diff --git a/.gitattributes b/.gitattributes
index 2e285d4dc0175d36955b3608aca70029f795c2c1..92030287fde7e0d517219816a635f4abba81cc99 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -226,3 +226,4 @@ data_all_eng_slimpj/shuffled/split/split_finalac/part-18.finalac filter=lfs diff
 data_all_eng_slimpj/shuffled/split/split_finalac/part-13.finalac filter=lfs diff=lfs merge=lfs -text
 data_all_eng_slimpj/shuffled/split/split_finalac/part-19.finalac filter=lfs diff=lfs merge=lfs -text
 data_all_eng_slimpj/shuffled/split/split_finalac/part-12.finalac filter=lfs diff=lfs merge=lfs -text
+data_all_eng_slimpj/shuffled/split/split_finalac/part-04.finalac filter=lfs diff=lfs merge=lfs -text
diff --git a/data_all_eng_slimpj/shuffled/split/split_finalac/part-04.finalac b/data_all_eng_slimpj/shuffled/split/split_finalac/part-04.finalac
new file mode 100644
index 0000000000000000000000000000000000000000..8e4096ed9a47145de3c8bec31f38f48b394a0d63
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split/split_finalac/part-04.finalac
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b11b4f11a776ff5030be9c04b87bd2ffc1e3ebb87741cef86834c79b0cc483d4
+size 12576661698
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzign b/data_all_eng_slimpj/shuffled/split2/finalzign
new file mode 100644
index 0000000000000000000000000000000000000000..f690b470c31017bad9729d754ca965ce3fd7358e
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzign
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\n\nRobot exploration problem is defined as making a robot or multi-robots explore unknown cluttered environments (i.e., office environment, forests, ruins, etc.) autonomously with specific goals. \nThe goal can be classified as: (1) Maximizing the knowledge of the unknown environments, i.e., acquiring a map of the world \\cite{thrun2002probabilistic}, \\cite{28_background_info}. (2) Searching a static or moving object without prior information about the world. \nWhile solving the exploration problems with the second goal can combine the prior information of the target object, such as the semantic information, it also needs to fulfill the first goal. \n\nThe frontier-based methods \\cite{21_yamauchi1997frontier}, \\cite{22_gonzalez2002navigation} have been widely used to solve the robot exploration problem. \n\\cite{21_yamauchi1997frontier} adopts a greedy strategy, which may lead to an inefficient overall path.\nMany approaches have been proposed to consider more performance metrics (i.e. information gain, etc.) \\cite{22_gonzalez2002navigation}, \\cite{23_bourgault2002information}, \\cite{33_basilico2011exploration}. \nHowever, these approaches are designed and evaluated in a limited number of environments. Therefore, they may fail to generalize to other environments whose layouts are different.\n\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=0.2]{.\/imgs\/4D_pointclouds.png}\n\t\\caption{The example of 4D point-clouds-like information. (a) shows a map example in $HouseExpo$, where the black, gray, and white areas denote unknown space, free space, and obstacle space, respectively. (b) shows the global map in our algorithm, where the map is obtained by homogeneous transformations. The map's center is the robot start location, and the map's x-coordinate is the same as the robot start orientation. (c) shows the 4D point-clouds-like information generated based on the global map. The x, y, z coordinate denote x location, y location and distance information, respectively. The color denotes frontier information, where red denotes obstacles and blue denotes frontiers.}\n\t\\label{fig:label_pointcloud}\n\\end{figure}\n\nCompared with these classical methods, machine learning-based methods exhibit the advantages of learning from various data.\nDeep Reinforcement Learning (DRL), which uses a neural network to approximate the agent's policy during the interactions with the environments \\cite{sutton2018reinforcement}, gains more and more attention in the application of games \\cite{DQN2015}, robotics \\cite{rl_env_robo}, etc.\nWhen applied to robot exploration problems, most research works \\cite{MaxM2018}, \\cite{31_chen2019self} {design the state space as the form of image} and use Convolution Neural Networks (CNN).\nFor example, in \\cite{MaxM2018}, CNN is utilized as a mapping from the local observation of the robot to the next optimal action.\n\nHowever, the size of CNN's input images is fixed, which results in the following limitations: \n(1) If input images represent the global information, the size of the overall explored map needs to be pre-defined to prevent input images from failing to fully containing all the map information. \n(2) If input images represent the local information, which fails to convey all the state information, the recurrent neural networks (RNN) or memory networks need to be adopted. \nUnfortunately, the robot exploration problem in this formulation requires relatively long-term planning, which is still a tough problem that has not been perfectly solved.\n\nIn this paper, to deal with the aforementioned problems, we present a novel state representation method, which relies on 4D point-clouds-like information of variable size. \nThese information have the same data structure as point clouds and consists of 2D points' location information, and the corresponding 1D frontier and 1D distance information, as shown in Fig.\\ref{fig:label_pointcloud}.\nWe also designs the corresponding training framework, which bases on the deep Q-Learning method with variable action space.\nBy replacing the image observation with 4D point-clouds-like information, our proposed exploration model can deal with unknown maps of arbitrary size.\nBased on dynamic graph CNN (DGCNN) \\cite{wang2019dynamic}, which is one of the typical neural network structure that process point clouds information, our proposed neural network takes 4D point-clouds-like information as input and outputs the expected value of each frontier, which can guide the robot to the frontier with the highest value.\nThis neural network is trained in a way similar to DQN in the $HouseExpo$ environment \\cite{li2019houseexpo}, which is a fast exploration simulation platform that includes data of many 2D indoor layouts. The experiment shows that our exploration model can achieve a relatively good performance, compared with the baseline in \\cite{li2019houseexpo}, state-of-the-art in \\cite{Weight2019}, classical methods in \\cite{21_yamauchi1997frontier}, \\cite{22_gonzalez2002navigation} and a random method.\n\n\\subsection{Original Contributions}\nThe contributions of this paper are threefold. \nFirst, we propose a novel state representation method using 4D point-clouds-like information to solve the aforementioned problems in Section \\ref{sec:relatedwork}.\nAlthough point clouds have been utilized in motion planning and navigation (\\cite{27_2Dpointclouds}, \\cite{30_ObstacleResp}), our work is different from these two papers in two main parts: \n(1) We use point clouds to represent the global information while they represent the local observation.\n(2) Our action space is to select a frontier point from the frontier set of variable size, while their action space contains control commands.\nSecond, we design the corresponding state function based on DGCNN \\cite{wang2019dynamic}, and the training framework based on DQN \\cite{DQN2015}. \nThe novelty is that our action space's size is variable, which makes our neural network converge in a faster way.\nThird, we demonstrate the performance of the proposed method on a wide variety of environments, which the model has not seen before, and includes maps whose size is much larger than maps in the training set. \n\nThe remainder of this paper is organized as follows. \nWe first introduce the related work in Section \\ref{sec:relatedwork}.\nThen we formulate the frontier-based robot exploration problem and DRL exploration problem in Section \\ref{sec:formulation}. \nAfter that, the framework of our proposed method are detailed in Section \\ref{sec:alg}.\nIn Section \\ref{sec:exp}, we demonstrate the performance of our proposed method through a series of simulation experiments. \nAt last, we conclude the work of this paper and discuss directions for future work in section \\ref{sec:conclude}.\n\n\\section{Related Work}\n\\label{sec:relatedwork}\nIn \\cite{21_yamauchi1997frontier}, the classical frontier method is defined, where an occupancy map is utilized in which each cell is placed into one of three classes: open, unknown and occupied.\nThen frontiers are defined as the boundaries between open areas and unknown areas. \nThe robot can constantly gain new information about the world by moving to successive frontiers, while the problem of selecting which frontiers at a specific stage remains to be solved. \nTherefore, in a frontier-based setting, solving the exploration problem is equivalent to finding an efficient exploration strategy that can determine the optimal frontier for the robot to explore.  \nA greedy exploration strategy is utilized in \\cite{21_yamauchi1997frontier} to select the nearest unvisited, accessible frontiers. \nThe experiment results in that paper show that the greedy strategy is short-sighted and can waste lots of time, especially when missing a nearby frontier that will disappear at once if selected (this case is illustrated in the experiment part).\n\nMany DRL techniques have been applied into the robot exploration problem in several previous works.\nIn a typical DRL framework \\cite{sutton2018reinforcement}, the agent interacts with the environment by taking actions and receiving rewards from the environment. \nThrough this trial-and-error manner, the agent can learn an optimal policy eventually.\nIn \\cite{MLiu2016}, a CNN network is trained under the DQN framework with RGB-D sensor images as input to make the robot learn obstacle avoidance ability during exploration. \nAlthough avoiding obstacles is important, this paper does not apply DRL to learn the exploration strategy.\nThe work in \\cite{Weight2019} combines frontier-based exploration with DRL to learn an exploration strategy directly. \nThe state information includes the global occupancy map, robot locations and frontiers, while the action is to output the weight of a cost function that evaluates the goodness of each frontier. \nThe cost function includes distance and information gain. \nBy adjusting the weight, the relative importance of each term can be changed. \nHowever, the terms of the cost function rely on human knowledge and may not be applicable in other situations. \nIn \\cite{2_li2019deep}, the state space is similar to the one in \\cite{Weight2019}, while the action is to select a point from the global map.\nHowever, the map size can vary dramatically from one environment to the next. \nIt losses generality when setting the maximum map size before exploring the environments. \n\nIn \\cite{MaxM2018} and \\cite{31_chen2019self}, a local map, which is centered at the robot's current location, is extracted from the global map to represent current state information.\nBy using a local map, \\cite{MaxM2018} trains the robot to select actions in ``turn left, turn right, move forward'', while \\cite{31_chen2019self} learns to select points in the free space of the local map. \nLocal map being state space can eliminate the limitation of global map size, but the current local map fails to contain all the information. \nIn \\cite{MaxM2018}, the robot tends to get trapped in an explored room when there is no frontier in the local map, because the robot has no idea where the frontiers are.\nThe training process in \\cite{31_chen2019self} needs to drive the robot to the nearest frontier when the local map contains no frontier information, although a RNN network is integrated into their framework. \nThis human intervention adopts a greedy strategy and can not guarantee an optimal or near-optimal solution. \nWhen utilizing local observations, the robot exploration problem requires the DRL approach to have a long-term memory.\nNeural map in \\cite{17_parisotto2018neural} is proposed to tackle simple memory architecture problems in DRL.\nBesides, Neural SLAM in \\cite{13_zhang2017neural} embeds traditional SLAM into attention-based external memory architecture.\nHowever, the memory architectures in \\cite{17_parisotto2018neural} and \\cite{13_zhang2017neural} are based on the fixed size of the global map.\nIt is difficult to be applied to unknown environments whose size may be quite large compared with maps in training sets.\nUnlike the aforementioned methods, our method uses the 4D point-clouds-like information to represent the global state information, which does not suffer from both the map size limitation and the simple memory problem. \nAs far as we know, our method is the first to apply point clouds to robot exploration problems. \nTherefore, we also design a respective DRL training framework to map the exploration strategy directly from point clouds.\n\n\n\\section{Problem Formulation}\n\\label{sec:formulation}\n\nOur work aims to develop and train a neural network that can take 4D point-clouds-like information as input and generate efficient policy to guide the exploration process of a robot equipped with a laser scanner. \nThe network should take into account the information about explored areas, occupied areas, and unexplored frontiers. \nIn this paper, the robot exploration problem is to make a robot equipped with a limited-range laser scanner explore unknown environments autonomously.\n\n\\subsection{Frontier-based Robot Exploration Problem}\n\\label{sec:formulation_A}\nIn the robot exploration problem, a 2D occupancy map is most frequently adopted to store the explored environment information. \nDefine the explored 2D occupancy map at step ${t}$ as ${M_t}$.\nEach grid in ${M_t}$ can be classified into the following three states: free grid ${M_t}$, occupied grid ${E_t}$, and unknown grid ${U_t}$. \nAccording to \\cite{21_yamauchi1997frontier}, frontiers ${F_t}$ are defined as the boundaries between the free space ${E_t}$ and unknown space ${U_t}$.\nMany existing DRL exploration frameworks learn a mapping from ${M_t}$ and ${F_t}$ to robot movement commands which can avoid obstacles and navigate to specific locations.\nAlthough this end-to-end framework has a simple structure, it is difficult to train.\nInstead, our method learns a policy network that can directly determine which frontier to explore, which is similar to \\cite{Weight2019} and \\cite{2_li2019deep}.\nAt step $t$, a target frontier is selected from ${F_t}$ based on an exploration strategy and current explored map ${M_t}$. \nOnce the change of the explored map is larger than the threshold, the robot is stopped, and the explored map at step $t+1$ ${M_{t+1}}$ is obtained.\nBy moving to selected frontiers constantly, the robot will explore more unknown areas until no accessible frontier exists. \n\nBecause ${M_t}$ can be represented as an image, it is commonly used to directly represent the state information.\nAs explained in Section \\ref{sec:relatedwork}, a novel state representation method with 4D point-clouds-like information is proposed instead.\nThe 4D point-clouds-like information at step $t$ is defined as a 4-dimensional point cloud set with $n$ points, denoted by $X_t = \\{ x_1^t, ..., x_n^t \\} \\subset \\mathbb{R}^4$.\nEach point contains 4D coordinates $x_i^t = \\left( x_i, y_i, b_i, d_i\\right)$, where $x_i, y_i$ denotes the location of the point, $d_i$ denotes the distance from the point to the robot location without collision, $b_i \\in \\{ 0, 1\\}$ denotes whether point $(x_i, y_i)$ in $M_t$ belongs to frontier or not.\n\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=0.53]{imgs\/MDP_framework.png}\n\t\\caption{The framework of the proposed method, which consists of five components: (a) A simulator adopted from $HouseExpo$ \\cite{li2019houseexpo}, which receives and executes a robot movement command and outputs the new map in $HouseExpo$ coordinate; (b) The modified Dijkstra algorithm to extract the contour of the free space; (c) The state represented by 4D point-clouds-like information; (d) The policy network which processes the state information and estimates the value of frontiers; (e) The A* algorithm that finds a path connecting the current robot location to the goal frontier and a simple path tracking algorithm that generates the corresponding robot movement commands.}\n\t\\label{fig:label_framework}\n\\end{figure}\n\n\\subsection{DRL exploration formulation}\n\\label{sec:DRL_formulation}\nThe robot exploration problem can be formulated as a Markov Decision Process (MDP), which can be modeled as a tuple $(\\mathcal{S}, \\mathcal{A}, \\mathcal{T}, \\mathcal{R}, \\gamma)$.\nThe state space ${\\mathcal{S}}$ at step $t$ is defined by 4D point cloud $X_t$, which can be divided into frontier set $F_t$ and obstacle set $O_t$.\nThe action space ${\\mathcal{A}_t}$ at step $t$ is the frontier set $F_t$, and the action is to select a point $f_t$ from $F_t$, which is the goal of the navigation module implemented by $A^{*}$ \\cite{Hart1968Astar}.\nWhen the robot take an action $f_t$ from the action space, the state $X_t$ will transit to state $X_{t+1}$ according to the stochastic state transition probability ${\\mathcal{T}(X_t, f_t, X_{t+1})} = p(X_{t+1} | X_t, f_t)$.\nThen the robot will receive an immediate reward $r_t = \\mathcal{R}(X_t, f_t)$.\nThe discount factor $\\gamma \\in [0, 1]$ adjusts the relative importance of immediate and future reward.\nThe objective of DRL algorithms is to learn a policy $\\pi (f_t | X_t)$ that can select actions to maximize the expected reward, which is defined as the accumulated $\\gamma-$discounted rewards over time.\n\nBecause the action space varies according to the size of frontier set $F_t$, it is difficult to design a neural network that maps the state to the action directly.\nThe value-based RL is more suitable to this formulation. \nIn value-based RL, a vector of action values, which are the expected rewards after taking actions in state $X_t$ under policy $\\pi$, can be estimated by a deep Q network (DQN) $Q_{\\pi}(X_t, f_t; \\theta) = \\mathbb{E}[\\sum_{i=t}^{\\infty}{\\gamma}^{i-t}r_i | X_t, f_t]$, where $\\theta$ are the parameters of the muti-layered neural network.\nThe optimal policy is to take action that has the highest action value:\n$f_{t}^{*}=\\mathop{\\text{argmax}}_{f_t}Q_{\\pi}(X_t,f_t; \\theta)$.\nDQN \\cite{DQN2015} is a novel variant of Q-learning, which utilizes two key ideas: \nexperience reply and target network. \nThe DQN tends to overestimate action values, which can be tackled by double DQN in \\cite{doubleDQN}.\nDouble DQN select an action the same as DQN selects, while estimate this action's value by the target network.\n\n\\section{Algorithm}\n\\label{sec:alg}\n\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=0.3]{.\/imgs\/PointCloud_Generation2.png}\n\t\\caption{The illustration of the 4D point-clouds-like information generation process. (a) presents the map where the black, gray, white, blue points denote obstacles, unknown space, free space, and robot location. In (b), the contour of free space, which is denoted by green points, is generated by the modified Dijkstra algorithm. The number on each point indicates the distance from this point to the robot location. In (c), the points in the contour set are divided into frontier or obstacle sets, which are denoted in dark green and light green, respectively. In (d), the 4D point-clouds-like information are extracted from the image (c). The point clouds include location, frontier flag, and distance information.}\n\t\\label{fig:label_illustration_h}\n\\end{figure}\n\nIn this section, we present the framework of our method and illustrate its key components in detail. \n\n\\subsection{Framework Overview}\nThe typical DRL framework is adopted, where the robot interacts with the environment step by step to learn an exploration strategy. \nThe environment in this framework is based on $HouseExpo$ \\cite{li2019houseexpo}.\nThe state and action space of the original $HouseExpo$ environment is the local observation and robot movement commands, respectively. \nWhen incorporated into our framework, $HouseExpo$ receives a sequence of robot movement command and outputs the global map once the change of the explored map is larger than the threshold, which is detailed in Section \\ref{sec:formulation_A}.\nAs shown in Fig. \\ref{fig:label_framework}, the 4D point-clouds-like information can be obtained by a modified Dijkstra algorithm. \nAfter the policy network outputting the goal point, the $A^{*}$ algorithm is implemented to find the path connecting the robot location to the goal point. \nThen a simple path tracking algorithm is applied to generate the sequence of robot movement commands.\n\n\n\\subsection{Frontier Detection and Distance Computation}\n\\label{sec:frontier_dectect}\nComputing the distances from the robot location to points in the frontier set without collision will be time-consuming if each distance is obtained by running the $A^{*}$ algorithm once. \nInstead, we modify the Dijkstra algorithm to detect frontiers and compute distance at the same time by sharing the search information.  \nDenote the ``open list'' and ``close list'' as $L_o$ and $L_c$, respectively.\nThe open list contains points that need to be searched, while the close list contains points that have been searched.\nDefine the contour list as $L_f$, which contains the location and the cost of points that belong to frontier or obstacle.\nOnly points in the free space of map $M_t$ are walkable. \nThe goal of this modified algorithm is to extract the contour of free space and obtain the distance information simultaneously.\nAs shown in Algorithm 1, the start point with the cost of zero, which is decided by the robot location, is added to $L_o$. \nWhile the open list is not empty, the algorithm repeats searching 8 points, denoted by $p_{near}$, adjacent to current point $p_{cur}$.\nThe differences from Dijkstra algorithms are: \n(1) If $p_{near}$ belongs to occupied or unknown space, add $p_{cur}$ to frontier list $L_f$, as shown in line 10 of Algorithm 1.\n(2) Instead of stopping when the goal is found, the algorithm terminates until $L_o$ contains zero points.\nAfter the algorithm ends, the contour list contains points that are frontiers or boundaries between free space and obstacle space.\nPoints in the contour list can be classified by their neighboring information into frontier or obstacle set, which is shown in Fig. \\ref{fig:label_illustration_h}.\n\n\\begin{algorithm}[h]\n\\caption{Modified Dijkstra Algorithm}\n\\begin{algorithmic}[1]\n\\STATE $L_o \\leftarrow \\{ p_{start}\\}, Cost( p_{start}) = 0;$ \n\\WHILE {$L_o \\neq \\phi$}\n\\STATE $p_{cur} \\leftarrow minCost(L_o)$;\n\\STATE $L_c \\leftarrow L_c \\cup p_{cur}, L_o \\leftarrow L_o \\backslash p_{cur}$;\n\\FOR{$p_{near}$ in 8 points adjacent to $p_{cur}$}\n\\STATE $cost_{near} = Cost(p_{cur}) + distance(p_{near}, p_{cur})$\n\\IF{$p_{near} \\in L_c$}\n\\STATE continue;\n\\ELSIF{$p_{near}$ is not walkable}\n\\STATE $L_f \\leftarrow L_f \\cup p_{cur}$;\n\\ELSIF{$p_{near} \\notin L_o$}\n\\STATE $L_o \\leftarrow L_o \\cup p_{near}$\n\\STATE $Cost(p_{near}) = cost_{near}$;\n\\ELSIF{$p_{near} \\in L_o$ and $Cost(p_{near})>cost_{near}$}\n\\STATE $Cost(p_{near})=cost_{near}$\n\\ENDIF\n\\ENDFOR\n\\ENDWHILE \n\\label{code:recentEnd}\n\\end{algorithmic}\n\\end{algorithm}\n\n\\begin{figure*}[t]\n\t\n\t\\centering\n\t\\includegraphics[scale=0.48]{imgs\/network_structure2.png}\n\t\\caption{The architecture of our proposed neural network. The input point clouds are classified into two categories: frontier set denoted by dark blue and obstacle set denoted by red. The edge convolution operation $EdgeConv$ is denoted by a light blue block, which is used to extract local features around each point in the input set. The feature sets of frontiers and obstacles, which are generated by $EdgeConv$ operations, are denoted by light green and green. The MLP operation is to extract one point's feature by only considering this point's information. After several $EdgeConv$ operations and one MLP operation, a max-pooling operation is applied to generate the global information, which is shown in light yellow.}\n\t\\label{fig:label_network_structure}\n\\end{figure*}\n\n\\subsection{Network with Point Clouds as Input}\n\\label{sec:DQN_architecture}\nIn this section, the architecture of the state-action value network with 4D point-clouds-like information as input is detailed.\nThe architecture is modified from DGCNN in Segmentation task \\cite{wang2019dynamic}, which proposes edge convolution (EdgeConv) operation to extract the local information of point clouds.\nThe EdgeConv operation includes two steps for each point in the input set: (1) construct a local graph including the center point and its k-nearest neighbors; (2) apply convolution-like operations on edges which connect each neighbor to the center point.\nThe $(D_{in}, D_{out})$ EdgeConv operation takes the point set $(N, D_{in})$ as input and outputs the feature set $(N, D_{out})$, where $D_{in}$ and $D_{out}$ denote the dimension of input and output set, and $N$ denotes the number of points in the input set.\nDifferent from DGCNN and other typical networks processing point cloud such as PointNet \\cite{qi2017pointnet}, which have the same input and output point number, our network takes the frontier and obstacle set as input and only outputs the value of points from the frontier set.\nThe reason for this special treatment is to decrease the action space's size to make the network converge in a faster manner.\n\nThe network takes as input $N_f + N_w$ points at time step $t$, which includes $N_f$ frontier points and $N_w$ obstacle points, which are denoted as $F_t = \\{ x_1^t, ..., x_{N_f}^t \\}$ and $O_t = \\{ x_{N_f+1}^t, ..., x_{N_f+N_w}^t \\}$ respectively.\nThe output is a vector of estimated value of each action $Q_{\\pi}(F_t, O_t, \\cdot; \\theta)$.\nThe network architecture contains multiple EdgeConv layers and multi-layer perceptron (mlp) layers.\nAt one EdgeConv layer, the feature set is extracted from the input set. \nThen all features in this edge feature set are aggregated to compute the output EdgeConv feature for each corresponding point.\nAt a mlp layer, the data of each point is operated on independently to obtain the information of one point, which is the same as the mlp in PointNet \\cite{qi2017pointnet}.\nAfter 4 EdgeConv layers, the outputs of all EdgeConv layers are aggregated and processed by a mlp layer to generate a 1D global descriptor, which encodes the global information of input points.\nThen this 1D global descriptor is concatenated with the outputs of all EdgeConv layers.\nAfter that, points that belong to the obstacle set are ignored, and the points from the frontier set are processed by three mlp layers to generate scores for each point.\n\n\n\\subsection{Learning framework based on DQN}\nAs described in Section \\ref{sec:DRL_formulation}, the DQN is a neural network that for a given state $X_t$ outputs a vector of action values.\nThe network architecture of DQN is detailed in Section \\ref{sec:DQN_architecture}, where the state $X_t$ in point clouds format contains frontier and obstacle sets.\nUnder a given policy $\\pi(f_t|F_t,O_t)$, the true value of an action $f_t$ in state $X_t = \\{F_t, O_t \\}$ is: $Q_{\\pi}(X_t, f_t; \\theta) \\equiv \\mathbb{E}[\\sum_{i=t}^{\\infty}{\\gamma}^{i-t}r_i | X_t, f_t]$. \nThe target is to make the estimate from the frontier network converge to the true value. \nThe parameters of the action-value function can be updated in a gradient decent way, after taking action $f_t$ in state $X_t$ and observing the next state $X_{t+1}$ and immediate reward $r_{t+1}$: \n\\begin{eqnarray}\\label{update_Q}\n\t\\theta_{t+1} = \\theta_t + \\alpha (G_t - Q_{\\pi}(X_t, f_t; \\theta_t)),\n\\end{eqnarray}\nwhere $\\alpha$ is the learning rate and the target $G_t$ is defined as \n\\begin{eqnarray}\\label{target}\n\tG_t = r_{t+1}+\\gamma Q_{\\pi}(X_{t+1}, \\mathop{\\text{argmax}}_{f}Q(X_{t+1}, f; \\theta_t); \\theta_t^{'}),\n\\end{eqnarray}\nwhere $\\theta^{'}$ denotes the parameter of the target network, which is updated periodically by $\\theta^{'} = \\theta$.\n\nTo make the estimate from our network converge to the true value, a typical DQN framework \\cite{DQN2015} can be adopted. \nFor each step $t$, the tuple $(X_t, f_t, X_{t+1}, r_{t+1})$ is saved in a reply buffer.  \nThe parameters can be updated by equation \\ref{update_Q} and \\ref{target} given the tuple sampled from the reply buffer.\n\n\nThe reward signal in the DRL framework helps the robot know at a certain state $X_t$ whether an action $f_t$ is appropriate to take.\nTo make the robot able to explore unknown environments successfully, we define the following reward function:\n\n\\begin{equation}\\label{reward_all}\nr_t = r_{area}^t + r_{frontier}^t + r_{action}^t.\n\\end{equation}\nThe term $r_{area}^t$ equals the newly discovered area at time $t$, which is designed to encourage the robot to explore unknown areas.\nThe term $r_{action}^t$ provides a consistent penalization signal to the robot when a movement command is taken. \nThis reward encourages the robot to explore unknown environments with a relatively short length of overall path.\nThe term $r_{frontier}^t$ is designed to guide the robot to reduce the number of frontiers, as defined in equation \\ref{reward_f}:\n\\begin{equation}\\label{reward_f}\nr_{frontier}^t = \\left\\{\n\\begin{aligned}\n 1,  N_{frontier}^t < N_{frontier}^{t-1}\\\\\n 0,  N_{frontier}^t \\geq N_{frontier}^{t-1}.\n\\end{aligned}\n\\right.\n\\end{equation}\nwhere $N_{frontier}^t$ denotes the number of frontier group at time $t$.\n\n\n\\section{Training Details and Simulation Experiments}\n\\label{sec:exp}\nIn this section, we first detail the training process of our DRL agent. \nThen we validate the feasibility of our proposed method in robot exploration problem by two sets of experiments:\n(1) a comparison with five other exploration methods, (2) a test of scalability where maps of larger size compared with training set are to be explored.\n\n\\subsection{Training Details}\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=0.3]{.\/imgs\/HouseExpo_traindata25.png}\n\t\\caption{Some map samples from training set. The black and white pixels represent obstacle and free space respectively.}\n\t\\label{fig:label_mapsample}\n\\end{figure}\n\nTo learn a general exploration strategy, the robot is trained in the $HouseExpo$ environment where 100 maps with different shapes and features are to be explored.\nThe robot is equipped with a 2m range laser scanner with a 180 degree field of view. \nThe noise of laser range measurement is simulated by the Gaussian distribution with a mean of 0 and a standard deviation of 0.02m.\nAs an episode starts, a map is randomly selected from the training set, and the robot start pose, including the location and pose, is also set randomly.\nIn the beginning, the circle area centered at the start location is explored by making the robot rotate for 360 degree.\nThen at each step, a goal frontier point is selected from the frontier set under the policy of our proposed method.\nA* algorithm is applied to find a feasible path connecting the current robot location to the goal frontier. \nA simple path tracking algorithm is used to find the robot commands to follow the planned path: moving to the nearest unvisited path point $p_{near}$, and replanning the path if the distance between the robot and $p_{near}$ is larger than a fixed threshold.\nAn episode ends if the explored ratio of the whole map is over ${95\\%}$.\n\n\\begin{table}[!htbp]\n\\caption{Parameters in Training}\n\\centering\n\\begin{tabular}{cccc}\n    \\toprule\n    \\multicolumn{2}{c}{HouseExpo} & \\multicolumn{2}{c}{Training} \\\\\n    \\hline\n    Laser range & $2m$ & Discount factor $\\gamma$ & 0.99 \\\\\n    \\hline\n    Laser field of view & $180^{\\circ}$ & Target network update f & 4000 steps \\\\\n    \\hline\n    Robot radius & $0.15m$ & Learning rate & 0.001 \\\\\n    \\hline\n    Linear step length & $0.3m$ & Replay buffer size & 50000 \\\\\n    \\hline\n    Angular step length & $15^{\\circ}$ & Exploration rate $\\epsilon$ & 15000\\\\\n    \\hline\n    Meter2pixel & $16$ & Learning starts & 3000\\\\\n    \\bottomrule\n\\end{tabular}\n\\end{table}\n\nSome training map samples are shown in Fig. \\ref{fig:label_mapsample}. \nThe largest size of a map in the training set is 256 by 256.\nBecause the size of state information $X_t$ changes at each time and batch update method requires point clouds with same size, currently, it is not realistic to train the model in a batch-update way.\nIn typical point clouds classification training process, the size of all the point clouds data are pre-processed to the same size.\nHowever, these operations will change the original data's spatial information in our method.\nInstead, for each step, the network parameters are updated 32 times with a batch size equal to 1.\nLearning parameters are listed in Table 1. \nThe training process is performed on a computer with Intel i7-7820X CPU and GeForce GTX 1080Ti GPU.\nThe training starts at 2000 steps and ends after 90000 update steps, which takes 72 hours.\n\n\\subsection{Comparison Study}\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=0.65]{imgs\/HouseExpo_test_data.png}\n\t\\caption{Four maps for testing. The size of map1, map2, map3 and map4 is (234, 191), (231, 200), (255, 174) and (235, 174), respectively. }\n\t\\label{fig:test_data}\n\\end{figure}\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=0.34]{imgs\/comparision.png}\n\t\\caption{The path length's data of each method on four test maps. For each map, each method is tested for 100 times with the same randomly initialized robot start locations.}\n\t\\label{fig:length_comparision}\n\\end{figure}\n\nBesides our proposed method, we also test the performance of the weight tuning method in \\cite{Weight2019}, a cost-based method in \\cite{22_gonzalez2002navigation}, a method with greedy strategy in  \\cite{21_yamauchi1997frontier}, a method utilizing a random policy and the baseline in \\cite{li2019houseexpo}, which we denote as the weight method, cost method, greedy method, random method and baseline, respectively.\nTo compare the performance of different methods, we use 4 maps as a testing set, as shown in Fig. \\ref{fig:test_data}.\nFor each test map, we conduct 100 trials by setting robot initial locations randomly for each trail.\n\nThe \\emph{random method} selects a frontier point from the frontier set randomly.\nThe \\emph{greedy method} chooses the nearest frontier point.\nThe \\emph{baseline} utilizes a CNN which directly determines the robot movement commands by the current local observation.\n\nThe \\emph{cost method} evaluates the scalar value of frontiers by a cost function considering distance and information gain information. \n\\begin{equation}\\label{cost_method}\ncost = wd+(1-w)(1-g),\n\\end{equation}\nwhere $w$ is the weight that adjusts the relative importance of costs. \n$d$ and $g$ denote the normalized distance and information gain of a frontier.\nAt each step, after obtaining the frontier set as detailed in Section \\ref{sec:frontier_dectect}, the k-means method is adopted to cluster the points in the frontier set to find frontier centers. \nTo reduce the runtime of computing information gains, we only compute the information gain for each frontier center.\nThe information gain is computed by the area of the unknown space to be explored if this frontier center is selected \\cite{22_gonzalez2002navigation}.\nThe weight in the cost method is fixed to 0.5, which fails to be optimal in environments with different structures and features.\n\nThe \\emph{weight method} can learn to adjust the value of the weight in equation \\ref{cost_method} under the same training framework as our proposed method.\nThe structure of the neural network in weight method is presented in Fig. \\ref{fig:label_network_structure}, which takes the 4D point-clouds-like information as input and outputs a scalar value.\n\n\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=0.9]{imgs\/comparision_result2.png}\n\t\\caption{The representative exploration trials of six different methods on map1 with the same robot start locations and poses. The bright red denotes the start state and the dark red denotes the end state. The green point denotes the locations where the robot made decisions to choose which frontiers to explore. As the step increases, the brightness of green points becomes darker and darker. The baseline's result doesn't have green points because its action is to choose a robot movement command.}\n\t\\label{fig:map_compare}\n\\end{figure}\n\nWe select the length of overall paths, which are recorded after $95\\%$ of areas are explored, as the metric to evaluate the relative performance of the six exploration methods. \nThe length of overall paths can indicate the efficiency of the exploration methods.\nThe box plot in Fig. \\ref{fig:length_comparision} is utilized to visualize the path length's data of each exploration method on four test maps. \nThe baseline is not considered here because the baseline sometimes fails to explore the whole environment, which will be explained later. \nThree values of this metric are used to analyze the experiment results: (1) the average, (2) the minimum value, (3) the variance.\nOur proposed method has the minimum average length of overall paths for all four test maps.\nThe minimum length of the proposed method in each map is also smaller than other five methods.\nThis indicates that the exploration strategy of our proposed method is more effective and efficient than the other five methods.\nThe random method has the largest variance and average value for each map because it has more chances to sway between two or more frontier groups. \nThat is why the overall path of the random method in Fig. \\ref{fig:map_compare} is the most disorganized.\nThe weight method has a lower average and minimum value compared with the cost method in all test maps, due to the advantages of learning from rich data.\nHowever, the weight method only adjusts a weight value to change the relative importance of distance and information gain. \nIf the computation of the information gain is not accurate or another related cost exists, the weight method fails to fully demonstrate the advantages of learning.\nInstead, our proposed method can learn useful information, including information gain, by learning to estimate the value of frontiers, which is the reason that our proposed method outperforms the weight method.\n\nFig. \\ref{fig:map_compare} shows an example of the overall paths of six different methods when exploring the map1 with the same starting pose.\nEach episode ended once the explored ratio was more than 0.95.\nThe proposed method explored the environment with the shortest path.\nThe explored ratio of the total map according to the length of the current path is shown in Fig. \\ref{fig:label_explored_ratio}.\nThe greedy method's curve has a horizontal line when the explored ratio is near 0.95. \nThis is because the greedy method missed a nearby frontier which would disappear at once if selected. \nHowever, the greedy method chose the nearest frontier instead, which made the robot travel to that missed frontier again and resulted in a longer path.\nFor example, in Fig. \\ref{fig:map_compare}, the greedy method chose to explore the point C instead of the point A, when the robot was at point B. This decision made the robot travel to the point A later, thus making the overall path longer.\nThe baseline's curve also exhibits a horizontal line in Fig. \\ref{fig:label_explored_ratio}, which is quite long.\nThe baseline's local observation contained no frontier information when the surroundings were all explored (in the left part of the environment shown in Fig. \\ref{fig:map_compare}).\nTherefore, at this situation, the baseline could only take ``random'' action (i.e. travelling along the wall) to find the existing frontiers, which would waste lots of travelling distances and may fail to explore the whole environment.\n\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=0.38]{imgs\/explored_ratio.png}\n\t\\caption{The ratio of the area explored and the area of the whole map with respect to the current path's length. The test map is map1 and the start locations is the same as Fig. \\ref{fig:map_compare}.}\n\t\\label{fig:label_explored_ratio}\n\n\\end{figure}\n\n\\subsection{Scalability Study}\n\nIn this section, a map size of (531, 201) is used to test the performance of our proposed method in larger environments compared with maps in the training set. \nIf the network's input is fixed size images, the map needs to be padded into a (531, 531) image, which is a low-efficient state representation way. \nThen a downscaling operation of the image is required to make the size of the image input the same as the requirement of the neural network, e.g. (256,256).\nAlthough the neural network can process the state data by downscaling, the quality of the input data decreases.\nTherefore, the network fails to work once the scaled input contains much less necessary information than the original image.\nFig. \\ref{fig:label_scalabilityTest} presents the overall path generated by our method without downscaling the map size.\nOur proposed method, which takes point clouds as input, has better robustness in maps with large scales because of the following two reasons.\nFirst, we incorporate the distance information into point clouds, which can help neural networks learn which part of point clouds are walkable.\nAlthough the image representation can also have a fourth channel as distance information, the scaling operation can make some important obstacles or free points disappear, which changes the structure of the map.\nSecondly, the number of pixels in an image increases exponentially as the size of the image increase.\nThe number of points in point clouds equals the number of pixels that represent an obstacle or frontier in a map, which is not an exponential relation unless all the pixels in a map are obstacles or frontiers.\n\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[scale=1.2]{.\/imgs\/path_1998.png}\n\t\\caption{The result of the scalability test. The map size is (531, 201). The meaning of points' color is the same as Fig. \\ref{fig:map_compare}}\n\t\\label{fig:label_scalabilityTest}\n\\end{figure}\n\n\\section{Conclusions And Future Work}\n\\label{sec:conclude}\n\n\n\nIn this paper, we present a novel state representation method using 4D point-clouds-like information and design the framework to learn an efficient exploration strategy.\nOur proposed method can solve the problems that come with using images as observations.\nThe experiments demonstrate the effectiveness of our proposed method, compared with other five commonly used methods.\nFor the future work, other network structures and RL algorithms can be modified and applied to the robot exploration problem with point clouds as input.\nThe converge speed of training may also be improved by optimizing the training techniques.\nBesides, the multi-robot exploration problem may also use point clouds to represent the global information. \n\n\n\\addtolength{\\textheight}{-8cm}  \n                                 \n                                 \n                                 \n                                 \n                                 \n\n\n\n\n\n\n\\bibliographystyle{IEEEtran}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{sec:INTRO}\nRelational Reinforcement Learning (RRL) has been investigated in early 2000s by works such as \\cite{bryant1999combining,dvzeroski1998relational,dvzeroski2001relational} among others. \nThe main idea behind RRL is to describe the environment in terms of objects and relations. \nOne of the first practical implementation of this idea was proposed by \\cite{dvzeroski1998relational} and later was improved in \\cite{dvzeroski2001relational} based on a modification to Q-Learning algorithm \\cite{watkins1992q} via the standard relational tree-learning algorithm TILDE \\cite{blockeel1998top}. As shown in \\cite{dvzeroski2001relational}, the RRL system allows for  very natural and human readable decision making and policy evaluations. More importantly, the use of variables in ILP system, makes it possible to learn generally formed policies and strategies. Since these policies and actions  are not directly associated with any particular instance and entity, this approach leads to a generalization capability beyond what is possible in most typical RL systems.\nGenerally speaking RRL framework offers several benefits over the traditional RL: (i) The learned policy is usually human interpretable, and hence can be viewed, verified and even tweaked by an expert observer. (ii) The learned program can generalize better than the classical RL counterpart. (iii) Since the language for the state representation is chosen by the expert, it is possible to incorporate inductive biases into learning. This can be a significant improvement in complex problems as it might be used to manipulate the agent to choose certain actions without accessing the reward function, (iv) It allows for the incorporation of higher level concepts and prior background knowledge. \n\nIn recent years and with the advent of the new deep learning techniques, significant progress has been made to the classical Q-learning RL framework. By using algorithms such as deep Q-learning and its variants \\cite{mnih2013playing,van2016deep}, as well as Policy learning algorithms such A2C and A3C \\cite{mnih2016asynchronous}, more complex problems are now been tackled. However, the classical RRL framework cannot be easily employed to tackle  large scale and complex scenes that exist in recent RL problems. \nSince standard RRL framework is in not usually able to learn from complex visual scenes and cannot be easily combined with differentiable deep neural\nIn particular, none of the inherent benefits of RRL have been materialized in the deep learning frameworks thus far. This is because existing RRL frameworks usually are not designed to learn from complex visual scenes and cannot be easily combined with differentiable deep neural networks.\nIn ~\\cite{payani2019Learning} a novel ILP solver was introduced which uses Neural-Logical Network (NLN)~\\cite{payani2018} for constructing a differentiable neural-logic ILP solver (dNL-ILP). The key aspect of this dNL-ILP solver is a differentiable deduction engine which is at the core of the proposed RRL framework. \nAs such, the resulting differentiable RRL framework can be used similar to deep RL in an end-to-end learning paradigm, trainable via the typical gradient optimizers. Further, in contrast to the early RRL frameworks, this framework is flexible and can learn from ambiguous and fuzzy information. Finally, it can be combined with deep learning techniques such as CNNs to extract relational information from the visual scenes. \nIn the next section we briefly introduce the differentiable dNL-ILP solver. In section, \\ref{sec:RRL} we show how this framework can be used to design a differentiable RRL framework. Experiments will be presented next, followed by the conclusion.\n\n\\section{Differentiable ILP via neural logic networks}\n\\label{sec:dNL-ILP}\n \nIn this section, we briefly present the basic design of the differentiable dNL-ILP which is at the core of the proposed RRL. More detailed presentation of dNL-ILP could be found in \\cite{payani2019Learning}.\nLogic programming is a paradigm in which we use formal logic (and usually first-order-logic) to describe relations between facts and rules of a program domain. In logic programming, rules are usually written as clauses of the form $H \\leftarrow B_1,\\,B_2,\\,\\dots,\\,B_m$, \nwhere $H$ is called \\texttt{head} of the clause and $B_1,\\,B_2,\\,\\dots,\\,B_m$ is called \\texttt{body} of the clause. A clause of this form expresses that if all the atoms $B_i$ in the \\texttt{body} are true, the \\texttt{head} is necessarily true.\nEach of the terms $H$ and $B$ is made of \\texttt{atoms}. Each \\texttt{atom} is created by applying an $n$-ary Boolean function called \\texttt{predicate} to some constants or variables. A \\texttt{predicate} states the relation between some variables or constants in the logic program. We use lowercase letters for constants (instances) and uppercase letters for variables. \nTo avoid technical details, we consider a simple logic program. Assume that a directed graph is defined using a series of facts in the form of  \\texttt{edge(X,Y)} where for example \\texttt{edge(a,b)} states that there is an edge from node \\texttt{a} to the node \\texttt{b}. As an example, the graph in Fig. \\ref{fig:connected_graph} can be represented as \\texttt{\\{edge(a,b), edge(b,c), edge(c,d), edge(d,b)\\}}.\n\\begin{figure}\n\t\\centering\n\t\\includegraphics[width=0.2\\textwidth]{cnt.png}\n\t\\caption{Connected graph example}\n\t\\label{fig:connected_graph}\n\t\\vspace{-.16in}\n\\end{figure}\nAssume that our task is to learn the \\texttt{cnt(X,Y)} predicate from a series of examples, where \\texttt{cnt(X,Y)} is true if there is a directed path from node \\texttt{X} to node \\texttt{Y}. The set of positive examples in graph depicted in Fig. \\ref{fig:connected_graph} is $\\mathcal{P}=$ \\texttt{\\{cnt(a,b), cnt(a,c), cnt(a,d), cnt(b,b),cnt(b,c), cnt(b,d),\\dots\\}}. Similarly the set of negative examples  $\\mathcal{N}$ includes atoms such as \\texttt{\\{cnt(a,a),cnt(b,a),\\dots\\}}.\n\nIt is easy to verify that the predicate \\texttt{cnt} defined as below satisfies all the provided examples (entails the positive examples and rejects the negative one):\n\\begin{align}\n\\text{cnt(X,Y)} &\\leftarrow \\text{edge(X,Y)} \\nonumber\\\\\n\\text{cnt(X,Y)} &\\leftarrow \\text{edge(X,Z),\\,\\,cnt(Z,Y)}\n\\label{eq:cnt}\n\\end{align}\nIn fact by applying each of the above two rules to the constants in the program we can produce all the consequences of such hypothesis\nIf we allow for formulas with 3 variables (\\texttt{X,Y,Z}) as in (\\ref{eq:cnt}), we can easily enumerate all the possible symbolic atoms that could be used in the body of each clause. In our working example, this corresponds to $\\mathbb{I}_{cnt}=$\\texttt{\\{edge(X,X), edge(X,Y), edge(X,Z), \\dots, cnt(Z,Y), cnt(Z,Z)\\}}. \nAs the size of the problem grows, considering all the possibilities becomes unfeasible. Consequently, almost all ILP systems use some form of rule templates to reduce the possible combinations. For example, the dILP \\cite{evans2018learning} model, allows for the clauses (in the body) of at most two atoms in each clause predicate. \nIn \\cite{payani2019Learning}, a novel approach was introduced to alleviate the above limitation and to allow for learning arbitrary complex predicate formulas. The main idea behind this approach is to use multiplicative neurons \\cite{payani2018} that are capable of learning and representing Boolean logic. Consider the fuzzy notion of Boolean algebra where fuzzy Boolean value are represented as a real value in range $[0,1]$, where True and False are represented by 1 and 0, respectively. Let $\\bar{x}$ be the logical `NOT' of $x$. \n\\begin{figure}[tb]\n\t\\centering\n\t\\subfloat[][]{\n\t\t\\small\n\t\t\\vspace{-5mm}\n\t\t\\begin{tabular}{|c|c|c|}\n\t\t\t\\hline  \n\t\t\t$x_i$ & $m_i$ & $F_c$ \\\\ \t\\toprule  \n\t\t\t0 & 0 & 1 \\\\ \\hline\n\t\t\t0 & 1 & 0 \\\\ \\hline\n\t\t\t1 & 0 & 1 \\\\ \\hline\n\t\t\t1 & 1 & 1 \\\\ \\hline\n\t\t\\end{tabular}\n\t\t\\label{fig:Fc}%\n\t}%\n\t\\qquad\n\t\\subfloat[][]{\n\t\t\\small\n\t\t\\begin{tabular}{|c|c|c|}\n\t\t\t\\hline\t \n\t\t\t$x_i$ & $m_i$ & $F_d$ \\\\   \t\\toprule\n\t\t\t0 & 0 & 0 \\\\ \\hline\n\t\t\t0 & 1 & 0 \\\\ \\hline\n\t\t\t1 & 0 & 0 \\\\ \\hline\n\t\t\t1 & 1 & 1 \\\\ \\hline\n\t\t\\end{tabular}\n\t\t\\label{fig:Fd}%\n\t}\n\t\\caption{Truth table of $F_c(\\cdot)$ and $F_d(\\cdot)$ functions}%\n\t\\label{fig:FcFd}%\n\\end{figure}\nLet $\\boldsymbol{x}^n \\in \\{0,1\\}^n$ be the input vector for a logical neuron. we can associate a trainable Boolean membership weight $m_i$ to each input elements $x_i$ from vector $\\boldsymbol{x}^n$. Consider Boolean function $F_c(x_i,m_i)$ with the truth table as in Fig. \\ref{fig:Fc} which is able to include (exclude) each element  $x_i$ in (out of) the conjunction function $f_{conj}(\\boldsymbol{x}^n)$. This design ensures the incorporation of each element $x_i$ in the conjunction function only when the corresponding membership weight $m_i$ is $1$. Consequently, the  neural conjunction function $f_{conj}$ can be defined as:\n\\vspace{-2mm}\n\\begin{align}\n\\label{eq:conj}\nf_{conj}(\\boldsymbol{x}^n) &= \\prod_{i=1}^{n} F_c(x_i,m_i) \\nonumber \\\\\n\\text{where, }  \\quad F_c(x_i,m_i) &= \\overline{\\overline{x_i} m_i } = 1 - m_i ( 1 - x_i) \n\\end{align}\nLikewise, a neural disjunction function $f_{disj}(\\boldsymbol{x}^n) $  can be defined using the auxiliary function $F_d$ with the truth table as in Fig. ~\\ref{fig:Fd}. \nBy cascading a layer of $N$ neural conjunction functions with a layer of $N$ neural disjunction functions, we can construct a differentiable function to be used for representing and learning a Boolean Disjunctive Normal Form (DNF). \n\ndNL-ILP employs these differentiable Boolean functions (e.g. dNL-DNF) to represent and learn predicate functions. Each dNL function can be seen as a parameterized symbolic formula where the (fuzzy) contribution of each symbol (atom) in the learned hypothesis is controlled by the trainable membership weights (e.g., $w_i$ where $m_i = sigmoid(w_i)$). If we start from the background facts ( e.g. all the groundings of predicate \\texttt{edge(X,Y)} in the graph example and apply the parameterized hypothesis we arrive at some new consequences (e.g., forward chaining). After repeating this process to obtain all possible consequences, we can update the parameters in dNL by minimizing the  cross entropy between the desired outcome (provided positive and negative examples) and the deduced consequences. \n\nAn ILP description of a problem in this framework consist of these elements:\n\\begin{enumerate}\n\t\\item The set of constants in the program. In example of Fig. \\ref{fig:connected_graph}, this consists of $\\mathcal{C}=$\\texttt{\\{a,b,c,d\\}}\n\t\\item The set of background facts. In the graph example above this consists of groundings of predicate \\texttt{edge(X,Y)}, i.e., $\\mathcal{B}=$\\texttt{\\{edge(a,b), edge(b,c), edge(c,d), edge(d,b)\\}}\n\t\n\t\\item The definition of auxiliary predicates. In the simple example of graph we did not include any auxiliary predicates. However, in more complex example they would greatly reduce the complexity of the problem.\n\t\n\t\\item The signature of the target hypothesis. In the graph example, This signature indicates the target hypothesis is 2-ary predicate \\texttt{cnt(X,Y)} and in the symbolic representation of this Boolean function we are allowed to use three variables \\texttt{X,Y,Z}. \n\t\n\n\n\t\n\\end{enumerate}\nIn addition to the aforementioned elements, some parameters such as intial values for the membership weights ($m_i=sigmoid(w_i)$), as well as the number of steps of forward chaining should be provided. Furthermore, in dNL-ILP the memberships are fuzzy Boolean values between 0 and 1. As shown in \\cite{payani2019Learning}, for ambiguous problems where a definite Boolean hypothesis may not be found which could satisfy all the examples, there is no guaranty that the membership weights converge to zero or 1. In applications where our only goal is to find a successful hypothesis this result is satisfactory. However, if the interpretability of the learned hypothesis is by itself a goal in learning, we may need to encourage the membership weights to converge to 0 and 1 by adding a penalty term:\n\\begin{equation}\n\\text{interpretability penalty} \\propto m_i(1-m_i)\\label{eq:interpret}\n\\end{equation}\n\n\\section{Relational Reinforcement Learning via dNL-ILP}\n\\label{sec:RRL}\n \n\nEarly works on RRL \\cite{dvzeroski2001relational,van2005survey} mainly relied on access to the explicit representation of states and actions  in terms of relational predicate language. In the most successful instances of these approaches, a regression tree algorithm is usually used in combination with a  modified version of Q-Learning algorithms. \nThe fundamental limitation of the traditional RRL approaches is that the employed ILP solvers are not differentiable. Therefore, those approaches are typically only applicable the problems for which the explicit relational representation of states and actions is provided. Alternatively, deep RL models, due to recent advancement in deep networks, have been successfully applied to the much more complex problems. These models are able to learn from raw images without relying on any access to the explicit representation of the scene. However, the existing RRL counterparts are falling behind such desirable developments in deep RL. \n\nIn this paper, we establish that differentiable dNL-ILP provides a platform to combine RRL  with deep learning methods, constructing a new RRL framework with the best of both worlds. This new RRL system allows the model to learn from the complex visual information received from the environment and extract intermediate explicit relational representation from the raw images by using the typical deep learning models such as convolutional networks. \n\\begin{figure*}\n\t\\centering\n\t\\includegraphics[width=0.85\\textwidth]{boxworld_states2.png}\n\t\\caption{States representation in the form of predicates in BoxWorld game,  before and after an action}\n\t\\label{fig:boxworld}\n\\end{figure*}\nAlthough the dNL-ILP can also be used to formulate RL algorithms such as deep Q-learning, we focus only on deep policy gradient learning algorithm. This formulation is very desirable because it makes the learned policy to be interpretable by human. \nOne of the other advantages of using policy gradient in our RRL framework is that it enables us to restrict actions according to some rules obtained either from human preferences or from problem requirements. This in turn makes it possible to account for human preferences or to avoid certain pitfalls, e.g.,  as in safe AI.\n\nIn our RRL framework, although we use the generic formulation of the policy gradient with the ability to learn stochastic policy, certain key aspects are different from the traditional deep policy gradient methods, namely state representation, language bias and action representation. In the following, we will explain these concepts in the context of BoxWorld game. In this game, the agent's task is to learn how to stack the boxes on top of each other (in a certain order). For illustration, consider the simplified version of the game as in Fig.\\ref{fig:boxworld} where there are only three boxes labeled as \\texttt{a,b}, and \\texttt{c}. A box can be on top of another or on the \\texttt{floor}. A box can be moved if it is not covered by another box and can be either placed on the floor or on top of another uncovered box. For this game, the environment state can be fully explained via the predicate \\texttt{on(X,Y)}. Fig. \\ref{fig:boxworld} shows the state representation of the scene before and after an  action (indicated by the predicate \\texttt{move(c,b)}). In the following we discuss each distinct elements of the proposed framework using the BoxWorld environment. \nFig.~\\ref{fig:ilp_rrl_diag} displays the overall design of our proposed RRL framework. In the following we discuss the elements of this RRL system.\n\n\\begin{figure*}[h]\n\t\\centering\n\t\\includegraphics[width=.95\\textwidth]{.\/rrl_diag.png}\n\t\\vspace{-5mm}\n\t\\caption{Learning explicit relational information from images in our proposed RRL; Images are processed to obtain explicit representation and dNL-ILP engine learns and expresses the desired policy (actions)}\n\t\\label{fig:ilp_rrl_diag}\n\\end{figure*}\n\\begin{figure*}\n\t\\centering\n\t\\includegraphics[width=1\\textwidth]{.\/language_state6.png}\n\n\n\t\\vspace{-10mm}\n\t\\caption{Transforming low-level state representation to high-level form via auxiliary predicates}\n\t\\label{fig:ilp_rrl_state}\n\\end{figure*}\n\\begin{figure*} \n\t\\centering    \n\t\\subfloat[A sample from CLEVER datset]{\n\t\t\\includegraphics[width=.55\\textwidth]{.\/clevr.png}\n\t\n\t}\n\t\\subfloat[A sample from sort-of-CLEVER datset]{\n\t\t\\includegraphics[width=.28\\textwidth]{.\/sclevr.png}\n\t\t\\label{subfig:sortofclever}\n\t\n\t}\n\t\\vspace{-2mm}\n\t\\caption{Extracting relational information from visual scene \\cite{santoro2017simple}}\n\t\\label{fig:ilp_RELATIONAL}\n\t\n\\end{figure*}\n\\subsection{State Representation}\n\\label{subsec:STATE-REP}\nIn the previous approaches to the RRL \\cite{dvzeroski1998relational,dvzeroski2001relational,jiang2019neural}, state of the environment is expressed in an explicit relational format in the form of predicate logic. This significantly limits the applicability of RRL in complex environments where such representations are not available. Our goal in this section is to develop a method in which the explicit representation of states can be learned via typical deep learning techniques in a form that will support the policy learning via our differentiable dNL-ILP. \nAs a result, we can utilize the various benefits of the RRL discipline without being restricted only to the environments with explicitly represented states.\n\nFor example, consider the BoxWorld environment explained earlier where the predicate\n\\texttt{on(X,Y)} is used to represent the state explicitly in the relational form (as shown in Fig.\\ref{fig:boxworld}). \nPast works in RRL relied on access to explicit relational representation of states, i.e.,\nall the groundings of the state representation predicates. \nSince this example has 4 constants, i.e. $\\mathcal{C}=$\\texttt{\\{a,b,c,floor\\}}, these groundings would be the binary values (`true' or `false') for the atoms \\texttt{on(a,a), on(a,b), on(a,c), on(a,floor), \\dots, on(floor,floor)}. \nIn recent years, extracting relational information from visual scenes has been investigated.\nFig. \\ref{fig:ilp_RELATIONAL} shows two types of relational representation extracted from images in~\\cite{santoro2017simple}. \nThe idea is to first process the images through multiple CNN networks. The last layer of the convolutional network chain is treated as the feature vector and is usually augmented with some non-local information such as absolute position of each point in the final layer of the CNN network. This feature map is then fed into a relational learning unit which is tasked with extracting non-local features.\nVarious techniques have been then introduced recently for learning these non-local information from the local feature maps, namely, self attention network models \\cite{vaswani2017attention,santoro2017simple} as well as graph networks \\cite{narayanan2017graph2vec,allamanis2017learning}. Unfortunately, none of the resulting presentations from past works is in the form of predicates needed in ILP.\n\n\nIn our approach, we use similar networks discussed earlier to extract non-local information. However given the relational nature of state representation in our RRL model, we consider three strategies in order to facilitate learning the desired relational state from images. Namely:\n\\begin{enumerate}\n\t\\item \\textbf{Finding a suitable state representation:} In our BoxWorld example, we used the \\texttt{on(X,Y)} to represent the state of the environment. However, learning this predicate requires inferring relation among various objects in the scene. As shown by previous works (e.g., \\cite{santoro2017simple}), this is a difficult task even in the context of a fully supervised setting (i.e., all the labels are provided) which is not applicable here. Alternatively, we propose to use lower-level relation for state representation and build higher level representation via predicate language. In the game of BoxWorld as an example, we can describe states by the respective position of each box. In particular, we  define two predicates \\texttt{posH(X,Y)} and \\texttt{posV(X,Y)} such that variable $X$ is associated with the individual box, whereas $Y$ indicate horizontal or vertical coordinates of the box, respectively. Fig.~ \\ref{fig:ilp_rrl_state} shows how this new lower-level representations can be transformed into the higher level description by the appropriate predicate language: \n\t\\begin{align}\n\t\\text{on(X, Y)} &\\leftarrow \\text{posH(X, Z)}, \\text{posH(Y, T)}, \\nonumber\\\\ &\\text{inc(T, Z)}, \\text{sameH(X, Y)} \\nonumber\\\\\n\t\\text{sameH(X, Y)} &\\leftarrow \\text{posH(X, Z)}, \\text{posH(Y, Z)}\n\t\\label{eq:on}\n\t\\end{align}\n\t\\item \\textbf{State constraints:} When applicable, we may incorporate relational constraint in the form of a penalty term in the loss function. For example, in our BoxWorld example we can notice that \\text{posY(floor)} should be always 0. In general, the choice of relational language makes it possible to pose constraints based on our knowledge regarding the scene. Enforcing these constraints does not necessarily speed up the learning as we will show in the BoxWorld experiment in Section \\ref{subsec:BoxWorld}. However, it will ensure that the (learned) state representation and consequently the learned relational policy resemble our desired structure of the problem.\n\t\\item \\textbf{Semi-supervised setting:} While it is not desirable to label every single scene that may happen during learning, in most cases it is possible to provide a few labeled scene to help the model to learn the desired state representation faster. These reference points  can then be incorporated to the loss function to encourage the network to learn a representation that matches to those provided labeled scenes. We have used a similar approach in Asterix experiment (see appendix \\ref{app:asterix}) to significantly increase the speed of learning.\n\\end{enumerate}\n\n\n\n\\subsection{Action Representation}\n\\label{subsec:ACTION-REP}\nWe formulate the policy gradient in a form that allows the learning of the actions via one (or multiple) target predicates. These predicates exploit the background facts, the state representation predicates, as well as auxiliary predicates to incorporate higher level concepts. \nIn a typical Deep policy gradient (DPG) learning, the probability distributions of actions are usually learned by applying a multi layer perception with a \\texttt{softmax} activation function in the last layer. In our proposed RRL, the action probability distributions can usually be directly associated with groundings of an appropriate predicate. For example, in  BoxWorld example in Fig.\\ref{fig:boxworld}, we define a predicate \\texttt{move(A,B)} and associate the actions of the agent with the groundings of this predicate. In an ideal case, where there is deterministic solution to the RRL problem, the predicate \\texttt{move(A,B)} may be learned in such a way that, at each state, only the grounding (corresponding to the correct action) would result 1 ('true') and all the other groundings of this predicate become 0. In such a scenario, the agent will follow the learned logic deterministically. Alternatively, we may get more than one grounding with value equal to 1 or we get some fuzzy values in the range of $[0,1]$. \nIn those cases, we estimate the probability distribution of actions similar to the standard deep policy learning by applying a \\texttt{softmax} function to the valuation vector of the learned predicate \\texttt{move} (i.e., the value of \\texttt{move(X,Y)} for \\texttt{X,Y}$\\in$ \\texttt{\\{a,b,c,floor\\}}).  \n\n\\section{Experiments}\n\\label{sec:EXPERIMENTS}\nIn this section we explore the features of the proposed RRL framework via several examples. We have implemented\\footnote{The python implementation of the algorithms in this paper\n\tis available at \\url{https:\/\/github.com\/dnlRRL2020\/RRL}} the models using Tensorflow \\cite{abadi2016tensorflow}.\n\\subsection{BoxWorld Experiment}\n\\label{subsec:BoxWorld}\nBoxWorld environment has been widely used as a benchmark in past RRL systems \\cite{dvzeroski2001relational,van2005survey,jiang2019neural}. In these systems the state of the environment is usually given as an explicitly relational data via groundings of the predicate \\texttt{on(X,Y)}. While ILP based systems are usually able to solve variations of this environments, they rely on explicit representation of state and they cannot infer the state from the image. Here, we consider the task of stacking boxes on top of each other. We increase the difficulty of the problem compared to the previous examples \\cite{dvzeroski2001relational,van2005survey,jiang2019neural} by considering the order of boxes and requiring that the stack is formed on top of the blue box (the blue box should be on the floor). To make sure the models learn generalization, we randomly place boxes on the floor in the beginning of each episode. We consider up to 5 boxes. Hence, the scene constants in our ILP setup is the set \\texttt{\\{a,b,c,d,e,floor\\}}. The dimension of the observation images is 64x64x3 and no explicit relational information is available for the agents. The action space for the problem involving  $n$ boxes is $(n+1)\\times (n+1)$ corresponding to all possibilities of moving a box (or the floor) on top of another box or the floor. Obviously some of the actions are not permitted, e.g., placing the floor on top of a box or moving a box that is already covered by another box. \n\n\\paragraph{Comparing to Baseline:}\nIn the first experiment, we compare the performance of the proposed RRL technique to a baseline. For the baseline we consider standard deep A2C (with up to 10 agents) and we use the implementation in \\texttt{stable-baseline} library \\cite{stable-baselines}. We considered both MLP and CNN policies for the deep RL but we report the results for the CNN policy because of its superior performance. \nFor the proposed RRL system, we use two convolutional layers with the kernel size of 3 and strides of 2 with $tanh$ activation function. We apply two layers of MLP with \\texttt{softmax} activation functions to learn the groundings of the predicates \\texttt{posH(X,Y)} and \\texttt{posV(X,Y)}. Our presumed grid is $(n+1)\\times(n+1)$ and we allow for positional constants  \\texttt{\\{0,1,\\dots,n\\}} to represent the locations in the grid in our ILP setting. \nAs constraint we add penalty terms to make sure \\texttt{posV(floor,0)} is True. We use vanilla gradient policy learning and to generate actions we define a learnable hypothesis predicate \\texttt{move(X,Y)}. Since we have $n+1$ box constants (including floor), the groundings of this hypothesis correspond to the  $(n+1)\\times(n+1)$ possible actions. Since the value of these groundings in dNL-ILP will be between 0 and 1, we generate \\texttt{softmax} logits by multiplying these outputs by a large constant $c$ (e.g., $c=10$). For the  target predicate \\texttt{move(X,Y)}, we allows for 6 rules in learning ( corresponding to dNL-DNF function with 6 disjunctions). The complete list of auxiliary predicates and parameters and weights used in the two models are given in appendix \\ref{app:box}. As indicated in Fig. \\ref{fig:ilp_rrl_state} and  defined in (\\ref{eq:on}), we introduce predicate \\texttt{on(X,Y)} as a function of the low-level state representation predicates \\texttt{posV(X,Y)} and \\texttt{posH(X,Y)}. We also introduce higher level concepts using these predicates to define the aboveness (i.e., \\texttt{above(X,Y)}) as well as \\texttt{isCovered(X,Y)}. \nFig. \\ref{fig:box_cmp} compares the average success per episode for the two models for the two cases of $n=4$ and $n=5$. The results shows that for the case of $n=4$, both models are able to learn a successful policy after around 7000 episodes. For the more difficult case of $n=5$, our proposed approach converges after around 20K episodes \nwhereas  it takes more than 130K episodes for the A2C approach to converge, and even then it fluctuates and does not always succeed.\n\\paragraph{Effect of background knowledge:}\nContrary to the standard deep RL, in an RRL approach, we can introduce our prior knowledge into the problem via the powerful predicate language. By defining the structure of the problem via ILP, we can explicitly introduce inductive biases \\cite{battaglia2018relational} which would restrict the possible form of the solution. We can speed up the learning process or shape the possible learnable actions even further by incorporating background knowledge. \nTo examine the impact of the background knowledge on the speed of learning, \nwe consider three cases for the BoxWorld problem involving $n=4$ boxes. The baseline model (RRL1) is as described before. In RRL2, we add another auxiliary predicate which defines the movable states as:\n\n\\begin{align*}\n\\text{movable(X,Y)} \\leftarrow \\neg \\text{isCovered(X)}, \\neg \\text{isCovered(Y)},  \\\\\\neg \\text{same(A,B)}, \\neg \\text{isfloor(X)}, \\neg \\text{on(X,Y)}\n\\end{align*}\nwhere $\\neg$ indicates the negate of a term. In the third model (RRL3), we go one step further, and we force the target predicate \\text{move(X,Y)} to incorporate the predicate \\texttt{movable(X,Y)} in each of the conjunction terms. \nFig. \\ref{fig:box_bk} compares the learning performance of these models in terms of average success rate (between [0,1]) vs the number of episodes.\n\\begin{figure}\n\t\\centering\n\t\\includegraphics[width=0.380\\textwidth]{box_mlp.png}\n\t\\vspace{-2mm}\n\t\\caption{Comparing deep A2C and the proposed model on BoxWorld task}\n\t\\label{fig:box_cmp}\n\\end{figure}\n\\begin{figure}\n\t\\centering\n\t\\includegraphics[width=0.380\\textwidth]{b4_bk.png}\n\t\\vspace{-2mm}\n\t\\caption{Effect of background knowledge on learning BoxWorld}\n\t\\label{fig:box_bk}\n\\end{figure}\n\\paragraph{Interpretability:}\nIn the previous experiments, we did not consider the interpretability of the learned hypothesis. Since all the weights are fuzzy values, even though the learned hypothesis is still a parameterized symbolic function, it does not necessarily represent a valid Boolean formula. \nTo achieve an interpretable result we add a small penalty as described in (\\ref{eq:interpret}). We also add a few more state constraints to make sure the learned representation follow our presumed grid notations (see Appendix \\ref{app:box} for details). The learned action predicate is found as: \n\\begin{align*}\n\\text{move(X, Y)} &\\leftarrow  \\text{moveable(X, Y)},\\, \\neg \\text{lower(X, Y)} \\\\\n\\text{move(X, Y)} &\\leftarrow   \\text{moveable(X, Y)},\\, \\text{isBlue(Y)} \\\\\n\\text{lower(X, Y)}  &\\leftarrow  \\text{posV(X, Z)},\\, \\text{posV(Y, T)},\\, \\text{lessthan(Z, T)}  \n\\end{align*}\n\n\\subsection{GridWorld Experiment}\n\\label{subsec:GridWorld}\n\\begin{figure}\n\t\\centering\n\t\\includegraphics[width=0.4\\textwidth]{gridworld.png}\n\t\\caption{GridWorld environment \\cite{zambaldi2018relational}} \\label{fig:ilp_gridworld}\n\t\\label{fig:ilp_boxworldaction}\n\\end{figure}\nWe use the GridWorld environment introduced in \\cite{zambaldi2018relational} for this experiment. This environment is consisted of a $12\\times12$ grid with keys and boxes randomly scattered. It also have an agent, represented by a single dark gray square box. The boxes are represented by two adjacent colors. The square on the right represents the box's lock type whose color indicates which key can be used to open that lock. The square on the left indicates the content of the box which is inaccessible while the box is locked. The agent must collect the key before accessing the box.\nWhen the agent has a key, provided that it walks over the lock box with the same color as its key, it can open the lock box, and then it must enter to the left box to acquire the new key which is inside the left box.\nThe agent cannot get the new key prior to successfully opening the lock box on the right side of the key box.\nThe goal is for the agent to open the gem box colored as white. We consider two difficulty levels. In the simple scenario, there is no (dead-end) branch. In the more difficult version, there can be one branch of dead end. An example of the environment and the branching scenarios is depicted in Fig.~\\ref{fig:ilp_gridworld}.\nThis is a very difficult task involving complex reasoning. Indeed, in the original work it was shown that a multi agent A3C combined with a non-local learning attention model could only start to learn after processing $5\\times10^8$ episodes. To make this problem easier to tackle, \nwe modify the action space to include the location of any point in the grid instead of directional actions. Given this definition of the problem, the agent's task is to give the location of the next move inside the rectangular grid. Hence, the dimension of the action space is $144=12\\times12$. \nFor this environment, we define the predicates \\texttt{color(X,Y,C)}, where $X,Y\\in\\{1,\\dots12\\}$, $C\\in\\{1,\\dots,10\\}$ and \\texttt{hasKey(C)} to represent the state. Here, variables $X,Y$ denote the coordinates, and the variable $C$ is for the color. Similar to the BoxWorld game, we included a few auxiliary predicates such as \\texttt{isBackground(X,Y)}, \\texttt{isAgent(X,Y)} and \\texttt{isGem(X,Y)} as part of the background knowledge. The representational power of ILP allows us to incorporate our prior knowledge about the problem into the model. As such we can include some higher level auxiliary helper predicates such as :\n\\begin{align*}\n\\text{isItem(X, Y)}&\\leftarrow \\ \\neg \\text{isBackground(X, Y)}, \\neg \\text{isAgent(X, Y)} \\\\\n\\text{locked(X, Y)}&\\leftarrow \\  \\text{isItem(X, Y)}, \\text{isItem(X,Z)}, \\text{inc(Y, Z)}\n\\end{align*}\nwhere predicate \\texttt{inc(X,Y)} defines increments for integers (i.e., \\texttt{inc(n,n+1)} is true for every integer n). \nThe list of all auxiliary predicates used in this experiment as well as the parameters of the neural networks used in this experiment are given in Appendix \\ref{app:grid}. \nSimilar to previous experiments we consider two models, an A2C agent as the baseline and our proposed RRL model using the ILP language described in Appendix \\ref{app:grid}.\n\\begin{table}[ht]\n\t\\caption{Number of training episodes required for convergence }\n\t\\label{tbl:results_block}\n\t\\centering \n\t\\begin{tabular} { l  c  c c c c c c }\n\t\t\\toprule\n\t\tmodel &   Without Branch & With Branch\\\\ \t\t\n\t\t\\midrule\n\t\tproposed RRL & 700   & 4500  \\\\\n\t\tA2C &  $> 10^8$ & $> 10^8$ \\\\\n\t\t\\bottomrule\n\t\\end{tabular}\n\\end{table}\n\\begin{figure}\n\t\\centering\n\t\\includegraphics[width=0.35\\textwidth]{bl_bk.png}\n\t\\vspace{-2mm}\n\t\\caption{Effect of background knowledge on learning GridWorld}\n\t\\label{fig:grid_bk}\n\\end{figure}\nWe listed the number of episodes it takes to converge in each setting in Table\\ref{tbl:results_block}. As the results suggest, the proposed approach can learn the solution in both settings very fast. On the contrary, the standard deep A2C was not able to converge after $10^8$ episodes. \nThis example restates the fact that incorporating our prior knowledge regarding the problem can significantly speed up the learning process.\n\nFurther, similar to the BoxWorld experiment, we study the importance of our background knowledge in the learning. In the first task (RRL1), we evaluate our model on the non-branching task by enforcing the action to include the $isItem(X,Y)$ predicate. In RRL2, we do not enforce this. As shown in Fig\\ref{fig:grid_bk}, RRL1 model learns 4 times faster than RRL2. Arguably, this is because, enforcing the inclusion of  $isItem(X,Y)$ in the action hypothesis reduces the possibility of exploring irrelevant moves (i.e., moving to a location without any item).\n\\subsection{Relational Reasoning}\n\\label{subsec:SORTOFCLEVER}\nCombining dNL-ILP with standard deep learning techniques is not limited to the RRL settings. In fact, the same approach can be used in other \nareas in which we wish to reason about the relations of objects.\nTo showcase this, we consider the relational reasoning task involving the Sort-of-CLEVR \\cite{santoro2017simple} dataset. This dataset (See Fig.\\ref{subfig:sortofclever}) consists of 2D images of some colored objects. The shape fo each object is either a rectangle or a circle and each image contains up to 6 objects.  The questions are hard-coded as fixed-length binary strings. Questions are either non-relational (e.g, \"what is the color of the green object?\") or relational (e.g., \"what is the shape of the nearest object to the green object?\"). In \\cite{santoro2017simple}, the authors combined a CNN generated feature map with a special type of attention based non-local network in order to solve the problem. We use the same CNN network and similar to the GridWorld experiment, we learn the state representation using predicate \\texttt{color(X,Y,C)} (the color of each cell in the grid) as well as \\texttt{isCircle(X,Y)} which learn if the shape of an object is circle or not. Our proposed approach reaches the accuracy of 99\\% on this dataset compared to the 94\\% for the non-local approach presented in \\cite{santoro2017simple}. The details of the model and the list of predicates in our ILP implementation is given in appendix \\ref{app:relational}.\n\n\n\\section{Conclusion}\n\\label{sec:Conclusion}\nIn this paper, we proposed a novel deep Relational Reinforcement Learning (RRL) model based on a differentiable Inductive Logic Programming (ILP) that can effectively learn relational information from image. We showed how this model can take the expert background knowledge and incorporate it into the learning problem using appropriate predicates. The differentiable ILP allows an end to end optimization of the entire framework for learning the policy in RRL. We showed the performance of the proposed RRL framework using environments such as BoxWorld and GridWorld.\n\n\n\n\n\n\n\\nocite{langley00}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nIn many data science problems, data are available through different views. Generally, the views represent different measurement modalities such as audio and video, or the same text that may be available in different languages. Our main interest here is neuroimaging where recordings are made from multiple subjects. In particular, it is of interest to find common patterns or responses that are shared between subjects when they receive the same stimulation or perform the same cognitive task \\citep{chen2015reduced,richard2020modeling}. \n\nA popular line of work to perform such shared response modeling is group Independent Component Analysis (ICA) methods. The fastest methods~\\cite{calhoun2001method, varoquaux2009canica} are among the most popular, yet they are not grounded on principled probabilistic models for the multiview setting. \nMore principled approaches exist~\\cite{richard2020modeling, guo2008unified}, but they do not model subject-specific deviations from the shared response. However, such deviations are expected in most neuroimaging settings, as the magnitude of the response may differ from subject to subject \\cite{penny2007random}, as may any noise due to heartbeats, respiratory artefacts or head movements~\\cite{liu2016noise}.\nFurthermore, most GroupICA methods are typically unable to separate components whose density is close to a Gaussian.\n\nIndependent vector analysis (IVA)~\\cite{lee2008independent, anderson2011joint} is a powerful framework where components are independent within views but each component of a given view can depend on the corresponding component in other views. \nHowever, current implementations such as IVA-L~\\cite{lee2008independent},\nIVA-G~\\cite{anderson2011joint}, IVA-L-SOS~\\cite{bhinge2019extraction}, IVA-GGD~\\cite{anderson2014independent} or\nIVA with Kotz distribution~\\cite{anderson2013independent} estimate only the\nview-specific components, and do not model or extract a shared response which is\nthe main focus in this work.\n\nOn the other hand, the shared response model~\\cite{chen2015reduced} is a popular approach to perform shared response modeling, yet it imposes orthogonality constrains that are restrictive and not biologically plausible.\n\nIn this work we introduce Shared ICA (ShICA), where each view is modeled as a linear transform of shared independent components contaminated by additive Gaussian noise. ShICA allows the principled extraction of the shared components (or responses) in addition to view-specific components. \nSince it is based on a statistically sound noise model, it enables optimal inference (minimum mean square error, MMSE) of the shared responses.\n\nLet us note that ShICA is no longer the method of choice when the concept of common response is either not useful or not applicable. \nNevertheless, we believe that the ability to extract a common response is an important feature in most contexts because it highlights a stereotypical brain response to a stimulus. Moreover, finding commonality between subjects reduces often unwanted inter-subject variability.\n\nThe paper is organized as follows.\nWe first analyse the theoretical properties of the ShICA model, before providing inference algorithms.\nWe exhibit necessary and sufficient conditions for the ShICA model to be identifiable (previous work only shows local identifiability~\\cite{anderson2014independent}), in the presence of Gaussian or non-Gaussian components. \nWe then use Multiset CCA to fit the model when all the components are assumed to\nbe Gaussian. We exhibit necessary and sufficient conditions for Multiset CCA to\nbe able to recover the unmixing matrices (previous work only gives sufficient\nconditions~\\cite{li2009joint}). In addition, we provide instances of the problem where Multiset CCA cannot recover the mixing matrices while the model is identifiable.\nWe next point out a practical problem : even a small sampling noise\ncan lead to large error in the estimation of unmixing matrices when Multiset CCA is used. To\naddress this issue and recover the correct unmixing matrices, we propose to\napply joint diagonalization to the result of Multiset CCA yielding a new method\ncalled ShICA-J.\nWe further introduce ShICA-ML, a maximum likelihood estimator of ShICA that models non-Gaussian components using a Gaussian mixture model. \nWhile ShICA-ML yields more accurate components, ShICA-J is significantly faster and offers a great initialization to ShICA-ML.\nExperiments on fMRI and MEG data demonstrate that the method outperforms existing GroupICA and IVA methods.\n\n\n\\section{Shared ICA (ShICA): an identifiable multi-view model}\n\\paragraph{Notation} We write vectors in bold letter $\\vb$ and scalars in lower case $a$. Upper case letters $M$ are used to denote\nmatrices. We denote $|M|$ the absolute value of the determinant of $M$. $\\xb \\sim \\Ncal(\\mub, \\Sigma)$ means that $\\xb \\in \\mathbb{R}^k$ follows\na multivariate normal distribution of mean $\\mub \\in \\mathbb{R}^k$ and\ncovariance $\\Sigma \\in \\mathbb{R}^{k \\times k}$. The $j, j$ entry of a diagonal matrix $\\Sigma_i$ is denoted $\\Sigma_{ij}$, the $j$ entry of $\\yb_i$ is denoted $y_{ij}$. Lastly, $\\delta$ is the Kronecker delta.\n\n\\paragraph{Model Definition} In the following, $\\xb_1, \\dots ,\\xb_m \\in \\bbR^p$ denote the $m$ observed random vectors obtained from the $m$ different views. We posit the following generative model, called Shared ICA (ShICA): for $i= 1\\dots m$\n\\begin{equation}\n  \\label{eq:model}\n   \\xb_i = A_i(\\sbb + \\nb_i)\n\\end{equation}\nwhere $\\sbb \\in \\mathbb{R}^{p}$ contains the latent variables called \\emph{shared components}, $A_1,\\dots, A_m\\in\\bbR^{p\\times p}$ are the invertible mixing matrices, and $\\nb_i \\in\n\\mathbb{R}^{p}$ are \\emph{individual noises}. The individual noises model both the deviations of a view  from the mean ---i.e.\\ individual differences--- and measurement noise. Importantly, we explicitly model both the shared components and the individual differences in a probabilistic framework to enable an optimal inference of the parameters and the responses.\n\nWe assume that the shared components are statistically independent, and that the individual noises are Gaussian and independent from the shared components:\n$p(\\sbb) = \\prod_{j=1}^p p(s_j)$ and $\\nb_i \\sim\\mathcal{N}(0, \\Sigma_i)$, where the matrices $\\Sigma_i$ are assumed diagonal and positive. Without loss of generality, components are assumed to have unit variance $\\bbE[\\sbb \\sbb^{\\top}] = I_p$. We further assume that there are at least 3 views: $m \\geq 3$. \n\nIn contrast to almost all existing works, we assume that some components (possibly all of them) may be Gaussian, and denote $\\mathcal{G}$ the set of Gaussian components: $\\sbb_j \\sim \\mathcal{N}(0, 1)$ for $j \\in \\mathcal{G}$. The other components are non-Gaussian: for $j\\notin \\mathcal{G}$, $\\sbb_j$ is non-Gaussian.\n\n\n\\paragraph{Identifiability} The parameters of the model are $\\Theta = (A_1, \\dots, A_m, \\Sigma_1, \\dots, \\Sigma_m)$. We are interested in the identifiability of this model: given observations $\\xb_1,\\dots, \\xb_m$ generated with parameters $\\Theta$, are there some other $\\Theta'$ that may generate the same observations?\nLet us consider the following assumption that requires that the individual noises for Gaussian components are sufficiently diverse:\n\\begin{assumption}[Noise diversity in Gaussian components]\n\\label{ass:diversity}\nFor all $j, j' \\in \\mathcal{G}, j \\neq j'$, the sequences $(\\Sigma_{ij})_{i=1 \\dots m}$ and $(\\Sigma_{ij'})_{i=1 \\dots m}$ are different where $\\Sigma_{ij}$ is the $j, j$ entry of $\\Sigma_i$\n\\end{assumption}\n\nIt is readily seen that there is one trivial set of indeterminacies in the problem: if $P \\in \\mathbb{R}^{p \\times p}$ is a sign and permutation matrix (i.e. a matrix which has one $\\pm 1$ coefficient on each row and column, and $0$'s elsewhere) the parameters $(A_1 P, \\dots, A_m P, P^{\\top}\\Sigma_1 P, \\dots, P^{\\top} \\Sigma_m P)$ also generate $\\xb_1,\\dots, \\xb_m$. The following theorem shows that under the above assumption, these are the only indeterminacies of the problem.\n\n\\begin{theorem}[Identifiability]\n\\label{thm:identif}\nWe make Assumption~\\ref{ass:diversity}. We let $\\Theta'=(A_1', \\dots, A_m', \\Sigma_1', \\dots,\\Sigma_m')$ another set of parameters, and assume that they also generate $\\xb_1,\\dots, \\xb_m$. Then, there exists a sign and permutation matrix $P$ such that for all $i$, $A_i'=A_iP$, and $\\Sigma_i'= P^{\\top} \\Sigma_i P$.\n\\end{theorem}\nThe proof is in Appendix~\\ref{proof:identif}. Identifiability in the Gaussian case is a consequence of the identifiability results in~\\cite{via2011joint} and in the general case, local identifiability results can be derived from the work of ~\\cite{anderson2014independent}. \nHowever local identifiability only shows that for a given set of parameters there exists a neighborhood in which no other set of parameters can generate the same observations~\\cite{rothenberg1971identification}. In contrast, the proof of Theorem~\\ref{thm:identif} shows global identifiability.\n\nTheorem~\\ref{thm:identif} shows that the task of recovering the parameters from the observations is a well-posed problem, under the sufficient condition of Assumption~\\ref{ass:diversity}.  We also note that Assumption~\\ref{ass:diversity} is necessary for identifiability. For instance, if $j$ and $j'$ are two Gaussian components such that $\\Sigma_{ij} = \\Sigma_{ij'}$ for all $i$, then a global rotation of the components $j, j'$ yields the same covariance matrices. The current work assumes $m \\geq 3$, in appendix~\\ref{app:identifiability} we give an identifiability result for $m=2$, under stronger conditions.\n\n\n\n\\section{Estimation of components with noise diversity via joint-diagonalization}\n\nWe now consider the computational problem of efficient parameter inference. This section considers components with noise diversity, while the next section deals with non-Gaussian components.\n\n\n\\subsection{Parameter estimation with Multiset CCA}\nIf we assume that the components are all Gaussian,\nthe covariance of the observations given by\n$C_{ij}=  \\bbE[\\xb_i\\xb_j^\\top] = A_i(I_p + \\delta_{ij}\\Sigma_i)A_j^{\\top}\\enspace\n$ are sufficient statistics and methods using only second order information, like Multiset CCA, are candidates to estimate the parameters of the model.\nConsider the\nmatrix $\\mathcal{C} \\in \\bbR^{pm \\times pm}$ containing $m \\times m$ blocks of size $p\n\\times p$\nsuch that the block $i,j$ is given by $C_{ij}$. Consider the matrix $\\mathcal{D}$ identical to $\\mathcal{C}$ excepts that the non-diagonal blocks are filled with zeros:\n\\begin{equation}\n  \\mathcal{C} = \\begin{bmatrix}\n    C_{11} & \\dots & C_{1m}\\\\\n    \\vdots & \\ddots & \\vdots \\\\\n    C_{m1} &\\dots & C_{mm} \n  \\end{bmatrix}\n  ,\\enspace\n  \\mathcal{D} = \\begin{bmatrix}\n    C_{11} & \\dots & 0\\\\\n    \\vdots & \\ddots & \\vdots \\\\\n    0 &\\dots & C_{mm} \n  \\end{bmatrix}. \n\\end{equation} \nGeneralized CCA consists of the following generalized eigenvalue problem:\n\\begin{equation}\n\\label{eq:eigv}\n    \\mathcal{C} \\ub = \\lambda \\mathcal{D}\\ub,\\enspace \\lambda > 0,\\enspace \\ub\\in\\bbR^{pm} \\enspace .\n\\end{equation}\n  \nConsider the matrix $U = [\\ub^1, \\dots, \\ub^p] \\in \\mathbb{R}^{mp \\times p}$ formed by concatenating the $p$ leading eigenvectors of the previous problem ranked in decreasing eigenvalue order. Then, consider $U$ to be formed of $m$ blocks of size $p \\times p$ stacked vertically and define $(W^i)^{\\top}$ to be the $i$-th block. These $m$ matrices are the output of Multiset CCA. We also denote $\\lambda_1 \\geq \\dots \\geq \\lambda_p$ the $p$ leading eigenvalues of the problem.\n \n\nAn application of the results of \\cite{li2009joint} shows that Multiset CCA recovers the mixing matrices of ShICA under some assumptions.\n\\begin{proposition}[Sufficient condition for solving ShICA via Multiset CCA~\\cite{li2009joint}]\nLet $r_{ijk} = (1 + \\Sigma_{ik})^{-\\frac12} (1 + \\Sigma_{jk})^{-\\frac12}$.\nAssume that $(r_{ijk})_k$ is non-increasing. Assume that the maximum eigenvalue $\\nu_k$ of matrix $R^{(k)}$ of general element $(r_{ijk})_{ij}$ is such that  $\\nu_k = \\lambda_k$ \n.\nAssume that $\\lambda_1 \\dots \\lambda_p$ are distinct.\nThen, there exists scale matrices $\\Gamma_i$ such that $W_i = \n\\Gamma_i A_i^{-1}$ for all $i$.\n\\end{proposition}\nThis proposition gives a sufficient condition for solving ShICA with Multiset CCA. It needs a particular structure for the noise covariances as well as specific ordering for the eigenvalues. The next theorem shows that we only need $\\lambda_1 \\dots \\lambda_p$ to be distinct for Multiset CCA to solve ShICA:\n\\begin{assumption}[Unique eigenvalues]\n  \\label{ass:uniqueeig}\n$\\lambda_1 \\dots \\lambda_p$ are distinct.\n\\end{assumption}\n\\begin{theorem}\n  \\label{th:eig}\n  We only make\n  Assumption~\\ref{ass:uniqueeig}. Then, there exists a permutation matrix $P$ and scale matrices $\\Gamma_i$ such that $W_i = P\\Gamma_i A_i^{-1}$ for all $i$.\n\\end{theorem}\nThe proof is in Appendix~\\ref{proof:eig}. This theorem means that solving the generalized eigenvalue problem~\\eqref{eq:eigv} allows to recover the mixing matrices up to a scaling and permutation: this form of generalized CCA recovers the parameters of the statistical model.\nNote that Assumption~\\ref{ass:uniqueeig} is also a necessary condition. Indeed, if two eigenvalues are identical, the eigenvalue problem is not uniquely determined.\n\nWe have two different Assumptions, \\ref{ass:diversity} and \\ref{ass:uniqueeig}, the first of which guarantees theoretical identifiability as per Theorem~\\ref{thm:identif} and the second guarantees consistent estimation by Multiset CCA as per Theorem~\\ref{th:eig}. Next we will discuss their connections, and show some limitations of the Multiset CCA approach. To begin with, we have the following result about the eigenvalues of the problem~\\eqref{eq:eigv} and the $\\Sigma_{ij}$.\n\\begin{proposition}\n  \\label{prop:eigvals_from_noise}\n  For $j\\leq p$, let $\\lambda_j$ the largest solution of $ \\sum_{i=1}^m\\frac{1}{\\lambda_j(1 + \\Sigma_{ij}) -\\Sigma_{ij}}=1$. Then, $\\lambda_1, \\dots, \\lambda_p$ are the $p$ largest eigenvalues of problem~\\eqref{eq:eigv}.\n\\end{proposition}\nIt is easy to see that we then have $\\lambda_1, \\dots, \\lambda_p$ greater than $1$, while the remaining eigenvalues are lower than $1$.\nFrom this proposition, two things appear clearly. First, Assumption~\\ref{ass:uniqueeig} implies Assumption~\\ref{ass:diversity}.\nIndeed, if the $\\lambda_j$'s are distinct, then the sequences $(\\Sigma_{ij})_i$ must also be different from the previous proposition.\nThis is expected as from Theorem~\\ref{th:eig}, Assumption~\\ref{ass:uniqueeig} implies identifiability, which in turn implies Assumption~\\ref{ass:diversity}.\n\nProp.~\\ref{prop:eigvals_from_noise} also allows us to derive cases where Assumption~\\ref{ass:diversity} holds but not Assumption~\\ref{ass:uniqueeig}. The following Proposition gives a simple case where the model is identifiable but it cannot be solved using Multiset CCA:\n\\begin{proposition}\n\\label{counter}\nAssume that for two integers $j, j'$, the sequence $(\\Sigma_{ij})_i$ is a permutation of $(\\Sigma_{ij'})_i$, i.e. that there exists a permutation of $\\{1,\\dots, p\\}$, $\\pi$, such that for all $i$, $\\Sigma_{ij} = \\Sigma_{\\pi(i)j'}$.  Then, $\\lambda_j = \\lambda_{j'}$.\n\\end{proposition}\nIn this setting, Assumption~\\ref{ass:diversity} holds so ShICA is identifiable, while Assumption~\\ref{ass:uniqueeig} does not hold, so Multiset CCA cannot recover the unmixing matrices.\n\n\n\n\n\\subsection{Sampling noise and improved estimation with joint diagonalization} \\label{sec:samplingnoise}\n\nThe consistency theory for Multiset CCA developed above is conducted under the assumption that the\ncovariances $C_{ij}$ are the true covariances of the model, and not\napproximations obtained from observed samples. In practice, however, a serious limitation of Multiset CCA is that even a slight error of estimation on the covariances, due to ``sampling noise'', can yield a large error in the estimation of the unmixing matrices, as will be shown next.\n\nWe begin with an empirical illustration. We take $m=3$, $p=2$, and $\\Sigma_i$ such that $\\lambda_1 = 2 + \\varepsilon$ and $\\lambda_2 =2$ for $\\varepsilon > 0$.\nIn this way, we can control the \\emph{eigen-gap} of the problem, $\\varepsilon$.\nWe take $W_i$ the outputs of Multiset CCA applied to the true covariances $C_{ij}$.\nThen, we generate a perturbation $\\Delta = \\delta \\cdot S$, where $S$ is a random positive symmetric $pm \\times pm$ matrix of norm $1$, and $\\delta >0$ controls the scale of the perturbation. \nWe take $\\Delta_{ij}$ the $p\\times p$ block of $\\Delta$ in position $(i, j)$, and $\\tilde{W}_i$ the output of Multiset CCA applied to the covariances $C_{ij} + \\Delta_{ij}$.\nWe finally compute the sum of the Amari distance between the $W_i$ and $\\tilde{W}_i$: the Amari distance measures how close the two matrices are, up to scale and permutation~\\cite{amari1996new}.\n\\begin{wrapfigure}{r}{.4\\textwidth}\n \n  \\centering\n  \\includegraphics[width=.99\\linewidth]{figures\/multicca_gap_jd.pdf}\n  \\caption{Amari distance between true mixing matrices and estimates of Multiset\n    CCA when covariances are perturbed. Different solid curves correspond to different\n    eigen-gaps. The black dotted line shows the chance level. When the gap is small, a small perturbation can lead to complete mixing. Joint-diagonalization (colored dotted lines) fixes the problem.}\n  \\label{fig:cca_gap}\n \n  \\end{wrapfigure}\nFig~\\ref{fig:cca_gap} displays the median Amari distance over 100 random repetitions, as the perturbation scale $\\delta$ increases. The different curves correspond to different values of the eigen-gap $\\varepsilon$. We see clearly that the robustness of Multiset CCA critically depends on the eigen-gap, and when it is small, even a small perturbation of the input (due, for instance, to sampling noise) leads to large estimation errors.\n\n\nThis problem is very general and well studied~\\cite{stewart1973error}: the mapping from matrices to (generalized) eigenvectors is highly non-smooth.\nHowever, the gist of our method is that the \\emph{span} of the leading $p$ eigenvectors is smooth, as long as there is a large enough gap between  $\\lambda_p$ and $\\lambda_{p+1}$.\nFor our specific problem we have the following bounds, derived from Prop.~\\ref{prop:eigvals_from_noise}.\n\\begin{proposition}\n  We let $\\sigma_{\\max} = \\max_{ij}\\Sigma_{ij}$ and $\\sigma_{\\min} = \\min_{ij}\\Sigma_{ij}$. Then, $\\lambda_p \\geq 1 + \\frac{m-1}{1+\\sigma_{\\max}}$, while $\\lambda_{p+1}\\leq 1 - \\frac{1}{1 + \\sigma_{min}}$.\n\\end{proposition}\nAs a consequence, we have $\\lambda_{p} -\\lambda_{p+1} \\geq \\frac{m-1}{1+\\sigma_{\\max}} + \\frac{1}{1+ \\sigma_{\\min}}\\geq \\frac m{1+ \\sigma_{\\max}}$: the gap between these eigenvalues increases with $m$, and decreases with the noise power.\n\n\\begin{wrapfigure}{l}{.45\\textwidth}\n\\begin{minipage}{.45\\textwidth}\n  \\begin{algorithm}[H]\n  \\caption{ShICA-J}\n  \\label{algo:shicaj}\n    \\begin{algorithmic}\n       \\STATE {\\bfseries Input :} Covariances $\\tilde{C}_{ij} = \\bbE[\\xb_i\\xb_j^{\\top}]$\n       \\STATE $(\\tilde{W}_i)_i \\leftarrow \\mathrm{MultisetCCA}((\\tilde{C}_{ij})_{ij})$\n       \\STATE  $Q \\leftarrow \\mathrm{JointDiag}((\\tilde{W}_i\\tilde{C}_{ii}\\tilde{W}_i^{\\top})_i)$\n       \\STATE $\\Gamma_{ij} \\leftarrow Q\\tilde{W}_i\\tilde{C}_{ij}W_j^\\top Q^\\top$\n       \\STATE $(\\Phi_i)_i \\leftarrow \\mathrm{Scaling}((\\Gamma_{ij})_{ij})$\n         \\STATE \\textbf{Return : } Unmixing matrices $(\\Phi_iQ\\tilde{W}_i)_i$.\n        \\end{algorithmic}\n  \\end{algorithm}\n\\end{minipage}\n\\end{wrapfigure}\nIn this setting, when the magnitude of the perturbation $\\Delta$ is smaller than $\\lambda_{p}-\\lambda_{p+1}$, ~\\cite{stewart1973error} indicates that $\\mathrm{Span}([W_1, \\dots, W_m]^{\\top})\\simeq \\mathrm{Span}([\\tilde{W}_1,\\dots, \\tilde{W}_m]^\\top)$, where $[W_1, \\dots, W_m]^{\\top}\\in\\bbR^{pm\\times p}$ is the vertical concatenation of the $W_i$'s.\nIn turn, this shows that there exists a matrix $Q\\in\\bbR^{p\\times p}$ such that\n\\begin{equation}\n    \\label{eq:justif_jd}\n    W_i \\simeq Q\\tilde{W}_i\\enspace \\text{for all} \\enspace i.\n\\end{equation}\nWe propose to use joint-diagonalization to recover the matrix $Q$. Given the $\\tilde{W}_i$'s, we consider the set of symmetric matrices $\\tilde{K}_i = \\tilde{W}_i\\tilde{C}_{ii}\\tilde{W}_i^{\\top}$, where $\\tilde{C}_{ii}$ is the contaminated covariance of $\\xb_i$. Following Eq.~\\eqref{eq:justif_jd}, we have $Q\\tilde{K}_iQ^{\\top} = W_i \\tilde{C}_{ii}W_i^{\\top}$, and using Theorem~\\ref{th:eig}, we have $Q\\tilde{K}_iQ^{\\top} = P\\Gamma_i A_i^{-1}\\tilde{C}_{ii}A_i^{-\\top}\\Gamma_iP^{\\top}$. Since $\\tilde{C}_{ii}$ is close to $C_{ii} = A_i (I_p + \\Sigma_i)A_i^\\top$, the matrix $P\\Gamma_i A_i^{-1}\\tilde{C}_{ii}A_i^{-\\top}\\Gamma_iP^{\\top}$ is almost diagonal.\nIn other words, the matrix $Q$ is an approximate diagonalizer of the $\\tilde{K}_i$'s, and we approximate $Q$ by joint-diagonalization of the $\\tilde{K}_i$'s. In Fig~\\ref{fig:cca_gap}, we see that this procedure mitigates the problems of multiset-CCA, and gets uniformly better performance regardless of the eigen-gap.\nIn practice, we use a fast joint-diagonalization algorithm~\\cite{ablin2018beyond} to minimize a joint-diagonalization criterion for positive symmetric matrices~\\cite{pham2001joint}. The estimated unmixing matrices $U_i = Q\\tilde{W}_i$ correspond to the true unmixing matrices only up to some scaling which may be different from subject to subject: the information that the components are of unit variance is lost. As a consequence, naive averaging of the recovered components may lead to inconsistant estimation. We now describe a procedure to recover the correct scale of the individual components across subjects.\n\n\\textbf{Scale estimation}\nWe form the matrices $\\Gamma_{ij} = U_i\\tilde{C}_{ij}U_j^\\top$. In order to estimate the scalings, we solve $\n\\min_{(\\Phi_i)} \\sum_{i\\neq j} \\| \\Phi_i \\diag(\\Gamma_{ij}) \\Phi_j - I_p \\|_F^2$\nwhere the $\\Phi_i$ are diagonal matrices.\nThis function is readily minimized with respect to one of the $\\Phi_i$ by the formula\n$\\Phi_i = \\frac{\\sum_{j \\neq i} \\Phi_j \\diag(Y_{ij})}{\\sum_{j \\neq i} \\Phi_j^2 \\diag(Y_{ij})^2}$ (derivations in Appendix~\\ref{app:fixedpoint}). We then iterate the previous formula over $i$ until convergence.\nThe final estimates of the unmixing matrices are given by\n$(\\Phi_i U_i)_{i=1}^m$. The full procedure, called ShICA-J, is summarized in Algorithm~\\ref{algo:shicaj}.\n\n\\subsection{Estimation of noise covariances}\n\nIn practice, it is important to estimate noise covariances $\\Sigma_i$ in order to take advantage of the fact that some views are noisier than others. As it is well known in classical factor analysis, modelling noise variances allows the model to virtually discard variables, or subjects, that are particularly noisy. \n\nUsing the ShICA model with Gaussian components, we derive an estimate for the noise covariances directly from maximum likelihood. We use an expectation-maximization (EM) algorithm, which is especially fast because noise updates are in closed-form. Following derivations given in appendix~\\ref{conditional_density}, the sufficient statistics in the E-step are given by \n\\begin{align}\n\\label{mmse1}\n\\EE[\\sbb|\\xb]= \\left(\\sum_{i=1}^m \\Sigma_i^{-1}  + I \\right)^{-1}  \\sum_{i=1}^m \\left(\\Sigma_i^{-1} \\yb_i \\right)\n     && \\VV[\\sbb|\\xb]= (\\sum_{i=1}^m \\Sigma_i^{-1}  + I)^{-1}\n\\end{align}\nIncorporating the M-step we get the following updates that only depend on the covariance matrices:\n$\n\\Sigma_i \\leftarrow \\diag(\\hat{C_{ii}} - 2 \\VV[\\sbb | \\xb]  \\sum_{j=1}^m \\Sigma_j^{-1} \\hat{C}_{ji}  + \\VV[\\sbb | \\xb]  \\sum_{j = 1}^m \\sum_{l = 1}^m \\left(\\Sigma_j^{-1} \\hat{C}_{jl} \\Sigma_l^{-1} \\right) \\VV[\\sbb | \\xb] + \\VV[\\sbb | \\xb])\n$\n\n\\section{ShICA-ML: Maximum likelihood for non-Gaussian components}\nShICA-J only uses second order statistics. However, the ShICA model~\\eqref{eq:model} allows for non-Gaussian components. We now propose an algorithm for fitting the ShICA model that combines covariance information with non-Gaussianity in the estimation to optimally separate both Gaussian and non-Gaussian components.\nWe estimate the parameters by maximum likelihood. Since most non-Gaussian\ncomponents in real data are super-Gaussian~\\cite{delorme2012independent, calhoun2006unmixing}, we assume that the non-Gaussian components $\\sbb$ have the super-Gaussian density \\\\ $p(s_j) = \\frac12\\left(\\mathcal{N}( s_j; 0, \\frac12) + \\mathcal{N}( s_j; 0, \\frac{3}{2})\\right) \\enspace.$\n\nWe propose to maximize the log-likelihood using a generalized\nEM~\\cite{neal1998view, dempster1977maximum}. Derivations are available in Appendix~\\ref{app:emestep}. Like in the previous section, the E-step is in closed-form yielding the following sufficient statistics:\n\\begin{align}\n\\label{mmse2}\n  \\EE[s_j | \\xb] = \\frac{\\sum_{\\alpha \\in \\{\\frac12, \\frac32\\}} \\theta_{\\alpha} \\frac{\\alpha \\bar{y}_{j}}{\\alpha + \\bar{\\Sigma_{j}}}}{\\sum_{\\alpha \\in \\{0.5, 1.5\\}} \\theta_{\\alpha}} \\enspace \\text{ and } \\enspace \\VV[s_j | \\xb] = \\frac{\\sum_{\\alpha \\in \\{\\frac12, \\frac32\\}} \\theta_{\\alpha} \\frac{\\bar{\\Sigma_{j}}\\alpha}{\\alpha + \\bar{\\Sigma_{j}}}}{\\sum_{\\alpha \\in \\{0.5, 1.5\\}} \\theta_{\\alpha}}  \n\\end{align}\n    where $\\theta_{\\alpha} = \\Ncal(\\bar{y}_{j}; 0 , \\bar{\\Sigma}_{j} + \\alpha)$, \n    $\\bar{y}_j = \\frac{\\sum_i \\Sigma_{ij}^{-1} y_{ij}}{ \\sum_i\n      \\Sigma_{ij}^{-1}}$ and $\\bar{\\Sigma_{j}} = (\\sum_i\n    \\Sigma_{ij}^{-1})^{-1}$ with $\\yb_i = W_i \\xb_i$.\nNoise updates are in closed-form and given by:\n$\\Sigma_i \\leftarrow  \\diag((\\yb_i - \\EE[\\sbb | \\xb]) (\\yb_i - \\EE[\\sbb | \\xb])^{\\top}+ \\VV[\\sbb | \\xb])$.\nHowever, no closed-form is available for the updates of unmixing matrices. We therefore perform quasi-Newton updates given by\n$W_i \\leftarrow (I - \\rho (\\widehat{\\mathcal{H}^{W_i}})^{-1} \\mathcal{G}^{W_i}) W_i$ where $\\rho \\in \\mathbb{R}$ is chosen by backtracking line-search,\n$\\widehat{\\mathcal{H}^{W_i}_{a, b, c, d}} =  \\delta_{ad} \\delta_{bc} +\n\\delta_{ac} \\delta_{bd}\\frac{(y_{ib})^2}{\\Sigma_{ia}}$\nis an approximation of the Hessian\nof the negative complete likelihood and $\\mathcal{G}^{W_i} = -I + (\\Sigma_i)^{-1}(\\yb_i - \\mathbb{E}[\\sbb|\\xb])(\\yb_i)^{\\top}$ is the gradient.\n\nWe alternate between computing the statistics $\\mathbb{E}[\\sbb|\\xb]$, \n$\\mathbb{V}[\\sbb|\\xb]$ (E-step) and updates of parameters $\\Sigma_i$ and $W_i$ for $i=1 \\dots m$ (M-step). Let us highlight that our EM algorithm and in particular the E-step resembles the one used in~\\cite{moulines1997maximum}. However because they assume noise on the sensors and not on the components, their formula for $\\EE[\\sbb| \\xb]$ involves a sum with $2^p$ terms whereas we have only $2$ terms. The resulting method is called ShICA-ML.\n\n\\paragraph{Minimum mean square error estimates in ShICA}\nIn ShICA-J as well as in ShICA-ML, we have a closed-form for the expected components given the data $\\EE[\\sbb | \\xb]$, shown in equation~\\eqref{mmse1} and~\\eqref{mmse2} respectively. This provides minimum mean square error estimates of the shared components, and is an important benefit of explicitly modelling shared components in a probabilistic framework.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n  \n\n\\section{Related Work}\nShICA combines theory and methods coming from different branches of ``component analysis''. It can be viewed as a GroupICA method, as an extension of Multiset CCA, as an Independent Vector Analysis method or, crucially, as an extension of the shared response model. In the setting studied here, ShICA improves upon all existing methods.\n\n\\paragraph{GroupICA}\nGroupICA methods extract independent components from multiple datasets. In its original form\\cite{calhoun2001method}, views are concatenated and then a PCA is applied yielding reduced data on which ICA is applied. One can also reduce the data using Multiset CCA instead of PCA, giving a method called \\emph{CanICA}~\\cite{varoquaux2009canica}. Other works~\\cite{Esposito05NI, Hyva11NI} apply ICA separately on the datasets and attempt to match the decompositions afterwards.\nAlthough these works provide very fast methods, they do not rely on a well defined model like ShICA.\nOther GroupICA methods impose some structure on the mixing matrices such as the tensorial method of~\\cite{beckmann2005tensorial} or the group tensor model in~\\cite{guo2008unified} (which assumes identical mixing matrices up to a scaling) or \\cite{svensen2002ica} (which assumes identical mixing matrices but different components). In ShICA the mixing matrices are only constrained to be invertible.\nLastly, maximum-likelihood based methods exist such as\n\\emph{MultiViewICA}~\\cite{richard2020modeling} (MVICA) or the full model\nof~\\cite{guo2008unified}.\nThese methods are weaker than ShICA as they use the same noise covariance across views and lack a principled method for shared response inference.\n\n\\paragraph{Multiset CCA}\nIn its basic formulation, CCA identifies a shared space between two datasets.\nThe extension to more than two datasets is ambiguous, and many\ndifferent generalized CCA methods have been proposed. \\cite{kettenring1971canonical} introduces 6 objective functions that reduce to CCA when $m=2$ and \\cite{nielsen2002multiset} considered 4 different possible constrains leading to 24 different formulations of Multiset CCA. The formulation used in ShICA-J is refered to in~\\cite{nielsen2002multiset} as SUMCORR with constraint 4 which is one of the fastest as it reduces to solving a generalized eigenvalue problem. The fact that CCA solves a well defined probabilistic model has first been studied in~\\cite{bach2005probabilistic} where it is shown that CCA is identical to multiple battery factor analysis~\\cite{browne1980factor} (restricted to 2 views). This latter formulation differs from our model in that the noise is added on the sensors and not on the components which makes the model unidentifiable. Identifiable variants and\ngeneralizations can be obtained by imposing sparsity on the mixing matrices such as in~\\cite{archambeau2008sparse, klami2014group, witten2009extensions} or non-negativity~\\cite{DELEUS2011143}.\nThe work in~\\cite{li2009joint} exhibits a set of sufficient (but not necessary) conditions under which a well defined model can be learnt by the formulation of Multiset CCA used in ShICA-J. The set of conditions we exhibit in this work are necessary and sufficient. We further emphasize that basic Multiset CCA provides a poor estimator as explained in Section~\\ref{sec:samplingnoise}.\n\n\\paragraph{Independent vector analysis}\nIndependent vector analysis~\\cite{lee2008independent} (IVA) models the data as a linear mixture of independent components $\\xb_i = A_i \\sbb_i$ where each component $s_{ij}$ of a given view $i$ can depend on the corresponding component in other views ($(s_{ij})_{i=1}^m$ are not independent).\nPractical implementations of this very general idea assume a distribution for\n$p((s_{ij})_{i=1}^m)$. In IVA-L~\\cite{lee2008independent}, $p((s_{ij})_{i=1}^m)\n\\propto \\exp(-\\sqrt{\\sum_i (s_{ij})^2})$ (so the variance of each component in\neach view is assumed to be the same), in IVA-G~\\cite{anderson2011joint} or\nin~\\cite{via2011maximum}, $p((s_{ij})_{i=1}^m) \\sim \\mathcal{N}(0, R_{ss})$\nand~\\cite{engberg2016independent} proposed a normal inverse-Gamma density.\nLet us also mention IVA-L-SOS~\\cite{bhinge2019extraction}, IVA-GGD~\\cite{anderson2014independent} and\nIVA with Kotz distribution~\\cite{anderson2013independent} that assume a\nnon-Gaussian density general enough so that they can use both second and higher\norder statistics to extract view-specific components.\nThe model of ShICA can be seen as an instance of IVA\nwhich specifically enables extraction of shared components from the subject specific components, unlike previous versions of IVA. In fact, ShICA comes with minimum mean square error estimates for the shared components\nthat is often the quantity of interest.\nThe IVA theory provides global identifiability conditions in the Gaussian case (IVA-G)~\\cite{via2011joint} and local identifiability conditions in the general case~\\cite{anderson2014independent} from which local identifiability conditions of ShICA could be derived. However, in this work, we provide global identifiability conditions for ShICA.\nLastly, IVA can be performed using joint diagonalization of cross covariances~\\cite{li2011joint, congedo2012orthogonal} although multiple matrices have to be learnt and cross-covariances are not necessarily symmetric positive definite which makes the algorithm slower and less principled.\n\n\\paragraph{Shared response model}\nShICA extracts shared components from multiple datasets, which is also the goal\nof the shared response model (SRM)~\\cite{chen2015reduced}. The robust\nSRM~\\cite{turek2018capturing} also allows to capture subject specific noise.\nHowever these models impose orthogonality constraints on the mixing matrices\nwhile ShICA does not.\nDeep variants of SRM exist such\nas~\\cite{chen2016convolutional} but while they release the orthogonality\nconstrain, they are not very easy to train or interpret and have many\nhyper-parameters to tune. ShICA leverages ICA theory to provide a much more powerful model of shared responses.\n\n\\paragraph{Limitations}\nThe main limitation of this work is that the model cannot reduce the dimension inside each view : there are as many estimated sources as sensors. This might be problematic when the number of sensors is very high. In line with other methods, view-specific  dimension reduction has to be done by some external method, typically view-specific PCA. Using specialized methods for the estimation of covariances should also be of interest for ShICA-J, where it only relies on sample covariances. Finally, ShICA-ML uses a simple model of a super-Gaussian distribution, while modelling the non-gaussianities in more detail in ShICA-ML should improve the performance.\n\n\\section{Experiments}\nExperiments used Nilearn~\\cite{abraham2014machine} and MNE~\\cite{gramfort2013meg} for fMRI and MEG data\nprocessing respectively, as well as the scientific Python ecosystem:\nMatplotlib~\\cite{hunter2007matplotlib}, Scikit-learn~\\cite{pedregosa2011scikit},\nNumpy~\\cite{harris2020array} and Scipy~\\cite{2020SciPy-NMeth}. We use the Picard algorithm for non-Gaussian ICA~\\cite{ablin2018faster}, and mvlearn for multi-view ICA~\\cite{perry2020mvlearn}. The above libraries use open-source licenses. fMRI experiments used the following datasets: sherlock~\\cite{chen2017shared}, forrest~\\cite{hanke2014high} , raiders~\\cite{ibc} and gallant~\\cite{ibc}. The data we use do not contain offensive content or identifiable information and consent was obtained before data collection. Computations were run on a large server using up to 100 GB of RAM and 20 CPUs in parallel.\n\\paragraph{Separation performance}\n\\label{sec:rotation}\nIn the following synthetic experiments, data are generated according to model~\\eqref{eq:model} with $p=4$ components and $m=5$ views and mixing matrices are generated by sampling coefficients from a standardized Gaussian.\nGaussian components are generated from a standardized Gaussian and their noise\nhas standard deviation $\\Sigma_i^{\\frac12}$ (obtained by sampling from a uniform\ndensity between $0$ and $1$) while non-Gaussian components are generated from a\nLaplace distribution and their noise standard deviations are equal. We study 3\ncases where either all components are Gaussian, all components are non-Gaussian\nor half of the components are Gaussian and half are non-Gaussian.\nWe vary the\nnumber of samples $n$ between $10^2$ and $10^5$ and display in\nFig~\\ref{exp:rotation} the mean Amari distance across subjects between the true unmixing\nmatrices and estimates of algorithms as a function of $n$.\nThe experiment is repeated $100$ times using different seeds. We report the median result and error bars represent the first and last deciles.\n\\begin{figure}\n  \\centering\n  \\includegraphics[width=\\textwidth]{.\/figures\/identifiability2.pdf}\n  \\caption{\\textbf{Separation performance}: Algorithms are fit on data following model~\\ref{eq:model} \\textbf{(a)} Gaussian components with noise diversity \\textbf{(b)} Non-Gaussian components without noise diversity \\textbf{(c)} Half of the components are Gaussian with noise diversity, the other half is non-Gaussian without noise diversity. }\n  \\label{exp:rotation}\n\\end{figure}\n\nWhen all components are Gaussian (Fig.~\\ref{exp:rotation}~(a)), CanICA cannot\nseparate the components at all. In contrast ShICA-J, ShICA-ML, Multiset CCA and\nMVICA are able to separate them, but Multiset CCA needs many more samples than\nShICA-J or ShICA-ML to reach a low amari distance, which shows that correcting for the rotation due to sampling noise improves the results. Looking at error bars, we also see that the performance of Multiset CCA varies quite a lot with the random seeds: this shows that depending on the sampling noise, the rotation can be very different from identity.\nMVICA needs even more sample than Multiset CCA to reach a low amari distance but\nstill outperforms CanICA.\n\nWhen none of the components are Gaussian (Fig.~\\ref{exp:rotation}~(b)), only\nCanICA, ShICA-ML and MVICA are able to separate the components, as other methods do not make use of non-Gaussianity.\nFinally, in the hybrid case (Fig.~\\ref{exp:rotation}~(c)), ShICA-ML is able to\nseparate the components as it can make use of both non-Gaussianity and noise\ndiversity. MVICA is a lot less reliable than ShICA-ML, it is uniformly worse and\nerror bars are very large showing that for some seeds it gives poor results.\nCanICA, ShICA-J and MultisetCCA cannot separate the components at all.\nAdditional experiments illustrating the separation powers of algorithms are available in Appendix~\\ref{app:separation}.\n\n\nAs we can see, MVICA can separate Gaussian components to some extent and therefore does not completely fail when Gaussian and non-Gaussian components are present. However MVICA is a lot less reliable than ShICA-ML: MVICA is uniformly worse than ShICA-ML and the error bars are very large showing that for some seeds it gives poor results.\n\n\\paragraph{Computation time}\n\n\n\\begin{figure}\n  \\centering\n  \\begin{subfigure}[b]{0.49\\textwidth}\n      \\centering\n      \\includegraphics[width=\\textwidth]{.\/figures\/synthetic_gaussian_timings.pdf}\n      \\caption{}\n      \\label{exp:syn_timings}\n  \\end{subfigure}\n  \\hfill\n  \\begin{subfigure}[b]{0.45\\textwidth}\n    \\centering\n    \\includegraphics[width=\\textwidth]{.\/figures\/inter_subject_stability.pdf}\n    \\caption{}\n    \\label{fig:eeg_intragroup_variability}\n\\end{subfigure}\n     \\caption{\\textbf{Left: Computation time.} Algorithms are fit on data generated from model~\\eqref{eq:model} with a super-Gaussian density. For different values of the number of samples, we plot the Amari distance and the fitting time. Thick lines link median values across seeds. \\textbf{Right: Robustness w.r.t intra-subject variability in MEG.}\n     (\\textbf{top}) $\\ell_2$ distance between shared components corresponding to the same stimuli in different trials.  (\\textbf{bottom}) Fitting time.}\n\\end{figure}\nWe generate components using a slightly super Gaussian density: $s_j = d(x)$ with $d(x) = x |x|^{0.2}$ and $x \\sim \\mathcal{N}(0, 1)$. We vary the number of samples $n$ between $10^2$ and $10^4$. We compute the mean Amari distance across subjects and record the computation time. The experiment is repeated $40$ times. We plot the Amari distance as a function of the computation time in Fig~\\ref{exp:syn_timings}. Each point corresponds to the Amari distance\/computation time for a given number of samples and a given seed. We then consider for a given number of samples, the median Amari distance and computation time across seeds and plot them in the form of a thick line.  From Fig~\\ref{exp:syn_timings}, we see that ShICA-J is the method of choice when speed is a concern while ShICA-ML yields the best performance in terms of Amari distance at the cost of an increased computation time. The thick lines for ShICA-J and Multiset CCA are quasi-flat, indicating that the number of samples does not have a strong impact on the fitting time as these methods only work with covariances. On the other hand CanICA or MVICA computation time is more sensitive to the number of samples.\n\n\n\n\n\\paragraph{Robustness w.r.t intra-subject variability in MEG}\n\nIn the following experiments we consider the Cam-CAN\ndataset~\\cite{taylor2017cambridge}. We use the magnetometer data from the MEG of\n$m=100$ subjects chosen randomly among 496.\nIn appendix~\\ref{app:preprocessing}\nwe give more information about Cam-CAN dataset.\nEach subject is repeatedly presented three audio-visual stimuli. \nFor each stimulus, we divide the trials into two sets and within each set,\nthe MEG signal is averaged across trials to isolate the evoked response. This\nprocedure yields 6 chunks of individual data (2 per stimulus).\nWe study the similarity between shared components corresponding to repetitions of the same stimulus. This gives a measure of robustness of each ICA algorithm with respect\nto intra-subject variability.\nData are first reduced using a subject-specific PCA with $p=10$ components.\nThe initial dimensionality of the data before PCA is $102$ as we only use the 102 magnetometers.\nAlgorithms are run 10 times with different seeds on the 6 chunks of data,\nand shared components are extracted.\nWhen two chunks of data correspond to repetitions of the same stimulus they should yield similar\ncomponents.\nFor each component and for each stimulus, we therefore measure the $\\ell_2$\ndistance between the two repetitions of the stimulus.\n This yields $300$ distances per algorithm that are\nplotted on Fig~\\ref{fig:eeg_intragroup_variability}.\n\nThe components recovered by ShICA-ML have a much lower variability than other approaches. The performance of ShICA-J is competitive with MVICA while being much faster to fit. Multiset CCA yields satisfying results compared with ShICA-J. However we see that the number of components that do not match at all across trials is greater in Multiset CCA.\n   \nAdditional experiments on MEG data are available in Appendix~\\ref{app:phantom}.\n\n\n\n\\paragraph{Reconstructing the BOLD signal of missing subjects}\n\\begin{wrapfigure}{l}{.42\\textwidth}\n  \\centering\n  \\includegraphics[width=0.99\\linewidth]{.\/figures\/reconstruction.pdf}\n  \\includegraphics[width=0.99\\linewidth]{.\/figures\/reconstruction_timings.pdf}\n  \n  \\caption{\\textbf{Reconstructing the BOLD signal of\n      missing subjects}. (\\textbf{top}) Mean $R^2$ score between reconstructed data and true\n    data. (\\textbf{bottom}) Fitting time.\n   \n    }\n  \\label{fig:reconstruction}\n\\end{wrapfigure}\nWe reproduce the experimental pipeline of~\\cite{richard2020modeling} to benchmark GroupICA methods using their ability to reconstruct fMRI data of a left-out subject.\nThe preprocessing involves a dimension reduction step performed using the shared response model~\\cite{chen2015reduced}. Detailed preprocessing pipeline is described in Appendix~\\ref{app:preprocessing}. We call an \\emph{unmixing operator} the product of the dimension\nreduction operator and an unmixing matrix and a \\emph{mixing operator} its pseudoinverse. There is one unmixing operator and one mixing operator per view.\nThe unmixing operators are learned using all subjects\nand $80\\%$ of the runs. Then they are applied on the remaining $20\\%$ of the runs using $80\\%$\nof the subjects yielding unmixed data from which shared components are\nextracted.\nThe unmixed data are combined by averaging (for SRM and other baselines) or using the MMSE estimate for ShICA-J and ShICA-ML.\nWe\nthen apply the mixing operator of the remaining $20\\%$ subjects on the shared components to reconstruct their data.\nReconstruction accuracy is measured via the coefficient of determination, \\aka $R^2$ score, that\nyields for each voxel the relative discrepancy between the true time course and the predicted one.\nFor each compared algorithm, the experiment is run 25 times with different seeds to obtain error bars. We report the mean $R^2$ score across voxels in a region of interest (see Appendix~\\ref{app:preprocessing} for details)\n and display the results in Fig~\\ref{fig:reconstruction}. The error bars represent a $95\\%$ confidence interval.\nThe chance level is given by the $R^2$ score of an algorithm that samples the\ncoefficients of its unmixing matrices and dimension reduction operators from a\nstandardized Gaussian. The median chance level is below $10^{-3}$ on all\ndatasets.\nShICA-ML yields the best $R^2$ score in all datasets and for any number of\ncomponents. ShICA-J yields competitive results with respect to MVICA\nwhile being much faster to fit. A popular benchmark especially in the SRM\ncommunity is the time-segment matching experiment~\\cite{chen2015reduced}: we\ninclude such experiments in Appendix~\\ref{app:timesegment}.\nIn\nappendix~\\ref{app:table}, we give the performance of ShICA-ML, ShICA-J and MVICA\nin form of a table.\n\n\n\n\n\\section{Conclusion, Future work and Societal impact}\n\nWe introduced the ShICA model as a principled unifying solution to the problems of shared response modelling and GroupICA. ShICA is able to use both the diversity of Gaussian variances and non-Gaussianity for optimal estimation. We presented two algorithms to fit the model: ShICA-J, a fast algorithm that uses noise diversity, and ShICA-ML, a maximum likelihood approach that can use non-Gaussianity on top of noise diversity. ShICA algorithms come with principled procedures for shared components estimation, as well as adaptation and estimation of noise levels in each view (subject) and component. On simulated data, ShICA clearly outperforms all competing methods in terms of the trade-off between statistical accuracy and computation time. On brain imaging data, ShICA gives more stable decompositions for comparable computation times, and more accurately predicts the data of one subject from the data of other subjects, making it a good candidate to perform transfer learning. \nOur code is available at \\url{https:\/\/github.com\/hugorichard\/ShICA}.\n\\footnote{Regarding the ethical aspects of this work, we think this work presents exactly the same issues as any brain imaging analysis method related to ICA.}\n\\clearpage\n\\paragraph{Acknowledgement and funding disclosure}\nThis work has received funding\nfrom the European Union's Horizon 2020 Framework Programme for Research and Innovation under\nthe Specific Grant Agreement No. 945539 (Human Brain Project SGA3), the KARAIB AI chair\n(ANR-20-CHIA-0025-01), the Grant SLAB ERC-StG-676943 and the BrAIN AI chair (ANR-20-CHIA-0016). PA acknowledges funding by the French government under management of Agence Nationale de la Recherche as part of the \"Investissements d'avenir\" program, reference ANR19-P3IA-0001 (PRAIRIE 3IA Institute). AH received funding from a CIFAR Fellowship. \n\n\n\n\\bibliographystyle{plain}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nIn quantum information science,\nmany figures of merit such as fidelity and von Neumann entropy \\cite{Nielsen2010} are utilized to characterize a quantum state.\nQuantum state tomography (QST) \\cite{James2001},\nby which a quantum density operator of an unknown quantum state is identified,\nis the most comprehensive method for deriving them.\nRecently, QST for photonic high-dimensional quantum states (qudits) \\cite{Thew2002} has been intensively investigated for\nentanglements based on orbital angular momentum \\cite{Agnew2011},\nfrequency bins \\cite{Bernhard2013},\nand time-energy uncertainty \\cite{Richart2014}.\nObservation of high-dimensional multipartite entanglement has also been reported \\cite{Malik2016}.\nFor time-bin qudits, which are promising candidates for transmission over an optical fiber,\nQST based on the conversion between time-bin states and polarization states has been performed \\cite{Nowierski2015}.\nQST generally requires $(d^2 - 1)$ different measurements for a state in $d$ dimensional Hilbert spaces\nbecause a general mixed state is characterized by $(d^2 - 1)$ real numbers.\nThus, it is important to reduce the number of measurement settings for high-dimensional QST.\nFor time-bin qubits,\nQST has been performed with a single delay Mach-Zehnder interferometer (MZI) \\cite{Takesue2009},\nwhich simultaneously constructed measurements projecting on two time-bin basis states and a superposition state of the time-bin basis.\nIn this paper, we propose an efficient scheme to implement QST for time-bin qudits utilizing cascaded delay MZIs \\cite{Ikuta2016a,Richart2012}.\nThanks to the simultaneous construction of the different measurements,\nthe number of measurement settings scales linearly with dimension $d$.\n\n\n\n\n\\section{\\label{sec:QSTDetail}Measurements with cascaded MZIs}\n\\subsection{\\label{sec:BasicQST}Basic concept}\n\nFirst, we give a general description of QST.\nA $d$-dimensional density operator $\\op{\\rho}$ can be expressed as $\\op{\\rho} = \\sum_{i=0}^{d^2-1} g_i \\op{G}_i$,\nwhere $\\op{G}_i$ is the generalized Gell-Mann matrix defined in \\cite{Thew2002}\nand $g_i$ is a real number.\n$g_0$ is usually fixed to $1\/d$ to be $\\mathrm{Tr}\\left( \\op{\\rho} \\right) = 1$,\nbecause $\\op{G}_i$ is traceless for $i \\geq 1$ and $\\op{G}_0$ is the identity operator $\\op{I}_d$.\nWhen we repeat a measurement represented by a projector $\\op{P}_j$ for $N$ photons,\nthe expected values of the photon counts $n_j^E$ is given by\n\\begin{equation}\nn_j^E = N \\mathrm{Tr} \\left( \\op{P}_j \\op{\\rho} \\right) = N \\sum_{i = 0}^{d^2 - 1} A_{ij} g_i\t,\t\\label{eq:ConceptOfQST}\n\\end{equation}\nwhere $A_{ij} = \\mathrm{Tr} \\left( \\op{P}_j \\op{G}_i \\right)$.\nWe can estimate $N$ and $g_i$ by multiplying the inverse matrix of $A_{ij}$ from the left of \\eref{eq:ConceptOfQST}.\nThus, the problem remaining to complete QST is how to prepare a set of measurements\nthat correspond to $\\op{P}_j$ for constructing $A_{ij}$ with rank $d^2$.\n\nTo prepare such a set of measurements for time-bin qudits,\nwe use cascaded MZIs.\n\\Fref{fig:CMZI} shows the concept of the measurements with the cascaded MZIs for a four-dimensional time-bin state.\n\\begin{figure}[htbp]\n\\centering\n\\includegraphics[width=\\linewidth]{figure01_ConceptOfCMZI.eps}\n\\caption{Concept of QST utilizing cascaded MZIs.}\n\\label{fig:CMZI}\n\\end{figure}\nThe 2-bit delay MZI has time delay $2T$ and phase difference $\\theta_2$,\nwhere $T$ denotes the temporal interval of time slots constituting the time-bin basis\nand $\\theta_2$ is the phase difference between the short and the long arms of the 2-bit delay MZI.\nThe 1-bit delay MZI has time delay $T$ and phase difference $\\theta_1$.\nThe output ports of the 2-bit delay MZI, $p_{2x}$ and $p_{2y}$, are connected to the input port of the 1-bit delay MZI and photon detector D2, respectively.\nThe output port of the 1-bit delay MZI, $p_{1x}$, is connected to photon detector D1,\nand the other output port, $p_{1y}$, is terminated.\nWhen the time-bin qudit is launched into the cascaded MZIs,\nD1 can detect a photon in a superposition of four different input states.\nOn the other hand,\nD2 cannot,\nbut it can detect a photon projected on the time-bin basis, which D1 cannot.\nTherefore, the information obtained from D1 and D2 are intrinsically different.\nWe utilize the number of photons detected by D1 and D2 at different detection times as $n_j^E$ in \\eref{eq:ConceptOfQST}.\n\nIn what follows, we describe the measurements by the cascaded MZIs in more detail.\nThe basis for the four-dimensional time-bin state is given by state $\\ket{k} (k \\in [0, 3])$\nin which a photon exists in the $k$th time slot.\nWhen pure state $\\ket{k}$ is launched into the 2-bit delay MZI,\nthe output state at port $p_{2x}$ is $\\op{M}_{2x} \\ket{k}$,\nwhere generalized measurement operator $\\op{M}_{2x}$ is given by\n\\begin{equation}\n\\op{M}_{2x} = \\frac{1}{2} \\sum_{k=0}^3 \\left( \\ket{k} + e^{i \\theta_2} \\ket{k+2} \\right) \\bra{k}\t\t.\n\\end{equation}\nSimilarly,\nwe can obtain the operators representing the measurements of each MZI at ports $p_{2y}, p_{1x}$, and $p_{1y}$ as follows.\n\\begin{eqnarray}\n\\op{M}_{2y} &=& \\frac{1}{2} \\sum_{k=0}^3 \\left( - \\ket{k} + e^{i \\theta_2} \\ket{k+2} \\right) \\bra{k}\t\t,\t\\\\\n\\op{M}_{1x} &=& \\frac{1}{2} \\sum_{k=0}^5 \\left( \\ket{k} + e^{i \\theta_1} \\ket{k+1} \\right) \\bra{k}\t\t,\t\\\\\n\\op{M}_{1y} &=& \\frac{1}{2} \\sum_{k=0}^5 \\left( -\\ket{k} + e^{i \\theta_1} \\ket{k+1} \\right) \\bra{k}\t\t.\n\\end{eqnarray}\n\nPhoton detectors D1 and D2 detect a photon at different detection times, $t_l$, for $l \\in [0, 6]$,\nwhich correspond to the projection measurements $\\op{M}_D = \\ket{l} \\! \\bra{l}$.\nTherefore,\nthe expected value $n^E_{D1 l \\theta_1 \\theta_2}$ of the photons detected by D1 at time $t_l$ is given by\n\\begin{eqnarray}\nn^E_{D1 l \\theta_1 \\theta_2} &=& N \\mathrm{Tr} \\left(\n\t\\op{M}_D\n\t\t\\op{M}_{1x}\n\t\t\t\\op{M}_{2x}\n\t\t\t\t\\op{\\rho}\n\t\t\t\\op{M}_{2x}^{\\dag}\n\t\t\\op{M}_{1x}^{\\dag}\n\t\\op{M}_D^{\\dag}\n\\right)\t\t\\\\\n\t&=& N \\mathrm{Tr} \\left( \\op{E}_{l \\theta_1 \\theta_2}^{D1} \\op{\\rho} \\right)\t\t,\t\\label{eq:E(Count)ltt}\n\\end{eqnarray}\nwhere we define the element of the positive operator valued measure\n$\\op{E}_{l \\theta_1 \\theta_2}^{D1} = \\op{M}_{2x}^{\\dag} \\op{M}_{1x}^{\\dag} \\op{M}_D^{\\dag} \\op{M}_D \\op{M}_{1x} \\op{M}_{2x}$.\nThe element of the positive operator valued measure for D2 is similarly defined as \n$\\op{E}_{l \\theta_1 \\theta_2}^{D2} = \\op{M}_{2y}^{\\dag} \\op{M}_D^{\\dag} \\op{M}_D \\op{M}_{2y}$.\nTo see what the measurement is performed by $\\op{E}_{l \\theta_1 \\theta_2}^{DX}$ for $DX \\in \\{D1, D2\\}$,\nit is convenient to estimate the simplified forms of $\\op{M}_D \\op{M}_{1x} \\op{M}_{2x}$ and $\\op{M}_D \\op{M}_{2y}$.\nFortunately,\n$\\op{M}_D$ is the projection onto the $l$th time slot for output states;\nthus, they have the simplified forms as $w_{DX l} \\ket{l} \\bra{\\psi^{DX}_{l \\theta_1 \\theta_2}}$,\nwhere $w_{DX l}$ is a complex weight\nand $\\ket{\\psi^{DX}_{l \\theta_1 \\theta_2}}$ is a normalized state in four-dimensional state.\nAll the simplified forms of the measurement operators are summarized in \\tref{tab:OpList}.\nTherefore,\n$\\op{E}_{l \\theta_1 \\theta_2}^{DX}$ returns the measurement result by the projector $\\ket{\\psi^{DX}_{l \\theta_1 \\theta_2}} \\bra{\\psi^{DX}_{l \\theta_1 \\theta_2}}$,\nexcluding the difference in weight $|w_{DX l}|^2$.\nThe simplified forms are easier to understand,\nbut the multiplication forms like $\\op{M}_D \\op{M}_{1x} \\op{M}_{2x}$ are more convenient for expanding the dimension\nor compensating for the imperfections due to measurement equipment as described later.\n\n\n\\begin{table}\n\t\\caption{\\label{tab:OpList}Measurement operators at different detection times and detector.}\n\t\\begin{indented}\n\t\\lineup\n\t\\item[]\n\t\t\\begin{tabular}{@{}ccr@{}r@{}r@{}r@{}r@{}r}\n\t\t\t\\br\n\t\t\tDetector & Detection time & \\multicolumn{6}{c}{Measurement operator}\t\\\\\n\t\t\t\\mr\n\t\t\tD1 & $t_0$ & $\\frac{1}{4} \\ket{0}$ & & $\\bra{0}$ &&& \\\\\n\t\t\t & $t_1$ & $\\frac{1}{4} \\ket{1}$ & $($ & $\\bra{1}$ & $+e^{i \\theta_1}\\bra{0}$ && $)$\t\\\\\n\t\t\t & $t_2$ & $\\frac{1}{4} \\ket{2}$ & $($ & $\\bra{2}$ & $+e^{i \\theta_1}\\bra{1}$ & $+e^{i \\theta_2}\\bra{0}$ & $)$\t\\\\\n\t\t\t & $t_3$ & $\\frac{1}{4} \\ket{3}$ & $($ & $\\bra{3}$ & $+e^{i \\theta_1}\\bra{2}$ & $+e^{i \\theta_2}\\bra{1}$ & $+e^{i (\\theta_1 + \\theta_2)}\\bra{0})$\t\\\\\n\t\t\t & $t_4$ & $\\frac{1}{4} \\ket{4}$ & $($ && $e^{i \\theta_1}\\bra{3}$ & $+e^{i \\theta_2}\\bra{2}$ & $+e^{i (\\theta_1 + \\theta_2)}\\bra{1})$\t\\\\\n\t\t\t & $t_5$ & $\\frac{1}{4} \\ket{5}$ & $($ &&& $e^{i \\theta_2}\\bra{3}$ & $+e^{i (\\theta_1 + \\theta_2)}\\bra{2})$\t\\\\\n\t\t\t & $t_6$ & $\\frac{1}{4} \\ket{6}$ & $($ &&&& $e^{i (\\theta_1 + \\theta_2)}\\bra{3})$\t\\\\\n\t\t\t\\cline{2-8}\n\t\t\tD2 & $t_0$ & $-\\frac{1}{2} \\ket{0}$ && $\\bra{0}$ &&&\t\t\\\\\n\t\t\t & $t_1$ & $-\\frac{1}{2} \\ket{1}$ && $\\bra{1}$ &&&\t\t\\\\\n\t\t\t & $t_2$ & $-\\frac{1}{2} \\ket{2}$ & $($ & $\\bra{2}$ && $-e^{i \\theta_2}\\bra{0}$ & $)$\t\\\\\n\t\t\t & $t_3$ & $-\\frac{1}{2} \\ket{3}$ & $($ & $\\bra{3}$ && $-e^{i \\theta_2}\\bra{1}$ & $)$\t\\\\\n\t\t\t & $t_4$ & $-\\frac{1}{2} \\ket{4}$ & $($ &&& $-e^{i \\theta_2}\\bra{2}$ & $)$\t\\\\\n\t\t\t & $t_5$ & $-\\frac{1}{2} \\ket{5}$ & $($ &&& $-e^{i \\theta_2}\\bra{3}$ & $)$\t\\\\\n\t\t\t\\br\n\t\t\\end{tabular}\n\t\\end{indented}\n\\end{table}\n\n\n\nAs in the QST for qubits,\nwe need to rotate $\\theta_1$ and $\\theta_2$ to complete the QST for qudits.\nWe use the same combinations of phase differences $\\theta_1$ and $\\theta_2$ utilized\nfor the time-energy entangled qudits \\cite{Richart2014}.\nThe total Hilbert space of the time-energy entangled qudits is spanned by two different logical qubits.\nOne is the qubit defined by the short and the long arms of the 1-bit delay MZI,\nand the other is the qubit defined by the short and the long arms of the 2-bit delay MZI.\nTherefore,\nthe high-dimensional QST is performed by the combination of the QST for logical qubits.\nSetting the phase differences between the arms at $0$ and $\\pi\/2$ corresponds\nto the measurements by the Pauli matrices $\\sigma_x$ and $\\sigma_y$ \\cite{Nielsen2010} for logical qubits, respectively.\nTherefore, combinations of phase differences $(\\theta_1, \\theta_2) = (0,0), (0, \\pi\/2), (\\pi\/2, 0)$, and $(\\pi\/2, \\pi\/2)$\nare sufficient to obtain the information about the phase of the qudits.\n\nOn the other hand,\nQST for qubits usually requires a measurement corresponding to the Pauli matrix $\\sigma_z$,\nwhich implies that it requires measurements without interference.\nThe measurement corresponding to $\\sigma_z$ for both the logical qubits are performed by D2 at $t_0, t_1, t_4$ and $t_5$,\nbecause the states $\\ket{\\psi^{D2}_{l \\theta_1 \\theta_2}}$ at these times are single time-bin basis states that correspond to eigenstates of $\\sigma_z$.\nHowever,\nwe need to prepare not only a $\\sigma_z \\otimes \\sigma_z$ measurement for logical qubits that doesn't completely interfere\nbut also measurements that partially interfere like a $\\sigma_z \\otimes \\sigma_x$ measurement.\nFrom this point,\nthe measurements by D1 at different detection times play an important role in the proposed scheme,\nbecause the interference pattern of the measurement $\\op{E}_{l \\theta_1 \\theta_2}^{D1}$ depends on detection time $t_l$ as shown in \\fref{fig:CMZI} and \\tref{tab:OpList}.\nIn other words,\nthe combination of the time-bin basis constituting $\\ket{\\psi^{D1}_{l \\theta_1 \\theta_2}}$ varies depending on the detection time.\nThe measurement at $t_0$ by D1 corresponds to the projection onto the single time-bin basis $\\ket{0}$,\nthe measurement at $t_1$ by D1 corresponds to the projection onto a superposition of $\\ket{0}$ and $\\ket{1}$, and so on.\n\n\nConsidering these characteristics of $\\op{E}_{l \\theta_1 \\theta_2}^{DX}$ described above,\nit is expected that the QST for time-bin qudits can be performed only by switching $\\theta_1$ and $\\theta_2$,\nwhich is confirmed by comparing \\eref{eq:ConceptOfQST} and \\eref{eq:E(Count)ltt}\nand by estimating the rank of $A_{ij}$.\nThe proposed scheme can be extended to general $d$-dimensional QST by adding extra MZIs.\nThe number of the MZIs for $d$-dimensional QST is $K$ given by $\\lceil \\log_2 d \\rceil$,\nwhere $\\lceil x \\rceil$ is the ceiling function for $x \\in \\mathbb{R}$.\nThe $K$ delay MZIs have different delay times $2^{i-1} T$ and phase differences $\\theta_i$ for $1 \\leq i \\leq K$.\nEach $\\theta_i$ takes $0$ and $\\pi \/ 2$ independently;\nthus, the number of measurement settings scales linearly with $d$.\n\nIt should be noted that we can implement QST for time-bin qudits without D2,\nwhich is confirmed from the rank of $A_{ij}$.\nHowever,\nD2 not only detects the photon which would be lost without it\nbut also collects information different from that obtained by D1.\nFor example,\nD1 cannot implement the measurement corresponding to the projection onto $\\ket{1}$, which D2 can.\nThis implies that D2 observes the same state from a different angle on the high-dimensional Bloch sphere.\nTherefore, the addition of D2 effectively improves the accuracy of the QST in the same measurement time.\n\n\n\n\\subsection{\\label{sec:LossComp}Compensation for imperfections}\n\nThe measurements described in subsection \\ref{sec:BasicQST} are ideal ones without imperfection.\nIn practice,\nthere are no ideal 50 : 50 beam splitters and no photon detectors with $100 \\%$ detection efficiency.\nFurthermore, when we utilize delay MZIs made with planar light wave circuit technology (PLC),\nthe difference in the optical path length between the long and the short arms causes imperfection due to medium loss.\nHowever,\nthe following modifications of the measurement operators can compensate for such imperfections:\n\\begin{eqnarray}\n\\op{M}_{2x} &=& \\frac{\\sum_{k=0}^3 \\left( \\ket{k} + \\sqrt{\\mathit{\\Delta} \\eta_{2x} } e^{i \\theta_2} \\ket{k+2} \\right) \\bra{k}}{\\sqrt{2\\left( 1+\\mathit{\\Delta} \\eta_{2x} \\right)}} \t\t,\t\\label{eq:CompM2x}\t\\\\\n\\op{M}_{2y} &=& \\frac{\\sum_{k=0}^3 \\left( - \\ket{k} + \\sqrt{\\mathit{\\Delta} \\eta_{2y} } e^{i \\theta_2} \\ket{k+2} \\right) \\bra{k}}{\\sqrt{2\\left( 1+\\mathit{\\Delta} \\eta_{2y} \\right)}} \t\t,\t\\label{eq:CompM2y}\t\\\\\n\\op{M}_{1x} &=& \\frac{\\sum_{k=0}^5 \\left( \\ket{k} + \\sqrt{\\mathit{\\Delta} \\eta_{1x} } e^{i \\theta_1} \\ket{k+1} \\right) \\bra{k}}{\\sqrt{2\\left( 1+\\mathit{\\Delta} \\eta_{1x} \\right)}} \t\t,\t\\label{eq:CompM1x}\t\\\\\n\\op{M}_{1y} &=& \\frac{\\sum_{k=0}^5 \\left( -\\ket{k} + \\sqrt{\\mathit{\\Delta} \\eta_{1y} } e^{i \\theta_1} \\ket{k+1} \\right) \\bra{k}}{\\sqrt{2\\left( 1+\\mathit{\\Delta} \\eta_{1y} \\right)}} \t\t,\t\\label{eq:CompM1y}\t\\\\\n\\op{E}_{l \\theta_1 \\theta_2}^{D1} &=& \\mathit{\\Delta} \\eta_{1} \\op{M}_{2x}^{\\dag} \\op{M}_{1x}^{\\dag} \\op{M}_D^{\\dag} \\op{M}_D \\op{M}_{1x} \\op{M}_{2x}\t,\t\\label{eq:CompED1}\t\\\\\n\\op{E}_{l \\theta_1 \\theta_2}^{D2} &=& \\op{M}_{2y}^{\\dag} \\op{M}_D^{\\dag} \\op{M}_D \\op{M}_{2y}\t,\t\\label{eq:CompED2}\n\\end{eqnarray}\nwhere $\\mathit{\\Delta} \\eta_{2x}, \\mathit{\\Delta} \\eta_{2y}, \\mathit{\\Delta} \\eta_{1x}, \\mathit{\\Delta} \\eta_{1y},$ and $\\mathit{\\Delta} \\eta_{1}$ are relative transmittances.\nRelative transmittances are the ratios between the transmittances depending on the optical paths and detectors.\nWe utilizes the relative values rather than absolute ones for experimental and theoretical convenience.\nThe use of the relative values decreases the expected value of the total photon number $N$ obtained by QST;\nthus, it is not an accurate modification in this sense.\nHowever,\nthe expected density operator $\\op{\\rho}$ will not change because $\\op{\\rho}$ is determined by the relative values of the photon counts.\nTherefore,\nthe use of the relative values is justified for the purpose of QST.\n\n\n\n\\subsection{\\label{sec:MLE}Maximum likelihood estimation}\n\nAs we mentioned in subsection \\ref{sec:BasicQST},\nQST for time-bin qudits can be performed by linear conversion of \\eref{eq:ConceptOfQST}.\nHowever,\nit is well known that\nthe density operator obtained by linear conversion does not often satisfy positivity,\nwhich implies the estimated density operator is unphysical \\cite{James2001}.\nMaximum likelihood estimation (MLE) is often used to avoid this problem \\cite{Agnew2011,James2001,Richart2014,Takesue2009}.\nFirst,\nwe use another representation of $\\op{\\rho}$ to enforce positivity as follows:\n\\begin{eqnarray}\n\\op{\\rho} &=& \\frac{\\op{R}^\\dag \\op{R}}{ \\mathrm{Tr} \\left( \\op{R}^\\dag \\op{R} \\right)}\t\t,\t\\\\\nN &=& \\mathrm{Tr} \\left( \\op{R}^\\dag \\op{R} \\right)\t,\n\\end{eqnarray}\nwhere $\\op{R}$ is an operator having a triangular form \\cite{James2001}.\nMLE is performed by finding $\\op{R}$ that minimizes the likelihood function $L\\left(\\op{R}\\right)$ given by\n\\begin{equation}\nL\\left(\\op{R}\\right) = \\sum_j \\left[ \\frac{\\left(n_j^M - n_j^E \\right)^2}{n_j^E} + \\ln n_j^E\t\\right]\t,\t\\label{eq:MLE}\n\\end{equation}\nwhere $n_j^M$ is the measured photon count and $n_j^E$ is the expected photon count in \\eref{eq:ConceptOfQST}.\nThe summation over $j$ is calculated for $j$ indicating different measurements.\nNote that we add $\\ln n_j^E$ to the likelihood function given in \\cite{James2001}.\nThe likelihood function is derived from the probability of obtaining a set of photon counts $n_j^M$,\nwhich is given by\n\\begin{equation}\nP = \\frac{1}{N_{norm}} \\prod_j \\exp \\left[ - \\frac{\\left(n_j^M - n_j^E \\right)^2}{2 \\sigma_j^2} \\right]\t,\n\\end{equation}\nwhere $N_{norm}$ is the normalization constant and $\\sigma_j \\approx \\sqrt{n_j^E}$ is the standard deviation for the $j$th measurement.\nHowever,\nthe normalization constant $N_{norm}$ can be approximated by $\\prod_j \\sqrt{2\\pi}\\sigma_j$ with Gaussian approximation,\nwhich leads to the additional term  $\\ln n_j^E$.\nTo perform MLE according to \\eref{eq:MLE},\nwe need to precisely map $n^E_{D1 l \\theta_1 \\theta_2}$ and $n^E_{D2 l \\theta_1 \\theta_2}$ to $n_j^E$\nbecause the intrinsically same measurements exist in the measurement settings.\nFor example,\nthe measurement at $t_0$ by D1 corresponding to the projection onto $\\ket{0}$ does not depend on $\\theta_1$ and $\\theta_2$.\nFor this purpose,\nwe introduce space $V_j$,\nwhich satisfies the following conditions:\n\\begin{eqnarray}\n^\\forall \\left(DX, l, \\theta_1, \\theta_2 \\right) \\in V_j \\ , \\ ^\\forall \\left( DX', l', \\theta_1', \\theta_2' \\right) \\in V_{j'}\t\\nonumber\\\\\n\\frac{\\op{E}_{l \\theta_1 \\theta_2}^{DX}}{\\mathrm{Tr} \\left( \\op{E}_{l \\theta_1 \\theta_2}^{DX} \\right)}\n=\n\\frac{\\op{E}_{l' \\theta_1' \\theta_2'}^{DX'}}{\\mathrm{Tr} \\left( \\op{E}_{l' \\theta_1' \\theta_2'}^{DX'} \\right)}\n\\qquad\n\\mbox{for}\n\\qquad\nj=j'\t,\t\t\\label{eq:Vcondition1}\n\\\\\n\\frac{\\op{E}_{l \\theta_1 \\theta_2}^{DX}}{\\mathrm{Tr} \\left( \\op{E}_{l \\theta_1 \\theta_2}^{DX} \\right)}\n\\neq\n\\frac{\\op{E}_{l' \\theta_1' \\theta_2'}^{DX'}}{\\mathrm{Tr} \\left( \\op{E}_{l' \\theta_1' \\theta_2'}^{DX'} \\right)}\n\\qquad\n\\mbox{for}\n\\qquad\n j \\neq j'\t.\t\\label{eq:Vcondition2}\n\\end{eqnarray}\nSpace $V_j$ is numerically generated via a comparison according to \\eref{eq:Vcondition1} and \\eref{eq:Vcondition2}.\nBy utilizing $V_j$,\nwe can map $n^E_{D1 l \\theta_1 \\theta_2}$ and $n^E_{D2 l \\theta_1 \\theta_2}$ to $n_j^E$ as follows:\n\\begin{eqnarray}\nn_j^E &=& \\sum_{\\left(DX, l, \\theta_1, \\theta_2 \\right) \\in V_j} n^E_{D1 l \\theta_1 \\theta_2}\t\t\\\\\n&=& N \\mathrm{Tr} \\left( \\op{E}_{j} \\op{\\rho} \\right)\t,\n\\end{eqnarray}\nwhere $\\op{E}_{j} = \\sum_{\\left(DX, l, \\theta_1, \\theta_2 \\right) \\in V_j} \\op{E}_{l \\theta_1 \\theta_2}^{DX}$.\nSimilarly, we obtain $n_j^M$,\nand now we can perform the QST for time-bin qudits by MLE.\n\n\n\\subsection{\\label{SumOfProc}Summary}\n\n\nHere,\nwe summarize the proposed QST procedure.\n\n\nFirst,\nwe measure the relative transmittances\n$\\mathit{\\Delta} \\eta_{2x}, \\mathit{\\Delta} \\eta_{2y}, \\mathit{\\Delta} \\eta_{1x}, \\mathit{\\Delta} \\eta_{1y},$ and $\\mathit{\\Delta} \\eta_{1}$,\nwith which we estimate the measurement operators $\\op{E}_{l \\theta_1 \\theta_2}^{DX}$ according to\n\\eref{eq:CompM2x}--\\eref{eq:CompED2}.\nThen,\nwe generate space $V_j$ from $\\op{E}_{l \\theta_1 \\theta_2}^{DX}$ according to \\eref{eq:Vcondition1} and \\eref{eq:Vcondition2}\nand prepare $\\op{E}_{j} = \\sum_{\\left(DX, l, \\theta_1, \\theta_2 \\right) \\in V_j} \\op{E}_{l \\theta_1 \\theta_2}^{DX}$.\n\n\n\nNext,\nwe perform photon count measurement\nby switching combinations of phase differences $(\\theta_1, \\theta_2) = (0,0), (0, \\pi\/2), (\\pi\/2, 0)$, and $(\\pi\/2, \\pi\/2)$\nand obtain $n^M_{DX l \\theta_1 \\theta_2}$.\nAfter the measurement,\n$n^M_{DX l \\theta_1 \\theta_2}$ is reduced into $n_j^M$ by using space $V_j$.\n\n\nFinally,\nwe find $\\op{R}$ minimizing the likelihood function $L\\left(\\op{R}\\right)$ with $n_j^M$ and $\\op{E}_{j}$\nand obtain the reconstructed density operator $\\op{\\rho}$.\nWhen we perform the QST for the multi-photon state,\nwe extend the procedure as in \\cite{James2001,Thew2002}\nby replacing $\\op{E}_{l \\theta_1 \\theta_2}^{DX}$ and $n^M_{DX l \\theta_1 \\theta_2}$ with its tensor production and coincidence count,\nrespectively.\n\n\n\\section{Experimental setup}\n\n\\begin{figure}[htbp]\n\\centering\n\\includegraphics[width=\\linewidth]{figure02_ExpSetup.eps}\n\\caption{Experimental setup.\nCW: Continuous wave laser.\nIM: Intensity modulator.\nEDFA: Erbium-doped fiber amplifier.\nPC: Polarization controller.\nFBG: Fiber Bragg grating filter.\nVATT: Optical variable attenuator.\nPPLN: Periodically poled lithium niobate waveguide.\nBPF: Optical band-pass filter.\nWDM: Wavelength demultiplexing filter.\nPol: Polarizer.\n2-bit delay MZI, 1-bit delay MZI (Delay Mach-Zehnder interferometers were fabricated using PLC technology.)\nSNSPD: Superconducting nanowire single-photon detector.\n}\n\\label{fig:ExpSetup}\n\\end{figure}\n\n\\Fref{fig:ExpSetup} shows the experimental setup.\nFirst,\nwe generate a continuous-wave light with a wavelength of 1551.1 nm and a coherence time of $\\sim$10 $\\mu$s,\nwhich is modulated into four-sequential pulses by an intensity modulator.\nThe repetition frequency, the temporal interval, and the pulse duration are 125 MHz, 1 ns, and 100 ps, respectively.\nThese pulses are amplified by an erbium-doped fiber amplifier (EDFA),\nand then the average power of the pulses are adjusted by an optical variable attenuator.\nThey are launched into a periodically poled lithium niobate (PPLN) waveguide,\nwhere 780-nm pump pulses are generated via second harmonic generation.\nThe 780-nm pump pulses are launched into another PPLN waveguide to generate a four-dimensional maximally entangled state through spontaneous parametric down-conversion.\nA fiber Bragg grating filter and two optical band-pass filters are located after the EDFA and the PPLN waveguides, respectively.\nThe fiber Bragg grating filter eliminates amplified spontaneous emission noise from the EDFA,\nand the first and the second band-pass filters eliminate the 1551.1- and the 780-nm pump pulses, respectively.\nThe generated entangled photons are separated by a wavelength demultiplexing filter into a signal and an idler photon whose wavelengths are 1555 and 1547 nm, respectively.\nEach separated photon is launched into the cascaded MZIs followed by two superconducting nanowire single-photon detectors (SNSPDs),\nwhere the QST described in \\sref{sec:QSTDetail} is performed.\nThe cascaded MZIs are composed of a 2-bit delay MZI and a 1-bit delay MZI fabricated by using PLC technology.\nThe phase differences of the 2- and 1-bit delay MZIs are controlled via the thermo-optic effect caused by electrical heaters attached to the waveguides.\nEach MZI shows a $>20$-dB extinction ratio thanks to the stability of the PLC \\cite{Takesue2005, Honjo2004}.\nPolarization controllers and polarizers are located in front of each MZI to operate the MZIs for one polarization.\nChannels 1 and 2 (3 and 4) of the SNSPDs are connected to the 1- and the 2-bit delay MZIs for the signal (idler) photon, respectively.\nThe photon detection events from the SNSPDs are recorded by a time-interval analyzer\nand analyzed by a conventional computer.\nThe detection efficiencies of the SNSPDs for channels 1, 2, 3, and 4 are $40, 56, 34$, and $43$ \\%, respectively,\nand the dark count rate for all channels is $<30$ cps.\n\n\\section{Results}\n\n\\subsection{Measurement of relative transmittance}\n\\begin{figure}[htbp]\n\\centering\n\\includegraphics[width=\\linewidth]{figure03_Marge.eps}\n\\caption{Histograms of single counts for single photon generated by single pump pulse\nfor the detector's (a) channel 1, (b) channel 2, (c) channel 3, and (d) channel 4.}\n\\label{fig:DiffEta}\n\\end{figure}\n\nWe first measured the relative transmittances between the arms of the MZIs---$\\mathit{\\Delta} \\eta_{2x}, \\mathit{\\Delta} \\eta_{2y},$ and $\\mathit{\\Delta} \\eta_{1x}$---for the signal and the idler photon.\nTo measure these values,\nwe generated a single pulse using the intensity modulator instead of four-sequential ones,\nbecause the photons generated by the single pulse don't interfere at the MZIs.\n\\Fref{fig:DiffEta} shows the histograms of single photon counts for each detector channel.\nThe four peaks in \\fref{fig:DiffEta}(a) and (c) correspond to the single counts for finding a photon in detection times $t_0$, $t_1$, $t_2$, and $t_3$, respectively.\nSimilarly,\nthe two peaks in \\fref{fig:DiffEta}(b) and (d) correspond to the single counts for finding a photon in detection times $t_0$ and $t_2$, respectively.\nWe calculated the relative transmittances from these single counts.\nFor example,\nsingle count $S^1_l$ at detection time $t_l$ for channel 1 satisfies the following relation:\n\\begin{equation}\nS^1_0 : S^1_1 : S^1_2 : S^1_3 = 1 : \\mathit{\\Delta} \\eta_{1x}^s : \\mathit{\\Delta} \\eta_{2x}^s : \\mathit{\\Delta} \\eta_{1x}^s \\mathit{\\Delta} \\eta_{2x}^s\t,\n\\end{equation}\nwhere $\\mathit{\\Delta} \\eta_{2x}^s$ and $\\mathit{\\Delta} \\eta_{1x}^s$ are the relative transmittances for the signal photon.\nTherefore,\nthe relative transmittances were estimated as\n$\\mathit{\\Delta} \\eta_{2x}^s = \\left( S^1_2 + S^1_3 \\right) \/ \\left( S^1_0 + S^1_1 \\right)$\nand\n$\\mathit{\\Delta} \\eta_{1x}^s = \\left( S^1_1 + S^1_3 \\right) \/ \\left( S^1_0 + S^1_2 \\right)$.\nSimilarly,\nwe calculated the other relative transmittances,\nwhich are summarized in \\tref{tab:DiffEta}.\nWe didn't measure $\\mathit{\\Delta} \\eta_{1y}$\nbecause output port $p_{1y}$ was terminated\nand thus didn't affect the result of our experiment.\nThe values summarized in \\tref{tab:DiffEta} were utilized for the QST described in the next section.\n\n\\begin{table}\n\t\\caption{\\label{tab:DiffEta}Summary of the relative transmittance.}\n\t\\begin{indented}\n\t\\lineup\n\t\\item[]\n\t\t\\begin{tabular}{@{}crr}\n\t\t\t\\br\n\t\t\t & Signal & Idler\t\\\\\n\t\t\t\\mr\n\t\t\t$\\mathit{\\Delta} \\eta_{2x}$ & 1.009\\0 & 0.8495\t\\\\\n\t\t\t$\\mathit{\\Delta} \\eta_{2y}$ & 0.8300 & 0.8302\t\\\\\n\t\t\t$\\mathit{\\Delta} \\eta_{1x}$ & 1.063\\0 & 0.9669\t\\\\\n\t\t\t\\br\n\t\t\\end{tabular}\n\t\\end{indented}\n\\end{table}\n\n\\subsection{QST for the time-bin entangled qudits}\n\n\n\\begin{figure}[htbp]\n\\centering\n\\includegraphics[width=\\linewidth]{figure04_rho_merge.eps}\n\\caption{(a) Real parts and (b) imaginary parts of measured density operator $\\op{\\rho}$.}\n\\label{fig:Rho}\n\\end{figure}\n\nWe then generated the four-dimensional maximally entangled state $\\ket{\\Psi_{MES}^4 (\\phi)}$ by utilizing the four-sequential pump pulses.\nThe state is given by\n\\begin{equation}\n\\ket{\\Psi_{MES}^4 (\\phi)} = \\frac{1}{2} \\sum_{k=0}^3 \\exp (i \\phi k ) \\ket{k}_s \\otimes \\ket{k}_i \t,\n\\end{equation}\nwhere $\\ket{k}_s$ and $\\ket{k}_i$ denote the time-bin basis for the signal and idler photon, respectively,\nand $\\phi$ denotes the relative phase between the product states $\\ket{k}_s \\otimes \\ket{k}_i$\ndue to the phases of the pump pulses for SPDC.\nThe pump pulses were generated from the CW laser;\nthus, the phase is proportional to $k$ and determined by the frequency and the temporal interval of the time slots.\nIt should be noted that we can control the phase of the entangled state by modulating that of the pump pulses.\nIn our setup,\nthe CW laser had a coherence time of $\\sim$10 $\\mu$sec,\nwhich implies that, in principle, we can extend the dimension of the entangled photons $d$ up to $10^3\\sim10^4$.\nThe measured single photon count rates for detector channels 1, 2, 3, and 4 were\n17.1, 72.4, 20.6, and 82.1 kcps, respectively.\nFrom these single photon count rates,\nthe relative transmittances between the detectors $\\mathit{\\Delta} \\eta_{1}$ for the signal and idler photon\nwere estimated to be 0.474 and 0.501, respectively.\nThe average photon number per qudit was 0.02,\nand the measurement time for one measurement setting was 10 sec.\nWe employed coincidence counts for arbitrary combinations of detection times between the signal and the idler photon with 16 measurement settings,\nwith which the QST for a single qudit described in \\sref{sec:QSTDetail} was extended to the QST for two qudits.\n\n\nWe performed the QST for the entangled qudits fifteen times.\n\\Fref{fig:Rho} shows one of the measured density operators $\\op{\\rho}$.\nAll measured coincidence counts and reconstructed operators in the fifteen trials are provided in the supplementary material.\nNote that we utilized $\\op{U}\\op{\\rho}\\op{U}^\\dag$ instead of $\\op{\\rho}$ so that the visualized operator would be close to $\\ket{\\Psi_{MES}^4 (0)}$,\nwhere the local unitary operator $\\op{U}$ for the signal photon is given by $\\sum_k \\exp (-i \\phi' k) \\ket{k}_s\\bra{k}_s$.\nBoth the real and the imaginary parts of the measured operator showed characteristics close to $\\ket{\\Psi_{MES}^4 (0)}$,\nand the elements of the operator that were 0 for $\\ket{\\Psi_{MES}^4 (0)}$ were suppressed.\n\n\n\\begin{table}\n\t\\caption{\\label{tab:FigOfMerit}Average quantities derived from measured $\\op{\\rho}$ for the fifteen experimental trials.\n\tThe critical values to violate the CGLMP inequality are also summarized.}\n\t\\begin{indented}\n\t\\lineup\n\t\\item[]\n\t\t\\begin{tabular}{@{}crr}\n\t\t\t\\br\n\t\t\t & Measured & Critical \\\\\n\t\t\t\\mr\n\t\t\tFidelity & $F(\\op{\\rho}, \\op{\\sigma}) = \\m $ 0.950 $\\pm$ 0.003 & $> 0.710$ \\\\\n\t\t\tTrace distance & $D(\\op{\\rho}, \\op{\\sigma}) = \\m $ 0.068 $\\pm$ 0.003 & $< 0.290$ \\\\\n\t\t\tLinear entropy & $H_{lin}(\\op{\\rho}) = \\m $ 0.093 $\\pm$ 0.006 & $< 0.490$ \\\\\n\t\t\tVon Neumann entropy & $H_{vn}(\\op{\\rho}) = \\m $ 0.343 $\\pm$ 0.016 & $< 2.002$ \\\\\n\t\t\t\\multirow{2}{*}{Conditional entropy} & $H_{c}(\\op{\\rho}|s) = - $ 1.654 $\\pm$ 0.016 & $< 0.002$ \\\\\n\t\t\t & $H_{c}(\\op{\\rho}|i) = - $ 1.653 $\\pm$ 0.016 & $< 0.002$ \\\\\n\t\t\t\\br\n\t\t\\end{tabular}\n\t\\end{indented}\n\\end{table}\n\nTo evaluate the measured operators more quantitatively,\nwe derived five figures of merit from $\\op{\\rho}$:\nfidelity $F(\\op{\\rho}, \\op{\\sigma})$,\ntrace distance $D(\\op{\\rho}, \\op{\\sigma})$,\nlinear entropy $H_{lin}(\\op{\\rho})$,\nvon Neumann entropy $H_{vn}(\\op{\\rho})$,\nand conditional entropy $H_{c}(\\op{\\rho}|X)$ \\cite{Nielsen2010,James2001}.\nHere, we employed the following definitions:\n\\begin{eqnarray}\nF(\\op{\\rho}, \\op{\\sigma}) &=& \\left[ \\Tr \\sqrt{ \\sqrt{\\op{\\sigma}} \\op{\\rho} \\sqrt{\\op{\\sigma}}}\\right]^2\t,\t\\\\\nD(\\op{\\rho}, \\op{\\sigma}) &=& \\frac{1}{2} \\Tr \\sqrt{\\left(\\op{\\rho} - \\op{\\sigma}\\right)^2}\t,\t\\\\\nH_{lin}(\\op{\\rho}) &=& 1 - \\Tr \\left( \\op{\\rho}^2 \\right)\t,\t\\\\\nH_{vn}(\\op{\\rho}) &=& - \\Tr \\left( \\op{\\rho} \\log_2 \\op{\\rho}\\right)\t,\t\\\\\nH_{c}(\\op{\\rho}|X) &=& H_{vn}(\\op{\\rho}) - H_{vn}(\\op{\\rho}_X)\t,\n\\end{eqnarray}\nwhere $\\op{\\sigma}$ is given by$\\ket{\\Psi_{MES}^4 (\\phi)} \\bra{\\Psi_{MES}^4 (\\phi)}$ with $\\phi$,\nwhich maximizes $F(\\op{\\rho}, \\op{\\sigma})$ or minimizes $D(\\op{\\rho}, \\op{\\sigma})$,\n$X \\in \\{s, i \\}$ denotes the signal and idler photon, respectively,\nand $\\op{\\rho}_X$ is the reduced density operator for $X$.\nThe average values of these quantities are summarized in \\tref{tab:FigOfMerit}.\nThe errors in \\tref{tab:FigOfMerit} were estimated as standard deviations in the fifteen experimental trials.\nTherefore,\nthey included the statistical characteristics of the coincidence counts and all the effects due to the experimental imperfections as well.\nThe measured fidelity and trace distance showed that the reconstructed operators were close to the target state $\\ket{\\Psi_{MES}^4 (\\phi)}$.\nNote that this is the first time fidelity $>0.90$ has been reported for entangled qudits \\cite{Agnew2011,Bernhard2013,Nowierski2015,Richart2014}.\nThe measured linear entropy and von Neumann entropy were low,\nwhich implies that the reconstructed operators were close to the pure state and that small disturbances occurred in the proposed QST scheme.\nFurthermore,\nthe measured conditional entropies were negative,\nwhich confirmed that the signal and the idler photons were entangled \\cite{Horodecki1996a,Horodecki1996}.\n\nTo evaluate the quality of entangled qudits,\nmany previous experiments employed the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality test,\nwhich is a generalized Bell inequality for entangled qudits \\cite{Collins2002,Dada2011a}.\nIf we assume symmetric noise,\ndepolarized entangled state $\\op{\\rho}_{mix}$ is given by\n\\begin{equation}\n\\op{\\rho}_{mix} = p \\ket{\\Psi_{MES}^4 (0)} \\bra{\\Psi_{MES}^4 (0)} + (1 - p) \\frac{\\op{I}_{16}}{16}\t,\t\t\\label{eq:MixedMES}\n\\end{equation}\nwhere $p$ is a probability and $\\op{I}_{16}$ is the identity operator in the 16-dimensional Hilbert space.\nThe condition $p > 0.69055$ is a criterion to violate the CGLMP inequality.\nTherefore,\nthe quantities derived from $\\op{\\rho}_{mix}$ with $p = 0.69055$ can be considered as the critical values for the evaluation of the entangled qudits.\nThese critical values are also summarized in \\tref{tab:FigOfMerit},\nwhich shows that all of the measured values satisfied the conditions to violate the CGLMP inequality.\nThus,\nwe confirmed that the proposed QST scheme based on cascaded MZIs successfully reconstructed the quantum density operator of the time-bin entangled qudits\nwith only 16 measurement settings.\n\n\n\n\\section{Conclusion}\nWe proposed QST for time-bin qudits based on cascaded MZIs,\nwith which the number of measurement settings scales linearly with dimension $d$.\nWe generated a four-dimensional maximally entangled time-bin state\nand confirmed that the proposed scheme successfully reconstructed the density operator with only 16 measurement settings.\nAll the quantities derived from the reconstructed state were close to the ideal ones,\nand the fidelity of 0.950 is the first time fidelity $>0.90$ has been achieved for entangled qudits.\nWe hope that our result will lead to advanced quantum information processing utilizing high-dimensional quantum systems.\n\n\n\n\n\\ack\nWe thank T. Inagaki and F. Morikoshi for fruitful discussions.\n\n\n\n\n\\section*{References}\n\n\\bibliographystyle{iopart-num}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nA natural description of the dynamics of chaotic systems is in \nterms of evolving probability densities~\\cite{Lasota}. \nOn this level the  time evolution in maps is governed by the linear Frobenius--Perron\noperator and the dynamical problem is solved by the determination of the spectral decomposition of this\noperator. In recent years, several authors have constructed complete and explicit spectral\ndecompositions of the Frobenius--Perron operator of a variety of model\nsystems~\\cite{firstgenspec,scndgenspec}.  The most useful decompositions contain in\ntheir spectrum the decay rates characterizing the approach to equilibrium of the system.  \nFor one-dimensional piecewise-linear Markov maps such decompositions\nare constructed in function spaces spanned by polynomials.  The dual space of these polynomials\nare generalized function spaces and so the decompositions are known as generalized\nspectral decompositions~\\cite{Deanbook}.  \n\nChaotic systems often contain a control parameter that characterizes\nthe strength of the chaos.  A simple model system with such a control\nparameter is the well-known tent map with varying height~\\cite{Schuster}.  \nThe tent map with height $h$ on the unit interval is given by\n\\begin{equation} \\label{generaltent}\n{\\rm T}(x) = \\left\\{ \\begin{array}{lc} \n\\alpha x & 0 \\leq x < \\frac{1}{2} \\\\ \\noalign{\\vskip4pt} \n\\alpha(1-x) & \\frac{1}{2} \\leq x < 1,\n\\end{array} \\right.\n\\end{equation}\nwhere the parameter $\\alpha \\equiv 2 h$. In Figure 1 the map (\\ref{generaltent}) with \nheight $\\sqrt{2}\/2$ is shown.  Note that the map acts on the unit interval $[0,1)$ but\nhas images on $[0,h]$. \n\\begin{figure}[htb]\n\\begin{center}\n\\scalebox{.5}[.5]{\\includegraphics{fig13.eps}}\n\\parbox{5in}{\\caption{\\small The tent map at $\\alpha = \\protect\\sqrt{2}$.  For this value of\n$\\alpha$ iterates of the critical point define four intervals around which the dynamics is\norganized, as discussed in Section 2.}}\n\\end{center}\n\\end{figure}\nAs characterized by its Lyapunov exponent, $\\log\\alpha$,\nthe map (\\ref{generaltent}) switches abruptly chaotic as the\nheight is raised past $1\/2$.   We are interested in the chaotic regime where $1\/2 < h \\leq 1$, i.e.,\n$1 < \\alpha \\leq 2$.  Similar to the well-known universality of the quadratic map, it has recently \nbeen reported~\\cite{Moon} that the tent map also governs the low-dimensional behavior of a\nwide class of nonlinear phenomena.  Specifically, it was found that the dynamics  of the\nGinzburg--Landau equation, in its description of the modulational instability of a wave train, is\nreducible to the tent map.  Under this reduction, varying the height in\n(\\ref{generaltent}) corresponds to varying the wavelength of the initial modulational instability.   \n\nOur interest is in the\nstatistical properties of the iterates of the tent map and in evolving probability\ndensities.  The Frobenius--Perron operator, $U$, corresponding to a map, ${\\rm S}(x)$, defined on the\nunit interval evolves a probability density, $\\rho(x,t)$ by one time step as\n\\begin{equation}\n\\rho(x,t+1) = U \\rho(x,t) \\equiv \\int_0^1 dx'\\, \\delta(x - {\\rm S}(x')) \\, \\rho(x',t).\n\\end{equation}\nEvaluating the integral gives a sum of contributions from the inverse branches of ${\\rm S}(x)$.  \nThe Frobenius--Perron operator corresponding to the map (\\ref{generaltent}) acts explicitly on a\ndensity $\\rho(x)$ as\n\\begin{equation} \\label{gententfpop}\nU_{\\rm T} \\rho(x) = \\frac{1}{\\alpha}\\left[ \\rho\\left(\n\\frac{x}{\\alpha} \\right) + \\rho\\left(\\frac{\\alpha - x}{\\alpha} \n\\right) \\right]\\Theta \\left(\\frac{\\alpha}{2} - x \\right),   \n\\end{equation}\nwhere \n\\begin{equation} \n\\Theta(a-x) = \\left\\{ \\begin{array}{lc} \n1 & x \\leq a \\\\\n0 & x > a.\n\\end{array} \\right. \n\\end{equation}\nThe step function appears here because the map has\nno inverse images for $x>\\alpha\/2$.\nFor $\\alpha=2$ the map has images on the\nwhole unit interval.  For this value of $\\alpha$ the invariant density (being the stationary\nsolution of (\\ref{gententfpop})) is\nuniform on the whole unit interval.  As $\\alpha$ is lowered the\ninvariant density is supported only on a subset of the interval\n$[\\alpha(1-\\alpha\/2),\\alpha\/2]$, i.e., from the\nsecond iterate to the first iterate of the critical point $x_c \\equiv 1\/2$. The invariant density is\ndiscontinuous at all values of the  trajectory of the critical point. If the critical trajectory is\nperiodic (or eventually periodic) there will be a finite number of discontinuities. \n\nFor $\\alpha \\geq \\sqrt{2}$ the invariant density has nonvanishing support on all of\n$[\\alpha(1-\\alpha\/2),\\alpha\/2]$.  As $\\alpha$ is decreased past this critical value,\n$\\alpha_{1}$, the invariant density breaks up into two bands with a gap in the\nmiddle. Decreasing $\\alpha$ past $\\alpha_{2} = 2^{1\/4}$ causes the invariant\ndensity to break up into 4 bands. In general the\ninvariant density has\n$2^n$ bands as $\\alpha$ is decreased past $\\alpha_{n} = 2^{2^{-n}}$. \nThese values of $\\alpha$ are called the band-splitting \npoints~\\cite{bsps}. \nThis is illustrated in Figure 2.\n\\begin{figure}[htb]\n\\begin{center}\n\\scalebox{0.73}[0.73]{\\includegraphics{bif.eps}}\n\\parbox{5in}{\\caption{\\small Bifurcation plot of the tent map with varying height showing\nthe formation of bands as the height, parametrized by $\\alpha=2h$ on the horizontal axis,\nis lowered.  The vertical axis is the subset $[\\alpha(1-\\alpha\/2),\\alpha\/2]$ of the\none-dimensional phase space.  In (a) the shaded regions indicate where the invariant\ndensity has nonvanishing support.  At this resolution we see up to the formation of the\nfour bands at $\\alpha=2^{1\/4}$ but higher band-splitting points are not resolved.  In (b) iterates\nof the critical trajectory as a function of $\\alpha$ are plotted.  These are seen to\ndetermine the band structure in (a).}}\n\\end{center}\n\\end{figure}\nAt the band-splitting points the critical trajectory is eventually \nperiodic and the invariant density is constant in each band and thus piecewise-constant\nover the unit interval.  But a general initial density will also have persistent oscillating\ncomponents among the bands.  This feature is known as asymptotic periodicity~\\cite{Lasota}.\n\nWe want to determine the spectral decomposition of the Frobenius--Perron operator so that we may\nexpand a density or correlation function in terms of its eigenmodes.  In order to do this we need\nthe dual states or left eigenstates of $U$.  These correspond to the right eigenstates of the\nadjoint of $U$, which is known as the Koopman operator~\\cite{Lasota}.  The Koopman operator,\n$K=U^\\dagger$, acts on a phase space function $A(x)$ as\n\\begin{equation} \\label{koopman}\nK A(x) = A({\\rm T}(x)),\n\\end{equation}\nwhere ${\\rm T}(x)$ is the rule for the map, such as~(\\ref{generaltent}).\nFor decompositions of one-dimensional, chaotic, Markov maps in spaces spanned by polynomials the\nKoopman operator has eigenstates that are generalized functions or\neigenfunctionals~\\cite{firstgenspec,scndgenspec,Deanbook}.  \n\nThe decay of the $x$-autocorrelation function for the tent map at the \nband-splitting points and at values of $\\alpha$\nclose to band-splitting points was calculated in~\\cite{Mori}.   \nThe tent map has also been studied by\nDorfle~\\cite{Dorfle} at arbitrary values of $\\alpha$ in several function spaces\nbut he does not provide explicit complete spectral decompositions.\nThe asymptotic periodicity of the system has been studied by Provatas and Mackey~\\cite{ProvMac}. \nSince as $t \\to \\infty$ the density is supported only within $[\\alpha(1-\\alpha\/2),\\alpha\/2]$\nall these authors have only considered the map in that region and neglected transient behavior onto\nit.   That is sufficient if one only considers the behavior of time correlation functions; but for\nthe general evolution of densities and observables in a nonequilibrium statistical mechanics context\nthis transient behavior must not be neglected since, as will be seen, the slowest decay\nmodes originate from this part of the dynamics.\n\nIn the next section we construct the spectral decomposition of the\nFrobenius--Perron operator at the first band-splitting point.   In Section 3 the decomposition at all\nthe band-splitting points is constructed using the self-similarity of the map at higher\nband-splitting points to the map at lower band-splitting points.  \\section{The first band-splitting point}\n\nFrom (\\ref{generaltent}) the map at the first band-splitting point corresponding to the\nheight $h=\\sqrt{2}\/2$ or $\\alpha=\\sqrt{2}$ is\n\\begin{equation} \\label{mapatfbsp}\n{\\rm{T}}_{1}(x) = \\left\\{ \\begin{array}{lc} \n\\sqrt{2} \\, x & 0 \\leq x < \\frac{1}{2} \\\\ \\noalign{\\vskip4pt} \n\\sqrt{2} \\, (1-x) & \\frac{1}{2} \\leq x < 1,\n\\end{array} \\right.\n\\end{equation}\nwhich is shown in Figure 1.\nThe dynamics is organized around four\nintervals determined by the trajectory of the critical point.  At the third iteration\nthe critical trajectory settles onto the fixed point, $x^*=2-\\sqrt{2}$.  The four\nintervals: ${\\rm{I}}=[0,{\\rm{T}}_{1}^{(2)}(x_{\\rm c}))$, \n${\\rm{II}}=[{\\rm{T}}_{1}^{(2)}(x_{\\rm c}),{\\rm{T}}_{1}^{(3)}(x_{\\rm c}))$\n${\\rm{III}}=[{\\rm{T}}_{1}^{(3)}(x_{\\rm c}),{\\rm{T}}_{1}^{(1)}(x_{\\rm c}))$ and\n${\\rm{IV}}=[{\\rm{T}}_{1}^{(1)}(x_{\\rm c}),1)$,  define a minimal Markov partition\nfor the map. (These intervals are indicated in Figure 1.)  Any point in the interior of\ninterval ${\\rm{IV}}$ is mapped onto some point in interval ${\\rm{I}}$ in one\niteration.  Under successive iterations all points in the interior of ${\\rm{I}}$ are\neventually mapped into ${\\rm{II}}$. Any point in interval $\\rm{II}$ maps into interval\n$\\rm{III}$ in one iteration and any point in interval $\\rm{III}$ maps into\n$\\rm{II}$ in one iteration.  Thus the union of the intervals $\\rm{II}$ and $\\rm{III}$ \nform the attracting set $\\Omega$. \n\nThe Frobenius--Perron operator for the map (\\ref{mapatfbsp}) acts on \na density as \n\\begin{equation} \\label{op}\nU_{\\rm T_1} \\rho(x) = \\frac{1}{\\sqrt{2}}\\left[ \\rho\\bigg(\n\\frac{x}{\\sqrt{2}} \\bigg) + \\rho\\bigg(\\frac{\\sqrt{2} - x}{\\sqrt{2}} \n\\bigg) \\right]\\Theta \\bigg( \\frac{\\sqrt{2}}{2} - x \\bigg).   \n\\end{equation}\nA general initial density continuous over the unit interval develops\ndiscontinuities at the endpoints of the four intervals described above. \nWe thus choose a function space to consider $U_{\\rm T_1}$ in as the space\nof piecewise-polynomial functions where the pieces are  the four\nintervals described above.  The invariant density has support only in\n$\\Omega$. \n\nThe fact that points oscillate between the intervals $\\rm{II}$ and $\\rm{III}$ means\nthat a general density will have a persistent oscillating component between these two\nintervals under time evolution.  This property  we will sometimes refer to in the\npresent context as the ``flip property\", since the part of the density in $\\rm{II}$\nwill all be in $\\rm{III}$ (with stretching) in the next time step and vice-versa. The parts of the\ninitial density with support in the intervals\n${\\rm{I}}$ and $\\rm{IV}$ will decay onto $\\Omega$.  Since we will use the eigenfunctions on\n$\\Omega$ to determine those on its complement, we first consider the decomposition on $\\Omega$.\n\n\\subsection{Evolution on the attractor}\n\nFor convenience $\\Omega$ is stretched\nonto the interval $[0,1)$. At the end of the computation we will rescale all\nresults back to $\\Omega$. The linear function that makes the stretch is\n\\begin{equation} \\label{phi}\n\\phi(x) = \n(2\/x^{*}) x - \\sqrt{2},\n\\end{equation}\nwhere ${\\rm{T}}_{1}^{(2)}(x_{\\rm c}) \\leq x < {\\rm{T}}_{1}^{(1)}(x_{\\rm c})$.\nThe transformation (\\ref{phi}) is a homeomorphism so that it begets a new\nmap ${\\rm R_1}$ topologically conjugate to the part of ${\\rm T_1}$ on $\\Omega$ as\n$\\rm{R}_{1} = \\phi \\circ {\\rm{T}}_{1} \\circ \\phi^{-1}$\ngiven by \n\\begin{equation} \\label{rescaled}\n{\\rm{R}}_{1}(x) = \\left\\{ \\begin{array}{lc}\n\\sqrt{2} \\, x + x^{*} & 0 \\leq x < x^{*} \\! \/2 \\\\ \\noalign{\\vskip4pt}\n\\sqrt{2} \\, (1-x) & x^{*} \\! \/2 \\leq x < 1, \n\\end{array} \\right.\n\\end{equation}\nwhere $x^{*} = 2 - \\sqrt{2}$ is the fixed point of the map ${\\rm{R}}_{1}(x)$,\nwhich is the same as\nthe fixed point of the map ${\\rm{T}}_{1}(x)$. Under this transformation, the\nintervals $\\rm{II}$ and $\\rm{III}$\nare stretched to the intervals ${\\rm{A}} \\equiv [0,x^{*})$ and ${\\rm{B}} \\equiv\n[x^{*},1)$ respectively. The map ${\\rm{R}}_{1}(x)$ is shown in Figure 3.   \n\\begin{figure}[htb]\n\\begin{center}\n\\scalebox{.5}[.5]{\\includegraphics{fig21.eps}}\n\\parbox{5in}{\\caption{\\small The rescaled Tent map at the first band-splitting point.}}\n\\end{center}\n\\end{figure}\n\nThe Frobenius--Perron operator corresponding to the\nrescaled map\n$\\rm{R}_{1}$ acts on a density as\n\\begin{equation} \\label{ur1}\nU_{\\rm{R}_{1}} \\rho(x) = \\frac{1}{\\sqrt{2}}\\left[ \\rho\\bigg(\n\\frac{\\sqrt{2} - x}{\\sqrt{2}} \\bigg) + \\rho\\bigg(\\frac{x - x^{*}}{\\sqrt{2}} \n\\bigg)\\Theta(x - x^{*}) \\right].  \n\\end{equation}\nThe flip property of $\\rm T_1$ is inherited by $\\rm R_1$ in that the inverse image of\n$\\rm A$ is $\\rm B$ and vice-versa.  This suggests that a simpler analysis will be\nobtained by considering the map corresponding to two iterations of $\\rm R_1$.  This map,\n${\\rm{G}}_{1} \\equiv \\rm{R}_{1} \\circ \\rm{R}_{1}$, is given by \n\\begin{equation}\n{\\rm G}_{1}(x) = \\left\\{ \n\\begin{array}{lc} \n-2x + x^{*} & 0 \\leq x < x^{*} \\! \/2 \\\\ \\noalign{\\vskip4pt}\n 2x - x^{*}  & x^{*} \\! \/2 \\leq x < (1+x^*)\/2 \\\\ \\noalign{\\vskip4pt}\n-2x + (2 + x^{*}) & (1+x^*)\/2 \\leq x < 1.\n\\end{array} \\right. \n\\end{equation}\nThe flip property of $\\rm{R}_{1}$ means that ${\\rm{G}}_{1}$\nis metrically  decomposable into two independent maps on the intervals\n$\\rm{A}$ and\n$\\rm{B}$, as is clear from Figure 4. From now on in this section we shall\ndrop the subscript $1$ on the maps $\\rm R_1$ and $\\rm G_1$; it being\nunderstood that we are referring to these maps at the first\nband-splitting point. \n\\begin{figure}[htb]\n\\begin{center}\n\\scalebox{.5}[.5]{\\includegraphics{fig31.eps}}\n\\end{center}\n\\parbox{5in}{\\caption{\\small The map ${\\rm{G_{1}}}={\\rm{R_{1} \\circ R_{1}}}$ is metrically\ndecomposable into two parts each conjugate to the tent map with unit height.} }\n\\end{figure}\n\n\nThe map ${\\rm G}$ restricted to $\\rm{A}$ is just a rescaling (with a\nflip) of the tent map with full height, ${\\rm T}_0$,  i.e., the map\n(\\ref{generaltent}) with $\\alpha=2$. This is expressed in terms of a\ntopological conjugacy as\n\\begin{equation}\n{\\rm{G}}_{\\rm{A}}(x) = \\phi^{-1}_{\\rm{A}}(x) \\circ {\\rm{T_0}}(x) \\circ\n\\phi_{\\rm{A}}(x),\n\\end{equation}\nwhere\nthe conjugating function $\\phi_{\\rm{A}}(x)$ is \n\\begin{equation}\n\\phi_{\\rm{A}}(x) = 1 - \\frac{x}{x^*},\n\\end{equation}\nand $x \\in [0, x^{*})$.\nSimilarly the map on $\\rm B$ is topologically conjugate to ${\\rm T}_0$ as\n\\begin{equation}\n{\\rm{G}}_{\\rm{B}}(x) = \\phi^{-1}_{\\rm{B}}(x) \\circ {\\rm{T}}_{0}(x) \\circ\n\\phi_{\\rm{B}}(x),\n\\end{equation}\nwhere the conjugating function $\\phi_{\\rm B}(x)$ is \n\\begin{equation}\n\\begin{array}{lc}\n\\phi_{\\rm{B}}(x) = \n(\\sqrt{2}\/x^{*})x - \\sqrt{2} ,\n\\end{array} \n\\end{equation}\nand here $x \\in [x^{*}, 1)$.\nThese conjugacies are useful for us because the\nspectral decompositions of maps that are topologically conjugate are simply\nrelated, as is reviewed in Appendix A.\nThe generalized spectral decomposition of $\\rm{T_{0}}$ has been\npreviously determined~\\cite{Gonzalo,fox} and is reviewed\nin Appendix B.  \n\nFollowing the discussion in those appendices gives the right eigenvectors of\n$\\rm{G}_{\\rm{A}}$ and $\\rm{G}_{\\rm{B}}$ as\n\\alpheqn\n\\begin{eqnarray} \\label{Gvecsaa}\n| 2^{-2j} \\rangle_{\\rm{G}_{\\rm{A}}} & = & \\frac{1}{x^{*}}\nB_{2j}\\left( \\frac{x^{*} - x}{2x^{*}} \\right)\\chi_{\\rm{A}} \\\\ \\label{Gvecsab}\n| 0_{2j+1} \\rangle_{\\rm{G}_{\\rm{A}}} & = & \\frac{1}{x^{*}}\nE_{2j+1}\\left( \\frac{x}{x^{*}} \\right)\\chi_{\\rm{A}}, \n\\end{eqnarray}\n\\reseteqn\n\\alpheqn\n\\begin{eqnarray} \\label{Gvecsba}\n| 2^{-2j} \\rangle_{\\rm{G}_{\\rm{B}}} & = & \\frac{\\sqrt{2}}{x^{*}}\nB_{2j}\\left( \\frac{x - x^{*}}{\\sqrt{2}x^{*}} \\right)\\chi_{\\rm{B}} \\\\ \\label{Gvecsbb}\n| 0_{2j+1} \\rangle_{\\rm{G}_{\\rm{B}}} & = & \\frac{\\sqrt{2}}{x^{*}}\nE_{2j+1}\\left( \\frac{\\sqrt{2}}{x^{*}}\\left( x-x^{*} \\right) \\right)\n\\chi_{\\rm{B}},\n\\end{eqnarray}\n\\reseteqn\nwhere the associated eigenvalue is the argument of the\nket vector with $|0_{2j+1}\\rangle$ meaning a null eigenpolynomial of degree $2j+1$\nand $\\chi_{\\rm{A}}$ and $\\chi_{\\rm{B}}$ are indicator functions on the intervals\n$\\rm{A}$ and $\\rm{B}$ respectively.  Due to the metric decomposability of $\\rm G$ these\nstates are eigenstates of $U_{\\rm G}$ as well.\n\nSimilarly, the left eigenvectors of\n$\\rm{G}_{\\rm{A}}$ and $\\rm{G}_{\\rm{B}}$ are the generalized functions\n\\alpheqn \n\\begin{eqnarray} \\label{lgvecaa}\n\\langle 2^{-2j} |_{\\rm{G}_{\\rm{A}}} & = & \n\\frac{(-1)^{2j-1}\\left( 2x^{*} \\right)^{2j}}{(2j)!}\\left[\n\\delta^{(2j-1)}_{-}(x - x^{*}) - \\delta^{(2j-1)}_{+}(x) \\right] \\\\ \\label{lgvecab}\n\\langle 0_{2j+1} |_{\\rm{G}_{\\rm{A}}} & = & -\\frac{\\left(x^{*}\\right)^{2j+2}}\n{(2j+1)!}\\delta^{(2j+1)}_{+}\\left( x \\right),  \n\\end{eqnarray}\n\\reseteqn\n\\alpheqn\n\\begin{eqnarray} \\label{lgvecba}\n\\langle 2^{-2j} |_{\\rm G_B} \n& = & \\frac{(-1)^{2j-1}\\left( \\sqrt{2} \\, x^{*} \\right)^{2j}}{(2j)!}\\left[\n\\delta^{(2j-1)}_{-}(x - 1) - \\delta^{(2j-1)}_{+}\n(x - x^{*}) \\right] \\\\ \\label{lgvecbb}\n\\langle 0_{2j+1} |_{\\rm G_B} & = & \\frac{-1}{(2j+1)!}\n\\left( \\frac{x^{*}}{\\sqrt{2}} \\right)^{2j+2}\n\\delta^{(2j+1)}_{-}\\left( x - 1 \\right),\n\\end{eqnarray}\n\\reseteqn\nwhere the definitions of $\\delta_{\\pm}$ are given in Appendix B.\n\nSince $U_{\\rm{G}} = U^{2}_{\\rm{R}}$ the spectrum of $U_{\\rm{R}}$ is a subset of\n$\\{0,\\pm 2^{-j} \\}$. Consider a non-zero eigenvalue, \n${2}^{-2j}$, of $U_{\\rm{G}}$. There are two\neigenvectors associated with this eigenvalue, each a polynomial of\norder $2j$. Since the function space on which $U_{\\rm{R}}$ acts has two basis\nelements for each degree $j$, i.e., an $j^{\\rm th}$ degree polynomial in ${\\rm A}$ and an\n$j^{\\rm th}$ degree polynomial in\n${\\rm B}$, there should be either two eigenvectors or one eigenvector and one Jordan\nvector that are polynomials of degree $2j$, associated with either one or both the\neigenvalues $\\{ +2^{-j},-2^{-j} \\}$. Since $U_{\\rm{G}}$ does not have any Jordan vectors\nit follows that $U_{\\rm{R}}$ doesn't either (for non-zero eigenvalues). \nThe eigenvalues of $U_{\\rm R}$ cannot be twofold degenerate since that\nwould imply that all the eigenvectors of\n$U_{\\rm{G}}$ are also  eigenvectors of $U_{\\rm{R}}$, which is impossible since $\\rm{G}$ is\nmetrically decomposable and $\\rm{R}$ has the flip property. Therefore the\nnon-zero eigenvalues of $\\rm{R}$ are  $+2^{-j}$ and $-2^{-j}$.\n\nThe eigenvectors of\n$U_{\\rm{R}}$ with eigenvalue $\\pm 2^{-j}$ are in the eigenspace \nspanned by the two eigenvectors of $U_{\\rm{G}}$ corresponding to\n$+ 2^{-2j}$. Thus they will be linear combinations as\n\\alpheqn \n\\begin{equation} \\label{reigenforma}\n|{+2^{-j}} \\rangle_{\\rm{R}} = \\frac{1}{2} \\left( |{+2^{-2j}}\n\\rangle_{\\rm{G}_{\\rm{A}}} + c_{j}|{+2^{-2j}} \\rangle_{\\rm{G}_{\\rm{B}}} \\right)\n\\end{equation}\nand\n\\begin{equation}\n|{-2^{-j}} \\rangle_{\\rm{R}} = \\frac{1}{2} \\left( |{+2^{-2j}} \\label{reigenformb}\n\\rangle_{\\rm{G}_{\\rm{A}}} + d_{j}|{+2^{-2j}} \\rangle_{\\rm{G}_{\\rm{B}}} \\right) , \n\\end{equation}\n\\reseteqn\nwhere the coefficent of $1\/2$ is put for convenient normalization.  To determine\n$c_j$ we use that $|{+2^{-j}} \\rangle_{\\rm R}$ is an eigenvector of \n$U_{\\rm{R}}$ as\n\\begin{equation}\nU_{\\rm{R}}\\left[ |{+2^{-2j}} \\rangle_{\\rm{G}_{\\rm{A}}} + \nc_{j}|{+2^{-2j}} \\rangle_{\\rm{G}_{\\rm{B}}} \\right] =\n2^{-j}\\left[ |{+2^{-2j}}\\rangle_{\\rm{G}_{\\rm{A}}} + \nc_{j}|{+2^{-2j}} \\rangle_{\\rm{G}_{\\rm{B}}} \\right]. \n\\end{equation}\nThe flip property tells us that \n\\begin{equation} \\label{nn}\nU_{\\rm{R}}\\left[ c_{j}|{+2^{-2j}} \\rangle_{\\rm{G}_{\\rm{B}}} \\right]\n = 2^{-j}|{+2^{-2j}}\\rangle_{\\rm{G}_{\\rm{A}}}. \n\\end{equation}\nSubstituting the explicit form (\\ref{Gvecsaa}) of $|{+2^{-2j}} \\rangle_{\\rm{G}_{\\rm{A}}}$\nand (\\ref{Gvecsba}) of $|{+2^{-2j}} \\rangle_{\\rm{G}_{\\rm{B}}}$ in (\\ref{nn})  and solving\nfor $c_{j}$ we find that\n$c_{j} = 2^{-j}$. A similar analysis  shows that $d_{j} = -2^{-j}$. Hence \n\\begin{equation} \\label{fbspurstates}\n|{\\pm 2^{-j}} \\rangle_{\\rm R}  =  \\frac{1}{2 x^*}\\left( B_{2j}\\left( \\frac\n{x^{*} - x}{2x^{*}} \\right)\\chi_{\\rm{A}} \\pm \\frac{\\sqrt{2}}{2^{j}}B_{2j}\\left(\n\\frac {x - x^{*}}{\\sqrt{2}x^{*}} \\right)\\chi_{\\rm{B}} \\right). \n\\end{equation}\n\nThe invariant state, corresponding to the invariant density of $U_{\\rm R}$ is\n\\begin{equation}\n|{+1}\\rangle_{\\rm R} = \\frac{1}{2 x^*}(\\chi_{\\rm A} + \\sqrt{2} \\, \\chi_{\\rm B}).\n\\end{equation}\nThis state carries all the probability under evolution of $U_{\\rm R}$ and any density\nwill have this component.  The state\n\\begin{equation}\n|{-1}\\rangle_{\\rm R} = \\frac{1}{2 x^*}(\\chi_{\\rm A} - \\sqrt{2} \\, \\chi_{\\rm B})\n\\end{equation}\nis the asymptotically periodic state.  Only it and the invariant density survives as $t\n\\to \\infty$; but $|{-1}\\rangle_{\\rm R}$, like decaying states, doesn't carry any probability. \nIt does keep the memory though of the projection of the initial density on\n$|{-1}\\rangle_{\\rm R}$, which is a special property of asymptotically periodic\nsystems~\\cite{Lasota}.\n  \n\nNow we consider the null space of $\\rm{U_{R}}$.  The map $\\rm{G}$ has two independent\nnull vectors (one in $\\rm A$ and one in $\\rm B$) for each odd degree.  \nThis implies that\n$\\rm{R}$ can have either a corresponding $2 \\times 2$ Jordan block \nor have 2 independent eigenvectors for each odd degree. The latter case is not possible\nsince null vectors of $\\rm{R}$ cannot have support in interval $\\rm{B}$ because only one\nof the terms on the rhs of (\\ref{ur1}) acts on  functions in $\\rm B$.\nThus there is a $2 \\times 2$ Jordan block for each odd degree associated with\neigenvalue $0$.\n\nConsider the action of $U_{\\rm G}\n=U^{2}_{\\rm{R}}$ on a null state, $| 0_{2j+1}\\rangle_{\\rm{G_{A}}}$, of\n$\\rm{G_A}$ as  \n\\begin{equation} \nU_{\\rm{R}}\\Big[ U_{\\rm{R}}|0_{2j+1} \\rangle_{\\rm{G}_A} \\Big] = 0.\n\\end{equation} \nThe function inside the square brackets has support only in $\\rm B$, and\n$U_{\\rm{R}}$ acting on any non-zero function with support in $\\rm B$ cannot vanish\nin one iteration. Thus $|0_{2j+1} \\rangle_{\\rm R}=|0_{2j+1} \\rangle_{\\rm\nG_A}$ is a null vector of $U_{\\rm{R}}$ with explicit form given in\n(\\ref{Gvecsab})\n\nThe Jordan vector, $|0_{J_{2j+1}} \\rangle_{\\rm R}$, associated with this eigenvector\nsatisfies\n\\begin{equation} \\label{q}\n U_{\\rm{R}}| 0_{J_{2j+1}} \\rangle_{\\rm{R}} = | 0_{2j+1}\n\\rangle_{\\rm{R}}.\n\\end{equation} \nWe may choose the Jordan vector to have support only\nin ${\\rm B}$ as\n\\begin{equation} \\label{qq}\n| 0_{J_{2j+1}} \\rangle_{\\rm{R}} = \\eta_{2j+1}| 0_{2j+1}\n\\rangle_{\\rm{G}_{\\rm{B}}},\n\\end{equation} \nwhere $\\eta_{2j+1}$ is a constant to be determined.  \nTo determine $\\eta_{2j+1}$ we apply $U_{\\rm R}$ on (\\ref{qq}) and use (\\ref{q}) and the\nexplicit forms (\\ref{Gvecsab}) and (\\ref{Gvecsbb}) (remembering that\n$|0_{2j+1} \\rangle_{\\rm R}=|0_{2j+1} \\rangle_{\\rm G_A}$) to obtain\n$\\eta_{2j+1} = -1$.\n\n\\subsubsection{Left eigenstates of $U_{\\rm{R}}$}\n\nThe left eigenstates of $U_{\\rm{R}}$ with non-zero eigenvalues may be determined by an\napproach similar to the one used to find the right eigenstates.  \nThe result is\n\\begin{eqnarray}\n\\langle \\pm 2^{-j}|_{\\rm{R}} & = & \\frac{\\left( 2x^{*} \\right)^{2j}}\n{(2j)!} \\left[ \\delta^{(2j-1)}_{+}(x) - \\delta^{(2j-1)}_{-}(x - x^{*})\n\\right. \\nonumber \\\\ & & \\left. \\hskip50pt\n\\pm \\delta^{(2j-1)}_{+}(x - x^{*}) \\mp \\delta^{(2j-1)}_{-}(x - 1) \\right].\n\\end{eqnarray} \nThe left states with zero eigenvalues are like the right states identical to those\nof $U_{\\rm G}$ (except for the factor of $-1$ for the dual state of the Jordan vector) as\n\\alpheqn  \n\\begin{eqnarray}\n\\left\\langle 0_{2j+1} \\right|_{\\rm R} & = &  \n\\left\\langle 0_{2j+1} \\right|_{\\rm G_A} \\\\\n\\langle 0_{J_{2j+1}} |_{\\rm{R}} & = & \n- \\left\\langle 0_{2j+1} \\right|_{\\rm G_B}. \n\\end{eqnarray}\n\\reseteqn\nNote that $\\langle 0_{J_{2j+1}} |_{\\rm{R}}$ is an eigenstate of the Koopman operator\nand $\\left\\langle 0_{2j+1} \\right|_{\\rm{R}}$ is a Jordan state.  \n\n\n\n\\subsection{Decay onto the attractor}\n\nAs noted before, initial densities with support in the intervals $\\rm{I}$ and\/or\n$\\rm{IV}$ will decay into $\\Omega$. Consider a density with support\nonly in $\\rm{IV}$ at $t=0$.  At $t=1$  the density has support only in ${\\rm{I}}$.  Thus\nany eigenvector of $U_{\\rm T_1}$ with support in $\\rm{IV}$ can only have\neigenvalue\n$0$.  To determine such an eigenvector we write an ansatz for it as \n\\begin{equation} \\label{aa}\n| 0_j \\rangle_{\\rm{IV}} =\nf_{{\\rm{I}},j}(x)\\chi_{{\\rm{I}}} +\nf_{{\\rm{II}},j}(x)\\chi_{\\rm{II}}\n+ f_{{\\rm{III}},j}(x)\\chi_{\\rm{III}} + f_{{\\rm{IV}},j}(x)\\chi_{\\rm{IV}},\n\\end{equation}\nwhere the subscript $\\rm IV$ on the ket denotes that it\ndescribes decay out of interval $\\rm IV$ and we take $f_{{\\rm IV},j}(x)$ as a\npolynomial of order $j$. Applying $U_{\\rm T_1}$ to (\\ref{aa}) and collecting terms that are\nmultiplied  by the same indicator function we get\n\\begin{eqnarray} \\label{aaa}\nU_{\\rm T_1}|0_j \\rangle_{\\rm{IV}} & = & \n\\left[ f_{{\\rm{I}},j} \\left( \\frac{x}{\\sqrt{2}} \n\\right) + f_{{\\rm{IV}},j}\\left(1- \\frac{x}{\\sqrt{2}} \n\\right) \\right]\\chi_{{\\rm{I}}} \\nonumber \\\\\n &  & \\mbox{} + \\left[ f_{{\\rm{I}},j} \\left(\n\\frac{x}{\\sqrt{2}} \n\\right) + f_{{\\rm{III}},j}\\left(1- \\frac{x}{\\sqrt{2}} \\right) \\right]\n\\chi_{\\rm{II}} \\nonumber \\\\ \n&  & \\mbox{} + \\left[ f_{{\\rm{II}},j} \\left( \\frac{x}{\\sqrt{2}} \n\\right) + f_{{\\rm{II}},j}\\left(1- \\frac{x}{\\sqrt{2}} \\right)\n\\right]\\chi_{\\rm{III}}.\n\\end{eqnarray} \nSince $|0_j \\rangle_{\\rm{IV}}$ is a null eigenstate the coefficients of each of the\nindicator functions must vanish. Since\n$f_{{\\rm{IV}},j}$ is a polynomial of degree\n$j$, it follows that \n$f_{{\\rm{I}},j}$ and\n$f_{{\\rm{III}},j}$ are also polynomials of degree $j$. We choose\n$f_{{\\rm{II}},j}$ to be zero.  Clearly,\n$f_{{\\rm{III}},j}=f_{{\\rm{IV}},j}$ and choosing it as\n$(x-1)^j$ fixes $f_{{\\rm{I}},j}$.  We thus have \n\\begin{equation} \\label{rt1} \n| 0_j  \\rangle_{\\rm{IV}} = (-1)^{j+1}x^j\\chi_{\\rm{\\rm{I}}} +\n(x-1)^j(\\chi_{\\rm{III}} + \\chi_{\\rm{IV}}). \n\\end{equation} \nWe note that because of the degeneracy associated\nwith eigenvalue $0$ in interval $\\rm{IV}$, this choice of eigenvectors is not\nunique. The left eigenstates (given below) associated with this choice of\nright  eigenvectors is unique and therefore when we expand an arbitrary \ndensity in terms of the right eigenvectors, the expansion coefficents \nare uniquely defined.\n\nThe action of $U_{\\rm T_1}$ on a function with support only \non $\\rm{\\rm{I}}$ is given by\n\\begin{equation} U_{\\rm T_1} [f(x)\\chi_{\\rm{I}}] = \\frac{1}{\\sqrt{2}}\nf(x\/\\sqrt{2}) ( \\chi_{\\rm{I}} + \\chi_{\\rm{II}}).\n\\end{equation} \nActing with $U_{\\rm T_1}$ on a monomial in $\\rm{I}$ gives\n\\begin{equation} \\label{ind}\n U_{\\rm T_1} [x^{j}\\chi_{\\rm I}] =\n\\frac{x^{j}}{(\\sqrt{2})^{j+1}} (\\chi_{\\rm{\\rm{I}}} + \\chi_{\\rm{II}}), \n\\end{equation}\nso that the eigenvectors of $U_{\\rm T_1}$ with support in $\\rm{I}$\nare monomials in $\\rm{I}$.\nTo determine their form in the other intervals we again write an ansatz as\nwe did for the eigenvectors with support in $\\rm{IV}$ as\n\\begin{equation} \\label{haha} \n| 2^{-(j+1)\/2}\n\\rangle_{{\\rm{I}}} = x^{j}\\chi_{{\\rm{I}}} + g_{{\\rm II},j}(x) \\chi_{\\rm{II}} +\ng_{{\\rm III},j}(x)\\chi_{\\rm{III}},\n\\end{equation}\nwhere the associated eigenvalue, appearing as the argument of the ket, is seen from (\\ref{ind}). In\nequation (\\ref{haha}) and below the subscript $\\rm I$ on a ket implies that\nit describes decay out of region ${\\rm I}$. Note that the\n$j=0$ mode here is the slowest decay mode in this system. Since $U_{\\rm T_1}$\ndoes not raise the degree of the polynomial it acts on, \n$g_{{\\rm II},j}(x)$ and $g_{{\\rm III},j}(x)$ are polynomials of degree $j$. Applying\n$U_{\\rm T_1}$ to (\\ref{haha}) and using (\\ref{ind}) and the fact that the function on\nthe rhs of (\\ref{haha}) is an eigenvector with eigenvalue\n$2^{-(j+1)\/2}$, we find that \n\\begin{equation}  \\label{form1}\nU_{\\rm T_1} ( g_{{\\rm II},j}(x)\\chi_{\\rm{II}} + g_{{\\rm III},j}(x)\\chi_{\\rm{III}}) =\n2^{-(j+1)\/2}  (g_{{\\rm II},j}(x)\\chi_{\\rm{II}} + g_{{\\rm III},j}(x)\\chi_{\\rm{III}}\n-x^{j}\\chi_{\\rm{II}}). \n\\end{equation}\nThe determination of $g_{{\\rm II},j}(x)$ \nand $g_{{\\rm III},j}(x)$ is described in Appendix C \n\nThe explicit form of the first few of these eigenvectors is\n\\alpheqn\n\\begin{eqnarray} \\label{firstfew}\n| 2^{-1\/2}\\rangle_{\\rm I} & = & \\chi_{{\\rm{I}}} +\n\\frac{1}{2(1-\\sqrt{2})}|1\\rangle_{\\Omega} + \\frac{1}{2(1+\\sqrt{2})}|{-1\\rangle_\\Omega} \\\\\n| 2^{-1}\\rangle_{\\rm I} & = & x \\, \\chi_{\\rm{I}} -\n\\frac{1}{4(x^*)}|1\\rangle_\\Omega + \\frac{1}{12}|{-1\\rangle_\\Omega} +\n\\frac{(x^*)^2}{2}|0\\rangle_\\Omega \\\\ \n|2^{-3\/2}\\rangle_{\\rm I} & = & x^2 \\,\\chi_{\\rm{I}} -\n\\frac{\\sqrt{2}x^*}{12}|1\\rangle_\\Omega +\n\\frac{(9\\sqrt{2}-8)x^*}{84}|-1\\rangle_\\Omega + \n\\frac{\\sqrt{2}(x^*)^3}{2}|0\\rangle_{\\Omega} \\\\ \n& & \\mbox{}\\hspace{1cm} - \\frac{\\sqrt{2}(x^*)^3}{2}|2^{-1}\\rangle_\\Omega +\n\\frac{(x^*)^4}{2(1+\\sqrt{2})}|{-2^{-1}\\rangle_\\Omega}.\n\\end{eqnarray}\n\\reseteqn \nThe subscript $\\Omega$ on a ket implies that it is a right state of \n$U_{\\rm R}$ which has been rescaled into the attractor, $\\Omega$, of $U_{\\rm T_1}$.\nThe explicit form of these states is given in Table~1.\n\n\\subsection{Left eigenstates of $U_{\\rm T_1}$}\n\nIt is easily seen that the left states given by \n\\begin{equation} \\label{lt1}\n\\langle 0_j |_{\\rm{IV}} = \\frac{(-1)^j}{j!}\\delta_{-}^{(j)}(x-1)\n\\end{equation}\nform a bi-orthonormal set with the null states in~(\\ref{rt1}).\nThese left states are also orthogonal to all the other right states of $U_{\\rm T_1}$.\nThe left states associated with the transient decay states out of $\\rm{I}$ are given by\n\\begin{equation} \\label{l1}\n\\langle {2}^{-(j+1)\/2}|_{\\rm I} = \\frac{1}{j!}\n\\left[ (-1)^j\\delta_{+}^{(j)}(x) + \\delta_{-}^{(j)}(x-1) \\right]. \n\\end{equation}\n\nThe left states of $U_{\\rm R}$ are not the left states of $U_{\\rm T_1}$, even though\nthe right states of $U_{\\rm R}$ are also right states of $U_{\\rm T_1}$. This is\nbecause $U_{\\rm T_1}$ acting on a density contained within $\\Omega$ will\ncontinue to be in $\\Omega$.  But in general the\nKoopman operator, $K_{\\rm T_1}$, acting on a function with support only in $\\Omega$\nwill result in the function having support outside $\\Omega$ too.\nThe left states of $U_{\\rm R}$ scaled back to $\\Omega$ form a bi-orthonormal set with the\nright states contained in $\\Omega$, but they are not orthogonal to the transient\nstates that decay into $\\Omega$.   To make them so we use Gram--Schmidt orthogonalization.  The\nresults are given in Table 1.  \n\n\\subsection{The spectral decomposition}\n\nUsing all the eigenstates and eigenvalues given in Table~1 we may write\nthe action of $U_{\\rm T_1}^t$ in terms of its spectral decomposition as\n\\begin{eqnarray} \\label{specdec}\nU_{\\rm T_1}^{t} & = & | 1 \\rangle\\langle 1 |_{\\Omega} + \n(-1)^t|{-1 \\rangle}\\langle{-1 |_\\Omega} + \\sum_{j=0}^{\\infty}\n\\left( 2^{-(2j+1)\/2} \\right)^t|2^{-(2j+1)\/2}\\rangle\\langle\n2^{-(2j+1)\/2}|_{\\rm{I}} \\nonumber \\\\ \n& & + \\sum_{j=1}^{\\infty}(2^{-j})^t \\left[ | {+2^{-j}}\n\\rangle\\langle {+2^{-j} |_\\Omega} +\n|2^{-j}\\rangle\\langle 2^{-j}|_{\\rm{I}} \\right] \\nonumber \\\\ \n& & + \\sum_{j=1}^{\\infty}(-2^{-j})^t | {-2^{-j}}\n\\rangle\\langle {-2^{-j} |_\\Omega} +\n\\sum_{j=0}^{\\infty}\\delta_{1,t} | 0_{2j+1}\n\\rangle\\langle 0_{J_{2j+1}} |_\\Omega \\nonumber \\\\ \n& & + \\sum_{j=0}^{\\infty}\\delta_{0,t} \\left[ |0_{2j+1}\n\\rangle\\langle 0_{2j+1} |_{\\Omega} + |0_{J_{2j+1}}\n\\rangle\\langle 0_{J_{2j+1}} |_{\\Omega} + |0_j\n\\rangle\\langle 0_j|_{\\rm{IV}} \\right], \n\\end{eqnarray}\nwhere the subscript on the bra states also identifies their dual ket states.\n\n\\clearpage\n\n \n\\begin{table}[p!] \n\\[\n\\begin{array}{|c|c|l|l|} \\hline \n\\mbox{eigenvalue} & \\mbox{degeneracy} & \\mbox{symbol} & \\mbox{eigenvector} \\\\ \\hline \n1 & 1 & | 1 \\rangle_{\\Omega} & \\chi_{\\rm{II}} + \\sqrt{2}\\chi_{\\rm{III}} \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n &  & \\langle 1 |_{\\Omega} & \\frac{(x^*)^2}{2}(\\chi_{\\rm{II}} + \\chi_{\\rm{III}}) \\\\\n& & & \\mbox{}-\\sum_{k=0}^{\\infty}\\left(a_{0,k}\\langle 2^{-(k+1)\/2}|_{\\rm{I}} +\n\\alpha_{0,k}'\\left\\langle 0_k \\right|_{\\rm{IV}} \\right) \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n\\hline \n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n-1 & 1 & | {-1 \\rangle_\\Omega} & \\chi_{\\rm{II}} - \\sqrt{2}\\chi_{\\rm{III}} \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n &  & \\langle -1 |_{\\Omega} & \\frac{(x^*)^2}{2}(\\chi_{\\rm{II}} - \\chi_{\\rm{III}}) \\\\\n& & &\\mbox{}-\n\\sum_{k=0}^{\\infty}\\left( b_{0,k}\\langle 2^{-(k+1)\/2}|_{\\rm{I}} -\n\\alpha_{0,k}'\\left\\langle 0_k \\right|_{\\rm{IV}} \\right) \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n\\hline\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n+\\frac{1}{2^j} & 1 & |{+ 2^{-j} \\rangle_\\Omega} &\nB_{2j}\\left( \\frac{x^* - \\phi(x)}{2x^*} \\right)\\chi_{\\rm{II}} +\n\\frac{\\sqrt{2}}{2^j}B_{2j}\\left( \\frac{\\phi(x) -\nx^*}{\\sqrt{2}x^*}\\right)\\chi_{\\rm{III}} \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n &  & \\langle +2^{-j} |_{\\Omega} & \\frac{\\left( x^{*} \\right)^{4j-2}}\n{(2j)!} \\left[ \\delta^{(2j-1)}_{+}(x-{\\rm{T}}^{(2)}(x_c))\n - \\delta^{(2j-1)}_{-}(x -x^{*}) \\right. \\\\ \n& & & \\mbox{} \\left. \n + \\delta^{(2j-1)}_{+}(x - x^{*}) -\n\\delta^{(2j-1)}_{-}(x - {\\rm{T}}^{(1)}(x_c)) \\right] \\\\ & & & - \n\\sum_{k=2j}^{\\infty}\\left( a_{j,k}\\langle 2^{-(k+1)\/2}|_{\\rm{{I}}} +\n\\alpha_{j,k}'\\left\\langle 0_k \\right|_{\\rm{IV}} \\right) \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n \\hline   \n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n-\\frac{1}{2^j} & 1 & |{- 2^{-j} \\rangle_\\Omega} &\nB_{2j}\\left( \\frac{x^* - \\phi(x)}{2x^*} \\right)\\chi_{\\rm{II}} -\n\\frac{\\sqrt{2}}{2^j}B_{2j}\\left( \\frac{\\phi(x) -\nx^*}{\\sqrt{2}x^*}\\right)\\chi_{\\rm{III}} \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n &  & \\langle -2^{-j} |_{\\Omega} &  \\frac{\\left( x^{*}\n\\right)^{4j-2}} {(2j)!} \\left[ \\delta^{(2j-1)}_{+}(x-{\\rm{T}}^{(2)}(x_c))\n- \\delta^{(2j-1)}_{-}(x - x^{*}) \\right. \\\\\n& &  & \\mbox{} \\left. \n - \\delta^{(2j-1)}_{+}(x - x^{*})  +\n\\delta^{(2j-1)}_{-}(x - {\\rm{T}}^{(1)}(x_c)) \\right] \\\\ & & & - \n\\sum_{k=2j}^{\\infty}\\left( b_{j,k}\\langle 2^{-(k+1)\/2}|_{\\rm{I}} - \\alpha_{j,k}'\\left\\langle\n0_k \\right|_{\\rm{IV}} \\right) \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n \\hline  \n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n0 & \\infty & | 0_{2j+1} \\rangle_{\\Omega} & E_{2j+1}\\left(\n\\frac{\\phi(x)}{x^*} \\right)\\chi_{\\rm{II}} \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n & ( 2 \\times 2 & \\left\\langle 0_{2j+1} \\right|_{\\Omega} &\n-\\left(\\frac{x^*}{\\sqrt{2}}\\right)^{4j+2}\\frac{1}{(2j+1)!}\n\\delta^{(2j+1)}_{+}(x-{\\rm{T}}^{(2)}(x_c)) \\\\\n& \\mbox{Jordan} & &\\mbox{} - \\sum_{k=2j+1}^{\\infty}c_{j,k}\n\\langle 2^{-(k+1)\/2}|_{\\rm{I}} \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n & \\mbox{blocks})  & | 0_{J_{2j+1}} \\rangle_{\\Omega} &\n-\\sqrt{2}\\left(E_{2j+1}\\left(\n\\frac{\\sqrt{2}}{x^*} (\\phi(x) - x^*)\\right)\\right)\\chi_{\\rm{III}} \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n & & \\left\\langle 0_{J_{2j+1}} \\right|_{\\Omega} &\n\\frac{(x^*)^{4j+2}}{\\sqrt{2}(2\\sqrt{2})^{2j+1}}\\frac{1}{(2j+1)!}\n\\delta^{(2j+1)}_{-}(x-{\\rm{T}}^{(1)}(x_c)) \\\\\n& & & \\mbox{}-\n\\sum_{k=2j+1}^{\\infty}\\gamma^{'}_{j,k}\\left\\langle 0_{k}\\right|_{\\rm{IV}}\n\\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n \\hline \n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n\\left( \\frac{1}{\\sqrt{2}}\\right)^{j+1} & 1 & |2^{-(j+1)\/2}\\rangle_{\\rm{I}} &\nx^j\\chi_{\\rm{I}} +\n\\sum_{i=0}a_{i,j}| 2^{-i}\\rangle + b_{i,j}|\n-2^{-i}\\rangle + c_{i,j}|0_i\\rangle \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n & & \\langle 2^{-(j+1)\/2}|_{\\rm{I}} & \\frac{1}{j!}\n\\left( (-1)^j\\delta^{(j)}(x) + \\delta^{(j)}(x-1) \\right) \\\\ \n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n\\hline \n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\\n0 & \\infty & |\n0_j \\rangle_{\\rm{IV}} &   (-1)^{j+1}x^j\\chi_{\\rm{I}} + (x-1)^{j}\\left(\n\\chi_{\\rm{III}} + \\chi_{\\rm{IV}} \\right) \\\\\n\\vspace{-1mm}& \\vspace{-1mm} & \\vspace{-1mm} & \\vspace{-1mm}\\\\ \n & & \\left\\langle 0_j \\right|_{\\rm{IV}} & \\frac{(-1)^j}{j!}\n\\delta^{(j)}(x-1)  \\\\ \\hline\n \\end{array} \\]\n\\caption{\\small Elements of the spectral decomposition of the tent map at the first band splitting\npoint. The constants $a_{i,j}\\equiv\\langle\n{2^{-i}}|_{\\Omega}(2)^{-(j+1)\/2}\n\\rangle_{\\rm{I}}$, $b_{i,j}\\equiv\\langle\n-{2^{-i}}|_{\\Omega}(2)^{-(j+1)\/2}\n\\rangle_{\\rm{I}}$ and $c_{i,j}\\equiv\\langle\n0_i|_{\\Omega}(2)^{-(j+1)\/2}\n\\rangle_{\\rm{I}}$ and are given in Appendix C.  The\nconstants $\\alpha_{i,j}'\\equiv\\langle\n+{2^{-i}}|_\\Omega 0_j \\rangle_{\\rm{IV}}$, $\\beta_{i,j}'\\equiv\\langle -{2^{-i}}|_\\Omega 0_j\n\\rangle_{\\rm{IV}}=-\\alpha_{i,j}'$ and $\\gamma_{i,j}'\\equiv\\langle 0_{J_i}|_\\Omega 0_j\n\\rangle_{\\rm{IV}}$ and\n$\\phi(x)$ is defined in (\\ref{phi}).}\n\\end{table}\n\n\n\\clearpage\n \n\n\n\n\n\n\n\n\\section{Higher band-splitting points}\n\nWe can determine the spectral decomposition of the tent map at any\nband-splitting point (bsp) by generalizing the approach used in the previous\nsection for the first bsp. For the rescaled map at\n$\\alpha = \\sqrt{2}$ we found that by considering its square\nit separated into two parts that were\ndirectly related by a simple change of scale (including a reflection for one\npart) to the tent map at full height where\n$\\alpha = 2$. This relationship also holds generally~\\cite{ProvMac,Heidel}\nbetween the map at the\n$n^{\\rm{th}}$ bsp,\n$(\\alpha_{n} = 2^{2^{-n}})$, and the $(n-1)^{\\rm{th}}$ bsp, \n$(\\alpha_{n-1} = 2^{2^{-(n-1)}} = \\alpha_{n}^2)$.\n\nThe tent map at $\\alpha_n$ on the interval\n$[ {\\rm{T}}^{(2)}_n (x_c), {\\rm{T}}^{(1)}_n (x_c))$,\nwhich contains the attractor, is first stretched to the \nunit interval $[0,1)$ to make the rescaled map ${\\rm R}_n$. \nThe linear function\nthat makes this  stretch is \n\\begin{equation} \\label{genphi}\n\\phi_n (x) = \\frac{2x - \\alpha_n (2 - \\alpha_n)}{\\alpha_n(\\alpha_n - 1)}.\n\\end{equation} \nUnder (\\ref{genphi}) the map ${\\rm{T}}_{n}$ transforms to \n${\\rm{R}}_n = \\phi_n \\circ {\\rm{T}}_n \\circ \\phi^{-1}_n$ and\nis  given by \n\\begin{equation} \\label{genr}\n{\\rm{R}}_n (x) = \\left\\{ \\begin{array}{lc}\n2-\\alpha_n (1-x) & 0 \\leq x < (\\alpha_n -1)\/ \\alpha_n \\\\\n\\noalign{\\vskip4pt}\n\\alpha_n (1- x) & (\\alpha_n -1)\/ \\alpha_n \\leq x < 1. \n\\end{array} \\right.\n\\end{equation}\n\nWe then compose ${\\rm{R}}_n$ with itself to obtain\n${\\rm{G}}_n \\equiv {\\rm{R}}_n \\circ {\\rm{R}}_n$. \nAs is illustrated in Figure 5 for the $2^{\\rm{nd}}$ bsp, 1t can be shown easily that in general: \n\\newline\n(a) ${\\rm{G}}_n(x)$ in the interval \n$X_{n, {\\rm A}} \\equiv [0,{\\rm{R}}_n^{(4)}(x_c))$ is\ntopologically conjugate to\n${\\rm{R}}_{n-1}$ (the rescaled map at higher height) in the interval\n$[0,1)$ as \n\\begin{equation} \\label{imp1}\n{\\rm{R}}_{n-1}  =  \\phi_{n,\\rm{A}}\n\\circ {\\rm{G}}_{n,\\rm{A}} \\circ \\phi_{n,\\rm{A}}^{-1} , \n\\end{equation}\nwhere\n\\begin{equation} \\label{impc1}\n\\phi_{n,\\rm{A}}  =  1 - \\frac{x}{\\alpha_n (\\alpha_n -1)},\n \\;\\;\\;\\;\\; x \\in X_{n, {\\rm A}}.\n\\end{equation}\n(b) ${\\rm{G}}_n(x)$ in the interval \n$X_{n, {\\rm B}} \\equiv [{\\rm{R}}_n^{(3)}(x_c),1)$ is\ntopologically conjugate to\n${\\rm{R}}_{n-1}$ in the interval $[0,1)$ as\n\\begin{equation} \\label{imp2}\n{\\rm{R}}_{n-1}  = \\phi_{n,\\rm{B}} \\circ\n{\\rm{G}}_{n,\\rm{B}} \\circ \\phi_{n,\\rm{B}}^{-1},  \n\\end{equation}\nwhere\n\\begin{equation} \\label{impc2}\n\\phi_{n,\\rm{B}}  =  \\frac{x-(2-\\alpha_n)}{\\alpha_n -1},\n \\;\\;\\;\\;\\; x \\in X_{n, {\\rm B}}. \n\\end{equation}\n\\begin{figure}[htb]\n\\begin{center}\n\\scalebox{.5}[.5]{\\includegraphics{fig41.eps}}\n\\parbox{5in}{\\caption{\\small At the second band-splitting point, ${\\rm{G_{2}}}$ \nis conjugate in $X_{2,{\\rm A}}$ and $X_{2,{\\rm B}}$ to\n$\\rm{R_{1}}$ shown in  Figure 3. The central transient region \nis shown as $X_{2,{\\rm C}}$.}}\n\\end{center}\n\\end{figure}\n\n\nAt the $n^{\\rm{th}}$  bsp the critical trajectory is eventually periodic with period\n$2^{n-1}$ ($n \\geq 1$), and therefore the number of discontinuities that appear\nunder time evolution of an initially smooth density is finite. Equations (\\ref{imp1}) --\n(\\ref{impc2}) imply that the band structure at the $n^{\\rm{th}}$ bsp consists of 2 scaled\ncopies of the band structure at the $(n-1)^{\\rm{th}}$ bsp separated by the\ninterval $[ {\\rm{R}}_{n}^{(4)}(x_c),{\\rm{R}}_{n}^{(3)}(x_c))  \\equiv\nX_{n, {\\rm C}}$, which makes one band. Therefore we have the following\n recursion relation for $S_n$, the number of bands at the $n^{{\\rm th}}$ bsp\nfor the map ${\\rm R}_{n}$,\n\\begin{equation}\nS_{n} = 2 S_{n-1} + 1 ,  \n\\end{equation}\nfor $n \\geq 2$,\nwhere $ S_{1} = 2$. Solving this recursion relation gives \n\\begin{equation}\\label{bandno}\nS_{n} = 2^n + 2^{n-1} - 1, \n\\end{equation}\nfor $n \\geq 1$.\nOf the $S_n$ bands, the invariant density has support only on $2^n$\nbands. The density is transient on the other\n$2^{n-1} -1$ bands. The function space we consider at the $n^{\\rm{th}}$ bsp is\npiecewise polynomial, with each piece extending over one band. \n\n\\subsection{Decomposition on the attractor}\n\nAssociated with the $2^n$ bands that make up \n$\\Omega_{n}$, the attractor at the $n^{\\rm{th}}$ bsp, are  $2^n$\n eigen\/Jordan vectors of each polynomial  degree\n$j$. We denote an element in the spectrum of\n$U_{{\\rm R}_n}$ associated with states on $\\Omega_{n}$ as $\\lambda^{n}_{k,j}$ and the right\neigen\/Jordan vector associated with it as $ |\\lambda^{n}_{k,j} \\rangle$. The\nsuperscript $n$ stands for the order of the band-splitting point. The index\n$k$ is an integer from $1$ to $2^n$ and distinguishes between the $2^n$\nindependent eigen\/Jordan vectors of degree $j$, at the $n^{\\rm{th}}$ bsp. \n\nSince ${\\rm G}_{n,{\\rm A}}$ and ${\\rm G}_{n,{\\rm B}}$  are topologically conjugate \nto ${\\rm R}_{n-1}$  all three share the same spectrum. The map ${\\rm G}_n$ is\nthe union of ${\\rm G}_{n,{\\rm A}}$, ${\\rm G}_{n,{\\rm B}}$ and the \npart of ${\\rm{G}}_{n}$ on the central transient interval $X_{n,{\\rm C}}$.\nThe spectrum of ${\\rm{R}}_{n}$ on $\\Omega_{n}$ is determined from the\nspectrum of ${\\rm{G}}_{n}$ on $\\Omega_{n}$. Consider a non-zero eigenvalue\n$\\lambda^{n-1}_{k,2j}$ of ${\\rm R}_{n-1}$ (we will show later that as at the\nfirst bsp the right states corresponding to non-zero eigenvalues\non the attractor are even-order polynomials), which is\nalso an eigenvalue of ${\\rm{G}}_{n}$ with degeneracy 2 \n(one for ${\\rm G}_{n,{\\rm A}}$ and one for ${\\rm G}_{n,{\\rm B}}$). \nUsing arguments parallel to those that we used at the first bsp\nwe deduce that  ${\\rm{R}}_{n}$ has two distinct eigenvalues \n$+\\sqrt{\\lambda^{n-1}_{k,2j}}$ and $-\\sqrt{\\lambda^{n-1}_{k,2j}}$. By induction \n${\\rm{R}}_{n+1}$ on $\\Omega_{n+1}$ has in its spectrum the eigenvalues\n$+(\\lambda^{n-1}_{k,2j})^{1\/4}$, $-(\\lambda^{n-1}_{k,2j})^{1\/4}$,\n$+i(\\lambda^{n-1}_{k,2j})^{1\/4}$ and  $-i(\\lambda^{n-1}_{k,2j})^{1\/4}$.\nThus from\nthe non-zero eigenvalues at the $0^{\\rm{th}}$ bsp we can determine \nthe non-zero eigenvalues at the\n$n^{\\rm {th}}$ bsp by taking square roots of $2^{-2j}$\nrecursively, $n$ times. Thus \n\\begin{equation} \\label{eig1}\n\\lambda^{n}_{k,2j} =\n\\left(\\frac{1}{2}\\right)^{{2j}\/{2^n}}\\mbox{exp}\\left(\\frac{2\\pi\nik}{2^n}\n\\right),\n\\end{equation}\nwhere $k=1,2,\\ldots,2^n$ and $j=0,1,2,\\ldots$ .\nNote that for $k \\leq 2^{n-1}$ \n\\begin{equation} \\label{minus}\n\\lambda^{n}_{k,2j} = -\\lambda^{n}_{k+2^{n-1},2j}.\n\\end{equation}\n\nAt the $0^{\\rm{th}}$ bsp the eigenvalue $0$ is infinitely degenerate with\nan associated eigenpolynomial of odd degree for each occurence of the\neigenvalue.  In the previous section we saw that at the $1^{\\rm st}$ bsp \nthere are an infinite number of  $2 \\times 2$ Jordan blocks associated with\neigenvalue zero, one each for each odd degree.  We will show by explicit\nconstruction below that this trend continues and at the $n^{\\rm{th}}$ bsp, ${\\rm R}_{n}$\nhas a $2^n \\times 2^n$ Jordan block for every odd degree.  \n\n\\subsubsection{Right states on the attractor}\n\nTo determine the right states on $\\Omega_{n}$ with non-zero eigenvalues we begin similar to\n$(20)$ by writing\nthe right states at the\n$n^{\\rm{th}}$ bsp in terms of those at the $(n-1)^{\\rm th}$ bsp as \n\\alpheqn \n\\begin{eqnarray}\n |\\lambda^{n}_{k,2j} \\rangle & = & |\\lambda^{n-1}_{k,2j}\n\\rangle_{{\\rm G}_{n,{\\rm A}}} +c^{n}_{k,2j} |\\lambda^{n-1}_{k,2j}\n\\rangle_{{\\rm G}_{n,{\\rm B}}} \\\\ \n |\\lambda^{n}_{k+2^{n-1},2j} \\rangle & = & |\\lambda^{n-1}_{k,2j}\n\\rangle_{{\\rm G}_{n,{\\rm A}}} +d^{n}_{k,2j} |\\lambda^{n-1}_{k,2j}\n\\rangle_{{\\rm G}_{n,{\\rm B}}},\n\\end{eqnarray}\n\\reseteqn\nwhere  $k = 1,2,\\ldots,2^{n-1}$. In equation (52) and\nin the remaining part of this subsection kets without\nany subscript denote right states of  ${\\rm{R}}$ at the appropriate bsp. \nConjugacies (\\ref{imp1}) and (\\ref{imp2}) imply that the eigenvectors \nof ${\\rm G}_{n,{\\rm A}}$ and ${\\rm G}_{n,{\\rm B}}$ are related to those \nof ${\\rm R}_{n-1}$ as\n\\alpheqn \n\\begin{eqnarray}\n|\\lambda^{n-1}_{k,2j}\\rangle_{{\\rm G}_{n,{\\rm A}}} & = & \nU_{\\phi^{-1}_{n,\\rm{A}}} |\\lambda^{n-1}_{k,2j} \\rangle \\\\ \n|\\lambda^{n-1}_{k,2j}\\rangle_{{\\rm G}_{n,{\\rm B}}} & = & \nU_{\\phi^{-1}_{n,\\rm{B}}} |\\lambda^{n-1}_{k,2j} \\rangle. \n\\end{eqnarray}\n\\reseteqn\nUsing this in (52) gives\n\\alpheqn \n\\begin{eqnarray} \\label{onea} \n |\\lambda^{n}_{k,2j} \\rangle & =\n& U_{\\phi^{-1}_{n,\\rm{A}}} |\n\\lambda^{n-1}_{k,2j} \\rangle +c^{n}_{k,2j}U_{\\phi^{-1}_{n,\\rm{B}}} \n |\\lambda^{n-1}_{k,2j} \\rangle \\\\  \\label{oneb}\n |\\lambda^{n}_{k+2^{n-1},2j} \\rangle & =\n& U_{\\phi^{-1}_{n,\\rm{A}}} |\n\\lambda^{n-1}_{k,2j} \\rangle +d^{n}_{k,2j}U_{\\phi^{-1}_{n,\\rm{B}}} \n|\\lambda^{n-1}_{k,2j} \\rangle.  \n\\end{eqnarray}\n\\reseteqn\nThe state $U_{\\phi^{-1}_{n,\\rm{A}}}|\\lambda^{n-1}_{k,2j} \\rangle$\nhas support only in $X_{n,{\\rm{A}}}$ and \n$U_{\\phi^{-1}_{n,\\rm{B}}} |\\lambda^{n-1}_{k,2j}\n\\rangle$ has support only in $X_{n,{\\rm{B}}}$. \n\nWe now use the relation\n\\begin{equation} \\label{pmyst}\n {\\rm{R}}_{n}\\circ \\phi_{n,\\rm{B}}^{-1} = \\phi_{n,\\rm{A}}^{-1}, \n\\end{equation}\nwhich implies that \n\\begin{equation} \\label{myst}\nU_{{\\rm{R}}_{n}}U_{\\phi_{n,\\rm{B}}^{-1}} =\nU_{\\phi_{n,\\rm{A}}^{-1}}.\n\\end{equation} \n(Even though (\\ref{pmyst}) and (\\ref{myst}) are written \nspecifically at the band-splitting points, they are valid for all\n$\\alpha \\in (1,2]$.)\nActing on (54) by $U_{{\\rm{R}}_n}$ and using (\\ref{myst}) we get\n\\alpheqn\n\\begin{eqnarray} \\label{xiaoa}\n\\lambda^{n}_{k,2j} | \\lambda^{n}_{k,2j} \\rangle & =\n& U_{{\\rm{R}}_n}U_{\\phi^{-1}_{n,\\rm{A}}}|\n\\lambda^{n-1}_{k,2j} \\rangle +c^{n}_{k,2j}U_{\\phi^{-1}_{n,\\rm{A}}} \n |\\lambda^{n-1}_{k,2j} \\rangle \\\\ \\label{xiaob} \n-\\lambda^{n}_{k,2j}| \\lambda^{n}_{k+2^{n-1},2j} \\rangle & =\n& U_{{\\rm{R}}_n}U_{\\phi^{-1}_{n,\\rm{A}}} |\n\\lambda^{n-1}_{k,2j} \\rangle +d^{n}_{k,2j}U_{\\phi^{-1}_{n,\\rm{A}}} \n |\\lambda^{n-1}_{k,2j} \\rangle,  \n\\end{eqnarray}\n\\reseteqn\nwhere (\\ref{minus}) has been used on the lhs of (\\ref{xiaob}).  Since\n$U_{{\\rm{R}}_n}$ has the flip property that any function with support \nonly in $X_{n,\\rm{B}}$ will go entirely to\n$X_{n,\\rm{A}}$ in one iteration and vice-versa we know that\n$U_{{\\rm{R}}_n}U_{\\phi^{-1}_{n,\\rm{A}}}|\\lambda^{n-1}_{k,2j} \\rangle$\n has support only in $X_{n,{\\rm{B}}}$ and $U_{\\phi^{-1}_{n,\\rm{A}}} \n|\\lambda^{n-1}_{k,2j} \\rangle$ has support only in $X_{n,\\rm{A}}$.\nMultiplying (\\ref{onea}) by $\\lambda^{n}_{k,2j}$ and (\\ref{oneb}) by\n$-\\lambda^{n}_{k,2j}$ and identifying the components with support only\nin $X_{n,{\\rm A}}$ with the corresponding components in (57)\ngives\n\\alpheqn\n\\begin{eqnarray}\nc^{n}_{k,2j}U_{\\phi^{-1}_{n,\\rm{A}}} \n |\\lambda^{n-1}_{k,2j} \\rangle & = & \\lambda^{n}_{k,2j}\nU_{\\phi^{-1}_{n,\\rm{A}}} |\\lambda^{n-1}_{k,2j} \\rangle \\\\ \nd^{n}_{k,2j}U_{\\phi^{-1}_{n,\\rm{A}}} \n |\\lambda^{n-1}_{k,2j} \\rangle & = & -\\lambda^{n}_{k,2j}\nU_{\\phi^{-1}_{n,\\rm{A}}}|\\lambda^{n-1}_{k,2j} \\rangle,\n\\end{eqnarray}\n\\reseteqn\nshowing that $c^{n}_{k,2j} = \\lambda^{n}_{k,2j}$ and $d^{n}_{k,2j} = -\\lambda^{n}_{k,2j}$. \nUsing this result gives the pair of recursion relations\n\\alpheqn\n\\begin{eqnarray} \\label{three}\n| \\lambda^{n}_{k,2j} \\rangle & =\n& \\left( U_{\\phi^{-1}_{n,\\rm{A}}}\n+\\lambda^{n}_{k,2j}U_{\\phi^{-1}_{n,\\rm{B}}} \\right) \n |\\lambda^{n-1}_{k,2j} \\rangle \\\\ \n| \\lambda^{n}_{k+2^{n-1},2j} \\rangle & =\n& \\left( U_{\\phi^{-1}_{n,\\rm{A}}} \n-\\lambda^{n}_{k,2j}U_{\\phi^{-1}_{n,\\rm{B}}} \\right)\n |\\lambda^{n-1}_{k,2j} \\rangle ,\n\\end{eqnarray}\n\\reseteqn \nwhich express the right states at the $n^{\\rm{th}}$ bsp in terms \nof those at the $(n-1)^{\\rm{th}}$ bsp. \n\nThese recursion relations can be solved to write the right\nstates at the\n$n^{\\rm{th}}$ bsp in terms of the right states at the $0^{\\rm{th}}$ ($\\alpha =\n2$) bsp. For notational convenience we define\n\\begin{equation} \\label{four}\n\\begin{array}{lcl}\n\\widehat{{\\rm{A}}}_{i} & \\equiv & U_{\\phi^{-1}_{i,{\\rm{A}}}} \\\\\n\\widehat{{\\rm B}}_{i} & \\equiv & U_{\\phi^{-1}_{i,{\\rm{B}}}} \\\\\n\\widehat{{\\rm B}}^{n}_{k,2j,i} & \\equiv &\n\\left(\\lambda^{n}_{k,2j}\\right)^{i}\\widehat{{\\rm{B}}}_{i}\n\\end{array}\\end{equation}\nLet $\\sigma_i$ ($i=1,2,\\dots,n$) be either $0$ or $1$ and we define $\\widehat\n{\\Pi}_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_1}$ to be an ordered \n$n$-product of $\\widehat{{\\rm{A}}}_{i}$'s and $\\widehat{{\\rm\nB}}^{n}_{k,2j,i}$'s, where if $\\sigma_i = 1$ then the $i^{\\rm {th}}$\nlocation in the $n$-product (counting from the right) will be taken by\n$\\widehat{{\\rm B}}^{n}_{k,2j,i}$  and if $\\sigma_i = 0$ then the $i^{\\rm {th}}$\nlocation will be taken by  $\\widehat{{\\rm{A}}}_{i}$. Solving (59)\ngives  \n\\begin{equation} \\label{five}\n| \\lambda^{n}_{k,2j} \\rangle = \n\\sum_{\\{\\sigma \\}}\\widehat{\\Pi}_{\\sigma_n\\sigma_{n-1}...\\sigma_1} |\n\\lambda^{0}_{1,2j} \\rangle.\n\\end{equation}\nThe sum in (\\ref{five}) is over all possible $\\sigma$-strings \nof $0$'s and $1$'s of length $n$ and so consists of\n$2^n$ terms ($n$-products). The order of the operators in each $n$-product \nmust be strictly observed \nsince the operators involved do not commute. \n\nTo illustrate (\\ref{five}) we write it out explicitly for $n = 1$ and $2$.\nFor $n=1$ (\\ref{five}) gives\n\\begin{equation} \\label{example1}\n| \\lambda^{1}_{k,2j} \\rangle = \\widehat{\\rm{A}}_{1} |\n\\lambda^{0}_{1,2j} \\rangle + \\widehat{\\rm B}^{1}_{k,2j,1} |\n\\lambda^{0}_{1,2j} \\rangle.\n\\end{equation}\nThis agrees with the expression (\\ref{fbspurstates})\n(corresponding to $k=1$ and $k=2$) we had for the\nright eigenstates at the first bsp. \nFor  $n=2$ (\\ref{five}) gives\n\\begin{eqnarray}\n| \\lambda^{2}_{k,2j}\\rangle & = &\n\\widehat{\\rm{A}}_{2}\\widehat{\\rm{A}}_{1} |\n\\lambda^{0}_{1,2j} \\rangle + \\widehat{\\rm{A}}_{2}\\widehat{\\rm B}^{2}_{k,2j,1} |\n\\lambda^{0}_{1,2j} \\rangle  \\nonumber \\\\\n& & \\mbox{} + \\widehat{\\rm B}^{2}_{k,2j,2} \\widehat{\\rm A}_{1} |\n\\lambda^{0}_{1,2j} \\rangle + \\widehat{\\rm B}^{2}_{k,2j,2}\\widehat{\\rm B}^{2}_{k,2j,1}\n | \\lambda^{0}_{1,2j} \\rangle.\n\\end{eqnarray}\n\nNow we prove by induction that there is a $2^n \\times\n2^n$ Jordan block associated with the eigenvalue $0$ at the $n^{\\rm{th}}$ bsp for\neach odd order $2j+1$. In section 2 it was shown that this statement is\ntrue for the first bsp.  Assume that this statement is true at the $(n-1)^{\\rm{th}}$ bsp.\nWe denote the Jordan vectors as $| 0^{n-1}_{k,2j+1} \\rangle$ where \n$k=2,3,\\dots,2^{n-1}$ ($| 0^{n-1}_{1,2j+1} \\rangle$ is the eigenvector of the block).  They satisfy\n\\alpheqn\n\\begin{eqnarray} \\label{jorddef}\nU_{{\\rm R}_n}| 0^{n-1}_{k,2j+1} \\rangle & = & | 0^{n-1}_{k-1,2j+1}\n\\rangle, \\;\\;\\;\\;\\;\\;\\;\\; k \\neq 1  \\\\ \nU_{{\\rm R}_n} | 0^{n-1}_{1,2j+1} \\rangle & = & 0.\n\\end{eqnarray}\n\\reseteqn \nSince we are assuming that $U_{{\\rm{R}}_{n-1}}$ has $2^{n-1} \\times 2^{n-1}$ \nJordan blocks, the conjugacies \n(\\ref{imp1}) and (\\ref{imp2}) imply that ${\\rm{G}}_{n,{\\rm A}}$ and ${\\rm{G}}_{n,{\\rm B}}$\nboth have $2^{n-1} \\times 2^{n-1}$ Jordan blocks with states given by\n\\alpheqn \n\\begin{eqnarray} \n| 0^{n}_{k,2j+1} \\rangle_{{\\rm{G}}_{n,A}} & = & \n\\widehat{{\\rm{A}}}_{n}| 0^{n-1}_{k,2j+1} \\rangle \\\\ \n| 0^{n}_{k,2j+1} \\rangle_{{\\rm{G}}_{n,B}} & = & \\label{jzerob}\n\\widehat{{\\rm{B}}}_{n}| 0^{n-1}_{k,2j+1} \\rangle,\n\\end{eqnarray}\n\\reseteqn\nwhere $k=1,2,\\dots,2^{n-1}$. Since \n${{\\rm{G}}_{n}}$ on $\\Omega_{n}$ has two $2^{n-1} \\times 2^{n-1}$ Jordan blocks\nfor each $j$, ${{\\rm{R}}_{n}}$ on $\\Omega_{n}$ can either have two \n$2^{n-1} \\times 2^{n-1}$ Jordan blocks for each $j$ or have one $2^{n}\n\\times 2^{n}$ Jordan block for each $j$. The first case implies that \n$U_{{\\rm R}_n}$ have two null vectors $| 0^{n}_{1,2j+1}\n\\rangle_{{\\rm{G}}_{n,{\\rm A}}}$ and $| 0^{n}_{1,2j+1}\n\\rangle_{{\\rm{G}}_{n,{\\rm B}}}$for each $j$. But $U_{{\\rm R}_n}\n| 0^{n}_{1,2j+1} \\rangle_{{\\rm{G}}_{n,{\\rm B}}} \\neq 0$, since no function with\nsupport in $X_{n,\\rm{B}}$ can vanish in one iteration under\n$U_{{\\rm R}_n}$.  Therefore \n$U_{{\\rm R}_n}$ has a $2^n \\times 2^n$ Jordan block for \neach odd degree $2j+1$. This\ncompletes the proof by induction. \n\nA null state of $U_{{\\rm R}_n}$ has to be a null state of\n$U_{{\\rm G}_n}$ too. Therefore the null state of\n$U_{{\\rm R}_n}$ for each $j$ is given by \n\\begin{equation} \\label{z1}\n| 0^{n}_{1,2j+1} \\rangle  =  \n\\widehat{{\\rm{A}}}_{n}| 0^{n-1}_{1,2j+1} \\rangle.\n\\end{equation}\nWe use the relation \n\\begin{equation}\n{\\rm R}_n \\circ \\phi^{-1}_{n, {\\rm A}} = \n\\phi^{-1}_{n, {\\rm B}} \\circ {\\rm R}_{n-1}\n\\end{equation}\nwhich implies that\n\\begin{equation} \\label{myst1}\nU_{{\\rm R}_n}\\widehat{{\\rm{A}}}_{n} =  \n\\widehat{{\\rm{B}}}_{n}U_{{\\rm R}_{n-1}}.\n\\end{equation}\nUnlike (\\ref{myst}), equation (\\ref{myst1}) \nis true only at the band-splitting points. Equation (\\ref{myst1}) can be used to\nverify that if we act on both sides of (\\ref{z1}) by $U_{{\\rm R}_n}$ its rhs reduces to zero.\n\nThe right state $| 0^{n}_{1,2j+1} \\rangle_{{\\rm G}_{n,{\\rm B}}}$ \nis a good candidate for the Jordan state $| 0^{n}_{2,2j+1} \\rangle$ since under one iteration by \n$U_{{\\rm R}_n}$ it will have support only in $X_{n, \\rm{A}}$ and under \ntwo iterations of $U_{{\\rm R}_n}$ it will vanish. Tentatively, from \n(\\ref{jzerob}) we write \n\\begin{equation} \\label{z2}\n| 0^{n}_{2,2j+1} \\rangle  =  \n\\widehat{{\\rm{B}}}_{n} | 0^{n-1}_{1,2j+1} \\rangle.\n\\end{equation}\nThis guess for the Jordan state can be verified by using \nrelation (\\ref{myst}).  Similarly (\\ref{myst1})\ncan be used to show that \n\\begin{equation} \\label{z3}\n| 0^{n}_{3,2j+1} \\rangle  = \n\\widehat{{\\rm{A}}}_{n}| 0^{n-1}_{2,2j+1} \\rangle.\n\\end{equation}\nand equation (\\ref{myst}) can be used to show that \n\\begin{equation} \\label{z4}\n| 0^{n}_{4,2j+1} \\rangle  =  \n\\widehat{{\\rm{B}}}_{n}| 0^{n-1}_{2,2j+1} \\rangle.\n\\end{equation}\nIn general, we find \n\\begin{eqnarray} \\label{r1}\n| 0^{n}_{k,2j+1} \\rangle & = & \n\\widehat{{\\rm{A}}}_{n} | 0^{n-1}_{\\lceil k\/2 \\rceil,2j+1} \\rangle \\;\\;\\;\\;\n\\mbox{for} \\; k \\; \\mbox{odd} \\\\ \\nonumber\n| 0^{n}_{k,2j+1} \\rangle & = & \n\\widehat{{\\rm{B}}}_{n} | 0^{n-1}_{k\/2 ,2j+1} \\rangle \\;\\;\\;\\;\\;\\;\n\\mbox{for} \\; k \\; \\mbox{even}\n\\end{eqnarray}\nwhere $k=1,2,\\dots,2^n$ and $\\lceil q \\rceil$ is the ceiling function ($q$ if it is an integer or\nelse the next greatest integer). \nThese recursions are illustrated in Figure~6 up to $n=2$.\n\\setlength{\\unitlength}{1mm}\n\\begin{figure}\n\\begin{center}\n\\begin{picture}(67,60)\n\\put(67,33){$|0^{0}_{1,2j+1}\\rangle$}\n\\put(66,34){\\vector(-1,1){15}}\n\\put(66,34){\\vector(-1,-1){15}}\n\\put(58,43){${\\widehat{\\rm A}}_{1}$}\n\\put(58,22){${\\widehat{\\rm B}}_{1}$}\n\\put(36,49){$|0^{1}_{1,2j+1}\\rangle$}\n\\put(36,18){$|0^{1}_{2,2j+1}\\rangle$}\n\\put(35,50){\\vector(-2,1){20}}\n\\put(35,50){\\vector(-2,-1){20}}\n\\put(35,19){\\vector(-2,1){20}}\n\\put(35,19){\\vector(-2,-1){20}}\n\\put(24,56.5){${\\widehat{\\rm A}}_{2}$}\n\\put(24,9){${\\widehat{\\rm B}}_{2}$}\n\\put(24,40){${\\widehat{\\rm B}}_{2}$}\n\\put(24,25){${\\widehat{\\rm A}}_{2}$}\n\\put(0,60){$|0^{2}_{1,2j+1}\\rangle$}\n\\put(0,39){$|0^{2}_{2,2j+1}\\rangle$}\n\\put(0,28){$|0^{2}_{3,2j+1}\\rangle$}\n\\put(0,8){$|0^{2}_{4,2j+1}\\rangle$}\n\\put(2,0){$n=2$}\n\\put(38,0){$n=1$}\n\\put(69,0){$n=0$}\n\\end{picture}\n\\parbox{5in}{\\caption{\\small States associated with eigenvalue zero obtained from the\naction of $\\widehat{{\\rm{A}}}_{n}$ and $\\widehat{{\\rm{B}}}_{n}$ on $|0^{n-1}_{k,2j+1}\\rangle$. }}\n\\end{center}\n\\end{figure}\nThis recursion relation can then be solved to write the eigen\/Jordan\nvectors at the $n^{\\rm{th}}$ bsp in terms of the null vectors at the $0^{\\rm{th}}$ bsp.\n To write down a compact solution we define $\\Pi_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_1}$, which is\nsimilar to the $\\widehat {\\Pi}_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_1}$ previously defined. \n We define $\\Pi_{\\sigma_n\\sigma_{n-1}...\\sigma_1}$ to be an ordered \n$n$-product of $\\widehat{{\\rm{A}}}_{i}$'s and $\\widehat{{\\rm{B}}}_{i}$'s.\nIf $\\sigma_i = 1$ then the $i^{\\rm {th}}$ location in the $n$-product\n(counting from the right) will be taken by  $\\widehat{{\\rm{B}}}_{i}$  and if\n$\\sigma_i = 0$ then the $i^{\\rm {th}}$ location will be taken by \n$\\widehat{{\\rm{A}}}_{i}$. With each $\\Pi_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_1}$\nwe associate a binary\nnumber formed from the string of $1$'s and $0$'s as  $\\kappa = \\sigma_n\\sigma_{n-1}\\dots\\sigma_1 +1$.\nSolving the recursion relation (\\ref{r1}) we get\n\\begin{equation} \\label{jord}\n| 0^{n}_{\\kappa,2j+1} \\rangle = \\Pi_{\\sigma_n\\sigma_{n-1}...\\sigma_1}\n| 0^{0}_{1,2j+1} \\rangle,\n\\end{equation}\nwhere $| 0^{0}_{1,2j+1} \\rangle$ is the null vector of degree $2j+1$ of the\ntent map with full height, and $\\kappa$ here is the decimal equivalent of the binary $\\kappa$,\nwhich ranges from $1$ to $2^n$. \n\n\\subsubsection{Left states on the attractor}\nWe obtain the left states, $ \\langle \\lambda^{n}_{k,j}\n|$, which are orthonormal to the right states given by\n(\\ref{five}) and (\\ref{jord})\nby taking the duals of those expressions.\nThe dual expression of (\\ref{five}) gives the left \nstates corresponding to the non-zero eigenvalues as \n\\begin{equation}\n\\langle \\lambda^{n}_{k,2j} | =\n\\sum_{\\{\\sigma\\}}\\widehat{\\Pi}^{\\dag}_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_1}\n\\frac{\\langle\n\\lambda^{0}_{1,2j}|}{2^n},\n\\end{equation}\nwhere the $n$-product here is of $(\\widehat{{\\rm{A}}}_{i}^{-1})^{\\dag}$'s and \n$((\\widehat{{\\rm B}}^{n}_{k,2j,i})^{-1})^{\\dag}$'s and the factor of $1\/2^n$ is put for\nnormalization. The left states corresponding to the Jordan vectors associated with the\neigenvalue $0$ are \n\\begin{equation} \\label{leftjord}\n\\langle 0^{n}_{\\kappa,2j+1} | =\n\\Pi^{\\dag}_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_1} \\langle 0^{0}_{1,2j+1}|,\n\\end{equation}\nwhere ${\\Pi^{\\dag}_{\\sigma_n\\sigma_{n-1}...\\sigma_1}}$ is an \nordered $n$-product of $(\\widehat{{\\rm{A}}}_{i}^{-1})^{\\dag}$'s and \n$(\\widehat{{\\rm B}}_{i}^{-1})^{\\dag}$'s.\n\n\\subsection{Decay onto the attractor of the rescaled map}\n\nWe saw in section 2.1 that $\\rm{R}_{1}$ has no transient bands. \nThe band structure of $\\rm{G}_2$\nconsists of two scaled copies of that of $\\rm{R}_{1}$ separated by the central interval  \n$X_{2,{\\rm C}}$. This central interval is a transient band of $\\rm{R}_{2}$. Since\n${\\rm{G}}_{3,{\\rm A}}$ and ${\\rm{G}}_{3,{\\rm B}}$ have a band structure similar to\nthat of ${\\rm{R}}_{2}$ both of them have a transient interval also. We refer\nto these two transient bands as peripheral transients since in\naddition there is a central transient in the interval $X_{3,{\\rm C}}$. \nIn general, as discussed below (\\ref{bandno}),\nat the $n^{\\rm{th}}$ bsp ${\\rm{R}}_{n}$ has $2^{n-1} - 1$ transient bands, of which \n$2^{n-1} - 2$ are peripheral transient bands. At each bsp\nall transient bands except the central one are rescaled versions of\nthe central transient bands at previous band-splitting points.\n\\begin{figure}[htb]\n\\begin{center}\n\\scalebox{.5}[.5]{\\includegraphics{fig51.eps}}\n\\parbox{5in}{\\caption{\\small Band structure at the $1^{\\rm{st}}$, $2^{\\rm{nd}}$ and \n$3^{\\rm{rd}}$ band-splitting points. The central transient $X_{2,{\\rm C}}$ at the $2^{\\rm{nd}}$\nbsp transforms into two peripheral transients at the $3^{\\rm{rd}}$ bsp.}}\n\\end{center}\n\\end{figure} \n\nUnder the map ${\\rm{R}}_{n}$ the inverse image of any point in the central\ninterval $X_{n,{\\rm C}}$ is contained within the interval itself. This implies that if\na function initially has no support in $X_{n,{\\rm C}}$, it will continue to have no\nsupport in $X_{n,{\\rm C}}$ under repeated iterations by $U_{{\\rm R}_n}$.\nThe spectrum and the form of the eigen\/Jordan vector in\nthe central interval at all the band-splitting points can be obtained by\ninspection. We notice that \n\\begin{equation} \\label{trans1}\nU_{{\\rm R}_n}\\left[ \\left(x-x^{*}_{n}\\right)^{j}\\chi_{n,{\\rm C}}\\right] =\n(-1)^{j}\\left(\\frac{1}{\\alpha_{n}}\\right)^{j+1}\\left\\{\\left(x-x^{*}_{n}\\right)^{j}\n\\chi_{n,{\\rm C}} +\n\\left(x-x^{*}_{n}\\right)^{j}\\chi_{n,b} \\right\\},\n\\end{equation}\nwhere $\\chi_{n,{\\rm C}}$ is the indicator function on \n$X_{n,{\\rm C}}$ and $\\chi_{n,b} =1$ if \n$x \\in [{\\rm{R}}^{(3)}_{n}(x_c), {\\rm{R}}^{(5)}_{n}(x_c) )$ and $0$ otherwise. The\nform of the eigen\/Jordan vector in $X_{n,{\\rm C}}$ \nassociated with decay out of the central interval is thus\n$\\left(x-x^{*}_{n}\\right)^{j}$. The complete form will be determined below.\nThe eigenvalues associated with decay out of\nthe central transient at the $n^{\\rm{th}}$ bsp are seen by (\\ref{trans1}) to be\n\\begin{equation} \\label{trans2}\n\\phi^{n,0}_{1,j} = (-1)^{j}\\left(\\frac{1}{\\alpha_{n}}\\right)^{j+1}\n\\end{equation}\n \nNext we obtain the complete spectrum at the $n^{\\rm{th}}$ bsp associated with\nthe decay out of all the transient regions onto $\\Omega_{n}$. This is done\nby transforming all the central transients at band-splitting points of\norder less than $n$.  Of all the peripheral transient bands at the $n^{\\rm th}$\nbsp, $2^{n-2}$ of these are\n$(n-2)$ times rescaled versions of the central transient at  ${\\rm{R}}_{2}$,  $2^{n-3}$\nof these are $(n-3)$ times rescaled versions of the central transient at \n${\\rm{R}}_{3}$ and so on up to $2$ of these peripheral transients being rescaled\nversions of the central transient at the $(n-1)^{\\rm{th}}$ bsp.\nThis is shown in Figure~7 up to $n=3$.\nWe denote the transient eigenvalues at the $n^{\\rm{th}}$ bsp by\n$\\phi^{n,l}_{k,j}$, where $l$ indicates that it was obtained from the\ncentral transient at the $(n-l)^{\\rm th}$ bsp, where \n$l=0,1,2,\\dots,n-2$, $k$ is\nan integer from $1$ to $2^l$, $j=0,1,2,3,\\dots,$ and as before the right state \n$|\\phi^{n,l}_{k,j} \\rangle$ is piecewise-polynomial of degree $j$ in each of\nthe pieces. The eigenvalues are obtained in a similar fashion to (\\ref{eig1}) as  \n\\begin{equation} \\label{eig2} \\phi^{n,l}_{k,j} =\n\\left(\\phi^{n-l,0}_{1,j}\\right)^{{1}\/{2^l}}\\mbox{exp}\\left(\n\\frac{2\\pi ik}{2^l}\\right),\n\\end{equation}\nwhere the $\\phi^{n,0}_{1,j}$ are given by (\\ref{trans2}). \nFor even values of $j$ there are degeneracies in the spectrum while for odd\nvalues of $j$ there are no degeneracies.  We consider first the states associated\nwith the degenerate eigenvalues.\n\n\\subsubsection{Transient right states of even degree}\nAs seen in (\\ref{eig2}), for a given $l$ (with $n$ and $2j$ fixed) there are $2^l$ distinct\neigenvalues indexed by $k$.  At each integer step ($l$) all\nthe eigenvalues of the previous step ($l-1$) are present and $2^{l-1}$ new eigenvalues \nappear.  But identical eigenvalues from different steps have disparate $k$ values.\nIt is convenient to rearrange the $k$ index so that degenerate eigenvalues share\nthe same $k$.\\footnote{This can be accomplished by choosing the new $k$'s asssociated\nwith the $l^{\\rm th}$ step as $k_{2i-1}^l = k_i^{l-1}$ and \n$k_{2i}^l = k_{2i-1}^l + 2^{l-1}$, where $i=1,\\dots,2^{l-1}$ denotes the order of its appearance and\n$k_1^0=1$.} Table 2 contains $\\phi^{5,l}_{k,0}$ for all possible values of \n$l$ and $k$, arranged to illustrate the reordering in $k$.\n\n\\begin{table}[htbp!]\n\\[\n\\begin{array}{|l|cccccccc|} \\hline\n & k=1 & k=2 & k=3 & k=4 & k=5 & k=6 & k=7 & k=8 \\\\ \\hline\n& \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} \n& \\vspace{-0.4mm} & \\vspace{-0.4mm} &  \\\\\n\\phi^{5,0}_{k,0} & \\varphi & & & & & & &  \\\\\n& \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} \n& \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\\\\n\\phi^{5,1}_{k,0} & \\varphi & -\\varphi & & & & & &  \\\\ \n& \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} \n& \\vspace{-0.4mm} & \\vspace{-0.4mm} &\\\\\n\\phi^{5,2}_{k,0} & \\varphi & -\\varphi & i\\varphi & -i\\varphi & & & &  \\\\ \n& \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\vspace{-0.4mm} \n& \\vspace{-0.4mm} & \\vspace{-0.4mm} & \\\\\n\\phi^{5,3}_{k,0} & \\varphi & -\\varphi & i\\varphi & -i\\varphi & \n\\varphi\\exp\\big( \\frac{\\pi i}{4} \\big) &\n\\varphi\\exp\\big( \\frac{3\\pi i}{4} \\big) &\n\\varphi\\exp\\big( \\frac{5\\pi i}{4} \\big)& \n\\varphi\\exp\\big( \\frac{7\\pi i}{4} \\big) \\\\\n\\hline\n\\end{array}\n\\]\n\\caption{Transient spectrum at the $5^{\\rm{th}}$ bsp with $j=0$. The\nconstant $\\varphi \\equiv 1\/\\alpha_{5}$.} \\end{table}\n\nNext we ask if there are independent eigenvectors\nassociated with the degenerate eigenvalues. \nUsing the same procedure used to find the right eigenvectors\ndecaying out of region $\\rm{I}$ it can be shown that in the rescaled map,\nfor $n > 2$ there is no eigenpolynomial of even degree with support in the central\ntransient. This means that the right states associated with $\\phi^{n,0}_{1,2j}$\nare Jordan vectors, for $n > 2$.  For $n = 2$, decay out of the central\ntransient is described by eigenvectors for all values of $j$. Since the right states associated\nwith \n$\\phi^{3,1}_{k,j}$, $\\phi^{4,2}_{k,j}$,\\dots,$\\phi^{n,n-2}_{k,j}$ are transformed\nversions of $| \\phi^{2,0}_{1,j} \\rangle$, these are also eigenvectors. For\n$n \\geq 3$ decay out of the central transient is described by Jordan \nvectors for even values\nof $j$. Therefore all the peripheral transients which are related by conjugacies\n(\\ref{imp1}) and (\\ref{imp2}) to these central transients are also Jordan\nvectors. Hence associated with the transient spectrum are Jordan blocks whose sizes correspond to the\nalgebraic multiplicity of the eigenvalues. Thus from Table 2 we see that at the $5^{\\rm{th}}$ bsp\nthere is a $4 \\times 4$ Jordan block associated with\n$\\phi^{5,0}_{1,2j}$, a $3 \\times 3$ Jordan block associated with $\\phi^{5,1}_{2,2j}$ and so on. At\nthe $n^{\\rm{th}}$ bsp the largest Jordan block in the transient spectrum is\nassociated with $\\phi^{n,0}_{1,2j}$ and is of size $n-1 \\times n-1$. Since \n$\\phi^{n,0}_{1,0}$ is the largest eigenvalue with modulus less than 1 in the\nspectrum of $U_{\\rm R_n}$, it corresponds to the slowest decay mode. Since there is a Jordan block\nassociated with $\\phi^{n,0}_{1,0}$ this decay is modified exponential (polynomial factors in $t$\ntimes exponential decay).\n\nIn general (for even $j$) we have Jordan vectors for $l\\leq n-3$ and eigenvectors for $l=n-2$ as\n\\begin{eqnarray} \\label{t5}\nU_{{\\rm R}_n}|\\phi^{n,l}_{k,2j} \\rangle & = & \\phi^{n,l}_{k,2j}\n|\\phi^{n,l}_{k,2j} \\rangle + |\\phi^{n,l+1}_{k,2j}\n\\rangle \\;\\;\\;\\;\\;\\;\\;\\; n \\geq 3, \\; l \\leq n-3 \\nonumber \\\\ \\noalign{\\vskip4pt}\nU_{{\\rm R}_n}|\\phi^{n,n-2}_{k,2j} \\rangle & = & \\phi^{n,n-2}_{k,2j}\n|\\phi^{n,n-2}_{k,2j} \\rangle \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; n \\geq 2. \n\\end{eqnarray}\nBy inspection we have\nalready obtained the form of the Jordan state in the central region in\n(\\ref{trans1}).  We have\n\\begin{equation} \\label{t6} | \\phi^{n,0}_{1,2j} \\rangle =\na_{n,2j}\\left(x-x^*_n\\right)^{2j}\\chi_{n,{\\rm C}} + f_{n,2j}(x)   \\end{equation}\nwhere $f_{n,2j}(x)$ is piecewise polynomial with degree $2j$ over each of the\n$S_{n}$ intervals (excluding the central interval\n$X_{n, {\\rm C}}$) at the $n^{\\rm{th}}$ bsp.  Since a Jordan vector multiplied by a\nscalar doesn't remain a Jordan vector (with respect to the same eigenvector in the block)\nwe do not have the freedom to choose\nthe $a_{n,2j}$'s to be $1$ as we did in (\\ref{haha}).   Using (\\ref{trans1})\nand (\\ref{t5}) we know that if (\\ref{t6}) is to be a Jordan vector the\narbitrary functions $f_{n,2j}(x)$ must satisfy \n\\begin{equation} \\label{t1} U_{{\\rm R}_n}\nf_{n,2j}(x) = \\phi^{n,0}_{1,2j}\\left[ f_{n,2j}(x) -\na_{n,2j}\\left(x-x^{*}_{n}\\right)^{2j}\\chi_{n, b}\n\\right] + | \\phi^{n,1}_{1,2j} \\rangle\n\\end{equation}\nA formal approach to determine the $a_{n, 2j}$'s and $f_{n, 2j}(x)$ is \ndescribed in Appendix D.\n\nTo find the eigenstates corresponding to the peripheral transients\nwe transform the central transient eigenstates at the $2^{\\rm{nd}}$ bsp\nto all the higher band-splitting points. We define \n\\begin{equation}\n\\check{\\rm B}^{n,n-2}_{k,2j,i} = \\left( \\phi^{n,n-2}_{k,2j} \\right)^{i}\\widehat{\\rm B}_{i},\n\\end{equation}\nand $\\check{\\Pi}_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_{3}}$ is an ordered product of \n$n-2$ operators $\\widehat{\\rm A}_{i}$ and $\\check{\\rm B}^{n,n-2}_{k,2j,i}$ ($i\n= 3,4,\\dots,n$). If $\\sigma_i = 0$ the $i^{\\rm th}$ place in the\nproduct is taken by  $\\widehat{\\rm A}_{i}$ and if $\\sigma_i = 1$ the $i^{\\rm\nth}$ place in the  product is taken by  $\\check{\\rm B}^{n,n-2}_{k,2j,i}$.\nFollowing the same procedure  used to obtain (\\ref{five}) we find that the transient\neigenvectors, $| \\phi^{n,n-2}_{k,2j}\\rangle$, $(n\\geq 3)$, are given by\n\\begin{equation} \\label{transeig}\n| \\phi^{n,n-2}_{k,2j} \\rangle = \\sum_{\\{ \\sigma\\}}\n\\check{\\Pi}_{\\sigma_n \\sigma_{n-1}\\dots\\sigma_3}\n| \\phi^{2,0}_{1,j} \\rangle\n\\end{equation}\n\n\nTo find the Jordan states corresponding to the peripheral transients, \n$| \\phi^{n,l}_{k,2j} \\rangle$ for $1 \\leq l \\leq n-3$, \nwe use an approach similar to that used to find the\nJordan vectors  describing decay out of the central transient, \n$| \\phi^{n,0}_{1,2j} \\rangle $. To clarify the notation we \nnote that $| \\phi^{n,1}_{k,2j} \\rangle $ does not\nhave support in the central transient band, but has \nsupport over all the other transient and attracting bands. Similarly\n$| \\phi^{n,2}_{k,2j} \\rangle $ has support on all bands except the\ncentral transient band and the two transient bands that are related by a single\ntransformation to the central transient at the $(n-1)^{\\rm{th}}$ bsp. This\npattern continues and $| \\phi^{n,n-2}_{k,2j} \\rangle$ has support\non all the attracting bands and the $2^{n-2}$ transient bands that are related\nby transformations to the central transient at the $2^{\\rm{nd}}$ bsp. Following\n(\\ref{t6}) and using the fact that the peripheral transients at the\n$n^{\\rm{th}}$ bsp are transformed versions of the transients at the\n$(n-1)^{\\rm{th}}$ bsp we write\n\\begin{equation} \\label{jord10}\n| \\phi^{n,l}_{k,2j} \\rangle  = a^{n,l}_{k,2j}\\left( \n\\widehat{\\rm A}_n| \\phi^{n-1,l-1}_{\\lceil k\/2 \\rceil,2j} \\rangle +\n\\phi^{n,l}_{k,2j} \\widehat{\\rm B}_n | \\phi^{n-1,l-1}_{\\lceil k\/2 \\rceil,2j}\n\\rangle \\right) + g^{n,l}_{k,2j}(x)\n\\end{equation}\nwhere $g^{n,l}_{k,2j}(x)$ is piecewise polynomial of degree $2j$. The\npolynomial  $g^{n,l}_{k,2j}(x)$ can be obtained using the procedure similar to\nthe one described in Appendix D. We present here the\nsolution only for the simplest case,\n\\begin{equation} \\label{jord14}\n| \\phi^{n,n-3}_{k,2j} \\rangle = 2 \\, \\phi^{n,n-3}_{k,2j} \\left(\n\\widehat{\\rm A}_n| \\phi^{n-1,n-4}_{\\lceil k\/2 \\rceil,2j} \\rangle\n + \\phi^{n,n-3}_{k,2j}\n\\widehat{\\rm B}_n| \\phi^{n-1,n-4}_{\\lceil k\/2 \\rceil,2j} \\rangle\n\\right) - \\frac{1}{2 \\, \\phi^{n,n-3}_{k,2j}}\n| \\phi^{n,n-2}_{k',2j} \\rangle\n\\end{equation}\nwhere $k'=k+1$ if $k$ is odd and $k'=k-1$ if $k$ is even. The recursion\nrelations for the other Jordan vectors involve more terms, and in general\nto find all the Jordan vectors at the $n^{\\rm{th}}$ bsp one must know\nall the Jordan vectors at the $(n-1)^{\\rm{th}}$ bsp. Also at a particular\nbsp to determine $| \\phi^{n,l}_{k,2j} \\rangle $ one must know \nall the $| \\phi^{n,l'}_{k,2j} \\rangle $ for $l' < l$. So\ngenerally one proceeds in the following order\n$| \\phi^{2,0}_{1,2j} \\rangle $, $|\n\\phi^{3,1}_{k,2j}\\rangle $, $| \\phi^{3,0}_{1,2j}\\rangle $,\n$| \\phi^{4,2}_{k,2j} \\rangle $, $|\n\\phi^{4,1}_{k,2j}\\rangle \\dots $. The transient eigenvectors can be\nobtained directly from (\\ref{transeig}) without regard to this order.\n\n\\subsubsection{Transient Right states of odd degree}\n\nFor odd values of $j$ the transient spectrum at the $n^{\\rm th}$ bsp, \ngiven by equation (\\ref{eig2}), is nondegenerate. We first find the \neigenvectors with support in the central transient bands, at all the\nband-splitting points. By inspection we have already obtained the form \nof the eigenvector in the central transient in (\\ref{trans1}) so that\n\\begin{equation} \\label{oddj}\n| \\phi^{n,0}_{1,2j+1} \\rangle = \\left( x-x^{*}_{n} \\right)^{2j+1} \\chi_{n,C} \n+ f_{n,2j+1}(x),\n\\end{equation}\nwhere $f_{n,2j+1}(x)$ is a polynomial of degree $2j+1$ in each of the \n$S_n$ intervals excluding the central interval.  For this expression is to be an \neigenvector $f_{n,2j+1}(x)$  must satisfy\n\\begin{equation} \\label{oddj1}\nU_{{\\rm R}_n}\nf_{n,2j+1}(x) = \\phi^{n,0}_{1,2j+1}\\left[ f_{n,2j+1}(x) -\n\\left(x-x^{*}_{n}\\right)^{2j+1}\\chi_{n, b}\n\\right]. \n\\end{equation}\nThis equation for $f_{n,2j+1}(x)$ is similar to equation (\\ref{t1}), except\nthat it has one term less on the rhs, and may be solved using the procedure\noutlined in Appendix~D.\n\nOnce the $| \\phi^{n,0}_{1,2j+1} \\rangle$ are known the eigenvector\ncorresponding to any $| \\phi^{n,l}_{k,2j+1} \\rangle$ can be written as \n\\begin{equation}\n| \\phi^{n,l}_{k,2j+1} \\rangle = \\sum_{\\{ \\sigma \\}\n}\\check{\\Pi}_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_{n-l+1}}\n|\\phi^{n-l,0}_{1,2j+1} \\rangle,\n\\end{equation}\nwhere $\\check{\\Pi}_{\\sigma_n\\sigma_{n-1}\\dots\\sigma_{n-l+1}}$ \n is an ordered product of \n$l$ operators $\\widehat{\\rm A}_{i}$ and $\\check{\\rm B}^{n,l}_{k,2j,i}$ ($i =\nn-l+1,\\dots,n$). The  $\\check{\\rm B}^{n,l}_{k,2j,i}$ operators are defined\nhere as \n\\begin{equation}\n\\check{\\rm B}^{n,l}_{k,2j,i} \\equiv  \\left(\\phi^{n,l}_{k,2j+1}\\right)^i\n \\widehat{\\rm B}_i\n\\end{equation}\nIf $\\sigma_i = 0$ the\n$i^{\\rm th}$ place in the product is taken by \n$\\widehat{\\rm A}_{i}$ and if $\\sigma_i = 1$ the $i^{\\rm th}$ place in the \nproduct is taken by  $\\check{\\rm B}^{n,l}_{k,2j,i}$. The sum is over all\npossible strings of $0$'s and $1$'s of length $l$.\n\n\\subsubsection{Left States}\n \nThe left states  $\\langle \\phi^{n,l}_{k,j} |$ form a  bi-orthonormal set with all\nthe previously obtained right states at the $n^{\\rm{th}}$ bsp as\n\\alpheqn\n\\begin{eqnarray}\n\\langle \\phi^{n,l}_{k,j} | \\lambda^{n}_{k'j'}  \n\\rangle & = & 0 \\\\ \n\\langle \\phi^{n,l}_{k,j} | \\phi^{n,l'}_{k'j'}  \n\\rangle & = & \\delta_{ll'}\\delta_{kk'}\\delta_{jj'}.\n\\end{eqnarray}\n\\reseteqn\nAmong the right states only the states with $l=0$ have support in the central transient band.\nFrom (\\ref{t6}) we see that the associated left states are \n\\alpheqn\n\\begin{eqnarray}\n\\langle \\phi^{n,0}_{1,2j} | & = & \\frac{1}\n{a_{n,2j}}\\delta^{(2j)}\\left( x - x^{*}_{n} \\right) \\\\ \n\\langle \\phi^{n,0}_{1,2j+1} | & = & \n-\\delta^{(2j+1)}\\left( x - x^{*}_{n} \\right).\n\\end{eqnarray}\n\\reseteqn\nThe left states corresponding to the peripheral transients at \nthe $n^{\\rm{th}}$ bsp, $\\langle \\phi^{n,l}_{k,j} |$,\nare found by transforming the left states at the \n$(n-1)^{\\rm{th}}$ bsp, \n$\\langle \\phi^{n-1,l-1}_{\\lceil k\/2 \\rceil,j} |$.\nThen the entire set at the $n^{\\rm{th}}$ bsp has to be orthonormalized\nusing a Gram--Schmidt procedure.\n\n\\subsection{Back to ${\\rm T}_n(x)$}\n\nGoing back to the tent map ${\\rm{T}}_{n}(x)$, we transform\nall the right states of ${\\rm{R}}_{n}(x)$ by $U_{\\phi^{-1}_{n}}$ and the left states by\n$K_{\\phi_{n}}$. The states describing decay out of \n$[ {\\rm{T}}_{n}^{(3)}(x_{c}),1 ]$ are null states. \nThe eigenvalues describing decay out of \n$[ 0,{\\rm{T}}_{n}^{(4)}(x_{c})]$ are \n$\\phi_j^n \\equiv \\left( \\frac{1}{\\alpha_{n}}\\right)^{j+1}$ and have\nassociated polynomial eigenvectors of degree $j$.  For $j$ even this part of the spectrum overlaps\nwith the spectrum describing decay of transients of ${\\rm R}_n$. There are Jordan vectors associated\nwith this part of the spectrum; denoting them as\n$| \\phi^{n}_{2j} \\rangle$ we have\n\\alpheqn\n\\begin{eqnarray}\nU_{{\\rm T}_n}| \\phi^{n}_{2j} \\rangle = \\phi^{n}_{2j}\n| \\phi^{n}_{2j} \\rangle +| \\phi^{n,0}_{1,2j} \n\\rangle \\\\ \nU_{{\\rm T}_n}| \\phi^{n}_{2j+1}\\rangle = \\phi^{n}_{2j+1}\n| \\phi^{n}_{2j+1} \\rangle .\n\\end{eqnarray}\n\\reseteqn\nThese right states can be determined by an extension of the \nmethods used in\nSection 2.2 to determine the eigenstates describing \ndecay out of interval $\\rm{I}$ for the tent map at the first bsp.\n\n\\section{Conclusion}\n\nWe have presented the generalized spectral\ndecomoposition of the Frobenius--Perron\noperator of the tent map at the\nband-splitting points. The right eigenstates are\npiecewise-polynomial functions and the left eigenstates\nare generalized functions. The \nspectrum is discrete and gives the\ncharacteristic decay times of the map.  From the decomposition\none can calculate correlations of arbitrary polynomials (as\nwell as functions expandable in terms of the polynomial \neigenstates).  Furthermore, since the modes corresponding\nto transient decay onto the attractor have been obtained, the\nfull nonequilibrium dynamics of initial probability densities\nis accessible.\n\nThe slowest decay mode, corresponding to the\neigenvalue $\\alpha_{n}^{-1}$ at the\n$n^{\\rm th}$ bsp, describes decay onto the\nattractor. At the $n^{\\rm th}$ bsp there is an \n$n \\times n$ Jordan block associated with this\neigenvalue and therefore the decay is modified\nexponential. The asymptotic periodicity\nof the map is clearly reflected in the\nspectrum as at the $n^{\\rm th}$ bsp, all the \n$n^{\\rm th}$ roots of unity are part of the\nspectrum.  Our analytic solution of density \nevolution in this system may be useful for \ncomparision with the behavior of systems governed by the Ginzburg--Landau\nequation since a component of its dynamics~\\cite{Moon} can be reduced to the tent map.\n\n\\section*{Acknowledgements}\n\nWe thank I.~Prigogine for his support and encouragement and G.E.~Ord\\'{o}\\~{n}ez\nfor several useful discussions and his comments on the manuscript.\nWe acknowledge US\nDepartment of Energy grant no. FG03-94ER14465,  \nthe Welch Foundation\ngrant no. F-0365 and the European Communities Commision (contract no.\n27155.1\/BAS) for support of this work.\n\\section*{Appendix A: Topological conjugacy}\n\nIn this appendix we review the spectral decompositions \nof maps related by a coordinate \ntransformation~\\cite{Deanbook}. Let ${\\rm{T}}: X \\rightarrow X$ be a map defined on the\ninterval\n$X$. Transforming the interval $X$ by the one-to-one, \nonto, continuous function $\\phi : X \\rightarrow Y$ gives a new map, ${\\rm{S}}:Y\n\\rightarrow Y$.  This map is determined as\n\\begin{equation}\ny_{t+1} = \\phi(x_{t+1}) = \\phi({\\rm T}(x_t)) \\equiv {\\rm S}(y_t).\n\\end{equation}\nUsing that $\\phi$ has an inverse gives\n\\begin{equation}\n\\phi({\\rm T}(x_t)) = \\phi({\\rm T}(\\phi^{-1}(\\phi(x_t)))) \n= \\phi \\circ {\\rm T} \\circ \\phi^{-1}(y_t),\n\\end{equation}\nso that\n\\begin{equation} \\label{strel}\n{\\rm S} = \\phi \\circ {\\rm T} \\circ \\phi^{-1}.\n\\end{equation}\nThe maps ${\\rm{T}}$ and ${\\rm{S}}$ are said to be topologically \nconjugate to each other. \n\nThe Koopman operator, $K_{\\rm{S}}$,\ncorresponding to ${\\rm{S}}$ is given from (\\ref{strel}) by \n\\begin{equation} \\label{kooprel}\n K_{\\rm{S}} = K^{-1}_{\\phi}K_{\\rm{T}}K_{\\phi},\n\\end{equation}\nwhere we have used the fact that $K_{\\phi^{-1}} = K^{-1}_{\\phi}$.\nThe Frobenius--Perron operator, $U_{\\rm{S}}$, coresponding to ${\\rm{S}}$\nis the adjoint of $K_{\\rm{S}}$. Taking the adjoint of (\\ref{kooprel})\nand using $(K_{\\phi}^{-1})^{\\dagger} = (K_{\\phi}^{\\dagger})^{-1}$ gives\n\\begin{equation} \\label{frobrel}\nU_{\\rm{S}} = U_{\\phi} U_{\\rm{T}} U^{-1}_{\\phi}.\n\\end{equation}\nSince $U_{\\rm S}$ and $U_{\\rm T}$ are related by the similarity (\\ref{frobrel})\nthe spectrum of $U_{\\rm S}$ is identical to that of $U_{\\rm T}$ and eigenstates\ntransform as\n\\begin{equation} \\label{app2}\n\\left| \\lambda_{n} \\right\\rangle_{\\rm{S}} = U_{\\phi}\\left| \\lambda_{n}\n\\right\\rangle_{\\rm{T}},\n\\end{equation}\nwhere we use a Dirac-style bra-ket notation for the states.\nFrom (\\ref{kooprel}) the left states transform as \n\\begin{equation} \\label{app3}\n\\left\\langle \\lambda_{n} \\right|_{\\rm{S}} = \nK_{\\phi^{-1}} \\left\\langle \\lambda_{n} \\right|_{\\rm{T}}.\n\\end{equation}\nJordan states of the maps are also related as in (\\ref{app2}) and (\\ref{app3}) and\nboth the algebraic and geometric multiplicities of the eigenvalues are preserved \nunder conjugacy.\n\n\\section*{Appendix B: The tent map with unit height}\n\nThe Frobenius--Perron operator of the tent map with unit height is given by \n\\begin{equation}\nU_{\\rm{T_{0}}}\\rho(x) = \\frac{1}{2}\\left[ \\rho \\left( \\frac{x}{2} \\right)\n + \\rho\\left( \\frac{2-x}{2} \\right) \\right].\n\\end{equation}\nThe operator $U_{\\rm T_0}$ admits polynomial eigenstates with support on the\nwhole unit interval. Associated with eigenpolynomials of order\n$2j$ are the nonzero eigenvalues  $2^{-2j}$. There\nis an infinite degeneracy of the eigenvalue $0$ with an independent\nodd-order eigenpolynomial associated with each occurence of the eigenvalue. \nThus, the odd-order eigenpolynomials are not unique but we choose them as Euler\npolynomials so that the associated left eigendistributions take a simple form.\nThe right eigenvectors of $U_{\\rm T_0}$ are~\\cite{Gonzalo,fox}\n\\alpheqn \n\\begin{eqnarray}\n|2^{-2j}\\rangle_{{\\rm{T}}_{0}} & = & \nB_{2j}(x\/2)  \\\\\n| 0_{2j+1} \\rangle_{\\rm T_0} & = &  E_{2j+1}(x), \n\\end{eqnarray}\n\\reseteqn\nwhere $B_{j}(x)$ is the Bernoulli polynomial of order $j$ and \n$E_{j}(x)$ is the Euler polynomial of order $j$~\\cite{Absteg}.\nThe corresponding left states are\n\\alpheqn\n\\begin{eqnarray}\n\\langle {2^{-2j}}|_{\\rm{T}_{0}} & = & \n2^{2j}\\widetilde B_{2j} (x)  \\\\\n\\left\\langle 0_{2j+1} \\right|_{\\rm{T}_{0}} & = & \n\\frac{-1}{(2j+1)!}\\delta^{(2j+1)}_{-}(x-1),\n\\end{eqnarray}\n\\reseteqn\nwhere $\\tilde B_0(x) = 1$ and for $j\\geq 1$\n\\begin{equation} \n\\widetilde B_{2j} (x) \\equiv \\frac{(-1)^{2j-1}}{(2j)!}\\left[ \n\\delta^{(2j-1)}_{-}(x-1) - \\delta^{(2j-1)}_{+}(x) \\right],  \n\\end{equation}\nwhere the action of $\\delta^{(m)}_\\pm (x-c)$ on a sufficently differentiable\nfunction $f(x)$ is given by \n\\begin{equation}\n\\int_a^b dx \\, \\delta^{(m)}_{\\pm}(x-c) f(x) =\n\\lim_{\\epsilon \\rightarrow 0} (-1)^{m} f^{(m)}(c \\pm \\epsilon),\n\\end{equation}\nfor $a \\leq c \\leq b$ and $\\epsilon$ is a positive infinitesimal.\n\nThe time evolution of a density is expressed in terms of the spectral decomposition of\n$U_{\\rm T_0}$ as\n\\begin{equation}\nU_{\\rm T_0}^t \\, \\rho(x) = \\sum_{j=0}^\\infty\n\\left[ (2^{-2j})^t |2^{-2j}\\rangle \\langle 2^{-2j}| \\rho \\rangle\n+ \\delta_{t,0} | 0_{2j+1} \\rangle \\langle 0_{2j+1}| \\rho \\rangle \\right],\n\\end{equation}\nwhere the bilinear form is defined by\n\\begin{equation}\n\\langle f | g \\rangle \\equiv \\int_0^1 dx \\, f^*(x) g(x).\n\\end{equation}\n\n\\section*{Appendix C: Calculation of transient right states}\n\nTo determine the functions \n$g_{{\\rm II},j}(x)$ and $g_{{\\rm III},j}(x)$, which appear\non the rhs of (\\ref{form1}) we expand \n$g_{{\\rm II},j}(x)\\chi_{\\rm{II}} + g_{{\\rm III},j}(x)\\chi_{\\rm{III}}$ in terms of the\neigenstates given in Table 1 of $U_{\\rm T_1}$ on the attractor as \n\\begin{eqnarray} \\label{expand1}\ng_{{\\rm II},j}(x)\\chi_{\\rm{II}} + g_{{\\rm III},j}(x)\\chi_{\\rm{III}} & = &\n\\sum_{i=1}^{\\lfloor j\/2\n\\rfloor} a_{i,j}|{+2^{-i}} \\rangle_{\\Omega} + \n\\sum_{i=1}^{\\lfloor j\/2\\rfloor}\n b_{i,j}|{-2^{-i}} \\rangle_{\\Omega} \\nonumber \\\\\n & & \\mbox{} + \\sum_{i=1}^{\\lfloor\n\\frac{j-1}{2} \\rfloor} c_{i,j}| 0_{2i+1} \\rangle_{\\Omega} +\n\\sum_{i=1}^{\\lfloor\n\\frac{j-1}{2} \\rfloor} d_{i,j}| 0_{J_{2i+1}} \\rangle_{\\Omega},  \n\\end{eqnarray}\nwhere $\\lfloor x \\rfloor$ denotes the integer\npart (floor) of the real number $x$.\nThen acting with $U_{\\rm T_1}$ gives\n\\begin{eqnarray} \\label{expand2}\nU_{{\\rm{T_1}}} \\left( g_{{\\rm II},j}(x)\\chi_{\\rm{II}} + g_{{\\rm\nIII},j}(x)\\chi_{\\rm{III}}\n\\right) & = &\n\\sum_{i=1}^{\\lfloor j\/2\n\\rfloor} \\frac{a_{i,j}}{2^i}|{+2^{-i}} \\rangle_{\\Omega} - \n\\sum_{i=1}^{\\lfloor j\/2\\rfloor}\n \\frac{b_{i,j}}{2^i}|{-2^{-i}} \\rangle_{\\Omega} \\nonumber \\\\\n& & \\mbox{} + \\sum_{i=1}^{\\lfloor\n\\frac{j-1}{2} \\rfloor} d_{i,j}| 0_{2i+1} \\rangle_{\\Omega}.  \n\\end{eqnarray} \nWe substitute (\\ref{expand1}) \nand (\\ref{expand2}) into (\\ref{form1}) and act on (\\ref{form1}) by all the left states\non the attractor in succession. Using orthonormality we obtain the\nfollowing equations for the expansion coefficients:\n\\alpheqn\n\\begin{eqnarray} \\label{form2}\n\\frac{a_{i,j}}{2^i} + \\alpha_{i,j} & = & 2^{-(j+1)\/2} \\, a_{i,j} \\\\\n\\frac{b_{i,j}}{2^i} - \\beta_{i,j} & = & -2^{-(j+1)\/2} \\, b_{i,j} \\\\ \nd_{i,j} + \\gamma_{i,j} & = &  2^{-(j+1)\/2} \\, c_{i,j} \\\\\nd_{i,j} & = &  0,\n\\end{eqnarray}\n\\reseteqn \nwhere\n\\alpheqn\n\\begin{eqnarray} \\label{def}\n\\alpha_{i,j} & \\equiv & 2^{-(j+1)\/2} \n\\langle{+2^{-i}}| x^j\\chi_{\\rm{II}} \\rangle  \\\\ \n\\beta_{i,j} & \\equiv & 2^{-(j+1)\/2}\n\\langle{-2^{-i}}| x^j\\chi_{\\rm{II}} \\rangle  = \n\\alpha_{i,j}  \\\\ \n\\gamma_{i,j} & \\equiv & 2^{-(j+1)\/2}\n\\langle 0_i |  x^j\\chi_{\\rm{II}} \\rangle,\n\\end{eqnarray}\n\\reseteqn\nand we used $\\langle 0_{J_i}| x^j\\chi_{\\rm{II}} \\rangle = 0$ because \n$\\langle 0_{J_i}|$ has support only in $\\chi_{\\rm III}$.  \nExplicit evaluation of $\\langle +\\frac{1}{2^i}|\nx^j\\chi_{\\rm{II}} \\rangle$ gives\n\\begin{equation}\n\\langle +\\frac{1}{2^i}| x^j\\chi_{\\rm{II}} \\rangle  =  \n\\left\\{ \\begin{array}{lc} \\frac{\\sqrt{2}}{2(\\sqrt{2}-1)(j+1)} \n((2 - \\sqrt{2})^j -1 )\n& i=0  \\\\ \\noalign{\\vskip4pt}\n0  & 2i-1 \\geq j  \\\\ \\noalign{\\vskip4pt}\n-\\frac{j!(2 - \\sqrt{2})^{j+2i-1}}{(2i)!(j-2i+1)!}(2^{(j-2i+1)\/2} -1) & 2i-1 < j.  \n\\end{array} \\right.\n\\end{equation}\nEvaluation of $\\langle 0_i |  x^j\\chi_{\\rm{II}} \\rangle$ gives\n\\begin{equation}\n\\langle 0_i |  x^j\\chi_{\\rm{II}} \\rangle = \n\\left\\{ \\begin{array}{lc} \\frac{j!}{(2i+1)!(j-2i-1)!}(\n\\sqrt{2} -1 )^{j+2i+1} & 2i+1 \\leq j \\\\ \\noalign{\\vskip4pt}\n0 & \\mbox{otherwise} .\n\\end{array} \\right.\n\\end{equation}\nThese results are then\nused in (109) to determine the expansion coefficients for the transient\neigenstates with support in region $\\rm I$.  \n\n\n\\section*{Appendix D: Transient right states at higher bsps}\n\nWe expand the arbitrary functions $f_{n,2j}(x)$ in terms of the\ntransient and non-transient eigenvectors of $U_{{\\rm R}_n}$. The\nnon-transient eigenvectors are given in (\\ref{five}) and (\\ref{jord}). The\ntransient eigenvectors will be transformed versions of the central\neigenvectors at the previous band-splitting points. The expansion is\n\\begin{eqnarray} \\label{t2}\nf_{n,2j}(x) & = &\n\\sum_{k=1}^{2^n}\\sum_{j^{'}=1}^{j} b^{n,2j}_{k,2j^{'}}\n| \\lambda^{n}_{k,2j^{'}} \\rangle +\n\\sum_{k=1}^{2^n}\\sum_{j^{'}=1}^{j-1} c^{n,2j}_{k,j^{'}}\n| 0^{n}_{k,2j^{'}+1} \\rangle \\nonumber \\\\\n & & + \\sum_{l=1}^{n-2}\\sum_{k=1}^{2^l}\\sum_{j^{'}=1}^{j}\nd^{n,l,2j}_{k,j^{'}}\n| \\phi^{n,l}_{k,2j^{'}} \\rangle + \\sum_{l=1}^{n-2}\\sum_{k=1}^{2^l}\n\\sum_{j^{'}=1}^{j-1} e^{n,l,2j}_{k,j^{'}}\n| \\phi^{n,l}_{k,2j^{'}+1} \\rangle.\n\\end{eqnarray}\nSince $d^{n,n-2,2j}_{1,j}$ is the coefficent of the eigenvector of the\nJordan block it can be set to zero.  \nApplying $U_{{\\rm R}_n}$ to the function $f_{n,2j}(x)$ we get\n\\begin{eqnarray} \\label{t3}\n\\lefteqn{U_{{\\rm R}_n} f_{n,2j}(x)  =  \n\\sum_{k=1}^{2^n}\\sum_{j^{'}=1}^{j}b^{n,2j}_{k,j^{'}}\n\\lambda^{n}_{k,2j^{'}}| \\lambda^{n}_{k,2j^{'}}\\rangle \n+\\sum_{k=1}^{2^{n}-1}\\sum_{j^{'}=1}^{j-1}\nc^{n,2j}_{k+1,j^{'}}\n| 0^{n}_{k,2j^{'}+1} \\rangle } \\hspace{20pt} \\nonumber \\\\\n& & \\mbox{} \n  + \\sum_{l=1}^{n-2}\\sum_{k=1}^{2^l}\\sum_{j^{'}=1}^{j}\nd^{n,l,2j}_{k,j^{'}}\n\\phi^{n,l}_{k,2j^{'}}| \\phi^{n,l}_{k,2j^{'}} \\rangle + \\sum_{l=2}^{n-2}\\sum_{k=1}^{2^{l-1}}\\sum_{j^{'}=1}^{j}\nd^{n,l-1,2j}_{k,j^{'}}\n\\phi^{n,l}_{k,2j^{'}}| \\phi^{n,l}_{k,2j^{'}} \\rangle \\nonumber \\\\\n & &\\mbox{}  \n+ \\sum_{l=1}^{n-2}\\sum_{k=1}^{2^l}\\sum_{j^{'}=1}^{j}\ne^{n,l,2j}_{k,j^{'}}\n\\phi^{n,l}_{k,2j^{'}+1}| \\phi^{n,l}_{k,2j^{'}+1} \\rangle\n\\end{eqnarray} \nWe substitute (\\ref{t3}) and (\\ref{t2}) into (\\ref{t1}) and\nhit both sides of the equation with $\\langle \\lambda^{n}_{k,2j^{'}}|$,\n$\\langle 0^{n}_{k,2j^{'}+1} |$, $\\langle\n\\phi^{n,l}_{k,2j^{'}+1} |$ and $\\langle\n\\phi^{n,l}_{k,2j^{'}} |$ successively.  Letting\n\\alpheqn\n\\begin{eqnarray}\n\\alpha^{n,2j}_{k,j'} & \\equiv & \\langle \\lambda^{n}_{k,2j'} |\n\\left(x-x^*_n \\right)^2j\\chi_{b,n} \\rangle \\\\\n\\beta^{n,2j}_{k,j'} & \\equiv & \\langle 0^{n}_{k,2j'+1} |\n\\left(x-x^*_n \\right)^{2j}\\chi_{b,n} \\rangle \\\\\n\\gamma^{n,l,2j}_{k,j'} & \\equiv & \\langle \\phi^{n,l}_{k,2j'}|\n\\left(x-x^*_n \\right)^{2j}\\chi_{b,n} \\rangle \n\\end{eqnarray}\n\\reseteqn \nwe obtain the following equations for the expansion coefficents\n$a_{n,j}$, $b^{n,2j}_{k,j^{'}}$, $c^{n,2j}_{k,j^{'}}$,\n$d^{n,l,2j}_{k,j^{'}}$ and $e^{n,l,2j}_{k,j'}$\n\\begin{eqnarray} \\label{t4}\nb^{n,2j}_{k,j'}\\lambda^{n}_{k,2j'} & = & \\phi^{n,0}_{1,j}\\left(\nb^{n,2j}_{k,j'} - \\alpha^{n,2j}_{k,j'} \\right) \\nonumber \\\\\nc^{n,2j}_{k+1,j^{'}} & = & \\phi^{n,0}_{1,j}\\left(\nc^{n,2j}_{k,j'} - \\beta^{n,2j}_{k,j'} \\right) \\nonumber \\\\\na_{n,2j}\\phi^{n,0}_{1,2j}\\gamma^{n,1,2j}_{1,j} & = & 1 \\nonumber \\\\\ne^{n,l,2j}_{k,j'}\\phi^{n,l}_{k,2j'+1} & = & \\phi^{n,0}_{1,j}\\left(\ne^{n,l,2j}_{k,j'} - \\delta^{n,l,2j}_{k,j'} \\right).\n\\end{eqnarray}\nThe equations for $d^{n,l,2j}_{k,j'}$ differ depending on the values of\n$l,k$ and $j'$. For $k=1$, $j'=j$ and $l=2,3,\\dots,n-2$\n\\begin{eqnarray} \n  d^{n,l-1,2j}_{1,j} & = & a_{n,2j}\\phi^{n,0}_{1,2j}\\gamma^{n,l,2j}_{1,j} \\nonumber \\\\\n  d^{n,n-2,2j}_{1,j} & = & 0.\n\\end{eqnarray}\nWhen $j \\neq j'$, $k \\neq 1$ and $l=1$ we have\n\\begin{equation} \nd^{n,1,2j}_{k,j'}\\left(\n\\phi^{n,0}_{1,2j} - \\phi^{n,1}_{k,2j'} \\right)\n= a_{n,j}\\phi^{n,0}_{1,2j}\\gamma^{n,1,2j}_{k,j'}.  \n\\end{equation}\nWhen $j \\neq j'$, $k \\neq 1$ and $l=2,3,\\dots,n-2$ we have\n\\begin{equation} \\label{t7}\n d^{n,l,2j}_{k,j'}\\left(\n\\phi^{n,0}_{1,2j} - \\phi^{n,l}_{k,2j'} \\right) - d^{n,l-1,2j}_{k,j'} =\na_{n,2j}\\phi^{n,0}_{1,2j}\\gamma^{n,l,2j}_{k,j'}. \n\\end{equation}\n\nThe equations (\\ref{t4}) -- (\\ref{t7}) for $a_{n,2j}$, \n$b^{n,2j}_{k,j'}$, $c^{n,2j}_{k,j'}$ \n$d^{n,l,2j}_{k,j'}$ and $e^{n,l,2j}_{k,j'}$ are either uncoupled or are coupled in a simple\nmanner and can be solved explicitly to find the expansion coeffients. Plugging\nthese coefficents into (\\ref{t2}) and (\\ref{t6}) we get all the Jordan\nstates with support in the central transient, for all $n > 2$. For $n = 2$\nset all the $d^{l,j}_{2,k,j'} = 0$, $e^{n,l,2j}_{k,j'} = 0$ and $a_{2,j} = 1$ and solve for\n$b^{j}_{n,k,j'}$, $c^{j}_{n,k,j'}$ from (\\ref{t7}) to obtain the\neigenvectors with support in the central transient at the second bsp.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzljq b/data_all_eng_slimpj/shuffled/split2/finalzljq
new file mode 100644
index 0000000000000000000000000000000000000000..170652e477e0244cbbaf1b49135211f9fb967078
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzljq
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\n\nThe Space Telescope Imaging Spectrograph (STIS) (Kimble et al.\\ \\markcite{kimble97}1997;\nWoodgate et al.\\ \\markcite{woodgate98}1998; Walborn \\& Baum \\markcite{walborn98}1998) was used during the Hubble\nDeep Field -- South (HDF--S) (Williams et al.\\ \\markcite{williams99}1999) observations\nfor ultraviolet spectroscopy (Ferguson et al.\\ \\markcite{ferguson99}1999) and ultraviolet\nand optical imaging. In this paper we present the imaging data.\n\nThe Hubble Deep Field -- North (HDF--N) (Williams et al.\\ \\markcite{williams96}1996) is the\nbest studied field on the sky, with $>$1~Msec of Hubble Space\nTelescope (HST) observing time (including follow-up observations\nby Thompson et al.\\ \\markcite{thompson99}1999 and Dickinson et al.\\ \\markcite{dickinson99}1999), and countless\nobservations with ground-based telescopes (e.g., Cohen et al.\\ \\markcite{cohen96}1996;\nConnolly et al.\\ \\markcite{connolly97}1997). Results obtained to date include a measurement\nof the ultraviolet luminosity density of the universe at $z>2$\n(Madau et al.\\ \\markcite{madau96}1996), the morphological distribution of faint galaxies\n(Abraham et al.\\ \\markcite{abraham96}1996), galaxy-galaxy lensing (Hudson et al.\\ \\markcite{hudson98}1998), and\nhalo star counts (Elson, Santiago \\& Gilmore \\markcite{elson96}1996). See Ferguson \\markcite{ferguson98}(1998) and\nLivio, Fall \\& Madau \\markcite{livio98}(1998) for reviews and further references. The HDF--S\ndiffers from the HDF--N in several ways. First, the installation\nof STIS and NICMOS on HST in 1997 February has enabled parallel\nobservations with three cameras. In addition to the STIS data, the\nHDF--S dataset includes deep WFPC2 imaging (Casertano et al.\\ \\markcite{casertano99}1999),\ndeep near-infrared imaging (Fruchter et al.\\ \\markcite{fruchter99}1999), and wider-area\nflanking field observations (Lucas et al.\\ \\markcite{lucas99}1999). Second, the STIS\nobservations were centered on QSO J2233-606, at $z \\approx 2.24$,\nto obtain spectroscopy. Finally, the field was chosen in the southern\nHST continuous viewing zone in order to enable follow-up observations\nwith ground-based telescopes in the southern hemisphere.\n\nIn section 2 we describe the observations. In section 3 we describe\nthe techniques we used to reduce the CCD images. In section 4 we\ndescribe the reduction of the MAMA images. In section 5 we describe\nthe procedures used to catalog the images. In section 6 we present\nsome statistics of the data, including galaxy number counts and color\ndistributions. Our purpose in this paper is to produce a useful\nreference for detailed analysis of the STIS images. Thus for the\nmost part we refrain from model comparisons and speculation on the\nsignificance of the results. We expect the STIS images to be useful\nfor addressing a wide variety of astronomical topics, including\nthe sizes of the faintest galaxies, the ultraviolet-optical color\nevolution of galaxies, the number of faint stars and white dwarfs\nin the galactic halo, and the relation between absorption line\nsystems seen in the QSO spectrum and galaxies near to the line of\nsight. We also expect the observations to be useful for studying\nsources very close to the quasar, and perhaps for detecting the\nhost galaxy of the quasar. However, this may require a re-reduction\nof the images, as the quasar is saturated in all of the CCD exposures,\nand there are significant problems with scattered light and\nreflections.\n\n\\section{Description of the observations}\n\nThe images presented here were taken in 4 different modes, 50CCD\n(Figure~\\ref{logclr}), F28X50LP (Figure~\\ref{loglp}), NUVQTZ\n(Figure~\\ref{lognuv}), and FUVQTZ (Figure~\\ref{logfuv}). The 50CCD\nand F28X50LP modes used the Charge Coupled Device (CCD) detector.\nThe 50CCD is a clear, filterless mode, while the F28X50LP mode uses\na long-pass filter beginning at about 5500{\\AA}. The FUVQTZ and\nNUVQTZ used the Multi-Anode Microchannel Array (MAMA) detectors as\nimagers with the quartz filter. The quartz filter was selected to\nreduce the sky noise due to airglow to levels below the dark noise. The\neffective areas of the 4 modes are plotted in Figure~\\ref{filttrans},\nalong with a pseudo-$B_{430}$ bandpass constructed from the 50CCD\nand F28X50LP fluxes. The MAMA field of view is a square, $25\\arcsec$\non a side, and was dithered so that the observations include data\non a field approximately $30\\arcsec$ square. The 50CCD mode is\nfilterless imaging with a CCD. The field of view is a square\n$50\\arcsec$ on a side, and the dithering extends to a square\n$60\\arcsec$ on a side. The F28X50LP is a long-pass filter that\nvignettes the field of view of the CCD to a rectangle $28\\times\n50\\arcsec$. The observations were dithered to image the entire\nfield of view of the 50CCD observations, although the exposure time\nper point on the sky is thus approximately half the total exposure\ntime spent in this mode. The original pixel scale is\n$0.0244\\arcsec$~pix$^{-1}$ for the MAMA images, and\n$0.05071\\arcsec$~pix$^{-1}$ for the CCD images. The final combined\nimages have a scale of $0.025\\arcsec$~pix$^{-1}$ in all cases.\nTable~\\ref{obstab} describes the observations. The filterless 50CCD\nobservations correspond roughly to V+I, and reach a depth of 29.4\nAB magnitudes at $10\\sigma$ in a 0.2 square arcsecond aperture (320\ndrizzled pixels). This is the deepest exposure ever made in the\nUV-optical wavelength region.\n\n\\subsection{Selection of the Field}\n\nSelection of the field is described by Williams et al.\\ \\markcite{williams99}(1999). The QSO\nis at RA~=~$\\rm 22^h33^m37.5883^s$, Dec~=~$-60^{\\circ} 33\\arcmin\n29.128\\arcsec$ (J2000). The errors on this position are estimated\nto be less than 40 milli-arcseconds (Zacharias et al.\\ \\markcite{zacharias98}1998). The\nposition of the QSO on the 50CCD and F28X50LP images is x=1206.61,\ny=1206.32, and on the MAMA images is x=806.61, y=806.32.\n\n\\subsection{Test Data}\n\nTest observations of the field were made in 1997 October. \nThese data are not used in the present analysis. While the test\nexposures do not add significantly to the exposure time, they would\nprovide a one-year baseline for proper motion studies of the brighter\nobjects.\n\n\\subsection{Observing Plan}\n\nThe STIS observations were scheduled so that the CCD was used in the\norbits that were impacted by the South Atlantic Anomaly, and the\nMAMAs were used in the clear orbits. The observations were made in the\ncontinuous viewing zone, and therefore were all made close to the\nlimb of the Earth. The G430M spectroscopy, all of which was read-noise\nlimited, was done during the day or bright part of the orbit, while\nthe CCD imaging was all done during the night or dark part of the\norbit. The MAMA imaging, done with the quartz filter, is insensitive\nto scattered Earth light, and was therefore done during bright time. A\nmore detailed discussion of the scheduling issues is given by\nWilliams et al.\\ \\markcite{williams99}(1999). The sky levels in the 50CCD images were\napproximately twice the square of the read noise, so these data are\nmarginally sky noise limited. The MAMA images are limited by the dark\nnoise.\n\n\\subsection{Dithering and Rotation}\n\nThe images were dithered in right ascension (RA) and declination\n(Dec) in order to sample the sky at the sub-pixel level. In addition,\nvariations in rotation of about $\\pm 1$ degree were used to provide\nadditional dithering for the WFPC2 and NICMOS fields during the\nSTIS spectroscopic observations. The STIS imaging observations were\ninterspersed with the STIS spectroscopic observations; therefore,\nall of the images were dithered in rotation as well as RA and Dec.\n\n\\subsection{CR-SPLIT and pointing strategy}\n\nThe CCD exposures were split into 2 or 3 {\\sc cr-split}s that each\nhave the same RA, Dec, and rotation. This facilitates cosmic ray\nremoval, although as discussed below, this was only used in the\nfirst iteration of the data reduction. The final 50CCD image is\nthe combination of 193 exposures making up 67 {\\sc cr-split}\npointings. After standard pipeline processing, (including bias and\ndark subtraction, and flatfielding), each exposure is given a {\\sc\nflt} file extension, and the cosmic-ray rejected combinations of\neach {\\sc cr-split} is given a {\\sc crj} file extension. The final\nF28X50LP image is the combination of 66 exposures making up 23 {\\sc\ncr-split} pointings. The F28X50LP image included 12 pointings at\nthe northern part of the field, one pointing at the middle of the\nfield, and 10 pointings at the southern half of the field.\n\n\\subsection{PSF observations}\n\nIn order to allow for PSF subtraction of the QSO present in the\ncenter of the STIS 50CCD image, two SAO stars of about 10~mag were\nobserved in the filterless 50CCD mode before and after the main\nHDF-S campaign. The stars are SAO 255267, a G2 star, and SAO 255271,\nan F8 star, respectively. These targets have spectral energy\ndistributions in the STIS CCD sensitivity range similar to that of\nthe QSO. For each star, 32 different {\\sc cr-split} exposures were taken.\nThe following strategy was used: (i) four different exposure times\nbetween 0.1 s and 5 s for each {\\sc cr-split} frame, to ensure high\nsignal-to-noise in the wings while not saturating the center; (ii)\na four-position dither pattern with quarter-pixel sampling and\n{\\sc cr-split} at each pointing with each exposure time; (iii) use of\ngain=4, to insure no saturation in the A-to-D conversion. During\nthe observations for SAO255267, a failure in the guide star\nacquisition procedure caused the loss of its long-exposure (5~s)\nimages. Gain=4 has a well-documented large scale pattern noise that\nmust be removed, e.g., by Fourier filtering, before a reliable PSF\ncan be produced. These data are not discussed further in this paper,\nbut are available from the HST archive for further analysis.\n\n\\section{Reduction of the CCD Images}\n\n\\subsection{Bias, Darks, Flats and Masks}\n\nStandard processing of CCD images involves bias and dark subtraction,\nflatfielding, and masking of detector defects. The bias calibration\nfile used for the HDF-S was constructed from 285 individual exposures,\ncombined together with cosmic-ray and hot-pixel trail rejection.\n\nThe dark file was constructed from a ``superdark'' frame and a\n``delta'' dark frame. The superdark is the cosmic-ray rejected\ncombination of over 100 individual 1200~s dark exposures taken\nover the several months preceding the HDF-S campaign. The delta\ndark adds into this high S\/N dark frame the pixels that are more\nthan $5\\sigma$ from the mean in the superdark-subtracted combination\nof 14 dark exposures taken during the HDF-S campaign. Calibration\nof the images with this dark frame removes most of the hot pixels\nbut still leaves several hundred in each image.\n\nAn image mask was constructed to remove the remaining hot pixels\nand detector features. The individual cosmic-ray rejected HDF-S\n50CCD exposures were averaged together without registration. The\nremaining hot pixels were identified with the IRAF\\footnote[12]{IRAF\nis distributed by the National Optical Astronomy Observatories,\nwhich are operated by the Association of Universities for Research\nin Astronomy, Inc., under cooperative agreement with the National\nScience Foundation.} {\\sc cosmicrays} task. These pixels were\nincluded in a mask that was used to reject pixels during the\n{\\sc drizzle} phase. Pixels that were more than $5\\sigma$ below the mean\nsky background were also masked, as were the 30 worst hot pixel\ntrails, and the unilluminated portions of the detector around the\nedges. Hot pixel trails run along columns and are caused by high\ndark current in a single pixel along the column.\n\nFlatfielding was carried out by the IRAF\/STSDAS {\\sc calstis}\npipeline using two reference files. The first, the {\\sc pflat}\ncorrects for small-scale pixel-to-pixel sensitivity variations,\nbut is smooth on large scales. This file was created from ground-test\ndata but comparisons to a preliminary version of the on-orbit flat\nrevealed only a few places where the difference was more than 1\\%.\nThe CCD also shows a 5-10\\% decrease in sensitivity near the edges\ndue to vignetting. This illumination pattern was corrected by a\nlow-order fit to a sky flat constructed from the flanking field\nobservations.\n\n\\subsection{Shifts and rotations}\n\nAfter pipeline processing, the CCD images were reduced using the\nIRAF\/STSDAS package {\\sc dither}, and test versions called {\\sc\nxdither}, and {\\sc xditherii}. These packages include the {\\sc\ndrizzle} software (Fruchter \\& Hook \\markcite{fruchterhook98}1998; Fruchter et al.\\ \\markcite{fruchteretal98}1998;\nFruchter \\markcite{fruchter98}1998). We used {\\sc drizzle} version 1.2, dated 1998\nFebruary. The test versions differ from the previously released\nversion primarily in their ability to remove cosmic rays from each\nindividual exposure, and include tasks that have not yet been\nreleased.\n\nThe {\\sc xditherii} package uses an iterative process to reject cosmic\nrays and determine the x and y sub-pixel shifts, which we summarize\nhere. The standard pipeline rejects cosmic rays using each {\\sc\ncr-split} of 2 or 3 images. The resulting {\\sc crj} files are used\nas the first iteration, we determine the x and y shifts, and the\nfiles are median combined. The resulting preliminary combination\nis then shifted back into the frame of each of the original exposures\n({\\sc flt} files), and a new cosmic ray mask is made. By comparing\neach exposure to a high signal-to-noise combination of all of the\ndata, we are less likely to leave cosmic ray residuals. The x and\ny shifts are determined at each iteration as well.\n\nThe rotations used in combining the data were determined from the\n{\\sc roll\\_avg} parameter in the jitter files, using the program\n{\\sc bearing}. We did not seek to improve on these rotations via\ncross-correlation or any other method. We did use cross-correlation\nto determine the x and y shifts.\n\nDetermination of the sub-pixel x and y shifts was done with an\niterative procedure. The first iteration was obtained by determining\nthe centroid of the bright point source just west of the QSO, using\nthe pipeline cosmic-ray rejected {\\sc crj} files. We could not use\ncross-correlation in this first iteration, because the very bright\nstar on the southern edge of the field was present on images taken\nat some, but not all, dither positions, which corrupted the\ncross-correlation. The source we used for centroiding was clearly\nvisible on all of the 50CCD and F28X50LP frames.\n\nUsing these shifts (which were accurate to better than 1 pixel),\nwe created a preliminary combined image. After pipeline processing\nand cosmic ray rejection, the {\\sc drizzle} program was used to\nshift and rotate each {sc crj} file onto individual outputs, without\ncombining them. We then used the task {\\sc imcombine} to create a\nmedian combination of the files. This preliminary image was then\nshifted and rotated back into the frame of each individual exposure\nusing the {\\sc xdither} task, {\\sc blot}, ready for the next iteration\nof the cosmic-ray rejection procedure. \n\n\\subsection{Cosmic ray rejection}\n\nIn this iteration, we discarded the {\\sc crj} files, and went back\nto the {\\sc flt} files, in which each exposure had undergone bias\nand dark subtraction and flatfielding, but not cosmic-ray rejection.\nEach exposure was compared to the blotted image, and a cosmic-ray\nmask for that exposure was created from all of the pixels that\ndiffered (positively or negatively) by more than a given threshold\nfrom the blotted image. In the version 1.0 released 50CCD image,\nthis threshold was set to be $5\\sigma$. However, we believe that\na small error in the sky level determination, introduced by the\namplifier ringing correction discussed below, meant that our \nrejection was approximately at the $3\\sigma$ level.\nThe cosmic ray masks were multiplied by the hot pixel masks discussed\nabove, and resulted in about 8\\% of the pixels being masked as\neither cosmic rays or hot pixels. This is, perhaps, overly\nconservative. A less conservative cut (after correcting the error\nin the sky value) would result in slightly higher exposure time\nper pixel, and thus an improvement of 1-2\\% in the signal to noise\nratio. The cosmic ray mask was combined with the hot pixel and\ncosmetic defect mask.\n\nThis problem with the sky value was corrected in the F28X50LP image,\nand a $3\\sigma$ level was used in the cosmic ray rejection.\n\n\\subsection{Amplifier ringing correction}\n\nHorizontal features due to amplifier ringing, varying in pattern\nfrom image to image, were present in most of the STIS CCD frames.\nWhen a pixel saw a highly saturated signal, the bias level was\ndepressed in the readout for the next few rows. The very high\nsignals causing this ringing came from hot pixels and from the\nsaturated QSO. The signal-to-noise ratio in the overscan region of\nthe detector was not sufficient to remove these features well. We\nremoved them with a procedure that subtracted on a row-by-row basis,\nfrom each individual image, the weighted average of the background\nas derived from the innermost 800 columns after masking and rejecting\n``contaminated'' pixels. The masks included all visible sources,\nhot pixels, and cosmic-ray hits. The source mask was determined\nfrom the initial registered median-combined image, shifted back to\nthe reference frame of each of the individual images. For the\nunmasked pixels in each row, the 50 highest and lowest were rejected\nand the mean of the remaining pixels was subtracted from the each\npixel in that row.\n\nHeavily smoothing the images reveals very slight horizontal residuals\nthat were not removed by the present choice of parameters in this\nprocess.\n\n\\subsection{Drizzling it all together}\n\nThe final image combination was done by drizzling the amplifier-ringing\ncorrected pipeline products together onto a single output image.\nThe exposures were weighted by the square of the exposure time,\ndivided by the variance, which is (sky+rn$^2$+dark). The rotations\nwere corrected so that North is in the +y direction, and the scale\nused was 0.492999 original CCD pixels per output pixel so that the\nfinal pixel scale is exactly 0.025 arcsec\/pixel. For the 50CCD data\nwe used a {\\sc pixfrac}=0.1, which is approximately equivalent to\ninterleaving, where each input pixel falls on a single output pixel.\nFor the F28X50LP data we used {\\sc pixfrac}=0.6, as a smaller {\\sc\npixfrac} left visible holes in the final image. See Fruchter \\& Hook \\markcite{fruchterhook98}(1998)\nfor a discussion of the meaning of the {\\sc drizzle} parameters. The\npoint spread functions of bright, non-saturated point sources are\nshown in Figure~\\ref{psf}. The sources selected are the point source\njust to the west of the quasar in the 50CCD and F28X50LP images,\nand the QSO in the MAMA images.\n\nThe final image is given in counts per second, which can be converted\nto magnitudes on the {\\sc stmag} system using the photometric\nzeropoints given by the {\\sc photflam} parameter supplied in the\nimage headers. We used the pipeline photometric zeropoints for the\n50CCD  and MAMA images, but revised the F28X50LP zeropoint by 0.1\nmagnitude based on a comparison of STIS photometry of the HST\ncalibration field in $\\omega$ Centauri with the ground-based\nphotometry of Walker \\markcite{walker94}(1994). The zeropoints in the AB magnitude\nsystem which we used are 26.386, 25.291, 23.887, and 21.539, for\nthe 50CCD, F28X50LP, NUVQTZ and FUVQTZ respectively. We also supply\nthe weight image, which is the sum of the weights falling on each\npixel. For the F28X50LP image, we supply an exposure-time image,\nwhich is the total exposure time contributing to each pixel. We\nhave multiplied this image by the area of the output pixels. The\nworld coordinate system in the headers was corrected so that North\nis exactly in the +y direction, and the pixel scale is exactly\n0.025 arcsec\/pixel.\n\n\\subsection{Window reflection}\n\nA window in the STIS CCD reflects slightly out-of-focus light from\nbright sources to the +x, $-$y direction (SW on the HDF-S images).\nThe QSO is saturated in every 50CCD and F28X50LP exposure. The\nwindow reflection of the QSO is clearly visible in the F28X50LP\nimage, but has been partially removed from the 50CCD image by the\ncosmic-ray rejection procedure. We wish to emphasize that it has\nonly been partially removed, and there are remaining residuals.\nThese residuals should not be mistaken for galaxies near the QSO,\nnor should they be mistaken for the host galaxy of the QSO. There\nis additional reflected light from the QSO (and from the bright\nstar at the southern edge) evident in the images. We believe that\nthe version 1.0 released images are not appropriate for searching\nfor objects very close to or underlying the QSO, and that such a\nsearch would require re-processing the raw data with particular\nattention paid to the window reflection, other reflected light,\nand to the PSF of the QSO. The diffraction spikes of the QSO are\nsmeared in the final images by the rotation of the individual\nexposures.\n\n\\section{Reduction of the MAMA Images}\n\nThe near-UV and far-UV images are respectively the weighted averages\nof 12 and 25 registered frames, with total exposure times of 22616~s\nand 52124~s. The MAMAs do not suffer from read noise or cosmic\nrays, and the quasar is not saturated in any of the UV data. However,\nthe MAMAs do have calibration issues that must be addressed.\n\n\\subsection{Flats, Dark Counts, and Geometric Correction}\n\nPrior to combination, all frames were processed with CALSTIS,\nincluding updated high-resolution pixel-to-pixel flat field files\nfor both UV detectors. Geometric correction and rescaling were\napplied in the final combinations via the {\\sc drizzle} program. The\nquartz filter changes the far-UV plate scale relative to that in\nthe far-UV clear mode, and so the relative scale between MAMA\nimaging modes was determined from calibration images of the globular\ncluster NGC~6681.\n\nDark subtraction for the near-UV image was done by subtracting a\nscaled and flat-fielded dark image from each near-UV frame. The\nscale for the dark image was determined by inspection of the\nright-hand corners of the near-UV image, because these portions of\nthe detector are occulted by the aperture mask and thus only register\ndark counts. For the far-UV images, {\\sc calstis} removes a nearly flat\ndark frame, but the upper left-hand quadrant of STIS far-UV frames\ncontains a residual glow in the dark current after nominal calibration.\nThis glow varies from frame to frame and also appears to change\nshape slightly with time. To remove the residual dark current, the\n16 far-UV frames with the highest count rates in the glow region\nwere co-added without object registration but with individual object\nmasks for the only two obvious objects in the far-UV frames (the\nquasar and bright spiral NNE of the quasar). We then fit the result\nwith a cubic spline to produce a glow profile. This profile was\nthen scaled to the residual glow in each processed frame and\nsubtracted prior to the final drizzle. Even during observations\nwith a strong dark glow, where the dark count rate is an order of\nmagnitude higher than normal, it is still very low, reaching rates\nno higher than $6\\times 10^{-5}$cts~sec$^{-1}$~pix$^{-1}$. The glow\nthus appears as a higher concentration of ones in a sea of zeros,\nand the subtraction of a smooth glow profile from such quantized\ndata over-subtracts from the zeros and under-subtracts from the\nones. These effects are visible in the corrected data, even when\nsmoothed out considerably in the final drizzled far-UV image. A\nlow-resolution flat-field correction was applied to the far-UV\nframes after subtraction of the residual dark glow. The near-UV\nframes require no low-resolution flat field correction.\n\n\\subsection{Shifts and Rotations}\n\nCurrently, geometrically corrected NUVQTZ and FUVQTZ frames do not\nhave the same plate scale.  Although geometric correction, rotation,\nand rescaling is applied during the final summation of individual\ncalibrated frames, we first produced a set of calibrated frames that\nincluded these corrections, in order to accurately determine the\nrelative shifts between them; this information was then used in\nconjunction with these corrections in the final drizzle.  All near-UV\nand far-UV frames were geometrically corrected, rescaled to\n$0.025\\arcsec~pix^{-1}$, and rotated to align North with the +y image\naxis. The roll angle specified in the jitter files was used to\ndetermine the relative roll between frames, and the mean difference\nbetween the planned roll and the jitter roll determined the absolute\nrotation. It is difficult to determine accurate roll angles from the\nimages themselves, because of the scarcity of objects in the MAMA\nimages. All near-UV and far-UV frames were then cross-correlated\nagainst one of the far-UV frames to provide shifts in the output\ncoordinate system. Note that centroiding on the quasar in all far-UV\nand near-UV frames yields the same shifts as cross-correlation, within\n0.1 pixel.\n\n\\subsection{Drizzling}\n\nThe calibrated frames were drizzled to a $1600 \\times 1600$ pixel\nimage, including the above corrections, rescaling, rotations, and\nshifts. We updated the world coordinate system in the image headers\nto exactly reflect the plate scale, alignment, and the astrometry\nof the quasar.\n\nFor both the far-UV and near-UV frames, individual pixels in each\nframe were weighted by the ratio of the exposure time squared to\nthe dark count variance; this weights the exposures by (S\/N)$^2$\nfor sources that are fainter than the background. Although the\nvariations in the far-UV dark profile are smooth, the near-UV dark\nprofile is an actual sum of dark frames, and so we smoothed the\nnear-UV dark profile to determine the weights. With this weighting\nalgorithm, pixels in the upper left-hand quadrant of a given far-UV\nimage contribute less when the dark glow is high, and contribute\nmore when it is low. The statistical errors (cts~s$^{-1}$) in the\nfinal drizzled image, for objects below the background (e.g.,\nobjects other than the quasar), are given by the square root of\nthe final drizzled weights file.\n\nThe drizzle ``dropsize'' ({\\sc pixfrac}) was 0.6, thus improving the\nresolution over a {\\sc pixfrac} of 1.0 (which would be equivalent to\nsimple shift-and-add). The $1600 \\times 1600$ pixel format contains\nall dither positions, and pixels outside of the dither pattern\nare at a count rate of zero. The pixel mask for each near-UV input\nframe included the occulted corners of the detector, a small number\nof hot pixels, and pixels with relatively low response (those with\nvalues $\\le$ 0.75 in the high-resolution flat field). The pixel\nmask for each far-UV frame included hot pixels and all pixels\nflagged in the data quality file for that frame. When every input\npixel drizzled onto a given output pixel was masked, that\npixel was set to zero.\n\n\\subsection{Window Reflection}\n\nAs with the CCD, a window reflection of the QSO\nappears in the near-UV image. This reflection appears $\\approx 0.2\\arcsec$\neast of the QSO itself, and should not be considered an astronomical object.\n \n\\section{Cataloging}\n\n\\subsection{Cataloging the Optical Images}\n\nThe catalog was created using the {\\sc SExtractor} package\n(Bertin \\& Arnouts \\markcite{bertin96}1996), revision of 1998 November 19, with some minor\nmodifications that were done for this application. We used two\nseparate runs of {\\sc SExtractor}, and manually merged the resulting\noutput catalogs. The first run used a set of parameters selected\nto optimize the detection of faint sources while not splitting what\nappeared to the eye to be substructure in a single object. We varied\nthe parameters {\\sc detect\\_thresh}, {\\sc deblend\\_mincont}, {\\sc\nback\\_size}, and {\\sc back\\_filtersize}. We decided to use a\ndetection threshold corresponding to an isophote of $0.65\\sigma$.\nSources were required a minimum area of 16 connected pixels above\nthis threshold. Deblending was done when the flux in the fainter\nobject was a minimum of 0.03 times the flux in the brighter object.\nThe background map was constructed on a grid of 60 pixels, and\nsubsequently filtered with a $3\\times3$ median filter. Prior to\ncataloging, the image was convolved with a Gaussian kernel with\nfull width half maximum of 3.4 pixels. As discussed in\nFruchter \\& Hook \\markcite{fruchterhook98}(1998), the effects of drizzling on the photometry\nis no more than 2\\%, and in our well-sampled 50CCD field, the\neffects should be much less than this. This effect is smaller than\nother uncertainties in the photometry of extended objects.\n\nThe second run of {\\sc SExtractor} was optimized to detect objects\nthat lay near the QSO and the bright star at the southern edge of\nthe image. These objects tend to be blended in with the point source\nat the lower detection threshold. Although our catalog might include\ngalaxies that are associated with absorption lines in the quasar\nspectrum, we did not attempt to subtract the quasar light from the\nimage, and so the catalog does not include objects within $3\\arcsec$\nof the quasar. The parameters used for the second run were the same\nas for the first run, with the exception of the {\\sc detect\\_thresh}\nparameter, which was set to $3.25\\sigma$. This parameter not only\nsets the minimum flux level for detection, but also is the isophote\nused to determine the extent of the object. Several objects fall\nbetween the $0.65\\sigma$ isophote and the $3.25\\sigma$ isophote of\nthe quasar. These are not deblended on the first {\\sc SExtractor}\nrun, because their fluxes are below 0.03 of the quasar flux, but\nare detected (without the need for deblending) on the second run.\nObjects near the quasar detected in the second run were added to\nthe catalog generated by the first run, and flagged accordingly.\nObjects from the second run that were not confused with the quasar\nor the bright star were not included. The isophotal photometry of\nobjects from the second run will not be consistent with the photometry\nof objects from the first run, because a different isophote was\nused. Eight objects were added to the catalog in this way.\n\nIn addition, 26 objects from the first {\\sc SExtractor} run \nwere clearly spurious due to the diffraction spikes of the QSO and \nthe bright star. These were manually deleted from the catalog. \n\nPhotometry of the F28X50LP image was done with {\\sc SExtractor}\nrun in two-image mode, in which the objects were detected and\nidentified on the 50CCD image, but the photometry was done in the\nother band. Isophotes and elliptical apertures are thus determined\nby the extent of the objects on the 50CCD images. Objects detected\nin the F28X50LP image but not on the 50CCD image are impossible,\nsince it has a lower throughput and shorter exposure time.\n\n\n\\subsection{Cataloging the Ultraviolet Images}\n\nFluxes in the UV were calculated outside of {\\sc SExtractor} because\nit had some problems handling quantized low-signal data. To determine\nthe gross flux, we summed the countrate within the area for each\nobject appearing in the {\\sc SExtractor} 50CCD segmentation map.\nWe then created an object mask by ``growing'' each object in the\nsegmentation map, using the IDL routine {\\sc dilate}, until it\nsubtended an area three times its original size. The resulting mask\nexcludes faint emission outside of the {\\sc SExtractor} isophotes\nfor all known objects in the field. The sky was calculated from\nthose exposed pixels within a $151 \\times 151$ pixel box centered\non each object, excluding pixels from the mask. The mean countrate\nper pixel in this sky region was used to determine the background\nfor each object (the median is not a useful quantity when dealing\nwith very low quantized signals), and thus the net flux. Statistical\nerrors per pixel for objects at or below the background are determined\nfrom the {\\sc drizzle} weight image raised to the $-1\/2$ power.\nThe statistical errors for the gross flux and sky flux were calculated\nusing this pixel map of statistical errors, and thus underestimate\nthe errors for bright objects such as the quasar.\n\nSome objects that are fully-exposed in the CCD image do not fall\nentirely within the exposed area of the MAMA images; for these\nobjects, we calculated the UV flux in the exposed area only, without\ncorrecting for the incomplete exposure, and flagged such objects\naccordingly. Objects were also flagged if the sky-box described\nabove did not contain at least 100 pixels (e.g., the quasar). For\nthese objects, we calculated a global sky value from a larger $685\n\\times 670$ pixel box, roughly centered in each MAMA image, that\nonly includes areas fully exposed in the dither pattern, and excludes\npixels in the object mask. When the net flux incorporates this\nglobal sky value, they have been flagged accordingly. We do not\nexpect or see any evidence for objects in the ultraviolet images\nthat do not appear on the 50CCD image.\n\n\\subsection{The Catalog}\n\nThe catalog is presented in Table~\\ref{cattab}, which contains a\nsubset of the photometry. The full catalogs are available on the World\nWide Web. For each object we report the following parameters:\n\n{\\bf ID:} The {\\sc SExtractor} identification number. The objects\nin the list have been sorted by right ascension (first) and\ndeclination (second), and thus are no longer in catalog order. In\naddition, the numbers are no longer continuous, as some of the object\nidentifications from the first {\\sc SExtractor} run have been\nremoved. Objects from the second {\\sc SExtractor} run have had\n10000 added to their identification numbers. These identification\nnumbers provide a cross-reference to the segmentation maps.\n\n{\\bf HDFS\\_J22r$-$60d:} The minutes and seconds of right ascension\nand declination, from which can be constructed the catalog name of\neach object. To these must be added 22 hours (RA) and $-60$ degrees\n(Dec). The first object in the catalog is HDFS\\_J223333.69$-$603346.0,\nat RA 22$^h$ 33$^m$ 33.69$^s$, Dec 60$\\deg$ 33$\\arcmin$\n46.0$\\arcsec$, epoch J2000.\n\n{\\bf x, y:} The x and y pixel positions of the object on the 50CCD and\nF28X50LP images. To get the x and y pixel positions on the MAMA\nimages, subtract 400 from each.\n\n{\\bf $m_i$, $m_a$:} The isophotal ($m_i$) and ``mag\\_auto'' ($m_a$)\n50CCD magnitudes. The magnitudes are given in the AB system\n(Oke \\markcite{oke71}1971), where $m = -2.5 log f_{\\nu} - 48.60$. The isophotal\nmagnitude is determined from the sum of the counts within the\ndetection isophote, set to be 0.65$\\sigma$. The ``mag\\_auto'' is\nan elliptical Kron \\markcite{kron80}(1980) magnitude, determined from the sum of\nthe counts in an elliptical aperture. The semi-major axis of \nthis aperture is defined by 2.5 times the first\nmoments of the flux distribution within an ellipse roughly twice the\nisophotal radius. However if the aperture defined this way \nwould have a semi-major axis smaller than than 3.5 pixels, a\n3.5 pixel value is used.\n\n{\\bf clr-lp:} Isophotal color, 50CCD$-$F28X50LP, in the AB magnitude\nsystem, as determined in the 50CCD isophote. {\\sc SExtractor} was\nrun in two-image mode to determine the photometry in the F28X50LP\nimage, using the 50CCD image as the detection image. When the\nmeasured F28X50LP flux is less than $2\\sigma$, we determine an\nupper limit to the color using the flux plus $2\\sigma$ when the\nmeasured flux is positive, and $2\\sigma$ when the measured flux is\nnegative. We did not clip the 50CCD photometry.\n\n{\\bf nuv-clr, fuv-clr:} Isophotal colors, NUVQTZ-50CCD and\nFUVQTZ-50CCD, in the AB magnitude system. Photometry in the MAMA\nimages are discussed above. Photometry of objects falling partially\noutside the MAMA image are flagged and should not be considered\nreliable. When the measured flux is less than $2\\sigma$, we give\nlower limits to the color as discussed above.\n\n{\\bf $r_h$:} The half-light radius of the object in the 50CCD image,\ngiven in milli-arcseconds. The half-light radius was determined by\n{\\sc SExtractor} to be the radius at which a circular aperture\ncontains half of the flux in the ``mag\\_auto'' elliptical aperture.\n\n{\\bf s\/g:} A star-galaxy classification parameter determined by a\nneural network within {\\sc SExtractor}, and based upon the morphology\nof the object in the 50CCD images (see Bertin \\& Arnouts \\markcite{bertin96}1996 for a detailed\ndescription of the neural network). Classifications near 1.0 are\nmore like a point source, while classifications near 0.0 are more\nextended.\n\n{\\bf flags:} Flags are explained in the table notes, and include both\nthe flags returned by {\\sc SExtractor}, and additional flags we\nadded while constructing the catalog.\n\n\\section{Statistics}\n\nIn this section we present several statistics of the data compiled\nfrom the catalog.\n\n\\subsection{Source Counts}\n\nThe source counts in the 50CCD image are given in Table~\\ref{nctable},\nand plotted as a function of AB magnitude in Figure~\\ref{numcts},\nwhere they are compared with the galaxy counts from the HDF-N WFPC2\nobservations, as compiled by Williams et al.\\ \\markcite{williams96}(1996). The counts are\ncompiled directly from the catalog, although all flagged regions\nhave been excluded, so that the counts do not include objects near\nthe edge of the image, or near the quasar. We plot only the Poissonian\nerrors, although there might be an additional component due to\nlarge-scale structure. We plot all sources, including both galaxies\nand stars, although we do not expect stars to contribute substantially\nto the source counts. No corrections for detection completeness\nhave been made, and the counts continue to rise until fainter than\n30~mag. The turnover fainter than this is due to incompleteness;\nthe counts do not turn over for astrophysical or cosmological\nreasons. \n\n\\subsection{Colors and Dropouts}\n\nThe 50CCD-F28X50LP colors of objects in the STIS images are plotted\nas points in Figure~\\ref{lpcolor}. Flagged objects have been removed\nfrom the sample. For comparison, we plot K--corrected (no-evolution)\ncolors of the template galaxies in the Kinney et al.\\ \\markcite{kinney96}(1996) sample\nas a function of redshift on the left of the figure. The LP filter is\nable to distinguish blue galaxies at $z<2.5$, but becomes\ndominated by the noise for blue galaxies fainter than 28~mag, and\nloses color resolution at $z>3$, where the Ly$\\alpha$ forest\ndominates the color in these bandpasses.\n\nBecause the F28X50LP bandpass is entirely contained within the\n50CCD bandpass, it is possible, by subtracting an appropriately\nscaled version of the measured F28X50LP flux from the 50CCD flux,\nto construct a pseudo-$B_{430}$ measurement (see Figure~\\ref{filttrans}).\nThis pseudo-$B_{430}$ is combined with the NUVQTZ and the F28X50LP\nmeasurements in a color-color diagram in Figure~\\ref{nuvdrop}. NUV\ndrop-outs, indicated on this figure by the dashed line, are those\nobjects with blue colors in the visible, but red colors in the UV,\nindicative of galaxies at $z>\\sim 1.5$. These galaxies show blue\ncolors characteristic of rapid star formation, while the red NUV\nto optical color is due to the Lyman break and absorption by the\nLy$\\alpha$ forest. The selection criteria were determined using\nthe models of Madau et al.\\ \\markcite{madau96}(1996). In an inset to Figure~\\ref{nuvdrop},\nwe plot the efficiency of these criteria for selecting galaxies of\nhigh redshift. The solid line is the fraction of all of the models\nthat meet these criteria, while the dotted line is the fraction of\nthose models with ages $<10^8$ years and foreground-screen extinction\nless than $A_B = 2$. These criteria are very efficient at finding\nyoung, star-forming galaxies at $1.5 < z < 3.5$. We have removed\npoint sources from this figure, including the bright object just\nwest of the QSO, which is extremely red and is likely to be an M\nstar.\n\nIn Figure~\\ref{fuvdrop} we give a FUV-NUV vs NUV-50CCD color-color\nplot showing FUV dropouts, where the Lyman break is passing through\nthe FUV bandpass at $z>0.6$. Of the 17 galaxies in the MAMA field with\nNUV magnitudes brighter than 28.4, only 3 have a clear signature of a\nLyman break at $0.6<z<1.5$. However, the upper limits are sufficiently\nweak that roughly half the sample could be at $z>0.6$.\n\n\\section{Conclusions}\n\nWe have presented the STIS imaging observations that were done as\npart of the Hubble Deep Field -- South campaign. The 50CCD image is\nthe deepest image ever made in the UV-optical wavelength region,\nand achieves a point source resolution near the diffraction limit\nof the HST. We have presented the catalog, and some statistics of\nthe data. These data will be useful for the study of the number and\nsizes of faint galaxies, the UV-optical color evolution of galaxies,\nthe number of faint stars and white dwarfs in the galactic halo, and\nthe relation between absorption line systems seen in the QSO spectrum\nand galaxies near to the line of sight. Follow-up observations of\nthe HDF-South fields by southern hemisphere ground-based telescopes,\nby HST, and by other space missions will also greatly increase our\nunderstanding of the processes of galaxy formation and evolution.\n\nThe images and catalog presented here are available on the World Wide\nWeb at: $<$http:\/\/www.stsci.edu\/ftp\/science\/hdfsouth\/hdfs.html$>$.\n\n\\bigskip\n\n\\acknowledgments\n\nWe would like to thank all of the people who contributed to making the\nHDF-South campaign a success, including those who helped to identify a\ntarget quasar in the southern CVZ, and those who helped in planning\nand scheduling the observations. JPG, TMB, and HIT wish to acknowledge\nfunding by the Space Telescope Imaging Spectrograph Investigation\nDefinition Team through the National Optical Astronomical Observatories,\nand by the Goddard Space Flight Center. CLM and CMC wish to acknowledge\nsupport by NASA through Hubble Fellowship grants awarded by STScI.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{References}}\n\\bibpunct{(}{)}{;}{a}{,}{;}\n\n\\newcommand{\\citepos}[1]{}\n\\renewcommand{\\citepos}[1]{\\citeauthor{#1}'s (\\citeyear{#1})}\n\n\\begin{document}\n\n\n\n\n\\title{Yet Another Statistical Analysis of Bob Ross Paintings}\n\n\\author{Christopher Steven Marcum, PhD \\\\ National Institutes of Health}\n\\date{\\today{}}\n\\maketitle\n\n\\abstract{\nIn this paper, we analyze a sample of clippings from paintings by the late artist Bob Ross. Previous work focused on the qualitative themes of his paintings \\citep{hickey2014sawb}; here, we expand on that line of research by considering the colorspace and luminosity values as our data. Our results demonstrate the subtle aesthetics of the average Ross painting, the common variation shared by his paintings, and the structure of the relationships between each painting in our sample. We reveal, for the first time, renderings of the average paintings and introduce ``eigenross'' components to identify and evaluate shared variance. Additionally, all data and code are embedded in this document to encourage future research, and, in the spirit of Bob Ross, to teach others how to do so.\n{\\\\{\\linebreak \\bf Keywords}: art, Bob Ross, paintings, linear subspace}\n}\n\n\\doublespace\n\n\\section{Introduction}\nPainter Bob Ross (1942--1995) was an icon of American art education. For over a decade, his television program, \\emph{The Joy of Painting}, taught and entertained millions of Americans tuning in to the half-hour show on PBS. In the course of his art career, Ross is estimated to have painted upward of $25,000$ paintings. As a master of the Alexander ``wet-on-wet'' oil painting technique, Ross's iconic ``happy'' clouds, mountains, streams, and, of course, trees were laid down on canvas in a matter of seconds. Recently, his set of paintings became the subject of a popular blog post titled ``A Statistical Analysis of the Work of Bob Ross'' by Walt Hickey on Nate Silver's pop-stat site \\href{http:\/\/fivethirtyeight.com\/features\/a-statistical-analysis-of-the-work-of-bob-ross\/}{fivethirtyeight.com}. The post ``went viral'' on social media sites and is the inspiration for the current work. \n\nAs a commendable digest, Hickey's approach to Ross's work should rightly be characterized as a statistical analysis of qualitative features, subjects, and themes of the paintings. He enumerates the frequency distribution of various aesthetic elements (trees, rocks, hills, etc) and, with great levity, calculates and describes the conditional probability that Ross paints one element given that he's already painted another  More, Hickey delved into the voluminous library of episodes of \\emph{The Joy of Painting} to determine such statistical anomalies of the presence of humans (n=2), and chimneys (n=1), in Ross's work. Hickey also employed the k-means clustering algorithm on the data represented by these features to determine unique subsets of paintings. In this paper, we take a different approach that advances this prior work in a quantitative analysis of digital representations of Ross's paintings.\n\nIn particular, we consider a different set of research questions to be addressed by formal statistical analysis. First, what does the ``average'' Bob Ross painting look like? Here, we diverge from Hickey's approach, which describes the ``typical'' Ross painting, the features of which may be quantified using conditional probabilities as he did. Instead, we specifically want to describe average tendency in the red-green-blue colorspace of digital representations of Ross's work. That is, can we render a representation of the central tendency for Ross's work by averaging over his paintings? Second, we ask what is the common variation shared across Bob Ross's paintings? The answer to this question will shed light on the commonly held belief that Ross has a relatively standardized theme. Finally, we ask to what extent are separate Bob Ross paintings correlated with one another: what is the relationship \\emph{between} Bob Ross paintings? \n\nFinally, this manuscript serves a didactic purpose: it illustrates how to conduct comparative quantitative research with completely reproducible results from image data packaged with the manuscript. To this end, this paper was prepared using the Sweave interface between Latex and R on a Linux operating system and the code generating the analysis is embedded in both the compiled pdf and the source. Additionally, an archive of the data can be found deposited online at the journal.\n\n\\section{Data}\nThe first thirty images returned from a Google image search of \\linebreak ``bob+ross+paintings'' in large format (as defined by Google) and attributed to Bob Ross were downloaded on November 1st, 2014.  The selection criteria also included that the \\emph{Ross} signature be present or, alternatively, that the painting could be verified against the catalog of known Bob Ross paintings from the \\emph{Joy of Painting} television program which is validated by comparison with the archive on \\href{http:\/\/www.tv.com\/shows\/the-joy-of-painting\/forums\/pictures-of-every-painting-15711-691600\/}{tv.com}. Each image was saved using a br\\%d.jp*g naming precedent, where br stands for bobross, \\%d is an integer from $1$ to $30$ and $*$ is either null or the letter $e$ depending on the image source, which is used by the following embedded script.\n\nNext, each image was cropped down to a square 550 by 550 pixels. This was automatically achieved by drawing the clipping window about the Cartesian center pixel (detected via gravity method) of each image using imagemagick and a Bourne-shell loop. The following snippet demonstrates the code, which was saved to a file called ConvertAllImages.sh. Thus, comparisons made between images are done on the pixel subset contained within this clipping window.\n\n\\begin{verbatim}\n#!\/bin\/sh\nlist=`ls br*jp*`\ni=1\nfor image in $list; do\nconvert $image -gravity center -crop 550X550+0+0 $i.jpg\ni=$((i+1))\ndone\n\\end{verbatim}\n\nThe resulting library of clipped images can be found in Table~\\ref{mat}. The intensity values of each image's three channels (red, green, and blue) was read on a pixel-by-pixel basis and stored as a three dimensional array (with dimensions $[550,550,3]$) using the ``jpeg'' library for \\texttt{R}. These arrays contain the data used in the subsequent analysis. The images are sampled at 100 dpi.\n\n\\section{Analysis}\n\nOur primary research question is, ``what does the average Bob Ross painting look like?'' To address this, we integrate over the respective channel indexes in the data array to obtain the mean value for each red, green, and blue channel among the 30 clippings. The resulting figure is rendered as a raster image and displayed in Figure~\\ref{res1}.  Despite considerable apparent variation in the supporting set of images, this average (while quite abstract in detail) clearly shows a preference gradient for blues and pinks at the top of the image and greens and browns at the bottom. One can also detect the faint gray outlines of the trunks and branches in Ross' ``Happy Trees'' rising from the bottom toward the top of the image, suggesting that Happy Trees have low alignment variance as we'd expect. The lower and upper 95\\% confidence range in these images only validates the consistency in the pixel-by-pixel averages; though, we note that the darker saturation of browns, grays, and blacks Ross used in his buildings is readily apparent in the lower bound image rendering.\n\nSecond, while the average is interesting, it fails to account for the variation in Ross' bucolic landscapes and cannot address the second research question: ``what is the common variation shared across Bob Ross' paintings?'' To examine this, we consider the eigenspace among the covariances across the dataset.  We derive a set of orthonormal vectors that best describe the shared variance across the distribution of the data---we'll call these vectors the eigenrosses. Specifically, using simple principal components analysis, we project the data back onto the eigenrosses and compare shared variances in the highly loading eigenross components. This classic approach is used in a wide variety of data reduction and statistical applications including, factor analysis, spectral analysis, and face-detection software (i.e., vis-a-vis eigenfaces methods). We conduct this for each of the three color channels as well as a flattened (monochromatic) version of the covariances---the flattened version is derived by averaging each channel with respect to each pixel, which is the Gaussian method of converting to grayscale used by most image manipulation software.\n\nThe proportion of shared variances from the eigenross components is plotted in Figure~\\ref{res2}. Interestingly, despite the commonly held belief that Ross' paintings are relatively similar, the plot demonstrates considerable variation---it's not until the fifth eigenross component is reached until 50\\% of common variation across the whole set is attained for all channels including the flattened version (in gray). However, the first two components jointly explain more than 30\\% of the variance. We can explore this further by rendering images from these components.\n\nEach of the first five eigenross components is displayed in Figure~\\ref{eigenross}. As these are channel-independent orthonormal transformations we cannot recombine the red, green, and blue eigenross components in a reasonable way; thus, the components are plotted separately. Lighter colored areas indicate lower pixel-by-pixel shared variance across the set of clippings in that channel. Examination of the first two components demonstrates a clear preference for upper sky and lower foreground shared variation in the red and blue channels, and a clear foreground preference in the greens. The remainder of the eigenross components appear to differentiate trees, mountains, and buildings in an order different for each channel.\n\nFinally, to address the third question, ``what is the relationship between Bob Ross paintings'' we simply examine the correlation structure using a network perspective. Specifically, we posit a relationship between two paintings if the product of red, green, and blue channel correlations is greater than or equal to $0.3^3$; in other words, two paintings are said to be related if the total correlation between them is moderate by classical standards \\citep{cohen1988spab}. The resulting network is depicted in Figure~\\ref{network}. \n\nNearly half (n=12) of the data are isolates in this network. The isolates include the three paintings that feature buildings. In the connected component, there are two clusters, bridged by the relationship between paintings 16 and 28. Paintings, 1 and 16 appear to be the most central. These qualitative interpretations of the plot are confirmed quantitatively in Table~\\ref{net}, which reports degree (number of connections), betweenness (number of non-redundant shortest-paths), and closeness (measure of being in the middle of the network) centrality scores for the paintings in the connected component of the network \\citep{wasserman&faust1994snam}. \n\n\\section{Conclusion}\nAs we mark the $20^{th}$ anniversary of Bob Ross's death this year, the popularity of \\textit{The Joy of Painting} is again on the rise. Various public tributes have surfaced recently, including a video mash-up set to music called ``Happy Trees'' by PBS on YouTube, the selection of a Bob Ross themed costume as the winner of the Smithsonian National Zoo's Annual ``Night of the living zoo '' Costume Contest in 2013, a weekly ``Bob Ross Night'' in Missoula \\url{http:\/\/www.zootownarts.org\/bobross}, and now two statistical analyses (one qualitative and one quantitative) of his work. \n\nIn this paper, we've conducted yet another statistical analysis of Bob Ross paintings. Rather than examine the qualitative features of the subjects as prior work has done, we used the quantitative values of the colorspace in digital representations of the paintings as our data. We've demonstrated the subtle aesthetics of the average Bob Ross painting, the common variance shared by a set of Ross's work, and the structure of relationships between this sample using relatively simple quantitative techniques. \n\nFinally, there are a number of limitations with the current approach. First, we consider only a very small sample (n=30) of the publicly available set of Ross's work, a corpus many thousands of paintings in number. Future work may wish to expand this dataset. Indeed, the techniques employed here may be used to identify specific works attributed to an artist in a larger corpus of mixed artists' work \\citep{cutzu3&2005dpp}. Second, to standardize the dataset we take only the innermost central region; thus, we have a sample within a sample. It's possible that this strategy does not fully represent the variety of work encompassed by the whole lot---however, given the high spectral variability reported in our results, we believe this strategy is indeed representative of his works. Third, the source digital images that we collected from the internet were not rendered in a uniform manner; in an ideal data scenario, digital reproductions would have been obtained using the same high-resolution equipment in a controlled lighting environment. This gives rise to random errors in the channel values. However, these limitations did not impede evaluation of the research questions set forth here. As a proof-of-concept, the fact that our methods were able to recover discernible features in both the average and the variance of the set of paintings lends confidence to our results. We leave it to future research to further this approach by mitigating these limitations with a larger, more  standardized, sample. Additionally, future research should take a mixed-methods approach to statistically combine the results of qualitative and quantitative analysis of a body of art in this manner.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\n\n\\section{Introduction}\nFew-shot learning~\\cite{fei2006one, fink2005object, wu2010towards, lake2015human, wang2020generalizing} is the learning problem where a learner experiences only a limited number of examples as supervision.\nIn computer vision, it has been most actively studied for the tasks of image classification~\\cite{alexnet, vgg, resnet} and semantic segmentation~\\cite{deeplab, fcn, deconvnet, unet} among many others~\\cite{han2021query, ojha2021few, ramon2021h3d, yue2021prototypical, zhao2021few}.\nFew-shot classification (FS-C\\xspace) aims to classify a query image into target classes when a few support examples are given for each target class. \nFew-shot segmentation (FS-S\\xspace) is to segment out the target class regions on the query image in a similar setup.\nWhile being closely related to each other~\\cite{li2009towards, yao2012describing, zhou2019collaborative},\nthese two few-shot learning problems have so far been treated individually.\nFurthermore, the conventional setups for the few-shot problems, FS-C\\xspace and FS-S\\xspace, are limited and do not reflect realistic scenarios; \nFS-C\\xspace~\\cite{matchingnet, ravi2016optimization, koch2015siamese} presumes that the query always contains one of the target classes in classification, while FS-S\\xspace~\\cite{shaban2017oslsm, rakelly2018cofcn, hu2019amcg} allows the presence of multiple classes but does not handle the absence of the target classes in segmentation.\nThese respective limitations prevent few-shot learning from generalizing to and evaluating on more realistic cases in the wild. \nFor example, when a query image without any target class is given as in \\figref{fig:teaser}, FS-S\\xspace learners typically segment out arbitrary salient objects in the query.\n\nTo address the aforementioned issues, we introduce the \\textit{integrative task of few-shot classification and segmentation} (FS-CS\\xspace) that combines the two few-shot learning problems into a multi-label and background-aware prediction problem. \nGiven a query image and a few-shot support set for target classes,  FS-CS\\xspace aims to \\textit{identify the presence of each target class} and \\textit{predict its foreground mask} from the query.\nUnlike FS-C\\xspace and FS-S\\xspace, it does not presume either the class exclusiveness in classification or the presence of all the target classes in segmentation.\n\n\n\nAs a learning framework for FS-CS\\xspace, we propose {\\em integrative few-shot learning} (iFSL\\xspace) that learns to construct shared foreground maps for both classification and segmentation.\nIt naturally combines multi-label classification and pixel-wise segmentation by sharing class-wise foreground maps and also allows to learn with class tags or segmentation annotations. \nFor effective iFSL\\xspace, we design the {\\em attentive squeeze network} (ASNet\\xspace) that computes semantic correlation tensors between the query and the support image features and then transforms the tensor into a foreground map by strided self-attention. \nIt generates reliable foreground maps for iFSL\\xspace by leveraging multi-layer neural features~\\cite{hpf, hsnet} and global self-attention~\\cite{transformers, vit}. \nIn experiments, we demonstrate the efficacy of the iFSL\\xspace framework on FS-CS\\xspace and compare ASNet\\xspace with recent methods~\\cite{xie2021few, wu2021learning, hsnet, xie2021scale}.\nOur method significantly improves over the other methods on FS-CS\\xspace in terms of classification and segmentation accuracy and also outperforms the recent FS-S\\xspace methods on the conventional FS-S\\xspace.\nWe also cross-validate the task transferability between the FS-C\\xspace, FS-S\\xspace, and FS-CS\\xspace learners, and show the FS-CS\\xspace learners effectively generalize when transferred to the FS-C\\xspace and FS-S\\xspace tasks.\n\n\n\nOur contribution is summarized as follows:\n\\begin{itemize}\n    \\item We introduce the task of \\textit{integrative few-shot classification and segmentation} (FS-CS\\xspace), which combines few-shot classification and few-shot segmentation into an integrative task by addressing their limitations.\n    \\item We propose the \\textit{integrative few-shot learning framework} (iFSL\\xspace), which learns to both classify and segment a query image using class-wise foreground maps.\n    \\item We design the \\textit{attentive squeeze network} (ASNet\\xspace),\n    which squeezes semantic correlations into a foreground map for iFSL\\xspace via strided global self-attention.\n    \\item We show in extensive experiments that the framework, iFSL\\xspace, and the architecture, ASNet\\xspace, are both effective, achieving a significant gain on FS-S\\xspace as well as FS-CS\\xspace.\n\\end{itemize}\n\n\n\n\n\\section{Related work}\n\\smallbreakparagraph{Few-shot classification (FS-C\\xspace)}.\nRecent FS-C\\xspace methods typically learn neural networks that maximize positive class similarity and suppress the rest to predict the most probable class.\nSuch a similarity function is obtained by a) meta-learning embedding functions~\\cite{koch2015siamese, matchingnet, protonet, allen2019infinite, tewam, can, feat, deepemd, renet}, b) meta-learning to optimize classifier weights~\\cite{maml, leo, mtl}, or c) transfer learning~\\cite{closer, rfs, dhillon2019baseline, wang2020few, negmargin, gidaris2018dynamic, qi2018low, rodriguez2020embedding}, all of which aim to generalize to unseen classes.\nThis conventional formulation is applicable if a query image corresponds to no less or more than a single class among target classes.\nTo generalize FS-C\\xspace to classify images associated with either none or multiple classes,\nwe employ the multi-label classification~\\cite{mccallum1999multi, boutell2004learning, cole2021multi, lanchantin2021general, durand2019learning}.\nWhile the conventional FS-C\\xspace methods make use of the class uniqueness property via using the categorical cross-entropy, we instead devise a learning framework that compares the binary relationship between the query and each support image individually and estimates a binary presence of the corresponding class.\n\n\n\n\n\\smallbreakparagraph{Few-shot semantic segmentation (FS-S\\xspace)}.\nA prevalent FS-S\\xspace approach is learning to match a query feature map with a set of support feature embeddings that are obtained by collapsing spatial dimensions at the cost of spatial structures~\\cite{wang2019panet, zhang2021self, siam2019amp, yang2021mining, liu2021anti, dong2018few, nguyen2019fwb, zhang2019canet, gairola2020simpropnet, yang2020pmm, liu2020ppnet}.\nRecent methods~\\cite{zhang2019pgnet, xie2021scale, xie2021few, wu2021learning, tian2020pfenet} focus on learning structural details by leveraging dense feature correlation tensors between the query and each support.\nHSNet~\\cite{hsnet} learns to squeeze a dense feature correlation tensor and transform it to a segmentation mask via high-dimensional convolutions that analyze the local correlation patterns on the correlation pyramid.\nWe inherit the idea of learning to squeeze correlations and improve it by analyzing the spatial context of the correlation with effective global self-attention~\\cite{transformers}.  \nNote that several methods~\\cite{yang2020brinet, wang2020dan, sun2021boosting} adopt non-local self-attention~\\cite{nlsa} of the query-key-value interaction for FS-S\\xspace, but they are distinct from ours in the sense that they learn to transform image feature maps, whereas our method focuses on transforming dense correlation maps via self-attention.\n\nFS-S\\xspace has been predominantly investigated as an one-way segmentation task, \\ie, foreground or background segmentation, since the task is defined so that every target (support) class object appears in query images, thus being not straightforward to extend to a multi-class problem in the wild.\nConsequently, most work on FS-S\\xspace except for a few~\\cite{wang2019panet, tian2020differentiable, liu2020ppnet, dong2018few} focuses on the one-way segmentation, where the work of \\cite{tian2020differentiable, dong2018few} among the few presents two-way segmentation results from person-and-object images only, \\eg, images containing (person, dog) or (person, table).\n\n\n\\smallbreakparagraph{Comparison with other few-shot approaches.}\nHere we contrast FS-CS\\xspace with other loosely-related work for generalized few-shot learning.\nFew-shot open-set classification~\\cite{liu2020few} brings the idea of the open-set problem~\\cite{scheirer2012toward, fei2016breaking} to few-shot classification by allowing a query to have no target classes.\nThis formulation enables background-aware classification as in FS-CS\\xspace, whereas multi-label classification is not considered.\nThe work of \\cite{tian2020generalized, ganea2021incremental} generalizes few-shot segmentation to a multi-class task, but it is mainly studied under the umbrella of incremental learning~\\cite{mccloskey1989catastrophic, rebuffi2017icarl, castro2018end}.\nThe work of \\cite{siam2020weakly} investigates weakly-supervised few-shot segmentation using image-level vision and language supervision, while FS-CS\\xspace uses visual supervision only.\nThe aforementioned tasks generalize few-shot learning but differ from FS-CS\\xspace in the sense that FS-CS\\xspace integrates two related problems under more general and relaxed constraints.\n\\section{Problem formulation}\n\\label{sec:ourtask}\nGiven a query image and a few support images for target classes, we aim to {\\em identify the presence} of each class and {\\em predict its foreground mask} from the query (\\figref{fig:teaser}), which we call the {\\em integrative few-shot classification and segmentation} (FS-CS\\xspace).  \nSpecifically, let us assume a target (support) class set $\\mathcal{C}_{\\text{s}}$ of $N$ classes and its support set $\\mathcal{S}=\\{ (\\mathbf{x}_{\\text{s}}^{(i)}, y_{\\text{s}}^{(i)}) | y_{\\text{s}}^{(i)} \\in \\mathcal{C}_{\\text{s}} \\}^{NK}_{i=1}$, which contains $K$ labeled instances for each of the $N$ classes, \\ie, $N$-way $K$-shot~\\cite{matchingnet, ravi2016optimization}. \nThe label $y_{\\text{s}}^{(i)}$ is either a class tag (weak label) or a segmentation annotation (strong label). \nFor a given query image $\\mathbf{x}$, we aim to identify the multi-hot class occurrence $\\mathbf{y}_\\text{C}$ and also predict the segmentation mask $\\mathbf{Y}_\\text{S}$ corresponding to the classes. \nWe assume the class set of the query $\\mathcal{C}$ is a subset of the target class set, \\ie, $\\mathcal{C} \\subseteq \\mathcal{C}_{\\text{s}}$, thus it is also possible to obtain $\\mathbf{y}_\\text{C} = \\varnothing$ and $\\mathbf{Y}_\\text{S} = \\varnothing$. \nThis naturally generalizes the existing few-shot classification~\\cite{matchingnet, protonet} and few-shot segmentation~\\cite{shaban2017oslsm, rakelly2018cofcn}. \n\n\n\n\\smallbreakparagraph{Multi-label background-aware prediction.}\nThe conventional formulation of few-shot classification (FS-C\\xspace)~\\cite{matchingnet, protonet, maml} assigns the query to one class among the target classes exclusively and ignores the possibility of the query belonging to none or multiple target classes. \nFS-CS\\xspace tackle this limitation and generalizes FS-C\\xspace to multi-label classification with a background class. \nA multi-label few-shot classification learner $f_{\\text{C}}$ compares semantic similarities between the query and the support images and estimates class-wise occurrences: $\\hat{\\mathbf{y}}_{\\text{C}} = f_{\\text{C}}(\\mathbf{x}, \\mathcal{S}; \\theta)$ where $\\hat{\\mathbf{y}}_{\\text{C}}$ is an $N$-dimensional multi-hot vector each entry of which indicates the occurrence of the corresponding target class.\nNote that the query is classified into a \\textit{background} class if none of the target classes were detected.  \nThanks to the relaxed constraint on the query, \\ie, the query not always belonging to exactly one class, FS-CS\\xspace is more general than FS-C\\xspace.\n\n\n\n\\smallbreakparagraph{Integration of classification and segmentation.}\nFS-CS\\xspace integrates multi-label few-shot classification with semantic segmentation by adopting pixel-level spatial reasoning.\nWhile the conventional FS-S\\xspace~\\cite{shaban2017oslsm, rakelly2018cofcn, wang2019panet, siam2019amp, nguyen2019fwb} assumes the query class set exactly matches the support class set,\n\\ie, $\\mathcal{C} = \\mathcal{C}_{\\text{s}}$,\nFS-CS\\xspace relaxes the assumption such that the query class set can be a subset of the support class set,\n\\ie, $\\mathcal{C} \\subseteq \\mathcal{C}_{\\text{s}}$.\nIn this generalized segmentation setup along with classification, an integrative FS-CS\\xspace learner $f$ estimates both class-wise occurrences and their semantic segmentation maps: $\\{ \\hat{\\mathbf{y}}_{\\text{C}}, \\hat{\\mathbf{Y}}_{\\text{S}}\\} = f(\\mathbf{x}, \\mathcal{S} ; \\theta)$.\nThis combined and generalized formulation gives a high degree of freedom to both of the few-shot learning tasks, which has been missing in the literature;\nthe integrative few-shot learner can predict multi-label background-aware class occurrences and segmentation maps simultaneously under a relaxed constraint on the few-shot episodes.\n\n\\section{Integrative Few-Shot Learning (iFSL\\xspace)}\n\\label{sec:ourmethod}\nTo solve the FS-CS\\xspace problem, we propose an effective learning framework, \\textit{integrative few-shot learning (iFSL\\xspace)}.\nThe iFSL\\xspace framework is designed to jointly solve few-shot classification and few-shot segmentation using either a class tag or a segmentation supervision.\nThe integrative few-shot learner $f$ takes as input the query image $\\mathbf{x}$ and the support set $\\mathcal{S}$ and then produces as output the class-wise foreground maps.\nThe set of class-wise foreground maps $\\mathcal{Y}$ is comprised of $\\mathbf{Y}^{(n)} \\in \\mathbb{R}^{H \\times W}$ for $N$ classes: \n\\begin{align}\n\\mathcal{Y} = f(\\mathbf{x}, \\mathcal{S}; \\theta) = \\{ \\mathbf{Y}^{(n)}\\}_{n=1}^{N},\n\\label{eq:foreground_mask}\n\\end{align}\nwhere $H \\times W$ denotes the size of each map and $\\theta$ is parameters to be meta-learned.\nThe output at each position on the map represents the probability of the position being on a foreground region of the corresponding class.\n\n\\smallbreakparagraph{Inference.}\niFSL\\xspace infers both class-wise occurrences and segmentation masks on top of the set of foreground maps $\\mathcal{Y}$.\nFor class-wise occurrences, a multi-hot vector $\\hat{\\mathbf{y}}_\\text{C} \\in \\mathbb{R}^{N}$ is predicted via max pooling followed by thresholding:\n\\begin{align}\n\\hat{\\mathbf{y}}_{\\text{C}}^{(n)} &= \n\\begin{cases}\n  1  \\text{\\; if \\,} \\max_{\\mathbf{p} \\in [H] \\times [W]} \\mathbf{Y}^{(n)}(\\mathbf{p}) \\geq \\delta,\\\\\n  0 \\text{\\; otherwise,}\n\\end{cases}\n\\label{eq:predict_class}\n\\end{align}\nwhere $\\mathbf{p}$ denotes a 2D position, $\\delta$ is a threshold, and $[ k ]$ denotes a set of integers from 1 to $k$, \\ie, $[k] = \\{1,\\! 2,\\! \\cdots,\\! k\\}$.\nWe find that inference with average pooling is prone to miss small objects in multi-label classification and thus choose to use max pooling.\nThe detected class at any position on the spatial map signifies the presence of the class.  \n\nFor segmentation, a segmentation probability tensor $\\mathbf{Y}_{\\text{S}} \\in \\mathbb{R}^{ H \\times W \\times (N + 1)}$ is derived from the class-wise foreground maps.\nAs the background class is not given as a separate support, we estimate the background map in the context of the given supports;  we combine $N$ class-wise background maps into \\textit{an episodic background map} on the fly. \nSpecifically, we compute the episodic background map $\\mathbf{Y}_{\\text{bg}}$ by averaging the probability maps of not being foreground and then concatenate it with the class-wise foreground maps to obtain a segmentation probability tensor $\\mathbf{Y}_{\\text{S}}$: \n\\begin{align}\n\\mathbf{Y}_{\\text{bg}} &= \\frac{1}{N} \\sum_{n=1}^{N}(\\mathbf{1} - \\mathbf{Y}^{(n)}), \\label{eq:bg_mask}\\\\\n\\mathbf{Y}_{\\text{S}} &= \\left[ \\mathbf{Y} || \\mathbf{Y}_{\\text{bg}} \\right] \\in \\mathbb{R}^{ H \\times W \\times (N + 1)}.\n\\label{eq:merge_mask}\n\\end{align}\nThe final segmentation mask $\\hat{\\mathbf{Y}}_\\text{S} \\in \\mathbb{R}^{H \\times W}$ is obtained by computing the most probable class label for each position:\n\\begin{equation}\n\\hat{\\mathbf{Y}}_\\text{S} = \\argmax_{n \\in [N + 1]} \\mathbf{Y}_{\\text{S}}.\n\\label{eq:predict_mask}\n\\end{equation}\n\n\n\\smallbreakparagraph{Learning objective.}\nThe iFSL\\xspace framework allows a learner to be trained using a class tag or a segmentation annotation using the classification loss or segmentation loss, respectively.\nThe classification loss is formulated as the average binary cross-entropy between the spatially average-pooled class scores and its ground-truth class label:\n\\begin{align}\n    \\mathcal{L}_{\\text{C}} &= -\\frac{1}{N}\\sum_{n=1}^{N}\\mathbf{y}_{\\text{gt}}^{(n)} \\log \\frac{1}{H W}\\sum_{\\scriptscriptstyle{\\mathbf{p} \\in [H] \\! \\times \\! [W]}} \\mathbf{Y}^{(n)}(\\mathbf{p}), \n        \\label{eq:loss_cls_final}\n\\end{align}\nwhere $\\mathbf{y}_\\text{gt}$ denotes the multi-hot encoded ground-truth class.\n\nThe segmentation loss is formulated as the average cross-entropy between the class distribution at each individual position and its ground-truth segmentation annotation:\n\\begin{align}\n    \\mathcal{L}_{\\text{S}} &= - \\frac{1}{(N + 1)}\\frac{1}{H W} \\sum_{n=1}^{N + 1}\\sum_{\\scriptscriptstyle{\\mathbf{p} \\in [H] \\! \\times \\! [W]}} \\mathbf{Y}_\\text{gt}^{(n)}(\\mathbf{p}) \\log \\mathbf{Y}_{\\text{S}}^{(n)}(\\mathbf{p}), \n        \\label{eq:loss_seg_final}\n\\end{align} where $\\mathbf{Y}_\\text{gt}$ denotes the ground-truth segmentation mask. \n\nThese two losses share a similar goal of classification but differ in whether to classify each \\textit{image} or each \\textit{pixel}. Either of them is thus chosen according to the given level of supervision for training.\n\n\\section{Model architecture}\nIn this section, we present \\textit{Attentive Squeeze Network} (ASNet\\xspace) of an effective iFSL\\xspace model.\nThe main building block of ASNet\\xspace is the attentive squeeze layer (AS\\xspace layer), which is a high-order self-attention layer that takes a correlation tensor and returns another level of correlational representation.\nASNet\\xspace takes as input the pyramidal cross-correlation tensors between a query and a support image feature pyramids, \\ie, a hypercorrelation~\\cite{hsnet}.\nThe pyramidal correlations are fed to pyramidal AS\\xspace layers that gradually squeeze the spatial dimensions of the support image, and the pyramidal outputs are merged to a final foreground map in a bottom-up pathway~\\cite{hsnet, fpn, refinenet}.\n\\figureref{fig:overview}~illustrates the overall process of ASNet\\xspace.\nThe $N$-way output maps are computed in parallel and collected to prepare the class-wise foreground maps in \\eqref{eq:foreground_mask} for iFSL\\xspace.\n\n\n\\subsection{Attentive Squeeze Network (ASNet)}\n\\smallbreakparagraph{Hypercorrelation construction.}\nOur method first constructs $NK$ hypercorrelations~\\cite{hsnet} between a query and each $NK$ support image and then learns to generate a foreground segmentation mask \\wrt each support input.\nTo prepare the input hypercorrelations, an episode, \\ie, a query and a support set, is enumerated into a paired list of the query, a support image, and a support label: $\\{(\\mathbf{x}, (\\mathbf{x}_{\\text{s}}^{(i)}, y_{\\text{s}}^{(i)})) \\}_{i=1}^{NK}$.\nThe input image is fed to stacked convolutional layers in a CNN and its mid- to high-level output feature maps are collected to build a feature pyramid $\\{\\mathbf{F}^{(l)}\\}_{l=1}^{L}$, where $l$ denotes the index of a unit layer, \\eg, $\\texttt{Bottleneck}$ layer in ResNet50~\\cite{resnet}.\nWe then compute cosine similarity between each pair of feature maps from the pair of query and support feature pyramids to obtain 4D correlation tensors of size $H_{\\text{q}}^{(l)} \\times W_{\\text{q}}^{(l)} \\times H_{\\text{s}}^{(l)} \\times W_{\\text{s}}^{(l)}$, which is followed by ReLU~\\cite{relu}:\n\\begin{equation}\n\\mathbf{C}^{(l)}(\\mathbf{p}_{\\text{q}}, \\mathbf{p}_{\\text{s}}) = \\mathrm{ReLU}\\left( \\frac{\\mathbf{F}_{\\text{q}}^{(l)}(\\mathbf{p}_{\\text{q}}) \\cdot \\mathbf{F}_{\\text{s}}^{(l)}(\\mathbf{p}_{\\text{s}})}{||\\mathbf{F}_{\\text{q}}^{(l)}(\\mathbf{p}_{\\text{q}})|| \\, ||\\mathbf{F}_{\\text{s}}^{(l)}(\\mathbf{p}_{\\text{s}})||} \\right).\n\\end{equation}\nThese $L$ correlation tensors are grouped by $P$ groups of the identical spatial sizes, and then the tensors in each group are concatenated along a new channel dimension to build a hypercorrelation pyramid: $\\{\\mathbf{C}^{(p)} | \\mathbf{C}^{(p)} \\in \\mathbb{R}^{ H_{\\text{q}}^{(p)} \\times W_{\\text{q}}^{(p)} \\times H_{\\text{s}}^{(p)} \\times W_{\\text{s}}^{(p)} \\times C_{\\text{in}}^{(p)}}  \\}_{p=1}^{P}$ such that the channel size $C_{\\text{in}}^{(p)}$ corresponds to the number of concatenated tensors in the $p_{\\text{th}}$ group. \nWe denote the first two spatial dimensions of the correlation tensor, \\ie, $\\mathbb{R}^{H_{\\text{q}} \\times W_{\\text{q}}}$, as query dimensions, and the last two spatial dimensions, \\ie, $\\mathbb{R}^{H_{\\text{s}} \\times W_{\\text{s}}}$, as support dimensions hereafter.\n\n\n\\smallbreakparagraph{Attentive squeeze layer (AS\\xspace layer).}\nThe AS\\xspace layer transforms a correlation tensor to another with a smaller support dimension via strided self-attention. \nThe tensor is recast as a matrix with each element representing a support pattern.\nGiven a correlation tensor $\\mathbf{C} \\in \\mathbb{R}^{H_{\\text{q}} \\times W_{\\text{q}} \\times H_{\\text{s}} \\times W_{\\text{s}} \\times C_{\\text{in}} }$ in a hypercorrelation pyramid, we start by reshaping the correlation tensor as a block matrix of size $H_{\\text{q}} \\times W_{\\text{q}}$ with each element corresponding to a correlation tensor of $\\mathbf{C}(\\mathbf{x}_{\\text{q}}) \\in \\mathbb{R}^{H_{\\text{s}} \\times W_{\\text{s}} \\times C_{\\text{in}} }$ on the query position $\\mathbf{x}_{\\text{q}}$ such that \n\\begin{equation}\n\\mathbf{C}^{\\text{block}} = \n\\begin{bmatrix} \n    \\mathbf{C}((1, 1)) & \\hdots & \\mathbf{C}((1, W_{\\text{q}})) \\\\\n    \\vdots & \\ddots & \\vdots   \\\\\n    \\mathbf{C}((H_{\\text{q}}, 1)) &  \\hdots & \\mathbf{C}((H_{\\text{q}}, W_{\\text{q}})) \n\\end{bmatrix}\n\\label{eq:block_matrix}\n.\n\\end{equation}\nWe call each element a \\textit{support correlation tensor}.\nThe goal of an AS\\xspace layer is to analyze the global context of each support correlation tensor and extract a correlational representation with a reduced support dimension while the query dimension is preserved: \n$\\mathbb{R}^{ H_{\\text{q}} \\times W_{\\text{q}} \\times H_{\\text{s}} \\times W_{\\text{s}} \\times C_{\\text{in}} } \\rightarrow \\mathbb{R}^{H_{\\text{q}} \\times W_{\\text{q}} \\times H_{\\text{s}}' \\times W_{\\text{s}}' \\times C_{\\text{out}} }$, where $H_{\\text{s}}' \\leq H_{\\text{s}}$ and $W_{\\text{s}}' \\leq W_{\\text{s}}$.\nTo learn a holistic pattern of each support correlation, we adopt the global self-attention mechanism~\\cite{transformers} for correlational feature transform.\nThe self-attention weights are shared across all query positions and processed in parallel.\n\n\nLet us denote a support correlation tensor on any query position $\\mathbf{x}_{\\text{q}}$ by  $\\mathbf{C}^{{\\text{s}}} = \\mathbf{C}^{\\text{block}}(\\mathbf{x}_{\\text{q}})$ for notational brevity as all positions share the following computation.\nThe self-attention computation starts by embedding a support correlation tensor $\\mathbf{C}^{{\\text{s}}}$ to a target\n\\footnote{\nIn this section, we adapt the term ``target'' to indicate the ``query'' embedding in the context of self-attention learning~\\cite{transformers, vit, lsa, pvt, lrnet} to avoid homonymous confusion with the ``query'' image to be segmented.\n}\n, key, value triplet: \n$\n\\mathbf{T}, \\mathbf{K}, \\mathbf{V} \\in \\mathbb{R}^{ H_{\\text{s}}' \\times W_{\\text{s}}' \\times C_{\\text{hd}}},\n$\nusing three convolutions of which strides greater than or equal to one to govern the output size.\nThe resultant target and key correlational representations, $\\mathbf{T}$ and $\\mathbf{K}$, are then used to compute an attention context.\nThe attention context is computed as following matrix multiplication:\n\\begin{equation}\n\\mathbf{A} = \\mathbf{T} \\mathbf{K}^{\\top} \\in \\mathbb{R}^{H_{\\text{s}}' \\times W_{\\text{s}}' \\times H_{\\text{s}}' \\times W_{\\text{s}}'}.\n\\label{eq:sixd_attn}\n\\end{equation}\nNext, the attention context is normalized by softmax such that the votes on key foreground positions sum to one with masking attention by the support mask annotation $\\mathbf{Y}_{\\text{s}}$ if available to attend more on the foreground region:\n\\begin{align*}\n\\bar{\\mathbf{A}}(\\mathbf{p}_{\\text{t}}, \\mathbf{p}_{\\text{k}}) = \\frac{\\exp \\left( \\mathbf{A}(\\mathbf{p}_{\\text{t}}, \\mathbf{p}_{\\text{k}}) \\mathbf{Y}_{\\text{s}}(\\mathbf{p}_{\\text{k}}) \\right)}{\\sum_{\\mathbf{p}_{\\text{k}}'}\\exp \\left( \\mathbf{A}(\\mathbf{p}_{\\text{t}}, \\mathbf{p}'_{\\text{k}}) \\mathbf{Y}_{\\text{s}}(\\mathbf{p}'_{\\text{k}}) \\right)},\n\\end{align*}\n\\begin{equation}\n\\text{where\\, } \\mathbf{Y}_{\\text{s}}(\\mathbf{p}_{\\text{k}}) =\n\\begin{cases}\n  1 \\quad \\; \\; \\text{if} \\; \\mathbf{p}_{\\text{k}} \\in [H'_{\\text{s}}] \\times [W'_{\\text{s}}] \\text{ is foreground,} \\\\    \n  - \\infty  \\; \\text{otherwise.}\n\\end{cases} \n\\label{eq:masked_attn}\n\\end{equation}\nThe masked attention context $\\bar{\\mathbf{A}}$ is then used to aggregate\nthe value embedding $\\mathbf{V}$:\n\\begin{equation}\n\\mathbf{C}^{{\\text{s}}}_{{\\text{A}}} = \\bar{\\mathbf{A}} \\mathbf{V} \\in \\mathbb{R}^{ H_{\\text{s}}' \\times W_{\\text{s}}' \\times C_{\\text{hd}} }.\n\\label{eq:agg}\n\\end{equation}\nThe attended representation is fed to an MLP layer, $\\mathbf{W}_{\\text{o}}$, and added to the input.\nIn case the input and output dimensions mismatch, the input is optionally fed to a convolutional layer, $\\mathbf{W}_{\\text{I}}$.\nThe addition is followed by an activation layer $\\varphi(\\cdot)$ consisting of a group normalization~\\cite{groupnorm} and a ReLU activation~\\cite{relu}:\n\\begin{equation}\n\\mathbf{C}^{{\\text{s}}}_{\\text{o}} = \\varphi(\\mathbf{W}_{\\text{o}}(\\mathbf{C}^{{\\text{s}}}_{\\text{A}}) + \\mathbf{W}_{\\text{I}}(\\mathbf{C}^{{\\text{s}}}) ) \\in \\mathbb{R}^{  H_{\\text{s}}' \\times W_{\\text{s}}' \\times C_{\\text{out}}}.\n\\end{equation}\nThe output is then fed to another MLP that concludes a unit operation of an AS\\xspace layer:\n\\begin{equation}\n\\mathbf{C}^{{\\text{s}} \\prime} = \\varphi(\\mathbf{W}_\\text{FF}(\\mathbf{C}^{{\\text{s}}}_{\\text{o}}) + \\mathbf{C}^{{\\text{s}}}_{\\text{o}}) \\in \\mathbb{R}^{ H_{\\text{s}}' \\times W_{\\text{s}}' \\times C_{\\text{out}}},\n\\end{equation}\nwhich is embedded to the corresponding query position in the block matrix of \\eqref{eq:block_matrix}.\nNote that the AS\\xspace layer can be stacked to progressively reduce the size of support correlation tensor, $H_{\\text{s}}' \\times W_{\\text{s}}'$, to a smaller size.\nThe overall pipeline of AS\\xspace layer is illustrated in the supplementary material.\n\n\n\n\\smallbreakparagraph{Multi-layer fusion.}\nThe pyramid correlational representations are merged from the coarsest to the finest level by cascading a pair-wise operation of the following three steps: upsampling, addition, and non-linear transform.\nWe first bi-linearly upsample the bottommost correlational representation to the query spatial dimension of its adjacent earlier one and then add the two representations to obtain a mixed one $\\mathbf{C}^{\\text{mix}}$.\nThe mixed representation is fed to two sequential AS\\xspace layers until it becomes a point feature of size $H_{\\text{s}}' = W_{\\text{s}}'=1$, which is fed to the subsequent pyramidal fusion.\nThe output from the earliest fusion layer is fed to a convolutional decoder, which consists of interleaved 2D convolution and bi-linear upsampling that map the $C$-dimensional channel to 2 (foreground and background) and the output spatial size to the input query image size.\nSee \\figref{fig:overview} for the overall process of multi-layer fusion.\n\n\n\n\n\n\n\\smallbreakparagraph{Class-wise foreground map computation.}\nThe $K$-shot output foreground activation maps are averaged to produce a mask prediction for each class.\nThe averaged output map is normalized by softmax over the two channels of the binary segmentation map to obtain a foreground probability prediction $\\mathbf{Y}^{(n)} \\in \\mathbb{R}^{H \\times W}$.\n\n\n\\section{Experiments}\nIn this section we report our experimental results regarding the FS-CS\\xspace task, the iFSL\\xspace framework, as well as the  ASNet\\xspace after briefly describing implementation details and evaluation benchmarks.\nSee the supplementary material for additional results, analyses, and experimental details.\n\n\n\n\n\n\\subsection{Experimental setups}\n\\smallbreakparagraph{Experimental settings.}\nWe select ResNet50 and ResNet-101~\\cite{resnet} pretrained on ImageNet~\\cite{russakovsky2015imagenet} as our backbone networks for a fair comparison with other methods and freeze the backbone during training as similarly as the previous work~\\cite{tian2020pfenet, hsnet}.\nWe train models using Adam~\\cite{adam} optimizer with learning rate of $10^{-4}$ and $10^{-3}$ for the classification loss and the segmentation loss, respectively.\nWe train all models with 1-way 1-shot training episodes and evaluate the models on arbitrary $N$-way $K$-shot episodes.\nFor inferring class occurrences, we use a threshold $\\delta = 0.5$.\nAll the AS\\xspace layers are implemented as multi-head attention with 8 heads. \nThe number of correlation pyramid is set to $P=3$.\n\n\n\n\\smallbreakparagraph{Dataset.}\nFor the new task of FS-CS\\xspace,\nwe construct a benchmark adopting the images and splits from the two widely-used FS-S\\xspace datasets, Pascal-5$^{i}$~\\cite{shaban2017oslsm, pascal} and COCO-20$^{i}$~\\cite{nguyen2019fwb, coco}, which are also suitable for multi-label classification~\\cite{wang2017multi}.\nWithin each fold, we construct an episode by randomly sampling a query and an $N$-way $K$-shot support set that annotates the query with $N$-way class labels and an $(N\\!+\\!1)$-way segmentation mask in the context of the support set.\nFor the FS-S\\xspace task, we also use Pascal-5$^{i}$ and COCO-20$^{i}$ following the same data splits as \\cite{shaban2017oslsm} and \\cite{nguyen2019fwb}, respectively.\n\n\\smallbreakparagraph{Evaluation.}\nEach dataset is split into four mutually disjoint class sets and cross-validated.\nFor multi-label classification evaluation metrics, we use the 0\/1 exact ratio $\\mathrm{ER} = \\mathbbm{1} [\\mathbf{y}_{\\text{gt}} = \\mathbf{y}_{\\text{C}} ]$~\\cite{durand2019learning}.\nIn the supplementary material, we also report the results in accuracy $\\mathrm{acc} = \\frac{1}{N} \\sum_n \\mathbbm{1} [\\mathbf{y}_{\\text{gt}}^{(n)} =  \\mathbf{y}^{(n)}_{\\text{C}} ]$.\nFor segmentation, we use mean IoU $\\mathrm{mIoU} = \\frac{1}{C}\\sum_c \\mathrm{IoU}_c$~\\cite{shaban2017oslsm, wang2019panet}, where $\\mathrm{IoU}_c$ denotes an IoU value of $c_{\\text{th}}$ class.\n\n\n\n\n\\begin{figure}[t!]\n\t\\centering\n\t\\small\n    \\includegraphics[width=0.97\\linewidth]{fig\/qual2way.pdf}\n    \\vspace{-1mm}\n\t\\caption{2-way 1-shot segmentation results of ASNet\\xspace on FS-CS\\xspace.\n\tThe examples cover all three cases of $\\mathcal{C}  =  \\varnothing$, $\\mathcal{C} \\subset \\mathcal{C}_{\\text{s}}$, and $\\mathcal{C} = \\mathcal{C}_{\\text{s}}$.\n\tThe images are resized to square shape for visualization.\n    \\vspace{-4mm}\n}\n\\label{fig:qual2way}\n\\end{figure}\n\n\n\n\n\n\n\\subsection{Experimental evaluation of iFSL\\xspace on FS-CS\\xspace}\nIn this subsection, we investigate the iFSL\\xspace learning framework on the FS-CS\\xspace task.\nAll ablation studies are conducted using ResNet50 on Pascal-$i^5$ and evaluated in 1-way 1-shot setup unless specified otherwise.\nNote that it is difficult to present a fair and direct comparison between the conventional FS-C\\xspace and our few-shot classification task since FS-C\\xspace is always evaluated on single-label classification benchmarks~\\cite{matchingnet, tieredimagenet, cifarfs, metaoptnet, metadataset}, whereas our task is evaluated on multi-label benchmarks~\\cite{pascal, coco}, which are irreducible to a single-label one in general. \n\n\n\n\\smallbreakparagraph{Effectiveness of iFSL\\xspace on FS-CS\\xspace.}\nWe validate the iFSL\\xspace framework on FS-CS\\xspace and also compare the performance of ASNet\\xspace with those of three recent state-of-the-art methods, PANet~\\cite{wang2019panet}, PFENet~\\cite{tian2020pfenet}, and HSNet~\\cite{hsnet}, which are originally proposed for the conventional FS-S\\xspace task; all the models are trained by iFSL\\xspace for a fair comparison.  \nNote that we exclude the background merging step (Eqs.~\\ref{eq:bg_mask} and \\ref{eq:merge_mask}) for PANet as its own pipeline produces a multi-class output including background.\nTables \\ref{table:ipa} and \\ref{table:ico} validate the iFSL\\xspace framework on the FS-CS\\xspace task quantitatively, where our ASNet\\xspace surpasses other methods on both 1-way and 2-way setups in terms of few-shot classification as well as the segmentation performance.\nThe 2-way segmentation results are also qualitatively demonstrated in \\figref{fig:qual2way} visualizing exhaustive inclusion relations between a query class set $\\mathcal{C}$ and a target (support) class set $\\mathcal{C}_{\\text{s}}$ in a 2-way setup.\n\n\n\n\\begin{figure}[t!]\n\t\\centering\n\t\\small\n    \\includegraphics[width=0.9\\linewidth]{fig\/multiway_legend.pdf}\n    \\vspace{-3mm}\n    \\includegraphics[width=0.49\\linewidth]{fig\/multiway_er_bar.pdf} \\hfill\n    \\includegraphics[width=0.49\\linewidth]{fig\/multiway_miou_bar.pdf}\n    \\caption{$N$-way 1-shot FS-CS\\xspace performance comparison of four methods by varying $N$ from 1 to 5.\n\t}\n\\label{fig:multiway}\n\\end{figure}\n\n\\smallbreakparagraph{Weakly-supervised iFSL\\xspace.}\nThe iFSL\\xspace framework is versatile across the level of supervision: weak labels (class tags) or strong labels (segmentation masks).\nAssuming weak labels are available but strong labels are not, ASNet\\xspace is trainable with the classification learning objective of iFSL\\xspace (Eq.~\\ref{eq:loss_cls_final}) and its results are presented as $\\text{ASNet\\xspace}_{\\text{w}}$ in \\tableref{table:ipa}.\n$\\text{ASNet\\xspace}_{\\text{w}}$ performs on par with ASNet\\xspace in terms of classification ER (82.0\\% \\textit{vs.}~84.9\\% on 1-way 1-shot), but performs ineffectively on the segmentation task (15.0\\% \\textit{vs.}~52.3\\% on 1-way 1-shot).\nThe result implies that the class tag labels are sufficient for a model to recognize the class occurrences, but are weak to endorse model's precise spatial recognition ability.\n\n\n\n\n\\smallbreakparagraph{Multi-class scalability of FS-CS\\xspace.}\nIn addition, FS-CS\\xspace is extensible to a multi-class problem with arbitrary numbers of classes, while FS-S\\xspace is not as flexible as FS-CS\\xspace in the wild.\nFigure~\\ref{fig:multiway} compares the FS-CS\\xspace performances of four methods by varying the $N$-way classes from one to five, where the other experimental setup follows the same one as in \\tableref{table:ipa}.\nOur ASNet\\xspace shows consistently better performances than other methods on FS-CS\\xspace in varying number of classes.\n\n\n\n\n\\smallbreakparagraph{Robustness of FS-CS\\xspace against task transfer.}\nWe evaluate the transferability between FS-CS\\xspace, FS-C\\xspace, and FS-S\\xspace by training a model on one task and evaluating it on the other task.\nThe results are compared in \\figref{fig:task_transfer} in which `$\\text{FS-S\\xspace} \\rightarrow$ FS-CS\\xspace' represents the result where the model trained on the $\\text{FS-S\\xspace}$ task (with the guarantee of support class presence) is evaluated on the FS-CS\\xspace setup.\nTo construct training and validation splits for FS-C\\xspace or FS-S\\xspace, we sample episodes that satisfy the constraint of support class occurrences~\\footnote{We sample 2-way 1-shot episodes having a single positive class for training on FS-C\\xspace or evaluating on FS-C\\xspace.\nWe collect 1-way 1-shot episodes sampled from the same class for training on FS-S\\xspace or evaluating on FS-S\\xspace.}. \nFor training FS-C\\xspace models, we use the class tag supervision only. \nAll the other settings are fixed the same, \\eg, we use ASNet\\xspace with ResNet50 and Pascal-$i^5$.\n\nThe results show that FS-CS\\xspace learners, \\ie, models trained on FS-CS\\xspace, are transferable to the two conventional few-shot learning tasks and yet overcome their shortcomings.\nThe transferability between few-shot classification tasks, \\ie, FS-C\\xspace and $\\text{FS-CS\\xspace}_{\\text{w}}$, is presented in \\figref{fig:task_transfer}(a).\nOn this setup, the $\\text{FS-CS\\xspace}_{\\text{w}}$ learner is evaluated by predicting a higher class response between the two classes, although it is trained using the multi-label classification objective.\nThe FS-CS\\xspace learner closely competes with the FS-C\\xspace learner on FS-C\\xspace in terms of classification accuracy.\nIn contrast, the task transfer between segmentation tasks, FS-S\\xspace and FS-CS\\xspace, results in asymmetric outcomes as shown in \\figref{fig:task_transfer}(b)~and~(c).\nThe FS-CS\\xspace learner shows relatively small performance drop on FS-S\\xspace, however, the FS-S\\xspace learner suffers a severe performance drop on FS-CS\\xspace.\nQualitative examples in \\figref{fig:teaser} demonstrate that the FS-S\\xspace learner predicts a vast number of false-positive pixels and results in poor performances.\nIn contrast, the FS-CS\\xspace learner successfully distinguishes the region of interest by analyzing the semantic relevance of the query objects between the support set.\n\n\\input{table\/task_transfer}\n\\input{table\/f1pa}\n\\input{table\/f2co}\n\n\\input{table\/ablation}\n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection{Comparison with recent FS-S\\xspace methods on FS-S\\xspace}\nTables~\\ref{table:fpa} and \\ref{table:fco} compare the results of the recent few-shot semantic segmentation methods and ASNet\\xspace on the conventional FS-S\\xspace task.\nAll model performances in the tables are taken from corresponding papers, and the numbers of learnable parameters are either taken from papers or counted from their official sources of implementation.\nFor a fair comparison with each other, some methods that incorporate extra unlabeled images~\\cite{yang2021mining, liu2020ppnet} are reported as their model performances measured in the absence of the extra data.\nNote that ASNet\\xspace in Tables~\\ref{table:fpa} and \\ref{table:fco} is trained and evaluated following the FS-S\\xspace setup, not the proposed FS-CS\\xspace one.\n\nThe results verify that ASNet\\xspace outperforms the existing methods including the most recent ones~\\cite{wu2021learning, xie2021few, yang2021mining}.\nEspecially, the methods that cast few-shot segmentation as the task of correlation feature transform, ASNet and HSNet~\\cite{hsnet}, outperform other visual feature transform methods, indicating that learning correlations is beneficial for both FS-CS\\xspace and FS-S\\xspace.\nNote that ASNet\\xspace is the most lightweight among others as ASNet\\xspace processes correlation features that have smaller channel dimensions, \\eg, at most 128, than visual features, \\eg, at most 2048 in ResNet50.\n\n\n\n\n\n\n\\subsection{Analyses on the model architecture}\nWe perform ablation studies on the model architecture to reveal the benefit of each component.\nWe replace the global self-attention in the ASNet\\xspace layer with the local self-attention~\\cite{lsa} to see the effect of the global self-attention~(\\tableref{table:ablation_architecture}\\texttt{a}).\nThe local self-attention variant is compatible with the global ASNet\\xspace in terms of the classification exact ratio but degrades the segmentation mIoU significantly, signifying the importance of the learning the global context of feature correlations.\nNext, we ablate the attention masking in \\eqref{eq:masked_attn}, which verifies that the attention masking prior is effective~(\\tableref{table:ablation_architecture}\\texttt{b}).\nLastly, we replace the multi-layer fusion path with spatial average pooling over the support dimensions followed by element-wise addition~(\\tableref{table:ablation_architecture}\\texttt{c}), and the result indicates that it is crucial to fuse outputs from the multi-layer correlations to precisely estimate class occurrence and segmentation masks.\n\n\n\n\\section{Discussion}\nWe have introduced the integrative task of few-shot classification and segmentation (FS-CS\\xspace) that generalizes two existing few-shot learning problems.\nOur proposed integrative few-shot learning (iFSL\\xspace) framework is shown to be effective on FS-CS\\xspace, in addition, our proposed attentive squeeze network (ASNet\\xspace) outperforms recent state-of-the-art methods on both FS-CS\\xspace and FS-S\\xspace.\nThe iFSL\\xspace design allows a model to learn either with weak or strong labels, that being said, \nlearning our method with weak labels achieves low segmentation performances. \nThis result opens a future direction of effectively boosting the segmentation performance leveraging weak labels in the absence of strong labels for FS-CS\\xspace.\n\n\n\n\\section{Supplementary Material}\n\n\n\\subsection{Detailed model architecture}\nThe comprehensive configuration of attentive squeeze network is summarized in \\tableref{table:asnet}, and its building block, attentive squeeze layer, is depicted in \\figref{fig:aslayer}.\nThe channel sizes of the input correlation $\\{C_\\text{in}^{(1)}, C_\\text{in}^{(2)}, C_\\text{in}^{(3)}\\}$ corresponds to $\\{4, 6, 3\\}$, $\\{4, 23, 3\\}$, $\\{3, 3, 1\\}$ for ResNet50~\\cite{resnet}, ResNet101, VGG-16~\\cite{vgg}, respectively.\n\n\n\\subsection{Implementation details}\nOur framework is implemented on PyTorch~\\cite{pytorch} using the PyTorch Lightning~\\cite{falcon2019pytorch} framework.\nTo reproduce the existing methods, we heavily borrow publicly available code bases.~\\footnote{PANet~\\cite{wang2019panet}: \\url{https:\/\/github.com\/kaixin96\/PANet} \\\\ PFENet~\\cite{tian2020pfenet}: \\url{https:\/\/github.com\/dvlab-research\/PFENet} \\\\\nHSNet~\\cite{hsnet}: \\url{https:\/\/github.com\/juhongm999\/hsnet}}\nWe set the officially provided hyper-parameters for each method while sharing generic techniques for all the methods, \\eg, excluding images of small support objects for support sets or switching the role between the query and the support during training. \nNVIDIA GeForce RTX 2080 Ti GPUs or NVIDIA TITAN Xp GPUs are used in all experiments, where we train models using two GPUs on Pascal-$5^{i}$~\\cite{shaban2017oslsm} while using four GPUs on COCO-$20^{i}$~\\cite{nguyen2019fwb}.\nModel training is halt either when it reaches the maximum $500_{\\text{th}}$ epoch or when it starts to overfit.\nWe resize input images to $400 \\times 400$ without any data augmentation strategies during both training and testing time for all methods.\nFor segmentation evaluation, we recover the two-channel output foreground map to its original image size by bilinear interpolation.\nPascal-$5^{i}$ and COCO-$20^{i}$ is derived from Pascal Visual Object Classes 2012~\\cite{pascal} and Microsoft Common Object in Context 2014~\\cite{coco}, respectively.\nTo construct episodes from datasets, we sample support sets such that one of the query classes is included in the support set by the probability of 0.5 to balance the ratio of background episodes across arbitrary benchmarks.\n\n\n\n\\begin{figure}[t!]\n\t\\centering\n\t\\small\n    \\includegraphics[width=\\linewidth]{supp\/fig\/aslayer.pdf}\n   \n    \\vspace{-5mm}\n\t\\caption{Illustration of the proposed attentive squeeze layer (Sec.~5.1. in the main paper).\n\tThe shape of each output tensor is denoted next to arrows.\n    }\n\\label{fig:aslayer}\n\\end{figure}\n\n\\newcommand{\\plh}{%\n  {\\ooalign{$\\phantom{0}$\\cr\\hidewidth$\\scriptstyle\\times$\\cr}}%\n}\n\n\\begin{table}[t!]\n    \\centering\n    \\setlength{\\extrarowheight}{-2.0pt}\n    \\scalebox{0.70}{\n        \\begin{tabular}{ccc}\n            \\toprule\n            $p = 1$ & $p = 2$ & $p = 3$ \\\\ \n            $\\frac{H}{8}\\plh\\frac{H}{8}\\plh\\frac{H}{8}\\plh\\frac{H}{8}\\plh C_\\text{in}^{(1)}$ & $\\frac{H}{16}\\plh\\frac{H}{16}\\plh\\frac{H}{16}\\plh\\frac{H}{16}\\plh C_\\text{in}^{(2)}$ & $\\frac{H}{32}\\plh\\frac{H}{32}\\plh\\frac{H}{32}\\plh\\frac{H}{32}\\plh C_\\text{in}^{(3)}$ \\\\ \n            \\midrule\n            {[pool support dims. by half]} & & \\\\\n            $\\mathrm{AS}(C_\\text{in}^{(1)}\\rightarrow32, 5, 4, 2)$ & $\\mathrm{AS}(C_\\text{in}^{(2)}\\rightarrow32, 5, 4, 2)$ & $\\mathrm{AS}(C_\\text{in}^{(3)}\\rightarrow32, 5, 4, 2)$ \\\\\n            $\\mathrm{AS}(32\\rightarrow128, 5, 4, 2$) & $\\mathrm{AS}(32\\rightarrow128, 5, 4, 2$) & $\\mathrm{AS}(32\\rightarrow128, 3, 2, 1$) \\\\\n            {[pool support dims.]} & & \\\\\n            {[upsample query dims.]} & & \\\\\n            \\multicolumn{2}{c}{ {[element-wise addition]} } & \\\\\n            \\multicolumn{2}{c}{ $\\mathrm{AS}(128\\rightarrow128, 1, 1, 0)$ } & \\\\\n            \\multicolumn{2}{c}{ $\\mathrm{AS}(128\\rightarrow128, 2, 1, 0)$ } & \\\\\n            \\multicolumn{2}{c}{ {[upsample query dims.]} } \\\\\n            & \\multicolumn{2}{c}{ {[element-wise addition]} } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{AS}(128\\rightarrow128, 1, 1, 0)$ } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{AS}(128\\rightarrow128, 2, 1, 0)$ } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{conv}(128\\rightarrow128, 3, 1, 1)$ } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{ReLU}$ } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{conv}(128\\rightarrow64, 3, 1, 1)$ } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{ReLU}$ } \\\\\n            & \\multicolumn{2}{c}{ {[upsample query dims.]} } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{conv}(64\\rightarrow64, 3, 1, 1)$ } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{ReLU}$ } \\\\\n            & \\multicolumn{2}{c}{ $\\mathrm{conv}(64\\rightarrow2, 3, 1, 1)$ } \\\\\n            & \\multicolumn{2}{c}{ {[interpolate query dims. to the input size]} } \\\\\n            \\bottomrule\n        \\end{tabular}\n    }  \n    \\caption{Comprehensive configuration of ASNet\\xspace of which overview is illustrated in Fig.~2 in the main paper.\n    The top of the table is the input of the model and the detailed architecture of the model below it.\n    $\\mathrm{AS}(C_{\\text{in}} \\rightarrow C_{\\text{out}}, k, s, p)$ denotes an AS\\xspace layer of the kernel size ($k$), stride ($s$), padding size ($p$) for the convolutional embedding with the input channel ($C_{\\text{in}}$) and output channel~($C_{\\text{out}}$). \\label{table:asnet}\n    }\n\\end{table}\n\n\n\n\n\\subsection{Further analyses}\nIn this subsection we provide supplementary analyses on the iFSL\\xspace framework and ASNet\\xspace.\nAll experimental results are obtained using ResNet50 on Pascal-$5^{i}$ and evaluated with 1-way 1-shot episodes unless specified otherwise.\n\n\\begin{figure}[t!]\n\t\\centering\n\t\\small\n    \\includegraphics[width=0.9\\linewidth]{supp\/fig\/cls_thr.pdf}\n\t\\caption{Classification threshold $\\delta$ and its effects.\n    }\n\\label{fig:cls_thr}\n\\vspace{-3mm}\n\\end{figure}\n\n\n\\smallbreakparagraph{The classification occurrence threshold $\\delta$.}\nEquation~2 in the main paper describes the process of detecting object classes on the shared foreground map by thresholding the highest foreground probability response on each foreground map.\nAs the foreground probability is bounded from 0 to 1, we set the threshold $\\delta=0.5$ for simplicity.\nA high threshold value makes a classifier reject insufficient probabilities as class presences.\nFigure~\\ref{fig:cls_thr} shows the classification 0\/1 exact ratios by varying the threshold, which reaches the highest classification performance around $\\delta=0.5$ and $0.6$.\nFine-tuning the threshold for the best classification performance is not the focus of this work, thus we opt for the most straightforward threshold $\\delta=0.5$ for all experiments.\n\n\n\n\n\\begin{figure}[t!]\n\t\\centering\n\t\\small\n\t\\includegraphics[width=0.99\\linewidth]{supp\/fig\/bg.pdf}\n\t\\caption{Visualization of background map for each support class and the merged background map $\\mathbf{Y}_{\\text{bg}}$ for the query.\n\tHigh background response is illustrated in black.\n\t}\n\\label{fig:bg}\n\\vspace{-3mm}\n\\end{figure}\n\n\\smallbreakparagraph{Visualization of $\\mathbf{Y}_{\\text{bg}}$.}\nFigure~\\ref{fig:bg} visually demonstrates the background merging step of iFSL\\xspace in Eq.~(3) in the main paper.\nThe background maps are taken from the 2-way 1-shot episodes.\nThe background response of the negative class is relatively even, \\ie, the majority of pixels are estimated as background, whereas the background response of the positive class highly contributes to the merged background map.\n\n\n\n\n\n\\input{supp\/table\/clsplussegloss}\n\n\\input{supp\/table\/ipa101}\n\n\n\n\\smallbreakparagraph{iFSL\\xspace with weak labels, strong labels, and both.}\n\\tableref{table:clsplussegloss} compares FS-CS\\xspace performances of three ASNets each of which trained with the classification loss (Eq.~(6) in the main paper), the segmentation loss (Eq.~(7) in the main paper), or both.\nThe loss is chosen upon the level of supervisions on support sets; classification tags (weak labels) or segmentation annotations (strong labels).\nWe observe that neither the classification nor segmentation performances deviate significantly between $\\mathcal{L}_{\\text{S}}$ and $\\mathcal{L}_{\\text{C}} + \\mathcal{L}_{\\text{S}}$;\ntheir performances are not even 0.3\\%p different.\nAs a segmentation annotation is a dense form of classification tags, thus the classification loss influences insignificantly when the segmentation loss is used for training.\nWe thus choose to use the segmentation loss exclusively in the presence of segmentation annotations.\n\n\n\n\n\\subsection{Additional results}\nHere we provide several extra experimental results that are omitted in the main paper due to the lack of space.\nThe contents include results using other backbone networks, another evaluation metric, and $K$ shots where $K > 1$.\n\n\n\n\\smallbreakparagraph{iFSL\\xspace on FS-CS\\xspace using ResNet101.}\nWe include the FS-CS\\xspace results of the iFSL\\xspace framework on Pascal-$5^{i}$ using ResNet101~\\cite{resnet} in \\tableref{table:ipa101}, which is missing in the main paper due to the page limit.  \nAll other experimental setups are matched with those of Table~1 in the main paper except for the backbone network.\nASNet\\xspace also shows greater performances than the previous methods on both classification and segmentation tasks with another backbone.\n\n\n\n\\input{supp\/table\/acc}\n\\smallbreakparagraph{FS-CS\\xspace classification metrics: 0\/1 exact ratio and accuracy.}\n\\tableref{table:ipa50_acc} presents the results of two classification evaluation metrics of FS-CS\\xspace: 0\/1 exact ratio~\\cite{durand2019learning} and classification accuracy.\nThe classification accuracy metric takes the average of correct predictions for each class for each query, while 0\/1 exact ratio measures the binary correctness for all classes for each query, thus being stricter than the accuracy; the exact formulations are in Sec.~6.1. of the main paper.\nASNet\\xspace shows higher classification performance in both classification metrics than others.\n\n\\input{supp\/table\/ipa50_5shot}\n\\input{supp\/table\/ipa101_5shot}\n\n\n\n\\smallbreakparagraph{iFSL\\xspace on 5-shot FS-CS\\xspace.}\nTables~\\ref{table:ipa50_5shot} and \\ref{table:ipa101_5shot} compares four different methods on the 1-way 5-shot and 2-way 5-shot FS-CS\\xspace setups, which are missing in the main paper due to the page limit.\nAll other experimental setups are matched with those of Table~1 in the main paper except for the number of support samples for each class, \\ie, varying $K$ shots.\nASNet\\xspace also outperforms other methods on the multi-shot setups.\n\n\n\n\n\n\n\n\\input{supp\/table\/fpavgg}\n\n\n\\input{supp\/table\/multiway}\n\n\n\\smallbreakparagraph{ASNet\\xspace on FS-S\\xspace using VGG-16.}\n\\tableref{table:fpavgg} compares the recent state-of-the-art methods and ASNet\\xspace on FS-S\\xspace using VGG-16~\\cite{vgg}.\nWe train and evaluate ASNet\\xspace with the FS-S\\xspace problem setup to fairly compare with the recent methods.\nAll the other experimental variables are detailed in Sec.~6.3. and Table~3 of the main paper.\nASNet\\xspace consistently shows outstanding performances using the VGG-16 backbone network as observed in experimnets using ResNets.\n\n\n\n\n\\begin{figure*}[t!]\n\t\\centering\n\t\\small\n\t\\includegraphics[width=\\linewidth]{supp\/fig\/2way_extra_coco_v1.pdf}\n\t\\caption{2-way 1-shot FS-CS\\xspace segmentation prediction maps on the COCO-$20^{i}$ benchmark.}\n\\label{fig:2way_extra_coco}\n\\end{figure*}\n\n\n\\smallbreakparagraph{Qualitative results.}\nWe attach additional segmentation predictions of ASNet\\xspace learned with the iFSL\\xspace framework on the FS-CS\\xspace task in \\figref{fig:2way_extra_coco}.\nWe observe that ASNet\\xspace successfully predicts segmentation maps at challenging scenarios in the wild such as a) segmenting tiny objects, b) segmenting non-salient objects, c) segmenting multiple objects, and d) segmenting a query given a small support object annotation.\n\n\n\n\n\n\n\\begin{figure*}[t!]\n\t\\centering\n\t\\small\n\t\\includegraphics[width=0.80\\linewidth]{supp\/fig\/fssfscs.pdf}\n\t\\caption{2-way 1-shot FS-CS\\xspace segmentation prediction maps of $\\text{ASNet}_{\\text{FS-S\\xspace}}$ and $\\text{ASNet}_{\\text{FS-CS\\xspace}}$.}\n\\label{fig:fssfcss}\n\\end{figure*}\n\n\n\\smallbreakparagraph{Qualitative results of $\\text{ASNet}_{\\text{FS-S\\xspace}}$.}\nFigure~\\ref{fig:fssfcss} visualizes typical failure cases of the $\\text{ASNet}_{\\text{FS-S\\xspace}}$ model in comparison with $\\text{ASNet}_{\\text{FS-CS\\xspace}}$; these examples qualitatively show the severe performance drop of $\\text{ASNet}_{\\text{FS-S\\xspace}}$ on FS-CS\\xspace, which is quantitatively presented in Fig.~5~(b) of the main paper.\nSharing the same architecture of ASNet\\xspace, each model is trained on either FS-S\\xspace or FS-CS\\xspace setup and evaluated on the 2-way 1-shot FS-CS\\xspace setup.\nThe results demonstrate that $\\text{ASNet}_{\\text{FS-S\\xspace}}$ is unaware of object classes and gives foreground predictions on any existing objects, whereas $\\text{ASNet}_{\\text{FS-CS\\xspace}}$ effectively distinguishes the object classes based on the support classes and produces clean and adequate segmentation maps.\n\n\n\n\n\n\n\\input{supp\/table\/ico50_foldwise}\n\\input{supp\/table\/fco50_foldwise}\n\\smallbreakparagraph{Fold-wise results on COCO-$\\mathbf{20^{i}}$.}\nTables~\\ref{table:ico50_foldwise} and \\ref{table:fco50_foldwise} present fold-wise performance comparison on the FS-CS\\xspace and FS-S\\xspace tasks, respectively.\nWe validate that ASNet\\xspace outperforms the competitors by large margins in both the FS-CS\\xspace and FS-S\\xspace tasks on the challenging COCO-$20^{i}$ benchmark.\n\n\n\n\n\n\\smallbreakparagraph{Numerical performances of Fig.~4 in the main paper.}\nWe report the numerical performances of the Fig.~4 in the main paper in \\tableref{table:multiway} as a reference for following research.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nDealing with nonlinear phenomena has become one of the predominant issues for mechanical engineers, in the objective of virtual testing. Whether they are geometrical or related to the material behavior, nonlinearities can be treated by a combination of Newton and linear solvers. Newton algorithms can be modified, secant, quasi-Newton \\cite{crisfield1979faster,deuflhard1975relaxation,dennis1977quasi,zhang1982modified}, depending mostly on the complexity of tangent operators computation. If the meshed structure has a large number of degrees of freedom, linear solvers are chosen to be iterative and parallel, belonging to the class of Domain Decomposition Methods for instance \\cite{mandel1993balancing,le1994domain,rixen1999simple,farhat2001feti,gosselet2006non}.\n\nThis article focuses on the nonlinear substructuring and condensation method, which has been investigated in previous studies \\cite{cresta2007nonlinear,pebrel2008nonlinear,bordeu2009balancing,negrello2016substructured}. The substructured formulation involves a choice of interface transmission conditions, which can be either primal, dual or mixed, referring either to interface displacements, nodal interface reactions, or a linear combination of the two previous types -- i.e. Robin interface conditions. In this context, the mixed formulation has shown good efficiency \\cite{cresta2008decomposition,pebrel2009etude,hinojosa2014domain,negrello2016substructured}, mostly due to a sound choice of the parameter introduced in the linear combination of interface conditions. Being homogeneous to a stiffness, and often refered to as an \\textit{interface impedance}, this parameter can indeed be optimized, depending on the mechanical problem \\cite{lions1990schwarz}. However, the computational cost of the optimal value involves in general storage and manipulation of global matrices, and is consequently not affordable in the framework of parallel computations. \n\nThe interface impedance, in DDM methods for structural mechanics, should model, from the point of view of one  substructure, its interactions with the complement of the whole structure. In order to achieve good convergence rates without degrading computational speed, interface impedance can generally be approximated either by \\textit{short scale} or \\textit{long scale} formulations, depending on the predominant phenomena which must be accounted for. In the mechanical context, for instance, a common \\textit{short scale} approximation can be built by assembling interface stiffness of the neighbors \\cite{cresta2008decomposition, pebrel2009etude, hinojosa2014domain, negrello2016substructured}.\n \nHowever, filtering long range interactions gives quite a coarse approximation of interface impedance, and does not give an accurate representation of the environment of each substructure. A good evaluation of the remainder of the structure should indeed couple these two strategies. Starting from this consideration, we propose here a new construction process of the interface impedance, based on a ``spring in series'' modeling of the structure, which couples the \\textit{long} and \\textit{short} range interactions with the structure. The heuristic we develop is strongly influenced by the availability of the various terms involved in our approximation. \n\nThe first section of this paper introduces the reference (mechanical or thermal) problem and the notations used in the following. A succinct presentation of the nonlinear substructuring and condensation method then recalls the principles of its mixed formulation: how the interface nonlinear condensed problem is built from nonlinear local equilibriums, and the basics of the whole solving process, involving a global Newton algorithm combined with two internal solvers (parallel local Newton algorithms and a multi-scale linear preconditioned Krylov solver for tangent interface system). At Section~\\ref{sec:new_heuristic}, the question of finding a relevant Robin parameter for mixed interface conditions is developed, mainly based on the observation that for each substructure, the optimal interface impedance is the nonlinear discretized \\textit{Dirichlet-to-Neumann} operator of its complementary part. The new heuristic is then introduced, starting from the model of two springs in series, and a possible nonlinear multi-scale interpretation is given. The details of the two-scale approximation can be found at subsection \\ref{ssec:two_scale}, its efficiency is evaluated at last section on several academic numerical examples.\n\n\\section{Reference problem, notations}\n\n\\subsection{Global nonlinear problem}\n\nWe consider here a nonlinear partial differential equation on a domain $\\Omega$, representative of a structural mechanical or thermal problem, with Dirichlet conditions on the part $\\partial \\Omega_u \\neq \\varnothing$ of its boundary, and Neumann conditions on the complementary part $\\partial \\Omega_F$. After discretization with the Finite Element method, the problem to be solved reads:\n\\begin{equation}\\label{eq:nl_problem}\nf_{int}(u) + f_{ext} = 0\n\\end{equation}\nVector $f_{ext}$ takes into account boundary conditions (Dirichlet or Neumann) and dead loads, operator $f_{int}$ refers to the discretization of homogeneous partial differential equation.\n\n\\begin{remark} In linear elasticity, under the small perturbations hypothesis, one has:\n\\begin{equation*}\nf_{int}(u) = -Ku\n\\end{equation*}\nwith $K$ the stiffness matrix of the structure.\n\\end{remark}\n\n\\subsection{Substructuring}\n\nClassical DDM notations will be used -- see figure \\ref{fig:notations}: global domain $\\Omega$ is partitioned into $N_s$ subdomains $\\Omega\\ensuremath{^{(s)}}$. For each subdomain, a trace operator $t\\ensuremath{^{(s)}}$ restricts local quantities $x\\ensuremath{^{(s)}}$ defined on $\\Omega\\ensuremath{^{(s)}}$ to boundary quantities $x\\ensuremath{^{(s)}}_b$ defined on $\\Gamma\\ensuremath{^{(s)}} \\equiv \\partial \\Omega\\ensuremath{^{(s)}} \\backslash \\partial \\Omega$:\n\\begin{equation*}\nx\\ensuremath{^{(s)}}_b = t\\ensuremath{^{(s)}} u\\ensuremath{^{(s)}} = x\\ensuremath{^{(s)}}_{\\vert \\Gamma\\ensuremath{^{(s)}}}\n\\end{equation*}\nQuantities defined on internal nodes (belonging to $\\Omega\\ensuremath{^{(s)}} \\backslash \\Gamma\\ensuremath{^{(s)}}$) are written with subscript $i$:  $x\\ensuremath{^{(s)}}_i$.\n\nGlobal primal (resp. dual) interface are noted $\\Gamma_A$ (resp $\\Gamma_B$).\nPrimal assembly operators $A\\ensuremath{^{(s)}}$ are defined as canonical prolongation operators from $\\Gamma\\ensuremath{^{(s)}}$ to $\\Gamma_A$: $A\\ensuremath{^{(s)}}$ is a full-ranked boolean matrix of size $n_A \\times n_b\\ensuremath{^{(s)}}$ - where $n_A$ is the size of global primal interface $\\Gamma_A$ and $n_b\\ensuremath{^{(s)}}$ the number of boundary degrees of freedom belonging to subdomain $\\Omega\\ensuremath{^{(s)}}$. \n\\begin{figure}[ht]\n\\begin{center}\n\\hspace{-0.5cm}\\subfloat[Subdomains]{\\includegraphics[width=4cm]{graph_2a.pdf}}\n\\subfloat[Local interface]{\\includegraphics[width=4cm]{graph_2b.pdf}}\n\\subfloat[Interface nodes]{\\includegraphics[width=3.5cm]{graph_2c.pdf}}\n\\subfloat[Interface connexions]{\\includegraphics[width=3.5cm]{graph_2d.pdf}}\n\n\\hspace{-0.75cm}\\subfloat{\\includegraphics[width=14.5cm]{matrices.pdf}}\n\\end{center}\n\\caption{Local numberings, interface numberings, trace and assembly operators}\n\\label{fig:notations}\n\\end{figure}\n\nDiamond notations are used in the following: for a  domain $\\Omega$ substructured in $N_s$ subdomains $\\left( \\Omega\\ensuremath{^{(s)}} \\right)$, concatenated local variables are superscripted $\\ensuremath{^{\\diamondvert}}$, $\\ensuremath{^{\\diamondminus}}$ or $\\ensuremath{^{\\diamondbackslash}}$, depending on the alignment.\n\\begin{equation*}\n\\begin{aligned}\nx\\ensuremath{^{\\diamondvert}} = & \\begin{pmatrix} \nx^{(1)} \\\\\n\\vdots \\\\\n x^{(N_{s})} \\end{pmatrix},\\qquad x\\ensuremath{^{\\diamondminus}} = \\begin{pmatrix}\n{x^{(1)}} \\, \\ldots \\, {x^{(N_{s})}} \\end{pmatrix},\\qquad\n M\\ensuremath{^{\\diamondbackslash}} = \\begin{pmatrix} \nM^{(1)} & 0   & 0 \\\\\n0 & \\ddots &  0  \\\\\n0 & 0  & M^{(N_{s})} \\\\\n\\end{pmatrix} \\\\\n\\end{aligned}\n\\end{equation*}\nAny matrix $B\\ensuremath{^{(s)}}$ satisfying $\\text{Range}(B\\ensuremath{^{\\diamondminus^T}}) = \\text{Ker}(A\\ensuremath{^{\\diamondminus}})$ can be assigned to dual assembly operator -- see figure~\\ref{fig:notations} for the most classical choice. \n\n\n\\section{Nonlinear substructuring and condensation: mixed formulation} \n\nThis section recalls the principle of nonlinear substructuring and condensation, which is explained in details in \\cite{negrello2016substructured}.\n\n\\subsection{Formulation of the condensed problem}\n\n Nonlinear problem \\eqref{eq:nl_problem} is decomposed into $N_s$ nonlinear subproblems:\n\\begin{equation*}\nf_{int}\\ensuremath{^{\\diamondvert}}(u\\ensuremath{^{\\diamondvert}}) + f_{ext}\\ensuremath{^{\\diamondvert}} + t\\ensuremath{^{\\diamondbackslash^T}} \\lambda\\ensuremath{^{\\diamondvert}}_b = 0\\ensuremath{^{\\diamondvert}}\n\\end{equation*}\nwhere $\\lambda\\ensuremath{^{(s)}}_b$ is the unknown local interface nodal reaction, introduced to represent interactions of the subdomain $\\Omega\\ensuremath{^{(s)}}$ with neighboring subdomains.\n\nTransmission conditions hold:\n\\begin{equation*}\n\\left\\lbrace \\begin{aligned}\nB\\ensuremath{^{\\diamondminus}} u\\ensuremath{^{\\diamondvert}}_b = 0 \\\\\nA\\ensuremath{^{\\diamondminus}} \\lambda\\ensuremath{^{\\diamondvert}}_b = 0\n\\end{aligned} \\right.\n\\end{equation*}\n\nThe mixed formulation consists in introducing a new interface unknown:\n\\begin{equation*}\n\\mu\\ensuremath{^{\\diamondvert}}_b = \\lambda\\ensuremath{^{\\diamondvert}}_b + Q\\ensuremath{^{\\diamondbackslash}}_b u\\ensuremath{^{\\diamondvert}}_b\n\\end{equation*}\nwhere the matrix $Q\\ensuremath{^{\\diamondbackslash}}_b$ is a parameter of the method. It has to be symmetric positive definite, and can be interpreted as a stiffness added to the interface, per subdomain: $Q\\ensuremath{^{\\diamondbackslash}}_b$ is called \\textit{interface impedance}. \\medskip\n\nLocal equilibriums can then be reformulated as:\n\\begin{equation}\\label{eq:local_eq}\nf_{int}\\ensuremath{^{\\diamondvert}}(u\\ensuremath{^{\\diamondvert}}) + f_{ext}\\ensuremath{^{\\diamondvert}} + t\\ensuremath{^{\\diamondbackslash^T}} \\left( \\mu_b\\ensuremath{^{\\diamondvert}} - Q\\ensuremath{^{\\diamondbackslash}}_b u\\ensuremath{^{\\diamondvert}}_b \\right) = 0\n\\end{equation}\nWe assume the existence, at least locally, of a nonlinear mixed analogue $H\\ensuremath{^{\\diamondvert}}_{nl}$ of the Schur complement (ie. a discrete Robin-to-Dirichlet operator):\n\\begin{equation}\\label{eq:local_eq_H}\nu\\ensuremath{^{\\diamondvert}}_b = H\\ensuremath{^{\\diamondvert}}_{nl}\\left( \\mu\\ensuremath{^{\\diamondvert}}_b; Q\\ensuremath{^{\\diamondbackslash}}_b, f\\ensuremath{^{\\diamondvert}}_{ext} \\right)\n\\end{equation}\n\\begin{prop} The tangent operator~$H\\ensuremath{^{\\diamondbackslash}}_{t}$ to~$H\\ensuremath{^{\\diamondvert}}_{nl}$ can be explicitly computed in function of the tangent stiffness~$K\\ensuremath{^{\\diamondbackslash}}_t$:\n\\begin{equation*}\n\\begin{aligned}\n H\\ensuremath{^{\\diamondbackslash}}_t = \\frac{\\partial H\\ensuremath{^{\\diamondvert}}_{nl}}{\\partial \\mu\\ensuremath{^{\\diamondvert}}_b} = t\\ensuremath{^{\\diamondbackslash}} \\left( K_t\\ensuremath{^{\\diamondbackslash}} + t\\ensuremath{^{\\diamondbackslash^T}} Q\\ensuremath{^{\\diamondbackslash}}_b t\\ensuremath{^{\\diamondbackslash}} \\right)^{-1} t\\ensuremath{^{\\diamondbackslash^T}} \\\\\n\\end{aligned}\n\\end{equation*}\nMoreover, in the linear case, the Robin-to-Dirichlet operator written $H\\ensuremath{^{\\diamondvert}}_{l}$ is  affine, with the constant term associated with external forces:\n\\begin{equation*}\n\\begin{aligned}\n& H\\ensuremath{^{\\diamondvert}}_l \\left( \\mu\\ensuremath{^{\\diamondvert}}_b; Q\\ensuremath{^{\\diamondbackslash}}_b, f\\ensuremath{^{\\diamondvert}}_{ext} \\right) = H\\ensuremath{^{\\diamondbackslash}}_t \\mu\\ensuremath{^{\\diamondvert}}_b + b\\ensuremath{^{\\diamondvert}}_m \\\\\n\\text{with }& b\\ensuremath{^{\\diamondvert}}_m = t\\ensuremath{^{\\diamondbackslash}} \\left( K\\ensuremath{^{\\diamondbackslash}} + t\\ensuremath{^{\\diamondbackslash^T}} Q\\ensuremath{^{\\diamondbackslash}}_b t\\ensuremath{^{\\diamondbackslash}} \\right)^{-1} f\\ensuremath{^{\\diamondvert}}_{ext}\n\\end{aligned}\n\\end{equation*}\n\\end{prop}\n\n\\begin{remark} \nFor the upcoming discussion, we will make use of the nonlinear primal Schur complement (Dirichlet-to-Neumann, noted $S_{nl}\\ensuremath{^{(s)}}$) which is such that $\\lambda_b\\ensuremath{^{(s)}}=S_{nl}\\ensuremath{^{(s)}}(u_b\\ensuremath{^{(s)}};f_{ext}\\ensuremath{^{(s)}})$. The tangent primal Schur complement can be computed from the tangent stiffness matrix:\n\\begin{equation*}\nS_t\\ensuremath{^{(s)}}=K\\ensuremath{^{(s)}}_{t_{bb}}-K\\ensuremath{^{(s)}}_{t_{bi}}{K\\ensuremath{^{(s)}}_{t_{ii}}}^{-1}K\\ensuremath{^{(s)}}_{t_{ib}}\n\\end{equation*}\nand we have $H_t\\ensuremath{^{\\diamondbackslash}} = (S\\ensuremath{^{\\diamondbackslash}}_t + Q\\ensuremath{^{\\diamondbackslash}}_b)^{-1}$. Note that the tangent dual Schur complement (Neumann-to-Dirichlet) can be written as ${S_t\\ensuremath{^{(s)}}}^{\\dagger} = t\\ensuremath{^{(s)}}{K_t\\ensuremath{^{(s)}}}^{\\dagger}{t\\ensuremath{^{(s)}}}^T$. In the linear case, the primal Schur complement is an affine operator with the constant term due to the external load:\n\\begin{equation*}\n\\begin{aligned}\n& S\\ensuremath{^{\\diamondvert}}_l \\left( u\\ensuremath{^{\\diamondvert}}_b; f\\ensuremath{^{\\diamondvert}}_{ext} \\right) = S\\ensuremath{^{\\diamondbackslash}}_t u\\ensuremath{^{\\diamondvert}}_b + b\\ensuremath{^{\\diamondvert}}_p \\\\\n\\text{with }& b\\ensuremath{^{\\diamondvert}}_p = f_{ext_b}\\ensuremath{^{\\diamondvert}} - K\\ensuremath{^{(s)}}_{t_{bi}}{K\\ensuremath{^{(s)}}_{t_{ii}}}^{-1}f_{ext_i}\\ensuremath{^{\\diamondvert}} = (S_t\\ensuremath{^{\\diamondbackslash}}+Q_b\\ensuremath{^{\\diamondbackslash}})b_m\\ensuremath{^{\\diamondvert}}\n\\end{aligned}\n\\end{equation*}\n\\end{remark}\n\nThanks to the  complementarity between balanced and continuous quantities, and to the symmetry positive definiteness of $Q\\ensuremath{^{\\diamondbackslash}}_b$, any boundary displacement (defined independently on neighboring subdomains) can be split in a unique way into a continuous field belonging to $\\text{Ker}\\left( B\\ensuremath{^{\\diamondminus}} \\right)$ and a balanced field belonging to $\\text{Ker}\\left( A\\ensuremath{^{\\diamondminus}} Q\\ensuremath{^{\\diamondbackslash}}_b \\right)$. Thus, the transmission conditions can be written in terms of $\\mu\\ensuremath{^{\\diamondvert}}_b$ and $u\\ensuremath{^{\\diamondvert}}_b$, and gathered in a single equation:\n\\begin{equation*}\nA\\ensuremath{^{\\diamondminus^T}} \\left( A\\ensuremath{^{\\diamondminus}} Q\\ensuremath{^{\\diamondbackslash}}_b A\\ensuremath{^{\\diamondminus^T}} \\right)^{-1} A\\ensuremath{^{\\diamondminus}} \\mu\\ensuremath{^{\\diamondvert}}_b - u\\ensuremath{^{\\diamondvert}}_b = 0\n\\end{equation*}\n\nFinally, interface condensed problem reads:\n\\begin{equation}\\label{eq:interf_pb}\nR\\ensuremath{^{\\diamondvert}}_b(\\mu_b\\ensuremath{^{\\diamondvert}}) \\equiv A\\ensuremath{^{\\diamondminus^T}} \\left( A\\ensuremath{^{\\diamondminus}} Q\\ensuremath{^{\\diamondbackslash}}_b A\\ensuremath{^{\\diamondminus^T}} \\right)^{-1} A\\ensuremath{^{\\diamondminus}} \\mu\\ensuremath{^{\\diamondvert}}_b - H\\ensuremath{^{\\diamondvert}}_{nl} \\left( \\mu\\ensuremath{^{\\diamondvert}}_b; Q\\ensuremath{^{\\diamondbackslash}}_b, f\\ensuremath{^{\\diamondvert}}_{ext} \\right) = 0\n\\end{equation} \n\n\\subsection{Solving strategy}\n\n\\subsubsection{Newton-Krylov algorithm}\n\nNonlinear substructuring and condensation results in applying a global Newton algorithm to interface problem \\eqref{eq:interf_pb} instead of problem \\eqref{eq:nl_problem}. Three steps are then involved in the solving process:\n\\begin{enumerate}[label=(\\roman*)]\n\\item Local solutions of nonlinear equilibriums \\eqref{eq:local_eq} are computed by applying local Newton algorithms.\n\\item The interface mixed residual is assembled.\n\\item The interface tangent problem is solved by a DDM solver.\n\\end{enumerate}\nNewton global algorithm can be written, with previous notations:\n\\begin{equation*}\n\\left\\lbrace \\begin{aligned}\n&\\frac{\\partial R\\ensuremath{^{\\diamondvert}}_b}{\\partial \\mu_b\\ensuremath{^{\\diamondvert}}} d\\mu\\ensuremath{^{\\diamondvert}}_b + R\\ensuremath{^{\\diamondvert}}_b = 0 \\\\\n&\\mu\\ensuremath{^{\\diamondvert}}_b  += d\\mu\\ensuremath{^{\\diamondvert}}_b\n\\end{aligned} \\right.\n\\end{equation*}\nTangent problem then reads:\n\\begin{equation}\\label{eq:tg_pb}\n\\left( A\\ensuremath{^{\\diamondminus^T}} \\left( A\\ensuremath{^{\\diamondminus}} Q\\ensuremath{^{\\diamondbackslash}}_b A\\ensuremath{^{\\diamondminus^T}} \\right)^{-1} A\\ensuremath{^{\\diamondminus}} - H\\ensuremath{^{\\diamondbackslash}}_t \\right) d\\mu\\ensuremath{^{\\diamondvert}}_b = H\\ensuremath{^{\\diamondvert}}_{nl} \\left( \\mu\\ensuremath{^{\\diamondvert}}_b, Q\\ensuremath{^{\\diamondbackslash}}_b, f\\ensuremath{^{\\diamondvert}}_{ext} \\right) - A\\ensuremath{^{\\diamondminus^T}} \\left( A\\ensuremath{^{\\diamondminus}} Q\\ensuremath{^{\\diamondbackslash}}_b A\\ensuremath{^{\\diamondminus^T}} \\right)^{-1} A\\ensuremath{^{\\diamondminus}} \\mu\\ensuremath{^{\\diamondvert}}_b\n\\end{equation}\n\n\\subsubsection{Alternative formulation}\\label{sec:altern_formul}\nTangent problem \\eqref{eq:tg_pb} could be treated by a FETI-2LM solver \\cite{roux2009feti}. An equivalent formulation of problem \\eqref{eq:interf_pb} is also possible, where the boundary interface unknown $\\mu\\ensuremath{^{\\diamondvert}}_b$ is replaced by a couple of interface unknowns $\\left( f_B, v_A \\right)$, $f_B$ being a nodal reaction and $v_A$ an interface displacement. Couple $\\left( f_B, v_A \\right)$ is made unique by imposing the three following conditions:\n\\begin{itemize}[label=$\\circ$]\n\\item $f_B$ is balanced\n\\item $v_A$ is continuous \n\\item $\\mu\\ensuremath{^{\\diamondvert}}_b = B\\ensuremath{^{\\diamondminus^T}} f_B + Q\\ensuremath{^{\\diamondbackslash}}_b A\\ensuremath{^{\\diamondminus^T}} v_A$\n\\end{itemize}\nWith this formulation, tangent problem is expressed by:\n\\begin{equation}\\label{eq:pb_tg2}\n\\begin{aligned}\n&\\left(A\\ensuremath{^{\\diamondminus}} S\\ensuremath{^{\\diamondbackslash}}_t A\\ensuremath{^{\\diamondminus^T}}\\right) dv_A  = A\\ensuremath{^{\\diamondminus}} \\left( Q\\ensuremath{^{\\diamondbackslash}}_b + S\\ensuremath{^{\\diamondbackslash}}_t \\right) b\\ensuremath{^{\\diamondvert}}_m \\\\\n\\text{with }&b\\ensuremath{^{\\diamondvert}}_m = H\\ensuremath{^{\\diamondvert}}_{nl} \\left( \\mu\\ensuremath{^{\\diamondvert}}_b; Q\\ensuremath{^{\\diamondbackslash}}_b, f\\ensuremath{^{\\diamondvert}}_{ext} \\right) - A\\ensuremath{^{\\diamondminus^T}} v_A\n\\end{aligned}\n\\end{equation}\nEquation \\eqref{eq:pb_tg2} has the exact form of a BDD \\cite{mandel1993balancing} problem. It can thus conveniently be solved with usual preconditioner and coarse problem. The following quantities can then be deduced:\n\\begin{equation}\\label{eq:recup_mu_u_lam}\n\\begin{aligned}\n& d\\mu_b\\ensuremath{^{\\diamondvert}} = S_t\\ensuremath{^{\\diamondbackslash}} A\\ensuremath{^{\\diamondminus^T}} dv_A - A\\ensuremath{^{\\diamondminus}} \\left( Q\\ensuremath{^{\\diamondbackslash}}_b + S_t\\ensuremath{^{\\diamondbackslash}} \\right) b_m\\ensuremath{^{\\diamondvert}} \\\\\n& du\\ensuremath{^{\\diamondvert}} = \\left( K_t\\ensuremath{^{\\diamondbackslash}} + t\\ensuremath{^{\\diamondbackslash^T}} Q_b\\ensuremath{^{\\diamondbackslash}} t\\ensuremath{^{\\diamondbackslash}} \\right)^{-1} t\\ensuremath{^{\\diamondbackslash^T}} \\left( A\\ensuremath{^{\\diamondminus}} \\left[ Q\\ensuremath{^{\\diamondbackslash}}_b + S_t\\ensuremath{^{\\diamondbackslash}} \\right] b_m\\ensuremath{^{\\diamondvert}} + d\\mu_b\\ensuremath{^{\\diamondvert}} \\right) \\\\\n& du_b\\ensuremath{^{\\diamondvert}} = t\\ensuremath{^{\\diamondbackslash}} du\\ensuremath{^{\\diamondvert}} \\\\\n& d\\lambda_b\\ensuremath{^{\\diamondvert}} = S_t\\ensuremath{^{\\diamondbackslash}} du_b\\ensuremath{^{\\diamondvert}} - A\\ensuremath{^{\\diamondminus}} \\left( Q\\ensuremath{^{\\diamondbackslash}}_b + S_t\\ensuremath{^{\\diamondbackslash}} \\right) b_m\\ensuremath{^{\\diamondvert}} = d\\mu_b\\ensuremath{^{\\diamondvert}} - Q\\ensuremath{^{\\diamondbackslash}}_b du_b\\ensuremath{^{\\diamondvert}}\n\\end{aligned}\n\\end{equation}\n\n\n\\subsubsection{Typical algorithm}\n\nAlgorithm~\\ref{alg:robin-bdd} sums up the main steps of the method with the mixed nonlinear local problems and primal tangent solver. For simplicity reasons, only one load increment was considered.\n\nAs can be seen in this algorithm, several convergence thresholds are needed:\n\\begin{itemize}\n\\item Global convergence criterion $\\varepsilon_{NG}$: since our approach is mixed, the criterion not only controls the quality of the subdomains balance (as in a standard Newton approach) but also the continuity of the interface displacement which is measured by an appropriate norm written $\\|\\cdot\\|_B$. \n\\item Local nonlinear thresholds $\\varepsilon_{NL}\\ensuremath{^{\\diamondvert}}$, which are associated with the Newton processes carried out independently on subdomains.\n\\item The global linear threshold of the domain decomposition (Krylov)  solver $\\varepsilon_{K}$ (here BDD). \n\\end{itemize}\nThe other parameters of the method are the initializations of the various iterative solvers and the choice of the impedance matrices $Q_b\\ensuremath{^{\\diamondbackslash}}$. \n\n\\begin{algorithm2e}[!ht]\n\\DontPrintSemicolon\n\\KwSty{Define:}\\;\n$r_{nl}^{m\\diamondvert}(u\\ensuremath{^{\\diamondvert}},\\mu_b\\ensuremath{^{\\diamondvert}}) = f_{int}\\ensuremath{^{\\diamondvert}}(u\\ensuremath{^{\\diamondvert}})-t\\ensuremath{^{\\diamondbackslash^T}} Q_b\\ensuremath{^{\\diamondbackslash}} t\\ensuremath{^{\\diamondbackslash}} u\\ensuremath{^{\\diamondvert}} + t\\ensuremath{^{\\diamondbackslash^T}} \\mu_b\\ensuremath{^{\\diamondvert}}+ f\\ensuremath{^{\\diamondvert}}_{ext}$\\;\n\\BlankLine\n\\KwSty{Initialization:}\\;\n$(u_0\\ensuremath{^{\\diamondvert}},\\lambda_{b_0}\\ensuremath{^{\\diamondvert}})$ such that $B\\ensuremath{^{\\diamondminus}} t\\ensuremath{^{\\diamondbackslash}} u_0\\ensuremath{^{\\diamondvert}}=0$ and $A\\ensuremath{^{\\diamondminus}} \\lambda_{b_0}\\ensuremath{^{\\diamondvert}}=0$\\;\n\\KwSty{Set} $k=0$\\;\n\\KwSty{Define} $\\mu_{b_k}\\ensuremath{^{\\diamondvert}}= \\lambda_{b_k}\\ensuremath{^{\\diamondvert}} + Q_b\\ensuremath{^{\\diamondbackslash}} t\\ensuremath{^{\\diamondbackslash}} u_k\\ensuremath{^{\\diamondvert}}$\\;\n\\While{$\\| r_{nl}^{m\\diamondvert}(u_k\\ensuremath{^{\\diamondvert}},\\mu_{b_k}\\ensuremath{^{\\diamondvert}})\\|+ \\| B\\ensuremath{^{\\diamondminus}} t\\ensuremath{^{\\diamondbackslash}} u\\ensuremath{^{\\diamondvert}}\\|_{B}>\\varepsilon_{NG}$ }{%\n  \\KwSty{Local nonlinear step}:  \\\n   \\KwSty{Set} $u_{k,0}\\ensuremath{^{\\diamondvert}}=u_{k}\\ensuremath{^{\\diamondvert}}$ and  $j=0$\\; \n  \\While{$\\| r_{nl}^{m\\diamondvert}(u_{k,j}\\ensuremath{^{\\diamondvert}},\\mu_{b_k}\\ensuremath{^{\\diamondvert}})\\|>\\varepsilon\\ensuremath{^{\\diamondvert}}_{NL}$}{\n    $u_{k,j+1}\\ensuremath{^{\\diamondvert}}=u_{k,j}\\ensuremath{^{\\diamondvert}}-\\left(K_{t_{k,j}}\\ensuremath{^{\\diamondbackslash}} + t\\ensuremath{^{\\diamondbackslash^T}} Q_b\\ensuremath{^{\\diamondbackslash}} t\\ensuremath{^{\\diamondbackslash}} \\right)^{-1} r_{nl}^{m\\diamondvert}( u_{k,j}\\ensuremath{^{\\diamondvert}}, \\mu_{b_k}\\ensuremath{^{\\diamondvert}})$ \\;\n    \\KwSty{Set} $j=j+1$\n  }\n  \\KwSty{Linear right-hand side}:\\;\n  $b_{m_k}\\ensuremath{^{\\diamondvert}} = A\\ensuremath{^{\\diamondminus^T}} \\left( A\\ensuremath{^{\\diamondminus}} Q_b\\ensuremath{^{\\diamondbackslash}} A\\ensuremath{^{\\diamondminus^T}} \\right)^{-1} A\\ensuremath{^{\\diamondminus}} \\mu_{b_k}\\ensuremath{^{\\diamondvert}} -t\\ensuremath{^{\\diamondbackslash}} u_{k,j}\\ensuremath{^{\\diamondvert}} $\\;\n  $b_{p_k}\\ensuremath{^{\\diamondvert}} = (S_{t_{k,j}}\\ensuremath{^{\\diamondbackslash}} + Q_b\\ensuremath{^{\\diamondbackslash}})b_{m_k}\\ensuremath{^{\\diamondvert}} $\\;\n  \\KwSty{Global linear step}:\\;\n  \\KwSty{Set} $dv_A^{0}=0$ and  $i=0$\\; \n  \\While{$\\|b\\ensuremath{^{\\diamondvert}}_{p_k}-\\left( A\\ensuremath{^{\\diamondminus}}\\; S_{t_{k,j}}\\ensuremath{^{\\diamondbackslash}} A\\ensuremath{^{\\diamondminus^T}} \\right) dv^i\\|>\\varepsilon_{K}$}{\n    Make BDD iterations (index $i$)\n  }\n  \\KwSty{Set} $u_{k+1}\\ensuremath{^{\\diamondvert}} = u_k\\ensuremath{^{\\diamondvert}} + du_k^{i\\diamondvert}$ and $  \\lambda_{b_{k+1}}\\ensuremath{^{\\diamondvert}} = \\lambda_{b_k}\\ensuremath{^{\\diamondvert}} + d\\lambda_{b_k}^{i\\diamondvert}$ using \\eqref{eq:recup_mu_u_lam}\\;\n  \\KwSty{Set} $k=k+1$\\;\n}\n\\caption{Mixed nonlinear approach with BDD tangent solver}\n\\label{alg:robin-bdd}\n\\end{algorithm2e}\n\n\n\n\\section{New heuristic for the interface impedance}\\label{sec:new_heuristic}\n\n\\subsection{Motivation}\\label{ssec:motivation}\n\n\nThe parameter $Q\\ensuremath{^{\\diamondbackslash}}_b$ is involved all along the solving, and a special care should be paid to its computation. \n\n\\medskip\n\nIn order to frame the ideas, let us consider the Robin-Robin algorithm with stationary iteration, in the nonlinear case, with nonlinear impedance. Starting from the initial guess $\\mu_b\\ensuremath{^{\\diamondvert}}=0$, we have the iterations of Algorithm~\\ref{alg:robin-robin}.\n\n\\SetNlSty{texttt}{(}{)}\n\\begin{algorithm2e}[ht]\n\t\\DontPrintSemicolon\n\\nl Parallel solve: $S_{nl}\\ensuremath{^{\\diamondvert}}(u_b\\ensuremath{^{\\diamondvert}};f\\ensuremath{^{\\diamondvert}}_{ext})+Q_{nl}\\ensuremath{^{\\diamondvert}}(u_b\\ensuremath{^{\\diamondvert}})= \\mu_b\\ensuremath{^{\\diamondvert}}$\\;\n\\nl Parallel post-processing: $\\lambda_b\\ensuremath{^{\\diamondvert}} = S_{nl}\\ensuremath{^{\\diamondvert}}(u_b\\ensuremath{^{\\diamondvert}};f\\ensuremath{^{\\diamondvert}}_{ext}) = \\mu_b\\ensuremath{^{\\diamondvert}}-Q_{nl}\\ensuremath{^{\\diamondvert}}(u_b\\ensuremath{^{\\diamondvert}})$\\;\n\\nl Assembly: $\\bar{u}_b\\ensuremath{^{\\diamondvert}} = A\\ensuremath{^{\\diamondminus^T}} \\tilde{A}\\ensuremath{^{\\diamondminus}} u_b\\ensuremath{^{\\diamondvert}}$, and $\\bar{\\lambda}_b\\ensuremath{^{\\diamondvert}} = \\left( I - \\tilde{A}\\ensuremath{^{\\diamondminus^T}} A\\ensuremath{^{\\diamondminus}} \\right) \\lambda_b\\ensuremath{^{\\diamondvert}}$\\;\n\\nl Parallel update of interface unknown: $\\mu_b\\ensuremath{^{\\diamondvert}} = Q_{nl}\\ensuremath{^{\\diamondvert}}(  \\bar{u}_b\\ensuremath{^{\\diamondvert}})  + \\bar{\\lambda}_b\\ensuremath{^{\\diamondvert}}$\\;\n\\caption{Robin-Robin stationary iteration}\n\\label{alg:robin-robin}\n\\end{algorithm2e}\t\n\n\\medskip\n\nAssembled quantities $\\bar{u}_b\\ensuremath{^{\\diamondvert}}$ and $\\bar{\\lambda}_b\\ensuremath{^{\\diamondvert}}$ are defined such that the interface conditions can be written as:\n\\begin{equation}\\label{eq:new_interf_cond}\nu_b\\ensuremath{^{\\diamondvert}}  = \\bar{u}_b\\ensuremath{^{\\diamondvert}} \\text{ and }\n\\lambda_b\\ensuremath{^{\\diamondvert}}  = \\bar{\\lambda}_b\\ensuremath{^{\\diamondvert}}\n\\end{equation}\nand we assume the nonlinear local operators $Q_{nl}\\ensuremath{^{\\diamondvert}}$ to be such that the equivalence between \\eqref{eq:new_interf_cond} and the following equation is ensured:\n\\begin{equation}\\label{eq:intQnl}\n\\left(Q_{nl}\\ensuremath{^{\\diamondvert}}(u_b\\ensuremath{^{\\diamondvert}}) - Q_{nl}\\ensuremath{^{\\diamondvert}}(\\bar{u}_b\\ensuremath{^{\\diamondvert}})\\right) + \\left(\\lambda_b\\ensuremath{^{\\diamondvert}}-\\bar{\\lambda}_b\\ensuremath{^{\\diamondvert}}\\right)=0\n\\end{equation}\n\n\nConsidering a given subdomain $\\Omega\\ensuremath{^{(j)}}$, and writing $\\Omega\\ensuremath{^{(\\overline{j})}}$ its complement, we can condense the whole problem on its interface; the boundary displacement $u_b\\ensuremath{^{(j)}}$ must then be the solution to:\n\\begin{equation*}\nS_{nl}\\ensuremath{^{(j)}}(u_b\\ensuremath{^{(j)}};f_{ext}\\ensuremath{^{(j)}}) + S_{nl}\\ensuremath{^{(\\overline{j})}}(u_b\\ensuremath{^{(j)}};f_{ext}\\ensuremath{^{(\\overline{j})}}) =0\n\\end{equation*}\nComparing this equation with line~(1) of algorithm~\\ref{alg:robin-robin}, one can see that, starting from a zero initial guess $\\mu_b\\ensuremath{^{(j)}}=0$, the method converges in only one iteration with $Q_{nl}\\ensuremath{^{(j)}} = S_{nl}\\ensuremath{^{(\\overline{j})}}$: the ideal impedance is the Dirichlet-to-Neumann operator of the complement. \\medskip\n\nIn order to further discuss the problem, we now consider the linear case, and we recall that we have:  $S_{l}\\ensuremath{^{(j)}}(u_b\\ensuremath{^{(j)}}) = S_{t}\\ensuremath{^{(\\overline{j})}} u_b\\ensuremath{^{(j)}} + b_p\\ensuremath{^{(\\overline{j})}}$. In that case, the optimal impedance is thus an affine operator whose linear part (which we will write $Q_b\\ensuremath{^{(j)}}$ in agreement with the development of previous section) accounts for the stiffness of the complement domain, whereas the constant part accounts for the external load on the complement part. Note that another point of view is to use a strictly linear impedance together with a good (non-zero) initialization for $\\mu_b\\ensuremath{^{\\diamondvert}}$ which should account for the external load on the complement domain.\n\nThe construction of a good constant part for the impedance is usually realized, in the linear case, by the introduction of a well-chosen coarse problem; this is discussed in subsection~\\ref{ssec:multi}. \nIn the nonlinear case, building a coarse problem which would connect all subdomains during their inner Newton loop seems complex; more, it would break the independent computations. It looks simpler to rely on a good initialization in order to propagate the right-hand side: this can be done at low cost by easing accuracy constraints in the first inner Newton loop (adapting $\\varepsilon_{NL}$), and then using the multiscale solver of the global linear step. Note that in \\cite{klawonn2017new} a coarse problem is built for nonlinear versions of FETIDP and BDDC but, again, it mainly serves to find a good initialization before independent parallel nonlinear solves.\n\nWe now focus on the construction of $Q_b\\ensuremath{^{\\diamondbackslash}}$, i.e. the linear part of the impedance. In the linear case,  one can show \\cite{magoules2004optimal,gander2011optimal} that for a slab-wise  decomposition of the structure (or a tree-like decomposition, i.e. whose connectivity graph has no cycles), the setting $Q_b\\ensuremath{^{(j)}} = S_t\\ensuremath{^{(\\overline{j})}}$ is optimal, in the sense that the convergence is reached in a maximum number of iterations equal to the number of subdomains (iterations are only needed to propagate the right-hand side). If the convenient coarse grid is added, convergence can be extremely fast. For an arbitrary decomposition, the optimality of such a setting can theoretically be lost, because of the unclear propagation rate of the right-hand side \\cite{nier1998remarques,gander2011optimal}. However, the pertinence of this value still seems to be ongoing, especially being given the difficulty to define a more relevant setting for a matrix operator $Q_t\\ensuremath{^{\\diamondbackslash}}$.\n\n\\medskip\n\n\nStarting from these considerations, let us further analyze the terms of the following expression of the interface impedance for a given subdomain $\\Omega\\ensuremath{^{(j)}}$:\n\\begin{equation}\\label{eq:opti_qb_lin}\nQ_t\\ensuremath{^{(j)}} = S_t\\ensuremath{^{(\\overline{j})}} = K_{bb}\\ensuremath{^{(\\overline{j})}} - K_{bi}\\ensuremath{^{(\\overline{j})}} K_{ii}\\ensuremath{^{(\\overline{j})^{-1}}} K_{ib}\\ensuremath{^{(\\overline{j})}}\n\\end{equation}\n\n\nThe first term, $ K\\ensuremath{^{(\\overline{j})}}_{bb}$, accounts for very local interactions. It is sparse, and exactly has the fill-in of matrix $K_{bb}\\ensuremath{^{(j)}}$. The second term, $K\\ensuremath{^{(\\overline{j})}}_{bi} {K\\ensuremath{^{(\\overline{j})}}_{ii}}^{-1} K\\ensuremath{^{(\\overline{j})}}_{ib}$, accounts for long range interactions, it depends on the whole structure (geometry and material), and couples all degrees of freedom together via in-depth interactions. It is thus a full matrix; this property can be seen as the consequence of the pseudo-differentiability of the underlying Steklov-Poincar\u00e9 operator of which the Schur complement is the discretization. It is important to note the minus sign: the short range part is very stiff and the global effects mitigate it. \n\nObviously, formula~\\eqref{eq:opti_qb_lin} is intractable in a distributed environment. However, different strategies have been investigated to compute  approximations at low cost -- see next subsection for a quick review.\n\n\\medskip\nIn the nonlinear context, the use of a linear impedance is of course non-optimal. Moreover, the best linear impedance probably resembles the Schur complement of the remainder of the subdomain in the final configuration, which is of course unknown a priori. Our aim is then to try to find a heuristic which gives an easy-to-compute approximation of the formula~\\eqref{eq:opti_qb_lin} to be applied to the initial tangent stiffness. \n\n\n\n\\subsection{Quick review}\\label{ssec:review}\n\nThe question of finding a good approximation of the Schur complement of a domain is at the core of mixed domain decomposition methods like optimized Schwarz methods \\cite{gander2006osm} or the Latin method \\cite{ladeveze2000micro}. Studies have proved that they needed to reproduce short-range effects (like local heterogeneity) but also structural effects (like the anisotropy induced by the slenderness of plate structures \\cite{SAAVEDRA.2012.1}). When one wishes to choose an invariant scalar (or tensor in case of anisotropy) for each interface, it can be beneficial to use a coarse model for its estimation \\cite{SAAVEDRA.2016.hal.1}. A possibility in order to better model short-range interaction between interface nodes is to use Ventcell conditions instead of simple Robin conditions \\cite{Hoang2014}; this enables to recover the same sparsity for the impedance as for the stiffness of the subdomain. An extreme strategy is to use (scalar) Robin conditions on the Riesz' image of the normal flux leading to a fully populated impedance matrix \\cite{DESMEURE.2011.3.1}. A more reasonable strategy is to use a strip approximation of the Schur complement \\cite{magoules_algebraic_2006}, which can also be computed by adding elements to the subdomains \\cite{Oumaziz2017}, in the spirit of restricted additive Schwarz methods \\cite{cai1999restricted}. \n\n\nFrom an algebraic point of view, short range approximation $ K\\ensuremath{^{(\\overline{j})}}_{t_{bb}}$ (or even $ \\operatorname{diag}(K\\ensuremath{^{(\\overline{j})}}_{t_{bb}})$) is sometimes used for FETI's preconditioner \\cite{Far94bis}, where it is called lumped approximation. \nLet $\\text{neigh}(j)$ be the set of the neighbors of subdomain $j$, we have\n\\begin{equation}\\label{eq:ktbb_neigh}\n\\text{lumped: }K_{t_{bb},l}\\ensuremath{^{\\text{neigh}(j)}} \\equiv K_{t_{bb}}\\ensuremath{^{(\\overline{j})}} = A\\ensuremath{^{(j)^T}} \\left( \\sum_{s \\in \\text{neigh}(j)} A\\ensuremath{^{(s)}} K\\ensuremath{^{(s)}}_{t_{bb}} A\\ensuremath{^{(s)^T}} \\right) A\\ensuremath{^{(j)}}\n\\end{equation}\nor even:\n\\begin{equation}\\label{eq:ktbb_neigh_diag}\n\\text{superlumped: }K_{t_{bb},sl}\\ensuremath{^{\\text{neigh}(j)}} \\equiv \\operatorname{diag}\\left(K_{t_{bb}}\\ensuremath{^{(\\overline{j})}}\\right) = A\\ensuremath{^{(j)^T}} \\left( \\sum_{s \\in \\text{neigh}(j)} A\\ensuremath{^{(s)}} \\operatorname{diag}\\left(K\\ensuremath{^{(s)}}_{t_{bb}}\\right) A\\ensuremath{^{(s)^T}} \\right) A\\ensuremath{^{(j)}}\n\\end{equation}\nBeing an assembly among a few subdomains of sparse block-diagonal matrices, this term is quite cheap to compute, and does not require any extra-computations, since local tangent stiffnesses are calculated anyway at each iteration of the solving process. The efficiency of the simple approximation \\eqref{eq:ktbb_neigh} has been studied, in the context of nonlinear substructuring and condensation, in some research works \\cite{cresta2007nonlinear, hinojosa2014domain, negrello2016substructured}, and has given good results when tested on rather homogeneous structures of standard shape. \\medskip\n\n\nIn the domain decomposition framework for linear problems, long range interactions are taken into account thanks to the coarse grid problems \\cite{Far94bis,mandel1993balancing,nouy03b}, which enables the method to comply with Saint-Venant's principle. These are closely related to projection techniques inspired by homogenization \\cite{ibrahimbegovic2003strong, feyel2000fe, ladeveze2000micro, guidault2007two, guidault2008multiscale} in order to get low rank approximations. Let $U$ be an orthonormal basis of a well chosen subspace of displacements, the approximation can be written as:\n\\begin{equation}\\label{eq:long_scale}\nS\\ensuremath{^{(\\overline{j})}} \\simeq U (U^T S\\ensuremath{^{(\\overline{j})}} U) U^T\n\\end{equation}\nSaint-Venant's principle imposes $U$ to contain at least the rigid body motions of $\\Omega\\ensuremath{^{(j)}}$, for computational efficiency it can be complemented by affine deformation modes or by displacements defined independently by interfaces.\\medskip\n\n\nHowever, if \\textit{short range} approximations do not provide enough information to give a good representation of the faraway structure influence on a substructure $\\Omega\\ensuremath{^{(j)}}$, neither do \\textit{long range} approximation give a good estimation of the near-field response to a sollicitation. Besides, in the context of small displacements, a lack of precision on the close structure is more problematic than the filtering of long range interactions: predominant mechanical reactions usually come from nearby elements of the mesh.\n \nThe best strategy for $Q\\ensuremath{^{(j)}}_b$ would combine both \\textit{short} and \\textit{long} range formulations, however this version has not been much investigated yet. In particular it is not that easy to ensure the positivity of the impedance if the two approximations are computed independently. In \\cite{gendre2011two} an expensive scale separation was introduced in the context of non intrusive global\/local computations where $\\Omega\\ensuremath{^{(\\overline{j})}}$ was somehow available (which is not the case in our distributed framework). We propose here a new expression for parameter $Q\\ensuremath{^{(j)}}_b$, in the context of nonlinear substructuring and condensation with mixed interface conditions, which combines short and long scale formulations, at low computational cost.\n\n\n\\subsection{Spring in series model}\\label{ssec:springs}\n\nOur heuristic for the impedance relies on the simple observation that finding a two-scale approximation of the flexibility of $\\Omega\\ensuremath{^{(\\overline{j})}}$ may be more patent than for the stiffness. It is inspired by the simple model of two springs assembled in series: one spring models the stiffness of the neighboring subdomains whereas the second models the stiffness of the faraway subdomains (see figure \\ref{fig:springs_series}). The resulting equivalent flexibility is the sum of the two flexibilities. \n\\begin{figure}[ht]\n\\begin{center}\n\\includegraphics{spring_series.pdf}\n\\end{center}\n\\caption{Springs in series model}\n\\label{fig:springs_series}\n\\end{figure}\nIn practice, in order to recover the structure of \\eqref{eq:opti_qb_lin}, while remaining tractable, we propose the local flexibility ${S_t\\ensuremath{^{\\text{neigh}(j)}}}^{-1}$ to be the inverse of a sparse matrix, and the long-range flexibility ${S_t^{\\text{far}(j)}}^{-1}$ to be low-rank. The latter condition is also motivated by \\cite{bebendorf2003existence,amestoy2016complexity}, where it is shown that low-rank approximants of fully populated inverse operators, arising from FE discretization of elliptic problems, can be derived from the hierarchical-matrices theory. Typically we have:\n\\begin{equation}\\label{eq:flex2terms}\n\\begin{aligned}\n{Q_b\\ensuremath{^{(j)}}}^{-1} = {K_{t_{bb}}\\ensuremath{^{\\text{neigh}(j)}}}^{-1} + A\\ensuremath{^{(j)^T}} V F V^T A\\ensuremath{^{(j)}}\n\\end{aligned}\n\\end{equation}\nwhere $K_{t_{bb}}\\ensuremath{^{\\text{neigh}(j)}}$ can refer for instance to expressions \\eqref{eq:ktbb_neigh} or \\eqref{eq:ktbb_neigh_diag}, $F$ is a small-sized $m \\times m$ square matrix, and $V$ an interface vectors basis of size $n_A \\times m$. Writing $V\\ensuremath{^{(j)}} = A\\ensuremath{^{(j)^T}} V$ the local contribution of basis $V$, expression \\eqref{eq:flex2terms} can be inversed using the Sherman-Morrisson formula:\n\\begin{equation}\n\\begin{aligned}\nQ_b\\ensuremath{^{(j)}} = K_{t_{bb}}\\ensuremath{^{\\text{neigh}(j)}} - \\underset{W_b\\ensuremath{^{(j)}}}{\\underbrace{ K_{t_{bb}}\\ensuremath{^{\\text{neigh}(j)}} V\\ensuremath{^{(j)}}}} \\, \\, \\underset{ {M\\ensuremath{^{(j)}}}^{-1} }{\\underbrace{ \\left( F^{-1} + V\\ensuremath{^{(j)^T}} K_{t_{bb}}\\ensuremath{^{\\text{neigh}(j)}} V\\ensuremath{^{(j)}} \\right)^{-1}}} \\, \\, \\underset{W_b\\ensuremath{^{(j)^T}}}{\\underbrace{ V\\ensuremath{^{(j)^T}} K_{t_{bb}}\\ensuremath{^{\\text{neigh}(j)}} }}\n\\end{aligned}\n\\end{equation} \nThis stiffness is a sparse matrix corrected by a low-rank term; then, when solving the (generalized) Robin problems, the Sherman-Morrisson formula can be used again:\n\\begin{equation}\n\\begin{aligned}\n\\text{let } \\tilde{K}_t\\ensuremath{^{(j)}} & \\equiv (K_t\\ensuremath{^{(j)}}+ t\\ensuremath{^{(j)^T}} {K_{t_{bb}}^{\\text{neigh}(j)} } t\\ensuremath{^{(j)}})  \n\\text{ and } W\\ensuremath{^{(j)}}  \\equiv t\\ensuremath{^{(j)^T}} W_b\\ensuremath{^{(j)}}:\\\\\n(K_t\\ensuremath{^{(j)}}+ t\\ensuremath{^{(j)^T}} Q_b\\ensuremath{^{(j)}} t\\ensuremath{^{(j)}})^{-1} & = \\tilde{K}_t^{(j)^{-1}} + \\tilde{K}_t^{(j)^{-1}} W\\ensuremath{^{(j)}} \\left(M\\ensuremath{^{(j)}} - W\\ensuremath{^{(j)^T}} \\tilde{K}_t^{-1} W\\ensuremath{^{(j)}} \\right)^{-1} W\\ensuremath{^{(j)^T}} \\tilde{K}_t^{(j)^{-1}}\n\\end{aligned}\n\\end{equation} \nThe short-range term enables to regularize the problem without impairing the sparsity of the stiffness matrix.\n\n\\subsection{A multi-scale interpretation}\\label{ssec:multi}\n\n\nIn the spirit of \\cite{oumaziz2}, we can derive a multi-scale interpretation of the additive form \\eqref{eq:flex2terms} adopted for the interface impedance. \n\nStarting from Algorithm~\\ref{alg:robin-robin}, a macroscopic condition, inspired from the Latin method, can be imposed on the nodal reactions: the nodal reactions should satisfy a weak form of the interface balance, defined by a macroscopic basis $C_A$:\n\\begin{equation}\\label{eq:macro_const}\nC_A^T A\\ensuremath{^{\\diamondminus}} \\lambda_b\\ensuremath{^{\\diamondvert}} = 0\n\\end{equation}\nIn the linear case, this condition can be enforced by the introduction of a Lagrange multiplier $\\alpha$ (details can be found in \\cite{oumaziz2}) in the interface condition \\eqref{eq:intQnl}:\n\\begin{equation*}\n\\lambda_b\\ensuremath{^{\\diamondvert}} - \\bar{\\lambda}_b\\ensuremath{^{\\diamondvert}} + Q_b\\ensuremath{^{\\diamondbackslash}} \\left( u_b\\ensuremath{^{\\diamondvert}} - \\bar{u}_b\\ensuremath{^{\\diamondvert}} \\right) + Q_b\\ensuremath{^{\\diamondbackslash}} A\\ensuremath{^{\\diamondminus^T}} C_A \\alpha = 0\n\\end{equation*}\nAfter algebraic calculations, writing local equilibriums with this new condition leads to:\n\\begin{equation*}\n\\left[ K\\ensuremath{^{\\diamondbackslash}} + t\\ensuremath{^{\\diamondbackslash^T}} Q_b\\ensuremath{^{\\diamondbackslash}} \\left( I\\ensuremath{^{\\diamondbackslash}} - P_{C_A}\\ensuremath{^{\\diamondbackslash}} \\right) t\\ensuremath{^{\\diamondbackslash}} \\right] u\\ensuremath{^{\\diamondvert}} = f_{ext}\\ensuremath{^{\\diamondvert}} + t\\ensuremath{^{\\diamondbackslash^T}} \\left[ \\bar{\\lambda}_b\\ensuremath{^{\\diamondvert}} + Q_b\\ensuremath{^{\\diamondbackslash}} \\left( I\\ensuremath{^{\\diamondbackslash}} - P_{C_A}\\ensuremath{^{\\diamondbackslash}} \\right) \\bar{u}_b\\ensuremath{^{\\diamondvert}} \\right]\n\\end{equation*}\nwhere $P_{C_A}\\ensuremath{^{\\diamondbackslash}} = A\\ensuremath{^{\\diamondminus^T}} C_A \\left( C_A^T A\\ensuremath{^{\\diamondminus}} Q_b\\ensuremath{^{\\diamondbackslash}} A\\ensuremath{^{\\diamondminus^T}} C_A \\right)^{-1} C_A^T A\\ensuremath{^{\\diamondminus}} Q_b\\ensuremath{^{\\diamondbackslash}}$ is a projector on the low-dimension subspace $\\operatorname{Range}(A\\ensuremath{^{\\diamondminus^T}} C_A)$.\n\nNot only the coarse space associated to the macroscopic constraint \\eqref{eq:macro_const} results in the propagation of the right-hand side on the whole structure ($P_{C_A}\\ensuremath{^{\\diamondbackslash}}$ is not sparse) but also in the modification of the impedance by the symmetric negative low rank term $-Q_b\\ensuremath{^{\\diamondbackslash}} P_{C_A}\\ensuremath{^{\\diamondbackslash}}$.\n\n\\medskip\n\n\nIn our nonlinear context, considering the basic setting $Q_b\\ensuremath{^{(j)}} = K_{t_{bb}}\\ensuremath{^{\\text{neigh}(j)}}$ \\eqref{eq:ktbb_neigh} or \\eqref{eq:ktbb_neigh_diag}, the modification $\\bar{Q}_b\\ensuremath{^{\\diamondbackslash}} = K_{t_{bb}}\\ensuremath{^{\\text{neigh}(j)}} - W_b\\ensuremath{^{(j)}} M\\ensuremath{^{(j)^{-1}}} W_b\\ensuremath{^{(j)^T}}$ proposed in \\eqref{eq:flex2terms} can be seen as the introduction of a multi-scale computation inside the mixed nonlinear substructuring and condensation method. As said earlier, the propagation of the right-hand side is ensured by a well-built initialization, which can be realized by adapting the inner Newton criterion $\\epsilon_{NL}$ at each global iteration.\n\n\n\n\n\\subsection{Two-scale approximation of the flexibility}\\label{ssec:two_scale}\n\n\\subsubsection{General idea}\n\nFrom previous analysis, we try to derive an approximation of the (linear) optimal flexibility \\eqref{eq:opti_qb_lin} which takes the additive form of \\eqref{eq:flex2terms}. Being given a substructure $\\Omega\\ensuremath{^{(j)}}$, we write $S_A\\ensuremath{^{(\\overline{j})}} = \\sum_{s \\neq j} A\\ensuremath{^{(s)}} S_t\\ensuremath{^{(s)}} A\\ensuremath{^{(s)^T}}$ the assembly of local tangent Schur complements on the remainder $\\Omega\\ensuremath{^{(\\overline{j})}}$.\n\nUsing the quotient and the inverse formulas for the Schur complement, we have:\n\\begin{equation}\\label{eq:flexSt}\n{S_t\\ensuremath{^{(\\overline{j})}}}^{-1} = \\left( {S_A\\ensuremath{^{(\\overline{j})}}}^{-1} \\right)_{bb} = A\\ensuremath{^{(j)^T}} {S_A\\ensuremath{^{(\\overline{j})}}}^{-1} A\\ensuremath{^{(j)}}\n\\end{equation}\n\n\\begin{remark}\nWe here assume a substructuring ensuring the inversibility of $S_A\\ensuremath{^{(\\overline{j})}}$ and $S_t\\ensuremath{^{(\\overline{j})}}$, i.e. Dirichlet conditions are not concentrated on only one subdomain, and the complementary part of each subdomain is connected. In practice, this is almost always the case; if not, a simple subdivision can overcome the problem.\n\\end{remark}\n\n\\medskip\n\nClassical preconditioners of BDD-algorithm can then be used as approximations of the inverse of $S_A\\ensuremath{^{(\\overline{j})}}$. \nWe hence introduce $\\hat{G}_A\\ensuremath{^{(\\overline{j})}} = \\left[\\, \\ldots, \\, \\hat{A}\\ensuremath{^{(s)}}_j R_b\\ensuremath{^{(s)}}, \\, \\ldots \\, \\right]_{s \\neq j}$ the concatenation of the scaled local traces of rigid body motions ($R_b\\ensuremath{^{(s)}}$) of subdomains belonging to $\\Omega\\ensuremath{^{(\\overline{j})}}$, with $\\hat{A}\\ensuremath{^{(s)}}_j$ scaled assembly operators taking into account the absence of matter inside subdomain $\\Omega\\ensuremath{^{(j)}}$. Considering the classical definition of scaled assembly operators $\\tilde{A}\\ensuremath{^{(s)}}$ \\cite{klawonn2001feti}, modified operators $\\hat{A}\\ensuremath{^{(s)}}_j$ can be defined as:\n\\begin{equation*}\n\\begin{aligned}\n \\hat{A}\\ensuremath{^{(s)}}_j = & \\left\\lbrace \\,\\,\\, \\begin{aligned} \\left( A\\ensuremath{^{\\diamondminus}} \\Delta\\ensuremath{^{\\diamondbackslash}} A\\ensuremath{^{\\diamondminus^T}} - A\\ensuremath{^{(j)}} \\Delta\\ensuremath{^{(j)}} A\\ensuremath{^{(j)^T}} \\right)^{-1} A\\ensuremath{^{(s)}} \\Delta\\ensuremath{^{(s)}} \\quad \\text{ if } s \\neq j \\\\\n0 \\quad \\text{ if } s = j \\end{aligned} \\right. \\\\\n& \\hspace{0.5cm} \\text{ with } \\,\\, \\Delta\\ensuremath{^{(s)}} \\equiv \\operatorname{diag} \\left( K_{t_{bb}}\\ensuremath{^{(s)}} \\right)\n\\end{aligned}\n\\end{equation*}\n\n\nLet $P_A\\ensuremath{^{(\\overline{j})}}$ be the $S_A\\ensuremath{^{(\\overline{j})}}$-orthogonal projector on $\\operatorname{Ker}\\left( \\hat{G}_A\\ensuremath{^{(\\overline{j})^T}} S_A\\ensuremath{^{(\\overline{j})}} \\right)$:\n\\begin{align*}\n P_A\\ensuremath{^{(\\overline{j})}} = I - \\hat{G}_A\\ensuremath{^{(\\overline{j})}} \\left( \\hat{G}_A\\ensuremath{^{(\\overline{j})^T}} S_A\\ensuremath{^{(\\overline{j})}} \\hat{G}_A\\ensuremath{^{(\\overline{j})}} \\right)^{-1} \\hat{G}_A\\ensuremath{^{(\\overline{j})^T}} S_A\\ensuremath{^{(\\overline{j})}} \n\\end{align*}\nwe have:\n\\begin{equation}\\label{eq:sep_inv_proj}\nS_A\\ensuremath{^{(\\overline{j})^{-1}}} =  P_A\\ensuremath{^{(\\overline{j})}} S_A\\ensuremath{^{(\\overline{j})^{-1}}} P_A\\ensuremath{^{(\\overline{j})^T}} + \\left( I - P_A\\ensuremath{^{(\\overline{j})}} \\right) S_A\\ensuremath{^{(\\overline{j})^{-1}}} \\left( I - P_A\\ensuremath{^{(\\overline{j})}} \\right)^T \n\\end{equation}\nThe BDD-theory states that in the first term, $S_A\\ensuremath{^{(\\overline{j})^{-1}}}$ can be conveniently approximated by a scaled sum of local inverses\\footnote{The GENEO theory \\cite{SPILLANE:2013:FETI_GenEO_IJNME} states that, if needed, computable extra modes shall be inserted in $\\hat{G}_A\\ensuremath{^{(\\overline{j})}}$ in order to maintain the quality of the approximation.}.\nAfter developing and factorizing, we have a first approximation of the flexibility:\n\\begin{equation}\\label{eq:expr_inv_st}\n\\begin{aligned}\nQ_{BDD}\\ensuremath{^{(j)^{-1}}} \\equiv A\\ensuremath{^{(j)^T}} \\left( P_A\\ensuremath{^{(\\overline{j})}} \\sum_{s \\neq j} \\hat{A}\\ensuremath{^{(s)}}_j {S_t\\ensuremath{^{(s)}}}^{\\dagger} \\hat{A}\\ensuremath{^{(s)^T}}_j P_A\\ensuremath{^{(\\overline{j})^T}} +  \\hat{G}_A\\ensuremath{^{(\\overline{j})}} \\left( \\hat{G}_A\\ensuremath{^{(\\overline{j})^T}} S_A\\ensuremath{^{(\\overline{j})}} \\hat{G}_A\\ensuremath{^{(\\overline{j})}} \\right)^{-1} \\hat{G}_A\\ensuremath{^{(\\overline{j})^T}} \\right) A\\ensuremath{^{(j)}} \\\\\n\\end{aligned}\n\\end{equation}\n\n\n\n\\subsubsection{Long range interactions term}\n\nThe second term of expression \\eqref{eq:expr_inv_st}, written $\\hat{F}_{A,2}\\ensuremath{^{(j)}}$, is a matrix of low rank $m^{(j)}$, where  $m^{(j)}$ is the number of neighbors rigid body motions.  It could be used as is, however its computation involves the inversion of quantity $\\hat{G}_A\\ensuremath{^{(\\overline{j})^T}} S_A\\ensuremath{^{(\\overline{j})}} \\hat{G}_A\\ensuremath{^{(\\overline{j})}}$, an interface matrix of rank $m\\ensuremath{^{(\\overline{j})}}$, where $m\\ensuremath{^{(\\overline{j})}}$ is the number of local rigid body modes of the whole remainder $\\Omega\\ensuremath{^{(\\overline{j})}}$. In the context of large structures with a high number of subdomains, $m^{(\\overline{j})}$ can increase drastically; saving the computation and factorization of such a matrix could then become quite interesting. Moreover, during the computation of the structure coarse problem, a close quantity is already assembled and factorized: the matrix $\\tilde{G}_A^T S_A \\tilde{G}_A$ -- with $S_A \\equiv \\sum_{s=1}^{N_s} A\\ensuremath{^{(s)}} S\\ensuremath{^{(s)}} A\\ensuremath{^{(s)^T}}$ and $\\tilde{G}_A \\equiv \\left[ \\ldots , \\, \\tilde{A}\\ensuremath{^{(s)}} R_b\\ensuremath{^{(s)}}, \\, \\ldots \\right]$. Compared to $\\hat{G}\\ensuremath{^{(\\overline{j})^T}} S_A\\ensuremath{^{(\\overline{j})}} \\hat{G}\\ensuremath{^{(\\overline{j})}}$, the addition of the local term linked to $\\Omega\\ensuremath{^{(j)}}$ in $\\tilde{G}_A^T S_A \\tilde{G}_A$ somewhat balances the classical scaling on its boundary (taking into account non-existant matter inside $\\Omega\\ensuremath{^{(j)}}$), we thus propose:\n\\begin{equation*}\n\\hat{F}_{A,2}\\ensuremath{^{(j)}} \\simeq A\\ensuremath{^{(j)^T}} \\hat{G}_A\\ensuremath{^{(\\overline{j})}} \\left( \\tilde{G}_A^T S_A \\tilde{G}_A \\right)^{-1} \\hat{G}_A\\ensuremath{^{(\\overline{j})^T}} A\\ensuremath{^{(j)}} \\equiv \\tilde{F}_{A,2}\\ensuremath{^{(j)}}\n\\end{equation*}\n\n\\subsubsection{Short range interactions term}\n\nThe first term of expression \\eqref{eq:expr_inv_st}, written $\\hat{F}_{A,1}\\ensuremath{^{(j)}}$, can also be simplified. First, for numerical efficiency, a diagonal lumping technique is used to approximate the local Schur complements (as explained in section \\ref{ssec:review}). Then, in order to preserve sparsity, the projectors are removed. Assuming stiffness scaling is used we then directly recover the inverse of the superlumped stiffness of the neighbors:\n\\begin{equation}\\label{eq:tild_ktbb}\n\\begin{aligned}\n\\hat{F}_{A,1}\\ensuremath{^{(j)}} & \\simeq A\\ensuremath{^{(j)^T}} \\sum_{s \\in \\text{neigh}(j)} \\hat{A}\\ensuremath{^{(s)}}_j \\operatorname{diag}\\left( K_{t_{bb}}\\ensuremath{^{(s)}} \\right)^{-1} \\hat{A}\\ensuremath{^{(s)^T}}_j A\\ensuremath{^{(j)}} \\\\ \n& = A\\ensuremath{^{(j)^T}} \\left( \\sum_{s \\in \\text{neigh}(j)} A\\ensuremath{^{(s)}} \\operatorname{diag} \\left( K_{t_{bb}}\\ensuremath{^{(s)}} \\right) A\\ensuremath{^{(s)^T}} \\right)^{-1} A\\ensuremath{^{(j)}} = K_{t_{bb},\\, sl}\\ensuremath{^{\\text{neigh}(j)^{-1}}}\n\\end{aligned}\n\\end{equation}\n\n\\subsubsection{Scaling issue}\n\nA way to avoid building the modified scaled assembly operators $\\hat{A}\\ensuremath{^{(s)}}_j$ is to notice that for $s \\neq j$, the following relation holds between modified and classical scaling operators $\\tilde{A}\\ensuremath{^{(s)}}$ \\cite{klawonn2001feti}:\n\\begin{equation*}\n\\begin{aligned}\nA\\ensuremath{^{(j)^T}} \\hat{A}_j\\ensuremath{^{(s)}} & = \\tilde{D}\\ensuremath{^{(j)}} A\\ensuremath{^{(j)^T}} \\tilde{A}\\ensuremath{^{(s)}} \\\\\n\\text{with }\\tilde{D}\\ensuremath{^{(j)}} \\equiv A\\ensuremath{^{(j)^T}} \\left( A\\ensuremath{^{\\diamondminus}} \\Delta\\ensuremath{^{\\diamondbackslash}} A\\ensuremath{^{\\diamondminus^T}} \\right) & \\left( A\\ensuremath{^{\\diamondminus}} \\Delta\\ensuremath{^{\\diamondbackslash}} A\\ensuremath{^{\\diamondminus^T}} - A\\ensuremath{^{(j)}} \\Delta\\ensuremath{^{(j)}} A\\ensuremath{^{(j)^T}} \\right)^{-1} A\\ensuremath{^{(j)}}\n\\end{aligned}\n\\end{equation*}\nand we observe that the local diagonal matrix $\\tilde{D}\\ensuremath{^{(j)}}$ can be \nextracted without cost from $\\tilde{A}\\ensuremath{^{(j)}}$:\n\\begin{equation*}\n\\tilde{D}\\ensuremath{^{(j)}} = A\\ensuremath{^{(j)^T}} \\left( I - A\\ensuremath{^{(j)}} \\tilde{A}\\ensuremath{^{(j)^T}} \\right)^{-1} A\\ensuremath{^{(j)}}\n\\end{equation*}\n\\begin{remark}\nWith evident notations, for a scaling based on the material stiffness, the diagonal coefficient of $\\tilde{D}\\ensuremath{^{(j)}}$ associated with degree of freedom $x$ is equal to:\n\\begin{equation*}\n\\begin{aligned} \n\\tilde{D}\\ensuremath{^{(j)}}_{xx} = \\dfrac{ \\sum_s K_{t_{xx}}\\ensuremath{^{(s)}} }{ \\sum_{s \\neq j } K_{t_{xx}}\\ensuremath{^{(s)}} } = \\left( 1 - \\dfrac{K_{t_{xx}}\\ensuremath{^{(j)}} }{ \\sum_s K_{t_{xx}}\\ensuremath{^{(s)}}} \\right)^{-1} = \\left( 1 - \\tilde{A}\\ensuremath{^{(j)}}_x \\right)^{-1}\n\\end{aligned}\n\\end{equation*}\\qed\n\\end{remark}\n\\medskip\n\n\n\\noindent \\textit{Final expression.} To conclude, we propose the following two-scale impedance:\n\\begin{equation}\\label{eq:final_expr_qb}\n\\left( Q\\ensuremath{^{(j)}}_{b, \\,2s} \\right)^{-1} = K_{t_{bb},\\,sl}\\ensuremath{^{\\text{neigh}(j)^{-1}}} + \\tilde{D}\\ensuremath{^{(j)}} A\\ensuremath{^{(j)^T}} \\tilde{G}_A\\ensuremath{^{(\\overline{j})}} \\left( \\tilde{G}_A^T S_A \\tilde{G}_A \\right)^{-1} \\tilde{G}_A\\ensuremath{^{(\\overline{j})^T}} A\\ensuremath{^{(j)}} \\tilde{D}\\ensuremath{^{(j)}}\n\\end{equation}\n\n\n\\subsection{Attempt to enrich the short-range approximation}\\label{ssec:Qritz}\n\nThe short range part of the impedance, corresponding to the sparse approximation of $\\hat{F}_{A,1}\\ensuremath{^{(j)}}$ by $K_{t_{bb},\\,sl}\\ensuremath{^{\\text{neigh}(j)^{-1}}}$, seems very crude. In particular, we most probably underestimate the flexibility of the neighbors by using a diagonal operator.\n\nWe believe it is worth mentioning the tentative improvement which consisted in adding another low rank term:\n\\begin{equation*}\n\\hat{F}_{A,1}\\ensuremath{^{(j)}} \\simeq K_{t_{bb},\\,sl}\\ensuremath{^{\\text{neigh}(j)^{-1}}} + \\tilde{D}\\ensuremath{^{(j)}} A\\ensuremath{^{(j)^T}} V_k \\Theta_k V_k^T A\\ensuremath{^{(j)}} \\tilde{D}\\ensuremath{^{(j)}}\n\\end{equation*}\nwhere $\\Theta_k$ is a diagonal matrix and $V_k$ an orthonormal basis, approximations of the eigen-elements of $S_A\\ensuremath{^{(\\overline{j})^{-1}}}$ associated with the higher part of the spectrum. They could be obtained at a moderate cost by post-processing the tangent BDD iterations in the spirit of \\cite{gosselet2013total} (but considering the classical eigenvalues instead of the generalized ones). \n\nThis low rank term could be concatenated with the one associated with rigid body motions $\\tilde{F}_{A,2}\\ensuremath{^{(j)}}$, and thus did not modify the usability of the approximation.  \nWe observed that it led to a stiffness which was closer to our reference $S_t\\ensuremath{^{(\\overline{j})^{-1}}}$ (measured with the Frobenius norm). But in practice when using it as the impedance in our numerical experiments, the reduction achieved in iterations numbers was not worth the additional cost of the enrichment term -- this is why we do not present it in detail. This ``improvement'' may be more useful on other classes of nonlinear problems for which it would be important not to overestimate the stiffness of the remainder of the structure.\n\n\n\n\n\\section{Results}\n\n\\subsection{Two test cases}\\label{sec:two_test_cases}\n\n\nThe efficiency of the expression \\eqref{eq:final_expr_qb} is evaluated on two numerical test cases. First test case is a bi-material beam with bending load, represented on figure~\\ref{fig:test_case_bimat}. Material and geometrical parameters are given in table \\ref{tab:params_tests_case}: one of the two materials is chosen to be elastoplastic with linear hardening, the other one is chosen to remain elastic. Load is applied with imposed displacement on the edge defined by $x=L$.\n\nSecond test case is a homogeneous multiperforated beam with bending load, represented on figure~\\ref{fig:test_case_multiperf}. Material and geometrical parameters are given in table \\ref{tab:params_tests_case}: material is chosen to be  elastoplastic with linear hardening. Load is applied with imposed displacement $u_D$ on the edge defined by $x=L$.\n\n\n\\begin{figure}[!ht]\n\\includegraphics[width=\\textwidth]{test_case_betarme2.pdf}\n\\caption{Bi-material beam: partition and loading}\n\\label{fig:test_case_bimat}\n\\end{figure}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics[width=15cm]{test_case_multiperf.pdf}\n\\end{center}\n\\caption{Multiperforated beam: partition and loading}\n\\label{fig:test_case_multiperf}\n\\end{figure}\n\n\n\\begin{table}[ht]\n\\begin{center}\n\\begin{minipage}{0.56\\linewidth}\n\\begin{tabular}{|c:c|c|}\n\\hline \\hline\n\\multicolumn{3}{|c|}{Bi-material beam} \\\\\n\\hline \\hline\n\\multicolumn{3}{|c|}{ Material parameters} \\\\\n\\hline \\hline\n & Material 1 & Material 2 \\\\\nYoung & $E_1 = 420e2$ & $E_2 = 210e6$ \\\\\nPoisson coefficient & $\\nu_1 = 0.3$ & $\\nu_2 = 0.3$ \\\\\nElastic limit & & $\\sigma_{0_2} = 420e3$ \\\\\nHardening coefficient & & $h_2 = 1e3$   \\\\\n\\hline \\hline\n\\multicolumn{3}{|c|}{Geometrical parameters} \\\\\n\\hline \\hline\nTotal length & \\multicolumn{2}{:c|}{L $ = 13$} \\\\\nTotal height & \\multicolumn{2}{:c|}{H $ = 2$} \\\\\nHeight of an armature & \\multicolumn{2}{:c|}{H$_\\text{a} = 0.25$} \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{minipage}\n\\begin{minipage}{0.43\\linewidth}\n\\begin{tabular}{|c:c|}\n\\hline \\hline\n\\multicolumn{2}{|c|}{Multiperforated beam} \\\\\n\\hline \\hline\n\\multicolumn{2}{|c|}{ Material parameters} \\\\\n\\hline \\hline\n & \\\\\nYoung & $E = 210e6$ \\\\\nPoisson coefficient &  $\\nu = 0.3$ \\\\\nElastic limit & $\\sigma_0 = 420e3$ \\\\\nHardening coefficient & $h = 1e6$ \\\\\n\\hline \\hline\n\\multicolumn{2}{|c|}{Geometrical parameters} \\\\\n\\hline \\hline\nLength & L $ = 10$ \\\\\nHeight & H $ = 1$ \\\\\nHole radius & r $ = 2\/30$ \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{minipage}\n\\caption{Material and geometrical parameters}\n\\label{tab:params_tests_case}\n\\end{center}\n\\end{table}\n\n\n\n\n\n\\subsection{Elastic analysis}\n\nThe ultimate goal of this paper is to assess the performance of the new impedance \\eqref{eq:final_expr_qb} in the nonlinear multi-scale distributed context. Before we reach that point, a preliminary mono-scale elastic study is performed in order to verify that the heuristic developed in previous sections is actually able to capture both short and long range interactions within the structure.\n\nSollicitations are here keeped low enough to remain in the elastic domain of every materials: bi-material beam and multiperforated beam are both submitted to a bending load of intensity $u_D = 1.5 \\,\\, 10^{-3}$. More, decomposition is for now only performed along $x$-axis (multiple points will be involved in next section, where the nonlinear multi-scale context is considered). One of the interest of the elastic linear case with slab-wise decomposition relies on the ability to express the optimal interface impedance: $Q_b\\ensuremath{^{(j)}} = S_t\\ensuremath{^{(\\overline{j})}}$ (see \\ref{ssec:motivation}). Even if the computational cost of this parameter would be, in a real situation, absolutely not affordable in the context of parallel resolutions, it was calculated here for the purpose of our analysis. A comparison with an optimal reference can thus be made for the two following expressions:\n\\begin{itemize}[label=$\\circ$]\n\\item a classical choice $K_{bb,l}\\ensuremath{^{\\text{neigh}(j)}}$: see \\eqref{eq:ktbb_neigh}\n\\item the new expression $Q_{b,\\,2s}\\ensuremath{^{(j)}}$: see \\eqref{eq:final_expr_qb}\n\\end{itemize}\nBeing given the alternative formulation we chose for the mixed nonlinear substructuring and condensation method (see section \\ref{sec:altern_formul}), an elastic resolution would be strictly equivalent to a primal BDD resolution. Therefore, no comparison of different interface impedances is possible with Algorithm~\\ref{alg:robin-bdd}. A mono-scale FETI-2LM solver \\cite{roux2009feti} was hence implemented, corresponding to the first formulation of the mixed interface problem with the $\\mu_b\\ensuremath{^{\\diamondvert}}$ unknown \\eqref{eq:tg_pb}. This algorithm enables to solve linear problems with Robin interface transmission conditions. \n\nNote that an optimal coarse problem could be added in order to recover an efficient multi-scale solver \\cite{dubois2012optimized,haferssas2015robust,loisel2015optimized}. However, this augmentation strategy would make it impossible to discern the efficiency of the long range interactions term of our two-scale impedance. Again, our aim is not to compete with augmented Krylov solvers for linear problems but to find an alternative way, compatible with nonlinear problems, to introduce long-range effects. The mono-scale formulation is thus preserved in order to evaluate the  ability of \\eqref{eq:final_expr_qb} to introduce in local equilibriums information related to the interactions with the far structure, in a linear context where the optimal parameter is known. \n\n\n\\begin{table}[!ht]\n\\begin{center}\n\\subfloat[Bi-material beam]{\\includegraphics[width=10cm]{results_lin_bimat.pdf}\\label{subtab:results_lin_bimat}} \\qquad\n\\subfloat[Multiperforated beam]{\\includegraphics[width=10cm]{results_lin_multiperf.pdf}\\label{subtab:results_lin_multiperf}}\n\\end{center}\n\\caption{Comparison of the three interface impedances: linear behavior}\n\\label{tab:results_lin}\n\\end{table}\n\nResults are given on table \\ref{tab:results_lin} for the two previously introduced test cases. \n\n\nAs expected, for both test cases, the optimal interface impedance $S_t^{(\\overline{j})}$ rounds off the resolution after a number of iterations equal to the number of subdomains minus one. Being given the repartition of the subdomains (no multiple points) and the absence of a coarse problem, this is the best convergence rate that can be achieved: mixed transmission conditions with interface impedance $S_t^{(\\overline{j})}$ is optimal.\n\nThe classical choice $K_{bb,l}^{\\text{neigh}(j)}$ does not involve any information on the long range interactions of a subdomain with the faraway structure inside local equilibriums: the number of iterations drastically increases along with the number of substructures. \n\nThe new expression $Q_{b,2s}^{(j)}$ introduced in this paper highly reduces the numbers of FETI-2LM iterations, compared to classical choice $K_{bb,l}^{\\text{neigh}(j)}$: gains are between 77 and 98\\%. This should mostly be due to the additive form of expression \\eqref{eq:final_expr_qb}, with the introduction of a long range interactions-term in the flexibility -- obviously, the absence of coarse problem in the resolution reinforces the benefits of this term. The forthcoming nonlinear study, based on algorithm \\ref{alg:robin-bdd}, will replace this expression in a context of multiscale computation. \n\nPerformance of expression $Q_{b,2s}^{(j)}$ is evidently not as good as that of optimal expression $S_t^{(\\overline{j})}$, but the increase in iterations numbers is only of about ten times the optimal iterations number (while it reaches about hundreds times the optimal iterations number for $K_{bb,l}^{\\text{neigh}(j)}$). We also recall that interface impedance $S_t^{(\\overline{j})}$ can not be computed in parallel resolutions: expression $Q_{b,2s}^{(j)}$, at the contrary, is fully and easily tractable.\n\n\nThe expression introduced here to evaluate the interface impedance thus seems, at least in the linear case, to achieve great performance at very low cost. \n\n\\begin{remark} As said earlier, the second effect of multiscale approaches (beside modifying the Robin condition), lies in the instantaneous propagation of the right-hand side. In our approach, the absence of a coarse problem is somehow compensated by the presence of tangent interface systems (solved with state of the start multi-scale BDD method). As an example, we initialized our linear FETI-2LM solver with the fields resulting from one BDD iteration. For the multiperforated beam split in 15 subdomains, the number of FETI-2LM iterations goes from 113 to 89, which is significant (for less subdomains, the coarse problem is too small to bring any valuable piece of information). In the spirit of \\cite{negrello2016substructured}, a tuned setting of the solvers' thresholds (synchronized with the evolution of the global residual, i.e. the precision of the global solution) could perform a good compromise between a global spread of the information and independent computations.\n\n\\end{remark}\n\n\\subsection{Plastic analysis}\\label{sec:it_numbers}\n\nThe evaluation of the performance of expression \\eqref{eq:final_expr_qb}  is continued with a plastic evolution study. The two test cases are submitted to bending loads, applied incrementally. Bi-material beam loading is decomposed as follows:\n\\begin{align}\nu_D & = \\left[ 0.05, \\, \\, 0.1, \\, \\, 0.15, \\, \\, 0.2, \\, \\, 0.25, \\, \\, 0.3, \\, \\, 0.35, \\, \\, 0.375, \\, \\, 0.4, \\, \\, 0.425, \\, \\, 0.45 \\right] u_{max} \\label{eq:load_incre_bimat}\\\\\nu_{max} & = 7.1 \\nonumber\n\\end{align}\nFor multiperforated beam loading, the incremental decomposition is set to:\n\\begin{align}\nu_D & = \\left[ 0.4, \\, \\, 0.6, \\, \\, 0.8, \\, \\, 1, \\, \\, 1.15, \\, \\, 1.3, \\, \\, 1.45, \\, \\, 1.5 \\right] u_{max} \\label{eq:load_incre_multiperf} \\\\\nu_{max} & = 0.275 \\nonumber\n\\end{align}\n\\begin{remark} \nFor the sake of clarity, every over load increment \\eqref{eq:load_incre_bimat} and \\eqref{eq:load_incre_multiperf} is represented in the forthcoming results tables. \n\\end{remark}\n\nThe substructuring of the bi-material beam involves 13 subdomains along $x$-axis, while multiperforated beam is decomposed into 30 subdomains with multiple points (see figures~\\ref{fig:test_case_bimat} and~\\ref{fig:test_case_multiperf}).\n\n\nNumbers of Krylov iterations, cumulated over global Newton loops and load increments, are stored for the three interface impedances $S_t^{(\\overline{j})}$, $K_{bb,l}^{\\text{neigh}(j)}$ and $Q_{b,2s}^{(j)}$ and the two test cases in tables \\ref{tab:iter_bimat} and \\ref{tab:iter_multiperf}. Indeed, performance of the solver is in particular linked to the number of processor communications, which are directly proportional to the number of Krylov iterations. \n\nThe computation of local tangent operators, at each global iteration, is also a costly operation. The numbers of global Newton iterations, cumulated over load increments, are thus also stored for each expression of the interface impedance and the two test cases. Note that in these cases, the number of Krylov iterations is almost constant per linear system, the cumulated numbers of Krylov iterations are thus nearly proportional to the numbers of global Newton iterations; the latter are therefore only stored for the last load increment. \n\nA fourth approach has been added to the study, written NKS in both tables, and corresponding to the ``classical'' resolution process used in nonlinear structural mechanical problems: a global Newton algorithm, combined with a linear DD solver for the tangent systems. The main difference between the nonlinear substructuring and condensation method and this classical technique resides in the nonlinear\/linear algorithms used for local resolutions. The resulting comparisons with approaches $S_t^{(\\overline{j})}$, $K_{bb,l}^{\\text{neigh}(j)}$ and $Q_{b,2s}^{(j)}$ hence represent the gains that can be achieved with the mixed nonlinear substructuring and condensation method, in the more general framework of nonlinear solvers. \\medskip\n\n\n\n\\begin{table}[!ht]\n\\begin{center}\n\\begin{minipage}{\\linewidth}\n\\begin{center}\n\\begin{tabular}{|c|cccccc|c|}\n\\hline\n\\multicolumn{7}{|c|}{Krylov} & Global Newton \\\\\n\\hline\nload inc. & 0.05 & 0.15 & 0.25 & 0.35 & 0.4 & 0.45 & 0.45\\\\\n\\hline\n$S_t^{(\\overline{j})}$ & 37 & 229 & x &  &  &  & x \\\\\n$K_{bb,l}^{\\text{neigh}(j)}$ & 36 & 259 & 598 & 978 & 1357 & 1772 & 47 \\\\\n$Q_{b,2s}^{(j)}$ & 37 & 266 & 580 & 891 & 1204 & 1514 & 39 \\\\\n\\hline\n\\hline\nNKS & 74 & 296 & 633 & 970 & 1344 & 1795 & 48 \\\\\n\\hline\n\\multicolumn{8}{c}{ } \\\\\n\\hline\n\\multicolumn{8}{|c|}{Gains (\\%) } \\\\\n\\hline\n$Q_{b,2s}^{(j)}$ vs. $K_{bb,l}^{\\text{neigh}(j)}$ & -3 & -3 & 3 & 9 & 11 & 15 & 17 \\\\\n\\hline\n\\hline\n$Q_{b,2s}^{(j)}$ vs. NKS & 50 & 10 & 8 & 8 & 10 & 16 & 19 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{minipage}\n\\end{center}\n\\caption{Bi-material beam: Krylov cumulated iterations over load increments, global Newton cumulated iterations}\n\\label{tab:iter_bimat}\n\\end{table}\n\n\n\\begin{table}[!ht]\n\\begin{center}\n\\begin{minipage}{\\linewidth}\n\\begin{center}\n\\begin{tabular}{|c|cccc|c|}\n\\hline\n\\multicolumn{5}{|c|}{Krylov} & Global Newton\\\\\n\\hline\nload inc. & 0.6 & 1 & 1.3 & 1.5 & 1.5\\\\\n\\hline\n$S_t^{(\\overline{j})}$ & 48 & 172 & 322 & 481 & 30 \\\\\n$K_{bb,l}^{\\text{neigh}(j)}$ & 61 & 212 & 373 & 548 & 35 \\\\\n$Q_{b,2s}^{(j)}$ & 48 & 170 & 300 & 438 & 28 \\\\\n\\hline\n\\hline\nNKS & 73 & 222 & 385 & 561 & 36 \\\\\n\\hline\n\\multicolumn{6}{c}{ } \\\\\n\\hline\n\\multicolumn{6}{|c|}{Gains (\\%)} \\\\\n\\hline\n$Q_{b,2s}^{(j)}$ vs. $K_{bb,l}^{\\text{neigh}(j)}$ & 21 & 20 & 20 & 20 & 20 \\\\\n$Q_{b,2s}^{(j)}$ vs. $S_t^{(\\overline{j})}$ & 0 & 1 & 7 & 9 & 7 \\\\\n\\hline\n\\hline\n$Q_{b,2s}^{(j)}$ vs. NKS & 34 & 23 & 22 & 22 & 22 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{minipage}\n\\end{center}\n\\caption{Multiperforated beam: Krylov cumulated iterations over load increments, global Newton cumulated iterations}\n\\label{tab:iter_multiperf}\n\\end{table}\n\n\nA first preliminary observation compares results for interface impedance $S_t^{(\\overline{j})}$ in the linear and the nonlinear case: the primitive guess we made about $S_t^{(\\overline{j})}$ being the best possible approximation we could analytically define of the interface impedance value was mistaken in the nonlinear formulation. For bi-material beam for instance, the resolution ended up with a divergence in the local Newton solvers, caused by fake high levels of plasticity inside subdomains, artifacts of the resolution -- this may be due to an excessively soft interface impedance, which lets the material deform more than necessary. \n\nSecondly, although our first guess was apparently misguided, the additive expression we derived from it seems to behave very satisfyingly: best performance is now achieved -- in the nonlinear process -- with the new expression of interface impedance $Q_{b,2s}^{(j)}$. Gains in terms of Krylov cumulated iterations, compared to classical interface impedance $K_{bb,l}^{\\text{neigh}(j)}$, vary from 15\\% to 20\\% at the end of the resolution: a benefit which should represent a non negligible decrease in CPU time for large structure problems (where each communication operation can be highly time-consuming). Compared to the interface impedance $S_t^{(\\overline{j})}$ -- which is not computationally affordable in practice, -- only the multiperforated beam can be effectively studied (convergence was not reached for bi-material beam): gains, for approach $Q_{b,2s}^{(j)}$, reach up 9\\% at the end of the resolution -- in terms of cumulated numbers of Krylov iterations. \n\n\\begin{remark}\nBi-material beam was meshed with 25~789 degrees of freedom, and its substructuring into 13 subdomains involved 984 interface degrees of freedom. Multiperforated beam was meshed with 30~515 degrees of freedom, and its substructuring into 30 subdomains involved 1641 interface degrees of freedom. Despite the relative smallness of these test cases, we expect them to be representative of computations on larger structures. Unfortunately our Octave-based code did not allow meaningful time measurements and large scale computations. Moreover, limiting communication as we try to do would be even more appreciable on computations involving many processors. The number of Krylov iterations seems to be the fairest and most reliable performance measurement.\n\\end{remark}\n\nComparison with classic method shows similar results for both test cases: at the end of the resolution, gains vary from 16 to 22\\% for Krylov cumulated iterations, and from 19 to 22\\% for global Newton cumulated iterations. This gain corresponds to the overall performance of the nonlinear substructuring and condensation method that can be achieved with mixed approach, compared to classical procedures. \n\n\n\\begin{remark}\nThe rather limited performance of mixed nonlinear substructuring and condensation method with classical interface impedance $K_{bb,l}^{\\text{neigh}(j)}$, compared to the classical resolution method, can be noticed in the above two examples. This lack of efficiency can probably be imputed to the difficulty of giving full account of long range phenomena with a short-scale interface impedance, whereas they prevail in the case of local heterogeneity (bi-material beam) and slenderness of plate structures (multiperforated beam).\n\\end{remark}\n\n\\subsection{Coupling with SRKS-method}\n\n\nAn augmentation strategy of Krylov subspaces, at each global nonlinear iteration, is possible by extracting Ritz vectors and values at the end of each Krylov solving and re-using them to construct an augmentation basis for the following Krylov iterations. The so-called TRKS method \\cite{gosselet2013total} reuses all of the produced Ritz vectors, while SRKS method \\cite{gosselet2013total} consists in selecting the Ritz values which are good enough approximations of tangent operator eigenvalues, and the corresponding Ritz vectors. SRKS method was implemented and its coupling with nonlinear substructuring and condensation method was studied for both test cases defined at section \\ref{sec:two_test_cases}. \n\nResults are given in tables \\ref{tab:iter_bimat_SRKS} and \\ref{tab:iter_multiperf_SRKS}. \n\n\n\n\n\\begin{table}[!ht]\n\\begin{center}\n\\begin{tabular}{|c|cccccc:c|}\n\\hline\n\\multicolumn{8}{|c|}{Krylov}\\\\\n\\hline\n\\multicolumn{7}{|c:}{ with SRKS } & wo SRKS \\\\\n\\hline\nload inc. & 0.05 & 0.15 & 0.25 & 0.35 & 0.4 & 0.45 & 0.45 \\\\\n\\hline\n$S_t^{(\\overline{j})}$ & 37 & 97 & x &  &  &  & x \\\\\n$K_{bb,l}^{\\text{neigh}(j)}$ & 36 & 113 & 218 & 339 & 452 & 578 & 1772 \\\\ \n$Q_{b,2s}^{(j)}$ & 37 & 98 & 197 & 304 & 398 & 492 & 1514 \\\\\n\\hline\n\\hline\nNKS & 53 & 130 & 245 & 370 & 492 & 648 & 1795 \\\\\n\\hline\n\\multicolumn{8}{c}{ } \\\\\n\\hline\n\\multicolumn{8}{|c|}{Gains (\\%)} \\\\\n\\hline\n$Q_{b,2s}^{(j)}$ vs. $K_{bb,l}^{\\text{neigh}(j)}$ & -3 & 13 & 10 & 10 & 12 & 15 & 15 \\\\\n\\hline\n\\hline\n$Q_{b,2s}^{\\text{neigh}(j)}$ vs. NKS & 30 & 25 & 20 & 18 & 19 & 24 & 16 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\caption{Bi-material beam, coupling with SRKS: Krylov cumulated iterations over load increments}\n\\label{tab:iter_bimat_SRKS}\n\\end{table}\n\n\\begin{table}[!ht]\n\\begin{center}\n\\begin{tabular}{|c|cccc:c|}\n\\hline\n\\multicolumn{6}{|c|}{Krylov} \\\\\n\\hline\n\\multicolumn{5}{|c:}{with SRKS} & wo SRKS \\\\\n\\hline\nload inc. & 0.6 & 1 & 1.3 & 1.5 & 1.5 \\\\\n\\hline\n$S_t^{(\\overline{j})}$ & 48 & 164 & 304 & 445 & 481 \\\\\n$K_{bb,l}^{\\text{neigh}(j)}$ & 61 & 201 & 351 & 506 & 548 \\\\\n$Q_{b,2s}^{(j)}$ & 47 & 159 & 280 & 410 & 438 \\\\\n\\hline\n\\hline\nNKS & 72 & 212 & 362 & 517 & 561 \\\\\n\\hline\n\\multicolumn{6}{c}{ } \\\\\n\\hline\n\\multicolumn{6}{|c|}{Gains (\\%) } \\\\\n\\hline\n$Q_{b,2s}^{(j)}$ vs. $K_{bb,l}^{\\text{neigh}(j)}$ & 20 & 20 & 20 & 20 & 20 \\\\\n$Q_{b,2s}^{(j)}$ vs. $S_t^{(\\overline{j})}$ & 2 & 3 & 8 & 8 & 9 \\\\\n\\hline\n\\hline\n$Q_{b,2s}^{(j)}$ vs. NKS & 35 & 25 & 23 & 21 & 22 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\caption{Multiperforated beam, coupling with SRKS: Krylov cumulated iterations over load increments}\n\\label{tab:iter_multiperf_SRKS}\n\\end{table}\n\n\n\n\n\nAs expected, SRKS leads to a global decrease of the number of Krylov iterations, observable by comparing the columns ''with'' and ''without'' SRKS of results tables. For the bi-material beam, Krylov iterations are reduced on average by 67\\% at last load increment; for multiperforated beam the average reduction is only close to 8\\% (a small number of Krylov iterations implies a small number of post-processed Ritz vectors: this could partly explain the less impressive efficiency of SRKS method on this test case). \n\nConcerning global Newton solver, the cumulated numbers of iterations remained constant with and without SRKS -- as expected, -- they were thus not presented again in this section. \n\nTables \\ref{tab:iter_bimat_SRKS} and \\ref{tab:iter_multiperf_SRKS} confirm observations of previous section. Even if the cumulated numbers of Krylov iterations are decreased thanks to SRKS, the overall gains generated by the new expression $Q_{b,2s}^{(j)}$ remain rather constant, and are even better for bi-material beam (indeed, the classic method NKS suffered from a slight degradation of its overall performance, and the gain of impedance $Q_{b,2s}^{(j)}$ compared to NKS reaches then 24\\% at the end of the resolution, in terms of Krylov cumulated iterations). \n\n\\section{Conclusion}\n\nA new approximation of the interface impedance has been developed, in the context of nonlinear substructuring and condensation methods with mixed approach. The expression of the interface impedance introduced here couples both short and long range interactions terms.\n\nThe procedure for building such a parameter consists in evaluating, for a given subdomain, the Schur tangent operator of the remainder of the structure (i.e. the optimal value in a linear context), which was originally the best analytic expression we could produce to approximate the optimal interface impedance in the nonlinear context. This evaluation involves a short scale term, basically consisting in the stiffness of the considered subdomain neighbors, and a long scale low rank term, composed of the projection of the Schur tangent operator into the space generated by rigid body modes, thereby capturing long range interactions with the faraway structure. \n\nPerformance of a FETI-2LM solver was studied on a linear case, where the Schur tangent operator of the remainder is exactly the optimal value for the interface impedance -- despite its intractability in practice in parallel resolution processes. Although, as expected, the new additive expression of the impedance did not produce as good results as this optimal value, it managed quite impressive gains, in particular compared to the classical choice made in this framework -- i.e. the stiffness assembled over the neighbors of a subdomain. \n\nPerformance of the mixed nonlinear substructuring and condensation method was also studied, on a plasticity case. Not only the exact computation of Schur tangent operator is not affordable in the framework of parallel distributed computations -- unlike the new expression we build, which was chosen to be inexpensively calculable in parallel, -- but it also was found to achieve not as good results as this new expression. This suggests that the level of accuracy obtained on the representation of a substructure environment with the additive expression of the interface impedance introduced here is increased. \n\nEventually, a study of the coupling of the resolution process with a selective reuse procedure of Krylov solver Ritz vectors (SRKS) tends to assess that performance of this new expression is maintained while numbers of Krylov iterations are decreased.\nAll these considerations are rather promising for implementations at larger scales.\n\n\n\\bibliographystyle{ieeetr}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\n\\section{Introduction}\n  \nThe BESIII\\xspace experiment is located at the Institute of High Energy Physics in Beijing. Symmetric \\ensuremath{e^+e^-}\\xspace collisions from Beijing Electron-Positron Collider (BEPCII) in an energy range between \\SI{2.0}{\\si{\\giga\\electronvolt}\\xspace} and \\SI{4.6}{\\si{\\giga\\electronvolt}\\xspace} are analyzed. The maximum luminosity of BEPCII of \\SI{1e33}{\\Lumi} at $\\sqrt{s}=$\\SI{3.773}{\\si{\\giga\\electronvolt}\\xspace} were surpassed in April 2016. \n\nThe detector measures charged track momenta with a relative precision of \\SI{0.5}{\\percent} (@\\SI{1.0}{\\si{\\giga\\electronvolt}\\xspace\/\\ensuremath{c}\\xspace}) using a multi-wire drift chamber in a \\SI{1}{\\tesla} magnetic field. Electromagnetic showers are measured in a caesium iodide calorimeter with a relative precision of \\SI{2.5}{\\percent} (@\\SI{1.0}{\\si{\\giga\\electronvolt}\\xspace}) and a good particle identification is achieved by combining information from energy loss in the drift chamber, from the time-of-flight system and from the calorimeter. Muons can be identified using 9 layers of resistive plate chambers integrated in the magnet return yoke. Details are provided elsewhere \\cite{Ablikim:2009aa}.\nBESIII\\xspace has collected large data samples in the tau-charm region. The interesting samples for the study of charmed hadrons are usually at a center-of-mass energy close to a threshold. The samples of interest for the analyses described in the following were recorded at the \\ensuremath{\\Dz {\\kern -0.16em \\Dzb}}\\xspace\/\\ensuremath{\\Dp {\\kern -0.16em \\Dm}}\\xspace threshold $(\\sqrt{s}=\\SI{3.773}{\\si{\\giga\\electronvolt}\\xspace})$ and at the \\ensuremath{\\Dsp{\\kern -0.16em \\Dsm}}\\xspace threshold $(\\sqrt{s}=\\SI{4.009}{\\si{\\giga\\electronvolt}\\xspace})$. Integrated luminosities of \\SI{2.81}{\\invfb} and \\SI{0.482}{\\invfb} were recorded, respectively.\n\n\\begin{figure}[tbp]\n   \\centering\n   \\begin{tikzpicture}\n\t \n\t  \\draw[draw=none, use as bounding box](0,1.5) rectangle (10.2cm,6cm);\n\t  \\begin{scope}[scale=0.5,color=black!70!white]\n\t\t \\coordinate (origin) at (9,9);\n\t\t \\draw[->] (origin) -- +(0:1) node[above] (n1) {z};\n\t\t \\draw[->] (origin) -- +(90:1) node[left] (n2) {y};\n\t\t\n\t  \\end{scope}\n\t  \\begin{scope}[line width=2pt]\n\t\t \\node[draw,black,rectangle,rounded corners=3pt,minimum size=3pt] (pv) at (5,3) {\\ensuremath{\\psi(3770)}\\xspace};\n\t\t \\draw[blue,->]  (1,3) node[below] {\\ensuremath{e^+}\\xspace} -- (pv);\n\t\t \\draw[blue,->]  (9,3) node[above] {\\en} -- (pv);\n\t\t\n\t\t \\node[draw,red,circle,minimum size=3pt, label=below:$\\ensuremath{\\kern 0.2em\\overline{\\kern -0.2em D}\\rule{0pt}{1.5ex}^0}\\xspace_{tag}$] (Dbarvtx) at (6.5,2.5) {};\n\t\t \\draw[black,dashed,-]  (pv) -- (Dbarvtx);\n\t\t \\draw[->,line width=1.5pt,black!60!white]  (Dbarvtx) -- +(5:2cm); \n\t\t \\draw[->,line width=1.5pt,black!60!white]  (Dbarvtx) -- +(-5:2cm) node[right] {hadrons}; \n\t\t \\draw[->,line width=1.5pt,black!60!white]  (Dbarvtx) -- +(-15:2cm); \n\t\t \\draw[->,line width=1.5pt,black!60!white]  (Dbarvtx) -- +(-25:2cm); \n\t\t\n\t\t \\node[draw,red,circle,minimum size=3pt, label=above right:$\\ensuremath{D^0}\\xspace$] (Dvtx) at (3.5,3.5) {};\n\t\t \\node[draw,black!60!white,fill,circle,minimum size=0pt] (KSvtx) at ($ (Dvtx) + (182:1.5) $) {};\n\t\t \\draw[black!60!white,dashed,-]  (Dvtx) -- (KSvtx);\n\t\t \\draw[black,dashed,-]  (pv) -- (Dvtx);\n\t\t \\draw[black!60!white]  (KSvtx) -- +(190:1) node[left] {$l^+$};\n\t\t \\draw[black!60!white,dashed]  (KSvtx) -- +(170:1) node[left] {$\\nu_l$};\n\t\t \\draw[black!60!white]  (Dvtx) -- +(150:2) node[left] {};\n\t\t \\draw[black!60!white,-]  (Dvtx) -- +(120:2) node[left] {hadrons};\n\t  \\end{scope}\n\t \n\t\t\n\t\t\t  \n\t\t\t\t \n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t \n\t\t\n\t \n   \\end{tikzpicture}\n   \\caption{\\ensuremath{\\psi(3770)}\\xspace decay topology in the \\ensuremath{\\psi(3770)}\\xspace rest frame. An undetected particle track can be reconstructed using the constrained kinematics of the decay. Typical tag modes for \\ensuremath{C\\!P}\\xspace and flavour eigenstates are listed.}\n   \\label{fig:psiprprdecay}\n\\end{figure}\nThe at-threshold decay topology at a center-of-mass energy of \\SI{3.773}{\\si{\\giga\\electronvolt}\\xspace} is illustrated in \\cref{fig:psiprprdecay}. A pair of mesons is produced and it is possible to conclude from the decay of one meson (so-called tag meson) properties of the second decay. For instance in case of neutral \\ensuremath{D}\\xspace decays the flavour or the \\ensuremath{C\\!P}\\xspace quantum numbers of the signal decay can be measured, even if the signal final state does not provide this information. In case of charged \\ensuremath{D}\\xspace decays the reconstruction of both decays is used to reduce the background and furthermore if undetected particles are involved in the signal decay the four momenta of those can be reconstructed. In particular the study of leptonic and semi-leptonic decays benefits from this. The reconstruction of both decays in each event is referred to as double tag technique.\n\nIn the following we present the measurements of the \\ensuremath{D^+_s}\\xspace decay constant (\\cref{sec:dsmunu}), first evidence of the decay $\\ensuremath{D^+}\\xspace\\ensuremath{\\rightarrow}\\xspace\\tau\\ensuremath{\\nu_\\tau}\\xspace$ (\\cref{sec:dptaunu}) and the analysis of the decay $\\ensuremath{D^0}\\xspace\\ensuremath{\\rightarrow}\\xspace\\KSL\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)$ (\\cref{sec:dzkspizpiz}).\n\\section{Pure leptonic $\\ensuremath{D_{s(d)}}\\xspace^+$ decays}\n\\label{sec:pureLeptonicD}\nThe pure leptonic decay of charged \\ensuremath{D_{s(d)}}\\xspace mesons proceeds via the annihilation of \\ensuremath{c}\\xspace and \\ensuremath{\\overline s}\\xspace(\\ensuremath{\\overline d}\\xspace) to a virtual \\ensuremath{W^\\pm}\\xspace boson and its decay to $l^+\\nu_l$. The decay rate can be parametrized as:\n\\begin{align}\n\t\\Gamma(\\ensuremath{D_{s(d)}}\\xspace\\ensuremath{\\rightarrow}\\xspace l^+\\nu_l) = \\frac{G_F^2}{8\\pi} f_{\\ensuremath{D_{s(d)}}\\xspace}^2 m_l^2 m_{\\ensuremath{D_{s(d)}}\\xspace} \\left( 1-\\frac{m_l^2}{m^2_{\\ensuremath{D_{s(d)}}\\xspace}}\\right)^2 \\abs{V_{cs(d)}}^2.\n   \\label{eqn:ds:decayRate}\n\\end{align}\nWith the Fermi constant $G_F$, the lepton mass $m_l$, the corresponding CKM matrix element $\\abs{V_{cs(d)}}^2$, the \\ensuremath{D_{s(d)}}\\xspace mass $m_{\\ensuremath{D_{s(d)}}\\xspace}$ and the decay constant $f_{\\ensuremath{D_{s(d)}}\\xspace}^2$. The decay constant parametrizes the \\ensuremath{\\mathrm{QCD}}\\xspace effects on the decay. From the measurement of the decay width $\\Gamma(\\ensuremath{D_{s(d)}}\\xspace\\ensuremath{\\rightarrow}\\xspace l^+\\nu_l)$ the decay constant $f_{\\ensuremath{D_{s(d)}}\\xspace}^2$ can be extracted. \n\nThe branching fraction can be measured via the previously described double tag technique. In each event the tag decay is reconstructed via numerous decay channels. The number of events that contain a tag candidate is denoted by $N_{\\text{tag}}$. Among those events the signal decay is reconstructed and the number of events that contain a tag decay and a signal decay is denoted by $N_{\\text{sig,tag}}$. The branching fraction is given by:\n\\begin{align}\n   {\\ensuremath{\\mathcal B}}\\xspace(\\ensuremath{D_{s(d)}}\\xspace\\ensuremath{\\rightarrow}\\xspace l^+\\nu_l) = \\frac{N_{\\text{sig,tag}}}{\\epsilon_{\\text{sig,tag}}}\\times\\frac{\\epsilon_{\\text{tag}}}{N_{\\text{tag}}}.\n   \\label{eqn:ds:bf}\n\\end{align}\nThe efficiencies for reconstruction and selection $\\epsilon_i$ are obtained from simulation.\nSince the final state contains a neutrino which is not detected the signal yield is determined using the missing mass:\n\\begin{align}\n   MM^2 = \\frac{\\left(E_{\\text{beam}}-E_\\mu\\right)^2}{c^4} - \\frac{\\left(-\\vec{p}_{\\ensuremath{D_{s(d)}}\\xspace}-\\vec{p}_{\\ensuremath{\\mu^+}\\xspace}\\right)^2}{\\ensuremath{c}\\xspace^2}.\n\\end{align}\nThe beam energy is denoted by $E_{\\text{beam}}$ and the reconstructed momentum of the tag \\ensuremath{D_{s(d)}}\\xspace decay candidate by $\\vec{p}_{\\ensuremath{D_{s(d)}}\\xspace}$.\n\n\\pagebreak\n\\subsection{$\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\mu^+\\ensuremath{\\nu_\\mu}\\xspace$ and $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\tau^+\\ensuremath{\\nu_\\tau}\\xspace$}\n\\label{sec:dsmunu}\nThe distribution of $MM^2$ of $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\mu^+\\ensuremath{\\nu_\\mu}\\xspace$ and $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\tau^+\\ensuremath{\\nu_\\tau}\\xspace$ is shown in \\cref{fig:ds:missingMass}. The \\ensuremath{\\tau^+}\\xspace is reconstructed via its decay to $\\ensuremath{\\pi^+}\\xspace\\ensuremath{\\nub_\\tau}\\xspace$. The yield is determined via a simultaneous fit to signal and sideband regions whereas the sideband regions are defined in the \\ensuremath{\\Dbar^+_s}\\xspace mass spectrum of the tag candidate. The $\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace$ signal is shown as red dotted curve and the $\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace$ signal as black dot-dashed curve. Background from misreconstructed tag \\ensuremath{D^+_s}\\xspace decays and background from non-\\ensuremath{\\Dsp{\\kern -0.16em \\Dsm}}\\xspace events is shown as green short dashed and violet long dashed curve, respectively.\nWithin a sample of \\num{15127(321)} events which contain a tag candidate we find \\num{69.3(93)} $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace$ decays and \\num{32.5(43)} $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace$ decays. In the fitting procedure the ratio of $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace$ to $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace$ was constraint to its Standard model prediction. The yields are corrected for radiative effects and we obtain:\n\\begin{align}\n   {\\ensuremath{\\mathcal B}}\\xspace(\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace) &= \\SIerrs{0.495}{0.067}{0.026}{\\percent} \\nonumber\\\\\n   {\\ensuremath{\\mathcal B}}\\xspace(\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace) &= \\SIerrs{4.83}{0.65}{0.26}{\\percent}.\n\\end{align}\n\\begin{wrapfigure}[21]{r}{0.35\\textwidth}\n   \\centering\n   \\includegraphics[width=0.35\\textwidth]{Dslnu}\n   \\caption{$MM^2$ distribution of $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\mu^+\\ensuremath{\\nu_\\mu}\\xspace$ and $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\tau^+\\ensuremath{\\nu_\\tau}\\xspace$. Signal (a) and sideband (b) regions are shown.}\n   \\label{fig:ds:missingMass}\n\\end{wrapfigure}\nThe branching fractions  {\\ensuremath{\\mathcal B}}\\xspace($\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace$) and  {\\ensuremath{\\mathcal B}}\\xspace($\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace$) are consistent with the world average within \\num{1} and \\num{1.5} standard deviations, respectively.\nFurthermore, the branching fractions are consistently determined using a fitting method which does not rely on the ratio of $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace$ to $\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace$. For further details we refer to \\cite{Ablikim:2016duz}.\n\nUsing ${\\ensuremath{\\mathcal B}}\\xspace(\\ensuremath{D^+_s}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace)$ the decay constant $f_{\\ensuremath{D^+_s}\\xspace}$ is determined using \\cref{eqn:ds:decayRate}:\n\\begin{align}\n   f_{\\ensuremath{D^+_s}\\xspace} = \\SIerrs{241.0}{16.3}{6.5}{\\si{\\mega\\electronvolt}\\xspace}.\n\\end{align}\nThe CKM matrix element $\\abs{V_{cd}}=\\num{0.97425(22)}$ \\cite{Agashe:2014kda} and the \\ensuremath{D^+_s}\\xspace lifetime \\cite{Agashe:2014kda} is used. A good agreement with LQCD calculations is found. Result are published in \\cite{Ablikim:2016duz}\n\n\\subsection{$\\ensuremath{D^+}\\xspace\\ensuremath{\\rightarrow}\\xspace\\tau^+\\ensuremath{\\nu_\\tau}\\xspace$}\n\\label{sec:dptaunu}\nThe $MM^2$ distribution of $\\ensuremath{D^+}\\xspace\\ensuremath{\\rightarrow}\\xspace\\tau^+\\ensuremath{\\nu_\\tau}\\xspace$ is shown in \\cref{fig:MMsqDptaunu}. The most severe background to the signal channel is $\\mu^+\\ensuremath{\\nu_\\mu}\\xspace$. To distinguish signal and background in a fitting procedure we use the difference in energy deposit of pions and muons in the electromagnetic calorimeter (EMC). We split the sample into events with an energy deposit larger and sample $\\SI{300}{\\si{\\mega\\electronvolt}\\xspace}$. As shown in \\cref{fig:MMsqDptaunu}(b) above $\\SI{300}{\\si{\\mega\\electronvolt}\\xspace}$ the number of $\\mu^+\\ensuremath{\\nu_\\mu}\\xspace$ events is reduced compared to the number of $\\tau^+\\ensuremath{\\nu_\\tau}\\xspace$ events.\n\\begin{figure}[tb]\n\t\\centering\n\t\\subfloat[$E_{EMC} \\leq \\SI{300}{\\si{\\mega\\electronvolt}\\xspace}$]{\n\t\\includegraphics[width=0.45\\textwidth]{dptaunuLow}}\n\t\\subfloat[$E_{EMC} > \\SI{300}{\\si{\\mega\\electronvolt}\\xspace}$]{\n\t\\includegraphics[width=0.45\\textwidth]{dptaunuHigh}}\n\t\\caption{$MM^2$ distribution for the decay $\\ensuremath{D^+}\\xspace\\ensuremath{\\rightarrow}\\xspace\\tau^+\\ensuremath{\\nu_\\tau}\\xspace$. The signal is shown as solid orange line. Background comes mainly from \\ensuremath{D^+}\\xspace decays to $\\mu^+\\ensuremath{\\nu_\\mu}\\xspace$ (solid black) and to $\\ensuremath{\\pi^+}\\xspace\\KL$ (dashed blue).}\n\t\\label{fig:MMsqDptaunu}\n\\end{figure}\n\nWe obtain a preliminary signal yield of \\SI{137(27)} events. The significance of the signal is larger than \\SI{4}{\\stdDev}. The preliminary branching fraction is given by:\n\\begin{align}\n\t{\\ensuremath{\\mathcal B}}\\xspace(\\ensuremath{D^+}\\xspace\\ensuremath{\\rightarrow}\\xspace\\tau^+\\ensuremath{\\nu_\\tau}\\xspace) = \\SI{1.20(24)}{\\timesten{-3}}.\n\\end{align}\nFurthermore, we extract the ratio of $\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace$ to $\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace$ decays:\n\\begin{align}\n\tR := \\frac{\\Gamma(\\ensuremath{D^+}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace)}{\\Gamma(\\ensuremath{D^+}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace)} = \\num{3.21(64)}. \n\\end{align}\nThe result is consistent with the Standard Model prediction.\n\n\\section{Analysis of the decay $\\ensuremath{D^0}\\xspace\\ensuremath{\\rightarrow}\\xspace\\KSL\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)$}\n\\label{sec:dzkspizpiz}\nWe present preliminary results of the branching measurement of the decays $\\ensuremath{D^0}\\xspace\\ensuremath{\\rightarrow}\\xspace\\KSL\\ensuremath{\\pi^0}\\xspace$ and $\\ensuremath{D^0}\\xspace\\ensuremath{\\rightarrow}\\xspace\\KSL\\ensuremath{\\pi^0}\\xspace$. Furthermore we determine the \\ensuremath{D^0}\\xspace mixing parameter $y_{\\ensuremath{C\\!P}\\xspace}$ using the \\ensuremath{C\\!P}\\xspace eigenstates $\\KS\\ensuremath{\\pi^0}\\xspace$ and $\\KL\\ensuremath{\\pi^0}\\xspace$. The challenge in this channel is the reconstruction of the \\KL decay since its long decay time signals of its decay products in the drift chamber is very unlikely. We use the constraint kinematics at the \\ensuremath{\\Dz {\\kern -0.16em \\Dzb}}\\xspace threshold to predict the \\KL four-momentum and furthermore require a certain energy deposit in the electromagnetic calorimeter.\n\nThe branching fraction of a \\ensuremath{C\\!P}\\xspace eigenstate can be measured in a self-normalization way using Cabibbo favoured (CF) tag channels. We define:\n\\begin{align}\n\tM^\\pm = \\frac{N_{CF,CP\\pm}}{\\epsilon_{CF,CP\\pm}}\\frac{\\epsilon_{CF}}{N_{CF}}.\t\n\\end{align}\nThe yields of double of double and single tag events is denoted by $N_{CF,CP\\pm}$ and $N_{CF}$ and the corresponding reconstruction efficiencies by $\\epsilon_{CF,CP\\pm}$ and $\\epsilon_{CF}$.\nThe branching fraction is given by:\n\\begin{align}\n\t{\\ensuremath{\\mathcal B}}\\xspace_{\\ensuremath{C\\!P}\\xspace\\pm} = \\frac{1}{1\\mp C_{f}} M^\\pm, \\qquad C_f = \\frac{M^- - M^+}{M^- + M^+}.\n\\end{align}\n\nWe use the flavour tag channels $\\ensuremath{K^-}\\xspace\\ensuremath{\\pi^+}\\xspace$, $\\ensuremath{K^-}\\xspace\\ensuremath{\\pi^+}\\xspace\\ensuremath{\\pi^-}\\xspace\\ensuremath{\\pi^+}\\xspace$ and $\\ensuremath{K^-}\\xspace\\ensuremath{\\pi^+}\\xspace\\ensuremath{\\pi^0}\\xspace$. The double tag yields and the preliminary branching fractions are listed in \\cref{tab:dzkspizpizBF}. The branching fractions of the final states $\\KSL\\ensuremath{\\pi^0}\\xspace$ and $\\KS\\ensuremath{\\pi^0}\\xspace\\piz$ are consistent with the PDG average \\cite{Agashe:2014kda} and the branching fraction to $\\KS\\ensuremath{\\pi^0}\\xspace\\piz$ is the first accurate measurement.\n\nFrom the branching fractions we can calculate the asymmetry between the \\ensuremath{C\\!P}\\xspace eigenstates:\n\\begin{align}\n\tR_{\\ensuremath{K^0}\\xspace\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)} = \\frac{{\\ensuremath{\\mathcal B}}\\xspace_{\\KS\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)}-{\\ensuremath{\\mathcal B}}\\xspace_{\\KL\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)}}{{\\ensuremath{\\mathcal B}}\\xspace_{\\KS\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)}+{\\ensuremath{\\mathcal B}}\\xspace_{\\KL\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)}}.\n\\end{align}\nThe results are also listed in \\cref{tab:dzkspizpizBF}.\n\\begin{table}[tbp]\n\t\\centering\n\t\\caption{Double tag yields and branching fractions of \\ensuremath{C\\!P}\\xspace eigenstates $\\KSL\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)$. Uncertainties are statistical only.}\n\t\\label{tab:dzkspizpizBF}\n\t\\begin{tabular}{|c|c|c|c|c|}\n\t\t\\hline\n\t\tChannel & \\ensuremath{C\\!P}\\xspace &$N_{CF,CP\\pm}$&  ${\\ensuremath{\\mathcal B}}\\xspace_{\\ensuremath{C\\!P}\\xspace\\pm}$& R\\\\\n\t\t\\hline\n\t\t\\KS\\ensuremath{\\pi^0}\\xspace & $+$ &\\num{7141(91)}& \\num{1.230(020)} & \\multirow{2}{*}{\\num{0.1077(125)}} \\\\\n\t\t\\KL\\ensuremath{\\pi^0}\\xspace & $-$ &\\num{6678(118)}& \\num{0.991(019)} &  \\\\\n\t\t\\hline\n\t\t\\KS\\ensuremath{\\pi^0}\\xspace\\piz & $+$ &\\num{2623(60)}& \\num{0.975(24)} & \\multirow{2}{*}{\\num{-0.0929(209)}} \\\\\n\t\t\\KL\\ensuremath{\\pi^0}\\xspace\\piz & $-$ &\\num{2136(69)}& \\num{1.18(04)} &  \\\\\n\t\t\\hline\n\t\\end{tabular}\n\\end{table}\n\n\\pagebreak\n\\subsection{Measurement of $y_{CP}$}\nUsing the final states $\\KS\\ensuremath{\\pi^0}\\xspace$ and $\\KL\\ensuremath{\\pi^0}\\xspace$ we determine the \\ensuremath{D^0}\\xspace mixing parameter $y_{\\ensuremath{C\\!P}\\xspace}$. The branching ratio of a \\ensuremath{C\\!P}\\xspace eigenstate is connected to the branching ratio of a pure flavour eigenstate via:\n\\begin{align}\n\t{\\ensuremath{\\mathcal B}}\\xspace_{\\ensuremath{C\\!P}\\xspace} \\approx {\\ensuremath{\\mathcal B}}\\xspace_{\\text{flavour}} (1\\mp y_{\\ensuremath{C\\!P}\\xspace}). \t\n\\end{align}\nThe parameter $y_{\\ensuremath{C\\!P}\\xspace}$ is then given by the asymmetry of branching ratios of \\ensuremath{C\\!P}\\xspace even and odd states to pure flavour states f:\n\\begin{align}\n\ty_{\\ensuremath{C\\!P}\\xspace} = \\frac{{\\ensuremath{\\mathcal B}}\\xspace_{-;f} - {\\ensuremath{\\mathcal B}}\\xspace_{+;f}}{{\\ensuremath{\\mathcal B}}\\xspace_{-;f} + {\\ensuremath{\\mathcal B}}\\xspace_{+;f}}.\n\\end{align}\nThe previously mentioned Cabibbo favoured final states are not pure flavour eigenstates. Therefore, we use the semi-leptonic decay to $\\ensuremath{K^-}\\xspace e^+\\ensuremath{\\nu_e}\\xspace$.\nWe obtain a preliminary value of:\n\\begin{align}\n\ty_{\\ensuremath{C\\!P}\\xspace} = \\SI{0.98(243)}{\\percent}.\n\\end{align}\nWe quote statistical uncertainty only. The result is in agreement with a previous measurement of BESIII\\xspace \\cite{Ablikim:2015hih} as well as with the HFAG average \\cite{arXiv:1612.07233}. Results are preliminary and we quote statistical uncertainties only.\n\n\\section{Summary}\nThe BESIII\\xspace experiment has collected large data sample at charm-related thresholds. The constraint kinematics at those energies allow the reconstruction of (semi-) leptonic decays with low background. Furthermore, the quantum entanglement of \\ensuremath{\\Dz {\\kern -0.16em \\Dzb}}\\xspace at threshold provides a unique laboratory for the analysis of \\ensuremath{C\\!P}\\xspace eigenstates. \nWe present the analysis of the leptonic decay of \\ensuremath{D^+_s}\\xspace to $\\ensuremath{\\mu^+}\\xspace\\ensuremath{\\nu_\\mu}\\xspace$ and $\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace$ with the measurement of branching fractions of the derived \\ensuremath{D^+_s}\\xspace form factor. Recently, BESIII\\xspace has found preliminary evidence of the decay \\ensuremath{D^+}\\xspace\\ensuremath{\\rightarrow}\\xspace\\ensuremath{\\tau^+}\\xspace\\ensuremath{\\nu_\\tau}\\xspace with a statistical significance above \\SI{4}{\\stdDev}. \nThe analysis of the $\\ensuremath{D^0}\\xspace\\ensuremath{\\rightarrow}\\xspace\\KSL\\ensuremath{\\pi^0}\\xspace(\\ensuremath{\\pi^0}\\xspace)$ includes the measurement of the branching fractions and using the decays to $\\KSL\\ensuremath{\\pi^0}\\xspace$ the measurement of the \\ensuremath{D^0}\\xspace mixing parameter $y_{\\ensuremath{C\\!P}\\xspace}$.\n\\section*{References}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzascm b/data_all_eng_slimpj/shuffled/split2/finalzzascm
new file mode 100644
index 0000000000000000000000000000000000000000..a427072b205660462ccda25887e23d4f69b548fc
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzascm
@@ -0,0 +1,5 @@
+{"text":"\\section{Sample}\n\\label{sec:sample}\n\nThe sample is composed of 70 archival {\\it Hubble Space Telescope}\n({\\it HST}) images of low-redshift QSOs.  They have redshifts between $0.06 \\leq z \\leq 0.46$ and total\n(host plus nucleus) absolute magnitudes brighter than $M_V \\leq -23$.\nFurthermore, they must have been observed with the\n{\\it HST}'s Wide-Field Planetary Camera 2 (WFPC2), using broad-band\nfilters, and have images publicly available in the {\\it HST} archives\nas of 1999.  This brings our sample to 70 QSOs.\nRather than restrict our study to a specific class of QSOs, we impose\nno physical criteria on the QSOs beyond those of magnitude and\nredshift.  Thus we are able to study a broad range of properties and\ndraw general conclusions.  The images are reduced and the physical parameters fitted \nas described by Hamilton et al.~(2002).\n\n\\section{The ``Fundamental Plane'' of QSOs}\n\\label{sec:fp}\n\nFor our Principal Components Analysis (PCA), we use a restricted sample of those QSOs for which we\nhave all of the following parameters: $M_V\\mathrm{(nuc)}$,  $L_X$, \n$r_{1\/2}$, and $\\mu_e$, where $\\mu_e$ is the effective\nsurface magnitude of the galactic bulge.  We further\nrequire that each QSO have a modeled, spheroidal bulge (the entire\ngalaxy, in the case of elliptical hosts).  These qualifications\nrestrict the sample to 42 QSOs.\n\n\nWe can perform two PCAs, an optical one using $M_V\\mathrm{(nuc)}$,  \n$\\log r_{1\/2}$, and $\\mu_e$ as the parameters, and an x-ray one that \nsubstitutes $\\log L_X$ for the nuclear luminosity.\nFrom the optical PCA performed on this sample of 42 objects, \nwe find that 96.1\\% of the variance can be explained with just the first two\nprincipal axes, and therefore the QSOs mostly lie in a plane within this parameter\nspace.  This we consider to be a fundamental plane (FP) for QSOs.  \nFor the corresponding x-ray results, the first two principal axes explain \n95.2\\% of the variance in the sample, and we find here an x-ray QSO fundamental plane.\nThe individual subsamples of QSOs (radio-loud or radio-quiet, with spiral or elliptical hosts, and all \ncombinations of these) \nare also examined in this way, and they show fundamental planes, as well.\n\n\nWe obtain the optical and x-ray formulae for the full sample's fundamental plane:\n\\begin{equation}\n\tM_V\\mathrm{(nuc)} = -77.5 + 3.14 \\mu_e - 14.2 \\log\n\tr_{1\/2}\n\t\\label{equ:oall-physical}\n\\end{equation}\n\\begin{equation}\n\t\\log L_X = 79.3 - 2.03 \\mu_e + 8.74 \\log\n\tr_{1\/2} \\mbox{ .} \n\t\\label{equ:xall-physical}\n\\end{equation}\nViews of the optical and x-ray fundamental planes, with the QSO data points superimposed, \nare displayed in Figure~\\ref{fig:fp-phys}.  Note that the host properties describe the horizontal and the nuclear luminosity the vertical in these plots.  Figure~\\ref{fig:fp-rms} illustrates the precision of the \nQSO fundamental plane in both forms, with the plane plotted against \nthe measured host sizes.  Its highest precision is found when solving for $\\log r_{1\/2}$.\n\n\n\n\\section{Discussion}\n\\label{sec:discussion}\n\n\\subsection{Possible Derivation}\nThe fundamental plane for QSOs shows a relationship between the\nnuclear and host features that goes beyond the simple (and weak) correlation of nuclear and\nhost luminosities.  This behavior may be connected to other, known\nrelations between the objects.\nFor example, there is already a well-studied\nfundamental plane for normal, elliptical galaxies (Djorgovski \\&\nDavis~1987; Dressler et al.~1987) that incorporates galaxy size, $r_{1\/2}$, central velocity dispersion,\n$\\sigma_c$, and effective surface magnitude,\n$\\mu_e$.\n\nLet us take a $V$-band measurement of the normal galaxy fundamental plane \n(Scodeggio et al.~1998), \n$\\log r_{1\/2} = 1.35 \\log \\sigma_c + 0.35 \\mu_e + \\mathit{Constant}$.  \nThe ratio of the coefficients of $\\log r_{1\/2}$ to $\\mu_e$ differs by about 37\\% between the QSO\noptical fundamental plane and the normal galaxy FP, and the QSO x-ray FP\nshows a 34\\% difference.  Still, there is a formal similarity between\nthe QSO and normal fundamental planes, which might point to a link between \nthe host galaxy's central velocity\ndispersion and the nuclear luminosity of the QSO.  This\ncould derive from the fueling mechanism of QSOs, if the movement of gas\nto the center of the galaxy and the black hole is related to the\nvelocity dispersion.  \n\n\nIt is therefore tempting to try to derive the\nQSO fundamental plane directly from the elliptical galaxy fundamental\nplane, but we find two problems with this approach, both arising from the relation of black hole mass to nuclear luminosity.  Using the\nvelocity dispersion to black hole mass relation of Merritt \\& Ferrarese~(2001),\n$ \\mathcal{M}_{BH}=1.3 \\times 10^8 \n\t\\left( \\sigma_c \/ 200 \\mbox{ km s}^{-1} \\right)^{4.72} \n\t\\mathcal{M}_{\\odot} $\nwe can put the elliptical galaxy fundamental plane in terms of black hole mass.  \nUsing the observed (but weak) correlation between black hole mass and \nnuclear luminosity in our sample, $M_V\\mathrm{(nuc)} = -1.98 \\log \\left( \\mathcal{M}_{\\mathrm{BH}} \/ \\mathcal{M}_{\\odot} \\right) -6.90$ and \n$\\log L_X = 2.77 \\log \\left( \\mathcal{M}_{\\mathrm{BH}} \/ \\mathcal{M}_{\\odot} \\right) + 19.8$,\nwe obtain\n\\begin{equation}\n\tM_V\\mathrm{(nuc)} = \\mathit{Constant} + 2.5 \\mu_e - 7.14 \\log r_{1\/2}\n\\end{equation}\n\\begin{equation}\n\t\\log L_X = \\mathit{Constant} - 3.5 \\mu_e + 10 \\log r_{1\/2} \\mbox{ .}\n\\end{equation}\nThese are our attempts to derive the QSO optical fundamental plane from the normal galaxy FP.\nThe optical form differs from the actual QSO FP, equation~(\\ref{equ:oall-physical}), \ncompletely outside the propagated errors, but \nthe x-ray form is within the errors of equation~(\\ref{equ:xall-physical}).\n\n\nBut any derivation of the QSO fundamental plane has an additional problem.  \nAs mentioned before, the QSO fundamental plane for the full sample is \ncomposed of individual FPs of the several subsamples.  Some subsample FPs \nactually slope in the opposite direction from the overall QSO FP.\nFor example, in the optical form, the FP of radio-quiets in elliptical hosts \nslopes in the opposite direction.  \nAnd in the x-ray form, the radio-quiet subsamples slope oppositely \nfrom the overall sample.\nYet these differences cannot be accounted for by different correlations of \nnuclear luminosity with black hole mass.  \nThe poor correlation of black hole mass with nuclear luminosity lies in contrast with the \nrelatively thin QSO fundamental plane.  \nFurthermore, Woo \\& Urry~(2002) suggest that the apparent correlations \nbetween black hole mass and nuclear luminosity are merely artifacts of \nsample selection.\nRegardless of how we take this interpretation, the relationship between \nblack hole mass and nuclear luminosity remains the missing link in any \nderivation of the QSO fundamental plane.\n\n\\subsection{Arrangement of Subsample Planes}\n\nThe insight into the origins of this new fundamental plane relationship might come from\nthe comparison of the QSO subsample FPs.  The thickness of the overall QSO\nfundamental plane appears partly to be the result of the superposition of\nthe subsamples' planes.\nBecause the QSO FP mathematically describes a link between the host and the \nnucleus, it seems reasonable to suppose that the slope of the plane depends on the \nphysical nature of this link.  The fueling mechanism at a QSO's core would seem to be the most directly related to this, depending on how we define ``fueling mechanism.''  \nWe could encompass within this term the details of the structure and dynamics of the accretion disk, as well as question of whether the QSO is efficiently or inefficiently fueled.\n\nIt is intriguing that as we change from one class to another, the fundamental plane \nessentially pivots about an axis, so the differences are mostly reduced to a single dimension, \nthe slope (or gradient) relative to the $\\mu_e$--$\\log r_{1\/2}$ plane.\nThe gradient directions, projected onto the $\\mu_e$--$\\log r_{1\/2}$ plane, are almost all \neither aligned (or anti-aligned, for those with opposite slope).  \nThe optical subsample gradient directions are never more \nthan 3.8 degrees away from that of the full sample, and in the x-ray form, they never exceed  \na 6.4 degree deviation.\n\nRadio-loudness has the strongest effect on the slopes.  In the x-ray form, the subsample FPs \nare almost evenly divided between those aligned with the full sample and those anti-aligned.  \nIn the optical form, only radio-quiets in elliptical hosts tilt opposite to the full sample.\nThis effect is interesting because we are seeing a stark difference between the radio-loud and \nradio-quiet nuclei in the hosts of the same morphology.\n\nIt would be interesting to find if the different QSO FP orientations described above come \nabout from different fueling mechanisms that might be found in the various subsamples.\nWe see, for instance, that radio-quiet and radio-loud QSOs are characterized by very \ndifferent slopes in their x-ray FPs, but the understanding of what makes these QSO types differ \nis still too limited to speculate further here.  In our ongoing research, we are expanding the \nfundamental plane study to other types of AGN.  \nWe can then compare their FP orientations with those of the different QSO\nsubsamples, which may teach us more about the physics underlying the QSO fundamental plane.\n\n\\section{Future Work}\n\nWe should ask if lower luminosity classes of AGN (such as Seyferts or LLAGN) also have \nfundamental planes of this sort.  If they do, how do they compare with that of QSOs?  We can \nimagine four possibilities:\n\\begin{enumerate}\n\\item{They share the same fundamental plane as QSOs.  This would indicate that AGN power \nscales with the host properties, even across AGN types, and would support some form of \nunification.}\n\n\\item{The plane is parallel to that of QSOs, but shifted to lower nuclear luminosities.  This would \nshow that these host properties don't determine the AGN class, and a given galaxy could \nhost different types.}\n\n\\item{The plane is tilted with respect to that of QSOs.  Then the fundamental plane slope would \nbe characteristic of the AGN type, possibly supporting the idea that the slope is tied to the \naccretion mechanism.}\n\n\\item{There is no fundamental plane whatsoever.  In that case, this type of fundamental plane \nwould be a unique property of QSOs.  High-luminosity objects would be more closely \nconnected with their host properties.}\n\\end{enumerate}\n\nAny of these outcomes would teach us something useful.\n\n\\begin{figure}\n\\scalebox{0.675}{\\includegraphics{ofp2.eps}}\n\\scalebox{0.675}{\\includegraphics{xfp2.eps}}\n\\caption{\nViews of the optical (left) and x-ray (right) QSO\nfundamental planes, showing the individual QSOs (points) and the plane fitted to the overall sample.  The host properties are the horizontal axes, while nuclear luminosity is vertical.   \nThe shading of the planes is proportional to nuclear luminosity, ranging from black (faint) to white (bright).  \nNote that only those points lying above the plane are visible here.  \nIn the axis labels, ``M'' is $M_V\\mathrm{(nuc)}$, ``X'' is $\\log L_X$, \n``$\\mu$'' is $\\mu_e$, and ``r'' is $\\log r_{1\/2}$.\n}\n\\label{fig:fp-phys}\n\\end{figure}\n\n\n\\begin{figure}\n\\scalebox{0.34}{\\includegraphics{fp-errors-rx.eps}}\n\\scalebox{0.34}{\\includegraphics{fp-errors-ro.eps}}\n\\caption{Overall QSO fundamental plane (vertical\naxis), plotted against the measured host galaxy size ($\\log r_{1\/2}$, horizontal\naxis).  Points on the diagonal line show perfect correspondence.  \nThe left figure uses the QSO fundamental plane in its optical form, while the right\nfigure uses the x-ray form.  The QSO fundamental plane is most precise when solved for the host size.}\n\\label{fig:fp-rms}\n\\end{figure}\n\n\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nThree types of fourth order Painlev\\'{e} type ordinary differential equations have been studied \\cite{FS,NY1,S}.\nThey are extensions of the Painlev\\'{e} equations $P_{\\rm{II}},\\ldots,P_{\\rm{VI}}$ and expressed as Hamiltonian systems\n\\[\n\t\\mathcal{H}^{X_n^{(1)}}:\\quad\n\t\\frac{dq_i}{dt} = \\frac{\\partial H^{X_n^{(1)}}}{\\partial p_i},\\quad\n\t\\frac{dp_i}{dt} = -\\frac{\\partial H^{X_n^{(1)}}}{\\partial q_i}\\quad\n\t(i=1,2),\n\\]\nwith the Coupled Hamiltonians\n\\[\\begin{split}\n\tH^{A_4^{(1)}} &= H_{\\rm{IV}}(q_1,p_1;\\alpha_2,\\alpha_1)\n\t+ H_{\\rm{IV}}(q_2,p_2;\\alpha_4,\\alpha_1+\\alpha_3) + 2q_1p_1p_2,\\\\\n\ttH^{A_5^{(1)}} &= H_{\\rm{V}}(q_1,p_1;\\alpha_2,\\alpha_1,\\alpha_1+\\alpha_3)\\\\\n\t&\\quad + H_{\\rm{V}}(q_2,p_2;\\alpha_4,\\alpha_1+\\alpha_3,\\alpha_1+\\alpha_3)\n\t+ 2q_1p_1(q_2-1)p_2,\\\\\n\tt(t-1)H^{D_6^{(1)}} &= H_{\\rm{VI}}(q_1,p_1;\\alpha_0,\\alpha_3+\\alpha_5,\n\t\\alpha_3+\\alpha_6,\\alpha_2(\\alpha_1+\\alpha_2))\\\\\n\t&\\quad + H_{\\rm{VI}}(q_2,p_2;\\alpha_0+\\alpha_3,\\alpha_5,\\alpha_6,\n\t\\alpha_4(\\alpha_1+2\\alpha_2+\\alpha_3+\\alpha_4))\\\\\n\t&\\quad + 2(q_1-t)p_1q_2\\{(q_2-1)p_2+\\alpha_4\\},\n\\end{split}\\]\nwhere\n\\[\\begin{split}\n\tH_{\\rm{IV}}(q,p;a,b) &= qp(p-q-t) - aq - bp,\\\\\n\tH_{\\rm{V}}(q,p;a,b,c) &= q(q-1)p(p+t) + atq + bp - cqp,\\\\\n\tH_{\\rm{VI}}(q,p;a,b,c,d) &= q(q-1)(q-t)p^2 - \\{(a-1)q(q-1)\\\\\n\t&\\quad +bq(q-t)+c(q-1)(q-t)\\}p + dq.\n\\end{split}\\]\nBut complete classification of fourth order Painlev\\'{e} systems is not achieved, so that the existence of unknown ones is expected.\nIn this article, we derive a class of fourth order Painlev\\'{e} systems from the Drinfeld-Sokolov hierarchies of type $A_n^{(1)}$ by similarity reductions.\n\nThe Drinfeld-Sokolov hierarchies are extensions of the KdV (or mKdV) hierarchy for the affine Lie algebras \\cite{DS}.\nFor type $A_n^{(1)}$, they imply several Painlev\\'{e} systems by similarity reductions \\cite{AS,KIK,KK1,KK2,NY1}; {\\it see Table 1}.\\DSPainleveKnown\nSuch fact clarifies the origines of several properties of the Painlev\\'{e} systems, Lax pairs, affine Weyl group symmetries and particular solutions in terms of the Schur polynomials.\n\nThe Drinfeld-Sokolov hierarchies are characterized by the Heisenberg subalgebras, that is maximal nilpotent subalgebras, of the affine Lie algebras.\nAnd the isomorphism classes of the Heisenberg subalgebras are in one-to-one correspondence with the conjugacy classes of the finite Weyl group {\\rm\\cite{KP}}.\nIn this article, we choose the {\\it regular} conjugacy classes of $W(A_n)$ and consider their associated hierarchies, called {\\it type I hierarchies} \\cite{GHM}.\nIn the notation of \\cite{DF}, the regular conjugacy classes of $W(A_n)$ correspond to the partitions $(p,\\ldots,p)$ and $(p,\\ldots,p,1)$.\nFor the derivation of fourth order Painlev\\'{e} systems, we investigate the partitions $(2,2)$, $(3,1)$, $(4,1)$, $(2,2,1)$ and $(3,3)$; {\\it see Table 2}.\\DSPainleveResult\n\nOne of impotant results in this article is the derivation of a new Painlev\\'{e} system.\nIt is expressed as a Hamiltonian system\n\\begin{equation}\\label{Eq:CP6}\n\t\\frac{dq_i}{dt} = \\frac{\\partial H_c}{\\partial p_i},\\quad\n\t\\frac{dp_i}{dt} = -\\frac{\\partial H_c}{\\partial q_i}\\quad (i=1,2),\n\\end{equation}\nwith a Coupled Hamiltonian\n\\begin{equation}\\begin{split}\\label{Eq:CP6_Ham}\n\tt(t-1)H_c &= H_{\\rm{VI}}(q_1,p_1;\\alpha_2,\\alpha_0+\\alpha_4,\n\t\\alpha_3+\\alpha_5-\\eta,\\eta\\alpha_1)\\\\\n\t&\\quad + H_{\\rm{VI}}(q_2,p_2;\\alpha_0+\\alpha_2,\\alpha_4,\n\t\\alpha_1+\\alpha_3-\\eta,\\eta\\alpha_5)\\\\\n\t&\\quad\n\t+ (q_1-t)(q_2-1)\\left\\{(q_1p_1+\\alpha_1)p_2+p_1(p_2q_2+\\alpha_5)\\right\\}.\n\\end{split}\\end{equation}\nThis system admits affine Weyl group symmetry of type $A_5^{(1)}$; see Appendix \\ref{Sec:AffWey}.\nOn the other hand, the system $\\mathcal{H}^{D_6^{(1)}}$ admits one of type $D_6^{(1)}$.\nThe relation between those two coupled Painlev\\'{e} VI systems is not clarified.\n\n\\begin{rem}\nFor the partition $(1,\\ldots,1)$ of $n+2$, we have the Garnier system in $n$-variables {\\rm\\cite{KK2}}.\nAlso for each partition $(5,1)$ and $(2,2,2)$, a system of sixth order is derived{\\rm;} we do not give the explicit formula here.\nThus we conjecture that any more fourth order Painlev\\'{e} system do not arise from the type I hierarchy.\n\\end{rem}\n\nThis article is organized as follows.\nIn Section \\ref{Sec:AffLie}, we recall the affine Lie algebra of type $A^{(1)}_n$ and realize it in a flamework of a central extension of the loop algebra $\\mathfrak{sl}_{n+1}[z,z^{-1}]$.\nIn Section \\ref{Sec:Heisenberg}, the Heisenberg subalgebra of $\\widehat{\\mathfrak{sl}}_{n+1}$ corresponding to the partition $\\mathbf{n}$ is introduced.\nIn Section \\ref{Sec:D-S}, we formulate the Drinfeld-Sokolov hierarchies and their similarity reductions.\nIn Section \\ref{Sec:Deri_CP6} and \\ref{Sec:Deri_Others}, the Painlev\\'{e} systems are derived from the Drinfeld-Sokolov hierarchies.\nIn Appendix \\ref{Sec:Lax}, we give explicit descriptions of Lax pairs by means of a bases of $\\widehat{\\mathfrak{sl}}_{n+1}$.\nIn Appendix \\ref{Sec:AffWey}, we discuss a group of symmetries for the system \\eqref{Eq:CP6} with \\eqref{Eq:CP6_Ham}.\n\n\n\\section{Affine Lie algebra}\\label{Sec:AffLie}\n\nIn this section, we recall the affine Lie algebra of type $A^{(1)}_n$ and realize it in a flamework of a central extension of the loop algebra $\\mathfrak{sl}_{n+1}[z,z^{-1}]$.\n\nIn the notation of \\cite{Kac}, the affine Lie algebra $\\mathfrak{g}=\\mathfrak{g}(A^{(1)}_n)$ is generated by the Chevalley generators $e_i,f_i,\\alpha_i^{\\vee}$ $(i=0,\\ldots,n)$ and the scaling element $d$ with the fundamental relations\n\\[\\begin{split}\n\t&(\\mathrm{ad}e_i)^{1-a_{i,j}}(e_j)=0,\\quad\n\t(\\mathrm{ad}f_i)^{1-a_{i,j}}(f_j)=0\\quad (i\\neq j),\\\\\n\t&[\\alpha_i^{\\vee},\\alpha_j^{\\vee}]=0,\\quad\n\t[\\alpha_i^{\\vee},e_j]=a_{i,j}e_j,\\quad\n\t[\\alpha_i^{\\vee},f_j]=-a_{i,j}f_j,\\quad\n\t[e_i,f_j]=\\delta_{i,j}\\alpha_i^{\\vee},\\\\\n\t&[d,\\alpha_i^{\\vee}]=0,\\quad [d,e_i]=\\delta_{i,0}e_0,\\quad\n\t[d,f_i]=-\\delta_{i,0}f_0,\n\\end{split}\\]\nfor $i,j=0,\\ldots,n$.\nThe generalized Cartan matrix $A=\\left[a_{i,j}\\right]_{i,j=0}^{n}$ for $\\mathfrak{g}$ is defined by\n\\[\\begin{array}{llll}\n\ta_{i,i}=2& (i=0,\\ldots,n),\\\\[4pt]\n\ta_{i,i+1}=a_{n,0}=a_{i+1,i}=a_{0,n}=-1& (i=0,\\ldots,n-1),\\\\[4pt]\n\ta_{i,j}=0& (\\text{otherwise}).\n\\end{array}\\]\nWe denote the Cartan subalgebra of $\\mathfrak{g}$ by\n\\[\n\t\\mathfrak{h} = \\mathbb{C}\\alpha_0^{\\vee}\\oplus\\mathbb{C}\\alpha_1^{\\vee}\n\t\\oplus\\cdots\\oplus\\mathbb{C}\\alpha_n^{\\vee}\\oplus\\mathbb{C}d\n\t= \\mathfrak{h}'\\oplus\\mathbb{C}d.\n\\]\nThe normalized invariant form $(\\cdot|\\cdot):\\mathfrak{g}\\times\\mathfrak{g}\\to\\mathbb{C}$ is determined by the conditions\n\\[\\begin{array}{lll}\n\t(\\alpha_i^{\\vee}|\\alpha_j^{\\vee}) = a_{i,j},& (e_i|f_j) = \\delta_{i,j},&\n\t(\\alpha_i^{\\vee}|e_j) = (\\alpha_i^{\\vee}|f_j) = 0,\\\\[4pt]\n\t(d|d) = 0,& (d|\\alpha_j^{\\vee}) = \\delta_{0,j},& (d|e_j) = (d|f_j) = 0,\n\\end{array}\\]\nfor $i,j=0,\\ldots,n$.\n\nLet $\\mathfrak{n}_{+}$ and $\\mathfrak{n}_{-}$ be the subalgebras of $\\mathfrak{g}$ generated by $e_i$ and $f_i$ $(i=0,\\ldots,n)$ respectively.\nThen the Borel subalgebra $\\mathfrak{b}_{+}$ of $\\mathfrak{g}$ is defined by $\\mathfrak{b}_{+}=\\mathfrak{h}\\oplus\\mathfrak{n}_{+}$.\nNote that we have the triangular decomposition\n\\[\n\t\\mathfrak{g} = \\mathfrak{n}_{-}\\oplus\\mathfrak{h}\\oplus\\mathfrak{n}_{+}\n\t= \\mathfrak{n}_{-}\\oplus\\mathfrak{b}_{+}.\n\\]\nThe corresponding infinite demensional groups are defined by\n\\[\n\tN_{\\pm} = \\exp(\\mathfrak{n}_{\\pm}^*),\\quad H = \\exp(\\mathfrak{h}'),\\quad\n\tB_{+} = HN_{+},\n\\]\nwhere $\\mathfrak{n}_{\\pm}^*$ are completions of $\\mathfrak{n}_{\\pm}$ respectively.\n\nLet $\\mathbf{s}=(s_0,\\ldots,s_n)$ be a vector of non-negative integers.\nWe consider a gradation $\\mathfrak{g}=\\bigoplus_{k\\in\\mathbb{Z}}\\mathfrak{g}_k(\\mathbf{s})$ of type $\\mathbf{s}$ by setting\n\\[\n\t\\deg\\mathfrak{h}=0,\\quad \\deg e_i=s_i,\\quad \\deg f_i=-s_i\\quad\n\t(i=0,\\ldots,n).\n\\]\nWith an element $\\vartheta(\\mathbf{s})\\in\\mathfrak{h}$ such that\n\\[\n\t(\\vartheta(\\mathbf{s})|\\alpha_i^{\\vee}) = s_i\\quad (i=0,\\ldots,n),\n\\]\nthis gradation is defined by\n\\[\n\t\\mathfrak{g}_k(\\mathbf{s}) = \\left\\{x\\in\\mathfrak{g}\\bigm|\n\t[\\vartheta(\\mathbf{s}),x]=kx\\right\\}\\quad (k\\in\\mathbb{Z}).\n\\]\nWe denote by\n\\[\n\t\\mathfrak{g}_{<k}(\\mathbf{s}) = \\bigoplus_{l<k}\\mathfrak{g}_l(\\mathbf{s}),\\quad\n\t\\mathfrak{g}_{\\geq k}(\\mathbf{s}) = \\bigoplus_{l\\geq k}\\mathfrak{g}_l(\\mathbf{s}).\n\\]\nNote that a gradation $\\mathbf{s}_p=(1,\\ldots,1)$, called {\\it the principal gradation}, implies\n\\[\n\t\\mathfrak{g}_{<0}(\\mathbf{s}_p) = \\mathfrak{n}_{-},\\quad\n\t\\mathfrak{g}_{\\geq0}(\\mathbf{s}_p) = \\mathfrak{b}_{+}.\n\\]\n\nThe affine Lie algebra $\\mathfrak{g}$ can be identified with\n\\[\n\t\\widehat{\\mathfrak{sl}}_{n+1} = \\mathfrak{sl}_{n+1}[z,z^{-1}]\\oplus\\mathbb{C}z\\frac{d}{dz}\n\t\\oplus\\mathbb{C}K,\n\\]\nwhere $K$ is a canonical central element.\nIn a flamework of $\\widehat{\\mathfrak{sl}}_{n+1}$, the Chevalley generators and the scaling element are given by\n\\[\\begin{split}\n\t&e_i = E_{i,i+1},\\quad f_i = E_{i+1,i},\\quad\n\t\\alpha^{\\vee}_i = E_{i,i} - E_{i+1,i+1}\\quad (i=1,\\ldots,n),\\\\\n\t&e_0 = zE_{n+1,1},\\quad f_0 = z^{-1}E_{1,n+1},\\quad\n\t\\alpha^{\\vee}_0 = E_{n+1,n+1} - E_{1,1} + K,\\quad d = z\\frac{d}{dz},\n\\end{split}\\]\nwhere $E_{i,j}=\\left(\\delta_{i,r}\\delta_{j,s}\\right)_{r,s=1}^{n+1}$ are matrix units.\nThe Lie bracket is defined by\n\\[\\begin{split}\n\t&[z^kX,z^lY] = z^{k+l}(XY-YX) + k\\delta_{k+l,0}\\mathrm{tr}(XY)K,\n\\end{split}\\]\nwhere $X,Y\\in\\mathfrak{sl}_{n+1}$.\n\n\n\\section{Heisenberg subalgebra}\\label{Sec:Heisenberg}\n\nFor type $A_n^{(1)}$, the isomorphism classes of the Heisenberg subalgebras are in one-to-one correspondence with the partitions of $n+1$.\nIn this section, we introduce the Heisenberg subalgebra of $\\widehat{\\mathfrak{sl}}_{n+1}$ corresponding to the partition $\\mathbf{n}$ following the manner in \\cite{KL}.\n\nLet $\\mathbf{n}=(n_1,n_2,\\ldots,n_r,n_{r+1},\\ldots,n_s)$ be a partition of $n+1$ with $n_1\\geq n_2\\geq\\ldots\\geq n_r>n_{r+1}=\\ldots=n_s=1$.\nConsider a partition of matrix corresponding to $\\mathbf{n}$\n\\[\n\t\\begin{bmatrix}\n\t\tB_{11}& B_{12}& \\cdots& B_{1s}\\\\\n\t\tB_{21}& B_{22}& \\cdots& B_{2s}\\\\\n\t\t\\vdots& \\vdots& \\ddots& \\vdots\\\\\n\t\tB_{s1}& B_{s2}& \\cdots& B_{ss}\n\t\\end{bmatrix},\n\\]\nwhere each block $B_{ij}$ is an $n_i\\times n_j$-matrix.\nWith this blockform, we define matricies $\\Lambda_i'\\in\\widehat{\\mathfrak{sl}}_{n+1}$ $(i=1,\\ldots,r)$ by\n\\[\n\t\\Lambda_i' = \\begin{bmatrix}\n\t\tO& & \\cdots& & O\\\\ & & & & \\\\ \\vdots& & B_{ii}& & \\vdots\\\\\n\t\t& & & & \\\\ O& & \\cdots& & O\n\t\\end{bmatrix},\\quad\n\tB_{ii} = \\begin{bmatrix}\n\t\t0& 1& 0& \\cdots& 0\\\\ 0& 0& 1& & 0\\\\ \\vdots& \\vdots& & \\ddots& \\\\\n\t\t0& 0& 0& & 1\\\\ z& 0& 0& \\cdots& 0\n\t\\end{bmatrix},\n\\]\ndiagonal matricies $H_j'\\in\\widehat{\\mathfrak{sl}}_{n+1}$ $(i=j,\\ldots,s-1)$ by\n\\[\n\tH_j' = n_{j+1}z^{-1}(\\Lambda_j')^{n_j}\n\t- n_jz^{-1}(\\Lambda_{j+1}')^{n_{j+1}},\n\\]\nand a diagonal matrix $\\eta_{\\mathbf{n}}'\\in\\widehat{\\mathfrak{sl}}_{n+1}$ by\n\\[\n\tB_{ii} = \\frac{1}{2n_i}\\mathrm{diag}(n_i-1,n_i-3,\\ldots,-n_i+1)\\quad\n\t(i=1,\\ldots,r).\n\\]\n\nDenoting the matrix $\\eta_{\\mathbf{n}}'$ by $\\mathrm{diag}(\\eta_1',\\eta_2',\\ldots,\\eta_{n+1}')$, we consider a permutation\n\\[\n\t\\sigma = \\left(\\begin{array}{llll}\n\t\t\\eta_1'& \\eta_2'& \\ldots& \\eta_{n+1}'\\\\[4pt]\n\t\t\\eta_1& \\eta_2& \\ldots& \\eta_{n+1}\n\t\\end{array}\\right),\n\\]\nsuch that $\\eta_1\\geq\\eta_2\\geq\\ldots\\geq\\eta_{n+1}$.\nThis permutation can be lifted to the transformation $\\sigma$ acting on the matricies $\\Lambda_i'$ and $H_j'$.\nWe set\n\\[\n\t\\Lambda_i = \\sigma(\\Lambda_i')\\quad (i=1,\\ldots,r),\\quad\n\tH_j = \\sigma(H_j')\\quad (j=1,\\ldots,s-1).\n\\]\nThen the Heisenberg subalgebra of $\\widehat{\\mathfrak{sl}}_{n+1}$ corresponding to the partition $\\mathbf{n}$ is defined by\n\\[\n\t\\mathfrak{s}_\\mathbf{n} = \\bigoplus_{i=1}^{r}\n\t\\bigoplus_{k\\in\\mathbb{Z}\\setminus n_i\\mathbb{Z}}\\mathbb{C}\\Lambda_i^k\n\t\\oplus\\bigoplus_{j=1}^{s-1}\\bigoplus_{k\\in\\mathbb{Z}\\setminus\\{0\\}}\n\t\\mathbb{C}z^kH_j\\oplus\\mathbb{C}K.\n\\]\n\nLet $N_{\\mathbf{n}}'$ be the least common multiple of $n_1,\\ldots,n_s$.\nAlso let\n\\[\n\tN_{\\mathbf{n}} = \\left\\{\\begin{array}{ll}\n\t\tN_{\\mathbf{n}}'&\n\t\t\\text{if $\\displaystyle N_{\\mathbf{n}}'\\left(\\frac{1}{n_i}+\\frac{1}{n_j}\\right)\n\t\t\\in2\\mathbb{Z}$ for $\\forall(i,j)$}\\\\[12pt]\n\t\t2N_{\\mathbf{n}}'& \\text{otherwise}\n\t\\end{array}\\right..\n\\]\nWe consider a operator corresponding to $\\mathbf{n}$\n\\[\n\t\\vartheta_{\\mathbf{n}}\n\t= N_{\\mathbf{n}}\\left(z\\frac{d}{dz}+\\mathrm{ad}\\eta_{\\mathbf{n}}\\right),\n\\]\nwhere $\\eta_{\\mathbf{n}}=\\sigma(\\eta_{\\mathbf{n}}')$.\nThen the operator $\\vartheta_{\\mathbf{n}}$ implies a gradation $\\mathbf{s}=(s_0,\\ldots,s_n)$ as follows:\n\\[\n\t\\vartheta_{\\mathbf{n}}(e_i) = s_ie_i\\quad (i=0,\\ldots,n).\n\\]\nNote that the Heisenberg subalgebra $\\mathfrak{s}_\\mathbf{n}$ admits the gradation $\\mathbf{s}$ defined by $\\vartheta_{\\mathbf{n}}$.\n\n\n\\section{Drinfeld-Sokolov hierarchy}\\label{Sec:D-S}\n\nIn this section, we formulate the Drinfeld-Sokolov hierarchy associated with the Heisenberg subalgebra $\\mathfrak{s}_\\mathbf{n}$.\nIts similarity reduction is also formulated.\n\nLet $\\Lambda_i$ and $H_j$ be the generators for $\\mathfrak{s}_\\mathbf{n}$ given in Section \\ref{Sec:Heisenberg}.\nIntroducing time variables $t_{i,k}$ $(i=1,\\ldots,r;k\\in\\mathbb{N})$, we consider an $N_{-}B_{+}$-valued function $G=G(t_{1,1},t_{1,2},\\ldots)$ defined by\n\\[\n\tG = \\exp\\left(\\sum_{i=1}^r\\sum_{k=1}^{\\infty}t_{i,k}\\Lambda_i^k\\right)G(0).\n\\]\nHere we assume the $\\mathbf{n}$-reduced condition\n\\[\n\tt_{i,l}=0\\quad (i=1,\\ldots,r;l\\in n_i\\mathbb{N}).\n\\]\nThen we have a system of partial differential equations\n\\begin{equation}\\label{Eq:DS_exp}\n\t\\partial_{i,k}(G) = \\Lambda_i^kG\\quad (i=1,\\ldots,r;k\\in\\mathbb{N}),\n\\end{equation}\nwhere $\\partial_{i,k}=\\partial\/\\partial t_{i,k}$\nVia the trianglar decomposition\n\\[\n\tG = W^{-1}Z,\\quad W\\in N_{-},\\quad Z\\in B_{+},\n\\]\nthe system \\eqref{Eq:DS_exp} implies {\\it a Sato equation}\n\\begin{equation}\\label{Eq:Sato}\n\t\\partial_{i,k}(W) = B_{i,k}W - W\\Lambda_i^k\\quad\n\t(i=1,\\ldots,r;k\\in\\mathbb{N}),\n\\end{equation}\nwhere $B_{i,k}$ stands for the $b_{+}$-component of $W\\Lambda_i^kW^{-1}$.\nThe compatibility condition of \\eqref{Eq:Sato} gives the Drinfeld-Sokolov hierarchy\n\\begin{equation}\\label{Eq:DS}\n\t\\left[\\partial_{i,k}-B_{i,k},\\partial_{j,l}-B_{j,l}\\right] = 0\\quad\n\t(i,j=1,\\ldots,r;k,l\\in\\mathbb{N}).\n\\end{equation}\n\nUnder the system \\eqref{Eq:Sato}, we consider an equation\n\\begin{equation}\\label{Eq:Sato_SR}\n\t(\\vartheta_{\\mathbf{n}}-\\mathrm{ad}\\rho)(W)\n\t= \\sum_{i=1}^r\\sum_{k=1}^{\\infty}d_ikt_{i,k}\\partial_{i,k}(W),\n\\end{equation}\nwhere $d_i=\\deg\\Lambda_i$ $(i=1,\\ldots,r)$ and $\\rho=\\sum_{j=1}^{s-1}\\rho_jH_j$.\nNote that each $\\rho_j$ is independent of time vatiables $t_{i,k}$.\nThe compatibility condition of \\eqref{Eq:Sato} and \\eqref{Eq:Sato_SR} gives\n\\begin{equation}\\label{Eq:DS_SR}\n\t\\left[\\vartheta_{\\mathbf{n}}-M,\\partial_{i,k}-B_{i,k}\\right] = 0\\quad\n\t(i=1,\\ldots,r;k\\in\\mathbb{N}),\n\\end{equation}\nwhere\n\\[\n\tM = \\rho + \\sum_{i=1}^r\\sum_{k=1}^{\\infty}d_ikt_{i,k}B_{i,k}.\n\\]\nWe call the systems \\eqref{Eq:DS} and \\eqref{Eq:DS_SR} a similarity reduction of the Drinfeld-Sokolov hierarchy.\n\n\\begin{rem}\\label{Rem:Lax}\nThe similarity reduction can be regarded as the compatibility condition of a Lax form\n\\[\n\t\\partial_{i,k}(\\Psi) = B_{i,k}\\Psi\\quad (i=1,\\ldots,r;k\\in\\mathbb{N}),\\quad\n\t\\vartheta_{\\mathbf{n}}(\\Psi) = M\\Psi.\n\\]\nHere an $N_{-}B_{+}$-valued function $\\Psi$ is given by\n\\[\n\t\\Psi = W\\exp\\left(\\sum_{i=1}^r\\sum_{k=1}^{\\infty}t_{i,k}\\Lambda_i^k\\right).\n\\]\n\\end{rem}\n\n\n\\section{Derivation of Coupled $P_{\\rm{VI}}$}\\label{Sec:Deri_CP6}\n\nIn this section, we derive the Painlev\\'{e} system \\eqref{Eq:CP6} with \\eqref{Eq:CP6_Ham} from the Drinfeld-Sokolov hierarchies for $\\mathfrak{s}_{(3,3)}$ and $\\mathfrak{s}_{(2,2,1)}$ by similarity reductions.\n\n\n\\subsection{For the partition $(3,3)$}\\label{Sec:System33}\n\nAt first, we define the Heisenberg subalgebra $\\mathfrak{s}_{(3,3)}$ of $\\mathfrak{g}(A^{(1)}_5)$.\nLet\n\\[\n\t\\Lambda_1 = e_{1,2} + e_{3,4} + e_{5,0},\\quad\n\t\\Lambda_2 = e_{0,1} + e_{2,3} + e_{4,5},\\quad\n\tH_1 = \\alpha^{\\vee}_1 + \\alpha^{\\vee}_3 + \\alpha^{\\vee}_5,\n\\]\nwhere\n\\[\n\te_{i_1,i_2,\\ldots,i_{n-1},i_n} = \\mathrm{ad}e_{i_1}\\mathrm{ad}e_{i_2}\n\t\\ldots\\mathrm{ad}e_{i_{n-1}}(e_{i_n}).\n\\]\nThen we have\n\\[\n\t\\mathfrak{s}_{(3,3)} = \\bigoplus_{k\\in\\mathbb{Z}\\setminus3\\mathbb{Z}}\n\t\\mathbb{C}\\Lambda_1^k\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus3\\mathbb{Z}}\n\t\\mathbb{C}\\Lambda_2^k\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus\\{0\\}}\n\t\\mathbb{C}z^kH_1\\oplus\\mathbb{C}K.\n\\]\nThe grade operator for $\\mathfrak{s}_{(3,3)}$ is given by\n\\[\n\t\\vartheta_{(3,3)} = 3\\left(z\\frac{d}{dz}+\\mathrm{ad}\\eta_{(3,3)}\\right),\n\\]\nwhere\n\\[\n\t\\eta_{(3,3)} = \\frac{1}{3}(\\alpha^{\\vee}_1+2\\alpha^{\\vee}_2+2\\alpha^{\\vee}_3\n\t+2\\alpha^{\\vee}_4+\\alpha^{\\vee}_5).\n\\]\nIt follows that $\\mathfrak{s}_{(3,3)}$ admits the gradation of type $\\mathbf{s}=(1,0,1,0,1,0)$, namely\n\\[\n\t\\vartheta_{(3,3)}(e_i) = e_i\\quad (i=0,2,4),\\quad\n\t\\vartheta_{(3,3)}(e_j) = 0\\quad (j=1,3,5).\n\\]\nNote that\n\\[\n\t\\mathfrak{g}_{\\geq0}(1,0,1,0,1,0) = \\mathbb{C}f_1\\oplus\\mathbb{C}f_3\n\t\\oplus\\mathbb{C}f_5\\oplus\\mathfrak{b}_{+}.\n\\]\n\nWe now assume $t_{2,1}=1$ and $t_{1,k}=t_{2,k}=0$ $(k\\geq2)$.\nThen the similarity reduction \\eqref{Eq:DS} and \\eqref{Eq:DS_SR} for $\\mathfrak{s}_{(3,3)}$ is expressed as\n\\begin{equation}\\label{Eq:DS_SR_33_b}\n\t\\left[\\vartheta_{(3,3)}-M,\\partial_{1,1}-B_{1,1}\\right] = 0.\n\\end{equation}\nHere the $\\mathfrak{b}_{+}$-valued functions $M$ and $B_{1,1}$ are defined by\n\\begin{equation}\\begin{split}\\label{Eq:DS_SR_33_b_BM}\n\tM &= \\vartheta_{(3,3)}(W)W^{-1}\n\t+ W(\\rho_1H_1+t_{1,1}\\Lambda_1+\\Lambda_2)W^{-1},\\\\\n\tB_{1,1} &= \\partial_{1,1}(W)W^{-1} + W\\Lambda_1W^{-1},\n\\end{split}\\end{equation}\nwhere $W$ is an $N_{-}$-valued function; its explicit formula is given below.\nIn the following, we derive the Painlev\\'{e} system from the system \\eqref{Eq:DS_SR_33_b} with \\eqref{Eq:DS_SR_33_b_BM}.\n\nWe denote by\n\\[\n\tW = \\exp(\\omega_0)\\exp(\\omega_{-1})\\exp(\\omega_{<-1}),\n\\]\nwhere\n\\[\\begin{split}\n\t\\omega_0 &= -w_1f_1 - w_3f_3 - w_5f_5,\\\\\n\t\\omega_{-1} &= -w_0f_0 - w_2f_2 - w_4f_4 - w_{0,1}f_{0,1} - w_{1,2}f_{1,2}\n\t- w_{2,3}f_{2,3} - w_{3,4}f_{3,4}\\\\\n\t&\\quad - w_{4,5}f_{4,5} - w_{5,0}f_{5,0} - w_{1,2,3}f_{1,2,3}\n\t- w_{3,4,5}f_{3,4,5} - w_{5,0,1}f_{5,0,1},\n\\end{split}\\]\nand $\\omega_{<-1}\\in\\mathfrak{g}_{<-1}(1,0,1,0,1,0)$.\nThen the $\\mathfrak{b}_{+}$-valued function $M$ is described as\n\\[\\begin{split}\n\tM &= \\kappa_0\\alpha^{\\vee}_0 + \\kappa_1\\alpha^{\\vee}_1\n\t+ \\kappa_2\\alpha^{\\vee}_2 + \\kappa_3\\alpha^{\\vee}_3\n\t+ \\kappa_4\\alpha^{\\vee}_4 + \\kappa_5\\alpha^{\\vee}_5 - (t_{1,1}w_5-w_1)e_0\n\t+ \\varphi_1e_1\\\\\n\t&\\quad - (t_{1,1}w_1-w_3)e_2 + \\varphi_3e_3 - (t_{1,1}w_3-w_5)e_4\n\t+ \\varphi_5e_5 + t_{1,1}\\Lambda_1 + \\Lambda_2,\\\\\n\\end{split}\\]\nwith dependent variables\n\\[\n\t\\varphi_1 = t_{1,1}w_2 - w_0,\\quad \\varphi_3= t_{1,1}w_4 - w_2,\\quad\n\t\\varphi_5 = t_{1,1}w_0 - w_4,\n\\]\nand parameters\n\\[\\begin{split}\n\t&\\kappa_0 = -t_{1,1}w_{5,0} - w_{0,1},\\quad\n\t\\kappa_1 = t_{1,1}(w_1w_2-w_{1,2}) - (w_0w_1+w_{0,1}) + \\rho_1,\\\\\n\t&\\kappa_2 = -t_{1,1}w_{1,2} - w_{2,3},\\quad\n\t\\kappa_3 = t_{1,1}(w_3w_4-w_{3,4}) - (w_2w_3+w_{2,3}) + \\rho_1,\\\\\n\t&\\kappa_4 = -t_{1,1}w_{3,4} - w_{4,5},\\quad\n\t\\kappa_5 = t_{1,1}(w_0w_5-w_{5,0}) - (w_4w_5+w_{4,5}) + \\rho_1.\n\\end{split}\\]\nNote that\n\\[\n\t\\partial_{1,1}(\\kappa_i) = 0\\quad (i=0,\\ldots,5).\n\\]\nWe also remark that\n\\[\n\tw_1\\varphi_1 + w_3\\varphi_3 + w_5\\varphi_5 + \\kappa_0 - \\kappa_1\n\t+ \\kappa_2 - \\kappa_3 + \\kappa_4 - \\kappa_5 + 3\\rho_1 = 0.\n\\]\nThe $\\mathfrak{b}_{+}$-valued function $B_{1,1}$ is described as\n\\[\\begin{split}\n\tB_{1,1} &= u_0K + (u_1+w_1x_1)\\alpha^{\\vee}_1 + u_2\\alpha^{\\vee}_2\n\t+ (u_3+w_3x_3)\\alpha^{\\vee}_3 + u_4\\alpha^{\\vee}_4\\\\\n\t&\\quad + w_5x_5\\alpha^{\\vee}_5 - w_5e_0 + x_1e_1 - w_1e_2 + x_3e_3\n\t- w_3e_4 + x_5e_5 + \\Lambda_1,\n\\end{split}\\]\nwhere\n\\[\\begin{split}\n\t&u_1 = \\frac{-2w_1\\varphi_1+w_3\\varphi_3+w_5\\varphi_5\n\t-2\\kappa_0+2\\kappa_1+\\kappa_2-\\kappa_3+\\kappa_4-\\kappa_5}{3t_{1,1}},\\\\\n\t&u_2 = -\\frac{w_1\\varphi_1+\\kappa_0-\\kappa_1+\\rho_1}{t_{1,1}},\\\\\n\t&u_3 = \\frac{-w_1\\varphi_1-w_3\\varphi_3+2w_5\\varphi_5\n\t-\\kappa_0+\\kappa_1-\\kappa_2+\\kappa_3+2\\kappa_4-2\\kappa_5}{3t_{1,1}},\\\\\n\t&u_4 = \\frac{w_5\\varphi_5+\\kappa_4-\\kappa_5+\\rho_1}{t_{1,1}},\\quad\n\tx_1 = \\frac{t_{1,1}^2\\varphi_1+t_{1,1}\\varphi_5+\\varphi_3}{t_{1,1}^3-1},\\\\\n\t&x_3 = \\frac{t_{1,1}^2\\varphi_3+t_{1,1}\\varphi_1+\\varphi_5}\n\t{t_{1,1}^3-1},\\quad\n\tx_5 = \\frac{t_{1,1}^2\\varphi_5+t_{1,1}\\varphi_3+\\varphi_1}{t_{1,1}^3-1}.\n\\end{split}\\]\nHence the system \\eqref{Eq:DS_SR_33_b} with \\eqref{Eq:DS_SR_33_b_BM} can be expressed as a system of ordinary differential equations in terms of the variabes $\\varphi_1,\\varphi_5,w_1,w_3,w_5$; we do not give its explicit formula.\n\nLet\n\\[\n\tq_1 = \\frac{w_1}{t_{1,1}^2w_3},\\quad\n\tp_1 = \\frac{t_{1,1}^2w_3\\varphi_1}{3},\\quad\n\tq_2 = \\frac{w_5}{t_{1,1}w_3},\\quad\n\tp_2 = \\frac{t_{1,1}w_3\\varphi_5}{3},\\quad t = \\frac{1}{t_{1,1}^3}.\n\\]\nWe also set\n\\[\\begin{split}\n\t&\\alpha_0 = \\frac{1}{3}(1-2\\kappa_0+\\kappa_1+\\kappa_5),\\quad\n\t\\alpha_1 = \\frac{1}{3}(\\kappa_0-2\\kappa_1+\\kappa_2),\\\\\n\t&\\alpha_2 = \\frac{1}{3}(1+\\kappa_1-2\\kappa_2+\\kappa_3),\\quad\n\t\\alpha_3 = \\frac{1}{3}(\\kappa_2-2\\kappa_3+\\kappa_4),\\\\\n\t&\\alpha_4 = \\frac{1}{3}(1+\\kappa_3-2\\kappa_4+\\kappa_5),\\quad\n\t\\alpha_5 = \\frac{1}{3}(\\kappa_0+\\kappa_4-2\\kappa_5),\n\\end{split}\\]\nand\n\\[\n\t\\eta = \\rho_1 + \\frac{1}{2}(\\alpha_1+\\alpha_3+\\alpha_5).\n\\]\nThen we have\n\n\\begin{thm}\nThe system \\eqref{Eq:DS_SR_33_b} with \\eqref{Eq:DS_SR_33_b_BM} gives the Painlev\\'{e} system \\eqref{Eq:CP6} with \\eqref{Eq:CP6_Ham}.\nFurthermore, $w_3$ satisfies the completely integrable Pfaffian equation\n\\[\\begin{split}\n\tt(t-1)\\frac{d}{dt}\\log w_3 &= -(q_1-1)(q_1-t)p_1 - (q_2-1)(q_2-t)p_2\\\\\n\t&\\quad - \\alpha_1q_1 - \\alpha_5q_2\n\t+ \\frac{1}{3}(\\alpha_1+\\alpha_2-\\alpha_3-\\alpha_4+2\\eta)t\\\\\n\t&\\quad - \\frac{1}{3}(\\alpha_1+\\alpha_2+2\\alpha_3-\\alpha_4-4\\eta).\n\\end{split}\\]\n\\end{thm}\n\n\n\\subsection{For the partition $(2,2,1)$}\\label{Sec:System221}\n\nThe Heisenberg subalgebra $\\mathfrak{s}_{(2,2,1)}$ of $\\mathfrak{g}(A^{(1)}_4)$ is defined by\n\\[\n\t\\mathfrak{s}_{(2,2,1)} = \\bigoplus_{k\\in\\mathbb{Z}\\setminus2\\mathbb{Z}}\n\t\\mathbb{C}\\Lambda_1^k\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus2\\mathbb{Z}}\n\t\\mathbb{C}\\Lambda_2^k\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus\\{0\\}}\n\t\\mathbb{C}z^kH_1\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus\\{0\\}}\n\t\\mathbb{C}z^kH_2\\oplus\\mathbb{C}K,\n\\]\nwith\n\\[\\begin{array}{ll}\n\t\\Lambda_1 = e_{4,0} + e_{1,2,3},& \\Lambda_2 = e_{0,1} + e_{2,3,4},\\\\[4pt]\n\tH_1 = \\alpha^{\\vee}_1 + \\alpha^{\\vee}_2 - \\alpha^{\\vee}_3,&\n\tH_2 = -\\alpha^{\\vee}_2 + \\alpha^{\\vee}_3 + \\alpha^{\\vee}_4.\n\\end{array}\\]\nThe subalgebra $\\mathfrak{s}_{(2,2,1)}$ admits the gradation of type $\\mathbf{s}=(2,0,1,1,0)$ with the grade operator\n\\[\n\t\\vartheta_{(2,2,1)}\n\t= 4\\left(z\\frac{d}{dz}+\\mathrm{ad}\\eta_{(2,2,1)}\\right),\\quad\n\t\\eta_{(2,2,1)} = \\frac{1}{4}\n\t(\\alpha^{\\vee}_1+2\\alpha^{\\vee}_2+2\\alpha^{\\vee}_3+\\alpha^{\\vee}_4).\n\\]\nNote that\n\\[\n\t\\mathfrak{g}_{\\geq0}(2,0,1,1,0)\n\t= \\mathbb{C}f_1\\oplus\\mathbb{C}f_4\\oplus\\mathfrak{b}_{+}.\n\\]\n\nWe now assume $t_{1,2}=1$ and $t_{1,k}=t_{2,k}=0$ $(k\\geq3)$.\nThen the similarity reduction \\eqref{Eq:DS_SR} for $\\mathfrak{s}_{(2,2,1)}$ is expressed as\n\\begin{equation}\\label{Eq:DS_SR_221_b}\n\t\\left[\\vartheta_{(2,2,1)}-M,\\partial_{1,1}-B_{1,1}\\right] = 0,\n\\end{equation}\nwith\n\\begin{equation}\\begin{split}\\label{Eq:DS_SR_221_b_BM}\n\tM &= \\vartheta_{(2,2,1)}(W)W^{-1}\n\t+ W(\\rho_1H_1+\\rho_2H_2+2t_{1,1}\\Lambda_1+2\\Lambda_2)W^{-1},\\\\\n\tB_{1,1} &= \\partial_{1,1}(W)W^{-1} + W\\Lambda_1W^{-1}.\n\\end{split}\\end{equation}\n\nLet\n\\[\n\tW = \\exp(\\omega_0)\\exp(\\omega_{-1})\\exp(\\omega_{-2})\\exp(\\omega_{<-2}),\n\\]\nwhere\n\\[\\begin{split}\n\t\\omega_0 &= -w_1f_1 - w_4f_4,\\\\\n\t\\omega_{-1} &= -w_2f_2 - w_3f_3 - w_{1,2}f_{1,2} - w_{3,4}f_{3,4},\\\\\n\t\\omega_{-2} &= -w_0f_0 - w_{0,1}f_{0,1} - w_{2,3}f_{2,3} - w_{4,0}f_{4,0}\\\\\n\t&\\quad - w_{1,2,3}f_{1,2,3} - w_{2,3,4}f_{2,3,4} - w_{4,0,1}f_{4,0,1}\n\t- w_{1,2,3,4}f_{1,2,3,4},\n\\end{split}\\]\nand $\\omega_{<-2}\\in\\mathfrak{g}_{<-2}(2,0,1,1,0)$.\nThen the system \\eqref{Eq:DS_SR_221_b_BM} gives explicit formulas of $M,B_{1,1}$ as follows:\n\\[\\begin{split}\n\tM &= \\kappa_0\\alpha^{\\vee}_0 + \\kappa_1\\alpha^{\\vee}_1\n\t+ \\kappa_2\\alpha^{\\vee}_2 + \\kappa_3\\alpha^{\\vee}_3\n\t+ \\kappa_4\\alpha^{\\vee}_4 + 2(w_1-t_{1,1}w_4)e_0\\\\\n\t&\\quad + \\varphi_1e_1 + (\\varphi_2-w_1\\varphi_{1,2})e_2\n\t+ (\\varphi_3+w_4\\varphi_{3,4})e_3 + \\varphi_4e_4\\\\\n\t&\\quad + \\varphi_{1,2}e_{1,2} + 2(t_{1,1}w_1-w_4)e_{2,3}\n\t- \\varphi_{3,4}e_{3,4} + 2t_{1,1}\\Lambda_1 + 2\\Lambda_2,\\\\\n\tB_{1,1} &= u_0K + (u_2+w_1x_1)\\alpha^{\\vee}_1 + u_2\\alpha^{\\vee}_2\n\t+ u_3\\alpha^{\\vee}_3 + w_4x_4\\alpha^{\\vee}_4 - w_4e_0\\\\\n\t&\\quad + x_1e_1 - w_1x_{1,2}e_2 + \\frac{\\varphi_3}{2t_{1,1}}e_3 + x_4e_4\n\t+ x_{1,2}e_{1,2} - w_1e_{2,3} + \\Lambda_1,\n\\end{split}\\]\nwhere\n\\[\\begin{split}\n\t&\\varphi_1 = -2w_0 + t_{1,1}w_2w_3 - 2t_{1,1}w_{2,3},\\quad\n\t\\varphi_2 = -2w_{3,4},\\quad \\varphi_3 = 2t_{1,1}w_{1,2},\\\\\n\t&\\varphi_4 = 2t_{1,1}w_0 + w_2w_3 + 2w_{2,3},\\quad\n\t\\varphi_{1,2} = 2t_{1,1}w_3,\\quad \\varphi_{3,4} = -2w_2,\n\\end{split}\\]\nand\n\\[\\begin{split}\n\t&u_2 = -\\frac{w_1\\varphi_1+\\kappa_0-\\kappa_1+\\rho_1}{2t_{1,1}},\\quad\n\tu_3 = \\frac{w_4\\varphi_4+\\kappa_3-\\kappa_4+\\rho_1}{2t_{1,1}},\\\\\n\t&x_1 = \\frac{(t_{1,1}\\varphi_1+\\varphi_4)\\varphi_3\n\t+(w_1\\varphi_1+w_4\\varphi_4+\\kappa_0-\\kappa_1+\\kappa_3-\\kappa_4+2\\rho_1)\n\t\\varphi_{3,4}}{2(t_{1,1}^2-1)\\varphi_3},\\\\\n\t&x_4 = \\frac{(\\varphi_1+t_{1,1}\\varphi_4)\\varphi_3+t_{1,1}\n\t(w_1\\varphi_1+w_4\\varphi_4+\\kappa_0-\\kappa_1+\\kappa_3-\\kappa_4+2\\rho_1)\n\t\\varphi_{3,4}}{2(t_{1,1}^2-1)\\varphi_3},\\\\\n\t&x_{1,2} = \\frac{w_1\\varphi_1+w_4\\varphi_4+\\kappa_0-\\kappa_1+\\kappa_3\n\t-\\kappa_4+2\\rho_1}{\\varphi_3}.\n\\end{split}\\]\nNote that $\\kappa_0,\\ldots,\\kappa_4$ are constants.\nWe also remark that\n\\[\\begin{split}\n\t&\\varphi_2\\varphi_{3,4} + 2(w_1\\varphi_1+w_4\\varphi_4+\\kappa_0-\\kappa_1\n\t+\\kappa_2-\\kappa_4+2\\rho_2) = 0,\\\\\n\t&\\varphi_3\\varphi_{1,2} - 2t_{1,1}(w_1\\varphi_1+w_4\\varphi_4+\\kappa_0\n\t-\\kappa_1+\\kappa_3-\\kappa_4+2\\rho_1) = 0.\n\\end{split}\\]\nHence the system \\eqref{Eq:DS_SR_221_b} can be expressed as a system of ordinary differential equations in terms of the variables $\\varphi_1,\\varphi_3,\\varphi_4,\\varphi_{3,4},w_1,w_4$.\n\nLet\n\\[\\begin{split}\n\t&q_1 = -\\frac{t_{1,1}^2\\varphi_{3,4}w_4}{\\varphi_3},\\quad\n\tp_1 = -\\frac{\\varphi_3\\varphi_4}{4t_{1,1}^2\\varphi_{3,4}},\\\\\n\t&q_2 = -\\frac{t_{1,1}\\varphi_{3,4}w_1}{\\varphi_3},\\quad\n\tp_2 = -\\frac{\\varphi_3\\varphi_1}{4t_{1,1}\\varphi_{3,4}},\\quad\n\tt = t_{1,1}^2.\n\\end{split}\\]\nWe also set\n\\[\\begin{split}\n\t&\\alpha_0 = \\frac{1}{4}(2-2\\kappa_0+\\kappa_1+\\kappa_4),\\quad\n\t\\alpha_1 = \\frac{1}{4}(\\kappa_0+\\kappa_3-2\\kappa_4),\\\\\n\t&\\alpha_2 = \\frac{1}{4}(1+\\kappa_2-2\\kappa_3+\\kappa_4),\\quad\n\t\\alpha_3 = \\frac{1}{4}(-\\kappa_2+\\kappa_3+2\\rho_1-2\\rho_2),\\\\\n\t&\\alpha_4 = \\frac{1}{4}(1+\\kappa_1-\\kappa_2-2\\rho_1+2\\rho_2),\\quad\n\t\\alpha_5 = \\frac{1}{4}(\\kappa_0-2\\kappa_1+\\kappa_2),\\\\\n\t&\\eta\n\t= \\frac{1}{4}(2\\kappa_0-2\\kappa_1+2\\kappa_3-2\\kappa_4+3\\rho_1-\\rho_2).\n\\end{split}\\]\nThen we have\n\n\\begin{thm}\nThe system \\eqref{Eq:DS_SR_221_b} with \\eqref{Eq:DS_SR_221_b_BM} gives the Painlev\\'{e} system \\eqref{Eq:CP6} with \\eqref{Eq:CP6_Ham}.\nFurthermore, $\\varphi_3$ and $\\varphi_{3,4}$ satisfy the completely integrable Pfaffian equations\n\\[\\begin{split}\n\tt(t-1)\\frac{d}{dt}\\log\\varphi_3 &= -q_1(q_1-t)p_1 - q_2(q_2-t)p_2\n\t- \\alpha_1q_1 - \\alpha_5q_2\\\\\n\t&\\quad + \\frac{1}{4}\n\t(1+2\\alpha_2-2\\alpha_3-2\\alpha_4-2\\alpha_5+6\\eta)t\\\\\n\t&\\quad - \\frac{1}{4}\n\t(1+2\\alpha_2+2\\alpha_3-2\\alpha_4-2\\alpha_5+2\\eta),\\\\\n\tt(t-1)\\frac{d}{dt}\\log\\varphi_{3,4} &= -(q_1-t)p_1 - (q_2-t)p_2 - \\eta.\n\\end{split}\\]\n\\end{thm}\n\n\n\\section{Derivation of other systems}\\label{Sec:Deri_Others}\n\nIn this section, we discuss the derivation of the Painlev\\'{e} systems for $\\mathfrak{s}_{(2,2)}$, $\\mathfrak{s}_{(3,1)}$ and $\\mathfrak{s}_{(4,1)}$ by a similar manner as in Section \\ref{Sec:Deri_CP6}.\n\n\n\\subsection{For the partition $(2,2)$}\\label{Sec:System22}\n\nThe Heisenberg subalgebra $\\mathfrak{s}_{(2,2)}$ of $\\mathfrak{g}(A^{(1)}_3)$ is defined by\n\\[\n\t\\mathfrak{s}_{(2,2)} = \\bigoplus_{k\\in\\mathbb{Z}\\setminus2\\mathbb{Z}}\n\t\\mathbb{C}\\Lambda_1^k\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus2\\mathbb{Z}}\n\t\\mathbb{C}\\Lambda_2^k\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus\\{0\\}}\n\t\\mathbb{C}z^kH_1\\oplus\\mathbb{C}K,\n\\]\nwith\n\\[\n\t\\Lambda_1 = e_{1,2} + e_{3,0},\\quad\n\t\\Lambda_2 = e_{0,1} + e_{2,3},\\quad\n\tH_1 = \\alpha^{\\vee}_1 + \\alpha^{\\vee}_3.\n\\]\nThe subalgebra $\\mathfrak{s}_{(2,2)}$ admits the gradation of type $\\mathbf{s}=(1,0,1,0)$ with the grade operator\n\\[\n\t\\vartheta_{(2,2)}\n\t= 2\\left(z\\frac{d}{dz}+\\mathrm{ad}\\eta_{(2,2)}\\right),\\quad\n\t\\eta_{(2,2)}\n\t= \\frac{1}{2}(\\alpha^{\\vee}_1+2\\alpha^{\\vee}_2+\\alpha^{\\vee}_3).\n\\]\nNote that\n\\[\n\t\\mathfrak{g}_{\\geq0}(1,0,1,0) = \\mathbb{C}f_1\\oplus\\mathbb{C}f_3\\oplus\\mathfrak{b}_{+}.\n\\]\n\nWe now assume $t_{1,2}=1$ and $t_{1,k}=t_{2,k}=0$ $(k\\geq3)$.\nThen the similarity reduction \\eqref{Eq:DS_SR} for $\\mathfrak{s}_{(2,2)}$ is expressed as\n\\begin{equation}\\label{Eq:DS_SR_22_b}\n\t\\left[\\vartheta_{(2,2)}-M,\\partial_{1,1}-B_{1,1}\\right] = 0,\n\\end{equation}\nwith\n\\begin{equation}\\begin{split}\\label{Eq:DS_SR_22_b_BM}\n\tM &= \\vartheta_{(2,2)}(W)W^{-1}\n\t+ W(\\rho_1H_1+t_{1,1}\\Lambda_1+\\Lambda_2)W^{-1},\\\\\n\tB_{1,1} &= \\partial_{1,1}(W)W^{-1} + W\\Lambda_1W^{-1}.\n\\end{split}\\end{equation}\n\nLet\n\\[\n\tW = \\exp(\\omega_0)\\exp(\\omega_{-1})\\exp(\\omega_{<-1}),\n\\]\nwhere\n\\[\\begin{split}\n\t\\omega_{0} &= -w_1f_1 - w_3f_3,\\\\\n\t\\omega_{-1} &= -w_0f_0 - w_2f_2 - w_{0,2}f_{0,2} - w_{1,2}f_{1,2}\\\\\n\t&\\quad - w_{2,3}f_{2,3} - w_{3,0}f_{3,0} - w_{1,2,3}f_{1,2,3}\n\t- w_{3,0,1}f_{3,0,1},\n\\end{split}\\]\nand $\\omega_{<-1}\\in\\mathfrak{g}_{<-1}(1,0,1,0)$.\nThen the system \\eqref{Eq:DS_SR_22_b_BM} gives explicit formulas of $M,B_{1,1}$ as follows:\n\\[\\begin{split}\n\tM &= \\kappa_0\\alpha^{\\vee}_0 + \\kappa_1\\alpha^{\\vee}_1\n\t+ \\kappa_2\\alpha^{\\vee}_2 + \\kappa_3\\alpha^{\\vee}_3 + (w_1-t_{1,1}w_3)e_0\\\\\n\t&\\quad + \\varphi_1e_1 + (w_3-t_{1,1}w_1)e_2 + \\varphi_3e_3\n\t+ t_{1,1}\\Lambda_1 + \\Lambda_2,\\\\\n\tB_{1,1} &= u_0K + u_1\\alpha^{\\vee}_1 + u_2\\alpha^{\\vee}_2\n\t+ w_3x_3\\alpha^{\\vee}_3 + w_1e_0 + x_1e_1 + w_3e_2 + x_3e_3 + \\Lambda_1,\n\\end{split}\\]\nwhere\n\\[\n\t\\varphi_1 = t_{1,1}w_2 - w_0,\\quad \\varphi_3 = t_{1,1}w_0 - w_2,\n\\]\nand\n\\[\\begin{split}\n\tu_1 &= \\frac{w_1}{t_{1,1}}x_3\n\t- \\frac{\\kappa_0-\\kappa_1+\\rho_1}{t_{1,1}},\\quad\n\tu_2 = \\frac{w_3\\varphi_3+\\kappa_2-\\kappa_3+\\rho_1}{t_{1,1}},\\\\\n\tx_1 &= \\frac{(w_1-t_{1,1}w_3)\\varphi_3\n\t-(\\kappa_0-\\kappa_1+\\kappa_2-\\kappa_3+2\\rho_1)t_{1,1}}{(t_{1,1}^2-1)w_1},\\\\\n\tx_3 &= \\frac{(t_{1,1}w_1-w_3)\\varphi_3\n\t-(\\kappa_0-\\kappa_1+\\kappa_2-\\kappa_3+2\\rho_1)}{(t_{1,1}^2-1)w_1}.\n\\end{split}\\]\nNote that $\\kappa_0,\\ldots,\\kappa_3$ are constants.\nWe also remark that\n\\[\n\tw_1\\varphi_1 + w_3\\varphi_3 + \\kappa_0 - \\kappa_1 + \\kappa_2 - \\kappa_3\n\t+ 2\\rho_1 = 0.\n\\]\nHence the system \\eqref{Eq:DS_SR_22_b} can be expressed as a system of ordinary differential equations in terms of the variables $\\varphi_3,w_1,w_3$.\n\nLet\n\\[\n\tp = \\frac{w_1\\varphi_3}{2t_{1,1}},\\quad q = \\frac{t_{1,1}w_3}{w_1},\\quad\n\tt = t_{1,1}^2.\n\\]\nWe also set\n\\[\\begin{split}\n\t&\\alpha_0 = \\displaystyle\\frac{1}{2}(1+\\kappa_1-2\\kappa_2+\\kappa_3),\\quad\n\t\\alpha_1 = \\displaystyle\\frac{1}{2}(-\\kappa_1+\\kappa_3+2\\rho_1),\\\\\n\t&\\alpha_2 = \\kappa_0 + \\kappa_2 - 2\\kappa_3,\\quad\n\t\\alpha_3 = \\displaystyle\\frac{1}{2}(1-2\\kappa_0+\\kappa_1+\\kappa_3),\\\\\n\t&\\alpha_4 = \\displaystyle\\frac{1}{2}(-\\kappa_1+\\kappa_3-2\\rho_1),\n\\end{split}\\]\nand\n\\[\n\ta = \\alpha_0,\\quad b = \\alpha_3,\\quad c = \\alpha_4,\\quad\n\td = \\alpha_2(\\alpha_1+\\alpha_2).\n\\]\nThen we have\n\n\\begin{thm}\nThe system \\eqref{Eq:DS_SR_22_b} with \\eqref{Eq:DS_SR_22_b_BM} gives the sixth Painlev\\'{e} equation.\nFurthermore, $w_1$ satisfies the completely integrable Pfaffian equation\n\\[\\begin{split}\n\tt(t-1)\\frac{d}{dt}\\log w_1 &= -(q-1)(q-t)p - \\alpha_2q\\\\\n\t&\\quad + \\frac{1}{4}(1+2\\alpha_1-2\\alpha_3-4\\alpha_4)t\n\t- \\frac{1}{4}(1-2\\alpha_1-4\\alpha_2-2\\alpha_3).\n\\end{split}\\]\n\\end{thm}\n\n\n\\subsection{For the partition $(3,1)$}\\label{Sec:System31}\n\nThe Heisenberg subalgebra $\\mathfrak{s}_{(3,1)}$ of $\\mathfrak{g}(A^{(1)}_3)$ is defined by\n\\[\n\t\\mathfrak{s}_{(3,1)} = \\bigoplus_{k\\in\\mathbb{Z}\\setminus3\\mathbb{Z}}\n\t\\mathbb{C}\\Lambda_1^k\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus\\{0\\}}\n\t\\mathbb{C}z^kH_1\\oplus\\mathbb{C}K,\n\\]\nwith\n\\[\n\t\\Lambda_1 = e_0 + e_1 + e_{2,3},\\quad\n\tH_1 = \\alpha^{\\vee}_1 + 2\\alpha^{\\vee}_2 - \\alpha^{\\vee}_3.\n\\]\nThe subalgebra $\\mathfrak{s}_{(3,1)}$ admits the gradation of type $\\mathbf{s}=(1,1,0,1)$ with the grade operator\n\\[\n\t\\vartheta_{(3,1)}\n\t= 3z\\left(\\frac{d}{dz}+\\mathrm{ad}\\eta_{(3,1)}\\right),\\quad\n\t\\eta_{(3,1)} = \\frac{1}{3}(\\alpha^{\\vee}_1+\\alpha^{\\vee}_2+\\alpha^{\\vee}_3).\n\\]\nNote that\n\\[\n\t\\mathfrak{g}_{\\geq0}(1,1,0,1) = \\mathbb{C}f_2\\oplus\\mathfrak{b}_{+}.\n\\]\n\nWe now assume $t_{1,2}=1$ and $t_{1,k}=0$ $(k\\geq3)$.\nThen the similarity reduction \\eqref{Eq:DS_SR} for $\\mathfrak{s}_{(3,1)}$ is expressed as\n\\begin{equation}\\label{Eq:DS_SR_31_b}\n\t\\left[\\vartheta_{(3,1)}-M,\\partial_{1,1}-B_{1,1}\\right] = 0,\n\\end{equation}\nwith\n\\begin{equation}\\begin{split}\\label{Eq:DS_SR_31_b_BM}\n\tM &= \\vartheta_{(3,1)}(W)W^{-1}\n\t+ W(\\rho_1H_1+t_{1,1}\\Lambda_1+2\\Lambda_1^2)W^{-1},\\\\\n\tB_{1,1} &= \\partial_{1,1}(W)W^{-1} + W\\Lambda_1W^{-1}.\n\\end{split}\\end{equation}\n\nLet\n\\[\n\tW = \\exp(-w_2f_2)\\exp(\\omega_{-1})\\exp(\\omega_{-2})\\exp(\\omega_{<-2}),\n\\]\nwhere\n\\[\\begin{split}\n\t\\omega_{-1} &= -w_0f_0 - w_1f_1 - w_3f_3 - w_{1,2}f_{1,2}\n\t- w_{2,3}f_{2,3},\\\\\n\t\\omega_{-2} &= -w_{0,1}f_{0,1} - w_{3,0}f_{3,0} - w_{0,1,2}f_{0,1,2} \n\t- w_{1,2,3}f_{1,2,3} - w_{2,3,0}f_{2,3,0},\n\\end{split}\\]\nand $\\omega_{<-2}\\in\\mathfrak{g}_{<-2}(1,1,0,1)$.\nThen the system \\eqref{Eq:DS_SR_31_b_BM} gives explicit formulas of $M,B_{1,1}$ as follows:\n\\[\\begin{split}\n\tM &= \\kappa_0\\alpha^{\\vee}_0 + \\kappa_1\\alpha^{\\vee}_1\n\t+ \\kappa_2\\alpha^{\\vee}_2 + \\kappa_3\\alpha^{\\vee}_3 + \\varphi_0e_0\n\t+ (\\varphi_1+w_2\\varphi_{1,2})e_1\\\\\n\t&\\quad + \\varphi_2e_2 + (\\varphi_3-w_2\\varphi_{2,3})e_3\n\t+ \\varphi_{1,2}e_{1,2} + \\varphi_{2,3}e_{2,3} - 2w_2e_{3,0}\n\t+ 2\\Lambda_1^2,\\\\\n\tB_{1,1} &= u_3K - \\frac{\\varphi_1-t_{1,1}}{2}\\alpha^{\\vee}_0\n\t+ \\frac{\\varphi_0-t_{1,1}}{2}\\alpha^{\\vee}_1\n\t+ \\frac{w_2\\varphi_{1,2}}{2}\\alpha^{\\vee}_2\n\t+ \\frac{\\varphi_{1,2}}{2}e_2 - w_2e_3 + \\Lambda_1,\n\\end{split}\\]\nwhere\n\\[\\begin{split}\n\t&\\varphi_0 = 2w_1 + 2w_{2,3} + t_{1,1},\\quad\n\t\\varphi_1 = -2w_0 - 2w_{2,3} + t_{1,1},\\\\\n\t&\\varphi_2 = (w_0-2w_1+t_{1,1})w_3 - 2w_{3,0},\\quad \\varphi_3 = 2w_{1,2},\\\\\n\t&\\varphi_{1,2} = 2w_3,\\quad \\varphi_{2,3} = 2w_0 - 2w_1 + t_{1,1}.\n\\end{split}\\]\nNote that $\\kappa_0,\\ldots,\\kappa_4$ are constants.\nWe also remark that\n\\[\n\t2w_2\\varphi_2 - \\varphi_3\\varphi_{1,2} = 2(\\kappa_2-\\kappa_3-3\\rho_1),\\quad\n\t\\varphi_0 + \\varphi_1 + \\varphi_{2,3} = 3t_{1,1}.\n\\]\nHence the system \\eqref{Eq:DS_SR_31_b} can be expressed as a system of ordinary differential equations in terms of the variables $\\varphi_0,\\varphi_1,\\varphi_2,\\varphi_{1,2},w_2$.\n\nLet\n\\[\n\tq_1 = -\\frac{w_2\\varphi_{1,2}}{\\sqrt{6}},\\quad\n\tp_1 = -\\frac{2\\varphi_2}{\\sqrt{6}\\varphi_{1,2}},\\quad\n\tq_2 = \\frac{\\varphi_1}{\\sqrt{6}},\\quad\n\tp_2 = -\\frac{\\varphi_0}{\\sqrt{6}},\\quad t = -\\frac{\\sqrt{6}t_{1,1}}{2}.\n\\]\nWe also set\n\\[\\begin{split}\n\t&\\alpha_1 = \\displaystyle\\frac{1}{3}(\\kappa_2-\\kappa_3-3\\rho_1),\\quad\n\t\\alpha_2 = \\displaystyle\\frac{1}{3}(\\kappa_1-2\\kappa_2+\\kappa_3),\\\\\n\t&\\alpha_3 = \\displaystyle\\frac{1}{3}(1+\\kappa_0-2\\kappa_1+\\kappa_2),\\quad\n\t\\alpha_4 = \\displaystyle\\frac{1}{3}(1-2\\kappa_0+\\kappa_1+\\kappa_3).\n\\end{split}\\]\nThen we have\n\n\\begin{thm}\nThe system \\eqref{Eq:DS_SR_31_b} with \\eqref{Eq:DS_SR_31_b_BM} gives the Painlev\\'{e} system $\\mathcal{H}^{A_4^{(1)}}$.\nFurthermore, $\\varphi_{1,2}$ satisfies the completely integrable Pfaffian equation\n\\[\n\t\\frac{d}{dt}\\log\\varphi_{1,2} = p_1 + p_2 - \\frac{2}{3}t.\n\\]\n\\end{thm}\n\n\n\\subsection{For the partition $(4,1)$}\\label{Sec:System41}\n\nThe Heisenberg subalgebra $\\mathfrak{s}_{(4,1)}$ of $\\mathfrak{g}(A^{(1)}_4)$ is defined by\n\\[\n\t\\mathfrak{s}_{(4,1)} = \\bigoplus_{k\\in\\mathbb{Z}\\setminus4\\mathbb{Z}}\n\t\\mathbb{C}\\Lambda_1^k\\oplus\\bigoplus_{k\\in\\mathbb{Z}\\setminus\\{0\\}}\n\t\\mathbb{C}z^kH_1\\oplus\\mathbb{C}K,\n\\]\nwith\n\\[\n\t\\Lambda_1 = e_0 + e_1 + e_4 + e_{2,3},\\quad\n\tH_1 = \\alpha^{\\vee}_1 + 2\\alpha^{\\vee}_2 - 2\\alpha^{\\vee}_3\n\t- \\alpha^{\\vee}_4.\n\\]\nThe subalgebra $\\mathfrak{s}_{(4,1)}$ admits the gradation of type $\\mathbf{s}=(2,2,1,1,2)$ with the grade operator\n\\[\n\t\\vartheta_{(4,1)}\n\t= 8\\left(z\\frac{d}{dz}+\\mathrm{ad}\\eta_{(4,1)}\\right),\\quad\n\t\\eta_{(4,1)} = \\frac{1}{8}\n\t(3\\alpha^{\\vee}_1+4\\alpha^{\\vee}_2+4\\alpha^{\\vee}_3+3\\alpha^{\\vee}_4).\n\\]\nNote that\n\\[\n\t\\mathfrak{g}_{\\geq0}(2,2,1,1,2) = \\mathfrak{b}_{+}.\n\\]\n\nWe now assume $t_{1,2}=1$ and $t_{1,k}=0$ $(k\\geq3)$.\nThen the similarity reduction \\eqref{Eq:DS_SR} for $\\mathfrak{s}_{(4,1)}$ is expressed as\n\\begin{equation}\\label{Eq:DS_SR_41_b}\n\t\\left[\\vartheta_{(4,1)}-M,\\partial_{1,1}-B_{1,1}\\right] = 0,\n\\end{equation}\nwith\n\\begin{equation}\\begin{split}\\label{Eq:DS_SR_41_b_BM}\n\tM &= \\vartheta_{(4,1)}(W)W^{-1}\n\t+ W(\\rho_1H_1+2t_{1,1}\\Lambda_1+4\\Lambda_1^2)W^{-1},\\\\\n\tB_{1,1} &= \\partial_{1,1}(W)W^{-1} + W\\Lambda_1W^{-1}.\n\\end{split}\\end{equation}\n\nLet\n\\[\n\tW = \\exp(\\omega_{-1})\\exp(\\omega_{-2})\\exp(\\omega_{-3})\\exp(\\omega_{-4})\n\t\\exp(\\omega_{<-4}),\n\\]\nwhere\n\\[\\begin{split}\n\t\\omega_{-1} &= -w_2f_2 - w_3f_3,\\\\\n\t\\omega_{-2} &= -w_0f_0 - w_1f_1 - w_4f_4 - w_{2,3}f_{2,3},\\\\\n\t\\omega_{-3} &= -w_{1,2}f_{1,2} - w_{3,4}f_{3,4},\\\\\n\t\\omega_{-4} &= -w_{0,1}f_{0,1} - w_{4,0}f_{4,0} - w_{1,2,3}f_{1,2,3}\n\t- w_{2,3,4}f_{2,3,4},\n\\end{split}\\]\nand $\\omega_{<-4}\\in\\mathfrak{g}_{<-4}(2,2,1,1,2)$.\nThen the system \\eqref{Eq:DS_SR_41_b_BM} gives explicit formulas of $M,B_{1,1}$ as follows:\n\\[\\begin{split}\n\tM &= \\kappa_0\\alpha^{\\vee}_0 + \\kappa_1\\alpha^{\\vee}_1\n\t+ \\kappa_2\\alpha^{\\vee}_2 + \\kappa_3\\alpha^{\\vee}_3\n\t+ \\kappa_4\\alpha^{\\vee}_4 + \\varphi_0e_0 + \\varphi_1e_1\\\\\n\t&\\quad + \\varphi_2e_2 + \\varphi_3e_3 + \\varphi_4e_4\n\t+ \\varphi_{1,2}e_{1,2} + \\varphi_{2,3}e_{2,3} + \\varphi_{3,4}e_{3,4}\n\t+ 4\\Lambda_1^2,\\\\\n\tB_{1,1} &= u_4K + u_0\\alpha^{\\vee}_0\n\t+ \\frac{\\varphi_0-2t_{1,1}}{4}\\alpha^{\\vee}_1 + u_2\\alpha^{\\vee}_2\n\t+ u_3\\alpha^{\\vee}_3 + \\frac{\\varphi_{1,2}}{4}e_2\n\t+ \\frac{\\varphi_{3,4}}{4}e_3 + \\Lambda_1,\n\\end{split}\\]\nwhere\n\\[\\begin{split}\n\t&\\varphi_0 = 4w_1 - 4w_4 + 2t_{1,1},\\quad\n\t\\varphi_1 = -4w_0 + 2w_2w_3 - 4w_{2,3} + 2t_{1,1},\\\\\n\t&\\varphi_2 = -2(2w_1-w_4-t_{1,1})w_3 - 4w_{3,4},\\quad\n\t\\varphi_3 = 2(w_1-2w_4-t_{1,1})w_2 + 4w_{1,2},\\\\\n\t&\\varphi_{1,2} = 4w_3,\\quad \\varphi_{2,3} = -4w_1 + 4w_4 + 2t_{1,1},\\quad\n\t\\varphi_{3,4} = -4w_2,\n\\end{split}\\]\nand\n\\[\\begin{split}\n\t64t_{1,1}u_0 &= (\\varphi_0-4t_{1,1})(4\\varphi_1+\\varphi_{1,2}\\varphi_{3,4})\n\t+ 4\\varphi_2\\varphi_{3,4}\\\\\n\t&\\quad + 16t_{1,1}^2 + 16(\\kappa_0-\\kappa_1+\\kappa_2-\\kappa_4-2\\rho_1),\\\\\n\t64t_{1,1}u_2 &= \\varphi_0(4\\varphi_1+\\varphi_{1,2}\\varphi_{3,4})\n\t+ 4(\\varphi_2-t_{1,1}\\varphi_{1,2})\\varphi_{3,4}\\\\\n\t&\\quad - 16t_{1,1}^2 + 16(\\kappa_0-\\kappa_1+\\kappa_2-\\kappa_4-2\\rho_1),\\\\\n\t64t_{1,1}u_3 &= \\varphi_0(4\\varphi_1+\\varphi_{1,2}\\varphi_{3,4})\n\t+ 4\\varphi_2\\varphi_{3,4}\\\\\n\t&\\quad - 16t_{1,1}^2 + 16(\\kappa_0-\\kappa_1+\\kappa_2-\\kappa_4-2\\rho_1).\n\\end{split}\\]\nNote that $\\kappa_0,\\ldots,\\kappa_4$ are constants.\nWe also remark that\n\\[\\begin{split}\n\t&(\\varphi_0-4t_{1,1})\\varphi_{1,2}\\varphi_{3,4} + 4\\varphi_3\\varphi_{1,2}\n\t+ 4\\varphi_2\\varphi_{3,4} = 16(-\\kappa_2+\\kappa_3+4\\rho_1),\\\\\n\t&4\\varphi_1 + 4\\varphi_4 + \\varphi_{1,2}\\varphi_{3,4} = 16t_{1,1},\\quad\n\t\\varphi_0 + \\varphi_{2,3} = 4t_{1,1}.\n\\end{split}\\]\nHence the system \\eqref{Eq:DS_SR_41_b} can be described as a system of ordinary differential equations in terms of the variables $\\varphi_0,\\varphi_1,\\varphi_2,\\varphi_{1,2},\\varphi_{3,4}$.\n\nLet\n\\[\\begin{split}\n\t&q_1 = \\frac{\\varphi_0}{4t_{1,1}},\\quad p_1 = \\frac{t_{1,1}\\varphi_1}{8},\\\\\n\t&q_2 = \\frac{\\varphi_0}{4t_{1,1}}\n\t+ \\frac{\\varphi_2}{t_{1,1}\\varphi_{1,2}},\\quad\n\tp_2 = \\frac{t_{1,1}\\varphi_{1,2}\\varphi_{3,4}}{32},\\quad\n\tt = -\\frac{t_{1,1}^2}{2}.\n\\end{split}\\]\nWe also set\n\\[\\begin{split}\n\t&\\alpha_1 = \\frac{1}{8}(2-2\\kappa_0+\\kappa_1+\\kappa_4),\\quad\n\t\\alpha_2 = \\frac{1}{8}(2+\\kappa_0-2\\kappa_1+\\kappa_2),\\\\\n\t&\\alpha_3 = \\frac{1}{8}(1+\\kappa_1-2\\kappa_2+\\kappa_3),\\quad\n\t\\alpha_4 = \\frac{1}{8}(\\kappa_2-\\kappa_3-4\\rho_1),\\\\\n\t&\\alpha_5 = \\frac{1}{8}(1-\\kappa_3+\\kappa_4+4\\rho_1).\n\\end{split}\\]\nThen we have\n\n\\begin{thm}\nThe system \\eqref{Eq:DS_SR_41_b} with \\eqref{Eq:DS_SR_41_b_BM} gives the Painlev\\'{e} system $\\mathcal{H}^{A_5^{(1)}}$.\nFurthermore, $\\varphi_{1,2}$ satisfies the completely integrable Pfaffian equation\n\\[\n\tt\\frac{d}{dt}\\log\\varphi_{1,2} = -q_1p_1 - q_2p_2 + tq_2 - \\frac{3}{4}t\n\t- \\frac{1+2\\alpha_1+2\\alpha_3+2\\alpha_5}{4}.\n\\]\n\\end{thm}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nThe Edelweiss experiment searches for the WIMP candidates of the Dark Matter. The set-up is located in LSM in the French Alps which provides a shielding factor of $\\sim$4800~m.w.e. The detection principle is based on measuring energy of the recoil nucleus originating from the WIMP elastic scattering. Bolometers of pure natural Ge are used both as the detectors and the target material. These detectors cooled down to about 20~mK allow to measure simultaneously heat and ionization signals. Due to the quenching of the ionization signal present for nuclear recoils one achieves a very high discrimination of $\\beta$ and $\\gamma$ background from the recoil candidates \\cite{defay08}. However, neutrons coming from the natural radioactivity or induced by the remaining muons can still mimic the nuclear recoil signal of WIMP events and thus can not be discriminated in the same way as $\\beta$'s and $\\gamma$'s. Therefore, this type of background requires special careful investigation. The knowledge of it also becomes highly important in view of large 1-tonne scale experiments like EURECA \\cite{kraus08}.\n\n\\section{Neutron background}\nFor kinematic reasons, not every neutron can mimic the WIMP nuclear recoil event but only those who have an energy of 0.5\\--10~MeV when they reach the Ge bolometers. Such neutrons appearing due to natural radioactivity in the surrounding (e.g. U\/Th contamination) can be avoided by using a passive hydrogen-rich moderator (50~cm polyethylene shield in case of Edelweiss) and in addition by radiopurity selection of materials to be used. Monitoring of the ambient neutron flux in proximity of the Edelweiss experimental set-up is performed with the help of $^3$He gas detectors. This measurement yields a flux of about $2\\cdot10^{-6}$~n\/cm$^2$\/day \\cite{yakushev08} which is in good agreement with the previously measured value \\cite{fiorucci07}. Another part of the neutron background is caused by muon interactions in the rock and in fact everywhere in the set-up (especially in high-Z materials such as the gamma shield based on lead). High energy neutrons (well above 10~MeV) created in such deep inelastic scattering (DIS) processes further lead to the production of secondary neutrons with energies below 10~MeV. The effect of this $\\mu-$induced neutron component is commonly reduced by tagging the original muons. In Edelweiss experiment the plastic scintillator modules covering the full bolometer set-up act as the muon veto \\cite{chantelauze07}. Full simulations of the Edelweiss set-up including the muon veto were performed in GEANT4 in order to estimate the influence of muons for the Dark Matter search. These simulations involve muon generation to reproduce the muon flux specific for LSM and allow to get complete event topology \\cite{horn07}. It was shown then that muons which miss the veto can still induce some neutrons reaching the bolometers and giving rise to WIMP-like events not vetoed by the muon system. To verify these simulations one has to normalize them to the experimental data, i.e. one needs explicit $\\mu-$induced neutron measurements. One way to achieve this is to check the rate of events which are in coincidence between muon veto and the bolometers. This rate currently measured in Edelweiss is about 0.03~events\/kg\/day and it is reasonably well reproduced in the simulations. However, the rareness of these coincidence events makes it hard to get enough statistics to draw a reliable conclusion. A dedicated detector based on liquid scintillator was thus designed and installed in 2008 in LSM.\n\n\\section{A detector for muon-induced neutrons}\n\\label{sec:nc-detector}\n\n\\begin{figure}[!ht]\n\t\\centering\n\t\t\\includegraphics[width=0.72\\textwidth]{figs\/nc-detector-fin.pdf}\n\t\\caption{General scheme of the neutron counter (side view): 1-tonne of Gd-loaded liquid scintillator viewed by 16 PMTs of 8-inch and 6 PMTs of 2-inch diameter. A layer of lead bricks below the liquid scintillator volume acts as an effective target for muons and high energy neutrons.}\n\t\\label{fig:nc-detector}\t\n\\end{figure}\n\nThe measuring principle of $\\mu$-induced neutrons is based on registering thermalized neutrons in coincidence with the incoming muon or by detecting a multiple neutron event (secondary neutrons produced in a $\\mu$-induced particle showers). To efficiently observe neutrons, a liquid scintillator of 1~m$^3$ volume (50x100x200~cm$^3$) loaded with Gadolinium (St.~Gobain Bicron BC525) is used as a core of the detector. The neutron capture process on Gd results in several gammas with 8~MeV sum energy. The scintillator volume is viewed from each of the two module ends by 8 photomultiplier tubes (PMT) of 8-inch diameter (Fig.~\\ref{fig:nc-detector}). These PMTs are optimized to register the light produced after the neutron capture. In addition, the system is equipped with 6 smaller PMTs (2-inch diameter) to register muons crossing the neutron detector (these muons create much more light and thus the 8-inch PMTs will saturate). The scintillator and PMTs are placed in one plexiglass container divided into three parts: the central one for the scintillator itself and two side ones filled with paraffin in which the PMTs are immersed. This plexiglass chamber is then placed in an aluminum vessel as secondary safety container. Finally, the system is surrounded by iron plates to reflect a fraction of neutrons back to the scintillator. In order to enhance the neutron production (up to a factor of 10 comparing to rock) a 10~cm thick layer of lead bricks is put underneath the detector. On top of the counter, a plastic scintillator module (same type as the muon veto of Edelweiss) is installed. The complete system is positioned right near the western wall of the Edelweiss muon veto. Based on the currently measured muon flux in the lab, the expected count rate of muon-induced neutrons is about few counts per day. \n\nThe GEANT4 simulations mentioned above were extended to optimize the neutron set-up before going for construction. Additionally, a smaller prototype (25x25x250~cm$^3$) was built beforehand in Karlsruhe in order to test mechanical properties, handling of liquids and gas as well as to study light collection, PMTs and overall performance. This prototype also allowed to develop a LED system to monitor over time the light properties of the scintillator and stability of PMTs. There are in total 8 LEDs ($\\lambda=$425~nm) placed at different positions. These LEDs are operated via VME-based PC commands and regularly fired one by one. The data from the groups of opposite PMTs are then analyzed. \n\nThe neutron counter is also equipped with safety sensors because of the pseudocumene based scintillator. This includes vapor sensors to check the internal and surrounding atmosphere, two leak sensors in the aluminum vessel, one temperature meter immersed in the paraffin volume and one outside of the counter. Signals of the vapor sensors are incorporated into LSM safety system which takes care of an alarm activation in the lab. One can as well monitor these sensors using the LabVIEW$^{\\tt{TM}}$-based program (\\underline{Ka}rlsruhe \\underline{C}ontrol of \\underline{S}afety or KA-CS) installed on Linux computer (SuSE~10.3) (Fig.~\\ref{fig:nc-ka-cs}). This software notifies users by email in case of an alarm due to a failure or passing of specified thresholds.\n\n\nThe neutron detector described was successfully installed in LSM in September 2008 and as for the time of writing, it is under intensive commissioning.\n\n\\begin{figure}\n\t\\centering\n\t\t\\includegraphics[width=0.62\\textwidth]{figs\/nc-ka-cs.pdf}\n\t\\caption{Principle scheme of KA-CS system for safety monitoring: sensors are continuously read via NI-6221 DAQ card by the LabVIEW program installed on Linux computer.}\n\t\\label{fig:nc-ka-cs}\n\\end{figure}\n\n\\section{Conclusion}\nImproved sensitivity of Dark Matter search experiments requires much better knowledge of the background conditions. Activity of the Edelweiss collaboration concerning the neutron background studies was presented, in particular the new detector for the $\\mu$-induced neutrons was described. \n\n\\section{Acknowledgements}\nThis work is in part supported by the German Research Foundation (DFG) through the Trans\\-regional Collaborative Research Center SFB-TR27 as well as by the EU contract RII3-CT-2004-506222.\n\n\n\\section{...}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nLet $G$ be a finite group which is a transitive subgroup of a certain symmetry group $S_{d+1}$. A number field $K$ of degree $d+1$ is called a $G$-field if its Galois closure $\\widehat{K}$ over $\\mathbb{Q}$ is a $G$-Galois extension. For a $G$-field $K$, we attach the Artin L-function\n$$\nL(s,\\rho,K)=\\frac{\\zeta_K(s)}{\\zeta(s)}=\\sum_{n=1}^\\infty a_{\\rho}(n)n^{-s},\n$$\nwhere $\\rho$ is $d$-dimensional representation of $G$. Note that $-1\\leq a_{\\rho}(p)\\leq d$.\nIf $G=S_{d+1}$, $\\rho$ is the $d$-dimensional standard representation of $S_{d+1}$.\nLet $L(X)^{r_2}$ be the set of $G$-fields $K$ with $ |d_K| <X$ and signature $(r_1,r_2)$.\nIn this paper, we restrict to the case $G=S_{d+1}$, and consider the sum $\\sum_{p\\leq x} a_{\\rho}(p)$ in the family of $S_{d+1}$-fields, $L(X)^{r_2}$ and show that under the counting conjectures (\\ref{estimate}) and (\\ref{estimate1}),\nit has the Gaussian distribution, namely, for a continuous real function $h$ on $\\Bbb R$, if $\\frac {\\log X}{\\log x}\\to\\infty$ as $x\\to\\infty$,\n\n\\begin{equation}\\label{main-id}\n\\frac 1{\\#L(X)^{r_2}} \\sum_{L(s,\\rho,K)\\in L(X)^{r_2}} h\\left(\\frac {\\sum_{p\\leq x} a_{\\rho}(p)}{\\sqrt{\\pi(x)}}\\right)\n\\longrightarrow \\frac 1{\\sqrt{2\\pi}}\\int_{-\\infty}^\\infty h(t)e^{-\\frac {t^2}2}\\, dt.\n\\end{equation}\nWhen $L(X)^{r_2}$ is replaced by $\\mathcal F_k$, the family of all normalized holomorphic Hecke eigen cusp forms of weight $k$ with respect to $SL_2(\\Bbb Z)$,\nNagoshi \\cite{N} showed that if $\\frac {\\log k}{\\log x}\\to\\infty$ as $x\\to\\infty$,\n\n\\begin{equation}\\label{N}\n\\frac 1{\\#\\mathcal F_k} \\sum_{f\\in \\mathcal F_k} h\\left(\\frac {\\sum_{p\\leq x} a_{f}(p)}{\\sqrt{\\pi(x)}}\\right)\n\\longrightarrow \\frac 1{\\sqrt{2\\pi}}\\int_{-\\infty}^\\infty h(t)e^{-\\frac {t^2}2}\\, dt,\n\\end{equation}\nand called it central limit theorem.\n\nHere we note that we do not need the Artin conjecture nor the strong Artin conjecture in the proof of (\\ref{main-id}).\nThe estimates (\\ref{estimate}) and (\\ref{estimate1}) are proved by Taniguchi and Thorne \\cite{TT} for $S_3$ fields.\nFor $G=S_4, S_5$, the estimate (\\ref{estimate}) was proved in \\cite{BBP} and \\cite{ST}, resp.\nWe prove (\\ref{estimate1}) in Sections \\ref{S_5} and \\ref{S_4}. Hence (\\ref{main-id}) is unconditional for $S_3, S_4$ and $S_5$-fields.\nThese estimates will be used in computing the $n$-level densities of Artin $L$-functions \\cite{CK}, \\cite{CK1}.\n\nWe also study the distribution of the prime sums\n$\\sum_{p\\leq x} a_{\\rho}(p)^r$ for a positive integer $r$. The effective Chebotarev density theorem implies the analogue of Sato-Tate distribution. Namely, $\\frac 1{\\pi(x)}\\sum_{p\\leq x} a_{\\rho}(p)^r\\to n_r$ as $x\\to\\infty$, where $n_r$ is the multiplicity of the trivial representation in $\\rho^r$.\n\nWe also study distribution of $\\sum_{p\\leq x} a_{f}(p)$ for $f\\in S_k(N)$, the set of normalized Hecke eigen cusp forms of weight $k$ with respect to $\\Gamma_0(N)$ with the trivial central character. We prove the Gaussian distribution as $N\\to\\infty$.\n\n\\section{Counting $S_{d+1}$-fields with local conditions}\n\nLet $\\mathcal S = (LC_{p})$ be a finite set of local\nconditions. $LC_p=\\mathcal S_{p,C}$ means that $p$ is unramified in $K$ and the conjugacy class of $\\text{Frob}_p$ is $C$. Let $|\\mathcal S_{p,C}|=\\frac {|C|}{|G|(1+f(p))}$ for some positive function $f(p)$ which satisfies\n$f(p)=O(\\frac 1p)$. There are also several splitting types of ramified primes, which are denoted by $r_1,r_2,\\cdots,r_w$. If $LC_p=\\mathcal S_{p,r_i}$, then it means that $p$ is ramified and its splitting type is $r_i$. Assume that we can choose explicit positive functions $c_1(p),c_2(p), \\cdots, c_w(p)$ with $\\sum_{i=1}^w c_i(p)=f(p)$. Define $|\\mathcal{S}_{p,r_i}|=\\frac{c_i(p)}{1+f(p)}$ and $|\\mathcal S|=\\prod_p |LC_p|$.\n\nLet $L(X;\\mathcal S)^{r_2}$ be the set of $S_{d+1}$-fields $K$ with $ |d_K| <X$ and the local condition\n$\\mathcal S$.\n\nThen assume that\n\\begin{eqnarray} \\label{estimate}\n|L(X)^{r_2}| &=& A(r_2) X +O(X^{\\delta}),\\\\\n|L(X;\\mathcal S)^{r_2}| &=& |\\mathcal S| A(r_2) X + O\\left(\\left(\\prod_{p \\in S} p \\right)^{\\gamma} X^{\\delta} \\right),\\label{estimate1}\n\\end{eqnarray}\nfor some positive constant $\\delta$ and $\\gamma$, and the implied constant is uniformly bounded for $p$ and local conditions at $p$.\n\nThis assumption is satisfied when $G=S_3, S_4$ and $S_5$. When $G=S_3$, Taniguchi and Thorne \\cite{TT} obtained more precise results:\nLet $L(X)^\\pm$ be the set of cubic fields $K$ with $ \\pm d_K <X$. Then\n\\begin{equation*}\n|L(X)^\\pm|=\\frac{C^{\\pm}}{12 \\zeta(3)}X + \\frac{4 K^{\\pm}}{5 \\Gamma(2\/3)^3}X^{5\/6}+O(X^{7\/9+\\epsilon}),\n\\end{equation*}\nwhere $C^{-}=3$, $C^+=1$, $K^-=\\sqrt{3}$, and $K^+=1$. Here, we count only one cubic field from three conjugate fields. Let $TS_p, PS_p,$ and $IN_p$ be the local conditions of $p$ which means that $p$ is totally split, partially split and inert respectively. Let $S=\\{LC_{p_i}| i=1,2,\\cdots,u \\}$ be a set of local conditions at $p_i$. Then\n\\begin{eqnarray*}\n|LC_p|=\\left\\{ \\begin{array}{cc}\n\\frac{1\/6}{1+1\/p+1\/p^2} & \\mbox{if $LC_p=TS_p$},\\\\\n\\frac{3\/6}{1+1\/p+1\/p^2} & \\mbox{if $LC_p=PS_p$},\\\\\n\\frac{2\/6}{1+1\/p+1\/p^2} & \\mbox{if $LC_p=IN_p$},\\\\\n\\frac{1\/p}{1+1\/p+1\/p^2} & \\mbox{if $p$ is partially ramified},\\\\\n\\frac{1\/p^2}{1+1\/p+1\/p^2} & \\mbox{if $p$ is totally ramified}.\n\\end{array}\\right.\n\\end{eqnarray*}\nand $|L(X; \\mathcal S)^{\\pm}| = |\\mathcal S| A^\\pm X + O(E_{\\mathcal S}(X))$, where $A^\\pm=C_1\\frac{C^{\\pm}}{12 \\zeta(3)}$, and\n\\begin{eqnarray*}\nE_{\\mathcal S}(X)=\\left\\{ \\begin{array}{lcc}\nX^{5\/6} & \\mbox{ if $(\\prod_{ p \\in \\mathcal S} p^{\\frac{8}{9}e_p}) < X^{\\frac{1}{16}}$, }\\\\\n( \\prod_{p \\in \\mathcal S}p^{\\frac{8}{9}e_p})X^{\\frac 79+\\epsilon} & \\mbox{ if $(\\prod_{ p \\in \\mathcal S} p^{\\frac{8}{9}e_p}) \\geq X^{\\frac{1}{16}}$, }\\\n\\end{array}\\right.\n\\end{eqnarray*}\nwhere $e_p=1$ if $p$ is unramified and otherwise, $e_p=2$.\n\nFor $G=S_4, S_5$, the estimate (\\ref{estimate}) was proved in \\cite{BBP} and \\cite{ST}.\nWe prove (\\ref{estimate1}) in Sections \\ref{S_5} and \\ref{S_4}.\n\nWe identify $L(X)^{r_2}$ with the set of Artin $L$-functions $L(s,\\rho,K)$ where $K$ is a $G$-field with $|d_K| <X$ with signature $(r_1,r_2)$. Here we count only one $G$-field for each $d+1$ conjugate fields.\nThroughout the article, we\nimplicitly assume that the size of $L(X)^{r_2}$ is same with the number of number fields which\nsatisfy the requirements of $L(X)^{r_2}$. This claim deals with arithmetic equivalence of number\nfields. Two number fields $K_1$ and $K_2$ are arithmetically equivalent if $\\zeta_{K_1}(s) = \\zeta_{K_2}(s)$. We say\nthat a number field K is arithmetically solitary if $\\zeta_K(s) = \\zeta_F(s)$ implies that $K$ and $F$ are\nconjugate. It is known that $S_d$-fields and $A_d$ fields are arithmetically solitary. See Chapter\nII in \\cite{Kl}.\n\nFor simplicity, we denote $L(s,\\rho,K)\\in L(X)^{r_2}$ by\n$\\rho\\in L(X)$.\n\n\\section{Central limit theorem of Artin L-functions}\n\nConsider, for a continuous real function $h$ on $\\Bbb R$,\n\n\\begin{equation}\\label{central}\n\\frac 1{\\#L(X)} \\sum_{\\rho\\in L(X)} h\\left(\\frac {\\sum_{p\\leq x} a_{\\rho}(p)}{\\sqrt{\\pi(x)}}\\right).\n\\end{equation}\nWe assume that $x$ grows more slowly than $X$; namely, $\\frac {\\log X}{\\log x}\\longrightarrow \\infty$ as $x\\to\\infty$. So for an arbitrary positive real number $a$, we have $X>x^a$.\n\nBy Theorem 25.8 and Theorem 30.2 (the method of moments) in \\cite{B}, it is enough to consider $h(x)=x^r$.\nConsider\n\\begin{equation}\\label{central-limit}\n\\sum_{\\rho\\in L(X)} \\left(\\frac {\\sum_{p\\leq x} a_\\rho(p)}{\\sqrt{\\pi(x)}}\\right)^r.\n\\end{equation}\n\nBy multinomial formula,\n$$\\left(\\sum_{p\\leq x} a_{\\rho}(p)\\right)^r=\\sum_{u=1}^r {\\sum}^{(1)}_{(r_1,...,r_u)} \\frac {r!}{r_1!\\cdots r_u!} \\frac 1{u!} {\\sum}^{(2)}_{(p_1,...,p_u)} a_{\\rho}(p_1)^{r_1}\\cdots a_{\\rho}(p_u)^{r_u},\n$$\nwhere $\\sum_{(r_1,...,r_u)}^{(1)}$ means the sum over the $u$-tuples $(r_1,...,r_u)$ of positive integers such that $r_1+\\cdots+r_u=r$, and $\\sum_{(p_1,...,p_u)}^{(2)}$ means the sum over the $u$-tuples $(p_1,...,p_u)$ of distinct primes such that $p_i\\leq x$ for each $i$.\nThen\n$$(\\ref{central-limit})=\\pi(x)^{-\\frac r2} \\sum_{u=1}^r \\frac 1{u!} {\\sum}^{(1)}_{(r_1,...,r_u)} \\frac {r!}{r_1!\\cdots r_u!}  {\\sum}^{(2)}_{(p_1,...,p_u)} \\left(\\sum_{\\rho\\in L(X)} a_{\\rho}(p_1)^{r_1}\\cdots a_{\\rho}(p_u)^{r_u}\\right).\n$$\n\nNow we claim that except when $r$ is even, $u=\\frac r2$, and $r_1=\\cdots=r_u=2$, it gives rise to the error term.\n\nNow suppose $r_i\\geq 2$ for all $i$, and $r_j>2$ for some $j$. Then since $r_1+\\cdots+r_u=r$, $u\\leq\\frac {r-1}2.$ Hence by the trivial estimate,\nsuch term is majorized by\n$$\\pi(x)^{-\\frac r2} \\sum_{u=1}^r \\frac 1{u!} {\\sum}_{(r_1,...,r_u)}^{(1)}\\frac {r!}{r_1!\\cdots r_u!} d^{r_1+\\cdots+r_u} |L(X)| \\pi(x)^u\n\\ll_r \\pi(x)^{-\\frac 12} |L(X)| \\sum_{u=1}^r \\frac 1{u!}  d^r \\ll_{r,d} X \\pi(x)^{-\\frac 12}.\n$$\nThis gives rise to the error term.\n\nSuppose $r_i\\leq 2$ for all $i$.\nSuppose $r_i=1$ for some $i$. We may assume that $r_1=1$.\n\nLet $N$ be the number of conjugacy classes of $G$, and partition the sum $\\sum_{\\rho\\in L(X)}$ into $(N+w)^{u}$ sums, namely, given\n$(\\mathcal S_1,...,\\mathcal S_{u})$, where $\\mathcal S_i$ is either $\\mathcal S_{p_i,C}$ or $\\mathcal S_{p_i,r_j}$,\nwe consider the set of $\\rho\\in L(X)$ with the local conditions $\\mathcal S_i$ for each $i$. Note that in each such partition, $a_{\\rho}(p_1)^{r_1}\\cdots a_{\\rho}(p_u)^{r_u}$ remains a constant.\n\nSuppose $p_1$ is unramified, and fix the splitting types of $p_2,\\cdots,p_u$, and let $\\text{Frob}_{p_1}$ runs through the conjugacy classes of $G$. Then by (\\ref{estimate1}), the sum of such $N$ partitions is\n$$\\sum_C \\left(\\frac{|C|a_\\rho(p_1)}{|G|(1+f(p_1))} A(\\mathcal S_2,...,\\mathcal S_{u})X + O((p_1\\cdots p_u)^\\gamma X^\\delta) \\right),\n$$\nfor a constant $A(\\mathcal S_2,...,\\mathcal S_u)$.\nLet $\\chi_\\rho$ be the character of $\\rho$. Then $a_{\\rho}(p)=\\chi_{\\rho}(g)$, where $g=\\text{Frob}_p$. By orthogonality of characters,\n$\\sum_C |C| a_{\\rho}(p_1)=\\sum_{g\\in G} \\chi_\\rho(g)=0$. Hence the above sum is\n$O((p_1\\cdots p_u)^\\gamma X^\\delta)$, and it is majorized by $\\pi(x)^{-\\frac r2+u}x^{\\gamma u} X^{\\delta}.$\n\nHence we can assume that $r_i\\leq 2$ for each $i$, and $p_j$ is ramified when $r_j=1$. Suppose $r_1+\\cdots+r_{v}+r_{v+1}+\\cdots+r_u=r$, $r_1=\\cdots=r_v=1$ and $r_{v+1}=\\cdots=r_u=2$. Then $u-v\\leq \\frac {r-1}2$, and $p_1,...,p_v$ are ramified.\nThe partition of fixed splitting types of $p_{v+1},...,p_u$ is majorized by\n$$\n\\prod_{i=1}^v \\frac {f(p_i)}{1+f(p_i)} B(\\mathcal S_{v+1},...,\\mathcal S_u)X + O((p_1\\cdots p_u)^\\gamma X^\\delta),\n$$\nfor some constant $B(\\mathcal S_{v+1},...,\\mathcal S_u)$.\nSince $\\frac {f(p)}{1+f(p)}\\ll \\frac 1p$, it contributes to\n$$\\pi(x)^{u-v-\\frac r2}(\\log\\log x)^v X+ \\pi(x)^{-\\frac r2+u}x^{\\gamma u} X^{\\delta}\\ll  X (\\log\\log x)^v \\pi(x)^{-\\frac 12}+\\pi(x)^{-\\frac r2+u}x^{\\gamma u} X^{\\delta}.\n$$\n\nNow let $r$ be even, $u=\\frac r2$, and $r_1=\\cdots=r_u=2$. If one of $p_1,p_2, \\cdots , p_u$ is ramified, their contribution is\nmajorized by $X \\pi(x)^{-1}\\log\\log x.$\nNow we assume that all primes are unramified. Then the corresponding term is\n\\begin{equation}\\label{main}\n\\pi(x)^{-\\frac r2} \\frac 1{u!} \\frac {r!}{2^u} \\sum_{(p_1,...,p_u)}^{(2)} \\left(\\sum_{L(s,\\rho)\\in L(X)} a_{\\rho}(p_1)^2\\cdots a_{\\rho}(p_u)^2\\right).\n\\end{equation}\n\nLet $N$ be the number of conjugacy classes of $G$, and partition the sum $\\sum_{\\rho\\in L(X)}$ into $N^u$ sums\nwhere $(C_1,...,C_u)$ is the set of $\\rho\\in L(X)$ such that $\\text{Frob}_{p_i}\\in C_i$ for each $i$.\nThen,\n\\begin{eqnarray*}\n&& \\sum_{\\rho\\in L(X)} a_{\\rho}(p_1)^2\\cdots a_{\\rho}(p_u)^2=\\sum_{(C_1,...,C_u)} \\chi_{\\rho}(p_1)^2\\cdots \\chi_{\\rho}(p_u)^2\n\\left(\\sum_{\\rho\\in L(X)\\atop \\text{Frob}_{p_i}\\in C_i} 1\\right) \\\\\n&& =\\sum_{(C_1,...,C_u)} \\chi_{\\rho}(p_1)^2\\cdots \\chi_{\\rho}(p_u)^2 \\left(\\prod_{i=1}^u \\frac {|C_i|}{|G|(1+f(p_i))} |L(X)|+O((p_1\\cdots p_u)^\\gamma X^{\\delta})\\right).\n\\end{eqnarray*}\nNow\n$$\n\\sum_{(C_1,...,C_u)} \\chi_{\\rho}(p_1)^2\\cdots \\chi_{\\rho}(p_u)^2 \\prod_{i=1}^u \\frac {|C_i|}{|G|(1+f(p_i))}=\\prod_{i=1}^u \\left(\\sum_{C_i} \\frac {\\chi_{\\rho}(p_i)^2|C_i|}{|G|(1+f(p_i))}\\right).\n$$\nHere $\\chi_{\\rho}(p)^2=\\chi_{\\rho^2}(p)=\\chi_{Sym^2\\rho}(p)+\\chi_{\\wedge^2\\rho}(p)$. We observed in \\cite{CK} that since $\\rho$ is an irreducible real self-dual representation,\n$Sym^2\\rho$ contains the trivial representation and\n$\\wedge^2\\rho$ does not contain the trivial representation (\\cite{JL}, page 274). Hence $\\chi_{\\rho}(p)^2=1+\\sum_{j=1}^l \\eta_j(p)$, where $\\eta_j$'s are non-trivial irreducible characters of $G$. By the orthogonality of characters, for each $j$, $\\sum_C |C|\\eta_j(p)=\\sum_{g\\in G} \\eta_i(g)=0$. Hence $\\sum_{C} \\chi_{\\rho}(p)^2|C|=|G|.$\nTherefore,\n\\begin{eqnarray*}\n&& {\\sum}_{(p_1,...,p_u)}^{(2)} \\left(\\sum_{\\rho\\in L(X)} a_{\\rho}(p_1)^2\\cdots a_{\\rho}(p_u)^2\\right) \\\\\n&=& \\pi(x)^u |L(X)| + O(\\pi(x)^{u-1} |L(X)|\\log\\log x) + O(\\pi(x)^u x^{\\gamma u} X^{\\delta}).\n\\end{eqnarray*}\n\nNote\n$$\\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^{\\infty} t^r e^{-\\frac{t^2}{2}}dt = \\begin{cases} \\frac{r!}{(r\/2)! 2^{r\/2}}, & \\text{if $r$ is even,}\\\\\n0, & \\text{if $r$ is odd}\\end{cases}.\n$$\nHence we have proved\n\\begin{theorem}\\label{Artin}\nSuppose $\\frac {\\log X}{\\log x}\\longrightarrow \\infty$ as $x\\to\\infty$. Then\n$$\n\\frac 1{|L(X)|} \\sum_{\\rho\\in L(X)} \\left(\\frac {\\sum_{p\\leq x} a_{\\rho}(p)}{\\sqrt{\\pi(x)}}\\right)^r\n=\\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^{\\infty} t^r e^{-\\frac{t^2}{2}}dt + O\\left(\\frac {(\\log\\log x)^r}{\\pi(x)^{\\frac 12}}\\right).\n$$\n\\end{theorem}\n\nThis proves (\\ref{main-id}).\n\n\\section{Central Limit Theorem for Hecke eigenforms; Level aspect}\n\nIn this section, in analogy to (\\ref{N}),\nwe consider central limit theorem for modular form $L$-functions with the trivial central character with respect to congruence subgroups as the level goes to infinity. We follow \\cite{N} closely. For $k\\geq 2$, let $S_k(N)$ be the set of normalized Hecke eigen cusp forms of weight $k$ with respect to $\\Gamma_0(N)$ with the trivial central character.\nLet $f(z)=\\sum_{n=1}^\\infty a_f(n)n^{\\frac {k-1}2} e^{2\\pi inz}$; $a_f(mn)=a_f(m)a_f(n)$, if $(m,n)=1$; $a_f(1)=1$; $a_f(p^j)=a_f(p)a_f(p^{j-1})-a_f(p^{j-2})$.\n\nWe show\n\\begin{theorem} \\label{Hecke}\nFor a continuous real function $h$ on $\\Bbb R$, (assume that $\\frac {\\log N}{\\log x}\\longrightarrow \\infty$ as $x\\to\\infty$.)\n\n$$\n\\frac 1{\\#S_k(N)} \\sum_{f\\in S_k(N)} h\\left(\\frac {\\sum_{p\\leq x} a_f(p)}{\\sqrt{\\pi(x)}}\\right)\\longrightarrow \\frac 1{\\sqrt{2\\pi}}\\int_{-\\infty}^\\infty h(t) e^{-\\frac {t^2}2}\\, dt\\quad \\text{as $x\\to\\infty$}.\n$$\n\\end{theorem}\n\nWe have, from \\cite{Se},\n\n\\begin{lemma} Suppose $k\\geq 2$. Let $S_k(N,\\chi)$ be the set of normalized Hecke eigen cusp forms of weight $k$ with respect to $\\Gamma_0(N)$ with a character $\\chi$ (mod $N$). Then\n$$\\sum_{f\\in S_k(N,\\chi)} a_f(n)=\\frac {k-1}{12} \\chi(\\sqrt{n}) n^{-\\frac 12} \\psi(N)+O(n^{c}N^{\\frac 12} d(N)),\n$$\nfor some constant $c$, independent of $n, N$.\n\\end{lemma}\n\nHere $\\psi(N)=N \\prod_{l | N} (1+\\frac 1l)$,\nand $d(N)$ is the number of positive divisors of $N$. Note that $\\psi(N)=|SL_2(\\Bbb Z): \\Gamma_0(N)|$.\nHere $\\chi(x)=0$ if $x$ is not a positive integer prime to $N$. In particular, if $n$ is not a square,\n$\\sum_{f\\in S_k(N,\\chi)} a_f(n)=O(n^{c}N^{\\frac 12} d(N)).$ Taking $n=1$ and $\\chi=1$, we have\n$$\\#S_k(N)=\\frac {k-1}{12} \\psi(N)+O(N^{\\frac 12}d(N)).\n$$\n\nWe need to compute, for a positive integer $r$,\n\\begin{equation}\\label{central-limit-h}\n\\sum_{f\\in S_k(N)} \\left(\\frac {\\sum_{p\\leq x} a_f(p)}{\\sqrt{\\pi(x)}}\\right)^r.\n\\end{equation}\n\nBy multinomial formula,\n$$(\\ref{central-limit-h})=\\pi(x)^{-\\frac r2} \\sum_{u=1}^r \\frac 1{u!} {\\sum}_{(r_1,...,r_u)}^{(1)} \\frac {r!}{r_1!\\cdots r_u!} {\\sum}_{(p_1,...,p_u)}^{(2)} \\left(\\sum_{f\\in S_k(N)} a_f(p_1)^{r_1}\\cdots a_f(p_u)^{r_u}\\right).\n$$\n\nNow we claim that except when $r$ is even, $u=\\frac r2$, and $r_1=\\cdots=r_u=2$, it gives rise to the error term.\n\nBy \\cite{N}, Lemma 2, we can show that\n$a_f(p)^n=\\sum_{j=0}^n h_n(j)a_f(p^j)$, where $h_n(j)=0$ if $n$ is odd and $j$ is even, or if $n$ is even and $j$ is odd.\nFor $u$-tuples $(r_1,...,r_u)$ and $(p_1,...,p_u)$, we define\n\\begin{eqnarray*}\nA(r_1,...,r_u) &=& {\\sum}_{(p_1,...,p_u)}^{(2)} B(r_1,...,r_u; p_1,...,p_u),\\\\\n B(r_1,...,r_u; p_1,...,p_u) &=& \\sum_{f\\in S_k(N)} a_f(p_1)^{r_1}\\cdots a_f(p_u)^{r_u}.\n\\end{eqnarray*}\n\nThen\n$$\nB(r_1,...,r_u; p_1,...,p_u)=\\sum_{0\\leq j_r\\leq r_1,...,0\\leq j_u\\leq r_u} h_{r_1}(j_1)\\cdots h_{r_u}(j_u) \\sum_{f\\in S_k(N)} a_f(p_1^{j_1}\\cdots p_u^{j_u}).\n$$\n\nAs in \\cite{N}, if $r_l$ is odd for some $l$, $A(r_1,...,r_u)\\ll N^{\\frac 12}d(N) \\pi(x)^u x^{cur}.$\n\t\nNow let $r_1=\\cdots=r_u=2$. Then $r$ is even, and $u=\\frac r2$.\n\n$$A(r_1,...,r_u)=\\pi(x)^{\\frac r2} \\#S_k(N)+O(\\pi(x)^{\\frac r2-1}(\\log\\log x)^{\\frac r2}\\#S_k(N)).\n$$\n\nNow suppose that all $r_i$'s are even, and $r_i>2$ for some $i$. Then $u\\leq \\frac r2-1$.\nThen\n$$A(r_1,...,r_u)\\ll \\pi(x)^{-1}\\#S_k(N).\n$$\n\nHence, as in Theorem \\ref{Artin}, we have\n\\begin{prop} Assume that $\\frac {\\log N}{\\log x}\\longrightarrow \\infty$ as $x\\to\\infty$. Then\n$$\n\\frac{1}{\\#S_k(N)} \\sum_{f\\in S_k(N)} \\left(\\frac {\\sum_{p\\leq x} a_f(p)}{\\sqrt{\\pi(x)}}\\right)^r\n=\\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^{\\infty} t^r e^{-\\frac{t^2}{2}}dt + O\\left(\\frac {(\\log\\log x)^{\\frac r2}}{\\pi(x)}\\right).\n$$\n\\end{prop}\nThis proves Theorem \\ref{Hecke}\n\n\\section{Analogues of Sato-Tate distribution}\n\nFor a Hecke eigenform $f\\in \\mathcal F_k$, Sato-Tate conjecture says that for a continuous real function $h$ on $[-2,2]$,\n$$\n\\frac 1{\\pi(x)} \\sum_{p\\leq x} h(a_{f}(p))\\longrightarrow \\frac 1{2\\pi}\\int_{-2}^2 h(t) \\sqrt{4-t^2}\\, dt,\\quad \\text{as $x\\to\\infty$}.\n$$\nLet $a_f(p)=2\\cos\\theta_f(p)$ for $\\theta_f(p)\\in [0,\\pi]$. Then\n$\\{\\theta_f(p)\\}$ is uniformly distributed with respect to the measure $\\frac 2{\\pi}\\sin^2\\theta \\, d\\theta$ on $[0,\\pi]$. This is proved in \\cite{BGHT}.\n\nFor a vertical Sato-Tate distribution, one can consider, for a fixed prime $p$,\n\\begin{equation} \\label{CDF}\n\\sum_{f\\in \\mathcal F_k} a_{f}(p)^n.\n\\end{equation}\n\nConrey-Duke-Farmer \\cite{CDF} proved, for a holomorphic form of weight $k$,\n$$\\sum_{f\\in \\mathcal F_k} a_f(p)^n=\\frac k{6\\pi} \\left(1+\\frac 1p\\right)\\int_0^\\pi 2^n \\cos^n\\theta \\frac {\\sin^2\\theta}{(1-\\frac 1{p})^2+\\frac 4p \\sin^2\\theta} \\, d\\theta+O(p^{\\frac n2+\\epsilon}).\n$$\n\nThis implies that $\\{\\theta_f(p), f\\in \\mathcal F_k\\}$ is uniformly distributed with respect to the measure\n$$\\frac 2{\\pi} \\left(1+\\frac 1p\\right)\\frac {\\sin^2\\theta}{(1-\\frac 1p)^2+\\frac 4p \\sin^2 \\theta} \\, d\\theta.\n$$\n\nFor Artin $L$-function analogue of Sato-Tate distribution, we consider, for $r\\geq 1$,\n\n\\begin{equation}\\label{Sato-Tate}\n\\frac 1{\\pi(x)} \\sum_{p\\leq x} a_{\\rho}(p)^r.\n\\end{equation}\n\nIn our case, note that $-1\\leq a_{\\rho}(p)\\leq d$.\nBy effective Chebotarev density theorem (cf. \\cite{Se1}, page 132), for $\\log x\\gg |G|(\\log \\left|d_{\\widehat{K}}\\right| )^2$,\n\\begin{equation*}\\label{chebo}\n\\sum_{p\\leq x \\atop \\text{Frob}_p\\in C} 1=\\frac {|C|}{|G|} \\pi(x)+O\\left(\\pi(x^{\\beta})\\right)+O\\left(x e^{-c |G|^{-\\frac 12} (\\log x)^{\\frac 12}}\\right),\n\\end{equation*}\nwhere $\\beta$ is an exceptional zero of $\\zeta_{\\widehat{K}}(s)$ such that $1-\\beta\\leq \\frac 14\\log d_{\\widehat{K}}$, if it exists. Hence\n\n$$\\sum_{p\\leq x} a_{\\rho}(p)^r=\\sum_C a_{\\rho}(p)^r \\left(\\sum_{p\\leq x\\atop \\text{Frob}_p\\in C} 1\\right)\n=\\sum_C a_{\\rho}(p)^r \\frac {|C|}{|G|} \\pi(x)+ O(\\pi(x^{\\beta})+x e^{-c |G|^{-\\frac 12} (\\log x)^{\\frac 12}}).\n$$\n\nNow $\\sum_C |C| a_{\\rho}(p)^r=\\sum_{g\\in G} \\chi_{\\rho}(g)^r$ and $\\chi_{\\rho}(g)^r=\\chi_{\\rho^r}(g)$.\nNote that\n$$\\frac 1{|G|}\\sum_{g\\in G} \\chi_{\\rho^r}(g)=n_r,\n$$\nwhich is the multiplicity of the trivial representation in $\\rho^r$. Hence\n$$\\sum_{p\\leq x} a_{\\rho}(p)^r=n_r \\pi(x)+O(\\pi(x^{\\beta})+x e^{-c |G|^{-\\frac 12} (\\log x)^{\\frac 12}}).\n$$\nTherefore,\n$$\\frac 1{\\pi(x)} \\sum_{p\\leq x} a_{\\rho}(p)^r\\longrightarrow n_r, \\quad \\text{as $x\\to\\infty$}.\n$$\n\nFor vertical Sato-Tate distribution, for a fixed prime $p$, consider\n$$\\frac 1{|L(X)|} \\sum_{\\rho\\in L(X)} a_{\\rho}(p)^r.\n$$\nThen by (\\ref{estimate1}),\n\\begin{eqnarray*}\n&& \\sum_{\\rho\\in L(X)} a_{\\rho}(p)^r=\\sum_C a_{\\rho}(p)^r \\left(\\sum_{\\rho\\in L(X)\\atop \\text{Frob}_p\\in C} 1\\right)+ a_{\\rho}(p)^r\n\\left(\\sum_{\\rho\\in L(X)\\atop \\text{$p$ is ramified}}  1 \\right) \\\\\n&&\n=\\frac {|L(X)|}{|G|(1+f(p))} \\sum_C |C| a_{\\rho}(p)^r +O(p^\\gamma X^\\delta)+O\\left(\\frac Xp\\right)\n=\\frac {|L(X)| n_r}{1+f(p)}+O(p^\\gamma X^\\delta)+O\\left(\\frac Xp\\right).\n\\end{eqnarray*}\nSo if $X>p^{\\frac {1+\\gamma}{1-\\delta}}$,\n$$\\frac 1{|L(X)|} \\sum_{\\rho\\in L(X)} a_{\\rho}(p)^r=\\frac {n_r}{1+f(p)}+O(p^{-1}).\n$$\n\n\\section{Counting $S_5$ quintic fields with local conditions}\\label{S_5}\n\nShankar and Tsimerman \\cite{ST} recently counted $S_5$ quintic fields with a power saving error terms. For $i=0,1,2$, let $N_5^{(i)}(X)$ be the number of $S_5$ quintic fields of signature $(5-2i,i)$ with $|d_K| < X$. Then they showed\n\\begin{eqnarray*}\nN_5^{(i)}(X)= D_i X+ O_{\\epsilon}\\left( X^{\\frac{399}{400}+\\epsilon }\\right),\n\\end{eqnarray*}\nwhere $D_i=d_i \\prod_p (1+ p^{-2} -p^{-4} -p^{-5})$ and $d_0,d_1,d_2$ are $\\frac{1}{240}, \\frac{1}{24}$ and $\\frac{1}{16}$, respectively.\n\nWe can count quintic fields with finitely many local conditions. Let $C$ be a conjugacy class of $S_5$ and $f(p)=p^{-1}+2p^{-2}+2p^{-3}+p^{-4}$. Let $\\mathcal S=\\{ LC_p \\}$ be a finite set of local conditions. Define\n $|\\mathcal S_{p,C}|=\\frac {|C|}{|G|(1+f(p))}$, $|\\mathcal S_{p,r_i} |=\\frac {c_i(p)}{(1+f(p))}$, and $|\\mathcal S|=\\prod_p |LC_p|$, where $c_i(p)$'s are given explicitly at the end of this section.\n\n\\begin{theorem} Let $N_5^{(i)}(X,\\mathcal S)$ be the number of $S_5$ quintic fields of signature $(5-2i,i)$ with $|d_K| < X$, and with the local condition $\\mathcal S$. Then\n\\begin{eqnarray*}\nN_5^{(i)}(X,\\mathcal S)= |\\mathcal S| D_i X+ O_{\\epsilon}\\left(\\left(\\prod_{p\\in \\mathcal S} p \\right)^{2-\\epsilon} X^{\\frac{199}{200}+\\epsilon }\\right).\n\\end{eqnarray*}\n\\end{theorem}\n\nWe follow the notations in \\cite{ST}.  Let $V_{\\mathbb{Z}}$ be the space of $4$-tuples of $5 \\times 5$ alternating matrices with integer coefficients. The group $G_\\mathbb{Z} = GL_4(\\mathbb{Z}) \\times SL_5(\\mathbb{Z})$ acts on $V_\\mathbb{Z}$ via\n$$\n(g_4,g_5) \\cdot ( A, B, C, D)^t = g_4 ( g_5 A g_5^t, g_5 B g_5^t,g_5 C g_5^t,g_5 D g_5^t)^t.\n$$\nHere $g_4\\cdot (A,B,C,D)^t$ means $(a_1 (A,B,C,D)^t, a_2 (A,B,C,D)^t, a_3 (A,B,C,D)^t, a_4 (A,B,C,D)^t)$, where $a_i$ is the $i$th row of $g_4$.\n\nThere is a canonical bijection between the set of $G_\\mathbb{Z}$-equivalence classes of elements $(A,B,C,D) \\in V_{\\mathbb{Z}}$, and the set of isomorphism classes of pairs of $(R,R')$, where $R$ is a quintic ring and $R'$ is a sextic resolvent ring of $R$. (See \\cite{B08}.)\nLet $\\mathcal V$ be an element of $V_{\\mathbb{Z}}$.  Over the residue field $\\mathbb{F}_p$, the element $\\mathcal V$ determines a quintic\n$\\mathbb{F}_p$-algebra $R(\\mathcal V)\/(p)$. Let us define the splitting symbol $(\\mathcal V,p)$ by\n$$\n(\\mathcal V,p)=(f_1^{e_1}f_2^{e_2} \\cdots ),\n$$\nwhenever $R(\\mathcal V)\/(p) \\cong \\mathbb{F}_{p^{f_1}}[t_1]\/(t_1^{e_1}) \\oplus \\mathbb{F}_{p^{f_2}}[t_2]\/(t_2^{e_2}) \\oplus \\cdots$. Then there are 17 possible splitting types for $(\\mathcal V,p)$; $(11111),$ $(1112),$ $(122),$ $(113),$ $(23),$ $(14),$ $(5),$ $(1^2111),$ $(1^212),$ $(1^23),$ $(1^21^21),$ $(2^21),$ $(1^311),$ $(1^32),$ $(1^31^2),$ $(1^41),$ and $(1^5)$. Let $\\sigma$ be one of 17 splitting types. Then define $T_p(\\sigma)$ to be the set of $\\mathcal V\\in V_{\\mathbb{Z}}$ such that $(\\mathcal V,p)=\\sigma$ and $U_p(\\sigma)$ to be the set of elements in $T_p(\\sigma)$ corresponding to quintic rings that are maximal at $p$. The set $U_p(\\sigma)$ is defined by congruence conditions on coefficients of $\\mathcal V$ modulo $p^2$. Let $\\mu(U_p(\\sigma))$ be the $p$-adic density of $\\mathcal S$ in $V_{\\mathbb{Z}_p}$. They are computed in Lemma 4 in \\cite{B08}. Let ${U}_p$ denote the union of the 17 $U_p(\\sigma)$. Then Lemma 20 of \\cite{B08} implies that\n\\begin{eqnarray*}\n\\mu({U_p})=(p-1)^8p^{12}(p+1)^4(p^2+1)^2(p^2+p+1)^2(p^4+p^3+p^2+p+1)(p^4+p^3+2p^2+2p+1)\/p^{40}.\n\\end{eqnarray*}\n\nNote that\n$$d_i \\zeta(2)^2\\zeta(3)^2\\zeta(4)^2\\zeta(5) \\prod_p \\mu({U_p}) = d_i \\prod_p (1+p^{-2}-p^{-4}-p^{-5}),\n$$\nwhich is the coefficient of the main term in counting quintic fields.  Here we need to interpret $\\mu({U_p})$ in the following way:\n$U_p$ can be considered as a subset of $(\\mathbb{Z}\/q^2 \\mathbb{Z})^{40}$, or the union of $k$ translates of $p^2 V_{\\mathbb{Z}}$, where $k$ is the size of the set. Here $k$ is $\\mu(U_p)q^{80}$.\nLet ${W}_p$ be the complement of ${U_p}$ in $V_{\\mathbb{Z}}$, then $\\mu({W}_p)=1- \\mu({U_p})$.  Then $W_p$ is the union of $\\mu({W}_p)q^{80}$ translates of $q^2V_{\\mathbb{Z}}$.\n\nFor $q$ square-free, let $W_q \\subset V_{\\mathbb{Z}}$ be the set of elements corresponding to quintic rings that are not maximal at each prime dividing $q$. Then $W_q$ is the union of $\\prod_{p \\mid q} \\mu(W_p) \\cdot q^{80}$ translates of $q^2 V_{\\mathbb{Z}}$ by the Chinese Remainder Theorem.\n\nLet $V_{\\mathbb{Z}}^{ndeg}$ denote the set of elements in $V_{\\mathbb{Z}}$ that correspond to orders in $S_5$-fields, and let $V_{\\mathbb{Z}}^{deg}$ be the complement of $V_{\\mathbb{Z}}^{ndeg}$.\nA point in $V_{\\mathbb{Z}}$ corresponds to a maximal order in an $S_5$ quintic fields precisely if it is in $ \\cap_p U_p \\cap V_{\\mathbb{Z}}^{ndeg}$. For a $G_\\mathbb{Z}$-invariant subset $S$ of $V_{\\mathbb{Z}}$, let $N(S,X)$ denote the number of irreducible $G_\\mathbb{Z}$-orbits in $S^{ndeg}:=S \\cap V_{\\mathbb{Z}}^{ndeg}$ having discriminant bounded by $X$.  For a set $S$ which is not $G_\\mathbb{Z}$-invariant, we can define $N^*(S,X)$ which also counts the orbits of degenerate points in $S$.\n\nNow we choose a finite set of primes $\\{p_1,p_2, \\cdots, p_n \\}$. And choose a splitting type $\\sigma_{p_k}$ for each $p_k$, $k=1,2,\\cdots, n$. Define $U'_p$ to be $U_p$ if $p \\neq p_k$, $k=1,2,\\cdots, n$. If $p=p_k$ for some $k$, then $U'_p=U_p(\\sigma_{p_k})$.   Let $W'_p$ be the complement of $U'_p$. Then $W'_q$ is the union of $\\prod_{p \\mid q} \\mu(W'_p) \\cdot q^{80}$ translates of $q^2 V_{\\mathbb{Z}}$.\n\nLet $N_5^{(i)}(X, \\{ \\sigma_{p_k} \\}_{k=1,2,\\cdots,n})$ be the number of $S_5$ quintic fields of signature $(5-2i,i)$ with $|d_K|<X$ and the splitting types of $p_k$'s are $\\sigma_{p_k}$ for $k=1,2,\\cdots,n$.\nThen by inclusion-exclusion method,\n$$N_5^{(i)}(X, \\{ \\sigma_{p_k} \\}_{k=1,2,\\cdots,n})=\\sum_{q} \\mu(q) N( W'_q \\cap V_{\\mathbb{Z}}^{(i)}, X).$$\n\nWe use two estimates of $N(W'_q \\cap V_{\\mathbb{Z}}^{(i)}, X)$ for small $q$'s and large $q$'s separately. Lemma 3 in \\cite{ST} says that\n$N(W_q, X)=O_\\epsilon(X\/q^{2-\\epsilon})$ and it implies that $N(W'_q,X) \\ll_\\epsilon (p_1 p_2 \\cdots p_n)^{2-\\epsilon} \\frac{X}{q^{2-\\epsilon}}$ for $q$ square-free. If $L$ is a translate of $mV_{\\mathbb{Z}}$, then we have\n\\begin{eqnarray}\nN^*( \\{ x \\in L \\cap V_{\\mathbb{Z}}^{(i)} : a_{12} \\neq 0\\}, X)=c_i \\frac{X}{m^{40}} + O\\left(m^{-39}X^{\\frac{39}{40}}\\right),\n\\end{eqnarray}\nwhere $c_i = d_i \\zeta(2)^2\\zeta(3)^2\\zeta(4)^2\\zeta(5)$. (See Equation 28 in \\cite{B10}.)\nSince $W'_q$ is an union of $\\prod_{p \\mid q} \\mu(W'_p) \\cdot q^{80}$ translates of $q^2 V_{\\mathbb{Z}}$,\n\\begin{eqnarray*}\nN^*( \\{ x \\in W'_q \\cap V_{\\mathbb{Z}}^{(i)} : a_{12} \\neq 0\\}, X)\n=\\prod_{p \\mid q} \\mu(W'_p) \\cdot c_i X + O\\left(q^2X^{\\frac{39}{40}}\\right)\n =\\mu(W'_q)\\cdot c_i X + O\\left(q^2X^{\\frac{39}{40}}\\right).\n\\end{eqnarray*}\n\nThen\n\\begin{eqnarray*}\n&& N_5^{(i)}(X, \\{ \\sigma_{p_i} \\}_{i=1,2,\\cdots,n})=\\sum_{q} \\mu(q) N( W'_q \\cap V_{\\mathbb{Z}}^{(i)}, X)\\\\\n&&= \\sum_{q \\leq Q} \\left( \\mu(W'_q) \\cdot c_i X + O\\left( q^2 X^{ \\frac{39}{40} } \\right) - \\mu(q)N_{12}^*(W_q \\cap V_{\\mathbb{Z}}^{deg,(i)},X)  \\right) + \\sum_{ q > Q} O_\\epsilon \\left( (p_1 p_2 \\cdots p_n)^{2-\\epsilon}  \\frac{X}{q^{2-\\epsilon} } \\right)\\\\\n&&=\\sum_{q \\leq Q} \\left( \\mu(W'_q) \\cdot c_i X - \\mu(q)N_{12}^*(W_q \\cap V_{\\mathbb{Z}}^{deg,(i)},X)  \\right)\n+ O_\\epsilon \\left( (p_1 p_2 \\cdots p_n)^{2-\\epsilon} X\/Q^{1-\\epsilon} + X^{\\frac{39}{40}}Q^{3+\\epsilon} \\right)\\\\\n&&= \\sum_q c_i \\mu(W'_q)X + (p_1 p_2 \\cdots p_n)^{2-\\epsilon} O_\\epsilon \\left( X\/Q^{1-\\epsilon}+X^{\\frac{39}{40}}Q^{3+\\epsilon} + X^{\\frac{199}{200}Q^{1+\\epsilon}}\\right)\\\\\n&&= c_i \\prod_p (1- \\mu(W'_q)) X + (p_1 p_2 \\cdots p_n)^{2-\\epsilon} O_\\epsilon \\left( X\/Q^{1-\\epsilon}+X^{\\frac{39}{40}}Q^{3+\\epsilon} + X^{\\frac{199}{200}Q^{1+\\epsilon}}\\right)\\\\\n&&= c_i \\prod_p (\\mu(U'_q)) X + (p_1 p_2 \\cdots p_n)^{2-\\epsilon}O_\\epsilon \\left( X\/Q^{1-\\epsilon}+X^{\\frac{39}{40}}Q^{3+\\epsilon} + X^{\\frac{199}{200}Q^{1+\\epsilon}}\\right).\n\\end{eqnarray*}\n\nPutting $Q=X^{\\frac{1}{400}}$, we have\n$$(p_1 p_2 \\cdots p_n)^{2-\\epsilon}O_\\epsilon \\left( X\/Q^{1-\\epsilon}+X^{\\frac{39}{40}}Q^{3+\\epsilon} + X^{\\frac{199}{200}Q^{1+\\epsilon}}\\right) \\ll_\\epsilon (p_1 p_2 \\cdots p_n)^{2-\\epsilon} X^{\\frac{399}{400}+\\epsilon}.\n$$\n Note that\n \\begin{eqnarray*}\n c_i \\prod_p (\\mu(U'_q)) &=& \\prod_{k=1}^n \\frac{\\mu(U_p(\\sigma_{p_k}))}{\\mu(U_{p_k})} c_i \\prod_p \\mu(U_p)=  \\prod_{k=1}^n \\frac{\\mu(U_p(\\sigma_{p_k}))}{\\mu(U_{p_k})} d_i \\prod_p \\left( 1+ p^{-2} -p^{-4} -p^{-5} \\right).\n\\end{eqnarray*}\n\nFrom Lemma 20 in \\cite{B08}, we can see that, for $f(p)=p^{-1}+2p^{-2}+2p^{-3}+p^{-4}$,\n$$\n\\frac{\\mu(U_p(\\sigma))}{\\mu(U_p)} = \\frac{1\/120}{1+f(p)},\\:\\frac{1\/12}{1+f(p)},\\:\\frac{1\/8}{1+f(p)},\\:\\frac{1\/6}{1+f(p)},\\: \\frac{1\/6}{1+f(p)},\\:\\frac{1\/4}{1+f(p)},\\:\\mbox{and }\\frac{1\/5}{1+f(p)}\n$$\nfor $\\sigma=(11111),(1112),(122),(113),(23),(14),(5),$ respectively, and\n\\begin{eqnarray*}\n\\frac{\\mu(U_p(\\sigma))}{\\mu(U_p)}& =& \\frac{1\/6 \\cdot 1\/p}{1+f(p)},\\:\\frac{1\/2 \\cdot 1\/p}{1+f(p)},\\:\\frac{1\/3 \\cdot 1\/p}{1+f(p)},\\:\\frac{1\/2 \\cdot 1\/p^2}{1+f(p)},\\: \\frac{1\/2 \\cdot 1\/p^2}{1+f(p)},\\:\\frac{1\/2 \\cdot 1\/p^2}{1+f(p)},\\frac{1\/2 \\cdot 1\/p^2}{1+f(p)},\\\\\n & & \\frac{1\/p^3}{1+f(p)},\\:\\frac{1\/p^3}{1+f(p)},\\:\\mbox{ and } \\frac{1\/p^4}{1+f(p)}\n\\end{eqnarray*}\nfor $\\sigma=(1^2111),(1^212),(1^23),(1^21^21),(2^2 1),(1^3 11),(1^3 2),(1^3 1^2), (1^4 1), (1^5),$ respectively. Hence we have proved the theorem. \n\n\\section{Counting $S_4$ quartic fields with local conditions}\\label{S_4}\n\nIn \\cite{BBP}, Belabas, Bhargava and Pomerance obtained a power saving error term for counting $S_4$ quartic fields. For $i=0,1$,\nlet $N_4^{(i)}(X)$ be the number of isomorphism classes of $S_4$-quartic fields of signature $(4-2i,i)$ with $|d_K|<X$. Then\n\\begin{eqnarray*}\nN_4^{(i)}(X)= D_i X + O(X^{23\/24+\\epsilon}),\n\\end{eqnarray*}\nwhere $D_i=d_i \\prod_{p} ( 1+p^{-2} -p^{-3} - p^{-4})$, and\n$d_0=\\frac{1}{48},d_1=\\frac{1}{8},$ and $d_0=\\frac{1}{16}$.\n\nLet $V_{\\mathbb{Z}}$ be the space of pairs of $(A,B)$ of integral ternary quadratic forms. The group $G_\\mathbb{Z}=GL_2(\\mathbb{Z}) \\times SL_3(\\mathbb{Z})$ acts on $V_{\\mathbb{Z}}$ in the following way.\nFor $g_2 \\in GL_2(\\mathbb{Z})$ and $g_3 \\in SL_3(\\mathbb{Z})$,\n\\begin{eqnarray*}\n(g_2,g_3)\\cdot (A,B)^t=g_2( g_3Ag_3^t, g_3Bg_3^t)^t.\n\\end{eqnarray*}\nHere $g_2\\cdot (A,B)$ means that $(a_1 (A,B)^t, a_2 (A,B)^t)$, where $a_i$ is the $i$th row of $g_2$.\n\nThere is a canonical bijection between the set of $G_\\mathbb{Z}$-equivalence classes of elements $(A,B) \\in V_{\\mathbb{Z}}$, and the set of isomorphism classes of pairs of $(Q,R)$, where $Q$ is a quartic ring and $R'$ is a cubic resolvent ring of $Q$. (See \\cite{B04}.)\n\nA prime $p$ has 11 possible splitting type in an $S_4$ quartic field $K$. They are $(1111),$ $(112),$ $(13),$ $(4),$ $(22),$ $(1^211),$ $(1^21^2),$ $(1^22),$ $(2^2),$ $(1^31),$ and $(1^4)$. As we did in the previous section, we can define $U_p(\\sigma)$ and $U_p$, resp. and\n$\\mu(U_p(\\sigma))$'s are computed in Lemma 23, \\cite{B04}.\n\nUsing their result, Yang \\cite{yang} was able to count $S_4$ quartic fields with one local condition with a power saving error term. He showed that\n\\begin{eqnarray*}\nN_4^{(i)}(X, \\sigma_p)= \\frac{\\mu(U_p(\\sigma_p))}{\\mu(U_p)}D_iX + O\\left(p^2X^{\\frac{143}{144}+\\epsilon}\\right).\n\\end{eqnarray*}\n\nBy the same argument in the previous section, we can extend Yang's result to the case of finitely many local conditions:\n\\begin{eqnarray*}\nN_4^{(i)}(X, \\{\\sigma_{p_k} \\}_{k=1,2,\\cdots,n} ) = \\left( \\prod_{k=1}\\frac{\\mu(U_p(\\sigma_{p_k}))}{\\mu(U_{p_k})} \\right) D_i X +\nO\\left( (p_1\\cdots p_k)^2 X^{\\frac{143}{144}+\\epsilon}\\right).\n\\end{eqnarray*}\n\nFrom Lemma 23 in \\cite{B04}, we can see that, for $f(p)=p^{-1}+2p^{-2}+p^{-3}$,\n$$\n\\frac{\\mu(U_p(\\sigma))}{\\mu(U_p)} = \\frac{1\/24}{1+f(p)},\\:\\frac{1\/4}{1+f(p)},\\:\\frac{1\/3}{1+f(p)},\\:\\frac{1\/8}{1+f(p)},\\: \\mbox{and }\\frac{1\/4}{1+f(p)}\n$$\nfor $\\sigma=(1111),(112),(13),(22),(4),$ respectively, and\n$$\n\\frac{\\mu(U_p(\\sigma))}{\\mu(U_p)} = \\frac{1\/2 \\cdot 1\/p}{1+f(p)},\\:\\frac{1\/2 \\cdot 1\/p}{1+f(p)},\\:\\frac{1\/2 \\cdot 1\/p^2}{1+f(p)},\\:\\frac{1\/2 \\cdot 1\/p^2}{1+f(p)},\\:\\frac{1\/p^2}{1+f(p)},\\: \\mbox{and }\\frac{1\/p^3}{1+f(p)}\n$$\nfor $\\sigma=(1^211),(1^22),(1^21^2),(2^2),(1^31), (1^4),$ respectively.  Hence we have proved\n\n\\begin{theorem} Let $N_4^{(i)}(X,\\mathcal S)$ be the number of $S_4$ quartic fields of signature $(4-2i,i)$ with $|d_K| < X$, and with the local condition $\\mathcal S$. Then\n\\begin{eqnarray*}\nN_4^{(i)}(X,\\mathcal S)= |\\mathcal S| D_i X+ O_{\\epsilon}\\left(\\left(\\prod_{p\\in \\mathcal S} p \\right)^2 X^{\\frac{143}{144}+\\epsilon }\\right).\n\\end{eqnarray*}\n\\end{theorem}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction} \\label{sec:intro}\n\nWith large spectroscopic surveys, we have access to precise individual chemical element abundance measurements for 10$^5$-10$^6$ stars. The \\project{\\textsc{galah}}\\ survey \\citep{Buder2018} provides stellar parameters and up to 23 abundances for 342,682 stars, and the \\project{Gaia--\\textsc{eso}}\\ survey \\citep{Gilmore2012} measures detailed abundances for 12 elements in about 10,000 field stars. Another example of the current depth of observational data is the 16th data release of Apache Point Observatory Galactic Evolution Experiment (\\project{\\textsc{apogee}}) survey, which contains information for 437,485 unique stars and more than 20 abundances \\citep{apogeedr16, 2020AJ....160..120J}. \n\nFor the Milky Way, we can use large spectroscopic surveys to catalogue an ensemble of measurements. These include precise stellar metallicities and abundances ([Fe\/H], [X\/Fe]) and imprecise ages, as well as current day positions and orbital parameters. These numbers can be used to work toward the reconstruction of the initial state of the Milky Way. While the chemical abundances of stars are birth properties, stars move over time and their dynamical properties change \\citep[e.g.][]{2012MNRAS.426.2089R}. Chemical tagging utilizes the unchanging chemical abundances to identify star formation groups \\citep{2002freeman-BH}. This is in theory possible as birth clusters up to $10^5 M_\\odot$ are anticipated to be chemically homogeneous \\citep{BH2010}. Chemical tagging has great promise \\citep[e.g.][]{Hogg2016,2016martell}, however, it has been shown to be difficult due to the need for extremely large sample sizes \\citep{Ting2015} and high precision data \\citep{2013Lindegren}.  \n\nIn paper I of this series \\citep{2020Ratcliffe}, we examined the distribution of clusters defined in a 19-dimensional chemical abundance space for 27,000 red clump \\project{\\textsc{apogee}}\\ DR14 stars in the Milky Way's disk \\citep{bovy2014apogee}. Using a non-parametric agglomerative hierarchical clustering method, we determined that the groups defined in abundance space are spatially separated as a function of age.\n\nYet, to reconstruct the disk in the past, we need to know where the stars were born, which we can not measure directly from data. Recently, we have access to some of the largest and highest resolution samples of zoom-in Milky Way-like simulations (e.g. NIHAO-UHD, \\cite{2020buck_NIHAO-UHD}; AURGIA, \\cite{2017Auriga}; FIRE2, \\cite{2018FIRE2}). We also now have access to more abundance information in simulations, with g8.26e11\\ from the NIHAO-UHD suite providing information for 15 abundances and Ananke from \\cite{2020FIRE_sanderson} having information for 11 abundances. Thus, now in simulations, we have access to the full set of properties to trace formation and evolution of disks (e.g. [Fe\/H], [X\/Fe], age, and their origin as indicated by their birth radii within the galactic disk,  $R_\\text{birth}$). This enables us to use simulations to investigate and understand the dependencies and relationships between these properties in disk galaxies, under particular initial conditions and evolutionary events. \n\nSome work has examined $R_\\text{birth}$\\ in simulations in an attempt to better understand the Milky Way's formation. With the use of an N-body simulation, \\cite{2021Bird_avr} found that the age--$R_\\text{birth}$\\ trends are a clear sign of the inside-out disc growth of their simulation, in addition to a correlation between $R_\\text{birth}$\\ and birth kinematics. \\cite{2021Johnson} find that in their hybrid hydrodynamical simulation there is a relationship between age, abundances, and $R_\\text{birth}$\\ in the solar neighborhood, and that the low-$\\alpha$ sequence represents a superposition of populations achieved by radial migration rather than an evolutionary sequence. See also \\cite{2020_buckchemical}.\n\nIn this paper, we use simulations to explore the physical meaning of clusters of stars defined only in ([Fe\/H], [X\/Fe]) space in the observational data. The questions we wish to answer are (i) do abundances link to birth associations, and if so does it rely on star formation processes, (ii) how does the presence of observational errors and sample size effect results, (iii) are results dependent on clustering methods used, and (iv) is there a relationship between stellar birth properties and their abundances? Milky Way analogue simulations are a good tool to investigate the questions we pose and qualitatively represent formation processes of our Galaxy. Both observations and hydrodynamical simulations of Milky Way analogues show that from about z=1, stellar disks form inside-out, with on-going enrichment and star formation across the disk until late times \\citep[e.g.][]{Haywood2013, 2020FIRE_sanderson}.\n\nThe numerical relationship between $R_\\text{birth}$, abundances, and age in the Milky Way has been investigated before. \\cite{2018Minchev_rbirth} proposed a method to infer stellar birth radii from age and metallicity for observational data by projecting stars to the metallicity gradient corresponding to their age. Similarly, \\cite{Frankel2018} invert the age--metallicity relation to find birth radii for the low-$\\alpha$ sequence. \\cite{Ness2019} also suggest that \\mbox{$\\rm [Fe\/H]$}, age, and high- or low-$\\alpha$ sequence membership is all that is needed to infer a star's $R_\\text{birth}$. However, since $R_\\text{birth}$\\ is unable to be measured observationally, none of these methods have been tested. Using simulations, we can study the link between chemical composition at birth ([Fe\/H], [X\/Fe]), birth time (t$_\\text{birth}$, or age) and birth location ($R_\\text{birth}$). \n\nThis paper is organized as follows. In Section \\ref{sec:data} we discuss the two simulations that this paper focuses on. Clustering methods used in this work are described in Section \\ref{sec:methods}. Section \\ref{sec:results_clustering} explores how chemically similar stars separate into discrete groups in the age--$R_\\text{birth}$\\ plane, while Section \\ref{sec:results_errors} explores how these results change under sampling and observational errors. Our last results section, Section \\ref{sec:results_regression}, quantifies the relationship between (\\mbox{$\\rm [Fe\/H]$}, \\mbox{$\\rm [X\/Fe]$}) and age, and (\\mbox{$\\rm [Fe\/H]$}, \\mbox{$\\rm [X\/Fe]$}, age) and $R_\\text{birth}$\\ using simple second order polynomial regressions. Finally, Sections \\ref{sec:discussion} and \\ref{sec:conclusion} present the discussion and conclusions of this analysis.\n\n\\section{Simulations} \\label{sec:data}\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=.95\\textwidth]{buck_selection.pdf}\\\\\n     \\includegraphics[width=.95\\textwidth]{buckHD_selection.pdf}\n\\caption{Selection cuts of the (\\textbf{top}) 2d, and (\\textbf{bottom}) 15d simulations in the (\\textbf{left}) velocity and (\\textbf{right}) spatial planes. The black circle in the Toomre diagram marks where we defined the separation for the kinematically different disk and halo stars. Spatially, we define disk stars to have $|z|\\leq 0.5$ kpc and $4 \\leq$ \\mbox{$R_{\\text{GAL}}$}\\ $\\leq 12$ kpc, shown in the right of the figure.}\n\\label{fig:selection_cuts}\n\\end{figure*}\n\nIn this paper, we focus on two simulations --- one with only two chemical abundances available (g7.55e11, 2d) and another with 15 chemical abundances (g8.26e11, 15d). We include both the high and low-dimensional simulations to investigate how stellar birth information is able to be captured in a few versus large vector of abundances.\n\nThe 2- and 15-dimensional simulations are taken from the Numerical Investigation of a Hundred Astronomical Objects (NIHAO) simulation suite \\citep{2015MNRAS.454...83W}, and are part of the NIHAO-UHD suite \\citep{2020buck_NIHAO-UHD,Buck2019}. The simulations were performed with the smooth particle hydrodynamics solver GASOLINE2 \\citep{2017gasoline2}. They are both spiral disk galaxies with bulges, and were bulge dominated until redshift $z\\geq 1$, with prominant stellar disks forming about 7-8 Gyr ago \\citep{2020buck_NIHAO-UHD}. The 2-dimensional simulation has a stellar particle mass of 0.093 $\\times 10^5 M_\\odot$, while the 15-dimensional simulation has a stellar particle mass of 1.06 $\\times 10^5 M_\\odot$. For more details, see \\cite{2020buck_NIHAO-UHD} for g7.55e11\\ and \\cite{2021BuckHD_chemEnrich} for g8.26e11. \\footnote{The redshift zero snapshot and halo catalogue of the 2d simulation is publicly available for download here: \\url{{https:\/\/tobibu.github.io\/##sim_data}}. Additional files, e.g. the birth positions and higher redshift snapshots, as well as the 15d simulation snapshots can be shared upon request.}\n\nThere are two main differences between the simulations --- resolution and chemical enrichment prescription. As seen from the particle masses, the 2d simulation has a higher mass resolution while the 15d simulation is at fiducial resolution. However, NIHAO galaxies are numerically well converged, so for the purpose of this work the resolution difference should not matter. The other difference is a detail in the numerics. The 15d simulation has an updated chemical enrichment prescription as described in \\cite{2021BuckHD_chemEnrich} which allows us to trace the 15 elements investigated here. This does not affect global properties of the galaxy such as stellar mass, star formation history, or disk size much.\n\nOne other difference is that the two galaxies have slightly different formation histories as they are two different realizations of $\\Lambda$CDM initial conditions. This mainly affects the accretion history and the final stellar mass or disk size. However, what is important for this work is that the stellar disk properties of these simulations --- such as stellar mass, size, and rotation --- agree with observations of the Milky Way and local galaxies \\citep{2020buck_NIHAO-UHD}. Furthermore, the age and $R_\\text{birth}$\\ distribution in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ abundance plane is very similar to that observed in the Milky Way \\citep[e.g.][]{yuxi2021universal, 2018Minchev_rbirth}.\n\nThe 2-dimensional abundance simulation has abundance information for \\mbox{$\\rm [Fe\/H]$}\\ and [O\/Fe]. The 15-dimensional simulation has the abundances of 15 elements from five different families --- five iron peak elements (Fe, V, Cr, Mn, Co), two light elements (C, N), two light odd-z elements (Al, P), five $\\alpha$-elements (O, Mg, S, Si, Ne), and one s-process element (Ba). Both simulations show a bimodality in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane. The high- and low-$\\alpha$ sequences in both simulations are a consequence of a gas-rich merger --- the high-$\\alpha$ sequence evolves first in the early galaxy, while the low-$\\alpha$ sequence forms after the gas-rich merger dilutes the interstellar medium's metallicity \\citep{2020_buckchemical}. \n\n\\subsection{Selection Cuts}\\label{sec:selection_cuts}\nWe focus our analysis on the present day disk. We first select stars that overlap in space with the disk by imposing limits of  $|z| \\leq 0.5$ kpc and 4 kpc $\\leq$ \\mbox{$R_{\\text{GAL}}$}\\ $\\leq$ 12 kpc, though are results are consistent for other spatial cuts. We then determine stars that are current disk members using 3-dimensional velocity space. We model a two component Gaussian mixture model in $(v_\\theta, v_r, v_z)$ --- similar to the approach taken by \\cite{2019ApJ...874...67B} and \\cite{2018MNRAS.477.4915O} to model simulations in kinematic space using GSF \\citep{2018ascl.soft06008O} --- and define disk stars to have a Mahalanobis distance less than 2 from the center of the corresponding Gaussian distribution. Figure \\ref{fig:selection_cuts} shows these selection cuts in the equivalent Toomre diagram and $x-y$ plane for both simulations. Finally, we do an additional cut of $R_\\text{birth} \\leq 15$ kpc to ensure we are not looking at infalling debris.\n\nAdditionally, since the abundances cover different ranges, we make quality cuts on our abundance data in the scaled ([Fe\/H], [X\/Fe]) space, where the transformed abundances have mean 0 and a standard deviation of 1. Since the goal of this paper is to focus on global properties between abundances, age, and $R_\\text{birth}$, we remove outliers by only selecting stars that have scaled abundances between -4 and 4. Our final sample sizes are 229,045 and 44,359 particles for the 2- and 15-dimensional simulations respectively.\n\n\\subsection{Birth Properties in the Abundance plane} \\label{sec:abundancePlane}\nFigure \\ref{fig:siml_3panel} shows the simulation data in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane after the selection cuts discussed above. Due to the formation history, both simulations have obvious trends in $R_\\text{birth}$\\ and age (middle and right columns). For a given value of \\mbox{$\\rm [\\alpha\/Fe]$}, $R_\\text{birth}$\\ increases as \\mbox{$\\rm [Fe\/H]$}\\ decreases. Similarly, for a given value of \\mbox{$\\rm [Fe\/H]$}, age increases as \\mbox{$\\rm [\\alpha\/Fe]$}\\ increases. As discussed in \\cite{2020_buckchemical}, the horizontal age gradient and the diagonal radius separation in [$\\alpha$\/Fe]--[Fe\/H] are simply a reflection of star formation in the disk happening at different radii, where metallicity decreases with increasing radii. \n\nThe left column of Figure \\ref{fig:siml_3panel} shows the density structure of the two simulations. For the 2-dimensional simulation (top left), there are density ridges which follow along different age tracks, whereas, there is no noticeable substructure in the 15-dimensional simulation (bottom left), presumably due to its lower mass resolution. The left panel of Figure \\ref{fig:siml_3panel} also shows that the footprint of the 15-dimensional simulation is different than the 2-dimensional simulation. Most noticeably, the spread in this plane primarily captures high-$\\alpha$ stars for the 15-dimensional simulation. The structural differences between the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ planes of the 2d and 15d simulations are due to slight differences in their formation history (discussed above) and the different set of chemical yields for chemical enrichment (see \\cite{2021BuckHD_chemEnrich} for discussion on the impact of yield tables and tracks in this abundance plane).\n\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=.97\\textwidth]{buck_3panel.pdf}\\\\\n     \\includegraphics[width=1\\textwidth]{buckHD_3panel.pdf}\n\\caption{The \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane of the (\\textbf{top}) 2-dimensional, and (\\textbf{bottom}) 15-dimensional simulation colored by (\\textbf{left}) density, (\\textbf{middle}) birth radius, and (\\textbf{right}) age. The two simulations have a different footprint in this abundance plane (discussed in Section \\ref{sec:data}), but both clearly have $R_\\text{birth}$\\ and age trends due to their formation history.}\n\\label{fig:siml_3panel}\n\\end{figure*}\n\n\\section{Clustering Methods} \\label{sec:methods}\n\nWe focus on two different clustering methods: agglomerative hierarchical clustering using Ward's minimum variance criterion \\citep{ward1963hierarchical} and EnLink \\citep{2009EnLink}. While both are nonparametric approaches, hierarchical clustering has the advantage of being simpler with only one tuning parameter --- the distance metric. On the other hand, EnLink needs two input parameters, but is able to fit complex structures since it has a locally adaptive distance metric. \n\nUnlike other clustering methods, hierarchical clustering and EnLink are nonparametric and thus do not force clusters to fit specific distributions. Additionally, other clustering methods, such as  K-means \\citep{hartigan1979algorithm}, require prior knowledge for how many clusters comprise the data, whereas the two methods focused on in this work do not. Particularly in the high dimensional space of the 15d simulation --- where we cannot visualize all 15 abundance dimensions at once --- choosing the wrong number of clusters could give rise to misleading results for a method requiring the number of clusters beforehand.\n\n\\subsection{Hierarchical Clustering --- tree based clustering with a fixed distance metric}\\label{sec:methods_hierarchical}\nFollowing the same methodology \\cite{2020Ratcliffe} used with observational red clump DR14 \\project{\\textsc{apogee}}\\ data, we use agglomerative hierarchical clustering using Ward's minimum variance criterion \\citep{ward1963hierarchical} as one of the ways to combine the most chemically similar stars. Specifically, we use the Ward2 algorithm described in \\cite{kaufman2009finding} and \\cite{murtagh2011ward}. We conceptually describe the algorithm here, and refer the reader to \\cite{2020Ratcliffe} for a more in depth explanation. \n\nThe algorithm begins with each star as its own cluster, and at each step we combine the pair of clusters that leads to a minimum increase in total within-cluster variance until only one large cluster containing all the stars remains. The output is a tree showing the combination of groups at each step, called a dendrogram. Thus, the user decides the number of clusters to separate the data into after seeing the linking structure of the data.\n\n\\subsection{EnLink --- density-based clustering with an adaptive metric}\\label{sec:methods_enlink}\nEnLink is a nonparametric hierarchical clustering algorithm built on a locally adaptive distance metric and hence able to identify complex structures in the data. The full data set is first divided via a binary-partitioning algorithm which uses an entropy criterion to preferentially bisect dimensions that contain  maximum information \\citep[``EnBid\"][]{2006MNRAS.373.1293S}. This approach allows a nonparametric definition of ``local\" regions in the data set from which the adaptive metric --- with flexible scales and orientations --- can then be derived (see \\cite{2009EnLink} for full details). It is this metric that defines the distance between particles subsequently.\n\nEnLink partners the adaptive distance metric machinery with IsoDen \\citep{pfitzner1997halo}, which is a density-based clustering algorithm. Conceptually, clusters can be thought of as regions around high density peaks that are separated from one another by lower density regions. Thus, as we lower the isodensity contours when examining a high density region, we stay within the cluster until we encounter a lower density region that connects to another high density region. Then, as the isodensity contour continues to lower, a new group encompassing both clusters is formed. Continuing in this fashion forms a hierarchy of density-based parent-child clusters. \n\nEnLink has two user specified parameters: the number of nearest neighbors used in calculating density ($k_\\text{den}$) and the threshold significance level when comparing the high and low density levels of parent-child clusters ($S_\\text{th}$). Since the goal of our analysis is not to find the best clustering, but rather to investigate the stability of our results, we choose to vary $k_\\text{den}$ from 30 to 1,000, and $S_\\text{th}$ is such that the expected number of groups due to Poisson noise is 0.5, 1, and 2. We did not observe major differences in our results.\n\n\\section{Results I: Abundance clusters form groups of ($R_\\text{birth}$, age)} \\label{sec:results_clustering}\n\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=1\\textwidth]{buck_contour3panel.pdf}\\\\\n     \\includegraphics[width=1\\textwidth]{buckHD_contour3panel.pdf}\\\\\n     \\includegraphics[width=1\\textwidth]{15in2d.pdf}\n\\caption{(\\textbf{Left}) The median overlap percentage for clusters in the age--$R_\\text{birth}$\\ plane as a function of the number of clusters determined by hierarchical clustering for the (\\textbf{top}) 2-dimensional, and (\\textbf{middle}) 15-dimensional simulation.  Each point is determined by calculating the median percent each cluster overlaps with the other clusters at the 50\\% contour level in the age--$R_\\text{birth}$\\ plane. The grey ribbon represents one standard deviation about the median overlap percentages. The 50\\% contour lines of clusters projected into the (\\textbf{middle}) \\mbox{$\\rm [\\alpha\/Fe]$}\\--\\mbox{$\\rm [Fe\/H]$}\\ plane, and (\\textbf{right}) age--$R_\\text{birth}$\\ plane. There are seven and eight clusters for the 2- and 15-dimensional simulations respectively. The (\\textbf{bottom}) row shows the results for clustering in only the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane of the 15d simulation (labeled ``Projected\") in comparison to clustering in the full 15-dimensional chemical space and the 2d simulation.}\n\\label{fig:contour_3panel}\n\\end{figure*}\n\nIn this section, we investigate the birth properties of clusters defined in a 2-dimensional (Section \\ref{sec:results_2d}) and 15-dimensional (Section \\ref{sec:results_tagsHD}) chemical abundance space. We examine the amount each cluster overlaps in birth time and space from 2 to 15 clusters determined using both the 2d and 15d simulations.\n\n\n\\subsection{Two Abundances Tag Distinct Ages and $R_\\text{birth}$}\\label{sec:results_2d}\n\nAs mentioned in Section \\ref{sec:methods_hierarchical}, hierarchical clustering produces a dendrogram showing how stars in abundance space combine, starting from each star being its own group to one cluster containing every star. After the linking structure is determined, the user then specifies how many clusters to separate the sample into. Walking down the tree --- and thus increasing the number of clusters --- corresponds to one group being separated to form two new clusters at each step. For a given number of $k$ clusters defined in the 2- or 15-dimensional abundance space, we determine the contour level that contains 50\\% of the stars within each abundance cluster after projecting into the age--$R_\\text{birth}$\\ plane. We then calculate the percent that each 50\\% contour level overlaps with the other $k-1$ cluster's 50\\% contour levels by laying down a fine grid and comparing the number of points in just the $i$th cluster to the number of points that fall in more than just the $i$th cluster. For the $i$th cluster, the overlap percentage is defined as the percent of area that is common between the 50\\% contour region of the $i$th cluster and the 50\\% contour regions of the other $k-1$ clusters. \n\nThe top left panel of Figure \\ref{fig:contour_3panel} shows the median of these overlap percentages and standard deviation of the $k$ overlap percentages as a function of the number of clusters found in the 2-dimensional simulation using hierarchical clustering. We see that clusters defined solely using two abundances show consistently low overlap in birth time and space for up to 10 clusters at the 50\\% contour level (and up to seven clusters at the 75\\% contour level, which is not shown). \n\nThe middle and right panels of the top row in Figure \\ref{fig:contour_3panel} show the seven clusters in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ and $R_\\text{birth}$--age planes at the 50\\% contour level. We can see that the clusters found using two abundances separate diagonally, both as a function of age and $R_\\text{birth}$. We believe that this primarily is a consequence of formation history, as the low-$\\alpha$ stars have gradients in abundances, age, and $R_\\text{birth}$.\n\n\\subsubsection{Using EnLink to Leverage Density Structure in the 2d Simulation} \\label{sec:enlink_2d}\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=.85\\textwidth]{buck2d_contourEnlinkPanel.pdf}\n\\caption{Seven clusters found using the density based nonparametric method EnLink in the 2-dimensional abundance space of g7.55e11\\ projected into the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ and age--$R_\\text{birth}$\\ planes. All stars are assigned to a cluster, and each contour captures 50\\% of the stars within the cluster. The clusters now follow the density ridges discussed in Section \\ref{sec:abundancePlane} and show more separation in the age--$R_\\text{birth}$\\ plane than those clusters found using hierarchical clustering. The median amount each cluster overlaps is 1\\%.}\n\\label{fig:enlink_clusters}\n\\end{figure*}\n\n\nIn the 2-dimensional abundance space of g7.55e11, we can see streaks of higher density regions along the different age bins (see top left of Figure \\ref{fig:siml_3panel}). Hierarchical clustering does not leverage the density of the simulation in abundance space and thus is unable to capture the streak formations (see top middle of Figure \\ref{fig:contour_3panel}). Therefore, to include this structure as information in assignment of cluster groups, we employ a density based clustering method with an adaptive distance metric to use the ridge-like structure in association of groups.\n\nAs discussed in Section \\ref{sec:methods_enlink}, EnLink has the number of nearest neighbors used to determine the density at a point and the maximum number of spurious clusters created by noise as input parameters. We find that the cluster separation in the age--$R_\\text{birth}$\\ plane is fairly stable when we focus on allowing either 0.5 or 1 spurious clusters and 30 to 1,000 nearest neighbors, with the majority of EnLink clusters having a median overlap percent of below 25\\% at the 75\\% contour level, and near 0\\% at the 50\\% contour level.\n\nFigure \\ref{fig:enlink_clusters} shows the 50\\% contours in the abundance and age--$R_\\text{birth}$\\ planes for seven clusters and parameter settings 260 nearest neighbors and a maximum of one spurious cluster. We can clearly see that EnLink captures the streaks of overdensity in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane better than hierarchical clustering, and in doing so we see better separation in the age--$R_\\text{birth}$\\ plane, with a median overlap percentage of only 1\\%. Since EnLink traces the higher density ridges, and the ridges trace different age bins, the cluster separation in the age--$R_\\text{birth}$\\ plane no longer follows the diagonal trends given by hierarchical clustering. Each group primarily lives in a unique birth time and place, though there is some overlap with the middle aged clusters, possibly due to not fine tuning the algorithm. Overall we conclude that for the 2-dimensional high resolution simulation, using a density based method with an adaptive metric is desirable for the best results.\n \n\n\\subsection{Additional nucleosynthetic families and abundances provide more information about birth properties}\\label{sec:results_tagsHD}\n\nSo far we have demonstrated that just two abundances (\\mbox{$\\rm [\\alpha\/Fe]$}\\ and \\mbox{$\\rm [Fe\/H]$}) can trace separate ages and birth radii. We now investigate how additional abundances, including additional nucleosynthetic families, strengthens this result. The list of abundances and their families is given in Section \\ref{sec:data}. Due to the difficult problem of estimating density in a high dimensional space, in addition to the issue of tuning the algorithm, we do not use EnLink to cluster in 15 dimensions, and instead focus on hierarchical clustering.\n\nAs shown in the middle left panel of Figure \\ref{fig:contour_3panel}, clusters defined in the chemical space of 15 abundances show more separation in the age--$R_\\text{birth}$\\ plane than the clusters defined in the abundance space of the 2-dimensional simulation. These exhibit separation for 13 clusters at the 50\\% contour level, and eight clusters at the 75\\% contour level (not shown). As shown in the middle and right columns of the middle row of Figure \\ref{fig:contour_3panel}, the clusters comprised of older stars (which trace the high-$\\alpha$ stars) primarily show separation as a function of age, whereas the younger low-$\\alpha$ stars show separation in both $R_\\text{birth}$\\ and age. This shows that high-$\\alpha$ stars were all born near the Galactic center, whereas the low-$\\alpha$ stars were born at different radii and times throughout the galaxy.\n\nComparing these results to the 2-dimensional simulation (top left of Figure \\ref{fig:contour_3panel}), we see that clusters defined in the 15-dimensional abundance space using hierarchical clustering overlap less in age and $R_\\text{birth}$. In particular, for up to nine clusters, the 15-dimensional clusters are predominantly distinct in birth time and space at the 50\\% contour level, whereas in 2-dimensions the clusters have some overlap even for as few as four clusters. \n\n\\subsection{Comparing groups in 2d and 15d}\n\nIn the previous section (Section \\ref{sec:results_tagsHD}) we showed that clusters defined in the 15-dimensional abundance space of g8.26e11\\ showed more separation in age and $R_\\text{birth}$\\ than clusters defined in the 2-dimensional abundance space of g7.55e11. Here we show the results of clustering in just the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane of the 15-dimensional simulation are consistent to those of the 2-dimensional simulation. \n\nThe bottom left of Figure \\ref{fig:contour_3panel} shows that the amount abundance clusters overlap in the age--$R_\\text{birth}$\\ plane is similar between the 2-dimensional simulation (red) and the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane of the 15-dimensional simulation (black; labeled ``projected\"). As the simulations are split into more clusters, both consistently show less distinction in (age, $R_\\text{birth}$). On the other hand, the clusters defined in the full 15-dimensional simulation retain separate ages and birth radii for up to nine clusters. This shows that more separate birth information is retained in abundance clusters when more abundances are included, and therefore we claim abundance clusters being more separate in age and $R_\\text{birth}$\\ is due to additional abundance information, and not an artifact of different simulation history or resolution.\n\nFigure \\ref{fig:15in2d_heatmap} compares eight clusters defined in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane of the 15-dimensional simulation to eight clusters defined in the full 15-dimensional abundance space. The clusters are arranged in order of age, with cluster 1 being the oldest and cluster 8 being the youngest. The oldest clusters share the most stars between the two simulations, whereas the middle aged and youngest clusters are more muddled. \n\n\n\\subsection{A grid in \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ separates birth properties less effectively}\n\\label{sec:results_whyCluster}\n\nSo far we focused on how chemically similar stars differ in birth time and space using clustering methods. Now we motivate why using a clustering method is needed for grouping stars.\n\nFigure \\ref{fig:clusterVgrid} shows the median and standard deviation of the percent cluster overlap for both the 2-dimensional and 15-dimensional simulations when separating the stars using different grouping methods. We compare hierarchical clustering with laying down a Cartesian grid in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane. The number of \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ bins are chosen to produce four, seven\/eight (for 2\/15d simulations respectively), and twelve clusters. We also show the results of EnLink for the 2-dimensional simulation. The left panel of Figure \\ref{fig:clusterVgrid} shows that when only two dimensions of abundance information are known, we do not gain any more knowledge of birth properties from using a simple clustering method than if we were to create bins by laying down a Cartesian grid across the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane. The clusters retain more separate birth properties when leveraging density with an adaptive distance metric, however the errors are higher than that of binning and hierarchical clustering. \n\n\\begin{figure}\n     \\includegraphics[width=0.45\\textwidth]{15in2d_heatmap.pdf}\n\\caption{Comparison of the number of stars shared between eight clusters defined in all 15 abundances versus just (\\mbox{$\\rm [\\alpha\/Fe]$}, \\mbox{$\\rm [Fe\/H]$}) of the 15-dimensional simulation. The clusters are arranged in order of age, with cluster 1 being the oldest and cluster 8 being the youngest. The percent of stars shared between clusters is determined by counting the number of stars found in the projected group that are in the 15-dimensional group, and then dividing by the number of stars in the projected group.}\n\\label{fig:15in2d_heatmap}\n\\end{figure}\n\nThe right panel of Figure \\ref{fig:clusterVgrid} reveals that when higher dimensional abundance information is available, there is a noticeable difference between only looking at stars separated using a grid in \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ versus using a clustering method in the full abundance space. Not only does clustering in 15 dimensions produce less overlap in the age--$R_\\text{birth}$\\ plane, but based on the smaller standard deviation, groups defined using hierarchical clustering produce consistently small overlap between clusters whereas groups defined by binning in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane produce a large range of amount clusters overlap in birth time and place.\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=0.47\\textwidth]{buck_clusterVgrid.pdf}\n     \\includegraphics[width=0.47\\textwidth]{buckHD_clusterVgrid.pdf}\n\\caption{Each point and error bar represents the median and standard deviation of the amount clusters overlap with one another in the age--$R_\\text{birth}$\\ plane. Comparing three different ways of combining stars in chemical space (a grid laid out in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane, hierarchical clustering, and EnLink) shows that if we only have 2 abundances available (\\textbf{left}), then groups of chemically similar stars determined via hierarchical clustering and gridding on average show similar separation in the age--$R_\\text{birth}$\\ plane. Leveraging the density in the abundance plane allows for even better separation in birth time and space. When we include more abundances and nucleosynthetic channels (\\textbf{right}), we find that hierarchical clustering done in 15 dimensions yields more distinct groups in age--$R_\\text{birth}$\\ than gridding in the visual two dimensions. Note that EnLink was inconclusive in 15 dimensions due to the curse of dimensionality and also only reported seven clusters for the 2d simulation, and therefore no EnLink result is shown for the 15-dimensional simulation or for four and twelve clusters for the 2d simulation.}\n\\label{fig:clusterVgrid}\n\\end{figure*}\n\nFigure \\ref{fig:meanRbirthVage_feh} compares the mean and standard deviation of (age, $R_\\text{birth}$) of each cluster determined using two different methods: hierarchical clustering (left) and binning in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane (right) to create a cartesian grid. This figure demonstrates that clusters defined using hierarchical clustering preserve physical interpretation and agree with expected trends, namely we see a clear metallicity gradient as a function of age for a given $R_\\text{birth}$\\ when stars are separated using hierarchical clustering. The trend is not as obvious to see when stars are separated in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane with a grid. Additionally, we see that clusters defined using a clustering method tend to have less overlap, and the overlap they do have is consistent among nearly all the clusters. However for the groups defined via a grid, the overlap between clusters is irregular, with some groups being mainly separate and others completely overlapping multiple groups.\n\nAdditionally, particularly for the 15-dimensional simulation, the age dispersion for each cluster when defined using hierarchical clustering is much smaller than when clusters are separated using a grid. This again shows that the groups found using hierarchical clustering represent different physical groups in time.\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=.95\\textwidth]{buck_meanRbirthVAge_feh.pdf}\\\\\n     \\includegraphics[width=.95\\textwidth]{buckHD_meanRbirthVAge_feh.pdf}\n    \\caption{Seven and eight clusters separated using (\\textbf{left}) hierarchical clustering (\\textbf{right}) and gridding in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane for the (\\textbf{top}) 2-dimensional and (\\textbf{bottom}) 15-dimensional simulation respectively projected into the $R_\\text{birth}$--age plane. Each point represents the mean (age, $R_\\text{birth}$) for each cluster, colored by the mean metallicity. Error bars shown are 1-$\\sigma$ standard deviations. Groups defined using hierarchical clustering show a metalicity gradient for a given $R_\\text{birth}$, suggesting that the clusters are physically meaningful. Groups defined in mono-\\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ bins do not show a metalicity gradient, and have larger dispersions in age.}\n\\label{fig:meanRbirthVage_feh}\n\\end{figure*}\n\n\\section{Results II: Clustering in Observational Data} \\label{sec:results_errors}\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=.88\\textwidth]{buck_err.pdf}\\\\\n     \\includegraphics[width=.86\\textwidth]{buckHD_err.pdf}\n\\caption{The black points and line correspond to the median percent that clusters defined in an error-convolved (\\textbf{top}) 2-dimensional and (\\textbf{bottom}) 15-dimensional abundance space overlap in the age--$R_\\text{birth}$\\ plane. For each star, new abundance measurements are drawn from a normal distribution with the true abundance value as the mean and a standard deviation of (\\textbf{left}) 0.02 dex and (\\textbf{right}) 0.05 dex. The grey ribbon captures one standard deviation about the median percent that clusters overlap in the age--$R_\\text{birth}$\\ plane. When simulating errors of 0.02 dex, clusters still stay separated in the age--$R_\\text{birth}$\\ plane and the separation is comparable to that given by clusters found with no abundance error (grey points and line). Adding an error of 0.05 dex in each dimension affects our ability of finding separate birth information slightly more in the 2-dimensional simulation than the 15-dimensional simulation.}\n\\label{fig:error}\n\\end{figure*}\n\n\nSection \\ref{sec:results_clustering} showed that under certain formation conditions and no observational limitations, that abundances trace stellar birth information $R_\\text{birth}$\\ and age. In this section we examine some of the consequences of observational limitations. \n\n\\subsection{Incorporating Measurement Uncertainty}\n\nCurrent day element abundance measurements are reported with uncertainties of $\\approx$ 0.02-0.05 dex \\citep{apogeedr16,2020AJ....160..120J}. Consequently, we examine how the clustering changes once we incorporate errors in the chemical abundances and how this impacts our ability to trace birth properties with observational data.\n\nFor each star in both the 2d and 15d simulations, we redraw a new set of element abundances, each from a Gaussian distribution where the standard deviation is representative of the measurement uncertainty. We test two precision regimes: $\\sigma_{\\mbox{err}}$ = 0.02 and 0.05 dex. The left column of Figure \\ref{fig:error} shows the overlap in the age--$R_\\text{birth}$\\ plane of clusters defined in the 2-dimensional (top) and 15-dimensional (bottom) abundance simulations when the abundances are modified with an equivalent of 0.02 dex error in each abundance direction (black points and line). With the current best observational error of $\\sigma_{\\mbox{err}}$ = 0.02 dex, the clusters defined in both the 2-dimensional and 15-dimensional abundance space retain separate birth properties, similar to the overlap found when the simulations have no error added (grey points and line). When abundances are redrawn with  observational errors of $\\sigma_{\\mbox{err}}$ = 0.05 dex for each data point (right column), we find that the majority of clusters from the higher dimensional simulation retain more separate birth information compared to those found in the 2-dimensional simulation.\n\n\n\\subsection{Modifying the sample size} \\label{sec:results_suberrors}\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=1\\textwidth]{subErr_bootstrap.pdf}\n\\caption{The mean percent of 50 subsampling replications that clusters defined in a 30,000 stellar sample of an error-convolved 2-dimensional (red) and 15-dimensional (blue) abundance space overlap in the age--$R_\\text{birth}$\\ plane. The errors added are equivalent to the observational best case scenario (\\textbf{middle}, 0.02 dex) and average observational error (\\textbf{right}, 0.05 dex) in each dimension. \\textbf{Left} has no error added. The ribbon shows one standard deviation in percent overlap for the 50 monte carlo simulations.}\n\\label{fig:subError}\n\\end{figure*}\n\nWhile current large surveys have captured many millions of stars, we have so far examined only about 30,000 stars with precise abundance measurements, within a narrow evolutionary state \\citep[e.g. \\project{\\textsc{apogee}}\\ DR14 RC catalog][]{bovy2014apogee}. To test more generally how useful chemical abundances are for linking to birth properties, we need to examine the impact of sample size.\n\nSo far in this work, we have been working with $\\sim$229,000 and $\\sim$44,000 star particles for the 2d and 15d simulations respectively. Now we examine how the clusters defined in abundance space --- both with and without the addition of errors --- change in the age--$R_\\text{birth}$\\ plane for a random sub-sample of 30,000 stars throughout the whole disk. Figure \\ref{fig:subError} shows the percent overlap for both the 2-dimensional (red) and 15-dimensional (blue) subsampled simulations with no error (left), the equivalent of 0.02 dex error (middle) and 0.05 dex error (right) in each dimension. In order to test the consistency of these results, we subsample with 50 replications. The mean and standard deviation of the median percent overlap are shown as a point and ribbon.\n\nWe can see from Figure \\ref{fig:subError} that as error increases, the amount the 2-dimensional clusters overlap in the age--$R_\\text{birth}$\\ plane also increases. This indicates that for the sample size and error used in paper I of this series \\citep{2020Ratcliffe}, only two abundance dimensions are not enough to recover separate birth time and place groups observationally for more than $\\approx$ 6 clusters. \n\nOn the other hand, the clusters in the 15-dimensional subsample are less affected by error than the 2-dimensional simulation. We can see that as error increases, the amount each cluster overlaps with other clusters in the age--$R_\\text{birth}$\\ plane stays more consistent than the clusters in the 2-dimensional subsampled simulation. While the clusters from both simulations trace less birth information in the presence of subsampling, we see that the recovery of separate birth place and time clusters is still possible with the inclusion of more abundances and nucleosynthetic families, especially for a smaller number ($\\leq\\,\\approx$10) of clusters.\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=1\\textwidth]{buck_RbirthXfe.pdf}\n\\caption{(\\textbf{Left}) The \\mbox{$\\rm [Fe\/H]$}--$R_\\text{birth}$\\ plane colored by age for the 2-dimensional simulation. The black lines and grey area mark off the solar metallicity stars, which we consider to be $\\pm$0.05 dex in \\mbox{$\\rm [Fe\/H]$}. (\\textbf{Right}) the running mean of [O\/Fe] of the solar metallicity stars across $R_\\text{birth}$\\ colored by age selected from within the horizontal lines at left. We see that for a given bin of metallicity, stars of different ages separate out and form either approximately quadratic or linear relations.}\n\\label{fig:Rbirthxfe_2d}\n\\end{figure*}\n\n\\section{Results III: Modeling how observable stellar properties relate to birth properties} \\label{sec:results_regression}\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=0.92\\textwidth]{buckHD_RbirthXfe.pdf}\n\\caption{(\\textbf{Top left})  The \\mbox{$\\rm [Fe\/H]$}--$R_\\text{birth}$\\ plane colored by age for the 15-dimensional simulation. The black lines and grey area mark off the solar metallicity stars, which we consider to be $\\pm$0.05 dex in \\mbox{$\\rm [Fe\/H]$}. All other plots show the running mean of \\mbox{$\\rm [X\/Fe]$}\\ of the solar metallicity stars accross $R_\\text{birth}$\\ colored by age. Similar to the 2-dimensional simulation shown in Figure \\ref{fig:Rbirthxfe_2d}, solar metallicity stars of different ages separate into approximately quadratic or linear curves.}\n\\label{fig:Rbirthxfe_hd}\n\\end{figure*}\n\nIn the previous sections, we showed that clusters in abundance space correspond to discrete groups in birth time and space. Now we quantify how chemical abundances relate to age and $R_\\text{birth}$.\n\nThe left panel of Figure \\ref{fig:Rbirthxfe_2d} shows the 2-dimensional simulation in the \\mbox{$\\rm [Fe\/H]$}--$R_\\text{birth}$\\ plane, with each point colored by the star's age. In order to visually examine if an age--abundance--$R_\\text{birth}$\\ relationship exists, we examine running \\mbox{$\\rm [X\/Fe]$}\\ means of solar metallicity stars (which are taken to be stars within the grey band) as a function of $R_\\text{birth}$, divided into age bins. The right panel of Figure \\ref{fig:Rbirthxfe_2d} shows that for the 2-dimensional simulation, there is a strong age--\\mbox{$\\rm [\\alpha\/Fe]$}\\ relation in solar metallicity stars that is approximately quadratic for older stars and linear for younger stars. Thus, given a fixed \\mbox{$\\rm [Fe\/H]$}, we anticipate that ages can be determined from abundances. Similarly for the 15-dimensional simulation shown in Figure \\ref{fig:Rbirthxfe_hd}, each age group has its own unique polynomial trend in [X\/Fe]--$R_\\text{birth}$.\n\nThis visual analysis done in Figures \\ref{fig:Rbirthxfe_2d} and \\ref{fig:Rbirthxfe_hd} leads to the conclusion that ages can be determined from abundances alone. To quantify this relationship, we use a simple second order polynomial to estimate age from ([X\/Fe], [Fe\/H]). The model for the 2-dimensional simulation is\n\\begin{align*}\n    age = & a_1 \\mbox{$\\rm [Fe\/H]$}^2 + a_2 \\mbox{$\\rm [\\alpha\/Fe]$}^2 + \\\\\n          & a_3\\mbox{$\\rm [Fe\/H]$}\\times\\mbox{$\\rm [\\alpha\/Fe]$}\\ + a_4 \\mbox{$\\rm [Fe\/H]$} +\\\\\n          & a_5 \\mbox{$\\rm [\\alpha\/Fe]$} + a_0,\n\\end{align*}\n\nwhere the $a_i$s are the coefficients. The model for the 15-dimensional simulation is similar, however with the inclusion of more abundances. The left column of Figure \\ref{fig:regression} shows the inferred age from the polynomial regression versus the true age of stars in the simulation. Even with just two abundances (top row), we are able to estimate age within $\\pm$0.52 Gyr. With the addition of more abundance information (bottom row), we find that we are able to accurately estimate age from 15 abundances to within $\\pm$0.06 Gyr. \n\nWe also wish to test how well we can quantify the relationship between age, $R_\\text{birth}$, and abundances. Given the low $R_\\text{birth}$\\ dispersion in the \\mbox{$\\rm [Fe\/H]$}--age plane shown in Figure \\ref{fig:RbirthDisps}, we use a second order polynomial model to estimate $R_\\text{birth}$\\ from (\\mbox{$\\rm [Fe\/H]$}, age). The model for both simulations is\n\\begin{align*}\n    r_\\text{birth} = & a_1 \\mbox{$\\rm [Fe\/H]$}^2 + a_2 age^2 + a_3 \\mbox{$\\rm [Fe\/H]$}\\times age +\\\\\n          & a_4 age + a_5 \\mbox{$\\rm [Fe\/H]$} + a_0,\n\\end{align*}\nwhere the $a_i$s are the coefficients.\nThe right panels of Figure \\ref{fig:regression} reveals that we can predict $R_\\text{birth}$\\ to within $\\pm$1.24 kpc for the 2-dimensional simulation (top) and within $\\pm$1.17 kpc for the 15-dimensional simulation (bottom). The inclusion of the additional abundances increases the accuracy by 0.06 kpc for the 15-dimensional simulation and only 0.01 kpc for the 2-dimensional simulation. We again see that additional abundance information helps inform more about stellar birth properties, however the difference is not as drastic as it was in estimating age.\n\nWhile we do not fit for the best model, we believe that this simple second order polynomial relationship between age, abundances, and $R_\\text{birth}$\\ cannot be drastically improved upon. For a given value of \\mbox{$\\rm [Fe\/H]$}, \\mbox{$\\rm [X\/Fe]$}, and age, we find that the intrinsic dispersion in $R_\\text{birth}$\\ is $\\approx$ 1.1 kpc for the 15d simulation and $\\approx$ 1.2 kpc for the 2d simulation. Thus, ages and abundances alone will not be able to estimate $R_\\text{birth}$\\ more accurately. This could be due to asymmetries causing abundance distributions to not lie in perfect annuli about the galactic center, reducing the tightness of the relationship between $R_\\text{birth}$\\ and abundances.\n\n\n\n\nWith the inclusion of 0.05 dex abundance error, we find that our age estimates decrease in accuracy to about $\\pm 0.76$ Gyr for the 15d simulation. With the addition of 0.05 dex abundance error and age error of 30\\%, the $R_\\text{birth}$\\ accuracy of the 15d simulation decreases to $\\pm 1.31$ kpc. This shows that according to our model, estimating $R_\\text{birth}$\\ from abundances and age is less sensitive to noise than estimating age from abundances.\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=.9\\textwidth]{buck_regression.pdf}\\\\\n     \\includegraphics[width=.9\\textwidth]{buckHD_regression_poly.pdf}\n\\caption{(\\textbf{Left}) The inferred age of the (\\textbf{top}) 2-dimensional and (\\textbf{bottom}) 15-dimensional simulation using a second order polynomial in (\\mbox{$\\rm [Fe\/H]$}, \\mbox{$\\rm [X\/Fe]$}) plotted against the true age of the star. With the additional abundance information provided in the 15d simulation, we are able to accurately and precisely estimate age, showing that abundances are chemical clocks. (\\textbf{Right}) Inferred $R_\\text{birth}$\\ of the (\\textbf{top}) 2-dimensional and (\\textbf{bottom}) 15-dimensional simulation using a second order polynomial in (\\mbox{$\\rm [Fe\/H]$}, age) plotted against the true $R_\\text{birth}$\\ of the stars. With just \\mbox{$\\rm [Fe\/H]$}\\ and age, we can infer a star's $R_\\text{birth}$\\ to within just over 1 kpc.}\n\\label{fig:regression}\n\\end{figure*}\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=0.98\\textwidth]{buck2d_RbDisp2.pdf}\\\\\n     \\includegraphics[width=0.98\\textwidth]{buckHD_RbDisp2.pdf}\\\\\n\\caption{The \\mbox{$\\rm [Fe\/H]$}--age plane colored by (\\textbf{left}) $R_\\text{birth}$\\ and (\\textbf{right}) $R_\\text{birth}$\\ dispersion for the (\\textbf{top}) 2- and (\\textbf{bottom}) 15-dimensional simulations. The low dispersion in this plane indicates that \\mbox{$\\rm [Fe\/H]$}\\ and age alone can determine $R_\\text{birth}$\\ accurately.}\n\\label{fig:RbirthDisps}\n\\end{figure*}\n\n\n\\section{Discussion --- Implications for future applications to the Milky Way}\\label{sec:discussion}\n\nPaper I of this series \\citep{2020Ratcliffe} used hierarchical clustering in the 19-dimensional abundance space of 30,000 red clump stars in the Milky Way catalogued by \\project{\\textsc{apogee}}\\ DR14. In that work, we found that up to six clusters have statistically significant different mean ages and distinct spatial distributions. The goal of this work is aimed to interpret those results and determine if clusters observed in chemical space correspond to physically meaningful groups. With the use of simulations, we are able to test the potential and current ability of linking current stellar properties (\\mbox{$\\rm [Fe\/H]$}, \\mbox{$\\rm [X\/Fe]$}) to their birth properties ($R_\\text{birth}$, age). \n\n\\subsection{Empirical Context}\n\nThe simulations used in this work (2-dimensional g7.55e11\\ and 15-dimensional g8.26e11) are Milky Way analogs from the NIHAO-UHD suite. Both simulations were bulge-dominated systems up to redshift $z\\geq 1$ with prominent stellar disks forming 7-8 Gyr ago. The formation of the $\\alpha-$sequences was due to a gas-rich merger, with the high-$\\alpha$ sequence forming during the early galaxy and the low-$\\alpha$ sequence forming after the merger. The main differences between these simulations are a slightly different formation history (sampling valid formation histories of Milky Way like galaxies) as well as an updated chemical enrichment prescription for the 15d model galaxy. The modification made to chemical enrichment prescriptions are described in \\citet{2021BuckHD_chemEnrich} and enabled us to follow 15 different elements while at the same time leaving global galaxy properties such as star formation history, stellar mass, and disk size unaffected. We believe that these simulations are representative of the Milky Way due to their formation history and age gradient in the abundance plane.\n\nEven though simulations provide us with particles and not individual stars, they allow us to examine the relationship between observable chemical properties, age, and birth location. Thus we focus on disk particles in our work.\n\n\\subsection{Clustering Approaches}\\label{sec:discussion_clustering}\n\nIn this work, we focused on three ways of grouping stars --- hierarchical clustering, EnLink, and binning in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane. Section \\ref{sec:results_whyCluster} shows that binning in just (\\mbox{$\\rm [Fe\/H]$}, \\mbox{$\\rm [\\alpha\/Fe]$}) does not effectively link abundance information to birth properties, especially when there is higher dimensional abundance data available. \n\nOf the clustering methods we explore, hierarchical clustering is advantageous for observational work. Section \\ref{sec:enlink_2d} shows that leveraging density with an adaptive distance metric in the 2-dimensional simulation is the best way for chemical clusters to correspond to distinct groups in the age--$R_\\text{birth}$\\ plane. However, due to the curse of dimensionality, leveraging density in a 15-dimensional space is difficult and unrealistic. We attempted to run EnLink in the 15-dimensional chemical abundance space, however clustering results were inconclusive and did not define many stars to a cluster. Additionally, for EnLink (or any other density based clustering method) to be used correctly on Milky Way catalogs, the survey selection function would need to be accounted for, as the selection function would possibly alter the distribution of stars in abundance space. Furthermore, we found that EnLink performed poorly when the density structure in the 2-dimensional abundance plane vanished after the addition of observational uncertainty. \n\n\\subsection{Likelihood of success --- Comparison to other simulations}\\label{sec:victor}\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=\\textwidth]{victor_3panel.pdf}\\\\\n\\caption{The \\mbox{$\\rm [\\alpha\/Fe]$}\\--\\mbox{$\\rm [Fe\/H]$}\\ plane colored by (\\textbf{left}) density, (\\textbf{middle}) $R_\\text{birth}$, (\\textbf{right}) age for the \\cite{2021Silva_simulation} simulation using clumpy star formation. The formation history produces quadratic age and $R_\\text{birth}$\\ distributions in the abundance plane, and causes the simple relationship between age, $R_\\text{birth}$, and clustered abundances to disappear.}\n\\label{fig:victor}\n\\end{figure*}\n\n\nIn this paper, we have focused on the relationship between abundances and birth properties of stars when the chemical bimodality is caused by a merger and successive dilution of the interstellar medium. We also consider the relationship when a galaxy is formed by clumpy star formation\\footnote{Note, the galaxies simulated within the NIHAO project also go through a clumpy phase \\citep{Buck2017} in agreement with observed clumpy galaxies at high redshift. However, for the NIHAO feedback scheme those clumps are agglomerations of young stars and only appear in stellar light not in stellar mass.}. We examine the $N$-body+Smooth Particle Hydrodynamics simulation of the formation of an isolated galaxy outlined in \\cite{2021Silva_simulation}. Star-forming clumps at high redshift start forming low-$\\alpha$ stars, then quickly self-enrich in $\\alpha$-elements due to their high star formation rate density and produce the high-$\\alpha$ sequence while the low-$\\alpha$ sequence is produced by radially distributed star formation. After about 4 Gyr, the clumps become less efficient, and the high-$\\alpha$ sequence stops growing \\citep{Clarke2019}. For more detailed information of the simulation, see \\cite{2021Silva_simulation} and \\cite{2021MNRAS.503.1418F}.\n\nFigure \\ref{fig:victor} shows the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane for a 230,000 particle subsample of simulation M2\\_c\\_nb, which undergoes clumpy star formation. Similar to the 2- and 15-dimensional simulations, there is a linear trend between the abundances and $R_\\text{birth}$, where $R_\\text{birth}$\\ decreases as \\mbox{$\\rm [Fe\/H]$}\\ increases. Age, however, does not appear to have a simple relationship between the two abundances. For instance, age decreases as \\mbox{$\\rm [\\alpha\/Fe]$}\\ decreases for solar metallicity stars at higher values of \\mbox{$\\rm [\\alpha\/Fe]$}, but the relationship is reversed for lower \\mbox{$\\rm [\\alpha\/Fe]$}.\n\nWe find that in this simulation, age and \\mbox{$\\rm [Fe\/H]$}\\ are able to predict $R_\\text{birth}$\\ within $\\pm0.72$ kpc --- about 40\\% better than the precision for the 2- and 15-dimensional simulations focused on in this work. Again, we also see that the addition of other abundances does not notably change our ability to estimate $R_\\text{birth}$, where the accuracy only increases by 0.01 kpc when \\mbox{$\\rm [\\alpha\/Fe]$}\\ is included in the regression. This shows that the formation history in all three simulations sets an underlying relationship with age, \\mbox{$\\rm [Fe\/H]$}, and $R_\\text{birth}$, where if we know the metallicity and age of a star, we can determine where it was born. \n\nHowever, while [Fe\/H] and age are a link to $R_\\text{birth}$, in this particular simulation the star formation history gives rise to a more complex relationship between the abundances ([Fe\/H], \\mbox{$\\rm [\\alpha\/Fe]$}) and age (Figure \\ref{fig:victor}). Therefore chemically similar groups of stars identified using hierarchical clustering no longer correspond to separate groups in the age--$R_\\text{birth}$\\ plane in this scenario.\n\nIn order to determine the ability to extend our conclusions to the Milky Way, we compare the Milky Way's age and age dispersion in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane to the three simulations with simulated ``observational\" ages by redrawing from a normal distribution with their true age as the mean and a standard deviation of $\\approx 2.6$ Gyr --- the median uncertainty of low-$\\alpha$ stars from the \\cite{yuxi2021universal} catalog. When simulating observational ages for the 2- and 15-dimensional simulations, the dispersion in age across \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ is uniformly low (see middle rows of Figure \\ref{fig:ageDisp}), while M2\\_c\\_nb has an increase in age dispersion as \\mbox{$\\rm [\\alpha\/Fe]$}\\ decreases (see bottom row of Figure \\ref{fig:ageDisp}). The Milky Way (shown in the top row of the same figure using ages and abundances from \\cite{yuxi2021universal}) has a consistently small dispersion in age of about 2-3 Gyr, with the dispersion being slightly smaller for low (\\mbox{$\\rm [Fe\/H]$}, \\mbox{$\\rm [\\alpha\/Fe]$}) --- the reverse of M2\\_c\\_nb's dispersion trends. On the other hand, similar to the 2d and 15d simulations focused on in this paper, the age of the stars in the Milky Way increases as \\mbox{$\\rm [\\alpha\/Fe]$}\\ increases for a given value of \\mbox{$\\rm [Fe\/H]$}.\n\nThe question of which simulation most closely matches the Milky Way's star formation history still requires further investigation. The selection cuts described in Section \\ref{sec:selection_cuts} produce different density trends in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane for the three simulations and observational data, where some samples have both high- and low-$\\alpha$ stars (e.g. the 15-dimensional simulation), while others primarily consist of stars with lower values of \\mbox{$\\rm [\\alpha\/Fe]$}\\ (e.g. M2\\_c\\_nb). There is room for exploration into how the Milky Way compares to the different \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ trends each simulation produces with different selection cuts, however, we find that our results are consistent under different cuts to capture disk stars.\n\nThis exploration shows that resolving distinct birth properties of chemically similar stars requires a small dispersion in age and $R_\\text{birth}$\\ trends in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane. Since the Milky Way has been shown to have age trends in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ abundance plane with small dispersion, we believe the conclusions we have drawn in this paper are relevant to the Milky Way. We conclude that the six clusters found in our previous work \\citep{2020Ratcliffe} using hierarchical clustering in the 19-dimensional \\project{\\textsc{apogee}}\\ red clump sample form discrete groups in birth time and place.\n\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=.7\\textwidth]{ageDisp_LowAlpherr.pdf}\n\\caption{(\\textbf{Top}) The Milky Way in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane using \\cite{yuxi2021universal} ages and abundances. The right panel shows the standard deviation of ages within each bin. The ages for the (\\textbf{second from top}) 2d simulation,  (\\textbf{third from top}) 15d simulation and (\\textbf{bottom}) M2\\_c\\_nb are redrawn from a normal distribution with their true age as the mean and a standard deviation equivalent to the median uncertainty of low-$\\alpha$ stars from the \\cite{yuxi2021universal} catalog. Only bins containing at least ten stars are shown in each plot above.}\n\\label{fig:ageDisp}\n\\end{figure*}\n\n\\subsection{Limitations and future work}\n\nThere are some limitations to our approach. In Section \\ref{sec:results_suberrors} we discuss the effect of subsampling data with observational errors. However, we do not take into account the complexity of survey selection functions. Additionally, in Section \\ref{sec:results_errors} we explore how errors affect our clustering results by adding 0.02 dex or 0.05 dex error to every abundance. Realistically though, some abundances are measured more accurately than others. \n\nSection \\ref{sec:discussion_clustering} discussed how density based clustering failed when structure vanished due to measurement error or in the high dimensional abundance space. For future work, combining hierarchical clustering with an adaptive distance metric would be interesting to explore. Partnering an adaptive distance metric with hierarchical clustering would avoid the problems of estimating density and determining the best distance metric in a high dimensional abundance space, and could potentially provide even more striking results. \n\nAs simulation resolution continues to increase, in the future it would also be useful to explore if satellite debris could be picked up by abundance clustering and complement clustering analysis done in action space \\citep[such as in ][]{2021arXiv210408185W}. In the simulations we use in this study, only $\\approx$ 20 stellar particles have $R_\\text{birth}$ $\\geq$ 20 kpc. With future datasets and simulations in mind, testing to see if accreted material differ in abundance space could be useful to determine accreted debris in the Milky Way. \n\n\\section{Summary and Conclusions}\\label{sec:conclusion}\nOur main results are summarized below: \n\n\\begin{itemize}\n    \\item We find with just \\mbox{$\\rm [Fe\/H]$}\\ and \\mbox{$\\rm [\\alpha\/Fe]$}\\ alone we can trace separate $R_\\text{birth}$--age clusters, with the separation being more distinct when we include more abundances, as demonstrated by our 15 element simulation g8.26e11\\ where we find nearly completely separate groups for up to $\\approx$ 10 clusters (Figure \\ref{fig:contour_3panel}). Considering current day observational uncertainty and sampling constraints, higher dimensional abundance data is necessary to trace birth properties from chemical abundance data. Clusters from the subsampled 2-dimensional abundance simulation with 0.05 dex error had substantial overlap with other clusters in the age--$R_\\text{birth}$\\ plane. On the other hand, clusters found in the subsampled 15d simulation with 0.05 dex error had almost no overlap in age and $R_\\text{birth}$\\ when finding six or fewer clusters (Section \\ref{sec:results_errors}; Figure \\ref{fig:subError}). \n    \n    \\item The clusters found in this paper presumably trace not only separate areas in the age--$R_\\text{birth}$\\ plane, but also link to different underlying physical properties. Stars separated by hierarchical clustering preserved a clear metallicity gradient as a function of age for a given $R_\\text{birth}$, whereas groups defined by binning in the \\mbox{$\\rm [\\alpha\/Fe]$}--\\mbox{$\\rm [Fe\/H]$}\\ plane lost the \\mbox{$\\rm [Fe\/H]$}\\ gradient and increased their age dispersion (Figure \\ref{fig:meanRbirthVage_feh}).\n    \n    \\item Chemical clusters of high- and low-$\\alpha$ stars separate differently in the age--$R_\\text{birth}$\\ plane. Clusters defined with low-$\\alpha$ stars separate both as a function of age and $R_\\text{birth}$, showing low-$\\alpha$ stars are born throughout the galaxy at different radii. High-$\\alpha$ stars are older ($> 7$ Gyr) and are born near the galactic center, but separate as a function of age (see Figures \\ref{fig:contour_3panel} and \\ref{fig:enlink_clusters}). \n    \n    \\item Using a simple second order polynomial regression, we quantify the relationship between observable abundance labels and birth property outputs (Section \\ref{sec:results_regression}). We model age as a function of (\\mbox{$\\rm [Fe\/H]$}, \\mbox{$\\rm [X\/Fe]$}), and can infer a star's age to a precision of $\\pm 0.52$ Gyr for the 2-dimensional abundance simulation and $\\pm 0.06$ Gyr for the 15-dimensional abundance simulation. We also model $R_\\text{birth}$\\ as a function of (\\mbox{$\\rm [Fe\/H]$}, age), and infer it to a precision of $\\pm 1.24$ kpc and $\\pm 1.17$ kpc for the 2- and 15-dimensional abundance simulations respectively. \n    \n    \\item The ability to reconstruct stellar groups born in different times and places from their abundances is determined by the formation history of the galaxy. When formation conditions lead to age and $R_\\text{birth}$\\ trends in the abundance plane with small dispersion, we find that there is a simple connection between clustered abundances and discrete birth times and places. Under clumpy star formation however, the simple relationship vanishes (Section \\ref{sec:victor}). \n    \n    \\item Our comparison of three simulations implies that the low dispersion of age  across the \\mbox{$\\rm [\\alpha\/Fe]$}-\\mbox{$\\rm [Fe\/H]$}\\ plane of the Milky Way indicates that the Milky Way's star formation history is sufficiently quiet and that clustering in abundance will correspond to birth associations in time and location (Figure \\ref{fig:ageDisp}).\n    \n\\end{itemize}\n\nWe seek to examine how abundance structure links to birth properties. We find that there is a simple relationship between age and chemical abundances, which agrees with previous work \\citep[e.g.][]{Ness2019}. $R_\\text{birth}$\\ cannot be tested as we can do for age --- we never have direct access to this quantity in observations. From our regression however, we see age and ([Fe\/H], \\mbox{$\\rm [X\/Fe]$}) link us to $R_\\text{birth}$\\ in the simulations. Indeed this analytical formalism has been adopted in models of radial migration \\citep[e.g.][]{Frankel2018,2019minchev}. We examine the $R_\\text{birth}$--age distribution further using the idea of abundance clustering, which we seek to see if it links to underlying physical processes. \n\nThis work highlights how we might use clustering of high dimensional abundance measurements in large surveys to infer groups of different birth place and time, and the impact of measurement uncertainty in working with the observational data. \n\n\\section{Acknowledgements} \nMelissa K Ness acknowledges support from the Sloan Foundation Fellowship. \nTobias Buck acknowledges support from the European Research Council under ERC-CoG grant CRAGSMAN-646955. This research made use of {\\sc{pynbody}} \\citet{pynbody}.\nWe gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (www.lrz.de).\nThis research was carried out on the High Performance Computing resources at New York University Abu Dhabi. We greatly appreciate the contributions of all these computing allocations.\nK.V.J. is supported by NSF grant AST-1715582.\nB.S. is supported by NSF grant DMS-2015376.\nVPD and LBS are supported by STFC Consolidated grant \\#ST\/R000786\/1\n\n\n\\section{Appendix - additional figures}\nHere we include abundance--age plots colored by $R_\\text{birth}$\\ for both the 2d and 15d simulations. These plots are similar to Figures \\ref{fig:Rbirthxfe_2d} and \\ref{fig:Rbirthxfe_hd}, however the coloring and x-axis are switched. \n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=\\textwidth]{buck_AgeXfe.pdf}\n\\caption{(\\textbf{Left}) The \\mbox{$\\rm [Fe\/H]$}--age plane colored by $R_\\text{birth}$\\ for the 2-dimensional simulation. The black lines and grey area mark off the solar metallicity stars, which we consider to be $\\pm$0.05 dex in \\mbox{$\\rm [Fe\/H]$}. (\\textbf{Right}) the running mean of [O\/Fe] of the solar metallicity stars across age colored by $R_\\text{birth}$\\ selected from within the horizontal lines at left. For a given bin of metallicity, stars clearly have a polynomial trend in \\mbox{$\\rm [X\/Fe]$}--age.}\n\\label{fig:Agexfe}\n\\end{figure*}\n\n\\begin{figure*}\n     \\centering\n     \\includegraphics[width=0.92\\textwidth]{buckHD_AgeXfe.pdf}\n\\caption{(\\textbf{Top left})  The \\mbox{$\\rm [Fe\/H]$}--age plane colored by $R_\\text{birth}$\\ for the 15-dimensional simulation. The black lines and grey area mark off the solar metallicity stars, which we consider to be $\\pm$0.05 dex in \\mbox{$\\rm [Fe\/H]$}. All other plots show the running mean of \\mbox{$\\rm [X\/Fe]$}\\ of the solar metallicity stars accross age colored by $R_\\text{birth}$. Similar to the 2-dimensional simulation shown in Figure \\ref{fig:Agexfe}, solar metallicity stars of different ages separate into different polynomial curves.}\n\\label{fig:Agexfe_hd}\n\\end{figure*}\n\n\\pagebreak\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzetup b/data_all_eng_slimpj/shuffled/split2/finalzzetup
new file mode 100644
index 0000000000000000000000000000000000000000..51dd9def5ddb0ffa385f8844472624695288ae3e
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzetup
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\n The  very innovative  proposal by F. Wilczek \\cite{W} to look for quantum time crystals has raised great interest, but their possible existence has been denied \\cite{B, WO}. The aim of this note is to partly refine Wilczek proposal, in such a way to overcome the objections of Refs. \\cite{B, WO},  and to exhibit explicit examples of quantum time crystals.  \n\n In our opinion, misleading prejudices affect the issue of possible breaking of time translations. One critical point is the widespread belief that the only criterion of spontaneous symmetry breaking is the non-invariance of a ground state correlation function and  this would a priori preclude the breaking of time translations.    \n\nAs a matter of fact, quite generally, a symmetry $\\b$ defined as a mapping  of the quantum canonical variables, more generally of (the algebra of) the observables generated by them, fails to define a symmetry of the states of a given realization or phase of the system (i.e. it does not define a Wigner symmetry), if it cannot be described by a unitary operator in the corresponding Hilbert space.\n\n   For an explicit easily checkable criterion of symmetry breaking, in terms of non-invariant expectations,  one has to consider pure states (since invariant  expectations of a mixed state do not exclude symmetry breaking) and therefore  the  characterization of a pure phase as an irreducible (more generally factorial) representation of the algebra of observables enters in a decisive way.  Irreducibility implies that all the operators which commute with the observables must be represented by multiples of the identity. In order to cover the finite temperature case (where irreducibility fails) this condition is only required to apply to the  set of observables which commute with all the observables (briefly the {\\em center} of the algebra of the observables);  in this more general case the representation is said to be {\\em factorial} and provides the general definition of a pure phase. \n\nClearly, in order to relate the breaking of time translations to non-invariant expectations one must consider a state which is not an eigenstate of the (finite volume) Hamiltonian, e.g. a superposition of eigenstates, \nbut obviously additional conditions are needed. \n\nThey are easily identified if \n \\,\\,i) a group $\\T$ of translations is defined on the observables and ii) the following minimal locality condition (asymptotic abelianess)  is satisfied for any pair of observables $A, \\,B$ and any translation $T \\in \\T$\n$$ \\limn [\\,T^n(A), \\,B\\,] = 0.$$ In the following, we shall always consider pure phases of quantum systems satisfying i) and ii). \n\nIn this case, if a state $\\omega$ invariant under $\\T$ belongs to the pure phase $\\Gamma$, it is the unique $\\T$-invariant  state,  equivalently the cluster property holds \\cite{FSB}\n$$ \\limn \\langle T^n(A)\\,B\\rangle = \\langle A \\rangle\\langle B \\rangle, $$\nwhere  $\\langle C \\rangle \\eqq \\omega(C)$ denotes the expectation of the state $\\omega$.\n\nThis allows for a simple criterion of spontaneous breaking of a symmetry $\\b$ which commutes with the group of translations $\\T$ (called an internal symmetry): \n\n\\noindent {\\em an internal symmetry $\\b$ is spontaneously broken in the pure phase $\\Gamma$ if and only if one of the correlation functions of (the translationally invariant state) $\\omega$ $\\in \\Gamma$ is not invariant under} $\\b$, \n\\be{\\langle \\b(A) \\rangle \\neq \\langle A \\rangle,}\\ee equivalently $$\\limn \\langle T^n (\\b(A)) B \\rangle  - \\langle A \\rangle \\langle B \\rangle \\neq 0.$$ \n  In fact, if $\\omega$ is invariant under $\\b$, by a general result $\\b$ may be described by a unitary operator $U_\\b$ in the  Hilbert space $\\H_\\Gamma$ which describes $\\Gamma$, i.e. $\\b$ defines a Wigner symmetry of $\\Gamma$;  conversely, the transformed state state $\\omega_\\b$, defined by $\\omega_\\b(A) \\eqq \\omega(\\b(A)) \\neq \\omega(A)$, is invariant under $\\T$ (because so is $\\omega$ and $\\b$ commutes with $\\T$), and by eq.\\,(1) and the uniqueness  of the translationally invariant state in $\\Gamma$ $\\omega_\\b$ must  belong to a different phase (and therefore $\\b $ cannot be described by a unitary operator). If such a uniqueness property (crucially related to the pure phases) does not hold one cannot  exclude the existence of a unitary operator $U_\\b$ which relates the corresponding state vectors $\\Psi{\\omega_\\b} = U_\\b \\Psi_\\omega$, in $\\H_\\Gamma$.  \n\nIt is worthwhile to stress that such a criterion of symmetry breaking, which crucially uses invariance under a group of translations, does not require that $\\omega$ is the ground state, even if invariance under a group of translations (not necessarily the full group of translations!) is generically shared  by ground states, and therefore it may be used for the breaking of time translations in a pure phase.      \n\n\\section{A mechanism for realizing quantum time crystals. A spin model}  \nThe next issue is the identification of pure phases defined by a translationally invariant state, which is not invariant under time translations. A possible practical way is to consider a quantum system defined by a Hamiltonian $H$ and a corresponding translationally invariant ground state $\\omega$, which defines a pure phase. Then, one switches on an interaction $V$, typically with an external field, formally $H \\mapsto H + V$, such that $\\omega $ is no longer invariant under the time evolution $\\a_t$ defined on the observables  $A$\n by the infinite volume limit of (volume-)cutoffed  Hamiltonian groups \n\\be{ \\at(A) = \\limn e^{i (H + V)_n t} \\,A\\,e^{-i (H + V)_n t},}\\ee\n $n$ indexing the cutoff. The crucial condition is that $\\at$ maps observables into observables. \n In this way, one may  obtain a spontaneous breaking of time translations. \n\nTo explicitly check this,  the following criterion may be useful: \n\n{\\em In a pure phase defined by a state $\\om$  invariant under a group of translations  $\\T$,  an internal   symmetry $\\b$   is spontaneously broken if and only if  there is \na symmetry breaking order parameter $\\om(\\b(A)) \\neq \\om(A)$, for some observable $A$ or, equivalently,  \nthere is an average or macroscopic  observable\n\\be{ A_{av} \\eqq \\limN \\frac{1}{N} \\sum_{i = 1}^N T^i(A)), \\text{ for }T \\in \\T, }\\ee with  non-invariant expectation   $\\omega(\\b(A_{av})) \\neq \\omega(A_{av}) = \\omega(A)$.} \n\n\nEq.\\,(3) immediately implies symmetry breaking, since, by asymptotic abelianess  $A_{av}$ commutes with all the observables so that it is represented by a multiple of the identity in each pure phase and therefore therefore $\\b$ cannot be implemented by a unitary operator $U_\\b$, which would leave $A_{av}$ invariant. \n\nIt is worthwhile to note that the non-invariance of  expectations  of average\/macroscopic observables  on a translationally invariant state is much easier to control, in particular for detecting the breaking of time translations.  \n\n\nA simple prototype of quantum time crystals is provided by a Heisenberg (lattice) ferromagnet described by a spin one-half Hamiltonian with nearest neighbor coupling $H$. The translationally invariant state $\\omega_x$ with all the spins  pointing in the $x$-direction defines an irreducible representation of the observables and a pure phase $\\Gamma$, satisfying i) and ii).\n\nThen, one  introduces the interaction $H_1$ with a uniform magnetic field ${\\bf h}$ pointing in the $z$-direction. Since $H$ and $H_1$ commute one gets \n\\be{ \\langle \\a_t(\\sigma_{x, av}) \\rangle  = \\cos(|{\\bf h}| t) = \\langle \\sigma^i_{x}(t) \\rangle.}\\ee\nBy the above criterion, this implies the breaking of time translations, leaving unbroken the group of time translations with $t = (\\ume + n) \\pi \/|{\\bf h}|$, with $\\,\\,n \\in \\mathbb Z,$  ({\\em quantum time crystal}). For such a conclusion, a crucial  role has been played by the  thermodynamical limit  and by the translational invariance of the state, a point which has not been realized by Watanabe and Oshikawa in their discussion of a simplified version of such a model. Clearly, the impossibility of describing $\\a_t$ by a unitary operator in $\\H_\\Gamma$ prevents the definition of an Hamiltonian there.\n\nThe general lesson from this relatively simple model is that if in a given pure phase the average  observables undergo a periodic  motion, one has a breaking of time translations with residual invariance under periodic translations, exactly as it happens for the breaking of space translations in a crystal. \nThus, the occurence of time crystals does not appear as a very odd, if not impossible, phenomenon as argued in the literature \\cite{B,WO}.\n\n\n\\section{An example of time periodicity enforced by topology}\n  A similar mechanism may be realized in the model, discussed by Wilczek \\cite{W},  of a charged particle with charge $q$ and unit mass confined to a ring  of unit radius that is threaded by (magnetic) flux $2 \\pi \\alpha\/q$.\n\n\n \n\n\n\n\n  \n\nWhen $\\a = 0$ the model becomes the familiar quantum mechanical model of  a particle on a ring. In the textbook presentations, it is not sufficiently emphasized that the non-trivial topology of the circle has a strong impact on the identification of the algebra of observables $\\A$, which is restricted to be the algebra generated by the canonical momentum $p$ and by periodic functions of the angle $\\ph$, conveniently by $U((n\\ph) \\eqq e^{ i n \\ph},$ $ n \\in \\mathbb{ Z}$ \\cite{WA}.\n\n Since the observable $V( 2 \\pi) \\eqq e^{ i 2 \\pi \\,p}$ commutes with all the observables, its spectrum,  i.e.  the expectation $\\langle V(2 \\pi) \\rangle_\\theta = e^{i \\theta}$, $\\theta \\in [ 0, 2 \\pi)$ mod $2 \\pi$, labels the  irreducible representations of (the algebra of) the observables hereafter called {\\em $\\theta$-sectors}, all $\\theta$'s being  allowed \\cite{Autoagg}.\nThe mapping  \n$$\\rho^\\theta:    U(n) \\,\\mapsto \\,U(n), \\,\\,V(\\b) \\eqq e^{ i \\b \\,p} \\,\\mapsto \\,V(\\b)\\,e^{ i  \\tilde{\\theta}\\, \\b}, \\,\\,\\,\\tilde{\\theta} \\eqq \\theta\/2 \\pi,$$    defines a symmetry of the observables, which is broken in each $\\theta$ sector, since it does not leave the central element $V(2 \\pi)$ invariant. The structure is very similar of that of QCD, with $V(2 n \\pi)$ playing the role of the large gauge transformations and $\\rho^\\theta$ the chiral transformations \\cite{FS, FS2}.\n \nFor $\\a \\neq 0$ the  dynamics $\\a^\\a(t)$ is given by \n$\\a^\\a(t) = \\rho^{ -2 \\pi\\,\\a}\\,\\a^0(t)\\,\\rho^{ 2 \\pi\\,\\a}$, with $\\a^0(t)$ the dynamics induced by $H_0 = \\ume p^2$. The spectrum of the corresponding Hamiltonian $H^\\a$ in each $\\theta$ sector coincides with the spectrum of $H^0$ in the sector $\\theta - \\a$.\n\nAs remarked above, to realize a spontaneous symmetry breaking of time translations it is enough to introduce a coupling of $\\ph$ with an external field $h$:\n$H^{\\a,h} =  H^\\a + h \\ph.$\nSuch a Hamiltonian does not belong to the algebra of observables, but nevertheless the corresponding time evolution $\\a^{\\a,h}(t)$ maps the algebra of observables $\\A$ into itself, as required,  for physical consistency.\nIn fact, by using  Zassenhaus' formula, one easily gets \n $$\\a^{\\a, h}(t)(U(n)) = e^{- i \\ume  t^2 h (p - \\a)}\\,\\a^\\a(t)(U(n))\\, e^{ i \\ume  t^2 h (p - \\a)} \\in \\A,$$\n \\be{\\a^{\\a, h}(t)(V(\\b)) = V(\\b)\\,e^{i \\b\\, h\\,t}, \\,\\,\\,\n\\a^{\\a, h}(t)(V(2 \\pi)) = V(2 \\pi)\\,e^{i 2 \\pi h\\,t}.}\\ee \nHence, $\\a^{\\a, h}(t)$ is broken in each $\\theta$ sector, leaving  as residual invariance group the time translations with $t = n\/h, \\,n \\in \\mathbb Z$.\n\nThe non-trivial topology of the circle plays a crucial role for the symmetry breaking in such a finite dimensional model; in the (reducible) representation with a decompactified $\\ph$, given by $L^2(\\mathbb R, d \\ph)$, the dynamics  $\\a^{\\a, h}(t)$ is implemented by unitary operators, which, however, do not leave each $\\theta$ sector invariant.     \n\n\\section{Breaking of time translations in many-particle Wilczek model}\nFor a many particle extension of the model discussed above, consider $N$ copies of the Wilczek model, e.g. by considering $N$ coaxial rings with the same unit radius, labeled by the index $i$,  with the following Hamiltonian:\n$ H^{\\a, V, N} = \\sum_{i = 1}^N( H^\\a_i + V(\\ph_i)),$\nwith $V(\\ph_i)$ a periodic function, to guarantee that  the corresponding time evolution $\\a^{\\a, V, N}(t)$ maps observables into observables \\cite{WF}. \n\nIn order to find phases with broken time translations in the $N \\ra \\infty$  limit, consider the product state  $\\Psi_0^N \\eqq \\prod_{i = 1}^N \\,\\Psi_0^i$, with $\\Psi_0^i = (2 \\pi)^{-\\ume} \\,e^{i \\a \\ph_i}$ the ground state of $H^{\\a, i}$ (one might as well take the product of the same $\\theta$ state for each index $i$). Clearly, in the thermodynamical limit such a state defines a pure phase and it is invariant under the group of ``translations'' of the index $i$, so that the criterion of Section 2 applies. \n\nTo this purpose, one may consider  \n the following observable\n$$ P_N = \\frac{1}{N} \\sum_{i = 1}^N f(\\ph_i)\\,p_i\\,f(\\ph_i) \\eqq \\frac{1}{N}\\sum_{i = 1}^N p_i^f,$$    \nwith $f$ a regular function of compact support in $[0, 2 \\pi]$, with periodic extension $f(\\ph_i + 2 \\pi) = f(\\ph_i)$; the observable $p_i^f$ describes a momentum localized in the support of $f$ and its expectation on the corresponding  $\\Psi_0^i $ is $\\langle p_i^f \\rangle_i = \\a\\,(2 \\pi)^{-1} \\int _0^{2 \\pi} d \\ph_i\\,|f(\\ph_i)|^2 \\neq 0$, and is independent of the index $i$. \n\n Furthermore, denoting by $\\a^{\\a, V, N}(t)$ the time evolution defined by $H^{\\a, V, N}$ and by $\\langle \\ldots \\rangle_{\\a, N}$ the expectation on the above product state, one has \n\n$$ \\frac{d}{d t} \\langle \\a^{\\a, V, N}(t)(p_i^f) \\rangle_{\\a, N}|_{t = 0} =  \\int _0^{2 \\pi} \\frac{d \\ph_i}{2 \\pi} \\,|f(\\ph_i)|^2 \\,\\frac{d V(\\ph_i)}{d \\ph_i},$$\nhaving used that $\\Psi_0^i$ is the ground state  of the kinetic Hamiltonian $H_i^{\\a}$. For a given  potential one can always find $f$ such that  the right hand side does not vanish (thanks to the fact that $\\Psi_0^i$ is not an eigenstate of $H_i^{\\a, V}$). \n\nAs in the example of spin systems, in the  infinite particle limit the  average  observable\n$$P_{av} = \\limN \\frac{1}{N} \\sum_{i = 1}^N p_i^f$$  commutes with  the observables, it is not zero in the (factorial) representation defined by the above product state in the limit $N \\ra \\infty$, $\\langle P_{av} \\rangle_{\\a, \\infty} = \\langle p_i^f \\rangle_{\\a, \\infty}$,   and \n\\be{ d\/dt \\langle   \\a^{\\a, V, \\infty}(t)(P_{av}) \\rangle_{\\a, \\infty}|_{t = 0}  \\neq 0.}\\ee\nThus, such an average  observable has a non-trivial time evolution and therefore time translations are broken \n in such a  representation.\n\nAnother possibility is to consider the average\/macroscopic observable \n$$ F(\\ph)_{av} \\eqq \\limN \\frac{1}{N} \\sum_{i=1}^N F(\\ph_i),$$\nwith $F$ a regular periodic function of compact support.\n\nProceeding as before one gets \n$$d\/dt \\langle \\a^{\\a, V, N}(t)(F(\\ph_i)) \\rangle_{\\a, N}|_{t = 0} = 0, $$\n\\be{(d\/dt)^2 \\langle \\a^{\\a, V, N}(t)(F(\\ph_i)) \\rangle_{\\a, N}|_{t = 0} = -  \\langle V'(\\ph_i)\\,F'(\\ph_i) \\rangle_{\\a, N },\n}\\ee where the prime denotes the derivative with respect to $\\ph_i$. The right hand side is independent of $i$ and different from zero for all periodic functions $F$, with derivative which is  not orthogonal to $V'$;  therefore the same result holds for $F(\\ph)_{av}$ in the $N \\ra \\infty$ limit. By the above criterion, this implies the breaking of time translations.  \n\nThe conclusions do not change if the interaction $V$  also contains a particle-particle interaction term $V_{p-p} = \\sum_{i<j} v(\\ph_i - \\ph_j)$, with $v$ a periodic function, since this term does not contribute to the right hand sides of eqs.\\,(6, 7).\n\nF. S. is grateful to Giovanni Morchio for very useful discussions.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nWell-quasi-order is a strong structural property of permutation classes, and until recently, it was conceivable that there might be only countably many classes with this property. However, it can be seen from the recent work of Oudrar, Pouzet, and Zaguia~\\cite{oudrar:minimal-prime-ages:} that there are uncountably many well-quasi-ordered permutation classes.\nOur main result goes further.\nWe show that one can find uncountably many well-quasi-ordered permutation classes with distinct enumerations, which implies that these enumerations cannot all be nice. We defer definitions and context for our main theorem until later in this introduction, but state it now.\n\n\\begin{theorem}\n\\label{thm-wqo-not-algebraic}\nThere are uncountably many distinct enumerations of well-quasi-ordered permutation classes.\n\\end{theorem}\n\nOur proof of Theorem~\\ref{thm-wqo-not-algebraic} builds on a construction from Pouzet's 1978 thesis concerning factor-closed sets of binary words~\\cite{pouzet:sur-la-theorie-:}. Section~\\ref{sec-pouzet-factors} establishes a number of properties of this construction, while the work after that exploits these in the permutation context. \n\nBesides underpinning the proof of Theorem~\\ref{thm-wqo-not-algebraic}, the properties we establish about Pouzet's construction also imply a result concerning subwords of infinite binary sequences. Specifically, we are able to find uncountably many such sequences, each having distinct linear complexity functions. We defer the formal statement and necessary definitions for this result until Section~\\ref{sec-sequences}.\n\nThe rest of this introduction provides the permutation-specific definitions and context for Theorem~\\ref{thm-wqo-not-algebraic}. We think of permutations in one-line notation, so a \\emph{permutation of length $n$} is simply an ordering of the set $\\{1,2,\\dots,n\\}$. The permutation~$\\pi$ \\emph{contains} the permutation~$\\sigma$ of length $k$ if~$\\pi$ has a subsequence of length $k$ that is \\emph{order isomorphic} to~$\\sigma$, by which we mean that the subsequence has the same pairwise comparisons as~$\\sigma$. For example,~$\\pi=372694185$ contains~$\\sigma=32514$, as witnessed by its subsequence $32918$, but~$\\pi$ avoids $54321$ because it has no decreasing subsequence of length five. If~$\\pi$ contains~$\\sigma$, then we sometimes say that~$\\sigma$ is a \\emph{subpermutation} of~$\\pi$.\n\nA \\emph{permutation class} is a downset of permutations in this order. In other words, if $\\mathcal{C}$ is a permutation class,~$\\pi\\in\\mathcal{C}$, and~$\\sigma\\le\\pi$, then we must also have~$\\sigma\\in\\mathcal{C}$. Every permutation class can be described by a unique \\emph{basis}, which consists of the minimal permutations \\emph{not} in the class. Every basis of a class is necessarily an \\emph{antichain}, meaning that none of its members is contained in another. As there are infinite antichains of permutations, there are infinitely-based permutation classes. A permutation class is \\emph{well-quasi-ordered} (\\emph{wqo} for short, or \\emph{belordonn{\\'e}} in French) if it does not contain an infinite antichain.\n\nWith $\\mathcal{C}_n$ denoting the set of permutations of length $n$ in the class $\\mathcal{C}$, the generating function of the class is\n\\[\n\t\\sum_{n\\ge 0} |\\mathcal{C}_n|x^n=\\sum_{\\pi\\in\\mathcal{C}} x^{|\\pi|},\n\\]\nwhere here $|\\pi|$ denotes the length of~$\\pi$. We are often interested in whether this generating function~$f(x)$ is \\emph{rational} (if~$f(x)=p(x)\/q(x)$ for polynomials $p$ and $q$), \\emph{algebraic} (if there is a polynomial~$p(x,y)\\in\\mathbb{Q}[x,y]$ such that $p(x,f(x))=0$), or \\emph{D-finite} (if $f(x)$ and its derivatives span a finite dimensional vector space over $\\mathbb{Q}(x)$).\n\nIn their 1996 paper, Noonan and Zeilberger~\\cite{noonan:the-enumeration:} conjectured that every finitely-based permutation class has a D-finite generating function. Note that the finite basis hypothesis here is clearly necessary---because there are infinite antichains of permutations, there are uncountably many different enumerations of permutations, but only countably many D-finite generating functions with rational coefficients. The Noonan--Zeilberger conjecture had begun to seem unlikely, and in 2005, Zeilberger himself conjectured that it was false~\\cite{elder:problems-and-co:}. However, it was not until 2015 that the conjecture was disproved by Garrabrant and Pak~\\cite{Garrabrant:Pattern-avoidan:}, a short version of which appeared in the proceedings of~\\emph{SODA~2016}~\\cite{garrabrant:permutation-pat:}%\n\\footnote{The proof of Garrabrant and Pak does not provide a concrete counterexample to the Noonan--Zeilberger conjecture. Many believe that the class of $1324$-avoiding permutations does not have a D-finite generating function because it is suspected to have the wrong asymptotics for such a generating function~\\cite{conway:on-the-growth-r:,conway:1324-avoiding-p:}. The same type of analysis applies to several other classes avoiding a single permutation of length five, as shown by Clisby, Conway, Guttmann, and Inoue~\\cite{clisby:classical-lengt:}. That said, for the sake of providing a concrete counterexample to the Noonan--Zeilberger conjecture, it may be preferable to consider classes with more basis elements, and thus more structure. Several potential counterexamples along these lines were identified in the work of Albert, Homberger, Pantone, Shar, and Vatter~\\cite{albert:generating-perm:}. Others have later been identified by B\\'ona and Pantone~\\cite{bona:permutations-av:long-mono}.}%\n\\footnote{In an interview published in 2021~\\cite{mansour:interview-with-:stanley}, Stanley singled out the results of Garrabrant and Pak, saying ``a topic within enumerative combinatorics that seems ripe for further investigation is developing a theory for showing that a given generating function (in one variable) does \\emph{not} have some desirable property, such as being D-finite or differentially algebraic. There are a number of results in this area, but nothing approaching a general theory. The most significant work in this direction (in my opinion) is the disproof of the Noonan--Zeilberger conjecture by Scott Garrabrant and Igor Pak.''}.\n\nThus we know that some permutation classes fail to have nice enumerations (by an elementary argument because there are infinite antichains of permutations), and the Garrabrant--Pak result shows that some \\emph{finitely-based} permutation classes even fail to have nice enumerations. In a similar direction, at the same conference at which he conjectured that the Noonan--Zeilberger conjecture was false, Zeilberger asked for necessary and sufficient conditions for classes to have rational\/algebraic\/D-finite\/... generating functions~\\cite{elder:problems-and-co:}. However, the results of Albert, Brignall, and Vatter~\\cite{albert:large-infinite-:} indicate that this question is likely to be intractable.\n\n\\begin{theorem}[Albert, Brignall, and Vatter~\\cite{albert:large-infinite-:}]\n\\label{thm-contained-rational}\nEvery permutation class except for the class of all permutations is contained in a class with a rational generating function%\n\\footnote{The proof of Theorem~\\ref{thm-contained-rational} employs Marcus and Tardos's resolution of the Stanley--Wilf conjecture~\\cite{marcus:excluded-permut:}, and can be viewed as a strengthening of this result.}.\n\\end{theorem}\n\nThis result shows that we cannot expect nice structure from permutation classes with rational generating functions. On the other hand, certain notions of structure do have enumerative consequences; one such example is due to Albert and Atkinson~\\cite{albert:simple-permutat:}, who showed that permutation classes containing only finitely many simple permutations have algebraic generating functions.\n\nWe say that a permutation class is \\emph{strongly algebraic} (or \\emph{h{\\'e}r{\\'e}ditairement alg{\\'e}brique} in French~\\cite{oudrar:sur-lenumeratio:}) if it and all its subclasses have algebraic generating functions. By an elementary counting argument, it follows that strongly-algebraic permutation classes must be wqo. Thus it was natural to wonder if the converse might hold as well, a conjecture that appears to have been first stated in the literature by the second author.\n\n\\begin{falseconjecture}[Vatter~{\\cite[Conjecture 12.3.4]{vatter:permutation-cla:}}]\n\\label{conj-wqo-algebraic}\nA permutation class is strongly algebraic if and only if it is well-quasi-ordered.\n\\end{falseconjecture}\n\nTheorem~\\ref{thm-wqo-not-algebraic} shows that this conjecture is false, because there are too many wqo permutation classes with distinct enumerations for them all to have algebraic generating functions. Indeed, there are too many for them all to even have D-finite generating functions%\n\\footnote{Note that the classes we construct in the proof of Theorem~\\ref{thm-wqo-not-algebraic} are almost certainly infinitely based, and thus are unlikely to represent additional counterexamples to Noonan and Zeilberger's false conjecture.}.\n\nWe remark that while our results show that wqo is not enough to guarantee algebraicity, a stronger notion known as \\emph{labelled well-quasi-order} (\\emph{lwqo} for short, or \\emph{h{\\'e}r{\\'e}ditairement belordonn{\\'e}} in French) might be. While this notion is implicit in the classic papers of Higman~\\cite{higman:ordering-by-div:} and Kruskal~\\cite{kruskal:well-quasi-orde:}, it was not until the work of Pouzet in the 1970s (in particular, his 1972 paper~\\cite{pouzet:un-bel-ordre-da:}) that it was studied explicitly. Recently it has been shown that lwqo nicely explains many structural results about permutation classes~\\cite{brignall:labelled-well-q:}. We leave the following question for future research.\n\n\\begin{question}\n\\label{ques-lwqo-algebraic}\nDoes every lwqo permutation class have an algebraic generating function?\n\\end{question}\n\nAt the very least, Question~\\ref{ques-lwqo-algebraic} will not fall to an argument such as the one we use here to disprove False Conjecture~\\ref{conj-wqo-algebraic}, as there are only countably many lwqo permutation classes, which is a corollary of them all being finitely based, see~\\cite[Proposition 2.3]{brignall:labelled-well-q:}. A slightly weaker version of Question~\\ref{ques-lwqo-algebraic} has been conjectured by Oudrar~\\cite[page 87]{oudrar:sur-lenumeratio:}.\n\nThe rest of this paper is organized as follows. Pouzet's construction, and properties of the resulting (uncountably large) collection of factor-closed binary languages, are given in Section~\\ref{sec-pouzet-factors}. In Sections~\\ref{sec-rightward-yearning} and~\\ref{sec-construction} we show how each such language can be used to construct a permutation class of a particular type, via ``pin sequences''. After establishing decomposition properties of the permutations that these classes contain in Sections~\\ref{sec-decomp} and~\\ref{sec-indecomposable}, we show in Section~\\ref{sec-wqo} that each such class is well-quasi-ordered. To complete the proof of Theorem~\\ref{thm-wqo-not-algebraic}, in Section~\\ref{sec-enum} we show that any two such permutation classes constructed from distinct languages cannot have the same enumeration sequence. Section~\\ref{sec-sequences}, which relies only on Section~\\ref{sec-pouzet-factors}, covers the result concerning binary sequences. Some closing remarks are given in Section~\\ref{sec-concluding}.\n\n\\section{Words Under the Factor Order}\n\\label{sec-pouzet-factors}\n\\newcommand{\\overline{\\alpha}}{\\overline{\\alpha}}\n\nWhile the construction described in this section, which is adapted from Pouzet's thesis~\\cite[page~64]{pouzet:sur-la-theorie-:}, can be defined more generally, we specialize it to the binary alphabet $\\{0,1\\}$. We are interested here in the \\emph{factor order} on the set of all finite binary words, $\\{0,1\\}^\\ast$, in which $u\\le w$ if $u$ occurs as a \\emph{factor} (or \\emph{consecutive subword}) of~$w$. In other words,~$u\\le w$ in this order if~$w=w_1uw_2$ for some (possibly empty) words~$w_1,w_2\\in\\{0,1\\}^\\ast$. This poset is \\emph{not} wqo in general, because, for example, the words $11$, $101$, $1001$, $\\dots$ form an infinite antichain.\n\n\n\nFor a binary word $\\gamma = \\gamma_1\\cdots\\gamma_n$, the \\emph{complement} (sometimes referred to as the \\emph{ones complement}) is the word $\\overline\\gamma = \\overline\\gamma_1\\cdots\\overline\\gamma_n$ formed by inverting every letter of $\\gamma$, so\n\\(\n\t\\overline\\gamma_i = 1-\\gamma_i\n\\)\nfor all $1\\le i\\le n$.\nWe now describe Pouzet's construction. While it takes a bit of preparation, this will eventually give us uncountably many wqo sets of binary words that are all closed downward in the factor order, each of which has a different enumeration sequence.\n\nLet $(s_k)_{k\\in\\mathbb{N}}$ be a sequence of positive integers. We construct the infinite sequence~$(\\alpha^{\\exparen{s_k}}_i)_{i\\in\\mathbb{N}}$ of binary words by setting\n\\[\n\t\\alpha^{\\exparen{s_k}}_1=01\n\\]\nand, for $i\\ge 1$, defining\n\\[\n\t\t\\alpha^{\\exparen{s_k}}_{i+1}\n\t\t\t=\n\t\t\t\\LaTeXunderbrace{\\alpha^{\\exparen{s_k}}_{i}\\cdots \\alpha^{\\exparen{s_k}}_{i}}_{\\text{$s_{i}$ copies}}\n\t\t\t\\LaTeXunderbrace{\\overline{\\alpha}^{\\exparen{s_k}}_{i}\\cdots \\overline{\\alpha}^{\\exparen{s_k}}_{i}}_{\\text{$s_{i}$ copies}}\n\t\t\t=\n\t\t\t\\left(\\alpha^{\\exparen{s_k}}_{i}\\right)^{s_i}\n\t\t\t\\left(\\overline{\\alpha}^{\\exparen{s_k}}_{i}\\right)^{s_i}.\n\\]\n\nIn the case where $s=(1,1,1,\\dots)$, the sequence~$\\alpha^{\\exparen{s_k}}_i$ is a prefix of the well-known Prouhet--Thue--Morse sequence (see~\\cite{allouche:the-ubiquitous-:}):\n\\[\n\t\\begin{array}{rl}\n\ti\t&\\alpha^{(1,1,1,\\dots)}_i\t\\\\[2pt]\n\t\\hline\\\\[-10pt]\n\t1\t&01\t\t\t\t\t\t\\\\\n\t2\t&01\\,10\t\t\t\t\t\\\\\n\t3\t&0110\\,1001\t\t\t\t\\\\\n\t4\t&01101001\\,10010110\t\n\t\\end{array}\n\\]\nThis example illustrates several features of the construction that hold for arbitrary sequences $(s_k)$. First, we can read the lengths of these words directly from the construction:\n\\[\n\t|\\alpha^{\\exparen{s_k}}_i|= 2^is_1s_2\\cdots s_{i-1}.\n\\]\nSecond, the first letter of~$\\alpha^{\\exparen{s_k}}_i$ is always $0$, while the last letter alternates with $i$.\n\n\\begin{observation}\\label{obs-last-letters}\nThe last letter of~$\\alpha^{\\exparen{s_k}}_i$ is 0 if and only if $i$ is even.\n\\end{observation}\n\n\n\n\nOf particular interest to us is the language\n\\[\n\t\\L^{\\exparen{s_k}}\n\t=\n\t\\{w\\::\\:\\text{$w$ is a factor of~$\\alpha^{\\exparen{s_k}}_i$ for some $i\\ge 1$}\\}.\n\\]\nBy definition, we include the empty word $\\varepsilon$ in~$\\L^{\\exparen{s_k}}$. \n\nNote that for any sequence $(s_k)$ and indices $i\\le j$, the word~$\\alpha^{\\exparen{s_k}}_j$ can be expressed as a sequence of concatenations of the words~$\\alpha^{\\exparen{s_k}}_i$ and~$\\overline{\\alpha}^{\\exparen{s_k}}_i$. That is, whenever $i\\le j$, then~$\\alpha^{\\exparen{s_k}}_j$ can be expressed as a word over the alphabet $\\{\\alpha^{\\exparen{s_k}}_i, \\overline{\\alpha}^{\\exparen{s_k}}_i\\}$, and we use this viewpoint several times in what follows. One consequence is that if~$w$ is a factor of~$\\alpha^{\\exparen{s_k}}_i$ for some $i$, then it is also a factor of~$\\alpha^{\\exparen{s_k}}_j$ for all~$j\\ge i$. Thus, the language~$\\L^{\\exparen{s_k}}$ can also be defined as the set of all words that appear as factors of~$\\alpha^{\\exparen{s_k}}_i$ for all sufficiently large values of $i$. \n\nIn the other direction, the next result, which is also essentially from Pouzet's thesis, guarantees that \nall sufficiently long words in~$\\L^{\\exparen{s_k}}$ actually contain~$\\alpha^{\\exparen{s_k}}_i$.\n\n\\begin{proposition}\\label{prop-contains-alpha}\nFor every sequence $(s_k)$ of positive integers, there exists a function $f^{\\exparen{s_k}}(i)$ such that every word in~$w\\in \\L^{\\exparen{s_k}}$ of length at least $f^{\\exparen{s_k}}(i)$ contains~$\\alpha^{\\exparen{s_k}}_i$ as a factor.\n\\end{proposition}\n\n\\begin{proof}\nLet~$\\alpha=\\alpha^{\\exparen{s_k}}_{i+1}$. We claim that we can take\n\\[\n\tf^{\\exparen{s_k}}(i)=2|\\alpha|=2^{i+2}s_1s_2\\cdots s_{i}.\n\\]\nTo see this, let~$w\\in\\L^{\\exparen{s_k}}$ have length at least $f^{\\exparen{s_k}}(i)$. As\n\\[\n\t|w|\\ge f^{\\exparen{s_k}}(i)>|\\alpha^{\\exparen{s_k}}_i|,\n\\]\nwe see that~$w$ must be a factor of~$\\alpha^{\\exparen{s_k}}_j$ for some $j\\ge i+1$. All such words are composed of concatenations of~$\\alpha$ with its complement~$\\overline{\\alpha}$, and thus~$w$ must contain either~$\\alpha$ or~$\\overline{\\alpha}$ as a factor, since~$w$ is at least twice as long as both. The result follows because each of~$\\alpha$ and~$\\overline{\\alpha}$ contain~$\\alpha^{\\exparen{s_k}}_i$ as a factor.\n\\end{proof}\n\nThat these languages are wqo follows readily from Proposition~\\ref{prop-contains-alpha}.\n\n\\begin{proposition}\n\\label{prop-Lsk-wqo}\nFor every sequence $(s_k)$ of positive integers, the set~$\\L^{\\exparen{s_k}}\\subseteq\\{0,1\\}^\\ast$ of words is wqo under the factor order.\n\\end{proposition}\n\n\n\\begin{proof}\nSuppose to the contrary that there were an infinite antichain~$w_1$,~$w_2$, $\\dots$ of words from~$\\L^{\\exparen{s_k}}$.\nThe word~$w_1$ is contained in~$\\alpha^{\\exparen{s_k}}_i$ for some index $i$ because it lies in~$\\L^{\\exparen{s_k}}$. Letting $f^{\\exparen{s_k}}(i)$ denote the function from Proposition~\\ref{prop-contains-alpha}, we see that every word in~$\\L^{\\exparen{s_k}}$ of length at least $f^{\\exparen{s_k}}(i)$ contains~$\\alpha^{\\exparen{s_k}}_i$ as a factor, and hence also contains~$w_1$ as a factor. It follows that there is some index~$j$ such that~${|w_j|\\geq f^{\\exparen{s_k}}(i)}$, from which we conclude that~$w_1$ is a factor of~$w_j$, which contradicts our assumption that these words form an infinite antichain.\n\\end{proof}\n\nPouzet~\\cite{pouzet:sur-la-theorie-:} established that when $(s_k)$ and $(t_k)$ are distinct sequences, then~$\\L^{\\exparen{s_k}}$ and~$\\L^{\\exparen{t_k}}$ are distinct languages. As there are uncountably many sequences of positive integers, there must then be uncountably many wqo factor-closed languages over a binary alphabet. For our enumerative goal, we require something a bit more precise: not only must~$\\L^{\\exparen{s_k}}$ and~$\\L^{\\exparen{t_k}}$ be distinct languages, but there must be some length where one language contains more words of that length than the other. In fact, the result we prove is stronger still: the set of words of some given length in one language is a \\emph{proper subset} of the words of that length in the other.\n\nBefore we state and prove this, however, we require a technical characterisation of the possible embeddings of~$\\alpha^{\\exparen{s_k}}_i$ in~$\\alpha^{\\exparen{s_k}}_j$ for given $i$ and any $j>i$. We again adopt the viewpoint that~$\\alpha_j^{\\exparen{s_k}}$ can be regarded as a word over the alphabet $\\{\\alpha_i^{\\exparen{s_k}},\\overline{\\alpha}_i^{\\exparen{s_k}}\\}$, but to ease exposition let us use~$\\alpha_i^\\ast$ and~$\\overline{\\alpha}_i^\\ast$ to denote the \\emph{letters}, and~$\\alpha_j^\\ast$ the word over $\\{\\alpha_i^\\ast,\\overline{\\alpha}_i^\\ast\\}$, with the property that the binary word~$\\alpha_j^{\\exparen{s_k}}$ is equal to~$\\alpha_j^\\ast$ after performing the substitutions~$\\alpha_i^\\ast\\mapsto \\alpha_i$ and~$\\overline{\\alpha}_i^\\ast\\mapsto\\overline{\\alpha}_i$. \n\n\\begin{proposition}\\label{prop-alpha-i-embeddings}%\nFor every sequence $(s_k)$ of positive integers and integers $i<j$, the only factors of~$\\alpha^{\\exparen{s_k}}_j$ that are equal to~$\\alpha^{\\exparen{s_k}}_i$ are given by \n\\begin{enumerate}[label=(\\roman*)]\n\\item the terms corresponding to a letter~$\\alpha^{\\ast}_i$ of~$\\alpha_j^\\ast$, and \n\\item the middle terms corresponding to a pair of letters~$\\overline{\\alpha}^{\\ast}_i\\overline{\\alpha}^{\\ast}_i$ in~$\\alpha_j^\\ast$.\n\\end{enumerate}\nAn analogous statement holds for factors of~$\\alpha_j^{\\exparen{s_k}}$ that are equal to~$\\overline{\\alpha}^{\\exparen{s_k}}_i$.\n\\end{proposition}\n\n\\begin{proof}\nSince we are dealing with a single sequence $(s_k)$ in this proof, we drop the $(s_k)$ superscript throughout.\n\nIt is clear that any occurrence of~$\\alpha_i^\\ast$ in~$\\alpha_j^\\ast$ corresponds to a factor of~$\\alpha_j$ equal to~$\\alpha_i$. Similarly, we have\n\\[\n\t\\overline{\\alpha}_i\\overline{\\alpha}_i = (\\overline{\\alpha}_{i-1}^{s_{i-1}}\\alpha_{i-1}^{s_{i-1}})(\\overline{\\alpha}_{i-1}^{s_{i-1}}\\alpha_{i-1}^{s_{i-1}}) = \\overline{\\alpha}_{i-1}^{s_{i-1}}\\alpha_{i}\\alpha_{i-1}^{s_{i-1}},\n\\]\nwhich demonstrates that the middle terms of~$\\overline{\\alpha}_i\\overline{\\alpha}_i$ are equal to~$\\alpha_i$.\n\nTo show that these are the only factors, we proceed by induction on $i$. In the case $i=1$, we have~$\\alpha_i=01$ and~$\\overline{\\alpha}_i=10$. For any $j>1$, fix an occurrence of $01$ in~$\\alpha_j$. If this occurrence starts on an odd-numbered letter of~$\\alpha_j$, then in~$\\alpha_j^\\ast$ this occurrence corresponds either to the letter~$\\alpha_1^\\ast$ or~$\\overline{\\alpha}_1^\\ast$, but it clearly cannot be the second of these. If, on the other hand, this occurrence starts on an even-numbered letter of~$\\alpha_j$, then this occurrence straddles two letters of~$\\alpha_j^\\ast$. By inspection, the only possibility is~$\\overline{\\alpha}_i^\\ast\\overline{\\alpha}_i^\\ast$. A similar argument applies for the occurrences of~$\\overline{\\alpha}_i$ in~$\\alpha_j$, and this completes the base case.\n\nSuppose that the proposition is true for some $i\\geq 1$. Take $j> i+1$, and consider an occurrence of~$\\alpha_{i+1}$ in~$\\alpha_j$. Since~$\\alpha_{i+1} = \\alpha_{i}^{s_{i}}\\overline{\\alpha}_{i}^{s_{i}}$, we begin by considering the occurrences of~$\\alpha_{i}^{s_{i}}$ and~$\\overline{\\alpha}_{i}^{s_{i}}$ in~$\\alpha_j$. \n\nBy induction, the only occurrences of~$\\alpha_i$ in~$\\alpha_j$ are as given in the proposition. Consequently, the only occurrences of~$\\alpha_i^{s_i}$ in~$\\alpha_j$ correspond to factors $(\\alpha_i^\\ast)^{s_i}$ in~$\\alpha_j^\\ast$, or the middle terms of the binary word corresponding to $(\\overline{\\alpha}_i^\\ast)^{s_i+1}$. A similar statement holds for the occurrences of~$\\overline{\\alpha}_i^{s_i}$ in~$\\alpha_j$.\n\nWe now consider the possible positions for our occurrence of~$\\alpha_{i+1} = \\alpha_{i}^{s_{i}}\\overline{\\alpha}_{i}^{s_{i}}$ in~$\\alpha_j$. If the first half (the word~$\\alpha_{i}^{s_{i}}$) appears in the middle of some factor of the form~$\\overline{\\alpha}_i^{s_i+1}$, then the second half of the word,~$\\overline{\\alpha}_i^{s_i}$ does not embed. Similarly, if the second half of the word embeds in the middle of a factor of the form~$\\alpha_i^{s_i+1}$ then the first half cannot embed. Therefore, the only embeddings of~$\\alpha_{i+1}$ in~$\\alpha_j$ must correspond precisely to instances of the factor $(\\alpha_i^\\ast)^{s_i}(\\overline{\\alpha}_i^\\ast)^{s_i}$ in~$\\alpha_j^\\ast$. A similar statement applies to~$\\overline{\\alpha}_{i+1}$. \n\nFinally, by construction,~$\\alpha_j^\\ast$ is composed of factors of the form $(\\alpha_i^\\ast)^{s_i}(\\overline{\\alpha}_i^\\ast)^{s_i}$ and $(\\overline{\\alpha}_i^\\ast)^{s_i}(\\alpha_i^\\ast)^{s_i}$. These correspond to the words~$\\alpha_{i+1}$ and~$\\overline{\\alpha}_{i+1}$ that can be used to make up~$\\alpha_j$, from which the inductive step follows. \n\\end{proof}\n\nWe now state the main result of this section; we prove it after considering an example.\n\n\\begin{proposition}\n\\label{prop-words-distinct-enum}\nSuppose that $(s_k)$ and $(t_k)$ are distinct sequences of positive integers, and that~$(s_k)$ lexicographically precedes $(t_k)$. Then there exists an integer $M\\ge 3$ such that~$\\L^{\\exparen{s_k}}_n = \\L^{\\exparen{t_k}}_n$ for all~${n<M}$, but~$\\L^{\\exparen{s_k}}_M\\supsetneq \\L^{\\exparen{t_k}}_M$.\n\\end{proposition}\n\nWe note that the ``inequalities'' in Proposition~\\ref{prop-words-distinct-enum} are in some sense reversed---we assume that $(s_k)$ precedes $(t_k)$ in lexicographical order, and then it follows that~$\\L^{\\exparen{s_k}}_M$ is \\emph{larger} than~$\\L^{\\exparen{t_k}}_M$. We illustrate this with the concrete example where the sequences are $(1,1,1,\\dots)$ and $(2,1,1,\\dots)$. In this case the construction gives us the table below.\n\\[\n\t\\begin{array}{rll}\\\\\n\ti&\\alpha^{(1,1,1,\\dots)}_i&\\alpha^{(2,1,1,\\dots)}_i\\\\[2pt]\n\t\\hline\\\\[-10pt]\n\t1&01\t\t\t\t\t&01\t\\\\\n\t2&01\\,10\t\t\t\t&01\\,01\\,10\\,10\\\\\n\t3&0110\\,1001\t\t\t&01011010\\,10100101\\\\\n\t4&01101001\\,10010110\t&0101101010100101\\,1010010101011010\n\t\\end{array}\n\\]\nOne can check that the languages~$\\L^{(1,1,1,\\dots)}$ and~$\\L^{(2,1,1,\\dots)}$ agree up to and including length $3$:\n\\[\n\\begin{array}{lclcl}\n\t\\L^{(2,1,1,\\dots)}_0&=&\\L^{(1,1,1,\\dots)}_0\t&=&\t\\{\\varepsilon\\},\\\\[2pt]\n\t\\L^{(2,1,1,\\dots)}_1&=&\\L^{(1,1,1,\\dots)}_1\t&=&\t\\{0, 1\\},\\\\[2pt]\n\t\\L^{(2,1,1,\\dots)}_2&=&\\L^{(1,1,1,\\dots)}_2\t&=&\t\\{00, 01, 10, 11\\},\\\\[2pt]\n\t\\L^{(2,1,1,\\dots)}_3&=&\\L^{(1,1,1,\\dots)}_3\t&=&\t\\{001, 010, 011, 100, 101, 110\\};\n\\end{array}\n\\]\nbut they differ at length $4$:\n\\[\n\t\\begin{array}{lcl}\n\t\t\\L^{(2,1,1,\\dots)}_4\t\t&=&\t\\{0010, 0100, 0101, 0110, 1001, 1010, 1011, 1101\\},\\\\[4pt]\n\t\t\\L^{(1,1,1,\\dots)}_4\t\t&=&\t\\{0010, 0100, 0101, 0110, 1001, 1010, 1011, 1101, 0011, 1100\\}.\n\t\\end{array}\n\\]\nHence, in this case Proposition~\\ref{prop-words-distinct-enum} holds with $M=4$. We conclude this section by proving Proposition~\\ref{prop-words-distinct-enum}, and then we begin translating Pouzet's construction to the permutation context in the next section.\n\n\\begin{proof}[Proof of Proposition~\\ref{prop-words-distinct-enum}]\nLet $(s_k)$ and $(t_k)$ be as in the statement of the result, and choose $I$ so that~${s_i=t_i}$ for all indices $i<I$, but $s_I<t_I$. We claim that we may take ${M=2^{I}s_1s_2\\cdots s_I+2}$. Note that~$M\\ge 4$.\nFor convenience, set~$\\alpha=\\alpha^{\\exparen{s_k}}_{I}$, and note that $|\\alpha|=2^{I}s_1\\cdots s_{I-1}$, and that~${M=s_I|\\alpha|+2}$.\n\nFirst consider a word~$w$ of length $i<M$ in~$\\L^{\\exparen{s_k}}$, and let $j>I$ be such that~$\\alpha_j^{\\exparen{s_k}}$ contains~$w$. Now view~$\\alpha_j^{\\exparen{s_k}}$ as a sequence of concatenations of~$\\alpha^{s_I}$ and~$\\overline{\\alpha}^{s_I}$. Since~$w$ has length at most $s_I|\\alpha|+1$, it follows that~$w$ embeds in~$\\alpha_j^{\\exparen{s_k}}$ in at most two terms of this concatenation. That is,~$w$ appears as a factor in one of the following words:\n\\[\n\t\\alpha^{s_I}\\alpha^{s_I},\\quad\n\t\\alpha^{s_I}\\overline{\\alpha}^{s_I},\\quad\n\t\\overline{\\alpha}^{s_I}\\alpha^{s_I},\\quad\n\t\\overline{\\alpha}^{s_I}\\overline{\\alpha}^{s_I}\n\\]\nIn fact, containment in one of these four words is a precise characterization of the words of length at most $M-1$ in~$\\L^{\\exparen{s_k}}$, since all four words appear in~$\\alpha_{I+3}^{\\exparen{s_k}}$:\n\\[\n\t\\alpha_{I+3}^{\\exparen{s_k}} = \\big(\n\t\t\\left(\\alpha^{s_I}\\overline{\\alpha}^{s_I}\\right)^{s_{I+1}}\n\t\t\\left(\\overline{\\alpha}^{s_I}\\alpha^{s_I}\\right)^{s_{I+1}}\\big)^{s_{I+2}}\n\t\\big(\n\t\t\\left(\\overline{\\alpha}^{s_I}\\alpha^{s_I}\\right)^{s_{I+1}}\n\t\t\\left(\\alpha^{s_I}\\overline{\\alpha}^{s_I}\\right)^{s_{I+1}}\\big)^{s_{I+2}}\n\\]\nFurthermore, since $t_I > s_I$, all four of these words also appear in~$\\L^{\\exparen{t_k}}$, and this establishes that~$\\L^{\\exparen{s_k}}$ and~$\\L^{\\exparen{t_k}}$ contain the same words up to length $M-1$.\n\nWe now turn our attention to the words of length $M$. First, any word~$w$ of length $M$ that embeds in one of the four words\n\\[\n\t\\alpha^{s_I}\\alpha^{s_I},\\quad\n\t\\alpha^{s_I}\\overline{\\alpha}^{s_I},\\quad\n\t\\overline{\\alpha}^{s_I}\\alpha^{s_I},\\quad\n\t\\overline{\\alpha}^{s_I}\\overline{\\alpha}^{s_I}\n\\]\nwill lie in both~$\\L^{\\exparen{s_k}}$ and~$\\L^{\\exparen{t_k}}$, by the same argument as before. \nAny other word of length $M$ must be formed from a copy of~$\\alpha^{s_I}$ or~$\\overline{\\alpha}^{s_I}$, with exactly one letter before and one after. That is, the only remaining words to consider are the following:\n\\begin{gather*} \n0\\alpha^{s_I}0,\\quad\n1\\alpha^{s_I}0,\\quad\n0\\alpha^{s_I}1,\\quad\n1\\alpha^{s_I}1,\\\\\n0\\overline{\\alpha}^{s_I}0,\\quad\n1\\overline{\\alpha}^{s_I}0,\\quad\n0\\overline{\\alpha}^{s_I}1,\\quad\n1\\overline{\\alpha}^{s_I}1.\t\n\\end{gather*}\nLet us assume that $I$ is even; the case where $I$ is odd is analogous. By Observation~\\ref{obs-last-letters}, the word~$\\alpha$ both begins and ends with 0. The following table summarizes whether each of the eight words above belongs to~$\\L^{\\exparen{s_k}}$ and~$\\L^{\\exparen{t_k}}$, and if so illustrates how it arises (note that the words specified in the second and third columns are factors of~$\\alpha_{I+3}^{\\exparen{s_k}}$ and~$\\alpha_{I+3}^{\\exparen{t_k}}$, respectively.\n\n\\begin{center}\n\\begin{tabular}{c@{\\qquad}l@{\\qquad}l}\nword \t\t\t\t&in~$\\L^{\\exparen{s_k}}$, factor of\t&in~$\\L^{\\exparen{t_k}}$, factor of\\\\\n\\hline\\\\[-10pt]\n$0\\alpha^{s_I}0$\t&$\\overline{\\alpha}^{s_I}\\overline{\\alpha}^{s_I}$ (see below)\t\t\t\t&$\\alpha^{t_I}\\alpha^{t_I}$\\\\\n$1\\alpha^{s_I}0$\t&$\\overline{\\alpha}^{s_I}\\alpha^{s_I}\\alpha^{s_I}$\t&$\\overline{\\alpha}^{t_I}\\alpha^{t_I}$\\\\\n$0\\alpha^{s_I}1$\t&$\\alpha^{s_I}\\alpha^{s_I}\\overline{\\alpha}^{s_I}$\t&$\\alpha^{t_I}\\overline{\\alpha}^{t_I}$\\\\\n$1\\alpha^{s_I}1$\t&$\\overline{\\alpha}^{s_I}\\alpha^{s_I}\\overline{\\alpha}^{s_I}$&Not in set (see below)\\\\\n$0\\overline{\\alpha}^{s_I}0$\t&$\\alpha^{s_I}\\overline{\\alpha}^{s_I}\\alpha^{s_I}$\t&Not in set (see below)\\\\\n$1\\overline{\\alpha}^{s_I}0$\t&$\\overline{\\alpha}^{s_I}\\overline{\\alpha}^{s_I}\\alpha^{s_I}$\t&$\\overline{\\alpha}^{t_I}\\alpha^{t_I}$\\\\\n$0\\overline{\\alpha}^{s_I}1$\t&$\\alpha^{s_I}\\overline{\\alpha}^{s_I}\\overline{\\alpha}^{s_I}$\t&$\\alpha^{t_I}\\overline{\\alpha}^{t_I}$\\\\\n$1\\overline{\\alpha}^{s_I}1$\t&$\\alpha^{s_I}\\alpha^{s_I}$ (see below)\t\t&$\\overline{\\alpha}^{t_I}\\overline{\\alpha}^{t_I}$\n\\end{tabular}\n\\end{center}\nThere remain four entries in the above table to consider. Let us begin first with the word $0\\alpha^{s_I}0$. Proposition~\\ref{prop-alpha-i-embeddings} tells us that~$\\alpha$ embeds in the middle of~$\\overline{\\alpha}\\alphabar$, and thus~$\\alpha^{s_I}$ embeds in the middle of~$\\overline{\\alpha}^{s_I}\\overline{\\alpha}^{s_I}$. Furthermore, the letter immediately to the left of this embedding is the last letter of~$\\overline{\\alpha}_{I-1}^{\\exparen{s_k}}$, which is 0 by Observation~\\ref{obs-last-letters} (since we are assuming that $I-1$ is odd). Similarly, the first letter after this embedding is the first letter of~$\\overline{\\alpha}_{I-1}^{\\exparen{s_k}}$, which is also 0, and hence $0\\alpha^{s_I}0$ is a factor of~$\\overline{\\alpha}^{s_I}\\overline{\\alpha}^{s_I}$.\n\nA similar argument can be applied to show that $1\\overline{\\alpha}^{s_I}1\\in\\L^{\\exparen{s_k}}$, and this establishes that~${\\L_M^{\\exparen{s_k}}\\supseteq \\L_M^{\\exparen{t_k}}}$.\n\nOur final task is to show that neither $1\\alpha^{s_I}1$ nor $0\\overline{\\alpha}^{s_I}0$ lies in~$\\L^{\\exparen{t_k}}$. We consider only $1\\alpha^{s_I}1$, the case for the other word being entirely analogous. \n\nBy Proposition~\\ref{prop-alpha-i-embeddings}, the only factors of~$\\alpha_j^{\\exparen{t_k}}$ that are equal to~$\\alpha$ are either given by the \\emph{letter}~$\\alpha$, or appear in the middle of the pair of letters~$\\overline{\\alpha}\\alphabar$, when we express~$\\alpha_j^{\\exparen{t_k}}$ as a word over $\\{\\alpha,\\overline{\\alpha}\\}$. Thus, the binary word~$\\alpha^{s_I}$ appears as a factor of~$\\alpha_j^{\\exparen{t_k}}$ only as the sequence of letters~$\\alpha^{s_I}$, or in the middle of~$\\overline{\\alpha}^{s_I+1}$.\nIn this latter embedding, the letter in~$\\overline{\\alpha}^{s_I+1}$ that lies immediately to the left of such an embedding is the last letter of~$\\overline{\\alpha}_{I-1}^{\\exparen{s_k}}$, which we have already established is equal to 0. Thus $1\\alpha^{s_I}1$ does not appear in the middle of~$\\overline{\\alpha}^{s_I+1}$.\n\nThe only remaining possibility is that $1\\alpha^{s_I}1$ embeds into~$\\alpha_j^{\\exparen{t_k}}$ precisely as~$\\alpha^{s_I}$, together with one extra letter on either side. Now~$\\alpha_j^{\\exparen{t_k}}$ can be written as a word comprising factors of the form~$\\alpha^{t_I}$ and~$\\overline{\\alpha}^{t_I}$. Since $t_I > s_I$, we are forced to embed either the letter 1 on the left of $1\\alpha^{s_I}1$ as the rightmost letter of~$\\alpha$, or the letter 1 on the right of $1\\alpha^{s_I}1$ as the leftmost letter of~$\\alpha$. Since~$\\alpha$ both begins and ends with 0, however, neither case is possible. Thus $1\\alpha^{s_I}1$ does not embed into~$\\alpha_j^{\\exparen{t_k}}$, from which we conclude that $1\\alpha^{s_I}1\\not\\in\\L^{\\exparen{t_k}}$, as required.\n\\end{proof}\n\n\n\\section{Rightward-Yearning Pin Sequences}\n\\label{sec-rightward-yearning}\n\nOur tool for translating the results about Pouzet's languages~$\\L^{\\exparen{s_k}}$ to the permutation context are the pin sequences first introduced by Brignall, Huczynska, and Vatter~\\cite{brignall:decomposing-sim:}. These are best described with a pictorial description of the permutation pattern order. The \\emph{plot} of the permutation~$\\pi$ is the set $\\{(i,\\pi(i))\\}$ of points. Clearly every plot of a permutation is \\emph{generic} in the sense that no two of its points share the same $x$- or $y$-coordinate. Conversely, every finite generic set of points in the plane is order isomorphic to the plot of a unique permutation, in the sense that two sets of points in the plane are \\emph{order isomorphic} if the axes can be stretched and shrunk to transform one of the sets into the other.\n\nAn \\emph{axis-parallel rectangle} is any rectangle in the plane with sides parallel to the $x$- and $y$-axes. The \\emph{rectangular hull} of a set of points in the plane is defined as the smallest axis-parallel rectangle containing them. Given a sequence $(p_1, \\dots, p_i)$ of points in the plane, a \\emph{proper pin} for this sequence is a point $p$ that lies outside their rectangular hull and \\emph{separates} $p_i$ from $\\{p_1,\\dots,p_{i-1}\\}$, meaning that $p$ lies either horizontally or vertically between $p_i$ and the rectangular hull of $\\{p_1,\\dots,p_{i-1}\\}$. A \\emph{proper pin sequence} is then constructed by starting with two points $p_1$ and $p_2$ (whose placement we discuss later), choosing $p_3$ to be a proper pin for $(p_1,p_2)$, then choosing $p_4$ to be a proper pin for $(p_1,p_2,p_3)$, and so on. We describe pins as either \\emph{left}, \\emph{right}, \\emph{up}, or \\emph{down} based on their position relative to the rectangular hull of $\\{p_1,\\dots,p_{i}\\}$. Note that the direction of a pin uniquely specifies its position relative to the previous points in a pin sequence. We specify pin sequences with the alphabet $\\{\\mathsf{l},\\r,\\u,\\d\\}$.\n\nIt follows from their definition that proper pin sequences must turn by $90^\\circ$ with each pin. In other words, an up pin may be immediately followed by a left or a right pin, but not by another up pin or by a down pin. As our goal is to encode binary strings as proper pin sequences, we \\emph{could} therefore translate each $0$ into left or down and each $1$ into right or up, with the choices determined by the previous pin. If we were to do this, we might for example have the correspondence\n\\[\n\t01101001\n\t\\mapsto\n\t\\mathsf{drululdr}.\n\\]\n\nWhile we suspect that our results would remain true with this translation from binary words to proper pin sequences, they would undoubtably be more troublesome to prove. Instead, we restrict our attention to \\emph{rightward-yearning pin sequences}, which we define to be the pin sequences made up only of right, up, and down pins. This means, because proper pin sequences must turn by $90^\\circ$ with every pin, that every second pin in a rightward-yearning pin sequence must be a right pin. For the other pins, we translate $0$ to be a down pin and $1$ to be an up pin. \nThus in this correspondence, we would have\n\\[\n\t01101001\n\t\\mapsto\n\t\\mathsf{drururdrurdrdrur}.\n\\]\n\nIn fact, we encode our pin sequences slightly differently than this. For reasons that will become apparent later, we subscript the letter encoding each right pin by the type of pin immediately preceding it. This enlarges our alphabet to $\\{\\rd,\\ru,\\d,\\u\\}$, and our previous example becomes\n\\[\n\t01101001\n\t\\mapsto\n\t\\mathsf{d r_d u r_u u r_u d r_d u r_u d r_d d r_d u r_u}.\n\\]\n(This pin sequence is plotted in Figure~\\ref{fig-rightward-yearning}.) We stress that the subscripts on our encodings of down pins do not affect the actual pin sequences; these subscripts instead inform us where the corresponding points lie in the plane.\n\n\\begin{figure}\n\\begin{center}\n\\begin{tikzpicture}[scale=0.3]\n\\node[openpoint] (orig) at (0,-0.5) {};\n\\foreach \\y [count=\\x] in {-2,1,-1,3,0,-4,2,5,-3,-6,4,-8,-5,7,-7,6}\n\t\\node[point] (\\y) at (\\x,\\y) {};\n\\foreach \\node [count=\\n,remember=\\node as \\prevnode (initially orig)] in {-2,-1,1,0,3,2,-4,-3,5,4,-6,-5,-8,-7,7,6} {\n\t\\ifodd\\n\n\t\t\\draw (\\prevnode-|\\node) -- ++(0,0.5)-- ++(0,-1) -- (\\node);\n\t\\else\n\t\t\\draw (\\prevnode|-\\node) -- ++(-0.5,0) -- (\\node);\n\t\\fi\n\t}\n\\end{tikzpicture}\n\\end{center}\n\\caption{The rightward-yearning pin sequence associated to the word $\\mathsf{d r_d u r_u u r_u d r_d u r_u d r_d d r_d u r_u}$.}\n\\label{fig-rightward-yearning}\n\\end{figure}\n\nIt remains to explain how to start a pin sequence. In the present work, we start every pin sequence with a point called an \\emph{origin} and labelled by $p_0$. \\emph{Importantly, we do not consider the origin $p_0$ to be part of the resulting rightward-yearning pin sequence.} \n\nFor the first real pin, $p_1$, if it has encoding $\\u$ or $\\mathsf{r_u}$, then $p_1$ appears above and to the right of $p_0$. Analogously, if $p_1$ has encoding $\\d$ or $\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace$, then it is placed below and to the right of $p_0$. In either case, the second pin $p_2$ slices the rectangular hull of $(p_0,p_1)$ in the direction indicated by its encoding.\n\nAs our pin sequences progress only to the right, this origin $p_0$ lies to the left of all other pins of the pin sequence, and will lie below all pins whose encoding is $\\mathsf{u}$ or $\\mathsf{r_u}$, and above all pins whose encoding is $\\mathsf{d}$ or $\\mathsf{r_d}$. In this way, the origin partitions each of the entries of the pin sequence into two groups: those above and below the $x$-axis. This means that our pin sequences could be considered a very simple type of \\emph{grid pin sequence} (as first considered by Brignall~\\cite{brignall:grid-classes-an:}), but we do not adopt this viewpoint.\n\n\nGiven any word~$w\\in\\{\\rd,\\ru,\\d,\\u\\}^n$ in which the letters alternate between $\\{\\d,\\u\\}$ and $\\{\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace,\\mathsf{r_u}\\}$, we take the \\emph{rightward-yearning pin sequence defined by~$w$} to be the permutation $\\tau_w^\\circ$ that is order isomorphic to the set $\\{p_1,p_2,\\dots,p_n\\}$ of points defined by the word~$w$. Thus $|\\tau_w^\\circ|=|w|=n$.\n\nAs is demonstrated in Section~\\ref{sec-decomp}, in order to discuss subpermutations of rightward-yearning pin sequences, it is necessary to also introduce the permutations $\\tau_w^\\bullet$ that include the origin as an extra point. We take $\\tau^\\bullet_w$ to be the permutation that is order isomorphic to the set $\\{p_0,p_1,p_2,\\dots,p_n\\}$ of points defined by the word~$w$, so $|\\tau_w^\\bullet|=|w|+1=n+1$.\n\n\n\\section{The Construction}\\label{sec-construction}\n\nWe now have the necessary background to describe the family of permutation classes used to prove Theorem~\\ref{thm-wqo-not-algebraic}.\n\nGiven a binary word~$w\\in\\{0,1\\}^\\ast$, we denote by $\\rho(w)$ the word (of twice the length as~$w$) over the alphabet $\\{\\rd,\\ru,\\d,\\u\\}$ that is obtained by performing the substitutions\n\\[\n\t0\\leftarrow \\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\n\t\\quad\n\t\\text{and}\n\t\\quad\n\t1\\leftarrow \\u\\mathsf{r_u};\n\\]\nthat is, replacing occurrences of $0$ by $\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace$ and occurrences of $1$ by $\\u\\mathsf{r_u}$.\nWe are frequently interested only in the image of $\\rho$ and factors of those words, and so we define the language\n\\begin{align*}\n\t\\P\t\t\t&=\n\t\t\\text{the factor closure of $\\rho(\\{0,1\\}^\\ast)$}.\\\\\n\\intertext{Our construction itself requires us to restrict to the binary words of Section~\\ref{sec-pouzet-factors}, for which we recall that}\n\t\\L^{\\exparen{s_k}}\t&=\n\t\t\\text{the factor-closed wqo languages of Section~\\ref{sec-pouzet-factors}}.\\\\\n\\intertext{We then consider the factors of the image under $\\rho$ of those languages, and the class of permutations to which they correspond:}\n\t\\P^{\\exparen{s_k}}\t&=\n\t\t\\text{the factor closure of $\\rho(\\L^{\\exparen{s_k}})$ and}\\\\\n\t\\mathcal{C}^{\\exparen{s_k}}\t&=\n\t\t\\text{the downward closure of $\\{\\psi_w^\\circ\\::\\: w\\in\\P^{\\exparen{s_k}}\\}$}.\n\\end{align*}\n\nIt follows from the definitions that $\\P$,~$\\L^{\\exparen{s_k}}$, and $\\P^{\\exparen{s_k}}$ are closed under taking factors, while $\\mathcal{C}^{\\exparen{s_k}}$ is closed under taking subpermutations, and is thus a permutation class. What remains to do is to establish that the classes $\\mathcal{C}^{\\exparen{s_k}}$ are wqo, and that if the sequences $(s_k)$ and $(t_k)$ differ, then the resulting classes $\\mathcal{C}^{\\exparen{s_k}}$ and $\\mathcal{C}^{\\exparen{t_k}}$ have different enumerations. These two results will follow by lifting the analogous results about the languages~$\\L^{\\exparen{s_k}}$, Propositions~\\ref{prop-Lsk-wqo} and \\ref{prop-words-distinct-enum}, to this context. In order to do this, we must first establish a decomposition result for the members of $\\mathcal{C}^{\\exparen{s_k}}$ in the next section. Before that, we make a simple observation now that we have the terminology to express it.\n\n\\begin{proposition}\n\\label{prop-Psk-to-Csk}\nSuppose that $v$ is a factor of~$w$ for words $v,w\\in\\P$. Then the permutation~$\\psi_w^\\circ$ contains the permutation~$\\psi_v^\\circ$ and the permutation~$\\psi_w^\\bullet$ contains the permutation~$\\psi_v^\\bullet$.\n\\end{proposition}\n\\begin{proof}\nFix a factor of $v$ in $w$. The pins of $\\psi_w^\\circ$ corresponding to this factor are in the same relative position to each other as the pins of~$\\psi_v^\\circ$, which verifies the claim for this pair of permutations. For the version of the result with origins, we note that the origin in~$\\psi_w^\\bullet$ is in the same relative position to the pins that correspond to a factor of $v$ in~$w$ as the origin in~$\\psi_v^\\bullet$ is in relative to the rest of the pins of that permutation.\n\\end{proof}\n\n\n\\section{A Decomposition}\n\\label{sec-decomp}\n\nWe frame the discussion in this section as considering the effect of deleting points from rightward-yearning pin sequences. There are essentially three types of pins we can delete: the first pin, the last pin, or an interior pin. We handle these cases below in order of their difficulty, for a word~$w\\in\\{\\rd,\\ru,\\d,\\u\\}^n$.\n\\begin{itemize}\n\\item To delete the last pin from a pin sequence, we simply don't create it in the first place. Thus the permutation obtained from~$\\psi^\\circ_w$ by deleting the point corresponding to $p_n$ is~$\\psi^\\circ_{w(1)\\cdots w(n-1)}$.\n\\item The same argument as above holds for the first pin, so the permutation obtained from~$\\psi^\\circ_w$ by deleting the point corresponding to the first pin is~$\\psi^\\circ_{w(2)\\cdots w(n)}$. \n\\item Deleting the $i$\\th pin from~$\\psi^\\circ_w$ for some index $2\\le i\\le n-2$ corresponds to replacing the origin in the permutation~$\\psi^\\bullet_{w(i+1)\\cdots w(n)}$ with the permutation~$\\psi^\\circ_{w(1)\\cdots w(i-1)}$.\n\\end{itemize}\nWe call the operation in this last case \\emph{inflating the origin}, and this case is the reason we introduced the permutations~$\\psi^\\bullet_w$ in Section~\\ref{sec-rightward-yearning} in the first place. The process of removing pins from the permutations~$\\psi^\\bullet_w$ is also needed, but is entirely analogous to the above, and will be handled once we have introduced some additional notation.\n\nInflating origins is similar to the sum of two permutations. Recall that given a permutation~$\\sigma$ of length $m$ and another permutation~$\\psi$ of length $n$, their \\emph{sum} is the permutation denoted by~$\\sigma\\oplus\\tau$ and defined by\n\\[\n\t(\\sigma\\oplus\\tau)(i)\n\t=\n\t\\left\\{\\begin{array}{ll}\n\t\\sigma(i)&\\text{if $1\\le i\\le m$,}\\\\\n\t\\tau(i-m)+m&\\text{if $m+1\\le i\\le m+n$.}\n\t\\end{array}\\right.\n\\]\n\nThe origin in~$\\psi^\\bullet_w$ is always the leftmost point, so we define the more general operation of inflating the first entry of a permutation. Suppose that~$\\sigma$ is a permutation of length $m$ and that $\\tau$ is a permutation of length $n+1$. Then~$\\sigma\\boxplus\\tau$ is the permutation of length $m+n$ obtained by inflating the first entry of $\\tau$ by~$\\sigma$. Formulaically, it is defined by\n\\[\n\t(\\sigma\\boxplus\\tau)(i)\n\t=\n\t\\left\\{\\begin{array}{ll}\n\t\\sigma(i)+\\tau(1)-1&\\text{if $1\\le i\\le m$,}\\\\\n\t\\tau(i-m+1)&\\text{if $m< i\\le m+n$ and $\\tau(i-m+1)<\\tau(1)$, and}\\\\\n\t\\tau(i-m+1)+m-1&\\text{if $m< i\\le m+n$ and $\\tau(i-m+1)>\\tau(1)$.}\n\t\\end{array}\\right.\n\\]\nSee Figure~\\ref{fig-interior-pin} for an example.\n\n\\begin{figure}\n{\\centering\n\\begin{tikzpicture}[scale=0.25]\n\\node[openpoint] (orig) at (0,0) {};\n\\foreach \\y [count=\\x] in {-2,2,-1,-4,1,4,-3,-6,3,-5}\n\t\\node[point] (\\y) at (\\x,\\y) {};\n\\foreach \\node [count=\\n,remember=\\node as \\prevnode (initially orig)] in {-2,-1,2,1,-4,-3,4,3,-6,-5} {\n\t\\ifodd\\n\n\t\t\\draw (\\prevnode-|\\node) -- ++(0,0.5)-- ++(0,-1) -- (\\node);\n\t\\else\n\t\t\\draw (\\prevnode|-\\node) -- ++(-0.5,0) -- (\\node);\n\t\\fi\n\t}\n\\node[openpoint,minimum width=4pt+3pt] at (-4) {};\n\\node[draw=none,fill=none] at (12,-1) {$\\rightarrow$};\n\\begin{scope}[shift={(15,-0.5)}]\n\\draw[fill=black!10,draw=none] (-0.5,-2.5) rectangle (4.5,2.5);\n\\node[openpoint] (orig) at (0,0) {};\n\\coordinate (-40) at (4,-4);\n\\foreach \\y [count=\\x] in {-2,2,-1,1\n\t\\node[point] (\\y) at (\\x,\\y) {};\n\\foreach \\y [count=\\x] in {4,-3,-5,3,-4}\n\t\\node[point] (\\y) at (\\x+4,\\y) {};\n\\foreach \\node [count=\\n,remember=\\node as \\prevnode (initially orig)] in {-2,-1,2,1,4,3} \n\t\\ifodd\\n\n\t\t\\draw (\\prevnode-|\\node) -- ++(0,0.5)-- ++(0,-1) -- (\\node);\n\t\\else\n\t\t\\draw (\\prevnode|-\\node) -- ++(-0.5,0) -- (\\node);\n\t\\fi\n\t}\n\\foreach \\node [count=\\n,remember=\\node as \\prevnode (initially -40)] in {-3,4,3,-5,-4} {\n\t\\ifodd\\n\n\t\t\\draw (\\prevnode|-\\node) -- ++(-0.5,0) -- (\\node);\n\t\\else\n\t\t\\draw (\\prevnode-|\\node) -- ++(0,0.5)-- ++(0,-1) -- (\\node);\n\t\\fi\n\t}\n\\end{scope}\n\\end{tikzpicture}\\par}\n\\caption{Deleting the circled interior pin from~$\\psi^\\circ_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u\\mathsf{r_u}\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u\\mathsf{r_u}\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace}$ results in~$\\psi^\\circ_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u\\mathsf{r_u}}\\boxplus\\psi^\\bullet_{\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u\\mathsf{r_u}\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace}$.}\\label{fig-interior-pin}\n\\end{figure}\n\nFrom our previous discussion, it follows that if we delete the $i$th pin from~$\\psi^\\circ_w$, where~$w\\in\\{\\rd,\\ru,\\d,\\u\\}^{n}$ and $2\\le i\\le n-1$, then we obtain the permutation\n\\[\n\t\\psi^\\circ_{w(1)\\cdots w(i-1)}\\boxplus \\psi^\\bullet_{w(i+1)\\cdots w(n)}.\n\\]\nIndeed, letting $\\varepsilon$ denote the empty word or empty permutation (as dictated by the context), and with the understanding that~$\\psi^\\circ_\\varepsilon=\\varepsilon$ while~$\\psi^\\bullet_\\varepsilon=1$, we see that for \\emph{any} $1\\le i\\le n$, the result of deleting the point corresponding to the $i$th pin $p_i$ from~$\\psi^\\circ_w$ is~$\\psi^\\circ_{w(1)\\cdots w(i-1)}\\boxplus\\psi^\\bullet_{w(i+1)\\cdots w(n)}$.\n\nAs noted earlier, we must also describe how to delete points from the permutations~$\\psi^\\bullet_w$, which follows by the same analysis. If we delete the origin $p_0$ from~$\\psi^\\bullet_w$, we obviously obtain the permutation~$\\psi^\\circ_w$.\nOtherwise, if~$w\\in\\{\\rd,\\ru,\\d,\\u\\}^{n}$ and $1\\le i\\le n$, then the result of deleting the point corresponding to the $i$th pin $p_i$ from~$\\psi^\\bullet_w$ is\n\\[\n\t\\psi^\\bullet_{w(1)\\cdots w(i-1)}\\boxplus\\psi^\\bullet_{w(i+1)\\cdots w(n)}.\n\\]\n\nOur next result puts this decomposition in the form we need it later. Note that we needn't include parentheses in the statement of this result because the operation $\\boxplus$ is associative.\n\n\\begin{proposition}\\label{prop-boxplus-decomp}\nFor any subpermutation~$\\pi$ of the rightward-yearning pin sequence~$\\psi^\\circ_w$, there exist nonempty words~$w_1$, $\\dots$,~$w_k\\in\\P$, each appearing as a factor in~$w$, such that\n\\[\n\t\\pi=\n\t\\psi^\\circ_{w_1}\\boxplus\\psi^\\bullet_{w_2}\\boxplus\\cdots\\boxplus\\psi^\\bullet_{w_k}.\n\\]\n\\end{proposition}\n\n\\begin{proof}\n\tFix a particular embedding of~$\\pi$ in~$\\psi_w^\\circ$, and delete the entries of~$\\psi_w^\\circ$ that are not involved in this embedding one at a time. At each step of this process, we have a permutation of the form~$\\psi^\\circ_{u_1}\\boxplus\\psi^\\bullet_{u_2}\\boxplus\\cdots\\boxplus\\psi^\\bullet_{u_\\ell}$ for some choice of words $u_1$, $\\dots$, $u_\\ell\\in \\P$ (which we may assume, by induction, appear as factors in the word~$w$), from which we must delete some specific entry. This entry must be a non-origin pin of either~$\\psi^\\circ_{u_1}$ or one of the~$\\psi^\\bullet_{u_j}$, and we've shown above that any such deletion results in another permutation of the desired form. The fact that each of the resulting words is a factor of~$w$ also follows by this inductive argument.\n\\end{proof}\n\n\nWe are now able to describe the decomposition of all permutations in some class $\\mathcal{C}^{\\exparen{s_k}}$ in terms of permutations defined by words from the language $\\P^{\\exparen{s_k}}$.\n\n\\begin{theorem}\n\\label{thm-Csk-description}\nLet $(s_k)$ be a sequence of positive integers. The class $\\mathcal{C}^{\\exparen{s_k}}$ consists precisely of those permutations~$\\pi$ that can be expressed as\n\\[\n\t\\pi=\\psi^\\circ_{v_1}\\boxplus\\psi^\\bullet_{v_2}\\boxplus\\cdots\\boxplus\\psi^\\bullet_{v_\\ell}\n\\]\nfor words $v_1$, $v_2$, $\\dots$, $v_\\ell\\in\\P^{\\exparen{s_k}}$ with $|v_1|+|v_2|+\\cdots+|v_\\ell|=|\\pi|$.\n\\end{theorem}\n\n\\begin{proof}\nLet~$\\pi\\in\\mathcal{C}^{\\exparen{s_k}}_n$. By the definition of $\\mathcal{C}^{\\exparen{s_k}}$, there is some word~$w\\in\\P^{\\exparen{s_k}}$ such that~$\\pi$ is contained in the permutation~$\\psi^\\circ_w$. By Proposition~\\ref{prop-boxplus-decomp}, it follows that there exist words $v_1$, $v_2$, $\\dots$, $v_\\ell$, each appearing as a factor of~$w$, such that \n\\[\n\t\\pi=\\psi^\\circ_{v_1}\\boxplus\\psi^\\bullet_{v_2}\\boxplus\\cdots\\boxplus\\psi^\\bullet_{v_\\ell}.\n\\]\nSince each $v_i$ is a factor of~$w\\in\\P^{\\exparen{s_k}}$, it follows that each $v_i\\in\\P^{\\exparen{s_k}}$. It is similarly clear that $|v_1|+|v_2|+\\cdots+|v_\\ell|=|\\pi|$.\n\nConversely, we consider a permutation~$\\pi$ as in the statement of the theorem and appeal to the properties of the language~$\\L^{\\exparen{s_k}}$. By definition, for each $v_i\\in\\P^{\\exparen{s_k}}$, there exists an integer $j_i$ such that $v_i$ is a factor of $\\rho(\\alpha_{j_i}^{\\exparen{s_k}})$. Set $m=\\max\\{j_1,\\dots,j_\\ell\\}$, so that each of $v_1$, $\\dots$, $v_\\ell$ appears as a factor in $\\rho(\\alpha_m^{\\exparen{s_k}})$.\n\nLetting $f^{\\exparen{s_k}}$ denote the function from Proposition~\\ref{prop-contains-alpha}, we see from that result that every (binary) word of length at least $f^{\\exparen{s_k}}(m)$ in~$\\L^{\\exparen{s_k}}$ contains $\\alpha_m^{\\exparen{s_k}}$. It follows that every word in $\\P^{\\exparen{s_k}}$ of length at least $2f^{\\exparen{s_k}}(m)+2$ contains $\\rho(\\alpha_m^{\\exparen{s_k}})$, and thus also contains all of $v_1$, $v_2$, $\\dots$, $v_\\ell$. (The ``$+2$'' here is due to the fact that the first and last letter of a word in $\\P$ need not be part of a factor of the form $\\rho(u)$.) It follows that every word in $\\P^{\\exparen{s_k}}$ of length at least $\\ell\\cdot(2f^{\\exparen{s_k}}(m)+2)+(\\ell-1)$ must contain a word~$w$ of the form\n\\[\n\tw = v_1x_1v_2x_2\\cdots x_{\\ell-1}v_\\ell\n\\]\nwhere $x_1$, $\\dots$, $x_{\\ell-1}$ are arbitrary non-empty words. Thus~$\\pi$ is a subpermutation of~$\\psi^\\circ_w$.\n\\end{proof}\n\nIt is tempting to conclude from Theorem~\\ref{thm-Csk-description} that each $\\mathcal{C}^{\\exparen{s_k}}$ is $\\boxplus$-closed in the sense that~${\\sigma,\\tau\\in\\mathcal{C}^{\\exparen{s_k}}}$ implies that~$\\sigma\\boxplus\\tau\\in\\mathcal{C}^{\\exparen{s_k}}$, but we need to be careful: if we simply inflate the first entry of $\\tau$ by~$\\sigma$, then what results is not guaranteed to lie in $\\mathcal{C}^{\\exparen{s_k}}$, since it is not necessarily the case that $\\tau$ can be described in such a way that its first entry can act as a (non-phantom) origin. However, since~${\\tau\\in\\mathcal{C}^{\\exparen{s_k}}}$, Theorem~\\ref{thm-Csk-description} tells us that we can write\n\\[\n\t\\tau=\\psi^\\circ_{v_1}\\boxplus\\psi^\\bullet_{v_2}\\boxplus\\cdots\\boxplus\\psi^\\bullet_{v_\\ell}.\n\\]\nfor some $v_1$, $v_2$, $\\dots$, $v_\\ell$ in $\\P^{\\exparen{s_k}}$, and then Theorem~\\ref{thm-Csk-description} tells us that\n\\[\n\t\\sigma\\boxplus \\psi^\\bullet_{v_1}\\boxplus\\psi^\\bullet_{v_2}\\boxplus\\cdots\\boxplus\\psi^\\bullet_{v_\\ell}\n\t\t\\in\\mathcal{C}^{\\exparen{s_k}}.\n\\]\n\n\n\\section{Indecomposable Permutations}\\label{sec-indecomposable}\n\nOne calls a permutation \\emph{sum decomposable} if it can be expressed as the sum of two shorter permutations, and \\emph{sum indecomposable} otherwise. We analogously call a permutation \\emph{$\\boxplus$-decomposable} if it can be expressed as~$\\sigma\\boxplus\\tau$ for two shorter permutations each of length at least two, and \\emph{$\\boxplus$-indecomposable} otherwise. (We must require that both~$\\sigma$ and $\\tau$ have length at least $2$ to avoid trivial decompositions, because $1\\boxplus\\pi=\\pi\\boxplus 1=\\pi$.)\n\n\\begin{table}\n\\[\n\t\\begin{array}{@{}c@{\\quad}c@{}}\n\t\t\\begin{array}{rcll}\n\t\t\\hline\\\\[-10pt]\n\t\t1\t\t&=&\\psi_\\u^\\circ=\\psi_\\d^\\circ=\\psi_\\r^\\circ\t\t&\\text{$\\boxplus$-indecomposable}\\\\[2pt]\n\t\t\\hline\\\\[-10pt]\n\t\t12\t\t&=&\\psi_{\\r\\d}^\\circ=\\psi_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace}^\\circ\t\t&\\text{$\\boxplus$-indecomposable}\\\\\n\t\t21\t\t&=&\\psi_{\\r\\u}^\\circ=\\psi_{\\u\\mathsf{r_u}}^\\circ\t\t\t&\\text{$\\boxplus$-indecomposable}\\\\[2pt]\n\t\t\\hline\\\\[-10pt]\n\t\t123\t\t&=&12\\boxplus 12\\\\\n\t\t132\t\t&=&\\psi_{\\r\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace}^\\circ=\\psi_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u}^\\circ\t\t\t&\\text{$\\boxplus$-indecomposable}\\\\\n\t\t213\t\t&=&21\\boxplus 12=\\psi_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\d}^\\circ\\\\\n\t\t231\t\t&=&12\\boxplus 21=\\psi_{\\u\\mathsf{r_u}\\u}^\\circ\\\\\n\t\t312\t\t&=&\\psi_{\\u\\mathsf{r_u}\\d}^\\circ=\\psi_{\\r\\u\\mathsf{r_u}}^\\circ\t\t\t&\\text{$\\boxplus$-indecomposable}\\\\\n\t\t321\t\t&=&21\\boxplus 21\\\\[2pt]\n\t\t\\hline\\\\[19.625pt]\n\t\t\\end{array}\n\t&\n\t\t\\begin{array}{rcll}\n\t\t\\hline\\\\[-10pt]\n\t\t1234\t&=&12\\boxplus 12\\boxplus 12\\\\\n\t\t1243\t&=&12\\boxplus 132\\\\\n\t\t1324\t&=&132\\boxplus 12\\\\\n\t\t1342\t&=&\\psi_{\\r\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u}^\\circ\t\t\t\t\t&\\text{$\\boxplus$-indecomposable}\\\\\n\t\t1423\t&=&\\psi_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u\\mathsf{r_u}}^\\circ\t\t&\\text{$\\boxplus$-indecomposable}\\\\\n\t\t1432\t& &\t\t\t\t\t\t\t\t\t&\\text{$\\boxplus$-indecomposable}\\\\[2pt]\n\t\t\\hline\\\\[-10pt]\n\t\t2134\t&=&21\\boxplus 12\\boxplus 12\\\\\n\t\t2143\t&=&21\\boxplus 132\\\\\n\t\t2314\t&=&12\\boxplus 21\\boxplus 12\\\\\n\t\t2341\t&=&12\\boxplus 12\\boxplus 21\\\\\n\t\t2413\t&=&\\psi_{\\u\\mathsf{r_u}\\u\\mathsf{r_u}}^\\circ=\\psi_{\\r\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\d}^\\circ&\\text{$\\boxplus$-indecomposable}\\\\\n\t\t2431\t&=&132\\boxplus 21\\\\[2pt]\n\t\t\\hline\n\t\t\\end{array}\n\t\\end{array}\n\\]\n\\caption{Decompositions of permutations of lengths at most four. An initial letter $\\r$ corresponds to either $\\mathsf{r_u}$ or $\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace$.}\n\\label{table-short-decomps}\n\\end{table}\n\nTable~\\ref{table-short-decomps} shows the decomposition of permutations of lengths at most four, as well as their expressions of the form of~$\\psi_w^\\circ$, for those permutations that can be expressed that way. To cut the number of cases in half, when considering permutations of length four we utilize the fact that these concepts are invariant under \\emph{complementation} of permutations (flipping their plots upside down).\n\nFrom Table~\\ref{table-short-decomps} we see that there are eight $\\boxplus$-indecomposable permutations of length four ($1342$, $1423$, $1432$, $2413$, and their complements). In this table, an initial letter $\\r$ corresponds to either $\\mathsf{r_u}$ or $\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace$, so of the permutations of length four, only $1423$ and its complement $4132$ have unique representations of the form~$\\psi_w$, while the other six $\\boxplus$-indecomposable permutations do not. The permutation $1432$ and its complement $4123$ in fact cannot be expressed in terms of $\\boxplus$ and permutations of the form~$\\psi^\\circ_w$ at all. This means that these two permutations are not subpermutations of any rightward-yearning pin sequence, and thus they do not arise in the classes we construct.\n\nWe show next that all sufficiently long rightward-yearning pin sequences are $\\boxplus$-indecomposable. The bound $|w|\\ge 4$ is necessary because, as shown in Table~\\ref{table-short-decomps},~$\\psi_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\d}^\\circ=213=21\\boxplus 12$ and, symmetrically,~$\\psi_{\\u\\mathsf{r_u}\\u}^\\circ=231=12\\boxplus 21$.\n\n\\begin{lemma}\\label{lem-pins-box-indecomposable}\nSuppose that~$w\\in\\P$. If $|w|\\ge 3$, then~$\\psi_w^\\bullet$ is $\\boxplus$-indecomposable. If $|w|\\ge 4$, then~$\\psi_w^\\circ$ is also $\\boxplus$-indecomposable.\n\\end{lemma}\n\n\n\\begin{proof}\nWe proceed by induction on the length of~$w$. The base case for the claim about~$\\psi_w^\\circ$ follows from examining Table~\\ref{table-short-decomps} for~$\\psi_w^\\circ$. For the claim about~$\\psi_w^\\bullet$, the base case follows by the following computations:~$\\psi^\\bullet_{\\u\\mathsf{r_u}\\u}=1342$, $\\psi^\\bullet_{\\u\\mathsf{r_u}\\d}=\\psi^\\bullet_{\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u\\mathsf{r_u}}=2413$, $\\psi^\\bullet_{\\mathsf{r_u}\\u\\mathsf{r_u}}=1423$, $\\psi^\\bullet_{\\mathsf{r_u}\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace}=\\psi^\\bullet_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u}=3142$, $\\psi^\\bullet_{\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\d}=4213$, and $\\psi^\\bullet_{\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace}=4132$.\n\nNow let $v$ denote the prefix of~$w$ comprising all but the last letter, and suppose by induction that~$\\psi_u^\\bullet$ (resp.,~$\\psi_u^\\circ$) is $\\boxplus$-indecomposable.\nThe only way in which~$\\psi_w^\\circ$ (resp.,~$\\psi_{w}^\\bullet$) could be $\\boxplus$-decomposable is if the last letter corresponds to a point that is inserted northeast or southeast of all of~$\\psi_{v}^\\circ$ (resp.,~$\\psi_{v}^\\bullet$), or if it is inserted next to the origin. Neither case is possible since pins must separate the predecessor pin from all the earlier ones. This means that the final pin cannot be placed in the top-right or bottom-right corner of~$\\psi_w^\\circ$ (resp.\\,$\\psi_{w}^\\bullet$), and also, since $|\\psi_v^\\circ|\\ge 4$ (resp., $|\\psi_v^\\bullet|\\ge 4$), there are at least two other pins whose positions come between the origin and the final pin. Thus~$\\psi_w^\\circ$ and~$\\psi_w^\\bullet$ are $\\boxplus$-indecomposable.\n\\end{proof}\n\nNext we show that, except for a small number of shorter permutations, all of the $\\boxplus$-indecomposable permutations that arise in our classes $\\mathcal{C}^{\\exparen{s_k}}$ are of the form~$\\psi^\\circ_w$.\n\n\\begin{proposition}\\label{prop-boxplus-indecomp}\nA subpermutation~$\\pi$ of a rightward-yearning pin sequence is $\\boxplus$-indecomposable if and only if~$\\pi\\in\\{1,12,21,132,312\\}$ or~$\\pi=\\psi_w^\\circ$ for some word~$w\\in\\P$ with $|w|\\ge 4$.\n\\end{proposition}\n\n\\begin{proof}\nFor permutations of lengths at most three, the result follows from an examination of Table~\\ref{table-short-decomps}. Now suppose that~$\\pi$ is a subpermutation of a rightward-yearning pin sequence and $|\\pi|\\ge 4$. If~$\\pi=\\psi^\\circ_w$ for some word~$w\\in\\P$, then $|w|\\ge 4$, so Lemma~\\ref{lem-pins-box-indecomposable} shows that~$\\pi$ is $\\boxplus$-indecomposable. Conversely, suppose that~$\\pi$ is $\\boxplus$-indecomposable. Since~$\\pi$ is a subpermutation of a rightward-yearning pin sequence, Proposition~\\ref{prop-boxplus-decomp} shows that there are nonempty words~$w_1$, $\\dots$,~$w_k\\in\\P$ such that\n\\[\n\t\\pi=\n\t\\psi_{w_1}^\\circ\\boxplus\\psi_{w_2}^\\bullet\\boxplus\\cdots\\boxplus\\psi_{w_k}^\\bullet.\n\\]\nObviously, the only way that~$\\pi$ could be $\\boxplus$-indecomposable in this case would be if all of the words~$w_i$ except one were empty. If~$w_j$ is the nonempty word then, by noting that~$\\psi_\\varepsilon^\\bullet=1$ and~$\\psi_\\varepsilon^\\circ\\boxplus\\psi_w^\\bullet =\\psi_w^\\circ$, we have~$\\pi=\\psi_{w_j}^\\circ$, and thus $|w_j|=|\\pi|\\ge 4$, completing the proof.\n\\end{proof}\n\nFinally, we investigate the uniqueness of the words encoding these $\\boxplus$-indecomposable permutations.  In this direction, we are primarily interested in the uniqueness of words for permutations without an origin, but it is easier to first establish the result for permutations with an origin. Note that the bound $|w|\\geq 4$ is best possible because~$\\psi^\\bullet_{\\u\\mathsf{r_u}\\d}=\\psi^\\bullet_{\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u\\mathsf{r_u}}=2413$.\n\n\\begin{table}\n\\[\n\t\\begin{array}{c|c}\n\t\tw&\\psi_w^\\bullet\\\\\n\t\t\\hline\\\\[-10pt]\n\t\t\\mathsf{ur_uur_u}&13524\\\\\n\t\t\\mathsf{ur_udr_d}&35142\\\\\n\t\t\\mathsf{r_uur_uu}&14253\\\\\n\t\t\\mathsf{r_uur_ud}&25314\\\\\n\t\t\\mathsf{r_udr_du}&31452\\\\\n\t\t\\mathsf{r_udr_dd}&42513\n\t\\end{array}\n\t\\quad\\quad\\quad\n\t\\begin{array}{c|c}\n\t\tw&\\psi_w^\\bullet\\\\\n\t\t\\hline\\\\[-10pt]\n\t\t\\mathsf{dr_dur_u}&31524\\\\\n\t\t\\mathsf{dr_ddr_d}&53142\\\\\n\t\t\\mathsf{r_dur_uu}&24153\\\\\n\t\t\\mathsf{r_dur_ud}&35214\\\\\n\t\t\\mathsf{r_ddr_du}&41352\\\\\n\t\t\\mathsf{r_ddr_dd}&52413\n\t\\end{array}\n\\]\n\\caption{The 12 words of length 4 in $\\P$ and their corresponding permutations~$\\psi_w^\\bullet$.}\n\\label{table-short-words-with-origin}\n\\end{table}%\n\n\\begin{proposition}\\label{prop-long-perms-have-unique-words}\nIf~$\\psi_v^\\bullet=\\psi_w^\\bullet$ for words $v,w\\in\\P$ satisfying $|v|=|w|\\ge 4$, then $v=w$.\n\\end{proposition}%\n\n\\begin{proof}\nWe proceed by induction on $|v|=|w|$. The base case of $|v|=|w|=4$ follows from an examination of Table~\\ref{table-short-words-with-origin}. Now suppose that $|v|=|w|\\ge 5$. Note that the first entry of~$\\psi_v^\\bullet$ must correspond to the origin $p_0$, and every entry of~$\\psi_v^\\bullet$ that lies above the origin must correspond to $\\u$ or $\\mathsf{r_u}$, while every entry that lies below the origin must correspond to $\\d$ or $\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace$.\n\nConsider the rightmost entry of~$\\psi_v^\\bullet$, which we may assume lies above the origin as the other case follows by a symmetrical argument. In this case, the last right step in both $v$ and~$w$ is encoded by the letter $\\mathsf{r_u}$, and this letter is either the final or penultimate letter of both $v$ and~$w$.\n\nIf $\\mathsf{r_u}$ is the final letter of both $v$ and~$w$, then we can remove it---the permutations are still equal, and thus by induction, so are the words $v$ and~$w$ with the last letter removed from each. Similarly, if $\\mathsf{r_u}$ is the penultimate letter in both $v$ and~$w$, then the final letter of each word must be the same (corresponding to the second to last entry of~$\\psi_v^\\bullet=\\psi_w^\\bullet$), and again we can remove it and apply induction. In either case, we conclude that $v=w$.\n\nIt remains to consider the case where, without loss of generality, $\\mathsf{r_u}$ is the final letter of $v$, and the penultimate letter of~$w$. Thus we have, say, $v=x\\mathsf{r_u}$ and~$w=y\\mathsf{r_u} z$ where $x$ and $y$ are words of lengths at least four and three, respectively, and $z\\in\\{\\u,\\d\\}$. Removing the rightmost point of~$\\psi_v^\\bullet=\\psi_{w}^\\bullet$ corresponds in each case to removing this final $\\mathsf{r_u}$. In the case of~$\\psi_v^\\bullet$, this leaves us with~$\\psi_x^\\bullet$, since $\\mathsf{r_u}$ was the last pin, whereas for~$\\psi_{w}^\\bullet$ we obtain~$\\psi_y^\\bullet\\boxplus\\psi_z^\\bullet$ since $\\mathsf{r_u}$ was an interior pin. However, we must have~$\\psi_x^\\bullet=\\psi_y^\\bullet\\boxplus\\psi_z^\\bullet$, and this is impossible since~$\\psi_x^\\bullet$ is $\\boxplus$-indecomposable by Lemma~\\ref{lem-pins-box-indecomposable}, while~$\\psi_y^\\bullet\\boxplus\\psi_z^\\bullet$ is not.\n\\end{proof}\n\nFor pin sequences without an origin, the analogous result must account for the fact that~${\\psi^\\circ_{\\mathsf{r_u} x}=\\psi^\\circ_{\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace x}}$ for all words $x\\in\\P$. Additionally, we note that~$\\psi_{\\u\\mathsf{r_u}\\u\\mathsf{r_u}}^\\circ=\\psi_{\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\d}^\\circ=2413$, so our result must start with words of length $5$.\n\n\\begin{proposition}\\label{prop-long-perms-have-unique-words-norigin}\nIf~$\\psi^\\circ_v=\\psi^\\circ_w$ for words $v,w\\in\\P$ satisfying $|v|=|w|\\ge 5$, then either~${v=w}$, or~${v=\\mathsf{r_u} x}$ and ${w=\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace x}$ for some word~$x\\in\\P$.\n\\end{proposition}\n\n\\begin{proof}\nConsider a word $v\\in\\P$ of length at least 5. We first claim that there exists a function~${\\phi \\::\\: \\P\\to\\P}$ with $|\\phi(v)|=|v|-1$ such that~$\\psi^\\circ_v=\\psi^\\bullet_{\\phi(v)}$.\n\nTo establish the claim, we recall that~$\\psi^\\circ_v=\\psi^\\circ_\\varepsilon\\boxplus\\psi^\\bullet_v$, and consider the effect of deleting the origin from~$\\psi^\\bullet_v$. The second-leftmost entry of~$\\psi^\\bullet_v$ becomes the new origin, and its position relative to the rest of the permutation depends upon the first few letters of $v$. The following chart defines the function~$\\phi$ for words of length at least 3, and in each case it is straightforward to verify that~$\\psi_v^\\circ=\\psi_{\\phi(v)}^\\bullet$.\n\\[\\begin{array}{ccc}\n\tv&\\quad&\\phi(v)\\\\\n\t\\hline\n\t\\u\\mathsf{r_u} x&&\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace x\\\\\n\t\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace x&&\\mathsf{r_u} x\\\\\n\t\\begin{aligned} \\mathsf{r_u}\\u\\mathsf{r_u} x\\\\[-3pt] \\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\u\\mathsf{r_u} x\\end{aligned}&\\Big\\}&\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace x\\\\\n\t\\begin{aligned} \\mathsf{r_u}\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace x\\\\[-3pt] \\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace x\\end{aligned}&\\Big\\}&\\u\\mathsf{r_u} x\n\\end{array}\\]\n(It would be possible to define~$\\phi$ explicitly for shorter words as well, but we do not need to do so.)\n\nNow consider words $v,w$ of length $\\ge 5$ such that~$\\psi^\\circ_v=\\psi^\\circ_w$. We have \n\\[\n\t\\psi^\\bullet_{\\phi(v)}=\\psi^\\circ_v=\\psi^\\circ_w=\\psi^\\bullet_{\\phi(w)},\n\\]\nand since $|\\phi(v)|=|v|-1 \\ge 4$, Proposition~\\ref{prop-long-perms-have-unique-words} implies that~$\\phi(v)=\\phi(w)$. By the definition of~$\\phi$, it now follows that either $v=w$, or $v$ and~$w$ differ only in their first letter, as required. \n\\end{proof}\n\n\n\nThe combination of Theorem~\\ref{thm-Csk-description} with Propositions~\\ref{prop-long-perms-have-unique-words} and~\\ref{prop-long-perms-have-unique-words-norigin} provide us with a guarantee that any permutation~$\\pi\\in\\mathcal{C}^{\\exparen{s_k}}$ corresponds to an almost-unique collection of words $v_1$, $v_2$, $\\dots$, $v_\\ell\\in\\P^{\\exparen{s_k}}$, providing $|v_1|\\ge 5$ and $|v_i|\\ge 4$ for $i\\ge 2$. If such criteria are met, then the only possible ambiguity arises in the first letter of $v_1$.\n\n\n\\section{Well-Quasi-Order}\n\\label{sec-wqo}\n\nThe fact that the classes $\\mathcal{C}^{\\exparen{s_k}}$ are, in a sense, ``$\\boxplus$ closed'' enables us to establish that these classes are all wqo, although this takes a bit of preparation. Recall that the binary languages~$\\L^{\\exparen{s_k}}$ are wqo under the factor order by Proposition~\\ref{prop-Lsk-wqo}. First we must lift this property to our pin sequence languages $\\P^{\\exparen{s_k}}$.\n\n\\begin{proposition}\n\\label{prop-Psk-wqo}\nFor every sequence $(s_k)$ of positive integers, the set $\\P^{\\exparen{s_k}}\\subseteq\\{\\rd,\\ru,\\d,\\u\\}^\\ast$ of words is wqo under the factor order.\n\\end{proposition}\n\\begin{proof}\nGiven any word~$w$, we define $\\Delta_L(w)$ to be the word obtained by removing the first letter of~$w$ (assuming that~$w$ is nonempty). If $u$ is contained as a factor in~$w$, it follows that $\\Delta_L(u)$ is contained as a factor in $\\Delta_L(w)$. Therefore, if the language $\\mathcal{S}$ is wqo under the factor order, then the language $\\Delta_L(\\mathcal{S})$ is wqo under the factor order. We similarly define $\\Delta_R(w)$ to be the word obtained by removing the last letter of~$w$.\n\nBy definition, for every word $v\\in\\P^{\\exparen{s_k}}$, there is some word~$w\\in\\L^{\\exparen{s_k}}$ for which $v$ is a factor of $\\rho(w)$. Indeed, if we take~$w$ to be minimal, then $v$ comprises all but possibly the first and last letter of $\\rho(w)$. Thus we can express $\\P^{\\exparen{s_k}}$ as\n\\[\n\t\\P^{\\exparen{s_k}}\n\t=\n\t\\rho(\\L^{\\exparen{s_k}})\n\t\\cup\\Delta_L(\\rho(\\L^{\\exparen{s_k}}))\n\t\\cup\\Delta_R(\\rho(\\L^{\\exparen{s_k}}))\n\t\\cup\\Delta_L(\\Delta_R(\\rho(\\L^{\\exparen{s_k}}))).\n\\]\nThis shows that $\\P^{\\exparen{s_k}}$ is the union of four wqo posets, and is therefore wqo itself.\n\\end{proof}\n\nTo go from the languages $\\P^{\\exparen{s_k}}\\subseteq\\{\\rd,\\ru,\\d,\\u\\}^\\ast$ to the permutation classes $\\mathcal{C}^{\\exparen{s_k}}$, we need to first recall the setting and statement of Higman's lemma. Given a poset $(X,\\le)$, we denote by $X^\\ast$ the set (or language) of all words with letters from $X$. The \\emph{generalized subword order} on $X^\\ast$ is defined by stipulating that the word $v=v(1)\\cdots v(k)$ is contained in the word~$w=w(1)\\cdots w(n)$ if and only if~$w$ has a subsequence~$w({i_1})w({i_2})\\cdots w({i_k})$ such that $v(j)\\le w({i_j})$ for all indices $j$. The following is a weakened version of Higman's original result.\n\n\\newtheorem*{higmans-lemma}{\\rm \\textbf{Higman's lemma}~\\cite{higman:ordering-by-div:}}\n\\begin{higmans-lemma}\nIf $(X,\\le)$ is wqo, then $X^\\ast$ is also wqo, under the generalized subword order.\n\\end{higmans-lemma}\n\nHigman's lemma immediately implies (via Proposition~\\ref{prop-Psk-wqo}) that the poset $(\\P^{\\exparen{s_k}})^\\ast$ is wqo under the generalized subword order. Note that in this poset, the ``letters'' of a ``word'' are in fact words from~$\\P^{\\exparen{s_k}}$ (which are themselves defined over the alphabet $\\{\\rd,\\ru,\\d,\\u\\}$).\n\nNow define a mapping~$\\phi\\::\\: (\\P^{\\exparen{s_k}})^\\ast\\to\\mathcal{C}^{\\exparen{s_k}}$ by\n\\[\n\t\\Phi(w)\n\t=\n\t\\psi_{w(1)}^\\circ\\boxplus\\psi_{w(2)}^\\bullet\\boxplus\\cdots\\boxplus\\psi_{w(k)}^\\bullet.\n\\]\nProposition~\\ref{prop-Psk-to-Csk} shows that the mappings~$w\\mapsto\\psi_w^\\circ$ and~$w\\mapsto\\psi_w^\\bullet$ are both order-preserving, and it then follows from the definition of $\\boxplus$ that~$\\phi$ is order-preserving. Theorem~\\ref{thm-Csk-description} further implies that~$\\phi$ maps surjectively onto $\\mathcal{C}^{\\exparen{s_k}}$.\n\nThe main result of this section then follows from the general fact that if the domain of an order-preserving mapping is wqo, then its range must be as well. (This fact is easily proved by contradiction, for one could pull back any infinite antichain in the range of such a mapping to find an infinite antichain in its domain.)\n\n\\begin{proposition}\n\\label{prop-Csk-wqo}\nFor every sequence $(s_k)$ of positive integers, the permutation class $\\mathcal{C}^{\\exparen{s_k}}$ is wqo.\n\\end{proposition}\n\n\n\\section{Distinct Enumerations}\n\\label{sec-enum}\n\nHaving shown that the classes $\\mathcal{C}^{\\exparen{s_k}}$ are all wqo, we now finish the proof of our main theorem by establishing that they have distinct enumerations.\n\n\\begin{theorem}\n\\label{thm-distinct-enum}\n\tSuppose that $(s_k)$ and $(t_k)$ are distinct sequences of positive integers, and that $(s_k)$ lexicographically precedes $(t_k)$. Then there exists an integer $N$ such that \n\t\\[\n\t\t\\bigcup_{n\\le N}\\mathcal{C}_n^{\\exparen{t_k}} \\subsetneq \\bigcup_{n\\le N}\\mathcal{C}_n^{\\exparen{s_k}}.\n\t\\]\n\tIn particular, the classes $\\mathcal{C}^{\\exparen{s_k}}$ and $\\mathcal{C}^{\\exparen{t_k}}$ have distinct enumeration sequences. \n\\end{theorem}\n\n\\begin{proof}\nLet $M$ be the integer from Proposition~\\ref{prop-words-distinct-enum}, so~$\\L^{\\exparen{s_k}}_n = \\L^{\\exparen{t_k}}_n$ for all $n<M$, but~$\\L^{\\exparen{t_k}}_M\\subsetneq \\L^{\\exparen{s_k}}_M$. We claim that $N=2M-1$ satisfies the requirements of the theorem. Since $M\\ge 3$, we have $N\\ge 5$.\n\nFirst, let~$\\pi\\in\\mathcal{C}^{\\exparen{t_k}}$ be a permutation of length $n\\le N$.  By Theorem~\\ref{thm-Csk-description}, we have\n\\[\t\\pi=\\psi^\\circ_{v_1}\\boxplus\\psi^\\bullet_{v_2}\\boxplus\\cdots\\boxplus\\psi^\\bullet_{v_\\ell}\n\\] \nfor words $v_1$, $v_2$, $\\dots$, $v_\\ell \\in\\P^{\\exparen{t_k}}$ with $|v_1|+\\cdots +|v_\\ell|=n$.\n\nFor each $v_i$ (for $i=1,2,\\dots,\\ell$), take a shortest word~$w_i\\in\\L^{\\exparen{t_k}}$ such that~$v_i$ is a factor of $\\rho(w_i)$. Now~$v_i$ can have at most two fewer letters than $\\rho(w_i)$, and thus $2|w_i|= |\\rho(w_i)| \\le |v_i|+2$. Furthermore, since $|v_i|\\le N=2M-1$, we conclude that $|w_i| \\le M$. By Proposition~\\ref{prop-words-distinct-enum}, we have~$w_i\\in \\L^{\\exparen{s_k}}$. Thus~${\\rho(w_i)\\in \\P^{\\exparen{s_k}}}$, and since~$v_i$ is a factor of $\\rho(w_i)$, it follows that $v_i\\in\\P^{\\exparen{s_k}}$. Thus $v_1$, $v_2$, $\\dots$, $v_\\ell$ all lie in $\\P^{\\exparen{s_k}}$, and hence~$\\pi\\in\\mathcal{C}^{\\exparen{s_k}}$ by Theorem~\\ref{thm-Csk-description}. This establishes that $\\mathcal{C}^{\\exparen{t_k}}_n\\subseteq \\mathcal{C}^{\\exparen{s_k}}_n$ for all $n\\le N$.\n\nIt remains to exhibit a permutation~$\\pi\\in\\mathcal{C}^{\\exparen{s_k}}\\setminus\\mathcal{C}^{\\exparen{t_k}}$ of length at most $N$. Take a word~${w\\in \\L^{\\exparen{s_k}}_M\\setminus\\L^{\\exparen{t_k}}_M}$, whose existence is guaranteed by Proposition~\\ref{prop-words-distinct-enum}. The word $\\rho(w)$ clearly lies in $\\P^{\\exparen{s_k}}$. However, it cannot lie in $\\P^{\\exparen{t_k}}$, as this would imply that there exists $u\\in\\L^{\\exparen{t_k}}$ such that $\\rho(w)$ is a factor of $\\rho(u)$, which would mean that~$w$ is a factor of $u$, and hence that~$w\\in\\L^{\\exparen{t_k}}$. \n\nThe word $\\rho(w)$ ends with $\\u\\mathsf{r_u}$ or $\\d\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace$. In either case, let $x$ be the word obtained by removing its last letter. Again, $x$ clearly lies in $\\P^{\\exparen{s_k}}$, but it cannot lie in $\\P^{\\exparen{t_k}}$, as any word that contains $x$ as a proper factor would also have to contain $\\rho(w)$, and we have already established that $\\rho(w)\\not\\in\\P^{\\exparen{t_k}}$. We now have a word $x$ of length $2M-1=N$ that lies in $\\P^{\\exparen{s_k}}\\setminus\\P^{\\exparen{t_k}}$ and which begins with $\\u$ or $\\d$.\n\nWe now consider the permutation~$\\pi=\\psi_x^\\circ$, which by definition lies in $\\mathcal{C}^{\\exparen{s_k}}_N$. Since~$N\\ge 5$, by Proposition~\\ref{prop-boxplus-indecomp} we have that~$\\pi$ is $\\boxplus$-indecomposable. \n\nSuppose that~$\\pi\\in\\mathcal{C}^{\\exparen{t_k}}_N$. As~$\\pi$ is $\\boxplus$-indecomposable, Theorem~\\ref{thm-Csk-description} tells us that~$\\pi=\\psi^\\circ_y$ for some~${y\\in\\P^{\\exparen{t_k}}}$. Now~$\\psi^\\circ_y = \\pi = \\psi^\\circ_x$ has length at least 5, and thus by Proposition~\\ref{prop-long-perms-have-unique-words-norigin} we must have either that $x=y$, or that $x$ and $y$ are identical after their first letter, which in each case must be~$\\mathsf{r_u}$ or~$\\ensuremath{^{\\text{\\scriptsize rd}}}\\xspace$. However, by construction,~$x$ begins with~$\\u$ or~$\\d$, and so in fact we must have $y=x$, and hence~$x\\in\\P^{\\exparen{t_k}}$, a contradiction. Thus,~$\\pi\\not\\in\\mathcal{C}^{\\exparen{t_k}}_N$ and the proof is complete.\n\\end{proof}\n\n\\section{Binary Sequences with Distinct Complexity Functions}\\label{sec-sequences}\n\nIn this short section, we consider a consequence of the work in Section~\\ref{sec-pouzet-factors} in the study of countably infinite binary words (commonly referred to as \\emph{sequences}). For a binary sequence $\\mathbf{w}$, the \\emph{complexity} of $\\mathbf{w}$ is the function that counts the number of words of length $n$ contained (as factors) in $\\mathbf{w}$. \n\nThe main result of this section is as follows. After the statement of the theorem, we introduce only the bare minimum in terminology, and refer the reader to, for example, Durand, Leroy, and Richomme~\\cite{durand:do-the-properties:} for a fuller treatment. \n\n\\begin{theorem}\\label{thm-words-distinct-complexity}\nLet $S=\\{\\sigma,\\mu\\}$ where $\\sigma$ and $\\mu$ are constant-length morphisms defined by \n\\[\n\\mu : {}\n\t\\begin{cases}\n\t\t0 \\mapsto 01\\\\\n\t\t1 \\mapsto 10\n\t\\end{cases}\n\t\\quad\\text{and}\\quad\n\\sigma : {}\n\t\\begin{cases}\n\t\t0 \\mapsto 00\\\\\n\t\t1 \\mapsto 11.\n\t\\end{cases}\n\\]\nThe collection of $S$-adic sequences contains uncountably many sequences with distinct complexity functions. \n\\end{theorem}\n\nNote that the morphism $\\mu$ is the \\emph{Thue--Morse morphism}. That is, the Thue--Morse sequence is a fixed point of $\\mu$.\n\nGiven a binary sequence $\\mathbf{w}$, an \\emph{$S$-adic representation} of $\\mathbf{w}$ is a sequence $(\\sigma_n)_{n\\in\\mathbb{N}}$ of morphisms (known as a \\emph{directive word}) where $\\sigma_n\\in S$, together with a sequence of letters $(a_n)_{n\\in\\mathbb{N}}$ from $\\{0,1\\}$, such that \n\\[\n\t\\mathbf{w} = \\lim_{n\\to\\infty} \\sigma_1\\cdots \\sigma_n(a_na_na_n\\cdots).\n\\]\nIn this case, we may say that $\\mathbf{w}$ is an \\emph{$S$-adic sequence}. Our interest in these sequences relates to the set of finite factors that they contain. Given a sequence $\\mathbf{w}$, let\n\\[\n\t\\L^\\mathbf{w}_n = \\{\\text{factors of }\\mathbf{w}\\text{ of length }n\\}.\n\\]\nNote that the union of these sets, $\\L^\\mathbf{w} = \\bigcup \\L^\\mathbf{w}_n$, is a factor-closed language. We now have the following result. It is likely that the restriction to sequences comprising only powers of two in this result can be avoided if we replace our set of morphisms $S=\\{\\mu,\\sigma\\}$ by something more complicated, but we do not require this.\n\n\n\\begin{proposition}\\label{prop-language-to-s-adic}\nLet $(s_k)_{k\\in\\mathbb{N}}$ be a sequence of positive integers where each term is a power of two, that is,~$s_i\\in \\{2^n : n\\geq 0\\}$. Then there exists an $S$-adic sequence $\\mathbf{w}$ such that $\\L^{\\mathbf{w}} = \\L^{\\exparen{s_k}}$. \n\\end{proposition}\n\nNote that Theorem~\\ref{thm-words-distinct-complexity} follows immediately from the above proposition, when combined with Proposition~\\ref{prop-words-distinct-enum}. \n\n\\begin{proof}\nFor $k\\geq 0$, consider the morphism $\\mu_k = \\mu\\sigma^k$. By definition, we have\n\\[\n\\mu_k : {}\n\t\\begin{cases}\n\t\t0 \\mapsto (01)^{2^k}\\\\\n\t\t1 \\mapsto (10)^{2^k}.\n\t\\end{cases}\n\\]\nGiven a sequence $(s_k)_{k\\in\\mathbb{N}}$ of powers of two, let $t_k = \\log_2(s_k)$. \nWe claim that $\\L^{\\mathbf{w}} = \\L^{\\exparen{s_k}}$, where $\\mathbf{w}$ is the $S$-adic sequence defined by the directive word $\\mu\\sigma^{t_1}\\mu\\sigma^{t_2}\\cdots$ and the all-zero sequence $0,0,\\dots$. \n\nTo establish the claim, first note (for example, by induction) that\n\\[\\mu_{t_1} \\cdots \\mu_{t_{i}}(0) = \\left( \\alpha_{i}^{\\exparen{s_k}}\\right)^{s_{i+1}}\\quad \\text{and}\\quad \\mu_{t_1} \\cdots \\mu_{t_{i}}(1) = \\left( \\overline{\\alpha}_{i}^{\\exparen{s_k}}\\right)^{s_{i+1}}.\\]\nAs a consequence, the sequence $\\mathbf{w}$ can be written as a word in $\\left\\{\\alpha_{i}^{\\exparen{s_k}},\\overline{\\alpha}_{i}^{\\exparen{s_k}}\\right\\}^*$, for any $i\\geq 1$. It follows immediately that $\\alpha_{i}^{\\exparen{s_k}}\\in\\L^\\mathbf{w}$ for all $i$, and by definition of $\\L^{\\exparen{s_k}}$, this establishes that $\\L^{\\exparen{s_k}}\\subseteq \\L^{\\mathbf{w}}$.\n\nFor the reverse containment, consider a word $\\gamma \\in \\L^\\mathbf{w}$. Fix any $i$ so that $|\\gamma| \\leq |\\alpha_i^{\\exparen{s_k}}|$, and consider~$\\mathbf{w}$ as a sequence in $\\left\\{\\alpha_{i}^{\\exparen{s_k}},\\overline{\\alpha}_{i}^{\\exparen{s_k}}\\right\\}^*$. Since $\\gamma$ is a factor of $\\mathbf{w}$, it follows that $\\gamma$ is either a factor of \n\\[\n\\alpha_i^{\\exparen{s_k}}\\text{ or }\\overline\\alpha_i^{\\exparen{s_k}}, \n\\]\nor it `straddles' two such factors, and thus is a factor of one of \n\\[\n\t\\alpha_i^{\\exparen{s_k}}\\alpha_i^{\\exparen{s_k}},\\quad\n\t\\alpha_i^{\\exparen{s_k}}\\overline\\alpha_i^{\\exparen{s_k}},\\quad\n\t\\overline\\alpha_i^{\\exparen{s_k}}\\alpha_i^{\\exparen{s_k}}\\text{ or}\\quad\n\t\\overline\\alpha_i^{\\exparen{s_k}}\\overline\\alpha_i^{\\exparen{s_k}}.\n\\]\nIn any case, all of these words are in $\\L^{\\exparen{s_k}}$, thus $\\gamma\\in\\L^{\\exparen{s_k}}$. Hence $\\L^\\mathbf{w}\\subseteq\\L^{\\exparen{s_k}}$, completing the proof.\\end{proof}\n\nWe finish this section by briefly noting another property of the $S$-adic sequences above, namely that we can bound the complexity of all these $S$-adic sequences by a linear function.\n\n\\begin{proposition}\nLet $S=\\{\\mu,\\sigma\\}$, and let $\\mathbf{w}\\in \\{0,1\\}^*$ be any $S$-adic sequence. Then $|\\L^\\mathbf{w}_n|\\leq 8n$.\n\\end{proposition}\n\n\\begin{proof}\nThis follows directly from Corollary~2.1 in \\cite{durand:corrigendum:}, which states the following: for a finite alphabet~$A$, a letter~$a\\in A$, and a sequence of morphisms $(\\sigma_n:\\{0,1\\}\\to \\{0,1\\}^*)_{n\\in\\mathbb{N}}$ of constant length~$\\ell$, the complexity of $\\mathbf{w} = \\lim \\sigma_1\\cdots\\sigma_n(aa\\cdots)$ is at most $\\ell|A|^2n$.\n\\end{proof}\n\n\n\\section{Concluding Remarks}\\label{sec-concluding}\n\nOur main result, established in Sections~\\ref{sec-wqo} and \\ref{sec-enum}, disproves False Conjecture~\\ref{conj-wqo-algebraic} by showing that there are too many different enumerations of wqo permutation classes for them all to have algebraic generating functions. However, the weaker Question~\\ref{ques-lwqo-algebraic}, which asks if every lwqo permutation class has an algebraic generating function, might still be true. Unfortunately, there are wqo-but-not-lwqo permutation classes that are strongly algebraic, so unlike False Conjecture~\\ref{conj-wqo-algebraic}, a positive resolution to this question would not give a structural characterization of the strongly-algebraic classes.\n\nThe permutations we have used to build our counterexamples $\\mathcal{C}^{\\exparen{s_k}}$ are all proper pin sequences or subpermutations thereof. As mentioned in the text, pin sequences were first defined by Brignall, Huczynska, and Vatter~\\cite{brignall:decomposing-sim:}, although our language-theoretical approach is influenced by Brignall, Ru\\v{s}kuc, and Vatter~\\cite{brignall:simple-permutat:decide:}. It was conjectured~\\cite[Conjecture 16]{brignall:simple-permutat:decide:} that the class of all proper pin sequences and their subpermutations has a rational generating function, and that conjecture was later proved by Bassino, Bouvel, and Rossin~\\cite{bassino:enumeration-of-:}, who also showed that this class has an infinite basis. Thus all of the classes we have used to disprove False Conjecture~\\ref{conj-wqo-algebraic} are contained in a class with a rational generating function (though this should not be too surprising, as Theorem~\\ref{thm-contained-rational} guarantees that such a class must exist).\n\nFor the remainder of the conclusion we discuss a much rougher notion of enumeration, that of growth rates. The \\emph{upper growth rate} of the permutation class is defined by\n\\[\n\t\\overline{\\gr}(\\mathcal{C}) = \\limsup_{n\\to\\infty}\\sqrt[n]{|\\mathcal{C}_n|}.\n\\]\nWhen the limit superior above is actually a limit (as has been conjectured is always the case%\n\\footnote{A weaker version of this conjecture, applying only to finitely-based permutation classes, was explicitly asked by the second author at the conference \\emph{Permutation Patterns 2005}~\\cite[Section~4]{elder:problems-and-co:}, but that may not be the first time it was posed. A stronger conjecture, stated in the context of ordered graphs, has been posed by Balogh, Bollob\\'as, and Morris~\\cite[Conjecture 8.1]{balogh:hereditary-prop:ordgraphs}.}),\nthen we call this the \\emph{proper growth rate} of the class and denote it by $\\mathrm{gr}(\\mathcal{C})$.\n\nThere has been extensive research on the set of all possible growth rates of permutation classes and at what growth rates certain phenomena first appear~\\cite{albert:growing-at-a-pe:,bevan:intervals-of-pe:,huczynska:grid-classes-an:,kaiser:on-growth-rates:,pantone:growth-rates-of:,vatter:permutation-cla:lambda:,vatter:small-permutati:,vatter:growth-rates-of:}. For example, the smallest non-wqo permutation class (equivalently, the infinite antichain whose downward closure has the smallest possible growth rate) has growth rate denoted by $\\kappa$, the largest real root of $x^3-2x^2-1$, which is approximately $2.21$. Furthermore, it has been established that every permutation class of growth rate smaller than $\\kappa$ has a rational generating function~\\cite[Section~8]{albert:inflations-of-g:}. Thus it may be interesting to determine the growth rates of the classes $\\mathcal{C}^{\\exparen{s_k}}$, or perhaps more ambitiously, to answer the following question.\n\n\\begin{question}\nWhat is the smallest real number $\\omega$ such that there is a wqo permutation class of growth rate $\\omega$ that fails to have an algebraic generating function?\n\\end{question}\n\nIt is not difficult to show that the classes $\\mathcal{C}^{\\exparen{s_k}}$ have \\emph{proper} growth rates, as we now explain. This follows from a Fekete's lemma argument that seems to have first been stated in the permutation context by Arratia~\\cite{arratia:on-the-stanley-:}%\n\\footnote{Although it seems likely given his some of his writing~\\cite[Problem~28]{chvatal:selected-combin:} that Knuth was aware of this application of Fekete's lemma in 1972.}.\nWe use the multiplicative form of Fekete's lemma, which states that if the sequence~$(a_n)$ of positive real numbers satisfies $a_{m+n}\\ge a_ma_n$ for all~$m$ and~$n$ (that is, if it is supermultiplicative), then~$\\lim\\sqrt[n]{a_n}$ exists and equals $\\sup\\sqrt[n]{a_n}$. \n\n\\begin{proposition}\nFor every sequence $(s_k)$ of positive integers, the permutation class $\\mathcal{C}^{\\exparen{s_k}}$ has a growth rate.\t\n\\end{proposition}\n\n\\begin{proof}\nTheorem~\\ref{thm-Csk-description} states that $\\mathcal{C}^{\\exparen{s_k}}$ consists precisely of the permutations of the form\n\\[\n\t\\psi^\\circ_{v_1}\\boxplus\\psi^\\bullet_{v_2}\\boxplus\\cdots\\boxplus\\psi^\\bullet_{v_\\ell}\n\\]\nfor words $v_1$, $v_2$, $\\dots$, $v_\\ell\\in\\P^{\\exparen{s_k}}$. Take~$\\pi\\in\\mathcal{C}^{\\exparen{s_k}}_m$,~$\\sigma\\in\\mathcal{C}^{\\exparen{s_k}}_n$, and express~$\\sigma$ as\n\\[\n\t\\sigma\n\t=\n\t\t\\tau^\\circ_{w_1}\\boxplus\\tau^\\bullet_{w_2}\\boxplus\\cdots\\boxplus\\tau^\\bullet_{w_\\ell}\n\\]\nfor some words~$w_1$, $\\dots$,~$w_\\ell\\in\\P^{\\exparen{s_k}}$. The mapping that sends the pair $(\\pi,\\sigma)$ to the permutation\n\\[\n\t\\pi\\boxplus\\tau^\\bullet_{w_1}\\boxplus\\tau^\\bullet_{w_2}\\boxplus\\cdots\\boxplus\\tau^\\bullet_{w_\\ell}\\in\\mathcal{C}^{\\exparen{s_k}}_{m+n}\n\\]\nis an injection from $\\mathcal{C}^{\\exparen{s_k}}_m\\times \\mathcal{C}^{\\exparen{s_k}}_n$ to $\\mathcal{C}^{\\exparen{s_k}}_{m+n}$, and thus~$\\lim\\sqrt[n]{|\\mathcal{C}^{\\exparen{s_k}}_n|}$ exists by Fekete's lemma.\n\\end{proof}\n\nWe leave open the question of what the growth rates of the classes $\\mathcal{C}^{\\exparen{s_k}}$ actually are, and whether these growth rates even depend on the choice of the sequence $(s_k)$.\n\n\\minisec{Acknowledgements}\nWe thank Dan Rust and Reem Yassawi for useful discussions.\n\n\n\\setlength{\\bibsep}{4pt}\n\n\n\\def$'${$'$}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\\section{Introduction}\n\\label{sec:introduction}\n\\input{sections\/introduction}\n\n\\section{Related Work}\n\\label{sec:related}\n\\input{sections\/related}\n\n\\section{Our General Framework for UDA}\n\\label{sec:components}\n\\input{sections\/components}\n\n\n\\section{Experiments}\n\\label{sec:analysis}\n\\input{sections\/analysis}\n\n\n\\section{Generalization to Multi-Source}\n\\label{sec:generalization}\n\\input{sections\/generalization}\n\n\\section{Conclusions}\n\\label{sec:conclusion}\n\\input{sections\/conclusions}\n\n\n\n{\\small\n\\bibliographystyle{ieee_fullname}\n\n\\subsection{Experimental Setup}\n\\label{sec:expsetup}\nWe now present the datasets used for the experiments in the three domain shift scenarios. \n\n\\myparagraph{Adverse weather.} For this scenario, we use Cityscapes \\cite{city} as the source dataset. It contains 3,475 real urban images, with 2,975 images used for training and 500 for the validation. Foggy version of Cityscapes \\cite{foggy} is used as the target dataset. \nHighest fog intensity (least visibility) images are used in our experiments, matching prior work~\\cite{GPA}. \nBoth datasets have 8 different categories. \nFollowing \\cite{da_faster_rcnn}, we used the tightest bounding box of an instance segmentation mask as ground truth box. This scenario is referred to as \\emph{Foggy}.\n\n\\myparagraph{Synthetic to real.} SIM10k~\\cite{sim10k} is a simulated dataset that contains  10,000 synthetic images.\nIn this dataset, we use all 58,701 car bounding boxes available as the source data during training. For the target data and evaluation, we use Cityscapes~\\cite{city} and only consider the car instances. This scenario is referred to as \\emph{Sim2Real}.\n\n\\myparagraph{Cross camera.} In this scenario, we use real the dataset of KITTI~\\cite{kitti} as our source data. KITTI contains 7,481 images and we use all of them for training. Similar to the previous scenarios, we use Cityscapes~\\cite{city} as target data. \n\nIn all experiments, we use mean average precision (mAP) with IoU threshold of 0.5 for evaluation. We compare our approach with the following prior works: DA \\cite{da_faster_rcnn}, DivMatch \\cite{diversify_and_match}, SW-DA \\cite{strong-weak}, SC-DA \\cite{zhu_cvpr19_selective_alignment} and MTOR \\cite{mean_teacher}.\n\n\\myparagraph{Implementation details.} We set the shorter side of the image to 600 pixels, following the Faster R-CNN implementation \\cite{ren2015faster}. Our Faster R-CNN network, as well as all the prior works we compare to, utilize ResNet-50~\\cite{he2016deep} as the backbone. Models using adversarial training are first trained with learning rate 0.001 for 50K iterations, then with learning rate 0.0001 for 20K more iterations and we report the final performance. Each batch is composed of 2 images, one from each domain. A momentum of 0.9 and a weight decay of 0.0005 is used. With the mentioned setting, maximum ~10k MB of memory needed and one NVIDIA Tesla V100-PCIE GPU is used.\nFor training contrastive learning models, we employ the code provided by \\cite{GPA} and we follow its exact settings for running experiments. Both methods are implemented with PyTorch~\\cite{pytorch}.   \n\n\n\\subsection{Analysis of UDA Components}\n\\label{subsec:res_experimental_analysis}\nIn this section we analyze the various design choices of alignment mechanisms~(\\Tableref{ablation_cl_at}), image-level alignment~(\\Tableref{tab:imglevel}), aggregation levels and aggregation mechanisms~(\\Tableref{tab:ablation_foggy_sim}) when  bulding UDA models.\n\nIn Table~\\ref{ablation_cl_at}, we compare CL and AT domain alignment paradigms in the \\emph{Sim2Real} scenario.\nFaster R-CNN is the baseline model which is only trained on the source and tested on the target. Single and Multiple Group(s) are shown as SG and MG. CA represents Class Agnostic, which means that class information is not used when constructing the groups. \nCL using SG as aggregation level, improves the performance over the source-only model ($33.2\\%$ vs $31.9\\%$).\nSimilarly, applying CL with MG ($36.9\\%$) or MG+CA ($42.6\\%$) setup further improves  model performance.\nAT  outperforms CL in each of these three scenarios (fifth to seventh rows of \\Tableref{ablation_cl_at}).\nApplying AT on the SG results in a large improvements over the baseline ($40.8\\%$ vs $31.9\\%$).\nSimilarly, AT heavily outperforms CL for the MG setting ($43.1\\%$ vs $36.9\\%$). \nSame trend is observed in MG+CA as well, with AT outperforming CL ($45.6\\%$ vs $42.6\\%$). \nThis large margin reveals that allowing the network to freely align the group representatives with AT, leads to a larger performance gain compared to explicitly matching the groups to nearest neighbors across domains using CL. \nBased on these results, we use AT for the rest of experiments.\n\n\\begin{table}\n    \\centering\n    \\scalebox{0.9}{\n    \\setlength{\\tabcolsep}{5.0mm}\n    \\begin{tabular}{lcc}\n    \t\\toprule[1.0pt]\n    \t Method & Agg. Levels & \\emph{car} AP \\\\\n    \t\\cmidrule(lr){1-1}\\cmidrule(lr){2-2}\\cmidrule(lr){3-3\n    \tFaster R-CNN & --- & 31.9\\\\\\cmidrule(lr){1-1}\\cmidrule(lr){2-2}\\cmidrule(lr){3-3\n    \t\\multirow{3}{*}{\\parbox{2.0cm}{Contrastive losses}} & SG & 33.2\\\\\n    \t& MG & 36.9 \\\\\n    \t& MG+CA & 42.6 \\\\\n        \\cmidrule(lr){1-1}\\cmidrule(lr){2-2}\\cmidrule(lr){3-3\n        \\multirow{3}{*}{\\parbox{2.0cm}{Adversarial training}} & SG & 40.8 \\\\\n    \t & MG & 43.1 \\\\\n    \t & MG+CA & 45.6 \\\\\n    \t\\bottomrule[1.0pt]\n    \\end{tabular}}\n    \\vspace{1mm}\n    \\caption{\\textbf{Sim2Real:} Analyzing the choice of alignment mechanism, comparing adversarial training against contrastive learning across different aggregation conditions (SG: Single Group, MG: Multiple Groups, CA: Class Agnostic ). Note that all results here only use instance level alignment.}\n   \n    \\label{ablation_cl_at}\n\\end{table}\n\n\n\n\\begin{figure*}\n\t\\centering\n\t\\setlength{\\tabcolsep}{0.02mm}\n\t\\begin{tabular}{cccc}\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/src_only\/srconly_10.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/src_only\/srconly_14.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/src_only\/srconly_12.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/src_only\/srconly_13.png}\\\\\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/iou\/iou_10.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/iou\/iou_14.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/iou\/iou_12.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/iou\/iou_13.png}\\\\\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/cosine\/cosine_10.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/cosine\/cosine_14.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/cosine\/cosine_12.png}&\n\t \\includegraphics[valign = c,width=0.22\\linewidth]{figures\/cosine\/cosine_13.png}\\\\\n\t\\end{tabular}\n\n\t\\caption{Qualitative results. Sim2Real scenario. First row: Faster R-CNN, second row: ViSGA (iou) and, last row: ViSGA (cosine). True positives and missed objects are shown as cyan and red boxes respectively. We can clearly see that Faster R-CNN model misses many objects. This improves in the second row, with the model based on grouping proposals with spatial overlap. However, ViSGA\\xspace model powered by similarity-based aggregation does even better, recovering almost all missed objects.\n\t} \n\t\\vspace{0mm}\n\t\\label{fig:qualitative_results}\n\\end{figure*}\n\\begin{table}\n    \\centering\n    \\scalebox{0.9}{\n    \\setlength{\\tabcolsep}{4.0mm}\n    \\begin{tabular}{cccc}\n    \t\\toprule[1.0pt]\n    \t Image-level & SG & MG & MG+CA\\\\\n    \t\\cmidrule(lr){1-1}\\cmidrule(lr){2-4}\n    \t\\xmark & \\bf40.8& 43.1& 45.6\\\\\n    \t\\cmark & 39.5& \\bf 44.9& \\bf 49.3\\\\\n    \t\\bottomrule[1.0pt]\n    \\end{tabular}}\n    \\vspace{1mm}\n    \\caption{\\textbf{Sim2Real:} Analyzing the effect of image-level alignment.}\n   \n    \\label{tab:imglevel}\n    \\vspace{0mm}\n\\end{table}\n\\myparagraph{Do we need image-level alignment?} \\Tableref{tab:imglevel} presents the comparison of model performance with image-level alignment added on top of the instance-level alignment presented before. \nThis comparison is done using AT across different aggregation levels. \nWe see that image-level alignment brings clear added improvement on both multi-group models, while degrading slightly on the single group model. \nOn the single group model, the instance-level alignment is happening at a global level since all the instances are aggregated into a single group before inducing alignment. Adding an extra alignment will not help further and could possibly induce noise, as seen in the results ($40.8\\%$ vs $39.5\\%$). However, on models with multiple groups, instance level AT focuses on local feature alignment, and hence adding global alignment with image-level AT is beneficial. Thus, we use image-level alignment for the remaining of the experimental section.\n\n\\begin{table}\n     \\centering\n     \\scalebox{0.9}{\n   \n\t\\begin{tabular}{*{2}{c} cc}\n\t\t\\toprule[1.0pt]\n\t\n\t\tAggr.\\ levels & Aggr.\\ mechanism &  Foggy& Sim2Real \\\\\\cmidrule(lr){1-1}\\cmidrule(lr){2-2}\\cmidrule(lr){3-4}\n\t\tProposals & No grouping & 38.5  & 39.0 \\\\\\cmidrule(lr){1-1}\\cmidrule(lr){2-2}\\cmidrule(lr){3-4\n\t\tSG & \\multirow{4}{*}{Cosine} & 33.7 & 39.5 \\\\\n\t\tMG (adaptive) &  & 41.8  & 44.9 \\\\\n\t\tMG+CA (adaptive) & & \\textbf{43.3} & \\textbf{49.3}\\\\\n\t\tMG+CA (fixed) & & 42.5 & 49.0\n\t\t \\\\\\cmidrule(lr){1-1}\\cmidrule(lr){2-2}\\cmidrule(lr){3-4\n\t\tMG+CA (adaptive) & IoU & 41.9 & 44.8\\\\\n\t\t\\bottomrule[1.0pt]\n\t\\end{tabular}}\n\t\\vspace{1mm}\n\t\\caption{\n\t\\textbf{Sim2Real \\& Foggy:} Analyzing the choice of different aggregation levels and mechanisms.}\n    \\label{tab:ablation_foggy_sim}\n    \\vspace{0mm}\n\\end{table}\n\n\n\n\\myparagraph{Aggregation levels \\& mechanisms.} Next, we study the process of aggregating instance proposals into groups before performing alignment. We compare the effect of both the number of groups as well as the mechanism used to aggregate proposals into groups. Table~\\ref{tab:ablation_foggy_sim}, \nfirst row shows results using original proposals without any grouping for the instance level alignment. \nAggregating instances into a SG per category causes a significant drop in performance, indicating that the condensing features into one vector may not be a useful approach. \nHowever, MG setup based on visual similarity (Cosine), is beneficial ($41.8\\%$ vs $38.5\\%$ on \\emph{Foggy} and $44.9\\%$ vs $39.0\\%$ on \\emph{Sim2real} ).\nPerformance is further improved by ignoring the predicted class-label ($43.3\\%$ on \\emph{Foggy} and $49.3\\%$ on \\emph{Sim2real}) and compared to the last set with MG, this shows that noisy pseudo labels (in MG) can be harmful to the clustering process and may have negative impact on the alignment.\nBoth the above models use cluster radius parameter to let the model vary the number of groups adaptively over the course of training.\nHere, we do not compare different clustering methods directly. However, we also experiment with fixing the number of clusters, as shown in \\emph{MG+CA (fixed)}. we perform a sweep of the number of clusters hyper-parameter and report the best numbers here (full results can be found in supplementary, figure 4). \nThis model performs slightly worse than \\emph{MG+CA (adaptive)}, indicating that the flexibility from adaptive number of clusters is beneficial.\n\nFinally in the last row, \nby using spatial overlap~(using IoU) to cluster instances~(as proposed in~\\cite{GPA, zheng_cvpr20_prototype}), we see that the performance drops by 1.4\\% and 4.5\\% on \\emph{Foggy} and \\emph{Sim2Real} respectively, compared to using visual similarity based clustering~(MG+CA (adaptive)). These large drops show that our visual similarity based grouping is a better way to accumulates proposals, since it allows grouping distant instances and avoids redundant group representatives.\n\n\\subsection{Comparison with SOTA}\n\\label{sec:comppriorwork}\n\nIn this section, we evaluate the best design choices embedded in our ViSGA\\xspace  \nand compare it to prior works in each of these domains in \\secref{sec:related}.\nViSGA\\xspace incorporates image-level alignment and adversarial training framework along with the novel group alignment of visual similarity based class-agnostic clusters.\n\\begin{table}[t]\n     \\centering\n     \\scalebox{0.8}{\n   \n\t\\begin{tabular}{{c}cc}\n\t\t\\toprule[1.0pt]\n\t\tMethods &  Cross Camera & Sim2Real \\\\\\cmidrule(lr){1-1}\\cmidrule(lr){2-3}\n\t\tFaster R-CNN  & 32.5  & 31.9 \\\\\\cmidrule(lr){1-1}\\cmidrule(lr){2-3\n\t\tDA-Faster \\cite{da_faster_rcnn} & 41.8 & 41.9 \\\\\n\t\tDivMatch \\cite{diversify_and_match} & 42.7  & 43.9 \\\\\n\t\tSW-DA \\cite{strong-weak} & 43.2 & 44.6\\\\\n\t\tSC-DA \\cite{zhu_cvpr19_selective_alignment} & 43.6 & 45.1\\\\\n\t\tMTOR \\cite{mean_teacher} & - & 46.6\\\\\n\t\tGPA (Only RCNN) \\cite{GPA} & 46.1 & 44.8\\\\\n\t\tGPA \\cite{GPA} & 47.9 & 47.6\\\\\n\t\t\\cmidrule(lr){1-1}\\cmidrule(lr){2-3\n\t\tOurs & 47.6 & \\textbf{49.3}\\\\\n\t\t\\bottomrule[1.0pt]\n\t\\end{tabular}\n\t}\n\t\\vspace{1mm}\n\t\\caption{Experimental results (\\%) of \\emph{Sim2Real \\& Cross Camera}.} \\label{eval_sim10k_kitti_city}\n\\end{table}\n\n\n\n\n\nTable~\\ref{eval_sim10k_kitti_city} shows the results for the \\emph{Sim2Real} and \\emph{Cross Camera} scenarios on \\emph{Car} class. \nThe adaption is challenging on \\emph{Sim2Real} due to relatively large domain shift between source and target. However, as shown in the table, our approach outperforms other methods by a fair margin ($49.3\\%$ vs $47.6\\%$ by the closest model, GPA).\nFor Cross Camera scenario, our approach has competitive performance compared to GPA\\cite{GPA}, while out-performing other approaches.\nIn Table~\\ref{eval_foggy_cs}, ViSGA\\xspace achieves SOTA results, with large improvements over other recent work. \nIt outperforms the GPA method~\\cite{GPA} ($43.3\\%$ vs $39.5\\%$) based on prototype matching, highlighting the importance of our design choices --- multiple similarity based class-agnostic groups and adversarial training.\nIn summary, the good performance shown by our model across three datasets with state-of-the-art results in two of them, provides evidence that our similarity-based method is successful in aligning instance level representations. \n\\begin{table}[]\n\\center\n\\scalebox{0.85}{\n\\tabcolsep=1.5pt\n\\begin{tabular}{ c | c c c c c c c c | c}\n  \\hlineB{3}\n   Methods & prsn & rider & car & truck & bus & train & mcycle & bicycle & mAP \\\\ \\hline\n   Faster R-CNN & 27.2 & 31.8 & 32.5 & 16.0 & 25.5 & 5.6 & 19.9 & 27 & 22.8\\\\\\hline\n  DA-Faster \\cite{da_faster_rcnn} & 29.2 & 40.4 & 43.4 & 19.7 & 38.3 & 28.5 & 23.7 & 32.7 & 32.0 \\\\\n  DivMatch \\cite{diversify_and_match} & 31.8 & 40.5 & 51.0 & 20.9 & 41.8 & 34.3 & 26.6 & 32.4 & 34.9 \\\\\n  SW-DA \\cite{strong-weak} & 31.8 & 44.3 & 48.9 & 21.0 & 43.8 & 28.0 & 28.9 & 35.8 & 35.3 \\\\\n  SC-DA \\cite{zhu_cvpr19_selective_alignment} & 33.8 & 42.1 & 52.1 & 26.8 & 42.5 & 26.5 & 29.2 & 34.5 & 35.9 \\\\\n  MTOR \\cite{mean_teacher} & 30.6 & 41.4 & 44.0 & 21.9 & 38.6 & 40.6 & 28.3 & 35.6 & 35.1 \\\\\n  GPA \\cite{GPA}  & 32.9 & \\textbf{46.7} & 54.1 & 24.7 & 45.7 & 41.1 & \\textbf{32.4} & 38.7 & 39.5 \\\\ \\hline\n    Ours & \\textbf{38.8} &  45.9 & \\textbf{57.2}  & \\textbf{29.9} & \\textbf{50.2} & \\textbf{51.9} &  31.9 & \\textbf{40.9}  & \\textbf{43.3}\\\\\n  \\bottomrule[1.0pt]\n\\end{tabular}}\n\\vspace{1mm}\n\\caption{Experimental results of (\\%) \\emph{Foggy}.}\n\\vspace{0mm}\n\\label{eval_foggy_cs}\n\\end{table}\n\n\n\n\n\n\\myparagraph{Qualitative analysis of ViSGA\\xspace.} \n\\Figref{fig:qualitative_results} compares the detection outputs of Faster R-CNN and ViSGA\\xspace models with different aggregation mechanisms, on \\emph{Sim2Real} scenario. \n\\Figref{fig:cluster_analysis} shows the evolution of the number of groups during ViSGA\\xspace training, on \\emph{Foggy} and \\emph{Sim2Real}\nWhile the number of initial groups are similar in both cases, the number of clusters on Sim2Real drops-off quickly and settles around 50 clusters when the best model performance is achieved.\nIn contrast, in \\emph{Foggy}, the number of clusters increases and is plateaus around 180, where the best performance is achieved. \nThis difference can be understood by noting that the \\emph{Foggy} scenario has 8 categories compared to only one category in Sim2real. \nHence the model needs more clusters in \\emph{Foggy}\n\\begin{figure}[t]\n\t\\centering\n\t\\includegraphics[width=0.30\\textwidth]{figures\/clusters_foggy_sim2real.png}\n\t\\caption{Evolution of number of groups during training for our ViSGA\\xspace model. Orange and blue dashed lines show the best training stops for Foggy and Sim2Real respectively. } \n\t\\label{fig:cluster_analysis}\n\t\\vspace{0mm}\n\\end{figure}\nIn figure~\\ref{sensitivity_analysis} shows experimental results measuring the sensitivity of the cluster radius parameter.\nWe can observe that for \\emph{Sim2Real} the network performs well when the threshold is low but it is relatively sensitive to high or very low radius values (no grouping). \nThis might be due to the large shift between synthetic images and real images. \nIn addition, a low cluster radius creates many single member clusters, reducing information aggregation. \nIn contrast, the performance is not very sensitive to various radius values on \\emph{Foggy}, where the domain gap is smaller. \nAdditionally, figure 6 in the supplement presents a tSNE  \\cite{van2008visualizing} visualizations of source and target feature distribution, to visually illustrate how ViSGA\\xspace prioritizes foreground alignment. This is also supported by figure 4 in the supplement, which shows that foreground objects get allocated more clusters and hence are prioritized for alignment.\n\n\\myparagraph{Computational Overhead.} The extra training time cost of our method, from computing the distances between the features of each proposal, is relatively small (eg.  one batch runtime is 0.79 for ViSGA\\xspace compared 0.62 for w\/o ViSGA\\xspace). ViSGA\\xspace has no overhead during inference. Note that contrastive learning based methods, e.g., GPA, also compute the distance between proposals in each domain.\n\\begin{figure}\n\t\\centering\n\t\\includegraphics[width=0.35\\textwidth]{figures\/chart_sensitivity_analyses.pdf}\n\t\\caption{Sensitivity analysis of cluster radius parameter.}\n\t\\label{sensitivity_analysis}\n\t\\vspace{-2mm}\n\\end{figure}\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection{Overview} \nOur  generalized UDA framework comprises  of three main components.\nFirst is a standard object detection network, Faster R-CNN, which takes an input image and produces bounding boxes and labels for all object instances present in the image. \nThe second component is an image-level domain adaptation loss which encourages alignment of the global image representation in the backbone network.\nThe third component is an instance-level domain adaptation loss which induces alignment of representations of each object instance. \nThis is illustrated in \\figref{fig:overall}. \nThus, the overall training objective of the method can be written as:\n\\begin{equation}\n\\mathcal{L} = \\mathcal{L}_{det} + \\lambda_1 \\mathcal{L}_{img}+\\lambda_2\\mathcal{L}_{inst}, \n\\label{eqn:final_loss}\n\\end{equation}\nwhere, $\\mathcal{L}_{det}$ is the supervised training loss for the detector, $\\mathcal{L}_{img}$ and $\\mathcal{L}_{inst}$ are the image-level and instance-level domain adaptation (DA) losses respectively, $\\lambda_1$ and $\\lambda_2$ are trade-off parameters. For methods that do not apply instant level alignment $\\lambda_2$ is set to zero. Note that $\\mathcal{L}_{det}$ is only applicable in the source domain where ground-truth bounding box annotations are available. \n\n\\myparagraph{Detection network.} Following the convention set by early work on cross-domain object detection, we deploy Faster R-CNN \\cite{da_faster_rcnn} as the object detection network in both, our method and the analysis. \nIt consists of a Region Proposal Network (RPN) and a detection head. Both networks are trained with two loss terms each, a regression loss for bounding box estimation and a classification loss for label prediction. Thus the detection loss $\\mathcal{L}_{det}$ for Faster R-CNN is composed of $\\mathcal{L}_{RPN}$ and $\\mathcal{L}_{head}$. \n\\subsection{How to Induce Alignment?}\n\\label{subsec:alignment_mechanism}\nThe role of the domain adaptation losses ($\\mathcal{L}_{img}, \\mathcal{L}_{inst}$) is to induce alignment between the model's representation of source and target domain inputs. \nDownstream blocks that use such invariant representation (here for example RPN and the detection heads), \n would be domain-agnostic and perform equally well in both domains.\nWhile adversarial training has been the dominant paradigm for reducing the discrepancy between feature distributions~\\cite{da_faster_rcnn, strong-weak, zhu_cvpr19_selective_alignment}, recently contrastive losses have been proposed to match source and target features \\cite{GPA, kang2019contrastive}. We present these approaches in this subsection and compare them in our experimental analysis~(\\secref{subsec:res_experimental_analysis}).\n\n\\myparagraph{Adversarial training.}\nThe key idea in Adversarial Training~(AT) based UDA methods is to learn domain invariant representations by fooling a discriminator which is trained to predict the input data domain based on the detector features. \nThis approach is usually class-agnostic, ignoring the features class information and focusing on domain-level alignment. \nSpecifically, the features $F_d$ of domain $d$ ($d=0$ for source and $d=1$ for target) is fed to the discriminator $\\mathcal{D}$ which predicts the domain of the extracted features. \nThe discriminator is trained by minimizing the cross-entropy loss as below.\n\\begin{equation}\n    \\mathcal{L}_{disc} = -d\\log(\\mathcal{D}(F_{d})) - (1-d)\\log(1- \\mathcal{D}(F_{d})). \n    \\label{eq:disc}\n\\end{equation}\nSince we want to adapt the features of the two domains to be indistinguishable by the discriminator, we have to maximize the loss in \\eqnsref{eq:disc} w.r.t the features $F_d$. This is achieved by incorporating a gradient reverse layer (GRL) \\cite{grl_ganin}, before features are input to the discriminator.\n\n\\myparagraph{Contrastive learning.} \nAs an alternative to AT, one can apply max-margin contrastive losses to align source and target features by leveraging the class information.\nThe main idea here is to push features from the same class closer and push apart features belonging to different classes across domains.\nWhen matching a single feature vector $F_d^i$~per class $i$ in each domain $d \\in (0,1)$, the max-margin contrastive loss takes the form: \n\\small\n\\begin{equation} \\label{eq:max_margin}\n\t\\begin{split}\n    \\mathcal{L}_{CL} = \\sum_i^C \\left[ ||F_0^{i} - F_1^{i}||_2^2 + \\sum_{j, j\\neq i}^C max\\{0, m - ||F_0^{i} - F_1^{j}||_2^2\\}\\right] \n\t\\end{split}\n\\end{equation}\n\\normalsize\nwhere $C$ is the number of classes and $m$ is the margin.  \nSince target data is unlabeled, the class prediction by the detector is used as a pseudo-label in \\cite{GPA} to apply \\eqnref{eq:max_margin}.\nIn our analysis, we also study the effect of ignoring this class information. \nThis can be achieved by considering only two sets of vectors of cardinality $N_0$ and $N_1$, possibly unequal number ($N_0 \\neq N_1$), from source and target domains to align.  \nTo apply contrastive losses here, we make a simple modification. \nInstead of matching class-specific features across domains, we match the proposals from one domain to the closest features (nn) of the other domain~(\\ref{eq:max_margin_proposal_nn}) and minimize the distance between their representations~(\\ref{eq:max_margin_proposal}), as shown below.\n\\begin{small}\n\t\\begin{align} \\label{eq:max_margin_proposal_nn}\n        \\text{nn}(i) &= \\text{argmin}_{j<N_1} ||F_0^{i} - F_1^{j}|| \\\\\n        \\label{eq:max_margin_proposal}\n        \\begin{split}\n            \\mathcal{L}_{CL} &= \\sum_i^{N_0} \\big[ ||F_0^{i} - F_1^{\\text{nn}(i)}||_2^2 \n            \\\\&+ \\sum_{j, j\\neq \\text{nn}(i)}^{N_1} max\\{0, m - ||F_0^{i} - F_1^{j}||_2^2\\} \\big].\n        \\end{split}\n\t\\end{align}\n\\end{small}\nIn our method, we utilize AT, avoiding  potential noise as a result of the reliance on unstable pseudo-labels during the alignment process. Our  aggregation strategy can leverage proposals similarities and possible embedded class-information as we explain in the sequel. \n\\subsection{What Features to Align?}\n\\label{subsec:feature_levels}\nIn detection, two main levels of feature alignment can be considered: 1)  image-level features output by the backbone network and 2)  instance-level or object-level features obtained after pooling each region-of-interest proposed by the RPN network. \nThe predominant approach aims for complete alignment at instance-level, i.e.\\ the representation of every proposed object, in source or target domain, should be domain agnostic. \nThis might be difficult to achieve, especially when complete alignment is challenging for the model, and when the source or target data during alignment contains some domain-specific outliers, e.g.\\ specific backgrounds only found in a simulation domain. \nTo address this, recent works aggregate the proposals on each of the source and target before applying feature alignment~\\cite{GPA, zheng_cvpr20_prototype, zhu_cvpr19_selective_alignment}.\nBoth~\\cite{GPA} and \\cite{zheng_cvpr20_prototype} take it to the other extreme, by collapsing the instances into a single prototype per category.\nWhile~\\cite{GPA} merges prototypes based on spatial overlap using intersection-over-union (IoU) and class labels, \\cite{zheng_cvpr20_prototype} only uses class labels to mean pool proposals into prototypes.\nIn contrast~\\cite{zhu_cvpr19_selective_alignment} treads a middle ground by merging proposals into many discriminative regions, but still only using spatial overlap as the merging criteria.\n\nIn our analysis in \\secref{subsec:res_experimental_analysis}, we compare the effectiveness of different components of this aggregation including 1) spatial grouping vs similarity based grouping (discussed in \\secref{sec:visga}) 2) using class information vs class agnostic and 3) single prototypes vs multiple groups.\n\\subsection{Similarity-based Group Alignment} \n\\label{sec:visga}\nIn this section, we propose a novel similarity-based grouping to aggregate object proposals before performing alignment.\nWe first aggregate proposals based on visual similarity into varying number of feature groups.\nAT is then applied to align the mean embeddings of the groups extracted from the source and target domains. \nThis simple yet effective change brings three key benefits. \nFirst, adversarial training at group level enables our model to coarsely align the main feature clusters, instead of attempting complete alignment of all instances which might be infeasible.\nSecond, in contrast to the spatial overlap used in \\cite{GPA, zhu_cvpr19_selective_alignment}, visual similarity-based clustering allows our model to group objects which are located far away in the image, but look similar. \nNote that this still groups heavily overlapping proposals, since they tend to also be visually similar. Hence, it avoids producing duplicate visually similar groups.\nBy using visual similarity, we do not depend on the pseudo-labels different from  previous approaches~\\cite{GPA, zheng_cvpr20_prototype}.  \nThe pseudo-labels tend to be noisy,   thus avoiding such dependency can be beneficial especially in early training.\nMoreover, when similar proposals are aggregated, we can implicitly leverage class information since the aggregated proposals are likely to be of the same class. \nFinally, by adaptively varying the number of groups, instead of using single prototypes, our model retains sufficient capacity to represent intra-domain variance. \n\n\n\\myparagraph{Similarity-based clustering.} To perform similarity-based clustering, we take as input the $N$ proposals generated by RPN and their fixed feature vectors denoted by $f\\in \\mathbb{R}^{N \\times m}$.\nIn order to discover the main feature groups, we cluster these features using  hierarchical agglomerative clustering. Starting bottom-up, each proposal is considered as an individual cluster. Then, at each step, the two closest clusters according to a distance metric are merged together. We utilize cosine distance as our merging metric:\n\\begin{equation} \\label{eq:metric}\ndistance (z_{i} , z_{j}) =1 - \\frac{z_{i} . z_{j}}{||z_{i}|| \\ ||z_{j}||}, \n\\end{equation}\n\\noindent where $z_{i}$ and $z_{j}$ show $i$-th and $j$-th proposal's feature embeddings. In contrast to recent work~\\cite{GPA}, which uses spatial overlap~(measure by IoU) to group together instances, using cosine similarity enables us to pair instances which are located far from each other, but are visually similar.\nMerging is stopped when dissimilarity within a cluster, as defined by a \\emph{linkage function}, exceeds the cluster radius parameter $\\tau$. We apply the complete-linkage heuristic~\\cite{defays1977efficient}, which ensures that the farthest distance of two members is smaller than $\\tau$.\n\\begin{equation} \\label{eq:linkage}\n\\text{MaxLink}(A,B) = \\ max \\{ dist(a,b) : a\\in A, b\\in B\\},\n\\end{equation}\n\\noindent where A, B are two sets of proposals' features in two clusters and $dist$ is the cosine distance. \nThis hierarchical clustering approach allows our model to adaptively change the number of feature groups during training, instead of having a fixed number of cluster like in k-means. \nOnce the clustering has converged, instances assigned to each cluster are pooled to construct a representative embedding $Z_{c_i}$:\n\\begin{equation} \nZ_{c_i} = \\frac{\\sum_{i=0}^{N_{c_i}} \\, z_i}{N_{c_i}},\n\\end{equation}\n\\noindent where $N_{c_i}$ is the number of instances assigned to the cluster $c_i$. \nThe group representative $Z_{c_i}$ is fed to a group-level discriminator and adversarial training is applied to align groups from the two domains using \\eqnref{eq:disc}.\n\nFinally, our method~(ViSGA\\xspace) combines image and instance-level alignment of aggregated proposals via adversarial training as illustrated in Fig.\\ref{fig:teaser}.\n\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction} \nThe spin galvanic effect (SGE), i.e  \nspin polarization-charge current interconversion, is currently the focus of intensive theoretical and applied research~\\cite{Ganichev2016}. Quite generally, in the absence of inversion symmetry, polar and axial vectors may transform similarly and hence a coupling between the spin polarization and the charge current density can occur~\\cite{Ivchenko1978}. In solid-state systems, as in semiconductors and metals, the key microscopic mechanism  is provided by the spin-orbit coupling (SOC)~\\cite{Edelstein90,Aronov89}.  Both the Rashba and the Dresselhaus spin-orbit coupling  (RSOC and DSOC, respectively), have been considered. RSOC arises as a result of the structure inversion asymmetry (SIA) in a semiconductor quantum well or at a metal interface.\nRSOC was first proposed for non-centrosymmetric wurtzite semiconductors~\\cite{Rashba} and, later, also for 2D electron gases~\\cite{bychkov1984properties}. Besides, spin-dependent splitting in heterojunctions has provided the basis for the spin transistors~\\cite{DattaDas}. RSOC may be seen as arising from the   Zeeman interaction between the magnetic moment component parallel to the spin and the effective magnetic field moving with the electron~\\cite{Newperspectives}. Recently, RSOC was detected in new materials such as metal surfaces, bulk and interfaces materials of semiconductors~\\cite{1,2,3,4,5,13} and heavy metals~\\cite{3}. Moreover, RSOC plays an important role even in more exotic areas like\nthe emergence of topological states in insulators and Majorana fermions in topological superconductors~\\cite{Hasan,Beenakker}. \nDSOC, on the other hand, arises in the bulk as a consequence of the bulk inversion asymmetry (BIA)~\\cite{Dresselhaus55}. \n\nThe  inverse SGE manifests as a non-equilibrium spin polarization due to an applied electric field. In solid-state systems, dissipation due to disorder created by impurities and imperfections leads to steady-state conditions with a DC charge current proportional to the applied electric field. In this linear-response regime, both the charge current and the non-equilibrium spin polarization are proportional to the electric field~\\cite{Edelstein90,rai2014microscopic}. In such a situation the electron drift velocity remains much smaller than the Fermi velocity, and the spin polarization also remains small. Recently, Vignale and Tokatly~\\cite{vignale2016theory} have considered the case of a perfectly clean two-dimensional electron gas (2DEG) with RSOC and have provided an elegant exact solution of the associated model, which allows to analyze the SGE and its inverse in the nonlinear regime, where electrons can be accelerated to high velocities.\n\nWhile the discussion on disorder-free systems might appear purely academic, there exists the possibility of investigating spin-orbit coupling effects in cold atoms~\\cite{114}, that are free from strong disorder. However, the synthetic fields produced on atoms by the action of Raman fields~ \\cite{zhu2006spin,Liu09,lin2011spin, su2016rashba} result in an anisotropic coupling, which can be seen as a combination of RSOC and DSOC.\n\nIn this paper we extend the theory of Vignale and Tokatly of nonlinear effects in inverse SGE to anisotropic spin-orbit couplings in the presence of a Zeeman field. We demonstrate that adding this complexity still allows for an analytical solution of the model, and its phenomenology can be fully analyzed.  In  particular, we investigate the dynamics of the spins in the adiabatic regime with Rashba spin-orbit coupling. To investigate the spin-dependent evolution we directly solve the Schr\\\"odinger equation in terms of spinors and present the analytical solutions. In addition, we describe the average non-equilibrium spin polarization and tunability of the system for different values of the two Rashba coefficients. We then compare the result with the adiabatically-approximated spin polarization.\n\n\n\n\n\n\\section{ The model  and its solution}  \nWe consider a collection of spin-one half atoms, which is driven by a constant and homogeneous electric field defined,  in a vector gauge, from the vector potential ${\\bf A}=-E\\,t\\,\\hat{\\textbf{x}}$. \nDue to the  translational invariance of the system, the system single-particle eigenstates are plane waves with a given momentum. \nThe system evolution is then governed by the Hamiltonian:\n\\begin{equation}\n\\begin{aligned}\nH({\\bf p},t)= H_0+H_{SO}+H_{E}+H_{ext},\n\\end{aligned}\n\\label{3}\n\\end{equation}\n\\noindent where $H_0= \\frac{1}{2m}[{\\bf p}+e{\\bf A}]^2$ corresponds to the kinetic part and $H_{SO}$ is Rashba spin-orbit interacting term: $H_{SO}= \\alpha_1\\,\\sigma_x\\,p_y-\\alpha_2\\,\\sigma_y\\,p_x$,\n$p_{x,y}$  being the in-plane  components of the momentum operator and $\\sigma_{x,y}$  the Pauli matrices  associated to the spin degree of freedom~\\cite{note1}. {\\color{black} This coupling produces the same effects as a magenetic field, which we will call Rashba field. In the standard treatment of RSOC and DSOC, one would have instead Hamiltonians of the kind $H_{RSOC}= \\alpha\\,(\\sigma_x\\,p_y-\\sigma_y\\,p_x)$, and $H_{DSOC}= \\beta\\,(\\sigma_x\\,p_y+\\sigma_y\\,p_x)$, respectively. The asymmetric case we are treating can then be considered as a combination of the two effects with strengths $\\alpha=(\\alpha_1+\\alpha_2)\/2$ and $\\beta=(\\alpha_1-\\alpha_2)\/2$. When the electric field is applied, minimal coupling results in an Edelstein term $H_E=\\alpha_2eEt \\,\\sigma_y$, which amounts to the presence of an effective field growing with time. In addition, we also include a Zeeman coupling with an external magnetic field $H_{ext}=-\\mu_B{\\bf B}\\cdot{\\boldsymbol{\\sigma}}$. \nThe occurrence of such coupling terms is not uniquely attributed to the application of actual fields and the simultaneous presence of RSOC and DSOC mechanisms: these may be effective descriptions. For cold atom systems, the Hamiltonian (\\ref{3}) is derived from a single-particle Hamiltonian where two hyperfine states of the ground level are coupled via Raman lasers, whose phase and intensity depend on the position. The projection of the Hamiltonian onto the manifold of these two states generates the non-Abelian gauge potential~\\cite{zhu2006spin,Liu09}. The rotation of the spin axes in this gauge potential reveals asymmetric spin-orbit coupling, which can be viewed as a combination of Rashba and Dresselhaus spin-orbit couplings.}\n\n\n\n\nTo begin with, we consider  the effect of having two different Rashba coefficients $\\alpha_1$ and $\\alpha_2$; in the absence of external fields, the eigenvalues of the spin-orbit part of the Hamiltonian read\n\\begin{equation}\n\\label{p}\nE_{1,2}=\\frac{p^2}{2m}\\mp\\sqrt{\\alpha_1^2p_y^2+\\alpha_2^2p_x^2}{\\ }\n\\end{equation}\n\\noindent being $p_x= p\\,\\cos\\theta$ and $p_y= p\\,\\sin\\theta$. The different coefficients break the circular symmetry of the constant energy contour of the pure RSOC: the absolute value of the momentum now explictly depends on the angle $\\theta$ between the $x$ axis and $\\hat{\\textbf{p}}$, giving an elongated shape to the contours:\n \\begin{equation}\np_{1,2}(\\theta, p_0)=\\sqrt{m^2\\alpha^2 (\\theta)+p_0^2}\\pm m \\alpha (\\theta)\n\\label{momentum}\n\\end{equation}\nwith $\\alpha (\\theta)=\\sqrt{\\alpha_1^2 \\sin^2 (\\theta)+\\alpha_2^2 \\cos^2 (\\theta)}$ and $p_0^2\/2m$ defining the energy of the contour and the Fermi momentum in the absence of SOC, Fig.~\\ref{ellipse}.\nFurthermore, the spin helicity of the eigenstates is no longer perpendicular to the momentum.\n\nThe implication of this asymmetry for the spin polarization dynamics can be assessed by directly solving the  Schr\\\"{o}dinger equation for the Hamiltonian in Eq.~({\\ref{3}}). \nFor a given Fermi momentum $p_0=p_F$, the energy levels with $p<p_2(\\theta,p_F)$ have both spin states occupied and then do not contribute to the spin dynamics. Hence, \nwe  consider only the states with $p_2(\\theta, p_F)<p<p_1(\\theta,p_F)$. \n\n\nThe interacting and free parts of the Hamiltonian ({\\ref{3}}) can be written as a $2\\times2$ matrix; following Ref.\\cite{vignale2016theory} the y axis is  taken as the quantization direction for spin~\\cite{note2}:\n\\begin{widetext}\n\\begin{equation*}\nH=\\begin{pmatrix}\n-\\alpha_2 \\,p\\,\\cos\\theta+\\alpha_2\\,eEt-\\mu_B B_y & -\\alpha_1\\,p\\,\\sin\\theta+\\mu_B (B_x+iB_z)\\\\\n-\\alpha_1\\,p\\,\\sin\\theta+\\mu_B (B_x-iB_z) & \\alpha_2\\,p\\,\\cos\\theta-\\alpha_2\\,eEt+\\mu_B B_y\n\\end{pmatrix}.\n\\end{equation*}\n\\end{widetext}\n\n\\begin{figure}\n\t\\includegraphics[width=0.9\\linewidth]{FermiSurfaces.pdf}\n\t\\caption{\\textbf{Fermi surfaces with  anisotropic SOC.} The Fermi surfaces associated to the two lower momentum $p_2(p_F,\\theta)$, and to the higher  momentum $p_1(p_F,\\theta)$ are shown as a function of the momentum components (in units of $p_F$). Here we set $m\\alpha_2=0.1p_F$, and $\\alpha_1\/\\alpha_2=1\/4$. States below $p_2(p_F,\\theta)$ are fully occupied (dark blue region), thus we only consider the contribution of states in the light blue region.}\n\t\\label{ellipse}\n\\end{figure}\n\nThe above form is the one for the Landau-Zener problem\\cite{Zener1932}, where the energy difference of two coupled levels varies linearly in time.  \nThe combination $\\alpha_2\\,eEt$ enters as an effective magnetic field due to the electric field. Following Ref.\\cite{vignale2016theory} we refer to this term as the Edelstein field.\nThe two relevant energy scales are the kinetic energy $p^2\/2m$ and {\\color{black} the work $eE L_{SOC}$ performed by the electric field the over the spin-orbit length $L_{SOC}= \\hbar (2m\\alpha_2)^{-1}$. In the absence of relaxation, this is the most relevant length scale}.\nIn the following for the sake of simplicity we take units such that $\\hbar =1$.\nNotice  that in the present anisotropic SOC, we must consider the SOC length in the same direction as the applied field.  It is then useful to introduce an adiabaticity parameter $\\gamma_p$ defined as the ratio of the above energy scales\n\\begin{equation}\n\\label{adiabaticity}\n\\gamma_p =\\frac{ e E L_{SOC}}{p^2\/2m}=\\gamma_0\\frac{p_0^2}{p^2},\n\\end{equation}\nwhere $\\gamma_0=\\frac{eE}{\\alpha_2 p_0^2}$.\nThe value of $\\gamma_p$ controls how fast the spin system reacts to the electric field.\nBy resorting to the natural units of energy $\\alpha_2 p \\sqrt{\\gamma_p}$, we introduce the following dimensionless quantities\n\\begin{equation}\n\\begin{aligned}\n&\\tau = {\\alpha_2p\\sqrt{\\gamma_p}} \\ t {\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ }\n\\tau_p=\\frac{\\cos\\theta}{\\sqrt{\\gamma_p}}\\\\\n&\\Delta_p=\\frac{\\sin\\theta}{\\sqrt{\\gamma_p}}\\frac{\\alpha_1}{\\alpha_2}{\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ }\n\\xi_{x,y,z}=\\frac{\\mu_BB_{x,y,z}}{\\alpha_2 \\, p\\, \\sqrt{\\gamma_p}}.\n\\end{aligned}\n\\label{5}\n\\end{equation}\n After the changes the Hamiltonian takes the form\n\\begin{equation}\nH_p(\\tau) = \\begin{pmatrix}\n\\tau-\\tau_p-\\xi_y & -\\Delta_p+\\xi_x+i\\xi_z \\\\\n-\\Delta_p+\\xi_x-i\\xi_z& -(\\tau-\\tau_p-\\xi_y)\n\\end{pmatrix}.\n\\end{equation}\n\n\nWe then look for the solution of the time-dependent Schr\\\"{o}dinger equation as a spinor with the two amplitudes $U(\\tau-\\tau_p-\\xi_y)$ and $V(\\tau-\\tau_p-\\xi_y)$\n\n\\begin{equation}\n\\ket{\\Psi(\\tau)}=U(\\tau-\\tau_p-\\xi_y)\\ket \\uparrow+V(\\tau-\\tau_p-\\xi_y)\\ket\\downarrow\n\\label{7}\n\\end{equation}\nin terms of which the Schr\\\"odinger equation becomes\n\\begin{equation}\n\\left\\{\n\\begin{aligned}\ni\\dot U(\\tau)&=\\tau U(\\tau)-\\tilde \\Delta_p\\,V(\\tau),\\\\\ni\\dot V(\\tau)&=-\\tau V(\\tau)-\\tilde\\Delta_p^*\\,U(\\tau),\n\\end{aligned}\n\\right.\n\\label{SysEq}\n\\end{equation}\nwhere $\\tilde\\Delta_p =\\Delta_p-(\\xi_x+i\\xi_z)$.\nBy rescaling the time variable as $z=\\sqrt{2}e^{-i\\frac{3\\pi}{4}}\\tau$\nand introducing the parameters $\\nu_+=\\frac{\\tilde\\Delta_p}{\\sqrt{2}}e^{-i\\frac{3\\pi}{4}}$,   $\\nu_-=\\frac{\\tilde\\Delta_p^*}{\\sqrt{2}}e^{i\\frac{\\pi}{4}}$,\nand $\\nu =\\nu_+\\nu_-=-\\frac{i}{2}|\\tilde\\Delta_p|^2$\nour system of equations becomes\n\\begin{equation}\n\\left\\{\n\\begin{aligned}\n\\dot{U}(z)+\\frac{z}{2}U(z)-\\nu_+V(z)=0\\\\\n\\dot{V}(z)-\\frac{z}{2}V(z)+\\nu_-U(z)=0,\n\\end{aligned}\n\\right.\n\\end{equation}\nwhose solution can be found in terms of parabolic cylinder functions by writing\n\\begin{equation}\n\t\\begin{aligned}\n\t\t&U(z)=D(\\nu,z),\\\\\n\t\t&V(z)=\\nu_-D(\\nu-1,z).\n\t\\end{aligned}\n\t\\label{sol1}\n\\end{equation}\n\n\nWe emphasize that the above represents the extension to the anisotropic case of the\n  solution originally found by Ref. \\cite{vignale2016theory}. \nIn the full normalized form,  two mutually orthogonal solutions read\n\\begin{equation}\n\t\\begin{aligned}\n\t\t&U^{(1)}(\\tau)=e^{-\\pi |\\tilde \\Delta_p|^2\/8}D(\\nu,z),\\\\\n\t\t&V^{(1)}(\\tau)=e^{-\\pi |\\tilde \\Delta_p|^2\/8}\\nu_- D(\\nu-1,z),\\\\\n\t\t&U^{(2)}(\\tau)=-[V^{(1)}(\\tau)]^*,\\\\\n\t\t&V^{(2)}(\\tau)=[U^{(1)}(\\tau)]^*.\n\t\\end{aligned}\n\t\\label{ind_sol}\n\\end{equation}\nThe chosen initial conditions, obtained by solving the Hamiltonian at $\\tau =0$, are,\nwith $\\tilde\\tau_p=\\tau_p+\\xi_y$,\n\\begin{equation}\n\\label{sys}\n\\begin{aligned}\n   U(-\\tilde\\tau_p)= U_0\\equiv\\sqrt{\\frac{1}{2}\\left(1+\\frac{\\tilde\\tau_p}{\\sqrt{\\tilde\\tau_p^2+|\\tilde\\Delta_p|^2}} \\right)    },\\\\\n   V(-\\tilde \\tau_p)=V_0\\equiv e^{-i {\\text {Arg}}(\\tilde\\Delta_p)}\\sqrt{\\frac{1}{2}\\left(1-\\frac{\\tilde\\tau_p}{\\sqrt{\\tilde\\tau_p^2+|\\tilde\\Delta_p|^2}}  \\right)    }.\n\\end{aligned}\n\\end{equation}\n\nThe above boundary conditions must be imposed on the general solution, which can be written as a linear combination of the two independent solutions (\\ref{ind_sol}) with coefficients $A_p$ and $B_p$.\nOne then gets\n\\begin{equation*}\n\t\\begin{aligned}\n\t\t&A_p=U_0[U^{(1)}(-\\tilde \\tau_p)]^*+V_0[V^{(1)}(-\\tilde \\tau_p)]^*\\\\\n\t\t&B_p=V_0\\,U^{(1)}(-\\tilde \\tau_p)-U_0\\,V^{(1)}(-\\tilde \\tau_p).\n\t\\end{aligned}\n\\end{equation*}\n\n\n\n\n\\begin{figure}\n\t\\centering\n\t\\begin{tabular}{@{}p{\\linewidth}}\n\t\\subfigimg[width=\\linewidth]{(a)}{g01.pdf} \\\\\n\t\t\\vspace{0.25cm}\n\t\\subfigimg[width=\\linewidth]{(b)}{g10.pdf}\n\t\\end{tabular}\n\t\\caption{\\textbf{Spin polarization component $S^y_{\\bf p}$ in different regimes.} Spin $y$-component as a function of time from the solutions of Eq.\\ref{SysEq} at fixed momentum and $\\theta=\\frac{\\pi}{2}$. The $z$-component of magnetic field is $B_z=0.3$.  (a) Adiabatic regime with $\\gamma_0=0.1$: the Rashba coefficients are $2\\alpha_1=\\alpha_2$ (orange), $\\alpha_1=2\\alpha_2$ (green), $0.95\\alpha_1=1.05\\alpha_2$ (purple) and $4\\alpha_1=\\alpha_2$ (gray). (b) Quasiadiabatic ($\\gamma_0=1$) and nonadiabatic ($\\gamma_0=10$): Rashba coefficients are $\\alpha_1=2\\alpha_2$ (orange, purple) and $2\\alpha_1=\\alpha_2$ (green, gray).}\n\t\\label{Comp}\n\\end{figure}\n\n\\section{Spin polarization} \nTo compute the spin polarization along the \\textit{y} direction we use $S^{y}=\\Psi^{\\dagger}\\sigma_z\\Psi$ and the analytical solution of the system (\\ref{SysEq}), by recalling that the spin quantization axis has been chosen along the $y$ direction~\\cite{note2}. Thus, for a given absolute value of the momentum in Eq.(\\ref{momentum}), and for $\\theta=\\frac{\\pi}{2}$, the spin along the $y$ direction reads  $S^y_{\\bf p}(\\tau,p,\\theta)=|U(\\tau-\\tau_p+\\xi_z)|^2-\\frac{1}{2}$. The numerical computation of the component $S^y_{\\bf p}$ as a function of time in different regimes is shown in Fig.\\ref{Comp}. \nIn the adiabatic regime (Fig.\\ref{Comp}a) when $\\gamma_0=0.1$ the component along \\textit{y} direction of the spin polarization $S^y_{\\bf p}$ {\\color{black} converges} slowly, with different timescales depending on the relative value of $\\alpha_1$ and $\\alpha_2$; these also dictate the  frequency of the oscillations. \n\\textcolor{black}{The spin adiabatically converges due to the presence of the external electric field.\n\nInitially the spin follows the Rashba field and points in the same direction. With time, the adiabatic influence of the external electric field causes the spin to respond. After a characteristic time, such an influence exceeds that of the Rashba field, thus the spin points along the direction of the electric field. In practice, we observe the saturation of the spin polarization for a given  magnitude of the external electric field.} In the quasiadiabatic or nonadiabatic regimes (Fig.\\ref{Comp}b) with $\\gamma_0=1$ and $\\gamma_0=10$, respectively, convergence occurs more rapidly, with the same qualitative differences due to the distinct coefficients $\\alpha_1$ and $\\alpha_2$. \n\n\\begin{figure*}\n\t\\centering\n\t\\begin{tabular}{@{}p{0.48\\linewidth}@{\\qquad}p{0.48\\linewidth}@{}}\n\t\t\\subfigimg[width=\\linewidth]{(a)}{Fig2a.pdf} &\n\t\t\\subfigimg[width=\\linewidth]{(b)}{Fig2b.pdf}\n\t\\end{tabular}\n\t\\caption{\\footnotesize \\textbf{Total spin polarization in adiabatic regime $\\gamma_0=0.1$.} Total spin polarization  $S^y(t)$ as a function of time $t$ for cold atomic system. (a) Rashba coefficients  $(\\alpha_1,\\,\\alpha_2)$, with $\\alpha_1>\\alpha_2$, from the upper to the lower curve are blue (1.00001, 0.99999), orange (1.05, 0.95), green (2, 1), red (3, 1) and purple (4, 1). (b) Rashba coefficients $(\\alpha_1,\\,\\alpha_2)$, with $\\alpha_1<\\alpha_2$, from the upper to the lower curve are blue (0.99, 1.01), orange (1, 1.5), green (1, 2), red (1, 3) and purple (1, 4).}\n\t\\label{Total}%\n\\end{figure*}\n\n\\begin{figure}[bpht!]\n\t\\includegraphics[width=8.5cm, height=5.2cm]{Fig3.pdf}\\\\\n\t\\caption{\\footnotesize \\textbf{Adiabatic approximation of the spin polarization.}  $S^y_{ad}$ as a function of time with fixed adiabatic parameter $\\gamma_0=0.1$ and different ratios of Rashba coefficients $k=\\frac{\\alpha_1}{\\alpha_2}$ with components of magnetic field {\\bf B} = (0.1, 0.2, 0.3) for the purple ($k=0.98$), red ($k=2$), orange ($k=3$), green ($k=0.5$) and yellow ($k=4$) curves. The blue curve is taken at {\\bf B} = 0 and $\\alpha_1=\\alpha_2$, which corresponds to the characteristic result for 2DEG.}\n\t\\label{Adiabatic}\n\\end{figure}\n\nWe now turn our attention to the total spin polarization. Differently from Vignale and Tokatly~\\cite{vignale2016theory}, who kept the momentum from Eq.~(\\ref{momentum}) fixed  at the Fermi level, assuming that the difference between $p_1$ and $p_2$ is small, we do not fix the momentum in our computation, i.e. the anisotropic case that we consider has the additional variable $p$. We consider the integration within the asymmetric region limited by the energies $E_1(p(\\theta,p_F))$ and $E_2(p(\\theta,p_F))$, and the Fermi level inthe absence of SOC lays in this region. Thus, the total spin polarization must be integrated as\n\n\\begin{equation}\n\tS^y (\\tau)=\\sum_{s=1,2} \\int \\ \\frac{d^2p}{(2\\pi)^2} \\ (-1)^{s-1} \\ S^y_{\\bf p}(\\tau) \\Theta \\left(\\frac{p_F^2}{2m}-E_s({\\bf p}) \\right)\n\t\\label{Integr}\n\\end{equation} \nwhere $\\Theta \\left(\\frac{p_F^2}{2m}-E_s({\\bf p}) \\right)$ is the Heaviside step function. This means that the total spin polarization can be computed by integrating $S^y_{\\bf p}$ over all the angles and averaging over the momentum $p(\\theta,p_0)$ as\n\t\\begin{equation}\n\t\tS^y ( \\tau)= \\int_{0}^{2\\pi} \\ \\frac{d\\theta}{2\\pi}\\int_{p_2(\\theta,p_0)}^{p_1(\\theta,p_0)} \\ \\frac{p\\,dp}{2\\pi} \\ S^y_{\\bf p}(\\tau,p,\\theta)\n\t\t\\label{Integr1}\n\t\\end{equation}\n\n\n\nFig.\\ref{Total} shows the total spin polarization $S^y$ for the two ratios of Rashba coefficients $\\alpha_1>\\alpha_2$ (Fig.\\ref{Total}a) and $\\alpha_1<\\alpha_2$ (Fig.\\ref{Total}b) in the adiabatic regime $\\gamma_0=0.1$. To evaluate Eq.(\\ref{Integr}) we consider $m=1$, $p_F=2$ and {\\bf B}=(0.1, 0.2, 0.3).\nThe blue and orange curves in Fig.\\ref{Total}a, corresponding to the case $\\alpha_1\\simeq\\alpha_2$, reach a steady condition soon, meaning that the spin direction follows that induced by the electric field. Besides, it confirms the theoretical prediction of the spin polarization for 2DEG with Rashba spin-orbit and Edelstein effect \\cite{vignale2016theory}. The violet and red curves in Fig.\\ref{Total}a are the total spin polarizations for $\\alpha_1=2\\alpha_2$, $\\alpha_1=3\\alpha_2$, and $\\alpha_1=4\\alpha_2$: they respond very slowly to the influence of an external electric field $E$, hence the steady state of the atomic spin takes longer to build up, depending on the ratio of Rashba coefficients. From Fig.\\ref{Total}b we observe that all the curves respond faster than in the case $\\alpha_1>\\alpha_2$, since saturation occurs in shorter times: only the blue ($1.01\\alpha_1=0.99\\alpha_2$), orange ($1.5\\alpha_1=\\alpha_2$) and green ($2\\alpha_1=\\alpha_2$) curves have a longer build-up time.\n\n\n\n\nNow let us consider the adiabatic approximation and compare it with the solutions in the adiabatic regime of weak electric field $E$. Note that we calculate the spin polarization $S^y_{{\\bf p},ad}$ with regard to the lower eigenstate of the system, which means that for all times the system under adiabatical process of the external electric field remains in the instantaneous lower eigenstate. This approach allows to obtain the result of the evolution considering time $\\tau$ as a parameter in the calculations. To this purpose we solve the system of equations (\\ref{SysEq}) taking into account only the eigenvalue for the lowest state. The component of the approximated spin polarization in the adiabatic regime can be found as\n\t\n\\begin{equation}\nS^y_{{\\bf p},ad}=\\frac{1}{2}\\frac{|\\tilde\\Delta_p|^2-\\left(\\tau-\\tilde\\tau_p+\\sqrt{|\\tilde\\Delta_p|^2+\\tilde\\tau_p^2}\\right)^2}{|\\tilde\\Delta_p|^2+\\left(\\tau-\\tilde\\tau_p+\\sqrt{|\\tilde\\Delta_p|^2+\\tilde\\tau_p^2}\\right)^2}\n\\end{equation}\n\nFig.\\ref{Adiabatic} shows the evolution of total spin polarization for a cold atomic system together with that in 2DEG (blue) with {\\bf B} = 0 and $\\alpha_1=\\alpha_2$ with $k=\\frac{\\alpha_1}{\\alpha_2}$, retrieved by integrating numerically over the angles and averaging over the momentum $p$ as in Eq.(\\ref{Integr1}) with the substitution of $S^y_{\\bf p}(\\tau,p,\\theta)$ with its adiabatic expression $S^y_{{\\bf p},ad}$.\n\n\nAs we can see from Fig.\\ref{Adiabatic} the blue curve in the long times coincides with the purple one ($k=0.98$), but in the small times the presence of \\textcolor{black}{Rashba SOC field}\nmakes the latter lay higher than the one for the 2DEG. The green curve ($k=0.5$) saturates quite fast with the small times and even slightly faster than the one for 2DEG, which means that the Edelstein field is more significant than Rashba field. The red ($k=2$), orange ($k=3$) and yellow curve ($k=4$) decline in the slower way and their saturation happens much later in comparison to the purple and green curve, showing that Rashba field still prevails. \n\n\nThe results obtained from the adiabatic approximation qualitatively coincide with the results calculated from the exact solution, and have the identical subsiding behavior in both small and large ratio of SOC parameters $k$. \nThe artificial pseudospin states in cold atoms with Rashba spin-orbit coupling show a longer lifetime, highlighting their better tunability compared with 2DEG. \n\n\n\n\n\n\n\n\n\n\\section{Discussion} In contrast to solid-state matter, where Rashba spin-orbit coupling depends on the SOC of the material, in cold atoms this type of coupling can be generated synthetically and manipulated externally. The application of artificial gauge fields in quantum gases with neutral atoms provides a series of advantages: lack of disorder compared to 2DEG, convenience for studying many-body systems, external tunability and longer lifetime of pseudospin states. Moreover, a synthetic magnetic field cannot be influenced by a real field due to the absence of dynamical degrees of freedom. In addition, the gauge fields allow to observe a non-equilibrium spin dynamics in many-particle interactions without complications due to the disorder, as we have for 2DEG or other systems in condensed matter systems. \n\nWe described analytically the model of cold atoms in the presence of RSOC and DSOC, \\textcolor{black}{weak electric field and external magnetic field represented as a Zeeman field.} After finding the solutions in terms of parabolic cylinder functions and the component of spin polarization, we integrate over all the angles and average over the momentum. Results show that when the ratio of SOC coefficients is $\\alpha_1>\\alpha_2$ the total spin polarization relaxes much more slowly than for the inverse ratio. Besides, the adiabatic approximation shows that the total spin polarization $S^y_{ad}$ is tunable much better and has longer lifetime of the atomic spin state than the spin state in 2DEG.\n\nWhile our scheme does not suffer from the heating problem, it may have a problem with the limited lifetime of the pseudospin states, due to atomic collisions which induce a decay of the degenerate dark states into those of lower energy. This difficulty can be addressed, however, by introducing external magnetic fields and weak electric fields. Our results can enable further investigations on spin current, spin Hall effect in cold atoms or other effects requiring stable spin states and large tunability. \n\n{\\bf Acknowledgements}  We thank G. Vignale, C. Tassi, and A. Sheikhabadi for discussion.\n\n\n\\bigskip\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Why hadron-hadron scattering?}\n\n\nIn 1966, Weinberg considered pion scattering off hadrons\nusing current algebra techniques~\\cite{Weinberg:1966kf}.\nFor  pion scattering on a target with mass $m_t$ and isospin $T_t$,\nthe corresponding scattering lengths for total isospin $T$ read\n\\begin{equation}\na_T = -\\frac{L}{1+ M_\\pi\/m_t}\\, \\left[T(T+1) -T_t(T_t+1) -2 \\right]~,\n\\end{equation}\nwith $M_\\pi$ the charged pion mass. For pion scattering on a \npion [``the more complicated case''], he found\n\\begin{equation}\na_0 = \\frac{7}{4}L ~, ~~~ a_2 =\n-\\frac{1}{2}L~, ~~~\nL = \\frac{g_V^2 M_\\pi}{8\\pi F_\\pi^2} \\simeq 0.1 \\, M_\\pi^{-1}~,\n\\end{equation}\nwith $g_V \\simeq 1$ the vector coupling and $F_\\pi \\simeq 92\\,$MeV the\nweak pion decay constant. The predictions were on one side amazing \ndue to their extreme simplicity and on the other side surprising,\nas one believed that scattering lengths should be of the order\nof 1~fm, the typical hadronic length scale - and not much smaller\nas given by these equations. The physics behind this suppression\nis well understood - the Goldstone boson nature of the pions requires\ndecoupling from any given field as external momenta go to zero (in the\nlimit of vanishing quark \/ pion masses). Corrections to these \npredictions can be worked out consistently in chiral perturbation theory\n(CHPT) and variants thereof, as will be discussed in the next sections. \n CHPT is the effective field theory (EFT) of the Standard Model at low energies\nand allows one to systematically explore the consequences of the\nspontaneous and explicit chiral symmetry breaking in QCD. Given the aims\nand scope of this meeting, it is therefore natural to ask: what have \nwe learned  since the seminal work of Weinberg? In the following, \nI will give a very personal answer to this question and hopefully \nconvince the reader\nthat hadron-hadron scattering is a fine tool to gain insight into the\nstrong interactions in the nonperturbative regime.\n\n\\section{Chiral symmetry and the essence of chiral perturbation theory}\n\nThis section serves as a warm up -- as CHPT and extensions thereof will be\nused to analyze various hadron-hadron scattering processes, a few remarks are\nin order.\nAs already stated, CHPT  explores the consequences of chiral symmetry breaking\nin QCD. As in any effective field theory, a power counting based on the scale\nseparation lets one organize the string of contributions to a given matrix\nelement or Greens function. The power of chiral symmetry manifests itself in\nthe relations between many processes. A particularly nice example of this are\nthe next-to-leading order low-energy constants (LECs) of the chiral effective\npion-nucleon Lagrangian, commonly denoted as $c_i$. These can e.g. be\ndetermined  from data on low energy pion-nucleon scattering to some precision.\nThey can then be used in the chiral EFT description of the nuclear \nforces, as they\nplay an important role in the two-pion exchange contributions of the\ntwo-nucleon forces and also in the leading long-range part of the \nthree-nucleon force. It is also important to stress that while the number\nof LECs increases with higher orders, this is not necessarily \nprolific for basic processes. E.g., elastic $\\pi\\pi$ scattering to\none loop features four LECs, at two loops there are only 2 \nnew  LECs, as all other ${\\cal O}(p^6)$ local operators \nsimply lead to a quark mass renormalizations of the  ${\\cal O}(p^4)$ \nLECs. Further, the predictions of CHPT can  \nbe sharpened by combining it with other methods such as dispersion relations,\ncoupled-channel approaches, lattice simulations and so on. As I will show,\nthis can lead to incredibly precise predictions in some cases, but one\nshould be aware that there is no free lunch - as will be discussed in the following. \n\n\n\\section{Lesson 1: Pion-pion scattering}\n\n Elastic pion-pion scattering ($\\pi\\pi\\to\\pi\\pi$) is the purest process \nin two-flavor chiral dynamics as the up and the down quark masses are\nreally small compared to any other hadronic mass scale. At threshold \nthe scattering amplitude is given in terms of two numbers, the \nscattering lengths $a_0$ and $a_2$. Most interesting is the history\nof the prediction for $a_0$: At   leading order (LO) (tree graphs in CHPT)\none has $a_0 = 0.16$ \\cite{Weinberg:1966kf}. The NLO (one-loop) corrections\nwere worked out by Gasser and Leutwyler in 1983, $a_0 = 0.20 \\pm 0.01$\n\\cite{Gasser:1983kx}. The fairly large correction can be understood\nin terms of the strong $\\pi\\pi$ final-state interactions in this partial\nwave. At  NNLO (2-loops), one finds $a_0 = 0.217 \\pm 0.009$ \n\\cite{Bijnens:1995yn} and this was considerably sharpened by \nmatching the  2-loop representation to the Roy equation solution,\nresulting in $a_0 = 0.220 \\pm 0.005$ \\cite{Colangelo:2000jc}. This is an\namazingly precise prediction for a low-energy QCD observable. Incidentally,\na similarly accurate prediction was achieved for $a_2$, \n$a_2 = -0.0444 \\pm 0.0010$, but here the corrections \nto the LO result, $a_2^{\\rm LO} = -0.0042$, are very small due to \nthe very weak $\\pi\\pi$ interactions\nin isospin~2. This visible improvement in accuracy compared to the two-loop\npredictions was due to the inclusion of data from higher energies in the\ndispersion relations with better accuracy than this is possible through the\nfinite number of LECs. Also, the two scattering lengths serve as subtraction\nconstants in the Roy equations and are thus much tighter constrained than\nin the pure chiral expansion. \n\n\\begin{SCfigure}[][t]\n\\includegraphics[width=0.54\\textwidth]{a0a2_201202.pdf}~~~~~\n\\caption{Theoretical predictions for the S-wave $\\pi\\pi$\n  scattering lengths in comparison to experimental data \n as well as direct and indirect lattice determinations. Figure\ncourtesy of Heiri Leutwyler \\cite{Heiri}.\n}\n\\label{fig:pipi}\n\\end{SCfigure}\n\nGiven such precise predictions - how about\nexperiment? The analysis of the $\\pi\\pi$ final-state interactions  in\n$K_{e4}$ and the cusp in $K^0\\to 3\\pi^0$ decays has proven to lead to the most precise\ndeterminations of the scattering lengths. An alternative it the measurement\nof lifetime of pionium, but this is experimentally more difficult and thus\nless accurate. From kaon decays using a particularly tailored non-relativistic\nEFT \\cite{Gasser:2011ju}, one obtains ~$a_0^0 = 0.2210\\pm \n0.0047_{\\rm stat}\\pm 0.0040_{\\rm sys}$ and $a_0^2 = -0.0429\\pm \n0.0044_{\\rm stat}\\pm 0.0028_{\\rm sys}$ \\cite{Batley:2010zza}.\nThe pionium lifetime measurement leads to $|a_0^0-a_0^2| = \n0.2533^{+0.0080}_{-0.0078}{}^{+0.0078}_{-0.0073}$, where the first\/second error\nis statistical\/systematic \\cite{Adeva:2011tc}. The agreement with the\nprediction from Ref.~\\cite{Colangelo:2000jc} is stunning.  In addition, there\nare direct and indirect lattice determinations of these fundamental\nparameters. Here, ``direct'' refers to using the L\\\"uscher method \nand extracting the scattering length from the measured energy shift \nwhile ``indirect'' means that\nthe LECs $\\ell_3$ and $\\ell_4$ have been extracted from the pion decay constant\nand mass whereas $\\ell_{1,2}$ have been taken from other sources. The grand\npicture is presented in Fig.~\\ref{fig:pipi}  and shows a \nbeautiful consistency.\nThis is truly  one of the finest tests of the Standard Model at low energies.\nHowever, not all is well --  a direct lattice determination of $a_0$ is still\nmissing and the lattice practitioners are urged to provide this so important\nnumber. Such a calculation is, of course, technically challenging because\nof the disconnected diagrams, but time is ripe for doing it.\n\n\n\\section{Lesson 2: Pion-kaon scattering}\n\nThe purest scattering process in chiral dynamics involving strange\nquarks is elastic pion-kaon scattering, $\\pi K\\to\\pi K$. Again, at \nthreshold the scattering amplitude is given in terms of two numbers,\nnamely the scattering lengths $a_{1\/2}$ and  $a_{3\/2}$.  Before \ndiscussing the status of the $\\pi K$ scattering lengths, I want to\naddress a few mysteries surrounding the $s$ quark. In standard \nthree-flavor CHPT, it is treated like the $u,d$ quarks. However: \nis the strange quark really light as $m_s \\sim 100~{\\rm MeV}\n\\sim \\Lambda_{\\rm QCD}$? This is reflected in the expansion parameter: \n$\\xi_s = {M_K^2}\/{(4\\pi F_\\pi)^2} \\simeq\n0.18$, which is much bigger than its SU(2) equivalent: \n$\\xi = {M_\\pi^2}\/{(4\\pi F_\\pi)^2} \\simeq 0.014$.\nIn fact,  many predictions of SU(3) CHPT work quite well, but\nthere are also indications of bad convergence in some recent \nlattice calculations, see e.g. Refs.~\\cite{Boyle:2007qe,Allton:2008pn}.\nA possible solution to this is offered by reordering techniques,\nsee~\\cite{Bernard:2010ex}.\nAlso, since many years there have been speculations that the\nthree-flavor condensate $\\Sigma(3)$ is very much suppressed compared to its\ntwo-flavor cousin $\\Sigma(2)$. E.g. Moussallam performed a sum rule study\nand found a sizeable suppression, $\\Sigma (3) =  \\Sigma (2) \n[1-0.54\\pm 0.27]$ \\cite{Moussallam:1999aq}\nwhereas a recent lattice study finds a more standard relation\n$\\Sigma (3) = \\Sigma(2) [1-0.23\\pm 0.39]$ \\cite{Fukaya:2010na}.\nNote that in both cases the uncertainties are large.\nThe history of the CHPT predictions for the scattering lengths\n\\begin{table}[t]\n\\begin{center}\n\\begin{tabular}{|l|c|c|c|c|}\n\\hline\n & Tree \\cite{Weinberg:1966kf,Griffith:1969ph}   \n &  1-loop \\cite{Bernard:1990kx,Bernard:1990kw}\n &  2-loop \\cite{Bijnens:2004bu}\n & RS \\cite{Buettiker:2003pp} \\\\\n\\hline\n$a_0^{1\/2}$ & +0.14 & $+0.18\\pm 0.03$ & +0.220 [0.17 \\ldots 0.225] &\n    $+0.224\\pm 0.022$\\\\\n$a_0^{3\/2}$ & $-0.07$ & $-0.05\\pm 0.02$ & $-0.047 [-0.075 \\ldots -0.04]$ \n    & $-0.0448\\pm 0.0077$\\\\\n\\hline\n\\end{tabular}\n\\caption{Chiral predictions at LO, NLO and NNLO for the $\\pi K$\nscattering lengths and from Roy-Steiner (RS) equations. The \nuncertainty for the 2-loop results is taken from the various\nparameter variations discussed in \\cite{Bijnens:2004bu}.}\n\\label{tab:piK}\n\\vspace{-0.5cm}\n\\end{center}\n\\end{table}\nis given in Tab.~\\ref{tab:piK} together with the results of the\nRoy-Steiner (RS) equations  \\cite{Buettiker:2003pp}. The agreement\nof the two-loop predictions (central values) is quite satisfactory, \nbut  the precision achieved in the RS framework is not as good as\nin the case of $\\pi\\pi$ scattering. This is largely due to the worse\nand partly inconsistent data base. Similarly, the scattering lengths\nextracted from these data are not very precise and fairly scattered,\nsee e.g. Fig.~1 in Ref.~\\cite{Bernard:1990kx}. More recent measurements\nin D- and B-meson decays with high statistics \n\\cite{Poluektov:2004mf,Aitala:2005yh,Link:2009ng,Aubert:2008bd}\nallow in principle for a better determination of $a_{1\/2}$ and  $a_{3\/2}$,\nbut none of these has performed an isospin decomposition. This is\nurgently called for. In principle, lattice QCD can have some impact here.\nHowever, the present situation as summarized for $a_{1\/2}$ in\nFig.~\\ref{fig:Kpi} (the date are taken from the\nrecent paper \\cite{Lang:2012sv}, see also the references therein) is everything\nbut satisfactory, there is a large spread of the results. For $a_{3\/2}$,\nthere is better agreement between the lattice results but also some\ntension with the value obtained from the RS analysis. Clearly, more\nwork is needed to clear up the situation for this process.\n\\begin{SCfigure}[][t]\n\\includegraphics[width=0.54\\textwidth]{a_piK_overview.pdf}~~~~~\n\\caption{The S-wave $\\pi K$ scattering lengths  from the lattice \nin comparison to LO and NLO CHPT and Roy-Steiner determinations. \nData as collected in Ref.~\\cite{Lang:2012sv}. For better comparison, \nthe scattering lengths are normalized to the reduced mass \n$\\mu_{\\pi K}$ of the pion-kaon system.\n}\n\\label{fig:Kpi}\n\\end{SCfigure}\n  \n\n\n\\section{Lesson 3: Pion-nucleon scattering}\n\nLet me now turn to elastic pion-nucleon scattering, $\\pi N\\to\\pi N$, which\nis the simplest (and also the most fundamental) scattering process \ninvolving nucleons. As in the case of\npion-kaon scattering, one has total isospin 1\/2 and 3\/2. Often used\nare the isoscalar and isovector scattering length, $a^+$ and $a^-$,\nrespectively, with $a_{3\/2} = a^+ - a^-$ and $a_{1\/2} = a^+ + 2a^-$.\nThe LO prediction for the isoscalar\/isovector scattering length\nis quite intriguing: \n\\begin{equation}\na_{\\rm LO}^+ = 0~,~~ a_{\\rm LO}^- =\n\\frac{1}{1+M_\\pi\/m_p}\\frac{M_\\pi^2}{8\\pi F_\\pi^2} = 79.5 \\cdot 10^{-3}\/M_\\pi~.\n\\end{equation}\nMuch is known about the chiral corrections to these results that were\nfirst addressed in \\cite{Bernard:1993fp}. While the  chiral expansion \nfor $a^-$ converges fast \\cite{Bernard:1995pa},\nthere are large cancellations in $a^+$, so that even its sign is \nnot known from scattering data, see e.g. table~3 in \\cite{Fettes:2000xg}\n(see also the more recent work in Ref.~\\cite{Alarcon:2012kn}). \nHowever, there is a wonderful\nalternative to get a hand on these scattering lengths, namely hadronic atoms.\nThese are electromagnetic bound states of two oppositely charged hadrons.\nDue to the large spatial extent of these objects, the strong interactions \nlead to small perturbations in the observed level spectrum. In particular,\nthere is a shift of the ground state energy ($\\Delta E_{1s}$) and further, \ndue to channel coupling, this level acquires a width $\\Gamma_{1s}$. \nDue to the small three-momenta in such a system, we are dealing essentially with \nscattering at zero energy or, stated differently, the energy shift and \nwidth can be expressed in terms of the corresponding scattering lengths.\nThere are many species of such hadronic atoms, like pionium ($\\pi^+\\pi^-$)\nalready discussed, pionic hydrogen  ($\\pi^- p$), pionic deuterium  ($\\pi^- d$)\nand their kaonic cousins ($K^- p, K^- d$). Hadronic atoms  can be analyzed \nmost systematically and precisely in suitably tailored non-relativistic\nEFTs, see \\cite{Gasser:2007zt} for a comprehensive review. For the case\nof pion-nucleon scattering, the corresponding high-precision theoretical\nframework for pionic hydrogen and pionic deuterium has been provided\nin Refs.~\\cite{Gasser:2002am} and \\cite{Baru:2011bw}, respectively (see\nalso the contribution from Martin Hoferichter to these proceedings). On the\nexperimental side, superb experiments have been performed at PSI for\nmany years, culminating in precise measurements of the energy shift and\nwidth of pionic hydrogen \\cite{Gotta:2008zza} and the energy shift \nin pionic deuterium \\cite{Strauch:2010vu}. \n\\begin{SCfigure}[][t]\n\\includegraphics[width=0.40\\textwidth]{bands1_mod.pdf}~~~~~~~\n\\caption{Extraction of the isoscalar and isovector\nscattering lengths from pionic hydrogen and deuterium.\nHere, $\\tilde{a}^+ = a^+ +\\frac{1}{1+M_\\pi\/m_p}\\times $\n$\\left\\{\\frac{\\Delta M_\\pi^2}{\\pi F_\\pi}c_1 - \n2\\alpha f_1\\right\\},$ with $\\Delta M_\\pi^2 = M_\\pi^2 -\nM_{\\pi^0}^2$, $\\alpha$ the fine structure constant and\n$c_1$\/$f_1$ are strong\/electromagnetitic NLO LECs with\n$c_1 \\simeq 0.9\\,$GeV$^{-1}$ and $|f_1| \\leq 1.4$~GeV$^{-1}$.\nFigure courtesy of Martin Hoferichter.\n}\n\\label{fig:piN}\n\\end{SCfigure}\nThe analysis of these data within these EFTs leads to\na very precise extaction of the scattering lengths  \\cite{Baru:2011bw}\n\\begin{equation}\na^+ =(7.6 \\pm 3.1) \\cdot 10^{-3}\/M_\\pi~, ~~~\na^-=(86.1 \\pm 0.9) \\cdot 10^{-3}\/M_\\pi~.\n\\end{equation}\nNote that the value for the isovector scattering length differs by just 8\\% form\nthe LO value, whereas the isocalar one is positive and only slightly larger in\nvalue than various contributions to it. This underlines that {\\sl only} within a\nconsistent framework like the employed EFT one is able to extract this value.\nAlso, using the GMO sum rule, the authors of \\cite{Baru:2011bw} find a precise\nvalue for the pion-nucleon coupling constant, ${g_{\\pi N}^2}\/(4\\pi) =\n13.69(12)(15)$, where the first error stems from the scattering lengths and\nthe second one from the integral over the $\\pi^- p$ cross section. This is\nconsistent with other determinations from pion-nucleon scattering or from\nperipheral nucleon-nucleon phase shifts.\n \n\n\\section{Lesson 4: Antikaon-nucleon scattering}\n\nNext, I consider the reaction $K^-p \\to K^- p$. It is a fundamental scattering \nprocess with strange quarks involving baryons. The dynamics of this process\nis driven by channel couplings and leads to the dynamic generation of the\n$\\Lambda (1405)$ resonance \\cite{Dalitz:1959dn,Dalitz:1960du}\nthat resides between the $\\pi \\Sigma$ and $\\bar K\nN$ thresholds and is certainly not a simple three-quark state. This reaction\nis therefore a major playground of {\\em unitarized CHPT (UCHPT)}. Due to the open\nchannels below the $K^-p$ threshold, the two scattering lengths $a_0$ and $a_1$\nare complex-valued quantities, which means that in this case we deal with four\nnumbers. Before continuing,\nit is important to point out the differences between CHPT and unitarized\nversions thereof.   CHPT is an exact representation of the chiral Greens function of\nQCD, which expands matrix elements in powers of small momenta and quark masses.\nCrossing and analyticity are in general fulfilled (if a proper regularization\nscheme is employed), whereas\ndue to the underlying power counting, unitarity is fulfilled perturbatively.\nCHPT is formulated in terms of the lowest-lying hadronic degrees of freedom\nand all effects from resonances are subsumed in the low-energy constants.\nIf one wants to describe resonances explicitely -- as it is the case here --\nsome resummation scheme that fulfills 2-body unitarity exactly is needed. \nThere are various formalism available\nto achieve that, mostly based on Lippman-Schwinger or Bethe-Salpeter equations.\nIn general, one gives up crossing symmetry and also some\nmodel-dependence is induced as there is a cornucopia of unitarization schemes.\nFurther, the power counting is not applied to the reaction amplitude but\nrather to the kernel of the scattering equation, as\nit is e.g. frequently and successfully done in chiral nuclear effective field\ntheory. Having said that, it is also important to stress that UCHPT has been\nquite successful in describing various scattering processes and the dynamic\ngenerations of resonances like the  $\\Lambda(1405)$, $S_{11}(1535)$,\n$S_{11}(1650)$,  and others. \n\nBut back to $K^-p$ scattering. A long-standing puzzle in these field,\nnamely the inconsistency of the DEAR kaonic hydrogen data with the\nscattering data (first pointed out in \\cite{Meissner:2004jr} and then \nconfirmed by many others)  was recently resolved by the fine experiment\nof the SIDDHARTA collaboration, who measured the properties of\nkaonic hydrogen with high precision, $\\Delta E_{1s} = -283 \\pm 36 {\\rm (stat)} \n\\pm 6 {\\rm (syst)}$~eV and $\\Gamma_{1s} = 541 \\pm 89 {\\rm (stat)} \\pm \n22 {\\rm (syst)}$~eV \\cite{Bazzi:2011zj}. Based on this, the\n kaonic hydrogen and the older scattering data can now be analyzed\n consistently, using the  chiral Lagrangian at NLO, as shown by the\nthree groups \\cite{Ikeda:2011pi,Ikeda:2012au,Mai:2012dt,Guo:2012vv}\n(see also \\cite{Cieply:2011nq}). Here, I report the results from \nRef.~\\cite{Mai:2012dt}. 14 LECs and 3 subtraction constants were fitted\nto scattering data in the channels $K^-p \\to K^-p$, $\\bar K^0n$,\n$\\Sigma^\\pm\\pi^\\mp$, and $\\Sigma^0\\pi^0$ for laboratory momenta\n${p_{\\rm lab} \\leq 300}$~MeV together with  the SIDDHARTA data.\nThis allows for  good description of the antikaon-proton cross section data \nand an accurate determination of the  scattering lengths, \n\\begin{equation}\\label{eq:a}\na_0  = -1.81^{+0.30}_{-0.28} + i~ 0.92^{+0.29}_{-0.23}~{\\rm\n  fm}~, ~~~\na_1 = +0.48^{+0.12}_{-0.11} + i~ 0.87^{+0.26}_{-0.20}~{\\rm fm}~.\n\\end{equation}\nThe improvement as compared to using scattering data only \n\\cite{Borasoy:2006sr} is clearly visible in Fig.~\\ref{fig:KN} (left panel).\nThese numbers are similar to the ones reported by Ikeda et al.\n\\cite{Ikeda:2011pi,Ikeda:2012au}. Therefore, \nthese fundamental chiral SU(3) parameters have now been\ndetermined with about an accuracy of $\\sim~15\\%$.\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.44\\textwidth]{a0a1-nur.pdf}\n~~~~~~~~\\includegraphics[width=0.4\\textwidth]{PWA_nur.pdf}\n\\caption{Left panel: Real and imaginary part of the isospin $T=0$ \n    and $T=1$ ${KN\\to KN}$\n    scattering lengths. The light shaded (green) areas correspond to the \n    $1\\sigma$ region of \\cite{Mai:2012dt} around the central value (full circles). \n    The darker (blue) areas correspond to the $1\\sigma$ region around central \n    value (empty circle) from Ref.~\\cite{Borasoy:2006sr}.\n    Right panel: Real and imaginary part of the $K^-p\\to K^-p$ scattering\n    amplitude. The shaded band indicates the uncertainty of the calculation. \n    The data point at $W_{\\rm cms}=M_K+m_p$ is determined from the energy\n    shift and width of kaonic hydrogen from the SIDDHARTA experiment.\n}\n\\label{fig:KN}\n\\end{figure}\nOne can extrapolate the amplitudes of elastic $K^-p$\nscattering to the subthreshold region, i.e. center-of-mass energies\n$1330 \\leq W_{\\rm cms} \\leq 1450$ MeV. The result is presented in the right\npanel of Fig.~\\ref{fig:KN}.\nFor both real and imaginary parts of the amplitude the maximum lies close\nto the $KN$ threshold and is quite narrow, which indicates the presence of a close-by pole. \nIt is also worth mentioning that the error band gets smaller for lower\nenergies, different to the recent analysis by Ikeda et al.~\\cite{Ikeda:2011pi,Ikeda:2012au}.\nWe note that although Ikeda et al. and  \\cite{Mai:2012dt} describe the scattering and bound\nstate data equally well, the subthreshold amplitude is very different. This is\npresumably due to the different approximation made in these two approaches.\nTherefore, a truly model-independent determination of this subthreshold\namplitude is not yet available.\n\n\\section{Lesson 5: Goldstone boson scattering off {\\boldmath$D$} and\n{\\boldmath$D^\\star$}-mesons}\n\nFinally, let us consider scattering the Goldstone boson octet $(\\pi, K ,\\eta)$  \noff the $D$-meson triplet $(D^0, D^+, D_s^+)$. This involves the\npositive-parity  scalar charm-strange  meson $D_{s0}^*(2317)$ which\nhas a very narrow, isospin-violating width and is interpreted by \nsome groups as a molecular $DK$ state. Here, we are mostly interested \nin the scattering length in the channel with $(S,I)=(1,0)$, as its \nvalue can tell us something about the possible nature of the scalar \nmeson. As I will show, this field enjoys a  healthy interplay of \nlattice QCD and UCHPT. But a few general remarks on the calculation\nof the scattering process $\\phi D \\to\\phi D$ are in order. This is \nan interesting problem, as it involves a variety of scales and is \nalso multi-faceted. First, light particles related to the chiral \nsymmetry of QCD are involved, thus we can perform a chiral expansion \nin momenta and quark masses. Second, as the $D$-meson contain charm \nquarks, we can exploit heavy quark symmetry and perform an expansion \nin $1\/m_c$. Third, one must consistently include isospin-violation\neffects. These are on one hand generated by the strong interactions \n($m_d \\neq m_u$) and on the other hand of electromagnetic origin ($q_u \\neq q_d$).\nIn total, one has to consider 16 channels with different total strangeness and\nisospin. Some of these are perturbative, but most are non-perturbative and\nrequire resummation, which can lead to the dynamical generation of\nmolecules. \n\nBefore addressing the actual calculations, let me discuss the relation\nbetween the scattering length $a$ and the nature of the state under\nconsideration, see Refs.~\\cite{Weinberg:1965zz,Baru:2003qq}\nfor a derivation:\n\\begin{equation}\n a = -2 \\left( \\frac{1-Z}{2-Z} \\right) \\frac1{\\sqrt{2\\mu\\epsilon}} \\left(\n 1+\\mathcal{O}(\\sqrt{2\\mu\\epsilon}\/\\beta) \\right),\n \\label{eq:weinberg}\n\\end{equation}\nwhere $\\mu$ and $\\epsilon$ are the reduced mass of the two-hadron \nsystem and the binding energy, respectively, and $Z$ is the wave function\nrenormalization constant ($0 \\leq Z\\leq 1$).\n Corrections of the above equation come from neglecting the range of\nforces, $1\/\\beta$, which contains information of the $D_s\\eta$ channel.\nWere the $D_{s0}^*(2317)$ a pure $DK$ bound state ($Z=0$), the value of \nthe $DK(I=0)$ scattering length would be $a=-1.05$~fm.\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.84\\textwidth]{fit5p3data.pdf}~~~~~\n\\caption{Fit to lattice data for various channels \nwith 5 parameters. The subtraction constant is \ndetermined from fixing the pole in the $(S,I)=(1,0)$ channel to \n2317.8~MeV. The points at the highest pion mass in each channel are not fitted.\n}\n\\label{fig:Dpi}\n\\end{figure}\nIn \\cite{Liu:2012zya}, new lattice data using the MILC plus Fermilab actions\nfor the channels $D\\bar K (-1,1), (-1,0)$, $D_sK(2,1\/2)$, $D\\pi(0,3\/2)$ and\n$D\\pi(1,1)$ were analyzed based on the UCHPT formalism developed in\n\\cite{Guo:2009ct} (for related work, see \n\\cite{Liu:2009uz,Geng:2010vw,Cleven:2010aw,Wang:2012bu}).\nThese are more data than previously available allowing \nin particular for the inclusion of $N_c$-suppressed operators\nof the NLO effective Lagrangian (there are 5 LECs at this\norder from which 3 are formally subleading in $1\/N_c$ and one subtraction\nconstant).\nIf one requires the $D_{s0}^* (2317)$ to be a $DK$-molecule by a proper\nchoice of the subtraction constant (i.e. having \na pole at the proper mass in this channel), \none has 5 fit parameters that describe the lattice data well, \nsee Fig.~\\ref{fig:Dpi}. In this fit, all parameters come out of natural \nsize and the  large-$N_c$ hierarchy obeyed. The scattering length \nin the $DK(I=0)$ channel comes out as\n$a(DK(I=0)) = -0.85^{+0.07}_{-0.05}~\\mbox{fm}$, which is consistent\nwith the molecular interpretation (for a more detailed discussion,\nalso concerning a different fit procedure, see \\cite{Liu:2012zya}).\nHaving pinned down all the LECs, one finds an improved prediction \nfor the isospin-violating width \n$\\Gamma(D_{s0}^* (2317)^+ \\to D_s^+ \\pi^0) = (89\\pm 27)\\,{\\rm keV}\\,$\n(for earlier work in the molecular picture, see \n\\cite{Faessler:2007gv,Lutz:2007sk,Guo:2008gp}).\nThis is very different from typical quark model predictions,\nwhich find this width to be about a few keV \\cite{Godfrey:2003kg},\nand thus an accurate  measurement of this quantity is called for.\nI wish to end with a few remarks on the $D_{s1}(2460)$. As\n$M_{D_{s1}(2460)}{-}M_{D_{s0}^*(2317)} \\simeq M_{D^*}{-}M_D$, it is most\nlikely a $D^\\star K$ molecule (if the $D^\\star_{s0} (2317)$\nis a $DK$ molecule).  Goldstone boson scattering off $D$- \nand $D^\\star$-mesons was considered in \\cite{Cleven:2010aw}.\nThe most interesting observation made concerns the\nmass and binding energy of a molecular state of a heavy meson $(H)$\nand a kaon. As its mass is given by $M_{\\rm mol} = M_K + M_H - \\epsilon$,\nthe mass should depend linearly on the kaon mass, very different\nfrom a genuine multi-quark state, whose mass depends linearly on the\nstrange quark and thus quadratically on the kaon mass. This behaviour\ncan, of course, be investigated on the lattice.\n\n\\section{Short summary \\& outlook}\n\nAs I have shown, there has been much progress in our understanding of\nhadron-hadron scattering lengths since Weinberg's seminal paper in 1966.\nMost advanced is theory and experiment in the case of pion-pion scattering.\nHere, lattice QCD still has to provide an acccurate number for $a_0$.\nMatters are much less satisfactory for pion-kaon scattering - as both \nexperiment and lattice QCD have to deliver more precise values for \nboth scattering lengths. A measurement of the properties of $\\pi K$ atoms\nwould certainly be very welcome \\cite{Adeva:2009zz,Schacher}.\nVery different to that, the combination of\nchiral EFTs with precision data has led to a high precision determination\nof the pion-nucleon scattering lengths $a^+$ and $a^-$. This should \nchallenge lattice practioners to provide a similarly accurate ab initio\ncalculation. In case of antikaon-nucleon scattering, there has been\nrecent progress by analysing scattering data and kaonic hydrogen data\nprovided by SIDDHARTA and the corresponding scattering lengths are now\nknown with an accuracy of about 15\\%. Here, a measurement of kaonic deuterium\nwould provide further stringent constraints \n\\cite{Doring:2011xc,Shevchenko:2012np,Faber:2010iw}. Finally,  including \ncharm quarks, the interplay of unitarized CHPT and lattice QCD complemented\nby experiment can deepen our understanding of heavy-light systems, thus\nproviding a bridge from chiral dynamics to the physics of heavy quark flavors.\n\n\\section*{Acknowledgements}\n\nI thank all my collaborators for sharing their insight into the\ntopics discussed here.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzflia b/data_all_eng_slimpj/shuffled/split2/finalzzflia
new file mode 100644
index 0000000000000000000000000000000000000000..08f5d9474a2231a6188248ab1f4aecc48927860e
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzflia
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\nOver past decades, much attentions focus on multitemporal Synthetic Aperture Radar (SAR) image change detection, since a SAR is capable of working in all-time and all-weather without the influence of extremely bad weather and the cloud. \nIn a past decade, most traditional SAR image change detection methods are developed how to extract changed areas from a difference image (DI), which suppose to include the information of changed regions. The DI calculated by the log-ratio (LR) \\cite{bazi2006automatic} is usually subject to the speckle and it is challenging to extract the accurate and clear information on the changed region. To tackle this issue, sparse learning\\cite{wang2016sar} was recently proposed learning robust features from the noisy DI. Wang et al.\\cite{wang2019can} analyzed the affects of the SAR image speckle on change detection and proposed a sparse learning-based method for SAR image change detection.\n\nRecently, deep neural networks have been successfully employed to computer vision and remote sensing image analysis due to its ability to exploiting essential and robust structural features on categories of objects. It also has been introduced into the field of change detection. Gong et al\\cite{Gong2017Change} proposed a deep neural network for SAR image change detection. Gao et al. \\cite{gao2016automatic} proposed a simple convolutional neural network, known as PCA-Net, exploring robust features on the changed regions from the noisy DI. However, the performance of these two unsupervised methods are limited without the correct guidance. To tackle this issue, Wang et al. \\cite{wang2018imbalanced} proposed a supervised PCA-Net to improve the performance by carefully collecting typical training samples, which obtains state-of-arts performance of bitemporal SAR image change detection. However, this two-layer convolutional neural network is low efficient, since the convolutional kernels are trained or generated by a Principle Component Analysis (PCA) decomposition. Recently, Li et al. \\cite{li2019deep} proposed a convolutional neural network (CNN) for SAR image change detection based on both unsupervised and supervised learning. Zhao et al. \\cite{zhao2017novel} proposed a bitemporal PolSAR image change detection by a joint classification and a similarity measurement.  Currently, it is still an open problem to extract the changed regions from the noisy DI. \n{Nowadays, a large volume of SAR images are acquired by satellites and it is imperative to develop an efficient model that can produce promising results of SAR image interpretation. Most above networks are too heavy and cost much computational burden. It is strongly required to develop a lightweight convolutional neural network.}\n\n {Recently, several lite networks are proposed to improve the inference efficiency. Howard et al. and Sandler et al. proposed two lite networks MobileNetV1 \\cite{howard2017mobilenets} and MobileNetV2 \\cite{sandler2018mobilenetv2} for visual category. Recently, Howard et al. proposed to search for MobileNetV3 \\cite{howard2019searching}. Tan et al. \\cite{tan2019efficientnet} proposed an efficient network for visual category. These lite networks have been extensively employed to visual category and the experimental results show that they can achieve comparable performance with heavy networks, but with low latency and network capacity. It can be potentially performed on edge devices with low power. Most recently, Chen et al.\\cite{chen2020a} proposed a lightweight multiscale spatial pooling network for bitemporal SAR image change detection. \n\nFollowing the idea of the lightweight neural network, in this letter, we focus on the application of lite networks in SAR image change detection. To achieve this, we propose a lite CNN for SAR image change detection. In the proposed network, bottleneck layers are introduced to reduce the number of output channel. Furthermore, the dilated convolutional layers\\cite{li2018csrnet} are introduced to enlarge receptive field with a few of non-zero entries in the kernel, which reduces the number of network parameters. We verify the proposed network by comparing other conventional CNN. Compared with the lightweight network in \\cite{chen2020a}, the proposed network is more robust with the residual and bottleneck structure. Experimental results on four sets of bitemporal SAR image show that our proposed method obtain comparable performance with CNN, while being much more efficient than CNNs. }\n\nThe rest of paper will be organized as follows. We will introduce our proposed method in Section 2. Then the proposed method will be verified on four datasets in Section 3. Finally, we will draw a conclusion in Section 4. \n\n\n\\section{Proposed Method}\n{Given bitemporal SAR images ${\\bf I}_1$ and ${\\bf I}_2$, the DI can be generated as follows}\n \\begin{equation}\\label{di}\n {\\bf I}_{DI} = {\\bf I}_1 \\ominus {\\bf I}_2\n \\end{equation}\n {where $\\ominus$ denote the difference operator.  However, most existing difference operator is subject to the speckle. \nThen we will propose a lightweight convolutional neural network to exploit the changed regions from the noisy DI.}\n\n\n\\begin{figure}[!htb]\n\\centering\n\\includegraphics[width=\\textwidth]{fig1.png}\n\\caption{The framework of the proposed network.(a)Network Architecture. (b) Bottleneck for encoder. (c)Bottleneck for decoder.}\n\\label{framework}\n\\end{figure}\n\n\\begin{table}[!htbp]\n\\centering\n\\caption{The tensors of all the layers.}\n\\label{tab:network}\n\\begin{tabular}{cccccccc}\n\\toprule\n Layer Name & Tensor Size & & Layer Name & Tensor Size & & Layer Name & Tensor Size   \\\\\n  \\hline\n   \\multicolumn{8}{c}{Initial Block} \\\\\nInput& (32,32,1) \\\\ \n Conv&(16,16,13) & & \n Max-pooling & (16,16,1) && \n Concatenation & (16,16,14) \\\\\n \\hline\n  \\multicolumn{8}{c}{Group 1} \\\\\nBottleNeck 1.0&(8,8,64) & &\nBottleNeck 1.1&(8,8,64) & &\nBottleNeck 1.2&(8,8,64)\\\\\nBottleNeck 1.3&(8,8,64) & &\nBottleNeck 1.4&(8,8,64) \\\\\n\\hline\n \\multicolumn{8}{c}{Group 2} \\\\\nBottleNeck 2.0&(4,4,128) & &\nBottleNeck 2.1&(4,4,128) & &\nBottleNeck 2.2&(4,4,128)\\\\\nBottleNeck 2.3&(4,4,128) & &\nBottleNeck 2.4&(4,4,128) & &\nBottleNeck 2.5&(4,4,128) \\\\\nBottleNeck 2.6&(4,4,128) & &\nBottleNeck 2.7&(4,4,128)& &\nBottleNeck 2.8&(4,4,128) \\\\\n\\hline\n \\multicolumn{8}{c}{Group 3} \\\\\nBottleNeck 3.0&(4,4,128) & &\nBottleNeck 3.1&(4,4,128) & &\nBottleNeck 3.2&(4,4,128)\\\\\nBottleNeck 3.3&(4,4,128) & &\nBottleNeck 3.4&(4,4,128) & &\nBottleNeck 3.5&(4,4,128)\\\\\nBottleNeck 3.6&(4,4,128) & &\nBottleNeck 3.7&(4,4,128)\\\\\n\\hline\n\\multicolumn{8}{c}{Group 4} \\\\\nBottleNeck 4.0&(8,8,64) & &\nBottleNeck 4.1&(8,8,64) & &\nBottleNeck 4.2&(8,8,64)\\\\\n\\hline\n\\multicolumn{8}{c}{Group 5} \\\\\nBottleNeck 5.0&(16,16,16) & &\nBottleNeck 5.1&(16,16,16) \\\\\n\\hline\n\\multicolumn{8}{c}{Output} \\\\\nConv&(32,32,2) \\\\\n  \\bottomrule\n\\end{tabular}\n\\end{table}\n\n\nThe whole framework of the proposed network can illustrated in Fig.\\ref{framework}(a). It is shown that the network consists of five groups of bottleneck layers \\cite{lin2013network} with an 1$\\times$1 kernels, illustrated by variety of colorful bars, among which the former three ones work as the encoder, and the latter two ones as the decoder. {The tensors of all layers are listed in Table \\ref{tab:network}.}\n\n\nIn the forward process, the network takes a patch of DI as the input. Firstly, the input data go through a normal convolutional layer and a max-pooling (MP) layer, respectively and then the outputs are concatenated. Next, the contact activations go through the decoder with three groups bottleneck layers. The essential structure of a bottleneck of encoder can be illustrated in Fig.\\ref{framework}(b). It is shown that a bottleneck layer is constructed by a small residual block, including a maxpooling path and a convolutional path. More specifically, the convolutional path consists of two 1$\\times$1 convolutions and one main convolution. The main convolution will vary with the various function of the bottleneck. It can be a normal convolution, a dilated convolution \\cite{li2018csrnet} or an asymmetrical convolution\\cite{szegedy2016rethinking}. {The tensors inside the encoding bottleneck are listed in Table \\ref{tab:bo_en}.}   \n\\begin{table}[!htbp]\n\\centering\n\\caption{The tensors inside an encoding bottleneck layer.}\n\\label{tab:bo_en}\n\\begin{tabular}{ccccc}\n\\toprule\n Layer Name & Tensor Size & & Layer Name & Tensor Size   \\\\\n  \\hline\n  Input& (16,16,14) \\\\\n  \\hline\n  \\multicolumn{5}{c}{Branch 1} \\\\\n Conv1& (8,8,16) &&\nConv2&(8,8,16) \\\\\nConv3&(8,8,64) &&\nDropout&(8,8,64) \\\\\n\\hline\n\\multicolumn{5}{c}{Branch 2} \\\\\nMax-pooling&(8,8,14) & &\nPadding&(8,8,64)\\\\\n\\multicolumn{5}{c}{Output} \\\\\n\\hline\nAddition & (8,8,64)\\\\\n  \\bottomrule\n\\end{tabular}\n\\end{table}\n\\begin{table}[!htbp]\n\\centering\n\\caption{The tensors inside a decoding bottleneck layer.}\n\\label{tab:bo_de}\n\\begin{tabular}{ccccc}\n\\toprule\n Layer Name & Tensor Size & & Layer Name & Tensor Size   \\\\\n  \\hline\n  Input& (4,4,128) \\\\\n  \\hline\n  \\multicolumn{5}{c}{Branch 1} \\\\\nConv1& (4,4,16) &&\nConv2&(8,8,16) \\\\\nConv3&(8,8,64) \\\\\n\\hline\n\\multicolumn{5}{c}{Branch 2} \\\\\nConv&(4,4,64) & &\nUp-Sampling&(8,8,64)\\\\\n\\multicolumn{5}{c}{Output} \\\\\n\\hline\nAddition & (8,8,64)\\\\\n  \\bottomrule\n\\end{tabular}\n\\end{table}\n\n The first group consist a down-sampling bottleneck and four normal convolutional bottleneck layers. In the normal bottleneck layers, the main convolution component is default set as the main normal convolutional layer. Especially, in the down-sampling bottleneck, the main convolutional component is set as a normal convolution kernel with 3$\\times$3 and the 1$\\times$1 convolution component is replaced by a 2$\\times$2 one. In the next two groups, to exploit the spatial context, we insert the bottleneck layers with asymmetrical and dilated convolution layers with various kernel sizes among the normal bottleneck, where the kernel sizes are set 2, 4, 8 and 16, respectively, as shown the digits below the green bars. In these bottleneck layers, the main convolutional layers are replaced by the dilated convolutional layers, where the kernels are sparse and most entries are zeros. Furthermore, the bottleneck layers with asymmetric convolution layers are also insert between the dilated and normal convolutional layer, illustrated by the blue bars. After encoding, the sizes of feature maps decrease as the one fourth as the original image. \n\nIn the decoding part, the context information collected by the encoder will be propagated to the pixel level. To achieve this, inspired by the idea of U-Net \\cite{ronneberger2015u}, we schedule a upsampling layer and two bottleneck layers. The essential structure of bottleneck for decoder can be illustrated in Fig.\\ref{framework}(c). Similar to the bottleneck for the encoder, the bottleneck for the decoder contains a pooling path and a convolution path. The former includes a maxpooling layer and a 1$\\times$1 convolution, while the latter includes two 1$\\times$1 convolutional layers and a 3$\\times$3 convolutional layer. Especially, when the bottleneck layer is used for upsampling, the 3$\\times$3 convolution component, illustrated by the yellow bar, will be replaced by a 3$\\times$3 transpose convolution \\cite{dumoulin2016guide}. Then the bottleneck will do the 2x upsampling. Trough two groups of decoding bottleneck layers, the feature map will be recover the same size as the input image. {The tensors inside the decoding bottleneck are listed in Table \\ref{tab:bo_de}.}  Finally, we put a 2$\\times$2 convolutional layer to get the probability map of two categories. \n\n\\begin{figure}[!htb]\n\\centering\n\\includegraphics[width=\\textwidth]{fig2.png}\n\\caption{Four sets of bitemporal SAR images. The first two rows are bitemporal images and the last row is the DIs. (a) YR-A. (b) YR-B. (c) Sendai-A. (d) Sendai-B. }\n\\label{fig2}\n\\end{figure}\n\n\\section{Experimental Results}\n\\label{sec:experiment}\n\\subsection{Experiment Datasets}\nIn this paper, the proposed method is verified on four sets of bitemporal SAR images. Two scenes (YR-A and YR-B) are from bitemporal Yellow River SAR images \\cite{Gong2017Change} acquired by the Radarsat-2 satellite in 2008 and 2009, respectively. Their image sizes are 306 $\\times$ 291 and 400 $\\times$ 350, respectively. Other two are parts of TerraSAR-X images acquired prior to (on Oct. 20, 2010) and after (on May 6, 2011) the Sendai earthquake in Japan \\cite{Cui2016A}. Their sizes (Sendai-A and Sendai-B) are 590 $\\times$687 and 689 $\\times$ 734, respectively. These four datasets are shown in Fig.\\ref{fig2}). These four datasets are quite challenging, such as the linear-shape changed regions in YR-B dataset and complex scene in both Sendai-A and Sendai-B datasets. \n\n\\begin{table}[!htbp]\n\\centering\n\\caption{The number of training samples.}\n\\label{tab:nos}\n\\begin{tabular}{ccccc}\n\\toprule\n  Dataset & YR-A & YR-B & Sendai-A & Sendai-B   \\\\\n  \\hline\n  No. Samples& 3596 & 6205 & 15375 & 20294 \\\\\n  \\bottomrule\n\\end{tabular}\n\\end{table}\n\\begin{figure}[!htb]\n\\centering\n\\includegraphics[width=0.6\\textwidth]{fig3.png}\n\\caption{The variations of loss and accuracies.}\n\\label{fig:loss}\n\\end{figure}\n\n\\subsection{Implementations}\n{\nWe have introduced a lite CNN for change detection for bitemporal SAR images. We first generate the DI by the Eq.(\\ref{di}) and the difference operator is implemented by the neighborhood-based LR operator \\cite{gong2011neighborhood}. \nTo train the network, we collect a training dataset according to the method in \\cite{wang2018imbalanced}. The numbers of training samples for each dataset are listed in Table \\ref{tab:nos}.\n\nMore specifically, the patchsize of each sample is set as 32 $\\times$ 32 and 8 samples are fed in each training step. Additionally, the network is trained by an end-to-end back-propagation manner and the loss is set as {the binary entropy function defined in \\cite{sadowski2016notes}}. \nThe training is optimized by the Adam algorithm \\cite{kingma2014adam} in the training stage, where the initial learning rate is set as 0.005. \nThe training is performed on the PyTorch platform built on the Ubuntu 16.04 installed in a PC with a 16 GB DDR memory and an NVIDIA TITAN Xp Graphics Processing Unit of 11 GB memory. The training process will converge at around 15 epochs. We show the variations of loss values and accuracies of training process in Fig.\\ref{fig:loss}.\n}\n\\subsection{Comparison Experiments}\nTo verify the benefits of the proposed method, it is compared with the unsupervised PCA-Net (U-PCA-Net)\\cite{gao2016automatic}, the supervised PCA-Net (S-PCA-Net) \\cite{wang2018imbalanced} which achieves the state-of-arts performance on SAR image change detection. We also compare the proposed method with the deep neural network (DNN) method \\cite{Gong2017Change} and CNN \\cite{li2019deep}. Among these methods, DNN and U-PCA-Net are unsupervised methods,while S-PCA-Net, CNN and the proposed method are supervised ones. \n\nThe performance of the compared methods is evaluated by probabilistic Missed Alarm (pMA), probabilistic False Alarm (pFA) and kappa coefficient, where pFA (pMA) are calculated by the ratios between FA (MA) and the number of Non-Changed pixels (NC)\\cite{wang2019can}. \n\n\\begin{figure}[!thb]\n\\centering\n\\includegraphics[width=\\textwidth]{fig4.png}\n\\caption{The visual comparison results. (a)U-PCA-Net. (b)S-PCA-Net. (c)DNN. (d) CNN. (e)Lite CNN. (f)Reference. }\n\\label{fig3}\n\\end{figure}\n\\begin{figure}[!htb]\n\\centering\n\\includegraphics[width=\\textwidth]{fig5.png}\n\\caption{The quantitative evaluations of compared methods.(a) MA. (b)FA. (c) Kappa. }\n\\label{eva}\n\\end{figure}\n\\subsection{Experiment Results on Individual Dataset Change Detection}\nIn this experiment, for the supervised learning methods, we collect the training samples from an individual dataset, which covers 30\\% areas of the whole image frame. The rest part is employed for testing.  \n\nThe visual comparison results are shown in Fig.\\ref{fig3}. It is shown that for the YR-A dataset, S-PCA-Net, DNN and Lite CNN get less noisy but more completed changed regions. Lite CNN can get more clear boundary of changed regions than DNN. For the YR-B dataset, Lite CNN can get more completed changed regions, especially the line at the bottom of the image. Other methods can not get the completed changed regions. For the Sendai-A dataset with complex scene, S-PCA-Net and the Lite CNN are less subject to the speckle and the background and get more clear changed regions, while other compared methods are subjected to the speckle and background and they are almost failed. Moreover, compared with S-PCA-Net, Lite CNN get better inner regional consistence.  For the Sendai-B dataset, Lite CNN gets more accurate changed regions than other methods. \n\n\nMoreover, we show the quantitative evaluations in Fig.\\ref{eva}. {It is shown in Fig.\\ref{eva} (a) that the proposed Lite CNN gets a lower pMA on YR-A, Sendai-A and Sendai-B dataset, while the CNN gets a lower pMA on YR-B dataset. It is shown in Fig.\\ref{eva} (b) that the proposed Lite CNN gets a lower pFA on Sendai-B dataset, while S-PCA-Net gets a lower pFA on YR-A, YR-B and Sendai-A dataset. }\nIt is shown in Fig.\\ref{eva} (c) that on the YR-A dataset, S-PCA-Net gets the best kappa among all the methods, while the Lite CNN gets the comparable kappas with other methods, except S-PCA-Net. On the YR-B dataset, Lite CNN gets the comparable kappas with other methods. However, on both Sendai-A and Sendai-B datasets, the Lite CNN performs better than other methods in terms of pMA and kappas.  \n\n\\begin{figure*}[!hbt]\n\\centering\n\\includegraphics[width=\\textwidth]{fig6.png}\n\\caption{The visual comparison results. (a) S-PCA-Net. (b) CNN. (c) Lite CNN. (d) Reference. }\n\\label{fig4}\n\\end{figure*}\n\\begin{figure*}[!htb]\n\\centering\n\\includegraphics[width=\\textwidth]{fig7.png}\n\\caption{The quantitative evaluations of compared methods.(a) MA. (b)FA. (c) Kappa.}\n\\label{eva2}\n\\end{figure*}\n\\subsection{Experiment Results on Cross-dataset Change Detection}\nTo further compare the proposed method with other supervised learning methods, S-PCA-Net and CNN, we perform the comparisons on the cross-dataset change detection, where the network trained on several datasets is applied to an unknown testing dataset. More specifically, to achieve this, this experiment is conducted through the leave-one-out manner, i.e. each dataset alternative is selected as the testing dataset and others as training datasets. \n\nThe visual comparisons are shown in Fig.\\ref{fig4}. It is shown that on the YR-A dataset Lite CNN gets more clear visual result with less noisy spots.  On the YR-B dataset, Lite CNN performs better than CNN, but not better than S-PCA-Net. There is many miss alarms in the results of Lite CNN. On both Sendai-A and Sendai-B datasets, Lite CNN gets better results than other two methods. \n\n{The quantitative evaluations in terms of pFA, pMA and Kappa are shown in Fig.\\ref{eva2}. It is shown in Fig.\\ref{eva2}(a) that the S-PCA-Net gets a lower pMA on all datasets. It is shown in Fig.\\ref{eva2}(b) that the Lite CNN gets a lower pFA on the Sendai-A dataset, while S-PCA-Net gets a lower pFA on the YR-A dataset and CNN gets a lower pFA on the YR-B and Sendai-B dataset.} It is shown in Fig.\\ref{eva2}(c) that Lite CNN performs better than CNN but comparable with S-PCA-Net on YR-A and YR-B datasets. However, Lite CNN shows great advantages over other two methods on Sendai-A and Sendai-B datasets. It indicates that the Lite CNN performs better than other two methods in model generalization, especially on challenging datasets with complex scenes.\n\\begin{table}[!htbp]\n\\centering\n\\caption{The training times of compared methods.}\n\\label{time}\n\\begin{tabular}{lccc}\n\\toprule\n Methods & S-PCA-Net & CNN& Lite CNN   \\\\\n  \\hline\nTimes& ~3 h & 30 mins. &15 mins. \\\\ \n  \\bottomrule\n\\end{tabular}\n\\end{table}\n\\subsection{Discussion}\nFrom the above comparisons, it is shown that Lite CNN can obtain comparable performance with other method on the YR-A and YR-B datasets. On the challenging datasets, e.g. Sendai-A and Sendai-B, Lite CNN outperforms other methods. Moreover, it has better ability to model generalization. Moreover, Lite CNN is more computationally efficient than S-PCA-Net and CNN. The training times of three supervised learning methods are compared in Table \\ref{time}. It is shown that Lite CNN is easy to train and take less time than S-PCA-Net and CNN, while S-PCA-Net takes longer time, since the convolutional kernel is generated by the principle component analysis decomposition. \n\nOverall, Lite CNN can obtain comparable or even better performance than S-PCA-Net and CNN. It is also more computationally efficient than other two methods. It is expected that Lite CNN is more practical in change detection, especially for the requirement of real-time detection.\n\n\\section{Conclusion}\n\\label{sec:conlusion}\nIn this paper, we develop a lightweight convolutional neural network for bitemporal SAR image change detection. The proposed network consists of groups of bottlenecks layers which exploit the image feature. To verify the benefits of our proposed method, we compare it with several traditional neural networks and the comparisons are performed on fours sets of bitemporal SAR images. The experimental results show that our proposed method Lite CNN performs better than other two methods on cross-dataset change detection, especially when the scene is complex. Furthermore, Lite CNN is a lightweight network, which is more computationally efficient than CNN and S-PCA-Net. In the future, we will further optimize Lite CNN and make it more efficient on the edge device. \n\n \\section*{Acknowledgment}\n This work was supported by the State Key Program of National Natural Science of China (No. 61836009), the National Natural Science Foundation of China (No. 61701361, 61806154), the Major Research Plan of National Natural Science Foundation of China (No. 91838303), the Open Fund of Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University (Grant No. IPIU2019006), the Natural Science Basic Research Plan in Shaanxi Province of China (No.2018JM6083) and the Open Fund of State Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University (No. 17E02).\n\n\n\\bibliographystyle{spiejour}  \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{sec:intro}\nA function $g:\\mathcal{I}\\subseteq\\mathbb{R}\\to\\mathbb{R}$ is said to be convex on the\ninterval $\\mathcal{I}$, if the inequality\n\\begin{align}\\label{eq:11}\ng(\\eta\\,x+(1-\\eta)y)\\leq \\eta\\,g(x)+(1-\\eta)g(y)\n\\end{align}\nholds for all $x,y\\in\\mathcal{I}$ and $\\eta\\in[0,1]$.  We say that $g$ is concave, provided $-g$ is convex.\n\nFor convex functions \\eqref{eq:11}, many equalities and inequalities have been established, {\\em e.g.},\nOstrowski type inequality \\cite{7}, Opial inequality \\cite{Farid}, Hardy type inequality \\cite{8}, Olsen type \ninequality \\cite{9}, Gagliardo-Nirenberg type inequality \\cite{10}, midpoint and trapezoidal type inequalities \n\\cite{6,Mohammed9} and the Hermite--Hadamard type (HH-type) inequality \\cite{5} that will be used in our study, \nwhich is defined by:\n\\begin{align}\\label{eq:12}\ng\\left(\\frac{u+v}{2}\\right)&\\leq \\frac{1}{v-u}\\int_u^v g(x)dx\\leq \\frac{g(u)+g(v)}{2},\n\\end{align}\nwhere $g:\\mathcal{I}\\subseteq\\mathbb{R}\\to\\mathbb{R}$ is assumed to be a convex function on  \n$\\mathcal{I}$ where $a, b\\in \\mathcal{I}$ with $u<v$.\n\nA huge number of researchers in the field of applied and pure mathematics have devoted their efforts to\nmodify, generalize, refine, and extend the Hermite--Hadamard inequality \\eqref{eq:12} for convex and other \nclasses of convex functions; see for further details \\cite{5,16,17,18,4}.\n\nIn 2013, the HH-type inequality \\eqref{eq:12} has been generalised to fractional integrals of Riemann--Liouville \ntype by Sarikaya et al \\cite{1}. Their result is as follows, for an $L^1$ convex function \n$f:[u,v]\\to\\mathbb{R}$, and for any $\\mu>0$:\n\\begin{align}\\label{eq:13}\ng\\left(\\frac{u+v}{2}\\right)&\\leq \\frac{\\Gamma(\\mu+2)}{2(v-u)^\\mu}\\left[I^{\\mu}_{u^+}g(v)\n+I^{\\mu}_{v^-}g(u)\\right]\\leq \\frac{g(u)+g(v)}{2},\n\\end{align}\nwhere $I^{\\mu}_{u^+}$ and $I^{\\mu}_{v^-}$ denote left-sided and right-sided \nRiemann-Liouville fractional integrals of order $\\mu>0$, respectively, defined as~\\cite{11}:\n\\begin{align}\\label{eq:14}\n\\begin{aligned}\nI^{\\mu}_{u^+}g(x)=\\frac{1}{\\Gamma(\\mu)}\\int_u^x (x-t)^{\\mu-1}g(t)dt, \\quad x>u,\n\\\\\nI^{\\mu}_{v^-}g(x)=\\frac{1}{\\Gamma(\\mu)}\\int_x^v (t-x)^{\\mu-1}g(t)dt, \\quad x<v.\n\\end{aligned}\n\\end{align}\nIf we take $\\mu=1$ in \\eqref{eq:13} we obtain \\eqref{eq:12}, it is clear that inequality \\eqref{eq:13} \nis a generalization of Hermite--Hadamard inequality \\eqref{eq:12}.\nMany further results have been derived from this \\cite{14,24,Mohammed6,Mohammed7,Mohammed4,2}, \nincluding in different types of fractional calculus, e.g. for tempered fractional integrals \\cite{Mohammed10}, \nthose of Hilfer type \\cite{basci-baleanu}, for those models of fractional calculus involving Mittag-Leffler \nkernels \\cite{Fernandez-Mohammed}, and for fractional integrals with respect to functions \\cite{Mohammed5}. \nBut so far such inequalities have not been investigated for fractional integrals of a twice differentiable\nconvex function with respect to a monotone function. For this reason, we recall the Riemann--Liouville \nfractional integrals of a function with respect to a monotone function.\n\\begin{definition}\\label{def:11}\nLet $(u,v)\\subseteq(-\\infty,\\infty)$ be a finite or infinite interval of the real-axis $\\mathbb{R}$ and \n$\\mu>0$. Let $\\psi(x)$ be an increasing and positive monotone function on the interval $(u,v]$ with a \ncontinuous derivative $\\psi'(x)$ on the interval $(u,v)$. Then the left and right-sided \n$\\psi$-Riemann--Liouville fractional integrals of a function $g$ with respect to another function $\\psi(x)$ \non $[u,v]$ are defined by \\cite{11,19,20}:\n\\begin{align}\\label{eq:15}\n\\begin{aligned}\nI^{\\mu:\\psi}_{u^+}g(x)=\\frac{1}{\\Gamma(\\mu)}\\int_{u}^{x} \\psi'(t)(\\psi(x)-\\psi(t))^{\\mu-1}g(t)dt,\n\\\\\nI^{\\mu:\\psi}_{v^-}g(x)=\\frac{1}{\\Gamma(\\mu)}\\int_{x}^{v} \\psi'(t)(\\psi(t)-\\psi(x))^{\\mu-1}g(t)dt.\n\\end{aligned}\n\\end{align}\nIt is important to note that if we set $\\psi(x)=x$ in \\eqref{eq:15}, then $\\psi$-Riemann--Liouville \nfractional integral reduces to Riemann--Liouville fractional integral \\eqref{eq:14}.\n\\end{definition}\n\nAs we said, in this study we investigate several inequalities of midpoint type for Riemann--Liouville \nfractional integrals of twice differentiable convex functions with respect to increasing functions.\n\\section{Main Results}\nOur main results follow the following lemma:\n\\begin{lemma}\\label{lem:31}\nLet $g:[u,v]\\subseteq\\mathbb{R}\\to\\mathbb{R}$ be a differentiable function and $g''\\in L_1[u,v]$ with \n$0\\leq u<v$. If $\\psi(x)$ is an increasing and positive monotone function on $(u,v]$ and its derivative \n$\\psi'(x)$ is continuous on $(u,v)$, then for $\\mu\\in(0,1)$ we have\n\\begin{align}\\label{eq:31}\n\\begin{aligned}\n\\sigma_{\\mu,\\psi}(g;u,v)&=\\frac{2^{\\mu-1}}{(v-u)^{\\mu}}\\Biggl[\n\\int_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)}^{\\psi^{-1}(v)}\\psi'(t)(v-\\psi(t))^{\\mu+1}(g''\\circ \\psi)(t)dt\n\\\\\n&-\\int_{\\psi^{-1}(u)}^{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)} \\psi'(t)(\\psi(t)-u)^{\\mu+1}\n(g''\\circ \\psi)(t)dt\\Biggr],\n\\end{aligned}\n\\end{align}\nwhere\n\\begin{align*}\n\\sigma_{\\mu,\\psi}(g;u,v)&=\\frac{2^{\\mu-1}\\Gamma(\\mu+2)}{(v-u)^\\mu}\n\\left[I^{\\mu:\\psi}_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)^+}\n(g\\circ \\psi)\\left(\\psi^{-1}(v)\\right)+I^{\\mu:\\psi}_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)^-}\n(g\\circ \\psi)\\left(\\psi^{-1}(u)\\right)\\right]\n-(\\mu+1)g\\left(\\frac{u+v}{2}\\right).\n\\end{align*}\n\\end{lemma}\n\\begin{proof}\nFrom Definition \\ref{def:11} we have\n\\begin{align*}\n\\hbar_{1}:=\\frac{2^{\\mu-1}\\Gamma(\\mu+2)}{(v-u)^\\mu}\nI^{\\mu:\\psi}_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)^+}(g\\circ \\psi)\\left(\\psi^{-1}(v)\\right)\n&=\\frac{\\mu(\\mu+1)2^{\\mu-1}}{(v-u)^\\mu}\\int_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)}^{\\psi^{-1}(v)} \n\\psi'(t)(v-\\psi(t))^{\\mu-1}(g\\circ \\psi)(t)dt\n\\\\\n&=-\\frac{(\\mu+1)2^{\\mu-1}}{(v-u)^\\mu}\\int_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)}^{\\psi^{-1}(v)} \n(g\\circ \\psi)(t)d(v-\\psi(t))^{\\mu}.\n\\end{align*}\nIntegrating by parts twice, we have\n\\begin{align}\\label{eq:32}\n\\hbar_{1}&=\\frac{\\mu+1}{2}g\\left(\\frac{u+v}{2}\\right)+\\frac{(\\mu+1)2^{\\mu-1}}{(v-u)^\\mu}\n\\int_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)}^{\\psi^{-1}(v)}\\psi'(t)(v-\\psi(t))^{\\mu}(g'\\circ \\psi)(t)dt\n\\nonumber\\\\\n&=\\frac{\\mu+1}{2}g\\left(\\frac{u+v}{2}\\right)+\\frac{1}{2}g'\\left(\\frac{u+v}{2}\\right)\n+\\frac{(\\mu+1)2^{\\mu-1}}{(v-u)^\\mu}\n\\int_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)}^{\\psi^{-1}(v)}\\psi'(t)(v-\\psi(t))^{\\mu+1}(g''\\circ \\psi)(t)dt\n\\end{align}\nAnalogously\n\\begin{align}\\label{eq:33}\n\\hbar_{2}&:=\\frac{2^{\\mu-1}\\Gamma(\\mu+1)}{(v-u)^\\mu}\nI^{\\mu:\\psi}_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)^+}(g\\circ \\psi)\\left(\\psi^{-1}(v)\\right)\n\\nonumber\\\\\n&=\\frac{\\mu+1}{2}g\\left(\\frac{u+v}{2}\\right)-\\frac{1}{2}g'\\left(\\frac{u+v}{2}\\right)\n-\\frac{2^{\\mu-1}}{(v-u)^\\mu}\n\\int_{\\psi^{-1}(u)}^{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)} \\psi'(t)(\\psi(t)-u)^{\\mu+1}(g''\\circ \\psi)(t)dt.\n\\end{align}\nIt follows from \\eqref{eq:32} and \\eqref{eq:33} that\n\\begin{align*}\n\\hbar_{1}+\\hbar_{2}-(\\mu+1)g\\left(\\frac{u+v}{2}\\right)\n&=\\frac{2^{\\mu-1}}{(v-u)^{\\mu}}\\Biggl[\n\\int_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)}^{\\psi^{-1}(v)}\\psi'(t)(v-\\psi(t))^{\\mu+1}(g''\\circ \\psi)(t)dt\n\\\\\n&-\\int_{\\psi^{-1}(u)}^{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)} \\psi'(t)(\\psi(t)-u)^{\\mu+1}\n(g''\\circ \\psi)(t)dt\\Biggr].\n\\end{align*}\nThis completes the proof of Lemma \\ref{lem:31}.\n\\end{proof}\n\\begin{corollary}\\label{cor:31}\nWith the similar assumptions of Lemma \\ref{lem:31} if\n\\begin{enumerate}\n\\item $\\psi(x)=x$, we have\n\\begin{align*}\n&\\frac{2^{\\mu-1}\\Gamma(\\mu+2)}{(v-u)^\\mu}\\left[I^{\\mu}_{\\left(\\frac{u+v}{2}\\right)^+}g(v)\n+I^{\\mu}_{\\left(\\frac{u+v}{2}\\right)^-}g(u)\\right]-(\\mu+1)g\\left(\\frac{u+v}{2}\\right)\n\\\\\n&=\\frac{(v-u)^2}{8}\\Biggl[\\int_{0}^{1}t^{\\mu+1}g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)dt\n+\\int_{0}^{1}t^{\\mu+1}g''\\left(\\frac{2-t}{2}u+\\frac{t}{2}v\\right)dt\\Biggr],\n\\end{align*}\nwhich is obtained by Tomar et al. \\cite{21}.\n\\item $\\psi(x)=x$ and $\\mu=1$, we have\n\\begin{align*}\n&\\frac{1}{v-u}\\int_{u}^{v}g(x)dx-g\\left(\\frac{u+v}{2}\\right)\n=\\frac{(v-u)^2}{16}\\Biggl[\\int_{0}^{1}t^{2}g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)dt\n+\\int_{0}^{1}t^{2}g''\\left(\\frac{2-t}{2}u+\\frac{t}{2}v\\right)dt\\Biggr],\n\\end{align*}\n\\end{enumerate}\nwhich is obtained by Sarikaya and Kiris \\cite{22}.\n\\end{corollary}\n\\begin{theorem}\\label{th:31}\nLet $g:[u,v]\\subseteq\\mathbb{R}\\to\\mathbb{R}$ be a differentiable function and $g''\\in L_1[u,v]$ with \n$0\\leq u<v$. Suppose that $|g''|$ is convex on $[u,v]$, $\\psi(x)$ is an increasing and positive monotone \nfunction on $(u,v]$ and its derivative $\\psi'(x)$ is continuous on $(u,v)$, then for $\\mu\\in(0,1)$ we have\n\\begin{align}\\label{eq:34}\n\\begin{aligned}\n\\left|\\sigma_{\\mu,\\psi}(g;u,v)\\right|\n&\\leq\\frac{(v-u)^2}{8}\\left(\\frac{1}{\\mu+2}\\right)^{1-\\frac{1}{q}}\n\\Biggl\\{\\left[\\frac{1}{2(\\mu+3)}|g''(u)|^q+\\left(\\frac{1}{\\mu+2}-\\frac{1}{2(\\mu+3)}\\right)\n|g''(v)|^q\\right]^{\\frac{1}{q}}\n\\\\\n&+\\left[\\left(\\frac{1}{\\mu+2}-\\frac{1}{2(\\mu+3)}\\right)|g''(u)|^q\n+\\frac{1}{2(\\mu+3)}|g''(v)|^q\\right]^{\\frac{1}{q}}\\Biggr\\}\n\\end{aligned}\n\\end{align}\nfor $q\\geq 1$.\n\\end{theorem}\n\\begin{proof}\nSuppose that $q=1$. By means of Lemma \\ref{lem:31} and Definition \\ref{def:11}, we get\n\\begin{align}\\label{eq:35}\n\\sigma_{\\mu,\\psi}(g;u,v)&=\\frac{2^{\\mu-1}}{(v-u)^{\\mu}}\\Biggl[\n\\int_{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)}^{\\psi^{-1}(v)}\\psi'(t_{1})(v-\\psi(t_{1}))^{\\mu+1}\n(g''\\circ \\psi)(t_{1})dt_{1}\n\\nonumber \\\\\n&-\\int_{\\psi^{-1}(u)}^{\\psi^{-1}\\left(\\frac{u+v}{2}\\right)} \\psi'(t_{2})(\\psi(t_{2})-u)^{\\mu+1}\n(g''\\circ \\psi)(t_{2})dt_{2}\\Biggr].\n\\end{align}\nChange the variables $x_{1}=\\frac{2(v-\\psi(t_{1}))}{v-u}$ and $x_{2}=\\frac{2(\\psi(t_{2})-u)}{v-u}$ and then\nset $t=x_{1}=x_{2}$ into the resulting equality, then \\eqref{eq:35} becomes\n\\begin{align*}\n\\sigma_{\\mu,\\psi}(g;u,v)&=\\frac{(v-u)^2}{8}\\Biggl[\n\\int_{0}^{1}t^{\\mu+1}g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)dt\n+\\int_{0}^{1}t^{\\mu+1}g''\\left(\\frac{2-t}{2}u+\\frac{t}{2}v\\right)dt\\Biggr],\n\\end{align*}\nthat is\n\\begin{align}\\label{eq:36}\n\\left|\\sigma_{\\mu,\\psi}(g;u,v)\\right|&\\leq\\frac{(v-u)^2}{8}\\Biggl[\n\\int_{0}^{1}t^{\\mu+1}\\left(\\left|g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)\\right|\n+\\left|g''\\left(\\frac{2-t}{2}u+\\frac{t}{2}v\\right)\\right|\\right) dt\\Biggr].\n\\end{align}\nBy using the convexity of $|g''|$, then inequality \\eqref{eq:36} gives \n\\begin{align*}\n\\left|\\sigma_{\\mu,\\psi}(g;u,v)\\right|&\\leq\\frac{(v-u)^2}{8}\\Biggl[\n\\int_{0}^{1}t^{\\mu+1}\\left(\\left|g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)\\right|\n+\\left|g''\\left(\\frac{2-t}{2}u+\\frac{t}{2}v\\right)\\right|\\right) dt\\Biggr]\n\\nonumber \\\\\n&\\leq\\frac{(v-u)^2}{8}\\left(|g''(u)|\\int_{0}^{1}\\frac{1}{2}t^{\\mu+2} dt\n+|g''(v)|\\int_{0}^{1}\\frac{2-t}{2}t^{\\mu+1} dt \\right.\n\\nonumber \\\\\n&+\\left.|g''(v)|\\int_{0}^{1}\\frac{1}{2}t^{\\mu+2} dt\n+|g''(u)|\\int_{0}^{1}\\frac{2-t}{2}t^{\\mu+1} dt \\right)\n\\nonumber \\\\\n&=\\frac{(v-u)^2}{8(\\mu+2)}\\left(|g''(u)|+|g''(v)|\\right).\n\\end{align*}\nThis gives \\eqref{eq:34} for $q=1$.\n\nNow, suppose that $q>1$. Using inequality of \\eqref{eq:36}, convexity of $|g''|^q$ and the power--mean's \ninequality for $q>1$, we have\n\\begin{align}\\label{eq:314}\n\\int_{0}^{1}t^{\\mu+1}\\left|g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)\\right|dt\n&=\\int_{0}^{1}t^{\\mu+1-\\frac{\\mu+1}{q}}\\left[t^{\\frac{\\mu+1}{q}}\n\\left|g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)\\right|\\right]dt\n\\nonumber \\\\\n&\\leq \\left(\\int_{0}^{1}t^{\\mu+1}\\right)^{1-\\frac{1}{q}}\n\\left(\\int_{0}^{1}t^{\\mu+1}\\left|g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)\\right|^{q}dt\n\\right)^{\\frac{1}{q}}\n\\nonumber \\\\\n&\\leq \\left(\\frac{1}{\\mu+2}\\right)^{1-\\frac{1}{q}}\n\\left(\\int_{0}^{1}\\left(\\frac{t^{\\mu+2}}{2}|g''(u)|^{q}+\\frac{2t^{\\mu+1}-t^{\\mu+2}}{2}|g''(v)|^{q}\n\\right)dt\\right)^{\\frac{1}{q}}\n\\nonumber \\\\\n&=\\left(\\frac{1}{\\mu+2}\\right)^{1-\\frac{1}{q}}\n\\left[\\frac{1}{2(\\mu+3)}|g''(u)|^q+\\left(\\frac{1}{\\mu+2}-\\frac{1}{2(\\mu+3)}\\right)\n|g''(v)|^q\\right]^{\\frac{1}{q}}.\n\\end{align}\nIn the same manner, we get\n\\begin{align}\\label{eq:315}\n&\\int_{0}^{1}t^{\\mu+1}\\left|g''\\left(\\frac{2-t}{2}u+\\frac{t}{2}v\\right)\\right|dt\n\\leq \\left(\\frac{1}{\\mu+2}\\right)^{1-\\frac{1}{q}}\n\\left[\\left(\\frac{1}{\\mu+2}-\\frac{1}{2(\\mu+3)}\\right)|g''(u)|^q\n+\\frac{1}{2(\\mu+3)}|g''(v)|^q\\right]^{\\frac{1}{q}}.\n\\end{align}\nUsing \\eqref{eq:314} and \\eqref{eq:315} in \\eqref{eq:36} we obtain \\eqref{eq:34} for $q>1$.\nThus the proof of theorem \\ref{th:31} is completed.\n\\end{proof}\n\\begin{corollary} \\label{cor:32}\nWith the similar assumptions of Theorem \\ref{th:31} if\n\\begin{enumerate}\n\\item $\\psi(x)=x$, we have\n\\begin{align*}\n&\\left|\\frac{2^{\\mu-1}\\Gamma(\\mu+2)}{(v-u)^\\mu}\\left[I^{\\mu}_{\\left(\\frac{u+v}{2}\\right)^+}g(v)\n+I^{\\mu}_{\\left(\\frac{u+v}{2}\\right)^-}g(u)\\right]-(\\mu+1)g\\left(\\frac{u+v}{2}\\right)\\right|\n\\\\\n&\\leq\\frac{(v-u)^2}{8}\\left(\\frac{1}{\\mu+2}\\right)^{1-\\frac{1}{q}}\n\\Biggl\\{\\left[\\frac{1}{2(\\mu+3)}|g''(u)|^q+\\left(\\frac{1}{\\mu+2}-\\frac{1}{2(\\mu+3)}\\right)\n|g''(v)|^q\\right]^{\\frac{1}{q}}\n\\\\\n&+\\left[\\left(\\frac{1}{\\mu+2}-\\frac{1}{2(\\mu+3)}\\right)|g''(u)|^q\n+\\frac{1}{2(\\mu+3)}|g''(v)|^q\\right]^{\\frac{1}{q}}\\Biggr\\},\n\\end{align*}\nwhich is obtained by Tomar et al. \\cite{21}.\n\\item $\\psi(x)=x$ and $\\mu=1$, we have\n\\begin{align*}\n&\\left|\\frac{1}{v-u}\\int_{u}^{v}g(x)dx-g\\left(\\frac{u+v}{2}\\right)\\right|\n\\leq\\frac{(v-u)^2}{48}\\Biggl[\\left(\\frac{3|g''(u)|^q+5|g''(v)|^q}{8}\\right)^{\\frac{1}{q}}\n+\\left(\\frac{5|g''(u)|^q+3|g''(v)|^q}{8}\\right)^{\\frac{1}{q}}\\Biggr],\n\\end{align*}\nwhich is obtained by Sarikaya et al. \\cite{23}.\n\\item $\\psi(x)=x$ and $q=1$, we have\n\\begin{align*}\n&\\left|\\frac{2^{\\mu-1}\\Gamma(\\mu+2)}{(v-u)^\\mu}\\left[I^{\\mu}_{\\left(\\frac{u+v}{2}\\right)^+}g(v)\n+I^{\\mu}_{\\left(\\frac{u+v}{2}\\right)^-}g(u)\\right]-(\\mu+1)g\\left(\\frac{u+v}{2}\\right)\\right|\n\\leq\\frac{(v-u)^2}{8(\\mu+2)}\\biggl(|g''(u)|+|g''(v)|\\biggr),\n\\end{align*}\nwhich is obtained by Tomar et al. \\cite{21}.\n\\item $\\psi(x)=x, \\mu=1$ and $q=1$, we have\n\\begin{align*}\n&\\left|\\frac{1}{v-u}\\int_{u}^{v}g(x)dx-g\\left(\\frac{u+v}{2}\\right)\\right|\n\\leq\\frac{(v-u)^2}{24}\\left(\\frac{|g''(u)|+|g''(v)}{2}\\right),\n\\end{align*}\n\\end{enumerate}\nwhich is obtained by Sarikaya et al. \\cite{23}.\n\\end{corollary}\n\\begin{theorem}\\label{th:32}\nLet $g:[u,v]\\subseteq\\mathbb{R}\\to\\mathbb{R}$ be a differentiable function and $g''\\in L_1[u,v]$ with \n$0\\leq u<v$. Suppose that $|g''|^q$ is convex on $[u,v]$, $\\psi(x)$ is an increasing and positive monotone \nfunction on $(u,v]$ and its derivative $\\psi'(x)$ is continuous on $(u,v)$, then for $\\mu\\in(0,1)$ we have\n\\begin{align}\\label{eq:37}\n\\begin{aligned}\n\\left|\\sigma_{\\mu,\\psi}(g;u,v)\\right|\n&\\leq\\frac{(v-u)^2}{8}\\left(\\frac{2}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\n\\Biggl[\\left(\\frac{|g''(u)|^q+3|g''(v)|^q}{4}\\right)^{\\frac{1}{q}}\n+\\left(\\frac{3|g''(u)|^q+|g''(v)|^q}{4}\\right)^{\\frac{1}{q}}\\Biggr]\n\\\\\n&\\leq\\frac{(v-u)^2}{8}\\left(\\frac{2}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\\bigl(|g''(u)|+|g''(v)|\\bigr),\n\\end{aligned}\n\\end{align}\nsuch that $q>1$ and $\\frac{1}{p}+\\frac{1}{q}=1$.\n\\end{theorem}\n\\begin{proof}\nBy using the Holder's inequality, we have\n\\begin{align}\\label{eq:38}\n\\int_{0}^{1}t^{\\mu+1}\\left|g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)\\right|dt\n&\\leq \\left(\\int_{0}^{1}t^{(\\mu+1)p}\\right)^{\\frac{1}{p}}\n\\left(\\int_{0}^{1}\\left|g''\\left(\\frac{t}{2}u+\\frac{2-t}{2}v\\right)\\right|^{q}dt\\right)^{\\frac{1}{q}}\n\\nonumber \\\\\n&\\leq \\left(\\frac{1}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\n\\left(\\int_{0}^{1}\\left(\\frac{t}{2}|g''(u)|^{q}+\\frac{2-t}{2}|g''(v)|^{q}\\right)\ndt\\right)^{\\frac{1}{q}}\n\\nonumber \\\\\n&=\\left(\\frac{1}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\n\\left(\\frac{|g''(u)|^{q}+3|g''(v)|^{q}}{4}\\right)^{\\frac{1}{q}}.\n\\end{align}\nSimilarly, we have\n\\begin{align}\\label{eq:39}\n\\int_{0}^{1}t^{\\mu+1}\\left|g''\\left(\\frac{2-t}{2}u+\\frac{t}{2}v\\right)\\right|dt\n&\\leq \\left(\\frac{1}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\n\\left(\\frac{3|g''(u)|^{q}+|g''(v)|^{q}}{4}\\right)^{\\frac{1}{q}}.\n\\end{align}\nThus, the inequalities \\eqref{eq:36}, \\eqref{eq:38} and \\eqref{eq:39} complete the proof of\nthe first inequality of \\eqref{eq:37}.\n\nTo prove the second inequality of \\eqref{eq:37}, we apply the formula \n\\begin{align*}\n\\sum_{i=1}^{n}\\left(c_i+d_i\\right)^m\\leq \\sum_{i=1}^{n}c_i^m+\\sum_{i=1}^{n}+d_i^m, \\quad 0\\leq m<1\n\\end{align*}\nfor $c_{1}=3|g''(u)|^{q}, c_{2}=|g''(u)|^{q}, d_{1}=|g''(v)|^{q}, d_{2}=3|g''(v)|^{q}$ and $m=\\frac{1}{q}$.\nThen \\eqref{eq:36} gives\n\\begin{align*}\n\\left|\\sigma_{\\mu,\\psi}(g;u,v)\\right|\n&\\leq\\frac{(v-u)^2}{8}\\left(\\frac{1}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\n\\Biggl[\\left(\\frac{|g''(u)|^q+3|g''(v)|^q}{4}\\right)^{\\frac{1}{q}}\n+\\left(\\frac{3|g''(u)|^q+|g''(v)|^q}{4}\\right)^{\\frac{1}{q}}\\Biggr]\n\\\\\n&\\leq\\frac{(v-u)^2\\left(3^{\\frac{1}{q}}+1\\right)}{16}\\left(\\frac{1}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\n\\bigl[|g''(u)|+|g''(v)|\\bigr]\n\\\\\n&\\leq\\frac{(v-u)^2}{8}\\left(\\frac{1}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\\bigl(|g''(u)|+|g''(v)|\\bigr).\n\\end{align*}\nHence the proof of Theorem \\ref{th:32} is completed.\n\\end{proof}\n\\begin{corollary}\\label{cor:33}\nWith the similar assumptions of Theorem \\ref{th:32}, if\n\\begin{enumerate}\n\\item $\\psi(x)=x$, we have\n\\begin{align*}\n&\\left|\\frac{2^{\\mu-1}\\Gamma(\\mu+2)}{(v-u)^\\mu}\\left[I^{\\mu}_{\\left(\\frac{u+v}{2}\\right)^+}g(v)\n+I^{\\mu}_{\\left(\\frac{u+v}{2}\\right)^-}g(u)\\right]-(\\mu+1)g\\left(\\frac{u+v}{2}\\right)\\right|\n\\\\\n&\\leq\\frac{(v-u)^2}{8}\\left(\\frac{2}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\n\\Biggl[\\left(\\frac{|g''(u)|^q+3|g''(v)|^q}{4}\\right)^{\\frac{1}{q}}\n+\\left(\\frac{3|g''(u)|^q+|g''(v)|^q}{4}\\right)^{\\frac{1}{q}}\\Biggr]\n\\\\\n&\\leq\\frac{(v-u)^2}{8}\\left(\\frac{2}{(\\mu+1)p+1}\\right)^{\\frac{1}{p}}\\bigl(|g''(u)|+|g''(v)|\\bigr),\n\\end{align*}\nwhich is obtained by Tomar et al. \\cite{21}.\n\\item $\\psi(x)=x$ and $\\mu=1$, we have\n\\begin{align*}\n\\left|\\frac{1}{v-u}\\int_{u}^{v}g(x)dx-g\\left(\\frac{u+v}{2}\\right)\\right|\n&\\leq\\frac{(v-u)^2}{16(2p+1)^{\\frac{1}{p}}}\n\\Biggl[\\left(\\frac{|g''(u)|^q+3|g''(v)|^q}{4}\\right)^{\\frac{1}{q}}\n+\\left(\\frac{3|g''(u)|^q+|g''(v)|^q}{4}\\right)^{\\frac{1}{q}}\\Biggr]\n\\\\\n&\\leq\\frac{(v-u)^2}{2^{2+\\frac{2}{q}}(2p+1)^{\\frac{1}{p}}}\\bigl(|g''(u)|+|g''(v)|\\bigr),\n\\end{align*}\n\\end{enumerate}\nwhich is obtained by Sarikaya et al. \\cite{23}.\n\\end{corollary}\n\\begin{corollary}\\label{cor:34}\nFrom Theorems \\ref{th:31}--\\ref{th:32}, we obtain the following inequality for $\\psi(x)=x, \\mu=1$ and $q>1$:\n\\begin{align*}\n\\left|\\frac{1}{v-u}\\int_{u}^{v}g(x)dx-g\\left(\\frac{u+v}{2}\\right)\\right|\n&\\leq(v-u)^2\\min\\{\\delta_{1},\\delta_{2}\\}\\bigl(|g''(u)|+|g''(v)|\\bigr),\n\\end{align*}\nwhere $\\delta_{1}=\\frac{1}{24}$ and $\\delta_{2}=\\frac{1}{2^{2+\\frac{2}{q}}(2p+1)^{\\frac{1}{p}}}$\nsuch that $p=\\frac{q}{q-1}$.\n\\end{corollary}\n\\section{Applications}\nIn this section some applications are presented to demonstrate usefulness of our obtained results in the\nprevious sections. \n\\subsection{Applications to special means}\nLet $u$ and $v$ be two arbitrary positive real numbers, then consider the following special means:\n\\begin{enumerate}\n\\item[(i)] The arithmetic mean:\n\\[A=A(u,v)=\\frac{u+v}{2}.\\]\n\\item[(ii)] The inverse arithmetic mean:\n\\[H=H(u,v)=\\frac{2}{\\frac{1}{u}+\\frac{1}{v}}, \\quad u,v\\neq 0.\\]\n\\item[(iii)] The geometric mean:\n\\[G=G(u,v)=\\sqrt{u\\,v}.\\]\n\\item[(iv)] The logarithmic mean:\n\\[L(u,v)=\\frac{v-u}{\\log(v)-\\log(u)}, \\quad u\\neq v.\\]\n\\item[(v)] The generalized logarithmic mean:\n\\[L_{n}(u,v)=\\left[\\frac{v^{n+1}-u^{n+1}}{(v-u)(n+1)}\\right]^{\\frac{1}{n}}, \n\\quad n\\in\\mathbb{Z}\\setminus\\{-1,0\\}.\\]\n\\end{enumerate}\n\\begin{proposition}\\label{prop:1}\nLet $|n|\\geq 3$ and $u, v\\in\\mathbb{R}$ with $0<u<v$, then\n\\begin{align}\\label{eq:prop1}\n\\left|A^{n}(u,v)-L_{n}^{n}(u,v)\\right|\\leq \\frac{(v-u)^2|n(n-1)|}{3\\cdot 4^{\\frac{1}{q}+2}}\\left[\nA^{\\frac{1}{q}}\\left(3|u|^{(n-2)q},5|v|^{(n-2)q}\\right)\n+A^{\\frac{1}{q}}\\left(5|u|^{(n-2)q},3|v|^{(n-2)q}\\right)\\right],\n\\end{align}\nfor $q\\geq 1$.\n\\end{proposition}\n\\begin{proof}\nApply Corollary \\ref{cor:32} part (2) for $g(x)=x^n$, where $n$ as specified above.\n\\end{proof}\n\\begin{proposition}\\label{prop:2}\nLet $u, v\\in\\mathbb{R}$ with $0<u<v$, then\n\\begin{align}\\label{eq:prop2}\n\\left|A^{-1}(u,v)-L^{-1}(u,v)\\right|\\leq \\frac{(v-u)^2}{3\\cdot 4^{\\frac{1}{q}+2}}\\left[\nA^{\\frac{1}{q}}\\left(3|u|^{-3q},5|v|^{-3q}\\right)\n+A^{\\frac{1}{q}}\\left(5|u|^{-3q},3|v|^{-3q}\\right)\\right],\n\\end{align}\nfor $q\\geq 1$.\n\\end{proposition}\n\\begin{proof}\nApply Corollary \\ref{cor:32} part (2) for $g(x)=\\frac{1}{x}, x\\neq 0$.\n\\end{proof}\n\\begin{proposition}\\label{prop:3}\nLet $|n|\\geq 3$ and $u, v\\in\\mathbb{R}$ with $0<u<v$, then\n\\begin{align}\\label{eq:prop31}\n&\\left|H^{-n}(v,u)-L_{n}^{n}\\left(v^{-1},u^{-1}\\right)\\right|\n\\nonumber\\\\\n&\\leq \\frac{\\left(v^{-1}-u^{-1}\\right)^2|n(n-1)|}{3\\cdot 4^{\\frac{1}{q}+2}}\\left[\nH^{\\frac{-1}{q}}\\left(3|u|^{(n-2)q},5|v|^{(n-2)q}\\right)\n+H^{\\frac{-1}{q}}\\left(5|u|^{(n-2)q},3|v|^{(n-2)q}\\right)\\right],\n\\end{align}\nand\n\\begin{align}\\label{eq:prop32}\n\\left|H(v,u)-L^{-1}\\left(v^{-1},u^{-1}\\right)\\right|\\leq \n\\frac{\\left(v^{-1}-u^{-1}\\right)^2}{3\\cdot 4^{\\frac{1}{q}+2}}\\left[\nH^{\\frac{-1}{q}}\\left(3|u|^{-3q},5|v|^{-3q}\\right)\n+H^{\\frac{-1}{q}}\\left(5|u|^{-3q},3|v|^{-3q}\\right)\\right],\n\\end{align}\nfor $q\\geq 1$.\n\\end{proposition}\n\\begin{proof}\nObserve that $A^{-1}\\left(u^{-1},v^{-1}\\right)=H(u,v)=\\frac{2}{\\frac{1}{u}+\\frac{1}{v}}$.\nSo, Make the change of variables $u\\to v^{-1}$ and $v\\to u^{-1}$ in the inequalities\n\\eqref{eq:prop1} and \\eqref{eq:prop2}, we can deduce the desired inequalities \\eqref{eq:prop31} and \n\\eqref{eq:prop32} respectively.\n\\end{proof}\n\\begin{proposition}\\label{prop:4}\nLet $u, v\\in\\mathbb{R}$ with $0<u<v$, then\n\\begin{align}\\label{eq:prop4}\n\\left|G^{-2}(u,v)-A^{-2}(u,v)\\right|\\leq \\frac{(b-a)^2}{2\\cdot 4^{\\frac{1}{q}+1}}\\left[\nA^{\\frac{1}{q}}\\left(3|u|^{-3q},5|v|^{-3q}\\right)\n+A^{\\frac{1}{q}}\\left(5|u|^{-3q},3|v|^{-3q}\\right)\\right],\n\\end{align}\nfor $q\\geq 1$.\n\\end{proposition}\n\\begin{proof}\nApply Corollary \\ref{cor:32} part (2) for $g(x)=x^2$.\n\\end{proof}\n\nNow, we give an application to a midpoint formula. Let $d$ be a partition\n$u=x_{0}<x_{1}<\\cdots<x_{m-1}<x_{m}=v$ of the interval $[a,b]$ and consider the quadrature formula\n\\begin{align*}\n\\int_{a}^{b}g(x)dx=T(g,d)+E(g,d),\n\\end{align*}\nwhere\n\\begin{align*}\nT(g,d)=\\sum_{j=0}^{m-1}g\\left(\\frac{x_{j}+x_{j+1}}{2}\\right)(x_{j+1}-x_{j})\n\\end{align*}\nis the midpoint version and $E(g,d)$ denotes the associated approximation error. Here, we\npresent some error estimates for the midpoint formula.\n\\begin{proposition}\\label{prop:5}\nLet $g:[u,v]\\to\\mathbb{R}$ be a differentiable mapping on $(u,v)$ with $u<v$. Suppose that $|g''|^q, q\\geq 1$ \nbe a convex function, then for every partition of $[u,v]$ the midpoint error satisfies\n\\begin{align}\\label{eq:prop5}\n\\left|E(g,d)\\right|\\leq \\min\\{\\delta_{1},\\delta_{2}\\}\\,\\sum_{j=0}^{m-1}(x_{j+1}-x_{j})^{2}\n\\bigl(|g''(x_{j})|+|g''(x_{j+1})|\\bigr).\n\\end{align}\n\\end{proposition}\n\\begin{proof}\nFrom Corollary \\ref{cor:34}, we have\n\\begin{align*}\n\\left|\\int_{x_{j}}^{x_{j+1}}g(x)dx-(x_{j+1}-x_{j})g\\left(\\frac{x_{j}+x_{j+1}}{2}\\right)\\right|\n\\leq \\min\\{\\delta_{1},\\delta_{2}\\}\\,(x_{j+1}-x_{j})^{2}\\bigl(|g''(x_{j})|+|g''(x_{j+1})|\\bigr)\n\\end{align*}\nSumming over $j$ from $0$ to $m-1$ and taking into account that $|g''|$ is convex, we\nobtain, by the triangle inequality, that\n\\begin{align*}\n\\left|\\int_{a}^{b}g(x)dx-T(g,d)\\right|&=\\left|\\sum_{j=0}^{m-1}\n\\left[\\int_{x_{j}}^{x_{j+1}}g(x)dx-(x_{j+1}-x_{j})g\\left(\\frac{x_{j}+x_{j+1}}{2}\\right)\\right]\\right|\n\\\\\n&\\leq \\sum_{j=0}^{m-1}\\left|\n\\int_{x_{j}}^{x_{j+1}}g(x)dx-(x_{j+1}-x_{j})g\\left(\\frac{x_{j}+x_{j+1}}{2}\\right)\\right|\n\\\\\n&\\leq \\min\\{\\delta_{1},\\delta_{2}\\}\\,\\sum_{j=0}^{m-1}(x_{j+1}-x_{j})^{2}\n\\bigl(|g''(x_{j})|+|g''(x_{j+1})|\\bigr).\n\\end{align*}\nThis ends the proof.\n\\end{proof}\n\\subsection{Modified Bessel functions}\nLet the function $\\mathcal{I}_{p}:\\mathbb{R}\\to[1,\\infty)$ be defined by\n\\begin{align*}\n\\mathcal{I}_{p}(x)=2^{p}\\Gamma(p+1)x^{-v}I_{p}(x),\\quad x\\in\\mathbb{R}.\n\\end{align*}\nFor this we recall the modified Bessel function of the first kind $\\mathcal{I}_{p}$ which is defined \nas \\cite{25}:\n\\begin{align*}\n\\mathcal{I}_{p}(x)&=\\sum_{n\\geq 0}\\frac{\\left(\\frac{x}{2}\\right)^{p+2n}}{n!\\Gamma(p+n+1)}.\n\\end{align*} \nThe first and the $n$th order derivative formula of $\\mathcal{I}_{p}(x)$ are, respectively, given by \\cite{26}:\n\\begin{align}\\label{eq:prop61}\n\\mathcal{I}'_{p}(x)&=\\frac{x}{2(p+1)}\\mathcal{I}_{p+1}(x),\n\\\\\n\\frac{\\partial^{n}\\mathcal{I}_{p}(x)}{\\partial x^{n}}&=2^{n-2p}\\sqrt{\\pi}x^{p-n}\\Gamma(p+1)\\,\n_{2}F_{3}\\left(\\frac{p+1}{2},\\frac{p+2}{2};\\frac{p+1-n}{2},\\frac{p+2-n}{2},p+1;\\frac{x^2}{4}\\right),\n\\label{eq:prop62}\n\\end{align}\nwhere $_{2}F_{3}\\left(\\cdot,\\cdot;\\cdot,\\cdot,\\cdot;\\cdot\\right)$ is the hypergeometric function defined \nby \\cite{26}:\n\\begin{align}\\label{eq:prop63}\n&_{2}F_{3}\\left(\\frac{p+1}{2},\\frac{p+2}{2};\\frac{p+1-n}{2},\\frac{p+2-n}{2},p+1;\\frac{x^2}{4}\\right)\n=\\sum_{k=0}^{\\infty}\\frac{\\left(\\frac{p+1}{2}\\right)_{k}\\left(\\frac{p+2}{2}\\right)_{k}}\n{\\left(\\frac{p-2}{2}\\right)_{k}\\left(\\frac{p-1}{2}\\right)_{k}(p+1)_{k}}\\frac{x^{2k}}{4^{k}\\,(k)!},\n\\end{align}\nwhere, for some parameter $\\nu$, the Pochhammer symbol $(\\nu)_{k}$ is defined as\n\\begin{align*}\n(\\nu)_{0}=1,\\quad (\\nu)_{k}=\\nu(\\nu+1)\\cdots(\\nu+k-1), \\quad k=1,2,...\n\\end{align*}\n\\begin{proposition}\nLet $u,v\\in\\mathbb{R}$ with $0<u<v$, then for each $p>-1$ we have\n\\begin{align}\\label{eq:prop64}\n&\\left|\\frac{\\mathcal{I}_{p}(v)-\\mathcal{I}_{p}(u)}{v-u}\n-\\frac{a+b}{4(p+1)}\\mathcal{I}_{p+1}\\left(\\frac{u+v}{2}\\right)\\right|\n\\leq (v-u)^{2}\\min\\{\\delta_{1},\\delta_{2}\\}\\, 2^{3-2p}\\sqrt{\\pi}\\Gamma(p+1)\n\\nonumber \\\\\n&\\times\\Biggl(\\left|a\\right|^{p-3}\n\\left|\\,_{2}F_{3}\\left(\\frac{p+1}{2},\\frac{p+2}{2};\\frac{p+1-n}{2},\\frac{p+2-n}{2},p+1;\\frac{a^2}{4}\\right)\n\\right|\n\\nonumber \\\\\n&+\\left|b\\right|^{p-3}\n\\left|\\,_{2}F_{3}\\left(\\frac{p+1}{2},\\frac{p+2}{2};\\frac{p+1-n}{2},\\frac{p+2-n}{2},p+1;\\frac{b^2}{4}\\right)\n\\right|\\Biggr).\n\\end{align}\n\\end{proposition}\n\\begin{proof}\nLet $g(x)=\\mathcal{I}'_{p}(x)$. Note that the function $x\\mapsto\\mathcal{I}'''_{p}(x)$ is convex on the \ninterval $[0,\\infty)$ for each $p>-1$. Using Corollary \\ref{cor:34} and \\eqref{eq:prop61}--\\eqref{eq:prop62}, \nwe obtain the desired inequality \\eqref{eq:prop64} immediately.\n\\end{proof}\n\\section{Conclusion}\nIn this paper, we established some new integral inequalities of midpoint type for convex functions with \nrespect to increasing functions involving Riemann--Liouville fractional integrals. It can be noted from \nCorollary \\ref{cor:31}--\\ref{cor:33} that our results are a generalization of all obtained results in\n\\cite{21,22,23}.\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{sec:intro}\n\nIn the current paradigm of galaxy formation, it is believed that virtually all\ngalaxies initially form  as `disks' owing to the cooling  of gas with non-zero\nangular momentum in  virialized dark matter haloes. This  smooth gas accretion\ndominates  the galactic  gas supply  and hence  the fuel  for  star formation.\nGalaxies that  reside in the  centers of lower  mass halos, those  with masses\nless than  $M_{halo} \\lower.7ex\\hbox{\\ltsima}  3\\times 10^{11} \\>h^{-1}\\rm M_\\odot$,  accrete gas  through very\nefficient  cold  mode accretion,  i.e.  gas that  is  never  heated (Keres  et\nal. 2005,  Keres et  al. 2008).   The central galaxies  that reside  in larger\nhalos accrete their  gas through the classic, but less  efficient, hot mode of\naccretion where  the gas is shock  heated to near the  virial temperature near\nthe virial  radius and then  must cool to  be accreted by the  central galaxy.\nHence the  naive expectation would be  that dwarf galaxies  should be actively\nstar forming and blue.\n\nHowever, when a small halo is accreted by a larger halo, i.e.  when it becomes\na  subhalo,  the central  galaxy  that  formed in  the  small  halo becomes  a\nsatellite galaxy and may experience a number of environmental effects that may\nchange its  properties.  For instance,  the diffuse gas  originally associated\nwith  the  subhalo  may  be  stripped,  thus  removing  the  fuel  for  future\nstar-formation  (e.g.   Larson,  Tinsley  \\& Caldwell  1980).   This  process,\nreferred to as strangulation (Balogh \\&  Morris 2000), can result in a gradual\ndecline of the  star formation rate in the satellite  galaxy, making it redder\nwith  the passage of  time.  If  the external  pressure is  sufficiently high,\nram-pressure  stripping  may  also be  able  to  remove  the entire  cold  gas\nreservoir of the satellite (e.g.  Gunn \\& Gott 1972), causing a fast quenching\nof its  star formation.  A satellite  galaxy is also subject  to tidal heating\nand stripping and  galaxy harassment (Moore et al 1996),  which may also cause\nthe  satellite to  lose  its fuel  for  star formation.   These processes  are\nbelieved  to have  played  an important  role  in the  evolution of  satellite\ngalaxies, and to  be responsible, to a large extent,  for the relation between\ngalaxy  properties  and  their  environment. Indeed,  satellite  galaxies  are\ngenerally  found to  be redder  and  somewhat more  concentrated than  central\ngalaxies  with similar  stellar masses  (e.g.  van  den Bosch  et  al.  2008a;\nWeinmann et al.  2008; Yang et al.  2008b; c; Guo et al. 2009).\n\nFurthermore, recent investigations  based on cosmological $N$-body simulations\nhave shown  that a significant fraction  of dark matter haloes  that are close\nto, but  beyond the  virial radius  of, a more  massive neighboring  halo, are\nphysically connected  to their neighbor.  As  shown by Lin et  al.  (2003) and\nmore  recently  by  Ludlow  et  al.   (2008), some  low-mass  halos  are  {\\it\nphysically} associated  with more massive halos,  in the sense  that they were\nonce subhalos  within the virial radii  of these more  massive progenitors and\nhave subsequently been ejected.  This  population of halos was found to extend\nbeyond three times the virial radii  of their host halos, and represents about\n$10\\%$ of the entire population of low-mass halos (Wang, Mo \\& Jing 2008).  If\ngalaxies have managed to form in the progenitors of these ejected halos, it is\nlikely that  the same environmental processes operating  on satellite galaxies\nmay also  have affected the properties  of these galaxies.   In particular, we\nwould  expect the  presence of  a red  population of  faint galaxies  that are\nclosely associated with massive halos that once hosted them.\n\nGalaxies are observed to be bimodal in the color-magnitude plane: red galaxies\nwith  very little  star formation  (the red  sequence) and  blue  star forming\ngalaxies that are typically disky (the blue cloud) (e.g. Kauffman et al. 2003,\nBaldry  et  al.  2004)  Extrapolating  the observed  division  line  (Yang  et\nal.  2008a) to  dwarf galaxies  we surprisingly  find that  for  central dwarf\ngalaxies in the SDSS, with $r$-band magnitudes between -14.46 and -17.05, just\nover 1\/4 are red.   In this paper we will investigate the  nature of these red\ndwarf galaxies.   Quantifying the spatial  distribution of this  population of\ngalaxies is  clearly important, because it  allows us to  determine whether or\nnot they  can be  explained as  a population of  satellite galaxies  that were\nejected from larger halos.\n\nIn this  paper, we use the galaxy  group catalogue constructed by  Yang et al.\n(2007)  from  the  Sloan  Digital   Sky  Survey  Data  Release  4  (SDSS  DR4;\nAdelman-McCarthy  {et al.~}  2006) to  study  the  distribution  of central  dwarf\ngalaxies around massive halos.  The structure of this paper is as follows.  In\n\\S\\ref{sec_data} we briefly describe the  criteria used to select galaxies and\ngalaxy  groups.  In \\S\\ref{sec_analyze}  we study  the radial  distribution of\ndwarf  galaxies around  their nearest  neighbor  halos and  its dependence  on\ngalaxy color  and concentration. Some  systematic effects that may  change our\nresults are discussed in \\S\\ref{sec_systematics}.  In \\S\\ref{sec_mock}, we use\nmock catalogues to  test the reliability of our results  and to quantify their\nimplications.   Finally, in  \\S\\ref{sec_discussion}, we  present  some further\ndiscussion regarding our results.\n\n\\section{Observational Data}\n\\label{sec_data}\n\n\\subsection{Samples of Galaxy Groups}\n\nOur analysis uses the galaxy group catalogues of Yang {et al.~} (2007), which were\nconstructed from the New York University Value-Added Galaxy Catalog (NYU-VAGC,\nsee Blanton {et al.~} 2005b) based on  the Sloan Digital Sky Survey Data Release 4\n(SDSS DR4;  Adelman-McCarthy {et al.~}  2006).  Only galaxies  in the  Main Galaxy\nSample with redshifts in the range $0.01 \\leq z \\leq 0.20$ and with a redshift\ncompleteness ${\\cal C}  > 0.7$  were used.  Three  sets of group  catalogues were\nconstructed using a  modified version of an adaptive  halo-based group finder,\nwhich was optimized  to assign galaxies into groups  according to their common\ndark matter halos (Yang {et al.~} 2005).   For our study here, we use group sample\nII, in  which only galaxies  with spectroscopic redshifts (either  provided by\nthe SDSS or taken from alternative  surveys) are used. We have tested, though,\nthat  using group  sample III,  which also  includes galaxies  that  have been\nmissed owing to fiber collisions, does not have a significant impact on any of\nour results.\n\nFor each group in the catalogue, Yang {et al.~} (2007) estimated the corresponding\nhalo mass using either the ranking of its characteristic luminosity (this mass\nis denoted by  $M_L$) or using the  ranking of its stellar mass  (this mass is\ndenoted by  $M_S$).  Throughout this paper,  we use $M_S$ as  our halo masses.\nWe  have also  tested that  using $M_L$  instead does  not change  any  of our\nresults.  As described in Yang {et al.~} (2007), the characteristic luminosity and\nstellar  mass of a  group are  defined to  be the  total luminosity  and total\nstellar  mass of  all group  members, respectively,  with $\\>^{0.1}{\\rm M}_r-5\\log h  \\leq -19.5$.\nThus, groups whose member galaxies are all fainter than $\\>^{0.1}{\\rm M}_r-5\\log h = -19.5$ cannot\nbe assigned halo masses according to  the ranking.  For these groups, the halo\nmasses are estimated in the following  way.  In Yang {et al.~} (2008b) it is shown\nthat the  stellar masses of central  galaxies are tightly  correlated with the\nmasses of their host haloes.  The mean of this relation is well described by\n\\begin{equation}\\label{eq:Ms_fit}\nM_{\\ast} = M_0\n\\frac { (M_h\/M_1)^{\\alpha +\\beta} }{(1+M_h\/M_1)^\\beta } \\,,\n\\end{equation}\nwhere $M_{\\ast}$  and $M_h$ are the  central galaxy stellar mass  and the host\nhalo mass of  the group, respectively, and ($\\log  M_0$, $\\log M_1$, $\\alpha$,\n$\\beta$) = (10.306, 11.040, 0.315, 4.543).  For groups that cannot be assigned\na halo  mass according  to the stellar-mass  (luminosity) ranking, we  use the\nabove relation  to obtain  $M_h$ through the  stellar masses of  their central\ngalaxies.\n\n\n\\subsection{Galaxy Samples}\n\\label{sec:samples}\n\\begin{deluxetable*}{lccccccccc}\n\\tabletypesize{\\scriptsize}\n\\tablecaption{Galaxy Samples \\label{tab1}} \\tablewidth{0pt} \\tablehead{ID &\n  $\\>^{0.1}{\\rm M}_r-5\\log h$ & $N_{\\rm total}$ & $N_{\\rm cent}$ & $N_{\\rm sat}$ &\n  $f_{\\rm red,cent}$ &  $f_{\\rm red,sat}$ & $f^b_{\\rm red,cent}$ & $f^b_{\\rm\n    red,sat}$ &  $f^b(r_{\\rm p}\/R_{180})\\le 3$ \\\\\n  (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10)} \\startdata\nS1       & (-14.46,-16.36] & 1500 & 1103 & 397 & 13.69\\% & 37.53\\% & 33.79\\% &\n         53.42\\% & 34.60\\%\\\\\nS2       & (-16.36,-16.78] & 1500 & 1081 & 419 & 13.69\\% & 36.28\\% & 22.50\\% &\n         47.02\\% & 47.46\\%\\\\\nS3       & (-16.78,-17.05] & 1500 & 1008 & 492 & 10.20\\% & 40.24\\% & 19.51\\% &\n         52.64\\% & 47.72\\%\\\\\nS1+S2+S3 & (-14.46,-17.05] & 4500 & 3192 & 1308 & 12.59\\% & 38.15\\% & 25.49\\% &\n         51.08\\% & 41.63\\% \\\\\n\\cline{1-10}\\\\\nS4 & & 1500 & 1080 & 420 & 13.51\\% & 37.02\\% \\enddata\n\n\n\\tablecomments{Column 1 indicates  the sample ID. Column 2  lists the absolute\n  magnitude range  of each  sample.  Columns  3 to 5,  indicate the  number of\n  total, central and satellite galaxies in each sample, respectively.  Columns\n  6  and  7 list  the  red fractions  among  central  and satellite  galaxies,\n  respectively, where the  red galaxies are defined to be  the reddest 20\\% of\n  all the galaxies. Column 8 lists  the red fraction of central dwarf galaxies\n  where the red galaxies are defined by extrapolating the division between red\n  sequence and blue cloud galaxies from  Yang et al.  (2008a).  Column 9 lists\n  also  this red fraction,  but for  the satellite  dwarf galaxies.  Column 10\n  lists the  fraction of those (in  Column 8) central red  dwarf galaxies that\n  have $r_{\\rm p}\/R_{180}\\le 3$. }\n\\end{deluxetable*}\n\n\nGroup catalogue II consists of 369447 galaxies, which are assigned into 301237\ngroups.  The  majority, 271420, of the  groups contain only  one member, i.e.,\nall  of them  are the  central galaxies  of the  groups.  The  remaining 98027\ngalaxies are in groups  with more than one member, and 29817  of them are {\\it\ncentral} galaxies  (the brightest one in  each group).  We refer  to the other\n68210 galaxies as {\\it satellites} (Yang et al.  2007).\n\nFrom  our galaxy  sample,  we select  three  subsamples of  dwarf galaxies  as\nfollows.  We  rank order all  galaxies according to their  absolute magnitudes\n(in the $r$-band, $K$- and evolution- corrected to redshift $z=0.1$), starting\nwith the  faintest galaxy. The 1500  galaxies with the highest  rank (i.e. the\n1500 faintest galaxies) make up our first sample, called S1, The galaxies with\nranks  1501-3000 make  up sample  S2, and  those with  ranks  3001-4500 sample\nS3. Table~\\ref{tab1}  lists the (sequential) absolute magnitude  ranges of all\nthree samples, as well as the  numbers of central and satellite galaxies. Note\nthat all the galaxies in S1, S2  and S3 are fainter than $\\>^{0.1}{\\rm M}_r-5\\log h = -17.05$.  In\nwhat  follows  we refer  to  all  galaxies in  these  three  samples as  dwarf\ngalaxies.\n\n\\begin{figure} \\plotone{f1.eps}\n  \\caption{The  color-magnitude  distribution  of  dwarf  galaxies  (including\n    central and  satellite galaxies).  In  four panels the dwarf  galaxies are\n    separated  into  20\\%,  30\\%,   40\\%,  50\\%  red  galaxies  as  indicated,\n    respectively.  The vertical dashed lines  in the upper-left panel show the\n    separation criteria of samples S1, S2 and S3.} \\label{fig:col}\n\\end{figure}\n\nTo  study how the  spatial distribution  of dwarf  galaxies depends  on galaxy\ncolor, we  separate each of  the samples,  S1, S2, and  S3, into red  and blue\nsubsamples. In particular, we define a color cut\n\\begin{equation}\\label{colcut}\n^{0.1}(g-r) = a + b~(\\>^{0.1}{\\rm M}_r-5\\log h)\\,,\n\\end{equation}\nand we  adjust the parameters  $a$ and  $b$ such that  samples S1, S2,  and S3\nroughly have the  same fractions of galaxies, $f_{\\rm  red}$, redder than this\nparticular cut. We  consider four values for $f_{\\rm  red}$: 20\\%, 30\\%, 40\\%,\nand  50\\%,  for  which  we  obtain  [a,  b]=[-0.421,-0.060],  [-0.423,-0.055],\n[-0.375,-0.049] and  [-0.313,-0.043], respectively.   Thus, if $f_{\\rm  red} =\n20$\\% it means  that the red subsamples of  S1, S2 and S3 each  consist of the\n20\\%  reddest galaxies  in their  particular samples,  etc.  Fig~\\ref{fig:col}\nshows the color-magnitude  relations of galaxies in S1,  S2 and S3 (delineated\nby vertical dashed  lines).  The four panels correspond  to the four different\nvalues  of $f_{\\rm  red}$, as  indicated,  and the  solid line  in each  panel\ncorresponds to the color cut of Eq.~(\\ref{colcut}) used in each case.\n\n\nIn Table~\\ref{tab1}  we list,  for each sample,  the red fractions  of central\n($f_{\\rm  red,cent}$) and  satellite galaxies  ($f_{\\rm red,sat}$).   Here red\ngalaxies are defined to be the reddest 20\\% of all galaxies (both centrals and\nsatellites) in our sample of dwarf galaxies.  Clearly, dwarf galaxies that are\nsatellites have a  much higher red fraction than  central dwarf galaxies.  For\ncomparison, extrapolating the observed  division line between the red sequence\nand the blue cloud  from Yang et al. (2008a) down to  dwarf galaxies one would\nfind that  33.8\\%, 22.5\\%, and 19.5\\% of  the central galaxies in  the S1, S2,\nand S3  samples, respectively, were red.   While in total, there  are more red\ncentral  dwarfs than  red satellite  dwarfs, which  is so  far  not predicted,\ne.g.  by halo  occupation  models (Brown  et  al. 2008).  Note that  different\ndefinition of  red galaxies may change  these fractions (e.g.  with respect to\nthe galaxies  of similar stellar masses),  however not the  general results we\nfind in this paper.\n\n\n\n\\section {The distribution of central dwarfs}\n\\label{sec_analyze}\n\n\\begin{figure} \\plotone{f2.eps}\n  \\caption{Fractions of the red central  galaxies near more massive halos as a\n    function of  projected distance $r_{\\rm p}\/R_{180}$.   The four panels  show the\n    results  of  the color  subsamples  with 20\\%,  30\\%,  40\\%  and 50\\%  red\n    galaxies, respectively.   The related color  subsample separation criteria\n    are shown in  Fig.  \\ref{fig:col}.  The different lines  correspond to the\n    different  samples  as indicated.   The  fit  long-dashed,  green line  is\n    described in  the text. For comparison,  we show the fraction  of red {\\it\n      satellite} galaxies  that are within  the same luminosity ranges  as the\n    central galaxies  at $r_{\\rm p}\/R_{180}=0$. The  small window within  each panel\n    shows the number counts of dwarf  central (or satellite) galaxies in S1 as\n    a function of $r_{\\rm p}\/R_{180}$: black  histogram for all galaxies and shaded,\n    red histogram for red galaxies. } \\label{fig:f_r}\n\\end{figure}\n\n\nIn this  section, we  investigate how central  dwarf galaxies  are distributed\nwith respect to their nearest more massive halo (i.e.  more massive than their\nown halo).   Since the  distances of galaxies  based on redshifts  suffer from\nredshift distortions, we separate the  distance between a central dwarf galaxy\nand its  nearest more massive  halo into two  components: $\\pi$, which  is the\nseparation along the line-of-sight, and  $r_{\\rm p}$, which is the separation in the\nperpendicular direction.\n\nFor each  group in  the catalogue, we  use the  assigned halo mass,  $M_S$, to\nestimate its halo radius, $R_{180}=[3M_{S}\/(4\\pi*180\\bar{\\rho})]^{1\/3}$, which\nfollows from defining  the mean mass density within a halo  as $180$ times the\naverage density of the universe,  $\\bar{\\rho}$.  We search around each central\ndwarf   galaxy,  within   a  line-of-sight   separation  $|\\pi|   =  15\\>h^{-1}{\\rm {Mpc}}$,\n\\footnote{Tests have shown that  changing the line-of-sight separation for the\nsearch  from $|\\pi|  \\le 15\\>h^{-1}{\\rm {Mpc}}$  to  $|\\pi| \\le  10\\>h^{-1}{\\rm {Mpc}}$ or  to $|\\pi|  \\le\n20\\>h^{-1}{\\rm {Mpc}}$ does not  have a significant impact on any of  our results.}  for the\ngroup  that has  (i) a  halo mass  larger  than that  of the  dwarf galaxy  in\nquestion and (ii)  the lowest value of $r_{\\rm p}\/R_{180}$  (with $R_{180}$ the halo\nradius of  the group).   The central  galaxy is then  said to  be at  a scaled\n`distance' $r_{\\rm p}\/R_{180}$ from  a massive halo, and the halo  is referred to as\nthe nearest halo of the galaxy.  We use this scaled distance because $R_{180}$\nis the  only important length  scale related to  the dynamics of  a virialized\nhalo.\n\n\\subsection{Color Dependence}\n\nFig.~\\ref{fig:f_r} shows  the fraction $N_{\\rm red}\/N_{\\rm  total}$ of central\ndwarf  galaxies  that   are  red  as  a  function   of  the  scaled  distance,\n$r_{\\rm p}\/R_{180}$,  to their  nearest halos.  Here  $N_{\\rm total}$  is the  total\nnumber  of dwarf  galaxies  in each  sample  (S1, S2  or S3)  in  that bin  of\n$r_{\\rm p}\/R_{180}$, and $N_{\\rm red}$ is the  number of those galaxies that are red\naccording to the criterion used. The  numbers are shown in the small window in\neach  panel (the black  histogram for  $N_{\\rm total}$,  and the  red, hatched\nhistogram for  $N_{\\rm red}$).  The four  panels show the  results for $f_{\\rm\nred} =  20$\\%, 30\\%, 40\\% and 50\\%.   In each panel, the  different lines show\nthe results  obtained for the three samples,  S1, S2, and S3,  as indicated in\nthe  upper-left  panel.   The  error-bars  are obtained  using  100  bootstrap\nresamplings  (Barrow, Bhavsar,  \\& Sonoda  1984; Mo,  Jing \\&  B\\\"orner 1992).\nGalaxies are counted in bins  specified by $N-0.5 \\leq r_{\\rm p}\/R_{180} \\leq N+0.5$\n(for  $N=2, 3,... ,7$),  and $0\\leq  r_{\\rm p}\/R_{180} \\leq  N+0.5$ for  $N=1$.  For\ncomparison, the data point at  $r_{\\rm p}\/R_{180} =0$, indicates the fraction of red\n{\\it  satellite} galaxies  within the  same  luminosity range  as the  central\ngalaxies.   Note that  the results  obtained  for S1,  S2, and  S3 are  almost\nidentical, indicating  that the spatial distribution of  dwarf galaxies around\nmassive haloes does not depend on their luminosities.  However, if we consider\nmuch  brighter galaxies,  e.g. at  $\\>^{0.1}{\\rm M}_r-5\\log h \\sim  -18.5$, the  radial dependence\nstarts to level off.\n\nThere  is a  clear  trend that  the  fraction of  red  central dwarf  galaxies\nincreases with decreasing  scaled distance to the nearest  halo.  The fraction\nof the  20\\% reddest population at  $r_{\\rm p}\/R_{180}\\ga 4$ is around  5\\% to 10\\%,\nincreases systematically to  $\\sim 25$\\% at $r_{\\rm p}\/R_{180}\\sim 1$,  and to $\\sim\n40$\\% at  $r_{\\rm p}\/R_{180} = 0$ for  the satellite galaxies.  For  the other three\ncases (with $f_{\\rm  red} =30$\\%, 40\\% and 50\\%),  the fraction also decreases\nwith $r_{\\rm p}\/R_{180}$, but  reaches a higher level at  large $r_{\\rm p}\/R_{180}$.  This\nindicates  that the less  red galaxies  in these  subsamples are  not strongly\nassociated  with massive  halos.  We  quantify  the association  of red  dwarf\ngalaxies with massive halos by fitting  the data obtained from S3 shown in the\nfour  panels  simultaneously with  a  function $f=a+b\\times\\exp(-x\/2)$,  where\n$x=r_{\\rm p}\/R_{180}$.   In the  fit we  subtract a  constant of,  $0.1$,  $0.2$ and\n$0.3$,  from  the  data  for  the  30\\%, 40\\%  and  50\\%  reddest  subsamples,\nrespectively, to account for the component that is not closely associated with\nmassive halos.  The best fit  results, with $a=0.045$ and $b=0.356$, are shown\nin each panel of Fig.  \\ref{fig:f_r} as the green, long-dashed lines.  We have\nalso checked the radial distribution  of the central dwarf galaxies when using\n$f_{\\rm red} = 15$\\%  to define the subsample of red dwarfs.  In this case, we\nfind less  than a  5\\% decrease  in the red  fraction at  large $r_{\\rm p}\/R_{180}$,\nindicating that the  5\\% least red galaxies in the  20\\% reddest subsample are\nnot randomly but more closely  distributed relative to the massive halos. Thus\nthe overall  results suggest that the  $15\\%$ - $20\\%$  reddest dwarf galaxies\nare  quite  distinct from  the  other  dwarfs, in  that  they  reveal a  clear\npreference to reside close to their  nearest more massive dark matter halo. In\naddition,  the non-zero  red fraction  at large  $r_{\\rm p}\/R_{180}$  indicates that\nthere is a  $\\sim 5\\%$ tail of red dwarfs  randomly distributed throughout the\nbackground population,  especially in  the voids, due  to some  processes that\nshut down the star formation. A similar trend has also been found by Cooper et\nal. (2007)  from the DEEP2  survey, however for  more massive galaxies  in low\ndensity regions at  higher redshifts. In \\S\\ref{sec_mock}, we  use mock galaxy\nredshift  surveys  constructed   from  cosmological  $N$-body  simulations  to\nquantify this connection.\n\n\n\\subsection{Concentration Dependence}\n\nApart from a  color dependence, we also check  whether the radial distribution\nof dwarf galaxies with respect to their nearest more massive dark matter halos\ndepends on their surface brightness profiles.  To this end, we split our dwarf\ngalaxies into  two subsamples  according to the  value of  their concentration\nparameter $C=r_{90}\/r_{50}$.   Here $r_{90}$ and  $r_{50}$ are the  radii that\ncontain 90  and 50 percent of  the Petrosian $r$-band  flux, respectively.  As\nshown in Strateva {et al.~} (2001), $C$ is a reasonable proxy for the Hubble type,\nwith $C>2.6$  corresponding to  early-type galaxies.  We,  therefore, separate\ngalaxies  into  high  ($C>2.6$)   and  low  ($C\\le  2.6$)  concentrations,  as\nillustrated in  the lower-right panel of  Fig.~\\ref{fig:concen}.  Roughly 20\\%\nof the dwarf galaxies thus end up in the high-concentration subsample.\n\nThe lower-right  panel of Fig.~\\ref{fig:f_con} shows the  fraction of galaxies\nin this high-concentration  subsample as a function of  the scaled distance to\nthe  nearest  more  massive  halo.   Unlike the  reddest  galaxies,  the  most\nconcentrated galaxies  have a radial distribution  that is similar  to that of\nthe total  population of central  dwarf galaxies.  Note however,  for brighter\ngalaxies,  especially   in  and  around   clusters,  there  is  a   so  called\nmorphology-radius relation  (e.g., Dressler et  al. 1997), which  according to\nPark \\& Hwang  (2008) may be largely induced by the  interaction of the target\ngalaxy with its nearest (early-type) neighbor galaxy.\n\n\n\\section{Systematics}\n\\label{sec_systematics}\n\nBefore we proceed to study the origin of the central red dwarf galaxies, there\nare a number of issues that need to be addressed. An obvious worry is that the\ngroup  finder is  not perfect,  and has  misclassified a  number  of satellite\ngalaxies as central galaxies.  We will  discuss this issue in more detail with\nthe  help of  mock galaxy  and group  catalogs in  \\S\\ref{sec_mock}.   In this\nsection we discuss systematics that can be addressed without the need for mock\ncatalogs.\n\n\n\\subsection{Stellar Mass Dependence}\n\\begin{figure} \\plotone{f3.eps}\n  \\caption{Upper-left panel:  the color-stellar mass distribution  of the 20\\%\n    red (`x'-crosses) and  80\\% blue (`+'-crosses) dwarf galaxies  in terms of\n    {\\it similar  stellar masses}.  Upper-right panel: the  same set  of dwarf\n    galaxies  as  in  the  upper-left  panel, but  separated  into  20\\%  blue\n    (`x'-crosses) and 80\\% red  (`+'-crosses).  Lower-left panel: the same set\n    of dwarf  galaxies as in the  upper-left panel, but  randomly selected and\n    separated  into  20\\% (`x'-crosses)  and  80\\% (`+'-crosses)  populations.\n    Lower-right panel:  the concentration-magnitude distribution  of the dwarf\n    galaxies, which  are separated into $\\sim  20\\%$ high and  $\\sim 80\\%$ low\n    concentration populations by $C=2.6$. } \\label{fig:concen}\n\\end{figure}\n\n\\begin{figure} \\plotone{f4.eps}\n  \\caption{Similar  to   Fig.   \\ref{fig:f_r},  but   with  related  subsample\n    separation  criteria shown in  Fig.  \\ref{fig:concen}.   Upper-left panel:\n    fraction of the red central galaxies near more massive halos as a function\n    of $r_{\\rm p}\/R_{180}$, where the 20\\% red population is defined with respect to\n    the  similar stellar  mass galaxies.   Upper-right panel:  similar  to the\n    upper-left  panel but  for the  20\\% blue  population.   Lower-left panel:\n    similar  to the  upper-left  panel  but for  the  20\\% random  population.\n    Lower-right  panel: fraction  of  the high  concentration $C>2.6$  central\n    galaxies    near    more    massive     halos    as    a    function    of\n    $r_{\\rm p}\/R_{180}$. } \\label{fig:f_con}\n\\end{figure}\n\nFor a given luminosity, redder galaxies  are expected to have a larger stellar\nmass.  The color separation used above  may thus introduce a bias in the sense\nthat galaxies  in the  redder subsample are  systematically more  massive.  To\ncheck  whether or  not  the color  distribution  we obtained  in the  previous\nsection is  robust when the dwarf  galaxies are selected in  a similar stellar\nmass bin,  we construct  a controlled subsample  S4, where stellar  masses for\ngalaxies are  estimated using the  relation between the  stellar mass-to-light\nratio  and color  obtained by  Bell et  al.(2003). Note  that the  survey {\\it\nmagnitude limit} of the SDSS  observation corresponds to a higher (lower) {\\it\nstellar  mass limit} for  the redder  (bluer) galaxies.   In general,  one can\nconstruct a  stellar mass limit  sample (and hence  the subsample S4)  for all\n(including both red and blue) galaxies  by adopting the stellar mass limit (as\na function  of redshift)  for the  reddest galaxies (see  Appendix of  van den\nBosch et  al. 2008b), which, however,  may significantly reduce  the number of\ndwarf galaxies in our sample.  Instead, as a rough approximation, we construct\nsubsample S4 as  follows (with the hidden assumption that  if the galaxies are\ncomplete  in  both  luminosity  and  stellar  mass  they  have  similar  color\ndistributions and thus similar red and blue fractions). First, we separate all\nthe dwarf galaxies  into red and blue populations: the  reddest 20\\% being red\nand the  rest being blue,  using the separation  line shown in  the upper-left\npanel of  Fig ~\\ref{fig:col}. Next,  for each of  the (1500$\\times$20\\%$=300$)\nred  galaxies in  S1, we  randomly  select four  blue galaxies  from the  blue\npopulation with stellar masses within  $\\Delta \\log M_{\\ast}=0.025$ of the red\ngalaxy.  This yields a  blue control sample of (1500$\\times$80\\%$=1200$) dwarf\ngalaxies, which  has the  same stellar mass  distribution as the  20\\% reddest\ngalaxies. The  control subsample  S4 so constructed  has exactly the  same red\nfraction of dwarf  galaxies as S1, but now with respect  to blue galaxies with\nsimilar stellar  masses.  The upper-left panel  of Fig.~\\ref{fig:concen} shows\nthe color-stellar mass relation for S4, split into red and blue galaxies.\n\n\nFor comparison, we also form the following two subsamples from S4.  In one, we\nrandomly select 20\\% of the galaxies from S4; in the other, we select the 20\\%\nbluest  galaxies that  have  the same  stellar  mass distribution  as all  the\ngalaxies  in  sample  S4.   The  color-stellar mass  relations  of  these  two\nsubsamples  are  shown  in  the  lower-left and  upper-right  panels  of  Fig.\n\\ref{fig:concen}, respectively.\n\nThe upper-left panel of Fig. \\ref{fig:f_con} shows $N_{\\rm red}\/N_{\\rm total}$\nas a  function of  $r_{\\rm p}\/R_{180}$ obtained using  sample S4.  Fitting  the data\nagain with  the function  $f=a+ b \\times\\exp(-x\/2)$,  we obtain  $a=0.053$ and\n$b=0.309$,  and the  corresponding model  is shown  as the  long-dashed curve.\nThis  dependence  on  the  scaled  distance, $x\\equiv  r_{\\rm p}\/R_{180}$,  is  only\nslightly  weaker  than  that  for  the  corresponding  luminosity  sample  S1,\nindicating that the bias caused by the stellar-mass difference between the red\nand blue subsamples is not important.\n\nThe  upper-right  and lower-left  panels  of  Fig.   \\ref{fig:f_con} show  the\nresults obtained for the 20\\% bluest galaxies and for the 20\\% random galaxies\n(as  defined above).   For  these two  cases  there is  no significant  radial\ndependence.  Although  one expects  such a lack  of radial dependence  for the\nrandom subsample,  it does indicate  that there are no  significant systematic\nerrors in our  analysis.  The lack of a radial dependence  for the 20\\% bluest\nsubsample is  due to the  fact that only  the $\\sim 15-20\\%$  reddest galaxies\nreveal a radial distribution that is peaked towards smaller $r_{\\rm p}\/R_{180}$.\n\n\n\\subsection{Dependence on the Mass of the Nearest Neighbor}\n\n\\begin{figure} \\plotone{f5.eps}\n  \\caption{The nearest neighbor to host  halo mass ratio $M_n\/M_h$ - projected\n    distance  $r_{\\rm p}\/R_{180}$  distribution of  the  dwarf  central galaxies  in\n    samples S1+S2+S3. The triangles and  crosses show the red and blue central\n    galaxies, respectively, where the red population is defined to be the 20\\%\n    reddest all galaxies.  }  \\label{fig:mass_rp}\n\\end{figure}\n\\begin{figure} \\plotone{f6.eps}\n  \\caption{Similar  to Fig.  \\ref{fig:f_r}, but  for all  galaxies  in samples\n    S1+S2+S3 within different central-nearest halo systems.  In each panel the\n    selection criteria,  $M_n\/M_h$, is indicated.  Here the  results are shown\n    for  the fraction  of the  20\\% red  population. For  comparison,  in each\n    panel, we  also show as  the symbols with  solid line the results  for all\n    central-nearest halo systems.  } \\label{fig:M_n}\n\\end{figure}\n\nIn our  analysis above, the ``nearest  more massive halo'' of  a central dwarf\ngalaxy  is defined  as the  halo with  a line-of-sight  separation  $|\\pi| \\le\n15\\>h^{-1}{\\rm {Mpc}}$ which  has (i) a  mass that  is more massive  than that of  the dwarf\ngalaxy,    and   (ii)    the    smallest   value    of   $r_{\\rm p}\/R_{180}$    (see\nsection~\\ref{sec_analyze}).   This implies  that  some of  these nearest  more\nmassive halos may  have masses that are only slightly larger  than that of the\ndwarf galaxy under consideration.\n\nIn what follows  we use $M_h$ to refer  to the halo mass of  the central dwarf\ngalaxy, and $M_n$ to refer to the  mass of its nearest more massive halo.  For\nour  combined sample  (S1 +  S2 +  S3)  the average  value of  $M_h$ is  about\n$10^{10.9}\\>h^{-1}\\rm M_\\odot$.   Fig.~\\ref{fig:mass_rp}  shows the  ratio  $M_n\/M_h$ as  a\nfunction of the  scaled distance $r_{\\rm p}\/R_{180}$ for all  central dwarf galaxies\nin S1+S2+S3.  Here the results for  the 20\\% reddest galaxies are shown as red\ntriangles, while the other 80\\% are indicated by blue crosses. Note that there\nis a very large amount of scatter  in $M_n\/M_h$, ranging from unity to well in\nexcess of 1000.\n\nIt is  interesting to investigate whether  the color dependence  of the radial\ndistribution of central dwarfs with respect to their nearest more massive halo\ndepends on $M_n$. This can provide  valuable insight into the actual origin of\nthis color  dependence.  We  therefore proceed as  follows.  We  first combine\nsamples  S1+S2+S3,  and then  calculate  the  fraction  of central  red  dwarf\ngalaxies  that   belong  to   the  20\\%  reddest   subsample  as  we   did  in\n\\S\\ref{sec_analyze}. However,  now we only select systems  for which $M_n\/M_h$\nis  restricted  to  [1,2],  [2,4],  [4,8] or  $\\log  [M_n\/  \\>h^{-1}\\rm M_\\odot]\\ge  12.0$,\nrespectively.  The results are shown  in the four panels of Fig.~\\ref{fig:M_n}\nas indicated. For comparison we also show, in each panel, the results obtained\nfor all systems (i.e.  $M_n\/M_h >  1$).  A comparison of all four panels shows\nthat  there is  a clear,  albeit  somewhat weak,  dependence of  the trend  on\n$M_n\/M_h$.  Overall,  the colors of  central dwarf galaxies are  most strongly\naffected by nearest neighbor halos that are  more massive. In the case of $1 <\nM_n\/M_h \\leq 2$ (upper-left panel),  the central dwarf galaxies have a $N_{\\rm\nred}\/N_{\\rm  total}$ that  is almost  independent of  $r_{\\rm p}\/R_{180}$,  and much\nlower  than that  of the  dwarf satellites.   On the  other hand,  the central\ndwarfs that are distributed around  halos more massive than $10^{12.0} \\>h^{-1}\\rm M_\\odot$\n(lower-right panel), have  a radial dependence that is  somewhat stronger than\nthat for all systems.\n\n\\subsection{Survey Edge Effect}\n\\begin{figure} \\plotone{f7.eps}\n  \\caption{Similar to Fig. \\ref{fig:f_r}, but  here we compare the results for\n    all  galaxies  in samples  S1+S2+S3,  with  and  without edge  effects  by\n    removing   the  central   dwarf  galaxies   that  are   near   the  survey\n    edge. } \\label{fig:edge}\n\\end{figure}\n\nSince the  SDSS is  not a full-sky  survey, and  since our group  catalogue is\nconstructed using  only galaxies  with redshifts $0.01  \\leq z \\leq  0.2$, our\nresults may  be influenced by  edge effects of  the survey: for  central dwarf\ngalaxies near an edge of the  survey, there is an enhanced probability that it\nis actually  a satellite (or central)  galaxy in a more  massive group (halo),\nbut for  which all other members  just happen to  lie beyond the edges  of the\nsurvey. Although  we tried to take  these effects into  account when assigning\nhalo masses to our  groups (see Yang et al. 2007 for  details), it could still\nbe that  a significant fraction of  our central dwarf galaxies  are in reality\nmisclassified centrals or satellites owes to the survey geometry.\n\nTo check the  impact of these edge  effects, we follow Yang et  al.  (2007) by\nmeasuring the edge parameter $f_{\\rm edge}$.  For each central dwarf galaxy in\nS1+S2+S3, we randomly  distribute $500$ points within a  radius $1\\>h^{-1}{\\rm {Mpc}}$. Next\nwe apply  the SDSS DR4  survey mask and  remove those random points  that fall\noutside of the region where the  completeness ${\\cal C} > 0.7$.  For each central\ndwarf galaxy we then compute the number of remaining points, $N_{\\rm remain}$,\nand we  define $f_{\\rm edge}=N_{\\rm remain}\/500$  as a measure  for the volume\naround the  central dwarf galaxy that  lies within the survey  edges.  To test\nthe  impact of  edge effects  on our  measurements in  \\S\\ref{sec_analyze}, we\nremove those  central dwarf galaxies  with $f_{\\rm edge}\\le 0.8$  (about 13\\%)\nand recalculate the radial distribution of the remaining central galaxies. The\nresult is shown in Fig.  \\ref{fig:edge} (dashed line), compared to the results\nfor  all the  central dwarfs,  independent of  their value  of  $f_{\\rm edge}$\n(solid  line).    Clearly,  the  two  curves   are  almost  indistinguishable,\nindicating that our results are not an artifact of survey edge effects.\n\n\\section{Test with mock samples}\n\\label{sec_mock}\n\n\\begin{figure} \\plotone{f8.eps}\n  \\caption{Similar to Fig \\ref{fig:f_r}, but here we compare the observational\n    and mock results.  The  upper-left, upper-right and lower-left panels show\n    the  results  for all  host-nearest  halo  systems  using different  color\n    models: Case  I, II and III  as indicated (see text).   In the lower-right\n    panel, we show results for those central-nearest halo systems with $M_n\\ge\n    10^{12.0}\\>h^{-1}\\rm M_\\odot$ using color model Case III but with different parameters.\n    In  each  panel, the  symbols  connected  with  dashed lines  are  results\n    obtained from  the mock  galaxy and group  catalogues where the  halos are\n    assumed to be  spherical. The symbols connected with  dot-dashed lines are\n    results obtained from the mock galaxy and group catalogues where the halos\n    are  assumed  to  follow a  triaxial  Jing  \\&  Suto (2002)  profile.  For\n    reference, in  each panel we also  show, as the dots  connected with solid\n    lines, the  results we obtained for  the SDSS samples  S1+S2+S3.  See text\n    for details.  } \\label{fig:mock}\n\\end{figure}\n\nOne  potential problem  with the  results presented  above is  that  the group\nfinder used  to identify  galaxy groups  is not perfect.   Hence, some  of the\ndwarf  galaxies  classified as  central  galaxies  may  in fact  be  satellite\ngalaxies.   To test  the severity  of such  effects and  to quantify  the true\nassociation between central dwarf galaxies  and their nearby massive halos, we\napply  the same  analysis to  mock samples  and compare  the results  with the\nobservational  data that  we have  obtained.  Here  we use  the mock  SDSS DR4\ngalaxy and  group catalogues that  are constructed by  Yang et al.   (2007) to\ntest the performance of the group  finder.  Following Yang et al.  (2004), the\nmock  galaxy catalogue  is constructed  by  populating dark  matter haloes  in\nnumerical  simulations of  the standard  $\\Lambda$CDM model  with  galaxies of\ndifferent luminosities, using the  conditional luminosity function (CLF) model\nof  Cacciato et  al.  (2008).  The cosmological  parameters  adopted here  are\nconsistent with the  three-year data release of the  WMAP mission: $\\Omega_m =\n0.238$,  $\\Omega_{\\Lambda}=0.762$, $n_s=0.951$,  $h=0.73$  and $\\sigma_8=0.75$\n(Spergel et al.  2007).  This CLF describes the  halo occupation statistics of\nSDSS galaxies, and accurately matches the SDSS luminosity function, as well as\nthe clustering and  galaxy-galaxy lensing data of SDSS  galaxies as a function\nof their luminosity.  Next a mock redshift survey is constructed mimicking the\nsky  coverage of  the SDSS  DR4  and taking  detailed account  of the  angular\nvariations in the magnitude limits and  completeness of the data (see Li {et al.~}\n2007  for details).  Finally  we construct  a group  catalogue from  this mock\nredshift survey, using  the same halo-based group finder as  for the real SDSS\nDR4.\n\nTo  test the  impact of  contamination on  our observational  results obtained\nabove, we consider three models for the distribution of red dwarf galaxies:\n\\begin{itemize}\n\\item Case I: Here we assume that a fraction, $f_{\\rm red, sat}$, of true {\\it\n    satellite}  dwarf  galaxies are  red,  but  that  all true  central  dwarf\n  galaxies are blue.\n\\item Case  II: Same as Case  I, but here  we assume that a  fraction, $f_{\\rm\n    red, cent}$, of true central dwarf galaxies are also red and have the same\n  spatial distribution as blue central dwarfs.\n\\item  Case III: Similar  to Case  II, but  here we  assume that  $f_{\\rm red,\n    cent}$ depends on  the distance of the central galaxy  to its nearest more\n  massive halo, according  to $f_{\\rm red, cent}(r)= a+b\\times\\exp(-(y-1)\/2)$.\n  Here $a$ and $b$ are constants and $y=r\/R_{180}$.\n\\end{itemize}\nThese models  are used to assign  a color to  each of the mock  dwarf galaxies\naccording to their  positions in real space and their  true membership of host\nhalos.\n\nAs for the  observational data, we select the 4500  faintest galaxies from the\nmock   group   catalogue,   using   the   same  criteria   as   described   in\nSubsection~\\ref{sec:samples}.   We  choose the  observational  result for  the\ncentral  galaxies  in  S1+S2+S3  (shown   as  the  dots  with  error  bars  in\nFig.~\\ref{fig:M_n} to compare  with our models.  As discussed  in the previous\nsection,  this result  is  representative  of the  distribution  of red  dwarf\ngalaxies with respect to their nearest  more massive halos.  For all Cases (I,\nII and III), we adopt $f_{\\rm red,  sat}=0.38$ so that the red fraction of the\nsatellite  galaxies  is  consistent  with  the SDSS  data  (repeated  in  Fig.\n\\ref{fig:mock} as a solid line).  In  Case II we set $f_{\\rm red, cent}=0.07$,\nso that the red fraction of  the central galaxies at large projected distance,\n$r_{\\rm p}\/R_{180}\\ge  4$, is  roughly  the  same as  the  observational data.   The\ncorresponding  results obtained  from Case  I  and Case  II are  shown in  the\nupper-left and  upper-right panels of Fig.   \\ref{fig:mock}, respectively.  It\nis clear  that in Case  I, in  which the only  red dwarfs are  satellites, the\nfraction of  false central  galaxies in  the mock catalogue  is too  small too\nmatch the observational data at  $r_{\\rm p}\/R_{180}\\ga 1$.  For Case II, although by\nconstruction the  fraction of red  central galaxies matches  the observational\nresults at large $r_{\\rm p}\/R_{180}\\ge 4$,  the model underestimates the fraction of\nred central  galaxies at  intermediate $r_{\\rm p}\/R_{180}$.  These  results indicate\nthat (i) not  all red dwarf galaxies are satellites, and  (ii) the central red\ndwarf  galaxies have  a different  distribution than  the total  central dwarf\npopulation.\n\nNow, let us  look at Case III. We have experimented  with different values for\n$a$  and $b$,  and found  that  the following  set of  parameters matches  the\nobservational  data  reasonably   well:  $(a,b)=(0.05,  0.36)$.   The  results\nobtained from the mock catalogue using  this set of model parameters are shown\nin the lower-left  panel of Fig. \\ref{fig:mock}.  This  shows that the central\nred dwarf galaxies are correlated with massive halos on scales given by $(y-1)\n\\la 2$ (i.e.  $r\\la 3 R_{180}$).\n\nFinally, as  we did for the  observational sample, we can  also obtain $f_{\\rm\nred, cent}(r)$  for dwarf  galaxies near halos  of different masses  using the\nmock sample  Case III. As an  illustration, we consider the  case with $M_n\\ge\n10^{12.0}\\>h^{-1}\\rm M_\\odot$. The model  for $f_{\\rm red, cent}(r)$ that  best matches the\nobservational  result has $(a,b)=(0.05,  0.45)$ and  is slightly  steeper than\nthat  obtained for  the  case without  any  restrictions on  $M_n$. The  model\nprediction obtained from the mock sample  is shown in the lower-right panel of\nFig. \\ref{fig:mock} along with the corresponding observational data.\n\nIn the mock catalogue considered above, the distribution of satellite galaxies\nin individual halos  is assumed to be spherically symmetric  and to follow the\nNFW  (Navarro,  Frenk \\&  White  1997)  profile (see  Yang  et  al.  2004  for\ndetails).  In  reality, the distribution  of satellite galaxies  in individual\nhalos  may not be  spherical, which  may cause  further contaminations  of the\ngroup  memberships  selected by  the  group finder.   To  test  this, we  have\nconstructed  a mock  catalogue  assuming that  the  distribution of  satellite\ngalaxies in individual halos is triaxial,  with axis ratios given by the model\nof Jing  \\& Suto (2002) for  CDM halos.  We  found a slightly higher  level of\ncontamination in  this new mock catalogue, but  it does not change  any of our\nresults   significantly.     As   an   illustration,   in    each   panel   of\nFig. \\ref{fig:mock}  we also  show the results  for non-spherical  halos using\nsymbols  connected with  dot-dashed lines.   We obtain  for Case  III slightly\nweaker radial dependence with $(a,b)=(0.05,0.34)$ and $(a,b)=(0.05,0.43)$, for\nthe cases shown in the lower-left and lower-right panels, respectively.\n\n\\section{Discussion}\n\\label{sec_discussion}\n\n\nWe set out to understand why  about 1\/4 of {\\it central} dwarf galaxies, those\nwith $r$-band magnitudes between -14.46 and -17.05, are red when one defines a\ndwarf  galaxy to be  red by  extrapolating the  division between  red sequence\ngalaxies and the blue cloud, as determined by Yang et al. (2008a) for brighter\ngalaxies, down to  dwarf magnitudes. Current models of  galaxy formation would\nnaively  expect such  galaxies  to be  blue  since they  would be  efficiently\naccreting  gas through  cold mode  accretion  and rapidly  converting it  into\nstars.\n\nIn a recent study,  Ludlow et al.  (2008; see also Lin  et al.  2003) analysed\nthe  properties of subhalos  in galaxy-sized  cold dark  matter halos  using a\nsuite  of cosmological N-body  simulations. The  subhalos in  their definition\nrefer to the whole population  of subhalos physically associated with the main\nsystem, including both subhalos that are found within the virial radius of the\nhost halo  at the  present time, and  halos that  were once within  the virial\nradius of  the main  progenitor of  the host and  have survived  as self-bound\nentities until $z=0$.  They found that such populations can extend beyond {\\it\nthree times}  the virial radius, and  contain objects on  extreme orbits, with\nsome  approaching the nominal  escape speed  from the  system. On  average the\nsubhalos identified  within the  virial radius represent  only about  {\\it one\nhalf} of all  associated subhalos, and many relatively  central halos may have\nactually been ejected  in the past from a more  massive system. Since galaxies\nare assumed  to form in  dark matter  halos, it is  interesting to see  if the\nresults we obtain here can be  understood in terms of galaxy formation in this\npopulation of subhalos.\n\nAccording to  the current theory  of galaxy formation, satellite  galaxies can\nexperience various environmental effects  that can quench their star formation\nand make them  red (e.g., van den Bosch et al.  2008b and references therein).\nBecause the galaxies in ejected subhalos have also been satellite galaxies, at\nleast  for some period  of time,  they are  likely to  have been  subjected to\nsimilar environmental effects, and thus  to have experienced some quenching of\ntheir star  formation rates.  It is  thus likely that  the association  of red\ndwarf  galaxies  with  massive  halos   presented  here  is  produced  by  the\nassociation of ejected subhalos with their (former) hosts.\n\nAs shown in  Table~\\ref{tab1}, about 30\\% of the  dwarf galaxies are satellite\ngalaxies. According  to the results obtained  by Ludlow et  al.  (2008), there\nshould  thus  also  be a  significant  fraction  of  dwarf galaxies  that  are\nphysically associated with nearby more  massive halos out to about three times\nthe virial  radius.  If  these associated galaxies  (now outside  their hosts)\nhave properties similar to the satellite galaxies, we would expect an enhanced\nfraction of  red dwarf  galaxies that are  distributed outside  massive halos.\nThis is qualitatively consistent with our findings presented above and also as\nshown in Table~\\ref{tab1}.  However, since the observational data are obtained\nin redshift space and based on  galaxy groups that may contain interlopers and\nmay  be incomplete,  a detailed  comparison between  the data  and  the models\nrequires  the construction of  mock catalogues  that make  use of  the subhalo\npopulation and contain all the observational selection effects.\n\nThe fact that central dwarf  galaxies have concentrations that are independent\nof their distances  to the nearest massive halos  indicates that the processes\nthat causes  them to become  red does not  have a significant impact  on their\nstructure.  This  is similar to the results  obtained by van den  Bosch et al.\n(2008a) who  found that the transformation mechanisms  operating on satellites\naffect color more  than structure (see also Kauffmann et  al. 2004; Blanton et\nal. 2005a; Ball, Loveday \\& Brunner 2008; Weinmann et al.  2008).  Once again,\nthis  similarity between red  dwarfs that  are satellites  and those  that are\ncentrals suggests that both populations  may have experienced similar kinds of\nenvironmental effects.\n\nHowever, as shown  in Table~\\ref{tab1}, in the S1+S2+S3  sample less than 42\\%\nof the  red dwarf central galaxies  have $r_{\\rm p}\/R_{180}\\le 3$.   In other words,\nmore than  58\\% of the red  dwarf central galaxies  are not close enough  to a\nlarger halo so that they could  have been preprocessed there, becoming red and\nthen subsequently being ejected.  The origin of this population of central red\ndwarf galaxies,  which is almost 10\\%  of the combined  S1+S2+S3 dwarf sample,\nstill  remains a  mystery within  the standard  paradigm of  galaxy formation.\nFurthermore,  if we had  used stellar  mass instead  of $r$-band  magnitude to\ndefine our dwarf  sample, the percentage of galaxies  in this population would\nlikely increase.  This population of isolated red dwarfs are not merely a dust\nreddened star forming  population seen near edge-on because  their axis ratios\nare  consistent with  a randomly  oriented population.  Although as  Croton \\&\nFarrar  (2008)  probed  the origin  of  the  red  dwarfs  in voids  using  the\nsemi-analytical  models, they only  found $\\sim  0.4\\%$ of  the dwarfs  in the\ntotal population  are red  centrals in  voids. While here  we find  that $\\sim\n10\\%$ dwarfs  are red centrals  without close neighbours  with $r_{\\rm p}\/R_{180}\\le\n3$.\n\nAn outstanding problem  for all galaxy formation models  concerns the low mass\nslope of  the galaxy mass  function.  CDM models  in general predict  too many\nlow-mass dark matter haloes compared to  the number of low mass galaxies.  The\nmass function of dark matter haloes,  $n(M)$, scales with halo mass roughly as\n$n(M)\\propto M^{-2}$ at the low-mass end.  This is in strong contrast with the\nobserved  luminosity function  of galaxies,  $\\Phi  (L)$, which  has a  rather\nshallow shape  at the faint end,  with $\\Phi(L) \\propto  L^{-1}$. To reconcile\nthis difference  one usually  invokes some form  of feedback within  these low\nmass halos.  If the feedback mechanism were to prevent gas from entering these\nhalos  at  late times,  such  galaxies would  appear  red.   For example,  the\npreheating mechanism of Mo et al. (2005), where gas is preheated by gas shocks\nwithin the  forming large scale structures  in which the low  mass dark matter\nhalos themselves are forming, has this feature.  Therefore, this population of\nisolated, red, central dwarf galaxies  could represent the tail of the process\nthat prevents  the vast majority  of low mass  dark matter halos  from forming\ngalaxies  and  their further  study  could shed  new  light  on the  mechanism\nresponsible.\n\n\n\\acknowledgements We thank the referee Darren Croton for helpful comments that\nimproved the presentation of this  paper. YW acknowledges the support of China\nPostdoctoral  Science Foundation.  This  work  is supported  by  the {\\it  One\nHundred  Talents}  project,  Shanghai  Pujiang Program  (No.  07pj14102),  973\nProgram (No.   2007CB815402), the CAS Knowledge Innovation  Program (Grant No.\nKJCX2-YW-T05) and  grants from NSFC (Nos.  10533030,  10673023, 10821302). HJM\nwould like to acknowledge the support of NSF AST-0607535, NASA AISR-126270 and\nNSF IIS-0611948.  NSK and D.H.M. would like to acknowledge the support of NASA\nLTSA NAG5-13102.\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section*{Figures}\n\n\\begin{figure}[H]\n \\includegraphics[width=1.\\linewidth]{overlay}\n    \\caption{\n    Panels \\textbf{(a) and (b)} are all-sky views\n    in Mollweide projection in\n    Galactic coordinates of longitude $\\ell$ and latitude $b$ with east to the left, with the ROI marked by the dotted box.\n    Panels \\textbf{(c)--(e)} are in a cylindrical projection and zoom in on the ROI.\n    %\n    \\textbf{{\\bf The Fermi Bubbles, including the Cocoon sub-structure, and the Sgr dSph galaxy}.\n    Panels (a) and (c)} display \n    the $\\gamma$-ray spatial template for the Fermi Bubbles\\cite{Ackermann2014} in arbitrary units with linear colour scale, highlighting the cocoon.\n    \\textbf{Panels (b) and (d)}\n    show the angular density of RR Lyrae stars with line-of-sight distances $>20$ kpc from the {\\it Gaia} Data Release 2 (DR2), in arbitrary units with logarithmic scaling; the Sgr dSph, Sgr stream, and the Large and Small Magellanic Clouds are clearly visible. The proper motion of the {Sgr~dSph~} is upwards in this figure. The dashed ellipses in panels (a)-(d) mark the same coordinates in each panel, and highlight both the cocoon and the Sgr dSph.\n    \\textbf{Panel (e)} shows contours of RR Lyrae surface density overlaid on the Fermi Bubbles template shown as the coloured background.\n    }\n    \\label{fig:SgrdSphOverlay}\n\\end{figure}\n\n\n\n\n\n\\begin{figure}[H]\n    \\centering\n        \\includegraphics[width=\\linewidth]{plotSgrSpectrumDataPlusFit}\n\\caption{ \n{\\bf Measured $\\gamma$-ray spectral brightness distributions of the {Sgr~dSph~} and the surrounding Fermi Bubbles}. \nThe black, dashed line \nshows a differential number flux obeying\n$dN_\\gamma\/dE_\\gamma \\propto E_\\gamma^{-2.1}$.\nThese data \nare as obtained by us in our {{\\em Fermi}-LAT} \\ data analysis as described in Methods. \nWe have converted luminosities to surface brightnesses \nadopting source solid angles of $\\Omega_{\\rm Sgr \\ dSph} = 9.6 \\times 10^{-3}$ sr, \nand $\\Omega_{\\rm FB} = 0.49$ sr, with the latter set by the $40^\\circ \\times 40^\\circ$ region of interest (ROI), not the intrinsic sizes of the Bubbles (which are larger than the ROI).\nError bars show $1\\sigma$ errors; for the Sgr dSph, the error bars incorporate both statistical and systematic errors added in quadrature.\nThe smooth blue curves show (solid) the best fit combined (magnetospheric + IC) and (dashed) the best fit magnetospheric spectra.\n}\n\\label{fig:luminosities}\n\\end{figure}\n\n\\begin{figure}[H]\n    \\centering\n\\includegraphics[width=\\linewidth]{plotLgammaOvrMstar.pdf}\n\\caption{{\\bf {$\\gamma$-ray} \\ luminosity\nnormalised to stellar mass for various structures whose emission is plausibly dominated by MSPs.}\nThe `Sgr magneto.' datum shows our\nbest-fit magnetospheric luminosity per stellar mass\n(the spectrum shown as the dashed blue curve in \\autoref{fig:luminosities})\nwhile the `Sgr tot' datum is the total, directly-measured luminosity. Globular cluster (`GC') measurements are from ref.~\\cite{Song2021}, while the remaining data (collated by ref.~\\cite{Song2021}) are from ref.~\\cite{Macias2019} (nuclear bulge of the Milky Way, `NB'), ref.~\\cite{Ackermann2017} (M31), and ref.~\\cite{Bartels2018} (Milky Way disc). \nError bars show 1$\\sigma$ errors.\nThe horizontal, dashed, grey curves show\nthe predicted total \n{$\\gamma$-ray} \\ luminosity per unit stellar mass\nat the nominated efficiencies, $f_{\\rm \\gamma,tot} = \\{0.1, 0.9\\}$, \ngiven an MSP spin-down power per unit stellar mass of\n$2 \\times 10^{28}$   erg\/s\/$M_{\\odot}$ as\nwe infer from ref.~\\cite{Sudoh2020}.}\n\\label{fig:LgammaOvrMstar}\n\\end{figure}\n\n\n\\begin{table}\n    \\centering\n    \\small\n    \\begin{tabular}{llll@{\\qquad\\qquad}rrrr}\n    \\hline\\hline\n    \\multicolumn{4}{c}{Template choices} & \\multicolumn{4}{c}{Results} \\\\\n    Hadr. \/ Bremss. & IC & FB & Sgr dSph &\n    $-\\log(\\mathcal{L}_{\\rm Base})$  & $-\\log(\\mathcal{L}_{{\\rm Base}+{\\rm  Sgr}})$  &  $\\mbox{TS}_{\\rm Source}$& Significance \\\\[0.5ex] \\hline \n    \\multicolumn{8}{c}{Default model} \\\\[0.5ex]\n    HD & 3D & S & Model I & 866680.6 &866633.0  & 95.2  &  $8.1\\;\\sigma$ \\\\[0.5ex] \\hline\n    \\multicolumn{8}{c}{Alternative background templates} \\\\[0.5ex]\n    HD & 2D A & S & Model I   &  866847.1    & 866810.9  & 72.3  &  $6.9\\;\\sigma$ \\\\\n    HD & 2D B & S & Model I &  867234.9  &867192.1  & 85.8 &  $7.8\\;\\sigma$ \\\\\n    HD & 2D C & S & Model I &  866909.4  & 866868.5  & 81.7  & $7.4\\;\\sigma$ \\\\\n    Interpolated & 3D & S & Model I   & 867595.4     & 867567.4  & 56.0 & $5.8\\;\\sigma$ \\\\\n    GALPROP & 3D & S & Model I & 866690.5   &  866640.8 & 99.5  & $8.3\\;\\sigma$ \\\\[0.5ex] \\hline\n    \\multicolumn{8}{c}{Flat FB template} \\\\[0.5ex]\n    HD & 3D & U & Model I & 867271.7 & 867060.1 & 423.2 &  $19.1\\;\\sigma$ \\\\\n    HD & 2D A & U & Model I & 867284.2 &867122.9 & 322.5 &  $16.5\\;\\sigma$ \\\\\n    HD & 2D B & U & Model I & 867624.3 & 867464.0& 320.7 & $16.4\\;\\sigma$ \\\\\n    HD & 2D C & U & Model I & 867322.7 &867158.2 &329.0 & $16.6\\;\\sigma$ \\\\\n    Interpolated & 3D & U & Model I & 867287.4 & 867081.2& 412.4 & $18.9\\;\\sigma$ \\\\\n    GALPROP & 3D & U & Model I & 868214.6 & 868040.9& 347.6  & $17.2\\;\\sigma$ \\\\[0.5ex]\\hline\n    \\multicolumn{8}{c}{Alternative Sgr dSph templates} \\\\[0.5ex]\n    HD & 3D & S & Model II & 866680.6 & 866626.3 & 108.5  & $8.7\\;\\sigma$ \\\\\n    HD & 3D & S & Model III & 866680.6 & 866647.5 & 66.1  & $6.4\\;\\sigma$ \\\\\n    HD & 3D & S & Model IV & 866680.6 & 866678.2 & 4.8 & $0.4\\;\\sigma$ \\\\\n    HD & 3D & S & Model V & 866680.6 &866644.9 & 71.5  & $6.7\\;\\sigma$ \\\\\n    HD & 3D & U & Model II & 867271.7 & 866970.7  & 602.1  & $23.2\\;\\sigma$ \\\\\n    HD & 3D & U & Model III & 867271.7 & 866994.1  & 555.3 & $22.2\\;\\sigma$ \\\\\n    HD & 3D & U & Model IV & 867271.7 & 867152.2 & 239.1 & $14.0\\;\\sigma$ \\\\\n    HD & 3D & U & Model V & 867271.7 & 866993.3 & 556.9   & $22.2\\;\\sigma$ \\\\\n    \\hline\\hline\n    \\end{tabular}\n    \\caption{Template analysis results comparing {\\it baseline} to {\\it baseline + Sgr dSph} models. \n    Columns (1) - (3) specify the {baseline} templates used for Galactic hadronic \/ bremsstrahlung emission, inverse Compton emission, and the Fermi Bubbles, respectively.\n    %\n    Column (4) specifies {source} templates\n    describing the Sgr dSph (see Methods for details). Columns (5) and (6) give the log likelihood for the baseline model (without the Sgr dSph) and the baseline + Sgr dSph model, and columns (7) and (8) give the test statistic with which the baseline + Sgr dSph model is preferred, and the corresponding statistical significance of that preference. \n    %\n    The improvement in TS going from $\\{\\rm HD, 3D, U , Model \\ I\\}$ to $\\{\\rm HD, 3D, S , Model \\ I\\}$ is $\\Delta$TS = 854.2, equivalent to 28.0 $\\sigma$.\n    Note that Sgr dSph model IV -- which generates a statistically insignificant improvement to the baseline for one particular combination in the last cluster -- is the sparsest stellar template, containing only 675 stars.\n    }\n    \\label{tab:loglikelihood}\n\\end{table}\n\n\n\\clearpage\n\n\\newrefsegment\n\n\\section*{Methods}\n\\label{sec:Methods}\n\nOur analysis pipeline consists of three steps: (1) data and template selection, (2) fitting, and (3) spectral modeling. \n\n\\subsection*{\nData and template selection\n}\n\\label{sec:fermidata}\n\nWe use eight years of LAT data,  selecting \\texttt{Pass 8 UltraCleanVeto} class events in the energy range from 500 MeV to 177.4 GeV. We choose the limit at low energy to mitigate both the impact of {$\\gamma$-ray} \\ leakage from the Earth's limb  and the increasing width of the point-spread function at lower energies.\nWe spatially bin the data to a resolution of $0.2^\\circ$, and divide it into 15 energy bins; the 13 lowest-energy of these are equally spaced in log energy, while the 2 highest-energy are twice that width in order to improve the signal to noise.\nWe select data obtained over the same observation period as that used in the construction of the Fourth Fermi Catalogue (4FGL)\\cite{Fermi-LAT:4FGL} (August 4, 2008 to August 2, 2016).\nThe region of interest (ROI) of our analysis is a square region defined by $-45^\\circ\\leq b \\leq -5^\\circ$, and $30^\\circ \\geq \\ell \\geq -10^\\circ$ (\\autoref{fig:SgrdSphOverlay}). \nThis sky region fully contains the Fermi cocoon substructure but avoids the Galactic plane ($|b|\\leq 5^\\circ$) where uncertainties are largest. Because the ROI is of modest size, we allow the Galactic diffuse emission (GDE)\ntemplates greater freedom to reproduce potential features in the data. \nWe carry out all data reduction and analysis using the standard  \n\\textsc{Fermitools v1.0.1}\\footnote{\\url{https:\/\/github.com\/fermi-lat\/Fermitools-conda\/wiki}} \nsoftware package.\nWe model the performance of the LAT with the \\texttt{P8R3\\_ULTRACLEANVETO\\_V2} Instrument Response Functions (IRFs).\n\nWe fit the spatial distribution of the ROI data as the sum of a series of templates for different components of the emission. For all the templates we consider, we define a ``baseline'' model that includes only known point and diffuse emission sources, to which we compare a ``baseline + Sgr dSph'' model that includes those templates plus the Sgr dSph. Our baseline models, following the approach of Ref.~\\cite{Abazajian:2020}, contain the following templates: (1) diffuse isotropic emission, (2) point sources, (3) emission from the Sun and Moon, (4) Loop I, (5) the Galactic Centre Excess, (6) Galactic cosmic ray-driven hadronic and bremsstrahlung emission, (7) inverse Compton emission, and (8) the \\textit{Fermi} Bubbles; baseline + Sgr dSph models also include a Sgr dSph template.\n\n\nOur templates for the first five emission sources are straightforward, and we adopt a single template for each of them throughout our analysis. Since our data selection is identical to that used to construct the 4FGL, we adopt the standard isotropic background and point source models provided as part of the catalogue \\cite{Fermi-LAT:4FGL}, \\texttt{iso$_{-}$P8R3$_{-}$ULTRACLEANVETO$_{-}$V2$_{-}$v1.txt}, and \\texttt{gll\\_psc\\_v20.fit}, respectively; the latter includes 177 $\\gamma$ ray point sources within our ROI. We similarly adopt the standard Sun and Moon templates provided. For the foreground structure Loop I, we adopt the model of Ref.~\\cite{Wolleben:2007}. Finally, given that the low-latitude boundary of our ROI overlaps with the spatial tail of the Galactic Centre Excess (GCE), we include the `Boxy Bulge' template of Ref.~\\cite{Freudenreich1998}, which has been shown \\cite{Macias2018,Bartels2018,Macias2019} to provide a good description of the observed GCE away from the nuclear Bulge region (which is outside our ROI). The inclusion of this template in our ROI model has only a small impact on our results.\n\nThe remaining templates require more care. The dominant source of $\\gamma$-rays within the ROI is hadronic and bremsstrahlung emission resulting from the interaction of Milky Way cosmic ray (CR) protons and electrons with interstellar gas; the emission rate is proportional to the product of the gas density and the CR flux. We model this distribution using three alternative approaches. Our preferred approach follows that described in Ref.~\\cite{Macias2018}. We assume that the spatial distribution of $\\gamma$-ray emission traces the gas distribution from the hydrodynamical model of Ref.~\\cite{Pohl2008}, which gives a more realistic description of the inner Galaxy than alternatives. To normalise the emission, we divide the Galaxy into four rings spanning the radial ranges $0-3.5$ kpc, $3.5-8.0$ kpc, $8.0-10.0$ kpc, and $10.0-50.0$ kpc, within which we treat the emission per unit gas mass in each of our 15 energy bins as a constant to be fit. We refer to the template produced in this way as the ``HD'' model. Our first alternative is to use the same procedure of dividing the Galaxy into rings, but describe the gas distribution within those rings using a template constructed from interpolated maps of Galactic H~\\textsc{i} and H$_2$, following the approach described in Appendix B of Ref.~\\cite{Ackermann2012}; we refer to this as the ``Interpolated'' approach. Our third alternative, the ``GALPROP'' model, is the SA50 model described by Ref.~\\cite{Johannesson:2018bit}, which prescribes the full-sky hadronic CR emission distribution.\n\nWe similarly need a model for diffuse, Galactic IC emission -- the second largest source of background -- which is a product of the CR electron flux and the interstellar radiation field (ISRF). As with hadronic emission, we consider four alternative distributions. Our default choice is the SA50 model described by Ref.~\\cite{Johannesson:2018bit}, which includes 3D models for the ISRF~\\cite{Porter:2017vaa}. We therefore refer to this as the ``3D'' model. However, unlike in Ref.~\\cite{Johannesson:2018bit}, we use this model only to obtain the spatial distribution of the emission, not its normalisation or energy dependence. Instead, we obtain these in the same way as for our baseline hadronic emission model, i.e., we divide the Galaxy into four rings and leave the total amount of emission in each ring at each energy as a free parameter to be fit to the data; this approach reduces the sensitivity of our results to uncertainties in the electron injection spectrum and ISRF normalisation. Our three alternatives to this are models ``2D A'', ``2D B'', and ``2D C'', corresponding to models A, B, and C as described by Ref.~\\cite{Ackermann:2014usa}, which model IC emission over the full sky under a variety of assumptions about CR injection and propagation, but rely on a 2D model for the ISRF.\n\nThe final component of our baseline template is a model for the Fermi Bubbles themselves, which are one of the strongest sources of foreground emission in high latitude regions of the ROI. The FBs are themselves defined as highly statistically-significant and spatially-coherent residuals in the inner Galaxy that remain once other sources are modelled out in all-sky {$\\gamma$-ray} \\ analyses. The FBs are not reliably traced by emission at any other wavelength, so we do not have an {\\it a priori} model with which to guide the construction of a spatial template of these structures. However, one characteristic that renders the FBs distinct from other large angular scale diffuse $\\gamma$-ray structures is their hard {$\\gamma$-ray} \\ spectrum. Indeed, the state-of-the-art, {\\it structured} spatial template for them generated by the {\\it Fermi} Collaboration\\cite{Ackermann2014} -- the templates one would normally employ in large ROI, inner Galaxy {{\\em Fermi}-LAT} \\ analyses --  were constructed using a spectral component analysis. That study recovered a number of regions of apparent substructure within the solid angle of the FBs,  most notably substructure overlapping the previously-discovered\\cite{Su2012,Selig2015} ``cocoon'' which, as we have discussed here, is largely coincident with the Sgr dSph. Of course, a potential issue with constructing a phenomenological, spectrally-defined model for the FBs is that, if there happens to be an extended, spectrally-similar source coincident with the FBs, it will tend to be incorporated into the template. For this reason Ref.~\\cite{Ackermann2014} suggest using a flat FB template when searching for new structures. Despite this proposal, our default analysis uses the more conservative choice of a structured FB template. However, we also run tests using an unstructured template for comparison, and to understand the systematic uncertainties associated with the choice of template. We refer to these two cases as the ``U'' (Unstructured) and ``S'' (Structured) FB templates, respectively.\n\nFinally, our baseline + Sgr dSph models require a template for the Sgr dSph. Our templates trace the distribution of bright stars in the dwarf, which we construct from five alternative stellar catalogues, all based on different selections from \\textit{Gaia} Data Release 2; we refer to the resulting templates as models I - V, and show them in E.D.~\\autoref{fig:Stellartemplates}. Full details on how we construct each of these templates are provided in  S.I.~sec.~2. Model I, our default choice, comes from the catalogue of $2.26\\times 10^5$ Sgr dSph candidate member stars from Ref.~\\cite{Vasiliev2020}; the majority of the catalogue consists of red clump stars. Model II uses the catalogue of RR Lyrae stars in the Sagittarius Stream from Ref.~\\cite{Ibataetal:2020}, which we have down-selected to a sample of 2369 stars whose kinematics are consistent with being members of the Sgr dSph itself. Model III uses the catalogue of $1.31\\times 10^4$ RR Lyrae stars belonging to the Sgr dSph provided by Ref.~\\cite{Iorio2019}. Finally, models IV and V come from the nGC3 and Strip catalogues of RR Lyrae stars from Ref.~\\cite{Ramosetal:2020}; the former contains 675 stars with higher purity but lower completeness, while the latter contains 4812 stars of higher completeness but lower purity.\n\n\\subsection*{Fitting procedure}\n\nOur fitting method follows that introduced in Refs.~\\cite{Macias2018, Macias2019}, and treats each of the 15 energy bins as independent, thereby removing the need to assume any particular spectral shape for each component and allowing the spectra to be determined solely by the data. Our data to be fit consist of the observed $\\gamma$-ray photon counts in each spatial pixel $i$ and energy bin $n$, which we denote $\\Phi_{n,i,\\rm obs}$, where\n$n$ goes from 1 to 15, and the index $i$ runs over the positions $(\\ell_i,b_i)$ of all spatial pixels within the ROI. For a given choice of template, we write the corresponding model-predicted $\\gamma$-ray counts as $\\Phi_{n,i,\\rm mod} = \\sum_c \\mathcal{N}_{n,c} R_{n,i} \\Phi_{c,i}$, where $R_{n,i}$ is the instrument response for each pixel and energy bin (computed assuming an $E^{-2}$ spectrum within the bin), and $\\Phi_{c,i}$ is the value of template component $c$ evaluated at pixel $i$; for baseline models, we have a total of 8 components, while for baseline + Sgr dSph models we have 9. Note that $\\Phi_{c,i}$ is a function of $i$ but not of $n$, i.e., we assume that the spatial distribution of each template component is the same at all energies, except for the IC templates, for which an energy-dependent morphology is predicted by our GALPROP simulations. Without loss of generality we further normalise each template component as $\\sum_i \\Phi_{c,i} = 1$, in which case $\\mathcal{N}_{n,c}$ is simply the total number of photons contributed by component $c$ in energy bin $n$, integrated over the full ROI; the values of $\\mathcal{N}_{n,c}$ are the parameters to be fit. We find the best fit by maximising the usual Poisson likelihood function\n\\begin{equation}\n    \\ln\\mathcal{L}_n = \\sum_{i} \\frac{\\Phi_{n,i,\\rm mod}^{\\Phi_{n,i,\\rm obs}} e^{-\\Phi_{n,i,\\rm mod}}}{\\Phi_{n,i,\\rm obs}!},\n    \\label{eq:log-likelihood}\n\\end{equation}\nusing the \\texttt{pylikelihood} routine, the standard maximum-likelihood method in \\texttt{FermiTools}. Note that, since each energy bin $n$ is independent, we carry out the likelihood maximisation bin-by-bin.\n\n\nWe perform all fits in pairs, one for a baseline model containing only known emission sources, and one for a baseline + Sgr dSph model containing the same known sources plus a component tracing the Sgr dSph. The set of paired fits we perform in this manner is shown in \\autoref{tab:loglikelihood}. We compare the quality of these baseline and baseline + Sgr dSph fits by defining the test statistic $\\mathrm{TS}_n = -2\\ln(\\mathcal{L}_{n,\\rm base}\/\\mathcal{L}_{n,\\rm base+Sgr})$; the total test statistic for all energy bins is simply $\\mathrm{TS} = \\sum_n \\mathrm{TS}_n$. We can assign a $p$-value to a particular value of the TS by noting that baseline + Sgr dSph models have 15 additional degrees of freedom compared to baseline models: the value of $\\mathcal{N}_{n,c}$ for the component $c$ corresponding to the Sgr dSph, evaluated at each of the  \n15 energy bins. In this case, the mixture distribution formula gives\\cite{Macias2018}\n\\begin{equation}\n    p(\\mathrm{TS}) = 2^{-N} \\left[\\delta(\\mathrm{TS}) + \\sum_{n=1}^N \\binom{N}{n} \\chi^2_n(\\mathrm{TS})\\right],\n\\end{equation}\nwhere $N = 15$  is the difference in number of degrees of freedom, \n$\\binom{N}{n}$ is the binomial coefficient, $\\delta$ is the Dirac delta function, and $\\chi^2_n$ is the usual $\\chi^2$ distribution with $n$ degrees of freedom. The corresponding statistical significance (in $\\sigma$ units) is\\cite{Macias2018}:\n\\begin{equation}\n\\label{eq:numberofsigmas}\n\\mbox{Number of $\\sigma$}\\equiv \\sqrt{\\rm InverseCDF\\left(\\chi_1^2,{\\rm CDF}\\left[p(\\mbox{TS}),\\hat{{\\rm TS}}\\right]\\right)},\n\\end{equation}\nwhere (InverseCDF) CDF is the (inverse) cumulative distribution function and the first argument of each of these functions is the distribution function, the second is the value at which the CDF is evaluated, and the total TS is denoted by $\\hat{\\rm TS}$. For 15 extra degrees of freedom, a 5$\\sigma$ detection corresponds to $\\mbox{TS}=46.1$. (Additional details of these formulae are given in S.I. Sec.~2 of Ref.~\\cite{Macias2018}.) We report values of $\\mathcal{L}_{\\rm base}$, $\\mathcal{L}_{\\rm base+Sgr}$, $\\mathrm{TS}$, and the significance level for all the templates we try in \\autoref{tab:loglikelihood}.\n\nA final step in our fitting chain is to assess the uncertainties. For our default choice of baseline + Sgr dSph model (first row in \\autoref{tab:loglikelihood}), our maximum likelihood analysis returns the central value $\\mathcal{N}^{\\rm def}_n$ on the total $\\gamma$-ray flux in the $n$th energy bin attributed to the Sgr dSph, and also yields an uncertainty $\\sigma^{\\rm def}_{\\mathcal{N},n}$ on this quantity. This represents the statistical error arising from measurement uncertainties. However, there are also systematic uncertainties stemming from our imperfect knowledge of the templates characterising the other emission sources. To estimate these, we examine the five alternative models listed in \\autoref{tab:loglikelihood} as ``Alternative background templates'', where we use different templates for the hadronic plus bremsstrahlung and inverse Compton backgrounds. Each of these models $m$ also returns a central value $\\mathcal{N}_n^m$ and an uncertainty $\\sigma_{\\mathcal{N},n}^m$ on the Sgr dSph flux. We use the uncertainty-weighted dispersion of these models as an estimate of the systematic uncertainty (e.g.,ref.~\\cite{Ackermann2018}):\n\\begin{equation}\n    \\delta\\mathcal{N}_n = \\sqrt{\\frac{1}{\\sum_m \\left(\\sigma_{\\mathcal{N},n}^m\\right)^{-2}} \\sum_m \\left(\\sigma_{\\mathcal{N},n}^m\\right)^{-2} \\left(\\mathcal{N}_n^{\\rm def} - \\mathcal{N}^m_n\\right)^2},\n\\end{equation}\nwhere the sums run over the $m=6-1$ alternative models. We take the total uncertainty on the Sgr dSph flux in each energy bin to be a quadrature sum of the systematic and statistical uncertainties, i.e., $(\\sigma^{\\rm def,tot}_{\\mathcal{N},n})^2 = (\\sigma^{\\rm def}_{\\mathcal{N},n})^2 + \\delta\\mathcal{N}_n^2$. We plot the central values and uncertainties of the fluxes for the default model derived in this manner in \\autoref{fig:luminosities}.\n\nWe have carried out several validation tests of this pipeline, which we describe in the Supplementary Information (SI).\n\n\n\n\n\\subsection*{Spectral modelling}\n\n\nWe model the observed Sgr dSph $\\gamma$-ray spectrum as a combination of prompt magnetospheric MSP emission and IC emission from {$e^\\pm$}~escaping MSP magnetospheres. We construct this model as follows. The prompt component is due to curvature radiation from {$e^\\pm$}~in within MSP magnetospheres. \nThe {$e^\\pm$}~energy distribution can be approximated as an exponentially-truncated power law \\cite{Abdo2013,Song2021}\n\\begin{equation}\n    \\frac{dN_{\\mathrm{MSP},e^\\pm}}{dE_{e^\\pm}} \\propto E_{e^\\pm}^{\\gamma_\\mathrm{MSP}} \\exp\\left(-\\frac{E_{e^\\pm}}{E_{\\mathrm{cut},e^\\pm}}\\right),\n\\label{eq:promptSpec}\n\\end{equation}\nand curvature radiation from these particles has a rate of photon emission per unit energy per unit time\n\\begin{equation}\n    \\frac{d\\dot{N}_{\\rm \\gamma,prompt}}{dE_\\gamma} = \\mathcal{N}\\left(L_{\\gamma,\\mathrm{prompt}}\\right) E_\\gamma^{\\alpha} \\exp\\left(-\\frac{E_\\gamma}{E_{\\rm cut, prompt}} \\right),\n\\label{eq:cutoffpwrlaw}\n\\end{equation}\nwhere $E_\\gamma$ is the photon energy, $\\mathcal{N}(L_{\\gamma,\\mathrm{prompt}})$ is a normalisation factor chosen so that the prompt component has total luminosity $L_{\\gamma,\\mathrm{prompt}}$, the index $\\alpha$ is related to that of the {$e^\\pm$}~distribution by $\\alpha = (\\gamma_{\\rm MSP} - 1)\/3$, and the photon cutoff energy is related to the {$e^\\pm$}~cutoff energy by \\cite{Baring2011}\n\\begin{equation}\nE_{\\rm cut,prompt} = \\frac{3 \\hbar c}{2 \\rho_c}   \\left(\\frac{E_{\\rm cut,e^\\pm}}{m_e}\\right)^3 \\simeq 2.0 \\ {\\rm GeV} \\ \\left(\\frac{\\rho_c}{\\rm 30 \\ km}\\right)^{-1} \\left(\\frac{E_{\\rm cut,e^\\pm}}{\\rm 3 \\ TeV}\\right)^3\n\\label{eq:EcutPrompt}\n\\end{equation}\nwhere $m_e$ is the electron mass, $\\rho_c$ is the radius of curvature of the magnetic field lines, and the other symbols have the usual meanings. Given the rather small magnetospheres, we expect $\\rho_c$ to be a small multiple of the $\\sim$ 10 km neutron star characteristic radius; henceforth we set $\\rho_c =$ 30 km. Empirically, $L_{\\gamma,\\rm prompt}$ is $\\sim 10\\%$ of the total MSP spin-down power \\cite{Abdo2013}.\n\n\n\nA larger proportion of the spin-down power goes into a wind of {$e^\\pm$}~escaping the magnetosphere. In the ultra-low density environment of the Sgr dSph, ionization and bremmstrahlung losses for this population, which occur at a rate proportional to the gas density, are negligible. Synchrotron losses, which scale as the magnetic energy density, will also be negligible; as noted in the main text, observed magnetic fields in dwarf galaxies are very weak \\cite{Regis2015}, and we can also set a firm upper limit on the Sgr dSph magnetic field strength simply by noting that the magnetic pressure cannot exceed the gravitational pressure provided by the stars since, if it did, that magnetic field, and the gas to which it is attached, would blow out of the galaxy in a dynamical time. The gravitational pressure is $P \\approx (\\pi\/2) G \\Sigma^2$, where $\\Sigma = M\/\\pi R^2$ is the surface density, and using our fiducial numbers $M = 10^8$ M$_{\\odot}$ and $R = 2.6$ kpc gives an upper limit on the magnetic energy density 0.06 eV \/ cm$^3$; non-zero gas or cosmic ray pressure would lower this estimate even further. This is a factor of four smaller than the energy density of the CMB, implying that synchrotron losses are at most a 20\\% effect, and can therefore be neglected.\n\nThis analysis implies that the only significant loss mechanism for these {$e^\\pm$}~is IC emission, resulting in a steady-state {$e^\\pm$}~energy distribution\n\\begin{equation}\n\\frac{dN_{e^\\pm}}{dE_{e^\\pm}} \\propto E_{e^\\pm}^\\gamma \\exp\\left(-\\frac{E_{e^\\pm}}{E_{\\mathrm{cut},e^\\pm}}\\right),\n\\end{equation}\nwhere $\\gamma = \\gamma_{\\rm MSP}-1$. We compute the IC photon distribution produced by these particles following ref.~\\cite{Khangulyan2014}, assuming that ISRF of the {Sgr~dSph~} is the sum of the CMB \nand two subdominant contributions, one consisting of light escaping from the Milky Way and the other a dilute stellar blackbody radiation field due to the stars of the dwarf.\nWe estimate the Milky Way contribution to the photon field at position of the dwarf using GalProp \\cite{Porter:2017vaa},\nwhich predicts a total energy density of $0.095$ eV\/cm$^3$ (compared to 0.26 eV\/cm$^{-3}$ for the CMB), comprised of 5 dilute black bodies\nwith colour temperatures and dilution factors\n$\\{ T_{\\rm rad},\\kappa \\}$ as follows: \n$\\{40 \\ {\\rm K }, 1.4 \\times 10^{-6} \\},\n\\{430 \\ {\\rm K }, 3.0 \\times 10^{-11} \\},\n\\{3400 \\ {\\rm K }, 4.3 \\times 10^{-14} \\},\n\\{6400 \\ {\\rm K }, 4.0 \\times 10^{-15} \\},$\nand\n$ \\{26000 \\ {\\rm K }, 8.0 \\times 10^{-18} \\}\n$.\nWe characterise the intrinsic light field of the dwarf as having a\ncolour temperature 3500 K and dilution factor of $7.0\\times 10^{-15}$ (giving energy density $0.005$ eV cm$^{-3}$; these choices are those expected for a spherical region of radius 2.6 kpc and stellar luminosity $2\\times 10^8$ $L_\\odot$, the approximate parameters of the Sgr dSph).\nThis yields an IC spectrum\n\\begin{equation}\n    \\frac{d\\dot{N}_{\\gamma,\\mathrm{IC}}}{dE_\\gamma} = \\mathcal{N}\\left(L_{\\gamma,\\rm IC}\\right) F\\left(\\gamma,E_{\\mathrm{cut},e^\\pm}\\right),\n\\end{equation}\nwhere $\\mathcal{N}\\left(L_{\\gamma,\\rm IC}\\right)$ is again a normalisation chosen to ensure that the total IC luminosity is $L_{\\gamma,\\rm IC}$, and $F\\left(\\gamma,E_{\\mathrm{cut},e^\\pm}\\right)$ is the functional form given by equation 14 of ref.~\\cite{Khangulyan2014}, which depends on the {$e^\\pm$}~spectral index $\\gamma$ and cutoff energy $E_{\\mathrm{cut},e^\\pm}$.\n\n\n\nCombining the prompt and IC components, we may therefore write the complete emission spectrum as\n\\begin{equation}\n    \\frac{d\\dot{N}_\\gamma}{dE_\\gamma} = \\mathcal{N}\\left(L_{\\gamma,\\mathrm{prompt}}\\right) E_\\gamma^{\\alpha} \\exp\\left(-\\frac{E_\\gamma}{E_{\\rm cut, prompt}} \\right) + \\mathcal{N}\\left(L_{\\gamma,\\rm IC}\\right) F\\left(\\gamma,E_{\\mathrm{cut},e^\\pm}\\right).\n\\end{equation}\nThis model is characterised by four free parameters: the total prompt plus IC luminosity $L_{\\gamma,\\rm tot} = L_{\\gamma,\\rm prompt} + L_{\\gamma,\\rm IC}$, the ratio of the prompt and IC luminosities $f = L_{\\gamma,\\rm prompt}\/L_{\\gamma,\\rm IC}$, the spectral index $\\alpha$ of the prompt component (which in turn fixes the other two spectral indices $\\gamma_{\\rm MSP}$ and $\\gamma$), and the cutoff energy for the prompt component $E_{\\rm cut, prompt}$ (which then fixes the {$e^\\pm$}~cutoff energy $E_{\\mathrm{cut},e^\\pm}$).\nNote that we make the simplest assumption that $\\alpha$ and $E_{\\rm cut, prompt}$ are uniform across the MSP population.\nIn reality, there may be a distribution of these properties but the parameteric form of \\autoref{eq:promptSpec}\nprovides a good description, in general, \nof both individual MSP spectra and the\naggregate spectra of GC MSP populations \\cite{Song2021}.\n\n\nWe fit the observed {Sgr~dSph~}~spectrum to this model using a standard $\\chi^2$ minimisation, using the combined statistical plus systematic uncertainty.\nWe obtain an excellent fit: the minimum $\\chi^2$ is 7.7 for 15 (data points) - 4 (fit parameters) = 11 (degrees of freedom, dof) or a reduced $\\chi^2$ of 0.70.\nWe report the best-fitting parameters in E.D.~\\autoref{tab:table1}, and plot the result best-fit spectra over the data in \\autoref{fig:luminosities}; we show the best-fit estimate (with $\\pm 1\\sigma$ confidence region) for the magnetospheric luminosity per stellar mass of the {Sgr~dSph~} MSPs in \\autoref{fig:LgammaOvrMstar}. \n\nWe also carry out an additional consistency check, by comparing our best-fit parameters describing the prompt emission -- $\\alpha$ and $E_{\\rm cut,prompt}$ -- to direct measurements of the prompt component from nearby, resolved MSPs \\cite{Abdo2013,Song2021}, and to measurements of GCs, whose emission is likely dominated by unresolved MSPs \\cite{Song2021}. We carry out this comparison in E.D.~\\autoref{fig:FitContours}. In this figure, we show joint confidence intervals on $\\alpha$ and $E_{\\rm cut,prompt}$ from our fit. For comparison, we construct confidence intervals for $\\alpha$ and $E_{\\rm cut,prompt}$ from observations using the sample of ref.~\\cite{Song2021}, who fit the prompt emission from 40 GCs and 110 individually-resolved MSPs. We draw 100,000 Monte Carlo samples from these fits, treating the stated uncertainties as Gaussian, and construct contours in the $(E_{\\rm cut,prompt}, \\alpha)$ plane containing 68\\%, 95\\%, and 99\\% of the sample points. As the plot shows, the confidence region from our fit is fully consistent with the confidence regions from the observations, indicating that our best-fit parameters are fully consistent with those typically observed for MSPs and GCs.\n\n\n\\section*{Data availability}\n\nAll data analysed for this study are publicly available.\nIn particular, {{\\em Fermi}-LAT} \\ data are available from \\url{https:\/\/fermi.gsfc.nasa.gov\/ssc\/data\/} and Gaia data are available from \\url{https:\/\/gea.esac.esa.int\/archive\/}.\nThe statistical pipeline, astrophysical templates, and gamma-ray observations necessary to reproduce our main results are publicly available in the following zenodo repository: \\url{10.5281\/zenodo.6210967}.\n\n\n\\section*{Code availability}\n\n{{\\em Fermi}-LAT} \\ data used in our study were reduced and analysed  using the standard  \n\\textsc{Fermitools v1.0.1}\nsoftware package available from \\url{https:\/\/github.com\/fermi-lat\/Fermitools-conda\/wiki}.\nThe performance of the {{\\em Fermi}-LAT} \\ was modelled with the \\texttt{P8R3\\_ULTRACLEANVETO\\_V2} Instrument Response Functions (IRFs).\nSpectral analysis and fitting was performed using custom \\textsc{MATHEMATICA}\ncode created by the authors which is available upon reasonable request.\n\n\\clearpage\n\n\n\\section*{Acknowledgements}\n\nRMC acknowledges \nsupport from the Australian Government through the Australian Research Council, award\nDP190101258 (shared with MRK)\nand hospitality from the Virginia Institute of Technology, the Max-Planck Institut f\\\"ur Kernphysik, and the GRAPPA Institute at the University of Amsterdam supported by the Kavli IPMU at the University of Tokyo. \nO.M. is supported by the GRAPPA Prize Fellowship and JSPS KAKENHI Grant Numbers JP17H04836, JP18H04340, JP18H04578, and JP20K14463.\nThis work was supported by World Premier International Research Centre Initiative (WPI Initiative), MEXT, Japan. \nADM acknowledges support from the Australian Government through a Future Fellowship from the Australian Research Council, award FT160100206.\nM.R.K. acknowledges support from the Australian Government through the Australian Research Council, award\nDP190101258 (shared with RMC) and\nFT180100375.\nThe work of S.H.\\ is supported by the U.S.\\ Department of Energy Office of Science under award number DE-SC0020262 and NSF Grant No.\\ AST-1908960 and No.\\ PHY-1914409. The work of DS is supported by the U.S.\\ Department of Energy Office of Science under award number DE-SC0020262. \nT.V. and A.R.D. acknowledge the support of the Australian Research Council's Centre of Excellence for Dark Matter Particle Physics (CDM) CE200100008.\nAJR acknowledges support from the Australian Government through the Australian Research Council, award FT170100243.\nRMC thanks Elly Berkhuijsen, Rainer Beck, Ron Ekers, Matt Roth, and Thomas Siegert for useful communications.\n\n\n\\section*{Author contributions statement}\n\nR.M.C. initiated the project and led the spectral analysis and theoretical interpretation. \nO.M constructed the astrophysical templates, designed the analysis pipeline, and performed the data analysis of  $\\gamma$ ray observations.\nD.M., M.R.K., C.G., R.J.T., F.A., J.A.H., S.A., S.H., A.G., M.R., L.F., and A.R. provided theoretical insights and interpretation, and advice about statistical analysis.\nT.V. and A.R.D. provided insights on the expected distribution of dark matter.\nR-Z.Y. performed an initial {$\\gamma$-ray} \\ data analysis.\nM.D.F helped with radio data.\nThe main text was written by RMC, MRK, and O.M. and the Methods section was written by O.M., R.M.C., and MRK.\nAll authors were involved in the interpretation of the results and all reviewed the manuscript.\n\n\n\n\\section*{Additional information}\n\nTo include, in this order: \\textbf{Accession codes} (where applicable); . \n\n\\subsection*{Competing interests}\n\nThe authors declare no competing interests.\n\n\n\n\\clearpage\n\n\n\\section*{Extended Data}\n\\setcounter{figure}{0}\n\\setcounter{table}{0}\n\n\\renewcommand{\\figurename}{Extended Data Figure}\n\\renewcommand{\\tablename}{Extended Data Table}\n\n\n\\begin{figure*}[ht!]\n\\centering\n\\begin{tabular}{lll}\n\\includegraphics[width=0.33\\textwidth]{Sgr_Stream_VasilevBelokurov.pdf} & \\includegraphics[width=0.33\\textwidth]{Sgr_Stream_Strasbourg.pdf}  & \\includegraphics[width=0.33\\textwidth]{Sgr_Stream_Iorio.pdf}\\\\\n\\includegraphics[width=0.33\\textwidth]{Sgr_Stream_BarcelonaI.pdf} & \\includegraphics[width=0.33\\textwidth]{Sgr_Stream_BarcelonaII.pdf}  & \\\\\n\\end{tabular}\n\\caption{The stellar density templates for the Sgr dSph used in this study. Each map has been normalized, so the units are arbitrary; the color scale is logarithmic. Morphological differences among the templates are due to different stellar candidates (red clump or RR Lyrae), search algorithms, and search target (the dwarf remnant or the stream).  \nData sources are as follows: \nModel I, ref.~\\cite{Vasiliev2020};\nModel II, ref.~\\cite{Ibataetal:2020};\nModel III, ref.~\\cite{Iorio2019};\nModel IV and Model V, ref.~\\cite{Ramosetal:2020}.\nDetailed descriptions of these templates are given in the S.I.~sec.~2.}\n\\label{fig:Stellartemplates}\n\\end{figure*}\n\n\n\n\\begin{figure}[t!]\n\\centering\n\\includegraphics[scale=0.3]{grid_MC_loglikes.pdf} \\\\\n\\caption{Goodness of fit computation for the best-fitting baseline + Sgr dSph model using our preferred set of templates (first entry in \\autoref{tab:loglikelihood}). In each of the 15 panels, one for each of the energy bins in our analysis pipeline, the blue histograms show the distribution of $-\\ln\\mathcal{L}$ values produced in 100 Monte Carlo trials where we use our pipeline to fit a mock data set produced by drawing photons from the same set of templates used in the fit; orange dashed vertical lines show the 68\\% confidence range of this distribution, and black dashed vertical lines show the mean. Under the null hypothesis that our best-fitting model for the real \\textit{Fermi} observations is a true representation of the data, and that disagreements between the model and the data are solely the result of photon counting statistics, the log-likelihood values for our best-fitting model should be drawn from the distributions shown by the blue histograms. For comparison, the red vertical line shows the actual measured log likelihoods for our best fit. The fact that these measured values are well within the range spanned by the Monte Carlo trials\nindicates that we cannot rule out the null hypothesis, indicating that our model is as good a fit to the data as could be expected given the finite number of photons that \\textit{Fermi} has observed.\n}\\label{fig:fitvalidation}\n\\end{figure}\n\n\n\\begin{figure*}[ht!]\n\\centering\n\\begin{tabular}{lll}\n\\includegraphics[width=0.32\\textwidth]{row_1a.pdf} & \\includegraphics[width=0.294\\textwidth]{row_1b.pdf}  & \\includegraphics[width=0.294\\textwidth]{row_1c.pdf}\\\\\n\\includegraphics[width=0.32\\textwidth]{row_2a.pdf} & \\includegraphics[width=0.294\\textwidth]{row_2b.pdf}  & \\includegraphics[width=0.294\\textwidth]{row_2c.pdf}\\\\\n\\includegraphics[width=0.32\\textwidth]{row_3a.pdf} & \\includegraphics[width=0.294\\textwidth]{row_3b.pdf}  & \\includegraphics[width=0.294\\textwidth]{row_3c.pdf}\n\\end{tabular}\n\\caption{Measured photon counts (left), best-fit baseline + {Sgr~dSph~} model (middle), and the fractional residuals $(Data-Model)\/Model$ (right). The images were constructed by summing the corresponding energy bins over the energy ranges displayed on top of each panel: [0.5, 1.0] GeV, [1.0, 4.0] GeV, [4.0, 15.8] GeV, from top to bottom. The maps have been smoothed with Gaussian filters of radii $1.0^\\circ$, $0.8^\\circ$, and $0.5^\\circ$ for each energy range displayed, respectively\n(where these angular scales are determined by the {{\\em Fermi}-LAT} \\ point spread function at the low-edge of the energy interval for the former two, while the latter is determined by the angular resolution of the gas maps).\nThe spectrum of baseline + {Sgr~dSph~} model components shown here can be seen in ~\\autoref{fig:totalspectra}. The 4FGL~\\cite{Fermi-LAT:4FGL} {$\\gamma$-ray} \\ point sources included in the baseline model are represented by the red circles.\n}\n\\label{fig:Residuals}\n\\end{figure*}\n\n\\begin{figure}\n\\centering\n\\begin{tabular}{cc}\n\\includegraphics[scale=0.7]{Injection_mismodeling_GDE.pdf} &\\includegraphics[scale=0.7]{Injection_MC_StrucFB_Fit_FlatFB.pdf}\\\\\n\\includegraphics[scale=0.7]{RecoveredSpectra_GDE.pdf} & \\includegraphics[scale=0.7]{RecoveredSpectra_FBs.pdf} \n\\end{tabular}\\caption{\nResults from our template mismatch tests. Each of the coloured lines shows the results of a test where we generate synthetic data with one set of templates, and attempt to recover the Sgr dSph in those data using a different set. In the upper two panels, the horizontal axis shows the true, energy-integrated Sgr dSph photon flux in the synthetic data, while the vertical axis shows the value (with $1 \\sigma$ statistical error bars) retrieved by our pipeline; the black dashed lines indicate perfect recovery of the input, and the vertical bands show the photon flux we measure for the Sgr dSph in the real \\textit{Fermi} data. In the bottom two panels we plot the recovered energy flux in each energy bin (with $1 \\sigma$ statistical error bars), for the case where the injected photon flux most closely matches the real Sgr dSph flux; the black dashed line again shows perfect recovery of the injected signal. The left panels show experiments where we mismatch the Galactic hadronic and IC templates, while the right panels show experiments where we mismatch the FB templates; see Methods for details.\n}\\label{fig:injectionrecovery}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{tabular}{lll}\n\\includegraphics[scale=0.65]{Results_rotation_around_center.pdf}  & \\includegraphics[scale=0.65]{Results_rotation_around_GC.pdf}   & \\includegraphics[scale=0.123]{translation_StructFBs.pdf}\n\\end{tabular}\\caption{\nResults of our rotation and translation tests. \\textit{Left:} change in TS when repeating the analysis using the default baseline + Sgr dSph model, but with the Sgr dSph rotated about its centre by the indicated angle (blue points); TS values $>0$ indicate an improved fit (dashed grey line), with $\\mbox{TS} = 46.1$ corresponding to a $5\\sigma$-significant improvement (red dashed line). \n\\textit{Centre:} same as the left panel, but for tests with the Sgr dSph template rotated about the Milky Way centre, rather than its own centre. \\textit{Right:} tests for translation of the Sgr dSph template. The true position of the Sgr dSph centre is the center of the plot, and the colour in each pixel indicates the change in TS if we displace the Sgr dSph centre to the indicated position; the maximum shown, at a displacement $\\Delta b \\approx -4^\\circ$, has $\\mbox{TS} = 40.8$, corresponding to $4.5\\sigma$ significance. For comparison, white contours show the original, unshifted Sgr dSph template, and the green arrow shows the direction anti-parallel to the Sgr dSph's proper motion, back along its past trajectory; red arrows show the projection of the green arrow in the $\\ell$ and $b$ directions.\n}\\label{fig:rotationAndTranslationTests}    \n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\includegraphics[scale=1]{Sgr_Sph_StructuredFBs_spectra_systematics.pdf}\\\\\n\\caption{{Sgr~dSph~} spectra derived from template analysis using different Galactic diffuse emission models; in all cases the spectrum shown is the flux averaged over the entire ROI, not the flux within the footprint of the Sgr dSph template. The fiducial model is our default choice (first entry in Table~\\ref{tab:loglikelihood}), while other lines correspond to alternate foregrounds -- models 2D A (red), 2D B (black), and 2D C (blue) for the Galactic IC foreground, and models Interpolated (dark green) and GALPROP 3D-gas (light green) for the Galactic hadronic + bremsstrahlung foreground. The error bars display $1\\sigma$ statistical errors. See Table~\\ref{tab:loglikelihood} and text for details.}\n\\label{fig:SgrSpecVar}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\includegraphics[scale=1]{Total_measured_spectra_RoI.pdf}\\\\ \n\\caption{\nContribution of each template component to the $\\gamma$-ray spectrum averaged over the entire ROI, for our default baseline + {Sgr~dSph~} model. Components shown are as follows: $\\pi^0+\\mbox{brems}$ is the Galactic hadronic plus bremsstrahlung foreground, ICS is the Galactic inverse Compton foreground, 4FGL indicates point sources from the 4th \\textit{Fermi} catalogue, Fermi Bubbles indicates the structured Fermi Bubble template, isotropic is the isotropic $\\gamma$-ray background, ``other'' includes the Sun and Moon, Loop I, and the Galactic Centre Excess, and Sgr stream indicates the Sgr dSph.\nThe error bars display $1\\sigma$ statistical errors.\n}\n\\label{fig:totalspectra}\n\\end{figure}\n\n\n\n\\begin{figure}\n    \\centering\n        \\includegraphics[width=0.5\\linewidth]{plotSpectralFitContours.pdf}\n\\caption{ \nFilled contours indicate the best-fit region for the spectral  parameters $E_{\\rm cut,prompt}$ and $\\alpha$\nthat determine the shape of the magnetospheric emission from the Sgr dSph; the outer, coloured region shows the 2$\\sigma$ region, the inner shows the 1$\\sigma$ region, and the red point marks the best fit.\nThe dotted and dashed contours describe the 1, 2, and 3 $\\sigma$ confidence regions measured in ref~\\cite{Song2021} for globular clusters (GCs) and individual resolved MSPs, respectively, constructed from the observations as described in Methods.\n}\n\\label{fig:FitContours}\n\\end{figure}\n\n\\begin{figure}\n \\includegraphics[width=1.\\linewidth]{plotLgammaOvrMstarVstSimple}\n    \\caption{\n{\\bf Data:} $\\gamma$-ray luminosity per stellar mass for a number of stellar systems (cf.~fig.~3 main text) versus mean stellar age of those systems. The mean stellar ages have been determined from empirically-determined star formation histories for all these objects (data sources as follows: {Sgr~dSph~} \\cite{Weisz2014}, M31 \\cite{Williams2017}, Galactic Bulge \\cite{Bernard2018}, NB \\cite{Nogueras-Lara2020} and ref.~\\cite{Weisz2013} for the LMC). The globular cluster datum (`GCs') is plotted at the mean measured {$\\gamma$-ray} \\ luminosity for the 27 systems analysed in ref.~\\cite{Song2021} divided by their stellar masses, and the age is the luminosity-weighted mean age for the 31 systems analysed in ref.~\\cite{Wu2022} (while the error bars for this datum show the standard deviations of these measurements for each population). The purple datum shows the secondary electron plus positron luminosity of the Milky Way (`disk $e^\\pm$') as inferred in ref.~\\cite{Strong2010} and adopting a disk stellar mass of $5.2 \\times 10^{10} \\ M_{\\odot}$\\cite{Bland_Hawthorn_2016}. {\\bf Model curve:} The solid blue curve shows the evolution with time (since the initial, burst-like star formation event) of the total spin-down power generated by a population of MSPs (normalised to the stellar mass expected to host that same population) according to the recent binary population synthesis modelling presented in ref.~\\cite{Gautam2021} (with the blue band indicating the estimated the $\\pm 1 \\sigma$ error on this quantity dominated by the uncertainties in the overall stellar binarity fraction). The {\\bf dashed red line} is an approximate fit to the solid blue line described by $5.0 \\times 10^{28}$ $ \\exp(-t\/t_{\\rm decay})$ \\ erg$\/s\/M_{\\odot}$ with $t_{\\rm decay} = 3$ Gyr. The dashed blue curve shows 10\\% of the mass-normalised spin-down power (with the error band suppressed for clarity). The {\\bf brown, dashed, horizontal line} shows the total power (per unit stellar mass) from MSP spin-down we infer from the study by Sudoh et al.~\\cite{Sudoh2020} of radio continuum emission from massive, quiescent galaxies (with expected mean stellar ages $>8-10$ Gyr; see the main text for more details).\n}\n\\label{fig:plotLgammaOvrMstarVstSimple}\n\\end{figure}\n\n\\begin{table}[ht!]\n    \\centering\n    \\begin{tabular}{ccccc}\n    \\hline\n     quantity & best-fit & 68\\% c.l.  & units & literature   \\\\\n     &&&& value(s)  \\\\\n    \\hline\n   $l_0 \\equiv L_{\\rm \\gamma,tot}\/M_\\star$ & $5.2 $ & $[4.4 , 6.0]$ & $10^{28}$ erg\/s\/$M_{\\odot}$ \n    & $\\sim (1-10)$ \\cite{Sudoh2020}   \\\\\n    $f = L_{\\rm \\gamma,prompt}\/L_{\\rm \\gamma,IC}$ & $0.83 $ & $[0.59, 1.3]$ & --- &  $\\sim 0.1$\\cite{Sudoh2020} \\\\\n    $\\alpha$ & $0.039 $ & $[-0.38,0.62]$ & --- & $-0.88 \\pm 0.44$\\cite{Song2021} \\\\\n    $E_{\\rm cut, prompt}$ & $1.0 $ & $[0.74, 1.3]$ & GeV & \n    $1.91^{+0.85}_{-0.59} \\pm 0.44$ \\cite{Song2021} \\\\\n    \\hline\n    \\end{tabular}\n    \\caption{Best fit spectral parameters with $\\pm 1\\sigma$ confidence regions as determined from $\\chi^2$ fitting to the measured {$\\gamma$-ray} \\ spectrum of the Sgr dSph. \n    %\n    The parameter $l_0$ is calculated using a stellar mass\n    $M_\\star = 10^8 M_{\\odot}$ \\cite{Vasiliev2021} for the Sgr dSph.\n    %\n    See also E.D. \\autoref{fig:FitContours}\n    %\n    }\n    \\label{tab:table1}\n\\end{table}\n\n\n\n\n\\clearpage\n\n\n\\printbibliography[segment=\\therefsegment,title={Methods and Extended Data References}, check=onlynew]\n\n\\clearpage\n\n\\newrefsegment\n\n\\renewcommand{\\figurename}{Supplementary Information Figure}\n\\renewcommand{\\tablename}{Supplementary Information Table}\n\n\\setcounter{figure}{0}\n\\setcounter{table}{0}\n\n\\section*{Supplementary Information}\n\n\\section{Chance overlap calculation}\n\\label{sec:overlap}\n\nIn the main text we estimate the probability of a chance overlap between cocoon {$\\gamma$-ray} \\ structure and {Sgr~dSph~} to be $\\approx 1\\%$.\nThis follows simply from noting that the solid angle of the Bubbles is around 0.7 sr\\cite{Ackermann2014} and the cocoon covers $\\lesssim$20\\% of this solid angle, so the chance probability for an overlap if these objects were placed randomly on the sky is $\\lesssim 0.2 \\times 0.7\/(4 \\pi) \\sim 0.012$. However, this is a generous upper limit; it does not take into account that, as revealed by the template analysis, there is a much more detailed correspondence between the {$\\gamma$-ray} \\ substructure and the stellar distribution not accounted for here. Moreover, the naive 1\\% estimate does include a `look-elsewhere' correction: the Milky Way is surrounded by satellite galaxies and there are apparently other regions of sub-structure within the Fermi Bubbles.\nHowever, not only is the cocoon the brightest and first-discovered region of sub-structure \\cite{Su2012}, it is also the only region that has been reliably detected by independent analyses \\cite{Selig2015,Ackermann2014}, and is visibly-evident in \nindependently-produced\n{$\\gamma$-ray}\\ maps \\cite{Yang2014,deBoer2015}.\nThe {Sgr~dSph~} is also a special object: it is the\nbrightest MW satellite not yet (prior to this work) detected in $\\gamma$-rays. \n(In fact, not only is the {Sgr~dSph~} the brightest satellite undiscovered in $\\gamma$-rays, it is substantially brighter than the next brightest galaxy\\footnote{The list of all the MW satellites with apparent magnitude $m<10$ includes 8 objects,\nthe brightest two, the LMC and SMC, with $m \\sim 0.3$ and $\\sim 2.1$, respectively, are already detected in $\\gamma$-rays.\nThe next brightest is the {Sgr~dSph~} with  $m \\sim 3$; after that come Fornax, Sculptor, and Leo I with $m \\sim 7.3, 8.7$ and 10.0\nand angular diameters of $0.24^\\circ, 0.51^\\circ$ and $0.11^\\circ$, respectively, which, even assuming they could be detected, would at best only appear marginally extended to {{\\em Fermi}-LAT}.}.)\nOverall, we have a spatial overlap\n(and detailed morphological correspondence as argued elsewhere) between \nthe brightest region of substructure within the {\\it Fermi} Bubbles\nand the Sgr dSph, the\nsecond closest, third-most massive, third brightest, and third most angularly extended satellite galaxy of the MW.\n\n\\begin{comment}\n\\section{Full description of templates}\n\\label{sec:templates}\n\n\n\\begin{table*}[!htbp]\\caption{{\\bf List of (baseline) spatial templates considered in our maximum likelihood runs. \\label{Tab:templates}}}\n\\begin{adjustbox}{width=1.0\\textwidth, center}\n\\centering\\begin{threeparttable}\n \\scriptsize\n\\begin{tabular}{llr}\n\\hline\\hline\nTemplates  & Summary description & Reference\\\\\\hline \nHadronic and Bremsstrahlung   &  Three alternative models: (i) 3D templates predicted by \\texttt{GALPROP v56}  (``{\\bf GALPROP}'')\n  & \\\\\n$\\gamma$ rays  &  (ii) hydrodynamical gas (``{\\bf HD}''), and (iii) interpolated gas templates (``{\\bf Interpolated}''). & \\\\\n &  These consist of H{\\tiny I},  H\\boldmath$_{2}$, and dust correction column density maps. & \\\\\n&  The H{\\tiny I} and H\\boldmath$_{2}$ maps are divided in four rings each. In the case of the  dust maps,\\\\\n& we use two total residual maps with different $E(B-V)$ magnitude cuts. & ~\\cite{Macias2018, Macias2019}\\\\\n &&\\\\\nInverse Compton  & Used various alternatives models: (i) three kinds of 2D ICS maps; a standard one (``{\\bf 2D A}''),      & \\\\\n$\\gamma$ rays & another that assumes spatially variable diffusion (``{\\bf 2D B}''), and one including a central source  &\\\\\n& of electrons (``{\\bf 2D C}''), (ii) a 3D ICS map$^\\dagger$ divided in four rings (``{\\bf 3D}'')  &  \\cite{Porter:2017vaa,Ackermann:2014usa}\\\\\n&&\\\\\n\\textit{Fermi} bubbles&  (i) Flat\/unstructured FBs template (``{\\bf U}''), and (ii) structured FBs template (``{\\bf S}'') &~\\cite{Macias2019}\\\\\n&&\\\\\nLoop I& Analytical model & \\cite{Wolleben:2007}\\\\\nGalactic centre excess& Stellar distribution model based on Freudenreich 1998 (F98)  & \\cite{Freudenreich1998}\\\\\nPoint sources & 4FGL catalogue of $\\gamma$-ray point sources \n({\\it gll\\textunderscore psc\\textunderscore v20.fit})& \\cite{Fermi-LAT:4FGL}\\\\\nSun and Moon & Models constructed in the 4FGL catalog&\\cite{Fermi-LAT:4FGL} \\\\\nIsotropic emission& \\texttt{iso$_{-}$P8R3$_{-}$ULTRAC.L.EANVETO$_{-}$V2$_{-}$v1.txt}&\\\\\n\\hline\\hline\n\\end{tabular}\n\\begin{tablenotes}\n\\item  The interstellar gas maps are divided in four rings of sizes ($0-3.5$, $3.5-8.0$, $8.0-10.0$, and $10.0-50.0$ kpc). The 3D ICS map are divided in rings of the same size as the gas maps. The 2D ICS maps correspond to ICS (Model A), ICS (Model B), and ICS (Model B) introduced in Ref.~\\cite{Ackermann:2014usa}. The baseline model considered in this work includes: (a) the hydrodynamical gas maps divided in rings, (b) the 3D ICS maps divided divided in rings, (c) the structured FBs template, (d) Loop I, (e) the F98 stellar template, (f) tailor-made maps for the Sun and the Moon, (g) an isotropic emission template, and (h) the 4FGL point sources. Note that in our bin-by-bin analysis procedure, only the normalisation of each template is varied in the fit. Since the energy bins are small, the fit results are independent of the assumed template spectra.  \\end{tablenotes}\n\\end{threeparttable}\n\\end{adjustbox}\n\\end{table*}\n\n\n\n\n\nHere we provide full details for how we construct all the templates that we use in our analysis.\n\n\\subsection{Hadronic plus bremsstrahlung models}\n\\label{sec:GDEdescrip}\n\nAs discussed in Methods, the dominant source of {$\\gamma$-ray} s from the ROI is hadronic and bremsstrahlung emission resulting from the interaction of CR protons and electrons with interstellar gas.\nWe model this component with three alternative templates: HD (hydrodynamic), Interpolated, and 3D (GALPROP); \nof these, the hydrodynamical template provides the best fit to the inner Galaxy {$\\gamma$-ray} \\ sky and is used in our baseline analysis.\n\nIn detail, the models we investigated for the gas-correlated {$\\gamma$-ray} \\ emission are as follows:\n\\begin{itemize}\n    \\item {\\bf Interpolated gas maps}:  these assume that the hadronic and bremsstrahlung components can be phenomenologically modelled with a linear combination of atomic hydrogen, molecular hydrogen, and dust residual maps. These are divided in four Galactocentric rings (four rings of H$_{\\rm I}$, four rings of H$_{2}$, and two residual dust maps---see also Table~\\ref{Tab:templates}) to account for potential uncertainties in the CR densities. The method used to create the interpolated gas maps is given in Appendix B of Ref.~\\cite{Ackermann2012}, which we have faithfully reproduced in~\\cite{Macias2018}. \n    %\n    The main objective of this method is to estimate the gas column density in the direction of the inner Galaxy\n    where the non-axisymmetric gravitational potential of the Galactic bar induces non-circular gas orbits.\n    %\n    Such interpolated gas maps are the standard interstellar gas distribution models employed in most studies by the Fermi team.\n    \n    \\item {\\bf Hydrodynamical gas maps}: these were constructed using a suite of hydrodynamical simulations of interstellar gas flow~\\cite{Pohl2008} that generate physically-motivated solutions for the gas kinematics in the direction of the inner Galaxy.  \n    The hydrodynamical gas maps provide a much better fit to the Galactic centre data than the interpolated gas maps\\cite{Macias2018}. Nevertheless, the main purpose of using alternative gas models in our study is evaluating the impact that these have in the inferred properties of the Sgr dSph. We note that the hydrodynamical maps are divided in the same ring scheme (four rings of H$_{\\rm I}$, four rings of H$_{2}$, and two residual dust maps) as the interpolated gas maps.\n    \n    \n    \\item {\\bf 3D gas (GALPROP)}: to generate alternative templates for the hadronic and bremsstrahlung gamma-ray emission, we reproduced one of the models proposed in Ref.~\\cite{Johannesson:2018bit} (Model SA50 in Table 5 of that reference) using \\texttt{GALPROP V56}~\\cite{Porter:2017vaa,Johannesson:2018bit}. The latest release of this software contains new 3D spatial density models of atomic and molecular hydrogen. These include the effects of several Galactic structures such as the spiral arms, and the Galactic disk. Note that in this case, we do not divide the resulting hadronic and bremsstrahlung maps in rings so that we are able to explore the effects that a less flexible Galactic diffuse emission model has in our results. \n\\end{itemize}\n\nFor the IC background component, we again generated and tested alternative maps, in particular, 2D and 3D variants.\nUncertainties in the IC component become more important in the high latitude regions \\cite{Ackermann:2014usa}. \n\nIn detail, models we investigated for diffuse IC emission are:\n\\begin{itemize}\n    \\item {\\bf 3D IC} maps divided in four rings: for these we utilized \\texttt{GALPROP~V56}, the propagation parameter setup  SA50 (see Table 5 in Ref.~\\cite{Johannesson:2018bit}), and the same ring subdivisions as those of the interstellar gas maps (see Table~\\ref{Tab:templates}). The advantage of the new 3D IC maps (over the ones constructed with previous versions of the code), is that it now incorporates fully 3D models for the interstellar radiation fields (ISRF)~\\cite{Porter:2017vaa}; hence avoiding potential biases introduced by the previously implicitly-assumed Galactocentric symmetry. Also, since the 3D IC maps can be divided in rings, we are able to reduce the impact of modelling assumptions such as the characteristics of the electron injection spectrum, and the normalisation of the ISRF.\n    \n    \\item {\\bf 2D IC} maps: we used the three different  IC maps constructed in Ref.~\\cite{Ackermann:2014usa} (Model A, B, and C). These were computed with an older version of the CR propagation code (\\texttt{GALPROP V54}), assume Galactocentric symmetry of the CR halo, and are monolithic (i.e., not divided in rings). These models encapsulate a wide range of uncertainties in the CR source distribution, CR injection spectra, the diffusion coefficient, Galactic magnetic fields, and a central source of electrons.\n\\end{itemize}\n\\end{comment}\n\n\n\\section{Construction of the Sgr dSph templates}\n\\label{sec:stellarmapsDetails}\n\nHere we provide detailed descriptions of \nhow we construct the Sgr dSph templates shown in E.D.~\\autoref{fig:Stellartemplates}.\n\n\\subsubsection*{Model I:} \n\nWe extract this template from the stellar catalogue constructed in Ref.~\\cite{Vasiliev2020}, which was derived using photometric and astrometric data from {\\it Gaia} Data Release 2 (DR2), and kinematic measurements from various other surveys. The catalogue consists of a list of $2.26\\times 10^5$ candidate member stars of the {Sgr~dSph~} remnant, which are reliably separated from the field stars. Every object in the catalogue has an extinction-corrected G-band magnitude larger than 18, and more than half of the objects in this catalogue are classified as red clump stars. Note that Ref.~\\cite{Vasiliev2020} adapted their procedure to reproduce the observed properties of the {Sgr~dSph~} remnant, not the stream, which is why the first panel of E.D.~\\autoref{fig:Stellartemplates} only shows the remnant. We show profiles of stellar number count along the long and short axes of the dwarf for this template in S.I.~\\autoref{fig:profile_longaxis}. \n\n\\begin{figure*}[t!]\n    \\centering\n    \\includegraphics[scale=0.15]{Long_axis_star_profile.pdf}\n    \\includegraphics[scale=0.15]{Short_axis_star_profile.pdf}\n    \\caption{Star count profiles for Model I, showing number of stars measured in bins of angular distance from the gravitational centre of the dwarf along its long (top) and short (bottom) axes. In the inset images (which are identical to the first panel of \\autoref{fig:Stellartemplates}), we mark the gravitational centre of the dwarf with a cyan circle, and show the long and short axes along which we measure the profiles as white bands.}\n    \\label{fig:profile_longaxis}\n\\end{figure*}\n\n\n\\subsubsection*{Model II:}\n\nOur second template comes from ref.~\\cite{Ibataetal:2020}. Instead of red clump stars, this study selected a sample of RR Lyrae stars from {\\it Gaia} DR2 data, for which distances are accurately measured. Also, rather than focusing on member stars of the {Sgr~dSph~} remnant, Ref.~\\cite{Ibataetal:2020} used the \\textsc{streamfinder} algorithm to single out stars with high probability of belonging to the Sagittarius Stream. By using the kinematic properties of the stars in that study, we constructed a template containing 2369 RR Lyrae stars (cf. \\autoref{fig:Stellartemplates}) in our ROI. Note that the stellar number count in this map is approximately two orders of magnitude smaller than that in Model I.   \n\n\\subsubsection*{Model III:}\n\nRef.~\\cite{Iorio2019} performed an all-sky analysis of RR Lyrae stars  (in {\\it Gaia} DR2 data) belonging to globular clusters, dwarf spheroidal galaxies, streams, and the Magellanic Clouds. Our Model III template is a subset of their data identified as belonging to the Sgr dSph, selected to reproduce their Fig.~1 (bottom-right). It includes $1.31\\times 10^4$ RR Lyrae stars in our ROI. \n\n\\subsubsection*{Model IV and Model V:}\n\nRef.~\\cite{Ramosetal:2020} developed two empirical catalogues of RR Lyrae stars in {\\it Gaia} DR2 data, which form the basis for our final two templates. The first (Model IV), corresponds to the nGC3 sample, which is characterized for its lower-completeness and higher-purity. This template contains 675 stars in our ROI. The second (Model V), is the Strip sample, containing higher-completeness, but lower purity. The total number of stars in our ROI for this model is 4812.\n\n\n\n\n\n\n\\section{Validation tests}\n\\label{ssec:validation}\n\n\nWhile our template analysis indicates a strong statistical preference for emission tracing the Sgr dSph, we also carry out five further validation tests to check the robustness of the result.\n\nFirst, we check whether the residuals between the baseline + {Sgr~dSph~} source model and the {\\it Fermi} data from our ROI are consistent with the level expected simply as a result of photon counting statistics, using a method similar to that of Ref.~\\cite{Buschmann2020}. Under the null hypothesis that the {\\it Fermi} data are a Poisson draw from our best-fit baseline + {Sgr~dSph~} model (i.e., that our model is correct, and any differences between it and the actual data are simply due to shot noise), we can determine the expected distribution of $\\ln\\mathcal{L}_n$ values via Monte Carlo. For each Monte Carlo trial, we draw a set of mock photon counts $\\Phi_{n,i,\\rm mock}$ in each pixel and energy bin from our best-fitting model (multiplied by the instrument response function), and then compute the energy-dependent log-likelihood for this mock data set using the same pipeline we use on the real data. We repeat this procedure 100 times, and plot the distribution of log-likelihood values it produces \nas the blue histograms\nin E.D. \\autoref{fig:fitvalidation}. These\nhistograms represent the expected log likelihood in each energy bin under the null hypothesis. We then compare this to the actual value of $\\ln\\mathcal{L}_n$ we measure for our model as compared to the real \\textit{Fermi} data. The plot shows that our measured log-likelihood falls squarely within the range expected under the null hypothesis, and we therefore conclude that the residuals between our model and the real data are consistent with being solely the result of photon counting statistics. \n\nIn addition to testing whether the residuals between model and data are consistent with simply being shot noise when we sum over all pixels (which is what the likelihood measures), we can also examine the residuals as a function of position. We do so in E.D.~\\autoref{fig:Residuals}, which shows the measured \\textit{Fermi} counts in our ROI (summed in three energy bins) in the first column, our best-fitting baseline + {Sgr~dSph~} model in the second column, and fractional residuals [$(\\rm{Data}-\\rm{Model})\/\\rm{Model}$] in the third column. The images are smoothed with a $0.5^\\circ$ Gaussian kernel, since this is roughly the resolution of our interstellar gas maps~\\cite{Macias2018,Macias2019}. The plot shows that, on a point-by-point basis, our models reproduce the data within $\\sim 10\\%$ over most of the ROI. \nThere are, however, a few small patches of correlated residuals, which are only at the $\\sim 30\\%$ level, and are far from the Sgr dSph region. \nThis points to the existence of real structure in the Fermi Bubbles that is not yet perfectly modelled, but given the small level of the residuals and the distance between them and the signal in which we are interested, this modelling imperfection has little impact on our results.\n\n\n\n\n\nAs our second validation test, we evaluate the sensitivity of our pipeline to uncertainties in our templates for Galactic diffuse emission, and we verify that our pipeline can recover synthetic signals similar to the Sgr dSph even when our templates are imperfect. Recall that we have three components of Galactic diffuse emission for which the templates are at least somewhat uncertain: hadronic + bremsstrahlung emission (for which our template can be HD, Interpolated, or GALPROP), Galactic IC emission (for which the template can be 3D, 2D A, 2D B, or 2D C), and the Fermi Bubbles (for which the template can be S, structured, or U, unstructured). \nWe test the sensitivity of our fits to these template choices as follows. First, we generate a set of mock background data by drawing a random realisation of photon counts from one combination of these templates, and on top of this we add a synthetic Sgr dSph signal; the Sgr dSph photons follow the spatial morphology of our Sgr dSph model I template, have a spectral shape $dN_\\gamma\/dE_\\gamma \\propto E_\\gamma^{-2}$, and have a normalisation that we vary systematically from $\\approx 10^{-11}$ ph cm$^{-2}$ s$^{-1}$ (integrated over all energies) to $\\approx 10^{-5}$ ph cm$^{-2}$ s$^{-1}$; our best-fit Sgr dSph photon flux falls in the middle of this range, $\\approx 2\\times 10^{-8}$ ph cm$^{-2}$ s$^{-1}$. Then we use our pipeline to recover the flux of the Sgr dSph from the synthetic map, but using a \\textit{different} set of templates for Galactic diffuse emission to the ones used to generate the synthetic data. Comparing the recovered Sgr dSph spectrum to the injected one reveals how well our pipeline performs when the input diffuse emission templates are not exactly correct. We carry out this experiment with four diffuse emission template combinations: (1) synthetic data generated from GALPROP + 3D + S, analysed using HD + 3D + S; (2) synthetic data generated from HD + 2D A + S, analysed using HD + 3D + S; (3) synthetic data generated from HD + 3D + S, analysed using HD + 3D + U; (4) synthetic data generated using HD + 3D + S, analysed using HD + 3D but no template for the FBs at all.\n\nWe show the results for the first two of these experiments in the two left panels of E.~D.~\\autoref{fig:injectionrecovery}; the top left panel shows the recovered energy-integrated photon flux compared to the injected flux, while the bottom left shows the recovered spectra when the input flux is $\\approx 2 \\times 10^{-8}$ ph cm$^{-2}$ s$^{-1}$. The plot shows that our pipeline yields excellent agreement between the injected and recovered signals for both the integrated flux and the spectrum unless the Sgr dSph signal is $\\sim 1$ order of magnitude weaker than our estimate. In no circumstance does our pipeline produce a false signal comparable in magnitude to our observed one. The two right panels of E.~D.~\\autoref{fig:injectionrecovery} show the third and fourth tests, where we mismatch the FB template. Here the effects are somewhat larger, but still relatively minor: if we create synthetic data with the S Fermi Bubble template (so that there is structure corresponding to the cocoon), and then analyse it using either the U template or no FB template at all, then we make a factor of $\\sim 2-3$ level error in the absolute flux, but no substantial error in the spectral shape. This test suggests that our detection of the Sgr dSph is very robust, but that we have a factor of $\\sim 2-3$ uncertainty in its absolute flux, stemming from our imperfect knowledge of the foreground FBs.\n\n\n\n\nThe third validation test we perform is to check whether a fit using the observed stellar distribution of the Sgr dSph as a template performs better than one using a purely geometric template placed at the same position; if the emission really is tracing the stars of the dwarf, and is not merely a chance overlap, a template matching the shape of the dwarf should perform better than a purely geometric distribution. For this purpose we consider disc-shaped templates of varying radii, centred at Galactic coordinates $(\\ell,b)=(5.61^\\circ, -14.09^\\circ)$ --- the dynamical centre of the Sgr dSph -- and repeat our standard procedure of comparing baseline models to baseline + Sgr dSph models, using these geometric templates in place of the Sgr dSph stellar templates. We use our fiducial choices for all other templates (hadronic and bremmstrahlung emission, galactic IC emission, and the Fermi Bubbles).\n\nWe show the results of this experiment in S.I.~\\autoref{tab:geometric_templates}. We find that geometric templates do perform better than baseline models with no Sgr dSph component, but, as expected, even the best geometric template (for a disc of radius $r=2.0^\\circ$) yields significantly less fit improvement ($TS=63.8$) than our fiducial stellar template ($TS=95.2$); this difference in test statistic, $\\Delta\\, TS = 31.4$, corresponds to the Sgr dSph template being preferred at $3.7\\sigma$ significance. Moreover, this result becomes even stronger if we notice two additional points. First, because we tried a wide range of radii for the geometric models, the geometric templates effectively provide an extra degree of freedom that the Sgr dSph template, which is fixed by observations, lacks. Because we fix the template radius while performing each fit, we do not treat the varying radius as an extra degree of freedom when computing the test statistic, but if we did so, then the difference in performance between the geometric and stellar templates would be even larger. Second, the geometric model that gives the best fit to the data is in fact the one whose radius most closely approximates the actual size of the core of the Sgr dSph. Indeed, Fig.~\\ref{fig:profile_longaxis} (bottom) shows that, in the direction of the short axis, the Sgr dSph stellar profile falls off steeply $\\sim 2^\\circ-3^\\circ$ away from the Sgr dSph centre. Thus the geometric template that gives the best match to the observations happens to be the one that most closely approximates the actual distribution of stars in the Sgr dSph.\n\n\\begin{table}[h!]\n    \\centering\n    \\small\n    \\begin{tabular}{llll@{\\qquad\\qquad}rrrr}\n    \\hline\\hline\n    \\multicolumn{4}{c}{Template choices} & \\multicolumn{4}{c}{Results} \\\\\n    Hadr. \/ Bremss. & IC & FB & Sgr dSph &\n    $-\\log(\\mathcal{L}_{\\rm Base})$  & $-\\log(\\mathcal{L}_{{\\rm Base}+{\\rm  Sgr}})$  &  $\\mbox{TS}_{\\rm Source}$& Significance \\\\[0.5ex] \\hline \n    \\multicolumn{8}{c}{Default model} \\\\[0.5ex]\n    HD & 3D & S & Model I & 866680.6 &866633.0  & 95.2  &  $8.1\\;\\sigma$\n    \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=0.5^\\circ$) & 866680.6 & 866666.1  & 28.9  &  $3.5\\;\\sigma$\n    \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=1.0^\\circ$) & 866680.6 & 866661.3 & 38.6  &  $4.4\\;\\sigma$\n    \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=2.0^\\circ$) & 866680.6 & 866648.7 & 63.8  &  $6.3\\;\\sigma$\n    \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=3.0^\\circ$) & 866680.6 & 866654.9  &  51.4   &  $5.4\\;\\sigma$\n    \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=4.0^\\circ$) & 866680.6 & 866658.1  & 45.0  &  $4.9\\;\\sigma$\n    \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=5.0^\\circ$) & 866680.6 &  866661.3 & 38.6 &  $4.4\\;\\sigma$\n    \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=6.0^\\circ$) & 866680.6 & 866669.3 & 22.7  &  $2.8\\;\\sigma$\n    \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=7.0^\\circ$) & 866680.6 & 866670.4 & 20.4  &  $2.6\\;\\sigma$\n    \\\\[0.5ex]\n   \n    HD & 3D & S & Disc ($r=9.0^\\circ$) & 866680.6 & 866664.9 & 31.4  &  $3.7\\;\\sigma$ \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=11.0^\\circ$) & 866680.6 & 866665.8 & 29.6  &  $3.6\\;\\sigma$ \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=13.0^\\circ$) & 866680.6 & 866673.0 & 15.2  &  $1.9\\;\\sigma$ \\\\[0.5ex]\n    HD & 3D & S & Disc ($r=15.0^\\circ$) & 866680.6 & 866676.5 & 8.3  &  $0.9\\;\\sigma$ \\\\[0.5ex]\n    \\hline\\hline\n    \\end{tabular}\n    \\caption{Same as \\autoref{tab:loglikelihood} in the main letter, except that here we compare the results for our fiducial stellar template for the Sgr dSph (Model I, top row) to results using disc templates of various angular radii centred at the dynamical centre of the Sgr dSph. }\n    \\label{tab:geometric_templates}\n\\end{table}\n\n\nOur \nfourth\nvalidation test is to check whether our fit degrades if we artificially rotate or translate the Sgr dSph template; if the signal we are detecting really does come from the Sgr dSph, the best fit should be for a template that traces its actual orientation and position, while rotated or shifted templates should produce progressively worse fits. This check is significant in part because Ref.~\\cite{Ackermann2014} performed similar rotation analysis for the hypothesis that the cocoon is tracing a jet from Sgr A$^*$, and found that there was no preference for a jet oriented toward Sgr A$^*$ over one oriented in some other way; they took this as evidence against the jet hypothesis. To check if the Sgr dSph template performs better on this test, we first rerun our analysis pipeline for our default set of templates (first line in \\autoref{tab:loglikelihood}), but with the Sgr dSph template rotated about its core. For each rotation angle we compute the TS, and compare to the TS of the original, unrotated model. We plot the result of this experiment in the left panel of E.D.~\\autoref{fig:rotationAndTranslationTests}. It is clear that, as expected, the fit is best when we use the actual orientation of the Sgr dSph, and degrades as we increase the rotation. Next, we carry out a similar procedure, but this time rather than rotating the Sgr dSph template about its core, we rotate around the centre of the Galaxy, thereby both translating and rotating the template. (This latter test was motivated by the particular alignment of the Sgr Stream with the previously claimed collimated jets from the Galaxy's supermassive black hole~\\cite{Su2012}.) We show the results in the middle panel of E.D.~\\autoref{fig:rotationAndTranslationTests}, and, again as expected, the TS strongly favours the true location and orientation of the Sgr dSph. Finally, we translate the Sgr dSph while leaving its orientation unchanged. We show the TS for displaced Sgr dSph in the right panel of E.D.~\\autoref{fig:rotationAndTranslationTests}. In this case the fit improves if we do displace the Sgr dSph from its true position by $\\approx 4^\\circ$ south. The amount by which the shift is favoured is fairly significant -- the TS improved by 40.8, which corresponds to $4.5\\sigma$ significance. Interestingly, the direction of the displacement is within a few degrees of the direction anti-parallel to the Sgr dSph's proper motion, suggesting that the dwarf's $\\gamma$-ray signal trails it slightly on its orbit.\nIf IC-emitting CR {$e^\\pm$} \\ are largely responsible for the observed {Sgr~dSph~} {$\\gamma$-ray} \\ signal as suggested by our spectral modelling, a systematic displacement of this signal southward by $\\sim 4^\\circ$ from the stars of {Sgr~dSph~} is quite reasonable as we have explained elsewhere (and see \\autoref{sec:CRtrans}).\n\n\n\n\n\n\n\\section{Transport of IC-emitting CR $e^\\pm$}\n\\label{sec:CRtrans}\n\nWe have seen that, while our pipeline detects a signal from the Sgr dSph at very high statistical significance, the fit improves even more (by $\\approx 4.5\\sigma$) if we displace the Sgr dSph template $\\approx 4^\\circ$ from its actual position (corresponding to 1.9 kpc at the distance of the Sgr dSph), in a direction very close to anti-parallel to the dwarf's proper motion. Here we demonstrate that a displacement of this type is expected in a model where the $\\gamma$-ray signal from the Sgr dSph is powered by MSPs. Part of the MSP signal emerges directly from the MSP magnetospheres, and thus traces the stellar component of the Sgr dSph. However, the majority of the observed signal is, in our model, IC emission powered by {$e^\\pm$}~escaping MSP magnetospheres and interacting with the CMB. The time between when {$e^\\pm$}~leave MSPs and when they IC scatter to produce $\\gamma$-ray photons is non-negligible: the CMB is dominated by photons with energies $\\sim k_{\\rm B}T_{\\rm CMB}$ (with $T_{\\rm CMB}=2.7$ K), so IC photons with energies of $\\sim 1-100$ GeV must be produced by {$e^\\pm$}~with energies $E_{e^\\pm} \\sim 0.6-6$ TeV. The characteristic IC loss time for such particles is\n\\begin{equation}\n    t_{\\rm IC} = \\frac{3 m_e^2 c^3}{4 \\sigma_{\\rm T} E_{e^\\pm} U_{\\rm CMB}} = 1.2\\left(\\frac{E_{e^\\pm}}{\\mbox{TeV}}\\right)^{-1}\\mbox{ Myr},\n\\end{equation}\nwhere $m_e$ is the electron mass, $c$ is the speed of light, $\\sigma_{\\rm T}$ is the Thomson cross section, and $U_{\\rm CMB} = a_R T_{\\rm CMB}^4 = 0.25$ eV cm$^{-3}$ is the energy density of the CMB.\n\nDuring this time, the {$e^\\pm$}~will have the opportunity to move a significant distance prior to producing $\\gamma$-rays, due to both bulk gas motion and CR flow relative to the gas. \nWith regard to bulk advection, we note that the proper speed of the {Sgr~dSph~} is $\\approx 260$ km s$^{-1}$, and we therefore expect an effective wind of Galactic halo gas to be blowing through (or, at least, around) the dwarf at approximately this speed.\nThis wind would advect the IC-radiating {$e^\\pm$} \\ southward.\nQuantitatively, the extent of the angular displacement of an IC {$\\gamma$-ray} \\ signal at $E_\\gamma$\n\\begin{equation}\n    \\Delta \\theta_{\\rm adv}(E_\\gamma) \\simeq 1.0^\\circ \\left(\\frac{E_\\gamma}{\\rm GeV}\\right)^{-1} \n    \\left(\\frac{v_{\\rm prop}}{\\rm 260 \\ km\/s}\\right)\n\\end{equation}\nwhere $v_{\\rm prop}$ is the proper motion on the sky.\nThus advection is expected to generate a \nsouthward displacement of $\\sim 1^\\circ$.\n\n\nThis is less than the displacement we observe, but advection is also likely less important than CR transport through the gas. While the diffusion coefficient for CRs in the galactic halo is very poorly known, we can make an order of magnitude estimate by adopting\nthe functional form for the diffusion coefficient given in ref~\\cite{Gabici2007} which is normalised to $3 \\times 10^{27}$ cm$^2$ s$^{-1}$ for a 1 GeV CR in a 3 $\\mu$G field. Then the expected diffusive displacement of the IC-radiating {$e^\\pm$}~is\n\\begin{equation}\n    \\Delta \\theta_{\\rm diff}(E_\\gamma) \\simeq 3.5^\\circ \\left(\\frac{E_\\gamma}{\\rm GeV}\\right)^{-0.12} \n    \\left(\\frac{B}{\\rm 0.1 \\ \\mu G}\\right)^{-0.27} .\n\\end{equation}\nWhile this is roughly the correct amount of displacement to reproduce what we observe, if the diffusion were isotropic then we would still not have explained the systematic offset between the dwarf and the displaced location picked out by our template analysis. However, we do not expect isotropic diffusion in the environment of the Sgr dSph. Simulations of objects plunging through diffuse halo gas indicate that a generic outcome of such interactions is the development of a coherent magneto-tail back along the objects' direction of motion \\cite{Dursi2008}. Such a structure formed by the Sgr dSph plunging through the Milky Way's halo would naturally explain why, rather than being isotropic, the diffusive transport is primarily backwards along the dwarf's trajectory.\n\n\n\\section{Energetics of the Sgr dSph MSP population}\n\\label{ssec:energetics}\n\n\nAs discussed in the main text, \nthe {$\\gamma$-ray} \\ luminosity per stellar mass we measure for the {Sgr~dSph~} \\ is substantially brighter than we measure for the Galactic Bulge, Galactic disk, or M31, but is substantially dimmer than is observed for globular clusters.\nIndeed, in \\autoref{fig:LgammaOvrMstar}, {Sgr~dSph~} \\ appears as a transition object between gas-poor, low metallicity, low star formation rate, and relatively low stellar mass systems on the left side and relatively gas rich and massive systems (some with appreciable star formation) on the right side.\nIn order to investigate more deeply how the $\\gamma$-ray luminosity of the Sgr dSph compares to that of other observed systems, and to theoretical expectations, in \\autoref{fig:plotLgammaOvrMstarVstSimple} we collect measurements of $\\gamma$-ray luminosity per unit stellar mass versus approximate age for a range of observed systems, and compare these measurements to model predictions. For the observed systems we include M31, the Milky Way bulge and nuclear bulge, the mean of Milky Way globular clusters, and the Milky Way disc; for the latter we have included both the $\\gamma$-ray emission directly measured from MSPs, and the observed {$e^\\pm$}~luminosity of the disc, which may include a significant MSP contribution. As in \\autoref{fig:LgammaOvrMstar}, we see that the Sgr dSph is intermediate between the metal-rich galactic systems -- M31, the Milky Way disc and bulge -- and the globular clusters (GCs). However, the figure also reveals a clear trend that galactic systems dim as a function of age, with Sgr dSph as both the youngest and the most luminous of the galactic systems.\n\n\nThe trend with age is consistent with theoretical expectations, indicated by the blue band in \\autoref{fig:plotLgammaOvrMstarVstSimple} which shows the prediction of a binary population synthesis (BPS) model \\cite{Gautam2021} for the total spin-down power per unit stellar mass liberated by magnetic braking of MSPs. Some of this power should emerge as prompt emission, and some as {$e^\\pm$} \\ injected into the ISM; the lower dashed blue line shows 10\\% of the total spin-down power, a rough estimate for the prompt component. In this particular calculation, the MSPs derive from Accretion Induced Collapse, the population is assumed to be of Solar metallicity, and each binary evolves independently (i.e., the `field star' limit is assumed). Based on the predictions of this model, and the estimated age of the Sgr dSph, we estimate that the $\\gamma$-ray signal we have detected can be explained by the presence of $\\approx 650$ MSPs in the galaxy. Given that the overall {$\\gamma$-ray} \\ luminosity of an MSP population is bounded by the spin-down power, it is evident from the figure that the expected energetics appear to be elegantly sufficient to power the signal from {Sgr~dSph~} \\ given the (relatively young) mean age of its stars; this age difference naturally explains why the Sgr dSph should be more luminous per unit mass than M31 or components of the Milky Way.\n\n\nIt is also noteworthy that the GCs are considerably more luminous per unit mass than both the BPS model and the Sgr dSph. The extremely high brightness of GCs is plausibly explained by some combination of dynamical effects, which lead to dynamical hardening of binaries and thence a higher production rate of MSPs, and metallicity effects, which lead to higher MSP production because metal-poor stars have weaker winds and thus experience less mass loss during their main sequence lifetimes than Solar-metallicity stars \\cite{Ruiter2019}. The former effect would not occur in the Sgr dSph, but the latter would, since the Sgr dSph has a metallicity $\\log_{10}(Z_{\\rm Sgr}\/Z_\\odot) \\simeq -0.9$ \\cite{Vasiliev2020}, where $Z_\\odot$ is the solar metallicity, which is comparable to typical GC metallicities.\n\n\n\n\nThe final comparison we show in \\autoref{fig:plotLgammaOvrMstarVstSimple} is with the MSP power inferred by Sudoh et al.\\cite{Sudoh2020} in massive, quiescent galaxies ($M_*>10^{9.5}$ M$_\\odot$, star formation rate $< 0.1$ M$_\\odot$ yr$^{-1}$). Such galaxies typically have stellar population ages $\\gtrsim 8-10$ Gyr \\cite{McDermid2015,Pacifici2016,Sudoh2020}, and Sudoh et al.~show that they produce anomalously-large synchrotron emission, which they attribute to radiation from {$e^\\pm$} \\ injected by MSPs; they infer an injection power $1.8\\times 10^{28}$ erg$\/$s$\/M_{\\odot}$, which we show as the brown dashed line in \\autoref{fig:plotLgammaOvrMstarVstSimple}. We see that this estimate is consistent both with the BPS model and comparable to the luminosity we infer for the Sgr dSph.\n\n\nOur overall conclusion is that the MSP luminosity we have derived for the Sgr dSph is fully consistent with both theoretical expectations and with a wide variety of observed systems. The Sgr dSph is more luminous per unit mass than the Milky Way or M31, but this is easily explained by its youth and low metallicity, and it is comparably- or less-luminous than other observed systems that are of comparable age or metallicity.\n\n\n\n\n\\section{Astrophysical {$\\gamma$-ray} \\ emission from other dSphs}\n\nOn the basis of the normalisation ($L_{\\gamma}\/M_\\star$) supplied by the Sgr dSph $\\gamma$-ray detection, we can make \nrough predictions for the astrophysical $\\gamma$-ray fluxes from a number of other dSph systems, simply by assuming this normalisation applies to them as well; future work should be based on full theoretical models including metallicity and age effects, but the simple calculation we present here can serve as a guide to the system for which such investigations are likely to be fruitful.\nOur predictions can, in turn, be compared to i) actual observational upper limits to the {$\\gamma$-ray} \\ fluxes from these dSphs  and ii) (model-dependent) predictions for the (WIMP) dark-matter-driven {$\\gamma$-ray} \\ fluxes from the same satellite galaxies. For this purpose we use the data assembled in Winter et al.~\\cite{Winter2016} for the distances, stellar masses, \nand MSP- and DM-driven fluxes for a population of 30 dSphs satellites of the Milky Way. These authors derive their MSP fluxes by extrapolating the $\\gamma$-ray luminosity function of resolved Milky Way MSPs; their result implies that at energies above 500 GeV, galaxies should produce an MSP photon flux per unit stellar mass of $\\approx 6.3\\times 10^{29}$ s$^{-1}$ M$_\\odot^{-1}$, roughly a factor of 40 smaller than the $\\approx 2.5\\times 10^{31}$ s$^{-1}$ M$_\\odot^{-1}$ we detect for the Sgr dSph. We report our revised estimates dwarf spheroidals' MSP luminosity in S.I.~\\autoref{tab:dsph_fluxes}. This finding has two implications, which we explore below: first, for some dwarfs this brings the predicted {$\\gamma$-ray}~flux close to current observational upper limits, suggesting that a more detailed analysis of \\textit{Fermi}-LAT data might yield a detection. Second, in some dSph galaxies, the predicted MSP flux is comparable to or exceeds the {$\\gamma$-ray}~fluxes that might be expected from dark matter annihilation.\n\n\n\n\\begin{table}\n\\begin{tabular}{lcc}\n\\hline\nGalaxy name & Predicted MSP flux & Predicted DM flux \\\\\n& (cm$^{-2}$ s$^{-1}$) & (cm$^{-2}$ s$^{-1}$) \\\\\n\\hline\nFornax & $2.38\\times 10^{-10}$ & $2.06\\times 10^{-11}$ \\\\\nSculptor & $1.10\\times 10^{-10}$ & $5.18\\times 10^{-11}$ \\\\\nSextans & $1.96\\times 10^{-11}$ & $3.27\\times 10^{-11}$ \\\\\nUrsa Minor & $1.95\\times 10^{-11}$ & $8.20\\times 10^{-11}$ \\\\\nLeo I & $1.59\\times 10^{-11}$ & $6.52\\times 10^{-12}$ \\\\\nDraco & $1.18\\times 10^{-11}$ & $8.20\\times 10^{-11}$ \\\\\nCarina & $8.12\\times 10^{-12}$ & $1.64\\times 10^{-11}$ \\\\\nLeo II & $4.54\\times 10^{-12}$ & $5.18\\times 10^{-12}$ \\\\\nBootes I & $1.36\\times 10^{-12}$ & $2.06\\times 10^{-11}$ \\\\\nCanes Ven. I & $1.33\\times 10^{-12}$ & $6.52\\times 10^{-12}$ \\\\\nUrsa Major II & $1.10\\times 10^{-12}$ & $2.59\\times 10^{-10}$ \\\\\nReticulum II & $5.27\\times 10^{-13}$ & $2.59\\times 10^{-10}$ \\\\\nComa Ber. & $5.19\\times 10^{-13}$ & $1.30\\times 10^{-10}$ \\\\\nHercules & $4.48\\times 10^{-13}$ & $1.64\\times 10^{-11}$ \\\\\nUrsa Major I & $4.25\\times 10^{-13}$ & $2.59\\times 10^{-11}$ \\\\\nTucana III & $2.67\\times 10^{-13}$ & $2.59\\times 10^{-10}$ \\\\\nGrus II & $2.53\\times 10^{-13}$ & $6.52\\times 10^{-11}$ \\\\\nTucana IV & $1.99\\times 10^{-13}$ & $6.52\\times 10^{-11}$ \\\\\nTucana II & $1.88\\times 10^{-13}$ & $8.20\\times 10^{-11}$ \\\\\nEridanus II & $1.60\\times 10^{-13}$ & $2.59\\times 10^{-12}$ \\\\\nWillman I & $1.45\\times 10^{-13}$ & $1.64\\times 10^{-10}$ \\\\\nSegue 1 & $1.34\\times 10^{-13}$ & $4.11\\times 10^{-10}$ \\\\\nLeo IV & $7.53\\times 10^{-14}$ & $1.03\\times 10^{-11}$ \\\\\nHorologium I & $6.65\\times 10^{-14}$ & $3.27\\times 10^{-11}$ \\\\\nPhoenix II & $6.55\\times 10^{-14}$ & $3.27\\times 10^{-11}$ \\\\\nCanes Ven. II & $6.51\\times 10^{-14}$ & $1.03\\times 10^{-11}$ \\\\\nReticulum III & $4.95\\times 10^{-14}$ & $2.06\\times 10^{-11}$ \\\\\nColumba I & $3.91\\times 10^{-14}$ & $5.18\\times 10^{-12}$ \\\\\nIndus I & $3.50\\times 10^{-14}$ & $2.59\\times 10^{-11}$ \\\\\nIndus II & $2.24\\times 10^{-14}$ & $3.27\\times 10^{-12}$ \\\\\n\\hline\n\\end{tabular}\n\\caption{\n\\label{tab:dsph_fluxes}\nPredicted MSP photon and dark matter annihilation photon fluxes at energies $E_\\gamma > 500$ MeV from nearby dSph galaxies, taken from the sample of ref.~\\cite{Winter2016}. Column 1: galaxy name; column 2: predicted MSP photon flux based on the Sgr dSph (see SI for details); column 3: DM annihalation flux predicted by ref.~\\cite{Winter2016}.\n}\n\\end{table}\n\n\n\n\n\n\n\n\\subsection{omparison with existing upper bounds}\n\n\n\nTo estimate whether other dwarf spheroidals might be detectable, we compare our differential flux predictions (incorporating both prompt and IC emission where, for simplicity, we make the approximation that the CMB-dominated ISRF of the {Sgr~dSph~} \\ also pertains in each other dSph under consideration)\nagainst the results from ref.~\\cite{Mazziotta2012}\\footnote{This is the most recent publication we can find that explicitly tabulates bin-by-bin, numerical 95\\% confidence upper limits on the differential flux received by a number of dSphs that also appear in the compilation of ref.~\\cite{Winter2016}}. On the basis of this comparison, we do not predict {$\\gamma$-ray} \\ emission from any dSph that surpasses the upper limits from ref.~\\cite{Mazziotta2012}. However two dSphs reach a significant fraction of the relevant upper limit in at least one energy bin (of width $log_{10}(\\Delta E$\/GeV) = 0.5): Fornax (which reaches 0.24 of the upper limit for the energy bin centred at 1.36 GeV) and Sculptor (which reaches 0.09 of the upper limit for the energy bin centred at 2.46 GeV). Furthermore, the results of ref.~\\cite{Mazziotta2012} were obtained using Pass7 {{\\em Fermi}-LAT} \\ data accumulated over only the first 3 years of {{\\em Fermi}-LAT} \\ operation. On the basis of, e.g., the results of ref.~\\cite{Ackermann2015} we expect that updated upper limits (Pass8, 15 years data) should be at least a factor of 4 more stringent. This makes Fornax and Sculptor both very interesting targets for a future study, though we remind the reader that our predictions are predicated on a normalisation obtained from the {Sgr~dSph~} \\ detection that may be somewhat over-optimistic because it ignores the stellar age effects evidenced in \\autoref{fig:plotLgammaOvrMstarVstSimple}\\footnote{The stellar population of Sculptor, in particular, is significantly older \\cite{Bettinelli2019} than that of Sagittarius, giving the MSP population more time to have spun down, though Fornax, on the other, has experienced some significant and relatively recent star formation \\cite{Rusakov2021}, like Sagittarius, qualifying it as a particularly compelling target for {$\\gamma$-ray} \\ observation.}. After these two, the brightest expected  dSphs are Sextans, Ursa Minor, Leo I, and Draco. These may also be interesting targets, though we note that we expect that they are almost one order of magnitude dimmer than Fornax and Sculptor.\n\n\n\\subsection{Comparison with predicted DM annihilation fluxes}\n\n\nWinter et al.\\cite{Winter2016} estimate DM annihilation fluxes for nearby dSphs using a DM annihilation cross section derived by assuming that the the Galactic Centre Excess (GCE) is a DM signal. We caution that this is likely only an upper limit, since of course our finding for the Sgr dSph suggests that some or all of the GCE is in fact due to MSPs (see also ref.~\\cite{Gautam2021}). Nonetheless, we proceed with our calculation using the Winter et al.~estimate precisely because it represents an upper limit on the DM signal. Comparing the MSP and DM signals estimated in S.I.~\\autoref{tab:dsph_fluxes} leads us to the important finding that, in contrast to the results obtained by Winter et al., there are three dSphs for which the MSP-driven $> 500$ MeV photon number flux exceeds the predicted DM flux (viz., Fornax by $\\sim$12; Leo I by $\\sim$2.4; and Sculptor by $\\sim$2.1) and three more where it exceeds $\\sim 1\/2$ the DM flux (viz., Leo \\\nII with 0.89; Sextans with 0.60; and Carina with 0.50 of the DM flux).\nA clear implication of these, albeit preliminary, results is that these targets should be avoided in the quest to better constrain putative WIMP DM self-annihilation cross-sections. By contrast, there remain other dSphs where the expected DM signal remains comfortably much larger than the MSP signal; these are more promising targets.\n\n\n\n\n\n\n\\clearpage\n\n\\printbibliography[segment=\\therefsegment,title={Supplementary Information References}, check=onlynew]\n\n\n\\end{document}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nObservations of high-redshift quasars probe the growth of supermassive\nblack holes (SMBH) and their connection to galaxy formation at the earliest\ncosmic epochs. \nThe discovery of strong submillimeter\/millimeter [(sub)mm] dust \ncontinuum in about 30\\% of the quasars known at z$\\sim$6 provides the \nfirst evidence of active star formation in young quasar host \ngalaxies at the end of the reionization era \\citep{bertoldi03a,bertoldi03b,petric03,priddey03,\nrobson04,wang07,wang08}. The star formation rates \nestimated from the FIR luminosities (a few $\\rm 10^{12}$ \nto $\\rm 10^{13}\\, L_{\\odot}$) are on the order of $\\rm 10^{2}$ \nto $\\rm 10^{3}\\,M_{\\odot}\\,yr^{-1}$, which are comparable to the typical \nvalues found in so-called submillimeter galaxies at $\\rm z=2\\sim3$ \n\\citep{scott02,greve05,kovacs06}. The spatially resolved [C {\\small II}] \nline emission from one of the most FIR luminous z$\\sim$6 quasars, SDSS \nJ114816.64+525150.3 (hereafter J1148+5251), further suggests a high star formation surface density \nof $\\rm \\sim1000\\,M_{\\odot}\\,yr^{-1}\\,kpc^{-2}$ over the central \n1.5 kpc region of the quasar host galaxy \\citep{maiolino05,walter09}. \n\nMolecular CO (6-5) line emission has been detected in ten of the \nFIR luminous z$\\sim$6 quasars (\\citealp{bertoldi03b,walter03,carilli07,\nwang10}, 2011, in prep.),   \nindicating the existence of highly-excited molecular \ngas in the quasar hosts. The CO (3-2), (6-5), and (7-6) transitions \ndetected in the z=6.42 quasar J1148+5251 reveal a molecular gas \ncomponent on scales of $\\sim$5 kpc in the host galaxy with CO \nexcitation conditions similar to those found in local starburst \ngalaxies and CO-detected quasars at lower redshifts \\citep{bertoldi03b,walter04,riechers09}. \n\nEmission in the low-order CO transitions ($\\rm J\\leq2$) from the z$\\sim$6 quasar host \ngalaxies is poorly constrained due to the limited sensitivity and \nfrequency coverage of the previous instruments \\citep{wagg08,wang10}. \nThe new Ka band receivers on the Expanded Very Large Array (EVLA, \\citealp{perley11}) open an  \nimportant frequency window for studies of the cold molecular gas in high-redshift \ngalaxies (e.g., \\citealp{ivison10,ivison11,riechers10}). In this paper, we report \nour EVLA observations of the CO (2-1) line emission in five z$\\sim$6 \nquasars \\citep{fan04,fan06,willott10a,willott10b} \nThree of them are from the Sloan Digital Sky Survey (SDSS, \\citealp{fan04,fan06}), \nwith two objects, SDSS J084035.09+562419.9 and SDSS J092721.82+200123.7, \npreviously detected in strong ($\\rm >3\\,mJy$) 250 \nGHz dust continuum and molecular CO (6-5) and (5-4) line emission. \nAnother object, SDSS J162331.81+311200.5, was detected in the [C {\\small II}] \nline, but undetected in millimeter dust \ncontinuum and high-J CO transitions (Bertoldi et al. 2011, in prep.).\nThe other two objects are from the Canada-France High-z Quasar\nSurvey (CFHQS, \\citealp{willott10a,willott10b}) and do not have published CO observations yet. \nOne of them, CFHQS 142952.17+544717.6, was detected in 250 GHz dust continuum \n(Omont et al. 2011, in prep.). We describe the observations in Section 2, present \nthe results in Section 3, and discuss the CO excitation and host galaxy \nevolution properties of the detections in Section 4. A $\\rm \\Lambda$-CDM\ncosmology with $\\rm H_{0}=71km\\ s^{-1}\\ Mpc^{-1}$, $\\rm\n\\Omega_{M}=0.27$ and $\\rm \\Omega_{\\Lambda}=0.73$ is adopted throughout this\npaper \\citep{spergel07}.\n\n\\section{Observations}\n\nThe observations were carried out using the Ka-band receiver on the EVLA \nin 2010 in the D, DnC, and C configurations. \nThe WIDAR correlator in Open Shared Risk Observing mode provided a maximum \nbandwidth of 128 MHz and a resolution of 2 MHz in each of the two \nbasebands (A\/C and B\/D intermediate frequency [IF] bands). The A\/C IFs \ncould not be tuned below 32 GHz. The redshifts and observing frequencies \nof the CO (2-1) line of the five targets are estimated with previous detections of the CO (6-5), \n[C {\\small II}], or quasar UV lines (\\citealt{carilli07,wang10};  \nBertoldi et al 2011, in prep.). For the \nthree sources with redshifts of $\\rm z\\leq6.2$ [corresponding to redshifted CO (2-1) line \nfrequencies of $\\rm \\nu_{obs}\\geq32$ GHz], we use the two 128 MHz IF pairs overlapped \nby 30 MHz and cover a total bandwidth of 226 MHz (i.e., $\\sim$2000 $\\rm km\\,s^{-1}$ \nin velocity and $\\rm \\sim0.05$ in redshift at $\\rm z=6$)\\footnote{10 MHz overlap and a total \nbandwidth of 246 MHz for J1429+5447.}. \nFor the other two objects with $\\rm z>6.2$, we \ncentered the 128 MHz window of the B\/D IF pairs on the line frequency \nand observed the continuum at $\\geq$32 GHz with the other window. \nThe observing time is 15 to 20 hours for each of the five targets (see Table 1).\nFlux calibrations were performed using the standard VLA \ncalibrators, 3C286 and 3C48, and we use 5-minute \nscan loops between targets and phase calibrators to calibrate the phase. \nThe data were reduced with AIPS, and the  \nspatial resolutions (FWHM) of the final images are typically 2$''$ for data taken in the \nD configuration and 0.7$''$ for the C configuration. \n\n\\section{Result}\n\nCO (2-1) line emission has been detected in two of the \nfive z$\\sim$6 quasars, J0927+2001 and J1429+5447, and marginally \ndetected in J0840+5624. We present all the observing parameters and \nmeasurements in Table 1. The detailed results are listed below.\n\n{\\bf J0927+2001} Toward this source strong dust continuum \nat 850 GHz, 250 GHz, and 85 GHz, and CO (6-5) and (5-4) line emission \nwere detected \\citep{carilli07,wang10}. We have \ndetected the CO (2-1) line and the emission distribution (averaged \nover a velocity range of 880 $\\rm km\\,s^{-1}$) along with a spectrum is \nshown in Figure 2. The line peak emission centeroid is consistent with the optical \nquasar position and the peaks of the high-J CO lines.  \nThe line width (FWHM) and redshift fitted with a single Gaussian \nprofile are $\\rm 590\\pm130\\,km\\,s^{-1}$ and $\\rm 5.7716\\pm0.0012$\nwhich are in good agreement with the measurements   \nfrom the high-order CO transitions ($\\rm z=5.7722\\pm0.0006$ and \n$\\rm FWHM=600\\pm70\\,km\\,s^{-1}$, \\citealt{carilli07}). \nThe line emission appears marginally \nresolved by the $\\rm 2.19''\\times1.96''$ synthesized beam with a peak \nsurface brightness of $\\rm 147\\pm21\\, \\mu Jy\\,beam^{-1}$ and a total \nintensity of $\\rm 230\\pm45\\,\\mu Jy$, with a source size of \n$\\rm (2.7''\\pm0.4'')\\times(2.4''\\pm0.3'')$ determined from a fit with a two-dimensional \nGaussian distribution (the deconvolved source size \nis about $\\rm 1.7''\\times 1.4''$, or $\\rm 10\\,kpc\\times8\\,kpc$). \nThe corresponding line fluxes and luminosities (Table 1) are higher than the upper limits estimated from\nprevious GBT observations, but are still consistent given the large\nuncertainties and baseline feature contamination in the GBT data \\citep{wagg08,wang10}.\n\n{\\bf J1429+5447} Toward this object strong radio continuum \nemission was detected in the FIRST survey \\citep{becker95} \nand recent VLBI observations \\citep{frey11}, making it the\nstrongest radio source among the known z$\\sim$6 quasars and the \nmost distant radio-loud quasar. It has also been detected in \ndust continuum at 250 GHz with a flux density of $\\rm \\sim3$ mJy \n(Omont et al. 2011, in prep.). \nWe have detected both CO (2-1) line emission and \ncontinuum emission at the line frequency. The \ncontinuum source is unresolved by the $\\rm 0.71''\\times0.67''$ synthesized \nbeam and the flux density averaged over the line-free channels at 32 GHz \nis $\\rm 257\\pm15$ $\\mu$Jy. We subtract the continuum by performing \nlinear fitting to the visibility data, \nusing the UVLIN task in AIPS. The CO line emission is resolved into two \npeaks with a spatial separation of $\\sim$1.2$''$ (6.9 kpc at the\nquasar redshift), and the optical and radio quasar positions are \nconsistent with the west peak (Figure 3). \nA Gaussian fit to the spectra yields a redshift \nof $\\rm z=6.1831\\pm0.0007$ and a line width \nof $\\rm FWHM=280\\pm70\\,km\\,s^{-1}$ for the west source, \nand $\\rm z=6.1837\\pm0.0015$ and $\\rm FWHM=400\\pm140\\,km\\,s^{-1}$ for the east source. \nThe line fluxes estimated with the peak surface brightness on \nthe velocity-averaged map averaging over a velocity range of \n$\\rm \\sim450\\,km\\,s^{-1}$ are $\\rm 0.065\\pm0.011\\,Jy\\,km\\,s^{-1}$ \nand $\\rm 0.050\\pm0.013\\,Jy\\,km\\,s^{-1}$\nfor the west and east components, respectively. However, \na two-dimensional Gaussian distribution fitted to the east component suggest \npossible extension with a source size of $\\rm (1.1''\\pm0.2'')\\times(0.7''\\pm0.2'')$, \nwhich should be checked with deeper observations at higher spatial resolution.\n\n{\\bf J0840+5624} This source was detected\nin (sub)mm dust continuum emission and CO\n(6-5) and (5-4) line emission; it has the broadest line width,\n$\\rm FWHM=860\\,km\\,s^{-1}$, among the CO-detected\nz$\\sim$6 quasars \\citep{wang07,wang10}. We observed the line\nat the redshift of $\\rm z=5.8441\\pm0.0013$ derived\nfrom the high-order CO detections and find no clear detection\nin a velocity-averaged map averaging over 1070 $\\rm km\\,s^{-1}$ made at the\nfull resolution of $\\rm 1.09''\\times0.76''$. At a lower resolution\nof $\\rm 2.19''\\times1.96''$, marginal signal ($\\rm 2.8\\sigma$)\nappears on the map (Figure 1), with a double-peaked\nmophology along the east-west direction. The optical quasar position\nis 0.8$''$ away from the east peak. We plot the spectrum at the position\nof east peak in the right panel of Figure 1, and there is only very\nmarginal signal (1 to 2$\\sigma$) over $\\rm \\sim-500$\nto $\\rm 500\\,km\\,s^{-1}$, i.e., the typical velocity range of the CO (6-5)\nand (5-4) line emission \\citep{wang10}.\nThe CO (2-1) line flux estimated with the surface\nbrightness of the east peak is $\\rm 0.062\\pm0.022\\,Jy\\,km\\,s^{-1}$ (Table 1).\nHowever, the signal is indeed marginal and deeper observations with a wider\nbandwidth are required to improve the measurement.\n\n{\\bf J0210$-$0456} This object is the highest\nredshift quasar known to date with $\\rm z=6.438\\pm0.004$ determined\nfrom the object's $\\rm Mg\\,{\\small II}\\,\\lambda2798\\AA$ line emission \\citep{willott10b}.\nWe searched for CO (2-1) line emission in the 128 MHz window centered at\nthe $\\rm Mg\\,{\\small II}$ redshift but did not detect it.\nHere we assume a line width of $\\rm 800\\,km\\,s^{-1}$, which is the\ntypical full width at zero intensity ($\\rm v_{FWZI}$) value found with\nsamples of high-z CO-detected quasars \\citep{coppin08,wang10}\nto estimate the upper limit of the line intensity.\nThe $\\rm 1\\sigma$ rms noise level on the map averaged over this velocity range\nis $\\rm \\sigma_{rms} =16\\,\\mu Jy\\,beam^{-1}$, and the $\\rm 3\\sigma$ upper limit of the line\nflux is estimated as $\\rm 3\\sigma_{rms} v_{FWZI}=0.038\\,Jy\\,km\\,s^{-1}$.\nThe corresponding 3$\\sigma$ upper limit of\nthe line luminosity is $\\rm {L'}_{CO(2-1)}<1.28\\times10^{10}\\,K\\,km\\,s^{-1}\\,pc^2$ \n(see equation (3) in \\citealt{solomon05}). However, we cannot rule out that \nthe $\\rm Mg\\,{\\small II}$ line emission is significantly offset \nfrom the quasar host galaxy redshift and CO (2-1) line falls outside the 128 MHz window. \nThe continuum emission is \nalso undetected with the other window centered at 32.1 GHz, and the \nchannel-averaged map yields a 3$\\sigma$ upper limit of $\\rm <54\\,\\mu Jy$.\n\n{\\bf J1623+3112} This object is detected in $\\rm [C\\,{\\small II}]$ 158$\\mu$m  \nfine structure line emission by Bertoldi et al. (2011, in prep.), \nbut undetected in 250 GHz dust continuum \\citep{wang07}. We searched for the CO (2-1) line in \nthe 128 MHz-bandwidth window centered at the $\\rm [C\\,{\\small II}]$ \nredshift of $\\rm z=6.2605\\pm0.0005$ and did not detect the line. \nThe rms on the map averaged over a velocity range of \n$\\rm 800\\,km\\,s^{-1}$ is $\\rm 26\\,\\mu Jy\\,beam^{-1}$. This yields \na 3$\\sigma$ upper limit of $\\rm <0.062\\,Jy\\,km\\,s^{-1}$ for the line flux  \nand $\\rm <2.0\\times10^{10}\\,K\\,km\\,s^{-1}\\,pc^2$ for the line luminosity. \nThe 3$\\sigma$ upper limit of the continuum emission at 35 GHz \nmeasured with A\/C IFs is $\\rm <75\\,\\mu Jy$. \n\n\\section{Discussion}\n\nWe have observed molecular CO (2-1) line emission toward five quasars \nat z$\\sim$6 using the EVLA, and detections\/marginal detection have been \nobtained from the three objects that have strong FIR dust \ncontinuum emission. This is consistent with the picture of massive star \nformation fueling by huge amount of molecular gas in these young \nquasar hosts. The detection of $\\rm [C\\,{\\small II}]$ in J1623+3112 is \nalso likely to be a sign of star formation, but the current sensitivity \nof our EVLA observations cannot detect molecular CO from the host galaxy. \nJ0927+2001 and J0840+5624, were  \npreviously detected strongly in the CO (6-5) and (5-4) transitions. \nCO (2-1) line emission has been detected and marginally \nresolved in the host galaxy of J0927+2001 over a scale of $\\sim$10 kpc. \nThe molecular gas masses ($\\rm M_{gas}$) estimated from the CO (2-1) line\npeak surface brightness and the total intensity on the velocity-averaged\nmap are listed in Table 1, assuming a CO luminosity-to-gas mass conversion factor\nof $\\rm \\alpha=0.8 M_{\\odot}\\,(K\\,km\\,s^{-1}\\,pc^{2})^{-1}$ appropriate\nfor local ultraluminous infrared galaxies \\citep{solomon97,downes98}.\nThese estimates are 1.7 and 2.5 times higher than the  \nvalue of $\\rm (1.8\\pm0.3)\\times10^{10}\\,M_{\\odot}$ estimated\nfrom the high-order CO transitions \\citep{carilli07,wang10}. \nWe plot the CO excitation ladder of this source in Figure 4,\ntogether with the results of Large Velocity Gradient (LVG) modeling\nof the highly-excited molecular gas components \n(gas densities of \norder $\\rm 10^{4}\\,cm^{-3}$, kinetic temperatures of 50 to 60 K, \nand peak at $\\rm J\\geq6$) \nfound in other high-z FIR and CO luminous\nquasars and nearby starburst galaxies \\citep{riechers06,riechers09,gusten06}.\nWe normalize the models to the high-order CO transitions. \nThe CO (2-1) line flux measured with the peak surface \nbrightness on the velocity-averaged map is consistent\/marginally consistent \nwith the values expected by these single-component models, while the total line flux \nintegrated over the line-emitting area falls above all the models. This may suggest \nthe exsitence of additional low excitation gas in the central $\\rm \\sim10\\,kpc$ region \nas was found in the submillimeter galaxy AzTEC-3\nat z=5.3 \\citep{riechers10} and the nearby starburst \ngalaxy M82 \\citep{weiss05}. However, there are still large \nuncertainties in the measurements of all the three transitions, \nand observations of other CO transitions are necessary to \naddress if there are multiple CO excitation components in the quasar host galaxy. \nOur observations show no evidence of excess CO (2-1) line emission and additional \nlow excitation component in the host galaxy of J0840+5624. \n\nThe C array imaging of the CO (2-1) line emission from J1429+5447 has \nresolved the molecular gas into two distinct peaks, with a spatial separation \nof $\\sim$6.9 kpc; the quasar position is consistent with the West peak. \nThere is no clear velocity offset ($\\rm 26\\pm60\\,km\\,s^{-1}$) between \nthe two components. These results suggest a gas-rich, major merging \nsystem with two distinct components that are comparable in CO luminosity and \nmolecular gas mass. The west component of this system \nis in a radio-loud quasar phase. Similar quasar-starburst systems with \nmultiple CO emission peaks were previously found in \nthe CO luminous quasars BRI 1202$-$0725 at z=4.7 \\citep{omont96,carilli02}, \nBRI 1335$-$0417 at z=4.4 \\citep{riechers08}  \nand J1148+5251 at z=6.42 \\citep{walter04}. These systems demonstrate  \nthe early phase of quasar-galaxy formation in which both AGN and starburst \nactivities are triggered by major mergers and the molecular gas in the \nnuclear region is not fully coalesced \\citep{narayanan08}. We will \nexpect further high-resolution observations with the EVLA in C or B \narray to constrain the gas surface density and dynamics, \nand with ALMA or the PdBI to resolve the dust continuum and distributed \nstar formation in these young quasar host galaxies.\n\n\\acknowledgments \nThis work is based on observations carried out with the Expanded Very Large \nArray (NRAO). The National\nRadio Astronomy Observatory (NRAO) is a facility of the National\nScience Foundation operated under cooperative agreement by Associated\nUniversities, Inc. We acknowledge support from the Max-Planck Society\nand the Alexander von Humboldt Foundation through the Max-Planck-Forschungspreis\n2005. Dominik A. Riechers acknowledges support from NASA through Hubble\nFellowship grant HST-HF-51235.01 awarded by the Space Telescope Science\nInstitute, which is operated by the Association of Universities for\nResearch in Astronomy, Inc., for NASA, under contract NAS 5-26555.\nM. A. Strauss acknowledges the support of NSF grant Ast-0707266.\n{\\it Facilities:} \\facility{EVLA}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzhiyd b/data_all_eng_slimpj/shuffled/split2/finalzzhiyd
new file mode 100644
index 0000000000000000000000000000000000000000..42196099d0d096739e6ef7df9a0cbcdc04080708
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzhiyd
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\n\\subsection{Summary of Results}\n \nThis paper proposes an approach to the Crepant Resolution Conjecture for open Gromov-Witten invariants, and supports it with a series of results and verifications about threefold $A_n$-singularities and their resolutions.\\\\\n\nLet $\\mathcal{Z}$ be a smooth toric Calabi--Yau Deligne--Mumford stack with\ngenerically trivial stabilizers and let $L$ be an Aganagic-Vafa brane\n(Sec. \\ref{sec:ogw}). Fix a Calabi--Yau torus action $T$ on $\\mathcal{Z}$ and\ndenote by $\\Delta_\\mathcal{Z}$ the free module over $H^\\bullet(BT)$ spanned by\nthe $T$-equivariant lifts of orbifold cohomology classes\nof Chen--Ruan degree at most two. We define\n(Sec. \\ref{ssec:dcrc}) a family of elements of Givental space,\n\\beq\n\\widehat{\\mathcal{F}}_{L,\\mathcal{Z}}^{\\rm disk}: H_T^\\bullet(\\mathcal{Z}) \\to \\mathcal{H}_\\mathcal{Z} =  H_T^\\bullet(\\mathcal{Z})((z^{-1})),\n\\eeq\nwhich we call the \\textit{winding neutral disk potential}.  Upon appropriate\nspecializations of the variable $z$, $\\widehat{\\mathcal{F}}^{\\rm disk}_{L,\\mathcal{Z}}$ encodes disk\ninvariants of $(\\mathcal{Z},L)$ at any winding $d$. \\\\\n\nConsider a \\textit{crepant\n  resolution diagram} $\\mathcal{X} \\to X \\leftarrow Y$, where $X$ is the coarse moduli\nspace of $\\mathcal{X}$ and $Y$ is a crepant resolution of the singularities of $X$. A\nLagrangian boundary condition $L$ is chosen on $\\mathcal{X}$ and  we denote by $L'$\nits transform in $Y$. \nOur\nversion of the open crepant resolution conjecture is a comparison of the (restricted) winding neutral disk potentials.\n\n\\begin{proposal}[The OCRC]\nThere exists a $\\mathbb{C}((z^{-1}))$-linear map of Givental spaces\n$\\mathbb{O}: \\mathcal{H}_\\mathcal{X} \\to \\mathcal{H}_Y$ and analytic functions $\\mathfrak{h}_\\mathcal{X}: \\Delta_\\mathcal{X}\n\\to \\mathbb{C}$, $\\mathfrak{h}_Y: \\Delta_Y \\to \\mathbb{C}$ such that\n\\beq\n\\mathfrak{h}_Y^{1\/z}{\\widehat \\mathcal{F}_{L,Y}^{\\rm disk}}\\big|_{\\Delta_Y}= \\mathfrak{h}_\\mathcal{X}^{1\/z} \\mathbb{O}\\circ \\widehat \\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}\\big|_{\\Delta_\\mathcal{X}}\n\\eeq\nupon analytic continuation of quantum cohomology parameters.\n\\end{proposal}\n\nFurther, we conjecture (Conjecture \\ref{conj:iri}) that both $\\mathbb{O}$ and\n$\\mathfrak{h}_\\bullet$ are completely determined\nby the classical toric geometry of $\\mathcal{X}$ and $Y$. In particular, we give a \nprediction for the transformation $\\mathbb{O}$ depending on a choice of identification of the\n$K$-theory lattices of $\\mathcal{X}$ and $Y$. \\\\\n\nWhen $\\mathcal{X}$ is a Hard Lefschetz\nCalabi--Yau orbifold, the OCRC extends to functions on all of $H_T^\\bullet(\\mathcal{Z})$.\nTogether with WDVV, this gives a Bryan--Graber-type statement for potentials encoding invariants from genus $0$ maps with an arbitrary number of boundary components:\n\n\\begin{prop1}\nLet $\\mathcal{X} \\rightarrow X \\leftarrow Y$ be a Hard Lefschetz diagram for which the OCRC  holds. Defining  $\\mathbb{O}^{\\otimes n}= \\mathbb{O}(z_1)\\otimes\\ldots\\otimes \\mathbb{O}(z_n)$, we have:\n\\beq\n{\\widehat \\mathcal{F}_{L',Y}^{n}}= \\mathbb{O}^{\\otimes n}\\circ \\widehat \\mathcal{F}_{L,\\mathcal{X}}^{n},\n\\eeq\nwhere $\\widehat \\mathcal{F}^{n}$ is the $n$-boundary  components analog of $\\widehat\n\\mathcal{F}^{\\rm disk}$  defined in \\eqref{mholepot}. \\\\\n\\end{prop1}\n\n\nConsider now the family of threefold $A_n$ singularities, where $\\mathcal{X}=[\\mathbb{C}^2\/\\mathbb{Z}_{n+1}]\\times \\mathbb{C}$ and $Y$ is its canonical minimal\nresolution. \n\\begin{mt1}\nThe OCRC  and Conjecture \\ref{conj:iri} hold for the $A_n$-singularities for any choice of Aganagic-Vafa brane on $\\mathcal{X}$.\n\\end{mt1}\nThe main theorem is an immediate consequence of Proposition \\ref{prop:wncrc}\nand Theorem \\ref{thm:sympl}. From it we deduce a series of comparisons of\ngenerating functions in the spirit of Bryan-Graber's  formulation of the CRC. \\\\\n\nIn \\eqref{cohdp} we define the \\textit{cohomological disk potential}\n$\\mathcal{F}_{L}^{\\rm disk}$ - a cohomology valued generating function for disk\ninvariants that ``remembers\" the twisting and the attaching fixed point of an\norbi-disk map. We also consider the coarser \\textit{scalar disk potential}\n(see \\eqref{sdp}), which keeps track of the winding of the orbimaps but\nforgets the twisting and attaching point.\nThere are essentially two different choices for the Lagrangian boundary condition on $\\mathcal{X}$; the simpler case occurs when $L$ intersects one of the effective legs of the orbifold. In this case we have the following result.\n\\begin{cocrceff}\nIdentifying identically the winding parameters and setting $\\mathbb{O}_\\mathbb{Z}(\\mathbf{1_k})=P_{n+1}$ for every $k$, we have:\n\\beq\n\\mathcal{F}_{L',Y}^{\\rm disk}(t,y,\\vec{w}) = \\mathbb{O}_\\mathbb{Z} \\circ \\mathcal{F}_{L,\\mathcal{X}}^{\\rm\n  disk}(t,y,\\vec{w}). \n  \\eeq\n\\end{cocrceff}\nIt is immediate to observe that the scalar disk potentials coincide (Corollary \\ref{cor:esc}).\\\\\n\nThe case when $L$ intersects the ineffective leg of the orbifold is more subtle.\n\\begin{cocrcgerby}\nWe exhibit a matrix  $\\mathbb{O}_\\mathbb{Z}$ of roots of unity and  a specialization of the winding parameters depending on the equivariant weights such that\n\\beq\n\\mathcal{F}_{L',Y}^{\\rm disk}(t,y,\\vec{w}) = \\mathbb{O}_\\mathbb{Z} \\circ \\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}(t,y,\\vec{w}) .\n\\eeq\n\\end{cocrcgerby}\nThe comparison of scalar potentials in this case does not hold\nanymore. Because of the special form of the matrix $\\mathbb{O}_\\mathbb{Z}$ we  deduce in\nCorollary \\ref{cor:sc} that the scalar disk potential for $Y$ corresponds to\nthe contribution to the potential for $\\mathcal{X}$ by the untwisted disk maps. \nAs the $A_n$-singularities satisfy the Hard Lefschetz condition, it is\nan exercise in book-keeping to extend the statements of Theorems \\ref{thm:dcrccoh}\nand \\ref{thm:dcrccoheff} to  compare generating functions for arbitrary genus\nzero open invariants, even treating all boundary Lagrangian conditions at the\nsame time. \\\\\n\nIn order to prove our main theorem, we must establish a fully equivariant\nversion of the symplectomorphism of Givental spaces which verifies the closed\nCRC for the $A_n$ geometries. Our analysis is centered on a new global\ndescription of the gravitational quantum cohomology of these targets which enjoys a number of remarkable features, and\nmay have an independent interest {\\it per se}.\n\n\n\\begin{thmmir}\nBy identifying the $A$-model moduli space with a genus zero double Hurwitz space, we construct a global quantum $D$-module $(\\mathcal{F}_{\\lambda,\\phi}, T\\mathcal{F}_{\\lambda,\\phi}, \\nabla^{(g,z)},H(,)_{g})$ which is locally isomorphic to $\\mathrm{QDM}(\\mathcal{X})$ and $\\mathrm{QDM}(Y)$ in appropriate neighborhoods of the orbifold and large complex structure points.\n\\end{thmmir} \n \n\n\\subsection{Context, Motivation and Further Discussion}\n\nOpen Gromov-Witten (GW) theory \nintends to study holomorphic maps from bordered Riemann surfaces, where the image of the boundary is constrained\n to lie in a Lagrangian submanifold of the target. While some general foundational\n work has been done \\cite{Solomon:2006dx, MR2425184}, at this point most\n of the results in the theory rely on additional structure. In \\cite{hht1, hht2}  Lagrangian Floer theory is employed to study the case when the boundary condition is a fiber of the moment map.\nIn the toric context, a mathematical approach\n\\cite{Katz:2001vm, Diaconescu:2003qa, MR2861610,r:lgoa} to construct operatively\na virtual counting theory of open maps is via the use of localization. \nA variety of striking relations have been verified connecting open GW theory and several other types of invariants,\nincluding open $B$-model invariants and matrix models \\cite{Aganagic:2000gs,\n  Aganagic:2001nx, Lerche:2001cw, Bouchard:2007ys, fang2012open}, quantum knot invariants\n\\cite{Gopakumar:1998ki, Marino:2001re}, and ordinary\nGromov--Witten and Donaldson--Thomas theory via ``gluing along the boundary''  \\cite{Aganagic:2003db,\n  Li:2004uf, moop}.\\\\\n\nSince Ruan's influential conjecture \\cite{MR2234886}, an intensely studied\nproblem in Gromov--Witten theory has been to determine the relation between GW invariants of target spaces\nrelated by a crepant birational transformation (CRC). The most general\nformulation of the CRC is framed in terms of Givental formalism\n(\\cite{MR2529944}, \\cite[Conj 4.1]{coates2007quantum}); the conjecture has been proved in\na  number of examples \\cite{MR2510741, MR2529944, MR2486673} and has by now gained folklore status, with\na general proof in the toric setting announced for some time \\cite{ccit2}. A natural question one can ask is whether\nsimilar relations exist in the context of open Gromov--Witten theory. Within\nthe toric realm, physics arguments based on open mirror symmetry\n\\cite{Bouchard:2007ys, Bouchard:2008gu, Brini:2008rh} have given strong indications that\nsome version of the Bryan--Graber \\cite{MR2483931} statement of the crepant\nresolution conjecture should hold at the level of disk invariants. This was\nproven explicitly for the crepant resolution of the Calabi--Yau orbifold $[\\mathbb{C}^3\/\\mathbb{Z}_2]$\nin \\cite{cavalieri2011open}. \nAround the same time, it was suggested \n\\cite{Brini:2011ij, talk-banff} that a general statement of a Crepant Resolution\nConjecture for open invariants  should have a natural formulation within\nGivental's formalism, as in \\cite{MR2510741, coates2007quantum}. Some implications of this\nphilosophy were verified in\n\\cite{Brini:2011ij} for the crepant resolution $\\mathcal{O}_{\\mathbb{P}^2}(-3)$ of the orbifold\n$[\\mathbb{C}^3\/\\mathbb{Z}_3]$. \\\\\n\nThe OCRC we propose here is a natural\nextension to open Gromov--Witten theory of the Coates--Corti--Iritani--Tseng\napproach \\cite{MR2529944} to Ruan's conjecture.\nThe  observation that the disk function of \\cite{MR2861610,r:lgoa} can be interpreted as an endomorphism of Givental space makes the OCRC statement follow almost tautologically from  the Coates--Corti--Iritani--Tseng\/Ruan picture of the ordinary \nCRC via toric mirror symmetry \\cite{MR2510741}. \nThe more striking aspect of our conjecture is then that the linear function $\\mathbb{O}$ comparing the winding neutral disk potentials is considerably simpler than the symplectomorphism $\\mathbb{U}_{\\rho}^{\\X,Y}$  in the closed CRC and it is characterized in terms of {\\it purely classical data}: essentially,  the equivariant Chern characters of $\\mathcal{X}$ and $Y$. This is closely related to Iritani's proposal \\cite{MR2553377} that the analytic continuation for the flat sections of the global quantum $D$-module is realized via the composition of $K$-theoretic central charges;  our disk endomorphisms are very close to just being  inverses to the $\\Gamma$ factors appearing in Iritani's central charges and therefore ``undo\" most of the transcendentality of $\\mathbb{U}_{\\rho}^{\\X,Y}$. \\\\\n\nIritani's proposal is inspired and consistent with the idea of  global mirror\nsymmetry, i.e. that there should be a global quantum $D$-module on the\n$A$-model moduli space which locally agrees with the Frobenius structure given\nby quantum cohomology. In order to verify Iritani's proposal in the fully\nequivariant setting, we construct explicitly such a global structure. Motivated by the connection of the Gromov--Witten theory of $A_n$ to certain integrable systems \\cite{agps}, we realize the Dubrovin\nlocal system as a system of one-dimensional hypergeometric periods.  As a\nspecial feature of this case, structure constants of quantum cohomology\nare rational in exponentiated flat coordinates (or, equivalently, the inverse\nmirror map is a rational function of the $B$-model variables).  Moreover, the $n$-dimensional\noscillating integrals describing the periods of the system reduce to Euler--Pochhammer line integrals in the\ncomplex plane. As a consequence, the computation of the analytic\ncontinuation of flat sections is drastically\nsimplified with respect to the standard toric mirror symmetry methods. Furthermore, in this context integral structures in\nequivariant cohomology emerge naturally from the interpretation of flat\nsections of the Dubrovin connection as twisted period maps. The\nDeligne--Mostow monodromy of hypergeometric periods translates then to an\naction of the colored braid group \nin equivariant\n$K$-theory. \nAn enticing speculation is that, upon mirror symmetry, this may correspond to\nautoequivalences of $D_T^b(Y)$ and surject to the\nSeidel--Thomas braid group action \\cite{MR1831820} in the\nnon-equivariant limit.\n\n\\begin{comment}\n Indeed, in\n\\cite{MR1831820} the authors famously constructed a faithful\nrepresentation of the braid group $B_{n+1}$ in terms of derived equivalences of $D^b(Y)$\ninduced by spherical twists. It is natural to speculate that our monodromy\ndescription of the global quantum $D$-module in Section~\\ref{sec:monodromy}\nsurjects to the Seidel--Thomas braid group, and recovers it in the non-equivariant limit.\n\\end{comment}\n\n\n\\subsection*{Acknowledgements} We are particularly grateful to Tom Coates for\nhis collaboration at the initial stages of this project, and the many\nenlightening conversations that followed. We would also like to thank Hiroshi\nIritani, Yunfeng Jiang, \\'Etienne Mann, Stefano Romano and Ed Segal for useful\ndiscussions and\/or\ncorrespondence. This project originated from discussions at the Banff Workshop on ``New recursion\nformulae and integrability for Calabi--Yau manifolds'', October 2011; we are\ngrateful to the organizers for the kind invitation and the great scientific\natmosphere at BIRS.   A.~B.~has been supported by a Marie Curie Intra-European Fellowship\nunder Project n$^\\circ$ 274345 (GROWINT).  R.~C.~ has been supported by NSF grant DMS-1101549. Partial support from the GNFM-INdAM under the\nProject ``Geometria e fisica dei sistemi integrabili'' is also acknowledged. \\\\\n\n\n\\section{Background}\n\nThis section gathers  background for the formulation of\nthe open string Crepant Resolution Conjecture of\nSection~\\ref{sec:ocrc} and its proof in Section~\\ref{sec:j}. We give a self-contained account of the\nquantum $D$-module\/Givental space approach to the study of the closed string\nCrepant Resolution Conjecture in genus zero along the lines of\nCoates--Corti--Iritani--Tseng \\cite{MR2510741} and Iritani\n\\cite{MR2553377} (Section~\\ref{sec:qdm}). Section~\\ref{sec:ogw} provides an overview of open Gromov--Witten theory for\ntoric Calabi--Yau threefolds \\`a la Katz--Liu as well as its extension to toric\norbifolds. Section~\\ref{sec:an} collects relevant material on\nthe classical and quantum geometry of $A_n$-resolutions. \\\\\n\nThe content of Section~\\ref{sec:qdm} is surveyed in Iritani's\nexcellent review article \\cite{MR2683208}, to which the reader is referred for\nfurther details. For a more comprehensive introduction to the open\nGromov--Witten theory for toric orbifolds, see e.g. \\cite{MR2861610, r:lgoa}.\n\n\n\\subsection[Quantum $D$-modules and the CRC]{Quantum $D$-modules and the Crepant Resolution Conjecture}\n\\label{sec:qdm}\n\n\n\n\nLet $\\mathcal{Z}$ be a smooth Deligne--Mumford stack with coarse moduli\nspace $Z$ and suppose that $\\mathcal{Z}$ carries an algebraic $T\\simeq\\mathbb{C}^*$ action with\nzero-dimensional \nfixed loci.  Write $I\\mathcal{Z}$ for the inertia stack of $\\mathcal{Z}$, \n$\\mathrm{inv}:I\\mathcal{Z}\\to I\\mathcal{Z}$ for its canonical involution and\n$i:I\\mathcal{Z}^T\\hookrightarrow I\\mathcal{Z}$ for\nthe inclusion of the $T$-fixed loci into $I\\mathcal{Z}$. \nThe equivariant Chen--Ruan cohomology ring $H(\\mathcal{Z}) \\triangleq H^{\\bullet}_{T,CR}(\\mathcal{Z})$ of $\\mathcal{Z}$ is a finite rank free module over\nthe $T$-equivariant cohomology of a point $H_T(\\mathrm{pt})\\simeq\n\\mathbb{C}[\\nu]$, where $\\nu=c_1(\\mathcal{O}_{BT}(1))$; we define\n$N_\\mathcal{Z} \\triangleq\\operatorname{rank}_{\\mathbb{C}[\\nu]} H(\\mathcal{Z})$. We furthermore suppose\nthat odd cohomology groups vanish in all degrees. \\\\\n\n\nThe $T$-action on $\\mathcal{Z}$ gives a non-degenerate inner product on\n$H(\\mathcal{Z})$ via the equivariant orbifold Poincar\\'e pairing\n\\beq\n\\eta(\\theta_1,\\theta_2)_{\\mathcal{Z}} \\triangleq \\int_{I\\mathcal{Z}^T}\\frac{i^*(\\theta_1 \\cup \\mathrm{inv}^*\n  \\theta_2)}{e(N_{I\\mathcal{Z}^T\/I\\mathcal{Z}})},\n\\label{eq:pair}\n\\eeq\nand it induces a torus action on the moduli\nspace $\\overline{\\mathcal M_{g,n}}(\\mathcal{Z}, \\beta)$ of degree $\\beta$ twisted stable maps\n\\cite{MR2450211, MR1950941} from genus $g$ orbicurves to $\\mathcal{Z}$. For classes $\\theta_1, \\dots, \\theta_n\\in H(\\mathcal{Z})$ and\nintegers $r_1, \\dots, r_n \\in \\mathbb{N}$, the Gromov--Witten\ninvariants of $\\mathcal{Z}$\n\\bea\n\\left\\langle \\sigma_{r_1}(\\theta_1) \\dots \\sigma_{r_n}(\\theta_n) \\right\\rangle_{g,n,\\beta}^\\mathcal{Z}\n& \\triangleq & \\int_{[\\overline{\\mathcal M_{g,n}}(\\mathcal{Z},\n    \\beta)]_T^{\\rm vir}} \\prod_{i=1}^n \\mathrm{\\operatorname{ev}}^*_i \\theta_i\n\\psi_i^{r_i}, \\label{eq:gwdesc} \\\\\n\\left\\langle \\theta_1 \\dots \\theta_n \\right\\rangle_{g,n,\\beta}^\\mathcal{Z} & \\triangleq & \\left\\langle \\sigma_{0}(\\theta_1) \\dots\n\\sigma_{0}(\\theta_n) \\right\\rangle_{g,n,\\beta}^\\mathcal{Z}, \n\\label{eq:gwprim}\n\\end{eqnarray}\ndefine a sequence of multi-linear functions on $H(\\mathcal{Z})$ with values in the\nfield of fractions $\\mathbb{C}(\\nu)$ of $H_T({\\rm pt})$. The correlators \\eqref{eq:gwprim}\n(respectively, \\eqref{eq:gwdesc} with $r_i>0$) are the {\\it\n  primary} (respectively, {\\it descendent}) Gromov--Witten invariants of\n$\\mathcal{Z}$. \\\\\n\nFix a basis\n$\\{\\phi_i\\}_{i=0}^{N_\\mathcal{Z}-1}$ of $H(\\mathcal{Z})$ such that $\\phi_0=\\mathbf{1}_\\mathcal{Z}$\nand $\\phi_j$, $1\\leq j \\leq b_2(Z)$ are untwisted Poincar\\'e duals of $T$-equivariant divisors\nin $Z$. Denote by $\\{\\phi^i\\}_{i=0}^{N_\\mathcal{Z}-1}$ the dual basis with respect to the pairing \\eqref{eq:pair}.  Let $\\tau=\\sum\\tau_i\\phi_i$ denote a general point of $H(\\mathcal{Z})$.  The WDVV equation for primary Gromov--Witten invariants \\eqref{eq:gwprim} defines a family of associative\ndeformations $\\circ_\\tau$ of the $T$-equivariant Chen--Ruan cohomology ring of $\\mathcal{Z}$ via\n\\beq\n\\eta\\l(\\theta_1 \\circ_\\tau \\theta_2, \\theta_3\\r)_{\\mathcal{Z}} \\triangleq \\left\\langle\\bra \\theta_1, \\theta_2, \\theta_3 \\right\\rangle\\ket_{0,3}^\\mathcal{Z}(\\tau)\n\\eeq\nwhere\n\\beq\n\\left\\langle\\bra \\theta_1, \\dots, \\theta_k \\right\\rangle\\ket_{0,k}^\\mathcal{Z}(\\tau) \\triangleq \\sum_{\\beta}\\sum_{n\\geq 0} \\frac{\\big\\langle \\theta_1,\\dots,\\theta_k,\n  \\overbrace{\\tau,\\tau,\\ldots,\\tau}^{\\text{$n$\n        times}} \\big\\rangle_{0,n+k,\\beta}^\\mathcal{Z}}{n!} \\in \\mathbb{C}((\\nu)) ,\n\\eeq\nand the index $\\beta$ ranges over the cone of effective curve classes\n$\\mathrm{Eff}(\\mathcal{Z}) \\subset H_2(Z, \\mathbb{Q})$; we denote by $l_\\mathcal{Z} \\triangleq b_2(Z)$\nits dimension. \\\\\n\n\nBy the Divisor Axiom \\cite{MR2450211} this can be rewritten as\n\\beq\n\\eta\\l(\\theta_1 \\circ_\\tau \\theta_2, \\theta_3\\r)_{\\mathcal{Z}}= \\sum_{\\beta\\in \\mathrm{Eff}(\\mathcal{Z}), n\\geq 0} \\frac{\\big\\langle \\theta_1,\\theta_2,\\theta_3,\n  \\overbrace{\\tau',\\tau',\\ldots,\\tau'}^{\\text{$n$\n        times}} \\big\\rangle_{0,n+3,\\beta}^\\mathcal{Z}}{n!}\\mathrm{e}^{\\tau_{0,2} \\cdot \\beta}\n\\label{eq:qprod2}\n\\eeq\nwhere we have decomposed $\\tau=\\sum_{i=0}^{N_\\mathcal{Z}-1} \\tau_i \\phi_i = \\tau_{0,2}+\\tau'$ as\n\\bea\n\\tau_{0,2} &=& \\sum_{i=1}^{l_\\mathcal{Z}} \\tau_{i} \\phi_{i}, \\\\\n\\tau' &=& \\tau_0 \\mathbf{1}_\\mathcal{Z} + \\sum_{i=l_\\mathcal{Z}+1}^{N_\\mathcal{Z}-1} \\tau_i \\phi_i.\n\\label{eq:Tprime}\n\\end{eqnarray}\n\nThe quantum product \\eqref{eq:qprod2} is a formal Taylor series in $(\\tau',\n\\mathrm{e}^{\\tau_{0,2}})$. Suppose that it is actually {\\it convergent} in a contractible\nopen set $U \\ni (0,0)$; this is the case for many toric orbifolds\n\\cite{MR1653024, Coates:2012vs} and,\nas we  see explicitly, for\nall the examples of Section~\\ref{sec:an}. Then the quantum product $\\circ_\\tau$ is an\nanalytic deformation of the Chen--Ruan cup product $\\cup_{\\rm CR}$, to which\nit reduces in the limit $\\tau' \\to 0$, $\\mathfrak{Re}(\\tau_{0,2}) \\to -\\infty$. Thus, the holomorphic\nfamily of rings $H(\\mathcal{Z}) \\times U \\to U$, together with the inner pairing \\eqref{eq:pair} and the\nassociative product \\eqref{eq:qprod2}, gives $U$ the structure of a\n(non-conformal) Frobenius manifold $QH(\\mathcal{Z})\\triangleq(U, \\eta, \\circ_\\tau)$\n\\cite{Dubrovin:1994hc}; this is the {\\it quantum cohomology ring} of $\\mathcal{Z}$. We  refer to the Chen--Ruan limit $\\tau' \\to 0$, $\\mathfrak{Re}(\\tau_{0,2})\n\\to -\\infty$ as the {\\it large radius limit point} of $\\mathcal{Z}$. \\\\\n\n\nAssigning a Frobenius structure on $U$ is tantamount to endowing the trivial\ncohomology bundle $TU \\simeq H(\\mathcal{Z}) \\times U \\to U$ with a flat\npencil of affine connections \\cite[Lecture\n  6]{Dubrovin:1994hc}. Denote by $\\nabla^{(\\eta)}$ the Levi--Civita connection\nassociated to the Poincar\\'e pairing on $H(\\mathcal{Z})$; in Cartesian coordinates\nfor $U\\subset H(\\mathcal{Z})$ this reduces to the ordinary de Rham differential\n$\\nabla^{(\\eta)}=d$. Consider then the one parameter family of covariant\nderivatives on $TU$\n\\beq\n\\nabla^{(\\eta,z)}_X \\triangleq  \\nabla^{(\\eta)}_X+z^{-1} X \\circ_\\tau.\n\\label{eq:defconn1}\n\\eeq\nThe fact that the quantum product is commutative, associative and integrable implies that\n$R_{\\nabla^{(\\eta,z)}}=T_{\\nabla^{(\\eta,z)}}=0$ identically in $z$; this is equivalent to the WDVV\nequations for the genus zero Gromov--Witten potential. The equation for the horizontal\nsections of $\\nabla^{(\\eta,z)}$,\n\\beq\n\\nabla^{(\\eta,z)} \\omega =0,\n\\label{eq:QDE}\n\\eeq\nis a rank-$N_\\mathcal{Z}$ holonomic system of\ncoupled linear PDEs. We  denote by $\\mathcal{S}_\\mathcal{Z}$ the vector space of solutions\nof \\eqref{eq:QDE}: a $\\mathbb{C}((z))$-basis of $\\mathcal{S}_\\mathcal{Z}$ is by definition given by the gradient of\na flat frame $\\tilde \\tau (\\tau,z)$ for the deformed connection\n$\\nabla^{(\\eta,z)}$. The Poincar\\'e\npairing induces a non-degenerate inner product $H(s_1,s_2)_{\\mathcal{Z}}$ on $\\mathcal{S}_\\mathcal{Z}$ via\n\\beq\nH(s_1, s_2)_\\mathcal{Z} \\triangleq \\eta(s_1(\\tau, -z),s_2(\\tau,z))_\\mathcal{Z}.\n\\label{eq:pairDmod}\n\\eeq\nThe triple $\\mathrm{QDM}(\\mathcal{Z})\\triangleq(U,\\nabla^{(\\eta,z)}, H(,)_\\mathcal{Z})$ defines a {\\it\n  quantum D-module} structure on $U$, and the system \\eqref{eq:QDE} is the {\\it quantum differential\n    equation} (in short, QDE) of $\\mathcal{Z}$. \n\\begin{rmk}\n\\label{rmk:fuchsLR}\nNotice that the assumption that the quantum product\n  \\eqref{eq:qprod2} is analytic in $(\\tau',\\mathrm{e}^{\\tau_{0,2}})$ around the large radius\n  limit point translates into the statement that the QDE \\eqref{eq:QDE} has a\n  Fuchsian singularity along $\\cup_{i=1}^{l_\\mathcal{Z}} \\{q_i\\triangleq\\mathrm{e}^{\\tau_i}=0\\}$. \\\\\n\\end{rmk}\nIn the same way in which the genus zero primary theory of $\\mathcal{Z}$ defines a quantum\n$D$-module structure on $H(\\mathcal{Z}) \\times U$, the genus zero gravitational\ninvariants \\eqref{eq:gwdesc} furnish a basis of horizontal sections\nof $\\nabla^{(\\eta,z)}$ \\cite{MR1408320}.  For every $\\theta\\in\nH(\\mathcal{Z})$, a flat section of the $D$-module is given by an\n$\\mathrm{End}(H(\\mathcal{Z}))$-valued function $S_\\mathcal{Z}(\\tau,z):H(\\mathcal{Z})\\to \\mathcal{S}_\\mathcal{Z}$ defined as\n\\beq\nS_\\mathcal{Z}(\\tau,z)\\theta \\triangleq \\theta-\\sum_{k=1}^{N_\\mathcal{Z}}\\phi^k\\left\\langle\\bra\\phi_k,\\frac{\\theta}{z+\\psi}\\right\\rangle\\ket_{0,2}^\\mathcal{Z}(\\tau)\n\\label{eq:fundsol}\n\\eeq\nwhere $\\psi$ is a cotangent line class and we expand the denominator as a\ngeometric series\n$\\frac{1}{z+\\psi}=\\frac{1}{z}\\sum\\left(-\\frac{\\psi}{z}\\right)^k$. We call the\npair  $(\\mathrm{QDM}(\\mathcal{Z}), S_\\mathcal{Z})$ a {\\it calibration} of the Frobenius structure\n$(H(\\mathcal{Z}), \\circ_\\tau, \\eta)$. \\\\\n\nThe flows of coordinate vectors for the flat frame of $TH(\\mathcal{Z})$ induced by\n$S_\\mathcal{Z}(\\tau,z)$ give a basis of deformed flat coordinates\n of\n$\\nabla^{(\\eta,z)}$, which is defined uniquely up to an additive $z$-dependent\n constant. A canonical basis is obtained upon applying the String Axiom:\ndefine the {\\it $J$-function} $J^\\mathcal{Z}(\\tau,z):U \\times \\mathbb{C} \\to H(\\mathcal{Z})$ by\n\\beq\nJ^\\mathcal{Z}(\\tau,z) \\triangleq zS_\\mathcal{Z}(\\tau,-z)^*\\mathbf{1}_\\mathcal{Z}\n\\label{eq:Jfun1}\n\\eeq\nwhere $S_\\mathcal{Z}(\\tau,z)^*$ denotes the adjoint to $S_\\mathcal{Z}(\\tau,z)$ under $H(-,-)_\\mathcal{Z}$. Explicitly, \n\\beq\n\\label{eq:resj}\nJ^\\mathcal{Z}(\\tau,z) = (z+\\tau_0)\\mathbf{1}_\\mathcal{Z}+\\tau_1\\phi_1+...+\\tau_{N_\\mathcal{Z}} \\phi_{N_\\mathcal{Z}}+\\sum_{k=1}^{N_\\mathcal{Z}} \\phi^k\\left\\langle\\bra\n\\frac{\\phi_k}{z-\\psi_{n+1}}\\right\\rangle\\ket_{0,1}^\\mathcal{Z}(\\tau).\n\\eeq\nComponents of $J^\\mathcal{Z}(\\tau,z)$ in the $\\phi$-basis give flat coordinates of\n\\eqref{eq:defconn1}; this is a consequence of \\eqref{eq:Jfun1} combined with\nthe String Equation. From \\eqref{eq:resj}, the undeformed flat coordinate system is obtained in the\nlimit $z\\to\\infty$ as\n\\beq\n\\lim_{z\\to \\infty}  \\l(J^\\mathcal{Z}(\\tau,z)-z \\mathbf{1}_\\mathcal{Z}\\r) = \\tau.\n\\eeq\n\\\\\n\nBy Remark~\\ref{rmk:fuchsLR}, a loop around the origin in the variables $q_i=\\mathrm{e}^{\\tau_i}$\ngives a non-trivial monodromy action on the $J$-function. Setting $\\tau'=0$ in \\eqref{eq:resj} and applying the Divisor\nAxiom then gives \\cite[Proposition~10.2.3]{MR1677117}\n\\bea\n& J^{\\mathcal{Z}, \\rm small}(\\tau_{0,2},z)  \\triangleq  J^\\mathcal{Z}(\\tau,z)\\Big|_{\\tau'=0} \\nn \\\\\n=& z \\mathrm{e}^{\\tau_1 \\phi_1\/z}\\dots\\mathrm{e}^{\\tau_{l_\\mathcal{Z}} \\phi_{l_\\mathcal{Z}}\/z}\n\\l(\\mathbf{1}_\\mathcal{Z}+ \\sum_{\\beta,k}\\mathrm{e}^{\\tau_1 \\beta_1}\\dots\\mathrm{e}^{\\tau_{l_\\mathcal{Z}}\\beta_{l_\\mathcal{Z}}}\\phi^k\\left\\langle\n\\frac{\\phi_k}{z(z-\\psi_{1})}\\right\\rangle_{0,1,\\beta}^\\mathcal{Z}\\r).\n\\label{eq:Jred}\n\\end{eqnarray}\nIn our situation\nwhere the $T$-action has only zero-dimensional fixed loci $\\{P_i\\}_{i=1}^{N_\\mathcal{Z}}$, write \n\\beq\n\\phi_i \\to \\sum_{j=1}^{N_\\mathcal{Z}} c_{ij}(\\nu) P_j, \\quad i=1, \\dots, l_\\mathcal{Z},\n\\eeq\nfor the image of $\\{\\phi_i \\in H^2(\\mathcal{Z}, \\mathbb{C})\\}_{i=1}^{l_\\mathcal{Z}}$ under the\nAtiyah--Bott isomorphism.\n \n  The image of each $\\phi_i$ is concentrated on the fixed point cohomology classes with trivial isotropy which \n    are idempotents of the\nclassical Chen-Ruan cup\n  product on $H(\\mathcal{Z})$. Therefore, the components of the $J$-function in the fixed points basis\n\\beq\nJ^{\\mathcal{Z}, \\rm small}(\\tau_{0,2},z) =: \\sum_{j=1}^{N_\\mathcal{Z}} J_j^{\\mathcal{Z}, \\rm small}(\\tau_{0,2},z) P_j\n\\eeq\nsatisfy\n\\beq\nJ_j^{\\mathcal{Z}, \\rm small}(\\tau_{0,2},z) = z \\mathrm{e}^{\\sum_{i=1}^{l_\\mathcal{Z}} \\tau_i\n  c_{ij}\/z}\\l(1+\\mathcal{O}\\l(\\mathrm{e}^{\\tau_{0,2}}\\r)\\r)\n\\label{eq:Jloc}\n\\eeq\nwhere the $\\mathcal{O}\\l(\\mathrm{e}^{\\tau_{0,2}}\\r)$ term on the right hand side is an analytic power\nseries around $\\mathrm{e}^{\\tau_{0,2}}=0$ by \\eqref{eq:Jred} and the assumption of convergence\nof the quantum product. The localized basis $\\{P_j\\}_{j=1}^{N_\\mathcal{Z}}$ therefore\ndiagonalizes the monodromy around large radius: by \\eqref{eq:Jloc}, each\n$J_j^{\\mathcal{Z}, \\rm small}(\\tau_{0,2},z)$ is an eigenvector of the monodromy around a loop in the\n$q_i$-plane encircling the large radius\nlimit of $\\mathcal{Z}$ with eigenvalue $\\mathrm{e}^{2\\pi\\mathrm{i} c_{ij}\/z}$.\n\n\n\\subsubsection{Global mirror symmetry and the closed CRC}\n\n\n\n\n \nConsider a toric  Gorenstein orbifold $\\mathcal{X}$, and let $X \\leftarrow Y$ be a crepant resolution of its coarse moduli space.\nRuan's Crepant Resolution Conjecture  can be phrased as the existence of a {\\it global quantum $D$-module}\nunderlying the quantum differential systems of $\\mathcal{X}$ and $Y$. This is a 4-tuple\n$(\\mathcal M_A, F, \\nabla, H(,)_F)$ with\n\\bit\n\\item $\\mathcal M_A$ a complex quasi-projective variety\n \n \n \n \n\\item $F\\to \\mathcal M_A$ a rank-$N_\\mathcal{Z}$ holomorphic vector bundle on $\\mathcal M_A$; \n\\item $\\nabla$ a flat $\\mathcal{O}_{\\mathcal M_A}$-connection on $F$;\n\\item $H(,)_F \\in \\mathrm{End}(F)$ a non-degenerate $\\nabla$-flat inner product.\n\\end{itemize}\nIn the quantum $D$-module picture, the Crepant Resolution\nConjecture states that there exist open subsets $V_\\mathcal{X}$, $V_Y \\subset \\mathcal M_A$\nand functions $\\mathfrak{h}_\\mathcal{X}, \\mathfrak{h}_Y \\in \\mathcal{O}_{\\mathcal M_A}$\nsuch that \nthe global\n$D$-module $(\\mathcal M_A, F, \\nabla, H(,)_F)$ is locally isomorphic to $\\mathrm{QDM}(\\mathcal{X})$ and\n$\\mathrm{QDM}(Y)$:\n\\bea\n(\\mathcal M_A, F, \\nabla \\circ \\mathfrak{h}_\\mathcal{X}^{1\/z} , H(,)_F)\\big|_{V_\\mathcal{X}} &\\simeq &\\mathrm{QDM}(\\mathcal{X}), \\\\\n(\\mathcal M_A, F, \\nabla \\circ \\mathfrak{h}_Y^{1\/z} , H(,)_F)\\big|_{V_Y} &\\simeq &\\mathrm{QDM}(Y).\n\\end{eqnarray}\nNotice that the Dubrovin connections on $TH(\\mathcal{X})$ and $TH(Y)$ correspond to\ndifferent trivialization of the global flat system $\\nabla$ when $\\mathfrak{h}_\\mathcal{X}\\neq\n\\mathfrak{h}_Y$. \nAny 1-chain $\\rho$ in $\\mathcal M_A$ gives an analytic continuation map\nof $\\nabla$-flat sections \n$\\mathbb{U}^{\\mathcal{X}, Y}_{\\mathcal{S},\\rho}:\\Gamma(V_Y, \\mathcal{O}(F)) \\to \\Gamma(V_\\mathcal{X}, \\mathcal{O}(F))$,\nwhich is an isometry of $H(,)_F$ \nand identifies the quantum $D$-modules of\n$\\mathcal{X}$ and $Y$.\n\\begin{rmk}\nWhen $\\mathfrak{h}_{\\mathcal{X}}\\neq \\mathfrak{h}_{Y}$, the induced Frobenius structures on $H(\\mathcal{X})$ and\n$H(Y)$ are inequivalent. A sufficient condition \\cite{MR2529944} for the two Frobenius\nstructures to coincide is given by the Hard Lefschetz criterion for $\\mathcal{X} \\to X$:\n\\beq\n\\mathrm{age}(\\theta) - \\mathrm{age}(\\mathrm{inv}^*\\theta) = 0\n\\eeq\nfor any class $\\theta\\in H(\\mathcal{X})$.\n\\end{rmk}\n\n\\begin{rmk}\nSuppose that\n$c_1(\\mathcal{Z})\\geq 0$ and that the coarse moduli space $Z$ is a\nsemi-projective toric variety given by a GIT quotient of $\\mathbb{C}^{\\dim\\mathcal{Z}+l_\\mathcal{Z}}$ by $(\\mathbb{C}^*)^{l_\\mathcal{Z}}$.\nIn this setting, the global quantum $D$-module arises naturally in the\nform of the GKZ system associated to $\\mathcal{Z}$ \\cite{MR1653024,\n  MR2271990, ccit2}. The scaling factor $\\mathfrak{h}_\\mathcal{Z}^{1\/z}$ then measures the\ndiscrepancy between the small $J$-function and the canonical basis-vector of\n  solutions of the GKZ system (the {\\it $I$-function}), restriced to zero\n  twisted insertions:\n\\beq\n\\mathfrak{h}_\\mathcal{Z}^{1\/z}(\\tau_{0,2}) J^{\\mathcal{Z}, \\rm small}(\\tau_{0,2}, z) =\nI^\\mathcal{Z}({\\frak a}(\\tau_{0,2}),z),\n\\label{eq:scalingIJ}\n\\eeq\nwhere ${\\frak a}(\\tau_{0,2})$ is the inverse mirror map. As a consequence of \\eqref{eq:scalingIJ}, the\nscaling factor $\\mathfrak{h}_{\\mathcal{Z}}$ is \ndetermined by the toric data defining $\\mathcal{Z}$ \\cite{MR1653024,\n  MR2529944, ccit2}. Let $\\Xi_i\\in H^2(Z)$ be the $T$-equivariant Poincar\\'e dual of the reduction to the quotient of the $i^{\\rm th}$\ncoordinate hyperplane in $\\mathbb{C}^{\\dim\\mathcal{Z}+l_\\mathcal{Z}}$ and write\n$\\zeta^{(j)}_i=\\mathrm{Coeff}_{\\phi_j}\\Xi_i \\in \\mathbb{C}[\\nu]$ for the coefficient of the projection of\n$\\Xi_i$ along $\\phi_j\\in H(\\mathcal{Z})$ for $j=0, \\dots, l_\\mathcal{Z}$. Defining, for every\n$\\beta$, $D_i(\\beta) \\triangleq \\int_\\beta \\Xi_i$ and $J^\\pm_\\beta\\triangleq\\l\\{j \\in\n\\{1,\\dots,\\dim\\mathcal{Z}+l_\\mathcal{Z} \\} | \\pm D_j(\\beta)>0\\r\\}$, we have\n\\bea\n\\tau_l &=& \\log{{\\frak a}_l} + \\sum_{\\beta\\in \\mathrm{Eff}(\\mathcal{Z})}{\\frak a}^\\beta \\frac{\\prod_{j_{-}\\in\n    J^-_\\beta}(-1)^{D_{j_{-}}(\\beta)} |D_{j_{-}}(\\beta)|!}{\\prod_{j_{+}\\in\n    J^+_\\beta}D_{j_{+}}(\\beta)!}\\sum_{k_{-}\\in\n  J^-_\\beta}\\frac{-\\zeta^{(l)}_{k_{-}}}{D_{k_{-}}(\\beta)}, \\quad l=1,\\dots,\nl_\\mathcal{Z}, \n\\end{eqnarray}\n\\bea\n\\mathfrak{h}_\\mathcal{Z} &=& \\exp\\l[\\sum_{\\beta\\in \\mathrm{Eff}(\\mathcal{Z})}{\\frak a}^\\beta \\frac{\\prod_{j_{-}\\in\n    J^-_\\beta}(-1)^{D_{j_{-}}(\\beta)} |D_{j_{-}}(\\beta)|!}{\\prod_{j_{+}\\in\n    J^+_\\beta}D_{j_{+}}(\\beta)!}\\sum_{k_{-}\\in J^-_\\beta}\\frac{-\\zeta^{(0)}_{k_{-}}}{D_{k_{-}}(\\beta)}\\r].\n\\end{eqnarray}\n\\end{rmk}\n\n\n\\subsubsection{Givental's symplectic formalism}\n\\label{sec:givental}\n\nThe global quantum D-module picture is intimately connected to\n the CRC statement of \\cite{MR2510741, coates2007quantum}. In view of our\n statement of the OCRC in Section \\ref{sec:ocrc}, we find it useful to spell\n it out here. Givental's symplectic space $(H_\\mathcal{Z},\\Omega_\\mathcal{Z})$ is the infinite dimensional vector space\n\\beq\n\\mathcal{H}_\\mathcal{Z}\\triangleq H(\\mathcal{Z})\\otimes\\mathcal{O}(\\mathbb{C}^*)\n\\eeq\nalong with the symplectic form\n\\beq\n\\Omega_\\mathcal{Z}(f,g)\\triangleq \\Res_{z=0} \\eta(f(-z),g(z))_\\mathcal{Z}.\n\\label{eq:sympform}\n\\eeq\nA general point of $\\mathcal{H}_\\mathcal{Z}$ can be written as\n\\beq\n\\sum_{k\\geq 0}\\sum_{\\alpha=0}^{N_\\mathcal{Z}-1} q_{k,\\alpha} \\phi_\\alpha z^k+\\sum_{l\\geq 0}\\sum_{\\beta=0}^{N_\\mathcal{Z}-1} p_{l,\\beta} \\phi_\\beta z^{-k-1}.\n\\eeq\nNotice that $\\{q_{k,\\alpha}, p_{l,\\beta}\\}$ are Darboux coordinates for\n\\eqref{eq:sympform}; call $\\mathcal{H}_\\mathcal{Z}^+$ the Lagrangian subpace spanned by\n$q_{k,\\alpha}$. The generating function of genus zero descendent Gromov--Witten invariants of\n$\\mathcal{Z}$,\n\\beq\n\\mathcal{F}_0^\\mathcal{Z} \\triangleq \\sum_{n=0}^\\infty \\sum_{\\beta \\in \\mathrm{Eff}(\\mathcal{Z})}\\sum_{\\substack{a_1, \\dots a_n \\\\ p_1\n    \\dots p_n}} \\frac{\\prod_{i=1}^n \\tau_{a_i,r_i}}{n!}\\left\\langle\n\\sigma_{r_1}(\\phi_{a_1}) \\dots \\sigma_{r_n}(\\phi_{a_n}) \\right\\rangle_{0,n,\\beta}^\\mathcal{Z},\n\\label{eq:descpot}\n\\eeq\nis the germ of an analytic function on $\\mathcal{H}_\\mathcal{Z}^+$ upon identifying\n$\\tau_{0,0}=q_{0,0}+1$, $\\tau_{\\alpha,n}=q_{\\alpha,n}$; under the assumption of convergence\nof the quantum product, coefficients of monomials in $\\tau_{\\alpha,n}$ with\n$\\deg_{\\rm CR} \\phi_\\alpha \\neq 0$, $n > 0$ are analytic functions of $\\mathrm{e}^{\\tau_{0,2}}$\nin a neighbourhood of the origin. The graph of the differential of\n\\eqref{eq:descpot}, \n\\beq\np_{l,\\beta}=\\frac{{\\partial}\\mathcal{F}_0^\\mathcal{Z}}{{\\partial} q^{l,\\beta}},\n\\eeq\nthen yields a formal germ of a Lagrangian submanifold $\\mathcal{L}_\\mathcal{Z}$ (in\nfact, a ruled cone, as a consequence of the genus zero Gromov--Witten axioms),\ndepending analytically on the small quantum cohomology variables\n$\\tau_{0,2}$. By the equations defining the cone, the $J$-function $J^\\mathcal{Z}(\\tau,-z)$ yields a family of\nelements of $\\mathcal{L}_\\mathbb{Z}$ parameterized by $\\tau \\in H(\\mathcal{Z})$, which is uniquely\ndetermined by its large $z$ asymptotics $J(\\tau, -z)=-z+\\tau + \\mathcal{O}(z^{-1})$. Conversely, the genus zero topological recursion relations imply that $\\mathcal{L}_\\mathcal{Z}$ can be reconstructed entirely from $J^\\mathcal{Z}(\\tau, z)$.\n\\\\\n\nThe Crepant Resolution Conjecture has a natural formulation in terms of\nmorphisms of Givental spaces, as pointed out by\nCoates--Corti--Iritani--Tseng (CCIT) \\cite{MR2510741} and further explored by Coates--Ruan\n\\cite{coates2007quantum}. \n\\begin{conj}[\\cite{MR2510741}, \\cite{coates2007quantum}]\nThere exists $\\mathbb{C}((z^{-1}))$-linear symplectic\nisomorphism of Givental spaces $\\mathbb{U}_\\rho^{\\mathcal{X},Y}:\\mathcal{H}_\\mathcal{X}\\rightarrow \\mathcal{H}_Y,$\nmatching the Lagrangian cones of $\\mathcal{X}$ and $Y$ upon a suitable analytic\ncontinuation of small quantum cohomology parameters:\n\\beq\n\\mathbb{U}_{\\rho}^{\\X,Y}(\\mathcal{L}_\\mathcal{X})=\\mathcal{L}_Y.\n\\eeq\n\\end{conj}\nThis version of the CRC is equivalent to the quantum $D$-module approach via the\nfundamental solutions, which give a canonical $z$-linear identification\n\\beq\\label{eq:givetosect}\nS_\\mathcal{Z}(\\tau,z):\\mathcal{H}_\\mathcal{Z}\\stackrel{\\cong}{\\longrightarrow}\\mathcal{S}_\\mathcal{Z}.\n\\eeq\ntranslating the analytic continuation map $\\mathbb{U}_{\\mathcal{S},\\rho}^{\\mathcal{X},Y}$ to a\nlinear isomorphism of Givental spaces which is symplectic, as\n$\\mathbb{U}_{\\mathcal{S},\\rho}^{\\mathcal{X},Y}$ preserves the pairing \\eqref{eq:pairDmod}. \n\\\\\n\nSuppose now that $c_1(\\mathcal{X})=0$, $\\mathrm{dim}_\\mathbb{C}\\mathcal{X}=3$ and assume further that\nthe $J$-functions $J^\\mathcal{Z}$, for $\\mathcal{Z}$ either $\\mathcal{X}$ or $Y$, and $\\mathbb{U}_{\\rho}^{\\X,Y}$ admit well-defined non-equivariant limits,\n\\beq\nJ_{\\rm n-eq}^\\mathcal{Z}(\\tau,z) \\triangleq \\lim_{\\nu\\to 0}J^\\mathcal{Z}(\\tau,z), \\qquad \\mathbb{U}^{\\mathcal{X},Y}_{\\rho,0} \\triangleq \\lim_{\\nu\\to 0} \\mathbb{U}_{\\rho}^{\\X,Y}. \n\\eeq\nBy homogeneity, $\\mathrm{e}^{-\\tau_0\/z} J_{\\rm n-eq}^\\mathcal{Z}(\\tau,z)$ is a Laurent\npolynomial of the form \\cite[\\S10.3.2]{MR1677117}\n\\beq\nJ_{\\rm n-eq}^\\mathcal{Z}(\\tau,z) = \\mathrm{e}^{-\\tau_0\/z}\\l(z + \\sum_{i=1}^{N_\\mathcal{Z}-1}\\l(\\tau_i  +\n\\frac{\\mathfrak{f_i}^\\mathcal{Z}(\\tau)}{z}\\r)\\phi_i + \\frac{\\mathfrak{g}^\\mathcal{Z}(\\tau)}{z^2}\\mathbf{1}_\\mathcal{Z}\\r),\n\\eeq\nwhere $\\mathfrak{f}^\\mathcal{Z}(\\tau)$ and $\\mathfrak{g}^\\mathcal{Z}(\\tau)$ are\nanalytic functions around the large radius limit point of $\\mathcal{Z}$. Restricting $J_{\\rm n-eq}^\\mathcal{Z}(\\tau,z)$\nto $\\Delta_\\mathcal{Z}$ and picking up a branch $\\rho$ of analytic continuation of the\nquantum parameters, the vector valued analytic function $\\mathcal{I}_\\rho^{\\mathcal{X},Y}$\ndefined by\n\\beq\n\\begin{xy}\n(0,20)*+{\\Delta_\\mathcal{X}}=\"a\"; (40,20)*+{\\Delta_Y}=\"b\";\n(0,0)*+{\\mathcal{H}_\\mathcal{X}}=\"c\"; (40,0)*+{\\mathcal{H}_Y}=\"d\";\n{\\ar^{\\mathcal{I}_\\rho^{\\mathcal{X},Y}} \"a\";\"b\"};\n{\\ar_{J_{\\rm n-eq}^\\mathcal{X}\\big|_{\\Delta_\\mathcal{X}}} \"a\";\"c\"};{\\ar^{J_{\\rm n-eq}^Y\\big|_{\\Delta_Y}} \"b\";\"d\"};\n{\\ar^{ \\mathfrak{h}_\\mathcal{X}^{1\/z}\\mathbb{U}^{\\mathcal{X},Y}_{\\rho,0}   \\mathfrak{h}_Y^{-1\/z}} \"c\";\"d\"};\n\\end{xy}\n\\label{eq:iddelta}\n\\eeq\ngives an analytic\nisomorphism\\footnote{Explicitly,  matrix entries $(\\mathbb{U}^{\\mathcal{X},Y}_{\\rho,0})_{ij}$ of\n$\\mathbb{U}^{\\mathcal{X},Y}_{\\rho,0}$ are monomials in $z$; call $\\mathfrak{u}_{ij}$ the\ncoefficient of such monomial. Then \\eqref{eq:iddelta} boils down to the\nstatement that quantum cohomology parameters \n$\\tau^\\bullet_i$ in $\\Delta_\\bullet$ for $i=1, \\dots, l_Y$ are identified as \n\\beq\n\\tau^Y_i = (\\mathcal{I}^{\\mathcal{X},Y}_\\rho \\tau^\\mathcal{X})_i \\triangleq\n\\mathfrak{u}_{i0}+\n\\sum_{j=1}^{l_Y}\\mathfrak{u}_{ij} \\tau_{j}^\\mathcal{X}+\n\\sum_{k=l_Y+1}^{N_Y-1}\\mathfrak{u}_{ik} \\mathfrak{f}^\\mathcal{X}_k(\\tau^\\mathcal{X}).\n\\label{eq:changevargen}\n\\eeq\nSince $\\deg (\\mathbb{U}^{\\mathcal{X},Y}_{\\rho,0})_{ij}>0$ for $j>l_Y$, in the Hard Lefschetz\ncase the condition that the coefficients of $\\mathbb{U}_{\\rho}^{\\X,Y}$ are Taylor series in $1\/z$\nimplies that $\\mathfrak{u}_{ik}=0$ for $k>l_Y$.\n} between neighbourhoods $V_\\mathcal{X}$, $V_Y$ of the\nprojections of the large radius points of $\\mathcal{X}$ and $Y$ to $\\Delta_\\mathcal{X}$ and\n$\\Delta_Y$. \nWhen $\\mathcal{X}$ satisfies the Hard--Lefschetz condition, the coefficients of $\\mathbb{U}_{\\rho}^{\\X,Y}$ contain\nonly non-positive powers of $z$  \\cite{coates2007quantum} and the non-equivariant limit coincides with the\n$z\\to\\infty$ limit; then the isomorphism\n$\\mathcal{I}_\\rho^{\\mathcal{X},Y}$ extends to an affine linear\n change of variables\n$\\widehat{\\mathcal{I}}_\\rho^{\\mathcal{X},Y}:H(\\mathcal{X})\\to H(Y)$ at the level of the full\ncohomology rings of $\\mathcal{X}$ and $Y$, which is \nan isomorphism of Frobenius\nmanifolds.\n\n\n\n\\subsubsection{Integral structures and the CRC}\n\\label{sec:intstr}\n\nIn \\cite{MR2553377}, Iritani uses $K$-groups to define an integral structure\nin the quantum D-module associated to the Gromov--Witten theory of a smooth\nDeligne--Mumford stack $\\mathcal{Z}$;  we recall \n the discussion in \\cite{MR2553377, MR2683208}, adapting\nit to the equivariant setting. \\\\\n\nWrite $K(\\mathcal{Z})$ for the Grothendieck group of topological vector bundles\n$V\\to\\mathcal{Z}$ and consider the map $\\Psi:K(\\mathcal{Z})\\to H(\\mathcal{Z})\\otimes\\mathbb{C}((z^{-1}))$ given by \n\\beq\\label{eq:stackymukai}\n\\Psi(V)\\triangleq (2\\pi)^{-\\frac{\\dim\\mathcal{Z}}{2}}z^{-\\mu} \\widehat\\Gamma_\\mathcal{Z}\\cup(2\\pi\\mathrm{i})^{\\deg\/2}\\mathrm{inv}^*\\mathrm{ch}(V),\n\\eeq\nwhere $\\mathrm{ch}(V)$ is the orbifold Chern character, $\\cup$ is the topological cup\nproduct on $I\\mathcal{Z}$, and \n\\bea\n\\label{eq:gammaT}\n\\widehat\\Gamma_\\mathcal{Z} &\\triangleq & \\bigoplus_v\\prod_f\\prod_\\delta\\Gamma(1-f+\\delta), \\\\\n\\mu & \\triangleq &\\left(\\frac{1}{2}\\deg(\\phi)-\\frac{3}{2}\\right)\\phi,\n\\end{eqnarray}\nwhere the sum in \\eqref{eq:gammaT} is over all connected components of the inertia stack, the left\nproduct is over the eigenbundles in a decomposition of the tangent bundle $T\\mathcal{Z}$\nwith respect to the stabilizer action (with $f$ the weight of the action on the eigenspace), and the\nright product is over all of the Chern roots $\\delta$ of the\neigenbundle. Via the fundamental solution \\eqref{eq:fundsol} this induces a map\nto the space of flat sections of $\\mathrm{QDM}(\\mathcal{Z})$; its image is a lattice \\cite{MR2553377}\nin $\\mathcal{S}_\\mathcal{Z}$, which Iritani dubs the {\\it $K$-theory integral structure} of\n  $QH(\\mathcal{Z})=(H(\\mathcal{Z}) , \\eta, \\circ_\\tau)$. This implies the existence of an integral\n  local system underlying $\\mathrm{QDM}(\\mathcal{Z})$ induced by the $K$-theory of\n  $\\mathcal{Z}$. \\\\\n\nIritani's theory has important implications for the Crepant Resolution\nConjecture. At the level of integral structures, the analytic continuation map\n$\\mathbb{U}_{\\mathcal{S},\\rho}^{\\mathcal{X}, Y}$ of flat sections should be induced by an isomorphism\n$\\mathbb{U}_{K,\\rho}^{\\mathcal{X},Y}: K(Y) \\to K(\\mathcal{X})$ at the $K$-group level,\n\\beq\\label{eq:intstructure}\n\\begin{xy}\n(0,20)*+{K(\\mathcal{X})}=\"a\"; (40,20)*+{K(Y)}=\"b\"\n(0,0)*+{\\mathcal{S}_\\mathcal{X}}=\"c\"; (40,0)*+{\\mathcal{S}_Y}=\"d\";%\n{\\ar^{\\mathbb{U}_{K,\\rho}^{\\mathcal{X},Y}} \"a\";\"b\"};\n{\\ar_{S_\\mathcal{X}(x,z)\\Psi_\\mathcal{X}} \"a\";\"c\"};{\\ar^{S_Y(t,z)\\Psi_Y} \"b\";\"d\"};\n{\\ar^{  \\mathfrak{h}_Y^{1\/z}\\mathbb{U}_{\\mathcal{S},\\rho}^{\\mathcal{X},Y} \\mathfrak{h}_\\mathcal{X}^{-1\/z}} \"c\";\"d\"};\n\\end{xy}\n\\eeq\n\n\nThe Crepant Resolution Conjecture can then be phrased in terms of the\nexistence of an identification of the integral structures underlying\nquantum cohomology. In \\cite{MR2553377}, it is conjectured that\n$\\mathbb{U}_{K,\\rho}^{\\mathcal{X},Y}$ should be induced by a natural geometric\ncorrespondence between $K$-groups (see also \\cite{MR2271990} for earlier work\nin this context). In terms of Givental's symplectic formalism, we have \n\\beq\\label{eq:iritanisymp}\n\\mathbb{U}_\\rho^{\\mathcal{X},Y}=\\Psi_Y\\circ\\mathbb{U}_{K,\\rho}^{\\mathcal{X},Y}\\circ\\Psi_\\mathcal{X}^{-1}.\n\\eeq\n\n\n\\subsection{Open Gromov--Witten theory}\n\\label{sec:ogw}\n\nFor a three-dimensional toric Calabi--Yau variety, open Gromov-Witten invariants \nare defined ``via\nlocalization\" in \\cite{Katz:2001vm, Diaconescu:2003qa}. This theory\nhas been first introduced for orbifold targets in \\cite{MR2861610} and developed in\nfull generality in \\cite{r:lgoa} (see also \\cite{fang2012open} for recent\nresults in this context). \n   Boundary conditions are given by choosing special type of Lagrangian\n   submanifolds introduced by Aganagic--Vafa in\n   \\cite{Aganagic:2000gs}.  These Lagrangians are defined locally in a formal neighborhood of each torus invariant line: in particular if $p$ is a torus fixed point adjacent to the torus fixed line $l$, and the local coordinates at $p$ are $(z,u,v)$, then $L$ is defined to be the fixed points of the anti-holomorphic involution\n   \\beq\n   (z,u,v)\\rightarrow (1\/\\overline{z}, \\overline{zu}, \\overline{zv})\n   \\eeq\n   defined away from $z=0$.  Boundary conditions can then be thought of as ``formal'' ways\n   of decorating the web diagram of the toric target. \\\\\n     \n Loci of fixed maps are described in terms of closed\ncurves mapping to the compact edges of the web diagram in the usual way and disks mapping rigidly to\nthe torus invariant lines with Lagrangian conditions. Beside Hodge integrals coming from the contracting\ncurves, the contribution of each fixed locus to the invariants has a factor\nfor each disk, which is constructed as follows. The map from the disk to a neighborhood\nof its image is viewed as the quotient  via an involution of a map of a\nrational curve to a canonical target. The obstruction theory in ordinary\nGromov-Witten theory admits a natural $\\mathbb{Z}_2$ action, and the equivariant Euler\nclass of the involution invariant part of the obstruction theory is chosen as\nthe localization contribution from the disk \\cite[Section~2.2]{MR2861610}, \\cite[Section~2.4]{r:lgoa}. This construction is efficiently\nencoded via the introduction of a ``disk function\", which we now review in the\ncontext of cyclic isotropy  (see \\cite[Section~3.3]{r:lgoa} for the general\ncase of finite abelian isotropy groups). \\\\\n\nLet $\\mathcal{Z}$ be a  three-dimensional CY toric orbifold,  $p$ a fixed point such\nthat a neighborhood is isomorphic to $[\\mathbb{C}^3\/\\mathbb{Z}_{n+1}]$, with representation\nweights $(m_1, m_2,m_3)$ and CY torus weights  $(w_1,w_2,w_3)$. Define ${n_{e}}=\n(n+1)\/\\gcd(m_1,n+1)$ to be the size of the effective part of the action along\nthe first coordinate axis. \n\n  There exist a map from an orbi-disk mapping to the first coordinate axis with winding $d$ and twisting $k$ if the compatibility condition \n\\beq\n\\frac{d}{{n_{e}}}-\\frac{km_1}{n+1}\\in \\mathbb{Z}\n\\label{compat}\n\\eeq\nis satisfied. In this case the positively oriented disk function  is\n\\begin{equation}\nD_k^+(d;\\vec{w})=\n\\left( \\frac{ {n_{e}}w_1}{d} \\right)^{\\text{age}(k)-1}\\frac{{n_{e}}}{d(n+1)\\left\\lfloor \\frac{d}{{n_{e}}} \\right\\rfloor !}\\frac{\\Gamma\\left( \\frac{dw_{2}}{{n_{e}}w_1}+\\left\\langle \\frac{k m_{3}}{n+1} \\right\\rangle + \\frac{d}{{n_{e}}} \\right)}{\\Gamma\\left( \\frac{dw_{2}}{{n_{e}}w_1}-\\left\\langle \\frac{k m_{2}}{n+1} \\right\\rangle +1 \\right)}.\n\\end{equation}\nThe negatively oriented disk function is obtained by switching the indices $2$\nand $3$. By renaming the coordinate axes this definition applies to the\ngeneral boundary condition. \\\\\n\nIn \\cite{r:lgoa} the disk function is used to construct the GW orbifold\ntopological vertex, a building block for open and closed GW invariants of\n$\\mathcal{Z}$. The disk potential is efficiently expressed in terms of the\ndisk and of the $J$ function of $\\mathcal{Z}$. Fix a Lagrangian boundary condition $L$\nwhich we assume to be on the first coordinate axis in the local chart ( $\\cong [\\mathbb{C}^3\/\\mathbb{Z}_{n+1}]$) around the\npoint $p$. Denote by $\\{\\mathbf{1_{p,k}}\\}_{k=1,...,n+1}$ the part of the localized basis for $H(\\mathcal{Z})$ supported at  $p$.\nRaising indices using the orbifold\nPoincar\\'e pairing, and extending the disk function to be a cohomology valued\nfunction\n\\begin{equation}\n\\mathcal{D}^+(d;\\vec{w})=\\sum_{k=1}^{n+1}D_k^+(d;\\vec{w}) \\mathbf{1_p^k},\n\\end{equation}\nthe (genus zero) \\textit{scalar disk potential} is obtained by contraction with the $J$ function:\n\\bea\nF_{L}^{\\rm disk}(\\tau,y,\\vec{w}) &\\triangleq & \\sum_d\\frac{y^d}{d!}\\sum_n\n\\frac{1}{n!}\\langle \\tau, \\ldots, \\tau \\rangle_{0,n}^{L,d} \\nn \\\\\n&=& \\sum_d \\frac{y^d}{d!}\\left( \\mathcal{D}^+(d;\\vec{w}), J^\\mathcal{Z}\\left(\\tau,\\frac{gw_1}{d}\\right)\\right)_{\\mathcal{Z}},\n\\label{sdp}\n\\end{eqnarray}\nwhere we denoted by $\\langle \\tau, \\ldots, \\tau \\rangle_{0,n}^{L,d}$ the disk\ninvariants with boundary condition $L$, winding $d$\nand $n$ general cohomological insertions.\n\\begin{rmk}\nWe may consider the disk potential relative to multiple Lagrangian boundary conditions. In that case, we define the disk function  by adding the disk functions for each Lagrangian, and we introduce a winding variable for each boundary condition. \n\\end{rmk}\n\n\\begin{rmk}\nIt is not conceptually difficult (but book-keeping intensive) to express the general genus zero open potential in terms of appropriate contractions of arbitrary copies of these disk functions with the full descendant Gromov-Witten potential of $\\mathcal{Z}$.\n\\end{rmk}\n\n\n\\subsection{$A_n$ resolutions}\n\\label{sec:an}\n\n\\subsubsection{GIT Quotients}\n\\label{sec:GIT}\n\nHere we review the relevant toric geometry concerning our targets.  Let\n$\\mathcal{X}\\triangleq[\\mathbb{C}^3\/\\mathbb{Z}_{n+1}]$ be the 3-fold $A_n$ singularity and $Y$ its resolution.\nThe toric fan for $\\mathcal{X}$ has rays $(0,0,1)$, $(1,0,0)$, and $(1,n+1,0)$, while\nthe fan for $Y$ is obtained by adding the rays $(1,1,0)$, $(1,2,0)$,...,\n$(1,n,0)$.  The divisor class group is described by the short exact sequence\n\\beq\n0\\longrightarrow\\mathbb{Z}^{n}\\stackrel{M^T}{\\longrightarrow}\\mathbb{Z}^{n+3}\\stackrel{N}{\\longrightarrow}\\mathbb{Z}^3\\longrightarrow\n0,\n\\label{eq:divclass}\n\\eeq\nwhere\n\\beq\nM=\\left[ \\begin{array}{cccccccc}\n1 & -2 & 1 & 0 & 0 &... &0 & 0\\\\\n0 & 1 & -2 & 1 & 0 &... &0 & 0\\\\\n\\vdots & &\\ddots & &\\ddots & && \\vdots\\\\\n0 &... & 0 & 0 & 1 & -2 & 1 & 0\n\\end{array}\n\\right]\n,\\hspace{.5cm} N=\\left[ \\begin{array}{cccccc}\n1 & 1 & 1 &  & 1 & 0\\\\\n0 & 1 & 2 & ... & n+1 & 0\\\\\n0 & 0 & 0 & & 0 & 1\n\\end{array}.\n\\right]\n\\label{eq:MN}\n\\eeq\n\\\\\nBoth $\\mathcal{X}$ and $Y$ are GIT quotients: \n\\bea\\label{orbgit}\n\\mathcal{X} &=& \\left[\\frac{\\mathbb{C}^{n+3}\\setminus V(x_1\\cdot...\\cdot\n    x_n)}{(\\mathbb{C}^*)^n}\\right], \\\\\nY &=& \\frac{\\mathbb{C}^{n+3}\\setminus V(I_1, \\dots, I_n),\n}{(\\mathbb{C}^*)^n}\n\\label{resgit}\n\\end{eqnarray}\nwhere \n\\beq\nI_i=\\prod_{j=0, j \\neq i-1, i}^{n+1} x_i,\n\\eeq\nand the torus action is specified by $M$. \nFrom the quotient \\eqref{orbgit}, we can compute pseudo-coordinates on the orbifold\n\\begin{equation}\\label{orbcoords}\n\\left[\\begin{array}{c}\nz_1\\\\\nz_2\\\\\nz_3\n\\end{array}\\right]\n=\n\\left[\\begin{array}{c}\nx_0x_1^{\\frac{n}{n+1}}x_2^{\\frac{n-1}{n+1}}\\cdot...\\cdot x_n^{\\frac{1}{n+1}}\\\\\nx_1^{\\frac{1}{n+1}}x_2^{\\frac{2}{n+1}}\\cdot...\\cdot x_n^{\\frac{n}{n+1}}x_{n+1}\\\\\nx_{n+2}\n\\end{array}\\right].\n\\end{equation}\nThese coordinates are only defined up to a choice of $(n+1)^{\\rm st}$\nroot of unity for each $x_i$.  This accounts for a residual $\\mathbb{Z}_{n+1}\\subset\n(\\mathbb{C}^*)^n$ acting with dual representations on the first two coordinates.  We\nidentify this residual $\\mathbb{Z}_{n+1}$ as the subgroup generated by \n$\\left(\\omega,\\omega^2, \\dots, \\omega^n\\right)\\in(\\mathbb{C}^*)^n$, where\n  $\\omega=\\mathrm{e}^{\\frac{2\\pi \\mathrm{i} }{n+1}}$. This realizes the quotient\n\\eqref{orbgit} as the 3-fold $A_n$ singularity where $\\mathbb{Z}_{n+1}=\\langle \\omega\n\\rangle$ acts by $\\omega \\cdot(z_1,z_2,z_3)=(\\omega z_1,\\omega^{-1} z_2,z_3)$.  \n\n\\begin{rmk}\\label{dualrmk}\nThe weights of the $\\mathbb{Z}_{n+1}$ action on the corresponding fibers of $T\\mathcal{X}$ are\ninverse to the weights on the local coordinates because a local trivialization\nof the tangent bundle is given by $\\frac{\\partial}{\\partial z^\\alpha}$ where\n$z^\\alpha$ are the local coordinates. \\\\\n\\end{rmk}\n\n\n\\begin{figure}\n\\centering\n\\includegraphics{webdiagrama3.pdf}\n\\caption{The toric web diagrams for $Y$ and $\\mathcal{X}$ for $n=3$. Fixed points and invariants lines are labelled, together with the relevant torus and representation weights.}\n\\label{fig:web}\n\\end{figure}\n\nThe geometry of the space $Y$ is captured by the toric web diagram in Figure\n\\ref{fig:web}.  In particular, $Y$ has $n+1$ torus fixed points (corresponding\nto the $n+1$ 3-dimensional cones in the fan) and a chain of $n$ torus\ninvariant lines connecting these points.  We label the points\n$p_1$,...,$p_{n+1}$ where $p_i$ correspondes to the cone spanned by $(0,0,1)$,\n$(1,i-1,0)$, and $(1,i,0)$ and we label the torus invariant lines by\n$L_1$,...,$L_n$ where $L_i$ connects $p_i$ to $p_{i+1}$.  We also denote by\n$L_0$ and $L_{n+1}$ the torus invariant (affine) lines corresponding to the\n2-dimensional cones spanned by the rays $(1,0,0), (0,0,1)$ and $(1,n,0),\n(0,0,1)$, respectively. From the quotient \\eqref{resgit} we compute\nhomogeneous coordinates on the line $L_i$\n\\begin{equation}\\label{projcoords}\n\\left[\\begin{array}{c}\nx_0^ix_1^{i-1}\\cdot...\\cdot x_{i-1}\\\\\nx_{n+1}^{n+1-i}x_{n-1}^{n-i}\\cdot...\\cdot x_{i+1}\n\\end{array}\\right]\n\\end{equation}\nwhere $p_i\\leftrightarrow[0:1]$ and $p_{i+1}\\leftrightarrow[1:0]$. \\\\\n\n\nOn the resolution, $H_2(Y)$ is generated by the torus invariant lines $L_i$.\nDefine $\\gamma_i\\in H^2(Y)$ to be dual to $L_i$.  The $\\gamma_i$ form a\nbasis of $H^2(Y)$;  denote the corresponding line bundles by $\\mathcal{O}(\\gamma_i)$.\nNote that $\\mathcal{O}(\\gamma_i)$ restricts to $\\mathcal{O}(1)$ on $L_i$ and $\\mathcal{O}$ on $L_j$ if\n$j\\neq i$ and this uniquely determines the line bundle $\\mathcal{O}(\\gamma_i)$. On the\norbifold, line bundles correspond to $\\mathbb{Z}_{n+1}$ equivariant line bundles on\n$\\mathbb{C}^3$.  We denote $\\mathcal{O}_k$ the line bundle where $\\mathbb{Z}_{n+1}$ acts on fibers\nwith weight $\\omega^k$;  then, for example,  $T_\\mathcal{X}=\\mathcal{O}_{-1}\\oplus\\mathcal{O}_{1}\\oplus\\mathcal{O}_0$ where the subscripts are computed modulo $n+1$ (c.f. Remark \\ref{dualrmk}).\n\n\\subsubsection{Classical equivariant geometry}\\label{sec:elb}\n\nGiven that we are working with noncompact targets, all of our quantum\ncomputations utilize Atiyah-Bott localization with respect to an additional\n$T=\\mathbb{C}^*$ action on our spaces. Let $T$ act on $\\mathbb{C}^{n+3}$ with weights $(\\alpha_1,0,...,0,\\alpha_2,-\\alpha_1-\\alpha_2)$.  Then the induced action on the orbifold and resolution can be read off from the local coordinates in \\eqref{orbcoords} and \\eqref{projcoords}.  In particular, the three weights on the fibers of $T_\\mathcal{X}$ are $-\\alpha_1,-\\alpha_2, \\alpha_1+\\alpha_2$.  The $T$-equivariant Chen-Ruan cohomology $H(\\mathcal{X})$ is\nby definition the $T$-equivariant cohomology of the inertia stack\n$\\mathcal{I}\\mathcal{X}$. The latter has components  $\\mathcal{X}_1, \\dots, \\mathcal{X}_n, \\mathcal{X}_{n+1}$, the last being the untwisted sector\\footnote{While it is more common to index the untwisted sector by $0$, we make this choice of notation for the sake of the computations of Section \\ref{sec:j}, where certain matrices are triangular with this ordering.}: \n\\bea\n\\mathcal{X}_k &=& [\\mathbb{C}\/\\mathbb{Z}_{n+1}], \\quad 1\\leq k \\leq n, \\nonumber \\\\\n\\mathcal{X}_{n+1} &=& [\\mathbb{C}^3\/\\mathbb{Z}_{n+1}]\n\\end{eqnarray}\nWriting $\\mathbf{1}_k$, $k=1, \\dots, n+1$ for the fundamental class of\n$\\mathcal{X}_k$ we obtain a $\\mathbb{C}(\\nu)$ basis of $H(\\mathcal{X})$; the age-shifted grading\nassigns degree $0$ to the fundamental class of the untwisted sector, and\ndegree $1$ to every twisted sector. \nThe Atiyah-Bott localization isomorphism is trivial, i.e. the fundamental class on each twisted sector is identified with the unique $T$-fixed point on that sector.  We abuse notation and use $\\mathbf{1}_k$ to also denote the fixed point basis. \nThe equivariant Chen-Ruan pairing in orbifold cohomology is\n\\beq\n\\eta\\l(\\mathbf{1}_i, \\mathbf{1}_j\\r)_\\mathcal{X} = \\frac{\\delta_{i,n+1}\\delta_{j,n+1}+\\alpha_1\\alpha_2 \\delta_{i+j,n+1}}{\\alpha_1 \\alpha_2(\\alpha_1+\\alpha_2)(n+1)}.\n\\eeq\n\\\\\n\nOn the resolution $Y$, the three weights on the tangent bundle at $p_i$ are \\beq(w_i^-,w_i^+,\\alpha_1+\\alpha_2)\\triangleq((i-1)\\alpha_1+(-n+i-2)\\alpha_2,-i\\alpha_1+(n+1-i)\\alpha_2,\\alpha_1+\\alpha_2).\\eeq\nMoreover, $\\mathcal{O}(\\gamma_j)$ is canonically linearized via the homogeneous coordinates in \\eqref{orbcoords}.  The weight of $\\mathcal{O}(\\gamma_i)$ at the fixed point $p_i$ is\n\\begin{equation}\\label{canwts}\n\\begin{cases}\n(n+1-j)\\alpha_2 & i\\leq j,\\\\\nj\\alpha_1 & i>j.\n\\end{cases}\n\\end{equation}\nDenote by $\\{P_i\\}_{i=1}^{n+1}$ the equivariant cohomology classes\ncorresponding to the fixed points of $Y$.  Choosing the canonical\nlinearization given in \\eqref{canwts}, the Atiyah-Bott localization\nisomorphism on $Y$ is given by\n\\bea\n\\label{eq:ab1}\n\\gamma_j &\\longrightarrow & \\sum_{i\\leq j}(n+1-j)\\alpha_2 P_i +\n\\sum_{i>j}j\\alpha_1P_i, \\\\\n\\gamma_{n+1} & \\longrightarrow &\\sum_{i=1}^{n+1}P_i.\n\\label{eq:ab2}\n\\end{eqnarray}\nwhere $\\gamma_{n+1}$ is the fundamental class on $Y$.  \nGenus zero, degree zero GW invariants are given by equivariant triple\nintersections on $Y$,\n\\beq\n\\left\\langle \\gamma_i, \\gamma_j, \\gamma_k  \\right\\rangle^Y_{0,3,0} = \\int_Y\\gamma_i\\cup\\gamma_j\\cup\\gamma_k.\n\\eeq\nWith $i\\leq j \\leq k<n+1$, \\eqref{eq:ab1}-\\eqref{eq:ab2} yield\n\\bea\n\\left\\langle \\gamma_{n+1}, \\gamma_{n+1}, \\gamma_{n+1}  \\right\\rangle^Y_{0,3,0} &=&\n\\frac{1}{(n+1)\\alpha_1\\alpha_2(\\alpha_1+\\alpha_2)},\\label{ccorr1}\\\\\n\\left\\langle \\gamma_{n+1}, \\gamma_{n+1}, \\gamma_i  \\right\\rangle^Y_{0,3,0} &=&\n0,\\\\\n\\left\\langle \\gamma_{n+1}, \\gamma_i, \\gamma_j  \\right\\rangle^Y_{0,3,0} &=&\n\\frac{i(n+1-j)}{-(n+1)(\\alpha_1+\\alpha_2)}, \\label{eq:eqpair}\\\\\n\\left\\langle \\gamma_i, \\gamma_j, \\gamma_k  \\right\\rangle^Y_{0,3,0} &=&\n-\\frac{ij(n+1-k)\\alpha_1+i(n+1-j)(n+1-k)\\alpha_2}{(n+1)(\\alpha_1+\\alpha_2)}\\label{ccorr4}.\n\\end{eqnarray}\nThe $T$-equivariant pairing $\\eta\\l(\\gamma_i,\\gamma_j\\r)_Y$ is given by \\eqref{eq:eqpair} and diagonalizes in the fixed point basis:\n\\beq\n\\eta\\l(P_i,P_j\\r)_Y=\\frac{\\delta_{i,j}}{w_i^-w_i^+(\\alpha_1+\\alpha_2)}.\n\\eeq\n\n\n\\subsubsection{Quantum equivariant geometry}\n\n We compute the genus $0$ GW invariants of $Y$ via localization (extending the computations of \\cite{MR2411404} to a more general torus action):\n\\begin{equation}\\label{qcorr}\n\\langle \\gamma_{i_1},....,\\gamma_{i_l} \\rangle_{0,l,\\beta} = \\begin{cases}\n-\\frac{1}{d^3} & \\text{if } \\beta= d(L_j+...+L_k) \\text{ with } j\\leq\\min\\{i_\\alpha\\}\\leq\\max\\{i_\\alpha\\}\\leq k,\\\\\n0 &\\text{else.}\n\\end{cases} \n\\end{equation}\nDenote by $\\Phi = \\sum_{i=1}^{n+1} t_i \\gamma_i$ a general\ncohomology class $\\Phi \\in H(Y)$.  The equivariant three-point correlators used to define the quantum cohomology can be computed from \\eqref{ccorr1}-\\eqref{ccorr4}, \\eqref{qcorr}, and the divisor equation (with $\\leq i\\leq j\\leq k\\leq n+1$):\n\\begin{equation}\\label{eq:yukY}\n\\left\\langle\\bra \\gamma_i,\\gamma_j,\\gamma_k\\right\\rangle\\ket_{0,3}^Y(t)=\\int_Y\\gamma_i\\cup\\gamma_j\\cup\\gamma_k-\\sum_{l\\leq i \\leq k \\leq m}\\frac{\\mathrm{e}^{t_l+...+t_m}}{1-\\mathrm{e}^{t_l+...+t_m}}.\n\\end{equation}\n\nThe equivariant quantum cohomology of $\\mathcal{X}$ can then be computed from the following result, which is proven in the appendix of \\cite{MR2510741}.\n\n\\begin{thm}[Coates-Corti-Iritani-Tseng]\\label{thm:crc}\nLet $\\log\\rho:[0,1]\\to H^2(Y)$ be a path in $H^2(Y)$ such that $\\rho$ is a\nstraight line in the K\\\"ahler cone of $Y$ connecting \n\\bea\n\\rho_i(0) &=& 0,  \\\\\n\\rho_i(1) &=& \\omega^{-i}.\n\\end{eqnarray}\nThen upon analytic continuation in the quantum\nparameters $t_i$ along $\\rho$, the quantum products for $\\mathcal{X}$ and $Y$ coincide\nafter the affine-linear change of variables\n\\beq\nt_i=\\l(\\widehat{\\mathcal{I}}^{\\mathcal{X},Y}_\\rho x\\r)_i = \\begin{cases}\n-\\frac{2\\pi\\mathrm{i}}{n+1}+\\sum_{k=1}^{n}\\frac{\\omega^{-ik}(\\omega^{\\frac{k}{2}}-\\omega^{-\\frac{k}{2}})}{n+1}x_k &0<i<n+1\\\\\nx_{n+1}, & i=n+1\\\\\n\\end{cases}\n\\label{eq:changevar}\n\\eeq\nand the linear isomorphism $\\mathbb{U}_{\\rho,0}^{\\mathcal{X}, Y}:H_{T}^{\\rm orb}(\\mathcal{X})\\rightarrow H_T(Y)$\n\\begin{align*}\n\\mathbf{1}_k &\\rightarrow\n\\sum_{i=1}^n\\frac{\\omega^{-ik}(\\omega^{\\frac{k}{2}}-\\omega^{-\\frac{k}{2}})}{n+1}\\gamma_i, \n\\\\\n\\mathbf{1}_{n+1} &\\rightarrow \\gamma_{n+1}.\n\\end{align*}\nFurthermore, $\\mathbb{U}_{\\rho,0}^{\\mathcal{X}, Y}$ \npreserves the equivariant\nPoincar\\'e pairings of $\\mathcal{X}$ and $Y$. \\\\\n\\end{thm}\n\n\\begin{comment} The subscript $0$ in $\\mathbb{U}_{\\rho,0}^{\\mathcal{X}, Y}$ is motivated by the fact that this is the $z \\to\n  \\infty$ limit of the symplectomorphism $\\mathbb{U}_{\\rho}^{\\mathcal{X}, Y}$ sending the formal\n  Lagrangian cone $\\mathcal{L}_\\mathcal{X}$ to $\\mathcal{L}_Y$,\n\\beq\n\\mathbb{U}_{\\rho,0}^{\\mathcal{X}, Y} = \\lim_{z \\to \\infty} \\mathbb{U}_{\\rho}^{\\mathcal{X}, Y}(z),\n\\eeq\nwhich matches the calibrations of the full Frobenius structures. Its expression will be\ncomputed in Section~\\ref{sec:j}.\n\\end{comment}\n\n\n\n\\section{The Open Crepant Resolution Conjecture}\n\\label{sec:ocrc}\n\\subsection{The disk function, revisited}\n\\label{ssec:dcrc}\n\nWe  reinterpret the disk function as an endomorphism of Givental space. First we homogenize Iritani's Gamma class \\eqref{eq:gammaT} and make it of degree zero:\n\\beq\n\\widehat \\Gamma_\\mathcal{Z}(z) \\triangleq z^{-\\frac{1}{2} \\deg}\\widehat \\Gamma_\\mathcal{Z} \\triangleq \\sum \\widehat \\Gamma_\\mathcal{Z}^k \\mathbf{1_{p,k}},\n\\label{irihomo}\n\\eeq\nwhere the second equality defines  $\\widehat \\Gamma_\\mathcal{Z}^k$ as the  $\\mathbf{1_{p,k}}$-coefficient of  $\\widehat \\Gamma_\\mathcal{Z}(z)$. With notation as in Section~\\ref{sec:ogw}, \n\\begin{equation}\n\\widehat \\mathcal{D}_\\mathcal{Z}^+(z;\\vec{w})(\\mathbf{1_{p,k}})\\triangleq \\frac{\\pi }{w_1(n+1)\\sin\\left(\\pi\\left(\\left\\langle \\frac{km_{3}}{n+1} \\right\\rangle -\\frac{w_{3}}{z}\\right)\\right)} \\frac{1}{ \\widehat \\Gamma_\\mathcal{Z}^k }\\mathbf{1_{p,k}}.\n\\label{eq:dr}\n\\end{equation}\n\nThe natural basis of inertia components gives  a basis of eigenvectors for the linear transformation $\\widehat \\mathcal{D}_\\mathcal{Z}^+: \\mathcal{H}_\\mathcal{Z} \\to \\mathcal{H}_\\mathcal{Z}$.\n\n\\begin{lem}\nThe $k$-th eigenvalue of $\\widehat \\mathcal{D}_\\mathcal{Z}^+$ coincides with $ D_k (d;\\vec{w})$ when $z= n_ew_1\/d$ and the winding\/twisting compatibility condition is met:\n\\beq\n\\delta_{1,\\exp\\left({2\\pi i \\left(\\frac{d}{n_e}-\\frac{km_1}{n+1}\\right)}\\right)}\n\\left(\\widehat \\mathcal{D}_\\mathcal{Z}^+\\left(\\frac{n_ew_1}{d};\\vec{w}\\right)(\\mathbf{1_{p,k}}),\\mathbf{1_{p}^k} \\right)_\\mathcal{Z} = D_k (d;\\vec{w})\n\\eeq\n\\end{lem}\n\\begin{proof}\nThis formula follows from the explicit expression of $\\widehat\\Gamma_\\mathcal{Z}$ in the localization\/inertia basis, manipulated via the identity $\\Gamma(\\star)\\Gamma(1-\\star)= \\frac{\\pi}{\\sin(\\pi\\star)}$. The Calabi-Yau condition $w_1+w_2+w_3=0$ is also used. The $\\delta$ factor encodes the degree\/twisting condition.\n\\end{proof}\n\nLet now $\\mathcal{X} \\rightarrow X \\leftarrow Y$ be a diagram of toric Calabi--Yau\nthreefolds for which the CCIT\/Coates--Ruan version of the closed crepant\nresolution conjecture holds.\nChoose a\nLagrangian boundary condition $L_\\mathcal{X}$ in $\\mathcal{X}$ and denote by $L_Y$ the transform of\nsuch condition in $Y$; notice that in general this can consist of several Lagrangian\nboundary conditions. We have the following\n\\begin{prop}\nThere exists a $\\mathbb{C}((z^{-1}))$-linear transformation $\\mathbb{O}: \\mathcal{H}_\\mathcal{X} \\to \\mathcal{H}_Y$ of Givental spaces such that\n\\beq\n\\widehat\\mathcal{D}_Y^+ \\circ \\mathbb{U}_{\\rho}^{\\X,Y} = \\mathbb{O} \\circ \\widehat\\mathcal{D}_\\mathcal{X}^+.\n\\eeq\n\\label{prop:o}\n\\end{prop}\n\nThis proposition is trivial, as $\\mathbb{O}$ can be constructed as $\\widehat\\mathcal{D}_Y^+ \\circ \\mathbb{U}_{\\rho}^{\\X,Y}\\circ ( \\widehat\\mathcal{D}_\\mathcal{X}^+)^{-1}$. However we observe that interesting open crepant resolution statements follow from this simple fact, and that $\\mathbb{O}$ is a  simpler object than $\\mathbb{U}_{\\rho}^{\\X,Y}$, and for a good reason: our disk function almost completely ``undoes\" the transcendental part in Iritani's central charge. We make this precise in the following  observation.\n\n\\begin{lem}\nReferring to equations \\eqref{eq:gammaT} and \\eqref{eq:dr} for the relevant definitions, we have\n\\bea\n \\Theta_\\mathcal{Z}(\\mathbf{1_{p,k}}) &\\triangleq & z^{-\\mu}\\widehat\\Gamma_\\mathcal{Z} \\cup\n \\widehat\\mathcal{D}_\\mathcal{Z}^+ (\\mathbf{1_{p,k}}) \\nn \\\\ &=& \\frac{z^{\\frac{3}{2}}\\pi }{w_1(n+1)\\sin\\left(\\pi\\left(\\left\\langle \\frac{km_{3}}{n+1} \\right\\rangle -\\frac{w_{3}}{z}\\right)\\right)} \\mathbf{1_{p,k}}\n\\label{Theta}\n\\end{eqnarray}\n\\label{lem:ga}\n\\end{lem}\n\nIn the hypotheses and notation of Proposition \\ref{prop:o}, note that $\\mathcal{X}$ and $Y$ must be related by variation of GIT, and therefore they are quotients of a common space $Z=\\mathbb{C}^{l_Y+3}$. Consider a \\textit{grade restriction window}\\footnote{We borrow the terminology from \\cite{ed:window}. See also \\cite{bfk:window} and \\cite{hhp:window}.} $\\mathfrak{W}\\subset K(Z)$: a set of equivariant bundles on $Z$ that descend bijectively to bases for  $K(\\mathcal{X})\\otimes \\mathbb{C}$ and $K(Y)\\otimes \\mathbb{C}$. Combining Lemma \\ref{lem:ga} with Iritani's proposal \\eqref{eq:iritanisymp}, we obtain the following prediction.\n\\begin{conj}\nDenote by $\\widehat{CH}_\\bullet= z^{-\\frac{1}{2}\\deg }CH_\\bullet$ the  (homogenized) matrix of Chern characters in the bases given by $\\mathfrak{W}$. Let $\\Theta_\\bullet$ be as in equation \\eqref{Theta}. Then:\n\\beq\n\\mathbb{O}= \\Theta_Y\\circ\\widehat{CH}_Y \\circ \\widehat{CH}^{-1}_\\mathcal{X} \\circ {\\Theta_\\mathcal{X}}^{-1}.\n\\eeq\n\\label{conj:iri}\n\\end{conj}\n\n\nWe verify Conjecture~\\ref{conj:iri} for the resolution of $A_n$ singularities in Section \\ref{sec:An}. We also note that while we are formulating the statement in the case of cyclic isotropy to keep notation lighter, it is not hard to write an analog prediction in a completely general toric setting.\\\\\n\nHaving modified our perspective on the disk functions, we also update our take\non open disk invariants to remember the twisting of the map at the origin of\nthe disk. In correlator notation, denote  $\\langle \\tau, \\ldots, \\tau \\rangle_{0,n}^{L,d,k}$ the disk\ninvariants with Lagrangian boundary condition $L$, winding $d$, twisting $k$ \nand $n$ cohomology insertions. We then define the \\textit{cohomological disk potential} as a cohomology valued function, which is expressed as a composition of the $J$ function with the  disk function \\eqref{eq:dr}:\n\\bea\n\\mathcal{F}_{L}^{\\rm disk}(\\tau,y,\\vec{w}) & \\triangleq &\\sum_d\\frac{y^d}{d!}\\sum_n\n\\frac{1}{n!}\\langle \\tau, \\ldots, \\tau \\rangle_{0,n}^{L,d,k}\\mathbf{1_{p,k}}, \\nn \\\\\n&=& \\sum_d \\delta_{1,\\exp\\left({2\\pi \\mathrm{i} \\left(\\frac{d}{n_e}-\\frac{km_1}{n+1}\\right)}\\right)}\\frac{y^d}{d!}\\widehat \\mathcal{D}_\\mathcal{Z}^+\\circ J^\\mathcal{Z}\\left(\\tau,\\frac{n_ew_1}{d},\\vec{w}\\right).\n\\label{cohdp}\n\\end{eqnarray}\nWe define a section of Givental space that  contains equivalent information to the disk potential:\n\\begin{equation}\n\\widehat \\mathcal{F}_{L}^{\\rm disk}(t,z,\\vec{w}) \\triangleq \\widehat \\mathcal{D}_\\mathcal{Z}^+ \\circ J^\\mathcal{Z}\\left(\\tau,z;\\vec{w}\\right).\n\\end{equation}\n\n\\begin{figure}[tb]\n$$\n\\xymatrix{\n{\\mathcal{H}_\\mathcal{X}}   \\ar[rrrrr]^\\mathbb{O} &  &   &   & & \\mathcal{H}_Y \\\\\n\\\\\n\\mathcal{H}_\\mathcal{X}  \\ar[rrrrr]^{\\mathbb{U}_{\\rho}^{\\X,Y}} \\ar[uu]_{\\widehat\\mathcal{D}_\\mathcal{X}}& &   &   & & \\mathcal{H}_Y \\ar[uu]^{\\widehat\\mathcal{D}_Y}\\\\\n& & \n\\Delta_\\mathcal{X}  \\ar[ull]_{\\mathfrak{h}^{1\/z}_{\\mathcal{X}} J^\\mathcal{X}} \\ar@\/^6pc\/[uuull]^{\\mathfrak{h}^{1\/z}_{\\mathcal{X}} \\widehat \\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}}  \n\\ar[r]^{\\mathcal{I}^{\\mathcal{X},Y}_\\rho} &\n\\Delta_Y   \\ar[urr]^-{\\mathfrak{h}^{1\/z}_{Y}\\widetilde J^Y}\n\\ar@\/_6pc\/[uuurr]_{{\\mathfrak{h}^{1\/z}_{Y} \\widehat \\mathcal{F}_{L,Y}^{\\rm disk}}} & \n}\n$$\n\\caption{Open potential comparison diagram. \nIn the Hard Lefschetz case this same diagram holds with the $\\mathfrak{h}$ factors omitted, and $\\Delta_\\bullet$ identified with the full cohomologies of either target.}\n\\label{diag}\n\\end{figure}\n\nWe call $\\widehat \\mathcal{F}_{L}^{\\rm disk}(t,z,\\vec{w}) $ the \\textit{winding\n  neutral disk potential}. For any pair of integers $k$ and $d$ satisfying\n\\eqref{compat}, the twisting $k$ and winding $d$ part of the disk potential\nis obtained by substituting $z=\\frac{n_ew_1}{d}$. A general ``disk crepant\nresolution statement\" that follows from the closed CRC is a comparison of\nwinding-neutral potentials, as illustrated in Figure~\\ref{diag}. \n\n\\begin{prop}\nLet $\\mathcal{X} \\rightarrow X \\leftarrow Y$ be a  diagram for which the\nCCIT\/Coates--Ruan form of the closed crepant resolution conjecture\nholds and identify quantum parameters in $\\Delta_\\mathcal{X}$ and\n  $\\Delta_Y$ via $\\mathcal{I}_\\rho^{\\mathcal{X},Y}$ as in \\eqref{eq:iddelta}. Then: \n\\beq\n\\mathfrak{h}^{1\/z}_Y {\\widehat \\mathcal{F}_{L,Y}^{\\rm disk}}\\big|_{\\Delta_Y}= \\mathfrak{h}^{1\/z}_\\mathcal{X} \\mathbb{O}\\circ \\widehat \\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}\\big|_{\\Delta_\\mathcal{X}}.\n\\label{eq:dcrc}\n\\eeq\nAssume further that $\\mathcal{X}$ satisfies the Hard Lefschetz condition and\nidentify cohomologies via the affine linear change of variables $\\widehat{\\mathcal{I}}_\\rho^{\\mathcal{X},Y}$. Then:\n\\beq\n{\\widehat \\mathcal{F}_{L,Y}^{\\rm disk}}=\\mathbb{O}\\circ \\widehat \\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}.\n\\eeq\n\\label{prop:wncrc}\n\\end{prop}\nHere we also understand that the winding-neutral disk potential of $Y$ is\nanalytically continued appropriately (we suppressed the tilde to avoid\nexcessive proliferation of superscripts). \n\n\\begin{rmk}\nAt the level of cohomological disk\npotentials, the normalization factors $\\mathfrak{h}_\\mathcal{X}$ and $\\mathfrak{h}_Y$ enter as a\nredefinition of the winding number variable $y$ in \\eqref{cohdp} depending on small quantum cohomology parameters; this is the manifestation\nof the the so-called {\\it open mirror map} in the physics literature on open\nstring mirror symmetry \\cite{Lerche:2001cw,\n  Aganagic:2001nx, Bouchard:2007ys, Brini:2011ij}. \n\\end{rmk}\n\n\\begin{rmk}\nThe statement of the proposition in principle hinges on the very possibility to identify\nquantum parameters as in \\eqref{eq:iddelta}-\\eqref{eq:changevargen}. In fact, the existence of the non-equivariant limits of\n  $\\mathbb{U}_{\\rho}^{\\X,Y}$ and the $J$-functions in our case is guaranteed by the fact that we restrict\n  to torus actions acting trivially on the canonical bundle of $\\mathcal{X}$ and $Y$; see e.g.~\\cite{moop}.\\\\\n\\end{rmk}\n\n\\subsection{The Hard Lefschetz OCRC}\n\n\nIn the Hard Lefschetz case the comparison of disk potentials naturally extends to the full genus zero open potential. We first define the \\textit{n-holes winding neutral potential}, a function from $H(\\mathcal{Z})$ to the $n$-th tensor power of Givental space $\\mathcal{H}_\\mathcal{Z}^{\\otimes n}= H(\\mathcal{Z})((z_1^{-1}))\\otimes\\ldots \\otimes H(\\mathcal{Z})((z_n^{-1}))$:\n\\beq\n\\widehat \\mathcal{F}^n_{L}(\\tau,z_1,\\ldots,z_n,\\vec{w}) \\triangleq \\widehat \\mathcal{D}_\\mathcal{Z}^{+\\otimes n} \\circ J^\\mathcal{Z}_n\\left(\\tau,z_1,\\ldots, z_n;\\vec{w}\\right),\n\\label{mholepot}\n\\eeq\nwhere $J^\\mathcal{Z}_n$ encodes $n$-point descendent invariants:\n\\beq\nJ^\\mathcal{Z}_n(\\tau,\\mathbf{z}; \\vec{w})\\triangleq \\left\\langle\\bra\n\\frac{\\phi_{\\alpha_1}}{z_1-\\psi_1}, \\dots,  \\frac{\\phi_{\\alpha_n}}{z_n-\\psi_n}\n\\right\\rangle\\ket_{0,n}\\phi^{\\alpha_1}\\otimes\\cdots\\otimes\\phi^{\\alpha_n}.\n\\label{eq:JZn}\n\\eeq\nIn \\eqref{eq:JZn}, we denoted $\\mathbf{z}=(z_1,\\dots,z_n)$ and a sum over repeated\nGreek indices is intended.  \nJust as in the disk case, one can now define a winding neutral open potential by summing over all integers $n$ and a cohomological open potential by introducing winding variables and summing over appropriate specializations of the $z$ variables. For a pair or spaces $\\mathcal{X}$ and $Y$ in a Hard Lefschetz CRC diagram then the respective potentials can be compared as in Section~\\ref{ssec:dcrc} - this all follows  from the comparison of the $n$-holes winding neutral potential, which we now spell out with care.\n\n\\begin{thm}\\label{thm:manyholes}\nLet $\\mathcal{X} \\rightarrow X \\leftarrow Y$ be a Hard Lefschetz diagram for which the closed crepant resolution conjecture holds. With all notation as in Proposition \\ref{prop:wncrc}, and  $\\mathbb{O}^{\\otimes n}= \\mathbb{O}(z_1)\\otimes\\ldots\\otimes \\mathbb{O}(z_n)$, we have:\n\\beq\n{\\widehat \\mathcal{F}_{L',Y}^{n}}= \\mathbb{O}^{\\otimes n}\\circ \\widehat \\mathcal{F}_{L,\\mathcal{X}}^{n}\n\\eeq\n\\end{thm}\n\n\\begin{proof}\nThe proof follows from the fact that the $n$-th tensor power of the\nsymplectomorphism $\\mathbb{U}_{\\rho}^{\\X,Y}$  compares the $J_n$'s:\n\\beq\n{ J^{Y}_{n}}= {\\mathbb{U}_{\\rho}^{\\X,Y}}^{\\otimes n}\\circ J^{\\mathcal{X}}_{n}.\n\\label{ujn}\n\\eeq \nFor $\\mathcal{Z}$ either $\\mathcal{X}$ or $Y$, define\n\\bea\nL_\\mathcal{Z}^n(\\tau,\\mathbf{z}) & \\triangleq  & \\mathrm{d} J^\\mathcal{Z}_n(\\tau,\\mathbf{z}) = \\left(\n\\frac{\\partial J^\\mathcal{Z}_n(\\tau,\\mathbf{z})}{\\partial \\tau_\\beta} \\right)\\otimes\n\\phi^\\beta \\nn \\\\ &=& \\left\\langle\\bra \\frac{\\phi_{\\alpha_1}}{z_1-\\psi_1}, \\dots,  \\frac{\\phi_{\\alpha_n}}{z_n-\\psi_n}, \\phi_\\beta \\right\\rangle\\ket_{0,n+1}\\phi^{\\alpha_1}\\otimes\\cdots\\otimes\\phi^{\\alpha_n}\\otimes\\phi^\\beta.\n\\end{eqnarray}\n\nHere $\\mathrm{d}$ is the total differential, and the second equality is its expression in coordinates with the natural identification of $\\mathrm{d}\\tau_\\beta$ with $\\phi^\\beta$. Since the total differential is a coordinate independent operator, we have the following.\n\n\\begin{lem}\\label{lem:op}\nAfter the change of variables and the linear isomorphism prescribed in the closed CRC (e.g. Theorem \\ref{thm:crc} for the $A_n$ resolutions), we have an equivalence of operators:\n\\beq\n\\sum_{1\\leq k\\leq n+1}\\left( \\frac{\\partial(-)}{\\partial x_k}\n\\right)\\otimes\\mathbf{1}^k =\\sum_{1\\leq i\\leq n+1}\\left( \\frac{\\partial(-)}{\\partial\n  t_i} \\right)\\otimes\\gamma^i. \\\\\n\\eeq\n\\end{lem}\n\n\n\n\n\nNow we deduce \\eqref{ujn}  by induction.  The result holds for $n=1$\n(this is the statement of the closed CRC), assume it holds for all $m<n$.  Define $\\widehat\\mathbb{U}^m(z_1,\n\\ldots, z_{m+1})\\triangleq{\\mathbb{U}_{\\rho}^{\\X,Y}}^{\\otimes m}(z_1, \\ldots, z_m)\\otimes\\mathbb{U}_0(z_{m+1})$.\nIt follows from Lemma \\ref{lem:op} that $\\widehat\\mathbb{U}^m(\\left( L_\\mathcal{X}^m(x,\\mathbf{z})\n\\right)=L_Y^m(t,\\mathbf{z})$ for all $m<n$. \\\\\n\nFor $\\mathcal{Z}$ either $\\mathcal{X}$ or $Y$, the WDVV relations give:\n\\bea\n& & D(1, n+1|2,n+2)\n\\left\\langle\\bra\\frac{\\phi_{\\alpha_1}}{z_1-\\psi_1}\\cdots\n\\frac{\\phi_{\\alpha_n}}{z_n-\\psi_n} \\mathbf{1}_\\mathcal{Z}\\cdot\\mathbf{1}_\\mathcal{Z}\\right\\rangle\\ket_{0,n+2} \\nn \\\\\n&=& D(1,2|n+1,n+2)\n\\left\\langle\\bra\\frac{\\phi_{\\alpha_1}}{z_1-\\psi_1}\\cdots \\frac{\\phi_{\\alpha_n}}{z_n-\\psi_n} \\mathbf{1}_\\mathcal{Z}\\cdot\\mathbf{1}_\\mathcal{Z}\\right\\rangle\\ket_{0,n+2},\n\\label{eq:wdvv}\n\\end{eqnarray}\n where $D(i,j|k,l)$ is the divisor in the moduli space which separates the points $i,j$ from $k,l$ (pull-back of the class of a boundary point in $\\overline{M}_{0,4}$).  Expanding \\eqref{eq:wdvv}, we have\n\n\\begin{align}\n\\sum_{1\\in J \\atop 2\\notin J}&\\left( \\left\\langle\\bra \\mathbf{1}_\\mathcal{Z}\\cdot\\prod_{i\\in J}\\frac{\\phi_{\\alpha_i}}{z_i-\\psi_i}\\cdot\\phi_\\beta \\right\\rangle\\ket_{0,|J|+2}\\phi^\\beta,  \\left\\langle\\bra \\mathbf{1}_\\mathcal{Z}\\cdot\\prod_{i\\notin J}\\frac{\\phi_{\\alpha_i}}{z_i-\\psi_i}\\cdot\\phi_\\epsilon \\right\\rangle\\ket_{0,|J^c|+2}\\phi^\\epsilon \\right)_\\mathcal{Z}\n\\nonumber\\\\\n&=\\sum_{1,2\\in J}\\left( \n\\left\\langle\\bra \\prod_{i\\in J}\\frac{\\phi_{\\alpha_i}}{z_i-\\psi_i}\\cdot\\phi_\\beta \\right\\rangle\\ket_{0,|J|+1}\\phi^\\beta\n,\n\\left\\langle\\bra \\mathbf{1}_\\mathcal{Z}\\cdot\\mathbf{1}_\\mathcal{Z}\\cdot\\prod_{i\\not\\in J}\\frac{\\phi_{\\alpha_i}}{z_i-\\psi_i}\\cdot\\phi_\\epsilon \\right\\rangle\\ket_{0,|J^c|+3}\\phi^\\epsilon   \\right)_\\mathcal{Z}\n\\end{align}\nwhere the sum index $J$ ranges over  subsets of $\\{1,...,n\\}$.  Applying the string equation to eliminate the fundamental class insertions and summing over all $\\alpha_i$, we obtain the relation\n\\begin{align}\\label{lemrel}\n\\sum_{1\\in J \\atop 2\\notin J}&\\left( \\left( \\sum_{i\\in J} \\frac{1}{z_i} \\right) L_\\mathcal{Z}^{|J|}(\\tau,\\mathbf{z}_J), \\left( \\sum_{i\\notin J} \\frac{1}{z_i} \\right) L_\\mathcal{Z}^{|J^c|}(\\tau,\\mathbf{z}_{J^c}) \\right)_\\mathcal{Z} \\nonumber\\\\\n&=\\sum_{1,2\\in J \\atop J^c\\neq\\emptyset}\\left(\n L_\\mathcal{Z}^{|J|}(\\tau,\\mathbf{z}_{J}) \n ,\n  \\left( \\sum_{i\\notin J} \\frac{1}{z_i} \\right)^2 L_\\mathcal{Z}^{|J^c|}(\\tau,\\mathbf{z}_{J^c})\n \\right)_\\mathcal{Z}\n+\\left( \\sum_{1\\leq i\\leq n} \\frac{1}{z_i} \\right) J^\\mathcal{Z}_n(\\tau,\\mathbf{z})\n\\end{align}\nwhere $(-,-)_\\mathcal{Z}$ is extended by applying Poincar\\'e pairing on the last coordinate and tensoring the remaining coordinates in the appropriate order.  Equation \\eqref{lemrel} allows us to write $J_n$ for either $\\mathcal{X}$ or $Y$ in terms of $L^m$ with $m<n$.  Since $\\widehat\\mathbb{U}^m$ identifies $L_\\mathcal{X}^m$ with $L_Y^m$ and $\\mathbb{U}_0$ preserves the Poincar\\'e pairing, it follows that ${\\mathbb{U}_{\\rho}^{\\X,Y}}^{\\otimes n}(\\mathbf{z})(J^\\mathcal{X}_n(x,\\mathbf{z}))=J^Y_n(t,\\mathbf{z})$.\n\\end{proof}\n\n\n\\section{OCRC for $A_n$ resolutions}\n\\label{sec:An}\n\nFor the  pairs $(\\mathcal{X},Y)=\\left([\\mathbb{C}^{3}\/\\mathbb{Z}_{n+1}],A_n\\right)$, Propositions \\ref{prop:wncrc} and \\ref{thm:manyholes} imply a Bryan-Graber type CRC statement comparing the open GW potentials.  Notice that since $\\mathcal{X}$ is a Hard Lefschetz orbifold we do not have to deal with the normalization factors $\\mathfrak{h}_\\bullet$.\nIn Sections \\ref{sec:ia} and \\ref{sec:ea} we study the two essentially distinct types of Lagrangian boundary conditions.\n\n\n\n\n\n\\subsection{Equivariant  $\\mathbb{U}_{\\rho}^{\\X,Y}$ and Integral Structures}\n\\label{sec:u}\nWe write the equivariant version of the symplectomorphism $\\mathbb{U}_{\\rho}^{\\X,Y}$.\n\n\\begin{thm}\nWith notation as in Theorem~\\ref{thm:crc}, let $\\widetilde{J}^Y(z)$ denote the analytic continuation of $J^Y$ along the path $\\rho$ to the\npoint $\\rho(1)$ composed with the identification \\eqref{eq:changevar} of\nquantum parameters. Then the linear transformation\n\\beq\n\\label{eq:Uiri}\n\\mathbb{U}_{\\rho}^{\\X,Y}\\mathbf{1_k}=\\sum_i P_i\\frac{1}{(n+1)}\\frac{\\widehat\\Gamma_Y^i}{\\widehat\\Gamma_\\mathcal{X}^k}\\left( \\sum_{j=0}^{i-1}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i}\\frac{j\\alpha_1}{z}}+\\sum_{j=i}^{n}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i}\\frac{(n+1-j)\\alpha_2}{z}} \\right)\n\\eeq\nis a linear isomorphism of Givental spaces such that\n\\beq\n\\widetilde{J}^Y= \\mathbb{U}_{\\rho}^{\\X,Y}\\circ {J}^\\mathcal{X}.\n\\eeq\n\\label{thm:sympl}\n\\end{thm}\n\nThe proof of this theorem in the equivariant setting is a consequence of our computations in Section~\\ref{sec:j}. \n\n\n\\begin{rmk}\nIn \\eqref{eq:stackymukai} we can replace the operator $z^{-\\mu}$ by the ``homogenization\noperator\" $z^{-\\frac{1}{2}\\deg}$ since the additional $z^{\\frac{3}{2}}$ part\ncontributes two canceling scalar factors. \\\\\n\\end{rmk}\n\nWe observe now that this result is compatible with Iritani's proposal\n\\eqref{eq:iritanisymp}. We first describe the canonical identification\n$\\mathbb{U}_{K,\\rho}^{\\mathcal{X},Y}$. Denote by $\\mathcal{O}(\\lambda_k)$ the geometrically trivial line bundle on $\\mathbb{C}^{n+3}$ where the torus $(\\mathbb{C}^*)^n$ acts via the $k$th factor with weight $-1$ and the torus $T$ acts trivially.  We define our grade restriction window $\\mathfrak{W}\\subset K(\\mathbb{C}^{n+3})$ to be the subgroup generated by the $\\mathcal{O}(\\lambda_k)$.  Using the description of the local coordinates in Section \\ref{sec:GIT}, we compute that the quotient \\eqref{orbgit} identifies $\\mathcal{O}(\\lambda_k)$ with $\\mathcal{O}_{-k}$ (with trivial $T$-action) and the quotient \\eqref{resgit} identifies $\\mathcal{O}(\\lambda_k)$ with $\\mathcal{O}(\\gamma_k)$ (with canonical linearization \\eqref{canwts}).  Therefore, we define $\\mathbb{U}_{K,\\rho}^{\\mathcal{X},Y}$ by identifying\n\\begin{align}\n\\mathcal{O}_Y&\\leftrightarrow\\mathcal{O}_\\mathcal{X}\\\\\n\\mathcal{O}(\\gamma_k)&\\leftrightarrow\\mathcal{O}_{-k}\n\\end{align}\nwhere the $T$-linearizations are trivial on the orbifold and canonical on the\nresolution. \\\\\n\nOn the orbifold, all of the bundles $\\mathcal{O}_j$ are linearized trivially, so the higher Chern classes vanish.  The orbifold Chern characters are:\n\\beq\n(2\\pi\\mathrm{i})^{\\deg\/2}I^*\\mathrm{ch}(\\mathcal{O}_j)=\\sum_{k=1}^{n+1}\\omega^{-jk}\\mathbf{1}_k.\n\\eeq\nThe $\\Gamma$ class is\n\\begin{align}\nz^{-\\frac{1}{2}\\deg}\\hat\\Gamma_\\mathcal{X}=\\Gamma&\\left(1+\\frac{\\alpha_1+\\alpha_2}{z}\\right)\\\\\n&\\hspace{-1cm}\\cdot\\left[ \\sum_{k=1}^n \\Gamma\\left(1-\\frac{k}{n+1}-\\frac{\\alpha_1}{z}\\right)\\Gamma\\left(\\frac{k}{n+1}-\\frac{\\alpha_2}{z}\\right)\\frac{\\mathbf{1}_k}{z}\n+\n\\Gamma\\left(1-\\frac{\\alpha_1}{z}\\right)\\Gamma\\left(1-\\frac{\\alpha_2}{z}\\right)\\mathbf{1}_{n+1}\\right]\n\\end{align}\n\nOn the resolution, the Chern roots at each $P_i$ are the weights of the action on the fiber above that point:\n\\beq\n(2\\pi\\mathrm{i})^{\\deg\/2}\\mathrm{ch}(\\mathcal{O}(\\gamma_j))=\\sum_{i=1}^{j}\\mathrm{e}^{2\\pi\\mathrm{i}(n+1-j)\\alpha_2}P_i+\\sum_{i=j+1}^{n+1}\\mathrm{e}^{2\\pi\\mathrm{i}\n  j\\alpha_1}P_i\n\\eeq\nand\n\\beq\n(2\\pi\\mathrm{i})^{\\deg\/2}\\mathrm{ch}(\\mathcal{O})=\\sum_{i=1}^{n+1}P_i.\n\\eeq\nThe $\\Gamma$ class is\n\\beq\nz^{-\\frac{1}{2}\\deg}\\hat\\Gamma_Y=\\Gamma\\left(1+\\frac{\\alpha_1+\\alpha_2}{z}\\right)\\left[ \\sum_{i=1}^{n+1} \\Gamma\\left(1+\\frac{w_i^+}{z} \\right)\\Gamma\\left( 1+\\frac{w_i^-}{z} \\right) P_i\\right]\n\\eeq\nWith this information one can compute \\eqref{eq:iritanisymp} and obtain the formula in Theorem \\ref{thm:sympl}. \\\\\n\nWe now derive explicit disk potential CRC statements for the two distinct types of Lagrangian boundary conditions.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection{$L$ intersects the ineffective axis}\n\\label{sec:ia}\nWe impose a Lagrangian boundary condition on the gerby leg of the orbifold (the third coordinate axis - $m_3=0$); correspondingly there are $n+1$ boundary conditions $L'$ on the resolution, intersecting the horizontal torus fixed lines  in Figure~\\ref{fig:web}.\n\\begin{thm}\nConsider the cohomological disk potentials $\\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}(t,y,\\vec{w}) $ and $\\mathcal{F}_{L',Y}^{\\rm disk}(t,y_{P_1}, \\dots, y_{P_{n+1}},\\vec{w})$.\nChoosing the bases $\\mathbf{1_k}$ and $P_i$ (where $k$ and $i$ both range from $1$ to $n+1$), define a linear transformation \n$\n\\mathbb{O}_\\mathbb{Z}:H(\\mathcal{X}) \\to H(Y)\n$\n by the matrix\n\\beq\n\\mathbb{O}_{\\mathbb{Z}\\ i,k} = \\left\\{\\begin{array}{ll}- \\omega^{\\left(\\frac{1}{2}-i\\right)k} & k\\not=n+1\\\\-1 & k=n+1.\\end{array}\\right.\n\\eeq\nAfter the identification of variables from Theorem \\ref{thm:crc}, and the specialization of winding parameters\n\\beq\ny_{P_i}= e^{\\pi\\mathrm{i}\\left[\\frac{w_i^-+(2i-1)\\alpha_1}{\\alpha_1+\\alpha_2}\\right]}y\n\\label{wvcov}\n\\eeq\nwe have\n\\beq\n\\mathcal{F}_{L',Y}^{\\rm disk}(t,y,\\vec{w}) = \\mathbb{O}_\\mathbb{Z} \\circ \\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}(t,y,\\vec{w}) .\n\\eeq\n\\label{thm:dcrccoh}\n\\end{thm}\n\n\\begin{proof}\n\nFrom equation \\eqref{eq:dr}, we have\n\n\\beq\n\\widehat \\mathcal{D}_{L,\\mathcal{X}}^+(z;\\vec{w})(\\mathbf{1_{k}})=\\sum_{k=1}^{n+1}\\frac{\\pi\\mathbf{1}_k}{(n+1)(\\alpha_1+\\alpha_2)\\sin\\left(\\pi\\left(\\left\\langle\\frac{k}{n+1}\\right\\rangle+\\frac{\\alpha_2}{z}\\right)\\right)\\widehat\\Gamma_\\mathcal{X}^k}\n\\eeq\n\n\nand\n\\beq\n\\widehat \\mathcal{D}_{L',Y}^+(z;\\vec{w})(P_i)=\\sum_{i=1}^{n+1}\\frac{\\pi P_i}{(\\alpha_1+\\alpha_2)\\sin\\left(\\pi\\left(-\\frac{w_i^-}{z}\\right)\\right)\\widehat\\Gamma_Y^i}\\eeq\n\nThe transformation $\\mathbb{O}$ is now obtained as $\\widehat\\mathcal{D}^+_Y\\circ\\mathbb{U}_{\\rho}^{\\X,Y}\\circ \\left(\\mathcal{D}^+_\\mathcal{X}\\right)^{-1}$:\n\n\\beq\n\\mathbb{O}(\\mathbf{1_k})= \\sum_{i=1}^{n+1} \\left[\\frac{\\sin\\left(\\pi\\left(\\left\\langle\\frac{k}{n+1}\\right\\rangle+\\frac{\\alpha_2}{z}\\right)\\right)}{\\sin\\left(\\pi\\left(-\\frac{w_i^-}{z}\\right)\\right)}\\left(\\sum_{j=0}^{i-1}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i}\\frac{j\\alpha_1}{z}}+\\sum_{j=i}^{n}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i}\\frac{(n+1-j)\\alpha_2}{z}} \\right)\\right] P_i.\n\\eeq\nWe now specialize  $z=\\frac{\\alpha_1+\\alpha_2}{d}$, for $d\\in \\mathbb{Z}$. The $i,k$ coefficient for $k\\neq n+1$ is:\n\\bea\n\\mathbb{O}_{i,k} &=&\\frac{\\sin\\left(\\pi\\left(\\frac{k}{n+1}+1-\\frac{d\\alpha_1}{\\alpha_1+\\alpha_2}\\right)\\right)}{\\sin\\left(\\pi\\left(-d\\frac{(n+1)\\alpha_1}{\\alpha_1+\\alpha_2}+d(n-i+2)\\right)\\right)}\\Bigg(\\sum_{j=0}^{i-1}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i}\n  j\\frac{\\alpha_1}{\\alpha_1+\\alpha_2}d} \\nn \\\\ &+& \\sum_{j=i}^{n}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i}(n+1-j)(1-\\frac{\\alpha_1}{\\alpha_1+\\alpha_2})d}\n\\Bigg)\\nn \\\\\n&=& (-1)^{d(n-i+2)}\\frac{\\omega^{k\/2}\\mathrm{e}^{-\\pi\\mathrm{i}\n    \\frac{\\alpha_1}{\\alpha_1+\\alpha_2}d}-\\omega^{-k\/2}\\mathrm{e}^{\\pi\\mathrm{i}\n    \\frac{\\alpha_1}{\\alpha_1+\\alpha_2}d}}{\\mathrm{e}^{\\pi\\mathrm{i} (n+1)\\frac{\\alpha_1}{\\alpha_1+\\alpha_2}d}-\\mathrm{e}^{-\\pi\\mathrm{i}\n    (n+1){\\frac{\\alpha_1}{\\alpha_1+\\alpha_2}d}}}\\sum_{j=-(n+1)+i}^{i-1}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i}\n  j\\frac{\\alpha_1}{\\alpha_1+\\alpha_2}d}\\nn \\\\\n&=& (-1)^{d(n-i+2)+1}\\omega^{\\left(\\frac{1}{2}-i\\right)k}\\mathrm{e}^{\\pi\\mathrm{i}(2i-n-2)\\frac{\\alpha_1}{\\alpha_1+\\alpha_2}d}\n\\nn \\\\\n&=& (-1) e^{d\\pi\\mathrm{i}\\left[n-i+2 +(2i-n-2)\\frac{\\alpha_1}{\\alpha_1+\\alpha_2}\\right]} \\omega^{\\left(\\frac{1}{2}-i\\right)k}.\n\\end{eqnarray}\nFor $k=n+1$\n\\beq\n\\mathbb{O}_{i,n+1}=(-1) e^{d\\pi\\mathrm{i}\\left[n-i+2 +(2i-n-2)\\frac{\\alpha_1}{\\alpha_1+\\alpha_2}\\right]}.\n\\eeq\nTo go from the second to the third line of this string of equations one notes that the product of the numerator of the fraction with the summation gives a telescoping sum; the residual terms have a factor canceling  the denominator and leaving the expression in the third line.\nIt is now immediate to see that we can incorporate the part of the transformation that depends multiplicatively on $d$ into a specialization of the winding variables, and that the remaining linear map is precisely $\\mathbb{O}_\\mathbb{Z}$. \n\\end{proof}\nFrom this formulation  of the disk  CRC one can deduce  a statement about scalar disk potentials which essentially says that the scalar potential of the resolution compares with the untwisted disk potential on the orbifold. \n\\begin{cor}\nWith all notation as in Theorem \\ref{thm:dcrccoh}:\n\\beq\n\\left( \\mathcal{F}_{L',Y}^{\\rm disk}(t,y,\\vec{w}),\\sum_{i=1}^{n+1}P^i\\right)_Y = -\\frac{1}{n+1}\\left(\\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}(t,y,\\vec{w}),\\mathbf{1^{n+1}}\\right)_\\mathcal{X}\n\\eeq\n\\label{cor:sc}\n\\end{cor}\n\\begin{proof}\nThis statement amounts to the fact that  the coefficients of all but the last column of matrix $\\mathbb{O}_\\mathbb{Z}$ add to zero. \n\\end{proof}\n\\subsection{$L$ intersects the effective axis}\n\\label{sec:ea}\n\nWe impose  our boundary condition $L$ on the first coordinate axis, which is  an effective quotient of $\\mathbb{C}$ with representation weight  $m_1=-1$ and torus weight $-\\alpha_1$. We can obtain results for the boundary condition on the second axis by switching $\\alpha_1$ with $\\alpha_2$, $m_1$ with $m_2$ and $+$ with $-$ in the orientation of the disks. In this case there is only one corresponding boundary condition $L'$ on the resolution, which intersects the (diagonal) non compact leg incident to $P_{n+1}$ in Figure~\\ref{fig:web}.\n\n\n\\begin{thm}\nConsider the cohomological disk potentials $\\mathcal{F}_{L,\\mathcal{X}}^{\\rm disk}(t,y,\\vec{w}) $ and $\\mathcal{F}_{L',Y}^{\\rm disk}(t, y_{P_{n+1}},\\vec{w})$.\nChoosing the bases $\\mathbf{1_k}$ and $P_i$ (where $k$ and $i$ both range from $1$ to $n+1$), define $\\mathbb{O}_\\mathbb{Z}(\\mathbf{1_k})=P_{n+1}$ for every $k$.\nAfter the identification of variables from Theorem \\ref{thm:crc}, and the identification of winding parameters $y=y_{P_{n+1}}$\nwe have\n\\beq\n\\mathcal{F}_{L',Y}^{\\rm disk}(t,y,\\vec{w}) = \\mathbb{O}_\\mathbb{Z} \\circ \\mathcal{F}_{L,\\mathcal{X}}^{\\rm\n  disk}(t,y,\\vec{w}). \\\\\n\\eeq\n\\label{thm:dcrccoheff}\n\\end{thm}\nWe obtain as an immediate corollary a comparison among scalar potentials.\n\\begin{cor}\nSetting $y=y_{P_{n+1}}$, we have\n\\beq\nF_{L',Y}^{\\rm disk}(t,y,\\vec{w}) = F_{L,\\mathcal{X}}^{\\rm disk}(t,y,\\vec{w}) .\n\\eeq\n\\label{cor:esc}\n\\end{cor}\n\n\\begin{proof}\nThe orbifold disk endomorphism is:\n\\beq\n\\widehat\\mathcal{D}^+_\\mathcal{X}(z;\\vec{w})(\\mathbf{1_k})=\\frac{\\pi}{-\\alpha_1(n+1)\\sin\\left(\\pi\\left(-\\frac{\\alpha_1+\\alpha_2}{z}\\right)\\right)\\widehat\\Gamma_\\mathcal{X}^k}\\mathbf{1}_k\n\\eeq\n\n\nThe resolution disk endomorphism  is\n\\beq\n\\widehat\\mathcal{D}^+_\\mathcal{X}(z;\\vec{w})(P_i) =\\frac{\\pi}{-(n+1)\\alpha_1\\sin\\left(\\pi\\left(-\\frac{\\alpha_1+\\alpha_2}{z}\\right)\\right)\\widehat\\Gamma_Y^{n+1}} \\delta_{i,n+1}P_{n+1}\n\\eeq\n\nWe can now compute $\\mathbb{O}$:\n\\beq\n\\mathbb{O}(\\mathbf{1_k})= \\frac{1}{n+1}\\left(\\sum_{j=0}^{n}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i}\\frac{j\\alpha_1}{z}}\\right)P_{n+i}.\n\\eeq\n\nSpecializing $z=\\frac{-(n+1)\\alpha_1}{d}$ for any positive integer $d$, we obtain:\n\n\\beq\n\\mathbb{O}_{n+1,k}=\\frac{1}{n+1}\\sum_{j=0}^{n}\\omega^{-jk}\\mathrm{e}^{2\\pi\\mathrm{i} j\\frac{-d}{n+1}}=\\delta_{k,-d\\mod n+1},\n\\eeq\nwhich implies the statement of the theorem.\n\n\\end{proof}\n\n\n\n\n\\section{One-dimensional mirror symmetry}\n\\label{sec:j}\n\nIn this section we exhibit a novel mirror symmetry description of the\nequivariant quantum cohomology of $A_n$ singularities in terms of a weak\nFrobenius manifold structure on a genus zero double Hurwitz space. In physics\nterminology, this is a logarithmic\nLandau--Ginzburg model on the sphere, akin to the Hori--Iqbal--Vafa spectral curves of\nnon-equivariant Gromov--Witten theory \\cite{Hori:2000ck} and the one-dimensional mirror\nof equivariant local $\\mathbb{C}\\mathbb{P}^1$  \\cite{Brini:2011ff}. This enables us to give\na complete description of the global quantum $D$-module and to determine\nexplicitly the\nform of the isomorphism between the calibrated Frobenius structures at the large\nvolume points of $\\mathcal{X}$ and $Y$.\n\\subsection{Weak Frobenius structures on double Hurwitz spaces}\n\\begin{comment}\n\\begin{defn}\nLet $C\\simeq \\mathbb{P}^1$, $\\lambda:C \\to \\mathbb{P}^1$ a marked rational function and write $(\\lambda)\\in\\mathrm{Div}(\\mathbb{P}^1)$\nfor the principal divisor associated to $\\lambda$.\nThe double Hurwitz space $\\mathcal{H}_{\\lambda}$ \nis the moduli space of covers \n\\beq\n\\xymatrix{C \\ar[r]^\\sim \\ar[rd]_\\lambda & C' \\ar[d]^{\\lambda'} \\\\ & \\mathbb{P}^1}\n\\eeq\nwith ramification profile above $0$ and $\\infty$ specified by $(\\lambda)$.\n\\end{defn}\n{\\color{red} I object a bit to this definition of Hurwitz space:  $\\lambda$ is one point parameterized not an invariant of the moduli space. Same for the divisor of $\\lambda$. The invariant is the ramification profile over $0$ and $\\infty$. Here is what I would do instead.}\n{\\color{blue}\n\\end{comment}\n\\begin{defn}\nLet  $\\mathbf{x}\\in \\mathbb{Z}^{n+3}$ be a vector of integers  adding to $0$. The double Hurwitz space $\\mathcal{H}_\\lambda \\triangleq \\mathcal M_0( \\mathbb{P}^1; \\mathbf{x})$ parameterizes isomorphism classes of covers $\\lambda$ of the projective line by a smooth genus $0$ curve $C$, with marked ramification profile over $0$ and $\\infty$ specified by $\\mathbf{x}$. This means that  the principal divisor of  $\\lambda$ is of the form\n$$\n(\\lambda)= \\sum x_i P_i.\n$$\nWe denote by $\\pi$ and $\\lambda$ the universal family and universal map, and by $\\Sigma_i$ the sections marking the $i$-th point in $(\\lambda)$:\n\\beq\n\\xymatrix{\\mathbb{P}^1  \\ar[d]  \\ar@{^{(}->}[r]& \\mathcal{U}\\ar[d]^\\pi  \\ar[r]^{\\lambda}  &  \\mathbb{P}^1 \\\\\n                     [\\lambda]  \\ar@{^{(}->}[r]^{pt.}   \\ar@\/^1pc\/[u]^{P_i}&                                             \\mathcal{H}_\\lambda  \\ar@\/^1pc\/[u]^{\\Sigma_i}& \n}\n\\eeq\n\\end{defn}\n\n\\begin{rem}\nA genus zero double Hurwitz space is naturally isomorphic to $M_{0,n+3}$, and is therefore an open set in affine space $\\mathbb{A}^n$. This is the only case that we utilize and it may seem overly sophisticated to use the language of moduli spaces to then work on such a simple object. We choose to do so to connect to the work of Dubrovin \\cite{Dubrovin:1992eu, Dubrovin:1994hc} and Romano \\cite{2012arXiv1210.2312R} (after Saito \\cite{MR723468}; see also \\cite{Krichever:1992qe}), who  studied\nexistence and construction of Frobenius structures  on  arbitrary double Hurwitz spaces. \n\\end{rem}\nLet \n$\\phi\\in \\Omega^1_{C}(\\log (\\lambda))$ be a meromorphic one form having simple poles at the support of $(\\lambda)$ with\nconstant residues; we call $(\\lambda, \\phi)$ respectively the {\\it\n  superpotential} and the {\\it quasi-momentum differential} of $\\mathcal{H}_\\lambda$.\nBorrowing the terminology from \\cite{2012arXiv1210.2312R, phdthesis-romano},\nwe say that an analytic Frobenius manifold structure $(\\mathcal{F}, \\circ, \\eta)$ on\na complex manifold $\\mathcal{F}$ is\n{\\it weak} if\n\\ben\n\\item the $\\circ$-multiplication gives a commutative and associative\nunital $\\mathcal{O}$-algebra structure\non the space of holomorphic vector fields on $\\mathcal{F}$;\n\\item the metric $\\eta$ provides a flat\n  pairing which is Frobenius w.r.t. to $\\circ$;\n\\item the algebra structure\nadmits a {\\it potential}, meaning that the 3-tensor\n\\beq\nR(X,Y,Z) \\triangleq \\eta(X,Y \\circ Z)\n\\eeq\nsatisfies the integrability condition\n\\beq\n(\\nabla^{(\\eta)} R)_{[\\alpha \\beta] \\gamma\\delta}=0.\n\\eeq\n\\end{enumerate}\nIn particular, this encompasses non-quasihomogeneous solutions of\nWDVV, and solutions without a flat identity element.\n\n\\begin{prop}[\\cite{2012arXiv1210.2312R}]\nFor vector fields $X$, $Y$, $Z \\in \\mathfrak{X}(\\mathcal{H}_\\lambda)$, define the\nnon-degenerate symmetric pairing $g$ and quantum product $\\star$ as\n\\bea\n\\label{eq:gmetr}\ng(X,Y) &\\triangleq & \\sum_{P\\in\\mathrm{supp}(\\lambda)}\\Res_P\\frac{X(\\log\\lambda)\n  Y(\\log\\lambda)}{\\mathrm{d}_\\pi \\log\\lambda}\\phi^2, \\\\\ng(X,Y \\star Z) &\\triangleq & \\sum_{P\\in\\mathrm{supp}(\\lambda)}\\Res_P\\frac{X(\\log\\lambda)\n  Y(\\log\\lambda) Z(\\log\\lambda)}{\\mathrm{d}_\\pi \\log\\lambda}\\phi^2,\n\\label{eq:star}\n\\end{eqnarray}\nwhere $\\mathrm{d}_\\pi$ denotes the relative differential with respect to the\nuniversal family (i.e. the differential in the fiber direction). Then the triple $\\mathcal{F}_{\\lambda,\\phi}=\\l(\\mathcal{H}_{\\lambda}, \\star, g\\r)$ endows\n$\\mathcal{H}_{\\lambda}$ with a weak Frobenius manifold structure.\n\\end{prop}\n\\begin{rmk}\n\\label{rmk:adual}\nEquations \\eqref{eq:gmetr}-\\eqref{eq:star} are the\nDijkgraaf--Verlinde--Verlinde formulae \\cite{Dijkgraaf:1990dj} for a\ntopological Landau--Ginzburg model on a sphere with $\\log\\lambda(q)$ as its\nsuperpotential. The case in which $\\lambda(q)$ itself is used as the\nsuperpotential gives rise to a {\\it different} Frobenius manifold structure,\nwhich is the case originally studied in \\cite[Lecture 5]{Dubrovin:1994hc}; the\nsituation at hand is its Dubrovin-dual\nin the sense of \\cite{MR2070050}, where $g$ plays the role of the\nintersection form and $\\star$ the dual product. \n\\end{rmk}\n\n\\subsubsection[Twisted periods and the QDE]{Twisted periods and the quantum\n  differential equation}\n\nThe quantum $D$-module associated to $\\mathcal{F}_{\\lambda, \\phi}$,\n\\beq\n\\nabla^{(g,z)} \\omega =0,\n\\label{eq:QDELG}\n\\eeq\nwhere\n\\beq\n\\label{eq:defconn}\n\\nabla^{(g,z)}_X(Y,z) \\triangleq  \\nabla^{(g)}_X Y+z^{-1} X \\star Y\n\\eeq\nenjoys a neat description in terms of the Landau--Ginzburg data $(\\lambda, \\phi)$:\nin particular, flat frames for \\eqref{eq:QDELG} can be computed from the\ntwisted Picard--Lefschetz theory of $\\lambda$ \\cite{MR936695, MR2070050, Brini:2011ff}.\nIn contrast with the classical Picard--Lefschetz theory,\nthis corresponds to\nconsidering cycles $\\gamma \\in H_1(\\mathbb{C} \\setminus H,\n\\mathbf{L})$ in the {\\it complement} of the zero-dimensional hypersurface\n$H=\\lambda^{-1}(0)$ cut\nby $\\lambda$,\nwhere the linear local system $\\mathbf{L}$ is defined by multiplication by\n$\\mathrm{e}^{2\\pi\\mathrm{i}\/z}$ when moving along a simple loop around\nany single point of $H$. Elements $\\gamma$ of the homology group with coefficients twisted by ${\\bf L}$\nare the {\\it twisted cycles} of $\\lambda$. \\\\\n\nOscillating integrals around a basis of twisted cycles of\nthe form\n\\beq\n\\Pi_{\\lambda, \\phi, \\gamma}(z) \\triangleq  \\int_\\gamma \\lambda^{1\/z} \\phi\n\\label{eq:periods}\n\\eeq\nare called {\\it\n  twisted periods}\\footnote{To be completely consistent with\n  \\cite{MR2070050} we should more correctly call these the {\\it\n  twisted periods}  of $\\mathcal{F}_{\\mathrm{e}^\\lambda,\\phi}$. See Remark \\ref{rmk:adual}.}\nof $\\mathcal{F}_{\\lambda,\\phi}$. Denote by $\\mathrm{Sol}_{\\lambda,\n  \\phi}$ the solution space of \\eqref{eq:QDELG},\n\\beq\n\\mathrm{Sol}_{\\lambda,\n  \\phi} = \\{s \\in \\mathfrak{X}(\\mathcal{F}_{\\lambda,\\phi}), \\nabla^{(g,z)}s=0 \\}.\n\\eeq\nWe have the following\n\\begin{prop}[Dubrovin, \\cite{MR2070050}]\n\\label{thm:tp}\nThe solution space of the quantum differential equations of\n$\\mathcal{F}_{\\lambda,\\phi}$ is generated by gradients of the twisted periods\n\\eqref{eq:periods}\n\\beq\n\\mathrm{Sol}_{\\lambda, \\phi} = \\mathrm{span}_{\\mathbb{C}((z))}\n\\{\\nabla^{(g)} \\Pi_{\\lambda,\\phi,\\gamma} \\}_{\\gamma \\in H_1(\\mathbb{C} \\setminus H,\n\\mathbf{L})}\n\\eeq\n\\end{prop}\nIn particular, Proposition \\ref{thm:tp} implies that the quantum $D$-modules arising from weak Frobenius structures on genus zero\ndouble Hurwitz spaces are described by systems of period integrals of\ngeneralized hypergeometric type. \\\\\n\n\\begin{rmk}\nSince $\\lambda$ is a genus zero covering map, in an affine chart parametrized by $q\\in\\mathbb{C}$ its logarithm takes the\nform \n\\beq\n\\log\\lambda = \\sum_{i}a_i \\log(q-q_i),\n\\label{eq:logl}\n\\eeq\nwhere $a_i\\in \\mathbb{Z}$. In fact, the existence of the weak Frobenius structure\n\\eqref{eq:gmetr}-\\eqref{eq:star} extends \\cite{phdthesis-romano} to the case where $\\mathrm{d}_\\pi\\log\\lambda$\nis a meromorphic function on $C$; this in particular encompasses the case where $a_i\\in\n\\mathbb{C}$ in \\eqref{eq:logl}. As far as flat coordinates of the deformed connection\n$\\nabla^{(g,z)}$ are concerned, Proposition~\\ref{thm:tp} continues to hold,\n the only proviso being that the locally constant sheaf ${\\bf L}$ be replaced\n with the unique local system specified by the monodromy weights $a_i\/z$ in\n \\eqref{eq:periods}, \\eqref{eq:logl}. \\\\\n\\end{rmk}\n\n\\subsection{A one-dimensional Landau--Ginzburg mirror}\n\nIt is known that the quantum $D$-modules associated to the equivariant Gromov--Witten theory of\nthe $A_n$-singularity $\\mathcal{X}$ and its resolution $Y$ admit a Landau--Ginzburg\ndescription in terms of $n$-dimensional oscillating integrals\n\\cite{MR1408320, MR1328251, MR2700280, MR2529944}. We provide here an alternative description\nvia one-dimensional twisted periods of a genus zero double Hurwitz space\n$\\mathcal{F}_{\\lambda, \\phi}$. \\\\\n\n\nLet  $\\mathcal M_A$ be $M_{0,n+3}$. By choosing the last three sections  to be the constant sections $0, 1, \\infty$, we realize  $\\mathcal M_A$ as an open subset of $\\mathbb{A}^{n}$ and trivialize the universal family. \nIn homogeneous coordinates $[u_0:\\dots:u_n]$ for $\\mathbb{P}^n$,\n\\beq\n\\mathcal M_A= \\mathbb{P}^n\\setminus \\mathrm{Proj} \\frac{\\mathbb{C}[u_0, \\dots, u_n]}{{\\left\\langle\n    u_i(u_j-u_k)\\right\\rangle}} \\triangleq  \\mathbb{P}^n\\setminus \\mathrm{discr} \\mathcal M_A .\n \\label{eq:discr}\n\\eeq\nLet\n$\\kappa_i=u_i\/u_0$, $i=1, \\dots, n$ be a set of global coordinates on $\\mathcal M_A$\nand $q$ be an affine coordinate on the fibers of the universal\nfamily. We give $\\mathbb{C}\\times \\mathcal M_A$ the structure of a one parameter family of double Hurwitz spaces by specifying the pair $(\\lambda, \\phi)$; we call \n$\\kappa_0$ the coordinate in the first factor, and define \n\\beq\n\\lambda(\\kappa_0, \\ldots \\kappa_n, q) = C_n(\\kappa)\n\\frac{q^{(n+1)\\alpha_1}}{\\left(1-q\\right)^{\\alpha_1+\\alpha_2}} \\prod _{k=1}^{n}\n\\left(1-q\\kappa_k\\right)^{-\\alpha_1-\\alpha_2}, \n\\label{eq:superpot}\n\\eeq\n\\beq\n\\phi(q) = \\frac{1}{\\alpha_1+\\alpha_2}\\frac{\\mathrm{d} q}{q},\n\\label{eq:primeform}\n\\eeq\nand\n\\bea\nC_n(\\kappa) &\\triangleq&   \\prod_{j=0}^n \\kappa_j^{\\alpha_1}.\n\\end{eqnarray}\nThen Eqs.~\\eqref{eq:gmetr}-\\eqref{eq:star} and\n\\eqref{eq:superpot}-\\eqref{eq:primeform} define a Frobenius structure $\\mathcal{F}_{\\lambda,\n  \\phi}$ on $\\mathbb{C}\\times\\mathcal M_A$; the discriminant ideal in \\eqref{eq:discr}\ncoincides with the locus where the $D$-module \\eqref{eq:defconn} is singular,\nand the irreducible components $V(\\kappa_i-\\kappa_j)$, for $i,j>0$, correspond to the loci where the\n$\\star$-product \\eqref{eq:star} blows-up. We have the following\n\\begin{thm}\n\\label{thm:mirror}\n\\ben\n\\item Let \n\\bea\n\\label{eq:kappa0Y}\n\\kappa_0 &=& \\mathrm{e}^{(t_{n+1}+\\delta_Y)\/\\alpha_1}, \\\\\n\\label{eq:kappaY}\n\\kappa_j &=& \\prod_{i=j}^n \\mathrm{e}^{t_i}, \\quad 1\\leq j\\leq n.\n\\end{eqnarray}\nwhere $\\delta_Y$ is an arbitrary constant. Then, in a neighbourhood $V_Y$ of $\\{ \\mathrm{e}^{t_i}=0\\}$, \n\\beq\n \\mathcal{F}_{\\lambda,\\phi} \\simeq QH_T(Y).\n\\eeq\n\\item Let\n\\bea\n\\label{eq:kappa0X}\n\\kappa_0 &=& \\mathrm{e}^{(x_{n+1}+\\delta_\\mathcal{X})\/\\alpha_1}, \\\\\n\\kappa_j &=& \\exp\\l[-\\frac{2\\mathrm{i}}{n+1}\\l(\\pi j+ \\sum_{k=1}^n\n  \\mathrm{e}^{-\\frac{\\mathrm{i} \\pi  k (j-1)}{n+1}} \\sin \\left(\\frac{\\pi  j\n    k}{n+1}\\right)x_k\\r)\\r], \\quad 1\\leq k\\leq n. \n\\label{eq:kappakX}\n\\end{eqnarray}\nwhere $\\delta_\\mathcal{X}$ is an arbitrary constant. Then, in a neighbourhood $V_\\mathcal{X}$ of $\\{x_i=0\\}$,\n\\beq\n \\mathcal{F}_{\\lambda,\\phi} \\simeq QH_T(\\mathcal{X}).\n\\eeq\n\\end{enumerate}\n\\end{thm}\n\\begin{proof} The proof is a straightforward computation from the\n  Landau--Ginzburg formulae \\eqref{eq:gmetr}-\\eqref{eq:star}.\n\\ben\n\\item \nConsider the three-point\ncorrelator $R(\\kappa_i {\\partial}_i, \\kappa_j {\\partial}_j, \\kappa_k {\\partial}_k)$, where\n${\\partial}_k \\triangleq \\frac{{\\partial}}{{\\partial} \\kappa_k}$, and define\n\\bea\nR^{(l)}_{i,j,k} &\\triangleq& \\Res_{q=\\kappa_l^{-1}} \\frac{\\kappa_i \\frac{{\\partial} \\ln\\lambda}{{\\partial} \\kappa_i}\n  \\kappa_j\\frac{{\\partial} \\ln\\lambda}{{\\partial} \\kappa_j} \\kappa_k \\frac{{\\partial}\n    \\ln\\lambda}{{\\partial} \\kappa_k} }{(\\alpha_1+\\alpha_2)^2 q \\frac{{\\partial} \\ln\\lambda}{{\\partial} q}}\\frac{\\mathrm{d} q}{q}.\n\\end{eqnarray}\nInspection shows that $R^{(l)}_{ijk}=0$ unless $l=i=j$, $l=i=k$ or\n$l=j=k$. Assume w.l.o.g. $l=j=i$, and suppose that $i,k>0$. We compute\n\\bea\n\\label{eq:lgqu1}\nR^{(i)}_{i,i,k}\n&=& \n\\frac{\\kappa_i}{\\kappa_k-\\kappa_i}+\\frac{\\alpha_2}{\\alpha_1+\\alpha_2}, \\\\\n\\label{eq:lgqu2}\nR^{(i)}_{i,i,i}\n\\begin{comment}\n&=& \\Res_{q=\\kappa_i^{-1}} \\Bigg\\{\\frac{(\\alpha_1+\\alpha_2\n  q\\kappa_i)^3}{(\\alpha_1+\\alpha_2)^3(1-q\\kappa_i)^2}\n \\frac{1}{\\frac{(n+1)\\alpha_1 (1-\\kappa_i\n     q)}{\\alpha_1+\\alpha_2}+\\frac{q(1-\\kappa_i q)}{1-q}+\\kappa_i q+\\sum_{l\\neq\n     i}^n\\frac{\\kappa_l\n  q(1-\\kappa_i q)}{1-\\kappa_l q}}\\frac{\\mathrm{d} q}{q}\\Bigg\\} \\nn \\\\\n&=& \\Res_{q=\\kappa_i^{-1}} \\Bigg\\{\\frac{(\\alpha_1+\\alpha_2\n  q\\kappa_i)^3}{(\\alpha_1+\\alpha_2)^3(\\kappa_i^{-1}-q)^2 \\kappa_i^2}\n \\frac{1}{\\kappa_i   q^2}\n\\frac{1}{1-(q-\\kappa_i^{-1})\n\\l[ \\frac{(n+1)\\alpha_1}{q(\\alpha_1+\\alpha_2)}\n+\\frac{1}{1-q}\n   +\\sum_{l\\neq i}^n\\frac{\\kappa_l}{1-\\kappa_l q}\\r]}\\mathrm{d} q \\Bigg\\} \n\\nn \\\\\n&=& \\Res_{q=\\kappa_i^{-1}} \\Bigg\\{\\frac{(\\alpha_2-2\\alpha_1)(\\alpha_1+\\alpha_2)^2}{(\\alpha_1+\\alpha_2)^3(q-\\kappa_i^{-1})}\n \\mathrm{d} q \n+\\frac{(\\alpha_1+\\alpha_2)^3}{(\\alpha_1+\\alpha_2)^3(q-\\kappa_i^{-1}) \\kappa_i^2}\n \\frac{1}{\\kappa_i   q^2} \\nn \\\\\n& & \n\\l[\\frac{(n+1)\\alpha_1}{q(\\alpha_1+\\alpha_2)}\n+\\frac{1}{1-q}\n   +\\sum_{l\\neq i}^n\\frac{\\kappa_l}{1-\\kappa_l q}\\r] \\mathrm{d} q \\Bigg\\} \n\\nn \\\\\n\\end{comment}\n&=& \\frac{(n-1) \\alpha_1+\\alpha_2}{\\alpha_1+\\alpha_2}+\n\\sum_{l\\neq i}^{n+1}\\frac{\\kappa_l}{\\kappa_i-\\kappa_l}, \\\\\nR^{(i)}_{0,i,i} \n&=& -\\frac{1}{\\alpha_1+\\alpha_2}.\n\\end{eqnarray}\nMoreover, for all $i$, $j$ and $k$ we have\n\\bea\nR^{(0)}_{i,j,k} &\\triangleq& \\Res_{q=0} \\frac{\\kappa_i \\frac{{\\partial} \\ln\\lambda}{{\\partial} \\kappa_i}\n  \\kappa_j\\frac{{\\partial} \\ln\\lambda}{{\\partial} \\kappa_j} \\kappa_k \\frac{{\\partial}\n    \\ln\\lambda}{{\\partial} \\kappa_k} }{(\\alpha_1+\\alpha_2)^2 q \\frac{{\\partial} \\ln\\lambda}{{\\partial} q}}\\frac{\\mathrm{d}\n  q}{q},\\nn \\\\\n&=& \\frac{\\alpha_1^{2-\\delta_{i,n+1}-\\delta_{j,n+1}-\\delta_{k,n+1}}}{(n+1)(\\alpha_1+\\alpha_2)^2} \\\\\nR^{(\\infty)}_{i,j,k} &\\triangleq& \\Res_{q=\\infty} \\frac{\\kappa_i \\frac{{\\partial} \\ln\\lambda}{{\\partial} \\kappa_i}\n  \\kappa_j\\frac{{\\partial} \\ln\\lambda}{{\\partial} \\kappa_j} \\kappa_k \\frac{{\\partial}\n    \\ln\\lambda}{{\\partial} \\kappa_k} }{(\\alpha_1+\\alpha_2)^2 q \\frac{{\\partial} \\ln\\lambda}{{\\partial} q}}\\frac{\\mathrm{d}\n  q}{q},\\nn \\\\\n&=& -\\frac{(-\\alpha_2)^{2-\\delta_{i,n+1}-\\delta_{j,n+1}-\\delta_{k,n+1}}}{(n+1)(\\alpha_1+\\alpha_2)^2}. \n\\label{eq:resinf}\n\\begin{comment}\n\\\\\nR^{(0)}_{0,0,0} &\\triangleq& \\Res_{q=0} \\frac{1}{(\\alpha_1+\\alpha_2)^2}\\frac{1}{(n+1)\\alpha_1+\\l(\\alpha_1+\\alpha_2\\r) \\sum_{l=1}^{n+1}\\frac{\\kappa_l\n  q}{1-\\kappa_l q}}\\frac{\\mathrm{d}\n  q}{q},\\nn \\\\\n&=& \\frac{1}{(\\alpha_1+\\alpha_2)^2  (n+1)\\alpha_1} \\\\\nR^{(\\infty)}_{0,0,0} &\\triangleq& \\Res_{q=\\infty} \\frac{1}{(\\alpha_1+\\alpha_2)^2}\\frac{1}{(n+1)\\alpha_1+\\l(\\alpha_1+\\alpha_2\\r) \\sum_{l=1}^{n+1}\\frac{\\kappa_l\n  q}{1-\\kappa_l q}}\\frac{\\mathrm{d}\n  q}{q},\\nn \\\\\n&=& \\frac{1}{(\\alpha_1+\\alpha_2)^2  (n+1)\\alpha_2}\n\\\\\nR^{(0)}_{0,0,i} &\\triangleq& \\Res_{q=0} \\frac{\\alpha_1+\\alpha_2 q\\kappa_i}{(\\alpha_1+\\alpha_2)^2(1-q\\kappa_i)}\\frac{1}{(n+1)\\alpha_1+\\l(\\alpha_1+\\alpha_2\\r) \\sum_{l=1}^{n+1}\\frac{\\kappa_l\n  q}{1-\\kappa_l q}}\\frac{\\mathrm{d}\n  q}{q},\\nn \\\\\n&=& \\frac{1}{(\\alpha_1+\\alpha_2)^2  (n+1)} \\\\\nR^{(\\infty)}_{0,0,i} &\\triangleq& \\Res_{q=\\infty} \\frac{\\alpha_1+\\alpha_2 q\\kappa_i}{(\\alpha_1+\\alpha_2)^2(1-q\\kappa_i)}\\frac{1}{(n+1)\\alpha_1+\\l(\\alpha_1+\\alpha_2\\r) \\sum_{l=1}^{n+1}\\frac{\\kappa_l\n  q}{1-\\kappa_l q}}\\frac{\\mathrm{d}\n  q}{q},\\nn \\\\\n&=& -\\frac{1}{(\\alpha_1+\\alpha_2)^2  (n+1)} \n\\\\\nR^{(0)}_{0,j,i} &\\triangleq& \\Res_{q=0} \\frac{(\\alpha_1+\\alpha_2 q\\kappa_i)(\\alpha_1+\\alpha_2 q\\kappa_j)}{(\\alpha_1+\\alpha_2)^2(1-q\\kappa_i)(1-q\\kappa_j)}\\frac{1}{(n+1)\\alpha_1+\\l(\\alpha_1+\\alpha_2\\r) \\sum_{l=1}^{n+1}\\frac{\\kappa_l\n  q}{1-\\kappa_l q}}\\frac{\\mathrm{d}\n  q}{q},\\nn \\\\\n&=& \\frac{\\alpha_1}{(\\alpha_1+\\alpha_2)^2  (n+1)} \\\\\nR^{(\\infty)}_{0,j,i} &\\triangleq& \\Res_{q=\\infty} \\frac{(\\alpha_1+\\alpha_2 q\\kappa_i)(\\alpha_1+\\alpha_2 q\\kappa_j)}{(\\alpha_1+\\alpha_2)^2(1-q\\kappa_i)(1-q\\kappa_j)}\\frac{1}{(n+1)\\alpha_1+\\l(\\alpha_1+\\alpha_2\\r) \\sum_{l=1}^{n+1}\\frac{\\kappa_l\n  q}{1-\\kappa_l q}}\\frac{\\mathrm{d}\n  q}{q},\\nn \\\\\n&=& \\frac{\\alpha_2}{(\\alpha_1+\\alpha_2)^2  (n+1)} \n\\\\\n\\end{comment}\n\\end{eqnarray}\nIt is immediate to see that \\eqref{eq:lgqu1}-\\eqref{eq:lgqu2} under the\nidentification \\eqref{eq:kappaY} imply that the quantum part of the\nthree-point correlator $R({\\partial}_{t_{i_1}}{\\partial}_{t_{i_2}}{\\partial}_{t_{i_3}})$\ncoincides with that of $\\left\\langle\\bra p_{i_1}, p_{i_2}, p_{i_3} \\right\\rangle\\ket^Y_{0}$ in\n\\eqref{eq:yukY}. A tedious, but straightforward computation shows that\n\\eqref{eq:lgqu1}-\\eqref{eq:resinf} yield the expressions\nfor the classical triple intersection numbers of $Y$. \\\\\n\\item This  is a consequence of the computation above and Theorem \\ref{thm:crc}.\n\\end{enumerate}\n\\end{proof}\n\\begin{figure}\n\\includegraphics{pochcont.pdf}\n\\caption{The double loop contour $\\gamma_4$ for $n=4$.}\n\\label{fig:pochcont}\n\\end{figure}\n\n\\begin{rmk}\nThe freedom of shift by $\\delta_\\mathcal{X}$ and $\\delta_Y$ respectively along\n$H^0(\\mathcal{X})$ and $H^0(Y)$ in \\eqref{eq:kappa0Y},\n\\eqref{eq:kappa0X} is a consequence of the restriction of the String Axiom to the small phase\nspace. We  set $\\delta_\\mathcal{X}=\\delta_Y=0$ throughout this section, but it will turn\nout to be useful to reinstate the shifts in the computations of Section~\\ref{sec:compsymp}.\n\\label{rmk:string}\n\\end{rmk}\n\n\n\\begin{rmk}\nIt should be possible to infer the form of the superpotential\n\\eqref{eq:superpot} from the equivariant GKZ system of $\\mathcal{X}$ and $Y$ by\narguments similar to the non-equivariant case (see e.g. \\cite[Appendix\n  A]{MR2510741}). The conceptual path we followed to conjecture the form\n\\eqref{eq:superpot} for a candidate dual Landau--Ginzburg model parallels the study of\nthe equivariant local $\\mathbb{CP}^1$ theory in \\cite{Brini:2011ff}; there, the\nexistence of a relation with a reduction of the 2-dimensional Toda hierarchy allows to derive\na Landau--Ginzburg mirror model through the dispersionless Lax formalism for\n2-Toda. More generally, $(n,m)$-graded reductions \\cite{phdthesis-romano} of $2$-Toda are believed to be relevant for the\nequivariant Gromov--Witten theory of local $\\mathbb{P}(n,m)$ \\cite{agps}; the\ndegenerate limit $m=0$ corresponds to the threefold $A_n$ singularity. In this case, the\ndispersionless 2-Toda Lax function reduces to \\eqref{eq:superpot}. \\\\\n\\end{rmk}\n\n\\subsection{The global quantum $D$-module}\n\\label{sec:globdpic}\n\nAn immediate corollary of Theorem~\\ref{thm:mirror} and Proposition~\\ref{thm:tp} is a concrete description of a global quantum $D$-module $(\\mathcal M_A, F, \\nabla,\nH(,)_g)$ interpolating between $\\mathrm{QDM}(\\mathcal{X})$ and $\\mathrm{QDM}(Y)$. Let\n$F \\triangleq T\\mathcal{F}_{\\lambda, \\phi}$ be\nendowed with the family of connections $\\nabla=\\nabla^{(g,z)}$ as in\n\\eqref{eq:defconn} and for $\\nabla$-flat sections $s_1$, $s_2$ let\n\\beq\nH(s_1, s_2)_g = g(s_1(\\kappa, -z),s_2(\\kappa,z))\n\\eeq\nLet now $V_\\mathcal{X}$ and $V_Y$ be neighbourhoods of $\\{\\kappa_i=\\omega^{-i}\\}$ and\n$\\{\\kappa_i=0\\}$ respectively. Then Theorem~\\ref{thm:mirror} can be rephrased\nas\n\\bea\n(\\mathcal{F}_{\\lambda,\\phi}, T\\mathcal{F}_{\\lambda,\\phi}, \\nabla^{(g,z)},H(,)_{g})|_{V_\\mathcal{X}} &\\simeq &\n\\mathrm{QDM}(\\mathcal{X}), \\\\\n(\\mathcal{F}_{\\lambda,\\phi}, T\\mathcal{F}_{\\lambda,\\phi}, \\nabla^{(g,z)},H(,)_{g})|_{V_Y} &\\simeq &\n\\mathrm{QDM}(Y),\n\\end{eqnarray}\nthat is, the twisted period system of $\\mathcal{F}_{\\lambda,\\phi}$ is a global quantum\n$D$-module connecting the genus zero descendent theory of $\\mathcal{X}$ and $Y$; the\ntwisted periods \\eqref{eq:periods} thus define a global flat frame for the\nquantum differential equations of $\\mathcal{X}$ and $Y$ upon analytic continuation in\nthe $\\kappa$-variables, \n\\beq\n\\mathrm{Sol}_{\\lambda,\\phi}|_{V_\\mathcal{X}} = \\mathcal{S}_\\mathcal{X}, \\quad \n\\mathrm{Sol}_{\\lambda,\\phi}|_{V_Y} = \\mathcal{S}_Y. \n\\eeq\n\n\nA canonical basis of $\\mathrm{Sol}_{\\lambda,\\phi}$ can be\n  constructed as follows.\nFor the superpotential \\eqref{eq:superpot}, the twisted homology $H_1(\\mathbb{C}\n  \\setminus \\lambda^{-1}(0), \\mathbf{L})$ is generated \\cite{MR1424469} by Pochhammer double\n  loop contours $\\{\\xi_i\\}_{i=1}^{n+1}$ encircling the origin\n  $q=0$ and $q=\\kappa_i^{-1}$, $i=1, \\dots, n+1$, as in Figure~\\ref{fig:pochcont} (alternatively $\\xi_i=[\\rho_0,\\rho_i]$, where the $\\rho$'s are simple oriented loops around each of the punctures). Then the integrals\n\n\n\\bea\n\\Pi_i^{(n)}(\\kappa,z) & \\triangleq & \\frac{1}{(1-\\mathrm{e}^{2\\pi\\mathrm{i} a})(1-\\mathrm{e}^{-2\\pi\\mathrm{i} b})}\\int_{\\xi_i} \\lambda^{1\/z}(q) \\frac{\\mathrm{d} q}{q} \\nn\n\\\\ &=& \\frac{C_n(\\kappa)^{\\frac{1}{z}}}{(1-\\mathrm{e}^{2\\pi\\mathrm{i} a})(1-\\mathrm{e}^{-2\\pi\\mathrm{i} b})} \\int_{\\xi_i}\nq^{a} (1-q)^{-b} \\prod _{k=1}^n \\left(1-q\n\\kappa_k\\right)^{-b}\\frac{\\mathrm{d} q}{q} \\nn \\\\\n&=& \n\\frac{C_n(\\kappa)^{\\frac{1}{z}} \\kappa_i^{-a}}{(1-\\mathrm{e}^{2\\pi\\mathrm{i} a})(1-\\mathrm{e}^{-2\\pi\\mathrm{i} b})} \n \\int_{\\xi_{n+1}} q^{a} (1-q)^{-b}\\left(1-q\/\\kappa_i\\right)^{-b}\n\\prod_{k\\neq i}^n \\left(1-q \\kappa_k\/\\kappa_i\\right)^{-b} \\frac{\\mathrm{d} q}{q} \\nn \\\\\n\\label{eq:eulerint}\n\\end{eqnarray}\nwhere we defined\n\\bea\na & \\triangleq & \\frac{(n+1) \\alpha_1}{z}, \\\\\nb & \\triangleq & \\frac{\\alpha_1+\\alpha_2}{z},\n\\end{eqnarray}\ngive a basis of twisted periods of $\\mathcal{F}_{\\lambda, \\phi}$; when $\\Re(a)>0$, $\\Re\n(b)<1$ they reduce to line integrals along chains connecting $q=0$ to\n$q=\\kappa_i^{-1}$. \\\\\n\n\nThe integrals \\eqref{eq:eulerint} can be given very explicit expressions in\nterms of known generalized hypergeometric functions \\cite{MR0422713}. Namely, we have\n\\bea\n\\Pi_i^{(n)}(\\kappa,z) &=& \n\\frac{\\Gamma(a)\\Gamma(1-b)}{\\Gamma(1+a-b)} C_n(\\kappa)^{\\frac{1}{z}}\n\\kappa_i^{-a}\n \\nn \\\\\n&\\times & \n\\Phi^{(n)}\\l(a,b,1+a-b;\n\\frac{1}{\\kappa_i},  \\frac{\\kappa_1}{\\kappa_i}, \\dots,\n\\frac{\\kappa_n}{\\kappa_i}\\r), \\quad 1\\leq i\\leq n, \\label{eq:pilaur1} \\\\\n\\Pi_{n+1}^{(n)}(\\kappa,z) &=& \\frac{\\Gamma(a)\\Gamma(1-b)}{\\Gamma(1+a-b)}  C_n(\\kappa)^{\\frac{1}{z}}\n\\Phi^{(n)}(a,b,1+a-b;\n\\kappa_1, \\dots, \\kappa_n),\n\\label{eq:pilaur2}\n\\end{eqnarray}\nwhere we defined\n\\beq\n\\label{eq:Phi}\n\\Phi^{(M)}(a, b, c, w_1, \\dots, w_M) \\triangleq  F_D^{(M)}(a; b, \\dots, b; c; w_1, \\dots, w_{M}),\n\\eeq\nand $F_D^{(M)}(a; b_1, \\dots, b_M; c; w_1, \\dots, w_M)$ in \\eqref{eq:Phi} is the\ngeneralized hypergeometric Lauricella function  of type $D$ \\cite{lauric}:\n\\beq\nF_D^{(M)}(a; b_1, \\dots, b_M; c; w_1, \\dots, w_M) \\triangleq \\sum_{i_1, \\dots, i_M}\n\\frac{(a)_{\\sum_j i_j}}{(c)_{\\sum_j i_j}}\\prod_{j=1}^M \\frac{(b_j)_{i_j} w_j^{i_j}}{i_j!}.\n\\label{eq:FD}\n\\eeq\nIn \\eqref{eq:FD}, we used the Pochhammer symbol $(x)_m$ to denote the ratio $(x)_m=\n\\Gamma(x+m)\/\\Gamma(x)$. \\\\\n\n\n\\begin{rmk}\nThat flat sections of $\\mathrm{QDM}(\\mathcal{X})$ and $\\mathrm{QDM}(Y)$ are solutions of a GKZ-type\nsystem, and therefore take the form of generalized hypergeometric functions in\n$B$-model variables, is a direct consequence of equivariant mirror symmetry for toric\nDeligne--Mumford stacks; see \\cite[Appendix A]{MR2510741} for the case under\nstudy here, and \\cite{ccit2} for the general case. Less expected, however, is the fact that flat sections of $\\mathrm{QDM}(\\mathcal{X})$ and $\\mathrm{QDM}(Y)$ are\nhypergeometric functions in {\\it exponentiated flat variables} for \\eqref{eq:pair},\nthat is, in $A$-model variables. This is a consequence of the particular form\n\\eqref{eq:yukY}, \\eqref{eq:lgqu1}-\\eqref{eq:lgqu2}\nof the quantum product: this depends {\\it rationally} on the variables\nin the K\\\"ahler cone for $Y$ in such a way that the quantum differential equation\n\\eqref{eq:QDE} for $Y$ (and therefore $\\mathcal{X}$, via \\eqref{eq:changevar}) becomes a\ngeneralized hypergeometric system in exponentiated flat coordinates. From the vantage\npoint of mirror symmetry, the rational dependence of the $A$-model three-point\ncorrelators on the quantum parameters can be regarded as an epiphenomenon of the Hard Lefschetz\ncondition, which ensures that the inverse mirror map is a rational\nfunction of the $B$-model variables. \n\\end{rmk}\n\n\\begin{rmk}\nAs a further surprising peculiarity of the\ncase of $A_n$ singularities,\nintegral representations of the flat sections have a {\\it simpler}\ndescription in $A$-model variables: the one-dimensional Euler integrals\n\\eqref{eq:eulerint} replace here the $n$-fold Mellin-Barnes contour integrals\nthat represent solutions of the corresponding GKZ system \\cite{MR2510741,\n  MR2700280}. This technical advantage is crucial for our\ncalculations of Section~\\ref{sec:compsymp}.\n  The reader may find a comparison of the Hurwitz mirror with the traditional\napproach of toric mirror symmetry in \\cite{bcr2013}.  \\\\\n\\end{rmk}\n\n\\subsubsection{Example: $n=2$ and the Appell system}\n\\label{sec:appell}\n\nIn this case the quantum $D$-module has rank three. We factor out the dependence on $C_2(\\kappa)$ in\n\\eqref{eq:pilaur1}-\\eqref{eq:pilaur2} for the flat coordinates of the deformed\nconnection as\n\\beq\nf(\\kappa_1,\\kappa_2,z)  \\triangleq (\\kappa_0\\kappa_1\\kappa_2)^{-a\/3} \\tilde t(\\kappa_0,\n\\kappa_1, \\kappa_2, z).\n\\label{eq:fdefn2}\n\\eeq\nThe flatness equations for $\\nabla^{(g,z)}$ for $n=2$ reduce to a\nhypergeometric Appell $F_1$ system \\cite{MR0422713} for $f$:\n\\bea\n\\label{eq:F1eq1}\n(\\kappa_1-\\kappa_2){\\partial}_1  {\\partial}_2 f -b ({\\partial}_1-{\\partial}_2)f &=& 0,  \\\\\n\\bigg[\\kappa_1(1-\\kappa_1)\\theta_1^2 +\\kappa_2(1-\\kappa_1){\\partial}_{12}  \n+(a+1-2b){\\partial}_1  &+& \\nn \\\\  -(a+1+2b) \\kappa_1 {\\partial}_1   -b \\kappa_2{\\partial}_2 -a b \\bigg]f &=&\n0. \n\\label{eq:F1eq2}\n\\end{eqnarray}\nFor $n=2$, the twisted periods \\eqref{eq:pilaur1}-\\eqref{eq:pilaur2} reduce to\nAppell $F_1$ functions \\cite{MR0422713}\n\\bea\n\\Pi_1^{(2)}(\\kappa_0,\\kappa_1,\\kappa_2,z) &=& \\frac{\\Gamma(a)\\Gamma(1-b)}{\\Gamma(1+a-b)} C_2(\\kappa)^{\\frac{1}{z}}\n\\kappa_1^{-a}\n\\Phi^{(2)}\\l(a,b,b, 1+a-b;\n\\frac{1}{\\kappa_1}, \\frac{\\kappa_2}{\\kappa_1} \\r) \\nn \\\\\n&=& \\frac{\\Gamma(a)\\Gamma(1-b)}{\\Gamma(1+a-b)} (\\kappa_0\\kappa_2)^{a\/3} \\kappa_1^{-a\/3}\n\\, F_1\\l(a,b,b,1+a-b,\\frac{1}{\\kappa_1},\n\\frac{\\kappa_2}{\\kappa_1}\\r) \\label{eq:twistn2a} \\\\\n\\Pi_2^{(2)}(\\kappa_0,\\kappa_1,\\kappa_2,z) &=&\n\\Pi_1^{(2)}(\\kappa_0,\\kappa_2,\\kappa_1,z) \\\\\n\\Pi_2^{(3)}(\\kappa_0,\\kappa_2,\\kappa_1,z)\n&=& \\frac{\\Gamma(a)\\Gamma(1-b)}{\\Gamma(1+a-b)} (\\kappa_0 \\kappa_1 \\kappa_2)^{a\/3} \\,\nF_1\\l(a,b,b, 1+a-b,\\kappa_1, \\kappa_2\\r) \\label{eq:twistn2b}\n\\end{eqnarray}\nwhere\n\\beq\nF_1\\l(a,b_1,b_2, c,x,y\\r) \\triangleq \\sum_{i_1, i_2 \\geq 0}\n\\frac{(a)_{i_1+i_2}}{(c)_{i_1+i_2}}\\frac{(b_1)_{i_1}\n  x^{i_1}}{i_1!}\\frac{(b_2)_{i_2} y^{i_2}}{i_2!}.\n\\eeq\nIt is straightforward to check that \\eqref{eq:twistn2a}-\\eqref{eq:twistn2b} yield a complete set of\nsolutions of \\eqref{eq:F1eq1}-\\eqref{eq:F1eq2}. \\\\\n\nIn this case, irreducible components of the discriminant locus are given by the lines $\\kappa_1=\\kappa_2$ and\n$\\kappa_i=0,1,\\infty$, $i=1,2$. Its moduli space is depicted in\nFigure~\\ref{fig:modspace2}. The large radius point of $\\mathcal{X}$\n$(\\kappa_1,\\kappa_2)=(\\mathrm{e}^{4\\pi \\mathrm{i}\/3},\\mathrm{e}^{2\\pi \\mathrm{i}\/3})$, denoted OP in Figure~\\ref{fig:modspace2}, is a regular point of the quantum $D$-module\n\\eqref{eq:F1eq1}-\\eqref{eq:F1eq2}, and the Fuchsian singularities\n$(\\kappa_1,\\kappa_2)=(0,0)$ and $(\\infty, \\infty)$ correspond to two\ncopies of the large radius point (henceforth, LR) of $Y$, referred to as LR1 and LR2 in\nFigure~\\ref{fig:modspace2}. The Frobenius structure induced around the latter two\npoints are canonically isomorphic to $QH_T(Y)$, and they are related to one another\nby the involution $\\kappa_i \\to -\\kappa_i$. In contrast with the $n=1$ case\n\\cite{cavalieri2011open, bcr2013}, where the Appell system reduces to the\nGauss ${}_2 F_1$-system, it is\nimpossible here \\cite{MR0422713} to provide a local solution around LR of the Appell system\n\\eqref{eq:F1eq1}-\\eqref{eq:F1eq2} in terms of Appell $F_1$-functions only;\nsee Appendix~\\ref{sec:anFD} for a discussion of this point. \nRepresenting eigenvectors of the monodromy around LR in\ngeneral in terms of the twisted period basis will be the subject of the first\npart of the proof of Theorem \\ref{thm:sympl} in the next section.\n\n\n\\begin{figure}[t]\n\\includegraphics{modspace2.pdf}\n\\caption{The K\\\"ahler moduli space of the $A_2$ singularity in $A$-model\n  coordinates.}\n\\label{fig:modspace2}\n\\end{figure}\n\n\\subsection{Proof of Theorem \\ref{thm:sympl}\n}\n\\label{sec:compsymp}\nLet $\\rho$ be a straight line in $\\mathcal M_A$ connecting the large radius point\n$\\{\\kappa_j=0\\}$ of $Y$ to\nthe one of $\\mathcal{X}$, given by $\\{\\kappa_j=\\omega^{-j}\\}$, with zero winding number\naround all irreducible components of the discriminant locus of $\\mathcal M_A$. We compute  the analytic\ncontinuation map $\\mathbb{U}_\\rho^{\\mathcal{X}, Y} : \\mathcal{H}_\\mathcal{X} \\to \\mathcal{H}_Y$ that identifies the\ncorresponding flat frames and Lagrangian cones upon analytic continuation\nalong $\\rho$. \\\\\n\nDefine the period map $\\Omega$:%\n\\beq\n\\bary{ccccc}\n\\Omega &:& H_1\\l(\\mathbb{C} \\setminus (\\lambda), \\mathbf{L}\\r) & \\to &\n\\mathcal{O}_{\\mathcal{F}_{\\lambda, \\phi}}, \\\\\n& & \\xi & \\to & \\int_\\xi \\lambda^{1\/z} \\phi,\n\\eary\n\\label{eq:periodmap}\n\\eeq\nand denote by $\\Pi^{(n)}$ as in \\eqref{eq:eulerint} the image of the\nbasis $\\xi$ of twisted cycles of Section~\\ref{sec:globdpic} under the period map. The horizontality \\eqref{eq:fundsol}-\\eqref{eq:Jfun1} of the $J$-functions of\n$\\mathcal{X}$ and $Y$, the String Equation for $\\mathcal{X}$ and $Y$, and Proposition~\\eqref{thm:tp} together state that $J^\\mathcal{X}$,\n$J^Y$ and $\\Pi^{(n)}$ are three\ndifferent $\\mathbb{C}(\\mathrm{e}^{\\mathrm{i} \\pi a}, \\mathrm{e}^{\\mathrm{i}\\pi b}, z)$-bases of deformed flat coordinates of $\\nabla^{(g,z)}$ under the identifications\n\\eqref{eq:kappa0Y}-\\eqref{eq:kappaY},\n\\eqref{eq:kappa0X}-\\eqref{eq:kappakX}. This entails, for every $\\rho$, the\nexistence of two \n$\\mathbb{C}(\\mathrm{e}^{\\mathrm{i} \\pi a}, \\mathrm{e}^{\\mathrm{i} \\pi b}, z)$-linear maps $A$, $B$\n\\beq\n\\bary{ccccc}\n\\nabla^{(\\eta_Y)} A \\Omega & : & H_1\\l(\\mathbb{C} \\setminus (\\lambda), \\mathbf{L}\\r) & \\to & \\mathcal{S}_Y, \\\\\n\\nabla^{(\\eta_\\mathcal{X})}B^{-1} \\Omega & : & H_1\\l(\\mathbb{C} \\setminus (\\lambda), \\mathbf{L}\\r) & \\to &\n\\mathcal{S}_\\mathcal{X},\n\\label{eq:AB}\n\\eary\n\\eeq\nsuch that\n\\bea\n\\label{eq:pijy}\nA \\Pi^{(n)} &=&  J_Y, \\\\\nB J_\\mathcal{X} &=&  \\Pi^{(n)}.\n\\label{eq:pijx}\n\\end{eqnarray}\nIn particular,\n\\beq\n\\mathbb{U}_\\rho^{\\mathcal{X}, Y} = A B. \n\\label{eq:UBA}\n\\eeq\n\\\\\n\n$A$ sends the twisted period basis $\\Pi^{(n)}$ to a basis of eigenvectors of the\nmonodromy around the large radius point of $Y$ normalized as in\n\\eqref{eq:Jloc}. We compute $A$\nby investigating the leading asymptotics of the twisted periods\n\\eqref{eq:pilaur1}-\\eqref{eq:pilaur2} around the large radius point of $Y$; as in the example of\nSection~\\ref{sec:appell}, we denote the latter by LR. \\\\\n\n\nIn $\\mathbb{C}^m$ with coordinates $(w_1, \\dots, w_m)$, let $\\chi_i$, for\nevery $i=1, \\dots, m$, be a path connecting the point at\ninfinity $W^\\infty_i$,\n\\beq\nW_i^\\infty\\triangleq(\\overbrace{0,\\dots, 0}^{\\text{$i$ times}}, \\overbrace{\\infty,\\dots,\n  \\infty}^{\\text{$m-i$ times}}),\n\\eeq\nwith zero winding number along $w_i=w_j$ ($i \\neq j$) and $w_i=0,1$. We want\nto compute the analytic continuation along $\\chi_i$ of the\nLauricella function \n$F_D^{(m)}(a,b_1, \\dots, b_n, c, w_1, \\dots, w_i, w_{i+1}^{-1}, \\dots, w_m^{-1})$\nfrom an open ball centered on $W^\\infty_i$ to the origin \n$W^\\infty_0=(0, \\dots, 0)$ in the sector where $w_i \\ll 1$,\n$w_i\/w_j \\ll 1$ for $i<j$. One strategy to do this is by performing the\ncontinuation in each individual variable $w_j$, $j>i$ appearing in \\eqref{eq:FD} through an iterated\nuse of Goursat's identity \\eqref{eq:2F1conn}.  The final result is\n\\eqref{eq:fdinf}; we refer the reader to Appendix \\ref{sec:anFD} for the\ndetails of the derivation. \\\\\n\nIn our case, Eq.~\\eqref{eq:fdinf} (see also Remark~\\ref{rmk:relabel}) implies, around $w_i=\\infty$, that\n\\bea\n\\Phi^{(m)}(a, b, c; w_1, \\dots, w_m) & \\sim & \n\\sum_{j=0}^{m-1}\\Gamma\\l[\\bary{ccc}c, & a-j b, & (j+1)\n  b-a \\\\ a, & b, & c-a \\eary\\r] \\nn \\\\ & & \\prod_{i=1}^j (-w_{m-i+1})^{-b}\n(-w_{m-j})^{-a+j b}\\nn \\\\ &+& \\prod_{j=1}^m (-w_j)^{-b}\n\\Gamma\\l[\\bary{cc}c, & a-m b \\\\ a, & c-m b \\eary\\r].\n\\end{eqnarray}\nwhen $w_i \\sim 0$, $w_i\/w_j \\sim 0$ for $j>i$. In particular, at the level of twisted periods this entails\n\\bea\n\\Pi_{n-k}^{(n)} & \\sim & C_n(\\kappa)^{\\frac{1}{z}}\n\\kappa_{n-k}^{-a}\n\\frac{\\Gamma(a)\\Gamma(1-b)}{\\Gamma(1+a-b)} \n\\Phi^{(k+1)}\\l(a,b,1+a-b, \\frac{\\kappa_{n-k+1}}{\\kappa_{n-k}},\n \\dots, \\frac{\\kappa_{n}}{\\kappa_{n-k}}, \\frac{1}{\\kappa_{n-k}} \\r)\n\\nn \\\\\n& \\sim &  \nC_n(\\kappa)^{\\frac{1}{z}}\n\\kappa_{n-k}^{-a}\n\\Bigg\\{\n\\frac{\\Gamma(a)\\Gamma(b-a)}{\\Gamma(b)} \\l(-\\kappa_{n-k}\\r)^{a}  \\nn \\\\ &+& \n\\sum_{j=1}^{k}\\frac{\\Gamma(a-j b)\\Gamma((j+1) b-a)}{\\Gamma(b)}\n\\l(-\\frac{\\kappa_{n+1-j}}{\\kappa_{n-k}}\\r)^{-a+j b} (-\\kappa_{n-k})^{b} \\prod_{i=1}^{j-1} \\l(-\\frac{\\kappa_{n+1-i}}{\\kappa_{n-k}}\\r)^{-b}\n\\nn \\\\ &+& \\kappa_{n-k}^{(k+1) b} \n\\frac{\\Gamma(1-b)\\Gamma(a-(k+1) b)}{\\Gamma(1+a-(k+2) b)} \\prod_{j=n-k+1}^{n} (-\\kappa_j)^{-b}\\Bigg\\}\n\\nn \\\\\n& \\sim &  \nC_n(\\kappa)^{\\frac{1}{z}}\n\\Bigg\\{\n\\sum_{j=0}^{k}\\frac{\\Gamma(a-j b)\\Gamma((j+1) b-a)}{\\Gamma(b)} (-1)^a \\l(\\kappa_{n+1-j}\\r)^{-a+j b} \\prod_{i=1}^{j-1} \\l(\\kappa_{n+1-i}\\r)^{-b}\n\\nn \\\\ &+& (-1)^{(k+1) b}\n\\frac{\\Gamma(1-b)\\Gamma(a-(k+1) b)}{\\Gamma(1+a-(k+2) b)}\\kappa_{n-k}^{(k+1)\n  b-a} \\prod_{j=n-k+1}^{n} (\\kappa_j)^{-b} \\Bigg\\}.\n\\label{eq:dectp}\n\\end{eqnarray}\nin a neighbourhood of $\\kappa=0$ given by $|\\kappa_i| \\ll 1$,\n$\\kappa_i\/\\kappa_j \\ll 1$ for $j>i$; notice that in cohomology coordinates\n\\eqref{eq:kappaY} for $Y$, this becomes an actual open ball $|q|\\ll 1$ around the point\nof classical limit $q_i = \\mathrm{e}^{t_i}=0$. Now, from the discussion of\nSection~\\ref{sec:GIT} and Eqns.~\\eqref{eq:Jred}, \\eqref{eq:kappaY}, around\nthe limit point of classical cohomology the $J$-function of $Y$ behaves as\n\\beq\nJ^Y_{p_i} = z C_n(\\kappa)^{\\frac{1}{z}} \\kappa_i^{(n-i+1)b-a}\\prod_{j=i+1}^n(\\kappa_j)^{-b}\\l(1+\\mathcal{O}(\\mathrm{e}^{t})\\r).\n\\label{eq:Jred2}\n\\eeq\nThen we can read off from \\eqref{eq:dectp}-\\eqref{eq:Jred2} the decomposition of each twisted period\n$\\Pi_i^{(n)}$ in terms of eigenvectors of the monodromy around LR, and in\nparticular, in terms of the localized components of the $J$-function. Explicitly,\n\\beq\n\\Pi^{(n)} = A^{-1} J^Y,\n\\eeq\nwhere\n\\beq\nA^{-1}_{ji} = \\left\\{\\bary{cl} (-1)^{(n-i+1) b}\n\\frac{\\Gamma(1-b)\\Gamma(a-(n-i+1) b)}{z \\Gamma(1+a-(n-i+2) b)} & \\mathrm{for}\n\\quad i=j, \\\\\n(-1)^a\\frac{\\Gamma(a-(n-i+1) b)\\Gamma((n-i+2) b-a)}{z \\Gamma(b)}  & \\mathrm{for}\n\\quad j<i,  \\\\\n0 & j>i.\n  \\eary\\right. \n\\label{eq:matrAINV}\n\\eeq\nIts inverse reads\n\\beq\nA_{ij} = \\left\\{\\bary{cl} \\mathrm{e}^{\\pi\\mathrm{i} (n-i+1) b}\n\\frac{z \\Gamma(1+a-(n-i+2) b)\\Gamma(1-a+(n-i+1) b)\\sin(a+(n-i+1) b)}{\\Gamma(1-b)\\pi} & i=j, \\\\\n\\mathrm{e}^{-i \\pi  (a-b (2 n-2j+3))} \\frac{z \\sin (\\pi  b)  \\Gamma (1-a+b (n+1-i)) \\Gamma (1+a-b (n-i+2))}{\\pi  \\Gamma (1-b)}\n & j>i,  \\\\\n0 & j<i.\n  \\eary\\right.\n\\label{eq:matrA}\n\\eeq\n\\\\\n\nConsider now the situation at the orbifold point (as before, denoted OP) given\nby $\\{\\kappa_j=\\omega^{-j}\\}$. Since by \\eqref{eq:resj},\n\\bea\nJ^\\mathcal{X}(0,z) &=& z \\mathbf{1}_0, \\\\\n\\frac{{\\partial} J^\\mathcal{X}}{{\\partial} x_k}(0,z) &=& \\mathbf{1}_{\\frac{k}{n+1}},\n\\end{eqnarray}\nto compute the operator $B$ in \\eqref{eq:AB} it suffices to evaluate the expansion of the Lauricella functions \\eqref{eq:pilaur1}-\\eqref{eq:pilaur2}\nat OP to linear order in $x_k$, $k=0, \\dots, n$, where it is implicit that principal branches are chosen in\n\\eqref{eq:eulerint} for all $k$; this corresponds to the assumption that the\n1-chain $\\rho$ has trivial winding number around the boundary divisors of $\\mathcal M_A$.\nFrom \\eqref{eq:kappakX}, \\eqref{eq:eulerint}, one has \n\\bea\n\\Pi_j^{(n)}(\\kappa,z)\\Big|_{x=0} &=& \n\\omega^{(j-n\/2) a}\n\\frac{\\Gamma(a)\\Gamma(1-b)}{\\Gamma(1+a-b)} \n\\Phi^{(n)}\\l(a,b, 1+a-b;\n\\omega, \\dots, \\omega^n \\r) \\nn \\\\ &=& \\frac{\n\\omega^{(j-n\/2) a}}{n+1}\n\\frac{\\Gamma(a\/(n+1))\\Gamma(1-b)}{\\Gamma(1-b+a\/(n+1))}, \\qquad j=1, \\dots, n+1.\n\\end{eqnarray}\nSimilarly, a short computation shows that \n\\bea\n\\kappa_k\\frac{{\\partial} \\Pi_j^{(n)}}{{\\partial} \\kappa_k}(0,z) \n&=& -\\frac{\\omega^{(j-n\/2)a}}{n+1} \\sum_{l=1}^{n}\\omega^{(j-k)l}\n\\frac{\\Gamma\\l(\\frac{a+l}{n+1}\\r)\\Gamma(1-b)}{\\Gamma\\l(\\frac{a+l}{n+1}-b\\r)},\n\\\\\n\\frac{{\\partial} \\Pi_j^{(n)}}{{\\partial} x_k}(\\kappa,z)\\bigg|_{x=0} &=& \n-\\frac{\\omega^{(j-n\/2) a -jk +k\/2}}{n+1} \n\\frac{\\Gamma\\l(\\frac{a-k}{n+1}+1\\r)\\Gamma(1-b)}{\\Gamma\\l(\\frac{a-k}{n+1}+1-b\\r)}.\n\\end{eqnarray}\nIn matrix form we have: \n\\beq\n\\Pi^{(n)} = B J^\\mathcal{X} = D_1 V D_2 J^\\mathcal{X}\n\\label{eq:matrB1}\n\\eeq\nwhere\n\\bea\n(D_1)_{jk} &=& \\omega^{(j-n\/2) a}\\delta_{jk}  \\\\\n(D_2)_{jk} &=&  \\delta_{jk}\\left\\{\\bary{cc} -\\omega^{k\/2} \n\\frac{\\Gamma\\l(\\frac{a-k}{n+1}+1\\r)\\Gamma(1-b)}{\\Gamma\\l(\\frac{a-k}{n+1}+1-b\\r)} &\n\\mathrm{for} \\quad 1\\leq k\\leq n\n\\\\ \\frac{\\Gamma(a\/(n+1))\\Gamma(1-b)}{z\n  \\Gamma(1-b+a\/(n+1))} & \\mathrm{for} \\quad\nk=n+1 \\eary\\right.  \\\\\nV_{jk} &=& \\frac{\\omega^{-jk}}{n+1}\n\\label{eq:matrB2}\n\\end{eqnarray}\n\\begin{comment}\nWe can invert this explicitly as\n\\beq\nJ^\\mathcal{X} = B \\Pi\n\\eeq\nwith \n\\bea\nV_{ik} & = &\n\\omega^{ik}  \\\\\n\\label{eq:matrB1}\nB_{ik} &\\triangleq& (D_2 V D_1)_{ik} \\nn \\\\ \n&=&\n-\\omega^{(n\/2-k)a + ik-i\/2}\n\\frac{\\Gamma\\l(\\frac{a-i}{n+1}+1-b\\r)}{\\Gamma\\l(\\frac{a-i}{n+1}+1\\r)\\Gamma(1-b)},\n\\quad i \\leq n  \\\\\nB_{n+1,k} &=& z \\omega^{(n\/2-k)a}\n \\frac{\\Gamma(1-b+a\/(n+1))}{\\Gamma(a\/(n+1))\\Gamma(1-b)}.\n\\label{eq:matrB2}\n\\end{eqnarray}\n\\end{comment}\nPiecing \\eqref{eq:matrA} and \\eqref{eq:matrB1}-\\eqref{eq:matrB2} together\nyields\\footnote{This amounts to a rather tedious exercise in telescoping sums and additions of roots of unity. The computation can be made available upon request.} \\eqref{eq:Uiri}, up to a scalar factor of $\\omega^{a}$. By\nRemark~\\ref{rmk:string}, this corresponds to our freedom of a String Equation\nshift along either of $H^0(\\mathcal{X})$ and $H^0(Y)$. Setting\n$\\delta_\\mathcal{X}-\\delta_Y=2\\pi\\mathrm{i}\\alpha_1$ in \\eqref{eq:kappa0Y}, \\eqref{eq:kappa0X} concludes the proof.\n\n{\\begin{flushright} $\\square$ \\end{flushright}}\n\n\\begin{comment}\n\\begin{thm}\nLet $\\rho$ be a straight line in $\\mathcal M_A$ connecting {\\rm LR} to {\\rm OP}. Then,\nin the bases $\\{p_i\\}_{i=1}^{n+1}$ for $Y$ and $\\{\\mathbf{1}_{\\left\\langle\n  \\frac{i}{n+1}\\right\\rangle}\\}_{i=1}^{n+1}$ for $\\mathcal{X}$, $\\mathbb{U}^{\\mathcal{X},Y}_\\rho : S_Y \\to\nS_\\mathcal{X}$ is given by\n\\beq\n(\\mathbb{U}^{\\mathcal{X},Y}_\\rho\n\\eeq\n\\end{thm}\n\\end{comment}\n\n\\subsection{Monodromy and equivariant integral structures}\n\\label{sec:monodromy}\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics{monodromy.pdf}\n\\caption{The path $\\sigma_{13}$ in $\\pi_1(\\mathcal M_A)$ for $n=4$.}\n\\label{fig:mono}\n\\end{figure}\n\nThe expression \\eqref{eq:Uiri} for\nthe symplectomorphism $\\mathbb{U}_\\rho^{\\mathcal{X}, Y}$ was obtained for the analytic\ncontinuation path $\\rho$ of Theorem~\\ref{thm:crc}. Fixing a\nreference point $m_0=(\\widetilde{\\kappa_1}, \\dots, \\widetilde{\\kappa_n})\n\\in\\mathcal M_A$, for a general path $\\rho \\circ \\sigma$ with $[\\sigma] \\in \\pi_1(\\mathcal M_A, m_0)$\nwe get a composition \n\\beq\n\\mathbb{U}_{\\rho\\circ\\sigma}^{\\mathcal{X}, Y} = \\mathbb{U}_\\rho^{\\mathcal{X}, Y} M_\\sigma\n\\eeq\nwhere $M_\\sigma : \\pi_1(\\mathcal M_A,m_0) \\to \\mathrm{End}(\\mathrm{Sol}_{\\lambda,\\phi})$\nis the monodromy representation of the fundamental group of $\\mathcal M_A$ in the space\nof solutions of the Lauricella system $F_D^{(n)}$. \\\\\n\nBy definition \\eqref{eq:discr}, $\\mathcal M_A$ is the configuration space of $n$\ndistinct points\nin $\\mathbb{P}^1\\setminus\\{0,1,\\infty\\}$. Therefore, its fundamental group coincides\nwith the genus zero pure mapping class group \\cite{0006.03401, MR613935}\n\\beq\n\\pi_1(\\mathcal M_A) \\simeq \\mathrm{PB}_{n+2}\/Z(\\mathrm{PB}_{n+2});\n\\eeq\nwhere $\\mathrm{PB}_{n+2}$ denotes the pure braid group in $n+2$ strands and\n$Z(\\mathrm{PB}_{n+2})\\simeq \\mathbb{Z}_2$ is its center. Writing $\\widetilde{\\kappa_i}=0,1,\n\\infty$ for $i=n+1$, $n+2$ and $n+3$ respectively, generators $P_{ij}$, $i=1, \\dots, n+3$,\n$j=1, \\dots, n$  of $\\mathrm{PB}_{n+2}$ are in bijection with paths\n$\\sigma_{ij}:[0,1]\\to\\mathcal M_A$ given by lifts to $\\mathcal M_A$ of closed contours in the\n$j^{\\rm th}$ affine coordinate plane that start at\n$\\kappa_j=\\widetilde{\\kappa_j}$, turn counterclockwise around\n$\\widetilde{\\kappa_i}$ (and around no other point) and then return to their\noriginal position, as in Figure~\\ref{fig:mono}.  \\\\\n\nThe image of the period map \\eqref{eq:periodmap}, by Proposition~\\ref{thm:tp},\nis a lattice in $\\mathrm{Sol}_{\\lambda,\\phi}$:\n\\beq\n\\mathrm{Sol}_{\\lambda,\\phi} = \\nabla^{(g)}\\Omega\\l(H_1\\l(\\mathbb{C}\\setminus (\\lambda),\n\\mathbf{L}\\r)\\r) \\otimes_{\\mathbb{Z}(\\mathrm{e}^{\\mathrm{i} \\pi a},\\mathrm{e}^{\\mathrm{i} \\pi b})}\\mathbb{C}(\\mathrm{e}^{\\mathrm{i} \\pi a},\\mathrm{e}^{\\mathrm{i} \\pi b},z),\n\\eeq\nand by \\eqref{eq:matrA},\n\\eqref{eq:matrB1}-\\eqref{eq:matrB2} the induced morphism $H_1(\\mathbb{C}\\setminus\n(\\lambda), {\\bf L}) \\simeq K(Y) $ is a lattice isomorphism. The\nmonodromy action on $\\mathrm{Sol}_{\\lambda, \\phi}$, at the level of\nequivariant $K$-groups, is given by lattice automorphisms $\\pi_1(\\mathcal M_A) \\to\n\\mathrm{Aut}_{\\mathbb{Z}(\\mathrm{e}^{\\mathrm{i} \\pi a},\\mathrm{e}^{\\mathrm{i} \\pi b})} K(Y)$;\nthis can be verified explicitly from the form of the monodromy matrices in the\ntwisted period basis \\cite{MR2962392}. It would be fascinating to trace the origin of this pure braid group action on the quantum\n$D$-module as coming from an action of the braid group at the level\nof the equivariant derived category of coherent sheaves on $\\mathcal{X}$ and $Y$, as\nin \\cite{MR1831820}.\n\n\\begin{figure}\n\\includegraphics{modspace1.pdf}\n\\caption{The K\\\"ahler moduli space of the $A_1$ singularity in $A$-model\n  coordinates. LR1 and LR2 indicate the large radius points $\\kappa=0, \\infty$\nrespectively, CP is the conifold point, and OP is the orbifold\npoint. Circuits around LR1-2 and CP generate the monodromy group of the global\nquantum $D$-module. The dashed segment depicts the analytic continuation path $\\rho$ of\nTheorem~\\ref{thm:crc} and \\ref{thm:sympl}.}\n\\label{fig:modspace1}\n\\end{figure}\n\\subsubsection{Example: $n=1$}\n\nIn this case the action on $K(Y)$ is given by the classical monodromy of the\nGauss system for $c=a-b+1$. With reference to Figure~\\ref{fig:modspace1}, we\nhave in the standard basis $\\{\\mathcal{O}_Y, \\mathcal{O}_Y(1)\\}$ for $K(Y)$,\n\\bea\nM_{\\rm LR1} &=& \n\\l(\n\\begin{array}{cc}\n \\mathrm{e}^{-\\mathrm{i} a \\pi } \\left(\\mathrm{e}^{2 \\mathrm{i} a \\pi }+\\mathrm{e}^{2 \\mathrm{i} b \\pi }\\right) & \\mathrm{e}^{2 \\mathrm{i} b \\pi } \\\\\n -1 & 0 \\\\\n\\end{array}\\r), \\\\ \nM_{\\rm CP} &=&\n\\left(\n\\begin{array}{cc}\n 1 & -2 \\mathrm{i} \\mathrm{e}^{-\\mathrm{i} (a-b) \\pi } \\sin (b \\pi ) \\\\\n -\\mathrm{e}^{-\\mathrm{i} (a+2 b) \\pi } \\left(-1+\\mathrm{e}^{2 \\mathrm{i} b \\pi }\\right) & \\mathrm{e}^{-2 \\mathrm{i} (a+b) \\pi } \\left(-1+\\mathrm{e}^{2 \\mathrm{i} b \\pi }\\right)^2+1 \\\\\n\\end{array}\n\\right), \\\\\nM_{\\rm LR2}\n&=&\n\\left(\n\\begin{array}{cc}\n 2 \\cos (a \\pi ) & 1-\\mathrm{e}^{-2 \\mathrm{i} a \\pi } \\left(-1+\\mathrm{e}^{2 \\mathrm{i} b \\pi }\\right) \\\\\n -1 & 2 \\mathrm{i} \\mathrm{e}^{-\\mathrm{i} (a-b) \\pi } \\sin (b \\pi ) \\\\\n\\end{array}\n\\right),\n\\end{eqnarray} \nfor the large radius and the conifold monodromy of $\\mathrm{QDM}(Y)$. It is\nstraightforward to check that they induce symplectic automorphisms of the Givental\nvector space $\\mathcal{H}(Y)$.\n\\begin{rmk}\nIn the non-equivariant limit the conifold monodromy becomes trivial. As a\nresult, the monodromy group reduces to the integers, being generated by the\nGalois action around the large radius limit point of $Y$. This is consistent\nwith the fact that $\\mathrm{B}_2\\simeq \\mathbb{Z}$ in \\cite{MR1831820}.\n\\end{rmk}\n\n\\begin{appendix}\n\\section{Analytic continuation of Lauricella $F_D^{(N)}$}\n\\label{sec:anFD}\nConsider the Lauricella function $F_D^{(M+N)}(a; b_1, \\dots,  b_{M+N}; c; z_1, \n\\dots,z_M, w_1, \\dots, w_N)$ around $P=(0,0, \\dots, \\infty, \\dots,\n\\infty)$. We  are interested in the leading terms of the asymptotics of\nthis function in the region $\\Omega_{M+N}$ defined as\n\\beq\n\\label{eq:omegaMN}\n\\Omega_{M+N}\n\\triangleq B(P,\\epsilon) \\bigcap_{i<j} H_{ij} \n\\eeq\ngiven by the intersection of the ball $B(P,\\epsilon)$ with the interior of the real hyperquadrics\n\\beq\nH_{ij} \\triangleq \\l\\{ (z,w) \\in \\mathbb{C}^{M+N}  \\big| |w_i\/w_j| < \\epsilon\\r\\}.\n\\eeq\nAs our interest is confined to the\n{\\it leading} asymptotics only, we can assume w.l.o.g. that $M=0$. \\\\\n\nFollowing \\cite[Chapter~6]{MR0422713}, start from the power series expression\n\\eqref{eq:FD} and perform the sum w.r.t. $w_N$\n\\bea\nF_D^{(N)}(a; b_1, \\dots, b_N; c; w_1, \\dots, w_N) &=& \\sum_{i_1, \\dots, i_{N-1}}\n\\frac{(a)_{\\sum_{j=1}^{N-1} i_j}}{(c)_{\\sum_{j=1}^{N-1} i_j}}\\prod_{j=1}^{N-1}\n\\frac{(b_j)_{i_j} w_j^{i_j}}{i_j!} \\nn \\\\ & & {}_2F_1\\l(a+\\sum_{j=1}^{N-1} i_j, b_N, c+\\sum_{j=1}^{N-1} i_j,w_N\\r) .\n\\label{eq:FD2F1}\n\\end{eqnarray}\nThe main idea then is to apply the connection formula for the inner Gauss\nfunction \n\\bea\n\\, _2F_1(a,b;c;z) &=& \\frac{(-z)^{-a} \\Gamma (c) \\Gamma (b-a) \\,\n  _2F_1\\left(a,a-c+1;a-b+1;\\frac{1}{z}\\right)}{\\Gamma (b) \\Gamma (c-a)} \\nn\n\\\\ &+& \\frac{(-z)^{-b} \\Gamma (c) \\Gamma (a-b) \\,\n   _2F_1\\left(b,b-c+1;-a+b+1;\\frac{1}{z}\\right)}{\\Gamma (a) \\Gamma (c-b)}\n\\label{eq:2F1conn}\n\\end{eqnarray}\nto analytically continue it to $|z|=|w_N|>1$; in doing so, we fix a path of\nanalytic continuation by choosing the principal branch for both the power functions\n$(-z)^{-a}$ and $(-z)^{-b}$ in \\eqref{eq:2F1conn} and continue $\\,\n_2F_1(a,b;c;z)$ to $|z>1|$ along a path that has winding number zero around\nthe Fuchsian singularity at $z=1$. As a power series in $w_N$ the analytic continuation\nof \n\\eqref{eq:FD2F1} around $w_N=\\infty$ then reads\n\\bea\n& & F_D^{(N)}(a; b_1, \\dots, b_N; c; w_1, \\dots, w_N) = (-w_N)^{-a}\n\\Gamma\\l[\\bary{cc}c, & b_N-a \\\\ b_N, & c-a \\eary\\r] \\nn \\\\ & &  F_D^{(N)}\\l(a; b_1, \\dots,\nb_{N-1}, 1-c+a; 1-b_N+a,\\frac{w_1}{w_N}, \\dots, \\frac{1}{w_N}\\r) \n+\n(-w_N)^{-b_N}\n\\Gamma\\l[\\bary{cc}c, & a-b_N \\\\ a, & c-b_N \\eary\\r] \\nn \\\\ & & C_N^{(N-1)}\\l(b_1, \\dots,\nb_{N}, 1-c+b_N; a-b_N,-w_1,-w_2, \\dots, \\frac{1}{w_N}\\r),\n\\label{eq:FDcont1}\n\\end{eqnarray}\nwhere we defined \\cite[Chapter~3]{MR0422713}\n\\bea\nC_N^{(k)}\\l(b_1, \\dots,\nb_{N}, a; a',x_1, \\dots, x_N\\r) & \\triangleq & \\sum_{i_1, \\dots, i_{N}}\n(a)_{\\alpha_N^{(k)}(\\mathbf{i})}(a')_{-\\alpha_N^{(k)}(\\mathbf{i})} \\prod_{j=1}^{N}\n\\frac{(b_j)_{i_j} w_j^{i_j}}{i_j!} \n\\end{eqnarray}\nand \n\\bea\n\\alpha_N^{(k)}(\\mathbf{i}) &\\triangleq& \\sum_{j=k+1}^{N} i_j-\\sum_{j=1}^{k} i_j,\\\\\n\\Gamma\\l[\\bary{ccc}a_1, & \\dots, & a_m \\\\ b_1, & \\dots, & b_n \\eary\\r] &\\triangleq&\n\\frac{\\prod_{i=1}^m \\Gamma(a_i)}{\\prod_{i=1}^l\\Gamma(b_i)}.\n\\end{eqnarray}\nNow, notice that the $F_D^{(N-1)}$ function in the r.h.s. of \\eqref{eq:FDcont1} is\nanalytic in $\\Omega_N$; there is nothing more that should be done there. The\nanalytic continuation of the $C_N^{(N-1)}$ function is instead much more involved (see\n\\cite{MR0422713} for a complete treatment of the $N=3$ case); but as all we\nare interested in is the leading term of the expansion around $P$ in\n$\\Omega_N$ we isolate the $\\mathcal{O}(1)$ term in its $1\/w_N$ expansion to find\n\\bea\n& & C_N^{(N-1)}\\l(b_1, \\dots,\nb_{N}, 1-c+b_N; a-b_N,-w_1,-w_2, \\dots, \\frac{1}{w_N}\\r) = \\nn \\\\\n&=& F_D^{(N-1)}\\l(a-b_N,b_1, \\dots,\nb_{N-1}, c-b_N; w_1, \\dots, w_{N-1}\\r)+ \\mathcal{O}\\l(\\frac{1}{w_{N}}\\r)\n\\label{eq:CNFD}\n\\end{eqnarray}\nWe are done: by \\eqref{eq:CNFD}, the form of the leading terms in the expansion of\n$F_D^{(N)}$ inside $\\Omega_N$ can be found recursively by iterating $N$ times the\nprocedure we have followed in \\eqref{eq:FD2F1}-\\eqref{eq:CNFD}; as at each step \\eqref{eq:2F1conn}-\\eqref{eq:CNFD} generate\none additional term, we end up with a sum of $N+1$ monomials each having\npower-like monodromy around $P$. Explicitly:\n\\bea\nF_D^{(N)}(a; b_1, \\dots, b_N; c; w_1, \\dots, w_N) & \\sim & \n\\sum_{j=0}^{N-1}\\Gamma\\l[\\bary{ccc}c, & a-\\sum_{i=N-j+1}^N b_i, & \\sum_{i=n-j}^N\n  b_i-a \\\\ a, & b_{N-j}, & c-a \\eary\\r] \\nn \\\\ & & \\prod_{i=1}^j (-w_{N-i+1})^{-b_{N-i+1}}\n(-w_{N-j})^{-a+\\sum_{i=N-j+1}^Nb_i}\\nn \\\\ &+& \\prod_{i=1}^N (-w_i)^{-b_i}\n\\Gamma\\l[\\bary{cc}c, & a-\\sum_{i=1}^N b_j \\\\ a, & c-\\sum_{i=1}^N b_j \\eary\\r].\n\\label{eq:fdinf}\n\\end{eqnarray}\n\n\\begin{rmk}\nThe analytic continuation to some other sectors of the ball $B(P,\\epsilon)$ is\nstraightforward. In particular we can replace the condition $w_i\/w_j \\sim 0$\nfor $j>i$ by its reciprocal $w_j\/w_i \\sim 0$; this amounts to relabeling $b_i\n\\to b_{N-i+1}$ in \\eqref{eq:fdinf}.\n\\label{rmk:relabel}\n\\end{rmk}\n\n\\begin{rmk} When $a=-d$ for $d\\in \\mathbb{Z}^+$, the function $F_D^{(N)}$ reduces to\n  a polynomial in $w_1, \\dots, w_N$. In this case the arguments above reduce\n  to a formula of Toscano \\cite{MR0340663} for Lauricella polynomials:\n\\bea\n& & F_D^{(N)}(-d; b_1, \\dots, b_N; c; w_1, \\dots, w_N)  \\nn \\\\ &=& (-w_N)^{d}\\frac{(b)_d}{(c)_d}\n F_D^{(N)}\\l(-d; b_1, b_2 \\dots,\nb_{N-1};1-d-c, 1-d-b_N,\\frac{w_1}{w_N}, \\dots, \\frac{1}{w_N}\\r).\n\\label{eq:FDtosc}\n\\end{eqnarray}\n\\label{rmk:toscano}\n\\end{rmk}\n\\begin{comment}\n\\section{GKZ mirror symmetry}\n\\label{sec:tms}\n\\subsection{$I$-functions and the Picard--Fuchs system}\n\nIt is instructive to compare the hypergeometric form of the $\\nabla$-flat\nsections \\eqref{eq:pilaur1}-\\eqref{eq:pilaur2} in $A$-model variables with the\ngeneralized hypergeometric functions that arise from solutions of the\nmirror GKZ system. \\\\\n\nLet us start from $n=1$. If we dualize \\eqref{eq:divclass},\n\\beq\n0\\longrightarrow\\mathbb{Z}^3\\stackrel{\\l(\\bary{ccc} 1 & 0 & 0 \\\\ 1 & 1 & 0 \\\\ 1 & 2 & 0 \\\\\n  0 & 0 & 1\\eary\\r)}{\\longrightarrow}\\mathbb{Z}^{4}\\stackrel{\\l( \\bary{cccc} 1 & -2 &\n  1 & 0 \\eary\\r)}{\\longrightarrow}\\mathbb{Z}\\longrightarrow\n0,\n\\label{eq:divclass2}\n\\eeq\ngives us the chamber decomposition depicted in Figure~\\ref{fig:bmod1} (the\n{\\it secondary fan} of $\\mathcal{X}$ and $Y$).\n\\begin{figure}[h]\n\\centering\n\\includegraphics{bmod1.pdf}\n\\caption{The secondary fan for the case $n=1$.}\n\\label{fig:bmod1}\n\\end{figure}\nThe {\\it B-model moduli space} $\\mathcal M_B$ is the toric orbifold corresponding to the\none-dimensional fan in Figure~\\ref{fig:bmod1}. From \\eqref{eq:divclass2}, we have\n$\\mathcal M_B \\simeq \\mathbb{P}(1,2)$: the northern (smooth) hemisphere of the orbifold projective line\ncorresponds to the right hand chamber in Figure~\\ref{fig:bmod1}, which gives rise\nto the resolution $Y = (K\\oplus\\mathcal{O})_{\\mathbb{P}^1}$; conversely for the southern\nhemisphere and the singularity $\\mathcal{X}=[\\mathbb{C}^3\/\\mathbb{Z}_2]$. Let $y_s$ be a coordinate\npatch for the smooth patch, and $y_o$ for the orbifold patch, so that\n$y_s=1\/y_o^2$; the large volume points for $Y$ and $\\mathcal{X}$ correspond to $y_s=0$\nand $y_o=0$ respectively. The Picard--Fuchs operator $\\mathcal{D}$ for $\\mathcal{X}$ and $Y$ reads \\cite{MR2510741}\n\\bea\n\\label{eq:GKZX1}\n\\mathcal{D} &=& z \\theta_o (z\\theta_o -z)- y_o^2 \\l(\\alpha_1-\\frac{z}{2}\n\\theta_o\\r)\\l(\\alpha_2-\\frac{z}{2} \\theta_o\\r), \\qquad \\theta_o =\n\\frac{{\\partial}}{{\\partial} y_o}, \\\\\n&=& 2 z  \\theta_s (2 z\\theta_s +z)- y_s^{-1}\\l(\\alpha_1+z \\theta_s\\r)\\l(\\alpha_2+z \\theta_s\\r), \\qquad \\theta_s =\n\\frac{{\\partial}}{{\\partial} y_s}.\n\\label{eq:GKZY1}\n\\end{eqnarray}\nConsider the patch of $\\mathcal M_B$ first and define the $I$-function\nof $Y$ as the cohomology valued series\n\\bea\nI^{K_{\\mathbb{P}^1}\\oplus\\mathcal{O}_{\\mathbb{P}^1}}(y_s,z) & \\triangleq &  z y_s^{p\/z}\\left[1+\\sum_{d>0}\n2 p y_s^{d} \\frac{\\Gamma(\\frac{2 p}{z}+2d)}{\\Gamma(\\frac{2\n    p}{z}+1)}\n\\frac{\\Gamma(\\frac{p+z+\\alpha_1}{z})}{\\Gamma(\\frac{p+z+\\alpha_1}{z}+d)} \n\\frac{\\Gamma(\\frac{p+z+\\alpha_2}{z})}{\\Gamma(\\frac{p+z+\\alpha_2}{z}+d)}\\right],\n\\nn \\\\\n&=& y_s^{\\alpha_1\/z}\\left[z+2\\alpha_1\\sum_{d>0}\n  \\frac{y_s^{d}}{d!} \\frac{\\Gamma(2d+\\frac{2\\alpha_1}{z})}{\\Gamma(1+\\frac{2\n    \\alpha_1}{z})}\n\\frac{\\Gamma(\\frac{z-\\alpha_2+\\alpha_1}{z})}{\\Gamma(\\frac{z-\\alpha_2+\\alpha_1}{z}+d)}\\right]\nP_2 + (1 \\leftrightarrow 2), \\nn \\\\\n&=& z y_s^{\\alpha_1\/z} \\, _2F_1\\l(\\frac{\\alpha_1}{z}, \\frac{1}{2}+\\frac{\\alpha_1}{z}, \\frac{\\alpha_1-\\alpha_2}{z}, 4 y_s\\r) P_2\n+ (1 \\leftrightarrow 2),\n\\label{eq:IY2F1}\n\\end{eqnarray}\nwhere $p=c_1(\\mathcal{O}_{\\mathbb{P}^1}(1))=\\alpha_2 P_1+\\alpha_1 P_2$ is the hyperplane class and\n$\\{P_1, P_2\\}$ is the localized basis for $H_T(Y)$ of Section~\\ref{sec:GIT}\n(that is, the equivariant classes corresponding to the North and the South\npole of the base $\\mathbb{P}^1$). Then the components of $I^Y$ are a basis of\nsolutions of \\eqref{eq:GKZY1}, and under the mirror map\n\\beq\ny_s = \\frac{\\mathrm{e}^{t}}{(1+\\mathrm{e}^{t})^2}\n\\label{eq:mirmap1}\n\\eeq\nit gives \\cite{MR2276766} a family of elements of the cone $\\mathcal{L}_Y$ of $Y$ such that\n\\beq\nI^Y(y_s(t),-z) = -z + t + \\mathcal{O}\\l(\\frac{1}{z}\\r).\n\\eeq\nThen\n\\beq\nJ^Y(t,z)|_{t_0=0} = I^Y(y_s(t),z),\n\\eeq\nas can be verified upon plugging \\eqref{eq:mirmap1} into \\eqref{eq:IY2F1},\nusing\n\\beq\n _2F_1(a,b;a-b+1;z)=(1-z)^{-a} \\,\n   _2F_1\\left(\\frac{a}{2},\\frac{a+1}{2}-b;a-b+1;-\\frac{4\n   z}{(1-z)^2}\\right)\n\\eeq\nand comparing with \\eqref{eq:t1LR1}-\\eqref{eq:t1LR2}. \\\\\n\nSimilarly, in the orbifold chamber we define\n\\bea\nI^{[\\mathbb{C}^3\/\\mathbb{Z}_2]}(y_o,z) & \\triangleq & z \\Bigg[\\sum_{k\\geq 0}\n  \\frac{y_o^{2k}}{(2k)!}\\prod_{r=0}^{k-1}\\l(\\frac{\\alpha_1}{z}-r\\r)\\l(\\frac{\\alpha_2}{z}-r\\r) \\mathbf{1}_0\n  \\nn \\\\\n&+& \\sum_{k\\geq 0}\n  \\frac{y_o^{2k+1}}{(2k+1)!}\\prod_{r=0}^{k-1}\\l(\\frac{\\alpha_1}{z}-r-\\frac{1}{2}\\r)\\l(\\frac{\\alpha_2}{z}-r-\\frac{1}{2}\\r) \\mathbf{1}_{1\/2}\n\\Bigg], \\nn \\\\\n &=& z \\, _2F_1\\l(\\alpha_1, \\alpha_2, \\frac{1}{2}, \\frac{y_o^2}{4}\\r) \\mathbf{1}_0 + y_o\n\\, _2F_1\\l(\\alpha_1+\\frac{1}{2}, \\alpha_2+\\frac{1}{2}, \\frac{3}{2}, \\frac{y_o^2}{4}\\r) \\mathbf{1}_{1\/2}.\n\\end{eqnarray}\nAs before,\n\\beq\nJ^\\mathcal{X}(x,z)|_{x_0=0} = I^\\mathcal{X}(y_o(x),z).\n\\eeq\n\\begin{rmk}\nNotice that the orbifold point $y_o=0$ in the $B$-model moduli space is a\nFuchsian singularity for \\eqref{eq:GKZX1} with critical exponents\n$(0,1\/2)$, and therefore $\\mathbb{Z}_2$ monodromy. This is unlike the orbifold point in the $A$-model, which is a\nsmooth point for the Dubrovin connection, since the projection map\n$y_s:\\mathcal M_A\\to\\mathcal M_B$ realizes $\\mathcal M_A$ as a double cover of $\\mathcal M_B$ branched at the conifold and the orbifold point.\n\\end{rmk}\nFor general $n$, the $B$-model moduli space is the projective toric\nDeligne--Mumford stack associated to the simplicial stacky fan with rays given\nby the columns of $M$ in \\eqref{eq:MN}. The large volume chamber,\ncorresponding to the stability condition \\eqref{resgit}, is the chamber with\nmaximal cones \n\\beq\n\\sigma_i=\\l\\{ \\bary{ccc} M_{\\bullet,i} & \\mathrm{for} & 1\\leq i <n, \\\\\nM_{\\bullet,n+3} & \\mathrm{for} & i=n,\n \\eary\\r.\n\\eeq\nwhere $M_{\\bullet, k}$ denotes the $k^{\\rm th}$ column of $M$. The $I$-function here reads \\cite{MR2510741}\n\\bea\nI^Y(y_s,z) &=& z \\l(\\prod_{i=1}^n y_{s,i}^{p_i\/z}\\r) \\sum_d \\Bigg[ \n\\frac{\\prod_{m\\leq 0}( \\alpha_1+p_1 + m z)}{\\prod_{m\\leq d_1}( \\alpha_1+p_1 + m z) }\n\\frac{\\prod_{m\\leq 0}( \\alpha_2+p_n + m z)}{\\prod_{m\\leq d_n}( \\alpha_2+p_n + m z) }\n\\nn \\\\\n& \\times & \n\\prod_{j=1}^{n}\\frac{\\prod_{m\\leq 0}( \\epsilon_j + m z)}{\\prod_{m\\leq\n    d_{j+1}-2d_j+d_{j-1}}( \\epsilon_j + m z) } y_{s,j}^{d_j}\\Bigg],\n\\label{eq:IYn}\n\\end{eqnarray}\nwhere \n$\\epsilon_j =\np_{j+1}-2 p_j + p_{j-1}$ for $1<j<n$ and we set $p_{-1}=p_{n+1}=0$ and\n$d_{-1}=d_{n+1}=0$. As shown in \\cite{MR2510741}, we have\n\\beq\nJ^Y(t,z)|_{t_0=0}=I^Y(y_s,z)\n\\eeq\nunder the mirror map $t=t(y_s)$, where\n\\beq\nt(y_s)=\\lim_{z\\to\\infty}\\l(I^Y(y_s,z)-z\\r).\n\\eeq\n\\\\\nThe orbifold chamber of $\\mathcal M_B$ is spanned by\n$\\{\\sigma_i=M_{\\bullet, i+1}\\}_{i=1}^n$. The orbifold coordinate patch $y_0$ is related\nto the resolution patch as $y_{s,i}= y_{o,i+1}y_{o,i}^{-2}y_{o,i-1}$, where\n$y_{o,0}=y_{o,n+1}=1$. In these variables, the $I$-function of $\\mathcal{X}$ is a rank\ntwo twist \\cite{MR2578300} of the Jarvis--Kimura $I$-function of $B\\mathbb{Z}_{n+1}$ \\cite{MR1950944}:\n\\beq\nI^\\mathcal{X}(y_o,z)=\n\\sum_{k_i\\geq 0}\\prod_{j=1,2}\\prod_{\\stackrel{D_j(k)<l_j\\leq 0}{\\left\\langle l_j \\right\\rangle = D_j(k)}} (\\alpha_j+l_j z) \\prod_{i=1}^n \\frac{y_{o,i}^{k_i}}{z^{k_i} k_i!}\\mathbf{1}_{\\left\\langle -D_2(k)\\right\\rangle}\n\\eeq\nwhere $D_1(k)=1\/n \\sum(i-n)k_i$, $D_2(k)=\\sum k_i -D_1(k)$.\n\n\\subsection{Analytic continuation}\nThe standard approach to the analytic continuation of solutions of the GKZ\nsystem is given by the Mellin--Barnes method \\cite{MR2271990, MR2700280,\n  MR2486673}. Fix one monomial $y_{s,1}^{d_1}\\dots y_{s,n-1}^{d_{n-1}}$ in\n\\eqref{eq:IYn} and consider its coefficient $I^Y_{d_1, \\dots,\n  d_{n-1}}(y_{s,n},z)$ as a formal power series in\n$y_n$. Upon replacing all Gamma functions $\\Gamma(\\alpha+d_n\\beta)$ using\n$\\Gamma(x) \\Gamma(1-x)= \\pi\/\\sin(\\pi x)$ until all factors have $d_n>0$, the\nresulting series converges for $|y_{s,n}|<R_{d_1, \\dots, d_{n-1}}$ \nsmall enough, to a hypergeometric Fox $H$-function given by the Mellin--Barnes integral\n\\bea\nI^Y_{d_1, \\dots,\n  d_{n-1}}(y_{s,n},z) & \\propto & H^{2,1}_{2,2}\\l(\\frac{1}{y_{s,n}} \\bigg|\n\\bary{cc}\n (0,1); & (1+\\epsilon_{n-1}\/z,2) \\\\\n(0,1), (-d_{n-1}-\\epsilon_{n-1}\/z, 2); & -\n\\eary\n \\r)\n \\nn \\\\\n&=& \n\\frac{1}{2\\pi\\mathrm{i}}\\int_{C_n} \ny_{s,n}^s\n\\frac{\\Gamma(s)\\Gamma(1-s)\\Gamma\\l(2s-d_{n-1}-\\frac{\\epsilon_{n-1}}{z}\\r)}{\\Gamma\\l(1+2s+\\frac{\\epsilon_{n}}{z}\\r)}\n\\end{eqnarray}\nwhere the contour $C_n$ is a loop beginning at $\\gamma -\\mathrm{i} \\infty$ and ending\nat $\\gamma+\\mathrm{i}\\infty$ with $\\gamma\\in\\mathbb{R}^+$, circling counterclockwise around $s=-n$\nand clockwise around $-n\/2 +\nd_{n-1}\/2+\\frac{\\epsilon_{n-1}}{2z}$, $s\\in\\mathbb{N}$. For $|y_{s,n}|<R_{d_1,\n  \\dots, d_{n-1}}$, we can close the contour around\nthe negative real axis, which gives back \\eqref{eq:IYn}. Closing instead the\ncontour around the half-line $-x + d_{n-1}\/2+\\frac{\\epsilon_{n-1}}{2z}$, $x\n\\in \\mathbb{R}^+$, analytically continues \\eqref{eq:IYn} to the chamber where\n$|y_{s,n}|>R_{d_1, \\dots, d_{n-1}}$. Iterating this procedure gives analytic\ncontinuation formulae for $I^Y(y_s,z)$ to other chambers of $\\mathcal M_B$. \\\\\n\nFor example, start from $n=1$ and rewrite \n\\beq\nI^{K_{\\mathbb{P}^1}\\oplus\\mathcal{O}_{\\mathbb{P}^1}}(y_s,z) =\n\\Theta(\\alpha_1,\\alpha_2,z) y_s^{-\\alpha_1\/z} \n \\sum_{d\\geq 0}\n  \\frac{y_s^{d}}{d!}\n  \\frac{\\Gamma(2d-\\frac{2\\alpha_1}{z})}{\\Gamma(\\frac{z+\\alpha_2-\\alpha_1}{z}+d)}\n  P_2 + (1 \\leftrightarrow 2)\n\\eeq\nwhere $\\Theta(\\alpha_1,\\alpha_2,z)=-2 \\alpha_1 \n \\frac{\\Gamma(\\frac{z+\\alpha_2-\\alpha_1}{z})}{\\Gamma(1-\\frac{2\n    \\alpha_1}{z})}$. This converges when $|y_s|<1\/4$. Let $C$ be the contour in\n the complex $s$-plane  depicted in Fig. \\ref{fig:contc3z2}, and consider the integral\n\\beq\n\\mathcal{I}(y_s,z) = \n\\int_{C} \\mathrm{d} s\\frac{y_s^{s}}{\\Gamma(s+1)} \\frac{\\Gamma(s)\\Gamma(1-s)\n  \\Gamma(2s-\\frac{2\\alpha_1}{z})}{\\Gamma(\\frac{z+\\alpha_2-\\alpha_1}{z}+s)} P_2 + (1 \\leftrightarrow 2)\n\\eeq\n\\begin{figure}[t]\n\\centering\n\\includegraphics[scale=0.8]{analytic.pdf}\n\\caption{The contour $C$.}\n\\label{fig:contc3z2}\n\\end{figure}\nWhen $|y_s|<1\/4$, we close the contour to the right and pick up residues at\n$s=n\\geq 0$. This gives\n$I^N_{K_{\\mathbb{P}^1}\\oplus\\mathcal{O}_{\\mathbb{P}^1}}(y_s,z) y_s^{\\alpha_1\/z} \/\n\\Theta(\\alpha_1,\\alpha_2,z)$. When $|y_s|>1\/4$, we close the contour to the right\nand pick up residues at $s=-n\/2+\\alpha_1\/z$. We obtain\n\\bea\n\\tilde I_{K_{\\mathbb{P}^1}\\oplus\\mathcal{O}_{\\mathbb{P}^1}}(y_s,z) &=& -\\frac{\\Theta(\\alpha_1,\\alpha_2,z)}{2}\n \\sum_{n\\geq 0}\n  \\frac{(-y_o)^{n}}{n!} \\frac{\\Gamma(n\/2-\\alpha_1\/z)}{\\Gamma(1-n\/2+\\alpha_2\/z)} P_2 + (1 \\leftrightarrow 2)\n\\end{eqnarray}\nThe symplectomorphism $\\mathbb{U}^{\\mathcal{X}, Y}: \\mathcal{L}_{[\\mathbb{C}^3\/\\mathbb{Z}_2]}\\to\n\\mathcal{L}_{(K+\\mathcal{O})_{\\mathbb{P}^1}}$ relating the cones of $\\mathcal{X}$ and $Y$ is designed so that\n$U(I^{[\\mathbb{C}^3\/\\mathbb{Z}_2]}(y_o, -z)) = \\tilde\nI^{K_{\\mathbb{P}^1}\\oplus\\mathcal{O}_{\\mathbb{P}^1}}(y_s,-z)$. As $U$ is\nindependent of $y_o$, we equate the first few powers of $y_o$ on both sides. We\nhave\n\\beq\nI^{[\\mathbb{C}^3\/\\mathbb{Z}_2]}(y_o, -z) = -z \\mathbf{1}_0 - z y_o \\l(\\frac{\\alpha_1}{z}+\\frac{1}{2}\\r)\\l(\\frac{\\alpha_2}{z}+\\frac{1}{2}\\r)\\mathbf{1}_{\\frac{1}{2}}+\\mathcal{O}\\l(y_o^2\\r)\n\\eeq\nand thus\n\\bea\n\\mathbb{U}^{\\mathcal{X},Y}\\l(\\mathbf{1}_0\\r) &=& \n\\frac{\\alpha_1  \\Gamma \\left(\\frac{\\alpha_1}{z}\\right) \\Gamma \\left(\\frac{z+\\alpha_1-\\alpha_2}{z}\\right)}{\\Gamma \\left(\\frac{2 \\alpha_1}{z}+1\\right) \\Gamma \\left(1-\\frac{\\alpha_2}{z}\\right)}P_2+\\frac{\\alpha_2\n    \\Gamma \\left(\\frac{\\alpha_2}{z}\\right) \\Gamma \\left(\\frac{z-\\alpha_1+\\alpha_2}{z}\\right)}{\\Gamma\n   \\left(1-\\frac{\\alpha_1}{z}\\right) \\Gamma \\left(\\frac{2\n     \\alpha_2}{z}+1\\right)} P_1, \\\\\n\\mathbb{U}^{\\mathcal{X},Y}\\l(\\mathbf{1}_{\\frac{1}{2}}\\r) &=& \n\\sqrt{\\pi } z^2 \\left(\\frac{4^{-\\frac{\\alpha_1}{z}} \\Gamma \\left(\\frac{z+\\alpha_1-\\alpha_2}{z}\\right)}{\\Gamma\n   \\left(\\frac{\\alpha_1}{z}\\right) \\Gamma \\left(\\frac{1}{2}-\\frac{\\alpha_2}{z}\\right)}P_2+\\frac{ 4^{-\\frac{\\alpha_2}{z}}\n   \\Gamma \\left(\\frac{z-\\alpha_1+\\alpha_2}{z}\\right)}{\\Gamma \\left(\\frac{1}{2}-\\frac{\\alpha_1}{z}\\right) \\Gamma\n   \\left(\\frac{\\alpha_2}{z}\\right)}P_1\\right)\n\\end{eqnarray}\n\n\\begin{rmk}\nWorking parametrically in $n$, the analytic continuation of the $n$-fold Mellin--Barnes\nintegral representation of \\eqref{eq:IYn} becomes practically unwieldy, as it\nwould require to iterate this procedure for every chamber that is crossed in\nthe process (which are $n$ in our case). \n\\end{rmk}\n\\end{comment}\n\\end{appendix}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\\label{secIntro}\nThe class of adaptive importance sampling (AIS) methods is a key Monte Carlo methodology for estimating integrals that cannot be obtained in closed form \\citep{robert2004monte}. This problem arises in many settings, such as Bayesian signal processing and machine learning \\citep{bugallo2015adaptive, bugallo2017adaptive} or optimal control, \\citep{kappen2016adaptive} where the quantities of interest are usually defined as intractable expectations. Adaptive importance samplers are versions of classical importance samplers (IS) which iteratively improve the proposals to generate samples better suited to the estimation problem at hand. Its variants include, for example, \\textit{population Monte Carlo} methods \\citep{cappe2004population} and adaptive mixture importance sampling \\citep{cappe2008adaptive}. Since there has been a surge of papers on the topic of AIS recently, a comprehensive review is beyond the scope of this article; see e.g. \\cite{bugallo2017adaptive} for a recent review.\n\nDue to the popularity of the adaptive importance samplers, their theoretical performance has also received attention in the past few years. The same as conventional IS methods, AIS schemes enjoy the classical $\\mathcal{O}(1\/\\sqrt{N})$ convergence rate of the $L_2$ error, where $N$ is the number of Monte Carlo samples used in the approximations, see e.g. \\cite{robert2004monte} and \\cite{agapiou2017importance}. However, since an adaptation is performed over the iterations and the goal of this adaptation is to improve the proposal quality, an insightful convergence result would provide a bound which explicitly depends on the number of iterations, $t$, (which sometimes we refer to as \\textit{time}) and the number of samples, $N$. Although there are convergence results of adaptive methods (see \\cite{douc2007convergence} for a convergence theory for population Monte Carlo based on minimizing Kullback-Leibler divergence), none of the available results yields an explicit bound of the error in terms of the number of iterations and the number of particles at the same time.\n\nOne difficulty of proving such a result for adaptive mixture samplers is that the adaptive mixtures form an interacting particle system and it is unclear what kind of adaptation they perform or whether the adapted proposals actually get closer to the target for some metric. An alternative to adaptation using mixtures is the idea of minimizing a cost function in order to adapt the proposal. This idea has been popular in the literature, in particular, minimizing the variance of the weight function has received significant attention, see, e.g., \\citet{arouna2004adaptative,arouna2004robbins, kawai2008adaptive, lapeyre2011framework, ryu2014adaptive, kawai2017acceleration, kawai2018optimizing}. Relevant to us, in particular, is the work of \\citet{ryu2014adaptive}, who have have proposed an algorithm called Convex Adaptive Monte Carlo (Convex AdaMC). This scheme is based on minimizing the variance of the IS estimator, which is a quantity related to the $\\chi^2$ divergence between the target and the proposal. \\citet{ryu2014adaptive} have shown that the variance of the IS estimator is a convex function of the parameters of the proposal when the latter is chosen within the exponential family. Based on this observation, \\citet{ryu2014adaptive} have formulated Convex AdaMC, which draws one sample at each iteration and construct the IS estimator, which requires access to the normalised target. They proved a central limit theorem (CLT) for the resulting sampler. The idea has been further extended for self-normalised importance samplers by \\citet{ryu2016convex}, who considered minimising the $\\alpha$-divergence between the target and an exponential family. Similarly, \\citet{ryu2016convex} proved a CLT for the resulting sampler. Similar ideas were also considered by \\citet{kawai2017acceleration, kawai2018optimizing}, who also aimed at minimizing the variance expression. Similarly, \\citet{kawai2018optimizing} showed that the variance of the weight function is convex when the proposal family is suitably chosen and provided general conditions for such proposals. \\citet{kawai2018optimizing} has also developed an adaptation technique based on the stochastic approximation, which is similar to the scheme we analyse in this paper. {There have been other results also considering $\\chi^2$ divergence and relating it to the necessary sample size of the IS methods, see, e.g., \\citet{sanz2018importance}. Following the approach of \\citet{chatterjee2018sample}, \\citet{sanz2018importance} considers and ties the necessary sample size to $\\chi^2$-divergence, in particular, shows that the necessary sample size grows with $\\chi^2$-divergence, hence implying that minimizing it can lead to more efficient importance sampling procedures.}\n\nIn this work, we develop and analyse a family of adaptive importance samplers, coined \\textit{optimised adaptive importance samplers} (OAIS), which relies on a particular adaptation strategy based on convex optimisation. We adapt the proposal with respect to a quantity (essentially the $\\chi^2$-divergence between the target and the proposal) that also happens to be the constant in the error bounds of the IS (see, e.g., \\citep{agapiou2017importance}). Assuming that proposal distributions belong to the exponential family, we recast the adaptation of the proposal as a convex optimisation problem and then develop a procedure which essentially optimises the $L_2$ error bound of the algorithm. By using results from convex optimisation, we obtain error rates depending on the number of iterations, denoted as $t$, and the number of Monte Carlo samples, denoted as $N$, together. In this way, we explicitly display the trade-off between these two essential quantities. To the best of our knowledge, none of the papers on the topic provides convergence rates depending explicitly on the number of iterations and the number of particles together, as we do herein.\n\nThe paper is organised as follows. In Sec.~\\ref{sec:AISintro}, we introduce the problem definition, the IS and the AIS algorithms. In Sec.~\\ref{sec:theAlg}, we introduce the OAIS algorithms. In Sec.~\\ref{sec:analysis}, we provide the theoretical results regarding optimised AIS and show its convergence using results from convex optimisation. Finally, we make some concluding remarks in Sec.~\\ref{sec:conc}.\n\n\\subsection*{Notation}\n\nFor $L\\in{\\mathbb N}$, we use the shorthand $[L] = \\{1,\\ldots,L\\}$. We denote the state space as ${\\mathsf X}$ and assume ${\\mathsf X} \\subseteq {\\mathbb R}^{d_x}$, $d_x \\ge 1$. The space of bounded real-valued functions and the set of probability measures on space ${\\mathsf X}$ are denoted as $B({\\mathsf X})$ and ${\\mathcal P}({\\mathsf X})$, respectively. Given $\\varphi\\in B({\\mathsf X})$ and $\\pi\\in{\\mathcal P}({\\mathsf X})$, the expectation of $\\varphi$ with respect to (w.r.t.) $\\pi$ is written as $(\\varphi,\\pi) = \\int \\varphi(x) \\pi(\\mbox{d}x)$ or ${\\mathbb E}_\\pi[\\varphi(X)]$. The variance of $\\varphi$ w.r.t. $\\pi$ is defined as $\\var_\\pi(\\varphi) = (\\varphi^2,\\pi) - (\\varphi,\\pi)^2$. If $\\varphi\\in B({\\mathsf X})$, then $\\|\\varphi\\|_\\infty = \\sup_{x\\in{\\mathsf X}} |\\varphi(x)| < \\infty$. The unnormalised density associated to $\\pi$ is denoted with $\\Pi(x)$. We denote the proposal as $q_\\theta \\in {\\mathcal P}({\\mathsf X})$, with an explicit dependence on the parameter $\\theta\\in\\Theta$. The parameter space is assumed to be a subset of $d_\\theta$-dimensional Euclidean space, i.e., $\\Theta \\subseteq {\\mathbb R}^{d_\\theta}$. \n\nWhenever necessary we denote both the probability measures, $\\pi$ and $q_\\theta$, and their densities with the same notation. To be specific, we assume that both $\\pi(\\mbox{d}x)$ and $q_\\theta(\\mbox{d}x)$ are absolutely continuous with respect to the Lebesgue measure and we denote their associated densities as $\\pi(x)$ and $q_\\theta(x)$. The use of either the measure or the density will be clear from both the argument (sets or points, respectively) and the context.\n\n\\section{Background}\\label{sec:AISintro}\n\nIn this section, we review importance and adaptive importance samplers.\n\n\\subsection{Importance sampling}\n\nConsider a target density $\\pi \\in {\\mathcal P}({\\mathsf X})$ and a bounded function $\\varphi \\in B({\\mathsf X})$. Often, the main interest is to compute an integral of the form\n\\begin{align}\\label{eq:ProbDefn}\n(\\varphi,\\pi) = \\int_{\\mathsf X} \\varphi(x) \\pi(x) \\mbox{d}x.\n\\end{align}\nWhile perfect Monte Carlo can be used to estimate this expectation when it is possible to sample exactly from $\\pi(x)$, this is in general not tractable. Hereafter, we consider the cases when the target can be evaluated exactly and up to a normalising constant, respectively.\n\nImportance sampling (IS) uses a proposal distribution which is easy to sample and evaluate. The method consists in weighting these samples, in order to correct the discrepancy between the target and the proposal, and finally constructing an estimator of the integral. To be precise, let $q_\\theta\\in{\\mathcal P}({\\mathsf X})$ be the proposal which is parameterized by the vector $\\theta\\in\\Theta$. The unnormalised target density is denoted as $\\Pi:{\\mathsf X} \\to {\\mathbb R}_+$. Therefore, we have\n\\begin{align*}\n\\pi(x) = \\frac{\\Pi(x)}{Z_\\pi},\n\\end{align*}\nwhere $Z_\\pi :=\\int_{\\mathsf X} \\Pi(x) {\\mathrm{d}} x < \\infty$. Next, we define functions $w_\\theta, W_\\theta:{\\mathsf X} \\times \\Theta \\to {\\mathbb R}_+$ as\n\\begin{align*}\nw_\\theta(x) = \\frac{\\pi(x)}{q_\\theta(x)} \\quad \\textnormal{and} \\quad W_\\theta(x) = \\frac{\\Pi(x)}{q_\\theta(x)},\n\\end{align*}\nrespectively. For a chosen proposal $q_\\theta$, the IS proceeds as follows. First, a set of independent and identically distributed (iid) samples $\\{x^{(i)}\\}_{i=1}^N$ is generated from $q_\\theta$. When $\\pi(x)$ can be evaluated, one constructs the empirical approximation of the probability measure $\\pi$, denoted $\\pi_\\theta^N$, as\n\\begin{align*}\n\\pi_\\theta^N(\\mbox{d}x) = \\frac{1}{N} \\sum_{i=1}^N w_\\theta(x^{(i)})\\delta_{x^{(i)}}(\\mbox{d}x),\n\\end{align*}\nwhere $\\delta_{x'}(\\mbox{d}x)$ denotes the Dirac delta measure that places unit probability mass at $x=x'$. For this case, the IS estimate of the integral in \\eqref{eq:ProbDefn} can be given as\n\\begin{align}\\label{eq:ISestimate}\n(\\varphi,\\pi^N_\\theta) = \\frac{1}{N} \\sum_{i=1}^N w_\\theta(x^{(i)}) \\varphi(x^{(i)}).\n\\end{align}\nHowever, in most practical cases, the target density $\\pi(x)$ can only be evaluated up to an unknown normalizing proportionality constant (i.e., we can evaluate $\\Pi(x)$ but not $Z_\\pi$). In this case, we construct the empirical measure $\\pi^N_\\theta$ as\n\\begin{align*}\n\\pi_\\theta^N(\\mbox{d}x) = \\sum_{i=1}^N \\mathsf{w}_\\theta^{(i)} \\delta_{x^{(i)}}(\\mbox{d}x),\n\\end{align*}\nwhere\n\\begin{align*}\n\\mathsf{w}_\\theta^{(i)} = \\frac{W_\\theta(x^{(i)})}{\\sum_{j=1}^N W_\\theta(x^{(j)})}.\n\\end{align*}\nFinally this construction leads to the so called self-normalizing importance sampling (SNIS) estimator\n\\begin{align}\\label{eq:SNISestimate}\n(\\varphi,\\pi^N_\\theta) = \\sum_{i=1}^N \\mathsf{w}_\\theta^{(i)} \\varphi(x^{(i)}).\n\\end{align}\nAlthough the IS estimator \\eqref{eq:ISestimate} is unbiased, the SNIS estimator \\eqref{eq:SNISestimate} is in general biased. However, the bias and the MSE vanish with a rate $\\mathcal{O}(1\/N)$, therefore providing guarantees of convergence as $N\\to\\infty$. Crucially for us, the MSE of both estimators. {For clarity, below we present an MSE bound for the (more general) SNIS estimator \\eqref{eq:SNISestimate} which is adapted from \\citet{agapiou2017importance}.}\n\\begin{thm}\\label{thm:ISfund}\nAssume that $(W_\\theta^2,q_\\theta) < \\infty$. Then for any $\\varphi\\in B({\\mathsf X})$, we have\n\\begin{align}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{\\theta}^N)\\right)^2\\right] \\leq \\frac{c_\\varphi \\rho(\\theta)}{{N}},\n\\label{eqThm1-1}\n\\end{align}\nwhere $c_\\varphi = 4\\|\\varphi\\|_\\infty^2$ and the function $\\rho:\\Theta \\to [\\rho^\\star,\\infty)$ is defined as\n\\begin{align}\n\\rho(\\theta) = {\\mathbb E}_{q_\\theta}\\left[\\frac{\\pi^2(X)}{q^2_\\theta(X)}\\right],\n\\label{eqThm1-2}\n\\end{align}\nwhere $\\rho^\\star := \\inf_{\\theta\\in\\Theta} \\rho(\\theta) \\geq 1$.\n\\end{thm}\n\\begin{proof}\nSee Appendix \\ref{app:proofIS} for a self-contained proof.\n\\end{proof}\n\\begin{rem} For the IS estimator \\eqref{eq:ISestimate}, this bound can be improved so that $c_\\varphi~=~\\|\\varphi\\|_\\infty^2$. However, this improvement does not effect our results in this paper, hence we present a single bound of the form in \\eqref{eqThm1-1} for the estimators \\eqref{eq:ISestimate} and \\eqref{eq:SNISestimate} for conciseness. $\\square$\n\\end{rem}\n\\begin{rem}\\label{rem:relationToChi} As pointed out by \\cite{agapiou2017importance}, the function $\\rho$ is essentially the $\\chi^2$ divergence between $\\pi$ and $q_\\theta$, i.e.,\n\\begin{align*}\n\\rho(\\theta) := \\chi^2(\\pi || q_\\theta) + 1.\n\\end{align*}\nNote that $\\rho(\\theta)$ can also be expressed in terms of the variance of the weight function $w_\\theta$, which coincides with the $\\chi^2$-divergence, i.e.,\n\\begin{align*}\n\\rho(\\theta) = \\var_{q_\\theta}(w_\\theta(X)) + 1.\n\\end{align*}\nTherefore, minimizing $\\rho(\\theta)$ is equivalent to minimizing $\\chi^2$-divergence and the variance of the weight function $w_\\theta$, i.e., $\\var_{q_\\theta}(w_\\theta(X))$. $\\square$\n\\end{rem}\n\\begin{rem} Remark~\\ref{rem:relationToChi} implies that, when both $\\pi$  and $q_\\theta$ belong {to the same parametric family (i.e., there exists $\\theta \\in \\Theta$ such that $\\pi=q_\\theta$),} one readily obtains\n\\begin{align*}\n\\rho^\\star := \\inf_{\\theta\\in\\Theta} \\rho(\\theta) = 1. \\quad \\square\n\\end{align*}\n\\end{rem}\n\\begin{rem} For the IS estimator \\eqref{eq:ISestimate}, the bound in Theorem~\\ref{thm:ISfund} can be modified so that it holds for unbounded test functions $\\varphi$ as well; see, e.g. \\citet{ryu2014adaptive}. Therefore, a similar quantity to $\\rho(\\theta)$, which includes $\\varphi$ whilst still retaining convexity, can be optimised for this case. Unfortunately, obtaining such a bound is not straightforward for the SNIS estimator \\eqref{eq:SNISestimate} as shown by \\citet{agapiou2017importance}. In order to significantly simplify the presentation, we restrict ourselves to the class of bounded test functions, i.e., we assume $\\|\\varphi\\|_\\infty < \\infty$. $\\square$\n\\end{rem}\n{Finally, we present a bias result from \\citet{agapiou2017importance}.\n\\begin{thm}\\label{thm:SNISbias}\nAssume that $(W_\\theta^2,q_\\theta) < \\infty$. Then for any $\\varphi\\in B({\\mathsf X})$, we have\n\\begin{align*}\n\\left| {\\mathbb E}\\left[(\\varphi,\\pi_{\\theta}^N)\\right] - (\\varphi,\\pi) \\right| \\leq \\frac{\\bar{c}_\\varphi \\rho(\\theta)}{{N}},\n\\end{align*}\nwhere $\\bar{c}_\\varphi = 12\\|\\varphi\\|_\\infty^2$ and the function $\\rho:\\Theta \\to [\\rho^\\star,\\infty)$ is the same as in Theorem~\\ref{thm:ISfund}.\n\\end{thm}\n\\begin{proof}\nSee Theorem 2.1 in \\citet{agapiou2017importance}.\n\\end{proof}}\n\\subsection{Parametric adaptive importance samplers}\nStandard importance sampling may be inefficient in practice when the proposal is poorly calibrated with respect to the target. In particular, as implied by the error bound provided in Theorem~\\ref{thm:ISfund}, the error made by the IS estimator can be high if the $\\chi^2$-divergence between the target and the proposal is large. Therefore, it is more common to employ an iterative version of importance sampling, also called as \\textit{adaptive importance sampling} (AIS). The AIS algorithms are importance sampling methods which aim at iteratively improving the proposal distributions. More specifically, the AIS methods specify a sequence of proposals $(q_t)_{t\\geq 1}$ and perform importance sampling at each iteration. The aim is to improve the proposal so that the samples are better matched with the target, which results in less variance and more accuracy in the estimators. There are several variants, the most popular one being population Monte Carlo methods \\citep{cappe2004population} which uses previous samples in the proposal.\n\n\\begin{algorithm}[t]\n\\begin{algorithmic}[1]\n\\caption{Parametric AIS}\\label{alg:ParametricAIS}\n\\State Choose a parametric proposal $q_{\\theta}$ with initial parameter $\\theta=\\theta_0$.\n\\For{$t\\geq 1$}\n\\State Adapt the proposal,\n\\begin{align*}\n\\theta_t = \\mathcal{T}_t(\\theta_{t-1}),\n\\end{align*}\n\\State Sample,\n\\begin{align*}\nx_t^{(i)} \\sim q_{\\theta_t}, \\quad \\textnormal{for } i = 1,\\ldots,N,\n\\end{align*}\n\\State Compute weights,\n\\begin{align*}\n\\mathsf{w}_{\\theta_t}^{(i)} = \\frac{W_{\\theta_t}(x_t^{(i)})}{\\sum_{i=1}^N W_{\\theta_t}(x_t^{(i)})}, \\quad \\textnormal{where} \\quad W_{\\theta_t}^{(i)} = \\frac{\\Pi(x_t^{(i)})}{q_{\\theta_t}(x^{(i)})}.\n\\end{align*}\n\\State Report the point-mass probability measure\n\\begin{align*}\n{\\pi}_{\\theta_t}^N({\\mathrm{d}} x) = \\sum_{i=1}^N \\mathsf{w}_{\\theta_t}^{(i)} \\delta_{x_t^{(i)}}({\\mathrm{d}} x),\n\\end{align*}\nand the estimator\n\\begin{align*}\n(\\varphi,{\\pi}_{\\theta_t}^N) = \\sum_{i=1}^N \\mathsf{w}_{\\theta_t}^{(i)} \\varphi(x_t^{(i)}).\n\\end{align*}\n\\EndFor\n\\end{algorithmic}\n\\end{algorithm}\n\nIn this section, we review one particular AIS, which we refer to as \\textit{parametric AIS}. In this variant, the proposal distribution is a parametric distribution, denoted $q_\\theta$. Over time, this parameter $\\theta$ is updated (or \\textit{optimised}) with respect to a predefined criterion resulting in a sequence $(\\theta_t)_{t\\geq 1}$. This yields a sequence of proposal distributions denoted as $(q_{\\theta_t})_{t\\geq 1}$.\n\nOne iteration of the algorithm goes as follows. Assume at time $t-1$ we are given a proposal distribution $q_{\\theta_{t-1}}$. At time $t$, we first update the parameter of this proposal,\n\\begin{align*}\n\\theta_t = \\mathcal{T}_t(\\theta_{t-1}),\n\\end{align*}\nwhere $\\{\\mathcal{T}_t:\\Theta \\to \\Theta, t\\geq 1\\}$, is a sequence of (deterministic or stochastic) maps, e.g., gradient mappings, constructed so that they minimise a certain cost function. Then, in the same way we have done in conventional IS, we sample\n\\begin{align*}\nx_t^{(i)} \\sim q_{\\theta_t}({\\mathrm{d}} x), \\quad \\textnormal{for } i = 1,\\ldots,N,\n\\end{align*}\ncompute weights\n\\begin{align*}\n\\mathsf{w}_{\\theta_t}^{(i)} = \\frac{W_{\\theta_t}(x_t^{(i)})}{\\sum_{i=1}^N W_{\\theta_t}(x_t^{(i)})},\n\\end{align*}\nand finally construct the empirical measure\n\\begin{align*}\n\\pi_{\\theta_t}^N({\\mathrm{d}} x) = \\sum_{i=1}^N \\mathsf{w}_{\\theta_t}^{(i)} \\delta_{x_t^{(i)}}({\\mathrm{d}} x).\n\\end{align*}\nThe estimator of the integral \\eqref{eq:ProbDefn} is then computed as in Eq. \\eqref{eq:SNISestimate}. \n\nThe full procedure of the parametric AIS method is summarized in Algorithm~\\ref{alg:ParametricAIS}. Since this is a valid IS scheme, this algorithm enjoys the same guarantee provided in Theorem~\\ref{thm:ISfund}. In particular, we have the following theorem.\n\\begin{thm}\\label{thm:ISfundAIS}\nAssume that, given a sequence of proposals $(q_{\\theta_t})_{t\\geq 1} \\in {\\mathcal P}({\\mathsf X})$, we have $(W_{\\theta_t}^2,q_{\\theta_t}) < \\infty$ for every $t$. Then for any $\\varphi\\in B({\\mathsf X})$, we have\n\\begin{align*}\n{\\mathbb E}\\left[\\left|(\\varphi,\\pi) - (\\varphi,\\pi_{\\theta_t}^N)\\right|^2\\right] \\leq \\frac{c_\\varphi \\rho(\\theta_t)}{{N}},\n\\end{align*}\nwhere $c_\\varphi = 4 \\|\\varphi\\|_\\infty^2$ and the function $\\rho(\\theta_t):\\Theta \\to [\\rho^\\star,\\infty)$ is defined as in Eq. \\eqref{eqThm1-2}.\n\\end{thm}\n\\begin{proof}\nThe proof is identical to the proof of Theorem~\\ref{thm:ISfund}. We have just re-stated the result to introduce the iteration index $t$.\n\\end{proof}\nHowever, this theorem does not give an insight of what happens as the number of iterations increases, i.e., when $t\\to\\infty$, with the bound. Ideally, the adaptation of the AIS should improve this bound with time. In other words, in the ideal case, the error should decrease as $t$ grows. Fortunately, Theorem~\\ref{thm:ISfundAIS} suggests that the maps $\\mathcal{T}_t:\\Theta\\to\\Theta$ can be chosen so that the function $\\rho$ is minimised over time. More specifically, the sequence $(\\theta_t)_{t\\geq 1}$ can be chosen so that it leads to a decreasing sequence (at least in expectation) $(\\rho(\\theta_t))_{t\\geq 1}$. In the following sections, we will summarize the deterministic and stochastic strategies to achieve this aim.\n\\begin{rem}\\label{remR} We define the unnormalised version of $\\rho(\\theta)$ and denote it as $R(\\theta)$. It is characterised as follows\n\\begin{align*}\n\\rho(\\theta) = \\frac{R(\\theta)}{Z_\\pi^2} \\quad \\textnormal{where} \\quad Z_\\pi = \\int_{\\mathsf X} \\Pi(x) {\\mathrm{d}} x < \\infty.\n\\end{align*}\nHence, $R(\\theta)$ can also be expressed as\n\\begin{align}\\label{eq:Rtheta}\nR(\\theta) = {\\mathbb E}_{q_{\\theta}} \\left[\\frac{\\Pi^2(X)}{q_{\\theta}^2(X)}\\right].\n\\end{align} $\\square$\n\\end{rem}\n\n\n\\subsection{AIS with exponential family proposals}\\label{sec:expFamily}\n\nFollowing \\cite{ryu2014adaptive}, we note that when $q_\\theta$ is chosen as an exponential family density, the function $\\rho(\\theta)$ is convex. In particular, we define\n\\begin{align}\\label{eq:PropDefineExp}\nq_\\theta(x) = \\exp(\\theta^\\top T(x) - A(\\theta)) h(x),\n\\end{align}\nwhere $A: {\\mathbb R}^{d_\\theta}\\to{\\mathbb R} \\cup \\{\\infty\\}$ is the log of the normalization constant, i.e.,\n\\begin{align*}\nA(\\theta) = \\log \\int \\exp(\\theta^\\top T(x)) h(x) \\mbox{d}x,\n\\end{align*}\nwhile $T:{\\mathbb R}^{d_x}\\to{\\mathbb R}^{d_\\theta}$ and $h:{\\mathbb R}^{d_x}\\to{\\mathbb R}_+$. Then we have the following lemma adapted from \\cite{ryu2014adaptive}.\n\\begin{lem}\\label{prop:rhoconvex} Let $q_\\theta$ be chosen as in \\eqref{eq:PropDefineExp}. Then $\\rho:\\Theta \\to [\\rho^\\star,\\infty)$ is convex, i.e., for any $\\theta_1,\\theta_2\\in\\Theta$ and $\\lambda \\in [0,1]$, the following inequality holds\n\\begin{align*}\n\\rho(\\lambda\\theta_1 + (1-\\lambda) \\theta_2) \\leq \\lambda \\rho(\\theta_1) + (1-\\lambda) \\rho(\\theta_2).\n\\end{align*}\n\\end{lem}\n\\begin{proof}\nSee Appendix \\ref{app:proofLemma1} for a self-contained proof.\n\\end{proof}\nLemma~\\ref{prop:rhoconvex} shows that $\\rho$ is a convex function, therefore, optimising it could give us provably convergent algorithms (as $t$ increases). Next lemma, borrowed from \\citet{ryu2014adaptive}, shows that $\\rho$ is differentiable and its gradient can indeed be computed as an expectation.\n{\\begin{lem}\\label{lem:GradientRho} The gradient $\\nabla\\rho(\\theta)$ can be written as\n\\begin{align}\\label{eq:gradRho}\n\\nabla \\rho(\\theta) = {\\mathbb E}_{q_\\theta} \\left[(\\nabla A(\\theta) - T(X)) \\frac{\\pi^2(X)}{q_\\theta^2(X)}\\right].\n\\end{align}\n\\end{lem}}\n\\begin{proof}\nThe proof is straightforward since $q_\\theta$ is from an exponential family and $A(\\theta)$ is differentiable.\n\\end{proof}\n\\begin{rem} Note that Eqs.~\\eqref{eq:Rtheta} and \\eqref{eq:gradRho} together imply that\n\\begin{align}\\label{eq:gradR}\n\\nabla R(\\theta) = {\\mathbb E}_{q_\\theta} \\left[(\\nabla A(\\theta) - T(X)) \\frac{\\Pi^2(X)}{q_\\theta^2(X)}\\right].\n\\end{align}\nWe also note (see Remark~\\ref{remR}) that\n\\begin{align}\\label{eq:RelGrads}\n\\nabla R(\\theta) = Z_\\pi^2 \\nabla \\rho(\\theta).\n\\end{align}\n$\\square$\n\\end{rem}\nIn the following sections, we assume that $\\rho(\\theta)$ is a convex function. Thus Lemma~\\ref{prop:rhoconvex} constitutes an important motivation for our approach. We leave general proposals which lead to nonconvex $\\rho(\\theta)$ for future work.\n\n\n\\section{Algorithms}\\label{sec:theAlg}\n\nIn this section, we describe adaptation strategies based on minimizing $\\rho(\\theta)$. In particular, we design maps $\\mathcal{T}_t:\\Theta\\to\\Theta$, for $t\\geq 1$, for scenarios where\n\\begin{itemize}\n\\setlength{\\itemindent}{2em}\n\\item[(i)] the gradient of $\\rho(\\theta)$ can be exactly computed,\n\\item[(ii)] an unbiased estimate of the gradient of $\\rho(\\theta)$ can be obtained, and\n\\item[(iii)] an unbiased estimate of the gradient of $R(\\theta)$ can be obtained.\n\\end{itemize}\nScenario (i) is unrealistic in practice but gives us a guideline in order to further develop the idea. {In particular, the error bounds for the more complicated cases follow the same structure as this case. Therefore, the results obtained in case (i) provide a good qualitative understanding of the results introduced later.} Scenario (ii) can be realized in cases where it is possible to evaluate $\\pi(x)$, in which case the IS leads to unbiased estimators. Scenario (iii) is what a practitioner would most often encounter: the target can only be evaluated up to the normalizing constant, i.e., $\\Pi(x)$ can be evaluated but $\\pi(x)$ cannot.\n\n{We finally remark that, for the cases where we assume a stochastic gradient can be obtained for $\\rho$ and $R$ (namely, the case (ii) and the case (iii) respectively), we consider two possible algorithms to perform adaptation. The first method is a \\textit{vanilla} SGD algorithm \\citep{bottou2016optimization} and the second method is a SGD scheme with iterate averaging \\citep{schmidt2017minimizing}. While vanilla SGD is easier to implement and algorithmically related to population-based Monte Carlo methods, iterate averaged SGD results in a better theoretical bound and it has some desirable variance reduction properties.}\n\n\n\n\\subsection{Exact gradient OAIS}\n\nWe first introduce the OAIS scheme where we assume that the exact gradients of $\\rho(\\theta)$ are available. Since $\\rho$ is defined as an expectation (an integral), this assumption is unrealistic. However, the results we can prove for this procedure shed light onto the results that will be proved for practical scenarios in the following sections.\n\nIn particular, in this scheme, given $\\theta_{t-1}$, we specify $\\mathcal{T}_t$ as\n\\begin{align}\\label{eq:exactOAIS}\n\\theta_t = \\mathcal{T}_t(\\theta_{t-1}) = \\mathsf{Proj}_\\Theta(\\theta_{t-1} - \\gamma \\nabla \\rho(\\theta_{t-1})),\n\\end{align}\nwhere $\\gamma > 0$ is the step-size parameter of the map and $\\mathsf{Proj}_\\Theta$ denotes projection onto the compact parameter space $\\Theta$. This is a classical gradient descent scheme on $\\rho(\\theta)$. In Section \\ref{ssErrorsExactGrad}, we provide non-asymptotic results for this scheme. However, as we have noted, this idea does not lead to a practical scheme and cannot be used in most cases in practice as the gradients of $\\rho$ in exact form are rarely available.\n\\begin{rem} {We use a projection operator in Eq.~\\eqref{eq:exactOAIS} because we assume throughout the analysis in Section~\\ref{sec:analysis} that the parameter space $\\Theta$ is compact.}\n$\\square$\n\\end{rem}\n\n{\\subsection{Stochastic gradient OAIS}}\n\n{Although it has a nice and simple form, exact-gradient OAIS is often intractable as, in most practical cases, the gradient can only be estimated. In this section, we first look at the case where $\\pi(x)$  can be evaluated, which means that an unbiased estimate of $\\nabla \\rho(\\theta)$ can be obtained. Then we consider the general case, where one can only evaluate $\\Pi(x)$ and can obtain an unbiased estimate of $\\nabla R(\\theta)$.}\n\n{In the following subsections, we consider an algorithm where the gradient is estimated using samples which can also be used to construct importance sampling estimators. The procedure is outlined in Algorithm \\ref{alg:SGDAIS} for the case in which only $\\Pi(x)$ can be evaluated and $\\nabla R(\\theta)$ is estimated.}\n\n{\\subsubsection{Normalised case}}\n\n{If we assume that the density $\\pi(x)$ can be evaluated exactly, then the algorithm can be described as follows. Given $(\\theta_k)_{1\\leq k\\leq t-1}$, at iteration $t$ we compute the next parameter iterate as\n\\begin{align*}\n\\theta_t = \\mathsf{Proj}_{\\Theta}(\\theta_{t-1} - \\gamma_t g_t),\n\\end{align*}\nwhere $g_t$ is an unbiased estimator of $\\nabla \\rho(\\theta_{t-1})$. We note that, due to the analytical form of $\\nabla \\rho$ (see Eq. \\eqref{eq:gradRho}), the samples and weights generated at iteration $t-1$, i.e., $\\left\\{ x_{t-1}^{(i)}, w_{\\theta_{t-1}}(x_{t-1}^{(i)}) \\right\\}_{i=1}^N$ can be reused to estimate the gradient. This makes an algorithmic connection to the population Monte Carlo methods where previous samples and weights are used to adapt the proposal \\citep{cappe2004population}.}\n\n{Given the updated parameter $\\theta_t$, the algorithm first samples from the updated proposal $x_t^{(i)} \\sim q_{\\theta_t}$, $i=1, \\ldots, N$, and then proceeds to construct the IS estimator as in \\eqref{eq:ISestimate}. Namely, \n\\begin{align}\n(\\varphi,\\pi^N_{{\\theta}_t}) = \\frac{1}{N} \\sum_{i=1}^N w_{{\\theta}_t}({x}_t^{(i)}) \\varphi({x}_t^{(i)}).\n\\label{eqEstimator_1}\n\\end{align}}\n\n{\\begin{algorithm}[tb!]\n\\begin{algorithmic}[1]\n\\caption{Stochastic gradient OAIS}\\label{alg:vanillaSGDAIS}\n\\State Choose a parametric proposal $q_{\\theta}$ with initial parameter $\\theta=\\theta_0$.\n\\For{$t\\geq 1$}\n\\State Update the proposal parameter,\n\\begin{align*}\n\\theta_t = \\mathsf{Proj}_\\Theta(\\theta_{t-1} - \\gamma_t \\tilde{g}_t)\n\\end{align*}\nwhere $\\tilde{g}_t$ is computed by approximating the expectation in Eq. \\eqref{eq:gradR} using the samples $x_{t-1}^{(i)}$ and weights $\\mathsf{w}_{\\theta_{t-1}}^{(i)} = \\Pi( x_{t-1}^{(i)} ) q_{\\theta_{t-1}}(x_{t-1}^{(i)})^{-1}$, $i=1, ..., N$.\n\\State Sample,\n\\begin{align*}\n{x}_t^{(i)} \\sim q_{{\\theta}_t}, \\quad \\textnormal{for } i = 1,\\ldots,N,\n\\end{align*}\n\\State Compute weights,\n\\begin{align*}\n\\mathsf{w}_{{\\theta}_t}^{(i)} = \\frac{W_{{\\theta}_t}({x}_t^{(i)})}{\\sum_{i=1}^N W_{{\\theta}_t}({x}_t^{(i)})}.\n\\end{align*}\n\\State Report,\n\\begin{align*}\n{\\pi}_{{\\theta}_t}^N({\\mathrm{d}} x) = \\sum_{i=1}^N \\mathsf{w}_{{\\theta}_t}^{(i)} \\delta_{{x}_t^{(i)}}({\\mathrm{d}} x),\n\\end{align*}\nand\n\\begin{align*}\n(\\varphi,{\\pi}_{{\\theta}_t}^N) = \\sum_{i=1}^N \\mathsf{w}_{{\\theta}_t}^{(i)} \\varphi({x}_t^{(i)}).\n\\end{align*}\n\\EndFor\n\\end{algorithmic}\n\\end{algorithm}}\n\n{\\subsubsection{Self-normalised case}}\n\n{For the general case, where we can only evaluate $\\Pi(x)$, the algorithm proceeds similarly. Given $(\\theta_k)_{1\\leq k\\leq t-1}$, the method proceeds by first updating the parameter\n\\begin{align*}\n\\theta_t = \\mathsf{Proj}_{\\Theta}(\\theta_{t-1} - \\gamma_t \\tilde{g}_t),\n\\end{align*}\nwhere $\\tilde{g}_t$ is an unbiased estimator of $\\nabla R(\\theta_{t-1})$. Given the updated parameter, we first sample $x_t^{(i)} \\sim q_{\\theta_t}$, $i=1, ..., N$, and then construct the SNIS estimate as in \\eqref{eq:SNISestimate}, i.e., \n\\begin{align*}\n(\\varphi,\\pi^N_{{\\theta}_t}) = \\sum_{i=1}^N \\mathsf{w}^{(i)}_{{\\theta}_t} \\varphi({x}_t^{(i)}).\n\\end{align*}\nwhere\n\\begin{align*}\n\\mathsf{w}_{{\\theta}_t}^{(i)} = \\frac{W_{{\\theta}_t}({x}^{(i)})}{\\sum_{j=1}^N W_{{\\theta}_t}({x}^{(j)})},\n\\end{align*}}\n\n\\subsection{Stochastic gradient OAIS with averaged iterates}\n\n{Next, we describe a variant of the stochastic gradient OAIS that uses averages of the iterates generated by the SGD scheme \\citep{schmidt2017minimizing} in order to compute the proposal densities, generate samples and compute weights. In Section \\ref{sec:analysis} we show that the convergence rate for this method is better than the rate that can be guaranteed for Algorithm \\ref{alg:vanillaSGDAIS}.}\n\n\\subsubsection{Normalised case}\n\nWe assume first that the density $\\pi(x)$ can be evaluated. At the beginning of the $t$-th iteration, the algorithm has generated the sequence $(\\theta_k)_{1\\leq k \\leq t-1}$. First, in order to perform the adaptive importance sampling steps, we set\n\\begin{align}\\label{eq:AveragingSGD}\n\\bar{\\theta}_t = \\frac{1}{t}\\sum_{k=0}^{t-1} \\theta_k\n\\end{align}\nand sample $\\bar{x}_{t}^{(i)} \\sim q_{\\bar{\\theta}_t}$ for $i = 1,\\ldots,N$. Following the standard parametric AIS procedure (Algorithm~\\ref{alg:ParametricAIS}), we obtain the estimate of $(\\varphi,\\pi)$ as,\n\\begin{align*}\n(\\varphi,\\pi^N_{\\bar{\\theta}_t}) = \\frac{1}{N} \\sum_{i=1}^N w_{\\bar{\\theta}_t}(\\bar{x}_t^{(i)}) \\varphi(\\bar{x}_t^{(i)}).\n\\end{align*}\nNext, we update the parameter vector using the projected stochastic gradient step\n\\begin{align}\\label{eq:recSgdAdaptNorm}\n\\theta_t = \\mathcal{T}_t(\\theta_{t-1}) = \\mathsf{Proj}_\\Theta(\\theta_{t-1} - \\gamma_t g_t),\n\\end{align}\nwhere $g_t$ is an unbiased estimate of $\\nabla\\rho(\\theta_{t-1})$, i.e., ${\\mathbb E}[g_t] = \\nabla \\rho(\\theta_{t-1})$ and $\\mathsf{Proj}_\\Theta$ denotes  projection onto the set $\\Theta$. Note that in order to estimate this gradient using \\eqref{eq:gradRho}, we sample $x_t^{(i)} \\sim q_{\\theta_{t-1}}$ for $i = 1, \\ldots, N$, and estimate the expectation in \\eqref{eq:gradRho}. It is worth noting that the samples $\\{ x_t^{(i)} \\}_{i=1}^M$ are different from the samples $\\{ \\bar x_t^{(i)} \\}_{i=1}^N$ used to estimate $(\\varphi,\\pi)$.\n\n\\subsubsection{Self-normalised case}\n\n\\begin{algorithm}[tb!]\n\\begin{algorithmic}[1]\n\\caption{Stochastic gradient OAIS with averaged iterates}\\label{alg:SGDAIS}\n\\State Choose a parametric proposal $q_{\\theta}$ with initial parameter $\\theta = \\theta_0$.\n\\For{$t\\geq 1$}\n\\State Compute the average parameter vector\n\\begin{align*}\n\\bar{\\theta}_t = \\frac{1}{t} \\sum_{k=0}^{t-1} \\theta_k\n\\end{align*}\n\\State Sample,\n\\begin{align*}\n\\bar{x}_t^{(i)} \\sim q_{\\bar{\\theta}_t}, \\quad \\textnormal{for } i = 1,\\ldots,N,\n\\end{align*}\n\\State Compute weights,\n\\begin{align*}\n\\mathsf{w}_{\\bar{\\theta}_t}^{(i)} = \\frac{W_{\\bar{\\theta}_t}(\\bar{x}_t^{(i)})}{\\sum_{i=1}^N W_{\\bar{\\theta}_t}(\\bar{x}_t^{(i)})}.\n\\end{align*}\n\\State Report the point-mass probability measure\n\\begin{align*}\n{\\pi}_{\\bar{\\theta}_t}^N({\\mathrm{d}} x) = \\sum_{i=1}^N \\mathsf{w}_{\\bar{\\theta}_t}^{(i)} \\delta_{\\bar{x}_t^{(i)}}({\\mathrm{d}} x),\n\\end{align*}\nand the estimator\n\\begin{align*}\n(\\varphi,{\\pi}_{\\bar{\\theta}_t}^N) = \\sum_{i=1}^N \\mathsf{w}_{\\bar{\\theta}_t}^{(i)} \\varphi(\\bar{x}_t^{(i)}).\n\\end{align*}\n\\State Update the parameter vector,\n\\begin{align*}\n\\theta_t = \\mathsf{Proj}_\\Theta(\\theta_{t-1} - \\gamma_t \\tilde{g}_t)\n\\end{align*}\nwhere $\\tilde g_t$ is an estimate of $\\nabla R(\\theta_{t-1})$ computed by approximating the expectation in Eq. \\eqref{eq:gradR} using a set of iid samples ${x}_t^{(i)} \\sim q_{\\theta_{t-1}}$, $i=1, ..., N$.\n\\EndFor\n\\end{algorithmic}\n\\end{algorithm}\nIn general, $\\pi(x)$ cannot be evaluated exactly, hence a stochastic unbiased estimate of $\\nabla\\rho(\\theta)$ cannot be obtained. When the target can only be evaluated up to a normalisation constant, i.e., only $\\Pi(x)$ can be computed, we can use the SNIS procedure as explained in Section~\\ref{sec:AISintro}. Therefore, we introduce here the most general version of the stochastic method, coined \\textit{stochastic gradient OAIS}, which uses the averaged iterates in \\eqref{eq:AveragingSGD} to construct the proposal functions. The scheme is outlined in Algorithm \\ref{alg:SGDAIS}.\n\nTo run this algorithm, given the parameter vector $\\bar{\\theta}_t$ in \\eqref{eq:AveragingSGD}, we first generate a set of samples $\\{\\bar{x}_t^{(i)}\\}_{i=1}^N$ from the proposal $q_{\\bar{\\theta}_t}$. Then the integral estimate given by the SNIS can be written as,\n\\begin{align*}\n(\\varphi,\\pi^N_{\\bar{\\theta}_t}) =  \\sum_{i=1}^N \\mathsf{w}_{\\bar{\\theta}_t}^{(i)} \\varphi(\\bar{x}_t^{(i)}),\n\\end{align*}\nwhere\n\\begin{align*}\n\\mathsf{w}_{\\bar{\\theta}_t}^{(i)} = \\frac{W_{\\bar{\\theta}_t}(\\bar{x}^{(i)})}{\\sum_{j=1}^N W_{\\bar{\\theta}_t}(\\bar{x}^{(j)})}.\n\\end{align*}\nFinally, for the adaptation step, we obtain the unbiased estimate of the gradient $\\nabla R(\\theta)$ and adapt the parameter as\n\\begin{align}\\label{eq:SgdUnnormalizedAdapt}\n\\theta_t = \\mathsf{Proj}_\\Theta(\\theta_{t-1} - \\gamma_t \\tilde{g}_t)\n\\end{align}\nwhere $\\tilde{g}_t$ is an unbiased estimate of $\\nabla R(\\theta_{t-1})$, i.e., ${\\mathbb E}[\\tilde{g}_t] = \\nabla R(\\theta_{t-1})$. Note that, as in the normalised case, this gradient is estimated by approximating the expectation in \\eqref{eq:gradR} using iid samples $x_t^{(i)} \\sim q_{\\theta_{t-1}}$, $i = 1,\\ldots,N$. These samples are different, again, from the set $\\{ \\bar x_t^{(i)} \\}_{i=1}^N$ employed to estimate $(\\varphi,\\pi)$.\n{\n\\begin{rem}\nIn Algorithm \\ref{alg:SGDAIS} the samples $\\{ \\bar x_t^{(i)} \\}_{i=1}^N$ drawn from the proposal distribution $q_{\\bar \\theta_{t-1}}({\\mathrm{d}} x)$ are \\textit{not} used to compute the gradient estimator $\\tilde g_t$ which, in turn, is needed to generate the next iterate $\\theta_t$. Therefore, if we can afford to generate $T$ iterates, $\\theta_0, \\ldots, \\theta_{T-1}$, with $T$ known before hand, and we are only interested in the estimator $(\\varphi,\\pi_{\\bar \\theta_T}^N)$ obtained at the last iteration (once the proposal function has been optimized) then it is be possible to skip steps 3--6 in Algorithm  \\ref{alg:SGDAIS} up to time $T-1$. Only at time $t=T$, we would compute the average parameter vector $\\bar \\theta_T$, sample $\\bar x_T^{(i)}$ from the proposal $q_{\\bar \\theta_T}({\\mathrm{d}} x)$ and generate the point-mass probability measure $\\pi_{\\bar \\theta_T}^N$ and the estimator $(\\varphi,\\pi_{\\bar \\theta_T}^N)$ .\n\\end{rem}\n}\n\n\\section{Analysis}\\label{sec:analysis}\n\nTheorem~\\ref{thm:ISfund} yields an intuitive result about the performance of IS methods in terms of the divergence between the target $\\pi$ and the proposal $q_\\theta$. We now apply ideas from convex optimisation theory in order to minimize $\\rho(\\theta)$ and obtain finite-time, finite-sample convergence rates for the AIS procedures outlined in Section \\ref{sec:theAlg}.\n\n\\subsection{Convergence rate with exact gradients} \\label{ssErrorsExactGrad}\n\nLet us first assume that we can compute the gradient of $\\rho(\\theta)$ exactly. In particular, we consider the update rule in Eq. \\eqref{eq:exactOAIS}. For the sake of the analysis, we impose some regularity assumptions on the $\\rho(\\theta)$.\n\n{\n\\begin{assumption}\\label{ass:LipschitzCont}\nLet $\\rho(\\theta)$ be a convex function with Lipschitz derivatives in the compact space $\\Theta$. To be specific, $\\rho$ is convex and differentiable, and there exists a constant $L<\\infty$ such that\n\\begin{eqnarray}\n\\|\\nabla \\rho(\\theta) - \\nabla \\rho(\\theta')\\|_2 &\\leq& L \\|\\theta - \\theta'\\|_2 \\nonumber\n\\end{eqnarray}\nfor any $\\theta,\\theta' \\in \\Theta$.\n\\end{assumption}\n}\n\n{\n\\begin{rem} Assumption \\ref{ass:LipschitzCont} holds when the density $q_\\theta(x)$ belongs to an exponential family (see Section~\\ref{sec:expFamily}) and $\\Theta$ is compact \\citep{ryu2014adaptive}, even if it may not hold in general for $\\theta \\in {\\mathbb R}^{d_\\theta}$. $\\square$\n\\end{rem}\n}\n\n\\begin{lem}\\label{lem:GDconv} If Assumption~\\ref{ass:LipschitzCont} holds and we set a step-size $\\gamma \\leq 1\/L$, then the inequality\n\\begin{align}\n\\rho(\\theta_t) - \\rho^\\star \\leq \\frac{\\|\\theta_0 - \\theta^\\star\\|^2}{2\\gamma t},\n\\label{eqLem3-1}\n\\end{align}\nis satisfied for the sequence $\\{\\theta_t\\}_{t\\ge 0}$ generated by the recursion \\eqref{eq:exactOAIS} where $\\theta^\\star$ is a minimum of $\\rho$.\n\\end{lem}\n\\begin{proof}\nSee, e.g., \\cite{nesterov2013introductory}.\n\\end{proof}\n\nThis rate in \\eqref{eqLem3-1} is one of the most fundamental results in convex optimisation. Lemma \\ref{lem:GDconv} enables us to prove the following result for the MSE of the AIS estimator adapted using exact gradient descent in Eq. \\eqref{eqEstimator_1}.\n\n\\begin{thm}\\label{thm:GD} Let Assumption~\\ref{ass:LipschitzCont} hold and construct the sequence $(\\theta_t)_{t\\geq 1}$ using recursion \\eqref{eq:exactOAIS}, where $(q_{\\theta_t})_{t\\geq 1}$ is the sequence of proposal distributions. Then, the inequality\n\\begin{align}\\label{ineq:gOAISbound}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{\\theta_t}^N)\\right)^2\\right] &\\leq \\frac{c_\\varphi \\|\\theta_0 - \\theta^\\star\\|_2^2}{2 \\gamma t {N}} +  \\frac{c_\\varphi \\rho^\\star}{{N}}\n\\end{align}\nis satisfied, where $c_\\varphi = 4 \\|\\varphi\\|_\\infty^2$, $0 < \\gamma \\leq 1\/L$ and $L$ is the Lipschitz constant of the gradient $\\nabla\\rho(\\theta)$ in Assumption \\ref{ass:LipschitzCont}.\n\\end{thm}\n\n\\begin{proof}\nSee Appendix \\ref{app:thm:GD}.\n\\end{proof}\n\n\\begin{rem}\\label{remGDasymptote} Theorem~\\ref{thm:GD} sheds light onto several facts. We first note that $\\rho^\\star$ in the error bound \\eqref{ineq:gOAISbound} can be interpreted as an indicator of the quality of the parametric proposal. We recall that $\\rho^\\star = 1$ when both $\\pi$ and $q_\\theta$ belong to the same exponential family. For this special case, Theorem~\\ref{thm:GD} implies that\n\\begin{align*}\n\\lim_{t\\to\\infty} \\left\\|(\\varphi,\\pi) - (\\varphi,\\pi_{\\theta_t}^N)\\right\\|_2 \\leq \\mathcal{O}\\left(\\frac{1}{\\sqrt{N}}\\right).\n\\end{align*}\nIn other words, when the target and the proposal are both from the exponential family, this adaptation strategy is leading to an \\textit{asymptotically optimal} Monte Carlo estimator (optimal meaning that we attain the same rate as a Monte Carlo estimator with $N$ iid samples from $\\pi$). On the other hand, when $\\pi$ and $q_\\theta$ do not belong to the same family, we obtain\n\\begin{align*}\n\\lim_{t\\to\\infty} \\left\\|(\\varphi,\\pi) - (\\varphi,\\pi_{\\theta_t}^N)\\right\\|_2 \\leq \\mathcal{O}\\left(\\sqrt{\\frac{\\rho^\\star}{N}}\\right),\n\\end{align*}\ni.e., the $L_2$ rate is again asymptotically optimal, but the constant in the error bound is worse (bigger) by a factor $\\sqrt{\\rho^\\star}>1$. $\\square$\n\\end{rem}\n\nThis bound shows that as $t\\to\\infty$, what we are left with is essentially the minimum attainable IS error for a given parametric family $\\{q_\\theta\\}_{\\theta\\in\\Theta}$. Intuitively, when the proposal $q_\\theta$ is from a different parametric family than $\\pi$, the gradient OAIS optimises the error bound in order to obtain the best possible proposal. In particular, the MSE has two components: First an $\\mathcal{O}(1\/tN)$ component which can be made to vanish over time by improving the proposal and a second $\\mathcal{O}(1\/N)$ component which is related to $\\rho^\\star$. The quantity $\\rho^\\star$ is related to the minimum $\\chi^2$-divergence between the target and proposal. This means that the discrepancy between the target and \\textit{optimal} proposal (according to the $\\chi^2$-divergence) can only be tackled by increasing $N$. This intuition is the same for the schemes we analyse in the next sections, although the rate with respect to the number of iterations necessarily worsens because of the uncertainty in the gradient estimators.\n\n\\begin{rem} When $\\gamma = 1\/L$, Theorem~\\ref{thm:GD} implies that if $t = \\mathcal{O}({L}\/{\\rho^\\star})$ and $N = \\mathcal{O}(\\rho^\\star \/ \\varepsilon)$, for some $\\varepsilon>0$, then we have\n\\begin{align*}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{\\theta_t}^N)\\right)^2\\right] &\\leq \\mathcal{O}(\\varepsilon).\n\\end{align*}\nWe remark that once we choose the number of samples $N = \\mathcal{O}(\\rho^\\star\/\\varepsilon)$, the number of iterations $t$ for adaptation is independent of $N$ and $\\varepsilon$. $\\square$\n\\end{rem}\n\n\\begin{rem} One can use different maps $\\mathcal{T}_t$ for optimisation. For example, one can use Nesterov's accelerated gradient descent (which has more parameters than just a step size), in which case, one could prove (by a similar argument) the inequality \\citep{nesterov2013introductory}\n\\begin{align*}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{\\theta_t}^N)\\right)^2\\right] &\\leq \\mathcal{O}\\left(\\frac{1}{t^2 {N}} +  \\frac{\\rho^\\star}{{N}}\\right).\n\\end{align*}\nThis is an improved convergence rate, going from $\\mathcal{O}(1\/t)$ to $\\mathcal{O}(1\/t^2)$ in the first term of the bound. $\\square$\n\\end{rem}\n\n\\subsection{Convergence rate with averaged SGD iterates} \\label{ssConvergence-Averaged-Iterates}\n\nWhile, for the purpose of analysis, it is convenient to assume that the minimization of $\\rho(\\theta)$ can be done deterministically, this is rarely the case in practice. The `best' realistic case is that we can obtain an unbiased estimator of the gradient. {Hence, we address this scenario, under the assumption that the actual gradient functions $\\nabla \\rho$ and $\\nabla R$ are bounded in $\\Theta$ (i.e., $\\rho(\\theta)$ is Lipschitz in $\\Theta$).}\n\n{\\begin{assumption}\\label{ass:BoundedGradient} The gradient functions $\\nabla \\rho(\\theta)$ and $\\nabla R(\\theta)$ are bounded in $\\Theta$. To be specific, there exist finite constants $G_\\rho$ and $G_R$ such that\n\\begin{eqnarray}\n\\sup_{\\theta\\in\\Theta} \\|\\nabla \\rho(\\theta)\\|_2 &<& G_\\rho <\\infty \\quad \\text{and} \\nonumber\\\\\n\\sup_{\\theta\\in\\Theta} \\|\\nabla R(\\theta)\\|_2 &<& G_R < \\infty. \\nonumber\n\\end{eqnarray}\n\\end{assumption}}\n\n{We note that this is a mild assumption in the case of interest in this paper, where $\\Theta \\subset {\\mathbb R}^{d_\\theta}$ is assumed to be compact.}\n\n\n\\subsubsection{Normalised target}\\label{sec:NormalisedIS}\n\nFirst, we assume that we can evaluate $\\pi(x)$, which means that at iteration $t$, we can obtain an unbiased estimate of $\\nabla \\rho(\\theta_{t-1})$, denoted $g_t$. We use the optimisation algorithms called \\textit{stochastic gradient} methods, which use stochastic and unbiased estimates of the gradients to optimise a given cost function \\citep{RobbinsMonro}. Particularly, we focus on optimised samplers using stochastic gradient descent (SGD) as an adaptation strategy.\n\n{We start proving that the stochastic gradient estimates $(g_t)_{t\\geq 0}$ have a finite mean-squared error (MSE) w.r.t. the true gradients. To prove this result, we need an additional regularity condition.}\n{\\begin{assumption}\\label{ass:SupSupBound} \nThe normalised target and proposal densities satisfy the inequality  \n\\begin{align*}\n\\sup_{\\theta\\in\\Theta} {\\mathbb E}_{q_\\theta}\\left[ \\left|\\frac{\\pi^2(X)}{q_\\theta^2(X)} \\frac{\\partial \\log q_\\theta}{\\partial \\theta_j}(X) \\right|^2 \\right] =: D_\\pi^j < \\infty.\n\\end{align*}\nfor $j=1, \\ldots, d_\\theta$. We denote $D_\\pi := \\max_{j \\in \\{1,\\ldots,d_\\theta\\}} D_\\pi^j < \\infty$.\n\\end{assumption}}\n\n{\n\\begin{rem} \\label{remSupSup}\nLet us rewrite $D_\\pi^j$ in Assumption \\ref{ass:SupSupBound} in terms of the weight function, namely\n\\begin{align*}\nD_\\pi^j = \\sup_{\\theta\\in\\Theta} {\\mathbb E}_{q_\\theta} \\left[ \\left| w_\\theta^2(X) \\frac{\\partial \\log q_\\theta}{\\partial \\theta_j}(X) \\right|^2 \\right].\n\\end{align*}\nWhen $q_\\theta(x)$ belongs to the exponential family, we readily obtain\n\\begin{align*}\nD_\\pi^j = \\sup_{\\theta\\in\\Theta} {\\mathbb E}_{q_\\theta} \\left[ w_\\theta^4(X) \\left( \\frac{\\partial A(\\theta)}{\\partial \\theta_i} -T_i(X) \\right)^2 \\right],\n\\end{align*}\nwhere $T_i(X)$ is the $i$-th sufficient statistic for $q_\\theta(x)$. Let us construct a bounding function for the weights of the form\n$$\nK(\\theta) := \\sup_{x \\in {\\sf X}} w_\\theta(x).\n$$\nIf we choose the compact space $\\Theta$ in such a way that $K(\\theta)$ is bounded, then we readily have\n\\begin{align*}\nD_\\pi^j &\\le  \\sup_{\\theta\\in\\Theta} K^4(\\theta) {\\mathbb E}_{q_\\theta} \\left[ \\left( \\frac{\\partial A(\\theta)}{\\partial \\theta_i} -T_i(X) \\right)^2 \\right] \\\\\n&\\le \\| K \\|_\\infty^4 \\text{Var}( T_i(X) ),\n\\end{align*}\nwhere we have used the fact that $\\frac{\\partial^m A(\\theta)}{\\partial \\theta_i} = {\\mathbb E}_{q_{\\theta}}\\left[ T_i^m(X) \\right]$. Therefore, if the weights remain bounded in $\\Theta$, a sufficient condition for Assumption \\ref{ass:SupSupBound} to hold is that the sufficient statistics of the proposal distribution all have finite variances, i.e., $\\max_{i \\in \\{1, \\ldots, d_\\theta\\} } T_i(X) < \\infty$.\n\\\\ \\\\\n{There are alternative conditions that, when satisfied, lead to Assumption \\ref{ass:SupSupBound} holding true. As an example, in Appendix \\ref{apRho2} we provide an alternative sufficient condition in terms of the function $\\rho_2(\\theta):={\\mathbb E}[ w_\\theta^4(X) ]$.}\n\\end{rem}\n}\n\nNow we show that when $g_t$ is an iid Monte Carlo estimator of $\\nabla \\rho$, we have the following finite-sample bound for the MSE.\n{\\begin{lem}\\label{lem:GradientMonteCarlo}\nIf Assumption~\\ref{ass:SupSupBound} holds, the following inequality holds,\n\\begin{align*}\n{\\mathbb E}[\\| g_t  - \\nabla \\rho(\\theta_{t-1})\\|_2^2] \\leq \\frac{d_\\theta c_{\\rho} D_\\pi}{N},\n\\end{align*}\nwhere $d_\\theta$ is the parameter dimension and $c_\\rho, D_\\pi < \\infty$ are constant w.r.t. $N$.\n\\end{lem}\n\\begin{proof}\nSee Appendix~\\ref{app:lem:GradientMonteCarlo}.\n\\end{proof}}\n\nIn order to obtain convergence rates for the estimator $(\\varphi,\\pi_{\\bar \\theta_t}^N)$ we first recall a classical result for the SGD (see, e.g., \\cite{bubeck2015convex}).\n\\begin{lem}\\label{lem:SGDconv} \n{Let Assumptions \\ref{ass:BoundedGradient} and \\ref{ass:SupSupBound} hold, apply recursion \\eqref{eq:recSgdAdaptNorm} and let $(g_t)_{t\\geq 0}$ be the stochastic gradient estimates in Lemma~\\ref{lem:GradientMonteCarlo}}. If we choose the step-size sequence $\\gamma_k = \\alpha \/ \\sqrt{k}$, $1\\leq k \\leq t$, for any $\\alpha > 0$, then\n{\\begin{align}\\label{eq:SGDrate}\n{\\mathbb E}[\\rho(\\bar{\\theta}_t) - \\rho^\\star] \\leq \\frac{{\\mathbb E}\\|\\theta_0 - \\theta^\\star\\|_2^2}{2\\alpha\\sqrt{t}} + \\frac{\\alpha d_\\theta c_\\rho D_\\pi}{\\sqrt{t} N} +  \\frac{\\alpha G^2_\\rho}{\\sqrt{t}},\n\\end{align}}\nwhere $\\bar{\\theta}_t = \\frac{1}{t}\\sum_{k=0}^{t-1} \\theta_k$.\n\\end{lem}\n\n\\begin{proof}\nSee Appendix \\ref{app:lem:SGDconv} for a self-contained proof.\n\\end{proof}\n\nWe can now state the first core result of the paper, which is the convergence rate for the AIS algorithm using a SGD adaptation of the parameter vectors $\\theta_t$.\n\\begin{thm}\\label{thm:SGDAIS} \nLet Assumptions \\ref{ass:BoundedGradient} and \\ref{ass:SupSupBound} hold, let the sequence $(\\theta_t)_{t\\geq 1}$ be computed using \\eqref{eq:recSgdAdaptNorm} and construct the averaged iterates $\\bar{\\theta}_t = \\frac{1}{t} \\sum_{k=0}^{t-1} \\theta_k$. Then, the sequence of proposal distributions $(q_{\\bar{\\theta}_t})_{t\\geq 1}$ satisfies the inequality\n{\\begin{align}\\label{eq:rateSGDAIS}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{\\bar{\\theta}_t}^N)\\right)^2\\right] &\\leq \\frac{c_1}{\\sqrt{t}N} + \\frac{c_2}{\\sqrt{t} N^2} + \\frac{c_3}{\\sqrt{t} N} + \\frac{c_4}{N}\n\\end{align}\nfor $t \\ge 1$ and any $\\varphi \\in B({\\sf X})$, where\n\\begin{align*}\nc_1 &= \\frac{c_\\varphi {\\mathbb E}\\|\\theta_0 - \\theta^\\star\\|_2^2}{2 \\alpha}, \\\\ \nc_2 &= {c_\\varphi c_\\rho \\alpha d_\\theta D_\\pi}, \\\\\nc_3 &={c_\\varphi \\alpha G_\\rho^2}, \\\\\nc_4 &={c_\\varphi \\rho^\\star},\n\\end{align*}\nand $c_\\varphi = 4\\|\\varphi\\|_\\infty^2$ are finite constants independent of $t$ and $N$.}\n\\end{thm}\n\n\\begin{proof}\nSee Appendix \\ref{app:thm:SGDAIS}.\n\\end{proof}\n\n\\begin{rem} \nNote that the expectation on the left hand side of  \\eqref{eq:rateSGDAIS} is taken w.r.t. the distribution of the measure-valued random variable $\\pi_{\\bar \\theta_t}^N$. $\\square$\n\\end{rem}\n\nTheorem~\\ref{thm:SGDAIS} can be interpreted similarly to Theorem~\\ref{thm:GD}. One can see that the overall rate of the MSE bound is $\\mathcal{O}\\left({1}\/{\\sqrt{t}N} + {1}\/{N}\\right)$. This means that, as $t\\to\\infty$, we are only left with a rate that is optimal for the AIS for a given parametric proposal family. In particular, again, $\\rho^\\star$ is related to the minimal $\\chi^2$-divergence between the target $\\pi$ and the parametric proposal $q_\\theta$. When the proposal and the target are from the same family, we are back to the case $\\rho^\\star = 1$, thus the adaptation leads to the optimal Monte Carlo rate $\\mathcal{O}(1\/\\sqrt{N})$ for the $L_2$ error within this setting as well.\n\n\\subsubsection{Self-normalised estimators}\n\nWe have noted that it is possible to obtain an unbiased estimate of $\\nabla\\rho(\\theta)$ when the normalised target $\\pi(x)$ can be evaluated. However, if we can only evaluate the unnormalised density $\\Pi(x)$ instead of $\\pi(x)$ and use the self-normalized IS estimator, the estimate of $\\nabla\\rho(\\theta)$ is no longer unbiased. We refer to Sec.~5  of \\cite{tadic2017asymptotic} for stochastic optimisation with biased gradients for adaptive Monte Carlo, where the discussion revolves around minimizing the Kullback-Leibler divergence rather than the $\\chi^2$-divergence. The results presented in \\cite{tadic2017asymptotic}, however, are asymptotic, while herein we are interested in finite-time bounds. Due to the structure of the AIS scheme, it is possible to avoid working with biased gradient estimators. In particular, we can implement the proposed AIS schemes using unbiased estimators of $\\nabla R(\\theta)$ instead of biased estimators of $\\nabla \\rho(\\theta)$. Since optimizing the unnormalised function $R(\\theta)$ leads to the same minima as optimizing the normalised function $\\rho(\\theta)$, we can simply use $\\nabla R(\\theta)$ for the adaptation in the self-normalised case.\n\nSimilar to the argument in Section \\ref{sec:NormalisedIS}, we first start the assumption below, which is the obvious counterpart of Assumption \\ref{ass:SupSupBound}.\n{\\begin{assumption}\\label{ass:SupSupBoundPi} \nThe unnormalized target $\\Pi(x)$ and the proposal densities $q_\\theta(x)$ satisfy the inequalities\n\\begin{align*}\n\\sup_{\\theta\\in\\Theta} {\\mathbb E}_{q_\\theta} \\left[ \\left| \\frac{\\Pi^2(X)}{q_\\theta^2(X)} \\frac{\\partial \\log q_\\theta}{\\partial \\theta_j}(X) \\right|^2 \\right] =: D_\\Pi^j < \\infty\n\\end{align*}\nfor $j=1, \\ldots, d_\\theta$. We denote $D_\\Pi : = \\frac{1}{d_\\theta} \\sum_{j=1}^{d_\\theta} D_\\Pi^j < \\infty$.\n\\end{assumption}}\n\nRemark \\ref{remSupSup} holds directly for Assumption \\ref{ass:SupSupBoundPi} as long as $Z_\\pi<\\infty$. {Next, we prove an MSE bound for the stochastic gradients $(\\tilde{g}_t)_{t\\geq 0}$ employed in recursion \\eqref{eq:SgdUnnormalizedAdapt}, i.e., the unbiased stochastic estimates of $\\nabla R(\\theta)$.}\n\n{\n\\begin{lem}\\label{lem:GradientMonteCarloR}\nIf Assumptions \\ref{ass:BoundedGradient} and \\ref{ass:SupSupBoundPi} hold, the inequality\n\\begin{align*}\n{\\mathbb E}[\\| \\tilde{g}_t  - \\nabla R(\\theta_{t-1})\\|_2^2] \\leq \\frac{d_\\theta c_R D_\\Pi}{N},\n\\end{align*}\nis satisfied, where $c_R, D_\\Pi < \\infty$ are constants w.r.t. of $N$.\n\\end{lem}\n\\begin{proof}\nThe proof is identical to the proof of Lemma~\\ref{lem:GradientMonteCarlo}.\n\\end{proof}\n}\n\nWe can now obtain explicit rates for the convergence of the unnormalized function $R(\\bar \\theta_t)$, evaluated at the averaged iterates $\\bar \\theta_t$. \n\n\\begin{lem}\\label{lem:SGDBiasedconv} \nIf Assumptions \\ref{ass:BoundedGradient} and \\ref{ass:SupSupBoundPi} hold and the sequence $(\\theta_t)_{t\\ge 1}$ is computed via recursion \\eqref{eq:SgdUnnormalizedAdapt}, with step-sizes $\\gamma_k = \\beta \/ \\sqrt{k}$ for $1\\leq k \\leq t$ and $\\beta > 0$, we obtain the inequality\n{\\begin{align}\\label{eq:UnnormRate}\n{\\mathbb E}[R(\\bar{\\theta}_t) - R ^\\star] \\leq \\frac{{\\mathbb E} \\|\\theta_0 - \\theta^\\star\\|_2^2}{2 \\beta \\sqrt{t}} + \\frac{\\beta d_\\theta c_R D_\\Pi}{\\sqrt{t} N} +  \\frac{\\beta G^2_R}{\\sqrt{t}}\n\\end{align}}\nwhere $c_R,D_\\Pi<\\infty$ are constants w.r.t. $t$ and $N$. Relationship \\ref{eq:UnnormRate} implies that\n{\\begin{align}\\label{eq:NormRateWithNormConsts}\n{\\mathbb E}[\\rho(\\bar{\\theta}_t) - \\rho^\\star] \\leq \n\\frac{{\\mathbb E} \\|\\theta_0 - \\theta^\\star\\|_2^2}{2 \\beta Z_\\pi^2 \\sqrt{t}} + \\frac{\\beta d_\\theta c_R D_\\Pi}{Z_\\pi^2 \\sqrt{t} N} +  \\frac{\\beta G^2_R}{Z_\\pi^2 \\sqrt{t}}.\n\\end{align}}\n\\end{lem}\n\\begin{proof} The proof of the rate in \\eqref{eq:UnnormRate} is identical to the proof of Lemma~\\ref{lem:SGDconv}. The rate in \\eqref{eq:NormRateWithNormConsts} follows by observing that $\\rho(\\theta) = R(\\theta) \/ Z_\\pi^2$ for every $\\theta\\in\\Theta$.\n\\end{proof}\n\nFinally, using Lemma~\\ref{lem:SGDBiasedconv}, we can state our main result: an explicit error rate for the MSE of Algorithm~\\ref{alg:SGDAIS} as a function of the number of iterations $t$ and the number of samples $N$.\n\n\\begin{thm}\\label{thm:SGDAISUN} \nLet Assumptions \\ref{ass:BoundedGradient} and \\ref{ass:SupSupBoundPi} hold and let the sequence $(\\theta_t)_{t\\ge 1}$ be computed via recursion \\eqref{eq:SgdUnnormalizedAdapt}, with step-sizes $\\gamma_k = \\beta \/ \\sqrt{k}$ for $1\\leq k \\leq t$ and $\\beta > 0$. We have the following inequality for the sequence of proposal distributions $(q_{\\bar{\\theta}_t})_{t\\geq 1}$,\n{\\begin{align}\\label{eq:rateUnnormAIS}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{\\bar{\\theta}_t}^N)\\right)^2\\right] &\\leq \\frac{C_1}{\\sqrt{t} N} + \\frac{C_2}{\\sqrt{t}N^2} + \\frac{C_3}{\\sqrt{t} N} + \\frac{C_4}{N},\n\\end{align}\nwhere\n\\begin{align*}\nC_1 &= \\frac{c_\\varphi {\\mathbb E}\\|\\theta_0 - \\theta^\\star\\|_2^2}{2 \\beta Z_\\pi^2}, \\\\\nC_2 &= \\frac{c_\\varphi \\beta c_R d_\\theta D_\\Pi}{Z_\\pi^2}, \\\\\nC_3 &= \\frac{c_\\varphi \\beta G^2_R}{Z_\\pi^2}, \\\\\nC_4 &= {c_\\varphi \\rho^\\star},\n\\end{align*}\nand $c_\\varphi = 4\\|\\varphi\\|_\\infty^2$ are finite constants independent of $t$ and $N$.}\n\\end{thm}\n\\begin{proof}\nThe proof follows from Lemma~\\ref{lem:SGDBiasedconv} and mimicking the exact same steps as in the proof of Theorem~\\ref{thm:SGDAIS}.\n\\end{proof}\n\n\\begin{rem} \nTheorem~\\ref{thm:SGDAISUN}, as in Remark~\\ref{remGDasymptote}, provides relevant insights regarding the performance of the stochastic gradient OAIS algorithm. In particular, for a general target $\\pi$, we obtain\n\\begin{align*}\n\\lim_{t\\to\\infty} \\left\\|(\\varphi,\\pi) - (\\varphi,\\pi_{\\bar{\\theta}_t}^N)\\right\\|_2 = \\mathcal{O}\\left(\\sqrt{\\frac{\\rho^\\star}{N}}\\right).\n\\end{align*}\nThis result shows that the $L_2$ error is asymptotically optimal. As in previous cases, if the target $\\pi$ is in the exponential family, then the asymptotic convergence rate is $\\mathcal{O}(1\/\\sqrt{N})$ as $t \\to \\infty$. $\\square$\n\\end{rem}\n\n\\begin{rem} \nTheorem~\\ref{thm:SGDAISUN} also yields a practical heuristic to tune the step-size and the number of particles together. Assume that $0 < \\beta < 1$ and let $N = 1\/\\beta$ (which we assume to be an integer without loss of generality). In this case, the rate \\eqref{eq:rateUnnormAIS} simplifies into\n\\begin{align*}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{\\bar{\\theta}_t}^N)\\right)^2\\right] &\\leq \\frac{c_\\varphi {\\mathbb E}\\|\\theta_0 - \\theta^\\star\\|_2^2}{2 Z_\\pi^2 \\sqrt{t}} + \\frac{c_\\varphi \\beta^3 c_R d_\\theta D_\\Pi}{Z_\\pi^2 \\sqrt{t}} + \\frac{c_\\varphi \\beta^2 G^2_R}{Z_\\pi^2\\sqrt{t}} + c_\\varphi \\rho^\\star \\beta\n\\end{align*}\nNow, if we let $t = \\mathcal{O}(1\/\\beta^2)$ we readily obtain\n\\begin{align*}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{\\bar{\\theta}_t}^N)\\right)^2\\right] &\\leq \\mathcal{O}(\\beta).\n\\end{align*}\nTherefore, one can control the error using the step-size of the optimisation scheme provided that other parameters of the algorithm are chosen accordingly. The same argument also holds for Theorem~\\ref{thm:SGDAIS}. $\\square$\n\\end{rem}\n\n\\begin{rem} \n{It is not straightforward to compare the rates in inequality \\eqref{eq:rateUnnormAIS} (for the unnormalized target $\\Pi(x)$) and inequality \\eqref{eq:rateSGDAIS} (for the normalized target $\\pi(x)$). Even if \\eqref{eq:rateUnnormAIS} may ``look better'' by a constant factor compared to the rate in  \\eqref{eq:rateSGDAIS}, this is usually not the case. Indeed, the variance of the errors in the unnormalised gradient estimators is typically higher and this reflects on the variance of the moment estimators. Another way to look at this issue is to realise that, very often, $Z_\\pi << 1$, which makes the bound in \\eqref{eq:rateUnnormAIS} much greater than the bound in \\eqref{eq:rateSGDAIS}.}\n\\end{rem}\n\n{Finally, we can adapt Theorem~\\ref{thm:SNISbias} to our case, providing a convergence rate of the bias of the importance sampler given by Algorithm~\\ref{alg:SGDAIS}.}\n\n{\\begin{thm}\\label{thm:SGDAISbias}\nUnder the setting of Theorem~\\ref{thm:SGDAISUN}, we have\n\\begin{align}\\label{eq:rateUnnormAISbias}\n\\left| {\\mathbb E}\\left[(\\varphi,\\pi_{\\bar{\\theta}_t}^N)\\right] - (\\varphi, \\pi)\\right| &\\leq \\frac{3C_1}{\\sqrt{t} N} + \\frac{3C_2}{\\sqrt{t}N^2} + \\frac{3C_3}{\\sqrt{t} N} + \\frac{3C_4}{N},\n\\end{align}\nwhere $C_1,C_2,C_3,C_4$ are finite constants given in Theorem~\\ref{thm:SGDAISUN} and independent of $t$ and $N$.\n\\end{thm}}\n\\begin{proof}\nThe proof follows from Theorem~\\ref{thm:SNISbias} and mimicking the same proof technique used to prove Theorem~\\ref{thm:SGDAISUN}.\n\\end{proof}\n\n\\subsection{Convergence rate with vanilla SGD}\n\n{The arguments of Section \\ref{ssConvergence-Averaged-Iterates} can be carried over to the analysis of Algorithm \\ref{alg:vanillaSGDAIS}, where the proposal functions $q_{\\theta_t}(x)$ are constructed using the iterates $\\theta_t$ rather than the averages $\\bar \\theta_t$. Unfortunately, achieving the optimal $\\mathcal{O}(1\/\\sqrt{t})$ rate for the vanilla SGD is difficult in general. The best available rate without significant restrictions on the step-size is given by \\citet{shamir2013stochastic}. In particular, we can adapt \\citet[Theorem~2]{shamir2013stochastic} to our setting in order to state the following lemma.\n\\begin{lem}\\label{lem:vanillaSGDconv} \nApply recursion \\eqref{eq:SgdUnnormalizedAdapt} for the computation of the iterates $(\\theta_t)_{t\\ge 1}$, choose the step-sizes $\\gamma_k = \\beta \/ \\sqrt{k}$ for $1\\leq k \\leq t$, where $\\beta > 0$, and let Assumptions \\ref{ass:BoundedGradient} and \\ref{ass:SupSupBoundPi} hold. Then, we have the inequality\n\\begin{align}\n{\\mathbb E}[R({\\theta}_t) - R ^\\star] \\leq \\left(\\frac{D^2}{\\beta \\sqrt{t}} + \\frac{\\beta d_\\theta c_R D_\\Pi}{\\sqrt{t} N} +  \\frac{\\beta G^2_R}{\\sqrt{t}}\\right) (2  + \\log t),\n\\end{align}\nwhere $D := \\sup_{\\theta,\\theta' \\in \\Theta} \\|\\theta - \\theta'\\| < \\infty$. This in turn implies that\n{\\begin{align}\n{\\mathbb E}[\\rho({\\theta}_t) - \\rho^\\star] \\leq \n\\left(\\frac{D^2}{\\beta \\sqrt{t}} + \\frac{\\beta d_\\theta c_R D_\\Pi}{\\sqrt{t} N} +  \\frac{\\beta G^2_R}{\\sqrt{t}}\\right)\\frac{(2  + \\log t)}{Z_\\pi^2}.\n\\end{align}}\n\\end{lem}}\n\\begin{proof}\nIt is straightforward to prove this result using \\citet[Theorem~2]{shamir2013stochastic} and the proof of Lemma~\\ref{lem:SGDconv}.\n\\end{proof}\n{The obtained rate is, in general, $\\mathcal{O}\\left( \\frac{\\log t}{\\sqrt{t}}\\right)$. This is known to be suboptimal and it can be improved to the {information-theoretical optimal} $\\mathcal{O}(1\/\\sqrt{t})$ rate by choosing a specific step-size scheduling, see, e.g., \\citet{jain2019making}. {However, in this case, the scheduling of $(\\gamma_t)_{t\\geq 1}$ depends directly on the total number of iterates to be generated, in such a way that the error $\\mathcal{O}(1\/\\sqrt{t})$ is guaranteed only for the {\\em last} iterate, at the final time $t$.}}\n\nWe can extend Lemma \\ref{lem:vanillaSGDconv} to obtain the following result.\n\n{\\begin{thm}\\label{thm:vanillaSGDAIS} \nApply recursion \\eqref{eq:SgdUnnormalizedAdapt} for the computation of the iterates $(\\theta_t)_{t\\ge 1}$, choose the step-sizes $\\gamma_k = \\beta \/ \\sqrt{k}$ for $1\\leq k \\leq t$, where $\\beta > 0$, and let Assumptions \\ref{ass:BoundedGradient} and \\ref{ass:SupSupBoundPi} hold. If we construct the sequence of proposal distributions $(q_{{\\theta}_t})_{t\\geq 1}$ be the sequence of proposal distributions we obtain the following MSE bounds\n\\begin{align}\n{\\mathbb E}\\left[\\left((\\varphi,\\pi) - (\\varphi,\\pi_{{\\theta}_t}^N)\\right)^2\\right] &\\le \\left(\n\t\\frac{C_1}{\\sqrt{t} N} + \\frac{C_2}{\\sqrt{t}N^2} + \n\t\\frac{C_3}{\\sqrt{t} N}\n\\right)(2 + \\log t) + \\frac{C_4}{N},\n\\label{eq:rateUnnormAIS-2}\n\\end{align}\nwhere\n\\begin{align*}\nC_1 &= \\frac{c_\\varphi D^2}{2 \\beta Z_\\pi^2}, \\\\\nC_2 &= \\frac{c_\\varphi \\beta c_R d_\\theta D_\\Pi}{Z_\\pi^2}, \\\\\nC_3 &= \\frac{c_\\varphi \\beta G^2_R}{Z_\\pi^2},  \\\\\nC_4 &= {c_\\varphi \\rho^\\star},\n\\end{align*}\nand $c_\\varphi = 4\\|\\varphi\\|_\\infty^2$ are finite constants independent of $t$ and $N$.\n\\end{thm}}\n\\begin{proof}\nThe proof follows from Lemma~\\ref{lem:vanillaSGDconv} with the exact same steps as in the proof of Theorem~\\ref{thm:SGDAIS}.\n\\end{proof}\n{Finally, it is also straightforward to adapt the bias result in Theorem~\\ref{thm:SGDAISbias} to this case, which results in the similar bound. We skip it for space reasons and also because it has the same form as in Theorem~\\ref{thm:SGDAISbias} with an extra $\\log t$ factor.}\n\n\\section{Conclusions}\\label{sec:conc}\nWe have presented and analysed \\textit{optimised} parametric adaptive importance samplers and provided non-asymptotic convergence bounds for the MSE of these samplers. Our results display the precise interplay between the number of iterations $t$ and the number of samples $N$. In particular, we have shown that the optimised samplers converge to an optimal proposal as $t\\to\\infty$, leading to an asymptotic rate of $\\mathcal{O}(\\sqrt{\\rho^\\star\/N})$. This intuitively shows that the number of samples $N$ should be set in proportion to the minimum $\\chi^2$-divergence between the target and the exponential family proposal, as we have shown that the adaptation (in the sense of minimising $\\chi^2$-divergence or, equivalently, the variance of the weight function) cannot improve the error rate beyond $\\mathcal{O}(\\sqrt{\\rho^\\star\/N})$. The error rates in this regime may be dominated by how close the target is to the exponential family.\n\nNote that the algorithms we have analysed require constant computational load at each iteration and the computational load does not increase with $t$ as we do not re-use the samples in past iterations. Such schemes, however, can also be considered and analysed in the same manner. More specifically, in the present setup the computational cost of each iteration depends on the cost of evaluating $\\Pi(x)$.\n\nOur work opens up several other paths for research. One direction is to analyse the methods with more advanced optimisation algorithms. Another challenging direction is to consider more general proposals than the natural exponential family, which may lead to non-convex optimisation problems of adaptation. Analysing and providing guarantees for this general case would provide foundational insights for general adaptive importance sampling procedures. Also, as shown by \\citet{ryu2016convex}, similar theorems can also be proved for $\\alpha$-divergences.\n\nAnother related piece of work arises from variational inference \\citep{wainwright2008graphical}. In particular, \\citet{dieng2017variational} have recently considered performing variational inference by minimising the $\\chi^2$-divergence, which is close to the setting in this paper. In particular, the variational approximation of the target distribution in the variational setting coincides with the proposal distribution we consider within the importance sampling context in this paper. This also implies that our results may be used to obtain finite-time guarantees for the expectations estimated using the variational approximations of target distributions.\n\nFinally, the adaptation procedure can be modified to handle the non-convex case as well. In particular, the SGD step can be converted into a stochastic gradient Langevin dynamics (SGLD) step. The SGLD method can be used as a global optimiser when $\\rho$ and $R$ are non-convex and a global convergence rate can be obtained using the standard SGLD results, see, e.g., \\citet{raginsky2017non,zhang2019nonasymptotic}. Global convergence results for other adaptation schemes such as stochastic gradient Hamiltonian Monte Carlo (SGHMC) can also be achieved using results from nonconvex optimisation literature, see, e.g., \\citet{akyildiz2020nonasymptotic}.\n\\section*{Acknowledgements}\n\\\"O.~D.~A. is funded by the Lloyds Register Foundation programme on Data Centric Engineering through the London Air Quality project. This work was supported by The Alan Turing Institute for Data Science and AI under EPSRC grant EP\/N510129\/1. J.~M. acknowledges the support of the Spanish \\textit{Agencia Estatal de Investigaci\\'on} (awards TEC2015-69868-C2-1-R ADVENTURE and RTI2018-099655-B-I00 CLARA) and the Office of Naval Research (award no. N00014-19-1-2226).\n\n\n\n\n\n\n\\clearpage\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction and Statement of Results}\nIt has long been known that, given an ergodic invertible probability measure preserving system, a Rohlin tower may be constructed with base independent of a given partition of the underlying space(\\cite{Roh:52}, \\cite{Roh:65}). In \\cite{Alp:79}, meanwhile, S. Alpern proved a `multiple' Rohlin tower theorem (see \\cite{EP:97} for an easy proof) whose full statement we will not give, but which has the following corollary of interest: \n\n\\begin{thm}\\label{thm:alp}\nLet $N \\in \\ensuremath{\\mathbb N} $ and \\ensuremath{\\epsilon > 0\\;} be given. For any ergodic invertible measure-preserving transformation $T$ of a Lebesgue probability space $(X, \\mathcal B, \\mu)$, there exists a Rohlin tower of height $N$ with base $B$ and error set $E$ with $\\mu(E) < \\ensuremath{\\epsilon} $, so that $T(E) \\subset B$. \n\\end{thm}\n\nA {\\em Rohlin tower of height} $N$ {\\em with base} $B$ {\\em and error set} $E$ is characterized by the collection of sets \n$\\{B, TB, \\dots, T^{N-1}B, E\\}$ forming a partition of $X$. If in addition $T(E) \\subset B$, we shall say {\\bf Alpern Tower}.\nIt is our goal to show that for ergodic transformations on $(X, \\ensuremath{\\mathcal B} , \\mu)$, given a finite measurable partition $\\mathbb P$ of $X$, an Alpern tower may be constructed with base $B$ independent of $\\mathbb P$. Precisely:\n\n\\begin{bigthm}\n\\label{mainthm}\nLet $(X, \\mathcal B, \\mu)$ be a Lebesgue probability space, and suppose $\\mathbb P$ is a finite measurable partition of $X$.   For any ergodic invertible measure-preserving transformation $T$ of $X$, $N \\in \\ensuremath{\\mathbb N} $, \nthere exists a Rohlin tower of height $N$ with base $B$ and error set $E$ such that $T(E) \\subset B$ and $B$ is independent of $\\mathbb P$.  \n\\end{bigthm}\n\nWe do not specify the size of the error set; but the process of constructing our tower makes it clear that the error set may be made arbitrarily small. \n\n\n\\section{Proof of main result}\n\nFor the remainder of the paper, $(X, \\mathcal B, \\mu)$ will be a fixed Lebesgue probability space and  $T:X \\to X$ will be an invertible ergodic measure-preserving transformation on $X$. All mentioned sets will be measurable and we will adopt a cavalier attitude toward null sets. In particular, ``partition'' will typically mean ``measurable partition modulo null sets''. \n\\begin{defn}\nBy a {\\em tower over B} we will mean a set $B \\subset X$, called the {\\em base}, and a countable partition $B = B_1 \\cup B_2 \\cup \\cdots$, together with their images  $T^iB_j$, $0 \\le i < j$, such that the family $\\{T^iB_j : 0 \\le i < j\\}$ consists in pairwise disjoint sets. If this family partitions $X$, we will say that the tower is {\\em exhaustive}. \n\\end{defn}\n\nIf a tower over $B$ is exhaustive and $B = B_N \\cup B_{N+1}$, we shall speak of an {\\em exhaustive Alpern tower of height} $\\{N, N+1\\}$, as in such a case, \n$\\{B, TB, \\ldots, T^{N-1}B, E=T^N B_{N+1}\\}$ partitions $X$ with $T(E) \\subset B$. So \nwe may re-phrase Theorem 1 as: \\medskip\n\n\\noindent {\\em {\\bf Theorem \\ref{mainthm}:} Let $(X, \\mathcal B, \\mu)$ be a Lebesgue probability space and suppose $\\mathbb P$ is a finite measurable partition of $X$.   For any ergodic invertible measure-preserving transformation $T$ of $X$, $N \\in \\ensuremath{\\mathbb N} $, one may find an exhaustive Alpern tower of height $\\{N, N+1\\}$ having base independent of $\\mathbb P$.} \\medskip\n\n\\noindent We require a lemma (and a corollary).  \n\n\n\n\\begin{lem}\\label{lem:m}\nLet $M \\in \\ensuremath{\\mathbb N} $ and let $\\ensuremath{\\mathbb P}  = \\{P_1, \\dots, P_t\\}$ be a partition of $X$ with $\\mu(P_i) > 0$ for each $i$. There exists a set $S$ of positive measure so that if $x \\in S$ with first return $n(x) = n$, say, then $|\\{x, Tx, \\dots, T^{n-1}x\\} \\cap P_i | \\ge M, 1 \\le i \\le t$.  \n\\end{lem}\n\\proof  For almost every $x$ we may find $K(x)$ so that for each $i$ between $1$ and $t$ we have $|\\{x, Tx, \\dots, T^{K(x) - 1}x\\} \\cap P_i| \\ge M$. Since almost all of $X$ is the countable union (over $k \\in \\ensuremath{\\mathbb N} $) of $\\{x: K(x) = k\\}$, there exists some fixed $K$ so that the set $A = \\{x: K(x) \\le K\\}$ has positive measure. If $C \\subset A$ has very small measure ($\\mu(C) < 1\/K$) then the average first-return time of $x \\in C$ to $C$ is $\\frac{1}{\\mu(C)} > K$, so we can find $S \\subset C$ with $\\mu(S) > 0$  so that $S, TS, \\dots, T^{K - 1}S$ are pairwise disjoint. \\hfill\\ensuremath{_\\blacksquare} \n\n\n\\begin{cor}\\label{cor:B}\n Let $M \\in \\ensuremath{\\mathbb N} $ and $\\ensuremath{\\mathbb P}  = \\{P_1, \\dots, P_t\\}$ be a partition of $X$ with $\\mu(P_i) > 0$ for each $i$. There is a tower having base \n$S = S_{tM} \\cup S_{tM+1} \\cup \\cdots$ where for each $x \\in S_r$, $|\\{x, Tx, \\dots, T^{r - 1}x\\} \\cap P_i| \\ge M$ for all $1 \\le i \\le t$.  \n\\end{cor}\n\\proof Let $S$, $K$  be as in Lemma \\ref{lem:m} and choose any $k \\ge K$. \\hfill\\ensuremath{_\\blacksquare}  \\medskip\n\nWe turn now to the proof of Theorem \\ref{mainthm}. Fix a partition $\\ensuremath{\\mathbb P}  = \\{P_1, \\dots, P_t\\}$, an arbitrary natural number $N$, and $\\epsilon >0$. Set $m_i = \\mu(P_i)$, and assume (without loss of generality) that $0 < m_1 \\le m_2 \\le \\dots \\le m_t$. Select and fix $M > \\frac{3N^3t}{m_1}$. Let $S$ be as in Corollary \\ref{cor:B} for this $M$; hence $S = S_{tM} \\cup S_{tM+1} \\cup \\cdots$.  (Some $S_i$ may be empty, of course.) For each non-empty $S_R$, partition $S_R$ by $\\ensuremath{\\mathbb P} $-name of length $R$. (Recall that $x, y$ in $S_R$ have the same $\\ensuremath{\\mathbb P} $-name of length $R$ if $T^ix$ and $T^iy$ lie in the same cell of \\ensuremath{\\mathbb P}  for $0 \\le i < R$.) Let $C$ be the base of one of the resulting columns; hence, every $x \\in C$ has the same $\\ensuremath{\\mathbb P} $-name of length $R$ (for some $R\\ge tM$), and the length $R$ orbit of each $x \\in C$ meets each $P_i$ at least $M$ times. \n\nPartition $C$ into pieces $C^{(1)}, C^{(2)}\\dots$, $C^{(t)}$ whose measures will be determined later. Then partition each $C^{(i)}$ into $N$ equal measure pieces, $C^{(i)} = C^{(i)}_1 \\cup C^{(i)}_2 \\cup \\dots \\cup C^{(i)}_N$. \n\nNow we fix $(R,C)$ and focus our attention on the height $R$ {\\em column} over a single $C^{(i)}$ and its height $R$ {\\em subcolumns} over $C^{(i)}_j$, $1\\leq j\\leq N$. We refer to the sets $T^rC^{(i)}$, $0 \\le r < R$, as {\\em levels} and to the sets $T^rC^{(i)}_j$ as {\\em rungs}. We are going to build a portion of $B$ by carefully selecting some rungs from the subcolumns under consideration. As we move through the various subcolumns, we need to have gaps of length $N$ or $N+1$ between selections. Now to specifics. We want \nto have our $\\ensuremath{C^{(i)}}$-selections form a ``staircase'' of height $N$ starting at level $N^2 - N$. That is, at height $(N-1)N$, the rung over $C^{(i)}_1$ is the only one selected; at height $N(N-1) + 1$, the rung over $C^{(i)}_2$ is the only one selected; etc., so that at height $N^2-1$, the rung over $C^{(i)}_N$ is the only one selected.  \n\nThis is easy to accomplish. First, we select each base rung $C^{(i)}_j$, $j = 1, 2, \\dots, N$ (i.e., the rungs in the zeroth level). Over $C^{(i)}_1$, we then select $N-1$ additional rungs with gaps of length $N$; that is, we select the rungs at heights $N$, $2N, \\dots, (N-1)N$. Over $C^{(i)}_2$ we select $N-2$ rungs with gap $N$, then a rung with gap $N+1$.  We continue in this fashion, choosing one less gap of length $N$ and one more of length $N+1$ in each subsequent subcolumn. In the last subcolumn (that over $C^{(i)}_N$) we are thus choosing rungs with gaps of length $N+1$ a total of $N-1$ times.  See the left side of \nFigure \\ref{pic:bottom} for the case $N = 4$.\n\nNow we perform a similar procedure moving down from the top, so as to obtain a staircase starting at height $R-(N^2-1)$. \nNote that there are either $N$ or $N-1$ unselected rungs at the top of each subcolunm. See the right side of Figure \\ref{pic:bottom}. \n\n\n\n\n\\begin{figure}[hbtp]\n\n\\caption[Bottom of Tower for $N = 4$]\n   {Bottom, Top of Tower for $N = 4$}\n\\setlength{\\unitlength}{.2in}\n\n\\begin{picture}(20,20)(0,0) \n\\label{pic:bottom}\n\\put(0, 0){$C^{(i)}_1 \\hspace{4mm} C^{(i)}_2 \\hspace{4mm}  C^{(i)}_3 \\hspace{3.3mm} C^{(i)}_4$}\n\\multiput(0,2)(0,1){16}{\\line(1,0){1}}\n\\multiput(2,2)(0,1){16}{\\line(1,0){1}}\n\\multiput(4,2)(0,1){16}{\\line(1,0){1}}\n\\multiput(6,2)(0,1){16}{\\line(1,0){1}}\n\\put(4,18){\\vdots}\n\\linethickness{1mm}\n\\multiput(0,2)(0,4){4}{\\line(1,0){1}}\n\\multiput(2, 2)(0,4){3}{\\line(1,0){1}}\n\\put(2, 15){\\line(1,0){1}}\n\\multiput(4, 2)(0,4){2}{\\line(1,0){1}}\n\\multiput(4, 11)(0, 5){2}{\\line(1, 0){1}}\n\\put(4, 16){\\line(1,0){1}}\n\\multiput(6, 2)(0,5){4}{\\line(1,0){1}}\n\n\\linethickness{.2mm}\n\\put(13, 1.5){\\vdots}\n\\multiput(10,3)(0,1){15}{\\line(1,0){1}}\n\\multiput(12,3)(0,1){15}{\\line(1,0){1}}\n\\multiput(14,3)(0,1){15}{\\line(1,0){1}}\n\\multiput(16,3)(0,1){15}{\\line(1,0){1}}\n\\linethickness{1mm}\n\\multiput(10, 3)(0,5){3}{\\line(1,0){1}}\n\\multiput(12, 4)(0,5){3}{\\line(1,0){1}}\n\\multiput(14, 5)(0,5){2}{\\line(1,0){1}}\n\\put(14, 14){\\line(1,0){1}}\n\\multiput(16,6)(0,4){2}{\\line(1,0){1}}\n\\put(16,14){\\line(1,0){1}}\n\n\\end{picture}\n\n\\end{figure} \\medskip\n\nNext, we want to select rungs through the middle of the tower so as to iterate the staircase pattern all the way up, except that we will skip certain levels (i.e. not select any of their rungs), continuing the staircase pattern where we left off with the following rung. As we want to match stride with the staircase already selected at the top, the total number of levels skipped in the middle section will be constrained to a certain residue class modulo $N$, and as we want the selected rungs to form a portion of an Alpern tower of height $\\{N, N+1\\}$, we cannot skip any two levels with fewer than $N$ levels between them.\n\nSome terminology: an {\\em appearance} of $P_j$ in \\ensuremath{C^{(i)}}\\ is just a level of \\ensuremath{C^{(i)}}\\ that is contained in $P_j$.  \nA {\\em selection} of $P_j$ is just a selected rung in a subcolumn of \\ensuremath{C^{(i)}}\\ that is contained in $P_j$. The {\\em net skips} of $P_j$ in the tower over \n\\ensuremath{C^{(i)}}\\ is defined as \\[ S_j(\\ensuremath{C^{(i)}}) = (\\# \\textnormal{ of appearances of $P_j$) } - (\\# \\textnormal{ of selections of $P_j$)}.\\] \nFor example, looking at Figure \\ref{pic:bottom}, one sees that $4$ zeroth level rungs are selected. So if the zeroth level belongs to $P_j$, the zeroth level \ncontribution to $S_j(\\ensuremath{C^{(i)}})$ is $-3$ (one appearance and 4 selections).\n\n \n \n\nLet $\\delta = 2(N-1)(N-2)$ and choose $\\gamma$ with \n\\begin{displaymath}{\\delta\\over m_1}+N > \\gamma \\ge {\\delta\\over m_1} \\quad \\mbox{and} \\quad (t-1)\\delta + \\gamma \\equiv R ~(\\hspace{-2.2ex}\\mod N).\n\\end{displaymath} \nOver \\ensuremath{C^{(i)}}, we skip a quantity of ``middle'' levels belonging to each $P_j$ (for $j \\neq i$) sufficient to ensure that $S_j(\\ensuremath{C^{(i)}})=\\delta$ for $j\\neq i$ and $S_i(\\ensuremath{C^{(i)}})=\\gamma$. (Note that $P_j$ cannot have been skipped more than $\\delta$ times in the outer rungs.) This is not delicate; one can just enact the selection greedily. That is to say, travel up the tower, beginning at level $N^2$, skipping rungs that belong to cells requiring additional skips whenever there's been no too-recent skip. Since each $P_j$ appears at least $M>{3N^3t\\over m_1}$ times, and we need only $\\gamma +(t-1)\\delta\\le {2N^2t\\over m_1}$ net skips, we'll find all the skips we need. \n\n\nWe have not specified the relative masses of the bases of the columns $\\ensuremath{C^{(i)}}$. Set\n\\begin{equation}\n\\label{bi} b_j = \\frac{\\mu(P_j)(\\gamma + (t-1)\\delta) - \\delta}{\\gamma - \\delta} \\; \n\\end{equation}\nand put $\\mu(\\ensuremath{C^{(i)}})= b_i \\mu(C)$, $1\\leq i\\leq t$. Our choice of $\\gamma$ ensures that $b_i\\ge 0$ for each $i$, and one easily checks that $\\sum b_i=1$, so this is coherent.\n\nLet $B_{C}$ be the union of the rungs selected from the columns over $C$ \n(this includes each of the rungs selected from each of the $N$ subcolumns over $\\ensuremath{C^{(i)}}$, $1\\le i\\le t$) \nand put $B=\\bigcup_{C} B_{C}$. (Here $C$ runs over the bases of the columns corresponding to every $\\ensuremath{\\mathbb P} $-name of length $R$ for every $R\\geq tM$.) It\nis clear that $B$ forms the base of an Alpern tower of height $\\{N, N+1\\}$. It remains to show that $B$ is independent of $\\ensuremath{\\mathbb P} $, which we will do by constructing a set $A$, disjoint from $B$, such that both $A$ and $A\\cup B$ can be shown to be independent of $\\ensuremath{\\mathbb P} $. \n \nHere is how $A$ is constructed. Consider again the tower over $\\ensuremath{C^{(i)}}$. This tower had $R$ levels and $RN$ rungs, some of which were selected for the base $B$. We now choose $\\gamma +(t-1)\\delta$ additional rungs for the set $A$. For each $j\\neq i$, $\\delta$ of these rungs should be contained in $P_j$, with the remaining $\\gamma$ contained in $P_i$. (We don't worry about gaps and whatnot; just choose any such collection of rungs disjoint from the family of $B$ selections.) \nDenote the union of the these additional rungs (in all of the columns over $\\ensuremath{C^{(i)}}$, $1\\leq i\\leq t$) by $A_{C}$. Finally, put $A=\\bigcup _{C} A_{C}$. \n\nThat $A\\cup B$ is independent of $\\ensuremath{\\mathbb P} $ is a consequence of the fact that for each $\\ensuremath{C^{(i)}}$, the number appearances of $P_j$ in the column over $\\ensuremath{C^{(i)}}$ is \nprecisely the number of $B$-selections from $P_j$ plus the number of $A$-selections from $P_j$. Accordingly, the relative masses of the cells of $\\ensuremath{\\mathbb P} $ restricted to $A\\cup B$ are equal to the relative frequencies of the appearances of the cells of $\\ensuremath{\\mathbb P} $ in the column over $\\ensuremath{C^{(i)}}$. Therefore, since the proportion of the column that is selected for $A\\cup B$ is independent of $\\ensuremath{C^{(i)}}$ (in fact is always equal to ${1\\over N}$), and since the columns over the various $\\ensuremath{C^{(i)}}$ exhaust $X$, $A\\cup B$ is independent of $\\ensuremath{\\mathbb P} $ (in fact $\\mu\\big(P_j \\cap (A\\cup B)\\big) = {1\\over N} \\mu(P_j)$, $1\\leq j\\leq t$).\n\nThat $A$ is independent of $\\ensuremath{\\mathbb P} $, meanwhile, is a consequence of equation (\\ref{bi}). Fixing $C$ and recalling that $b_i = {\\mu(\\ensuremath{C^{(i)}})\\over \\mu(C)}$, \nthat there were $\\delta$ \n$P_j$-rungs in the column over $\\ensuremath{C^{(i)}}$ selected for $A$, $i\\neq j$, and that there were $\\gamma$ $P_i$-rungs in the column over $\\ensuremath{C^{(i)}}$ selected for $A$, \nthe relative mass of $P_i$ among the $A$-selections in the tower over $C$ is \n\\[ r_i = \\frac{b_i \\gamma + (1-b_i)\\delta}{\\gamma + (t-1)\\delta} .\\]\nBut, solving for $\\mu(P_i)$ in equation (\\ref{bi}), one gets that\n\\[ \\mu(P_i) = \\frac{b_i \\gamma + (1-b_i)\\delta}{\\gamma + (t-1)\\delta} \\]\nas well. So the intersection of $A$ with the column over $C$ is independent of $\\ensuremath{\\mathbb P} $. That this is true for every $C$ gives independence of $A$ from $\\ensuremath{\\mathbb P} $ simpliciter. \\hfill\\ensuremath{_\\blacksquare} \n\n\n\n\\providecommand{\\bysame}{\\leavevmode\\hbox to3em{\\hrulefill}\\thinspace}\n\\providecommand{\\MR}{\\relax\\ifhmode\\unskip\\space\\fi MR }\n\\providecommand{\\MRhref}[2]{%\n  \\href{http:\/\/www.ams.org\/mathscinet-getitem?mr=#1}{#2}\n}\n\\providecommand{\\href}[2]{#2}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{\\bf Introduction}\n\\bigskip\n\nDenote by $S^{1} = \\mathbb{R}\/\\mathbb{Z}$ the circle and  $p :\n\\mathbb{R}\\longrightarrow S^{1}$ the canonical projection. Let  $f$\n be an orientation preserving homeomorphism of $S^{1}$. The homeomorphism  $f$ admits a lift $\\widehat{f} :\n\\mathbb{R}\\longrightarrow \\mathbb{R}$  that is an increasing\nhomeomorphism of  $\\mathbb{R}$  such that $p\\circ\\widehat{f} =\nf\\circ p$. Conversely, the projection of such a homeomorphism of\n$\\mathbb{R}$ is an orientation preserving homeomorphism of\n$S^{1}$. Let  $x\\in S^{1}$. We call \\emph{orbit} of  $x$  by  $f$\nthe subset $O_{f}(x) = \\{f^{n}(x): n\\in\\mathbb{Z} \\}$. Historically, the study of the dynamics of \ncircle homeomorphisms was\ninitiated by Poincar\\'e (\\cite{hP}, 1886), who introduced the\nrotation number of a homeomorphism $f$  of $S^{1}$ as $\\rho (f) =\n\\underset{n\\to +\\infty}{\\lim}\\frac{\\widehat{f}^{n}(\\widehat{x}) -\n\\widehat{x}}{n}~(\\textrm{mod } 1)$, where $\\widehat{x}\\in\n\\mathbb{R}$ such that $p(\\widehat{x})= x$. Poincar\\'e shows that\nthis limit exists and does not depend on neither $x$ nor the lift\n$\\widehat{f}$ of $f$. We say that $f$ is semi-conjugate to the\nrotation  $R_{\\rho(f)}$ if there exists an orientation preserving\nsurjective continuous map $h: S^{1}\\longrightarrow S^{1}$ of degree\none such that $h\\circ f = R_{\\rho(f)}\\circ h$.\n\n{\\it Poincar\\'e's theorem.} Let  $f$  be an homeomorphism of $S^{1}$\nwith irrational rotation number $\\rho(f)$. Then $f$ is\nsemi-conjugate to the rotation  $R_{\\rho(f)}$.\n\nA natural question is whether the semi-conjugation $h$ could be\nimproved to be a conjugation, that is $h$ to be an homeomorphism. In\nthis case, we say that $f$ is topologically conjugate to the\nrotation $R_{\\rho(f)}$. In this direction, Denjoy (\\cite{aD32})\nproves the following:\n\\medskip\n\n{\\it Denjoy's theorem \\cite{aD32}}. Every $C^{2}$-diffeomorphism $f$\nof $S^{1}$ with irrational rotation number $\\rho(f)$ is\ntopologically conjugate to the rotation $R_{\\rho(f)}$.\n\\medskip\n\nDenjoy asked whether or not $C^{2}$-diffeomorphisms $f$ of $S^{1}$\nare ergodic with respect to the Lebesgue measure $m$ ($f$ is said to\nbe ergodic with respect to $m$ if any $f$-invariant measurable set\n$A$ has measure $m(A)$ equal to $0$ or $1$). Simultaneously, Herman\nand Katok gave a positive answer to this question:\n\\medskip\n\n{\\it Herman-Katok's theorem} (\\cite{yKdO89}, \\cite{bHaK95}). Every\n$C^{2}$-diffeomorphism  $f$  with irrational rotation number is\nergodic with respect to the Lebesgue measure $m$.\n\\medskip\n\nIt is well known that an homeomorphism  $f$ of  $S^{1}$  with\nirrational rotation number preserves a unique normalized measure on\n$S^{1}$, denoted by  $\\mu_{f}$. If  $\\widehat{h}$ is the lift of\n$h$,  by taking  $\\widehat{h}(0) = 0$,  the conjugating\nhomeomorphism  $h$ is unique and related to $\\mu_{f}$ by\n$h(x)=p(\\mu_{f}([0,x])) \\in S^{1}$ for $x \\in S^{1}$. Uniqueness of\n$\\mu_{f}$ implies that $\\mu_{f}$ is either singular, or absolutely\ncontinuous with respect to  $m$, in this second case, $h$ is an\nabsolutely continuous function. Recall that $\\mu_{f}$ is said to be\n\\textit{singular} with respect to the Lebesgue measure $m$ on\n$S^{1}$ if there exists a measurable subset $E$ of $S^{1}$ such that\n$\\mu_{f}(E) = 1$ and $m(E) = 0$.\n In fact, if $\\mu_{f}$  is absolutely continuous with respect to\n the Lebesgue measure $m$ and  $f$ is a  $C^{2}$-diffeomorphism,\n $\\mu_{f}$ is necessarily equivalent to  $m$  as a consequence of Herman-Katok's theorem\n above (i.e. $m$ is absolutely continuous with respect to $\\mu_{f}$\n and conversely).\n\\medskip\nIn the sequel we deote by $\\mathbb{R}^{\\ast}=\\mathbb{R}\\backslash\n\\{0\\}$ and  $\\mathbb{N}^{\\ast}=\\mathbb{N}\\backslash \\{0\\}$.\n\n\\textit{Definition}. A real number  $\\alpha\\in ]0, 1[$ is called\n\\textit{Diophantine with exponent $\\delta\\geq 0$} if there is a\nconstant $c(\\alpha)>0$ such that\n$$ \\ (1) \\qquad \\qquad \\arrowvert\\alpha -\\dfrac{p}{q}\\arrowvert\\geq \\dfrac{c(\\alpha)}{q^{2+\\delta}}\\qquad \\textrm{ for any }\\  \\dfrac{p}{q}\\in \\mathbb{Q}.$$\n\\medskip\n\\\n\\\\\nA number that is neither rational nor Diophantine is called a\n\\textit{Liouville number}. \\\n\\\\\n Every real number $\\alpha\\in ]0, 1[$ has a continued fraction expansion\nrepresented by\n$$\\alpha = \\frac{1}{a_{1}+ \\frac{1}{a_{2}+ \\dots}}: =\n[a_{1},a_{2},\\dots,a_{n},\\dots]$$ \\\n\\\\\nwhere  $a_{m} \\in \\mathbb{N}^{\\ast}$, $m\\in \\mathbb{N}^{*}$ are\ncalled \\textit{partial quotients} of $\\alpha$. When ($a_{m})_{m\\in\n\\mathbb{N}}$ is bounded, $\\alpha$ is said to be of \\textit{bounded\ntype}. This is equivalent to the fact that $(1)$ holds with $\\delta\n= 0$.\n\\medskip\n\nThe problem of smoothness of the conjugacy $h$ of smooth\ndiffeomorphisms to rotations is now very well understood (see for\ninstance \\cite{mH79}, \\cite{yKdO89}, \\cite{kmKyS89}, \\cite{KT09},\n\\cite{jcY84}).\n\n\n\n\\medskip\n\n\n\nWe refer the reader to the books \\cite{aN10} and \\cite{wDvS91} for a\nthorough account on circle homeomorphisms.\n\\smallskip\n\nThe situation is more complicated for circle homeomorphisms with\nbreak points or shortly, class $P$-homeomorphisms (see the\ndefinition below). This class are known to satisfy the conclusion of\nDenjoy's theorem (Corollary 2.6) (see also \\cite{yKdO89};\n\\cite{mH79}, chapter VI) and, with additional regularity, of\nHerman-Katok's theorem (see \\cite{kaA06}). However,\nKatznelson-Ornstein's theorem \\cite{yKdO89} cannot be extended in\ngeneral to class $P$. The study of the regularity of the invariant\nmeasures of class $P$-homeomorphisms arises then naturally.\n\\bigskip\n\n\\textbf{Class  $P$-homeomorphisms} \\\\\nThe following definition is du to M.R. Herman.\n\\begin{defn}(see \\cite{mH79}, p.74) An orientation preserving homeomorphism $f$ of $S^{1}$ is called a \\emph{class  $P$}-homeomorphism if it is differentiable\nexcept at finitely many points, the so called \\textit{break points}\nof $f$, at which left and right derivatives (denoted, respectively,\nby $\\textrm{Df}_{-}$ and $\\textrm{Df}_{+}$) exist and such that the\nderivative  $\\textrm{Df}: S^{1} \\longrightarrow \\mathbb{R}_{+}^{*}$\nhas the following properties:\n\\begin{itemize}\n\\item [\\textbullet] there exist two constants  $0<a<b<+\\infty$  such that: $a<\\textrm{Df}(x)<b,$  for every $x$, where $\\textrm{Df}$  exists,\n\n\\item [\\textbullet]  $a <\\textrm{Df}_{+}(c)< b$ and  $a<\\textrm{Df}_{-}(c)< b$  at the break points $c$.\n\n\\item [\\textbullet]  $\\log \\textrm{Df}$  has bounded variation on  $S^{1}$.\n\\end{itemize}\n\\end{defn}\n\\medskip\n\nWe pointed out that the third condition implies the two ones.\n\\medskip\nThe ratio $\\sigma_{f}(c): =\n\\dfrac{\\textrm{Df}_{-}(c)}{\\textrm{Df}_{+}(c)}$  is called the\n\\emph{$f$-jump} in $c$.\n\\medskip\n\n Denote by\n\\begin{itemize}\n \\item [\\textbullet] $C(f) = \\{c_{0}, c_{1}, c_{2},\\dots, c_{p}\\}$  the set of break points of $f$ in\n$S^{1}$\n\n \\item [\\textbullet] $c_{p+1}: = c_{0}$.\n\n \\item [\\textbullet] $\\pi_{s, O_{f}(c)}(f): =  \\underset{x\\in C(f)\\cap O_{f}(c)}{\\prod}\\sigma_{f}(x)$,\nfor every $c\\in S^{1}$. \\\n\\\\\n \\item [\\textbullet] $\\pi_{s}(f)$ the product of $f$-jumps in the break points of $f$:\n$$\\pi_{s}(f) =  \\underset{c\\in C(f)}{\\prod}\\sigma_{f}(c).$$\n\\\\\n\\item [\\textbullet] $SO(f)=\\{O_{f}(c):~c \\in C(f)~\\textrm{and}~\\pi_{s, O_{f}(c)}(f)\\neq 1\\}$\n\n\\end{itemize}\n\\bigskip\n\nThe total variation of $\\log \\textrm{Df}$ we denote by $V =\n\\textrm{Var}(\\log \\textrm{Df})$. We have $$~V : \\ = \\\n\\sum_{j=0}^{p}\\textrm{Var}_{[c_{j},c_{j+1}]}\\log \\textrm{Df} +\n|\\log(\\sigma_{f}(c_{j}))|< +\\infty.$$ In this case,  $V$ is the\ntotal variation of  $\\log \\textrm{Df}$,  $\\log \\textrm{Df}_{-}$,\n$\\log \\textrm{Df}_{+}$.\n\\bigskip\n\nWe notice the following properties:\n\\begin{itemize}\n \\item [\\textbullet] If $f$ is a class $P$-homeomorphism of $S^{1}$ which is $C^{1}$ on $S^{1}$ then $f$ is a $C^{1}$-diffeomorphism.\n\n\\item [\\textbullet] If $f$ is a class $P$-homeomorphism of $S^{1}$ then $D^{2}f \\in L^{1}(S^{1})$: Indeed, this follows from\n(\\cite{HS}, Theorem $18.14$, p. 284) since $\\textrm{Df}$ has bounded\nvariation on $S^{1}$.\n\n\\item [\\textbullet] If $f$ is a class $P$-homeomorphism of $S^{1}$ and $\\textrm{Df}$ is absolutely continuous on every connected interval of $S^{1}\\backslash C(f)$ then $f\\in C^{1}(S^{1}\n\\backslash C(f))$.\n\\end{itemize}\n\n Among the simplest examples of class $P$-homeomorphisms, there are:\n\\medskip\n\n\\textbullet \\; $C^{2}$-diffeomorphisms,\n\n\\textbullet \\; Piecewise linear $\\textrm{PL}$-homeomorphisms.\n\nAn orientation preserving homeomorphism $f$ of $S^{1}$ is called a\n\\emph{PL-homeomorphism} if $f$ is differentiable except at finitely\nmany break points $(c_{i})_{1\\leq i\\leq p}$ of $S^{1}$  such that\nthe derivative  $\\textrm{Df}$ is constant on each  $]c_{i}, \\\nc_{i+1}[$.\n\\bigskip\n\nDenote by\n\\begin{itemize}\n\n\\item [\\textbullet] $\\mathcal{P}(S^{1})$ the set of class $P$-homeomorphisms of $S^{1}$.\n\n\\item [\\textbullet] $\\textrm{PL}(S^{1})$ the set of orientation preserving piecewise linear $\\textrm{PL}$-homeomorphisms of $S^{1}$.\n\\end{itemize}\n\\medskip\nWe notice that $\\mathcal{P}(S^{1})$ is a group which contains\n$\\textrm{PL}(S^{1})$ (cf. \\cite{am08}).\n\\bigskip\n\n\\begin{defn}\\cite{am15}  Let  $f\\in \\mathcal{P}(S^{1})$. We say that $f$ has the \\textit{($D$)-property}\nif the product of $f$-jumps at the break points of each orbit is\ntrivial, that is  $\\pi_{s, O_{f}(c)}(f)= 1$, for every $c\\in C(f)$.\n\\end{defn}\n\\medskip\n\nIn particular, if $f$ has the ($D$)-property, then $\\pi_{s}(f) = 1$.\nConversely, if all break points belong to the same orbit and\n$\\pi_{s}(f) = 1$ then  $f$ has the ($D$)-property.\n \\bigskip\n\n Let  $f\\in \\mathcal{P}(S^{1})$. We say that $f$ satisfies the \\textit{Katznelson-Ornstein (KO)} if\n $\\textrm{Df}$ is absolutely continuous on every continuity interval of $\\textrm{Df}$.\n\n\n\\medskip\n\n\n\\medskip\n\n\n\\textbullet ~~ Recently, there has been a significant progress in\nthe problem of the regularity of the conjugating map between two\nclass $P$-homeomorphisms with the \\textit{same}\nirrational rotation number. The case of two class $P$-homeomorphisms with one break point and with the\nsame jump, was studied by Khanin and\nKhmelev in \\cite{KhKm} and by Teplinskii and Khanin in \\cite{TK}.\n\n\\medskip\n\n\\textbullet ~~ The case of two class $P$-homeomorphisms with \\textit{one} break point and with\n\\textit{distinct} jumps, was studied by Dzhalilov, Akin and Temir in\n\\cite{AHS10}. Their results show that the conjugation map between two such maps is singular.\n\n\\textbullet ~~ The case of two class $P$-homeomorphisms with \\textit{two} break points was studied by Akhadkulov,\nDzhalilov and Mayer in \\cite{HAD11} (see Corollary \\ref{c:14}).\n\\medskip\n\n\n\\textbullet ~~ The case of \\textit{several} break point with\n\\textit{distinct total jumps}, was studied by Dzhalilov, Mayer and Safarov in\n\\cite{DMS}, and independently by the first author in \\cite{A}.\nTheir results show that the conjugation map between two such maps is singular:\n\n{\\it Theorem $($\\cite{A}, \\cite{DMS}$)$} \\textit{Let $f$ and $g$ be two class $P$-homeomorphisms of the circle $S^{1}$ and same\nirrational rotation number. Assume that $f$ and $g$ satisfy that satisfy the Katznelson-Ornstein (KO).\nIf $\\pi_{s}(f)\\neq \\pi_{s}(g)$ then the homeomorphism map $h$ conjugating $f$ and $g$ is a singular function i.e. it is continuous on $S^{1}$ and $\\textrm{Dh}(x)=0$ a.e. with respect to the Lebesgue measure.}\n\\bigskip\n\n\\begin{defn}\nWe say that two class $P$-homeomorphisms $f$ and $g$ of the circle\n$S^{1}$ are \\textit{break-equivalent} if there exists a topological\nconjugating $h$ such that\n\\begin{itemize}\n \\item[(1)] ~~ $h(\\mathrm{SO}(f)) = \\mathrm{SO}(g)$ \\ and\n \\item[(2)] ~~ $\\pi_{s, O_{g}(h(c))}(g) = \\pi_{s, O_{f}(c)}(f)$, ~~ \\textrm{for all}~~ $c\\in\nC(f)$\n\\end{itemize}\n\\end{defn}\n\\medskip\n\nIn particular, if all points of $C(f)$ (resp. $C(g)$) are on pairwise\ndistinct orbits then\n\n- $\\mathrm{card}(\\mathrm{SO}(f)) = \\mathrm{card}(C(f))$\n(resp. $\\mathrm{card}(\\mathrm{SO}(g))=\\mathrm{card}(C(g))$),\n\n- $f$ and $g$ are break-equivalent if there exists a topological\nconjugation $h$ from $f$ to $g$ such that:\n\\begin{itemize}\n \\item[(1)] ~~ $h(C(f))=C(g)$ \\ and\n \\item[(2)] ~~ $\\sigma_{g}(h(c))=\\sigma_{f}(c) ~~ \\textrm{for all} ~~ c \\in C(f).$\n\\end{itemize}\n\\bigskip\n\nThis definition coincides with that of \\cite{KcDs}. It is easy to see\nthat if there is a $C^{1}-$ conjugation between $f$ and $g$ then $f$\nand $g$ are break-equivalent. The case of break-equivalent\n$C^{2+\\alpha}$ homeomorphisms $f$ and $g$ with\n$\\pi_{s}(f)=\\pi_{s}(g)=1$ and some combinatorial conditions was\nstudy by Cunha-Smania in \\cite{KcDs}. It was proved that any two\nsuch homeomorphisms are $C^{1}-$ conjugated.\n\\bigskip\n\\\\\nIn the present paper we consider \\textit{non break equivalent}\nclass $P$-homeomorphisms having \\textit{several break points} with\ncoinciding irrational rotation number of bounded type. The main purpose is to prove the following:\n\n\\\n\\\\\n{\\bf Main Theorem }(Nonrigidity). \\textit{Let $f$ and $g$ be two\nclass $P$-homeomorphisms of the circle $S^{1}$ with several break\npoints that satisfy the Katznelson-Ornstein (KO) and they have the\nsame irrational rotation number of bounded type. If $f$ and $g$ are not break equivalent then\nthe homeomorphism $h$ conjugating $f$ to $g$ is a singular function\ni.e. it is continuous on $S^{1}$ and $\\textrm{Dh}(x)=0$ a.e. with\nrespect to the Lebesgue measure}.\n\\medskip\n\nAs a consequence we have\n\\medskip\n\n\\begin{cor}\\label{c:12}  Let $f$ and $g$ satisfy the assumptions of the main theorem. If \\textrm{card} $(SO(f))\\neq $ \\textrm{card} $(SO(g))$ then\nthe map conjugating $f$ to $g$ is a singular function. In particular, this hold if $f$ (resp. $g$) has exactly $n$\nbreak points (resp. $m$ break points) lying on pairwise distinct \n$f$-orbits (resp. $g$-orbits) with $n, m\\in \\mathbb{N}$, $n\\neq m$.\n\\end{cor}\n\\bigskip\n\n\\begin{cor}\\label{c:13}  Let $f$ and $g$ satisfy the assumptions of the main theorem. If there is some point $d \\in SO(f)$\nsuch that $\\pi_{s,O_{g}(d)}(g) \\notin \\{\\pi_{s,O_{f(c)}}(f): ~~c \\in\nC(f)\\}$ then the map $h$ conjugating $f$ to $g$ is singular.\n\\end{cor}\nIn particular, for \\textit{non break equivalent} homeomorphisms with\ntwo break points, we get, as consequence:\n\\medskip\n\n\\begin{cor}\\label{c:14} $($Akhadkulov-Dzhalilov-Noorani's theorem$)$ \\cite{ADN}\nLet $f_{i} \\in \\mathcal{P}(S^{1}),~i=1,2$ be circle homeomorphisms with\ntwo break points $a_{i},~b_{i}$. Assume that $f_{i},~i=1,2$ satisfy\nthe Katznelson-Ornstein (KO) condition and $D^{2}f_{i}\\in\nL^{p}(S^{1})$ for some $p>1$. Assume that:\n\\begin{itemize}\n  \\item [(i)] The rotation numbers $\\rho(f_{i})$ of $f_{i},~i=1,2$\nare irrational of bounded type and coincide\n$\\rho(f_{1})=\\rho(f_{2})=\\rho, ~\\rho \\in \\mathbb{R}\\backslash\n\\mathbb{Q}$,\n  \\item [(ii)] $\\sigma_{f_{1}}(a_{1}) \\notin\n\\{\\sigma_{f_{2}}(a_{2}),~\\sigma_{f_{2}}(b_{2})\\}$,\n  \\item [(iii)]\n$\\sigma_{f_{1}}(a_{1})~\\sigma_{f_{1}}(b_{1})=\\sigma_{f_{1}}(a_{2})~\\sigma_{f_{1}}(b_{2})$,\n  \\item [(iv)] The break points of $f_{i},~i=1,2$ do not lie on the\nsame orbit,\n\\end{itemize}\nThen the map $h$ conjugating $f_{1}$ to $f_{2}$ is singular.\n\\end{cor}\n\\medskip\n\n\\begin{cor}\\label{c:15}\nLet $f$ and $g$ satisfy the assumptions of the main theorem. Then:\n\\begin{itemize}\n    \\item [(i)] If $g$ does not have the $(D)-$ property and $f$ has\nthe $(D)-$ property then the map conjugating $f$ to $g$ is\nsingular.\n    \\item [(ii)] If $f$ and $g$ have the $(D)-$property and $D^{2}f,~D^{2}g \\in\nL^{p}(S^{1})$ for some $p>1$ then the map conjugating $f$ to $g$ is\nabsolutely continuous.\n  \\end{itemize}\n\\end{cor}\n\\medskip\n\nIn particular:\n\\medskip\n\n\\begin{cor} $($Adouani-Marzougui's theorem $($\\cite{am12}, Theorem B$)$$)$\\label{c:16}\nLet $f$  satisfies the assumptions of the main theorem. Then:\n\\begin{itemize}\n    \\item [(i)] If $f$ does not have the $(D)$-property then the invariant measure $\\mu_{f}$ is singular with respect\nto the Lebesgue measure $m$.\n    \\item [(ii)] If $f$ has the $(D)$-property and $D^{2}f \\in\nL^{p}(S^{1})$ for some $p>1$, then the measure $\\mu_{f}$ is\nequivalent to the Lebesgue measure $m$.\n  \\end{itemize}\n\\end{cor}\n\\medskip\n\n\\begin{cor} $($\\cite{am12}, Corollary 1.5$)$ \\label{c:17} Let $f\\in \\mathrm{PL}(S^{1})$\nhave irrational rotation number $\\alpha$ of bounded type. Then the following are equivalent:\n\\begin{itemize}\n \\item [(i)] $f$ has the ($D$)-property\n\n \\item [(ii)] The measure $\\mu_{f}$ is equivalent to the Lebesgue measure $m$.\n\\end{itemize}\n\\end{cor}\n\\medskip\n\n\\textbf{Remark.} The main Theorem and in particular Corollary \\ref{c:17}  cannot be extended to rotation number not of bounded type, since very recently,\nTeplinsky \\cite{aT15} constructs an example of a (PL) circle homeomorphism with $4$ non-trivial break points\nlying on different orbits that has invariant measure equivalent to the Lebesgue measure $m$.\nThe rotation number for such example can be chosen either Diophantine or Liouvillean, but not of bounded type.\n\n\\section{\\bf Notations and preliminary results}\n\\bigskip\n\n \\textit{\\bf 2.1. Dynamical partitions}. Let  $f$ be a homeomorphism of  $S^{1}$  with irrational rotation number  $\\alpha = \\rho(f)$.\nWe identify $\\alpha$ to its lift $\\widehat{\\alpha}$ in $]0, 1[$. Let\n$(a_{n})_{n\\in \\mathbb{N}^{\\ast}}$ be the partial quotients of\n$\\alpha$ in the continued fractions expansion. For $n\\in\n\\mathbb{N}^{\\ast}$, the fractions $[a_{1},a_{2},\\dots,a_{n}]$ are\nwritten in the form of irreducible fractions $\\frac{p_{n}}{q_{n}}$.\nThe sequence $\\frac{p_{n}}{q_{n}}$ converges to $\\alpha$ and we say\nthat $\\frac{p_{n}}{q_{n}}$ are \\textit{rational approximations} of\n$\\alpha$. Their denominators $q_{n}$ satisfy the following recursion\nrelation:\n$$q_{n} = a_{n}q_{n-1}+q_{n-2}, ~n\\geq 2, ~q_{0}=1, ~q_{1}=a_{1}.$$\n\nLet $x_{0}\\in S^{1}$ fixed. Denote by:\n\n$$\\Delta_{0}^{(n)}(x_{0}) = \\begin{cases}\n{[x_{0}, f^{q_{n}}(x_{0})]}, &\\text{ if  $n$  is  even }  \\\\\n{[f^{q_{n}}(x_{0}), x_{0}]}, &\\text{ if  $n$  is  odd }\n\\end{cases}$$\n\\\n\\\\\n$$\\Delta_{i}^{(n)}(x_{0}) : \\ = f^{i}\\left(\\Delta_{0}^{(n)}(x_{0})\\right), \\ i\\in \\mathbb{Z}$$\n\\medskip\n\n\\textit{In all the sequel, we deal with the case $n$ odd} (the case\n$n$ even is obtained by reversing the orientation of $S^{1}$).\n\\smallskip\n\nWe have then:\n\\medskip\n\n\\begin{lem}[See \\cite{yS94}]\\label{l:23} The segments  $\\Delta_{i}^{(n-1)}(x_{0}) = f^{i}\\left(\\Delta_{0}^{(n-1)}(x_{0})\\right), \\ 0\\leq\ni<q_{n}$  and  $\\Delta_{j}^{(n)}(x_{0}) =\nf^{j}\\left(\\Delta_{0}^{(n)}(x_{0})\\right), \\ 0\\leq j<q_{n-1}$ cover\n$S^{1}$ and that their interiors are mutually disjoint.\n\\end{lem}\n\\medskip\n\nThe partition denoted by $\\xi_{n}(x_{0}): =\n\\big\\{\\Delta_{i}^{(n-1)}(x_{0}); \\ \\Delta_{j}^{(n)}(x_{0}), \\ 0\\leq\ni<q_{n}, \\ 0\\leq j<q_{n-1}\\big\\}$  is called the \\textit{$n$-th\ndynamical partition} of the point $x_{0}$. It is defined by the\norder of points $x_{0}, \\dots, f^{q_{n-1}+q_{n}-1}(x_{0})$. The\nprocess of passing from $\\xi_{n}(x_{0})$ to $\\xi_{n+1}(x_{0})$ is\ndescribed by remaining intact the elements\n $\\Delta_{j}^{(n)}(x_{0})$, while each element $\\Delta_{i}^{(n-1)}(x_{0})$, ($0\\leq i<q_{n}$) is partitioned into $a_{n+1}+1$ sub-segments; since  $q_{n+1} = a_{n+1}q_{n}+q_{n-1}$:\n$$\\Delta_{i}^{(n-1)}(x_{0}) = \\Delta_{i}^{(n+1)}(x_{0})~\\cup~\\bigcup_{s=0}^{a_{n+1}-1}\n \\Delta_{i+q_{n-1}+sq_{n}}^{(n)}(x_{0})$$\nFor every  $n\\geq 1,~\\xi_{n+1}(x_{0})$  is finer than\n$\\xi_{n}(x_{0})$ in the following sense: every element\n$\\xi_{n}(x_{0})$ is a union of elements  $\\xi_{n+1}(x_{0})$.\n\\medskip\n\nThe following lemmas are easy to check.\n\\begin{lem}\\label{l:24} Let  $n\\geq 1$  be an integer and $y_{1}\\in\nS^{1}$. Set $y_{2} = f^{q_{n-1}}(y_{1})$,  $y_{3} =\nf^{q_{n-1}}(y_{2})$, $\\Delta_{i}^{(n-1)}(y_{1}) = f^{i}([y_{1},\ny_{2}])$  and  $\\Delta_{j}^{(n-1)}(y_{2}) = f^{j}([y_{2}, y_{3}])$,\n$0\\leq i, \\ j < q_{n}$. Then $\\Delta_{i}^{(n-1)}(y_{1})\\cap\n\\Delta_{j}^{(n-1)}(y_{2})$ has non empty interior if and only if\n\\textit{one} of the following conditions holds:\n\\medskip\n\n\\item \\begin{enumerate}\n\\item  $j = i-q_{n-1}$ and $q_{n-1}\\leq i<q_{n}$; in this case we have\n$$\\Delta_{i}^{(n-1)}(y_{1}) = \\Delta_{j}^{(n-1)}(y_{2}).$$\n\\item  $j = q_{n}-q_{n-1}+i$ and $0\\leq i<q_{n-1}$; in this case we have\n\n$$\\Delta_{j}^{(n-1)}(y_{2}) = f^{q_{n}}(\\Delta_{i}^{(n-1)}(y_{1})).$$\n\\end{enumerate}\n\\end{lem}\n\\medskip\n\\bigskip\n\n\n\\begin{lem}\\label{l:25} Let  $n\\geq 1$  be an integer and  $y_{1}\\in\nS^{1}$. Set  $y_{2} = f^{q_{n-1}}(y_{1})$,  $y_{3} =\nf^{q_{n-1}}(y_{2})$. Then for every  $x\\in S^{1}\\backslash\nO_{f}(y_{1})$, there exists a unique $0\\leq i = i_{n}(x) <q_{n}$\nsuch that $x\\in f^{i}(]y_{1},y_{2}[)~\\cup\nf^{\\varphi_{n}(i)}(]y_{2},y_{3}[)$ where $\\varphi_{n}:\n[0,q_{n}[\\longrightarrow [0,q_{n}[$  is a bijective map given by:\n\n$$\\varphi_{n}(i) =\n\\begin{cases}\nq_{n}-q_{n-1}+i,~ &\\hbox{if} \\ \\ ~~0\\leq i<q_{n-1}\\\\\ni-q_{n-1},~ &\\hbox{if} \\ \\ ~~q_{n-1}\\leq i<q_{n}\n\\end{cases}$$\n\\end{lem}\n\\medskip\n\\bigskip\n\n\\textit{\\bf 2.2. Useful inequalities.} The proof of the following\nresults are based on the dynamical partition of  $S^{1}$.\n\\bigskip\n\n{\\it Finzi distortion Lemma}~\\cite{aF50}. Let  $f\\in\n\\mathcal{P}(S^{1})$  with irrational rotation number. For all  $z\\in\nS^{1}$;  $x,~y\\in [z,~f^{q_{n-1}}(z)]$ and for all integer $0\\leq k\n\\leq q_{n}$, we have:\n$$~e^{-V}\\leq\\frac{\\textrm{Df}^{k}(x)}{\\textrm{Df}^{k}(y)}\\leq\ne^{V}.$$\n\n\\\n\\\\\nNotice that Finzi distortion Lemma is used for the proof of\nHerman-Katok's theorem.\n\\medskip\n\nThe following Lemma plays a key role for studying metrical\nproperties of the homeomorphism $f$:\n\\bigskip\n\n{\\it Denjoy's inequality}. Let $f\\in \\mathcal{P}(S^{1})$ with\nirrational rotation number. For all $x\\in S^{1}$  and all $n\\in\n\\mathbb{N}$, we have  $$e^{-V}\\leq \\textrm{Df}^{q_{n}}(x)\\leq\ne^{V}$$ where $V= \\textrm{Var}(\\log \\textrm{Df})$.\n\\medskip\n\nThe proof of this inequality results from Finzi distortion Lemma. It\ncan be also obtained by applying Denjoy-Koksma's inequality to the\nfonction  $\\log \\textrm{Df}$ (cf. Herman \\cite{mH79}).\n\\medskip\n\nHere and further on, by $m([a,b])$ we mean the smallest length of the two\narcs $[a,b]$ and $[b,a]$ on $S^{1}$.\n\nUsing Denjoy's inequality, one has:\n\\medskip\n\n\\begin{cor}[Geometric inequality]\\label{c:24} There exists a constant $C>0$ such that for any $x_{0}\\in S^{1}$, $n\\geq 1$ and any element\n$\\Delta^{(n)}$ of the dynamical partition $\\xi_{n}(x_{0})$, we have\n\\; $m(\\Delta^{(n)})\\leq C\\lambda^{n}$, where $\\lambda =\n(1+e^{-V})^{-\\frac{1}{2}}< 1$.\n\\end{cor}\n\\medskip\n\nFrom Corollary \\ref{c:24} it follows that every orbit of every $x\\in\nS^{1}$ is dense in $S^{1}$ and this implies the following\ngeneralization of the classical Denjoy theorem:\n\\medskip\n\n\\begin{cor}[Denjoy's theorem: the class P] Let $f\\in \\mathcal{P}(S^{1})$ with irrational rotation number $\\alpha = \\rho(f)$.\nThen $f$ is topologically conjugate to the  rotation $R_{\\alpha}$.\n\\end{cor}\n\\medskip\n\nIn the following Lemma we have to compare the lengths of iterates\ndifferent of intervals.\n\\medskip\n\n\\begin{lem}\\label{l:31} Let $f\\in \\mathcal{P}(S^{1})$ with irrational rotation number $\\alpha = \\rho(f)$.\nLet  $n\\in \\mathbb{N}^{*}$  and  $z_{1}\\in S^{1}$. Set $z_{2} =\nf^{q_{n-1}}(z_{1}), \\ z_{3} = f^{q_{n-1}}(z_{2})$. Then for any\nsegments  $K_{1}, \\ K_{2}\\subset [z_{1},z_{3}]$, one has:\\\\\n\n$$e^{-2V}\\dfrac{m(K_{1})}{m(K_{2})}\\leq\n\\dfrac{m(f^{j}(K_{1}))}{m(f^{j}(K_{2}))}\\leq\ne^{2V}\\dfrac{m(K_{1})}{m(K_{2})}$$ for all \\; $j=-q_{n}, \\dots\n,0,\\dots, q_{n}$.\n\\end{lem}\n\\medskip\n\n\\begin{proof} If  $j= q_{n}$,  Lemma \\ref{l:31} is a consequence of Denjoy's inequality.\nWe suppose that  $0\\leq j<q_{n}$. Let  $\\mathcal{L}$ be the set of\nsegments in  $[z_{1},z_{2}]$\n or in  $[z_{2},z_{3}]$. If  $K\\in \\mathcal{L}$ then  $K\\subset\n[z,f^{q_{n-1}}(z)]$  with  $z=z_{1}~\\textrm{or}~z=z_{2}$.\n\n Since $$\\frac{m(f^{j}(K))}{\\textrm{Df}^{j}(z_{2})} = \\int_{K}\\frac{\\textrm{Df}^{j}(t)}{\\textrm{Df}^{j}(z_{2})}dm(t),$$\n\\medskip\n\nby Finzi distortion Lemma applied to $f$  on $[z,f^{q_{n-1}}(z)]$,\nwe get:\n\n   $$e^{-V}\\leq \\frac{\\textrm{Df}^{j}(t)}{\\textrm{Df}^{j}(z_{2})}\\leq\ne^{V}, \\ \\textrm{ for every } \\ t\\in K.$$\n\\medskip\n\nBy integrate this last inequality, we obtain\n\\begin{equation}e^{-V}m(K)\\leq\n\\frac{m(f^{j}(K))}{\\textrm{Df}^{j}(z_{2})}\\leq e^{V}m(K)\n\\end{equation}\n\\medskip\n\nLet  $K_{1}, \\ K_{2}\\subset [z_{1},z_{3}]$  be two segments. We\ndistinguish three cases:\n\\medskip\n\na) $K_{1}\\in \\mathcal{L}$  and  $K_{2}\\in \\mathcal{L}$: in this\ncase, the inequality (2.1) implies: \\\\\n$$e^{-V}m(K_{1})\\leq\n\\frac{m(f^{j}(K_{1}))}{\\textrm{Df}^{j}(z_{2})}\\leq\ne^{V}m(K_{1})$$~~and~~\n$$e^{-V}m(K_{2})\\leq \\frac{m(f^{j}(K_{2}))}{\\textrm{Df}^{j}(z_{2})}\\leq\ne^{V}m(K_{2}),$$ \\\\\ntherefore\n$$e^{-2V}\\frac{m(K_{1})}{m(K_{2})}\\leq\\frac{m(f^{j}(K_{1}))}{m(f^{j}(K_{2}))}\n \\leq e^{2V}\\frac{m(K_{1})}{m(K_{2})}.$$\n\\medskip\n\nb) $K_{1}\\notin \\mathcal{L}$ and $K_{2}\\in \\mathcal{L}$: in this\ncase, take $K_{1} = K_{1}^{\\prime}\\cup K_{1}^{\\prime\\prime}$  where\n$K_{1}^{\\prime}\\subset [z_{1},z_{2}]$ and\n$K_{1}^{\\prime\\prime}\\subset [z_{2},z_{4}]$ are two segments, then\n$K_{1}^{\\prime}\\in \\mathcal{L}$ and\n$K_{1}^{\\prime\\prime}\\in\\mathcal{L}$. By ~ a), we see that\n\\\\\n$$e^{-2V}\\frac{m(K_{1}^{\\prime})}{m(K_{2})}\\leq\\frac{m(f^{j}(K_{1}^{\\prime}))}{m(f^{j}(K_{2}))}\n \\leq e^{2V}\\frac{m(K_{1}^{\\prime})}{m(K_{2})}$$ and\n $$e^{-2V}\\frac{m(K_{1}^{\\prime\\prime})}{m(K_{2})}\\leq\\frac{m(f^{j}(K_{1}^{\\prime\\prime}))}{m(f^{j}(K_{2}))}\n \\leq e^{2V}\\frac{m(K_{1}^{\\prime\\prime})}{m(K_{2})}.$$\n\\medskip\n\nAdding these inequalities, we get\n  $$e^{-2V}\\frac{m(K_{1})}{m(K_{2})}\\leq\\frac{m(f^{j}(K_{1}))}{m(f^{j}(K_{2}))}\n \\leq e^{2V}\\frac{m(K_{1})}{m(K_{2})}.$$\n\\medskip\n\nc) $K_{1}\\notin \\mathcal{L}$  and  $K_{2}\\notin \\mathcal{L}$: in\nthis case, take  $K_{2} = K_{2}^{\\prime}\\cup K_{2}^{\\prime\\prime}$\nwhere  $K_{2}^{\\prime}\\subset [z_{1},z_{2}]$ and\n$K_{2}^{\\prime\\prime}\\subset [z_{2},z_{3}]$ are two segments. By\napplying ~ b) to  $K_{1}$  and\n $K_{2}^{\\prime}$ (resp. $K_{2}^{\\prime\\prime}$), we obtain the inequality of the Lemma.\nApply the same result to $f^{-1}$ instead of $f$ (since the\nconvergent sequences of the continued fractions of $\\varrho(f^{-1})=1-\\varrho(f)$\nand $\\varrho(f)$ have the same denominators).\n\\end{proof}\n\\bigskip\n\n\\textit{\\bf 2.3. Some ratio tools.} Let us introduce the notion of\nratio distortion with respect to a homeomorphism.\n\\medskip\n\n\\begin{defn} Let  $x_{1},x_{2},x_{3}$  be real numbers such that  $x_{1}<x_{2}<x_{3}$.\n\\medskip\n\\\n\\\\\ni)  The \\textit{ratio} of the triple ($x_{1},x_{2},x_{3}$) is the\nreal number defined as\n\n $$\\textrm{r}(x_{1},x_{2},x_{3}) =\n\\frac{x_{2}-x_{1}}{x_{3}-x_{2}}.$$\n\n\\\n\\\\\nii) The \\textit{ratio distortion} of the triple\n($x_{1},x_{2},x_{3}$) with respect to a strictly increasing function\n$F: \\mathbb{R}\\longrightarrow \\mathbb{R}$  is the real number\ndefined as\n\n$$\\textrm{Dr}_{F}(x_{1},x_{2},x_{3}) =\n\\frac{\\textrm{r}(F(x_{1}),F(x_{2}),F(x_{3}))}{r(x_{1},x_{2},x_{3})}\n= \\frac{F(x_{2})-F(x_{1})}{x_{2}-x_{1}}\n\\frac{x_{3}-x_{2}}{F(x_{3})-F(x_{2})}$$\n\\end{defn}\n\\medskip\n\nNotice that:\n\\medskip\n\n- The ratio $\\textrm{r}$ is translation invariant:\n$$\\textrm{r}(x_{1}+a,x_{2}+a,x_{3}+a) = \\textrm{r}(x_{1},x_{2},x_{3}), \\ a\\in \\mathbb{R}.$$\n\n- The ratio distortion $\\textrm{Dr}$ is multiplicative with respect\nto composition: for two functions $F$ and $G$ on $\\mathbb{R}$, we\nhave\n$$\\textrm{Dr}_{G\\circ F}(x_{1},x_{2},x_{3}) = \\textrm{Dr}_{G}(F(x_{1}),F(x_{2}),F(x_{3}))\\textrm{Dr}_{F}(x_{1},x_{2},x_{3}).$$\n\\medskip\n\nLet $z_{1},z_{2},z_{3}\\in S^{1}$ with lifts $\\widehat{z_{1}}, \\\n\\widehat{z_{2}}, \\ \\widehat{z_{3}}$ and $z_{1}\\prec z_{2}\\prec\nz_{3}\\prec z_{1}$  ordered on $S^{1}$. Define\n\n$$\\widetilde{z_{i}}:=\n\\begin{cases}\n    \\widehat{z_{i}}, & \\ \\textrm{ if } \\  \\widehat{z_{1}}< \\widehat{z_{i}} <1\\\\\n    1+\\widehat{z_{i}}, & \\ \\textrm{ if } \\  0\\leq \\widehat{z_{i}}< \\widehat{z_{1}}\n \\end{cases}$$\n\\\n\\\\\nwhere $i=2,3$. Obviously we have $\\widetilde{z_{1}} <\n\\widetilde{z_{2}} < \\widetilde{z_{3}}$. The vector\n$(\\widetilde{z_{1}},\\widetilde{z_{2}},\\widetilde{z_{3}}) \\in\n\\mathbb{R}^{3}$ is called the\\textit{ lifted vector } of\n$(z_{1},z_{2}, z_{3})\\in (S^{1})^{3}$.\n\nConsider now a homeomorphism $f$ of $S^{1}$  with lift\n$\\widehat{f}$. We define the \\textit{ratio distortion} of the triple\n$(z_{1},z_{2},z_{3})$, $z_{1},z_{2},z_{3}\\in S^{1}$ with respect to\n$f$  by\n$$\\textrm{Dr}_{f}(z_{1},z_{2},z_{3}): = \\textrm{Dr}_{\\widehat{f}}(\\widetilde{z_{1}},\\widetilde{z_{2}},\\widetilde{z_{3}})$$  where\n$(\\widetilde{z_{1}},\\widetilde{z_{2}},\\widetilde{z_{3}})$ is the\nlifted vector of $(z_{1},z_{2}, z_{3})$. This definition is\nindependent of the lift of $f$  since the ratio is translation invariant.\n\\medskip\n\n\\begin{defn}\\label{d:32} Let $R>1$ be a real number and $x_{0}\\in S^{1}$. We say that a triple\n$(z_{1},z_{2},z_{3})$~ of~ $S^{1}$ ($z_{1}\\prec z_{2}\\prec z_{3})$\n satisfies the conditions $(a)$~~\\textrm{and}~~$(b)$ for the point $x_{0}$ and\nthe constant $R$ if:\\\\\n\\medskip\n\n\\begin{itemize}\n \\item [(a)]: $R^{-1}\\leq\\dfrac{m([z_{2},~z_{3}])}{m([z_{1},~z_{2}])}\\leq R$\n\\\n\\\\\n\\item [(b)]: $\\underset{1\\leq i\\leq 3}{\\max}~m([x_{0},z_{i}])\\leq R m([z_{1},z_{2}])$\n\\end{itemize}\n\\end{defn}\n\\medskip\n\nWe call two intervals in $S^{1}$ $R$-\\textit{comparable} if the\nratio of their lenghts is in $[R^{-1}, R]$.\n\\bigskip\n\\medskip\n\n\\textit{\\bf 2.4. Reduction.} In this subsection, we will reduce any\nhomeomorphism $f\\in \\mathcal{P}(S^{1})$ with several break (or\nnon-break)\n points to the one with break points lying on different orbits.\n\\medskip\n\n\\begin{defn} Let $c\\in C(f)$. A \\emph{maximal $f$-connection} of  $c$ is a segment\n\\ $[f^{-p}(c),\\dots, f^{q}(c)]:= \\{f^{s}(c): \\ -p \\leq s\\leq q\\}$\nof the orbit  $O_{f}(c)$  which contains all the break points of $f$\ncontained on  $O_{f}(c)$  and such that  $f^{-p}(c)$  (resp.\n$f^{q}(c)$)  is the first (resp. last) break point of  $f$  on\n$O_{f}(c)$.\n\\end{defn}\n\\medskip\n\\\n\\\\\n We have the following properties:\n\\medskip\n\\\n\\\\\n- Two break points of $f$ are on the same maximal $f$-connection, if\nand only if, they are on the same orbit.\n\n- Two distinct maximal $f$-connections are disjoint.\n\\bigskip\n\nDenote by \\\n\\\\\n\\begin{itemize}\n\n\n \\item [-]  $ M_{i}(f) = [c_{i},\\dots, f^{N_{i}}(c_{i})], \\ (N_{i}\\in \\mathbb{N}),$ the maximal $f$-connections of\n$c_{i}\\in C(f)$, ($0\\leq i\\leq p$).\n\n \\item [-]  M$(f) = \\coprod _{i=0}^{p}M_{i}(f)$.\n\\end{itemize}\n\\medskip\nSo, we have the decomposition: $C(f) = \\coprod_{i=0}^{p} C_{i}(f)$\nwhere,  $C_{i}(f) = C(f)\\cap M_{i}(f), \\ 0\\leq i\\leq p$. We also\nhave $$\\underset{d\\in C_{i}(f)}\\prod \\sigma_{f}(d) = \\underset{d\\in\nM_{i}(f)}\\prod \\sigma_{f}(d).$$\n\\medskip\n\\\n\\\\\n\\begin{prop}[\\cite{am15}, Theorem 2.1]\\label{p:623}\nLet $f\\in \\mathcal{P}(S^{1})$ with irrational rotation number, and\nlet $\\big(k_{0},\\dots,k_{p}\\big)\\in \\mathbb{Z}^{p+1}$. Then there\nexists a piecewise quadratic homeomorphism $K\\in \\mathcal{P}(S^{1})$\nsuch that $F:= K \\circ f \\circ K^{-1}\\in \\mathcal{P}(S^{1})$ with\n$C(F) \\subset \\{K(f^{k_{i}}(c_{i}))= F^{k_{i}}(K(c_{i})); i=0,1,\n\\dots, p\\}$ and such that $\\sigma_{F}(F^{k_{i}}(K(c_{i}))) =\n\\pi_{s,O_{f}(c_{i})}(f),~i=0,1, \\dots, p$.\n\\end{prop}\n\\medskip\n\n\\begin{cor}[\\cite{am15}, Corollary 2.3]\\label{c:21} Let $f\\in \\mathcal{P}(S^{1})$ with irrational rotation number.\nSuppose that $f$ satisfies the (KO) condition. Then, there exists a\npiecewise quadratic homeomorphism $K\\in \\mathcal{P}(S^{1})$ such\nthat: $F = K\\circ f \\circ K^{-1}\\in \\mathcal{P}(S^{1})$ with $C(F)\\subset\\{K(c_{0}),\\dots,K(c_{p})\\}$, where $c_{0},\\dots, c_{p}\\in C(f)$\nare on pairwise distinct orbits.\n\\end{cor}\n\\medskip\n\n\nIn particular, we have:\n\\medskip\n\n\\begin{cor}\\label{c:22} Let $f$, $K$ and $F$ as in Corollary \\ref{c:21}.\n\\begin{itemize}\n\\item [(i)] If $f$ does not satisfy the ($D$)-property, then there exists\n$0\\leq i\\leq p$  such that $K(c_{i})$ is the unique break point of\n$F$ in its orbit.\n \\item [(ii)] If $f$ satisfies the ($D$)-property then $F$ is a $C^{1}$-diffeomorphism with $\\mathrm{DF}$ absolutely continuous on\n$S^{1}$.\n\\end{itemize}\n\\end{cor}\n\\medskip\n\\bigskip\n\n\\begin{prop}\\label{p:23} Let $f, ~g\\in \\mathcal{P}(S^{1})$ and have the same irrational rotation number such that the break points of\n$f$ (resp. $g$) belong to pairwise distinct $f$-orbits (resp.\n$g$-orbits). Let $h$ be the conjugating homeomorphism from $f$ to\n$g$. Then there exist an integer $q\\geq p$,\n$c_{0},c_{1},\\dots,c_{q}; \\ d_{0},d_{1},\\dots,d_{q}$ belong to pairwise distinct orbits $f$-orbits and $g$-orbits respectively\nsuch that $C(f)\\subset \\{c_{0},c_{1},\\dots,c_{q}\\}$,\n$C(g)\\subset \\{d_{0},d_{1},\\dots,d_{q}\\}$, and a homeomorphism $u$\nof $S^{1}$ such that $G: = u \\circ f \\circ u^{-1}\\in\n\\mathcal{P}(S^{1})$ has break points belong to pairwise distinct\n$G$-orbits and satisfies\n\\\\\n\\begin{itemize}\n\n \\item [(i)]  $C(G)\\subset \\{u(c_{i}): ~i=0,1, \\dots, q\\}$.\n \\item [(ii)] $\\sigma_{G}(u(c_{i})) = \\sigma_{g}(d_{i})~,~i=0,1, \\dots, q$.\n \\item [(iii)] $\\pi_{s}(G)=\\pi_{s}(g)$.\n \\item [(iii)] $h$ is singular if and only if so is $u$.\n\\end{itemize}\n\\end{prop}\n\\medskip\n\\\n\\\\\n\\textit{From now on we denote by \\ \\ $B:=  \\{c_{0},\\dots, c_{q}\\}$} and $c_{0}=c$.\n\\medskip\n\nIn the sequel, we may assume that $f, ~g\\in \\mathcal{P}(S^{1})$ have\nthe same irrational rotation number $\\alpha$ and satisfy the\nfollowing:\n\\medskip\n\n- The points of $B$ belong to pairwise distinct $f-$ orbits.\n\n- The break points of $g$ belong to pairwise distinct $g$-orbits.\n\n- $C(f)\\subset B$.\n\n- The maps $f, ~g$ satisfy the Katznelson-Ornstein (KO) condition.\n\n- The conjugating $h$ is such that $C(g)\\subset h(B)$.\n\\bigskip\n\\medskip\n\n\\section{\\bf Primary Cells}\n\\medskip\n\\medskip\n\nLet  $x_{0}\\in S^{1}$ and $f\\in \\mathcal{P}(S^{1})$\nwith irrational rotation number $\\alpha =\\rho(f)$. Let $c\\in B$\nand $n$ an odd integer. By Lemma \\ref{l:23}, either $c\\in\n\\Delta^{(n-1)}_{i_{n}(c)}(x_{0})$ for some $0\\leq i_{n}(c) < q_{n}$\nor $c\\in\\Delta^{(n)}_{i_{n}(c)}(x_{0})$ for some $0\\leq i_{n}(c)<\nq_{n-1}$. Set\n\n\\[\\ y_{2} = f^{-i_{n}(c)}(c), \\ y_{1} =\nf^{-q_{n-1}}(y_{2}), \\ y_{3} = f^{q_{n-1}}(y_{2}).\\]\n\\smallskip\n\nNotice that $y_{1},y_{2}$ and $y_{3}$ are defined with respect to\n$f,x_{0},c$ and the number $i_{n}(c)$ depends on $x_{0}$.\n\\medskip\n\nLet $\\delta > 0$ and $U_{\\delta}(x_{0})$ a\n$\\delta$-neighbourhood of $x_{0}$.\n\\medskip\n\n\\begin{prop}$($cf. \\cite{am12}, Proposition 3.1$)$ \\label{p:41} Under the notations above, there exists $N = N(x_{0}, \\delta)\\in \\mathbb{N}$ such that for all $n\\geq N$, there is\na triple $(y_{1},y_{2},y_{3})=(y_{1}(n),y_{2}(n),y_{3}(n))_{n\\geq\nN}$ with the following properties:\n\\medskip\n\n \\begin{itemize}\n \\item [(c-0)] $\\left(y_{1},y_{2},y_{3}\\right) \\left(\\mathrm{resp}.\n ~ (f^{q_{n}}\\left(y_{1}),f^{q_{n}}(y_{2}),f^{q_{n}}(y_{3}\\right)\\right))_{n\\geq N}\\subset\nU_{\\delta}(x_{0})$\\\\\n\n\\item [(c-1)] $~y_{2} \\in \\Delta^{(n-1)}_{0}(x_{0})~\\mathrm{ or }~y_{2}\\in \\Delta^{(n)}_{0}(x_{0})$\\\\\n\n \\item [(c-2)] $~m\\left(f^{j}([y_{1},y_{3}])\\right)\\leq K\\lambda^{n}$, for every $0\\leq j<q_{n}$, where $\\lambda = (1+e^{-V})^{-\\frac{1}{2}}$  and  $K$ a constant independent of  $n$.\n\n \\item [(c-3)] $~\\sum_{j=0}^{q_{n}-1}m\\left(f^{j}([y_{1},y_{3}])\\right)\\leq 2$\\\\\n\n \\item [(c-4)] The triples  $\\left(y_{1},y_{2},y_{3}\\right)$~ and\n$(f^{q_{n}}(y_{1}),f^{q_{n}}(y_{2}),f^{q_{n}}(y_{3}))$ satisfy\nconditions $(a)$ and $(b)$ of definition \\ref{d:32} for\n$x_{0}$ and the constant $R = e^{3V}+ e^{V}+1$.\\\\\n\n \\item [(c-5)] \\begin{itemize}\n\\item [-] $f^{i}([y_{1},~y_{3}])$ does not contain $c$ for every $0\\leq i\\neq i_{n}(c)<q_{n}$.\n\\item [-] $f^{i_{n}(c)}([y_{1},y_{3}])$ does not contain any break point of $f$ other than $c$.\n \\end{itemize}\n\n\\end{itemize}\n\\end{prop}\n\\medskip\n\n\\textbf{Definition $($primary cell$)$}. The triple\n$\\left(y_{1},y_{2},y_{3}\\right)$ given in Proposition \\ref{p:41} is\ncalled a \\textit{primary cell associated to  $(f,x_{0},c,\\delta,N)$}\nfor the constant $R = e^{3V}+ e^{V}+1$.\n\\bigskip\n\nIn the sequel, set $\\mathbb{N}_{0}=\\{n \\in \\mathbb{N}~,~n \\geq N\\}$.\n\nLet $c \\in B$, $d\\notin O_{f}(c)$ and\n$\\left(y_{1},y_{2},y_{3}\\right): =\n(y_{1}(n),y_{2}(n),y_{3}(n))_{n\\in \\mathbb{N}_{0}}$ be the primary cell\nassociated to  $(f,x_{0},c,\\delta,N)$. By Lemma \\ref{l:25} and for\nevery and $n\\in \\mathbb{N}_{0}$, denote by\n\n$$t_{n}(d)   = \\dfrac{m([f^{-i_{n}(d)}(d), y_{2}])}{m([f^{j_{n}(d)-i_{n}(d)}(y_{2}), y_{2}])}$$\n\\\\\nwhere \\;$j_{n}(d) =\n\\varphi_{n}(i_{n}(d))$ and $i_{n}(d)$ is the unique integer $0 \\leq\ni_{n}(d)<q_{n}$ such that $d \\in f^{i_{n}(d)}([y_{1}, y_{2}])$ or $d\n\\in f^{j_{n}(d)}([y_{1},y_{2}])$.\n\\bigskip\n\nOne always has $f^{-i_{n}(d)}(d)\\in [f^{q_{n}}y_{1}, y_{2}]$.\nIndeed, by Lemma \\ref{l:25}, there exists a unique $0\\leq i_{n}(d) <\nq_{n}$ such that either\n $d\\in f^{i_{n}(d)}([y_{1}, y_{2}])$ or $d\\in f^{j_{n}(d)}([y_{2}, y_{3}])$. In the first case, $f^{-i_{n}(d)}(d)\\in [y_{1}, y_{2}]$ and in the second case, $f^{-i_{n}(d)}(d)\\in [f^{q_{n}}y_{1}, f^{q_{n}}y_{2}]\\subset [f^{q_{n}}y_{1}, y_{2}]$.\nOne can write $$t_{n}(d)   = \\left\\{\n\\begin{array}{ll}\n       \\dfrac{m([f^{-i_{n}(d)}(d), y_{2}])}{m([y_{1}, y_{2}])}, & \\hbox{if }q_{n-1}\\leq i_{n}(d)< q_{n} \\\\\\\\\n    \\dfrac{m([f^{-i_{n}(d)}(d), y_{2}])}{m([f^{q_{n}}y_{1}, y_{2}])}, & \\hbox{if } 0\\leq i_{n}(d)< q_{n-1}\n\\end{array}\n\\right.\n$$\n\\medskip\n\nLet $d\\in B\\backslash\\{c\\}$ and $A$ be an infinite subset of $\\mathbb{N}_{0}$. Denote by\n\\medskip\n\n\\textbullet \\; $T(d, A)$ the set of limit points of $(t_{n}(d))_{n\\in A}$. Therefore\n $T(d, A)\\subset [0,1]$.\n\\medskip\n\nWe say that $d$ satisfies:\n\\medskip\n\n\\textbullet \\; The $P_{1}(d,A)$-property if $T(d, A)\\cap ~]0,1[\\neq \\emptyset$\nand for every $n\\in A, ~0 \\leq i_{n}(d) <q_{n-1}$.\n\n\\textbullet \\; The $P_{2}(d,A)$-property if $T(d, A)\\cap ~]0,1[\\neq \\emptyset$\nand for every $n \\in A, ~q_{n-1} \\leq i_{n}(d) <q_{n}$.\n\\bigskip\n\\medskip\n\nSet \\begin{align*} Q_{11}( A) & = \\{d\\in B\\backslash \\{c\\}:\n~\\textrm{d ~satisfies ~the } P_{1}(d, A)-\\textrm{property}\n\\}\\\\\nQ_{12}(A) & = \\{d\\in B\\backslash \\{c\\}:  ~\\textrm{d ~satisfies ~the\n} P_{2}(d, A)-\\textrm{property}\n\\}\\\\\nQ_{1}(A) & = Q_{11}(A)\\cup Q_{12}(A)\\\\\nQ_{2}(A) & = \\{d\\in B\\backslash \\{c\\}:  T(d, A) = \\{0\\}\\}\\\\\nQ_{3}( A) & = \\{d\\in B\\backslash \\{c\\}: T(d, A) = \\{1\\}\\}\\\\\nQ_{4}( A) & = \\{d\\in B\\backslash \\{c\\}: T(d, A) = \\{0,1\\}\\}\n\\end{align*}\n\\bigskip\n\n\\begin{prop}\\label{p:461}\nAssume that the rotation number $\\rho(f)$ of $f$ is of bounded type. Then for every points $c, c_{1}$ in\n$B(f)$, $c_{1}\\notin O_{f}(c)$, there exists an infinite subset $\\mathbb{M}_{c,c_{1}}$ of\n$\\mathbb{N}_{0}$ such that $c_{1}\\in Q_{1}(\\mathbb{M}_{c,c_{1}})$.\n\\end{prop}\n\\medskip\n\nWe need two lemmas.\n\\medskip\n\n\\begin{lem}\\label{l:4611}\nLet $0\\leq k<q_{n+1}+q_{n}$ be an integer. Then\n$\\Delta_{0}^{(n-1)}(c)\\cap \\Delta^{(n)}_{k}(c)$ has non empty\ninterior if and only if $k=q_{n-1}+q_{n+1}$ or $k = q_{n-1}+jq_{n}$ for some $0\\leq j\\leq\na_{n+1}$.\n\\end{lem}\n\\smallskip\n\n\\begin{proof}\n- Assume that $k=q_{n-1}+q_{n+1}$ or $k = q_{n-1}+jq_{n}$ for some $0\\leq j \\leq\na_{n+1}$. Since $$\\Delta_{0}^{(n-1)}(c)= \\Delta_{0}^{(n+1)}(c) \\coprod_{0 \\leq\nj<a_{n+1} }~~\\Delta^{(n)}_{q_{n-1}+jq_{n}}(c),$$ so we have\n$$\\Delta_{0}^{(n-1)}(c)\\cap \\Delta^{(n)}_{k}(c) = \\begin{cases}\n\\Delta^{(n)}_{k}(c), & \\textrm{if } k=q_{n-1}+jq_{n} \\ \\textrm{ with } 0\\leq j <a_{n+1}, \\\\\n [c,f^{q_{n+1}}(c)], & \\textrm{if } k=q_{n+1}, \\\\\n [f^{q_{n-1}+q_{n}+q_{n+1}}(c),f^{q_{n-1}}(c)], & \\textrm{if } k=q_{n-1}+q_{n+1}.\n\\end{cases}$$\n\nIn either case, $\\Delta_{0}^{(n-1)}(c)\\cap \\Delta^{(n)}_{k}(c)$ has non empty\ninterior. Conversely we distinguish two cases:\n\n- $0 \\leq k< q_{n+1}$: if $k \\notin\n\\{q_{n-1}+jq_{n}:~0\\leq j< a_{n+1}\\}$, then by Lemma\n\\ref{l:23}, $\\Delta_{0}^{(n-1)}(c)\\cap \\Delta^{(n)}_{k}(c)$ has\nempty interior.\n\n- $q_{n+1}\\leq k< q_{n+1}+q_{n}$: If $k\\notin \\{q_{n+1}, q_{n-1}+q_{n+1}\\}$, then $k=l+q_{n+1}$ with $1\\leq l< q_{n}$ and \n$l\\neq q_{n-1}$. Thus we have\n\\begin{align*}\nf^{-q_{n+1}}\\left(\\Delta_{0}^{(n-1)}(c)\\cap\n\\Delta^{(n)}_{k}(c)\\right)=[f^{-q_{n+1}}(c),~f^{-q_{n+1}+q_{n-1}}(c)]\\cap\n\\Delta^{(n)}_{l}(c)\\\\\n \\subset \\left(\\Delta_{0}^{(n)}(c)\\cup\n\\Delta_{0}^{(n-1)}(c)\\right)\\cap \\Delta^{(n)}_{l}(c)\n\\end{align*}\nHence $\\Delta_{0}^{(n-1)}(c)\\cap \\Delta^{(n)}_{k}(c)$ has empty\ninterior.\n\\end{proof}\n\\medskip\n\n\\begin{lem}\\label{l:4612}\nLet $0 \\leq k < (a_{n+1}+2)q_{n}$ be an integer. Then\n$\\Delta^{(n-1)}_{k}(c)\\cap \\Delta_{0}^{(n)}(c)$ has non empty\ninterior if and only if $k = q_{n}+q_{n+1}$ or $k = jq_{n}$ for some\n$1\\leq j\\leq a_{n+1}+1$.\n\\end{lem}\n\\medskip\n\n\\begin{proof} We have $$\\Delta_{0}^{(n)}(c)\\cap \\Delta^{(n-1)}_{k}(c) = \\begin{cases}\n\\Delta_{0}^{(n)}(c), & \\textrm{if }  k=jq_{n} \\textrm{ with } \\  1 \\leq j \\leq a_{n+1}, \\\\\n[f^{q_{n}}(c),f^{q_{n}+q_{n+1}}(c)], & \\textrm{if } k=(a_{n+1}+1)q_{n}, \\\\\n[f^{q_{n}+q_{n+1}}(c),c], & \\textrm{if } k= q_{n}+q_{n+1}.\n\\end{cases}$$\nHence $\\Delta_{0}^{(n)}(c)\\cap \\Delta^{(n-1)}_{k}(c)$ has non empty interior. Conversely, we distinguish three cases:\n\n- $0 \\leq k< q_{n}$: In this case, by Lemma \\ref{l:23}, $\\Delta^{(n-1)}_{k}(c)\\cap \\Delta_{0}^{(n)}(c)$ has empty\ninterior.\n\n-  $q_{n}\\leq k < (a_{n+1}+1)q_{n}$: If $k\\notin \\{ jq_{n}: \\ 1\\leq j \\leq a_{n+1}\\}$, then $k=l+jq_{n}$ with $1\\leq l <q_{n}$ \nand $1\\leq j\\leq a_{n+1}$. Thus we have \n$$f^{-jq_{n}}\\left(\\Delta^{(n-1)}_{k}(c)\\cap\n\\Delta_{0}^{(n)}(c)\\right)=\\Delta^{(n-1)}_{l}(c)\\cap\nf^{-jq_{n}}(\\Delta_{0}^{(n)}(c))\\subset \\Delta^{(n-1)}_{l}(c)\\cap\n\\Delta_{0}^{(n-1)}(c),$$ so  $\\Delta^{(n-1)}_{k}(c)\\cap\n\\Delta_{0}^{(n)}(c)$ has empty interior.\n\n-  $(a_{n+1}+1)q_{n}\\leq k < (a_{n+1}+2)q_{n}$: If $k\\notin \\{(a_{n+1}+1)q_{n}, \\ q_{n+1}+q_{n}\\}$, then $k=l+(a_{n+1}+1)q_{n}$ \nwith $1 \\leq l<q_{n}$ and $l\\neq\nq_{n-1}$. Thus we have\n\\begin{align*}\nf^{-(a_{n+1}+1)q_{n}}\\left(\\Delta^{(n-1)}_{k}(c)\\cap\n\\Delta_{0}^{(n)}(c)\\right) & = \\Delta^{(n-1)}_{l}(c)\\cap\nf^{-(a_{n+1}+1)q_{n}}(\\Delta_{0}^{(n)}(c))\\\\\n& \\subset \\Delta^{(n-1)}_{l}(c)\\cap \\left(\\Delta^{(n-1)}_{0}(c)\\cup\nf^{q_{n-1}}(\\Delta_{0}^{(n-1)}(c))\\right).\n\\end{align*}\n\n Hence $\\Delta^{(n-1)}_{k}(c)\\cap \\Delta_{0}^{(n)}(c)$ has empty\ninterior.\n\\end{proof}\n\\bigskip\n\n\\textit{Proof of Proposition \\ref{p:461}}. Suppose that there exist two distinct points $c,c_{1}$ in $B(f)$\nsuch that for any infinite subset $M$ of $\\mathbb{N}_{0}$ we have $T(c_{1}, M)\\subset \\{0,1\\}$. In particular for\n$M= \\mathbb{N}_{0}$. So we have three possible cases.\n\\medskip\n\n\\textbf{Case 1}: $T(c_{1}, \\mathbb{N}_{0})=\\{0\\}$ i.e. $c_{1}\\in\nQ_{2}(\\mathbb{N}_{0})$. Since $$f^{-i_{n}(c_{1})}(c_{1})\\in\n[f^{q_{n}}(y_{1}),~y_{2}] = \\Delta_{0}^{(n)}(y_{1})\\cup\n\\Delta_{0}^{(n-1)}(y_{1}),$$ $$m(\\Delta_{0}^{(n-1)}(y_{1}))\\leq\nm([f^{q_{n}}(y_{1}),~y_{2}])\\leq\n(1+e^{V})m(\\Delta_{0}^{(n-1)}(y_{1}))$$ and $$\\lim_{n \\to\n+\\infty}~\\frac{m([f^{-i_{n}(c_{1})}(c_{1}),~\ny_{2}])}{m([f^{q_{n}}(y_{1}),~y_{2}])}=0,$$ there exists an integer\n$n_{0}\\in \\mathbb{N}$ such that for every $n\\geq n_{0},\n~f^{-i_{n}(c_{1})}(c_{1})\\in \\Delta_{0}^{(n-1)}(y_{1})$ and\n$$\\lim_{n\\to +\\infty}~\\frac{m([f^{-i_{n}(c_{1})}(c_{1}),~y_{2}])}{m(\\Delta_{0}^{(n-1)}(y_{1}))}=0.$$\nFor $n\\in \\mathbb{N}$, set\n\\medskip\n\n\\[ ~ s_{n}: = i_{n}(c_{1})-i_{n}(c)-q_{n-1}\\]\n\n\\[l_{n}: = \\frac{m(\\Delta^{(n)}_{s_{n}}(c))}{m(\\Delta^{(n-1)}_{s_{n}}(c))}, ~~~~ \\ \n b_{n}: = \\frac{m([c_{1},~f^{s_{n}+q_{n-1}}(c)])}{m(\\Delta^{(n-1)}_{s_{n}}(c))}\\]\n\\medskip\n\nThen $-q_{n}<s_{n}+q_{n-1}<q_{n}$ and by (Lemma \\ref{l:31} and\nDenjoy's inequality), we have for every $n\\geq n_{0},~~c_{1}\\in\n\\Delta^{(n-1)}_{s_{n}}(c)$ and\n\\begin{equation}\\label{(3.1)}\n\\lim_{n\\to +\\infty} b_{n}=0\n\\end{equation}\nIn particular, for every $n\\geq n_{0}$, $c_{1}$ is an interior point\nof $\\Delta^{(n-1)}_{s_{n}}(c)\\cap \\Delta^{(n)}_{s_{n+1}}(c)$ and\nhence $\\Delta_{0}^{(n-1)}(c)\\cap \\Delta^{(n)}_{s_{n+1}-s_{n}}(c)$\nhas a non empty interior.\n\n\\medskip\n\n- If $s_{n+1}-s_{n} \\geq 0$, then $s_{n+1}-s_{n} <\nq_{n+1}-(q_{n}-q_{n-1})$ and by Lemma \\ref{l:4611}\n$$s_{n+1}-s_{n}\\in \\left\\{ q_{n-1}+jq_{n}: 0\\leq j<\na_{n+1}\\right\\}$$\n\\medskip\n\n-If $s_{n+1}-s_{n} \\leq 0$, then $s_{n}-s_{n+1} < (a_{n+1}+1)q_{n}$\nand by Lemma \\ref{l:4612}\n$$s_{n+1}-s_{n}\\in \\{-jq_{n}: \\ 1\\leq j\\leq a_{n+1}\\}.$$\n\\bigskip\n\nLet $n\\geq n_{0}$. Since $\\Delta^{(n-1)}_{s_{n}}(c)\\subset\n\\bigcup_{0 \\leq j \\leq\na_{n+1}}~f^{q_{n-1}+jq_{n}}(\\Delta^{(n)}_{s_{n}}(c))$, so by\nDenjoy's inequality, we have\n$$\\frac{m(\\Delta^{(n-1)}_{s_{n}}(c))}{m(\\Delta^{(n)}_{s_{n}}(c))}<\n\\sum_{0\\leq j\\leq a_{n+1}}~e^{(1+j)V}$$\n\nSo, $$l_{n}^{-1}< \\frac{e^{V}}{e^{V}-1}~(e^{(1+a_{n+1})V}-1)$$\n\nHence,\n\\begin{equation}\\label{(3.2)}\n  \\textrm{If}~~ \\lim_{n\\to + \\infty }l_{n}=0 \\ \\textrm{ then } ~ \\lim_{n\\to + \\infty }a_{n+1} = +\\infty\n\\end{equation}\n\\medskip\n\nWe distinguish four sub-cases.\n\\bigskip\n\nCase 1.1: $s_{n+1}-s_{n} \\in \\{q_{n-1}+jq_{n}~:~ 1\\leq j<\na_{n+1}\\}$. Then by the Denjoy's inequality, we have\n\\begin{align*}\nl_{n} & \\leq\ne^{V}\\frac{m(\\Delta^{(n)}_{s_{n}+q_{n-1}}(c))}{m(\\Delta^{(n-1)}_{s_{n}}(c))}\\\\\n& \\leq\ne^{V}\\frac{m([c_{1},~f^{s_{n}+q_{n-1}}(c)])}{m(\\Delta^{(n-1)}_{s_{n}}(c))} \\\\\n& = e^{V}b_{n}\n\\end{align*}\n\n(since $c_{1} \\in \\Delta^{(n-1)}_{s_{n}}(c)\\backslash\n\\Delta^{(n)}_{s_{n}+q_{n-1}}(c)$).\\\\\n\\medskip\n\nCase 1.2: $s_{n+1}-s_{n}=q_{n-1}$. Then by the Denjoy's inequality, we have\n\\begin{align*}l_{n}& \\leq e^{V}\\frac{m(\\Delta^{(n)}_{s_{n+1}}(c))}{m(\\Delta^{(n-1)}_{s_{n}}(c))} \\\\\n& \\leq e^{V}\\frac{m([f^{s_{n+1}+q_{n}}(c),~c_{1}])}{m(\\Delta^{(n)}_{s_{n+1}}(c))}+\ne^{V}\\frac{m([c_{1},~f^{s_{n}+q_{n-1}}(c)])}{m(\\Delta^{(n-1)}_{s_{n}}(c))} \\\\\n& = e^{V}(b_{n}+b_{n+1})\n\\end{align*}\n(since $c_{1}\\in\n\\Delta^{(n)}_{s_{n+1}}(c) = \\Delta^{(n)}_{s_{n}+q_{n-1}}(c)\\subset\n\\Delta^{(n-1)}_{s_{n}}(c)$).\\\\\n\\medskip\n\nCase 1.3: $s_{n+1}-s_{n} \\in \\{-jq_{n}~:~1 \\leq j < a_{n+1} \\}$. Then by\nthe Denjoy's inequality, we have\n\\begin{align*} l_{n}& \\leq e^{V}\\frac{m(\\Delta^{(n)}_{s_{n}+q_{n-1}}(c))}{m(\\Delta^{(n-1)}_{s_{n}}(c))}\\\\\n& \\leq e^{V}\\frac{m([c_{1},~f^{s_{n}+q_{n-1}}(c)])}{m(\\Delta^{(n-1)}_{s_{n}}(c))} \\\\\n& = e^{V}b_{n}\n\\end{align*}\n(since $c_{1} \\in \\Delta^{(n-1)}_{s_{n}}(c)\\backslash\n\\Delta^{(n)}_{s_{n}+q_{n-1}}(c)$ as in Case 1.1).\\\\\n\\medskip\n\nCase 1.4: $s_{n+1}-s_{n} = q_{n-1}-q_{n+1}$. Then by the Denjoy's iequality, we have\n\n\\begin{align*}\nl_{n} & = \\frac{m(f^{-q_{n-1}+q_{n+1}}(\\Delta^{(n)}_{s_{n+1}}(c)))}{m(\\Delta^{(n-1)}_{s_{n}}(c))}\\\\\n& \\leq e^{2V}\n\\frac{m(\\Delta^{(n)}_{s_{n+1}}(c))}{m(\\Delta^{(n-1)}_{s_{n}}(c))}\\\\\n& \\leq e^{2V}\\frac{m([f^{s_{n+1}+q_{n}}(c),~c_{1}])}{m(\\Delta^{(n-1)}_{s_{n}}(c))}+ \ne^{2V}\\frac{m([c_{1},~f^{s_{n+1}}(c)])}{m(\\Delta^{(n-1)}_{s_{n}}(c))}\\\\\n& \\leq e^{2V}\\frac{m([f^{s_{n+1}+q_{n}}(c),~c_{1}])}{m(\\Delta^{(n)}_{s_{n+1}}(c))}+\ne^{2V}\\frac{m([c_{1},~f^{s_{n}+q_{n-1}}(c)])}{m(\\Delta^{(n-1)}_{s_{n}}(c))}\\\\\n& \\leq e^{2V}(b_{n}+b_{n+1})\n\\end{align*}\n(since $c_{1} \\in\n\\Delta^{(n)}_{s_{n+1}}(c) = f^{-q_{n+1}}(\\Delta^{(n)}_{s_{n}+q_{n-1}}(c))\n\\subset \\Delta^{(n-1)}_{s_{n}}(c)$).\\\\\n\nIn either of the four cases above, we conclude that for every $n\\geq n_{0}$,~$$l_{n}\\leq\ne^{2V}(b_{n}+b_{n+1}).$$ So by the assertions (\\ref{(3.1)}) and\n(\\ref{(3.2)}) we obtain that\n$\\underset{n\\to + \\infty}\\lim ~a_{n+1} = +\\infty,$ a contradiction with that $\\rho(f)$ is of bounded type.\\\\\n\\medskip\n\n\\textbf{Case 2}: $ T(c_{1}, \\mathbb{N}_{0}) = \\{1\\}$ i.e. $c_{1}\\in\nQ_{3}(\\mathbb{N}_{0})$. In this case, there\nexists $n_{1}\\in \\mathbb{N}$ such that for all $n\\geq\nn_{1}, ~f^{-j_{n}(c_{1})}(c_{1})\\in \\Delta^{(n-1)}(y_{2})$ and\n$$\\lim_{n\\to +\\infty}~\\frac{m([y_{2},~f^{-j_{n}(c_{1})}(c_{1})])}{m(\\Delta^{(n-1)}_{0}(y_{2}))} = 0.$$\n\nFor $n\\geq n_{1}$, set\n\\medskip\n\n\\[r_{n}: = j_{n}(c_{1})-i_{n}(c)\\]\n\n\\[l^{\\prime}_{n}:= \\frac{m(\\Delta^{(n)}_{r_{n}}(c))}{m(\\Delta^{(n-1)}_{r_{n}}(c))}, ~~~~ \\ \nb^{\\prime}_{n}:= \\frac{m([f^{r_{n}}(c),~c_{1}])}{m(\\Delta^{(n-1)}_{r_{n}}(c))}\\]\n\\medskip\n\nThen $-q_{n}<r_{n}<q_{n}$ and by Lemma \\ref{l:31}, we have for every\n$n\\geq n_{1}$, $~c_{1} \\in \\Delta^{(n-1)}_{r_{n}}(c)$ and\n$$\\lim_{n\\to+\\infty}~b^{\\prime}_{n}=0$$ In particular, for every $n\\geq\nn_{1}$,~ $c_{1}~~ \\textrm{is an interior point of}~~\n\\Delta^{(n-1)}_{r_{n}}(c)\\cap \\Delta^{(n)}_{r_{n+1}}(c)$ and\n$$-q_{n+1}<r_{n+1}-r_{n}<q_{n+1}.$$\n\n- If $r_{n+1}-r_{n} \\geq 0$, then by Lemma \\ref{l:4611}  $$r_{n+1}-r_{n}\\in\n\\{ q_{n-1}+jq_{n}: 0\\leq j< a_{n+1}\\}.$$\n\n-If $r_{n+1}-r_{n}\\leq 0$, then by Lemma \\ref{l:4612}  $$r_{n+1}-r_{n}\\in\n\\{ -jq_{n}: 1\\leq j\\leq a_{n+1}\\}.$$\n\nWe distinguish four sub-cases.\n\\medskip\n\nCase 2.1: $r_{n+1}-r_{n} \\in \\{q_{n-1}+jq_{n}:~0 \\leq j <\na_{n+1}-1\\}$. Then by the Denjoy's inequality, we have\n$$l^{\\prime}_{n} \\leq e^{V}\n \\frac{m(f^{-q_{n}}(\\Delta^{(n)}_{r_{n}}(c)))}{m(\\Delta^{(n-1)}_{r_{n}}(c))} \\leq\n e^{V} b^{\\prime}_{n}$$\n(since $f^{-q_{n}}(\\Delta^{(n)}_{r_{n}}(c))\\subset\n[f^{r_{n}}(c),~c_{1}]$).\\\\\n\\medskip\n\nCase 2.2: $r_{n+1}-r_{n} = q_{n+1}-q_{n}$ (i.e. $j=a_{n+1}-1$).\n Then by the Denjoy's inequality, we have\n\\begin{align*}\nl^{\\prime}_{n} & =\n \\frac{m(f^{-q_{n+1}+q_{n}}(\\Delta^{(n)}_{r_{n+1}}(c)))}{m(\\Delta^{(n-1)}_{r_{n}}(c))}\\\\\n & \\leq\n e^{2V} \\frac{m(\\Delta^{(n)}_{r_{n+1}}(c))}{m(\\Delta^{(n-1)}_{r_{n}}(c))} \\\\\n & \\leq e^{2V}\\left(\\frac{m([f^{r_{n}}(c),~c_{1}])}{m(\\Delta^{(n-1)}_{r_{n}}(c))}+\n\\frac{m([c_{1},~f^{r_{n+1}}(c)])}{m(\\Delta^{(n)}_{r_{n+1}}(c))}\\right)\\\\\n& = e^{2V}(b^{\\prime}_{n}+b^{\\prime}_{n+1})\n\\end{align*}\n(since $c_{1} \\in \\Delta^{(n)}_{r_{n+1}}(c) \\subset\n\\Delta^{(n-1)}_{r_{n}}(c)$).\n\\bigskip\n\nCase 2.3: $r_{n+1}-r_{n}\\in \\{-jq_{n}:~2\\leq j\\leq a_{n+1}\\}$. Then\nby the Denjoy's inequality, we have\n\n\\begin{align*}l^{\\prime}_{n} & \\leq e^{V}\n \\frac{m(f^{-q_{n}}(\\Delta^{(n)}_{r_{n}}(c)))}{m(\\Delta^{(n-1)}_{r_{n}}(c))} \\\\\n & \\leq\n e^{V} \\frac{m([f^{r_{n}}(c),~c_{1}])}{m(\\Delta^{(n-1)}_{r_{n}}(c))} \\\\\n & = e^{V}b^{\\prime}_{n}\n \\end{align*}\n(since $f^{-q_{n}}(\\Delta^{(n)}_{r_{n}}(c))\\subset [f^{r_{n}}(c),~c_{1}]$).\\\\\n\nCase 2.4: $r_{n+1}-r_{n}=-q_{n}$ (i.e. $j=1$). Then by the Denjoy's inequality,\nwe have\n\\begin{align*}\nl^{\\prime}_{n} & =\n \\frac{m(f^{-q_{n}}(\\Delta^{(n)}_{r_{n+1}}(c)))}{m(\\Delta^{(n-1)}_{r_{n}}(c))}\\\\\n & \\leq\n e^{V} \\frac{m(\\Delta^{(n)}_{r_{n+1}}(c))}{m(\\Delta^{(n-1)}_{r_{n}}(c))} \\\\\n & \\leq e^{V}\\left(\\frac{m([f^{r_{n}}(c),~c_{1}])}{m(\\Delta^{(n-1)}_{r_{n}}(c))}+\n\\frac{m([c_{1},~f^{r_{n+1}}(c)])}{m(\\Delta^{(n)}_{r_{n+1}}(c))}\\right)\\\\\n& = e^{V}(b^{\\prime}_{n}+b^{\\prime}_{n+1})\n\\end{align*}\n(since $c_{1} \\in \\Delta^{(n)}_{r_{n+1}}(c) \\subset\n\\Delta^{(n-1)}_{r_{n}}(c)$).\n\\bigskip\n\nIn either of the four cases [2.1$-$2.4] above, we conclude that for every $n\\geq n_{0}$,~$$l^{\\prime}_{n}\\leq\ne^{2V}(b^{\\prime}_{n} + b^{\\prime}_{n+1}).$$ So as in Case 1, we\nconclude that  $\\underset{n\\to\n+\\infty}\\lim ~a_{n+1} = +\\infty$, a contradiction with that $\\rho(f)$ is of bounded type.\\\\\n\\medskip\n\n\\textbf{Case 3}: $T(c_{1}, \\mathbb{N}_{0})=\\{0,1\\}$. In this case,\nthere exists an infinite subset\n$M_{1}$ of $\\mathbb{N}_{0}$ such that $c_{1}\\in Q_{2}(M_{1})\\cap Q_{3}(M_{2})$, where $M_{2} = \\mathbb{N}_{0}\\backslash M_{1}$.\nHence there exists $n_{1}\\in \\mathbb{N}_{0}$ such that for all $n\\geq\nn_{1}, n\\in M_{1}$, $c_{1}$ is an interior point\nof $\\Delta^{(n-1)}_{s_{n}}(c)$ and there\nexists $n_{2}\\in \\mathbb{N}_{0}$ such that for all $n\\geq\nn_{2}, n\\in M_{2}$, $c_{1}$ is an interior point of $\\Delta^{(n-1)}_{r_{n}}(c)$. We distinguish the following cases.\n\\bigskip\n\n\\textit{Case 3.1}:  $(n, n+1)\\in M_{1}\\times M_{1}$ (resp. $(n, n+1)\\in M_{2}\\times M_{2}$) holds for infinitely many $n$, say\n$n\\in M_{1}^{\\prime}\\subset M_{1}$ (resp. $M_{2}^{\\prime}\\subset M_{2}$) with  $M_{1}^{\\prime}$ (resp. $M_{2}^{\\prime}$) infinite.\nIn this case, $c_{1}$ is an interior point of $\\Delta^{(n-1)}_{s_{n}}(c)\\cap \\Delta^{(n)}_{s_{n+1}}(c)$ (resp.\n$\\Delta^{(n-1)}_{r_{n}}(c)\\cap\n\\Delta^{(n)}_{r_{n+1}}(c)$) for $n\\in M_{1}^{\\prime}$ (resp. $n\\in M_{2}^{\\prime}$). Hence as in Cases 1 and 2,\nwe obtain that $$\\underset{n\\to\n+\\infty, n\\in M_{1}^{\\prime}}\\lim ~a_{n+1} = +\\infty \\ (\\textrm{resp}. \\underset{n\\to\n+\\infty, n\\in M_{2}^{\\prime}}\\lim ~a_{n+1} = +\\infty).$$\n\\bigskip\n\n\\textit{Case 3.2}: $(n, n+1)\\in M_{1}\\times M_{2}$ holds for infinitely many $n$. In this case, $c_{1}$ is an interior point of\n$\\Delta^{(n-1)}_{s_{n}}(c)\\cap \\Delta^{(n)}_{r_{n+1}}(c)$. Hence we have one of the following sub-cases.\n\\bigskip\n\n $A_{1}$: $r_{n+1}-s_{n}\\in \\{q_{n-1}+jq_{n}: ~1\\leq j\\leq a_{n+1}\\}$. In this case, we have, by the Denjoy's inequality:\n\\begin{equation*}\nl_{n} \\leq e^{V}\\frac{m([c_{1},~f^{s_{n}+q_{n-1}}(c)])}{m(\\Delta^{(n-1)}_{s_{n}}(c))}=e^{V}b_{n}\n\\end{equation*}\n(since $f^{q_{n-1}}(\\Delta^{(n)}_{s_{n}}(c))\\subset [c_{1},~f^{s_{n}+q_{n-1}}(c)])$.\\\\\n\\medskip\n\n$A_{2}$:  $r_{n+1}-s_{n}\\in \\{-jq_{n}:~1\\leq j\\leq a_{n+1}-1\\}$. In this case, \\begin{equation*}\nl_{n} \\leq e^{3V}\\frac{m([c_{1},~f^{s_{n}+q_{n-1}}(c)])}{m(\\Delta^{(n-1)}_{s_{n}}(c))}=e^{3V}b_{n}\n\\end{equation*}\n(since $f^{-(q_{n+1}-q_{n-1})}(\\Delta^{(n)}_{s_{n}}(c))\\subset\n[c_{1},~f^{s_{n}+q_{n-1}}(c)])$.\n\\medskip\n\n$A_{3}$:   $r_{n+1}-s_{n}= q_{n-1}$.\n\\bigskip\n\n\\textit{Case 3.3}:  $(n, n+1)\\in M_{2}\\times M_{1}$ holds for infinitely many $n$. In this case,\n$c_{1}$ is an interior point of $\\Delta^{(n-1)}_{r_{n}}(c)\\cap \\Delta^{(n)}_{s_{n+1}}(c)$. Hence we have one of the following sub-cases.\n\\bigskip\n\n$B_{1}$: $s_{n+1}-r_{n}\\in \\{q_{n-1}+jq_{n}: ~0\\leq j\\leq a_{n+1}-2\\}$. In this case, by the Denjoy's inequality, we have\n\\[l^{\\prime}_{n} \\leq e^{3V}b^{\\prime}_{n} \\ ( \\textrm{since } \\ f^{q_{n+1}-q_{n}}(\\Delta^{(n)}_{r_{n}}(c))\\subset\n[f^{r_{n}}(c),~c_{1}]).\\]\n\\medskip\n\n$B_{2}$:  $s_{n+1}-r_{n}\\in \\{-jq_{n}: ~2\\leq j\\leq a_{n+1}+1\\}$. In this case, by the Denjoy's inequality, we have\n\\[l^{\\prime}_{n} \\leq e^{V}b^{\\prime}_{n} \\ (\\textrm{since} f^{-q_{n}}(\\Delta^{(n)}_{r_{n}}(c))\\subset [f^{r_{n}}(c),~c_{1}]).\\]\n\\medskip\n\n$B_{3}$:  $s_{n+1}-r_{n} = -q_{n}$.\n\\bigskip\n\\medskip\n\n\\textit{Claim.} One of the cases $A_{1}$, $A_{2}$, $B_{1}$ and $B_{2}$ holds for infinitely many $n$.\n\\medskip\n\nIndeed, on the contrary, the cases $A_{3}$ and $B_{3}$ hold in particular for\ninfinitely many $n \\in \\mathbb{N}_{0}$. So for every $n\\in M_{1}$, we\nhave $n+1\\in M_{2}$ and $r_{n+1} = s_{n} + q_{n-1}$ and for every\n$n\\in M_{2}$, we have $n+1\\in M_{1}$ and $s_{n+1}-r_{n}= -q_{n}$. So\nfor every $n\\in M_{1}$, we have $n+1\\in M_{2}$, $n+2\\in M_{1}$ and\n$n+3\\in M_{2}$. Hence $r_{n+1}-s_{n+2}= q_{n+1}$ and\n$r_{n+3}-s_{n+2}= q_{n+1}$, so $r_{n+1} = r_{n+3}$, for every $n\\in\nM_{1}$. Thus $(r_{n})_{n\\in M_{2}}$ is a constant $r\\in \\mathbb{Z}$.\nIt follows that $c_{1}\\in \\Delta^{(n-1)}_{r}(c)$ for every $n\\in\nM_{2}$ and hence $m\\left([f^{-r}(c_{1}), c]\\right)\\leq\nm\\left(\\Delta^{(n-1)}_{0}(c)\\right)$. Since $\\underset{n\\to\n+\\infty}\\lim m\\left(\\Delta^{(n-1)}_{0}(c)\\right) = 0$, so $c_{1} =\nf^{r}(c)$, this contradicts the hypothesis $c_{1}\\notin O_{f}(c)$.\n\\bigskip\n\nIf $A_{1}$ (resp. $A_{2}$) holds for infinitely many $n$, say $n\\in M_{1}^{\\prime\\prime}\\subset M_{1}$ (resp.\n$M_{1}^{\\prime\\prime\\prime}$)\nwith  $M_{1}^{\\prime\\prime}$ (resp. $M_{1}^{\\prime\\prime\\prime}$) infinite,\nso as in Cases 1 and 2,\nwe obtain that $$\\underset{n\\to\n+\\infty, n\\in M_{1}^{\\prime\\prime}}\\lim ~a_{n+1} = +\\infty ~(\\textrm{resp}. \\underset{n\\to\n+\\infty, n\\in M_{1}^{\\prime\\prime\\prime}}\\lim ~a_{n+1} = +\\infty).$$\n\\medskip\n\\medskip\nIf $B_{1}$ (resp. $B_{2}$) holds for infinitely many $n$, say $n\\in M_{2}^{\\prime\\prime}\\subset M_{2}$\n(resp. $M_{2}^{\\prime\\prime\\prime}\\subset M_{2}$) with\n$M_{2}^{\\prime\\prime}$ (resp. $M_{2}^{\\prime\\prime\\prime}$) infinite, so similarily as for $A_{1}$ and  $A_{2}$,\nwe obtain that $$\\underset{n\\to\n+\\infty, n\\in M_{2}^{\\prime\\prime}}\\lim ~a_{n+1} = +\\infty ~ (\\textrm{resp}. \\underset{n\\to\n+\\infty, n\\in M_{2}^{\\prime\\prime\\prime}}\\lim ~a_{n+1} = +\\infty.)$$\\\\\n\nIn either of the three cases [3.1$-$3.3] above, we get a contradiction with that\n$\\rho(f)$ is of bounded type. We conclude that the Case 3 doesn't occur and so $Q_{4}( \\mathbb{N}_{0})=\\emptyset$. \\qed\n\n\\bigskip\n\\bigskip\n\nIn the sequel,\nwe write for simplicity $\\mathbb{N}_{0}$ instead of $\\mathbb{N}_{c,c_{1}}$ and we denote by\n\n $$E(c_{1},c):= \\{c\\}\\cup Q_{2}(\\mathbb{N}_{0})\\cup Q_{3}(\\mathbb{N}_{0})$$\n\nSo one has\n$$B\\backslash\\{c\\} = Q_{1}( \\mathbb{N}_{0})\\ \\amalg~Q_{2}( \\mathbb{N}_{0}) \\\n\\amalg~Q_{3}(\\mathbb{N}_{0})  .$$\n\\medskip\n\nFor $a \\in S^{1},~n \\in \\mathbb{N}_{0}$ and $\\gamma >0,$ set\n\\medskip\n\n\\textbullet ~ $~l_{n}: = m(\\Delta^{(n)}(y_{1}))$\\\\\n\n\\textbullet ~ $V^{(f)}_{n,\\gamma}(a):=[a-\\gamma ~l_{n-1},~a+\\gamma\n~l_{n-1}]$ \\\\\n\n \\textbullet ~ $k_{n}(d)=\\begin{cases}\n\n                      i_{n}(d), & \\textrm{if}~d \\in \\{c\\} \\cup Q_{2}(\\mathbb{N}_{0}) \\\\\n                      j_{n}(d), & \\textrm{if}~d \\in Q_{3}(\\mathbb{N}_{0})\n                                               \\end{cases}$\n\\medskip\n\\medskip\n\n\\begin{prop}\\label{p:47} There exists a positive constant $\\gamma_{0}>0$ such that:\n\\medskip\n\n\\begin{enumerate}\n  \\item For every $d\\in E(c_{1},c)$ and every $0<\\gamma< \\gamma_{0}$, there exists\n$n_{\\gamma} \\in \\mathbb{N}_{0}\n  $ such that for any $n \\in \\mathbb{N}_{0},~n \\geq n_{\\gamma}$ there exists a unique integer $0 \\leq k_{n}(d)<q_{n}$ such that\n\n  $$f^{-k_{n}(d)}(d) \\in V^{(f)}_{n,\\gamma}(f^{-i_{n}(c)}(c))\\subset  ]y_{1},y_{3}[$$\n\n  \\item For every $n \\in \\mathbb{N}_{0},~\\bigcup\\limits_{i=0}^{q_{n}-1} f^{-i}\\big(B\\backslash E(c_{1},c)\\big)\\subset S^{1}\\backslash\n  V^{(f)}_{n,\\gamma_{0}}(f^{-i_{n}(c)}(c))$.\\\\\n\\item For every $~d \\in Q_{11}( \\mathbb{N}_{0})$ \\textrm{and } $n\\in \\mathbb{N}_{0}$, \\textrm{we have } $f^{-i_{n}(d)}(d)\\in\n~]f^{q_{n}}(y_{1})+\\gamma_{0}l_{n-1}, y_{2}-\\gamma_{0}l_{n-1}[$.\\\\\n   \\item For every $~d \\in Q_{12}( \\mathbb{N}_{0})$ \\textrm{and }$n\\in \\mathbb{N}_{0}$, \\textrm{we have }\n$f^{-j_{n}(d)}(d) \\in ~]y_{2}+\\gamma_{0}l_{n-1},\ny_{3}-\\gamma_{0}l_{n-1}[$.\n\\end{enumerate}\n\\end{prop}\n\\medskip\n\n\\begin{proof} Let $d\\in B\\backslash \\{c\\}$.\n\nAssertion (1): The\nintervals $f^{i_{n}(d)}([y_{1},~y_{2}])$ and\n$f^{j_{n}(d)}([y_{2},~y_{3}])$ are comparable (that is there is a\npositive constant $0<K<1$ such that $K \\leq\n\\dfrac{m(f^{i_{n}(d)}([y_{1},~y_{2}]))}{m(f^{j_{n}(d)}([y_{2},~y_{3}]))}\n\\leq K^{-1}$ for every $n \\in \\mathbb{N}_{0}$) and are comparable to\ntheir union $[f^{j_{n}(d)}(y_{2}),~f^{i_{n}(d)}(y_{2})]$ which\nimplies, by Lemma \\ref{l:31} and Denjoy's inequality, that the\nfour intervals\n$[y_{1},~y_{2}],~[y_{2},~y_{3}],~[f^{j_{n}(d)-i_{n}(d)}(y_{2}),y_{2}],~[y_{2},~f^{i_{n}(d)-j_{n}(d)}(y_{2})]$\nare comparable. In particular, the ratios\n$\\dfrac{m([f^{-i_{n}(d)}(d),~y_{2}])}{m([y_{1},~y_{2}])}$ and\n$\\dfrac{m([f^{-i_{n}(d)}(d),~y_{2}])}{m([f^{j_{n}(d)-i_{n}(d)}(y_{2}),~y_{2}])}=t_{n}(d)$ are comparable.\nSo, for $d\\in Q_{2}(\\mathbb{N}_{0}),~\\lim_{n \\to +\\infty}\n~t_{n}(d)=0$ which is equivalent to the assertion:\n$$\\forall ~\\gamma >0,~\\exists ~ n_{\\gamma} \\in \\mathbb{N}_{0}\n~\\textrm{such that for every }~n \\geq n_{\\gamma},~ n \\in\n\\mathbb{N}_{0}~:~f^{-i_{n}(d)}(d) \\in V^{(f)}_{n,\\gamma}(y_{2}).\n$$\n$\\bullet$ ~ Similarly, the ratios\n$\\dfrac{m([y_{2},~f^{-j_{n}(d)}(d)])}{m([y_{1},~y_{2}])}$ and\n$\\dfrac{m([y_{2},~f^{-j_{n}(d)}(d)])}{m([y_{2},~f^{i_{n}(d)-j_{n}(d)}(y_{2})])}$\nare comparable, which is comparable to the\nratio\n$\\dfrac{m([f^{j_{n}(d)-i_{n}(d)}(y_{2}),~f^{-i_{n}(d)}(d)])}{m([f^{j_{n}(d)-i_{n}(d)}(y_{2}),~y_{2}])}\n=1-t_{n}(d)\n$ (by the Lemma \\ref{l:31}). So, for $d \\in Q_{3}(\\mathbb{N}_{0}),~\\lim_{n \\to +\\infty}\n~t_{n}(d)=1$, which is equivalent to the assertion:\n$$\\forall ~\\gamma >0,~\\exists ~ n_{\\gamma}\\in \\mathbb{N}_{0}\n~\\textrm{such that for every }~n \\geq n_{\\gamma},~ n \\in\n\\mathbb{N}_{0}:~f^{-j_{n}(d)}(d) \\in V^{(f)}_{n,\\gamma}(y_{2}).\n$$\n\nAssertion (2): Let $d \\in Q_{1}(\\mathbb{N}_{0})$. There exists\n$0<\\gamma (d)<1$ such that for every $n \\in \\mathbb{N}_{0},~t_{n}(d)\n\\geq \\gamma (d) ~ \\textrm{and}~1-t_{n}(d) \\geq  \\gamma (d) $. Since\n$Q_{1}(\\mathbb{N}_{0})$ is finite there exists $0<\\gamma_{0}<1$ and\nan infinite subset $M_{2}$  of $\\mathbb{N}_{0}$\n($\\mathbb{N}_{0}\\backslash M_{2}$ is finite) such that the points\n$f^{-i_{n}(d)}(d)$ and $f^{-j_{n}(d)}(d)$ are contained in the set\n$S^{1}\\backslash V^{(f)}_{n,\\gamma_{0}}(y_{2})$ for all $d\\in\nQ_{1}(M_{2})$  and $n \\in M_{2}$. By Lemma \\ref{l:25}, $~ d\\notin f^{i}\n([y_{1},~y_{2}])\\cup f^{j} ([y_{2},~y_{3}])$, for every $0\n\\leq i < q_{n}, ~i \\neq i_{n}(d), ~j = \\varphi_{n}(i)$. Hence, for every $0\n\\leq i <q_{n}, ~i \\neq i_{n}(d):~f^{-i}(d) \\notin [y_{1},~y_{2}]$\nand every $0 \\leq j <q_{n},~j \\neq\nj_{n}(d)=\\varphi_{n}(i_{n}(d)): f^{-j}(d)\\notin [y_{2},~y_{3}]$. In\nparticular, for every $0 \\leq i <q_{n},~i \\neq i_{n}(d),~i \\neq\nj_{n}(d): ~f^{-i}(d) \\notin [y_{1},~y_{3}]$. So $f^{-i}(d) \\notin\nV^{(f)}_{n,\\gamma_{0}}(y_{2})$ since\n$V^{(f)}_{n,\\gamma_{0}}(y_{2})\\subset [y_{1},~y_{3}]$. Then\n$\\bigcup_{0 \\leq i <q_{n}}f^{-i}(B\\backslash E(c_{1},c))\\subset\nS^{1}\n\\backslash V^{(f)}_{n,\\gamma_{0}}(y_{2})$.\n\\bigskip\n\nWrite $\\mathbb{N}_{0}$ instead of $M_{2}$.\n\\\n\\\\\n\nAssertion (3): Let $d \\in Q_{11}(\\mathbb{N}_{0})$. Then there exist\nan integer ~ $n(d) \\in \\mathbb{N}_{0}$ such that for every $n\\in\n\\mathbb{N}_{0}~( n \\geq n(d))~,~0 \\leq i_{n}(d)< q_{n-1}$,\n\n\\begin{align*}\nf^{-i_{n}(d)}(d) \\in [y_{1},~y_{2}]\\cup\nf^{j_{n}(d)-i_{n}(d)}([y_{2},~y_{3}])&=[y_{1},~y_{2}]\\cup\n[f^{q_{n}}(y_{1}),~f^{q_{n}}(y_{2})]\\\\\\\\\n& =[f^{q_{n}}(y_{1}),y_{2}]\n\\end{align*}\n and\n$$\\gamma_{0} \\leq\nt_{n}(d)=\\dfrac{m([f^{-i_{n}(d)}(d),~y_{2}])}{m([f^{q_{n}}(y_{1}),~y_{2}])}\n\\leq 1-\\gamma_{0}.$$\n\\medskip\n\\\n\\\\\nSince the intervals $[f^{q_{n}}(y_{1}),~y_{2}]$ and $[y_{1},~y_{2}]$\nare comparable, there exists ~ $0 <\\gamma_{1}<\\gamma_{0}$ and an\ninteger $n^{\\prime}(d) \\in \\mathbb{N}_{0}$ such that for all \\ $d\\in\n\\mathbb{N}_{0}$ and $n \\geq n^{\\prime}(d)$: $f^{-i_{n}(d)}(d) \\in\n[f^{q_{n}}(y_{1})+\\gamma_{1}l_{n-1},~y_{2}-\\gamma_{1}l_{n-1}]$.\nSince $Q_{11}(\\mathbb{N}_{0})$ is finite, there exists an integer\n$n_{1} \\in \\mathbb{N}_{0}$ such that for all \\ $d\\in Q_{11}(\n\\mathbb{N}_{0})$ and $n\\in \\mathbb{N}_{0},~n \\geq n_{1}$:\n$$f^{-i_{n}(d)}(d) \\in\n[f^{q_{n}}(y_{1})+\\gamma_{1}l_{n-1},~y_{2}-\\gamma_{1}l_{n-1}].$$\n\\medskip\n\\\n\\\\\nAssertion (4): Let $d\\in Q_{12}( \\mathbb{N}_{0})$. Then there exist\nan integer ~ $n(d) \\in \\mathbb{N}_{0}$ such that for every $n\\in \\mathbb{N}_{0}, \\ n \\geq n(d)$,  $q_{n-1} \\leq i_{n}(d) <\nq_{n}$, $f^{-j_{n}(d)}(d) \\in [y_{2},~y_{3}]$ and\n$$\\gamma_{0} \\leq\nt_{n}(d) = \\dfrac{m([f^{-i_{n}(d)}(d),~y_{2}])}{m([y_{1},~y_{2}])}\n\\leq 1-\\gamma_{0}.$$\n\\medskip\n\\\n\\\\\nSince the ratios\n$$\\dfrac{m([f^{-j_{n}(d)}(d), ~y_{3}])}{m([y_{2},~y_{3}])}\n~~~~~~~~~ \\  \\textrm{ and } \\ ~~~~~~~~~~~\n\\dfrac{m([f^{-i_{n}(d)}(d),~y_{2}])}{m([y_{1},~y_{2}])}$$\n\\medskip\n\\\n\\\\\n are comparable, there exists $0 <\\gamma_{2}<\\gamma_{0}$ such that\n$f^{-j_{n}(d)}(d) \\in\n[y_{2}+\\gamma_{2}l_{n-1},~y_{3}-\\gamma_{2}l_{n-1}], \\ \\textrm{for\nall } \\ d\\in Q_{12}(\\mathbb{N}_{0})$. Since $Q_{12}(\\mathbb{N}_{0})$\nis finite, there exists an integer ~ $n_{2} \\in \\mathbb{N}_{0}$ such\nthat $\\textrm{for all } \\ d\\in Q_{12}(\\mathbb{N}_{0})$ and $n\\in\n\\mathbb{N}_{0},~n \\geq n_{2}$:  $$f^{-j_{n}(d)}(d) \\in\n[y_{2}+\\gamma_{2}l_{n-1},~y_{3}-\\gamma_{2}l_{n-1}]$$\n\\end{proof}\n\n\\begin{cor}\\label{c:37}\nFor every $d \\in E(c_{1},c)$,  we have \\[\\lim_{n \\to + \\infty,~n \\in\n\\mathbb{N}_{0}}\\dfrac{m([f^{-k_{n}(d)}(d),~y_{2}])}{m([y_{1},~y_{2}])}\n=0 \\]\n\\end{cor}\n\\medskip\n\n\\begin{proof} It is a consequence of Proposition \\ref{p:47}.\n\\end{proof}\n\\medskip\n\n\\\n\\\\\n\\section{\\bf Secondary Cells}\n\nWe introduce in this section a new triple $(z_{1},z_{2},z_{3})$ in\n$U_{\\delta}(x_{0})$ depending on two real parameters $\\beta$ and\n$\\gamma$. Let $\\beta,~\\gamma \\in ]0,\\gamma_{0}[~(\\beta <\\gamma)$.\nFor $n \\in \\mathbb{N}_{0}~(n \\geq n_{\\beta}),~$ we define the points\n$z_{1},z_{2},z_{3}\\in S^{1}$ ($z_{1}\\prec z_{2}\\prec z_{3})$ as\nfollows: $z_{2} = y_{2}$ and $z_{1}, ~z_{3}\\in\nV^{(f)}_{n,\\gamma}(z_{2})\\backslash V^{(f)}_{n,\\beta}(z_{2})$ i.e.\n\n$$\\beta\\leq \\frac{m([z_{1},z_{2}])}{m([y_{1},y_{2}])}\\leq\n\\gamma ~\\textrm{and }~\\beta\\leq\n\\frac{m([z_{2},z_{3}])}{m([y_{1},y_{2}])}\\leq \\gamma $$\n\\bigskip\n\n\\textbf{Definition (secondary cell)}. The triple\n$(z_{1},~z_{2},~z_{3})$ is called a $(\\beta,\\gamma)$-derived cell\nassociated to $(f,x_{0},c,\\mathbb{N}_{0},\\delta)$.\n\\medskip\n\n\n\\begin{prop}\\label{p:42} Under the notations above, for every $n \\in \\mathbb{N}_{0},~n \\geq n_{\\beta} $ we have:\n\\begin{itemize}\n \\item [(0)] $[z_{1},z_{3}]\\subset  V^{(f)}_{n,\\gamma}(y_{2})\\subset [y_{1},y_{3}]$.\n\n \\item [(1)] For any $d\\in E(c_{1},c)$, there exists a unique $0\\leq k_{n}(d)<q_{n}$ such that $f^{-k_{n}(d)}(d)\\in  V^{(f)}_{n,\\frac{1}{4}\\beta}(y_{2})$.\n\n \\item [(2)] $~m\\left(f^{j}([z_{1},z_{3}])\\right)\\leq K\\lambda^{n}$, for every $0\\leq j<q_{n}$, where\n$\\lambda = (1+e^{-V})^{-\\frac{1}{2}}$ and  $K$ is a constant\nindependent of $n$, $V= \\textrm{Var}(\\log(\\mathrm{Df}))$.\n\n \\item [(3)] $~\\sum_{j=0}^{q_{n}-1}m\\left(f^{j}([z_{1},z_{3}])\\right)\\leq\n2$.\n\n \\item [(4)] The triples  $\\big(z_{1},z_{2},z_{3}\\big)$~ and\n$(f^{q_{n}}\\big(z_{1}),f^{q_{n}}(z_{2}),f^{q_{n}}(z_{3})\\big)$\nsatisfy conditions  $(a)$  and  $(b)$ of Definition \\ref{d:32} for\n$x_{0}$  and the constant $R(\\beta)  = ~\\frac{Re^{2V}}{\\beta}$,\nwhere $R=e^{3V}+e^{V}+1$.\n\n \\item [(5)] $f^{i}([z_{1},z_{3}])$ does not contain any  point of $B$, for every $0\\leq i< q_{n}$ and $i\\neq k_{n}(d),~d \\in\nE(c_{1},c)$.\n\n\\item [(6)] For every $d\\in E(c_{1},c),~d \\in\nf^{k_{n}(d)}(]z_{1},z_{3}[)$.\n\n\\end{itemize}\n\\end{prop}\n\\medskip\n\n\\begin{proof}\nAssertion (0): This results from the definition of $\\big(z_{1},z_{2},z_{3}\\big)$, for $\\gamma$ small.\\\\\n\nAssertion (1): This follows from the Assertion (1) in Proposition \\ref{p:47}.\\\\\n\nAssertions (2) and (3) hold since $[z_{1},z_{3}]\\subset\n[y_{1},y_{3}]$ and by applying the same proof to\n$\\big(y_{1},y_{2},y_{3}\\big)$ instead of\n$\\big(y_{1},y_{2},y_{3}\\big)$ of the properties (c-2) and (c-3) of Proposition \\ref{p:41}.\\\\\nAssertion (4): We have\n$$\\dfrac{\\beta}{\\gamma} = \\dfrac{\\beta m([y_{1},y_{2}])}{\\gamma\nm([y_{1},y_{2}])} \\leq \\dfrac{m([z_{2},z_{3}])}{m([z_{1},z_{2}])}\n\\leq \\dfrac{\\gamma m([y_{1},y_{2}])}{\\beta m([y_{1},y_{2}])} =\n\\dfrac{\\gamma}{\\beta}.$$\n\nThen by Lemma \\ref{l:31}, we get\n\\bigskip\n\n\\begin{align*}\n  e^{-2V}\\dfrac{\\beta}{\\gamma} & = e^{-2V}\\dfrac{\\beta m([y_{1},y_{2}])}{\\gamma m([y_{1},y_{2}])} \\\\\n& \\leq e^{-2V}\\dfrac{m([z_{2},z_{3}])}{m([z_{1},z_{2}])} \\leq\n\\dfrac{m(f^{q_{n}}([z_{2},z_{3}]))}{m(f^{q_{n}}([z_{1},z_{2}]))}\\\\\n& \\leq  e^{2V}\\dfrac{m([z_{2},z_{3}])}{m([z_{1},z_{2}])} \\\\\n& \\leq e^{2V}\\dfrac{\\gamma m([y_{1},y_{2}])}{\\beta m([y_{1},y_{2}])}\n= e^{2V} \\dfrac{\\gamma}{\\beta}.\n\\end{align*}\n\\\\\\\\\n\n Hence $\\big(z_{1},z_{2},z_{3}\\big)$ satisfies conditions (a) and (b) of Definition \\ref{d:32} for the\nconstant $R(\\beta, \\gamma) = \\dfrac{R}{\\beta}e^{2V}$. On the other\nhand, since $[z_{1},z_{3}]\\subset [f^{q_{n}}(y_{1}),y_{3}],~x_{0}\\in\n[f^{q_{n}}(y_{1}),y_{3}]$ and\n\n$\\max \\left(m([f^{q_{n}}(y_{1}),x_{0}]); m([x_{0},y_{3}])\\right)\\leq R\nm([y_{1},y_{2}]),$ it follows that $$\\underset{1\\leq i\\leq 3}\\max(\nm([x_{0},z_{i}])\\leq\n\\max\\left(m([f^{q_{n}}(y_{1}),x_{0}]);m([x_{0},y_{3}])\\right)\\leq R\nm([y_{1},y_{2}])\\leq \\dfrac{R}{\\beta}m([z_{1},z_{2}]).$$\n\nFurthermore, as $[z_{1},z_{3}]\\subset ] y_{1},y_{3}[ $ then\n$f^{q_{n}}([z_{1},z_{3}])\\subset f^{q_{n}}(] y_{1},y_{3}[)$\n\\\\\n\nSince $x_{0}\\in [f^{q_{n}}(y_{1}),y_{3}]~ \\textrm{and} ~ f^{q_{n}}(]\ny_{1},y_{3}[)\\cup f^{q_{n-1}} ( ]f^{q_{n}}(y_{1}),y_{2}[ )\\cup\nf^{q_{n}-q_{n-1}}( ] y_{2},y_{3}[)\\subset [f^{q_{n}}(y_{1}),y_{3}],$\n\nwe get\n\n\\begin{align*}\n\\underset{1\\leq i\\leq 3}\\max m([f^{q_{n}}(z_{i}),x_{0}])&\\leq\n\\max\\left (m([f^{q_{n}}(y_{1}),x_{0}]);m([x_{0},y_{3}])\\right )\\\\\n& \\leq\n\\dfrac{R}{\\beta}m([z_{1},z_{2}]) \\\\\n& \\leq \\dfrac{R}{\\beta}e^{2V}m(f^{q_{n}}([z_{1},z_{2}])~~\n(\\textrm{by Denjoy's inequality} ).\n\\end{align*}\n Therefore\n\n$\\big(f^{q_{n}}(z_{1}),f^{q_{n}}(z_{2}),f^{q_{n}}(z_{3})\\big)$\nsatisfies conditions (a) and (b) of Definition \\ref{d:32} for the\nconstant $R(\\beta,\\gamma) = \\dfrac{R}{\\beta}e^{2V}$. \\\\\n\nAssertion (5): If $d\\in  B$ and $0\\leq i < q_{n}$ be an integer such\nthat $d\\in f^{i}([z_{1},z_{3}])$ then $f^{-i}(d)\\in\n[z_{1},z_{3}]\\subset V^{(f)}_{n,\\gamma}(y_{2})\\subset\nV^{(f)}_{n,\\gamma_{0}}(y_{2})$. According to the Assertion (2) of\nPropositions \\ref{p:47}, we obtain $f^{-i}(d)\\notin\n\\bigcup\\limits_{j=0}^{q_{n}-1} f^{-j}\\big(B\\backslash E(c_{1},c)\n\\big)$, $0\\leq i < q_{n}$. In particular, $f^{-i}(d)\\notin\nf^{-i}\\big(B\\backslash E(c_{1},c) \\big)$. Hence $d\\in E(c_{1},c)$\nsuch that $0\\leq i < q_{n}$ and $f^{-i}(d) \\in\nV^{(f)}_{n,\\gamma}(y_{2})$. By Assertion (1), $i=k_{n}(d)$.\\\\\n\nAssertion (6) is a consequence of Assertions (0) and (1).\n\\end{proof}\n\\medskip\n\n\\begin{prop}[\\cite{A}, Proposition 4.2]\\label{p:46} Let $\\left(y_{1},y_{2},y_{3}\\right)\\subset\nU_{\\delta}(x_{0})$ be the primary cell and $(z_{1},z_{2},z_{3})$ an\n$(\\beta,\\gamma)$ secondary cell associated to\n$(f,x_{0},c,\\mathbb{N}_{0})$. Let $h$ be the homeomorphism\nconjugating $f$ to $g$ and assume that it admits in $x_{0}$ a positive\nderivative $\\textrm{Dh}(x_{0})>0$. Then the following properties hold:\n\n\\begin{itemize}\n \\item [(1)] $(h(y_{1}),h(y_{2}),h(y_{3}))$ is a\nprimary cell associated to $(g,h(x_{0}),h(c),\\mathbb{N}_{0})$.\n\n\\item [(2)] $(h(z_{1}),h(z_{2}),h(z_{3}))$ is a $(\\frac{\\beta}{2},2\\gamma)$-derived cell associated to\n$(g,h(x_{0}),h(c),\\mathbb{N}_{0})$.\n\n\\item [(3)] There is an integer $n_{\\gamma} \\in \\mathbb{N}_{0}$ such\nthat for every $n \\in \\mathbb{N}_{0},~n \\geq n_{\\gamma}$ :\n$$h \\big(V^{(f)}_{n,\\gamma}(y_{2}) \\big) \\subset V^{(g)}_{n,2\\gamma}\\big(h(y_{2})\\big)\n\\subset h \\big(V^{(f)}_{n,4\\gamma}(y_{2}) \\big)$$\n\\end{itemize}\n\\end{prop}\n\\medskip\n\n\\begin{prop}\\label{p:43} Under the notations of Proposition \\ref{p:46}, for every $n\n\\in \\mathbb{N}_{0},~n \\geq n_{\\beta} $ we have:\n\\medskip\n\\begin{itemize}\n\n \\item [(h-0)] $[h(z_{1}),h(z_{3})]\\subset  V^{(g)}_{n,2\\gamma}(h(y_{2}))\\subset\n[h(y_{1}),h(y_{3})]$.\n\n \\item [(h-1)] For any $d \\in E(c_{1},c)$, $k_{n}(d)$ is the unique integer in $ [0,~q_{n}[$ such that\n$g^{-k_{n}(d)}(h(d))\\in  V^{(g)}_{n,\\frac{1}{2}\\beta}(h(y_{2}))$.\n\n \\item [(h-2)] $~m\\left(g^{j}([h(z_{1}),h(z_{3})])\\right)\\leq K^{\\prime}(\\lambda^{\\prime})^{n}$, for every  $0\\leq\nj<q_{n}$,\nwhere $\\lambda^{\\prime} = (1+e^{-V^{\\prime}})^{-\\frac{1}{2}}$ and\n$K^{\\prime}$ is a constant independent of  $n$,\n$V^{\\prime}=\\textrm{Var}(\\log(Dg))$.\n\n \\item [(h-3)] $~\\sum_{j=0}^{q_{n}-1}m\\left(g^{j}([h(z_{1}),h(z_{3})])\\right)\\leq 2$\n\n \\item [(h-4)] $g^{i}([h(z_{1}),h(z_{3})])$ does not contain any break point of $h(B)$ for every $0\\leq i< q_{n}$ and $i\\neq k_{n}(d),\n~d \\in E(c_{1},c)$.\n\n\\item [(h-5)] For every $d\\in E(c_{1},c)$,\n\n$$ \\lim_{n\\to\n+\\infty}\\dfrac{m\\big([g^{-k_{n}(d)}(h(d)),h(y_{2})]\\big)}{m\n\\big([h(y_{1}),h(y_{2}) ] \\big)} = 0 $$\n\n\\item [(h-6)] For every $d \\in E(c_{1},c),~h(d) \\in\ng^{k_{n}(d)}(]h(z_{1}),h(z_{3})[)$.\n\n\\end{itemize}\n\\end{prop}\n\\medskip\n\n\\begin{proof} Assertion $($h-0$)$ is a consequence of Proposition\n\\ref{p:46}, (3).\n\\\n\\\\\n\n(h-1$)$: Let $d\\in E(c_{1},c)$, by Proposition \\ref{p:42} (1), there\nexists  $0\\leq k_{n}(d)<q_{n}$ such that $f^{-k_{n}(d)}(d)\\in\nV^{(f)}_{n,\\frac{1}{4}\\beta}(z_{2})$; then $g^{-k_{n}(d)}(h(d)) =\nh(f^{-k_{n}(d)}(d))\\in h(V^{(f)}_{n,\\frac{1}{4}\\beta}(z_{2}))\\subset\nV^{(g)}_{n,\\frac{1}{2}\\beta}(h(z_{2}))$ for every $n\\geq\nn^{\\prime\\prime}_{\\beta},~~n \\in \\mathbb{N}_{0}$. Uniqueness: If\n~~$0 \\leq i,j < q_{n}$ satisfy $g^{-i}(h(d)),~g^{-j}(h(d))\\in\nV^{(g)}_{n,2\\gamma}(h(z_{2}))$, then $f^{-i}(d), ~f^{-j}(d)\\in\nh^{-1}\\big( V^{(g)}_{n,\\gamma}(h(z_{2})\\big)\\subset V^{(f)}_{n,2\\gamma}(z_{2})$. Therefore by Proposition \\ref{p:42} (1), $i=j$.\\\\\n\\\n\\\\\n$($h-2$)$ and $($h-3$)$: by Proposition \\ref{p:46}, (2),\n$(h(z_{1}),h(z_{2}),h(z_{3}))$ is a\n$(\\frac{\\beta}{2},2\\gamma)$-derived cell associated to\n$(g,h(x_{0}),h(c),\\mathbb{N}_{0})$. Therefore, the proof is similar to Proposition \\ref{p:42}, \\textit{(2)} and \\textit{(3)} by replacing $f$ by $g$.\\\\\n\\\n\\\\\n$($h-4$)$: Let $0\\leq i<q_{n}$ and assume that\n$g^{i}\\big([h(z_{1}),h(z_{3})] \\big)$ contains a break point\n$d^{\\prime} = h(d)$ of $g$ for a break point $d$ of $f$, then\n$f^{i}\\big([z_{1},z_{3}] \\big)$ contains the break point $d$ of $f$.\nBy Proposition \\ref{p:42}, (1) and (5), we have $d\\in\nE(c_{1},c)$ and $i = k_{n}(d)$.\n\\\n\\\\\n$($h-5$)$: Let  $d \\in E(c_{1},c)$ and $\\gamma >0$. By Proposition\n\\ref{p:41} (6), there is an integer $n_{\\gamma}^{\\prime} \\in \\mathbb{N}_{0}$\nsuch that for every $n \\in \\mathbb{N}_{0},~n \\geq n_{\\gamma}^{\\prime}$ :\n$f^{-k_{n}(d)}(d) \\in V^{(f)}(y_{2})$. On the other hand, by\nProposition \\ref{p:46}, (3), there is an integer $n_{\\gamma} \\in\n\\mathbb{N}_{0},~n_{\\gamma}\\geq n_{\\gamma}^{\\prime}$ such that for every $n\n\\in \\mathbb{N}_{0},~n \\geq n_{\\gamma}$ : $ h\n\\big(V^{(f)}_{n,\\frac{\\gamma}{2}}(y_{2}) \\big) \\subset\nV^{(g)}_{n,\\gamma}(h(y_{2}))$. As $g^{-k_{n}(d)}(h(d)) =\nh(f^{-k_{n}(d)}(d))$, it follows that $g^{-k_{n}(d)}(h(d))\\in\nV^{(g)}_{n,\\gamma}(h(y_{2}))$ for every $n \\geq n_{\\gamma},~n \\in\n\\mathbb{N}_{0}$. Since $\\gamma>0$ is arbitrary, so, $$ \\lim_{n \\to\n+\\infty} \\dfrac{m\\big([g^{-k_{n}(d)}(h(d)),h(y_{2}) ] \\big)}{m\n\\big([h(y_{1}),h(y_{2}) ] \\big)}=0\n$$\n$($h-6$)$ is a consequence of Assertions ($h-0$) and ($h-1$).\n\\end{proof}\n\\medskip\n\n\\section{\\bf Control of distortions}\n\\medskip\n\n\\begin{prop}[\\cite{A}, Proposition 5.1]\\label{p:2} Let $\\mathbb{N}_{0}$ and $\\gamma_{0}$ are as in Proposition \\ref{p:47}. Let\n$\\beta,~\\gamma \\in ]0,\\gamma_{0}[~(\\beta <\\gamma)$. Assume that the\nconjugation homeomorphism $h$ from $f$ to $g$ admits at $x_{0}$ a\npositive derivative $\\mathrm{Dh}(x_{0}) = \\omega_{0} >0$. Then there\nexists an integer $n_{\\beta} \\in \\mathbb{N}_{0}$ such that: for\nevery $n\\in \\mathbb{N}_{0}, \\ n\\geq n_{\\beta},$ we have\n\n$$\\left|\n\\dfrac{\\mathrm{Dr}_{g^{q_{n}}}\\big(h(z_{1}),h(z_{2}),h(z_{3})\\big)}{\\mathrm{Dr}_{f^{q_{n}}}(z_{1},z_{2},z_{3})}\n- 1\\right|\\leq \\dfrac{2}{1-\\gamma_{0}}\\beta$$\n\\end{prop}\n\\bigskip\n\\\n\\\\\n\nThe next proposition is an another distortion control which is\nopposite to the one of Proposition \\ref{p:2}, this allows us to\nprove that the conjugation from $f$ to $g$ is singular with respect\nto the Lebesgue measure.\n\n\\begin{prop}\n\\label{p:44} Assume that the irrational rotation number\nof $f$ is of bounded type. Let $c, c_{1}$ in $B(f)$,  $c\\neq c_{1}$,  $\\mathbb{N}_{0}$ and $\\gamma_{0}$ are as in\nProposition \\ref{p:47}. Then\nfor any $\\varepsilon >0$, there exists $0<\\gamma<\\gamma_{0}$ such\nthat for any $\\beta \\in ]0,\\gamma[$ there exists $n_{\\beta} \\in\n\\mathbb{N}_{0}$ such that for all $n \\geq n_{\\beta},~n \\in\n\\mathbb{N}_{0}$ the ($\\beta,\\gamma$) secondary cell\n$(z_{1},z_{2},z_{3})$ associated to\n$(f,x_{0},c,\\mathbb{N}_{0},\\delta)$ satisfies the following\ninequality\n$$ \\left| \\dfrac{\\textrm{Dr}_{g^{q_{n}}}\\left(h(z_{1}),h(z_{2}),h(z_{3})\\right)}{\\textrm{Dr}_{f^{q_{n}}}(z_{1},z_{2},z_{3})}-\n\\Pi(c_{1},c) \\right|\\leq A \\ \\varepsilon, ~~\\textrm{for some\nconstant}  \\; A> 0,$$\n\nwhere\n$$\\Pi(c_{1},c)=\n \\underset{d\\in E (c_{1},c)}\\prod \\dfrac{\\sigma_{g}(h(d))}{\\sigma_{f}(d)}.$$\n\\end{prop}\n\\medskip\n\nThe proof of the proposition \\ref{p:44} is an elaboration of the proof of (\\cite{A}, Proposition 5.3) and so we only\ndescribe the changes that are necessary.\n\\medskip\n\n\\begin{lem}\\label{l:49q}\nAssume that the\nrotation number $\\alpha$ of $f$ is of bounded type. Let $c_{1} \\in C(f)\\backslash \\{c\\}$, $u_{0}$, $\\gamma_{c,c_{1}}$ and\n$\\mathbb{N}_{0}$ as in Proposition \\ref{p:47}. Let $h$ be the conjugating from $f$ to $R_{\\alpha}$:\n$h\\circ f= R_{\\alpha}\\circ h$. Assume that Dh$(x_{0})>0$. Then for any $\\varepsilon >0$,\nthere exists $\\eta >0$ such that for any $u\\in ]0,\\eta[$ there exists $n_{u,r} \\in\n\\mathbb{N}_{c,c_{1}}$ such that for any $n \\in \\mathbb{N}_{c,c_{1}},\\ n\\geq\nn_{u,r}$: the $($r,u$)$-derived cell $(z_{1},z_{2},z_{3})$ associated to\n$(f,x_{0},c)$ satisfies\n\\\n\\\\\n$$\\arrowvert\\textrm{Dcr}_{f^{q_{n}}}(z_{1},z_{2},z_{3})-\n\\Pi_{f}(c,c_{1})\\arrowvert\\leq C_{1}\\varepsilon,$$ where $$\\Pi_{f}(c,c_{1})= \\underset{b\\in E (c_{1},c)}\\prod\n\\sigma_{f}(b)$$ and \\; $C_{1}$ is a positive constant.\n\\end{lem}\n\\bigskip\n\n\n\\begin{proof}\nLet $\\varepsilon>0$. Since $\\textrm{Df}$ is absolutely continuous on\nevery interval $[c_{i},c_{i+1}]~(0 \\leq i \\leq p)$, there exists a\nreal $0<\\eta_{0}<e^{2V}\\gamma_{0}$ such that for every disjoint\nintervals $([a_{j},b_{j}])_{j \\in J}$ of continuity intervals of\n$\\textrm{Df}$ (these later are the $[c_{i},c_{i+1}]~(0 \\leq i \\leq\np)$) such that if $\\sum_{j \\in J}|a_{j}-b_{j}|<\\eta_{0}$ then\n$\\sum_{j \\in J}|\\textrm{Df}(a_{j})-\\textrm{Df}(b_{j})|<\\varepsilon$.\nLet $0<\\beta<\\gamma<\\frac{1}{5}e^{-2V}\\eta_{0}$ and\n$(z_{1},z_{2},z_{3})$ be the $(\\beta , \\gamma)$-derived cell\nassociated\nto $(f,x_{0},c,\\mathbb{N}_{0})$. For $n\\in \\mathbb{N}_{0}$, denote the following:\\\\\n\n \\textbullet ~ $I:= \\{0,1,\\dots,q_{n}-1\\}\\backslash \\{k_{n}(d):~d \\in E(c_{1},c)\\}$.\\\\\n\n\\textbullet ~ $D_{i}(f):=\n\\textrm{Dcr}_{f}\\big(f^{i}(z_{1}),f^{i}(z_{2}),f^{i}(z_{3})\\big),~0\n\\leq\ni<q_{n}$.\\\\\n\n\\textbullet ~ $P:= \\prod_{i\\in I}D_{i}(f)~~;~~ P_{1}:= \\prod_{d\\in\nE(c_{1},c)}D_{k_{n}(d)}(f)$.\\\\\n\n\\textbullet ~ $D_{n}(f):=\n\\textrm{Dcr}_{f^{q_{n}}}(z_{1},z_{2},z_{3})$.\n\\medskip\n\nOne has $D_{n}(f) = PP_{1}$.\n\\bigskip\n\n\\textbf{Step 1}. We consider $D_{i}(f),~i \\in I$. By Proposition\n\\ref{p:42} (5), $\\textrm{Df}$ is continuous on the interval\n$[f^{i}(z_{1}),f^{i}(z_{3})]$. Then by the mean value theorem, there\nexist $a_{i}\\in ]f^{i}(z_{1}),f^{i}(z_{2})[$ and $b_{i}\\in\n]f^{i}(z_{2}),f^{i}(z_{3})[$ such that $D_{i}(f)=\n\\dfrac{\\textrm{Df}(a_{i})}{\\textrm{Df}(b_{i})} $. Since\n$\\big([a_{i},f^{i}(z_{2})] \\big)_{i\\in I}$ are disjoint intervals of\ncontinuity of $\\textrm{Df}$, by Lemma \\ref{l:31}, they satisfy the\ninequalities :\\\\\\\\\n\n$\\begin{array}{ll}\n   \\sum_{i\\in I}m([a_{i},f^{i}(z_{2})]) & \\leq \\sum_{i \\in I}m([f^{i}(z_{1}),f^{i}(z_{2})])\n\\\\\\\\\n\n   & \\leq \\sum_{i\\in I} e^{2V} \\dfrac{m([z_{1},z_{2}])}{m([y_{1},y_{2}])}\nm([f^{i}(y_{1}),f^{i}(y_{2})])\\\\\\\\\n\n   & \\leq e^{2V}\\gamma \\sum_{i\\in I}m([f^{i}(y_{1}),f^{i}(y_{2})])\\\\\n & \\leq e^{2V}\\gamma \\\\\n& \\leq \\eta_{0}.\n \\end{array}\n$ \\\\\n\nConsequently\n\n\\begin{equation}\\label{(1)}\n    \\sum_{i\\in I} |\\textrm{Df}(f^{i}(z_{2}))-\\textrm{Df}(a_{i})|\\leq \\varepsilon\n\\end{equation}\n\\medskip\n\nAlso, $\\big([f^{i}(z_{2}),b_{i}] \\big)_{i\\in I}$ are disjoint intervals of continuity of $\\textrm{Df}$, so by Lemma \\ref{l:31}, they satisfy:\\\\\n\n$\\begin{array}{ll}\n   \\sum_{i\\in I}m([f^{i}(z_{2}),b_{i}]) & \\leq \\sum_{i\\in I}m([f^{i}(z_{2}),f^{i}(z_{3})])\n\\\\\\\\\n\n   & \\leq \\sum_{i\\in I} e^{2V} \\dfrac{m([z_{2},z_{3}])}{m([y_{1},y_{2}])}\nm([f^{i}(y_{1}),f^{i}(y_{2})])\\\\\\\\\n\n   & \\leq e^{2V}\\gamma \\sum_{i\\in I}m([f^{i}(y_{1}),f^{i}(y_{2})])\n\\leq \\eta_{0}.\n \\end{array}\n$ \\\\\\\\\nConsequently\n\n\\begin{equation}\\label{(2)}\n    \\sum_{i \\in I} |\\textrm{Df}(f^{i}(z_{2}))-\\textrm{Df}(b_{i})| \\leq \\varepsilon\n\\end{equation}\n\\medskip\n\nCombining (\\ref{(1)}) and (\\ref{(2)}), we get\n\n\\begin{equation}\\label{(3)}\n    \\sum_{i \\in I} |\\textrm{Df}(b_{i})-\\textrm{Df}(a_{i})|\\leq 2\\varepsilon .\n\\end{equation}\n\nSet $D^{\\ast}_{i}(f):= \\max\\big(D_{i}(f),(D_{i}(f))^{-1}\\big)$ and\n$P^{\\ast}:= \\prod_{i\\in I} D^{\\ast}_{i}(f)$.\n\\medskip\n\nSince $\\textrm{Df}$ takes its values in $[m_{1},M_{1}]~~(m_{1}>0)$, the following properties hold:\\\\\n\n$0\\leq D^{\\ast}_{i}(f)-1 \\leq \\dfrac{1}{m_{1}}\n|\\textrm{Df}(b_{i})-\\textrm{Df}(a_{i})|$.\\\\\n\n$\\sum_{i \\in I} |D^{\\ast}_{i}(f)-1|\\leq \\dfrac{2}{m_{1}}\n\\varepsilon$.\\\\\n\n$ |\\log D_{i}(f)|= \\log D^{\\ast}_{i}(f)\\leq D^{\\ast}_{i}(f)-1$\\\\\n\n$\\dfrac{1}{P^{\\ast}} \\leq P \\leq P^{\\ast}$.\\\\\n\nIt follows that\n\\begin{equation}\\label{(4)}\n    e^{-C_{0}\\varepsilon} \\leq P \\leq e^{C_{0}\\varepsilon}\n \\, \\, \\ \\textrm{where}  \\, \\, C_{0} = \\dfrac{2}{m_{1}}.\n\\end{equation}\n\\medskip\n\n\\textbf{Step 2}. We consider $D_{k_{n}(d)}(f),~d\\in E(c_{1},c)$. We have $d \\in ~ ]f^{k_{n}(d)}(z_{1}),f^{k_{n}(d)}(z_{3})[$.\\\\\n\n\\textbf{Case 2a}. $d\\in ]f^{k_{n}(d)}(z_{1}),f^{k_{n}(d)}(z_{2})[$\nwith $k_{n}(d)=i_{n}(d)$. By Proposition \\ref{p:42} (5),\n$\\textrm{Df}$ is continuous on the intervals\n$[f^{k_{n}(d)}(z_{1}),d],~[d,f^{k_{n}(d)}(z_{2})]$ and\n$[f^{k_{n}(d)}(z_{2}),f^{k_{n}(d)}(z_{3})]$; by the mean value\ntheorem there exist $t_{1}\\in ]f^{k_{n}(d)}(z_{1}),d[,~t_{2} \\in\n]d,f^{k_{n}(d)}(z_{2})[$ and $t_{3} \\in\n]f^{k_{n}(d)}(z_{2}),f^{k_{n}(d)}(z_{3})[$ such that\n$$D_{k_{n}(d)}(f) = (1-r_{n}(d))\\dfrac{\\textrm{Df}(t_{1})}{\\textrm{Df}(t_{3})}+r_{n}(d)\\dfrac{\\textrm{Df}(t_{2})}{\\textrm{Df}(t_{3})}$$\n~~where~~$$r_{n}(d) =\n\\dfrac{m([d,f^{k_{n}(d)}(z_{2})])}{m([f^{k_{n}(d)}(z_{1}),f^{k_{n}(d)}(z_{2})])}.$$\n\nWe have\n\\medskip\n\n $\\begin{array}{ll}\n           |D_{k_{n}(d)}(f)-\\sigma_{f}(d)| & \\leq |\\dfrac{\\textrm{Df}(t_{1})}{\\textrm{Df}(t_{3})}-\\dfrac{D_{-}f(d)}{D_{+}f(d)}|+\nr_{n}(d)\\dfrac{|\\textrm{Df}(t_{1})-\\textrm{Df}(t_{2})|}{\\textrm{Df}(t_{3})}\\end{array}\n$\n\\medskip\n\nSince $$\\begin{array}{ll}\n|\\dfrac{\\textrm{Df}(t_{1})}{\\textrm{Df}(t_{3})}-\\dfrac{D_{-}f(d)}{D_{+}f(d)}|\n\\leq \\dfrac{M_{1}}{m_{1}^{2}} \\big(\n|\\textrm{Df}(t_{1})-D_{-}f(d)|+|\\textrm{Df}(t_{3})-D_{+}f(d)|\\big),\n\\end{array}$$\n\\medskip\n\nand by Lemma \\ref{l:31}\n\\medskip\n\n$$\\begin{array}{ll}\n r_{n}(d)     & = \\dfrac{m \\big(f^{k_{n}(d)}([f^{-k_{n}(d)}(d),z_{2}]) \\big)}{m \\big(f^{k_{n}(d)}([z_{1},z_{2}]\n\\big)}\\\\\\\\\n    & \\leq e^{2V}\\dfrac{m ([f^{-k_{n}(d)}(d),z_{2}]) }{m ([z_{1},z_{2}])} \\\\\\\\\n& \\leq e^{2V}\\dfrac{m ([y_{1},y_{2}]) }{m ([z_{1},z_{2}])}\\times\n\\dfrac{m ([f^{-k_{n}(d)}(d),z_{2}]) }{m ([y_{1},y_{2}])} \\\\\\\\\n& \\leq \\dfrac{e^{2V}}{\\beta} s_{n}(d)\n \\end{array}$$\n\nwith ~~~~\n$$s_{n}(d):= \\dfrac{m ([f^{-k_{n}(d)}(d),z_{2}]) }{l\n([y_{1},y_{2}])}.$$\n\\medskip\n\nIt follows that:\n\n$$|D_{k_{n}(d)}(f)-\\sigma_{f}(d)| \\leq K_{0} \\big(\n\\dfrac{s_{n}(d)}{\\beta}+|\\textrm{Df}(t_{1})-D_{-}f(d)|+|\\textrm{Df}(t_{3})-D_{+}f(d)|\n \\big)$$\nwhere\n\n$K_{0}=\\max(\\dfrac{M_{1}}{m_{1}}e^{2V},\\dfrac{M_{1}}{m_{1}^{2}})$.\n\\medskip\n\nSince $\\underset{n\\to +\\infty}\\lim s_{n}(d)=0$ (Corollary\n\\ref{c:37}), there exists $n_{d,\\beta} \\in \\mathbb{N}_{0}$ such that\nfor any $n \\in \\mathbb{N}_{0},~ n \\geq n_{d,\\beta}$, one has\n$s_{n}(d)< \\beta\\varepsilon $. The intervals\n$(]t_{1},d[;~]d,t_{3}[)_{d\\in E(c_{1},c)}$ are disjoint intervals of\ncontinuity of $\\textrm{Df}$,  they satisfy  by Lemma \\ref{l:31}:\n\\bigskip\n\n $\n\\begin{array}{ll}\n m([t_{1},d])+m([d,t_{3}]) & \\leq 2 m([f^{k_{n}(d)}(z_{1}),f^{k_{n}(d)}(z_{2})])+m([f^{k_{n}(d)}(z_{2}),f^{k_{n}(d)}(z_{3})])\\\\\\\\\n\n & \\leq 3 e^{2V}\\gamma m([f^{k_{n}(d)}(y_{1}),f^{k_{n}(d)}(y_{2})])\\\\\\\\\n\n  & \\leq 3 e^{2V} \\gamma < \\eta_{0}\n\\end{array}\n$\n\n So, $$ |\\textrm{Df}(t_{1})-D_{-}f(d)|+|\\textrm{Df}(t_{3})-D_{+}f(d)|< \\varepsilon $$\n\\medskip\n\nHence, there exists $n_{d,\\beta} \\in \\mathbb{N}_{0}$ such that for\nevery $n \\in \\mathbb{N}_{0}$, $n \\geq n_{d,\\beta}$,\n\n\\begin{equation}\\label{(5)}\n    |D_{k_{n}(d)}(f)-\\sigma_{f}(d)|\\leq 2 K_{0}\\varepsilon\n\\end{equation}\n\\smallskip\n\n\\textbf{Case 2b}. $d\\in ]f^{k_{n}(d)}(z_{2}),f^{k_{n}(d)}(z_{3})[$\nwith $k_{n}(d)=j_{n}(d)$. By Proposition \\ref{p:42} (b-5),\n$\\textrm{Df}$ is continuous on the intervals\n$[f^{k_{n}(d)}(z_{1}),f^{k_{n}(d)}(z_{2})],~[f^{k_{n}(d)}(z_{2}),d]$\nand $[d,f^{k_{n}(d)}(z_{3})]$. By the mean value theorem, there\nexist $s_{1} \\in ]d, f^{k_{n}(d)}(z_{3})[,~s_{2} \\in\n]f^{k_{n}(d)}(z_{2}),d[$ and $s_{3} \\in\n]f^{k_{n}(d)}(z_{1}),f^{k_{n}(d)}(z_{2})[$ such that\n$$D_{k_{n}(d)}^{-1}(f)=(1-r^{\\prime}_{n}(d))\\dfrac{\\textrm{Df}(s_{1})}{\\textrm{Df}(s_{3})}+r^{\\prime}_{n}(d)\\dfrac{\\textrm{Df}(s_{2})}{\\textrm{Df}(s_{3})}$$\nwhere\n$$r^{\\prime}_{n}(d) = \\dfrac{m[f^{k_{n}(d)}(z_{2}),d])}{m[f^{k_{n}(d)}(z_{2}),f^{k_{n}(d)}(z_{3})])}.\n$$\n\\medskip\n\nAs in Case 2a, we have\n\\medskip\n\n $\\begin{array}{ll}\n           |D_{k_{n}(d)}(f)^{-1}-\\sigma_{f}(d)^{-1}| & \\leq |\\dfrac{\\textrm{Df}(s_{1})}{\\textrm{Df}(s_{3})}-\\dfrac{D_{+}f(d)}{D_{-}f(d)}|+\nr^{\\prime}_{n}(d)\n\\dfrac{|\\textrm{Df}(s_{1})-\\textrm{Df}(s_{2})|}{\\textrm{Df}(s_{3})}\\end{array}\n$\n\\bigskip\n\nSince $\\begin{array}{ll}\n|\\dfrac{\\textrm{Df}(s_{1})}{\\textrm{Df}(s_{3})}-\\dfrac{D_{+}f(d)}{D_{-}f(d)}|\\leq\n\\dfrac{M_{1}}{m_{1}^{2}}\n\\big(|\\textrm{Df}(s_{1})-D_{+}f(d)|+|\\textrm{Df}(s_{3})-D_{-}f(d)|\n\\big),\\end{array} $ \\\n\\\\\n\\medskip\n\nand by Lemma \\ref{l:31}\n\\medskip\n\n$$\\begin{array}{ll}\n r^{\\prime}_{n}(d) & = \\dfrac{m \\big(f^{k_{n}(d)}([z_{2},f^{-k_{n}(d)}(d)]) \\big)}{m \\big(f^{k_{n}(d)}([z_{2},z_{3}]\n\\big)}\\\\\\\\\n    & \\leq e^{2V}\\dfrac{m ([z_{2},f^{-k_{n}(d)}(d)]) }{m ([z_{2},z_{3}])} \\\\\\\\\n& \\leq e^{2V}\\dfrac{m ([y_{1},y_{2}]) }{m([z_{2},z_{3}])}\\times\n\\dfrac{m ([z_{2},f^{-k_{n}(d)}(d)]) }{m ([y_{1},y_{2}])} \\\\\\\\\n& \\leq \\dfrac{e^{2V}}{\\beta} s_{n}^{\\prime}(d),\\end{array}\n$$ where $$s_{n}^{\\prime}(d):= \\dfrac{m ([z_{2},f^{-k_{n}(d)}(d)]) }{m\n([y_{1},y_{2}])}.$$ \\\n\\\\\n\nIt follows that $$|D_{k_{n}(d)}(f)^{-1}-\\sigma_{f}(d)^{-1}| \\leq\nK_{0} \\big(\n\\dfrac{s_{n}^{\\prime}(d)}{\\beta}+|\\textrm{Df}(s_{1})-D_{+}f(d)|+|\\textrm{Df}(s_{3})-D_{-}f(d)|\n \\big)$$\nwhere $$K_{0} =\n\\max(\\dfrac{M_{1}}{m_{1}}e^{2V},\\dfrac{M_{1}}{m_{1}^{2}}).$$ By\nCorollary \\ref{c:37} : $\\underset{n\\to +\\infty}\\lim\ns_{n}^{\\prime}(d)=0$. Hence, there exists $n_{d,\\beta} \\in\n\\mathbb{N}_{0}$ such that for every $n\\in \\mathbb{N}_{0}, \\ n \\geq\nn_{d,\\beta}$,~~ $s_{n}^{\\prime}(d)< \\beta\\varepsilon $. The\nintervals $(]d,s_{1}[;~]s_{3},d[)_{d\\in E(c_{1},c)}$ are disjoint\nintervals of\ncontinuity of $\\textrm{Df}$, they satisfy, by Lemma \\ref{l:31}, \\\\\n\\medskip\n\n $\\begin{array}{ll}\n m([d,s_{1}])+m([s_{3},d]) & \\leq    m([f^{k_{n}(d)}(z_{1}),f^{k_{n}(d)}(z_{2})])+ 2m([f^{k_{n}(d)}(z_{2}),f^{k_{n}(d)}(z_{3})])\\\\\\\\\n\n & \\leq 3e^{2V}\\gamma m([f^{k_{n}(d)}(y_{1}),f^{k_{n}(d)}(y_{2})])\\\\\\\\\n\n  & \\leq 3e^{2V}\\gamma < \\eta_{0}\n\\end{array}\n$\n\n So, $$|\\textrm{Df}(s_{1})-D_{+}f(d)|+|\\textrm{Df}(s_{3})-D_{-}f(d)|< \\varepsilon $$\n\\medskip\n\nHence, there exists $n_{d,\\beta}\\in \\mathbb{N}_{0}$ such that for\nevery $n \\in \\mathbb{N}_{0}, n\\geq n_{d,\\beta}$,\n\n\\begin{equation}\\label{(6)}\n    |D_{k_{n}(d)}(f)^{-1}-\\sigma_{f}(d)^{-1}| \\leq 2 K_{0}\\varepsilon\n\\end{equation}\n\\medskip\n\nTherefore from the cases 2a and 2b, we conclude that there exists\n$n_{d,\\beta} \\in \\mathbb{N}_{0}$ such that for every $n \\in\n\\mathbb{N}_{0},~n \\geq n_{d,\\beta}$,\n\\medskip\n\n\\begin{equation}\\label{(7)}\n     |D_{k_{n}(d)}(f)-\\sigma_{f}(d)| \\leq  K_{0}\\varepsilon\n\\end{equation}\n\\medskip\n\nSince $E(c_{1},c)$ is finite, there exists $n_{\\beta} \\in\n\\mathbb{N}_{0}$ such that for every $n \\in \\mathbb{N}_{0}, ~n \\geq\nn_{\\beta}$,\n\n\\begin{equation}\\label{(8)}\n   |\\prod_{d \\in E(c_{1},c)}~D_{k_{n}(d)}(f)-\\prod_{d \\in\nE(c_{1},c)}~\\sigma_{f}(d)| \\leq \\varepsilon\n\\end{equation}\n\\medskip\n\nHence, (\\ref{(4)}) and (\\ref{(8)}) imply that: there exist $n_{\\beta} \\in \\mathbb{N}_{0}$ such that for every $n \\in\n\\mathbb{N}_{0},~n \\geq n_{\\beta}$,\n\n\\begin{equation}\\label{(9)}\n    |Dcr_{f^{q_{n}}}(z_{1},z_{2},z_{3})-\\nu(c) | \\leq C_{1}\\varepsilon\n\\end{equation}\n\\medskip\n\nwhere $\\nu(c) = \\prod_{d\\in E(c_{1},c)}~\\sigma_{f}(d)$ and $C_{1}$ is a\npositive constant.\n\\end{proof}\n\\bigskip\n\n\\begin{lem}\n\\label{l:49} Under the hypothesis of Proposition \\ref{p:44}, for any $\\varepsilon >0$, there exists\n$0<\\gamma<\\gamma_{0}$, such that for any $\\beta \\in ]0,\\gamma[$,\nthere exist $n_{\\beta}\\in \\mathbb{M}_{0}$ such that for any $n\\in\n\\mathbb{M}_{0}, ~n\\geq n_{\\beta}$, the ($\\beta,\\gamma$)-secondary\ncell $(z_{1},z_{2},z_{3})$ associated to $(f,x_{0},b,\\mathbb{M}_{0}, \\delta)$ satisfies\n\n$$\\arrowvert\\textrm{Dr}_{g^{q_{n}(b)}}(h(z_{1}),h(z_{2}),h(z_{3}))-\n\\Pi_{g}(h(c), h(c_{1}))\\arrowvert\\leq C_{2}\\varepsilon$$\n\\medskip\n\nwhere \\ $\\Pi_{g}(h(c), h(c_{1})) = \\underset{d\\in E (c_{1},c)}\\prod \\sigma_{g}(h(d))$ and \\; $C_{2}$ is a\npositive constant.\n\\end{lem}\n\\medskip\n\n\\begin{proof} The proof is a consequence of Lemma \\ref{l:49q} and (Proposition \\ref{p:43}, (h-5)) applied to\nthe ($\\frac{\\beta}{2},\\gamma$)-derived cell\n$(h(z_{1}),h(z_{2}),h(z_{3}))$ associated to $(g,h(x_{0}),h(c),\n\\mathbb{N}_{0})$ instead of the ($\\beta,\\gamma$)-derived cell\n$(z_{1},z_{2},z_{3})$ associated to $(f,x_{0},c,\\mathbb{N}_{0})$.\n \\end{proof}\n\\medskip\n\\\n\\\\\n{\\it Proof of Proposition \\ref{p:44}}. The proof results from the\nLemmas \\ref{l:49q} and \\ref{l:49}. \\qed\n\\bigskip\n\n   \\section{\\bf Proof of Main Theorem }\n   \\medskip\n\nLet $f, ~g\\in \\mathcal{P}(S^{1})$ with the same irrational rotation number $\\alpha$ of bounded type.\nSuppose that $f$ and $g$ satisfy the (KO) condition. By Corollary \\ref{c:21}, there exist two\n piecewise quadratic homeomorphisms $K, L\\in \\mathcal{P}(S^{1})$ such that $F= L \\circ f \\circ L^{-1}$ and\n $G = K \\circ g \\circ K^{-1}$ have the following properties:\n\n   \\begin{enumerate}\n     \\item $F, G\\in \\mathcal{P}(S^{1})$ and have the same irrational rotation number $\\alpha$,\n\n     \\item  The break points of $F$ (resp. $G$) are on \\textit{pairwise distinct} $F$-orbits (resp. $G$-orbits),\n\n     \\item $F$ and $G$ satisfy the (KO) condition,\n\n     \\item Let $h$ the conjugating map between $f$ and $g$ ~ i.e. $h \\circ f = g \\circ h$ and set $v = K \\circ h \\circ L^{-1}$. Then\n\n     \\subitem - $v$ is an absolutely continuous (resp. a singular) function if and only if so is $h$.\n\n    \\subitem - $v\\circ F= G\\circ v$.\n   \\end{enumerate}\n\n   Therefore, we may assume that all break points of $f$ (resp. $g$) are on \\textit{pairwise distinct} $f$-orbits\n   (resp. $g$-orbits). Now by Proposition \\ref{p:23}, there exists a\n   homeomorphism $u$ of $S^{1}$ such that $G= u\\circ f\\circ u^{-1}\\in  \\mathcal{P}(S^{1})$ with the following properties:\n\n   \\\n   \\\\\n   \\textbullet ~ $C(f)\\subset B:= \\{c_{i}: ~i=0,1, \\dots, q\\}$, ($q\\geq p$). \\\\\n   \\textbullet ~ $C(G)\\subset u(B):=\\{u(c_{i}): ~i=0,1, \\dots, q\\}$. \\\\\n   \\textbullet ~ $\\sigma_{G}(u(c_{i})) = \\sigma_{g}(d_{i})~,~i=0,1, \\dots, q$.\\\\\n   \\textbullet ~ $\\pi_{s}(G)=\\pi_{s}(g)$.\\\\\n   \\textbullet ~ $h$ is singular if and only if so is $u$.\n   \\medskip\n\n   So we may assume that $u=h$ and $G=g$.\n\\\n\\\\\n   To show that the conjugation homeomorphism $h$ from $f$ to $g$ is singular with respect to the Lebesgue measure $m$, it\n   suffices to prove that its derivative $\\textrm{Dh}$ is zero on\n   a set of Lebesgue total measure. Assume on the contrary that $h$ admits at a point $x_{0}$ a positive derivative $Dh(x_{0})>0$.\n\\bigskip\n\nLet $\\varepsilon >0, ~c \\in B$. For $0<\\beta<\\gamma <\\gamma_{0}$,\nwrite:\n\n$$D_{n}(\\beta, \\gamma):= \\dfrac{\\textrm{Dr}_{g^{q_{n}}}\\big(h(z_{1}),h(z_{2}), h(z_{3}) \\big)}{\\textrm{Dr}_{f^{q_{n}}}\\big(z_{1},z_{2}, z_{3} \\big)} $$\n\\medskip\n\nBy Proposition \\ref{p:2}, there exists $n_{\\beta} \\in\n\\mathbb{N}_{0}$ such that for every $n\\in \\mathbb{N}_{0},~n\\geq\nn_{\\beta}$:\n\n\\begin{equation}\\label{(10)}\n    |D_{n}(\\beta, \\gamma)-1| \\leq \\dfrac{2}{1-\\gamma_{0}}\\beta\n\\end{equation}\n\\medskip\n\nBy Proposition \\ref{p:44}, there exists\n$\\gamma_{\\varepsilon}<\\gamma_{0}$ such that for every\n$0<\\beta<\\gamma_{\\varepsilon}$ there exists\n$n_{\\beta}(\\varepsilon)\\in \\mathbb{N}_{0}$ such that for every $n\\in\n\\mathbb{N}_{0},~~n\\geq n_{\\beta}(\\varepsilon)$, the $(\\beta,\\gamma)$\nsecondary cell $(z_{1},z_{2},z_{3})\\ (\\gamma<\\gamma_{\\varepsilon})$-\nassociated to $(f,x_{0},c,\\mathbb{N}_{0},\\delta)$ satisfies:\n\n\\begin{equation}\\label{(11)}\n   |D_{n}(\\beta, \\gamma)-\\Pi(c_{1},c)| \\leq A \\varepsilon,\n\\end{equation}\n\\\n\\\\\nwhere $$\\Pi(c_{1},c):= \\underset{d \\in\nE(c_{1},c)}\\prod~\\dfrac{\\sigma_{g}(h(d))}{\\sigma_{f}(d)}$$ and $A$\nis a positive\nconstant.\\\\\n\nLet $\\beta < \\gamma <\\gamma_{\\varepsilon}$ and $n \\in\n\\mathbb{N}_{0}, ~n \\geq n_{\\beta}(\\varepsilon)$. Then (\\ref{(10)})\nand (\\ref{(11)}) imply that\n\\bigskip\n\n$ \\begin{array}{lll}\n            |\\Pi(c_{1},c)-1| & \\leq |D_{n}(\\beta, \\gamma)-1|+|D_{n}(\\beta,\n\\gamma)-\\Pi(c_{1},c)| & \\leq \\dfrac{2\\beta}{1-\\gamma_{0}}+A\n\\varepsilon\n\n  \\end{array}$\n\\bigskip\n\nSince $\\varepsilon$ and $ \\beta $ are arbitrary, it follows that $\\Pi(c_{1},c)=1$. i.e.\n\\begin{equation}\\label{(12)}\n   \\prod_{d\\in E(c_{1},c)} ~\\dfrac{\\sigma_{g}(h(d))}{\\sigma_{f}(d)}=1\n\\end{equation}\nSince $c_{1}, c \\in B$,~~$c_{1}\\neq c~$ are arbitrary, so for every\n$(i,k)\\in \\{0,1, \\dots,~q \\}^{2}~~(i \\neq k),$ one has\n$$\\underset{d\\in E(c_{k}, c_{i})}\\prod~\\dfrac{\\sigma_{g}(h(d))}{\\sigma_{f}(d)}=1$$\n\nAs by Proposition \\ref{p:461}, $c_{k} \\notin E(c_{k},c_{i})$, so we have $$\\underset{0 \\leq j \\leq q\n}\\prod~\\big (\\dfrac{\\sigma_{g}(h(c_{j}))}{\\sigma_{f}(c_{j})}\n\\big)^{e(i,k,j)}=1,$$\n\nwhere $e(i,k,j) \\in \\{0,1\\}$ with\n$$\\varepsilon(i,k,i)=1 \\textrm{and } \\varepsilon(i,k,k)=0.$$\nIt follows that for every $(i,k)\\in \\{0,1, \\dots,~q \\}^{2}, \\ i\\neq\nk$, we have\n\n$$\\underset{0 \\leq j \\leq q}\\sum~ e (i,k,j)~\\log\\left(\\dfrac{\\sigma_{g}(h(c_{j}))}{\\sigma_{f}(c_{j})}\\right)=0.$$\n\\medskip\n \\\n\\\\\n\nFor $(i,j,k) \\in \\{0, \\dots, q\\}^{3}$, set\n$$\\varepsilon_{k+i(q+1),j}\n    =\\left\\{\n                            \\begin{array}{ll}\n                         e (i,k,j) & \\textrm{if} ~~i \\neq k,~~j \\neq i ~~\\textrm{and}~~j\\neq\nk,\n\\\\\\\\\n                       1 &  \\textrm{if} ~~i \\neq k ~~\\textrm{and}~~j=\ni,\n\\\\\\\\\n                          0 & \\textrm{if} ~~i \\neq k\n~~\\textrm{and}~~j=k,\n\\\\\\\\\n0   &   \\textrm{if} ~~i = k\n                   \\end{array}\n         \\right.\n$$\n\nIt follows that for every $(i,k) \\in \\{0, \\dots,\nq\\}^{2}$,~~$$\\sum_{j=0}^{q}\\varepsilon_{k+i(q+1),j}\\log\\left(\\frac{\\sigma_{g}(h(c_{j}))}{\\sigma_{f}(c_{j})}\\right)=0\n$$\n\nSet $A_{q+1}=(a_{l,j})_{0\\leq l<(q+1)^{2},~0 \\leq j<q}\\in\n\\mathcal{M}_{(q+1)^{2},~q+1}(\\{0,1\\})$  the matrix defined by\n$a_{l,j}=\\varepsilon_{k+i(q+1),j}~$, where $l=k+i(q+1)$ with $0\\leq\ni,~k \\leq q$. The matrix $A_{q+1}$ has a rank $q+1$ (see \\cite{am12}, Lemma 6.1). Therefore for every\n$j\\in \\{0,1, \\dots,~q\\}$, $\\sigma_{g}(h(c_{j}))=\\sigma_{f}(c_{j})$. Hence $f$ and $g$ are break-equivalent, a contradiction. \nThe proof is complete. \\qed\n\\\n\\\\\n\n\\textit{Proof of Corollary \\ref{c:12}}. This follows from the fact that if\n$f$ and $g$ do not have the same number of singular orbits then $f$ and\n$g$ are not break-equivalent. \\qed\n\\\n\\\\\n\n\\textit{Proof of Corollary  \\ref{c:13}}. Suppose that $f$ and $g$ are\nbreak-equivalent. After reduction, one can suppose that $\\textrm{SO}(f)= C(f)$ and $\\textrm{SO}(g)= C(g)$. Then for every $d \\in C(g)$, there is $e \\in C(f)$\nsuch that $d=h(e)$ and $\\sigma_{g}(d)=\\sigma_{f}(e)$ i.e.\n$\\sigma_{g}(d) \\in \\{\\sigma_{f}(c):~c \\in C(f)\\}$, this\ncontradicts the hypothesis of the corollary.\\qed\n\\\n\\\\\n\n\\textit{Proof of Corollary  \\ref{c:14}}. This follows from the fact that the\ncondition (ii) satisfies the assumption of Corollary \\ref{c:13}. \\qed\n\\\n\\\\\n\n\\textit{Proof of Corollary  \\ref{c:15}}. \\textit{Proof of (i)}. Since $g$\ndoes not have the $(D)-$ property and $f$ has the $(D)-$ property,\nso there exists a point $d \\in C(g)$ such that\n$\\pi_{s,O_{g}(d)}(d)\\neq 1$ and $\\pi_{s,O_{f}(c)}(f)= 1$ for every\n$c \\in C(f)$. We conclude by Corollary \\ref{c:13}.\n\\\n\\\\\n\n \\textit{Proof of (ii)}. By Corollary \\ref{c:21}, $f$ is conjugate\nto a class P-homeomorphism $F=K \\circ f \\circ K^{-1}$ through a\npiecewise quadratic class $P$ homeomorphism $K$ of $S^{1}$. Since\n$f$ satisfies the $D-$ property, $\\pi_{s,O_{f}(c)}(f)=\n1=\\sigma_{F}(K(c))$ for every $c \\in C(f)$. Thus, $F$ is a $C^{1}$-\ndiffeomorphism. Moreover, $\\textrm{DF}$ is absolutely continuous on $S^{1}$\nand $D^{2}F \\in L^{p}(S^{1})$ for some $p>1$. By\nKatznelson-Ornstein's theorem, $\\mu_{F}$ is equivalent to the\nLebesgue measure $m$ and so is $\\mu_{f}$. Hence there exists an\nabsolutely continuous map $\\varphi$ such that $\\varphi \\circ f=\nR_{\\rho(f)} \\circ \\varphi$. Similarly, there exists an absolutely\ncontinuous map $\\psi$ such that $\\psi \\circ g = R_{\\rho(f)} \\circ\n\\psi$. In addition, $\\psi^{-1}$ is absolutely continuous. It\nfollows that $(\\psi \\circ h\\circ\\varphi^{-1}) \\circ\nR_{\\rho(f)}=R_{\\rho(f)}\\circ (\\psi\\circ h\\circ \\varphi^{-1})$. As\n$\\rho(f)$ is irational then $\\psi\\circ h\\circ\n\\varphi^{-1}=R_{\\beta}$ a rotation, for some $\\beta \\in S^{1}$.\nTherefore $h= \\psi^{-1}\\circ R_{\\beta}\\circ \\varphi$, which is an\nabsolutely continuous map. This completes the proof. \\qed\n\\\n\\\\\n\n\\textit{Proof of Corollary  \\ref{c:16}}. The proof follows easily from\nCorollary \\ref{c:15} by taking $g$ the rotation $R_{\\rho(f)}$. \\qed\n\n\n\n\\bigskip\n\n\\bibliographystyle{amsplain}\n\\bigskip\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{sec:intro}\nIn recent years, the atmospheric~\\cite{sk}, solar~\\cite{solar}, \nreactor~\\cite{kamland}, and accelerator~\\cite{k2k, minos_first} experiments \nhave provided convincing evidence of neutrino oscillations and \ntherefore have demonstrated that neutrinos have non--zero masses.  This phenomenon \nis the first clear example of new physics beyond the Standard Model which \nassumes neutrinos are massless particles.  Three \ngeneration neutrino oscillations are described by six independent parameters: \nthree mixing angles ${\\rm sin^2\\theta}_{12}, \n{\\rm sin^2\\theta}_{23},  {\\rm sin^2\\theta}_{13}$,  two mass-squared \ndifferences $\\Delta m^2_{21} = m^2_2 - m^2_1$ and \n$\\Delta m^2_{23} = m^2_3 - m^2_2$, and one complex phase $\\delta$. \nBoth mass differences and two mixing \nangles ($\\theta_{12}$ and $\\theta_{23}$) are measured. The mixing angle \n$\\theta_{13}$ was found to be small and only an upper limit was \nobtained~\\cite{chooz,k2k_theta_13}. Presently nothing is known \nabout the CP violating Dirac phase $\\delta$. The near--future neutrino\noscillation experiments will be focused on the measurements of the unknown \nneutrino  parameters: $\\theta_{13}$, mass hierarchy, and  \n$\\delta$. Another important goal of these experiments is  to \nmeasure the known mixing parameters more precisely.\n\n\\section{Principles of T2K}\n\\label{sec:t2k}\nThe T2K (Tokai--to--Kamioka) experiment~\\cite{t2k}   will use a \nhigh intensity  off--axis neutrino \nbeam generated by a 50 GeV  (initially 30 GeV) proton beam at  JPARC \n(Japan Proton Accelerator Research Complex), SuperKamiokande  as a far \nneutrino \ndetector, and  a set of dedicated neutrino detectors    located \nat a distance of 280 m from the pion production target  to\nmeasure the properties of the unoscillated neutrino beam.  The schematic view \nof the T2K setup is shown in Fig.~\\ref{fig:t2k_setup}.\n\\begin{figure}[h]\n\\centering\\includegraphics[width=14cm,angle=0]{t2k_setup.eps}\n \\caption{General layout  of the T2K experiment. The basic elements are \n the neutrino beam line, muon monitor, near neutrino detector at 280 meters  \n from the pion production target, and the far neutrino detector \n SuperKamiokande. Possible future 2km near detector  is also shown.}\n\\label{fig:t2k_setup}\n\\end{figure}\n The first phase of \n T2K   has two main goals: a sensitive \nmeasurement of ${\\rm\\theta}_{13}$  and  a more accurate determination of the \nparameters ${\\rm sin^22\\theta}_{23}$ and $\\Delta m^2_{23}$ than any previous\nexperiment. \n\nThe probability of $\\nu_{\\mu}$ transition to  $\\nu_e$  can be approximately \ngiven by\n\\begin{equation}\nP(\\nu_{\\mu}\\to \\nu_e) \\approx 4{\\rm cos}^2\\theta_{13}{\\rm sin}^2\\theta_{13}\n{\\rm sin}^2\\theta_{23}{\\rm sin}^2\\Bigl\n(\\frac{1.27\\Delta m^2_{13}({\\rm eV}^2)L({\\rm km})}{E_{\\nu}({\\rm GeV})}\\Bigr),\n\\label{eq:p(numu-nue)}\n\\end{equation}\nwhere $L$ is the $\\nu$ flight distance, and $E_{\\nu}$ is the neutrino energy.\nIt follows from this expression, the maximum sensitivity to the\n$\\nu_{\\mu}\\to \\nu_e$ transition is expected around the oscillation maximum \nfor $\\Delta m_{13} \\simeq \\Delta m_{23} = \\Delta m_{atm} \\simeq 2.5\\times\n10^{-3}$. Based on this value, the neutrino peak energy in T2K should be  tuned \nto  $\\leq 1$ GeV to\nmaximize the sensitivity for muon neutrino \noscillations  for a baseline of 295 km. \n\nT2K will adopt an \noff--axis beam configuration in which neutrino energy is almost independent of \npion energy and quasi-monochromatic neutrino spectrum can be achieved. \nThe neutrino beam  is produced \nfrom pion decays in a 94 m  decay tunnel filled with 1 atm He gas at an\nangle of \n$2.5^{\\circ}$  with respect to the proton beam axis, providing a  narrow neutrino \nspectrum  with mean neutrino energies from 0.7 to  0.9 GeV, as shown in \nFig.~\\ref{fig:t2k_nu_beam}. \n\\begin{figure}[h]\n\\centering\\includegraphics[width=10cm,angle=0]{nu_beam.eps}\n\\caption{Neutrino energy spectra at $0^{\\circ}$ and  different \noff-axis angles.}\n\\label{fig:t2k_nu_beam}\n\\end{figure}\nThe high energy tail is considerably reduced at $2.5^{\\circ}$ in \ncomparison with\nthe standard on-axis wide-band beam. This minimizes the neutral \ncurrent $\\pi^0$ background  in the $\\nu_e$ appearance search.\nMoreover, the intrinsic contamination of $\\nu_e$'s from muon and\nkaon decays  is expected to be about 0.4\\% around the peak energy.\n\nTo achieve T2K  goals,  precise measurements \nof the   neutrino flux, spectrum and \ninteraction cross sections are needed. For these purposes, the near detector \ncomplex (ND280)~\\cite{nd280}  will \nbe built at a distance of 280 m from the target along the line defined by the \naverage pion decay point and  SK (see Fig.~\\ref{fig:t2k_setup}). \nThis complex has two detectors: an on-axis detector (neutrino beam\nmonitor)    and  an off--axis detector. Physics \nrequirements for ND280  \ncan be briefly summarized as \nfollows: the absolute energy scale of the neutrino spectrum  must\nbe calibrated with 2\\% precision, and the neutrino flux monitored \nwith \nbetter than 5\\% accuracy. The  momentum resolution of muons from the \ncharged current quasi-elastic interactions~(CCQE) should be less than 10\\%, and the \nthreshold for \ndetection of recoil protons  is required to be about 200~MeV\/c. The \n$\\nu_e$ fraction should be measured with an uncertainty of $\\leq 10$\\%.\nA measurement of  the neutrino  beam direction, with a precision much better \nthan 1 mrad, is required from the on-axis detector.  \n\n\\section{Near neutrino detectors}\n\\label{sec:nd280}\n\\subsection{On-axis neutrino monitor}\nThe role of the  on-axis neutrino detector~(INGRID) is to monitor the neutrino \nbeam direction and profile on a day to day basis. It consists of $7 + 7$ \nidentical modules, arranged to form a cross-configuration, and 2 diagonal modules, \n as shown in   Fig.~\\ref{fig:ingrid}.\n \\begin{figure}[h]\n\\centering\\includegraphics[width=13cm,angle=0]{ingrid_combined.eps}   \n\\caption{(a) schematic view of INGRID; (b) segmented iron-scintillator \nsandwich module; (c) a  charged current  neutrino interaction with muon \ntrack.}\n\\label{fig:ingrid}\n\\end{figure}\nINGRID samples the neutrino beam profile with an area of $9\\times 9$ m$^2$.\nEach  iron-scintillator sandwich module covers an area of $125 \\times 125$ cm$^2$ \nand weighs 10 tons. The module consists of ten 6.5 cm-thick  \niron layers and 11\nscintillator tracking  planes, and is surrounded by four veto counters. Each\ntracking plane has one vertical and one horizontal scintillator layer \ncomposed  of $5\\times 1\\times\n121$ cm$^3$  scintillator slabs.\nEach scintillator has a central hole to insert a wavelength shifting~(WLS) \nfiber for light \ncollection and routing to a photosensor. \n The total mass of INGRID is $\\sim 160$ tons.\nA typical  event rate  detected by the center module  every spill is expected \nto  be  about 0.5 per ton, i.e. the whole INGRID will detect more  than $10^5$\nneutrino events\/day. In order to minimize the systematic from the uncertainty \nof the off-axis angle, the neutrino beam direction will be monitored by \nINGRID with a precision of $<< 1$ mrad each day at designed intensity.\n \n\\subsection{Off-axis near detector}\nThe off-axis detector (Fig.~\\ref{fig:nd280})\n\\begin{figure}[h]\n\\centering\\includegraphics[width=10cm,angle=0]{nd2.eps}   \n\\caption{The cutaway view of the T2K  near detector.}\n\\label{fig:nd280}\n\\end{figure}\n includes the UA1 \nmagnet operating with a magnetic field of 0.2 T, \na Pi-Zero detector (POD), a tracking detector which includes  time projection \nchambers (TPC's) and fine grained scintillator detectors (FGD's), an \nelectromagnetic calorimeter\n(Ecal), and a side muon range detector~(SMRD).   \n\n \\subsubsection{Photosensors}\n Wavelength \nshifting  fibers will be widely used for  readout of all \nscintillator detectors which are the main active element of  the ND280  \ndetector.  \n A magnetic field environment and  limited  space inside the \nUA1 magnet put serious constraints for the usage of standard photodetectors \nsuch as traditional multi-anode photomultipliers. Since the ND280 has about \n60k individual readout channels, the cost of \nphotosensors is also very important. \n After studying several candidates, \na multi-pixel avalanche photo-diode operating in the \nlimited Geiger multiplication mode was selected as the baseline detector.  These \n novel devices  \nare compact, well matched to spectral emission of WLS fibers, and insensitive \nto magnetic fields~\\cite{gm1,gm2,andreev}. The required  parameters for these\nphotosensors from all ND280 subdetectors can be summarized as follows: \nan active area diameter of $\\sim 1$ mm, photon detection efficiency for green \nlight\n$\\geq 20$\\% , pixels number $> 400$, and a dark rate at operating \nconditions $\\leq 1$ \nMHz. The gain should be  $(0.5-1.0)\\times 10^6$, \nthe cross$-$talk $\\sim10$\\%, and \npulse width  should be less than 100 ns to meet  the spill structure of the \nJPARC proton beam.  For \ncalibration and control  purposes, it is very desirable  to obtain well separated  \nsingle photoelectron peaks in amplitude spectra  at operating temperature.\n\nAfter a R\\&D study of 3 years,  a Hamamatsu  MPPC was  chosen  as the \nphotosensor for ND280. The description of this device\nand its parameters can be found in Ref.~\\cite{hamamatsu}. \nThe final T2K version is a 667 pixel MPPC with a sensitive area \nof $1.3\\times 1.3$ mm$^2$ (Fig.~\\ref{fig:mppc}). \n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[width=9cm,angle=0]{mppc_new_a.eps}\n\\includegraphics[width=6cm,angle=0]{mppc_new_b.eps}\n\\end{center}\n\\caption{(a) The photograph of a 667 pixel MPPC:  a magnified face view of \nan MPPC  with a sensitive area of $1.3\\times 1.3$ mm$^2$ (left),\nthe package of this MPPC (right); (b) ADC spectrum from an LED \nsignal. Clearly separated peaks at equal intervals correspond to 0, 1, 2, \n3... fired pixels.}\n\\label{fig:mppc}\n\\end{figure}\n These devices\ndemonstrated  good performance at room temperature: a low cross-talk  value of about 10\\%, \na photon detection \nefficiency for green light of $\\geq 25$\\%,   a low dark rate of $\\sim 0.3$ \nMHz at the operating voltage, a high gain of about \n $0.7\\times 10^6$, and a pulse width of less than 50 ns.  \n \n\\subsubsection{POD}\nThe POD is optimized for measurement of the inclusive  $\\pi^0$ production by  \n$\\nu_{\\mu}$ interactions on oxygen and  will be installed in the upstream end of the \nmagnet. The cross section measurements on an oxygen target will be achieved by \nusing the following POD geometry: the upstream and downstream regions are\nconfigured as electromagnetic calorimeters providing energy containment and\nactive veto, and the central region of the POD provides the fiducial mass for \nthe $\\pi^0$ measurements (Fig.~\\ref{fig:pod}(a)).\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[width=6.2cm,angle=0]{pod_a.eps}\n\\includegraphics[width=7.5cm,angle=0]{pod_b_c.eps}\n\\end{center}\n\\caption{(a) POD schematic view: the central region is constructed of\nalternating water target and scintillator tracking layers; (b) one layer of \nthe target region; (c) a  neutral current\n$\\pi^0$ event in POD. The horizontal and vertical axes are in centimeters. }\n\\label{fig:pod}\n\\end{figure}\n The schematic view of a plane of the POD target is shown in \n Fig.~\\ref{fig:pod}(b).\nIt consists of alternating water target layers of about 3 cm-thick  and \ntracking layers composed of X-Y extruded triangular shaped scintillator bars of \n17 mm in height and 32.5 mm at the base and a central hole for a WLS fiber.  \n A thin sheet of brass\n($\\sim 1.6$ mm-thick) is sandwiched in the 26 X-Y tracking layers of the target\nregion. The  upstream and downstream regions have 7 X-Y scintillator layers \nwith 4 mm-thick lead radiators between them.\n  The POD has a total mass \nof approximately 17 tons with a fiducial mass of about 3 tons of water and \n8 tons of other materials. \n The tests of light yield of the POD\nscintillators with MPPC's connected to one end of a Y11 WLS fiber \n showed good results. The light yields for a minimum \nionizing particles~(MIP) are 19.8 p.e.\/MeV and 8.7 p.e.\/MeV at 25 and 205 cm  \nfrom the MPPC, respectively. With the mirrored  far end of the WLS fiber, \nthe light yield \nof 15.7 p.e.\/MeV is much greater than the 5 p.e.\/MeV required for \nefficient reconstruction of electromagnetic showers.\n\nOxygen cross\nsection measurements will be made by comparing the interaction rate of events \ncollected with water in the target region  versus similar running \nperiods with water removed from the target region. A typical neutral current \nevent with  a $\\pi^0$ is shown in Fig.~\\ref{fig:pod}(c) in which a neutral pion is\naccompanied by a neutron.\nThe energy resolution for events fully contained in the active\ntarget  is expected to be about 10\\% + 3.5\\%\/$\\sqrt{{\\rm GeV}}$ and \nthe reconstruction efficiency of a $\\pi^0$ with a momentum $\\geq 200$ MeV\/c\nis expected to be approximately 33\\%.\n\n\\subsubsection{ND280 tracker}\nThe ND280 tracker consists of three TPC's and two FGD's, as shown in \nFig.~~\\ref{fig:nd280}. Its main function is \nto measure the  muon and electron  neutrino beam fluxes and  energy spectra, \nplus\nvarious \ncharged current cross sections.  The tracker is designed to  accurately \nmeasure CCQE events, the main \nprocess  at the T2K peak neutrino energy, \n\\begin{equation}\n\\nu_{\\mu} + n \\to \\mu^- + p.\n\\label{eq:ccqe}\n\\end{equation}\n In order to measure this process the reconstruction of both\n proton and muon  is useful. The proton will be primarily identified and measured \n by the FGD while the muon will be measured by the TPC.  The initial neutrino energy \n will be reconstructed from the muon momentum. The  measurements of CCQE events \n will be used for flux normalization in the  oscillation analysis. \\\\\n \n{\\it FGD.} The ND280 will \ncontain two FGD's, each \nwith dimensions $1.84\\times 1.84\\times 0.3$ m$^3$ resulting in a  total target \nmass of about 2.0 tons.  \nThe first FGD will be an active scintillator detector, similar to the \nSciBar detector~\\cite{scibar} of the K2K experiment. \nIt consists of thirty scintillator layers of 192  \n$0.96\\times 0.96 \\times 184$ cm$^3$ extruded  \nscintillator bars which are   arranged \nin alternating vertical and horizontal layers perpendicular to the beam\ndirection.  The second FGD is composed of seven X-Y \nsandwiches  of scintillator \nlayers alternating with six 3-cm thick layers of water. The weight of the  \nscintillator is 0.56 ton and  of water, 0.44 ton. The readout of each\nscintillator bar  is provided by an MPPC connected to one end of a WLS fiber \ninserted in \na central hole. \nA beam test of scintillator bars performed at TRIUMF showed that the light yield\nfor 120 MeV\/c pions, muons, electrons will be more than 10 p.e. at the far end \nfrom a photosensor without mirroring the far end of the fiber. The  \nmirroring  increases the light yield by $\\geq 80$\\%,\nguaranteeing a detection efficiency of more \nthan 99\\% for  minimum ionizing particles. The FGD  allows a clear\nseparation between protons and pions using dE\/dx information and tagging \nMichel electrons from the decay of short-ranged pions.\nComparing the interaction rates in both FGD's permits separate measurement \nof neutrino cross sections on carbon and on water.\nAbout $4\\times 10^5$ \nneutrino interactions are expected in both FGD modules for a one year exposure \nwith $10^{21}$ protons on target.\n\n{\\it TPC.} The primary purpose  of the TPC   is \nto measure the 3-momenta of muons produced in  CCQE interactions in the FGD. \n The TPC will use a \nlow diffusion gas  to obtain the \nmomentum resolution of $\\leq 10$\\% for particles below 1 GeV\/c. A 700 $\\mu$m \nspace point resolution per ``row'' of pads  is required to achieve this momentum resolution. \nThe absolute energy scale will be checked at the 2\\% level using the invariant \nmass of neutral kaons produced in DIS neutrino interactions and decaying in the\nTPC volume. A good dE\/dx resolution of $< 10$\\% \nis expected for 72 cm long tracks which will provide better than 5$\\sigma$ \nseparation between muon and electron tracks \nin the momenta range 0.3-1.0 GeV\/c. \n\nThe  three TPC modules  are \nrectangular boxes with outer \ndimensions of approximately $2.5\\times 2.5$ m$^2$ in the plane perpendicular \nto the neutrino beam direction, and 0.9 m along the beam direction. A simplified\ndrawing of the TPC is shown in Fig.~\\ref{fig:tpc}.\n\\begin{figure}[h]\n\\centering\\includegraphics[width=8cm,angle=0]{tpc3d.eps}   \n\\caption{The layout of TPC showing the inner and outer boxes and the \ncentral cathode.}\n\\label{fig:tpc}\n\\end{figure}\nThe TPC modules are operated at an electric field of 200 V\/cm. \nThe central cathode, which divides the drift space into two halves to limit the \nmaximum drift distance to $\\sim 1$ m, will be  at a potential of -25 kV. The\nbaseline gas choice is Ar(95\\%)--CF$_4$(3\\%)--iC$_4$H$_{10}$(2\\%).\n\n \nThe `bulk' Micromegas detectors will be used to instrument the TPC readout\nplane. The active surface area  of the  \nMicromegas \nmodule is  $359\\times 342$ mm$^2$ with 1726 active pads of $9.7\\times 6.9$ \nmm$^2$.  12  Micromegas modules   will be used for each\nreadout plane of the TPC.\n In total, the 3 TPC's will consist of 72 modules with  $\\sim 124000$ readout \nchannels. \n\nThe first prototypes of Micromegas detectors have been tested with cosmic \nmuons in the former HARP \nfield cage setup with a magnetic field~\\cite{micromegas}  and demonstrated good\nmomentum resolution of 8.3\\% at 1 GeV\/c. A dE\/dx resolution of \nabout 12\\%  for track lengthes of about 40 cm and a good \nuniformity of $\\sigma = 3.4$\\% for  the gain $\\sim 1000$  have been obtained. \n\nA typical CCQE event for neutrino interaction in FGD1 is shown in \nFig.~\\ref{fig:ccqe_track}.\n\\begin{figure}[h]\n\\centering\\includegraphics[width=9cm,angle=0]{ccqe_track_new.eps}   \n\\caption{Typical CCQE event in the tracker.}\n\\label{fig:ccqe_track}\n\\end{figure}\nThe   reconstruction efficiency of CCQE \nevents produced in the FGD with a track in the TPC is estimated to be about \n50\\% at a $E_{\\nu} \\sim 0.7$ GeV.\n\n\\subsubsection{Electromagnetic calorimeter}\nThe Electromagnetic calorimeter (Ecal) shown in Fig.~\\ref{fig:ecal} \n\\begin{figure}[h]\n\\centering\\includegraphics[width=7cm,angle=0]{ecal.eps}   \n\\caption{Basic structure of the electromagnetic calorimeter.}\n\\label{fig:ecal}\n\\end{figure}\nconsists of two sections. \nOne surrounds the POD (POD Ecal) for detectioning photons and muons escaping the \nPOD, and the second section, surrounding the FGD's and TPC's  (TEcal), detects \nparticles leaving the tracking volume. \n\nTEcal modules are made of 4 cm-wide, 1 cm-thick plastic\nscintillator bars arranged in 32 layers and separated by 31 layers of 1.75\nmm-thick lead sheets.  The orientation of the bars alternates between layers \nso that the bars in any layer are perpendicular to the bars in the two adjacent \nones. This bar width allows good $\\pi^0$ reconstruction efficiency and provides \nthe spatial resolution required for reconstruction  of the direction  of detected\nphotons. The active length of the TEcal along the neutrino beam is 384 cm and  \nthe total depth   is 50 cm corresponding to 10.5$X_0$. TEcal has two side\nmodules, one on each side of the UA1 iron yokes, one top and one \nbottom modules, each is split into two (left and right) so that they can move \nwith the magnet yoke when the magnet opens.\nAll scintillator \nbars have a hole in the center with a 1 mm WLS fiber inserted in it. All \nlong bars running along the neutrino beam are readout by an MPPC at each end\n(double-end readout), while all shorter bars (perpendicular to the neutrino\nbeam) are mirrored at one end and readout by an MPPC at the other (single-end\nreadout). The downstream Ecal is a single module with the same granularity \nas TEcal modules with an effective depth of 11$X_0$. It is located at the \ndownstream end of the magnet and covers \nan active surface area of $2\\times 2$ m$^2$. All bars have double-ended readout. \nThe total weight of the TEcal and downstream Ecal is 28.3 tons. \n\n The POD Ecal has modules with coarser segmentation and less total $X_0$ and \n does not provide good energy and spatial resolution required for $\\pi^0$ \n reconstruction. These modules consist of 6 scintillator layers separated by \n 5 layers of 5 mm-thick lead converters resulting in an effective depth of \n $4.5X_0$. \n \n The energy resolution of TEcal, dominated by sampling fluctuations, is\n estimated to be about 7.5\\%\/$\\sqrt{E(\\rm GeV)}$ for energies up to \n 5 GeV.  TEcal is expected to provide good electron\/pion separation. An\n efficiency of 90\\% for electrons is expected with 95\\% pion rejection. \n \n\\subsubsection{Side muon range detector}\nMuons which escape at large angles with respect to the neutrino \nbeam can not be measured by the TPC's. However, they will intersect in the iron yoke \nand therefore a muon's momentum can be obtained from its range by \ninstrumenting the iron at various depths.  About 40\\% of muons from \nCCQE reactions and about 15\\% of muons from  \ncharge current \nnon-quasi-elastic reactions  are expected to enter the SMRD.  In addition, \nthe SMRD will be used to veto events from \nneutrino interactions in the magnet and  in walls of the ND280 pit and will \nprovide a cosmic trigger \nfor calibration of inner detectors. \n\nThe UA1 iron yoke  \nconsists of 16 C-shaped elements made of sixteen 5 cm thick iron plates, with \n1.7 cm air gap between the plates and is segmented in 12 azimuthal sections. \nThe active component of the SMRD will consist of 0.7 cm thick scintillator slabs\nsandwiched between the iron plates of the magnet yokes. \nDetails of the extrusion of the scintillator slabs  and the method  of \netching the plastic surface by a chemical agent   can be found \nin Ref.~\\cite{extrusion}. For the readout, we  employ a \nsingle WLS fiber embedded in a serpentine shaped (S--shape)\ngroove, as shown in Fig.~\\ref{fig:smrd_counter}.\n\\begin{figure}[h]\n\\centering\\includegraphics[width=12cm,angle=0]{smrd_counter_1.eps}   \n\\caption{The  SMRD counter with embedded Kuraray Y11 WLS fiber.}\n\\label{fig:smrd_counter}\n\\end{figure}\n  Such a \nshape allows the fiber to collect the scintillation light over the whole \nsurface of a scintillator slab~\\cite{smrd_nim}. Two MPPC's are  coupled to \nboth ends of a  \nWLS fiber glued into the S--shape \ngroove. The detector performance has been tested using cosmic muons. Typical \nADC spectra for  \nMIP's obtained with $1.0\\times 1.0$ mm$^2$ MPPC's are  \nshown in Fig.~\\ref{fig:adc_smrd_spectra}. \n\\begin{figure}[h]\n\\centering\\includegraphics[width=11cm,angle=0]{good_spectra.ps}   \n\\caption{The ADC spectra of the SMRD counter  for  minimum ionizing \nparticles measured at 22$^{\\circ}$C. The light yield (sum of both ends) is \nequal to 58 p.e.}\n\\label{fig:adc_smrd_spectra}\n\\end{figure}\nThe SMRD counters tests  resulted in a high detection efficiency measurement \nof \ngreater than 99\\%, a time resolution of about 1 ns, and a spatial resolution \nalong the slab of about 8 cm   for minimum ionizing particles.\n\\section{Conclusion}\nThe T2K experiment has  a rich physics potential  and provides an excellent  \nopportunity to greatly extend our  understanding of neutrino properties.\nTo achieve the physics goals of T2K, the complex of near neutrino detectors  \nneeded for measurement of the unoscillated neutrino beam properties \nis under construction. The on-axis detector will be ready  to accept the first \nneutrino beam in April 2009, the installation and commissioning  of the whole \noff-axis detector  will be finished during 2009. The T2K experiment is \nexpected to start data taking in 2009.  \n \n{\\bf Acknowledgments.} I thank M.~Gonin, A.~Grant,  D.~Karlen, T.~Nakaya, \nV.~Paolone and  M.~Yokoyama for providing material for the talk and useful \ncomments on the manuscript.  This work was supported in part by  \nthe ``Neutrino Physics'' Program \n of the Russian Academy of  Sciences and by the RFBR (Russia)\/JSPS (Japan) \n grant \\#08-02-91206.\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzziazr b/data_all_eng_slimpj/shuffled/split2/finalzziazr
new file mode 100644
index 0000000000000000000000000000000000000000..491bb18e6ca3d1d4c1a402c7ce79d0554d8b6682
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzziazr
@@ -0,0 +1,5 @@
+{"text":"\\section{Unconventional d.c. and optical conductivities}\n\\label{sec:intro}\n\nIt is an observed fact that several chemically diverse families of unconventional materials exhibit a low temperature resistivity that is linear in temperature, when tuned to what appear to be quantum critical points.\nIllustrative recent experimental data can be found for cuprates, pnictides, heavy fermions, ruthenates and organic superconductors -- see \\cite{Sachdev:2011cs} for an overview and references. While it is likely that there may be more than one explanation for this behavior, the universality of the temperature dependence of the resistivity seen in the phase diagrams of these materials strongly motivates the search for robust physical mechanisms that can reproduce the observations.\n\nIn this paper we show, in the context of the holographic correspondence, that the structure of superradiant instabilities of extremal black hole horizons leads universally to a linear in temperature resistivity when these systems are tuned to the quantum critical point mediating the instability. This mechanism will be described in some generality. We go on to illustrate the process in a particular model that captures additional features of several of the unconventional materials of interest: the resistivity will be due to scattering off modes that are becoming unstable, and which are supported at nonzero momentum. One can take these modes to model the spin density and charge density wave instabilities appearing in the phase diagrams of \\cite{Sachdev:2011cs}.\n\nThat the resistivity is linear rather than, say, quadratic in temperature is only half of the mystery. Unlike conventional metals, many of the materials of interest fail to exhibit resistivity saturation as the temperature is increased. The resistivity increases unabated with temperature through the Mott-Ioffe-Regel limit. The materials are consequently known as bad metals \\cite{Emery:1995zz}. This fact becomes particularly confusing when considered in conjunction with the dependence of the in-plane (frequency dependent) optical conductivity on temperature. In conventional metals, the optical conductivity exhibits a Drude peak that broadens as the temperature is increased. Resistivity saturation occurs when the spectral weight is smeared out over the whole of the bandwidth and the Drude peak effectively disappears \\cite{hussey}. In several classes of unconventional materials that do not exhibit saturation, the Drude peak is accompanied by an extended tail that falls off slowly at large frequencies up to the bandwidth scale \\cite{basov}. At the would-be saturation temperature, the Drude peak is observed to melt into this broader feature \\cite{hussey, basov}. The d.c.$\\,$resistivity, however, continues to increase linearly in temperature with the same slope, irrespectively of whether or not there is an associated Drude peak! The conundrum is served: Does the linear in temperature resistivity originate in Drude-like (i.e. momentum-relaxing) scattering or not?\n\nThe answer to this question is again likely to be material dependent. The picture of resistivity saturation outline above may not be correct. Nonetheless, the characterization of bad metals as metals that do not exhibit a zero frequency collective mode encourages the notion that the resistivity might be controlled by quantum critical physics, presumably responsible for the extended tail in the spectral density, rather than be sensitive to the mechanism of momentum relaxation. Such a picture is likely to have trouble with the fact that at lower temperatures a very sharp Drude peak is observed on top of the broader feature, see e.g. \\cite{boris} for measurements in optimally doped YBCO. The mechanism of linear resistivity presented in this paper will be quantum critical in nature, and we will assume that the Drude peak has been swamped by the critical degrees of freedom.\n\nFigure \\ref{fig:optical} below illustrates the above discussion.\n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[width = \\textwidth]{OpticalConductivity.pdf}\\caption{Theorist's schematic view of the optical conductivity in bad metals at lower temperatures (left) and higher temperatures (right). As the temperature is raised, spectral weight is shifted from the Drude peak into the broad tail and to interband energy scales. The linear in temperature d.c.$\\,$resistivity does not notice the melting of the Drude peak.\n\\label{fig:optical}}\n\\end{center}\n\\end{figure}\n\n\\section{Extremal horizons and BKT transitions}\n\\label{sec:bkt}\n\nIn quantum theories with a holographically dual description, the strongly interacting physics is described by classical gravitational dynamics in a dual spacetime with one extra spatial dimension. The extra dimension geometrically implements the renormalization group flow. In particular, the far interior of the spacetime describes the far IR, or lowest energy scales, of the dual quantum system \\cite{Hartnoll:2011fn}. In many holographic models placed at a finite charge density, $\\langle J^t \\rangle \\neq 0$, the far IR geometry is characterized by an emergent scaling symmetry that indicates a power law specific heat at low temperatures, and hence the presence of gapless degrees of freedom \\cite{Hartnoll:2011fn}. Working in two spatial dimensions for concreteness, the general scale invariant form of the metric is \\cite{Kachru:2008yh}\n\\begin{equation}\\label{eq:scalingIR}\nds^2_{\\text{IR}} = L^2_{\\text{IR}} \\left(\\frac{- dt^2 + d\\r^2}{\\r^2} + \\frac{dx^2 + dy^2}{\\r^{2\/z}} \\right) \\,.\n\\end{equation}\nThis spacetime admits the scaling symmetry $\\{t,\\r\\} \\to \\lambda \\{t,\\r\\}, \\vec x \\to \\lambda^{1\/z} \\vec x$. Therefore $z$ is the dynamical critical exponent. For simplicity we will not discuss here the more general class of metrics describing hyperscaling violation \\cite{Charmousis:2010zz, Huijse:2011ef}, although our considerations apply to those spacetimes also. Holographic IR scaling spacetimes typically arise over a finite range of parameter space and therefore describe critical phases.\n\nIn a scaling geometry of the form (\\ref{eq:scalingIR}), all the operators ${\\mathcal{O}}$ in the low energy theory have an energy scaling dimension $\\Delta$. This dimension determines the spectral weight (imaginary part of the retarded Green's function) in the regime $\\w \\ll T \\ll \\mu$ to be\n\\begin{equation}\\label{eq:im}\n\\lim_{\\w \\to 0}\\frac{1}{\\w} \\text{Im} \\, G_{{\\mathcal{O}} {\\mathcal{O}}}^R(\\w,T) \\sim T^{2 \\Delta - 2 - 2\/z}\\,.\n\\end{equation}\nHere the chemical potential $\\mu$ has been used to indicate the UV scale. Physics well below that scale is captured by the low energy spacetime (\\ref{eq:scalingIR}) and is amenable to dimensional analysis. We also used the fact that the spectral weight is odd in frequency for bosonic operators. In general, the above spectral weight is evaluated at zero momentum, $k=0$. A slight generalization is possible in the case of $z = \\infty$. In this case, space does not scale and so the momentum $k$ is dimensionless and can be nonzero. The scaling dimension becomes\nmomentum dependent: $\\Delta(k)$.\n\nAccording to the basic holographic dictionary \\cite{Witten:1998qj, Gubser:1998bc}, each operator ${\\mathcal{O}}$ is dual to a field $\\phi$ in the IR spacetime. For simplicity, to start with, consider the case in which $\\phi$ is a scalar field with mass $m$ that is not coupled to other fields at a linearized level. By solving the bulk wave equation in the geometry (\\ref{eq:scalingIR}) and reading off the scaling behavior from the solution as $\\rho \\to 0$, one\nimmediately finds\n\\begin{equation}\\label{eq:delta}\n\\Delta =  \\frac{2 + z}{2 z} + \\nu \\equiv \\frac{2 + z}{2 z} + \\sqrt{L^2_\\text{IR} m^2 + \\frac{(2+z)^2}{4 z^2}} \\,.\n\\end{equation}\nThe parameter $\\nu$ introduced here will appear repeatedly below.\nIn the case of $z = \\infty$, the mass $m^2$ can be momentum dependent. In this expression we see that if the mass squared satisfies the generalized Breitenlohner-Freedman bound\n\\begin{equation}\\label{eq:bf}\nL^2_\\text{IR} m^2 > -  \\frac{(2+z)^2}{4 z^2} \\,,\n\\end{equation}\nthen the scaling dimension $\\Delta$ is real.\n\nThe quantity $L^2_\\text{IR} m^2$ can be tuned by varying UV parameters. In particular, we can imagine tuning these parameters such that the mass squared drops below the bound (\\ref{eq:bf}), and the scaling dimension becomes complex. It is well understood by now that this triggers an interesting quantum phase transition in which the operator ${\\mathcal{O}}$ condenses once the mass squared of $\\phi$ becomes too negative. We will return to the nature of the transition very shortly, but first we notice that precisely at the critical point, where the square root in (\\ref{eq:delta}) vanishes and $\\nu = 0$, then from (\\ref{eq:im}) and (\\ref{eq:delta}) we have\n\\begin{equation}\\label{eq:critical}\n\\lim_{\\w \\to 0}\\frac{1}{\\w} \\text{Im} \\, G_{{\\mathcal{O}} {\\mathcal{O}}}^R(\\w) \\sim \\frac{1}{T} \\,.\n\\end{equation}\nThis expression, which has been previously emphasized in \\cite{Iqbal:2011aj, Vegh:2011aa}, will be at the heart of the linear resistivity above a quantum critical point that we will discuss in the following section. Previous interest in this expression is due to the fact that it resembles the spectral weight of the bosonic mode underlying the marginal Fermi liquid phenomenology of the cuprates \\cite{Varma:1989zz}. It is not quite the same, however, because in general (\\ref{eq:critical}) only holds at $k=0$. Even in the case of $z = \\infty$, because the dimension $\\Delta$ is $k$ dependent -- this is why these systems were termed semi-locally critical in \\cite{Iqbal:2011in}, rather than fully locally critical -- the full spectral density will have a nontrivial $k$ dependence, and (\\ref{eq:critical}) will only hold for one value of $k$ at a time. The absence of a $k$ dependence is crucial for the marginal Fermi liquid, as the mode is coupled to a Fermi surface, which has spectral weight at a nonzero $k=k_F$ that is set by UV dynamics. In contrast, our framework will operate entirely at the level of currents, which control the holographic charge dynamics at leading classical order in the bulk, and will not involve explicit discussion of Fermi surfaces.\n\nThe association of complex IR scaling dimensions to instabilities was first made in the context of holographic superconductors \\cite{Hartnoll:2008kx, Denef:2009tp, Gubser:2008pf}. In cases where the operator ${\\mathcal{O}}$ carries a charge, the instability can be understood as a cousin of the superradiant instabilities of charged black holes, driven by pair production of quanta near the horizon and leading to a discharging of the black hole \\cite{Hartnoll:2011fn}.\nIt was later realized that the quantum phase transition mediating this instability was of Berezinskii-Kosterlitz-Thouless (BKT) type.  For instance, when the mass squared is just below the bound (\\ref{eq:bf}), the temperature below which the instability occurs scales like\n\\begin{equation}\\label{eq:tc}\nT_c \\sim \\mu \\, e^{- \\pi\/\\sqrt{-\\nu^2}} \\,.\n\\end{equation}\nSimilar exponential hierarchies control quantities such as the condensate just below the critical mass squared.\nSuch zero temperature BKT transitions were first discussed in \\cite{Kaplan:2009kr}.\nUnlike the conventional BKT transition, they can occur in any dimension and are not tied to an interpretation of vortex unbinding, but rather describe the merger of a UV and IR fixed point. These transitions were subsequently noted to be rather generic in holographic settings \\cite{Jensen:2010ga, Iqbal:2010eh} and to admit a `semi-holographic' description \\cite{Jensen:2011af, Iqbal:2011aj}, in which the only role of holography is to provide a critical IR sector in which the transition occurs \\cite{Faulkner:2010tq}. Our discussion in the following section will be essentially semi-holographic in nature, being independent of most details of the UV region of the bulk geometry. In \\S \\ref{sec:broader} of the discussion section we will take a further step back from holography and comment on the validity of the result we have just described for general BKT transitions.\n\nThere are two key points we would like the reader to take from the above. Firstly, that given a `critical phase' with an IR scaling symmetry described by the metric (\\ref{eq:scalingIR}) one can induce a quantum phase transition by tuning the dimension of an operator to become complex. Secondly, at the corresponding quantum critical point, the spectral density of this operator has the temperature dependence (\\ref{eq:critical}). This last statement holds at $k=0$ for finite $z$, and at some specific $k_\\star$ when $z = \\infty$.\n\n\\section{Mechanism of linear resistivity}\n\\label{sec:mechanism}\n\nThe d.c.$\\,$conductivity is given by\n\\begin{equation}\\label{eq:sigma}\n\\sigma  = \\lim_{\\w \\to 0} \\frac{1}{\\w} \\, \\text{Im} \\, G^R_{J^x J^x}(\\w,T) \\,.\n\\end{equation}\nAt a nonzero charge density $\\langle J^t \\rangle$ and if momentum is conserved, this quantity is problematic because, in addition to the contribution (\\ref{eq:sigma}), there is a delta function in the dissipative conductivity at $\\w = 0$. In order to relax momentum over experimental timescales, the charge carriers must either be parametrically diluted or must interact with parametrically heavier degrees of freedom \\cite{Hartnoll:2012rj}. The result is the broadening of the delta function into a Drude peak. The contribution of the Drude peak to the d.c. conductivity is intimately connected to the mechanism by which momentum is relaxed. For instance, umklapp scattering in a Fermi liquid gives rise to the celebrated $T^2$ dependence of the resistivity. Instead, we would like the d.c.$\\,$conductivity to be dominated by the universal quantum critical dynamics underlying the spectral weight (\\ref{eq:critical}). This can happen if the Drude peak contribution is swamped by the zero frequency limit of an extended tail that arises from scattering off critical modes. As we discussed in \\S \\ref{sec:intro} above, this may be the case in bad metallic regimes.\n\nIt is sometimes asserted that the presence of a Drude peak is synonymous with a quasiparticle description of transport. This is not quite correct. The essential requirement for a Drude peak is a hierarchy of time scales, whereby the momentum relaxation timescale is much longer than any other timescale in the system. This is particularly clear in hydrodynamic or memory matrix approaches, e.g. \\cite{Hartnoll:2007ih, Hartnoll:2012rj}. In the presence of such a hierarchy, strongly correlated systems without a quasiparticle description will still exhibit a Drude peak. Conversely, \nthe absence of a Drude peak simply requires that momentum is being dumped by the charge carriers at a rate comparable to all other interactions. In such circumstances, the spectral weight from the delta function is transferred into the critical tail or indeed to interband energy scales. Strong interactions are presumably important here to maintain a metallic character and avoid localization \\cite{Emery:1995zz}. In the concrete model we consider in the following section, we assume that such a process is occurring in our system, without disrupting the momentum-conserving interactions that we consider, so that in effect we can ignore the delta function contribution to the conductivity. More generally, we can imagine that momentum-relaxing processes are already part of the critical system that is undergoing the quantum critical BKT transition.\n\nIf $J^x$ itself were the operator undergoing the BKT transition, then combining (\\ref{eq:critical}) and (\\ref{eq:sigma}) would directly give a linear in temperature resistivity at the critical point. Such a phase transition would correspond to the spontaneous generation of a uniform current and presumably requires spontaneous symmetry breaking of the global $U(1)$ symmetry. We are not aware of holographic, or other, models where this occurs. However, it is easy for the IR critical behavior (\\ref{eq:critical}) to get communicated to the current operator via operators that are irrelevant from the IR quantum critical point of view.\n\nThe IR scaling geometry (\\ref{eq:scalingIR}) is generically deformed by irrelevant operators that drive a renormalization group flow up towards the finite density UV fixed point or cutoff. In the IR scaling regime, before these irrelevant operators kick in, we can imagine diagonalizing the equations of motion for a generic perturbation of the background to obtain decoupled gauge invariant fields $\\Phi_I$. Near the boundary ($\\rho \\to 0$) of the IR geometry, these satisfy\n\\begin{equation}\\label{eq:GIR}\n\\Phi^I(\\rho) \\sim c^I \\Big( \\rho^{1+2\/z-\\Delta_I} + \\rho^{\\Delta_I} \\, {\\mathcal G}^R_I(\\w,T) \\Big) \\,.\n\\end{equation}\nHere ${\\mathcal G}^R_I(\\w,T)$ is the IR Green's function, the $c^I$ are constants, and $\\Delta_I$ is the IR dimension of the operator. We have allowed a temperature $T \\ll \\mu$ that only affects the IR spacetime. One of these dimensions $\\Delta_I$ is assumed to undergo a BKT transition of the form described in the previous section.\n\nAway from the IR geometry, the irrelevant operators will typically couple these perturbations. However, in the regime of interest $\\w,T \\ll \\mu$, this coupling does not introduce any additional non-analytic temperature or frequency dependence. In appendix \\ref{eq:matching} we show that a generalization of the usual matching procedure of e.g.\n\\cite{Faulkner:2011tm} implies that to leading order at low frequencies and temperatures\\footnote{To be precise, as explained in the appendix, equation (\\ref{eq:imgsum}) holds when the $\\nu_I$'s are real, that is, on the stable side of the quantum critical point. When some of the $\\nu_I$'s are imaginary, the general expression has a complicated logarithmic dependence on $T$ and $\\w$.}\n\\begin{equation}\\label{eq:imgsum}\n\\text{Im} \\, G^R_{J^x J^x}(\\w,T) = \\sum_I d^I \\, \\text{Im} \\, {\\mathcal G}^R_I(\\w,T) \\,.\n\\end{equation}\nHere the real coefficients $d^I$ will generically be nonzero if the irrelevant operators mix the IR mode $\\Phi_I$ with the gauge field $A_x$. This is by no means automatic; the model of the following sections will achieve the required mixing by combining several interesting ingredients. In more familiar condensed matter language, we can think of the direct coupling in (\\ref{eq:imgsum}) between the current and a fluctuating order parameter as a cousin of the Aslamazov-Larkin process \\cite{al}, in this case mediated by irrelevant operators. The key fact is that we couple the fluctuating field directly to the current, not going via e.g. a fermionic self-energy. It is now immediate that if one of these IR operators undergoes a BKT transition, then the spectral weight (\\ref{eq:critical}), plugged into the matching formula (\\ref{eq:imgsum}) leads to a linear in temperature resistivity at the critical point\n\\begin{equation}\\label{eq:linearT}\nr = \\frac{1}{\\sigma} \\sim T \\,.\n\\end{equation}\nNote that, according to (\\ref{eq:im}) and (\\ref{eq:delta}), the contribution from a general IR operator ${\\mathcal{O}}_I$ to the conductivity is\n\\begin{equation}\\label{eq:2nu}\n\\sigma = T^{-1 + 2 \\nu_I} \\,.\n\\end{equation}\nRecall that $\\nu$ was defined in (\\ref{eq:delta}). Assuming we are in a stable phase, then we see that the contribution of all the other operators with $\\nu_I > 0$ are subleading in the sum (\\ref{eq:imgsum}) compared to the critical operator with $\\nu = 0$. The above discussion is depicted in figure \\ref{fig:phased} below.\n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=270pt]{PhaseDiagram.pdf}\\caption{Schematic phase diagram. The BKT quantum phase transition occurs at the boundary of a quantum critical phase when the scaling dimension of an operator becomes complex, signaling a condensation instability. If the unstable operator is coupled to the current via irrelevant operators, then above the critical point the quantum critical contribution to the resistivity is linear in temperature. Close to the critical point, the mode becoming unstable has a strong effect on the d.c.$\\,$and optical conductivities.\n\\label{fig:phased}}\n\\end{center}\n\\end{figure}\n\nWhile (\\ref{eq:2nu}) allows the critical operator to dominate at the critical point, away from the critical point, on the disordered side, it implies that the exponent of the resistivity will be $1 - 2 \\nu < 1$. Here $\\nu$ is the exponent of the critical operator away from the critical point. This is in contrast to experiments in all the unconventional materials of interest, which show that when detuned from criticality, the exponent of the resistivity increases towards the Fermi liquid $T^2$ behavior \\cite{Sachdev:2011cs}. To capture this behavior we would need to increase the scope of our model. The simplest way to do this would be to combine the critical tail contribution we are discussing with a more conventional Femi liquid Drude peak contribution. It may be that by coupling the critical operator to the Fermi liquid, along the marginal Fermi liquid lines of \\cite{Iqbal:2011aj, Vegh:2011aa} or otherwise, one can remove the $T^2$ contribution to the resistivity in the critical region of the phase diagram. For instance, very schematically, a form like\n\\begin{equation}\\label{eq:fudged}\n\\sigma \\sim \\nu \\, T^{-2} + T^{-1 + 2 \\nu} \\,,\n\\end{equation}\nwould start to look closer to the data.\n\nComplications with the Drude peak are removed if one looks at the optical conductivity. The scaling arguments above now imply that the dissipative conductivity scales like\n\\begin{equation}\\label{eq:sw}\n\\sigma \\sim \\w^{-1 + 2 \\nu} \\,.\n\\end{equation}\nThis gives the marginal Fermi liquid form\n\\begin{equation}\\label{eq:1w}\n\\sigma \\sim \\frac{1}{\\w} \\,,\n\\end{equation}\nat the critical point. This may be compatible with observations in e.g. YBCO \\cite{Varma:1989zz} and LSCO \\cite{lsco}. We discuss the optical conductivity in more detail below. It would be interesting to measure in detail the doping dependence of the power law tail of the optical conductivity in these materials, to assess the plausibility of a dependence like (\\ref{eq:sw}) close to the critical point. As we noted above, the expressions (\\ref{eq:sw}) and (\\ref{eq:2nu}) are strictly applicable only on the $\\nu > 0$ side of the quantum phase transition. It is a feature of these models that the d.c.$\\,$and optical conductivities have asymmetric behavior on opposite sides of the quantum critical point.\n\nThere may seem to be a tension in the fact that $J^x$ does not acquire a vacuum expectation value and yet its correlator couples at the lowest frequencies to the unstable mode according to (\\ref{eq:imgsum}). We will verify explicitly in our concrete model below that these two statements are compatible.\n\nThe mechanism of linear in temperature resistivity we have described is universal in the sense that it only depends on the onset of a holographic BKT quantum phase transition at the boundary of a quantum critical phase, combined with the presence of irrelevant operators that couple the IR critical operator to the current. The mechanism is independent of the details of the theory undergoing the transition and also of the UV completion of the critical theory. Beyond the tuning to the quantum critical point, no additional specification of dimensions of operators or dynamical critical exponents is necessary. In the remainder of this paper we describe a specific holographic realization of the scenario that we have just outlined.\n\n\\section{Lattices and finite wavevector instabilities}\n\\label{sec:lattice}\n\nA concrete holographic model realizing the mechanism outlined above can be achieved by combining three interesting ingredients that have been the focus of recent discussion:\n\n\\begin{itemize}\n\n\\item Vectorial instabilities occurring at finite wavevector $k_\\star > 0$ \\cite{Nakamura:2009tf, Donos:2011bh, Donos:2011qt}.\n\n\\item A (semi-) locally quantum critical sector in which all momenta are critical\n\\cite{Sachdev:2010um, McGreevy:2010zz, Iqbal:2011in}.\n\n\\item A lattice that is irrelevant in the IR scaling regime \\cite{Hartnoll:2012rj, Horowitz:2012ky, Liu:2012tr}.\n\n\\end{itemize}\n\n\\noindent The essential idea is that the irrelevant coupling to the lattice will communicate the finite wavevector instability to the $k=0$ electrical current. The instability at $k_\\star$ can have critical scaling because of the local quantum criticality.\n\nThe most important effect of a lattice is to broaden the delta function in the conductivity \\cite{Hartnoll:2012rj} into a Drude peak. Impurities will also achieve this effect \\cite{Hartnoll:2008hs}. Nonetheless, many of the interesting materials are believed to be very clean, and indeed, the Fermi liquid $T^2$ resistivity observed over large ranges of temperatures in these materials, away from the critical regions, presumably originates from umklapp scattering off the lattice rather than impurities plus interactions \\cite{maslov}. As we have stressed repeatedly, however, in this work we are not interested in the Drude peak contribution to the conductivity. The role of the lattice for us will be to mix modes with different wavevectors.\n\nWe will consider the following 3+1 dimensional bulk model \\cite{Donos:2011bh}\n\\begin{align}\\label{lagra1}\n\\mathcal{L}=&{\\textstyle{\\frac12}} R\\,\\ast 1-{\\textstyle{\\frac12}} \\,\\ast d\\varphi\\wedge d\\varphi-V\\left(\\varphi\\right) \\ast 1- {\\textstyle{\\frac12}} \\,\\tau\\left(\\varphi\\right) F\\wedge\\ast F-{\\textstyle{\\frac12}} \\,\\vartheta\\left(\\varphi\\right) F\\wedge F\\, ,\n\\end{align}\nwhere $F=dA$. This Lagrangian describes Einstein-Maxwell theory coupled to a pseudoscalar field with both dilatonic and axionic couplings to the field strength. The corresponding equations of motion are given by\n\\begin{align}\\label{eomi}\n&R_{\\mu\\nu}=\\partial_\\mu \\varphi\\partial_\\nu \\varphi+g_{\\mu\\nu}\\,V-\\tau\\,\\left(\\frac{1}{4}g_{\\mu\\nu}\\,F_{\\lambda\\rho}F^{\\lambda\\rho} -F_{\\mu\\rho}F_{\\nu}{}^{\\rho}\\right) \\,, \\nonumber \\\\\n&d\\left(\\tau\\ast F+\\vartheta F\\right)=0 \\,, \\nonumber \\\\\n&d\\ast d\\varphi+V'*1+\\frac{1}{2}\\tau'\\,F\\wedge\\ast F+\\frac{1}{2}\\vartheta'\\,F\\wedge F=0\\, .\n\\end{align}\nWe will assume that the three functions $V$, $\\tau$ and $\\vartheta$ have the following expansions\n\\begin{align}\\label{expans}\nV=-6+\\frac{1}{2}m_{s}^{2}\\,\\varphi^{2}+\\dots,\\qquad\n\\tau=1-\\frac{n}{12}\\,\\varphi^{2}+\\dots,\\qquad\n\\vartheta=\\frac{c_{1}}{2\\sqrt{3}}\\,\\varphi+\\dots\\, .\n\\end{align}\nIt is sufficient to know the action for the pseudoscalar to quadratic order, as it will only appear as a perturbation of the background. In (\\ref{expans}) we have furthermore set the asymptotic $AdS_4$ radius to $L^2 = 1\/2$. In the Lagrangian (\\ref{lagra1}) we already set both the Newton and Maxwell constants to unity.\nAll of these quantities can be scaled out of the equations of motion in this model.\n\nThe key feature of the theory (\\ref{lagra1}), to be described immediately below, is that it can develop vectorial instabilities, which involve the electric current. Closely related to this fact is that the instabilities of interest occur at nonzero wavevector $k_\\star$, avoiding the spontaneous generation of a homogeneous current, as we would expect. By subsequently introducing a lattice, that becomes irrelevant in the IR and does not disrupt the critical phase, we will communicate the effects of this instability to the spectral weight of the current operator, leading to strong temperature and frequency dependence in the conductivity.\n\n\\subsection{IR spectrum of excitations and instability}\n\\label{sec:irspectrum}\n\nThe equations of motion (\\ref{eomi}) admit the following $AdS_{2}\\times \\mathbb{R}^{2}$ black hole solution\n\\begin{equation}\\label{eq:AdS2_bh}\nds_{4}^{2} = -f\\,dt^{2}+\\frac{1}{12} \\left(\\frac{dr^{2}}{f}+dx^{2}+dy^{2}\\right) \\,, \\qquad A=\\left(r-r_{+}\\right)\\,dt \\,, \\qquad\n\\varphi=0 \\,.\n\\end{equation}\nHere the emblackening factor\n\\begin{equation}\nf=r^{2}-r_{+}^{2} \\,.\n\\end{equation}\nThe horizon of the black hole \\eqref{eq:AdS2_bh} is at $r=r_{+}$ and the temperature is $T = \\sqrt{3}\\,r_{+}\/\\pi$.\nThe boundary of $AdS_2$ is at $r \\to \\infty$. This will serve as our near horizon scaling geometry,\n as per our discussion in \\S \\ref{sec:bkt} above, which we have further\nplaced at a finite temperature. That the effects of the temperature are restricted to the IR scaling geometry implies that $T \\ll \\mu$, the UV scale. The scaling regime described by $AdS_{2}\\times \\mathbb{R}^{2}$ has dynamical critical exponent $z=\\infty$ and an associated ground state entropy density. This ground state entropy has tainted the reputation of $AdS_{2}\\times \\mathbb{R}^{2}$ as a ubiquitous tool in the applied holography effort. (Semi) local quantum criticality with $z=\\infty$ is in fact compatible with a vanishing ground state entropy density if hyperscaling is violated \\cite{Hartnoll:2012wm}. Holographic scaling geometries with $z=\\infty$ are the only currently known holographic duals (away from the probe limit) that share at leading bulk classical order the basic property of Fermi liquids of having spectral weight at low energies but finite momentum. It seems conceivable that $AdS_{2}\\times \\mathbb{R}^{2}$ may have the last laugh.\n\nAs usual, perturbations about the background can be decomposed into transverse and longitudinal sectors that decouple from each other. The finite wavevector instability occurs in the transverse channel. We can write the transverse perturbations around the exact solution \\eqref{eq:AdS2_bh} as\n\\begin{align}\\label{fluctuations}\n\\delta g_{ty}=h_{ty}\\left(t,r\\right)\\sin\\left(kx\\right) \\,, \\qquad \\delta g_{xy}=h_{xy}\\left(t,r\\right)\\cos\\left(kx\\right) \\,, \\nonumber \\\\\n\\delta A_{y}=a\\left(t,r\\right)\\sin\\left(kx\\right) \\,, \\qquad \\qquad \\delta \\varphi= w\\left(t,r\\right)\\cos\\left(kx\\right) \\,.\n\\end{align}\nThe equations of motion \\eqref{eomi} then yield the system of linear coupled equations\n\\begin{align}\n-k\\,\\partial_{t}h_{xy}+k^{2}\\,h_{ty}-f \\left(2\\,\\partial_{r}a+\\partial_{r}^{2}h_{ty}\\right)=0 \\,, \\nonumber \\\\\n2\\,\\partial_{t}a+12kf\\,\\partial_{r}h_{xy}+\\partial_{t}\\partial_{r}h_{ty}=0 \\,, \\nonumber \\\\\n-f^{-1}\\,\\partial_{t}^{2}h_{xy}+12\\,\\partial_{r}\\left(f\\partial_{r}h_{xy} \\right)+kf^{-1}\\,\\partial_{t}h_{ty}=0 \\,, \\nonumber \\\\\n-f^{-1}\\,\\partial_{t}^{2}a+12\\,\\partial_{r}\\left(f\\partial_{r}a \\right)-12k^{2}\\,a+c_{1}k\\,w+12\\,\\partial_{r}h_{ty}=0 \\,, \\nonumber \\\\\n-f^{-1}\\,\\partial_{t}^{2}w+12\\,\\partial_{r}\\left(f\\partial_{r}w \\right)-\\left(12k^{2}+m_{s}^{2}+n\\right)\\,w+12c_{1}k\\,a=0 \\,.\n\\end{align}\nIntroducing the new field $\\phi_{xy}$ through\n\\begin{equation}\n\\partial_{t}\\phi_{xy}=f\\,\\partial_{r}h_{xy} \\,,\n\\end{equation}\nthe system of equations \\eqref{fluctuations} leads to the linear system of equations\n\\begin{equation}\\label{eq:system}\n\\left(\\Box_{2}-M^{2}\\right)\\mathbf{v}=0 \\,,\n\\end{equation}\nwith ${\\bf v}=(\\phi_{xy},a,w)$ and the mass matrix\n\\begin{equation}\\label{mmfirstmod}\nM^{2}=\\left(\\begin{array}{ccc}12\\, k^{2} & 2\\,k & 0 \\\\144\\,k & 24+12\\,k^{2}  & -c_{1}k \\\\0 & -12\\,c_{1}k & 12\\,k^{2}+m_{s}^{2} + n\\end{array}\\right)\\, .\n\\end{equation}\nNote that the Maxwell field fluctuation decouples from the remainder at zero wavenumber, $k=0$.\nThe Laplacian appearing in equation \\eqref{eq:system} is with respect to the two dimensional metric\n\\begin{equation}\nds_{2}^{2}=-f\\,dt^{2}+\\frac{dr^{2}}{12\\,f} \\,.\n\\end{equation}\n\nThe linearly coupled system of equations \\eqref{eq:system} can be diagonalized to yield three independent modes\n\\begin{eqnarray}\n\\lefteqn{\\left(\\Box_{2}-\\mu_{i}^{2}\\right)\\,g_{i}=0}\\nonumber \\\\\n&& \\Rightarrow \\qquad  \\partial_{r}^{2}g_{i}+\\frac{f^{\\prime}}{f}\\,\\partial_{r}g_{i}-\\left(\\frac{1}{12\\,f^{2}}\\partial_{t}^{2}+\\frac{1}{12\\,f}\\mu_{i}^{2} \\right)g_{i}=0 \\,,\n\\end{eqnarray}\nwith $\\mu_{i}^{2}$ being the three eigenvalues of the mass matrix \\eqref{mmfirstmod}. If we go to frequency space by writing $g_{i}(t,r)=e^{-\\imath\\omega t} u_{i}(r)$, the solution with infalling boundary conditions at the horizon \\cite{Son:2002sd, Hartnoll:2009sz} is then\n\\begin{equation}\nu_{i}(r)=\\left(\\frac{2}{r_{+}}\\right)^{\\nu_{i}}\\,\\Gamma\\left(a_{i} \\right)\\Gamma\\left(1+\\nu_{i}\\right)f(r){}^{-\\imath \\frac{\\omega}{4\\sqrt{3}r_{+}}}r^{-a_{i}}\\,{}_{2}F_{1}\\left(\\frac{a_{i}}{2},\\frac{a_{i}+1}{2},1-\\nu_{i};\\frac{r_{+}^{2}}{r^{2}} \\right)-\\left(\\nu_{i}\\leftrightarrow -\\nu_{i}\\right) \\,,\n\\end{equation}\nwhere $a_{i}=\\frac{1}{2}-\\imath \\frac{\\omega}{2\\sqrt{3}r_{+}}-\\nu_{i}$ and $\\nu_{i}=\\frac{1}{2}\\sqrt{1+\\frac{1}{3}\\mu_{i}^{2}}$.\nBy expanding the above solution near the boundary of the $AdS_{2}$, i.e. as $r \\to \\infty$, we can read off the $AdS_{2}$ retarded Green's functions in the usual way (e.g. \\cite{Faulkner:2011tm}) to obtain\\footnote{The case $\\nu_i = 0$, which will be of particular interest below, should properly be treated independently, with the solution to the wave equation expressed in terms of a Legendre function. Correct result are obtained by continuation of the general results to $\\nu_i \\to 0$. In particular, the spectra density $\\text{Im} G^R \\sim \\w\/T$ at $\\nu_i = 0$.}\n\\begin{equation}\n\\mathcal{G}^R_{i}\\left(\\omega, T \\right)=-\\left(\\frac{\\pi}{2\\sqrt{3}} T \\right)^{2\\nu_{i}}\\frac{\\Gamma\\left(1-\\nu_{i}\\right)\\Gamma\\left(\\frac{1}{2}-\\imath\\frac{\\omega}{2\\pi T}+\\nu_{i}\\right)}{\\Gamma\\left(1+\\nu_{i}\\right)\\Gamma\\left(\\frac{1}{2}-\\imath\\frac{\\omega}{2\\pi T}-\\nu_{i}\\right)} \\,. \\label{eq:gads2}\n\\end{equation}\nThese have the expected form that is determined by the $SL(2,{{\\Bbb R}})$ symmetry of $AdS_{2}$. Again, see for instance \\cite{Faulkner:2011tm}. These are the IR Green's functions that will appear in the matching formula (\\ref{eq:imgsum}).\nThe perturbation includes the transverse current mode $\\d A_y(x)$, at nonzero momentum $k$. Below we will couple this mode to the homogeneous current using a lattice.\n\nFor small $\\omega$ we have\n\\begin{eqnarray}\n\\lefteqn{\\mathcal{G}^R_{i}\\left(\\omega\\right)=-\\left(\\frac{\\pi}{2\\sqrt{3}} T \\right)^{2\\nu_{i}}\\frac{\\Gamma\\left(1-\\nu_{i}\\right)\\Gamma\\left(\\frac{1}{2}+\\nu_{i}\\right)}{\\Gamma\\left(1+\\nu_{i}\\right)\\Gamma\\left(\\frac{1}{2}-\\nu_{i}\\right)}}\\nonumber \\\\\n&& +\\imath\\omega \\frac{1}{2}\\,\\left(\\frac{\\pi}{2\\sqrt{3}} \\right)^{2\\nu_{i}}\\,T^{2\\nu_{i}-1}\\frac{\\Gamma\\left(\\frac{1}{2}+\\nu_{i} \\right)\\Gamma\\left(1-\\nu_{i}\\right)}{\\Gamma\\left(\\frac{1}{2}-\\nu_{i}\\right)\\Gamma\\left(1+\\nu_{i}\\right)}\\,\\tan\\pi\\nu_{i} \\,.\n\\end{eqnarray}\nIf $\\nu_i$ is real, then taking the imaginary part we recover the scaling with temperature that we anticipated in (\\ref{eq:im}) above, using the expression (\\ref{eq:delta}) for $\\Delta$ in terms of $\\nu$.\nIn general, the eigenvalues of the matrix \\eqref{mmfirstmod} are slightly complicated functions of the wavenumber $k$, but are easily found numerically.\n\nTo illustrate the features of the spectrum of our theory, consider the special case where $m_{s}^{2}+n=0$.\n(We will in fact consider a different case for the numerics below.) In that case we have\n\\begin{align}\n\\nu_{1}=&\\frac{1}{2}\\sqrt{1+4\\,k^{2}} \\,, \\nonumber \\\\\n\\nu_{2}=&\\frac{1}{2}\\sqrt{5+4\\,k^{2}-\\frac{\\sqrt{12}}{3}\\sqrt{12+\\left(24+c_{1}^{2}\\right)k^{2}}} \\,, \\nonumber \\\\\n\\nu_{3}=&\\frac{1}{2}\\sqrt{5+4\\,k^{2}+\\frac{\\sqrt{12}}{3}\\sqrt{12+\\left(24+c_{1}^{2}\\right)k^{2}}} \\,.\\label{eq:nus}\n\\end{align}\nFrom the expressions above we can see that $\\nu_{2}^{2}$ has two minima at\n\\begin{equation}\nk^{\\pm}_\\text{min} = \\pm\\frac{1}{2\\sqrt{12}}\\,\\frac{c_{1}\\sqrt{48+c_{1}^{2}}}{\\sqrt{24+c_{1}^{2}}} \\,,\n\\end{equation}\nat which\n\\begin{equation}\n\\nu_{2\\,\\text{min}} = \\frac{1}{4}\\sqrt{12-\\frac{c_{1}^{2}}{3}-\\frac{192}{24+c_{1}^{2}}} \\,.\n\\end{equation}\nFor $c_{1}>2\\sqrt{6}$ we see that there is a range of $k$ for which $\\nu_{2}$ is imaginary.\nThese are the finite wavenumber instabilities that we shall use. For our purposes, it does not matter whether or not the range of unstable momenta extends down to $k=0$. What is important is that there are finite wavenumber instabilities involving the Maxwell field $\\d A_y$.\n\nEven when the system is stable, when $0<c_{1}<2\\sqrt{6}$, we see that, as opposed to the pure Einstein-Maxwell case, the dominant mode will have $\\nu_{2\\, \\text{min}}<1\/2$. This renders the finite wavenumber operators relevant in the IR. A lattice of such operators would lead to a strong backreaction on the IR geometry \\cite{Hartnoll:2012rj}. In the following subsection we will instead introduce a lattice for the charge density $J^t$, that will be seen to be irrelevant in the IR.\n\nWithin the IR geometry, neither $c_1$ nor the unstable range of $k$ is tunable. The wavenumber $k$ is dimensionless in the IR because of the local criticality. However, once the $AdS_2 \\times {{\\Bbb R}}^2$ geometry is realized as the IR of a full asymptotically $AdS_4$ spacetime, then we shall see that $k$ must appear in the UV-dimensionless combination $k\/\\sqrt{J^t}$, with $J^t$ being the total charge density in the system. By varying the charge density, which can be thought of as a proxy for varying the doping of an experimental system, we effectively vary the momentum that appears in the scaling IR Green's functions. In the following subsection we shall introduce a lattice wavenumber $k_L$. By keeping the lattice fixed and varying the charge density $J^t$, we will induce a BKT quantum phase transition in modes that couple via scattering off the lattice to the homogeneous current.\n\nThe scenario outlined in the previous paragraph, and to be fleshed out below, does not quite give a realization of the phase diagram of figure \\ref{fig:phased}: the system is either stable or unstable over some range of momentum and this fact cannot be tuned. What we will vary by varying $k\/\\sqrt{J^t}$ is whether the instability feeds through to the homogeneous current, our observable of interest. To truly realize the desired phase diagram of figure \\ref{fig:phased} we need to enlarge the model to allow e.g. the parameter in the action $c_1$ or the radius of the IR $AdS_2$ metric to be tunable from the UV. We do not see an obstacle to doing this, but will continue with our slightly simpler model in this paper.\n\n\\subsection{Lattice}\n\nThe previous subsection studied perturbations of a finite temperature scaling solution to the theory (\\ref{lagra1}). Following \\cite{Donos:2011bh} we exhibited an instability of this background, for $c_1$ sufficiently large, over a range of momenta, $k_A < k < k_B$. In this range the exponent $\\nu_2(k)$ in (\\ref{eq:nus}) is imaginary. At the boundary of this range of momenta $\\nu_2(k_{A\/B}) = 0$, leading to the universal spectral function (\\ref{eq:critical}). In this section we will couple this critical mode to the $k=0$ current by introducing a lattice that is irrelevant in the IR. We will furthermore explain how $k$ can be tuned to the critical values by varying the charge doping of the system.\n\nThe simplest and perhaps most natural lattice to consider is an `ionic lattice' in which the operator that couples to the lattice is the charge density $J^t$. That is, we introduce a spatial modulation to the chemical potential\n\\begin{equation}\\label{eq:AV}\nA_t^{(0)} = \\mu + V(x,y) \\,.\n\\end{equation}\nHolographically this is implemented by the usual UV boundary condition $\\lim_{r \\to \\infty} A_t = A_t^{(0)}$. In a purely electric background, we can consistently set the pseudoscalar $\\varphi = 0$ in the theory (\\ref{lagra1}). Therefore the background generated by the lattice is found by solving the Einstein-Maxwell equations (sans pseudoscalar) subject to the UV boundary condition. We shall do this numerically in a perturbative approximation in the following section. However, the essential physical features can be determined without an explicit background solution, as we proceed to show.\n\nThe charge density at any nonzero wavevector is an irrelevant perturbation about the $AdS_2 \\times {{\\Bbb R}}^2$ solution (\\ref{eq:AdS2_bh}) of Einstein-Maxwell theory \\cite{Edalati:2010pn, Hartnoll:2012rj}. Therefore, however strong the UV potential in (\\ref{eq:AV}), the effects of the lattice will always be small in the far IR. The IR Green's functions computed in the previous section are thus unchanged. The role of the lattice is only to mix the unstable finite wavenumber modes with the homogeneous current mode, according to our discussion in \\S \\ref{sec:mechanism}. To isolate this effect from Drude momentum-relaxation physics, we take the current to propagate in the $y$ direction, but the lattice to oscillate only in the $x$ direction, with wavenumber $k_L$\n\\begin{equation}\\label{eq:periodic}\nV(x,y) = V(x) = V\\left(x + \\frac{2\\pi}{k_L}\\right) \\,.\n\\end{equation}\n\nAccording to (\\ref{eq:sigma}), to obtain the conductivity we must calculate $\\text{Im} \\, G^R_{J^y J^y}(\\w,T)$\nat $k=0$. We are now taking the current to run in the $y$ rather than $x$ direction. This Green's function is holographically related to perturbations $\\delta A_y$ in the bulk. Even without a lattice, in a nonzero charge density spacetime, $\\delta A_y$ couples to $\\d g_{ty}$. With the lattice, inspection of the equations reveals that in the full spacetime the four modes $\\{\\delta A_y, \\delta g_{ty}, \\delta g_{xy}, \\delta \\varphi\\}$ are coupled at wavenumbers that are integer multiplies of $k_L$. These can be collected into three gauge-invariant modes for each wavenumber\n\\begin{equation}\nk_n = n \\, k_L \\,,\n\\end{equation}\nsatisfying second order equations of motion. In the IR, the different wavenumber modes decouple and obey the equations that we have solved in the previous subsetion. The upshot is that the general matching formula (\\ref{eq:imgsum}) becomes\n\\begin{equation}\n\\text{Im} \\, G^R_{J^y J^y}(\\w,T) = \\sum_{i,n} d^i_n \\, \\text{Im} \\, {\\mathcal G}^R_i(\\w,T, k_n) \\,.\n\\end{equation}\nHere the IR Green's functions ${\\mathcal G}^R_i$ are those obtained in (\\ref{eq:gads2}) above. Their wavenumber dependence is through $\\nu_i(k_n)$ in (\\ref{eq:nus}). The mixing is illustrated in figure \\ref{fig:lattice}  below.\n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=170pt]{Lattice.pdf}\\caption{The IR is tuned to the boundary of an instability condensing finite wavenumber vectorial modes. The lattice is imposed in the UV but irrelevant in the IR. Away from the locally critical IR region, the lattice mixes modes of different wavenumber and couples the unstable mode to the homogeneous electric current.\n\\label{fig:lattice}}\n\\end{center}\n\\end{figure}\n\nTo tune the system across the instability identified in the previous subsection, insofar as the conductivity is concerned (see the discussion at the end of \\S \\ref{sec:irspectrum}), we now need to vary $k_L$ so that one of the $k_n$ becomes equal to the wavenumbers $k_A$ or $k_B$ bounding the unstable region. Physically it is presumably not feasible to tune $k_L$ itself, as the material is fixed. However, in the formulae for $\\nu_i(k_n)$ in (\\ref{eq:nus}), a dimensionful quantity has been suppressed and lengths have been rescaled relative to natural lengths of the UV geometry \\cite{Hartnoll:2011fn}. This is possible because of the emergent $z = \\infty$ scaling, under which lengths are dimensionless.\nThe invariant dimensionless quantity to consider, from a UV perspective, is the ratio of momentum to the square root of the charge density: $k\/\\sqrt{J^t}$ \\cite{Hartnoll:2012rj}. The charge density $J^t$ corresponds to the total electric charge available for conduction. This can be tuned experimentally by doping the system. Doping is indeed the mechanism of tuning in the cuprate and pnictide unconventional superconductors. Thus, with $k_F$ fixed, doping the system will allow the dimensionless IR wavenumbers $k_n$ to be tuned through their critical values, communicating the BKT transition of interest into a linear in temperature resistivity (\\ref{eq:linearT}).\n\nThe optical conductivities in (\\ref{eq:sw}) and (\\ref{eq:1w}) now show that a lattice combined with local criticality and a mode on the verge of a finite wavenumber instability leads to a significant low energy spectral weight, ranging to $\\sigma \\sim \\w^{-1}$ at the critical point itself. A strong optical conductivity going like $\\sigma \\sim \\w^{-2\/3}$ was recently obtained in an impressive numerical holographic lattice computation in \\cite{Horowitz:2012ky}. The mechanism underlying these effects are quite different. The lattice scatterings captured in \\cite{Horowitz:2012ky} relaxed the current, resolving the Drude peak, while ours merely mix modes of differing transverse momenta. The tail  in the optical conductivity observed in \\cite{Horowitz:2012ky} is indeed a tail of the Drude peak itself, and would presumably not be there if momentum were conserved. Our tail is an additional feature due to scattering off IR critical modes. Remarkably the scaling $\\sigma \\sim \\w^{-2\/3}$ agrees with a reported measurement in BSCYCO \\cite{twothirds}. As we noted above, a $\\sigma \\sim \\w^{-1}$ scaling has been suggested for e.g.\nYBCO \\cite{Varma:1989zz} and LSCO \\cite{lsco}, although a sophisticated scaling analysis of the data comparable to that in BSCYCO \\cite{twothirds} remains to be performed. To substantiate these similarities, a connection to the underlying dynamics of the material is required. It is certainly of interest to combine these two effects of the lattice in a single model.\n\n\\section{Numerics: lattice deformed RN black hole}\n\nThe explicit realization of the mechanism for linear in temperature resistivity, and strong optical conductivities, of the previous section depended on various genericity assumptions about modes coupling to other modes. In this section we perform a numerical analysis with a lattice that will confirm all the assumptions made. To simplify the analysis, we work perturbatively (to second order) in the strength of the lattice. This allows us to use a large system of coupled ODEs rather than PDEs. The perturbative treatment is consistent and already contains all of the physics we wish to illustrate.\n\n\\subsection{The background lattice perturbation}\\label{sec:lattice_sol}\n\nIn the absence of a lattice, the full asymptotically $AdS_4$ background of the theory (\\ref{lagra1}) dually describing\na finite charge density, zero temperature state of matter is the extremal Reissner-Nordstr\\\"om black brane \\cite{Hartnoll:2011fn}\n\\begin{align}\\label{eq:RNbh}\nds^{2}_{4}&=-f\\,dt^{2}+f^{-1}\\,dr^{2}+r^{2}\\,\\left( dx^{2}+dy^{2}\\right) \\,, \\notag\\\\\nA&=\\,\\left(1-\\frac{r_{+}}{r} \\right)\\,dt \\,, \\notag\\\\\nf&=2r^{2}-\\left( 2r_{+}^{2}+\\frac{1}{2}\\right)\\frac{r_{+}}{r}+\\frac{r_{+}^{2}}{2r^{2}} \\,.\n\\end{align}\nWe wish to deform by introducing a chemical potential or ``ionic'' lattice. We achieve this by setting the boundary value of the Maxwell field to be (cf. (\\ref{eq:periodic}) above)\n\\begin{equation}\\label{eq:At_asympt}\n\\lim_{r \\to \\infty} A_{t}=1+\\lambda\\,\\cos\\left(k_{L}x\\right) \\,.\n\\end{equation}\nIn this subsection we set up the equations describing the effect of this deformation on the static background (\\ref{eq:RNbh}) to order $\\lambda^2$.\n\nChoosing to work in a radial gauge where $g_{r\\mu}=0$, we can see that the components of the metric that will be\naffected by the lattice deformation are $\\left\\{g_{tt},g_{rr},g_{xx},g_{yy} \\right\\}$. The nontrivial functional dependence of the metric components will be on the radial coordinate $r$ and the spatial coordinate $x$. There is a residual gauge symmetry generated by the vector $\\xi=\\xi^{r}\\,\\partial_{r}+\\xi^{x}\\,\\partial_{x}$ with $\\nabla_{r}\\xi_{x}+\\nabla_{x}\\xi_{r}$=0. These perturbations of the background remain within Einstein-Maxwell theory (that is, the pseudoscalar is not sourced). As shown in \\cite{Hartnoll:2012rj}, the $\\w = 0$ and finite $k$ perturbations of the near horizon $AdS_{2}\\times \\mathbb{R}^{2}$ geometry in Einstein-Maxwell theory are all irrelevant. This fact strongly suggests that the $AdS_{2}\\times \\mathbb{R}^{2}$ IR limit is not modified by the inclusion of a lattice. The magnitude of the effects of the lattice are tunable at the boundary and become small as $r \\to r_+$ in the interior. We therefore conclude that as far as the background is concerned, for small parameter $\\lambda$ we can consistently treat the backreaction of the metric and gauge field perturbatively at all radii.\n\nExpanding our field components in $\\lambda$ we can write\n\\begin{align}\\label{eq:lattice_perts}\nA_{t}&=1-\\frac{r_{+}}{r}+\\lambda\\,a^{(1,1)}\\,\\cos\\left(k_{L}x\\right)+\\lambda^{2}\\,\\left(a^{(2,0)}+a^{(2,2)}\\,\\cos\\left(2k_{L}x\\right) \\right)+O\\left(\\lambda^{3}\\right) \\,, \\notag\\\\\ng_{tt}&=-f\\,\\left[1+\\lambda\\,Q^{(1,1)}_{tt}\\,\\cos\\left(k_{L}x\\right)+\\lambda^{2}\\,\\left(Q^{(2,0)}_{tt}+Q^{(2,2)}_{tt}\\,\\cos\\left(2k_{L}x\\right) \\right) \\right]+O\\left(\\lambda^{3}\\right) \\,, \\notag\\\\\ng_{rr}&=f^{-1}\\,\\left[1+\\lambda\\,Q^{(1,1)}_{tt}\\,\\cos\\left(k_{L}x\\right)+\\lambda^{2}\\,\\left(Q^{(2,0)}_{tt}+Q^{(2,2)}_{tt}\\,\\cos\\left(2k_{L}x\\right) \\right) \\right]+O\\left(\\lambda^{3}\\right) \\,, \\notag\\\\\ng_{ii}&=r^{2}\\,\\left[1+\\lambda\\,Q^{(1,1)}_{ii}\\,\\cos\\left(k_{L}x\\right)+\\lambda^{2}\\,\\left(Q^{(2,0)}_{ii}+Q^{(2,2)}_{ii}\\,\\cos\\left(2k_{L}x\\right) \\right) \\right]+O\\left(\\lambda^{3}\\right) \\,,\n\\end{align}\nwhere $f$ is as in \\eqref{eq:RNbh} and the $a$ and $Q$ functions depend on $r$ only. We have used the residual gauge freedom mentioned above to fix the functions appearing in $g_{rr}$ in terms of the functions appearing in $g_{tt}$. From\nthe expansion above we have, computing the surface gravity, that the temperature is still given by\\footnote{We will later impose that the metric perturbations fall off at infinity, so that the normalization of time remains the same as for the $\\lambda=0$ case.} $4 \\pi T= \\left. f^{\\prime}\\right|_{r=r_{+}}$. Plugging the ansatz for the perturbations \\eqref{eq:lattice_perts} in the equations of motion we obtain\n\\begin{itemize}\n\\item At order $\\lambda$: second order differential equations for the perturbations $\\left\\{Q_{ii}^{(1,1)},a^{(1,1)}\\right\\}$ and an algebraic equation for $Q^{(1,1)}_{tt}$.\n\\item At order $\\lambda^{2}$: second order equations for $\\left\\{Q_{ii}^{(2,0)},Q_{ii}^{(2,2)},a^{(2,0)},a^{(2,2)}\\right\\}$, a first order equation for $Q^{(2,0)}_{tt}$ and an algebraic equation for $Q_{tt}^{(2,2)}$.\n\\end{itemize}\nWe will solve these equations numerically below. At this early point we note that for our purposes we will not need to solve for the functions $Q_{aa}^{(2,2)}$, where $a = t,x,y$, and $a^{(2,2)}$ but it should be noted that they are non-trivial by consistency of the equations of motion. In order to fully define the boundary value problem we now need to impose boundary conditions which will give us a regular near horizon geometry and with the right sources at the boundary of $AdS_{4}$.\n\nThe horizon is a singular point of the equations of motion and regularity of the solution imposes the following near horizon expansions at $r=r_{+}$\n\\begin{align}\\label{eq:nhb_exp}\nQ_{aa}^{(i,j)}&=Q_{aa(0)}^{(i,j)}+Q_{aa(1)}^{(i,j)}\\,\\left(r-r_{+}\\right)+\\cdots,\\quad a=t,x,y \\,, \\notag\\\\\na^{(i,j)}&=a^{(i,j)}_{(0)}\\,\\left(r-r_{+}\\right)+a^{(i,j)}_{(1)}\\,\\left(r-r_{+}\\right)^{2}+\\cdots \\,.\n\\end{align}\nPlugging the near horizon expansion \\eqref{eq:nhb_exp} into the equations of motion, we discover that the constants $a^{(i,j)}_{(0)}$,  $Q_{tt(0)}^{(2,0)}$ and $Q_{ii(0)}^{(i,j)}$ are constants of integration as well as a combination of $Q_{ii(1)}^{(1,1)}$ which we take to be the sum $s^{(1,1)} \\equiv Q_{xx(1)}^{(1,1)}+Q_{yy(1)}^{(1,1)}$.\n\nOn the other hand, at infinity we have the following schematic expansions\n\\begin{align}\\label{eq:asb_exp}\na^{(i,j)}&=A_{(0)}^{(i,j)}+A_{(1)}^{(i,j)}\\,r^{-1}+\\cdots \\,, \\notag\\\\\nQ_{xx}^{(1,1)}&=G_{xx(-1)}^{(1,1)}\\,r+G_{xx(0)}^{(1,1)}+\\cdots+G_{xx(3)}^{(1,1)}\\,r^{-3}+\\cdots \\,, \\notag\\\\\nQ_{yy}^{(1,1)}&=G_{xx(-1)}^{(1,1)}\\,r+G_{yy(0)}^{(1,1)}+\\cdots+5\\,G_{xx(3)}^{(1,1)}\\,r^{-3}+\\cdots \\,, \\notag\\\\\nQ_{ii}^{(2,0)}&=G_{ii(0)}^{(2,0)}+\\cdots+G_{ii(3)}^{(2,0)}\\,r^{-3}+\\cdots \\,, \\notag\\\\\nQ_{tt}^{(2,0)}&=G_{tt(0)}^{(2,0)}+\\cdots \\,.\n\\end{align}\nIn order to source the gauge field corresponding to the ionic lattice deformation \\eqref{eq:At_asympt} we need to set $A_{(0)}^{(i,j)}=\\delta^{i1}\\delta^{j1}\\,\\lambda$, which uniquely fixes the sources of the gauge field. The ionic lattice is the only deformation of the Reissner-Nordstrom black hole we would like to turn on and therefore we should also set $G_{xx(-1)}^{(1,1)}=G_{ii(0)}^{(1,1)}=G_{ii(0)}^{(2,0)}=G_{tt(0)}^{(2,0)}=0$.\n\nTo conclude this section we note that we will have a total of six second order differential equations\\footnote{As mentioned before, we don't need to solve for the functions $Q^{(2,2)}_{aa}$ and $a^{(2,2)}$.} in $\\left\\{Q_{ii}^{(1,1)},Q_{ii}^{(2,0)},a^{(1,1)},a^{(2,0)}\\right\\}$ and one first order differential equation in $Q_{tt}^{(2,0)}$. We have eight constants of integration from the horizon $\\left\\{Q_{ii(0)}^{(1,1)},s^{(1,1)},Q_{aa(0)}^{(2,0)},a_{(0)}^{(1,1)},a_{(0)}^{(2,0)}\\right\\}$ and five constants of integration from the asymptotic data $\\left\\{G_{xx(3)}^{(1,1)},G_{ii(3)}^{(2,0)},A_{(1)}^{(1,1)},A_{(1)}^{(2,0)}  \\right\\}$. This combination of differential order and number of constants of integration gives a unique solution  for any given temperature. We will describe the numerical shooting method we are using in \\S \\ref{sec:numerics}.\n\n\\subsection{The $\\lambda^{2}$ corrected current-current correlator}\n\\label{sec:corelator_cor}\n\nGiven the background whose construction we have just described, we now wish to compute the retarded Green's function $G^R_{J^y J^y}(\\w,T)$ at $k=0$ in the deformed background. As will immediately become clear, for a source for $J^y$ at $k=0$ to induce a response also in $J^y$ at $k=0$ via scattering off a finite wavenumber mode, it is necessary to go to second order in the lattice strength, which is why we have also considered the background to order $\\lambda^2$. To compute the Green's function, we consider the following time dependent perturbation\n\\begin{align}\\label{eq:current_pert}\n\\delta A_{y}&=e^{-\\imath \\omega t}\\left[ a_{y}^{(0,0)}+\\lambda\\,a_{y}^{(1,1)}\\,\\cos\\left(k_{L}x\\right)+\\lambda^{2}\\,\\left(a_{y}^{(2,0)}+a_{y}^{(2,2)}\\,\\cos\\left(2k_{L}x\\right) \\right)\\right]+O\\left(\\lambda^{3}\\right) \\,, \\notag\\\\\n\\delta\\varphi&=e^{-\\imath \\omega t}\\left[\\lambda\\,\\varphi^{(1,1)}\\,\\sin\\left(k_{L}x\\right)+\\lambda^{2}\\,\\varphi^{(2,2)}\\,\\sin\\left(2k_{L}x \\right)\\right]+O\\left(\\lambda^{3}\\right) \\,, \\notag\\\\\n\\delta g_{ty}&=e^{-\\imath \\omega t}r^{2}\\left[g_{ty}^{(0,0)}+\\lambda\\,g_{ty}^{(1,1)}\\,\\cos\\left(k_{L}x\\right)+\\lambda^{2}\\,\\left(g_{ty}^{(2,0)}+g_{ty}^{(2,2)}\\,\\cos\\left(2k_{L}y \\right) \\right)\\right]+O\\left(\\lambda^{3}\\right) \\,, \\notag\\\\\n\\delta g_{xy}&=e^{-\\imath \\omega t}r^{2}\\left[\\lambda\\,g_{xy}^{(1,1)}\\,\\sin\\left(k_{L}x\\right)+\\lambda^{2}\\,g_{xy}^{(2,2)}\\,\\sin\\left(2k_{L}x \\right)\\right]+O\\left(\\lambda^{3}\\right) \\,,\n\\end{align}\nwith all the functions $\\Phi^{(i,j)}$ depending on the radius $r$ only. The perturbation described by \\eqref{eq:current_pert} is consistent and we chose again to work in radial gauge. We will fix the constants of integration in this gauge and then perform a large gauge transformation that will bring the perturbation into a form where it will be manifest that we are only sourcing the $k=0$ component of the current $J_{y}$.\n\nPlugging the perturbation \\eqref{eq:current_pert} into the equations of motion we obtain\n\\begin{itemize}\n\\item Second order equations for $\\left\\{a_{y}^{(i,j)},\\varphi^{(i,j)},g_{xy}^{(i,j)} \\right\\}$ .\\notag \n\\item First order equations for $\\left\\{g_{ty}^{(i,j)}\\right\\}$ .\n\\end{itemize}\nRegular, infalling boundary conditions at the horizon gives the near horizon expansion\n\\begin{align}\\label{eq:nh_exp}\n\\varphi^{(i,j)}&=f^{-\\frac{\\imath \\omega}{4\\pi T}}\\,\\left[\\varphi_{(0)}^{(i,j)}+\\varphi_{(1)}^{(i,j)}\\,\\left(r-r_{+}\\right)+\\cdots\\right] \\,, \\notag\\\\\na_{y}^{(i,j)}&=f^{-\\frac{\\imath \\omega}{4\\pi T}}\\,\\left[a_{y(0)}^{(i,j)}+a_{y(1)}^{(i,j)}\\,\\left(r-r_{+}\\right)+\\cdots\\right] \\,, \\notag\\\\\ng_{xy}^{(i,j)}&=f^{-\\frac{\\imath \\omega}{4\\pi T}}\\,\\left[g_{xy(0)}^{(i,j)}+g_{xy(1)}^{(i,j)}\\,\\left(r-r_{+}\\right)+\\cdots\\right] \\,, \\notag\\\\\ng_{ty}^{(i,j)}&=f^{-\\frac{\\imath \\omega}{4\\pi T}}\\left(r-r_{+}\\right)\\,\\left[g_{ty(0)}^{(i,j)}+g_{ty(1)}^{(i,j)}\\,\\left(r-r_{+}\\right)+\\cdots\\right] \\,.\n\\end{align}\nRegularity is seen to imply that all the constants of integration are fixed in terms of $\\left\\{\\varphi_{(0)}^{(i,j)}, a_{y(0)}^{(i,j)},g_{xy(0)}^{(i,j)}\\right\\}$. In particular, the $g_{ty(0)}^{(i,j)}$ are not independent.\n\nThe general asymptotic form of the solutions as $r \\to \\infty$ is found to be\\footnote{We chose to have $m_{s}^{2}=-4$ in the action \\eqref{lagra1}. Reinstating the asymptotic $AdS_4$ radius $L$, this corresponds to a mass squared $m^2 L^2 = - 2$.}\n\\begin{eqnarray}\\label{eq:as_exp}\n\\varphi^{(i,j)} & = & \\displaystyle \\frac{\\varPhi^{(i,j)}_{(1)}}{r}+\\frac{\\varPhi^{(i,j)}_{(2)}}{r^{2}}+\\cdots \\,, \\qquad g^{(i,j)}_{xy} = G^{(i,j)}_{xy(0)}+\\cdots +\\frac{G^{(i,j)}_{xy(3)}}{r^{3}}+\\cdots \\,,   \\notag\\\\\na^{(i,j)}_{y} &  = & \\displaystyle A^{(i,j)}_{y(0)}+\\frac{A^{(i,j)}_{y(1)}}{r}+\\cdots \\,,  \\qquad g^{(i,j)}_{ty}=G^{(i,j)}_{ty(0)}+\\cdots \\,.\n\\end{eqnarray}\nFor the bulk pseudoscalar $\\varphi$, the absence of a source requires that we impose\n$\\varPhi^{(i,j)}_{(1)}=0$ for a $\\Delta=2$ operator or $\\varPhi^{(i,j)}_{(2)}=0$ for a $\\Delta=1$ operator. We wish to source only the homogeneous mode of the $A_{y}$ component of the Maxwell field and furthermore at leading order in $\\lambda$ only, giving the boundary condition $A^{(i,j)}_{y(0)}=\\delta^{i,0}\\delta^{j,0}$.\n\nThe situation is slightly more involved with the constants $G^{(i,j)}_{xy(0)}$ and $G^{(i,j)}_{ty(0)}$. The first thought would be that one needs to set all these constants equal to zero since they represent non-normalisable modes for the bulk fields. A simple counting, however, reveals that this would overdefine the boundary value problem. \nAt the horizon we saw that $g_{ty(0)}^{(i,j)}$ was fixed by regularity in terms of the other integration constants. Consequently, at the boundary,\nthe constants $G^{(i,j)}_{ty(0)}$ will be uniquely fixed after specifying $G^{(i,j)}_{xy(0)}$, and demanding regularity at the horizon, and will in general be nonzero.\n\nWe will instead choose the constants $G^{(i,j)}_{ty(0)}$ and $G^{(i,j)}_{xy(0)}$ such that after a large coordinate transformation we will only have a source for the current. More specifically we impose\n \\begin{equation}\\label{eq:G_conds}\nj\\,k\\,G^{(i,j)}_{ty(0)}-\\imath\\, \\omega \\, G^{(i,j)}_{xy(0)}=0 \\,.\n \\end{equation}\nWe then perform the coordinate transformation\n\\begin{align}\\label{eq:large_diff_transf}\ny\\rightarrow y+e^{-\\imath \\omega t}\\sum_{i,j} \\lambda^{i} h^{(i,j)}\\,\\cos\\left(jkx \\right) \\,,\n\\end{align}\nwhere $h^{(i,j)}$ are functions of $r$ only. These functions are required to satisfy:\n\\begin{itemize}\n\\item Near the $AdS_{4}$ boundary they have the fall off\n\\begin{equation}\nh^{(i,j)}\\approx \\frac{1}{j \\, k}G_{xy(0)}^{(i,j)}+O\\left(r^{-5}\\ln r\\right) \\,.\n\\end{equation}\n\\item Near the horizon $r=r_{+}$ they have the infalling behavior\n\\begin{equation}\nh^{(i,j)}=f^{-\\frac{\\imath \\omega}{4\\pi T}}\\left(r-r_{+}\\right)\\,\\left[h_{(0)}^{(i,j)}+h_{(1)}^{(i,j)}\\,\\left(r-r_{+}\\right)+\\cdots \\right] \\,.\n\\end{equation}\n\\end{itemize}\nThe fall off condition in the UV:\n\\begin{itemize}\n\\item Removes the non-normalisable terms from the $g_{ty}$ and $g_{xy}$ components of the metric provided we satisfy \\eqref{eq:G_conds}.\n\\item It doesn't change the values of the VEVs for the various fields appearing in our ansatz.\n\\item It doesn't introduce new deformations coming from the $g_{ri}$ components.\n\\end{itemize}\n\nA particularly natural example of a coordinate transformation satisfying all of the above properties is one that maps our perturbations into the\nde Donder-Lorentz gauge\n\\begin{equation}\\label{eq:DeDonder_gauge}\n\\nabla_{\\mu}\\delta g^{\\mu\\nu}=0 \\,,\\quad \\nabla_{\\mu}\\delta A^{\\mu}=0 \\,.\n\\end{equation}\nHere $\\nabla$ is the connection with respect to the background solution we presented in \\S \\ref{sec:lattice_sol}. The gauge conditions \\eqref{eq:DeDonder_gauge} become second order differential equations for the functions $h^{(i,j)}$. The resulting solution satisfies all of our above requirements.\n\nThe quantity we are interested in calculating is the optical conductivity (\\ref{eq:sigma}). After taking into account the source of the gauge field specified by $A^{(i,j)}_{y(0)}=\\delta^{i,0}\\delta^{j,0}$, the retarded Green's function function is given by (up to a constant of proportionality)\n\\begin{equation}\nG^R_{J^y J^y}\\left(\\omega,k=0\\right)= \\sum_{i=0}\\lambda^{i}\\,A_{y(1)}^{(i,0)} \\,.\n\\end{equation}\nAs we will explain in more detail in \\S \\ref{sec:numerics}, for our purposes it will be sufficient to just consider the second order correction in $\\lambda$\n\\begin{equation}\\label{eq:curres}\nG^R_{J^y J^y}\\left(\\omega,k=0\\right)= A_{y(1)}^{(0,0)}+\\lambda^{2}\\,A_{y(1)}^{(2,0)} \\,.\n\\end{equation}\nThe first term $A^{(0,0)}_{y(1)}$ is the, by now well understood, current-current correlator evaluated in the extremal electric Reissner-Nordstr\\\"om background in Einstein-Maxwell theory \\cite{Hartnoll:2009sz}.\n\nOur aim is therefore to solve for the function $a_{y}^{(2,0)}$ and more specifically we would like to extract the constant $A_{y(1)}^{(2,0)}$ from it. After staring at the equations of motion one will notice that in order to achieve that we will not need to solve for the functions $a_{y}^{(2,2)}$, $g_{ty}^{(2,2)}$, $g_{xy}^{(2,2)}$ and $\\varphi^{(2,2)}$. The eight functions we will be solving for are $a_{y}^{(0,0)}$, $a_{y}^{(1,1)}$, $a_{y}^{(2,0)}$, $\\varphi^{(1,1)}$, $g_{ty}^{(0,0)}$, $g_{ty}^{(1,1)}$, $g_{ty}^{(2,0)}$ and $g_{xy}^{(1,1)}$ which satisfy five second order differential equations and three first order ones. In order to find a solution we have five constants of integration from the horizon data $\\left\\{a_{y(0)}^{(0,0)},a_{y(0)}^{(1,1)},a_{y(0)}^{(2,0)},\\varphi_{(0)}^{(1,1)},g_{xy(0)}^{(1,1)} \\right\\}$ and eight constants of integration from the asymptotic boundary $\\left\\{A_{y(1)}^{(0,0)},A_{y(1)}^{(1,1)},A_{y(1)}^{(2,0)},\\varPhi_{(1)}^{(1,1)},G^{(1,1)}_{xy(3)},G^{(0,0)}_{ty(0)},G^{(1,1)}_{ty(0)},G^{(2,0)}_{ty(0)}  \\right\\}$. This counting reveals that we will now have a unique solution for the perturbation once the background and the source have been fixed, including the frequency $\\omega$.\n\n\\subsection{Numerical results}\n\\label{sec:numerics}\n\nHaving set up the problem we would like to solve, we now employ a numerical shooting method appropriate for the case at hand. As we have outlined in \\S \\ref{sec:lattice_sol}, the first step of the calculation is to correct the background up to second order in $\\lambda$. To achieve this, we solve the equations of motion perturbatively order by order in $\\lambda$ which, as we explained, boils down to solving a system of six second order and one first order differential equations. The background solution will be uniquely specified by a set of thirteen constants $c_{1}=\\left\\{Q_{ii(0)}^{(1,1)},s^{(1,1)},Q_{aa(0)}^{(2,0)},a_{(0)}^{(1,1)},a_{(0)}^{(2,0)}\\right\\}$ and $c_{2}=\\left\\{G_{xx(3)}^{(1,1)},G_{ii(3)}^{(2,0)},A_{(1)}^{(1,1)},A_{(1)}^{(2,0)}  \\right\\}$.\n\nIn order to specify these constants, we numerically integrate the equations of motion from a distance close to the horizon $r=r_{+}+\\epsilon$ up to a finite radius in the bulk $r=r_{m}$, using the near horizon expansion \\eqref{eq:nhb_exp} as the initial conditions at $r=r_{+}+\\epsilon$. Following this procedure allows us to express the functions and their derivatives at $r=r_{m}$ as a function of the constants of integration $c_{1}$. We also integrate numerically the equations from a large radius $r=R$ down to the same point $r=r_{m}$ using the asymptotic expansion \\eqref{eq:asb_exp}, this time expressing the functions and their derivatives as a function of the constants of integration $c_{2}$. In order to get a solution in the full bulk we need to match the values of the functions and their derivatives we have found at $r=r_{m}$ by suitably adjusting the constants $c_{1}$ and $c_{2}$. A simple counting shows that this solution for the constants $c_{1}$ and $c_{2}$ will be unique i.e. the number of equations we will have from matching the two solutions will be thirteen.\n\nOnce we have specified the background we follow the same procedure to solve for the perturbation we described in \\S \\ref{sec:corelator_cor}. This time we will be using the near horizon expansion \\eqref{eq:nh_exp} and the asymptotic expansion \\eqref{eq:as_exp}. After matching the two solutions in the middle of the bulk, as we did for the background solution, we will have uniquely fixed the other thirteen constants of integration: the background constants $\\left\\{a_{y(0)}^{(0,0)},a_{y(0)}^{(1,1)},a_{y(0)}^{(2,0)},\\varphi_{(0)}^{(1,1)},g_{xy(0)}^{(1,1)} \\right\\}$ and the fluctuation constants $\\left\\{A_{y(1)}^{(0,0)},A_{y(1)}^{(1,1)},A_{y(1)}^{(2,0)},\\varPhi_{(1)}^{(1,1)},G^{(1,1)}_{xy(3)},G^{(0,0)}_{ty(0)},G^{(1,1)}_{ty(0)},G^{(2,0)}_{ty(0)}  \\right\\}$. In total we will have to specify twenty six constants of integration, thirteen for the background and thirteen for the perturbation. The constant we are ultimately interested in is $A_{y(1)}^{(2,0)}$ which will be precisely the $\\lambda^{2}$ correction of the current-current two-point function, according to (\\ref{eq:curres}). The $\\lambda^{2}$ correction to the conductivity will then be given by\n\\begin{equation}\\label{eq:cond_cor}\n\\sigma^{(2)}=\\frac{A_{y(1)}^{(2,0)}}{\\imath \\, \\omega} \\,.\n\\end{equation}\n\nFrom the spectral analysis of \\S \\ref{sec:irspectrum} and the matching argument, we expect that if an IR relevant or unstable operator mixes in the perturbation, we should see its imprint as a strong contribution to the d.c.$\\,$conductivity as we lower the system's temperature approaching extremality. To illustrate this we have fixed $n=36$ and $c_{1}\\approx 8.47$ in  the Lagrangian density \\eqref{lagra1}, recall we already put $m_s^2 = -4$. This choice gives exactly one value of momentum $k_{c}\\approx 1.27$ for which the corresponding IR mode saturates the $AdS_{2}$ BF bound, and no unstable modes.\\footnote{We have checked that for these values of the coefficients, there is also no instability localized away from the near horizon region.} The explicit expressions for the spectrum around the $AdS_{2}\\times \\mathbb{R}^2$ background solution is more complicated than the case with $n=4$ that we chose for illustrative purposes in section \\S \\ref{sec:irspectrum}. In figure \\ref{fig:nu} we present the dominant $\\nu(k)$ for this specific case demonstrating that at precisely $k_{c}$ we have a marginally stable mode with $\\nu=0$.\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=160pt]{nu.pdf}\\caption{Plot of the dominant exponent $\\nu$ as a function of $k$ for $n=36$, $m_s^2 = -4$ and $c_{1}\\approx 8.47$ illustrating the existence of a mode with $\\nu=0$ at $k_{c}\\approx 1.27$, and no unstable modes. \\label{fig:nu}}\n\\end{center}\n\\end{figure}\nThis tuning to the boundary of instability is one way to address the fact, discussed at the end of \\S \\ref{sec:irspectrum}, that the model we are studying typically has an instability, with the effect of dialing $k_L\/\\sqrt{J^t}$ being to determine whether the instability manifests itself in the conductivity or not.\nThough we will quote values of $k_L$ in this section, as measured in the IR theory which as $z=\\infty$ and hence dimensionless momenta, we should recall from \\S \\ref{sec:irspectrum} that the invariant UV quantity is $k_L\/\\sqrt{J^t}$, that can be tuned via doping. Ultimately one would like to extend the model so that the system can be tuned through the instability.\n\nFixing a small value for $\\omega$ (we take $\\w\/\\mu = 10^{-6}$) and solving the equations of motion as we described above, we have calculated the correction to the d.c.$\\,$conductivity due to lattice induced scatterings and we have plotted the result against temperature in figure \\ref{fig:dlogsdlogt}. As we have explained in previous sections, the expectation is that at low temperatures this should be dominated by a power law $\\sigma^{(2)}\\sim T^{2\\nu-1}$. The behaviour we observe for the two different values of lattice momentum we chose to study precisely matches our expectations.\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=180pt]{dLgsdLgT.pdf}\\caption{Plot of the logarithmic derivative of the temperature dependence of the d.c.$\\,$conductivity for $n=36$ and $c_{1}\\approx 8.47$. The top (red) curve has $k_L = 1.5$ and the bottom (blue) curve has $k_L = 1.27$.\nThese correspond to $\\nu =0$ and $\\nu \\approx 0.2$, respectively. At low temperatures the expected scaling $\\sigma^{(2)}\\sim T^{2\\nu-1}$ is recovered. \\label{fig:dlogsdlogt}}\n\\end{center}\n\\end{figure}\nIn particular, the critical case gives $\\sigma \\sim 1\/T$. We see that quite low temperatures are necessary in this model to reach the true scaling regime. These lower temperatures are costly to reach numerically. Figure \\ref{fig:dlogsdlogt} confirms that the various genericity assumptions we have made in the matching arguments are legitimate.\n\nWe now turn to the correction to the optical conductivity. For the same values of the constants $n$ and $c_{1}$ as before, we have fixed the lattice momentum to be precisely the value for which we have the marginally stable IR mode participating in the perturbation. We have plotted the correction of the optical conductivity as a function of the frequency $\\omega$ in figure \\ref{fig:OptCond} for two different low values of temperature $T$. We present these results in two plots. The first shows the optical conductivity up to high frequencies. The features one notices are an extended tail at low values of the frequency $\\omega$ and a regime of negative values. The negative regime implies that spectral weight is being transferred at interband energy scales. We will see in the following paragraph however that most of the spectral weight in the broad tail at intermediate energy scales is being extracted from the Drude peak. The second plot shows that the broad tail exhibits a power law falloff, again in agreement with our general expectations and matching arguments. If we fit the power law, we do not quite find the expected $\\sigma \\sim 1\/\\w$ for this critical $k_L$. This is because we are not at low enough temperatures to have reached the true scaling regime, as we saw in figure \\ref{fig:dlogsdlogt}. We have checked that as the temperature is lowered, the scaling tends towards the anticipated $\\sigma \\sim 1\/\\w$.\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=140pt]{OptCond.pdf}\\includegraphics[height=146pt]{LogLogOptCond.pdf}\\caption{The correction to the real part of the conductivity $\\mathrm{Re}\\left(\\sigma^{(2)} \\right)$ for $n=36$, $m_s^2 = -4$ and $c_{1}\\approx 8.47$ at $k_{L}=1.27$. The red (lower) curve has $T\/\\mu \\approx 0.01$ and the blue (top) curve has $T\/\\mu \\approx 0.006$. The left plot shows the redistribution of spectral weight at interband frequencies, while the right, log-log, plot shows the expected intermediate-low frequency scaling regime. \\label{fig:OptCond}}\n\\end{center}\n\\end{figure}\nWe can recall that the zeroth order optical conductivity (without a lattice), to which the results of figure \\ref{fig:OptCond} should be added, shows a featureless increase from zero at low frequencies to a constant at frequencies above $\\w$ \\cite{Hartnoll:2009sz}. In fact, it is a general feature of known extremal holographic backgrounds that the optical conductivity vanishes as a positive power of $\\w$ at low frequencies \\cite{Iizuka:2011hg}. Additional dynamics, such as the mixing with a critical mode we have implemented here, seems to be necessary to obtain an extended quantum critical tail such as that in figure \\ref{fig:OptCond}. We once again emphasize that this tail is not a Drude peak, there is still a delta function at $\\w = 0$, as we now discuss.\n\nLet us examine the spectral weight transfer more closely. The conductivity sum rule implies that the integral of the real part of the conductivity over the positive real axis should not change upon introducing our ionic lattice. Therefore, at each order in the $\\lambda$ expansion we can expect the correction to the conductivity to integrate to zero. This integral includes the contribution from the Drude peak delta function. The correction to the delta function can be read off from the zero frequency limit of the real part of the current current correlator. We can write\n\\begin{equation}\n\\mathrm{Re}\\,\\sigma^{(2)} = -\\pi \\, \\mathrm{Re}\\,G^{(2)}_{J^yJ^y}(0)\\,\\delta\\left(\\omega\\right) + \\frac{\\mathrm{Im}\\,G^{(2)}_{J^yJ^y}\\left(\\omega\\right)}{\\omega} \\,.\n\\end{equation}\nThe left hand plot in figure \\ref{fig:ReG} shows the real part of the current correlator at zero frequency as a function of temperature for two values of $\\nu$. From this plot we see that there is delta function with negative weight in the correction to the conductivity. This in turn shows that there is spectral weight transfer from the Drude peak to the broad tail. The spectral weight transfer to the broad tail increases with $T$ in one case and decreases with $T$ in another. The right hand plot in figure \\ref{fig:ReG} shows the integrated spectral weight\n\\begin{equation}\\label{eq:f_definition}\nf\\left(\\omega\\right)=-\\frac{\\pi}{2} \\mathrm{Re}\\,G^{(2)}(0)+\\int_{0^{+}}^{\\omega}d\\omega^{\\prime}\\,\\frac{\\mathrm{Im}\\,G^{(2)}\\left(\\omega^{\\prime}\\right)}{\\omega^{\\prime}} \\,,\n\\end{equation}\nplotted at the critical momentum for the two different temperatures considered. The function asymptotes to zero, confirming the sum rule and providing a nontrivial check of our numerics. From the integrated spectral weight we see that the weight lost from the Drude peak already balances out the broad tail contribution, while the negative region we noted before in figure \\ref{fig:OptCond} at higher frequencies is then balanced out by higher energy processes, and so seems not to be closely related to the critical power law tail.\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=140pt]{ReG.pdf}\\includegraphics[height=139pt]{fPlot.pdf}\\caption{Spectral weight transfer. The plots have\n$n=36$, $m_s^2 = -4$ and $c_{1}\\approx 8.47$. Left, the zero frequency limit of the real part of the Green's function correction $G^{(2)}_{J^yJ^y}$ as a function of temperature. The bottom (red) curve has $k_L = 1.5$ and the top (blue) curve has $k_L = 1.27$. The negative of this curve is the spectral weight extracted from the Drude peak. Right, the integrated spectral weight defined in \\eqref{eq:f_definition}. The red curve has $T\/\\mu \\approx 0.01$ and the blue curve has $T\/\\mu \\approx 0.006$. Both are at the critical lattice spacing $k_L = 1.27$. We see that the sum rule is satisfied after integrating up to a few times the UV scale $\\mu$.  \\label{fig:ReG} \\label{fig:fPlot}}\n\\end{center}\n\\end{figure}\nSpectral weight redistribution from Drude peak to broad tail is a key experimental feature in unconventional metals, e.g. \\cite{hussey, basov,boris, orenstein}.\n\nSpectral weight redistribution has recently been discussed in the context of fermionic quantum BKT transitions \\cite{pwp, pwp2}. There it has been suggested that the discrete scale invariance associated with the complex scaling dimensions in the unstable phase may be an underlying principle of the spectral weight redistribution occurring at Mott transitions.\n\nIn the remainder of this section we shall make some comments about the case in which there is an actual instability over some range of momenta.\nA first question to address is whether spontaneous homogeneous currents are generated via coupling to the lattice. According to the analysis around the Reissner-Nordstr\\\"om black hole of \\cite{Donos:2011bh}, the extremal near horizon version of which we repeated in \\S \\ref{sec:irspectrum}, we will have unstable modes at finite momenta. A perturbative analysis in $\\lambda$ reveals that these modes will be unstable  around the backgrounds we are considering here as well. It was shown in \\cite{Donos:2011bh} that a particular mode with wavenumber $k_{c}$ will first become unstable as we lower the temperature. Due to the presence of a lattice, we will now have the mixing of all modes with wavenumber $k_{c}+n\\,k_{L}$ where $k_{L}$ is the lattice wavenumber and $n$ is integer. One of the fields that will participate in the unstable perturbation will be the gauge field. The question now is what would happen in the case where $k_{c}=m\\,k_{L}$ for $m$ a positive integer. This is the critical case we are most interested in. Is a spontaneous homogeneous current generated? More generally, this question can be asked whenever $m \\, k_L$ lies within the range of unstable momenta. We considered this case and explicitly constructed numerically the unstable mode at next to leading order in $\\lambda$. Doing so revealed that the expectation value for the homogeneous current is zero to within our numerical accuracy. It seems that this result should be provable from general principles.\n\nWe have also studied the behavior of the conductivity close to the temperature where a striped phase transition occurs, assuming that our lattice is precisely such that $k_{c}=m\\,k_{L}$ so that the unstable mode is directly communicated to the current. We find that the d.c.$\\,$conductivity diverges as $\\mathrm{Re}\\left(\\sigma^{(2)}\\right)\\propto \\left(T-T_{c}^{\\left(0\\right)}\\right)^{-2}$ where $T_{c}^{\\left(0\\right)}$ is specified by the existence of a static mode around the $\\lambda=0$ background. The presence of a lattice will shift the critical temperature: $T_{c}=T_{c}^{\\left(0\\right)}+\\lambda^{2}\\,T_{c}^{\\left(2\\right)}+\\cdots$ \\cite{Flauger:2010tv}. The full correlator should diverge at $T_{c}$.\n\n\n\\section{Discussion}\n\nIn this discussion section we will reiterate the main points of our paper and simultaneously contextualize our results in terms of previous holographic and other theoretical work, highlighting potential experimental features.\n\n\\subsection{Broader perspective on linear resistivity, BKT and other models}\n\\label{sec:broader}\n\nIn \\S \\ref{sec:bkt} we described quantum BKT transitions from the standpoint of the near horizon geometry of an extremal black brane. In particular, the scaling dimension of the operator ${\\mathcal{O}}$ took the form $\\Delta = (2+z)\/(2z) + \\nu$, with $\\nu$ the square root of a quantity that becomes negative beyond the critical point. This type of formula is typical in holographic frameworks. The fact that $2 \\Delta = 1+2\/z$ when $\\nu=0$ underlies the scaling of the spectral weight at the critical point in (\\ref{eq:critical}): $\\lim_{\\w \\to 0} \\text{Im} \\, G_{{\\mathcal{O}} {\\mathcal{O}}}^R(\\w)\/\\w \\sim 1\/T$. In the large $N$ limit, in which the holographic description is classical, this implies that the `double trace' operator ${\\mathcal{O}} {\\mathcal{O}}$ is marginal.\n\nA more general field theoretical description of quantum BKT transitions \\cite{Kaplan:2009kr} is as a merger and subsequent annihilation of two fixed points of the RG flow. At the transition point, where the two fixed points merge, one can expect in general that there should be a marginal operator (that does not exponentiate -- this statement at the critical point is in addition to the marginal operator that is presumably necessary to dial the dimensions of operators). It seems likely therefore that ${\\mathcal{O}} {\\mathcal{O}}$ will be marginal in general. However, away from the large $N$ limit, or some other kind of generalized mean field description, the dimensions of operators do not add and therefore we cannot draw any conclusions about the dimension of ${\\mathcal{O}}$. It follows that ${\\mathcal{O}}$ will not in general have the dimension $\\Delta = (2+z)\/(2z)$ at the critical point, ultimately not leading to a linear resistivity. A BKT transition in itself therefore does not appear to be sufficient. On the other hand, if the operator that condenses does admit a mean field description, then our mechanism for a linear resistivity will automatically go through. Theories with holographic duals are one set of concrete examples where this is the case, even when the formula for the operator dimension is more complicated than (\\ref{eq:delta}). Other examples were given in \\cite{Kaplan:2009kr}.\nNote that ``mean field'' here does not imply that the transition is of mean field nature -- it is not -- rather that there exists a description in which the order parameter may be treated as a classical variable.\n\nBeyond BKT transitions, previously studied models have used a conceptually similar approach of coupling the electric current to degrees of freedom with a $1\/T$ spectral weight. For instance in \\cite{kiv2,kiv3} such degrees of freedom resided on a density of impurities tuned to a specific value of the impurity coupling for which the model becomes solvable. The ``Gaussianization'' of the model at their critical coupling is reminiscent of our observation above that a mean field description of the unstable operator at the BKT transition is necessary to obtain the required temperature dependence of the spectral weight. The model also shares the feature of our approach that the Drude contribution to the conductivity is hoped to be subdominant relative to the quantum critical contribution.\n\nA mean field limit was also tied to the emergence of a linear in temperature resistivity in Kondo lattice models, e.g. \\cite{sy, georges, Sachdev:2010um, Sachdev:2010uj}. These models are not dissimilar to those mentioned in the previous paragraph. A $1\/T$ spectral density of the localized spin excitations\nis fed into the  self energy of the conduction fermions, leading to marginal Fermi liquid phenomenology \\cite{Varma:1989zz}. Holographic realizations of similar models are mentioned in \\S \\ref{sec:holo} below, see \\cite{Sachdev:2010uj} for an extended comparison.\n\nIn short, the general strategy is to find a well-motivated $1\/T$ spectral density and then transfer this temperature dependence to the conductivity.\nThe holographic BKT transitions we have discussed provide a robust way to this, using irrelevant operators rather than explicit fermions to transfer the spectral weight, with the interesting behavior occurring at the boundary between a critical phase and an ordered phase.\n\n\n\\subsection{Experimental signatures of the mechanism}\n\nIncorporating the effects of a Drude peak will presumably be necessary to connect with key features of the phase diagrams of unconventional materials, such as the crossover to Fermi liquid behavior away from the critical point. However, it seems possible to distill at least three generic ingredients of the scenario we have outlined that may manifest themselves experimentally in one way or another.\n\nFirstly one could look for evidence of BKT scaling in quantities such as the critical temperature (\\ref{eq:tc}) or the expectation value of the condensed operator. In general, on the side of the critical point in the phase diagram where an operator condenses, one expects quantities to be controlled by a dynamically generated scale with an exponential dependence on the distance to the critical point \\cite{Kaplan:2009kr}.\n\nA second generic feature is likely to be an asymmetry in the optical and d.c.$\\,$conductivities, as well as other quantities that couple to the unstable mode, between the two sides of the quantum critical point. On the side where an operator condenses, at sufficiently low temperatures and frequencies, one expects only logarithmic corrections to the $1\/T$ and $1\/\\w$ scalings of the critical point itself. See appendix \\ref{eq:matching}. The other, disordered, side of the critical point should be characterized by varying power law dependences along the lines of equations (\\ref{eq:fudged}) and (\\ref{eq:sw}) above.\n\nThirdly, the nature of the transition, in which a scaling dimension becomes complex as two critical points annihilate \\cite{Kaplan:2009kr}, requires the existence of a critical phase in the IR, of which the BKT quantum critical point is a boundary. This critical phase should manifest itself in scaling behaviors such as (\\ref{eq:sw}) persisting down to arbitrarily low temperatures on the disordered side of the critical point. This scaling behavior may or may not require disentangling from other physics, such as superconductivity, present in the phase diagram.\n\n\\subsection{Context: linear resistivity in holography}\n\\label{sec:holo}\n\nThere exists a large body of interesting previous holographic work attempting to understand the origin of a linear in temperature d.c.$\\,$resistivity. These works can broadly be classified into two classes, depending on the fate of the translation-invariance delta function in the conductivity. When the conductivity is due to probe branes \\cite{Karch:2007pd, Hartnoll:2009ns} or probe fermions \\cite{Faulkner:2010zz, Kachru:2010dk}, the degrees of freedom of interest are taken to be a parametrically small part of a bigger system. In this case the charge carriers can dump their momentum elsewhere and it does not return on the `experimental' timescale. A second option, that avoids diluting the carriers, is to explicitly break translation invariance via parametrically heavy degrees of freedom such as impurities \\cite{Hartnoll:2008hs} or a lattice \\cite{Hartnoll:2012rj, Horowitz:2012ky}.\n\nFor both classes of models, the d.c.$\\,$ conductivity typically depends on parameters of the model. The dynamical critical exponent $z$ in \\cite{Hartnoll:2009ns} and the dimension of IR operators in \\cite{Faulkner:2010zz, Kachru:2010dk,Hartnoll:2008hs, Hartnoll:2012rj}. These models do not provide a compelling motivation, at least without additional input, for selecting the exponent that results in a linear resistivity. An interesting example of how additional input can help is \\cite{Jensen:2011su}, where the dimension of the impurity operator of interest is protected by supersymmetry. It is furthermore unclear if the probe limit is a reasonable approximation for the real world systems of interest.\n\nOur model has not addressed the fate of the delta function, but rather assumed that the corresponding Drude peak is swamped by a quantum critical contribution to the d.c. conductivity. We have suggested that this may be a reasonable starting point to discuss some bad metallic phases of matter. In contrast to the other models we find a linear in temperature resistivity occurring robustly and precisely where we would like it to: at a quantum critical point mediating the onset of an instability. The result is universal in the sense that it does not depend on the specific microscopic realization of the BKT transition. It does require, however, the existence of an irrelevant operator that can communicate the instability to the current correlators. We achieved such a coupling in \\S \\ref{sec:lattice} by having a vectorial instability at a finite wavenumber that was was communicated to the current via an irrelevant lattice.\n\n\\subsection{Open questions and future directions}\n\nThe essential feature of the holographic dynamics we have discussed is the BKT quantum phase transition.\nThe realization of such a BKT quantum phase transition in e.g. some Hubbard-like lattice model as a function of doping would of course be very exciting in bridging the gap between extremal horizons and the chemistry of unconventional materials.\n\nSuperconducting phases have been absent from our discussion thus far, and yet are a central feature of the most interesting bad metals. It seems reasonable to hope for a unified theory of bad metals and unconventional superconductivity. We can imagine two ways in which our mechanism could interplay with a superconducting instability. The first, a variant on a fairly conventional viewpoint, is simply that the superconducting instability could be triggered by coupling to the operator that develops the $1\/T$ spectral weight at the critical point. A second possibility is that the critical phase itself, out of which the BKT transition emerges, is tightly entwined with\nthe existence of a superconducting instability. It is common in holographic frameworks, see \\cite{Hartnoll:2012pp} for a recent discussion, for the IR of the superconducting phase to exhibit an emergent scaling symmetry. This could itself be the critical phase in which the BKT transition occurs. Such a picture would be, loosely speaking, in line with claims that the linear in T conductivity is associated to the existence of superconducting phases \\cite{taillefer}. These critical issues deserve further thought.\n\nClearly a pressing issue is to establish (experimentally?) whether the picture we have outlined in figure \\ref{fig:optical}, namely that in bad metals the Drude peak is swamped by an extended `critical' contribution, is reasonable in some circumstances. An alternative possibility is that the extended tail in fact falls rapidly to zero at $\\w \\approx 0$, so that for the strict d.c.$\\,$conductivity the Drude contribution always dominates. This would incorporate naturally the fact that the d.c.$\\,$conductivity is insensitive to the melting of an explicit Drude peak in the data.\nAgainst this scenario we can note that, at least in the holographic models we have studied, the quantum critical contribution to the conductivity does extend all the way down to $\\w=0$. An alternative possibility would be to build a model in which momentum relaxational process were built into the critical sector that the undergoes a BKT transition. In such a model we might hope to have our cake and eat it, simultaneously having a linear resistivity and incorporating the Drude peak physics.\n\nDrude physics could explicitly be incorporated into our model by making the lattice potential (\\ref{eq:AV}) periodic in both directions. One could imagine solving such a model numerically along the lines of \\cite{Horowitz:2012ky}. Because the lattice is irrelevant in the IR, the momentum relaxation rate is very slow and hence one's first thought is that there will always necessarily be a well-defined Drude peak \\cite{Hartnoll:2012rj}. However, sufficiently close to the BKT critical point, there is a further long timescale in the problem, the lifetime of the mode that is going unstable, and this may be able to transfer spectral weight out of the Drude peak and into the critical tail.\nWe made some preliminary remarks about this process in \\S \\ref{sec:numerics}. A more comprehensive holographic study of this point is desirable and has the potential to shed light on the nature of bad metals.\n\nThe particular model of a BKT transition that we constructed in \\S \\ref{sec:lattice} relied on local ($z=\\infty$) criticality to obtain critical physics at nonzero wavenumber that could then be coupled by a lattice onto the homogeneous electrical conductivity. It would be very interesting to see if this requirement can be relaxed by combining for instance BKT transitions with Fermi surface physics, or by finding a way to communicate BKT transitions to the electrical current without going via finite wavevector modes.\n\nThe essential role of holography in our work has been to provide a setting where BKT transitions occur naturally and where the interplay between instability in a strongly correlated medium, lattices and conduction can be studied in a theoretically controlled way. Holography is less able to incorporate more conventional Fermi liquid physics in a useful way. Any strategy to describe the full phase diagram and the crossover the Fermi liquid behavior will presumably have to involve a mix of distilled insights from holography and conventional Fermi liquid computations.\n\nFinally, the focus throughout this paper on the linear in temperature d.c.$\\,$resistivity, and possible application to bad metals,\nshould not obscure the more general points we have made. Two further take home messages are firstly that strong optical and d.c.$\\,$conductivities\ncan be achieved by coupling critical modes on the verge of an instability to the electrical current via irrelevant operators. Secondly, that (semi) local quantum criticality enables the effects of instabilities at nonzero wavevector to be efficiently coupled to e.g. the conductivity via lattice scattering.\n\n\n\\section*{Acknowledgements}\n\nWe have benefitted from discussions with Jerome Gauntlett, Chris Herzog, Steve Kivelson, John McGreevy, Mike Norman, Philip Phillips, Subir Sachdev, Dam Son and Jan Zaanen on topics related to those in this paper. We would also like to acknowledge the organizers of the Chicheley Hall meeting on ``Gravity, black holes and condensed matter'' for providing the stimulating setting where this collaboration was initiated. S.A.H. is partially funded by a Sloan research fellowship and by a DOE Early Career Award. A.D. is supported by an EPSRC fellowship.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\n\n\n\\section{Introduction}\n\nReinforcement Learning (RL) has demonstrated its effectiveness in a variety of tasks~\\cite{mnih2015human,openai2018openaifive,jaderberg2018human}. However, a common challenge for RL methods is their severe dependency on a well-designed reward signal.\nFortunately, the reward signals will be unnecessary if we consider to Learn from Demonstrations (LfD), or commonly known as Imitation Learning (IL)~\\cite{hussein2017imitation}. In this paper, we focus on the common setting of IL, where agents learn their policies from the samples of trajectories from the expert, without any further access to the expert or explicit rewards. \n\nClassic solutions for IL such as behavior cloning (BC)~\\cite{pomerleau1991efficient} aim to minimize 1-step deviation error along the provided expert trajectories with supervised learning, which suffers seriously from an extensive collection of expert data and compounding error caused by covariate shift ~\\cite{ross2010efficient,ross2011reduction}.\nAs an alternative, Inverse Reinforcement Learning (IRL)~\\cite{ng2000algorithms,abbeel2004apprenticeship,fu2017learning} tries to recover a reward function from the expert and subsequently train an RL policy under that, yet such a bi-level optimization scheme can result in high computational cost. \nThe recent solution as GAIL~\\cite{ho2016generative} derived from Max-Entropy IRL (MaxEnt IRL) formulates the IL problem as occupancy measure matching. GAIL takes advantage of GAN~\\cite{goodfellow2014generative} to minimize the Jensen-Shannon divergence between the agent's occupancy measures and the expert's while it also inherits the notorious defects of GAN, including training instability and mode dropping~\\cite{brock2018large}.\n\nAnalogous to IL, learning statistical models from given data and generating similar samples has been an important topic in the generative model community. Among them, recent energy-based models (EBMs) have gained much attention because of the simplicity and flexibility in likelihood estimation~\\cite{du2019implicit,song2019sliced}. \nIn this paper, we propose to leverage the advantages of EBMs to solve IL with a novel framework called Energy-Based Imitation Learning (EBIL), which addresses the problem via expert energy estimation in a two-step fashion: first estimates an unnormalized probability density (\\textit{a.k.a.} energy) of expert's occupancy measure through score matching, and then takes the energy to construct a surrogate reward function as a guidance for the agent to learn the desired policy. In experiments, we first verify our idea in a simple one-dimensional environment by visualizing the estimated reward and the induced policy; then we evaluate our algorithm on extensive high-dimensional continuous control benchmarks, showing that EBIL can always achieve comparable or better performance than SoTA methods.\n\nIn addition to the stability and flexibility of EBMs, EBIL also enjoys more efficiency thanks to the two-step training fashion that overcomes the undesired slow alternate training process as in IRL and GAIL.\nThough the underlying intuition behind our proposed methodology was to match the expert's occupancy measure through EBM, we surprisingly find that there indeed exists a non-trivial connection between our method and previous MaxEnt IRL methods. Thus we further provide a theoretical illustration of the relation between EBIL and MaxEnt IRL, showing that EBIL is a dual problem of MaxEnt IRL but simpler and more efficient. Compared with MaxEnt IRL, EBIL can provide more flexibility on the choice to train the expert's EBM and enable us to avoid the intractable estimation of the partition function.\nThe analysis, along with past works provides a holistic view of the role of EBM in imitation learning.\n\n\\section{Preliminaries}\nIn this section, we present the definition of reinforcement learning problem, imitation learning and energy-based models along with the notations.\n\n\\subsection{Maximum Entropy Reinforcement Learning}\n\nReinforcement Learning (RL) problems can be seen as Markov Decision Process (MDP), which is represented as a tuple $\\caM = \\langle \\caS, \\caA, P, \\rho_0, r, \\gamma \\rangle$, where $\\caS$ is the set of states, $\\caA$ represents the action space of the agent, $P: \\caS \\times \\caA \\times \\caS \\rightarrow \\mathbb{R}$ is the state transition probability distribution, $\\rho_0: \\caS\\rightarrow\\mathbb{R}$ is the distribution of the initial state $s^0$, and $\\gamma\\in [0,1]$ is the discounted factor. The agent holds its policy $\\pi(a|s): \\caS \\times \\caA \\rightarrow [0, 1]$ to make decisions and receive rewards defined as $r: \\caS \\times \\caA \\rightarrow \\mathbb{R}$. For an arbitrary function $f: \\langle s, a \\rangle \\rightarrow \\mathbb{R}$, it is easy to show that $\\bbE_\\pi[f(s,a)]=\\bbE_{s\\sim P, a\\sim \\pi}[f(s,a)]\\triangleq \\bbE \\left [\\sum_{t=0}^\\infty \\gamma^t f(s_t,a_t) \\right ]$, where $s_{0}\\sim \\rho_0$, $a_t\\sim\\pi(\\cdot|s_t)$, $s_{t+1}\\sim P(\\cdot|a_t,s_t)$. \n\nThe normal objective of RL is to get an optimal policy such that it can maximize its own total expected return $R \\triangleq \\bbE_\\pi[r(s,a)] = \\bbE \\left [\\sum_{t=0}^\\infty \\gamma^t r(s_t, a_t) \\right ]$, while Maximum Entropy Reinforcement Learning (MaxEnt RL) augments the objective with an entropy term to find a stochastic policy that can also maximize its entropy at each visited state~\\cite{ho2016generative,haarnoja2017reinforcement} as:\n\\begin{equation}\\label{eq:maxent-rl}\n    \\pi^* = \\argmax_{\\pi} \\bbE_\\pi\\left [r(s,a)\\right ]+\\alpha H(\\pi)~,\n\\end{equation}\nwhere $H(\\pi) \\triangleq E_{\\pi}[- \\log \\pi(a|s)]$ is the $\\gamma$-discounted causal entropy~\\cite{bloem2014infinite} and the temperature hyperparameter $\\alpha$ is used to determine the relative importance of entropy as a reward, we will let $\\alpha=1$ by default in the following part of this paper.\n\n\\iffalse\n\\begin{equation}\\label{eq:rl}\n    \\pi^* = \\argmax_{\\pi} \\bbE_\\pi \\left [r(s,a) \\right ]~. \n\\end{equation}\n\\fi\n\n\\textbf{Occupancy Measure.}\nThe agent generates trajectories, \\textit{i.e.}, state-action $(s,a)$ pairs when they interact with the environment with policy $\\pi$ lead to the definition of occupancy measure $\\rho_\\pi^{s,a}(s,a)$ or $\\rho_\\pi^{s}(s)$ as the density of occurrence of states or state-action pairs:\n\\begin{equation}\n\\begin{aligned}\n    \\rho_{\\pi}^{s,a}(s,a) &= \\sum_{t=0}^{\\infty}\\gamma^t P(s_t=s, a_t=s|\\pi)\\\\\n&= \\pi(a|s)\\sum_{t=0}^{\\infty}\\gamma^t P(s_t=s|\\pi)\n= \\pi(a|s)\\rho_{\\pi}^{s}(s)~,\n\\end{aligned}\n\\end{equation}\nwhich allows us to write that: $\\bbE_{\\pi}[\\boldsymbol{\\cdot}]=\\sum_{s,a}\\rho_{\\pi}^{s,a}(s,a)[\\boldsymbol{\\cdot} ]=\\bbE_{(s,a)\\sim \\rho_{\\pi}^{s,a}}[\\boldsymbol{\\cdot}]$.\nFor simplicity, we will denote $\\rho_\\pi^{s,a}$ as $\\rho_\\pi$ without further explanation in the following sections, and we have $\\rho_\\pi \\in \\caD\\triangleq\\{ \\rho_\\pi: \\pi\\in\\Pi \\}$. \n\n\\subsection{Imitation Learning}\n\nImitation learning (IL) \\cite{hussein2017imitation} studies the task of Learning from Demonstrations (LfD), which aims to learn a policy from expert demonstrations which typically consists the expert trajectories interacted with environments without receiving reward signals from environments. General IL objective tries to minimize the distance between the actions taken by policy $\\pi$ and expert policy $\\pi_E$:\n\\begin{equation}\\label{eq:il}\n\\pi^* = \\argmin_\\pi \\mathbb{E}_{s \\sim \\rho_{\\pi}^{s}}\\left [\\ell \\left ({\\pi_E}(\\cdot | s), \\pi(\\cdot | s)\\right )\\right ]~,\n\\end{equation}\nwhere $\\ell$ denotes some distance metric.\nHowever, as we do not ask the expert agent for further demonstrations, it is always hard to optimize \\eq{eq:il} with only expert trajectories accessible. Thus, Behavior Cloning (BC)~\\cite{pomerleau1991efficient} provides a straightforward method by learning the policy in a supervised way, where the objective is represented as a Maximum Likelihood Estimation (MLE):\n\\begin{equation}\n\\hat{\\pi}^* = \\argmin_\\pi \\mathbb{E}_{s \\sim \\rho_{\\pi_E}^s}\\left [\\ell \\left ({\\pi_E}(\\cdot | s), \\pi(\\cdot | s)\\right )\\right ]~,\n\\end{equation}\nwhich suffers from covariate shift problem for the i.i.d. state assumption.\n\nAnother branch of methods are under the basic idea of Inverse Reinforcement Learning (IRL) \\cite{ng2000algorithms} that tries to recover the reward function $r^*$ in the environments. An underlying assumption of IRL is that the reward function $r^*$ will evaluate the expert policy as the optimal policy in the environment. Formally,\n\\begin{equation}\\label{irl}\n\\pi^* = \\argmax_\\pi \\mathbb{E}_{(s,a) \\sim \\rho_{\\pi}}\\left [r^*(s,a)\\right ]~,\n\\end{equation}\nwhich suffers typically from a high complexity for its bi-level optimization and can cause ambiguity resulting in  different reward functions.\n\nDerived from Max-Entropy IRL (MaxEntIRL) which solves the ambiguity of normal IRL methods, generative Adversarial Imitation Learning (GAIL) \\cite{ho2016generative} shows that the objective of MaxEntIRL is a dual problem of occupancy measure matching, and thus can be solved through generative models such as GAN. Specifically, it shows that the policy learned by RL on the reward recovered by IRL can be characterized by\n\\begin{equation}\\label{eq:rl-irl}\n    \\begin{aligned}\n    {\\textnormal{l}} \\circ \\irl_\\psi(\\pi_E) = \\argmin_\\pi - H(\\pi) + \\psi^*(\\rho_\\pi - \\rho_{\\pi_E})~,\n    \\end{aligned}\n\\end{equation}\nwhere $\\psi$ is the regularizer, and $f^*:\\bbR^{\\caS\\times\\caA}\\rightarrow\\overline{\\bbR}$ is the convex conjugate for an arbitrary function $f:\\bbR^{\\caS\\times\\caA}\\rightarrow \\overline{\\bbR}$ given by $f^*(x)=\\sup_{y\\in\\bbR^{\\caS\\times\\caA}}x^Ty - f(y)$. \n\\eq{eq:rl-irl} shows that various settings of $\\psi$ can be seen as a distance metric leading to various solutions of imitation learning.\n\n\n\\subsection{Energy-Based Models}\n\\label{subsec:ebm}\n\nFor a random variable $X\\sim p(x)$, energy-based model (EBM) \\cite{lecun2006tutorial} builds the density of data by estimating the energy function $E(x)$ with sample $x$ as\n\\begin{equation}\n    \\begin{aligned}\n        p(x) = \\frac{1}{Z}\\exp(-E(x))~,\n    \\end{aligned}\n\\end{equation}\nwhere $Z=\\int\\exp(-E(x))dx$ is the partition function, which is normally intractable to compute exactly for\nhigh-dimensional $x$. The energy function $E$ can be seen as the unnormalized log-density of data which is always optimized to maximize the likelihood of the data. Typically, the estimation of the partition function $Z$ is computationally expensive, which requires sampling from the Boltzmann distribution $p(x)$ within the inner loop of learning. \n\n\\section{Imitation Learning via Expert Energy Estimation}\n\\label{sec:ebil}\n\nIn this section, we provide an energy-based perspective of IL and propose to learn the agent's policy via estimating the energy of the expert demonstrations.\n\n\\subsection{Energy-Based Imitation Learning}\n\\label{subsec:EBIL}\n\nIL requires to recover expert policy $\\pi_E$ from static demonstrations which consists of expert trajectories and cannot be further expanded by interacting with the expert agent. Instead of minimizing the distance between every action taken by agent policy and expert's based on expert trajectories as shown in \\eq{eq:il}, or find the policy which is optimal that achieves the maximum accumulated reward under unknown reward function, \\eq{eq:rl-irl} prescribes that we are able to formulate the problem of recovering expert policy based on its occupancy measure. Formally, denoting the set of policies as $\\Pi$ and the set of valid occupancy as measures $\\caD \\triangleq \\{ \\rho_\\pi>0 : \\pi \\in \\Pi \\}$, \\lm{lm:occupancy} shows the one-to-one correspondence between $\\Pi$ and $\\caD$:\n\n\\begin{lemma}[Theorem 2 of \\cite{syed2008apprenticeship}]\\label{lm:occupancy}\n    If $\\rho \\in \\caD$, then $\\rho$ is the occupancy measure for $\\pi_\\rho(a|s) \\triangleq \\frac{\\rho(s,a)}{\\sum_{a'}\\rho(s,a')}$, and $\\pi_\\rho$ is the only policy whose occupancy measure is $\\rho$.\n\\end{lemma}\n\\vspace{-2pt}\n\nThus, the occupancy measure can be used as an alternative in the general IL objective shown in \\eq{eq:il}. Applying KL divergence as the distance metric, we could construct the IL objective as minimizing the reverse KL divergence $\\kld$ of between the agent's occupancy measure and expert's:\n\\begin{equation}\\label{eq:kl-il}\n    \\pi^* = \\argmin_{\\pi} \\kld ( \\rho_\\pi \\| \\rho_{{\\pi_E}})~.\n\\end{equation}\n\\begin{proposition}\\label{prop:kl-il}\n    The optimal solution for the reverse KL divergence objective of IL shown in \\eq{eq:kl-il} is that $\\pi^*={\\pi_E}$.\n\\end{proposition}\n\\vspace{-6pt}\n\\begin{proof}\n    It is obvious that the solution of \\eq{eq:kl-il} is unique since $\\kld$ is convex for $\\rho_\\pi$, which achieves the optimal value iff $\\rho_\\pi = \\rho_{{\\pi_E}}$. According to \\lm{lm:occupancy}, we can recover policy ${\\pi_E}$ if we can recover the occupancy measure of expert policy.\n    Thus the optimal solution is that $\\pi^* = {\\pi_E}$.\n\\end{proof}\nConsidering to model the normalized occupancy measure with Boltzmann distribution, the density can be represented by an EBM as\n\\begin{equation}\\label{eq:ebm}\n    (1-\\gamma)\\rho_\\pi(s,a) = \\frac{1}{Z}\\exp(-E(s,a))~,\n\\end{equation}\nwhere leads to the following proposition.\n\\begin{proposition}\\label{prop:eb-il}\n    The reverse KL divergence objective of IL \\eq{eq:kl-il} is equivalent to the following of Energy-Based Imitation Learning (EBIL) objective \\eq{eq:eb-il}:\n\\iffalse\nThus we take \\eq{eq:ebm} into \\eq{eq:kl-il} for both policy $\\pi$ and ${\\pi_E}$, we get that: \n\\begin{equation}\\label{eq:kl-induce}\n    \\begin{aligned}\n        \\kld ( \\rho_\\pi \\| \\rho_{{\\pi_E}}) &= \\sum_{s,a} \\rho_\\pi(s,a) \\log \\frac{\\rho_\\pi(s,a)}{\\rho_{\\pi_E}(s,a)}\\\\\n        &= \\sum_{s,a}\\rho_\\pi\\left( \\log{\\rho_\\pi(s,a)} - \\log{\\frac{e^{-E_{\\pi_E}(s,a)}}{Z'}} \\right )\\\\\n        &= \\sum_{s,a}\\rho_\\pi\\left(E_{\\pi_E}(s,a)+\\log{\\rho_\\pi(s,a)} + \\log{Z'}\\right )\\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ]+\\sum_{s,a}\\rho_\\pi\\log{\\rho_\\pi(s,a)} + \\text{const}\\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ]+\\sum_{s,a}\\rho_\\pi\\log{\\rho_\\pi(s,a)} -\\log{\\sum_{s,a'}\\rho(s,a')}+ \\text{const}\\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ]+\\sum_{s,a}\\rho_\\pi\\log{\\left [ \\rho_\\pi(s,a)\/\\sum_{a'}\\rho(s,a')\\right ]}+ \\text{const}\\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ] - \\overline{H}\\left (\\rho_\\pi(s,a) \\right ) + \\text{const}\n       \n       \n       \n       \n       \n        ~,\n    \\end{aligned}\n\\end{equation}\nwhere $\\overline{H}=-\\sum_{s,a}\\rho_\\pi\\log{\\rho_\\pi(s,a)\/\\sum_{a'}\\rho(s,a')}$ is the entropy of the occupancy measure, $E_{\\pi_E}$ is the EBM of policy ${\\pi_E}$ and $Z'$ is its partition function.\n\\begin{lemma}[Lemma 3 of \\cite{ho2016generative}]\n   $\\overline{H}$ is strictly concave, and for all $\\pi \\in \\Pi$ and $\\rho \\in \\caD$, we have $H(\\pi) = \\overline{H}(\\rho_\\pi)$ and $\\overline{H}(\\rho)=H(\\pi_\\rho)$.\n\\end{lemma}\nThus, \\eq{eq:kl-il} in the end lead to the objective function of Energy-Based Imitation Learning (EBIL) as:\n\\fi\n\\begin{equation}\\label{eq:eb-il}\n\\pi^* = \\argmax_{\\pi} \\bbE_\\pi \\left[-E_{\\pi_E}(s,a)\\right ] + H(\\pi)~.\n\\end{equation}\n\\end{proposition}\n\\vspace{-6pt}\nThe proof of \\prop{prop:eb-il} is in \\ap{ap:eb-il}. A key observation is that \\eq{eq:eb-il} provides exactly the same form as the objective of MaxEnt RL shown in \\eq{eq:maxent-rl}, and thus we can just estimate the energy of expert data as a surrogate reward function without involving the intractable partition function $Z$\\footnote{One may notice that according to \\lm{lm:occupancy}, we can simply recover the expert policy directly through $\\pi^*=\\exp(-E(s,a))\/\\sum_{a'}{\\exp{(-E(s,a'))}}$. However, this may be hard to generalize to continuous or high-dimensional action space in practice. For more discussions one can refer to \\se{ap:ebil-sac}.}. Generally, we can choose the reward function as $r(s,a)=h(-E_{\\pi_E}(s,a))$ where $h$ is a monotonically increasing linear function to keep the objective of \\eq{eq:eb-il} still true. \n\nTherefore, EBIL that learns with MaxEnt RL using the expert energy function as the reward function aims to minimize the reverse KL divergence between the agent's occupancy measure and the expert's. It is worth noting that if we remove the entropy term to construct a standard RL objective, then it will collapse into minimizing the cross entropy of the occupancy measure rather than the KL divergence.\n\n\\subsection{Expert Energy Estimation with Demonstrations}\n\nAs described above, our reward function is determined by $E_{{\\pi_E}}(s,a)$, a learned energy function of the occupancy measure. In this section, we elaborate on how to estimate $E_{{\\pi_E}}(s,a)$ from expert demonstrations. \nSpecifically, in this paper, we leverage Deep Energy Estimator Networks (DEEN)~\\cite{saremi2018deep}, a scalable and efficient algorithm to directly estimate the energy of expert's occupancy measure of policy via a differentiable framework without involving the intractable estimation of the normalizing constant. Then we can take the estimated energy as the surrogate reward to train the agent policy.\n\nFormally, let the random variable $X=g(s,a)\\sim g(\\rho_{\\pi_E}(s,a))$. \nLet the random variable $Y$ be the noisy observation of $X$ that $y\\sim x+N(0, \\sigma^2I)$, \\textit{e.g.}, $y$ is derived from samples $x$ by adding with white Gaussian noise $\\xi\\sim N(0, \\sigma^2I)$. \nThe empirical Bayes least square estimator, \\textit{i.e.}, the optimal denoising function $g(y)$ for the white Gaussian noise, is solved as\n\\begin{equation}\n\\begin{aligned}\\label{eq:denoise}\n    g(y) = y + \\sigma^2\\nabla_y\\log{p(y)}~.\n\\end{aligned}\n\\end{equation}\nSuch a function can be trained with a feedforward neural network $\\hat{g}$ by denoising each sample $y_i \\in Y$ to recover $x_i \\in X$, which can be implemented with a Denoising Autoencoder (DAE)~\\cite{vincent2008extracting}. Then we can use the DAE $\\hat{g}$ to approximate the score function $\\nabla_y \\log p(y)$ of the corrupted distribution by $\\nabla_y \\log p(y) \\propto \\hat{g}(y) - y$~\\cite{robbins1955empirical,miyasawa1961empirical,raphan2011least}. However, one should note that the DAE does not provide the energy function but instead approximates the score function -- the gradient of $\\log \\rho_\\pi(s,a)$, which cannot be adopted as the vital reward function.\n\nThus, in order to estimate the EBM of expert's state-action pairs provided through demonstration data, we consider to parameterize the energy function $E_\\theta(y)$ with a neural network explicitly. As shown in \\cite{saremi2018deep}, such a network called DEEN can be trained by minimizing the following objective:\n\\begin{equation}\\label{eq:deen}\n    \\argmin_{\\theta} \\sum_{x_i\\in X, y_i\\in Y} \\left \\| x_i - y_i + \\sigma^2\\frac{\\partial E_\\theta(y=y_i)}{\\partial y} \\right \\|^2~,\n\\end{equation}\nwhich ensures the relation of score function $\\partial E_\\theta(y)\/\\partial y$ shown in \\eq{eq:denoise}. It is worth noting that the EBM estimates the energy of the noisy samples. This can be seen as a Parzen window estimation of $p(x)$ with variance $\\sigma^2$ as the smoothing parameter~\\cite{saremi2019neural,vincent2011connection}. A trivial problem here is that \\eq{eq:deen} requires the samples (state-action pairs) to be continuous so that the gradient can be accurately computed. Actually, EBIL can be easily expanded to discrete space by using other energy estimation methods, \\textit{e.g.}, Noise Contrastive Estimation~\\cite{gutmann2010noise}. In this work, we concentrate on the continuous space and leave the discrete version in the future.\n\nIn practice, we learn the EBM of expert data from off-line demonstrations and construct the reward function, which will be fixed until the end to help agent learn its policy with a normal RL procedure. Specifically, we construct the surrogate reward function $\\hat{r}(s,a)$ as follows:\n\\begin{equation}\\label{eq:reward}\n    \\hat{r}(s,a) = h(-E_{{\\pi_E}}(s,a))~,\n\\end{equation}\nwhere $h(x)$ is a monotonically increasing linear function, which can be specified for different environments.\nFormally, the overall EBIL algorithm is presented in \\alg{alg:EBIL} of \\ap{ap:algo} .\n\\section{Discussions}\n\\label{sec:discussion}\n\nIn this paper, we propose to estimate the energy function from expert demonstrations directly, then regard it as the surrogate reward function to force the agent to learn a good policy that can match the occupancy measure of the expert. Interestingly, MaxEnt IRL can be seen as a special implementation of EBM, which constructs the expert demonstrations as a Boltzmann distribution of the cost \/ reward function, and tries to extract optimal policy from it. In this section, we theoretically clarify the relation between EBIL and MaxEnt IRL, and show that EBIL actually can be seen as a simplified and efficient solution for MaxEnt IRL.\n\nIRL aims to recover a cost or reward, under which the set of demonstrations are near-optimal. However, the optimal solution is still underdefined. To that end, MaxEnt IRL resolves the reward ambiguity problem in normal IRL by employing the principle of maximum entropy~\\cite{ziebart2008maximum,ziebart2010modeling,bloem2014infinite}, which introduces probabilistic models to explain suboptimal behaviors as noise. More specifically, MaxEnt IRL models the paths in demonstrations using a Boltzmann distribution, where the energy is given by the unknown reward function $\\hat{r}^*$:\n\\begin{equation}\n\\label{eq:maxent-irl}\n    p_{\\hat{r}^*}(\\tau) = \\frac{1}{Z}\\exp{(\\hat{r}^*(\\tau))}~,\n\\end{equation}\nwhere $\\tau=\\{ s_0, a_0, \\cdots, s_T, a_T \\}$ is a trajectory of state-action pairs and $T$ is its length; $\\hat{r}^*(\\tau)=\\sum_{t}\\hat{r}^*(s_t,a_t)$ is the reward function, under which the expert demonstrations are optimal; $Z$ is the partition function.\\footnote{Note that \\eq{eq:maxent-irl} is formulated under the deterministic MDP setting. A general form for stochastic MDP is derived in \\cite{ziebart2008maximum,ziebart2010modeling} yet owns similar analysis: the probability of a trajectory is decomposed as the product of conditional probabilities of the states $s_t$, which can factor out of all likelihood ratios since they are not affected by the reward function.} Similar to other EBMs, the parameters of the reward function is optimized to maximize the likelihood of expert trajectories.\n\nUnder this model, ultimately we hope that our policy can generate any trajectories with the probability increases exponentially as the return gets higher, and we can obtain the desired optimal trajectories with the highest likelihood. Following previous work, we focus on the maximum casual entropy IRL \\cite{ziebart2008maximum,ziebart2010modeling}, which aims to maximize the entropy of the distribution over paths under the constraints of feature matching that can be regarded as the matching of the reward. Formally, maximum causal entropy IRL can be represented as the following optimization problem~\\cite{ho2016generative}:\n\\begin{equation}\\label{eq:irl-cas}\n\\begin{aligned}\n\\hat{r}^* &= \\argmax_{\\hat{r}} \\bbE_{{\\pi_E}}\\left [\\hat{r}(s,a) \\right ] - \\left ( \\max_{\\pi\\in\\Pi} \\bbE_{\\pi}\\left [\\hat{r}(s,a)\\right ] + H(\\pi) \\right ) ~,\n\\end{aligned}\n\\end{equation}\nwhere $H(\\pi) := \\mathbb{E}_\\pi [-\\log \\pi (a|s)]$ is the causal entropy~\\cite{bloem2014infinite} of the policy $\\pi$.\n\n\\subsection{EBIL is a Dual Problem of MaxEnt IRL}\n\nNow we first illustrate that EBIL (\\eq{eq:kl-il}) is a dual of the above MaxEnt IRL problem. The proof sketch is to show that EBIL is an instance of occupancy measure matching problem which has been proven to be a dual problem of MaxEnt IRL.\n\n\\begin{lemma}\\label{lm:dual}\nIRL is a dual of the following occupancy measure matching problem and the induced optimal policy is the primal optimum which matches the expert's occupancy measure $\\rho_{\\pi_E}$:\n\\begin{equation}\\label{eq:irl-dual}\n    \\min_{\\rho_\\pi\\in\\caD} \\overline{H}(\\rho_\\pi) \\text{ subject to } \\rho_\\pi(s,a) = \\rho_{\\pi_E}(s,a) \\text{ } \\forall s \\in \\caS, a \\in \\caA~.\n\\end{equation}\n\\end{lemma}\n\n\\begin{proposition}\\label{prop:ebil-dual}\n    The EBIL objective \\eq{eq:kl-il} is an instance of the occupancy measure matching problem \\eq{eq:irl-dual}.\n\\end{proposition}\n\nThe proof of \\lm{lm:dual} can be refered to the Section 3 of \\cite{ho2016generative}, and the proof of \\prop{prop:ebil-dual} is shown in \\ap{ap:ebil-dual}. Combining \\lm{lm:dual} and \\prop{prop:ebil-dual}, we have that EBIL is a dual problem of MaxEnt IRL. \n\n\\subsection{EBIL is More Efficient than IRL}\nNow we are going to illustrate why EBIL is a more efficient solution.\nRecall that the intuition of MaxEnt IRL is to regard the demonstrations as a Boltzmann distribution of the reward function, and then induce the optimal policy. Suppose that we have already recovered the optimal reward function $\\hat{r}^*$, then the optimal policy is induced by the following practical forward MaxEnt RL procedure:\n\\begin{equation}\\label{eq:rl-hr}\n    \\pi^* = \\argmax_{\\pi} \\bbE_\\pi\\left [\\hat{r}^*(s,a)\\right ]+ H(\\pi)~. \n\\end{equation}\nNow we further demonstrate that EBIL aims to seek the same policy, while through a simplified and more efficient training procedure.\n\n\\begin{proposition}\\label{prop:tau-kl}\n    Denote $\\tau$ and $\\tau_E$ are trajectories sampled by the agent and the expert respectively, and suppose we have the optimal reward function $\\hat{r}^*$, then the policy $\\pi^*$ induced by $\\hat{r}^*$ is the optimal solution to the following optimization problem: \n    \\begin{equation}\\label{eq:tau-kl}\n        \\begin{aligned}\n        \\min_\\pi \\kld(p(\\tau)\\|p(\\tau_E))~.\n        \\end{aligned}\n    \\end{equation}\n\\end{proposition}\n\n\\begin{proposition}\\label{prop:kl-kl}\n    The optimization problem \\eq{eq:tau-kl} is equivalent to the KL divergence IL objective \\eq{eq:kl-il} and the EBIL objective \\eq{eq:eb-il}.\n\\end{proposition}\n\nThe proof for these two propositions are in \\ap{ap:tau-kl} and \\ap{ap:kl-kl} separately. These two propositions together reveal the optimal policy obtained from EBIL is the same as the one from MaxEnt IRL when the optimal reward function is recovered. However, the latter one is indirect and much more computationally expensive. Primitively, as shown in \\eq{eq:irl-cas}, IRL methods are in fact aimed to recover the optimal reward function (served as an EBM) by maximum likelihood on the expert trajectories instead of directly learning the policy and cannot avoid estimating the non-trivial partition function $Z$, which is always hard, especially in high-dimensional spaces. The SoTA IRL method, AIRL\\cite{fu2017learning}, as we shown in \\se{sec:one-domain} and \\ap{ap:airl}, actually does not recover the energy. By contrast, EBIL is essentially a fixed-reward-based method that seeks to learn the policy guided by the pre-estimated energy of expert's occupancy measure, which shows much more efficiency and provides more flexible and general choices on training the expert's EBM.\n\nAs a supplementary statement, \\cite{finn2016connection} reveals the close relationship among Guided Cost Learning~\\cite{finn2016guided} (a sample-based algorithm of MaxEnt IRL), GAIL and EBMs. Besides, \\cite{ghasemipour2019divergence} also presents a unified perspective among previous IL algorithms and discuss in a divergence minimization view similar as ours shown in \\se{subsec:EBIL}. Therefore, all of these methods show connections among each other.\n\\section{Related Work}\n\nInstead of seeking to alternatively update the policy and the reward function as in IRL and GAIL, many recent works of IL aim to learn a fixed reward function directly from expert demonstrations and then apply a normal reinforcement learning procedure with that reward function. Although this idea can be found inherently in previous GMMIL work~\\cite{kim2018imitation} that utilizes the maximum mean discrepancy as the distance metric to guide training,\nit is recently proposed by Random Expert Distillation (RED) \\cite{wang2019red}, which employs the idea of Random Network Distillation\n\\cite{burda2018rnd} to estimate the support of expert policy, and compute the reward function by the loss of fitting a random neural network. \nIn addition, Disagreement-Regularized Imitation Learning \n\\cite{brantley2020disagreementregularized} constructs the reward function using the disagreement in their predictions of an ensemble of policies trained on the demonstration data, which is optimized together with a supervised behavioral cloning cost.\nInstead of using a learned reward function, the fixed reward of Soft-Q Imitation Learning\n\\cite{reddy2019softqil} applies constant rewards by setting positive rewards for the expert state-actions and zero rewards for other ones, which is optimized with the off-policy SQL algorithm~\\cite{haarnoja2018soft}.\n\nOur EBIL relies highly on EBMs, which have played an important role in a wide range of tasks including image modeling, trajectory modeling and continual online learning \\cite{Du2019generalization}. \nThanks to the appealing features, EBMs have been introduced into many RL literature, for instance, parameterized as value function~\\cite{sallans2004valueEBM}, employed in the actor-critic framework~\\cite{heess2012acEBMs}, applied to MaxEnt RL~\\cite{haarnoja2017reinforcement} and model-based RL regularization~\\cite{boney2019regularizing}. \nHowever, EBMs are always difficult to train due to the partition function \\cite{finn2016connection}. Nevertheless, recent works have tackled the problem of training large-scale EBMs on high-dimensional data, such as DEEN~\\cite{saremi2018deep} which is applied in our implementation. Except for DEEN, there still leaves plenty of choices for efficiently training EBMs \\cite{gutmann2012noise,Du2019generalization,nijkamp2019learn}. \n\\section{Experiments}\n\n\\subsection{Synthetic Task}\n\\label{sec:one-domain}\n\n\\begin{wrapfigure}{r}{0.4\\textwidth}\n\\vspace{-7pt}\n\\includegraphics[width=1\\linewidth]{figs\/KL-crop.pdf}\n\\vspace{-2pt}\n\\caption{The KL divergence between the agent trajectories and the expert during the learning procedure, which indicates that EBIL is much more stable than the other methods. The blue dash line represents the converged result of EBIL.}\n\\vspace{-14pt}\n\\label{fig:kl-div}\n\\end{wrapfigure}\n\nIn the synthetic task, we want to evaluate the qualitative performance of different IL methods by displaying the heat map of the learned reward and sampled trajectories. \nAs analyzed in Section~\\ref{sec:ebil} and \\ref{sec:discussion}, EBIL is capable of guiding the agent to recover the expert policy and correspondingly generate the high-quality trajectories. To demonstrate this point, we evaluate EBIL along with its counterparts (GAIL~\\cite{ho2016generative}, AIRL~\\cite{fu2017learning} and RED~\\cite{wang2019red}) on a synthetic environment where the agent tries to move in a one-dimensional space. \nSpecifically, the state space is $[ -0.5, 10.5 ]$ and the action space is $[-1, 1]$. The environment initializes the state at $0$, and we set the expert policy as static rule policies $\\pi_E = {\\mathcal{N}}(0.25, 0.06)$ when the state $s\\in [ -0.5, 5 )$, and $\\pi_E = {\\mathcal{N}}(0.75, 0.06)$ when $s\\in [ 5, 10.5 ]$. The sampled expert demonstration contains $40$ trajectories with up to $30$ timesteps in each one. \nFor all methods, we choose SAC \\cite{haarnoja2018soft} as the learning algorithm.\n\nWe plot the KL divergence between the agent's and the expert's trajectories during the training procedure in \\fig{fig:kl-div} and visualize the final estimated rewards with corresponding induced trajectories in \\fig{fig:heat_maps}.\nAs illustrated in \\fig{fig:ebil_heat} and \\fig{fig:kl-div}, the reward estimated by EBIL successfully captures the likelihood of the expert trajectories, and the induced policy quickly converge to the expert policy. By contrast, GAIL requires a noisy adversarial process to correct the policy. As a result, although GAIL achieves compatible final performance against EBIL~(\\fig{fig:gail_heat}), it suffers a slow, unstable training as shown in \\fig{fig:kl-div} and assigns arbitrary reward for some regions of the state-action space.\nIn addition, as suggested in \\fig{fig:airl_heat} and \\fig{fig:red_heat} respectively, under this simple one-dimensional domain, AIRL does not in fact recover the energy as meaningful rewards, and RED suffers from the diverged reward and fail to imitate the expert.\n\n\n\n\\begin{figure*}[!t]\n\\centering\n\\subfigure[Expert Trajectories]{\n\\begin{minipage}[b]{0.28\\linewidth}\n\\label{fig:expert_heat}\n\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/expert-crop.pdf}\n\\vspace{-0.8pt}\n\\end{minipage}\n}\n\\hspace{-10pt}\n\\subfigure[EBIL]{\n\\begin{minipage}[b]{0.155\\linewidth}\n\\label{fig:ebil_heat}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/ebil_reward_heat_40-crop.pdf}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/ebil_agent_heat_40_667-crop.pdf}\n\\end{minipage}\n}\n\\subfigure[GAIL]{\n\\begin{minipage}[b]{0.155\\linewidth}\n\\label{fig:gail_heat}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/gail_heat_40_19890-crop.pdf}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/gail_agent_heat_40_15000-crop.pdf}\n\\end{minipage}\n}\n\\subfigure[AIRL]{\n\\begin{minipage}[b]{0.155\\linewidth}\n\\label{fig:airl_heat}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/airl_heat_40_16000_1-crop.pdf}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/airl_agent_heat_40_16000-crop.pdf}\n\\end{minipage}\n}\n\\subfigure[RED]{\n\\begin{minipage}[b]{0.155\\linewidth}\n\\label{fig:red_heat}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/rnd_heat_40_499-crop.pdf}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/rnd_agent_heat_40_19999-crop.pdf}\n\\end{minipage}\n}\n\\vspace{-7pt}\n\\caption{Heat maps of the expert trajectories (leftmost), the (final) \\textit{estimated rewards} recovered by different methods (top) and the corresponding \\textit{induced policy} (bottom). The horizontal and the vertical axis denote the \\textit{state space} and the \\textit{action space} respectively. The red dotted line represents the position where the agent should change its policy. \nIt is worth noting that EBIL and RED both learn fixed reward functions, while GAIL and AIRL iteratively update the reward signals. We do not compare BC since it learns the policy via supervised learning without recovering any reward signals.}\n\\vspace{-20pt}\n\\label{fig:heat_maps}\n\\end{figure*}\n\n\n\n\\subsection{Mujoco Tasks}\n\nWe further test our method on five continuous control benchmarking Mujoco environments: Humanoid, Hopper, Walker2d and Swimmer and InvertedDoublePendulum. In this experiments, we still compare EBIL against GAIL, AIRL, GMMIL and RED, where we employ Trust Region Policy Optimization (TRPO)~\\cite{schulman2015trust} as the learning algorithm in the implementation for all evaluated methods. Expert agents are trained with OpenAI baselines version~\\cite{dhariwal2016openai} of Proximal Policy Optimization (PPO)~\\cite{schulman2017proximal}. Furthermore, we consider to sample 4 trajectories by the trained expert policy, as \\cite{ho2016generative,wang2019red} do.\nThe training curves along with more experiments are in \\ap{ap:exp}, showing the training stability of the algorithm.\n\nAs shown in \\tb{tab:mujoco}, EBIL achieves the best or comparable performance among all environments, indicating that the energy is able to become an excellent fixed reward function and is efficient to guide the agent to do imitation learning. It is worth noting that we do not apply BC initialization for all tasks. We surprisingly find that we are unsuccessful with AIRL on several environments even after extensive tuning, similar to the results in \\cite{liu2019state}.\n\n\\begin{table*}[t]\n\\vskip 0.15in\n\\caption{Comparison for different methods of the episodic true rewards on 5 continuous control benchmarks. The means and the standard deviations are evaluated over 50 runs.}\n\\vspace{-5pt}\n\\begin{center}\n\\begin{scriptsize}\n\\begin{tabular}{cccccc}\n\\toprule\n& Humanoid & Hopper & Walker2d & Swimmer & InvertedDoublePendulum\\\\\n\\midrule\nRandom & 100.38 $\\pm$ 28.25 & 14.21 $\\pm$ 11.20 & 0.18 $\\pm$ 4.35 & 0.89 $\\pm$ 10.96 & 49.57 $\\pm$ 16.88 \\\\\n\\hline\nBC & 178.74 $\\pm$ 55.88 & 28.04 $\\pm$ 2.73 & 312.04 $\\pm$ 83.83 & 5.93 $\\pm$ 16.77 & 138.81 $\\pm$ 39.99\\\\\nGAIL & 145.84 $\\pm$ 7.01  & 459.33 $\\pm$ 216.79  & 278.93 $\\pm$ 36.82  & 23.79 $\\pm$ 21.84  & 122.71 $\\pm$ 71.36 \\\\\nAIRL & 286.63 $\\pm$ 6.05 & 126.92 $\\pm$ 62.39  & 215.79 $\\pm$ 23.04  & -13.44 $\\pm$ 2.69 & 76.78 $\\pm$ 19.63 \\\\\nGMMIL & 416.83 $\\pm$ 59.46 & 1000.87 $\\pm$ 0.87 & 1585.91 $\\pm$ 575.72 & -0.73 $\\pm$ 3.28 & 4244.63 $\\pm$ 3228.14\\\\\nRED & 140.23 $\\pm$ 19.10 & 641.08 $\\pm$ 2.24 & 641.13 $\\pm$ 2.75 & -3.55 $\\pm$ 5.05 & 6400.19 $\\pm$ 4302.03 \\\\\n\\textbf{EBIL (Ours)} & \\textbf{472.22 $\\pm$ 107.72} & \\textbf{1040.99 $\\pm$ 0.53} & \\textbf{2334.55 $\\pm$ 633.91} & \\textbf{58.09 $\\pm$ 2.03} & \\textbf{8988.37$\\pm$ 1812.76}\\\\\n\\hline\nExpert (PPO) & 1515.36 $\\pm$ 683.59 & 1407.36 $\\pm$ 176.91 & 2637.27 $\\pm$ 1757.72 &  122.09  $\\pm$ 2.60 &  6129.10 $\\pm$ 3491.47 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:mujoco}\n\\end{scriptsize}\n\\end{center}\n\\vspace{-15pt}\n\\end{table*}\n\\section{Conclusion}\n\nIn this paper, we propose Energy-Based Imitation Learning (EBIL), which shows that it is feasible to compute a fixed reward function via directly estimating the expert's energy to help agents learn from the demonstrations. We further theoretically discuss the connections of our method with Maximum Entropy Inverse Reinforcement Learning (MaxEnt IRL) and reveal that EBIL is a dual problem of MaxEnt IRL which provides a simplified and efficient solution. We empirically show the comparable or better performance of EBIL against SoTA Imitation Learning (IL) algorithms in multiple tasks. Future work can focus on different energy estimation methods for expert demonstrations and exploring more properties of EBM in IL.\n\n\\clearpage\n\\section{Broader Impact}\n\nFor potential positive impacts, EBIL simplifies the learning procedure and increases the efficiency of IL, which can be applied into practical decision-making problems where agents are required to imitate demonstrated behaviors such as robotics and autonomous driving in the future work. However, negative consequences also exist since advances in automation led by IL may bring about workers who are engaged in repetitive tasks being displaced by robots. After all, teaching machines with amounts of expert demonstrations must be much cheaper than hiring hundreds of teachers and skillful employees. \n\\section{Algorithm}\n\\label{ap:algo}\n\\begin{algorithm}[!h]\n    \\caption{Energy-Based Imitation Learning}\n    \\label{alg:EBIL}\n    \\begin{algorithmic}[1]\n       \\STATE {\\bfseries Input:} Expert demonstration data $\\tau_E=\\{ (s_i, a_i) \\}_{i=1}^{N}$,  parameterized energy-based model $E_{\\phi}$, parameterized policy $\\pi_{\\theta}$;\n       \n       \\FOR{$k = 0, 1, 2, \\dotsc$}\n       \\STATE Optimize $\\phi$ with the objective in \\eq{eq:deen}.\n       \\ENDFOR\n       \n       Compute the surrogate reward function $\\hat{r}$ via \\eq{eq:reward}.\n       \n       \\FOR{$k = 0, 1, 2, \\dotsc$}\n       \\STATE Update $\\theta$ with a normal RL procedure using the surrogate reward function $\\hat{r}$.\n       \\ENDFOR\n       \n     \\RETURN {$\\pi$}\n    \\end{algorithmic}\n\\end{algorithm}\n\n\\section{Proofs}\n\n\\subsection{Proof of \\protect\\prop{prop:eb-il}}\n\\label{ap:eb-il}\nBefore showing the equivalence between the reverse KL divergence objective and the EBIL objective, we first present the following lemma.\n\\begin{lemma}[Lemma 3 of \\cite{ho2016generative}]\n   $\\overline{H}$ is strictly concave, and for all $\\pi \\in \\Pi$ and $\\rho \\in \\caD$, we have $H(\\pi) = \\overline{H}(\\rho_\\pi)$ and $\\overline{H}(\\rho)=H(\\pi_\\rho)$~,\nwhere $\\overline{H}\\left (\\rho \\right )=-\\sum_{s,a}\\rho_\\pi\\log{\\rho_\\pi(s,a)\/\\sum_{a'}\\rho_\\pi(s,a')}$ is the entropy of the occupancy measure.\n\\end{lemma}\n\n\\begin{proof}[Proof of \\protect\\prop{prop:eb-il}]\n\nTake \\eq{eq:ebm} into \\eq{eq:kl-il} for both policy ${\\pi_E}$, one can obtain that: \n\\begin{equation}\\label{eq:kl-induce}\n    \\begin{aligned}\n        \\kld ( \\rho_\\pi \\| \\rho_{{\\pi_E}}) &= \\sum_{s,a} \\rho_\\pi(s,a) \\log \\frac{\\rho_\\pi(s,a)}{\\rho_{\\pi_E}(s,a)}\\\\\n        &= \\sum_{s,a}\\rho_\\pi\\left( \\log{\\rho_\\pi(s,a)} - \\log{\\frac{e^{-E_{\\pi_E}(s,a)}}{(1-\\gamma)Z'}} \\right )\\\\\n        &= \\sum_{s,a}\\rho_\\pi\\left(E_{\\pi_E}(s,a)+\\log{\\rho_\\pi(s,a)} + \\log{(1-\\gamma)Z'}\\right )\\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ]+\\sum_{s,a}\\rho_\\pi\\log{\\rho_\\pi(s,a)} + \\text{const}\\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ]+\\sum_{s,a}\\rho_\\pi\\log{\\rho_\\pi(s,a)} -\\log{\\sum_{s,a'}\\rho_\\pi(s,a')} + \\log{\\sum_{s,a'}\\rho_\\pi(s,a')} + \\text{const}\\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ]+\\sum_{s,a}\\rho_\\pi\\log{\\left [ \\rho_\\pi(s,a)\/\\sum_{a'}\\rho_\\pi(s,a')\\right ]}+ \\text{const}\\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ] - \\overline{H}\\left (\\rho_\\pi \\right ) + \\text{const}\n        \\\\\n        &= \\bbE_\\pi \\left[E_{\\pi_E}(s,a)\\right ] - H(\\pi) + \\text{const}\n        ~,\n    \\end{aligned}\n\\end{equation}\nwhere $E_{\\pi_E}$ is the EBM of policy ${\\pi_E}$ and $Z'$ is its partition function. Therefore \\eq{eq:kl-il} in the end leads to the objective function of EBIL \\eq{eq:eb-il}:\n\\begin{equation}\\label{eq:kl-eq-ebil}\n    \\begin{aligned}\n    \\argmin_{\\pi} \\kld ( \\rho_\\pi \\| \\rho_{{\\pi_E}}) = \\argmax_{\\pi} \\bbE_\\pi \\left[-E_{\\pi_E}(s,a)\\right ] + H(\\pi)\n    \\end{aligned}\n\\end{equation}\n\\end{proof}\n\n\n\\subsection{Proof of \\protect\\prop{prop:ebil-dual}}\n\\label{ap:ebil-dual}\n\n\\begin{proof}[Proof of \\protect\\prop{prop:ebil-dual}]\n    Similarly as in \\cite{ho2016generative}, we would like to relax \\eq{eq:irl-dual} into the following form with the motivation from \\eq{eq:rl-irl}:\n    \\begin{equation}\n        \\min_{\\pi} d_\\psi(\\rho_\\pi,\\rho_{\\pi_E})- H(\\pi)~,\n    \\end{equation}\n    where we modify the IRL regularizer $\\psi$ so that $d_\\psi(\\rho_\\pi,\\rho_{\\pi_E}) \\triangleq \\psi^*(\\rho_\\pi - \\rho_{\\pi_E})$ is a smooth distance metric that penalizes violations in the difference between the occupancy measures.\n    By choosing $\\psi= \\bbE_{\\pi_E} [-1-\\log(r(s, a))+r(s, a)]$, we obtain $d_\\psi(\\rho_\\pi,\\rho_{\\pi_E})=D_{\\text{KL}}(\\rho_\\pi\\|\\rho_{\\pi_E})$\\footnote{Full derivations can be found in Appendix D of \\protect\\cite{ghasemipour2019divergence} and we replace $c(s,a)$ with $-r(s,a)$.}. Thus we have:\n    \\begin{equation}\\label{eq:kl-h}\n        \\min_{\\pi} D_{\\text{KL}}(\\rho_\\pi\\|\\rho_{\\pi_E})- H(\\pi)~.\n    \\end{equation}\n    Refer to \\eq{eq:kl-induce}, we have:\n    \\begin{equation}\n        D_{\\text{KL}}(\\rho_\\pi\\|\\rho_{\\pi_E}) = \\bbE_\\pi\\left[E_{\\pi_E}(s,a)\\right ] - H(\\pi) + \\text{const}~.\n    \\end{equation}\n    Thus, we can rewrite \\eq{eq:kl-h} as the following optimization problem:\n    \\begin{equation}\\label{eq:eb-il-2}\n    \\pi^* = \\argmax_{\\pi} \\bbE_\\pi \\left[-E_{\\pi_E}(s,a)\\right ] + 2H(\\pi)~,\n    \\end{equation}\n    which leads to the EBIL objective \\eq{eq:eb-il} with the temperature hyperparameter $\\alpha=2$.\n    This indicates that EBIL is a dual problem of the MaxEnt IRL problem.\n\\end{proof}\n\n\\subsection{Proof of \\protect\\prop{prop:tau-kl}}\n\\label{ap:tau-kl}\n\n\\begin{proof}[Proof of \\protect\\prop{prop:tau-kl}]\nSuppose we have recovered the optimal reward function $\\hat{r}$, then we can derive the objective of the KL divergence between the two trajectories into the forward MaxEnt RL procedure.\n\nWith chain rule, the induced trajectory distribution $p(\\tau)$ is given by\n\\begin{equation}\n     p(\\tau) = p(s_0)\\prod_{t=0}^{T}P(s_{t+1}|s_t,a_t)\\pi(a_t|s_t)~.\n\\end{equation}\n\nSuppose the desired expert trajectory distribution $p(\\tau_E)$ is given by\n\\begin{equation}\n\\begin{aligned}\np(\\tau) &\\propto p(s_0)\\prod_{t=0}^{T}P(s_{t+1}|s_t,a_t) \\exp(\\hat{r}^*(\\tau))\\\\\n&= p(s_0)\\prod_{t=0}^{T}P(s_{t+1}|s_t,a_t) \\exp(\\sum_{t=0}^{T}\\hat{r}^*(s_t, a_t))~,\n\\end{aligned}\n\\end{equation}\nnow we will show that the following optimization problem is equivalent to a forward MaxEnt RL procedure given the optimal reward $\\hat{r}^*$:\n\\begin{equation}\\label{eq:tau-kl-induce-1}\n\\begin{aligned}\n    \\kld(p(\\tau)\\|p(\\tau_E))&= \\sum_{\\tau\\sim\\pi} p(\\tau) \\log \\frac{p(\\tau)}{p(\\tau_E)}\\\\\n        &= \\sum_{\\tau\\sim\\pi}p(\\tau)\\left( \\log{p(\\tau)} - \\log{p(\\tau_E)} \\right )\\\\\n        &= \\bbE_{\\tau\\sim\\pi} \\left[ \\log p(s_0) + \\sum_{t=0}^T \\left (\\log P(s_{t+1}|s_t,a_t) + \\hat{r}^*(s_t, a_t)\\right ) - \\right. \\\\\n    &~~~~~\\left. \\log p(s_0) - \\sum_{t=0}^T \\left (\\log P(s_{t+1}|s_t,a_t) + \\log \\pi(a_t|s_t)\\right ) \\right] + \\text{const}\\\\\n    &= \\bbE_{\\tau \\sim p(\\tau)} \\left[ \\sum_{t=0}^T \\hat{r}^*(s_t, a_t) - \\pi(a_t|s_t)) \\right] + \\text{const} \\\\\n    &= \\sum_{t=0}^T \\bbE_{(s_t, a_t) \\sim \\rho(s_t, a_t)} [\\hat{r}^*(s_t,a_t) - \\log \\pi(a_t|s_t)] + \\text{const}~.\n\\end{aligned}\n\\end{equation}\n\nWithout loss of generality, we approximate the finite term $\\sum_{t=0}^T \\bbE_{(s_t, a_t)}$ with an infinite term $\\bbE_{\\pi}$ by the definition, and then we have\n\\begin{equation}\\label{eq:tau-kl-induce-2}\n\\begin{aligned}\n    \\kld(p(\\tau)\\|p(\\tau_E))\n    &\\approx \\bbE_{(s, a) \\sim \\rho(s, a)} [\\hat{r}^*(s,a) - \\log \\pi(a_t|s_t)] + \\text{const}\\\\\n    &= \\bbE_{\\pi} [\\hat{r}^*(s,a) - \\log \\pi(a|s)] + \\text{const}\\\\\n    &= \\bbE_{\\pi} [\\hat{r}^*(s,a)] - \\bbE_{\\pi}[\\log \\pi(a|s)] + \\text{const}\\\\\n    &= \\bbE_{\\pi} [\\hat{r}^*(s,a)] - H(\\pi) + \\text{const}~.\n\\end{aligned}\n\\end{equation}\n\nThus the objective \\eq{eq:tau-kl} is equivalent to the following optimization problem:\n\\begin{equation}\n    \\max_{\\pi} \\bbE_\\pi\\left [\\hat{r}^*(s,a)\\right ]+ H(\\pi)~, \n\\end{equation}\nwhich is exactly the objective of a forward MaxEnt RL procedure (\\eq{eq:rl-hr}). This indicates that when MaxEnt IRL recovers the optimal reward function, a forward RL learning which leads to the optimal (expert) policy is equivalent to minimize the reverse KL divergence between the trajectories sampled by the agent and by the expert.\n\\end{proof}\n\n\n\\subsection{Proof of \\protect\\prop{prop:kl-kl}}\n\\label{ap:kl-kl}\n\\begin{proof}[Proof of \\protect\\prop{prop:kl-kl}]\n    From the deviation \\eq{eq:tau-kl-induce-2}, we know that the optimization problem \\eq{eq:tau-kl} is equivalent to a forward MaxEnt RL problem \\eq{eq:rl-hr}. Let $r^*(s,a)=-E(s,a)$, and we will exactly get the EBIL objective \\eq{eq:eb-il}. \n    Note that the reverse KL divergence IL objective \\eq{eq:kl-il} can also be derived into the EBIL objective \\eq{eq:eb-il} followed \\eq{eq:kl-induce}. Thus \\eq{eq:tau-kl} is equivalent to both the reverse KL divergence IL objective \\eq{eq:kl-il} and the EBIL objective \\eq{eq:eb-il}.\n\\end{proof}\n\n\\section{Experiments}\n\\label{ap:exp}\n\\subsection{Hyperparameters}\n\nWe show the hyperparameters for both DEEN training and policy training on different tasks in \\tb{tab:hyperparameters}. Specifically, we use MLPs as the networks for training DEEN and the policy network.\n\n\\begin{table*}[htbp]\n\\caption{Important hyperparameters used in our experiments}\n\\label{tab:hyperparameters}\n\\centering\n\\resizebox{0.7\\textwidth}{!}{\n\\begin{tabular}{llcccccc}\n\\toprule\n& Hyperparameter & One-D. & Human. & Hop. & Walk. & Swim. & Invert. \\\\\n\\midrule\n\\multirow{4}{*}{Policy} & Hidden layers & 3 & 3 & 3 & 3 & 3 & 3 \\\\\n& Hidden Size & 200 & 200 & 200 & 200 & 200 & 200 \\\\\n& Iterations & 6000 & 6000 & 6000 & 6000 & 6000 & 6000 \\\\\n& Batch Size & 32 & 32 & 32 & 32 & 32 & 32 \\\\\n\\midrule\n\\multirow{6}{*}{DEEN} & Hidden layers & 3 & 3 & 3 & 4 & 3 & 3 \\\\\n& Hidden size & 200 & 200 & 200 & 200 & 200 & 200 \\\\\n& Epochs & 3000 & 3000 & 6000 & 500 & 1900  & 500 \\\\\n& Batch Size & 32 & 32 & 32 & 32 & 32 & 32 \\\\\n& Noise Scale $\\sigma$ & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 \\\\\n& Reward Scale $\\alpha$ & 1 & 1 & 5 & 1 & 1 & 1000 \\\\\n\\bottomrule\n\\end{tabular}}\n\\end{table*}\n\n\\subsection{Synthetic Task Training Procedure}\n\nWe demonstrate more training slices of the synthetic task in this section. \n\nWe analyze the learned behaviors during the training procedure of the synthetic task, as illustrated by visitation heatmaps in \\fig{fig:train-heat}. For each method, we choose to show four training stages from different training iterations. These figures provide more evidence that although GAIL can finally achieve good results, EBIL provides fast and stable training. By contrast, GMMIL and RED fail to achieve effective results during the whole training time.\\footnote{For better understanding how these methods learn reward signals, we also visualize the changes of estimated rewards during the training procedures. Videos can be seen at \\url{https:\/\/www.dropbox.com\/s\/0mrsoqyu040crdo\/video.zip?dl=0}.}\n\n\\begin{figure*}[htb]\n\\centering\n\\includegraphics[width=0.90\\linewidth]{figs\/policy-iter.pdf}\n\n\\caption{The induced policy during policy training procedures. In each figure the horizontal axis denotes the \\textit{state space}, and the vertical axis represents the \\textit{action space}. Methods from top to bottom are separately EBIL, GAIL, AIRL and RED and each one contains four training stages shown in one line. The color bar is the same as \\fig{fig:heat_maps}. The brighter the yellow color, the higher the visitation frequency.}\n\\vspace{-15pt}\n\\label{fig:train-heat}\n\\end{figure*}\n\n\\subsection{Training Curves}\n\\label{ap:curves-mujoco}\n\nWe plot the episodes averaged return during the training procedure in \\fig{fig:curves-mujoco}, where EBIL shows effective guidance to help agent learn good policies while owns stability on all environments in comparison to the other methods. In our experiments, we find that the training procedure of GAIL suffers from instability.\n\n\\begin{figure*}[h!]\n\\centering\n\\includegraphics[width=1\\linewidth]{.\/figs\/curves-mujoco.pdf}\n\n\\vspace{-3pt}\n\\caption{Training curves of GAIL, GMMIL, RED and EBIL on different continuous control benchmarking tasks, where the solid curves depict the mean and the shaded areas indicate the standard deviation. Each iterations contains 1024 timesteps.}\n\\vspace{-15pt}\n\\label{fig:curves-mujoco}\n\\end{figure*}\n\n\n\\subsection{Energy Evaluation}\n\\label{curves-energy}\n\nSince the loss function of DEEN cannot be directly used as an indicator to evaluate the quality of the learned energy network, we propose to evaluate the averaged energy value for expert trajectories and the random trajectories on different tasks. As shown in \\fig{fig:curves-energy}, DEEN finally converges in all experiments by differentiating the expert data. It is worth noting that in our experiments, we find that a well-trained energy network may be hard for agents to learn the expert policies on some environments. \nWe regard it as the ``sparse reward signals'' problem, as discussed in \\se{sec:one-domain}. By contrast, sometimes a ``half-trained'' model may provide smoother rewards, and can help the agent to learn more efficiently. Similar phenomenon also occurs when training the discriminator in GAN.\n\nWe will further analyze the training performance with energy models of different epochs in ablation study \\se{sec:abl-study}.\n\n\\begin{figure*}[h!]\n\n\\centering\n\\includegraphics[width=1\\linewidth]{.\/figs\/curves-energy.pdf}\n\n\\vspace{-33pt}\n\\caption{Energy evaluation curves on different mujoco tasks, where the red line represents for the average energy estimation on expert data and the blue is for random trajectories, which contain 100 trajectories separately. Note that lower energy values correspond to higher rewards. The min value is -1, and the max is 1 since we use \\textit{tanh} for the last layer of the DEEN network.}\n\\vspace{-15pt}\n\\label{fig:curves-energy}\n\\end{figure*}\n\n\n\\subsection{Ablation Study}\n\\label{sec:abl-study}\n\nTo further understand what the better energy model for learning a good policy is, we conduct ablation study on energy models trained from different epochs. The results are illustrated in \\fig{fig:ablation-energy}, which verify our intuition that a ``half-trained'' model can provide smoother rewards that solve the \"sparse reward`` problem, which is better for imitating the expert policy.\n\n\\begin{figure*}[h!]\n\\centering\n\\includegraphics[width=0.45\\linewidth]{.\/figs\/ablation-energy-hopper}\n\\includegraphics[width=0.45\\linewidth]{.\/figs\/ablation-energy-walker}\n\\vspace{-4pt}\n\\caption{The average episode rewards evaluated on Hopper-v2 and Walker2d-v2 by agents that are learned with energy models from different training epochs.}\n\\vspace{-15pt}\n\\label{fig:ablation-energy}\n\\end{figure*}\n\n\\section{Further Discussions}\n\n\\subsection{Surrogate Reward Functions}\n\nAs discussed in \\cite{kostrikov2018discriminator}, the reward function is highly related to the property of the task. Positive rewards may achieve better performance in the ``surviving'' style environment, and negative ones may take advantage in the ``per-step-penalty'' style environment. The different choices are common in those imitation learning works based on GAIL, which can use either $\\log(D)$ or $-\\log(1-D)$, where\n$D\\in [0,1]$ is the output of the discriminator, determined by the final ``\\textit{sigmoid}'' layer. In our work, we choose ``\\textit{tanh}'' as the final layer of the energy network, which in result leads the energy into a range of $[-1,1]$. In order to adapt to different environments while holding the good property of the energy, we can apply a monotonically increasing linear function $h$ as the surrogate reward function, which makes translation or scaling transformation on the energy outputs. It appears that in all of our tasks, the original energy signal does not show much ascendancy, and thus we choose different $h$ for these tasks.\n\nIn the one-dimension domain experiment, we choose to use the following surrogate reward function:\n\\begin{equation}\n    \\hat{r}(s,a)=h(x)=x+1~,\n\\end{equation}\nwhere $\\hat{r} \\in [0, 2]$ and $x=-E(s,a)$ is the energy function. Thus, the experts' state-action pair will get close-to-zero rewards at each step.\n\nIn mujoco tasks, we choose the surrogate reward function as:\n\\begin{equation}\n    \\hat{r}(s,a)=h(x)=(x+1)\/2~,\n\\end{equation}\nwhere $x=-E(s,a)$ is the energy function. Note that we construct this reward function to make a normalized reward $\\hat{r} \\in [0, 1]$ so that the non-expert's state-action pairs will gain near-zero rewards while the experts' get close-to-one rewards at each step regarding the output range of the energy is $[-1,1]$. In our experiments, similar rewards as the one-dimensional synthetic environment can also work well.\n\n\\subsection{AIRL Does Not Recover the Energy}\n\\label{ap:airl}\n\nAdversarial Inverse Reinforcement Learning (AIRL)\\cite{fu2017learning}, is a SoTA IRL method that apply an adversarial architecture similar as GAIL to solve the IRL problem. Formally, AIRL constructs the discriminator as \n\\begin{equation}\\label{eq:airl-dis}\nD(s,a) = \\frac{\\exp(f(s,a))}{\\exp(f(s,a)) + \\pi(a|s)}~.\n\\end{equation}\nThis is motivated by the former GCL-GAN work~\\cite{finn2016connection}, which proposes that one can apply GAN to train GCL that formulate the discriminator as\n\\begin{equation}\\label{eq:airl-dis}\nD(\\tau) = \\frac{\\frac{1}{Z}\\exp(c(\\tau))}{\\frac{1}{Z}\\exp(c(\\tau)) + \\pi(\\tau)}~,\n\\end{equation}\nwhere $\\tau$ denotes the trajectory. AIRL uses a surrogate reward\n\\begin{equation}\\label{eq:airl-reward}\n\\begin{aligned}\nr(s,a) &= \\log D(s,a) - \\log(1-D(s,a))\\\\\n&= f(s,a)-\\log{\\pi(a|s)}~,\n\\end{aligned}\n\\end{equation}\nwhich can be seen as an entropy-regularized reward function.\n\nHowever, the difference between \\eq{eq:airl-dis} and \\eq{eq:airl-reward} indicates that AIRL does not actually recover the expert's energy since they omit the partition function $Z$ which is important for estimating the energy. Also, the learning signal that drives the agent to learn a good policy is not a pure reward term but contains an entropy term itself. We visualize the different reward choice ($f(s,a)$ or $f(s,a)-\\log{\\pi(a|s)}$) in \\fig{fig:airlreward} as comparison, which verify our intuition that AIRL in fact does not recover the expert's energy as EBIL does.\n\n\\begin{figure*}[!t]\n\\centering\n\\subfigure[Reward as $f(s,a)-\\log{\\pi(a|s)}$]{\n\\begin{minipage}[b]{0.33\\linewidth}\n\\label{fig:logreward}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/airl_heat_40_16000_1-crop.pdf}\n\\end{minipage}\n}\n\\subfigure[Reward as $f(s,a)$]{\n\\begin{minipage}[b]{0.393\\linewidth}\n\\label{fig:freward}\n\\includegraphics[width=1\\linewidth]{figs\/heat-crop\/airl_heat_40_16000_0_bar-crop.pdf}\n\\end{minipage}\n}\n\\vspace{-7pt}\n\\caption{Heat maps of the different estimated rewards recovered by AIRL.}\n\\label{fig:airlreward}\n\\end{figure*}\n\n\\subsection{Discussions with MaxEnt RL Methods}\n\\label{ap:ebil-sac}\n\nSoft-Q Learning (SQL)~\\cite{haarnoja2017reinforcement} and Soft Actor-Critic (SAC)~\\cite{haarnoja2018soft} are two main approaches of MaxEnt RL, particularly, they propose to use a general energy-based form policy as:\n\\begin{equation}\\label{eq:softq}\n    \\pi(a_t|s_t) \\propto \\exp{(-E(s_t, a_t))}~.\n\\end{equation}\nTo connect the policy with soft versions of value functions and Q functions, they set the energy model $E(s_t,a_t) = -\\frac{1}{\\alpha}Q_{\\text{soft}}(s_t,a_t)$ where $\\alpha$ is the temperature parameter, such that the policy can be represented with the Q function which holds the highest probability at the action with the highest Q value, which essentially provides a soft version of the greedy policy. Thus, one can choose to optimize the soft Q function to obtain the optimal policy by minimizing the expected KL-divergence:\n\n\\begin{equation}\\label{eq:softac}\n    J(\\pi) = \\bbE_{s\\sim \\rho^s_{\\caD}}\\left[\\kld\\left( \\pi(\\cdot|s) \\big \\| \\frac{\\exp{(Q(s,\\cdot))}}{Z(s)} \\right) \\right ]~,\n\\end{equation}\nwhere $\\rho^s_{\\caD}$ is the distribution of previously sampled states and actions, or a replay buffer. Therefore, the second term in the KL-divergence in fact can be regarded as the target or the reference for the policy.\n\nConsider to use the KL-divergence as the distance metric in the general objective of IL shown in \\eq{eq:il}, then we get:\n\\begin{equation}\n\\begin{aligned}\n    \\pi^* &= \\argmin_\\pi \\mathbb{E}_{\\pi} \\left [\\kld \\left( \\pi(\\cdot|s) \\big \\| {\\pi_E}(\\cdot|s)  \\right) \\right ]~.\n\\end{aligned}\n\\end{equation}\nIf we choose to model the expert policy using the energy form of \\eq{eq:softq} then we get:\n\\begin{equation}\n\\begin{aligned}\\label{eq:softil}\n    \\pi^* &= \\argmin_\\pi \\mathbb{E}_{\\pi}\\left [\\kld \\left( \\pi(\\cdot|s) \\big \\| \\frac{\\exp{(-E_{\\pi_E}(s,a)})}{Z} \\right) \\right ]~.\n\\end{aligned}\n\\end{equation}\n\n\\begin{proposition}\n\\label{prop:ebil-sac}\n    The IL objective shown in \\eq{eq:softil} is equivalent to the EBIL objective shown in \\eq{eq:eb-il}.\n\\end{proposition}\n\\begin{proof}\n    Since \\eq{eq:eb-il} is equivalent to \\eq{eq:kl-il}, it holds the optimal solution such that $\\pi^*={\\pi_E}$ according to \\prop{prop:kl-il}. Also, it is easy to see that \\eq{eq:softil} has the same optimal solution such that $\\pi^*={\\pi_E}$.\n\\end{proof}\nThus, \\prop{prop:ebil-sac} reveals the relation between MaxEnt RL and EBIL. Specifically, EBIL employs the energy model learned from expert demonstrations as the target policy. The difference is that MaxEnt RL methods use the Q function to play the role of the energy function, construct it as the target policy, and iteratively update the Q function and the policy, while EBIL directly utilizes the energy function to model the expert occupancy measure and constructs the target policy. \n\nAs a result, it makes sense to directly optimize the policy by taking the energy model as the target policy instead of the reward function, which leads to the optimal solution as:\n\n\\begin{equation}\n    \\begin{aligned}\n        \\pi^*(a|s)&= \\frac{\\rho_{{\\pi_E}}(s,a)}{\\sum_{a'}\\rho_{{\\pi_E}}(s,a')}\\\\\n        &=\\frac{\\frac{1}{Z}\\exp(-E_{{\\pi_E}}(s,a))}{\\frac{1}{Z}\\sum_{a'}\\exp{(-E_{{\\pi_E}}(s,a'))}}\\\\\n        &=\\frac{\\exp(-E(s,a))}{\\sum_{a'}\\exp{(-E(s,a'))}}~.\n    \\end{aligned}\n\\end{equation}\nTherefore, the optimal solution can also be obtained through estimating the energy function and summing it over the action space, which may be intractable for high-dimensional or continuous action space. Nevertheless, this can be solved in simple scenarios.","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section[Preliminaries]{Preliminaries}\n\nIn this section we discuss a local  characterization of conformally flat hypersurfaces $f\\colon\\,M^3\\to\\mathbb{Q}^{4}(c)$ with three distinct principal curvatures \n and present  the examples of minimal conformally flat hypersurfaces in $\\mathbb{Q}^{4}(c)$ with three distinct principal curvatures given by generalized cones over Clifford tori. \n\n\\subsection{Characterization of conformally flat hypersurfaces}\n\n First we  recall the notion of holonomic hypersurfaces.  One says that a  hypersurface $f\\colon M^{n} \\to \\mathbb{Q}^{n+1}(c)$  is   \\emph{holonomic} if $M^n$ carries  global orthogonal coordinates  $(u_1,\\ldots, u_{n})$  such that the coordinate vector fields \n$\\partial_j=\\dfrac{\\partial}{\\partial u_j}$ diagonalize the second fundamental form $I\\!I$ of $f$. \n\nSet $v_j=\\|\\partial_j\\|$\n and define $V_{j} \\in C^{\\infty}(M)$, $1\\leq j\\leq n$, by \n $I\\!I(\\partial_j, \\partial_j)=V_jv_j$, $1\\leq j\\leq n$. \nThen the first and second fundamental forms of $f$ are\n\\begin{equation} \\label{fundforms}\nI=\\sum_{i=1}^nv_i^2du_i^2\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,I\\!I=\\sum_{i=1}^nV_iv_idu_i^2.\n\\end{equation} \nDenote $v=(v_1,\\ldots, v_n)$ and  $V=(V_{1},\\ldots, V_n)$. We call  $(v,V)$ the pair associated to $f$. \nThe next result is well known.\n\n\\begin{proposition}\\label{fund}\n The triple $(v,h,V)$, where \n $h_{ij}=\\frac{1}{v_i}\\frac{\\partial v_j}{\\partial u_i},$\n satisfies the  system of PDE's\n \n  \\begin{eqnarray}\\label{sistema-hol}\n \\left\\{\\begin{array}{l}\n  (i) \\ \\dfrac{\\partial v_i}{\\partial u_j}=h_{ji}v_j,\\,\\,\\,\\,\\,\\,\\,\\,\\,(ii) \\ \\dfrac{\\partial h_{ik}}{\\partial u_j}=h_{ij}h_{jk},\\vspace{1ex}\\\\\n  (iii) \\ \\dfrac{\\partial h_{ij}}{\\partial u_i} + \\dfrac{\\partial h_{ji}}{\\partial u_j} + \\sum_{k\\neq i,j} h_{ki}h_{kj} + \n   V_{i}V_{j}+cv_iv_j=0,\\vspace{1ex}\\\\\n  (iv) \\ \\dfrac{\\partial V_{i}}{\\partial u_j}=h_{ji}V_{j},\\,\\,\\,\\,1\\leq i \\neq j \\neq k \\neq i\\leq n.\n  \\end{array}\\right.\n \\end{eqnarray}\nConversely, if $(v,h,V)$ is a solution of $(\\ref{sistema-hol})$ on a simply connected open subset   $U \\subset {\\mathbb R}^{n}$, with  $v_i> 0$\neverywhere  for all $1\\leq i\\leq n$,\nthen there exists a holonomic hypersurface $f\\colon U \\to  \\mathbb{Q}^{n+1}(c)$  whose first and second fundamental forms are given by  $(\\ref{fundforms}).$\n\\end{proposition}\n\nThe following characterization of conformally flat hypersurfaces $f\\colon\\,M^3\\to\\mathbb{Q}^{4}(c)$ with three distinct principal curvatures  was given in \\cite{ct}, improving a theorem due to Hertrich-Jeromin \\cite{h-j}. \n\n\\begin{theorem}\\label{main3} Let $f\\colon\\,M^3\\to\\mathbb{Q}^{4}(c)$ \nbe a  holonomic hypersurface whose associated pair $(v, V)$ satisfies \n\\begin{equation} \\label{holo.flat}\\sum_{i=1}^3\\delta_iv_i^2=0, \\,\\,\\,\\,\\,\\,\\sum_{i=1}^3\\delta_iv_iV_i=0\\,\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,\\sum_{i=1}^3\\delta_iV_i^2=1, \n\\end{equation} \nwhere $(\\delta_1, \\delta_2, \\delta_3)= (1,-1, 1)$. Then $M^3$ is conformally flat and $f$ has three distinct principal curvatures. \n\nConversely, any conformally flat hypersurface $f\\colon\\,M^3\\to\\mathbb{Q}^{4}(c)$ with three distinct \nprincipal curvatures is locally a \nholonomic hypersurface whose associated pair $(v, V)$ satisfies $(\\ref{holo.flat}).$\n\\end{theorem}\n\n\n\nIt will be convenient to use the following equivalent version of Theorem~\\ref{main3}.\n\n\n\\begin{corollary}\\label{le:asspair}\nLet $f\\colon M^3\\to \\mathbb{Q}^4(c)$ be a holonomic hypersurface whose associated pair $(v,V)$ satisfies \n\\begin{equation}\\label{holo.flat.med.2}\n\\begin{array}{lcl}\nv_2^2=v_1^2+v_3^2,  & \\quad &\n\\displaystyle{V_2=-\\frac{1}{3}\\Big(\\frac{v_1}{v_3}-\\frac{v_3}{v_1}\\Big) + \\frac{v_2}{3}H}, \\vspace{.2cm} \\\\\n\\displaystyle{V_1=-\\frac{1}{3}\\Big(\\frac{v_2}{v_3}+\\frac{v_3}{v_2}\\Big) + \\frac{v_1}{3}H}, & \\quad &\n\\displaystyle{V_3=\\frac{1}{3}\\Big(\\frac{v_1}{v_2}+\\frac{v_2}{v_1}\\Big) + \\frac{v_3}{3}H},\n\\end{array}\n\\end{equation}\nwhere   $H$ is\nthe mean curvature function of $f$. Then $M^3$ is conformally flat and $f$ has three distinct principal curvatures. \n\nConversely, any conformally flat hypersurface $f\\colon\\,M^3\\to\\mathbb{Q}^{4}(c)$ with three distinct \nprincipal curvatures is locally a \nholonomic hypersurface whose associated pair $(v, V)$ satisfies $(\\ref{holo.flat.med.2}).$\n\\end{corollary}\n\\begin{proof} It suffices to show that equations (\\ref{holo.flat}) together with \n\\begin{equation}\\label{lem1.med}\n\\begin{array}{l}\nH=\\sum_{i=1}^3{V_iv_i^{-1}}\n\\end{array}\n\\end{equation}\nare equivalent to (\\ref{holo.flat.med.2}). For that, consider the Minkowski space ${\\mathbb L}^3$ endowed with the Lorentz inner product \n$$\\<(x_1,x_2,x_3), (y_1,y_2,y_3)\\> = x_1y_1-x_2y_2+x_3y_3.$$\nThen the conditions in  (\\ref{holo.flat}) say that  $v=(v_1, v_2, v_3)$ and $V=(V_1, V_2, V_3)$ are  orthogonal with respect to such inner product,  $v$ is light-like and $V$ is a unit space-like vector. Since $w=(-v_3,0,v_1)\\in {\\mathbb L}^3$ is orthogonal to $v,$ we have  $v^\\perp=\\mbox{span}\\{v,w\\}.$ As $V\\in v^{\\perp},$ we can write $V=av+bw$ for some  $a,b \\in C^{\\infty}(M^3)$. Note that  $V_2=av_2.$ \nUsing  $(\\ref{holo.flat})$ we obtain\n $$1=\\langle V,V \\rangle = \\langle av+bw,av+bw \\rangle=b^2\\langle w,w \\rangle=b^2v_2^2.$$ \n Thus $V=\\frac{V_2}{v_2}v+\\frac{\\lambda}{v_2}w,$ with $\\lambda=\\pm 1.$ Therefore \n\\begin{equation}\\label{V1.e.V3.med.}\n\\begin{array}{lll}\n\\displaystyle{V_1=\\frac{1}{v_2}(V_2v_1-\\lambda v_3)}\\qquad \\mbox{and} \\qquad \\displaystyle{V_3=\\frac{1}{v_2}(V_2v_3+\\lambda v_1)}.\n\\end{array}\n\\end{equation}\nSubstituting  (\\ref{V1.e.V3.med.}) in (\\ref{lem1.med}) \nwe obtain\n\\begin{equation}\\label{V2.med.}\n\\begin{array}{l}\n\\displaystyle{V_2=-\\frac{\\lambda}{3}\\Big(\\frac{v_1}{v_3}-\\frac{v_3}{v_1}\\Big) + \\frac{v_2}{3}H}.\n\\end{array}\n\\end{equation}\nSubstituting  (\\ref{V2.med.}) in (\\ref{V1.e.V3.med.}) yields \n$$V_1=-\\frac{\\lambda}{3}\\Big(\\frac{v_2}{v_3}+\\frac{v_3}{v_2}\\Big) + \\frac{v_1}{3}H \\,\\,\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,\nV_3=\\frac{\\lambda}{3}\\Big(\\frac{v_1}{v_2}+\\frac{v_2}{v_1}\\Big) + \\frac{v_3}{3}H,$$\nand changing the orientation, if necessary, we may assume that $\\lambda=1$.\\end{proof} \n\n\\subsection{Generalized cones over Clifford tori}\n\nFirst we show that, if  $g\\colon {\\mathbb R}^2 \\to {\\mathbb S}^3\\subset {\\mathbb R}^4$ is the Clifford torus parametrized by \n\\begin{equation} \\label{eq:g}\n  g(x_1,x_2)=\\frac{1}{\\sqrt{2}}(\\cos (\\sqrt{2} x_1), \\sin (\\sqrt{2} x_1),\\cos (\\sqrt{2} x_2), \\sin (\\sqrt{2} x_2)),\n  \\end{equation} \n   then the standard  cone\n$F\\colon (0, \\infty)\\times {\\mathbb R}^2\\to {\\mathbb R}^4$ over $g$ given by\n$$F(s,x)=sg(x),\\,\\,\\,\\,x=(x_1, x_2),$$\nis a minimal conformally flat hypersurface. \n\n\nThe first and second fundamental forms of $F$  with respect to the unit normal vector field \n$$\\eta(s, x_1, x_2)=\\frac{1}{\\sqrt{2}}(\\cos (\\sqrt{2} x_1), \\sin (\\sqrt{2} x_1),-\\cos (\\sqrt{2} x_2), -\\sin (\\sqrt{2} x_2))$$\nare\n$$\n\\begin{array}{lll}\nI=ds^2+ s^2(dx_1^2+dx_2^2) \\qquad \\text{and} \\qquad I\\!I= s(-dx^2_1+dx^2_2).\n\\end{array}\n$$\nIn terms of the new coordinates $u_1, u_2, u_3$, related to $s, x_1, x_2$ by\n$$\nu_2=\\log s,\\,\\,\\,\\,u_1=\\sqrt{2}x_1\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,u_3=\\sqrt{2}x_2,\n$$\nthe first and second fundamental forms of $F$ become\n$$I=\\frac{e^{2u_2}}{2}(du_1^2+2du_2^2+du_3^2)\\,\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,I\\!I=\\frac{e^{u_2}}{2}(-du_1^2+du_3^2),\n$$\nhence $F$ is a minimal conformally flat hypersurface with three distinct principal curvatures, one of which being zero.\\vspace{1ex}\n\nThe preceding example  can be extended to the case in which the ambient space is any space form, yielding  examples of minimal conformally flat hypersurfaces $f\\colon M^3\\to \\mathbb{Q}^4(c)$ with three distinct principal curvatures  also for $c\\neq 0$. \\vspace{.5ex}\n\n Start with the Clifford torus $g\\colon {\\mathbb R}^2\\to {\\mathbb S}^3\\subset {\\mathbb R}^4$ parametrized by (\\ref{eq:g}).\n  If $c>0$, define $F\\colon (0, \\pi\/\\sqrt{c})\\times {\\mathbb R}^2\\to {\\mathbb S}^4(c)\\subset {\\mathbb R}^5={\\mathbb R}^4\\times {\\mathbb R}$ by\n$$F(s,x)=\\frac{1}{\\sqrt{c}}(\\cos ({\\sqrt{c}}s) e_5+\\sin ({\\sqrt{c}}s) g(x)),$$\nwhere $x=(x_1, x_2)$ and $e_5$ is a unit vector spanning the factor ${\\mathbb R}$ in the orthogonal decomposition ${\\mathbb R}^5={\\mathbb R}^4\\times {\\mathbb R}$.\n\nNotice that, for each fixed $s=s_0$,  the map $F_{s_0}\\colon {\\mathbb R}^2\\to {\\mathbb S}^4(c)$, given by $F_{s_0}(x)=F(s_0, x)$, is also a Clifford torus \nin an umbilical hypersurface  ${\\mathbb S}^3(\\tilde c)\\subset {\\mathbb S}^4(c)$ with curvature $\\tilde c=c\/\\sin^2(\\sqrt{c}s_0)$, which has \n$$N_{s_0}=F_*\\frac{\\partial}{\\partial s}|_{s=s_0}=-\\sin(\\sqrt{c}s_0)e_5+\\cos(\\sqrt{c}s_0)g$$\nas a unit normal vector field along $F_{s_0}$. Notice also that\n$$F(s+s_0, x)=\\cos(\\sqrt{c}s)F_{s_0}(x)+\\sin(\\sqrt{c}s)N_{s_0}(x),$$\nthus $s\\mapsto F(s,x)$ parametrizes the geodesic in ${\\mathbb S}^4(c)$ through $F_{s_0}(x)$ tangent to $N_{s_0}(x)$ at $F_{s_0}(x)$.\nHence $F$ is a generalized cone over $F_{s_0}$.\n\nThe first and second fundamental forms of $F$  with respect to the unit normal vector field \n$$\\eta(s, x_1, x_2)=\\frac{1}{\\sqrt{2}}(\\cos (\\sqrt{2} x_1), \\sin (\\sqrt{2} x_1),-\\cos (\\sqrt{2} x_2), -\\sin (\\sqrt{2} x_2), 0)$$\nare\n$$\n\\begin{array}{lll}\n\\displaystyle{I=ds^2+ \\frac{1}{c}\\sin^2 ({\\sqrt{c}}s)(dx_1^2+dx_2^2)} \\;\\; \\mbox{and} \\;\\; \\displaystyle{I\\!I=\\frac{\\sin ({\\sqrt{c}}s)}{\\sqrt{c}}(-dx^2_1+dx^2_2)}.\n\\end{array}\n$$\nIn terms of the new coordinates $u_1, u_2, u_3$, related to $s, x_1, x_2$ by\n\\begin{equation} \\label{eq:uisxis}\n\\frac{du_2}{ds}=\\frac{\\sqrt{c}}{\\sin(\\sqrt{c}s)},\\,\\,\\,\\,u_1=\\sqrt{2}x_1\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,u_3=\\sqrt{2}x_2,\\end{equation} \nthe first and second fundamental forms of $F$ become\n\\begin{equation} \\label{eq:forms}\nI=\\frac{\\sin^2 \\theta}{2c}(du_1^2+2du_2^2+du_3^2)\\,\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,I\\!I=\\frac{\\sin \\theta}{2\\sqrt{c}}(-du_1^2+du_3^2),\n\\end{equation} \nwhere $\\theta=\\sqrt{c}s$, which, in view of the first equation in (\\ref{eq:uisxis}), \n  satisfies \n$$\\frac{d\\theta}{du_2}=\\sin \\theta.$$\nIt follows from (\\ref{eq:forms}) that $F$ is a minimal conformally flat hypersurface.\n\nIf $c<0$, define\n$F\\colon (0, \\infty)\\times {\\mathbb R}^2\\to \\mathbb{H}^4(c)\\subset {\\mathbb L}^5$ by\n$$F(s,x)=\\frac{1}{\\sqrt{-c}}(\\cosh ({\\sqrt{-c}}s) e_5+\\sinh ({\\sqrt{-c}}s) g(x)),$$\nwhere $x=(x_1, x_2)$,  $e_5$ is a unit time-like vector in ${\\mathbb L}^5$ and $e_5^\\perp$ is identified with ${\\mathbb R}^4$. \n\nAs in the previous case, for each fixed $s=s_0$  the map $F_{s_0}\\colon {\\mathbb R}^2\\to \\mathbb{H}^4(c)$, given by $F_{s_0}(x)=F(s_0, x)$, is also a Clifford torus \nin an umbilical hypersurface  ${\\mathbb S}^3(\\tilde c)\\subset \\mathbb{H}^4(c)$ with curvature $\\tilde c=-c\/\\sinh^2(\\sqrt{-c}s_0)$, and \n$F$ is a generalized cone over $F_{s_0}$.\n\nNow  the first and second fundamental forms of $F$ \nare\n$$I=ds^2+ \\frac{1}{-c}\\sinh^2 ({\\sqrt{-c}}s)(dx_1^2+dx_2^2)$$\nand\n$$I\\!I=\\frac{\\sinh ({\\sqrt{-c}}s)}{\\sqrt{-c}}(-dx^2_1+dx^2_2).$$\nIn terms of the new coordinates $u_1, u_2, u_3$, related to $s, x_1, x_2$ by\n$$\n\\frac{du_2}{ds}=\\frac{\\sqrt{-c}}{\\sinh(\\sqrt{-c}s)},\\,\\,\\,\\,u_1=\\sqrt{2}x_1\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,u_3=\\sqrt{2}x_2,\n$$\nthey become\n\\begin{equation} \\label{eq:formsb}I=\\frac{\\sinh^2 \\theta}{-2c}(du_1^2+2du_2^2+du_3^2)\\,\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,I\\!I=\\frac{\\sinh \\theta}{2\\sqrt{-c}}(-du_1^2+du_3^2),\\end{equation} \nwhere $\\theta(s)=\\sqrt{-c}s$\nsatisfies \n$$\\frac{d\\theta}{du_2}=\\sinh \\theta.$$\nIt follows from  (\\ref{eq:formsb}) that $F$ is a minimal conformally flat hypersurface with three distinct principal curvatures,\none of which being zero.\n\n\n\\section{The proofs of Theorems \\ref{thm:cmc} and \\ref{thm:minimalcneq0}}\n\nFirst we derive a system of PDE's for new unknown functions associated to a conformally flat hypersurface $f\\colon M^3\\to \\mathbb{Q}^4(c)$ with three distinct principal curvatures  under the assumption that \n$f$ has constant mean curvature.\n\n\n\n\\begin{proposition}\\label{flat.med.reduz.result.}\nLet $f\\colon M^3\\to \\mathbb{Q}^4(c)$ be a holonomic hypersurface with constant mean curvature $H$ whose associated pair  $(v,V)$ satisfies $(\\ref{holo.flat.med.2})$. Set $$(\\alpha_1,\\alpha_2,\\alpha_3)=\\Big(\\frac{1}{v_2}\\frac{\\partial v_2}{\\partial u_1},\\frac{1}{v_3}\\frac{\\partial v_3}{\\partial u_2},\\frac{1}{v_1}\\frac{\\partial v_1}{\\partial u_3}\\Big).$$ \nThen $v_1, v_2, v_3, \\alpha_1, \\alpha_2, \\alpha_3$ satisfy the differential equations  \n\\begin{equation} \\label{eq:e0}\\frac{\\partial v_1}{\\partial u_1}=\\frac{v_1}{v_2^4}(v_2^4+v_2^2v_3^2+v_3^4)\\alpha_1,\\,\\,\\,\\,\\,\\frac{\\partial v_2}{\\partial u_1}=v_2\\alpha_1,\\,\\,\\,\\,\\,\\frac{\\partial v_3}{\\partial u_1}=\\frac{v_3^5}{v_2^4}\\alpha_1,\\end{equation} \n\\begin{equation} \\label{eq:e0a}\\frac{\\partial v_1}{\\partial u_2}=\\frac{v_1^5}{v_3^4}\\alpha_2,\\,\\,\\,\\,\\,\\frac{\\partial v_2}{\\partial u_2}=\\frac{v_2}{v_3^4}(v_1^4-v_1^2v_3^2+v_3^4)\\alpha_2,\\,\\,\\,\\,\\,\\frac{\\partial v_3}{\\partial u_2}=v_3\\alpha_2,\\end{equation} \n\\begin{equation} \\label{eq:e0b}\\frac{\\partial v_1}{\\partial u_3}= v_1\\alpha_3,\\,\\,\\,\\,\\,\\frac{\\partial v_2}{\\partial u_3}=\\frac{v_2^5}{v_1^4}\\alpha_3,\\,\\,\\,\\,\\,\\frac{\\partial v_3}{\\partial u_3}=\\frac{v_3}{v_1^4}(v_1^4+v_1^2v_2^2+v_2^4)\\alpha_3,\\end{equation} \n\\begin{equation} \\label{eq:e1}\\begin{array}{l}\n{\\displaystyle \\frac{\\partial \\alpha_1}{\\partial u_1}  =  \\frac{1}{v_2^4}(3v_2^4-v_3^4)\\alpha_1^2 - \\frac{v_1^6}{v_3^8}(3v_1^2-2v_3^2)\\alpha_2^2 + \\frac{v_2^4}{v_1^2v_3^4}(3v_1^2+2v_2^2)\\alpha_3^2 }  \\vspace{.17cm} \\\\  \n{\\displaystyle +\\ \\frac{1}{9v_3^4}(5v_1^4+2v_2^2v_3^2)-  \\frac{v_1^2v_2^2}{v_3^2}c +  \\frac{v_1v_2}{18v_3^3}(v_2^2+v_3^2-2v_1v_2v_3H)H,} \\end{array}\n\\end{equation} \n\\begin{equation} \\label{eq:e1a}\\frac{\\partial \\alpha_2}{\\partial u_1}=2 \\frac{v_1^2}{v_2^2}\\alpha_1\\alpha_2,\\,\\,\\,\\,\\,\\frac{\\partial \\alpha_3}{\\partial u_1}=\n2 \\frac{v_3^2}{v_2^4}(4v_3^2+v_1^2)\\alpha_1\\alpha_3,\\end{equation} \n\\begin{equation} \\label{eq:e2}\\begin{array}{l}\n{\\displaystyle \\frac{\\partial \\alpha_2}{\\partial u_2} = -\\frac{v_3^4}{v_1^4v_2^2}(3v_2^2 + 2v_3^2) \\alpha_1^2 -\\frac{1}{v_3^4}(v_1^4 - 3v_3^4)\\alpha_2^2 - \\frac{v_2^6}{v_1^8}(2v_1^2+3v_2^2)\\alpha_3^2 } \\vspace{.17cm} \\\\ \n{\\displaystyle -\\frac{1}{9v_1^4}(5v_2^4-2v_1^2v_3^2)  +  \\frac{v_2^2v_3^2}{v_1^2}c - \\frac{v_2v_3}{18v_1^3}(v_1^2-v_3^2-2v_1v_2v_3H)H,} \n\\end{array}\n\\end{equation} \n\\begin{equation} \\label{eq:e2a}\\frac{\\partial \\alpha_1}{\\partial u_2}=2 \\frac{v_1^2}{v_3^4}(4v_1^2- v_2^2)\\alpha_1\\alpha_2,\\,\\,\\,\\,\\,\\frac{\\partial \\alpha_3}{\\partial u_2}=2 \\frac{v_2^2}{v_3^2}\\alpha_2\\alpha_3,\\end{equation} \n\\begin{equation} \\label{eq:e2b}\\frac{\\partial \\alpha_1}{\\partial u_3}=-2 \\frac{v_3^2}{v_1^2}\\alpha_1\\alpha_3,\\,\\,\\,\\,\\,\\frac{\\partial \\alpha_2}{\\partial u_3}=2 \\frac{v_2^2}{v_1^4}(4v_2^2- v_3^2)\\alpha_2\\alpha_3\\end{equation} \nand\n\\begin{equation} \\label{eq:e3}\\begin{array}{l}\n{\\displaystyle \\frac{\\partial \\alpha_3}{\\partial u_3} = \\frac{v_3^6}{v_2^8}(2v_2^2+3v_3^2)\\alpha_1^2 + \\frac{v_1^4}{v_2^4v_3^2}(2v_1^2-3v_3^2)\\alpha_2^2 + \\frac{1}{v_1^4}(3v_1^4-v_2^4)\\alpha_3^2 } \\vspace{.17cm} \\\\ \n{\\displaystyle + \\frac{1}{9v_2^4}(5v_3^4+2v_1^2v_2^2) - \\frac{v_1^2v_3^2}{v_2^2}c - \\frac{v_1v_3}{18v_2^3}(v_1^2+v_2^2+2v_1v_2v_3H)H,} \n\\end{array}\n\\end{equation} \nas well as the algebraic relations\n\\begin{equation}\\label{equ.alg.f.e.}\n\\begin{array}{l}\n\\displaystyle{\\Big(\\frac{30v_1}{v_2v_3^9} F  - \\frac{4v_1^4v_2^2}{v_3^6}(v_1^2-v_3^2)c + \\frac{v_1^3v_2}{18v_3^7} m_2 H \\Big)\\alpha_2 =0}, \\vspace{-.25cm} \\\\ \\\\\n\\displaystyle{\\Big( \\frac{30v_2}{v_1^9v_3}F  + \\frac{4v_2^4v_3^2}{v_1^6}(v_1^2+v_2^2)c + \\frac{v_3v_2^3}{18v_1^7} m_3 H \\Big)\\alpha_3=0} , \\vspace{-.25cm} \\\\ \\\\\n\\displaystyle{\\Big( \\frac{30v_3}{v_1v_2^9} F  - \\frac{4v_1^2v_3^4}{v_2^6}(v_2^2+v_3^2)c + \\frac{v_1v_3^3}{18v_2^7}m_1 H \\Big)\\alpha_1=0 ,}\n\\end{array}\n\\end{equation}\n where\n\\begin{equation*}\n\\begin{array}{rcl}\nm_1 &=& (v_2^2+4v_3^2)(4v_2^2+v_3^2)-8v_1v_2v_3(v_2^2+v_3^2)H,\\vspace{.2cm} \\\\\nm_2 &=& (v_1^2-4v_3^2)(4v_1^2-v_3^2)-8v_1v_2v_3(v_1^2-v_3^2)H, \\vspace{.2cm}\\\\\nm_3 &=& (v_1^2+4v_2^2)(4v_1^2+v_2^2)+8v_1v_2v_3(v_1^2+v_2^2)H, \\vspace{.2cm}\\\\\nF &=& \\displaystyle{\\frac{1}{27v_1v_2v_3}\\big[9v_1^2v_3^8(v_2^2+v_3^2)\\alpha_1^2  +   9v_1^8v_2^2(v_1^2-v_3^2)\\alpha_2^2  - 9v_2^8v_3^2(v_1^2+v_2^2)\\alpha_3^2} \\vspace{.2cm}\\\\\n &&  - \\ v_1^2v_2^2v_3^2(2v_1^2v_2^4-2v_1^2v_3^4-2v_2^2v_3^4-v_1^2v_2^2v_3^2)\\big].\n\\end{array}\n\\end{equation*}\n\\end{proposition}\n\\proof\nThe triple $(v,h,V),$ where $h_{ij}=\\frac{1}{v_i}\\frac{\\partial v_j}{\\partial u_i},$ satisfies the system of PDE's\n\\begin{equation}\\label{hol.flat.f.esp.}\n\\left\\{\\begin{array}{l}\\displaystyle{\n\\!\\!\\!(i) \\frac{\\partial v_i}{\\partial u_j}= h_{ji}v_j,  \\,\\,\\,\\,\\,\\,\\, (ii) \\frac{\\partial h_{ij}}{\\partial u_i} + \\frac{\\partial h_{ji}}{\\partial u_j} +h_{ki}h_{kj}+ V_iV_j + cv_iv_j =0}, \\vspace{.18cm}\\\\\n\\!\\!\\! \\displaystyle{(iii) \\frac{\\partial h_{ik}}{\\partial u_j}=h_{ij}h_{jk}, \\,\\,\\,\\,\\,\\,\\, (iv) \\frac{\\partial V_i}{\\partial u_j}=h_{ji}V_j, \\hspace{.5cm} 1\\leq i\\neq j\\neq k\\neq i \\leq 3,\\vspace{.18cm}}\\\\\n\\!\\!\\! \\displaystyle{(v) \\delta_i\\frac{\\partial v_i}{\\partial u_i}+ \\delta_jh_{ij}v_j +\\delta_kh_{ik}v_k=0, \\, \\ \\ (vi) \\delta_i\\frac{\\partial V_i}{\\partial u_i}+ \\delta_jh_{ij}V_j +\\delta_kh_{ik}V_k=0.}\n\\end{array}\\right. \\!\\!\\!\\!\\!\\!\\!\n\\end{equation}\nEquations  $(i)$, $(ii)$, $(iii)$ and $(iv)$ are due to the fact  that  $f$ is a holonomic hypersurface with $(v,V)$ as its associated pair, and  $(v)$ and $(vi)$ follow by differentiating (\\ref{holo.flat}).\n\nUsing   (\\ref{holo.flat.med.2}) and equations  $(i)$, $(iv)$, $(v)$ and $(vi)$ in  (\\ref{hol.flat.f.esp.}) one can show that\n\\begin{equation}\\label{rel.h-ki-kj}\n v_j^5h_{ki}=v_i^5h_{kj}, \\quad 1\\leq i\\neq j\\neq k\\neq i\\leq 3.\n\\end{equation}\nFrom $(i)$ and $(v)$ of (\\ref{hol.flat.f.esp.}), together with (\\ref{rel.h-ki-kj}), one  obtains the formulae for  the derivatives $\\frac{\\partial v_i}{\\partial u_j},$ $1\\leq i,j\\leq 3$. In a similar way, using  $(i)$, $(iii)$ and $(v)$, together with  (\\ref{rel.h-ki-kj}), one finds the derivatives $\\frac{\\partial \\alpha_i}{\\partial u_j},$ $1\\leq i\\neq j\\leq 3$.  In order to compute $\\frac{\\partial \\alpha_i}{\\partial u_i},$ $1\\leq i\\leq 3$, we note that equation  $(ii)$, together with (\\ref{rel.h-ki-kj}) and the remaining equations in (\\ref{hol.flat.f.esp.}), determines the   system of linear equations \n\\begin{equation*}\nMP=-B\n\\end{equation*}\nin the variables  $\\frac{\\partial \\alpha_i}{\\partial u_i},$ $1\\leq i\\leq 3$, where\n\\begin{displaymath}\nM= \\left( \\begin{array}{ccc}\n 9v_1^2v_2^4v_3^2 & \\frac{9v_1^8v_2^2}{v_3^2} & 0\\vspace{.17cm}\\\\\n \\frac{9v_1^2v_3^8}{v_2^2} & 0 & 9v_1^4v_2^2v_3^2 \\vspace{.17cm}\\\\\n 0 &  9v_1^2v_2^2v_3^4 & \\frac{9v_2^8v_3^2}{v_1^2}\n\\end{array}\\right)\\!\\!, \\quad P= \\left( \\begin{array}{c}\n\\frac{\\partial \\alpha_1}{\\partial u_1} \\vspace{.17cm}\\\\\n\\frac{\\partial \\alpha_2}{\\partial u_2} \\vspace{.17cm}\\\\\n\\frac{\\partial \\alpha_3}{\\partial u_3}\n\\end{array}\\right)\n\\end{displaymath}\nand\n\\begin{displaymath}\nB= \\left( \\begin{array}{r}\n- 9v_1^2v_3^4(v_2^2+v_3^2)\\alpha_1^2 + \\frac{9v_1^8v_2^2}{v_3^6}(4v_2^2+v_3^2)(v_1^2-v_3^2)\\alpha_2^2 + 9v_2^8\\alpha_3^2 \\\\- v_1^2v_2^2(2v_3^4-v_1^2v_2^2) + \\ 9v_1^4v_2^4v_3^2 c -  v_1^3v_2^3v_3(v_1^2+v_2^2-v_1v_2v_3H)H. \\vspace{0.32cm}\\\\\n - \\frac{9v_1^2v_3^8}{v_2^6}(4v_1^2+v_2^2)(v_2^2+v_3^2)\\alpha_1^2 + 9v_1^8\\alpha_2^2 - 9v_2^4v_3^2(v_1^2+v_2^2)\\alpha_3^2\\\\ - v_1^2v_3^2(2v_2^4+v_1^2v_3^2) + \\ 9v_1^4v_2^2v_3^4 c +  v_1^3v_2v_3^3(v_1^2-v_3^2+v_1v_2v_3H)H. \\vspace{0.32cm}\\\\\n 9v_3^8\\alpha_1^2 - 9v_1^4v_2^2(v_1^2-v_3^2)\\alpha_2^2 + \\frac{9v_2^8v_3^2}{v_1^6}(4v_3^2-v_1^2)(v_1^2+v_2^2)\\alpha_3^2 \\\\ - v_2^2v_3^2(2v_1^4-v_2^2v_3^2) + \\ 9v_1^2v_2^4v_3^4 c +  v_1v_2^3v_3^3(v_2^2+v_3^2+v_1v_2v_3H)H.\n\\end{array}\\right)\\!\\!.\n\\end{displaymath}\nOne can check that  \nsuch system has a unique solution given by (\\ref{eq:e1}), (\\ref{eq:e2}) and (\\ref{eq:e3}).\n\nFinally, computing the mixed derivatives  $\\frac{\\partial^2 \\alpha_i}{\\partial u_j\\partial u_k} = \\frac{\\partial^2 \\alpha_i}{\\partial u_k\\partial u_j},$ $1\\leq i,k,j\\leq 3$, from   (\\ref{hol.flat.f.esp.}) we obtain \n$$0=\\frac{\\partial^2 \\alpha_1}{\\partial u_2\\partial u_1} - \\frac{\\partial^2 \\alpha_1}{\\partial u_1\\partial u_2} = \\Big(\\frac{30v_1}{v_2v_3^9} F  - \\frac{4v_1^4v_2^2}{v_3^6}(v_1^2-v_3^2)c + \\frac{v_1^3v_2}{18v_3^7} m_2 H \\Big)\\alpha_2, \n$$\n$$\n0=\\frac{\\partial^2 \\alpha_2}{\\partial u_3\\partial u_2} - \\frac{\\partial^2 \\alpha_2}{\\partial u_2\\partial u_3} = \\Big( \\frac{30v_2}{v_1^9v_3}F  + \\frac{4v_2^4v_3^2}{v_1^6}(v_1^2+v_2^2)c + \\frac{v_3v_2^3}{18v_1^7} m_3 H \\Big)\\alpha_3 \n$$\nand\n$$\n 0=\\frac{\\partial^2 \\alpha_3}{\\partial u_1\\partial u_3} - \\frac{\\partial^2 \\alpha_3}{\\partial u_3\\partial u_1} = \\Big( \\frac{30v_3}{v_1v_2^9} F  - \\frac{4v_1^2v_3^4}{v_2^6}(v_2^2+v_3^2)c + \\frac{v_1v_3^3}{18v_2^7}m_1 H \\Big)\\alpha_1.\\qed\n $$\n \n \n \n In the  lemmata that follows we assume  the hypotheses of   Proposition \\ref{flat.med.reduz.result.} to be satisfied and use the notations therein.\n\n\\begin{lemma} \\label{le:v1equalv3} If $v_1=v_3$ everywhere then $H=0$.\n\\end{lemma}\n\\proof By the assumption and the first equation in (\\ref{holo.flat.med.2}) we have $v_2=\\sqrt{2}v_1$. We obtain from any two of the  equations in (\\ref{eq:e0})  that $\\alpha_1=0$, whereas any two of the  equations in (\\ref{eq:e0b}) imply that $\\alpha_3=0$.\nThen (\\ref{eq:e1}) and (\\ref{eq:e3}) give\n$$\n\\begin{array}{l}\n18 \\alpha_2^2 + 4 v_1^2 H^2 - 3 \\sqrt{2}v_1 H + 36 v_1^2 c -18=0, \\vspace{0.17cm} \\\\\n18 \\alpha_2^2 + 4 v_1^2 H^2 + 3 \\sqrt{2}v_1 H + 36 v_1^2 c -18=0,\n\\end{array}\n$$\nwhich imply that $H=0$. \\qed\n\n\n\\begin{lemma} \\label{le:alphaiszero} The functions $\\alpha_1, \\alpha_2, \\alpha_3$ can not vanish symultaneously on any open subset of $M^3$. \n\\end{lemma}\n\\proof  If $\\alpha_1, \\alpha_2, \\alpha_3$ all vanish on the open subset $U\\subset M^3$, then (\\ref{eq:e1}), (\\ref{eq:e2}) and (\\ref{eq:e3}) become \n\\begin{equation}\\label{cond.a1=a2=a3=0.1}\n\\begin{array}{l}\n2(5v_1^4+2v_2^2v_3^2) - 18v_1^2v_2^2v_3^2c +  v_1v_2v_3(v_2^2+v_3^2-2v_1v_2v_3H)H=0,\n\\end{array}\n\\end{equation}\n\\begin{equation}\\label{cond.a1=a2=a3=0.2}\n\\begin{array}{l}\n2(5v_2^4-2v_1^2v_3^2) - 18v_1^2v_2^2v_3^2c + v_1v_2v_3(v_1^2-v_3^2-2v_1v_2v_3H)H=0,\n\\end{array}\n\\end{equation}\n\\begin{equation}\\label{cond.a1=a2=a3=0.3}\n\\begin{array}{l}\n2(5v_3^4+2v_1^2v_2^2) -  18v_1^2v_2^2v_3^2c - v_1v_2v_3(v_1^2+v_2^2+2v_1v_2v_3H)H=0. \n\\end{array}\n\\end{equation}\nComparying (\\ref{cond.a1=a2=a3=0.1}) with  (\\ref{cond.a1=a2=a3=0.2}) and (\\ref{cond.a1=a2=a3=0.3}) yields, respectively, \n\\begin{equation}\\label{cond.a1=a2=a3=0.3.1}\n\\begin{array}{ll}\n\\displaystyle{H = \\frac{2(v_1^2+v_2^2)}{v_1v_2v_3} \\qquad {\\text{and}} \\qquad H=-\\frac{2(v_1^2-v_3^2)}{v_1v_2v_3}},\n\\end{array}\n\\end{equation}\nwhich is a contradiction. \\qed \n\n\\begin{lemma} \\label{le:alpha1alpha3} There does not exist any open subset of $M^3$ where  $v_1-v_3$ is nowhere vanishing and  $\\alpha_1=0=\\alpha_3$. \n\\end{lemma}\n\\proof Assume that  $\\alpha_1 = 0=\\alpha_3$ and that  $v_1-v_3$ does not  vanish on the open subset $U \\subset M^3$.\nBy Lemma \\ref{le:alphaiszero},  $\\alpha_2$ must be nonvanishing on an open dense subset $V\\subset U$.  Then equations (\\ref{eq:e0}), (\\ref{eq:e0a}), (\\ref{eq:e0b}), (\\ref{eq:e1a}), (\\ref{eq:e2a}) and (\\ref{eq:e2b}) reduce to the following  on $V$:\n\\begin{equation*}\n\\begin{array}{l}\n\\displaystyle{\\frac{\\partial v_i}{\\partial u_1}=\\frac{\\partial v_i}{\\partial u_3}=\\frac{\\partial \\alpha_i}{\\partial u_j}=0}, \\ \\ i,j=1,2,3,  \\ \\  \\ \\ i\\neq j, \\hspace{2.08cm}\n\\end{array}\n\\end{equation*}\n\\begin{equation}\\label{col.ex.f.e.1}\n\\begin{array}{l}\n\\displaystyle{\\frac{\\partial v_1}{\\partial u_2}=\\frac{v_1^5}{v_3^4}\\alpha_2, \\quad \n\\frac{\\partial v_2}{\\partial u_2}=\\frac{v_2}{v_3^4}(v_1^4-v_1^2v_3^2+v_3^4) \\alpha_2, \\quad\n\\frac{\\partial v_3}{\\partial u_2}=v_3\\alpha_2},\n\\end{array}\n\\end{equation}\nand, since $\\alpha_1=\\alpha_3=0,$ equations (\\ref{eq:e1}), (\\ref{eq:e2}) and (\\ref{eq:e3})  become, respectively, \n\\begin{equation}\\label{col.ex.f.e.2}\n\\begin{array}{l}\n\\displaystyle{\\frac{v_1^6}{v_3^8}(3v_1^2-2v_3^2)\\alpha_2^2 + \\frac{1}{9v_3^4}(5v_1^4+2v_2^2v_3^2) -  \\frac{v_1^2v_2^2}{v_3^2}c}  \\vspace{1ex}\\\\ \\hspace*{20ex}\\displaystyle{+\\frac{v_1v_2}{18v_3^3}(v_2^2+v_3^2-2v_1v_2v_3H)H =0},\n\\end{array}\n\\end{equation}\n\\begin{equation}\\label{col.ex.f.e.3}\n\\begin{array}{l}\n\\displaystyle{\\frac{\\partial \\alpha_2}{\\partial u_2} = -\\frac{1}{v_3^4}(v_1^4 - 3v_3^4)\\alpha_2^2 -\\frac{1}{9v_1^4}(5v_2^4-2v_1^2v_3^2)  +  \\frac{v_2^2v_3^2}{v_1^2}c} \\vspace{1ex}\\\\ \\hspace*{20ex}\\displaystyle{- \\frac{v_2v_3}{18v_1^3}(v_1^2-v_3^2-2v_1v_2v_3H)H},\n\\end{array}\n\\end{equation}\n\\begin{equation}\\label{col.ex.f.e.4}\n\\begin{array}{l}\n\\displaystyle{\\frac{v_1^4}{v_2^4v_3^2}(2v_1^2-3v_3^2)\\alpha_2^2 + \\frac{1}{9v_2^4}(5v_3^4+2v_1^2v_2^2) -  \\frac{v_1^2v_3^2}{v_2^2}c} \\vspace{1ex}\\\\ \\hspace*{20ex} \\displaystyle{-\\frac{v_1v_3}{18v_2^3}(v_1^2+v_2^2+2v_1v_2v_3H)H=0}. \n\\end{array}\n\\end{equation}\nMultiplying (\\ref{col.ex.f.e.2}) and   (\\ref{col.ex.f.e.4}) by  $2v_3^8$ and $3v_1^2v_2^4v_3^2$, respectively,  and  subtracting one\nfrom the  other, yield\n\\begin{equation}\n\\begin{array}{lcr}\\label{col.ex.f.e.5}\n\\displaystyle{\\alpha_2^2 = \\frac{1}{90 v_1^6}\\big[-2 v_1^2 v_2^2 v_3^2 (3 v_1^2 + 2 v_3^2)H^2 -  v_1 v_2 v_3  (6 v_1^4 + v_1^2 v_3^2 - 4 v_3^4)H} \\vspace{0.15cm} \\\\  \\hspace*{5ex} \\displaystyle{- \\ 18  v_1^2 v_2^2 v_3^2 (3 v_1^2 + 2 v_3^2)c + 2 (6 v_1^6 + 16 v_1^4 v_3^2 + 19 v_1^2 v_3^4 + 4 v_3^6)\\big]}.\n  \\end{array}\n\\end{equation} \nOn one hand, substituting (\\ref{col.ex.f.e.5}) in  (\\ref{col.ex.f.e.3}) we obtain\n\\begin{equation}\\label{col.ex.f.e.6}\n\\begin{array}{l}\n\\displaystyle{ \\frac{\\partial \\alpha_2}{\\partial u_2} = \\frac{1}{90 v_1^6 v_3^4}\\big[2 v_1^2 v_2^2 v_3^2 (3 v_1^6 + 2 v_1^4 v_3^2 - 4 v_1^2 v_3^4 - 6 v_3^6)H^2} \\vspace{0.1cm} \\\\\\hspace*{9ex} \\displaystyle{+ \\  v_1 v_2 v_3 (6 v_1^8 + v_1^6 v_3^2 - 27 v_1^4 v_3^4 + 2 v_1^2 v_3^6 + 12 v_3^8)H} \\vspace{0.1cm} \\\\\\hspace*{9ex} \\displaystyle{+ \\ 18 v_1^2 v_2^2 v_3^2 (3 v_1^6 + 2 v_1^4 v_3^2 - 4 v_1^2 v_3^4 - 6 v_3^6)c} \\vspace{0.1cm} \\\\\\hspace*{9ex} \\displaystyle{- \\ 4 (v_1^4 - v_3^4) (3 v_1^6 + 8 v_1^4 v_3^2 + 16 v_1^2 v_3^4 + 6 v_3^6)  \\big]}.\n\\end{array}\n\\end{equation}\nOn the other hand, differentiating  (\\ref{col.ex.f.e.5}) with respect to  $u_2$ and using  (\\ref{col.ex.f.e.1}) gives\n\\begin{equation}\\label{col.ex.f.e.7}\n\\begin{array}{l}\n\\displaystyle{\\alpha_2\\frac{\\partial \\alpha_2}{\\partial u_2} = -\\frac{\\alpha_2}{180 v_1^6 v_2 v_3^3} \\big[v_2^2(-4 v_1^2 v_2 v_3^3 (5 v_1^4 - 4 v_1^2 v_3^2 - 6 v_3^4)H^2} \\vspace{0.1cm} \\\\\\hspace*{9ex}  \\displaystyle{- \\ v_1 v_3^2 (8 v_1^6 - 27 v_1^4 v_3^2 - 8 v_1^2 v_3^4 + 24 v_3^6)H} \\vspace{1ex}\\\\\\hspace*{9ex}\\displaystyle{- \\ 36 v_1^2 v_2 v_3^3 (5 v_1^4 - 4 v_1^2 v_3^2 - 6 v_3^4)c}  \\vspace{1ex}\\\\\\hspace*{9ex}\\ \\displaystyle{+8 v_2 v_3  (v_1^2 - v_3^2) (v_2^2 + v_3^2) (8 v_1^2 + 3 v_3^2)\\big]}.\n\\end{array}\n\\end{equation}\nUsing that  $\\alpha_2\\neq 0$ and $v_1-v_3\\neq 0$ on  $V$, we obtain from   (\\ref{col.ex.f.e.6}) and (\\ref{col.ex.f.e.7}) that\n\\begin{equation}\\label{col.ex.f.e.8}\n\\begin{array}{l}\n\\displaystyle{ H^2 + \\frac{4 v_1^6 - 2 v_1^4 v_3^2 - 9 v_1^2 v_3^4 + 4 v_3^6}{4 v_1^3 v_2 v_3 (v_1^2 - v_3^2)}H - \\frac{2 v_2^2 (v_1^2 - v_3^2)}{v_1^4 v_3^2} + 9 c=0.}\n\\end{array}\n\\end{equation}\nDifferentiating (\\ref{col.ex.f.e.8}) with respect to $u_2,$ and using  (\\ref{col.ex.f.e.1}) we obtain\n\\begin{equation}\\label{col.ex.f.e.9}\n\\begin{array}{l}\nv_1 v_3 (22 v_1^6 - 11 v_1^4 v_3^2 - 4 v_1^2 v_3^4 + 8 v_3^6)H = -16  v_2^3 (v_1^2 - v_3^2)^2.\n\\end{array}\n\\end{equation}\nSince $v_1-v_3\\neq 0,$ we must have  $(22 v_1^6 - 11 v_1^4 v_3^2 - 4 v_1^2 v_3^4 + 8 v_3^6)\\neq 0$ on $V.$ Therefore,  (\\ref{col.ex.f.e.9}) implies   that\n\\begin{equation}\\label{col.ex.f.e.10}\n\\begin{array}{l}\n\\displaystyle{H = -\\frac{16  v_2^3 (v_1^2 - v_3^2)^2}{v_1 v_3 (22 v_1^6 - 11 v_1^4 v_3^2 - 4 v_1^2 v_3^4 + 8 v_3^6)}}.\n\\end{array}\n\\end{equation}\nFinally, differentiating  (\\ref{col.ex.f.e.10}) with respect to  $u_2$ and  using  (\\ref{col.ex.f.e.1}) we obtain\n\\begin{equation}\\label{col.ex.f.e.11}\n\\begin{array}{l}\n\\displaystyle{0 = -\\frac{1680  v_1^5v_2^3 (v_1^2 - v_3^2)^2}{v_3 (22 v_1^6 - 11 v_1^4 v_3^2 - 4 v_1^2 v_3^4 + 8 v_3^6)^2}\\alpha_2,}\n\\end{array}\n\\end{equation}\nwhich is a contradiction, for the right-hand-side of  (\\ref{col.ex.f.e.11}) is nonzero.\\qed \n\n\\begin{lemma} \\label{le:alpha2alphaj} There does not exist any open subset of $M^3$ where  $\\alpha_2=0=\\alpha_j$ for some $j\\in \\{1, 3\\}$.  \n\\end{lemma}\n\\proof We argue for the case in which $j=1$, the other case being similar. So, assume that  $\\alpha_1$ and $\\alpha_2$ vanish on an open subset  $U \\subset M^3$.  By Lemma \\ref{le:alphaiszero},  $\\alpha_3$ is nonzero on an open dense subset $V\\subset U$.  Equations (\\ref{eq:e1}) and (\\ref{eq:e2}) can be rewritten as follows on $V$: \n\n\\begin{equation}\\label{con.ad.f.e.5}\n\\begin{array}{l}\n\\displaystyle{\\frac{v_2^4}{v_1^2v_3^4}(3v_1^2+2v_2^2)\\alpha_3^2  + \\frac{1}{9v_3^4}(5v_1^4+2v_2^2v_3^2)  -  \\frac{v_1^2v_2^2}{v_3^2}c }\\vspace{1ex}\\\\ \\hspace*{20ex}\\displaystyle{+  \\frac{v_1v_2}{18v_3^3}(v_2^2+v_3^2-2v_1v_2v_3H)H =0}, \\vspace{0.17cm} \\\\\n\n\\displaystyle{- \\frac{v_2^6}{v_1^8}(2v_1^2+3v_2^2)\\alpha_3^2 -\\frac{1}{9v_1^4}(5v_2^4-2v_1^2v_3^2)  +  \\frac{v_2^2v_3^2}{v_1^2}c} \\vspace{1ex}\\\\ \\hspace*{20ex}\\displaystyle{- \\frac{v_2v_3}{18v_1^3}(v_1^2-v_3^2-2v_1v_2v_3H)H =0}.\n\\end{array}\n\\end{equation}\nEliminating $\\alpha_3^2$ from the equations in  (\\ref{con.ad.f.e.5}) yields\n\\begin{equation}\\label{con.ad.f.e.6}\n\\begin{array}{ll}\n\\displaystyle{H^2- \\frac{7 v_1^4 + 7 v_1^2 v_3^2 + 2 v_3^4}{2 v_1 v_2 v_3 (v_1^2 + v_2^2)} H - \\frac{ 2 v_3^2}{v_1^2 v_2^2} + 9 c =0}.\n\\end{array}\n\\end{equation}\nDifferentiating (\\ref{con.ad.f.e.6}) with respect to $u_3$ and using that $\\alpha_3\\neq 0$ we obtain\n\\begin{equation}\\label{con.ad.f.e.7}\n\\displaystyle{H=\\frac{8 v_3^3  (v_1^2 + v_2^2)}{v_1  v_2 (21 v_1^4 + 21 v_1^2 v_3^2 + 4 v_3^4)}}.\n\\end{equation}\nFinally, differentiating (\\ref{con.ad.f.e.7}) with respect to  $u_3$ and using the fact that  $H$ is constant we obtain \n\\begin{equation*}\n\\begin{array}{ll}\n\\displaystyle{0=\\frac{120 v_3^3 v_2 (v_1^2 + v_2^2) (7 v_1^4 + 7 v_1^2 v_3^2 + 2 v_3^4)}{v_1^3 (21 v_1^4 + 21 v_1^2 v_3^2 + 4 v_3^4)^2},}\n\\end{array}\n\\end{equation*}\nwhich is a contradiction. \\qed\n\n\\begin{lemma} \\label{le:alphaialphajneq0} If there exist $p\\in M^3$ and $1\\leq i\\neq j\\leq 3$  such that $\\alpha_i(p)\\neq 0\\neq \\alpha_j(p)$ then $H=0=c$.  \n\\end{lemma}\n\\proof  We give the proof for the case in which $i=1$ and $j=2$, the remaining ones being similar. Let $U\\subset M^3$ be an open neighborhood of $p$ where  $\\alpha_1$ and  $\\alpha_2$ are nowhere vanishing. Then  (\\ref{equ.alg.f.e.}) gives\n$$\\frac{30v_3}{v_1v_2^9} F  - \\frac{4v_1^2v_3^4}{v_2^6}(v_2^2+v_3^2)c + \\frac{v_1v_3^3}{18v_2^7}m_1 H=0   $$\nand \n$$ \\frac{30v_1}{v_2v_3^9} F  - \\frac{4v_1^4v_2^2}{v_3^6}(v_1^2-v_3^2)c + \\frac{v_1^3v_2}{18v_3^7} m_2 H =0,\n$$\nor equivalently,\n\\begin{equation}\\label{con.ad.f.e.2}\n\\left\\{\\begin{array}{l}\nF=-\\frac{1}{540}v_1^2v_2^2v_3^2[Hm_1-72cv_1v_2v_3(v_2^2+v_3^2)], \\vspace{0.18cm} \\\\\nF=-\\frac{1}{540}v_1^2v_2^2v_3^2[Hm_2-72cv_1v_2v_3(v_1^2-v_3^2)].\n\\end{array}\\right.\n\\end{equation}\nSubtracting one of the equations in  (\\ref{con.ad.f.e.2}) from the other we obtain \n\\begin{equation}\\label{con.ad.f.e.3}\n\\begin{array}{lll}\n\\displaystyle{H^2-\\frac{7(v_1^2 \\ + \\ v_2^2)}{8v_1v_2v_3}H+9c=0}.\n\\end{array}\n\\end{equation}\nDifferentiating  (\\ref{con.ad.f.e.3}) with respect to  $u_1$ we obtain \n\\begin{equation}\\label{con.ad.f.e.4}\n\\begin{array}{lll}\n\\displaystyle{\\frac{21v_3^3}{8v_1v_2^3}H\\alpha_1=0}.\n\\end{array}\n\\end{equation}\nSince  $\\alpha_1\\neq 0$,  equation  (\\ref{con.ad.f.e.4}) implies that  $H=0$, and hence $c=0$ by (\\ref{con.ad.f.e.3}). \\vspace{1ex}\\qed\n\n\n\n\\begin{lemma} \\label{le:v1neqv3} If $v_1\\neq v_3$ at some point of $M^3$ then $H=0=c$. \n\\end{lemma}\n\\proof  Assume that $v_1(p_0)\\neq v_3(p_0)$ for some  $p_0\\in M^3$, and hence that $v_1\\neq v_3$  on some open neighborhood  $U\\subset M^3$\nof $p_0$. By Lemma \\ref{le:alphaiszero}, there exist an open subset $U'\\subset U$ and $i\\in\\{1,2,3\\}$ such that  $\\alpha_i(p)\\neq 0$ for all $p\\in U'$.  It follows from Lemma \\ref{le:alpha1alpha3} and Lemma \\ref{le:alpha2alphaj} that there exist $q\\in U'$ and $j\\in\\{1,2,3\\}, \\ j\\neq i,$ such that   $\\alpha_j(q)\\neq 0$. Thus there exists $q\\in M^3$ such that  $\\alpha_i(q)\\neq 0$ and $\\alpha_j(q)\\neq 0, \\ i\\neq j,$ and the conclusion follows from Lemma \\ref{le:alphaialphajneq0}. \\vspace{2ex}\\qed\n\n\\noindent \\emph{Proof of Theorem $\\ref{thm:cmc}$:} Follows immediately from  Lemma \\ref{le:v1equalv3} and Lemma \\ref{le:v1neqv3}.\\vspace{2ex}\\qed\n\n\n\n\n\n\n\n\n\\noindent \\emph{Proof of Theorem $\\ref{thm:minimalcneq0}$:}  \nGiven $p\\in M^3$, let  $u_1, u_2, u_3$ be $U$ be local principal coordinates on an open neighborhood  $U$ of $p$  as in \nCorollary \\ref{le:asspair}. It follows from Lemma \\ref{le:v1neqv3}  that the associated pair $(v,V)$ satisfies $v_1=v_3$ on $U$. Thus $\\lambda_2$ vanishes on $U$, and hence everywhere on $M^3$ by analyticity. The statement is now a consequence of the next proposition. \\qed\n\n\\begin{proposition}\\label{thm:minimalpczero} Let $f\\colon M^{3} \\to \\mathbb{Q}^{4}(c)$  be a  conformally flat hypersurface with three distinct principal curvatures. If one of the principal curvatures is everywhere zero,   then either $c=0$ and $f$ is locally a cylinder over a surface $g\\colon M^2(\\bar c)\\to {\\mathbb R}^3$ with constant Gauss curvature $\\bar c\\neq 0$ or $f$ is locally   a generalized cone over a surface $g\\colon M^2(\\bar c)\\to \\mathbb{Q}^{3}(\\tilde c)$ with constant Gauss curvature $\\bar c\\neq \\tilde c$ in an umbilical hypersurface $\\mathbb{Q}^{3}(\\tilde c)\\subset \\mathbb{Q}^4(c)$, $\\tilde c\\geq c$, with $\\tilde c>0$ if $c=0$. If, in addition, $f$ is minimal, then $f(M^3)$ is an open subset of a generalized cone over a Clifford torus in an umbilical hypersurface $\\mathbb{Q}^{3}(\\tilde c)\\subset \\mathbb{Q}^4(c)$, $\\tilde c>0$, with $\\tilde c\\geq c$ if $c>0$.\n\\end{proposition}\n\\proof Let $e_1, e_2, e_3$\ndenote local  unit vector fields which are principal directions correspondent to the distinct\nprincipal curvatures $\\lambda_1, \\lambda_2, \\lambda_3$, respectively. Then conformal flatness of $M^3$ is\nequivalent to the relations\n\\begin{equation}  \\label{eq:uno}\n\\<\\nabla_{e_i}e_j,e_k\\>=0\n\\end{equation} \nand\n\\begin{equation}  \\label{eq:dos}\n(\\lambda_j-\\lambda_k)e_i(\\lambda_i)+(\\lambda_i-\\lambda_k)e_i(\\lambda_j)+ (\\lambda_j-\\lambda_i)e_i(\\lambda_k)=0,\n\\end{equation} \nfor all distinct indices $i, j, k$ (see \\cite{la}, p. 84). It follows from Codazzi's equation and (\\ref{eq:uno}) that\n\\begin{equation} \\label{eq:tres}\n\\nabla_{e_i}e_i=\\sum_{j\\neq i}(\\lambda_i-\\lambda_j)^{-1}e_j(\\lambda_i)e_j.\n\\end{equation} \nIf, say, $\\lambda_2=0$, then equation\n(\\ref{eq:dos}) yields\n$$\n\\lambda_3^{-1}e_2(\\lambda_3)=\\lambda_1^{-1}e_2(\\lambda_1):=\\varphi,\n$$\nhence the distribution $\\{e_2\\}^\\perp$ spanned by $e_1$ and $e_3$ is umbilical in $M^3$ by\n(\\ref{eq:tres}).\n\nIf $\\varphi$ is identically zero on $M^3$, then $\\{e_2\\}^\\perp$ is a totally geodesic distribution, and hence \n$M^3$ is locally isometric to a Riemannian product $I\\times M^2$ by the local de Rham theorem. Since $M^3$ is conformally flat, it follows that $M^2$ must have constant Gauss curvature. Moreover, \nby Molzan's theorem (see Corollary $17$ in \\cite{nol}), $f$ is locally an extrinsic product of isometric immersions of the factors, \nwhich is not possible if $c\\neq 0$ because $f$ has three distinct principal curvatures. Therefore $c=0$ and $f$ is locally a cylinder over a surface with constant Gauss curvature in ${\\mathbb R}^3$. \n\nIf $\\varphi$ is not identically zero on $M^3$, given $x\\in M^3$ let $\\sigma$ be the leaf of $\\{e_2\\}^\\perp$ containing $x$ and let $j\\colon\\sigma\\to M^3$ be the inclusion of  $\\sigma$  into $M^3$. Denote  $\\tilde g=f\\circ j$. \nThen the normal bundle $N_{\\tilde g}\\sigma$ of $\\tilde g$ splits as \n\\begin{equation*}\nN_{\\tilde g}\\sigma=f_*N_j\\sigma\\oplus N_fM=\\mbox{span}\\{f_*e_2\\}\\oplus N_fM\n\\end{equation*}\nand\n\\bea\n\\tilde \\nabla_X f_*e_2\\!\\!\\!&=&\\!\\!\\!f_*\\nabla_Xe_2+\\alpha^f(j_*X,e_2)\\\\\n\\!\\!\\!&=&\\!\\!\\!-\\varphi \\tilde{g}_*X\n\\eea\nfor all $X\\in \\mathfrak{X}(\\sigma)$, where $\\tilde \\nabla$ is the induced \nconnection on ${\\tilde g}^*T\\mathbb{Q}^4(c)$. It follows that the normal vector field $\\eta=f_*e_2$ of $\\tilde g$ \nis parallel with respect \nto the normal connection of $\\tilde g$, and that the shape operator of $\\tilde g$ with \nrespect to $\\eta$  is \ngiven by \n$A^{\\tilde g}_\\eta=\\varphi I$. \nIt is a standard fact that this implies  $\\tilde g(\\sigma)$ to be contained in an umbilical hypersurface $\\mathbb{Q}^{3}(\\tilde c)\\subset \\mathbb{Q}^4(c)$, $\\tilde c\\geq c$, that is,  there exist an umbilical hypersurface $i\\colon \\mathbb{Q}^{3}(\\tilde c)\\to \\mathbb{Q}^4(c)$   and an isometric immersion \n$g\\colon M^2=\\sigma\\to\\mathbb{Q}^3({\\tilde c})$ such that $\\tilde g=i\\circ g$. \nMoreover,  since at any $y\\in\\sigma$ the fiber $L(y)\\!=\\!\\mbox{span}\\{\\eta(y)\\}$  \ncoincides with the normal space of $i$ at $g(y)$, it follows that $f$ coincides with \nthe generalized cone over $g$ in a neighborhood of $x$. \n\nIn particular, $M^3$ is a warped product $I\\times_{\\rho}M^2$, and since $M^3$ is conformally flat, $M^2$ must have constant Gauss curvature. If, in addition, $f$ is minimal, then $g$ must be a Clifford torus in an umbilical hypersurface $\\mathbb{Q}^{3}(\\tilde c)\\subset \\mathbb{Q}^4(c)$, $\\tilde c>0$, with $\\tilde c\\geq c$ if $c>0$, and the preceding argument shows that $f(M^3)$ is an open subset of a generalized cone over~$g$.\\qed\n\n\\section{Proof of Theorem \\ref{thm:minimalceq0}}\nFirst we rewrite Proposition (\\ref{flat.med.reduz.result.}) when $H=0=c$ and state a converse to it.\n\n\\begin{proposition}\\label{flat.min.reduz.result.}\nLet $f\\colon M^3\\to {\\mathbb R}^4$ be a holonomic hypersurface whose associated pair  $(v,V)$ satisfies \n\\begin{equation} \\label{eq:vis}v_2^2=v_1^2+v_3^2\\end{equation}  and \n\\begin{equation}\\label{holo.flat.min.2}\n\\begin{array}{l}\n\\displaystyle{V_1=-\\frac{1}{3}\\Big(\\frac{v_2}{v_3}+\\frac{v_3}{v_2}\\Big)},\\quad\n\\displaystyle{V_2=-\\frac{1}{3}\\Big(\\frac{v_1}{v_3}-\\frac{v_3}{v_1}\\Big)}, \\quad\n\\displaystyle{V_3=\\frac{1}{3}\\Big(\\frac{v_1}{v_2}+\\frac{v_2}{v_1}\\Big)}.\n\\end{array}\n\\end{equation}\n Set $$\\alpha=(\\alpha_1,\\alpha_2,\\alpha_3)=\\Big(\\frac{1}{v_2}\\frac{\\partial v_2}{\\partial u_1},\\frac{1}{v_3}\\frac{\\partial v_3}{\\partial u_2},\\frac{1}{v_1}\\frac{\\partial v_1}{\\partial u_3}\\Big).$$\n Then  $\\phi=(v_1,v_2,v_3,\\alpha_1,\\alpha_2,\\alpha_3)$ satisfies the system of PDE's \n\\begin{equation}\\label{flat.min.reduz.}\n\\left\\{\\begin{array}{l}\n\\displaystyle{\\frac{\\partial \\phi}{\\partial u_1}=\\Big(\\frac{\\partial v_1}{\\partial u_1},v_2\\alpha_1, \\frac{v_3^5}{v_2^4}\\alpha_1,\\frac{\\partial\\alpha_1}{\\partial u_1},2 \\frac{v_1^2}{v_2^2}\\alpha_1\\alpha_2,2 \\frac{v_3^2}{v_2^4}(4v_3^2+v_1^2)\\alpha_1\\alpha_3 \\Big)}, \\vspace{.25cm}\\\\\n\\displaystyle{\\frac{\\partial \\phi}{\\partial u_2}=\\Big( \\frac{v_1^5}{v_3^4}\\alpha_2, \\frac{\\partial v_2}{\\partial u_2}, v_3\\alpha_2, 2 \\frac{v_1^2}{v_3^4}(4v_1^2- v_2^2)\\alpha_1\\alpha_2,\\frac{\\partial\\alpha_2}{\\partial u_2},2 \\frac{v_2^2}{v_3^2}\\alpha_2\\alpha_3 \\Big)},\\vspace{.25cm}\\\\\n\\displaystyle{\\frac{\\partial \\phi}{\\partial u_3}=\\Big(   v_1\\alpha_3,\\frac{v_2^5}{v_1^4}\\alpha_3, \\frac{\\partial v_3}{\\partial u_3}, -2 \\frac{v_3^2}{v_1^2}\\alpha_1\\alpha_3, 2 \\frac{v_2^2}{v_1^4}(4v_2^2- v_3^2)\\alpha_2\\alpha_3,\\frac{\\partial\\alpha_3}{\\partial u_3} \\Big),}\n\\end{array}\\right.\n\\end{equation}\nwhere\n$$\n\\begin{array}{l}\n\\displaystyle \\frac{\\partial v_1}{\\partial u_1}=\\frac{v_1}{v_2^4}(v_2^4+v_2^2v_3^2+v_3^4)\\alpha_1, \\;\\;\\;\n\\displaystyle \\frac{\\partial v_2}{\\partial u_2}=\\frac{v_2}{v_3^4}(v_1^4-v_1^2v_3^2+v_3^4)\\alpha_2, \\vspace{.2cm}\\\\\n\\displaystyle \\frac{\\partial v_3}{\\partial u_3}=\\frac{v_3}{v_1^4}(v_1^4+v_1^2v_2^2+v_2^4)\\alpha_3, \\vspace{.2cm}\\\\\n\\displaystyle{\\frac{\\partial \\alpha_1}{\\partial u_1} = \\frac{1}{v_2^4}(3v_2^4-v_3^4)\\alpha_1^2 - \\frac{v_1^6}{v_3^8}(3v_1^2-2v_3^2)\\alpha_2^2 + \\frac{v_2^4}{v_1^2v_3^4}(3v_1^2+2v_2^2)\\alpha_3^2} \\vspace{1ex}\\\\\\hspace*{6ex} \\displaystyle{+ \\frac{1}{9v_3^4}(5v_1^4+2v_2^2v_3^2)},\\vspace{.2cm}\\\\\n\\displaystyle{\\frac{\\partial \\alpha_2}{\\partial u_2} =-\\frac{v_3^4}{v_1^4v_2^2}(3v_2^2 + 2v_3^2) \\alpha_1^2 -\\frac{1}{v_3^4}(v_1^4 - 3v_3^4)\\alpha_2^2 - \\frac{v_2^6}{v_1^8}(2v_1^2+3v_2^2)\\alpha_3^2} \\vspace{1ex}\\\\\\hspace*{6ex}\\displaystyle{-\\frac{1}{9v_1^4}(5v_2^4-2v_1^2v_3^2)},\\vspace{.2cm}\\\\\n\\displaystyle{\\frac{\\partial \\alpha_3}{\\partial u_3} = \\frac{v_3^6}{v_2^8}(2v_2^2+3v_3^2)\\alpha_1^2 + \\frac{v_1^4}{v_2^4v_3^2}(2v_1^2-3v_3^2)\\alpha_2^2 + \\frac{1}{v_1^4}(3v_1^4-v_2^4)\\alpha_3^2} \\vspace{1ex}\\\\\\hspace*{6ex}\\displaystyle{+ \\frac{1}{9v_2^4}(5v_3^4+2v_1^2v_2^2)},\n\\end{array}\n$$\nas well as  the algebraic equation \n\\begin{equation}\\label{equ.chave}\n\\begin{array}{rcr}\n9v_1^2v_3^8(v_2^2+v_3^2)\\alpha_1^2  +   9v_1^8v_2^2(v_1^2-v_3^2)\\alpha_2^2  - 9v_2^8v_3^2(v_1^2+v_2^2)\\alpha_3^2 \\vspace{.2cm}\\\\\n  - \\ v_1^2v_2^2v_3^2(2v_1^2v_2^4-2v_1^2v_3^4-2v_2^2v_3^4-v_1^2v_2^2v_3^2) = 0.\n\\end{array}\n\\end{equation}\nConversely, if $\\phi=(v_1,v_2,v_3,\\alpha_1,\\alpha_2,\\alpha_3)$ is a solution of $(\\ref{flat.min.reduz.})$ satisfying (\\ref{eq:vis})  on an open simply-connected subset $U\\subset {\\mathbb R}^3$, then $\\phi$ satisfies  (\\ref{equ.chave}) and the  triple $(v, h, V)$, where $v=(v_1,v_2, v_3)$,  $V=(V_1, V_2, V_3)$ is given by $(\\ref{holo.flat.min.2})$ and $h=(h_{ij})$, with  $h_{ij}=\\frac{1}{v_i}\\frac{\\partial v_j}{\\partial u_i}$, $1\\leq i\\neq j\\leq 3$,  satisfies (\\ref{sistema-hol}),  and hence gives rise to a holonomic  hypersurface $f\\colon U\\to {\\mathbb R}^4$ whose associated pair $(v,V)$ satisfies (\\ref{eq:vis}) and  (\\ref{holo.flat.min.2}). \n\\end{proposition}\n\nIn view of Corollary \\ref{le:asspair} and Proposition \\ref{flat.min.reduz.result.}, minimal conformally flat hypersurfaces of ${\\mathbb R}^4$ are in correspondence with solutions $\\phi=(v_1,v_2,v_3,\\alpha_1,\\alpha_2,\\alpha_3)$  of (\\ref{flat.min.reduz.}) satisfying (\\ref{eq:vis}) and (\\ref{equ.chave}). We shall prove  that such solutions  are, in turn,  in correspondence with the leaves of a foliation of codimension one on the algebraic variety constructed in the next result. \n\n\n\\begin{proposition}\\label{prop.chave}  \nDefine $G,F:{\\mathbb R}^6={\\mathbb R}^3\\times {\\mathbb R}^3\\to{\\mathbb R}$  by  \n$$G(x,y)= x_2^2-x_1^2-x_3^2$$\n and\n\\begin{equation*}\n\\begin{array}{r}\nF(x,y)= 9x_1^2x_3^8(x_2^2+x_3^2)y_1^2 + 9x_1^8x_2^2(x_1^2-x_3^2)y_2^2 - 9x_2^8x_3^2(x_1^2+x_2^2)y_3^2 \\vspace{.2cm}\\\\\n  - x_1^2x_2^2x_3^2(2x_1^2x_2^4-2x_1^2x_3^4-2x_2^2x_3^4-x_1^2x_2^2x_3^2).\n\\end{array}\n\\end{equation*}\nLet\n$M^4:=F^{-1}(0)\\cap G^{-1}(0)\\cap\\{(x,y)\\in {\\mathbb R}^6;x_1>0,x_2>0,x_3>0\\,\\,\\mbox{and}\\,\\,y\\neq 0\\}$\nand let $\\ell_{\\pm}$ be the half lines in $M^4$ given by  $$\\ell_{\\pm}=\\{(x,y)\\in M^4\\;:\\; x=s(1, \\sqrt{2},1)\\,\\,\\mbox{for some $s>0$} \\,\\,\\mbox{and}\\,\\, y=(0,\\pm 1,0)\\}.$$ Then $\\tilde{M}^4=M^4\\setminus (\\ell_-\\cup \\ell_+)$ is a regular submanifold of ${\\mathbb R}^6$ and $\\ell_-\\cup \\ell_+$ is the singular set of $M^4$.\n\\end{proposition}\n\\proof If $p\\in M^4$ we have $\\nabla G(p)=\\big(-2x_1,2x_2,-2x_3,0,0,0\\big)$, while the components of $\\nabla F(p)$ are given by \n$$x_1\\frac{\\partial F}{\\partial x_1}(p)= 18x_1^8x_2^2(4x_1^2-3x_3^2)y_2^2 + 18x_2^{10}x_3^2y_3^2-2x_1^4x_2^2x_3^2(2x_2^4-x_2^2x_3^2-2x_3^4),$$\n$$x_2\\frac{\\partial F}{\\partial x_2}(p)=-18x_1^2x_3^{10}y_1^2-18x_2^8x_3^2(3x_1^2+4x_2^2)y_3^2 -2x_1^2x_2^4x_3^2(4x_1^2x_2^2-x_1^2x_3^2-2x_3^4),$$\n$$x_3\\frac{\\partial F}{\\partial x_3}(p)= 18x_1^2x_3^8 (3x_2^2+4x_3^2)y_1^2 - 18x_1^{10}x_2^2y_2^2 +2x_1^2x_2^2x_3^4(x_1^2x_2^2+4x_1^2x_3^2+4x_2^2x_3^2),$$\n$$\\frac{\\partial F}{\\partial y_1}(p)= 18x_1^2x_3^8(x_2^2+x_3^2)y_1,\\,\\,\\,\\,\\,\n\\frac{\\partial F}{\\partial y_2}(p)=18x_1^8 x_2^2(x_1^2-x_3^2)y_2$$\nand\n$$\\frac{\\partial F}{\\partial y_3}(p)=-18x_2^8(x_1^2+x_2^2)x_3^2y_3.$$\nThat  $M^4\\setminus (\\ell_+\\cup \\ell_-)$ is a smooth submanifold of ${\\mathbb R}^6$ and $\\ell_-\\cup \\ell_+$ is the singular set of $M^4$ is a consequence of the next two facts.\\vspace{1ex}\n\n\\noindent {\\bf Fact 1:}\n$\\nabla F(p)\\neq 0$ for all $p\\in M^4.$ \n\\proof If $\\nabla F(p)=0$ at $p=(x_1,x_2, x_3, y_1, y_2, y_3)$ then from $\\frac{\\partial F}{\\partial y_1}(p)=0$ it follows that  $y_1=0$, whereas \n$\\frac{\\partial F}{\\partial y_3}(p)=0$ implies that   $y_3=0$. Thus $y_2\\neq 0$, and hence   $x_3=x_1$ from $\\frac{\\partial F}{\\partial y_2}(p)=0$. Therefore $x_2=\\sqrt{2}x_1,$ and then  $0=\\frac{\\partial F}{\\partial x_2}(p)=-20\\sqrt{2}x_1^{11},$ which  contradicts the fact that $x_1>0$. \\vspace{1ex} \\\\\n\\noindent {\\bf Fact 2:} The subset $\\{p\\in M^4\\,:\\,\\nabla F(p)=a\\nabla G(p)\\,\\,\\,\\mbox{for some}\\,\\,\\,a\\in {\\mathbb R}-\\{0\\}\\}$ coincides with $\\ell_{-}\\cup \\ell_{+}.$ \n\\proof Assume that \n\\begin{equation} \\label{eq:nFnG}\\nabla F(p)=a\\nabla G(p)\\end{equation}  for some $a\\in {\\mathbb R}-\\{0\\}$. Equation  (\\ref{eq:nFnG})  gives us six equations, the last three of which yield $y_1=y_3=0$ and $x_3=x_1$. Since  $x_2^2=x_1^2+x_3^2,$ we obtain that $x_2=\\sqrt{2}x_1.$ Using this and the second of such equations we obtain that  $a=-10x_1^{10}.$ Finally, the first one implies that $y_2^2=1$. \\vspace{1ex} \\qed\n\n\\begin{proposition}\\label{prop.chaveb}  \nLet  $X_1,X_2,X_3\\colon M^4\\to{\\mathbb R}^6$ be defined by \n\\begin{equation*}\n\\begin{array}{lcl}\n\\displaystyle{X_1(p)=\\frac{1}{x_2^4}\\Big((x_2^4+x_2^2x_3^2+x_3^4)x_1y_1,x_2^5y_1, x_3^5y_1,x_2^4 A_1(p)},\\vspace{1ex}\\\\\\hspace*{13ex} 2 x_1^2x_2^2y_1y_2,(8x_3^2+2x_1^2)x_3^2y_1y_3\\Big), \\vspace{.2cm} \\\\\n\\displaystyle{X_2(p)=\\frac{1}{x_3^4}\\Big( x_1^5y_2,(x_1^4-x_1^2x_3^2+x_3^4)x_2y_2,x_3^5y_2} ,\\vspace{1ex}\\\\\\hspace*{13ex}(8x_1^2- 2x_2^2)x_1^2y_1y_2, x_3^4A_2(p),2 x_2^2x_3^2y_2y_3 \\Big), \\vspace{.2cm} \\\\\n\\displaystyle{X_3(p)=\\frac{1}{x_1^4}\\Big( x_1^5y_3,x_2^5y_3, (x_1^4+x_1^2x_2^2+x_2^4)x_3y_3,-2x_1^2x_3^2y_1y_3},\\vspace{1ex}\\\\\\hspace*{13ex}(8x_2^2-2 x_3^2)x_2^2y_2y_3,x_1^4A_3(p) \\Big),\n\\end{array}\n\\end{equation*}\n where \n\\begin{equation*}\n\\begin{array}{l}\n\\displaystyle{A_1(p) = \\frac{1}{x_2^4}(3x_2^4-x_3^4)y_1^2 - \\frac{x_1^6}{x_3^8}(3x_1^2-2x_3^2)y_2^2 + \\frac{x_2^4}{x_1^2x_3^4}(3x_1^2+2x_2^2)y_3^2} \\vspace{1ex}\\\\\\hspace*{10ex} \\displaystyle{+ \\frac{1}{9x_3^4}(5x_1^4+2x_2^2x_3^2)}, \n\\end{array}\n\\end{equation*}\n\\begin{equation*}\n\\begin{array}{l}\n\\displaystyle{A_2(p) =-\\frac{x_3^4}{x_1^4x_2^2}(3x_2^2 + 2x_3^2) y_1^2 -\\frac{1}{x_3^4}(x_1^4 - 3x_3^4)y_2^2 - \\frac{x_2^6}{x_1^8}(2x_1^2+3x_2^2)y_3^2} \\vspace{1ex}\\\\\\hspace*{10ex}\\displaystyle{-\\frac{1}{9x_1^4}(5x_2^4-2x_1^2x_3^2)},\n\\end{array}\n\\end{equation*}\n\\begin{equation*}\n\\begin{array}{l}\n\\displaystyle{A_3(p) = \\frac{x_3^6}{x_2^8}(2x_2^2+3x_3^2)y_1^2 + \\frac{x_1^4}{x_2^4x_3^2}(2x_1^2-3x_3^2)y_2^2 + \\frac{1}{x_1^4}(3x_1^4-x_2^4)y_3^2} \\vspace{1ex}\\\\\\hspace*{10ex}\\displaystyle{+ \\frac{1}{9x_2^4}(5x_3^4+2x_1^2x_2^2)}.\n\\end{array}\n\\end{equation*}\nThen the following assertions hold:\n\\begin{itemize}\n\\item[(i)]  $X_1(p),X_2(p),X_3(p)$ are linearly independent for all $p\\in~\\tilde M^4$.\n\\item[(ii)]   $\\{p\\in M^4;X_1(p)=0\\}=\\ell_-\\cup \\ell_+=\\{p\\in M^4;X_3(p)=0\\}$.\n\\item[(iii)] The vector fields  $X_1,X_2,X_3$ are everywhere tangent to  $\\tilde{M}^4$ and the curves \n $\\gamma_\\pm\\colon {\\mathbb R}\\to {\\mathbb R}^6$ given by  $\\gamma_\\pm(t)=(e^t,\\sqrt{2}e^t,e^t,0,\\pm 1,0)$,\n are integral curves of $X_2$ with $\\gamma_\\pm({\\mathbb R})=\\ell_\\pm$.\n \\item[(iv)] $[X_i, X_j]=0$ on $\\tilde{M}^4$ for all $1\\leq i\\neq j\\leq 3$.\n \\end{itemize}\n \\end{proposition}\n \\proof First notice that  $X_2(p)=0$ if and only if  $y_2=0$ and $A_2(p)=0$. Since $A_2(p)<0$ whenever $y_2=0$, it follows that\n $X_2(p)\\neq 0$ for all $p~\\in~M^4$. \n\nNow observe that  $X_1(p)=0$ if and only if $y_1=0$ and $A_1(p)=0$.  Thus, if  $p=(x_1, x_2, x_3, y_1, y_2, y_3)$ is such that $X_1(p)=0$ then  \n\\begin{equation*}\n\\left\\{ \\begin{array}{l}\nay_2^2+by_3^2 =c,\\vspace{.2cm}\\\\\ndy_2^2+ey_3^2 =f,\\vspace{.2cm}\\\\\nx_2^2=x_1^2+x_3^2,\n\\end{array}\\right.\n\\end{equation*}\n where\n$$a=9x_1^8x_2^4(3x_1^2-2x_3^2),\\,\\,\\,\\,b=-9x_2^8x_3^4(3x_1^2+2x_2^2),\\,\\,\\,\\, c= x_1^2x_2^4x_3^4(5x_1^4+2x_2^2x_3^2),$$\n$$ d=9x_1^8x_2^2(x_1^2-x_3^2),\\,\\,\\,\\, e=-9x_2^8x_3^2(x_1^2+x_2^2)$$\nand \n$$  f= x_1^2x_2^2x_3^2(2x_1^2x_2^4-2x_1^2x_3^2-2x_2^2x_3^4-x_1^2x_2^2x_3^2).$$\nSuch system has a unique solution given by\n\\begin{equation*}\ny_2^2=\\frac{x_3^8(x_1^2+x_2^2)^2}{9x_1^{12}} \\quad \\quad \\mbox{and} \\quad \\quad y_3^2=-\\frac{(x_1^2-x_3^2)^2}{9x_1^4}.\n\\end{equation*}\nThus we must have $y_3=0$, and hence  $x_1=x_3$ and $y_2=\\pm 1.$  It follows that the subset  $\\{p\\in M^4;X_1(p)=0\\}$  coincides with $\\ell_-\\cup \\ell_+$.\n\nIn a similar way one shows that the subset  $\\{p\\in M^4;X_3(p)=0\\}$  coincides with $\\ell_-\\cup \\ell_+$, and the proof of $(ii)$ is completed.\n\n\nTo prove $(i)$, first notice that  $X_1(p),X_2(p),X_3(p)$ are  pairwise linearly independent. This already implies that if $\\lambda_1,\\lambda_2,\\lambda_3\\in {\\mathbb R}$ are such that \n\\begin{equation}\\label{combina.linear}\n\\lambda_1X_1(p)+\\lambda_2X_2(p)+\\lambda_3X_3(p)=0\n\\end{equation}\nthen either $\\lambda_1=\\lambda_2=\\lambda_3=0$ ou $\\lambda_1\\neq 0,\\lambda_2\\neq 0$ e $\\lambda_3\\neq 0.$ We will show that the last possibility can not occur. \n\nEquation (\\ref{combina.linear}) gives the system of equations \n\\begin{displaymath}\n\\left\\{ \\begin{array}{ll}\nx_2^2x_3^4y_1\\lambda_1+x_1^6y_2\\lambda_2=0 \\vspace{.2cm}\\\\\nx_1^4x_3^2y_2\\lambda_2+x_2^6y_3\\lambda_3=0 \\vspace{.2cm}\\\\\n\\displaystyle{\\big[ A_1(p)-\\frac{2}{x_2^4}(3x_2^4+x_3^4+2x_2^2x_3^2)y_1^2\\big]\\lambda_1=0}\\vspace{.2cm} \\\\\n\\displaystyle{\\big[A_2(p)-\\frac{2}{x_3^4}(x_1^4+3x_3^4-2x_1^2x_3^2)y_2^2\\big]\\lambda_2=0} \\vspace{.2cm}\\\\\n\\displaystyle{\\big[ A_3(p)-\\frac{2}{x_1^4}(3x_1^4+x_2^4+2x_1^2x_2^2)y_3^2 \\big]\\lambda_3=0.}\n\\end{array}\\right.\n\\end{displaymath}\nThus, it suffices to prove that the system of equations\n\\begin{displaymath}\n\\left\\{ \\begin{array}{ll}\n\\displaystyle{ A_1(p)-\\frac{2}{x_2^4}(3x_2^4+x_3^4+2x_2^2x_3^2)y_1^2=0}\\vspace{.2cm} \\\\\n\\displaystyle{A_2(p)-\\frac{2}{x_3^4}(x_1^4+3x_3^4-2x_1^2x_3^2)y_2^2=0 }\\vspace{.2cm}\\\\\n \\displaystyle{A_3(p)-\\frac{2}{x_1^4}(3x_1^4+x_2^4+2x_1^2x_2^2)y_3^2 =0}\n\\end{array}\\right.\n\\end{displaymath}\nhas no solutions for $p=(x_1, x_2, x_3, y_1, y_2, y_3)\\in \\tilde{M}^4$. We write the preceding system as a linear system \n\\begin{displaymath}\n\\left\\{ \\begin{array}{rcl}\na_1y_1^2+a_2y_2^2+a_3y_3^2=a_4 \\vspace{.2cm}\\\\\nb_1y_1^2+b_2y_2^2+b_3y_3^2=b_4 \\vspace{.2cm}\\\\\nc_1y_1^2+c_2y_2^2+c_3y_3^2=c_4\n\\end{array}\\right.\n\\end{displaymath}\nin the variables $y_1^2,y_2^2$ and $y_3^2$, where\n\\begin{equation*}\n\\begin{array}{lll}\na_1= 9x_1^2x_3^8(3x_1^4+10x_2^2x_3^2), \\hspace{.6cm} & b_1= 9x_1^4x_3^8(3x_2^2+2x_3^2), \\vspace{.2cm}\\\\\n\na_2= 9x_1^8x_2^4(3x_1^2-2x_3^2),  & b_2= 9x_1^8x_2^2(3x_2^4-10x_1^2x_3^2), \\vspace{.2cm}\\\\\n\na_3= -9x_2^8x_3^4(3x_1^2+2x_2^2), & b_3=9x_2^8x_3^4(2x_1^2+3x_2^2), \\vspace{.2cm}\\\\\n\na_4= x_1^2x_2^4x_3^4(5x_1^4+2x_2^2x_3^2), & b_4= -x_1^4x_2^2x_3^4(5x_2^4-2x_1^2x_3^2), \n\\end{array}\n\\end{equation*}\nand\n\\begin{equation*}\n\\begin{array}{lll}\n c_1= 9x_1^4x_3^8(2x_2^2+3x_3^2),\\,\\,\\,\\,\\,\\,\\,\nc_2=9x_1^8x_2^4(2x_1^2-3x_3^2),\\vspace{.2cm}\\\\\n\n c_3=-9x_2^8x_3^2(3x_3^4+10x_1^2x_2^2),\\,\\,\\,\\,\\,\\,\\,\nc_4= -x_1^4x_2^4x_3^2(5x_3^4+2x_1^2x_2^2).\n\\end{array}\n\\end{equation*}\nSince\n\\begin{equation*}\n\\begin{array}{l}\n\\det\n\\left(\\!\\!\\begin{array}{ccc}\na_1 & a_2 & a_3 \\\\\nb_1 & b_2 & b_3 \\\\\nc_1 & c_2 & c_3\n\\end{array}\\!\\right)=656100x_1^{12}x_2^{12}x_3^{12}(x_3^4+x_1^2x_2^2)(x_1^2-x_2^2+x_3^2)=0\\vspace{.2cm}\\\\\n\n\\det\n\\left(\\!\\!\\begin{array}{ccc}\na_1 & a_2 & a_4 \\\\\nb_1 & b_2 & b_4 \\\\\nc_1 & c_2 & c_4\n\\end{array}\\!\\right)=-29160x_1^{14}x_3^{18}x_2^6(x_3^4+x_1^2x_2^2)\\neq 0,\n\\end{array}\n\\end{equation*}\nsuch system has no solutions. Thus $(i)$ is proved. \n\n\n\nNow, for $p\\in M^4$ we have \n\\begin{equation*}\n\\begin{array}{l}\n\\displaystyle{\\langle \\nabla F(p),X_1(p)\\rangle=\\frac{10y_1}{x_2^4}(x_2^4+x_3^4)F(p)=0=\\langle \\nabla G(p),X_1(p)\\rangle}\\vspace{.2cm} \\\\\n\\displaystyle{\\langle \\nabla F(p),X_2(p)\\rangle=\\frac{10y_2}{x_3^4}(x_1^4+x_3^4)F(p)=0=\\langle \\nabla G(p),X_2(p)\\rangle}\\vspace{.2cm} \\\\\n\\displaystyle{\\langle \\nabla F(p),X_3(p)\\rangle=\\frac{10y_3}{x_1^4}(x_1^4+x_2^4)F(p)=0= \\langle \\nabla G(p),X_3(p)\\rangle},\n\\end{array}\n\\end{equation*}\n hence $X_1,X_2,X_3$ are everywhere tangent to  $\\tilde{M}^4$. That  $\\gamma_\\pm$ is an integral curve of $X_2$  follows by \nchecking that  $X_2(\\gamma_\\pm(t))=(e^t,\\sqrt{2}e^t,e^t,0,0,0)=\\gamma'_\\pm(t)$.  Finally, a straightforward computation gives\n\\begin{equation*}\n\\begin{array}{l}\n\\displaystyle{[X_1,X_2](p)=\\Big(0,0,0,\\frac{10y_2}{9x_2^2x_3^{10}}F(p),\\frac{10y_1}{9x_1^6x_2^4x_3^2}F(p),0\\Big)=0} \\vspace{.2cm} \\\\\n\n\\displaystyle{[X_1,X_3](p)=\\Big(0,0,0,-\\frac{10y_3}{9x_1^4x_2^2x_3^6}F(p),0,-\\frac{10y_1}{9x_1^2x_2^{10}}F(p)\\Big)=0} \\vspace{.2cm} \\\\\n\n\\displaystyle{[X_2,X_3](p)=\\Big(0,0,0,0,\\frac{10y_3}{9x_1^{10}x_3^2}F(p),\\frac{10y_2}{9x_1^2x_2^6x_3^4}F(p)\\Big)=0}. \\qed\n\\end{array} \n\\end{equation*}\n\n\n\n\n\n\n \n\nThe proof of the next proposition is straightforward.\n\n\\begin{proposition}\\label{prop:involutions} $(i)$  For each  $\\epsilon=(\\epsilon_1, \\epsilon_2, \\epsilon_3)$,  $\\epsilon_j\\in \\{-1, 1\\}$ for $1\\leq j\\leq 3$, the map $\\Phi^{\\epsilon}\\colon \\tilde{M}^4\\to \\tilde{M}^4$  given by \n$$\\Phi^{\\epsilon}(x_1, x_2, x_3, y_1, y_2, y_3)=(x_1, x_2, x_3, \\epsilon_1y_1, \\epsilon_2y_2, \\epsilon_3y_3)$$\nsatisfies $\\Phi^{\\epsilon}_*X_j(p)=\\epsilon_jX_j(\\Phi^{\\epsilon}(p))$ for all $p\\in \\tilde{M}^4$.\\vspace{1ex}\\\\\n$(ii)$ The map $\\Psi\\colon \\tilde{M}^4\\to \\tilde{M}^4$  given by \n$$\\Psi(x_1, x_2, x_3, y_1, y_2, y_3)=\\bigg(x_3, x_2, x_1, \\frac{x_2^4}{x_1^4}y_3, \\frac{x_1^4}{x_3^4}y_2,\\frac{x_3^4}{x_2^4}y_1\\bigg)$$\nsatisfies \n$$\\Psi_*X_1(p)=X_3(\\Psi(p)),\\;\\;\\Psi_*X_2(p)=X_2(\\Psi(p))\\;\\;\\mbox{and}\\;\\;\\Psi_*X_3(p)=X_1(\\Psi(p))$$\n for all $p=(x_1, x_2, x_3, y_1, y_2, y_3)\\in \\tilde{M}^4$.\\vspace{1ex}\\\\\n$(iii)$ The maps $\\Psi$ and  $\\Phi^{\\epsilon}$, $\\epsilon\\in \\{-1, 1\\}\\times \\{-1, 1\\}\\times\\{-1, 1\\}$, generate a group of involutions\nof $\\tilde{M}^4$ isomorphic to $\\mathbb{Z}_2\\times \\mathbb{Z}_2\\times \\mathbb{Z}_2\\times \\mathbb{Z}_2$ that preserves the distribution ${\\cal D}$ spanned by the vector fields $X_1, X_2$ and $X_3$.\n\\end{proposition}\n\n\n\n\n\n\n\\noindent \\emph{Proof of Theorem \\ref{thm:minimalceq0}:} \nFirst we associate to each leaf $\\sigma$  of ${\\cal D}$ a  covering map $\\phi_\\sigma\\colon U_\\sigma\\to \\sigma$ from a simply-connected open subset $U_\\sigma\\subset {\\mathbb R}^3$ and a minimal immersion $f_\\sigma\\colon U_\\sigma\\to {\\mathbb R}^4$ with three distinct principal curvatures whose induced metric is conformally flat. \n\nFor any $q\\in \\tilde M^4$ and for $1\\leq i\\leq 3$ denote  by $\\tau_q^i\\colon J_q^i\\to \\tilde{M}^4$ the maximal integral curve of $X_i$ through $q$, that is, $0\\in J_q^i$, $\\tau^i_q(0)=q$,  $(\\tau^i_q)'(t)=X_i(\\tau^i_q(t))$ for all $t\\in J_q^i$, and $J_q^i$ is maximal with these properties. Let $${\\cal D}(X_i)=\\{(t, q)\\in {\\mathbb R}\\times \\tilde{M}^4\\,:\\, t\\in J^i_q\\}$$ and let $\\varphi^i\\colon  {\\cal D}(X_i)\\to \\tilde{M}^4$ be the flow of $X_i$, given by $\\varphi^i(t, q)=\\tau^i_q(t)$. For a fixed $p\\in \\sigma$ define $U_\\sigma=U_\\sigma(p)$ by\n$$U_\\sigma=\\{(u_1, u_2, u_3)\\,:\\, u_1\\in J^1_p, \\,u_2\\in J^2_{\\varphi^1(u_1, p)}, \\, u_3\\in J^3_{\\varphi^2(u_2,\\varphi^1(u_1, p))}\\}$$\nand $\\phi_\\sigma=\\phi^p_\\sigma$ by\n$$\\phi_\\sigma(u_1, u_2, u_3)=\\varphi^3(u_3, \\varphi^2(u_2,\\varphi^1(u_1, p))).$$\nThen  $0\\in U_\\sigma$,   $\\phi_\\sigma(0)=p$,  and for all $u\\in U_\\sigma$ we have\n\\begin{equation*\n\\frac{\\partial \\phi_\\sigma}{\\partial u_i}(u)=X_i(\\phi_\\sigma(u)), \\,\\, \\,\\,\\, 1\\leq i\\leq 3.\n\\end{equation*} \n  \nWe claim that $\\phi_\\sigma$ is a covering map onto $\\sigma$. Given $x\\in\\sigma$, let $\\tilde B_{2\\epsilon}(0)$ be an open \nball of radius $2\\epsilon$ centered at the origin such that\n$\\phi_\\sigma^x|_{\\tilde B_{2\\epsilon}(0)}$ is a diffeomorphism onto \n$B_{2\\epsilon}(x)=\\phi_\\sigma^x(\\tilde B_{2\\epsilon}(0))$. Since\n\\begin{equation} \\label{eq:psix0}\n\\phi_\\sigma^p(t+s)=\\varphi^3(t_3,\\varphi^2(t_2,\\varphi^1(t_1, \\phi_\\sigma^p(s))))=\\phi_\\sigma^{\\phi_\\sigma^p(s)}(t)\n\\end{equation} \nwhenever both sides are defined, where $t=(t_1,t_2,t_3)$ \nand $s=(s_1,s_2,s_3)$, if $x=\\phi_\\sigma^p(s)$, $s=(s_1,s_2, s_3)\\in U_\\sigma$, then for any \n$y=\\phi_\\sigma^x(t)\\in B_{2\\epsilon}(x)$, $t=(t_1,t_2,t_3)\\in \\tilde B_{2\\epsilon}(0)$, we have\n$$ y=\\phi_\\sigma^x(t)=\\phi_\\sigma^{\\phi_\\sigma^p(s)}(t)=\\phi_\\sigma^p(s+t).$$\nThis shows that  $B_{2\\epsilon}(x)\\subset \\phi_\\sigma^p(U_\\sigma)$ if  $x\\in \\phi_\\sigma^p(U_\\sigma)$, hence $\\phi_\\sigma^p(U_\\sigma)$ is open in $\\sigma$. But since $y=\\phi_\\sigma^x(t)$ if and only if $x=\\phi_\\sigma^y(-t)$, as follows from (\\ref{eq:psix0}), the same argument shows that\n$x\\in \\phi_\\sigma^p(U_\\sigma)$ if $y\\in \\phi_\\sigma^p(U_\\sigma)$ for some $y\\in B_{2\\epsilon}(x)$, and hence $\\sigma\\setminus \\phi_\\sigma^p(U_\\sigma)$ is also open. It follows that $\\phi_\\sigma^p$ is onto $\\sigma$.\n\n\n\n\nNow, for any $x\\in \\sigma$ write \n$$\n(\\phi_\\sigma^p)^{-1}(x)=\\cup_{\\alpha\\in A}\\tilde x_\\alpha,\n$$\n and for each $\\alpha\\in A$ let $\\tilde B_{2\\epsilon}(\\tilde x_\\alpha)$ denote \nthe open ball of radius $2\\epsilon$ centered at $\\tilde x_\\alpha$. Define \na map $\\psi_\\alpha\\colon B_{2\\epsilon}(x)\\to\\tilde B_{2\\epsilon}(\\tilde x_\\alpha)$\nby \n$$\n\\psi_\\alpha(y)=\\tilde x_\\alpha+(\\phi_\\sigma^x)^{-1}(y).\n$$\nBy (\\ref{eq:psix0}) we have \n\\bea\n\\phi_\\sigma^p(\\psi_\\alpha(y))\\!\\!\\!&=&\\!\\!\\!\\phi_\\sigma^p(\\tilde x_\\alpha+(\\phi_\\sigma^x)^{-1}(y))\\\\\n\\!\\!\\!&=&\\!\\!\\!\\phi_\\sigma^{\\phi_\\sigma^p(\\tilde x_\\alpha)}((\\phi_\\sigma^x)^{-1}(y))\\\\\n\\!\\!\\!&=&\\!\\!\\!\\phi_\\sigma^x((\\phi_\\sigma^x)^{-1}(y))\\\\\n\\!\\!\\!&=&\\!\\!\\!y\n\\eea\nfor all $y\\in B_{2\\epsilon}(x)$. Thus $\\phi_\\sigma^p$ is a diffeomorphism \nfrom $\\tilde B_{2\\epsilon}(\\tilde x_\\alpha)$ onto \n$B_{2\\epsilon}(x)$ having $\\psi_\\alpha$ as its inverse. \nIn particular, this implies that $\\tilde B_\\epsilon(\\tilde x_\\alpha)$ and \n$\\tilde B_\\epsilon(\\tilde x_\\beta)$ are disjoint if $\\alpha$ and \n$\\beta$ are distinct indices in $A$. Finally, it remains to check that \nif $\\tilde y\\in (\\phi_\\sigma^p)^{-1}(B_\\epsilon(x))$ then \n$\\tilde y\\in \\tilde B_\\epsilon(\\tilde x_\\alpha)$ for some $\\alpha\\in A$. \nThis follows from the fact that \n$$\n\\phi_\\sigma^p(\\tilde y-(\\phi_\\sigma^x)^{-1}(\\phi_\\sigma^p(\\tilde y)))=\\phi_\\sigma^{\\phi_\\sigma^p(\\tilde y)}\n(-(\\phi_\\sigma^x)^{-1}(\\phi_\\sigma^p(\\tilde y)))=x.\n$$\nFor the last equality, observe from (\\ref{eq:psix0})  that for all \n$x, y\\in \\sigma$ we have that $\\phi_\\sigma^x(t)=y$ if and only if $\\phi_\\sigma^y(-t)=x$.\n\n\n \nWriting $\\phi_\\sigma=(v_1,v_2,v_3,\\alpha_1,\\alpha_2,\\alpha_3)$, it follows that $\\phi_\\sigma$ satisfies  (\\ref{flat.min.reduz.}), as well as (\\ref{eq:vis}) and  (\\ref{equ.chave}). Defining $h_{ij}=\\frac{1}{v_i}\\frac{\\partial v_j}{\\partial u_i}$, $1\\leq i\\neq j\\leq 3$, and $V=(V_1, V_2, V_3)$ by (\\ref{holo.flat.min.2}),  it follows from  Proposition~\\ref{flat.min.reduz.result.} that the triple $(v, h, V)$, where $v=(v_1,v_2, v_3)$ and $h=(h_{ij})$,  satisfies (\\ref{sistema-hol}), and hence gives rise to a \n minimal conformally flat hypersurface $f_\\sigma\\colon U_\\sigma\\to {\\mathbb R}^4$ with three distinct principal curvatures by Corollary \\ref{le:asspair}. \n \n Given two distinct leaves $\\sigma$ and $\\tilde \\sigma$  of ${\\cal D}$, the corresponding immersions   $f_\\sigma$ and $f_{\\tilde \\sigma}$ are  congruent if and only if there exists a diffeomorphism $\\psi\\colon U_\\sigma\\to U_{\\tilde \\sigma}$ such that \n $$\\psi^*I_{\\tilde\\sigma}=I_\\sigma\\,\\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\psi^*I\\!I_{\\tilde\\sigma}=I\\!I_\\sigma$$\n where $I_\\sigma$ and $I\\!I_{\\sigma}$ are the first and second fundamental formulae of $f_\\sigma$, respectively, and $I_{\\tilde\\sigma}$, $I\\!I_{\\tilde\\sigma}$ are those of $f_{\\tilde \\sigma}$. A long but straightforward computation shows that, up to a translation,  either $\\psi$ coincides with the map given by\n $$\\psi_\\epsilon(u_1,u_2,u_3)=(\\epsilon_1u_1, \\epsilon_2u_2, \\epsilon_3u_3)$$ \n for some $\\epsilon=(\\epsilon_1, \\epsilon_2, \\epsilon_3)$ with $\\epsilon_i\\in \\{-1, 1\\}$ for $1\\leq i\\leq 3$, or it is the composition of such a map with the map given by\n $$\\theta(u_1, u_2, u_3)=(u_3, u_2, u_1).$$\n It is easy to check that this is the case if and only if  there exists $\\Theta\\in G$ such that  $\\phi_{\\tilde \\sigma}\\circ \\psi=\\Theta\\circ \\phi_{\\sigma}$. \n \n \n \n \n \n \n Now let $f\\colon M^3\\to {\\mathbb R}^4$ be a  minimal isometric immersion  with three distinct principal curvatures of a simply connected\n conformally flat Riemannian manifold. We shall prove that either $f(M^3)$ is an open subset of the cone over a Clifford torus in ${\\mathbb S}^3$ or there exist a leaf $\\sigma$ of ${\\cal D}$ and  a local diffeomorphism $\\rho\\colon M^3\\to V$ onto an open subset $V\\subset U_\\sigma$ \n such that $f$ is congruent to  $f_\\sigma\\circ \\rho$.\n \n First we associate to $f$ a map $\\phi_f\\colon M^3\\to M^4\\subset {\\mathbb R}^6$ as follows.\n Fix a unit normal vector field $N$ along $f$ and denote by $\\lambda_1<\\lambda_2<\\lambda_3$ the distinct principal curvatures of $f$ with respect to $N$. For each $1\\leq j\\leq 3$, the eigenspaces $E_{\\lambda_j}=\\ker (A-\\lambda_j I)$ associated to $\\lambda_j$, where $A$ is the shape operator with respect to $N$ and $I$ is the identity endomorphism, form a field of directions along $M^3$, and since $M^3$ is simply connected we can find a smooth global unit vector field $Y_j$ along $M^3$ such that $\\mbox{span}\\{Y_j\\}=E_{\\lambda_j}$. \nLet the functions $v_1, v_2, v_3$ be defined on $M^3$ by\n\\begin{equation} \\label{eq:globalvj}v_j=\\sqrt{\\frac{\\delta_j}{(\\lambda_j-\\lambda_i)(\\lambda_j-\\lambda_k)}},\\,\\,\\,\\delta_j=\\frac{(\\lambda_j-\\lambda_i)(\\lambda_j-\\lambda_k)}{|(\\lambda_j-\\lambda_i)(\\lambda_j-\\lambda_k)|}, \\,\\,\\,i\\neq j\\neq k\\neq i,\\end{equation} \nand let $\\alpha_1, \\alpha_2,\\alpha_3$ be given   by\n$$\\alpha_1=\\frac{v_1}{v_2}Y_1(v_2), \\,\\,\\,\\,\\alpha_2=\\frac{v_2}{v_3}Y_2(v_3)\\,\\,\\,\\mbox{and}\\,\\,\\,\\alpha_3=\\frac{v_3}{v_1}Y_3(v_1).$$ \nDefine $\\phi_f\\colon M^3\\to {\\mathbb R}^6$ by $\\phi_f=(v_1,v_2,v_3,\\alpha_1,\\alpha_2,\\alpha_3)$. \n\nNow, it follows from  Theorem \\ref{main3} that each point $p\\in M^3$ has a connected open neighborhood $U\\subset M^3$ endowed with principal coordinates $u_1, u_2, u_3$ such that the pair  $(v,V)$ associated to $f$  satisfies (\\ref{eq:vis}) and \n(\\ref{holo.flat.min.2}). Let $\\phi_U\\colon U\\to {\\mathbb R}^6$ be given by $\\phi_U=(v_1,v_2,v_3,\\alpha_1,\\alpha_2,\\alpha_3)$,\nwith $(\\alpha_1,\\alpha_2,\\alpha_3)=\\big(\\frac{1}{v_2}\\frac{\\partial v_2}{\\partial u_1},\\frac{1}{v_3}\\frac{\\partial v_3}{\\partial u_2},\\frac{1}{v_1}\\frac{\\partial v_1}{\\partial u_3}\\big)$. It is easy to check that $\\phi_f|_U=\\Theta\\circ \\phi_U$ for some $\\Theta\\in G$. \nOn the other hand, by  Proposition  \\ref{flat.min.reduz.result.} we have that $\\phi_U$  \n satisfies (\\ref{flat.min.reduz.}), as well as the algebraic equation \n(\\ref{equ.chave}).  \nIt follows  that $\\phi_U(U)\\subset M^4$ and that \n$$\\frac{\\partial \\phi_U}{\\partial u_i}(u)=X_i(\\phi_U(u)), \\,\\,\\, \\,\\,\\, 1\\leq i\\leq 3,$$\nfor all $u\\in U$. \nTherefore either $\\phi_U(U)$ is an open subset of a leaf $\\sigma_{U}$ of the distribution ${\\cal D}$ on $\\tilde M^4$ spanned by $X_1, X_2, X_3$, or $\\phi_U(U)$ is an open segment of either $\\ell_+$ or $\\ell_-$. If the latter possibility holds for some open subset $U\\subset M^3$, then $v_1=v_3$ on $U$, hence $\\lambda_2=0$ on $U$. By analyticity, $\\lambda_2=0$ on $M^3$, and hence Proposition \\ref{thm:minimalpczero} implies that  $f(M^3)$ is an open subset of a  cone over a Clifford torus in an umbilical hypersurface $\\mathbb{Q}^{3}(\\tilde c)\\subset {\\mathbb R}^4$, $\\tilde c>0$.\n\n\n\n\n\nOtherwise we have that each point $p\\in M^3$ has an open neighborhood $U\\subset M^3$ such that\n$\\phi_f(U)$ is an open subset of a leaf $\\sigma_{U}$ of  ${\\cal D}$. It follows that $\\phi_f(M^3)$ is an open subset of a leaf $\\sigma$ of  ${\\cal D}$. If $\\rho\\colon M^3\\to U_\\sigma$ is a lift of $\\phi_f$ with respect to $\\phi_\\sigma$, that is, $\\phi_f=\\phi_\\sigma\\circ \\rho$, then $\\rho$ is a local diffeomorphism such that $f$ and $f_\\sigma\\circ \\rho$ have the same first and second fundamental forms.\nTherefore $f$ is congruent to $f_\\sigma\\circ \\rho$.\\qed\n \n \n \n \n \n \n \n  \n\n\n\n\n\n\n ","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nLast decade witnessed an increased effort in the deployment of automated vehicle (AV) technology because it can enhance passenger safety, improve travel mobility, reduce fuel consumption, and maximize traffic throughput \\cite{VanderWerfShladover02, Askari_2016, Li_AAP_2017}. Early deployment dates back to research projects, such as DARPA challenges \\cite{Campbell_2010}, PATH program \\cite{Rajam_Shlad_2001}, Grand Cooperative Driving Challenges \\cite{GCDCIntro2011}. Meanwhile, the automotive industry made achievements in equipping production vehicles with advanced driver assistant systems (ADAS) technology. Currently attentions are attracted to AVs with higher levels of autonomy \\cite{SAE_J3016_2016}.\n\nThe ultimate objective is to navigate and guide AVs to destinations following driving conventions and rules.\nThe key components include perception, estimation, planning and control. Perception algorithms collect and process raw sensor (camera, radar, lidar, etc.) data, and convert them to human-readable physical data. Estimation algorithms \\cite{Farrell_2017, Wischnewski_2019, Bersani_AEIT_2019} typically apply sensor fusion technique to obtain clean and sound vehicle state estimations based on sensor characteristics. Planning \\cite{Karaman_IJRR_2011, Paden_TIV_2016} can be further divided into mission planning (or route planning), behavior planning (or decision making), and motion planning: i) mission planning algorithms select routes to destinations through given road networks based on requirements; ii) behavior planning generates appropriate driving behaviors in real-time according to driving conventions and rules, to guide the interaction with other road-users and infrastructures; iii) motion planning translates the generated behavior primitives into a trajectory based on vehicle states. Control algorithms utilize techniques from control theory \\cite{Karl_Richard_Feedback, Khalil_NC, Luenberger_1997, Ioannou_Sun_RAC, Yuri_SMC} that enable vehicles to follow aforementioned trajectories in longitudinal and lateral directions.\n\n\\IEEEpubidadjcol\n\nVehicle control performance highly depends on perception and estimation outcomes, among which lane perception and lane estimation \\cite{AHuang_phd, Fakhfakh_JAIHC_2020} are crucial. In longitudinal control, estimated lanes are needed to identify preceding in-path vehicles, and obtain maximum allowable speed based on road curvature at a preview distance. In lateral control, estimated lanes serve as desired paths for controllers to follow. In practice, lanes are typically perceived by cameras in real-time when high-resolution GPS or high-definition map are not installed. Perception algorithms detect lanes using techniques from computer vision or machine learning and then characterize them as polynomial functions \\cite{Xu_ECCV_2020, Liu_ICCV_2021_CondLaneNetAT, Wang_ECCV_2020, Tabelini_2021} in vehicle body-fixed frame. However, representing lanes as polynomial functions brings great inconvenience to practical estimation and control algorithms. On the one hand, estimation algorithms usually predict polynomial coefficients based on a nominal model, among which Kalman filter \\cite{Klmn_1960, Humpherys_2012, Zarchan_KF_2015, Pei_KF_2019} is the most famous. However, it is infeasible to mathematically derive such a model that characterizes the evolution of coefficients for polynomial functions. This is because: i) vehicle body-fixed frame is translating and rotating as the vehicle moves, and ii) polynomial function representation does not preserve the form in coordinate transformation.\nOn the other hand, iterative methods need to be applied when control algorithms extract attributes (curvature, heading, etc.) from polynomial function representation of lanes at a preview distance.\n\nThis paper attempts to resolve this problem by characterizing lanes with arc-length-based parametric representation. To ensure compatibility with current platforms, we still assume that perception algorithms provide polynomial function representation of lanes in vehicle body-fixed frame.\nThe major contributions are as follows. Firstly, we mathematically derived a transformation and its inverse that reveal the relationship between polynomial function representation and arc-length-based parametric representation. Secondly, it is shown that such parametric representation preserves the form in coordinate transformation. Therefore, we are able to derive a mathematical model to characterize the evolution of coefficients that can be used for prediction during locomotion. Moreover, to simulate the whole process of lane perception, lane estimation and control, we set up a novel simulation framework that includes: i) usage of curvature as a function of arc length to represent lanes based on differential geometry, ii) derivation of coefficients for polynomial function representation to simulate perception in vehicle body-fixed frame, and iii) transformation from absolute dynamics in earth-fixed frame to relative dynamics observable in camera-based control.\n\n\nThis paper is organized follows. In Section~\\ref{sec:prelim}, we start with preliminaries on coordinate transformation, vectorization operator and fundamental theory on curves. In Section~\\ref{sec:curv_repr}, we provide theoretical results on curve representations, and derive transformations between polynomial function representation and arc-length-based parametric representation.\nSection~\\ref{sec:veh_ctrl_setup} investigates camera-based vehicle control problem, and applies theoretical results in Section~\\ref{sec:curv_repr} to obtain an intrinsic linear model for lane estimation. Also, the dynamics describing absolute position and orientation in earth-fixed frame are transformed into those describing relative position and orientation observed in the camera field-of-view (FOV). A controller is introduced from \\cite{Wubing_LC_TIV_2022} to demonstrate that prediction based on the proposed lane estimation approach is adequate for control algorithms. In Section~\\ref{sec:res}, we first show how we set up simulation framework, and then conduct experiments to demonstrate the efficacy of the simulation framework and lane estimation approach. In Section~\\ref{sec:conclusion}, conclusions are drawn and future research directions are pointed out.\n\n\\section{Preliminaries\\label{sec:prelim}}\nIn this section, preliminaries are provided. In Section~\\ref{sec:coord_transf_gen}, we provide the coordinate transformation applied extensively in later chapters. In Section~\\ref{sec:vec_op}, the definition and theorem on vector operator of matrices are introduced. In Section~\\ref{sec:curv_repr_def}, polynomial function representation and arc-length-based parametric representation are discussed to approximate curves based on Taylor series.\n\n\\subsection{Coordinate Transformation \\label{sec:coord_transf_gen}}\n\nGiven two coordinate systems ($O$-$xyz$ and $Q$-$\\tau\\eta z$) as shown in Fig.~\\ref{fig:gen_coord_transf}, where the $Q$-$\\tau\\eta z$ frame is obtained by translating the $O$-$xyz$ frame with vector $\\pvec{OQ}$, and then rotating with angle $\\psi$, we recall the following theorem.\n\n\\begin{theorem}[Change of Coordinates]\\label{thm:gen_coord_transf}\n  Suppose the coordinates of $Q$ expressed in $O$-$xyz$ frame are\n  \\begin{align}\n    \\boldsymbol{d} &=\n    \\begin{bmatrix}\n      x_{\\rm Q} & y_{\\rm Q}\n    \\end{bmatrix}^{\\top}\\,,\n  \\end{align}\n  and the coordinates of an arbitrary point $P$ are\n  \\begin{align}\n    \\boldsymbol{r} &=\n    \\begin{bmatrix}\n      x_{\\rm P} & y_{\\rm P}\n    \\end{bmatrix}^{\\top}\\,,&\n    \\hat{\\boldsymbol{r}} &=\n    \\begin{bmatrix}\n      \\tau_{\\rm P} & \\eta_{\\rm P}\n    \\end{bmatrix}^{\\top}\\,,\n  \\end{align}\n  expressed in the $O$-$xyz$ and $Q$-$\\tau\\eta z$ frame, respectively, then one can change coordinates from $Q$-$\\tau\\eta z$ frame to $O$-$xyz$ frame by\n  \\begin{align}\n    \\boldsymbol{r} &= \\bfR\\, \\hat{\\boldsymbol{r}}+\\boldsymbol{d}\\,,\n  \\end{align}\n  where\n  \\begin{align}\n    \\bfR &=\n    \\begin{bmatrix}\n      \\cos\\psi  & -\\sin\\psi  \\\\ \\sin\\psi  &\\cos\\psi\n    \\end{bmatrix}\n  \\end{align}\n  is the rotation matrix.\n\\end{theorem}\n\n\\begin{figure}\n  \\centering\n \n  \\includegraphics[scale=0.5]{Fig01.pdf}\\\\\n  \\caption{Coordinate transformation.\\label{fig:gen_coord_transf}}\n\\end{figure}\n\n\\subsection{Vectorization of Matrices \\label{sec:vec_op}}\nVectorization of a matrix represents the operation that cuts the matrix into columns and stacks them sequentially as a column vector.\nOne can refer to \\cite{Laub2005} for more details. Here we recall the following definition and theorem.\n\n\\begin{definition}\\label{def:vec_op}\nLet $h_{i}\\in \\mathbb{R}^{n}$ denote the $i$-th column of matrix $\\bfH\\in \\mathbb{R}^{n\\times m}$, i.e., $\\bfH=[h_{1}\\quad h_{2}\\quad\\ldots\\quad\nh_{m}]$. The vector operator is defined as\n\\begin{equation}\\label{eqn:vec_def}\n  \\vectr(\\bfH)=\n  \\left[\n    \\begin{array}{cccc}\n      h_{1}^{\\rm T} & h_{2}^{\\rm T} &\\ldots & h_{m}^{\\rm T}\n    \\end{array}\n  \\right]^{\\rm T}\\in\n\\mathbb{R}^{mn}\\,.\n\\end{equation}\n\\end{definition}\n\n\\begin{theorem}\\label{thm:vec_kron_relation}\nFor any three matrices $\\mathbf{A}$, $\\mathbf{B}$ and $\\bfC$ where the matrix product\n$\\mathbf{ABC}$ is defined, we have\n\\begin{equation}\n  \\vectr(\\mathbf{A}\\mathbf{B}\\bfC)=(\\bfC^{\\rm T}\\otimes \\mathbf{A})\\vectr(\\mathbf{B})\\,,\n\\end{equation}\nwhere $\\otimes$ denotes Kronecker product.\n\\end{theorem}\n\n\\subsection{Curves in 2-D Space \\label{sec:curv_repr_def}}\nAccording to Taylor series, curves can be approximated with polynomials.\nIn practice, lanes are typically represented as 2-D curves in vehicle body-fixed frame.\nThus, in this part we discuss Taylor approximation for 2-D curves in $xy$-plane. The shorthand notation\n\\begin{align}\n  \\dfrac{\\diff^{0} y}{\\diff x^{0}}=y(x)\\,,\n\\end{align}\nis introduced, which will be kept throughout this paper.\n\n\\begin{definition}\n  Given a curve $\\mathcal{C}$ in $xy$-plane and a point $P$ on the curve whose coordinates are $(x_{0}, y(x_{0}))$, its $N$-th order polynomial function representation about point $P$ is its Taylor approximation at point $P$ until the $N$-th order, i.e.,\n  \\begin{equation}\n  \\begin{split}\\label{eqn:def_func_repr_algb_form}\n    \\mathcal{C}'&=\\{(x,\\, y)\\,|\\,\n    y(x;x_{0})=\\varphi_{0}+\\varphi_{1}\\, (x-x_{0}) +\\cdots \\\\\n    &+\\varphi_{N}\\, (x-x_{0})^{N}\\,,\\,x\\in\\mathbb{R}\\}\\,,\n  \\end{split}\n  \\end{equation}\n  where the coefficients are\n  \\begin{align}\\label{eqn:func_repr_coeff_def}\n    \\varphi_{n} &= \\dfrac{1}{n!}\\dfrac{\\diff^{n} y}{\\diff x^{n}}\\Big|_{x=x_{0}}\\,,\n  \\end{align}\n  for $n=0, 1, \\ldots, N$.\n\\end{definition}\n\n\\begin{definition}\n  Given a curve $\\mathcal{C}$ in $xy$-plane and a point $P$ on the curve, the $N$-th order parametric representation using arc length\n  \\begin{align}\\label{eqn:arc_length_def}\n    s &= \\int_{x_{0}}^{x}\\sqrt{1+\\Big(\\dfrac{\\diff y}{\\diff x}\\Big)^{2}}\\, \\diff x\\,,\n  \\end{align}\n  about point $P$ is its Taylor approximation with respect to arc length parameter $s$ at point $P$ until the $N$-th order, i.e.,\n  \\begin{equation}\\label{eqn:def_param_repr_algb_form}\n    \\begin{split}\n     \\mathcal{C}'&=\\{(x,\\, y)\\,|\\,\n      x(s; s_{0})=\\bar{\\phi}_{0}+\\bar{\\phi}_{1} \\,(s-s_{0})+\\cdots\\\\\n      & +\\bar{\\phi}_{N} \\,(s-s_{0})^{N},\\;\n      y(s; s_{0})=\\hat{\\phi}_{0}+\\hat{\\phi}_{1}\\, (s-s_{0})\\\\\n      & +\\cdots +\\hat{\\phi}_{N}\\, (s-s_{0})^{N},\\,s\\in\\mathbb{R}\\}\\,\n    \\end{split}\n  \\end{equation}\n  where $s_{0}$ is the corresponding arc length of point $P$, and the coefficients are\n  \\begin{align}\\label{eqn:param_repr_coeff_def}\n    \\bar{\\phi}_{n}&= \\dfrac{1}{n!}\\dfrac{\\diff^{n} x}{\\diff s^{n}}\\Big|_{s=s_{0}}\\,,&\n    \\hat{\\phi}_{n}&= \\dfrac{1}{n!}\\dfrac{\\diff^{n} y}{\\diff s^{n}}\\Big|_{s=s_{0}}\\,,\n  \\end{align}\n  for $n=0, 1, \\ldots, N$.\n\\end{definition}\n\nWe remark that in the  remainder of the paper polynomial function representation \\eqref{eqn:def_func_repr_algb_form} and arc-length-based parametric representation \\eqref{eqn:def_param_repr_algb_form} will be referred to as function representation and parametric representation, respectively. To simplify the notation, we rewrite \\eqref{eqn:def_func_repr_algb_form} into the matrix form, that is,\n\\begin{align}\\label{eqn:def_func_repr_matx_form}\n  \\mathcal{C}'&=\\{(x,\\, y)\\,|\\,y(x; x_{0})=\\boldsymbol{\\varphi}(x_{0})\\,\\boldsymbol{p}_{N}(x-x_{0})\\,,\\,x\\in\\mathbb{R}\\}\\,,\n\\end{align}\nwhere\n\\begin{equation}\n\\begin{split}\\label{eqn:func_repr_coeff_vec_def}\n    \\boldsymbol{\\varphi} & =\n    \\begin{bmatrix}\n      \\varphi_{0} &\\varphi_{1} & \\cdots & \\varphi_{N}\n    \\end{bmatrix}\\,,\\\\\n    \\boldsymbol{p}_{N}(x) & =\n    \\begin{bmatrix}\n      1 & x & \\cdots & x^{N}\n    \\end{bmatrix}^\\top \\,.\n\\end{split}\n\\end{equation}\nSimilarly, the matrix form of \\eqref{eqn:def_param_repr_algb_form} is\n\\begin{align}\\label{eqn:def_param_repr_matx_form}\n  \\mathcal{C}'&=\\{\\boldsymbol{r}\\,|\\,\n  \\boldsymbol{r}(s; s_{0})=\\boldsymbol{\\phi}(s_{0})\\,\\boldsymbol{p}_{N}(s-s_{0})\\,,\\,s\\in\\mathbb{R}\\}\\,,\n\\end{align}\nwhere\n\\begin{equation}\\label{eqn:param_repr_coeff_vec_def}\n\\begin{split}\n    \\boldsymbol{r}(s; s_{0}) & =\n    \\begin{bmatrix}\n      x(s; s_{0}) \\\\ y(s; s_{0})\n    \\end{bmatrix}\\,,\\enskip\n    \\boldsymbol{\\phi}  =\n    \\begin{bmatrix}\n      \\bar{\\phi}_{0} & \\bar{\\phi}_{1} & \\cdots & \\bar{\\phi}_{N} \\\\\n      \\hat{\\phi}_{0} & \\hat{\\phi}_{1} & \\cdots & \\hat{\\phi}_{N}\n    \\end{bmatrix}\\,,\n\\end{split}\n\\end{equation}\nand $\\boldsymbol{p}_{N}(\\cdot)$ uses the same definition in \\eqref{eqn:func_repr_coeff_vec_def}. Note that the dependency of coefficients ($\\boldsymbol{\\varphi}$ and $\\boldsymbol{\\phi}$) on the coordinates of point P ($x_{0}$ and $s_{0}$) is highlighted in the matrix form.\n\n\\begin{remark}\\label{remark:curv_repr_gen}\n  In 2-D space, a curve is uniquely determined if the curvature $\\kappa(s)$ is given for arbitrary arc length position $s$.\n\\end{remark}\n\\begin{IEEEproof}\n  For a general point $P$ on the curve, we assume that its coordinates, slope angle, curvature and arc length are $(x, y)$, $\\alpha$, $\\kappa$ and $s$, respectively.\n  Based on differential geometry, their relationship is described by\n  \\begin{equation}\\label{eqn:EOM_ref_path_ds}\n    \\begin{split}\n         x' &=\\cos\\alpha\\, ,\n         \\\\\n        y' &=\\sin\\alpha\\, ,\n        \\\\\n        \\alpha' &=\\kappa\\, ,\n    \\end{split}\n  \\end{equation}\n  where prime denotes differentiation with respect to $s$. Solving \\eqref{eqn:EOM_ref_path_ds} with initial conditions, one can obtain the tuple $(x, y,\\alpha)$ as functions of $s$ that characterizes the curve.\n\\end{IEEEproof}\n\n\\section{Representations of Curves \\label{sec:curv_repr}}\nThis part presents theoretical results on the representations of curves. Section~\\ref{sec:property_param_repr} shows that parametric representations have property of preserving the form in parameter shifting and coordinate transformation. Section~\\ref{sec:transform_repr} derives the changes of coefficients that reveal the relationship between function representation and parametric representation. In Section~\\ref{sec:coeff_repr_curves}, we derive the coefficients for both representations for the curve \\eqref{eqn:EOM_ref_path_ds} with known curvature at arbitrary arc length position.\n\n\\subsection{Properties of Parametric Representation \\label{sec:property_param_repr}}\n\\begin{theorem}[Conformal Representation in Shifting]\\label{thm:curve_param_repr_shift}\n   The parametric curve \\eqref{eqn:def_param_repr_matx_form} preserves its form when the Taylor expansion is shifted to parameter location $s_{1}=s_{0}+\\tilde{s}$. That is, $\\boldsymbol{r}(s; s_{0})$ can be rewritten into\n  \\begin{align}\n    \\boldsymbol{r}(s; s_{1}) &= \\boldsymbol{\\phi}(s_{1})\\,\\boldsymbol{p}_{N}(s-s_{1})\\,,\n  \\end{align}\n  where the change of coefficients is\n  \\begin{align}\n    \\boldsymbol{\\phi}^{\\top}(s_{1}) &= \\boldsymbol{T}(\\tilde{s})\\,\\boldsymbol{\\phi}^{\\top}(s_{0})\\,,\n  \\end{align}\n  and\n  \\begin{align}\\label{eqn:T_expansion}\n    \\boldsymbol{T}(\\tilde{s})&=\n    \\begin{bmatrix}\n    C_{0}^{0} &  C_{1}^{0}\\tilde{s} & C_{2}^{0}\\tilde{s}^{2} & \\cdots & C_{N}^{0}\\tilde{s}^{N}\\\\\n     &  C_{1}^{1} & C_{2}^{1}\\tilde{s} &\\cdots & C_{N}^{1}\\tilde{s}^{N-1}\\\\\n     &  & C_{2}^{2} &  \\ddots & \\vdots \\\\\n     &  &  & \\ddots  & C_{N}^{N-1}\\tilde{s}& \\\\\n     &  &  &  & C_{N}^{N}\n    \\end{bmatrix}.\n  \\end{align}\n  Here, $C_{N}^{k}$ represents the binomial coefficients and $C_{0}^{0}=1$.\n\\end{theorem}\n\\begin{IEEEproof}\n \n  Substituting ${s_{0}=s_{1}-\\tilde{s}}$ into \\eqref{eqn:def_param_repr_matx_form}, and then utilizing binomial theorem, one can obtain\n\\begin{align}\n  \\boldsymbol{r}&(s; s_{0})= \\boldsymbol{\\phi}(s_{0})\\,\\boldsymbol{p}_{N}(s-s_{0}) \\nonumber\\\\\n  &=\n  \\begin{bmatrix}\n    \\sum\\limits_{n=0}^{N} \\bar{\\phi}_{n} (s-s_{0})^{n}\\\\\n    \\sum\\limits_{n=0}^{N} \\hat{\\phi}_{n} (s-s_{0})^{n}\n  \\end{bmatrix}\n  =\n  \\begin{bmatrix}\n    \\sum\\limits_{n=0}^{N} \\bar{\\phi}_{n} (s-s_{1}+\\tilde{s})^{n}\\\\\n    \\sum\\limits_{n=0}^{N} \\hat{\\phi}_{n} (s-s_{1}+\\tilde{s})^{n}\n  \\end{bmatrix} \\nonumber\\\\\n  &=\n  \\begin{bmatrix}\n    \\sum\\limits_{n=0}^{N} \\bar{\\phi}_{n} \\sum\\limits_{m=0}^{n}C_{n}^{m}\\tilde{s}^{n-m}(s-s_{1})^{m}\\\\\n    \\sum\\limits_{n=0}^{N} \\hat{\\phi}_{n} \\sum\\limits_{m=0}^{n} C_{n}^{m}\\tilde{s}^{n-m}(s-s_{1})^{m}\n  \\end{bmatrix}\\\\\n  &=\n  \\begin{bmatrix}\n    \\sum\\limits_{m=0}^{N} \\Big(\\sum\\limits_{n=m}^{N} C_{n}^{m}\\tilde{s}^{n-m}\\bar{\\phi}_{n}\\Big)(s-s_{1})^{m}\\\\\n    \\sum\\limits_{m=0}^{N} \\Big(\\sum\\limits_{n=m}^{N} C_{n}^{m}\\tilde{s}^{n-m}\\hat{\\phi}_{n}\\Big)(s-s_{1})^{m}\n  \\end{bmatrix}\\,,\\nonumber\n\\end{align}\nwhich is the $N$-th order parametric curve about $s_{1}$. Comparing the coefficients, we obtain the change of coefficients.\n\\end{IEEEproof}\n\n\\begin{theorem}[Conformal Representation in Transformation] \\label{thm:curve_param_repr_conformal}\n  The parametric curve \\eqref{eqn:def_param_repr_matx_form} preserves its form in coordinate transformation. Suppose we are given two coordinate systems (frame $\\cFE_{1}$ and $\\cFE_{2}$), and the change of coordinates from $\\cFE_{2}$ to $\\cFE_{1}$ is\n  \\begin{align}\n    \\boldsymbol{r} &= \\bfR\\,\\hat{\\boldsymbol{r}} + \\bfd\\,,\n  \\end{align}\n  where $\\boldsymbol{r}$ and $\\hat{\\boldsymbol{r}}$ are the coordinates of an arbitrary point expressed in frame $\\cFE_{1}$ and $\\cFE_{2}$, respectively, $\\bfR$ is the rotation matrix, and $\\bfd$ is the origin of frame $\\cFE_{2}$ expressed in frame $\\cFE_{1}$.\n  Then the parametric curve \\eqref{eqn:def_param_repr_matx_form} expressed in frame $\\cFE_{1}$ possesses the same form when expressed in frame $\\cFE_{2}$, that is,\n  \\begin{align}\n    \\hat{\\boldsymbol{r}}(s; s_{0}) &=\\widehat{\\boldsymbol{\\phi}}(s_{0})\\,\\boldsymbol{p}_{N}(s-s_{0})\\,,\n  \\end{align}\n  where the change of coefficients is\n  \\begin{align}\n    \\widehat{\\boldsymbol{\\phi}}(s_{0})& = \\bfR^{\\top}\\big(\\boldsymbol{\\phi}(s_{0})-\\bfD \\big)\\,,\n  \\end{align}\n  and\n  \\begin{align}\n    \\bfD& = \\begin{bmatrix}\n      \\bfd & 0 & \\cdots & 0\n    \\end{bmatrix}\\in \\mathbb{R}^{2\\times (N+1)}\\,.\n  \\end{align}\n\\end{theorem}\n\\begin{IEEEproof}\n \n  Based on change of coordinates, the curve \\eqref{eqn:def_param_repr_matx_form} can be expressed in $\\cFE_{2}$ as\n\\begin{equation}\n  \\begin{split}\n    \\hat{\\boldsymbol{r}}(s; s_{0}) &= \\bfR^{\\top}\\boldsymbol{r}(s; s_{0})- \\bfR^{\\top}\\bfd\\,,\\\\\n    &=\\bfR^{\\top}\\boldsymbol{\\phi}(s_{0})\\,\\boldsymbol{p}_{N}(s-s_{0}) - \\bfR^{\\top}\\bfd\\,,\n  \\end{split}\n\\end{equation}\nBy noticing that\n\\begin{align}\n  \\bfd & = \\bfD\\,\\boldsymbol{p}_{N}(s-s_{0})\\,,\n\\end{align}\none can obtain the change of coefficients given in the theorem.\n\n\\end{IEEEproof}\n\n\\begin{remark}\\label{remark:func_repr_preserve_shift}\n  Function representation preserves its form in parameter shifting, but not in coordinate transformation.\n\\end{remark}\n\n\\subsection{Transformations between Function Representation and Parametric Representation \\label{sec:transform_repr}}\n\nIn this part, we derive the transformations between function representation and parametric representation.\nResults are only provided until the fifth-order, which is considered adequate in practice.\nThe following assumptions are made: i) Taylor series are expanded about the intersection between the curve and the $y$-axis (also referred to as $y$-intercept); ii) this $y$-intercept marks the starting point of arc length, i.e., $s=0$; and iii) the positive direction of arc length parameter $s$ corresponds to the positive direction of the $x$-axis. We obtain the following transformations based on those assumptions.\n\n\n\\begin{theorem}\\label{thm:curve_func_2_param_repr}\n  Given a curve with function representation \\eqref{eqn:def_func_repr_matx_form}, its parametric representation \\eqref{eqn:def_param_repr_matx_form} is uniquely determined in the same coordinate system. In other words, there exists a unique map $\\boldsymbol{\\phi}=\\boldsymbol{f}(\\boldsymbol{\\varphi})$. The coefficients until the fifth order are\n  \\begin{equation\n    \\begin{split}\n    \\bar{\\phi}_{0} &= 0\\,, \\qquad\\qquad\\qquad\\qquad\\quad\\enskip\\;\n    \\hat{\\phi}_{0} = \\varphi_{0}\\,,\\\\\n    \\bar{\\phi}_{1} &= \\dfrac{1}{\\lambda}\\,, \\qquad\\qquad\\qquad\\qquad\\quad\\enskip\n    \\hat{\\phi}_{1} = \\dfrac{\\varphi_{1}}{\\lambda}\\,,\\\\\n    \\bar{\\phi}_{2} &= -\\dfrac{\\varphi_{1} \\varphi_{2}}{\\lambda^{4}}\\,, \\qquad\\qquad\\qquad\\quad\n    \\hat{\\phi}_{2} =\\dfrac{\\varphi_{2}}{\\lambda^{4}}\\,,\\\\\n    \\bar{\\phi}_{3} &= \\dfrac{2 \\varphi_{2}^{2}-\\varphi_{1} \\varphi_{3}}{\\lambda^{5}}-\\dfrac{8 \\varphi_{2}^{2}}{3\\lambda^{7}}\\,,\\qquad\n    \\hat{\\phi}_{3} =\\dfrac{\\varphi_{3}}{\\lambda^{5}}- \\dfrac{8\\varphi_{1} \\varphi_{2}^{2}}{3\\lambda^{7}}\\,, \\\\\n    \\bar{\\phi}_{4} &= \\dfrac{5 \\varphi_{2} \\varphi_{3}-\\varphi_{1} \\varphi_{4}}{\\lambda^{6}}\n    -\\dfrac{10 \\varphi_{1} \\varphi_{2}^{3}+13 \\varphi_{2} \\varphi_{3}}{2\\lambda^{8}}\\\\\n     &+\\dfrac{28\\varphi_{1} \\varphi_{2}^{3}}{3\\lambda^{10}}\\,,\\\\\n    %\n    \\hat{\\phi}_{4} &=\\dfrac{\\varphi_{4}}{\\lambda^{6}}\n    +\\dfrac{16 \\varphi_{2}^{3}-13 \\varphi_{1} \\varphi_{2}\\varphi_{3}}{2\\lambda^{8}}\n    - \\dfrac{28\\varphi_{2}^{3}}{3\\lambda^{10}} \\,,\\\\\n    \\bar{\\phi}_{5} &= \\dfrac{3 \\varphi_{3}^{2}+6 \\varphi_{2} \\varphi_{4}-\\varphi_{1} \\varphi_{5}}{\\lambda^{7}}\\\\\n    &-\\dfrac{39 \\varphi_{3}^{2}+210 \\varphi_{1}\\varphi_{2}^{2} \\varphi_{3}+76 \\varphi_{2} \\varphi_{4}-140 \\varphi_{2}^{4}}{10\\lambda^{9}}\\\\\n    &+\\dfrac{188 \\varphi_{1} \\varphi_{2}^{2}\\varphi_{3}-248 \\varphi_{2}^{4}}{5\\lambda^{11}}\n    + \\dfrac{112\\varphi_{2}^{4}}{3\\lambda^{13}}\\,,\\\\\n    %\n    \\hat{\\phi}_{5} &=\\dfrac{\\varphi_{5}}{\\lambda^{7}}\n    +\\dfrac{326 \\varphi_{2}^{2} \\varphi_{3}-76 \\varphi_{1}\\varphi_{2} \\varphi_{4}-39 \\varphi_{1}\\varphi_{3}^{2}}{10\\lambda^{9}}\\\\\n    &-\\dfrac{128 \\varphi_{1}\\varphi_{2}^{4}+188 \\varphi_{2}^{2} \\varphi_{3}}{5\\lambda^{11}}+ \\dfrac{112\\varphi_{1}\\varphi_{2}^{4} }{3\\lambda^{13}}\\,,\n    \\end{split}\n  \\end{equation}\n  where\n  \\begin{align}\n    \\lambda &= \\sqrt{1+\\varphi_{1}^{2}}\\,.\n  \\end{align}\n\\end{theorem}\n\n\\begin{IEEEproof}\n \n  Based on the assumptions, we have\n\\begin{align}\\label{eqn:fun_repr_eval_0}\n   x (0)&=0\\,, &\n   y (0)&=\\varphi_{0}\\,,&\n   x '(s) &>0\\,.\n\\end{align}\nwhere $'$ denotes differentiation with respect to $s$, implying $\\bar{\\phi}_{0}$ and $\\hat{\\phi}_{0}$ given in the theorem.\nNotice that \\eqref{eqn:arc_length_def} yields\n\\begin{align}\\label{eqn:ds_comp_equality}\n  \\diff s^{2} &=\\diff  x ^{2}+\\diff  y ^{2} &\\Longrightarrow \\quad\n  ( x ')^{2}+( y ')^{2} &=1\\,,\n \n\\end{align}\nand the derivative of \\eqref{eqn:def_func_repr_algb_form} with respect to $s$ yields\n\\begin{align}\\label{eqn:fun_repr_deriv_1}\n   y ' &= \\varphi_{1}  x '+\\cdots +n\\varphi_{n}  x ^{n-1} x '\\,.\n\\end{align}\nEvaluating (\\ref{eqn:ds_comp_equality}, \\ref{eqn:fun_repr_deriv_1}) at $s=0$ and utilizing \\eqref{eqn:fun_repr_eval_0}, we obtain\n\\begin{align}\\label{eqn:fun_repr_deriv1_eval_0}\n   x '(0) &=\\dfrac{1}{\\sqrt{1+\\varphi_{1}^{2}}}\\,,&\n   y '(0) &=\\dfrac{\\varphi_{1}}{\\sqrt{1+\\varphi_{1}^{2}}}\\,,\n\\end{align}\nwhich implies $\\bar{\\phi}_{1}$ and $\\hat{\\phi}_{1}$ given in the theorem. Then taking the derivatives of (\\ref{eqn:ds_comp_equality}, \\ref{eqn:fun_repr_deriv_1}) with respect to $s$ yields\n\\begin{equation}\\label{eqn:fun_repr_deriv2}\n  \\begin{split}\n    & x ' x ''+ y ' y '' =0\\,,\\\\\n    & y '' = (\\varphi_{1} +\\cdots +n\\varphi_{n}  x ^{n-1}) x ''\\\\\n    &\\quad +\\big(2\\varphi_{2} +\\cdots +n(n-1)\\varphi_{n}  x ^{n-2}\\big)( x ')^{2}\\,.\n  \\end{split}\n\\end{equation}\nEvaluating (\\ref{eqn:fun_repr_deriv2}) at $s=0$ and utilizing (\\ref{eqn:fun_repr_eval_0}, \\ref{eqn:fun_repr_deriv1_eval_0}), we obtain\n\\begin{align}\\label{eqn:fun_repr_deriv2_eval_0}\n   x ''(0) &=-\\dfrac{2\\varphi_{1}\\varphi_{2}}{(1+\\varphi_{1}^{2})^{\\frac{3}{2}}}\\,,&\n   y ''(0) &=\\dfrac{2\\varphi_{2}}{(1+\\varphi_{1}^{2})^{\\frac{3}{2}}}\\,,\n\\end{align}\nwhich implies $\\bar{\\phi}_{2}$ and $\\hat{\\phi}_{2}$ given in the theorem.\nSimilarly, evaluating the derivative of (\\ref{eqn:fun_repr_deriv2}) at $s=0$ and then utilizing (\\ref{eqn:fun_repr_eval_0}, \\ref{eqn:fun_repr_deriv1_eval_0}, \\ref{eqn:fun_repr_deriv2_eval_0}), one can obtain an algebraic linear equation about $ x '''(0)$ and $ y '''(0)$ and thus obtain $\\bar{\\phi}_{3}$ and $\\hat{\\phi}_{3}$ . Following this procedure, we can derive all the derivatives and obtain the coefficients given in the theorem.\n\n\\end{IEEEproof}\n\n\\begin{theorem}\\label{thm:curve_param_2_func_repr}\n  Given a curve with parametric representation \\eqref{eqn:def_param_repr_matx_form}, its function representation \\eqref{eqn:def_func_repr_matx_form} is uniquely determined in the same coordinate system. In other words, there exists a unique map $\\boldsymbol{\\varphi}=\\boldsymbol{f}^{-1}(\\boldsymbol{\\phi})$.  The coefficients until the fifth-order are\n  \\begin{equation\n    \\begin{split}\n      \\varphi_{0} &= \\hat{\\phi}_{0}\\,,\\qquad\\,\n      \\varphi_{2} = \\dfrac{\\hat{\\phi}_{2} \\bar{\\phi}_{1}-\\hat{\\phi}_{1} \\bar{\\phi}_{2}}{\\bar{\\phi}_{1}^3}\\,,\\\\\n      \\varphi_{1} &= \\dfrac{\\hat{\\phi}_{1}}{\\bar{\\phi}_{1}}\\,,\\qquad\n      \\varphi_{3} = \\dfrac{\\hat{\\phi}_{3}}{\\bar{\\phi}_{1}^3}\n      -\\dfrac{\\hat{\\phi}_{1} \\bar{\\phi}_{3}+2 \\hat{\\phi}_{2} \\bar{\\phi}_{2}}{\\bar{\\phi}_{1}^4}\n      +\\dfrac{2 \\hat{\\phi }_{1} \\bar{\\phi}_{2}^2}{\\bar{\\phi}_{1}^5}\\,,\\\\\n      \\varphi_{4} &= \\dfrac{\\hat{\\phi}_{4}}{\\bar{\\phi}_{1}^4}\n      -\\dfrac{\\hat{\\phi}_{1} \\bar{\\phi}_{4}+2 \\hat{\\phi}_{2} \\bar{\\phi}_{3}+3 \\hat{\\phi}_{3} \\bar{\\phi}_{2}}{\\bar{\\phi}_{1}^5}\\\\\n      &+\\dfrac{5 \\bar{\\phi}_{2}(\\hat{\\phi}_{1} \\bar{\\phi}_{3} + \\hat{\\phi}_{2} \\bar{\\phi}_{2})}{\\bar{\\phi}_{1}^6}\n      -\\dfrac{5 \\hat{\\phi}_{1} \\bar{\\phi}_{2}^3}{\\bar{\\phi}_{1}^7}\\,,\\\\\n      \\varphi_{5} &=\\dfrac{\\hat{\\phi}_{5}}{\\bar{\\phi}_{1}^5}\n      -\\dfrac{\\hat{\\phi }_{1} \\bar{\\phi}_{5}+2 \\hat{\\phi}_{2} \\bar{\\phi}_{4}+3 \\hat{\\phi }_{3} \\bar{\\phi}_{3}+4 \\hat{\\phi}_{4} \\bar{\\phi}_{2}}{\\bar{\\phi }_{1}^6}\\\\\n      &+\\dfrac{3 \\hat{\\phi}_{1} (\\bar{\\phi}_{3}^2+2 \\bar{\\phi}_{2} \\bar{\\phi}_{4})+3\\bar{\\phi}_{2}(3 \\hat{\\phi}_{3} \\bar{\\phi}_{2}+4 \\hat{\\phi}_{2} \\bar{\\phi}_{3})}{\\bar{\\phi}_{1}^7}\\\\\n      &-\\dfrac{7 \\bar{\\phi}_{2}^{2}(3 \\hat{\\phi}_{1} \\bar{\\phi}_{3} +2 \\hat{\\phi}_{2} \\bar{\\phi}_{2})}{\\bar{\\phi}_{1}^8}\n      +\\dfrac{14 \\hat{\\phi}_{1} \\bar{\\phi}_{2}^4}{\\bar{\\phi}_{1}^9}\\,.\n    \\end{split}\n  \\end{equation}\n\\end{theorem}\n\n\\begin{IEEEproof}\n \n  Given the parametric representation \\eqref{eqn:def_param_repr_algb_form} of the curve, one can obtain the derivatives ($x'$, $y'$, $x''$, $y''$, ...) with respect to $s$ until the required order. Also, notice that\n\\begin{equation}\\label{eqn:proof_dyx}\n    \\dfrac{\\diff y}{\\diff x} =\\dfrac{y'}{x'}\\,,\n\\end{equation}\nand\n\\begin{equation}\\label{eqn:proof_dyx_recurv}\n    \\dfrac{\\diff^{n+1} y}{\\diff x^{n+1}} =\\dfrac{\\diff}{\\diff x}\\left(\\dfrac{\\diff^{n} y}{\\diff x^{n}}\\right)\n    =\\dfrac{\\left(\\frac{\\diff^{n} y}{\\diff x^{n}}\\right)'}{ x'}\\,, \\quad n=1,\\, 2,\\, 3,\\, \\ldots\n\\end{equation}\nCalculating the derivatives in (\\ref{eqn:proof_dyx}, \\ref{eqn:proof_dyx_recurv}) recursively and utilizing \\eqref{eqn:func_repr_coeff_def}, one can obtain the coefficients given in the theorem by noticing that $x_0=0$ implies $s=0$.\n\n\\end{IEEEproof}\n\n\\begin{remark}\nThe transformed representation is not necessarily equal to the original representation due to truncation errors in Taylor series, but can provide a very good approximation. This is because their derivatives are equal up until the specified order at the point where Taylor series are expanded.\n\\end{remark}\n\n\\subsection{Representations of a Given Curve \\label{sec:coeff_repr_curves}}\nIt is useful to derive the coefficients of parametric representation and function representation for curves described by \\eqref{eqn:EOM_ref_path_ds} with given $\\kappa(s)$. On the one hand, these coefficients can be used to validate the transformations derived in Section~\\ref{sec:transform_repr}. On the other hand, they can be used to simulate perception outcomes for camera-based control. In the following, we assume: i) the tuple $(x(s), y(s),\\alpha(s))$ are obtained with the given $\\kappa(s)$ according to \\eqref{eqn:EOM_ref_path_ds}; and ii) the representations are expanded about point $P$ whose arc length position is $s_{0}$. Other attributes at point P are\n\\begin{equation}\\label{eqn:gen_curv_P_loc}\n\\begin{split}\n    &x(s_{0}) =x_{0}\\,, \\enskip\n    y(s_{0}) =y_{0}\\,, \\enskip\n    \\alpha(s_{0}) =\\alpha_{0}\\,, \\enskip\n    \\kappa(s_{0}) =\\kappa_{0}\\,,\\\\\n    %\n    &\\dfrac{\\diff \\kappa}{\\diff s}(s_{0})=\\kappa'_{0}\\,,\\quad\n    \\dfrac{\\diff^{2} \\kappa}{\\diff s^{2}}(s_{0})=\\kappa''_{0}\\,,\\quad\n    \\dfrac{\\diff^{3} \\kappa}{\\diff s^{3}}(s_{0})=\\kappa'''_{0}\\,.\n\\end{split}\n\\end{equation}\n\n\n\\begin{theorem}\\label{thm:gen_curve_param_repr}\n  Given a curve in $xy$-plane with known ($x(s)$, $y(s)$, $\\alpha(s)$, $\\kappa(s)$), its parametric representation about point $P$ is unique. The coefficients until fifth-order are\n    \\begin{equation}\n      \\begin{split}\n        \\bar{\\phi}_{0}&=x_{0}\\,,\\qquad \\qquad \\qquad\\qquad\n        \\hat{\\phi}_{0}=y_{0}\\,,\\\\\n        \\bar{\\phi}_{1}&=\\cos\\alpha_{0}\\,,\\qquad\\hspace{45pt}\n        \\hat{\\phi}_{1}=\\sin\\alpha_{0}\\,,\\\\\n        \\bar{\\phi}_{2}&=-\\tfrac{1}{2}\\kappa_{0}\\sin\\alpha_{0}\\,,\\quad\\hspace{31pt}\n        \\hat{\\phi}_{2}=\\tfrac{1}{2}\\kappa_{0}\\cos\\alpha_{0}\\,,\\\\\n        \\bar{\\phi}_{3}&=-\\tfrac{1}{6}\\kappa_{0}^{2}\\cos\\alpha_{0}-\\tfrac{1}{6}\\kappa_{0}'\\sin\\alpha_{0}\\,,\\\\\n        \\hat{\\phi}_{3}&=-\\tfrac{1}{6}\\kappa_{0}^{2}\\sin\\alpha_{0}+\\tfrac{1}{6}\\kappa_{0}'\\cos\\alpha_{0}\\,,\\\\\n        \\bar{\\phi}_{4}&=-\\tfrac{1}{24}(\\kappa_{0}''-\\kappa_{0}^{3})\\sin\\alpha_{0}-\\tfrac{1}{8}\\kappa_{0}\\kappa_{0}'\\cos\\alpha_{0}\\,,\\\\\n        \\hat{\\phi}_{4}&=\\tfrac{1}{24}(\\kappa_{0}''-\\kappa_{0}^{3})\\cos\\alpha_{0}-\\tfrac{1}{8}\\kappa_{0}\\kappa_{0}'\\sin\\alpha_{0}\\,,\\\\\n        \\bar{\\phi}_{5}&=\\tfrac{1}{120}\\big(\\kappa_{0}^{4}-3(\\kappa_{0}')^{2}-4\\kappa_{0}\\kappa_{0}''\\big)\\cos\\alpha_{0}\\\\\n        &\\quad+\\tfrac{1}{120}(6\\kappa_{0}^{2}\\kappa_{0}'-\\kappa_{0}''')\\sin\\alpha_{0}\\,,\\\\\n        \\hat{\\phi}_{5}&=\\tfrac{1}{120}\\big(\\kappa_{0}^{4}-3(\\kappa_{0}')^{2}-4\\kappa_{0}\\kappa_{0}''\\big)\\sin\\alpha_{0}\\\\\n        &\\quad-\\tfrac{1}{120}(6\\kappa_{0}^{2}\\kappa_{0}'-\\kappa_{0}''')\\cos\\alpha_{0}\\,.\n      \\end{split}\n    \\end{equation}\n\\end{theorem}\n\\begin{IEEEproof}\n \n  Given an arbitrary point $(x, y)$ on the curve (\\ref{eqn:EOM_ref_path_ds}), the derivatives of the curve at that point are\n\\begin{equation}\\label{eqn:xy_derivs}\n  \\begin{split}\n    x' &= \\cos\\alpha\\,,\\qquad\\qquad\\qquad\\quad\\enskip\n    y' =\\sin\\alpha\\,,\\\\\n    x''&=-\\kappa\\sin\\alpha\\,,\\qquad\\qquad\\qquad\n    y''=\\kappa\\cos\\alpha\\,,\\\\\n    x'''&=-\\kappa^{2}\\cos\\alpha-\\kappa'\\sin\\alpha\\,,\\\\\n    x^{(4)}&=-(\\kappa''-\\kappa^{3})\\sin\\alpha-3\\kappa\\kappa'\\cos\\alpha\\,,\\\\\n    x^{(5)}&=\\big(\\kappa^{4}-3(\\kappa')^{2}-4\\kappa\\kappa''\\big)\\cos\\alpha\\\\\n    &+(6\\kappa^{2}\\kappa'-\\kappa''')\\sin\\alpha\\\\\n    y''' &=-\\kappa^{2}\\sin\\alpha+\\kappa'\\cos\\alpha\\,,\\\\\n    y^{(4)}&=(\\kappa''-\\kappa^{3})\\cos\\alpha-3\\kappa\\kappa'\\sin\\alpha\\,,\\\\\n    y^{(5)}&=\\big(\\kappa^{4}-3(\\kappa')^{2}-4\\kappa\\kappa''\\big)\\sin\\alpha\\\\\n    &-(6\\kappa^{2}\\kappa'-\\kappa''')\\cos\\alpha\\,.\n  \\end{split}\n\\end{equation}\nEvaluating \\eqref{eqn:xy_derivs} at point $P$ and utilizing \\eqref{eqn:param_repr_coeff_def}, we obtain the coefficients given in the theorem.\n\n\\end{IEEEproof}\n\n\n\\begin{theorem}\\label{thm:gen_curve_func_repr}\n  Given a curve in $xy$-plane with known ($x(s)$, $y(s)$, $\\alpha(s)$, $\\kappa(s)$), its function representation about point $P$ is unique. The coefficients until fifth-order are\n    \\begin{equation\n      \\begin{split}\n        \\varphi_{0} &= y_{0}\\,, \\qquad\\hspace{50pt}\n        \\varphi_{1} = \\tan\\alpha_{0}\\,,\\\\\n        \\varphi_{2} &= \\dfrac{\\kappa_{0}}{2\\cos^{3}\\alpha_{0}}\\,, \\qquad\\qquad\n        \\varphi_{3} = \\dfrac{\\kappa_{0}'+3\\kappa_{0}^{2}\\tan\\alpha_{0}}{6\\cos^{4}\\alpha_{0}}\n        \\,,\\\\\n        %\n        \\varphi_{4} &= \\dfrac{5\\kappa_{0}^3 }{8\\cos^{7}\\alpha_{0}}\n            +\\dfrac{\\kappa_{0}''-12 \\kappa_{0}^3+10 \\kappa_{0}\\kappa_{0}'\\tan\\alpha_{0} }{24\\cos^{5}\\alpha_{0}}  \\,,\\\\\n        \\varphi_{5} &= \\dfrac{7\\kappa_{0}^{2} (\\kappa_{0}'+\\kappa_{0}^{2}\\tan\\alpha_{0})}{8\\cos^{8}\\alpha_{0}}\n        +\\dfrac{\\kappa_{0}'''-86 \\kappa_{0}^{2} \\kappa_{0}'}{120\\cos^{6}\\alpha_{0}}\\\\\n        &+\\dfrac{ \\big(3\\kappa_{0}\\kappa_{0}''+2(\\kappa_{0}')^{2}-12\\kappa_{0}^{4}\\big) \\tan\\alpha_{0} }{24\\cos^{6}\\alpha_{0}}\n          \\,.\n      \\end{split}\n    \\end{equation}\n\\end{theorem}\n\\begin{IEEEproof}\n \n  Given an arbitrary point $(x, y)$ on the curve (\\ref{eqn:EOM_ref_path_ds}), the derivatives of the coordinates $x$ and $y$ with respect to $s$ at that point are given in \\eqref{eqn:xy_derivs}. Also, notice that the derivatives of $y$ with respect to $x$ are the same as those given in (\\ref{eqn:proof_dyx}, \\ref{eqn:proof_dyx_recurv}). Substituting \\eqref{eqn:xy_derivs} into (\\ref{eqn:proof_dyx}, \\ref{eqn:proof_dyx_recurv}), one can obtain the derivatives recursively until the required order. Then the coefficients can be obtained by evaluating these derivatives at point $P$ and utilizing \\eqref{eqn:func_repr_coeff_def}.\n\\end{IEEEproof}\n\n\\begin{remark}\nOne can verify that coefficients given in Theorem~\\ref{thm:gen_curve_param_repr} and \\ref{thm:gen_curve_func_repr} satisfy the transformations given in Theorem~\\ref{thm:curve_func_2_param_repr} and \\ref{thm:curve_param_2_func_repr}.\n\\end{remark}\n\n\\section{Application in Lateral Control \\label{sec:veh_ctrl_setup}}\nThis section applies arc-length-based parametric representation to camera-based lateral control problem. We first present a typical architecture using function representation, and discuss the related issues in lane estimation and control. Then a new architecture is proposed to use parametric representation that can facilitate and improve lane estimation as well as control-related information extraction.\n\nFig.~\\ref{fig:block_diag}(a) illustrates a typical architecture of camera-based vehicle control. At first, lanes are captured by cameras. Then perception applies lane detection algorithms using computer vision or machine learning techniques, and outputs coefficients $\\boldsymbol{\\varphi}$ that represent lanes with polynomial function representations. In the scenarios where perception is not perfect (noisy or corrupted) or temporarily unavailable, lane estimation becomes extremely important, which is achieved through predictors, observers or estimators. Those techniques require a model on the evolution of coefficients for prediction. For example, the orange box in Fig.~\\ref{fig:block_diag}(a) represents a typical Kalman filter implementation, which is decoupled into two steps: time update and measurement update. Time update step utilizes a model to predict a priori estimate of the coefficients, while the measurement update step generates a posteriori estimate based on the newest measurement and signal characteristics.\nHowever, when function representation is used, it is rather difficult to find such a model because: i) the vehicle body-fixed frame is translating and rotating due to vehicle movement; and ii) function representation does not preserve the form in coordinate transformation.\nTherefore, in practice it is common to use simple approximated models for prediction, such as $\\boldsymbol{\\varphi}_{k+1}=\\boldsymbol{\\varphi}_{k}$. These predictions only work for a very short period, and underlying inaccuracies in the model lead to unexpected behaviors due to the aforementioned issues.\nThe other issue appears when control algorithms need to extract state information with respect to lanes at a preview distance, such as lateral deviation, relative heading angle, road curvature, etc. Extracting such information requires numerical iterations for function representation because the preview distance is implicit in the representation.\n\n\\begin{figure}[!t]\n  \\centering\n \n  \\includegraphics[scale=1.2]{Fig02.pdf}\\\\\n  \\caption{Block diagrams of camera-based vehicle control. (a) A typical architecture using function representation. (b) Proposed architecture using arc-length-based parametric representation. }\\label{fig:block_diag}\n\\end{figure}\n\nThese issues can be resolved if arc-length-based parametric representation is utilized to characterize lanes.\nWhen the vehicle moves, the nice properties in Theorem~\\ref{thm:curve_param_repr_shift} and \\ref{thm:curve_param_repr_conformal} indicate an intrinsic linear model on the evolution of coefficients. Also, it is straightforward to extract information with respect to lanes at a preview distance since this distance is actually the arc length parameter explicitly used in the representation.\nFig.~\\ref{fig:block_diag}(b) proposes a new architecture for camera-based control problem using arc-length-based parametric representation.\nWe still assume perception outputs coefficients $\\boldsymbol{\\varphi}$ of polynomial function representation to ensure compatibility with current platforms. An additional step is introduced to transform function representation to parametric representation by applying Theorem~\\ref{thm:curve_func_2_param_repr}. Thus, we can derive an intrinsically linear model on the evolution of coefficients $\\boldsymbol{\\phi}$, and easily extract information needed by control algorithms. The details are provided in the remainder of this part. In Section~\\ref{sec:perception}, we introduce notations, and discuss lane representations and transformations. Section~\\ref{sec:estmation_lane} derives the model on the evolution of coefficients $\\boldsymbol{\\phi}$ for lane estimation. In Section~\\ref{sec:ctrl}, we introduce a vehicle dynamic model and a lateral controller as an example to demonstrate how to utilize the derived lane estimation model.\n\n\n\n\\subsection{Perception and Transformation \\label{sec:perception}}\n\n\nFig.~\\ref{fig:camera_control} depicts the camera-based perception of the path represented as the green dashed curve. Remark that in practice perception algorithms output representations of lane markers captured by cameras, which can be transformed into representations of lane centers. For simplicity, in this paper we use paths or lanes to indicate lane centers.\nWe also assume that the camera with FOV angle $2\\delta$ is mounted at point $Q$ along the longitudinal symmetry axis. The wheelbase length is $l$, and the distance from point $Q$ to the rear axle center is $d$. The light purple sector region denotes the FOV of the camera, which is also symmetric about the longitudinal axis. The closest on-path point observed in the camera is $\\Omega$. Note that the camera can only capture the segment  $\\mathcal{C}$ of the path within the FOV that is highlighted as the solid green curve beyond point $\\Omega$. In this part, we maintain the following notations:\n\\begin{enumerate}\n  \\item ${(x,y,z)}$ denotes the earth-fixed frame $\\cFE$.\n\n  \\item ${(\\tau, \\eta, z)}$ denotes the vehicle body-fixed frame $\\cFB$ with the origin located at $Q$. Axes $\\tau$ and $\\eta$ are along the longitudinal and lateral directions, with the corresponding unit vectors denoted as $\\unitvec[\\tau]$ and $\\unitvec[\\eta]$, respectively.\n\n  \\item The position of $Q$ is ($x_{Q}$, $y_{Q}$) expressed in $\\mathcal{F}$, and the vehicle heading angle is $\\psi$ with respect to the $x$-axis.\n\n  \\item The position of $\\Omega$ is ${(x_{\\rm \\Omega}, y_{\\rm \\Omega})}$ expressed in $\\mathcal{F}$, while the slope angle and curvature at point $\\Omega$ are $\\alpha_{\\rm \\Omega}$ and $\\kappa_{\\rm \\Omega}$, respectively.\n\n  \\item When it is needed to distinguish different time instants, subscripts $k$ or $k+1$ indicating time steps will be added to the points, axes, frames and time-varying variables.\n\\end{enumerate}\n\n\\begin{figure}[!t]\n  \\centering\n \n  \\includegraphics[scale=0.9]{Fig03.pdf}\\\\\n  \\caption{Schematics of camera-based vehicle control.\\label{fig:camera_control}}\n\\end{figure}\n\n\nPerception algorithms process the observed path segment $\\mathcal{C}$ and approximate it with a polynomial function\n\\begin{align}\\label{eqn:poly_func_repr_D}\n    \\mathcal{C}'=\\{(\\tau, \\eta)\\,|\\,\\eta = \\boldsymbol{\\varphi}(0)\\,\\boldsymbol{p}_{N}(\\tau)\\,,\\,\\tau\\in\\mathbb{R}\\}\\,,\n\\end{align}\nthat is expressed in frame $\\cFB$ and indicated by the red curve in Fig.~\\ref{fig:camera_control}.\nNote that point $D$ corresponding to $\\tau=0$ is invisible in the FOV since it is typically less than $180$ degrees. Strictly speaking, \\eqref{eqn:poly_func_repr_D} is not the Taylor approximation of $\\mathcal{C}$ about point $D$, but the expansion of Taylor approximation of $\\mathcal{C}$ about the closest on-path point (point $\\Omega$) in the FOV, that is,\n\\begin{align}\\label{eqn:poly_func_repr_omega}\n  \\mathcal{C}'=\\{(\\tau, \\eta)\\,|\\,\\eta = \\boldsymbol{\\varphi}(\\tau_{\\Omega})\\,\\boldsymbol{p}_{N}(\\tau-\\tau_{\\Omega})\\,,\\,\\tau\\in\\mathbb{R}\\}\\,.\n\\end{align}\nAccording to Remark~\\ref{remark:func_repr_preserve_shift}, the change of coefficients is\n\\begin{align}\n     \\boldsymbol{\\varphi}^\\top(0)&=\\boldsymbol{T}(-\\tau_{\\Omega})\\boldsymbol{\\varphi}^{\\top}(\\tau_{\\Omega})\\,,\n\\end{align}\nwhere $\\boldsymbol{T}(\\cdot)$ is the same as that given in \\eqref{eqn:T_expansion}.\n\nNext step is to transform function representation \\eqref{eqn:poly_func_repr_D} to arc-length-based parametric representation.\nIndeed, one should transform \\eqref{eqn:poly_func_repr_omega} to parametric representation about point $\\Omega$ since \\eqref{eqn:poly_func_repr_D} is the expansion of approximation \\eqref{eqn:poly_func_repr_omega} about point $\\Omega$.\nHowever, it is rather complicated to transform to parametric representation about point $\\Omega$; see proof of Theorem~\\ref{thm:curve_func_2_param_repr}. Also, transformation about point $\\Omega$ leads to the issue of floating origin of the arc length coordinate $s$ while the vehicle is moving. Therefore, we transform \\eqref{eqn:poly_func_repr_D} to parametric representation about point $D$, which is the $\\eta$-intercept of $\\mathcal{C}'$ in frame $\\cFB$.\nAs shown in Fig.~\\ref{fig:camera_control}, point $\\Omega$ is close to point $D$ when the following holds: i) the lateral deviation to the path is small; or ii) the camera has a relatively wide view. Applying Theorem~\\ref{thm:curve_func_2_param_repr}, we obtain the parametric representation of $\\mathcal{C}'$ given in \\eqref{eqn:poly_func_repr_D} about point $D$ as\n\\begin{align}\\label{eqn:param_repr_body_frame}\n  \\mathcal{C}'&=\\{\\bfr\\,|\\,\\bfr(s; 0)= \\boldsymbol{\\phi}(0)\\,\\boldsymbol{p}_{N}(s)\\,,\\,s\\in\\mathbb{R}\\}\\,,\n\\end{align}\nwhere $\\bfr = [\\tau, \\; \\eta]^\\top$ is the coordinates in frame $\\cFB$, the location of arc length coordinate $s=0$ corresponds to point $D$, and the change of coefficients is\n\\begin{align}\\label{eqn:param_repr_body_frame_coeff}\n  \\boldsymbol{\\phi}(0)&= \\boldsymbol{f}(\\boldsymbol{\\varphi}(0))\\,.\n\\end{align}\n\n\n\\subsection{Lane Estimation \\label{sec:estmation_lane}}\n\n\\begin{figure}\n  \\centering\n \n  \\includegraphics[scale=0.6]{Fig04.pdf}\\\\\n  \\caption{Vehicle movement from step $k$ to $k+1$.\\label{fig:lanepoly_time_evolve}}\n\\end{figure}\n\nFig.~\\ref{fig:lanepoly_time_evolve} depicts vehicle movement from time step $k$ to $k+1$. As mentioned earlier, Fig.~\\ref{fig:lanepoly_time_evolve} uses subscripts $k$ or $k+1$ on points, frames and time-varying variables to distinguish different instants; cf.~Fig.~\\ref{fig:camera_control}. Specifically, point $Q_{k}$, frame $\\cFB[k]$ with $\\tau_{k}\\eta_{k}z$ axis and point $D_{k}$ denote the location of the camera, the body-fixed frame and the $\\eta$-intercept of the lane at step $k$, respectively. The red curve $\\mathcal{C}'$ represents the curve \\eqref{eqn:param_repr_body_frame} at step $k$.\n$(x_{k}, y_{k})$ are the coordinates of $Q_{k}$ in the earth-fixed frame $\\cFE$, while $\\psi_{k}$ is the vehicle heading. $(\\tilde{x}_{k}, \\tilde{y}_{k})$ and $(\\tilde{\\tau}_{k}, \\tilde{\\eta}_{k})$ are the coordinates of the displacement vector $Q_{k}Q_{k+1}$ expressed in the earth-fixed frame $\\cFE$ and body-fixed frame $\\cFB[k]$, respectively. $\\tilde{\\psi}_{k}$ is the change of vehicle heading from step $k$ to step $k+1$. $s_{k}$ is the arc length coordinate at step $k$ such that $s_{k}=0$ corresponds to point $D_{k}$, while $\\tilde{s}_{k}$ represents the arc length distance from $D_{k}$ to $D_{k+1}$ along the curve $\\mathcal{C}'$. In summary,\n\\begin{equation}\\label{eqn:term_diff_k_to_k1}\n\\begin{split}\n  \\tilde{x}_{k} & = x_{k+1}-x_{k}\\,,\\qquad\n  \\tilde{y}_{k} = y_{k+1}-y_{k}\\,,\\\\\n  \\tilde{\\psi}_{k} & = \\psi_{k+1}-\\psi_{k}\\,,\\qquad\n  \\tilde{s}_{k} = s_{k}-s_{k+1}\\,.\n\\end{split}\n\\end{equation}\nIn the following we assume vehicle state changes $\\tilde{x}_{k}$, $\\tilde{y}_{k}$, $\\tilde{\\psi}_{k}$, $\\tilde{\\tau}_{k}$, $\\tilde{\\eta}_{k}$ and $\\tilde{s}_{k}$ are known, and will investigate the details on how to obtain them in Section~\\ref{sec:ctrl}.\n\nTo derive the evolution of coefficients in \\eqref{eqn:param_repr_body_frame}, we highlight the time-dependency and rewrite it for step $k$ as\n\\begin{align}\\label{eqn:param_repr_body_frame_k_in_k}\n  \\mathcal{C}'&=\\{\\bfr_{k}\\,|\\,\\bfr_{k}(s_{k}; 0) = \\boldsymbol{\\phi}_{k}(0)\\,\\boldsymbol{p}_{N}(s_{k})\\,,\\,s_{k}\\in \\mathbb{R\\}}\\,,\n\\end{align}\nwhich is the parametric representation using arc length coordinates $s_{k}$ about point $D_{k}$ in frame $\\cFB[k]$. The objective is to derive the new representation\n\\begin{equation}\\label{eqn:param_repr_body_frame_k+1}\n\\begin{split}\n    \\mathcal{C}'&=\\{\\bfr_{k+1}\\,|\\,\n  \\bfr_{k+1}(s_{k+1}; 0)= \\boldsymbol{\\phi}_{k+1}(0)\\,\\boldsymbol{p}_{N}(s_{k+1})\\,,\\, s_{k+1}\\in\\mathbb{R}\\}\\,,\n\\end{split}\n\\end{equation}\ngiven \\eqref{eqn:param_repr_body_frame_k_in_k} based on vehicle state changes from step $k$ to step $k+1$ such that the relationship between the coefficients $\\boldsymbol{\\phi}_{k}(0)$ and $\\boldsymbol{\\phi}_{k+1}(0)$ can be obtained. Note that \\eqref{eqn:param_repr_body_frame_k+1} is based on arc length coordinates $s_{k+1}$ about point $D_{k+1}$ in frame $\\cFB[k+1]$. Hence, three steps are performed sequentially in the following: i) coordinate transformation from frame $\\cFB[k]$ to frame $\\cFB[k+1]$; ii) shifting expansion point from $D_{k}$ to $D_{k+1}$; iii) changing coordinate from $s_{k}$ to $s_{k+1}$.\n\nAccording to Theorem~\\ref{thm:gen_coord_transf}, the change of coordinates from body-fixed frame $\\cFB[k+1]$ to $\\cFB[k]$ is\n\\begin{align}\\label{eqn:coord_transf_k_k_1}\n\\boldsymbol{r}_{k} &= \\bfR_{k}\\, \\boldsymbol{r}_{k+1}+\\boldsymbol{d}_{k}\\,,\n\\end{align}\nwhere\n\\begin{align}\n    \\bfR_{k} &=\n    \\begin{bmatrix}\n      \\cos\\tilde{\\psi}_{k}  & -\\sin\\tilde{\\psi}_{k}  \\\\ \\sin\\tilde{\\psi}_{k}  &\\cos\\tilde{\\psi}_{k}\n    \\end{bmatrix}\\,,&\n    \\bfd_{k} &=\n    \\begin{bmatrix}\n      \\tilde{\\tau}_{k}   \\\\ \\tilde{\\eta}_{k}\n    \\end{bmatrix}\\,.\n\\end{align}\nApplying Theorem~\\ref{thm:curve_param_repr_conformal} to curve \\eqref{eqn:param_repr_body_frame_k_in_k} with coordinate transformation \\eqref{eqn:coord_transf_k_k_1}, we obtain the parametric representation using arc length coordinates $s_{k}$ about point $D_{k}$ in frame $\\cFB[k+1]$ as\n\\begin{align}\\label{eqn:param_repr_body_frame_k_in_k+1}\n  \\mathcal{C}'&=\\{\\bfr_{k+1}\\,|\\,\n  \\bfr_{k+1}(s_{k}; 0)= \\widehat{\\boldsymbol{\\phi}}_{k}(0)\\,\\boldsymbol{p}_{N}(s_{k})\\,,\\,s_{k}\\in\\mathbb{R}\\}\\,,\n\\end{align}\nwhere the change of coefficients is\n\\begin{align}\\label{eqn:coeff_change_step_1}\n  \\widehat{\\boldsymbol{\\phi}}_{k}(0) & = \\bfR_{k}^{\\top}\\big(\\boldsymbol{\\phi}_{k}(0)-\\bfD_{k} \\big)\\,,\n\\end{align}\nand\n\\begin{align}\n\\bfD_{k} & = \\begin{bmatrix}\n  \\bfd_{k} & 0 & \\cdots & 0\n\\end{bmatrix}\\in \\mathbb{R}^{2\\times (N+1)}\\,.\n\\end{align}\n\nNotice that the expansion point has shifted from $D_{k}$ to $D_{k+1}$ with distance $\\tilde{s}_{k}$.\nApplying Theorem~\\ref{thm:curve_param_repr_shift} to \\eqref{eqn:param_repr_body_frame_k_in_k+1}, we obtain the parametric representation of $\\mathcal{C}'$ using arc length coordinates $s_{k}$ about point $D_{k+1}$ in frame $\\cFB[k+1]$ as\n\\begin{align}\\label{eqn:param_repr_body_frame_k_in_k+1_sk}\n \\mathcal{C}'&=\\{\\bfr_{k+1}\\,|\\,\n  \\bfr_{k+1}(s_{k}; \\tilde{s}_{k}) = \\widehat{\\boldsymbol{\\phi}}_{k}(\\tilde{s}_{k})\\,\\boldsymbol{p}_{N}(s_{k}-\\tilde{s}_{k})\\,,\\,s_{k}\\in\\mathbb{R}\\}\\,,\n\\end{align}\nwhere the change of coefficients is\n\\begin{align}\\label{eqn:coeff_change_step_2}\n  \\widehat{\\boldsymbol{\\phi}}_{k}^\\top(\\tilde{s}_{k})&=\\boldsymbol{T}(\\tilde{s}_{k})\\,\\widehat{\\boldsymbol{\\phi}}_{k}^\\top(0)\\,,\n\\end{align}\nwhere $\\boldsymbol{T}(\\cdot)$ is the same as that given in \\eqref{eqn:T_expansion}.\n\nNext utilizing \\eqref{eqn:term_diff_k_to_k1}, we can change coordinates from $s_{k}$ to $s_{k+1}$ to obtain the parametric representation \\eqref{eqn:param_repr_body_frame_k+1} where the change of coefficients is\n\\begin{align}\\label{eqn:coeff_change_step_3}\n  \\boldsymbol{\\phi}_{k+1}(0)&=\\widehat{\\boldsymbol{\\phi}}_{k}(\\tilde{s}_{k})\\,.\n\\end{align}\nIn summary, the evolution of coefficients in the parametric representation from step $k$ to step $k+1$ is\n\\begin{align}\\label{eqn:coeff_dyn_gen_equiv}\n  \\boldsymbol{\\phi}_{k+1}(0)&=\\bfR_{k}^{\\top}\\big(\\boldsymbol{\\phi}_{k}(0)-\\bfD_{k} \\big)\\, \\boldsymbol{T}^\\top(\\tilde{s}_{k})\\,,\n\\end{align}\ncf. (\\ref{eqn:coeff_change_step_1}, \\ref{eqn:coeff_change_step_2}, \\ref{eqn:coeff_change_step_3}), implying a linear relationship by nature.\n\n\\begin{remark}\nUtilizing vectorization operator and Theorem~\\ref{thm:vec_kron_relation}, one can rewrite \\eqref{eqn:coeff_dyn_gen_equiv} into the standard form of linear system\n\\begin{align}\n  \\boldsymbol{\\Phi}_{k+1}&=\\mathbf{A}_{k}\\boldsymbol{\\Phi}_{k}+\\mathbf{B}_{k}\\,,\n\\end{align}\nwhere\n\\begin{equation}\n  \\begin{split}\n    \\boldsymbol{\\Phi}_{k}&=\\vectr(\\boldsymbol{\\phi}_{k}(0))\\,, \\qquad\\qquad\n   \\mathbf{A}_{k} =\\boldsymbol{T}(\\tilde{s}_{k})\\otimes \\bfR_{k}^{\\top}\\,,\\\\\n   \\mathbf{B}_{k} &= -\\big(\\boldsymbol{T}(\\tilde{s}_{k})\\otimes \\bfR_{k}^{\\top}\\big)\\vectr(\\mathbf{D}_{k})\\,.\n  \\end{split}\n\\end{equation}\n\\end{remark}\n\n\n\\subsection{Vehicle Dynamics and Control \\label{sec:ctrl}}\n\nThe proposed architecture and model on the evolution of coefficients using arc-length-based parametric representation can be applied to any vehicle models with reasonable control algorithms that require lane estimation and information extraction. To demonstrate the work flow, in this part we provide an example on the model derived in \\cite{Wubing_ND_2022} using the path-following controller proposed in \\cite{Wubing_LC_TIV_2022}.\n\n\\subsubsection{Dynamics and Transformation on States\\label{sec:dyn_estimation_states}}\n\nIn general, vehicle dynamics describe the evolution of absolute position (e.g., $x_{\\rm Q},\\, y_{\\rm Q}$) and orientation (heading angle $\\psi$) in the earth-fixed frame $\\cFE$. They have different levels of complexity based on fidelity.\nHere, we consider the model derived in \\cite{Wubing_ND_2022} on the camera location point $Q$, that is\n\\begin{equation}\\label{eqn:EOM_point_Q}\n\\begin{split}\n\\dot{x}_{\\rm Q} &= V\\,\\cos\\psi-d\\,\\dfrac{V}{l}\\tan\\gamma \\sin\\psi\\, , \\\\\n\\dot{y}_{\\rm Q} &= V\\,\\sin\\psi+d\\,\\dfrac{V}{l}\\tan\\gamma \\cos\\psi\\, , \\\\\n\\dot{\\psi} &= \\dfrac{V}{l}\\,\\tan\\gamma\\, .\n\\end{split}\n\\end{equation}\nwhere $x_{\\rm Q}$, $y_{\\rm Q}$, ${\\psi}$, $l$ and $d$ utilize the same notations introduced in Section~\\ref{sec:perception}, $V$ is the constant longitudinal speed, and $\\gamma$ is the steering angle.\n\nTo facilitate control design, the vehicle dynamics \\eqref{eqn:EOM_point_Q} on absolute position ($x_{\\rm Q},\\, y_{\\rm Q}$) and orientation (heading angle $\\psi$) expressed in the earth-fixed frame $\\cFE$ can be transformed to dynamics on relative position and orientation with respect to the path. Such transformation allows us to obtain the evolution of arc length position, lateral deviation and relative heading with respect to lanes perceived in the camera. In this paper, we choose the following relative position and orientation as new states: i) the arc length $s_{\\Omega}$ that the vehicle has travelled along the lane; ii) the observed distance $\\varepsilon_{\\Omega}$ that characterizes the length of vector $\\pvec{\\Omega Q}$ (cf.~Fig.~\\ref{fig:camera_control}), whose sign is positive when $Q$ is on the left side of the path;\nand iii) the relative heading angle\n\\begin{align}\\label{eqn:rel_heading_def}\n  \\theta_{\\Omega} &= \\psi-\\alpha_{\\Omega}\\,,\n\\end{align}\nwith respect to point $\\Omega$ on the path.\nThe details on the state transformation are provided in Appendix~\\ref{append:coord_transf}, and the resulting transformed relative dynamics are\n\\begin{equation}\\label{eqn:transf_xy_se_diff_Q}\n  \\begin{split}\n    \\dot{s}_{\\Omega} &= \\dfrac{ V }{\\sin(\\delta-\\theta_{\\Omega})}\\big(\\sin\\delta+\\dfrac{d}{l}\\cos\\delta \\tan\\gamma\\big)\\\\\n    &+\\dfrac{|\\varepsilon_{\\Omega}|\\cos\\big(\\delta-\\sign(\\varepsilon_{\\Omega})\\,\\delta\\big)}{\\sin(\\delta-\\theta_{\\Omega})}\\dfrac{V}{ l}\\tan\\gamma\\,,\\\\\n    %\n    \\dot{\\varepsilon}_{\\Omega} &=\\dfrac{ V }{\\sin(\\delta-\\theta_{\\Omega})}\\big(\\sin\\theta_{\\Omega}+\\dfrac{d}{l}\\cos\\theta_{\\Omega} \\tan\\gamma\\big)\\\\\n    &+\\dfrac{|\\varepsilon_{\\Omega}|\\cos(\\delta-\\sign(\\varepsilon_{\\Omega})\\,\\theta_{\\Omega})}{\\sin(\\delta-\\theta_{\\Omega})}\\dfrac{V}{l}\\tan\\gamma\\,,\\\\\n    %\n    \\dot{\\theta}_{\\Omega} &=-\\dfrac{ V\\, \\kappa_{\\Omega}}{\\sin(\\delta-\\theta_{\\Omega})}\\big(\\sin\\delta+\\dfrac{d}{l}\\cos\\delta \\tan\\gamma\\big)\\\\\n    &+\\Big(1-\\dfrac{\\kappa_{\\Omega} |\\varepsilon_{\\Omega}|\\cos\\big(\\delta-\\sign(\\varepsilon_{\\Omega})\\,\\delta\\big)}{\\sin(\\delta-\\theta_{\\Omega})}\\Big)\\dfrac{V}{l}\\tan\\gamma\\,.\n  \\end{split}\n\\end{equation}\n\n\n\\subsubsection{Control}\n\nThe objective of a path-following controller is to generate desired steering angle $\\gamma_{\\rm des}$ such that point Q can follow the given path. In literature, there are many available controllers demonstrated to be effective in different scenarios. In this part we use the nonlinear controller proposed in \\cite{Wubing_LC_TIV_2022} as an example since cameras are typically mounted at the front of the vehicle.\nWe hightlight the key ideas of this controller, and refer readers to \\cite{Wubing_LC_TIV_2022} for more details on the design.\n\nWith the assumption that the steering angle $\\gamma$ can track any desired value $\\gamma_{\\rm des}$, that is, $\\gamma = \\gamma_{\\rm des}$,\nthe path-following controller is\n\\begin{align}\\label{eqn:lateral_controller}\n  \\gamma_{\\rm des} & = \\gamma_{\\rm ff} + \\gamma_{\\rm fb}\\,,\n\\end{align}\nwhich consists of a feedforward control law\n\\begin{align}\n  \\gamma_{\\rm ff} &= \\arctan \\dfrac{l\\,\\kappa_{\\rm D}}{\\sqrt{1-(d\\,\\kappa_{\\rm D})^{2}}}\\,, \\label{eqn:steer_controller_ff_sum}\n\\end{align}\nand a feedback control law\n\\begin{align}\\label{eqn:steer_controller_fb_sum}\n  \\gamma_{\\rm fb} &= \\gamma_{\\rm sat}\\cdot g \\Big( \\tfrac{k_{1}}{\\gamma_{\\rm sat}}\\big(\\theta_{\\rm D}-\\theta_{0}+\\arctan (k_{2}\\,\\varepsilon_{\\rm D})\\big)\\Big)\\,.\n\\end{align}\nHere, $\\kappa_{\\rm D}$ is the road curvature at point $D$, $\\theta_{\\rm D}$ is the relative heading angle with respect to point $D$ (cf.~\\eqref{eqn:rel_heading_def}), and ${\\varepsilon_{\\rm D}=-\\eta_{\\rm D}}$ is the $\\eta$-deviation of point $D$ where $\\eta_{\\rm D}$ indicates the $\\eta$-coordinate of point $D$ in frame $\\cFB$. In other words, $\\varepsilon_{\\rm D}$ characterizes the length of vector $\\pvec{D Q}$ (cf.~Fig.~\\ref{fig:camera_control}), and is positive when $\\pvec{D Q}$ points towards the positive $\\eta$-axis.\nAlso,\n\\begin{align}\\label{eqn:theta0_des}\n  \\theta_{0} & = -\\arcsin(d\\,\\kappa_{\\rm D})\\,\n\\end{align}\nis the desired yaw angle error, ($k_{1}$, $k_{2}$) are tunable control gains, $\\gamma_{\\rm sat}$ is the maximum allowable steering angle, and $g (x)$ denotes the wrapper function\n\\begin{equation}\n    g(x) =\\dfrac{2}{\\pi}\\arctan \\Big(\\dfrac{\\pi}{2} x\\Big)\\,. \\label{eqn:satfunction}\n\\end{equation}\nThe feedforward control essentially provides the estimated steering angle to handle a given road curvature $\\kappa_{\\rm D}$ whereas the feedback control makes corrections based on lateral deviation $\\varepsilon_{\\rm D}$ and yaw angle error $\\theta_{\\rm D}-\\theta_{0}$.\n\nThe controller (\\ref{eqn:lateral_controller}-\\ref{eqn:satfunction}) relies on the information about point $D$ or with respect to point $D$. We remark that point $D$ is not the closest on-path point to $Q$ as that used in \\cite{Wubing_LC_TIV_2022}, or the closest observable on-path point (point $\\Omega$) to $Q$ in the FOV. One can verify that when the road curvature is constant (i.e., $\\kappa_{\\rm D}=\\kappa^{\\ast}$), the closed loop system (\\ref{eqn:transf_xy_se_diff_Q}-\\ref{eqn:satfunction}) possesses the desired equilibrium\n\\begin{align}\\label{eqn:equilb}\n  s_{\\Omega}^{\\ast}=\\dfrac{V\\,t}{\\sqrt{1-(d\\,\\kappa^{\\ast})^{2}}}\\,,\\;\n  \\varepsilon_{\\Omega}^{\\ast}=0\\,,\\;\n  \\theta_{\\Omega}^{\\ast}=-\\arcsin(d\\,\\kappa^{\\ast})\\,,\n\\end{align}\nwhich can be stabilized with properly chosen gain $k_{1}$ and $k_{2}$. The equilibrium \\eqref{eqn:equilb} represents the scenario where the vehicle follows the given path perfectly with no lateral deviations.\nTo extract the information ($\\kappa_{\\rm D}$, $\\theta_{\\rm D}$, $\\varepsilon_{\\rm D}$) from representation \\eqref{eqn:param_repr_body_frame}, we provide the following lemma.\n\n\n\\begin{lemma}\\label{thm:terms_from_param_repr}\n  Given the parametric representation \\eqref{eqn:param_repr_body_frame} of the lane in frame $\\cFB$, the $\\eta$-deviation $\\varepsilon_{\\rm D}$, the relative heading angle $\\theta_{\\rm D}$, and the curvature $\\kappa_{\\rm D}$ at point $D$ are\n  \\begin{equation}\\label{eqn:extract_ctrl_info_from_repr}\n    \\begin{split}\n      \\varepsilon_{D} &=-\\hat{\\phi}_{0}\\,,\\,\\qquad\\qquad\\qquad\n      \\theta_{D} = -\\arctan \\dfrac{\\hat{\\phi}_{1}}{\\bar{\\phi}_{1}}\\,,\\,\\\\\n      \\kappa_{D} &= \\dfrac{2\\hat{\\phi}_{2}\\bar{\\phi}_{1}-2\\hat{\\phi}_{1}\\bar{\\phi}_{2}}{\\hat{\\phi}_{1}^{2}+\\bar{\\phi}_{1}^{2}}\\,.\n    \\end{split}\n  \\end{equation}\n\\end{lemma}\n\\begin{IEEEproof}\n  Given \\eqref{eqn:param_repr_body_frame}, we obtain the $\\eta$-deviation $\\varepsilon$, the relative heading angle $\\theta$, and the road curvature $\\kappa$ at an arbitrary point $P$ with a preview distance $s_{\\rm P}$ as\n  \\begin{equation}\\label{eqn:lemma_get_terms_from_repr}\n    \\begin{split}\n      \\varepsilon(s_{\\rm P}) &= -\\eta(s_{\\rm P}) \\,,\\qquad\n      \\theta(s_{\\rm P}) = -\\arctan \\dfrac{\\eta'(s_{\\rm P})}{\\tau'(s_{\\rm P})}\\,,\\\\\n      \\kappa(s_{\\rm P}) &= \\dfrac{\\eta''(s_{\\rm P})\\,\\tau'(s_{\\rm P})-\\eta'(s_{\\rm P})\\,\\tau''(s_{\\rm P})}{(\\eta'(s_{\\rm P}))^{2}+(\\tau'(s_{\\rm P}))^{2}}\\,,\n    \\end{split}\n  \\end{equation}\n  where the derivatives $\\eta'$, $\\tau'$, $\\eta''$ and $\\tau''$ can be obtained by differentiating \\eqref{eqn:param_repr_body_frame} with respect to $s$.\n  Point D marks the origin of arc length coordinate $s$. Thus, evaluating \\eqref{eqn:lemma_get_terms_from_repr} at $s_{\\rm P}=0$ yields \\eqref{eqn:extract_ctrl_info_from_repr} at point $D$.\n\\end{IEEEproof}\n\n\n\\subsubsection{Vehicle State Changes}\nIn the derivation of \\eqref{eqn:coeff_dyn_gen_equiv}, vehicle state changes $\\tilde{x}_{k}$, $\\tilde{y}_{k}$, $\\tilde{\\psi}_{k}$, $\\tilde{\\tau}_{k}$, $\\tilde{\\eta}_{k}$ and $\\tilde{s}_{k}$ are assumed to be known at each step in Section~\\ref{sec:estmation_lane}. In practice, they can be obtained based on a nominal vehicle dynamic model and sensor data. In this part we take model \\eqref{eqn:EOM_point_Q} as an example, and assume the longitudinal speed $V$ and yaw rate $\\omega=\\dot{\\psi}$ can be measured by onboard sensors. We rewrite model \\eqref{eqn:EOM_point_Q} into\n\\begin{equation}\\label{eqn:model_w_sensor_data}\n  \\begin{split}\n    \\dot{x}&= V\\cos\\psi -d\\, \\omega \\sin\\psi\\, ,\\\\\n    \\dot{y}&= V\\sin\\psi+d\\, \\omega\\cos\\psi\\,, \\\\\n    \\dot{\\psi}&=\\omega\\,.\n  \\end{split}\n\\end{equation}\nbased on measurable data $V$ and $\\omega$.\nApplying Euler method to integrate \\eqref{eqn:model_w_sensor_data} at step $k$, we obtain\n\\begin{equation}\\label{eqn:changes_x_y_psi}\n  \\begin{split}\n    \\tilde{x}_{k}&= (V_{k}\\cos\\psi_{k} -d\\, \\omega_{k} \\sin\\psi_{k})T\\,,\\\\\n    \\tilde{y}_{k}&= (V_{k}\\sin\\psi_{k}+d\\, \\omega_{k}\\cos\\psi_{k})T\\,,\\\\\n    \\tilde{\\psi}_{k}&=\\omega_{k} T\\,,\n  \\end{split}\n\\end{equation}\nwhere $T$ is the step size. Notice that $(\\tilde{x}_{k}, \\tilde{y}_{k})$ and $(\\tilde{\\tau}_{k}, \\tilde{\\eta}_{k})$ are the coordinates of displacement vector $Q_{k}Q_{k+1}$ expressed in earth-fixed frame $\\cFE$ and body-fixed frame $\\cFB[k]$, respectively. Thus, one can apply Theorem~\\ref{thm:gen_coord_transf} on coordinate transformation and obtain\n\\begin{align}\\label{eqn:changes_tau_eta_psi}\n\\tilde{\\tau}_{k}&= V_{k}T\\,,&\n\\tilde{\\eta}_{k}&= d\\, \\omega_{k} T\\,.\n\\end{align}\n\nNote that $\\tilde{s}_{k}$ is the arc length distance that point $D$ has travelled along the curve $\\mathcal{C}'$ from step $k$ to step $k+1$. Realizing that point $D$ coincides with point $\\Omega$ if $\\delta=\\frac{\\pi}{2}$, we can easily derive the evolution of $s_{\\rm D}$ from the relative dynamics \\eqref{eqn:transf_xy_se_diff_Q} that is transformed from \\eqref{eqn:EOM_point_Q}.\nBy setting $\\delta=\\frac{\\pi}{2}$ in \\eqref{eqn:transf_xy_se_diff_Q} and replacing point $\\Omega$ with point $D$, the evolution of $s_{\\rm D}$ becomes\n\\begin{equation}\n  \\begin{split}\\label{eqn:transf_xy_se_diff_D}\n    \\dot{s}_{\\rm D} &= \\dfrac{ V+\\omega\\,\\varepsilon_{\\rm D} }{\\cos\\theta_{\\rm D}}\\,,\n  \\end{split}\n\\end{equation}\nwhere yaw rate $\\omega=\\tfrac{V}{l}\\,\\tan\\gamma$ is utilized; cf.~\\eqref{eqn:model_w_sensor_data}.\nApplying Lemma~\\ref{thm:terms_from_param_repr} to the parametric representation \\eqref{eqn:param_repr_body_frame},\nthe $\\eta$-deviation $\\varepsilon_{D}$ and relative heading angle $\\theta_{D}$ can be obtained at step $k$. Thus, integrating \\eqref{eqn:transf_xy_se_diff_D} with Euler method yields\n\\begin{equation}\\label{eqn:changes_s}\n  \\tilde{s}_{k}=\\dfrac{V_{k}+\\omega_{k}\\,\\varepsilon_{\\textrm{D}_{k}}}{\\cos(\\theta_{\\textrm{D}_{k}})}\\,T\\,.\n\\end{equation}\n\n\n\n\\section{Results \\label{sec:res}}\nIn this section, simulations of the whole process explained in Section~\\ref{sec:veh_ctrl_setup} are performed to demonstrate the usage of arc-length-based parametric representation in lane estimation and vehicle control. In Section~\\ref{sec:sim_setup}, we start with the details on how we set up experiment scenarios and simulate lane perception in camera-based control. In Section~\\ref{sec:sim_res}, simulations with or without using model \\eqref{eqn:coeff_dyn_gen_equiv} for prediction are conducted for the path-following control problem and results indicate the efficacy and large potential of \\eqref{eqn:coeff_dyn_gen_equiv} in facilitating lane estimation in vehicle control.\n\n\n\\subsection{Simulation Setup\\label{sec:sim_setup}}\n\nThe model \\eqref{eqn:coeff_dyn_gen_equiv} integrated with the controller (\\ref{eqn:lateral_controller}-\\ref{eqn:satfunction}) is applicable to lane estimation in path-following problems where the path can have any reasonable shape. Remark~\\ref{remark:curv_repr_gen} indicates that a path can be fully described by $\\kappa(s)$. Also, if $\\kappa(s)$ has an analytical form, we can derive the coefficients for polynomial function representation \\eqref{eqn:poly_func_repr_D} given vehicle state with respect to the path. These coefficients can be used as: i) the output of perception algorithms at perception updating instants; and ii) the true values to compare against the predicted values when perception outcome is not available. Therefore, we consider the closed path used in \\cite{Wubing_ND_2022} and derive the coefficients for polynomial function representation in this part.\nThe curvature of the path is given as\n\\begin{align}\\label{eqn:curv_s_func}\n \\kappa(s) &= \\dfrac{\\kappa_{\\max}}{2}\\left(1-\\cos\\bigg(\\dfrac{2\\pi}{s_{\\rm T}}s\\bigg)\\right)\\ ,\n\\end{align}\nwhere $\\kappa_{\\max}$ is the maximum curvature along the path, and $s_{\\rm T}$ is the arc length period.\nThis path has $N$ corners and perimeter $Ns_{\\rm T}$ if\n\\begin{equation}\\label{eqn:curv_close_cond}\n \\kappa_{\\max}\\,s_{\\rm T}=\\dfrac{4\\pi}{N}\\ , \\quad N=2, 3, \\ldots \\ .\n\\end{equation}\n\nAs discussed in Section~\\ref{sec:perception}, perception algorithms provide representation \\eqref{eqn:poly_func_repr_D} of the lane in real-time, which can be viewed as the expansion of Taylor approximation \\eqref{eqn:poly_func_repr_omega} about point $\\Omega$ in the FOV.\nTo simulate perception, we need to derive the coefficients of function representation \\eqref{eqn:poly_func_repr_omega} in frame $\\cFB$ given the vehicle states and the path information \\eqref{eqn:curv_s_func}.\n\n\\begin{lemma}\\label{lemma:gen_curve_func_repr}\n    Given the current vehicle relative states ($s_{\\Omega}$, $\\varepsilon_{\\Omega}$ and $\\theta_{\\Omega}$) with respect to the path, and the half angle $\\delta$ of camera FOV, the lane segment $\\mathcal{C}$  can be approximated as function representation \\eqref{eqn:poly_func_repr_omega} in frame $\\cFB$ by applying Taylor series to point $\\Omega$, where $\\tau_{\\Omega}:=\\tau(s_{\\Omega})=|\\varepsilon_{\\Omega}| \\cos\\delta$ and\n    \\begin{equation}\\label{eqn:gen_curv_func_repr_coeff}\n      \\begin{split}\n        \\varphi_{0}(\\tau_{\\Omega}) &= -\\varepsilon_{\\Omega}\\sin\\delta\\,, \\quad\n        \\varphi_{1}(\\tau_{\\Omega}) = -\\tan\\theta_{\\Omega}\\,, \\\\\n        %\n        \\varphi_{2}(\\tau_{\\Omega}) &= \\dfrac{\\kappa_{\\Omega}}{2\\cos^{3}\\theta_{\\Omega}}\\,,\\quad\n        \\varphi_{3}(\\tau_{\\Omega}) = \\dfrac{\\kappa'_{\\Omega}-3\\kappa_{\\Omega}^{2}\\tan\\theta_{\\Omega}}{6\\cos^{4}\\theta_{\\Omega}}\\,,\\\\\n        %\n        \\varphi_{4}(\\tau_{\\Omega}) &= \\dfrac{5\\kappa_{\\Omega}^3}{8\\cos^{7}\\theta_{\\Omega}}\n        +\\dfrac{\\kappa''_{\\Omega}-12 \\kappa_{\\Omega}^{3}-10\\kappa_{\\Omega}\\kappa'_{\\Omega}\\tan\\theta_{\\Omega} }{24\\cos^{5}\\theta_{\\Omega}}  \\,,\\\\\n        %\n        \\varphi_{5}(\\tau_{\\Omega}) &=\n        \\dfrac{ 7\\kappa_{\\Omega}^{2} (\\kappa'_{\\Omega}-\\kappa_{\\Omega}^{2}\\tan \\theta_{\\Omega}) }{8\\cos^{8}\\theta_{\\Omega}}\n        +\\dfrac{\\kappa'''_{\\Omega}-86\\kappa_{\\Omega}^{2} \\kappa'_{\\Omega}}{120\\cos^{6}\\theta_{\\Omega}} \\\\\n        &+\\dfrac{\\big(12\\kappa_{\\Omega}^{4}-3\\kappa_{\\Omega}\\kappa''_{\\Omega}-2(\\kappa'_{\\Omega})^{2}\\big)\\tan\\theta_{\\Omega}}{24\\cos^{6}\\theta_{\\Omega}}\\,.\n      \\end{split}\n    \\end{equation}\n\\end{lemma}\n\\begin{IEEEproof}\n  See Appendix~\\ref{append:path_func_repr_body_frame}.\n\\end{IEEEproof}\n\n\n\\subsection{Simulation Results \\label{sec:sim_res}}\n\n\nIn this part, we simulate the whole process of perception, estimation and control explained in Section~\\ref{sec:veh_ctrl_setup} when the vehicle tries to follow the given path (\\ref{eqn:EOM_ref_path_ds}, \\ref{eqn:curv_s_func}) with camera-based perception. The controller (\\ref{eqn:lateral_controller}-\\ref{eqn:satfunction}) updates commands every $T$ seconds while perception provides the function representation \\eqref{eqn:poly_func_repr_D} every $T_{\\rm p}$ seconds. To demonstrate the efficacy of the proposed estimation algorithm, we also assume: i) $T_{\\rm p}$ is larger than $T$; ii) when the representation \\eqref{eqn:poly_func_repr_D} is not updated by perception, the controller may use the model \\eqref{eqn:coeff_dyn_gen_equiv} to update the parametric representation with the estimated state changes (\\ref{eqn:changes_x_y_psi}, \\ref{eqn:changes_tau_eta_psi}, \\ref{eqn:changes_s}) at each step; iii) the measurement \\eqref{eqn:poly_func_repr_D} is free of noise such that prediction using model \\eqref{eqn:coeff_dyn_gen_equiv} can be easily compared against true values without noise effects; and iv) the true values about coefficients of representation are obtained by calculating $\\boldsymbol{\\varphi}(\\tau_{\\Omega})$ using Lemma~\\ref{lemma:gen_curve_func_repr} at every control period with vehicle states ($s_{\\rm \\Omega}$, $\\varepsilon_{\\Omega}$, $\\theta_{\\Omega}$). The initial conditions are set to $s_{\\rm \\Omega}=0$ [m], $\\varepsilon_{\\Omega}=0.1$ [m], $\\theta_{\\Omega}=0$ [deg],  and the other parameters used in the simulations are provided in TABLE~\\ref{tab:params}.\n\n\\begin{table}[!t]\n\\begin{center}\n\\renewcommand{\\arraystretch}{1.3}\n\\rowcolors{1}{LightCyan}{LightMagenta}\n\\begin{tabular}{l|c|l}\n\\hline\\hline\n \\rowcolor{Gray}  Parameter & Value & Description\\\\\n \\hline\n $l$ [m]& $2.57$ & wheelbase length\\\\\n $d$ [m]& $2$ & distance from Q to rear axle center\\\\\n $\\delta$ [deg]& $60$ & half angle of camera FOV\\\\\n $k_{1}$ [m\/s]& $-l\/d$ & control gain\\\\\n $k_{2}$ [m$^{-1}$]& $0.02$ & control gain\\\\\n $\\gamma_{\\max}$ [deg]& $30$ & physical steering angle limit\\\\\n $s_{\\rm T}$ [m] & $250$ & arc length period of the path\\\\\n $N$ [1] & $4$ & number of corners for closed path\\\\\n $\\kappa_{\\max}$ [m$^{-1}$] & $0.004\\pi$ & maximum curvature of the path\\\\\n $V$ [m\/s] & 20 & longitudinal speed \\\\\n\n\\hline\\hline\n\\end{tabular}\n\\end{center}\n\\caption{Parameters used in the simulations. \\label{tab:params}}\n\\end{table}\n\n\nFig.~\\ref{fig:sim_50ms} shows the simulation results without using \\eqref{eqn:coeff_dyn_gen_equiv} to predict coefficients when $T=0.05$ [s] and $T_{\\rm p}=0.15$ [s]. That is, the controller outputs a new command at one step based on the updated lane representation from perception, and then holds this command for the following two steps. This is because when new representation is not available, the outdated one is still used by the controller which outputs the same command. This is a typical and easy solution when characterizing lanes using function representation \\eqref{eqn:poly_func_repr_D} directly, since the evolution of coefficients in such representation is not obtainable as explained in Section~\\ref{sec:veh_ctrl_setup}.\n\nIn panel (a), the dotted black curve denotes the closed path (\\ref{eqn:EOM_ref_path_ds}, \\ref{eqn:curv_s_func}), while the solid red curve represents the position of the vehicle at point $Q$. Panel (b) plots the lateral deviation $\\varepsilon_{\\Omega}$ using the blue curve, and the steering command $\\gamma_{\\rm des}$ using the red curve with the axis marked on the right. Panels (c, d, e) show the time profiles of the coefficients $\\hat{\\phi}_{0}$, $\\hat{\\phi}_{1}$ and $\\hat{\\phi}_{2}$, respectively, of the parametric representation \\eqref{eqn:param_repr_body_frame} when the vehicle moves along the path. The blue curves denote the measurement outputs of perception algorithm, while the red curves indicate the true values of those coefficients. We remark that: i) only the coefficients until the second order in the lateral direction are shown here since they contain more important information in lateral control than other coefficients; ii) although this represents the scenario using function representation, the coefficients are still transformed to facilitate comparison against parametric representation; and iii) the time profiles of other coefficients in the representation \\eqref{eqn:param_repr_body_frame} are similar and reveal similar results.\nFig.~\\ref{fig:sim_50ms}(a,b) indicate that the controller (\\ref{eqn:lateral_controller}-\\ref{eqn:theta0_des}) allows the vehicle to follow the given path with reasonable performance in this scenario. However, during simulation we also observe that when $T_{\\rm p}\\ge 0.2$ [s], vehicle using this controller is not able to follow the given path using the outdated lane information without prediction. This result implies a high requirement on lane perception latency especially when measurements may also be corrupted with noises in practice.\n\n\\begin{figure}\n  \\centering\n \n  \\includegraphics[scale=1.05]{Fig05.pdf}\\\\\n  \\caption{Simulation results for camera-based lateral control without prediction on lane representation when $T=0.05$ [s] and $T_{\\rm p}=0.15$ [s]. (a) Vehicle position and the closed path (\\ref{eqn:EOM_ref_path_ds}, \\ref{eqn:curv_s_func}) in ($x$, $y$)-plane. (b) lateral deviation $\\varepsilon_{\\Omega}$ and steering command $\\gamma_{\\rm des}$. (c, d, e) time profiles of coefficients in the parametric representation \\eqref{eqn:param_repr_body_frame} while the vehicle moves along the path. \\label{fig:sim_50ms}}\n\\end{figure}\n\n\\begin{figure}\n  \\centering\n \n  \\includegraphics[scale=1.05]{Fig06.pdf}\\\\\n  \\caption{Simulation results for camera-based lateral control using \\eqref{eqn:coeff_dyn_gen_equiv} for estimation on lane representation when $T=0.05$ [s] and $T_{\\rm p}=2$ [s]. (a) Vehicle position and the closed path (\\ref{eqn:EOM_ref_path_ds}, \\ref{eqn:curv_s_func}) in ($x$, $y$)-plane. (b) lateral deviation $\\varepsilon_{\\Omega}$ and steering command $\\gamma_{\\rm des}$. (c, d, e) time profiles of coefficients in the parametric representation \\eqref{eqn:param_repr_body_frame} while the vehicle moves along the path. \\label{fig:sim_2s}}\n\\end{figure}\n\nFig.~\\ref{fig:sim_2s} shows the simulation results when function representation \\eqref{eqn:poly_func_repr_D} is transformed to parametric representation and \\eqref{eqn:coeff_dyn_gen_equiv} is used to predict the coefficients at every control step in the absence of measurement. Here, the control period $T$ is still $0.05$ [s], but perception period $T_{\\rm p}$ is set to $2$ [s] to demonstrate the effectiveness. Besides the same layout and color scheme as those used in Fig.~\\ref{fig:sim_50ms}, panels (c,d,e) use blue dots to represent new measurements of coefficients from perception algorithm, and also zoomed-in plots to highlight the errors on coefficients between the predicted values and the true values. Fig.~\\ref{fig:sim_2s}(a,b) indicate that with such low perception updating rate, the controller still achieves reasonable performance in following the given path by predicting the new representation using \\eqref{eqn:coeff_dyn_gen_equiv}. Fig.~\\ref{fig:sim_2s}(c,d,e) show that prediction errors on the coefficients of higher orders are much smaller than those of lower orders. This is natural because errors on higher orders lead to less accurate prediction for the future than errors on lower orders. The zoomed-in plots illustrate that the estimation errors in the coefficients  $\\hat{\\phi}_{0}$, $\\hat{\\phi}_{1}$ and $\\hat{\\phi}_{2}$ become noticeable after predicting with \\eqref{eqn:coeff_dyn_gen_equiv} for about 0.3, 1.2, and 1.6 [s], respectively. The error in $\\hat{\\phi}_{0}$ leads to a noticeable offset in lateral deviation $\\varepsilon_{\\Omega}$ around $0.05$ [m] depicted in Fig.~\\ref{fig:sim_2s}(b).\nOne may notice that the vehicle travels 40 [m] during $2$ [s] prediction period since $V=20$ [m\/s]. Function representation \\eqref{eqn:poly_func_repr_D} is the Taylor approximation about point $\\Omega$ at the perception updating instant. The approximation error gradually becomes noticeable while the vehicle moves forward. Also, prediction with \\eqref{eqn:coeff_dyn_gen_equiv} requires estimated state changes (\\ref{eqn:changes_tau_eta_psi}, \\ref{eqn:changes_s}) using Euler integration that aggregates errors. Although the errors in Taylor approximation cannot be mitigated, the aggregation errors in Euler integration can be reduced by increasing the estimation frequency.\n\n\\begin{figure}\n  \\centering\n \n  \\includegraphics[scale=1.05]{Fig07.pdf}\\\\\n  \\caption{Comparison results for camera-based lateral control using \\eqref{eqn:coeff_dyn_gen_equiv} for estimation on lane representation when $T_{\\rm p}=2$ [s]. (a, c) $T=0.02$ [s]. (b, d) $T=0.01$ [s]. \\label{fig:sim_T_diff}}\n\\end{figure}\n\nFig.~\\ref{fig:sim_T_diff} shows the comparison results for the same scenario as that for Fig.~\\ref{fig:sim_2s} when perception updating period $T_{\\rm p}$ is still $2$ [s], but control updating period $T$ is reduced to $0.02$ [s] and $0.01$ [s] for panels (a,c) and (b,d), respectively.\nFig.~\\ref{fig:sim_2s}(c) and Fig.~\\ref{fig:sim_T_diff}(c,d) show that the error of $\\hat{\\phi}_{0}$ is decreased as control updating period $T$ decreases, which leads to decreased offset in lateral deviation $\\varepsilon_{\\Omega}$ depicted in Fig.~\\ref{fig:sim_2s}(b) and Fig.~\\ref{fig:sim_T_diff}(a,b).\n\nWe remark that in practice perception updating period is faster than $2$ [s], but the simulations shown here demonstrate the large potential in estimating lanes using parametric representation with \\eqref{eqn:coeff_dyn_gen_equiv}. This prediction can be used in the time update step in Kalman filter to get more accurate estimations, or as a pure prediction when measurements are temporarily not available. When noises and model mismatches appear in practice, performance degradation is inevitable. However, it is expected that prediction within $0.5\\sim 1$ [s] can still provide reasonable performance since integration aggregation is not long and the vehicle travelling distance is not far.\n\n\\section{Conclusion \\label{sec:conclusion}}\n\nThis paper revisited the fundamental mathematics on approximating curves as polynomial functions or parametric curves. It is shown that arc-length-based parametric representations possess the nice properties of preserving the form in coordinate transformation and parameter shifting. These properties have the potential in facilitating lane estimation for vehicle control since lanes are characterized as curves expressed in vehicle body-fixed frame by perception algorithms. As the vehicle moves, the body-fixed frame is translating and rotating. Thus, we proposed a new architecture using parametric representation in lane estimation and control. To ensure compatibility with most of current platforms, perception algorithms are still assumed to output coefficients of polynomial function representation. We derived the change of coefficients to transform polynomial function representation to arc-length-based parametric representation, and the evolution of coefficients using parametric representation. This evolution reveals an intrinsic linear relationship as the vehicles moves, which can be easily used for prediction or integrated with Kalman filters. We also set up a framework to simulate the whole process, including perception, estimation and control, for camera-based vehicle control problems. Simulation results indicate that controllers relying on predicted lanes using parametric representations can still achieve reasonably good performance at extremely low perception updating rate. These results are practically important in improving control performance with reduced perception updating rate, and obtaining better estimates when coefficients of representations are corrupted with noises. Future research directions may include lane estimation in the presence of noises and model mismatches, and field implementation with the proposed architecture and estimation model.\n\n\n\n\\bibliographystyle{IEEEtran}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nThe study of the interaction of Alfv\\'en waves (AWs) \nwith plasma inhomogeneities is \nimportant for\nboth astrophysical and laboratory plasmas.\nThis is because both AWs and inhomogeneities \noften coexist in these physical systems.\nAWs are believed to be\ngood candidates for plasma heating, energy and momentum transport.\nOn the one hand, in many physical situations AWs are easily excitable \n(e.g. through convective motion of the solar interior)\nand thus they are present in a number of astrophysical systems.\nOn the other hand, these waves dissipate due to \nthe shear viscosity as opposed to\ncompressive fast and slow magnetosonic waves which dissipate due to the\nbulk viscosity.\nIn astrophysical plasmas shear viscosity is extremely small\nas compared to bulk viscosity. Hence,\nAWs are notoriously difficult to dissipate.\nOne of the possibilities to improve AW dissipation is to introduce progressively\ndecreasing spatial scales, $\\delta l \\to 0$, into the system (recall that the \nclassical dissipation is $\\propto \\delta l^{-2}$). \nHeyvaerts and Priest have proposed (in the astrophysical context) one such \nmechanism, called \nAW phase mixing \\citep{hp83}. It occurs when a linearly polarised\nAW propagates in the plasma with a \none dimensional density inhomogeneity transverse \nto the uniform magnetic field.\nIn such a situation the initially plane AW front is progressively \ndistorted because of different Alfv\\'en speeds across the field. \nThis creates progressively stronger gradients\nacross the field (in the inhomogeneous regions \nthe transverse scale collapses to zero),\nand thus in the case of finite resistivity, dissipation is greatly enhanced.\nHence, it is believed that phase mixing can provide significant plasma\nheating. Phase mixing could be also important for laboratory plasmas.\n\\citet{hc74} proposed the heating of collisionless plasma by \nutilising spatial phase mixing by shear Alfv\\'en wave resonance and discussed potential \napplications to toroidal plasma.\nA significant amount of work has been done in the context of heating open\nmagnetic structures in the solar \ncorona \\citep{hp83,nph86,p91,nrm97,dmha00,bank00,tan01,hbw02,tn02,tna02,tnr03}.\nAll phase mixing studies so far have been performed in the MHD approximation,\nhowever, since the transverse scales in the AW collapse progressively to zero,\nthe MHD approximation is inevitably violated. \nThis happens when the transverse scale approaches\nthe ion gyro-radius $r_i$ and then electron gyro-radius $r_e$.\nThus, we proposed to study the phase mixing effect in the kinetic regime, i.e.\nwe go beyond a MHD approximation. Preliminary results were \nreported in \\citet{tss05}, where\nwe discovered a new mechanism for the acceleration of electrons\ndue to wave-particle interactions. This has important implications\nfor various space and laboratory plasmas, e.g. the \ncoronal heating problem and acceleration of the solar wind.\nIn this paper we present a full analysis of the discovered effect\nincluding an analysis of the broadening of the ion\ndistribution function due to the presence of Alfv\\'en waves and the generation of \ncompressive perturbations due to both\nweak non-linearity and plasma density inhomogeneity.\n\n\n\\section{The model}\nWe used 2D3V, the fully relativistic, electromagnetic, particle-in-cell (PIC)\ncode with MPI parallelisation, modified from the 3D3V TRISTAN code \\citep{b93}.\nThe system size is $L_x=5000 \\Delta$ and $L_y=200 \\Delta$, where\n$\\Delta(=1.0)$ is the grid size. The periodic boundary conditions for\n$x$- and $y$-directions are imposed on particles and fields. There are about\n478 million electrons and ions in the simulation. The average number of\nparticles per cell is 100 in low density regions (see below). \nThe thermal velocity of electrons is $v_{th,e}=0.1c$\nand for ions is $v_{th,i}=0.025c$.\nThe ion to electron\nmass ratio is $m_i\/m_e=16$. The time step is $\\omega_{pe} \\Delta t=0.05$. Here\n$\\omega_{pe}$ is the electron plasma frequency.\nThe Debye length is $v_{th,e}\/\\omega_{pe}=1.0$. The electron skin depth \nis $c\/\\omega_{pe}=10 \\Delta$, while the ion skin depth is $c\/\\omega_{pi}=40 \\Delta$.\nHere $\\omega_{pi}$ is the ion plasma frequency.\nThe electron Larmor radius is $v_{th,e}\/\\omega_{ce}=1.0 \\Delta$, while\nthe same for ions is $v_{th,i}\/\\omega_{ci}=4.0 \\Delta$.\nThe external uniform magnetic field, $B_0(=1.25)$,\nis in the $x$-direction and the initial\nelectric field is zero. \nThe ratio of electron cyclotron frequency to the electron plasma\nfrequency is $\\omega_{ce}\/\\omega_{pe}=1.0$, while the same for ions is\n$\\omega_{ci}\/\\omega_{pi}=0.25$. The latter ratio is essentially $V_A\/c$ -- the Alfv\\'en\nspeed normalised to the speed of light. Plasma $\\beta=2(\\omega_{pe}\/\\omega_{ce})^2(v_{th,e}\/c)^2=0.02$.\nHere all plasma parameters are quoted far away from the density \ninhomogeneity region. The dimensionless (normalised to some reference constant value of $n_0=100$ particles per cell) \nion and electron density inhomogeneity is described by\n\\begin{equation}\n {n_i(y)}=\n{n_e(y)}=1+3 \\exp\\left[-\\left(\\frac{y-100\\Delta}{50 \\Delta}\\right)^6\\right]\n\\equiv F(y).\n\\end{equation}\nThis means that in the central region (across the \n$y$-direction), the density is\nsmoothly enhanced by a factor of 4, and there are the \nstrongest density gradients having \na width of about ${50 \\Delta}$ around the \npoints $y=51.5 \\Delta$ and $y=148.5 \\Delta$.\nThe background temperature of ions and electrons, \nand their thermal velocities\nare varied accordingly\n\\begin{equation}\n{T_i(y)}\/{T_0}=\n{T_e(y)}\/{T_0}=F(y)^{-1},\n\\end{equation}\n\\begin{equation}\n {v_{th,i}}\/{v_{i0}}=\n{v_{th,e}}\/{v_{e0}}=F(y)^{-1\/2},\n\\end{equation}\nsuch that the thermal pressure remains constant. Since the background magnetic field\nalong the $x$-coordinate  is also constant, the total pressure remains constant too.\nThen we impose a current of the following form\n\\begin{equation}\n{\\partial_t E_y}=-J_0\\sin(\\omega_d t)\\left(1-\\exp\\left[-(t\/t_0)^2\\right]\\right),\n\\end{equation}\n\\begin{equation}\n{\\partial_t E_z}=-J_0\\cos(\\omega_d t)\\left(1-\\exp\\left[-(t\/t_0)^2\\right]\\right).\n\\end{equation}\nHere $\\omega_d$ is the driving frequency which was fixed at $\\omega_d=0.3\\omega_{ci}$.\nThis ensures that no significant ion-cyclotron damping is present. Also,\n$\\partial_t$ denotes the time derivative.\n$t_0$ is the onset time of the driver, which was fixed at $50 \/\\omega_{pe}$\ni.e.  $3.125 \/ \\omega_{ci}$. This means that the driver onset time is about 3 ion-cyclotron\nperiods. Imposing such a current on the system results in the generation of\nleft circularly polarised AW, which is driven at the left \nboundary of simulation box and has spatial width of $1 \\Delta$.\nThe initial amplitude of the current is such that \nthe relative AW amplitude is about 5 \\% of the background\n(in the low density homogeneous regions),\nthus the simulation is weakly non-linear.\n\n\\section{Main results}\n\nBecause no initial (perpendicular to the external magnetic field) velocity excitation\nwas imposed in addition to the above specified currents \n(cf. \\citet{tn02,dvl01,tt03,tt04}), \nthe circularly polarised AW excited (driven) at the left boundary\nis split into two circularly polarised AWs which travel in opposite directions. The dynamics of these\nwaves as well as other physical quantities is shown in Fig.~1.\n(cf. Fig.~1 from \\citet{tss05} where \n$B_z$ and $E_y$, the circularly polarised Alfv\\'en wave\ncomponents, were shown for three different times).\nA typical simulation, untill $t=875 \/ \\omega_{ce}=54.69 \/ \\omega_{ci}$ takes about 8 days\non the parallel 32 dual 2.4 GHz Xeon  processors.\nIt can be seen from the figure \nthat because of the periodic boundary conditions, a circularly polarised\nAW that was travelling to the left, reappeared \non the right side of the simulation box.\nThe dynamics of the AW ($B_z,E_y$) progresses in a similar manner as in the \nMHD, i.e. it phase mixes \\citep{hp83}.\nIn other words, the middle region (in $y$-coordinate), i.e. $50 \\Delta \\leq y \\leq 150 \\Delta$, travels \nslower because of the density enhancement (note that \n$V_A(y) \\propto 1\/\\sqrt{n_i(y)}$).\nThis obviously causes a \ndistortion of initially plain wave front and the creation of strong gradients\nin the regions around $y \\approx 50$ and $150$.\nIn the MHD approximation when resistivity, $\\eta$, is finite, \nthe AW is strongly dissipated in these regions. This effectively means that the outer and inner parts of the\ntravelling AW are detached from each other and propagate independently.\nThis is why the effect is called phase mixing -- after a long time (in the case\nof developed phase mixing), \nphases in the wave front become effectively uncorrelated.\nBefore \\citet{tss05}, it was not clear what to expect from our PIC simulation. \nThe code is collisionless and there\nare no sources of dissipation in it (apart from the \npossibility of wave-particle interactions).\nIt is evident from Fig.~1 that in the developed stage of phase mixing \n($t=54.69 \/ \\omega_{ci}$), the AW front is substantially damped in the strongest density\ngradient regions.\nContrary to the AW ($B_z$ and $E_y$) dynamics we do not see any phase mixing for \n$B_y$ and $E_z$. The latter two behave similarly.\nIt should be noted that $E_z$ contains both driven (see Eq.(4) above) and \nnon-linearly generated fast magnetosonic wave components, with the former being dominant over the\nlatter. \nSince $B_x$ is not driven, and initially its perturbations are absent,\nwe see only non-linearly generated slow magnetosonic perturbations confined to the\nregions of strongest density gradients (around $y\\approx50$ and $150$).\nNote that these also have rapidly decaying amplitude.\nAlso, we gather from Fig.~1 that the density perturbation ($\\approx 10$\\%)\nwhich is also generated through the weak non-linearity is present too.\nThese are propagating density oscillations with variation both in overall magnitude (perpendicular to the\nfigure plane) and across the $y$-coordinate, and they are mainly confined to the strongest density gradients regions\n(around $y\\approx 50$ and $150$).\nNote that dynamics of $B_x,B_y$ and $B_z$ with \nappropriate geometrical switching (because in our\ngeometry the uniform magnetic field lies along the $x$-coordinate)\nis in qualitative agreement with \\citet{bank00} (cf their Fig.~9).\nThe dynamics of remaining $E_x$ component is treated separately in the next figure.\nIt is the inhomogeneity of the medium $n_i(y)$, $V_A(y)$, i.e.\n$\\partial \/ \\partial y \\not = 0$, is the cause of weakly non-linear coupling of the AWs to the \ncompressive modes (see \\citet{nrm97,tan01} for further details).\n\n\\begin{figure*}\n\\centering\n \\epsfig{file=fig1a.eps,width=6cm}\n \\epsfig{file=fig1b.eps,width=6cm}\n \\epsfig{file=fig1c.eps,width=6cm}\n \\epsfig{file=fig1d.eps,width=6cm}\n \\epsfig{file=fig1e.eps,width=6cm}\n \\epsfig{file=fig1f.eps,width=6cm}\n\\caption{Contour (intensity) plots of electromagnetic field components and electron density \nat time $t=54.69 \/ \\omega_{ci}$ (developed stage of phase mixing). \nThe phase mixed Alfv\\'en wave components are $B_z$ and $E_y$. \nThe excitation source is at the left\nboundary. Because of periodic boundary conditions, the \nleft-propagating AW re-appears from the \nright side of the simulation box. Note how the (initially plain) AW is stretched because of \ndifferences in local Alfv\\'en speed across the \n$y$-coordinate. Significant ($\\approx 10$\\%) \ndensity fluctuations can be seen.}\n\\end{figure*}\n\n\nIn Fig.~2 we try to address the question of \nwhere the AW energy went? (as we saw strong\ndecay of AWs in the regions of strong density gradients).\nThus in Fig.~2 we plot $E_x$, the longitudinal\nelectrostatic field, and electron phase space ($V_x\/c$ vs. $x$ and $V_x\/c$ vs. $y$) for different \ntimes.\nIn the \nregions around $y \\approx 50$ and $150$, for later times, a significant electrostatic field\nis generated. This is the consequence of stretching of the \nAW front in those regions\nbecause of the difference in local Alfv\\'en speed.\nIn the middle column of this figure we see that exactly in those regions\nwhere $E_x$ is generated, \nmany electrons are accelerated along $x$-axis.\nWe also gather from the right column that for \nlater times ($t=54.69 \/ \\omega_{ci}$), the\nnumber of high velocity electrons is increased around the \nstrongest density gradient regions\n(around $y \\approx 50$ and $150$). Thus, the generated $E_x$ field is somewhat oblique\n(not exactly parallel to the external magnetic field).\nHence, we conclude that the \nenergy of the phase-mixed AW goes into acceleration of electrons.\nLine plots of $E_x$ show that this electrostatic field is strongly damped,\ni.e. the energy is channelled to electrons via Landau damping.\n\n\\begin{figure*}\n\\centering\n\\includegraphics[width=12cm]{fig2.eps}\n\\caption{Left column: contour plots of the generated electrostatic field $E_x$\nnearly parallel to the\nexternal magnetic field  at instances: \n$t=(0, 31.25, 54.69) \/ \\omega_{ci}$. Central column: $V_x\/c$ versus $x$ of electron phase\nspace at the same times. To reduce figure size, only electrons with $V_x > 0.15c$\nwere plotted. Right column: $V_x\/c$ versus $y$ of electron phase\nspace at the same times. Only electrons with $V_x > 0.12c$\nwere plotted (note the dip in the middle due to the \ndensity inhomogeneity across $y$-coordinate).}\n\\end{figure*}\n\n\n\nIn Fig.~3 we investigate ion phase space\n($V_z\/c$ vs. $x$ and $V_z\/c$ vs. $y$) for the different \ntimes. The reason for choice of $V_z$ will become clear below.\nWe gather from this plot that in $V_z\/c$ vs. $x$ phase space, clear\npropagating oscillations are present (left column). These oscillations \nare of the incompressible, Alfv\\'enic \"kink\" type, \ni.e. for those $x$s where there is an increase of\ngreater positive velocity ions, there is also a \ncorresponding decrease of lower negative velocity ions.\nIn the $V_z\/c$ vs. $y$ plot we also see no clear acceleration of\nions.\n\n\\begin{figure*}\n\\centering\n\\includegraphics[width=12cm]{fig3.eps}\n\\caption{Left column: $V_z\/c$ versus $x$ of ion phase\nspace at instances: \n$t=(0, 31.25, 54.69) \/ \\omega_{ci}$. \nRight column: $V_z\/c$ versus $y$ of ion phase\nspace at the same times. Only ions with $V_z > 0.03c$\nare plotted (note the dip in the middle due to the \ndensity inhomogeneity across the $y$-coordinate).}\n\\end{figure*}\n\n\n\nWe next look at the distribution functions of electrons and ions\nbefore and after the phase mixing took place.\nIn Fig.~4 we plot distribution functions of electrons and ions at $t=0$ and $t=54.69 \/ \\omega_{ci}$.\nNote that  at $t=0$  the distribution functions do not look as \npurely Maxwellian because\nof the fact that the \ntemperature varies across the $y$-coordinate (to keep total pressure\nconstant) and the graphs are produced for the entire simulation domain.\nAlso, note that for electrons in $f(V_x)$ there is \na substantial difference at $t=54.69 \/ \\omega_{ci}$\nto its original form because of the aforementioned \nelectron acceleration.\nWe see that the number of electrons having velocities $V_x=\\pm (0.1-0.3)c$ is increased.\nNote that the acceleration of electrons takes place mostly along\nthe external magnetic field (along the $x$-coordinate). Thus, very little electron acceleration \noccurs for $V_y$ or $V_z$ (solid and dotted curves practically overlap each other).\nFor the ions the situation is different: we see broadening of the ion velocity distribution functions\nin $V_z$  and $V_y$ (that is why we have chosen to present the \n$V_z$ component of ion phase space in Fig.~3).\n\\begin{figure*}\n\\centering\n\\includegraphics[width=12cm]{fig4.eps}\n\\caption{All three components of the distribution functions of electrons \n(top row) and ions (bottom row) \nat $t=0$ (dotted curves) and $t=54.69 \/ \\omega_{ci}$\n(solid curves), i.e. for the developed stage of phase mixing.}\n\\end{figure*}\n\n\n\nThe reason for this broadening of the ion distribution function becomes \nclear in Fig.~5 where we plot\nkinetic energy $x,y,z$ components ($\\propto V_{x,y,z}^2$) and total kinetic energies for\nelectrons (top row) and ions (bottom row). For ions we gather that $y$ and $z$ components of\nthe kinetic energy (bottom left figure) oscillate in anti-phase and their oscillatory part perfectly cancels \nout in the total energy (bottom right figure). Thus, the broadening of the $y$ and $z$ components of the\nion velocity distribution functions is due to the presence of AWs (usual wave broadening, which is actually observed\ne.g. in the solar corona and solar wind, \\cite{bd71,sbnm95,bpb00}), and hence there is no ion acceleration present.\nNote that $y$ and $z$ components and hence total kinetic energy of ions is monotonously increasing due to continuous\nAW driving. Note that no significant motion of ions along the field is present.\nFor electrons, on the other hand, we see a \nsignificant increase of the \n$x$ component (along the magnetic field) of kinetic energy\nwhich is due to the new electron acceleration mechanism discovered by us (cf. Fig.10).\nNote that for ions the $y$ component reaches lower values (than the \n$z$ component) because of lower AW velocity in the middle \npart of the simulation domain.\n\n\\begin{figure}[]\n\\resizebox{\\hsize}{!}{\\includegraphics{fig5.eps}} \n\\caption{Top row: kinetic energies (calculated  by $x$ (solid), $y$ (dotted), $z$ (dashed) velocity (squared) components) of \nelectrons (left), and total kinetic energy for electrons (right)\nas a function of time. Bottom row: As above but for ions. The units on $y$-axis are arbitrary.}\n\\end{figure}\n\n\n\nThe next step is to check whether the increase in electron velocities really comes from the\nresonant wave particle interactions. For this purpose in Fig.~6, left \npanel,  we plot two snapshots of the\nAlfv\\'en wave $B_z(x,y=148)$ component at instances $t=54.69 \/ \\omega_{ci}$ (solid line)\nand $t=46.87 \/ \\omega_{ci}$ (dotted line).\nThe distance between the two upper leftmost peaks (which is the distance \ntravelled by the\nwave in the time span between the snapshots) \nis about $\\delta L=150\\Delta=15(c\/\\omega_{pe})$.\nThe time difference between the snapshots is $\\delta t=7.82 \/ \\omega_{ci}$.\nThus, the \nmeasured AW speed at the point of the strongest density gradient ($y=148$)\nis $V_A^M=\\delta L \/\\delta t=0.12c$. We can also work out \nthe Alfv\\'en speed from theory.\nIn the homogeneous low density region the Alfv\\'en speed was set to be\n$V_A(\\infty)=0.25 c$. From Eq.(1) it follows that for $y=148$ the \ndensity is increased by a factor of\n$2.37$ which means that the Alfv\\'en wave speed at this position is\n$V_A(148)=0.25\/\\sqrt{2.37}c=0.16c$.\nThe measured ($0.12c$) and calculated ($0.16c$) Alfv\\'en speeds in the inhomogeneous regions \ndo not coincide. This is probably because  the \nAW front is decelerated (due to momentum conservation) \nas it passes on energy and momentum to the\nelectrons in the inhomogeneous regions (where electron acceleration takes place). \nHowever, this possibly is not the case if wave-particle interactions\nplay the same role as dissipation in  MHD \\citep{sg69}:\nThen wave-particle interactions would result only in the decrease of the AW\namplitude (dissipation) and not in its deceleration.\nIf we compare these values to Fig.~4 (top left panel for $f(V_x)$), we deduce\n that these are the\nvelocities $>0.12c$ above which electron numbers with higher velocities\nare greatly increased. This deviation peaks at about $0.25c$ which,\nin fact, corresponds to the Alfv\\'en speed in the lower density regions.\nThis can be explained by the fact the electron acceleration takes\nplace in  wide regions (cf. Fig.~2) along and around $y \\approx 148$ (and $y \\approx 51$) -- hence\nthe spread in the accelerated velocities.\nIn Fig.~6 we also plot a visual fit curve (dashed line) to \nquantify the amplitude decay law for the AW (at $t=54.69 \/ \\omega_{ci}$)\nin the strongest density inhomogeneity region.\nThe fitted (dashed) cure is represented by $0.056 \\exp \\left[ -\n\\left({x}\/{1250}\\right)^3\\right]$.\nThere is a surprising similarity of this fit with the \nMHD approximation results.\n\\citet{hp83} found that for large times (developed phase mixing),\nin the case of a harmonic driver, the amplitude decay law\nis given by $\\propto \\exp \\left[ -\n\\left(\\frac{\\eta \\omega^2 V_A^{\\prime 2}}{6 V_A^{5}}\\right)x^3\\right]$ which \nis much faster \nthan the usual resistivity dissipation\n$\\propto \\exp(-\\eta x)$. Here $V_A^{\\prime}$ is the derivative\nof the Alfv\\'en speed with respect to the $y$-coordinate.\nThe most interesting fact is that even in the kinetic approximation\nthe same $\\propto \\exp (-A x^3)$ law holds as in MHD.\n\n\n\\begin{figure*}\n\\centering\n\\includegraphics[width=12cm]{fig6.eps}\n\\caption{Left: two snapshots of the\nAlfv\\'en wave $B_z(x,y=148)$ component at instances $t=54.69 \/ \\omega_{ci}$ (solid line)\nand $t=46.87 \/ \\omega_{ci}$ (dotted line). The dashed line represents fit\n$0.056 \\exp \\left[ -\\left({x}\/{1250}\\right)^3\\right]$. Center: $B_z(x,y=10)$ \n(low density homogeneous region), $B_z(x,y=100)$ (high density homogeneous region).\nNote the\ndifferences in amplitudes and propagation speeds, which are consistent with the equilibrium\ndensity and thus Alfv\\'en speed dependence on $y$-coordinate.}\n\\end{figure*}\n\n\n\nIn MHD, finite resistivity and\nAlfv\\'en speed non-uniformity are responsible for the\nenhanced dissipation via phase mixing.\nIn our PIC simulations (kinetic phase mixing), however, we do not have dissipation\nand collisions (dissipation). Thus, in our case,\nwave-particle interactions play the same role as \nresistivity $\\eta$ in the MHD phase mixing \\citep{sg69}.\nNo significant AW dissipation\nwas found away from the density inhomogeneity regions (Fig.~6 middle and right panels, note also the\ndifferences in amplitudes and propagation speeds, which are consistent with the imposed density and hence Alfv\\'en speed variation\nacross the $y$-coordinate).\nThis has the same explanation as in the case of MHD --\nit is in the regions of density of inhomogeneities ($V_A^{\\prime}\\not=0$) \nthat the dissipation is greatly enhanced, while in the regions\nwhere $V_A^{\\prime}=0$ there is no substantial dissipation (apart from the \nclassical $\\propto \\exp(-\\eta x)$\none).\nIn the MHD approximation, the aforementioned amplitude decay law is derived\nfrom the diffusion equation, to which MHD equations reduce for large times (developed\nphase mixing \\citep{tnr03}). It seems that the kinetic description \nleads to the same type of diffusion equation.\nIt is unclear at this stage, however, what physical quantity \nwould play the role of resistivity $\\eta$ (from the MHD approximation) in the\nkinetic regime. \n\n\n\n\\subsection{Homogeneous plasma case}\n\nIn order to clarify the broadening of the ion velocity distribution function\n and also for a consistency check\nwe performed an additional simulation in the case of homogeneous plasma.\nNow the density was fixed at 100 ions\/electrons per cell in the entire simulation\ndomain and hence plasma temperature and thermal velocities were fixed too.\nIn such a set up no phase mixing should take place as the AW speed is uniform.\n\n\\begin{figure*}\n\\centering\n \\epsfig{file=fig7a.eps,width=6cm}\n \\epsfig{file=fig7b.eps,width=6cm}\n \\epsfig{file=fig7c.eps,width=6cm}\n \\epsfig{file=fig7d.eps,width=6cm}\n \\caption{As in Fig.~1 but for the case of homogeneous plasma density (no phase mixing).\n Note only non-zero (above noise level) components are plotted. There are no $B_x,E_x$ or density\n fluctuations present in this case.}\n\\end{figure*}\n\n\n\nIn Fig.~7 we plot the only non-zero (above noise level) components at $t=54.69 \/ \\omega_{ci}$, which\nare left circularly polarised AW fields: $B_z,B_y,E_z,E_y$. \nNote there are no $B_x,E_x$ or density fluctuations present in this case (cf. Fig.~1) as\nit is the plasma inhomogeneity that facilitates the coupling between  AW and the compressive\nmodes.\n\\begin{figure*}\n\\centering\n\\includegraphics[width=12cm]{fig8.eps}\n\\caption{As in Fig.~3 but for the case of homogeneous plasma density (no phase mixing).}\n\\end{figure*}\n\n\n\nIn Fig.~8 we plot ion phase space ($V_z\/c$ vs. $x$ and $V_z\/c$ vs. $y$) in the\nhomogeneous plasma case for different times (cf. Fig.~3). We gather from the graph that\npropagating, incompressible, Alfv\\'enic \"kink\" type oscillations are still present (left column),\nwhile no significant ion\nacceleration takes place (right column). This is better understood from Fig.~9 where we plot electron and ion \ndistribution functions for $t=0$ and $t=54.69 \/ \\omega_{ci}$ (as in Fig.~4) for the \nhomogeneous plasma case. \nThere are three noteworthy points: (i) no electron acceleration takes place because of\nthe absence of phase mixing; (ii) there is (as in the inhomogeneous case) broadening of the ion\nvelocity distribution functions (in $V_y$ and $V_z$) due to the present AW (wave broadening);\n(iii) The distribution now looks Maxwellian (cf. Fig.~4) because \nthe distribution function\nholds for the entire homogeneous region.\n\n\\begin{figure*}\n\\centering\n\\includegraphics[width=12cm]{fig9.eps}\n\\caption{As in Fig.~4 but for the case of homogeneous plasma density (no phase mixing).}\n\\end{figure*}\n\n\nIn Fig.~10  we plot the\nkinetic energy $x,y,z$ components ($\\propto V_{x,y,z}^2$) and \ntotal kinetic energy for\nelectrons (top row) and ions (bottom row). For ions we see (as in the inhomogeneous case) \nthat $y$ and $z$ components of\nthe kinetic energy (bottom left figure) oscillate in anti-phase and their oscillatory part perfectly cancels \nout in the total energy (bottom right figure). Thus, the broadening of the $y$ and $z$ components of the\nion velocity distribution functions is due to the presence of AWs, and, in turn, there is no ion acceleration.\nAgain the $y$ and $z$ components and hence the \ntotal kinetic energy of the ions is monotonously increasing due to continuous\nAW driving. No significant motion of ions along the field is present.\nFor electrons we do not observe any acceleration due to the absence of phase mixing (cf. Fig.5).\nNote that the $y$ component now attains the same values as the \n$z$ component (bottom left figure)\nbecause of the same AW velocity in the entire simulation domain.\n\n\\begin{figure}[]\n\\resizebox{\\hsize}{!}{\\includegraphics{fig10.eps}} \n\\caption{As in Fig.~5 but for the case of homogeneous plasma density (no phase mixing).} \n\\end{figure} \n\n\n\\section{Discussion}\n\nIn our preliminary work \\citep{tss05} we outlined the main results of our\nnewly-discovered mechanism of electron acceleration. Here we \npresented a more detailed analysis\nof the phenomenon. We have established the following:\n\n\\begin{itemize}\n\\item Progressive distortion of the Alfv\\'en wave front, due to the differences in \nlocal Alfv\\'en speed, generates oblique (nearly parallel to the magnetic\nfield) electrostatic fields, which accelerate electrons.\n\n\\item The amplitude decay law in the inhomogeneous regions, \nin the kinetic regime, is shown to be the same as in the MHD approximation \ndescribed by \\citet{hp83}.\n\n\\item The density perturbations ($\\approx 10$\\% of background)\nare generated due to both the weak non-linearity and plasma inhomogeneity. \nThese are propagating density oscillations with variations both \nin overall magnitude \nand across the $y$-coordinate. They are mainly confined to the strongest density gradients regions\n(around $y \\approx 50$ and $150$) i.e. edges of the density structure (e.g. boundary of a solar coronal loop). \nLongitudinal to the external magnetic field, $B_x$, perturbations are also generated in the\nsame manner, but with smaller ($\\approx 3$\\%) amplitudes.\n\n\\item Both in the homogeneous and inhomogeneous cases the presence \nof AWs causes broadening of the perpendicular \n(to the external magnetic field) ion velocity \ndistribution functions, while no ion acceleration is observed.\n\n\\end{itemize}\n\nIn the MHD approximation \n\\citet{hbw02} and \\citet{tnr03} showed that \nin the case of localised Alfv\\'en pulses,\nHeyvaerts and Priest's amplitude decay\nformula $\\propto \\exp (-A x^3)$ (which is true for\nharmonic AWs) is replaced by the power law $B_z \\propto x^{-3\/2}$. \nA natural next step forward\nwould be to check whether \nin the case of localised Alfv\\'en pulses the same power law holds\nin the kinetic regime.\n\nAfter this study was complete\nwe became aware of a study by \\citet{vh04}, who used a hybrid\ncode (electrons treated as a neutralising fluid, with ion\nkinetics retained) as opposed to our (fully kinetic) PIC code,\nto simulate resonant absorption. They found that \na planar (body) Alfv\\'en\nwave propagating at less than $90^{\\circ}$ to a background gradient  \nhas field lines which lose wave energy to another set of field lines by\ncross-field transport. Further, \\citet{v04} found that \nwhen perpendicular scales of the\norder of 10 proton inertial lengths ($10 c\/\\omega_{pi}$) \ndevelop from wave refraction\nin the vicinity of the resonant field lines, a non-propagating \ndensity fluctuation begins\nto grow to large amplitudes. This saturates by exciting highly \noblique, compressive and\nlow-frequency waves which dissipate and heat protons. \nThese processes lead to a faster development of small\nscales across the magnetic field, i.e. the phase mixing mechanism, \nstudied here.\n\n\n\\begin{acknowledgements}\nThe authors gratefully acknowledge support from\nCAMPUS (Campaign to Promote University of Salford) which funded\nJ.-I.S.'s one month fellowship to the Salford University \nthat made this project possible.\nDT acknowledges use of E. Copson Math cluster \nfunded by PPARC and University of St. Andrews.\nDT kindly acknowledges support from Nuffield Foundation \nthrough an award to newly appointed lecturers in Science,\nEngineering and Mathematics (NUF-NAL 04).\nThe authors would like to \nthank the referee, Dr. Bernie J. Vasquez, for pointing out some minor\ninconsistencies, which have been now corrected.\n\\end{acknowledgements}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzibts b/data_all_eng_slimpj/shuffled/split2/finalzzibts
new file mode 100644
index 0000000000000000000000000000000000000000..1a3ebe2f4906a88e9d35a52ffee8f53b2f2fb19d
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzibts
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction and summary of results}\n\nThe existence of dark matter and dark energy is now firmly established phenomenologically \\cite{Bradac,Spergel} but the theoretical understanding is far from complete.  Einstein equations require ``exotic\" components in the right hand side corresponding  to about $\\%96$ of the total energy density today. Understanding the microscopic nature of these extra components is one of the most challenging and important problems faced by theoretical physics at present.\n\nSupersymmetric and exotic particles in the standard model are the best candidates for dark matter (for a review see \\cite{Jungman}).  Several experiments are now being devised for a direct detection of these particles. Alternative descriptions based on modifications to gravity have also been explored with interesting results. See \\cite{Sanders,Bekenstein,Moffat,Ferreira,Ferreira2,Carroll}, and references quoted therein, for some of these efforts and its consequences. For a recent review of the Einstein aether theory see \\cite{Jacobson}.\n\nThe problem of dark energy is somehow more recent, although the issue of the cosmological constant has been around for a long time. The discovery of an accelerating Universe \\cite{Expansion} resulted in deep changes in cosmology. The simplest explanation for this phenomena is a small positive cosmological constant, but many other possibilities have been explored (see \\cite{Carroll2,Lima} for recent reviews).\n\n~\n\nIn this paper we consider an action for general relativity coupled to a Born-Infeld theory. The Born-Infeld theory has as fundamental variable a symmetric connection  $C^\\rho_{\\ \\mu\\nu}(x)$. $C^{\\mu}_{\\ \\nu\\rho}$ has the same symmetries and transformation properties of the Christoffel symbol but is independent from it. The action is\n\\begin{equation}\\label{I}\n  I[g_{\\mu\\nu},C^{\\mu}_{\\ \\nu\\rho},\\Psi]  = {1 \\over 16 \\pi G} \\int d^4x \\left[ \\sqrt{|g_{\\mu\\nu}|} R  + {2 \\over \\alpha l^2}\\sqrt{\\left|g_{\\mu\\nu}-l^2 K_{(\\mu\\nu)}\\right| } \\right] + \\int d^4x\\, {\\cal L}_m(\\Psi,g_{\\mu\\nu}),\n\\end{equation}\nwhere $|A_{\\mu\\nu}|$, for any $A_{\\mu\\nu}$, denotes the absolute value of the determinant of $A_{\\mu\\nu}$. $K_{\\mu\\nu}$ is the ``Ricci\" curvature associated to $C^{\\mu}_{\\ \\nu\\rho }(x)$,\n\\begin{equation}\\label{Kmn}\nK_{\\mu\\nu} \\equiv K^{\\alpha}_{\\ \\mu\\alpha\\nu } \\ \\ \\ \\   \\ \\  (K^{\\mu}_{\\ \\nu\\, \\alpha\\beta} = C ^{\\mu}_{\\ \\nu\\beta,\\alpha} + C^{\\mu}_{\\ \\sigma\\alpha} C^{\\sigma}_{ \\ \\nu\\beta} - [\\alpha \\leftrightarrow \\beta]).\n\\end{equation}\nBesides Newton's constant, the action (\\ref{I}) has two extra parameters: $l$ is a length and $\\alpha$ is dimensionless.  $\\Psi$ denotes all baryonic fields and ${\\cal L}_{{ m}}$ the baryonic Lagrangian.\n\nThe action (\\ref{I}) is similar in spirit although different in interpretation to the Born-Infeld gravity action proposed by Deser and Gibbons \\cite{Deser-Gibbons},\n\\begin{equation}\\label{IDG}\nI[g_{\\mu\\nu}]=\\int \\sqrt{|g_{\\mu\\nu} - l^2 R_{\\mu\\nu} + X_{\\mu\\nu}(R)|}\n\\end{equation}\nand elaborated in \\cite{DG2}.  As discussed in \\cite{Deser-Gibbons}, the term $X_{\\mu\\nu}(R)$ must be chosen such that the action is free of ghost, and free of Schwarzschild-like singularities. The action (\\ref{IDG}) is an action for pure gravity, and it can be seen as a natural extension to spin two of the scalar $\\sqrt{|g_{\\mu\\nu} + \\partial_\\mu \\phi \\partial_\\nu\\phi| }$ and vector $\\sqrt{|g_{\\mu\\nu} + F_{\\mu\\nu}|}$ Born-Infeld (BI) theories.  For the scalar and vector BI theories the equations of motion are of second order.  For the spin two theory this is not automatic and requires the addition of $X_{\\mu\\nu}$.\n\nThe action (\\ref{I}), on the other hand, gives rise to second order equations because $K_{\\mu\\nu}(C)$ depends on first derivatives of the field $C^{\\mu}_{\\ \\nu\\rho }$. This action, however, is not an action for pure gravity but gravity coupled to $C^{\\mu}_{\\ \\nu\\rho }$. The equations of motion are discussed in the appendix and in Sec. \\ref{Eq\/Sec} below.\n\nIt is known (e.g. \\cite{Fradkin-T}) that general relativity with cosmological constant is dual to Eddington's action \\cite{Eddington} $I[C]\\sim\\int \\sqrt{|K_{\\mu\\nu}|}$. The action (\\ref{I}) can then be interpreted as general relativity interacting with its own dual field theory.\n\nThe action (\\ref{I}) can also be motivated by looking at general relativity without metric \\cite{B}. This interpretation will be discussed in Sec. \\ref{Sec\/g=0}.\n\nOur main goal in this paper is to argue that the field $C^{\\mu}_{\\ \\nu\\rho}$ has good properties to represent dark matter and dark energy. We shall study the equations of motion following from (\\ref{I}) and prove the following properties.\n\\begin{enumerate}\n\\item\nFor a cosmological model, there exist solutions where the expansion factor $a(t)$ behaves as $a(t) \\sim e^{Ht}$ for large $t$, and as $a(t)\\sim t^{2\/3}$ for small $t$.\nThe equation of state for the fluid interpolates between $p=0$ and $p=-\\rho$.    The parameters in the solution can be adjusted such that this field contributes to $\\sim 23\\%$ of the total matter energy density and $\\sim \\%73$ of vacuum energy density, as required by observations \\footnote{Couplings between dark matter and energy have appeared in \\cite{Comelli}, and in \\cite{Bertolami} involving a Chapligyn gas.}.\n\n\\item\nFor a spherically symmetric configurations, the action (\\ref{I}) predicts asymptotically flat rotation curves, as required by galactic dynamics.  The parameters involved in this solution can also be adjusted to deal with realistic situations.\n\\end{enumerate}\n\n\nWe would like to stress the simplicity of this proposal. The ``Born-Infeld\" term is all we need to account for both dark energy and dark matter, at least for the problems described above.  More complicated tests, like lensing, fluctuations, and others will be discussed elsewhere \\cite{BFS,BRR}. See also \\cite{Davi}.\n\n\n\n\n\n\n\n\\section{The Equations of Motion}\n\n\n\\label{Eq\/Sec}\n\n\\subsection{A bi-metric theory}\n\nThe fields varied in the action (\\ref{I}) are the metric $g_{\\mu\\nu}$ and the connection $C^{\\mu}_{\\ \\nu\\rho }$.  Both fields are independent. At the level of the equations of motion, the connection $C^{\\mu}_{\\ \\nu\\rho }$ can be written in terms of a second metric $q_{\\mu\\nu}$. (The full action can also be written as a bi-metric theory \\cite{andy}.) This action then represent a bi-metric theory if gravity. This result follows closely the structure of Eddington's theory \\cite{Eddington}. We shall postpone a detailed derivation for the appendix and include here only the result.\n\nLet $q_{\\mu\\nu}(x)$ be a rank two invertible symmetric tensor satisfying the metricity condition\n\\begin{equation}\nD_\\rho q_{\\mu\\nu}=0\n\\end{equation}\n{\\it with respect to} $C^{\\mu}_{\\ \\nu\\rho }$.  Since $C^{\\mu}_{\\ \\nu\\rho }$ is symmetric  this implies $C^{\\mu}_{\\ \\nu\\rho} = {1 \\over 2} q^{\\mu\\alpha} ( q_{\\alpha\\nu,\\rho} + q_{\\alpha\\rho,\\nu} - q_{\\nu,\\rho,\\alpha} )$, and for every $q_{\\mu\\nu}$ there is a unique $C^{\\mu}_{\\ \\nu\\rho }$.\n\nThe equations of motion derived from the action (\\ref{I}) can be written completely in terms of $g_{\\mu\\nu}$ and $q_{\\mu\\nu}$, and take the very simple form\n\\begin{eqnarray}\nG_{\\mu\\nu} &=& - {1 \\over l^2} \\sqrt{{q}\\over g}\\, g_{\\mu\\alpha}\\,q^{\\alpha\\beta}\\,  g_{\\beta\\nu} + 8\\pi G\\, T^{{\\scriptscriptstyle (m)}}_{\\ \\ \\mu\\nu} \\label{ee} \\\\\nK_{\\mu\\nu} &=& {1 \\over l^2}( g_{\\mu\\nu} + \\alpha\\, q_{\\mu\\nu})  \\label{Ke}\n\\end{eqnarray}\n$T^{{\\scriptscriptstyle (m)}}_{\\ \\mu\\nu}$ is the energy momentum tensor associated to the baryonic Lagrangian ${\\cal L}_{{\\scriptscriptstyle (m)}}$. $q^{\\mu\\nu}$ is the inverse of $q_{\\mu\\nu}$. The derivation of these equations is left for the appendix.\n\n~\n\nEquation (\\ref{ee}) is the Einstein equation.  The first term in the right hand side is the contribution from the Born-Infeld action.  Our main goal will be to prove that this fluid can account for dark matter and dark energy.\n\n\n\\subsection{The de-Sitter solution} \\label{SecdeSitter}\n\nThe de-Sitter spacetime is an exact solution to this theory.  This can be seen as follows. (The de-Sitter spacetime is expected to be relevant after matter becomes negligible so we set here $T^{(m)}_{\\ \\mu\\nu}=0$.)\n\nSuppose there exists solutions of the equations of motion with $R_{\\mu\\nu}=\\Lambda g_{\\mu\\nu}$.  It is direct to see that this implies that both metrics must be proportional,\n\\begin{equation}\nq_{\\mu\\nu}(x) = \\gamma\\,  g_{\\mu\\nu}(x)\n\\end{equation}\nwith $\\gamma$ a constant. The constant $\\gamma$ can be computed as follows.\nReplacing in (\\ref{Ke}) we derive,\n\\begin{equation}\nR_{\\mu\\nu} = {1 \\over l^2}\\left( \\gamma \\alpha + 1 \\right) g_{\\mu\\nu}.\n\\end{equation}\nReplacing in (\\ref{ee}) (with $T^{(m)}_{\\mu\\nu}=0$) we derive\n\\begin{equation}\nR_{\\mu\\nu} = {\\gamma \\over l^2} g_{\\mu\\nu}\n\\end{equation}\nConsistency determines $\\gamma$,\n\\begin{equation}\n\\gamma = {1 \\over 1-\\alpha}.\n\\end{equation}\nThus, the Born-Infeld field can behave as a cosmological constant with the value\n\\begin{equation}\n\\Lambda = {1 \\over 1-\\alpha}\\, {1 \\over l^2}.\n\\end{equation}\nThe value $\\alpha=1$ is a critical point where cosmological solutions ceases to exist.\nCuriously, we shall see that a good fit for the Friedman equation requires $\\alpha$ to be close, but not equal, to one.\n\n\n\n\\section{Friedman cosmological models}\n\nThe evolution equation for the scale factor in flat cosmological models is given by the Friedman equation (neglecting radiation)\n\\begin{equation}\\label{Fr}\n{\\dot a^2 \\over a^2} = {\\Omega_{bm} + \\Omega_{dm} \\over a^3} + \\Omega_{\\Lambda}.\n\\end{equation}\nCurrent values for the (relative) densities of barionic matter $\\Omega_{bm}$, dark matter $\\Omega_{dm}$ and vacuum energy $\\Omega_\\Lambda$ are,\n\\begin{equation}\\label{Omega}\n\\Omega_{bm} \\simeq 0.04, \\ \\ \\ \\ \\ \\ \\  \\Omega_{dm} \\simeq 0.23, \\ \\ \\ \\ \\ \\ \\Omega_\\Lambda \\simeq 0.73.\n\\end{equation}\nAmong the components appearing in the right hand side of (\\ref{Fr}), only the $\\sim 0.04$ fraction of baryonic matter is theoretically well-understood. The other $0.23+0.73=0.96$ fraction remains a great mystery.\n\n\\subsection{Goal of this section}\n\n\n\nThe goal of this section is to demonstrate that the field $C^{\\mu}_{\\ \\nu\\rho }$ behaves like dark matter for small times, and as dark energy for larger times. In other words, its equation of state evolves from $p=0$ into $p=-\\rho$.  Adjusting the parameters $\\alpha$ and $l$, plus initial conditions, the Born-Infeld field can account for both the $\\Omega_{dm}$ and $\\Omega_{\\Lambda}$ contributions in (\\ref{Fr}). Thus, the action (\\ref{I}), is capable to reproduce the correct evolution of the scale factor without adding neither dark matter nor dark energy.\n\nOur approach does not shed any light into the particular values for $\\Omega_\\Lambda,\\Omega_{dm},\\Omega_{bm}$ and other cosmological parameters. We shall only prove that $l$ and $\\alpha$ can be chosen such that the predictions from (\\ref{I}) are consistent with the Friedman equation (\\ref{Fr}).   In particular we have chosen here to set $k=0$ and consider only flat models. There is no particular reason for the choice other than simplicity. A full analysis with a varying $k$ and including other developments will be reported in \\cite{BFS}.\n\n\n\\subsection{The ansatz and equations}\n\\label{Equations}\n\n\nTo solve (\\ref{ee}) and (\\ref{Ke}) we assume that both $g_{\\mu\\nu}$ and $q_{\\mu\\nu}$ are homogeneous, isotropic and with flat spatial sections.  Using the gauge freedom in the time coordinate to fix $g_{tt}=-1$, the ansatz for $g_{\\mu\\nu}$ and $q_{\\mu\\nu}$ is then,\n\\begin{eqnarray}\\label{FRW}\ng_{\\mu\\nu}dx^\\mu dx^\\nu &=& -  dt^2 + a(t)^2 (dx^2 + dy^2 + dz^2), \\\\\nq_{\\mu\\nu}dx^\\mu dx^\\nu &=& - X(t)^2 dt^2 + Y(t)^2 (dx^2 + dy^2 + dz^2)\\label{qFRW}\n\\end{eqnarray}\nwhere $a(t),X(t),Y(t)$ are arbitrary functions of time to be fixed by the equations of motion and initial conditions.\n\nAs usual for flat models, and to match the choice made in (\\ref{Fr}), we set\n\\begin{equation}\na(t) |_{ \\scriptscriptstyle today }=1, \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  H_0 = \\dot  a(t) |_{ \\scriptscriptstyle today }\n\\end{equation}\nand use $H_0$ to define a natural dimensionless time coordinate $H_0 t$.  The time coordinate in all expressions from now on refer to this choice.\n\nEquations (\\ref{ee},\\ref{Ke}) for the ansatz (\\ref{FRW},\\ref{qFRW}) become,\n\\begin{eqnarray}\n{\\dot a^2 \\over a^2} &=& {1 \\over 3l^2 H_0^2 } {Y^3\\over X}{1 \\over a^3} + {\\rho \\over \\rho_c} \\label{F} \\label{c1} \\\\\n\\left( {Y^3 \\over X} \\right)^. &=& 3 X Y a \\dot a  \\label{c2} \\\\\n{1 \\over X^2} {\\dot Y^2 \\over Y^2}  &=& {1 \\over 3l^2 H_0^2}\\left(  - {1 \\over 2 X^2} + \\alpha + {3 \\over 2} {a^2\\over Y^2}\\right), \\label{c3}\n\\end{eqnarray}\nplus second order equations related to (\\ref{c1}-\\ref{c3}) by Bianchi identities.\nWe have introduced the usual notation $\\rho_c = {3H_0^2 \\over 8\\pi G}$. $\\rho$ is the baryonic matter and we  shall assume\n\\begin{equation}\n{\\rho \\over \\rho_c} = {\\Omega_{bm} \\over a^3 }.\n\\end{equation}\n\nThe interpretation of equations (\\ref{c1}-\\ref{c3}) is straightforward. Equation (\\ref{F}) is the Friedman equation determining the time evolution of the scale factor $a(t)$.  The first term in the right hand side of (\\ref{c1}) is the contribution from the Born-Infeld field $C^{\\mu}_{\\ \\nu\\rho}$. Defining the density and pressure for the Born-Infeld field,\n\\begin{equation}\\label{rhop}\n\\rho_{{\\scriptscriptstyle BI}} = {1 \\over 8\\pi G l^2}{Y^3 \\over X} {1 \\over a^3}, \\ \\ \\ \\ \\ \\ \\ p_{{\\scriptscriptstyle BI}} = - {1 \\over 8\\pi G l^2} {XY \\over a}\n\\end{equation}\nthe right hand side of (\\ref{c1}) is simply ${1 \\over \\rho_{c}}(\\rho_{{\\scriptscriptstyle BI}} + \\rho)$.  Furthermore, in terms of $\\rho_{{\\scriptscriptstyle BI}}$ and $p_{{\\scriptscriptstyle BI}}$, equation (\\ref{c2}) takes the usual conservation form\n\\begin{equation}\n(\\rho_{{\\scriptscriptstyle BI}} a^3)^. = - p_{{\\scriptscriptstyle BI}} (a^3)^. .\n\\end{equation}\n\nEq. (\\ref{c3}) (``the Friedman equation for the metric $q_{\\mu\\nu}$\") provides the equation of state for $\\rho_{{\\scriptscriptstyle BI}}$ and $p_{{\\scriptscriptstyle BI}}$ allowing a full solution to the problem.  Note that using (\\ref{rhop}) the functions $X(t),Y(t)$ can be written in terms of $\\rho_{{\\scriptscriptstyle BI}}(t),p_{{\\scriptscriptstyle BI}}(t)$ and (\\ref{c3}) becomes a (differential) relation between these two functions. This equation of state thus have one free parameter represented as an initial condition.\n\nWe shall now show that $\\rho_{{\\scriptscriptstyle BI}}$ behaves like dark matter for small times, and like dark energy for large times.\n\n\n\\subsection{Asymptotic $a \\rightarrow 0$ and $a \\rightarrow \\infty$ behavior}\n\n\nDue to the complicated and non-linear character of equations (\\ref{c1}-\\ref{c3}) we shall study them by series expansions and numerically.\n\n~\n\nWe first  study the behavior for large values of $a$. In this regime, the baryonic matter density $\\rho \\sim a^{-3}$ does not contribute. (A radiation component would not contribute either.)  Neglecting the term $\\rho\/\\rho_c$, it is direct to see that the functions,\n\\begin{equation}\na(t) = a_0\\, e^{t\/C }, \\ \\ \\ \\ \\    X(t) = {1 \\over \\sqrt{1-\\alpha}} \\ \\ \\ \\ \\  Y(t) = {a_0 \\over \\sqrt{1-\\alpha}} \\, e^{t\/C},\n\\end{equation}\nwith $C = \\sqrt{3(1-\\alpha)}\\,l H_0$ provides an exact solution to (\\ref{c1}-\\ref{c3}). Thus, de-Sitter\\footnote{The existence of this exact solution is not at all surprising because  we already know that the general equations (\\ref{ee}) and (\\ref{Ke}) accepts solutions of the form $R_{\\mu\\nu} = \\Lambda g_{\\mu\\nu}$ when $q_{\\mu\\nu}$ is proportional to $g_{\\mu\\nu}$} space is a solution to (\\ref{c1}-\\ref{c3}) for large times. The constant $C$ measures the value of the associated vacuum density. In order for this solution to approach de-Sitter space with the correct exponent, we must impose\n\\begin{equation}\\label{LO}\n{1 \\over 3(1-\\alpha)l^2 H_0^2} = \\Omega_{\\Lambda}.\n\\end{equation}\n$H_0$ and $\\Omega_\\Lambda$ are determined by observations. This provides a first constraint on the parameters $l$ and $\\alpha$ entering in the action. We shall use (\\ref{LO}) to solve $l$ in terms of $\\alpha$.\n\n~\n\nNow, we study the $a(t) \\simeq 0$ region. In this regime, an exact solution is not available, but one can display a series expansion with the desired properties. The following series\n\\begin{equation}\na(t)= a_0\\, t^{2\/3} (1 + {\\cal O}(t^{4\/3})), \\ \\ \\ \\ \\ X(t) = x_0^3( 1 + {\\cal O}(t)), \\ \\ \\ \\ \\ Y(t) = x_0 (1 + {\\cal O}(t) )\n\\end{equation}\nprovide a solution to (\\ref{c1}-\\ref{c3}). The crucial point here is the exponent $t^{2\/3}$ in $a(t)$ meaning that $C^{\\mu}_{\\ \\nu\\rho}$ does indeed behave like matter for small times. The amount of dark matter is controlled by $a_0$.\n\n\\subsection{Numerical interpolation}\n\nOur final goal is to display a solution for $a(t)$ interpolating between $a(t)\\simeq t^{2\/3}$ for small $a(t)$ and $a(t)\\simeq e^{Ht}$ for large $a(t)$.  Furthermore, we would like this solution to exhibit the right amount of dark matter and dark energy.\nThis will be done by a numerical analysis.\n\n\n\nEquations (\\ref{c1}-\\ref{c3}) are of first order and thus we need to give three conditions $a_1=a(1)$, $X_1=X(1)$ and $Y_1=Y(1)$, plus the values of $\\alpha$ and $l$ to integrate them.  These are 5 parameters. However only two of them are independent. This can be seen as follows.\n\n\nFirst of all, for a flat model, we can choose $a(1)=1$. Second, in (\\ref{LO}), we already encounter one condition on the parameters to achieve the right evolution. Eq. (\\ref{LO}) allows to solve $l$ in terms of $\\alpha$. One extra condition follows by evaluating Eq. (\\ref{c1}) today,\n\\begin{equation}\n1 = {1 \\over 3 l^2 H_0^2} { Y_1^3 \\over X_1}  +  \\Omega_{bm},\n\\end{equation}\nfrom where we can solve $X_1$ in terms of $Y_1$ and $l$.  The remaining parameters are thus $\\alpha$ and $Y_1$.\n\n~\n\nWe have integrated (\\ref{c1}-\\ref{c3}) numerically varying $\\alpha$ and $Y_1$.  The resulting curve is compared with the evolution predicted by (\\ref{Fr},\\ref{Omega}). Our conclusions are the following.\n\n\\begin{enumerate}\n\n\\item\nFirst of all, there exists values of $\\alpha,Y_1$ such that the evolution predicted by (\\ref{Fr}) is almost undistinguishable from that following from (\\ref{c1}-\\ref{c3}), at least for the part of the Universe we can observe $0<t<1$. In Fig. \\ref{fig1}, the continuous line represents the Born-Infeld theory with $\\alpha=0.99$ and $Y_1 = 10.59$. The dots represents the Friedman evolution dictated by (\\ref{Fr}).\n\\begin{figure}[h]\n\\centerline{\\psfig{file=friedman.eps,width=6cm,angle=-90}}\n\\caption{ \\ $\\alpha=0.99, \\ Y_1=10.59$}\n\\label{fig1}\n\\end{figure}\nThe parameters were adjusted for a best fit, and in particular the big-bang occurs at $t=0.00731..$ in both theories.\n\n\\item  If $\\alpha$ is not close to one, there is no value of $Y_1$ to achieve a good fit with the Friedman equation.  The above picture corresponds to $\\alpha=0.99$. The value $\\alpha=0.9$ also gives a good fit, but smaller ones do not. $\\alpha>1$ does not work either.\n\nThe fact that $\\alpha \\sim 1$ to have a good fit is quite peculiar because the actual value $\\alpha=1$ is singular and the de-Sitter solution does not exist (See Sec. \\ref{SecdeSitter}).  In any case, recall that $\\alpha$ enters in the action as a coupling constant and is not subject to variations.  More testings on the theory should narrow the actual value of this parameter.\n\n\n\\item\nOf course no measurements exist for $t>1$, but it is interesting to explore the predictions of Born-Infeld theory to larger times. If one chooses the parameters such that the Big-Bang occurs at the same value of $t$ in both theories, then for large $t$ the expansion factor $a(t)$ grows slightly slower in the Born-Infeld theory.   Further details on this issue will be reported  elsewhere.\n\\end{enumerate}\n\n\n\n\\subsection{The evolution of the equation of state}\n\nAs we mention in Sec. \\ref{Equations}, the field $C^{\\mu}_{\\ \\nu\\rho}$ can be characterized by an energy density $\\rho_{{\\scriptscriptstyle BI}}$ and pressure $p_{{\\scriptscriptstyle BI}}$ whose expressions are given in (\\ref{rhop}).  The corresponding equation of state is,\n\\begin{equation}\n{p_{{\\scriptscriptstyle BI}} \\over \\rho_{{\\scriptscriptstyle BI}}} = - \\left( {a X \\over Y} \\right)^2\n\\end{equation}\nand we observe that the pressure is always negative.  Fig. \\ref{eqst} shows the evolution $0<t<3$ of the quotient $p_{{\\scriptscriptstyle BI}}\/\\rho_{{\\scriptscriptstyle BI}}$.\n\\begin{figure}[h]\n \\centerline{\\psfig{file=EquationState.eps,width=6cm,angle=-90 }}\n\\label{eqst}\n\\caption{ Evolution of the equation of state}\n\\end{figure}\nWe see clearly the interpolation between $p_{{\\scriptscriptstyle BI}}=0$ for small times, and $p_{{\\scriptscriptstyle BI}}=-\\rho_{{\\scriptscriptstyle BI}}$ for larger times.\n\n\n~\n\n\n\\section{Spherical symmetry and galactic rotation curves}\n\nIn this section we explore the action (\\ref{I}) on galactic scales where dark matter also plays an important role. (Dark energy is less relevant at this scale.) Stars orbiting galaxies have rotation curves not matching the observed luminous matter and this implies the existence of `dark matter'. See \\cite{Rubin} for a recent review. If the Born-Infeld theory (\\ref{I}) can be regarded as a good candidate for this exotic form of matter, it must account for these flat rotation curves.\n\nNumerical studies of matter interacting only gravitationally suggests the 2-parameter NFW \\cite{NFW} density profile for the dark matter halo,\n\\begin{equation}\\label{NFWp}\n\\rho_{{\\scriptscriptstyle NFW}}(r) = {a \\over r( 1 + r\/r_0)^2}.\n\\end{equation}\nThe density diverges at the origin but the total mass is finite. The rotation curve associated to this profile has a peak and decreases slowly with $r$.\n\nAnother popular density function is the (pseudo) Isothermic profile,\n\\begin{equation}\\label{ISOp}\n\\rho_{{\\scriptscriptstyle ISO}}(r) = {b \\over 1 + r^2\/r_0^2}\n\\end{equation}\nhaving a finite density at the origin. This halo leads to a rotation curve increasing  monotonically with an asymptotically flat region. See \\cite{deBlok} for an observational comparison of both profiles.\n\n~\n\n\nOur proposal is that the Born-Infeld field appearing in (\\ref{I}) can account for the dark matter present in galaxies. We shall prove that the action (\\ref{I}) gives rise to a rotation curve behaving like the NFW halo for small $r$, and as the (pseudo) Isothermal halo for large $r$.  In particular, the Born-Infeld theory yields an asymptotically flat rotation curve (at least to first order in the coupling constant).  To this end, we study in this section solutions with spherical symmetry to equations (\\ref{ee}-\\ref{Ke}).\n\n\\subsection{The ansatz and equations of motion}\n\n\nOur main interest is the `dark matter' contribution to the gravitational potential induced by $C^{\\mu}_{\\ \\nu\\rho}$.   We shall then neglect here the visible matter, set $T^{{\\scriptscriptstyle (m)}}_{\\ \\ \\mu\\nu}=0$ and study the solutions of\n\\begin{eqnarray}\nG_{\\mu\\nu} &=& - {1 \\over l^2} \\sqrt{{q}\\over g}\\, g_{\\mu\\alpha}\\,q^{\\alpha\\beta}\\,  g_{\\beta\\nu}\\, \\label{oee} \\\\\nK_{\\mu\\nu} &=& {1 \\over l^2}( g_{\\mu\\nu} + \\alpha\\, q_{\\mu\\nu})  \\label{oKe}\n\\end{eqnarray}\nwith spherical symmetry.\n\nFirst, note that since $g_{\\mu\\nu}$ and $q_{\\mu\\nu}$ are invertible, the right hand side of (\\ref{oee}) is different from zero at all points.  This represents a non-compact source.  Since for a galactic problem we expect the curvature to be very small, the right hand side of (\\ref{oee}) must be very small.  This is indeed true because\nthe parameter $l$ is of cosmological scale, and thus ${1 \\over l^2}$ is very small compared to any galactic scale.\n\nThis also means that we can treat the right hand side of (\\ref{oee}) and (\\ref{oKe}) as perturbations.  The parameter ${1 \\over l^2}$ measures the interaction between $g_{\\mu\\nu}$ and $q_{\\mu\\nu}$. If ${1 \\over l^2}\\rightarrow 0$, these two fields are decoupled and satisfy the order zero equations,\n\\begin{equation}\\label{zero}\nG_{\\mu\\nu}=0, \\ \\ \\ \\ \\ \\  K_{\\mu\\nu}=0\n\\end{equation}\n\nThe interactions can be incorporated perturbatively by expansions of the form,\n\\begin{eqnarray}\ng_{\\mu\\nu} &=& g_{\\mu\\nu}^{\\scriptscriptstyle{(0)}} + {1 \\over l^2 } \\, g_{\\mu\\nu}^{\\scriptscriptstyle{(1)}}  + {1 \\over l^4 } \\, g_{\\mu\\nu}^{\\scriptscriptstyle{(2)}} + \\cdots\\\\\nq_{\\mu\\nu} &=& q_{\\mu\\nu}^{\\scriptscriptstyle{(0)}} + {1 \\over l^2 } \\,q_{\\mu\\nu}^{\\scriptscriptstyle{(1)}}  + {1 \\over l^4}\\,  q_{\\mu\\nu}^{\\scriptscriptstyle{(2)}}\\, + \\cdots.\n\\end{eqnarray}\nwhere $g^{{\\scriptscriptstyle (0)}}_{\\mu\\nu}$ and $q^{{\\scriptscriptstyle (0)}}_{\\mu\\nu}$ satisfy the order zero equations (\\ref{zero}). [There exists a different perturbative scheme leading to a different sector of this theory. Instead of treating ${1 \\over l^2}$ as very small, one could start with the exact solution described in Sec. \\ref{SecdeSitter}, and study linearized fluctuations around that background. This yields a different set of solutions that will be studied elsewhere.]\n\n~\n\nWe start our discussion with the order zero fields  $g^{{\\scriptscriptstyle (0)}}_{\\mu\\nu}$ and $q^{{\\scriptscriptstyle (0)}}_{\\mu\\nu}$. The static, spherically symmetric solution to the order zero equation $G_{\\mu\\nu}=0$ is the Schwarzschild metric\n\\begin{equation}\\label{g0}\ng_{\\mu\\nu}^{\\scriptscriptstyle{(0)}}\\, dx^\\mu dx^\\nu  = -c^2\\left( 1 - {2MG \\over c^2 r} \\right)  dt^2 +  \\left( 1 - {2MG \\over c^2 r} \\right)^{-1} dr^2 + r^2d\\Omega^2.\n\\end{equation}\nHowever, $M$ represents the total baryonic mass and since we have set $T^{{\\scriptscriptstyle (m)}}_{\\ \\ \\mu\\nu}=0$ we also set\n\\begin{equation}\nM=0.\n\\end{equation}\nOur order zero $g^{{\\scriptscriptstyle (0)}}_{\\ \\mu\\nu}$ metric is thus flat space. The effects of baryonic matter can easily be incorporated at the end and will be studied in \\cite{BRR}.\n\n\nThe order zero equation for $q_{\\mu\\nu}$ is $K_{\\mu\\nu}=0$. The solution with spherical symmetry is also the Schwarzschild metric in the ``reciprocal\" metric $q_{\\mu\\nu}$,\n\\begin{equation}\\label{q0}\nq_{\\mu\\nu}^{\\scriptscriptstyle{(0)}}\\, dx^\\mu dx^\\nu    = -\\beta^2 c^2\\left( 1 - {w_0 \\over  \\tilde k(r)} \\right) dt^2 + \\left( 1 - {w_0 \\over \\tilde k(r)} \\right)^{-1}  \\tilde k'^2 dr^2  +  \\tilde k^2(r) d\\Omega^2.\n\\end{equation}\nHere, $\\tilde k(r)$ is an arbitrary function of $r$, $w_{0}$ is an arbitrary constant with dimensions of length (the $q_{\\mu\\nu}$ ``Schwarzschild radius\"), and $\\beta$ is a dimensionless constant.  This tensor solves $K_{\\mu\\nu}=0$ everywhere except at $\\tilde k=0$. Some comments on the metric (\\ref{q0}) are in order:\n\n\\begin{enumerate}\n\\item\nWe have chosen the radial coordinate $r$ such that $g^{{\\scriptscriptstyle (0)}}_{\\mu\\nu}$ has $r^2d\\Omega^2$ in the angular part. It is then {\\it not} correct to assume that the metric $q^{{\\scriptscriptstyle (0)}}_{\\mu\\nu}$ can also be written in terms of $r$ and with the same $r^2 d\\Omega^2$ in its angular part. This is role of the function $\\tilde k(r)$ which represents an arbitrary radial re-parametrization.  This function will be determined by the equations of motion.\n\n\\item\nIn the same way, the time scale $t$ is fixed in terms of the metric $g_{\\mu\\nu}$, and does not need to be the same for the metric $q_{\\mu\\nu}$. This the role of the dimensionless constant $\\beta$ entering in (\\ref{q0}). This constant will be important below.\n\n\\item\nIf $w_0\\neq 0$, the metric (\\ref{q0}) solves $K_{\\mu\\nu}=0$ everywhere, except at $k=0$. As we shall see below, the most interesting solution requires $w_0\\neq 0$, and explores $k(r)$ all the way to the horizon. This means that we are forced to interpret the metric (\\ref{q0}) as a black hole in the $q_{\\mu\\nu}$ space.  We shall restrict our discussion to the region,\n\\begin{equation}\n\\tilde k > w_0.\n\\end{equation}\n\\item\nFor $w_0\\neq 0$ it will be convenient to use a dimensionless radial coordinate,\n\\begin{equation}\nk \\equiv {\\tilde k \\over w_0}.\n\\end{equation}\nIn particular the horizon is now located at,\n\\begin{equation}\nk=1, \\ \\ \\ \\ \\ (\\mbox{horizon}).\n\\end{equation}\nFrom now on, all formulas refer to this coordinate.\n\n\n\\end{enumerate}\n\n\n~\n\nHaving chosen the zero order solutions to (\\ref{oee}) and (\\ref{oKe}), we now discuss the corrections induced but the right hand side of these equations. We only discuss here the first order correction to $g_{\\mu\\nu}$, proportional to ${1 \\over l^2}$. Since the right hand side of (\\ref{oee}) is already of order ${1 \\over l^2}$, it is enough to know $q_{\\mu\\nu}$ to order zero. [Note that $q_{\\mu\\nu}^{{\\scriptscriptstyle (0)}}$ contributes to $g_{\\mu\\nu}^{{\\scriptscriptstyle (1)}}$, $q_{\\mu\\nu}^{{\\scriptscriptstyle (1)}}$ contributes to $g_{\\mu\\nu}^{{\\scriptscriptstyle (2)}}$, and so on.]\n\n\nOur problem then reduces to replacing $q_{\\mu\\nu}$ given by (\\ref{q0}) in (\\ref{oee}) and solve for the metric $g_{\\mu\\nu}$ to first order in ${1 \\over l^2}$. The metric $g_{\\mu\\nu}$ must be spherically symmetric.  We then write,\n\\begin{eqnarray}\\label{metric}\nds^2 &=& -c^2\\left( 1 + {1 \\over c^2}\\Phi(r)\\right) dt^2 +\\left(1 - {2m(r) \\over c^2 r} \\right)^{-1} dr^2  + r^2d\\Omega^2,\n\\end{eqnarray}\nwith\n\\begin{eqnarray}\n  \\Phi &=& \\Phi^{{\\scriptscriptstyle (0)}} + {1 \\over l^2}\\, \\Phi^{{\\scriptscriptstyle (1)}} + {1 \\over l^4}\\, \\Phi^{{\\scriptscriptstyle (2)}} + \\cdots \\\\\n   m &=& m^{{\\scriptscriptstyle (0)}} + {1 \\over l^2}\\, m^{{\\scriptscriptstyle (1)}}  + {1 \\over l^4}\\, m^{{\\scriptscriptstyle (2)}} + \\cdots.\n\\end{eqnarray}\nAs we have already discussed, in the approximation with no baryonic matter, the zero order solution is simply flat space and thus\n\\begin{equation}\n \\Phi^{{\\scriptscriptstyle (0)}}=0, \\ \\ \\ \\  m^{{\\scriptscriptstyle (0)}}=0.\n\\end{equation}\n\nTo first order we obtain the equations,\n\\begin{eqnarray}\n    {dm^{{\\scriptscriptstyle (1)}} \\over dr} \\left(1 - {1 \\over k}\\right) - {w_0^3  c_0^2 \\over 2 \\beta}\\, k^2{d k \\over dr} &=& 0, \\label{g11}\\\\\n  \\beta c^2w_0 k^2\\left(1 - {1 \\over k}\\right)  + 2 {dk\\over dr} u^{{\\scriptscriptstyle (1)}} &=& 0, \\label{g22} \\\\\n  {du^{{\\scriptscriptstyle (1)}} \\over dr} + \\beta c^2 w_0\\,r\\, {dk \\over dr}  &=& 0, \\label{g33}\n\\end{eqnarray}\nwhere we have re-defined $\\Phi^{{\\scriptscriptstyle (1)}}(r)$ in terms of a new function $u^{{\\scriptscriptstyle (1)}}(r)$ by\n\\begin{equation}\\label{phi1}\nr{d\\Phi^{{\\scriptscriptstyle (1)}} \\over dr}=   u^{{\\scriptscriptstyle (1)}}(r) + {m^{{\\scriptscriptstyle (1)}}(r) \\over r}.\n\\end{equation}\n[To first order, the equations only depend on $\\Phi'$ and this is why this redefinition does not spoil locality.]\n\n\n\n\n\\subsection{Full parametric solution. Two branches}\n\nEquations (\\ref{g11}-\\ref{g33}) are three non-linear equations for the three unknowns $m^{{\\scriptscriptstyle (1)}}(r),u^{{\\scriptscriptstyle (1)}}(r)$ and $k(r)$.  A much simpler set of equations can be obtained by changing the independent variable from $r$ to $k$.\n\nWe define the functions $u^{{\\scriptscriptstyle (1)}}(k),m^{{\\scriptscriptstyle (1)}}(k)$ and $r(k)$. Also, for any $f(r)$,\n\\begin{equation}\n{df\\!(r) \\over dr}  = \\left. {df(k) \\over dk}\\right\/ {dr \\over dk}.\n\\end{equation}\nPerforming these substitutions,  equations (\\ref{g1}-\\ref{g3}) become linear for the unknowns $m^{{\\scriptscriptstyle (1)}}(k),u^{{\\scriptscriptstyle (1)}}(k)$ and $r(k)$,\n\\begin{eqnarray}\n    {dm^{{\\scriptscriptstyle (1)}} \\over dk} \\left(1 - {1 \\over k}\\right) - {w_0^3  c_0^2 \\over 2 \\beta}\\, k^2  &=& 0 \\label{g1}\\\\\n  \\beta c^2 w_0 k^2\\left(1 - {1 \\over k}\\right){dr \\over dk}  + 2\\, u^{{\\scriptscriptstyle (1)}} &=& 0 \\label{g2} \\\\\n  {du^{{\\scriptscriptstyle (1)}} \\over dk} + \\beta c^2 w_0\\,r   &=& 0 . \\label{g3}\n\\end{eqnarray}\nNote in particular that $m^{{\\scriptscriptstyle (1)}}$ has decoupled from $u^{{\\scriptscriptstyle (1)}}$ and $r(k)$. The general solution can be found in closed form,\n\\begin{eqnarray}\n  r(k) &=& A_0 \\left( -\\left(k - {1 \\over 2}\\right)\\ln\\left(1-{1 \\over k}\\right) -1\\right) + B_0 \\left(k - {1 \\over 2} \\right) \\label{rk} \\\\\n  u^{{\\scriptscriptstyle (1)}}(k) &=& {1 \\over 2} \\beta c^2 w_0 \\left[ A_0 \\left( k^2 \\left( 1- {1 \\over k} \\right) \\ln\\left( 1 - {1 \\over k}\\right) +  k - {1 \\over 2} \\right) - B_0 ( k^2 - k) \\right] \\label{uk} \\\\\n  m^{\\scriptscriptstyle (1)}(k) &=& {w_0^3c^2\\over 2\\beta}\\left( {1 \\over 3}k^3 + {1 \\over 2}k^2 + k + \\ln(k-1) - h_0 \\right) \\label{mk}\n\\end{eqnarray}\nwhere $A_0,B_0$ and $h_0$ are integration constants.   This solution is real for $k>1$, that is outside the horizon in the reciprocal space $q_{\\mu\\nu}$.\n\n~\n\nTo explore the properties of the different solutions we first note that the function $r(k)$ displayed in (\\ref{rk}) diverges at two different values of $k$,\n\\begin{equation}\nk = \\infty, \\ \\ \\ \\ \\ \\ \\ \\ \\mbox{and} \\ \\ \\  \\ \\ \\ \\ \\ k=1.\n\\end{equation}\n\nSince the function $r(k)$ is a coordinate change and must be globally defined at least in the range $0<r<\\infty$, the derivative $dr\/dk$ must be different from zero everywhere. Note that if $A_0$ and $B_0$ have the same sign, then the function $r(k)$ has a maximum or minimum, which is not allowed.  This leaves two simple cases:\n\n\\begin{itemize}\n\\item {\\bf Linear branch:} $A_0<0,B_0>0$. In this case, $r(k)$ diverges for large $k$, and becomes zero at some finite value $k=k_0$.  For $k<k_0$ the coordinate $r(k)$ is negative and thus this region is not physical. For large $k$ the solution rapidly approaches a linear behavior. The physical range of the coordinate $k$ in this case is\n\\begin{equation}\nk_0 \\leq k < \\infty.\n\\end{equation}\nHowever, it can be easily seen that $m^{{\\scriptscriptstyle (1)}}\/r$ diverges quadratically for large $r$. This behavior is unacceptable.  The same divergency is observed for the potential $\\Phi(r)$. From now on we shall exclude this case.\n\n\\item {\\bf Logarithmic branch:} $A_0>0,B_0<0$. In this case, $r(k)$ diverges at $k=1$ and becomes zero at some finite value $k=k_0$. The physical range of the coordinate $k$ in this case is\n\\begin{equation}\n1 > k \\geq k_0\n\\end{equation}\nThe most salient and peculiar property of this branch is that infinity is mapped to the horizon in the metric $q_{\\mu\\nu}$. There is a strong\/weak relationship between both fields. The details of this branch are studied in the following paragraphs.\n\n\n\n\\end{itemize}\n\nFig. \\ref{bran} shows the behavior of the function $r(k)$ for each branch.\n\n\\begin{figure}[h]\n\\centerline{\\psfig{file=branches.eps,width=10cm,angle=0}}\n\\caption{Two branches}\n\\label{bran}\n\\end{figure}\n\n\n\n\n\n\\subsection{The logarithmic branch and asymptotically flat rotation curves}\n\nThe most important property of this branch is that the rotation curves are asymptotically flat.  Let us recall the relation between the Newtonian potential appearing in (\\ref{metric}) and the rotation speed of a (non-relativistic) object at distance $r$,\n\\begin{equation}\\label{prof}\nv(r) = \\sqrt{ r {d\\Phi(r) \\over dr}}.\n\\end{equation}\n(This follows from the geodesic equation.) On the other hand, the derivative of the potential $\\Phi$, to first order in ${1 \\over l^2}$, is given in terms of $u^{{\\scriptscriptstyle (1)}}$ and $m^{{\\scriptscriptstyle (1)}}$ in (\\ref{phi1}).  The rotation curve can be expressed as a parametric function ,\n\\begin{equation}\nv(k) = {1 \\over l} \\sqrt{ u^{{\\scriptscriptstyle (1)}}(k) + {m^{{\\scriptscriptstyle (1)}}(k) \\over r(k)}}, \\ \\ \\ \\ \\ \\   r=r(k)\n\\end{equation}\nwhere $u^{{\\scriptscriptstyle (1)}}(k),m^{{\\scriptscriptstyle (1)}}(k)$ and $r(k)$ are given in (\\ref{rk}-\\ref{mk}).\n\nFrom these expression is it direct to compute the limit,\n\\begin{eqnarray}\\label{vinf0}\nv_{\\infty}^2 & \\equiv & \\lim_{k\\rightarrow 1} v^2(k) \\nonumber\\\\\n&=&  {w_0 (\\beta^2 A_0^2 - 4 w_0^2) \\over 4A_0 \\beta l^2}\\, c^2\n\\end{eqnarray}\nwhich is indeed finite.\n\nHowever, this is not the whole story. We need to impose boundary conditions at $r=0$ ($k=k_{0}$) to ensure that the solution and in particular the rotation curve (\\ref{prof}) is well-behaved there too. This will imply the following constraints and redefinitions of  the parameters $A_0,B_0$ and $h_0$.\n\n\\begin{enumerate}\n\\item\nWe first express $B_0$ in terms of $k_0$, the point where $r(k_0)=0$. This gives the following expression for $B_0$,\n\\begin{equation}\nB_0 = {A_0 \\over 2k_0-1} \\left((2k_0-1) \\ln\\left(1 - {1 \\over k_0} \\right) + 2\\right).\n\\end{equation}\n\\item\nSecond, ${m^{{\\scriptscriptstyle (1)}}}\\over r$ must be finite at $r=0$.  This implies  that $m^{{\\scriptscriptstyle (1)}}(k)$ must vanish at $k=k_0$ and this fixes $h_0$ to be \\begin{equation}\n h_0 = {1 \\over 3} k_0^3 + {1 \\over 2}k_0^2 + k_0 + \\ln(k_0-1)\n\\end{equation}\n\\item\nFinally, the orbital velocity of an object at $r=0$ must be zero. This implies that $u^{{\\scriptscriptstyle (1)}} + m^{{\\scriptscriptstyle (1)}}\/r$ evaluated at $k=k_0$ must vanish. This is achieved by choosing the constant $A_0$ to be\n\\begin{equation}\n A_0 = {2 w_0k_0^2 (2k_0-1) \\over \\beta}\n\\end{equation}\n\\end{enumerate}\nIn summary, boundary conditions at $r=0$ fix $B_0,A_0$ and $h_0$ in terms of a new parameter $k_0$. The full solution is then characterized by three remaining constants. The length scale $w_0$, and two dimensionless numbers $\\beta$ and $k_0$.\n\n\n\\subsection{A better parametrization and examples}\n\nThe solution we have found is still parameterized by several numbers. The functions $r(k),v(k)$ depend on $l,c,\\beta,w_0,k_0$.   The first two, $l,c$ enter in the action and cannot be varied. In fact $l$ has been already constrained by the cosmological analysis.  The other three remaining parameters can be chosen to match a desired physical situation.  Before plotting examples is it convenient to choose a different basis for these three arbitrary parameters.\n\nFirst, the asymptotic velocity $v_{\\infty}$ computed in (\\ref{vinf0}) in terms of $k_0$ is\n\\begin{equation}\\label{vinf}\nv^2_\\infty  = {4k_0^6-4k_0^5+ k_0^4 - 1 \\over 2(2k_0-1)k_0^2}\\, {w_0^2 \\over l^2}\\, c^2\n\\end{equation}\nThis parameter is of course a natural observable which can be identified easily for most galaxies. We use this equation and express $w_0$ in terms of $v_\\infty$,\n\\begin{equation}\\label{w0}\nw_0 = \\,\\sqrt{{2(2k_0-1)k_0^2 \\over 4k_0^6-4k_0^5+ k_0^4 - 1}}\\, {l\\, v_\\infty \\over c}\n\\end{equation}\nSecond, the dimensionless parameter $\\beta$, which enter in (\\ref{q0}), can be redefined as\n\\begin{equation}\n\\beta = {l \\, \\over r_0} { v_\\infty \\over c}.\n\\end{equation}\nwhere $r_0$ is an arbitrary parameter with dimensions of length.\n\n\nWith these definitions, the functions $r(k),v(k)$ take the convenient form\n\\begin{equation}\nr(k) = r_0 f_1(k,k_0), \\ \\ \\ \\ \\ \\   v(k) = v_\\infty f_2(k,k_0).\n\\end{equation}\nThe arbitrary constant $r_0$ sets the length scale while $v_\\infty$ set the velocity scale. Since both are arbitrary, they can be fixed to any desired values to fit realistic curves.   The constant $k_{0}$ controls the shape of the curve and how fast it grows. Since there are three independent parameters, there will be a degeneracy when fitting these curves with observational data (this will be discussed in \\cite{BRR}).\nThe explicit expressions for $f_1,f_2$ are not very illuminating, and can be derived directly from the solution (\\ref{rk}-\\ref{mk}). Of course $f_2$ satisfies $f_{2}(1,k_0)=1$.\n\n~\n\nFig. (\\ref{figg1}) shows examples of the curve with $v_\\infty=100km\/sec$, $r_0$ fixed, and varying $k_{0}$. The top curve corresponds to $k_0=1.5$. As $k_0$ increases we observe a slower growth of the rotation curve. All curves asymptotically reach the value $v_\\infty=100km\/sec$.  The horizontal axis is expressed in terms of $r\/r_0$, and choosing $r_0$ one can fit any desired length scale.\n\n\n\\begin{figure}[h]\n\\centerline{\\psfig{file=galactic.eps,width=6cm,angle=270}}\n\\caption{Rotation curves for $k_0=50,15,5,1.5$.      }\n\\label{figg1}\n\\end{figure}\n\nIt is interesting to note that for values of $k_0$ smaller than $k_0 \\simeq 1.5$, the curves change shape.  Fig. (\\ref{figg2}) shows the rotation curve for $k_0=1.5,1.03,1.003,1.0005$. The top curve corresponds to $k_{0}=1.5$. As $k_{0}$ becomes smaller, the rotation curves growths more slowly.\n\\begin{figure}[h]\n\\centerline{\\psfig{file=galactic2.eps,width=6cm,angle=270}}\n\\caption{Rotation curves for $k_0=1.5,1.03,1.003,1.0005$.      }\n\\label{figg2}\n\\end{figure}\n\nNote that one does not expect the curves to be asymptotically flat to all orders. The solutions discussed here are only the first order approximation in the coupling ${1 \\over l^2}$. The next orders are necessary to extrapolate the result to large values of $r$, comparable with $l$.  Also, the near horizon region for the metric  $q_{\\mu\\nu}$ is singular in Schwarzschild  coordinates and thus a proper analysis in regular coordinates may also change the behavior near infinity.\n\n\\subsection{Final remarks}\n\nWe end this section with two extra comments regarding the solutions with spherical symmetry.\n\n\n\n\\sub{Orders of magnitude and Solar System:} The solutions we have considered contain a length scale, $w_0$. This parameter was replaced in  (\\ref{w0}) by the final speed $v_\\infty$, which is a better observable.  It is however interesting to estimate the values of $w_0$ for a realistic situation. We set  $l \\sim 10^6 kpc$ (cosmological length), and ${v_{\\infty} \\over c} \\sim {1 \\over 3} 10^{-3}$, for a typical situation with $v_\\infty \\sim 100 km\/sec$. Fig. \\ref{figw0} shows $w_0$ as a function of $k_0$.\n\n\\begin{figure}[h]\n\\centerline{\\psfig{file=w0.eps,width=6cm,angle=270}}\n\\caption{$w_0$(kpc) as a function of $k_0$.      }\n\\label{figw0}\n\\end{figure}\n\nFor $k_{0} > 3 $, $w_0$ is equal to a few kpc.  This is a natural galactic scale. With an optimistic viewpoint one can thus assign to $w_0$ some physical meaning determined by the length of the object observed. In other words, the tensor $q_{\\mu\\nu}$ is a field whose natural length scale of variation is determined by the object.\n\nNow, the natural dimensionless parameter which controls the corrections from flat space is ${w_0 \\over l}$. If we believe that the value of $w_0$ is comparable to the object of study, then for Solar System experiments ${w_0 \\over l}$ is too small, and the effects of $C^{\\mu}_{\\ \\nu\\rho}$ should not contribute.\n\n~\n\n\\sub{Central density:} The central density associated to $C^{\\mu}_{\\ \\nu\\rho }$ diverges linearly, as the NFW profile (\\ref{NFWp}). This can be seen by solving (\\ref{g11}-\\ref{g33}), for small values of $r$, as a series expansion. The series,\n\\begin{eqnarray}\n  k(r) &=& k_0 - {\\beta (k_0-1) \\over w_0k_0 }\\ r + {\\cal O}(r^2) \\\\\n  m^{{\\scriptscriptstyle (1)}}(r) &=& -{w_0^2k_0^2 c^2 \\over 2} \\ r  + {\\cal O}(r^2) \\\\\n  u^{\\scriptscriptstyle (1)}(r) &=& {w_0^2k_0^2c^2 \\over 2} + {\\cal O}(r^2)\n\\end{eqnarray}\nsolve (\\ref{g11}-\\ref{g33}) with the boundary condition $v(r)\\rightarrow 0$ as $r\\rightarrow 0$. With this solution at hand we can compute the behavior of the associated mass density,\n\\begin{eqnarray}\n  4\\pi G\\, \\rho(r) &=& {1 \\over r^2}( r^2 \\Phi' )'  \\\\\n   &\\simeq & { 2(k_0-1)w_0 c^2 \\beta \\over l^2\\, r} + {\\cal O}(1)\n\\end{eqnarray}\nwith a linear divergency, as anticipated.\n\n\\section{Eddington action, the equivalence principle and $g_{\\mu\\nu}=0$}\n\n\\label{Sec\/g=0}\n\n\nOur proposal for dark matter and dark energy is summarized in the action (\\ref{I}). Once the action is written one can ``roll down\" exploring its predictions and consequences by usual methods. This is what we have done so far. However, it is also interesting to ``climb up\" and attempt a derivation, or at least a good motivation to include the Born-Infeld term in the gravitational action.\n\nWe start this section recalling a well-known effect. Consider a system of $N$ spins. If no external field is applied (and the temperature is not too small) the macroscopic average is $\\langle \\vec{S} \\rangle = 0$.  On the contrary, in the presence of an external field, $H_{ext}$, the symmetry is broken, the spins align and produce a non-zero macroscopic average $\\langle \\vec{S} \\rangle_{\\vec{H}_{ext}}\\neq 0$. It then follows that the total magnetic field felt by a charge $q$ is\n\\begin{equation}\n\\vec{H}_T = \\vec{H}_{ext} + \\langle \\vec{S} \\rangle_{\\vec{H}_{ext}}.\n\\end{equation}\nThe orbit of the charge will obey the Lorentz equation with $\\vec{H}_T$ not $\\vec{H}_{ext}$. If we did not know about spins the contribution $\\langle \\vec{S} \\rangle_{\\vec{H}_{ext}}$ would be interpreted as a sort of `dark' magnetic field. If the temperature is below the Curie temperature, the external field could be removed and the spins remain in their `ordered' state with $\\langle \\vec{S} \\rangle_0 \\neq 0$.\n\nLet us now describe an analog of this effect in the theory of gravity.  Topological manifolds are invariant under the full diffeomorphism group. Riemannian manifolds are invariant only under the subgroup of isometries of the metric. The state $g_{\\mu\\nu}=0$ represents the unbroken state of general relativity \\cite{Witten88}, and the  introduction of a metric breaks the symmetry. The natural geometrical analog of the external field $\\vec{H}_{ext}$ is the metric tensor $g_{\\mu\\nu}$. (See \\cite{Horowitz,Giddings,Guendelman} for other discussions on the state $g_{\\mu\\nu}=0$, and \\cite{Witten07} for a recent critical viewpoint.)\n\nWe shall treat the metric as an external field which can be switched on and off\\footnote{In this picture, the big-bang could be understood as a smooth transition from a manifold without metric into a Riemanian manifold.}. Our first goal is to explore fields that can be defined in the absence of a metric. The simplest example is given by a connection $C^{\\mu}_{\\ \\nu\\rho}(x)$.  In fact, Eddington introduced a purely affine theory a long time ago \\cite{Eddington},\n\\begin{equation}\\label{edd0}\nI_0[C] = \\kappa \\int d^4 x\\, \\sqrt{K_{\\mu\\nu}(C)}\n\\end{equation}\nwhere $K_{\\mu\\nu}$ is the curvature associated to the connection $C^{\\mu}_{\\ \\nu\\rho}(x)$ (see Eqn. (\\ref{Kmn})).  This action is invariant under spacetime diffeomorphism and yields second order differential equations for the field $C^{\\mu}_{\\ \\nu\\rho}$.  Eddington action was extensively studied as a purely affine theory of gravity, and also as a possible unification of gravity and electromagnetism \\cite{Eddington,Poplawski}. We take here a different interpretation and let the field $C^{\\mu}_{\\ \\nu\\rho}$ be an independent degree of freedom.\n\nWe now turn on the external field $g_{\\mu\\nu}$ and study the effects of both $g_{\\mu\\nu}$ and $C^{\\mu}_{\\ \\nu\\rho}$ on particles. The first problem is to determine  the action for the coupled system.  We do not want to introduce ghost or higher derivatives. The action  (\\ref{edd0}) is already free of anomalies. So we start by adding the standard Einstein-Hilbert action for $g_{\\mu\\nu}$ and consider\n\\begin{equation}\n\\int d^4 x  \\left( \\sqrt{g}R  + \\kappa \\sqrt{K_{\\mu\\nu}}\\  \\right).\n\\end{equation}\nWith this action, the fundamental fields $g_{\\mu\\nu}$ and $C^{\\mu}_{\\ \\nu\\rho}$ are decoupled. To make the theory more interesting we add interactions. The most attractive  theory (although not unique) having second order field equations is the Einstein-Born-Infeld action introduced in Eq. (\\ref{I}).\n\nAn important point now is to define the geodesic equation for the coupled system. In the presence of a metric $g_{\\mu\\nu}$ there is a natural affine connection $\\Gamma^{\\mu}_{\\ \\nu\\rho}$ represented by the Christoffel symbol,\n\\begin{equation}\\label{chr}\n\\Gamma^\\mu_{\\ \\nu\\rho} = {1 \\over 2}g^{\\mu\\sigma} ( g_{\\sigma\\nu,\\rho} + g_{\\sigma\\rho,\\nu} - g_{\\nu\\rho,\\sigma}).\n\\end{equation}\nThe question is, should geodesics be defined with respect to $C^{\\mu}_{\\ \\nu\\rho}$, $\\Gamma^{\\mu}_{\\ \\nu\\rho}$, both?  In order to comply with the equivalence principle we shall postulate that particles only couple to the metric and not to the connection $C^{\\mu}_{\\ \\nu\\rho }$.  The geodesic equation then take the usual form\n\\begin{equation}\\label{geo}\n\\ddot x^{\\mu} + \\Gamma^{\\mu}_{\\ \\alpha\\beta} \\dot x^\\alpha \\dot x^\\beta=0,\n\\end{equation}\nwhere $\\Gamma^{\\mu}_{\\ \\alpha\\beta}$ is the Christoffel symbol (\\ref{chr}).  Observe that the metric satisfies the equations (\\ref{ee}) and is coupled to the field $C^{\\mu}_{\\ \\nu\\rho }$. In this sense, $C^{\\mu}_{\\ \\nu\\rho }$ does contribute to $g_{\\mu\\nu}$ and indirectly affects the motion of particles. This is how the field $C$ can explain flat rotation curves.\n\nNow, the analogy with spin systems can be pushed a little bit further.  We have seen in the cosmological analysis that for large times the system approaches the de-Sitter solution (see Sec. \\ref{SecdeSitter}), and in particular the metric $q_{\\mu\\nu}$ becomes proportional to $g_{\\mu\\nu}$, $q_{\\mu\\nu}\\rightarrow \\lambda g_{\\mu\\nu}$. One can interpret this fact as analogous to the alignment of spins along the direction of the applied field, $\\langle \\vec{S} \\rangle  \\rightarrow \\lambda \\vec{H}_{ext}$. Of course, to support this interpretation one would need to consider generic initial conditions. This will be analyzed elsewhere.\n\nFinally, recall that when the external  magnetic field is removed, spins can have a spontaneous non-zero average $\\langle \\vec{S} \\rangle$, and this vector generates forces on charged particles.  Is there a gravitational analogue to this effect? The gravitational force is measured by the connection (\\ref{chr}), entering in the geodesic equation. The external field is the metric. Now, as the metric is removed, the Christoffel connection becomes ${0 \\over 0}$, with the same scaling weight in the numerator and denominator. For a large class of paths the limit is a finite function.  Since the only connection available at $g_{\\mu\\nu}=0$ is $C^{\\mu}_{\\ \\nu\\rho}$, it is tempting to conjecture that $\\Gamma^{\\mu}_{\\ \\nu\\rho} \\rightarrow C^{\\mu}_{\\ \\nu\\rho}$, as the metric is removed. In this way, the geodesic equation has a non-trivial limit when the metric vanishes, and particles will feel `forces'.  These are not forces in the usual sense because there is no metric.  (Although note that a geodesic equation, defined by parallel transport, can be introduced without a metric.)  The limit $g_{\\mu\\nu}\\rightarrow 0$ was the key ingredient employed in \\cite{B} for a different approach to understand dark matter as an effect associated to a topological manifold. To make these ideas precise a theory describing the process $g_{\\mu\\nu}\\rightarrow 0$ is necessary. We hope to come back to this interpretation in the future.\n\n\n\n\\section{Conclusions}\n\nDark matter and dark energy have unique properties and their understanding in one of the most crucial problems faced by theoretical physics today.   Dark matter does not interact with normal matter and this property has motivated us to look for fields which have this property somehow ``built in\". We have explored gravity coupled to connection $C^{\\mu}_{\\ \\nu\\alpha}$ field with a Born-Infeld action.\n\nThis theory comply with the main background properties normally attributed to dark matter and dark energy. First, the evolution of the scale factor in cosmological models has the right time dependence interpolating between pressureless matter and a cosmological constant.\n\nAt galactic scales dark energy is less relevant but dark matter still plays an important role. By an approximation valid for distances much smaller to the Hubble radius we have solved the equations of motion for spherical objects and find the expected rotation curves.  These curves satisfy the basic asymptotic flatness observed in galaxies providing new support for this proposal.\n\nWe have left several topics for the future. The stability of this theory and the study of primordial fluctuations are important to determine the CMB anisotropies. This will be reported in \\cite{BFS}.  On galactic scales a systematic fit with observational curves is necessary. This issue is presently under study and will be reported in \\cite{BRR}.\n\n\n\n\n\n\n\\section{Appendix. Derivation of the equations of motion}\n\n\nThe fields which are varied in the action (\\ref{I}) are the metric $g_{\\mu\\nu}$ and the connection $\\Gamma^{\\mu}_{\\ \\nu\\rho}$. The equations of motion for the metric follow by a straightforward variation of the action. The result is\n\\begin{equation}\\label{1}\nG_{\\mu\\nu} = \\sqrt{{|g_{\\mu\\nu}- l^2 K_{(\\mu\\nu)}| \\over |g_{\\mu\\nu}| }} \\ g_{\\mu\\alpha}\\left({1 \\over g-l^2 K }\\right)^{\\alpha\\beta} g_{\\beta\\nu} + 8\\pi G \\, T^{{\\scriptscriptstyle (m)}}_{\\mu\\nu}\n\\end{equation}\nThis equation can be drastically simplified by using the equation of motion for the connection $\\Gamma^{\\mu}_{\\ \\nu\\rho}$. This equation is derived in two steps.  First, since the action only depends on the curvature $K_{\\mu\\nu}$ once can compute the variation using the chain rule,\n\\begin{equation}\n{\\delta I \\over \\delta \\Gamma^{\\mu}_{ \\nu\\rho}} = \\int {\\delta I \\over \\delta K_{(\\alpha\\beta)}} \\, {\\delta K_{(\\alpha\\beta)} \\over \\delta \\Gamma^{\\mu}_{\\nu\\rho}}\n\\end{equation}\nJust like in Eddington \\cite{Eddington} theory one finds  by direct variation that the combination\n\\begin{equation}\\label{K00}\n\\sqrt{q}{q}^{\\mu\\nu}  \\equiv -{1 \\over \\alpha}\\sqrt{|g_{\\mu\\nu} - l^2 K_{\\mu\\nu}|} \\left({1 \\over g-l^2 K }\\right)^{\\mu\\nu}\n\\end{equation}\nsatisfies\n\\begin{equation}\nD_\\rho(\\sqrt{q}{q}^{\\mu\\nu})=0\n\\end{equation}\nwhere $D_\\rho$ is the covariant derivative built with the connection $\\Gamma_{{\\scriptscriptstyle 0}}$.  Since $\\Gamma^{\\mu}_{\\ \\nu\\rho}$ is symmetric, this equation imply\n\\begin{equation}\n\\Gamma^{\\mu}_{ \\nu\\rho} = {1 \\over 2} q^{\\mu\\alpha} ( q_{\\alpha\\nu,\\rho} + q_{\\alpha\\rho,\\nu} - q_{\\nu,\\rho,\\alpha} )\n\\end{equation}\nWe thus write $\\Gamma^{\\mu}_{\\ \\nu\\rho}$ in terms of $q_{\\mu\\nu}$. The equation (\\ref{K00})  now depends only on $q_{\\mu\\nu}$. Taking the determinant at both sides, and inverting one readily derives (\\ref{Ke}).\n\nThe final simplification follows by noticing that the right hand side of (\\ref{1}) contains $\\sqrt{q}q^{\\mu\\nu}$.  Thus, using (\\ref{K00}), Eq. (\\ref{1}) is transformed into (\\ref{ee}).\n\nThe analysis of these equations is greatly simplified by using the bi-metric formalism \\cite{andy}.\n\n~\n\n~\n\n\n\\section{Acknowledgements}\n\nThe author would like to thank S. Carlip, P. Ferreira, A.Gomberoff, M. Henneaux, A. Reisenegger, D. Rodrigues,  N. Rojas, C. Skordis and S. Theisen for useful comments and discussions.  The author was partially supported by Fondecyt Grants (Chile) \\#1060648 and \\#1051084.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nBerry in his pioneer work raised a fundamentally important concept known as\ngeometric phase (GP) in addition to the usual dynamic phase accumulated on\nthe wave function of a quantum system, provided that the Hamiltonian varies\nwith multi-parameters cyclically and adiabatically \\cite{Berry}. At the\npresent time the GP with extensive generalization along many directions has\nwide applications in various branches of physics \\cite{Berry2,Shapere,Bohm}.\n\nRecently, the close relation between GP and quantum phase transition (QPT)\nhas been gradually revealed \\cite{Carollo,Zhu,Hamma} and increasing interest\nhas been drawn to the role of GP in detecting QPT for various many-body\nsystems \\cite{Zhu08,Chen,interests}, which, as a matter of fact, is also a\nnew research field in condensed matter physics \\cite{Sachdev,Sondhi}. QPT\nusually describes an abrupt change in the ground state of a many-body system\ninduced by quantum fluctuations. The phase transition between ordered and\ndisordered phases is accompanied by symmetry breaking, which can also be\ncharacterized by Landau-type order parameters.\n\nOn the other hand, a new type of QPT called topological quantum phase\ntransitions (TQPT) has attracted much attention. The first non-trivial\nexample is the fractional quantum Hall effect \\cite{Tsui,Laughlin}. In the\nlast decade, several exactly soluble spin-models with the TQPT, such as the\ntoric-code model \\cite{Kitaev03}, the Wen-plaquette model \\cit\n{Wen-plaquette,Wen08} and the Kitaev model on a honeycomb lattice \\cit\n{Kitaev}, were found. In contrast to the conventional QPT governed by local\norder parameters \\cite{Sachdev}, the TQPT can be characterized only by the\ntopological order \\cite{WenBook}. As good examples to illustrate the\nunderlying physics, different methods are developed to describe the TQPT in\nthe Kitaev honeycomb model \\cite{T. Xiang07,T. Xiang08,H. D. Chen07,H. D.\nChen08,S. Yang,Gu}. In Ref. \\cite{T. Xiang07}, Feng \\textit{et.al.} obtained\nthe local order parameters of Landau type to characterize the phase\ntransition by introducing Jordan-Wigner and spin-duality transformations\ninto the Majorana representation of the honeycomb model. Gu \\textit{et.al.}\nshowed an exciting result of the ground-state fidelity susceptibility \\cit\n{S. Yang,Gu}, which can be used to identify the TQPT from the gapped $A$\nphase with Abelian anyon excitations to gapless $B$ phase with non-Abelian\nanyon excitations.\n\nQuite recently, Zhu \\cite{Zhu} showed that the ground-state GP in the $XY$\nmodel is non-analytic with a diverged derivative with respect to the field\nstrength at the critical value of magnetic field. Thereupon, the relation\nbetween the GP and the QPT is established. Nevertheless, much attention has\nbeen paid to the QPT, while effort devoted to the relation between the GP\nand the TQPT is very little. The present paper is devoted to exploiting the\nGP of the Kitaev honeycomb model as an essential tool to establish a\nrelation between the GP and the TQPT and reveal the novel quantum\ncriticality. Unlike the GP in the usual lattice-spin model for the QPT,\nwhich is generated by the single-spin rotation of each lattice-site, the\nsimultaneous rotation of linked two spins in one unit-cell seems crucial to\ndescribe the TQPT in the honeycomb model. The non-analyticity of GP at the\ncritical points with a divergent second-order derivative with respect to the\ncoupling parameters shows that the TQPT is the second-order transition and\ncan be well described by the GP.\n\nIn Sec. II, the ground state wave function and energy spectrum of the Kitaev\nhoneycomb model are presented. After introducing a correlated rotation of\ntwo $z$-link spins in each unit-cell, the ground-state GP and its\nderivatives are obtained explicitly in Sec. III. Sec. IV is devoted to\ninvestigating the scaling behavior of the GP. A brief summary and discussion\nare given in Sec. V.\n\n\\section{The Kitaev honeycomb model and spectrum}\n\nThe Kitaev honeycomb model shown in Fig. \\ref{fig1}(a) is firstly introduced\nto illustrate the topologically fault-tolerant quantum-information\nprocessing \\cite{Kitaev03,Kitaev,Nayak}. In this model, each spin located at\nvertices of the lattice interacts with three nearest-neighbor spins through\nthree types of bonds, depending on their directions. By using the Pauli\noperators $\\sigma ^{a}$ $(a=x,y,z)$, the corresponding Hamiltonian is\nwritten a\n\\begin{equation}\nH=-J_{x}\\!\\!\\!\\sum_{x\\mbox{-links}}\\!\\!\\!\\sigma _{j}^{x}\\sigma\n_{k}^{x}-J_{y}\\!\\!\\!\\sum_{y\\mbox{-links}}\\!\\!\\!\\sigma _{j}^{y}\\sigma\n_{k}^{y}-J_{z}\\!\\!\\!\\sum_{z\\mbox{-links}}\\!\\!\\!\\sigma _{j}^{z}\\sigma\n_{k}^{z},  \\label{Kitaev model}\n\\end{equation\nwhere $j$, $k$ denote the two ends of the corresponding bond, and $J_{a}$\nare coupling parameters. After introducing a special notation $K_{jk}=\\sigma\n_{j}^{a}\\sigma _{k}^{a}$, where the indexes $a$ depend on the types of links\nbetween sites $j$ and $k$ (so we also write it into $a_{jk}$ in the\nfollowing text for perspicuousness), Hamiltonian (\\ref{Kitaev model}) can be\nrewritten into a compact form\n\\begin{equation}\nH=-\\frac{1}{2}\\sum_{\\langle j,k\\rangle }J_{a_{jk}}K_{jk}.\n\\label{Kitaev modelK}\n\\end{equation}\n\n\\begin{figure}[h]\n\\centering \\vspace{0cm} \\hspace{0cm} \\scalebox{0.8}\n\\includegraphics{fig1.eps}}\n\\caption{(Color online) (a) Kitaev honeycomb model, in which one spin\ninteracts with three nearest-neighbor spins through three types of bonds,\ndepending on their direction. A unit-cell with $x$, $y$ and $z$ links and\ngraphic representation of Hamiltonian (\\protect\\ref{HM}) with Majorana\noperators are marked by the red dotted line. (b) Phase diagram of the model,\nwhere $A$ phase is gapped and $B$ phase is gapless.}\n\\label{fig1}\n\\end{figure}\n\nIt has been known that the Kitaev honeycomb model can be solved exactly by\nintroducing Majorana fermion operators, which are defined as \\cite{Kitaev,S.\nYang}\n\\begin{equation}\n\\sigma ^{x}=ib^{x}c,\\quad \\sigma ^{y}=ib^{y}c,\\quad \\sigma ^{z}=ib^{z}c.\n\\label{MajoranaFermion}\n\\end{equation\nGenerally, a set of Majorana operators $M=\\left\\{\nb^{x},b^{y},b^{z},c\\right\\} $ can be employed to describe a spin by two\nfermionic modes. They are Hermitian and obey the relations $m^{2}=1$ and \nmm^{\\prime }=-m^{\\prime }m$ for $m,m^{\\prime }\\in M$ and $m\\neq m^{\\prime }\n. Moreover, in the Hilbert space with a spin described by two fermionic\nmodes, the relation $b^{x}b^{y}b^{z}c\\left\\vert \\Psi \\right\\rangle\n=\\left\\vert \\Psi \\right\\rangle $\\ must be satisfied to ensure the obeying of\nthe same algebraic relations as $\\sigma^{x}$, $\\sigma ^{y}$, and $\\sigma\n^{z} $ \\cite{Kitaev}.\n\nDrawing on the operators (\\ref{MajoranaFermion}) to the Kitaev honeycomb\nmodel, Hamiltonian (\\ref{Kitaev modelK}) is given b\n\\begin{equation}\nH=\\frac{i}{2}\\sum_{\\langle j,k\\rangle}\\hat{u}_{jk}J_{a_{jk}}c_{j}c_{k},\n\\label{HM}\n\\end{equation}\nwhere $\\hat{u}_{jk}=ib_{j}^{a_{jk}}b_{k}^{a_{jk}}$. Fig. \\ref{fig1}(a) also\nshows the structure of Hamiltonian (\\ref{HM}), from which it can be seen\nthat $\\hat{u}_{jk}=-\\hat{u}_{kj}$. Since these operators $\\hat{u}_{jk}$\ncommute with the Hamiltonian (\\ref{HM}) and with each other, the Hilbert\nspace splits into two common eigenspaces of $\\hat{u}_{jk}$ with eigenvalues \nu_{jk}=\\pm1$. Thus, Hamiltonian (\\ref{HM}) is reduced to a quadratic\nMajorana fermionic Hamiltonian\n\\begin{equation}\nH=\\frac{i}{2}\\sum_{\\langle j,k\\rangle}u_{jk}J_{a_{jk}}c_{j}c_{k}.  \\label{HU}\n\\end{equation}\n\nWith a Fourier transformation\n\\begin{equation}\nc_{s,\\lambda}=\\frac{1}{\\sqrt{2L^{2}}}\\sum_{\\mathbf{q}}e^{i\\mathbf{q}\\cdo\n\\mathbf{r}_{s}}a_{\\mathbf{q},\\lambda},  \\label{Fourier}\n\\end{equation}\nwhere $s$ denotes a unit cell shown in Fig. \\ref{fig1}(a), $\\lambda $ refers\nto a position inside the cell, $r_{s}$ represents the coordinate of the unit\ncell, and $\\mathbf{q}$ are momenta of the system with finite system-size \n2L^{2}$, and a Bogoliubov transformation\n\\begin{equation}\n\\left\\{\n\\begin{array}{c}\nC_{\\mathbf{q},1}^{\\dag}=\\frac{1}{\\sqrt{2}}a_{-\\mathbf{q},1}-\\frac{1}{\\sqrt{2\n}A_{\\mathbf{q}}^{\\ast}a_{-\\mathbf{q},2}, \\\\\nC_{\\mathbf{q},2}^{\\dag}=\\frac{1}{\\sqrt{2}}A_{\\mathbf{q}}a_{-\\mathbf{q},1}\n\\frac{1}{\\sqrt{2}}a_{-\\mathbf{q},2}\n\\end{array}\n\\right.\n\\end{equation}\nwhere $A_{\\mathbf{q}}=\\sqrt{\\epsilon_{\\mathbf{q}}^{2}+\\Delta_{\\mathbf{q}}^{2\n}\/(\\Delta_{\\mathbf{q}}+i\\epsilon_{\\mathbf{q}})$, Hamiltonian (\\ref{HU}) is\ntransformed int\n\\begin{equation}\nH=\\sum_{\\mathbf{q}}\\sqrt{\\epsilon_{\\mathbf{q}}^{2}+\\Delta_{\\mathbf{q}}^{2}\n\\left( C_{\\mathbf{q},1}^{\\dagger}C_{\\mathbf{q},1}-C_{\\mathbf{q},2}^{\\dagger\n}C_{\\mathbf{q},2}\\right)  \\label{HC}\n\\end{equation}\nwith $\\epsilon_{\\mathbf{q}}=J_{x}\\cos q_{x}+J_{y}\\cos q_{y}+J_{z}$, and \n\\Delta_{\\mathbf{q}}=J_{x}\\sin q_{x}+J_{y}\\sin q_{y}$. In Hamiltonian (\\re\n{HC}), the momenta take the values \\cite{S. Yang\n\\begin{equation}\nq_{x\\left( y\\right) }=\\frac{2n\\pi}{L},n=-\\frac{L-1}{2},\\cdots,\\frac{L-1}{2},\n\\label{Values of q}\n\\end{equation}\nwhen the system size is chosen as $N=2L^{2}$ with $L$ being an odd integer.\nThus, the ground and the first-excited states are obtained by\n\n\\begin{align}\n\\left\\vert \\Psi_{0}\\right\\rangle & \\!\\!=\\prod_{\\mathbf{q}}C_{q,2}^{\\dagger\n}\\left\\vert 0\\right\\rangle =\\prod_{\\mathbf{q}}\\frac{1}{\\sqrt{2}}\\left( A_\n\\mathbf{q}}a_{-\\mathbf{q},1}+a_{-\\mathbf{q},2}\\right) \\left\\vert\n0\\right\\rangle ,  \\label{wavefunction} \\\\\n\\left\\vert \\Psi_{1}\\right\\rangle & \\!\\!=\\prod_{\\mathbf{q}}C_{q,1}^{\\dagger\n}\\left\\vert 0\\right\\rangle =\\prod_{\\mathbf{q}}\\frac{1}{\\sqrt{2}}\\left( a_{\n\\mathbf{q},1}-A_{\\mathbf{q}}^{\\ast}a_{-\\mathbf{q},2}\\right) \\! \\left\\vert\n0\\right\\rangle ,\n\\end{align}\nwith the energy eigenvalue\n\\begin{equation}\nE_{0,1}=\\pm\\sum_{\\mathbf{q}}\\sqrt{\\epsilon_{\\mathbf{q}}^{2}+\\Delta _{\\mathbf\nq}}^{2}},  \\label{EP}\n\\end{equation}\n\nIt has been shown that the Kitaev honeycomb model (\\ref{Kitaev model}) has a\nrich phase diagram including a gapped phase with Abelian anyonic excitations\n(called $A$ phase) and a gapless phase with non-Abelian anyonic excitations \n$B$ phase) \\cite{Kitaev}. In Fig. \\ref{fig1}(b), the two phases $A $ and $B$\nare separated by three transition lines, \\textit{i.e.}, $J_{x}=1\/2$, \nJ_{y}=1\/2$, and $J_{z}=1\/2$, which form a small triangle surrounding the $B$\nphase. Here, we only plot the energy spectrum (\\ref{EP}) as a function of \nJ_{z}$ for $J_{x}=J_{y}$ (the vertical dot-and-dash line in Fig. \\ref{fig1\n(b)) in Fig. \\ref{fig2}. It can be seen from Fig. \\ref{fig2} that the\nenergy-level degeneracy arises or lifts at certain points, which can be\nregarded as the possible critical points of QPT \\cite{Zhu,Sachdev}. In Fig.\n\\ref{fig2}(b, c, d), the degenerate points occur in the $B$ phase, but\ndisappear in the $A$ phase as shown in Fig. \\ref{fig2}(f). Moreover, the\nenergy spectrum may have asymptotic degeneracy at the phase diagram edge\nseen from Fig. \\ref{fig2}(a) when the size of system tends to infinity. The\nnon-analyticity points of ground state in $B$ phase are actual\nlevel-crossing points.\n\n\\begin{figure}[t]\n\\centering \\vspace{0cm} \\hspace{0cm} \\scalebox{0.88}\n\\includegraphics{fig2.eps}}.\n\\caption{Energy spectrum for the parameters $J_{x}=J_{y}$ (a) $J_{z}=0$, the\nspectrum indeed is degenerate in a larger system size; (b), (c), and (d) in \nB$ phase, for $J_{z}<1\/3$, $J_{z}=1\/3$, and $1\/3<J_{z}<1\/2$, respectively;\n(e) at the critical point of $J_{z}=1\/2$ and (f) in $A$ phase. It is clearly\nthat there is level-crossing in (b), (c) and (d).}\n\\label{fig2}\n\\end{figure}\n\n\\section{Geometric phase}\n\nIn general spin-chain systems characterized by Landau-type order parameters,\nthe GPs can be generated by adiabatic and cyclic evolutions with a rotation\nof each spin coupled with its neighbors in the certain parameter spaces \\cit\n{Zhu}. However, in the Kitaev honeycomb model, the two spins \n\\sigma_{s,\\lambda }$ and $\\sigma _{s,\\bar{\\lambda}}$ in the unit cell $s$ is\ncoupled with each other only by a $z$-link, as Fig. \\ref{fig1}(a) shows. As\na result, a simple rotation of a single-spin with the generator $\\sigma\n_{s,\\lambda }^{z}$ can only \"propagate\" along the horizontal spin-chain\nthrough the $x$- and $y$-link couplings but not along the vertical direction\nsince the rotation-generator of a single-spin $\\sigma _{s,\\lambda }^{z}$\ncommutes with the $z$-link spin-operators in the Hamiltonian between the\nhorizontal spin-chains. On other words, if using the above single-spin\nrotation, the Kitaev honeycomb model would be equivalent to a system of\nindependent multi-single-spin-chains. In order to obtain the GP of the\nKitaev honeycomb model, it should be introduced a correlated rotation of two\n$z$-link spins in each unit-cell\n\\begin{equation}\nU\\left( \\phi \\right) =\\exp \\left[ i\\phi R\\right] ,  \\label{Rotation}\n\\end{equation\nwher\n\\begin{equation}\nR=\\sum_{s}\\sum_{\\lambda }\\sigma _{s,\\lambda }^{z}\\sigma _{s,\\bar{\\lambda\n}^{z}  \\label{R expression}\n\\end{equation\nis the correlated rotation-generator, and $\\phi $ is the \"co-rotation\nangle\". Indeed, when the rotation operator is applied on the spin of $\\left(\ns,\\lambda \\right) $-th set, the spin operator $\\sigma _{s,\\bar{\\lambda}}^{z}$\nacts as a c-number because the spin operators on different sets commute each\nother. As a matter of fact, the correlated rotation-generator $R$ can\ngenerate a \"co-rotation\" of the $z$-link spins in each unit cell.\nFurthermore, under the gauge transformation (\\ref{Rotation}), the rotations\nof each spins in the 2D honeycomb Kitaev model become correlative and\nglobal. Hence it is possible to reveal the relation between the GP and the\nnonlocal TQPT by means of the correlated rotation. Then, the ground state\nwave function becomes\n\\begin{equation}\n\\left\\vert \\Psi _{0}^{\\prime }(\\phi )\\right\\rangle =U\\left( \\phi \\right)\n\\left\\vert \\Psi _{0}\\right\\rangle ,\n\\end{equation\nand correspondingly, the GP is given by \\cite{Liang\n\\begin{align}\n\\gamma & =-i{\\int\\nolimits_{0}^{2\\pi }}\\left\\langle \\Psi _{0}\\right\\vert\nU^{^{\\dag }}\\frac{d}{d\\phi }U\\left\\vert \\Psi _{0}\\right\\rangle d\\phi  \\notag\n\\\\\n& =-2\\pi \\left\\langle \\Psi _{0}\\right\\vert R\\left\\vert \\Psi\n_{0}\\right\\rangle .  \\label{BPOrigin}\n\\end{align\nIt can be seen that the GP for the Kitaev honeycomb model is proportional to\nthe expectation value of the correlated rotation $R$. Different from the\nlocal spin-correlation $\\sigma _{s,\\lambda }^{z}\\sigma _{s,\\bar{\\lambda\n}^{z} $, the sum over whole lattice-sites in $R$ leads to a global property,\nwhich is crucial for the topological QPT.\n\nIn terms of the Majorana fermion operators (\\ref{MajoranaFermion}), the\nrotation operator $R$ is given, after using the Fourier transformation (\\re\n{Fourier}), by $R=\\sum_{s,\\lambda}\\left( ib_{s,\\lambda}^{z}c_{s,\\lambda\n}\\right) \\left( ib_{s,\\bar{\\lambda}}^{z}c_{s,\\bar{\\lambda}}\\right)\n=\\sum_{s}\\left( -iu_{s,1;s,2}^{z}c_{s,1}c_{s,2}\\right) +\\sum_{s}\\left(\n-iu_{s,2;s,1}^{z}c_{s,2}c_{s,1}\\right) $. Under the restriction of vortex\nfree subspace, $u_{s,1;s,2}^{z}$ and $u_{s,2;s,1}^{z}$ are the good quantum\nnumbers, that is to say, $u_{s,1;s,2}^{z}=1$, and $u_{s,2;s,1}^{z}=-1$.\nThus, the rotation operator $R$ is finally obtained by\n\n\\begin{equation}\nR=\\frac{-i}{\\sqrt{2L^{2}}}\\sum_{\\mathbf{q}}\\left( a_{-\\mathbf{q},1}a_\n\\mathbf{q},2}-a_{-\\mathbf{q},2}a_{\\mathbf{q},1}\\right) .  \\label{R}\n\\end{equation}\nBy means of Eqs. (\\ref{wavefunction}), (\\ref{BPOrigin}), and (\\ref{R}), the\nground-state GP is given formally by\n\\begin{equation}\n\\gamma=\\frac{-2\\pi}{\\sqrt{2L^{2}}}\\sum_{\\mathbf{q}} \\mathop{\\rm Im} \\left(\n-A_{\\mathbf{q}}e^{2i\\mathbf{q}\\cdot\\mathbf{d}}+A_{\\mathbf{q}}^{\\ast}\\right) ,\n\\label{BP of R}\n\\end{equation}\nwhere $\\mathbf{d}$\\ is a vector from one site to another inside one cell. It\ncan be seen easily from Fig. \\ref{fig1}(a) that the vector is given by \n\\mathbf{d=}\\left( \\mathbf{n}_{1}+\\mathbf{n}_{2}\\right) \/3$. Inserting this\nvector $\\mathbf{d}$ into Eq. (\\ref{BP of R}), we hav\n\\begin{align}\n\\gamma & \\!\\! =\\!\\!\\frac{-2\\pi}{\\sqrt{2L^{2}}}\\sum_{\\mathbf{q}}\\mathop{\\rm\nIm}\\left( -A_{\\mathbf{q}}e^{\\frac{i}{3}\\left( 2q_{x}+2q_{y}\\right) }+A_\n\\mathbf{q}}^{\\ast}\\right)  \\notag \\\\\n& \\!\\! =\\!\\!\\frac{-2\\pi}{\\sqrt{2\\!L^{2}}}\\!\\!\\sum_{\\mathbf{q}}\\!\\frac \n\\epsilon_{\\mathbf{q}}\\!\\!\\left[ 1\\!\\!+\\!\\cos\\!\\frac{1}{3}\\!\\left(\n2q_{x}\\!\\!+\\!2q_{y}\\!\\right) \\right] \\!\\!-\\!\\!\\Delta_{\\mathbf{q}}\\sin \\\n\\frac{1}{3}\\!\\left( 2q_{x}\\!\\!+\\!2q_{y}\\right) }{\\sqrt{\\epsilon _{\\mathbf{q\n}^{2}+\\Delta_{\\mathbf{q}}^{2}}}  \\label{gammafinal}\n\\end{align}\n\n\\begin{figure}[h]\n\\centering \\vspace{0cm} \\hspace{0cm} \\scalebox{0.5}\n\\includegraphics{fig3.eps}}.\n\\caption{(Color online) Scaled GP with system size parameter $L=101$.}\n\\label{fig3}\n\\end{figure}\n\nEq. (\\ref{gammafinal}) is the main result of this paper. The scaled (or\naverage) GP $\\gamma\/L$ as a function of coupling parameters is shown in Fig.\n\\ref{fig3}, which distributes symmetrically with respect to the coupling\nparameters $J_{x}$ and $J_{y}$. For sake of simplicity, the scaled GP \n\\gamma\/L$ is replaced by $\\gamma$ in the following discussions. In order to\nsee the difference between $A$ and $B$ phases, $\\gamma$-variation with \nJ_{z} $ along a selected line $J_{x}=J_{y}$ in the phase diagram of Kitaev\n\\cite{Kitaev} (see Fig. \\ref{fig1}(b), the vertical dot-and-dash line) is\nplotted in Fig. \\ref{fig4}(a). It is shown that $\\gamma$ is smooth in $A$\nphase ($J_{z}>1\/2$) while becomes saltant in $B$ phase ($J_{z}<1\/2$) for the\nsize parameters $L=11$ (dark yellow line)$,$ $33$ (red), and $99$ (blue),\nrespectively. Moreover, all the data fall onto a single curve in $A$ phase,\nwhile the number of saltation increases with the system-size $L$ in $B$\nphase (see insets (1) and (2) of Fig. \\ref{fig4}(a) ). To be specific, the\nnumber of saltation for $L=33$ is three times than that for $L=11$ (see Fig.\n\\ref{fig4}(a)), and the same situation occurs in turn for $L=99$ and $33$.\n\n\\begin{figure*}[t]\n\\centering \\vspace{0cm} \\hspace{0cm} \\scalebox{1.0}\n\\includegraphics{fig4.eps}}\n\\caption{(Color online) (a) $\\protect\\gamma$ curve along the selected\nvariation path $J_{x}=J_{y}$ for $L=11,$ $33,$ and $99$. Both insets reveal\nthe increasing number of saltation in $B$ phase proportional to the system\nsize parameter $L$. (b) $g_{x}$ and (c) $g_{xx}$ as a function of $J_{z}$\nalong the variation path $J_{x}=J_{y}$ for system size parameters $L=101,303$\nand $909$. The two insets are local enlarged-pictures, which show the\nvibration in $B$ phase and the circumstances in the critical point\nrespectively.}\n\\label{fig4}\n\\end{figure*}\n\nIt is meaningful to consider the first-order partial derivative \ng_{_{\\beta}}=\\partial\\gamma\/\\partial J_{\\beta}$ ($\\beta=x,y$) of the GP \n\\gamma$. Since the GP $\\gamma$ in Eq. (\\ref{gammafinal}) is symmetric with\nrespect to $J_{x}$ and $J_{y}$, we only need to investigate $g_{x}$ (or\nequivalently $g_{y}$). The variation of $g_{x}$ with respect to $J_{z}$\nalong the selected path of $J_{x}=J_{y}$ from $B$ phase to $A$ phase is\nshown in Fig. \\ref{fig4}(b) for different system-size parameters $L=101$, \n303$ and $909$. It can be seen from Fig. \\ref{fig4}(b) that $g_{x}$\noscillates in $B$ phase with frequency (or number of peaks), which is\nproportional to $L$ (see inset (1) of Fig. \\ref{fig4}(b)). This rapid\nvariation of the GP $\\gamma$ (in the $B$ phase) has not yet been found, to\nour knowledge. However, a very similar behavior of fidelity susceptibility\nin the Kitaev model has been reported \\cite{S. Yang}. On the other hand, the\nvalue of $g_{x}$ at the critical point $J_{z}=1\/2$ increases with the\nsystem-size and sharply decays in $A$ phase (see inset (2) of Fig. \\ref{fig4\n(b) for detail). It is interesting to remark that the saltation of GP \n\\gamma $ in $B$ phase due to the complex structure of ground state with\ndegeneracy (Fig. \\ref{fig2} (b),(c),(d)) is not random rather has\nregulation, especially it tends to a regular oscillation above the point, \nJ_{z}=1\/3$ , (see inset (1) of Fig. \\ref{fig4}(b)). The oscillation\nfrequency depends linearly on the system size.\n\nTo show the non--analyticity of GP at the critical points explicitly the\nsecond-order derivative $g_{xx}$ of the GP $\\gamma$ with respect to the\ncoupling parameters is calculated. Fig. \\ref{fig4}(c) shows the variation of\n$g_{xx}$ with respect to $J_{z}$ along the variation path of $J_{z}=J_{y}$\nfor different system-size parameters $L=101$, $303$ and $909$. Inset (1)\nreveals the increase of peak-number of $g_{xx}$ in $B$ phase along with the\nsystem-size $L$ similar to $\\gamma$ and $g_{x}$ in behavior. The\nsecond-order derivative $g_{xx}$ is divergent at the critical point \nJ_{z}=1\/2$ as shown in inset (2) indicating that the TQPT of the Kitaev\nhoneycomb model is a second-order transition, While the QPT of the XY spin\nchain \\cite{Zhu,Zhu08} and the Dicke model \\cite{Zhu08,Chen} has been shown\nto be the first-order transition with the divergent first-order derivative\nof the GP. We conclude that the non-analytic GP $\\gamma$ can very well\ndescribe the TQPT in terms of the Landau phase-transition theory.\n\nSimilarly, we can also choose the variation path as $J_{z}=1\/4$ (dashed line\nin Fig. \\ref{fig1}(b)) with two critical points $J_{x}=1\/4$ and $J_{x}=1\/2$.\nQualitatively similar results are shown in Fig. \\ref{fig5} for different\nsize parameters $L=101$ (red line), $303$ (blue) and $707$ (dark),\nrespectively, where $\\gamma$-plot is a smooth curve in $A$ phase for \nJ_{x}<1\/4$ or $J_{x}>1\/2$ and becomes saltant in $B$ phase when \n1\/4<J_{x}<1\/2$ (Fig. \\ref{fig5}(a)). The plots of $g_{x}$ and $g_{xx}$ are\nrespectively shown in Fig. \\ref{fig5}(b) and (c) displaying the clear\nvibration in the $B$ phase. $g_{x}$ has a sharp peak at the critical points\nand $g_{xx}$ is divergent in the thermodynamic limit showing the\ncharacteristic of second-order phase transition. Inset of Fig. \\ref{fig5}(c)\nshows the detail of the vibration in the $B$ phase with the peak-number\nproportional to the system size.\n\n\\begin{figure}[h]\n\\centering \\vspace{0cm} \\hspace{0cm} \\scalebox{0.3}\n\\includegraphics{fig5.eps}}\n\\caption{(Color online) (a) $\\protect\\gamma$ curve, which is smooth in $A$\nphase and saltant in $B$ phase, (b) $g_{x}$ curve and (c) $g_{xx}$ as a\nfunction of $J_{x}$ for $J_{x}$ varying along the path $J_{z}=1\/4$, with\ncritical points at $J_{x}=1\/4$ and $J_{x}=1\/2$.}\n\\label{fig5}\n\\end{figure}\n\n\\section{Finite-size scaling}\n\nIn order to quantify the non-analytic nature of GP through the critical\npoints, and to further understand the quantum criticality, we investigate\nthe scaling behavior of the GP and its first-order and second-order\nderivatives by the finite size scaling analysis \\cite{Barber}. Since the GP\nof a many-body system is an extensive quantity, it usually depends on the\nsystem size in the non-critical region. In the vicinity of critical point (\nJ_{z}^{C}=1\/2$ here), the GP $\\gamma$ follows a power law\\cite{Lin}\n\n\\begin{equation}\n\\gamma \\propto {\\left\\vert J_{z}-J_{z}^{C}\\right\\vert }^{-\\alpha _{\\gamma }}\n\\label{alpha}\n\\end{equation\nwith $\\alpha $ being corresponding exponent. ${\\left\\vert\nJ_{z}-J_{z}^{C}\\right\\vert }$-dependence of $\\gamma $ in the left-hand side\nof critical point ( $J_{z}<J_{z}^{C}$ ) and right-hand side ( \nJ_{z}>J_{z}^{C})$ is respectively plotted in Fig. \\ref{fig6}(a) and (b) for\ndifferent system-size parameters $L=101$, $303$ and $909$. The corresponding\nexponents $\\alpha _{\\gamma }^{-}=-0.99934\\pm 0.00033$ (left-hand side) and \n\\alpha _{\\gamma }^{+}=-0.83538\\pm 0.00008$ (right-hand side) are obtained\nfrom Fig. \\ref{fig6}(a) and (b). Similarly, $g_{x}$ and $g_{xx}$ as a\nfunction of $|J_{z}-J_{z}^{C}|$ are plotted in Fig. \\ref{fig6}(c), (d) and\n(e), (f) for the gapless and gapped phases respectively, from which the\ncritical exponents $\\alpha _{g_{x}}^{-}=-0.17529\\pm 0.02056$, $\\alpha\n_{g_{xx}}^{-}=1.32523\\pm 0.01719$ (left) for B phase and $\\alpha\n_{g_{x}}^{+}=-0.48375\\pm 0.00033$, $\\alpha _{g_{xx}}^{+}=0.60687\\pm 0.00526$\n(right) for A phase are found. The fact of negative exponents $\\alpha\n_{\\gamma }^{\\pm }$, $\\alpha _{g_{x}}^{\\pm }$ and positive $\\alpha\n_{g_{xx}}^{\\pm }$ indicates that $\\gamma $ and $g_{x}$ are finite while \ng_{xx}$ is divergent at the critical point in the thermodynamic limit. Thus\nthe TQPT is a second-order phase transition characterized by the GP $\\gamma \n.\n\n\\begin{figure}[h]\n\\centering \\vspace{0cm} \\hspace{0cm} \\scalebox{1.0}\n\\includegraphics{fig6.eps}}\n\\caption{(Color online) Finite-size scaling analysis of the power-law\ndivergence for (a) GP $\\protect\\gamma$, (c) $g_{x}$, (e) $g_{xx}$ as a\nfunction of $|J_{z}-J_{z}^{C}|$ in the vicinity of critical point with\nsystem sizes $L=301,901$ and $1501$ on the left-hand side ($J_{z}<J_{z}^{C}\n) and (b), (d), (f) on the right-hand side ($J_{z}>J_{z}^{C}$) respectively.}\n\\label{fig6}\n\\end{figure}\n\n\\begin{figure}[h]\n\\centering \\vspace{0cm} \\hspace{0cm} \\scalebox{0.35}\n\\includegraphics{fig7.eps}}\n\\caption{(Color online) $L$-dependence of $J_{z}^{C}-J_{z}^{m}$ in\nlogarithmic coordinate for $L=901,951,...,1901$.}\n\\label{fig7}\n\\end{figure}\n\nThe position of maximum value of $\\gamma $ denoted by $J_{z}^{m}$ may not be\nlocated exactly at the critical point $J_{z}^{C}=1\/2$, but tends to it in\nthe thermodynamic limit $L\\rightarrow \\infty $, which is regarded as the\npseudocritical point \\cite{Barber}. The $J_{z}^{C}-J_{z}^{m}$ versus\ndifferent system-size $L=901,951,...,1901$ in a logarithmic coordinate is\nplotted in Fig. \\ref{fig7}, which is a straight line of slope $-0.37851\\pm\n0.00226$. It means that the $J_{z}^{m}$ tends toward to the critical point \nJ_{z}^{C}$ following the power-law decay\n\\begin{equation}\nJ_{z}^{C}-J_{z}^{m}\\propto L^{-0.37851}.\n\\end{equation}\n\nOn the other hand, the maximum value of $\\gamma $ at $J_{z}=J_{z}^{m}$ for a\nfinite-size system behaves as\n\\begin{equation}\n\\gamma ({J_{z}^{m}})\\propto {L}^{\\mu _{\\gamma }},\n\\end{equation\nwhich is shown in the inset of Fig. \\ref{fig8}(a) with a straight line in\nlogarithmic coordinate. The corresponding size-exponent is given by $\\mu\n_{\\gamma }=0.01148\\pm 0.00054$.\n\n\\begin{figure*}[t]\n\\centering \\vspace{0cm} \\hspace{0cm} \\scalebox{1.0}\n\\includegraphics{fig8.eps}}\n\\caption{(Color online) (a) $F_{\\protect\\gamma}$, (b) $F_{g_x}$, and (c) \nF_{g_{xx}}$ as a function of $L^{\\protect\\nu}\\left( J_{z}-J_{z}^{m}\\right)$\nfor $L=401,601,...,1601$. All the data fall on to a single curve\nrespectively. And the three insets in turn shows the variation of $\\protec\n\\gamma(J_{z}^{m})$, $g_{x}(J_{z}^{m})$, and $g_{xx}(J_{z}^{m})$ with respect\nto the system size-parameters $L=101,151,...,1901$.}\n\\label{fig8}\n\\end{figure*}\n\nSince the GP $\\gamma$ around its maximum position $J_{z}^{m}$ can be written\nas a simple function of $J_{z}^{m}-J_{z}$, it is possible to make all the\nvalue-data defined by a universal scaling function $F_{\\gamma}=\\left( {\\gamm\n}({J_{z}^{m}})-\\gamma\\right) \/\\gamma$ versus $L^{\\nu_{\\gamma}}\\left(\nJ_{z}-J_{z}^{m}\\right) $, namely,\n\\begin{equation}\nF_{\\gamma}=f\\left[ L^{\\nu_{\\gamma}}\\left( J_{z}^{m}-J_{z}\\right) \\right] ,\n\\end{equation}\nwhere $\\nu_{\\gamma}$ is a critical exponent that governs the divergence of\nthe correlation length. The values of $F_{\\gamma}$ for different system-size\nparameters $L$ fall onto a single curve as shown in Fig. \\ref{fig8}(a), from\nwhich we can extract the critical exponent $\\nu_{\\gamma}=-0.015$ numerically.\n\nIn fact, according to the scaling ansatz of a finite system \\cite{Barber,Lin\n, the critical exponent $\\nu $ can be determined by the relation $\\nu =\\mu\n\/\\alpha $. In terms of this relation, the critical exponents in $B$ and $A$\nphases are found as ${\\nu }_{\\gamma }^{-}=-0.01149$ and ${\\nu }_{\\gamma\n}^{+}=-0.01374$, which are consistent with the numerical result $\\nu\n_{\\gamma }$ extracted from Fig. \\ref{fig8}(a). Inset of Fig. \\ref{fig8}(b)\nis a plot of the maximum value of $g_{x}({J_{z}^{m}})$ as a function of $L$\n\\begin{equation}\ng_{x}({J_{z}^{m}})\\propto {L}^{\\mu _{g_{x}}}\n\\end{equation}\nin logarithmic coordinate, from which the size exponent $\\mu\n_{g_{x}}=0.01612\\pm 0.00094$ is found. The universal scaling function\n\\begin{equation}\nF_{g_{x}}=f\\left[ L^{\\nu _{g_{x}}}(J_{z}^{m}-J_{z})\\right]\n\\end{equation}\nis shown in Fig. \\ref{fig8}(b). We have the numerical value $\\nu\n_{g_{x}}=-0.040$ and the results determined by the relation $\\nu =\\mu\n\/\\alpha $ that $\\nu _{g_{x}}^{-}=-0.09196$, $\\nu _{g_{x}}^{+}=-0.03332$. The\ndeviation between $\\nu _{g}$ and $\\nu _{g_{xx}}^{-}$ may be due to the rapid\noscillation in the gapless $B$ phase. Similarly, the critical exponents of \ng_{xx}$ can be obtained from Fig. \\ref{fig8}(c) as $\\mu _{g_{xx}}=0.54570\\pm\n0.00237$, $\\nu _{g_{xx}}^{-}=0.410$ and $\\nu _{g_{xx}}^{+}=0.908$, and the\nresults determined by $\\nu =\\mu \/\\alpha $ are $\\nu _{g_{xx}}^{-}=0.41178$\nand $\\nu _{g_{xx}}^{+}=0.89920$ respectively.\n\n\\section{Summary and discussion}\n\nWe demonstrate that the ground-state GP generated by the correlated rotation\nof two linked-spins in a unit-cell indeed can be used to characterize the\nTQPT for the Kitaev honeycomb model. The non-analytic GP with a divergent\nsecond-order derivative at the critical points shows that the TQPT is a\nsecond-order phase-transition different from the $XY$ spin-chain \\cit\n{Zhu,Zhu08}, in which the first-order derivative of GP is divergent, and the\nLMG model\\cite{Zhu,Zhu08}, in which the GP itself is shown to be divergent.\nMoreover it is found that the GP is zigzagging with oscillating derivatives\nin the gapless $B$ phase, but is a smooth function in the gapped $A$ phase.\nThe scaling behavior of the non-analytic GP in the vicinity of critical\npoint is shown to exhibit the universality with negative exponents of both \n\\gamma$ and $g_{x}$ while a positive exponent of $g_{xx}$ indicating the\ncharacteristic of second-order phase transition.\n\n\\section*{Acknowledgments}\n\nThis work is supported by the NNSF of China under Grant Nos. 11075099 and\n11074154, ZJNSF under Grant No. Y6090001, and the 973 Program under Grant\nNo. 2006CB921603.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\t\\label{section1}\n\t\n\\begin{figure}\t\n\t\\begin{center}\n\t\t\\includegraphics[width=90mm]{Figure1.png}\n\t\t\\caption{Panel (a): Spatial positions of the stars in our sample, with the tidal radius ($r_t=10$\\arcmin) of M~54 over-plotted with a solid line. The open red symbols designate N-rich stars (the diamond symbol refers to a field star, while the open circle highlights the extra-tidal member of M~54). The lime circles designate the M~54 population analyzed in this work, while the black plus symbols designate the stars analyzed by \\citet{Nataf2019}. The empty grey `star' symbols designate the potential Sgr population from \\citet{Hayes2020}. The two concentric circles indicate 5 $r_{t}$ and 7 $r_{t}$ for reference. Panel (b): \\textit{Gaia} EDR3 proper motions of stars that have been associated with the Sgr stream: blue symbols for the  \\citet{Antoja2020} stars and open black `star' symbols for \\citet{Hayes2020} stars. The orbital path of Sgr is shown by the dotted (backward) and solid (forward) purple line in panels (a) and (b), with the thick and thin lines showing the central orbit, and one hundred ensemble of orbits that shows the more probable regions of the space, which are crossed more frequently by the simulated orbit, respectively. Panel (c): Color magnitude diagram from \\textit{Gaia} EDR3 photometry of our sample. The symbols are the same as in panels (a) and (b), except the white circles, which denotes the M~54 members from \\textit{Gaia} EDR3, selected on proper motions and within 3$\\arcmin$ from the cluster center. Panel (d): Radial velocities versus [Fe\/H] ratios determined from APOGEE-2\/\\texttt{ASPCAP} (black symbols) and our [Fe\/H] ratio determinations from \\texttt{BACCHUS} (green and red symbols) in the field around M~54. The [Fe\/H] APOGEE-2\/\\texttt{ASPCAP} determinations have been systematically offset by $\\sim$0.11 dex in order to compare with our [Fe\/H] \\texttt{BACCHUS}  determinations, as suggested in \\citep{Fernandez-Trincado2020c}.}\n\t\t\\label{Figure1}\n\t\\end{center}\n\\end{figure}\t\n\t\nThe Sagittarius (Sgr) dwarf spheroidal (dSph) galaxy is one of the closest massive satellites of the Milky Way (MW) \\citep{Ibata1994}, and has yielded a wealth of observational evidence of ongoing accretion by the MW in the form of persistent stellar debris and tidal streams discovered by \\citet{Mateo1996}, and extensively studied with photometric and spectroscopic observations over a huge range of distances ($\\sim$10--100 kpc) \\citep[see, e.g.,][]{Ibata2001, deBoer2015} using different stellar tracers--including Carbon stars \\citep{Totten1998}, the first all-sky map of the tails using 2MASS M-giants \\citep{Majewski2003}, red clump Stars \\citep{Correnti2010}, RR Lyrae stars \\citep{Newberg2003, Ramos2020}, and CN-strong stars \\citep{Hanke2020}, among other tracers, usually in small patches along the stream (see, e.g., \\citealt{Li2019}). These studies have been followed-up by numerical studies \\citep[see, e.g.,][]{Law2005, Vasiliev2020}, as well as by using precise astrometry from the \\textit{Gaia} second data release \\citep[Gaia DR2;][]{Brown2018}, based on proper motions alone \\citep{Antoja2020}. Its proximity provides a unique laboratory to study accretion in detail, through the tidally stripped streams that outflow from the Sgr system \\citep[][]{Hasselquist2017, Hasselquist2019, Hayes2020}.\n\t\t\nAs a natural result of such an accretion event, there is a claim in the literature that not only field stars but also GCs have been accreted \\citep[see, e.g.,][]{Massari2019}.  Some have been speculated to be lost in the disruption process, and may lie immersed in the Sgr stream.  Candidates include: M~54, Terzan 7, Arp 2, Terzan 8, Pal 12, Whiting 1, NGC 2419, NGC 6534, and NGC 4147 \\citep[e.g.,][]{Law2010a, Bellazzini2020}, but a firm connection is still under debate \\citep[e.g.,][]{Villanova2016, Tang2018, Huang2020, Yuan2020}. In this context, ``chemical tagging\" \\citep[e.g.,][]{Freeman2002}, which is based on the principle that the photospheric chemical compositions of stars reflect the site of their formation, is a promising route for investigation of this question.   \n\nWhile the abundances of light and heavy elements for individual stars in GCs have been widely explored \\citep[e.g.,][]{Pancino2017, Meszaros2020}, little is known about these abundances in disrupted GCs likely associated with the closest dwarf galaxies, such as Sgr \\citep{Karlsson2012}. Although some evidence for chemical anomalies has been detected towards the inner bulge and halo of the MW \\citep[see, e.g.,][]{Fernandez-Trincado2016b, Recio-Blanco2017, Schiavon2017, Fernandez-Trincado2017} and Local Group dwarf galaxies \\citep[see, e.g.,][]{Fernandez-Trincado2020b}, suggesting the presence of GCs in the form of disrupted remnants, alternative ways to produce these stars have been recently discussed \\citep{Bekki2019}.\n\nThis paper is outlined as follows. The high-resolution spectroscopic observations are discussed in Section \\ref{section2}. Section \\ref{section3} describes the sample associated with M~54, including a comparison with data from the literature. Section \\ref{section4} presents our estimated stellar parameters and derived chemical-abundance determinations. Section \\ref{section5} discusses the results, and our concluding remarks are presented in Section \\ref{section6}.\n  \n\\section{Data}\n\\label{section2}\n\n  We make use of the internal dataset (which includes all data taken through March 2020) of the second-generation Apache Point Observatory Galactic Evolution Experiment \\citep[APOGEE-2;][]{Majewski2017}, which includes the first observations from the Ir\\'en\\'ee du Pont 2.5-m Telescope at Las Campanas Observatory \\citep[APO-2S;][]{Bowen1973} in the Southern Hemisphere (Chile), and more observations from the Sloan 2.5-m Telescope at Apache Point Observatory \\citep[APO-2N;]{Gunn2006} in the Northern Hemisphere (New Mexico). The survey operates with two nearly identical spectrographs \\citep{Eisenstein2011, Wilson2012, Wilson2019}, collecting high-resolution ($R\\sim22,000$) spectra in the near-infrared textit{H}-band (1.5145--1.6960 $\\mu$m, vacuum wavelengths). This data set provides stellar parameters, chemical abundances, and radial velocity (RV) information for more than 600,000 sources, which include $\\sim$437,000 targets from the sixteenth data release \\citep[DR16;][]{Ahumada2020} of the fourth generation of the Sloan Digital Sky Survey \\citep[SDSS-IV;][]{Blanton2017}. APOGEE-2 target selection is described in full detail in \\citet{Zasowski2017} (APOGEE-2), Santana et al. (in prep.) (APO-2S), and Beaton et al. (in prep.) (APO-2N). \n  \n  APOGEE-2 spectra were reduced \\citep{Nidever2015} and analyzed using the APOGEE Stellar Parameters and Chemical Abundance Pipeline \\citep[ASPCAP;][]{Garcia2016, Holtzman2015, Holtzman2018, Henrik2018, Henrik2020}. The model grids for APOGEE-2 internal dataset are based on a complete set of \\texttt{MARCS} stellar atmospheres \\citep{Gustafsson2008}, which now extend to effective temperatures as low as 3200 K, and spectral synthesis using the \\texttt{Turbospectrum} code \\citep{Plez2012}. The APOGEE-2 spectra provide access to more than 26 chemical species, which are described in \\citet{Smith2013}, \\citet{Shetrone2015}, \\citet{Hasselquist2016}, \\citet{Cunha2017}, and \\citet{Holtzman2018}.  \n\n\\subsection{M~54 field}\n\\label{section3}\n\nThe APOGEE-2 field toward M~54 was previously examined in \\citet{Meszaros2020} based on public DR16 spectra. In that work, 22 stars were identified as potential members linked to M~54 based in the APOGEE-2 radial velocities \\citep{Nidever2015}, i.e., stars with RV within $3\\sigma _{RV,cluster}$, metallicity within $\\pm$0.5 dex around the cluster average, proper motion from the \\textit{Gaia} Early Data Release 3 \\citep[\\textit{Gaia} EDR3;][]{Brown2020} within 2.5$\\sigma$ around the cluster average proper motion, and located inside the cluster tidal radius, $r_{t}\\lesssim10$ arcmin, \\citep[][2010 edition]{Harris1996} were classified as potential members of M~54. However, only 7 out of 22 stars were spectroscopically examined with the \\texttt{BACCHUS} code in \\citet{Masseron2016}, since only these stars achieved a signal-to-noise (S\/N$>$70) sufficient to provide reliable abundance determinations.  \n\nThe post-APOGEE DR16 dataset provides incremental visits toward M~54, which has allowed to increase the signal-to-noise for 20 out of 22 of the potential cluster members. As a result, nitrogen, titanium, and nickel abundances can be now obtained from the stronger absorption features (as shown for $^{12}$C$^{14}$N lines as shown in Figure \\ref{Figure4}), and other chemical species can also be studied. \n\n\\citet{Nataf2019}, using APOGEE-2 DR14 data \\citep{Abolfathi2018} and abundance determinations from the \\texttt{Payne} pipeline \\citep{Ting2019}, have catalogued eight possible members from M~54. Two of those objects (2M18544275$-$3029012 and 2M18550740$-$3026052) were included in our study. The remaining six stars were rejected from our analysis for the following reasons. Six objects in \\citet{Nataf2019} were found to have low S\/N ($<$70) spectra, resulting in very uncertain CNO abundance ratios for many chemical species, since the molecular lines ($^{16}$OH, $^{12}$C$^{16}$O, and $^{12}$C$^{14}$N) are very weak. Secondly, 6 out of the 8 objects in \\citet{Nataf2019} exhibit [Fe\/H] $> -1.1$, and were recently classified as Sgr stars \\citep[see, e.g.,][]{Hayes2020}, which make them unlikely members of M~54.\n\nIn this study, we make use of the more recent spectra to examine the chemical composition of added stars to the abundance average of M~54. As in \\citet{Meszaros2020}, we also limit our discussion only to stars with S\/N$>70$.\n\n\\subsection{Extra-tidal stars}\n\nWe also report on the serendipitous discovery of two nitrogen-enhanced (N-rich) metal-poor stars beyond the tidal radius of M~54, as shown in pane (a) of Figure \\ref{Figure1}. APOGEE-2 stars in the stream$+$core Sagittarius (Sgr) system \\citep[see, e.g.,][]{Hasselquist2017, Hasselquist2019, Hayes2020} are highlighted as black open `star' symbols in pane (a) of Figure \\ref{Figure1}, while potential star members (blue symbols) of the stream$+$core Sgr system from \\citet[][]{Antoja2020} are also displayed in panel (a) of Figure \\ref{Figure1}. It is important to note that the [Fe\/H] abundance of APOGEE-2 Sgr stars are provided by the \\texttt{ASPCAP} pipeline \\citep[see][]{Hasselquist2017, Hasselquist2019, Hayes2020}. In order to compare with our [Fe\/H] determinations, an offset of $\\sim$0.11 dex was applied to \\texttt{ASPCAP} metallicities in panel (d) of Figure \\ref{Figure1}, as suggested in \\citet{Fernandez-Trincado2020c}.\n\nPanels (a) to (d) of Figure \\ref{Figure1} reveal that one (2M18565969$-$3106454) of the newly discovered N-rich stars meets the minimum criterion to be considered a potential extra-tidal star which has likely escaped the cluster potential, while the second N-rich star (2M18533777$-$3129187) has physical properties that are clearly offset from the M~54 population. In particular, this star is brighter than the typical population of M~54 (see panel (c) in Figure \\ref{Figure1}), and both proper motions and RV differ from the nominal proper motion and RV of the cluster as shown in panels (b) and (d) of Figures \\ref{Figure1}. It is likely that 2M18533777$-$3129187 is a foreground field star (hereafter N-rich field star). \n\n\n\\section{Stellar parameters and chemical-abundance determinations}\n \\label{section4}\n\nThe chemical analysis is very similar to that carried out by \\citet[][]{Fernandez-Trincado2019a, Fernandez-Trincado2019b, Fernandez-Trincado2019c, Fernandez-Trincado2019d, Fernandez-Trincado2020a, Fernandez-Trincado2020b, Fernandez-Trincado2020c, Fernandez-Trincado2020d, Fernandez-Trincado2021a}. The stellar parameters ($T_{\\rm eff}$, $\\log$ \\textit{g}, and first guess on metallicity) for the 20 cluster members with S\/N$>$70 were extracted from \\citet{Meszaros2020}, while we adopt the atmospheric parameters from the uncalibrated post-APOGEE DR16 values for the two stars beyond the cluster tidal radius. The elemental abundances and final errors in [Fe\/H] and [X\/Fe], astrometric and kinematic properties of our sample are listed in Tables \\ref{Table1},  \\ref{Table11}, and \\ref{Table2}, respectively. \n\nA consistent chemical-abundance analysis was then carried out with the \\texttt{BACCHUS} code \\citep{Masseron2016}, from which we obtained the metallicities from Fe I lines, and abundances for twelve other chemical species belonging to the light- (C, N), $\\alpha$- (O, Mg, Si, Ca, and Ti), Fe-peak (Ni), odd-Z (Al, K) and \\textit{s}-process (Ce, Nd) elements.\n\n \\begin{figure}\t\n \t\\begin{center}\n \t\t\\includegraphics[width=88mm]{Figure2.png}\n \t\t\\includegraphics[width=92mm]{Figure3.png}\n \t\t\\caption{{\\bf \\texttt{BACCHUS} elemental abundances}. Panel (a): The observed [X\/H] and [Fe\/H] abundance-density estimation (violin representation) of M~54 stars, and the observed abundance ratios of newly identified N-rich stars. The extra-tidal star from M~54 and a field star is highlighted with a black open circle and diamond, respectively. Each violin indicates with horizontal lines the median and limits of the distribution. The lime and dark violet violin representation refer to the abundance ratios of 20 stars (this work) and 7 stars from \\citet{Meszaros2020}, respectively. Panels (b)--(e): Distributions of light- (C,N), $\\alpha$- (Mg, Si) and odd-Z (Al) elements in different abundance planes. In each panel, the planes [Al\/Fe] -- [Mg\/Fe], [N\/Fe]--[C\/Fe], [Al\/Fe]--[Si\/Fe], [Si\/Fe]--[Mg\/Fe] are shown, respectively, for GCs from \\citet{Meszaros2020}. The black dotted line at [Al\/Fe] $=+0.3$ indicates the separation of FG and SG stars as proposed in \\citet{Meszaros2020}. The distribution of M~54 stars (lime squares) analyzed in this work are overlaid. The black open circle and diamond refer to the extra-tidal and field N-rich star, respectively. The plotted error bars show the typical abundance uncertainties.}\n \t\t\\label{Figure2}\n \t\\end{center}\n \\end{figure}\t\n \n   \\section{Results and discussion}\n \\label{section5}\n \n Panel (a) of Figure \\ref{Figure2} summarizes the chemical enrichment seen in M~54 stars analyzed in this work, and compares to the \\citet{Meszaros2020} determinations. The chemical composition of the two newly identified N-rich stars beyond the cluster tidal radius is also shown in the same figure. Overall, the chemical abundance of M~54 based on the added cluster stars is within the typical errors, and does not affect the science results presented in \\citet{Meszaros2020}, while the two external N-rich stars share chemical patterns similar to the M~54 population.\n \n For M~54, we find a mean metallicity $\\langle$[Fe\/H]$\\rangle = -1.30\\pm0.12$, which agrees well with \\citet{Meszaros2020}\\footnote{Note that here, and for the abundances described below, the number following the average abundance represents the one-sigma dispersion, not the error in the mean.}. The spread in [Fe\/H] increased from 0.04 to 0.12 dex, but it is still smaller than that reported in \\citet{Carretta2010}. Even if the measured scatter is larger than that reported by \\citet{Meszaros2020}, it does not seem to indicate the presence of a significant spread in [Fe\/H], and is similar to that observed in Galactic globular clusters (GCs) at similar metallicity, such as M~10 \\citep[see, e.g.,][]{Meszaros2020}. Nickel (an element that belongs to the Fe-group), exhibits a flat distribution as a function of [Fe\/H], similar to that observed in \\citet{Carretta2010}, and at odds with that observed in Sgr stars. \n \nRegarding the other chemical species, we find excellent agreement with the values provided by \\citet{Meszaros2020}, as can be seen in panel (a) of Figure \\ref{Figure2}, with the main difference that the added stars introduce a larger star-to-star scatter than previously measured. M~54 exhibits a modest enhancement in $\\alpha$-elements, with mean values for [O\/Fe], [Mg\/Fe], [Si\/Fe], [Ca\/Fe], and [Ti\/Fe] which is similar to what is seen in halo GCs: $\\langle$[O\/Fe]$\\rangle = +0.64\\pm0.36$ (14 stars); $\\langle$[Mg\/Fe]$\\rangle = +0.18\\pm0.11$ (18 stars); $\\langle$[Si\/Fe]$\\rangle = +0.26\\pm0.10$ (20 stars); $\\langle$[Ca\/Fe]$\\rangle = +0.25\\pm0.07$ (16 stars); and the new measured $\\langle$[Ti\/Fe]$\\rangle = +0.21\\pm0.21$ (16 stars), indicating a fast enrichment provided by supernovae (SNe) II events. Mean values are in good agreement with \\citet{Meszaros2020}, with the exception of oxygen, which displays the larger star-to-star spread expected in likely second-generation stars. \n\nWe also find that the [O\/Fe], [Mg\/Fe], and [Si\/Fe] ratios are almost flat as a function of the metallicity, while [Ca\/Fe] and [Ti\/Fe] ratios slightly increases as [Fe\/H] increases, similar to the behaviour found by \\citet{Carretta2010}. On the contrary, the $\\alpha$-element trend observed in Sgr stars \\citep[see, e.g.,][]{Carretta2010, McWilliam2013, Hasselquist2017, Hasselquist2019} differ from those seen in the population of M~54. Overall, the $\\alpha$-elements in the cluster are higher than seen in Sgr stars. In conclusion, the measured $\\alpha$-enrichment in this work support the previous hypothesis suggesting that the $\\alpha$-element in M~54 stars formed before the typical $e$-folding time for SN Ia contributing their ejecta to the gas pool \\citep[e.g.,][]{Carretta2010}. \n\nWe also found that some stars in M~54 appear to be quite Mg poor, with strong enrichment in aluminum and nitrogen, providing further evidence for the presence of second-generation stars in M~54, and the signature of very high temperatures achieved during H-burning \\citep[e.g.,][]{Carretta2010, Meszaros2020}. The odd-Z elements (Al and K) in M~54 exhibit an average $\\langle$[Al\/Fe]$\\rangle = +0.14\\pm0.37$ (19 stars) and $\\langle$[K\/Fe]$\\rangle = +0.15\\pm0.18$ (17 stars), with a clear anti-correlation in Al-Mg, as can be seen in in panel (b) of Figure \\ref{Figure2}, with moderate Mg depletions related to the enrichment in Al abundances, as the result of the conversion of Mg into Al during the Mg-Al cycle \\citep[e.g.,][]{Carretta2010, Denissenkov2015, Renzini2015, Pancino2017}. This pattern is evidently not present in the Sgr stars, where, on the contrary, \\texttt{ASPCAP} Mg and Al abundances are positively correlated with each other \\citep[see, e.g.,][]{Hasselquist2017, Hasselquist2019, Hayes2020}. \n\nWe derived average abundances for C and N in M~54, of $\\langle$[C\/Fe]$\\rangle = -0.36\\pm0.25$ (13 stars) and $\\langle$[N\/Fe]$\\rangle = +1.12\\pm0.48$ (17 stars). Most of the stars in M~54 are C deficient ([C\/Fe]$\\lesssim$+0.3) and N enhanced ([N\/Fe]$>+0.5$), but they do not exhibit the typical N-C anti-correlation (see panel (c) of Figure \\ref{Figure2}) seen in other GCs at similar metallicity \\citep[e.g.][]{Meszaros2020}, most probably due the lack of stars with low nitrogen abundances. On the contrary, an apparent continuous distribution of N abundances is present in M~54. This result indicates the prevalence of the multiple-population phenomenon in M~54 as previously suggested in the literature \\citep{Carretta2010, Milone2017, Sills2019, Meszaros2020}.\n\nAdditionally, we do not find any evidence for the presence of the K-Mg anti-correlation in M~54, as have been suggested to be present in a few Galactic GCs at similar metallicity \\citep{Meszaros2020}. Furthermore, a Si-Al correlation is slightly evident in M~54, as shown in panel (d) of Figure \\ref{Figure2}, and has a stubby Mg-Si distribution (see panel (e) of Figure \\ref{Figure2}), which is an indication of $^{28}$Si production from the result of a secondary leakage in the main Mg-Al cycle, which is instead absent in the Sgr stars.\n  \nFor the elements produced by neutron(\\textit{n})-capture processes (Ce II and Nd II), we find, on average, $\\langle$[Ce\/Fe]$\\rangle = +0.18\\pm0.13$ (10 stars) and [Nd\/Fe]$=+0.44$ (1 star). Overall, M~54 exhibits a modest enrichment in \\textit{s}-process elements, with a few stars as enhanced as $+0.4$, similar to that observed in Galactic GC stars at similar metallicity \\citep[see, e.g.,][]{Meszaros2020}, suggesting that it is possible that the \\textit{s}-process enrichment has been produced by a different source than the progenitor of the Mg-Al anti-correlations, possibly by low-mass asymptotic giant branch stars. Lastly, we find that [Ce\/Fe] ratios in M~54 are almost flat as a function of metrallicity. Unfortunately, Nd II is measured in only one star, which has been found to exhibit the modest enhancement, consistent with a moderate enrichment of \\textit{s}-process elements.\n\nFurthermore, we report the serendipitous discovery of two N-enhanced stars identified within $\\sim$7$r_t$ from M~54, as shown in panel (a) of Figure \\ref{Figure1}. Panel (a) of Figure \\ref{Figure2} show the collection of [X\/Fe] and [Fe\/H] abundance ratios for the two newly identified N-rich stars beyond the tidal radius of M~54. Both stars exhibit very similar chemical-abundance patterns as those seen in the population of M~54. A plausible explanation is that both stars were previous members of M~54, from which they have been ejected. However, this possibility seems unlikely for one of these extra-tidal stars (2M18533777$-$3129187), which was ruled out as a possible member of M~54. \n\nAs can be appreciated from inspection of panels (a) to (d) of Figure \\ref{Figure1}, the current position of 2M18533777$-$3129187 does not resemble the kinematic and astrometric properties \\citep[e.g.,][]{Antoja2020, Hayes2020} of Sgr+M~54 stars, nor the orbital path of Sgr\\footnote{The Sgr orbit was computed with the \\texttt{GravPot16} model, \\url{https:\/\/gravpot.utinam.cnrs.fr}, by adopting the same model configurations as described in \\citet{Fernandez-Trincado2020c}. For the Sgr centre, we adopt the heliocentric distance $d_{\\odot} =$ 26.5 kpc and heliocentric radial velocity $RV = 142$ km s$^{-1}$ from \\citet{Vasiliev2020b}, and proper motions from \\citet{Helmi2018}: $\\mu_{\\alpha}\\cos{\\delta} = -2.692$ mas yr$^{-1}$ and $\\mu_{\\delta} = -1.359$ mas yr$^{-1}$, with uncertainties assumed of the order of 10\\% in $d_{\\odot}$, $RV$, and proper motions.} . It is also the most luminous star in our sample, making it a likely foreground star. The possibility that this star was disrupted from M~54 and deposited in the inner Galaxy seems unlikely, as the perigalacticon of M~54 is located well beyond the solar radius \\citep[see, e.g.,][]{Baumgardt2019}. We   conclude that 2M18533777$-$3129187 is a N-enhanced field star born in a different progenitor than M~54, but with a similar chemical-enrichment history to this cluster.\n\n Aside from 2M18533777$-$3129187, there is another N-enhanced field star (2M18565969$-$3106454) located $\\sim{}5\\times{}r_{t}$ from the cluster center, which exhibits a stellar atmosphere strongly enriched in nitrogen ([N\/Fe]$>+1.4$), as extreme as M~54 stars, accompanied by a very low carbon abundance ([C\/Fe]$<-0.7$), and with discernible contributions from the \\textit{s}-process elements (Ce II). Since the [Al\/Fe] ratio is $>+0.5$, which is a 'typical' value for stars in GCs, and unlikely in dwarf galaxy populations, we conclude that 2M18565969$-$3106454 shares the same nucleosynthetic pathways of second-generation stars in M~54. \n \n2M18565969$-$3106454 is a potential extra-tidal star with kinematics and astrometric properties similar to that of M~54 stars, and exhibits unique chemical patterns comparable to that of genuine second-generation GC stars, which makes it very different from Sgr stars. On the other hand, N-rich stars are commonly observed to be more centrally concentrated in GCs \\citep[e.g.][]{Dalessandro2019} and as a consequence they have smaller probabilities to be tidally stripped. Thus, it is likely that the extra-tidal star could well be just a stripped M~54 star as many others in its surroundings. Our finding demonstrate that N-rich stars are a promising route for identifying the unambiguous chemical signatures of stars formed in GC-like environment which may lie immersed in the M~54+Sgr core and\/or Sgr stream, as well as confirm or discard the possible association of GCs to the Sgr stream \\citep{Bellazzini2020}. \n \nFollowing the same methodology as described in \\citet{Fernandez-Trincado2021b}, we compute the predicted number ($N_{N-rich}$) of N-rich field stars observed in APOGEE-2 toward M~54\/Sgr using the smooth halo density relations presented in \\citet{Horta2021}, and by adopting the same Monte Carlo implementation of the Von Neumann Rejection Technique \\citep[see e.g.,][]{Press2002} as in Eq. 7 in \\citep{Fernandez-Trincado2015a}. We find the expected number of observed N-rich halo stars beyond $d_{\\odot}\\gtrsim15$ kpc over the sky area of 1.5 degree radius centred in M~54, and with both astrometric and kinematic properties as M~54 to be $N_{N-rich}< 0.1$ (from 1000 Monte Carlo realisations). This yield a very low probability that the new identified extra-tidal N-rich star associated with M~54 is due to random fluctuations in the field. Furthermore, we also use the Besan\\c{}con galactic model \\citep{Robin2003} and the \\texttt{GravPot16} model \\citep{Fernandez-Trincado2020e} to explore the expectations for a \"default\" Milky Way along the RVs to the Sgr+M\\~54 surrounding field beyond  $d_{\\odot}\\gtrsim$ 15 kpc. The \"all\" sample is dominated by halo kinematics with a negligible contribution from the thin and thick disk beyond $RV \\gtrsim 120$ km s$^{-1}$.  Thus, our Milky Way simulated sample act to guide us in $RV$ space, confirming that the kinematics of the newly identified extra-tidal N-rich star differs from the disk population, with practically low contribution form the expected halo. , \n\n \\section{Concluding remarks}\n \\label{section6}\n\nWe present a spectroscopic analysis for 20 out 22 red giant stars that are members of M~54 from the internal APOGEE DR16 dataset. This study doubles the sample of stars with spectroscopic measurements for this cluster, and the new post-APOGEE DR16 spectra achieve high signal-to-noise (S\/N$>70$), allowing the addition of new chemical species not examined in previous studies \\citep[e.g.,][]{Meszaros2020} in the \\textit{H}-band--APOGEE-2 footprint. \n \n Overall, the chemical species re-examined in M~54 were found to be consistent with previous studies \\citep{Meszaros2020}, although most of them exhibit a large star-to-star scatter. We find that 15 out of the 20 stars investigated show a high [N\/Fe] abundance ratio ([N\/Fe]$\\gtrsim+0.5$), confirming the prevalence of the MPs phenomenon in M~54. Both [Ni\/Fe] and [Ti\/Fe], not previously examined in \\citet{Meszaros2020}, were found to be in good agreement with measurements in the literature. In particular, we confirm the [Ti\/Fe]~ratio slightly increases as [Fe\/H] increases, as has been reported in \\citet{Carretta2010}. We also find a large spread in [Al\/Fe], and the presence of a genuine second-generation star in M~54, which exhibits Mg deficiency ([Mg\/Fe]$<$0) accompanied with large enhancements in nitrogen and aluminum. In general, all chemical species examined in the M~54 members present distinguishable chemical behaviour compared with Sgr stars, suggesting a different chemical-evolution history that resembles other Galactic halo GCs at similar metallicity.\n\nFurthermore, we report on the serendipitous discovery of a potential extra-tidal star toward the surrounding regions of the M~54+Sgr core, which exhibits a strong enrichment in nitrogen comparable to that seen in M~54 stars. As far as we know this is the first study reporting on the unambiguous chemical signatures of stars formed in GC-like environment into a nearby satellite dwarf galaxy around the Milky Way. Finding out how many of such chemical unusual stars likely originated in GCs are present in dwarf galaxy systems, help to understand the link between GCs and their stellar streams \\citep[see e.g.,][]{Bellazzini2020}. \n\n\t\\begin{acknowledgements}  \n\tThe author is grateful for the enlightening feedback from the anonymous referee.\n\t J.G.F-T is supported by FONDECYT No. 3180210. \n\t T.C.B. acknowledges partial support for this work from grant PHY 14-30152: Physics Frontier Center \/ JINA Center for the Evolution of the Elements (JINA-CEE), awarded by the US National Science Foundation. \n\t D.M. is supported by the BASAL Center for Astrophysics and Associated Technologies (CATA) through grant AFB 170002, and by project FONDECYT Regular No. 1170121. \n\t S.V. gratefully acknowledges the support provided by Fondecyt regular No. 1170518. \n    D.G. gratefully acknowledges support from the Chilean Centro de Excelencia en Astrof\\'isica y Tecnolog\\'ias Afines (CATA) BASAL grant AFB-170002. D.G. also acknowledges financial support from the Direcci\\'on de Investigaci\\'on y Desarrollo de la Universidad de La Serena through the Programa de Incentivo a la Investigaci\\'on de Acad\\'emicos (PIA-DIDULS). \n\t A.R.-L. acknowledges financial support provided in Chile by Agencia Nacional de Investigaci\\'on y Desarrollo (ANID) through the FONDECYT project 1170476.\n\t B.B. acknowledge partial financial support from the Brazilian agencies CAPES-Financial code 001, CNPq, and FAPESP. \n\t \\\\\n\t\n\tThis work has made use of data from the European Space Agency (ESA) mission Gaia (\\url{http:\/\/www.cosmos.esa.int\/gaia}), processed by the Gaia Data Processing and Analysis Consortium (DPAC, \\url{http:\/\/www.cosmos.esa.int\/web\/gaia\/dpac\/consortium}). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.\\\\\n\t\n\tFunding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS- IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrof\\`{i}sica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) \/ University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut f\\\"{u}r Astrophysik Potsdam (AIP), Max-Planck-Institut f\\\"{u}r Astronomie (MPIA Heidelberg), Max-Planck-Institut f\\\"{u}r Astrophysik (MPA Garching), Max-Planck-Institut f\\\"{u}r Extraterrestrische Physik (MPE), National Astronomical Observatory of China, New Mexico State University, New York University, University of Notre Dame, Observat\\'{o}rio Nacional \/ MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Aut\\'{o}noma de M\\'{e}xico, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.\\\\\n\\end{acknowledgements}\n\t\n\\bibliographystyle{aa}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nThe magneto-rotational instability (MRI) is a powerful process to drive\nturbulence and angular momentum transport in protoplanetary disks, \nultimately enabling the accretion of matter onto the central object \\citep{bal91,haw91,bal98}.\nThere is vast literature studying this mechanism in local shearing box\nsimulations with an ideal MHD description\n\\citep{bra95,haw95,haw96,mat95,sto96,san04}. \\\\\nThe effect of non-ideal MHD on MRI, regarding the issue of resistive \nprotoplanetary disks, was mostly studied in\nlocal box simulations \\citep{bla94,jin96,san00,fle00,san02I,san02II,fle03,inu05,tur07,tur08,tur10}. \nThe various studies showed that at a \ncertain level of resistivity the MRI will be suppressed.\n\nUp to now there is no prescription of resistive profile \nin protoplanetary disks which applies for longer timescales.\nIt is known that the dust grains control the ionization level\nin protoplanetary disk. The particle cross section and dust-to-gas\nratio are most important parameters for defining the ionization level of\nthe gas \\citep{tur06,war07}.\nMost studies of non-ideal MRI turbulence use a static dust\ndistribution and neglect dust\ngrowth and evolution \\citep{sim09,tur06,tur07,dzy10}. But exactly in non-turbulent regions, the dust\n particles can grow, reducing quickly the cross section and so driving to\nbetter ionization levels enabling again MRI \\citep{zso10}. \nIn our study we focus on ideal MHD, which applies to sufficiently\nionized disk regions depleted of small dust grains. \nThis also applies to the innermost hot parts of \nprotoplanetary accretion disk and even extended radial regions \nas expected for transitional disks \\citep{chi07}.\nHere, an MRI turbulent ionization front starting at the inner rim of the \ndisk propagates radially outward and the disk get evacuated from\ninside-out.\\\\\n\nRecent results on the MRI obtained in local unstratified box simulations by \\citet{les07},\n\\citet{froII07}, \\citet{sim09} and \\citet{fro10} show that occurrence and saturation level of MRI in zero net flux simulations is controlled by the magnetic Prandtl number \\footnote{The ratio of viscosity vs.\\\nresistivity}. \nIdeal MHD simulations including stratification found at least convergence for zero-net flux local\nsimulations \\citep{dav10,fla10}. Here, the vertical resolution plays the key role for the convergence\n\\citep{shi10}. Despite the simplicity of box simulations and their interesting results obtained over the\nlast years, the study of radial extended structures are very restricted.\nFor instance, the aspect ratio of the boxes is known to influence the saturation level of turbulence \\citep{bod08}.\nBesides local box simulations, global simulations of MRI have also been performed\n\\citep{arm98,haw01I,ste01,haw01,arl01,fro06,lyr08,fro09}.\nThey confirmed the picture of a viscously spreading disk as a proxy for the action of MHD turbulence. \nRecently, the first global non-ideal MHD simulation \\citep{dzy10}, \nwhich included a radial dead-zone \/ active zone interface demonstrated the importance of the inner edge of the\ndead zone as a trap for planetesimals and even small planets.\\\\\n\nSo far only finite difference schemes as implemented in the ZEUS and Pencil\ncodes have been used to perform global simulations. \nHowever, a Godunov code would have several advantages over a finite difference scheme. \nWithout using any artificial viscosity the code solves \nthe MHD Riemann problem and can better handle the supersonic MHD turbulence in corona regions of the disk. Several papers recognized the importance of Godunov-type shock capturing upwind schemes for future astrophysical \nsimulations \\citep{sto05,fro06b,mig07,flo10}.\nIn this project we use the Godunov code PLUTO \\citep{mig09} to perform\nisothermal global MHD simulations of protoplanetary disks. \nIn future work, we\nwill switch on the total energy conservation property of this scheme and\ninclude radiation MHD to follow the temperature evolution in global disk.\\\\\nAn important issue in stratified global simulations is the\nrelatively low resolution per scale height compared to what is possible in local box simulations.\nIn addition, the extent of the azimuthal domain is often restricted to save computational time.\nThe first $2\\pi$ global disk simulations were performed by\n\\citet{arm98}, \\citet{haw00} and\n\\citet{arl01} for a short period of time.\nBut most of the global simulations were performed in restricted azimuthal domains like\n$\\pi\/4$ or $\\pi\/2$ \\citep{fro06,fro09,dzy10}. \nBy restricting the azimuthal domain one also restricts the largest possible mode in the\ndomain. One of the goal of this paper is to investigate whether these\nmodes affects the nonlinear state of the turbulence.\\\\\n\nThe standard viscous $\\alpha-$disk theory \\citep{sha73} introduces an effective turbulent viscosity \n $\\eta = \\rho \\nu = \\alpha P \/ \\Omega$ with the local thermal pressure $P$\nand the orbital frequency $\\Omega$,\narising from undefined magnetic or hydrodynamic processes,\ntransporting angular momentum outward and allowing mass accretion onto the star.\n\\citet{lyn74} calculated the radial mass accretion rate and the\nradial accretion velocity for a 1D viscous disk model as a local function of surface density $\\Sigma$ and the value for $\\alpha$.\nInterestingly 2D viscous disk models \\citep{kle92} showed the appearance of meridional\noutflows. Here, the mass flows radially outward near the\nmidplane compensated by increased radial inflow at upper layers of the disk to allow for net-accretion,\nfor $\\alpha < 0.05$. Much emphasis was given to this radial outflow and its role\nfor the radial transport for grains and chemical species over large distances and relative short time scales\n\\citep{kel04,cie09}.\\\\\nIn addition, we will investigate the onset of a vertical outflow\nas it was described in local box simulations \\citep{suz09,suz10} using a net\nflux vertical field. Such outflows can be launched in the\nmagnetized corona region of the MRI turbulent disk \\citep{mil00,mac00}.\nThey could have an important effect on the dissipation timescales of\naccretion disks and may be related to jet production from accretion\ndisks \\citep{fer06}.\nAn interesting property of MRI in stratified zero-net flux simulations is the emergence of\na \"butterfly\" pattern, an oscillating mean azimuthal magnetic field with an\nperiod of 10 local orbits. It was found in many local MRI simulations,\nrecently again by \\citet{dav10}, \\citet{gre10}, \\citet{fla10} and in global\nsimulations by \\citet{sor10} and \\citet{dzy10}.\nWe indeed identify such a \"butterfly\" pattern in our global runs, which was suggested to be linked to magnetic dynamo action in accretion disks \\citep{sor10,gre10}.\n\nOur paper is organized in the following way.\nIn Section 2 we will present our model setup and the numerical configuration.\nSection 3 contains the results\nSection 4 and 5 will provide a discussion, summary and outlook for our work.\n\\section{Model setup}\nThe setup follows closely the disk model which is presented by\n\\citet{fro06,fro09}.\nWe define the cylindrical radius with $R = r \\sin{(\\theta)}$ with the spherical\nradius $r$ and polar angle $\\theta$.\nThe initial density, pressure and azimuthal velocity are set to be in hydrostatic equilibrium.\n$$\\rho = \\rho_{0} \u00a0R^{-3\/2}\\exp{}\\Bigg(\\frac{\\sin{(\\theta)}-1}{(H\/R)^2}\\Bigg) $$\nwith $\\rho_{0} = 1.0$, $\\rm H\/R = c_0 = 0.07$.\\\\ \nWe choose an isothermal equation\nof state. The pressure is set to $P = c_{s}^2\\rho$ with $\\rm c_{s} =\nc_0\\cdot1\/\\sqrt{R}$.\nThe azimuthal velocity follows  $$V_{\\phi} = \\sqrt{\\frac{1}{r}}\\Bigg(1- \\frac{2.5}{\\sin(\\theta)}c^2_0 \\Bigg).$$\nFor the initial velocities $V_{R}$ and $V_{\\theta}$ we use a white noise\nperturbation amplitude of $V_{R,\\theta}^{Init} = 10^{-4} c_{s}$.\ufffd\nWe start the simulation with a pure toroidal magnetic seed field with constant plasma beta\n$\\beta = 2P \/ B^{2} = 25$.\nThe radial domain extends from 1 to 10 radial code units (CU)\\footnote{We refer to CU instead of a physical length unit because ideal MHD simulations without radiation transport\nare scale free. Thus our simulations could represent a disk from 1 to 10 AU as much as a disk from\n$0.1$ to 1 AU. Only explicit dust physics and radiative transfer will introduce a realistic physical scale.} with radial buffer zones from 1 to 2 CU\nand 9 to 10 CU.\nIn the buffer zones we use a linearly increasing resistivity. This damps \nthe magnetic field fluctuations and suppresses boundary interactions,\nespecially for the closed boundary runs. Our buffer\nzone follows mainly the ones used in global simulations by \\citep{fro06,fro09,dzy10}. \nThe $\\theta$ domain is set to $\\theta = \\pi\/2 \\pm 0.3 $, corresponding to $\\pm\n4.3 \\rm $ scale heights.\nWe calculated in total five disk models. Three models cover the complete $2\\pi$ azimuthal  domain (FC, FO and BO in Table 1) and \ntwo models are constrained to $\\pi\/4$ (PC, PO in Table 1). The simulation FO\nis also used for a test model FOR which is described later.\nThe simulation BO has the best resolution.\nOne subset of models has a closed boundary (FC and PC). Here we\nuse a reflective radial boundary with a sign flip\nfor the tangential magnetic fields and a periodic boundary condition for the $\\theta$ direction.\nA second subset of models has an outflow boundary condition (FO,PO and BO). Here, we use a relaxation function in the radial buffer zones which reestablishes gently the initial value of density over a time period of one local orbit. \nIn the buffer zones we set: $\\rho^{new} = \\rho - (\\rho-\\rho^{Init})\\cdot \\Delta\nt \/ T_{Orbits}$. \nOur outflow boundary condition projects the radial gradients\nin density, pressure and azimuthal velocity into the radial boundary and the\nvertical gradients in density and pressure at the $\\theta$ boundary. \nWe ensure to have no inflow velocities. For an inward pointing velocity\nwe mirror the values in the ghost cell to ensure no inward mass flux. \nThe $\\theta$ boundary condition for the magnetic field are also set up \nto be zero gradient, which approximates \"force-free\" - outflow conditions. \nWe also ensure the force free character of the tangential components for the radial boundary\nby adjusting the $1\/r$ profile in the magnetic field components in the ghost\ncells.\nThe normal component of the magnetic field in the ghost cells is always \nset to have $\\nabla \\cdot \\vec{B}$ = 0.\nWe set the CFL value to 0.33. Also higher CFL values were successfully tested and\nwill be used for future calculations.\nWe use a uniform grid with an aspect ratio of the individual cells at 5 CU of $1:0.67:1.74$\n$(\\Delta r: r\\Delta\\theta:r\\Delta\\phi)$.\nUsing a uniform grid instead of a logarithmic grid, where\n$\\Delta r\/r$ is constant, has the disadvantage that it will reduce the\naccuracy in the sense that the inner part of the disk is poorly resolved,\ncompared to the outer part of the disk: $H(1AU)\/\\Delta r < H(10AU)\/\\Delta r  $.\\\\ \nHowever for the uniform grid, the relative broad radial inner \nbuffer zone lies in the poorly resolved disk part and is excluded from\nanalysis.\nThe outer parts of the disk are, compared\nto a logarithmic grid with the same resolution, better resolved.  \nLogarithmic grid requires a much smaller buffer\nzone, e.g. a logarithmic grid would place one third of the total number of grid\ncells in the first ninth of the domain, between 1 and 2 AU.\nOf course, using a uniform grid will always restrict the range of the\nradial domain and for more radially extended simulation the need of a logarithmic grid is mandatory.\n\nFor all runs we employ the second order scheme in\nPLUTO with the HLLD Riemann solver \\citep{miy05}, piece-wise linear\nreconstruction and $2^{nd}$ order Runge Kutta time integration. \nWe treat the induction equation with the \"Constrained Transport\" (CT) method in combination with the upwind CT method described in\n\\citet{gar05}.\nThe detailed numerical configuration is presented in \\citet{flo10}.\nOur high resolution run BO was performed on a Blue-gene\/P cluster with 4096\ncores and was calculated\nfor over 1.5 million time steps which corresponds to 1.8 million CPU hours.\n\\begin{table}[th]\n\\begin{center}\n\\begin{tabular}{ccccc}\nModel name & Resolution ($R$ $\\theta$ $\\phi$) \u00a0& $\\phi$-range & Boundary & Orbits at 1 AU (Years)\\\\\n\\hline\n\\hline\nPC & 256 128 64 & $\\pi\/4$ & closed & 1435 \\\\\nPO & 256 128 64 & $\\pi\/4$ & open & 1519 \\\\\nFC & 256 128 512 & $2\\pi$ & closed & 1472 \\\\\nFO & 256 128 512 & \u00a0$2\\pi$ & open & 1526 \\\\\n\\hline\nFOR& 256 128 512 & $2\\pi$ & open & $1000-1448$ \\\\ \n\\hline\nBO& 384 192 768 & $2\\pi$ & open & $1247$ \n\\\\\n\\end{tabular}\n\\caption{MHD runs performed. (P - $\\pi\/4$; F - $2\\pi$; O - open boundary; C -\nclosed boundary; B - best resolved run.)}\n\\end{center}\n\\end{table}\n\\subsection{Code Units vs. Physical Units}\nIsothermal ideal MHD simulations are scale-invariant. \nOne has to define unit-variables to transform from code to cgs units. \nWe can set three independent values to \ndefine our problem. \nThis is gas density for which we choose for instance $\\rm \\rho_u = 10^{-10} g\/cm^3$, the radial\ndistance unity as length $1 CU = 1 AU$\nand the Keplerian velocity $\\rm v_u = \\sqrt{ G\\cdot M_{\\sun} \/ l_u}$ with the gravitational\nconstant $G$ and the solar mass $M_{\\sun}$.\n\nWith those three quantities, we translate the values for our measured surface density and mass accretion\nrate into cgs units. Using this values we derive at 1 AU at the midplane a gas density of\n$\\rm \\rho = 10^{-10} g\/cm^3$ with a Keplerian velocity of $\\rm v_K= 2.98* 10^6 cm\/s$. \nWith this the surface density becomes $524 g\/cm^2$ at 1AU.\nGas velocities and the Alfv\\'enic speed are always presented in units of the sound\nspeed for convenience.\n\n\n\\subsection{Turbulent stresses}\nThe $\\alpha$ parameter relates the turbulent stresses to \nthe local thermal pressure. For the calculation of the $\\alpha$ values\nwe measure the Reynolds and Maxwell\nstresses, which are the $R-\\phi$ components of the respective stress tensors. \nThe Reynolds stress is calculated as $\\rm T_{R}= \\overline{\\rho v'_{\\phi}v'_{R}} $\nand the Maxwell stress as $\\rm T_{M}= \\overline{B'_{\\phi}B'_{R}}\/ 4 \\pi $\nwith the turbulent velocity or magnetic fields, e.g., $\\rm v'_{\\phi} = v_{\\phi} - \\overline{v_{\\phi}}$.\nThe mean component of the velocity and magnetic field are always calculated\nonly along the azimuthal direction because of the radial and vertical gradients in the disk.\nIn our simulations, the amplitude of Maxwell stress is about three times the Reynolds stress.\nFor the total $\\alpha$ value we integrate the mass weighted stresses over the total domain\n$$ \\alpha = \\frac{ \\int \\rho \\Bigg( \\frac{v'_{\\phi}v'_{R}}{c^2_s} - \\frac{B'_{\\phi}B'_{R}}{4 \\pi \\rho c^2_s}\\Bigg)dV} {\\int \\rho dV}.$$\nThe respective turbulence enhanced viscosity can now be represented as $\\nu = \\alpha H c_s$\nwith the height of the disk $H$ and the sound speed $c_s$.\n\\begin{figure}\n\\hspace{-0.6cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-1A.ps,scale=0.46}\n\\psfig{figure=FIG-1C.ps,scale=0.46}\n\\end{minipage}\n\\hspace{4.0cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-1B.ps,scale=0.46}\n\\psfig{figure=FIG-1D.ps,scale=0.46}\n\\end{minipage}\n\\label{totalal}\n\\caption{Top left: Total stresses expressed as $\\alpha$-parameters for the $\\pi\/4$ models PC\nand PO and the $2\\pi$ models FC, FO and BO. The parameter is mass weighted\nand integrated for the domain (3-8 AU).\nTop right: Radial $\\alpha$ profile, time averaged between 300 and 1200 inner\norbits.\nFor the best resolution model BO, the profile follows roughly $\\sqrt{r}$ in the region B. \nRegion A and C are affected by boundary conditions and buffer zones.\nBottom left:  Vertical $\\alpha$ profile, averaged over time and space region ($II\/B$). \nBottom right: Evolution of the vertical distribution of azimuthally averaged Maxwell and Reynolds stress\n$T_S$ for a radius of 4 AU with\ntime. Colors are logarithmic values of the corresponding dynamical viscosity including the density profile.}\n\\end{figure}\n\\section{Results}\n\\subsection{Disk evolution}\nWe first describe the typical evolution for an azimuthal MRI (AMRI) \nin global disk simulation with open boundaries. \nThe AMRI simulation starts with a purely toroidal net magnetic field which \nbecomes MRI unstable on timescales of around 10 local orbits.\nAfter approximately 250 inner orbits, the disk reaches its maximum\n$\\alpha$ value of $0.01$.\nAt this time (equivalent to 10 local orbits at\nthe outer boundary of the undamped region) the disk has become fully turbulent.\nDuring this evolution, the initial magnetic flux decreases as it leaves the computational\ndomain in the vertical direction. \nStarting at approximately 250 inner orbits, there is an evolution of oscillating mean fields.\nFig. 1, top left, presents the mass weighted and domain integrated $\\alpha$ value \nover time for all models.\nDuring the time period between 800 and 1200 inner orbits, we get a\nrelatively constant $\\alpha$ value of $5\\cdot10^{-3}$ (model BO). \nWe mark three different time stages of the turbulent\ndisk evolution:\nIn period I (0 to 800 inner orbits), the turbulence is not yet saturated.\nAfter a strong initial rise due to the net azimuthal field the turbulent decays\nto a level where self-sustained turbulence is possible, e.g., the loss of magnetic flux\nin the vertical direction is balanced by the generation of magnetic flux in the turbulent flow.\nThe nature of this generation of magnetic fields can be an indication for dynamo action,\ne.g., an $\\alpha \\Omega$ dynamo\n\\citep{bra05,gre10}, but detailed studies of this effect will be subject to future work.\nIn period II, we have a quasi steady state of at least 400 inner orbits. \nDuring this time period, we do all our analysis. \nIn the period III, a comparison of the models becomes less useful.\nThe models with lower resolution and open boundary (PO and FO) \nshow a decreasing $\\alpha$-stress in time. Thus they are not useful for long time integrations past\n1200 inner orbits. In the closed models, on the other hand, the magnetic flux cannot escape vertically \n(PC and FC) and therefore, turbulence does not decay. \nOn the contrary, turbulence even increases in these runs as the flux in the box \ncannot efficiently escape.\\\\\nA closer view shows that the stress can oscillate locally on shorter time  scales.\nIn Fig. 1, bottom right, we plot the mass weighted stresses $\\alpha\\rho$ at 4 AU over height\nand local orbits. The strength of stresses locally oscillates with a period of around 5 local\norbits. The maxima in the stresses always appear first in the midplane and then propagate\nvertically. These oscillations in the stresses are connected to the $B_\\phi$ \"butterfly\" structures\nwhere the azimuthal mean field oscillates with a frequency of 10 local orbits (Fig. 13). \nEvery change of sign in the mean $B_\\phi$ is now correlated with a minimum in the stresses, \nwhich both occur every 5 local orbits.\nAt the same time this plot shows the importance of the stresses in a region up\nto 3 disk scale heights.\n\nAlthough one can always define a total $\\alpha$-parameter in the disk, the spatial\nvariations are enormous, especially in the vertical direction. \nThe vertical $\\alpha$ profile is plotted in Fig.1, bottom left. For model\nBO, the turbulent stress at the midplane increases from $2.0\\cdot 10^{-3}$\nup to $8\\cdot10^{-2}$ at 4 scale heights.\nThe simulations with moderate resolution show significant lower values around the midplane due\nto the lack of resolution there. For the closed models, the stresses in the\ncorona are artificially increased due to the periodic boundary.\\\\\n\n\\subsection{Radial profile of turbulent stress}\nBeside the vertical profile of turbulent stress, which has been already studied in local\nbox simulations, the radial profile of the turbulent stress can only be addressed in global\nsimulations.\nIn Fig. 1, top right, we present the radial $\\alpha$ profile, averaged\nbetween 300 and 1200 inner orbits.\nIn the inner buffer zones (1 - 2 AU) the $\\alpha$ values are practically zero because of the\nresistive damping. Starting from 2 AU $\\alpha$ rises until it levels off at\naround 3 AU. From 3 to 8 AU we obtain a radial $\\alpha$ profile which can be\napproximated by a $\\sqrt{r}$ dependence. Beyond 9 AU $\\alpha$ is again close to zero because of the damping applied there.\nWe mark three regions in radius (Fig. 1, top right, green lines).\nRegion A, extending from 1 to 3 AU, is affected by the buffer zone.\nRegion B, ranging from 3 to 8 AU shows the $\\sqrt{r}$ slope.\nRegion C, covering 8 to 10 AU, is again affected by the buffer zone.\nIn the following analysis, we will therefore concentrate on region B.\\\\\nIn order to have a radial force-free accretion disk, \nfields have to drop radially as $B \\propto r^{-1}$ (Fig. 12, top left).\nThis was also observed for magnetic fields in galactic disks \\citep{bec01} (Fig. 1).\nIf the most important toroidal field follows $\\propto r^{-1}$, \nthe radial Lorentz force vanishes:\n$$\\rm F_{radial} = - \\frac{1}{r^2\\rho} \\frac{\\partial r^2 B_{\\phi}^2}{\\partial\nr}.$$\nIn the case of $\\rm \\partial \\log{\\rho}\/\\partial \\log{r} = -1.5$\nand $\\partial \\log{c_s}\/\\partial \\log{r} = -0.5$ the $\\alpha$ value,\ndominated by the Maxwell stresses will then \nscale as $\\sqrt{r}$, which is actually matching the value that \nwe measure in our best resolved model (see Fig. 1, top right).\n\n\n\\subsection{Mass loss}\nThe models with open boundaries show a considerable mass loss over the course of our\nsimulations.\nA vertical outflow removes a substantial amount of mass. The\ntotal mass loss over time is presented in Fig. 5. The mass loss is\ndetermined in space region B. The closed models FC and PC loose there mass\ndue to radial mass movement. The open models loose there mass mainly due to\nthe vertical outflow. We will discuss this outflow in section 3.5 .\nTo check the possible impact of this mass loss onto the properties of the\nturbulence, we restarted run FO after 1000 inner orbits with the current\nvelocity and magnetic field configuration but the initial density distribution.\nWe call this model FOR (FO Restarted, Table 1).\nAfter restarting the simulation, the turbulence needs a couple of\ninner orbits to readjust the fully turbulent state.\nWe compared the mean total $\\alpha$ stress of the runs FO and FOR and found a comparable evolution \nof the $\\alpha$ values.  We measure $\\alpha = 1.4\\cdot10^{-3}$ for FOR and $\\alpha = 1.3\\cdot10^{-3}$ for FO in the time period\nfrom 1000 up to 1400 inner orbits. We conclude that the mass loss is not\nyet influencing the development and strength of turbulence. \n\\begin{figure}\n\\hspace{-0.6cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-2A.ps,scale=0.46}\n\\psfig{figure=FIG-2C.ps,scale=0.46}\n\\end{minipage}\n\\hspace{4.0cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-2B.ps,scale=0.46}\n\\psfig{figure=FIG-2D.ps,scale=0.46}\n\\end{minipage}\n\\label{surf}\n\\caption{Top left: The surface density profile after 1000 inner orbits for the $\\pi\/4$ model\nPO, the $2\\pi$ model FO and the high-resolution model BO. Dashed lines represent the surface\ndensity profile for the respective viscous disk model and the dotted line the initial profile. \nTop right: 2D contour plot of time and azimuthal averaged radial mass flow for model BO.\nThe red color indicates inward accretion to the star, blue color shows outward motion.\nWe do not observe a meridional flow.\nBottom left: Radial profile of the time-averaged radial mass flow for\nthe high-resolution model BO (solid line) and the viscous models. \nBottom right: 2D contour plot of $(\\Omega - \\Omega_0) \/ \\Omega_0$ over\nradius and time, averaged over azimuth at the midplane. The orbital frequency\nremains sub-Keplerian $(\\Omega_K - \\Omega_0) \/ \\Omega_0 = 0.012$.}\n\n\\end{figure}\n\\subsection{Viscous disk models}\nThe classical $\\alpha$ viscous disk model should reproduce the radial mass flow \nas it occurs in global MHD simulations of MRI turbulent disks.\n\\citet{bal99} have\nargued that the mean flow dynamics in MRI turbulence follows the\n$\\alpha$ prescription. \nTo further test this supposition, we performed a series of 2D HD viscous comparison simulations with the PLUTO code \nfor several of our 3D MHD runs. \nWe use the same resolution and the same initial setup. \nYet, the magnetic field evolution is now replaced by an explicit shear \nviscosity from the time averaged radial $\\alpha$ profile $\\nu (R) = \\alpha(R) H c_s$\nobtained from the MHD simulations (see Fig. 1 top right).\nFig. 2, top left, shows the surface density profile for the models PO,\nFO, model BO and the corresponding viscous\nmodel.\nThe surface density profile of the viscous runs follow nicely the respective MHD model\nprofile (Fig. 2, top left, dashed line) for the region that we use for analysis (3-8 AU).\nAll viscous models show a higher surface\ndensity profile than the open models BO, PO and FO, but of course\nin contrast to the MHD models the viscous models do not show any \nsubstantial vertical mass outflow.\nThe total radial mass flow (e.g. azimuthally and vertically integrated) is plotted as\na time average (0 - 1000 inner orbits) for \nthe high-resolution model B0 (Fig. 2, bottom left, solid line) and the respective viscous\nruns (Fig. 2, bottom left, dashed and dotted line). \nThe radial mass flow of the viscous run matches very well the flow obtained in the MHD model.\nA constant $\\alpha$ value will not reproduce the proper\nevolution of the MRI run. If we adopt for instance a constant $\\alpha$ value of $5\\cdot10^{-3}$, \nwhich would be the global mean value of the MHD run, we get a globally constant accretion rate of\n$\\rm 5.1\\cdot10^{-9} M_\\sun\/yr$.\nAs a sanity check for our viscosity module we compare this value to the \nanalytical estimates by \\citet{lyn74}: \n$$\\dot M(r) = 3 \\pi \\Sigma_g \\nu + 6 \\pi r \u00a0\\frac{\\partial(\\Sigma_g\\nu)}{\\partial r}$$\nand find a value very close to the time dependent viscous run of $\\dot M = 6\\cdot10^{-9}\n\\frac{M_{\\sun}}{yr}$,\nbased on a surface density profile of $\\rm \\Sigma_g = 524\\cdot R^{-0.5} [g\/cm^2]$ and our disk parameter\n$H=0.07*R$.\\\\\nIn Fig. 2, top right, we show the time and azimuthal average of \nthe accretion rate over radius and height. \nThere is a dominant inward accretion at the midplane (Fig. 2, top right, red\ncolor).\nThis result is in contrast to the viscous runs where we see the minimum of\naccretion and even a small outflow at the midplane \\citep{kle92,tak02}.\nAfter \\citet{tak02} (eq. 8) there are several possibilities which could change\nthe vertical profile of the radial velocity, and therefore the mean accretion\nflow. Radial and vertical gradients in the orbital frequency as well as a\nspatially varying $\\alpha$ will affect the vertical profile of the meridional outflow.\nFor the MHD simulations one has to include the vertical gradient as well as the time derivative of the orbital\nfrequency. Fig. 2, bottom right, demonstrate the change of the orbital frequency\nwith a period of around 50 local orbits at 5 AU.\\\\\nRadial mass flow and surface density evolution have shown that we can fit\nour MHD global models with a viscous disk model as long as we use \nan $\\alpha$ profile compatible with our MHD run.\nOf course, the disk spreading that we observe in our MHD run\nis partly due to the existence of our radial buffer zones,\nin which not only the fields decay, but also the $\\alpha$ stresses\nvanish. In a larger radial domain we can expect that also a larger\nregion of the disk will get into a steady state of accretion.\nHowever, one could also argue that in a realistic protoplanetary accretion disk\none will ultimately reach dead zones which behave similar as our\nbuffer zones. In that sense the active part of our global disk is \nembedded between two dead zones.\n\\begin{figure}\n\\hspace{-1.2cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-3A.ps,scale=0.56}\n\\end{minipage}\n\\hspace{4.2cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-3B.ps,scale=0.46}\n\\end{minipage}\n\\label{vel_spec3}\n\\caption{Left: Angle between the cylindrical radial and vertical velocity \nwith respect to the midplane axis ($V_R = -1$ and $V_Z = 0$) for the upper hemisphere.\nRight: Vertical mass outflow $\\rho v_z dA_z$ in units of $\\rm M_\\sun\/yr$ at 5 AU. \nThere is a mass outflow present above 3 scale\nheights. The evaporation time, $\\rm \\tau_{ev} = \\Sigma\/(\\rho v_z)$, was determined to 2070 local orbits.}\n\\end{figure}\n\n\\begin{figure}\n\\hspace{-1.2cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-4A.ps,scale=0.49}\n\\end{minipage}\n\\hspace{4.2cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-4B.ps,scale=0.46}\n\\end{minipage}\n\\label{vel_spec4}\n\\caption{Left: Logarithmic contour plot of the density, over plotted\nwith the velocity vector in the $R-\\theta$ plane for model BO. Both are averaged over azimuth and time\nand plotted for the upper disk hemisphere. The velocity vectors show a\n outflow pattern above two disk scale heights. The red line marks the optical depth of $\\tau = 1$ for our setup.\nRight: Vertical density profile at 5 AU after 1000 inner orbits for\nmodel BO (solid line), the respective viscous model (dashed line) and the \ninitial profile (dotted line). The optical depth of $\\tau = 1$ is around 2.8 scale\nheights for our model.}\n\\end{figure}\n\n\\begin{figure} \n\\hspace{-0.6cm}\n\\psfig{figure=FIG-5.ps,scale=0.46}\n\\label{totalmass}\n\\caption{Total mass plotted over time for all models. The mass is integrated in the\nspace region B (3-8 AU). The change of the mass for the closed models is due\nto radial movement. The mass loss for the open models is dominated by the vertical outflow.}\n\\end{figure}\n\n\n\\subsection{Vertical outflow}\nIn the previous section, we have seen that the MHD simulations point to the\npresence of an additional process besides turbulent \"viscous\" spreading that removes gas from the disk.\nFig. 4, right, shows the initial vertical density profile at 5 AU (dotted\nline), the respective profile for the MHD model BO (solid line) and the viscous HD run (dashed line) after 1000 inner orbits (90 local orbits).\nFor our model, the vertically integrated optical depth of $\\tau = 1$ is around 2.8 scale heights (Fig. 4, red line).\nFor the calculation of the optical depth, we used Rosseland mean opacities \\citep{dra84} with the temperature at 5 AU.\nThe additional magnetic pressure as well as the vertical mass flow, present in the MHD run, generates higher gas density \nabove 3 scale heights compared to the hydrostatic equilibrium.\nIn Fig. 4, left, we plotted a snapshot of the azimuthally averaged velocity \nfield, taken after 1000 inner orbits. The plot indicates a vertical outflow in the disk starting above \n2 scale heights. We measured the angle \nbetween the cylindrical radial velocity $V_R$ and the vertical velocity\n$V_Z$ for the mean and turbulent components (Fig. 3, left). \nThe angle is measured with respect to the midplane axis\n(pointing to the star, see Fig. 3, left, $V_R = -1$ and $V_Z = 0$).\nThe upper (red solid line) and the lower hemisphere (blue solid line) \npresent similar profiles. \nFrom the midplane up to $1.8$ scale heights, the turbulent velocity field is directed\nupwards but still pointing to the star. \nThe low angle of $10^{o}$ for the mean velocities shows the gas motion\npointing to the star and towards the midplane. \nAt $1.8$ scale heights the turbulent velocity is pointing away from the\nmidplane and the star.\nAlso the mean velocity angle changes quickly in the region between 1.6 and 2 scale heights \nto an outflow angle, e.g., steeper than $90^{o}$. This region coincides with the region where\nthe vertical outflow is launched \\citep{suz10}. \nAbove 2 scale heights the angle between the turbulent and the mean velocity\ncomponents stays above $90^{o}$, leading a vertical outflow with a small radial outward component.\nThe so-called dynamical evaporation time is the time to evacuate\nthe gas completely from the disk assuming no supply of matter. In our\nmodel the value is slightly larger than 2000 local orbits (Fig. 3, right)\nwhich provides a confirmation for the vertical outflow obtained by local box\nsimulations from \\citet{suz10} with a vertical net flux field.\n\n\nIn Fig. 3, right, we plotted the vertical mass flow over height at 5 AU.\nThe outflow starts at 2 scale heights and reaches mass fluxes of $\\rm 10^{-10} M_\\sun\/yr$ at 5 AU (model BO, solid line). The influence of the\npure outflow boundary is observed to cause the small outflow in the HD viscous run (dashed line).\nIn the midplane region, the disk reestablishes the hydrostatic \nequilibrium due to the radial mass loss at the midplane (Fig. 6, bottom\nright, red solid line). This drives to a small mean vertical motions visible\nin the vertical velocity (Fig. 6, bottom right, green dotted line).\n\nThe gas does leave the grid with Mach numbers of only\n0.5, which is significantly lower that the local escape velocity, which would be about Mach 20.\nEven the results indicate a stable vertical outflow, \nwithout including the sonic point and the Alfv\\'enic point in the simulation\nit is not possible to make prediction about the flow, leaving or returning to\nthe disk at larger radii.  \nThus the fate of the vertical outflow to be a disk wind or not will have to be determined in more detail \nin future simulations with a much broader vertically extent. For this study one would\nmost probably need an additional vertical field in the corona, which could support \nadditional propulsion effects like magneto-centrifugal acceleration.\n\\subsection{Velocity analysis}\nPlanet  formation processes in circumstellar accretion disk are strongly dependent on the\nstrength of the turbulence. Turbulence mixes gas and particles, diffuses or concentrates them \nand makes them collide \\citep{ilg04,joh05,joh07,bra08,cuz08,car10,bir10}.\nThe property of MHD turbulence that is important for planet formation are the turbulent velocity\nand density fluctuations of the gas.\nThe density fluctuations are around $10\\%$ and follow the results by\n\\citet{fro06}.\nThe spatial distribution of the fluctuating and mean part of the velocities \nis presented in Fig. 6.\nAll results are obtained for time averages from 800 to 1200 inner orbits\nand are given in units of the sound speed.\nSpatial averaging is performed in azimuth and between 3 and 7 AU for the vertical\nprofiles. The radial profiles are mass\nweighted. \nFig. 6, top left, shows the turbulent RMS velocity over radius. \nThe profile is roughly constant with a total RMS velocity\nof $0.1 c_s$, dominated by the radial turbulent velocity.\nThe vertical dependence of the turbulent velocity (Fig. 6 - right - top) shows a flat profile \naround $\\pm 1$ scale height above and below the\nmidplane for the radial and azimuthal velocity.\nBoth components increase above one scale height by an order of\nmagnitude.\nThe radial component dominates with $0.07 c_{s} $ around the midplane up to $0.3 c_{s} $ at 4 scale\nheights. \nThe azimuthal component follows with $0.05 c_{s} $ up to $0.2 c_{s}$ at 4 scale heights.\nOnly the $\\theta$-component does not show a flat profile around the\nmidplane and increases steadily from $0.02 c_{s} $ to $0.2 c_{s}$ at 4 scale heights,\nwhich is an effect of the density stratification.\nThe small decrease of the $\\theta$ component near the vertical boundary is due to the \noutflow boundary because it does not allow inflow velocities.\\\\\n\nA global picture of the total rms velocity is presented in Fig. 7.\nThe 3D picture is taken after 750 inner orbits and shows again the \ndifferent turbulent structures of the midplane and coronal region.  \nThere are also localized supersonic turbulent motions in the disk\ncorona (Fig. 7, white color). Compared to the turbulent velocity, the mean\nvelocities of the gas are two\norder of magnitude smaller. They show small but steady gas motions in the\ndisk. \nThe vertical dependence for the mean velocity (Fig. 6 right - bottom) \nshows the small inward motion (red solid line) as well as the change of $r$ and $\\theta$-velocity\ncomponents to an outflow configuration around 1.6 scale heights.\n\\begin{figure}\n\\hspace{-0.6cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-6A.ps,scale=0.46}\n\\psfig{figure=FIG-6C.ps,scale=0.46}\n\\end{minipage}\n\\hspace{4.0cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-6B.ps,scale=0.46}\n\\psfig{figure=FIG-6D.ps,scale=0.46}\n\\end{minipage}\n\\label{vel_turb}\n\\caption{Top left: RMS fluctuations of the velocity versus radius for model BO,\naveraged over time and azimuth. \nAll components show a roughly flat profile, dominated by the radial turbulent velocity.\nThe radial profiles are mass weighted. The time average is performed during time period II (Fig.1, top\nleft, green line).\nTop right: Turbulent velocity profile versus scale height for model\nBO, averaged over time and azimuth.\nThere is a flat profile visible in the range $\\pm 1.5$\nscale heights above and below the midplane.\nStarting at $1.5$ scale heights the turbulent velocity increases.\nBottom left: Energy power spectra $E_m\\cdot m^2$ for $\\pi\/4$ model PO (red dotted line),\n$2\\pi$ model FO (blue dashed line) and the high-resolution model BO (black solid line). \nBottom right: \u00a0Time average of the mean velocity over scale height.\n}\n\\end{figure}\n\n\n\\subsubsection{Kinetic spectra}\nNot all particles do couple alike to the turbulent gas flow. \nIn fact particles have a size-dependent friction or stopping time \\citep{wei77}.\nThis stopping time is also the time a particle needs to couple to the\nturbulent gas flow. \nBest coupled to turbulence are those particles, which have a coupling\ntime shorter then turbulent correlation time. \nParticle collision velocities are maximized for particles whose stopping time\ncoincides with the turbulent correlation time, e.g., the eddy turn over time.\nThis means that particles of different sizes couple to different length scales of the\nturbulent spectrum. Therefore, a study of planet formation processes needs \nnot only the mean turbulent velocity but also its spectral distribution.\\\\\nIn the global domain, only the $k_{\\phi}$ space of the spectra is\nwithout modifications accessible as only the $\\phi$ direction is periodic in space.\nThe investigation of the complete $k$-space for this model goes beyond the\nscope of this work.\nThe classical Kolmogorov theory predicts the scaling of the energy\nspectra per wavenumber: $E(k) \\propto v_k^2 k^{-1} \\propto \\epsilon^{2\/3} k^{-5\/3}$. \nWe calculate along azimuth $|v(k_\\phi)|^2 = |v_r(k_\\phi)|^2 +\n|v_\\theta(k_\\phi)|^2 + |v_\\phi(k_\\phi)|^2 $ with $v_r(k_\\phi) = \\left\n\\langle \\int_\\phi\nv_r(r,\\theta,\\phi)e^{-ik_{\\phi}\\phi} d\\phi \\right \\rangle$.\nThe average is done in radius (region B, Fig. 1) and height ($\\pm 0.5$ disk scale heights).\nFor our spectra we use the azimuthal wavenumber $\\rm m$ instead of $k$\nto be independent from radius: $k = 2\\pi\/\\lambda = m\/R$.\nIn Fig. 6, bottom left, we plotted the energy power spectra $E_m =\nv(m)^{2}\\cdot m$ with time and\nspace averaged over $\\pm 0.5$ scale heights around the midplane.\nIn our models we do not observe Kolmogorov inertial like range, $E_m\n\\cdot m^2 \\sim m^{1\/3}$.\nThe $2\\pi$ runs F0 and BO have most of the energy placed at $m=5$.\nThe high resolution model BO present a $k^{-1.2}$ dependence, starting from $m=5$ until\n$m=30$.\nThe $\\pi\/4$ run PO piles up the energy at its domain size ($m=8$), reaching higher\nenergy levels compared to the $2\\pi$ models FO and BO.\nThe velocity spectra for each component along the azimuth, \nplotted in Fig. 8, left, indicate that all velocity components have \nsimilar amplitude for the small scales and do not deviate \nby more than a factor of two at the largest scales.\nThe radial velocities peak at m equals 5, but \noverall the entire spectrum above m=20 is essentially flat.\nThe peak at m=5 could be connected to the production of shear waves in the simulations.\nThese shear or density waves are described in \\citet{hei09}.\nOn top of the shorter time scale of MRI turbulence, these long \"time scale\" shear waves\nare visible in the contour plot of the radial velocity in the $r-\\phi$ midplane (Fig. 8 right).\nThe shear wave structures drive the radial velocity up to $0.3 c_s$.\nIn the velocity spectra we see the start of the dissipation regime\nat $m=30-40$ for the high-resolution run BO. For the model BO, \nthis corresponds to 26 or rather 19 grid cells per wavelength, \nwhich is still well resolved by the code \\citep{flo10}.\nShearing waves are also visible in a $r-\\theta$ snapshot \nof the velocity (Fig. 9, left). Here we plot the azimuthal \nvelocity $V_\\phi - V_K$ as contour color, over-plotted with the velocity vectors.\nRed contour lines show Keplerian azimuthal velocities.\nSuper-Keplerian regions are important for dust particle migration.\nThey reverse the radial migration of particles, leading to their efficient\nconcentration and triggering parasitic instabilities in the dust layer, like\nthe streaming instability leading potentially to gravoturbulent planetesimal formation\n\\citep{kla08,joh07}.\nIn our simulation these super-Keplerian regions are not completely\naxisymmetric, but have\na large extension in the azimuthal direction of several scale heights.\nThe variation of the orbital frequency over time and space, presented in\nFig. 9, left, and Fig. 2, bottom right, are connected to zonal flows. They\nare observed and discussed in several local and global studies\n\\citep{joh09,dzy10}.\n\\subsection{Magnetic field analysis}\nThe azimuthal MRI generates a turbulent zero-net field configuration in the\ndisk.\nDespite the loss of mass and magnetic flux through the vertical\nboundary there is no sign of decay for the highest resolution case BO \n(Fig. 1, top left, bottom right).\nWe find well established turbulence. Fig. 9, right, presents a snapshot of the magnetic fields \nafter 750 inner orbits. \nThe $r-\\theta$ components are shown as vectors   \nwith the azimuthal magnetic field as background color. \n\\subsubsection{Magnetic energy spectrum}\nTo understand the magnetic turbulence at the midplane, we\ninvestigated the spectral distribution of the magnetic energy.\nThe magnetic energy power spectrum (Fig. 12 - bottom left) is plotted along\nthe azimuthal direction with the same time and space average as for the \nkinetic energy power spectra.\nWe plot the magnetic energy power spectra times the wave-number \n$m\\cdot B_m^2\/2P_{Init-5AU}$ to show where most of the \nmagnetic energy is located.\nFor all runs, most of the magnetic energy is\ndeposited in small scale magnetic turbulence. This was found in several\nrecent MRI simulations, latest in local box simulations by \\citet{dav10} and \\citep{fro10}.\nThe peak of the magnetic energy lies just above the dissipation regime.\nFor the $2\\pi$ model FO, the peak is located between \n$m=10$ and $m=20$, whereas for the high-resolution run BO this regime\nis shifted to $m=20$ and $m=30$. \nThe spectra follows closely the $m^{1.0}$ slope until the dissipation regime is reached.\nThe $\\pi\/4$ run does not resolve the scales where we observe this $m$ dependence. \nIn the restricted model PO most of the magnetic energy is again located \nat the scale of the domain size.\\\\\n\\subsubsection{Convergence}\nThe convergence of MRI is an important aspect in ongoing MRI research in\nlocal and global simulations. In local boxes, there was found convergence for\nthe large scale turbulence between 32 and 64 grid cells per scale height\n\\citep{dav10}. Due to the large domain in global simulations, it was up to now not feasible to reach\nsuch resolutions per scale height. Here the first resolution level is needed \nto reach a self sustaining turbulence, at least for\nsimulations with a zero-net flux toroidal field \\citep{fro06}. Comparing the\nresults from stratified local box simulations we can already give\npredictions for global simulations with such high resolutions per scale\nheight. \nIn comparison with the local box simulations by \\citet{dav10} we get a very\nsimilar profile of the magnetic energy with increasing resolution.\nWith higher resolution (FO to BO, Fig. 12, bottom left) the large scale magnetic energy decreases \nwhile the small scale energy increases. A doubled resolution as model BO should also\nshow convergence for the large scales. Doing this, we expect\nonly a weak decrease for the large scale modes, as presented in\n\\citet{dav10}, Fig. 3.\n\n\n\\subsubsection{Plasma beta}\nThe overall strength of the magnetic fields is best analyzed by this plasma beta\nvalue $\\beta = 2P\/B^2$.\nFig. 10 presents a 3D picture of the logarithmic plasma beta for the \n$r-\\theta$ components, taken at 750 inner orbits. \nThe two-phase structure of the disk is again visible.\nThe well established turbulence at the midplane has a broad distribution \nof high plasma beta values (Fig. 11 , top left).\nIn contrast, there are regions in the corona of the disk with plasma beta below unity (Fig. 10, black regions).\nThe azimuthal and time averaged plasma beta at the midplane lies around 400 (Fig. 11, bottom right).\nIn Fig. 11, top left, we plot the correlation of plasma beta over height in a scatter plot of all grid cells.\nWe find the distribution of beta values to be very narrow in the disk corona (1-10) but on the\nother hand to be much broader (10 - $10^4$) around the midplane, but strongly peaked around $\\beta$ = 500. \nThe value of plasma beta in the disk corona depends on several issues. A\nzero-net flux MRI turbulence with toroidal field produces lower magnetic\nfields in the corona. This was already shown in a very similar simulation by \\citet{fro06} (Fig. 8, solid line, model S2). \nIn contrast, a vertical initial field produces a stronger turbulence level\nwith plasma beta values below unity in the corona.\nThe boundary condition also affects the values in the corona.\nA closed boundary condition, e.g. periodic in the vertical direction \nwill accumulate large amount of magnetic flux in the corona and drive to a \nplasma beta value smaller then one (observed in model FC and PC). \nThe small increase of plasma beta above 3 disk scale\nheights is connected to the vertical outflow and the increase of gas\npressure and density in this area (Fig. 4, right). This effect has to be investigated in future work\nwith a much broader vertical extent.\nVery high plasma beta values in the midplane (Fig. 11, top left) indicate reconnection.\nTwo magnetic fields with different sign and comparable strength coming\ntoo close to each other, e.g., in the same grid cell, do reconnect. \nSuch reconnections are visible in single grid cells with nearly no magnetic field.\nFor our BO model, the reconnection zones reach plasma beta values up to $10^{11}$. \nThe heating due to reconnection in those regions is not covered in our\nisothermal model, but shall be a subject for future studies.\n\n\\begin{figure}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-7.ps,scale=0.22}\n\\end{minipage}\n\\label{vrm}\n\\caption{3D picture of turbulent RMS velocity at 750 inner orbits for model BO.\nThe white regions in the corona present super sonic turbulence.}\n\\end{figure}\n\\begin{figure}\n\\hspace{-0.6cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-8A.ps,scale=0.46}\n\\end{minipage}\n\\hspace{4.0cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-8B.ps,scale=0.46}\n\\end{minipage}\n\\label{vel_spec2}\n\\caption{Left: Velocity spectra in units of the sound speed for all three components\nat the midplane. Space and time averaged is again between 3 and 8 AU\nand between 800 and 1200 inner orbits. The radial velocity peaks at $m=3-5$\nfor both $2\\pi$ models.\nRight: Contour plot of the radial velocity at the midplane ($R-\\phi$ plane).\nLarge shear wave structures become visible. This snapshot is taken after 750\ninner orbits.}\n\\end{figure}\n\\begin{figure}\n\\hspace{-0.6cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-9A.ps,scale=0.46}\n\\end{minipage}\n\\hspace{4.0cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-9B.ps,scale=0.46}\n\\end{minipage}\n\\label{pow_spec}\n\\caption{Left: Contour plot of $V_\\phi - V_K$ for an azimuthal slice. The red\ncontour line encloses regions with Super-Keplerian velocity.\nOverplotted are the $r-\\theta$ velocity fields.\nRight: \u00a0Contour plot of $B_\\phi$ for an azimuthal slice.\nOverplotted are the $r-\\theta$ magnetic fields fields.\nBoth snapshots are taken after 750 inner orbits.\n}\n\\end{figure}\n\\begin{figure}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-10.ps,scale=0.22}\n\\end{minipage}\n\\label{pbeta}\n\\caption{3D picture of plasma beta after 750 inner orbits for model BO.\nThe black regions in the corona present plasma beta values below unity.}\n\\end{figure}\n\\begin{figure}\n\\hspace{-0.6cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-11A.ps,scale=0.46}\n\\psfig{figure=FIG-11C.ps,scale=0.46}\n\\end{minipage}\n\\hspace{4.0cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-11B.ps,scale=0.46}\n\\psfig{figure=FIG-11D.ps,scale=0.46}\n\\end{minipage}\n\\label{mag_turb2}\n\\caption{Top left: Distribution of plasma beta, $N(\\beta)\/N_{Total}$, over height at 750 inner orbits for model BO.\nThe color represents the relative number of grid cells, containing specific\nplasma beta values. At the midplane,\nthere is a wide distribution of plasma beta values between 10 and 10000.\nIn the coronal region the distribution becomes more narrow with values between 1 and 10.\nTop right: Contour plot of azimuthal and time averaged plasma beta of BO\nwith radial (bottom left) and vertical profile (bottom right).}\n\\end{figure}\n\\subsubsection{Spatial distribution}\nAs we already mentioned in section 3.2, the radial profile of the turbulent magnetic field\nhas a direct effect onto the radial profile of the Maxwell stress in the $\\alpha$ parameter.\nThe dominant turbulent azimuthal magnetic field goes as $1\/r$, as shown in a\nazimuthal and time average in Fig. 12, top left.\nThe saturated turbulent field is 4 times lower than the initial azimuthal field.\nAll values are normalized to the initial gas pressure at 5 AU at the midplane\nand the radial profiles are again mass weighted.\nThe vertical profile shows a constant distribution around $\\pm 2$ scale heights \nfrom the midplane until it decreases with height (Fig. 12, top right).\nIn contrast, the radial and $\\theta$ component show a local\nminimum at the midplane with a peak of turbulent magnetic field slightly\nabove 2 scale heights. \\\\\nThe turbulent magnetic fields are around 2 orders of magnitude larger than the\nmean fields. \nThe vertical profiles of mean magnetic fields over height are presented in Fig. 12, bottom right.\nThe radial magnetic field is anti-symmetric to the midplane and correlated\nwith the dominating azimuthal component.\nThe distribution of mean magnetic fields are connected to the \"butterfly\"\noscillations.\n\n\\subsubsection{Butterfly structure}\nThe butterfly pattern is a general property of MRI turbulence and  \nwas found in many local and global simulations, latest by\n\\citet{gre10}, \\citet{fla10}, \\citet{sor10} and \\citet{dzy10} .\nThe \"butterfly\" pattern becomes visible for the mean $B_\\phi$ evolution, \nplotted over disk height and time.\nIn Fig. 13, bottom, we plotted the $B_\\phi$ component of the magnetic field\naveraged over a small radius (4 - 5 AU) and over azimuth for model FO, left,\nand PO, right. \nWe see a clear \"butterfly\" pattern in both models. \nThis pattern is also visible in the total accretion stress with\ndoubled period (Fig. 1, bottom right). In comparison, the $\\pi\/4$ run shows \nno systematic and more violent picture of the butterfly. The amplitudes are stronger and \nit has mixed symmetry (Fig. 13, bottom right). Also the total magnetic flux\nevolution shows these properties for model PO (Fig. 13, top right). \nThe FO run presents a similar amplitude and period as the BO run. \nThe effect of the narrow azimuthal domain on the mean fields will be investigated in a follow-up work.\nThe reason of this butterfly structure and its role for the MRI is still under discussion. \nRecent studies show the connection to the MHD dynamo \\citep{gre10}\nand magnetic buoyancy \\citep{shi10}.\n\n\\begin{figure}\n\\hspace{-0.6cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-12A.ps,scale=0.46}\n\\psfig{figure=FIG-12C.ps,scale=0.46}\n\\end{minipage}\n\\hspace{4.0cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-12B.ps,scale=0.46}\n\\psfig{figure=FIG-12D,scale=0.46}\n\\end{minipage}\n\\label{mag_turb}\n\\caption{Top left: Time averaged turbulent magnetic field over radius for\nmodel BO. The turbulent field adjusts to the force-free $r^{-1}$ profile.\nTop right: Time-averaged turbulent magnetic field over scale height for\nmodel BO. The dominating turbulent azimuthal field represents the same flat profile\n$\\pm 1.5$ scale heights around the midplane as the velocity (Fig. 6, top\nright). The turbulent radial and $\\theta$ components represent a different profile with\nmaximum at 2.3 scale heights.\nBottom left: \u00a0Magnetic energy power spectra $B_m^2\\cdot m$ for $\\pi\/4$ model PO (red dotted line), $2\\pi$ model FO\n(blue dashed line) and the high-resolution model BO (black solid line).\nThe profile follows the $m^{1.0}$ slope until the dissipation range.\nBottom right: \u00a0Time-averaged mean magnetic field over height for \u00a0\u00a0\u00a0\u00a0\nmodel BO. The radial and azimuthal field show again anti-correlation.\nThe anti-symmetry for the upper and lower hemisphere could be correlated\nwith a $\\alpha$-$\\Omega$ MHD dynamo.\nAll radial profiles are mass weighted. The time averaged is performed in time\nperiod II (Fig.1, top left, green line).}\n\\end{figure}\n\\begin{figure} \n\\hspace{-0.6cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-13A.ps,scale=0.55}\n\\psfig{figure=FIG-13C.ps,scale=0.46}\n\\end{minipage}\n\\hspace{4.0cm}\n\\begin{minipage}{5cm}\n\\psfig{figure=FIG-13B.ps,scale=0.46}\n\\psfig{figure=FIG-13D.ps,scale=0.46}\n\\end{minipage}\n\\label{mag_spec2}\n\\caption{\nTop left: Total magnetic flux evolution integrated over the entire computational \ndomain (without the buffer zones) normalized over initial flux $B_\\phi$\nin the $2\\pi$ run FO and $\\pi\/4$ run PO (top right).\nBottom: Contour plot of $B_{\\phi}$ over disk height and time. The value is averaged over\nazimuth and radius (4 AU to 5 AU). Local \norbits are calculated at 4.5 AU. Bottom left: model FO. Bottom right: model\nPO. The butterfly pattern becomes visible. The $\\pi\/4$ model shows irregular and stronger amplitudes.}\n\\end{figure}\n\n\n\n\n\n\\section{Discussion}\nFor a number of aspects, our Godunov method confirms results previously\nobtained with a finite difference method as presented by \\citet{fro06}.\n\\begin{itemize}\n\\item A minimum amount of grid cells per scale height, which is about 25 grid\ncells, is needed to sustain turbulence, which was to be expected as both methods \npresent similar numerical behavior \\citep{flo10}. \nOtherwise the turbulent magnetic energy slowly decays in the nonlinear MRI\nevolution \\citep{fro06}. \nOur highest resolution model BO was able to sustain a constant level of\nturbulent stress for more than 400 inner orbits.\n\n\\item The toroidal magnetic net flux is quickly lost via an \n      open vertical boundary. Then, there is a oscillating zero-net\nflux field present in the disk.\n\n\\item The disks show a two layer structure of turbulence.\n\\end{itemize}\n\n\\subsection*{$\\alpha$-stress evolution}\nWe obtained a steady state $\\alpha$ value of about $5\\cdot10^{-3}$, which\nis comparable to the results obtained in \\citet{fro06}.\nThe time averaged radial profile of $\\alpha$ follows $\\sqrt{r}$.\nThis profile can be explained by the choice of our\nradial pressure (density and temperature) profile, in combination\nwith the resulting magnetic field profile which is\nforce free, $|B'_\\phi| \\propto r^{-1}$.\nFor this magnetic field profile, the net radial magnetic force\nvanishes. \nAny quasi steady state of disk turbulence must display this profile,\notherwise large scale radial readjustments in the density profile would occur.\nBoth $B'_\\phi$ and $B'_r$ determine the Maxwell stress $B'_\\phi B'_r $ to be $\\sim 1\/r^2$.\nFor the chosen $ \\partial \\ln{P} \/ \\partial \\ln {R} = -2.5$ this results in  $\\alpha \\sim B'_\\phi\nB'_r\/P \\sim \\sqrt{r}$.\\\\\nOf course, this profile is only valid for well-ionized accretion disk\nregions.\nThe radial $\\alpha$ profile in protoplanetary disks remains an open\nquestion. \nThe ionization rate, and possibly the MRI\nactivity, will be a function of radius and height \\citep{sem04,dzy10}. Furthermore, the pressure scale height \nwill vary with radius, and this also changes the MRI evolution.\nBoth effects will lead to different saturation levels for MRI turbulence\nat different radii and thus also to different $\\alpha$ values. \n\\subsection*{Magnetic energy convergence}\n\n\\citet{dav10}, \\citet{shi10} and \\citet{fla10} show in local box simulations \nthat the large scale magnetic energy converges for a resolution\nbetween 32 and 64 grid cells per pressure scale height (\\citet{dav10}, Fig. 3). \nOtherwise, the large scale magnetic energy decreases with increasing\nresolution.\nAt the current state we could only handle 25 cells per scale height in our global\nsimulations. We expect also a large scale \nconvergence of magnetic energy with 1.5(2.5) higher resolution.\nFuture calculations shall complete this point, but will be five times more computationally\nexpensive.\\\\\nWe can already conclude that our global magnetic energy spectra as well as the effect of increasing \nresolution (Fig, 12, bottom left, FO to BO) look very similar\nto the results presented in local box simulations. \nThe magnetic energy power spectra reveals that most of\nthe magnetic energy is deposited in the small turbulent scales.\nFor the model with a restricted azimuthal domain of $\\pi\/4$,\nthe largest energy scale is always the domain size.\n\\subsection*{Turbulent velocity}\nRecently observed turbulent velocities in TW Hya and HD 163296\n\\citep{hug10} fit nicely to our computed Mach numbers of 0.1 and 0.4 in the midplane and corona of the\ndisks.\\\\\nThe kinetic energy spectra as well as the velocity spectra along\nazimuth ($k_\\phi$ space) show a peak between $\\rm m=5$ and $6$ due to radial shear\nwaves.\nLatest results in local box MRI simulations presented\na $k^{-3\/2}$ slope for the kinetic energy power spectra \\citep{fro10}.\nSimilar as in \\citet{fro10}, our power-law fit \napplies only for a small range in k space.\nWe do not find a Kolmogorov type slope of $k^{-5\/3}$ (Fig. 6).\nFurther studies are needed, including the $k_r$ and $k_{\\theta}$.\\\\\nA Kolmogorov scaling was predicted for magnetic ISM turbulence by\n\\citet{gol95} and recently confirmed in numerical simulations by \\citet{ber10}.\nHowever, it only applies for the inertial range of incompressible\nisotropic turbulence. The driving of the turbulence via MRI,\nthe anisotropy of the turbulent eddies, the geometry and rotation of the disk \nand the compressibility of the gas\nmake it difficult to argue for a Kolmogorov scaling. \nWe expected a spectrum to be more or less deviating from this simple law.\n\n\\subsection*{Two-phase disk structure}\nWe observe that the accretion disks establish a two-phase structure:\\\\\n- The midplane region between $\\pm$ two scale heights shows a pretty\nconstant turbulent RMS velocity of about $10\\%$ of the local sound speed\n independent of radius or height.\nPart of the RMS velocity occurs due to global shear waves which have radial\npeak velocities of up to $30\\%$ of the local sound speed. \nThe amplitude of the azimuthal fluctuations in the magnetic\nfield is also independent of height ($\\pm$ two scale heights around the midplane) but develops a \n$1\/r$ profile in radius.\nThe midplane region shows a broad distribution of plasma beta values, \n$\\beta = \\frac{2P}{B^2}$, with a mean value of about 500 and a full width at\nhalf maximum of two order of magnitude.\\\\\n- In the coronal region, more than two scale heights above the midplane,\n the mean turbulent velocity reaches a Mach number of 0.5 with supersonic peaks up to 1.5. \nThe mean magnetic fields decrease in this region with height.\nThe disk corona shows a narrower distribution of the plasma beta values with most values between 1\nand 10. Here the magnetic fields are buoyant, gas and fields are\nexpelled from the disc.\nRelative high plasma beta ($\\beta > 1$) in the corona have been\nreported in \\citet{fro06} for global models of AMRI with open boundary. The\nmagnetic flux escapes through the vertical boundary with a remaining zero-net flux\nin the computational domain. This leads to the weakly magnetized corona (below equipartition).\\\\\n\n\n\\subsection*{Vertical outflow}\nOur models show a MRI driven vertical outflow.\nAbove 2 scale heights, the gas flow is directed vertically and radially \noutward, Fig. 3. The outflow velocity of the gas (measured at the vertical\nboundary) is still subsonic.\nThe disk evaporation time was determined at 5 AU to 2000 local orbits.\nThe launching region is located between 1.6 and 2 scale heights. \nThis results matches values obtained in local box simulations \\citep{suz09,suz10} with a\nvertical net-flux field.\\\\\nHowever, we are aware that a detailed study of the vertical outflows\nrequires \nmuch broader vertical extended\nsimulations to confirm that the gas is evacuated from the disk and not\nreturning.\nThese simulations should then include the sonic point or even the Alfv\\'enic point to give\nfurther insight into disk-wind and disk-jet interacting regions.\n\n\\subsection*{Meridional flows}\nOur present work shows that the meridional\noutflow at the midplane is only present in HD simulations, e.g., in\nviscous simulations with an $\\alpha$ value assumed to be constant in time and space.\nFor our MHD models, we find time variations of the orbital frequency of\naround 50 local orbits, which are not present in the viscous disk models\nand which prevent a steady radial outflow.\nA similar result, the absence of a meridional flow in global MHD simulations \nwas recently found by \\citet{fro11}.\\\\\nHowever, we confirm the more general picture of a viscous disk and \nshow that viscous disk models with a radial viscosity\nprofile can reproduce successfully the radial mass flow rate in global MRI turbulent stratified disks.\nClearly, the vertical mass flow cannot be described with such an HD\nmodel.\\\\\n\n\\subsection*{Mean field evolution}\nThe azimuthal MRI is self-sustaining in our zero net flux simulations with\nopen boundaries.\nThe fact that the total flux oscillates around zero could be due\nto the generation of a mean poloidal magnetic field by a turbulent toroidal\nfield. \nWe observe also an antisymmetric distribution of the mean magnetic fields in the upper and\nlower hemisphere which could be an indication for the action of an MHD dynamo in our global\nsimulations.\\\\\nThe existence of an $\\alpha$-$\\Omega$ MHD dynamo and its role for accretion\ndisks was investigated by \\citet{bra95}, \\citet{zie00}, \\citet{arl01},\n\\citet{bra07}, \\citet{les08} and \\citet{bla10}.\nThe temporal oscillations of the mean azimuthal field, plotted \nover height and time (Fig. 13), generates a butterfly pattern. \nLatest results connect the butterfly pattern with \na dynamo mechanisms \\citep{gre10}. \nWe present also a butterfly pattern with a period of 10 local orbits,\nindependent of the azimuthal extent.\nAdditionally, the butterfly structure is reflected in the temporal\nspatial fluctuations of the mean turbulent stresses with double period. \nA change of sign of the mean azimuthal field occurs every five local orbits, at the same time the \n$\\alpha$-stresses show a minimum (Fig. 1, bottom right).\\\\\nThe magnetic energy as well as the mean field evolution have shown\nthat the $\\pi\/4$ model does not capture the correct properties \nof the larger scale simulations. \n\\citet{haw00} also studied full $2\\pi$ and restricted $\\pi\/2$ models of\naccretion tori. However, a detailed study of the impact of different \nazimuthal domain extents is still needed and will be covered in future work.\n\n\\section{Summary}\nWe have performed full $2\\pi$ 3D stratified global MHD simulations of \naccretion disks with the Godunov code PLUTO.\nOur chosen disk parameter represent well-ionized proto-planetary disk\nregions. We obtain a quasi steady state zero-net flux MRI turbulence \nafter around 250 inner orbits.\n\n\\begin{itemize}\n\n\n\\item The second order Godunov scheme PLUTO including the HLLD Riemann\nsolver presents a similar nonlinear MRI evolution as finite difference\nschemes. There is also a need of about 25 grid cells per pressure\nscale height to reach a self-sustaining MRI turbulence in global zero net flux\nazimuthal MRI simulations.\n\n\\item We observe a total $\\alpha$ parameter of about $5\\cdot10^{-3}$,\nwhich remains constant for at least 400 inner orbits and scales with $\\sqrt{r}$ for our used pressure and\ndensity profile.\n\n\\item The turbulent magnetic fields show a $1\/r$ profile in radius, mainly\nvisible in the dominating toroidal magnetic field. This configuration is force free\nin the sense that there exist no large scale net force on the gas. This\nprofile determines the slope of the $\\alpha$ parameter.\n\n\\item The magnetic energy spectra is similar as in local box simulations.\nMost of the magnetic energy is placed in the smallest resolved turbulent\nscale. \n\n\\item The kinetic energy spectra as well as the velocity spectra peak for an\nazimuthal wavenumber between $\\rm m=3$ and $5$ due to shear waves, driving the\nradial velocity up to a Mach number of 0.3. We do not find a Kolmogorov type\nscaling in the $k_\\phi$ space.\n\n\\item The model with an azimuthal extent of only $\\pi\/4$ has most of the energy at the domain\nsize and does not show the same mean field evolution. \n\n\\item We observe a butterfly pattern with then local orbits independent of\nthe azimuthal extent. The butterfly period becomes also visible in the\nMaxwell stress with double period. The mean magnetic fields are\nantisymmetric for the two hemispheres.\n\n\\item At the midplane ($\\pm 2 $ disk scale heights), \nour turbulent RMS velocity presents a constant Mach number of 0.1\nindependent on radius. At the corona ($> 2$ disk scale heights), the\nturbulent velocity increases up to a Mach number of 0.5 at 4 scale heights.\n\n\\item The turbulent magnetic fields at the midplane present a broad plasma\nbeta distribution with a mean of about 500 $\\pm$ one order of magnitude.\nIn the corona the plasma beta is between unity and ten.\n\n\\item The turbulent and the mean velocities are pointing vertically and\nradially outward in the disk corona ($> 2$ disk scale heights). We observe a\nsteady vertical outflow for the open boundary models, dominating the radial\naccretion flow.\n\n\\item We do not see a meridional flow pointing radially outward at the\nmidplane in our MHD models. However, we reproduce our total radial mass flow\nin 2D viscous disk simulations with a radial dependent $\\alpha$-viscosity.\n\n\n\n\n \n\n\n\n\\end{itemize}\n\n\\section{Outlook}\n\nThis paper presents a huge data set of about 10 TBytes.\nThis means we will continue to analyze the data for different goals. \nOne study will deal with a closer investigation of dynamo properties in\nour global disk models. Another one will analyze the turbulent spectra in a\nbetter way to derive correlation times for the turbulence.\nWe will also fill the parameter space with $\\pi$ and $\\pi\/2$ models to\nidentify whether a subsection will be sufficient. Higher resolution is\nenvisioned to reach resolution per scale height comparable to recent stratified local\nbox simulations. Finally, our global MHD model will be the work horse for our\nfuture investigations of planet formation processes in circumstellar disks,\nlike collisions of boulders, planetesimal formation and planet migration.\\\\\nIn future runs, we also plan to use non-ideal MHD to include more realistic\nmagnetic Prandtl numbers and magnetic Reynolds numbers to understand the occurrence and\nsaturation level of the turbulence. Improving the thermodynamics is also\na must in future work, dealing with the proper ionization of the disk, like\ncapturing $p\\Delta V$ terms or magnetic dissipation as heat input.\n\n\\acknowledgments\nWe thank Andrea Mignone for very useful discussions about the numerical setup.\nWe thank Sebastien Fromang for the helpful comments on the global models and \non the manuscript.\nWe thank Alexei Kritsuk for the discussion about turbulent spectra.\nWe also thank Willy Kley for the comments on the viscous model.\nWe thank Frederic A. Rasio and an anonymous referee for the fast and very professional processing of\nthis work.\nH. Klahr, N. Dzyurkevich and M. Flock have been supported in part by the\nDeutsche Forschungsgemeinschaft DFG through grant DFG Forschergruppe 759\n\"The Formation of Planets. Neal Turner was supported by a\nNASA Solar Systems Origins grant through the Jet Propulsion\nLaboratory, California Institute of Technology, and by an Alexander\nvon Humboldt Foundation Fellowship for Experienced Researchers.\nThe Critical First Growth Phase\". Parallel\ncomputations have been performed on the PIA cluster of the MaxPlanck\nInstitute for Astronomy Heidelberg as well as the GENIUS Blue Gene\/P cluster\nboth located at the computing center of the MaxPlanck Society in Garching.\n\\bibliographystyle{apj}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{s_intro}\n\n\n\nGlobular clusters (GCs) host multiple populations of stars characterized by different spectroscopic and photometric signatures. Anti-correlations between the abundances of several elements such as C-N, Na-O, and sometimes Mg-Al have been reported at the surface of various types of stars, from the main sequence (MS) to the red giant branch (RGB) and the asymptotic giant branch (AGB) \\citep[e.g.,][]{Cohen1978,Peterson1980,sneden92,Kraft1994,Thevenin2001,gratton07,Gratton2019,Meszaros2015,carretta15,Carretta2019,Johnson2016,Pancino2017,Wang2017,Masseron2019}. These differences in chemical composition are thought to explain the various sequences observed in color-magnitude diagrams (CMDs) built with specific filters sensitive to atomic and molecular lines of the elements listed above \\citep[e.g.,][]{bedin04,piotto07,Bowman2017,nardiello18,marino19}. The discovery of these peculiarities (variations in chemical composition and discrete sequences in CMDs) turned GCs from textbook examples of clusters born in a single star forming event into complex structures the origin of which remains elusive.\n\n\nThe standard explanation\\footnote{Alternative possibilities exist but all rely at least partly on nucleosynthesis products of AGB or massive stars, see \\citet{marcolini09,elmegreen17}.} to these puzzling properties is the pollution of the original proto-cluster gas by a population of rapidly evolving stars more massive than the present-day GC members. Indeed, the abundance patterns observed are typical outcomes of nucleosynthesis at about 75 MK. More precisely, hydrogen burning through the CNO cycle, together with the Ne-Na and the Mg-Al chains, fully explains the anti-correlations \\citep{1988ATsir1525...11K,Denisenkov1990,prantzos07,Prantzos2017}. Potential polluters experiencing such nucleosynthesis phases are $\\sim$5-7.5~M$_{\\sun}$\\ AGB stars \\citep[e.g.,][]{ventura01,Ventura2009}, massive stars either rotating fast \\citep{decressin07,DecressinCM2007}, in binary systems \\citep{demink09,Izzard2013}, or in a red supergiant phase \\citep{szecsi19}, and super-massive stars \\citep{denis14}. Whatever the nature of the polluter, it should be objects present at early times of the GC history that have spread their nucleosynthesis products in the surrounding gas and out of which the stellar populations we see today were formed. Depending on the degree of mixing of the nucleosynthesis products with pristine gas, a range of chemical composition is predicted for the newly formed stars. The polluters have long disappeared because of their relatively high mass, and only low-mass stars either from the initial population formed out of original proto-GC gas or from the second population formed out of polluted material are still present. We usually refer to these two populations of stars as 1P (or 1G) and 2P (or 2G), standing for first and second population (generation), respectively.\n\nOne of the key differences in the predictions of the scenarios that invoke the different polluters listed above is the amount of helium that is inevitably ejected together with other nucleosynthesis products. Indeed, as hot hydrogen-burning is needed to explain the observed abundance patterns, helium is naturally produced and released too. On one hand, the fast-rotating massive star (FRMS) models of \\citet{decressin07}, developed  specifically to reproduce the observations of the GC NGC~6752, predict a wide range of Y for the ejecta, up to Y=0.8, and the test case\\footnote{The study focuses on one binary system made of a 20~M$_{\\sun}$\\ primary and a 15~M$_{\\sun}$\\ secondary star orbiting each other on a 12-day orbit, and with individual rotation periods synchronized on the orbital period.} of binary evolution presented by \\citet{demink09} also predicts a wide range of Y, up to 0.63.\nOn the other hand, models of \\citet{doherty14} indicate that nucleosynthesis in massive AGB stars should produce material with helium mass fraction of about 0.35--0.40, as a result of second dredge-up.  On the other hand, supermassive stars\ncan potentially release material rich in hot hydrogen-burning products but only mildly enriched in helium \\citep{denis14}, with a helium mass fraction close to that of the proto-cluster gas in the case where they form through the so-called runaway collision scenario \\citep{Gieles2018}.\n\nMeasuring the helium surface abundance from spectroscopy is not possible in most GC stars. Only hot horizontal branch (HB) stars display weak \\ion{He}{i} lines, and these are difficult to model and interpret. However, the helium surface abundance in these stars, with effective temperatures higher than $\\sim$11 000~K, is affected by atomic diffusion  \\citep[e.g.,][]{Michaud08,Quievy09}. Thus, the measured helium no longer represents the original chemical composition of the stars. The vast majority of GC stars are too cool to display any helium line in their spectra. Nevertheless, helium enrichment is detected in a few hot HB stars with $\\Delta$Y ---the difference between the highest Y of 2P stars and Y of 1P stars--- generally not larger than $\\sim$0.1 \\citep{villanova12,marino14}, although \\citet{pasquini11} and \\citet{dupree13} report a Y difference of up to 0.17 between two HB stars, of NGC~2808 and $\\omega$~Cen, respectively.\n\nA change in helium mass fraction affects the internal structure as well as the color and the brightness of stars because the opacity is modified. As a consequence, stars with the same mass, age, and metallicity but different Y have different effective temperatures ($T_{\\rm{eff}}$; the higher Y, the higher $T_{\\rm{eff}}$; e.g., \\citealt{IbenFaulkner1968,chantereau15,CassisiSalaris2020}). Their spectral energy distributions (SEDs) therefore peak at different wavelengths: stars with high Y have more flux at shorter wavelengths, and thus bluer colors. Consequently they are located to the left of stars with smaller Y in CMDs (e.g., \\citealt{sbordone11} and Sect.~\\ref{s_sed}). Variations in the helium content naturally lead to a widening of classical branches (MS, RGB, HB, AGB) in CMDs \\citep[e.g.,][]{Rood1973,Norris1981,DAntonaCaloi2004,DAntona2005ApJ,chantereau16}. In addition, the associated variations in (among others) C, N, and O abundances impact specific colors built with photometric filters encompassing lines sensitive to these elements. This further increases the separation between stars in CMDs, leading to the observed multiple and discrete sequences \\citep[e.g.,][]{Lardo2012,marino19}. \n\nComparison of observed and theoretical colors in filters mostly sensitive to $T_{\\rm{eff}}$, and thus Y, has been used to   indirectly constrain the amount of helium present at the surface of GC stars \\citep[e.g.,][]{piotto07,milone15}. \\citet{king12} report a maximum helium mass fraction of about 0.39$\\pm$0.02 in $\\omega$~Cen based on the analysis of MS stars. Using the Hubble Space Telescope (HST) ultra-violet (UV) survey of GCs \\citep[HUGS][]{piotto15,nardiello18}, \\citet{milone18} determined Y in 57 GCs. $\\Delta$Y ranges from nearly 0 to 0.124, corresponding to a maximum Y of about 0.38. \\citet{milone18} also show that $\\Delta$Y correlates with the cluster mass, with higher Y being determined in more massive clusters.\n\nAnother indirect constraint on the helium content of GCs comes from the morphology of their HB. Its different shape in clusters with similar general properties, such as M3 and M13 \\citep[e.g.,][]{ferraro97}, is difficult to explain. A spread in Y of HB stars is a viable possibility \\citep{rood73} and quantitative determinations give $\\Delta$Y between 0.02 and 0.15 on the HB, depending on the cluster \\citep{Caloi2005,lee05,dicri10,valcarce16,tailo16,denis17,vandenberg18,chantereau19}. \n\nThe presence of hot HB stars in GCs of early-type galaxies is also thought to be responsible for the existence of a so-called UV upturn \\citep{gr90}. This feature refers to the increase of flux below $\\sim$2500 \\AA\\ in galaxies that no longer form stars and that are made of low-mass MS and post-MS stars. These objects have SEDs that rapidly drop short of about 3500~\\AA. Hot HB stars, such as those seen in Galactic GCs, may explain the UV fluxes. \\citet{ali18} argued that if such hot HB stars are present because of a high helium content (as suggested by \\citealt{Meynet2008} for elliptical galaxies), there should be a redshift above which they would no longer be observed, having not yet sufficiently evolved. The position of this transition redshift can be used to constrain Y in hot HB stars. \\citet{ali18} showed that a value of $\\sim$0.45 would be compatible with the observed disappearance of the UV upturn with redshift.\n\nThus, modern estimates of Y in GCs indicate that the very helium-rich stars predicted in particular by the FRMS scenario are not detected. However, a key specificity of the FRMS model highlighted by \\citet{chantereau15} is that such He-rich objects evolve faster and differently compared to more classical stars. In particular, \\citet{chantereau16} showed that in a GC that would have been formed under the FRMS scenario, the distribution of stars quickly falls as Y increases (at ages typical of GCs, i.e., 9 to 13.5 Gyr). In practice, there should be little to no He-rich stars on the RGB and AGB of the cluster NGC~6752, for which the models of Chantereau et al. were tailored. This also naturally explains the lack of Na-rich AGB stars in some GCs \\citep{Campbell2013,Wang2016,Wang2017}, although observations reveal that the presence of 2P AGB stars can be affected by more than one  factor \\citep{Wang2017}.\n\nThe question therefore naturally arises as to whether the absence of very He-rich stars (i.e., Y$>$0.4) is a robust observational fact, or these stars simply escaped detection due to their exceptionally small number. In view of the discriminating nature of the helium content for various scenarios, it is important to investigate this potential issue, which we aim to do in the present study. In practice, we build on the work of \\citet{chantereau16} to compute synthetic clusters with the predicted distribution of multiple populations for NGC~6752. We compute synthetic spectra consistently with isochrones, produce synthetic photometry and CMDs, and perform determinations of the maximum Y values of these synthetic clusters in order to see if we recover or miss the highly enriched populations predicted by the model of Chantereau et al.\n\nOur paper is organized as follows: Sect.~\\ref{s_specphotom} presents the computation of synthetic spectra and photometry. We then discuss the behavior of our models with special emphasis on the effects of surface abundances on colors. We subsequently compare our predicted photometry to observations in various CMDs before moving to the determination of the maximum helium content in NGC~6752 and synthetic clusters in Sect.~\\ref{s_maxHe}. We discuss our results in Sect.~\\ref{s_disc} and give our conclusions in Sect.~\\ref{s_conc}.\n\n\\section{Spectral synthesis and synthetic photometry}\n\\label{s_specphotom}\n\nIn this section we first present our computations of synthetic spectra and the associated photometry (Sect.~\\ref{s_meth}). We then describe the effects of stellar parameters and surface abundances on both the SEDs and synthetic colors (Sect.~\\ref{s_sed}). We build synthetic CMDs and compare them with observations (Sect.~\\ref{s_compobs}).\n\n\n\\subsection{Method}\n\\label{s_meth}\n\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=9cm]{hrd_theo.eps}\n\\caption{Hertzsprung-Russell diagram with the isochrones of \\citet{chantereau15}. Different symbols and colors stand for different initial composition, especially different helium mass fraction. Symbols correspond to the points for which atmosphere models have been calculated.}\n\\label{hr_theo}\n\\end{figure}\n\nWe proceeded as in \\citet{martins20} to compute synthetic photometry. We relied on the evolutionary tracks and isochrones computed by \\citet{chantereau15} with the code STAREVOL.\nThese models are based on the FRMS scenario \\citep{decressin07} for the formation of multiple stellar populations in GCs. Each isochrone is characterized by a set of abundances that directly comes from the FRMS predictions. We refer to \\citet{chantereau15} for details. Each set of abundances is tailored to reproducing 1P and various 2P stars in NGC~6752, in which the abundances vary according to different degrees of pollution by FRMS. Figure~\\ref{hr_theo} shows the Hertzsprung-Russell diagram (HRD) with the isochrones we consider in the present work. Each isochrone is labeled according to its helium mass fraction (Y), but we stress that abundances of other elements are also varied (in particular, nitrogen is increased and carbon and oxygen are depleted when Y increases; see Appendix~\\ref{ap_chem}). We stress that the isochrones have been recomputed for a metallicity of $[Fe\/H]=-1.53$, which is slightly higher than the value of -1.75 used in \\citet{chantereau15}. This change was made to better match the metallicity of NGC~6752. \n\nAlong each isochrone we computed atmosphere models and synthetic spectra at ten points (see Fig.~\\ref{hr_theo}) using the codes ATLAS12 \\citep{kur14} and SYNTHE \\citep{kur05}. Our computations include the so-called predicted lines, that is, lines for which at least one of the energy levels comes from quantum mechanics calculation and not from laboratory measurements. These lines thus have approximate wavelengths, but their opacities have been shown to be of prime importance to reproducing observed SEDs \\citep{coelho14}. We adopted a microturbulent velocity of 1~km~s$^{-1}$\\ in all our calculations. \n\nTo convert the HRD into CMDs we computed synthetic photometry in the Vegamag system: \n\n\\begin{equation}\n  mX = -2.5 log (F_X\/F^{Vega}_X) = -2.5 log (F_X) + ZP^{Vega}_X\n\\label{eq_mX}\n,\\end{equation}\n\n\\noindent where $mX$ is the magnitude in the X filter and ZP the zero point. The average flux $F_X$ over the passband X was calculated according to \\citet{bohlin14}:\n\n\\begin{equation}\nF_X = \\frac{\\int \\lambda F_{\\lambda} R_X d\\lambda}{\\int \\lambda R_X d\\lambda}\n,\\end{equation}\n\n\\noindent where $R_X$ is the transmission curve of filter X\\footnote{Transmission curves were retrieved from the Spanish VO \\url{http:\/\/svo2.cab.inta-csic.es\/svo\/theory\/fps3\/}.}.\nThe zero point $ZP^{Vega}_X$ in Eq.~\\ref{eq_mX} was calculated using the Vega STScI reference spectrum\\footnote{File alf\\_lyr\\_stis\\_010.fits from \\url{ftp:\/\/ftp.stsci.edu\/cdbs\/current_calspec\/}.} and the appropriate transmission curve.\n\n\n\nFinally, for comparison with observations, we assumed a distance modulus of 13.18 for NGC~6752 based on the \\emph{Gaia} DR2 determination \\citep{helmi18}. This value is consistent with those found by \\citet{harris96} (13.19), \\citet{renzini96} (13.05) , and \\citet{gratton03} (13.24).\nPrior to synthetic photometry calculations, we reddened our SEDs using a color excess $E(B-V) = 0.060$ and A$_V$=3.2, adopting the extinction law of \\citet{ccm89}.\nThis choice best reproduces the turn-off (TO) and sub-giant region in the  m814W (m606W-m814W) CMD (see for instance Fig.~\\ref{cmd}). This is slightly larger than the value of 0.046$\\pm$0.005 reported by \\citet{gratton05} but close to the value of \\citet{shleg98}:  0.056.\n\n\n\n\\subsection{Spectral energy distributions}\n\\label{s_sed}\n\nIn this section we describe the effects of chemical composition on the SED. The goal is to identify spectral regions that are affected by certain species. We refer to \\citet{sbordone11} or \\citet{milone20}, among other recent studies, for similar descriptions.\n\nFigure~\\ref{comp_sed_L0p85} shows a selection of models at the bottom of the RGB, with luminosities equal to $10^{0.85}$~L$_{\\odot}$ (see Fig.~\\ref{hr_theo}). These spectra have different $T_{\\rm{eff}}$, surface gravities and chemical compositions (see Table~\\ref{tab_chem}). Because of the higher $T_{\\rm{eff}}$\\ in higher Y models, the SED peak is shifted towards shorter wavelengths. In the optical region, the slope of the SED becomes steeper (faster decline with wavelength) which translates into bluer colors. Variations in individual abundances of light elements (CNO) also changes the strength of absorption lines, mostly below 4500~\\AA. \n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[width=9cm]{comp_sed_L0p85.eps}\n\\caption{Spectral energy distributions of some of the models with \\ifmmode \\log \\frac{L}{L_{\\sun}} \\else $\\log \\frac{L}{L_{\\sun}}$\\fi~=~0.85 but different chemical compositions (and thus different $T_{\\rm{eff}}$\\ and $\\log g$). Different colors correspond to different models, identified by their helium mass fraction.}\n\\label{comp_sed_L0p85}\n\\end{figure}\n\nTo better separate the effects of light elements and helium on the SED, we show in Fig.~\\ref{comp_CNO} examples of spectra in which the abundances of C, N, and O have been varied by a factor of three, all other parameters being kept constant. A reduction of the carbon abundance translates into a weaker CH absorption between 4200 and 4400 \\AA. Conversely, an increase in the nitrogen content leads to a stronger NH absorption at 3300-3500 \\AA. The CN band around 3900 \\AA\\ is less affected. The OH absorption between 2800 and 3300 \\AA\\ reacts to a change in the oxygen content. Consequently, photometry in the HST filters F275W and F336W is affected by C, N, and O abundances \\citep{sbordone11,milone18,CassisiSalaris2020}. These filters have been used to build the so-called super color C$_{410}$=(m275W-m336W)-(m336W-m410M) \\citep{milone13}. This photometric diagnostic has been shown to be a powerful tool for separating multiple populations (see also following section). Filters F395N, F467M, F606W, F814W and to some extent F410M are relatively insensitive to variations in C, N, and O abundances. An important result of Fig.~\\ref{comp_CNO} is that C, N, and O abundances do not affect the global shape of the SED, but only specific wavelength regions that include molecular bands \\citep{milone13,Dotter2015}. \n\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=9cm]{comp_sed_effectCNO.eps}\n\\caption{Spectral energy distribution of two models with similar parameters except the C, N, and O abundances: the red line shows a model with C\/H reduced by a factor three (top panel), N\/H increased by a factor three (middle), and O\/H reduced by a factor three (bottom) compared to the initial model in black. The other parameters are: $T_{\\rm{eff}}$\\ = 5375 K, $\\log g$\\ = 3.37, Y=0.248. The gray solid lines indicate the transmission curves of the HST WFC3\/UVIS F275W, F336W, F395N, F410M, F467M, and ACS\/WFC F606W and F814W.}\n\\label{comp_CNO}\n\\end{figure}\n\n\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=9cm]{comp_sed_L0p85_effectcompo.eps}\n\\caption{Spectral energy distribution of three models with \\ifmmode \\log \\frac{L}{L_{\\sun}} \\else $\\log \\frac{L}{L_{\\sun}}$\\fi=0.85: one with Y=0.248, $T_{\\rm{eff}}$\\ = 5375 and $\\log g$\\ = 3.37 (black line); one with Y=0.400 and the same $T_{\\rm{eff}}$ \\ and $\\log g$\\ (green line); and the model with Y=0.400 and the associated $T_{\\rm{eff}}$\\ and $\\log g$\\ (5549 K and 3.31 respectively, red line).}\n\\label{comp_sed_L0p85_compo}\n\\end{figure}\n\n\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=9cm]{comp_Tstru_L0p85_effectcompo.eps}\n\\caption{Temperature as a function of Rosseland optical depth in the three models leading to the SEDs shown in Fig. \\ \\ref{comp_sed_L0p85}.}\n\\label{comp_Tstru_L0p85}\n\\end{figure}\n\n\n\nTo further quantify the effect of chemical composition (and in particular of Y) on the SED, in Fig.\\ \\ref{comp_sed_L0p85_compo} we compare  the SEDs of three models with the same luminosity but different chemical composition. We focus on the models with L=$10^{0.85}$~L$_{\\odot}$. We have chosen the models of the Y=0.248 and Y=0.400 sequence, to which we add a third model with the effective temperature and gravity of the Y=0.248 sequence, but the chemical composition of the Y=0.400 sequence. Hence, we are able to disentangle the effect of chemical composition on the effective temperature and logg on one side, and on the SED on the other side. Comparing the two models with $T_{\\rm{eff}}$\\ = 5375 K, we find the same trends as the ones drawn from Fig.\\ \\ref{comp_CNO}. It is mainly the CH, CN, NH and OH bands that are affected. The general shape of the SED is otherwise relatively similar in the two models. Hence, models with different helium content but similar $T_{\\rm{eff}}$\\ and surface gravity have very similar SEDs, except in regions containing lines involving C, N, and O. If we now compare the two models with the same composition but different effective temperature and surface gravity, we see a major modification of the SED. The hottest model has more (less) flux blueward (redward) of 6000 \\AA. This is mainly governed by the change in $T_{\\rm{eff}}$\\ which itself is due to the different helium content. Figure\\ \\ref{comp_Tstru_L0p85} shows the temperature structure in the three models. Changing only the chemical composition leads to a higher temperature in the inner atmosphere, but a similar structure in the outer parts. This effect is entirely dominated by the difference in the helium content: computing a model with $T_{\\rm{eff}}$\\ = 5375 K, $\\log g$\\ = 3.37, and the helium content of the Y=0.400 sequence but the abundances of all elements heavier than He from the Y=0.248 sequence leads to a temperature structure which is almost indistinguishable from that of the green model in Fig.\\ \\ref{comp_Tstru_L0p85}.  \nIf we now change both the chemical composition and the effective temperature\/surface gravity (red model), we obtain a global increase in the temperature at all depths in the atmosphere, which translates into a change of the SED. \n\nFrom these comparisons we conclude that the global shape of the SED is mainly sensitive to the effective temperature which itself depends critically on the helium content and its effect on opacities. The abundances of heavier elements affect certain portions of the SED but not its global shape. Variations in Y thus affect colors sensitive to the global shape of the SED. The filters F395N, F410M, F606W, and F814W should be relatively free of contamination by absorption lines of light elements, and can therefore be used to study the helium content \\citep{milone13,milone18,Dotter2015,CassisiSalaris2020}.\n\n\\subsection{Comparison with observed CMDs}\n\\label{s_compobs}\n\n\n\nIn this section we compare our synthetic photometry to the observed CMDs of NGC~6752. We use the data of \\citet{milone13} and of the HUGS survey \\citep{piotto15,nardiello18}. The goal is to see if synthetic colors reproduce observations and to identify potential failures.\n\nThe bottom-right panel of Fig.~\\ref{cmd} shows the m814W versus (m606W-m814W) CMD. Taking the Y=0.248 isochrone as a reference, we see that on average our synthetic photometry is able to reproduce the shape of the observed sub-giant branch and the bottom of the RGB. More specifically, the synthetic isochrone is located near the red part of the envelopes that define these branches, which are broadened because of intrinsic dispersion and the presence of multiple populations. The synthetic isochrone reproduces the TO relatively well.\nOn the upper RGB, the synthetic isochrone appears slightly too red compared to the observations, which could be due to the fact that the stellar evolution models were computed with an atmosphere treated in the gray, plane-parallel, and Eddington approximations. \n\n\n\n\\begin{figure*}[]\n  \\centering\n\\includegraphics[width=0.4\\textwidth]{cmd_275W_814W.eps}\n\\includegraphics[width=0.4\\textwidth]{cmd_336W_814W.eps}\n\n\\includegraphics[width=0.4\\textwidth]{cmd_410M_814W.eps}\n\\includegraphics[width=0.4\\textwidth]{cmd_C410_814W.eps}\n\n\\includegraphics[width=0.4\\textwidth]{cmd_467M_814W.eps}\n\\includegraphics[width=0.4\\textwidth]{cmd_606W_814W.eps} \n\\caption{Color-magnitude diagrams: In all panels, the ordinate axis is the magnitude in the ACS F814W filter. The abscissa axis is the difference between magnitude in the X filter and the magnitude in the ACS F814W filter, where X is the WFC3 F275W filter (top left panel), WFC3 F336W filter (top right panel), WFC3 F410M filter (middle left panel), WFC3 F467M filter (bottom left panel), and ACS 606W (bottom right panel). In the middle right panel, the abscissa axis is the color difference (m275W-m336W)-(m336W-m410M). In all panels, different symbols and colors correspond to models with different chemical composition, tagged by their helium content (Y). Gray points correspond to the photometric data of \\citet{milone13}, except in the bottom right panel where they are from the HUGS survey \\citep{piotto15,nardiello18}.}\n\\label{cmd}\n\\end{figure*}\n\nFigure~\\ref{cmd} shows several CMDs involving filters F275W, F336W, F410M, F467M and F814W. These filters are sensitive to the chemical composition as described in Sect.~\\ref{s_sed}. \nFocusing on the Y=0.248 isochrone we find, in general, relatively good qualitative agreement with observations. We note that in the m814W versus (m410M-m814W) diagram, the synthetic isochrone is located slightly too much to the red on the RGB (at least when compared to the m814W-(m275W-m814W) and m814W-(m336W-m814W) CMDs). In the (m336W-m814W) color the Y=0.248 isochrone is located roughly in the middle of the observed branch, for reasons that are explained in the following paragraph. The observed RGB is redder than the synthetic isochrone in the m814W versus C$_{410}$ diagram. This is likely the result of the small offsets seen in other CMDs that are amplified by the super color. All these (relatively) small offsets between observations and synthetic isochrones are due to different photometric calibrations between observations and synthetic colors and to limitations in the stellar evolution and spectral modeling. This likely has a small impact on the determination of the helium content of multiple populations, because only relative color differences are used and not absolute ones. However, it is important to keep in mind that full consistency is not achieved between observations and synthetic photometry.\n\n\nIncreasing Y globally leads to a shift of all isochrones to the left because of the increased $T_{\\rm{eff}}$. An exception is the m814W-(m336W-m814W) CMD where the isochrones move first to the right (Y=0.260 to Y=0.300) and then move back to the blue from Y=0.300  to Y=0.600. This is caused by the strong sensitivity of the F336W filter to the nitrogen abundance (see Sect.~\\ref{s_sed}). The N abundance increases rapidly when Y increases, which causes a deepening of the NH absorption band. Consequently, the (m336W-m814W) color is redder. At the same time, $T_{\\rm{eff}}$\\ increases because of the higher helium content. But at first, the effect of nitrogen is stronger, leading to a redder color. When Y reaches $\\sim$0.300, the nitrogen increase is not sufficient to counter-balance the effect of the higher $T_{\\rm{eff}}$\\ and the colors become bluer again. This effect, specific to the F336W filter, is not seen in the TO region of the CMD because at the corresponding $T_{\\rm{eff}}$\\ there is no molecular NH band in the  spectra of the stars investigated here. \n\n\n\n\\vspace{0.5cm}\n\nHaving presented and described our synthetic photometry of NGC~6752, we now turn to the main question tackled by this study: the maximum helium content.\n\n\n\\section{Maximum helium content}\n\\label{s_maxHe}\n\nIn this section, we investigate whether the current estimates of the maximum helium content of stars of the second population are true values or lower limits. More precisely, we study the possibility that highly enriched stars could be missed when studying multiple populations with HST photometry.\n\n\n\\subsection{Helium in NGC~6752}\n\\label{smax_ngc6752}\n\n\nIn a first step, we re-determine the maximum helium mass fraction difference in NGC~6752. We use a  similar method to that of \\citet{milone18} which we describe below. Briefly, we select the extreme populations, that is, the least and most chemically enriched ones, from the chromosome map \\citep{milone17}. We then estimate the helium mass fraction difference between these two populations in various CMDs using the theoretical isochrones and synthetic photometry presented in Sects.~\\ref{s_meth} and \\ref{s_sed}.\n\nTo build the chromosome map we first create the m814W versus (m275W-m814W) and m814W versus C$_{410}$ diagrams shown in the top panels of Fig.~\\ref{fidchmap6752}. We subsequently define the red and blue so-called fiducial lines that bracket the distribution of stars along the RGB. These lines are defined manually by selecting points along the red and blue envelopes and by applying a spline function over the selected points. The width of the RGB is set to the difference between the two fiducial lines at a magnitude of 14.9, corresponding to 2.0 magnitudes above the TO, in agreement with the definition of \\citet{milone17}. For each star on the RGB in the  m814W versus (m275W-m814W) and m814W versus C$_{410}$ diagrams, the quantities $\\Delta$(m275W-m814W) and $\\Delta (C_{410})$ are calculated according to equations 1 and 2 of \\citet{milone17}. We select stars with m814W magnitudes between 15.8 and 12.8 (dashed lines in Fig.~\\ref{fidchmap6752}) to cover the bottom of the RGB but avoid its part above the bump in the luminosity function where internal mixing can affect surface chemical composition \\citep[e.g.,][]{Briley1990,Shetrone2003,CZ2007,Lind2009,Henkel2017}. The resulting chromosome map is shown in the bottom panel of Fig.~\\ref{fidchmap6752}.\n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{fid_chmap_ngc6752.eps}\n\\caption{\\textit{Top left panel}: m814W versus (m275W-m814W) CMD of NGC~6752. \\textit{Top right panel}: m814W versus C$_{410}$ diagram. In both panels, the red and blue solid lines are the fiducial lines along the RGB. The horizontal dashed lines indicate the magnitude bin considered to build the chromosome map shown in the bottom panel. The horizontal dotted line marks the m814W value at which the width of the RGB is measured (see text). \\textit{Bottom panel}: Chromosome map ($\\Delta (C_{410})$ versus $\\Delta$ (m275W-m814W)) on the RGB. The dotted lines define boxes in which stars are considered either 1Pe (bottom right) or 2Pe (top left).}\n\\label{fidchmap6752}\n\\end{figure}\n\n\nFollowing the concept of \\citet{milone17}, we manually select the extreme 1Pe and 2Pe stars from the chromosome map by defining boxes respectively near the right-most and left-most parts of the stars' distribution, as illustrated in Fig.~\\ref{fidchmap6752}. We then study the color (and thus Y) differences between these two extreme populations in three CMDs:  m814W versus (m395N-m814W),  m814W versus (m410M-m814W), and  m814W versus (m467M-m814W). According to Sect.~\\ref{s_compobs} and \\citet{milone18} the colors (m395N-m814W), (m410M-m814W), and (m467M-m814W) depend almost exclusively on the helium content at the metallicity of NGC~6752. In addition, the color difference is the largest for the colors that involve filters located at sufficiently blue wavelengths to show sensitivity to effective temperature ---and thus Y--- variations (see Fig.~\\ref{comp_sed_L0p85} and middle panel of Fig.~5 of \\citealt{milone18}).\n\nFigure~\\ref{395m814_1G2G_6752} shows the m814W versus (m395N-m814W) diagram for the 1Pe and 2Pe stars (see Appendix \\ref{ap_dY} for the other CMDs). Building on \\citet{milone18} we define new fiducial lines along the two populations. We divide each distribution into m814W bins of 0.2 mag  in width. In each bin, we calculate the median m814W and (m395N-m814W). We subsequently perform a boxcar averaging, replacing each median point by the average of its three closest neighbours. This gives the filled circles in Fig.~\\ref{395m814_1G2G_6752}. Finally, we run a spline function over these new points to obtain the fiducial lines for each of the two extreme populations. The color difference between these lines is estimated at six m814W magnitudes: 15.2, 14.9, 14.6, 14.3, 14.0, and 13.7. We do not consider brighter stars for reasons that will be explained further below. Section~\\ref{ap_dY} of the Appendix shows the CMDs using the F410M and F467M filters. \n\n\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{delta395m814_ngc6752.eps}\n\\caption{m814W versus (m395N-m814W) CMD for the 1Pe (black) and 2Pe (red) populations selected in the chromosome map of Fig.~\\ref{fidchmap6752}. The filled circles are the points used to define the fiducial lines, which themselves are shown by the solid lines. See text for details. The horizontal dotted lines indicate the m814W magnitudes at which the color difference between the 2Pe and 1Pe fiducial lines is determined.}\n\\label{395m814_1G2G_6752}\n\\end{figure}\n\n\nOnce obtained, this set of six color differences is compared to theoretical values in Fig.~\\ref{Ydcol395_6752}. The latter are calculated from our synthetic photometry, including distance and extinction corrections appropriate for NGC~6752 as described in Sect.~\\ref{s_meth}. For each m814W magnitude, we determine the Y difference between the isochrones that match the (m395N-m814W) color difference determined from observations. We do this for the six selected m814W magnitudes and finally average the six determinations to yield the final Y difference. The standard deviation is taken as the uncertainty in this measurement. We perform this process for the three selected colors. The results are gathered in Table~\\ref{tab_he_ngc6752}. They are broadly consistent with the determination of \\citet{milone18} who quote a maximum Y difference of 0.042$\\pm$0.004. We note that our uncertainties are much larger. We tested the effect of varying the size of the boxes to select the 1Pe and 2Pe stars in the chromosome map. Increasing the size of 0.2 magnitudes does not affect the results. However, reducing the size (i.e., selecting fewer points, but at even more extreme positions) translates into an increase in $\\Delta$Y by between 0.015 and 0.020. However, at the same time, the uncertainties also increase by the same amount because of\nthe reduced number of stars, \n\n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{Y_dcol395_ngc6752.eps}\n\\caption{Determination of the helium mass fraction difference between 1Pe and 2Pe stars for the six magnitudes (see labels in panels) defined in Fig.~\\ref{395m814_1G2G_6752}. For each panel the filled circles are the theoretical values calculated from our isochrones and synthetic photometry. The black solid line is a linear regression to these values. The vertical gray line highlights the measured color difference between 1Pe and 2Pe fiducial lines. The horizontal dashed line indicates the corresponding Y difference read from the black solid line.}\n\\label{Ydcol395_6752}\n\\end{figure}\n\n\n\n\\begin{table}[ht]\n\\begin{center}\n  \\caption{Difference in the helium mass fraction Y between the 1Pe and 2Pe populations, for different colors and for the RGB and MS stars.}\n\\label{tab_he_ngc6752}\n\\begin{tabular}{lc}\n\\hline  \ncolor & $\\Delta$Y \\\\     \n\\hline\nRGB & \\\\\n(m395N-m814W)  & 0.039$\\pm$0.013 \\\\       \n(m410M-m814W)  & 0.052$\\pm$0.011 \\\\        \n(m467M-m814W)  & 0.068$\\pm$0.025 \\\\\n\\hline\nMS & \\\\\n(m395N-m814W)  & 0.042$\\pm$0.004 \\\\       \n(m410M-m814W)  & 0.047$\\pm$0.004 \\\\        \n(m467M-m814W)  & 0.049$\\pm$0.049 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nIn anticipation of the following section,  in Fig.~\\ref{fidchmap6752MS} and Table~\\ref{tab_he_ngc6752} we present the analysis of extreme populations on the MS of NGC~6752. The details of the analysis are presented in Sect.~\\ref{clu_W16}. The results indicate that the maximum helium mass fraction reported by \\citet{milone18} based on the RGB is also recovered for MS stars. These results are further discussed in Sect.\\ref{s_disc}.\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{fidchmap6752MS.eps}\n\\caption{Same as Fig.~\\ref{fidchmap6752} but for the MS of NGC~6752.}\n\\label{fidchmap6752MS}\n\\end{figure}\n\n\n\n\\subsection{Synthetic clusters}\n\\label{smax_synthclu}\n\nIn a second step, we build synthetic clusters to investigate whether or not we underestimate the maximum helium difference between extreme populations. \n\nWe first start by building synthetic CMDs. In practice, we draw artificial points along the isochrones in the m814W versus (m275W-m814W), m814W versus (m336W-m814W), m814W versus (m410M-m814W), m814W versus (m395N-m814W), and m814W versus (m467M-m814W) diagrams (see Fig.~\\ref{cmd}). We assume a magnitude distribution in the F814W filter similar to that of NGC~6752 (see Fig.~\\ref{distrib814}). We build clusters made of 9000 stars, ensuring a consistent number of stars on the RGB compared to NGC~6752.\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{distrib814.eps}\n\\caption{Distribution of stars according to their m814W magnitude in NGC~6752 (black) and in a typical synthetic cluster (red). The latter distribution results from random sampling using a Gaussian distribution.}\n\\label{distrib814}\n\\end{figure}\n\n\nFor each m814W magnitude drawn along the isochrone (in each diagram) we add a correction to the color (x-axis in each diagram) to introduce a dispersion on the theoretical isochrone. We estimate the correction in the following way. We retrieve photometry of NGC~6752 from the HUGS survey\\footnote{\\url{https:\/\/archive.stsci.edu\/prepds\/hugs\/}} and build the m814W versus (m275W-m814W), m814W versus (m336W-m814W), and m814W versus (m435W-m814W) diagrams. We select stars at m814W magnitudes of 14.9 and 16.5 (in a bin of size 0.2 magnitude). For these subgroups of stars and for each color, (m275W-m814W), (m336W-m814W), and (m435W-m814W), we take the standard deviation with respect to the median point as representative of the dispersion on the RGB and MS. We subsequently use these values to introduce a dispersion in the synthetic colors. For that we randomly draw a color correction by means of a Gaussian distribution centered on zero and characterized by the standard deviation determined above.\nIn the absence of photometric error for the m395N, m410M, and m467M magnitudes, we assume the dispersion in the colors (m395N-m814W), (m410M-m814W), and (m467M-m814W) is the same as in (m435W-m814W). We perform this process for all isochrones, that is, for all chemical compositions. We finally end up with a series of synthetic CMDs that are used to build synthetic clusters.\n\n\n\\subsubsection{Two chemical compositions}\n\\label{clu_2pop}\n\nWe build synthetic clusters by mixing populations of different chemical composition. We start with a cluster made up of one-third stars with Y=0.248, and two-thirds stars with Y=0.330. For the m814W versus (m275W-m814W) CMD, we therefore select 3000 stars from Y=0.248 isochrone in the synthetic m814W versus (m275W-m814W) just created, and 6000 stars from the Y=0.330 isochrone. We repeat the process for all five diagrams.\nWe then apply the same method as described in Sect.~\\ref{smax_ngc6752} to determine the maximum helium mass fraction difference in the synthetic cluster. We know by construction that it is equal to 0.082. We find that $\\Delta$Y=0.081$\\pm$0.002, 0.079$\\pm$0.002, and 0.070$\\pm$0.015 using the (m395N-m814W), (m410M-m814W), and (m467M-m814W) colors, respectively. We thus recover the input value ($\\Delta$Y=0.082) with a good level of confidence.\n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{fidchmap_unif0.eps}\n\\caption{Same as Fig.~\\ref{fidchmap6752} but for a synthetic cluster with one-third stars with  Y=0.248 and two-thirds stars with Y=0.260 to 0.600 with a flat distribution.}\n\\label{fidchmapunif0}\n\\end{figure}\n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{delta395m814_unif0.eps}\n\\caption{Same as Fig.~\\ref{395m814_1G2G_6752} but for a synthetic cluster with one-third stars with Y=0.248  and two-thirds stars with Y=0.260 to 0.600 with a flat distribution.}\n\\label{395m814_1G2G_unif0}\n\\end{figure}\n\n\n\\subsubsection{Uniform distribution among second population}\n\\label{clu_unif}\n\nWe then run another test by building a synthetic cluster still made up of one-third 1P stars (3000 data points) drawn from the Y=0.248 isochrone, but with the remaining two-thirds of 2P stars (i.e., 6000 data points) spread uniformly between isochrones with Y varying from 0.260 to 0.600. For that, we create the isochrones characterized by Y=0.430, 0.470, 0.500, 0.530, and 0.570 by linearly interpolating between the Y=0.400 and Y=0.600 isochrones. We create the five CMDs with these additional isochrones using the same method as described immediately above. We select 500 stars for each isochrone between 0.260 and 0.600, which is 5.5\\% per isochrone, to obtain the final synthetic cluster.\nWe then proceed as previously to determine $\\Delta$Y. Figure~\\ref{fidchmapunif0} shows the definition of the fiducial lines and the chromosome map, together with the selected 1Pe and 2Pe stars. Figure~\\ref{395m814_1G2G_unif0} shows the 1Pe and 2Pe stars in the m814W versus (m395N-m814W) diagram. Here, we face a problem: the number of 2Pe stars is too small to apply the automatic process for defining the fiducial line of the 2Pe population. We therefore select the fiducial line by hand\\footnote{We estimate the uncertainty on $\\Delta$Y resulting from the use of this manual process by performing ten repetitions on the same set of 1Pe and 2Pe populations. We find the uncertainty is of the order 0.004.}, as done in the first step of the process that leads to the chromosome map. We then determine the Y difference and we obtain $\\Delta$Y=0.362$\\pm$0.005. Using the other colors, (m410M-m814W) and (m467M-m814W), we obtain $\\Delta$Y=0.364$\\pm$0.008 and $\\Delta$Y=0.367$\\pm$0.007, respectively. The true Y difference, being 0.352, shows that we are able to measure it with good accuracy. \n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{distriW16.eps}\n\\caption{Black solid histogram: Relative fraction of stars as a function of their helium content on the lower RGB in the models of \\citet{chantereau16} and for an age of 13~Gyr. Red dashed histogram: Distribution we adopt to build synthetic clusters with populations as close as possible to those of \\citet{chantereau16}.}\n\\label{distriW16}\n\\end{figure}\n\n\n\\subsubsection{Distribution of Chantereau et al.}\n\\label{clu_W16}\n\n\nWe finally move to clusters made of populations similar to those presented by \\citet{chantereau16} within the framework of the FRMS scenario that fits the O-Na anti-correlation in NGC~6752, and which is the most extreme case in terms of He enrichment. We use the distribution of stars according to their helium content shown in Fig.~6 of \\citet{chantereau16}  for an age of 13 Gyr (at that age, their model predicts that 10$\\%$ of the stars should have Y$>$0.4, from an initial fraction of 21$\\%$). We adopt the distribution of the lower RGB as representative of the entire population of the cluster. Examination of Fig.~6 of \\citet{chantereau16} reveals that this is a fair approximation for the MS up to the upper RGB. As we do not have synthetic photometry for the full distribution of Y presented by Chantereau et al., we group bins of Y. This is illustrated in Fig.~\\ref{distriW16}. For instance,  in the bin with Y=0.30 we gather the stars of Chantereau et al. with Y=0.29, 0.30, and 0.31. In addition, we linearly extrapolated our isochrones beyond Y=0.6 (up to Y=0.72) using our Y=0.4 and Y=0.6 synthetic isochrones. For the populations with Y$>$0.6 in Fig.~\\ref{distriW16} we group stars in bins of  0.2 in width (e.g., the Y=0.64 bin gathers stars with Y=0.64 and 0.65 from the distribution of Chantereau et al.). The most enriched population has Y=0.72 in our clusters, corresponding to $\\Delta$Y=0.472. We built ten clusters.\n\nWe then perform the determination of the maximum helium mass fraction as in the previous example where a uniform distribution of stars with Y$>$0.248 was used. Figures~\\ref{fidchmapW16} and \\ref{395m814_W16} show the synthetic CMDs, chromosome map, and extreme populations in the m814W versus (m395M-m814W) CMD in a representative example. We gather the results in Table~\\ref{tab_he_synth} and Fig.~\\ref{deltaY}. For some realizations of our synthetic clusters, and for some colors, we derive enrichments that are marginally compatible with the input value $\\Delta$Y=0.472: we obtain $\\Delta$Y=0.437$\\pm$0.038 for cluster 8 using the color (m467M-m814W). However, the main result is that, on average, we determine a maximum $\\Delta$Y of about 0.43, which is smaller than the input value of 0.472. This is qualitatively understood by looking at Figs.~\\ref{distriW16} and \\ref{fidchmapW16}. Stars with Y$>$0.6 have an almost flat distribution which translates into the extended population in upper left part of the chromosome map. When picking the stars identified as the 2Pe population, and to ensure a sufficient number of stars in that population, we include the stars with the highest Y, but also some stars with slightly smaller Y. We therefore tend to create a population with an average Y that is smaller than 0.72. \n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{fidchmap_W16_000.eps}\n\\caption{Same as Fig.~\\ref{fidchmap6752} but for a synthetic cluster with the populations of \\citet{chantereau16}.}\n\\label{fidchmapW16}\n\\end{figure}\n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{delta395m814_W16_000.eps}\n\\caption{Same as Fig.~\\ref{395m814_1G2G_6752} but for a synthetic cluster with the populations of \\citet{chantereau16}.}\n\\label{395m814_W16}\n\\end{figure}\n\n\n\\begin{table}[t]\n\\begin{center}\n  \\caption{Helium difference recovered in ten synthetic clusters with a distribution of the population as in Fig.~\\ref{distriW16}. $\\Delta$Y$_{X}$ stands for the helium difference estimated from color ($X$-m814W) where $X$ is the magnitude in one of the filters F395N, F410M, or F467M.}\n\\label{tab_he_synth}\n\\begin{tabular}{cccc}\n\\hline  \ncluster id & $\\Delta$Y$_{395N}$ & $\\Delta$Y$_{410M}$ & $\\Delta$Y$_{467M}$ \\\\     \n\\hline\n0  &    0.444$\\pm$0.022 &   0.448$\\pm$0.014  &   0.468$\\pm$0.019 \\\\\n1  &    0.409$\\pm$0.007 &   0.411$\\pm$0.006  &   0.416$\\pm$0.007 \\\\\n2  &    0.411$\\pm$0.031 &   0.416$\\pm$0.021  &   0.434$\\pm$0.038 \\\\\n3  &    0.425$\\pm$0.027 &   0.434$\\pm$0.027  &   0.427$\\pm$0.051 \\\\\n4  &    0.420$\\pm$0.013 &   0.429$\\pm$0.008  &   0.436$\\pm$0.010 \\\\\n5  &    0.437$\\pm$0.025 &   0.438$\\pm$0.023  &   0.438$\\pm$0.011 \\\\\n6  &    0.417$\\pm$0.013 &   0.421$\\pm$0.009  &   0.430$\\pm$0.014 \\\\\n7  &    0.472$\\pm$0.010 &   0.472$\\pm$0.017  &   0.488$\\pm$0.011 \\\\\n8  &    0.457$\\pm$0.029 &   0.460$\\pm$0.020  &   0.492$\\pm$0.023 \\\\\n9  &    0.449$\\pm$0.021 &   0.460$\\pm$0.023  &   0.457$\\pm$0.019 \\\\\n\\hline\naverage & 0.430$\\pm$0.004  &  0.426$\\pm$0.004  &  0.441$\\pm$0.004 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{deltaY.eps}\n\\caption{Maximum helium difference $\\Delta$Y for ten synthetic clusters. Different symbols refer to different colors used for the determination. Blue (red) symbols stand for stars on the MS (RGB). The horizontal black solid line shows the true helium difference used to build the clusters.}\n\\label{deltaY}\n\\end{figure}\n\n\n\nTo further investigate this behavior, we show in Fig.~\\ref{chmapzoom2Ge} and Table~\\ref{tab_he_2Ge} the effect of the selection of 2Pe stars on the determination of the maximum helium difference. Choosing a larger population (population 2Pe(c)) translates into a decrease in $\\Delta$Y by $\\sim$0.03, as expected because of the inclusion of stars with less extreme Y in the 2Pe population. We also note that the values of $\\Delta$Y obtained with that selection of 2Pe stars are consistent with those obtained for other synthetic clusters reported in Table \\ref{tab_he_synth} and for which the 2Pe selection was more strict. Inversely, reducing the 2Pe population (2Pe(a) in Fig.~\\ref{chmapzoom2Ge}), but still keeping a number of stars sufficient to define the 2Pe fiducial line, leads to a larger $\\Delta$Y, which is consistent with the input value. \n\n\nFrom these experiments, we conclude that for distributions of multiple populations with small numbers of stars with large chemical enrichments, such as that of \\citet{chantereau16}, the derived maximum helium enrichment critically depends on the selection of the 2Pe population. We also find that we slightly underestimate the maximum Y of the cluster.\n\n\n\n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{plot_chmap_zoom_2Ge_000.eps}\n\\caption{Zoom into the upper left part of the chromosome map shown in the bottom panel of Fig.~\\ref{fidchmapW16}. The gray dotted lines mark the selection of 2Pe stars as in Fig.~\\ref{fidchmapW16}. The blue and red broken lines indicate alternative selections of 2Pe stars.}\n\\label{chmapzoom2Ge}\n\\end{figure}\n\n\\begin{table}[]\n\\begin{center}\n  \\caption{Effect of the selection of 2Pe stars (see Fig.~\\ref{chmapzoom2Ge}) on the determination of the maximum helium difference in synthetic cluster number 0. The first column gives the label of the 2Pe selection. The following columns give the helium difference estimated using the same three colors as in Table~\\ref{tab_he_synth}.}\n\\label{tab_he_2Ge}\n\\begin{tabular}{cccc}\n\\hline  \n2Pe selection & $\\Delta$Y$_{395N}$ & $\\Delta$Y$_{410M}$ & $\\Delta$Y$_{467M}$ \\\\     \n\\hline\n2Pe(a)  &       0.444$\\pm$0.022 &   0.448$\\pm$0.014  &   0.468$\\pm$0.019 \\\\\n2Pe(b)  &       0.458$\\pm$0.018 &   0.471$\\pm$0.011  &   0.489$\\pm$0.006 \\\\\n2Pe(c)  &       0.410$\\pm$0.040 &   0.410$\\pm$0.034  &   0.418$\\pm$0.032 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\\vspace{0.2cm}\n\n\\citet{chantereau16}  showed that the RGB contains less very enriched (Y$>$0.6) stars than the MS (see their Fig.~5).\nWe therefore expect that the determination of the maximum helium content of a GC using MS stars suffers less from the difficulties described above. To test this, we determined $\\Delta$Y as reported for RGB stars in Figs.~\\ref{fidchmapW16} and \\ref{395m814_W16} and Table~\\ref{tab_he_synth} but focusing on MS stars. Figure~\\ref{fidchmapW16_MS} illustrates our selection of stars: those with m814 magnitudes between 16.9 and 18.1. We estimate the width of the MS at m814=17.5. The 1Pe and 2Pe stars are extracted from the chromosome map as shown in the lower panel of Fig.~\\ref{fidchmapW16_MS}. The results are gathered in Table~\\ref{tab_he_synth_MS}. Compared to Table~\\ref{tab_he_synth} we see that the true helium mass fraction difference (0.472) is indeed better recovered when using MS stars. A graphical representation of this result is given in Fig.~\\ref{deltaY} where we see that depending on the cluster simulation, $\\Delta$Y based on RGB stars may be underestimated, while for MS stars, the input value is always recovered. We thus conclude that for GCs that would have stellar populations similar to those of \\citet{chantereau16}, the study of the maximum helium content should be preferentially performed on MS stars, provided sufficient data quality. \n\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{fidchmap_W16_000_MS.eps}\n\\caption{Same as Fig.~\\ref{fidchmapW16} but for MS stars.}\n\\label{fidchmapW16_MS}\n\\end{figure}\n\n\n\n\\begin{table}[]\n\\begin{center}\n  \\caption{Same as Table~\\ref{tab_he_synth} but for MS stars.}\n\\label{tab_he_synth_MS}\n\\begin{tabular}{cccc}\n\\hline  \ncluster id & $\\Delta$Y$_{395N}$ & $\\Delta$Y$_{410M}$ & $\\Delta$Y$_{467M}$ \\\\     \n\\hline\n0  &    0.464$\\pm$0.004 &   0.468$\\pm$0.005  &    0.478$\\pm$0.010 \\\\\n1  &    0.472$\\pm$0.007 &   0.478$\\pm$0.004  &    0.472$\\pm$0.009 \\\\\n2  &    0.468$\\pm$0.010 &   0.478$\\pm$0.007  &    0.482$\\pm$0.009 \\\\\n3  &    0.466$\\pm$0.009 &   0.474$\\pm$0.007  &    0.487$\\pm$0.006 \\\\\n4  &    0.473$\\pm$0.007 &   0.472$\\pm$0.010  &    0.473$\\pm$0.009 \\\\\n5  &    0.459$\\pm$0.005 &   0.474$\\pm$0.005  &    0.482$\\pm$0.003 \\\\\n6  &    0.468$\\pm$0.010 &   0.470$\\pm$0.011  &    0.475$\\pm$0.008 \\\\\n7  &    0.464$\\pm$0.008 &   0.464$\\pm$0.007  &    0.476$\\pm$0.013 \\\\\n8  &    0.466$\\pm$0.016 &   0.470$\\pm$0.015  &    0.481$\\pm$0.005 \\\\\n9  &    0.467$\\pm$0.006 &   0.478$\\pm$0.011  &    0.491$\\pm$0.006 \\\\\n\\hline\naverage & 0.465$\\pm$0.002  &  0.473$\\pm$0.002  &  0.482$\\pm$0.002 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\n\\subsubsection{Steep distribution}\n\\label{clu_steep}\n\n\nIn this section we try to answer the question of whether or not we can miss very helium-rich stars if multiple populations follow a steeper distribution than that presented by \\citet{chantereau16}. To this end, we define an artificial distribution as shown in Fig.~\\ref{distribsteep}. We start from the distribution of \\citet{chantereau16} between Y=0.248 and Y=0.29. We linearly interpolate their distribution in this range of Y, and then extrapolate the resulting distribution up to Y=0.400 (blue line in Fig.~\\ref{distribsteep}). We thus obtain a much steeper distribution of populations as a function of Y  than that of Chantereau et al. for Y$>$0.29. According to \\citet{milone18} and Sect.~\\ref{smax_ngc6752}, the maximum helium mass fraction observed in NGC~6752 is about 0.29. Our artificial distribution can therefore be seen as a test case where only a few stars with Y$>$0.29 are present in synthetic clusters. We then try to see if they are recovered or missed when determining $\\Delta$Y.\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{distribsteep.eps}\n\\caption{Black solid histogram: Relative fraction of stars as a function of their helium content on the lower RGB in the models of \\citet{chantereau16} and for an age of 13~Gyr. Blue solid line: Linear interpolation of Chantereau's distribution between Y=0.248 and 0.290, and extrapolation up to Y=0.400. Red dashed histogram: Adopted distribution based on the previous interpolation and re-scaling so that the sum of relative fractions is equal to 1.}\n\\label{distribsteep}\n\\end{figure}\n\n\nWe built ten synthetic clusters using the above distribution. We use only Y values for which isochrones are available, that is, Y=0.248, 0.260, 0.270, 0.300, 0.330, 0.370, and 0.400 (red bins in Fig.~\\ref{distribsteep}). We perform the $\\Delta$Y determination as in the previous sections. The results are gathered in Fig.~\\ref{deltaYsteep}. Using RGB stars, we are not able to recover the input value ($\\Delta$Y=0.152), but we can still detect stars with Y$>$0.29 (i.e., $\\Delta$Y=0.042). If present, and under the assumption that their distribution follows that described above, stars more helium-rich than Y=0.29 should therefore be detectable. On the MS, we confirm the trend seen in Sect.~\\ref{clu_W16} that higher values of $\\Delta$Y are recovered. However, with the present distribution, the maximum helium mass fraction of the cluster is also missed on the MS due to the very small number of highly enriched stars. This is different from Sect.~\\ref{clu_W16} where on the MS the initial value of $\\Delta$Y could be retrieved. \n\n\n\n\\begin{figure}[]\n\\centering\n\\includegraphics[width=0.49\\textwidth]{deltaYsteep.eps}\n\\caption{Same as Fig.~\\ref{deltaY} but for the distribution of the population described in Sect.~\\ref{clu_steep}. The gray area marks the observed value of $\\Delta$Y in NGC~6752.}\n\\label{deltaYsteep}\n\\end{figure}\n\n\n\\section{Discussion}\n\\label{s_disc}\n\nOur method for determining the maximum helium mass fraction in GCs is slightly less automated than that presented by \\citet{milone18}. In particular, the selection of the extreme 1Pe and 2Pe populations is made visually in our case, while it relies on a more sophisticated treatment in \\citet{milone18}. We tested the effect of the 2Pe selection in Sect.~\\ref{clu_W16} and Fig.~\\ref{chmapzoom2Ge}, and argue that the choice of 2Pe stars can affect the value of the maximum Y. However, qualitatively, stars much more He-rich than the observed limit of 0.042 are easily detected regardless of the 2Pe selection. In addition, the automated method of \\citet{milone18} works well when 2Pe stars are clearly identified by an overdensity in the chromosome map, but there are clusters for which no such overdensity is visible. For instance, the chromosome map of NGC~6752 itself, presented in the bottom panel of Fig.~\\ref{fidchmap6752}, shows a rather uniform distribution along the 2G sequence (i.e., from the bottom right corner up to the upper left corner). Hence, we argue that the choice of 2Pe stars in our study is not drastically different from \\citet{milone18}.\n\n\nHe-rich populations may be contaminated by blue stragglers and their descendants which would populate similar regions of CMDs. \\citet{marino19} showed that candidate evolved blue stragglers should be located preferentially along the 1P sequence, and thus would not contaminate 2Pe stars. However, one may wonder whether blue stragglers resulting from the merger of two 2P stars could produce stars along the 2P sequence too. This needs to be investigated further.  \nBinaries can also contaminate the 2P sequence. As shown by \\citet{martins20}, the presence of a companion among RGB stars will tend to displace a star up and left in the chromosome map. The magnitude of the displacement depends on the relative brightness and effective temperature of the two stars. Hence, stars along the 2G sequence, with medium Y but with a companion, may be moved to the position of single stars with higher Y. Consequently, the extremity of the 2G sequence may contain stars with less extreme Y. This could lead to overestimation of the maximum Y. The binary fraction among GCs is low, usually below 10\\% \\citep{sollima07,milone12,jb15}, and their effect on the maximum Y should therefore be limited; unless the number of very He-rich stars is also small, as in the distribution of \\citet{chantereau16}. In any case, if binaries are present, the maximum Y determined from photometry is probably overestimated.\n\n\nWith these limitations in mind, and given the results of the present study, it is unlikely that  NGC~6752 contains stars with Y$\\gtrsim$0.3. If multiple populations were formed as predicted by the FRMS scenario developed by \\citet{decressin07} and \\citet{chantereau15,chantereau16}, a wide distribution of Y, from 0.248 to 0.72, should be present among stars either on the MS or the RGB, with ~39$\\%$ of the stars with Y$>$0.3 and ~10$\\%$ with Y$>$0.4 at 13~Gyr. Our study reveals that while we may not retrieve the most helium-rich objects on the RGB, we should still be able to detect stars with Y as high as 0.65 (see Fig.~\\ref{deltaY}). This is clearly in contrast with results based on HST photometry indicating Y no higher than 0.3. We have shown that even in the case of a Y distribution much steeper than that predicted by \\citet{chantereau16} we would be able to find stars with helium enrichment beyond the observed value.\n\nA prediction of our study dedicated to NGC~6752 is that the maximum helium content of GC stars, if it follows a distribution where helium-rich stars are less numerous than helium-poor ones, is best determined on the MS rather than on the RGB. This is due to the faster evolution of He-rich stars and consequently the larger number of stars on the MS than on the RGB \\citep{dm73,dantona10,chantereau16}. \nHowever, the maximum Y we obtain on the MS using HST data of NGC~6752 does not indicate a significant difference compared to the value found on the RGB.\n\nAll in all, the present results strongly suggest that stars in NGC~6752 do not follow the distribution predicted by the FRMS model presented in \\citet{chantereau16}, and consequently, multiple populations were not likely formed out of material polluted by this type of object.\nThis conclusion applies only to NGC~6752, and additional studies of clusters with different ages, metallicities, and masses are required to see whether generalizations can be made. A wider study of this kind is necessary to investigate whether or not the current observational limit of Y$\\sim$0.4 is robust and to investigate whether or not it suffers from observational limitations. As recalled in Sect.~\\ref{s_intro}, this limit is a key prediction of some models, but also a building block of some others. In particular, the formation of multiple populations caused by pollution of material ejected from a super-massive star (SMS) originally {assumes} that the SMS stops its evolution when its core helium content reaches 0.4, and is further dislocated by instabilities and\/or strong stellar winds \\citep{denis14}. This assumption was dictated  by the observational fact that Y appears to be no higher than 0.4 in the most extreme GC populations. On the other hand, hot-hydrogen burning products with low helium abundances in agreement with the photometric constraints can be ejected by SMSs in the case where they are continuously rejuvenated by runaway stellar collisions \\citep{Gieles2018}.\n\nPollution by material produced in massive AGB stars predicts that the helium distribution among multiple populations reaches a maximum of $\\sim$0.38 \\citep[e.g.,][]{dercole10}. This is consistent with the current observational limit, and would make these objects good polluter candidates if other problems were not linked to their use, as summarized in \\citet{Renzini2015} and \\citet{bastianlardo18} for instance. Other important factors are the time constraints on the dilution by pristine material, as also highlighted by \\citet[][see also \\citealt{dercole16}]{dercole11}, and the mass budget issue \\citep[e.g.,][]{PC2006,Krause2016}. The transformation of the Na-O correlation in AGB ejecta into a Na-O anti-correlation, as seen in all GCs, also requires specific conditions for mixing of pristine material with nucleosynthesis products \\citep[e.g.,][]{Ventura2008,Karakas2010}. In addition, the C+N+O sum of AGB ejecta is not conserved \\citep{Decressin2009}, contrary to what is deduced from spectroscopic analysis of stars in NGC~6752 \\citep{yong15}. \n\nThe role of massive binaries in the multiple population phenomenon remains to be investigated. \\citet{demink09}  showed that these objects could potentially produce the required abundance patterns. But their study is limited to a 20+15 M$_{\\sun}$\\ system on a 12-day orbit and in which both components have reached synchronization. The average helium mass fraction of the ejecta of this binary system is 0.3. Material ejected at later phases of the system's evolution has Y as large as $\\sim$0.63 (see Fig.~1 of de Mink et al.). The average helium content is therefore consistent with the current maximum Y observed in GCs. However binary evolution depends not only on the properties and evolution of the  components, but also on the parameters of the  system (separation, eccentricity, mass ratio, mass transfer efficiency); see for example \\citet{menon20}. Additionally, the maximum central temperature of the considered mass domain does not reach the high values required to build the Mg-Al anti-correlation \\citep[e.g.,][]{prantzos07,Prantzos2017}. A wider study involving population synthesis is therefore required to assess the impact of massive binaries on the origin of multiple populations in GCs.  \n\n\n\n\n\n\\section{Conclusion}\n\\label{s_conc}\n\nIn this study, we investigated the determination of the maximum helium mass fraction in stars of the GC NGC~6752. Our goal was to decipher whether we really detect the most He-rich stars with present-day\nphotometric methods, or miss them.\nWe relied on the work of \\citet{chantereau16} who produced isochrones with various chemical compositions corresponding to different degrees of pollution by FRMS which is an extreme case in terms of He enrichment. We computed synthetic spectra along these isochrones using the atmosphere code ATLAS12 and the spectral synthesis code SYNTHE. The resulting spectra were used to compute synthetic photometry in the following HST filters: WFC3 F275W, WFC3 F336W, WFC3 F410M, WFC3 F467M, ACS F606W, and ACS F814W. We compared the synthetic colors with data of NGC~6752 obtained by \\citet{milone13}. The different CMDs are usually reasonably well reproduced, although offsets exist between synthetic and observed sequences (MS, TO, RGB).\n\nWe re-determined the maximum helium mass fraction of stars in NGC~6752 using a method very similar to that of \\citet{milone18}. Our results are consistent with those of Milone at al.\nWe built synthetic clusters with various populations characterized by their He content (they also have different composition in light elements). We validated our method on simple population distributions, ensuring that we are able to recover the input maximum Y. We subsequently created synthetic clusters following the distribution presented by \\citet{chantereau16}, that is, with stars with Y of between 0.248 and 0.72. We show that on the RGB, we slightly underestimate the maximum Y, but by a relatively small amount ($\\sim$0.05). On the MS, we retrieve the input value. In any case, even on the RGB the maximum Y we determine in synthetic clusters is higher than the observed value of 0.042$\\pm$0.004 \\citep{milone18}. We tested that even if populations followed a steeper Y distribution than that of \\citet{chantereau16}, stars with Y higher than 0.042 are recovered (in that case the maximum Y is underestimated both on the RGB and MS). Finally, we determined the maximum Y on the MS of NGC~6752 using HST data and find it to be consistent with the value obtained on the RGB.\n\nThese results indicate that multiple populations in NGC~6752 have a Y distribution that is very likely not that assumed by \\citet{chantereau16} in the framework of the FRMS scenario. Our results also show that in the specific case studied here, the maximum helium mass fraction determined from observations is probably the true value (i.e., there are no stars more He-rich in that cluster). \nWe stress that although we have focused on the specific case of pollution by FRMS, our results apply to any scenario that would predict a strong He enrichment among 2P stars \\citep{Salarisetal2006,Pietrinferni2009,Cassisi2013,Dotter2015}.\nOur results need to be extended to other clusters spanning a range of parameters (age, metallicity, mass) in order to confirm that FRMSs are not responsible for the multiple populations in GCs and to better constrain the scenario that produce them. \n\n\n\\section*{Acknowledgments}\n\nWe thank an anonymous referee for a positive report. We thank A. Milone for sharing HST photometry of NGC~6752 and for interesting discussions. This work was supported by the Swiss National Science Foundation (Project 200020-192039 PI C.C.). This work was supported by the Agence Nationale de la Recherche grant POPSYCLE number ANR-19-CE31-0022.\n\n\\bibliographystyle{aa}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzihft b/data_all_eng_slimpj/shuffled/split2/finalzzihft
new file mode 100644
index 0000000000000000000000000000000000000000..6f6b81c1b9b9b78f733ab4442a8d99bb158659a5
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzihft
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\nOne of the widely accepted mechanisms\nof planet formation is the core-nucleated instability theory (Perri \\& Cameron 1974; Haris 1978; Mizuno\net al. 1978; Stevenson 1982). According to this scenario, the massive gaseous atmosphere would\nbe accumulated in a runaway manner when the core mass reaches a critical value.\nIn static models, when heating balances cooling,\nrunaway accretion occurs when the planet is beyond the critical mass,\nbecause the envelope fails to hold hydrostatic equilibrium. Rafikov (2006) found\na broad range of critical mass ($0.1 M_{\\oplus} \\le M_{\\rm critical} \\le 100 M_{\\oplus}$)\ndue to various disk properties and planetesimal accretion rate.\nHowever, in dynamic or quasi-static models, the thermal disequilibrium\nrather than the hydrostatic disequilibrium plays the dominant role.\nThe runaway accretion occurs because the envelope becomes thermally unstable\nas the cooling timescale becomes catastrophically shorter.\nIn this case, the runaway accretion is driven by\nrunaway cooling (Bodenheimer \\& Pollack 1986; Lee et al. 2014; Piso \\& Youdin 2014).\nThree stages are involved in the formation process. In the first stage,\nrocky cores grow by rapid planetesimal accretion. In the second stage, the core's feeding zone is depleted of solids and the atmosphere grows gradually, regulated by the KH contraction. Finally, when the atmosphere reaches the crossover mass,\ngas runaway takes place and the planet gets inflated into a gas giant. The timescale of second stage is the longest among\nthe three and dominates whole formation process (Pollack et al. 1996).\n\n\nAbout 20\\% of Sun-like stars host super-Earths with radii of 1-4 $R_{\\oplus}$ at distance 0.05-0.3 AU (Howard et al. 2010; Batalha et al. 2013; Petigura et al. 2013).\nRadial velocity measurements (Weiss \\& Marcy 2014) and transit timing variations (Wu \\& Lithwick 2013) manifest that\n masses of these super-Earths are in the range of 2$-$20 $M_{\\oplus}$.\nThe abundance of super-Earths presents a puzzle for the core instability theory.\nThis theory indicates that when a protoplanet reaches the super-Earth size, two physical processes\nmake the survival of super-Earths difficult, leading to a planetary ``desert\" in this size range (Ida \\& Lin 2004).\nSuper-Earths would excite density waves in PPDs and give rise to rapid type I migration.\nThis type of migration would cause the planet to be engulfed by its host star if the disk\ninner edge touches the stellar surface.\nRecent studies have sought various remedies\nfor type I migration (Yu et al. 2010; Fung \\& Chiang 2017).\nPPDs are expected to have an inner edge at the stellar magnetosphere (e.g., Long et al. 2005). For planets undergoing disk-driven migration, they are expected to pile up near this edge. They would stay either at the edge because the gas runs out, or inside the edge down to 2:1 resonance because that's where the tidal torque will taper off, or outside the edge as the standing waves generated by wave reflection off the inner edge stall planet migration (Tsang 2011).\nIn this paper we would focus on another threat for super-Earths.\nSuper Earths have low mean density, which suggests that they must\nbe surrounded by gas envelopes (Rogers \\& Seager 2010).\nSince these observed super-Earths are in the range of critical mass,\nthey would trigger efficient gas runaway and accumulate massive gas envelope.\nThey would become gas giants. As a result, super-Earths are supposed to be rare.\nHowever, the Kepler's discovery wreck these predictions. Lee et al. (2014) has proposed\nmetallicity gradient inside the PPDs or late assembly of cores to\nresolve the puzzle of super-Earth formation. Lee \\& Chiang (2016) stressed\nthat the late core assembly in transitional PPDs is more consistent with\nobservations. In gas-poor environments, gas dynamical friction has\nweakened to allow proto-cores to stir one another and merge.\nIn addition, this formation scenario ensures that super-Earth cores accrete mass\nwith a few percent envelope mass fraction (EMF).\n\n\n\n\n\nGuillot \\& Showman (2002) argued that the dissipation of kinetic energy of atmospheric wind,\ndriven by intense irradiation, could bury heat inside the planet.\nMany studies extend this idea to explain the radius anomaly of hot Jupiters\n(Youdin \\& Mitchell 2010; Ginzburg \\& Sari 2015; Komacek \\& Youdin 2017).\nThese investigations focus on the late evolution after the disk dispersal.\nUnfortunately, this is invalid for the early evolution of super-Earths because they are still\nembedded within disks. The irradiation may not penetrate the\ndisk and is not able to bury heat in the exoplanets.\n\nHowever, we note that\ntidal interactions between the host star and planet can periodically perturb the planet\nand generate mechanical forcing of the fluid motions (Zahn 1977; Goldreich \\& Nicholson 1989).\nHeating by tidal dissipation in primordial super-Earth envelope can inhibit the gas cooling (Ginzburg \\& Sari 2017).\nThis mechanism requires the orbital eccentricity of super-Earths be continuously pumped.\nBut super-Earths may not be massive enough to clear a clean gap to excite orbital\neccentricity (Goldreich \\& Sari 2003).\nAnother important aspect about tidal interaction is that \ntidally-forced turbulent mixing would induce heat transport inside the planets.\nRecent laboratory experiment shows that turbulence could penetrate deep inside the\nplanet interior (Cabanes et al. 2017).\nBy combining laboratory measurements and high resolution simulations, Grannan et al. (2017)\nconfirmed the generation of bulk filling turbulence inside planet driven by tidal forcing.\nTurbulent mixing plays an essential role in heat transport in strongly stratified environments (Garaud \\& Kulenthirarajah 2016).\nThis motivates us to study the effects of turbulent diffusion on the planet's thermal evolution.\nPrior studies have noticed that the turbulent mixing induced by mechanical forcing\nleads to heat transport inside hot Jupiters (Youdin \\& Mitchell 2010).\nThese tides would produce appreciable thermal feedback and may lead to interior radiative zones, enhancing\ng-mode dissipations with a wide spectrum of resonances (Jermyn et al. 2017).\nWe find that the thermal feedback associated with the externally-forced turbulent stirring\nmay greatly alter the accretion history of super-Earths.\n\n\n\nIt is well known that the timescale of gas accretion is dictated by the KH timescale.\nIn other words, accretion is determined by the planet's ability to cool (Lee \\& Chiang 2015).\nIn this paper, we note that\nthe tidally-forced turbulent diffusion influences the heat transport inside the planet's envelope.\nThermal feedback would be induced by turbulent diffusion.\nThe heat transport associated with tidally-forced turbulent diffusion\nwould reduce the cooling luminosity\nand enhance the KH timescale.\nWe find that turbulent diffusion may have significant effects\non the planet accretion history\\footnote{In our\ncalculation, turbulent diffusion coefficient $\\mu_{\\rm turb}\\sim 10^{7} - 10^{9}$ cm$^2$ s$^{-1}$,\ncomparable to typical\n$\\mu_{\\rm turb}\\sim 10^{6}-10^{10}$ cm$^2$ s$^{-1}$ in solar system planets (de Pater \\& Lissauer  2001).}.\nBased on our calculations, we propose that tidally-forced turbulent diffusion would effectively\nhelp super-Earths evade growing into gas giants.\n\n\n\nThis paper is structured as follows. In section 2, we provide a brief description of the accreting\nplanet envelope with tidally-forced turbulent diffusion.\nIn section 3, we compare the planet interior thermal\nprofile with and without turbulent diffusion, discussing the thermal feedback\ninduced by turbulent diffusion, especially the shift of RCBs.\nIn section 4, we depict the cooling luminosity variations and onset of gas runaway.\nThe quasi-static Kelvin-Helmholtz evolution and critical turbulent diffusivity\nare discussed in Section 5. In Section 6, we discuss the mass loss\nmechanisms for super-Earths and the limitation of super-Earth formation by the turbulent diffusion.\nSummary and conclusions are given\nin Section 7.\n\n\\section{Accreting Envelope with Tidally-Forced Turbulence}\nSuper-Earths are susceptible to runaway accretion (Pollack et al. 1996).\nThe ability to accrete is determined by the planet's power to cool (Lee \\& Chiang 2015).\nHow super-Earths avoid rapid gas runaway\ndepends critically on the cooling history of planet, which is closely related to\nthe thermal structure of the envelope.\nIn the convectively stable region, the turbulent diffusion would induce heat transport within the planet.\nIn this section we will concentrate on the thermal feedback caused by tidally-induced turbulent diffusion.\n\n\\subsection{Thermal structure of Gaseous Envelope}\nSince the planet's ability to cool depends on planets' thermal structure of the envelope,\nwe first study the gaseous envelope structure of planets,  i.e.,  the distribution of pressure,\ntemperature, and mass around a protoplanetary core with mass $M_{\\rm c}$ embedded\nwithin the protoplanetary nebular.\nThe planet envelope (or, interchangeably ``atmosphere'') structure is governed by the following equations of mass\nconservation, hydrostatic equilibrium, thermal gradient, and energy conservation\n(Kippenhahn et al. 2012) :\n\\begin{equation}\n\\frac{d M_r}{d r} = 4 \\pi \\rho r^2 \\ ,\n\\end{equation}\n\\begin{equation}\n\\frac{d P}{d r} = - \\frac{G M_r}{r^2} \\rho \\ ,\n\\end{equation}\n\\begin{equation}\n\\frac{d T}{d r} = \\nabla_{\\rm } \\frac{T}{P} \\frac{d P}{d r} \\ ,\n\\end{equation}\n\\begin{equation}\n\\frac{d L}{d r} = \\frac{d M_r}{d r} \\left( \\epsilon - T\\frac{\\partial s}{\\partial t} \\right) \\ ,\n\\end{equation}\nwhere $G$  is  the gravitational constant, $P$ is the pressure, $\\rho$ is the density,\n$T$ is the temperature,  $L$ is the luminosity,\nand $M_r$ is the mass, including the core mass\nand the atmosphere mass,  enclosed inside the radius $r$,\n$M_r = M_{\\rm atm} + M_{\\rm c}$.\nThe symbol ``$\\nabla$\" denotes the temperature gradient\ninside the envelope.\nThe energy generation $\\epsilon$ is set to zero since there is no nuclear reaction\ninside the planet.\nThe above equations implicitly indicate\nthat the envelope quickly adjusts and dynamical timescale is shorter\nthan the accretion timescale (Rafikov 2006).\nNote that the right hand side term, $-T\\frac{\\partial s}{\\partial t}$, in the energy equation dictates the cooling process.\nReplacing the local energy equation by a global energy equation would greatly reduce the\nnumerical tasks and we need only deal with ODEs rather than PDEs\n(Piso \\& Youdin 2014; Lee et al. 2014). Details will be discussed in Section 3.\n\nThe energy transport in the convective region is very efficient and\nthe temperature gradient is\\footnote{This assumption is mainly made for simplicity\nof the models, they are not necessarily correct (Stevenson 1985; Leconte \\& Chabrier 2012).\nWe are working on including the mixing length theory (e.g Kippenhahn et al. 2012) to\nbetter quantify the issue of super-adiabaticity.}\n\\begin{equation}\n\\nabla = \\nabla_{\\rm ad} = \\left( \\frac{d \\ln T}{d \\ln P}\\right)_{\\rm ad} \\ .\n\\end{equation}\nThe convective and radiative layers of the envelope are specified by\nthe Schwarzschild criterion: the atmosphere is stable against\nconvection when $\\nabla < \\nabla_{\\rm ad} $ and convectively\nunstable when $\\nabla \\ge \\nabla_{\\rm ad} $. Since the convective energy\ntransport is efficient, $\\nabla = \\nabla_{\\rm ad}$ in the convective region.\nThe actual temperature gradient can be expressed as\n\\begin{equation}\n\\nabla_{\\rm } = \\min(\\nabla_{\\rm ad}, \\nabla_{\\rm rad}) \\ .\n\\end{equation}\nIn this paper, we adopt a polytropic index $\\gamma=7\/5$ for an ideal\ndiatomic gas and the adiabatic gradient $\\nabla_{\\rm ad} = (\\gamma-1)\/\\gamma$.\nNote that the realistic equation of state (EOS) would change the value of $\\nabla_{\\rm ad}$\nand the effects of realistic EOS will be left for future studies.\n\n\n\n\nThe radiative temperature gradient\n\\begin{equation}\n\\label{radTgrad}\n\\nabla_{\\rm rad} = \\frac{3 \\kappa L P}{64\\pi\\sigma G M_r T^4} \\ ,\n\\end{equation}\nwhere $\\kappa$ is the opacity. \nIn the upper part of the atmosphere, the exact\nvalue of $\\kappa$ is highly uncertain because the amount of dust and the dust size\ndistribution are not well constrained in PPDs.\nLee et al. (2014) studied both dusty and dust-free atmosphere and\nfound that the radiative-convective boundaries (RCBs) are determined by\nH$_2$ dissociation at an almost fixed temperature $\\sim$2500 K for dusty atmosphere.\nThey also found the for dust-free atmosphere, the radiative region keeps an almost\nisothermal temperature fixed by the envelope outer surface.\nTechnically, the opacity laws can be written as a power law as a function\nof pressure and temperature whether or not the total opacity is dominated\nby dust grains. For these reasons, we adopt a power law opacity\n(Rafikov 2006; Piso \\& Youdin 2014; Ginzburg et al. 2016), by assuming that\n\\begin{equation}\n\\kappa = \\kappa_0 (P\/P_0)^{\\alpha} (T\/T_0)^{\\beta} \\ .\n\\end{equation}\nHere we choose  $\\kappa_0 = 0.001$cm$^{2}$g$^{-1}$,  which allows our\nfiducial model without turbulent diffusion to possess properties of more\nsophisticated super-Earth models (Lee et al. 2014).\nWhat is important is the opacity near the RCB. In that sense,\nit is important to keep in mind that the power-law indices\n$\\alpha$ and $\\beta$ can change significantly within the envelope (and with distance from the star).\nWe have tried different choices of $\\alpha$ and $\\beta$. We find that, as long as the\nparameter $\\alpha$ and $\\beta$ satisfy $\\nabla_0 \\equiv \\frac{1+\\alpha}{4-\\beta} > \\nabla_{\\rm ad}$,\nour results are robust and insensitive to the choices we made\\footnote{\nIn later part of this paper, we present the results with $\\alpha=1$, $\\beta = 1$,\nwhich ensures the existence of the inner convective region and outer radiative region\ninside the planet gas envelope.  For details, please refer to discussions in Rafikov (2006)\nand  Youdin \\& Mitchell (2010).}.\n\n\n\n\n\n\n\nConventionally, it is believed that solid cores accrete planetesimal\nand gas simultaneously (Pollack et al. 1996; Bodenheimer et al.\n2000).\nHowever, estimation shows that the termination epoch\nof accretion of solids is well before the accretion of gas.\nThe dust coagulation timescale can be as short as\n$t_{\\rm coagulate} \\sim 10^4$ yr especially\nwhen the planet is close to the central host (Lee et al. 2014).\nThis timescale is much shorter than typical disk dispersal timescale ($\\sim$ 0.5$-$10 Myr).\nIn addition, calculations by\nLee \\& Chiang (2015) showed that planetesimal accretion does not generically prevent runaway.\nAs a result, it is physically valid to set the planetesimal\naccretion rate to zero ($L_{\\rm acc}=0$)\nwhen we study accreting super-Earths within the disk.\nIn this case, the core is free to cool and contract, and it is  extremely susceptible to the gas runaway.\n\n\n\nNote that the above differential equations are essentially identical\nto the usual planet interior structure equations. The distinction is the thermal\nfeedback generated by tidally-forced turbulent mixing inside the stably stratified region.\nMore specifically, $\\nabla_{\\rm rad}$ is affected by the turbulent diffusion, which will\nbe further discussed in the next section.\n\n\n\n\\subsection{Thermal Feedback by Tidally-Forced Turbulent Mixing}\nHow do super-Earths evade becoming gas giants?\nIn this paper, we propose a robust mechanism to avoid runaway accretion.\nDue to the tidal forcing, the planet's gas envelope would be stirred and\nthe turbulent motion may be initiated.\nDetailed analyses of these processes are rather complex\nand beyond the scope of this paper (e.g., Garaud \\& Kulenthirarajah 2016; Grannan et al. 2017).\nIn this paper, we try to constrain the turbulent diffusion\nthat is necessary to influentially affect the planet accretion timescale.\nWe find\nthat even weak turbulence would affect the planet accretion history significantly.\n\n\nSince the sound-crossing time is much shorter than\nthe time for heat to diffuse across the fluid blob, the blob conserves entropy (i.e. adiabatically) and keeps\npressure equilibrium with the ambient environments when it displaces over a radial\ndistance $\\ell$.\nThe temperature difference between the blob and its surroundings is\n\\begin{equation}\n\\delta T = \\left(\\frac{d T}{dr}\\bigg|_{\\rm ad} - \\frac{d T}{dr} \\right) \\ell =  - \\frac{\\ell  T}{c_p} \\frac{d s}{dr} \\ .\n\\end{equation}\nThe heat excess associated with these fluid blobs can be written\nas $\\delta q = \\rho c_p \\delta T$ and the corresponding turbulent heat flux is\n$F_{\\rm turb} = v \\delta q$, where $v$ is the characteristic speed of turbulent eddies.\nThe entropy gradient can be put down as\n\\begin{equation}\n\\frac{d s}{d r} = \\frac{ g}{T \\nabla_{\\rm ad} } (\\nabla_{\\rm ad} - \\nabla) \\ ,\n\\end{equation}\nwhere $g$ is the gravitational acceleration. This equation\nindicates that in the stably stratified region ($\\nabla < \\nabla_{\\rm ad}$),\nthe entropy gradient is positive ($ds\/dr>0$). The heat flux by turbulent mixing is\nthen\n\\begin{equation}\nF_{\\rm turb} = v\\delta q = \\rho c_p v \\delta T = - \\rho g v  \\ell\n \\left( 1- \\frac{\\nabla}{\\nabla_{\\rm ad}} \\right) \\ .\n\\end{equation}\nThe flux is negative for stable stratification.\nFor a thermal\nengine without external forcing, heat always flows from hot to cold regions.\nHowever, with external mechanical forcing by tides, heat flows from cold\nto hot regions becomes feasible (Youdin \\& Mitchell 2010).\nNote that the turbulent diffusion coefficient $\\mu_{\\rm turb} \\equiv v \\ell$\\footnote{Note that $\\mu_{\\rm turb} = K_{zz}$, a symbol widely used in the community of planetary atmospheres.} and the corresponding luminosity  is\n\\begin{equation}\nL_{\\rm turb} = 4 \\pi r^2  \\left[ - \\rho g \\mu_{\\rm turb}  \\left( 1- \\frac{\\nabla}{\\nabla_{\\rm ad}} \\right) \\right] \\ .\n\\end{equation}\nThe total luminosity is carried by two components, the radiative and the turbulent\n\\begin{equation}\nL = L_{\\rm rad} + L_{\\rm turb}   \\  .\n\\end{equation}\nWe note that the temperature gradient in the radiative region\ncan be arranged in a compact form as (see Appendix A for details),\n\\begin{equation}\n\\nabla^{\\rm }_{\\rm rad} = \\frac{1 + \\eta }{1\/\\nabla^{(0)}_{\\rm rad} + \\eta\/\\nabla_{\\rm ad}}  \\  .\n\\end{equation}\nIn the above equation,\n\\begin{equation}\n\\nabla^{(0)}_{\\rm rad} \\equiv \\frac{3 \\kappa P L}{64\\pi\\sigma G M_r T^4} \\ ,\n\\end{equation}\nand\n\\begin{equation}\n\\eta \\equiv \\frac{4 \\pi \\mu_{\\rm turb} G M_r \\rho}{L} = 4 \\pi \\left( \\frac{M_{\\rm c}}{M_{\\oplus}} \\right) \\nu_{\\rm turb} \\left(\\frac{M_r}{M_{\\rm c}} \\right)  \\left( \\frac{\\rho}{\\rho_{\\rm disk}} \\right)   \\ ,\n\\end{equation}\nwhere the superscript ``(0)\" indicates the radiative temperature gradient without turbulence\\footnote{This equation is actually\nthe same as the equation (\\ref{radTgrad}) in this paper.} and  $M_{\\rm c}$ is the mass of the solid core.\nIt can be readily shown that the following inequality holds in\nradiative region  $\\nabla^{(0)}_{\\rm rad} < \\nabla < \\nabla_{\\rm ad}$ (see Figure 3 for the\npseudo-adiabatic region).\nHere we stress that it is the turbulent diffusion driven by external tidal forcing that makes $\\nabla$\nsteeper than $\\nabla_{\\rm rad}^{(0)}$. This inequality has significant implications for\nthe thermal feedback induced by tidally-forced turbulent diffusion.\nAn interesting issue is that radiative zones would be enlarged and the cooling luminosity\nwould be greatly reduced.\n\nHere we define two dimensionless parameters\n\\begin{equation}\n\\label{turb_def}\n\\nu_{\\rm turb} \\equiv \\frac{\\mu_{\\rm turb}}{L\/(GM_{\\oplus}\\rho_{\\rm disk})} \\ , \\ \\zeta \\equiv \\frac{\\mu_{\\rm turb}} { H_p c_s} \\ .\n\\end{equation}\nThe two parameters represent the strength of turbulence. In the definition of $\\zeta$,\n$H_p\\equiv -d r\/d\\ln P$ and $c_s$ are pressure scale height and sound speed, respectively.\nIt is obvious that, if the turbulence in the radiative region is negligible, i.e., $\\eta = 0$,\nthe temperature gradient recovers its usual definition,\n$\\nabla_{\\rm rad} \\rightarrow \\nabla^{(0)}_{\\rm rad}$.\nIn section 5.1, we will give a physical estimation of the parameter $\\zeta$ based on our calculations. We will\nsee that small value of $\\zeta \\sim 10^{-6} - 10^{-5}$ has already appreciable effects on the\nformation of super-Earths. This mechanism is robust in the sense that even weak turbulence is\nadequate for it to operate.\nWe should keep in mind that one limitation is that the turbulence strength is parameterized,\nnot physically specified. This is an important issue which still remains to be addressed, i.e.,\nforcing turbulence induced by tides\nshould be investigated in further detail (Barker 2016; Grannan et al. 2017).\n\n\n\n\n\n\n\n\n\n\n\\subsection{Boundary Conditions}\nThe density and temperature at the outer boundary of the atmosphere are given\nby the nebular density and temperature. We adopt the minimum mass extrasolar nebula (MMEN) model\nof Chiang \\& Laughlin (2013). According to MMEN, the disk structure reads,\n\\begin{equation}\n\\rho_{\\rm disk}= 6\\times 10^{-6} \\left(\\frac{a}{0.1 {\\rm AU}} \\right)^{-2.9} {\\rm g \\ cm^{-3}} \\ ,\n\\end{equation}\n\\begin{equation}\nT_{\\rm disk} = 1000 \\left( \\frac{a}{0.1 {\\rm AU}} \\right)^{-3\/7} {\\rm K} \\ .\n\\end{equation}\n\nThe inner boundary lies at the surface of the inner core.\nThe core density is assumed to be $\\rho_{\\rm core} = 7$g cm$^{-3}$, the core mass\nis 5 $M_{\\oplus}$ and the core radius is $R_{\\rm core}$ = 1.6 $R_{\\oplus}$.\nThe outer boundary condition is chosen at the smaller of the Bondi radius and Hill radius,\nwhich are\n\\begin{equation}\nR_H \\approx 40 R_{\\oplus} \\left[ \\frac{(1+{\\rm EMF}) M_{\\rm core}}{5 M_{\\oplus}}\\right]^{1\/3} \\left( \\frac{a}{0.1 {\\rm AU}}\\right)  \\ ,\n\\end{equation}\n\\begin{equation}\nR_B \\approx 90 R_{\\oplus} \\left[ \\frac{(1+{\\rm EMF}) M_{\\rm core}}{5 M_{\\oplus}}\\right] \\left( \\frac{1000 {\\rm K}}{T}\\right)  \\ ,\n\\end{equation}\nrespectively.\n\n\n\n\n\n\\section{Thermal Properties of Gas Envelopes}\nSince the thermal cooling timescale is intimately related to the planet interior structure,\nwe first describe the interior structure of the gaseous envelope.\nTo avoid the complication induced by sandwiched convection-radiation structure\ninside the planet interior (Ginzburg \\& Sari 2015; Jermyn et al. 2017),\nwe simply consider a two-layer model, i.e.,\na convective interior and a radiative exterior (Piso \\& Youdin 2014).\n\nWe adopt the assumption that the luminosity, $L$, is spatially constant, which\nis valid in radiative region if the thermal relaxation timescale is shorter than thermal times in the rest\nof the atmosphere. The validation of such assumption is corroborated by\nPiso \\& Youdin (2014) and  Lee et al. (2014).\nTo get thermal profiles within the envelope, a luminosity $L$\nis required to obtain $\\nabla_{\\rm rad}$ before we numerically integrate the structure\nequations.\nThe spatially constant $L$ is treated as an eigenvalue of the ODEs.\nTo get the eigenvalue numerically, we first give a guess value of $L$ and\nre-iterate the integration until the mass at the core, $m(R_{\\rm c})$,\nmatches the actual mass $M_{\\rm c}$. Note that, once the luminosity is found,\nthe location of radiative-convective boundary (RCB) can be specified accordingly.\n\n\n\\subsection{Envelopes without Heat Transport by Turbulent Mixing}\nFor the convenience of comparison, we first consider a fiducial model, i.e.,\nan envelope without turbulence ($\\nu_{\\rm turb} = 0$).\nIn Figure \\ref{AtmProfile}, we show the radial profiles of pressure, temperature, and density of\nthe envelope for a 5$M_{\\oplus}$ core with increasing envelope mass during atmospheric growth.\nThe green, cyan and yellow curves denote the envelope mass fraction (EMF) = 0.1, 0.4, 0.8, respectively.\nThe thicker and thinner parts stand for the convective and radiative region, respectively.\nThe boundaries of the thicker and thinner part are the radiative-convective boundaries (RCBs).\nThe convective region is adiabatic.\nThe radiative region connects the lower entropy interior to the higher entropy exterior.\nIn Figure \\ref{AtmProfile}, we note that the pressure in the convection zone increases with\nenvelope mass, but the temperature only varies slightly.\nSince the entropy is $\\propto \\ln(T^{1\/\\nabla_{\\rm ad}}\/P)$,\nit is clear that, with increasing envelope mass,\nthe steady-state envelopes evolve in order of decreasing entropy (Marleau \\& Cumming 2014).\nThis is consistent with the cooling process that the envelope experiences,\nwhich allows the atmosphere to accrete more gas.\n\n\nLee et al. (2014) found that, for dusty atmosphere, the location of RCBs lies\nat an roughly fixed temperature where H$_2$ dissociates ($\\sim$ 2500K).\nIn Figure \\ref{AtmProfile}, the RCB lies at the bottom\nof the outermost radiative region and the temperatures at the RCBs are no longer 2500K.\nThis is because we adopt a grain-free atmosphere due to efficient grain coagulation (Ormel 2014).\nAccording to the middle panel of Figure \\ref{AtmProfile},\nwe find that grain-free atmosphere behaves differently from grain-rich atmosphere.\nThe outer radiative region is nearly isothermal, which implies that $T_{\\rm RCB} \\sim T_{\\rm out}$.\nSuch features have also been identified in Lee \\& Chiang (2015, 2016) and Inamdar \\& Schlichting (2015),\nwhich can be readily understood\nin terms of the following relation (Rafikov 2006; Piso \\& Youdin 2014)\n\\begin{equation}\n\\frac{T_{\\rm RCB}}{ \\ T_{\\rm out} }  \\sim \\left(1 - \\frac{\\nabla_{\\rm ad}}{\\nabla_0} \\right)^{-1\/(4-\\beta)}  \\sim 1 \\  .\n\\end{equation}\nThe term on the right hand side of this equation is around the order of unity.\nThis explains why the temperature at RCB, $T_{\\rm RCB} \\sim T_{\\rm out}$.\nWe would stress that, the above relation is only valid for atmosphere without turbulence.\nWhen heat transport by turbulent mixing is taken into account, the RCB is pushed inwards,\nand the temperature at the RCB ($T_{\\rm RCB}$) becomes higher.\n\n\n\nAt the early stage of accretion, the envelope mass is small and\nthe envelope can be well treated as non-self-gravitating.\nIn this case, simple analytic results can be derived (Rafikov 2006; Piso \\& Youdin 2014).\nThough the envelope we consider in this paper is self-gravitating, these analytical results\nare still very instructive to understand atmospheric evolution and interpret our\nnumerical results.  How the position of the RCBs\nvaries with envelope mass can be understood with the following relations (Piso \\& Youdin 2014),\n\\begin{equation}\n\\label{LMrelation}\n\\frac{M_{\\rm atm}}{M_{\\rm c}} = \\frac{P_{\\rm RCB}}{\\xi P_{\\rm M}}  \\ , \\\n\\frac{P_{\\rm RCB}}{ \\ P_{\\rm disk} } \\sim \\ e^{R_{\\rm B}\/R_{\\rm RCB} } \\ .\n\\end{equation}\nwhere $\\xi$ is a variable on the order of unity and $P_{\\rm M}$ is the characteristic pressure that is\nrelated to the core mass (Piso \\& Youdin 2014).\nIn the early stage of planet accretion, with the increase of envelope mass, the pressure at\nRCB would increase as well.\nAccordingly, the cooling luminosity would be reduced.\nWhen the self-gravity becomes important, the above relations no longer hold.\nThe stronger luminosity is necessary to support the more massive envelope.\nWith the increase of luminosity, the RCB would be shifted outward\nas shown in Figure \\ref{AtmProfile} (Ginzburg \\& Sari 2015).\n\n\n\n\\begin{figure}\n\\includegraphics[scale=0.75]{AtmProfileRevise.eps}\n\\caption{\\label{AtmProfile}\nThermal profiles around a planet core\nwith mass $M_{\\rm c} = 5 M_{\\oplus}$ at 0.1 AU.\nTurbulence is not included, $\\nu_{\\rm turb} = 0$.\nThe pressure, temperature, and density are shown in the upper, middle, and lower panels,\nrespectively.  In each panel,\nthe green, cyan, yellow lines stand for $M_{\\rm atm}\/M_{\\rm c} = $ 0.1, 0.4, 0.8,\nrespectively.\nWith the increase of envelope mass, the pressure at RCBs always increases.\nHowever, the position of RCBs inside the planet first decreases and then increases.\nThis non-monotonic behavior is\ndue to the effects of self-gravity (Piso \\& Youdin 2014).\nNote in particular that no pseudo-adiabatic region appears in the envelope (cf. Figure \\ref{AtmProfile_with_turb}).\n}\n\\end{figure}\n\n\n\n\\subsection{Envelopes with Heat Transport by Turbulent Mixing}\nIn this section, we explore how turbulence ($\\nu_{\\rm turb} \\neq 0$) changes the structure\nof the planet envelope.\nThe most interesting feature is that the turbulence would push the RCBs\ninwards and diminish the cooling luminosity.\nIn Figure \\ref{AtmProfile_with_turb}, we show the planet thermal profiles for envelope\nmass fraction, $M_{\\rm atm}\/M_{\\rm c} =$ 0.2, 0.4 and 0.8.\nThe core mass $M_{\\rm c}  = 5 M_{\\oplus}$.\nIn Figure \\ref{AtmProfile_with_turb}, we find that the difference\nis that a pseudo-adiabatic region appears.\nExplicitly, we point out the location of the pseudo-adiabatic region\nin the middle panel of Figure \\ref{AtmProfile_with_turb}.\nIn such regions, the temperature gradient is\nvery close to adiabatic gradient, but still smaller than adiabatic gradient (see Figure \\ref{TempGradVsP}).\n\nFrom middle panel of Figure \\ref{AtmProfile}, we see that,\nwhen the heat transport by turbulent diffusion is not included,\nthe RCB lies around the isothermal radiative region, $T_{\\rm RCB}\\sim T_{\\rm out}$.\nWhen turbulent diffusion is included, the temperature gradient would deviate\nfrom the isothermal approximation, which is most obvious by comparing middle panels of Figure\n\\ref{AtmProfile} and Figure \\ref{AtmProfile_with_turb}.\nWe can identify from Figure \\ref{TempGradVsP}, that the temperature gradient near\nRCBs is approaching $\\nabla_{\\rm ad}$ and clearly deviates from isothermal temperature\ngradient. Due to this temperature gradient deviation, a pseudo-adiabatic region appears.\nAs a result, the temperature at RCB becomes higher and RCBs would penetrate deeper inside\nthe envelope.\n\n\\begin{figure}\n\\includegraphics[scale=0.75]{AtmProfile_with_turbRevise.eps}\n\\caption{\\label{AtmProfile_with_turb}\nThe same as Figure \\ref{AtmProfile}, but for a turbulent envelope with $\\nu_{\\rm turb} = 0.016$.\nThe pseudo-adiabatic region is most clearly visible when comparing the middle panel of Figure 1 and Figure 2.\nDue to the presence of pseudo-adiabatic region, the RCBs are pushed inwards. The temperature at RCBs\nbecomes higher when heat transport by tidally-forced turbulent mixing is taken into account.\n}\n\\end{figure}\n\nTo better understand the effects of heat transport by turbulent mixing,  we compare the profiles of planet\nenvelope with and without turbulence. The results are shown in Figure \\ref{TempGradVsP}\nas red solid and blue dashed lines, respectively.\nThe upper panel shows the global variation of temperature with pressure\nwithin the envelope.\nIn this panel, the difference between the two cases with and without turbulence\nis hardly discernible.\nThe middle panel shows again the variation of temperature with pressure but\nfocuses on the localized region around the radiative-convective transition region.\nIt shows that the turbulent mixing smoothes\nthe transition toward the adiabat.\nThere would appear a pseudo-adiabatic region above the\nactual adiabatic region. This pseudo-adiabatic region pushes the RCB inward to higher pressure.\nTurbulent mixing leads to a more gradual approach to adiabat.\n\n\nThe turbulent diffusion in stably stratified region provides heating, instead\nof cooling so it is natural to expect that with turbulent diffusion taken into\naccount, the total cooling rate of envelope will decrease and KH\ncontraction timescale would be prolonged (see Figure \\ref{LVsMatm} for details).\n\n\n\n\n\\begin{figure}\n\\includegraphics[scale=0.65]{TempGradVsP.eps}\n\\caption{\\label{TempGradVsP}\nThermal profiles of planet envelope. The EMF  $M_{\\rm atm}\/M_{\\rm c} =  0.1 $.\n{\\it Upper panel:} The blue dashed curve represents the\nenvelope without turbulence.\nThe red solid curve denotes envelope with turbulence, $\\nu_{\\rm turb} = 0.016$.\nThe RCBs are denoted as blue and red dots.\nThe two temperature profiles are very similar and difficult to\ndistinguish.\n{\\it Middle panel:} To identify their differences,\nwe show the two profiles near the radiative-convective transition region.\nThe red curve shows a more gradual transition from the radiative\nto adiabatic region. The region between the blue dot and red dot is the\npseudo-adiabatic region.\n{\\it Bottom panel:} The ratio of temperature gradient to adiabatic gradient.\nThe region with $\\nabla\/\\nabla_{\\rm ad} = 1$ is the convection zone.\nThe region with $\\nabla\/\\nabla_{\\rm ad} < 1$ is the radiative zone.\nIn the pseudo-adiabatic region, $\\nabla$ is\nvery close to $\\nabla_{\\rm ad}$, but still smaller than $\\nabla_{\\rm ad}$.\nThe RCBs shift inwards  when heat transport by turbulent mixing\nis taken into account. The RCBs penetrate deeper with stronger turbulent mixing.\n }\n\\end{figure}\n\n\n\\section{Onset of Gas Runaway and Cooling Luminosity Variations}\nSince we are interested in the planet accretion history,\nit is necessary to investigate the luminosity with increasing envelope mass.\nIn the deep atmosphere, heat is advected by convective eddies.\nNear the surface, this could be achieved by diffusion. The surface temperature\ngradients would become shallower and a radiative region shows up.\nThe variations of luminosity with envelope mass is shown in Figure \\ref{LVsMatm}.\nWith the accumulation of envelope mass, the luminosity reaches a minimum.\nBeyond this minimum, the luminosity $L$ increases. As a result, the planet begins to cool at a very\nshort timescale and the envelope mass would grow super-linearly after this epoch.\nPhysically, it is natural to adopt the epoch when the minimum $L$ is reached as the\nonset of gas runaway, $t_{\\rm run}$.\n\nOn the right hand side of luminosity minimum, the luminosity-mass relation is relatively\neasy to understand. At this late stage of mass growth, the self-gravity\nof envelope appears to be prominent, and greater\nluminosity is necessary to support stronger gravity.\nHowever, on the left hand side of the luminosity minimum,\nthe mass of envelope is small and the planet is at the its early stage\nof mass growth.\nAt this early stage (envelope's self-gravity can be ignored),\nthe luminosity diminishes with a thicker radiative outer layer and more massive envelope.\nThis reduction in cooling luminosity is intimately related to the shift of RCBs.\nWhen the envelope self-gravity can be ignored,\nthe luminosity at RCB can be written as (Piso \\& Youdin 2014)\n\\begin{equation}\nL_{\\rm RCB} = \\frac{64\\pi \\sigma G M_{\\rm RCB} T^4_{\\rm RCB}}{3 \\kappa P_{\\rm RCB}} \\nabla_{\\rm ad}\n\\approx \\frac{L_{\\rm disk} P_{\\rm disk}}{P_{\\rm RCB}} \\ ,\n\\end{equation}\nwhere  $M_{\\rm RCB}$ and $L_{\\rm disk}$ reads\n\\begin{equation}\nM_{\\rm RCB} = \\frac{5\\pi^2}{4}\\rho_{\\rm RCB} R_{\\rm B}^{\\prime}\\sqrt{R_{\\rm RCB}} \\ , \\\nL_{\\rm disk} \\approx\n\\frac{64\\pi\\sigma G M_{\\rm RCB} T_{\\rm disk}^4}{3 \\kappa_{\\rm d} P_{\\rm disk}} \\nabla_{\\rm ad}  \\ .\n\\end{equation}\nThe above equations can be written in terms of known properties if the envelope\nmass is centrally concentrated (see, e.g., Lee \\& Chiang 2015).\nThis central concentration is physically expected since in deeper layers where temperatures\nrise above $\\sim2500$K, hydrogen molecules dissociate. As energy is spent on dissociating H$_2$\nmolecules rather than heating up the gas, the adiabatic index drops below 4\/3, to approach 1.\nThe upshot is that both the densities at the RCB and the radiative luminosity\ncan be written in terms of core properties and the temperature at the RCB.\n\n\nAs RCB deepens, the RCB becomes even more\noptically thick so it is harder to radiate energy away; as a result, the\nenvelope cools more slowly.\n\n\n\n\nIn Figure \\ref{LVsMatm}, we stress that two important aspects of thermal\nevolution during the planet accretion would be\naffected by turbulent mixing. The first is that it influences the luminosity.\nIn Figure \\ref{LVsMatm}, we know that when the turbulent diffusivity ($\\nu_{\\rm turb}$) is enhanced, the\ncooling luminosity would be reduced globally.\nThat is, for any particular value of envelope mass, the cooling luminosity for\nan envelope with turbulence is always below that without turbulence.\nWhen the turbulence is stronger, the luminosity becomes even smaller.\nThe second is that it changes the EMF at which the gas runaway occurs.\nIn Figure \\ref{LVsMatm}, our calculations show that,\nwhen the turbulence becomes stronger, the onset of gas runaway takes place\nat higher envelope mass fraction (EMF).\n\n\n\n\n\n\\begin{figure}\n\\includegraphics[scale=0.75]{LVsMatm.eps}\n\\caption{\\label{LVsMatm}\nThe luminosity $L$ varies non-monotonically with envelope mass.\nThe results for $\\nu_{\\rm turb} = 0,  0.005,  0.016$ are shown in\nblue solid, green dot-dashed, and red dashed lines, respectively.\nThe luminosity minimum is reached at $M_{\\rm atm}\/M_{\\rm c}$\n= 0.86, 1.16, 1.20, respectively.\nWhen the envelope mass is small, the increase of envelope mass\ncauses the luminosity to decrease. When the envelope mass is sufficiently large,\nthe self-gravity of gas envelope become important, and bigger\nluminosity $L$ is necessary to support stronger gravity. We choose\nthe luminosity minimum as the epoch when the runaway accretion sets in.\nWe note that two important aspects of thermal evolution during the planet accretion would be\naffected. With the enhanced turbulence, the cooling luminosity is reduced globally.\nWhen the turbulence becomes stronger, the onset of gas runaway occurs\nat a higher envelope mass fraction.\n}\n\\end{figure}\n\n\n\n\n\n\n\n\\section{Quasi-Static KH Evolution and Critical Turbulent Diffusivity}\n\nSince we ignore the accretion luminosity from the planetesimals,\nthe gravitational KH contraction is the only source for the cooling.\nThe gas accretion is regulated by the KH timescale.\nOur time evolution model\ncan follow the envelope mass growth up to the very early epoch of\nrunaway growth around the crossover mass.\nFortunately, Pollack et al. (1996) found that the timescale spent in the runaway accretion stage\nis orders of magnitude smaller than the KH timescale. The mass growth\ntimescale is  actually dominated by the KH stage. For this reason,\nour model can get rather accurate estimation of mass growth timescale of an accreting planet.\nIn this section, we will explore how the turbulent mixing affect the KH contraction timescale.\nFor strong turbulent diffusion, the heat transport may even inflate the planet (Youdin \\& Mitchell 2010).\nWe are not interested in planet inflation induced by strong turbulence in this paper. We find that even\nweak turbulence can already play an essential role to delay the KH contraction.\n\n\n\n\n\n\\subsection{ Time evolution: Temporally Connecting Snapshots }\nIn the previous section, we have obtained snapshots of envelope\nstructure for different envelope masses.\nTo estimate the accretion timescale,\nwe need to connect them temporally in order of increasing mass.\nThe gas accretion history can be followed\nby the cooling process (Piso \\& Youdin 2014).\nDetailed estimation shows the luminosity generated in the radiative\nregion can be safely ignored (Lee et al. 2014).\nIt is physically valid to assume the luminosity of the envelope is generated\nin the convective zone and the luminosity can be treated as constant in the\nouter radiative zone (Piso \\& Youdin 2014).\nThis would greatly simplify our evolutionary calculations.\nUnder such circumstances, we only need to solve a set of ordinary differential equations and connect\nthe solutions in time.\nLee \\& Chiang (2015) shows that it is physically valid to omit\nplanetesimal heating during the gas accretion of super-Earths.\nWhen there is no planetesimal accretion to power the gas envelope,\nthe time interval between two adjacent hydrostatic snapshots is the\ntime it spends to cool between them.\nIn addition to internal energy variations, gas accretion and envelope contraction\nalso bring about changes to the global energy budget.\nSpecifically, the time interval between two steady state solutions can be written as (Piso \\& Youdin 2014)\n\\begin{equation}\\label{budget}\n\\Delta t = \\frac{-\\Delta E + \\langle e\\rangle\\Delta M - \\langle P\\rangle\\Delta V_{\\langle M\\rangle}}{\\langle L\\rangle} \\ .\n\\end{equation}\nNote that the symbol $\\Delta$ designates the difference between\nthe two adjacent states and the bracket denotes the average of them.\nThe total energy $E$ consists of the internal energy and\nthe gravitational potential energy, which reads\n\\begin{equation}\nE = \\int_{M_c}^{M_{}} u \\ d M_r - \\int_{M_c}^{M_{}} \\frac{G M_r}{r} d M_r\\ ,\n\\end{equation}\nwhere $u$ is the specific internal energy, $u = c_{\\rm v} T$.  The second term in\nequation (\\ref{budget}) stands for contribution from gas accretion. The specific energy of the accreting gas\nis $e = - G M_r \/r + u$. The third term in equation (\\ref{budget}) accounts for $P dV$ work done by the envelope\ncontraction.\nAll terms are calculated at the RCB. Note in particular that the volume difference\nbetween two adjacent snapshots are performed at fixed mass.\nWe choose the fixed mass as the average of the masses at the RCB (Piso \\& Youdin 2014).\n\n\n\\begin{figure}\n\\includegraphics[scale=0.65]{timescale_new.eps}\n\\caption{\\label{timescale}\n{\\it Upper panel} :\nThe accretion history for $\\nu_{\\rm turb} =$ 0, 0.0016, 0.005, and 0.016 is shown\nas cyan dot-dashed, blue solid, green dotted, red dashed lines, respectively.\nThe initial time for the accretion is estimated as $t_0 = |E|\/L$.\nThe slightly different starting time is due\nto the luminosity decrease by the inclusion of turbulence (see Figure \\ref{LVsMatm}).\nThe initial EMF is around 6\\%, where the planet is nearly fully convective.\nDifferent color dots in the upper panel denote the epoch, $t_{\\rm run}$, when the gas runaway takes place.\nThe runaway time is $t_{\\rm run} =$ 4.04, 10, 18.4, and 48.3 Myrs,\nrespectively. The solid blue curve shows the critical solution, where $t_{\\rm run} = t_{\\rm disk}$.\nThe critical diffusivity for  $M_{\\rm core} = 5 M_{\\oplus}$ is\n$\\nu_{\\rm critical}\\sim 1.6\\times10^{-3}$ if $t_{\\rm disk}=10$ Myrs.\n{\\it Lower panel} : The critical $\\nu_{\\rm critical}$ for various core mass. For higher core\nmass, the critical $\\nu_{\\rm critical}$ is higher.\nWe note that a weak turbulence with small diffusivity,\n$\\mu_{\\rm turb} \\sim 10^{7} -10^{8}$ cm$^2$ s$^{-1}$, can already enhance\nthe runaway timescale and delay the gas runaway. \n}\n\\end{figure}\nIn the upper panel of Figure \\ref{timescale}, we shown the planet mass growth\nhistory for different turbulent diffusivity.\nIn our fiducial model without turbulence, $t_{\\rm run}\\sim$ 4.04 Myrs.\nBeyond this epoch, the gas runaway occurs.\nThe gas runaway is due to the fast increase of $L$ beyond $t_{\\rm run}$,\nwhich leads to a rapid cooling process on a shorter timescale.\nThe most intriguing feature is that\nthe runaway time is delayed and accretion timescale is prolonged\nwhen heat transport by tidally-forced turbulent mixing is taken into account.\nFor instance, when $\\nu_{\\rm turb} = 0.0016, 0.005, \\ 0.016$, the runaway time,\n$t_{\\rm run} = 10, \\ 18.4, \\ 48.3$ Myr, respectively.\nThe stronger the turbulence, the longer the gas runaway timescale.\n\nIn our calculations, we find that a small value of\n$\\nu_{\\rm turb}$, on the order of $10^{-3}$, can already appreciably affect\nthe cooling timescale of super-Earths.  Since $\\nu_{\\rm turb}$ is dimensionless,\nit is better to recover its physical value according to Equation (\\ref{turb_def}).\nTypically, luminosities for super-Earths are $L \\sim 10^{26}$erg\/s,\n$M_{\\oplus} = 5.97 \\times 10^{27}$g, and $\\rho_0 = 6\\times 10^{-6}$ g cm$^{-3}$.\nThen the term, $L\/(GM_{\\oplus}\\rho_0)$, defined in Equation (\\ref{turb_def})\nis approximately $ \\sim 4.2 \\times10^{10}$ cm$^2$ s$^{-1}$.\nFor the dimensionless diffusivity $\\nu_{\\rm turb} = 0.0016$, the physical diffusivity\nis approximately $\\mu_{\\rm turb} \\sim 4.2 \\times 10^{7}$ cm$^2$ s$^{-1}$.\nFor even larger $\\nu_{\\rm turb}$,\nthe K-H contraction timescale can be enhanced by orders of  magnitude.\nAccording to Figure \\ref{timescale}, it is evident that the turbulent diffusivity on the order\n$\\sim 10^7 - 10^{8}$ cm$^2$ s$^{-1}$ can already\nenhance the runaway timescale by an oder of magnitude.\nThe pressure scale height inside the planet is $H_p \\sim 10^9$ cm and the sound speed\nis $c_s \\sim 10^5$ cm s$^{-1}$. \nWe can get a physical sense how large the turbulent diffusivity is by estimating\nthe dimensionless parameter $\\zeta$ in Equation (\\ref{turb_def}).\nIn our calculation, the parameter $\\zeta$ is pretty small, on the order\nof $10^{-7}\\sim 10^{-6}$. This means that the turbulent diffusion\nnecessary to prolong the cooling timescale needs not to be very strong.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection{Critical Turbulence Diffusivity $\\nu_{\\rm critical}$ and Super-Earth Formation}\n\nA gas giant would be formed if the protoplanetary disk is still full of gas when\nthe planet enters the runaway accretion stage. However,\nif the runway time $t_{\\rm run}$ is longer than the disk lifetime $t_{\\rm disk}$,\nthe disk gas is depleted and the planet is unable to accrete sufficient gas to become a gas giant,\nthen a super-Earth may be formed.\nTwo timescales, $t_{\\rm run}$\nand $t_{\\rm disk}$, determine the ultimate destiny of the planet,\ni.e., whether the planet becomes a super-Earth\nor a gas giant. If $t_{\\rm run} < t_{\\rm disk}$, gas runaway occurs within the lifetime of\ndisk. The planet would get inflated by the runaway gas accretion and become a gas giant.\nOn the contrary, if $t_{\\rm run} > t_{\\rm disk}$, the disk disperses before the gas\nrunaway takes place. Because there is not enough gas material for the planet to accrete, the planet is\nunable to become a gas giant. Usually the disk life is about $5-10$ Myr.\nTo be specific, we take the disk lifetime as $t_{\\rm disk} = $ 10 Myrs throughout this paper.\n\nIn the upper panel of Figure \\ref{timescale}, the core mass fixed at $M_{\\rm core} = 5 M_{\\oplus}$.\nWe find that there exists a critical diffusivity $\\nu_{\\rm critical} = 1.6\\times 10^{-3}$.\nWhen $\\nu_{\\rm turb}> \\nu_{\\rm critical}$, the K-H contraction timescale\nbecomes longer than the disk lifetime and the core would not be able to experience the gas runaway.\nIn this case, the formation of gas giants can be avoided and the formation of super-Earths becomes viable.\nIn the lower panel of Fig. \\ref{timescale}, we show the variations of $\\nu_{\\rm critical}$\nwith $M_{\\rm core}$. The critical diffusivity becomes larger when the core mass increases.\nSpecifically, for a 10 Earth mass core, the critical dimensionless diffusivity is approximately\n$\\nu_{\\rm critical } = 3.2\\times10^{-2}$. The actual diffusivity is about $\\sim 10^{9}$ cm$^{2}$ s$^{-1}$.\n\n\n\n\n\n\n\n\n\n\\subsection{Variations of $\\nu_{\\rm critical}$ with Planet Location in PPDs }\nObservationally, the Kepler statistics show that $\\sim$20\\% of Sun-like stars harbors super-Earths\nat distance of 0.05-0.3 AU. By contrast, the occurrence rate\nfor hot Jupiters inside $\\sim 0.1$ AU is only 1\\%. To explain these observational features,\nwe consider how the turbulence affects the thermal evolution for planets\nat different locations in PPDs.\nThe turbulent mixing considered in this paper is driven by the tides raised by the host star.\nWe believe that the tidally-induced turbulent mixing inside the planet\nwould become weaker when the planet is farther away from the host star.\n\nLee et al. (2014) found that, for dusty disk, the runaway timescale is independent of\nthe orbital location. However, since dust can not persist in the envelope due to\ncoagulation and sedimentation (Ormel 2014; Mordasini 2014), \nthe runaway timescale is no longer independent of the orbital location.\nIn the upper panel of Figure \\ref{semimajor}, we show the accretion\nhistory for planets at three different locations. The core mass is $M_{\\rm c} = 6 M_{\\oplus}$.\nThe blue solid, green dot-dashed, and red dashed curves\ndesignate the temporal variations of envelope mass for  $a = $ 0.1AU, 1AU, and 5AU, respectively.\nThe turbulent diffusivity is  $\\nu_{\\rm turb} = 0.013$. The gas runaway occurs at\n$t_{\\rm run} $= 33.1, 3.2, and 1.7 Myrs.  It is clear that gas accretion\nonto cores is hastened for planets that are farther away from the central star.\nThis behaviour can be understood from the decrease in opacity\nat the RCB which makes the envelope more transparent, enhancing the rate of cooling\n(Lee \\& Chiang 2015; Inamdar \\& Schlichting 2015).\nThe planet at $a = $ 1AU  and 5 AU would become a gas giant due to\nrunaway accretion ($t_{\\rm run} < t_{\\rm disk}$).\nHowever, the planet in the inner region $a= $ 0.1 AU would become a super-Earth ($t_{\\rm run} > t_{\\rm disk}$).\nThe fact that atmospheres cool more rapidly at large distances as\ndust-free worlds has been used to explain the presence of extremely puffy, low mass planets\n(Inamdar \\& Schlichting 2015; Lee \\& Chiang 2016).\n\n\nWe explore the critical diffusivity, $\\nu_{\\rm critical}$, for planets at\ndifferent locations inside the minimum mass extrasolar nebula (MMEN).\nThe results are shown in the lower panel of Figure \\ref{semimajor}.\nIt shows that the critical diffusivity increases with the semi-major axis.\nWhen the planet is farther from the central star, $\\nu_{\\rm critical}$ becomes larger.\nThis means that the more distant planet requires stronger turbulence\nto lengthen the KH timescale and avoid gas runaway.\nFor tidally-induced forcing, we believe that the turbulent diffusion $\\nu_{\\rm turb}$ is determined by\nthe tides inside the planet raised by host star. The tides become weaker if the planet is farther away\nfrom the host star.\nOur proposed mechanism can naturally explain the formation of close-in super-Earth,\nwhile still ensuring the gas giant formation at larger orbital distance.\nWhen the planet is near the host star, tidally-forced turbulent mixing is stronger and $\\nu_{\\rm turb}$ would be larger.\nAccording to Figure \\ref{semimajor}, the required threshold $\\nu_{\\rm critical}$ is smaller,\nAs a result, the inequality $\\nu_{\\rm turb} > \\nu_{\\rm critical}$ can be more readily\nto satisfy and formation of super-Earth becomes possible.\nOn the contrary, when the planet is far from the host star, $\\nu_{\\rm turb}$ becomes smaller as the stirring by\ntides becomes weaker. The required threshold $\\nu_{\\rm critical}$ becomes larger.\nThe threshold to avoid gas runaway is more difficult to satisfy.\nThis indicates that, in the in-situ planet formation scenario,\nit is more readily to form close-in super-Earths\nand gas giants are more prone to appear in the outer region of PPDs.\nThe above implication is consistent with occurrence rate inferred from observations.\n\n\n\n\n\n\n\n\n\n\n\\begin{figure}\n\\includegraphics[scale=0.7]{semimajor_new.eps}\n\\caption{\\label{semimajor}\n{\\it Upper panel} : Variations of envelope mass with time.\nThe core mass is $M_{\\rm c} = 6 M_{\\oplus}$. The turbulent\ndiffusivity is $\\nu_{\\rm turb} = 0.01$. The blue solid, green dot-dashed, red dashed lines denote\nmass growth history for planets at 0.1 AU, 1 AU, and 5 AU, respectively.\nThe critical mass ratio at the epoch of runaway decreases for more distant planet.\nThe runaway time for the three different cases are 33.1, 3.2, and 1.7 Myr, respectively.\nIt is expected that for more distant planets, larger turbulent diffusivity is required to prevent\nrunaway gas accretion within $t_{\\rm disk} \\sim$ 10 Myrs.\n{\\it Lower panel} : The critical diffusivity, $\\nu_{\\rm critical}$, for different orbital locations, required\nto prevent gas runaway for disk lifetime $t_{\\rm disk} \\sim$ 10 Myrs.\nBeyond $\\nu_{\\rm critical}$, the KH timescale is longer than the disk lifetime.\nThe formation of super-Earths becomes possible.\n }\n\\end{figure}\n\n\n\n\n\n\\section{Mass Loss Mechanisms}\nObservation shows that super-Earths possess hydrogen and helium\nenvelopes containing only several percent of the planet's mass.\nHowever, we can see in Figure \\ref{timescale} that the planets accrete\nvery massive gas envelopes.\nThe planet core with $\\nu_{\\rm turb}=0$ reaches an envelope mass fraction (EMF)\nof $\\sim 0.8$ at the epoch of gas runaway.\nThe envelope mass is considerably higher than the mass inferred from observations.\nThese primordial super-Earths may experience\nsignificant mass loss during the post-formation evolution.\n\nHow super-Earths lose their mass still remains an open question.\nHere we briefly mention some possible ways to lose the envelope mass.\nThe first possibility is that close-in planets are exposed to intense XUV (extreme UV\nand X-ray) irradiation from their host stars. Photoevaporation\ncan significantly modify the structure of their atmosphere.\nOver the timescale of $\\sim 100$ Myrs, X-rays from host stars can photoevaporate\nthe super-Earth envelopes from initial EMF $\\sim 1$ to EMF of $\\sim 0.01-0.1$,\nwhich may naturally explain the differences between\nthe theoretical predictions and observational facts (e.g., Murray-Clay et al. 2009;\nOwen \\& Wu 2013; Owen \\& Wu 2017; Gaudi et al. 2017).\n\nGiant impact is the second possible mechanism to explain the mass loss,\nwhich is expected to be common because they are needed to provide\nlong-term orbital stability of planetary systems (Cossou et al. 2014).\nHydrodynamical simulations show that a single collision between similarly sized exoplanets\ncan easily reduce the envelope-to-core-mass ratio by a factor of two.\nSuper-Earths' asymptotic mass can be achieved by one or two giant impacts.\nUnder certain circumstances, almost 90\\% of the gas envelope can be\nlost during impact process (Liu et al. 2015; Inamdar \\& Schlichting 2016).\n\n\nMass transfer between the close-in planet and host star via Roche lobe represent the third way to\nreduce the planet mass (Valsecchi et al. 2015; Jia \\& Spruit 2017; Jackson et al. 2017).\nTidal dissipation can drive orbits of these primordial super-Earths to decay toward the Roche limit.\nThe mass transfer is quite rapid, potentially leading to complete removal of the gaseous envelope in a few Gyr,\nand leaving behind a super-Earth.\nMany gaseous exoplanets in short-period orbits are on the verge or are in the process of Roche-lobe overflow (RLO).\nThe coupled processes of orbital evolution and RLO likely shape the observed distribution of close-in exoplanets and may even be responsible for producing some of the short-period rocky planets. But recent calculations by Dosopoulou et al. (2017) challenged this idea by claiming that,  for high eccentric planets or retrograde planets, self-accretion by\nthe planet would slow down the mass loss rate via Roche lobe overflow.\n\n\nSuper-Earth envelope mass fractions range just 1-10\\% and more typically just $\\sim$1\\%\n(see Rogers \\& Seager 2010, Lopez \\& Fortney 2014, Wolfgang \\& Lopez 2015).\nThe mechanism discussed in this paper overpredicts the envelope mass fraction of super-Earths, often beyond 80\\%.\nPhotoevaporation, even around Sun-like stars, are only effective out to ~10 days and many super-Earths lie beyond this (see, e.g., Figure 8 of Owen \\& Wu 2013). Removal of $>$90\\% of the envelope by giant impact requires impact velocity that exceeds the escape velocity (see, e.g., Figure 3 of Inamdar \\& Schlichting 2016). Finally, Roche lobe overflow only works within ~2 stellar radii where the Roche radius is.\nLee \\& Chiang (2016) proposed that the late-time formation of cores ensures that super-Earth\ncores accrete a few percent envelope mass fraction, in agreement with the observations.\nThere is a clear difference in the expected final envelope mass fraction\nbetween their work and ours.\n\nVery recent works have revealed that planetary envelopes embedded within PPDs\nmay not be in hydrostatic balance, which slows down envelope growth. It\nis possible for a steady state gas flow enters\nthrough the poles and exits in the disc mid-plane (Lambrechts \\& Lega 2017).\nIn the presence of a magnetic field and weakly ionizing winds,\nohmic energy is dissipated more readily for lower-mass planets.\nOhmic dissipation would make super-Earths more vulnerable to atmospheric evaporation (Pu \\& Valencia 2017).\nThese findings may offer new explanations for the typical low-mass envelopes around the cores of Super-Earths.\nIn addition, we also note that the turbulent\ndiffusion mechanism may be still operating in the late core assembly scenario.\nIn the late core assembly scenario without turbulent diffusion, the asymptotic EMF is about 3-5\\% (Lee \\& Chiang 2016).\nWhen turbulent diffusion is taken into account, the EMF can be further reduced to 1\\%.\n\n\n\n\n\n\\section{Summary and Conclusion}\n\nIn this paper, we propose a new mechanism to avoid gas runaway for planet cores\nwithin the lifetime of disks.\nThe mechanism proposed in this paper is not subject the $\\kappa$ or $\\mu$\ncatastrophe (Lee \\& Chiang 2015). Tidal heating (Ginzburg \\& Sari 2017) requires\norbital eccentricity be continuously pumped up during super-Earth formation.\nOur mechanism does not depend on the orbital eccentricity of super-Earth.\nIncorporating this model into a population synthesis model may better constrain our\nunderstanding of the exoplanet formation (Ida  \\&Lin 2004; Jin \\& Mordasini 2017).\n\nWe have explored the effects of heat transport induced by tidal stirring on the thermal\nstructure of stably stratified, radiative layers of super-Earths,\nfocusing on their influences on the KH timescale.\nWhen we take turbulent stirring into account,\npseudo-adiabatic regions would show up within the radiative zone.\nThis may push the RCBs inwards.\nThe temperature, pressure at RCBs becomes higher and the cooling luminosity would be reduced.\nAs a result, the KH timescale would be enhanced.\nWe find that\nthere exist a critical turbulent diffusivity $\\nu_{\\rm critical}$. When\n$\\nu_{\\rm turb} > \\nu_{\\rm critical}$, the runaway time is greater than\nthe disk lifetime ($t_{\\rm run}  > t_{\\rm disk}$). Under such circumstances,\nthe onset of the planet gas runaway lags behind the disk gas depletion.\nSince the planet has not enough gas to accumulate, it can no longer grow\ninto a gas giant and become a super-Earth instead. In addition, we also investigate\nthe variations of $\\nu_{\\rm critical}$ with planet's semi-major axis in MMEN.\nOur calculations show that the condition for turbulence-induced formation of super-Earths\nis more readily satisfied in the inner disk region, but is harder to satisfy in the outer\ndisk region. The occurrence rate of super-Earths and gas giant is consistent our calculations.\n\n\nThe extent of radiative region has important implication\nfor the tidal dissipations inside the planet.\nThe turbulence pushes the RCBs inwards and produces enlarged radiative zones.\nSince the internal gravity waves can\npropagate inside the radiative zone, the variations of this resonant cavity\nwould significantly influence the dissipation of internal gravity waves.\nThis would greatly influence the propagation and dissipation of internal\ngravity waves inside the radiative zone (Jermyn et al. 2017).\nAnother effect is that the transition between convective zone to radiative zone is smoothed.\nThe radiative zone is thickened and\nthis bears important implications for the internal gravity wave\nexcitation and propagation (Lecoanet \\& Quataert 2013).\nThis would have appreciable effects on the thermal tides inside the planet.\nThese issues will be addressed in a further study.\n\n\nA limitation of this work is that the turbulence strength is not specified from first principle.\nAs a compromise, we parameterize the turbulence diffusion as a free parameter. We try\nto constrain the turbulence strength in terms of the planet thermal evolution. Interestingly,\nwe find the turbulence in the radiative region  have substantial effects on the planet\naccretion history.\nHow turbulence is initiated during the planet formation and how strong the turbulent diffusion\nis involve very complicated physical processes, which are worth further investigations.\n\n\nRealistic opacities and EOS have influential effects on\nthe planetary thermal structure and the core accretion process (e.g. Stevenson 1982;\nIkoma et al. 2000; Rafikov 2006),\nespecially for timescale of the KH timescale (Lee et al. 2014; Piso \\& Youdin 2014).\nOur simple prescription of opacity needs to be improved.\nGuillot et al. (1994)\nshowed that an convective layer lies between two adjacent radiative\nregion due to the opacity window near $\\sim$ 2000K.\nA relevant caveat is the existence of radiative zones sandwiched inside convective interior.\nSuch radiative windows are ignored in our two-layer models.\nIt would be interesting\nto consider how a downward turbulent heat flux would interact with such\na sandwiched region. In summary, how super-Earth envelope cooling\nhistory responds to more realistic opacities and EOS needs to be further investigated.\nCalculation with realistic EOS and opacity are underway and will be reported elsewhere.\n\n\nWe have found that the epoch of runaway accretion can be effectively\ndelayed by the turbulent diffusion within the stably stratified region. But we should be cautious that\nthe envelope mass fraction predicted by this mechanism is not fully consistent with observations.\nThe envelope mass fraction for planet embedded within the gas-rich MMEN is greater than 80\\%, much higher\nthan the typical super-Earth envelope.\nIt is difficult for the turbulent diffusion alone to make the envelope mass fraction be consistent with observations.\nAdditional physical process, such as giant impact, photo-evaporation, Roche-lobe overflow may be operating to\nreduce the envelope mass fraction during\nthe formation of super-Earth.  But these mass loss processes either operate on distances shorter\nthan most super-Earths or are applicable under certain circumstances. A promising mechanism for super-Earth formation\nis the late core assembly within the transitional PPDs. In this scenario, with the reduction of the\nPPD mass density, the envelope mass fraction can be as low as 3-5\\% (Lee \\& Chiang 2016). We note that the turbulent diffusion\nmay be still working in the late core assembly scenario. How turbulent diffusion affect the envelope\nmass fraction within transitional PPDs is an interesting issue worth further investigation.\n\n\n\\acknowledgments\nWe thank the anonymous referee for the thoughtful comments that greatly improve this paper.\nDiscussions about heat transport inside planet interior\nwith Yanqin Wu and Re'em Sari are highly appreciated.\nThis work has been supported by National Natural\nScience Foundation of China (Grants 11373064,  11521303, 11733010),\nYunnan Natural Science Foundation (Grant 2014HB048)\nand Yunnan Province (2017HC018).\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nLacunary generating functions appeared previously in a number of circumstances, including for example the treatment of Cauchy problems in partial differential equations~\\cite{babusci2017lacunary,penson2018quasi}. Here, we develop a rather general technique for the treatment of such generating functions, applicable to sequences $P=(p_n(x,y))_{n=0}^{\\infty}$ of polynomials $p_n(x,y)$, where $x$ is the generic variable and $y$ plays the role of a parameter. Such two-variable extensions of one-variable polynomials have been strongly advocated in~\\cite{babusci2010lectures}. They can be logically and consistently defined for all standard families of orthogonal polynomials such as Hermite, Laguerre, Chebyshev of first and second kind, Jacobi and Legendre polynomials~\\cite{babusci2017lacunary,babusci2010lectures,beals2016special}. Once such two-variable equivalents are properly defined, their one-variable variants are obtained by fixing the values of both variables to functions of one of the variables. The concrete example considered in this paper is given by the two-variable Hermite (or so-called Hermite-Kamp\\'{e} de F\\'{e}riet) polynomials $H_n(x,y)$~\\cite{kampe,dattoli1997evolution}, from which the standard one-variable Hermite polynomials $H_n(x)$ may be recovered via (see~\\eqref{eq:HPtwo} below for the definition of $H_n(x,y)$)\n\\begin{equation}\nH_n(x)=H_n(2x,-1)\\,.\n\\end{equation}\nWe will focus our particular attention onto the derivation of a general formula for the $K$-tuple $L$-shifted lacunary generating functions $\\cH_{K,L}(\\lambda;x,y)$ of the two-variable Hermite polynomials $H_n(x,y)$, which are defined (for $K=1,2,3,\\dotsc$ and $L=0,1,2,\\dotsc$) by\n\\begin{equation}\\label{eq:HLGFa}\n\\cH_{K,L}(\\lambda;x,y):=\\sum_{n=0}^{\\infty}\\frac{\\lambda^n}{n!}\\; H_{n\\cdot K+L}(x,y)\\,.\n\\end{equation}\nThe exponential generating functions of type~\\eqref{eq:HLGFa} for Hermite and other types polynomials are very sparsely known, and progress in obtaining new closed-form formulas has been painstakingly slow. A glance at standard reference tables~\\cite{prudnikov1992integrals} reveals only a few known examples. A number of results in this vein were obtained by combinatorial approaches initiated by D.~Foata and V.~Strehl in~\\cite{foataStrehl1984} supplemented by umbral methods, see~\\cite{dattoli2017operational} and references therein. This methodology culminated recently in a tandem study of various lacunary generating functions of Laguerre polynomials derived by purely umbral-type~\\cite{babusci2017lacunary} and purely combinatorial methods~\\cite{strehl2017lacunary}. Only a few results are currently available for lacunary generating functions of Hermite polynomials: the double lacunary case has been combinatorially re-derived by D.~Foata in~\\cite{foata1981some}, whereas the more challenging triple-lacunary generating function has been derived by both umbral and combinatorial methods in~\\cite{gessel2005triple}. Finally, several new lacunary generating functions for Legendre and Chebyshev polynomials were obtained recently by a combination of analytic and umbral methods in~\\cite{gorskalacunary}. To conclude our short survey of results known previously in the literature, let us comment that there exists a related result due to Nieto and Truax~\\cite{nieto1995arbitrary}, which (in the form adapted to the two-variable Hermite polynomials $H_n(x,y)$ as presented in~\\cite{dattoli1997evolution,dattoli1998operational}) reads for $K\\in \\bZ_{\\geq 1}$, $L\\in \\bZ_{\\geq 0}$ and $L<K$\n\\begin{subequations}\n\\begin{align}\n\\cS_{K,L}(\\lambda;x,y)&:=\\sum_{n=0}^{\\infty}\\frac{\\lambda^{n\\cdot K+L}}{(n\\cdot K+L)!}H_{n\\cdot K+L}(x,y)\\\\\n&=\\frac{1}{K}\\sum_{\\ell=1}^K\\; \\frac{e^{x\\tau_{\\ell}+y\\tau_{\\ell}^2}}{e^{2\\pi i \\ell L\/K}}\\,,\\quad \n\\tau_{\\ell}:=\\lambda e^{2\\pi i \\ell\/K}\\,.\n\\end{align}\n\\end{subequations}\nNote however that this type of generating function is not the lacunary exponential type studied in the present paper.\\\\\n\nWe believe to have extended the knowledge of these objects by providing a general methodology for the study of lacunary generating functions. Indeed, our results are obtained by specialization of a general algorithm developed by us here (see Lemma~1 and Corollary~1). Quite remarkably,  it takes as its input just the coefficients $g_{r,m}(y)$ of the \\emph{elementary} exponential generating functions $\\cG_{1,0}(\\lambda;x,y)$, defined via\n\\begin{subequations}\n\\begin{align}\n\\cG_{1,0}(\\lambda;x,y)&=\\sum_{n=0}^{\\infty}\\frac{\\lambda^n}{n!} p_n(x,y)\\\\\n&=\\sum_{r=0}^{\\infty}x^r\\sum_{m=0}^{\\infty}\\frac{\\lambda^{r+m}}{(r+m)!}\\; g_{r\\!,\\,m}(y)\\,,\n\\end{align}\n\\end{subequations}\nand returns (for arbitrary parameters $K=1,2,\\dotsc$ and $L=0,1,\\dotsc$) closed-form expressions for the $K$-tuple $L$-shifted lacunary generating functions $\\cG_{K,L}(\\lambda;x,y)$. Armed with this technique, we derive \\emph{all} lacunary generating functions $\\cH_{K,L}(\\lambda;x,y)$ for the two-variable Hermite polynomials $H_n(x,y)$ (see Theorem~\\ref{thm:HPlacK}, and also Table~\\ref{tab:HPlacFull} and Table~\\ref{tab:HPlacShift} for a number of examples).\\\\\n\nThe paper is structured as follows: in Section~\\ref{sec:Alg}, we derive our general algorithm for computing lacunary generating functions. These results are specialized in Section~\\ref{sec:HP} to the case of two-variable Hermite-polynomials. Additional details of the proofs are provided in Appendix~\\ref{app:proofs}. For the readers' convenience, an elementary Maple code for algorithmically verifying some of our explicit formulae of Table~\\ref{tab:HPlacFull} is given in Appendix~\\ref{app:Maple}.\n\n\n\\section{An algorithm for computing lacunary generating functions}\n\\label{sec:Alg}\n\nSuppose we are given a sequence of polynomials $p_n(x,y)$, for $n\\geq 0$, i.e.\\ one polynomial for each non-negative integer index $n$ and such that \n\\[\n\\deg_x(p_n(x,y))=n\\,.\n\\]\nTypically, we will consider the variable $y$ as a formal parameter, and focus on expansions in terms of the variable $x$. Note also that one could without additional complications admit multiple variables $y_1,y_2,\\dotsc$ instead of a single ``parameter'' variable $y$, so we will, without loss of generality, consider here only the case of a single ``parameter'' variable $y$.\\\\\n\nGiven a particular set of polynomials, one may compute the exponential generating function $\\cG(\\lambda;x,y)$ for this set as\n\\begin{subequations}\n\\begin{align}\n\\cG(\\lambda;x,y)&:=\\sum_{n=0}^{\\infty}\\frac{\\lambda^n}{n!} \\; p_n(x,y)\\label{eq:EGFa}\\\\\n&=\\sum_{r=0}^{\\infty} x^r \\sum_{m=0}^{\\infty} \\frac{\\lambda^{r+m}}{(r+m)!}\\; g_{r\\!,\\,m}(y)\\,. \\label{eq:EGFb}\n\\end{align}\n\\end{subequations}\nWhile the form as presented in~\\eqref{eq:EGFa} merely amounts to re-encoding of the information available via the explicit definition of the polynomials $p_n(x,y)$, the form~\\eqref{eq:EGFb} in fact necessitates a calculation: equation~\\eqref{eq:EGFa} must be expanded into powers of $x$ and then further in powers of the formal variable $\\lambda$, which (in the specific pairing of powers $\\lambda^{r+m}$ with $1\/(r+m)!$) defines a set of expansion coefficients $g_{r\\!,\\,m}(y)$. To provide a concrete example, we demonstrate the calculation for the case of the two-variable Hermite polynomials $H_n(x,y)$ that will play a central role later. Their exponential generating function $\\cH(\\lambda;x,y)$ reads~\\cite{babusci2010lectures,dattoli1997evolution}\n\\begin{equation}\\label{eq:EGFhp1}\n\\cH(\\lambda;x,y):=\\sum_{n=0}^{\\infty}\\frac{\\lambda^n}{n!} H_n(x,y)=e^{\\lambda x+\\lambda^2 y}\\,.\n\\end{equation}\nTo obtain the form as described in~\\eqref{eq:EGFb}, we expand the EGF first in terms of the variable $x$, and then in terms of the variable $\\lambda$:\n\\begin{equation}\n\\begin{aligned}\n\\cH(\\lambda;x,y)&=e^{\\lambda x+\\lambda^2 y}\\\\\n&=\\left(\\sum_{r=0}^{\\infty} x^r\\; \\tfrac{\\lambda^r}{r!}\\right)\\;e^{\\lambda^2 y}\\\\\n&=\\sum_{r=0}^{\\infty} x^r \\; \\sum_{m=0}^{\\infty} \\frac{\\lambda^{r+2m}}{r! m!}y^m\\\\\n&=\\sum_{r=0}^{\\infty} x^r \\; \\sum_{m=0}^{\\infty} \\frac{\\lambda^{r+2m}}{(r+2m)!}\\; \\left(\\frac{(r+2m)!\\; y^m}{r!m!}\\right)\\\\\n&=\\sum_{r=0}^{\\infty}x^r \\sum_{m=0}^{\\infty}\\frac{\\lambda^{r+2m}}{(r+2m)!}\\; h_{r\\!,\\,2m}(y)\\,.\n\\end{aligned}\n\\end{equation}\nConsequently, for these polynomials by comparison with the defining equation~\\eqref{eq:EGFb}, we find that $g_{r\\!,\\,m}(y)=0$ for $m$ odd, and \n\\begin{equation}\ng_{r\\!,\\,2m}(y)=\\frac{(r+2m)! y^m}{r!m!}\\,.\n\\end{equation}\n\n\nGiven again a set of polynomials $p_n(x,y)$, one may also define a more general family of generating functions, the so-called \\emph{$K$-tuple $L$-shifted lacunary generating functions} $\\cG_{K,L}(\\lambda;x,y)$ (for $K\\in \\bZ_{\\geq 1}$ and $L\\in \\bZ_{\\geq 0}$):\n\\begin{subequations}\n\\begin{align}\n\\cG_{K,L}(\\lambda;x,y)&:=\n\\sum_{n=0}^{\\infty}\\frac{\\lambda^n}{n!} \\; \np_{K\\cdot n+L}(x,y)\\label{eq:LGFa}\\\\\n&=\\sum_{r=0}^{\\infty} x^r \\sum_{m=0}^{\\infty} \\frac{\\lambda^{r+m}}{(r+m)!}\\; g^{(K,L)}_{r\\!,\\,m}(y)\\,. \\label{eq:LGFb}\n\\end{align}\n\\end{subequations}\nNote that by definition,\n\\begin{equation}\\label{eq:LGFegf}\n\\cG_{1,0}(\\lambda;x,y)\\equiv\\cG(\\lambda;x,y)\\,.\n\\end{equation}\n\nBefore we continue with further elaborations, we wish to clarify the precise framework within which the series rearrangements that are essential to our methods are well-posed.\n\n\\subsection{Summability}\\label{sec:sum}\n\nPolynomials or series of any sort are functions $M\\to k$ where $M$ is a set of monomials (a monoid\\footnote{The product of two monomials is a monomial, there exists a neutral for this multiplication, the void monomial.}) and $k$ its set of coefficients ($\\mathbb{R},\\mathbb{C}$ any ring as a ring of polynomials or series). In order to manipulate safely infinite sums, such as in the transition from~\\eqref{eq:EGFa} to the form~\\eqref{eq:EGFb}, these spaces are endowed with the notion of \\emph{summability}. \n\\begin{defn} A family of series $(S_i)_{i\\in I}$ is said {\\it summable} \\cite{reutenauer} if it is {\\it locally finite} \\cite{berstel} i.e. if \n\\begin{equation}\n(\\forall m\\in M)\\big(\\; \\vert\\{i\\in I|\\scal{S_i}{m}\\not=0\\}\\vert<\\infty\\;\\big)\\,,\n\\end{equation}\nwhere $\\scal{S_i}{m}$ stands for ``the coefficient of the monomial $m$ in $S_i$''.\\\\ \nIn this case ($(S_i)_{i\\in I}$ is summable) we say that $S=\\sum_{i\\in I}S_i$ where, for all $m\\in M$\n\\begin{equation}\n\\scal{S}{m}=\\sum_{i\\in I}\\scal{S_i}{m}\\,.\n\\end{equation}\n\\end{defn}  \n\\begin{remarks} i) In $k[|x]]$ (series of one variable) $M=\\{x^n\\}_{n\\geq 0}$, the family $\\{(x+x^2)^n\\}_{n\\geq 0}$  is summable (with sum $\\frac{1}{1-x-x^2}$), while $\\{(x+1)^n\\}_{n\\geq 0}$ is not.\\\\\nii) As an ``a posteriori'' justification, for all series $S$, one can easily check that the family \n$(\\scal{S}{m}\\,m)_{m\\in M}$ is summable with sum $S$, hence the additive notation can be rigorously set as \n\\begin{equation}\nS=\\sum_{m\\in M} \\scal{S}{m}\\,m\\,.\n\\end{equation}  \niii) The reader aware of topology will find that this notion is none other that the {\\rm summability for the topology of point-wise convergence (on $M$), $k$ being endowed with the discrete topology}~\\cite{GT1}.\\\\\niv) The sequence $\\Big((1+\\frac{x}{n})^{n}\\Big)_{n\\geq 1}$ converges towards $e^x$, but coefficient by coefficient, this is a coarser topology, with -- this time -- $\\mathbb{R}$ endowed with the usual topology, i.e.\\ Treves' topology~\\cite{SMF,treves}.          \n\\end{remarks}\n\n\n\nWe will now present first a closed-form equation that makes explicit the relationship between the expansion coefficients $g_{r,\\,m}^{(K,L)}(y)$, see equation~\\eqref{eq:LGFb}, and the expansion coefficients $g^{(1,0)}_{r,\\,m}(y)$ of the exponential generating function $\\cG_{1,0}(\\lambda;x,y)$, see equation~\\eqref{eq:LGFegf}. \n\n\\subsection{Lacunary shifts}\n\nIt follows directly from the definition given in~\\eqref{eq:LGFa} that the operator\n\\begin{equation}\n\\bS_L:=\\left(\\frac{\\partial}{\\partial \\lambda}\\right)^L\n\\end{equation}\nimplements the action of lacunary shifts on exponential generating functions $\\cG_{K,0}(\\lambda;x,y)$:\n\\begin{equation}\\label{eq:lacShift}\n\\bS_L \\left(\\cG_{K,0}(\\lambda;x,y)\\right)=\\sum_{n=L}^{\\infty}\\frac{\\lambda^{n-L}}{(n-L)!}\\; p_{n\\cdot K}(x,y)\n=\\sum_{n=0}^{\\infty}\\frac{\\lambda^{n}}{n!}\\; p_{n K+L}(x,y)=\\cG_{K,L}(\\lambda;x,y)\\,.\n\\end{equation}\nWhile it may be intricate in its own right to extract from this equation the lacunary expansion coefficients $g^{(1,L)}_{r,\\,m}(y)$ as defined in~\\eqref{eq:LGFb}, this computation is in principle straightforward. Therefore we will focus in this paper mostly on providing formulae for the lacunary dilatations characterized by an integer $K$. However, for the explicit application example as presented in Section~\\ref{sec:HP}, we will be able to take advantage of certain operational techniques particular to the Hermite polynomials in order to compute the lacunary shifts of their respective generating functions in closed form.\n\n\n\\subsection{Lacunary dilatations}\n\nAccording to the definition given in~\\eqref{eq:LGFa}, the so-called \\emph{$K$-fold lacunary dilatation} (for $K\\in \\bZ_{\\geq 1}$) is implemented by means of the (formal) operator, which acts on formal series $F(\\lambda)$ via\n\\begin{equation}\\label{def:lacD}\n\\bL_K(F(\\lambda)):=F(\\lambda)\\big\\vert_{\n\\lambda^n\\mapsto \n\\; \\delta_{(n \\Mod K),0}\n\\; \\frac{n!}{\\left(n\/K\\right)!}\\;\\lambda^{\\left(n\/K\\right)}}\\,.\n\\end{equation}\nConsequently, the action of $\\bL_K$ may be considered as a transformation of monomials in the spirit of Section~\\ref{sec:sum}. Indeed,\n\\begin{subequations}\\label{eq:lacDil}\n\\begin{align}\n\\bL_K\\left(\\cG_{1,L}(\\lambda;x,y)\\right)&=\\sum_{n= 0}^{\\infty}\\frac{\\lambda^n}{n!}\\;\\left(\\delta_{(n \\Mod K),0}\\;\\frac{n!}{(n\/K)!}\\;\\frac{\\lambda^{(n\/K)}}{\\lambda^n}\\right)\\; p_{n+L}(x,y)\\\\\n&=\\sum_{r=0}^{\\infty}\\frac{\\lambda ^r}{r!} p_{r\\cdot K+L}(x,y)=\\cG_{K,L}(\\lambda;x,y)\\,,\\label{eq:auxKa}\n\\end{align}\n\\end{subequations}\nwhere in~\\eqref{eq:auxKa}, $r=n\/K$.\\\\\n\nNote at this point that the operators $\\bS_L$ and $\\bL_K$ (for $K=1,2,\\dotsc$ and $L=0,1,\\dotsc$) allow to implement the derivation of arbitrary lacunary generating functions $\\cG_{K,L}(\\lambda;x,y)$ from the initial knowledge of the exponential generating function $\\cG_{1,0}(\\lambda;x,y)$ as defined in~\\eqref{eq:LGFegf}.\\\\\n\nAssume now that we are given either the exponential generating function $\\cG_{1,0}(\\lambda;x,y)$ of some polynomials $p_n(x,y)$, or the $L$-shifted version $\\cG_{1,L}(\\lambda;x,y)$ thereof, and introduce for notational simplicity the notation $\\cG(\\lambda;x,y)$ for either choice of generating function (in a slight abuse in light of previous notations). We thus assume that we are given an equation of the generic form \n\\begin{equation}\\label{eq:GFexcpansion}\n\\cG(\\lambda;x,y)=\\sum_{r=0}^{\\infty}x^r\\sum_{m=0}^{\\infty}\\frac{\\lambda^{r+m}}{(r+m)!}\\; g_{r\\!,\\,m}(y)\\,.\n\\end{equation}\nWith these notational preparations, computing a $K$-fold lacunary dilatation of $\\cG(\\lambda;x,y)$ amounts to extracting the coefficients $g^{(K,0)}_{r\\!,\\,m}(y)$ in explicit form via expanding $\\bL_K(\\cG(\\lambda;x,y))$ in powers of $x$, and then further in powers of $\\lambda$. The only technical tool necessary is an elementary procedure to resolve the summations over $\\Mod K$-classes involved in the definition.\n\n\\begin{restatable}{lem}{genKD}\\label{lem:KD}\nThe explicit form for the $K$-fold lacunary dilatation $\\bL_K(\\cG(\\lambda;x,y))$ ($K\\in \\bZ_{\\geq 1}$)  of a generating function $\\cG(\\lambda;x,y)$ with expansion coefficients $g_{r,m}(y)$ reads \n\\begin{equation}\\label{eq:KLGF}\n\\begin{aligned}\n\\cG_{K,0}(\\lambda;x,y)&=\\bL_K\\left(\\cG(\\lambda;x,y)\\right)\\\\\n&= \n\\sum_{s=0}^{\\infty} x^{s\\cdot K}\\sum_{q=0}^{\\infty}\\frac{\\lambda^{s+q}}{(s+q)!}\\;g_{s\\cdot K,\\,q\\cdot K}(y)\\\\\n&\\quad \n+\\sum_{\\alpha=1}^{K-1}\\sum_{s=0}^{\\infty} x^{(s+1)\\cdot K-\\alpha}\\sum_{q=0}^{\\infty}\\frac{\\lambda^{s+q+1}}{(s+q+1)!}\\; g_{(s+1)\\cdot K-\\alpha,\\,q\\cdot K+\\alpha}\\,.\n\\end{aligned}\n\\end{equation}\n\\end{restatable}\n\\begin{proof}\nThe argument follows from splitting the summation over $r$ in $\\bL_K(\\cG(\\lambda;x,y)$ (with $\\cG(\\lambda;x,y)$ expanded in the form described in~\\eqref{eq:EGFb}) into $\\Mod K$-classes, which consequently leads to a modification of the summation over the second index $m$. We refer the readers to Appendix~\\ref{app:lemP} for the precise details. \n\\end{proof}\n\nIn practical applications, it is often the case that the expansion coefficients $g_{r,m}$ have further structure, e.g.\\ as in the case of the Hermite polynomials (discussed in the next section) that only the coefficients with second index $m$ even are non-zero. We thus present the following corollary for this specific scenario, which will play an important role in the explicit calculation of closed-form expressions for the lacunary generating functions of the Hermite polynomials. Note also that one could easily adapt our approach to other scenarios in which the second indices $m$ fulfill a $\\Mod N$ constraint (for $N\\in \\bZ_{\\geq 3}$ some non-negative integer) via an entirely analogous argument.\n\n\\begin{restatable}{cor}{genKDcor}\\label{cor:KD}\nThe explicit form for the $K$-fold lacunary shift $\\bL_K(\\cG(\\lambda;x,y))$ ($K\\in \\bZ_{\\geq 1}$)  of a generating function $\\cG(\\lambda;x,y)$ with expansion coefficients $g_{r\\!,\\,m}(y)$ splits into a part which only contains summands with \\emph{even} second indices $m$ of $g_{r,m}(y)$ (marked ``part $E$'') and a part involving odd second indices only (marked ``part $O$''). It reads for the case $K=2T$ (with $T\\in \\bZ_{\\geq 1}$)\n\\begin{subequations}\\label{eq:KLGFeven}\n\\begin{align}\n\\bL_{K=2T}\\left(\\cG(\\lambda;x,y)\\right)&= {\\bigg[}^{\\text{part $E$}}\n\\sum_{s=0}^{\\infty} x^{s\\cdot K}\\sum_{q=0}^{\\infty}\n\\frac{\\lambda^{s+q}}{(s+q)!}\\; g_{s\\cdot K,\\,q\\cdot K}(y)\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T-1}\\sum_{s=0}^{\\infty} x^{(s+1)\\cdot K-2\\beta}\\sum_{q=0}^{\\infty}\\frac{\\lambda^{s+q+1}}{(s+q+1)!}\\; g_{(s+1)\\cdot K-2\\beta,\\,q\\cdot K+2\\beta}\\bigg]\\\\\n&\\quad+{\\bigg[}^{\\text{part $O$}}\n\\sum_{\\beta=1}^T\\sum_{s=0}^{\\infty}x^{(s+1)\\cdot K-2\\beta+1}\\sum_{q=0}^{\\infty}\\frac{\\lambda^{s+1+1}}{(s+q+1)!}\\; g_{(s+1)\\cdot K-2\\beta+1,\\,q\\cdot K+2\\beta-1}\\bigg]\\,,\n\\end{align}\n\\end{subequations}\nand for the case $K=2T+1$ (with $T\\in \\bZ_{\\geq 1}$)\n\\begin{subequations}\\label{eq:KLGFodd}\n\\begin{align}\n\\bL_{K=2T+1}\\left(\\cG(\\lambda;x,y)\\right)&= {\\bigg[}^{\\text{part $E$}}\\sum_{s=0}^{\\infty} x^{s\\cdot K}\\sum_{\\ell=0}^{\\infty}\n\\frac{\\lambda^{s+2\\ell}}{(s+2\\ell)!}\\; g_{s\\cdot K,\\,2\\ell \\cdot K}(y)\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T}\\sum_{s=0}^{\\infty} x^{(s+1)\\cdot K-2\\beta}\\sum_{\\ell=0}^{\\infty}\\frac{\\lambda^{s+2\\ell+1}}{(s+2\\ell+1)!}\\; g_{(s+1)\\cdot K-2\\beta,\\,2\\ell\\cdot K+2\\beta}\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T}\\sum_{s=0}^{\\infty} x^{(s+1)\\cdot K-2\\beta+1}\\sum_{\\ell=0}^{\\infty}\\frac{\\lambda^{s+2\\ell+2}}{(s+2\\ell+2)!}\\; g_{(s+1)\\cdot K-2\\beta+1,\\,(2\\ell+1)\\cdot K+2\\beta-1}\\bigg]\\\\\n&\\quad+{\\bigg[}^{\\text{part $O$}}\n\\sum_{s=0}^{\\infty} x^{s\\cdot K}\\sum_{\\ell=0}^{\\infty}\n\\frac{\\lambda^{s+2\\ell+1}}{(s+2\\ell+1)!}\\; g_{s\\cdot K,\\,(2\\ell+1) \\cdot K}(y)\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T}\\sum_{s=0}^{\\infty} x^{(s+1)\\cdot K-2\\beta+1}\n\\sum_{\\ell=0}^{\\infty}\\frac{\\lambda^{s+2\\ell+1}}{(s+2\\ell+1)!}\\; g_{(s+1)\\cdot K-2\\beta+1,\\,(2\\ell)\\cdot K+2\\beta-1}\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T}\\sum_{s=0}^{\\infty} x^{(s+1)\\cdot K-2\\beta}\\sum_{\\ell=0}^{\\infty}\\frac{\\lambda^{s+2\\ell+2}}{(s+2\\ell+2)!}\\; g_{(s+1)\\cdot K-2\\beta,\\,(2\\ell+1)\\cdot K+2\\beta}\\bigg]\\,.\n\\end{align}\n\\end{subequations}\n\\end{restatable}\n\\begin{proof}\nThe proof follows from a subdivision of summation ranges as detailed in Appendix~\\ref{app:corDproof}.\n\\end{proof}\n\n\n\\section{Hermite polynomials}\n\\label{sec:HP}\n\nDue to their paramount importance in special functions theory and in the development of operational techniques (cf.\\ e.g.~\\cite{dattoli1997evolution,dattoli2000generalized}), we will now present as an application of our general algorithm the computation of all higher order lacunary generating functions for the \\emph{Hermite-Kamp\\'{e} de F\\'{e}riet polynomials}~\\cite{kampe,dattoli1997evolution} (with $n\\in \\bZ_{\\geq0}$):\n\\begin{equation}\\label{eq:HPtwo}\nH_n(x,y):=e^{y\\frac{d^2}{dx^2}} x^n =n! \\sum_{k=0}^{\\lfloor \\frac{n}{2}\\rfloor}\\frac{x^{n-2k}y^k}{(n-2k)!k!}\\,.\n\\end{equation}\nIt is well-known that these polynomials possess the exponential generating function (compare~\\eqref{eq:EGFhp1})\n\\begin{subequations}\n\\begin{align}\n\\cH_{1,0}(\\lambda;x,y)&:=\\sum_{n=0}^{\\infty}\n\\frac{\\lambda^n}{n!}\nH_n(x,y)=e^{y\\frac{d^2}{dx^2}} e^{\\lambda x}\\label{eq:HPlac1s0}\\\\\n&=e^{\\lambda x + \\lambda^2 y}\\,.\n\\end{align}\n\\end{subequations}\nHere and from now on, we will take the notational convention that the generating functions $\\cG_{K,L}(\\lambda;x,y)$ for the two-variable Hermite polynomials $H_n(x,y)$ will be denoted $\\cH_{K,L}(\\lambda;x,y)$.\\\\\n\nThe above formula is a straightforward consequence of the Crofton identity~\\cite{crofton79} (see also~\\cite[Eq.~(I.3.17)]{dattoli1997evolution} and~\\cite{dattoli2000generalized}),  according to which, for $m\\in \\bZ_{\\geq 1}$, $\\lambda$ a formal variable and $f(x),g(x)$ formal power series in $x$, we have the following equality of operators (which are the expressions between $[\\dotsc]$):\n\\begin{equation}\\label{eq:crofton}\n\\left[\\exp\\left(\\lambda \\frac{d^m}{dx^m}\\right)f(x)\\right]g(x)=\\left[ f\\left(x + m\\lambda \\frac{d^{m-1}}{dx^{m-1}}\\right)\\exp\\left(\\lambda\\frac{d^m}{dx^m}\\right)\\right]g(x)\\,.\n\\end{equation}\nAs a second important consequence of this identity, we find a significant reduction of the complexity of determining the lacunary generating functions of the Hermite polynomials: surprisingly enough, instead of having to compute explicitly the shifts $\\cH_{1,L}(\\lambda;x,y)$ of the exponential generating function $\\cH_{1,0}(\\lambda;x,y)$, followed by application of Corollary~\\ref{cor:KD} to compute $\\cH_{K,L}(\\lambda;x,y)$, we can take advantage of operational techniques to derive an exponential generating for \\emph{all} shifts in closed form. Note that for some ranges of parameters (i.e.\\ for $K=1,2$ and $L\\in \\bZ_{\\geq 1}$), formulae equivalent to our result~\\eqref{eq:propHLGF} below have been presented already in~~\\cite{dattoli1997evolution,dattoli1998operational}.\n\n\n\\begin{prop}\\label{prop:LshiftHLGF}\nDefine the exponential generating function\\footnote{In a sense, $\\cR_K(\\mu;\\lambda;x,y)$ is the exponential generating function of other types of exponential generating functions, a slightly unusual, yet rather useful construct. Note also that these manipulations are admissible in the framework according to Section~\\ref{sec:sum}.} of the lacunary shifts $\\cH_{K,L}(\\lambda;x,y)$ of the $K$-tuple lacunary generating function $\\cH_{K,0}(\\lambda;x,y)$ of the polynomials $H_n(x,y)$ as\n\\begin{equation}\n\\begin{aligned}\n\\cR_K(\\mu;\\lambda;x,y)&:= \\sum_{L=0}^{\\infty}\\frac{\\mu^L}{L!} \\cH_{K,L}(\\lambda;x,y)\\\\\n&\\overset{\\eqref{eq:lacDil}}{=}\\sum_{L=0}^{\\infty}\\frac{\\mu^L}{L!} \\bL_K\\left(\\cH_{1,L}(\\lambda;x,y)\\right)\\\\\n&\\overset{\\eqref{eq:lacShift}}{=}\\sum_{L=0}^{\\infty}\\frac{\\mu^L}{L!} \\bL_K\\left(\\left(\\tfrac{\\partial}{\\partial\\lambda}\\right)^L\\left(\\cH_{1,0}(\\lambda;x,y)\\right)\\right)\\\\\n&=\\bL_K\\left(e^{\\mu \\frac{\\partial}{\\partial \\lambda}}\\cH_{1,0}(\\lambda;x,y)\\right)\\,.\n\\end{aligned}\n\\end{equation}\nThen by virtue of the Crofton identity and of a semi-linear normal-ordering technique~\\cite{dattoli1997evolution}, one finds that\n\\begin{equation}\\label{eq:propHLGF}\n\\boxed{\\cR_K(\\mu;\\lambda;x,y)=e^{\\mu x+\\mu^2 y}\\cH_{K,0}(\\lambda;x+2\\mu y,y)=\\cH_{1,0}(\\mu;x,y)\\cH_{K,0}(\\lambda;x+2\\mu y,y)\\,.}\n\\end{equation}\nConsequently, as one of the key results of this paper, we find that\n\\begin{equation}\\label{eq:HKLexpl}\n\\cH_{K,L}(\\lambda;x,y)=\\left[\\left(\\tfrac{\\partial}{\\partial\\mu}\\right)^L \\cR_K(\\mu;\\lambda;x,y)\\right]\\bigg\\vert_{\\mu\n\\mapsto0}\n\\end{equation}\n\\begin{proof}\nPartially evaluating the formula for $\\cH_K(\\mu;\\lambda;x,y)$,\n\\begin{subequations}\n\\begin{align}\n\\cR_K(\\mu;\\lambda;x,y)&=\\bL_K\\left(e^{\\mu \\frac{\\partial}{\\partial \\lambda}}\\cH_{1,0}(\\lambda;x,y)\\right)\\\\\n&\\overset{\\eqref{eq:HPlac1s0}}{=} \n\\bL_K\\left(e^{\\mu \\frac{\\partial}{\\partial \\lambda}}e^{y\\frac{d^2}{dx^2}}e^{\\lambda x}\\right)\\\\\n&=\\bL_K\\left(e^{y\\frac{d^2}{dx^2}}e^{\\mu \\frac{\\partial}{\\partial \\lambda}}e^{\\lambda x}\\right)\\\\\n&=\\bL_K\\left(e^{y\\frac{d^2}{dx^2}}e^{\\mu x}e^{\\lambda x}\\right)\\,,\\label{eq:shiftPropA}\n\\end{align}\n\\end{subequations}\nand applying the Crofton identity~\\eqref{eq:crofton} (to move the operator $\\exp(y\\frac{d^2}{dx^2})$ past the operator $\\exp(\\mu x)$) yields\n\\begin{equation}\n\\cR_K(\\mu;\\lambda;x,y)=\\bL_K\\left(e^{\\mu(x+2y\\frac{d}{dx})}e^{y\\frac{d^2}{dx^2}}e^{\\lambda x}\\right)\\,.\n\\end{equation}\nAt this point, note that the operator $\\exp(\\mu(x+2y\\tfrac{d}{dx}))$ is independent of the formal variable $\\lambda$, whence this operator and the lacunary dilatation operator $\\bL_K$ commute:\n\\begin{subequations}\n\\begin{align}\n\\cR_K(\\mu;\\lambda;x,y)&=e^{\\mu(x+2y\\frac{d}{dx})}\\left(\\bL_K\\left(e^{y\\frac{d^2}{dx^2}}e^{\\lambda x}\\right)\\right)\\\\\n&\\overset{\\eqref{eq:HPlac1s0}}{=}\ne^{\\mu(x+2y\\frac{d}{dx})}\\left(\\bL_K\\left(\\cH_{1,0}(\\lambda;x,y)\\right)\\right)\\\\\n&\\overset{\\eqref{eq:lacDil}}{=}e^{\\mu(x+2y\\frac{d}{dx})} \\cH_{K,0}(\\lambda;x,y)\\,.\n\\end{align}\n\\end{subequations}\nThis formula may be further improved via applying a certain semi-linear normal ordering technique (see Appendix~\\ref{app:SLNO} for the precise details) to obtain the final result as stated, whence for every formal power series $f(x)$ (and for $\\mu$ a formal variable),\n\\begin{equation}\n\\begin{aligned}\ne^{\\mu(x+2y\\frac{d}{dx})}f(x)&=g(\\mu;x)f(T(\\mu;x))\\\\\ng(\\mu;x)&=e^{\\mu x+\\mu^2 y}\\,,\\quad T(\\mu;x)=x+2\\mu y\\,.\n\\end{aligned}\n\\end{equation}\n\\end{proof}\n\\end{prop}\n\nDue to this proposition, our task of determining closed-form equations for all higher order lacunary generating functions $\\cH_{K,L}(\\lambda;x,y)$ effectively collapses to the slightly simpler task of determining the lacunary generating functions $\\cH_{K,0}(\\lambda;x,y)$ for $K\\in \\bZ_{\\geq 1}$. We will employ the generic algorithm as presented in Lemma~\\ref{lem:KD} in the variant as presented in Corollary~\\ref{cor:KD}, since the expansion coefficients $h^{(1,0)}_{r\\!,\\,m}(y)$ of the exponential generating function $\\cH_{1,0}(\\lambda;x,y)$ defined via\n\\begin{equation}\n\\cH_{1,0}(\\lambda;x,y):=\\sum_{n=0}^{\\infty}\\frac{\\lambda^n}{n!} H_n(x,y)=e^{\\lambda x+\\lambda^2 y}\n=\\sum_{r=0}^{\\infty}x^r \\sum_{m=0}^{\\infty}\\frac{\\lambda^{r+m}}{(r+m)!}\\; h^{(1,0)}_{r\\!,\\,m}(y)\n\\end{equation}\nfulfill\n\\begin{equation}\\label{eq:HPcoeffs}\nh^{(1,0)}_{r\\!,\\,m}(y)=\\delta_{(m\\Mod 2),0}\\; \\frac{(r+m)!y^{\\frac{m}{2}}}{r!(\\frac{m}{2})!}\\,.\n\\end{equation}\nThis entails in particular that our task further reduces to applying the explicit formula for the ``even parts'' (marked ``part $E$'') given in Corollary~\\ref{cor:KD} for $K=2T$ and $K=2T+1$, respectively.\\\\\n\nIt will further prove convenient to recall the \\emph{Gauss-Legendre multiplication formula}~\\cite[Eq.~5.5.6]{NIST:DLMF} for Gamma functions (for $n\\cdot z\\not\\in \\bZ_{\\leq 0}$),\n\\begin{equation}\\label{eq:GMF}\n\\Gamma(nz)=n^{nz-\\frac{1}{2}}(2\\pi)^{\\frac{(1-n)}{2}}\\prod_{j=0}^{n-1}\\Gamma\\left(z+\\frac{j}{n}\\right)\\,.\n\\end{equation} \nMore precisely, we will make use of the following variant of this formula: for $n(s+x),nx\\in \\bC\\setminus \\bZ_{\\leq 0}$, $n\\in \\bZ_{\\geq 2}$ and $s\\in \\bZ_{\\geq 0}$, we have that\n\\begin{equation}\\label{eq:GMFC}\n\\Gamma(n(s+x))=\\left(n^{s\\cdot n}\\right)\\Gamma(nx)\\;\\prod_{j=0}^{n-1}\\left(x+\\frac{j}{n}\\right)_s\\,,\n\\end{equation}\nwith the Pochhammer symbol $(a)_b$ defined according to the convention\n\\[\n(a)_b:=\\frac{\\Gamma(a+b)}{\\Gamma(a)}\\,.\n\\]\n\nLet us also fix notations for hypergeometric functions~\\cite{prudnikov1992integrals,beals2016special} as\n\\begin{equation}\n\\pFq{p}{q}{a_1,\\dotsc,a_p}{b_1,\\dotsc,b_q}{z}:=\\sum_{s=0}^{\\infty}\\frac{z^s}{s!}\\frac{(a_1)_s\\dotsc (a_p)_s}{(b_1)_s\\dotsc (b_q)_s}\\,,\n\\end{equation}\nand let us denote sequences in the form $\\seq{f_i}{1\\leq i\\leq n}$, such as in\n\\begin{equation}\n\\pFq{p}{q}{\\seq{a_i}{1\\leq i\\leq p}}{\\seq{b_j}{1\\leq i\\leq q}}{z}:=\\pFq{p}{q}{a_1,\\dotsc,a_p}{b_1,\\dotsc,b_q}{z}\\,.\n\\end{equation}\n\nWith these preparations, we are now in a position to state another key result of this paper, whence a closed-form expression for all $K$-tuple lacunary generating functions $\\cH_{K,0}(\\lambda;x,y)$ of the Hermite polynomials $H_n(x,y)$ in infinite-series form:\n\n\n\\begin{restatable}{thm}{HPlacK}\\label{thm:HPlacK}\nThe $K$-tuple lacunary generating functions $\\cH_{K,0}(\\lambda;x,y)$ read for $K=2T$ ($T\\in \\bZ_{\\geq 1}$)\n\\begin{equation}\n\\begin{aligned}\\label{eq:lacHPeven}\n\\cH_{K=2T,0}(\\lambda;x,y)&=\n\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^s}{s!}\\;x^{2T s}\\;\n\\pFq{(2T-1)}{(T-1)}{%\n\\seq{s+\\tfrac{j+1}{2T}}{0\\leq j\\leq 2T-2}}{%\n\\seq{\\tfrac{\\ell+1}{T}}{0\\leq \\ell\\leq T-2}}{\\lambda(4Ty)^T}\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T-1}\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^{s+1}}{(s+1)!}\\; \nx^{2T (s+1)-2\\beta}\\; y^{\\beta}\\;\\left(\\tfrac{(2T(s+1))!}{(2T(s+1)-2\\beta)!\\beta!}\\right)\\cdot\\\\\n&\\qquad\\cdot\n\\pFq{(2T-1)}{(T-1)}{\\seq{s+1+\\tfrac{j+1}{2T}}{0\\leq j\\leq 2T-2}}{%\n\\seq{\\tfrac{\\beta+\\ell+1}{T}}{\\stackrel{0\\leq\\ell\\leq T-1}{\\ell\\neq T-1-\\beta}}}{\\lambda(4Ty)^T}\\,,\n\\end{aligned}\n\\end{equation}\nand for $K=2T+1$ (with $T\\in \\bZ_{\\geq1}$)\n\\begin{equation}\n\\begin{aligned}\\label{eq:lacHPodd}\n\\cH_{K=2T+1,0}(\\lambda;x,y)&=\n\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^s}{s!}\\;x^{K s}\\;\n\\pFq{(2K-2)}{(K-1)}{\\seq{\\tfrac{s}{2}+\\tfrac{j+1}{2K}}{\\stackrel{0\\leq j\\leq 2K-2}{j\\neq K-1}}}{\\seq{\\tfrac{\\ell+1}{K}}{0\\leq \\ell \\leq K-2}}{\\tfrac{\\lambda^2(4Ky)^K}{4}}\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T}\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^{s+1}}{(s+1)!}\\; \nx^{K(s+1)-2\\beta}\\; y^{\\beta}\\;\\left(\\tfrac{(K(s+1))!}{(K(s+1)-2\\beta)!\\beta!}\\right)\\cdot\\\\\n&\\qquad\\cdot\n\\pFq{(2K-2)}{(K-1)}{\\seq{\\tfrac{s+1}{2}+\\tfrac{j+1}{2K}}{\\stackrel{0\\leq j\\leq 2K-2}{j\\neq K-1}}}{\\seq{\\tfrac{\\beta+\\ell+1}{K}}{\\stackrel{0\\leq \\ell\\leq K-1}{\\ell\\neq K-1-\\beta}}}{\\tfrac{\\lambda^2(4Ky)^K}{4}}\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T}\n\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^{s+2}}{(s+2)!}\\; \nx^{K(s+2)-2(T+\\beta)}\\; y^{T+\\beta}\\;\n\\left(\\tfrac{(K(s+2))!}{(K(s+2)-2(T+\\beta))!(T+\\beta)!}\\right)\\cdot\\\\\n&\\qquad\\cdot\n\\pFq{(2K-2)}{(K-1)}{\\seq{\\tfrac{s+2}{2}+\\tfrac{j+1}{2K}}{\\stackrel{0\\leq j\\leq 2K-2}{j\\neq K-1}}}{\n\\seq{\\tfrac{T+\\beta+\\ell+1}{K}}{\\stackrel{0\\leq \\ell\\leq K-1}{\\ell\\neq T-\\beta}}}{\\tfrac{\\lambda^2(4Ky)^K}{4}}\\,.\n\\end{aligned}\n\\end{equation}\n\\end{restatable}\n\\begin{proof}\nThe proof follows by specializing Corollary~\\ref{cor:KD} to the case at hand and by making repeated use of equation~\\eqref{eq:GMFC} in order to transform the resulting terms into the form presented in the theorem.\n\\end{proof}\n\nSince the precise details of the above calculations might be of independent interest to some of the readers, we present the case $K=4$ in the form of a worked example. Based on formula~\\eqref{eq:HPcoeffs} for the expansion coefficients $h^{(1,0)}_{r\\!,\\,m}$ of the exponential generating function $\\cH_{1,0}(\\lambda;x,y)$ of the Hermite polynomials $H_n(x,y)$, and taking advantage of Corollary~\\ref{cor:KD} (whence making use of the formula for even $K=2T$, of which moreover only the parts marked $part~E$ contribute in the case at hand), we obtain the following expression:\n\\begin{equation}\n\\begin{aligned}\\label{eq:H40step1}\n\\cH_{4,0}(\\lambda;x,y)&=\\sum_{s=0}^{\\infty} x^{4s}\\sum_{q=0}^{\\infty}\\frac{\\lambda^{s+q}}{(s+q)!}\\; h^{(1,0)}_{4s\\!,\\,4q}(y)\\\\\n&\\quad+\\sum_{s=0}^{\\infty} x^{4s+2}\\sum_{q=0}^{\\infty}\\frac{\\lambda^{s+q+1}}{(s+q+1)!}\\; h^{(1,0)}_{4s+2\\!,\\,4q+2}(y)\\\\\n&=\\sum_{s=0}^{\\infty} x^{4s}\\sum_{q=0}^{\\infty}\\frac{\\lambda^{s+q}(4(s+q))!y^{2q}}{(s+q)!(4s)!(2q)!}\\\\\n&\\quad+\\sum_{s=0}^{\\infty} x^{4s+2}\\sum_{q=0}^{\\infty}\\frac{\\lambda^{s+q+1}(4(s+q+1))!y^{2q+1}}{(s+q+1)!(4s+2)!(2q+1)!}\\,.\n\\end{aligned}\n\\end{equation}\nApplying formula~\\eqref{eq:GMFC} repeatedly, we find the auxiliary relations\n\\begin{align*}\n(4(s+q))!&=4^{4q}\\Gamma(4s+1)\\prod_{j=0}^3\\left(s+\\tfrac{j+1}{4}\\right)_q=4^{4q}(4s)!\\left(s+\\tfrac{3+1}{4}\\right)_q \\prod_{j=0}^{{\\color{blue}2}}\\left(s+\\tfrac{j+1}{4}\\right)_q\\\\\n&=\\tfrac{4^{4q}(4s)!(s+q)!}{q!} \\prod_{j=0}^{2}\\left(s+\\tfrac{j+1}{4}\\right)_q \\qquad(\\text{since }\\left(s+1\\right)_q=\\tfrac{\\Gamma(s+q+1)}{\\Gamma(s+1)})\\\\\n(2q)!\n&=2^{2q}\\Gamma(1)\\prod_{j=0}^1\\left(\\tfrac{j+1}{2}\\right)_q\n=4^q \\left(\\tfrac{1}{2}\\right)_q q! \\qquad(\\text{since }\\left(1\\right)_q\n=\\tfrac{\\Gamma(q+1)}{\\Gamma(1)}=q!)\\,,\\\\\n\\end{align*}%\nand analogously for $(4(s+q+1))!$ and $(2q+1)!$, respectively. Inserting these results into~\\eqref{eq:H40step1}, we recover the formula for $\\cH_{4,0}(\\lambda;x,y)$ as presented in Theorem~\\ref{thm:HPlacK} (see also Table~\\ref{tab:HPlacFull}):\n\\begin{equation}\n\\begin{aligned}\\label{eq:H40step2}\n\\cH_{4,0}(\\lambda;x,y)&=\n\\sum_{s=0}^{\\infty} x^{4s}\\sum_{q=0}^{\\infty}\\tfrac{\\lambda^{s+q}\\;4^{4q}(4s)!(s+q)!y^{2q}\\prod_{j=0}^{2}\\left(s+\\frac{j+1}{4}\\right)_q}{(s+q)!(4s)!s! 4^q \\left(\\frac{1}{2}\\right)_q q!}\\\\\n&\\quad\n+\\sum_{s=0}^{\\infty} x^{4s+2}\\sum_{q=0}^{\\infty}\\tfrac{\\lambda^{s+q+1}\\;4^{4q} (4(s+1))!(s+q+1)! y^{2q+1}\\prod_{j=0}^{2}\\left(s+1+\\frac{j+1}{4}\\right)_q}{(s+q+1)!(4s+2)!(s+1)!4^q q! \\left(\\frac{3}{2}\\right)_q}\\\\\n&=\n\\sum_{s=0}^{\\infty} \\tfrac{\\lambda^s}{s!}\\; x^{4s}\\sum_{q=0}^{\\infty}\\tfrac{(\\lambda (2^3y)^2)^{q}}{q!}\\;\\tfrac{\\prod_{j=0}^{2}\\left(s+\\frac{j+1}{4}\\right)_q}{ \\left(\\frac{1}{2}\\right)_q}\\\\\n&\\quad\n+\\sum_{s=0}^{\\infty} \\tfrac{\\lambda^{s+1}}{(s+1)!}\\;x^{4s+2}y\\;\\left(\\tfrac{(4(s+1))!}{(4(s+1)-2)!}\\right)\n\\sum_{q=0}^{\\infty}\\tfrac{(\\lambda (2^3y)^2)^{q}}{q!}\\;\\tfrac{\\prod_{j=0}^{2}\\left(s+1+\\frac{j+1}{4}\\right)_q}{ \\left(\\frac{3}{2}\\right)_q}\\\\\n&=\n\\sum_{s=0}^{\\infty} \\tfrac{\\lambda^s}{s!}\\; x^{4s}\n\\pFq{3}{1}{s+\\tfrac{1}{4},s+\\tfrac{2}{4},s+\\tfrac{3}{4}}{\\tfrac{1}{2}}{\\lambda y^22^6}\\\\\n&\\quad\n+\\sum_{s=0}^{\\infty} \\tfrac{\\lambda^{s+1}}{(s+1)!}\\;x^{4s+2}y\\;\\left(\\tfrac{(4(s+1))!}{(4(s+1)-2)!}\\right)\\;\\cdot\\\\\n&\\qquad \\cdot\\;\n\\pFq{3}{1}{s+1+\\tfrac{1}{4},s+1+\\tfrac{2}{4},s+1+\\tfrac{3}{4}}{\\tfrac{3}{2}}{\\lambda y^22^6}\\,.\n\\end{aligned}\n\\end{equation}\n\nNote in particular the appearance of Hermite polynomial expansion coefficients in the formulae for $\\cH_{K,0}(\\lambda;x,y)$ as presented in Theorem~\\ref{thm:HPlacK} -- for example, the fraction of factorials appearing in the second to last line of~\\eqref{eq:H40step2} coincides with the coefficient of the monomial $x^{4s+2}y$ of the Hermite polynomial $H_{4(s+1)}(x,y)$ (compare~\\eqref{eq:HPtwo}),\n\\[\nH_{4(s+1)}(x,y)=\\sum_{k=0}^{2(s+1)}\\frac{(4(s+1))!}{(4(s+1)-2k)!k!}\\; x^{4(s+1)-2k}y^k\\,.\n\\]\n\n\nCombining the results of Theorem~\\ref{thm:HPlacK} with the results of Proposition~\\ref{prop:LshiftHLGF}, we have at our disposal explicit formulae for all higher order lacunary generating functions of the Hermite polynomials $H_n(x,y)$.\n\n\n\\begin{restatable}{cor}{HPlacKL}\\label{cor:HPlacKL}\nThe $K$-tuple $L$-shifted lacunary generating functions $\\cH_{K,L}(\\lambda;x,y)$ read for $K=2T$ ($T\\in \\bZ_{\\geq 1}$) and $L\\in \\bZ_{\\geq 0}$\n\\begin{equation}\n\\begin{aligned}\\label{eq:lacHPevenLshifted}\n&\\cH_{K=2T,L}(\\lambda;x,y)\\\\\n&\\quad=\n\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^s}{s!}\\;\n\\left(\\sum_{q=0}^L q! \\binom{L}{q}\\binom{K s}{q}H_{L-q}(x,y)\\;x^{K s-q}(2y)^q\\right)\n\\;\\cdot\\\\\n&\\quad\\qquad \\cdot\\;\n\\pFq{(K-1)}{(T-1)}{%\n\\seq{s+\\tfrac{j+1}{K}}{0\\leq j\\leq K-2}}{%\n\\seq{\\tfrac{\\ell+1}{T}}{0\\leq \\ell\\leq T-2}}{\\lambda(2Ky)^T}\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T-1}\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^{s+1}}{(s+1)!}\\; \n\\bigg(\\sum_{q=0}^L q!\\binom{L}{q}\\binom{K (s+1)-2\\beta}{q} H_{L-q}(x,y)\\;\\cdot\\\\\n&\\hphantom{+\\sum_{\\beta=1}^{T-1}\\sum_{s\\geq 0}\\tfrac{\\lambda^{s+1}}{(s+1)!}}\\qquad\\cdot\\;x^{K (s+1)-2\\beta-q}\\; 2^q\\;y^{\\beta+q}\\bigg)\\;\n\\left(\\tfrac{(K(s+1))!}{(K(s+1)-2\\beta)!\\beta!}\\right)\\;\\cdot\\\\\n&\\hphantom{+\\sum_{\\beta=1}^{T-1}\\sum_{s\\geq 0}\\tfrac{\\lambda^{s+1}}{(s+1)!}}\\quad\\cdot\\;\n\\pFq{(K-1)}{(T-1)}{\\seq{s+1+\\tfrac{j+1}{K}}{0\\leq j\\leq K-2}}{%\n\\seq{\\tfrac{\\beta+\\ell+1}{T}}{\\stackrel{0\\leq\\ell\\leq T-1}{\\ell\\neq T-1-\\beta}}}{\\lambda(2Ky)^T}\\,,\n\\end{aligned}\n\\end{equation}\nand for $K=2T+1$ (with $T\\in \\bZ_{\\geq1}$)\n\\begin{equation}\n\\begin{aligned}\\label{eq:lacHPoddLshifted}\n&\\cH_{K=2T+1,L}(\\lambda;x,y)\\\\\n&\\quad=\n\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^s}{s!}\\;\\left(\\sum_{q=0}^L\nq!\\binom{L}{q}\\binom{K s}{q}H_{L-q}(x,y)\\;x^{K s-q}(2y)^q\\right)\\;\\cdot\\\\\n&\\quad\\qquad \\cdot\\;\\pFq{(2K-2)}{(K-1)}{\\seq{\\tfrac{s}{2}+\\tfrac{j+1}{2K}}{\\stackrel{0\\leq j\\leq 2K-2}{j\\neq K-1}}}{\\seq{\\tfrac{\\ell+1}{K}}{0\\leq \\ell \\leq K-2}}{\\tfrac{\\lambda^2(4Ky)^K}{4}}\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T}\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^{s+1}}{(s+1)!}\\; \n\\bigg(\\sum_{q=0}^L q!\\binom{L}{q}\\binom{K(s+1)-2\\beta}{q}H_{L-q}(x,y)\\; \\cdot\\\\\n&\\hphantom{+\\sum_{\\beta=1}^{T}\\sum_{s\\geq 0}\\tfrac{\\lambda^{s+1}}{(s+1)!}\\; \n}\\cdot\\;x^{K(s+1)-2\\beta-q}\\; 2^q\\;y^{\\beta+q}\\bigg)\\;\\left(\\tfrac{(K(s+1))!}{(K(s+1)-2\\beta)!\\beta!}\\right)\\;\\cdot\\\\\n&\\hphantom{+\\sum_{\\beta=1}^{T}\\sum_{s\\geq 0}\\tfrac{\\lambda^{s+1}}{(s+1)!}\\; \n}\\cdot\\;\\pFq{(2K-2)}{(K-1)}{\\seq{\\tfrac{s+1}{2}+\\tfrac{j+1}{2K}}{\\stackrel{0\\leq j\\leq 2K-2}{j\\neq K-1}}}{\\seq{\\tfrac{\\beta+\\ell+1}{K}}{\\stackrel{0\\leq \\ell\\leq K-1}{\\ell\\neq K-1-\\beta}}}{\\tfrac{\\lambda^2(4Ky)^K}{4}}\\\\\n&\\quad \n+\\sum_{\\beta=1}^{T}\n\\sum_{s=0}^{\\infty}\\tfrac{\\lambda^{s+2}}{(s+2)!}\\; \n\\bigg(\\sum_{q=0}^L q!\\binom{L}{q}\\binom{K(s+2)-2(T+\\beta)}{q} H_{L-q}(x,y) \\;\n\\cdot\\\\\n&\\hphantom{+\\sum_{\\beta=1}^{T}\n\\sum_{s\\geq 0}\\tfrac{\\lambda^{s+2}}{(s+2)!}\\; }\\quad\\cdot\n\\;x^{K(s+2)-2(T+\\beta)-q}\\;2^q\\; y^{T+\\beta+q}\\bigg)\\;\n\\left(\\tfrac{(K(s+2))!}{(K(s+2)-2(T+\\beta))!(T+\\beta)!}\\right)\\;\\cdot\\\\\n&\\hphantom{+\\sum_{\\beta=1}^{T}\n\\sum_{s\\geq 0}\\tfrac{\\lambda^{s+2}}{(s+2)!}\\;}\\quad\\cdot\\;\n\\pFq{(2K-2)}{(K-1)}{\\seq{\\tfrac{s+2}{2}+\\tfrac{j+1}{2K}}{\\stackrel{0\\leq j\\leq 2K-2}{j\\neq K-1}}}{\n\\seq{\\tfrac{T+\\beta+\\ell+1}{K}}{\\stackrel{0\\leq \\ell\\leq K-1}{\\ell\\neq T-\\beta}}}{\\tfrac{\\lambda^2(4Ky)^K}{4}}\\,.\n\\end{aligned}\n\\end{equation}\n\\end{restatable}\n\\begin{proof}\nSee Appendix~\\ref{app:proofLacKL} for the details. \n\\end{proof}\n\nFor the readers' convenience, we present some explicit results for $\\cH_{K,0}(\\lambda;x,y)$ in Table~\\ref{tab:HPlacFull}, as well as several examples of shifted lacunary generating functions $\\cH_{K,L}(\\lambda;x,y)$ (for $K=3,4$ and $L=1,2,3$) obtained via Corollary~\\ref{cor:HPlacKL} in Table~\\ref{tab:HPlacShift}. To the best of our knowledge, all of these results past $K=2$ are new.\n\n\\section{Conclusion}\n\nTaking advantage of the summability properties of exponential generating functions of polynomial sequences, we provide novel re-summation techniques combined with operational methods in order to compute higher order lacunary generating functions of polynomials of all types. The application of these techniques to the case of two-variable Hermite polynomials $H_n(x,y)$ furnished explicit formulae for an infinite set of $K$-tuple $L$-shifted lacunary generating functions $\\cH_{K,L}(\\lambda;x,y)$, which subsume the known expressions for $\\cH_{1,L}(\\lambda;x,y)$~\\cite{prudnikov1992integrals}, $\\cH_{2,0}(\\lambda;x,y)$~\\cite{foata1981some,foataStrehl1984,dattoli2017operational}\n and $\\cH_{3,0}(\\lambda;x,y)$~\\cite{gessel2005triple}. For the convenience of readers who would like to perform experimental mathematics around our methods, we provide some explicit examples for $\\cH_{K,0}(\\lambda;x,y)$ for $K=1,\\dotsc,10$ in Table~\\ref{tab:HPlacFull} as well as some Maple code in Appendix~\\ref{app:Maple}.\n \n\n\n\n\n{\\footnotesize\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nThe interaction between qubits and a cavity is ubiquitous in several\nbranches of physics ranging from quantum optics~\\cite{Scully}, to quantum information~\\cit\n{Wallraff}  to condensed-matter physics~\\cite{Leggett}. In early work on cavity quantum electrodynamics (QED),\nthe qubit-cavity coupling strength was much smaller than the cavity\ntransition frequency, the rotating-wave approximation (RWA) can be applied, and an analytical exact solution can be derived straightforwardly~\\cite{jaynes}.\nWith recent advances in the\ncircuit QED using superconducting qubits, it is possible to engineer\nsystems for which the qubits are so far detuned from the cavity, or are\ncoupled to the cavity in a ultra-strong coupling regime where the coupling\nstrength is comparable to the cavity transition frequency, that the RWA is demonstrated  to\nfail to describe the system correctly~\\cit\n{Niemczyk,pfd,fedorov,devoret,you,li}. The counter-rotating-wave (CRW)\ninteractions in the qubit-cavity systems are therefore expected to play a crucial role.\n\nUnder the RWA, the ground state  is simply a direct product of the low state of the qubit and the vacuum cavity.\nThe CRW interactions lead to a squeezed vacuum state containing virtual photons\n\\cite{Ashhab,ciuti}. The analytical exact study in the full model is highly nontrivial. There have been numerous theoretical studies on\none- and two-qubit and cavity coupling systems, including the adiabatic approximation~\\cit\n{Ashhab1,agarwal}, a Bargmann space technique~\\cite{Braak,Zhong}, an\nextended coherent-state method~\\cite{chen,mao15}, and a generalized RWA (GRWA)~\\cite{irish,zhang}. Recently there\nhave been interesting applications of the Dicke model~\\cite{dicke} with three\nqubits in the quantum information technology, such as the application of the Greenberger-Horne-Zeilinger states~\\cit\n{GHZ}. And the circuit QED has entered the deep-strong-coupling\nregime ~\\cite{Yoshihara}, so it is experimentally possible to\nrealize the three-qubit Dicke model in circuit QED in the ultra-strong-\nand deep-strong-coupling regime~\\cite{sonalo}. We will present an\nanalytical solution to a three-qubit Dicke model. However, explicit\nanalytic solutions to the three- and more-qubit Dicke model have not\nbeen extensively studied. Despite the fact that the exact solution to the\nthree-qubit  Dicke model has been given by a Bargmann space technique~\\cit\n{Braak1} where a numerical search for the zeros of very complicated\ntranscendental  functions is needed, an efficient, easy-to-implement\ntheoretical treatment remains elusive. In this paper, we extend the\nprevious GRWA in  the one-qubit Rabi model by Irish~\\cite{irish}  to\nthe three-qubit Dicke model. Including the CRW interactions, we\nsuccessfully derive a solvable Hamiltonian with the same form as the\nordinary RWA term. Therefore all eigenvalues and eigenstates can be\napproximately solved and can be implemented with great ease by\nexperimentalists.\n\n\n\n\nThere is on going interest in the genuine multipartite\nentanglement (GME) of the Dicke states for multiple qubits systems~\\cit\n{novo,horodecki}.\nMost of the existing studies of\nentanglement focus on bipartite entanglement in the reduced state of two parties of a multipartite system~\\cit\n{nielsen,roscilde,giamp,zurek}, which can be quantified through the von\nNeumann entropy~\\cite{wehrl,schu} and the concurrence characterizing qubit-qubit\nentanglement~\\cite{wang,vidal,zhang1}. However, bipartite entanglement can\nonly give a partial characterization. Multipartite entanglement is\nknown to be different from entanglement between all bipartitions~\\cit\n{ali,Guhne,bodoky}. Recently the\nbipartite entanglement decoherence has been studied in connection with a\nphenomenon termed entanglement sudden death, indicating that the bipartite\nentanglement can decay to zero abruptly during a finite period of time~\\cit\n{yu1}. Whether this property occurs for the dynamics of GME remains\nunexplored. So it is highly desirable to study both the bipartite\nentanglement and the GME for the multipartite entanglement in the more than\ntwo qubits system, where the three qubits and cavity coupling system can be\nserved as the most simple paradigm.\n\nThe paper is outlined as follows. In Sec.~II, we map the three-qubit Dicke\nmodel with the CRW interactions into a solvable Hamiltonian by the zeroth- and\nfirst-order approximation, giving an analytical expression of eigenvalues and\neigenstates. In Sec.III, we discuss dynamics of the GME for the multi-qubit\nentanglement and the concurrence for the qubit-qubit entanglement by our\nmethod. Finally, a brief summary is given in Sec.~IV.\n\n\\section{An analytical treatment to the three-qubit cavity system}\n\nThe Hamiltonian of the three-qubit Dicke model, which describes three\nidentical qubits coupled to a common harmonic cavity, is written as $\\left(\n\\hbar =1\\right) $\n\\begin{equation}\nH=-\\Delta J_{z}+\\omega a^{\\dagger }a+\\frac{g}{2}(a^{\\dagger\n}+a)(J_{+}+J_{-}),  \\label{ham1}\n\\end{equation\nwhere $a$ and $a^{\\dagger }$ are, respectively, the annihilation and\ncreation operators of the harmonic cavity with frequency $\\omega $, \nJ_{i}\\left( i=z,\\pm \\right) \\ $\\ is the angular momentum operator,\ndescribing the three qubits of level-splitting $\\Delta $ in terms of a\npseudospin of length $J=3\/2$, and $g$ denotes the collective qubit-cavity\ncoupling strength.\n\nIn the RWA, the CRW terms $a^{\\dagger }J_{+}$ and $aJ_{-}$ are neglected, and the Hamiltonian becomes\n\\begin{equation*}\nH_{\\mathtt{RWA}}=-\\Delta J_{z}+\\omega a^{\\dagger }a+\\frac{g}{2}(a^{\\dagger\n}J_{-}+aJ_{+}),\n\\end{equation*}\nwhich is restricted to relatively weak-coupling strength $g\\ll \\omega $, and\nto the qubit-cavity near resonance, $\\Delta \\approx \\omega $. Now, the\ninteraction couples only $|-\\frac{3}{2}\\rangle |n+2\\rangle $, $|-\\frac{1}{2\n\\rangle |n+1\\rangle $, $|\\frac{1}{2}\\rangle |n\\rangle $, and $|\\frac{3}{2\n\\rangle |n-1\\rangle $ for each $n$, which are the eigenstates of the noninteracting Hamiltonian $-\\Delta J_{z}+\\omega a^{\\dagger }a$. The whole Hilbert space can then be decomposed into the subspaces formed by these states which  can be diagonalized analytically. It is easy\nto write the following tri-diagonal matrix form:\n\\begin{widetext}\n\\begin{equation}\nH_{\\texttt{RWA}}=\\left(\n\\begin{array}{cccc}\n\\omega (n+2)+\\frac{3\\Delta }{2} & T_{n+1,n+2} & 0 & 0 \\\\\nT_{n+1,n+2} & \\omega (n+1)+\\frac{\\Delta }{2} & T_{n,n+1} & 0 \\\\\n0 & T_{n,n+1} & \\omega n-\\frac{\\Delta }{2} & T_{n-1,n} \\\\\n0 & 0 & T_{n-1,n} & \\omega (n-1)-\\frac{3\\Delta }{2\n\\end{array\n\\right) .  \\label{RWA}\n\\end{equation\n\\end{widetext}\nwhere\n\\begin{eqnarray*}\nT_{n+1,n+2}&&=g\\sqrt{3(n+2)}\/4,T_{n,n+1}=g\\sqrt{n+1}\/4, \\\\\nT_{n-1,n}&&=g\\sqrt{3n}\/4.\n\\end{eqnarray*}\n\nIf CRW terms $a^{\\dagger }J_{+}$ and $aJ_{-}$ are included, the Hilbert\nspace cannot be decomposed into the finite dimensional spaces, because the\ntotal excitation number $N=a^{\\dagger }a+J_{z}+3\/2$ is non-conserved and the\nsubspace for different index $n$ defined above is highly correlated. So\nanalytical solutions in this case should be highly non-trivial.\n\nThe Hamiltonian (\\ref{ham1}) including the CRW terms with a rotation around the \ny$ axis by an angle $\\pi\/2$ can be rewritten as\n\\begin{equation}\nH=\\Delta J_{x}+\\omega a^{\\dagger }a+g(a^{\\dagger }+a)J_{z}.  \\label{Ham}\n\\end{equation\nIntroducing a unitary transformation $U=\\exp \\left[ \\frac{g}{\\omega \nJ_{z}\\left( a^{\\dagger }-a\\right) \\right] $, one can obtain the transformed\nHamiltonian $H'_{SB}=H_{0}+H_{1}$, consisting of\n\\begin{eqnarray}  \\label{H_11}\nH_{0} &=&\\omega a^{\\dagger }a-\\frac{g^{2}}{\\omega }J_{z}^{2},  \\label{H_0} \\\\\nH_{1} &=&\\Delta \\left\\{ J_{x}\\cosh \\left[ \\frac{g}{\\omega }\\left( a^{\\dagger\n}-a\\right) \\right] +iJ_{y}\\sinh \\left[ \\frac{g}{\\omega }\\left( a^{\\dagger\n}-a\\right) \\right] \\right\\}.\\label{H_11}  \\notag \\\\\n\\end{eqnarray\nThen We can expand the even and odd functions $\\cosh (y)$ and $\\sinh (y)$, respectively, as\n$\\cosh \\left[ \\frac{g}{\\omega }\\left(\na^{\\dagger }-a\\right) \\right] =G_{0}\\left( a^{\\dagger }a\\right) +G_{1}\\left(\na^{\\dagger }a\\right) \\left( a^{\\dagger }\\right) ^{2}+a^{2}G_{1}\\left(\na^{\\dagger }a\\right) +...$ and $\\sinh \\left[ \\frac{g}{\\omega }\\left(\na^{\\dagger }-a\\right) \\right] =F_{1}\\left( a^{\\dagger }a\\right) a^{\\dagger\n}-aF_{1}\\left( a^{\\dagger }a\\right) +F_{2}\\left( a^{\\dagger }a\\right) \\left(\na^{\\dagger }\\right) ^{3}-a^{3}F_{2}\\left( a^{\\dagger }a\\right) +...$, where \nG_{i}(a^{\\dagger }a)(i=0,1,...)$ and $F_{j}(a^{\\dagger }a)(j=1,2,...)$ are\ncoefficients that depend on the cavity number operator $\\widehat{n}=a^{\\dagger}a$\nand the dimensionless parameter $g\/\\omega$. A different order of approximations can then be performed by\nneglecting some terms in the expansions.\n\n\\textsl{zeroth-order approximation:} In the zeroth-order approximation, we\nonly keep the first term $G_{0}\\left( a^{\\dagger }a\\right) $ in $\\cosh\n\\left[ \\frac{g}{\\omega }\\left( a^{\\dagger }-a\\right) \\right] $, and the Hamiltonian is approximated as\n\\begin{equation}\nH^{^{0th}}=\\omega a^{\\dagger }a-\\frac{g^{2}}{\\omega }J_{z}^{2}+\\Delta\nJ_{x}G_{0}\\left( a^{\\dagger }a\\right) .\n\\end{equation}\nIn the basis of the oscillator state $|n\\rangle$, the term $G_{0}\\left( a^{\\dagger }a\\right) $ only has\nnon-vanishing diagonal element\n\\begin{equation}\nG_{0}(n)=\\langle n|\\cosh \\left[ \\frac{g}{\\omega }\\left( a^{\\dagger\n}-a\\right) \\right] |n\\rangle =e^{-\\frac{g^{2}}{2\\omega ^{2}}}L_{n}(\\frac\ng^{2}}{\\omega ^{2}}),\n\\end{equation}\nwhere Laguerre polynomials $L_{n}^{m-n}(x)=\\sum_{i=0}^{\\min\n\\{m,n\\}}(-1)^{n-i}\\frac{m!x^{n-i}}{(m-i)!(n-i)!i!}$.\nNote that only the\noscillator number operator $\\widehat{n}$ appears, so the\nHilbert space can be decomposed into different $n$ manifolds spanned by the spin\nand cavity basis of $|-\\frac{3}{2}\\rangle |n\\rangle $, $|-\\frac{1}{2}\\rangle\n|n\\rangle $, $|\\frac{1}{2}\\rangle |n\\rangle $ and $|\\frac{3}{2}\\rangle\n|n\\rangle $. In the subspace containing only the $n$-th manifold, the\nHamiltonian takes the form\n\\begin{widetext}\n\\begin{equation}\\label{h0}\nH^{^{0th}}=\\left(\n\\begin{array}{cccc}\n\\omega n-\\frac{9g^{2}}{4\\omega } & \\frac{\\sqrt{3}}{2}\\Delta G_{0}(n) & 0 & 0\n\\\\\n\\frac{\\sqrt{3}}{2}\\Delta G_{0}(n) & \\omega n-\\frac{g^{2}}{4\\omega } & \\Delta\nG_{0}(n) & 0 \\\\\n0 & \\Delta G_{0}(n) & \\omega n-\\frac{g^{2}}{4\\omega } & \\frac{\\sqrt{3}}{2\n\\Delta G_{0}(n) \\\\\n0 & 0 & \\frac{\\sqrt{3}}{2}\\Delta G_{0}(n) & \\omega n-\\frac{9g^{2}}{4\\omega \n\\end{array\n\\right).\n\\end{equation\n\\end{widetext}\nThe corresponding eigenvalues\nand eigenvectors are straightforwardly given by respectively\n\\begin{eqnarray}  \\label{zeroenergy}\n\\varepsilon _{1,n} &=&\\omega n-\\frac{5g^{2}}{4\\omega }-\\frac{1}{2\nB_{n}-2\\chi _{1,n},  \\notag  \\label{zeroenergy} \\\\\n\\varepsilon _{2,n} &=&\\omega n-\\frac{5g^{2}}{4\\omega }+\\frac{1}{2\nB_{n}-2\\chi _{2,n},  \\notag \\\\\n\\varepsilon _{3,n} &=&\\omega n-\\frac{5g^{2}}{4\\omega }-\\frac{1}{2\nB_{n}+2\\chi _{1,n},  \\notag \\\\\n\\varepsilon _{4,n} &=&\\omega n-\\frac{5g^{2}}{4\\omega }+\\frac{1}{2\nB_{n}+2\\chi _{2,n},\n\\end{eqnarray\nand\n\\begin{eqnarray}\n|\\varphi _{1,n}\\rangle &\\varpropto &\\left(\n\\begin{array}{c}\n-1 \\\\\nK_{1,n} \\\\\n-K_{1,n} \\\\\n\n\\end{array\n\\right) ,|\\varphi _{2,n}\\rangle \\varpropto \\left(\n\\begin{array}{c}\n1 \\\\\n-K_{2,n} \\\\\n-K_{2,n} \\\\\n\n\\end{array\n\\right) ,  \\notag \\\\\n|\\varphi _{3,n}\\rangle &\\varpropto &\\left(\n\\begin{array}{c}\n-1 \\\\\nK_{3,n} \\\\\n-K_{3,n} \\\\\n\n\\end{array\n\\right) ,|\\varphi _{4,n}\\rangle \\varpropto \\left(\n\\begin{array}{c}\n1 \\\\\n-K_{4,n} \\\\\n-K_{4,n} \\\\\n\n\\end{array\n\\right) ,  \\label{eigenstates}\n\\end{eqnarray\nwhere\n\\begin{equation}\nK_{i,n}=\\\n\\begin{array}{c}\n\\frac{1}{\\sqrt{3}B_{n}}[-\\frac{2g^{2}}{\\omega }-(-1)^{i}B_{n}+4\\chi\n_{i,n}],(i=1,2) \\\\\n\\frac{1}{\\sqrt{3}B_{n}}[-\\frac{2g^{2}}{\\omega }-(-1)^{i}B_{n}-4\\chi\n_{i-2,n}],(i=3,4\n\\end{array\n,  \\label{ki}\n\\end{equation\nand\n\\begin{equation*}\n\\chi _{i,n}=\\sqrt{\\frac{g^{4}}{4\\omega ^{2}}+(-1)^{i}\\frac{g^{2}}{4\\omega \nB_{n}+\\frac{B_{n}^{2}}{4}}(i=1,2)\n\\end{equation*}\nwith $B_{n}=\\Delta G_{0}(n)$. Interestingly, the zeroth-order approximation is similar\nto the adiabatic approximation in the two-qubit system~\\cite{agarwal}, where the transition\nbetween different manifolds is not considered, and the $n$th state is only limited to the same $n$-th manifold.\n\n\nThe validity of the zeroth-order approximation is restricted to the large detuning regime $\\Delta\/\\omega\\ll1$.\nIn the zero detuning limiting, $\\Delta =0$, within the same manifold $n$, $|\\pm \\frac{3}\n2}\\rangle |n\\rangle $ and $|\\pm \\frac{1}{2}\\rangle |n\\rangle $ are nearly\ndegenerate. For a large\ndetuning $\\Delta\/\\omega\\ll1 $, it is reasonable to consider the qubit states with the same $n$\nmanifold coupled by the interaction.\nEspecially, for a strong coupling strength $g\/\\omega\\gg\\Delta\/\\omega$, the diagonal\nterms of the approximated Hamiltonian in Eq.(~\\ref{h0}) play a more dominant role than the off-diagonal terms dependent on $\\Delta$.\nAnd the high order terms in Eq.(~\\ref{H_11}) still can be neglected even in the strong coupling regimes.\nHence, the zeroth-order approximation is expected to work well from weak to strong coupling regimes for the large detuning case $\\Delta\/\\omega\\ll1$.\n\nThe zeroth-order energy spectrum is plotted in Fig.~\\re\n{energy level} with dash-dotted lines.\nIn large detuning regime $\\Delta\/\\omega =0.1$,\nthe zeroth-order results agree well with the numerical ones from weak to\nstrong coupling regimes in Fig.~\\ref{energy level}(a). But the\nRWA fails to give correct energies as the coupling strength $g\/\\omega$\nincreases. Because of the coupling of the qubit and the original oscillator, the latter should be displaced. Thus, the displaced oscillator state in\nthe zeroth-order approximation, $|n\\rangle _{j}=\\exp [\\frac{jg}{\\omega \n(a^{\\dagger}-a)]|n\\rangle (j=\\pm \\frac{3}{2},\\pm \\frac{1}{2})$, plays a more\nimportant role than the original oscillator state $|n\\rangle$ in the RWA,\nresulting in more accurate eigen-energies in Eq. (~\\ref{zeroenergy}) and\neigenfunctions in Eq. (~\\ref{eigenstates}). However, there is a noticeable\ndeviation of the zeroth-order approximated results for the resonance case \n\\Delta \/\\omega =1$, indicating that the higher-order terms in Eq. (\\ref{H_11\n) should be taken into account. Physically, qubit states with different $n$ manifolds should be coupled by the interactions.\n\n\\begin{center}\n\\begin{figure*}[tbp]\n\\includegraphics[scale=0.8]{elevel.eps}\n\\caption{(Color online) Energy levels obtained by the GRWA (dashed\nlines) for different $\\Delta\/\\protect\\omega =0.1$ (a), and $\\Delta\/\\protec\n\\omega =1$ (b). The energies by the numerically exact diagonalization (\nsolid lines), results of RWA (short dotted lines) and results obtained by\nthe zeroth-order approximation (dashed dotted lines) are plotted for\ncomparison.}\n\\label{energy level}\n\\end{figure*}\n\\end{center}\n\n\n\n\\textsl{First-order approximation:} Keeping the linear terms in $a$ and \na^{\\dag }$ and neglecting all higher order terms in the interaction Hamiltonian $H_{1}$(\\ref{H_11}) gives\n\\begin{equation}\nH_{1}=\\Delta \\{J_{x}G_{0}\\left( a^{\\dagger }a\\right) +iJ_{y}[F_{1}\\left(\na^{\\dagger }a\\right) a^{\\dagger }-aF_{1}\\left( a^{\\dagger }a\\right) ]\\}.\n\\label{H_1}\n\\end{equation\nThe term $F_{1}\\left( a^{\\dagger }a\\right) a^{\\dagger }$ describes the\nphoton hopping from state $\\left\\vert n\\right\\rangle $ to $\\left\\vert\nn+1\\right\\rangle $. It is reasonable to set $\\left\\langle n+1\\right\\vert\nR_{n+1,n}a^{\\dagger }\\left\\vert n\\right\\rangle =\\left\\langle n+1\\right\\vert\nF_{1}\\left( a^{\\dagger }a\\right) a^{\\dagger }\\left\\vert n\\right\\rangle $ by\n\\begin{eqnarray}\nR_{n+1,n} &=&\\left\\langle n+1\\right\\vert \\sinh \\left[ \\frac{g}{\\omega \n\\left( a^{\\dagger }-a\\right) \\right] \\left\\vert n\\right\\rangle \/\\sqrt{n+1}\n\\notag \\\\\n&=&\\frac{1}{n+1}\\frac{g}{\\omega }e^{-\\frac{g^{2}}{2\\omega ^{2}}}L_{n}^{1}\n\\frac{g^{2}}{\\omega ^{2}}).  \\label{Rn}\n\\end{eqnarray\nSimilarly, the term $aF_{1}\\left( a^{\\dagger }a\\right) $ only has non-vanishing\nelement $\\langle n\\left\\vert aF_{1}\\left( a^{\\dagger }a\\right) |n+1\\right\\rangle $.\nIt follows that the term $F_{1}\\left( a^{\\dagger\n}a\\right) a^{\\dagger }$\\ creates and $aF_{1}\\left( a^{\\dagger }a\\right) $\neliminates a single photon of the cavity. The physics process is similar to that described in\nthe RWA model, which facilitates the further analytic treatment.\n\nThe Hamiltonian now is $H^{1st}=H_{0}^{^{\\prime }}+H_{1}^{^{\\prime }}$:\n\\begin{eqnarray}\nH_{0}^{^{\\prime }} &=&\\omega a^{\\dagger }a-\\frac{g^{2}}{\\omega \nJ_{z}^{2}+\\Delta \\beta J_{x}, \\\\\nH_{1}^{^{\\prime }} &=&\\Delta J_{x}[G_{0}\\left( a^{\\dagger }a\\right) -\\beta\n]+iJ_{y}\\Delta \\lbrack F_{1}\\left( a^{\\dagger }a\\right) a^{\\dagger\n}-aF_{1}\\left( a^{\\dagger }a\\right) ],  \\notag\n\\end{eqnarray\nwhere $\\beta =G_{0}\\left( 0\\right) =e^{-\\frac{g^{2}}{2\\omega ^{2}}}$.\n\nSince the qubit and cavity in the noninteracting part $H_{0}^{^{\\prime }}$ are\ndecoupled, we apply a unitary transformation $S$ to diagonalize the qubit\npart in $H_{0}^{^{\\prime }}$\n\\begin{equation}\nS=\\left(\n\\begin{array}{cccc}\n-\\frac{1}{C_{1}} & \\frac{1}{C_{2}} & -\\frac{1}{C_{3}} & \\frac{1}{C_{4}} \\\\\n\\frac{K_{1}}{C_{1}} & -\\frac{K_{2}}{C_{2}} & \\frac{K_{3}}{C_{3}} & -\\frac\nK_{4}}{C_{4}} \\\\\n-\\frac{K_{1}}{C_{1}} & -\\frac{K_{2}}{C_{2}} & -\\frac{K_{3}}{C_{3}} & -\\frac\nK_{4}}{C_{4}} \\\\\n\\frac{1}{C_{1}} & \\frac{1}{C_{2}} & \\frac{1}{C_{3}} & \\frac{1}{C_{4}\n\\end{array\n\\right) ,\n\\end{equation\nwhere $K_{i}$ has been defined in Eq.(~\\ref{ki}) for $n=0$, and the\nnormalized parameter is $C_{i}=\\sqrt{2+2K_{i}^{2}}$.\nThe corresponding eigenvalues are $\\varepsilon_{i,0}$ in Eq.(~\\ref{zeroenergy}).\n\nIn terms of  the transformation $S^{\\dagger}H_{1}^{^{\\prime }}S$,\nthe Hamiltonian $H^{1st}$ of the three-qubit Dicke model can be approximated as\n\\begin{widetext}\n\\begin{eqnarray}\nH_{\\texttt{GRWA}} &=&\\omega a^{\\dagger }a+\\mu _{1}(a^{\\dagger }a)|-\\frac{3}{2}\\rangle \\langle -\\frac\n3}{2}|+\\mu _{2}(a^{\\dagger }a)|-\\frac{1}{2}\\rangle \\langle -\\frac{1}{2}|+\\mu _{3}(a^{\\dagger }a)|\\frac{1}{\n}\\rangle \\langle \\frac{1}{2}|+\\mu _{4}(a^{\\dagger }a)|\\frac{3}{2}\\rangle \\langle \\frac{3}{2\n|  \\nonumber  \\label{GRWAham} \\\\\n&&+\\Delta F_{1}\\left( a^{\\dagger }a\\right) [\\frac{-\\sqrt{3}K_{2}+K_{1}(\\sqrt\n3}+2K_{2})}{C_{1}C_{2}}(a|-\\frac{1}{2}\\rangle \\langle -\\frac{3}{2}|+h.c)  \\nonumber \\\\\n&&+\\frac{-\\sqrt{3}K_{3}+K_{2}(\\sqrt{3}-2K_{3})}{C_{2}C_{3}}(a|\\frac{1}{2\n\\rangle \\langle -\\frac{1}{2}|+h.c)\n\\nonumber \\\\\n&&+\\frac{-\\sqrt{3}K_{4}+K_{3}(\\sqrt{3}+2K_{4})}{C_{3}C_{4}}(a|\\frac{3}{2\n\\rangle \\langle \\frac{1}{2}|+h.c)],\n\\end{eqnarray}\n\\end{widetext}\nwhere $\\mu _{i}(a^{\\dagger }a)=\\varepsilon _{i,0}-\\Delta [G_{0}\\left( a^{\\dagger }a\\right) -\\beta ]\\frac{2K_{i}[\\sqrt{\n}-(-1)^{i}K_{i}]}{_{C_{i}^{2}}}$.\nThere are only the energy-conserving terms $(a|-\\frac{1}{2}\\rangle \\langle \n\\frac{3}{2}|+h.c)$, $(a|\\frac{1}{2}\\rangle \\langle -\\frac{1}{2}|+h.c)$, and \n(a|\\frac{3}{2}\\rangle \\langle \\frac{1}{2}|+h.c)$ with renormalized\ncoefficients, originating from the CRW terms $iJ_{y}[F_{1}\\left(\na^{\\dagger }a\\right) a^{\\dagger }-aF_{1}\\left( a^{\\dagger }a\\right)\n]$. The dominated effect of the original CRW terms is considered\nhere. Because it is the three-qubit Dicke model Hamiltonian in the same\nRWA form with renormalized coefficients, the present approach\nessentially borrows the basic idea of the GRWA  proposed by Irish\nfor the one-qubit model~\\cite{irish}.\n\n\nNote that the individual bosonic creation (annihilation) operator \na^{\\dagger }\\left( a\\right) $ appears in the GRWA, so the qubits\nstates with different oscillator number $n$, $n\\pm1$ and $n+2$ are coupled with each other. In the basis of $|-\\frac{3}{2}\\rangle |n+2\\rangle $, $|-\\frac{1}{2}\\rangle\n|n+1\\rangle $, $|\\frac{1}{2}\\rangle |n\\rangle $ and $|\\frac{3}{2}\\rangle\n|n-1\\rangle $ ($n>0$), the Hamiltonian $H_{\\texttt{GRWA}}$ can be written in the matrix form as\n\\begin{widetext}\n\\begin{equation}\nH_{\\texttt{GRWA}}=\\left(\n\\begin{array}{cccc}\n\\omega (n+2)+\\mu _{1}(n+2) & \\Delta R_{n+1,n+2}^{\\prime } & 0 & 0 \\\\\n\\Delta R_{n+1,n+2}^{\\prime } & \\omega (n+1)+\\mu _{2}(n+1) & \\Delta R_{n,n+1}^{\\prime }\n& 0 \\\\\n0 & \\Delta R_{n,n+1}^{\\prime } & \\omega n+\\mu _{3}(n) & \\Delta R_{n-1,n}^{\\prime } \\\\\n0 & 0 & \\Delta R_{n-1,n}^{\\prime } & \\omega (n-1)+\\mu _{4}(n-1\n\\end{array\n\\right) ,\n\\end{equation}\n\\end{widetext}with $R_{n+1,n+2}^{\\prime }=\\frac{-\\sqrt{3}K_{2}+K_{1}(\\sqrt{3\n+2K_{2})}{C_{1}C_{2}}R_{n+1,n+2}\\sqrt{n+2}$, $R_{n,n+1}^{\\prime }=\\frac{\n\\sqrt{3}K_{3}+K_{2}(\\sqrt{3}-2K_{3})}{C_{2}C_{3}}R_{n,n+1}\\sqrt{n+1}$ and \nR_{n-1,n}^{\\prime }=\\frac{-\\sqrt{3}K_{4}+K_{3}(\\sqrt{3}+2K_{4})}{C_{3}C_{4}\nR_{n-1,n}\\sqrt{n}$.\n\nTo this end, the GRWA can be also performed analytically  without more efforts than\nthose in the original Hamiltonian $H_{\\texttt{RWA}}$ in Eq.(\\ref{RWA}).\nThe displaced oscillator states $|n\\rangle _{m}$, $|n\\pm\n1\\rangle _{m}$ and $|n+2\\rangle _{m}$ depend upon the Dicke state \n|j,m\\rangle $, and are definitely different from both the RWA ones and the zeroth-order approximations where\nonly the state $|n\\rangle_{m}$ is considered. Hence, as $\\Delta\/\\omega$ increases,\nthe first-order correction provides an efficient, yet accurate analytical solution.\n\nThe ground-state energy for the ground state $|-\\frac{3}{2}\\rangle |0\\rangle\n$ is\n\\begin{equation}\nE_{0}=-\\frac{5g^2}{4\\omega}-\\frac{\\Delta }{2}e^{-\\frac{g^{2}}{2\\omega ^{2}}}-2\\chi _{1,0}.\n\\end{equation}\nThe first and second excited energies $\\{E_{0}^{k}\\}$ ($k=1,2$) can be given\nby expanding the GRWA Hamiltonian in the basis $|-\\frac{3}{2}\\rangle\n|1\\rangle$ and $|-\\frac{1}{2}\\rangle |0\\rangle$\n\\begin{equation}\nH_{\\mathtt{GRWA}}=\\left(\n\\begin{array}{cc}\n\\omega +\\mu _{1}(1) & \\Delta R_{0,1}^{\\prime } \\\\\n\\Delta R_{0,1}^{\\prime } & \\mu _{2}(0\n\\end{array\n\\right) .\n\\end{equation\nSimilarly, $H_{\\mathtt{GRWA}}$ is given in terms of $|-\\frac{3}{2}\\rangle\n|2\\rangle $, $|-\\frac{1}{2}\\rangle |1\\rangle $, $|\\frac{1}{2}\\rangle\n|0\\rangle $ as\n\\begin{equation}\nH_{\\mathtt{GRWA}}=\\left(\n\\begin{array}{ccc}\n2\\omega +\\mu _{1}(2) & \\Delta R_{1,2}^{\\prime } & 0 \\\\\n\\Delta R_{1,2}^{\\prime } & \\omega +\\mu _{2}(1) & \\Delta R_{0,1}^{\\prime } \\\\\n0 & \\Delta R_{0,1}^{\\prime } & \\mu _{3}(0\n\\end{array\n\\right) ,\n\\end{equation\nwhich provides three analytical excited energies $\\{E_{0}^{k}\\}$ ($k=3,4,5$).\n\nEnergies obtained by the GRWA are presented in dashed lines in Fig.~\\re\n{energy level}. Especially, for the resonance case $\\Delta =\\omega $, the GRWA results are much better than the zeroth-order results (blue dotted lines) in Fig.\\ref{energy level}(b). It ascribes to the effect of the coupling between states\nwith different manifolds. Our approach is basically a perturbative expansion\nin terms of $\\Delta\/\\omega$. As the increase of the $\\Delta \/\\omega$ ,\nthe high order terms in Eq.(5) still cannot be neglected in the intermediate and strong coupling regimes.\nSo the GRWA works reasonably well in the ultra-strong coupling regime $g\/\\omega<0.3$ at resonance.\nInterestingly, the level crossing is present in both the GRWA results\nand the exact ones. The RWA requires weak coupling due to the complete neglect of the CRW terms, which are\nqualitatively incorrect as the coupling strength increases. So the GRWA includes the dominant contribution of the CRW\nterms, exhibiting substantial improvement\nof energy levels over the RWA one. The RWA fails in particular to describe\nthe eigenstates, which should be more sensitive in the quantum entanglement\npresented in the next section.\n\n\\section{Quantum entanglement}\n\nIn the present three-qubit system, we study the GME for the multipartite entanglement and the concurrence for the bipartite\nentanglement. A fully separable three-particle state must contain no entanglement.\nIf the state is not fully separable, then it\ncontains some entanglement, but it might be still separable with respect to\ntwo-party configurations. For genuine multiparticle entangled states, all\nparticles are entangled and therefore GME is   very important   among various definition of entanglements.\n\n\nWe review the basic definitions of GME for the three qubits $A$, $B$, and $C$. A separable state is a mixture of product states with respect to a bipartition $A|BC$, that is $\\rho_{A|BC}^{sep}=\\sum_{j}p_j|\\varphi_A^j\\rangle\\langle\\varphi_A^j|\\otimes|\\varphi_{BC}^j\\rangle\\langle\\varphi_{BC}^j|$,\n where $p_j$ is a coefficient. Similarly, we denote other separable states for the two other bipartitions as $\\rho_{B|AC}^{sep}$ and $\\rho_{C|AB}^{sep}$. A biseparable state is a mixture of separable states, and combines the separable states $\\rho_{A|BC}^{sep}$, $\\rho_{B|AC}^{sep}$, and $\\rho_{C|AB}^{sep}$ with respect to all possible bipartitions. Any state that is not a biseparable state is called genuinely multipartite entangled.\n\nRecently, a powerful technique has been advanced to characterize multipartite entanglement using positive partial transpose (PPT) mixtures~\\cite{peres}. It is well known that a separable state is PPT, implying that its partial transpose is positive semidefinite.\nWe denote a PPT mixture of a tripartite state as a convex combination of PPT states $\\rho_{A|BC}^{PPT}$, $\\rho_{B|AC}^{PPT}$ and $\\rho_{C|AB}^{PPT}$\nwith respect to different bipartitions.\nThe set of PPT mixtures contains the set of\nbiseparable states. The advantage of using PPT mixtures instead of biseparable states is that the set of PPT mixtures\ncan be fully characterized by the linear semidefinite programming (SDP)~\\cite{boyd},\nwhich is a standard problem of constrained convex optimization theory.\n\nIn order to characterize PPT mixtures, a multipartite state which is not a PPT mixture can be detected by a decomposable entanglement witness $W$~\\cite{novo}. The witness operator is defined as $W=P_M+Q_M^{T_M}$ for all bipartitions $M|\\bar{M}$, where $P_M$, and $Q_M$ are positive semidefinite operators, and $T_M$ is the partial transpose with respect to $M$. This observable $W$ is positive on all PPT mixtures, but has a negative expectation value on at least one entangled state.\nTo find a fully decomposable witness for a given state $\\rho$, the convex optimization technique SDP\nbecomes important, since it allows us to optimize over all fully decomposable witnesses.\nHence, a state $\\rho$ is a PPT mixture only if the optimization problem~\\cite{novo},\n\\begin{equation}  \\label{minm}\n\\textrm{minimize:} {}{} \\mathtt{Tr}(W\\rho).\n\\end{equation}\nhas a positive solution. If the minimum in Eq. (~\\ref{minm}) is negative, $\\rho$ is\nnot a PPT mixture and hence is genuinely multipartite entangled.\nWe denote the absolute value of the above minimization as $E(\\rho)$. For solving the SDP we use the programs YALMIP and SDPT3~\\cite{yalmip,program}, which are freely available.\n\n\nNow we discuss the dynamics of the GME for the three-qubit entanglement.\nThe initial entangled three-qubit state is chosen as the W state with only one excitation\n\\begin{equation}\n|W\\rangle =\\frac{1}{\\sqrt{3}}(|100\\rangle +|010\\rangle +|001\\rangle ),\n\\label{initial state}\n\\end{equation\nwhich corresponds to the Dicke state $|D_{3}\\rangle =|-\\frac{1}{2\n\\rangle $. For the Hamiltonian (~\\ref{Ham}) with respect to the rotation around the \ny$ axis by the angle $\\pi\/2$, the initial Dicke state can be written as\n\\begin{equation}\n|D_{3}\\rangle =\\frac{1}{\\sqrt{8}}(-\\sqrt{3}|-\\frac{3}{2}\\rangle -|-\\frac{1}{\n}\\rangle +|\\frac{1}{2}\\rangle +\\sqrt{3}|\\frac{3}{2}\\rangle),\n\\label{initial state1}\n\\end{equation\nand the initial cavity state is the vacuum state $|0\\rangle $. Based on the\neigenstates $\\left\\{ |\\varphi _{k,n}\\rangle\\right\\} $ and eigenvalues \n\\left\\{ E_{n}^{k}\\right\\} $ in the GRWA and the zeroth-order approximation,\nthe wavefunction evolves from the initial state as $|\\phi (t)\\rangle\n=\\sum_{n,k}e^{-iE_{n}^{k}t}|\\varphi _{k,n}\\rangle \\langle \\varphi\n_{k,n}|D_{3}\\rangle $. And the three-qubit reduced state $\\rho (t)$ can be given by\ntracing out the cavity degrees of freedom\n\\begin{equation}\n\\rho (t)=\\texttt{Tr}_{\\mathtt{cavity\n}(|\\phi (t)\\rangle \\langle \\phi (t)|).\n\\end{equation}\nWe then calculate the absolute value of the minimum $E(\\rho )$ to detect the GME by solving the minimum in Eq.(~\\ref{minm}).\n\n\\begin{figure}[tbp]\n\\includegraphics[scale=0.45]{GMEDym.eps}\n\\caption{(Color online) Dynamics of the GME for three-qubit entanglement\nwith the initial W state for the ultrastrong-coupling strength $g\/\\protec\n\\omega=0.1$ with the different detuning $\\Delta\/\\protect\\omega=0.1$ (a) and \n\\Delta\/\\protect\\omega=1$ (b) by the GRWA method (dash-dotted lines),\nnumerical method (solid lines), RWA (short-dotted\nlines), and the zeroth-order approximation (dashed lines).}\n\\label{dynamics GEM}\n\\end{figure}\n\nFig.~\\ref{dynamics GEM} shows the $E(\\rho )$ plotted against parameter $\\Delta t\/(2\\pi)$ for different detunings $\\Delta\/\\omega$\nfor the ultra-strong-coupling strength $g\/\\omega =0.1$. For comparison, results from numerical exact\ndiagonalization and RWA are also shown. We observe a quasi-periodic behavior\nof the GME dynamics. $E(\\rho )$ decays from the initial entangled W state\nand falls off to a nonzero minimum value, implying no death of the three-qubit entanglement. The GME dynamics obtained by the\nGRWA are consistent with the numerical results, while the RWA results are\nqualitatively incorrect for the off-resonance case $\\Delta \/\\omega =0.1$ in\nFig.~\\ref{dynamics GEM} (a). The zeroth-order approximation, where only states within\nthe same manifold are included, works well for the off-resonance case \n\\Delta =0.1$ in Fig.~\\ref{dynamics GEM} (a) but not for the on-resonance\ncase in Fig.~\\ref{dynamics GEM} (b). The validity of the GRWA ascribes to the\ninclusion of the CRW interaction $iJ_{y}F_{1}\\left( a^{\\dagger }a\\right)\n(a^{\\dagger }-a)$.\n\n\nThe onset of the decay of the multipartite\nentanglement is due to the information loss of qubits dynamics to the cavity.\nOn the other hand, it is the interaction with the cavity that leads to the\nentanglement resurrection. The lost information will be transferred back to the qubit\nsubsystem after a finite time, which is associated with the ratio between the\ncoupling strength $g\/\\omega$ and the level-splitting of qubits $\\Delta\/\\omega$.\nAs the ratio $g\/\\Delta$ increases, the contributions of the qubit-cavity interaction become dominant\nand the lost entanglement will be transferred quickly from the cavity to qubits with\nless revivals time, as shown in Fig~\\ref{dynamics GEM} (a).\n\n\nMoreover, it is significant to study the different behavior of the multipartite entanglement and the bipartite entanglement.\nThe concurrence characterizes the\nentanglement between two qubits. Due to the symmetric Dicke states in the\nthree-qubit collective model, the concurrence is evaluated in terms of the\nexpectation values of the collective spin operators as $C=\\max\n\\{0,C_{y},C_{z}\\}$, where the quantity $C_{n}$ is defined for a given\ndirection $n(=y,z)$ as $C_{n}=\\frac{1}{2N(N-1)}\\{N^{2}-4\\langle\nS_{n}^{2}\\rangle -\\sqrt{[N(N-2)+4\\langle S_{n}^{2}\\rangle\n]^{2}-[4(N-1)\\langle S_{n}\\rangle ]^{2}}\\}$~\\cite{vidal}. From the dynamical\nwavefunction $|\\phi (t)\\rangle $, we can  easily evaluate the coefficients\nfor the qubit to remain in the $|j,m\\rangle $ state\n\\begin{equation}\\label{zeroprob}\nP_{m}^{0th}=\\sum_{n=0}^{\\infty\n}\\sum_{k=1}^{4}f_{n}(t)e^{-iE_{n}^{k}t},\n\\end{equation\nin  the zeroth-order approximation and\n\\begin{eqnarray}\\label{probability}\nP_{m}^{\\mathtt{GRWA}} &\\approx&\\sum_{n}^{\\infty\n}\\sum_{k=1}^{4}f_{n}^{k}(t)(e^{-iE_{n-2}^{k}t}+e^{-iE_{n-1}^{k}t}  \\notag \\\\\n&&+e^{-iE_{n}^{k}t}+e^{-iE_{n+1}^{k}t}),\n\\end{eqnarray\nin the GRWA. $f_{n}^{k}(t)$ is a dynamical parameter associated with the\ninitial state and the $k$-th eigenstates for each $n$. From $P_{m}^{\\mathtt{GRWA}}$ in Eq.(~\\ref{probability}), we\nobserve energy-level transitions among $E_{n-2}^{k}$, $E_{n\\pm 1}^{k}$ and \nE_{n}^{k}$ in the GRWA, which produce essential improvement of the dynamics\nover the zeroth-order ones in Eq.(~\\ref{zeroprob}). Since the average value of collective\nspin operators can be expressed by $P_m$, such as $4\\langle S_{y}^{2}\\rangle =4\\sqrt{3}({}_{-\\frac{3}{\n}}\\langle n-2|n\\rangle _{\\frac{1}{2}}P_{-\\frac{3}{2}}P_{\\frac{1}{2}}+{}_{\n\\frac{1}{2}}\\langle n-1|n+1\\rangle _{\\frac{3}{2}}P_{-\\frac{1}{2}}P_{\\frac{3}\n2}})-4(P_{-\\frac{1}{2}}^{2}+P_{\\frac{1}{2}}^{2})+3$, we calculate the concurrence $C$ by the zeroth-order approximation and the GRWA, respectively.\n\n\\begin{figure}[tbp]\n\\includegraphics[scale=0.7]{condyn.eps}\n\\caption{(Color online) Dynamics of the concurrence for the qubit-qubit\nentanglement with the initial W state for the ultrastrong coupling strength \ng\/\\protect\\omega=0.1$. The parameters are the same as in Fig.~\\protect\\re\n{dynamics GEM}.}\n\\label{dynamics concurrence}\n\\end{figure}\n\nWe plot the dynamics of the concurrence for different detunings $\\Delta \/\\omega =0.1$ and $1$ in\nFig.~\\ref{dynamics concurrence}. The initial W state gives the maximum\npairwise entanglement $C=2\/3$ of any Dicke states. Fig.~\\ref{dynamics\nconcurrence} (a) shows that dynamics of the concurrence by the zeroth-order\napproximation are similar to the numerical ones in the off-resonance case \n\\Delta \/\\omega =0.1$, in which the RWA results are invalid. The sudden death\nof the bipartite entanglement is observed in the resonance case in Fig.~\\re\n{dynamics concurrence} (b). The dynamics of the concurrence obtained by the\nGRWA is similar to the numerical results, exhibiting the disappearance of the\nentanglement for a period of time.\nHowever, there is no sudden death of the\nentanglement in the RWA case, indicating that the CRW terms are not negligible.\n\nVery interestingly, as shown in Fig.~\\ref{dynamics GEM}, the GME  for the three-qubit entanglement never vanishes, in sharp contrast with bipartite entanglement.\nDuring the vanishment of\nconcurrence, the GME is generally  small but still finite.\nIt follows  that the  two-qubit state is separable in the system, but the three-qubit state still contains residual entanglement. This may be one\nadvantage to using GME as a quantum information resource.\n\nFinally, it is significant to clarify why the GME of the tripartite entanglement behaves differently\nwith the concurrence of the bipartite entanglement. The well-known death of the concurrence\nis related to the disappearance of the entanglement in an arbitrary two-qubit subsystem, say A and B, while a deep understanding\nis associated with the question of whether there exists entanglement in the three-qubit system. Intuitively, we may think that entanglement is still stored in the bipartition $AB|C$. Negativity is used to detect the entanglement for this bipartition~\\cite{vidal2}, which\nfalls off to a nonzero minimum in Fig.~\\ref{entanglement}. It reveals that the state for the bipartition $AB|C$ is not a separable state. Similarly, those states with respect to other bipartitions $AC|B$ and $BC|A$ are not separable. Therefore, the three-qubit state stays in an entangled state and\nthe GME for the three-qubit entanglement never disappears during the death of the two-qubit entanglement. The theory of the multipartite entanglement is not fully developed and requires more insightful investigations into more- than two-party systems. We highlight here the different features of the multipartite entanglement and bipartite entanglement in the more- than two-qubit system, and have found that the GME is always robust at least in the qubits and single-mode cavity system.\n\\begin{figure}[tbp]\n\\includegraphics[scale=0.45]{compare.eps}\n\\caption{(Color online) GME for the three qubits A, B,C (dash-dotted line), negativity for the entanglement with respect to the bipartition $AB|C$ (solid line),\nand concurrence between A and B qubits (dashed line) obtained by the numerical method for \ng\/\\protect\\omega=0.1$ and $\\Delta\/\\protect\\omega =1$.}\n\\label{entanglement}\n\\end{figure}\n\n\\section{Conclusion}\n\nIn this work, we have extended the original GRWA by Irish for the one-qubit Rabi model to the three-qubit Dicke model by the unitary transformation. The zeroth-order approximation, equivalent to the adiabatic approximation,\nis suited for arbitrary coupling strengths for the large detuning case. The first-order approximation, also called GRWA,\nworks well in a wide range of coupling strength even on resonance and much better than the RWA ones. In the GRWA, the effective Hamiltonian with\nthe CRW interactions is evaluated as the same form of the ordinary RWA one, which facilitates the derivation of the explicit analytic solutions. All eigenvalues and eigenstates can be approximately given.\n\nBy the proposed GRWA scheme, we have also calculated the dynamics of concurrence for the bipartite entanglement and the GME for the multipartite entanglement, which are in quantitative agreement with the numerical ones. The well-known sudden death of the two-qubit entanglement is observed by our analytic solution.\nAn interesting phenomenon of entanglement is that the GME for the three-qubit entanglement decays to the nonzero minimum during the time window in which the two-qubit entanglement disappears, implying that three qubits remain entangled when the two-qubit state is separable.\nOur results indicate that the GME is the powerful entanglement to detect quantum correlations in multipartite systems that cannot be described via bipartite entanglement in subsystems of smaller particles.\nThere still exists many open problems to the theory of entanglement for multipartite systems due to much richer structure of the entanglement in a more- than two-party system. In particular, the dynamical behaviors for two kinds of\nentanglement may be explored in the multi-qubit realized in the recent\ncircuit QED systems in the ultra-strong coupling.\n\n\n\nIn the end of the preparation of the present work, we noted a recent paper\nby Mao et al. ~\\cite{mao} for the same model. We should say that the approach\nused there is the adiabatic approximation of the present work, i.e., the\nzeroth-order approximation.\n\n\\section{Acknowledgements}\n\nThis work was supported by National Natural Science Foundation of China\n(Grants No.11547305, and No.11474256), Chongqing Research Program of Basic Research and\nFrontier Technology (Grant No.cstc2015jcyjA00043), and Research Fund for the Central Universities\n(Grant No.106112016CDJXY300005).\n\n$^{*}$ Email:yuyuzh@cqu.edu.cn\n\n$^{\\dagger}$ Email:qhchen@zju.edu.cn\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nIn this paper, we are interested to solve the following unconstrained optimization problem:\n\\begin{eqnarray}\\label{general}\n\\min_{x\\in\\Bbb{R}^n}f(x),\n\\end{eqnarray}\nin which $f:\\Bbb{R}^n\\rightarrow \\Bbb{R}$ is a continuously differentiable function. There are various iterative \napproaches for solving (\\ref{general}) \\citep{Nocedal}. The Conjugate Gradient (CG) method is one such approach. The CG based methods\ndo not need any second-order information of the objective function. For a given point $x_0\\in \\Bbb{R}^n$, the iterative formula\ndescribing the  CG method is:\n\\begin{equation}\\label{iter}\nx_{k+1}=x_k+\\alpha_k d_k,\n\\end{equation}\nin which $x_k$ is current iterate point, $\\alpha_k$ is the step size, and $d_k$ is the search direction determined by:\n\\begin{eqnarray}\\label{dk}\nd_k=\\left\\{\n\\begin{array}{lr}\n-g_k\\qquad\\qquad\\quad\\qquad k=0,&\\\\\n-g_k+\\beta_{k-1}d_{k-1}\\qquad k\\geq 1,&\\\\\n\\end{array} \\right.\n\\end{eqnarray}\nwhere $g_k=\\nabla f(x_k)$ is the gradient of the objective function in the current iteration. The conjugate gradient parameter is $\\beta_k$, whose choice of different values leads to various CG methods.\nThe most well-known of the CG methods are the Hestenes-Stiefel (HS) method \\citep{hestenes}, Fletcher-Reeves (FR) method \\citep{Fletcher64},\nConjugate Descent (CD) \\citep{Fletcher13}, and Polak-Ribiere-Polyak (PRP) \\citep{prp}.\n\nThere are various approaches to determining a suitable  step size in each iteration such as Armijo line search, Goldstein line search, and Wolfe line search \\citep{Nocedal}. The Armijo line search finds the largest value of step size in each iteration such that the following inequality holds:\n\\begin{eqnarray}\\label{line}\nf(x_k+\\alpha_kd_k)\\leq f(x_k)+\\gamma\\alpha_kg_k^Td_k\n\\end{eqnarray}\nin which $\\gamma\\in(0,1)$ is a constant parameter.\nGrippo et al. \\citep{Grippo86} introduced a non-monotone Armijo-type line search technique as another way to compute step size.\nThe Incorporation of  the non-monotone strategy into the gradient and projected gradient  approaches, the conjugate gradient method, and the trust-region methods  has led to significant improvements to these methods. Zhang and Hager \\citep{Zhang04} gave some conditions to improve the convergence rate of this strategy. Ahookhosh et al. \\citep{Ahookhosh122} built on these results and investigated   a new non-monotone condition:\n\\begin{equation}\\label{amin}\nf(x_k+\\alpha_kd_k)\\leq R_k+\\gamma\\alpha_kg_k^T d_k,\n\\end{equation}\nwhere $R_k$ is defined by\n\\begin{eqnarray}\n& R_k=\\eta_k f_{l_k}+(1-\\eta_k)f_k, & \\label{rk}\\label{flk}\\\\\n& \\eta_k\\in[\\eta_{\\min},\\eta_{\\max}],~\\eta_{\\min}\\in[0, 1), \\ \\eta_{\\max}\\in[\\eta_{\\min},1], &  \\notag\\\\\n& f_{l_k}=\\max_{0\\leq j\\leq m_k}\\{f_{k-j}\\}, \\nonumber \\\\\n&  m_0=0, \\ \\ 0\\leq m_k\\leq \\min\\{m_{k-1}+1,N\\} \\mbox{ for some } N\\geq 0. \n\\end{eqnarray}\nNote that $\\eta_k$ is known as the non-monotone parameter and plays an essential role in the algorithm's convergence.\n\nAlthough this new non-monotone strategy in \\citep{Ahookhosh122} has some appealing properties, especially in functional performance, current algorithms based on this non-monotone strategy\nface the following challenges.\n\\begin{itemize}\n    \\item The existing schemes for determining the parameter $\\eta_k$ \nmay not reduce the value of the objective function significantly in initial iterations.\nTo overcome this drawback,  we propose a new scheme for choosing $\\eta_k$ \nbased on the gradient behaviour  of the objective function.\nThis can reduce the total  number of iterations.\n\\item Many evaluations of the objective function are needed to find \nthe step length $\\alpha_k$ in step $k$. \nTo make this step more efficient,  we use an adaptive and composite step length procedure from \\citep{Li19} to determine   the initial value of the step length in inner iterations.\n\\item The third issue is the global convergence for the non-monotone CG method. Most exiting CG methods use the Wolfe condition, which plays a vital role in establishing the global convergence of various CG methods \\citep{Nazareth01}. Wolfe line search is more expensive than the Armijo line search strategy. Here, we define a suitable conjugate gradient parameter so that the scheme proposed here has global convergence property.\n\n\\end{itemize}\n\n\n\n\n\n\n\n\nBy combining the outlined strategies, we propose a modification to the non-monotone line search method. Then, we incorporate this approach into the CG method and introduce a new non-monotone CG algorithm. We prove that our proposed algorithm has  global convergence. Finally, we compare our algorithm and eight other algorithms on standard tests  and non-negative matrix factorization instances. We utilize some criteria such as the number of objective function evaluations, the number of gradient evaluations, the number of iterations, and the CPU time to compare the performance of algorithms.\n\n\n\\section{An improved non-monotone line search algorithm} \\label{s:algorithm}\n\nThis section discusses the issues with the state of the art of non-monotone line search strategy, choice of the step sizes, and finally, the conjugate gradient parameter.\n\\subsection{A new scheme of choosing $\\eta_k$}\nRecall that the   non-monotone line search strategy is determined by equation \\eqref{amin} in step $k$.\nThe parameter $\\eta_k$ is involved in the non-monotone term (\\ref{flk})\nand its choice can have a significant impact on the performance of the algorithm. There are two common approaches for calculating \n$\\eta_k$.\nThe scheme proposed by Ahookhosh et al. \\citep{Ahookhosh122}  has been used in most of the existing non-monotone algorithms \\citep{Esmaeili,Ahookhosh_Nu,Amini_App14,Ahookhosh15}.\nThis strategy can be formulated as $\\eta_k=\\frac{1}{3}\\eta_0 (-\\frac{1}{2})^k+\\frac{2}{3}\\eta_0$ \nwhere $\\eta_0=0.15$ and the limit value of $\\eta_k$ is 0.1.\nThe other scheme proposed by Amini et al. \\citep{Amini14}, which depends on the behaviour of gradient is given by:\n\\begin{equation}\\label{Amini's_method}\n\\eta_0=0.95, \\ \\\n\\eta_{k}= \\left\\{\n\\begin{array}{ll}\n\\frac{2}{3}\\eta_{k-1} +0.01, & \\mbox{if }  ~\\|g_{k} \\|_{\\infty}\\leq 10^{-3}; \\\\\n\\max\\{ 0.99\\eta_{k-1},0.5\\}, & \\mbox{otherwise}.\n\\end{array} \\right.\n\\end{equation}\nTo illustrate the behaviour of $\\eta_k$ proposed in   \\citep{Ahookhosh122} and \\citep{Amini14}, we solve the problem $f(x)= (x_0-5)^2+\\sum_{i=1}^{40} (x_i-1)^2$ for $ x\\in \\Bbb{R}^{41}$. \nThe values of the parameter $\\eta_k$ corresponding to the two schemes are displayed in Fig.  \\ref{muk} (Left).\n \\begin{figure}[h!]\n\\centering\n \\includegraphics[width=.45\\textwidth]{a1.jpg}\n   \\includegraphics[width=.45\\textwidth]{a4.jpg}\n\\caption{(Left): Values of $\\eta_k$ proposed in   \\citep{Ahookhosh122} and \\citep{Amini14}, (Right): Values of $\\eta_k$ for the new scheme.}\n\\label{muk}\n\\end{figure}\nAs shown in Fig. \\ref{muk},  for the scheme proposed by Ahookhosh et al. \\citep{Ahookhosh122}, $\\eta_k$\nis close to $0.1$ after only a few  iterations. {Notice that  $\\eta_k$ in each iteration does not have any connection with the behaviour of the objective function. Thus this scheme is not effective.} In addition, there are two issues with the  scheme introduced by Amini et al. in \\citep{Amini14}.\nOne problem indicated by Fig. \\ref{muk} is that that $\\eta_k$ decreases relatively\nquickly for the first 65 iterations.\n{Since the algorithm requires the long iterations to solve his problem}, ideally $\\eta_k$ should be close to 1 for these initial iterations.\nThe second problem is that  the value of $\\eta_k$ remains the same  for a large number of iterations and it is not affected by  the behaviour of the objective function.\n\nTo avoid theses challenges, we propose an adaptive strategy for calculating the value of  $\\eta_k$:\n\\begin{equation} \\label{eq:etakn}\n\\eta_{k}=0.95\\sin\\left(\\frac{\\pi \\|g_{k}\\|}{1+2\\|g_{k}\\|}\\right)+0.01.\n\\end{equation}\nWhen $x_k$ is far away from the minimizer, we can reasonably assume that  $\\|g_k\\|$ is large. Thus the value  of $\\eta_k$ defined by \\eqref{eq:etakn} is close to 1.\nThis makes the scheme closer to the original non-monotone strategy in the initial iterations, providing a chance to reduce the value of the objective function more significantly in the initial iterations. On the other hand, when $x_k$ is close to the minimizer, $\\|g_k\\|$ is small, then the value of $\\eta_k$ is close to zero. Thus, the step length is small so that the new point stays in the neighbourhood of the optimal point. Thus the new scheme is closer to the  monotone strategy. We plot the behaviour of  $\\eta_k$ denoted by \\eqref{eq:etakn} in Fig. \\ref{muk} (Right), using the same values of the gradient for the optimization problem mentioned above.\n\n\\subsection{ New schemes for choosing $\\alpha_k$ }\nWe utilize a convex combination of the  Barzilai-Borwein (BB) step sizes to calculate an appropriate $\\alpha_k$ in each outer iteration as in  \\citep{Li19}. Our strategy calculates the value of  $\\alpha_k$,   using the following equation:\n\\begin{equation}\\label{newalpha}\n\\alpha_k^{{\\scriptscriptstyle \\textrm{CBB}}} =\\mu_k\\alpha^{(1)}_k+(1-\\mu_k)\\alpha^{(2)}_k,\n\\end{equation}\nwhere\n\\begin{eqnarray*}\n\t&\\alpha_k^{(1)}=\\frac{s_k^Ts_k}{s_k^Ty_k},\\quad \\alpha^{(2)}_k=\\frac{s_k^Ty_k}{y_k^Ty_k},\\quad s_k:=x_k-x_{k-1},\\quad y_k:=g_k-g_{k-1};&\\\\\n\t&\\mu_k=\\frac{K_2}{K_1+K_2}\\quad\n\tK_1=\\|\\alpha^{(1)}_k y_k-s_k\\|^2,\\quad K_2=\\|(\\alpha^{(2)}_k)^{-1}s_k-y_k\\|^2.&\n\\end{eqnarray*}\n\\subsection{Conjugate gradient parameter}\nHere, we propose the new conjugate gradient parameter given by:\n\\begin{eqnarray}\\label{cgpar}\n\\beta_k=\\omega \\frac{\\|g_k\\|}{\\|d_{k-1}\\|},\\quad \\omega \\in (0,1).\n\\end{eqnarray}\nThe complete algorithm  is in Appendix \\ref{AppA} (see Algorithm \\ref{alg1}). The next lemma proves a key property of   $\\beta_k$ which is very important in proving the algorithm's convergence. The proofs are in the Appendix \\ref{AppA}.\n\\begin{lemma}\\label{decent}\nFor the  search direction $d_k$ and the constant $c>0$ we have:\n\t\\begin{eqnarray}\n\td_k^Tg_k\\leq -c\\|g_k\\|.\n\t\\end{eqnarray}\n\\end{lemma}\n The following assumptions are used to analyze the convergence properties of  Algorithm \\ref{alg1}.\n\\begin{description}\n\t\\item[H1] The level set $\n\t\\mathcal{L}(x_0)=\\{x|f(x)\\leq f(x_0),~~~~x\\in \\Bbb{R}^n\\}$ is bounded set.\n\t\\item[H2] The gradient of objective function is Lipschitz continuous over an open convex set $C$ containing $\t\\mathcal{L}(x_0)$. That is:\n\t\\begin{equation*}\n\t\\|g(x)-g(y)\\|\\leq L\\|x-y\\|,\\qquad \\forall ~x,y\\in C.\n\t\\end{equation*}\n\\end{description}\nWe prove the following Theorem about the global convergence of Algorithm \\ref{alg1}, the proof of which follows from the Lemmas presented in \nthis section. Please see the appendix for the proofs.\n\n\n\\begin{theorem}\\label{glob}\n\t{Let $(H1)$, $(H2)$, and Lemmas \\ref{decent} and \\ref{aboveserch} hold. Then, for the\n\tsequence $\\{x_k\\}$ generated by Algorithm \\ref{alg1}, we have $\\lim_{k\\rightarrow \\infty} \\|g_k\\|=0.$\n}\\end{theorem}\n\n\n\\begin{lemma}\\label{aboveserch}\n\tSuppose that the search direction $d_k$ with the CG parameter $\\beta_k$ given by (\\ref{cgpar}) is generated by  Algorithm \\ref{alg1}. Then, an upper bound for $d_k$ is given by $\\|d_k\\|\\leq (1+\\omega)\\|g_k\\|.$\n\\end{lemma}\n\\begin{lemma}\\label{low-bou}\n\tSuppose that $x_k$ is not a stationary point of (\\ref{general}). Then there exists a constant\n\t\\begin{equation*}\n\t{\\lambda}=\\min \\left\\{\\beta_1\\rho,\\frac{2(1-\\omega)\\rho(1-\\gamma)}{L(1+\\omega)^2}\\right\\},\n\t\\end{equation*}\n\tsuch that $\\alpha_k\\geq {\\lambda}$.\n\\end{lemma}\n\n\n\n\\section{Numerical Results}\nIn this section we test the new algorithm to solve a set of standard optimization problems and the non-negative matrix factorization problem, which is a non-convex optimization problem. The implementation level details are  in Appendix \\ref{AppB}.\nTo  demonstrate the efficiency of the   proposed algorithm, we compare  our algorithm and eight other existing algorithms introduced in \\citep{Ahookhosh122,Amini14,Jiang,Zhang} on a set of $110$ standards test problems. To describe the behaviour of each strategy, we use\nperformance profiles proposed by  Dolan and Mor\u00e9 \\citep{Dolan}.\nNote that the performance profile for an algorithm  $p_s(\\tau): \\Bbb{R}\\mapsto [0, 1]$  is a non-decreasing, piece-wise constant function, continuous from the right at each breakpoint. Moreover, the value  $p_s(1)$ denotes the probability that the algorithm will win against the rest of the algorithm. More information  on the  performance profile is in Appendix \\ref{AppB}. We plot  the performance profile of each algorithm in terms of the total number of outer iteration and the  CPU time on the set of standard test problems in Fig. \\ref{results}.  \n \\begin{figure}[h!]\n\\centering\n \\includegraphics[width=.45\\textwidth]{1.jpg}\n   \\includegraphics[width=.45\\textwidth]{3.jpg}\n\\caption{(Left): Performance profiles of the total number of outer iterations, (Right): Performance profiles of CPU Time.}\n\\label{results}\n\\end{figure}\n\n\nWe also apply our algorithm  to solve the  Non-Negative Matrix Factorization (NMF)\nwhich has several applications in image processing such as face detection problems. \nGiven a non-negative matrix $V\\in\\Bbb{R}^{m\\times n}$, a NMF\nfinds two non-negative matrices\n$W\\in\\Bbb{R}^{m\\times k}$ and $H\\in\\Bbb{R}^{k\\times n}$ with\n$k\\ll\\min(m,n)$ such that $X\\approx WH$.  This problem can be formulated as\n\\begin{equation}\\label{opti-n}\n\\min_{W,H\\geq0} F(W,H)=\\frac{1}{2}\\|V-WH\\|_{F}^2.\n\\end{equation}\nEquation \\eqref{opti-n} is a non-convex optimization problem. We compare our method and Zhang's algorithm \\citep{Zhang} on  some random datasets and reported these results in Appendix \\ref{AppB}. \n\n\n\\section{Conclusion} In this paper, we introduced a new non-monotone conjugate gradient  algorithm based on efficient Barzilai-Borwein step size. We introduced a new non-monotone parameter based on gradient behaviour and determined by  a trigonometric function. We use a convex combination of the determined method to compute the step size value in each iteration.   We prove that the   proposed algorithm has global convergence. We implemented and tested our algorithm on a set of standard test problems and the non-negative matrix factorization problems. The   proposed algorithm can solve $98\\%$ of the test problems for a set of standard test instances. For the non-negative matrix factorization, the results indicate that our algorithm is more efficient compared to  Zhang' s method \\citep{Zhang}. \n\n\n\n\n\n\n\n\n\n\n\\bibliographystyle{unsrtnat}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\n\n\\section{Introduction}\n\nThe difference-of-log-Normals distribution, henceforth DLN, is the distribution arising when one subtracts a log-Normal random variable (RV) from another. To define the DLN, consider an RV $W$ such that \n\\begin{equation} \\label{eq:DLN}\nW = Y_{p} - Y_{n} = \\text{exp}(X_{p}) - \\text{exp}(X_{n}) \\ \\ \\text{with} \\ \\ \\pmb{X} = (X_{p},X_{n})^{T} \\sim \\mathcal{N}(\\pmb{\\mu},\\pmb{\\Sigma})\n\\end{equation}\nin which $\\pmb{X}$ is a bi-variate Normal with\n\\begin{equation} \\label{eq:BVN}\n\\pmb{\\mu} = \\begin{bmatrix} \\mu_p \\\\ \\mu_n \\end{bmatrix} \\ \\ \\ \n\\pmb{\\Sigma} = \\begin{bmatrix} \\sigma_p^2 & \\sigma_p\\cdot\\sigma_n\\cdot\\rho_{pn} \\\\ \\sigma_p\\cdot\\sigma_n\\cdot\\rho_{pn} & \\sigma_n^2 \\end{bmatrix}\n\\end{equation}\nWe say $W$ follows the five-parameter DLN distribution, $W \\sim \\text{DLN}(\\mu_p,\\sigma_p,\\mu_n,\\sigma_n,\\rho_{pn})$.\n\nThe companion paper \\cite{Parham2022} makes the case that the DLN is a \\emph{fundamental distribution in nature}, in the sense that it arises naturally in a plethora of disparate natural phenomena, similar to the Normal and log-Normal distributions. It shows that firm income, return, and growth are all well-described by the DLN, it further shows that city population growth, per-county GDP growth, and the per-industry per-Metro GDP growth all show remarkable fit to the DLN. \\cite{Parham2022} describes how the emergence of the DLN is a direct result of an application of the Central Limit Theorems and ``Gibrat's Law'' when applied to various economic phenomena. As the DLN is almost completely unexplored,\\footnote{At the time of writing, I was able to find only two statistical works considering it, \\cite{Lo2012} and \\cite{GulisashviliTankov2016}. Both papers concentrate on the sum of log-Normals but show their results hold for the difference of log-Normals as well, under some conditions.} this paper aims to fill the gap.\n\nThe next section fully characterizes the DLN distribution, deriving its PDF, CDF, central moments, and estimators for the distribution parameters given data. It also introduces an extension of the DLN to the multi-variate N-dimensional case using elliptical distribution theory. A full suite of computer code is provided for future use.\n\nNext, Section~\\ref{sec:Methods} discusses the difficulty of working with the raw DLN distribution, stemming from its characteristic ``double-exponential'' heavy tails. To alleviate this difficulty, I discuss the close link between the DLN and the Hyperbolic Sine (\\emph{sinh}) function and its inverse (\\emph{asinh}) and present the ADLN distribution - the DLN under an asinh transform. The section then considers the problem of measuring growth in DLN-distributed RVs. To that end, it generalizes the concept of growth, currently defined only for strictly positive RVs, to DLN RVs that are sometimes negative. I show that the appropriate growth concept for an RV (e.g. percentage, difference in logs, or DLN-growth) intimately depends on the RV's statistical distribution.\n\nSection~\\ref{sec:MC} explores the properties of the estimators presented via extensive Monte-Carlo experiments. It: (i) reports the empirical bias and variance of the moment estimators and the MLE parameter estimators; (ii) establishes critical values for the Kolmogorov-Smirnov and Anderson-Darling distributional tests for DLN RVs; and (iii) presents the relation between the measures of growth developed in Section~\\ref{sec:Methods}. \\comments{Finally, it discusses using the DLN as an approximating distribution, and presents evidence that the DLN is an excellent approximating distribution for several distributions, including the distributions arising from the sum of two DLN RVs, the multiplication of DLN by Normal RVs, and the multiplication of Normal by log-Normal RVs.}\n\n\n\n\\section{Definitions and properties}\n\\label{sec:Def}\n\nPrior to proceeding, and to fix ideas, Figure~\\ref{fig:DLNexam} presents several instances of the DLN distribution. Panel (a) presents and contrasts the standard Normal, standard DLN, and standard log-Normal. The uncorrelated standard DLN is defined as DLN(0,1,0,1,0), i.e. the difference between two exponentiated uncorrelated standard Normal RVs. Panel (b) shows the role of the correlation coefficient $\\rho_{pn}$ in the standard DLN, controlling tail-weight vs. peakedness. Panel (c) repeats the analysis of Panel (b) for a different parametrization common in practical applications, exhibiting the problem of dealing with heavy tails. Panel (d) presents the data of panel (c) in asinh space, showing how asinh resolves the problem of graphing heavy tails and why the ADLN distribution is useful in practice.\n\n\\RPprep{DLN Examples}{0}{0}{DLNexam}{%\n    This figure presents examples of the DLN distribution. Panel (a) graphs the PDFs of the standard Normal, log-Normal, and DLN. Panel (b) graphs the PDFs of standard DLN with different correlation coefficients $\\rho_{pn}$. Panel (c) presents the PDFs of a DLN with parameters $(3,2,2,2)$, common in practice, and varying correlation coefficients $\\rho_{pn}$. Panel (c) presents the PDF for the range $\\pm 10$, which is a significant truncation due to the long tails of this DLN. Panel (d) presents the same PDFs as Panel (c), but the x-axis is asinh-transformed, such that it spans the range sinh(-10) $\\approx$ -11,000 to sinh(10) $\\approx$ 11,000.\n}\n\\RPfig{%\n\t\\begin{tabular}{cc} \n\t\t\\subfigure[standard DLN, N, LN]{\\includegraphics[width=3in]{Img\/DLN_N_LN.pdf}} & \n\t\t\\subfigure[Std. DLN w\/ corrs]{\\includegraphics[width=3in]{Img\/SDLN_corrs.pdf}} \\\\ \\\\\n\t\t\\subfigure[DLN w\/ corrs]{\\includegraphics[width=3in]{Img\/DLN_corrs.pdf}} &\n\t\t\\subfigure[ADLN w\/ corrs]{\\includegraphics[width=3in]{Img\/ADLN_corrs.pdf}} \\\\ \\\\\n\t\\end{tabular}\n}\n\n\n\n\\subsection{PDF and CDF}\n\nThe PDF for the bi-variate Normal (BVN) RV $\\pmb{X}$ is well-known to be\n\\begin{equation} \\label{eq:PDFBVN}\nf_{BVN}(\\pmb{x}) = \\frac{\\lvert\\pmb{\\Sigma}\\rvert^{-\\frac{1}{2}}}{2\\pi}\\cdot \\text{exp}\\left(-\\frac{1}{2} (\\pmb{x}-\\pmb{\\mu})^{T} \\pmb{\\Sigma}^{-1} (\\pmb{x}-\\pmb{\\mu})\\right) = \\frac{\\lvert\\pmb{\\Sigma}\\rvert^{-\\frac{1}{2}}}{2\\pi}\\cdot \\text{exp}\\left(-\\frac{1}{2} \\lvert\\lvert\\pmb{x}-\\pmb{\\mu}\\rvert\\rvert_{\\pmb{\\Sigma}}\\right)\n\\end{equation} \nwith $\\lvert\\pmb{\\Sigma}\\rvert$ the determinant of $\\pmb{\\Sigma}$ and $\\lvert\\lvert\\pmb{x}\\rvert\\rvert_{\\pmb{\\Sigma}}$ the Euclidean norm of $\\pmb{x}$ under the Mahalanobis distance induced by $\\pmb{\\Sigma}$.\n\nThe PDF for the bi-variate log-Normal (BVLN) RV $\\pmb{Y} = (Y_{p},Y_{n})^{T}$ can be obtained by using the multivariate change of variables theorem. If $\\pmb{Y}=g(\\pmb{X})$ then\n\\begin{equation}\nf_{Y}(\\pmb{y}) = f_{X}(g^{-1}(\\pmb{y})) \\cdot \\lvert\\lvert J_{g^{-1}}(\\pmb{y})\\rvert\\rvert\n\\end{equation}\nwith $J_{g^{-1}}$ the Jacobian matrix of $g^{-1}(\\cdot)$ and $\\lvert\\lvert J_{g^{-1}}\\rvert\\rvert$ the absolute value of its determinant. Applying the theorem for $\\pmb{Y} = g(\\pmb{X}) = (\\text{exp}(X_p),\\text{exp}(X_n))^{T}$ we have $g^{-1}(\\pmb{y}) = (log(y_p),log(y_n))^{T}$ and $\\lvert\\lvert J_{g^{-1}}(\\pmb{y})\\rvert\\rvert = (y_p\\cdot y_n)^{-1}$. The PDF of a BVLN RV is then\n\\begin{equation} \\label{eq:PDFBVLN}\nf_{BVLN}(\\pmb{y}) = \\frac{\\lvert\\pmb{\\Sigma}\\rvert^{-\\frac{1}{2}}}{2\\pi y_p y_n} \\text{exp}\\left(-\\frac{1}{2}\\lvert\\lvert\\log(\\pmb{y})-\\pmb{\\mu}\\rvert\\rvert_{\\pmb{\\Sigma}}\\right)\n\\end{equation}\n\nWe can now define the cumulative distribution function (CDF) of the DLN distribution using the definition of the CDF of the difference of two RV\n\\begin{equation} \\label{eq:CDFDLN1}\n\\begin{split}\nF_{DLN}(w) & = P[W\\leq w] = P[y_{p} - y_{n} \\leq w] = P[y_{p} \\leq y_{n} + w] \\\\\n           & =  \\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{y_{n}+w}f_{BVLN}(y_{p},y_{n})dy_{p}dy_{n}\n\\end{split}\n\\end{equation}\nwhich can be differentiated w.r.t $w$ to yield the PDF\n\\begin{equation} \\label{eq:PDFDLN1}\nf_{DLN}(w) = \\int_{-\\infty}^{\\infty}f_{BVLN}(y+w,y)dy  =  \\int_{-\\infty}^{\\infty}f_{BVLN}(y,y-w)dy\n\\end{equation}\nbut because $f_{BVLN}(\\pmb{y})$ is non-zero only for $\\pmb{y}>0$, we limit the integration range\n\\begin{equation} \\label{eq:PDFDLN}\nf_{DLN}(w) = \\int_{\\text{max}(0,w)}^{\\infty}f_{BVLN}(y,y-w)dy\n\\end{equation}\nwhich yields the PDF of the DLN distribution.\n\nIt is well-known, however, that the integral in equation~\\ref{eq:PDFDLN} does not have a closed-form solution. The accompanying code suite evaluates it numerically, and also numerically evaluates the CDF using its definition\n\\begin{equation} \\label{eq:CDFDLN}\nF_{DLN}(w) = \\int_{-\\infty}^{w}f_{DLN}(y)dy\n\\end{equation}\n\n\\begin{sloppypar}\nFor the simpler case with difference of uncorrelated log-Normals, i.e. $\\rho_{pn}=0$, we can derive the PDF of the DLN via a characteristic function (CF) approach as well. In this case, we can write the CF of the DLN as ${\\varphi_{DLN}(t)=\\varphi_{LN}(t)\\cdot\\varphi_{LN}(-t)}$ with $\\varphi_{LN}(t)$ the CF of the log-Normal. Next, we can apply a Fourier transform to obtain the PDF,\n\\begin{equation} \\label{eq:PDFDLNCF}\nf_{DLN}(w) = \\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}e^{-i\\cdot t\\cdot w} \\cdot \\varphi_{DLN}(t)dt\n\\end{equation}\nUnfortunately, the log-Normal does not admit an analytical CF, and using Equation~\\ref{eq:PDFDLNCF} requires a numerical approximation for $\\varphi_{LN}(t)$ as well. \\cite{Gubner2006} provides a fast and accurate approximation method for the CF of the log-Normal which I use in the calculation of $f_{DLN}(w)$ when using this method.\n\\end{sloppypar}\n\n\n\\subsection{Moments}\n\\label{sec:Moms}\n\n\\subsubsection{MGF}\n\nThe moment generating function (MGF) of the DLN can be written as\n\\begin{equation} \\label{eq:MGFDLN}\nM_{W}(t) = \\mathbb{E}\\left[e^{tW}\\right] = \\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty}e^{tw}f_{BVLN}(y+w,y)dydw\n\\end{equation}\nbut this formulation has limited usability due to the lack of closed-form solution for the integrals. Instead, it is useful to characterize the moments directly, as we can obtain them in closed-form.\n\n\n\n\\subsubsection{Mean and variance}\n\nUsing the definitions of $\\pmb{\\mu}$ and $\\pmb{\\Sigma}$ in \\ref{eq:BVN}, define the mean and covariance of the BVLN RV, $\\pmb{\\hat{\\mu}}$ and $\\pmb{\\hat{\\Sigma}}$ (element-wise) as\n\\begin{equation} \\label{eq:BVLN}\n\\begin{split}\n\\pmb{\\hat{\\mu}}_{(i)} & = \\text{exp}\\left(\\pmb{\\mu}_{(i)} + \\frac{1}{2}\\pmb{\\Sigma}_{(i,i)}\\right) \\\\\n\\pmb{\\hat{\\Sigma}}_{(i,j)} & = \\text{exp}\\left(\\pmb{\\mu}_{(i)} + \\pmb{\\mu}_{(j)} + \\frac{1}{2}\\left(\\pmb{\\Sigma}_{(i,i)} + \\pmb{\\Sigma}_{(j,j)}\\right)\\right)\\cdot \\left( \\text{exp}\\left(\\pmb{\\Sigma}_{(i,j)}\\right)-1\\right) \\\\\n\\end{split}\n\\end{equation}\nNote that if $\\pmb{\\Sigma}$ is diagonal (i.e., $X_{p}$ and $X_{n}$ are uncorrelated) then $\\pmb{\\hat{\\Sigma}}$ will be diagonal as well. We are however interested in the general form of the DLN distribution. The identities regarding the expectation and variance of a sum of RV yield\n\\begin{equation} \\label{eq:MUDLN}\n\\mathbb{E}\\left[W\\right] = \\mathbb{E}\\left[Y_p\\right] - \\mathbb{E}\\left[Y_n\\right] = \\pmb{\\hat{\\mu}}_{(1)} - \\pmb{\\hat{\\mu}}_{(2)} = \\text{exp}(\\mu_p + \\frac{\\sigma_p^2}{2}) - \\text{exp}(\\mu_n + \\frac{\\sigma_n^2}{2})\n\\end{equation}\nand\n\\begin{equation} \\label{eq:SIGDLN}\n\\begin{split}\n\\text{Var}\\left[W\\right] & =\\mathbb{C}\\left[Y_p,Y_p\\right] + \\mathbb{C}\\left[Y_n,Y_n\\right] -2\\cdot\\mathbb{C}\\left[Y_p,Y_n\\right] = \\pmb{\\hat{\\Sigma}}_{(1,1)} + \\pmb{\\hat{\\Sigma}}_{(2,2)} - 2\\cdot\\pmb{\\hat{\\Sigma}}_{(1,2)} \\\\\n & = \\text{exp}\\left(2\\mu_{p}+\\sigma_p^2\\right)\\cdot\\left(exp\\left(\\sigma_p^2\\right) - 1\\right) \n   + \\text{exp}\\left(2\\mu_{n}+\\sigma_n^2\\right)\\cdot\\left(exp\\left(\\sigma_n^2\\right) - 1\\right) \\\\\n & - 2\\text{exp}\\left(\\mu_{p}+\\mu_{n}+\\frac{1}{2}(\\sigma_p^2+\\sigma_n^2)\\right)\n \\cdot\\left(\\text{exp}\\left(\\sigma_p\\sigma_n\\rho_{pn}\\right) - 1\\right)\n\\end{split}\n\\end{equation}\nwith $\\mathbb{C}$ the covariance operator of two general RV $U_{1},U_{2}$\n\\begin{equation} \\label{eq:COVAR}\n\\mathbb{C}\\left[U_{1},U_{2}\\right] = \\mathbb{E}\\left[(U_1 - \\mu_1)(U_2-\\mu_2)\\right]\n\\end{equation}\n\n\n\n\\subsubsection{Skewness and kurtosis}\n\nSkewness and kurtosis of the DLN can similarly be established using coskewness and cokurtosis (for overview, see e.g. \\cite{Miller2013}). Coskewness of three general RV $U_{1},U_{2},U_{3}$ is defined as\n\\begin{equation} \\label{eq:COSKEW}\n\\mathbb{S}\\left[U_{1},U_{2},U_{3}\\right] = \\frac{\\mathbb{E}\\left[(U_1 - \\mu_1)(U_2-\\mu_2)(U_3-\\mu_3)\\right]}{\\sigma_1\\sigma_2\\sigma_3}\n\\end{equation}\nand cokurtosis of four general RV $U_{1},U_{2},U_{3},U_{4}$ is defined as \n\\begin{equation} \\label{eq:COKURT}\n\\mathbb{K}\\left[U_{1},U_{2},U_{3},U_{4}\\right] = \\frac{\\mathbb{E}\\left[(U_1 - \\mu_1)(U_2-\\mu_2)(U_3-\\mu_3)(U_4-\\mu_4)\\right]}{\\sigma_1\\sigma_2\\sigma_3\\sigma_4}\n\\end{equation}\nwith the property that $\\mathbb{S}\\left[U,U,U\\right] = \\text{Skew}\\left[U\\right]$ and $\\mathbb{K}\\left[U,U,U,U\\right] = \\text{Kurt}\\left[U\\right]$. More importantly, it is simple to show that\n\\begin{equation} \\label{eq:SKEWDIFF}\n\\text{Skew}\\left[U-V\\right] = \\frac{\\sigma_U^3\\mathbb{S}\\left[U,U,U\\right] -3\\sigma_U^2\\sigma_V\\mathbb{S}\\left[U,U,V\\right]+3\\sigma_U\\sigma_V^2\\mathbb{S}\\left[U,V,V\\right] -\\sigma_V^3\\mathbb{S}\\left[V,V,V\\right]}{\\sigma_{U-V}^{3}}\n\\end{equation}\nand similarly\n\\begin{equation} \\label{eq:KURTDIFF}\n\\begin{split}\n\\text{Kurt}\\left[U-V\\right] & = \\frac{1}{\\sigma_{U-V}^{4}} [ \\sigma_U^4\\mathbb{K}\\left[U,U,U,U\\right] -4\\sigma_U^3\\sigma_V\\mathbb{K}\\left[U,U,U,V\\right] \\\\ & + 6\\sigma_U^2\\sigma_V^2\\mathbb{K}\\left[U,U,V,V\\right] -4\\sigma_U\\sigma_V^3\\mathbb{K}\\left[U,V,V,V\\right]+\\sigma_V^4\\mathbb{K}\\left[V,V,V,V\\right] ]\n\\end{split}\n\\end{equation}\nwith $\\sigma_{U-V} = \\text{Var}\\left[U-V\\right]^{\\frac{1}{2}}$ calculated using Equation~\\ref{eq:SIGDLN}. Evaluating the operators $\\mathbb{S}$ and $\\mathbb{K}$ for the case of DLN requires evaluating expressions of the general form $\\mathbb{E}\\left[Y_{p}^{i}Y_{n}^{j}\\right]$, which can be done via the MGF of the BVN distribution\n\\begin{equation} \\label{eq:EUVSimp}\n\\mathbb{E}\\left[Y_{p}^{i}Y_{n}^{j}\\right] = \\mathbb{E}\\left[e^{i X_p}e^{j X_n}\\right] = \\text{MGF}_{BVN}\\left(\\big[\\begin{smallmatrix} i \\\\ j \\end{smallmatrix}\\big] \\right) = \\mathbb{E}\\left[Y_{p}^{i}\\right]\\mathbb{E}\\left[Y_{n}^{j}\\right]e^{ij\\pmb{\\Sigma}_{(1,2)}}\n\\end{equation}\nwith $\\mathbb{E}\\left[Y_{p}^{i}\\right]=\\text{exp}\\left(i\\mu_{p} + \\frac{1}{2}i^2\\sigma_{p}^2\\right)$. This concludes the technical details of the derivation. \n\nThe method presented can be extended to higher central moments as well. The accompanying code suite includes functions that implement the equations above and use them to calculate the first five moments of the DLN given the parameters $(\\mu_p,\\sigma_p,\\mu_n,\\sigma_n,\\rho_{pn})$. Section~\\ref{sec:MC} later describes the results of Monte-Carlo experiments testing the empirical variance and bias of the moments as a function of sample size.\n\n\n\n\\subsection{Estimation}\n\\label{sec:Estim}\n\nGiven data $\\pmb{D} \\sim \\text{DLN}(\\pmb{\\Theta})$ with $\\pmb{\\Theta} = (\\mu_p,\\sigma_p,\\mu_n,\\sigma_n,\\rho_{pn})$, we would like to find an estimate $\\pmb{\\hat{\\Theta}}$ to the parameter vector $\\pmb{\\Theta}$. Experiments show that given an appropriate initial guess, the MLE estimates of $\\pmb{\\Theta}$ perform well in practice. The main parameter of difficulty is $\\rho_{pn}$. This parameter is akin to the shape parameter in the Stable distribution, which plays a similar role and is similarly difficult to estimate, see e.g. \\cite{FamaRoll1971}. It hence requires special care in the estimation.\n\nThe estimation code provided minimizes the negative log-likelihood of the data w.r.t the DLN PDF using a multi-start algorithm. The starting values for the first four parameters are fixed for all start points as:\n\\begin{equation} \\label{eq:ESTIM_GUESS}\n\\begin{bmatrix}\n\\mu_p \\\\ \\sigma_p \\\\ \\mu_n \\\\ \\sigma_n\n\\end{bmatrix} = \n\\begin{bmatrix}\n\\text{Median}\\left[\\text{log}\\left(\\pmb{D}\\right)\\right] \\ \\ \\text{for} \\ \\ \\pmb{D}>0 \\\\\n\\text{IQR}\\left[\\text{log}\\left(\\pmb{D}\\right)\\right]\/1.35 \\ \\ \\text{for} \\ \\ \\pmb{D}>0  \\\\\n\\text{Median}\\left[\\text{log}\\left(-\\pmb{D}\\right)\\right] \\ \\ \\text{for} \\ \\ \\pmb{D}<0  \\\\\n\\text{IQR}\\left[\\text{log}\\left(-\\pmb{D}\\right)\\right]\/1.35 \\ \\ \\text{for} \\ \\ \\pmb{D}<0  \\\\\n\\end{bmatrix}\n\\end{equation}\nwhile the initial guesses for $\\rho_{pn}$ are $(-0.8,-0.3,0,0.3,0.8)$. The estimator $\\pmb{\\hat{\\Theta}}$ is then the value which minimizes the negative log-likelihood in the multi-start algorithm. The estimator inherits asymptotic normality, consistency, and efficiency properties from the general M-estimator theory, as the dimension of $\\pmb{\\hat{\\Theta}}$ is fixed, the likelihood is smooth, and is supported on $\\mathbb{R}\\ \\forall \\pmb{\\hat{\\Theta}}$. A better estimation procedure for the parameters of the DLN might be merited, but is left for future work.\n\n\n\n\\subsection{The elliptical multi-variate DLN}\n\\label{sec:mvsdln}\n\nPractical applications of the DLN require the ability to work with multi-variate DLN RVs. I hence present an extension of the DLN to the multi-variate case using elliptical distribution theory, with the standard reference being \\cite{FangEtAl1990}.\n\n\\begin{sloppypar}\nThe method of elliptical distributions requires a symmetric baseline distribution. We will therefore focus our attention on the symmetric DLN case in which ${\\mu_p=\\mu_n\\equiv\\mu}$ and ${\\sigma_p = \\sigma_n\\equiv\\sigma}$, yielding the three parameter uni-variate symmetric distribution $\\text{SymDLN}(\\mu,\\sigma,\\rho)=\\text{DLN}(\\mu,\\sigma,\\mu,\\sigma,\\rho)$. I begin by defining a standardized N-dimensional elliptical DLN RV using SymDLN and the spherical decomposition of \\cite{CambanisEtAl1981}, and later extend it to a location-scale family of distributions.\n\\end{sloppypar}\n\nLet $\\mathbf{U}$ be an N-dimensional RV distributed uniformly on the unit hyper-sphere in $\\mathbb{R}^{N}$ and arranged as a column vector. Let $R\\geq0$ be a uni-variate RV independent of $\\mathbf{U}$ with PDF $f_{R}\\left(r\\right)$ to be derived momentarily, and let $\\mathbf{Z}=R\\cdot\\mathbf{U}$ be a standardized N-dimensional elliptical DLN RV. A common choice for $\\mathbf{U}$ is $\\widehat{\\mathbf{U}}\/\\lvert\\lvert\\widehat{\\mathbf{U}}\\rvert\\rvert_{2}$ with $\\widehat{\\mathbf{U}} \\sim MVN(\\mathbf{0}_N,\\mathbf{1}_N)$. $\\mathbf{U}$ captures a direction in $\\mathbb{R}^{N}$, and we have $\\sqrt{\\mathbf{U}^{T}\\cdot\\mathbf{U}} =  \\lvert\\lvert\\mathbf{U}\\rvert\\rvert_{2} \\equiv 1$, which implies $\\sqrt{\\mathbf{Z}^{T}\\cdot\\mathbf{Z}} =  \\lvert\\lvert\\mathbf{Z}\\rvert\\rvert_{2} = R$. We further know that the surface area of an N-sphere with radius $R$ is given by\n\\begin{equation} \\label{eq:Surface}\nS_{N}\\left(R\\right) = \\frac{2\\cdot\\pi^{\\frac{N}{2}}}{\\Gamma\\left(\\frac{N}{2}\\right)}\\cdot R^{N-1}\n\\end{equation}\nand can hence write the PDF of $\\mathbf{Z}$ as\n\\begin{equation} \\label{eq:fZPDF1}\nf_{\\mathbf{Z}}\\left(\\mathbf{z}\\right) = \\frac{f_{R}\\left(\\lvert\\lvert\\mathbf{z}\\rvert\\rvert_{2}\\right)}{S_{N}\\left(\\lvert\\lvert\\mathbf{z}\\rvert\\rvert_{2}\\right)} =  \\frac{\\Gamma\\left(\\frac{N}{2}\\right)\\cdot f_{R}\\left(\\lvert\\lvert\\mathbf{z}\\rvert\\rvert_{2}\\right)}{2\\cdot\\pi^{\\frac{N}{2}}\\cdot\\lvert\\lvert\\mathbf{z}\\rvert\\rvert_{2}^{N-1}}\n\\end{equation}\n\nWe require $f_{R}\\left(r\\right)$ and $f_{\\mathbf{Z}}\\left(\\mathbf{z}\\right)$ to be valid PDFs, which yields the conditions\n\\begin{equation} \\label{eq:RZcond}\n\\begin{split}\n& f_{R}\\left(r\\right) \\geq 0\\ \\forall\\ r\\in\\mathbb{R} \\\\\n& f_{\\mathbf{Z}}\\left(\\mathbf{z}\\right) \\geq 0\\ \\forall\\ \\mathbf{z}\\in\\mathbb{R}^{N} \\\\\n& \\int_{-\\infty}^{\\infty}f_{R}\\left(r\\right)\\ dr = 1 \\\\\n& \\int_{-\\infty}^{\\infty}\\cdot\\cdot\\cdot \\int_{-\\infty}^{\\infty} f_{\\mathbf{Z}}\\left(\\mathbf{z}\\right)\\  d\\mathbf{z}_{(N)}\\cdot\\cdot\\cdot d\\mathbf{z}_{(1)} = 1 \\\\\n\\end{split}\n\\end{equation}\nto those, we can add the condition that the properly normalized distribution of $f_{R}\\left(r\\right)$ will be SymDLN,\n\\begin{equation} \\label{eq:fRcond}\nf_{R}\\left(r\\right) = \\widetilde{M}_{N}\\left(r\\right)\\cdot f_{DLN}(r)\n\\end{equation}\nwith $\\widetilde{M}_{N}\\left(r\\right)$ chosen such that the conditions in Equation~\\ref{eq:RZcond} hold. Solving for this set of conditions yields\n\\begin{equation} \\label{eq:fR}\nf_{R}\\left(r\\right) = \\frac{r^{N-1}} {\\int_{0}^{\\infty}\\widetilde{r}^{N-1}\\cdot f_{DLN}\\left(\\widetilde{r}\\right)\\ d\\widetilde{r}}\\cdot f_{DLN}\\left(r\\right)\n\\end{equation}\nand\n\\begin{equation} \\label{eq:fZ}\nf_{\\mathbf{Z}}\\left(\\mathbf{z}\\right) =  \\frac{\\Gamma\\left(\\frac{N}{2}\\right)}{2\\cdot\\pi^{\\frac{N}{2}}\\cdot \\int_{0}^{\\infty}\\widetilde{r}^{N-1}\\cdot f_{DLN}\\left(\\widetilde{r}\\right)\\ d\\widetilde{r}}\\cdot f_{DLN}\\left(\\lvert\\lvert\\mathbf{z}\\rvert\\rvert_{2}\\right) = M_{N}\\cdot f_{DLN}\\left(\\lvert\\lvert\\mathbf{z}\\rvert\\rvert_{2}\\right)\n\\end{equation}\nwith $M_{N}$ a normalization constant depending only on the dimension N and the parameters of the baseline SymDLN$\\left(\\mu, \\sigma, \\rho\\right)$ being used. We can further use the definition of the CDF of $\\mathbf{Z}$ to write\n\\begin{equation} \\label{eq:FZ}\n\\begin{split}\nF_{\\mathbf{Z}}\\left(\\mathbf{z}\\right) & = \\int_{-\\infty}^{\\mathbf{z}_{(1)}}\\cdot\\cdot\\cdot \\int_{-\\infty}^{\\mathbf{z}_{(N)}} f_{\\mathbf{Z}}\\left(\\mathbf{\\widehat{z}}\\right)\\  d\\mathbf{\\widehat{z}}_{(N)}\\cdot\\cdot\\cdot d\\mathbf{\\widehat{z}}_{(1)} \\\\ \n& = \\int_{-\\infty}^{\\mathbf{z}_{(1)}}\\cdot\\cdot\\cdot \\int_{-\\infty}^{\\mathbf{z}_{(N)}} M_{N}\\cdot f_{\\mathbf{DLN}}\\left(\\lvert\\lvert\\mathbf{z}\\rvert\\rvert_{2}\\right)\\  d\\mathbf{\\widehat{z}}_{(N)}\\cdot\\cdot\\cdot d\\mathbf{\\widehat{z}}_{(1)} \\\\\n\\end{split}\n\\end{equation}\nwhich concludes the characterization of the standardized N-dimensional\nelliptical DLN RV.\n\nExtending the standardized N-dimensional DLN to a location-scale family of distributions is now straightforward. Let $\\widetilde{\\pmb{\\mu}}=\\left(\\mu_1 , \\mu_2 , ... , \\mu_N\\right)^{T}$ be a column vector of locations and let $\\widetilde{\\pmb{\\Sigma}}$ be a positive-semidefinite scaling matrix of rank $N$. Define \n\\begin{equation} \\label{eq:MVDLN}\n\\mathbf{W} = \\widetilde{\\pmb{\\mu}} + \\widetilde{\\pmb{\\Sigma}}^{\\frac{1}{2}}\\cdot\\mathbf{Z}\n\\end{equation}\nwith $\\widetilde{\\pmb{\\Sigma}}^{\\frac{1}{2}}$ denoting the eigendecomposition of $\\widetilde{\\pmb{\\Sigma}}$. The PDF of $\\mathbf{W}$ is then given by\n\\begin{equation} \\label{eq:PDFMVDLN}\n\\begin{split}\nf_\\mathbf{W}\\left(\\mathbf{w}\\right) & = \\lvert\\widetilde{\\pmb{\\Sigma}}\\rvert^{-\\frac{1}{2}}\\cdot f_{\\mathbf{Z}}\\left(\\widetilde{\\pmb{\\Sigma}}^{-\\frac{1}{2}}\\cdot\\left(\\mathbf{w}-\\widetilde{\\pmb{\\mu}}\\right)\\right) \\\\\n& = \\lvert\\widetilde{\\pmb{\\Sigma}}\\rvert^{-\\frac{1}{2}}\\cdot M_{N}\\cdot f_{DLN}\\left(\\sqrt{\\left(\\mathbf{w}-\\widetilde{\\pmb{\\mu}}\\right)^{T}\\cdot\\widetilde{\\pmb{\\Sigma}}^{-1}\\cdot\\left(\\mathbf{w}-\\widetilde{\\pmb{\\mu}}\\right)}\\right) \\\\\n& = \\lvert\\widetilde{\\pmb{\\Sigma}}\\rvert^{-\\frac{1}{2}}\\cdot M_{N}\\cdot f_{DLN}\\left(\\lvert\\lvert\\mathbf{w}-\\widetilde{\\pmb{\\mu}}\\rvert\\rvert_{\\widetilde{\\pmb{\\Sigma}}}\\right) \\\\\n\\end{split}\n\\end{equation}\nThe CDF of $\\mathbf{W}$ can similarly be written as\n\\begin{equation} \\label{eq:CDFMVDLN}\n\\begin{split}\nF_{\\mathbf{W}}\\left(\\mathbf{w}\\right) & = \\lvert\\widetilde{\\pmb{\\Sigma}}\\rvert^{-\\frac{1}{2}}\\cdot M_{N}\\cdot \\int_{-\\infty}^{\\mathbf{w}_{(1)}}\\cdot\\cdot\\cdot \\int_{-\\infty}^{\\mathbf{w}_{(N)}} f_{\\mathbf{DLN}}\\left(\\lvert\\lvert\\mathbf{w}-\\widetilde{\\pmb{\\mu}}\\rvert\\rvert_{\\widetilde{\\pmb{\\Sigma}}}\\right)\\  d\\mathbf{\\widehat{w}}_{(N)}\\cdot\\cdot\\cdot d\\mathbf{\\widehat{w}}_{(1)} \\\\\n\\end{split}\n\\end{equation}\nwhich characterizes a general elliptical multi-variate DLN RV.\n\nFinally, note that the scaling matrix $\\widetilde{\\pmb{\\Sigma}}$ is not the covariance matrix of $\\mathbf{W}$ due to the heavy-tails of $\\mathbf{W}$, similar to other heavy-tailed elliptical distributions such as the multi-variate Stable, t, or Laplace distributions. Further note that the normalization integral in Equation~\\ref{eq:fR} is numerically unstable for high values of N (e.g., $N\\geq 5$), and care should be taken when deriving the PDF of high-dimensional DLN RVs.\n\n\n\n\\section{Methods for heavy-tailed analysis}\n\\label{sec:Methods}\n\nAs discussed above, a main difficulty of working with the DLN distribution stems from its ``double exponential'' nature, i.e. the fact it exhibits exponential tails in both the positive and negative directions. The usual mitigation for a single exponential tail, applying a log transform, fails as the log is undefined on the negatives. This section describes how to extend methods applied to one-sided exponential tails to double-exponential distributions.\n\n\n\n\\subsection{Inverse-Hyperbolic-Sine space and the ADLN}\n\nA common alternative to using log-transforms is transforming the data using the Inverse Hyperbolic Sine (asinh). For a review of the use of asinh in economic applications see \\cite{BellemareWichman2020}. The hyperbolic sine and its inverse are given by\n\\begin{equation} \\label{eq:ASINH}\n\\begin{split}\n\\text{sinh}(x) & = \\frac{e^{x}-e^{-x}}{2} \\\\\n\\text{asinh}(x) & = \\log\\left(x+\\sqrt{1+x^2}\\right)\n\\end{split}\n\\end{equation}\nThe asinh transform has the following useful properties:\n\\begin{enumerate}\n    \\item Differentiable and strictly increasing in x.\n    \\item $\\text{asinh}(x)\\approx \\text{sign}(x)(\\log\\lvert x\\rvert + \\log(2))$, with the approximation error rapidly vanishing as $\\lvert x\\rvert$ increases.\\footnote{About 1\\% approximation error at $\\lvert x\\rvert$=4, and about 0.1\\% at $\\lvert x\\rvert$=10.}\n    \\item Odd function, such that $\\text{asinh}(-x) = -\\text{asinh}(x)$.\n    \\item Zero based, such that $\\text{asinh}(0)=0$\n\\end{enumerate}\nI.e., asinh is a bijection similar in flavor to the neglog transform:\n\\begin{equation} \\label{eq:NEGLOG}\n\\text{neglog}(x) =\\text{sign}(x)\\log(1+\\lvert x\\rvert)\n\\end{equation}\nbut with less distortion than the neglog around 0, at the cost of the fixed bias $\\log(2)\\approx 0.7$.\n\nIt is useful to note that any difference of exponentials function can be factored into an exponential multiplied by a Hyperbolic Sine, i.e., \n\\begin{equation} \\label{eq:NEGLOG}\ny =\\exp\\left(x_1\\right) - \\exp\\left(x_2\\right) = 2\\cdot\\exp\\left(\\frac{x_1 + x_2}{2}\\right)\\cdot\\text{sinh}\\left(\\frac{x_1 - x_2}{2}\\right)\n\\end{equation}\nwhich highlights the intimate intuitive relation between the sinh function and the DLN and Laplace distributions. All three are expressed in terms of difference of exponentials, leading to their characteristic ``double exponential'' nature. Sinh's inverse, the asinh, is hence a natural transform to apply to DLN and Laplace distributed RVs.\n\nAs asinh is differentiable and strictly increasing, the method of transformation applies. If $Z=\\text{asinh}(W)$ where $W\\sim DLN$ then $Z\\sim ADLN$, $W=\\text{sinh}(Z)$, and $\\frac{dZ}{dW} = \\left(1+\\text{sinh}(Z)^{2}\\right)^{-1\/2}$. We can now write the PDF for the ADLN distribution\n\\begin{equation} \\label{eq:PDFADLN}\nf_{ADLN}(z) = \\frac{f_{DLN}(\\text{sinh}(z))}{\\text{asinh}'(\\text{sinh}(z))} = f_{DLN}(\\text{sinh}(z))\\sqrt{1+\\text{sinh}(z)^2} \n\\end{equation}\nwhich allows analysis of $Z\\sim ADLN$, the transformed DLN RVs, whose histogram is more ``compact'' and easier to present.\n\nPanels (c) and (d) of Figure~\\ref{fig:DLNexam} present typical DLN distributions encountered in practice with linear (Panel c) and asinh (Panel d) horizontal axis. Panel (c) presents a truncated segment of the distribution. Due to the asinh transform, Panel (d) is able to present the entire distribution. The approximate log-Normality of the positive and negative sides of the DLN is not visible in Panel (c), but is made clear by the asinh transform in Panel (d).\n\n\n\n\\subsection{Growth in DLN-distributed variates}\n\\label{sec:Growth}\n\nHow does one measure growth in DLN-distributed RVs? A firm that had $\\$100M$ of income in year $1$ and $\\$120M$ of income in year $2$ has certainly grown its income. One can argue whether it is preferable to say the firm grew by $\\frac{120M}{100M}-1=0.2=20\\%$ or by $\\log(120M)-\\log(100M)=0.182$ log-points, yet the question itself is well-formed. But what if the firm had $-\\$100M$ of income (i.e., loss) in year $1$, and then $\\$120M$ of income in year $2$? What was its growth? This section aims to provide a rigorous answer to that question.\n\nTo begin, we require a definition of growth. \\cite{BarroSala-I-Martin2003} and \\cite{StudenyMeznik2013} define instantaneous growth of a time-continuous and \\emph{strictly positive} RV $Z(t)>0$ as \n\\begin{equation} \\label{eq:pergrowth}\n\\frac{dZ(t)\/dt}{Z(t)} = \\frac{Z'(t)}{Z(t)} \\approx \\frac{Z_{t+1}-Z_t}{Z_t}\n\\end{equation}\nwith the second part of the equation using the first-difference of discrete variables as an approximation to the derivative $Z'(t)$, which yields the well-known formulation of percentage growth in discrete variables. Generalizing this definition to $Z(t)\\in \\mathbb{R}$ yields:\n\\begin{equation} \\label{eq:pergrowth2}\nd\\% \\equiv \\frac{dZ(t)\/dt}{\\lvert Z(t)\\rvert} = \\frac{Z'(t)}{\\lvert Z(t)\\rvert} \\approx \\frac{Z_{t+1}-Z_t}{\\lvert Z_t\\rvert} \\ \\ \\text{for} \\ \\ Z(t) \\neq 0\n\\end{equation}\nwhich guarantees that $Z_{t+1}>Z_t$ will imply positive growth, regardless of the sign of $Z_t$. The approximate term $\\left(Z_{t+1}-Z_t\\right)\/\\lvert Z_t\\rvert$ is  \\emph{generalized percentage growth} (hereafter denoted d\\%), and is explosive if $\\lvert Z_t\\rvert\\to 0$, similar to ``traditional'' percentage growth.\n\nNext, it is instructive to consider the growth of a log-Normally distributed RV, as most measures of size encountered in firm dynamics (and elsewhere) are approximately log-Normally distributed. To that end, consider the following setting:\n\\begin{equation} \\label{eq:AR_LN}\n\\begin{split}\n& X_{t+1} = \\left(1-\\rho_X\\right)\\cdot\\mu_X + \\rho_X\\cdot X_{t} + \\epsilon^{X}_{t} \\\\\n& \\epsilon^{X}_{t} \\sim \\mathcal{N}(0,\\sigma_{X}^2) \\\\\n& Y_{t} = \\text{exp}\\left(X_{t}\\right)\n\\end{split}\n\\end{equation}\nIn which $X_{t}$ is a simple $AR(1)$ stochastic process, and hence distributes Normally, and $Y_{t}>0$ is log-Normally distributed. What is the growth in $Y_{t}$?\n\nApplying the definition, we have:\n\\begin{equation} \\label{eq:loggrowth}\n\\frac{Y'(t)}{\\lvert Y(t)\\rvert} = \\frac{Y(t)\\cdot X'(t)}{Y(t)} = X'(t) \\approx X_{t+1} - X_t = \\log(Y_{t+1}) - \\log(Y_{t}) \\equiv \\text{dlog}(Y_{t+1})\n\\end{equation}\nwhich yields the well-known formulation of growth as a difference in logs between consecutive values, denoted dlog(). The difference between Equations~\\ref{eq:pergrowth2} and~\\ref{eq:loggrowth} is in whether we differentiate before applying the first-difference approximation. Note that using percentage growth as in Equation~\\ref{eq:pergrowth2} in this case would yield:\n\\begin{equation} \\label{eq:pergrowthYt}\n\\frac{Y_{t+1}}{Y_t} - 1 = \\exp(X_{t+1} - X_t) - 1\n\\end{equation}\nor the general observation that percentage growth is a convex transform of log growth. It is further worth noting that $\\lim_{\\rho_X \\to 1} \\left(X_{t+1} - X_t\\right) = \\epsilon^{X}_{t}$. Log growth yields the innovation in the underlying AR(1) process, while percent growth yields the transformed value $\\exp(\\epsilon^{X}_{t})-1$. I.e., percent growth introduces a convexity bias relative to log growth in the case of a log-Normally distributed RV.\n\nConversely, using log growth to measure growth in a Normally distributed RV, even if said RV is strictly positive in practice, would introduce a similar but opposite ``concavity bias.'' To see that, consider the growth in $X(t)>0$, when measured in dlog terms:\n\\begin{equation} \\label{eq:loggrowthNorm}\n\\text{dlog}(X_{t+1}) = \\log(X_{t+1}) - \\log(X_t) = \\log\\left(\\frac{X_{t+1}}{X_t} -1 +1\\right) =  \\log\\left(\\frac{ X'(t)}{\\lvert X(t)\\rvert} + 1\\right)\n\\end{equation}\nPut differently, using dlog() to measure growth in $X$ yields the log of percent growth, which is the appropriate measure by the definition in Equations~\\ref{eq:pergrowth} and~\\ref{eq:pergrowth2}. Hence, the concept of growth used is closely related to the distribution being considered.\n\nNext, consider a similar setting, but for a DLN RV:\n\\begin{equation} \\label{eq:AR_DLN}\n\\begin{split}\n& X^{p}_{t+1} = \\left(1-\\rho_{p}\\right)\\cdot\\mu_{p} + \\rho_{p}\\cdot X_{t}^{p} + \\epsilon^{p}_{t} \\\\\n& X^{n}_{t+1} = \\left(1-\\rho_{n}\\right)\\cdot\\mu_{n} + \\rho_{n}\\cdot X_{t}^{n} + \\epsilon^{n}_{t} \\\\\n& (\\epsilon^{p}_{t},\\epsilon^{n}_{t})^{T} \\sim \\mathcal{N}\\left(\\pmb{0},\\pmb{\\Sigma}\\right) \\\\\n& Y^{p}_{t} = \\text{exp}\\left(X^{p}_{t}\\right) \\ \\ ; \\ \\ Y^{n}_{t} = \\text{exp}\\left(X^{n}_{t}\\right) \\\\\n& W_{t} = Y^{p}_{t} - Y^{n}_{t}\n\\end{split}\n\\end{equation}\nwith $\\pmb{\\Sigma}$ as in Equation~\\ref{eq:BVN}. By applying the generalized growth definition~\\ref{eq:pergrowth2}, we have:\n\\begin{equation} \\label{eq:DLNGROWTH}\n\\begin{split}\n\\frac{W'(t)}{\\lvert W(t)\\rvert} & = \\frac{Y^{p}(t)\\cdot dX^{p}(t)\/dt - Y^{n}(t)\\cdot dX^{n}(t)\/dt}{\\lvert W(t)\\rvert} \\approx \\frac{Y^{p}_{t}\\cdot\\left(X^{p}_{t+1} - X^{p}_{t}\\right) - Y^{n}_{t}\\cdot\\left(X^{n}_{t+1} - X^{n}_{t}\\right)}{\\lvert W(t)\\rvert} \\\\\n& = \\frac{Y^{p}_{t}\\cdot\\text{dlog}\\left(Y^{p}_{t+1}\\right) - Y^{n}_{t}\\cdot\\text{dlog}\\left(Y^{n}_{t+1}\\right)}{\\lvert Y^{p}_{t} - Y^{n}_{t}\\rvert}\n\\end{split}\n\\end{equation}\nwhich implies the growth of a DLN RV can be defined as a function of the levels and growth rates of its two component log-Normal RVs. Section~\\ref{sec:MC} conducts Monte-Carlo experiments to explore the relation between the measures of growth presented above for Normal, log-Normal, and DLN distributed RVs.\n\n\\comments{\n\\begin{equation} \\label{eq:DLNGROWTH}\n\\begin{split}\ng & = \\frac{200\\cdot\\left(\\log\\left(270\\right)-\\log\\left(200\\right)\\right) - 100\\cdot\\left(\\log\\left(120\\right)-\\log\\left(100\\right)\\right)}{\\lvert200 - 100\\rvert} = 0.4179 \\ dlnp\\  (\\approx 0.4055 \\ lp)  \\\\\ng & = \\frac{50\\cdot\\left(\\log\\left(270\\right)-\\log\\left(50\\right)\\right) - 100\\cdot\\left(\\log\\left(120\\right)-\\log\\left(100\\right)\\right)}{\\lvert50 - 100\\rvert} = 1.3218 \\ dlnp\n\\end{split}\n\\end{equation}\n}\n\n\n\n\\section{Monte-Carlo experiments}\n\\label{sec:MC}\n\nThis section reports the results of Monte-Carlo experiments designed to ascertain the properties of the moments, estimators, and measures discussed above. \\comments{, as well as present further results on the properties of the DLN as an approximating distribution.}\n\n\n\n\\subsection{Properties of estimators}\n\nI begin by exploring the moments and parameter estimators of Sections~\\ref{sec:Moms} and~\\ref{sec:Estim}. I concentrate the experiments on a region of the parameter space that arises in practical applications related to the theory of the firm:\n\\begin{equation} \\label{eq:MC_Region_1}\n\\pmb{Q}: \\ \\ \\left(\\mu_p,\\sigma_p,\\mu_n,\\sigma_n,\\rho_{pn}\\right) \\in \\left(\\left[-3,3\\right],\\left[0.5,2.5\\right],\\left[-3,3\\right],\\left[0.5,2.5\\right],\\left[-1,1\\right]\\right)\n\\end{equation}\n\n\\noindent The data collection\/creation for the Monte-Carlo analysis proceeds as follows.\\\\\n\\noindent For each $i \\in \\{1...N\\}$:\n\\begin{enumerate}\n    \\item Draw a parameter vector $\\pmb{\\Theta}_i\\in\\pmb{Q}$ with Uniform probability.\n    \\item Calculate the theoretical central moments based on $\\pmb{\\Theta}_i$ using the method of Section~\\ref{sec:Moms}.\n    \\item Draw $K$ observations $W_{i,k}\\sim\\text{DLN}(\\pmb{\\Theta}_i)$.\n    \\item Calculate the first five empirical central moments of $W_{i,k}$.\n    \\item Recalculate the first five empirical moments using iteratively smaller subsets of the $K$ observations.\\footnote{Specifically, I recalculate the moments based on the first $K\/2^s$ observations for $s\\in\\{1...11\\}$.}\n    \\item Estimate the parameters of $W_{i,k}$, denoted $\\pmb{\\widehat{\\Theta}}_i$, using the method of Section~\\ref{sec:Estim}.\n    \\item Calculate the Kolmogorov-Smirnov (K-S), Chi-square (C-2), and Anderson-Darling (A-D) test statistics based on $\\pmb{\\widehat{\\Theta}}_i$ and $W_{i,k}$.\n\\end{enumerate}\nI repeat the data creation process $N=70,000$ times. Within each loop, I draw $K=100,000$ observations $W_{i,k}\\sim\\text{DLN}(\\pmb{\\Theta}_i)$.\n\nPanel (a) of Table~\\ref{tab:MC1} presents the Monte-Carlo results for the moment estimators of Section~\\ref{sec:Moms}. It compares the theoretical moments derived in Step 2 of the Monte-Carlo experiment to the empirical moments derived in Step 4, concentrating on the first five moments of the distribution. The analysis is done in asinh space because the moments of the DLN explode quickly due to its heavy tails (similar to moments of the log-Normal, which are similarly considered in log space). The empirical and theoretical moments show high correlation, and the odd moments (mean or $1^{st}$ moment, skewness or $3^{rd}$ moment, and $5^{th}$ moment) exhibit no significant bias. The even moments (variance or $2^{nd}$, and kurtosis or $4^{th}$) show evidence of bias, which is fairly severe for kurtosis. Small-sample bias correction to the kurtosis estimator appears warranted, but is outside the scope of this work. The IQR of the difference between the theoretical and empirical moments is increasing with the moment degree, as expected.\n\n\\RPprep{Estimator Monte Carlo Experiments}{0}{0}{MC1}{%\n    This table presents results of estimator Monte-Carlo experiments with $N=70,000$ repetitions and $K=100,000$ observations drawn in each repetition. Panel (a) tests the moments estimators $\\widehat{M}_i\\ \\ i\\in\\{1...5\\}$ of Section~\\ref{sec:Moms} vs. the actual moments $M_i$, conducting all analysis in asinh space. It reports the general accuracy corr($\\text{asinh}(\\widehat{M}_i),\\text{asinh}(M_i)$); the bias median($\\text{asinh}(\\widehat{M}_i)-\\text{asinh}(M_i)$) ; and the accuracy IQR($\\text{asinh}(\\widehat{M}_i)-\\text{asinh}(M_i)$). Panel (b) reports similar statistics comparing the DLN parameter estimators of Section~\\ref{sec:Estim} $\\pmb{\\widehat{\\Theta}}$ and the actual parameters $\\pmb{\\Theta}$. Panel (c) reports the values of parameters a,b,c,d in the approximations $ICDF(p) = a\\cdot\\exp(b\\cdot p) + c\\cdot\\exp(d\\cdot p)$ for the ICDFs of the Kolmogorov-Smirnov, Chi-square, and Anderson-Darling test statistics for DLN RVs, as well as the approximation $R^2$.\n}\n\\RPtab{%\n    \\begin{tabularx}{\\linewidth}{Frrrrr}\n    \\toprule\n\t\\textit{Panel (a): Moment estimators} & $\\widehat{M}_1$ & $\\widehat{M}_2$ & $\\widehat{M}_3$ & $\\widehat{M}_4$ & $\\widehat{M}_5$ \\\\\n    \\midrule\n    Correlation                 &  0.9997  &  0.9929 &  0.9282 &  0.8238 &  0.8478 \\\\\n    Bias                        &  -0.0001 &  0.1092 & -0.0002 &  6.3410 & 0.0220 \\\\\n    Accuracy                    &  0.0217  &  0.4785 &  3.4480 &  8.5609 & 32.0236 \\\\ \\\\\n    \n\t\\textit{Panel (b): Parameter estimators} & $\\widehat{\\mu}_p$ & $\\widehat{\\sigma}_p$ & $\\widehat{\\mu}_n$ & $\\widehat{\\sigma}_n$ & $\\widehat{\\rho}_{pn}$ \\\\\n    \\midrule\n    Correlation                 &  0.9408 &  0.9619 &  0.9412 &  0.9623 &  0.9190 \\\\\n    Bias                        & -0.0034 &  0.0019 & -0.0043 &  0.0019 & -0.0048 \\\\\n    Accuracy                    &  0.0588 &  0.0251 &  0.0614 &  0.0259 &  0.0762 \\\\ \\\\\n\n    \\textit{Panel (c): ICDF approximations} & a & b & c & d & $R^2$ \\\\\n    \\midrule\n    Kolmogorov-Smirnov          & 6.75e-7 &  0.1553 & -6.7520 & -0.0011 &  0.9976 \\\\\n    Chi-square                  & 1.88e-8 &  0.1955 &  1.2080 &  0.0044 &  0.9920 \\\\\n    Anderson-Darling            & 1.18e-5 &  0.1350 & -5.7070 & -0.0060 &  0.9900 \\\\\n\t\\bottomrule\n    \\end{tabularx}\n}\n\nPanel (b) of Table~\\ref{tab:MC1} goes on to present the Monte-Carlo results for the parameter estimators of Section~\\ref{sec:Estim}. It compares the actual parameters drawn in Step 1 to the estimated parameters calculated in Step 6. The results indicate the estimation procedure is performing quite well. There is high correlation between the actual and estimated parameters, including the hard to estimate correlation parameter. The parameter estimates also exhibit no systematic bias and reasonably low estimation error IQR. These results imply the estimation procedure, while cumbersome, is able to capture the DLN parameters correctly.\n\nTo further explore the precision and small-sample bias of the moment estimators, Figure~\\ref{fig:MC1} presents the dependence of estimator quality on sample size. Panel (a) of the figure presents the dependence of the correlation between the theoretical and empirical moments on sample size. Kurtosis is even less precise than the $5^{th}$ moment, and is strongly influenced by sample size. Panel (b) of Figure~\\ref{fig:MC1} then presents the dependence of the bias on sample size. The $1^{st}$ and $3^{rd}$ moment estimators exhibit no small-sample bias. The $2^{nd}$ and $5^{th}$ exhibit small and rapidly decreasing bias. Kurtosis, again, shows high bias, only slowly decreasing with sample size.\n\n\\RPprep{Estimator Monte-Carlo experiments}{0}{1}{MC1}{%\n    This figure presents results of estimator Monte-Carlo experiments. Panel (a) graphs the dependence of the correlation between the theoretical and empirical moments on sample size. Panel (b) graphs the dependence of moment bias on sample size. Panel (c) presents the distribution of (log of) the K-S statistic in the simulations. Panels (d)-(f) then present the ICDF of the (log) K-S, C-2, and A-D statistics, along with the fitted curves.\n}\n\\RPfig{%\n\t\\begin{tabular}{ccc} \n\t\t\\subfigure[Corr($\\text{asinh}(\\widehat{M}_i),\\text{asinh}(M_i)$)] {\\includegraphics[width=2.5in]{Img\/Moment_Corr.pdf}} & \n\t\t\\subfigure[Median($\\text{asinh}(\\widehat{M}_i)-\\text{asinh}(M_i)$)] {\\includegraphics[width=2.5in]{Img\/Moment_Bias.pdf}} & \n\t\t\\subfigure[PDF of log K-S statistic] {\\includegraphics[width=2.5in]{Img\/KS_PDF.pdf}} \\\\ \\\\\n\t\t\\subfigure[ICDF of log K-S statistic]\n\t\t{\\includegraphics[width=2.5in]{Img\/KSfit.pdf}} &\n\t\t\\subfigure[ICDF of log C-2 statistic]\n\t\t{\\includegraphics[width=2.5in]{Img\/C2fit.pdf}} &\n\t\t\\subfigure[ICDF of log A-D statistic]\n\t\t{\\includegraphics[width=2.5in]{Img\/ADfit.pdf}} \\\\ \\\\\n\t\\end{tabular}\n}\n\n\n\n\\subsection{Test-statistic critical values}\n\\label{sec:TestStats}\n\nA second goal of the Monte-Carlo experiments is to establish critical values for test statistics of the hypothesis that some given data are drawn from a DLN distribution. This is especially important for the Anderson-Darling test statistic, whose critical values are well-known to strongly depend on the distribution being examined. See e.g. \\cite{Stephens1979}, \\cite{DAgostinoStephens1986} Chapter 4, and \\cite{JantschiBolboaca2018}.\n\nTo that end, I calculate the K-S, C-2, and A-D test statistics for each of the $N$ draws in the sample, as described in Step 8 above. To fix ideas, Panel (c) of Figure~\\ref{fig:MC1} presents the distribution of (log of) the K-S statistic in the Monte-Carlo experiment. I then calculate the inverse-CDF (ICDF) of the resulting distribution of (log of) each test statistic. Panels (d), (e), and (f) of Figure~\\ref{fig:MC1} present the ICDFs of the (log) K-S, C-2, and A-D test statistics, respectively. E.g., Panel (f) indicates that one should reject the hypothesis that given data are drawn from the DLN distribution (at a 5\\% confidence level) if the A-D statistic is higher than $\\text{exp}(ICDF(95)) = \\text{exp}(1.135) = 3.110$.\n\nTo move from calculating critical values to deriving a continuous mapping between p-values and test-statistic values, it is common in the literature discussed above to propose an ad-hoc functional form which is able to approximate the ICDF well. Once one estimates the approximating functional form using non-linear least-squares, one can use it to find the p-values associated with each test-statistic value, and vice-versa. Following experimentation, the functional form most closely able to replicate the resulting ICDFs is of the form:\n\\begin{equation} \\label{eq:Pvals}\nICDF(p) = a\\cdot\\text{exp}\\left(b\\cdot p\\right) + c\\cdot\\text{exp}\\left(d\\cdot p\\right)\n\\end{equation}\nwhich is a four-parameter sum (or difference, if $c<0$) of exponentials.\n\nPanels (d), (e), and (f) of Figure~\\ref{fig:MC1} include the fitted values of the functional form, and show that there is an excellent fit between the functional form and the empirical ICDFs. Panel (c) of Table~\\ref{tab:MC1} presents the values of the four approximating parameters for each of the (log) test statistics' ICDFs, and further reports the $R^2$ of the fit, which is above $0.99$ for all three statistics. Hence, one can safely use these functionals to derive p-values for tests of distributional hypotheses.\n\n\n\n\n\\subsection{Growth measures}\n\nA second set of Monte-Carlo experiments tests the relation between the growth measures described in Section~\\ref{sec:Growth}, for RVs distributed Normal, log-Normal, and DLN. To that end, I define three stochastic processes yielding stationary distributions distributed N, LN, and DLN. For each RV type, in each Monte-Carlo iteration, I draw random parameters for the distribution, simulate it forward, measure growth per-period using the different measures discussed above, and consider the relation between the random innovations $\\epsilon_t$ and the various growth measures.\n\nThe stochastic processes for $X$, $Y$, and $W$, distributed N, LN, and DLN, respectively, are as described in Equations~\\ref{eq:AR_LN} and~\\ref{eq:AR_DLN} above. The parameter regions are:\n\\begin{equation} \\label{eq:MC_Region_2}\n\\begin{split}\n\\pmb{Q}_{N}: & \\ \\ \\left(\\rho_{N},\\mu_{N},sd_{N}\\right) \\in \\left(\\left[0.60,0.99\\right],\\left[-100,100\\right],\\left[10,100\\right]\\right) \\\\\n\\pmb{Q}_{LN}: & \\ \\ \\left(\\rho_{LN},\\mu_{LN},sd_{LN}\\right) \\in \\left(\\left[0.60,0.99\\right],\\left[-3,3\\right],\\left[0.5,2.5\\right]\\right) \\\\\n\\pmb{Q}_{DLN}: & \\ \\ \\left(\\rho^{p,n}_{DLN},\\mu^{p,n}_{DLN},sd^{p,n}_{LN},\\rho^{pn}_{DLN}\\right) \\in \\left(\\left[0.60,0.99\\right],\\left[-3,3\\right],\\left[0.5,2.5\\right],\\left[-1,1\\right]\\right) \\\\\n\\end{split}\n\\end{equation}\nwith $\\sigma_{\\Box} = \\sqrt{sd_{\\Box}^2\\cdot\\left(1-\\rho_{\\Box}^2\\right)}$ for $\\Box \\in \\{N,LN,DLN\\}$.\n\n\\noindent The data collection\/creation for the second Monte-Carlo analysis proceeds as follows:\\\\\n\\noindent For each RV type $\\Box \\in \\{N,LN,DLN\\}$: \\\\\n\\noindent For each $i \\in \\{1...N\\}$:\n\\begin{enumerate}\n    \\item Draw a parameter vector $\\pmb{\\Theta}_i\\in\\pmb{Q}_\\Box$ with Uniform probability.\n    \\item Initialize the RV $Z_{\\Box,0}$ to $\\mu_\\Box$ for N, exp($\\mu_\\Box$) for LN, and $Z^{p,n}_{\\Box,0}$ at exp($\\mu^{p,n}_{\\Box,0}$) for DLN.\n    \\item Draw a shock vector of length $K+100$ (two correlated shock vectors for DLN).\n    \\item Simulate the process forward $K+100$ period based on its laws of motion.\n    \\item Drop the first 100 observation as burn-in.\n    \\item Calculate the set of growth measures from Section~\\ref{sec:Growth}.\n\\end{enumerate}\nI repeat the data creation process $N=10,000$ times, each for $K=1,000$ periods, yielding a total of $10M$ growth observations to be analyzed per distribution type.\n\nPanels (a),(b),(c) of Table~\\ref{tab:MC2} presents the correlations between different growth measures for N, LN, and DLN RVs, respectively. The panels also report correlations concentrating on strictly positive values (i.e., when $Z_{t}>0$ and $Z_{t+1}>0$) and when further avoiding tiny beginning values (i.e., $Z_t>1$). The appropriate concept of growth for Normally distributed RV is $\\epsilon_t\/\\lvert Z_{t}\\rvert$, and Panel (a) shows it is highly correlated with the generalized percentage growth measure. The panel further shows that using dlog as a measure of growth for Normal RVs is inaccurate. This fact is further highlighted by Panels (a) and (b) of Figure~\\ref{fig:MC2} which present the relation between the appropriate growth measure and the generalized percent (d\\%) and dlog measures, respectively. Panel (a) shows d\\% captures growth of Normal RVs well, and Panel (b) highlights the ``concavity bias'' arising from using the dlog measure rather than the d\\% measure. The dispersion around the 45-degree line in Panel (a) is driven by the mean-reversion term of the AR(1), which the growth concept ignores.\n\n\\RPprep{Growth Monte Carlo Experiments}{0}{0}{MC2}{%\n    This table presents results of growth Monte-Carlo experiments with $N=10,000$ repetitions and $K=1,000$ observations simulated forward in each repetition. Panels (a), (b), and (c) present results for N, LN, DLN, respectively. Within each panel, I report correlations between the following measures of growth: $\\epsilon_t$ the stochastic innovation underlying the growth at time $t$; $\\epsilon_t\/\\lvert Z_{t}\\rvert$ the relative stochastic innovation; d\\%($Z_{t+1}$)=$\\left(Z_{t+1} - Z_{t}\\right\/\\lvert Z_{t}\\rvert$ the generalized percentage growth; dlog($Z_{t+1}$)=log($Z_{t+1}$)-log($Z_{t}$) the log point growth; dDLN($Z_{t+1}$) the DLN growth formulation based on Equation~\\ref{eq:DLNGROWTH}.\n}\n\\RPtab{%\n    \\begin{tabularx}{\\linewidth}{Flllll}\n    \\toprule\n\t\\textit{Panel (a): N} & $\\epsilon_t$ & $\\epsilon_t\/\\lvert Z_{t}\\rvert$ & d\\%($Z_{t+1}$) & dlog($Z_{t+1}$) & \\\\\n    \\midrule\n    $\\epsilon_t$ \n    & 1.000 & 0.010 & 0.009 & 0.659$^{a}$ & \\\\\n    $\\epsilon_t\/\\lvert Z_{t}\\rvert$ \n    & 0.380$^{b}$ & 1.000 & 0.973 & 0.031$^{a}$ & \\\\\n    d\\%($Z_{t+1}$) \n    & 0.357$^{b}$ & 0.960$^{b}$ & 1.000 & 0.033$^{a}$ & \\\\\n    dlog($Z_{t+1}$) \n    & 0.712$^{b}$ & 0.590$^{b}$ & 0.617$^{b}$ & 1.000 & \\\\ \\\\\n\n\t\\textit{Panel (b): LN} & $\\epsilon_t$ & $\\epsilon_t\/\\lvert Z_{t}\\rvert$ & d\\%($Z_{t+1}$) & dlog($Z_{t+1}$) & \\\\\n    \\midrule\n    $\\epsilon_t$ \n    & 1.000 & 0.023$^{a}$ & 0.269$^{a}$ & 0.931$^{a}$ & \\\\\n    $\\epsilon_t\/\\lvert Z_{t}\\rvert$\n    & 0.644$^{b}$ & 1.000 & 0.097$^{a}$ & 0.023$^{a}$ & \\\\\n    d\\%($Z_{t+1}$) \n    & 0.381$^{b}$ & 0.363$^{b}$ & 1.000 & 0.295$^{a}$ & \\\\\n    dlog($Z_{t+1}$) \n    & 0.929$^{b}$ & 0.620$^{b}$ & 0.381$^{b}$ & 1.000 & \\\\ \\\\\n\n\t\\textit{Panel (c): DLN} & $\\widehat{\\epsilon}_t^c$ & $\\widehat{\\epsilon}_t\/\\lvert Z_{t}\\rvert^c$ & d\\%($Z_{t+1}$) & dlog($Z_{t+1}$) & dDLN($Z_{t+1}$) \\\\\n    \\midrule\n    $\\widehat{\\epsilon}_t^c$ \n    & 1.000 & 0.000$^{a}$ & 0.000$^{a}$ & 0.038$^{a}$ & 0.000$^{a}$ \\\\\n    $\\widehat{\\epsilon}_t\/\\lvert Z_{t}\\rvert^c$\n    & 0.043$^{b}$ & 1.000 & 0.652 & 0.022$^{a}$ & 0.944 \\\\\n    d\\%($Z_{t+1}$) \n    & 0.009$^{b}$ & 0.464$^{b}$ & 1.000 & 0.016$^{a}$ & 0.645 \\\\\n    dlog($Z_{t+1}$) \n    & 0.057$^{b}$ & 0.739$^{b}$ & 0.397$^{b}$ & 1.000 & 0.023$^{a}$ \\\\\n    dDLN($Z_{t+1}$)\n    & 0.040$^{b}$ & 0.931$^{b}$ & 0.455$^{b}$ & 0.797$^{b}$ & 1.000 \\\\ \\\\\n    \\bottomrule\n    \\end{tabularx}\n    \\begin{flushleft}\n    $^a$ For strictly positive values ($Z_{t}>0$ and $Z_{t+1}>0$) \\\\\n\t$^b$ For strictly positive and non-tiny initial values ($Z_{t}>1$ and $Z_{t+1}>0$) \\\\\n\t$^c$ For DLN, I define $\\widehat{\\epsilon}_t = \\left(Z_t^p\\cdot\\epsilon_t^p - Z_t^n\\cdot\\epsilon_t^n\\right)$ and $Z_t = Z_t^p - Z_t^n$\n    \\end{flushleft}\n}\n\n\\RPprep{Growth Monte-Carlo experiments}{1}{0}{MC2}{%\n    This figure presents results of growth Monte-Carlo experiments. Panels (a) and (b) graph the relation between the growth of a Normal RV and (a) generalized percentage growth d\\%($Z_{t+1}$)=$\\left(Z_{t+1} - Z_{t}\\right)\/\\lvert Z_{t}\\rvert$; (b) log point growth dlog($Z_{t+1}$)=log($Z_{t+1}$)-log($Z_{t}$). Panels (c) and (d) graph the relation between the growth of a log-Normal RV and (c) dlog($Z_{t+1}$) ; (d) d\\%($Z_{t+1}$). Panels (e) and (f) graph the relation between the growth of a DLN RV and (e) the DLN growth measure from Equation~\\ref{eq:DLNGROWTH}, dDLN($Z_{t+1}$); (f) d\\%($Z_{t+1}$).\n}\n\\RPfig{%\n\t\\begin{tabular}{cc} \n\t\t\\subfigure[N growth vs. d\\%$^a$] {\\includegraphics[width=2.5in]{Img\/N_grow_per.pdf}} & \n\t\t\\subfigure[N growth vs. dlog$^b$] {\\includegraphics[width=2.5in]{Img\/N_grow_dlog.pdf}} \\\\ \n\t\t\\subfigure[LN growth vs. dlog] {\\includegraphics[width=2.5in]{Img\/LN_grow_dlog.pdf}} & \n\t\t\\subfigure[LN growth vs. d\\%] {\\includegraphics[width=2.5in]{Img\/LN_grow_per.pdf}} \\\\ \t\t\n\t\t\\subfigure[DLN growth vs. dDLN$^a$] {\\includegraphics[width=2.5in]{Img\/DLN_grow_dDLN.pdf}} & \n\t\t\\subfigure[DLN growth vs. d\\%$^a$] {\\includegraphics[width=2.5in]{Img\/DLN_grow_per.pdf}} \\\\ \n\t\\end{tabular}\n    \\begin{flushleft}\n    $^a$ For non-tiny initial values ($\\lvert Z_{t}\\rvert>1$) \\\\\n\t$^b$ For strictly positive and non-tiny initial values ($Z_{t}>1$ and $Z_{t+1}>0$) \\\\\n    \\end{flushleft}\t\n}\n\nPanel (b) of Table~\\ref{tab:MC2} moves on to considering LN RVs. Here, the appropriate concept of growth is just $\\epsilon_t$, and the panel shows that dlog measures growth well, while d\\% suffers from a convexity bias and is a poor measure of growth. Panels (c) and (d) of Figure~\\ref{fig:MC2} make the convexity bias clear by plotting the relation between growth and dlog and between growth and d\\%, respectively.\n\nFinally, Panel (c) of Table~\\ref{tab:MC2} presents correlations between growth of DLN RVs and the growth measures. For DLN, the appropriate concept of growth is $\\left(Z_t^p\\cdot\\epsilon_t^p - Z_t^n\\cdot\\epsilon_t^n\\right)\/\\lvert Z_t^p-Z_t^n\\rvert$, and the panel shows that the growth formula for DLN derived in Equation~\\ref{eq:DLNGROWTH} captures it well. The panel also shows that dlog, which has limited usability for measuring DLN growth as it is limited to positive values, does poorly even when limited to positive values, and reaches a correlation of ~0.75 with DLN growth even when limiting to positive, non-tiny values. Panels (e) and (f) of Figure~\\ref{fig:MC2} show that dDLN is indeed an appropriate measures, while d\\% is an unbiased but noisy measure of DLN growth.\n\n\n\n\\comments{\n\\subsection{DLN as an approximating distribution}\n\nA third Monte-Carlo experiment tests how well the DLN distribution approximates several ``compound'' distributions arising in practice. The test is also useful in providing evidence that our tests have power to reject ``non-DLN'' distributions. The distributions I concentrate on are: (i) sum of two DLN RVs; (ii) multiplication of DLN by log-Normal RV; (iii) Division of DLN by log-Normal RV; (iv) multiplication of DLN by Normal RV; and (v) multiplication of Normal by log-Normal RV. The two distributions being compounded are independent of each other.\n\nFor all DLN RVs, I use the parameter region $\\pmb{Q}$ from Equation~\\ref{eq:MC_Region_1}. For Normal and log-Normal RVs, I use the following parameter regions:\n\\begin{equation} \\label{eq:MC_Region_3}\n\\begin{split}\n\\pmb{Q}_{\\widehat{N}}: \\ \\ & \\left(\\mu_N,\\sigma_N\\right) \\in \\left(\\left[-100,100\\right],\\left[10,100\\right]\\right) \\\\\n\\pmb{Q}_{\\widehat{LN}}: \\ \\ & \\left(\\mu_{LN},\\sigma_{LN}\\right) \\in \\left(\\left[-3,3\\right],\\left[0.5,2.5\\right]\\right) \\\\\n\\end{split}\n\\end{equation}\n\nThe data collection\/creation for the Monte-Carlo analysis in this section proceeds as follows: \\\\\nFor each $i \\in \\{1...N\\}$:\n\\begin{enumerate}\n    \\item Draw a first parameter vector $\\pmb{\\Theta}^1_i$, from the appropriate parameter range, with Uniform probability.\n    \\item Draw a second parameter vector $\\pmb{\\Theta}^2_i$, from the appropriate parameter range, with Uniform probability.\n    \\item Draw $K$ observations $X_{i,k}$ from the first distribution with parameter vector $\\pmb{\\Theta}^1_i$.\n    \\item Draw $K$ observations $Y_{i,k}$ from the second distribution with parameter vector $\\pmb{\\Theta}^2_i$.\n    \\item Calculate the compound RV values $W_{i,k}$ using $X_{i,k}$ and $Y_{i,k}$.\n    \\item Estimate the DLN parameters of $W_{i,k}$, denoted $\\pmb{\\hat{\\Theta}}_i$, using the method of Section~\\ref{sec:Estim}.\n    \\item Calculate the K-S, C-2, and A-D test statistics based on $\\pmb{\\hat{\\Theta}}_i$ and $W_{i,k}$.\n    \\item Calculate the p-values of the test statistics using the ICDF approximations from Section~\\ref{sec:TestStats}.\n\\end{enumerate}\n\nTable~\\ref{tab:MC3} presents the results of the analysis.\\rp{Need to refresh the table after the fixes to the dlnfit code.} For each compound distribution, Panel (a) presents the percent of Monte-Carlo repetitions rejected as DLN by each of the three distributional tests, at the 1\\%, 5\\%, and 10\\% confidence levels. Panels (b) and (c) present the (5,10,50)$^{th}$ percentiles of the test statistics and their accompanying p-values, respectively, across the Monte-Carlo experiments.\n\n\\RPprep{Approximation Monte Carlo Experiments}{0}{0}{MC3}{%\n    This table presents results of approximation Monte-Carlo experiments with $N=25,000$ repetitions and $K=100,000$ observations drawn in each repetition. For each compound distribution tested, Panel (a) reports the share of observations rejected as being DLN at the 1\\%, 5\\%, and 10\\% confidence levels using each of the three distributional tests K-S, C-2, and A-D. Panels (b) and (c) present the (5,10,50)$^{th}$ percentiles of the test statistics and their accompanying p-values, respectively, across all Monte-Carlo runs for each compound distribution.\n}\n\\RPtab{%\n    \\begin{tabularx}{\\linewidth}{Frrrrrrrrr}\n    \\toprule\n    & \\multicolumn{3}{c}{K-S} & \\multicolumn{3}{c}{C-2} & \\multicolumn{3}{c}{A-D} \\\\\n\t\\textit{Panel (a): rejected} & \\multicolumn{1}{c}{1\\%} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} & \\multicolumn{1}{c}{1\\%} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} & \\multicolumn{1}{c}{1\\%} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} \\\\\n    \\midrule\n    DLN + DLN   & 0.007 & 0.076 & 0.337 & 0.007 & 0.104 & 0.334 & 0.009 & 0.082 & 0.355 \\\\\n    DLN * LN    & 0.101 & 0.377 & 0.539 & 0.111 & 0.408 & 0.538 & 0.084 & 0.378 & 0.549 \\\\\n    DLN \/ LN    & 0.129 & 0.375 & 0.521 & 0.148 & 0.385 & 0.522 & 0.117 & 0.370 & 0.515 \\\\\n    DLN * N     & 0.001 & 0.148 & 0.690 & 0.001 & 0.385 & 0.753 & 0.001 & 0.178 & 0.668 \\\\\n    LN * N      & 0.000 & 0.070 & 0.324 & 0.000 & 0.080 & 0.270 & 0.000 & 0.086 & 0.353 \\\\ \\\\\n    \n\t\\textit{Panel (b): stats} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} & \\multicolumn{1}{c}{50\\%} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} & \\multicolumn{1}{c}{50\\%} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} & \\multicolumn{1}{c}{50\\%} \\\\\n    \\midrule\n    DLN + DLN   & 0.002 & 0.002 & 0.004 & 3.910 & 4.279 & 9.975 & 0.011 & 0.025 & 0.209 \\\\\n    DLN * LN    & 0.001 & 0.002 & 0.008 & 3.349 & 3.855 & 32.59 & 0.006 & 0.009 & 1.068 \\\\\n    DLN \/ LN    & 0.001 & 0.001 & 0.007 & 3.441 & 3.864 & 22.28 & 0.006 & 0.009 & 0.707 \\\\\n    DLN * N     & 0.002 & 0.002 & 0.009 & 4.170 & 4.657 & 56.31 & 0.011 & 0.018 & 1.358 \\\\\n    LN * N      & 0.001 & 0.001 & 0.002 & 3.233 & 3.660 & 5.321 & 0.008 & 0.010 & 0.042 \\\\ \\\\\n    \n\t\\textit{Panel (c): p-vals} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} & \\multicolumn{1}{c}{50\\%} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} & \\multicolumn{1}{c}{50\\%} & \\multicolumn{1}{c}{5\\%} & \\multicolumn{1}{c}{10\\%} & \\multicolumn{1}{c}{50\\%} \\\\\n    \\midrule\n    DLN + DLN   & 0.042 & 0.055 & 0.136 & 0.035 & 0.047 & 0.138 & 0.040 & 0.053 & 0.132 \\\\\n    DLN * LN    & 0.000 & 0.010 & 0.082 & 0.000 & 0.007 & 0.073 & 0.001 & 0.013 & 0.080 \\\\\n    DLN \/ LN    & 0.000 & 0.002 & 0.092 & 0.000 & 0.002 & 0.087 & 0.000 & 0.007 & 0.091 \\\\\n    DLN * N     & 0.041 & 0.046 & 0.072 & 0.030 & 0.034 & 0.057 & 0.039 & 0.046 & 0.074 \\\\\n    LN * N      & 0.044 & 0.058 & 0.238 & 0.047 & 0.056 & 0.315 & 0.040 & 0.055 & 0.247 \\\\\n\t\\bottomrule\n    \\end{tabularx}\n}\n\nThe results in Table~\\ref{tab:MC3} first establish that the distributional tests used have sufficient power to reject distributions that are non-DLN. In Panel (a), for each of the three test methods, about 30\\%-70\\% of Monte-Carlo repetitions are rejected as being DLN at the 10\\% confidence level. Even at the 5\\% level, around 40\\% of DLN*LN and DLN\/LN repetitions are rejected.\n\nSecond, the results in Table~\\ref{tab:MC3} indicate that DLN performs well as an approximating distribution for sum of DLN (DLN+DLN), multiplication of log-Normal by Normal (LN*N), and to a lesser extent multiplication of DLN by Normal (DLN*N). E.g., for these three compound distributions, the 5$^{th}$ percentile of p-values using all three tests is around $0.03$-$0.05$. DLN however performs poorly as an approximating distribution for the other two compound distributions, DLN*LN and DLN\/LN. For comparison, both of these compound distributions have 5$^{th}$ percentile of p-values around $0.000$-$0.001$.\n}\n\n\n\n\\section{Summary}\n\nThis paper presents the Difference-of-Log-Normals (DLN) distribution, stemming from the multiplicative CLT, and lays a methodological and quantitative foundation for the analysis of DLN-distributed phenomena. It begins by characterizing the distribution, defining its PDF and CDF, presenting estimators for its moments and parameters, and generalizing it to a elliptical multi-variate RVs.\n\nIt goes on to discuss mathematical methods useful in the analysis of DLN distributions. First, it shows the intimate intuitive relation between the DLN distribution and the Hyperbolic Sine, and why the Inverse Hyperbolic Sine (asinh) is a useful transform when dealing with ``double exponential'' RVs such as the DLN.\n\nNext, it considers the concept of growth for DLN RVs. It extends the classical definition of growth, applying only to positive RVs, to RVs $\\in \\mathbb{R}$. It then shows that the measure of growth used is dependant on the distribution of the data being measured. It makes the case that growth in Normal, log-Normal and DLN RVs should be measured using different measures of growth and develops the appropriate measure of growth for DLN RVs.\n\nThe paper reports the results of extensive Monte-Carlo experiments, aimed to establish the properties of the estimators and measures presented. It shows that the moment estimators have good accuracy, but highlights their small-sample bias, especially for the case of kurtosis. A small-sample bias-correction method for the kurtosis estimator is merited. It also shows that the parameter estimators proposed are reasonably accurate and unbiased. To enable accurate tests of whether some data are DLN, it establishes critical values and p-value estimators for three distributional tests: Kolmogorov-Smirnov, Chi-square, and Anderson-Darling.\n\nA second Monte-Carlo experiment verifies the generalized growth measures discussed indeed back-out the appropriate growth concept for Normal, log-Normal, and DLN distributions. It especially highlights the ``convexity\/concavity bias'' arising when applying the wrong measure of growth to an RV. Of importance here is the evidence that measuring growth of log-Normal RVs using percentage growth leads to a significant convexity bias. \\comments{A third Monte-Carlo experiment presents evidence that DLN is also a useful approximating distribution, able to approximate several compound distributions.}\n\n\n\n\n\n\n\n\n\n\n\\comments{\n\n\\subsection{Alternative parametrization}\n\\label{sec:Alt}\n\nConsider the following bijection:\n\\begin{equation} \\label{eq:REPARAM}\n\\begin{bmatrix}\n\\alpha \\\\ \\beta \\\\ \\gamma \\\\ \\delta \\\\ \\epsilon\n\\end{bmatrix}\n= \\text{asinh}\\left(\n\\begin{bmatrix}\n\\text{exp}\\left(\\mu_p+\\frac{\\sigma_p^2}{2}\\right) - \\text{exp}\\left(\\mu_n+\\frac{\\sigma_n^2}{2}\\right) \\\\\n\\text{exp}\\left(\\mu_p+\\frac{\\sigma_p^2}{2}\\right) + \\text{exp}\\left(\\mu_n+\\frac{\\sigma_n^2}{2}\\right) \\\\\n\\left(\\text{exp}\\left(\\sigma_p^2\\right)-1\\right)  - \\left(\\text{exp}\\left(\\sigma_n^2\\right)-1\\right)  \\\\\n\\left(\\text{exp}\\left(\\sigma_p^2\\right)-1\\right)  + \\left(\\text{exp}\\left(\\sigma_n^2\\right)-1\\right)  \\\\\n\\text{exp}\\left(\\sigma_p\\cdot\\sigma_n\\cdot\\rho_{pn}\\right)-1\n\\end{bmatrix}\\right)\n\\end{equation}\nwhich maps the parameter vector $\\pmb{\\Theta}_1 = (\\mu_p,\\sigma_p,\\mu_n,\\sigma_n,\\rho_{pn})$ to the parameter vector $\\pmb{\\Theta}_2 = (\\alpha,\\beta,\\gamma,\\delta,\\epsilon)$. This parametrization stems from Equations~\\ref{eq:MUDLN} and~\\ref{eq:SIGDLN}, in which the various terms appear. It further concentrates on the sums and differences of the terms, and applies an asinh transform to the parameter space. The transformed parameters in $\\pmb{\\Theta}_2$ correlate with the (asinh of the) first four moments of the DLN distribution described by the vector $\\pmb{\\Theta}_1$, as shown at the Monte-Carlo experiments in Section~\\ref{sec:MC}. This alternative parametrization is useful for implementing method-of-moments estimators for the parameters of the DLN.\n\nPanel (c) of the same table presents an analysis of the alternative parametrization described in Section~\\ref{sec:Alt}. The correlation between the alternative parameters and the predicted and actual moments is high for the first four parameters and respective moments, but is practically zero for the fifth parameter and moment. This indicates the fifth parameter in the alternative parametrization does not capture the associated moment. There is again significant bias in the even parameters relative to their corresponding moments.\n\nPanel (c) --- Alternative parameters & $\\alpha$ & $\\beta$ & $\\gamma$ & $\\delta$ & $\\epsilon$ \\\\\n\\midrule\n$\\widehat{M}_i$ Correlation &  1.0000 &  0.9280 &  0.8568 &  0.9682 &  0.0183 \\\\\n$\\widehat{M}_i$ Bias        &  0.0000 & -5.8456 & -0.0574 & -11.486 &  4.5365 \\\\\n$\\widehat{M}_i$ Accuracy    &  0.0000 &  4.2309 &  4.7317 &  7.6611 & 60.5636 \\\\\n$M_i$ Correlation           &  0.9994 &  0.9359 &  0.7638 &  0.7692 &  0.0081 \\\\\n$M_i$ Bias                  &  0.0001 & -5.4896 &  0.0160 & -3.7869 &  4.3550 \\\\\n$M_i$ Accuracy              &  0.0275 &  4.0366 &  2.1522 &  1.6222 & 26.3605 \\\\ \\\\\n\nPanel (c) compares the alternative parametrization of Section~\\ref{sec:Alt} $\\pmb{\\widetilde{\\Theta}}$ with the first five moment estimators and actual moments $\\widehat{M}_i$ and $M_i$.\n\nOur last distribution of interest is the firm income growth distribution (FIGD). Dealing with growth aspects of income presents a methodological issue, however, as our measures of growth are ill-equipped to describe growth in sometimes-negative values. I hence begin by extending the growth measures to deal with values in $(-\\infty,\\infty)$ rather than $(0,\\infty)$. To fix ideas, consider the following seven scenarios: a firm earns (i) \\$100 in period $t$ and \\$200 in period $t+1$, (ii) \\$100 in $t$ and \\$1 in $t+1$, (iii) \\$100 in $t$ and -\\$100 in $t+1$, (iv) -\\$100 in $t$ and \\$100 in $t+1$, (v) -\u00a210,000 in $t$ and \u00a210,000 in $t+1$, (vi) \\$0 in $t$ and \\$100 in $t+1$, (vii) \\$0 in $t$ and -\\$100 in $t+1$, .\n\nWhat was the growth in firm income in each scenario? The two standard ways in which to measure growth are percent change $d\\%(X_{t+1}) = (X_{t+1} - X_{t})\/X_{t}$, and log-point change $\\text{dlog}(X_{t+1}) = \\log(X_{t+1}) - \\log(X_{t})$. Using either method, the first two scenarios are well-defined. In scenario (i), income growth was (200-100)\/100 = 1 = 100\\%, or it was log(200)-log(100) = 0.693 = 69.3 log-points (lp). In scenario (ii), it was (1-100)\/100 = -99\\% or log(1)-log(100) = -461 lp. Note that log-point growth quickly tends to $-\\infty$ as we decrease firm income during the second period in scenario (ii) from $1$ to $0$.\n\nIn scenario (iii), one could say that percent growth was ((-100)-100\/100) = -2 = -200\\%, extending the definition of percent changes. But this extension leads percent growth in scenario (iv) to be -200\\% as well, even though firm income grew. A more intuitive extension of the percent concept is to use\n\\begin{equation} \\label{eq:gprecent}\n\\widetilde{d\\%}(X_{t+1}) = (X_{t+1} - X_{t})\/\\lvertX_{t}\\rvert\n\\end{equation}\nGrowth rates then become (i) 100\\%, (ii) -99\\%, (iii) -200\\%, (iv) 200\\%, (v) 200\\%, (vi) $-\\infty$, and (vii) $+\\infty$. This extension improves the direction (i.e. sign) of percent growth. As can be seen in scenario (v), it is also scale-invariant (i.e., not impacted by the unit of measurement). Yet growth rates from values close to zero remain explosive.\n\nCan we likewise extend the log-point growth concept? Using the inverse hyperbolic sine (asinh) again, we can define the growth in $X$ to be \n\\begin{equation} \\label{eq:dasinh}\n\\text{dasinh}(X_{t+1}) = \\text{asinh}(X_{t+1}) - \\text{asinh}(X_{t})\n\\end{equation}\nGrowth rates in the seven scenarios are then (i) 69.3 asinh points (ap), (ii) -442 ap, (iii) -1060 ap, (iv) +1060 ap, (v) +1980 ap (vi) +530 ap, (vii) -530 ap. This measure has several desirable properties: (a) growth to and from zero is well-defined and non-explosive, (b) growth from -X to X is double the growth from 0 to X, (c) growth from -X to X is the opposite of growth from X to -X, (d) growth between two positive values quickly approaches the proper log-point growth (due to the quickly decreasing approximation error of asinh discussed above). One downside of the measure is that it is scale-dependent when the two values being compared have opposite signs, as can be seen in scenario (v).\n\n}\n\n\\clearpage\n\\bibliographystyle{JFE}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzziueo b/data_all_eng_slimpj/shuffled/split2/finalzziueo
new file mode 100644
index 0000000000000000000000000000000000000000..7b2aa625952a0f61ebe2048b96661c8cea317a1f
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzziueo
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\nThe determination of the exact string theory low energy effective action is a very difficult problem in general. In the case of type II string theory on $\\mathds{R}^{1,10-d} \\times T^{d-1}$, the lowest order non-perturbative corrections could nonetheless have been computed  \\cite{Green:1997tv,Green:1997as,Kiritsis:1997em}. Although there is no non-perturbative formulation of the theory,  the constraints following from supersymmetry and $U$-duality have permitted to determine the non-perturbative low energy effective action from perturbative computations in string theory \\cite{D'Hoker:2005jc,Green:2008uj,Gomez:2013sla,Green:2014yxa,D'Hoker:2014gfa} and in eleven-dimensional supergravity \\cite{Green:1997as,Green:1999pu,Green:2005ba,Green:2008bf,Basu:2014uba}. The four-graviton amplitude allows in particular to determine the $\\nabla^{2k}R^4$ type correction in the effective action,\n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal L}\\sim  \\frac{1}{\\kappa^2}  R +\\sum_{p,q}  \\kappa^{2 \\frac{d-3+4p+6q}{9-d}}  E_{(p,q)} \\nabla^{4p+6q} R^4 +\\dots    \\ee \nwhere the dots stand for other terms including the supersymmetric completion, $(p,q)$ labels the different invariant combinations of derivatives compatible with supersymmetry according to the notations used in \\cite{Green:2010wi}, and $E_{(p,q)}$ are automorphic functions of the scalar fields defined on $E_{d(d)}(\\mathds{Z}) \\backslash E_{d(d)}\/ K_d$. For $(p,q) = (0,0)$, $(1,0)$ and $(0,1)$, the complete effective action at this order is determined by these functions ${\\cal E}_\\gra{p}{q}$, which have been extensively studied  \\cite{Review,Obers:1999um,Basu:2007ck,Green:2010kv,Green:2011vz,Fleig:2013psa,Minimal,D4R4,Gustafsson:2014iva,Pioline:2015yea}. \n\n$E_{(0,0)}$ is an Eisenstein series associated to the minimal unitary representation \\cite{Obers:1999um,Green:2010kv}, $E_{(1,0)}$ is an (or a sum of two) Eisenstein series associated to the next to minimal unitary representation(s) \\cite{Green:2010kv}, and both are therefore relatively well understood.  They are nonetheless very complicated functions, and the explicit expansion of $E_{(1,0)}$ in Fourier modes is not yet determined \\cite{Green:2011vz,Fleig:2013psa,Gustafsson:2014iva}. $E_{(0,1)}$ is not even an Eisenstein series, and was shown in \\cite{Green:2005ba} to satisfy to an inhomogeneous Poisson equation in type IIB. A proposal for this function in eight dimensions \\cite{Basu:2007ck}, suggested a split of the function into the sum of an Eisenstein series and an inhomogeneous solution, which was subsequently generalised in seven and six dimensions \\cite{Green:2010wi,Green:2010kv}, and  recently clarified in \\cite{Pioline:2015yea}. \n\nIn this paper we extend the analysis carried out in \\cite{Minimal,D4R4} to the study of $E_{(0,1)}$. We show that this function indeed splits into the sum of two functions that are associated to two distinct supersymmetry invariants, and therefore satisfy to inequivalent tensorial differential equations. In particular, the second satisfies to a homogeneous equation, which is solved by the Eisenstein function appearing in \\cite{Green:2010wi,Basu:2007ck,Pioline:2015yea}. One can distinguish the two functions by looking at specific higher point couplings that we identify. The new class of invariants generalises to an infinite class admitting a coupling in $F^{2k} \\nabla^4 R^4$, and we identify a unique Eisenstein function solving the corresponding tensorial differential equations in all dimensions greater than four. This function turns out to be compatible with perturbative string theory, and only admits three perturbative contributions in four dimensions, at 1-loop, $(k+2)$-loop, and $2k$-loop.  However, the only amplitude that seems to unambiguously distinguish it from others is the $(k+2)$-loop four-graviton amplitude in a non-trivial Ramond--Ramond background, which makes an explicit check extremely challenging. \n\n\nWe start with the analysis of the supersymmetry invariants in four dimensions. The two $\\nabla^6 R^4$ type invariants in the linear approximation are associated to two distinct classes of chiral primary operators of $SU(2,2|8)$ discussed in \\cite{Drummond:2003ex}. We identify the corresponding representations of $E_{7(7)}$ associated to nilpotent coadjoint orbits \\cite{E7Djo} that are summarised in figure \\ref{ClosureDiag}. \n\\begin{figure}[htbp]\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (1,0) node{\\textbullet};\n \\draw (1,0 - 1) node{\\textbullet};\n  \\draw (1,0 - 2)  node{\\textbullet};\n  \\draw (1,0 + 2)  node{\\textbullet};\n  \\draw (1,0 + 4)  node{\\textbullet};\n  \\draw (1 + 1,0 + 2.5)  node{\\textbullet};\n   \\draw (1 - 1,0 + 3.5)  node{\\textbullet};\n    \\draw (1 - 1 ,0 + 1) node{\\textbullet};\n   \n  \\draw (1 + 0.3,0 - 2) node{$R$};\n  \\draw (1 + 0.4,0 - 1) node{$R^4$};\n  \\draw (1 + 0.7,0) node{$ \\nabla^4 R^4$};\n  \\draw (1 - 1.9,0 + 1) node{$ {F}^{2k} \\nabla^4 R^4$};\n  \\draw (1 + 0.7 + 1,0 + 2.5) node{$ \\nabla^6 R^4$};\n  \\draw[-,draw=black,very thick](1,0) -- (1,0 + 2 );\n   \\draw[-,draw=black,very thick](1 - 1,0 + 1) -- (1 - 1,0 + 3.5);\n    \\draw[-,draw=black,very thick](1 - 1,0 + 3.5) -- (1,0 + 2);\n    \\draw[-,draw=black,very thick](1,0 + 2) -- (1 + 1,0 + 2.5);\n    \\draw[-,draw=black,very thick](1 + 1,0 + 2.5) -- (1,0 + 4);\n    \\draw[-,draw=black,very thick](1 - 1,0 + 3.5) -- (1,0 + 4);\n     \\draw[dashed,draw=black,very thick](1,0 + 4) -- (1,0 + 4.5);\n  \\draw[-,draw=black,very thick](1,0) -- (1 - 1,0 + 1);\n\\draw[-,draw=black,very thick] (1,0 - 1) -- (1,0);\n\\draw[-,draw=black,very thick] (1,0 - 2) -- (1,0 - 1);\n\\draw[<-,draw=black,thick] (1 - 3-1,0 + 5) -- (1 - 3 - 1,0 - 2);\n\\draw (1 - 3 + 0.2 - 1,0 - 2) node{$0$};\n\\draw (1 - 3- 1,0 - 2) node{-};\n\\draw (1 - 3- 1,0 - 1) node{-};\n\\draw (1 - 3- 1,0) node{-};\n\\draw (1 - 3- 1,0 + 2) node{-};\n\\draw (1 - 3- 1,0 + 1) node{-};\n\\draw (1 - 3- 1,0 + 2.5) node{-};\n\\draw (1 - 3- 1 ,0 + 3.5) node{-};\n\\draw (1 - 3 - 1,0 + 4) node{-};\n\\draw (1 - 3 + 0.3 - 1,0 - 1) node{$34$};\n\\draw (1 - 3 + 0.3 - 1,0) node{$52$};\n\\draw (1 - 3 + 0.3 - 1,0 + 1) node{$54$};\n\\draw (1 - 3 + 0.3 - 1,0 + 2) node{$64$};\n\\draw (1 - 3 + 0.3 - 1,0 + 2.5) node{$66$};\n\\draw (1 - 3 + 0.3 - 1,0 + 3.5) node{$70$};\n\\draw (1 - 3 + 0.3 - 1,0 + 4) node{$76$};\n\\draw (1 - 3 + 0.5 - 1,0 + 5) node{dim};\n\\end{tikzpicture}\n\\end{center}\n\\caption{\\small Closure diagram of nilpotent orbits  of $E_{7(7)}$ of  dimension smaller than 76.}\n\\label{ClosureDiag}\n\\end{figure}\nIn the linearised approximation, the $F^2 \\nabla^4 R^4$ type invariant does not carry a $\\nabla^6 R^4$ coupling, but we explain that the structure of the linearised invariant allows for this mixing at the non-linear level, and that the latter must occur because the two classes of invariants merge in one single $E_{8(8)}$ representation in three dimensions. We conclude that the exact threshold function in four dimensions takes the form\n\\begin{equation}}\\def\\ee{\\end{equation} E_{\\gra{0}{1}} = \\hat{{\\cal E}}_{\\grad{8}{1}{1}}  + \\frac{32}{189\\pi}\\hat{{E}}_{\\mbox{\\DEVII000000{5}}}\\ ,  \\ee\nwhere $\\hat{{\\cal E}}_{\\grad{8}{1}{1}}$ is the solution to the inhomogeneous differential equation \\eqref{E811Equation} that is consistent with perturbative string theory. The explicit relation between the tensorial differential equations and the associated nilpotent orbits permits us to determine the wavefront set of the associated functions, extending the results of \\cite{Green:2011vz,Fleig:2013psa} to the $\\nabla^6 R^4$ threshold function. It appears, as can be seen in figure \\ref{ClosureDiag}, that the two functions admit distinct wavefront sets. In particular we show that although $\\hat{{\\cal E}}_{\\grad{8}{1}{1}}$ is not an Eisenstein series, it admits the same wavefront set as $\\hat{{E}}{\\mbox{\\DEVII{\\mathnormal{6}}00000{\\mathfrak{0}}}}$.\n\n\nWe then consider the uplift of our results in higher dimensions, and exhibit that this general structure extends to all dimensions lower than eight, and is in perfect agreement with the exact threshold functions proposed in \\cite{Green:2010wi,Basu:2007ck,Pioline:2015yea}. In each dimension, the supersymmetry invariants transform in irreducible representations of $E_{d(d)}$, defined by the representation of $E_{d(d)}$ on the associated function on $E_{d(d)}\/ K_d$ satisfying to the relevant differential equations implied by supersymmetry. The inequivalent invariants are summarised in figure \\ref{DimensionMultiplets}.\n\\begin{figure}[htbp]\n\\center\n \\begin{tikzpicture}\n\\draw (1 - 1,0 + 5) node{$IIA$}; \\draw (1,0 + 5) node{$IIB$};   \\draw (1 + 2,0 + 5) node{$IIA$}; \\draw (1 + 3,0 + 5) node{$IIB$};\n \\draw (1 + 5,0 + 5) node{$IIA$}; \\draw (1 + 6,0 + 5) node{$IIB$};\n \n\\draw[-,draw=black, thick](1 - 1,0 + 4) -- (1 - 1,0 + 4.7); \\draw[-,draw=black, thick](1,0 + 4) -- (1,0 + 4.7);\n\\draw[-,draw=black, thick](1 + 2,0 + 4) -- (1 + 2,0 + 4.7); \\draw[-,draw=black, thick](1 + 3,0 + 4) -- (1 + 3,0 + 4.7);\n\\draw[-,draw=black, thick](1 + 5,0 + 4) -- (1  + 5,0 + 4.7); \\draw[-,draw=black, thick](1 + 6,0 + 4) -- (1 + 6,0 + 4.7);\n\\draw[dashed,draw=black, thick](1 + 7,0 + 4) -- (1 + 7,0 + 4.5);\n\\draw[-,draw=black, thick](1,0 + 4) -- (1 - 0.9,0 + 4.7);\n\\draw[-,draw=black, thick](1 + 3,0 + 4) -- (1 + 2.1,0 + 4.7);\n\n\\draw[dashed,draw=black, thick](1 + 2.5,0 - 1) -- (1 + 2.5,0 - 1.3);\n\\draw[dashed,draw=black, thick](1 - 0.5,0 - 1) -- (1 - 0.5,0 - 1.3);\n\\draw[dashed,draw=black, thick](1 + 3 + - 1 + 7.5\/2,0 - 1) -- (1 + - 1  + 3 + 7.5\/2 ,0 - 1.3);\n\n\\draw[<-,draw=black,thick] (1 - 3,0 + 6) -- (1 - 3,0 - 2);               \n\\draw (1 - 3,0 + 5) node{-};\n\\draw (1 - 3,0 + 4) node{-};   \\draw (1 + - 1,0 + 4) node{\\color{rouge}  \\textbullet};\\draw (1 + 1 + - 1,0 + 4) node{ \\textbullet};  \\draw (1 + - 1 + 3,0 + 4) node{\\textbullet};\\draw (1 + - 1 + 4,0 + 4) node{$\\circ$};\n\\draw (1 - 3,0 + 3) node{-};                \\draw (1 + - 1 + 0.5,0 + 3) node{\\textbullet};   \\draw (1 + - 1 + 3,0 + 3) node{\\textbullet};\\draw (1 + 4 + - 1 ,0 + 3) node{$\\circ$};\n\\draw (1 - 3,0 + 2) node{-};                \\draw (1 + - 1 + 0.5,0 + 2) node{\\textbullet};   \\draw (1 + - 1 + 3,0 + 2) node{\\textbullet};\\draw (1 + 4 + - 1,0 + 2) node{\\color{rouge} \\textbullet};\n\\draw (1 - 3,0 + 1) node{-};                \\draw (1 + - 1 + 0.5,0 + 1) node{\\textbullet};   \\draw (1 + - 1 + 3.5,0 + 1) node{\\textbullet};\n\\draw (1 - 3,0) node{-};\t\t\t    \\draw (1 + - 1 + 0.5,0) node{\\textbullet};         \\draw (1 + - 1 + 3.5,0) node{\\textbullet};\n\\draw (1 - 3,0 - 1) node{-};                 \\draw (1 + - 1 + 0.5 ,0 - 1) node{\\textbullet};   \\draw (1 + - 1 + 3.5,0 - 1) node{\\textbullet};\n\\draw (1 - 3 + 0.3,0 + 5) node{$10$};\n\\draw (1 - 3 + 0.3,0 + 4) node{$8$};\n\\draw (1 - 3 + 0.3,0 + 3) node{$7$};\n\\draw (1 - 3 + 0.3,0 + 2) node{$6$};\n\\draw (1 - 3 + 0.3,0 + 1) node{$5$};\n\\draw (1 - 3 + 0.3,0) node{$4$};\n\\draw (1 - 3 + 0.3,0 - 1) node{$3$};\n\\draw (1 - 3 + 0.5,0 + 6) node{dim};\n\n\\draw (1 + - 1 + 6\/2 + 7.5\/2 ,0 - 1) node{\\textbullet}; \n\\draw (1 + - 1 + 6 ,0 ) node{\\color{rouge}  \\textbullet}; \n\\draw (1 + - 1 + 7.5 ,0 ) node{ \\textbullet}; \n\\draw (1 + - 1 + 6 ,0 +1) node{$\\circ$}; \n\\draw (1 + - 1 + 7.5 ,0 +1) node{\\textbullet}; \n\\draw (1 + - 1 + 6 ,0 +2) node{$\\circ$}; \n\\draw (1 + - 1 + 7.5 ,0 +2) node{\\color{rouge} \\textbullet}; \n\\draw (1 + - 1 + 6 ,0 +3) node{$\\circ$}; \n\\draw (1 + - 1 + 7.5 ,0 +3) node{$\\circ$}; \n\\draw (1 + - 1 + 6 ,0 +4) node{$\\circ$}; \n\\draw (1 + - 1 + 7 ,0 +4) node{$\\circ$};\n\\draw (1 + - 1 + 8 ,0 +4) node{$\\circ$}; \n\n\\draw (1 + 0.5 + - 1,0 - 1.6) node{$R^4$};\n\\draw (1 + 3.5 + - 1,0 - 1.6) node{$\\nabla^4 R^4$};\n\\draw (1 + 6\/2 + 7.5\/2 + - 1,0 - 1.6) node{$\\nabla^6 R^4$};\n\n\\draw[-,draw=black, thick](1 + 8 + - 1,0  + 4) -- (1 + 0.5 + 7 + - 1,0 + 3);\n\\draw[-,draw=black, thick](1 + 0.5 + 6.5 + - 1,0  + 4) -- (1 + 0.5 + 7 - 1,0 + 3);\n\\draw[-,draw=black, thick](1 + 0.5 + - 1,0 -1) -- (1 + 0.5 + - 1,0 + 3);\n\\draw[-,draw=black, thick](1 + 3.5 + - 1 ,0 -1) -- (1 + 3.5 + - 1,0 + 1);\n\\draw[-,draw=black, thick](1 + 3 + 7.5\/2 + - 1 ,0 -1) -- (1 + 6 + - 1,0);\n\\draw[-,draw=black, thick](1 + 3 + 7.5\/2 + - 1 ,0 -1) -- (1 + 7.5 + - 1,0);\n\\draw[-,draw=black, thick](1 + 6 + - 1,0) -- (1 + 6 + - 1,0 + 4);\n\\draw[-,draw=black, thick](1 + 7.5 + - 1,0) -- (1 + 7.5 + - 1,0 + 3);\n\n\\draw[-,draw=black, thick](1 + 3.5 + - 1,0 + 1) -- (1 + - 1 + 4,0 + 2);  \\draw[-,draw=black, thick](1 + - 1 + 3.5,0 + 1) -- (1 + - 1 + 3,0 + 2);\n\\draw[-,draw=black, thick](1 + - 1 + 0.5,0 + 3) -- (1 + - 1 ,0 + 4); \\draw[-,draw=black, thick](1 + - 1 + 0.5,0 + 3) -- (1 + - 1 + 1,0 + 4);\n\n\\draw[-,draw=black, thick](1 + - 1 + 4,0 + 4) -- (1 + - 1 + 4,0 + 2);  \\draw[-,draw=black, thick](1 + - 1 + 3,0 + 4) -- (1 + - 1 + 3,0 + 2);\n\n\n\\end{tikzpicture}\n\n\n\\caption{\\label{DimensionMultiplets}\\small Each node corresponds to an inequivalent supersymmetry invariant, white if it cannot be written in harmonic superspace in the linearised approximation, and red if the corresponding harmonic superspace is chiral. For $\\nabla^6 R^4$, the links to 10 dimensions are valid for the homogeneous solution, while all the eight-dimensional invariants uplift to type IIA for the inhomogeneous solution.}\n\\end{figure}\nThe tensorial differential equations satisfied by Eisenstein functions relevant to our analysis are reviewed in the appendices. \n\n\\section{$\\mathcal{N}=8$ supergravity in four dimensions}\nMaximal supergravity includes 70 scalar fields parametrising the symmetric space $E_{7(7)} \/ SU_{\\scriptscriptstyle \\rm c}(8)$ \\cite{Cremmer:1979up}, and can be defined in superspace by promoting these fields to superfields $\\phi^\\upmu$ \\cite{Brink:1979nt,Howe:1981gz}. One defines the Maurer--Cartan form \n\\begin{equation}}\\def\\ee{\\end{equation} d {\\cal V} \\,  {\\cal V}^{-1} = \\left( \\begin{array}{cc}\\  2 \\delta_{[i}^{[k} \\omega^{l]}{}_{j]} \\ &\\  P_{ijkl} \\ \\\\ \\ P^{ijkl}\\ & -2 \\delta^{[i}_{[k} \\omega^{j]}{}_{l]} \\ \\end{array}\\right) \\ , \\ee\nwith  \n\\begin{equation}}\\def\\ee{\\end{equation} P^{ijkl} = \\frac{1}{24} \\varepsilon^{ijklpqrs} P_{pqrs} \\ . \\label{ComplexSelfual}\\ee\nThe metric on $E_{7(7)} \/ SU_{\\scriptscriptstyle \\rm c}(8)$ is defined as\n\\begin{equation}}\\def\\ee{\\end{equation} G_{\\upmu\\upnu}(\\phi) d\\phi^\\upmu d\\phi^\\upnu = \\frac{1}{3} P_{ijkl} P^{ijkl} \\ , \\ee\nand the derivative in tangent frame is defined such that for any function \n\\begin{equation}}\\def\\ee{\\end{equation} d {\\cal E} = 3 P^{ijkl} {\\cal D}_{ijkl} {\\cal E} \\ . \\ee\nThe superfields satisfy to\n\\begin{equation}}\\def\\ee{\\end{equation} D_\\alpha^i {\\cal E} = \\frac{1}{4} \\varepsilon^{ijklpqrs} \\chi_{\\alpha jkl} \\,  {\\cal D}_{pqrs} {\\cal E} \\ , \\qquad \\bar D_{\\adt i} {\\cal E} = 6 \\bar \\chi_{\\adt}^{jkl} \\,  {\\cal D}_{ijkl} {\\cal E} \\ , \\ee\nwhere $\\chi_{\\alpha ijk}$ is the Dirac superfield in Weyl components, and $\\bar \\chi_\\adt^{ijk}$ its complex conjugate. The expansion of the scalar fields include the 28 Maxwell field strengths $F_{\\alpha\\beta ij}$, the 8 Rarita--Schwinger field strengths $\\rho_{\\alpha\\beta\\gamma i}$ and the Weyl tensor $C_{\\alpha\\beta\\gamma\\delta}$, satisfying to $\\mathcal{N}=8$ supergravity classical (two derivatives) field equations. The supervielbeins are the solutions to the Bianchi identities defined such that the Riemann tensor is valued in $\\mathfrak{sl}(2,\\mathds{C}) \\oplus \\mathfrak{su}(8)$ and the $\\mathfrak{su}(8)$ component is identified with the scalar field curvature \\cite{Brink:1979nt,Howe:1981gz},\n\\begin{equation}}\\def\\ee{\\end{equation} R^i{}_j = \\frac{1}{3} P_{jklp} \\wedge P^{iklp} \\ . \\ee\nThe covariant derivative on $E_{7(7)} \/ SU_{\\scriptscriptstyle \\rm c}(8)$ in tangent frame satisfies to \n\\begin{equation}}\\def\\ee{\\end{equation} [ {\\cal D}^{ijkl} , {\\cal D}_{pqrs} ]  {\\cal D}_{tuvw}= - 24 \\delta^{ijkl}_{qrs][t} {\\cal D}_{uvw][p} + 3 \\delta^{ijkl}_{pqrs} {\\cal D}_{tuvw} \\ ,  \\label{Comut} \\ee\nand the Laplace operator is\n\\begin{equation}}\\def\\ee{\\end{equation} \\Delta = \\frac{1}{3} {\\cal D}^{ijkl} {\\cal D}_{ijkl} \\ . \\ee\nIn the linearised approximation, the scalar superfield $W_{ijkl}$ satisfies to the reality constraint \\eqref{ComplexSelfual} and to\n\\begin{equation}}\\def\\ee{\\end{equation} D_\\alpha^p W_{ijkl} = 2 \\delta^p_{[i} \\chi_{\\alpha jkl]} \\ , \\qquad \\bar D_{\\adt p } W_{ijkl} = \\frac{1}{12} \\varepsilon_{ijklpqrs} \\bar \\chi_\\adt^{qrs} \\ . \\ee \nIn this approximation the superfield $W^{ijkl}$ transforms in the minimal unitary representation of the superconformal group $SU(2,2|8)$ \\cite{Gunaydin:1984vz}. This property permits a complete classification of supersymmetry invariants in the linearised approximation in terms of irreducible representations of $SU(2,2|8)$ of Lorentz invariant top component \\cite{Drummond:2003ex,Drummond:2010fp}. In our analysis, we rely on the assumption of absence of supersymmetry anomaly, such that there is no algebraic obstruction to the extension of a linearised invariant to a full non-linear invariant. This implies a bijective correspondence between the set of linearised invariants and the non-linear invariants, such that one can deduce the explicit gradient expansion of the functions (or tensor functions) of the scalar fields on $E_{7(7)} \/ SU_{\\scriptscriptstyle \\rm c}(8)$ that determine the invariants.\n\\subsection{The standard $\\nabla^6 R^4$ type invariant}\\label{811D6R4}\nOne can define a $\\nabla^6 R^4$ type invariant in harmonic superspace, using the harmonic variables $u^1{}_i,\\, u^r{}_i,\\, u^8{}_i$ parametrising $SU(8)\/ S(U(1) \\times U(6)\\times U(1))$, such that $r=2$ to $7$ of $SU(6)$ \\cite{Drummond:2003ex,Drummond:2010fp,Hartwell:1994rp}. In this case the harmonic superspace integral can be defined at the non-linear level \\cite{Bossard:2011tq}, but we will only consider its linearised approximation. The superfield  in the ${\\bf 20}$ of $SU(6)$\n\\begin{equation}}\\def\\ee{\\end{equation} W_{rst} = u^i{}_8 u^j{}_r u^k{}_s u^l{}_t W_{ijkl} \\ , \\ee\nsatisfies to the G-analyticity constraints \n\\begin{equation}}\\def\\ee{\\end{equation} u^1{}_i D_\\alpha^i W_{rst} = 0   \\ , \\qquad u^i{}_8 \\bar D_{\\adt i} W_{rst} = 0 \\  . \\ee\nOne can therefore integrate any function of $W_{rst}$ on the associated analytic superspace. To understand the most general integrand, we must decompose monomials of $W_{rst}$ in irreducible representations of $SU(6)$. At quadratic order we have the representation $[0,0,2,0,0]$ and the combination \n\\begin{equation}}\\def\\ee{\\end{equation} W^{rtu} W_{stu} = \\frac{1}{6} \\varepsilon^{rtuvwx} W_{stu} W_{vwx} \\ee\nin the $[1,0,0,0,1]$. Because one obtains the $[0,0,2,0,0]$ by simply adding the Dynkin labels of $W_{rst}$, we will say that this representation is freely generated, whereas we shall consider the $[1,0,0,0,1]$ as a new generator at order two. At cubic order, we have the two elements freely generated by the ones already discussed, {\\it i.e.}\\  $[0,0,3,0,0]$ and $[1,0,1,0,1]$, and the additional combination \n\\begin{equation}}\\def\\ee{\\end{equation} W_{u[rs} W_{t]vw} W^{uvw} \\ , \\ee\nin the $[0,0,1,0,0]$. At quartic order we have the four elements freely generated by the ones already discussed, and the two additional elements \n\\begin{equation}}\\def\\ee{\\end{equation} W_{vw[r} W^{vw[t} W_{s]xy} W^{u]xy}  \\ , \\quad  W_{urs} W_{tvw} W^{uvw} W^{rst} \\ , \\ee\nthat decompose into the $[0,1,0,1,0]$ and the singlet representation. One checks that these elements freely generate the general polynomials in $W_{rst}$, such that the latter are labeled by five integers. \n\nTo integrate such a function in analytic superspace, one needs to consider these generating monomials with additional harmonic variables in order to compensate for the $S(U(1)\\times U(6)\\times U(1))$ representation, {\\it i.e.}\\  \n\\begin{eqnarray} \\label{Uintegral811}  \\int du\\,  u^8{}_i u^r{}_j u^s{}_k u^t{}_l W_{rst} &=& W_{ijkl} \\, , \\\\\n\\int du\\,  u^8{}_i u^s{}_j u_1{}^k u_r{}^l  W^{rtu} W_{stu}  &=& W_{ijpq} W^{klpq} - \\frac{1}{28} \\delta_{ij}^{kl} W_{pqrs} W^{pqrs}  \\, , \\nonumber \\\\*\n\\int du\\,  u_1{}^q u^8{}_p u^8{}_i u^r{}_j u^s{}_k u^t{}_l W_{u[rs} W_{t]vw} W^{uvw}   &=& W_{po[ij} W_{kl]mn} W^{qomn} - \\frac{|W|^2\\hspace{-1.7mm}}{108} \\scal{ \\delta_p^q W_{ijkl} - \\delta^p_{[i} W_{jkl]p}}    \\, , \\nonumber \\\\*\n\\int du u_1{}^k u_1{}^l u^8{}_i u^8{}_j  W_{urs} W_{tvw} W^{uvw} W^{rst} &=& W_{npq(i} W_{j)mp^\\prime q^\\prime} W^{np^\\prime q^\\prime(k} W^{l)pqm}  - \\delta_{(i}^{(k} \\delta_{j)}^{l)} ( \\dots ) \\ ,\\nonumber \n\\end{eqnarray}\nwhich are respectively in the $[0,0,0,1,0,0,0]$, the $[0,1,0,0,0,1,0]$, the $[1,0,0,1,0,0,1]$ and the $[2,0,0,0,0,0,2]$ irreducible representations of $SU(8)$, whereas  \n\\begin{equation}}\\def\\ee{\\end{equation} \\int du u_1{}^m u_1{}^n u^8{}_k u^8{}_l u^r{}_i u^s{}_j  u_t{}^p u_u{}^q  W_{vwr} W^{vwt} W_{sxy} W^{uxy}  = W_{i^\\prime j^\\prime [ij} W_{k]lk^\\prime l^\\prime} W^{i^\\prime j^\\prime [pq} W^{m]nk^\\prime l^\\prime} + \\dots \\label{Uintegral811B}\n\\ee\ngives rise to the fourth order monomial in the $[1,0,1,0,1,0,1]$ irreducible representation. \n\nOne obtains in this way that the harmonic superspace integral of a general monomial of order $n_1 + 2n_2 +3n_3+ 4n_4+4n_4^\\prime + 4$ in the $[n_2,n_4,n_1+n_3,n_4,n_2]$ of $SU(6)$ gives rise to a term in $\\nabla^6 R^4$ with a monomial of order $n_1 + 2n_2 +3n_3+ 4n_4+4n_4^\\prime $ in the $[n_3+n_4 +2n_4^\\prime,n_2,n_4,n_1+n_3,n_4,n_2,n_3+n_4 +2n_4^\\prime]$ of $SU(8)$, {\\it i.e.}\\  \n\\begin{eqnarray} &&\\int du  D^{14} \\bar D^{14} \\, F(u)_{\\scriptscriptstyle [n_3+n_4 +2n_4^\\prime,n_2,n_4,n_1+n_3,n_4,n_2,n_3+n_4 +2n_4^\\prime]}^{[ n_2,n_4,n_1+n_3,n_4,n_2]}  W^{n_1 + 2n_2 +3n_3+ 4n_4+4n_4^\\prime + 4}|_{[n_2,n_4,n_1+n_3,n_4,n_2]} \\nonumber \\\\*\n&&\\sim \\nabla^6 R^4  \\, W^{n_1 + 2n_2 +3n_3+ 4n_4+4n_4^\\prime }|_{[n_3+n_4 +2n_4^\\prime,n_2,n_4,n_1+n_3,n_4,n_2,n_3+n_4 +2n_4^\\prime]} +\\dots\\label{811Linear} \\end{eqnarray}\nwhere the function $F(u)$ is the function of the harmonic variable defined as a product of the generating functions defined in (\\ref{Uintegral811},\\ref{Uintegral811B}). One needs at least one quartic singlet in the G-analytic superfield to get a non-vanishing integral \\cite{Drummond:2003ex}. \n\nReferring to the one to one correspondence between linearised and non-linear invariants \\cite{Drummond:2003ex}, one deduces that the non-linear invariant must admit the same gradient expansion, {\\it i.e.}\\  \n\\begin{eqnarray}&&  {\\cal L}_\\grad811[{\\cal E}_\\grad811] \\nonumber \\\\*\n&=& \\hspace{-5mm}\\sum_{n_1,n_2,n_3,n_4,n_4^\\prime} \\hspace{-5mm} {\\cal D}^{n_1 + 2 n_2 + 3 n_3 + 4 n_4 + 4 n^\\prime_4 }_{\\scriptscriptstyle [n_3+n_4 +2n_4^\\prime,n_2,n_4,n_1+n_3,n_4,n_2,n_3+n_4 +2n_4^\\prime]} \\hspace{2mm} \n{\\cal E}_{\\grad{8}{1}{1}} \\, {\\cal L}^{\\scriptscriptstyle [n_3+n_4 +2n_4^\\prime,n_2,n_4,n_1+n_3,n_4,n_2,n_3+n_4 +2n_4^\\prime]}_\\grad811 \\hspace{5mm} \\  \\label{811GradExpand} \\end{eqnarray}\nwhere each $ {\\cal L}^{\\scriptscriptstyle [n_3+n_4 +2n_4^\\prime,n_2,n_4,n_1+n_3,n_4,n_2,n_3+n_4 +2n_4^\\prime]}_\\grad811$ is an $E_{7(7)}$ invariant superform in the corresponding representation of $SU(8)$. Note that although the irreducible representation remains unchanged under the substitution \n\\begin{equation}}\\def\\ee{\\end{equation} (n_1,n_3,n_4^\\prime) \\rightarrow(n_1+2, n_3-2,n_4^\\prime +1)\\ee\nthe corresponding superforms and the tensor structure of the derivative are different, and are really labelled by the five integers $n_1,n_2,n_3,n_4,n_4^\\prime$ without any further identification. Of course the mass dimension implies that these integers are bounded from above, and the maximal weight terms in $\\chi^{14} \\bar \\chi^{14}$ can only be in representations like $[2,6,0,8,0,6,2]$, $[2,6,1,6,1,6,2]$, \\dots $[2,10,0,0,0,10,2]$, \\dots $[11,1,0,0,0,1,11]$. \n\n\nThis gradient expansion implies in particular that the third order derivative of ${\\cal E}_\\grad811$ in the $[0,2,0,0,0,0,0]$ and its complex conjugate must vanish, {\\it i.e.}\\  \n\\begin{eqnarray}  \\Scal{ 4 {\\cal D}_{ijpq} {\\cal D}^{pqmn} {\\cal D}_{mnkl} - {\\cal D}_{ijkl} \\scal{ \\Delta + 24} } {\\cal E}_\\grad811 &=& 0 \\ , \\label{CubicC}\\nonumber \\\\*\n  \\Scal{ 4 {\\cal D}^{ijpq} {\\cal D}_{pqmn} {\\cal D}^{mnkl} - {\\cal D}^{ijkl} \\scal{ \\Delta + 24} } {\\cal E}_\\grad811 &=& 0 \\ .  \\end{eqnarray}\nThese equations imply all the higher order constraints on the function such that  its gradient expansion is in agreement with \\eqref{811GradExpand}. \nDefining the covariant derivative in tangent frame as a Lie algebra generator in the fundamental representation of $E_{7(7)}$, this equation reads equivalently \n\\begin{equation}}\\def\\ee{\\end{equation} {\\bf D}_{56}^{\\; 3} {\\cal E}_\\grad811  = {\\bf D}_{56} \\Scal{ 6 + \\tfrac{1}{4} \\Delta } {\\cal E}_\\grad811 \\ . \\label{Cubic56} \\ee\nThis implies in particular that all the Casimir operators are determined by the quadratic one such that \n\\begin{equation}}\\def\\ee{\\end{equation} {\\rm tr} \\scal{ {\\bf D}_{56}^{\\; 2+2n}} \\, {\\cal E}_\\grad811= 6 \\Delta \\scal{ 6 + \\tfrac{1}{4} \\Delta}^{n} {\\cal E}_\\grad811 \\ , \\ee\nbut the quadratic Casimir is not a priori determined by equation \\eqref{CubicC} alone. We will need to consider the other invariants to finally conclude that supersymmetry moreover implies \\cite{Green:2010kv}\n\\begin{equation}}\\def\\ee{\\end{equation}  \\Delta  {\\cal E}_\\grad811 = - 60  {\\cal E}_\\grad811 - ({\\cal E}_\\grad844)^2  \\ .\\label{Laplace811} \\ee\nEquation \\eqref{Cubic56} defines a qantization of the algebraic condition ${\\bf Q}_{56}^{\\; 3}=0$ associated to the complex nilpotent orbit of $E_{7}$ of Dynkin label \\DEVII{2}00000{\\mathfrak{0}}, while the condition that the fourth order derivative does not vanish generically in the ${\\scriptstyle [2,0,0,0,0,0,2]}$ distinguishes its real form of  $SU(8)$ Dynkin label [$\\scriptstyle \\mathfrak{2}\\mathfrak{0}\\mathfrak{0}\\mathfrak{0}\\mathfrak{0}\\mathfrak{0}\\mathfrak{2}$] \\cite{E7Djo}, which defines the graded decomposition of $SU(8)$ associated to the $(8,1,1)$ harmonic superspace we consider in this section. The property that the linearised structure does not permit to determine the eigenvalue of the Laplace operator in this case, implies that the quantization of the associated nilpotent orbit is not unique, and depends on one free parameter. This property follows from the fact that a nilpotent element of this kind can be obtained as the appropriate limit of a semi-simple element satisfying to the characteristic equation ${\\bf Q}_{56}^{\\; 3}=\\frac{1}{24} {\\rm tr}({\\bf Q}_{56}^{\\; 2}) {\\bf Q}_{56} $. \n\n\n\\subsection{$F^2 \\nabla^4 R^4$ type invariant and its relation to $\\nabla^6 R^4$}\n\\label{F2D4R4} \nAlthough the $\\nabla^6 R^4$ type invariant provides the unique supesymmetric invariant preserving $SU(8)$ one can write at this order, there is another class of invariants that can be defined form the chiral harmonic superspace defined in terms of the harmonic variables $u^{\\hat{r}}{}_i,\\, u^r{}_i$ parametrising $SU(8)\/S(U(2)\\times U(6))$ \\cite{Drummond:2003ex,Hartwell:1994rp},  with $\\hat{r},\\hat{s}$ equal to  $1, 2$ of $SU(2)$, and $r ,s$ running from $3$ to $8$ of $SU(6)$. One defines the superfield \n\\begin{equation}}\\def\\ee{\\end{equation}\nW^{rs} = u^1{}_i u^2{}_j u^r{}_k u^s{}_l W^{i j k l}\n\\ee\nthat satisfies to the G-analiticity constraint \n\\begin{equation}}\\def\\ee{\\end{equation} \nu^{\\hat{r}}{}_{i} \\bar D^i_\\alpha W^{rs} = 0 \\ . \n\\ee\nSimilarly as in the preceding section, the most general function of $W^{rs}$ is freely generated by the three monomials \n\\begin{equation}}\\def\\ee{\\end{equation} W^{rs} \\ , \\qquad \\frac{1}{2} \\varepsilon_{rstuvw} W^{tu} W^{vw} \\ , \\qquad \\frac{1}{2} \\varepsilon_{rstuvw} W^{rs} W^{tu} W^{vw} \\ . \\ee\nOne must supplement them with harmonic variables to preserve $S(U(2)\\times U(6))$ invariance, using \n\\begin{eqnarray} \\int du\\, u^i{}_1 u^j{}_2 u^k{}_r u^l{}_s \\, W^{rs} &=& W^{ijkl} \\ , \\\\\n \\int du\\, u^i{}_1 u^j{}_2 u^r{}_k u^s{}_l \\,  \\frac{1}{2} \\varepsilon_{rstuvw} W^{tu} W^{vw}  &=& W^{ijpq} W_{klpq} - \\frac{1}{28} \\delta^{ij}_{kl}W^{pqrs} W_{pqrs} \\ , \\nonumber \\\\*\n  \\int du\\, u^i{}_1 u^j{}_2 u^k{}_1 u^l{}_2 \\,  \\frac{1}{2} \\varepsilon_{rstuvw} W^{rs} W^{tu} W^{vw}  &=& W^{ijpq} W_{pqrs} W^{rskl}  - \\frac{1}{12} W^{ijkl} W_{pqrs} W^{pqrs}  \\ . \\nonumber\n\\end{eqnarray}\nOne only gets a non-trivial integral if the cubic $SU(6)$ singlet in $W^{rs}$ appears at least quadratically, which can be understood from the property that the associated chiral primary operator of $SU(2,2|8)$ is otherwise in a short representation \\cite{Drummond:2003ex}. Because the $U(1)$ weight of the measure is compensated by a single factor of this cubic $SU(6)$ singlet, it appears that there is no $SU(8)$ invariant that exists in this class. \n\n For a general monomial, one gets an invariant of the form \n\\begin{eqnarray}&&  \\int du \\bar D^{16}  D^{12}  \\, F(u)^{[0,n_1,0,n_2,0]}_{[0,n_2+2n_3+2,0,n_1,0,n_2,0]} \\, W^{n_1 + 2n_2 + 3n_3 + 6} |_{[0,n_1,0,n_2,0]}  \\\\\n&\\sim&W^{n_1 + 2n_2 + 3n_3}_{\\scriptscriptstyle [0,n_2+2n_3,0,n_1,0,n_2,0]} \\bar F^{2}_{\\scriptscriptstyle[0,2,0,0,0,0,0]} \\nabla^4 R^4+\\dots + W^{n_1+2n_2+n_3-22}_{\\scriptscriptstyle [0,n_2+2n_3-8,0,n_1-8,0,n_2-4,0]}\\bar \\chi^{16}_{\\scriptscriptstyle[0,8,0,4,0,0,0]}  \\chi^{12}_{\\scriptscriptstyle[0,2,0,4,0,4,0]} \\ , \\nonumber\\end{eqnarray}\nwhere all terms are projected to the $\\scriptstyle [0,n_2+2n_3+2,0,n_1,0,n_2,0]$ irreducible representation, and the term in $\\bar F^2$ is\n\\begin{equation}}\\def\\ee{\\end{equation} \\bar F_{\\adt\\bdt}^{ij} \\bar F^{\\adt\\bdt  kl}  -   \\bar F_{\\adt\\bdt}^{[ij} \\bar F^{kl]\\adt\\bdt} \\ . \\ee\nFor a generic function ${\\cal F}[W]$ of $W_{rs}$, one obtains\n\\begin{equation}}\\def\\ee{\\end{equation} D^{16} \\bar D^{12}  {\\cal F}[W] = \\sum_{n_1,n_2,n_3} \\frac{\\partial^{n_1+2n_2+3n_3+6} {\\cal F}[W]}{\\partial W^{n_1+2n_2+3n_3+6}}{}\\Big|_{[0,n_2,0,n_1,0]} {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{[0,n_1,0,n_2,0]\\ord{n_1+2n_2+3n_3+3}} \\ , \\ee  \nwhere the densities $ {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{[0,n_1,0,n_2,0]\\ord{n_1+2n_2+3n_3+3}}$ are of order $n_1+2n_2+3n_3+6$ in the fields and only depend on the scalar fields through their space-time derivative. The number $n_1+2n_2+3n_3+3$ is the $U(1)$ weight of the density. These densities determine by construction covariant superforms in the linearised approximation \\cite{Voronov,Gates:1997kr,Gates:1997ag}, such that \n\\begin{eqnarray} d^\\ord{0}  {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl} &=& 0 \\ ,  \\nonumber \\\\*\n\\Scal{ d^\\ord{0}  {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl,pqrs} + 3 P^{pqrs} \\wedge   {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl} }{}_{\\scriptscriptstyle [0,2,0,1,0,0,0]} &=& 0 \\ ,  \\nonumber \\\\*\n\\Scal{ d^\\ord{0}  {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl,pqrs,mntu} + 3 P^{pqrs} \\wedge   {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl,mntu} }{}_{\\scriptscriptstyle [0,2,0,2,0,0,0]} &=& 0 \\  , \\nonumber \\\\*\n\\Scal{ d^\\ord{0}  {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl,pq}{}_{rs}+18 P_{rsmn} \\wedge   {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl,pqmn} }{}_{\\scriptscriptstyle [0,3,0,0,0,1,0]} &=& 0 \\  ,\n\\end{eqnarray}\nwhere $d^\\ord{0}$ is the superspace exterior derivative in the linear approximation. At the next order, because \n\\begin{equation}}\\def\\ee{\\end{equation} d = \\sum_{n=0}^{\\infty} d^\\ord{n} \\ee\nsatisfies to $d^2=0$, one has \n\\begin{equation}}\\def\\ee{\\end{equation} \\{ d^\\ord{0},d^\\ord{1}\\} = 0\\ , \\ee\nand therefore \n\\begin{equation}}\\def\\ee{\\end{equation} d^\\ord{0} \\Scal{ d^\\ord{1}  {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl} } = 0 \\ . \\ee\nWe assume in this paper that the structure of superconformal multiplets implies the absence of supersymmetry anomaly, or equivalently that the fifth cohomology of $d^\\ord{0}$ is empty. Nevertheless, even if $d^\\ord{1}  {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl} $ only depends on the covariant superfields, nothing prevents its $d^\\ord{0}$ antecedent to depend explicitly on the scalar fields.  This implies in this case that\n\\begin{equation}}\\def\\ee{\\end{equation} d^\\ord{1}  {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl}  =-d^\\ord{0}  {\\cal L}_{\\grad820\\, \\ord{1}}^{ij,kl} +  P_{pqrs} \\wedge  {\\cal M}^{ij,kl,pqrs} + P^{pqij} \\wedge {\\cal M}_{pq}{}^{kl} + P^{pqkl} \\wedge {\\cal M}_{pq}{}^{ij} -2 P^{i]pq[k} \\wedge {\\cal M}_{pq}{}^{l][j} \\ , \\label{d1F2R4} \\ee\nwhere $ {\\cal L}_{\\grad820\\, \\ord{1}}^{ij,kl}$ is the covariant correction to the superform, whereas ${\\cal M}^{ij,kl,pqrs}$ and ${\\cal M}^{ij}{}_{kl}$ are superforms of order six in the fields in the $[0,2,0,1,0,0,0]$ and the $[0,1,0,0,0,1,0]$, respectively, that must satisfy to\n\\begin{eqnarray}\nd^\\ord{0} {\\cal M}^{ij,kl,pqrs} &=& \\scal{ P^{pqrs} \\wedge \\mathcal{N}^{ij,kl} }{}_{\\scriptscriptstyle [0,2,0,1,0,0,0]}\\ ,  \\nonumber \\\\*\nd^\\ord{0} {\\cal M}^{ij}{}_{kl} &=& P^{ijpq} \\wedge \\mathcal{N}_{klpq} - \\frac{1}{28} \\delta^{ij}_{kl} P^{pqrs} \\wedge \\mathcal{N}_{pqrs} \\ . \\end{eqnarray}\nIn order to have such corrections that could not be reabsorbed in a covariant correction as $ {\\cal L}_{\\grad820\\, \\ord{1}}^{ij,kl}$, one must have a corresponding short multiplet associated to a linearised invariant of the same dimension. The only candidate for a superform $ {\\cal M}^{ij,kl,pqrs}$ is $  {\\cal L}_{\\grad820\\, {\\rm \\scriptscriptstyle lin}}^{ij,kl,pqrs} $, but it is of order seven in the fields, and therefore  $ {\\cal M}^{ij,kl,pqrs}=0$ at this order. However, there is a candidate for $ {\\cal M}^{ij}{}_{kl} $ which is $  {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}ij}{}_{kl} $, the superform that appears in the $\\nabla^6 R^4$ type invariant discussed in the last section. Following \\eqref{811Linear}, we have \n\\begin{eqnarray} d^\\ord{0}  {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}   &=&  0 \\ , \\nonumber \\\\*\n d^\\ord{0}  {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{ijkl}   &=&  - 3 P^{ijkl} \\wedge   {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}  \\ , \\nonumber \\\\*\n d^\\ord{0}  {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{ijkl,pqrs}     &=&  - 3 \\scal{ P^{ijkl} \\wedge {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{pqrs}  }{}_{\\scriptscriptstyle [0,0,0,1,0,0,0]}  \\ , \\nonumber \\\\*\n   d^\\ord{0}   {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}ij}{}_{kl}  &=&  - 18 \\scal{ P_{klpq} \\wedge {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{ijpq}  }{}_{\\scriptscriptstyle [0,1,0,0,0,1,0]}   \\ ,\\label{Linear811}\n\\end{eqnarray}\nand therefore \n\\begin{eqnarray} && d^\\ord{0} \\Bigl(\\Scal{ W^{ijpq} W_{pqrs} W^{rskl}  - \\tfrac{1}{12} W^{ijkl} W_{pqrs} W^{pqrs} }   {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}  \\Bigr . \\nonumber \\\\*\n&&  \\qquad + W^{ijpq} W_{pqrs}   {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{rskl} + W^{ijpq} W^{klrs}  {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}{}_{pqrs}+  W^{klpq} W_{pqrs}   {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{rsij}     \\nonumber \\\\*\n&& \\hspace{10mm} \\Bigl . + 6 W^{pqij} {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}kl}{}_{pq} + 6 W^{pqkl} {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}ij}{}_{pq} -12 W^{i]pq[k} {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}l][j}{}_{pq} \\Bigr)\\nonumber \\\\*\n&=& 18 \\Scal{ P^{pqij}\\wedge  {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}kl}{}_{pq} + P^{pqkl} \\wedge {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}ij}{}_{pq} -2 P^{i]pq[k}\\wedge  {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}l][j}{}_{pq}} \\ , \\label{d0Cohom}\n \\end{eqnarray}\nsuch that $  {\\cal L}_{\\grad811\\, {\\rm \\scriptscriptstyle lin}}^{\\hspace{10mm}ij}{}_{kl} $ is indeed a consistent candidate. Moreover, the structure of the linearised $(8,1,1)$ invariant does not permit to have the tensor function $W^{ijpq} W_{pqrs} W^{rskl}$, such that \\eqref{d0Cohom} is not the exterior derivative of a superform that does not depend on the naked scalar fields (uncovered by a space-time derivative). It follows that such a correction, if it appeared in \\eqref{d1F2R4}, could not be reabsorbed in a redefinition of $ {\\cal L}_{\\grad820\\, \\ord{1}}^{ij,kl}$. \n\n\nIf this mixing between the $(8,2,0)$ and the $(8,1,1)$ superforms was not appearing at the non-linear level, then the action of the exterior derivative in the function of the scalar fields should not introduce lower derivative terms such that it should satisfy then to \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}^{ijpq} \\Scal{  4 {\\cal D}_{pqrs} {\\cal D}^{rsmn} {\\cal D}_{mnkl} - {\\cal D}_{pqkl} \\scal{ \\Delta + 24} } {\\cal E}_{\\grad{8}{2}{0}} = 0 \\ . \\label{D4Consistency} \\ee\nIf the mixing did appear, then the unicity of the linearised invariants \\eqref{Linear811} would imply that the corresponding non-linear superform should be the same as in \\eqref{811GradExpand}, such that once again the exterior derivative acting on $D^3_{\\scriptscriptstyle [0,2,0,0,0,0,0]} {\\cal E}_\\grad820$ should not generate lower derivative terms and one would conclude again that \\eqref{D4Consistency} must be satisfied. Therefore this equation must be satisfied in either cases.\n\n\nUsing moreover the property that the gradient expansion of the linearised invariant is inconsistent with the presence of the third order derivative in the $[1,0,0,1,0,0,1]$ of $SU(8)$, one requires\n\\begin{equation}}\\def\\ee{\\end{equation} \\Scal{ 36 {\\cal D}_{jr[kl} {\\cal D}^{irmn} {\\cal D}_{pq]mn} - \\delta^i_j {\\cal D}_{klpq} ( \\Delta + 42)   + \\delta^i_{[k} {\\cal D}_{lpq]j} ( \\Delta-120)} {\\cal E}_{\\grad{8}{2}{0}} = 0 \\ . \\label{CubicR} \n\\ee\nUsing this equation one computes independently of \\eqref{D4Consistency} that \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}^{ijpq} \\Scal{  4 {\\cal D}_{pqrs} {\\cal D}^{rsmn} {\\cal D}_{mnkl} - {\\cal D}_{pqkl} \\scal{ \\Delta + 24} } {\\cal E}_{\\grad{8}{2}{0}}  = \\frac{1}{12} \\Scal{ 28 {\\cal D}^{ijpq} {\\cal D}_{klpq} - 3 \\delta^{ij}_{kl} \\Delta} \\scal{ \\Delta + 60 } {\\cal E}_\\grad820 \\ee\nand we conclude that \\eqref{D4Consistency}  and \\eqref{CubicR} imply together\n\\begin{equation}}\\def\\ee{\\end{equation}  \\Delta {\\cal E}_\\grad820 = -60  {\\cal E}_\\grad820 \\ .\\label{Laplace820}  \\ee\nThis eigenvalue is such that the structure of the invariant is consistent with the mixing between the $(8,2,0)$ and the $(8,1,1)$ superforms. Only in this case can they reduce to the same invariant for a function ${\\cal E}_{\\grad{8}{2}{2}}$ satisfying to both \\eqref{CubicC} and \\eqref{CubicR}, as for the $\\nabla^4 R^4$ type invariant. \n\nWe are going to argue now that this chiral invariant must indeed include a $\\nabla^6 R^4$ coupling, because the two classes of invariants reduce to one single class in three dimensions. But before to do this, let us mention that \\eqref{CubicR} can be rewritten as\n\\begin{equation}}\\def\\ee{\\end{equation} {\\bf D}_{133}^{\\; 3} {\\cal E}_\\grad820 =\\frac{1}{3}   {\\bf D}_{133} \\Delta {\\cal E}_\\grad820 \\ , \\ee\nwhich defines a qantization of the algebraic eqation ${\\bf Q}_{133}^{\\; 3}=0$ associated to the complex nilpotent orbit of $E_{7}$ of Dynkin label \\DEVII{0}00000{\\mathfrak{2}} with the real form defined with the $SU(8)$ Dynkin label [$\\scriptstyle \\mathfrak{0}\\mathfrak{2}\\mathfrak{0}\\mathfrak{0}\\mathfrak{0}\\mathfrak{0}\\mathfrak{0}$] \\cite{E7Djo}, which defines the graded decomposition of $SU(8)$ associated to the $(8,2,0)$ harmonic superspace we consider in this section. In this case the choice of real form moreover implies that the complex charge in the ${\\bf 70}$ defining the nilpotent orbit through the Kostant--Sekiguchi correspondence satisfies to \n\\begin{equation}}\\def\\ee{\\end{equation} Q^{ijpq} Q_{pqmn} Q^{mnkl} = 0 \\ , \\ee\nsuch that it admits a unique quantization, with the eigenvalue of the Laplace operator $-60$. However, we will see in the following that the constraint \\eqref{D4Consistency} can be relaxed while keeping the property that the associated representation of $E_{7(7)}$ is a highest weight representation. \n\n\n\\subsection{Dimensional reduction to three dimensions}\nIn  three dimensions, the duality group is $E_{8(8)}$, of maximal compact subgroup $Spin(16)\/\\mathds{Z}_2$. We denote $i, j$ the $SO(16)$ vector indices and $A, B$ the positive chirality Weyl spinor indices. The covariant derivative in tangent frame is a chiral Weyl spinor, {\\it i.e.}\\  in the  \\WSOXVI00000001 representation. In the linearised approximation, the covariant fields all descend from the Weyl spinor scalar field, satisfying to \\cite{Greitz:2011vh}\n\\begin{equation}}\\def\\ee{\\end{equation}\nD_{\\alpha}^{i} W^{A} = \\Gamma^{i A \\dot{A}} \\chi_{\\alpha \\dot A} \\ . \n\\ee\nBoth four-dimensional $(8,1,1)$ and $(8,2,0)$ harmonic superspaces descend to the same $(16,2)$ harmonic superspace in three dimensions, defined through the introduction of harmonic variables parametrising $SO(16)\/(U(2) \\times SO(12))$ \\cite{Howe:1994ms}. The Weyl spinor representation decomposes with respect to $U(2) \\times Spin(12)$ as\n\\begin{equation}}\\def\\ee{\\end{equation} {\\bf 128} \\cong {\\bf 32}_+^{\\ord{-1}} \\oplus \\scal{ {\\bf 2}\\otimes {\\bf 32}_-}^\\ord{0} \\oplus {\\bf 32}_+^{\\ord{1}}\\ , \\label{128inD6} \\ee\nsuch that the grad $1$ Weyl spinor $W$ of $Spin(12)$ satisfies to a G-analyticity constraint with respect to the positive grad covariant derivative in the ${\\bf 2}$ of $U(2)$. The general polynomial in the $Spin(12)$ Weyl spinor is parametrised by four integers, just as for the rank three antisymmetric tensor of $SU(8)$ in section \\eqref{811D6R4}.\\footnote{This property follows from the fact that the classification of duality orbits of the black hole charges are the same in the $\\mathcal{N}=2$ supergravity theories of duality group $SO^*(12)$ and $SU(3,3)$ \\cite{Ferrara:1997uz}.} One computes in a similar way the general integral \n\\begin{eqnarray} && \\int du F(u)_{{\\mbox{\\WSOXVI0{n_3\\hspace{-0.5mm}\\mbox{+}n_4\\hspace{-0.5mm}\\mbox{+}2n_4^\\prime}0{n_2}0{n_4}0{n_1\\hspace{-0.5mm}\\mbox{+}n_3}} } }^{{\\mbox{\\WSOXII0{n_2}0{n_4}0{n_1\\hspace{-0.5mm}\\mbox{+}n_3}} }} D^{28}  W^{n_1 + 2n_2 +3n_3+ 4n_4+4n_4^\\prime + 4}|_{{\\mbox{\\WSOXII0{n_2}0{n_4}0{n_1\\hspace{-0.5mm}\\mbox{+}n_3}} }}  \\nonumber \\\\*\n&\\sim &\\nabla^{10} P^4  \\, W^{n_1 + 2n_2 +3n_3+ 4n_4+4n_4^\\prime }|_{{\\mbox{\\WSOXVI0{n_3\\hspace{-0.5mm}\\mbox{+}n_4\\hspace{-0.5mm}\\mbox{+}2n_4^\\prime}0{n_2}0{n_4}0{n_1\\hspace{-0.5mm}\\mbox{+}n_3}} } } +\\dots\\end{eqnarray}\nwhere $\\nabla^{10} P^4 $ is a $Spin(16)$ invariant quartic term in the scalar field momentum, that replaces the $\\nabla^6 R^4$ type term that vanishes modulo the equations of motion in three dimensions. In three dimensions it is not established if there is a one to one correspondence between non-linear and linear invariants defined as harmonic superspace integrals. Nevertheless, the class of invariants we discuss descends from four dimensions, and we can therefore assume they admit the same structure, {\\it i.e.}\\  \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal L}_\\gra{16}{2}[{\\cal E}_{\\gra{16}{2}}] = \\sum_{n_1,n_2,n_3,n_4,n_4^\\prime} {\\cal D}_{{\\mbox{\\WSOXVI0{n_3\\hspace{-0.5mm}\\mbox{+}n_4\\hspace{-0.5mm}\\mbox{+}2n_4^\\prime}0{n_2}0{n_4}0{n_1\\hspace{-0.5mm}\\mbox{+}n_3}} }} {\\cal E}_{\\gra{16}{2}}\\, {\\cal L}^{{\\mbox{\\WSOXVI0{n_3\\hspace{-0.5mm}\\mbox{+}n_4\\hspace{-0.5mm}\\mbox{+}2n_4^\\prime}0{n_2}0{n_4}0{n_1\\hspace{-0.5mm}\\mbox{+}n_3}} }}\\ .  \\ee\nThis expansion implies that the fourth order derivative of the function ${\\cal E}_{\\gra{16}{2}}$ restricted  to the \\WSOXVI10001000 must vanish, {\\it i.e.}\\  \\begin{equation}}\\def\\ee{\\end{equation} \\scal{ {\\cal D} \\Gamma_{i[jk}{}^r {\\cal D}} \\scal{ {\\cal D} \\Gamma_{lpq]r} {\\cal D} }{\\cal E}_{\\gra{16}{2}} = - \\delta_{i[j} \\scal{ {\\cal D} \\Gamma_{klpq]} {\\cal D}} ( \\Delta+48  ) {\\cal E}_{\\gra{16}{2}} \\ ,\\label{quarticE8}  \\ee\nwhere the Laplace operator $\\Delta$ is defined as\n\\begin{equation}}\\def\\ee{\\end{equation}\n\\Delta = {\\cal D}_{A} {\\cal D}^{A}\\ . \n\\ee\nBy dimensional reduction of the four-dimensional equation  \\eqref{Laplace820}, one computes that   \\begin{equation}}\\def\\ee{\\end{equation}\n\\Delta {\\cal E}_{\\gra{16}{2}} = - 198  {\\cal E}_{\\gra{16}{2}} \\ . \n\\ee\nOne can understand that the two kinds of 1\/8 BPS invariants discussed in the preceding section dimensionally reduce to this single class. If one consider the decomposition of \\eqref{128inD6} with respect to $U(6)\\subset Spin(12)$, one obtains for one embedding \n \\begin{equation}}\\def\\ee{\\end{equation} {\\bf 32}_+\\cong {\\bf  6}^\\ord{-2} \\oplus {\\bf 20}^\\ord{0} \\oplus  \\overline{\\bf 6}^\\ord{2}\\ , \\label{32inA5} \\ee\nsuch that the G-analytic superfield in the ${\\bf 32}_+$ includes the four-dimensional $(8,1,1)$ G-analytic scalar $W^{rst}$ as well as some components of the vector fields. A generic spinor of non-zero quartic invariant can be represented by $W^{rst}$. For the other embedding  $U(6)\\subset Spin(12)$, one gets\n \\begin{equation}}\\def\\ee{\\end{equation} {\\bf 32}_+\\cong  \\overline{\\bf  1}^\\ord{-3} \\oplus {\\bf 15}^\\ord{-1}  \\oplus \\overline{\\bf 15}^\\ord{1} \\oplus {\\bf 1}^\\ord{3}\\ , \\label{32inA5p} \\ee\nsuch that  the G-analytic superfield in the ${\\bf 32}_+$ includes the four-dimensional $(8,2,0)$ G-analytic scalar $W^{rs}$ as well as some components of the vector fields, and a Ehlers complex scalar parametrising the four-dimensional metric. The scalar field alone only parametrises a null spinor of $Spin(12)$ of vanishing quartic invariant, and only together with the Ehlers scalar field it can provide a representative of a generic spinor. One could have naively concluded that the function ${\\cal E}_\\grad820$ should give rise to a  function on $E_{8(8)}\/Spin_{\\scriptscriptstyle \\rm c}(16)$ satisfying moreover to \n\\begin{equation}}\\def\\ee{\\end{equation} 5\\scal{ {\\cal D} \\Gamma_{ijpq}  {\\cal D}} \\scal{ {\\cal D} \\Gamma^{klpq} {\\cal D}} {\\cal E} = - 20 \\scal{{\\cal D} \\Gamma_{ij}{}^{kl} {\\cal D}} \\scal{ \\Delta + 48 } {\\cal E}  + 28 \\delta_{ij}^{kl} \\Delta \\scal{\\Delta + 120} {\\cal E} \\ , \\ee\nbut this equation only admits solutions for functions satisfying to the Laplace equation\n\\begin{equation}}\\def\\ee{\\end{equation} \\Delta {\\cal E} = -210\\,  {\\cal E} \\ , \\ee\nexcepted for the functions satisfying to the quadratic and cubic constraints that define the $R^4$ and $\\nabla^4 R^4$ type invariants. We see therefore that this equation is incompatible with supersymmetry.\n\n It follows that both $(8,1,1)$ and $(8,2,0)$ type invariants dimensionally reduce to three-dimensional invariants depending of functions on $E_{8(8)}\/Spin_{\\scriptscriptstyle \\rm c}(16)$ that belong to the same representation of $E_{8(8)}$. Being in the same representation, they both carry a quartic component in the linearised approximation and they must both include a $\\nabla^6 R^4$ type term in their uplift to four dimensions. This proves that the mixing between the two different linearised structures must occur such that the non-linear $\\bar F^2 \\nabla^4 R^4$ type invariant cannot exist without including a $\\nabla^6 R^4$ type term as well. \n\nBefore to end this section on the three-dimensional theory, let us discuss the modification of the supersymmetry constraint due to the completion of the $R^4$ type invariant at the next order. As it is argued in \\cite{Green:2005ba}, the appearance of a $R^4$ correction with threshold function ${\\cal E}_\\gra{16}{8}$, will modify the Laplace equation with a non-zero right-hand-side, {\\it i.e.}\\  \n \\begin{equation}}\\def\\ee{\\end{equation}\n\\Delta {\\cal E}_{\\gra{16}{2}} = - 198  {\\cal E}_{\\gra{16}{2}} - {\\cal E}_{\\gra{16}{8}}^{\\; 2} \\ . \n\\ee\nBecause the function $ {\\cal E}_{\\gra{16}{8}}$ satisfies to \\cite{Minimal}\n\\begin{equation}}\\def\\ee{\\end{equation} \\scal{ {\\cal D} \\Gamma_{ijkl} {\\cal D}}  {\\cal E}_{\\gra{16}{8}} = 0 \\ , \\ee\nthe second derivative of its square must necessarily vanish in the  \\WSOXVI10001000, and we get accordingly a modification of \\eqref{quarticE8} to\n\\begin{equation}}\\def\\ee{\\end{equation} \\scal{ {\\cal D} \\Gamma_{i[jk}{}^r {\\cal D}} \\scal{ {\\cal D} \\Gamma_{lpq]r} {\\cal D} } {\\cal E}_{\\gra{16}{2}}= 150 \\delta_{i[j} \\scal{ {\\cal D} \\Gamma_{klpq]} {\\cal D}}  {\\cal E}_{\\gra{16}{2}} + \\delta_{i[j} \\scal{ {\\cal D} \\Gamma_{klpq]} {\\cal D}} {\\cal E}_{\\gra{16}{8}}^{\\; 2}\\ . \\ee\n\n\\subsection{$E_{7(7)}$ Eisenstein series}\nIn this section we shall discuss some properties of Einstein series that solve the differential equations we have derived for the $\\nabla^6 R^4$ type invariants.\n\n\\addtocontents{toc}{\\protect\\setcounter{tocdepth}{1}}\n\\subsubsection{Fundamental representation}\n\\addtocontents{toc}{\\protect\\setcounter{tocdepth}{2}}\nAs discussed in \\cite{Obers:1999um,D4R4}, one can define the Eisenstein series \n\\begin{equation}}\\def\\ee{\\end{equation} E_{\\mbox{\\DEVII000000s}} = \\sum_{\\vspace{-2mm}\\begin{array}{c}\\scriptstyle \\vspace{-4mm}  \\Gamma\\in \\mathds{Z}^{56} \\vspace{2mm}\\\\ \\scriptscriptstyle I_4^{\\prime\\prime}(\\Gamma)|_{\\bf 133}=0\\end{array}} |Z(\\Gamma)_{ij} Z(\\Gamma)^{ij}|^{-s} \\   , \\label{E56s} \\ee\nas a sum over the rank one integral charge vectors $\\Gamma$ in the ${\\bf 56}$ of $E_{7(7)}$ satisfying to the constraint that the quadratic tensor  $\\Gamma\\otimes \\Gamma$ vanishes  in the adjoint representation. This formula is rather useful to identify the differential equations satisfied by the Eisenstein function, because one can simply consider the case of one charge $\\Gamma$, with  $Z(\\Gamma)_{ij} = {\\cal V}_{ij}{}^I\\Gamma_I$, such that the quadratic constraint becomes \n\\begin{equation}}\\def\\ee{\\end{equation} Z_{[ij} Z_{kl]} = \\frac{1}{24} \\varepsilon_{ijklpqrs} Z^{pq} Z^{rs} \\ , \\qquad Z_{ik} Z^{jk} = \\frac{1}{8} \\delta_i^j Z_{kl} Z^{kl} \\ ,\\ee\nand the differential operator acts on $Z_{ij} $ as an element of $\\mathfrak{e}_{7(7)}$\n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{ijkl} Z^{pq} = 3 \\delta^{pq}_{[ij} Z_{kl]} \\ , \\qquad {\\cal D}_{ijkl} Z_{pq} = \\frac{1}{8} \\varepsilon_{ijklpqrs} Z^{rs} \\ . \\ee\nUsing the definition $|Z|^2 = Z_{ij} Z^{ij}$, one computes that the function $|Z|^{-2s}$ satisfies to \n\\begin{eqnarray} {\\cal D}_{ijpq} {\\cal D}^{klpq} |Z|^{-2s} &=& 2s(s-2) Z_{ij} Z^{kl} |Z|^{-2s-2} + \\frac{s(s-11)}{4} \\delta_{ij}^{kl} |Z|^{-2s} \\  , \\nonumber \\\\*\n{\\cal D}_{ijpq} {\\cal D}^{pqrs} {\\cal D}_{rskl} |Z|^{-2s} &=& - 3 s(s-2)(s-4) Z_{ij} Z_{kl} |Z|^{-2s-2} + \\frac{s^2-15s + 8}{4} {\\cal D}_{ijkl} |Z|^{-2s}  \\ , \\nonumber \\\\*\n {\\cal D}_{jr[kl} {\\cal D}^{irmn} {\\cal D}_{pq]mn} |Z|^{-2s} &=&\\frac{(s-2)(s-7)}{12}  \\delta^i_j{\\cal D}_{klpq}  |Z|^{-2s} -\\frac{ s^2-9s -40}{12} \\delta^i_{[k} {\\cal D}_{pql]j} |Z|^{-2s}  \\ , \\hspace{10mm} \\label{ConstraintsZs} \n\\end{eqnarray}\nand to the Laplace equation \n\\begin{equation}}\\def\\ee{\\end{equation} \\Delta |Z|^{-2s} = 3s(s-9) |Z|^{-2s} \\ . \\ee\nFor $s\\ne2,\\, 4$, the function admits a generic gradient expansion in the irreducible representations $[0,n_2+2n_3,0,n_1,0,n_2,0]$ and their complex conjugate. To exhibit this property, it is convenient to consider a restricted set of indices as follows \n\\begin{eqnarray} &&  \\scal{ {\\cal D}_{12ij} {\\cal D}^{ijkl} {\\cal D}_{kl12}}^{n_3} \\scal{  {\\cal D}_{12pq} {\\cal D}^{78pq}}^{n_2} \\scal{{\\cal D}_{1234}}^{n_1} |Z|^{-2s} \\\\ &=& \\tfrac{(s+n_1+n_2+n_3-1)!(s+n_2+n_3-3)!(s+n_3-5)!}{(s-1)!(s-3)!(s-5)!} \\scal{\\mbox{-}3 Z_{12}^{\\; 2}}^{n_3} \\scal{2 Z_{12} Z^{78}}^{n_2} \\scal{\\mbox{-}6 Z_{[12} Z_{34]}}^{n_1} |Z|^{-2(s+n_1+n_2+n_3)} \\, . \\nonumber \\label{GradExpandZs} \\end{eqnarray}\nOne computes moreover that for $m\\le n$ \n\\begin{eqnarray} &&  \\scal{{\\cal D}^{78ij} {\\cal D}_{ijkl} {\\cal D}^{kl78}}^{m} \\scal{{\\cal D}_{12pq} {\\cal D}^{pqrs} {\\cal D}_{rs12}}^n |Z|^{-2s} \\\\\n&=& \\tfrac{(s+n-1)!(s+n-3)!(s+n-5)!(s+n+m-1)!(s+n+m-3)!(s-n+m-5)!}{(s-1)!(s-3)!(s-5)!(s+n-1)!(s+n-3)!(s-n-5)!} \\scal{\\mbox{-}3 Z^{78\\; 2}}^{m} \\scal{\\mbox{-}3 Z_{12}^{\\; 2}}^{n}|Z|^{-2(s+n+m)} \\nonumber \\\\*\n&=&\\scal{\\mbox{-}\\tfrac{3}{2}}^{n+m} \\tfrac{(s+n-5)!(s+n+m-1)!(s+n+m-3)!(s-n+m-5)!}{(s+n-m-5)! (s+2n-1)!(s+2n-3)!(s-n-5 )! } \\scal{{\\cal D}_{12ij} {\\cal D}^{ijkl} {\\cal D}_{kl12}}^{n-m}\\scal{{\\cal D}_{12pq} {\\cal D}^{78pq}}^{n+m} |Z|^{-2s} \\nonumber  \\end{eqnarray}\nsuch that acting with a derivative operator in the conjugate representation $[0,0,0,0,0,2m,0]$ does not produce an independent tensor. One has in particular for $s$ an integer greater than $5$ \n\\begin{equation}}\\def\\ee{\\end{equation} \\scal{{\\cal D}^{78ij} {\\cal D}_{ijkl} {\\cal D}^{kl78}} \\scal{{\\cal D}_{12pq} {\\cal D}^{pqrs} {\\cal D}_{rs12}}^{s-4} |Z|^{-2s} = 0 \\ . \\ee\nThis equation is the equivalent on $E_{7(7)}\/SU_{\\scriptscriptstyle \\rm c}(8)$ of the equation on $SL(2)\/SO(2)$ \n\\begin{equation}}\\def\\ee{\\end{equation} \\bar {\\cal D} {\\cal D}^{s-1} E_{[s]} = 0 \\ ,  \\ee\nfor integral $s$, and we would like to see that the function $ E{\\mbox{\\DEVII000000s}}$ also decomposes somehow into a ``holomorphic'' part $ {\\cal F}_s$ and a ``anti-holomorphic'' part $\\bar {\\cal F}_s$, satisfying respectively to \n\\begin{equation}}\\def\\ee{\\end{equation} \\scal{{\\cal D}_{12pq} {\\cal D}^{pqrs} {\\cal D}_{rs12}}^{s-4} \\bar {\\cal F}_s = 0 \\ , \\qquad \\scal{{\\cal D}^{78ij} {\\cal D}_{ijkl} {\\cal D}^{kl78}}^{s-4} {\\cal F}_s = 0 \\  , \\ee\nsuch that \n\\begin{equation}}\\def\\ee{\\end{equation}   \\scal{{\\cal D}_{12pq} {\\cal D}^{pqrs} {\\cal D}_{rs12}}^{s-4} E_{\\mbox{\\DEVII000000s}} =  \\scal{{\\cal D}_{12pq} {\\cal D}^{pqrs} {\\cal D}_{rs12}}^{s-4} {\\cal F}_s  \\ , \\label{D3sF}  \\ee\nand respectively for the complex conjugate. By consistency, this requires for instance that acting with further derivatives on this tensor does not permit to get back lower order tensors with $n_3<s-4$ in \\eqref{GradExpandZs}. \n\n\nThrough representation theory, one obtains that \n\\begin{eqnarray}&&  {\\cal D}_{[0,0,0,1,0,0,0]} {\\cal D}^{n_1+2n_2+3n_3}_{[0,n_2+2n_3,0,n_1,0,n_2,0]} |Z|^{-2s} \\\\\n&\\sim& \\Bigl( {\\cal D}^{n_1+1+2n_2+3n_3}_{[0,n_2+2n_3,0,n_1+1,0,n_2,0]} +{\\cal D}^{n_1-1+2(n_2+1)+3n_3}_{[0,n_2+2n_3+1,0,n_1-1,0,n_2+1,0]}  +{\\cal D}^{n_1+2(n_2-1)+3(n_3+1)}_{[0,n_2+2n_3+1,0,n_1,0,n_2-1,0]}  \\Bigr . \\nonumber \\\\*\n&& \\Bigl . + {\\cal D}^{n_1-1+2n_2+3n_3}_{[0,n_2+2n_3,0,n_1-1,0,n_2,0]} +{\\cal D}^{n_1+1+2(n_2-1)+3n_3}_{[0,n_2+2n_3-1,0,n_1+1,0,n_2-1,0]}  +{\\cal D}^{n_1+2(n_2+1)+3(n_3-1)}_{[0,n_2+2n_3-1,0,n_1,0,n_2+1,0]} \\Bigr) |Z|^{-2s} \\nonumber\n\\end{eqnarray}\nfor some coefficients that are not specified. So the only way to reduce $n_3$, is to increase $n_2$ by $1$ unit. We will check this equation in the case $n_1=n_2=0$. The restriction of the derivative ${\\cal D}^{3n} |Z|^{-2s}$ to the $[0,2n,0,0,0,0,0]$ with two free indices reads \n\\begin{eqnarray} && {\\cal D}^{3n\\, [0,2n,0,0,0,0,0]}_{ij1^{2n-1}2^{2n-1}} |Z|^{-2s} \\nonumber \\\\*\n&=& \\tfrac{(s+n-1)!(s+n-3)!(s+n-5)!}{(s-1)!(s-3)!(s-5)!} \\frac{(-3)^n}{2n} \\Scal{ Z_{ij} Z_{12}^{\\; 2n-1} - (2n-1) Z_{1[i} Z_{j]2} Z_{12}^{\\; 2n-2}} |Z|^{-2(s+n)} \\ , \\end{eqnarray}\nand one computes that \n\\begin{eqnarray} && {\\cal D}^{78ij} \\frac{1}{2n}\\Scal{ Z_{ij} Z_{12}^{\\; 2n-1} - (2n-1) Z_{1[i} Z_{j]2} Z_{12}^{\\; 2n-2}} |Z|^{-2(s+n)} \\nonumber \\\\*\n&=& \\frac{(2n+5 ) ( n - s+4)}{8n} Z^{78} Z_{12}^{\\; 2n-1} |Z|^{-2s} \\ , \\end{eqnarray}\nsuch that \n\\begin{eqnarray}&&  {\\cal D}^{78ij} {\\cal D}^{3n\\, [0,2n,0,0,0,0,0]}_{ij1^{2n-1}2^{2n-1}} |Z|^{-2s} \\nonumber \\\\*\n& =& \\frac{3(s+n-5)(2n+5)(s-n-4)}{16n}   \\scal{ {\\cal D}_{12ij} {\\cal D}^{ijkl} {\\cal D}_{kl12}}^{n-1} \\scal{  {\\cal D}_{12pq} {\\cal D}^{78pq}} |Z|^{-2s} \\ . \\end{eqnarray}\nIn particular we have that \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}^{78ij} {\\cal D}^{3(s-4)\\, [0,2(s-4),0,0,0,0,0]}_{ij1^{2s-5}2^{2s-5}} |Z|^{-2s} = 0  \\ , \\label{ConsSF2k} \\ee\nconsistently with the assumption that no lower order tensor is produced out of the tensor function \\eqref{D3sF}. We conclude therefore that the tensor \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal F} \\hspace{-0.4mm} E_{[0,2(s-4),0,0,0,0,0]} = {\\cal D}^{3(s-4)}_{[0,2(s-4),0,0,0,0,0]} E_{\\mbox{\\DEVII000000s}} \\ , \\label{FE} \\ee\nis an $E_{7(7)}(\\mathds{Z})$ modular form that is in some sense holomorphic, such that its gradient expansion is restricted to derivative of this tensor in the symmetric representations $[0,n_2+2(n_3+s-4),0,n_1,0,n_2,0]$, {\\it i.e.}\\ \n\\begin{equation}}\\def\\ee{\\end{equation}  {\\cal D}^{n_1+2n_2+3n_3}_{[0,n_2+2n_3,0,n_1,0,n_2,0]}   {\\cal F} \\hspace{-0.4mm} E_{[0,2(s-4),0,0,0,0,0]}  \\in [0,n_2+2(n_3+s-4),0,n_1,0,n_2,0] \\ . \\ee\n\n\n\nUsing Langlands functional identity  \\cite{Green:2010kv}, one computes that the only integer values of $s\\ge5$ for which the function  diverges are  \n\\begin{eqnarray}   E_{\\mbox{\\DEVII000000{5\\mbox{+}\\epsilon}}} &=& \\frac{63}{16\\pi \\, \\epsilon} E_{\\mbox{\\DEVII0000004}} + \\hat{E}_{\\mbox{\\DEVII000000{5}}} + \\mathcal{O}(\\epsilon) \\ , \\label{DivergenceF2D4R4} \\nonumber \\\\*\nE_{\\mbox{\\DEVII000000{7\\mbox{+}\\epsilon}}} &=&\\frac{1\\, 964\\, 655 \\zeta(5)}{2048 \\pi^{5} \\, \\epsilon} E_{\\mbox{\\DEVII0000002}} + \\hat{E}_{\\mbox{\\DEVII000000{7}}} + \\mathcal{O}(\\epsilon) \\ , \\nonumber \\\\*\n E_{\\mbox{\\DEVII000000{9\\mbox{+}\\epsilon}}} &=& \\frac{12\\, 642\\, 554\\, 925 \\zeta(5)\\zeta(9)}{2\\, 097\\, 152 \\pi^{9}\\, \\epsilon} +\\hat{E}_{\\mbox{\\DEVII000000{9}}}+ \\mathcal{O}(\\epsilon) \\ . \\end{eqnarray}\nHowever, according to \\eqref{ConstraintsZs}, the function $E_{\\mbox{\\DEVII000000s}}$ satisfies to \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}^{3}_{[0,2,0,0,0,0,0]} E_{\\mbox{\\DEVII000000s}} = 0 \\ ,\\quad  \\mbox{for}\\, s=0,\\, 2,\\, 4 \\ , \\ee\nand it follows that the tensor $ {\\cal F} \\hspace{-0.4mm} E_{[0,2(s-4),0,0,0,0,0]}$ \\eqref{FE} is finite for all $s$. However, we have argued in the preceding section that the $\\bar F^2 \\nabla^4 R^4$ type invariant must include a  $\\nabla^6 R^4$ type term, which will be multiplied by the function itself. In this case the relevant Eisenstein function diverges, and one must regularise it such that the differential equation \\eqref{Laplace820} will be modified to\n\\begin{equation}}\\def\\ee{\\end{equation} \\Delta \\, \\hat{E}_{\\mbox{\\DEVII000000{5}}}   = - 60  \\, \\hat{E}_{\\mbox{\\DEVII000000{5}}} + \\frac{189}{16 \\pi}  E_{\\mbox{\\DEVII0000004}} \\ . \\ee\nSuch a correction is reminiscent of a 1-loop logarithm divergence of the $\\nabla^4 R^4$ type invariant form factor. \n\n\\addtocontents{toc}{\\protect\\setcounter{tocdepth}{1}}\n\\subsubsection{Adjoint representation}\n\\addtocontents{toc}{\\protect\\setcounter{tocdepth}{2}}\n\nOne can also consider the Eisenstein series \\footnote{We assume here that all the elements of $\\mathds{Z}^{133}$ are in the $E_{7(7)}(\\mathds{Z})$ orbit of a relative integer times a normalised representative of the continuous orbit. This property does not affect our conclusions in any case, which only requires the generating character to satisfy to the differential equations we discuss.}\n\\begin{equation}}\\def\\ee{\\end{equation} E_{\\mbox{\\DEVII{\\mathnormal{s}}00000{\\mathfrak{0}}}} =  \\sum_{{\\bf Q}\\in \\mathds{Z}^{133} |{\\bf Q}^2=0} \\scal{  X(Q)_{ijkl} X(Q)^{ijkl} }^{-s} \\ ,  \\ee \nas the sum over integral charges ${\\bf Q}\\in \\mathfrak{e}_{7(7)}$ satisfying to the constraint ${\\bf Q}^2 = 0 $, and such that the adjoint action of the coset representative ${\\cal V}$ on ${\\bf Q}$ decomposes into the anti-Hermitian traceless matrix $\\Lambda^i{}_j$ and the complex-selfdual antisymmetric tensor $X_{ijkl}$ satisfying to the constraints \n\\begin{eqnarray} \\Lambda^i{}_k \\Lambda^k{}_j &=& - \\frac{1}{48} \\delta^i_j X^{klpq} X_{klpq} \\ ,\\nonumber \\\\*\n\\Lambda^{[i}{}_{[k} \\Lambda^{j]}{}_{l]} &=& - \\frac{1}{2} X^{ijpq} X_{klpq}  + \\frac{1}{48} \\delta^{ij}_{kl} X^{pqrs} X_{pqrs} \\ , \\nonumber \\\\*\n\\Lambda^{[i}{}_p X^{j]pkl} &=& \\Lambda^{[k}{}_p X^{l]pij}  \\ . \\end{eqnarray}\nThe action of the derivative on these tensors is defined as the $\\mathfrak{e}_{7(7)}$ action \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{ijkl} X^{pqrs}  = 12 \\delta^{[pqr}_{[ijk} \\Lambda^{s]}{}_{l]} \\ , \\qquad \n{\\cal D}_{ijkl} \\Lambda^p{}_q = 2 \\delta^p_{[i} X_{jkl]q} + \\frac{1}{4} \\delta^p_q X_{ijkl} \\ . \\ee\nOne computes for $|X|^2 = X_{ijkl} X^{ijkl} $ that\n\\begin{eqnarray} {\\cal D}_{ijkl} |X|^2 &=& -24 X_{p[ijk} \\Lambda^p{}_{l]} \\ , \\qquad \\qquad\\qquad  {\\cal D}_{ijpq} X^{klpq} = 10 \\delta_{[i}^{[k} \\Lambda^{j]}{}_{l]} \\ , \\\\\n{\\cal D}_{ijpq} {\\cal D}^{klpq} |X|^2 &=& 30 X_{ijpq} X^{klpq} + 3 \\delta_{ij}^{kl} |X|^2 \\ , \\qquad {\\cal D}_{ijpq} |X|^2 {\\cal D}^{klpq} |X|^2 = 12 X_{ijpq} X^{klpq} |X|^2 \\ , \\nonumber \\end{eqnarray}\nwhich permits to derive that \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{ijpq} {\\cal D}^{klpq} |X|^{-2s} = 6s(2s-3) X_{ijpq} X^{klpq} |X|^{-2s-2} - 3 s\\delta_{ij}^{kl} |X|^{-2s} \\ . \\ee\nOne gets therefore a solution to the equation \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{ijpq} {\\cal D}^{klpq} {\\cal E}_\\grad844 = - \\frac{9}{2} \\delta_{ij}^{kl} {\\cal E}_\\grad844 \\ , \\label{R4Quadra} \\ee\nfor $s=\\frac{3}{2}$. One computes in general that \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{ijpq} {\\cal D}^{pqrs}{\\cal D}_{rskl} |X|^{-2s} = \\scal{ s^2 - \\tfrac{17}{2} s+6} {\\cal D}_{ijkl} |X|^{-2s} \\ , \\ee\nand the function satisfies to  \\eqref{CubicC} and its complex conjugate for all $s$. The restriction of the third order derivative to the $[1,0,0,1,0,0,1]$ gives\n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{1k[12} {\\cal D}_{34]ij} {\\cal D}^{8ijk} |X|^{-2s} = - \\frac{3}{4} s(2s-3)(2s-5) \\Lambda^8{}_1 X_{1234} |X|^{-2s-2} \\ , \\ee\nshowing that the function solves the cubic equation \\eqref{CubicR} for $s=\\frac{5}{2}$. These functions satisfy the same equations as their analog Eisenstein functions defined in the fundamental representation, consistently with the property that \\footnote{We are grateful to Axel Kleinschmidt who provided the explicit coefficients.}\n\\begin{equation}}\\def\\ee{\\end{equation}  E_{\\mbox{\\DEVII{\\frac{3}{2}}00000{\\mathfrak{0}}}}  = \\frac{2}{\\pi}   E_{\\mbox{\\DEVII{0}000002}} \\ , \\qquad  E_{\\mbox{\\DEVII{\\frac{5}{2}}00000{\\mathfrak{0}}}} = \\frac{8}{15\\pi}   E_{\\mbox{\\DEVII{0}000004}} \\ . \\ee \nOne can also consider the restriction of the fourth order derivative to the $[2,0,0,0,0,0,0,2]$ to vanish, which defines a further restriction on solutions to \\eqref{CubicC}. In this case one obtains \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}^{8kij} {\\cal D}_{1lij} {\\cal D}_{1kpq} {\\cal D}^{8lpq}   |X|^{-2s} = - \\frac{9}{2} s(2s-3)(2s-5)(s-4) \\Lambda^8{}_1 \\Lambda^8{}_1 |X|^{-2s-2} \\ , \\ee\nand this further restriction distinguishes the value $s=4$. \nWe have in general \n\\begin{equation}}\\def\\ee{\\end{equation} \\Delta  |X|^{-2s} = 2s(2s-17) |X|^{-2s}  \\ , \\ee\nand the function $E{\\mbox{\\DEVII{4}00000{\\mathfrak{0}}}}$ does not solve the 1\/8 BPS equation. \nUsing the same normalisation as   \\cite{Green:2010kv} with a factor of $2\\zeta(2s)$ in the definition of the Eisenstein function, one computes using Langlands formula \n\\begin{equation}}\\def\\ee{\\end{equation}  E_{\\mbox{\\DEVII{\\mathnormal{s}}00000{\\mathfrak{0}}}}   = \\pi^{\\frac{33}{2}} \\tfrac{\\Gamma(s-8) \\Gamma(s-\\stfrac{13}{2}) \\Gamma(s-\\stfrac{11}{2}) \\Gamma(2s-\\stfrac{17}{2}) \\zeta(2s-16) \\zeta(2s-13)\\zeta(2s-11) \\zeta(4s-17) }{ \\Gamma(s-\\stfrac{5}{2}) \\Gamma(s-\\stfrac{3}{2}) \\Gamma(s) \\Gamma(2s-8)\\zeta(17-2s)\\zeta(2s-5)\\zeta(2s-3)\\zeta(4s-16)} E_{\\mbox{{{\\tiny $ { \\left[ \\begin{array}{cccccc}  & & \\mathfrak{0} \\hspace{-0.7mm}&&& \\vspace{ -1.5mm} \\\\ \\stfrac{17}{2}\\mbox{-}s\\hspace{-0.7mm} &  \\mathfrak{0} \\hspace{-0.7mm}& \\mathfrak{0} \\hspace{-0.7mm} & \\mathfrak{0}\\hspace{-0.7mm}&\\mathfrak{0}\\hspace{-0.7mm}& \\mathfrak{0}  \\end{array}\\right] }$}}\n}} \\ . \\ee\n The function is singular for various values of $s$, {\\it i.e.}\\  $\\frac{9}{2}$, $\\frac{11}{2}$, $6$, $\\frac{13}{2}$, $7$, and $\\frac{17}{2}$, and in particular for $s=6$, which is the relevant value to solve equation \\eqref{CubicC} with \\eqref{Laplace811}. One should therefore consider the regularised series\n\\begin{equation}}\\def\\ee{\\end{equation} E_{\\mbox{{{\\tiny $ { \\left[ \\begin{array}{cccccc}  & & \\mathfrak{0} \\hspace{-0.7mm}&&& \\vspace{ -1.5mm} \\\\ 6\\mbox{+}\\epsilon\\hspace{-0.7mm} &  \\mathfrak{0} \\hspace{-0.7mm}& \\mathfrak{0} \\hspace{-0.7mm} & \\mathfrak{0}\\hspace{-0.7mm}&\\mathfrak{0}\\hspace{-0.7mm}& \\mathfrak{0}  \\end{array}\\right] }$}}}}= \\frac{\\pi^5}{8 \\zeta(9)\\, \\epsilon}  E_{\\mbox{{{\\tiny $ { \\left[ \\begin{array}{cccccc}  & & \\mathfrak{0} \\hspace{-0.7mm}&&& \\vspace{ -1.5mm} \\\\ \\frac{5}{2}\\hspace{-0.7mm} &  \\mathfrak{0} \\hspace{-0.7mm}& \\mathfrak{0} \\hspace{-0.7mm} & \\mathfrak{0}\\hspace{-0.7mm}&\\mathfrak{0}\\hspace{-0.7mm}& \\mathfrak{0}  \\end{array}\\right] }$}}}} +  \\hat{E}_{\\mbox{{{\\tiny $ { \\left[ \\begin{array}{cccccc}  & & \\mathfrak{0} \\hspace{-0.7mm}&&& \\vspace{ -1.5mm} \\\\ 6 \\hspace{-0.7mm} &  \\mathfrak{0} \\hspace{-0.7mm}& \\mathfrak{0} \\hspace{-0.7mm} & \\mathfrak{0}\\hspace{-0.7mm}&\\mathfrak{0}\\hspace{-0.7mm}& \\mathfrak{0}  \\end{array}\\right] }$}}}} + \\mathcal{O}(\\epsilon)\\ . \\ee\nHowever, we will see in the following that this function does not appear in string theory, similarly as the $\\nabla^6 R^4$ threshold function is not described by an Eisenstein series in type IIB supergravity. Nonetheless, some components of this function should appear, as we will argue in the following. \n\n\\subsection{$F^{2k} \\nabla^4 R^4$ type invariants}\nThe $F^2 \\nabla^4R^4$ type invariants we have discussed in section \\ref{F2D4R4} have a natural generalisation to higher order invariants. Considering the same chiral harmonic superspace defined in terms of the harmonic variables $u^{\\hat{r}}{}_i,\\, u^r{}_i$ parametrising $SU(8)\/S(U(2)\\times U(6))$ \\cite{Drummond:2003ex}, one can define the G-analytic superfields \n\\begin{equation}}\\def\\ee{\\end{equation} \\bar F_{\\adt\\bdt}^{12} = u^1{}_i u^2{}_j  F_{\\adt\\bdt}^{ij}\\  ,\\qquad  \\bar \\chi_\\adt^{12r} = u^1{}_i u^2{}_j u^r{}_k \\bar \\chi_\\adt^{ijk} \\ . \\ee\nThey do not permit to define directly chiral primary operators of $SU(2,2|8)$, because \n\\begin{equation}}\\def\\ee{\\end{equation} \\bar D_{\\adt t} W^{rs}  = \\delta_t^{[r} \\bar \\chi_\\adt^{12s]} \\ , \\qquad \\bar D_{\\adt r} \\chi_\\bdt^{12s} = \\delta_r^s \\bar F_{\\adt\\bdt}^{12} \\ . \\ee\nChiral primary operators are annihilated by the special supersymmetry generators at the origin, {\\it i.e.}\\  \n\\begin{equation}}\\def\\ee{\\end{equation} S_{\\dot{\\gamma}}^r \\bar F_{\\adt\\bdt}^{12} = \\varepsilon_{\\cdt(\\adt} \\bar \\chi_{\\bdt)}^{12r} \\ , \\qquad S_\\adt^r \\bar \\chi_\\bdt^{12s} = \\varepsilon_{\\adt\\bdt} W^{rs} \\ , \\qquad S_\\adt^t W^{rs} = 0 \\ . \\ee\nOne can enforce this property by defining a chiral primary as \n\\begin{equation}}\\def\\ee{\\end{equation} \\mathcal{O}^\\ord{k}_{{\\cal F}} = (S)^{12} \\Scal{  ( \\bar F_{\\adt\\bdt}^{12} \\bar F^{\\adt\\bdt 12} )^{2+k} {\\cal F}[W] } \\propto \\scal{ \\varepsilon_{rstuvw} W^{rs} W^{tu} W^{vw}}^2  ( \\bar F_{\\adt\\bdt}^{12} \\bar F^{\\adt\\bdt 12} )^{k-1}  {\\cal F}[W]+\\dots \\label{ChiralPrimary}   \\ee\nfor an arbitrary function ${\\cal F}$ of the G-analytic superfield $W^{rs}$. By construction such a chiral primary operator is never short, and defines a non-trivial integrand for the $(8,2,0)$ measure. Because one can consider an arbitrary representative up to a total fermionic derivative, one can as well consider the first term in \\eqref{ChiralPrimary} as the integrand. \n\nSo similarly as in section  \\ref{F2D4R4}, we get the general class of linearised invariants for an arbitrary positive integer $k$,\n\\begin{eqnarray}&&  \\int du \\bar D^{16}  D^{12}  \\, F(u)^{[0,n_1,0,n_2,0]}_{[0,n_2+2n_3+2k,0,n_1,0,n_2,0]} \\, \\bar F^{2k-2}\\, W^{n_1 + 2n_2 + 3n_3 + 6} |_{[0,n_1,0,n_2,0]}  \\\\\n&\\sim&W^{n_1 + 2n_2 + 3n_3}_{\\scriptscriptstyle [0,n_2+2n_3,0,n_1,0,n_2,0]} \\bar F^{2k}_{\\scriptscriptstyle[0,2k,0,0,0,0,0]} \\nabla^4 R^4+\\dots \\nonumber \\\\*\n&& \\hspace{10mm} + W^{n_1+2n_2+n_3-22}_{\\scriptscriptstyle [0,n_2+2n_3-8,0,n_1-8,0,n_2-4,0]} \\bar F^{2k-2}_{\\scriptscriptstyle [0,2k-2,0,0,0,0,0]} \\bar \\chi^{16}_{\\scriptscriptstyle[0,8,0,4,0,0,0]}  \\chi^{12}_{\\scriptscriptstyle[0,2,0,4,0,4,0]} \\ . \\nonumber\\end{eqnarray}\nWe conclude that the corresponding supersymmetry invariants admit the same gradient expansion in \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal L}^\\ord{k}_\\grad820[{\\cal E}_\\grad820^\\ord{k}] =\\sum_{n_1\\ge 0,n_2\\ge0,n_3\\ge k}  {\\cal D}^{n_1+2n_2+3n_3}_{[0,n_2,0,n_1,0,n_2+2n_3,0]} {\\cal E}_\\grad820^\\ord{k} \\, {\\cal L}^{k\\, [0,n_2+2n_3,0,n_1,0,n_2,0]}_\\grad820 \\ , \\ee\nfor a function ${\\cal E}_\\grad820^\\ord{k}$ satisfying to \\eqref{CubicR}, and $k\\ge2$. The coupling at the lowest number of points is then of the kind \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}^{3k}_{[0,0,0,0,0,2k,0]} {\\cal E}_\\grad820^\\ord{k} \\, {\\cal L}^{k\\, [0,2k,0,0,0,0,0]}_\\grad820 = {\\cal D}^{3k}_{[0,0,0,0,0,2k,0]} {\\cal E}_\\grad820^\\ord{k} \\, \\bar F^{2k}_{[0,2k,0,0,0,0,0]} \\, \\nabla^4 R^4 + \\dots \\ee\nIn principle one could expect to have a non-trivial mixing with another class of linearised invariant at the non-linear level, just as the one of the $\\bar F^2 \\nabla^4 R^4$ type invariant with the $\\nabla^6 R^4$ type invariant described in section  \\ref{F2D4R4}. However, there is no higher order chiral primary operator that can define a non-trivial  $(8,1,1)$ harmonic superspace integral, and we did not find any linearised invariant with the right structure to define a possible cohomology class as does \\eqref{d0Cohom}. Therefore we expect these invariants to have the same structure as the associated linearised invariants, {\\it i.e.}\\  to only contribute to $(4+2k)$-point amplitudes and higher. \n\n\nIndependently of this assumption, the structure of these invariants requires that the action of the derivative ${\\cal D}_{ijkl}$ on ${\\cal D}^{3k} {\\cal E}_\\grad820^\\ord{k}$ does not generate lower order derivatives of the function. This condition is precisely \\eqref{ConsSF2k}, and we conclude therefore that the eigenvalue of the Laplace operator is determined in the same way as\n\\begin{equation}}\\def\\ee{\\end{equation} \\Delta {\\cal E}_\\grad820^\\ord{k} = 3 (k+4)(k-5) {\\cal E}_\\grad820^\\ord{k} \\ , \\ee\nsuch that the function satisfies to \n\\begin{equation}}\\def\\ee{\\end{equation} 12 {\\cal D}_{jr[kl} {\\cal D}^{irmn} {\\cal D}_{pq]mn} {\\cal E}_\\grad820^\\ord{k} =  (k+2)(k-3)  \\delta^i_j {\\cal D}_{klpq}  {\\cal E}_\\grad820^\\ord{k}  - ( k(k-1) -60)  \\delta^i_{[k} {\\cal D}_{lpq]j} {\\cal E}_\\grad820^\\ord{k}\\ .  \\label{CubicK} \\ee\nIt is therefore tempting to conjecture that \n\\begin{equation}}\\def\\ee{\\end{equation}  {\\cal E}_\\grad820^\\ord{k} \\propto  E_{\\mbox{\\DEVII{0}00000{4\\mbox{+}k}}} \\ , \\label{EisF2k}  \\ee\nin the string theory effective action, and we will indeed show in section \\ref{StringPerturb} that this function admits a consistent perturbative string theory limit. Moreover, we will see in section \\ref{HigherDimensions} that it also admits an appropriate decompactification limit. \n\n\n\\subsection{Wavefront set and Poisson equation source term}\nWe have seen that there are two classes of $\\nabla^6 R^4$ type invariants in four dimensions, that preserve tree-level supersymmetry modulo the classical field equations. However, considering that the effective action already includes an $R^4$ type correction, we must take into account the action of the accordingly modified supersymmetry transformation on the $R^4$ type invariant itself. This is a very difficult task to carry out in practice, but one can nonetheless show general properties on these corrections. We recall that the $R^4$ type invariant admits the following gradient expansion in derivatives of the function ${\\cal E}_\\grad844$ \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal L}_\\grad844[{\\cal E}_\\grad844] = \\sum_{n=0}^{12} {\\cal D}^n_{[0,0,0,n,0,0,0]}  {\\cal E}_\\grad844 {\\cal L}_\\grad844^{[0,0,0,n,0,0,0]} , \\ee\nwith ${\\cal E}_\\grad844$ satisfying to \\eqref{R4Quadra}. The first order modification of the supersymmetry transformations will therefore necessarily admit the same gradient expansion in the function  ${\\cal E}_\\grad844$, such that\n\\begin{equation}}\\def\\ee{\\end{equation} \\delta = \\delta^\\ord{0} + \\sum_{n=0}^{12}   {\\cal D}^n_{[0,0,0,n,0,0,0]}  {\\cal E}_\\grad844 \\delta^{\\ord{1}\\, [0,0,0,n,0,0,0]} +\\dots \\ , \\ee\nwhere the dots stand for higher order corrections. It follows that the correction at second order will admit the expansion \n\\begin{eqnarray} && \\delta \\int {\\cal L}_\\grad844[{\\cal E}_\\grad844] \\nonumber \\\\*\n&=&  \\int \\Scal{ \\sum_{n=0}^{12}   {\\cal D}^n_{[0,0,0,n,0,0,0]}  {\\cal E}_\\grad844 \\delta^{\\ord{1}\\, [0,0,0,n,0,0,0]} } \\Scal{ \\sum_{m=0}^{12} {\\cal D}^m_{[0,0,0,m,0,0,0]}  {\\cal E}_\\grad844 {\\cal L}_\\grad844^{[0,0,0,m,0,0,0]} }  \\nonumber \\\\*\n&=& \\int \\sum_{m \\, n} \\sum_R   \\scal{ {\\cal D}^n_{[0,0,0,n,0,0,0]}  {\\cal E}_\\grad844 {\\cal D}^m_{[0,0,0,m,0,0,0]}{\\cal E}_\\grad844  }_R \\Psi^R_{m,n} \\,  \\end{eqnarray}\nwhere the sum over $R$ runs over all irreducible representations of $SU(8)$ in the tensor product  $[0,0,0,n,0,0,0]\\otimes [0,0,0,m,0,0,0]$, and $ \\Psi^R_{m,n} $ are understood to be $E_{7(7)}$ invariant densities function of the fields and their covariant derivatives in the irreducible representation $R$. One checks that all the appearing irreducible representations $R$ are self-conjugate, {\\it i.e.}\\   of the type $[n_4,n_3,n_2,n_1,n_2,n_3,n_4]$, by property of the tensor product $[0,0,0,n,0,0,0]\\otimes[0,0,0,m,0,0,0] $. The $\\bar F^2 \\nabla^4 R^4$ type invariant admits a gradient expansion with non-self conjugate irreducible representations, and all its components in self-conjugate representations do in fact coincide with ones appearing in the $(8,1,1)$ $\\nabla^6 R^4$ type invariant. It follows that the analysis of the supersymmetry constraints on the $\\bar F^2 \\nabla^4 R^4$ type invariant is not modified by the presence of the $R^4$ correction, and equations (\\ref{CubicR},\\ref{Laplace820}) are the exact equations to be solved by the corresponding function ${\\cal E}_\\grad820$ in the Wilsonian action. \n\nHowever, all the irreducible representations that appear in the gradient expansion \\eqref{811GradExpand} are included in the tensor product $[0,0,0,n,0,0,0]\\otimes[0,0,0,m,0,0,0] $ for $m$ and $n$ running from 1 to twelve, and the differential equations (\\ref{CubicC},\\ref{Laplace811}) must be modified in the presence of the $R^4$ type correction. Following the analysis carried out in \\cite{Green:2005ba,Green:2010kv}, we conclude that \n\\begin{equation}}\\def\\ee{\\end{equation}  \\Delta  {\\cal E}_\\grad811 = - 60  {\\cal E}_\\grad811  - ({\\cal E}_\\grad844)^2 \\ .\\label{Laplace811R4} \\ee\nAs explained in \\cite{Minimal}, this requires then to modify \\eqref{CubicC} to \n\\begin{eqnarray} {\\cal D}_{ijpq} {\\cal D}^{pqmn} {\\cal D}_{mnkl}  {\\cal E}_\\grad811 &=& - 9 {\\cal D}_{ijkl}   {\\cal E}_\\grad811 - \\frac{1}{2} {\\cal E}_\\grad844 {\\cal D}_{ijkl} {\\cal E}_\\grad844  \\ , \\label{CubicCR4}\\nonumber \\\\*\n {\\cal D}^{ijpq} {\\cal D}_{pqmn} {\\cal D}^{mnkl} {\\cal E}_\\grad811 &=& -9  {\\cal D}^{ijkl} {\\cal E}_\\grad811 - \\frac{1}{2} {\\cal E}_\\grad844 {\\cal D}^{ijkl} {\\cal E}_\\grad844 \\ . \\end{eqnarray}\nUsing in particular the tensor product \n\\begin{equation}}\\def\\ee{\\end{equation} {\\scriptstyle [0,0,0,2,0,0,0]}\\otimes {\\scriptstyle[0,0,0,1,0,0,0]}\\cong {\\scriptstyle [0,0,0,3,0,0,0]}\\oplus {\\scriptstyle [0,1,0,1,0,1,0] } \\oplus {\\scriptstyle [1,0,0,1,0,0,1] }\\oplus  {\\scriptstyle [0,0,1,1,1,0,0]}\\oplus  {\\scriptstyle [0,0,0,1,0,0,0]} \\nonumber \\ee\none shows that \n\\begin{equation}}\\def\\ee{\\end{equation} \\Scal{ 4 {\\cal D}_{ijpq} {\\cal D}^{pqmn} {\\cal D}_{mnkl} - {\\cal D}_{ijkl} \\scal{ \\Delta + 24} }   ({\\cal E}_\\grad844)^2 = 0 \\ , \\ee\nwhereas\n\\begin{equation}}\\def\\ee{\\end{equation} \\Scal{ 36 {\\cal D}_{jr[kl} {\\cal D}^{irmn} {\\cal D}_{pq]mn} - \\delta^i_j {\\cal D}_{klpq} ( \\Delta + 42)   + \\delta^i_{[k} {\\cal D}_{lpq]j} ( \\Delta-120)}   ({\\cal E}_\\grad844)^2  \\ne 0 \\ . \\ee\nWe therefore conclude that no higher derivative correction in $ ({\\cal E}_\\grad844)^2$ can consistently modify \\eqref{CubicCR4} without contradicting \\eqref{Laplace811R4}. \n\nThese properties of the source term in the Poisson equation \\eqref{Laplace811R4} can also be understood through the structure of the Fourier modes of these functions. In the decompactification limit, the Fourier modes of a function are the coefficients,  functions on $E_{6(6)}\/Sp_{\\scriptscriptstyle \\rm c}(4)$, of $e^{2\\pi i (q,a)}$, with the axion field $a$ in the ${\\bf 27}$ of the $E_{6(6)}$ subgroup. We have shown in \\cite{Minimal} that \\eqref{R4Quadra} implies then that the associated momenta are rank one vectors, {\\it i.e.}\\  using the cubic Jordan norm $3 \\, {\\rm det\\,}(q) = {\\rm tr} \\, q (q\\times q )$,\n\\begin{equation}}\\def\\ee{\\end{equation} q\\times q = 0\\ ,\\label{qxq} \\ee\n consistently with the properties of the $R^4$ threshold function.  If we consider the square of ${\\cal E}_\\grad844$, it admits by construction Fourier modes of momenta $q_1 + q_2$ where $q_1$ and $q_2$ satisfy to \\eqref{qxq}, such that \n \\begin{equation}}\\def\\ee{\\end{equation} {\\rm det\\,} (q_1+q_2) = {\\rm det\\,}(q_1) + {\\rm tr} \\, q_1 (q_2\\times q_2 )+ {\\rm tr} \\, q_2 (q_1\\times q_1 )+ {\\rm det\\,}(q_2) = 0 \\ , \\ee\nAs one can see in \\cite{Minimal}, equation \\eqref{Laplace811R4}  implies that the Fourier modes of the function ${\\cal E}_\\grad811$ must indeed carry momenta satisfying to the rank 2 constraint ${\\rm det\\,}(q)=0$, whereas the Fourier modes of the function ${\\cal E}_\\grad820$ are generic by construction in the parabolic decomposition. The  nilpotent orbit associated to  ${\\cal E}_\\grad820$  is indeed defined from the graded decomposition \n\\begin{equation}}\\def\\ee{\\end{equation} \\mathfrak{e}_{7(7)} \\cong \\overline{\\bf 27}^\\ord{-2}\\oplus \\scal{ \\mathfrak{gl}_1\\oplus \\mathfrak{e}_{6(6)}}^\\ord{0} \\oplus {\\bf 27}^\\ord{2}\\ , \\ee\nsuch that a representative of the nilpotent orbit is a generic element of the grad two component in the ${\\bf 27}$. \n\nConsidering instead the string theory limit, the non-abelian Fourier modes are defined over a Heisenberg algebra with $32$ momenta in the positive chirality Weyl spinor representation of $Spin(6,6)$ associated to Ramond--Ramond D-brane charge $Q$, and an additional momentum associated to the Neveu--Schwarz 5-brane charge $N_5$. The nilpotent orbit associated to ${\\cal E}_\\grad811$ is defined from the associated graded decomposition \n\\begin{equation}}\\def\\ee{\\end{equation} \\mathfrak{e}_{7(7)} \\cong{\\bf 1}^\\ord{-4}  \\oplus {\\bf 32}^\\ord{-2}\\oplus \\scal{ \\mathfrak{gl}_1\\oplus \\mathfrak{so}(6,6)}^\\ord{0} \\oplus {\\bf 32}^\\ord{2}\\oplus {\\bf 1}^\\ord{4} \\ . \\label{D6Grad}\\ee\nA representative of the nilpotent orbit is defined as a generic Weyl spinor in the grad 2 component \\cite{SpinorOrbits}, \n\\begin{equation}}\\def\\ee{\\end{equation} Q \\in Spin(6,6)\/ SU(2,4) \\ , \\quad {\\rm or}\\quad Q \\in Spin(6,6)\/ SL(6) \\ , \\label{OrbitsRank4}  \\ee\nto which one can add an arbitrary element of the grad 4 component $N_5$. This implies in particular that equation \\eqref{CubicCR4} does not imply any constraint on the Fourier modes. Equation \\eqref{R4Quadra} implies instead that $Q$ must be a rank 1 spinor, \\cite{SpinorOrbits}\n\\begin{equation}}\\def\\ee{\\end{equation}(Q^2)|_{\\bf 66} \\ \\hat{=}\\   (Q\\Gamma^{MN} Q) = 0 \\ , \\qquad Q \\in Spin(6,6)\/ \\scal{SL(6)\\ltimes \\mathds{R}^{15}} \\ , \\ee\n as for example the grad 3 singlet in the decomposition \n\\begin{eqnarray} \\mathfrak{so}(6,6) &\\cong& \\overline{\\bf 15}^\\ord{-2}\\oplus \\scal{ \\mathfrak{gl}_1\\oplus \\mathfrak{sl}_6}^\\ord{0} \\oplus {\\bf 15}^\\ord{2}\\ , \\nonumber \\\\* \n {\\bf 32}& \\cong& {\\bf 1}^\\ord{-3} \\oplus {\\bf 15}^\\ord{-1} \\oplus \\overline{\\bf 15}^\\ord{1} \\oplus  {\\bf 1}^\\ord{3} \\ . \n \\end{eqnarray}\nA generic rank 1 charge vector can always be rotated to the grad 3 component. Considering the sum of two rank one charges, respectively in the grad -3 and the grad 3 components, one obtains a generic rank 4 spinor of stabilizer $SL(6)\\subset Spin(6,6)$. All the rank four charges defined as the sum of two rank 1 charges with a non-trivial symplectic product can be written in this form. Therefore the right-hand-side in \\eqref{CubicCR4}  indeed sources generic Fourier modes of ${\\cal E}_\\grad811$. More precisely, all the Fourier modes with a negative quartic invariant $I_4(Q)\\le 0$ (belonging to the second orbit in \\eqref{OrbitsRank4}) are sourced by the function ${\\cal E}_\\grad{8}{1}{1}^{\\; 2}$, whereas the Fourier modes with a strictly positive quartic invariant $I_4(Q)$  (belonging to the first orbit in \\eqref{OrbitsRank4}) satisfy to a homogeneous equation. \n\nOn the contrary, a representative of the nilpotent orbit associated to ${\\cal E}_\\grad820$ satisfies that its third power in the adjoint representation vanishes, which according to \\eqref{D6Grad} implies that \\cite{SpinorOrbits}\n\\begin{equation}}\\def\\ee{\\end{equation} (Q^3)|_{{\\bf 32}}  \\ \\hat{=}\\  ( Q \\Gamma^{MN} Q  ) \\Gamma_{MN} Q = 0 \\ , \\quad Q \\in Spin(6,6)\/\\scal{ SL(2)\\times Spin(3,4)\\ltimes \\mathds{R}^{2\\times 8 +1}} \\ .\\label{Q3String}  \\ee \nThe relation with the Fourier modes is not completely straightforward in the presence of a non-trivial NS5-brane charge, because in that case the nilpotent subgroup is a non-abelian Heisemberg group, such that the corresponding Killing vector \n\\begin{equation}}\\def\\ee{\\end{equation} \\kappa_\\alpha = \\frac{\\partial\\, }{\\partial a^\\alpha} - \\frac{1}{2}C_{\\alpha\\beta} a^\\beta\\frac{\\partial\\, }{\\partial b} \\ , \\qquad k_5 = \\frac{\\partial\\, }{\\partial b} \\ , \\ee\nsatisfy to\n\\begin{equation}}\\def\\ee{\\end{equation} [ \\kappa_\\alpha , \\kappa_\\beta ] = C_{\\alpha\\beta} k_5 \\ , \\ee\nwhere $C_{\\alpha\\beta}$ is the antisymmetric charge conjugation matrix of $Spin(6,6)$. For a Fourier mode of vanishing NS5-brane charge, $k_5 {\\cal E}_{Q,0} = 0 $, and one can define the spinor charge $Q$ such that $\\kappa_\\alpha   {\\cal E}_{Q,0}  = i  Q_\\alpha  {\\cal E}_{Q,0}$, and $Q$ must satisfy to the same algebraic equations as the representatives of the nilpotent orbits associated to the differential equations. For a non-zero NS5-brane charge the relevant equations are more complicated, but still involve the Killing vector $\\kappa_\\alpha$ to the third order in the same combination. \n\n\nLet us now consider the M-theory limit, for which one considers the decomposition \n\\begin{equation}}\\def\\ee{\\end{equation} \\mathfrak{e}_{7(7)} \\cong{\\bf 7}^\\ord{-4}  \\oplus \\overline{\\bf 35}^\\ord{-2}\\oplus \\scal{ \\mathfrak{gl}_1\\oplus \\mathfrak{sl}_7}^\\ord{0} \\oplus {\\bf 35}^\\ord{2}\\oplus \\overline{\\bf 7}^\\ord{4} \\ , \\label{A6Grad}\\ee\nIn this case the nilpotent subgroup also generate a non-abelian Heisenberg type algebra \n\\begin{equation}}\\def\\ee{\\end{equation} \\kappa_{mnp} = \\frac{\\partial\\, }{\\partial a^{mnp} } - \\frac{1}{12} \\varepsilon_{mnpqrst} a^{qrs}  \\frac{\\partial\\, }{\\partial b_t } \\ , \\qquad k^m =  \\frac{\\partial\\, }{\\partial b_m }  \\ , \\ee\nsuch that \n\\begin{equation}}\\def\\ee{\\end{equation} [\\kappa_{mnp} ,\\kappa_{qrs}] = \\frac{1}{6}  \\varepsilon_{mnpqrst}  k^t \\ . \\ee\nFor a Fourier mode of vanishing M5-brane charge, $k^m  {\\cal E}_{q,0} = 0 $, and one can define the M2-brane charge $\\kappa_{mnp}  {\\cal E}_{q,0}  = i  q_{mnp}  {\\cal E}_{q,0}$. For a non-zero M5-brane charge $k^m  {\\cal E}_{q,p} = i p^m {\\cal E}_{q,p}  $ the relevant equations are more complicated, but still involve the Killing vector in a way similar as does the corresponding nilpotent orbit characteristic equation involves the algebraic charges. For a 1\/2 BPS charge satisfying to the quadratic constraint, one obtains \\cite{Lu:1997bg}\n\\begin{equation}}\\def\\ee{\\end{equation} \\varepsilon^{mnqrstu} q_{pqr} q_{stu} = 0 \\ , \\qquad q_{mnp} p^p = 0 \\ , \\ee\ngiving $17=13+4$ linearly independent solutions, with typical representative\n\\begin{equation}}\\def\\ee{\\end{equation} \\frac{1}{6} q_{mnp} dy^m \\wedge dy^n \\wedge dy^p = q_1 dy^1 \\wedge dy^2 \\wedge dy^3 \\ . \\ee\nThe cubic constraint in the adjoint representation implies \n\\begin{equation}}\\def\\ee{\\end{equation} \\varepsilon^{nrstuvw} q_{rst}q_{uv[p} q_{qm]w} = 0 \\ ,  \\qquad \\varepsilon^{mnqrstu} q_{pqr} q_{stu} p^p = 0 \\ , \\ee \nthat gives $27=21+6$ linearly independent solutions, with typical representative\n\\begin{equation}}\\def\\ee{\\end{equation}  \\frac{1}{6} q_{mnp} dy^m \\wedge dy^n \\wedge dy^p = dy^1 \\wedge \\scal{ q_1 dy^2 \\wedge dy^3 + q_2 dy^4 \\wedge dy^5 + q_3 dy^6 \\wedge dy^7}  \\ . \\label{Rank3} \\ee\n The cubic constraint in the fundamental implies instead \n\\begin{equation}}\\def\\ee{\\end{equation}  \\varepsilon^{mnrstuv} q_{mnr}q_{st(p} q_{q)uv} = 0 \\ , \\label{Rank4} \\ee\nthat gives $33=26+7$ linearly independent solutions, such that the $SL(7)$ M2-brane charge orbits are either \n\\begin{equation}}\\def\\ee{\\end{equation} q \\in SL(7,\\mathds{R})\/ (SL(3,\\mathds{C}) \\ltimes \\mathds{C}^3) \\ , \\quad {\\rm or}\\quad q\\in SL(7,\\mathds{R})\/ (SL(3,\\mathds{R}) \\ltimes \\mathds{R}^3)^{\\times 2}  \\ , \\label{SL7orbit} \\ee\nwith typical representative \n\\begin{equation}}\\def\\ee{\\end{equation}   \\frac{1}{6} q_{mnp} dy^m \\wedge dy^n \\wedge dy^p = q_1 dy^1 \\wedge  dy^2 \\wedge dy^3 + q_2 dy^1\\wedge  dy^4 \\wedge dy^5 + q_3 dy^2 \\wedge dy^6 \\wedge dy^4 + q_4 dy^3 \\wedge dy^5 \\wedge dy^6  \\ , \\ee \nand \n\\begin{equation}}\\def\\ee{\\end{equation}  \\frac{1}{2\\times 12^3}\\varepsilon^{pmnrstu}  \\varepsilon^{qm^\\prime n^\\prime r^\\prime s^\\prime t^\\prime u^\\prime } q_{mnr}q_{stm^\\prime} q_{n^\\prime r^\\prime u} q_{s^\\prime t^\\prime u^\\prime} =  q_1 q_2 q_3  q_4 \\delta^p_7 \\delta^q_7 \\ , \\ee\nsuch that the orbit \\eqref{SL7orbit} is determined by the sign of the eigenvalue of this rank one symmetric tensor, $I_4 =  q_1 q_2 q_3 q_4$. The generic sum of two rank one charges takes the form \n\\begin{equation}}\\def\\ee{\\end{equation} \\frac{1}{6} q_{mnp} dy^m \\wedge dy^n \\wedge dy^p = q_1 dy^1 \\wedge dy^2 \\wedge dy^3  + q_2dy^4 \\wedge dy^5 \\wedge dy^6 \\ ,\\ee\nand is a generic solution to \\eqref{Rank4} associated to the second orbit ({\\it i.e.}\\  $I_4<0$), and violates equation \\eqref{Rank3}. Therefore we confirm that a quadratic source in ${\\cal E}_\\grad{8}{4}{4}$ is in contradiction with the cubic equation satisfied by ${\\cal E}_\\grad{8}{2}{0}$, whereas it is consistent with the one satisfied by ${\\cal E}_\\grad{8}{1}{1}$. \n\n\n\n\n\n\n\nLet us now argue that all the invariants of the infinite series of $\\bar F^{2k} \\nabla^4 R^4$ do not get modified at the same order by lower order modifications to the supersymmetry transformations. By power counting, the next order correction to the $R^4$ type invariant and a $\\bar F^{2k} \\nabla^4 R^4$ type invariant can in principle contribute to a right-hand-side for the classical supersymmetry variation of a $\\bar F^{2k+6} \\nabla^4 R^4$ type invariant. So in principle one could expect that the function ${\\cal E}_\\grad820^\\ord{k}$ satisfies to a Poisson equation of the kind \n\\begin{multline} \\Delta {\\cal E}_\\grad820^\\ord{k} =3 (k+4)(k-5) {\\cal E}_\\grad820^\\ord{k}   - a^\\ord{k}_3 {\\cal E}_\\grad844 \\, {\\cal E}_\\grad820^\\ord{k-3} \\\\ - a^\\ord{k}_5   {\\cal E}_\\grad822 \\, {\\cal E}_\\grad820^\\ord{k-5} - a^\\ord{k}_6 ({\\cal E}_\\grad844)^2 \\, {\\cal E}_\\grad820^\\ord{k-6} - \\sum_{p=0}^{k-8} b^\\ord{k}_{p}   {\\cal E}_\\grad820^\\ord{k-8-p} {\\cal E}_\\grad820^\\ord{p} + \\dots \\end{multline}\nHowever, the solutions to the differential equation \\eqref{CubicK} admit restricted Fourier modes in the string theory limit, satisfying to \\eqref{Q3String} for a vanishing NS5-brane charge. As we have already explained, the product of two functions including non-perturbative corrections admits generic Fourier modes in the string theory limit, because the sum of two pure spinors can be a generic spinor. We see therefore that a source term modifying \\eqref{CubicK} would necessarily involve the third order differential operator such as to source these Fourier modes. Such a modification would destroy completely the structure of the equations, which would reduce then to some kind of Poisson equation. \n\n\n\\subsection{String theory perturbation theory}\n\\label{StringPerturb} \nIn order to deduce constraints on the contributions that can possibly appear in perturbative string theory, it is important to solve the differential equations satisfied by the threshold functions in the parabolic gauge with manifest T-duality symmetry \\eqref{D6Grad}. In this section we will solve these equations on an ansatz function depending only on the string theory dilaton $e^{2\\phi}$ and the scalar fields parametrising $SO(6,6)\/(SO(6)\\times SO(6))$. We have not computed explicitly the decomposition of the differential equations, but using the manifest covariance, and the known solutions for the $R^4$ and the $\\nabla^4 R^4$ threshold functions \\cite{Green:2010kv}, we can determine unambiguously all the unknown coefficients. \n\nWe define the covariant derivative ${\\cal D}_{a\\hat{b}}$ on $SO(6,6)\/(SO(6)\\times SO(6))$ in tangent frame, such that $a=1$ to $6$ of one $SO(6)$ and $\\hat{b}=1$ to $6$ of the other. It is convenient to define the covariant derivative as an $SU(4)\\times SU(4)$ tensor\n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{ij\\hat{k}\\hat{l}} = \\frac{1}{4} \\gamma^a{}_{ij} \\gamma^{\\hat{b}}{}_{\\hat{k}\\hat{l}} {\\cal D}_{a\\hat{b}} \\ , \\ee\nwith $i=1,\\, 4$ of one $SU(4)$ and $\\hat{\\imath}=1,\\, 4$ of the other. \n\nCalibrating the equations on the known solutions, one obtains that \n\\begin{equation}}\\def\\ee{\\end{equation} {\\bf D}_{56}^{\\;3} {\\cal E} = \\scal{ s^2 - \\tfrac{17}{2} s+6}    {\\bf D}_{56} {\\cal E} \\label{D563sString} \\ee\ndecomposes on $\\mathds{R}_+^* \\times SO(6,6)\/(SO(6)\\times SO(6))$ as\n\\begin{eqnarray}\\biggl(  \\Scal{  \\frac{1}{64} \\partial_\\phi^{\\; 3} + \\frac{17}{32} \\partial_\\phi^{\\; 2} + \\frac{3}{2} \\partial_\\phi -  {\\cal D}_{a\\hat{b}} {\\cal D}^{a\\hat{b}} } \\delta_a^b + \\Scal{ \\frac{3}{4} \\partial_\\phi + 6 } {\\cal D}_{a\\hat{c}} {\\cal D}^{b\\hat{c}} \\biggr) {\\cal E} &=&\\scal{ s^2 - \\tfrac{17}{2} s+6}   \\ \\delta_{a}^b \\,  \\frac{1}{4} \\partial_\\phi{\\cal E} \\ , \\qquad \\nonumber \\\\*\n\\biggl( {\\cal D}_{a\\hat{c}} {\\cal D}^{d\\hat{c}} {\\cal D}_{d\\hat{b}} + \\Scal{ \\frac{3}{16} \\partial_\\phi^{\\; 2} + \\frac{31}{8} \\partial_\\phi + 9 } {\\cal D}_{a\\hat{b}} \\biggr) {\\cal E} &=&\\scal{ s^2 - \\tfrac{17}{2} s+6}   {\\cal D}_{a\\hat{b}} {\\cal E}\\ ,  \\nonumber \\\\*\n\\biggl( 8 {\\cal D}_{ip}{}^{\\hat{k}\\hat{q}} {\\cal D}^{pr}{}_{\\hat{q}\\hat{s}} {\\cal D}_{jr}{}^{\\hat{l}\\hat{s}} + \\Scal{ \\frac{5}{4} \\partial_\\phi + 2} 2{\\cal D}_{ij}{}^{\\hat{k}\\hat{l}}\\biggr) {\\cal E} &=& 2\\scal{ s^2 - \\tfrac{17}{2} s+6}  {\\cal D}_{ij}{}^{\\hat{k}\\hat{l}} {\\cal E} \\ , \\ \n\\end{eqnarray}\nwhereas \n\\begin{equation}}\\def\\ee{\\end{equation} {\\bf D}_{133}^{\\;3} {\\cal E} =s(s-9)   {\\bf D}_{133} {\\cal E} \\label{AdjointEquation}  \\ee\ngives the components in the ${\\bf 32}$ of $Spin(6,6)$\n\\begin{eqnarray} \\biggl(\\Scal{ \\frac{1}{64} \\partial_\\phi^{\\; 3} + \\frac{5}{8} \\partial_\\phi^{\\; 2} - \\frac{5}{16} \\partial_\\phi - {\\cal D}_{pq{\\hat{r}\\hat{s}}} {\\cal D}^{pq{\\hat{r}\\hat{s}}} } \\delta_i^k \\delta_{\\hat{\\jmath}}^{\\hat{l}} + 3 ( \\partial_\\phi +6)  {\\cal D}_{ip\\hat{\\jmath}\\hat{q}} {\\cal D}^{kp\\hat{l}\\hat{q}} \\biggr) {\\cal E} &=& s(s-9) \\ \\delta_i^k \\delta_{\\hat{\\jmath}}^{\\hat{l}}\\,  \\frac{1}{4} \\partial_\\phi {\\cal E}\\ , \\qquad  \\nonumber \\\\*\n\\biggl(8  {\\cal D}_{ip\\hat{\\jmath}\\hat{q}} {\\cal D}^{pr\\hat{q}\\hat{s}}{\\cal D}_{kr\\hat{l}\\hat{s}} + \\Scal{ \\frac{3}{16} \\partial_\\phi^{\\; 3} + \\frac{31}{8} \\partial_\\phi}2 {\\cal D}_{ik\\hat{\\jmath}\\hat{l}} \\biggr) {\\cal E} &=&   2 s(s-9){\\cal D}_{ik\\hat{\\jmath}\\hat{l}} {\\cal E} \\ . \\label{D1333sString}\n \\end{eqnarray}\nThe $\\nabla^4 R^4$ threshold function solves \\eqref{D563sString} for $s=\\frac{3}{2}$ and \\eqref{D1333sString} for $s=4$. One reads directly from these equations, that a solution of type $e^{a\\phi} {\\cal E}_{D_6}$  on $\\mathds{R}_+^* \\times SO(6,6)\/(SO(6)\\times SO(6))$ must be such that ${\\cal E}_{D_6}$ satisfies to the quadratic equations in all fundamental representations ({\\it i.e.}\\  the vector and Weyl spinor of positive and negative chirality), unless $a=-6$ or $a=-8$. The only other solutions are therefore such that ${\\cal E}_{D_6}$ is either a constant, or solves \\eqref{MinimalD6}. One finds the unique  solution $e^{-10\\phi}$.  For the values $a=-8$, the function ${\\cal E}_{D_6}$ satisfies to a quadratic equation in the spinor representation, and solve \\eqref{VecD6} for $s=4$ (or $1$ which is equivalent). For $a=-6$, ${\\cal E}_{D_6}$ satisfies to a quadratic equation in the vector representation, and cubic equations in the two spinor representations, and must therefore satisfy to  \\eqref{NextMinimalD6}. We find therefore that supersymmetry and T-duality alone already determine the $\\nabla^4 R^4$ type corrections in perturbative string theory, up to three free coefficients, that are given in \\cite{Green:2010kv}\n\\begin{equation}}\\def\\ee{\\end{equation} \\frac{1}{2} {E}_{\\mbox{\\DEVII{\\frac{5}{2}}00000{\\mathfrak{0}}}}  = \\zeta(5) e^{-10\\phi}  + \\frac{4}{15\\pi} e^{-8\\phi} E_{\\mbox{\\WSOXII{4}00000}}  + \\frac{2}{3} e^{-6\\phi} E_{\\mbox{\\WSOXII{0}00020}} + \\mathcal{O}(e^{-e^{-\\phi}})  \\ . \\label{E4} \\ee\nThis confirms that supersymmetry alone already prevents any perturbative correction to the $\\nabla^4 R^4$ threshold function beyond 2-loop in perturbative string theory. \n\nThe functions defining the $\\bar F^{2k} \\nabla^4 R^4$ solve equation  \\eqref{D1333sString} for $s=k+4$. \nSimilarly one obtains the general $SO(6,6,\\mathds{Z})$ invariant solution \n \\begin{equation}}\\def\\ee{\\end{equation} {\\cal E}_\\grad820^\\ord{k} = c^\\ord{k}_1 e^{-2(k+4)\\phi} {E}_{\\mbox{\\WSOXIIT{k\\mbox{+}4}000{\\mathfrak{0}}0}}   + c_{k+2}^\\ord{k} e^{-6\\phi} {E}_{\\mbox{\\WSOXIIT{\\mathfrak{0}}000{k\\mbox{+}2}0}} +c^\\ord{k}_{2k}   e^{2(k-5)\\phi} {E}_{\\mbox{\\WSOXIIT{k}000{\\mathfrak{0}}0}} +\\mathcal{O}(e^{-e^{-\\phi}})  \\ .\\ee\nIt is quite remarkable that the only solutions we get all correspond to a strictly positive number of loops in perturbative string theory. After implementing the Weyl rescaling, one obtains indeed that $c^\\ord{k}_\\ell$ is a coefficient for a $\\ell$-loop correction in string theory for the $\\bar F^{2k} \\nabla^4 R^4$ threshold function. For $k=1$ and $k=2$, equation   \\eqref{D1333sString} is exact for the Wilsonian effective action (not taking into account linear corrections associated to logarithms in the complete effective action). $U$-duality therefore implies that ${\\cal E}_\\grad820$ must be an Eisenstein function as in \\eqref{EisF2k}. Assuming that our argumentation in the preceding section is correct, and that equation \\eqref{D1333sString} is satisfied for all $k$, we arrive at the conjecture that  the $\\bar F^{2k} \\nabla^4 R^4$ threshold function is defined by the Eisenstein series $E{\\mbox{\\DEVII{0}00000{4\\mbox{+}k}}}$ for all $k$. It is rather remarkable that this coupling would only get three corrections in perturbation theory, at 1-loop, $k+2$-loop and $2k$-loop. \n\n\nThis Eisenstein function diverges precisely for $k=1$, corresponding to the $\\bar F^2 \\nabla^4 R^4$ threshold related to the $\\nabla^6 R^4$  threshold function by supersymmetry.  One must therefore consider the regularised Eisenstein series \n\\begin{multline}  \\frac{16}{63} \\hat{{E}}_{\\mbox{\\DEVII000000{5}}} = \\frac{16}{63}e^{-10\\phi}  \\hat{E}_{\\mbox{\\WSOXIIT{5}000{\\mathfrak{0}}0}}-\\frac{15\\zeta(5)}{4} \\phi\\,  e^{-10\\phi}  + \\frac{1}{\\pi} e^{-8\\phi} \\Scal{ 2 \\phi  {E}_{\\mbox{\\WSOXIIT{4}000{\\mathfrak{0}}0}} - \\partial_s {E}_{\\mbox{\\WSOXIIT{s}000{\\mathfrak{0}}0}} \\big|_{s=4} }   \\\\ + \\frac{\\pi}{9} e^{-6\\phi} \\hat{E}_{\\mbox{\\WSOXIIT{\\mathfrak{0}}000{3}0}}  +   \\mathcal{O}(e^{-e^{-\\phi}}) \\ .  \\end{multline} \nHere we have fixed all the coefficients by consistency with \\eqref{DivergenceF2D4R4} and \\eqref{E4}. The logarithm of the dilaton indicates a divergence of the $\\nabla^4 R^4$ form factor into  $\\nabla^6 R^4$ in supergravity. Note nonetheless that the 3-loop contribution in the last line violate T-duality parity in $O(6,6,\\mathds{Z})$, and the string theory effective action must include the same function with opposite chirality. Because it is a three-loop contribution, it cannot come from the completion of the $R^4$ type invariant and it must appear as a solution to equation \\eqref{D563sString} for $s=6$. \n\nConsidering the general $SO(6,6,\\mathds{Z})$ invariant solution of \\eqref{D563sString}, one finds indeed \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal E}_\\grad811  =  c_{\\mbox{-}6}e^{-4s\\phi} + c_{\\mbox{-}\\frac{1}{2}}e^{-(2s+1)\\phi}{E}_{\\mbox{\\WSOXII{0}0000{\\mathnormal{s}\\mbox{-}\\hspace{-0.2mm}\\stfrac{1}{2}}}}  +c_1 e^{2(2s-17)\\phi}  +c_2 e^{-8\\phi} {E}_{\\mbox{\\WSOXII0{\\mathnormal{s}\\mbox{-}2}0000}}+ c_3 e^{2(s-9)\\phi} {E}_{\\mbox{\\WSOXII00000{\\mathnormal{s}\\mbox{-}3}}}  \\ee\nwhere the coefficients $c_\\ell$ are constants that would correspond to $\\ell$-loop contributions for the $\\nabla^6 R^4$ threshold function in string theory.  Note that the first two terms do not make sense in perturbative string theory. The corresponding Eisenstein function ${E}{\\mbox{\\DEVII{s}00000{\\mathfrak{0}}}}$ includes generically all these terms, and therefore cannot define the string theory threshold function, consistently with the property that \\eqref{D563sString} is corrected by a source term \\eqref{CubicCR4}. However, the three-loop contribution is not affected by the source term, and one can take seriously the last contribution, which is precisely the one required to restore  $O(6,6,\\mathds{Z})$ invariance  for $s=6$.\n\nThis is indeed confirmed by the expression obtained in \\cite{Pioline:2015yea} for the $\\nabla^6 R^4$ threshold function, and using these results we conclude therefore that the exact threshold function for the $\\nabla^6 R^4$ coupling is defined as\n\\begin{equation}}\\def\\ee{\\end{equation} E_{\\gra{0}{1}} = \\hat{{\\cal E}}_{\\grad{8}{1}{1}}  + \\frac{32}{189\\pi}\\hat{{E}}_{\\mbox{\\DEVII000000{5}}}\\ ,  \\ee\nwhere the function $ {\\cal E}_{\\grad{8}{1}{1}}$ solve the differential equation \n\\begin{eqnarray}\\label{E811Equation} \\Delta \\hat{{\\cal E}}_{\\grad{8}{1}{1}} &=& - 60 \\hat{{\\cal E}}_{\\grad{8}{1}{1}} - \\Scal{ {E}_{\\mbox{\\DEVII{\\mathnormal{\\tfrac{3}{2}}}00000{\\mathfrak{0}}}}}^2 + \\frac{35}{\\pi} \\Scal{ \\frac{1}{2}  {E}_{\\mbox{\\DEVII{\\mathnormal{\\tfrac{5}{2}}}00000{\\mathfrak{0}}}}}\\ \\\\\n {\\cal D}_{ijpq} {\\cal D}^{pqmn} {\\cal D}_{mnkl}  \\hat{{\\cal E}}_\\grad811 &=& - 9 {\\cal D}_{ijkl}   \\hat{{\\cal E}}_\\grad811 - \\frac{1}{2} {E}_{\\mbox{\\DEVII{\\mathnormal{\\tfrac{3}{2}}}00000{\\mathfrak{0}}}} {\\cal D}_{ijkl} {E}_{\\mbox{\\DEVII{\\mathnormal{\\tfrac{3}{2}}}00000{\\mathfrak{0}}}}  + \\frac{35}{4\\pi}   {\\cal D}_{ijkl}  \\Scal{ \\frac{1}{2}  {E}_{\\mbox{\\DEVII{\\mathnormal{\\tfrac{5}{2}}}00000{\\mathfrak{0}}}}}\\ , \\nonumber \\\\*\n {\\cal D}^{ijpq} {\\cal D}_{pqmn} {\\cal D}^{mnkl} \\hat{{\\cal E}}_\\grad811 &=& -9  {\\cal D}^{ijkl} \\hat{{\\cal E}}_\\grad811 - \\frac{1}{2}{E}_{\\mbox{\\DEVII{\\mathnormal{\\tfrac{3}{2}}}00000{\\mathfrak{0}}}} {\\cal D}^{ijkl} {E}_{\\mbox{\\DEVII{\\mathnormal{\\tfrac{3}{2}}}00000{\\mathfrak{0}}}} +\\frac{35}{4\\pi}   {\\cal D}^{ijkl}  \\Scal{ \\frac{1}{2}  {E}_{\\mbox{\\DEVII{\\mathnormal{\\tfrac{5}{2}}}00000{\\mathfrak{0}}}}}\\ . \\nonumber\n\\end{eqnarray}\nHere the anomalous right-hand-side is determined such as to coincide with the one obtained in \\cite{Pioline:2015yea} for the complete function $ E_{\\gra{0}{1}}$. These coefficients can also be directly computed from the properties of the Eisenstein functions and the structure of the differential equations \\cite{Axel}. \n\\section{Supergravity in higher dimensions}\n\\label{HigherDimensions}\nIn this section we will consider the extension of the results of the preceding section in five, six, seven and eight dimensions. We will see that the two $\\nabla^6 R^4$ type invariants both lift to higher dimensions, even if they cannot be defined as harmonic superspace integrals in the linearised approximation in general.\n\n\\subsection{$\\mathcal{N} =4$ supergravity in five dimensions}\nLet us recall in a first place some properties of maximal supergravity in five dimensions. The scalar fields parametrise the symmetric space $E_{6(6)}\/Sp(4)_{\\scriptscriptstyle \\rm c}$. We use  $i, j = 1, ..., 8$ as indices in the fundamental representation of  $Sp(4)$, and $\\O^{i j}$ defines the symplectic form with the normalisation $\\O^{i k} \\O_{j k} = \\delta^{i}_{j} $. The covariant derivative in tangent frame ${\\cal D}_{i j k l}$ is a symplectic traceless rank four antisymmetric tensor in the representation $[0,0,0,1]$ of $Sp(4)$.\n\n\n\\addtocontents{toc}{\\protect\\setcounter{tocdepth}{1}}\n\\subsubsection{Linearised $\\nabla^6 R^4$ type invariants}\n\\addtocontents{toc}{\\protect\\setcounter{tocdepth}{2}}\nIn five dimensions there is only one kind of 1\/8 BPS harmonic superspace integral that one can define \\cite{Bossard:2009sy}. For this purpose, one considers $Sp(4)\/(U(1)\\times Sp(3))$ harmonic variables $(u^{1}{}_{i}, u^{r}{}_{i}, u^{8}{}_{i})$ with $r = 2, ... ,7$ in the fundamental of  $Sp(3)$, and the decomposition \n\\begin{eqnarray}\n\\mathfrak{sp}(4) &\\cong& {\\bf 6}^\\ord{-1} \\oplus \\scal{ \\mathfrak{u}(1)\\oplus \\mathfrak{sp}(3)}^\\ord{0} \\oplus {\\bf 6}^\\ord{1} \\nonumber \\\\*\n{\\bf 42} &\\cong&  {\\bf 14}^{\\ord{-1}}_{3} \\oplus {\\bf 14}^{\\ord{0}}_{2} \\oplus {\\bf 14}^{\\ord{1}}_{3} \\ . \n\\end{eqnarray}\nOne defines the G-analytic superfield $W^{r s t}$ in the $[0,0,1]$ of $Sp(3)$\n\\begin{equation}}\\def\\ee{\\end{equation}\nW^{r s t} = u^{1}{}_{i}  u^{r}{}_{j} u^{s}{}_{j} u^{t}{}_{k} L^{i j k l} \\ , \n\\ee\nwhich satisfies the constraint \\begin{equation}}\\def\\ee{\\end{equation}\nu^1{}_{ i} D_{\\alpha}^{i} W^{r s t} = 0 \\ . \n\\ee\nFollowing the same reasoning as in section \\ref{811D6R4}, we consider a general monomial of $W^{rst}$ in an irreducible representation of $Sp(3)$. In this case we obtain equivalently that the monomials are freely generated by $W^{rst}$ in the $[0,0,1]$,  the elements \n\\begin{equation}}\\def\\ee{\\end{equation} W^{r t p} W^{s q r} \\O_{t q} \\O_{p r} \\ , \\ee\nin the $[2,0,0]$,\n\\begin{equation}}\\def\\ee{\\end{equation} W^{r p q} W^{s u}{}_{p} W^{t}{}_{q u} \\, , \\ee\nin the $[0,0,1]$, and  \n\\begin{equation}}\\def\\ee{\\end{equation} W^{r] t u} W^{[s}{}_{t u} W^{p] v w} W^{[q}{}_{v w} - {\\rm ``symp\\ trace\"} \\ , \\qquad W^{r s t} W^{p q}{}_{r} W^{u}{}_{s p} W{}_{t q u}\\ , \\ee\nrespectively in the $[0,2,0]$ and the singlet representation. The general linearised invariant takes therefore the form \n\\begin{eqnarray}\n&&  \\int du D^{28} F(u)^{[2n_2,2n_4,n_1 + n_3]}_{[2 n_3 + 2 n_{4} + 4 n'_{4}, 2n_2, 2n_4, n_1 + n_3]} W^{4 + n_1 + 2 n_2 + 3 n_3 + 4 n_4 + 4 n'_4}_{[2n_2,2n_4,n_1 + n_3]} \\nonumber \\\\*\n&=&   L^{n_1 + 2 n_2 + 3 n_3 + 4 n_4 + 4 n'_4}_{[2 n_3 + 2 n_{4} + 4 n'_{4}, 2n_2, 2n_4, n_1 + n_3]} \\scal{ \\nabla^6 R^4  + \\dots } + \\dots \n\\end{eqnarray}\nThe structure of these linearised invariants suggests that the complete non-linear invariant admits the following gradient expansion \n\\begin{equation}}\\def\\ee{\\end{equation}\n{\\cal L}_{\\gra{4}{1}}[ {\\cal E}_{\\gra{4}{1}}] = \\sum_{n_1,n_2,n_3,n_4,n_4^\\prime} {\\cal D}^{n_1 + 2 n_2 + 3 n_3 + 4 n_4 + 4 n'_4}_{[2 n_3 + 2 n_{4} + 4 n'_{4}, 2n_2, 2n_4, n_1 + n_3]} {\\cal E}_{\\gra{4}{1}} {\\cal L}_{\\gra{4}{1}}^{[2 n_3 + 2 n_{4} + 4 n'_{4}, 2n_2, 2n_4, n_1 + n_3]}\\ . \n\\ee\nThe consistency of this ansatz requires that the function ${\\cal E}_{\\gra{4}{1}} $ must be an eigenfunction of the Laplace operator, and that its third order derivative restricted to the $[0,2,0,0]$ is proportional to its second derivative in the same representation. This linearised analysis is consistent with the one of the $(8,1,1)$ type invariant in four dimensions, and we are going to see that the relevant equation is \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{ijpq} {\\cal D}^{pqrs} {\\cal D}_{rskl}  {\\cal E}_{\\gra{4}{1}} = \\frac{1}{4} {\\cal D}_{ijkl} \\scal{ 34 + \\Delta}  {\\cal E}_{\\gra{4}{1}}  \\ .\\ee\nHowever, the $(8,2,0)$ type invariants cannot be defined in the linearised approximation through a harmonic superspace integral, and we shall instead consider the uplift of the general invariant to five dimensions. \n\n\\subsubsection{Decompactification limit from four to five dimensions}\nWe are therefore going to solve the differential equations  \\eqref{CubicR} and \\eqref{E811Equation}  for a function depending only of the Levi subgroup $\\mathds{R}_*^+\\times  E_{6(6)}$ of the parabolic subgroup associated to the decompactification limit, such that \n\\begin{equation}}\\def\\ee{\\end{equation} \\mathfrak{e}_{7(7)}\\cong \\overline{\\bf 27}^\\ord{-2} \\oplus \\scal{ \\mathfrak{gl}_1 \\oplus \\mathfrak{e}_{6(6)} }^\\ord{0} \\oplus {\\bf 27}^\\ord{2} \\ , \\qquad \n{\\bf 56} \\cong {\\bf 1}^\\ord{-3} \\oplus {\\bf 27}^\\ord{-1} \\oplus \\overline{\\bf 27}^\\ord{1} \\oplus {\\bf 1}^\\ord{3} \\ .\\label{56E6}  \\ee\nFor this purpose we use the same conventions as in \\cite{Minimal}, such that the coset representative in $E_{7(7)}\/SU(8)_{\\scriptscriptstyle \\rm c}$ is defined as\n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal V} = \\left( \\begin{array}{cccc} \\ e^{3\\phi} \\ & \\ 0 \\ & \\ 0 \\ & \\ 0 \\\\\n0 &\\ e^{\\phi} V_{ij}{}^I \\ &0&0\\\\\n0&0& \\ e^{-\\phi} V^{ \\scriptscriptstyle \\rm{\\mbox{\\tiny-1}}}{}_I{}^{ij} \\ &0\\\\\n0&0&0& e^{-3\\phi} \\end{array}\\right) \\left( \\begin{array}{cccc} \\ 1 \\ & \\ a^J \\ & \\ \\tfrac{1}{2} t_{JKL} a^K a^L  \\ & \\ \\tfrac{1}{3} t_{KLP} a^K a^L a^P \\\\\n0 &\\ \\delta_I^J \\ &t_{IJK} a^K&\\tfrac{1}{2} t_{IKL} a^K a^L\\\\\n0&0& \\delta_J^I \\ &a^I \\\\\n0&0&0& 1 \\end{array}\\right)  \\ , \\label{corset_elem} \\ee\nwhere $V_{i j}{}^{I}$ is the coset representative in $E_{6(6)}$ with the $Sp(4)$ pair $ij$ being antisymmetric symplectic traceless and the index $I$ in the fundamental of $E_{6(6)}$. $t_{I J K}$ is the $E_{6(6)}$ invariant symmetric tensor normalised as in \\cite{Minimal}. We have already computed the decomposition of the cubic equation \\eqref{Cubic56} in \\cite{Minimal}, which is\n\\begin{eqnarray} \\Bigl( \\frac{1}{64} \\partial_\\phi^{\\; 3} + \\frac{21}{32} \\partial_\\phi^{\\; 2} +\\frac{9}{2} \\partial_\\phi - \\frac{3}{4} \\Delta \\Bigr) {\\cal E}_\\grad{8}{1}{1}   &=& -  \\frac{1}{4} \\partial_\\phi\\Scal{9 {\\cal E}_\\grad{8}{1}{1}  + \\frac{1}{4}   {\\cal E}_\\grad{8}{4}{4}^{\\; 2}}  \\\\\n \\biggl(  {\\cal D}_{ijpq} {\\cal D}^{pq}{}_{rs} {\\cal D}^{rskl}  + {\\cal D}_{ij}{}^{kl} \\Bigl( \\frac{1}{48} \\partial_\\phi^{\\; 2} + \\frac{27}{24} \\partial_\\phi + \\frac{7}{2} \\Bigr)  + {\\cal D}_{ijpq} {\\cal D}^{klpq} \\Bigl( \\frac{1}{4} \\partial_\\phi+3 \\Bigr)\\hspace{-32mm} && \\nonumber \\\\* +\\delta_{ij}^{kl} \\Bigl( \\frac{1}{12^3} \\partial_\\phi^{\\; 3} + \\frac{5}{96} \\partial_\\phi^{\\; 2} +\\frac{1}{6} \\partial_\\phi - \\frac{1}{4} \\Delta  \\Bigr) \n \\biggr) {\\cal E}_\\grad{8}{1}{1} &=& -  \\Bigl( \\frac{1}{12} \\delta_{ij}^{kl} \\partial_\\phi + {\\cal D}_{ij}{}^{kl} \\Bigr)  \\Scal{ 9 {\\cal E}_\\grad{8}{1}{1}  + \\frac{1}{4}   {\\cal E}_\\grad{8}{4}{4}^{\\; 2}} \\nonumber \\ ,\n \\end{eqnarray}\n where \n \\begin{equation}}\\def\\ee{\\end{equation}\n\\delta_{ij}^{kl} = \\delta_{[i}^{[k} \\delta_{j]}^{l]} - \\frac{1}{8} \\Omega_{ij} \\Omega^{k l} \\ , \\qquad \\Delta = \\frac{1}{3} {\\cal D}_{ijkl} {\\cal D}^{ijkl} \\ ,\n\\ee\nand indices are raised and lowered with the symplectic matrix $\\Omega_{ij}$.  Because of the Weyl rescaling required to stay in Einstein frame, the relevant radius power in the decompactification limit for a $\\nabla^{2n} R^4$ threshold function is such that  ${\\cal E}_{E_{7}} = e^{-( 6 + 2 n)\\phi} {\\cal E}_{E_6}$, and because we are interested in the constraint on the $\\nabla^{6} R^4$ threshold function, we use the ansatz \n \\begin{equation}}\\def\\ee{\\end{equation}\n {\\cal E}_{\\grad{8}{1}{1}} = e^{- 12 \\phi} {\\cal E}_{\\gra{8}{1}} \\ , \\qquad  {\\cal E}_\\grad844 = e^{-6 \\phi}  {\\cal E}_{\\gra{8}{4}} \\label{LaplaceE6}  \\ ,\n \\ee\nwhere $ {\\cal E}_{\\gra{8}{1}}$ and $ {\\cal E}_{\\gra{8}{4}}$ are functions on $E_{6(6)}\/Sp(4)_{\\scriptscriptstyle \\rm c}$. Using this ansatz, one derives \n \\begin{equation}}\\def\\ee{\\end{equation}\n\\Delta {\\cal E}_{\\gra{8}{1}} = - 18  {\\cal E}_{\\gra{8}{1}}  - {\\cal E}^{\\; 2}_{\\gra{8}{4}} \\ , \n \\ee\nand\n\\begin{equation}}\\def\\ee{\\end{equation}\n\\bigl( {\\cal D}_{ijpq} {\\cal D}^{pqrs} {\\cal D}_{rskl}  + 2  {\\cal D}_{i jkl} \\bigr) {\\cal E}_{\\gra{8}{1}} = - \\frac{1}{4}  {\\cal D}_{i jkl} {\\cal E}^{\\; 2}_{\\gra{8}{4}} \\ . \\label{D6R4E6} \n\\ee\nThese equations are satisfied by the 1\/8 BPS threshold functions in the Wilsonian effective action, but the U-duality invariant function appearing in the 1PI effective action satisfied to anomalous equations with additional terms linear in ${\\cal E}_\\gra{8}{4}$ in the right-hand-side \\cite{Pioline:2015yea}. \n\nWe shall now consider the uplift of the  $F^{2 k} \\nabla^4 R^4$ type invariants, but for this purpose it will be more convenient to consider directly the decompactification limit of the Eisenstein function  ${E}{\\mbox{\\DEVII000000{k\\mbox{+}4}}}$. We shall only consider the term with the correct power of the compactification radius $r$ to lift to a diffeomorphism invariant in five dimensions, as computed in appendix \\ref{E66Eis},\n\\begin{equation}}\\def\\ee{\\end{equation} \\int d^4 x \\, \\sqrt{-g} \\  {E}_{\\mbox{\\DEVII000000{k\\mbox{+}4}}}\\,  \\nabla^{4+2k} R^4 \\rightarrow  \\frac{\\pi^{\\frac{1}{2}} \\Gamma(k + \\frac{7}{2})}{\\Gamma(k+4)}   \\int d^5x \\, \\sqrt{-g}\\  E_{\\mbox{\\DEVI00000{k\\mbox{+}\\frac{7}{2}}}}   \\nabla^{4+2k} R^4 \\ . \\ee\nWe conclude in this way that the threshold function  ${\\cal E}_{\\frac{1}{8}}^\\ord{k}$ defining the $F^{2k} \\nabla^{4} R^4$ type invariants satisfies to \n\\begin{eqnarray}\n\\Scal{ {\\cal D}_{ijpq} {\\cal D}^{pq}{}_{rs} {\\cal D}^{rskl}  - \\frac{2k(k+1)-10}{3} {\\cal D}_{ij}{}^{kl}} {\\cal E}_{\\frac{1}{8}}^\\ord{k} &=&\n\\frac{k+2}{2} \\biggl({\\cal D}_{i j p q} {\\cal D}^{k lp q}  - \\frac{2(2 k-5) (2 k+7)}{27}  \\delta_{ij}^{kl} \\biggr) {\\cal E}_{\\frac{1}{8}}^\\ord{k} \\nonumber \\\\*\n\\Delta {\\cal E}_{\\frac{1}{8}}^\\ord{k} = \\frac{2}{3} (2 k-5) (2 k+7) {\\cal E}_{\\frac{1}{8}}^\\ord{k} \\ , && \\qquad {\\cal D}^{3}_{[2,0,0,1]} {\\cal E}_{\\frac{1}{8}}^\\ord{k} = 0 \\ . \\label{F2kD4R4E6}\n\\end{eqnarray}\nIt follows from representation theory that such equations are indeed implied by \\eqref{AdjointEquation}, and this explicit example permits to determine them uniquely. \n\nWe therefore obtain that the threshold function is the regularised Eisenstein series \n\\begin{equation}}\\def\\ee{\\end{equation} \\hat{{\\cal E}}_{\\frac{1}{8}}^\\ord{1} =   \\frac{5}{108} \\hat{E}_{\\mbox{\\DEVI00000{\\mbox{$\\frac{9}{2}$}}}} \\ , \\ee\nsuch that the exact $\\nabla^6 R^4$ threshold function $E_{(0,1)}$ is \n\\begin{equation}}\\def\\ee{\\end{equation} E_{(0,1)} =  \\hat{{\\cal E}}_{\\gra{8}{1}} +  \\frac{5}{108}  \\hat{E}_{\\mbox{\\DEVI00000{\\mbox{$\\frac{9}{2}$}}}}  \\ .\\ee\nThe series $E{\\mbox{\\DEVI00000{s}}}$ admits a pole at $s=\\frac{9}{2}$ proportional to the series $E{\\mbox{\\DEVI{\\mathnormal{\\mbox{$\\frac{3}{2}$}}}0000{\\mathfrak{0}}}}$ defining the $R^4$ threshold, exhibiting that the $R^4$ invariant form factor diverges at two loop into the $\\nabla^6 R^4$ form factor associated to the same function. This is in agreement with \\cite{Pioline:2015yea}, where the explicit coefficient is computed. \n\n\n\n\\subsection{$\\mathcal{N} = (2,2)$ supergravity in six dimensions}\nWe shall now discuss these invariants in $\\mathcal{N}=(2,2)$ supergravity in six dimensions. We recall that the scalar fields parametrise in this case  the symmetric space $SO(5,5) \/ ( SO(5) \\times SO(5) )$. \n\\subsubsection{Linearised invariant}\nIn the linearised approximation, the theory is defined from the scalar superfield $L^{ij \\hi \\hj}$ in the  $[0,1] \\times [0,1]$ of $Sp(2) \\times Sp(2)$, where $i,j $ and $\\hat{\\imath},\\hat{\\jmath}$ run from $1$ to $4$ in the fundamental of the two respective $Sp(2)$. One can define a $\\nabla^6 R^4$ type invariant by considering harmonic variables $u^{1}{}_{i}, u^{r}{}_{i} ,u^{4}{}_{i}$ parametrising $Sp(2)\/(U(1)\\times Sp(1))$ associated to one $Sp(2)$ factor, with $r=2,3$ of $Sp(1)$, such that \\begin{equation}}\\def\\ee{\\end{equation}\n\\mathfrak{sp}(2)  \\cong {\\bf 2}^\\ord{-1}  \\oplus \\scal{  \\mathfrak{u}(1)  \\oplus \\mathfrak{sp}(1) }^\\ord{0}\\oplus {\\bf 2}^\\ord{1}   \\ , \\qquad \n{\\bf 4}  \\cong{\\bf  1}^{\\ord{-1}} \\oplus {\\bf 2}^{\\ord{0}} \\oplus {\\bf 1}^{\\ord{1}} \\ . \\ee\nOne can in this way introduce the G-analytic superfield \\cite{Bossard:2009sy}\n\\begin{equation}}\\def\\ee{\\end{equation}\nW^{r \\hi \\hj} = u^{1}{}_{i} u^{r}{}_{j} L^{ij \\hi \\hj} \\ , \n\\ee\nthat transforms in the fundamental of $Sp(1)$ and as a vector of $SO(5) \\cong Sp(2)\/\\mathds{Z}_2$, and satisfies to the $1\/8$ BPS G-analyticity  constraint \n\\begin{equation}}\\def\\ee{\\end{equation}\nu^1{}_i D^{i}_{\\alpha} W^{r, \\hi \\hj} = 0 \\  . \n\\ee\nA general polynomial in $W^{r, \\hi \\hj}$ decomposes into irreducible representations of $Sp(1)\\times Sp(2)$. Similarly as in lower dimensions, one shows that the latter are freely generated by $W^{r, \\hi \\hj}$ itself in the $[1]\\times[0,1]$ of $SU(2)\\times Sp(2)$, the two quadratic monomials \\begin{equation}}\\def\\ee{\\end{equation} \nW^{r \\hi \\hj} W^{s}{}_{\\hi \\hj} \\ , \\qquad  W^{r \\hi \\hk} W_{r}{}^{\\hj}{}_{\\hk} \\ , \\ee\nin the $[2]$ and the $[2,0]$, respectively, the cubic monomial \n\\begin{equation}}\\def\\ee{\\end{equation}\n W^{s \\hi \\hj }W^{r \\hk \\hl} W_{s \\hk \\hl} \\ , \\ee\nin the $[1]\\times[0,1]$, and the two quartic monomials \n\\begin{equation}}\\def\\ee{\\end{equation}\nW^{s \\hi \\hat{p}}\\def\\hq{\\hat{q}} W_{s}{}^{\\hj}{}_{\\hat{p}}\\def\\hq{\\hat{q}}   W^{p}{}_{\\hk}{}^{\\hq} W_{p \\hl \\hq} - \\frac{1}{6} \\delta^{\\hi \\hj}_{\\hk \\hl} W^{s \\hi \\hat{p}}\\def\\hq{\\hat{q}} W_{s}{}^{\\hj}{}_{\\hat{p}}\\def\\hq{\\hat{q}}   W^{p}{}_{\\hi}{}^{\\hq} W_{p \\hj \\hq} \n\\ , \\quad  W^{s \\hi \\hat{p}}\\def\\hq{\\hat{q}} W_{s}{}^{\\hj}{}_{\\hat{p}}\\def\\hq{\\hat{q}}   W^{p}{}_{\\hi}{}^{\\hq} W_{p \\hj \\hq}  \\ , \\ee\nin the $[0,2]$ and the singlet representation, respectively. One concludes that the most general monomial is labeled by 6 integers, such that \n\\begin{eqnarray}\n && \\int du D^{12} \\bar{D}^{16} F(u)^{[n_1 + 2 n_2 + n_3] [2 n'_2, n_1 + n_3 + 2 n_4]}_{[ 2 n'_2 + 2 n_3  + 4 n_4 + 4 n'_4 ,n_1 + 2 n_2 + n_3] [2 n'_2, n_1 + n_3 + 2 n_4]} \nW^{4 + n_1 + 2 n_2 + 2 n'_2 + 3 n_3 + 4 n_4 + 4 n'_4}_{[n_1 + 2 n_2 + n_3] [2 n'_2, n_1 + n_3 + 2 n_4]} \\nonumber \\\\*\n&=&  L^{n_1 + 2 n_2 + 2 n'_2 + 3 n_3 + 4 n_4 + 4 n'_4}_{[ 2 n'_2 + 2 n_3  + 4 n_4 + 4 n'_4 ,n_1 + 2 n_2 + n_3] [2 n'_2, n_1 + n_3 + 2 n_4]}\\nabla^{6} R^{4} + \\dots \n\\end{eqnarray}\nThe linear analysis therefore suggests the form of the nonlinear invariant \n\\begin{eqnarray}\n&& {\\cal L}_{\\grad410}[ {\\cal E}_{\\grad410}] \\\\\n&=& \\sum_{\\substack{ n_1,n_2,n^\\prime_2\\\\ n_3 ,n_4,n_4^\\prime}} {\\cal D}^{n_1 + 2 n_2 + 2 n'_2 + 3 n_3 + 4 n_4 + 4 n'_4}_{\\scriptscriptstyle [ 2 n'_2 + 2 n_3  + 4 n_4 + 4 n'_4 ,n_1 + 2 n_2 + n_3] [2 n'_2, n_1 + n_3 + 2 n_4]} {\\cal E}_{\\grad410} \n{\\cal L}_{\\grad410}^{\\scriptscriptstyle [ 2 n'_2 + 2 n_3  + 4 n_4 + 4 n'_4 ,n_1 + 2 n_2 + n_3] [2 n'_2, n_1 + n_3 + 2 n_4]}\\nonumber \\\\*\n&& +  \\sum_{\\substack{ n_1,n_2,n^\\prime_2\\\\ n_3 ,n_4,n_4^\\prime}} {\\cal D}^{n_1 + 2 n_2 + 2 n'_2 + 3 n_3 + 4 n_4 + 4 n'_4}_{\\scriptscriptstyle[2 n'_2, n_1 + n_3 + 2 n_4] [ 2 n'_2 + 2 n_3  + 4 n_4 + 4 n'_4 ,n_1 + 2 n_2 + n_3] } {\\cal E}_{\\grad410} \n{\\cal L}_{\\grad410}^{\\scriptscriptstyle [2 n'_2, n_1 + n_3 + 2 n_4][2 n'_2 + 2 n_3  + 4 n_4 + 4 n'_4 ,n_1 + 2 n_2 + n_3] }\\nonumber\n\\end{eqnarray}\nwhere we consider the possibility of a mixing between the invariant ${\\cal L}_{\\grad410}$ with its conjugate obtained by exchanging the two $Sp(2)$ factors, according to the observation in \\cite{D4R4} for the $\\nabla^4 R^4$ type invariant in eight dimensions. \n\nFrom this structure one deduces that supersymmetry requires the function ${\\cal E}_{\\grad410}$ to be an eigenfunction of the Laplace operator, and to satisfy equations of the form \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}^3_{[2,0],[2,0]} {\\cal E}_{\\grad410} \\propto  {\\cal D}^{\\; 2}_{[2,0],[2,0]} {\\cal E}_{\\grad410} \\ , \\qquad  {\\cal D}^3_{[0,1],[0,1]} {\\cal E}_{\\grad410} \\propto  {\\cal D}_{[0,1],[0,1]} {\\cal E}_{\\grad410} \\ , \\ee\nas well has a highest weight constraint \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}^{2k}_{[0,0],[0,2k]}  {\\cal E}_{\\grad410} = 0 \\ , \\label{HighestWeight} \\ee\nfor some integer $k$. We will see in the next section that the standard $\\nabla^6 R^4$ type invariant threshold function indeed satisfies to these equations for $k=2$. \n\\subsubsection{Decompactification limit from five to six dimensions}\nWe are now going to solve the differential equations  \\eqref{D6R4E6} and \\eqref{F2kD4R4E6}  for a function depending only of the Levi subgroup $\\mathds{R}_*^+\\times  SO(5,5)$ of the parabolic subgroup associated to the decompactification limit, such that \n\\begin{equation}}\\def\\ee{\\end{equation} \\mathfrak{e}_{6(6)}\\cong {\\bf 16}^\\ord{-3} \\oplus \\scal{ \\mathfrak{gl}_1 \\oplus \\mathfrak{so}(5,5) }^\\ord{0} \\oplus \\overline{\\bf 16}^\\ord{3} \\ , \\qquad \n{\\bf 27} \\cong {\\bf 10}^\\ord{-2} \\oplus {\\bf 16}^\\ord{1} \\oplus {\\bf 1}^\\ord{4} \\ .\\label{27D5}  \\ee\nThe covariant derivative on $E_{6(6)}\/Sp_{\\scriptscriptstyle \\rm c}(4)$ acting on such a function takes the block diagonal form \n\\begin{equation}}\\def\\ee{\\end{equation}\n{\\bf D}_{27} = \\text{diag} \\biggl(\\tfrac{1}{6} \\partial_{\\phi}, {\\bf D}_{16}+ \\tfrac{1}{24} {\\bf\\mathds{1}}_{16} \\partial_{\\phi}, {\\bf D}_{10} - \\tfrac{1}{12} {\\bf\\mathds{1}}_{10} \\partial_{\\phi}  \\biggr) \\ . \n\\ee\nTo check the differential equations \\eqref{D6R4E6} and \\eqref{F2kD4R4E6} we need to compute the block diagonal decomposition of the higher order differential operators. In order to do this computation we consider a general ansatz and determine all the free coefficients by consistency with the various differential equations displayed in appendix \\ref{TensorEquationsEd}. We obtain in this way \n\\begin{multline}\n{\\bf D}^{\\; 2}_{27} = \\text{diag} \\biggl(\\tfrac{1}{6^2} \\partial^{\\; 2}_{\\phi} + \\tfrac{1}{2} \\partial_{\\phi}\\,  ,\\   {\\bf D}^{\\; 2}_{16} + \\tfrac{1}{2}  {\\bf D}_{16} \\bigl(\\tfrac{1}{6} \\partial_{\\phi}+1\\bigr)  + \\tfrac{1}{16}  {\\bf \\mathds{1}}_{16}  \\bigl( \\tfrac{1}{6^2}  \\partial^{\\; 2}_{\\phi} + 3 \\partial_{\\phi} \\bigr) \\, , \\\\\n {\\bf D}^{\\; 2}_{10} -  {\\bf D}_{10} \\bigl(  \\tfrac{1}{6} \\partial_{\\phi} +1 \\bigr) + \\tfrac{1}{4} {\\bf\\mathds{1}}_{10} \\bigl(  \\tfrac{1}{6^2} \\partial^{\\; 2}_{\\phi} + \\partial_{\\phi} \\bigr) \\biggr)\n\\end{multline}\nand\n\\begin{multline}\n{\\bf D}^{\\; 3}_{27} = \\text{diag} \\biggl(\\tfrac{1}{6^3} \\partial^{\\; 3}_{\\phi} + \\tfrac{3}{16} \\partial^{\\; 2}_{\\phi} + \\tfrac{5}{4} \\partial_{\\phi} - \\tfrac{1}{2} \\Delta \\,,\\\\\n {\\bf D}^{\\; 3}_{16}\n+\\tfrac{3}{4}  {\\bf D}^{\\; 2}_{16} \\bigl(\\tfrac{1}{6} \\partial_{\\phi} +2 \\bigr)+  {\\bf D}_{16} \\bigl( \\tfrac{3}{16}\\scal{ \\tfrac{1}{6^2} \\partial^{\\; 2}_{\\phi} +2  \\partial_{\\phi}}+1 \\bigr)+ \\tfrac{1}{64} {\\bf\\mathds{1}}_{16} \\bigl( \\tfrac{1}{6^3}  \\partial^{\\; 3}_{\\phi} + \\tfrac{1}{2} \\partial^{\\; 2}_{\\phi} - 8 \\Delta \\bigr) \\, , \\\\  {\\bf D}^{\\; 3}_{10} - \\tfrac{3}{2}  {\\bf D}^{\\; 2}_{10} \\bigl( \\tfrac{1}{6} \\partial_{\\phi}  +2 \\bigr) \n + {\\bf D}_{10} \\bigl(\\tfrac{3}{4}  \\scal{ \\tfrac{1}{6^2} \\partial^{\\; 2}_{\\phi} + \\partial_{\\phi} }+\\tfrac{5}{2} \\bigr)- \\tfrac{1}{8} \n {\\bf\\mathds{1}}_{10} \\bigl( \\tfrac{1}{6^3} \\partial^{\\; 3}_{\\phi} +\\tfrac{1}{4} \\partial^{\\; 2}_{\\phi} +\\partial_{\\phi}-2\\Delta \\bigr)  \\biggr) \\ ,\n\\end{multline}\nwhere $\\Delta \\equiv \\text{Tr}\\,  {\\bf D}_{10}^{\\; 2}$. In order to determine the constraints on the threshold function is six dimensions, we consider an ansatz with the appropriate power of the radius modulus $e^{-3\\phi}$ such as to compensate for the Weyl rescaling to Einstein frame, {\\it i.e.}\\  \n\\begin{equation}}\\def\\ee{\\end{equation}\n{\\cal E}_{\\gra84} = e^{-6 \\phi}{\\cal E}_{\\grad422}\\ ,  \\qquad {\\cal E}_{\\gra81} = e^{-12 \\phi} {\\cal E}_{\\grad410} \\ . \n\\ee\nThe singlet component of \\eqref{D6R4E6} gives directly the Poisson equation \n\\begin{equation}}\\def\\ee{\\end{equation} \\label{E6D_laplace}\n\\Delta {\\cal E}_{\\grad410}  = - {\\cal E}^{\\; 2}_{\\grad422} \\ , \n\\ee\nwhich is indeed consistent with \\eqref{LaplaceE6}. Working out spinor and the vector equations, using the Poisson equation \\eqref{E6D_laplace}, one obtains similarly \n\\begin{equation}}\\def\\ee{\\end{equation} \\label{E6D}\n\\biggl( {\\bf D}^{\\; 3}_{16} - \\frac{3}{4} {\\bf D}_{16} \\biggr) {\\cal E}_{\\grad410}  = - \\frac{1}{4} {\\bf D}_{16} {\\cal E}^{\\; 2}_{\\grad422} \\ , \\qquad \n\\biggl( {\\bf D}^{\\; 3}_{10} -\\frac{3}{2} {\\bf D}_{10} \\biggr) {\\cal E}_{\\grad410}   = - \\frac{1}{4}  {\\bf D}_{10} {\\cal E}^{\\; 2}_{\\grad422} \\ . \n\\ee\nThe only Eisenstein function that solves this homogenous equation (for ${\\cal E}_{\\grad422} =0$) is the Eisenstein series $\\hat{E}{\\text{\\DSOX0{\\mbox{$\\frac{7}{2}$}}000}}$, but its  expansion in the string theory limit is inconsistent with perturbation theory. As is computed in appendix \\ref{DnAdj}, one has moreover\n\\begin{equation}}\\def\\ee{\\end{equation}  D^d{}_{\\hat{a}}\\scal{  {\\cal D}_{(a}{}^{\\hat{b}} {\\cal D}_{b|\\hat{b}} {\\cal D}_{c}{}^{\\hat{c}} {\\cal D}_{d)\\hat{c}} }|_{[0,4]} \\hat{E}_{\\text{\\DSOX0{\\mbox{$\\frac{7}{2}$}}000}} = 0 \\ , \\ee\nwhich defines an integrability condition for the function to decompose into the sum of two functions satisfying to \\eqref{HighestWeight} and its conjugate obtained by exchange of the two $Sp(2)$ for $k=2$. \n\n\nLet us now consider the differential equation \\eqref{F2kD4R4E6} for the function ${\\cal E}^{(k)}_{\\frac{1}{8}\\, E_6}$ defining the  $F^{2k} \\nabla^{4} R^4$ threshold function in five dimensions. Diffeomorphism invariance in six dimensions requires an ansatz of the form \n\\begin{equation}}\\def\\ee{\\end{equation}\n{\\cal E}^{(k)}_{\\frac{1}{8}\\, E_{6}} = e^{- 2(k+5)\\phi} {\\cal E}^{(k)}_{\\frac{1}{8}\\, D_5} \\ , \n\\ee\nand using this ansatz, one obtains from the singlet component of \\eqref{F2kD4R4E6} the Laplace equation \n\\begin{equation}}\\def\\ee{\\end{equation}\n\\Delta {\\cal E}^{(k)}_{\\frac{1}{8}} = \\frac{5}{2}  (k+3)(k-1) {\\cal E}^{(k)}_{\\frac{1}{8}} \\ , \n\\ee\nwhere we removed the $D_5$ label for simplicity. The spinor and the vector equations give then\n\\begin{eqnarray}\n\\biggl( {\\bf D}^{\\; 3}_{16} -\\frac{13  (k+3) (k-1)+24}{16} {\\bf D}_{16}  \\biggr) {\\cal E}^{(k)}_{\\frac{1}{8}}   &=& - \\frac{3(k+1)}{4}  \\Scal{ {\\bf D}^{\\; 2}_{16} -\\frac{5 (k+3) (k-1)}{16}   \\mathds{1}_{16} } {\\cal E}^{(k)}_{\\frac{1}{8}} \\ , \\nonumber \\\\*\n {\\bf D}^{\\; 2}_{10}  \\, {\\cal E}^{(k)}_{\\frac{1}{8}} &=&  \\frac{ (k+3) (k-1)  }{4} \\mathds{1}_{10} \\, {\\cal E}^{(k)}_{\\frac{1}{8}}   \\ ,\n\\end{eqnarray}\nwhere we used that the even and odd powers of ${\\bf D}_{10}$ lie in different irreducible representations of $Sp(2)\\times Sp(2)$, and must therefore vanish separately. The unique Eisenstein function satisfying to this equation is \n\\begin{equation}}\\def\\ee{\\end{equation}\n{\\cal E}^{(k)}_{\\frac{1}{8}} \\propto E_{\\mbox{\\DSOX{0}000{\\mbox{$k$+$3$}}}}\\, , \n\\ee\nconsistently with the decompactification limit of the five-dimensional function \n\\begin{equation}}\\def\\ee{\\end{equation}   E_{\\mbox{\\DEVI00000{k\\mbox{+}\\frac{7}{2}}}}    =2 \\zeta(2k+7)  e^{-4(2k+7) \\phi }   + \\frac{\\pi^\\frac{1}{2} \\Gamma(k+3)}{\\Gamma(k + \\frac{7}{2})} e^{- (2k+10)\\phi} E_{\\mbox{\\DSOX{0}000{\\mbox{$k$+$3$}}}} + \\dots \\ee\nWe conclude therefore that the exact $\\nabla^6 R^4$ function is defined as\n\\begin{equation}}\\def\\ee{\\end{equation} E_{(0,1)}= \\hat{{\\cal E}}_\\grad{4}{1}{0}+ \\hat{{\\cal E}}_\\grad{4}{0}{1} + \\frac{8}{189} \\hat{E}_{\\mbox{\\DSOX{0}000{\\mbox{$4$}}}}\\ , \\ee\nwhere $\\hat{{\\cal E}}_\\grad{4}{1}{0}$ satisfies to \\eqref{E6D}, and to an anomalous Poisson equation with an additional constant source term. This function is consistent with \\cite{Pioline:2015yea}, where the second Eisenstein function appears with this normalisation, and the 2-loop five dimensional threshold function must indeed solve \\eqref{E6D}, because the equation is parity invariant with respect to $O(5,5)$. \n\n\n\n\n\\subsection{$\\mathcal{N} = 2$ supergravity in seven dimensions}\nNone of the $\\nabla^6 R^4$ type invariants can be defined in the linearised approximation as harmonic superspace integrals in seven dimensions. We will therefore consider the uplift of the four-dimensional invariants in the decompactification limit. In seven dimensions the scalar fields parametrize the symmetric space $SL(5)\/SO(5)$, and the covariant derivative ${\\cal D}_{ij}$ transforms as a symmetric traceless tensor of $SO(5)$, with  $i, j = 1,\\dots,5$ of $SO(5)$. We consider therefore the parabolic subgroup of $E_{7(7)}$ of semi-simple Levi subgroup $SL(5) \\times SL(3)$ associated to the decomposition \n\\begin{eqnarray} \\label{133Graded}\n\\mathfrak{e}_{7(7)} &\\cong&  \\bar{{\\bf 5} }^\\ord{-6} \\oplus  ( {\\bf 3} \\otimes {\\bf 5})^\\ord{-4}  \\oplus   ( \\bar{ \\bf 3} \\otimes {\\bf \\overline{10}})^\\ord{-2}  \\oplus \\scal{  \\mathfrak{gl}_1 \\oplus \\mathfrak{sl}_3 \\oplus \\mathfrak{sl}_5 }^\\ord{0} \\oplus ( { \\bf 3} \\otimes { \\bf 10})^\\ord{2}\n\\oplus (\\bar{ \\bf 3} \\otimes \\bar{ \\bf 5})^\\ord{4} \\oplus { \\bf 5}^\\ord{6} \\nonumber \\\\*\n{\\bf 56} &\\cong&\\overline{\\bf 3}^\\ord{-5} \\oplus {\\bf 10}^\\ord{-3} \\oplus ({\\bf 3}\\otimes  \\overline{\\bf  5})^\\ord{-1} \\oplus (\\overline{\\bf 3}\\otimes {\\bf 5})^\\ord{1} \\oplus \\overline{\\bf 10}^\\ord{3} \\oplus {\\bf 3}^\\ord{5}\\ . \n\\end{eqnarray}\nWe will use the same conventions as in \\cite{D4R4}, where the decompactification limit of equations  \\eqref{CubicR} and \\eqref{E811Equation}  is already discussed in details. We consider the ansatz \n \\begin{equation}}\\def\\ee{\\end{equation}\n {\\cal E}_{\\grad{8}{1}{1}} = e^{- 36 \\phi} {\\cal E}_{\\frac{1}{8}} \\ , \\qquad    {\\cal E}_{\\grad{8}{4}{4}} = e^{- 18 \\phi} {\\cal E}_{\\gra{4}{2}} \\ , \n \\ee\nwith $ {\\cal E}_{\\frac{1}{8}}$ and ${\\cal E}_{\\gra{4}{2}} $ defined on $SL(5)\/SO(5)$, and the appropriate power of the volume modulus $e^{-3\\phi}$ required by diffeomorphism invariance in seven dimensions. The ${\\bf 3}^\\ord{3}$ component of the equation reduces to the Poisson equation \n\\begin{equation}}\\def\\ee{\\end{equation}\\label{Laplace7D} \n\\Delta {\\cal E}_{\\frac{1}{8}} \\equiv  2 {\\cal D}^{ij} {\\cal D}_{ij} {\\cal E}_{\\frac{1}{8}}  = \\frac{42}{5} {\\cal E}_{\\frac{1}{8}} - {\\cal E}^{\\; 2}_{\\gra{4}{2}} \\ . \n\\ee\nUsing this equation in the $ (\\overline{\\bf 3}\\otimes {\\bf 5})^\\ord{1} $ component of \\eqref{E811Equation}, one obtains \n\\begin{equation}}\\def\\ee{\\end{equation}\\label{Vec7D} \n\\biggl( {\\cal D}_{i}{}^{k} {\\cal D}_{k}{}^{l}  {\\cal D}_{l}{}^{j} + \\frac{1}{5} {\\cal D}_{i}{}^{k} {\\cal D}_{k}{}^{j} - \\frac{1053}{400} {\\cal D}_{i}{}^{j} +\\frac{177}{500} \\delta_{i}^{j} \\biggr) {\\cal E}_{\\frac{1}{8}} =\n\\frac{1}{4} \\biggl(\\frac{1}{10} \\delta_{i}^{j} - {\\cal D}_{i}{}^{j} \\biggr) {\\cal E}^{\\; 2}_{\\gra{4}{2}}  \\ . \n\\ee\nUsing moreover these equations to simplify the $ \\overline{\\bf 10}^\\ord{3}$ components, one obtains \n\\begin{equation}}\\def\\ee{\\end{equation} \\label{Tens7D}   \\Scal{ 6{\\cal D}^{[i}{}_{[k} {\\cal D}^{j]}{}_{p} {\\cal D}^{p}{}_{l]}  + \\frac{3}{10} {\\cal D}^{[i}{}_{[k} {\\cal D}^{j]}{}_{l]}} {\\cal E}_{\\frac{1}{8}} = \\frac{3}{5}  \\delta^{[i}_{[k} \\biggl(  {\\cal D}^{j]}{}_p {\\cal D}^p{}_{l]}  -\\frac{71}{20}{\\cal D}^{j]}{}_{l]} + \\frac{9}{25}  \\delta_{l]}^{j]} \\biggr) {\\cal E}_{\\frac{1}{8}}  \\ . \\ee\nThe solution to the homogenous equation (with $ {\\cal E}_{\\gra{4}{2}} =0$) can be written as the Eisenstein function $E_{\\scriptscriptstyle [3, 0,0,\\frac{5}{2}]}$, using the formulae of Appendix \\ref{SL5Review}. \n\nWe consider now the $F^{2k} \\nabla^4 R^4$ threshold function, with the ansatz \n\\begin{equation}}\\def\\ee{\\end{equation}\n{\\cal E}_{\\grad820}^\\ord{k} = e^{-6(k +5) \\phi}{\\cal E}_{\\frac{1}{8}}^\\ord{k} \\ . \n\\ee\nAppropriate linear combinations of the grad 6 and 4 components of \\eqref{CubicR} in \\eqref{133Graded} give the two equations \n\\begin{eqnarray} \\biggl( {\\cal D}_{i}{}^{k} {\\cal D}_{k}{}^{l}  {\\cal D}_{l}{}^{j}  + \\frac{1}{2}  {\\cal D}_{i}{}^{k} {\\cal D}_{k}{}^{j}  \\biggr) {\\cal E}_{\\frac{1}{8}}^\\ord{k}  &=&\\biggl( \\frac{16 k(7k+20) + 75}{400} {\\cal D}_{i}{}^{j} +\\frac{3 k(k+5)(2k+5)}{125} \\delta_{i}^{j}- \\frac{1}{40}  \\delta_{i}^{j} \\Delta  \\biggr) {\\cal E}_{\\frac{1}{8}}^\\ord{k}   \\nonumber \\\\*\nk \\,   {\\cal D}_{i}{}^{k} {\\cal D}_{k}{}^{j}  {\\cal E}_{\\frac{1}{8}}^\\ord{k}  &=& \\biggl(k \\frac{4k+5}{20} {\\cal D}_{i}{}^{j} +\\frac{3k(k+5)(2k+5)}{25} \\delta_{i}^{j} - \\frac{1}{2}  \\delta_{i}^{j} \\Delta \\biggr)     {\\cal E}_{\\frac{1}{8}}^\\ord{k}   \\ .  \\end{eqnarray}\nFor $k\\ge 1$ we conclude that the function must satisfy to the quadratic equation\n\\begin{equation}}\\def\\ee{\\end{equation}  \\label{fundamental_1}\n{\\cal D}_{i}{}^{p} {\\cal D}_{p}{}^{j} {\\cal E}_{\\frac{1}{8}}^\\ord{k} = \\frac{4 k + 5}{20} {\\cal D}_{i}{}^{j} {\\cal E}_{\\frac{1}{8}}^\\ord{k} + \\frac{3 k (2k + 5)}{25} \\delta_{i}^{j} {\\cal E}_{\\frac{1}{8}}^\\ord{k} \\ , \n\\ee\nsuch that \n\\begin{equation}}\\def\\ee{\\end{equation}\n\\Delta {\\cal E}_{\\frac{1}{8}}^\\ord{k} = \\frac{6 k (2k + 5) }{5} {\\cal E}_{\\frac{1}{8}}^\\ord{k} \\ . \n\\ee\nOne can then check that all the other equations implied by  \\eqref{CubicR} are indeed satisfied provided that \\eqref{fundamental_1} is.  This equation is satisfied by the Eisenstein function $E_{\\scriptscriptstyle [0,0,k + \\frac{5}{2},0]}$, which appears in the decompactification limit of the corresponding Eisenstein function on $E_{7(7)}\/ SU_{\\scriptscriptstyle \\rm c}(8)$, {\\it i.e.}\\  \n\\begin{equation}}\\def\\ee{\\end{equation}\nE_{\\mbox{\\DEVII000000{k\\mbox{+}4}}} =e^{- 10(k+4) \\phi} E_{\\scriptscriptstyle [k+4,0]}  +  \\frac{\\pi^{\\frac{3}{2}}\\Gamma(k+\\frac{5}{2})}{\\Gamma(k+4)}  e^{- 6(k+5) \\phi} E_{\\scriptscriptstyle [0,0,k + \\frac{5}{2},0]} + \\dots \n\\ee\nwhere the Eisenstein series is normalised with an extra  $2\\zeta(2s)$ factor with respect to the Langlands normalisation. We conclude therefore that the exact $\\nabla^6 R^4$ threshold function is \n\\begin{equation}}\\def\\ee{\\end{equation}  E_{(0,1)}  = {\\cal E}_{\\frac{1}{8}}  + \\frac{5 \\pi}{378} E_{\\scriptscriptstyle [0,0,\\frac{7}{2},0]}  \\ ,\\ee\nwhere ${\\cal E}_{\\frac{1}{8}}$ is a solution to (\\ref{Laplace7D},\\ref{Vec7D},\\ref{Tens7D}) in agreement with \\cite{Green:2010wi}.\\footnote{Note that the normalisation of the Eisenstein function $E_{\\scriptscriptstyle [0,0,s,0]} $ does not include the additional factor of $\\zeta(2s-1)$ as in  \\cite{Green:2010wi}.}\n\n\n\n\\subsection{$\\mathcal{N} = 2$ supergravity in eight dimensions}\nWe shall now consider the oxidation of the  seven-dimensional  $\\nabla^6 R^4$ and $F^{2n} \\nabla^4 R^4$ type invariants to eight dimensions. Because there is a 1-loop divergence in eight dimensions, the exact $R^4$ threshold function differs from the Wilsonian effective action function. In the dimensional reduction, the divergence appears to be absorbed into the infinite sum of Kaluza--Klein states over the circle such that the function is finite in seven dimensions, but involves a logarithm of the radius modulus in the decompactification limit \\cite{Green:2010sp}. In order to consider the non-analytic terms in eight dimensions, we will take these logarithms into account in the decompactification limit. \n\n\n We shall use the same conventions as in \\cite{D4R4}, {\\it i.e.}\\  the complex scalar field $\\tau$ parametrises the coset representative $v_\\alpha{}^j \\in SL(2) \/ SO(2)$, with $\\alpha, \\beta = 1,2$ of $SO(2)$ and $i,j = 1,2$ of $SL(2)$, whereas the five real scalar fields $t$ parametrise the coset representative $V^{a}{}_J \\in SL(3)\/SO(3)$, with $a, b = 1,2,3$ of $SO(3)$ and $I, J = 1,2,3$ of $SL(3)$. The corresponding covariant derivative in tangent frame are then traceless symmetric tensors ${\\cal D}_{\\alpha \\beta}$ and  ${\\cal D}_{a b}$, respectively. In the decompactification limit, one writes the  $SL(5)\/SO(5)$ coset element in the parabolic gauge \n \\begin{equation}}\\def\\ee{\\end{equation}\n{\\cal V} = \\left( \\begin{array}{cc} \\ e^{-3\\phi} v^{ \\scriptscriptstyle \\rm{\\mbox{\\tiny-1}}}_j{}^\\alpha  \\ &  \\ 0 \\ \\\\ \n\\  e^{2\\phi} V^a{}_K a_j^K & \\ e^{2\\phi} V^{a}{}_J \\ \\end{array} \\right) \\ , \n\\ee\nassociated to the graded decomposition \n\\begin{equation}}\\def\\ee{\\end{equation} \\mathfrak{sl}_5 \\cong ( {\\bf 2}\\otimes \\overline{\\bf 3})^\\ord{-5} \\oplus \\scal{ \\mathfrak{gl}_1 \\oplus \\mathfrak{sl}_2 \\oplus \\mathfrak{sl}_3}^\\ord{0} \\oplus  ( {\\bf 2}\\otimes {\\bf 3})^\\ord{5} \\ . \\ee\nIn this way one computes that the covariant derivative over $SL(5)\/SO(5)$ in tangent frame acts on a function of $\\phi, \\tau,t$ as \\cite{D4R4}\n\\begin{equation}}\\def\\ee{\\end{equation} {\\bf D}_{5}  =\\text{diag} \\left( -  \\tfrac{1}{20} \\partial_\\phi  \\delta_\\alpha^\\beta - {{\\cal D}}_\\alpha{}^\\beta,  \\tfrac{1}{30} \\partial_\\phi \\delta_a^b +{\\cal D}_a{}^b \\right) \\  .  \\ee\nOne computes that the higher order derivative operators obtained as products of ${\\bf D}_{5} $ in the ${\\bf 5}$ of $SL(5)$ decompose similarly as\n\\begin{multline} {\\bf D}^{\\; 2}_{5} = \\text{diag} \\biggl(  {{\\cal D}}_\\alpha{}^\\beta \\scal{\\tfrac{1}{10} \\partial_\\phi+ \\tfrac{3}{4} }+ \\scal{  \\tfrac{1}{400} \\partial_\\phi^{\\; 2} + \\tfrac{1}{16} \\partial_\\phi + \\tfrac{1}{2} {\\cal D}_{\\gamma\\delta} {\\cal D}^{\\gamma\\delta}  }   \\delta_\\alpha^\\beta , \\hspace{3 cm} \\\\ \n  {\\cal D}_a{}^c {\\cal D}_c{}^b + {\\cal D}_a{}^b \\scal{ \\tfrac{1}{15} \\partial_\\phi+\\tfrac{1}{2}  } +\\scal{ \\tfrac{1}{900}  \\partial_\\phi^{\\; 2} + \\tfrac{1}{24} \\partial_\\phi  }  \\delta_a^b \\biggr) \\ , \\end{multline}\nand\n\\begin{multline} {\\bf D}^{\\;3}_{5} = \\text{diag} \\biggl( - \\tfrac{1}{4}  {{\\cal D}}_\\alpha{}^\\beta \\scal{ \\tfrac{3}{10^2} \\partial_{\\phi}^{\\; 2}+ \\tfrac{7}{10} \\partial_\\phi  +\\tfrac{9}{4} +2  {\\cal D}_{\\gamma \\delta} {\\cal D}^{\\gamma \\delta}} \\\\\n\\hspace{10mm} - \\tfrac{1}{8}  \\scal{ \\tfrac{1}{10^3} \\partial_\\phi^{\\; 3} +\\tfrac{1}{30} \\partial_\\phi^{\\; 2}+\\tfrac{1}{8} \\partial_\\phi + 6  {\\cal D}_{\\gamma \\delta} {\\cal D}^{\\gamma \\delta} \\scal{ \\tfrac{1}{10}  \\partial_\\phi +1} -2 {\\cal D}_{a b} {\\cal D}^{a b}}   \\delta_\\alpha^\\beta\\ ,  \\\\ \n  {\\cal D}_a{}^c {\\cal D}_c{}^d  {\\cal D}_d{}^b +{\\cal D}_a{}^c {\\cal D}_c{}^b \\scal{\\tfrac{1}{10} \\partial_{\\phi} + 1} + \\tfrac{1}{3} {\\cal D}_a{}^b \\scal{ \\tfrac{1}{10^2} \\partial_\\phi^{\\; 2} +  \\tfrac{11}{40}\\partial_\\phi + \\tfrac{3}{4} }\\\\ + \\tfrac{1}{8} \\scal{ \\tfrac{1}{15^3}  \\partial_\\phi^{\\; 3} + \\tfrac{1}{180} \\partial_\\phi^{\\; 2} -\\tfrac{1}{12} \\partial_\\phi -2 {\\cal D}_{\\alpha \\beta} {\\cal D}^{\\alpha \\beta} }  \\delta_a^b \\biggr) \\ . \\end{multline}\nWe can now solve equation \\eqref{Vec7D} in the docompactification limit, with $ {\\cal E}_{\\frac{1}{8}}(\\phi,\\tau,t)$ and \\cite{Green:2010wi}\n\\begin{equation}}\\def\\ee{\\end{equation}  {\\cal E}_{\\gra{4}{2}}  = e^{-6\\phi} \\Scal{ 2 \\hat{E}_{[1]}(\\tau) + \\hat{E}_{[\\stfrac{3}{2},0]}(t) - 20 \\pi ( \\phi - \\phi_0)} \\ , \\ee\nwhere $\\phi_0$ is a constant that depends on the renormalisation scheme. Using the property that \n\\begin{equation}}\\def\\ee{\\end{equation} {\\cal D}_{ac} {\\cal D}^{bc}   \\hat{E}_{[\\stfrac{3}{2},0]}(t)  = - \\frac{1}{4} {\\cal D}_a{}^b   \\hat{E}_{[\\stfrac{3}{2},0]}(t)  + \\frac{2\\pi}{3} \\ , \\qquad 2 {\\cal D}_{\\alpha\\beta} {\\cal D}^{\\alpha\\beta}  \\hat{E}_{[1]}(\\tau) = \\pi \\ , \\ee\none shows that the general solution to \\eqref{Vec7D}, as a function of $\\phi, \\tau$ and $t$ takes the general form \n\\begin{multline}  {\\cal E}_{\\frac{1}{8}}(\\phi,\\tau,t) = e^{-12\\phi} \\biggl(\\hat{{\\cal F}}_{[4]}(\\tau)  +\\hat{{\\cal F}}_{[4,-2 ]}(t) + \\frac{1}{3} \\hat{E}_{[1]}(\\tau) \\hat{E}_{[\\stfrac{3}{2},0]}(t) + \\frac{\\pi}{18} \\Scal { \\hat{E}_{[1]}(\\tau)  + \\frac{19\\pi}{12}} \\biggr . \\\\ \\biggl .  - \\frac{10\\pi}{3} ( \\phi - \\phi_0 ) \\Scal{2 \\hat{E}_{[1]}(\\tau) + \\hat{E}_{[\\stfrac{3}{2},0]}(t)  + \\frac{\\pi}{3}} + \\frac{100\\pi^2}{3} ( \\phi- \\phi_0)^2\\biggr)  \\ ,  \\end{multline} \nwhere ${\\cal F}_{[4]}(\\tau)$ and ${\\cal F}_{[4,-2 ]}(t)$ are solutions to \n\\begin{eqnarray} \\Delta\\hat{{\\cal F}}_{[4]}(\\tau) &=& 12\\hat{{\\cal F}}_{[4]}(\\tau)  - ( \\hat{E}_{[1]}(\\tau))^2 \\ , \\qquad  \\Delta\\hat{{\\cal F}}_{[4,-2 ]}(t)  = 12\\hat{{\\cal F}}_{[4,-2 ]}(t) -(  \\hat{E}_{[\\stfrac{3}{2},0]}(t) )^2 \\ , \\nonumber \\\\*\n{\\cal D}_{ac} {\\cal D}^{cd} {\\cal D}_{db} \\hat{{\\cal F}}_{[4,-2 ]}(t)  &=& \\frac{49}{16} {\\cal D}_{ab}\\hat{{\\cal F}}_{[4,-2 ]}(t) - \\frac{3}{2} \\delta_{ab}\\hat{{\\cal F}}_{[4,-2 ]}(t) - \\frac{1}{2}   \\hat{E}_{[\\stfrac{3}{2},0]}(t)  {\\cal D}_{ab}   \\hat{E}_{[\\stfrac{3}{2},0]}(t)  \\nonumber \\\\*\n&& \\hspace{30mm} + \\frac{1}{2} \\delta_{ab} \\Scal{ \\frac{1}{4} (  \\hat{E}_{[\\stfrac{3}{2},0]}(t) )^2 + \\frac{\\pi}{9}  \\hat{E}_{[\\stfrac{3}{2},0]}(t)  + \\frac{\\pi^2}{27} } \\ . \\end{eqnarray}\nHere the notation is used to emphasize that these solutions are defined modulo the homogeneous solutions $E_{[4]}(\\tau)$ and $E_{[4, -2]}(t)$, respectively, as one can see using the formulae of Appendix \\ref{SL3Equa}. Note nonetheless that these homogeneous solutions are inconsistent with the string  theory perturbation expansion, and the exact threshold function is uniquely determined by these equations and consistency with string theory \\cite{Basu:2007ck}. \n\nThe structure of the threshold function exhibits that there is a 1-loop divergence of the $R^4$ type invariant form factor proportional to the $\\nabla^6 R^4$ type invariant. This implies the presence of an addition renormalisation scheme ambiguity in the definition of the analytic part of the effective action. It appears that the renormalisation scheme used in \\cite{Green:2010wi,Basu:2007ck}, cannot be obtained by simply neglecting the terms in $\\phi-\\phi_0$, but one finds nonetheless that the threshold function only differs by terms proportional to the linear and the quadratic term in  $\\phi-\\phi_0$, {\\it i.e.}\\  \n\\begin{multline}  \\hat{ {\\cal E}}_{\\frac{1}{8}}(\\tau,t) = \\hat{{\\cal F}}_{[4]}(\\tau)  +\\hat{{\\cal F}}_{[4,-2 ]}(t) + \\frac{1}{3} \\hat{E}_{[1]}(\\tau) \\hat{E}_{[\\stfrac{3}{2},0]}(t) + \\frac{\\pi}{18} \\Scal { \\hat{E}_{[1]}(\\tau)  + \\frac{19\\pi}{12}}  \\\\ +\\frac{\\pi}{36}  \\Scal{2 \\hat{E}_{[1]}(\\tau) + \\hat{E}_{[\\stfrac{3}{2},0]}(t)  - \\frac{5\\pi}{2}} \\ . \\end{multline} \n\n\n\nLet us now consider the oxidation of the $F^{2k} \\nabla^4 R^4$ type invariants, {\\it i.e.}\\  solve the differential equation \\eqref{fundamental_1} for a function of the form $e^{- (10 + 2k) \\phi}{\\cal E}_{\\frac{1}{8}}^\\ord{k}(\\tau, t)$, as required by diffeomorphism invariance in eight dimensions. One obtains straightforwardly \n\\begin{eqnarray}\n  2 {\\cal D}_{\\alpha \\beta} {\\cal D}^{\\alpha \\beta} {\\cal E}^\\ord{k}_{\\frac{1}{8}}(\\tau,t)  &=& (1 + k) (2 + k){\\cal E}^\\ord{k}_{\\frac{1}{8}}(\\tau,t)   \\ ,  \\nonumber \\\\*\n{\\cal D}_{a}{}^{c} {\\cal D}_{c}{}^{b}{\\cal E}^\\ord{k}_{\\frac{1}{8}}(\\tau,t)  &=& \\frac{(5 + 4 k)}{12} {\\cal D}_{a}{}^{b}  {\\cal E}^\\ord{k}_{\\frac{1}{8}}(\\tau,t)+ \\frac{(2 + k)(1 + 2 k)}{9} \\delta_{a}^{b} {\\cal E}^\\ord{k}_{\\frac{1}{8}}(\\tau,t) \\ . \n\\end{eqnarray}\nUsing the results of Appendix \\ref{SL3Equa} one obtain that the solution can be written in terms of Eisenstein functions as\n\\begin{equation}}\\def\\ee{\\end{equation}\n{\\cal E}^\\ord{k}_{\\frac{1}{8}}(\\tau, t) \\propto  E_{[k + 2]}(\\tau) E_{[0, k+2]}(t) \\ , \n\\ee\nconsistently with the decompactification limit of the $SL(5)\/SO(5)$ Eisenstein function \\cite{D4R4},\n \\begin{multline}  E_{[0,0,k + \\stfrac{5}{2},0]} =2 \\zeta( 2k+5)\\zeta(2k+4)  e^{-6(2k+5) \\phi} + \\frac{2\\pi^2 \\zeta(2k+2)}{(2k+3)(k+1)}  e^{8k \\phi} E_{[k+\\stfrac{3}{2},0]}(t) \\\\  +\\frac{\\sqrt{\\pi} \\Gamma(k+2)}{2\\Gamma(k + \\stfrac{5}{2})}  e^{-2(k+5) \\phi} E_{[k+2]}(\\tau) E_{[0,k+2]}(t)  + \\mathcal{O}(e^{- e^{-5 \\phi}}) \\ . \\end{multline}\nThe sum of the two functions reproduces correctly the threshold function obtained in \\cite{Green:2010wi,Basu:2007ck}. \n\n\n\n\\section*{Acknowledgment}\nWe would like to thank Axel Kleinschmidt and Boris Pioline for useful discussions, and are particularly grateful to Axel Kleinschmidt for providing some explicit relations between Eisenstein series. \n\n        \n\n ","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nRecent changes of the law in China and Turkey mean that their current leaders (President Xi Jinping and President Recep Tayyip Erdo\\^{g}an respectively) may hold onto their positions indefinitely. Conversely, in other countries the leader may change relatively often; for instance the UK has had five different Prime Ministers between the years 2007-2019. Among smaller groups some, such as private companies, have a permanent leader while other groups, such as university departments or social societies, have more transient and flexible leadership structures. \n\nA notable feature of many human groups is that they often do not explicitly coerce their members to join a hierarchy. Instead, soft power and prestige play a strong role \\cite{sapolsky_social_2004,van_vugt_evolutionary_2015}, with status being an abstraction of more tangible material resources such as land, food, weapons or other commodities \\cite{lin_social_2002}. Status is then voluntarily conferred upon leaders by those they are allied with \\cite{hawley_ontogenesis_1999,henrich_evolution_2001,lin_social_2002,pratto_social_2006,castells_network_2011,fiske_virtuous_2014,henrich_secret_2015,van_vugt_evolutionary_2015}, with many of these alliances being asymmetric \\cite{hall_asymmetric_1985,henrich_evolution_2001,henrich_secret_2015,van_vugt_evolutionary_2015,holekamp_aggression_2016}. The member with the highest status usually deemed the leader \\cite{hawley_ontogenesis_1999,pratto_social_2006,fiske_virtuous_2014,van_vugt_evolutionary_2015}, creating hierarchical societies. What is not clear, however, is what factors determine why some groups have no leader, others have transient leaders and yet others have relatively permanent leaders.\n\nA notable example of a shift between different forms of leadership dynamics is found from evidence from the Neolithic Era. Before this era, human societies consisted of egalitarian hunter-gatherer groups where material resources such as food were shared relatively equally \\cite{jaeggi_reciprocity_2013}\nand leadership roles were facultative and of a temporary duration. There followed a transition to sedentary groups where high-status individuals had more resources but leaders still changed relatively regularly \\cite{bar-yosef_sedentary_2001}. Finally, hereditary leadership became institutionalised, where the role of a chief was passed down a paternal line, which monopolised most of the resources \\cite{earle_how_1997}. Many scholars argue that these shifts were due to social and technological developments, which meant that interactions between individuals became increasingly asymmetric. These asymmetries were likely due to control of agricultural surpluses \\cite{carneiro_theory_1970,testart_significance_1982,boone_competition_1992,kaplan_hillard_s._evolutionary_2009}, land \\cite{carneiro_theory_1970}, ideologies \\cite{cauvin_birth_2001}, or military units and weapons \\cite{earle_how_1997}.  In light of this evidence, the model we present here investigates how asymmetry in status interaction can generate the different classes of leadership dynamics observed during the Neolithic Era.\n\nNetwork analysis has proved to be a useful approach for studying the interactions of members of a population \\cite{lin_social_2002,latour_reassembling_2007,castells_network_2011}. Quantitative study of hierarchical networks studied is usually static in nature and they are presented as snapshots in time \\cite{padgett_robust_1993,albert_statistical_2002}. However, members of a population will often change their properties and who they interact with over time. Recently, a number of studies have concentrated on the dynamical properties of networks \\cite{gross_adaptive_2008,bryden_stability_2011}. To look at the factors behind different types of leadership dynamics, we build on this work to model a dynamic coevolutionary network which incorporates the status of individuals as properties of the nodes and links between individuals representing alliances.\n\n\\section{Model}\n\nThe model consists of a dynamic network of $n$ individuals and is based on the following five assumptions: 1. individuals are equivalent to one another in every way and are unable to coerce one another to form alliances; 2. each individual has a status level which depends on their associations with others, meaning that status is adjusted according to the status of those who they are linked to; 3. individuals share a proportion of their status amongst those they are linked with; 4. status can be asymmetrically passed from one individual to another; 5. individuals can change who they associate with according to the marginal utility of the associations.\n\nEach individual $i$ maintains a status $s_i$ which translates to how much influence they have within the group. Status acts as a multivariate aggregate of an individual's level of money, prestige (titles, jobs, etc), and ownership (land, valuable resources, etc). We assume that, to participate in society, an individual must maintain relationships where they choose a fixed number (constant for all individuals) of associations with other individuals. Consequently, in our model, each individual is given $\\lambda$ unidirectional `outgoing' links which are assigned to others in a network. Individuals can have any number of `incoming' links from others in the network. \n\nThe statuses of the individuals are updated according to their links in the status update stage, and individuals are then given an opportunity to rewire their links in the rewiring stage. The model is then run forward in time to observe the distribution of status and changes of that distribution amongst the individuals. We especially looked for `leader' individuals with high status and checked to see whether they were superceded by other leaders. We ran models until patterns of leadership dynamics had stabilised, or for a substantially long time (up to 5 million time steps) to check that new leaders were extremely unlikely to rise to high status.\n\n{\\bf Status update stage:} In the model, a proportion of $r$ of each individual's status is shared amongst each of its links (including both incoming and outgoing links). This formalisation of sharing status amongst links is based on Katz's prestige measure \\cite{katz_new_1953}. For each link, we calculate that link's status by adding the status contribution from the outgoing individual (for whom the link is outgoing) to the status contribution from the incoming individual. To model unequal alliances we introduce the \\emph{inequality parameter} $q$ which reassigns the link's status back to those linked to unequally. A proportion $q$ of a link's status is assigned to the incoming individual, with a proportion $(1-q)$ remaining with the outgoing individual. In this formulation, the total amount of status in the model is constant, and because every status is initialised at $s_i =1.0$, the sum always equals $n$, i.e., $\\sum_i s_i=n$.\n\n{\\bf Rewiring phase: } In order to maximise status, each individual determines the outgoing link which is worth the least value to itself.  This link is rewired randomly, with probability $w$, to an individual with whom they are not currently linked. The assumption of random rewiring reflects the fact that an individual is unlikely to be able to tell the value of an association with another until they have formed the link.\n\n\n\\section {Results}\n\nIn the following, we will present our analysis of the dynamics that result from the interplay between the processes outlined above. Simulations were run of the model choosing parameter values over a complete range. Depending on the parameters, we either observe relatively equal statuses among the population, or a relatively high status level for one or a few individuals. An example of a typical network with a single dominant individual can be seen in Fig. 1. \n\n\\begin {figure}\n  \\includegraphics[width=0.5\\textwidth]{figure_1.png}\n  \\caption{A plot of the network showing a single individual with a high level of status compared to the others. Individuals with higher status are lighter coloured and have larger circles. }\n\\end {figure}\n\nA key parameter in the model is the inequality parameter ($q$), which models an unequal transfer of status from a link originator to a link receiver. This parameter can represent how social and technological development in the Neolithic Era created inequalities in interactions. As we increase $q$, theory predicts different phases of dynamics in the model, which are shown in \\figreftext{2}. We dub the individual with the highest level of status as the leader. We find three different types of leadership dynamics in the model: No leader, transient leader(s), and permanent leader(s).\n\n\\begin {figure}\n  \\includegraphics[width=0.5\\textwidth]{figure_2.png}\n  \\caption{Increasing the inequality takes the model through five different phases. First there is effectively no leader at all (panel A). Then we see that a single individual can rise to a high leadership status, but this is transient and leaders are replaced by other individuals (panel B). The length of time that individuals stay as leader then increases as we increase $q$ until the leader is effectively permanently in charge (panel C). In the next phase, a second individual can rise to a high status alongside the first leader, but these individuals' leadership position is transient (panel D). Finally, two individuals share leadership status and remain so permanently (panel E). \nThe value of $q$ is shown, other parameters are $r=0.2$, $n=50$, $\\lambda=3$, $w=0.5$. }\n\\end {figure}\n\n\nThe dynamics shown in Fig. 2 panel B indicate that as one leader is removed, this can create a power vacuum which leads to a new leader quickly gaining status. We have produced a video animation of the model of this phase of the model which is available at www.youtube.com\/watch?v=LrQWDhjwsYA. To investigate how the model transitions in and out of this phase, we looked in more detail at how the numbers of leaders and the lengths of time that they were leaders varied over different levels of the inequality parameter ($q$). We calculated the distributions of the different numbers of leaders over a threshold status level ($s_i > 3.0$) and the median length of time new leaders stay over the threshold after they have become the highest status individual. These are plotted in \\figreftext{3} with varying numbers of links originating from each individual ($\\lambda$). The plot demonstrates there are ranges of the inequality parameter ($q$) where leader turnover is relatively high, but the number of leaders is relatively constant. This shows that there is a power-vacuum effect in our model.\n\n\\begin {figure}\n  \\includegraphics[width=0.5\\textwidth]{figure_3.png}\n  \\caption{During transient periods, as one leader loses status, another quickly replaces it. Increasing the inequality parameter increases the time that leaders stay above the status level. The lines in panel {\\bf A} show the mean numbers of leaders over a threshold status level throughout a complete run of the model. For each value of $q$, vertical boxes indicate the relative proportion of timesteps with each number of leaders, for instance the width of $\\approx 0.98$ at $q=0.532$ and $\\lambda=3$ indicates that there was generally only one leader above the threshold throughout the simulation. Panel {\\bf B} shows the mean time that an individual stays above the threshold after they have reached highest status.Leader turn over was quite high at $q=0.532$ with the average leader lasting 7000 time steps with simulations run over 2 million time steps. Parameters as in \\figreftext{2} unless shown.\n  }\n\\end{figure}\n\n\nTo understand the dynamics created by the model in more detail, we compare them to a simpler model of a branching process. Branching processes specify the rates at which an individual with $x_i$ links acquires or loses links. In such processes, we observe a power-law distribution of the number of links when the link gain rate is close to the loss rate. We observe such a power law distribution when this is the case in our model (see Fig. 4, panel A). The formation of a hump in the distribution to the right is also consistent with branching processes with a reflecting boundary. However, the results suggest our model is not simply a superposition of branching processes for each individual. A superposition would not explain why we find a power vacuum effect, where there is always a leader which changes identity over time (see, e.g., \\figreftext{3}, $q=0.532$, $\\lambda=3$). The reason the power vacuum happens is because the presence of a leader suppresses the others (see \\figreftext{4} panel {\\bf B}), which is due to the relatively high number of links to the leader.\n\n\n\\begin {figure}\n  \\includegraphics[width=0.5\\textwidth]{figure_4.png}\n  \\caption{Frequency distributions of the numbers of links to individuals demonstrate how individuals show critical behaviour of a branching process over a range of values of $q$ (panel {\\bf A}. There is a truncated power law distribution with exponent $\\approx -8.0$ on panel {\\bf A} at a relatively low level of $q=0.525$. At higher levels of $q$  we can see how dominant individuals will suppress others to subcritical behaviour (panel {\\bf B}). We can see how the rewiring of links to an extra leader between $q=0.54$ and $q=0.55$ (see \\figreftext{3} panel {\\bf A}) suppresses the frequencies of individuals with mid-range number of links as $q$ is increased. Parameters are the same as in \\figreftext{2}, $q$ as shown.  Simulations were run over 2 million time steps.}\n\\end{figure}\n\n\nIn order to check whether our model is consistent with evidence from the Neolithic Era, we looked to see if the increase in leadership time-length is consistent over a wide range of parameters and that our results can be found in large groups. We ran simulations over a wide range of parameters to investigate the role of each parameter on the dynamics. Over each simulation run, we recorded the number of times there was a change of leader. We counted new leaders when they hadn't been one of the previous $l-1$ leaders. Our results confirm that as we increased the inequality parameter, we recorded fewer leaders as individuals spend longer time periods as leader. The full range of parameters are presented in the Supplementary Material (see Figures S1-9).\n\n\\section{Discussion}\n\nThe model presented here demonstrates a rich set of leadership structure dynamics amongst individuals in a non-coercive environment. The model reveals an interesting phase where competition to be leader is suppressed by the temporary presence of one leader, meaning that when a leader loses status it will be quickly replaced. We show how the dynamics can depend on the level of inequality of alliances between individuals, and on the numbers of alliances an individual can form. This suggests that technology and social norms can modulate such a system and implies that self-organisation in a society can play a role in keeping a system near to an equilibrium point where leadership changes relatively frequently.\n\nThis work pushes forward our understanding of hierarchies in human networks. This is currently largely based on static networks which are formed by preferential-attachment where nodes are more likely to connect to other nodes which are already of high status \\cite{albert_statistical_2002}. Our model presents an alternative where the hierarchy is dynamic: nodes have high numbers of connections (alliances) at some points and then other nodes take over. \n\nThis work also contributes new insights into the Neolithic transitions in human societies from relatively flat power structures, through a period where leaders changed over time, to dominant institutionalised leaders \\cite{bar-yosef_sedentary_2001}.  Our model presents a potential explanation for this, given that status would be closely linked to control of food or other monopolisable resources. Contemporary to the political transitions were innovations in agriculture, which enabled a high status individual to control a large food surplus. These high status individuals were able to feed a large number of supporters at relatively little cost to themselves, for example funding a military, enabling them to maintain and eventually institutionalise their power.  Monopolisable resources could also be less tangible, such as religious authority \\cite{cauvin_birth_2001} however the evidence suggests these changes followed technological advances \\cite{whitehouse_complex_2019}. In either case, the growth of population size and the transition to a sedentary, agricultural, lifestyle would have made it more difficult for followers to leave their group and hence easier for a dominant individual to monopolise \\cite{carneiro_theory_1970,powers_evolutionary_2014}. These factors, especially the ability to monopolise resources, relate to a high level of the inequality parameter ($q$) in our model as the leader individual is able to form alliances where they exchange a small proportion of these resources to gain loyalty from their supporters.\n\nThe three phases of human leadership dynamics correspond to three phases identified in the organisational psychology literature. Lewin has identified three modes of leadership: Laissez Faire, Democratic and Autocratic \\cite{lewin_patterns_1939}. In this analysis, the Laissez Faire mode was found to be the case where there is no central resource to coordinate and corresponds to the no-leader phase. When there is a central resource, our model predicts that those individuals with higher status are able to control this central resource, and thus not lose out when more individuals join their group. This is because a controlled surplus of this central resource enables a leader to pay off many individuals and maintain their leadership \\cite{bueno_de_mesquita_logic_2005}. The ability to control a central resource means that such groups will switch from the Laissez Faire mode to more Democratic and Autocratic modes. \n\nIn this paper we focussed primarily on applying this model to develop insights regarding the Neolithic transitions from flat power structures to hierarchical societies.  Future work can build upon these foundations to examine whether this model can be applied to other changes in societal structure, such as the movements from monarchy toward parliamentary democracies in 18th-century Europe, or the transitions of Roman civilization betwween monarchy, through annually electing two concurrent consuls in the Roman Republic, to a single Imperator Caesar in the Roman Empire.  Other work might investigate the impact of relaxing some of our assumptions. For instance, exploring different rewiring rules where individuals have different numbers of links, or rewire to others based on a similar or higher levels of status or numbers of links. The model also can be extended in various ways to better represent the real-world contexts in which leadership dynamics operate; these could include representations of technological innovations, changes in social norms, or power struggles between potential leaders.  These extensions would enable us to develop the model further into a powerful exploratory tool for human leadership dynamics. \n\n\\bibliographystyle{unsrt}  \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\\section{Introduction}\n\\label{sec:intro}\n\nAn accurate description of excited nucleons and their interaction with probes such as photons at GeV energies has remained elusive for decades.   \nThe standard model~\\citep{Gross:1973id,Politzer:1973fx} underpins the structure of the \nnucleons and their excitations, but in the low-energy non-perturbative regime, competing semi-phenomenological models of specific\nreaction dynamics are all that are available.  Present-day  \nlattice QCD calculations~\\citep{Edwards:2011jj, Edwards:2012fx} and quark models~\\citep{Capstick:2000qj, Capstick:1998uh, Capstick:1986bm,Loring:2001kx,Glozman:1997ag, Giannini:2001kb} predict a richer baryon spectrum than experimentally observed~\\citep{Patrignani:2016xqp, Klempt:2009pi,Koniuk:1979vw}: the so-called {\\it missing resonance problem}.  There are theoretical approaches to the nucleon resonance spectrum that predict that some quark-model states do not exist, including models with quasi-stable diquarks~\\citep{Anselmino:1992vg},\nAdS\/QCD string-based models~\\citep{Brodsky:2006uq}, and ``molecular'' models in which some baryon resonances are dynamically generated from\nthe unitarized interaction among ground-state baryons and mesons~\\citep{Kolomeitsev:2003kt}.\nBut finding such missing states may in part be an experimental problem:  high-mass nucleon resonances may couple weakly to $\\pi N$ and may thus have escaped detection in the analysis of $\\pi N$ elastic scattering experiments.\nFurther, they are wide and overlapping,  and partial-wave analysis (PWA) of reaction data for specific final states remains difficult due to channel-coupling effects and insufficient experimental constraints.\nThe experimental results discussed here represent one step in the direction of adding constraints to the hyperon photoproduction database, which ultimately impacts models for nucleon excitations.  \n\nCross-section measurements alone are not enough to constrain PWA models of meson production amplitudes.  Polarization observables related to the spins of the beam photons, target, and recoiling baryons are also needed.\nPhotoproduction of pseudoscalar mesons is governed by four complex amplitudes that lead to an interaction cross sections and 15 spin observables~\\citep{Chew:1957tf, Barker:1975bp,Fasano:1992es, Chiang:1996em, Keaton:1996pe, Sandorfi:2010uv, Nys:2016uel}.  \nA \\textit{mathematically complete} experiment would require data, with negligible uncertainties, on a minimum of eight well-chosen observables at each center-of mass (c.m.) energy, $W$,  and meson polar angle, $\\cos \\theta_{c.m.}$. In practice, with realistically achievable uncertainties, measurements of many more are needed to select between competing partial wave solutions, and even knowledge of the sign of an asymmetry can provide valuable discrimination~\\cite{Sandorfi:2010uv}. Furthermore, avoiding ambiguities in PWA solutions requires measurements of observables from each spin configuration of the three combinations of beam-target, target-recoil, and beam-recoil polarization~\\cite{Sandorfi:2010uv, Nys:2016uel}.\n\nFurthermore, while isospin $I=3\/2$ transitions ($\\Delta^*$ excitations) can be studied with proton target data alone, both proton- and neutron-target\nobservables are necessary to study $I=1\/2$ transitions and isolate the separate $\\gamma p N^*$ proton and $\\gamma n N^*$ neutron photo-couplings~\\citep{Sandorfi:2013cya}.\nInformation from neutron targets is comparatively scarce~\\citep{ Anisovich:2017afs},  particularly in the hyperon channels~\\citep{Compton_PhysRevC.96.065201,  AnefalosPereira:2009zw},\nwhich is why the present measurement is of value.   Furthermore, the hyperon photoproduction channels   $\\gamma N\\rightarrow K \\Lambda (\\Sigma^{0})$\nare  attractive for analysis for two reasons.  First,  the threshold for two-body hyperon final states is at $W \\simeq 1.6$~GeV, above which lie numerous poorly known resonances.   Two-body strange decay modes, rather than cascading non-strange many-body decays, may be easier to interpret.\nSecond, the hyperon channels give easy access to recoil polarization observables on account of their self-analyzing weak decays.  While the present work  does not involve measurement of hyperon polarizations, previous work has shown the benefit of using such information to extract properties of higher-mass nucleon resonances~\\citep{Paterson:2016vmc,Bradford_CxCz, Bradford_xsec, McNabb, Anisovich:2007bq, Paterson:2016vmc, McCracken, Dey, Anisovich:2017ygb}.  Thus, \npursuing ``complete\" amplitude information in the hyperon photoproduction channels can be complimentary to the analogous quest in, say, pion photoproduction.\n\nIn this article, we present first-time measurements of the beam-target observable $E$ on a longitudinally polarized neutron bound in deuterium in the quasi-free reaction $\\gamma n(p) \\to K^0Y(p)$.\nThe helicity asymmetry $E$  is formally defined as the normalized difference in photoproduction yield between  antiparallel ($\\sigma^{A}$) and parallel ($\\sigma^{P}$) configurations, {\\it i.e.},  settings where the incident photon beam polarization is antialigned or aligned, respectively, with the longitudinal polarization of the target.  Following Ref.~\\cite{Barker:1975bp} and Ref.~\\cite{Sandorfi:2010uv}  write \n\\begin{equation}\nE=\\frac{\\sigma^{A}-\\sigma^{P}}{\\sigma^{A}+\\sigma^{P}}.\n\\end{equation}\nThis helicity asymmetry, $E$, is related to the  cross section by\n\\begin{equation}\n\\left(\\frac{d\\sigma}{d\\Omega}\\right)=\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{0}\\left(1-P_{T}P_{\\odot}E\\right),\n\\label{equation2}\n\\end{equation}\n %\nwhere $\\left(d\\sigma \/ d\\Omega\\right)_{0}$ is the differential cross section averaged over initial spin states and summed over the final states, and $P_{T}$\nand $P_{\\odot}$ are the target longitudinal and beam circular polarizations, respectively. \n\nThe asymmetry results obtained are compared with several model predictions.  The first is a single-channel effective Lagrangian approach,  \nKaonMAID~\\citep{Mart:1999ed,Lee:1999kd}, with parameter constraints largely imposed from SU(6).  Without experimental constraints on the $N^* \\Lambda K^0$ and  $\\gamma n N^*$ vertices, the reaction of interest is difficult to model accurately.   \nThe second model giving predictions for the present results is the data description given by  SAID~\\citep{SAID, Adelseck:1986fb}.   In general, SAID is more up to date than KaonMAID;  for the present reaction channels the SAID predictions are a polynomial fit to all available data  before  2008, assuming final state interactions for these polarization observables can be neglected~\\cite{strakovsky}.\nThe third  comparison is made to the multichannel K-matrix formalism of the  Bonn-Gatchina~\\citep{Anisovich:2012ct} group, which is the most up to date, being constrained by recent first-time measurements~\\citep{Compton_PhysRevC.96.065201}  of the differential cross section for the reaction $\\gamma n(p) \\to K^0\\Lambda (p)$  [with $(p)$ as the spectator proton].\n\n\n\\section{Experimental Procedures\n\\label{sec:Section-II}} \n\nThe experiment was performed at the Thomas Jefferson National Accelerator Facility (JLab) using the CEBAF Large Acceptance\nSpectrometer (CLAS)~\\citep{CLAS-NIM}.  \nThis setup has been used for several studies of $K^+$ photoproduction of  \nhyperonic final states on a proton target~\\citep{Bradford_CxCz, Bradford_xsec, McNabb, Moriya:2014kpv, Moriya:2013hwg, Moriya:2013eb, McCracken, Dey} \nand on an effective neutron (deuteron) target~\\citep{Compton_PhysRevC.96.065201,AnefalosPereira:2009zw}.\nThe present results stem from the so-called ``\\textit{g14}\" run period between December 2011 and May 2012, from which non-strange \nresults have been previously reported~\\citep{Ho:2017kca}.   \nThe CEBAF accelerator provided longitudinally polarized electron beams with energies of \n$E_{e}=2.281$, \n$2.257$, \nand $2.541$ GeV, \nand an \\textit{average} electron beam polarization for the present study of $P_{e}=0.82\\pm0.04$, which was measured routinely\nby the Hall-B M\\\"oller polarimeter~\\cite{Moller2}. The electron beam helicity was pseudorandomly flipped between +1 and $-1$ with a 960 Hz flip\nrate. The electron beam was incident on the thin gold radiator of the Hall-B Tagger system~\\citep{Sober} and produced circularly polarized\ntagged photons. The polarization of the photons was determined using the Maximon and Olsen formula~\\citep{Olsen:1959zz}\n\\begin{equation}\nP_{\\odot}=P_{e}\\frac{4k-k^{2}}{4-4k+3k^{2}},\n\\end{equation}\nwhere $P_{\\odot}$ and $P_{e}$ are the photon and electron polarizations, respectively, and $k=E_{\\gamma} \/ E_e$ is the ratio between\nthe photon energy and the electron beam energy. \n\nA 5-cm-long solid target of hydrogen deuteride (HD)  was used in the experiment~\\citep{Lowry:2016uwa,Bass:2013noa}.\nIt  achieved vector polarizations of   25\\%-30\\% for deuterons, i.e., for \n{\\it bound} neutrons in the deuteron with relaxation times of about a year.  \nThe polarized target was held at the center of CLAS using an in-beam cryostat that produced a 0.9~T holding field and operated at 50 mK.  The target polarization was monitored using nuclear magnetic resonance measurements~\\citep{Lowry:2016uwa}.   The orientation of the target longitudinal polarization direction was inverted between periods of data taking, either parallel or antiparallel to the direction of the incoming photon beam.   Background events from the unpolarizable target wall material and aluminum cooling wires~\\citep{Bass:2013noa} were removed using empty-target data, as discussed in Secs.~\\ref{sec:Section-IIIa} and~\\ref{sec:Section-IIIb}.\n\nThe specific reaction channel for this discussion came from events of the type $\\gamma d \\to \\pi^+ \\pi^- \\pi^- p (X)$ using a readout trigger requiring a minimum of two charged particles in different CLAS sectors.  After particle identification  we required  the ``spectator,\"  $X$, to be an undetected  low-momentum proton and possibly a photon, via the missing mass technique, as explained in the next section. In order to determine the $E$ asymmetry experimentally, the event yields in a given kinematic bin of $W$ and kaon center-of-mass angle were obtained by counting events with total c.m. helicity $h=$3\/2 (laboratory-frame antiparallel configuration), called $N_{A}$, and events with $h=$1\/2 (laboratory frame parallel configuration) called $N_{P}$, respectively. The $E$ observable \nwas then computed as \n\\begin{equation}\nE=\\frac{1}{\\overline{P_{T}}\\cdot\\overline{P_{\\odot}}}\\left(\\frac{N_{A}-N_{P}}{N_{A}+N_{P}}\\right),\n\\label{Eq_Eval}\n\\end{equation}\nwhere $\\overline{P_{T}}$ and $\\overline{P_{\\odot}}$ are the run-averaged\ntarget and beam polarizations, respectively. \n\n\n\n\\section{Data Analysis \n\\label{sec:Section-III}}\n\nThe performance of the system was extensively studied for a reaction with much higher count rates than the present one.   The nonstrange reaction  $\\gamma d \\to \\pi^- p (X) $ was investigated using many of the same analysis steps and methods discussed in this article to extract the $E$ observable for $\\gamma n \\to \\pi^- p$~\\citep{Ho:2017kca}.    The analysis steps outlined below were all tested on that reaction.   In particular, the boosted decision tree (BDT) selection procedure~\\cite{DruckerCortes, ROE2005577} used below was validated against alternative ``cut-based\" and kinematic fit  methods, with the result that the BDT procedure resulted in $\\sim30\\%$ larger yields of  signal events and therefore gave better statistical precision on the final $E$ asymmetry.\n\n\\subsection{Particle identification}\n\\label{sec:Section-IIIa}\n\nFor this particular analysis, we required that every selected event consists of at least two positive tracks and two negative tracks with associated photon tagger hits~\\cite{Sober}.\nThe CLAS detector system determined the path length, the charge type,\nthe momentum and the flight time for each track~\\citep{Sharabian,Mestayer,Smith}.\nFor each track of momentum $\\overrightarrow{p}$, we compared the measured time of flight, $TOF_{m}$, to a hadron's expected time of\nflight, $TOF_{h}$, for a pion and proton of identical momentum and path length. \nCLAS-standard cuts were placed on the difference between the measured and the expected time of flight, $\\triangle TOF=TOF_{m}-TOF_{h}$. We selected events for which the two positively charged particles were the proton and $\\pi^{+}$, and the two negatively charged were both  $\\pi^{-}$. Well-established CLAS fiducial cuts were applied to select events with good spatial reconstruction. \n\nEvents originating from unpolarized target material\\textit{\\footnotesize{}\\textemdash }aluminum cooling wires and polychlorotrifluoroethylene (pCTFE)\\textit{\\footnotesize{}\\textemdash } dilute $E$ and must be taken into account. A  period of data taking was dedicated to an \\textit{empty} target cell in\nwhich the HD material was not present. This set of data was used to study and remove the bulk of the target material background on the basis of a loose missing mass cut.   \nFigure \\ref{Z-vertex} shows the resulting reconstructed reaction vertex for four-track data along the beam line both for a full target and for an empty target scaled to match the counts in several downstream target foils. \nThe full-to-empty ratio of about 3.3:1 in the target region was important in selecting the optimal BDT cut discussed below.\n\n\\begin{figure}\n\\vspace{-0.5cm}\n\\includegraphics[width=0.5\\textwidth]{Z_vertex_RS2}\\protect\n\\vspace{-0.5cm}\n\\caption{The open histogram shows the vertex  distribution of events along the beam\nline for a full target is the open histogram. Dashed red lines show the nominal target boundaries.  The peaks at $z>0$ are from target-independent foils in the cryostat;  the positions of two are  highlighted with dotted blue lines~\\cite{Lowry:2016uwa}. The filled histogram shows the scaled target-empty  background  distribution.   \n\\label{Z-vertex} }\n\\end{figure}\n\nFigure \\ref{MMass} shows the resulting target-full  missing mass distribution for spectator $X$ in $\\gamma d\\rightarrow\\pi^{-}\\pi^{+}\\pi^{-}p(X)$,\nafter these cuts.  A clear peak corresponding to the spectator proton is seen at point 1 for events that produced a $\\Lambda$ particle.  A loose cut was applied to reject events with missing mass larger than 1.4 GeV\/c$^{2}$ at point 4 because of the presence of $\\Sigma^{0}\\rightarrow\\pi^{-}p(\\gamma)$ events. These have a 73-MeV photon in the final state in addition to the proton, and the distribution peaks at point 2 and has a kinematic tail to about point 3.\n\n\\begin{figure}[htbp]\n\\vspace{-0.5cm}\n\\includegraphics[width=0.5\\textwidth,height=0.35\\textwidth]{MMass_RS}\\protect\n\\vspace{-0.5cm}\n\\caption{The missing mass distribution, $\\gamma d\\rightarrow\\pi^{-}\\pi^{+}\\pi^{-}pX$\nafter PID cuts showing the dominant spectator proton peak at ``1.''   The magenta line at ``4'' indicates a loose event rejection for $m_X >  1.4$~GeV\/c$^2$. This rejects unambiguous\nbackground but keeps $\\Sigma^{0}\\rightarrow\\pi^{-}p(\\gamma)$ events in which both a proton and a photon are missing between ``2'' and ``3.''  (See text.)\n\\label{MMass} }\n\\end{figure}\n\n\n\\subsection{$K^{0}Y$ event selection using BDT analysis}\n\\label{sec:Section-IIIb}\n\nBecause of the small reaction cross section in this experiment, a method was needed to optimally isolate the events of interest with minimal statistics loss.\nThe multivariate analysis tool called the boosted decision tree (BDT)  approach was used to select the exclusive events of interest in this study.   Three steps were needed to achieve this result.  The first BDT was created to select events from both the \n$\\gamma d\\rightarrow\\pi^{-}\\pi^{+}\\pi^{-}p(p_{S})$ and the $\\gamma d\\rightarrow\\pi^{-}\\pi^{+}\\pi^{-}p(p_{S}\\gamma)$ final states, \nconsistent with quasi-free production from a deuteron.  This was to reject target-material background and events with a high missing momentum of the undetected spectator nucleon, $p_S$.  The second BDT was created to remove the nonstrange pionic background with the same final states, that is, to pick out events with $\\Lambda$ and  $\\Sigma^0$ intermediate-state particles.    The third BDT was to separate the $K^{0}\\Lambda$ and $K^{0}\\varSigma^{0}$ events. \n\nThis BDT algorithm is more efficient than a simple ``cut'' method in both rejecting background and keeping signal events~\\citep{ROE2005577,Ho-thesis}.  The method  builds a ``forest'' of \\textit{distinct} \\textit{decision trees} that are linked together by a \\textit{boosting} mechanism. Each decision tree constitutes a \\textit{disjunction} of logical conjunctions (i.e., a graphical representation of a set of \\textit{if-then-else} rules). Thus, the entire reaction phase-space is considered by every decision tree.  Before employing the BDT for signal and background classification, the BDT algorithm needs to be constructed (or trained) with \\textit{training} data\\textit{\\textemdash }wherein  the category of every event is definitively known. We used the ROOT implementation of the BDT algorithm ~\\citep{Hocker:2007zz}. \nEvery event processed by the constructed BDT algorithm is assigned a value of between $-1$ and +1 that\nquantifies how likely the processed event is a background event (closer to $-1$) or a signal event (closer to $+1$). An optimal cut on the\nBDT output is chosen to maximize the\\textit{ }$S\/\\sqrt{S+B}$ ratio, where $S$ and $B$ are the estimations, based on training data, of the initial number of signal\nand background events, respectively.\n\nThe initial assignment of the $\\pi^-$ particles to either $K^0$ or $\\Lambda$ decay was studied with Monte Carlo simulation, and a loose selection based on invariant masses was made.  Specific details of these cuts are given in Ref.~\\citep{Ho-thesis}. \n\nThe first BDT was trained using real empty-target data for the background training.   A signal Monte Carlo simulating quasifree hyperon production on the neutron was used for signal training data.  The momentum distribution of the spectator proton, $p_{s}$, followed the Hulth\\`en potential~\\citep{Cladis_PhysRev.87.425,Lamia:2012zz} for the deuteron. Based on this training, an optimal BDT cut  that maximized the estimated initial\\textit{ }$S\/\\sqrt{S+B}$ ratio was selected. Figure \\ref{Z_vertex_BDT} shows the total (blue histogram) and rejected (black histogram) events by the first BDT cut. In comparing  Figs.~\\ref{Z-vertex} and \\ref{Z_vertex_BDT}, two items should be noted. First, the BDT was trained to remove target-material background events with missing momentum not consistent with a Hulth\\`en distribution. Second, the BDT background-rejection efficiency was not perfect, leaving some target-material background events that were removed in a subsequent step (Sec.~\\ref{sec:Section-IIIc}). We then rejected events with $z>-2$~cm on the reaction vertex to remove remaining unambiguous background events due to various cryostat foils. \n\n\\begin{figure}[htbp]\n\\vspace{-0.5cm}\n\\includegraphics[width=0.5\\textwidth]{Z_vertex_BDT1_RS}\n\\vspace{-1.cm}\n\\protect\\caption{The reconstructed distribution of the reaction vertex along the beam\nline showing target-full events in the top histogram (blue) after loose $K^0Y^0$ selection  and the missing mass cut shown in Fig.~\\ref{MMass}.\nEvents selected by the first BDT are shown in the middle histogram (red), and rejected events in the bottom histogram  (black).\nThe magenta line indicates a loose cut to reject unambiguous target-material background. \n\\label{Z_vertex_BDT} }\n\\end{figure}\n\nThe second-step BDT was trained using a four-body phase-space $\\gamma d\\rightarrow\\pi^{-}\\pi^{+}\\pi^{-}p(p_{S})$\nsimulation as background training data and the $\\gamma d\\rightarrow K^{0}\\Lambda(p_{S})$ simulation as signal training data. There were two negative pions in each event:  one from the decay of the $K^0$ and one from the decay of the hyperon.   The goal of the BDT analysis was to use the available correlations among all particles to sort the pions correctly and to select events with decaying strange particles.   The main training variables at this stage of the analysis included the 3-momenta of all the particles and the detached decay vertices of the $K^0$s and the hyperons.  \nAfter the optimized BDT cut was placed, Fig.~\\ref{lambda K0 IM}  shows the total (red histogram) and\nrejected (black histogram) events after this second BDT analysis step.  The efficiency of the second BDT was less than 100\\%, thus, there are remaining\ntarget background events in the selected data sample.  The dips near the signal maxima in the background spectra show that the background is slightly undersubtracted. This issue is discussed and corrected below.  A fit with  a Breit-Wigner line shape and a polynomial was used to estimate  that the \nstrange-to-non-strange ratio of events in the data set at this stage was about 2.3:1 in the peak regions.\n\n\\begin{figure}[htpb]\n\\includegraphics[width=0.48\\textwidth]{IM_ppim_g2}\n\\includegraphics[width=0.48\\textwidth]{IM_pippim_g2}\n\n\\protect\\caption{Invariant $\\pi_{\\Lambda}^{-}p$ mass (top) and invariant $\\pi_{K^{0}}^{-}\\pi^{+}$\nmass (bottom) after target material background rejection by the first\nBDT cut. Black histograms show events rejected  by the second BDT cut.  Fits of the sum (red curve) of a Breit-Wigner line-shape (blue curve) and a third order polynomial (black curve) are shown.  The fits aid the discussion in the text but were not used in the subsequent analysis. \\label{lambda K0 IM} }\n\\end{figure}\n\nFor the final task, separating the  $K^{0}\\Lambda$ and $K^{0}\\varSigma^{0}$ channels, the third BDT was trained using $\\gamma d\\rightarrow K^{0}\\Sigma^{0}(p_{S})$ simulation as ``background'' training data and $\\gamma d\\rightarrow K^{0}\\Lambda(p_{S})$ simulation as ``signal'' training data. Note that the term background used here is just for semantic convenience, since both channels were retained after applying the third optimized BDT cut.\nFigure~\\ref{MMass_off_K0_simulation}  shows in the left [right] histogram the classification success of the third BDT on $\\gamma d\\rightarrow K^{0}\\Lambda(p_{S})$  [$\\gamma d\\rightarrow K^{0}\\Sigma^{0}(p_{S})$] simulation data. The histograms reveal that a small number of $K^{0}\\Lambda$ events  would be misclassified as $K^{0}\\varSigma^{0}$ events, and vice versa. In the next section, the correction for the contamination on both final\ndata sets is discussed. Figure \\ref{MMass_off_K0} shows the separation result from the third BDT on real data. \n\n\\begin{figure*}[t]\n\\includegraphics[width=0.5\\textwidth]{MM_pippim_K0Lambda_MC}\\includegraphics[width=0.5\\textwidth]{MM_pippim_K0Sigma0_MC}\\protect\n\\caption{Distributions of missing mass from the reconstructed $K^{0}$, $\\gamma n\\rightarrow\\pi_{K^{0}}^{-}\\pi^{+}X$\nfor simulation data, assuming that the target is an at-rest neutron.\nLeft: the magenta histogram represents events with correct $K^{0}\\Lambda$\nclassification, while the cyan histogram represents events with the wrong\n$K^{0}\\Sigma^{0}$classification. Right: the cyan histogram represents\nevents with the correct $K^{0}\\Sigma^{0}$~classification, while the magenta\nhistogram represents events with the wrong $K^{0}\\Lambda$ classification.\n\\label{MMass_off_K0_simulation} }\n\\end{figure*}\n\n\n\\begin{figure}[t]\n\\includegraphics[width=0.5\\textwidth]{MM_pippim}\\protect\\caption{Distribution of missing mass \nfrom the reconstructed $K^{0}$, $\\gamma n\\rightarrow\\pi_{K^{0}}^{-}\\pi^{+}X$\nfor real data, assuming that the target is an at-rest neutron,\nafter rejecting non-hyperon background by the second BDT cut.\nThe magenta (cyan) histogram was classified as $K^{0}\\Lambda$ ($K^{0}\\Sigma^{0}$)\nusing the third BDT selection step. \\label{MMass_off_K0} }\n\\end{figure}\n\n\\subsection{Corrections for remaining backgrounds and asymmetry calculation}\n\\label{sec:Section-IIIc}\n\nThe $E$ asymmetry values  for both target-material and non-strange background events were statistically\nconsistent with 0~\\citep{Ho-thesis}; therefore, we implemented an  approximation procedure\nto correct for the dilution effect from the remaining background.\nWe estimated two ratios: one for the remaining fraction of target background (TGT), $R^{TGT}$,  \nand one for the fraction of remaining nonstrange (NS) final-state events mixed with the hyperon events, $R^{NS}$.\nWe write \n$R^{TGT}= {N^{remain}} \/ {N^{HD}}$,\nand \n$R^{NS}={Y^{remain}}\/{Y^{K^{0}Y}}$.   \n$N^{remain}$ and $N^{HD}$ are the estimated number of remaining target-material background events\nand true deuteron events after the first BDT and $z=-2$~cm vertex cuts, respectively.\n$Y^{remain}$ and  $Y^{K^{0}Y}$ are the estimated number of remaining nonstrange  and true $K^{0}Y$ events after the second\nBDT cut, respectively. Next, let $Y_{BDT}$  be the number of events that passed the $z$-vertex cut and the first two BDT selections; then $Y_{BDT}$\ncan be partitioned into \n\\begin{align}\nY_{BDT}&=\\left(1+R^{NS}\\right)Y^{K^{0}Y} \\nonumber \\\\\n&=\\left(1+R^{NS}\\right)\\left[Y_{HD}^{K^{0}Y}+Y_{TGT}^{K^{0}Y}\\right],\\;\\label{eq:wideeq-2-3}\n\\end{align}\nsince $Y^{K^{0}Y}$ also comprises events from the remaining target-material\nbackground and the bound signal events.  If we further allow  \n$Y_{TGT}^{K^0 Y} \/ Y_{HD}^{K^0 Y} = N^{remain} \/ N^{HD} = R^{TGT}$,\nthen $Y_{BDT}$ can finally be expressed as\n\\begin{equation}\nY_{BDT}=\\left(1+R^{NS}\\right)\\left(1+R^{TGT}\\right)Y_{HD}^{K^{0}Y},\\;\\label{eq:wideeq-2}\n\\end{equation}\nor\n\\begin{equation}\nY_{HD}^{K^{0}Y}=\\left(1+R^{NS}\\right)^{-1}\\left(1+R^{TGT}\\right)^{-1}Y_{BDT}.\n\\label{eq:wideeq-2-1}\n\\end{equation}\nThese relations should remain valid for both $Y_{BDT}^{K^{0}\\Lambda}$ and $Y_{BDT}^{K^{0}\\Sigma^{0}}$, \nwhich are the $K^{0}\\Lambda$ and $K^{0}\\Sigma^{0}$ signal events from bound neutrons, respectively.  \nThe backgrounds that leak through the BDT filters will be helicity independent and will be subtracted in the numerator of Eq.~(\\ref{Eq_Eval}).  \nUsing Eq.~(\\ref{eq:wideeq-2-1}) to correct the summed yields in the denominator gives the corrected asymmetry as\n\\begin{equation}\nE_{corrected}^{K^{0}Y}=\\left(1+R^{NS}\\right)\n\\times\\left(1+R^{TGT}\\right)E_{BDT}^{K^{0}Y},\\;\\label{eq:wideeq-2-2}\n\\end{equation}\nwhere $E_{BDT}^{K^{0}Y}$ is obtained from $Y_{BDT}^{K^{0}Y}$ (or,\nmore exactly, $Y_{BDT}^{P}$ and $Y_{BDT}^{A}$\nof the $K^{0}Y$ parallel and antiparallel subsets). \nFrom the simulations we found average values of $R^{TGT}$ and $R^{NS}$ of 0.09  and 0.17, respectively, with some dependence on\nthe specific run period.\n\nNext we discuss a correction for the third BDT classification result.\nRecall that the third BDT selection separates the true signal $K^{0}Y$ events into two subsets: one is mostly $K^{0}\\Lambda$ events,\nand the other is mostly $K^{0}\\varSigma^{0}$. If we denote  $N_{\\Lambda}^{BDT}$ and $N_{\\Sigma^{0}}^{BDT}$ as the\nnumber of events the third BDT identified as $K^{0}\\Lambda$ and $K^{0}\\varSigma^{0}$ events, respectively, then we have the expressions\n\n\\begin{equation}\nN_{\\Lambda}^{BDT}=\\omega_{\\Lambda}N_{\\Lambda}^{true}+(1-\\omega_{\\Sigma^{0}})N_{\\Sigma^{0}}^{true},\\;\\label{eq:wideeq-3}\n\\end{equation}\n\\begin{equation}\nN_{\\Sigma^{0}}^{BDT}=(1-\\omega_{\\Lambda})N_{\\Lambda}^{true}+\\omega_{\\Sigma^{0}}N_{\\Sigma^{0}}^{true},\\;\\label{eq:wideeq-3-1}\n\\end{equation}\nwhere $\\omega_{\\Lambda}$ and $\\omega_{\\Sigma^{0}}$ are the fractions of events correctly identified: these values were\nestimated based on simulation data. After rearrangement, we arrive at the expressions \n\\begin{align}\nN_{\\Lambda}^{true}&=\\left[\\omega_{\\Lambda}-\\frac{(1-\\omega_{\\Sigma^{0}})}{\\omega_{\\Sigma^{0}}}(1-\\omega_{\\Lambda})\\right]^{-1} \\nonumber \\\\\n&\\times \\left[N_{\\Lambda}^{BDT}-\\frac{(1-\\omega_{\\Sigma^{0}})}{\\omega_{\\Sigma^{0}}}N_{\\Sigma^{0}}^{BDT}\\right],\\;\n\\label{eq:wideeq}\n\\end{align}\n\\begin{align}\nN_{\\Sigma^{0}}^{true}&=\\left[\\omega_{\\Sigma^{0}}-\\frac{(1-\\omega_{\\Lambda})}{\\omega_{\\Lambda}}(1-\\omega_{\\Sigma^{0}})\\right]^{-1} \\nonumber \\\\ \n&\\times \\left[N_{\\Sigma^{0}}^{BDT}-\\frac{(1-\\omega_{\\Lambda})}{\\omega_{\\Lambda}}N_{\\Lambda}^{BDT}\\right]\\;\n\\label{eq:wideeq-1}.\n\\end{align}\n\nThe \\textit{corrected} $E$ asymmetry was obtained using the derived $N_{\\Lambda}^{true}$ and $N_{\\Sigma^{0}}^{true}$ by using\nEq.~(\\ref{Eq_Eval}).  From the simulations we found average values of $\\omega_Y$ of 0.87 and 0.91 for $\\Lambda$ and $\\Sigma^0$ events, respectively.\n\nThe neutron polarization in the deuteron is smaller than the deuteron polarization because the deuteron wavefunction has, in addition to an $S$-wave component, a $D$-wave component in which the spin of the neutron need not be aligned with the deuteron spin.   This was studied using data for the $\\gamma n \\to \\pi^- p $ reaction and reported in our previous publication~\\citep{Ho:2017kca}.  It was found that for spectator recoil momenta of less than 100~MeV\/$c$ the correction was negligible.  Had we cut on the recoil momentum at 200~MeV\/$c$ rather than 100~MeV\/$c$, a measured dilution factor of $(8.6\\pm0.1)$\\%  would have been necessary for the nonstrange channel.   But different reaction channels  may exhibit different sensitivities to recoil momentum.  For the reaction under discussion here we could not afford the statistical loss by cutting on recoil momentum, and we elected to make a conservative correction based on the general considerations in \\citep{Ramachandran:1979ck}.  The neutron polarization can\nbe estimated as $P_{n}=P_{d}(1-\\frac{3}{2}P_{D})$, where $P_{n}$ and $P_{d}$ are neutron and deuteron polarizations, respectively, and $P_{D}$ denotes the deuteron $D$-state probability.  The latter is not strictly an observable and needs only to be treated consistently within a given $NN$ potential.\nFollowing  Ref.~\\citep{Ramachandran:1979ck}, we take the $D$-state contribution averaged over a range of $NN$ potentials as about  5\\%, which implies that the neutron polarization is  92.5\\% of the deuteron polarization, or a 7.5\\% dilution factor. \n\n\\subsection{Systematic Uncertainties}\n\nWe implemented four systematic studies to quantify the robustness of the trained BDT algorithms and the sensitivity of our results on\nthe  correction procedures introduced in the previous section.  \nTwo  tests studied the effect of loosening the first and the second BDT cuts, respectively.  One test focused on the sensitivity of the $E$ results on the third correction\\textit{\\textemdash }the correction procedure that was implemented to ``purify'' the final selected $K^{0}\\Sigma^{0}$($K^{0}\\Lambda$) sample.  Finally, we reduced the beam and target polarizations by one standard deviation of their respective total uncertainties (statistical and systematic) to study the changes in the $E$ results.\n\nFinally, we note a complication that could occur when summing $\\Lambda$ yields to create the $E$ asymmetries. The relative angular distribution between the $\\pi^-$ and the $p$ that are used to reconstruct a $\\Lambda$ carries information on the recoil polarization of the latter. When summed over azimuthal angles, this information is lost. However, limitations in detector acceptance could result in  incomplete integration, which in principle could introduce into Eq.~\\ref{equation2}  a dependence on six additional observables~\\cite{Sandorfi:2010uv}. The gaps in CLAS acceptance are modest, and due to the lower than expected production cross sections, the data below are presented in broad kinematic bins, which tends to dilute such effects. On the scale of our statistical uncertainties, such corrections are expected to be negligible and we have not attempted to correct for them.\n\n\n\n\\section{Results \\label{sec:Section-IV}}\n\nWe present here the results for the $E$ asymmetry in two $W$ energy bins. The lower bin is from 1.70 to 2.02 GeV and denoted $W_{1}$, while the higher bin is from 2.02 to 2.34 GeV and referred to  $W_{2}$.  Due to small cross sections for $K^0Y$ photoproduction, and to detector inefficiencies that are amplified by the  required identification of four charged particles, our statistics are  sufficient for only three bins in the $K^0$ center-of-mass production angle.  The measurements for the $\\gamma n \\to K^0 \\Lambda$ reaction  are plotted together with predictions from the KaonMAID, SAID, and Bonn-Gatchina (BnGa)  models in Fig.~\\ref{Ecostheta_K0L}.   The data show that the $K^0\\Lambda$ asymmetry is largely positive below 2~GeV and mostly negative above 2~GeV, without more discernible trends.   Values of $E$ must approach $+1$ at $\\cos \\theta^{c.m.}_{K^0}\\to \\pm 1$ to conserve angular momentum.   Thus, the values for $E$  in bin $W_2$ must change rather rapidly near the extreme angles.\n\n\nFor comparison, the PWA combine results from many experiments at different energies, and this results in varying degrees of sensitivity to energy and angle. This is illustrated in Fig.~\\ref{Ecostheta_K0L} by the SAID and BnGa PWA predictions at the limits of the energy bins. None of the models were tuned to these results;  that is, the models are all predictions based on  fits to previously published data on other observables.\nFirst, one observes that the data are not statistically strong enough to strongly discriminate among the models.  In the lower $W$ bin all three models\ncan be said to agree with the data.   In the higher $W$ bin the SAID model may be  slightly favored by the data among the three.\n\n\\begin{figure}[htbp]\n\\vspace{-0.5cm}\n\\includegraphics[angle=-90 , width=0.55\\textwidth, trim=0 3.5cm 0 0, clip]{e-k0-lambda-1.pdf}\n\\vspace{-10mm} \n\\caption{Helicity asymmetry  $E$ for the  ${K^{0}\\Lambda}$ final state (with combined statistical and systematic uncertainties) vs. $\\cos\\theta_{K^{0}}$   The asymmetries are shown with the neutron-target theoretical models KaonMaid ~\\citep{Mart:1999ed} (dashed red curve) and SAID~\\citep{SAID} (dot-dashed blue curve) and Bonn-Gatchina~\\citep{Anisovich:2007bq,Anisovich:2012ct} (solid black curve).  Because of the 0.32-GeV-wide $W$ bins, each model is represented by two curves, computed at the bin endpoint $W$ values, as labeled. \n\\label{Ecostheta_K0L} }\n\\end{figure}\n\nThe results for the $\\gamma n \\to K^0 \\Sigma^0$ channel are plotted in Fig.~\\ref{Ecostheta_K0S}, together with model predictions from SAID and Kaon-MAID.   In contrast to the $K^0 \\Lambda$  channel at lower $W$, here the data hint at less positive values for $E$.   \nIn the bin for  $W$ above 2 GeV, the data are also consistent with 0 for $K^0\\Sigma^0$, whereas the $K^0\\Lambda$ data tended to be negative.  In fact, the $K^0\\Sigma^0$ asymmetry is consistent with 0 in all available bins.   \nThe model comparisons show that the KaonMAID prediction for the $K^0\\Sigma^0$ channel in the higher $W$ bin are probably not consistent with the data, while the SAID result is consistent with the data.   For the $K^0\\Sigma^0$  case we do not have predictions from the Bonn-Gatchina model  because the unpolarized differential cross section has not been measured yet, and without it the model  does not have a prediction available. \n\n\\begin{figure}[htbp]\n\\vspace{-0.5cm}\n\\includegraphics[angle=-90 ,  width=0.55\\textwidth, trim=0 3.5cm 0 0, clip]{e-k0-sigma0-1.pdf}\n\\vspace{-10mm} \n\\caption{Helicity asymmetry  $E$ for the  ${K^{0}\\Sigma^0}$ final state (with combined statistical and systematic uncertainties) vs. $\\cos\\theta_{K^{0}}$ for two 0.32-GeV-wide  energy bands in $W$, as labeled. Model curves are as in Fig.~\\ref{Ecostheta_K0L}.\n\\label{Ecostheta_K0S} }\n\\end{figure}\nIn order to show  one other comparison between data and theory, we plot some of the present results for a neutron target together with the model predictions for the $K^+ \\Lambda$ reaction on a {\\textit {proton}} target in Fig.~\\ref{Ecostheta_K0L2}.  This is intended to show the difference in  the model predictions on protons versus neutrons.  One sees how different the three model predictions are for protons versus neutrons.   One notes that the predictions for the proton target calculations all tend to be closer to the new data we are presenting for a neutron target.   This suggests that calculations of the $E$ observable for a neutron target can be improved.   \nThus, we may expect these present results to have some impact on the further development of these models.\n\n\\begin{figure}[htbp]\n\\vspace{-0.5cm}\n\\includegraphics[angle=-90 ,  width=0.55\\textwidth, trim=0 3.5cm 0 0, clip]{e-k0-lambda-2.pdf}\n\\vspace{-10mm} \n\\caption{\nHelicity asymmetry  $E$ for the  ${K \\Lambda}$ final state vs. $\\cos\\theta_{K^{0}}$ for energy band  $W_2$.   Left: Data from Fig.~\\ref{Ecostheta_K0L} together with model  predictions for a neutron target. Right: Model calculations  for the $K^+ \\Lambda$ reaction on a proton target, as computed using KaonMaid~\\citep{Mart:1999ed} (dashed red curve),  SAID~\\citep{SAID} (dot-dashed blue curve) and Bonn-Gatchina~\\citep{Anisovich:2007bq,Anisovich:2012ct} (solid and dashed black curves).   Curves on the right are closer to the (reaction mismatched) data shown on the left.\n\\label{Ecostheta_K0L2} }\n\\end{figure}\n\nSo far unpublished CLAS results for the corresponding reaction $\\gamma p \\to K^+ \\Lambda$ have higher statistics and finer energy bins than the present results (since the identification of this final state requires the detection of fewer particles).   The present  $K^0 \\Lambda$ results are, within our uncertainties, similar to the $K^+\\Lambda$ asymmetries in Ref.~\\cite{LiamCasey}. The numerical values of the measured  $K^0 \\Lambda$  and $K^0 \\Sigma^0$ $E$ asymmetries, together with their statistical and systematic uncertainties, are reported in Table \\ref{Tab:E_sys_stat}.\n\n\\begin{table*}[htbp]\n\\hfill{}%\n\\begin{tabular}{ccccc}\n\\hline\\hline \n\\multicolumn{1}{c}{   } &  & \\multicolumn{3}{c}{$\\cos\\theta_{K^{0}}$}\\tabularnewline\n\\cline{3-5} \n\\multicolumn{1}{c}{} &  & $-$0.6 & 0.0 & $+$0.6\\tabularnewline\n\\hline \n\\multirow{2}{*}{$K^{0}\\Lambda$ } & $W_{1}$ & 0.834$\\pm$0.499$\\pm$0.287 & $-$0.144$\\pm$0.436$\\pm$0.098 & 1.066$\\pm$0.419$\\pm$0.231\\tabularnewline\n\\cline{2-5} \n & $W_{2}$ & $-$0.533$\\pm$0.752$\\pm$0.345 & $-$0.263$\\pm$0.618$\\pm$0.101 & $-$0.648$\\pm$0.464$\\pm$0.136\\tabularnewline\n\\hline \n\\multirow{2}{*}{$K^{0}\\Sigma^{0}$} & $W_{1}$ & $-$0.110$\\pm$0.723$\\pm$0.406 & 0.581$\\pm$0.539$\\pm$0.144 & $-$0.319$\\pm$0.541$\\pm$0.460\\tabularnewline\n\\cline{2-5} \n & $W_{2}$ & $-$0.471$\\pm$0.446$\\pm$0.391 & 0.0002$\\pm$0.317$\\pm$0.150 & 0.054$\\pm$0.281$\\pm$0.065\\tabularnewline\n\\hline \\hline\n\\end{tabular}\n\\hfill{}\n\n\\protect\\caption{Numerical values of the $E$ asymmetry measurements for the $K^{0}\\Lambda$\/$K^{0}\\Sigma^{0}$\nchannels. The uncertainties are statistical and systematic, respectively.  Center-of-mass energy ranges are $1.70 < W_1 < 2.02$~GeV and $2.02 < W_2 < 2.34$~GeV.\n\\label{Tab:E_sys_stat}}\n\\end{table*}\n\n\\section{Conclusions \\label{sec:Section-V}}\n\nWe have reported the first set of $E$ asymmetry measurements for the reaction $\\gamma d\\rightarrow K^{0}Y(p_{s})$ for 1.70~GeV$\\leq W \\leq$ 2.34~GeV. In particular, we have described the three-step BDT-based analysis method developed to select a clean sample of $p\\pi^{+}\\pi^{-}\\pi^{-}$ with intermediate hyperons. We have plotted the $E$ asymmetry as a function of $\\cos \\theta_{K^{0}}^{CM}$.\nSeveral systematic uncertainty tests led to the conclusion that statistical uncertainties dominated the final results.  The numerical values of the measured $E$ asymmetries and their statistical and systematic uncertainties are reported in Table \\ref{Tab:E_sys_stat}.\n\nEvidently,  this analysis is limited by the small cross sections of the channels of interest, leading to large uncertainties in the measurements of the $E$ asymmetry.  At present, comparison with several models makes no decisive selections among the model approaches.  \nOverall, the BnGa predictions are of a quality similar to that of the SAID predictions. The Kaon-MAID predictions for both channels seem less successful.  Among all three model comparisons, the distinction between proton- and neutron-target predictions are  differentiated by the data:  The proton-target predictions compare better than the neutron-target predictions with the experimental results.  In principle, this information is valuable since it hints at the necessary isospin decomposition of the hyperon photoproduction mechanism.   \n\nAt present, multipole analyses for $K^0Y$ channels are severely limited by the available data.   Higher statistical data on these channels for a number of other polarization  observables, from a much longer (unpolarized) target, have been collected during the $g13$ running period with CLAS and are under analysis.   A greater number of different polarization observables is generally more effective than precision at determining the  photoproduction amplitude~\\cite{Sandorfi:2010uv}.   When these $g13$ results become available, the present data on the beam-target $E$ asymmetry are likely to have a larger impact.   \n\n\\begin{acknowledgments}\nWe acknowledge the outstanding efforts of the staff of the Accelerator\nand Physics Divisions at Jefferson Lab who made this experiment\npossible. The work of the Medium Energy Physics group at Carnegie\nMellon University was supported by DOE Grant No. DE-FG02-87ER40315.  The\nSoutheastern Universities Research Association (SURA) operated the\nThomas Jefferson National Accelerator Facility for the United States\nDepartment of Energy under Contract No. DE-AC05-84ER40150.  Further\nsupport was provided by \nthe National Science Foundation, \nthe Chilean Comisi\\'on Nacional de Investigaci\\'on Cient\\'ifica y Tecnol\\'ogica (CONICYT),\nthe French Centre National de la Recherche Scientifique,\nthe French Commissariat \\`{a} l'Energie Atomique,\nthe Italian Istituto Nazionale di Fisica Nucleare,\nthe National Research Foundation of Korea,\nthe Scottish Universities Physics Alliance (SUPA),\nand the United Kingdom's Science and Technology Facilities Council.\n\\end{acknowledgments}\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nIn a previous communication$^1$ it was suggested that a typical elementary\nparticle, the electron can be considered to be what was termed a Quantum\nMechanical Black Hole (or QMBH), made up of a relativistic fluid of subconstituents,\ndescribed by the Kerr-Newman metric giving both its gravitational and\nelectromagnetic fields$^2$. It was pointed out that alternatively the QMBH could\nbe described as a relativistic vortex in the hydrodynamical formulation. It\nwas pointed out that the QMBH or vortex could also be thought of as a\nrelativisitc rotating shell.\\\\\nIn Section 2 we examine this model which explains several observed facts,\nwhile in Section 3 we try to explore the mechanism which triggers off the\nformation of these QMBH particles. In Section 4 we examine the cosmological\nimplications of the model and again discover that a surprisingly large\nnumber of observed facts are neatly explained. Finally in Section 5 we\nmake some comments and observations.\n\\section{Quantum Mechanical Black Holes}\nIf we adhoc treat an electron as a charged and spinning black hole, described\nby the Kerr-Newman metric, the pleasing fact which emerges is that this\nmetric describes the gravitational and electromagnetic field of an electron\nincluding the anomalous gyromagnetic ratio$^2$, $g=2.$\\\\\nHowever the horizon of the Kerr-Newman Black Hole becomes in this case\ncomplex$^3$,\n\\begin{equation}\nr_+ = \\frac{GM}{c^2} + \\imath b,b \\equiv (\\frac{G^2Q^2}{c^8} + a^2 -\n\\frac{G^2M^2}{c^4})^{1\/2}\\label{e1}\n\\end{equation}\nwhere $G$ is the gravitational constant, $M$ the mass and $a \\equiv L\/Mc,L$\nbeing the angular momentum. That is, we have a naked singularity apparently\ncontradicting the cosmic censorship conjecture. However, in the Quantum\nMechanical domain, (\\ref{e1}) can be seen to be meaningful.\\\\\nInfact, the position coordinate for a Dirac particle is\ngiven by$^4$\n\\begin{equation}\nx_\\imath = (c^2p_\\imath H^{-1} t + a_\\imath)+\\frac{\\imath}{2}\nc\\hbar (\\alpha_\\imath - cp_\\imath H^{-1})H^{-1},\n\\label{e2}\n\\end{equation}\nwhere $a_\\imath$ is an arbitrary constant and $c\\alpha_\\imath$ is the velocity operator\nwith eigen values $\\pm c$. The real part in (\\ref{e2}) is the usual position\nwhile the imaginary part arises from Zitterbewegung. Interestingly, in both\n(\\ref{e1}) and (\\ref{e2}), the imaginary part is of the order of $\\frac{\\hbar}\n{mc}$, the Compton wavelength, and leads to an immediate identification of\nthese two equations. We must remember that our physical measurements are\ngross - they are really measurements averaged over a width\nof the order $\\frac{\\hbar}{mc}$. Similarly, time measurements are imprecise\nto the tune $\\sim \\frac{\\hbar}{mc^2}$. Very precise measurements if possible,\nwould imply that all Dirac particles would have the velocity of light, or\nin the Quantum Field Theory atleast of Fermions, would lead to divergences.\n(This is closely related to the non-Hermiticity of position operators in\nrelativistic theory as can be seen from equation (\\ref{e2}) itself$^5$.\nPhysics begins after an averaging over the above unphysical\nspace-time intervals. In the process as is known (cf.ref.5), the imaginary\nor non-Hermitian part of the position operator in (\\ref{e2}) disappears.\nThat is in the case of the QMBH (Quantum Mechanical Black Hole), obtained by\nidentifying (\\ref{e1}) and (\\ref{e2}), the naked singularity is shielded\nby a Quantum Mechanical censor.\\\\\nTo examine this situation more closely we reverse the arguments after\nequation (\\ref{e2}), and consider instead the complex displacement,\n\\begin{equation}\nx^\\mu \\to x^\\mu + \\imath a^\\mu\\label{e3}\n\\end{equation}\nwhere $a^o \\approx \\frac{\\hbar}{2mc^2}, \\mbox{and} a^\\mu \\approx \\frac{\\hbar}{mc}$\nas before. That is, we probe into the QMBH or the Zitterbewegung region\ninside the Compton wavelength as suggested by (\\ref{e1}) and (\\ref{e2}).\nRemembering that $|a^\\mu| < < 1$, we have, for the wave function,\n\\begin{equation}\n\\psi (x^\\mu) \\to \\psi (x^\\mu + \\imath a^\\mu) = \\frac{a^\\mu}{\\hbar}\n[\\imath \\hbar \\frac{\\partial}{\\partial x^\\mu} + \\frac{\\hbar}{a^\\mu}]\n\\psi (x^\\mu)\\label{e4}\n\\end{equation}\nWe can identify from (\\ref{e4}), by comparison with the well known electromagnetism-\nmomentum coupling, the usual electrostatic charge as,\n\\begin{equation}\n\\Phi e = \\frac{\\hbar}{a^o} = mc^2\\label{e5}\n\\end{equation}\nIn the case of the electron, we can verify that the equality (\\ref{e5})\nis satisfied. Infact it was shown that from here we can get a rationale\nfor the value of the fine structure constant (cf.ref.1).\\\\\nWe next consider the spatial part of (\\ref{e3}), viz.,\n$$\\vec x \\to \\vec x + \\imath \\vec a, \\mbox{where} |\\vec a| = \\frac{\\hbar}{2mc},$$\ngiven the fact that the particle is now seen to have the charge $e$ (and mass\n$m$). As is well known this leads in General Relativity from the static Kerr\nmetric to the Kerr-Newman metric where the gravitational and electromagnetic\nfield of the particle is given correctly, including the anomalous factor\n$g = 2$. In General Relativity, the complex transformation (\\ref{e3}) and\nthe subsequent emergence of the Kerr-Newman metric has no clear explanation. Nor\nthe fact that, as noted by Newman$^6$ spin is the orbital angular momentum\nwith an imaginary shift of origin. But in the above context we can see the\nrationale: the origin of (\\ref{e3}) lies in the QMBH and Zitterbewegung\nprocesses inside the Compton wavelength.\\\\\nHowever the following question has to be clarified: How can an electron\ndescribed by the Quantum Dirac spinor $(\\theta_\\chi)$, where $\\theta$\ndenotes the positive energy two spinor and $\\chi$ the negative energy\ntwo spinor, be identified with the geometrodynamic Kerr-Newman Black\nHole characterised by the curved space time (without any doublevaluedness,\ncf.ref.2).\\\\\nWe observe that as is well known,$^7$ at and within the Compton wavelength\nit is the negative energy $\\chi$ that dominates. Further, under reflection,\nwhile $\\theta \\to \\theta, \\chi$ behaves like a psuedo-spinor,\\\\\n$$\\chi \\to -\\chi$$\nHence the operator $\\frac{\\partial}{\\partial x^\\mu}$ acting on $\\chi$, a\ndensity of weight $N = 1,$ has the following behaviour$^8$,\n\\begin{equation}\n\\frac{\\partial \\chi}{\\partial x^\\mu} \\to \\frac{1}{\\hbar} [\\hbar \\frac{\\partial}\n{\\partial x^\\mu} - NA^\\mu]\\chi\\label{e6}\n\\end{equation}\nwhere,\n\\begin{equation}\nA^\\mu = \\hbar \\Gamma_\\sigma^{\\mu \\sigma} = \\hbar \\frac{\\partial}{\\partial x^\\mu}\nlog (\\sqrt{|g|})\\label{e7}\n\\end{equation}\nAs before we can identify $NA^\\mu$ in (\\ref{e6}) with the electromagnetic\nfour potential. That $N = 1$, explains the fact that charge is discrete.\\\\\nIn this formulation, electromagnetism arises from the covariant derivative\nwhich is the result of the Quantum Mechanical behaviour of the negative\nenergy components of the Dirac spinor at the Compton wavelength scale. We can see\nat once how an electron can be associated with curvature and how the double\nconnectivity of spin half surfaces in the geometrodynamical formulation.\n(\\ref{e7}) strongly resembles Weyl's formulation for the unification\nof electromagnetism and gravitation$^9$. However it must be noted that the\noriginal Christofell symbol of Weyl contained two independent entities viz.\nthe metric tensor \\underline{and} the electromagnetic potential, so that there was\nreally no unification. In our formulation we have used only the Quantum\nMechanical psuedo spinor property.\\\\\nSo we could treat the Quantum Mechanical Black Hole as a relativistic fluid\nof subconstituents (or Ganeshas). In a linearized theory (cf.ref.2) we\nhave\n\\begin{equation}\ng_{\\mu v} = \\eta_{\\mu v} + h_{\\mu v}, h_{\\mu v} = \\int \\frac{4T_{\\mu v}(t -\n|\\vec x - \\vec x'|, \\vec x')}{|\\vec x - \\vec x'|}d^3 x'\\label{e8}\n\\end{equation}\nIt was then shown, (cf.ref.1), that not only do we recover the Quantum\nMechanical spin but using equation (\\ref{e7}) and (\\ref{e8}) that for\n$r = |\\vec x| >> |\\vec x'|$ we get\n\\begin{equation}\n\\frac{e'e}{r} = A_o \\sim \\frac{\\hbar c^3}{r} \\int \\rho \\omega d^3 x'\n\\sim (Gmc^3)\\frac{mc^2}{r}\\label{e9}\n\\end{equation}\nwhere $e' = 1 \\mbox{esu}$ corresponds to the charge $N = 1$ and $e$ is the\ntest charge. (\\ref{e9}) is correct and infact leads to the well known empirical result,\n\\begin{equation}\n\\frac{e^2}{Gm^2} \\sim 10^{40},\\label{e10}\n\\end{equation}\nThe above model gives a rationale for the left handedness of the neutrino,\nwhich can be treated as an electron with vanishing mass so that the\nCompton wavelength becomes arbitrarily large. For such a particle, we\nencounter in effect the region within the Compton wavelength with the pseudo\nspinorial property discussed above, that is left handedness.\\\\\nFinally it may be remarked that the electron, the positron and its special case the neutrino\nare the fundamental elementary particles which could be used to generate\nthe mass spectrum of elementary particles$^{10}$.\\\\\nWe now briefly examine why the Compton wavelength emerges as a fundamental\nlength. Our starting point could be the Dirac or Klein-Gordon equations. For\nsimplicity we consider the Klein-Gordon equation. It is well known that the\nposition operator is given by$^{5}$\n\\begin{equation}\n\\vec X_{op} = \\vec x_{op} - \\frac{\\imath \\hbar c^2}{2} \\frac{\\vec p}{E^2}\\label{e11}\n\\end{equation}\n(The Dirac equation also has a similar case).\\\\\nWe saw in (ref.1) that the imaginary part in equation (\\ref{e11}) which\nmakes $\\vec X_{op}$ non-Hermitian, and for the Dirac particle gives Zitterbewegung\ndisappears on averaging over intervals $\\Delta t \\sim \\frac{\\hbar}{mc^2} (\\mbox{and}\n\\Delta r \\sim \\frac{\\hbar}{mc})$ so that $\\vec X_{op}$ becomes Hermitian (this is\nalso the content of the Foldy-Wothuysen transformation). Our physics, as\npointed out begins after such an average or Hermitization. Our measurement\nin other words are necessarily gross to this extent - we will see this more\nclearly. From equation (\\ref{e11})\nwe now get\n\\begin{equation}\n\\hat X^2_{op} \\equiv \\frac{2m^3c^4}{\\hbar^2} X^2_{op} = \\frac{2m^3c^6}{\\hbar^2}\nx^2 + \\frac{p^2}{2m}\\label{e12}\n\\end{equation}\nMathematically equation (\\ref{e12}) shows that $\\hat X^2_{op}$ gives a problem\nidentical to the harmonic oscillator with quantized levels: Infact the quantized\n\"space-levels\" for $\\vec X^2_{op}$ turn out to be multiples of $(\\hbar\/mc)^2$!\nFrom here, we get $\\Delta t = \\frac{\\Delta x}{c} = \\frac{\\hbar}{mc^2}$.\n\\section{The formation of QMBH particles}\nWe now investigate how such QMBH can be formed. For this we digress\ntemporarily to vaccuum fluctuations. It is well known that there is a zero\npoint field (ZPF). According to QFT this arises due to the virtual quantum\neffects of the electromagnetic field already present. Whereas according to\nwhat has now come to be called Stochastic Electrodynamics (SED), it is\nthese ZPF that are primary and result in Quantum Mechanical primary effects\n$^{11}$. Many Quantum Mechanical effects can indeed be explained this way.\nWithout entering into the debate about the ZPF fluctuations for the moment, we observe that\nthe energy of the fluctuations of the magnetic field in a region of length\n$\\lambda$ is given by$^{2}$ $(\\vec E$ and $\\vec B$ are electromagnetic field\nstrengths)\n\\begin{equation}\nB^2 \\sim \\frac{\\hbar c}{\\lambda^4}\\label{e13}\n\\end{equation}\nIf $\\lambda$ as in the QMBH is taken to be the Compton wavelength,\n$\\frac{\\hbar}{mc}$ (\\ref{e13}) gives us for the energy in this volume\nof the order $\\lambda^3$,\\\\\n$$\\mbox{Total\\quad energy\\quad of\\quad QMBH\\quad}\\sim \\frac{\\hbar c}{\\lambda} =\nmc^2,$$\nexactly as required. In other words the entire energy of the QMBH\nof mass $m$ can be thought to have been generated by the fluctuations\nalone. Further the fluctuation in curvature over the length $l$ is given\nby$^{2}$,\n\\begin{equation}\n\\Delta R \\sim \\frac{L^*}{l^3},\\label{e14}\n\\end{equation}\nwhere $L^*$ is the Planck length of the order $10^{-33}cms$.\\\\\nFor the electron which we consider, $l$ is of the order of the Compton\nwavelength, that is $10^{-11}cms$. Substitution in (\\ref{e14}) therefore\ngives\n$$\\Delta R \\sim 1$$\nIn other words the entire curvature of the QMBH is also generated by these\nfluctuations. That is the QMBH can be thought to have been created by\nthese fluctuations alone.\\\\\nWithin the framework of QED, we can come to this conclusion in another\nway$^{12}$. It is known that the vaccuum energy of the electron field with\na cut off $k_{max}$ is given by,\n\\begin{equation}\n\\frac{\\mbox{Energy}}{\\mbox{Volume}} \\sim \\hbar c k^4_{max}\\label{e15}\n\\end{equation}\nThis is the same as equation (\\ref{e13}) encountered earlier. Also the\ninfinite energy of the vaccuum is avoided by the assumption of the cut\noff normally taken to be of the order of a typical Compton wavelength on\nthe ground that we do not know that the laws of electromagnetism are\nvalid beyond these high frequencies, that is within these length scales.\\\\\nBut the preceding discussion shows that it is natural to take $k_{max} =\n\\frac{mc}{\\hbar},$ the inverse Compton wavelength of the electron. The energy\nof the electron from equation (\\ref{e15}) then comes out to be\n$$E \\sim mc^2,$$\nas before. So we are led to the important conclusion that the\ninfinity of QED is avoided by the fact that QMBH are formed, rather than by\nthe arbitrary prescription of a cut off. Infact there is a further bonus\nand justification for the above interpretation. Let us use in (\\ref{e15})\nthe pion Compton wavelength as the cut off. The reason we choose the pion\nis that it is considered to be a typical elementary particle in the sense\nthat it plays a role in the strong interactions, and further it could\nbe used as a building block for developing a mass spectrum, and finally\nas seen in (ref.1) can be considered to be made up of an electron and\na positron. Then from (\\ref{e15}) we can recover the pion mass,\n$m_\\pi$ and moreover,\n\\begin{equation}\nNm_\\pi = M,\\label{e16}\n\\end{equation}\nwhere $N$ is the number of elementary\nparticles, typically pions, $N \\sim 10^{80}$ and $M$ is the mass\nof the universe,viz. $10^{56}gms$.\\\\\nIn other words, in our interpretation we have not only avoided the QED\ninfinity but have actually recovered the mass of the universe. We will return\nto this point shortly.\\\\\nWe now consider the same scenario from a third point of view, viz. from the\nstandpoint of Quantum Statistical Mechanics. Here also the spirit is that\nof randomness$^{13}$. A state can be written as\n\\begin{equation}\n\\psi = \\sum_{n} c_n \\phi_n,\\label{e17}\n\\end{equation}\nin terms of basic states $\\phi_n$ which\ncould be eigen states of energy for example, with eigen values $E_n$. It\nis known that (\\ref{e17}) can be written as\n\\begin{equation}\n\\psi = \\sum_{n} b_n \\phi_n\\label{e18}\n\\end{equation}\nwhere $|b_n|^2 = 1$ if $E<E_n<E+\\Delta$, and $= 0$ otherwise under the assumption\n\\begin{equation}\n\\overline{(c_n,c_m)} = 0, n \\ne m\\label{e19}\n\\end{equation}\n(Infact $n$ could stand for not a single state but for a set of states\n$n_\\imath$ and so also $m$). Here the bar denotes a time average over a\nsuitable interval. This is the well known Random Phase Axiom and arises\ndue to the total randomness amongst the phases $c_n$. Also the expectation\nvalue of any operator $O$ is given by\n\\begin{equation}\n<O> = \\sum_{n} |b_n|^2 (\\phi_n, O \\phi_n)\/ \\sum_{n} |b_n|^2\\label{e20}\n\\end{equation}\n(\\ref{e18}) and (\\ref{e20}) show that effectively we have incoherent states\n$\\phi_1, \\phi_2,....$ once averages over time intervals for the phases\n$c_n$ in (\\ref{e19})vanish owing to their relative randomness.\\\\\nIn the light of the preceding discussion of random fluctuations in the context of QMBH\nin SED and QED, we can interpret the above meaningfully: We can identify\n$\\phi_n$ with the ZPF. The time averages are the Zitterbewegung averages\nover intervals $\\sim \\frac{\\hbar}{mc^2}$. We then get disconnected or\nincoherent particles or QMBH from a single background of vaccuum\nfluctuations exactly as before. The incoherence arises because of the well\nknown random phase relation (\\ref{e19}) that is after averaging over the\nsuitable interval.\\\\\nBut in all of the above considerations, and in present day theory the question\nthat comes up is: How can we reconcile the fact that the various particles\nin the universe are not infact incoherent but rather occupy a single\ncoherent space-time. The answer which can now be seen to emerge in the\nlight of the above discussion is that all these particles are linked by\ninteraction. These interactions as pointed out in (ref.1) arise within\nthe Compton wavelength or Zitterbewegung region, that is in phenomena\nwithin the time scale $\\frac{\\hbar}{mc^2}$. It will be observed in the\nabove discussion that at these time scales the equation (\\ref{e19}) is\nno longer valid and we have to contend with equation (\\ref{e17}) rather\nthan equation (\\ref{e18}). So interactions arising within the\nCompton wavelength link or make coherent\nthe various particles.\\\\\nInfact all this is perfectly in tune with the QFT picture wherein the\ninteractions are caused by virtual particles with life time less than\n$\\frac{\\hbar}{mc^2}$. It may also be observed that in Wheeler's Geometrodynamical\nmodel$^{14}$, the various particles are linked by exactly such\nwormholes linking distant regions.\\\\\nIn the above formulation we could take $\\phi_n$ to be the particlets or Ganeshas instead of\nenergy eigen states, that is to be position eigen states and consider sets\n$$\\overline{(c_{n_\\imath}, c_{m_j})} = 0,$$\nexactly as before (cf.(\\ref{e19})). Each set $\\phi_{n_\\imath}$ defines a particle\n$P_n$ consisting of $n_\\imath$ Ganeshas or particlets. It is the link\nat $\\Delta t < \\hbar\/mc^2$ between $P_n$ and $P_m$ which puts otherwise incoherent particles into a\nsingle space-time, that is allows interactions.\\\\\nIn other words, a set of particles can be said to be in the same space-time\nif every particle interacts with atleast one other member of the set.\\\\\nFor completeness we mention that the above bunching could be carried out\nin principle for two\nor more universes. Thus a set of particles constitutes universe $U_1$ while\nanother set of particles constitute an incoherent universe $U_2$. Again the\nincoherence can be broken at a suitable time scale (cf.ref.15 for a pictorial\nmodel in terms of wormholes).\\\\\nThere is another way of looking at all this.\nWe first note that the space-time symmetry of relativity has acquired\na larger than life image. Infact our perception of the universe is\nessentially one of all space (or as much of it as possible) at one instant\nof time (cf.also ref.2). Further, time is essentially an ordering or sequencing\nof events. To understand time we must know on what basis this ordering is\ndone so that causality and other laws of physics hold or in other words we\nhave the universe of the physical hyperboloid.\\\\\nWe now approach this problem by trying to liberate the sequence of\nevents in time from any ordering at all. At first sight it would appear that\nthis approach would lead to a chaotic universe without physics that is\ncausality, interaction and so on. We will actually try to attempt to explain\nthe emergence of physics from such a, what may be called pre-space-time scenario. It must be\nnoted that both Special and General Relativity work in a deterministic\nspace-time. Even relativistic Quantum Mechanics and Quantum Field Theory\nassume the space-time of Special Relativity. Quantum Gravity on the other\nhand which has not yet proved to be a completely successful theory questions\nthis concept of space-time$^{16}$.\\\\\nWhile a random time sequence is ruled out at what may be called the macro\nlevel, in our case above the Compton wavelength, within the framework of\nQMBH and as seen above this is certainly possible below the Compton\nwavelength scale. Infact this is the content of non locality and non Hermiticity\nof the Zitterbewegung in the region of QMBH.\\\\\nSo we start with truly instantaneous point particles or particlets (or Ganeshas)\nwhich are therefore indistinguishable, (cf. ref.1) (and could be denoted by\n$\\phi_n$ of (\\ref{e17})). We then take a random sequence of such\nparticlets$^{13}$. Such a sequence for the interval $\\Delta t \\sim \\frac\n{\\hbar}{mc^2}$ in time collectively constitutes a particle that has come\ninto existence and is spread over a space interval of the order of the\nCompton wavelength. In other words we have made a transition from pre-\nspace-time to a particle in space-time. This is exactly the averaging over random phases in\nequation (\\ref{e19}). Hermiticity of position operators has now been\nrestored and we are back with the states $\\phi_n$ in equation\n(\\ref{e18}). All this is in the spirit that our usual time is such that,\nwith respect to it vaccuum fluctuations are perfectly random as pointed\nby Macrea$^{17}$. So the subconstituents of the relativistic fluid given\nin (\\ref{e8}) (or the Quantized Vortex in the hydrodynamical formulation\n(cf. ref.1)), are precisely these particlets.\\\\\nTo visualize the above consideration in greater detail we first consider strictly\npoint particles obtained by taking the random sequences over time\nintervals $\\sim \\frac{\\hbar}{mc^2}$. We consider an assembly of such truly\npoint particles which as yet we cannot treat either with Fermi-Dirac or\nBose-Einstein statistics but rather as a Maxwell-Boltzman distribution. If there\nare $N$ such particles in a volume $V$, it is known that$^{13}$, the volume\nper particle is of the order of,\n$$(\\frac{V}{N})^{1\/3} \\sim \\lambda_{thermal} \\approx \\frac{\\hbar}{\\sqrt{m^2c^2}} =\n\\frac{\\hbar}{mc},$$\nwhere we take the average velocity of each particle to be equal to $c$. Infact,\nthis is exactly what happens, as Dirac pointed out (cf. ref.4), for a truly\nhypothetical point electron, in the form of Zitterbewegung within the\nCompton wavelength.\\\\\nSo the Compton wavelength arises out of the (classical) statistical inability to\ncharacterise a point particle precisely: It is not that the particle has an\nextension per se. In this sense the Compton wavelength has a very\nCopenhagen character, except that it has been deduced on the basis of an\nassembly of particles rather than an isolated particle.\n\\section{The Universe of Fluctuations}\nThe question that arises is, what are the cosmological implications of the\nabove scenario, that is, if we treat the entire universe as arising from\nfluctuations, is this picture consistent with the observed universe? It\nturns out that not only is there no inconsistency, but on the contrary\na surprising number of correspondences emerge.\\\\\nThe first of these is what we have encountered a little earlier viz.\nthe fact that we recover the mass of the universe as in equation (\\ref{e16}).\\\\\nWe can next deduce another correspondence. The ZPF gives the correct\nspectral density viz.\n$$\\rho (\\omega) \\alpha \\omega^3$$\nand infact the Planck spectrum$^{18}$. We then get the total intensity\nof radiation from the fluctuating field due to a single star as$^{11}$,\n$$I(r) \\alpha \\frac{1}{r^2}$$\nIt then follows that given the observed isotropy and homogeneity of the\nuniverse at large, as is well known,\n\\begin{equation}\nM \\alpha R\\label{e21},\n\\end{equation}\nwhere $R$ is the radius of the universe.\\\\\nEquation (\\ref{e21}) is quite correct and infact poses a puzzle, as is\nwell known and it is to resolve this dependence that dark matter has\nbeen postulated$^{19}$ whereas in our formulation the correct mass radius\ndependence has emerged quite naturally without any other adhoc postulates.\\\\\nAs we have seen above the Compton wavelength of a typical particle, the pion viz $l_\\pi$ can be\ngiven in terms of the volume of uncertainity. However in actual observation\nthere is an apparent paradox. If the universe is $n$ dimensional then we\nshould have,\n$$Nl^n_\\pi \\sim R^n$$\nfor the universe itself. This relation is satisfied with $n = 2$ in which\ncase we get a relation that has been known emperically viz.,\n$$l_\\pi \\sim \\frac{R}{\\sqrt{N}}$$\n(Even Eddington had used this relation).\\\\\nSo in conjunction with (\\ref{e16}) we have an apparent paradox where the actual universe appears to be\ntwo dimensional. This will be resolved shortly and it will be seen that\nthere is no contradiction.\\\\\nAnother interesting consequence is as follows: According to our formulation\nthe gravitational potential energy of a pion in a three dimensional isotropic\nsphere of pions is given by\n$$\\frac{Gm_\\pi M}{R}$$\nThis should be equated with the energy of the pion viz. $m_\\pi c^2$. We then\nget,\n\\begin{equation}\n\\frac{GM}{c^2} = R,\\label{e22}\n\\end{equation}\na well known and observationally correct relation. In our formulation we\nget $m_\\pi$ from the ZPF and given $N$ we know $M$ so that from equation\n(\\ref{e22}) we can deduce the correct radius $R$ of the universe.\\\\\nProceeding further we observe that the fluctuations in the particle number $N$ itself is\nof the order $\\sqrt{N}^{13,20}$. Also $\\Delta t$ above is the typical\nfluctuating time. So we get,\n$$\\frac{dN}{dt} = \\frac{\\sqrt{N}}{\\Delta t} = \\frac{m_\\pi c^2}{\\hbar} \\sqrt{N}$$\nwhence as $t = 0, N = 0,$\n\\begin{equation}\n\\sqrt{N} = \\frac{2m_\\pi c^2}{\\hbar} .T\\label{e23}\n\\end{equation}\nwhere $T$ is the age of the universe $\\approx 10^{17}secs$. It is remarkable\nthat equation (\\ref{e23}) is indeed correct. One way of looking at this is\nthat not only the radius but also the age of the universe is correctly\ndetermined. As we saw before,\n$$R = \\frac{GM}{c^2} = \\frac{GNm_\\pi}{c^2}$$\nso that\n\\begin{equation}\n\\frac{dR}{dt} = \\frac{Gm_\\pi}{c^2} \\frac{dN}{dt} = \\frac{Gm^2_\\pi}{\\hbar} \\sqrt{N} = HR\\label{e24}\n\\end{equation}\nwhere\n\\begin{equation}\nH = \\frac{Gm_\\pi^3 c}{\\hbar^2}\\label{e25}\n\\end{equation}\nOne can easily verify that (\\ref{e25}) is satisfied for the Hubble constant so\nthat (\\ref{e24}) infact gives the Hubble's velocity distance relation.\\\\\nFurthermore from (\\ref{e25}) we deduce that,\n\\begin{equation}\nm_\\pi = (\\frac{\\hbar^2 H}{Gc})^{1\/3}\\label{e26}\n\\end{equation}\nIt is remarkable that equation (\\ref{e26}) is known to be true from a\npurely empirical standpoint$^{21}$. However we have actually deduced it in\nour formalism. Another way of interpreting equation (\\ref{e26}) is that\ngiven $m_\\pi$ (and $\\hbar, G$ and $c$) we can actually deduce the value of\n$H$ in our formalism.\\\\\nFrom Equation (\\ref{e24}), we deduce that,\n\\begin{equation}\n\\frac{d^2R}{dt^2} = H^2R\\label{e27}\n\\end{equation}\nThat is, effectively there is a cosmic repulsion. Infact, from (\\ref{e27}) we\ncan identify the cosmological constant as\n$$\\Lambda \\sim H^2$$\nwhich is not only consistent but agrees exactly with the limit on this constant\n(cf.ref.2).\\\\\nThe final correspondence is to do with an explanation for the microwave\ncosmic background radiation within the above framework of fluctuations. It\nis well known that the fluctuations of the Boltzmann $H$ function for interstellar\nspace is of the order of $10^{-11}secs^{13}$. These fluctuations can be\nimmediately related to the ZPF exactly as in the case of the Lamb shift\n(cf.ref.2). So $\\frac{\\hbar}{mc^2} = 10^{-11}$ or the associated wavelength\nviz.,\n$$\\frac{\\hbar}{mc} \\sim 0.3 cms,$$\nwhich corresponds to the cosmic background\nradiation$^{3}$. The same conclusion can be drawn from a statistical\ntreatment of interstellar Hydrogen$^{22}$.\n\\section{Comments}\n1. We could arrive at equation (\\ref{e13}) by a slightly different route\n(cf.ref.2). We could start with a single oscillator in the ground state\ndescribed by the wave function\n\\begin{equation}\n\\psi(x) = \\mbox{const} \\quad exp[-(m\\omega\/2 \\hbar)x^2]\\label{e28}\n\\end{equation}\nwhich would fluctuate with a space uncertainity of\n$$\\Delta x \\sim (\\hbar\/m\\omega)^{\\frac{1}{2}} = \\frac{\\hbar}{mc}$$\nThe electromagnetic ZPF could be treated as an infinite collection of\nindependent oscillators and we could recover equation (\\ref{e13}).\\\\\n2.Earlier we skirted the issue whether the ZPF is primary or secondary.\nWe now start either with the ZPF or with the pre-space-time background\nfield of the instantaneous particles (or Ganeshas). We could assign a\nprobability $p$ for them to appear in space-time and the probability\n$1-p = q$ for this not to happen. From here we get the probability for\n$N$ of them to appear as\n\\begin{equation}\n\\mbox{Probability}\\quad \\alpha \\quad exp \\quad [-\\mu^2 N^2]\\label{e29}\n\\end{equation}\nThis immediately ties up with the considerations following from equation\n(\\ref{e12}) (cf.ref.2), if we identify $N$ with $x$. The justification\nfor this can be seen by a comparison with $|\\psi (x)|^2$ from (\\ref{e28}):\nFrom (\\ref{e29}), the probability is non-negligible if\n$$\\Delta N \\sim \\frac{1}{\\mu},$$\nwhich turns out to be, from (\\ref{e28}),\n$$\\Delta N \\sim \\frac{1}{\\mu} \\approx \\frac{\\hbar}{mc},$$\nthe Compton wavelength. Thus once again we conclude from (\\ref{e29})\nthat a probabilistic fluctuational collection of instantaneous particlets\nfrom a pre-space-time background shows up as a particle in space-time.\\\\\nWheeler considers the algebra of propositions as providing the link\nbetween what he terms pre-geometry and geometrodynamics. In our formulation\nprobabilistic fluctuations lead to space-time and physics from\npre-space-time.\\\\\n3. It was pointed out that the equation\n\\begin{equation}\nl_\\pi \\sim \\frac{R}{\\sqrt{N}}\\label{e30}\n\\end{equation}\nsuggests that the universe is apparently two dimensional. This paradoxical\nresult is consistent with astrophysical data (cf.ref.19). We could resolve\nthe paradox as follows:\\\\\nWe start with the fact that the universe on the average is neutral. Further\nthe fluctuation in the number of electrons is $\\sim \\sqrt{N}$. So an extra\nelectrostatic potential energy is created which is balanced by (or in\nour formulation manifests itself as) the energy of the electron itself\n(cf.ref.20):\n$$\\frac{e^2\\sqrt{N}}{R} = mc^2$$\nwhich leads to the above relation.\\\\\nSo in the conventional theory, that is in the language of a fixed particle\nnumber universe, we would say that the universe is apparently two dimensional.\nBut once we recognise the fluctuations, the universe is really three\ndimensional. Infact the fundamental equation (\\ref{e10}) which was\nderived purely from the point of view of an isolated particle can also be\nderived on the basis of a \"two dimensional\" universe$^{23}$.\\\\\n4. The considerations of the previous section show that there exists, what\nmay be called a micro-macro nexus: Fundamental constants of Quantum Theory\nare tied up with constants from macro physics and cosmology. So the universe\nis holistic. It has a slightly different connotation from the Machian formulation,\nbecause the latter deals with a deterministic universe with rigid physical\nlaws.\\\\\nInfact from (\\ref{e30}), (\\ref{e22}) and (\\ref{e23}), we can deduce that,\n\\begin{equation}\n\\frac{2Gm_\\pi^3c}{\\hbar^2} = \\frac{1}{T}\\label{e31}\n\\end{equation}\nwhich is a variant of equation (\\ref{e10}), if we replace its right side\nby $\\sqrt{N}$. This may be interpreted as giving $e,G,c$ or $\\hbar$ in\nterms of $m_\\pi\\quad \\mbox{and}\\quad N$. More interestingly, (\\ref{e31})\ngives the variation of $G$, or more generally, the left side, with the\nage of the universe (cf.ref.2 for Dirac's conjecture in this connection).\\\\\n5. The quantization formula for space following from equation (\\ref{e12}),\nreflects an empirical formula deduced by Chacko$^{24}$ which can be used to\ngenerate a mass spectrum. It also vindicates a close connection between\nenergy and space-time: As pointed out (cf.ref.1) inertial mass arises from\nthe non local Zitterbewegung processes within the Compton wavelength$^{25}$.\\\\\n6. Finally we observe that inspite of similarities, the above scenario of\nfluctuations differs from steady-state cosmology and the $C$ field\nformulation$^{26}$.\n\\newpage\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nA citation network is an important source of analysis in science.\nCitations serve multiple purposes such as crediting an idea, signaling\nknowledge of the literature, or critiquing others' work \\citep{martyn1975citation}.\nWhen citations are thought of as impact, they inform tenure, promotion,\nand hiring decisions \\citep{meho2007impact}. Furthermore, scientists\nthemselves make decisions based on citations, such as which papers\nto read and which articles to cite. Citation practices and infrastructures\nare well-developed for journal articles and conference proceedings.\nHowever, there is much less development for dataset citation. This\ngap affects the increasingly important role that datasets play in\nscientific reproducibility \\citep{task2013out,belter2014measuring,robinson2016analyzing,park2018informal},\nwhere studies use them to confirm or extend the results of other research\n\\citep{sieber1995not,darby2012enabling}. One historical cause of\nthis gap is the difficulty in archiving datasets. While less problematic\ntoday, the citation practices for datasets take time to develop. Better\nalgorithmic approaches to track dataset usage could improve this state.\nIn this work, we hypothesize that a network flow algorithm could track\nusage more effectively if it propagates publication and dataset citations\ndifferently. With the implementation of this algorithm, then, it will\nbe possible to correct differences in citation behavior between these\ntwo types of artifacts, increasing the importance of datasets as first\nclass citizens of science.\n\nDifferent researchers use citation networks to evaluate the importance\nof authors \\citep{ding2009pagerank,ding2011applying,west2013author},\npapers \\citep{chen2007finding,ma2008bringing}, journals \\citep{bollen2006journal,bergstrom2007eigenfactor},\ninstitutions \\citep{fiala2013suborganizations} and even countries\n\\citep{fiala2012bibliometric}. The \\textsc{PageRank} algorithm \\citep{page1999pagerank}\nhas served as a base for much of these citation network-based evaluations.\nFor example, \\citet{bollen2006journal} proposed a weighted \\textsc{PageRank\n}to assess the prestige of journals, while \\citet{ding2009pagerank}\nand \\citet{ding2011applying} proposed a weighted \\textsc{PageRank\n}to measure the prestige of authors. \\citet{fiala2012time} defined\na time-aware \\textsc{PageRank }method for accurately ranking the most\nprominent computer scientists. \\citet{franceschet2017timerank} introduced\nan approach called \\textsc{TimeRank} for rating scholars at different\ntime points. \\textsc{TimeRank} updates the rating of scholars based\non the relative rating of the citing and cited scholars at the time\nof the citation. Citation networks are thus an important source of\ninformation for ranking homogenous types of nodes.\n\nHistorically, ranking datasets using citation networks is significantly\nmore challenging. These challenges have technical and social issues\nalike. First, datasets cost time and labor to prepare and to share,\nresulting in some articles failing to provide datasets \\citep{alsheikh2011public}.\nSecond, archiving and searching massive datasets is prohibitively\nexpensive and difficult. Third, scholars are not used to citing datasets.\nSurvey research shows that scholars value citing dataset \\citep{kratz2015researcher}\nyet they tend to cite the \\emph{article} rather than the dataset or\nthey merely mention the dataset without explicit reference \\citep{force2014encouraging}.\nTherefore, these reasons have prevented the proper assignment of credit\nto dataset usage.\n\nSeveral initiatives attempt to improve citation practices for datasets.\nIn 2014, the Joint Declaration Of Data Citation Principles was officially\nreleased. These principles, however, mainly focus on normalizing dataset\nreferences rather than normalizing storage and some other technical\nissues \\citep{altman2015introduction,callaghan2014joint,mooney2012anatomy}.\nFor instance, some researchers have suggested assigning specific DOIs\nto datasets to mitigate differences between datasets and articles\n\\citep{callaghan2012making}. Others have proposed to automatically\nidentify uncited or unreferenced datasets used in articles \\citep{boland2012identifying,kafkas2013database,ghavimi2016identifying}.\nAll these solutions try to make citation dataset behavior more standard\nor attempt to fix the citation network by estimating which data nodes\nare missing. Therefore, these solutions necessarily modify the source\nthat algorithms use to estimate impact.\n\nIn this article, we develop a method for assigning credit to datasets\nfrom citation networks of publications, assuming that dataset citations\nhave biases. Importantly, our method does not modify the source data\nfor the algorithms. The method does not rely on scientists explicitly\nciting datasets but infers their usage. We adapt the network flow\nalgorithm of \\citet{walker2007ranking} by including two types of\nnodes: datasets and publications. Our method simulates a random walker\nthat takes into account the differences between obsolescence rates\nof publications and datasets, and estimates the score of each dataset---the\n\\textsc{DataRank}. We use the metadata from the National Center for\nBioinformatics (NCBI) GenBank nucleic acid sequence and Figshare datasets\nto validate our method. We estimate the relative rank of the datasets\nwith the \\textsc{DataRank} algorithm and cross-validate it by predicting\nthe actual usage of them---number of visits to the NCBI dataset web\npages and downloads of Figshare datasets. We show that our method\nis better at predicting both types of usages compared to citations\nand has other qualitative advantages compared to alternatives. We\ndiscuss interpretations of our results and implications for data citation\ninfrastructures and future work.\n\n\\section{Why measure dataset impact?}\n\nScientists may be incentivized to adopt better and broader data sharing\nbehaviors if they, their peers, and institutions are able to measure\nthe impact of datasets (e.g., see \\citet{silvello2018theory} and\n\\citet{kidwell2016badges}). In this context, we review impact assessment\nconceptual frameworks and studies of usage statistics and crediting\nof scientific works more specifically. These areas of study aim to\ndevelop methods for scientific indicators of the usage and impact\nof scholarly outputs. Impact assessment research also derives empirical\ninsights from research products by assessing the dynamics and structures\nof connections between the outputs. These connections can inform better\npolicy-making for research data management, cyberinfrastructure implementation,\nand funding allocation.\n\nMethods for measuring usage and impact include a variety of different\ndimensions of impact, from social media to code use and institutional\nmetrics. Several of these approaches recognize the artificial distinction\nbetween the scientific process and product \\citep{priem2013scholarship}.\nFor example, altmetrics is one way to measure engagement with diverse\nresearch products and to estimate the impact of non-traditional outputs\n\\citep{priem2014altmetrics}. Researchers predict that it will soon\nbecome a part of the citation infrastructure to routinely track and\nvalue \\textquotedblleft citations to an online lab notebook, contributions\nto a software library, bookmarks to datasets from content-sharing\nsites such as Pinterest and Delicious\\textquotedblright{} \\citep[from ][]{priem2014altmetrics}.\nIn short, if science has made a difference, it will show up in a multiplicity\nof places. As such, a correspondingly wider range of metrics are needed\nto attribute credit to the many locations where research works reflect\ntheir value. For example, datasets contribute to thousands of papers\nin NCBI\\textquoteright s Gene Expression Omnibus and these attributions\nwill continue to accumulate, just like paper accumulate citations,\nfor a number of years after the datasets are publicly released \\citep{piwowar2011data,piwowar2013altmetrics}.\nEfforts to track these other sources of impact include ImpactStory,\nstatistics from FigShare, and Altmetric.com \\citep{robinson2017datacite}.\n\nCredit attribution efforts include those by federal agencies to expand\nthe definition of scientific works that are not publications. For\nexample, in 2013 the National Science Foundation (NSF) recognized\nthe importance of measuring scientific artifacts other than publications\nby asking researchers for \\textquotedblleft products\\textquotedblright{}\nrather than just publications . This represents a significant change\nin how scientists are evaluated \\citep{piwowar2013altmetrics}. Datasets,\nsoftware, and other non-traditional scientific works are now considered\nby the NSF as legitimate contributions to the publication record.\nFurthermore, real-time science is presented in several online mediums;\nalgorithms filter, rank, and disseminate scholarship as it happens.\nIn sum, the traditional journal article is increasingly being complemented\nby other scientific products \\citep{priem2013scholarship}.\n\nYet despite the crucial role of data in scientific discovery and innovation,\ndatasets do not get enough credit \\citep{silvello2018theory}. If\ncredit was properly accrued, researchers and funding agencies would\nuse this credit to track and justify work and funding to support datasets---consider\nthe recent Rich Context Competition which aimed at to filling this\ngap by detecting dataset mentions in full-text papers \\citep{zengnyu}.\nBecause these dataset mentions are not tracked by current citation\nnetworks, this leads to biases in dataset citations \\citep{robinson2016analyzing}.\nThe FAIR (findable, accessible, interoperable, reproducible) principles\nof open research data are one major initiative that is spearheading\nbetter practices with tracking digital assets such as datasets \\citep{wilkinson2016fair}.\nHowever, the initiative is theoretical, and lacks technical implementation\nfor data usage and impact assessment. There remains a need to establish\nmethods to better estimate dataset usage.\n\n\\section{Materials and methods}\n\n\\subsection{Datasets}\n\n\\subsubsection{OpenCitations Index (COCI)}\n\nThe OpenCitations index (COCI) is an index of Crossref's open DOI-to-DOI\ncitation data. We obtained a snapshot of COCI (November 2018 version),\nwhich contains approximately 450 million DOI-to-DOI citations. Specifically,\nCOCI contains information including citing DOI, cited DOI, the publication\ndate of citing DOI. The algorithm we proposed in the paper requires\nthe publication year. However, not all the DOIs in COCI have a publication\ndate. We will introduce Microsoft Academic Graph to fill this gap.\n\n\\subsubsection{Microsoft Academic Graph (MAG)}\n\nThe Microsoft Academic Graph is a large heterogeneous graph consisting\nof six types of entities: paper, author, institution, venue, event,\nand field of study \\citep{sinha2015overview}. Concretely, the description\nof a paper consists of DOI, title, abstract, published year, among\nother fields. We downloaded a copy of MAG in November 2019, which\ncontains 208,915,369 papers. As a supplement to COCI, we extract the\nDOI and published year from MAG to extend those DOIs in COCI without\na publication date.\n\n\\subsubsection{PMC Open Access Subset (PMC-OAS)}\n\nThe PubMed Central Open Access Subset is a collection of full-text\nopen access journal articles in biomedical and life sciences. We obtained\na snapshot of PMC-OAS in August 2019. It consists of about 2.5 million\nfull-text articles organized in well-structured XML files. The articles\nare identified by a unique id called PMID. We also obtained a mapping\nbetween PMIDs and DOIs from NCBI, which enabled us to integrate PMC-OAS\ninto the citation network.\n\n\\subsubsection{GenBank}\n\nGenBank is a genetic sequence database that contains an annotated\ncollection of all publicly available nucleotide sequences for almost\n420,000 formally described species \\citep{Sayers2019}. The information\nabout a nucleotide sequence in GenBank is organized as a record consisting\nof many data elements (fields) and stored in a flat-file (see Fig.\n\\ref{fig:sample-data-of}). The ACCESSION field contains the unique\nidentifier of the dataset. The last citation in the REFERENCE field\ncontains the information about the submitter, including the author\nlist and the date in which the dataset was introduced (e.g., ``16-JAN-1992''\nin Fig. \\ref{fig:sample-data-of}). We obtained a snapshot of the\nGenBank database (version 230) with 212,260,377 gene sequences. We\nremove those sequences without submission date. This left us with\n77,149,105 sequences.\n\nThe National Institutes of Health (NIH) provided us with number of\nvisits to a sequence's landing page for the top 1000 Nucleotide sequences\nduring the month of September 2012. We use these visits as a measure\nof real \\emph{usage.}\n\n\\begin{figure}\n\\begin{centering}\n\\includegraphics{genbank_record}\n\\par\\end{centering}\n\\caption{\\label{fig:sample-data-of} Sample record of a sequence submission\nfrom GenBank. The ACCESSION field is the unique identifier of a dataset.}\n\\end{figure}\n\n\n\\subsubsection{Figshare}\n\nFigshare is a multidisciplinary, open access research repository where\nresearchers can deposit and share their research output. Figshare\nallows users to upload various formats of research output, including\nfigures, datasets, and other media \\citep{thelwall2016figshare}.\nIn order to encourage data sharing, all research data made publicly\navailable has unlimited storage space and is allocated a DOI. This\nDOI is used by scientists to cite Figshare resources using traditional\ncitation methods. Figshare makes the research data publicly and permanently\navailable which mitigates the resource decay problem and improves\nresearch reproducibility \\citep{zeng2019deadscience}. A Figshare\nDOI contains the string 'figshare' (e.g., '10.6084\/m9.figshare.6741260').\nWe can leverage this feature to determine whether a publication cites\nFigshare resources by detecting Figshare-generated DOIs.\n\nFigshare also keeps track of dataset accesses, such as page views\nand dataset downloads. We get the downloads statistics of Figshare\nDOI from the Figshare Stats API\\footnote{https:\/\/docs.figshare.com\/\\#stats}\nand use it as a measure of real \\textit{usage}.\n\n\\subsection{Construction of citation network}\n\nThe citation networks in this paper consist of two types of nodes\nand two types of edges. The node is represented by the paper and the\ndataset and the edge is represented by the citation between two nodes.\nConcretely, papers cite each other to form paper-paper edges as datasets\ncan only be cited by papers which are represented by the paper-dataset\nedges. As shown in the construction workflow (Fig. \\ref{fig:Network-construction-workflow}),\nwe build the paper-paper citation network using COCI and MAG and build\ntwo separate paper-dataset edge sets using GenBank and Figshare. Then\nwe integrate the paper-dataset edge sets into the paper-paper citation\nnetwork to form two complete citation networks. The construction workflow\nis illustrated in Figure \\ref{fig:Network-construction-workflow}.\n\n\\begin{figure}\n\\begin{centering}\n\\includegraphics[width=1\\columnwidth]{network_construction}\n\\par\\end{centering}\n\\caption{\\label{fig:Network-construction-workflow}Citation network construction\nworkflow}\n\\end{figure}\n\n\n\\subsubsection{Paper-paper citation network}\n\nAs our proposed method takes the publication year into account, we\nneed to remove those edges without publication year. The DOI-DOI citation\nin COCI dataset provides us a skeleton of the citation network. Even\nthough COCI comes with a field named timespan which originally refers\nto the publication time span between the citing DOI and cited DOI,\nthis timespan leads to different results depending on the time granularity\n(i.e., year-only vs year+month). As explained above, we have to complement\nthe COCI dataset with MAG to complete the year of publication of cited\nand citing articles. By joining the COCI and MAG, we build a large\npaper-paper citation network consisting of 45,180,243 nodes and 443,055,788\nedges. As the usage data of GenBank only covers 2012 (see Genbank\nabove), we pruned the network to remove papers and datasets published\nafter 2012. For Figshare, we use all the nodes and edges. The statistics\nof the networks described above are listed in Table \\ref{tab:Statistics-of-network}.\n\n\\begin{table}\n\\caption{\\label{tab:Statistics-of-network}Statistics of article citation networks}\n\n\\centering{}%\n\\begin{tabular}{cccc}\n\\hline \nSources & Filter & Number of Nodes & Number of Edges\\tabularnewline\n\\hline \nCOCI (original) & N\/A & 46,534,424 & 449,840,585\\tabularnewline\nCOCI (filtered) & contains publication year & 21,689,394 & 203,884,791\\tabularnewline\nCOCI \\& MAG (for Figshare) & contains publication year & 45,180,243 & 443,055,788\\tabularnewline\nCOCI \\& MAG (for GenBank) & publication year \\ensuremath{\\le} 2012 & 30,304,869 & 212,410,743\\tabularnewline\n\\hline \n\\end{tabular}\n\\end{table}\n\n\n\\subsubsection{Paper-dataset citation network}\n\\begin{enumerate}\n\\item \\textbf{Constructing paper-dataset citations for GenBank. }As previously\ndescribed by \\citet{Sayers2019}, authors should use GenBank accession\nnumber with the version suffix as identifier to cite a GenBank data.\nThe accession number is usually mentioned in the body of the manuscript.\nThis practice enables us to extract GenBank dataset mention from the\nPMC-OAS dataset to build the paper-dataset citation network. \n\\begin{enumerate}\n\\item \\emph{Parsing XML file to extract full-text}\\textbf{. }We first parse\nthe XML files using XPath expressions to extract the PMID and the\nfull-text. We get 2,174,782 articles with PMID and full-text from\nPMC-OAS dataset.\n\\item \\emph{Matching the accession number to build paper-dataset citations}.\nAccording to the GenBank Accession Prefix Format, an accession number\nis composed of a fixed-number of letters plus a fixed-number of numerals\n(e.g., 1 letter + 5 numerals, 2 letters + 6 numerals). Based on the\nformat, we composed a regular expression to match individual mentions\nof accession numbers in the full-text. There are two kinds of accession\nnumber mentions: accession number only (e.g., U00096) and range of\naccession number (e.g., KK037225-KK037232). For the second kind, we\nexpanded the range to recover all the omitted accession numbers.\n\\end{enumerate}\n\\end{enumerate}\n\\begin{enumerate}[resume]\n\\item \\textbf{Extracting paper-dataset citation for Figshare. }As there\nis a string 'figshare' in a Figshare DOI, we can use a regular expression\nto search for them in COCI. \n\\begin{enumerate}\n\\item \\textit{Identifying Figshare DOI in the set of cited DOI. }In this\nstep, we extracted 918 Figshare DOIs as dataset candidates.\n\\item \\textit{Filtering by resource type. }Not all the Figshare DOIs are\ndatasets because Figshare supports many kinds of resources. We use\nthe Figshare Article API\\footnote{https:\/\/docs.figshare.com\/\\#public\\_article}\nto get the meta-data of a DOI. In the meta-data, there is a field\nindicating the resource type (type code 3 is dataset). After filtering\nthe candidates by resource type, we get 355 datasets.\n\\end{enumerate}\n\\end{enumerate}\n\n\\subsubsection{Visualization of citation network}\n\nFor the purpose of exploring this network, we sample about one thousand\nnodes and 1.5 thousand edges from the network. We observe four patterns\nof papers citing datasets (a dataset cannot cite anything): one-to-one,\none-to-many, many-to-one and many-to-many (Fig. \\ref{fig:network-of-sample}).\n\n\\begin{figure}\n\\begin{centering}\n\\includegraphics[width=1\\textwidth]{F1A_sampleData_colored}\n\\par\\end{centering}\n\\caption{\\label{fig:network-of-sample} Visualization of publication--dataset\ncitation network. Papers appear as red nodes and Datasets are green.\nThe lighter the color, the older the resource.}\n\\end{figure}\n\n\n\\subsection{Network models for scientific artifacts}\n\n\\subsubsection{\\textsc{NetworkFlow}}\n\nWe adapt the network model proposed in \\citet{walker2007ranking}.\nThis method, which we call \\textsc{NetworkFlow} here, is inspired\nby \\textsc{PageRank} and addresses the issue that citation networks\nare always directed back in time. In this model, each vertex in the\ngraph is a publication. The goal of this method is to propagate a\nvertex's impact through its citations.\n\nThis method simulates a set of researchers traversing publications\nthrough the citation network. It ranks publications by estimating\nthe average path length taken by researchers who traverse the network\nconsidering the age of resources and a stopping criterion. Mathematically,\nit defines a traffic function $T_{i}(\\tau_{\\text{pub}},\\alpha)$ for\neach paper. A starting paper is selected randomly with a probability\nthat exponentially decays in time with a \\emph{decay} parameter $\\tau_{\\text{paper}}$.\nEach occasion the researcher moves, it can stop with a probability\n$\\alpha$ or continue the search through the citation network with\na probability $1-\\alpha$. The predicted traffic $T_{i}$ is proportional\nto the rate at which the paper is accessed. The concrete functional\nform is as follows. The probability of starting at the $i$th node\nis \n\\begin{equation}\n\\rho_{i}\\propto\\exp\\left(-\\frac{\\text{age}_{i}}{\\tau_{\\text{pub}}}\\right)\\label{eq:starting-probability}\n\\end{equation}\n\nThen,\\textsc{ }the method defines a transition matrix from the citation\nnetwork as follows \n\\begin{equation}\nW_{ij}=\\begin{cases}\n\\frac{1}{k_{j}^{\\text{out}}} & \\text{if \\ensuremath{j} cites \\ensuremath{i}}\\\\\n0 & \\text{o.w.}\n\\end{cases}\\label{eq:transition-probability}\n\\end{equation}\nwhere $k_{j}^{\\text{out}}$ is the out-degree of the $j$th paper.\n\nThe average path length to all papers in the network starting from\na paper sampled from the distribution $\\rho$ is defined as \n\\begin{equation}\nT=I\\cdot\\rho+(1-\\alpha)W\\cdot\\rho+(1-\\alpha)^{2}W^{2}\\rho+\\cdots\\label{eq:average-path-length}\n\\end{equation}\n\nThe parameters $\\tau_{\\text{paper}}$ and $\\alpha$ are found by cross\nvalidation by predicting real traffic. In practice, this series can\nbe solved iteratively by computing the difference between $T_{t+1}$\nand $T_{t}$. For this and all algorithms used in this work, we stop\nthe iterations when the total absolute difference in rank between\ntwo consecutive iterations is less than $10^{-2}$ which typically\nrequired around 30 iterations.\n\n\\subsubsection{\\textsc{DataRank}}\n\nIn this article, we extend\\textsc{ NetworkFlow} to accommodate different\nkinds of nodes. The extension considers that the probability of starting\nat any single node should depend on whether the node is a publication\nor a dataset. This is, publications and datasets may vary in their\nrelevance period. We call this new algorithm \\textsc{DataRank}. Mathematically,\nwe redefine the starting probability in Eq. \\ref{eq:starting-probability}\nof the $i$th node as \n\\begin{equation}\n\\rho_{i}^{\\text{DataRank}}=\\begin{cases}\n\\exp\\left(-\\frac{\\text{age}_{i}}{\\tau_{\\text{pub}}}\\right) & \\text{if \\ensuremath{i} is a publication}\\\\\n\\exp\\left(-\\frac{\\text{age}_{i}}{\\tau_{\\text{dataset}}}\\right) & \\text{\\text{if \\ensuremath{i} is a dataset}}\n\\end{cases}\\label{eq:data-rank-starting}\n\\end{equation}\n\nThis initialization process is depicted in Figure \\ref{fig:Initialize-the-value}.\nHere, datasets have a smaller decay than papers. The size of the bubble\nindicates the initial flow as defined by Eq. \\ref{eq:data-rank-starting}.\nAfter initializing, we can easily find that nodes of the same type\nand same age have the same value, and that the younger a node is,\nthe bigger its value.\n\n\\begin{figure}\n\\begin{centering}\n\\includegraphics[width=0.95\\textwidth]{F2_data_paper_arrow}\n\\par\\end{centering}\n\\caption{\\label{fig:Initialize-the-value}Nodes after initialization. The size\nof the node represents its value, different color means different\nnode type: red nodes are papers and green nodes are datasets.}\n\\end{figure}\n\nNow, we estimate the traffic in a similar fashion but now the traffic\nof a node $T_{i}^{\\text{DataRank}}(\\tau_{\\text{pub}},\\tau_{\\text{dataset}},\\alpha)$\ndepends on three parameters that should be found by cross-validation\nwith the rest of the components of the method remaining the same (e.g.,\n\\eqref{transition-probability} and \\eqref{average-path-length}).\n\n\\subsubsection{\\textsc{DataRank-FB}}\n\nIn \\textsc{DataRank}, each time the walker moves, there are two options:\nto stop with a probability $\\alpha$ or to continue the search through\nthe reference list with a probability $1-\\alpha$. However, there\nmay exist a third choice: to continue the search through papers who\ncite the current paper. In other words, the researcher can move in\ntwo directions: forwards and backwards. We call this modified method\n\\textsc{DataRank-FB. }In this method, one may stop with a probability\n$\\alpha-\\beta$, continue the search forward with a probability $1-\\alpha$,\nand backward with a probability $\\beta$. To keep them within the\nunity simplex, the parameters must satisfy $\\alpha>0$, $\\beta>0$,\nand $\\alpha>\\beta$,\n\nThen\\textbf{\\textsc{, }}we define another transition matrix from the\ncitation network as follows \n\\begin{equation}\nM_{ij}=\\begin{cases}\n\\frac{1}{k_{j}^{\\text{in}}} & \\text{if \\ensuremath{j} cited by \\ensuremath{i}}\\\\\n0 & \\text{o.w.}\n\\end{cases}\\label{eq:transition-probability-1}\n\\end{equation}\nwhere $k_{j}^{\\text{in}}$ is the number of papers that cite $j$.\nWe update the average path length to all papers in the network starting\nfrom $\\rho$ as\n\n\\begin{equation}\nT=I\\cdot\\rho+(1-\\alpha)W\\cdot\\rho+\\beta M\\cdot\\rho+(1-\\alpha)^{2}W^{2}\\rho+\\beta^{2}M^{2}\\rho+\\cdots\\label{eq:average-path-length-1}\n\\end{equation}\n\n\n\\subsection{Other network models}\n\n\\subsubsection{\\textsc{PageRank}}\n\n\\textsc{PageRank} is a well-known and widely used webpage ranking\nalgorithm proposed by Google \\citep{page1999pagerank}. It uses the\ntopological structure of the web to determine the importance of a\nwebpage, independently of its content \\citep{bianchini2005inside}.\nFirst, it builds a network of the web through the link between webpages.\nSecond, each webpage is assigned a random value, which is then updated\nbased on the link relationships---an iterative process that will\neventually converge to a stationary value.\n\nThe mathematical formulation of \\textsc{PageRank} is\n\n\\begin{equation}\nPR(p_{i})=\\frac{1-d}{N}+d\\underset{p_{j}\\in M(p_{i})}{\\sum\\frac{PR(p_{j})}{L(p_{j})}},\\label{eq:pagerank-algorithm}\n\\end{equation}\nwhere $p_{1},p_{2},\\cdots,p_{N}$ are the webpages whose importance\nneed to be calculated, $M(p_{i})$ is the set of webpages that has\na link to page $p_{i}$, $L(p_{j})$ is the number of outbound links\non webpage $p_{j}$, and $N$ is the total number of webpages. The\nparameter $d$ is a dampening factor which ranges from 0 to 1 and\nis usually set to 0.85 \\citep{brin1998anatomy,page1999pagerank}.\n\n\\subsubsection{Modified \\textsc{PageRank}}\n\nConsidering that we have two types of resources in the network, we\nmodify the standard \\textsc{PageRank} to allow a different damping\nfactor for publication and for dataset. This amounts to modifying\nthe update equation to\n\n\\begin{equation}\nPR(p_{i})=\\frac{1-d_{data}}{N_{data}}+\\frac{1-d_{pub}}{N_{pub}}+d_{data}\\underset{p_{j}\\in M^{data}(p_{i})}{\\sum\\frac{PR(p_{j})}{L(p_{j})}}+d_{pub}\\underset{p_{k}\\in M^{pub}(p_{i})}{\\sum\\frac{PR(p_{k})}{L(p_{k})}},\\label{eq:modified-pagerank}\n\\end{equation}\nwhere $p_{1},p_{2},\\cdots,p_{N}$ are still the nodes whose importance\nneed to be calculated, $M^{data}(p_{i})$ is the set of datasets that\nhave a link to page $p_{i}$, $M^{pub}(p_{i})$ is the set of papers\nthat has a link to page $p_{i}$, $L(p_{j})$ is the number of outbound\nlinks on webpage $p_{j}$, and $N_{data},N_{pub}$ are the total size\nof datasets and paper collections, respectively. The parameter $d_{data}$\nis a damping factor for datasets and $d_{pub}$ is a damping factor\nfor paper sets.\n\n\\section{Results}\n\nWe aim at finding whether the estimation of the rank of a dataset\nbased on citation data is related to a real-world measure of relevance\nsuch as page views or downloads. We propose a method for estimating\nrankings that we call \\textbf{\\textsc{DataRank,}} which considers\ndifferences in citation dynamics for publications and datasets. We\nalso propose some variants to this method, and compare all of them\nto standard ranking algorithms. We use the data of visits of GenBank\ndatasets and downloads of Figshare datasets as measure of real usage.\nThus, we will investigate which of the methods work best for ranking\nthem.\n\n\\subsection{Properties of the citation networks}\n\n\\begin{figure}\n\\begin{centering}\n\\includegraphics[width=0.8\\textwidth]{Citation_network_publication_age_prob_dist}\n\\par\\end{centering}\n\\begin{centering}\n\\includegraphics[width=0.8\\textwidth]{Citation_network_received_citation_prob_dist}\n\\par\\end{centering}\n\\caption{\\label{fig:paper_network_age_citation_dist}Probability density of\nage and citations. Power laws describing the growth of both aspects\nof the network have parameters $k_{\\text{age}}\\approx-4.1$ and $k_{\\text{citations}}\\approx-2.16$.}\n\\end{figure}\n\nWe first examined some statistics of the paper--paper citation network\nand the paper--dataset citation network. Specifically, we examined\ndataset age because it determines the initial rank of a node and we\nexamine the citations because they control how ranks diffuse through\nthe network. We modeled publication age with respect to 2019 as a\npower law distribution $p(a)\\propto a^{-k}$ and we found the best\nparameter to be $k\\approx-4.1$ (SE=$0.07$, $p<0.001$, Fig. \\ref{fig:paper_network_age_citation_dist}\ntop panel). Similarly, the citation count can be modeled by a power\nlaw distribution $p(d)\\propto d^{-k}$ with parameter $k\\approx-2.16062$\n(SE=$0.012$, $p<0.001$, Fig. \\ref{fig:paper_network_age_citation_dist}\nbottom panel). While both distributions can be well described by power\nlaws, the age distribution had some out-of-trend dynamics for small\nage values because the number of publications is not growing as fast\nas the power law would predict. The networks thus is expanding fast\nin nodes (e.g., age) and highly skewed for citations.\n\n\\begin{figure}\n\\begin{centering}\n\\includegraphics[width=0.8\\textwidth]{genebank_usage}\n\\par\\end{centering}\n\\begin{centering}\n\\includegraphics[width=0.8\\textwidth]{figureshare_usage}\n\\par\\end{centering}\n\\caption{\\label{fig:pdf-of-figshare}Probability density function of usage\n(website visits for Genbank and downloads for Figshare)}\n\\end{figure}\n\nWe then wanted to examine differences in usage between Genbank and\nFigshare. We plotted the estimated probability density function of\nthis usage for both datasets as a log-log plot (Fig. \\ref{fig:pdf-of-figshare}).\nWhile the scale of usage is significantly different (i.e., overall\nGenBank is more used than Figshare), there seems to be a long-tail\npower law relationship in usage. The GeneBank dataset had a larger\nbut not significantly different scale parameter than Figshare ($k\\approx-1.416$,\nSE=0.2699, in GenBank and $k\\approx-1.125$, SE=0.0907, in Figshare,\nfor $p(u)\\propto u^{-k}$, two-sample t-test $t(220)=-1.05$, $p=0.29$).\nThere is a significant bias for downloads below a certain threshold,\nwhere smaller number of downloads are less frequent than expected\nby the power laws. However, both datasets show similar patterns suggesting\na common mechanism driving the dataset usage behavior.\n\n\\subsection{Prediction of real usage}\n\nOne of the real tests of whether the methods work is to predict how\nthey are related to real usage data. For each algorithm and set of\nparameters, we estimated the rank of networks' nodes. We then correlated\nthese ranks with real usage (i.e., web visits for GenBank and downloads\nfor Figshare). We now describe the best performance after these parameter\nsearch.\n\nWe performed a grid search with publication decay year $\\tau_{\\text{pub}}\\in\\left\\{ 1,5,10,20,30,50,70,100\\right\\} $,\nthe dataset decay year $\\tau_{\\text{dataset}}\\in\\left\\{ 1,5,10,20,30,50,70,100\\right\\} $,\nand alpha in $\\alpha\\in\\left\\{ 0.05,0.15\\right\\} $. The best model\nof \\textsc{DataRank} achieved a correlation of 0.3336 in Genbank which\nis slightly better than \\textsc{DataRank-FB} 0.3335, \\textsc{NetworkFlow}\n0.3327, \\textsc{PageRank} 0.3324, and Modified \\textsc{PageRank} 0.3327\n(Fig. \\ref{fig:result-correlation}). The best model of \\textsc{DataRank}\nachieves a correlation of 0.1078 in Figshare, which is substantially\nbetter than \\textsc{DataRank-FB} with 0.0723. The best absolute correlations\nby all the other methods only achieved negative correlations (\\textsc{NetworkFlow}\\textbf{\\textsc{=}}$-0.072$,\n\\textsc{PageRank}=$-0.073$, and Modified \\textsc{PageRank}=$-0.073$)---we\nselected models based on absolute correlation because it would produce\nthe best predictive performance. Taken together, \\textsc{DataRank}\nhas both better absolute correlation performance and highest correlation,\nsuggesting a superior ability to predict real usage.\n\n\\begin{figure}\n\\begin{centering}\n\\includegraphics[width=1\\textwidth]{correlation}\n\\par\\end{centering}\n\\caption{\\label{fig:result-correlation}Model comparison in correlation coefficient.\n\\textsc{DataRank} is able to predict better the real usage of datasets\ncompared to other variants.}\n\\end{figure}\n\n\n\\subsection{Interpretation of best-fit model}\n\nWe wanted to explore how \\textsc{DataRank} changes in performance\nacross the different parameters. This exploration allowed us to understand\nhow the parameters tell us something about the underlying characteristics\nof the citation networks.\n\nThe results across all parameters are shown in Figure \\ref{fig:Parameter-search}\nand we now describe general trends. For experiments on GenBank dataset,\nwe found the \\textsc{DataRank} model reaches its best with $\\tau_{\\text{pub}}=100$\nand $\\tau_{\\text{dataset}}=30$ (Fig. \\ref{fig:result-correlation}\ntop panel). However, for dataset decay, the performance reaches a\nplateau after around 20 years and it reaches its peak at 30 years.\nAfter 30 years, performance goes down slowly. In terms of publication\ndecay, the performance increases significantly before 20 years. After\n20 years, the performance enters into a steady but marginal increase.\nIn all the cases, the alpha at 0.05 is better than 0.15. For Figshare\ndataset, dataset decay has divergent patterns: for small publication\ndecays, dataset decay increases the performance. For large publication\ndecays, dataset decay decreases the performance. For publication decay,\nmore specifically, we observed an opposite trend compared to GenBank:\nthe performance goes down rapidly as the publication decay increases\n(Fig. \\ref{fig:result-correlation} bottom panel). However, similar\nto GenBank, it losses momentum after 20 years but still decreases\nsteadily.\n\nOne explanation for the differences between the best parameters for\nGenbank and Figshare is that dataset age and citation distribution\nhave different patterns. We perform an analysis to confirm this hypothesis.\nIndeed, we found that Figshare datasets are significantly younger\nthan Genbank datasets (bootstrapped difference between average age\n= $-4.80$ years, SE = 0.24, $p<0.001$). We also found that Figshare\ndataset citations are more uniform than Genbank dataset citations\nalthough not significantly different (bootstrapped difference in dataset\ncitation kurtosis = -44.34, SE = 48.74, $p=0.25$). The \\textsc{DataRank}\nalgorithm uses large values of dataset decay to propagate publication\ncitations over a longer time and small values of data decay to steer\nthose citations towards a concentrated set of top cited datasets.\nThis is the case of GenBank dataset dynamics. Figshare, comparatively,\nobeys opposite age and citation dynamics which \\textsc{DataRank} attempts\nto accommodate by using small values of publication decay and large\nvalues of dataset decays. Concretely, the best publication decay for\nGenbank is 100 and for Figshare is 1, and the best dataset decay for\nGenbank is 30 and for Figshare is 100. Taken together, \\textsc{DataRank}'s\nparameters offer inferential interpretation of the citation network\ndynamics, which can help us understand how they are distributed in\ntime and credit spaces.\n\n\\begin{figure}\n\\begin{centering}\n\\includegraphics[width=0.8\\textwidth]{genebank_parameter_search}\n\\par\\end{centering}\n\\begin{centering}\n\\includegraphics[width=0.8\\textwidth]{figshare_parameter_search}\n\\par\\end{centering}\n\\caption{\\label{fig:Parameter-search}Model performance during grid search\nwith publication decay time (years) $\\tau_{\\text{pub}}\\in\\left\\{ 1,5,10,20,30,50,70,100\\right\\} $,\nthe dataset decay time (years) $\\tau_{\\text{dataset}}\\in\\left\\{ 1,5,10,20,30,50,70,100\\right\\} $,\nand alpha in $\\alpha\\in\\left\\{ 0.05,0.15\\right\\} $}\n\n\\end{figure}\n\n\n\\section{Discussion}\n\nThe goal of this article is to better evaluate the importance of datasets\nthrough article citation network analysis. Compared with the mature\ncitation mechanisms of articles, referencing datasets is still in\nits infancy. Acknowledging the long time the practice of citing datasets\nwill take to be adopted, our research aims at recovering the true\nimportance of datasets even if their citations are biased compared\nto publications.\n\nScholars disagree on how to give credit to research outcomes. Regardless\nof how disputed citations are as a measure of credit \\citep[see][]{moed1985use,diamond1986citation,martin1996use,seglen1997impact,wallin2005bibliometric},\nthey complement other measures that are harder to quantify such as\npeer review assessment \\citep{meho2007impact,piwowar2007sharing}\nor real usage such as downloads \\citep{belter2014measuring}. Citations,\nhowever, are rarely used for datasets \\citep{altman2013evolution},\ngiving these important research outcomes less credit that they might\ndeserve. Our proposal aims at solving some of these issues by constructing\na network flow that is able to successfully predict real usage better\nthan other methods. While citations are not a perfect measure of credit,\nhaving a method that can at least attempt to predict usage is advantageous.\n\nPrevious research has examined ways of normalizing citations by time,\nfield, and quality. This relates to our \\textsc{DataRank} algorithm\nin that we are trying to normalize the citations by year and artifact\ntype. Similar work has been done in patent citations: \\citet{hall2001nber}\nattempt to eliminate the effects caused by year, field and year-field\ninteraction through dividing the number of citation received by a\ncertain patent by the corresponding year-field average number of citation\nof patents of each cohort in each field. \\citet{yang2015using} used\npatent citation networks to propagate citations and evaluate patent\nvalue. Other researchers have gone beyond time and field by also attempting\nto control by quality of the resource. Clarivate Analytics editors\nconsider other normalizing factors such as publishing standards, editorial\ncontent and citation information when creating the Data Citation Index\n(DCI) database \\citep{reuters2012repository}. However, a control\nlike this requires significantly more manual curation.\n\nWe found that the practice of following who cites an artifact (i.e.,\nbackward propagation) seemed to be not as important compared to following\na cited artifact (i.e., forward propagation). This is, the more specialized\n\\textsc{DataRank-FB} model (see Methods) did not produce higher predictability.\nThis lack of improvement could suggest that when scientists traverse\nthe network of citations, they seem to only follow one direction of\nthe graph (i.e., the reference list). This could be perhaps a limitation\nof the tools available to scientists to explore the citation network\nor because backward propagation changes constantly year after year.\nInitiatives that force the creation of identifiers (DOI) for datasets,\nsuch as the NERC Science Information Strategy Data Citation and Publication\nproject \\citep{callaghan2012making}, might change this pattern.\n\nWe find it useful to interpret the effect of different decay times\non the performance of \\textsc{DataRank}. The best-fitting parameters\nshow that \\textsc{DataRank} attempts to model the network temporal\nand topological dynamics differently for Genbank and Figshare. Because\nGenbank tends to have older datasets that have more concentrated citations\ncompared to Figshare, the large value in publication decay time and\nsmall value in dataset decay time produces rank distributions that\nmatch the underlying dynamics of Genbank (Fig. \\ref{fig:Parameter-search}).\nSimilarly, the alpha parameter, which controls the probability of\nthe random walk to stop, is larger for Figshare, intuitively suggesting\nthat due to the smaller network size and shorter temporal paths, a\nhigher probability of stopping should be in place (Fig. \\ref{fig:Parameter-search}).\nThus, \\textsc{DataRank} can help to interpret dataset citation behavior.\n\nThere are some shortcomings in our study. For GenBank and Fighsare,\nwe do not have a great deal of information on actual usage. There\nare 1000 records but we only located 693 in the publication network\nof Genbank and 355 datasets from Figshare. Also, there are significant\ndifferences in the information, with Figshare dataset being cited\nless often than GenBank. In the future, we will explore other data\nrepositories such as PANGEA, Animal QTLdb, and UK Data Archive, and\nwe will request updates about web visits to other GenBank sequences.\n\nOpen research datasets have little means for systematic attribution\neven in well-resourced disciplines, such as the biomedical community,\nand our proposal attempts to systematize this attribution more broadly\nwithout requiring changes in behavior. The lack of systematic benchmarking\ntools prevents good policy-making. Furthermore, it contributes to\nthe invisibility of digital objects and labor, an issue of serious\nconcern \\citep{scroggins2019labor}. When digital objects are not\nwell described, they tend to disappear from view. They fall to the\nbottom of classic search engine results when there are no mechanisms\nto assign credit to datasets. This lack of indexing creates an asymmetrical\nrepresentation of some kinds of objects of science and can be an obstacle\nto quality evaluation and data reuse. Thus \\textsc{DataRank} can be\nused to correct these asymmetrical discrepancies between articles\nand datasets.\n\nOur approach does not directly estimate true impact but predicts one\npossible measure of usage. However, this prediction could be a foundational\nstep toward developing technical and theoretical models of impact.\nAlso, in the literature, \\textquotedblleft impact\\textquotedblright{}\nis defined differently depending on the goal \\citep{piwowar2013altmetrics}.\nMetrics estimating impact can be defined through \\textquotedblleft use\\textquotedblright ,\n\\textquotedblleft reuse\\textquotedblright , or \\textquotedblleft engagement\\textquotedblright ,\nand have a range of proxies. For example, a download might measure\nuse while in another context it may only indicate viewing. Comparatively,\nthe edifice of citation standards in the realm of journal articles\nis relatively well-established, with refinements to the interpretation\nof citation behavior such as the relative value of citations \\citep{stuart2017data},\nthe disciplinary context \\citep{borgman1989bibliometrics}, and the\nin-text location \\citep{teplitskiy2018almost}. Nonetheless, usage\nserves as a proximal indicator of influence, and a first-order approximation\nof the impact of the scientific work. Recent work in developing impact\nassessment tools continue development and refinement \\citep{silvello2018theory}.\nHowever, existing evaluation mechanisms often fail where there are\nno direct or indirect measure for usage, which can be an important\nindicator of scientific impact. Clearly, our approach serves not only\nas a concrete tool to measure impact---albeit imperfectly---but\nalso as a vehicle to discuss why and how to measure impact on datasets.\n\n\\section{Conclusion}\n\nUnderstanding how datasets are used is an important topic in science.\nDatasets are becoming crucial for the reproduction of results and\nthe acceleration of scientific discoveries. Scientists, however, tend\nto dismiss citing datasets and therefore there is no proper measurement\nof how impactful datasets are. Our method uses the publication-publication\ncitation network to propagate the impact to the publication--dataset\ncitation network. Using two databases of real dataset networks, we\ndemonstrate how our method is able to predict actual usage more accurately\nthan other methods. Our results suggest that datasets have different\ncitation dynamics to those of publications. In sum, our study provides\na prescriptive model to understand how citations interact in publication\nand dataset citation networks and gives a concrete method for producing\nranks that are predictive of actual usage.\n\nOur study advances an investigation of datasets and publications with\nnovel ideas from network analysis. Our work puts together concepts\nfrom other popular network flow estimation algorithms such as \\textsc{PageRank}\n\\citep{brin1998anatomy} and \\textsc{NetworkFlow} \\citep{walker2007ranking}.\nWhile scientists might potentially take a great amount of time to\nchange their citation behavior, we could use techniques such as the\none put forth in this article to accelerate the credit assignment\nfor datasets. Ultimately, the need for tracking datasets will only\nbecome more pressing and therefore we must adapt or miss the opportunity\nto make datasets first-class citizens of science.\n\n\\section*{Acknowledgements}\n\nThe authors would like to thank the Dr. Kim Pruitt from National Center\nfor Biotechnology Information, NLM, NIH, DHHS. Tong Zeng was funded\nby the China Scholarship Council \\#201706190067. Sarah Bratt was partially\nfunded by National Science Foundation award \\#1561348. Daniel E. Acuna\nwas partially funded by the National Science Foundation awards \\#1800956.\n\n\\bibliographystyle{apalike}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzjcar b/data_all_eng_slimpj/shuffled/split2/finalzzjcar
new file mode 100644
index 0000000000000000000000000000000000000000..10b278b4330fc3c137ac6f6314b75518bdd2c127
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzjcar
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\n\\label{introduction}\nThe physical state and structure of the interstellar medium (ISM) are important parameters for understanding the star formation in a galaxy. In a typical star-forming region, young massive stars are born and start to illuminate their parental cloud. UV photons ionize the surrounding medium, creating H\\,{\\sc ii}\\xspace regions, while the transition to the neutral atomic or molecular phase occurs at higher visual extinction, where the material is more effectively shielded. Far-UV (FUV) photons control the chemical activity in these regions, namely the photodissociation region (PDR; \\citealt{tielens-1985}). By studying the latter, we can investigate the conditions of the molecular clouds, which in turn will be potential sites for the next episode of star formation. \n\nHow does the propagation of radiation and the ISM composition affect\nISM observables in low-metallicity galaxies? Addressing this question is important to understand the evolution of low-metallicity galaxies, which undergo more bursty star formation than normal galaxies. Nearby star-forming dwarf galaxies present distinct\nobservational signatures compared to well-studied disk galaxies. Dwarfs are usually metal poor, H\\,{\\sc i}\\xspace\\ rich, and molecule poor as\na result of large-scale photodissociation \\citep[e.g.,][]{kunth-2000,hunter-2012,schruba-2012}. Mid-IR (MIR) and far-IR (FIR) observations have revealed bright atomic lines from H\\,{\\sc ii}\\xspace regions ([S\\,{\\sc iii}]\\xspace, [Ne\\,{\\sc iii}]\\xspace, [Ne\\,{\\sc ii}]\\xspace, [O\\,{\\sc iii}]\\xspace, etc.) and PDRs ([C\\,{\\sc ii}]\\xspace, [O\\,{\\sc i}]\\xspace) \\citep[e.g.,][]{hunter-2001,madden-2006,wu-2008,hunt-2010,cormier-2015}. Their spectral energy distributions (SEDs) are also different from spiral and elliptical galaxies and indicative of altered dust properties, with a relatively low abundance of polycyclic aromatic hydrocarbons (PAHs) and perhaps a different dust composition \\citep[e.g.,][]{madden-2006,galliano-2008,remy-2013}. \nIt is still unknown, however, whether these differences between dwarf and disk galaxies are the direct result of recent star formation activity shaping the ISM or instead a consequence of the low-metallicity ISM that is independent of star formation activity. To answer this, one needs to observe tracers of the interplay between the ISM and various stages of star formation activity. While there are now a number of important studies available on PDR properties modeling FIR lines on large scales in various extragalactic environments \\citep[e.g.,][]{kaufman-2006,vasta-2010,gracia-carpio-2011,cormier-2012,parkin-2013} or in our Galaxy under solar-metallicity conditions \\citep[e.g.,][]{cubick-2008,bernard-salas-2012,bernard-salas-2015}, only a few studies are published on individual extragalactic regions \\citep{mookerjea-2011,lebouteiller-2012}. Of particular interest are dwarf galaxies, where the effect due to radiative feedback is expected to be most significant. \nThe goal of this paper is to investigate how the low-metallicity ISM reacts under the effects of star formation in regions that have undergone different histories. The nearby low-metallicity galaxy NGC\\,4214 provides an excellent environment to perform this experiment because it has well-separated star-forming centers, one hosting a super star cluster, which allows us to study the effects of extreme star-forming conditions on the surrounding ISM. \n\nNGC\\,4214 is a nearby irregular galaxy located 3\\,Mpc away \\citep{dalcanton-2009} with a metallicity of $\\sim$0.3\\,Z$_{\\odot}$ \\citep{kobulnicky-1996} and a wealth of ancillary data. It shows various morphological characteristics such as H\\,{\\sc i}\\xspace holes and shells and a spiral pattern \\citep{mcintyre-1998}. \nNGC\\,4214 is known to host two main, well-defined star-forming regions with recent activity (Fig.\\,\\ref{3color}). The largest of the two regions is found in the center of the galaxy (also referred to as NW or region~I) and contains several clusters, including a super star cluster, while the second region is found to the southeast (also referred to as SE or region~II) and is  younger and more compact. \nUsing near-IR, optical, and UV data, several studies have constrained the ages of the clusters in the two main regions, which show evidence for recent star formation \\citep{ubeda-2007,sollima-2013,sollima-2014}. \\cite{schruba-2012} have measured the ongoing SFR of NGC\\,4214 to be 0.12\\,M$_{\\odot}$\\,yr$^{-1}$. \nThe galaxy seems to have maintained its star formation in the past 10\\,Gyr at an average rate of $\\sim$0.02\\,M$_{\\odot}$\\,yr$^{-1}$, with a prolonged star formation episode that occurred about 3\\,Gyr ago and several shorter bursty events within the past Gyr at a rate of 0.05-0.12\\,M$_{\\odot}$\\,yr$^{-1}$ \\citep{mcquinn-2010,williams-2011}. \\par\n\n\n\\begin{figure}\n\\centering\n\\includegraphics[scale=0.52]{fig1.eps}\n\\centering\n\\caption{Three-color image of NGC\\,4214 using the HST WFC3 filters F438W (B, blue), F502N ([O\\,{\\sc iii}]\\xspace, green), and F657N (H$\\alpha$+[N\\,{\\sc ii}]\\xspace, red), downloaded from the Hubble Legacy Archive (\\protect\\url{http:\/\/hla.stsci.edu\/}).}\n\\label{3color}\n\\end{figure}\n\nIn this paper, we present observations of MIR and FIR fine-structure cooling lines in NGC\\,4214, which provide key diagnostics of the physical conditions of the ISM. We focus our analysis on the two main star-forming complexes. The line emission is analyzed with radiative transfer models to characterize the ISM conditions. We take into account directly observed star formation histories and explore how they affect the IR line emission. Photometry is used for the energy budget of the models. The structure of this paper is the following: Sect.~\\ref{data} describes the data, Sect.~\\ref{method} describes the model, and the results are presented in Sect.~\\ref{results}. We summarize and discuss our results in Sect.~\\ref{discussion}. \n\n\n\\section{Data}\n\\label{data}\n\\subsection{{\\it Herschel} data}\nWe used observations of NGC\\,4214 obtained by the PACS instrument \\citep{poglitsch-2010} onboard the \\textit{Herschel}\\xspace Space Observatory \\citep{pilbratt-2010} as part of the Dwarf Galaxy Survey \\citep{madden-2013}. The list of observations can be found in Table~\\ref{AOR}. The photometry data at 70$\\mu$m\\xspace, 100$\\mu$m\\xspace, and 160$\\mu$m\\xspace, with respective beam sizes (FWHM) of 5.6$^{\\prime\\prime}$\\xspace, 6.7$^{\\prime\\prime}$\\xspace, and 11.3$^{\\prime\\prime}$\\xspace, were published by \\cite{remy-2013}. These bands cover the peak of the SED originating from the reprocessed stellar light by the dust. \nThe spectroscopy comprises observations of the \\oiii88$\\mu$m\\xspace and \\nii122$\\mu$m\\xspace lines, which trace the ionized gas, as well as the \\cii157$\\mu$m\\xspace, \\oi63$\\mu$m\\xspace, and \\oi145$\\mu$m\\xspace lines, which trace the PDR. The data consist of small mappings of $5\\times5$ rasters separated by $\\sim$16$^{\\prime\\prime}$\\xspace for \\oiii88$\\mu$m\\xspace and \\oi63$\\mu$m\\xspace and $3\\times3$ rasters separated by $\\sim$24$^{\\prime\\prime}$\\xspace for the other lines, ensuring a uniform coverage of $1.6^{\\prime}\\times1.6^{\\prime}$. Originally presented in \\cite{cormier-2010}, the PACS spectral data were re-processed with the reduction and analysis software HIPE user release v.11 \\citep{ott-2010} and PACSman v.3.5 \\citep{lebouteiller-2012}. With the improved calibration and definition of the regions, flux maps are globally consistent with those published in \\cite{cormier-2010} and line ratios agree within 30\\%. Flux maps of the \\cii157$\\mu$m\\xspace and \\oi63$\\mu$m\\xspace lines are shown in Fig.\\,\\ref{mask}. The associated error maps include data and line-fitting uncertainties, but not calibration uncertainties, which are on the order of 15\\%. \nThe FWHM is 9.5$^{\\prime\\prime}$\\xspace below 100$\\mu$m\\xspace and 10$^{\\prime\\prime}$\\xspace, 11$^{\\prime\\prime}$\\xspace, 12$^{\\prime\\prime}$\\xspace at 122$\\mu$m\\xspace, 145$\\mu$m\\xspace, 160$\\mu$m\\xspace, respectively. All maps were convolved to the \\cii157$\\mu$m\\xspace resolution of $\\sim$12$^{\\prime\\prime}$\\xspace , which at the distance of NGC\\,4214 corresponds to a physical scale of 175\\,pc. \nIn both the photometry and spectroscopy data sets, the convolutions were performed using kernels provided by \\cite{aniano-2011}\\footnote{\\url{http:\/\/www.astro.princeton.edu\/~ganiano\/Kernels\/}}.\n\n\n\\begin{figure*}\n\\centering\n\\includegraphics[width=5.585cm]{fig2a.eps}\\hspace{-1mm}\n\\includegraphics[width=4.25cm]{fig2b.eps}\\hspace{-1mm}\n\\includegraphics[width=4.25cm]{fig2c.eps}\\hspace{-1mm}\n\\includegraphics[width=4.25cm]{fig2d.eps}\n\\centering\n\\caption{\nMaps of the \\cii157$\\mu$m\\xspace, \\oi63$\\mu$m\\xspace, \nand TIR emission in NGC\\,4214. Units are W\\,m$^{-2}$\\,sr$^{-1}$. \nThe two star-forming regions, as defined in Sect.~\\ref{sect:definesf}, \nare outlined with red contours. \nThe right panel shows the \\textit{Spitzer}\\xspace IRS mapping strategy. \nOrange: Long-High module coverage; \ncyan: Short-High module coverage; \ngray background: \\cii157$\\mu$m\\xspace map. \n}\n\\label{mask}\n\\end{figure*}\n\n\n\n\\subsection{{\\it Spitzer} data}\nNGC\\,4214 was observed with the three instruments onboard the \\textit{Spitzer}\\xspace space telescope \\citep{werner-2004}. We used the MIPS 24$\\mu$m\\xspace observations obtained within the Local Volume Legacy Survey \\citep{dale-2009} that were processed by \\cite{bendo-2012}. The MIPS 24$\\mu$m\\xspace map, which has an original FWHM of 5.9$^{\\prime\\prime}$\\xspace, was convolved to a resolution of $\\sim$12$^{\\prime\\prime}$\\xspace to match that of the PACS data. \\par\n\nThe IRS observations (program ID 3177, PI. Skillman) consist of small mappings of the two main star-forming regions in high-resolution mode \\citep{houck-2004}. We extracted the data from the \\textit{Spitzer}\\xspace Heritage Archive (see Table~\\ref{AOR}) and processed them with the software CUBISM v1.8 \\citep{smith-2007}. We used the default mapping procedure and bad pixel removal to produce spectral cubes with pixel sizes 2.26$^{\\prime\\prime}$\\xspace for the Short-High module and 4.46$^{\\prime\\prime}$\\xspace for the Long-High module. \nWe then created surface brightness maps for all spectral lines of interest -- \\siv10.5$\\mu$m\\xspace, \\neii12.8$\\mu$m\\xspace, \\neiii15.6$\\mu$m\\xspace, \\siii18.7$\\mu$m\\xspace, \\siii33.5$\\mu$m\\xspace, which all trace H\\,{\\sc ii}\\xspace regions -- in the following way: for each pixel of the cube, we extracted the signal with a range of $\\pm$0.7$\\mu$m\\xspace around the line and fit a polynomial of order two for the baseline and a Gaussian for the line with the IDL routine \\texttt{mpfit}. For a more stable fit, the peak of the Gaussian is required to be positive, the position of the peak is expected within one instrumental FWHM of the rest wavelength, and the width is limited to the instrumental resolution ($R=600$). Finally, we added random noise and iterated the fit $300$ times to estimate the best-fit parameters as the median of the resulting parameters and the error on those parameters as the standard deviation. \nError maps again include data and line-fitting uncertainties, but not calibration uncertainties, which are on the order of 5\\%. \nThe coverage of the star-forming regions of the galaxy in the IRS maps is only partial, as shown in Fig.\\,\\ref{mask}. No integrated values for the flux of the whole regions could be retrieved. To obtain a representative value for the line flux in each region, we regridded the IRS maps to that of the \\oiii88$\\mu$m\\xspace map. Then we selected the pixels that appear in both maps and scaled the emission of these pixels to the \\oiii88$\\mu$m\\xspace line to infer the corresponding line fluxes for the star-forming regions as a whole. \n\n\\begin{table}\n\\caption{List of \\textit{Herschel}\\xspace and \\textit{Spitzer}\\xspace observations.}\n\\label{AOR}\n \\centering\n\\vspace{-5pt}\n  \\begin{tabular}{l l}\n\\hline \\hline\n    \\vspace{-10pt}\\\\\n\\multicolumn{2}{c}{\\textit{Herschel}\\xspace data}\\\\\nInstrument & Observation Identification number (OBSID) \\\\\n\\hline\n    \\vspace{-10pt}\\\\\nPACS phot. & $1342211803$, $1342211804$, $1342211805$, \\\\\n & $1342211806$ \\\\\nPACS spec. & $1342187843$, $1342187844$, $1342187845$, \\\\\n & $1342188034$, $1342188035$, $1342188036$ \\\\\n\\hline \\hline\n    \\vspace{-10pt}\\\\\n\\multicolumn{2}{c}{\\textit{Spitzer}\\xspace data}\\\\\nInstrument & Astronomical Observation Request (AOR) \\\\\n\\hline\n    \\vspace{-10pt}\\\\\nMIPS 24$\\mu$m\\xspace & $22652672$, $22652928$, $22710528$, $22710784$ \\\\\n\\multicolumn{2}{l}{IRS Short-High} \\\\\n~On-source: & $10426368$, $10426624$, $10426880$, $10427136$ \\\\\n~Background: & $13728256$, $13729792$, $13730304$, $13730816$, \\\\\n& $13733120$, $13762304$, $13767424$, $13767936$, \\\\\n& $13768448$, $13768704$, $13769728$, $13770496$, \\\\\n& $13773568$\\\\\n\\multicolumn{2}{l}{IRS Long-High} \\\\\n~On-source: &$10424832$, $10425088$, $10425344$, $10425600$, \\\\\n& $10425856$, $10426112$, $10427392$\\\\\n~Background: & $13728768$, $13729792$, $13730304$, $13730816$, \\\\\n& $13733120$, $13763328$, $13764352$, $13765376$, \\\\\n&$13767424$, $13767936$, $13768448$, $13768704$,\\\\\n&  $13769728$, $13770496$, $13773568$\\\\\n\\hline \\hline\n\\end{tabular}\n\\end{table}\n\nWe focus on these selected IRS lines because they are among the brightest MIR fine-structure cooling lines and can be used as reliable diagnostics of the physical conditions in H\\,{\\sc ii}\\xspace regions. In general, the intensity or luminosity ratio of two lines of the same element but different ionization level is indicative of the radiation field hardness. Such diagnostics are the \\neiii15.6$\\mu$m\\xspace\/\\neii12.8$\\mu$m\\xspace or the \\siv10.5$\\mu$m\\xspace\/\\siii18.7$\\mu$m\\xspace ratios \\citep[e.g.,][]{verma-2003}, which are insensitive to the density because of their high critical densities (see Table~\\ref{fluxes}). Accordingly, species of the same ionization level but different transition are indicative of the electron density as a result of the different critical densities for each transition \\citep{osterbrock}. Examples are the \\siii18.7$\\mu$m\\xspace\/\\siii33.5$\\mu$m\\xspace, \\neiii15.6$\\mu$m\\xspace\/\\neiii36.0$\\mu$m\\xspace, or \\nii122$\\mu$m\\xspace\/\\nii205$\\mu$m\\xspace ratios \\citep[e.g.,][]{rubin-1994}. These diagnostics are insensitive to the temperature inside the H\\,{\\sc ii}\\xspace region. Unfortunately, the \\neiii36.0$\\mu$m\\xspace and \\nii205$\\mu$m\\xspace lines fall at the edge of the IRS and PACS wavelength ranges, respectively, where the spectra are too noisy to detect or derive a reliable line ratio for the two star-forming regions. Therefore we relied on the [S\\,{\\sc iii}]\\xspace line to probe the electron density.\n\n\n\n\\subsection{Total infrared luminosity map}\nTo construct a total infrared (TIR) luminosity map of the galaxy, we combined the MIPS 24$\\mu$m\\xspace and PACS 70, 100, and 160$\\mu$m\\xspace data, following \\cite{galametz-2013}: \n\\begin{equation}\nL_{\\rm TIR}=\\int_{3\\mu m}^{1\\,100\\mu m}L_{\\nu}d\\nu=\\sum c_i L_i\n.\\end{equation}\nWe used the values of the coefficients, $c_i$, from Table~3 of their paper: $[c_{24},c_{70},c_{100},c_{160}] = [2.064,0.539,0.277,0.938]$. This method, although slightly less accurate than a direct integration of a well-sampled SED, does not require degrading the resolution of our data beyond the PACS 160$\\mu$m\\xspace beam and is sufficient for our modeling purposes to estimate the energy budget in the star-forming regions. The $L_{\\rm TIR}$ map is shown in Fig.\\,\\ref{mask}.\n\n\n\n\\subsection{Defining the star-forming regions}\n\\label{sect:definesf}\nTo define the apertures for the main star-forming regions, we set a threshold for the signal-to-noise ratio (S\/N) equal to 5 in each individual PACS 70$\\mu$m\\xspace, 100$\\mu$m\\xspace, and 160$\\mu$m\\xspace photometry and PACS spectral map. We masked all pixels below this S\/N and drew the contours, which include all the remaining unmasked pixels separately for the photometry and the spectroscopy maps. Because the emission in the photometry maps is more extended, we kept the contours from the photometry and used these apertures throughout the analysis to define the two star-forming regions, as shown in Fig.\\,\\ref{mask}. This means that pixels in the spectroscopy maps that are below the S\/N threshold but within the region contours are still counted. \nThe fluxes and uncertainties for the line and TIR emission were measured taking into account all pixels in each region. They\nare reported in Table~\\ref{fluxes}. \nThe ISM emission (gas and dust) peaks in these two regions, and most of the line fluxes are twice as high in the central region as$\\text{ in}$ the southern region, except for \\neiii15.6$\\mu$m\\xspace (factor 1.3) and \\siv10.5$\\mu$m\\xspace, which have lower fluxes toward the central region. This hints at different physical conditions in the two regions, which we investigate with radiative transfer models. \n\n\\begin{table*}\n\\caption{Observed MIR and FIR fluxes for the line and broadband emission.\nUncertainties on the fluxes include data and line-fitting uncertainties, but not \ncalibration uncertainties, which are on the order of 5\\% for the \\textit{Spitzer}\\xspace lines and 15\\% for the \\textit{Herschel}\\xspace lines.\nCritical density and ionization potential values are taken from \\citet{cormier-2012}. \nCritical densities are noted [e] for collisions with electrons and [H] for collisions with hydrogen atoms.}\n\\label{fluxes}\n \\centering\n\\vspace{-5pt}\n  \\begin{tabular}{l c c c c c}\n\\hline\\hline\n    \\vspace{-10pt}\\\\\n &   & \\multicolumn{2}{c}{Flux $\\pm$ uncertainty} & & Ionization \\\\ \n Line   &  Wavelength   &       \\multicolumn{2}{c}{($\\times10^{-16}$ W~m$^{-2}$)} & Critical density  &  potential  \\\\ \n                &       ($\\mu$m\\xspace)          &       Region I          &       Region II & (cm$^{-3}$) &      (eV)    \\\\\n\\hline\n    \\vspace{-10pt}\\\\\n\\lbrack \\textsc{S\\,iv}] &       10.51 & $5.68\\pm0.21$           & $8.40\\pm0.10$   & $5\\times10^4$ [e]     & 34.79\\\\       \n\\lbrack Ne\\textsc{\\,ii}] &      12.81 & $8.98\\pm0.22$           & $4.13\\pm0.11$   & $7\\times10^5$ [e]     & 21.56\\\\\n\\lbrack Ne\\textsc{\\,iii}] &     15.56 & $18.70\\pm0.14$  & $14.25\\pm0.08$        & $3\\times10^5$ [e]       &40.96\\\\\n\\lbrack \\textsc{S\\,iii}] &      18.71 & $11.78\\pm0.20$  & $6.85\\pm0.08$ & $2\\times10^4$ [e]       & 23.34 \\\\\n\\lbrack \\textsc{S\\,iii}] &      33.48 & $18.71\\pm0.27$  & $8.20\\pm0.12$ & $7\\times10^3$ [e]       & 23.34\\\\\n\\lbrack \\textsc{O\\,i}] &        63.18 & $10.11\\pm0.35$  & $4.06\\pm0.21$ & $5\\times10^5$ [H]       & -\\\\\n\\lbrack \\textsc{O\\,iii}] &      88.36 & $31.86\\pm0.62$  & $13.50\\pm0.40$        & $5\\times10^2$ [e]       & 35.12\\\\\n\\lbrack \\textsc{N\\,ii}] &       121.90 &        $0.44\\pm0.20$           & $0.14\\pm0.08$   & $3\\times10^2$ [e]     & 14.53\\\\ \n\\lbrack \\textsc{O\\,i}] &        145.52 &        $0.65\\pm0.09$           & $0.32\\pm0.07$   & $1\\times10^5$ [H]     & -\\\\\n\\lbrack \\textsc{C\\,ii}] &       157.74 &        $26.34\\pm0.33$  & $10.05\\pm0.21$  & 50 [e], $3\\times10^3$ [H]     & 11.26\\\\\n\\hline\n\\end{tabular}\n\\begin{tabular}{l c c c}\n\\hline\n    \\vspace{-10pt}\\\\\n   &  & \\multicolumn{2}{c}{Flux density $\\pm$ uncertainty} \\\\\n Broadband      &       Wavelength      & \\multicolumn{2}{c}{(Jy)}\\\\\n                &               ($\\mu$m\\xspace)  &       Region I          &       Region II              \\\\\n\\hline\n    \\vspace{-10pt}\\\\\nMIPS  & 24 & $0.67\\pm0.01$ & $0.48\\pm0.01$ \\\\\nPACS & 70 & $7.36\\pm0.21$ &     $3.72\\pm0.12$ \\\\\nPACS & 100 & $7.91\\pm0.19$ & $4.10\\pm0.11$ \\\\\nPACS & 160 & $6.07\\pm0.10$ & $3.23\\pm0.06$ \\\\\n\\hline\n    \\vspace{-10pt}\\\\\n{$L_{\\rm TIR}$ (erg\\,s$^{-1}$)} & 3 -- 1100 & $5.25\\times10^{41}$ &       $3.02\\times10^{41}$     \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{table*}\n\n\\section{Description of the model}\n\\label{method}\n\\subsection{Model geometry and strategy}\nOur objective is to characterize the physical conditions of the ISM phases from which the IR emission arises in NGC\\,4214. To that end, we used the spectral synthesis code \\textsc{Cloudy} v.13, last described by \\cite{ferland-2013}. We performed a multiphase detailed modeling of the ISM for which we combined line and continuum emission, following the method described in \\cite{cormier-2012}. We considered the two main star-forming regions of NGC\\,4214: the most evolved central region (NW-I) and the southern region (SE-II). Here we present the main aspects of the model and how it is applied to each region. The components\/ISM phases of the model are \n\\begin{enumerate}\n         \\item a central source of radiation,\n         \\item an ionized medium component (H\\,{\\sc ii}\\xspace region) that surrounds the central source, \n         \\item a neutral medium (PDR) surrounding the H\\,{\\sc ii}\\xspace region.\n\\end{enumerate}\n\\noindent \nThis method assumes a single radiation source responsible for the observed SED of the studied region. In other words, we took all of the different sources (star clusters) and the surrounding clouds from which they have formed and represented them with one central source and one surrounding cloud. We thus targeted the integrated properties of each region. In practice, we mixed components of the ISM that have different composition and properties\nand blend them in a single system. \nThe applied geometry is spherical. The source is in the center and the illuminated face of the cloud lies at a certain distance that we call inner radius. In our case, the effective geometry is one-dimensional plane-parallel because the cloud forms a thin shell and its distance from the radiation source is large. \\par\n\nThe radiation source, representative of the stars that populate the clusters of the star-forming region, illuminates a cloud of dust and gas. It controls the ionization parameter, $U$, which characterizes the field and is defined as the ratio of the incident ionizing photon density to the hydrogen density. Hard UV photons from the source ionize hydrogen and form the H\\,{\\sc ii}\\xspace region. As this radiation is transmitted through the cloud, it is attenuated\nand thus becomes softer, which decreases its influence on ionization. However, it still controls the processes further in the cloud (in the PDR).\\par\n\nThe adopted strategy is to treat the H\\,{\\sc ii}\\xspace region first and then use the H\\,{\\sc ii}\\xspace region parameters as input for the PDR modeling. This allows for a self-consistent approach \\citep{abel-2005}, which is usually not directly available in standard PDR codes (see \\citealt{roellig-2007} for a comparison of PDR codes), and is important to accurately derive the radiation field that impinges\non the PDR. We first ran the simulation until the end of the H\\,{\\sc ii}\\xspace region, choosing to stop the simulation when the (electron) temperature reached 500\\,K to ensure that the model had transitioned to the atomic phase. We iterated to optimize our parameters so\nthat they matched the observed emission of known H\\,{\\sc ii}\\xspace region-diagnostic lines ([\\textsc{S\\,iv}]\\,10.5$\\mu$m\\xspace, [Ne\\textsc{\\,ii}]\\,12.8$\\mu$m\\xspace, [Ne\\textsc{\\,iii}]\\,15.6$\\mu$m\\xspace, [\\textsc{S\\,iii}]\\,18.7$\\mu$m\\xspace, [\\textsc{S\\,iii}]\\,33.5$\\mu$m\\xspace, \\oiii88$\\mu$m\\xspace, and \\nii122$\\mu$m\\xspace). Then we fed the result of this model to the PDR and compared the predictions to the remaining three PDR lines observed: \\oi63$\\mu$m\\xspace, \\oi145$\\mu$m\\xspace, and \\cii157$\\mu$m\\xspace, choosing a visual extinction of 10\\,mag as the stopping criterion. At this point, the gas temperature had fallen to roughly 10\\,K. \n\n\n\n\\subsection{Model parameters}\nWe constrained the properties of the star-forming regions by varying some of the parameters that control the physics of the models while keeping others fixed. The main parameters that we consider are\n\\begin{enumerate}\n  \\item a radiation field source: shape, age, luminosity (varied),\n  \\item the hydrogen density of the ISM, $n_{\\rm H}$ (varied),\n  \\item the ISM gas elemental abundances (fixed),\n  \\item the inner radius, $r_{\\rm in}$ (varied),\n  \\item the magnetic field, B (fixed),\n  \\item the turbulent velocity, $v_{\\rm turb}$ (fixed).\n\\end{enumerate}\n\\noindent Parameters that are fixed were set to values from the literature. The other parameters were varied inside a range whose width reflects the dispersion of published measurements or of the data. The main parameter of interest for this study is the radiation field, which was varied within a range guided by studies of the star formation history.\n\n\n\\subsubsection{Hydrogen density ($n_{\\rm H}$)}\n\\label{density}\nWe performed our simulations assuming pressure equilibrium. As the model proceeds through consecutive zones of the cloud, it keeps the pressure constant. Thus, the density of the medium varies to satisfy this equilibrium. The initial density that we specified in the models is the density at the illuminated face of the cloud, where the H\\,{\\sc ii}\\xspace region starts. The initial values and the range we probed are motivated by the observed \\siii18.7$\\mu$m\\xspace\/\\siii33.5$\\mu$m\\xspace ratio in the H\\,{\\sc ii}\\xspace region, which is\nknown to be sensitive to the electron density in the range 10$^2$-10$^4$\\,cm$^{-3}$ \\citep{rubin-1994}. We therefore let the initial density vary in the range 100-300\\,cm$^{-3}$ for the central region and 300-600\\,cm$^{-3}$ for the southern region with a common step of 25\\,cm$^{-3}$. By iterating this procedure, we constrained the best values for the density at the beginning of the H\\,{\\sc ii}\\xspace region.    \n\n\n\\subsubsection{Inner radius ($r_{\\rm in}$)}\nIn our spherical geometry, the source is at the center and is surrounded by a cloud. The illuminated face of the cloud lies at a certain distance $r_{\\rm in}$. This is not a strictly physically constrained parameter because the setup we used does not realistically model each cluster, but instead tries to mimic a whole region and reproduce its emission. The variation of this radius changes the photons flux and thus is expected to affect our results. We let $r_{\\rm in}$ vary from 1 to 100\\,pc for both regions.\n\n\n\\subsubsection{Elemental abundances}\nElemental abundances in the models were set to the observed values for oxygen, sulfur, nitrogen, and neon, taken from \\cite{kobulnicky-1996}. Some measurements partially cover our defined regions, and we adopted them as representative. Exclusively for carbon, we scaled its abundance according to the study on the dependence of $\\log(C\/O)$ on metallicity by \\cite{izotov-1999}. For other elements, we used the default ISM composition of \\textsc{Cloudy} and scaled the abundances to our metallicity (1\/3). The values used are indicated in Table~\\ref{elements}. \n\n\\begin{table}\n  \\caption{Elemental abundances in NGC\\,4214. \n  Values (in logarithmic scale) for NGC\\,4214 are taken from \\citet{kobulnicky-1996} and solar values from \\citet{asplund-2009}.}\n\\label{elements}\n \\centering\n\\vspace{-5pt}\n   \\begin{tabular}{c c c c}\n   \\hline \n    \\vspace{-10pt}\\\\\n        Abundance               & Region I      & Region II  & Solar value \\\\\n        \\hline\n    \\vspace{-10pt}\\\\\n        \\lbrack O\/H]            & $-3.795\\pm0.05$       & $-3.64\\pm0.04$        & $-3.31\\pm0.05$ \\\\\n        \\lbrack S\/H]            & $-5.380\\pm0.06$       & $-5.21\\pm0.06$        & $-4.88\\pm0.03$ \\\\\n        \\lbrack N\/H]            & $-5.094\\pm1.00$       & $-5.02\\pm0.10$        & $-4.17\\pm0.05$ \\\\\n        \\lbrack Ne\/H]           & $-4.535\\pm0.11$       & $-4.51\\pm0.08$        & $-4.07\\pm0.10$ \\\\\n        \\lbrack C\/H]            & $-4.295\\pm0.30$       & $-4.14\\pm0.30$        & $-3.57\\pm0.05$ \\\\\n        \\hline \n   \\end{tabular}\n \\end{table}\n\n\\subsubsection{Radiation field - shape and energy}\nWe used the code \\textsc{Starburst99}  \\citep{leitherer-2010} to produce a stellar population spectrum that serves as input for our models. We chose a Kroupa initial mass function between 0.08 and 120\\,M$_{\\odot}$ \\citep{kroupa-2001}, as done in \\cite{andrews-2013}, and Padova asymptotic giant branch tracks with Z=0.004. \nAs discussed above, we did not model each cluster individually, but we used integrated emission from the entire star-forming regions instead. We tried to be as close to the shape and intensity of the radiation field of the H\\,{\\sc ii}\\xspace regions as possible. Motivated by the star formation history of the galaxy presented in \\cite{mcquinn-2010} and \\cite{williams-2011}, we tested the following cases:\n\\begin{itemize}\n\\item For the central region, we considered two limiting scenarios: \n(i)~a single-burst star formation event and (ii)~a continuous star formation model, with SFR=0.07\\,${\\rm M_{\\odot}\\,yr^{-1}}$. The ages of the clusters were varied within a range of (i)~1-20\\,Myr (in steps of 0.5\\,Myr) and (ii)~200-1000\\,Myr (in steps of 200\\,Myr).\n\\item For the southern region, we considered a single-burst event with an age that varied from 1 to 20\\,Myr (in steps\nof 0.5\\,Myr).\n\\end{itemize}\n\\noindent\nA fixed mass of 10$^5$\\,M$_{\\odot}$ (typical cluster mass in \\citealt{sollima-2013}) was considered for the single bursts, where the stars are created at once (delta burst). Our value for the SFR (0.07\\,${\\rm M_{\\odot}\\,yr^{-1}}$) is representative of the `average' rate at which this galaxy formed stars within the past 1\\,Gyr of its history. The ages of the clusters in both regions were guided by values from \\cite{ubeda-2007}, \\cite{sollima-2013}, and \\cite{sollima-2014}. \\cite{ubeda-2007} found 2-7\\,Myr for region~I, along with extended clusters in the same region with ages of 150 to 190\\,Myr. In region~II, they found ages spreading around 2\\,Myr. \\cite{sollima-2013,sollima-2014} reported a larger spread in ages. In region~I, they obtained ages around a median of 14\\,Myr, and for the more extended clusters the ages lie between 10 and 300\\,Myr. For region~II, they found a median age of $\\sim$20\\,Myr. \\par\n\nFor the luminosity emitted from each region, we chose to use the TIR luminosity as a first approximation of the luminosity of the starburst. This choice implies the assumption that all radiation from the clusters in the region is reprocessed by the dust and thus emitted at longer wavelengths. In doing so, we kept in mind that there can be processes that we did not model (UV escape fraction or a diffuse ionized medium, for example) and that can contribute to this radiated energy (see Sect.~\\ref{discussion}). \n\n\n\\subsubsection{Magnetic field strength (B) and turbulent velocity ($v_{\\rm turb}$)}\nMagnetic fields and turbulence play an important role in structuring the ISM \\citep[e.g.,][]{mckee-2007}. When \\textsc{Cloudy} solves the pressure equilibrium for each zone of the modeled cloud, a magnetic pressure term equal to $\\displaystyle P_{\\rm B}=\\frac{B^2}{8\\pi}$ is included in the equation of state along with a turbulent pressure term equal to $\\displaystyle P_{\\rm turb}=2.8 \\cdot 10^6 \\cdot 3 \\cdot (\\frac{n_{\\rm H}}{10^5\\,{\\rm cm^{-3}}})(\\frac{v_{\\rm turb}}{\\rm {1\\,km\\,s^{-1}}})^2$~[cm$^{-3}$\\,K], for isotropic turbulent motions, where $n_{\\rm H}$ is the total hydrogen density and $v_{\\rm turb}$ is the turbulent velocity (see the {\\sc Hazy} documentation of \\textsc{Cloudy} for more information). \\par\n\nThe magnetic field of NGC\\,4214 was measured by \\cite{kepley-2011} using multiwavelength radio emission. The reported field strength in the center of the galaxy is 30\\,$\\mu$G, and the pressure term due to this field has the same order of magnitude as the hot gas and the gravitational contributions. Since it is not well known how the observed magnetic field might affect our observed line intensities, we excluded it from our default models and tested one case with a magnetic field strength of 30\\,$\\mu$G. \\par \n\nAnother potential energy source to consider can arise from the dissipation of turbulence. Turbulent energy is converted into thermal energy as it cascades from large scales to small scales through dissipation. However, we did not resolve size scales for which we can measure this. \n\\textsc{Cloudy} does not attempt to model the dissipation mechanism, but assumes a simple thermal energy source based on line width. The turbulent velocity was set to a value of 1.5\\,km\\,s$^{-1}$ by default in our models, and we tested two other cases: one case with an intermediate turbulent velocity ($v_{\\rm turb}$=3\\,km\\,s$^{-1}$ or FWHM=5\\,km\\,s$^{-1}$) that corresponds to the approximate line width observed in the CO(1-0) data by \\cite{walter-2001}, and one case with a high turbulent velocity ($v_{\\rm turb}$=50\\,km\\,s$^{-1}$) as found in the diffuse ionized gas by \\cite{WilcotsThurow-2001} and used also in \\cite{kepley-2011}.\n\nNevertheless, we explore the effects of excluding or including magnetic fields and turbulence in Sect.~\\ref{magn}. \n\n\n\\subsection{Determination of best-fitting models}\n\\label{minchi}\nWe aim to converge on a unique parameter set that best describes the conditions of the regions. We first ran models for which\nwe varied the parameters in a coarse grid to narrow down the parameter space, using ranges of values found in the literature to start with. We then used the \\textit{optimization} option of \\textsc{Cloudy}, which automatically varies the specified parameters in a finer grid to find the optimal solution.\n\nWe computed the average $\\chi ^2$, denoted $\\bar\\chi ^2$, for each model by comparing the observed fluxes of \\siv10.5$\\mu$m\\xspace, \\neiii15.6$\\mu$m\\xspace, \\siii18.7$\\mu$m\\xspace, \\siii33.5$\\mu$m\\xspace, and \\oiii88$\\mu$m\\xspace to the fluxes predicted from the radiative transfer calculation. These lines are the most luminous and most strongly correlated with the H\\,{\\sc ii}\\xspace region (as opposed to [N\\,{\\sc ii}]\\xspace and [Ne\\,{\\sc ii}]\\xspace which, from experience, can arise from other phases). We refer to these as the optimized lines in Table~\\ref{chi2ionic}. The goodness of the line emission fit is given by low $\\bar\\chi ^2$ values.\nThe \\textit{optimization} method of \\textsc{Cloudy} searches the minimum of $\\bar\\chi ^2$ that is defined as\n\\begin{align}\n   \\bar\\chi ^2=\\frac{1}{n}\\sum{\\chi_i ^2}=\\frac{1}{n}\\sum{\\frac{( M_i - O_i)^2}{(min\\{O_i;M_i\\} \\times \\sigma_i)^2}},\n\\end{align}\n\\noindent where $n$ is the number of lines optimized and $\\chi_i^2$ are the $\\chi^2$ values of the individual optimized lines.\nM$_i$ and O$_i$ are the modeled and observed fluxes, and $\\sigma_i$ is the fractional error on the observed flux (uncertainty\/flux) with calibration uncertainties added in quadrature to the measured uncertainties described in Sect.~\\ref{data}. We have five observables (the ionic lines listed above) and varied four parameters (cluster age, source luminosity, hydrogen density, and inner radius). \n\n\n\n\\section{Results}\n\\label{results}\nIn this section we present the model results for the two regions according to the star formation histories considered. Parameters of the best-fitting models and their corresponding $\\chi^2$ values are reported in Tables~\\ref{model} and \\ref{chi2ionic}, respectively. \n\n\n\\begin{table*}[!t]\n\\caption{Input parameters for the best-fitting models. \nValues are given at the illuminated face of the cloud. \nValues in parenthesis for the magnetic field strength \nand turbulent velocities are tested in Sect.~\\ref{magn}.}\n\\label{model}\n  \\centering\n\\vspace{-5pt}\n  \\begin{tabular}{l c c c}\n  \\hline \n    \\vspace{-10pt}\\\\\n  Parameter                             & \\multicolumn{2}{c}{Central region} & Southern region\\\\\n                                                & Single burst & Continuous & Single burst \\\\\n  \\hline\n    \\vspace{-10pt}\\\\\n  Density $n_{\\rm H}$ [cm$^{-3}$]               & 155           & 180             & 440   \\\\\n  Inner radius $r_{\\rm in}$ [pc]                        & 85.4                 & 62.1          & 22.3  \\\\\n  Stellar age t [Myr]                                   & 4.1                 & 440           & 3.9            \\\\\n  Total luminosity L [erg\\,s$^{-1}$]            & $1.15\\times10^{42}$ & $1.91\\times10^{42}$   & $5.25\\times10^{41}$   \\\\\n  Magnetic field B [$\\mu$G]                     & -                     & - (30)          & -             \\\\\n  Turbulent velocity $v_{\\rm turb}$ [km\\,s$^{-1}$]      & 1.5         & 1.5 (3, 50)   & 1.5           \\\\\n  \\hline \n  \\end{tabular}\n\\end{table*}\n\\begin{figure*}\n\\centering\n\\includegraphics[clip,trim=0 20mm 0 0,width=17cm,height=5cm]{fig3a}\n\\includegraphics[clip,trim=0 20mm 0 0,width=17cm,height=5cm]{fig3b}\n\\caption{Results for the central region (top panel) \nand for the southern region (bottom panel): line emission \nfor the H\\,{\\sc ii}\\xspace region (left side) and the PDR (right side), assuming \npressure equilibrium.\nGreen bars represent the observations, blue bars our single-burst model predictions, \nand gray bars with a dashed outline the continuous star formation model predictions.}\n\\label{h2bars}\n\\end{figure*}\n\n\\subsection{Line emission}\n\\label{modelresults}\n\\subsubsection{Central region (I): The single-burst model}\n\\label{SB}\nFor the single-burst star formation event, the best-fitting model of the central region has the following parameters: burst age of 4.1\\,Myr with luminosity $1.1\\times10^{42}$\\,erg\\,s$^{-1}$, density of 155\\,cm$^{-3}$, and $r_{\\rm in}\\simeq85$\\,pc. The corresponding ionization parameter at the illuminating face of the cloud is $\\log(U)=-2.7$. For the H\\,{\\sc ii}\\xspace region, all optimized lines are matched within $\\pm$30\\%, and \\neii12.8$\\mu$m\\xspace and \\nii122$\\mu$m\\xspace are underpredicted by a factor of $\\sim$8 and 3, respectively (see Fig.\\,\\ref{h2bars}, blue bars in the top panel). \nIn the PDR, the \\oi145$\\mu$m\\xspace and 63$\\mu$m\\xspace lines are overpredicted by a factor of $\\sim$2.5, and the \\cii157$\\mu$m\\xspace line is matched within 20\\%. We note that [C\\,{\\sc ii}]\\xspace emission can arise from both the neutral and the ionized phases of the ISM, with a potentially non-negligible contribution from the warm ionized medium in the Milky Way \\citep{heiles-1994}. The H\\,{\\sc ii}\\xspace region of our best-fitting model contributes negligibly to the predicted \\cii157$\\mu$m\\xspace and [O\\,{\\sc i}]\\xspace emission ($<$3\\%). The ultraviolet radiation field strength $G_0$ inside the PDR is $455$ in units of the equivalent \\cite{habing-1968} flux ($1\\,G_0 = 1.6\\times10^{-3}$\\,erg\\,cm$^{-2}$\\,s$^{-1}$). The input luminosity required by the model, which all comes out as $L_{\\rm TIR}$ in the PDR, is $\\text{about twice as}$  high\nas the observed $L_{\\rm TIR}$ in that region. \n\nThese results represent the simplifying case that the recent starburst dominates the star formation in this central region, so the line emission can be explained with a single burst. The age of the burst in the model nicely agrees with the range of ages from \\cite{ubeda-2007} and is at the younger end of ages from \\cite{sollima-2013,sollima-2014}.  \n\n\n\n\\subsubsection{Central region (I): The continuous star formation model}\nIn the continuous star formation scenario, the best-fitting model of the central region has the following parameters: stellar age of 440\\,Myr with luminosity $1.9\\times10^{42}$\\,erg\\,s$^{-1}$, density of 180\\,cm$^{-3}$, and $r_{\\rm in}\\simeq62$\\,pc. The ionization parameter is $\\log(U)=-2.5$. Line predictions for the H\\,{\\sc ii}\\xspace region and the PDR from this model solution are shown in Fig.\\,\\ref{h2bars} (gray bars). For all optimized lines (\\oiii88$\\mu$m\\xspace, \\siii18.7 and 33.5$\\mu$m\\xspace, \\siv10.5$\\mu$m\\xspace, and \\neiii15.6$\\mu$m\\xspace), the model matches the observations within $\\pm$20\\%. The two other ionic lines, \\neii12.8$\\mu$m\\xspace and \\nii122$\\mu$m\\xspace, are underpredicted by a factor of $\\sim$7 and 4. \nIn the PDR, [C\\,{\\sc ii}]\\xspace and the [O\\,{\\sc i}]\\xspace lines are matched within a factor of $\\sim$2. The contribution of the H\\,{\\sc ii}\\xspace region to the predicted PDR emission is only 1\\%. \nWe find $G_0\\simeq1.2\\times10^3$, which is higher than in the single-burst case. The luminosity of the model exceeds the observed $L_{\\rm TIR}$ by a factor of 3.5. \\par\n\nThe results represent the simplifying case of continuous star formation dominating this region, with the starbursts being embedded in it. The age of the model agrees well with the star formation event in the window 400-500\\,Myr ago reported by \\cite{mcquinn-2010}. \n\n\n \n\\subsubsection{Southern region (II)}\n\\label{southres}\nThe best-fitting model for the southern region is characterized by a burst age of 3.9\\,Myr with luminosity $5.3\\times10^{41}$\\,erg\\,s$^{-1}$, density of 440\\,cm$^{-3}$, and $r_{\\rm in}\\simeq22$\\,pc. The ionization parameter is $\\log(U)=-2.3$. Line predictions for the H\\,{\\sc ii}\\xspace region and the PDR are shown in the bottom panel of Fig.\\,\\ref{h2bars}. This burst found for the southern region is slightly younger than the burst in the central region, in agreement with \\cite{ubeda-2007}. In the H\\,{\\sc ii}\\xspace region, the \\oiii88$\\mu$m\\xspace, \\siii18.7 and 33.5$\\mu$m\\xspace, and \\siv10.5$\\mu$m\\xspace lines are reproduced within 30\\%, while \\neiii15.6$\\mu$m\\xspace, \\neii12.8$\\mu$m\\xspace, and  \\nii122$\\mu$m\\xspace are underpredicted by a factor of 1.7, 10, and 6, respectively. \nFeeding this model to the PDR, the \\cii157$\\mu$m\\xspace line is underpredicted by a factor of 3.4, while the [O\\,{\\sc i}]\\xspace lines are both overpredicted by a factor of $\\sim$2. The contribution of the H\\,{\\sc ii}\\xspace region to the PDR line emission is only 1\\%. $G_0$ is found to be about $3.2\\times10^3$, which is higher than in the central region. The luminosity of the model is 1.7 times higher than the observed $L_{\\rm TIR}$ in this region. \n\n\n\n\\subsubsection{Comparison to empirical line ratios}\nPhysical conditions in the H\\,{\\sc ii}\\xspace region are mainly determined by tracers of the radiation field strength ([Ne\\,{\\sc iii}]\\xspace\/[Ne\\,{\\sc ii}]\\xspace, [S\\,{\\sc iv}]\\xspace\/\\siii18.7$\\mu$m\\xspace) and of density (\\siii18.7$\\mu$m\\xspace\/\\siii33.5$\\mu$m\\xspace). We compare these well-known diagnostic ratios in the two star-forming regions in Table~\\ref{ratios}. In the southern region, ratios of [Ne\\,{\\sc iii}]\\xspace\/[Ne\\,{\\sc ii}]\\xspace and [S\\,{\\sc iv}]\\xspace\/\\siii18.7$\\mu$m\\xspace are observed to be about twice as high and \\siii18.7$\\mu$m\\xspace\/\\siii33.5$\\mu$m\\xspace marginally higher than in the central region, indicating that the radiation field is harder and the medium denser. This is indeed what we recover with our best-fitting models (Table~\\ref{model}), as they match the sulfur ratios well. \n\n\n\\begin{table}\n\\caption{$\\chi^2$ values for the two star-forming regions.}\n\\label{chi2ionic}\n \\centering\n\\vspace{-5pt}\n   \\begin{tabular}{l c c c}\n   \\hline \\hline\n    \\vspace{-10pt}\\\\\n        H\\,{\\sc ii}\\xspace region~~~  &\\multicolumn{2}{c}{Central region}    & \\hspace{-2mm}Southern region \\\\             \n                                & Burst         & \\hspace{-1mm}Continuous & Burst \\\\\n        \\hline\n    \\vspace{-10pt}\\\\\n        \\multicolumn{2}{l}{Individual $\\chi^2$ values:}         &                 &               \\\\\n        \\lbrack \\textsc{O\\,iii}] \\,88$\\mu$m\\xspace               & 0.01  & 0.03    & 0.01  \\\\\n        \\lbrack \\textsc{N\\,ii}]\\,122$\\mu$m\\xspace                & 12.58 & 44.63   & 82.56 \\\\\n        \\lbrack \\textsc{S\\,iii}]\\,18.7$\\mu$m\\xspace              & 2.24  & 2.38    & 37.69 \\\\\n        \\lbrack \\textsc{S\\,iii}]\\,33.5$\\mu$m\\xspace              & 8.10  & 6.99    & 31.89 \\\\\n        \\lbrack \\textsc{S\\,iv}]\\,10.5$\\mu$m\\xspace       & 0.76  & 0.70  & 4.94    \\\\\n        \\lbrack Ne\\textsc{\\,ii}]\\,12.8$\\mu$m\\xspace      & 14442.2       & 13842.6 & 58101.7       \\\\\n        \\lbrack Ne\\textsc{\\,iii}]\\,15.6$\\mu$m\\xspace     & 8.14  & 24.65         & 224.51        \\\\\n        \\hline\n    \\vspace{-10pt}\\\\\n        $\\bar\\chi^2$ (all ionic lines)          & 2067.72       & 1988.85 & 8354.76       \\\\\n        $\\bar\\chi^2$ (optimized lines) \\hspace{-4mm}          & 3.85  & 6.95  & 59.81   \\\\\n        \\hline\n        \\hline\n    \\vspace{-10pt}\\\\\n        PDR~~~  & \\multicolumn{2}{c}{Central region}    & \\hspace{-2mm}Southern region \\\\               \n                                & Burst         & \\hspace{-1mm}Continuous & Burst \\\\\n        \\hline\n    \\vspace{-10pt}\\\\\n        \\multicolumn{2}{l}{Individual $\\chi^2$ values:}         &                 &               \\\\\n        \\lbrack \\textsc{C\\,ii}]\\,157$\\mu$m\\xspace        & 1.57  & 31.83 & 258.63  \\\\\n        \\lbrack \\textsc{O\\,i}]\\,63$\\mu$m\\xspace  & 149.78        & 57.05 & 85.37   \\\\\n        \\lbrack \\textsc{O\\,i}]\\,145$\\mu$m\\xspace & 34.14 & 11.83 & 21.27 \\\\\n        \\hline\n    \\vspace{-10pt}\\\\\n        $\\bar\\chi^2$ (all PDR lines)    & 61.83 & 33.57 & 121.76        \\\\\n        \\hline \\hline\n   \\end{tabular}\n \\end{table}\n\\begin{table*}\n\\caption{Observed and predicted MIR line ratios for the two star-forming regions.\nThe [Ne\\,{\\sc iii}]\\xspace\/[Ne\\,{\\sc ii}]\\xspace and [S\\,{\\sc iv}]\\xspace\/[S\\,{\\sc iii}]\\xspace line ratios are indicative of the radiation field strength, \nand the ratio of the two [S\\,{\\sc iii}]\\xspace lines is a density diagnostic.}\n\\label{ratios}\n\\centering\n\\vspace{-5pt}\n   \\begin{tabular}{l c c c c c c c}\n   \\hline\n    \\vspace{-10pt}\\\\\nRatio           & & \\multicolumn{3}{c}{Central region}          & & \\multicolumn{2}{c}{Southern region} \\\\\n   & &   Observed &    Burst & Continuous                        & & Observed      & Burst \\\\\n   \\hline\n    \\vspace{-10pt}\\\\\n\\lbrack Ne\\textsc{\\,iii}]\/[Ne\\,{\\sc ii}]\\xspace& & 2.082        & 13.72 & 12.34          & & 3.448               &       28.955          \\\\  \n\\lbrack \\textsc{S\\,iv}]\/[\\textsc{S\\,iii}]18.7 & &       0.481 & 0.479 & 0.477                 & & 1.227  &  1.044\\\\\n\\lbrack \\textsc{S\\,iii}]18.7\/[\\textsc{S\\,iii}]33 & &  0.630  & 0.593         & 0.601         & & 0.835 & 0.846\\\\\n\\hline\n   \\end{tabular}\n  \\end{table*}\n\n\n\\subsection{Effects of magnetic fields and turbulence on the PDR temperature and density}\n\\label{magn}\nAfter determining the best parameters for the H\\,{\\sc ii}\\xspace regions, we explored the effect of cloud density on the PDR emission in more\ndetail. \nDensity is of critical importance in the emission output of the simulation because of the different critical densities of the observed lines. Density values quoted so far are representative of the H\\,{\\sc ii}\\xspace region and evolve inside the modeled cloud. Figure~\\ref{dens} shows hydrogen density profiles in the clouds for each case presented in Sect.~\\ref{modelresults}. The density starts at the initial value we set for each model in the H\\,{\\sc ii}\\xspace region, remaining practically at the same level throughout the H\\,{\\sc ii}\\xspace region. At the interface between the H\\,{\\sc ii}\\xspace region and the PDR, there is a jump in density required to keep the model in pressure equilibrium. When pressure is only determined by the gas pressure ($P_{\\rm gas}=n_{\\rm H}kT$; i.e., magnetic fields and turbulence are omitted), the temperature difference at the phase transition is balanced by a rise in density of 2-3 orders of magnitude. Within this frame, the effects of magnetic fields or turbulence, implemented as pressure terms in \\textsc{Cloudy}, can be understood as follows: when total pressure equilibrium is assumed, they give more support at the phase transition, thus preventing a large difference in density between the H\\,{\\sc ii}\\xspace region and the PDR and moderating the density increase at large optical depths. \nFor the model presented in Sect.~\\ref{modelresults}, where a low turbulence value is included but no magnetic fields, representative PDR densities are $2\\times10^4$\\,cm$^{-3}$ in the central region for both the single-burst and continuous star formation models, and $7\\times10^4$\\,cm$^{-3}$ in the southern region (see Fig.\\,\\ref{dens}). \n\n\\begin{figure}\n\\centering\n\\includegraphics[clip,width=8.2cm]{fig4.eps}\n\\vspace{-5pt}\n\\caption{Density profiles in the modeled clouds for the central and southern region, which include a turbulence pressure term ($v_{\\rm turb}$=1.5\\,km\\,s$^{-1}$). Note that the x-axis is logarithmic, so the H\\,{\\sc ii}\\xspace region (with a constant low density) occupies a thin layer of the cloud, stopping at low visual extinction ($\\sim$0.1\\,mag).}\n\\label{dens}\n\\end{figure}\n\n\nThe effects of magnetic field and turbulence on the cloud density, temperature, and line emission are shown in Fig.\\,\\ref{turb}. \nWe present a set of runs for our best-fitting model in the central region single-burst case (note that we recover similar behaviors for the central continuous and southern single-burst cases, as shown in Appendix~\\ref{appendixa}) with the magnetic field (B=30\\,$\\mu$G) and\/or the turbulence pressure ($v_{\\rm turb}$=1.5, 3, 50\\,km\\,s$^{-1}$) terms switched on. These terms have no impact on the ionic line emission because thermal pressure dominates the pressure balance in the H\\,{\\sc ii}\\xspace region, but they noticeably change the emission of the PDR lines. When only thermal pressure is considered, the gas density jumps to values $>3\\times10^4$\\,cm$^{-3}$ in the PDR and the [O\\,{\\sc i}]\\xspace lines are overpredicted by an order of magnitude (black bars and dotted line). \nWith only the magnetic field on, all three PDR lines are underpredicted by a factor of $\\sim$3 (orange bars), but their ratios are kept in the range observed thanks to the lower densities achieved ($2\\times10^3$\\,cm$^{-3}$). Comparing models with different turbulent velocities, we see that the [C\\,{\\sc ii}]\\xspace line is best matched for low\nor intermediate velocities because of their moderate densities ($\\sim10^4$\\,cm$^{-3}$) and slightly lower PDR temperatures (at $A_{\\rm V} \\simeq 1-3$\\,mag). Increasing the turbulent velocity reduces the predicted [O\\,{\\sc i}]\\xspace emission and PDR density. The high-turbulence model performs poorly because it has the most dramatic effect on the density and line emission. \n\nTo summarize, we find that the best case that simultaneously matches all three PDR lines in the central region is the model with intermediate turbulent velocity ($v_{\\rm turb}$=3\\,km\\,s$^{-1}$), which has a density of $8\\times10^3$\\,cm$^{-3}$, but we stress that the main effect of turbulence is to reduce the PDR density.\n\n\n\\begin{figure*}\n\\centering\n\\includegraphics[clip,width=\\textwidth,height=6cm]{fig5a.eps}\n\\includegraphics[clip,width=8cm]{fig5b.eps} \\hspace{1cm}\n\\includegraphics[clip,width=8cm]{fig5c.eps}\n\\vspace{-5pt}\n\\caption{Effect of turbulence and magnetic fields on the predicted line intensities (top panel), density, and temperature (bottom panels) in the modeled cloud for the central region single-burst case. Green bars: observations. Gray bars and solid lines: only low turbulence switched on ($v_{\\rm turb}$=1.5\\,km\\,s$^{-1}$, default model). Black bars and dotted lines: no magnetic fields and no turbulence. Orange bars and dashed lines: only magnetic field switched on (B=30\\,$\\mu$G). Red bars and dash-dotted line: only moderate turbulence switched on ($v_{\\rm turb}$=3\\,km\\,s$^{-1}$). Cyan bars and triple-dotted-dashed line: only high turbulence switched on ($v_{\\rm turb}$=50\\,km\\,s$^{-1}$).}\n\\label{turb}\n\\end{figure*}\n\n\n\n\\subsection{Input spectra and SED}\n\\label{insed}\nFigure~\\ref{spectra} shows the input and output SEDs of the models for the two regions. The input SED is the stellar spectrum of the illuminating source modeled with \\textsc{Starburst99} and also includes the CMB at millimeter wavelengths. In the central region, the stellar spectrum has a wider distribution for the continuous star formation model (red curve) than the single-burst star formation model (black curve), and it is more luminous in the near-IR regime due to the presence of old stars.  \nCompared to observations, all input SEDs fall above the GALEX FUV data because they are unattenuated, and the single-burst input SEDs fall below the 2MASS data because they lack old stars. In the central region, the input SED of the continuous model, on the other hand, agrees well with the 2MASS data. For better agreement with the FUV data, we estimated the level of extinction required to attenuate the input SEDs. We considered average extinction values $E(B-V)$ of 0.1, 0.05, and 0.1\\,mag for the central continuous central single-burst and southern single-burst models, respectively (dotted lines in Fig.\\,\\ref{spectra}), which are in the range of values found by \\cite{ubeda-2007b}. \n\nFocusing on the output SEDs of the models for the central region, it is anticipated that the level of the FIR continuum is different. The higher the input luminosity of the source, the higher the peak of the output SED. Moreover, as the dust temperature rises, the peak of the output SED is expected to shift to shorter wavelengths. For the continuous model, the higher FUV luminosity therefore\nprovides more dust heating, explaining the slight shift of its peak to shorter wavelengths. \nWe can compare the output SEDs to the observed PACS 70$\\mu$m\\xspace, 100$\\mu$m\\xspace, and 160$\\mu$m\\xspace fluxes. The models agree relatively well with observations for the southern region, but overpredict the FIR continuum emission in the central region.\nThis is not surprising because we used as input luminosity a higher value than the observed TIR flux and the modeled PDR has a high $A_{\\rm V}$. Better agreement with continuum observations requires a model that predicts a TIR flux lower by a factor of 2-3, for example, by reducing the covering factor of the PDR. We return to this in Sect.~\\ref{modelum}.\n\n\n\\begin{figure*}\n\\centering\n\\includegraphics[clip,trim=0 0 0.1cm 0,width=6.7cm]{fig6a.eps}\n\\includegraphics[clip,trim=1.95cm 0 0.1cm 0,width=5.75cm]{fig6b.eps}\n\\includegraphics[clip,trim=1.95cm 0 0.1cm 0,width=5.75cm]{fig6c.eps}\n\\vspace{-10pt}\n\\caption{Spectral energy distributions of the two star-forming regions: central region single-burst case (left panel), central region continuous case (middle panel), and southern region single-burst model (right panel). The black and blue curves correspond to the input and output SEDs, respectively. The dotted lines are the attenuated input SEDs. The data points are the photometry measurements from GALEX FUV, 2MASS J, H, K bands, MIPS 24\\,$\\mu$m\\xspace, and PACS at 70$\\mu$m\\xspace, 100$\\mu$m\\xspace, and 160\\,$\\mu$m\\xspace. In panels for the central region, the dashed curves are scaled versions of the output SEDs, considering a covering factor of $0.5$ for the PDR. }\n\\label{spectra}\n\\end{figure*}\n\n\n\n\\section{Discussion}\n\\label{discussion}\nWe have presented models for the two star-forming regions of NGC\\,4214 that work for most of the observed MIR and FIR lines. Some discrepancies remain between our models and observations ([Ne\\,{\\sc ii}]\\xspace, [N\\,{\\sc ii}]\\xspace, [C\\,{\\sc ii}]\\xspace\/[O\\,{\\sc i}]\\xspace, and $L_{\\rm TIR}$); these are not due to the choice of parameter space but rather to missing physics or components in our models. In this section, we discuss various aspects of our analysis: 1)~the discrepancies with observations, and we give clues to improve our models, 2)~which star formation scenario describes the data better, and 3)~how our ISM results relate to the known properties and evolution of the two regions.\n\n\n\\subsection{Discrepancies between models and observations}\n\\label{disclines}\n\\subsubsection{Ionic lines}\nIn our best-fitting models of the H\\,{\\sc ii}\\xspace region, the \\neii12.8$\\mu$m\\xspace and \\nii122$\\mu$m\\xspace lines are systematically underpredicted. These lines have lower excitation potentials (21.56 and 14.53\\,eV, respectively) than the other, better matched ionic lines, and can therefore be partially excited outside of the main H\\,{\\sc ii}\\xspace region. This effect can be significant in NGC\\,4214 because of the poor spatial resolution. \n\nDiscrepancies between the observed and modeled [Ne\\,{\\sc iii}]\\xspace\/[Ne\\,{\\sc ii}]\\xspace ratio, with the same amplitude as we found for NGC\\,4214, were reported by \\cite{martin-hernandez-2002} for H\\,{\\sc ii}\\xspace regions observed by ISO\/SWS (see their figure~2). These could again be related to a mixture of physical conditions within the ISO beam, which is also relatively large. For the starburst galaxy Haro\\,11, we have examined the effect of an additional low-ionization component (star of effective temperature 35\\,000\\,K and $n_{\\rm H}\\simeq 10^{1-3}$\\,cm$^{-3}$). This reproduced the observed \\neii12.8$\\mu$m\\xspace and \\nii122$\\mu$m\\xspace emission without significantly affecting the other ionic lines \\citep{cormier-2012}.\nAlternatively, given that the neon lines have the largest energy difference, they are more sensitive to the underlying stellar atmosphere models than the sulfur lines. Constraining those models is beyond the scope of this paper, and we relied on the sulfur lines as being more robust diagnostics of the H\\,{\\sc ii}\\xspace region conditions in NGC\\,4214 (i.e., models presented in Sect.~\\ref{modelresults}). \n\nWe also assessed the effect of including the \\neii12.8$\\mu$m\\xspace line in the best-fitting solution-tracking procedure for the southern region. This resulted in a solution where the \\neii12.8$\\mu$m\\xspace absolute flux was better reproduced (within a factor of 3). This model uses an older burst (5\\,Myr), higher density (500\\,cm$^{-3}$), and the same inner radius (20\\,pc). The corresponding ionization parameter is $\\log(U)=-2.4$, which is 0.1\\,dex lower than previously found. However, the model underpredicts the neon intensities by a factor of 2 and the [\\textsc{S\\,iv}]\/[\\textsc{S\\,iii}]\\,18.7$\\mu$m\\xspace ratio by a factor of $\\sim$4, while that ratio was matched within 20\\% without the [Ne\\,{\\sc ii}]\\xspace constraint. \n\n\n\\subsubsection{PDR lines}\nIn our default PDR solutions for both regions, [C\\,{\\sc ii}]\\xspace is systematically underpredicted compared to [O\\,{\\sc i}]\\xspace. The best PDR model, found in Sect.~\\ref{magn} for the central region single-burst case, includes a turbulent velocity of 3\\,km\\,s$^{-1}$. In the southern and central region continuous case, similar turbulent velocities also lead to better agreement with the [C\\,{\\sc ii}]\\xspace\/[O\\,{\\sc i}]\\xspace line ratios, but still underpredict the observed emission in absolute values (Appendix~\\ref{appendixa}).\n\nIn addition to the stars, X-rays can be a source of heating in the PDR and affect the FIR line emission. Point sources and diffuse X-ray emission have been reported in \\cite{hartwell-2004} and \\cite{ghosh-2006}. The identified point sources are not coincident with the peak of the FIR emission, and we therefore ignored them. The diffuse emission is mostly detected in the central region, with a luminosity of $3\\times 10^{38}$\\,erg\\,s$^{-1}$ \\citep{hartwell-2004}, which is lower than that of the starburst. We have tested the effect of this diffuse X-ray component on the PDR lines in the central region and found that it increases the predicted intensity of the [O\\,{\\sc i}]\\xspace lines by $\\sim$30\\% and the [C\\,{\\sc ii}]\\xspace intensity by less than 10\\%. As X-rays are not the main source of heating in the PDR, they do not help to produce significantly more [C\\,{\\sc ii}]\\xspace emission. \n\nWe further explored the possibility of [C\\,{\\sc ii}]\\xspace originating from a diffuse ionized component. We compared the [C\\,{\\sc ii}]\\xspace and \\nii122$\\mu$m\\xspace intensities and the PACS upper limit on the \\nii205$\\mu$m\\xspace line, which gives \\nii122$\\mu$m\\xspace\/\\nii205$\\mu$m\\xspace$>$1, to theoretical predictions assuming pure collisional regime. Following \\cite{bernard-salas-2012} and applying $C$ and $N$ elemental abundances observed in NGC\\,4214, we found that less than 16\\% of the total observed [C\\,{\\sc ii}]\\xspace emission arises in diffuse ionized gas. \\textit{Herschel}\\xspace SPIRE FTS observations of \\nii205$\\mu$m\\xspace toward the central region also indicate that \\nii122$\\mu$m\\xspace\/\\nii205$\\mu$m\\xspace$=$2.5 (priv. comm. R. Wu), which gives an ionized gas density of $\\sim$60\\,cm$^{-3}$ and a contribution of only 8\\% to the total [C\\,{\\sc ii}]\\xspace emission. Therefore, if a low-density ionized component is added to our current models to account for the missing [N\\,{\\sc ii}]\\xspace and [Ne\\,{\\sc ii}]\\xspace emission, this component will not contribute significantly to the [C\\,{\\sc ii}]\\xspace emission. Our best-fitting models for the central region also predict that the H\\,{\\sc ii}\\xspace region contributes less than a few percent to the [C\\,{\\sc ii}]\\xspace emission. \n\nThe [C\\,{\\sc ii}]\\xspace emission most likely arises from a neutral phase, but its conditions are not well described by our default PDR models. With the PDR tests performed in Sect.~\\ref{magn}, we have explored the effect of density on the PDR emission lines, but these lines are also sensitive to the radiation field strength. To reduce the radiation field intensity $G_0$ (not the hardness), we placed the PDR farther away by stopping the model at the H$^+$\/H\\,{\\sc i}\\xspace phase transition and resuming the calculation at a larger distance in the H\\,{\\sc i}\\xspace phase (note that this breaks the pressure equilibrium). The direct effect is to dilute the UV field before it reaches the PDR, as proposed by \\cite{israel-2011} and \\cite{cormier-2015}, which is equivalent to increasing the porosity of the medium. For the central single-burst central continuous and the southern single-burst cases, we increased the PDR distance by a factor of 2, 3, and 5 ($r_{\\rm in}$$\\simeq$170, 186, and 115\\,pc), respectively. This way, $G_0$ decreases to $\\sim$120 in all three cases, boosting the [C\\,{\\sc ii}]\\xspace emission, and the predicted [C\\,{\\sc ii}]\\xspace\/[O\\,{\\sc i}]\\xspace ratios match the observed ratios within 40\\% (Fig.~\\ref{pdrdist}). In absolute values, the [C\\,{\\sc ii}]\\xspace and [O\\,{\\sc i}]\\xspace intensities are 2 to 3 times too high,\nhowever. This can be compensated by a PDR covering factor lower than unity (see Sect.~\\ref{modelum} below). \n\nWe conclude that a moderate density, moderate $G_0$ neutral medium (compared to our dense, high $G_0$ default PDR model) with a\nlow turbulent velocity and a covering factor lower than unity is the most plausible origin for the observed [C\\,{\\sc ii}]\\xspace emission. \n\n\\begin{figure*}\n\\centering\n\\includegraphics[clip,trim=0 10mm 0 0,width=\\textwidth,height=5.8cm]{fig7.eps}\n\\vspace{-10pt}\n\\caption{Effect of changing the distance to the modeled cloud for the PDR calculation. The PDR distance is increased by a factor of 2, 3, and 5 for the central single-burst (left panel), central continuous (middle panel), and southern single-burst cases (right panel), respectively.}\n\\label{pdrdist}\n\\end{figure*}\n\n\n\\subsubsection{Model luminosity}\n\\label{modelum}\n\\cite{hermelo-2013} have fit the dust SED of the whole galaxy. In particular, their models require less UV luminosity than that observed to match the IR emission. They discussed possible explanations for this disagreement, proposing an escape of unattenuated UV radiation along with a particular geometry and dust properties in the galaxy. Such an argument of a UV escape fraction could also apply in our case. As seen in Fig.\\,\\ref{spectra}, the observed photometry data points in the FIR, which correspond to emission originating from the PDR, are lower than the modeled SED for the central region. This disagreement can indicate a different covering factor for the PDR. In our model, the PDR fully covers the sphere around the source (i.e., covering factor of unity). For the best-fitting models to better match the photometry, it could be that the PDR component is more porous, allowing radiation to escape the cloud. To illustrate this, we plot the resulting SEDs for the two models of the central region considering a PDR covering factor of 0.5 (dashed curves in Fig.\\,\\ref{spectra}).\n\nPart of the discrepancies in our results that we have discussed in this section~\\ref{disclines} originate in modeling each complex as a single cloud, which is imposed by the lack of spatial resolution in the observations. Clearly, future improvements are expected from observations with better spatial resolution. \n\n\n\\subsection{Central region: bursty or continuous star formation?}\n\\label{borc}\nThe star formation history of NGC\\,4214 over the last Gyr is complex. It shows bursts lasting for shorter or longer periods and a continuous `background', which takes place throughout this whole time window \\citep{mcquinn-2010,williams-2011}. In that sense, we could say that it is a rather hybrid star formation pattern. \nIn the central region, we have investigated cases of both a single-burst and a continuous star formation mode. However, when we use a single model to reproduce the observed line emission, we simplify the problem, since we do not take into account both modes. Hence arises the question of which of the two approaches is the most adequate to model the MIR-FIR line emission. \nWe have shown that both modes can satisfyingly reproduce the observed mid- and far-infrared line emission. By comparing the $\\bar\\chi^2$ values of the best-fitting models (Table~\\ref{chi2ionic}), we found that the single-burst case seems to globally\nperform better when considering the lines used in the optimization method. When including [N\\,{\\sc ii}]\\xspace and [Ne\\,{\\sc ii}]\\xspace, the two modes perform similarly, although the high $\\bar\\chi^2$ values are driven by the poor fit to the \\neii12.8$\\mu$m\\xspace line. \nFor the PDR, the continuous scenario gives a lower $\\bar\\chi^2$ , but the default PDR solutions are not optimum and can be fine-tuned for both modes (by lowering the density and $G_0$, see Sects.~\\ref{magn} and \\ref{disclines}). We conclude that both are limiting, simplifying cases of modeling the ISM in NGC\\,4214, with the continuous star formation model being marginally more accurate inside the PDR and the single-burst in the H\\,{\\sc ii}\\xspace region (without further refinement).\n\n\n\\subsection{Comparison between the two star-forming regions}\nHow do the ISM conditions that we have characterized in the two star-forming regions relate to their star formation properties? \nWe have found that the modeled cluster (radiation source) in the southern region contains younger stellar populations with a harder radiation field than that in the central region, in agreement with the results of \\cite{ubeda-2007}, for instance. The hydrogen density is also higher in the southern star-forming region, but the metallicities of the regions are very similar. The southern region is observed to be at a younger, more compact stage than the central region. The central region is more evolved\nand had time to expand, as observed by the presence of shells that may have swept away the dense material \\citep{walter-2001}, and is thus consistent with a more diffuse ISM. \n\nWe calculated the star formation rate surface densities for the two regions combining the GALEX FUV map and the \\textit{Spitzer}\\xspace 24$\\mu$m\\xspace map, as done in \\cite{leroy-2008}, with%\n\\begin{equation}\n\\label{sfcomp}\n\\begin{split}\n\\Sigma_{\\rm SFR} {\\rm [M_{\\odot}\\,yr^{-1}\\,kpc^{-2}]} = 3.2 \\cdot 10^{-3} \\cdot {\\rm I_{24}~[MJy\\,sr^{-1}]} \\\\ ~+~ 8.1 \\cdot 10^{-2} \\cdot {\\rm I_{\\rm FUV}~[MJy\\,sr^{-1}]}\n\\end{split}\n,\\end{equation}\n\\noindent where $\\Sigma_{\\rm SFR}$ is the SFR surface density and I$_{24}$ and I$_{\\rm FUV}$ the 24$\\mu$m\\xspace and FUV intensities. We also measured the atomic and molecular hydrogen content of the two regions using the 21cm map from THINGS\\footnote{\\url{http:\/\/www.mpia-hd.mpg.de\/THINGS\/Data.html}} \\citep{walter-2008} and the CO(1-0), CO(2-1) transition maps from \\cite{walter-2001} and HERACLES\\footnote{\\url{http:\/\/www.cv.nrao.edu\/~aleroy\/heracles_data\/}} \\citep{leroy-2009}, respectively. We used a conversion factor of $\\alpha_{\\rm CO}$=4.38~[M$_\\odot$\\,pc$^{-1}$\\,(K\\,km\\,s$^{-1}$)$^{-1}$] from CO(1-0) luminosity to H$_2$ mass. If we were to use a different conversion factor due to the low metallicity of these regions \\citep[e.g.,][]{schruba-2012}, this would not affect the relative comparison of the regions (see Table~\\ref{sfprops}). \nThe central region (I) has a total hydrogen content of M$_{\\rm gas,I}$=M$_{\\rm HI}$+M$_{\\rm H_2}$=2.05$\\times$10$^6\\,{\\rm M_\\odot}$ and a molecular (mass) fraction of $f_{\\rm mol,I}$=M$_{\\rm H_2}$\/M$_{\\rm HI}$=0.35. Integrating Eq.~\\ref{sfcomp} in the region, we find SFR$_{\\rm I}$=2.2$\\times$10$^{-2}\\,{\\rm M_\\odot\\,yr^{-1}}$. The southern region (II) has a higher total hydrogen content of M$_{\\rm gas,II}$=2.68$\\times$10$^6\\,{\\rm M_\\odot}$, an H$_2$ fraction $f_{\\rm mol,II}$=0.32, and SFR$_{\\rm II}$=1.9$\\times$10$^{-2}\\,{\\rm M_\\odot\\,yr^{-1}}$. \nTherefore the southern region has relatively more gas compared to its SFR than the central region. In terms of efficiency, SFR\/M$_{\\rm gas}$, it is about 50\\% lower in the southern region. \nThis could reflect a slightly more efficient, cluster-like star formation episode in the central region or simply encode a different evolutionary state as the SFR and gas masses are a strong function of time on scales of individual star-forming regions \\citep[e.g.,][]{schruba-2010}. The southern region being younger, it may still be in the process of forming stars. \n\n\n\\begin{table}\n  \\caption{Comparison of star formation properties.}\n\\label{sfprops}\n \\centering\n\\vspace{-5pt}\n   \\begin{tabular}{l c c c}\n   \\hline \n    \\vspace{-10pt}\\\\\n        Quantity                        & & Region I    & Region II   \\\\\n        \\hline\n    \\vspace{-10pt}\\\\\n        {$L_{\\rm CII}\/L_{\\rm TIR}$}     & & $5.4\\times10^{-3}$  & $3.6\\times10^{-3}$ \\\\\n        {$L_{\\rm CII}\/L_{\\rm CO(1-0)}$}         & & $6.7\\times10^4$     & $2.5\\times10^4$ \\\\\n        {M$_{\\rm gas=H_2+HI}$~$[$M$_\\odot]$}    & & $2.05\\times10^6$    & $2.68\\times10^6$ \\\\\n        {M$_{\\rm H_2}$\/M$_{\\rm HI}$}    & & 0.35        & 0.32 \\\\\n        {SFR~$[$M$_\\odot$\\,yr$^{-1}]$}  & & $2.2\\times10^{-2}$  & $1.9\\times10^{-2}$ \\\\\n        {SFE~$[$Gyr$^{-1}]$}    & & 10.7        & 7.1 \\\\\n        \\hline \n   \\end{tabular}\n \\end{table}\n\n\nThe main differences in ISM conditions that we extracted from our modeling relate to the H\\,{\\sc ii}\\xspace region properties. The emission lines are a factor of two lower in luminosity in the southern region, except [Ne\\,{\\sc iii}]\\xspace and [S\\,{\\sc iv}]\\xspace, which are proportionally higher in the southern region. By contrast, the PDR conditions in the two regions are similar ($n_{\\rm H}\\simeq10^4$\\,cm$^{-3}$ and $G_0\\simeq150$). Our modeling reflects conditions resulting from the recent star-forming event and has little predictive power regarding a different, future star-forming event. In particular, at the linear scale that we probe ($\\sim$175\\,pc), the PDR conditions are averaged over multiple star-forming clouds and not representative of the underlying, possibly different, substructure in individual molecular clouds. \nHowever, there is more PDR emission relative to CO in the central region, that is, high [C\\,{\\sc ii}]\\xspace\/CO and [O\\,{\\sc i}]\\xspace\/CO ratios \\citep[see also][]{cormier-2010}. \nAs found by \\cite{walter-2001}, CO emission is centrally concentrated in the south and more diffuse in the center. The concentration of molecular gas may be nourishing the current star formation episode in the south or is being observed at a pre-disruption stage with the same fate as the central region. \nThe increased porosity, which evidently is an intrinsic property of the low-metallicity ISM, is seen in both the central and southern star-forming regions. \nThe main evolution within the dense medium is seen in the covering factor of the PDR, which is found to be lower in the central, more evolved region than in the southern region, and in CO, which probably suffers more from photodissociation with time and its emission is seen farther away from the cluster center, but this cannot be modeled with our static approach. Observing an intermediate PDR tracer at the C$^+$\/CO transition, such as C\\,{\\sc i}, would help to test this evolution scenario. \n\n\n\n\\section{Conclusion}\nWe have investigated the physical conditions characterizing \nthe ISM of the dwarf irregular galaxy NGC\\,4214 by modeling \\textit{Spitzer}\\xspace \nand \\textit{Herschel}\\xspace observations of MIR and FIR fine-structure cooling lines. \nWe used the spectral synthesis code \\textsc{Cloudy} to \nself-consistently model the H\\,{\\sc ii}\\xspace region and PDR properties of the two main \nstar-forming regions in NGC\\,4214. \nWe summarize our results as follows: \n\\begin{itemize}\n\\item The ionized gas in the southern region is found to be $2.5$ \ntimes denser than in the central region (440\\,cm$^{-3}$ \nversus 170\\,cm$^{-3}$) and typified by a harder radiation field. \nOur best-fitting models of the H\\,{\\sc ii}\\xspace region+PDR reproduce most \nionic and neutral atomic lines, namely the \\oiii88$\\mu$m\\xspace, \\siii18.7 \nand 33.5$\\mu$m\\xspace, \\siv10.5$\\mu$m\\xspace, \\neiii15.6$\\mu$m\\xspace, and \\oi63$\\mu$m\\xspace lines, \nwithin a factor of $\\sim$2. \n\\item The observed \\nii122$\\mu$m\\xspace and \\neii12.8$\\mu$m\\xspace lines are \nthe most discrepant with our model solutions for the H\\,{\\sc ii}\\xspace region. \nA single model component seems too simplistic to account for all \nobserved lines simultaneously. Given the complexity of these star-forming regions, \na multi-component modeling would be more appropriate. \nIn particular, a lower excitation ionized gas component may be \nrequired to match the [N\\,{\\sc ii}]\\xspace and [Ne\\,{\\sc ii}]\\xspace emission in both regions. \n\\item Our H\\,{\\sc ii}\\xspace region models and the established observational \n[C\\,{\\sc ii}]\\xspace\/[N\\,{\\sc ii}]\\xspace line ratio used as a proxy for the fraction of [C\\,{\\sc ii}]\\xspace arising in the ionized gas \nboth indicate that the [C\\,{\\sc ii}]\\xspace emission is mostly associated with the PDR gas, \nwith only a $\\sim$10\\% contribution from the ionized gas. \n\\item Constant pressure models where thermal pressure dominates \nthe pressure equilibrium perform rather poorly for the PDR lines \nmostly because of the high densities and high $G_0$ values \nreached in the PDR. Including additional pressure terms, such as \nweak turbulent or magnetic pressure, or placing the \nPDR cloud farther away and reducing its covering factor, \nleads to a much improved reproduction of the observed line intensities. \n\\item Star formation histories have an effect on the predicted \nMIR-FIR line emission. We have explored the two simplifying cases \nof a bursty and a continuous star formation scenario. \nIn the central region, we found that the bursty scenario works marginally \nbetter for the H\\,{\\sc ii}\\xspace region and the continuous scenario for the PDR, \nalthough both modes can reproduce \nthe observations after refining the PDR conditions. \n\\item The H\\,{\\sc ii}\\xspace region modeling from IR emission is consistent with \nthe evolutionary stages of the regions found in previous studies: \nthe southern region is younger and more compact, while the central region \nis more evolved and diffuse. \nOn the linear scale of our study ($\\sim$175\\,pc), the PDR conditions \nof individual star-forming clouds are averaged out and do not echo \nthe observed differences between the two regions (stellar ages, H\\,{\\sc ii}\\xspace conditions, etc.). \nThe increased porosity of the star-forming regions appears \nas an intrinsic characteristic of the low-metallicity ISM, \nwhile the covering factor of the PDR, which is reduced \nin the central region, stands out as the main evolution tracer.\n\\end{itemize}\n\\vspace{3mm}\n\n\\begin{acknowledgements}\nWe would like to thank S. Hony for his help with the IRS data and \nfor fruitful discussion, F. Walter for providing us the CO(1-0) data, \nand S. Glover for his advice on turbulence issues.\nWe thank the referee for his or her comments on the manuscript.\nDC and FB acknowledge support from DFG grant BI 1546\/1-1.\nThis work is based in part on archival data obtained with the \nSpitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, \nCalifornia Institute of Technology under a contract with NASA.\n\\textit{Herschel}\\xspace is an ESA space observatory with science instruments \nprovided by European-led Principal Investigator consortia and \nwith important participation from NASA.\n\\end{acknowledgements}\n\n\n\\bibliographystyle{aa}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nA precise determination of Parton Distribution Functions (PDFs) with \nreliable estimate of their uncertainties is crucial for the success of \nthe physics program at the LHC experiments. \nOn the one hand PDF uncertainties are often the dominant theoretical \nuncertainties for many relevant signal and background \nprocesses~\\cite{Campbell:2006wx}. \nOn the other hand overestimated PDF errors might hinder \nthe discovery of new physics effects, as shown for example \nin~\\cite{Ferrag:2004ca}.\nTop physics at the LHC is no exception and both top pair and single-top\nproduction present complementary and interesting properties as far as PDF\ndetermination\/effects are concerned. This contribution aims to review\nsome of the implications of PDFs for top quark physics at the LHC.\n\nIn the first part of the contribution we summarize the present \nstatus of the predictions for $t\\bar{t}$, $t-$ and $s-$channel single-top \ncross-sections, computed using different PDF sets. We show how differences \nin the predictions can directly be traced to both differences in the parton \nluminosities, and the values of physical parameters used in the PDF \nanalyses, such as the strong coupling constant $\\alpha_s$ or the  \nthe $b$-quark mass, $m_b$.\nIn particular, we highlight the importance to account for the uncertainty \non the $b$-quark mass for accurate predictions of single-top production at \nthe LHC.\n\nIn the second part we study PDF induced correlations between PDFs and \n$t\\bar{t}$\/single-top cross-sections and between top and $W^\\pm$\/$Z^0$ \ncross-sections. \nWe briefly discuss how these correlations could be used in order to \nimprove the accuracy of top cross-section measurements with early data \nat the LHC.\nThese correlation studies are performed within the framework of the \nNNPDF parton analysis~\\cite{DelDebbio:2007ee,Ball:2008by,Ball:2009mk,\nBall:2010de}  which, by relying on Monte Carlo techniques \nfor the estimation of uncertainties, provides an ideal tool for such \nstatistical studies.\n\nThe baseline PDF set for the studies presented in this contribution\nis the recently released NNPDF2.0~\\cite{Ball:2010de}, the first NLO global \nfit using the NNPDF methodology. \n\n\\section{Top-quark production at the LHC}\n\n\\subsection{$t\\bar{t}$ production}\n\nTop pair production is the main channel for top quark production at Tevatron \nand LHC.\nIn Table~\\ref{tab:ttbar} we collect the predictions for the top pair\ncross-section at LHC 7 TeV at NLO computed with the MCFM code~\\cite{ref:MCFM} \nusing different PDF sets.\n\n\\begin{table}[ht!]\n  \\caption{Top pair cross-section at NLO with different PDF sets at \n    LHC 7 TeV.}\n  \\label{tab:ttbar}\n  \\begin{narrowtabular}{2cm}{c|c}\n    \\hline\n      CTEQ6.6~\\cite{Nadolsky:2008zw}  & 147.7 $\\pm$ 6.4 pb \\\\\n      MSTW2008~\\cite{Martin:2009iq}   & 159.0 $\\pm$ 4.7 pb \\\\\n      NNPDF2.0~\\cite{Ball:2010de}     & 160.0 $\\pm$ 5.9 pb \\\\\n    \\hline\n      ABKM09~\\cite{Alekhin:2009ni}    & 131.9 $\\pm$ 4.8 pb \\\\\n      HERAPDF1.0~\\cite{:2009wt}       & 136.4 $\\pm$ 4.7 pb \\\\\n    \\hline\n  \\end{narrowtabular}\n\\end{table}\n\nWe notice that the predictions from the three global fits, NNPDF2.0, CTEQ6.6 \nand MSTW08 agree at the 1-sigma level.\nThe differences with PDF sets based on reduced datasets, ABKM09 and HERAPDF1.0, \nare larger. \nWe note that top pair production depends strongly on the large-$x$ gluon, \nand thus using sets which do not include Tevatron jet data might lead to rather \ndifferent predictions for this observable.\nOne should notice that differences between the predictions from different PDF \nsets also arise from the use of different values for the strong coupling \nconstant $\\alpha_s$.  \nIt has been shown that using a common value of $\\alpha_s$ brings predictions\nfrom different groups for various LHC observables, including top pair \nproduction, in better agreement~\\cite{Demartin:2010er,Ubiali:2010xc}.\n\nOnce we subtract the difference introduced by different choices for $\\alpha_s$, \nthe remaining differences can be directly traced to differences in the PDF \nluminosities at the typical scale of the process.\nThis is illustrated in Fig.~\\ref{fig:gglumi}, where the gluon-gluon luminosity\nfor LHC at 7 TeV is plotted for the CTEQ6.6, MSTW2008 and NNPDF2.0 NLO sets.\nFor example, the lower value for the cross-section obtained using the CTEQ6.6\nset reflects the smaller $gg$ luminosity as compared to the other sets at\n$Q^2=m_t^2$.\n\\begin{figure}[ht!]\n  \\centering\n  \\includegraphics[width=7cm]{gglumi-7-rel-global}\n  \\caption{Gluon-gluon parton luminosities for CTEQ6.6, MSTW2008 and NNPDF2.0\n    including the associated PDF uncertainties. Results are showed as ratios\n    to NNPDF2.0.}\n  \\label{fig:gglumi}\n\\end{figure}\n\n\\subsection{Single-top production}\n\nNext we present predictions for single-top production at the LHC at 7 TeV.\nThese predictions for various PDF sets are collected in \nTable~\\ref{tab:singletop}, where we present results for both the $t$- \nand $s$-channel single-top cross-sections computed at NLO in QCD with \nthe MCFM code. We have used the $N_f=5$ (massless) calculation \nfor the results presented here, recently the $N_f=4$ calculation, which\nproperly takes into account the effects due to finite $b$-quark mass, also \nbecame available~\\cite{Campbell:2009ss}.\n\nWhile at the Tevatron the contributions of $t$- and $s$-channel $W$ exchange \nto single-top production are comparable in size, at the LHC $t$-channel \nproduction is by far the dominant production mechanism.\n\nFrom the point of view of testing the predictions from different PDF sets \n$t$-channel single-top is also very interesting due to the fact that, in the \nso called 5-flavour scheme ({\\it i.e.} a scheme where the $b$ is assumed to\nbe a parton in the proton) the cross-section at LO probes directly the \n$b$-quark PDF, which in turn is closely related to the gluon distribution \nfrom which it is generated radiatively.\n\nFrom Table~\\ref{tab:singletop} one notices that the central predictions from \nthe various PDF sets can differ by several times the quoted 1-sigma PDF \nuncertainty\\footnote{Note that for the ABKM09 prediction the uncertainty \nincludes the associated $\\alpha_s$, $m_c$ and $m_b$ uncertainties, which \ncannot be disentangled from the PDF uncertainties, and is thus much larger \nthan the one obtained using other PDF sets.}.\nThere are different contributions to this discrepancy. The first stems from \nthe different values of the strong coupling constant $\\alpha_S$ which are \nused by different parton sets. Since single-top production is mediated\nby electroweak gauge bosons, $\\alpha_s$ enters only in radiative corrections,\nunlike the case of $t\\bar{t}$ production discussed above, this\neffect is rather small.\n\nIn order to separate the differences in the single-top production \ncross-section which arise from the differences in the PDFs themselves\nand those from other physical parameters (like $m_b$ or $\\alpha_s$) which \nalso enter in the PDF analyses and in the computation of the partonic matrix \nelement, we plot in Fig.~\\ref{fig:bglumi} the $b$-gluon parton luminosity, \nwhich determines the LO cross-section, for the CTEQ6.6, MSTW2008 and \nNNPDF2.0 NLO sets. \nIt is clear that parton luminosities in the kinematic region relevant for \nsingle-top production differ by an amount much smaller than the cross-sections \nthemselves, suggesting that the differences indeed come from variations of \nother physical parameters which enter the PDF analysis.\n\nIndeed, it can be seen that the bulk of this difference is related to the \ndifferent values of the $b$-quark mass used in the fits by the different\ncollaborations. The NNPDF collaboration sets $m_b=4.3$ GeV, CTEQ uses \n$m_b=4.5$ GeV while the MSTW08 fit is performed setting $m_b=4.75$ GeV. \nIn order to substantiate our claim that the different values used the $b$-quark \nmass explain the bulk of the difference for the $t$-channel single-top \ncross-section, we produced two NNPDF2.0 sets with $m_b = 3.7$ GeV \nand  $m_b = 5.0$ GeV respectively. \nThe results for the $b$-gluon parton luminosities for these modified \nsets are shown in the right plot in Fig.~\\ref{fig:bglumi} and the \ncorresponding cross-sections for the $t$-channel single-top cross-section \nare collected in Table~\\ref{tab:singletop-mb}.\nIt is clear that the value of $m_b$ is anti-correlated with the $bg$ luminosity \nand the $t$-channel single-top cross-section.\n\nFrom Table~\\ref{tab:singletop-mb} one sees that variations of the $b$-quark \nmass of the order or $\\delta m_b\\sim 0.7$ GeV induce an uncertainty in the \ncross-section of $\\delta\\sigma \\sim 3$ pb.\nIf we take the PDG average as the best available determination of the $b$-quark\nmass and convert it from the \\hbox{$\\overline{\\rm MS}$} scheme to the pole mass scheme we obtain an\nuncertainty of approximately $\\delta m_b({\\rm PDG})\\sim 0.2$ GeV. Rescaling \nerrors, we are still left with an uncertainty in the $t$-channel single-top \ncross-section of $\\delta\\sigma \\sim 0.8$ pb, still larger than the typical \nnominal PDF uncertainties quoted in Table~\\ref{tab:singletop}. \nIt is also clear from Table~\\ref{tab:singletop-mb} and Fig.~\\ref{fig:bglumi} \nthat using a similar value of $m_b$ would bring the predictions from different \nPDF sets into much better agreement. The uncertainty due to $m_b$ should \nthus always be accounted for in the theoretical predictions for LHC single-top \nproduction.\n\n\\begin{table}[t!]\n  \\caption{Single-top cross-section at NLO with different PDF sets at \n    LHC 7 TeV.}\n  \\label{tab:singletop}\n  \\begin{narrowtabular}{2cm}{c|c|c}\n    \\hline\n                                    & $t$-channel            & $s$-channel   \\\\ \n    \\hline\n    CTEQ6.6~\\cite{Nadolsky:2008zw}  &  40.85 $\\pm$  0.50 pb & 2.33 $\\pm$ 0.05 pb\\\\\n    MSTW2008~\\cite{Martin:2009iq}   &  41.96 $\\pm$  0.26 pb & 2.38 $\\pm$ 0.04 pb\\\\\n    NNPDF2.0~\\cite{Ball:2010de}     &  44.33 $\\pm$  0.32 pb & 2.38 $\\pm$ 0.06 pb\\\\\n    \\hline\n    ABKM09~\\cite{Alekhin:2009ni}    &  43.17 $\\pm$  1.98 pb & 2.40 $\\pm$ 0.03 pb\\\\\n    HERAPDF1.0~\\cite{:2009wt}       &  40.04 $\\pm$  0.33 pb & 2.38 $\\pm$ 0.05 pb\\\\\n    \\hline\n  \\end{narrowtabular}\n\\end{table} \n\n\n\\begin{figure}[ht!]\n  \\centering\n  \\includegraphics[width=0.45\\textwidth]{bglumi-7-rel-global.eps}\\qquad\n  \\includegraphics[width=0.45\\textwidth]{bglumi-7-rel-nnpdf.eps}\n  \\caption{(left) $b$-gluon parton luminosities for CTEQ6.6, MSTW2008 and \n    NNPDF2.0, normalized to the NNPDF2.0 value. (right) $b$-gluon parton \n    luminosities for NNPDF2.0 fits with different values of the $b$-quark \n    mass normalized to the standard NNPDF2.0.}\n  \\label{fig:bglumi}\n\\end{figure}\n\n\\begin{table}[t!]\n  \\caption{$t$-channel single-top cross-section at NLO computed using NNPDF2.0 \n    sets with different values of the $b$-quark mass.}\n  \\label{tab:singletop-mb}\n  \\begin{narrowtabular}{2cm}{l|c}\n    \\hline\n    NNPDF2.0 ($m_b=3.7$ GeV) &  46.77 $\\pm$ 0.36 pb \\\\\n    NNPDF2.0 ($m_b=4.3$ GeV) &  44.33 $\\pm$ 0.32 pb \\\\\n    NNPDF2.0 ($m_b=5.0$ GeV) &  41.04 $\\pm$ 0.32 pb \\\\\n    \\hline\n  \\end{narrowtabular}\n\\end{table}\n\n\\section{PDF-induced correlations}\n\nIt is well known (see for example the discussion in \nRef.~\\cite{Nadolsky:2008zw,Ball:2008by}) that parton densities\ninduce correlations among different observables measured at hadron \ncolliders. \nThese can be the PDFs themselves, one PDF and a physical observable or \ntwo physical observables. The latter case is especially important from \nthe experimental point of view, since it allows to define measurement \nstrategies in which the PDF uncertainties between two observables cancel, \nfor example in the case in which these correlation between the two observables \nis maximal.\n\nIn the case of a PDF set based on the Monte Carlo method, like NNPDF, \nthe correlation coefficient $\\rho[A,B]$ for two observables $A$ and $B$ which \ndepend on PDFs is given by the standard expression for the correlation of two\nstochastic variables~\\cite{Ball:2008by,Demartin:2010er}\n\\begin{equation}\n  \\label{eq:correlation}\n  \\rho[A,B]=\\frac{\\langle A B\\rangle_{\\mathrm{rep}}\n    - \\langle A\\rangle_{\\mathrm{rep}}\\langle B\\rangle_{\\mathrm{rep}} }\n  {\\sigma_A\\sigma_B}\n\\end{equation}\nwhere the averages are taken over the ensemble of the $N_{\\mathrm{rep}}$ values \nof the observables computed with the different replicas of the PDF set, \nand $\\sigma_{A,B}$ are the standard deviations for the observables as computed \nfrom the MC ensemble.\nThe value of $\\rho$ characterizes whether two observables are correlated \n($\\rho \\approx 1$), anti-correlated ($\\rho \\approx -1$) or uncorrelated \n($\\rho\\approx 0$). In the following we present results for the NNPDF2.0 set, \nthe LHC cross-sections have been obtained as before using the MCFM code.\n\nAs a first example, we compute the correlation between the $t\\bar{t}$ and\n$t$-channel single-top cross-section at the LHC (7 TeV) and different PDFs\nat the factorization scale $\\mu_f=m_{\\mathrm{top}}$ as a function of $x$.\nThe results are plotted in Fig.~\\ref{fig:pdf_obs_corr}. \nThe most remarkable features are that the $t\\bar{t}$ cross-section at the \nLHC at 7 TeV is mostly correlated to the gluon distribution at $x\\sim 0.1$ \nand anti-correlated with it at small-$x$, with the same behaviour present \nfor sea quark PDFs,  generated radiatively from the gluon. \nWe note also that the $u$- and $d$-quark distributions are anti-correlated \nwith the cross-section at medium-\/large-$x$. \n\nAs for the case of the $t$-channel single-top cross-section, we point out \nthat the strong correlation with the gluon (and therefore with the $c$- \nand $b$-quark distributions) present for $t\\bar{t}$ is now milder \nand peaked at medium-$x$, $x\\sim 0.01$, and now we find a moderate \ncorrelation at medium-\/small-$x$ with the $u$ and $d$ PDFs, of the \nopposite sign as in the $t\\bar{t}$ cross-section. \nWe would like to stress as well the correlation of single-top\ncross-section and the $s$-,$\\bar{s}$-quark PDFs at medium-\/small-$x$, which \nis notably absent in the $t\\bar{t}$ case.\n\n\\begin{figure}[ht!]\n  \\centering\n  \\includegraphics[width=0.33\\textwidth,angle=270]{pdf_ttbar_corr}\\qquad\n  \\includegraphics[width=0.33\\textwidth,angle=270]{pdf_singletop_corr}\n  \\caption{Correlation between parton densities and $t\\bar{t}$ (left) \n    and $t$-channel single-top (right) cross-sections at the LHC 7 TeV. \n    The PDF set used is NNPDF2.0 and cross-sections have been\n    computed with MCFM.}\n  \\label{fig:pdf_obs_corr}\n\\end{figure}\n\nAs previously pointed out, the correlation coefficient \nEq.~(\\ref{eq:correlation}) can also be computed between two cross-sections, \nwhich is potentially relevant since in the case of a sizable correlation \nthe measurement of one of these observables would provide useful information \non the value of the other one. In this respect we have computed the \ncorrelation between the $t\\bar{t}$ and $t$-channel single-top cross-sections \non one side and $W^{\\pm}$ or $Z^0$ cross-sections at the LHC on the other.\nThe values for the correlation coefficients for the different pairs of \nobservables are collected in Table~\\ref{tab:obs_obs_corr} and the correlation \nellipses are plotted in Fig.~\\ref{tab:obs_obs_corr} for the $t\\bar{t}$ \ncross-section and in Fig.~\\ref{fig:singletop_VB_corr} for $t$-channel \nsingle-top.\n\n\\begin{table}[t!]\n  \\centering\n  \\begin{narrowtabular}{3cm}{c|c|c|c}\n    \\hline\n    $\\mathbf{\\rho}$     & $\\sigma_{W^+}$ & $\\sigma_{W^-}$ & $\\sigma_{Z^0}$\\\\\n    \\hline\n    $\\sigma_{t\\bar{t}}$ &   -0.716       &    -0.694      &   -0.773      \\\\\n    \\hline\n    $\\sigma_{t}$        &    0.330       &     0.140      &    0.240      \\\\\n    \\hline\n  \\end{narrowtabular}\n  \\caption{Correlation coefficients between $t\\bar{t}$ or $t$-channel \n    single-top and $W^{\\pm}$ or $Z^0$ cross-sections at the LHC 7 TeV in the\n    NNPDF2.0 analysis. }\n  \\label{tab:obs_obs_corr}\n\\end{table}\n\nBoth the values of $\\rho$ and the shape of the correlation ellipses show \na significant anti-correlation between the $t\\bar{t}$ cross-section and \nthe $W^\\pm$ and $Z^0$ ones.\nGiven the fact that the vector boson cross-sections at the LHC are \n${\\cal{O}}(10)$ times larger than the $t\\bar{t}$ cross-section and \nmore accurately known from the theoretical point of view, it is foreseeable \nto use those in order to better calibrate the top pair cross-section \nmeasurement in early data.\n\nOn the other hand the single-top cross-section shows a very mild \ncorrelation to the vector boson one thus rendering a similar approach based \non the precision measurement of EW bosons difficult. However, if one is able\nto identify other observables which should be measured with a similar\nprecision and that are correlated to the single-top cross-section, the\ndiscussion of the $t\\bar{t}$ case would also apply here.\n \n\\begin{figure}[t!]\n  \\centering\n  \\includegraphics[width=0.31\\textwidth]{Wminus-ttbar}\\quad\n  \\includegraphics[width=0.31\\textwidth]{Wplus-ttbar}\\quad\n  \\includegraphics[width=0.31\\textwidth]{Z-ttbar}\\quad\n  \\caption{Correlation between $t\\bar{t}$ and Electroweak Vector Boson cross \n    sections at the LHC 7 TeV. The cross-sections have been computed\nwith MCFM and the NNPDF2.0 parton set.}\n  \\label{fig:ttbar_VB_corr}\n\\end{figure}\n\n\\begin{figure}[t!]\n  \\centering\n  \\includegraphics[width=0.31\\textwidth,angle=90]{Wminus-singletop}\\quad\n  \\includegraphics[width=0.31\\textwidth]{Wplus-singletop}\\quad\n  \\includegraphics[width=0.31\\textwidth]{Z-singletop}\\quad\n  \\caption{Correlation between $t$-channel single-top and Electroweak Vector \n    Boson cross-sections at the LHC 7 TeV.  The cross-sections have\n been computed\nwith MCFM and the NNPDF2.0 parton set.}\n  \\label{fig:singletop_VB_corr}\n\\end{figure}\n\n\\section{Conclusions}\n\nThe quality of top physics results from the LHC experiments will be affected, \namong other factors, by our knowledge of Parton Distribution Functions and \ntheir uncertainties. In this contribution we have reviewed the present status \nof predictions for $t\\bar{t}$ and single-top cross-sections evaluated at \nNLO in QCD with different PDF sets and pointed out differences among them, \ntrying to elucidate the reasons for these differences. For the case of \nsingle-top production, we have shown that one important source of difference\namong predictions obtained using different PDF sets is the value of the \n$b$-quark mass $m_b$ used by the different collaborations. \n\nIn the second part we briefly discussed PDF-induced correlations between \nparton densities and top cross-sections and between the latter and \nelectroweak vector boson production cross-sections at the LHC at 7 TeV. \nThese correlation could be useful to define experimental strategies to \nmeasure the top quark cross-section in a way in which PDF uncertainties are \nreduced.\n\n\\acknowledgments\nAG would like to thank the organizers, and in particular Fabio Maltoni,\nfor the kind invitation to participate in a very nice and stimulating \nWorkshop and the HEPTOOLS European Network for providing the financial \nsupport for his participation.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{1. ISM computational complexity derivation}\n\n\n\nFor ISM, DG and SM, the bottleneck resides in the computation of the gradient.\n\\[ f ( W) = \\sum_{i, j} \\gamma_{i, j} e^{- \\frac{\\tmop{Tr} ( W^T A_{i, j}\n   W)}{2 \\sigma^2}} \\]\n\\[ \\frac{\\partial f}{\\partial W} = \\left[ \\sum_{i, j}  \\frac{\\gamma_{i,\n   j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( W^T A_{i, j} W)}{2 \\sigma^2}} A_{i, j}\n   \\right] W \\]\n\\[ \\frac{\\partial f}{\\partial W} = \\left[ \\sum_{i, j}  \\frac{\\gamma_{i,\n   j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( W^T \\Delta x_{i, j} \\Delta x_{i, j}^T\n   W)}{2 \\sigma^2}} A_{i, j} \\right] W \\]\nWhere $A_{i, j} = \\Delta x_{i, j} \\Delta x_{i, j}^T$. The variables have the\nfollowing dimensions.\n\\[ \\begin{array}{l}\n     x_{i, j} \\in \\mathbbm{R}^{d \\times 1}\\\\\n     W \\in \\mathbbm{R}^{d \\times q}\n   \\end{array} \\]\nTo compute a new $W$ with DG, we first mulitply $\\Delta x_{i, j}^T W$, which\nis $O ( d)$. Note that $W$ in DG is always 1 single column. Next, it\nmultiplies with its own transpose to yied $O ( d  + q^2)$. Then we\ncompute $A_{i, j}$ to get $O ( d + q^2 + d^2)$. Since this operation needs to\nbe added $n^2$ times, we get, $O ( n^2 ( d + q^2 + d^2))$. Since $d \\gg q$,\nthis notation reduces down to $O ( n^2 d^2)$. Let $T_1$ be the number of\niterations until convergence, then it becomes $O ( T_1 n^2 d^2)$. Lastly, in\nDG, this operation needs to be repeated $q$ times, hence, $O ( T_1 n^2 d^2\nq)$.\n\n\n\nTo compute a new $W$ with SM, we first mulitply $\\Delta x_{i, j}^T W$, which\nis $O ( d q)$. Next, it multiplies with its own transpose to yied $O ( d q\n + q^2)$. Then we compute $A_{i, j}$ to get $O ( d q + q^2 + d^2)$.\nSince this operation needs to be added $n^2$ times, we get, $O ( n^2 ( d q +\nq^2 + d^2))$. Since $d \\gg q$, this notation reduces down to $O ( n^2 d^2)$.\nThe SM method requires the computation of the inverse of $d \\times d$ matrix.\nSince inverses is cubic, it becomes $O ( n^2 d^2  + d^3)$. Lastly, let\n$T_2$ be the number of iterations until convergence, then it becomes $O ( T_2\n( n^2 d^2 + d^3))$.\n\n\n\nTo compute a new $W$ with ISM, we first mulitply $\\Delta x_{i, j}^T W$, which\nis $O ( d q)$. Next, it multiplies with its own transpose to yied $O ( d q\n + q^2)$. Then we compute $A_{i, j}$ to get $O ( d q + q^2 + d^2)$.\nSince this operation needs to be added $n^2$ times, we get, $O ( n^2 ( d q +\nq^2 + d^2))$. Since $d \\gg q$, this notation reduces down to $O ( n^2 d^2)$.\nThe ISM method requires the computation of the eigen decomposition of $d\n\\times d$ matrix. Since inverses is cubic, it becomes $O ( n^2 d^2  +\nd^3)$. Lastly, let $T_3$ be the number of iterations until convergence, then\nit becomes $O ( T_3 ( n^2 d^2 + d^3))$.\n\n\\end{document}\n\n\\section{GENERAL FORMATTING INSTRUCTIONS}\n\n\n\\end{document}\n\n\\section{GENERAL FORMATTING INSTRUCTIONS}\n\n\\end{document}\n\n\n\n\\section{Introduction}\n\nClustering, i.e., the process of grouping similar objects in a dataset together, is a classic problem. It is extensively used for exploratory data analysis.  Traditional clustering algorithms typically identify a single partitioning of a given dataset.  However, data is often multi-faceted and can be both interpreted and clustered through multiple viewpoints (or, {\\em views}).  For example, the same face data can be clustered based on either identity or based on pose.  In real applications, partitions generated by a clustering algorithm may not correspond to the view a user is interested in. \n\n\n\n\\iffalse\n\\fi\nIn this paper, we address the problem of finding an {\\em alternative clustering}, given a dataset and an existing, pre-computed clustering.  Ideally, one would like the alternative clustering to be {\\em novel} (i.e., non-redundant) w.r.t. the existing clustering to reveal a new viewpoint to the user.  Simultaneously, one would like the result to reveal partitions of high clustering {\\em quality}.\n Several recent papers propose algorithms for  alternative clustering~\\cite{gondek2007non,cui2010learning,dang2010generation,davidson2008finding,cui2007non,niu2014iterative}.  Among them, Kernel Dimension Alternative Clustering (KDAC) is a flexible approach, shown to have superior performance compared to several competitors~\\cite{niu2014iterative}. KDAC is as powerful as spectral clustering in discovering arbitrarily-shaped clusters (including ones that are not linearly separable) that are non-redundant w.r.t.~an existing clustering.  As an additional advantage, KDAC can simultaneously learn the subspace in which the alternative clustering resides. \n\nThe flexibility of KDAC comes at a price: the KDAC formulation involves optimizing a non-convex cost function constrained over the space of orthogonal matrices (i.e, the Stiefel manifold). Niu et al.~\\cite{niu2014iterative} proposed a Dimension Growth (DG) heuristic for solving this optimization problem, which is nevertheless highly computationally intensive. We elaborate on its complexity in Section~\\ref{gen_inst}; experimentally, DG is quite slow, with a convergence time of roughly $46$ hours on an Intel Xeon CPU, for a $624$ sample-sized face data (c.f.~Section~\\ref{sec:exp}).  This limits the applicability of KDAC in interactive exploratory data analysis settings, which often require results to be presented to a user within a few seconds.  It also limits the scalability of KDAC to large data.  Alternately, one can solve the KDAC optimization problem by gradient descent on a Stiefel manifold (SM)~\\cite{wen2013feasible}. However, given the lack of convexity, both DG or SM are prone to get trapped to local minima. Multiple iterations  with random initializations are required to ameliorate the effect of locality.  This increases computation time, and also decreases in effectiveness as the dimensionality of the data increases: the increase in dimension rapidly expands the search space and the abundance of local minima. As such, with both DG and SM, the clustering quality is negatively affected by an increase in dimension.\n\n\n\\iffalse\n\\fi\n\n{\\bf Our Contributions.}   \nMotivated by the above issues, we make the following contributions:\n\\begin{packeditemize}\n\\item We propose an Iterative Spectral Method (ISM), a \\emph{novel algorithm} for solving the non-convex optimization constrained on a Stiefel manifold problem inherent in KDAC. Our algorithm has  several highly desirable properties. First, it \\emph{significantly outperforms} traditional methods such as DG and SM in terms of both computation time and quality of the produced alternative clustering.  Second, the algorithm relies on an \\emph{intuitive use of iterative spectral decompositions}, making it  both easy  to  understand as well as easy to implement, using off-the-shelf libraries. \n\\item  ISM has a natural initialization, constructed through a Taylor approximation of the problem's Lagrangian. Therefore, high quality results can be obtained without random restarts in search of a better initialization. We show that this initialization is a contribution in its own right, as its use improves performance of competitor algorithms.\n\\item We provide \\emph{theoretical guarantees} on its fixed point.  In particular, we establish conditions under which  the fixed point of ISM satisfies both the 1st and 2nd order necessary conditions for local optimality. \n\\item We extensively evaluate the performance of ISM in solving KDAC with synthetic and real data under various clustering quality and cost measures.  Our results show an improvement in execution time by up to a factor of roughly $70$ and $10^5$, compared to SM and DG, respectively. At the same time, ISM  outperforms SM and DG in clustering quality measures along with significantly lower computational cost. \n\n\n\n\\end{packeditemize}\n\\section{Kernel Dimension Alternative Clustering (KDAC) }\n\\label{gen_inst}\n\nIn alternative clustering, a dataset is provided along with existing clustering labels. Given this\nas input, we seek a $\\emph{new}$ clustering that is (a) distinct from the existing clustering, and (b) has high quality with respect to a clustering quality measure.\nAn example illustrating this is shown in Figure   \\ref{fig:moon_illustrate}.  \nThis dataset comprises 400  points in $\\mathcal{R}^4$. Projected to the first two dimensions, the dataset contains two clusters of intertwining parabolas shown as Clustering A. Projected to the last two dimensions, the dataset contains two Gaussian clusters shown as Clustering B. Points clustered together in one view can be in different clusters in the alternative view. In alternative clustering, given (a) the dataset, and (b) one of the two possible clusterings (e.g., Clustering B), we wish to discover the alternative clustering illustrated by the different view.\n\n\\begin{figure}[ht] \n  \\centering\n  \\includegraphics[width=7cm,height=3cm]{{extras\/moon}}\n  \\caption{Four-dimensional moon dataset. Projection into the first two dimensions reveals different clusters than projection to the latter two dimensions.}\n  \\label{fig:moon_illustrate}\n\\end{figure}\n\n\n\nFormally, let $X \\in \\mathcal{R}^{n \\times d}$ be a dataset with $n$ samples and\n$d$ features, along with an existing clustering \n$Y \\in \\mathcal{R}^{n \\times k}$, where $k$ is\nthe number of clusters. If  $x_i$ belongs\nto cluster $j$, then $Y_{i, j}= 1$; otherwise, $Y_{i,j}=0$.\nWe wish to discover an alternative clustering $U \\in \\mathcal{R}^{n \\times k}$ \non some lower dimensional subspace of dimension $q \\ll d$.\nLet $W \\in \\mathcal{R}^{d \\times q}$ be a projection\nmatrix such that $ X W \\in \\mathcal{R}^{n \\times q}$.  \n\n\n\n\nWe seek the optimal projection $W$ and clustering  $U$ that \nmaximizes the statistical dependence between $X W$ with $U$, yielding a high clustering quality, while minimizing the\ndependence between $X W$ and $Y$, ensuring the novelty of the new clustering. \nDenoting DM as a Dependence Measure function, and using $\\lambda$ as a weighing constant, this optimization can be written as:  \n\\begin{subequations}\\label{eq:orig_objective}\n  \\begin{align}\n\\text{Maximize:}& \\quad\\tmop{DM} ( X W , U) - \\lambda \\tmop{DM} ( X W, Y),\\\\\n   \\text{s.t :}& \\quad W^T W = I, U^T U = I.\n\\end{align}\n\\end{subequations}  \nAs in spectral clustering, the labels of the alternative clustering are retrieved by performing $K$-means on matrix $U$, treating its rows as samples. \nThere are many potential choices for DM. The most well-known measures are correlation and mutual information (MI). While correlation performs well in many applications, it lacks the ability to measure non-linear relationships. Although there is clear relationship in Clustering A in Figure \\ref{fig:moon_illustrate}, correlation would mistakenly yield a value of nearly 0. \nAs a dependence measure, MI is superior in that it also measures non-linear relationships. However, due to the probabilistic nature of its formulation, a joint distribution is required. Depending on the distribution, the computation of MI can be prohibitive. \n\nFor these reasons, the Hilbert Schmidt Independence Criterion (HSIC) \\cite{gretton2005measuring} has been proposed for KDAC \\cite{niu2014iterative}. Like MI, it captures non-linear relationships. Unlike MI, HSIC does not require estimating a joint distribution, and it relaxes the need to discretize continuous variables. In addition, as shown by Niu et al.~\\cite{niu2014iterative}, \nHSIC is mathematically equivalent to spectral clustering, further implying that a high HSIC between the data and $U$ yields  high clustering quality.\nA visual comparison of HSIC and correlation  can be found in\nFigure \\ref{HSIC_capture_nonlinear} of Appendix \\ref{App:HSIC} in the supplement.\n\n\nUsing HSIC as a dependence measure, the objective of KDAC becomes \n\\begin{subequations}\\label{eq:main_objective}\n  \\begin{align}\n\\text{Maximize:}& \\quad\\tmop{HSIC} ( X W , U) - \\lambda \\tmop{HSIC} ( X W, Y),\\\\\n   \\text{subject to:}& \\quad W^T W = I, U^T U = I.\n\\end{align}\n\\end{subequations}  \nwhere\n$\\tmop{HSIC} ( X, Y) \\equiv \\frac{1}{(n-1)^2} \\tmop{Tr} ( K_{X} H K_Y H).$\nHere, the variables $K_{X}$ and $K_Y$ are Gram matrices, \nand the $H$ matrix is a\ncentering matrix where $H = I - \\frac{1}{n} \\bm{1}_n \\bm{1}^T_n$ with \n$\\bm{1}$ the $n$-sized  vector of all ones. \nThe elements of $K_{X}$ and $K_Y$\nare calculated by kernel functions $k_{X} ( x_i, x_j)$ and $k_Y ( y_i, y_j)$.  \n The kernel functions for $Y$ and $U$ used in KDAC are $K_Y = Y Y^T$ and $K_U = U U^T$, and the kernel function for $XW$ is  the Gaussian $k_{XW} ( x_i, x_j) = \\exp(- {\\tmop{Tr} [ ( x_i - x_j)^T\nW W^T ( x_i - x_j)]}\/{(2 \\sigma^2)})$. \nDue to the equivalence of HSIC and spectral clustering, the practice of normalizing the kernel $K_{XW}$ is adopted from spectral clustering by Niu et al.~\\cite{niu2014iterative}.   \nThat is, for $K_{XW}$ the unnormalized\nGram matrix, the normalized matrix is defined as $D^{- 1 \/ 2} K_{XW} D^{- 1 \/ 2}$ where $D=\\mathrm{diag}(\\bm{1}_n^TK_{XW})$ is a diagonal matrix whose elements are the  column-sums of $K_{XW}$.\n\n \n\\textbf{KDAC Algorithm.}\nThe optimization problem \\eqref{eq:main_objective} is non-convex. The KDAC algorithm solves (\\ref{eq:main_objective}) using alternate maximization between the variables $U$, $W$ and $D$, updating each while holding the other two fixed. After convergence, motivated by spectral clustering, $U$ is discretized via $K$-means to provide the alternative clustering. The algorithm proceeds in an iterative fashion,  summarized in Algorithm \\ref{KDAC_algorithm}. In each iteration, variables $D$, $U$, and $W$ are updated as follows:\n\n\\textbf{Updating D:} \nWhile holding $U$ and $W$ constant, $D$ is computed as  \n$D=\\mathrm{diag}(\\bm{1}_n^TK_{XW})$.\nMatrix $D$ is subsequently treated as a scaling constant throughout the rest of the iteration. \n\n\\textbf{Updating U:} \nHolding $W$ and $D$ constant and solving for $U$, (\\ref{eq:main_objective}) reduces to :\n\\begin{align} \\label{eq:spectral_clustering}\n     \\textstyle\\max_{U:U^TU=I}  \\tmop{Tr} ( U^T \\mathcal{Q} U), \n\\end{align}\nwhere  $\\mathcal{Q}= H D^{- 1 \/ 2} K_{XW} D^{- 1 \/ 2} H$. This is precisely spectral clustering~\\cite{von2007tutorial}: \n \\eqref{eq:spectral_clustering} can be solved by setting $U$'s columns to the $k$ most dominant eigenvectors of $\\mathcal{Q}$, which can be done in $O(n^3)$ time.\n\n\n   \n\\begin{algorithm}[t]\n    \\scriptsize\n    \\SetKwInOut{Input}{Input}\n    \\SetKwInOut{Output}{Output}\n    \\Input{dataset $X$, original clustering $Y$}\n    \\Output{alternative clustering $U$ }\n    Initialize $W_0$ using $W_{\\mathrm{init}}$ from (\\ref{eq:winit})\\\\\n    Initialize $U_0$ from original clustering\\\\\n    Initialize $D_0$ from $W$ and original clustering\\\\\n    \\While{($U$ not converged) or ($W$ not converged)}{\n        Update $D$ \\\\\n        Update $W$ by solving Equation (\\ref{eq:main_cost_function})\\\\\n        Update $U$ by solving Equation (\\ref{eq:spectral_clustering})\\\\\n\t}\n\tClustering Result $\\gets$ Apply K-means to $U$\n\t\\caption{KDAC Algorithm} \n\\label{KDAC_algorithm}\n\\end{algorithm}\n\\begin{algorithm}[t]\n    \\scriptsize\n    \\SetKwInOut{Input}{Input}\n    \\SetKwInOut{Output}{Output}\n    \\Input{$U$,$D$,$X$, $Y$}\n    \\Output{ $W^*$ }\n    Initialize $W_0$ to the previous value of $W$ in the master loop of KDAC.\\\\\n\t\\While{$W$ not converged}{\n\t\t$W \\gets \\mathop{\\mathrm{eig}}_{\\min} ( \\Phi ( W));$\\\\\n\t\n\t} \t\n\t\\caption{ISM Algorithm} \\label{masteralg}   \n\\end{algorithm}\n   \n   \n\n\n\\textbf{Updating W:} \nWhile holding $U$ and $D$ constant to solve for $W$, (\\ref{eq:main_objective}) reduces to:\n\\begin{subequations}\n\\label{eq:main_cost_function}\n\\begin{align} \n   \\text{Minimize:}\\quad&F(W) =- \\textstyle\\sum_{i, j} \\gamma_{i, j} e^{- \\frac{\\tmop{Tr} [ W^T A_{i, j}\n   W]}{2 \\sigma^2}}\\label{eq:mainobj}\\\\\n   \\text{subject to:}\\quad &W^TW=I\\label{eq:mainconstr}\n\\end{align}\n\\end{subequations}\nwhere $\\gamma_{i,j}$ are the elements of matrix $\\gamma = D^{- 1 \/ 2} H ( U U^T - \\lambda Y Y^T) H D^{- 1 \/ 2}$, and \n$A_{i, j} = ( x_i - x_j) ( x_i - x_j)^T$ (see Appendix \\ref{Cost_Derivation} in the supplement for the derivation). \nThis objective, along with a Stiefel Manifold constraint, $W^TW=I$, pose a challenging optimization problem as neither is convex. Niu et al.~\\cite{niu2014iterative} propose solving \\eqref{eq:main_cost_function} through an algorithm termed Dimensional Growth (DG). This algorithm solves for $W$ by computing individual columns of $W$ separately through gradient descent (GD). Given a set of computed columns, the next column is computed by GD projected to a subspace orthogonal to the span of computed set. Since DG is based on GD, the computational complexity is dominated by computing the gradient of \\eqref{eq:mainobj}. The latter is given by:\n\\begin{equation} \\label{eq:gradient_of_main_cost_function}\n\\nabla F(W) =\\textstyle\\sum^n_i \\sum_j^n  \\frac{\\gamma_{i, j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} [\n   W^T A_{i, j} W]}{2 \\sigma^2}} A_{i, j} W. \n\\end{equation}\nThe complexity of DG is $O(t_{DG} n^2d^2q)$, where $n$, $d$ are the dataset size and dimension, respectively, $q$ is the dimension of the subspace of the alternative clustering, and $t_{DG}$ is the number of iterations of gradient descent. The calculation of the gradient contributes the term $O(n^2d^2q)$. Although this computation is highly parallelizable, the algorithm still suffers from slow convergence rate. Therefore, $t_{DG}$ often dominates the computation cost.  \n\n\n\n\nAn alternative approach to optimize \\eqref{eq:main_cost_function} is through classic methods for performing optimization on the Stiefel Manifold (SM) \\cite{wen2013feasible}. The computational complexity of this algorithm is dominated by the computation of the gradient and a matrix inversion with $t_{SM}$ iterations.   This yields a complexity of $O(t_{SM} n^2 d^2 + t_{SM}d^3)$ for SM. Finally, as gradient methods applied to a non-convex objective, both SM and DG require multiple executions from random initialization points to find improved local minima. This approach becomes less effective as the dimension $d$ increases.\n\n\n\n\n\\section{An Iterative Spectral Method}\n\nThe computation of KDAC is dominated by the $W$ updates in Algorithm~\\ref{KDAC_algorithm}. Instead of using DG or SM to solve the optimization problem for $W$ in KDAC, we propose an Iterative Spectral Method (ISM).  Our algorithm is motivated from the following observations. The Lagrangian of \\eqref{eq:main_cost_function} is:\n \\begin{align*}\n      \\mathcal{L} ( W, \\Lambda) =& - \\textstyle\\sum_{i, j} \\gamma_{i, j} \\exp\\left(- \\frac{\\tmop{Tr}\n      (W^T A_{i, j} W)}{2 \\sigma^2}\\right)\\\\\n      &- \\frac{1}{2} \\tmop{Tr} ( \\Lambda ( W^T W -\n      I)) \\numberthis \\label{eq:lag}\n\\end{align*}\n    Setting $\\nabla_W \\mathcal{L}(W,\\Lambda)=0$ gives us the equation:\n\\begin{align}\\Phi(W)W = W \\Lambda,\\label{eq:balance} \\end{align}\nwhere \n\\begin{equation} \\label{eq:phi_equation}\n  \\Phi ( W) = \\textstyle\\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^2} \\exp(- \\frac{\\tmop{Tr} [ W^T A_{i, j}\n  W]}{2 \\sigma^2}) A_{i, j},\n\\end{equation}\nand $\\Lambda$ is a diagonal matrix.\n\nRecall that a feasible $W$, satisfying \\eqref{eq:mainconstr}, is orthonormal. \n\\eqref{eq:balance} is an eigenequation; thus, a stationary point $W$ of the Lagrangian \\eqref{eq:lag}  comprises of $q$ eigenvectors of $\\Phi(W)$ as columns.\nMotivated by this observation, ISM attempts to find such a $W$ in the following iterative fashion. Let $W_0$ be an initial  matrix. Given $W_k$ at iteration $k$, the matrix $W_{k+1}$  is computed as:\n$$W_{k+1} = \\textstyle\\mathop{\\mathrm{eig}}_{\\min} ( \\Phi ( W_k)), \\quad k=0,1,2,\\ldots,$$\nwhere the operator $\\mathop{\\mathrm{eig}}_{\\min} (A)$ returns a matrix whose columns are\nthe $q$ eigenvectors corresponding to the smallest eigenvalues of $A$.\n\n\nISM is summarized in Alg.~\\ref{masteralg}. Several important observations are in order. First, the algorithm ensures that $W_k$, for $k\\geq 1$, is feasible, by construction: selected eigenvectors are orthonormal and satisfy \\eqref{eq:mainconstr}. Second, it is also easy to see that a fixed point of the algorithm will also be a stationary point of the Lagrangian \\eqref{eq:lag} (see also~Lemma~\\ref{lemma:eig}). Though it is harder to prove,  selecting  eigenvectors corresponding to the \\emph{smallest} eigenvalues is key: we show that this is precisely the property that relates a fixed point of the algorithm to the local minimum  conditions (see Thm.~\\ref{thm:stationary}).\nFinally, ISM has several computational advantages. For $t_{ISM}$ iterations, the calculation of $\\Phi(W)$, and the ensuing eigendecomposition yields a complexity of $O(t_{ISM}( n^2 d^2 +  d^3))$. Since $q\\ll d$, various approximation methods \\cite{vladymyrov2016variational}\\cite{richtarikgeneralized}\\cite{lei2016coordinate} can be employed to find the few eigenvectors. For example, the Coordinate-wise Power Method\\cite{lei2016coordinate}, approximates the most dominant eigenvalue at $O(d)$ time, reducing ISM's complexity to $O(t_{ISM} n^2 d^2)$. This improvement is further confirmed experimentally (see Figure \\ref{fig:ND_vs_time}). Lastly, $t_{ISM}$ is magnitudes smaller than both $t_{DG}$ and $t_{SM}$. In general $t_{ISM} < 10$, while $t_{SM} > 50$ and $t_{DG} > 200$.\n\n \n\\subsection{Convergence Guarantees}\n\nAs mentioned above, the selection of the eigenvectors corresponding to the \\emph{smallest} eigenvalues of $\\Phi(W_k)$ is crucial for the establishment of a stationary point. Namely, we establish the following theorem:\n\\begin{theorem}\\label{thm:stationary}\n  For large enough $\\sigma$ (satisfying Inequality \\eqref{ineq:large_sigma_orig}), a fixed point $W^*$ of  Algorithm~\\ref{masteralg} satisfies the necessary conditions of a local minimum of \\eqref{eq:main_cost_function} if $\\Phi(W^*)$ is full rank.\n\\end{theorem}\n\\begin{proof}\nThe main body of the proof is organized into a series of lemmas proved in the supplement.\n\nOur first auxiliary lemma (from~\\cite{wright1999numerical}), establishes conditions necessary for a stationary point of the Lagrangian to  constitute local minimum. \n\\begin{lemma} \\label{lemma:2nd_order}\n  [Nocedal,Wright, Theorem 12.5~{\\cite{wright1999numerical}}] (2nd Order Necessary Conditions)\n    Consider the optimization problem:\n  $ \\min_{W : h (W) = 0} f (W), $\nwhere $f : \\mathbb{R}^{d \\times q} \\to \\mathbb{R}$ and $h :\n  \\mathcal{R}^{d \\times q} \\to \\mathbb{R}^{q \\times q}$ are twice continuously\n  differentiable. Let   $\\mathcal{L}$ be the Lagrangian of this optimization problem. Then, a local minimum must satisfy the following  conditions:\n  \\begin{subequations}\n \n    \\begin{align} \n    &\\nabla_W \\mathcal{L} (W^{\\ast}, \\Lambda^{\\ast}) = 0, \\label{eq:1st_W}\\\\\n    &\\nabla_{\\Lambda} \\mathcal{L} (W^{\\ast}, \\Lambda^{\\ast}) = 0, \\label{eq:1st_lambda}\\\\\n  \n \n \n \n   \n    \\begin{split}\n    \\tmop{Tr} ( Z^T &\\nabla_{W W}^2 \\mathcal{L}(W^{\\ast}, \\Lambda^{\\ast}) Z) \\geq 0 \\\\&\\tmop{for}   \\tmop{all} Z \\neq 0 , \\tmop{with} \n       \\nabla h (W^{\\ast})^T Z = 0.   \\label{eq:2nd_W}\n       \\end{split}\n    \\end{align}   \n \n  \\end{subequations}\n\\end{lemma}\nArmed with this result, we next characterize the properties of a fixed point of Algorithm \\ref{masteralg}:\n\\begin{lemma} \\label{basic_lemma}\n  Let $W^{\\ast}$ be a fixed point of Algorithm \\ref{masteralg}. Then it satisfies:\n \n   $ \\Phi ( W^{\\ast}) W^{\\ast} = W^{\\ast} \\Lambda^{\\ast},$\n \n  where $\\Lambda^{\\ast} \\in \\mathcal{R}^{q \\times q}$ is a diagonal matrix\n  containing the $q$ smallest eigenvalues of $\\Phi ( W^{\\ast})$ and\n\n  $W^{\\ast^T} W^{\\ast} = I. $\n \n\\end{lemma}\nThe proof can be found in Appendix \\ref{proof_of_lemma_2}.\nOur next result, whose proof is  in Appendix \\ref{proof_of_lemma_3}, states that \n a fixed point satisfies the 1st order conditions of Lemma \\ref{lemma:2nd_order}. \n\\begin{lemma} \\label{lemma:eig}\n  If $W^{\\ast}$ is a fixed point and $\\Lambda^{\\ast}$ is as defined in Lemma~\\ref{basic_lemma},\n  then $W^{\\ast}$, $\\Lambda^*$ satisfy the 1st order conditions (\\ref{eq:1st_W})(\\ref{eq:1st_lambda}) of Lemma \\ref{lemma:2nd_order}.\n\\end{lemma}\nOur last lemma, whose proof is in Appendix \\ref{proof_of_lemma_4}, establishes that a fixed point satisfies the 2nd order conditions of Lemma \\ref{lemma:2nd_order}, for large enough $\\sigma$.  \n\\begin{lemma} \\label{lemma:2nd_order_lemma}\n  If $W^{\\ast}$ is a fixed point, $\\Lambda^{\\ast}$ is as defined in Lemma~\\ref{basic_lemma}, and $\\Phi(W^*)$ is full rank,\n  then given a large enough $\\sigma$ (satisfying Inequality \\eqref{ineq:large_sigma_orig}), $W^{\\ast}$ and $\\Lambda^*$ satisfy the 2nd order condition (\\ref{eq:2nd_W}) of Lemma \\ref{lemma:2nd_order}.\n\\end{lemma}\n Thm.~\\ref{thm:stationary} therefore follows.\n\\end{proof}\n\n\nThm.~\\ref{thm:stationary} is stated in terms of a large enough $\\sigma$; we can characterize this constraint precisely. In the proof of Lemma~\\ref{lemma:2nd_order_lemma} we establish the following condition on $\\sigma$:\n\\begin{multline}\n   \\sigma^2 [\\min_i ( \\bar{\\Lambda^*}_i) -\\max_j(\\Lambda_j^*)] \\geq \\\\\n    \\sum_{i, j} \\frac{|\\gamma_{i, j}|}{\\sigma^2} e^{-\n   \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}}\\tmop{Tr} (A^T_{i,j}A_{ij}). \\label{ineq:large_sigma_orig}\n\\end{multline}\nHere, $\\Lambda^*$ is the set of $q$ smallest eigenvalues of $\\Phi(W)$, and $\\bar{\\Lambda^*}$ is the set of the remaining eigenvalues. The left-hand side (LHS) of the equation further motivates ISM's choice of  eigenvectors corresponding to the $q$ smallest eigenvalues. This selection guarantees that the LHS of the inequality is positive. Therefore, given a large enough $\\sigma$, Inequality \\eqref{ineq:large_sigma_orig} and the 2nd order condition is satisfied. \n\nFurthermore, this equation provides a reasonable suggestion for the value of $q$.  Since we wish to maximize the term $(\\min_i ( \\bar{\\Lambda^*}_i) -\\max_j(\\Lambda_j^*))$ to satisfy the inequality, the value $q$ should be set where this gap is maximized. More formally, we will defined\n\\begin{align}\n   \\delta_{gap}=\\min_i ( \\bar{\\Lambda^*}_i) -\\max_j(\\Lambda_j^*)\n   \\label{eq:eiggap}.\n\\end{align}\nas the eigengap.\n\n\n\n\n\n\n\\subsection{Spectral Initialization via Taylor Approximation}\n\\label{sec:initialization}\nISM admits a natural initialization point, constructed via a Taylor approximation of the objective. As we show experimentally in Section~\\ref{sec:exp}, this initialization is a contribution in its own right: it improves both clustering quality and convergence time for ISM \\emph{as well as} competitor algorithms.  To obtain a good initialization, observe that by using the 2nd order Taylor approximation of the objective function \\eqref{eq:mainobj} at $W=0$, the Lagrangian can be approximated by \n\\begin{align*}\n\\tilde{\\mathcal{L}}(W,\\Lambda) \\approx & -\\textstyle \\sum_{i, j} \\gamma_{i, j}  \\left( 1 - \\frac{\\tmop{Tr}\n   (W^T A_{i, j} W)}{2 \\sigma^2} \\right)\\\\\n   & + \\frac{1}{2} \\tmop{Tr} (\\Lambda (I -\n   W^T W)). \n\\end{align*}\n  Setting $\\nabla_W \\tilde{\\mathcal{L}}(W,\\Lambda)=0$ reduces the problem into a simple eigendecomposition, namely, the one defined by the system \n$\\left[ \\textstyle \\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^2} A_{i,\n   j} \\right] W = W \\Lambda .$\nHence, the 2nd order Taylor approximation of the original cost objective has a closed form global minimum that can be used as an initialization point, namely:\n\\begin{align}\n   \\textstyle W_{\\mathrm{init}}=\\mathrm{eig}_{\\min}( \\sum_{i, j} {\\gamma_{i, j}} A_{i,\n   j}\/{\\sigma^2})\\label{eq:winit}.\n\\end{align}\n\nWe use this spectral initialization (SI) in the first master iteration of KDAC. In subsequent master iterations, $W_0$ (the starting point of ISM) is set to be the last value to which ISM converged to previously.\n\n\n\n\n\\section{Scalability}\\label{sec:scalability}\n\\chieh{The scalability adventage of ISM is two folds. First, the most computational complex portion of the algorithm is the eigen decomposition of $\\Phi(W) \\in \\mathbb{R}^{d \\times d}$. Since $d<<N$, the scalability is decoupled from the size of the data. Even if high dimensional data is used, the eigendecomposition within ISM only requires q eigenvectors. Since $q << N$, there exist many techniques to approximate eigenvectors, e.g, the power method. There also exist off the shelf GPU implementations of eigendecomposition (MAGMA, cuBLAS). To further improve the speed, updates of U can also be improved via the Variational Nystrom method, Vladymyrov et al. ICML16. Our key contribution is to provide theoretical guarantees for the spectral method to leverage existing research and technology. Second,   the proposed initialization is intimately tied to the ISM method. It results from applying the 2nd order Taylor approximation to the objective to approximate a closed form solution of the global minimum. Having a starting point close to the global minimum simultaneously improves convergence rate and the quality of the solution.}\n\n\n\\section{Experimental Results}\\label{sec:exp}\nWe experimentally validate the performance of ISM in terms of both speed and clustering quality. The source code is publicly available at github\\footnote{https:\/\/github.com\/neu-spiral\/ISM}. Because \\cite{niu2014iterative} has already performed extensive comparisons of KDAC against other alternative clustering methods, this section will concentrate on comparing  ISM to competing models for optimizing KDAC: Dimensional Growth (DG)~\\cite{niu2014iterative} and gradient descent on the Stiefel Manifold (SM)~\\cite{wen2013feasible}. SM is a generic approach, while DG is the approach originally proposed to solve KDAC~\\cite{niu2014iterative}. \n\nIn addition to introducing a new algorithm for optimizing KDAC, we also proposed an intelligent initialization scheme based on Taylor approximation in Section \\ref{sec:initialization}, we call Spectral Initialization (SI).  We also investigate how SI effects the performance of the various algorithms compared to the standard random initialization (RI).\n\n\n\n\\begin{table}[h]\n\\tiny\n\\centering\n\\setlength\\tabcolsep{0.2pt}\n    \\begin{tabular}{c|c|c|c|c|c}\n    \\textbf{SG} \n        & NMI       $\\uparrow$\n        & CQ        $\\uparrow$\n        & Novelty   $\\downarrow$\n        & Cost      $\\downarrow$\n        & Time      $\\downarrow$\\\\\n    \\midrule\n        ISM SI\n        \t& \\textbf{1} \n        \t& \\textbf{2} \n        \t& \\textbf{0} \n        \t& -1.2\n        \t& \\textbf{0.02} \\\\\n        ISM RI\n        \t& 0.4$\\pm$0.49\n        \t& 1.6$\\pm$0.478\n        \t& \\textbf{0.0$\\pm$0.0} \n        \t& -1.48$\\pm$0.381\n        \t& 0.04$\\pm$0.01\\\\\n        SM SI\n        \t& \\textbf{1} \n        \t& 1.99\n        \t& \\textbf{0} \n        \t& \\textbf{-1.791} \n        \t& 0.404\\\\\n        SM RI\n        \t& \\textbf{1$\\pm$0.0} \n        \t& 1.79$\\pm$0.398\n        \t& \\textbf{0.0$\\pm$0.0} \n        \t& -1.59$\\pm$0.398\n        \t& 1.47$\\pm$1.521\\\\\n        DG SI\n        \t& 0\n        \t& 1.629\n        \t& 1\n        \t& -1.316\n        \t& 1.732\\\\\n        DG RI\n        \t& 0.93$\\pm$0.196\n        \t& 0.99$\\pm$0.0\n        \t& 0.03$\\pm$0.104\n        \t& -0.99$\\pm$0.0\n        \t& 1.51$\\pm$0.102\\\\\n    \\midrule\n    \\textbf{LG} \\\\\n        ISM SI\n        \t& \\textbf{1} \n        \t& \\textbf{1.9}\n        \t& \\textbf{0} \n        \t& 509\n        \t& 0.239\\\\\n        ISM RI\n        \t& 0.8$\\pm$0.4\n        \t& \\textbf{1.9$\\pm$0.011}\n        \t& \\textbf{0.0$\\pm$0.0} \n        \t& 605$\\pm$193\n        \t& \\textbf{0.18$\\pm$0.038} \\\\\n        SM SI\n        \t& \\textbf{1} \n        \t& 1.9\n        \t& \\textbf{0} \n        \t& 509\n        \t& 0.413\\\\\n        SM RI\n        \t& 0.4$\\pm$0.49\n        \t& 1.9$\\pm$0.031\n        \t& 0.6$\\pm$0.49\n        \t& 1095$\\pm$479\n        \t& 11.21$\\pm$11.01\\\\\n        DG SI\n        \t& \\textbf{1} \n        \t& \\textbf{1.9} \n        \t& \\textbf{0} \n        \t& 509.975\n        \t& 1595.174\\\\\n        DG RI\n        \t& 0.1$\\pm$0.32\n        \t& 0.61$\\pm$0.17\n        \t& 0.9$\\pm$0.32\n        \t& \\textbf{101.5$\\pm$30.8} \n        \t& 1688$\\pm$551\\\\\n     \\midrule\n    \\textbf{Moon} \\\\       \t\n        ISM SI\n        \t& \\textbf{1} \n        \t& \\textbf{2} \n        \t& \\textbf{0} \n        \t& \\textbf{149} \n        \t& \\textbf{0.575} \\\\\n        ISM RI\n        \t& 0.4$\\pm$0.4\n        \t& \\textbf{2.0$\\pm$0.0} \n        \t& 0.5$\\pm$0.5\n        \t& 269.98$\\pm$43\n        \t& 3.07$\\pm$1.4\\\\\n        SM SI\n        \t& \\textbf{1} \n        \t& 1.998\n        \t& \\textbf{0} \n        \t& \\textbf{149} \n        \t& 2.653\\\\\n        SM RI\n        \t& 0.27$\\pm$0.335\n        \t& \\textbf{2.0$\\pm$0.0} \n        \t& 0.5$\\pm$0.5\n        \t& 277$\\pm$18\n        \t& 258$\\pm$374\\\\\n        DG SI\n        \t& \\textbf{1} \n        \t& 1.998\n        \t& \\textbf{0} \n        \t& 149.697\n        \t& 359.188\\\\\n        DG RI\n        \t& 0.09$\\pm$0.3\n        \t& 1.27$\\pm$0.6\n        \t& 0.8$\\pm$0.4\n        \t& 161.65$\\pm$102\n        \t& 3212$\\pm$1368\\\\\n    \\midrule\n    \\textbf{MoonN} \\\\       \t       \t\n        ISM SI\n        \t& \\textbf{1} \n        \t& \\textbf{2} \n        \t& \\textbf{0} \n        \t& \\textbf{15.3} \n        \t& \\textbf{0.3} \\\\\n        ISM RI\n        \t& 0.91$\\pm$0.2\n        \t& \\textbf{2.0$\\pm$0} \n        \t& 0.04$\\pm$0.1\n        \t& 15.59$\\pm$0.8\n        \t& 0.55$\\pm$0.2\\\\\n        SM SI\n        \t& \\textbf{1} \n        \t& \\textbf{2} \n        \t& \\textbf{0} \n        \t& \\textbf{15.3} \n        \t& 0.452\\\\\n        SM RI\n        \t& 0.22$\\pm$0.4\n        \t& \\textbf{2.0$\\pm$0} \n        \t& 0.72$\\pm$0.4\n        \t& 17.7$\\pm$1\n        \t& 102$\\pm$48.5\\\\\n        DG SI\n        \t& \\textbf{1} \n        \t& \\textbf{2} \n        \t& \\textbf{0} \n        \t& 15.4\n        \t& 3836.3\\\\\n        DG RI\n        \t& 0$\\pm$0.0\n        \t& 1.6$\\pm$0.04\n        \t& 1.0$\\pm$0.0\n        \t& 16.2$\\pm$0.06\n        \t& 3588$\\pm$304\\\\\n    \\midrule\n    \\textbf{Flower} \\\\       \t\n        ISM SI\n        \t& \\textbf{-} \n        \t& \\textbf{0.41} \n        \t& \\textbf{0} \n        \t& 20\n        \t& \\textbf{0.04}\\\\\n        ISM RI\n        \t& \\textbf{-} \n        \t& \\textbf{0.41$\\pm$0.0} \n        \t& \\textbf{0.0$\\pm$0.0} \n        \t& 19.51$\\pm$0.0\n        \t& 0.1$\\pm$0.01 \\\\\n        SM SI\n        \t& \\textbf{-} \n        \t& \\textbf{0.41} \n        \t& \\textbf{0} \n        \t& 20\n        \t& 0.153\\\\\n        SM RI\n        \t& \\textbf{-} \n        \t& 0.3$\\pm$0.2\n        \t& 0.01$\\pm$0.012\n        \t& \\textbf{0.7$\\pm$0.5} \n        \t& 0.8$\\pm$0.6\\\\\n        DG SI\n        \t& \\textbf{-} \n        \t& \\textbf{0.41} \n        \t& \\textbf{0} \n        \t& 20\n        \t& 27.251\\\\\n        DG RI\n        \t& \\textbf{-} \n        \t& 0.35$\\pm$0.02\n        \t& 0.2$\\pm$0.4\n        \t& 20.6$\\pm$1\n        \t& 37.0$\\pm$5\\\\\n    \\midrule\n    \\textbf{Faces} \\\\       \t       \t       \t\n        ISM SI\n        \t& \\textbf{0.57} \n        \t& \\textbf{0.61} \n        \t& 0.004\n        \t& 59.6\n        \t& \\textbf{1.5} \\\\\n        ISM RI\n        \t& 0.56$\\pm$0.002\n        \t& \\textbf{0.61$\\pm$0.0} \n        \t& \\textbf{0.0$\\pm$0.0} \n        \t& 59.6$\\pm$0.118\n        \t& 1.51$\\pm$0.146\\\\\n        SM SI\n        \t& 0.562\n        \t& 0.608\n        \t& 0.004\n        \t& 59.559\n        \t& 7.96\\\\\n        SM RI\n        \t& \\textbf{0.57$\\pm$0.002} \n        \t& \\textbf{0.61$\\pm$0} \n        \t& 0.004$\\pm$0\n        \t& 59.7$\\pm$0.1\n        \t& 109$\\pm$35.2\\\\\n        DG SI\n        \t& 0.564\n        \t& 0.6\n        \t& 0.004\n        \t& 59.8\n        \t& 100591.071\\\\\n        DG RI\n        \t& 0.458$\\pm$0.045\n        \t& 0.565$\\pm$0.018\n        \t& 0.024$\\pm$0.018\n        \t& \\textbf{54.28$\\pm$3} \n        \t& 166070$\\pm$4342\\\\\n    \\midrule\n    \\textbf{WebKb} \\\\\n        ISM SI\n        \t& \\textbf{0.37} \n        \t& 0.286\n        \t& \\textbf{0} \n        \t& -0.273\n        \t& 231\\\\\n        ISM RI\n        \t& 0.29$\\pm$0.07\n        \t& 0.54$\\pm$0.2\n        \t& 0.01$\\pm$0.002\n        \t& -0.52$\\pm$0.2\n        \t& 137.45$\\pm$15.7\\\\\n        SM SI\n        \t& 0.048\n        \t& \\textbf{3.296} \n        \t& 0.034\n        \t& \\textbf{-3.159} \n        \t& \\textbf{9.945} \\\\\n        SM RI\n        \t& 0.33$\\pm$0.06\n        \t& 0.12$\\pm$0.005\n        \t& 0.008$\\pm$0.004\n        \t& -0.11$\\pm$0.004\n        \t& 13511$\\pm$13342\\\\\n        DG SI\n        \t& 0.048\n        \t& 1.066\n        \t& 0.034\n        \t& -1.019\n        \t& 199887.134\\\\\n        DG RI\n        \t& 0.23$\\pm$0\n        \t& 1.06$\\pm$0\n        \t& 0.1$\\pm$0.005\n        \t& 0.616$\\pm$0.04\n        \t& 727694$\\pm$41068\\\\    \n\\end{tabular}\n\\caption{\n The Normalized Mutual Information, Clustering Quality, and clustering novelty are abbreviated in the first 3 columns as NMI, CQ, and Novelty. The cost of the objective and run time is displayed in the last two columns. For each optimization technique, spectral initialization (SI) and random initialization (RI) are separately tested. With RI, 10 random initial points have been tested with their mean and std displayed. } \\label{experiment_table_and_figures}\n\\end{table}\n\n\n\n\n\n\n\n\n\n\\begin{figure}[!t] \n  \\centering\n  \\includegraphics[width=7.7cm,height=8.7cm]{{extras\/synthetic_data_results}} \n  \\caption{ Figure includes all original and alternative displayable clusterings. The face data is originally clustered by the identity of the individual. Here the average image of the alternative clustering is displayed. It is observable that the original and alternative clusters are all visually obvious clusters and provide alternative views.} \n  \\label{fig:results_figure}\n\\end{figure}\n\n\n\n\\begin{figure}[!t] \n  \\centering\n  \\includegraphics[width=0.7\\columnwidth]{{extras\/DimVTime_PolyFIt_slope}}\n  \\caption{Growth in dimension vs time in log\/log scale. A slope of 1 is linear growth.}\n  \\label{fig:ND_vs_time}\n\\end{figure}\n\n\\noindent\\textbf{Datasets.} We perform experiments on four synthetic and three real datasets.  The synthetic data are displayed in Figure \\ref{fig:results_figure}. Small Gaussian (SG) contains four Gaussian clusters with $40$ samples and two features shown at the top left of the figure. When this data is projected down to feature 2, the original clustering is created. Rotating this projection onto feature 1, the alternative clustering emerges. Large Gaussian (LG) contains four Gaussian clusters with $1000$ samples and four dimensions is shown in the top center location. The Gaussian clusters are rotated by $45$ degrees to reside in 3D, and the fourth dimension is generated from a uniform noise distribution. This synthetic data is designed to test the response of KDAC within a noisy environment.  \nWe generate two additional synthetic datasets shown in top right: Moon and Moon+Noise (MoonN). Both datasets have the first two dimensions as two parabolas and the second two dimensions as Gaussian clusters. The MoonN dataset further includes three noisy dimensions generated from a uniform distribution with 1000 samples.\nSince the Gaussian clusters have a compact structure and the parabolas have a non-linear structure, these datasets demonstrate KDAC's ability to handle mixed clustering structures in a uniformly noisy environment.\nDue to the novelty of alternative clustering, there has been very few public repository data that have at least two alternative labels. \nThe two traditional benchmark datasets are CMU's WebKB dataset~\\cite{cmu4universities} and face images from the UCI KDD repository~\\cite{bay2000uci}.  CMU's WebKB dataset consists of 1041 html pages from 4 universities. One labelling is based on universities, and an alternative labelling based on topic (course, faculty, project, student). After preprocessing by removing rare and stop words, we are left with 500 words. \nThe face dataset consists of $640$ images from $20$ people in four different poses. Each image has 32x30 pixels. Images are vectorized and PCA is then used to further condense the dataset by keeping 85\\% of the variance, resulting in a dataset of 624 samples and 20 features. \nWe set the existing clustering based on identity, and\nseek an alternative clustering   based on pose. The last real dataset is the Flower image by Alain Nicolas \\cite{particleoft}, a 350x256 pixel image. The RGB values of each pixel is taken as a single sample, with repeated samples removed. This results in a dataset of 256 samples and 3 features.\nAlthough this dataset does not have labels, the quality of the alternative clustering can be visually observed. With the exception of the high dimensional WebKB data, the remaining datasets are visualized in Figure \\ref{experiment_table_and_figures} (b).\n\n\\noindent\\textbf{Hyperparameter Tuning.}\nISM has 3 hyperparameters that require tuning, $q$, $\\lambda$, and $\\sigma$. The hyperparameter $q$ with a potential range of (0,$d$) is initially set to $k$, the number of clusters. A grid search was then conducted for $\\lambda \\in (0,10]$ and $\\sigma \\in (0,10]$ to find the highest CQ ($\\lambda$, $\\sigma$) pair that satisfies inequality (\\ref{ineq:large_sigma_orig}) at an increment of 0.01. In the event that Inequality (\\ref{ineq:large_sigma_orig}) cannot be satisfied, the highest CQ closest to satisfying (\\ref{ineq:large_sigma_orig}) is used. At this point, since $\\Phi(W^*)$ is computed, the $q$ value that maximizes the eigengap as defined in Eq(\\ref{eq:eiggap}) can be used if (\\ref{ineq:large_sigma_orig}) is not yet satisfied. Note that competing models do not have a natural way of selecting hyperparameters. Since all competing models optimize the same objective, we report all results using the same hyperparameters. To ensure reproducible experiments, the hyperparameters utilized in each experiment is provided in Appendix \\ref{App:Hyperparameters}.\n\n\\noindent\\textbf{Evaluation Method.} \nTo exhaustively evaluate ISM on KDAC, both external and internal measures have been recorded in Table~\\ref{experiment_table_and_figures}. More specifically, column 1 and 3 (NMI and Novelty) are external measures because they compare alternative cluster assignments against an externally known ground truth. To make the comparison, Normalized Mutual Information (NMI) as suggested by \\cite{strehl33knowledge} was used.  The NMI is a measure between 0 to 1 with 0 denoting no relationship and 1 as maximum relationship. Column 1 (NMI) is calculated by computing the NMI between the ground truth and the alternative cluster assignments. Column 3 (Novelty) is calculated by computing the NMI between the alternative cluster assignments against the original label. Ideally, we wish for the NMI of the alternative cluster assignments against the ground truth to be 1, and 0 against the original clustering.  If we let $U$ and $L$ be two clustering assignments, NMI can be calculated with $NMI(L,U) = \\frac{I(L,U)}{\\sqrt{H(L)H(U)}}$, where $I(L,U)$ is the mutual information between $L$ and $U$, and $H(L)$ and $H(U)$ are the entropies of $L$ and $U$ respectively. Lastly, since no ground truth exists for the Flower dataset, the NMI field is not applicable and indicated with a dash (-).\n\nColumns 2, 4 and 5 (CQ, Cost, Time) are internal measures used to evaluate ISM. They are internal measures since they are computed solely from the data and the algorithm with no external knowledge applied during the comparison. The clustering quality (CQ) is computed with $HSIC(XW,U)$ with $U$ as the clustering solution. This is equivalent to the spectral clustering objective with high values denoting high clustering quality. The cost quality records the objective function of KDAC in Eq. (\\ref{eq:main_objective}). The last column, Time, measures the execution time of the entire KDAC algorithm in seconds on an Intel Xeon E7 processor.\n\n\nIn Table~\\ref{experiment_table_and_figures}, we report the performance of the various methods: our ISM, SM, and DG, paired with two initialization schemes: our spectral initialization (SI) and random initialization (RI).  For random initialization, we repeat these 10 times and report the mean and standard deviation for each measure.  The optimal direction of each measure is denoted by the $\\uparrow\\downarrow$, with $\\uparrow$ denoting a preference towards larger values and $\\downarrow$ otherwise. For each field, the optimal result is printed in bold font.\n\n\n\n\\noindent\\textbf{Performance Comparison Results.} \nTable \\ref{experiment_table_and_figures} illustrates that ISM with SI outperforms its competitors in both internal and external quality measure for the first 3 columns. Since it is possible for the objective cost to achieve a low cost with a trivial solution based on different $(\\sigma, \\lambda)$ pairs, the objective should be low, but it is not always indicative of better clustering quality. This is demonstrated in the case of WebKb dataset, where SM+SI achieved a lower cost with a faster convergence. However, upon inspecting the clustering allocation in this case, we observed that it was a trivial classification, with almost all points in the same cluster.  Since the demand for a faster KDAC was the original motivator, special attention should be paid to the Time column. The execution time of ISM significantly outperforms the original approach (DG) as well as the standard approach (SM). This speed improvement is especially true in the Faces dataset where ISM improves the speed by 5 folds. \n\n\n\n\n\n\\noindent\\textbf{The Effect of Spectral Initialization.}\n By comparing SI against RI, we can isolate the effect of our proposed spectral initialization (SI). Comparing the rows, the spectral initialization improved both time and clustering quality for all methods. From this observation, we conclude that SI contributes to clustering quality by starting each algorithm at a desirable initialization. The convergence improvement came from placing each algorithm closer to the local minimum. Comparing all methods when using SI, we observed that ISM optimization still outperformed other algorithms in terms of time. From this, we conclude that the proposed SI has a greater impact on the clustering quality while the ISM optimization technique contribute towards faster convergence.\n\n\n\\iffalse\nIt is also important to point out that since ISM is a spectral method requiring only a few eigenvalues, it is possible to use  techniques such as the power method \\cite{richtarikgeneralized}, has shown strong improvement as the data scale.  However, the table contains a version purely based on the merits of ISM without extra improvements. Therefore, the source code that produced Table \\ref{experiment_table_and_figures} used only an off the shelf Numpy function for the eigendecomposition. \n\\fi\n\n\\noindent\\textbf{Scalability.}\nNote that KDAC consists of optimizing $U$ and $W$ from Eq. (\\ref{eq:main_objective}). Since the computational bottleneck resided in the optimization of $W$, ISM was designed to speed up this portion. The scalability analysis, therefore, will concentrate on only the optimization of $W$. ISM has a computational complexity of $O(t_{ISM}(n^2d^2+d^3)$ and the complexity can be divided into the calculation of the derivative and the eigendecomposition of $\\Phi(W)$. Although the derivative contributes to $O(n^2d^2)$, it is a highly parallelizable operation that can be rendered trivial through the usage of GPUs. Therefore, ISM's true bottleneck is not the number of samples ($n$), but the number of dimensions due to the $O(d^3)$ operation of eigendecomposition. As the dimensionality of the data increase, the complexity grows at a cubic rate. Yet, while this growth of dimensionality may exacerbate algorithms such as SM, the negative influence on ISM is limited. This is because the $O(d^3)$ term from SM came from a matrix inversion while ISM uses a spectral method. Since only very few eigenvalues are required, there exists many approximation algorithms to speed up the eigendecomposition \\cite{vladymyrov2016variational} \\cite{richtarikgeneralized}\\cite{lei2016coordinate}.  To demonstrate this point, Coordinate-wise Power Method (CPM) \\cite{lei2016coordinate} was implemented and compared to the eigendecomposition operation from Numpy. In this experiment, noisy dimensions of uniform distributions are added to the synthetic dataset of Large Gauss (LG) such that the total dimension increase in multiples of 2. As the dimension of the data grows exponentially, the time of execution is recorded in Figure \\ref{fig:ND_vs_time} in log scale. Given a log\/log scale, a slope of 1 is linear while a slope of 2 is quadratic. From studying the slope of each operation, the eigendecomposition from Numpy grows at a rate between linear and quadratic. However, by utilizing CPM, the growth becomes roughly linear. Therefore, the refinement of utilizing a spectral optimization method is a key reason for speed improvement.\n\n\n\n\n\n\\section{Conclusions}\n\nWe have proposed an iterative spectral optimization technique for solving a non-convex optimization problem while being constrained on a Stiefel manifold. This new technique demonstrates speed improvement for any algorithm that could be formulated into Eq (\\ref{eq:main_cost_function}). The ISM algorithm is easy to implement with existing software libraries. Due to the usage of the spectral method, approximation techniques from existing research could be deployed to further speed up the eigendecomposition. Accompanied with the algorithm are the theoretical guarantees that satisfy the first and second order necessary conditions for a local minimum. Besides these guarantees, we also proposed a natural initialization point based on Taylor approximation of the original cost function. Experiments on synthetic and real data confirmed that our proposed spectral initialization improved the performance of all the optimization algorithms, ISM, SM and DG. Simultaneously, the experiments demonstrate that our proposed ISM algorithm had the best convergence rate compared to competing models with up to 5 folds of speed improvement. Although we focus this paper on an important application of ISM, alternative clustering, the optimization algorithm proposed and guarantees can be extended to other optimization problems involving Gaussian-kernel like objectives constrained over the Stiefel manifold, which is a common formulation for dimensionality reduction with a kernel-based objective. \nUnderstanding whether ISM can be applied to such objectives and be leveraged to solve broader classes of problems is a natural future direction for this work. \n\n\n\\subsubsection*{Acknowledgements}\nWe would like to acknowledge support for this project from the NSF grant IIS-1546428. We would also like to thank Yale Chang for his insightful discussions. \n\n\n\\section{Derivation for Equation \\ref{eq:main_cost_function} }\nGiven the objective function,\n\\[ \\begin{array}{ll}\n     \\max & \\tmop{HSIC} ( X W , U) - \\lambda \\tmop{HSIC} ( X W, Y)\\\\\n     U, W & \\\\\n     s.t & W^T W = I , U^T U = I.\n   \\end{array} \\]\nUsing the HSIC measure defined, the objective function can be\nrewritten as\n\\[ \\begin{array}{lll}\n     \\tmop{HSIC} ( X W , U) - \\lambda \\tmop{HSIC} ( X W, Y) & = &\n     \\tmop{Tr} ( H  U U^T H D^{\\frac{-1}{2}} K_{XW} D^{\\frac{-1}{2}}) - \\lambda \\tmop{Tr} ( H Y Y^T H\n     D^{\\frac{-1}{2}} K_{XW} D^{\\frac{-1}{2}})\\\\\n     & = & \\tmop{Tr} ( D^{\\frac{-1}{2}} H ( U U^T - \\lambda Y Y^T) H D^{\\frac{-1}{2}} K_{XW})\\\\\n     & = & \\tmop{Tr} ( \\gamma K_{XW})\\\\\n     & = & \\sum_{i, j} \\gamma_{i, j} K_{X_{i, j}}.\n   \\end{array}  \\]\nwhere $\\gamma$ is a symmetric matrix and $\\gamma = H ( U U^T - \\lambda Y Y^T)\nH$. By substituting the Gaussian kernel for $K_{X_{i, j}}$, the objective\nfunction becomes\n\\[ \\begin{array}{l}\n     \\min\\\\\n     W\n   \\end{array} - \\sum_{i, j} \\gamma_{i, j} e^{- \\frac{\\tmop{Tr} [ W^T A_{i, j}\n   W]}{2 \\sigma^2}} \\begin{array}{llll}\n     &  & s.t & W^T W = I.\n   \\end{array} \\]\n\\label{Cost_Derivation}\n\\end{appendices}\n\n\n\n\n\n\n\n\n\n\\begin{appendices} \n    \\section{Proof for Lemma \\ref{basic_lemma} }\n    \\begin{proof}\n        Algorithm \\ref{masteralg} sets the smallest $q$ eigenvectors of $\\Phi ( W_k)$ as\n        $W_{k + 1}$. Since a fixed point $W^{\\ast}$ is reached when $W_k = W_{k + 1}$,\n        therefore $W^{\\ast}$ consists of the smallest eigenvectors of $\\Phi (\n        W^{\\ast})$ and $\\Lambda^{\\ast}$ corresponds with a diagonal matrix of eigenvavlues.\n        Since the eigenvectors of $\\Phi ( W^{\\ast})$ are orthonormal\n        , $W^{\\ast^T} W^{\\ast} = I$ is also satisfied.\n    \\end{proof}\n    \\label{proof_of_lemma_2}\n\\end{appendices}\n\n\n\n\n\\begin{appendices}\n\\section{Proof for Lemma \\ref{lemma:eig} }\n\\begin{proof}\n\n    Using Equation (\\ref{eq:main_cost_function}) as the objective function, the corresponding Lagrangian and its gradient is written as \n    \n    \\begin{align}\n      \\mathcal{L} ( W, \\Lambda) &= - \\sum_{i, j} \\gamma_{i, j} e^{- \\frac{\\tmop{Tr}\n      (W^T A_{i, j} W)}{2 \\sigma^2}} - \\frac{1}{2} \\tmop{Tr} ( \\Lambda ( W^T W -\n      I)) \\label{eq:lagrangian},\n    \\end{align}\n   and \n   \\begin{equation} \\label{eq:gradient_of_lagrangian}\n    \\nabla_W \\mathcal{L} ( W, \\Lambda) = \\sum_{i, j} \\frac{\\gamma_{i,\n      j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} (W^T A_{i, j} W)}{2 \\sigma^2}} A_{i, j} W\n      - W \\Lambda. \n    \\end{equation}\n   \n   \n  By setting the gradient of the Lagrangian to zero, and using the definition of $\\Phi(W)$ from Equation (\\ref{eq:phi_equation}), Equation (\\ref{eq:gradient_of_lagrangian}) can be written as\n    \\begin{equation}\\label{eig_relation} \n     \\Phi(W) W = W \\Lambda. \n    \\end{equation} \n    The gradient with respect to $\\Lambda$ is\n    \n    \\begin{align}\n        \\nabla_\\Lambda \\mathcal{L} ( W, \\Lambda) =  W^T W - I.\n    \\end{align}\n    \n    Setting this gradient of the Lagrangian also to zero, condition (\\ref{eq:1st_lambda}) is equivalent to\n     \n    \\begin{equation} \n        W^T W = I. \\label{prof:orth}\n    \\end{equation}\n     \n     By Lemma \\ref{basic_lemma}, a fixed point $W^*$ and its corresponding $\\Lambda^*$ satisfy (\\ref{eig_relation}) and (\\ref{prof:orth}), and the lemma follows.\n\\end{proof}\n\\label{proof_of_lemma_3}\n\\end{appendices}\n\n\n\\begin{appendices}\n\\section{Proof for Lemma \\ref{lemma:2nd_order_lemma} }\n\nThe proof for Lemma \\ref{lemma:2nd_order_lemma} relies on the following three sublemmas. The first two sublemmas demonstrate how the 2nd order conditions can be rewritten into a simpler form.  \nWith the simpler form, the third lemma demonstrates how the 2nd order conditions of a local minimum are satisfied given a large enough $\\sigma$.\n\n\\begin{sublemma}\\label{lemma:directional_derivate}\n\nLet the directional derivative in the direction of $Z$ be defined as \n\\begin{equation}\n  \\mathcal{D} f (W) [Z] := \\begin{array}{l}\n    \\lim\\\\\n    t \\rightarrow 0\n  \\end{array} \\frac{f (W + tZ) - f (W)}{t}.\n\\end{equation}\n\nThen the 2nd order condition of Lemma \\ref{lemma:2nd_order_lemma} can be written as \n\n\\begin{equation} \\label{cond:large_inequality}\n\\tmop{Tr} ( Z^T \\mathcal{D} \\nabla \\mathcal{L} [ Z]) = \\left\\{ \\sum_{i, j}\n   \\frac{\\gamma_{i, j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^*\n   )}{2 \\sigma^2}}  \\left[ \\tmop{Tr} ( Z^T A_{i, j} Z) -\n   \\frac{1}{\\sigma^2} \\tmop{Tr} ( Z^T A_{i, j} W^*)^2 \\right] \\right\\} -\n   \\tmop{Tr} ( Z^T Z \\Lambda^*),\n\\end{equation}\n\nfor all $Z$ such that \n\\begin{equation} \\label{cond:Zcondition}\nZ^T W^* + W^{*^T} Z = 0.\n\\end{equation}\n\n\\end{sublemma}\n\n\n\\begin{proof}\nObserve first that \n\\begin{equation}\n    \\nabla^2_{W^* W^*} \\mathcal{L} ( W^*, \\Lambda^*) Z = \n    \\mathcal{D} \\nabla \\mathcal{L} [ Z],\n\\end{equation}\n\nwhere the directional derivative of the gradient $\\mathcal{D} \\nabla \\mathcal{L} [ Z]$\nis given by \n\n\\[ \\mathcal{D} \\nabla \\mathcal{L} [ Z] = \\begin{array}{l}\n     \\lim\\\\\n     t \\rightarrow 0\n   \\end{array} \\frac{\\partial}{\\partial t} \\sum_{i, j} \\frac{\\gamma_{i,\n   j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( ( W^* + t Z)^T A_{i, j}  ( W^* + t Z))}{2\n   \\sigma^2}} A_{i, j}  ( W^* + t Z) - ( W^* + t Z) \\Lambda. \\]\n\nThis can be written as\n\\[ \\mathcal{D} \\nabla \\mathcal{L} [ Z] = T_1 + T_2 - T_3, \\]\nwhere\n\\begin{align}\n    T_1 &= \\begin{array}{l}\n        \\lim\\\\ t \\rightarrow 0\n        \\end{array} \\frac{\\partial}{\\partial t} \\sum_{i, j} \\frac{\\gamma_{i,\n        j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( ( W^* + t Z)^T A_{i, j}  ( W^* + t Z))}{2\n        \\sigma^2}} A_{i, j} W^*\\\\\n    &= \\begin{array}{l}\n        \\lim\\\\\n        t \\rightarrow 0\n        \\end{array} \\frac{\\partial}{\\partial t} \\sum_{i, j} \\frac{\\gamma_{i,\n        j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* + t Z^T A_{i, j} W^* +\n        t W^{*^T} A_{i, j} Z + t^2 Z^T A_{i, j} Z )}{2 \\sigma^2}} A_{i, j} W^*  \\\\\n    &= - \\sum_{i, j} \\frac{\\gamma_{i, j}}{2 \\sigma^4} e^{- \\frac{\\tmop{Tr} (\n        ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}} \\tmop{Tr} ( Z^T A_{i, j} W^* + W^{*^T}\n        A_{i, j} Z) A_{i, j} W^* \\\\\n    &= - \\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^4} e^{- \\frac{\\tmop{Tr} (\n   ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}} \\tmop{Tr} ( Z^T A_{i, j} W^*)\n   A_{i, j} W^* &    \\text{as $A_{i, j}=A_{i,j}^T$},\\\\\n    T_2 &= \\begin{array}{l}\n     \\lim\\\\\n     t \\rightarrow 0\n   \\end{array} \\frac{\\partial}{\\partial t} \\sum_{i, j} \\frac{\\gamma_{i,\n   j}}{\\sigma^2} t e^{- \\frac{\\tmop{Tr} ( ( W^* + t Z)^T A_{i, j}  ( W^* + t\n   Z))}{2 \\sigma^2}} A_{i, j} Z\\\\\n   &= \\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} (W^{*^T}\n   A_{i, j} W^*)}{2 \\sigma^2}} A_{i, j} Z, \\\\\n    T_3 &= \\begin{array}{l} \\lim\\\\ t \\rightarrow 0 \\end{array} \\frac{\\partial}{\\partial t}  ( W^* + t Z) \\Lambda\\\\\n    &= Z \\Lambda.\n\\end{align}\n\nHence, putting all three terms together yields\n\n\n\\begin{equation}\\label{eq:directional_gradient}\n\\mathcal{D} \\nabla \\mathcal{L} [ Z] = \\left\\{ \\sum_{i, j} \\frac{\\gamma_{i,\n   j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2\n   \\sigma^2}}  \\left[ A_{i, j} Z - \\frac{1}{\\sigma^2} \\tmop{Tr} ( Z^T A_{i, j}\n   W^*) A_{i, j} W^* \\right] \\right\\} - Z \\Lambda.\n\\end{equation}\n   \n     \n\n\\iffalse\nTo produce a formulation of condition (\\ref{eq:2nd_W}), Equation (\\ref{eq:directional_gradient}) needs to multiply by $Z^T$ and place trace around the expression. This results in \n\\fi\n\nHence,\n\n\\begin{equation}\n    \\tmop{Tr} (Z^T \\nabla^2_{W^* W^*} \\mathcal{L} ( W^*, \\Lambda^*) Z) = \n    \\tmop{Tr} ( Z^T \\mathcal{D} \\nabla \\mathcal{L} [ Z]) ,\n\\end{equation}\n\n\\begin{equation} \\label{trace_2nd_condition}\n   = \\left\\{ \\sum_{i, j}\n   \\frac{\\gamma_{i, j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^*\n   )}{2 \\sigma^2}}  \\left[ \\tmop{Tr} ( Z^T A_{i, j} Z) -\n   \\frac{1}{\\sigma^2} \\tmop{Tr} ( Z^T A_{i, j} W^*)^2 \\right] \\right\\} -\n   \\tmop{Tr} ( Z^T Z \\Lambda_W).   \n\\end{equation}\n\n\nNext, let $Z$ be such that $Z\\neq 0$ and $\\nabla h (W^{\\ast})^T Z = 0$, where\n\\begin{equation}\nh ( W^*) = W^{*^T} W^* - I.\n\\end{equation}\n\nTherefore, the constraint condition can be written on $Z$ in (\\ref{eq:2nd_W}) can be written as\n\n\n\\begin{align}\n\\begin{split}\n\\nabla h ( W^*)^T Z &= \\begin{array}{l} \\lim\\\\\n     t \\rightarrow 0\n   \\end{array} \\frac{\\partial}{\\partial t}  \\frac{( W^* + t Z)^T ( W^* + t Z) -\n   W^{*^T} W^*}{t}\\\\\n    &= Z^T W^* + W^{*^T} Z = 0. \\label{Zconclusion}\n\\end{split}\n\\end{align}\n\nUsing Equations (\\ref{trace_2nd_condition}) and (\\ref{Zconclusion})  lemma \\ref{lemma:directional_derivate} follows.\n\\end{proof}\n\n\n\nRecall from Lemma \\ref{basic_lemma} that $W^*$ consists\nof the $q$ eigenvectors \\ of $\\Phi (W^*)$ with the smallest eigenvalues. We define $\\bar{W^*} \\in \\mathcal{R}^{d \\times d - q}$ as all other eigenvectors of $\\Phi(W^*)$. \\ Because $Z$ has the same dimension as $W^*$, each\ncolumn of $Z$ resides in the space of $\\mathcal{R}^d$. Since the eigenvectors\nof $\\Phi (W^*)$ span $\\mathcal{R}^d$, each column of $Z$ can be represented\nas a linear combination of the eigenvectors of $\\Phi (W^*)$. In other words, each\ncolumn $z_i$ can therefore be written as $z_i = W^*P^{(i)}_W + \\bar{W^*}\nP^{(i)}_{\\bar{W^*}}$, where $P^{(i)}_{W^*} \\in \\mathcal{R}^{q \\times 1}$ and \\\n$P^{(i)}_{\\bar{W^*}} \\in \\mathcal{R}^{d - q \\times 1}$ \\ represents the\ncoordinates for the two sets of eigenvectors. Using the same notation, we also define $\\Lambda^* \\in\n\\mathcal{R}^{q \\times q}$ as the eigenvalues corresponding to $W^*$ and\n$\\bar{\\Lambda^*} \\in \\mathcal{R}^{d - q \\times d - q}$ as the eigenvalues\ncorresponding to $\\bar{W^*}$. The entire matrix $Z$ can therefore be\nrepresented as \n\\begin{equation} \\label{def:Z}\n  Z = \\bar{W^*} P_{\\bar{W^*}} + W^*P_{W^*}.\n\\end{equation}\n\n\nFurthermore, it can be easily shown that $P_{W^*}$ is a skew symmetric matrix, or $- P_{W^*} = P_{W^*}^T$. By  setting $Z$ from Equation (\\ref{cond:Zcondition}) into  (\\ref{def:Z}), the constraint can be rewritten as\n\n\\begin{align}\n[ P_{\\bar{W^*}}^T \\bar{W^*}^T + P_W^{*^T} W^{*^T}] W^* + W^{*^T} [ \\bar{W^*} P_{\\bar{W^*}} + W^* P_{W^*}] &= 0.\n\\end{align}\n\nSimplifying the equation yields the relationship\n\n\\begin{equation}\nP_W^{*^T} + P_{W^*} = 0.\n\\end{equation}\n\n\n\n\n\nUsing these definitions, we define the following sublemma.\n\n\\begin{sublemma}\\label{lemma:To_final_form}\nGiven a fixed point $W^*$ and a $Z$ satisfying condition (\\ref{cond:Zcondition}), the condition \n$\\tmop{Tr} ( Z^T \\mathcal{D} \\nabla \\mathcal{L} [ Z]) \\geq 0$ is equivalent to \n\\begin{equation} \\label{eq:inequality}\n   \\tmop{Tr} ( P_{\\bar{W^*}}^T \\bar{\\Lambda^*} P_{\\bar{W^*}}) - \\tmop{Tr} (\n   P_{\\bar{W^*}} \\Lambda^* P_{\\bar{W^*}}^T) \\geq C_2,\n\\end{equation}\nwhere \n\\begin{equation} \\label{def:C2}\n   C_2 = \\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^4} e^{-\n   \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}} \\tmop{Tr} (\n   Z^T A_{i, j} W^*)^2,\n\\end{equation}\n\n$P_{W^*}, P_{\\bar{W^*}}$ are given by Equation (\\ref{def:Z}), and $\\Lambda^*,\\bar{\\Lambda^*}$ are the diagonal matrices containing the bottom and top eigenvalues of $\\Phi(W^*)$ respectively.\n\n\n\n\\end{sublemma}\n\n\n\n\\begin{proof}\nBy condition  (\\ref{cond:large_inequality}), \n\\begin{align}\n    \\tmop{Tr} ( Z^T \\mathcal{D} \\nabla \\mathcal{L} [ Z]) &= C_1 - C_2 + C_3, \\label{eq:41} \n\\end{align}\nwhere\n\\begin{align*}\n    C_1  &= \\tmop{Tr} \\left( Z^T \\sum_{i, j} \\frac{\\gamma_{i,\n   j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2\n   \\sigma^2}} A_{i, j} Z \\right), \\\\\n   C_2 &= \\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^4} e^{-\n   \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}} \\tmop{Tr} (\n   Z^T A_{i, j} W^*)^2  \\label{eq:43},\\\\\n   C_3 &= - \\tmop{Tr} ( Z^T Z \\Lambda^*).\n\\end{align*}\n\n\n\n$C_1$ can be written as \n\n\\begin{align*}\n C_1 &= \\tmop{Tr} \\left( Z^T \\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^2} e^{-\n   \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}} A_{i, j} Z\n   \\right) &\\\\\n &=\\tmop{Tr} ( Z^T \\Phi ( W^*) [ \\bar{W^*} P_{\\bar{W^*}} + W^* P_{W^*}]) &\\\\\n &=\\tmop{Tr} ( Z^T [ \\Phi ( W^*)  \\bar{W^*} P_{\\bar{W^*}} + \\Phi ( W^*) W^* P_{W^*}])  & \\\\\n &=\\tmop{Tr} ( Z^T [ \\bar{W^*}  \\bar{\\Lambda} P_{\\bar{W^*}} + W^* \\Lambda P_{W^*}]) \n    & \\text{By definition of eigenvalues.} \\\\\n &= \\tmop{Tr} ( [ P_{\\bar{W^*}}^T \\bar{W^*} ^T + P_W^{*^T} W^{*^T} ] [ \\bar{W^*} \n   \\bar{\\Lambda} P_{\\bar{W^*}} + W^* \\Lambda P_{W^*}]) & \\text{Substitute for $Z$} \\\\\n &=\\tmop{Tr} ( P_{\\bar{W^*}}^T  \\bar{\\Lambda} P_{\\bar{W^*}} ) + \\tmop{Tr} ( P_{W^*}^T\n   \\Lambda P_W ) & \\text{Given $W^{*^T}W^*=I$, $\\bar{W^*}^TW^* =0 $}.\n\\end{align*}\n\n\n\nSimilarly\n\\begin{align*}\n    C_3 &= - \\tmop{Tr} ( Z^T Z \\Lambda) \\\\\n    &= - \\tmop{Tr} ( [ P_{\\bar{W^*}}^T \\bar{W^*} ^T + P_{W^*}^T W^{*^T}] \n        [ \\bar{W^*} P_{\\bar{W^*}} + W^* P_{W^*}] \\Lambda) \\\\\n    &= - \\tmop{Tr} ( [ P_{\\bar{W^*}}^T P_{\\bar{W^*}} + P_{W^*}^T P_{W^*}] \\Lambda)\\\\\n    &= - \\tmop{Tr} ( P_{\\bar{W^*}}^T P_{\\bar{W^*}} \\Lambda) - \n        \\tmop{Tr} ( P_{W^*}^T P_{W^*} \\Lambda).\n\\end{align*}\n\n\nBecause $P_{W^*}$ is a square skew symmetric matrix, the diagonal elements of $P_{W^*}\nP_{W^*}^T$ is the same as the diagonal of $P_{W^*} P_{W^*}^T$. From this observation, we\nconclude that $\\tmop{Tr} ( P_{W^*} P_{W^*}^T \\Lambda) = \\tmop{Tr} ( P_{W^*}^T P_{W^*}\n\\Lambda)$. Hence, \n\n\n\\begin{align*}\nC_3 = - \\tmop{Tr} ( P_{\\bar{W^*}} \\Lambda P_{\\bar{W^*}}^T ) -\n   \\tmop{Tr} ( P_{W^*}^T \\Lambda P_{W^*} ).\n\\end{align*}\n   \n\nPutting all 3 parts together yields\n\n\\begin{align}\n\\begin{split}\n    \\tmop{Tr} ( Z^T \\mathcal{D} \\nabla \\mathcal{L} [ Z]) &= \\tmop{Tr} (\n   P_{\\bar{W^*}}^T  \\bar{\\Lambda} P_{\\bar{W^*}} ) + \\tmop{Tr} ( P_{W^*}^T \\Lambda P_{W^*}\n   ) - C_2 - \\tmop{Tr} ( P_{\\bar{W^*}} \\Lambda P_{\\bar{W^*}}^T ) -\n   \\tmop{Tr} ( P_{W^*}^T \\Lambda P_{W^*} ) \\\\\n   &=\\tmop{Tr} ( P_{\\bar{W^*}}^T \\bar{\\Lambda} P_{\\bar{W^*}}) - \\tmop{Tr} (\n   P_{\\bar{W^*}} \\Lambda P_{\\bar{W^*}}^T) - C_2 .\n\\end{split}\n\\end{align}\n\n\n\nThe 2nd order condition (\\ref{eq:2nd_W}) is, therefore, satisfied, when   \n\\begin{equation} \\label{eq:58}\n   \\tmop{Tr} ( P_{\\bar{W^*}}^T \\bar{\\Lambda} P_{\\bar{W^*}}) - \\tmop{Tr} (\n   P_{\\bar{W^*}} \\Lambda P_{\\bar{W^*}}^T) \\geq C_2.\n\\end{equation}\n\n\\end{proof}\n\n\n\n\n\n\n\\begin{sublemma} \\label{large_enough_sigma}\n    Given $W^*$,$\\bar{W^*}$,$\\bar{\\Lambda^*}$, and $\\Lambda^*$ \n    as defined in Equation (\\ref{def:Z}), \n   if the corresponding smallest eigenvalue of $\\bar{\\Lambda^*}$ \n   is larger than the largest eigenvalue of $\\Lambda^*$, then given a large enough  $\\sigma$ the \n   condition (\\ref{eq:2nd_W}) of Lemma \\ref{lemma:2nd_order} is satisfied.\n\\end{sublemma}\n\n\\begin{proof}\nTo proof sublemma (\\ref{large_enough_sigma}), we provide bounds on each of the terms in \\eqref{eq:58}. Starting with $C_2$ defined at (\\ref{def:C2}). It has a trace term, $(\\tmop{Tr}(Z^TA_{ij}W^*))^2$ that can be rewritten as \n\n\\begin{equation}\\label{eq:60}\n  (\\tmop{Tr}(A_{ij}W^*Z^T))^2 = (\\tmop{Tr}(A_{ij}W^*P^T_{W^*}W^{*^T}+ A_{ij}W^*P^T_{\\bar{W^*}}\\bar{W^*}^T))^2.\n\\end{equation}\n\nSince $A_{ij}$ is symmetric and $W^*P^T_{W^*}W^{*^T}$ is skew-symmetric, then\nTr$(A_{ij}W^*P^T_{W^*}W^{*^T})=0$. Hence \n\n\\begin{align}\n   (\\tmop{Tr}(Z^TA_{ij}W^*))^2 & =  (\\tmop{Tr}(A_{ij}W^*Z^T))^2 \n    = (\\tmop{Tr}(A_{ij}W^*P^T_{\\bar{W^*}}\\bar{W^*}^T))^2 \\\\\n    &\\leq \\tmop{Tr}(A^T_{i,j}A_{ij})\\tmop{Tr}(P^T_{\\bar{W^*}}P_{\\bar{W^*}}) \n\\end{align}\n\nwhere the last inequality follows from Cauchy-Schwartz inequality and that fact that $W^{*^T}W^*=I$ and $\\bar{W^*}^T\\bar{W^*}=I$.\nThus, $C_2$ in \\eqref{eq:43} is bounded by\n\\begin{equation}\\label{eq:c2bound}\n   C_2 \\leq  \\sum_{i, j} \\frac{|\\gamma_{i, j}|}{\\sigma^4} e^{-\n   \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}} \\tmop{Tr} (\n    A^T_{i,j}A_{ij})\\tmop{Tr}(P^T_{\\bar{W^*}}P_{\\bar{W^*}})\n\\end{equation}\nSimilarly, the remaining terms in \\eqref{eq:41} can be bounded by\n\\begin{equation}\nC_1= \\tmop{Tr} ( P_{\\bar{W^*}}^T \\bar{\\Lambda^*} P_{\\bar{W^*}}) \\geq \\min_i\n    ( \\bar{\\Lambda^*}_i) \\tmop{Tr} ( P_{\\bar{W^*}} P_{\\bar{W^*}}^T) \n\\end{equation}\n\\begin{equation}\n C_3 = -\\tmop{Tr} ( P_{\\bar{W^*}} \\Lambda^* P^T_{\\bar{W^*}}) \\geq -\n     \\max_i ( \\Lambda_i^*) \\tmop{Tr} ( P_{\\bar{W^*}}^T P_{\\bar{W^*}}).\n\\end{equation}\n     \nUsing the bounds for each term, the Equation (\\ref{eq:58}) can be rewritten as\n\\begin{align}\n    [\\min_i ( \\bar{\\Lambda^*}_i) -\\max_j(\\Lambda_j^*)] \\tmop{Tr}(P^T_{\\bar{W^*}}P_{\\bar{W^*}}) &\\geq \n    \\sum_{i, j} \\frac{|\\gamma_{i, j}|}{\\sigma^4} e^{-\n   \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}}\n   \\tmop{Tr} (A^T_{i,j}A_{ij})\n   \\tmop{Tr}(P^T_{\\bar{W^*}}P_{\\bar{W^*}})\\\\\n   [\\min_i ( \\bar{\\Lambda^*}_i) -\\max_j(\\Lambda_j^*)] &\\geq \n    \\sum_{i, j} \\frac{|\\gamma_{i, j}|}{\\sigma^4} e^{-\n   \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}} \\tmop{Tr} (A^T_{i,j}A_{ij})\\label{eq:conclusion}\n\\end{align}\n\nIt should be noted that $\\Lambda^*$ is a function of $\\frac{1}{\\sigma^2}$. This relationship could be removed by multiplying both sides of the inequality by $\\sigma^*$ to yield\n\\begin{equation}\n   \\sigma^2 [\\min_i ( \\bar{\\Lambda^*}_i) -\\max_j(\\Lambda_j^*)] \\geq \n    \\sum_{i, j} \\frac{|\\gamma_{i, j}|}{\\sigma^2} e^{-\n   \\frac{\\tmop{Tr} ( ( W^{*^T} A_{i, j} W^* )}{2 \\sigma^2}}\\tmop{Tr} (A^T_{i,j}A_{ij}). \\label{ineq:large_sigma}\n\\end{equation} \n\nSince $\\sigma^2$ is always a positive value, as long as all the eigenvalues from $\\bar{\\Lambda^*}$ is larger than all the eigenvalues from $\\Lambda^*$, the left hand side of the equation will always be greater than 0. As $\\sigma \\rightarrow \\infty$, the right hand side approaches 0, and the  condition (\\ref{eq:2nd_W}) of Lemma \\ref{lemma:2nd_order} is satisfied. \n\\end{proof} \\label{proof_of_lemma_4}\n\n\nAs a side note, the eigen gap between min($\\bar{\\Lambda^*}$) and max($\\Lambda^*$) controls the range of potential $\\sigma$ values \u2014i.e. the larger the eigen gap the easier for $\\sigma$ to satisfy \\eqref{ineq:large_sigma}. Therefore, the ideal cutoff point should have a large eigen gap.\n\n\n\\end{appendices}\n\n\n\n\n\n\n\n\\newpage\n\\begin{appendices} \\label{Appendix:Convergence_plot}\n\\section{Convergence Plot from Experiments}\n\nFigure \\ref{fig:convergence} summarizes the convergence activity of various experiments. For each experiment, the top figure \nprovides the magnitude of the objective function. It can be seen \nthat the values converges towards a fixed point. The middle plot provide updates of the gradient of the Lagrangian. It can be seen that the gradient converges towards 0. The bottom plot shows the changes in $W$ during each iteration. The change in $W$ converge towards 0.\n\n\\begin{figure}[ht]\n  \\centering\n  \\includegraphics[width=14cm,height=14cm]{{extras\/Convergence_plot}}\n  \\caption{Convergence Results from the Experiments.}\n  \\label{fig:convergence}\n\\end{figure}\n\\end{appendices}\n\\newpage\n\n\n\n\n\n\\begin{appendices}\n\\section{Proof of Convergence}\n\nThe convergence property of ISM has been analyzed and yields the following theorem.\n\n\\begin{theorem}\n  A sequence $\\{W_k\\}_{k\\in \\mathbb{N}}$ generated by Algorithm~\\ref{masteralg} contains a convergent subsequence. \n \\end{theorem}\n \n\n\n\\begin{proof}\n\nAccording to Bolzano-Weierstrass theorem, if we can show that the sequences generated from\nthe 1st order relaxation is bounded, it has a convergent subsequence. If we\nstudy the Equation $\\Phi(W)$ more closely, the key driver of the sequence of $W_k$\nis the matrix $\\Phi$, therefore, if we can show that if this matrix is\nbounded, the sequence itself is also bounded. We look inside the construction\nof the matrix itself.\n\n\\[ \\Phi_{n + 1} = \\left[ \\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^2} e^{-\n   \\frac{\\tmop{Tr} (W_n^T A_{i, j} W_n)}{2 \\sigma^2}} A_{i, j} \\right] \\]\n\nFrom this equation, start with the matrix $A_{i, j} = ( x_i - x_j) ( x_i -\nx_j)^T$. Since $x_i, x_j$ are data points that are always centered and scaled\nto a variance of 1, the size of this matrix is always constrained. It also\nimplies that $A_{i, j}$ is a PSD matrix. From this, the exponential term is always limited between\nthe value of 0 and 1. The value of $\\sigma$ is a constant given from the\ninitialization stage. Lastly, we have the $\\gamma_{i, j}$ term. Since $\\gamma\n= D^{- 1 \/ 2} H ( U U^T - \\lambda Y Y^T) H D^{- 1 \/ 2}$. The degree matrix\ncame from the exponential kernel. Since the kernels are bounded, $D$ is also\nbounded. The centering matrix $H$ and the previous clustering result $Y$ can\nbe considered as bounded constants. Since the spectral embedding $U$ is a\northonormal matrix, it is always bounded. From this, given that the components\nof $\\Phi$ is bounded, the infinity norm of the $\\Phi$ is always bounded. The\neigenvalue matrix of $\\Lambda$ is therefore also bounded. Using the\nBolzano-Weierstrass Theorem, the sequence contains a convergent sub-sequence. Given that $\\Phi$ is a continuous function of $W$, by continuity, $W$ also has a convergent sub-sequence.\n\\end{proof}\n\\end{appendices}\n\n\n\n\\begin{appendices}\n\\section{Proof for the initialization}\nAlthough the proof was originally shown through the usage of the 2nd order Taylor Approximation. A simpler approach was later discovered to arrive to the same formulation faster. We first note that Taylor's Expansion around 0 of an exponential is \n\\[e^x=1+x+\\frac{x^2}{2!}+...  .\\]\n\nGiven the objective Lagrangian in eq \\eqref{eq:lag}, \\ we simplify the Lagrangian by using the Taylor approximation only on the problematic exponential term. The approximation is expanded up to the 1st order centering around 0 to yield \n\\[ \\mathcal{L} \\approx - \\sum_{i, j} \\gamma_{i, j}  \\left( 1 - \\frac{\\tmop{Tr}\n   (W^T A_{i, j} W)}{2 \\sigma^2} \\right) + \\frac{1}{2} \\tmop{Tr} (\\Lambda (I -\n   W^T W)) .\\]\nBy taking the derivative of the approximated Lagrangian and setting the derivative to zero, an eigenvalue\/eigenvector relationship emerges as\n\\[ \\Phi W =  \\left[ \\sum_{i, j} \\frac{\\gamma_{i, j}}{\\sigma^2} A_{i,\n   j} \\right] W_0 = W_0 \\Lambda .\\]\n   \nFrom this, we see that $\\Phi_0$ is no longer a function of $W$. Using this $\\Phi_0$ we can then calculate a closed form solution for $W_0$\n\\end{appendices}\n\n\n\n\\begin{appendices}\n\\section{Proof for the computational complexity}\n\n\nFor ISM, DG and SM, the bottleneck resides in the computation of the gradient.\n\\[ f ( W) = \\sum_{i, j} \\gamma_{i, j} e^{- \\frac{\\tmop{Tr} ( W^T A_{i, j}\n   W)}{2 \\sigma^2}} \\]\n\\[ \\frac{\\partial f}{\\partial W} = \\left[ \\sum_{i, j}  \\frac{\\gamma_{i,\n   j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( W^T A_{i, j} W)}{2 \\sigma^2}} A_{i, j}\n   \\right] W \\]\n\\[ \\frac{\\partial f}{\\partial W} = \\left[ \\sum_{i, j}  \\frac{\\gamma_{i,\n   j}}{\\sigma^2} e^{- \\frac{\\tmop{Tr} ( W^T \\Delta x_{i, j} \\Delta x_{i, j}^T\n   W)}{2 \\sigma^2}} A_{i, j} \\right] W \\]\nWhere $A_{i, j} = \\Delta x_{i, j} \\Delta x_{i, j}^T$. The variables have the\nfollowing dimensions.\n\\[ \\begin{array}{l}\n     x_{i, j} \\in \\mathcal{R}^{d \\times 1}\\\\\n     W \\in \\mathcal{R}^{d \\times q}\n   \\end{array} \\]\nTo compute a new $W$ with DG, we first mulitply $\\Delta x_{i, j}^T W$, which\nis $O ( d)$. Note that $W$ in DG is always 1 single column. Next, it\nmultiplies with its own transpose to yied $O ( d  + q^2)$. Then we\ncompute $A_{i, j}$ to get $O ( d + q^2 + d^2)$. Since this operation needs to\nbe added $n^2$ times, we get, $O ( n^2 ( d + q^2 + d^2))$. Since $d \\gg q$,\nthis notation reduces down to $O ( n^2 d^2)$. Let $T_1$ be the number of\niterations until convergence, then it becomes $O ( T_1 n^2 d^2)$. Lastly, in\nDG, this operation needs to be repeated $q$ times, hence, $O ( T_1 n^2 d^2\nq)$.\n\n\n\nTo compute a new $W$ with SM, we first mulitply $\\Delta x_{i, j}^T W$, which\nis $O ( d q)$. Next, it multiplies with its own transpose to yied $O ( d q\n + q^2)$. Then we compute $A_{i, j}$ to get $O ( d q + q^2 + d^2)$.\nSince this operation needs to be added $n^2$ times, we get, $O ( n^2 ( d q +\nq^2 + d^2))$. Since $d \\gg q$, this notation reduces down to $O ( n^2 d^2)$.\nThe SM method requires the computation of the inverse of $d \\times d$ matrix.\nSince inverses is cubic, it becomes $O ( n^2 d^2  + d^3)$. Lastly, let\n$T_2$ be the number of iterations until convergence, then it becomes $O ( T_2\n( n^2 d^2 + d^3))$.\n\n\n\nTo compute a new $W$ with ISM, we first mulitply $\\Delta x_{i, j}^T W$, which\nis $O ( d q)$. Next, it multiplies with its own transpose to yied $O ( d q\n + q^2)$. Then we compute $A_{i, j}$ to get $O ( d q + q^2 + d^2)$.\nSince this operation needs to be added $n^2$ times, we get, $O ( n^2 ( d q +\nq^2 + d^2))$. Since $d \\gg q$, this notation reduces down to $O ( n^2 d^2)$.\nThe ISM method requires the computation of the eigen decomposition of $d\n\\times d$ matrix. Since inverses is cubic, it becomes $O ( n^2 d^2  +\nd^3)$. Lastly, let $T_3$ be the number of iterations until convergence, then\nit becomes $O ( T_3 ( n^2 d^2 + d^3))$.\n\n\\end{appendices}\n\n\n\n\n\n\\begin{appendices} \n\\section{Measure of Non-linear Relationship by HSIC Versus Correlation}\n\nThe figure below demonstrates a visual comparison of HSIC and correlation. It can be seen that HSIC  measures non-linear relationships, while correlation does not. \n\\begin{figure}[ht]\n  \\centering\n  \\includegraphics[width=14cm,height=3cm]{{extras\/HSIC_example}}\n  \\caption{Showing that HSIC captures non-linear information.}\n  \\label{HSIC_capture_nonlinear}\n\\end{figure}\n\\label{App:HSIC}\n\\end{appendices}\n\n\n\n\n\n\n\n\n\n\\begin{appendices}\n\\section{Implementation Details of the Cost function}\n\nThe computation of the cost using the formulation below is slow if it is implemented using a loop. \n\\begin{equation}\n  \\begin{array}{ll}\n    \\min & - \\sum_{i, j} \\gamma_{i, j} e^{- \\frac{\\tmop{tr} ( W^T A_{i, j}\n    W)}{2 \\sigma^2}}\\\\\n    W & \\\\\n    s.t & W^T W = I\\\\\n    & W \\in \\mathbb{R}^{d \\times q}\\\\\n    & A \\in \\mathbb{R}^{d \\times d}\\\\\n    & \\gamma_{i, j} \\in \\mathbb{R}\n  \\end{array}\n\\end{equation}\n\nInstead, we use the original formulation to derive a faster way to compute the cost.\n\nStarting with the original cost function as\n\\[ \\tmop{cost} = \\tmop{HSIC} ( X W, U) - \\lambda \\tmop{HSIC} ( X W, Y) \\]\n\\[ \\tmop{cost} = \\tmop{Tr} ( D^{-1\/2}K_{XW} D^{-1\/2} H U U^T H) - \\lambda \\tmop{Tr} (D^{-1\/2}K_{XW} D^{-1\/2} H Y Y^T H) \\]\n\nWhen optimizing $U$, it is obvious that the 2nd portion does not effect the\noptimization. Therefore, $U$ can be solved using the following form.\n\\[ U = \\begin{array}{l}\n     \\tmop{argmin}\\\\\n     U\n   \\end{array} \\tmop{Tr} ( U^T H D^{- 1 \/ 2} K_{X W} D^{- 1 \/ 2} H U) \\]\n\n\nIf we are optimization for $W$, using the combination of the rotation property and the combination of the 2 traces, the cost can be written as \n\\[ \\tmop{cost} = \\tmop{Tr} ( [ D^{- 1 \/ 2} H ( U U^T - \\lambda Y Y^T) H D^{-\n   1 \/ 2}] K). \\]\n\n\nIn this form, it can be seen that the update of $W$ matrix will only affect\nthe kernel $K$ and the degree matrix $D$. Therefore, it makes sens to treat\nthe middle portion as a constant which we refer as $\\Psi$.\n\\[ \\tmop{cost} = \\tmop{Tr} ( [ D^{- 1 \/ 2} \\Psi D^{- 1 \/ 2}] K) \\]\n\n\nGiven that $[ D^{- 1 \/ 2} \\Psi D^{- 1 \/ 2}]$ is a symmetric matrix, from this\nform, we can convert the trace into an element wise product $\\odot$.\n\\[ \\tmop{cost} = \\sum_{i,j} ([ D^{- 1 \/ 2} \\Psi D^{- 1 \/ 2}] \\odot K )_{i,j} \\]\n\n\nTo further reduction the amount of operation, we let $d$ be a vector of the\ndiagonal elements of $D^{- 1 \/ 2}$, hence $d = \\tmop{diag} ( D^{- 1 \/ 2})$,\nthis equality hold.\n\\[ D^{- 1 \/ 2} \\Psi D^{- 1 \/ 2} = [ d d^T] \\odot \\Psi \\]\n\n\nTherefore, the final cost function can be written in its simplest form as :\n\\[ \\tmop{cost} = \\sum_{i,j} \\Gamma_{i,j} = \\sum_{i,j} (\\Psi \\odot [ d d^T] \\odot K )_{i,j} \\]\n\n\nDuring update, as $W$ update during each iteration, the matrix $\\Psi$ stays as\na constant while $d d^T$ and $K$ update. The benefit of this form minimize the\ncomplexity of the equation, while simplify cost into easily parallelizable\nmatrix multiplications. The equation also clearly separates the elements into\nportions that require an update and portions that does not.\n\\end{appendices}\n\n\n\n\\begin{appendices}\n\\section{Implementation Details of the Derivative}\nAs it was shown from previous sections, the gradient of our cost function using the Gaussian Kernel is \n\\[ \\nabla f ( W) = \\left[ \\frac{1}{\\sigma^2} \\sum \\gamma_{i, j} K_{i, j} A_{i, j} \\right] W  - 2W\\Lambda\\].\n\n\nIf we let $\\Psi = \\left[  \\frac{1}{2\\sigma^2}  \\gamma_{i, j} K_{i, j}  \\right]$ , it can be rewritten as \n\\[ \\nabla f ( W) = \n\\left[ \\sum \\Psi_{i, j} A_{i, j} \\right] W - W\\Lambda.\\]\n\nFrom this formulation, the optimal $W$ is equivalent to the eigenvectors of the $\\left[ \\sum \\Psi_{i, j} A_{i, j} \\right]$. According to ISM, the $q$ eigenvectors corresponding to the smallest eigenvalues is used for $W$. Since solving $\\sum \\Psi_{i, j} A_{i, j}$ using a loop is slow, we vectorize the formulation so that\n\n\\[ \\sum \\Psi_{i, j} A_{i, j} = X^T[D_{\\Psi} - \\Psi]X \\], \n\nwhere $D_\\Psi$ is the degree matrix of $Psi$ such that the diagonal elements are defined as\n\n\\[ d_{i,i} = \\sum_{j} \\Psi_{i,j} \\], \n\nand $X \\in \\mathbb{R}^{n \\times d}$ is the original data.\n\n\\end{appendices}\n\n\n\n\n\n\\begin{appendices} \n\\section{Hyperparameters Used in Each Experiment}\n    \\begin{table}[h]\n    \\centering\n        \\begin{tabular}{l|ccc}\n        & $\\sigma$ & $\\lambda$ & $q$ \\\\ \\cline{1-4}\n        Gauss A & 1 & 0.04 & 1 \\\\\n        Gauss B 200 & 5 & 2 & 3 \\\\\n        Moon 400 & 0.1 & 1 & 3 \\\\\n        Moon+N 200 & 0.2 & 0.1 & 6 \\\\\n        Flower & 2 & 10 & 2 \\\\\n        Face & 3.1 & 1 & 17 \\\\\n        Web KB & 18.7 & 0.057 & 4 \\\\\n        \\end{tabular}\n    \\end{table}\n    \\label{App:Hyperparameters}\n\\end{appendices}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\n\nThis paper is about the Newtonian model of gravitation,\nalso known as the classical $N$-body problem.\nWe start recalling the standard notation.\nLet $E$ be an Euclidean space,\nin which the punctual masses $m_1,\\dots,m_N>0$\nare moving under the action of the inverse-square law of universal gravitation.\nIf the components of $x=(r_1,\\dots,r_N)\\in E^N$\nare the positions of the bodies,\nthen we shall denote $r_{ij}=\\norm{r_i-r_j}_E$\nthe distance between bodies $i$ and $j$\nfor any pair $1\\leq i<j\\leq N$.\nThe Newton's equations can be written as $\\ddot x=\\nabla U(x)$,\nwhere $U:E^N\\to\\mathbb{R}\\cup\\set{+\\infty}$ is the \\emph{Newtonian potential}, \n\\[\nU(x)=\\;\\sum_{i<j}\\;m_i\\,m_j\\;r_{ij}^{-1}\\;,\n\\]\nand the gradient is taken with respect to the mass scalar product.\nA configuration $x\\in E^N$ is said to be without collisions if\n$U(x)<+\\infty$,\nthat is to say, whenever we have $r_{ij}\\neq 0$ for all $i\\neq j$.\nWe denote $\\Omega\\subset E^N$ the open and dense set of configurations without collisions.\nTherefore Newton's equations define an analytic local flow on\n$T\\Omega=\\Omega\\times E^N$,\nwith a first integral given by the energy constant\n\\[h=\\frac{1}{2}\\norm{\\dot x}^2-U(x)\\,.\\]\n\nOne of the main difficulties\nfor the analysis of the dynamics in this model is the uncertainty,\nfor a given motion,\nabout the presence of singularities after a finite amount of time.\nThat is to say,\nwe can not predict whether a certain evolution of the bodies\nwill be defined for all future time or not.\nWe recall that maximal solutions that end in finite time\nmust undergo collisions at the last moment,\nor to have an extremely complex behaviour called\npseudocollision (\\cite{Dia}, p.39).\nNotwithstanding,\nthe classification of all possible final evolutions was developed,\nfor motions assumed to be without singularities in the future,\nessentially in terms of\nthe asymptotic behaviour of the distance between the bodies.\nSome of the greatest contributions in this direction\nare undoubtedly those due to Chazy,\nand especially those that he obtained in the works\n\\cite{Cha1, Cha2} that we comment below.\nHowever,\nthis approach does not provide the existence of motions\nfor any type of final evolution.\n\nIn this paper we will be concerned with the class of\nhyperbolic motions,\nas defined by Chazy by analogy with the Keplerian case.\n\n\\begin{definition}\nHyperbolic motions are those such that\neach body has a different limit velocity vector, that is\n$\\dot{r}_i(t)\\to a_i\\in E$ as $t\\to +\\infty$,\nand $a_i\\neq a_j$ whenever $i\\neq j$. \n\\end{definition}\n\nIf $V$ is a normed vector space\nand $x(t)$ is a smooth curve in $V$\nwith asymptotic velocity $a\\in V$,\nthen we must have $x(t)=ta+o(t)$ as $t\\to +\\infty$,\nbut the converse is of course not true.\nHowever, for $V=E^N$ and $a=(a_1,\\dots,a_N)\\in\\Omega$,\nthe converse is satisfied\nby solutions of the Newtonian $N$-body problem\n(see Lemma \\ref{lema-cont.limitshape}).\nThus, hyperbolic motions are characterized as\n\\emph{motions without singularities in the future and such that\n $x(t)=ta+o(t)$ for some configuration $a\\in\\Omega$.}\n\nIt follows that for any hyperbolic motion we have\n$\\alpha t < r_{ij}(t) <  \\beta t$ for some positive constants,\nfor all $i<j$, and for all $t$ big enough.\nAs we will see,\nChazy proved that this weaker property\nalso characterizes hyperbolic motions. \n\nAs usual,\n$I(x)=\\inner{x}{x}=\\sum_i m_i\\inner{r_i}{r_i}_E$ will denote the\n\\emph{moment of inertia} of the configuration $x\\in E^N$\nwith respect to the origin of $E$.\nWhen the motion $x(t)$ is given,\nwe will use the notation $U(t)$ and $I(t)$\nfor the compositions $U(x(t))$ and $I(x(t))$ respectively.\nThus for an hyperbolic motion such that\n$x(t)=a t + o(t)$ as $t\\to +\\infty$ we have\n$U(t)\\to 0$, $I(t)\\sim I(a)\\,t^2$ and $2h=I(a)>0$.\n\nWe say that a motion $x(t)$ has \\emph{limit shape}\nwhen there is a time dependent similitude $S(t)$ of the space $E$\nsuch that $S(t)x(t)$ converges to some configuration $a\\neq 0$\n(here the action of $S(t)$ on $E^N$ is the diagonal one).\nThus the limit shape of an hyperbolic motion is the shape\nof his asymptotic velocity $a=\\lim_{t\\to +\\infty}t^{-1}x(t)$.\nNote that, in fact,\nthis represents a stronger way of having a limit shape,\nsince in this case the similarities are given by homotheties.\n\n\n\\subsection{Existence of hyperbolic motions}\n\\label{s-existence}\n\nThe only explicitly known hyperbolic motions\nare of the homographic type,\nmeaning that the configuration is\nall the time in the same similarity class.\nFor this kind of motion,\n$x(t)$ is all the time a central configuration,\nthat is, a critical point of $I^{1\/2}U$.\nThis is a strong limitation,\nfor instance the only central configurations for $N=3$\nare either equilateral or collinear.\nMoreover,\nthe Painlev\u00e9-Wintner conjecture states that up to similarity\nthere are always a finite number of central configurations.\nThe conjecture was confirmed by Hampton and Moeckel\n\\cite{HamMoe} in the case of four bodies,\nand by Albouy and Kaloshin \\cite{AlbKal}\nfor generic values of the masses in the planar five-body problem.\n\nOn the other hand,\nChazy proved in \\cite{Cha2} that the set of initial conditions\ngiving rise to hyperbolic motions is an open subset of $T\\Omega$,\nand moreover,\nthat the limit shape depends continuously on the initial condition\n(see Lemma \\ref{lema-cont.limitshape}).\nIn particular,\na motion close enough to some hyperbolic homographic motion\nis still hyperbolic.\nHowever, this does not allow us to draw conclusions\nabout the set of configurations that are realised as limit shapes.\nIn this paper we prove that \\emph{any} configuration\nwithout collisions is the limit shape of some hyperbolic motion.\nAt our knowledge, there are no results in this direction\nin the literature of the subject.\n\n\n\nAn important novelty in this work is the use of global viscosity solutions, in the sense introduced by Crandall, Evans and Lions \\cite{CraLio,CraEvaLio},\nfor the supercritical Hamilton-Jacobi equation\n\\begin{equation}\\tag{HJ}\\label{HJh}\nH(x,d_xu)=h \\qquad x\\in E^N,\n\\end{equation}\nwhere $H$\nis the Hamiltonian of the Newtonian $N$-body problem,\nand $h>0$.\n\nWe will found global viscosity solutions through a limit process\ninspired by the Gromov's construction of the ideal boundary\nof a complete locally compact metric space.\nTo do this,\nwe will have to generalize to the case $h>0$ the H\u00f6lder estimate\nfor the action potential discovered by the first author in\n\\cite{Mad1} in the case $h=0$.\nWith this new estimate we will remedy the loss of\nthe Lipschitz character of the viscosity subsolutions,\nwhich is due to the singularities of the Newtonian potential.\n\nIn a second step, we will show that the functions thus obtained\nare in fact fixed points of the Lax-Oleinik semigroup. \nMoreover,\nwe will prove that given any configuration without collisions\n$a\\in\\Omega$,\nthere are solutions of Equation (\\ref{HJh}) such that\nall its calibrating curves are hyperbolic motions\nhaving the shape of $a$ as limit shape.\nFollowing this method (developed in Sect. \\ref{s-HJ})\nwe get to our main result.\n\n\\begin{theorem}\n\\label{thm-princ}\nFor the Newtonian $N$-body problem in a space $E$\nof dimension at least two,\nthere are hyperbolic motions $x:[0,+\\infty)\\to E^N$ such that\n\\[x(t)=\\sqrt{2h}\\,t\\;a+o(t)\\quad\\text{ as }\\quad t\\to +\\infty,\\]\nfor any choice of $x_0=x(0)\\in E^N$,\nfor any configuration without collisions $a\\in\\Omega$ normalized by $\\norm{a}=1$,\nand for any choice of the energy constant $h>0$.  \n\\end{theorem}\n\nWe emphasize the fact that the initial configuration can be chosen \\emph{with} collisions.\nThis means that in such a case, the motion $x$ given by the theorem is continuous at $t=0$,\nand defines a maximal solution $x(t)\\in\\Omega$ for $t>0$. \nFor instance,\nchoosing $x_0=0\\in E^N$,\nthe theorem gives the existence of ejections from the total collision configuration,\nwith prescribed positive energy and arbitrarily chosen limit shape.\n\nMoreover, the well known Sundman's inequality (see Wintner \\cite{Win}) implies that motions with total collisions have zero angular momentum. \nTherefore, we deduce the following non trivial corollary.\n\n\\begin{corollary}\nFor any configuration without collisions $a\\in\\Omega$\nthere is a hyperbolic motion with zero angular momentum\nand asymptotic velocity $a$.  \n\\end{corollary}\n\n\nIt should be said that the hypothesis that excludes\nthe collinear case $\\dim E=1$ is only required to ensure\nthat action minimizing curves do not suffer collisions.\nThe avoidance of collisions is thus assured by the celebrated\nMarchal's Theorem that we state below in Sect. \\ref{s-var.setting}.\nThe collinear case could eventually be analyzed\nin the light of the results obtained by Yu and Zhang \\cite{YuZha}.\n\nTheorem \\ref{thm-princ} should be compared with that obtained\nby the authors in \\cite{MadVen} which concerns completely parabolic motions.\nWe recall that completely parabolic motions (as well as total collisions)\nhave a very special asymptotic behaviour.\nIn his work of 1918 \\cite{Cha1},\nChazy proves that the normalized configuration\nmust approximate the set of normal central configurations.\nUnder a hypothesis of non-degeneracy,\nhe also deduces the convergence to a particular central configuration. \nThis hypothesis is always satisfied in the three body problem.\nHowever,\na first counterexample with four bodies in the plane\nwas founded by Palmore \\cite{Pal},\nallowing thus the possibility of motions\nwith infinite spin (see Chenciner \\cite{Che1} p.281).\n\nIn all the cases, Chazy's Theorem prevents arbitrary limit shapes\nfor completely parabolic motions as well as for total collisions.\nIn this sense,\nlet us mention for instance the general result by Shub \\cite{Shu}\non the localisation of central configurations,\nshowing that they are isolated from the diagonals.\n\nWe should also mention that the confinement of the\nasymptotic configuration to the set of central configurations,\nboth for completely parabolic motions and for total collisions,\nextends to homogeneous potentials of degree $\\alpha\\in (-2,0)$.\nFor these potentials the mutual distances must grow like $t^{2\/(2-\\alpha)}$ in\nthe parabolic case, and must decay like $\\abs{t-t_0}^{2\/(2-\\alpha)}$\nin the case of a total collision at time $t=t_0$.\nOn the other hand,\nit is known that potentials giving rise to strong forces near collisions\ncan present motions of total collision with non-central asymptotic configurations.\nWe refer the reader to the comments on the subject by Chenciner in \\cite{Che3}\nabout the Jacobi-Banachiewitz potential, and to Arredondo et al. \\cite{ArPeChSt}\nfor related results on the dynamics of total collisions in the case of\nSchwarzschild and Manev potentials. \n\n\nLet us say that there is another natural way to prove the existence of hyperbolic motions, \nusing the fact that the Newtonian force vanishes when all mutual distances diverge.\nWe could call these motions \\emph{almost linear}.\nThe way to do that is as follows.\nSuppose first that $(x_0,a)\\in \\Omega\\times\\Omega$\nis such that the half-straight line given by $\\bar{x}(t)=x_0+ta$, $t>0$\nhas no collisions ($\\bar{x}(t)\\in\\Omega$ for all $t>0$).\nConsider now the motion $x(t)$ with initial condition\n$x(0)=x_0$ and $\\dot x(0)=\\alpha a$ for some positive constant $\\alpha$.\nIt is not difficult to prove that, for $\\alpha>0$ chosen big enough,\nthe trajectory $x(t)$ is defined for all $t>0$, and moreover,\nit is a hyperbolic motion with limit velocity $b\\in\\Omega$ close to $\\alpha a$.\nIn particular,\nthe limit shape of such a motion can be obtained\nas close as we want from the shape of $a$.\n\nThe previous construction is unsatisfactory for several reasons.\nFirst, we do not get exactly the desired limit shape but a close one.\nThis approximation can be made as good as we want,\nbut we lose the control of the energy constant $h$ of the motion,\nwhose order of magnitude is that of $\\alpha^2$.\nSecondly,\nit is not possible to apply this method when the half-straight line\n$\\bar{x}$ presents collisions.\nFor instance this is the case if we take $a=z_0-x_0$\nfor any choice of $z_0\\in E^N\\setminus\\Omega$.\nFinally,\neven if the homogeneity of the potential can be exploited\nto find a new hyperbolic motion\nwith a prescribed positive energy constant,\nand the same limit shape,\nwe lose the control on the initial configuration.\nIndeed,\nif $x$ is a hyperbolic motion defined for all $t\\geq 0$\nwith energy constant $h$,\nthen the motion $x_\\lambda$ defined by\n$x_\\lambda(t)=\\lambda\\,x(\\lambda^{-3\/2}t)$\nis still hyperbolic with energy constant $\\lambda^{-1}h$.\nMoreover, the limit shapes of $x$ and $x_\\lambda$ are the same,\nbut $x_\\lambda(0)=\\lambda x(0)$ meaning that\nthe initial configuration is dilated by the factor $\\lambda$.\n\n\n\n\n\n\n\\subsection{Other expansive motions}\n\\label{s-other}\n\nHyperbolic motions are part of the family of\n\\emph{expansive motions} which we define now.\nIn order to classify them,\nas well as for further later uses,\nwe summarize below a set of well-known facts\nabout the possible evolutions of the motions\nin the Newtonian $N$-body problem.\n\n\\begin{definition}\n[Expansive motion]\nA motion $x:[0,+\\infty)\\to \\Omega$ is said to be expansive\nwhen all the mutual distances diverge.\nThat is, when $r_{ij}(t)\\to+\\infty$ for all $i<j$.\nEquivalently, the motion is expansive if $U(t)\\to 0$.\n\\end{definition}\n\nWe will see that there are three well defined classes of expansive motions. \nFirst of all we must observe that,\nsince we $U(t)\\to 0$ implies $\\norm{\\dot x(t)}\\to\\sqrt{2h}$,\nexpansive motions can only occur with $h\\geq 0$.\n\nIn his pioneering work,\nJean Chazy proposed a classification of motions in terms of their final evolution.\nIn the Keplerian case there is only one distance function to consider,\nand the three classes of motions are elliptic, parabolic and hyperbolic.\nExtending the analysis for $N\\geq 3$,\nhe introduced several hybrid classes of motions,\nsuch as hyperbolic-elliptical in which some distances diverge and others remain bounded.\nIn his attempt to achieve a full classification,\nhe obtains the theoretical possibility of complex behaviours\nsuch as the so-called oscillatory motions or the superhyperbolic motions,\nsee Saari and Xia \\cite{SaaXia}.\nAfter the works of Chazy, and for quite some time,\nspecialists have doubted the existence of such motions\nbecause of his complex and paradoxical appearance. \nThe same can be said about the existence of pseudo-collision\nsingularities, which, as is well known, are impossible if $N=3$.\n\nLet us say that the existence results of oscillatory motions goes\nback to the work of Sitnikov \\cite{Sit} for the spatial restricted\nthree-body problem.\nThen, the main idea in this paper was extended to\nthe unrestricted problem by Alekseev\n(see Moser \\cite{Mos} for a more detailed explanation of this\nand other related developments).\nSitnikov's ideas were undoubtedly very important\nfor the construction of the first example of a motion\nwith a pseudo-collision singularity with five bodies by Xia \\cite{Xia}.\nWith respect to superhyperbolic motions we must say that,\nalthough there are no known examples of them,\nthey exist at least in a weak sense\nfor the collinear four-body problem\n(with regularisation of binary collisions) \\cite{SaaXia}.\n\nAs we will see, to achieve the proof of the announced results,\nit will be crucial to show that certain motions that will be obtained\nare not superhyperbolic,\nand that they do not suffer collisions nor pseudo-collisions.\n\nWe need to introduce two functions which play an important role\nin the classical description of the dynamics.\nFor a given motion, these two functions are\n\\[\nr(t)=\\min_{i<j}r_{ij}(t)\\quad \\text{ and }\\quad\nR(t)=\\max_{i<j}r_{ij}(t)\\,\n\\]\nthe minimum and the maximum separation between the bodies\nat time $t$.\nWe now recall some  facts concerning the possible behaviours\nof the trajectories as $t\\to +\\infty$ in terms of the behaviours\nof these functions.\n\nWe start by fixing some notation and making some remarks.\n\n\\begin{notation}\nGiven positive functions $f$ and $g$,\nwe will write $f\\approx g$ when the quotient of them\nis bounded between two positive constants.\n\\end{notation}\n\n\\begin{remark}\nIt is easy to see that $r\\approx U^{-1}$.\nMoreover, \n$R^2\\approx I_G$ where $I_G$  denotes the moment of inertia\nwith respect to the center of mass $G$ of the configuration.\nTo see this it suffices to write $I_G$\nin terms of the mutual distances.\n\\end{remark}\n\n\\begin{remark}\n\\label{rmk-configur.measure}\nThe function $\\mu=U\\,I_G\\,^{1\/2}$ is homogeneous\nof degree zero.\nSome authors call this function the\n\\emph{configurational measure}.\nAccording to the previous remark we have $\\mu\\approx R\\,r^{-1}$.\n\\end{remark}\n\n\\begin{remark}\nBy K\u00f6nig's decomposition we have that $I=I_G+M\\norm{G}_E^2$\nwhere $M$ is the total mass of the system.\nTherefore, using the Largange-Jacobi identity $\\ddot I=4h+2U$ we deduce that,\nif $h>0$ and the center of mass is at rest,\nthen $R(t)>At$ for some constant $A>0$.\n\\end{remark}\n\n\n\\begin{theorem*}[1922, Chazy \\cite{Cha2} pp. 39 -- 49]\nLet $x(t)$ be a motion with energy constant $h>0$ and defined for all $t>t_0$.\n\n\\begin{enumerate}\n\\item[(i)] The limit\n\\[\\lim_{t\\to +\\infty}R(t)\\,r(t)^{-1}=L\\in [1,+\\infty]\\]\nalways exists.\n\n\\item[(ii)] If $L<+\\infty$ then there is a configuration $a\\in\\Omega$,\nand some function $P$, which is analytic in a neighbourhood of $(0,0)$,\nsuch that for every $t$ large enough we have\n\\[x(t)=ta-\\log(t)\\,\\nabla U(a)+P(u,v)\\]\nwhere $u=1\/t$ and $v=\\log(t)\/t$.\n\\end{enumerate}\n\\end{theorem*}\n\nAs Chazy pointed out, surprisingly Poincar\u00e9 made the mistake of \nomitting the $\\log(t)$ order term in his\n\\emph{``M\u00e9thodes Nouvelles de la M\u00e9canique C\u00e9leste\"}.\n\nSubsequent advances in this subject were recorded much later,\nwhen Chazy's results on final evolutions were included\nin a more general description of motions.\nFrom this development we must recall the following theorems.\nNotice that none of them make assumptions\non the sign of the energy constant $h$.\n\n\\begin{theorem*}[1967, Pollard \\cite{Pol}]\nLet $x$ be a motion defined for all $t>t_0$.\nIf $r$ is bounded away from zero then we have that\n$R=O(t)$ as $t\\to +\\infty$.\nIn addition $R(t)\/t\\to +\\infty$ if and only if $r(t)\\to 0$.\n\\end{theorem*}\n\nThis leads to the following definition.\n\n\\begin{definition} A motion is said to be superhyperbolic when\n\\[\\limsup_{t\\to +\\infty}\\;R(t)\/t=+\\infty.\\]\n\\end{definition}\n\nA short time later it was proven that,\neither the quotient $R(t)\/t\\to +\\infty$,\nor $R=O(t)$ and the system expansion can be described more accurately.\n\n\\begin{theorem*}[1976, Marchal-Saari \\cite{MarSaa}]\nLet $x$ be a motion defined for all $t>t_0$.\nThen either $R(t)\/t \\to +\\infty$ and $r(t)\\to 0$,\nor there is a configuration $a\\in E^N$ such that $x(t)=ta+O(t^{2\/3})$.\nIn particular, for superhyperbolic motions the quotient $R(t)\/t$ diverges.\n\\end{theorem*}\n\nOf course this theorem does not provide much information\nin some cases, for instance if the motion is bounded then\nwe must have $a=0$.\nOn the other hand,\nit admits an interesting refinement concerning the\nthe behaviour of the subsystems.\nMore precisely,\nwhen $R(t)=O(t)$ and the configuration $a$ given by the theorem\nhas collisions the system decomposes naturally into subsystems,\nwithin which the distances between the bodies\ngrow at most like $t^{2\/3}$.\nConsidering the internal energy of each subsystem,\nMarchal and Saari (Ibid, Theorem 2 and corollary 4 pp.165-166)\ngave a decription of the possible dynamics\nthat can occur within the subsystems.\nFrom these results we can easily deduce the following.\n\n\\begin{theorem*}[1976, Marchal-Saari \\cite{MarSaa}]\nSuppose that $x(t)=ta+O(t^{2\/3})$ for some $a\\in E^N$,\nand that the motion is expansive.\nThen, for each pair $i<j$ such that $a_i=a_j$ we have $r_{ij}\\approx t^{2\/3}$.\n\\end{theorem*}\n\nNotice that we can always consider the \\emph{internal motion}\nof the system, that is, looking at the relative positions\nof the bodies with respect to their center of mass.\nThis gives a new motion with the same distance functions.\nMoreover,\nthe internal motion of an expansive motion is also expansive.\n\nAll the previous considerations allow us to classify expansive motions\naccording to the asymptotic order of growth of the distances between the bodies.\nSince an expansive motion is not superhyperbolic,\nwe can assume that it is of the form $x(t)=ta+O(t^{2\/3})$ for some $a\\in E^N$.\nMoreover, we can assume that the center of mass is at rest,\nmeaning that $G(a)=0$.\nWe get then the following three types.\n\n\\begin{enumerate}\n\\item[(H) ] \\emph{Hyperbolic} :\n$a\\in\\Omega$, and $r_{ij}\\approx t$ for all $i<j$\n\\item[(PH)] \\emph{Partially hyperbolic} :\n$a\\in E^N\\setminus\\Omega$ but $a\\neq 0$.\n\\item[(P) ] \\emph{Completely parabolic} :\n$a=0$, and $r_{ij}\\approx t^{2\/3}$ for all $i<j$.\n\\end{enumerate}\n\nLet $h_0$ be the energy constant of the above defined\ninternal motion.\nIt is clear that the first two types can only occur if $h_0>0$,\nwhile the third requires $h_0=0$.\n\nFinally,\nwe observe that Chazy's Theorem applies in the first two cases .\nIn these cases,\nthe limit shape of $x(t)$ is the shape of the configuration $a$\nand moreover,\nwe have $L<+\\infty$ if and only if $x$ is hyperbolic.\nOf course if $h_0>0$ and $L=+\\infty$ then\neither the motion is partially hyperbolic or it is not expansive.\n\n\n\n\n\n\n\n\n\\subsection{The geometric viewpoint}\n\\label{s-geom.view}\n\nWe explain now the geometric formulation\nand the geometrical meaning of this work\nwith respect to the Jacobi-Maupertuis metrics associated\nto the positive energy levels.\nSeveral technical details concerning these metrics are given\nin Sect. \\ref{s-jm.dist}.\nThe boundary notions are also discussed in Sect. \\ref{s-busemann}.\nIt may be useful for the reader to keep in mind\nthat reading this section can be postponed to the end.\n\nWe recall that for each $h\\geq 0$, the Jacobi-Maupertuis metric\nof level $h$ is a Riemannian metric defined\non the open set of configurations without collisions $\\Omega$.\nMore precisely,\nit is the metric defined by $j_h=2(h+U)\\,g_m$,\nwhere $g_m$ is the Euclidean metric in $E^N$\ngiven by the mass inner product.\nOur main theorem has a stronger version\nin geometric terms.\nActually Theorem \\ref{thm-princ} can be reformulated\nin the following way.\n\n\\begin{theorem}\\label{thm-princ.rays}\nFor any $h>0$, $p\\in E^N$ and $a\\in\\Omega$,\nthere is  geodesic ray of the Jacobi-Maupertuis metric of level $h$\nwith asymptotic direction $a$ and starting at $p$.\n\\end{theorem}\nThis formulation requires some explanations.\nThe Riemannian distance $d_h$ in $\\Omega$ is defined as usual\nas the infimum of the length functional among all the\npiecewise $C^1$ curves in $\\Omega$ joining two given points.\nWe will prove that $d_h$ can be extended\nto a distance $\\phi_h$ in $E^N$,\nwhich is a metric completion of $(\\Omega,d_h)$,\nand which also we call the Jacobi-Maupertuis distance.\nMoreover, we will prove that $\\phi_h$ is precisely the action\npotential defined in Sect. \\ref{s-var.setting}.\n\nThe minimizing geodesic curves can then be defined\nas the isometric immersions of compact intervals\n$[a,b]\\subset\\mathbb{R}$ within $E^N$.\nMoreover, we will say that a curve $\\gamma:[0,+\\infty)\\to E^N$\nis a geodesic ray\nfrom $p\\in E^N$, if $\\gamma(0)=p$ and each restriction\nto a compact interval is a minimizing geodesic.\nTo deduce this geometric version of our main theorem\nit will be enough to observe that the obtained\nhyperbolic motions can be reparametrized\ntaking the action as parameter to obtain geodesic rays.\n\nWe observe now the following interesting implication of\nChazy's Theorem.\n\\begin{remark}\n\\label{rmk-Chazy.implic}\nIf two given hyperbolic motions have the same asymptotic\ndirection, then they have a bounded difference.\nIndeed,\nif $x$ and $y$ are hyperbolic motions with the same asymptotic\ndirection, then the two unbounded terms\nof the Chazy's asymptotic development of $x$ and $y$ also agree.\n\\end{remark}\n\n\nWe recall that the Gromov boundary of a geodesic space\nis defined as the quotient set of the set of geodesic rays\nby the equivalence that identifies rays that are kept\nat bounded distance.\nFrom the previous remark,\nwe can deduce that two geodesic rays with asymptotic direction\ngiven by the same configuration $a\\in\\Omega$\ndefine the same point at the Gromov boundary.\n\n\\begin{notation}\nLet $\\phi_h:E^N\\times E^N\\to\\mathbb{R}^+$ be the Jacobi-Maupertuis\ndistance for the energy level $h\\geq 0$\nin the full space of configurations.\nWe will write $\\mathcal{G}_h$ for the corresponding Gromov boundary.\n\\end{notation}\n\nThe proof of the following corollary is given in Sect. \\ref{s-jm.dist}.\n\n\\begin{corollary}\\label{cor-Gr.boundary}\nIf $h>0$, then each class in $\\Omega_1=\\Omega\/\\mathbb{R}^+$\ndetermines a point in $\\mathcal{G}_h$ which is composed\nby all geodesic rays with asymptotic direction in this class.\n\\end{corollary}\n\n\nOn the other hand,\nif instead of the arc length we parametrize the geodesics\nby the dynamical parameter,\nthen it is natural to question the existence\nof non-hyperbolic geodesic rays.\nWe do not know if there are partially hyperbolic geodesic rays. \nNor do we know if a geodesic ray should be an expansive motion. \n\nIn what follows we denote $\\norm{v}_h$\nfor the norm  of $v\\in T\\Omega$ with respect to the metric $j_h$,\nand $\\norm{p}_h$ the dual norm of an element $p\\in T^*\\Omega$.\nIf $\\gamma:(a,b)\\to\\Omega$ is a geodesic\nparametrized by the arc length, then\n\\[\\norm{\\dot\\gamma(s)}_h^2=\n2(h+U(\\gamma(s))\\,\\norm{\\dot\\gamma(s)}^2=1\\]\nfor all $s\\in (a,b)$.\nTaking into account that $U\\approx r^{-1}$ we see that\nthe parametrization of motions as geodesics\nleads to slowed evolutions over passages near collisions.\nWe also note that for expansive geodesics we have\n$\\norm{\\dot\\gamma(s)}\\to 1\/\\sqrt{2h}$.\n\nFinally we make the following observations about the\nHamilton-Jacobi equation that we will solve in the weak sense.\nFirst, the equation (\\ref{HJh}) , that explicitly reads\n\\[\\frac{1}{2}\\norm{d_xu}^2-U(x)=h\\]\ncan be written in geometric terms, precisely as the eikonal equation\n\\[\n\\norm{d_xu}_h=\\frac{1}{\\sqrt{2(h+U(x))}}\\,\\norm{d_xu}=1\n\\]\nfor the Jacobi-Maupertuis metric.\nOn the other hand,\nthe solutions will be obtained as limits of weak subsolutions,\nwhich  can be viewed as $1$-Lipschitz functions for the\nJacobi-Maupertuis distance.\nWe will see that the set of viscosity subsolutions\nis the set of functions\n$u:E^N\\to\\mathbb{R}$ such that $u(x)-u(y)\\leq \\phi_h(x,y)$\nfor all $x,y\\in E^N$.\n\n\n\n\n\n\n\n\\section{Viscosity solutions of the Hamilton-Jacobi equation}\n\\label{s-HJ}\n\n\n\nThe \\emph{Hamiltonian} $H$ is defined over\n$T^*E^N\\simeq E^N\\times (E^*)^N$ as usual by\n\\[\nH(x,p)=\\frac{1}{2}\\norm{p}^2-U(x)\n\\]\nand taking the value $H(x,p)=-\\infty$\nwhenever the configuration $x$ has collisions.\nHere the norm is the dual norm with respect to the mass product,\n that is,\nfor $p=(p_1,\\dots,p_N)\\in (E^*)^N$\n\\[\n\\norm{p}^2=\nm_1^{-1}\\,\\norm{p_1}^2+\\dots+m_N^{-1}\\,\\norm{p_N}^2\\,,\n\\]\nthus in terms of the positions of the bodies\nequation (\\ref{HJh}) becomes\n\\[H(x,d_xu)=\n\\sum_{i=1}^N\\frac{1}{2\\,m_i}\\norm{\\frac{\\partial u}{\\partial r_i}}^2-\n\\;\\sum_{i<j}\\frac{m_im_j}{r_{ij}}\\; = h\\,.\\]\nAs is known,\nthe method of characteristics for this type of equations\nconsists in reducing the problem to the resolution\nof an ordinary differential equation,\nwhose solutions are precisely the characteristic curves.\nOnce these curves are determined,\nwe can obtain solutions by integration along these curves,\nfrom a cross section in which the solution value is given.\nOf course,\nhere the characteristics are precisely the solutions\nof the $N$-body problem and can not be computed.\nOur method will be the other way around:\nfirst we build a solution as a limit of subsolutions,\nand then we find characteristic curves\nassociated with that solution.\n\nWe will start by recalling\nthe notion of viscosity solution in our context.\nThere is an extremely wide literature on viscosity solutions due to\n the great diversity of situations in which they can be applied.\nFor a general and introductory presentation the books of Evans\n \\cite{Eva1} and Barles \\cite{Bar} are recommended.\nFor a broad view on the Lax-Oleinik semigroups\nwe suggest references \\cite{Ber,Eva2, Fat}.  \n\n\\begin{definition}[Viscosity solutions]\nWith respect to the Hamilton-Jacobi equation (\\ref{HJh}),\nwe say that a continuous function $u:E^N\\to\\mathbb{R}$ is a\n\\begin{enumerate}\n\\item \\emph{viscosity \\bf{subsolution}},\nif for any $\\psi\\in C^1(E^N)$ and for any configuration $x_0$\nat which $u-\\psi$ has a local maximum we have\n$H(x_0,d_{x_0}\\psi)\\leq h$.\n\n\\item \\emph{viscosity \\bf{supersolution}},\nif for any $\\psi\\in C^1(E^N)$ and for any configuration $x_0$\nat which $u-\\psi$ has a local minimum we have\n$H(x_0,d_{x_0}\\psi)\\geq h$.\n\n\\item \\emph{viscosity \\bf{solution}},\nas long as is both a subsolution and a supersolution.\n\\end{enumerate}\n\\end{definition}\n\n\\begin{remark}\nIt is clear that we get the same notions by taking test functions\n$\\psi$ defined on open subsets of $E^N$.\n\\end{remark}\n\n\\begin{remark}\nThe notion of viscosity solution is a generalization\nof the notion of classical solution.\nIndeed, if $u\\in C^1(E^N)$\nsatisfies the Hamilton-Jacobi equation everywhere,\nthen $u$ is a viscosity solution\nsince we can take $\\psi=u$ as a test function.\n\\end{remark}\n\nIf $u\\in C^0(E^N)$ is a viscosity solution,\nthen we have $H(x,d_xu)=h$\nat any point where $u$ is differentiable.\nThis follows from the fact that for any $C^0$ function $u$,\nthe differentiability at $x_0\\in E^N$\nimplies the existence of $C^1$ functions\n$\\psi^-$ and $\\psi^+$ such that $\\psi^-\\leq u \\leq \\psi^+$ and\n$\\psi^-(x_0)=u(x_0)=\\psi^+(x_0)$.\nAs we will see (Lemma \\ref{lema-visc.subsol.locLip}),\nin our case viscosity subsolutions are locally Lipschitz\nover the open and dense set $\\Omega\\subset E^N$\nof configurations without collisions.\nTherefore by Rademacher's Theorem\nthey are differentiable almost everywhere.\nBut, as is well known to the reader familiar with the subject,\nbeing a viscosity solution is a much more demanding property\nthan satisfying the equation almost everywhere.\n\n\n\\begin{remark}\nWe note that the participation of the unknown $u$\nin equation (\\ref{HJh}) is only through the derivatives $d_xu$.\nTherefore the set of classical solutions\nis preserved by addition of constants.\nAlso note that the same applies for the set of\nviscosity subsolutions and the set of viscosity supersolutions.\n\\end{remark}\n\nFrom now on,\nwe will use of the powerful interaction between\nthe Hamiltonian view of dynamics and the Lagrangian view.\nThe Hamilton-Jacobi equation provides a great bridge\nbetween the symplectic aspects of dynamics\nand the variational properties of trajectories.\n\nOnce the Lagrangian action is defined,\nwe will characterize the set of viscosity subsolutions\nas the set of functions satisfying a property of domination\nwith respect to the action.\nThen, the next step will be to prove the equicontinuity\nof the family of viscosity subsolutions\nby finding an estimate for an action potential.\n\n\n\n\n\\subsection{Action potentials and viscosity solutions} \n\\label{s-var.setting}\n\n\n\nThe \\emph{Lagrangian} is defined on\n$TE^N\\simeq E^N\\times E^N$ fiberwise\nas the convex dual of the Hamiltonian, that is\n\\[\nL(x,v)=\\sup\\set{p(v)-H(x,p)\\mid p\\in (E^*)^N}\n\\]\nor equivalently,\n\\[\nL(x,v)=\\frac{1}{2}\\norm{v}^2 + U(x)\\,,\n\\]\nso in particular it takes the value $L(x,v)=+\\infty$\nif $x$ has collisions.\nThe Lagrangian action will be considered\non absolutely continuous curves,\nand its value could be infinite.\nWe will use the following notation.\nFor $x,y\\in E^N$ and $\\tau>0$, let\n\\[\n\\mathcal{C}(x,y,\\tau)=\n\\set{\\gamma:[a,b]\\to E^N \\mid\\gamma(a)=\nx,\\,\\gamma(b)=y,\\,b-a=\\tau}\n\\]\nbe the set of absolutely continuous curves\ngoing from $x$ to $y$ in time $\\tau$,\nand\n\\[\n\\mathcal{C}(x,y)=\\bigcup_{\\tau>0}\\mathcal{C}(x,y,\\tau)\\,.\n\\]\nThe Lagrangian action of a curve $\\gamma\\in\\mathcal{C}(x,y,\\tau)$\nwill be denoted\n\\[\n\\mathcal{A}_L(\\gamma)=\\int_a^b L(\\gamma,\\dot\\gamma)\\,dt=\n\\int_a^b \\tfrac{1}{2}\\norm{\\dot\\gamma}^2+U(\\gamma)\\,dt\n\\]\n\nIt is well known that Tonelli's Theorem\non the lower semicontinuity of the action for convex Lagrangians\nextends to this setting.\nA proof can for instance be found in \\cite{daLMad} (Theorem 2.3).\nIn particular we have, for any pair of configurations $x,y\\in E^N$,\nthe existence of curves achieving the minimum value\n\\[\n\\phi(x,y,\\tau)=\n\\min\\set{\\mathcal{A}_L(\\gamma)\\mid \\gamma\\in\\mathcal{C}(x,y,\\tau)}\n\\]\nfor any $\\tau>0$.\nWhen $x\\neq y$ there also are curves reaching the minimum\n\\[\n\\phi(x,y)=\\min\\set{\\mathcal{A}_L(\\gamma)\\mid \\gamma\\in\\mathcal{C}(x,y)}\n=\\min\\set{\\phi(x,y,\\tau)\\mid \\tau>0}\n\\]\nIn the case $x=y$ we have\n$\\phi(x,x)=\\inf\\set{\\mathcal{A}_L(\\gamma)\\mid \\gamma\\in\\mathcal{C}(x,y)}=0$.\nWe call these functions on $E^N\\times E^N$ respectively\nthe \\emph{fixed time action potential} and the\n\\emph{free time} (or \\emph{critical}) \\emph{action potential}.\n\nAccording to the Hamilton's principle of least action,\nif a curve $\\gamma:[a,b]\\to E^N$ is a minimizer of the Lagrangian\naction in $\\mathcal{C}(x,y,\\tau)$ then $\\gamma$ satisfy Newton's\nequations at every time $t\\in [a,b]$ in which $\\gamma(t)$\nhas no collisions, i.e. whenever $\\gamma(t)\\in\\Omega$.\n\nOn the other hand,\nit is easy to see that there are curves\nboth with isolated collisions and finite action.  \nThis phenomenon,\nalready noticed by Poincar\u00e9 in \\cite{Poi}, prevented the use\nof the direct method of the calculus of variations\nin the $N$-body problem for a long time. \n\nA big breakthrough came from Marchal,\nwho gave the main idea needed to prove the following theorem.\nComplete proofs of this and more general versions were\nestablished by Chenciner \\cite{Che1}\nand  by Ferrario and Terracini \\cite{FerTer}.\n\n\\begin{theorem*}[2002, Marchal \\cite{Mar}]\nIf $\\gamma\\in\\mathcal{C}(x,y)$ is defined on some interval $[a,b]$,\nand satisfies $\\mathcal{A}_L(\\gamma)=\\phi(x,y,b-a)$,\nthen $\\gamma(t)\\in\\Omega$ for all $t\\in (a,b)$.\n\\end{theorem*}\nThanks to this advance,\nthe existence of countless periodic orbits has been established\nusing variational methods.\nAmong them, the celebrated three-body figure eight\ndue to Chenciner and Montgomery \\cite{CheMon}\nis undoubtedly the most representative example,\nalthough it was discovered somewhat before.\nMarchal's Theorem was also used to prove the nonexistence\nof entire free time minimizers \\cite{daLMad},\nor in geometric terms,\nthat the zero energy level has no straight lines.\nThe proof we provide below for our main result\ndepends crucially on Marchal's Theorem.\nOur results can thus be considered as a new application\nof Marchal's Theorem, this time in positive energy levels.\n\nWe must also define for $h>0$ the\n\\emph{supercritical action potential} as the function \n\\[\n\\phi_h(x,y)=\n\\inf\\set{\\mathcal{A}_{L+h}(\\gamma)\\mid \\gamma\\in\\mathcal{C}(x,y)}=\n\\inf\\set{\\phi(x,y,\\tau)+h\\tau\\mid \\tau>0}.\n\\]\n\nFor the reader familiar with the Aubry-Mather theory,\nthis definition should be reminiscent of the supercritical\naction potentials used by Ma\u00f1\u00e9 to define the critical value\nof a Tonelli Lagrangian on a compact manifold. \n\nAs before we prove\n(see Lemma \\ref{lema-JM.geod.complet} below),\nnow for $h>0$,\nthat given any pair of different configurations $x,y\\in E^N$,\nthe infimum in the definition of $\\phi_h(x,y)$\nis achieved by some curve $\\gamma\\in\\mathcal{C}(x,y)$,\nthat is, we have $\\phi_h(x,y)=\\mathcal{A}_{L+h}(\\gamma)$.\nIt follows that if $\\gamma$ is defined in $[0,\\tau]$,\nthen $\\gamma$ also minimizes $\\mathcal{A}_L$ in $\\mathcal{C}(x,y,\\tau)$\nand by Marchal's Theorem we conclude that $\\gamma$\navoid collisions,\ni.e. $\\gamma(t)\\in\\Omega$ for every $t\\in (0,\\tau)$.\n\n\n\\subsubsection{Dominated functions and viscosity subsolutions}\n\nLet us fix $h>0$\nand take a $C^1$ subsolution $u$ of $H(x,d_xu)=h$,\nthat is, such that $H(x,d_xu)\\leq h$ for all $x\\in E^N$.\nNotice now that,\nsince for any absolutely continuous curve\n$\\gamma:[a,b]\\to E^N$ we have\n\\[\nu(\\gamma(b))-u(\\gamma(a))=\n\\int_a^b d_{\\gamma}u(\\dot\\gamma)\\,dt\\,,\n\\]\nby Fenchel's inequality we also have\n\\[\nu(\\gamma(b))-u(\\gamma(a))\\leq\n\\int_a^b L(\\gamma,\\dot\\gamma)+\nH(\\gamma,d_{\\gamma}u)\\;dt\\;\\leq\n\\;\\mathcal{A}_{L+h}(\\gamma)\\,.\n\\]\nTherefore we can say that if $u$ is a $C^1$ subsolution,\nthen\n\\[\nu(x)-u(y)\\leq\n\\mathcal{A}_{L+h}(\\gamma)\n\\]\nfor any curve\n$\\gamma\\in\\mathcal{C}(x,y)$.\nThis motivates the following definition.\n\n\\begin{definition}[Dominated functions]\nWe said that $u\\in C^0(E^N)$ is dominated by $L+h$,\nand we will denote it by $u\\prec L+h$,\nif we have\n\\[\nu(y)-u(x)\\leq\n\\phi_h(x,y)\\quad\\text{ for all }\\quad x,y\\in E^N.\n\\]\n\\end{definition}\n\nThus we know that $C^1$ subsolutions are dominated functions.\nWe prove now the well-known fact that dominated functions\nare indeed viscosity subsolutions.\n\n\\begin{proposition}\n\\label{prop-dom.are.visc.ssol}\nIf $u\\prec L+h$ then $u$ is a viscosity subsolution of (\\ref{HJh}).\n\\end{proposition}\n\n\\begin{proof} \nLet $u\\prec L+h$ and consider a test function $\\psi\\in C^1(E^N)$.\nAssume that $u-\\psi$ has a local maximum\nat some configuration $x_0\\in E^N$.\nTherefore,\nfor all $x\\in E^N$ we have $\\psi(x_0)-\\psi(x) \\leq u(x_0)-u(x)$.\n\nOn the other hand,\nthe convexity and superlinearity of the Lagrangian\nimplies that there is a unique $v\\in E^N$ such that\n$H(x_0,d_{x_0}\\psi)=d_{x_0}\\psi (v)-L(x_0,v)$.\nTaking any smooth curve $x:(-\\delta,0]\\to E^N$\nsuch that $x(0)=x_0$ and\n$\\dot x(0)=v$ we can write, for $t\\in (-\\delta,0)$\n\\[\\frac{\\psi(x_0)-\\psi(x(t))}{-t}\\leq \\frac{u(x_0)-u(x(t))}{-t}\\leq\n\\;-\\frac{1}{t}\\;\\mathcal{A}_{L+h}\\left(x\\mid_{[t,0\\,]}\\right)\\]\nthus for $t\\to 0^-$ we get\n$d_{x_0}\\psi (v)\\leq L(x_0,v)+h$,\nthat is to say, $H(x_0,d_{x_0}\\psi)\\leq h$ as we had to prove.\n\\end{proof}\nActually, the converse can be proved.\nFor all that follows,\nwe will only need to consider dominated functions,\nand for this reason,\nit will no longer be necessary to manipulate test functions\nto verify the subsolution condition in the viscosity sense.\nHowever,\nfor the sake of completeness we give a proof of this converse.\n\nA first step is to prove that viscosity subsolutions\nare locally Lipschitz on the open, dense,\nand full measure set of configurations without collisions\n(for this we follow the book of\nBardi and Capuzzo-Dolcetta \\cite{BarCap}, Proposition 4.1, p. 62).\n\n\\begin{lemma}\n\\label{lema-visc.subsol.locLip}\nThe viscosity subsolutions of (\\ref{HJh})\nare locally Lipschitz on $\\Omega$.\n\\end{lemma}\n\n\\begin{proof}\nLet $u\\in C^0(E^N)$ be a viscosity subsolution and\nlet $z\\in\\Omega$.\nWe take a compact neighbourhood $W$ of $z$\nin which the Newtonian potential is bounded,\ni.e. such that $W\\subset\\Omega$.\nThus our Hamiltonian is coercive on $T^*W$,\nmeaning that given $h>0$ we can choose $\\rho>0$ for which,\nif $\\norm{p}>\\rho$ and $w\\in W$ then $H(w,p)>h$.\n\nWe choose now $r>0$ such that\nthe open ball $B(z,3r)$ is contained in $W$.\nLet $M=\\max\\set{u(x)-u(y)\\mid\\;x,y\\in W}$\nand take $k>0$ such that $2kr>M$.\n\nWe take now any configuration $y\\in B(z,r)$ and we define,\nin the closed ball $\\overline{B}_y=\\overline{B}(y,2r)$,\nthe function $\\psi_y(x)=u(y)+k\\norm{x-y}$.\nWe will use the function $\\psi_y$ as a test function in the open set\n$B^*_y=B(y,2r)\\setminus\\set{y}$.\nWe observe first that $u(y)-\\psi_y(y)=0$ and that\n$u-\\psi_y$ is negative in the boundary of $\\overline{B}_y$.\nTherefore the maximum of $u-\\psi_y$\nis achieved at some interior point\n$x_0\\in B(y,2r)$.\n\nSuppose that $x_0\\neq y$.\nSince $\\psi_y$ is smooth on $B^*_y$,\nand $u$ is a viscosity subsolution,\nwe must have $H(x_0,d_{x_0}\\psi_y)\\leq h$.\nTherefore we must also have $k=\\norm{d_{x_0}\\psi_y}\\leq\\rho$.\n\nWe conclude that, if we choose $k>\\rho$ such that $2rk>M$,\nthen for any $y\\in B(z,r)$\nthe maximum of $u-\\psi$ in $\\overline{B}_y$\nis achieved at $y$, meaning that $u(x)-u(y)\\leq k\\norm{x-y}$\nfor all $x\\in\\overline{B}_y$.\nThis proves that $u$ is $k$-Lipschitz on $B(z,r)$.\n\\end{proof}\n\n\\begin{remark}\n\\label{rmk-vssol.are.subsol.ae}\nBy Rademacher's Theorem, we know that any viscosity subsolution\nis differentiable almost everywhere in the open set $\\Omega$.\nIn addition, at every point of differentiability $x\\in\\Omega$\nwe have $H(x,d_xu)\\leq h$.\nTherefore, since $\\Omega$ has full measure in $E^N$,\nwe can say that viscosity subsolutions satisfies $H(x,d_xu)\\leq h$\nalmost everywhere in $E^N$.\n\\end{remark}\n\n\\begin{remark}\nWe observe that the local Lipschitz constant $k$ we have obtained\nin the proof depends, a priori,\non the chosen viscosity subsolution $u$.\nWe will see that this is not really the case.\nThis fact will result immediatly from the following proposition and\nTheorem \\ref{thm-phih.estim}.\n\\end{remark}\n\nWe can prove now that\nthe set of viscosity subsolutions of $H(x,d_xu)=h$\nand the set of dominated functions $u\\prec L+h$ coincide.\n\n\\begin{proposition}\n\\label{prop-visc.ssol.are.dom}\nIf $u$ is a viscosity subsolution of (\\ref{HJh}) then $u\\prec L+h$.\n\\end{proposition}\n\n\\begin{proof}\nLet $u:E^N\\to\\mathbb{R}$ be a viscosity subsolution.\nWe have to prove that\n\\[u(y)-u(x)\\leq \\mathcal{A}_{L+h}(\\gamma)\\quad\n\\text{ for all }x,y\\in E^N,\\;\\gamma\\in\\mathcal{C}(x,y)\\,.\\]\nWe start by showing the inequality for any segment\n$s(t)=x+t(y-x)$, $t\\in [0,1]$.\nNote first that in the case $y=x$ there is nothing to prove,\nsince the action is always positive.\nThus we can assume that $r=\\norm{y-x}>0$.\n\nWe know $H(x,d_xu)\\leq h$ is satisfied\non a full measure set $\\mathcal{D}\\subset E^N$\nin which $u$ is differentiable,\nsee Lemma \\ref{lema-visc.subsol.locLip}\nand Remark \\ref{rmk-vssol.are.subsol.ae}.\nAssuming that $s(t)\\in\\mathcal{D}$ for almost every $t\\in[0,1]$\nwe can write\n\\[\n\\frac{d}{dt}\\,u(s(t))=d_{s(t)}u\\,(y-x)\\quad\\text{ a.e. in }[0,1]\n\\]\nfrom which we deduce,\napplying Fenchel's inequality and integrating,\n\\[\nu(y)-u(x)\\leq\n\\int_0^1L(s(t),y-x)+H(s(t),d_{s(t)}u)\\;dt\\leq \\mathcal{A}_{L+h}(s)\\,.\n\\]\nOur assumption may not be satisfied.\nMoreover,\nit could even happen that all the segment\nis outside the set $\\mathcal{D}$ in which the derivatives of $u$ exist. \nThis happens for instance if $x$ and $y$ are configurations\nwith collisions and with the same colliding bodies.\nHowever Fubini's Theorem say us that our assumption is verified\nfor almost every $y\\in S_r=\\set{y\\in E^N\\mid \\norm{y-x}=r}$.\nThen \n\\[\nu(y)-u(x)\\leq \\mathcal{A}_{L+h}(s)\\quad\\text{ for almost }y\\in S_r\n\\]\nTaking into account that both $u$ and $\\mathcal{A}_{L+h}(s)$\nare continuous as functions of $y$,\nwe conclude that the previous inequality holds in fact,\nfor all $y\\in S_r$.\n\nWe remark that the same argument applies\nto any segment with constant speed,\nthat is to say, to any curve $s(t)=x+tv$, $t\\in [a,b]$.\nConcatenating these segments we deduce that the inequality\nalso holds for any piecewise affine curve\n$p\\in\\mathcal{C}(x,y)$. The proof is then achieved as follows.\n\nLet $\\gamma\\in\\mathcal{C}(x,y)$ be a curve such that\n$\\mathcal{A}_{L+h}(\\gamma)=\\phi_h(x,y)$.\nThe existence of such a curve is guaranteed by Lemma\n\\ref{lema-JM.geod.complet}.\nSince this curve is a minimizer of the Lagrangian action,\nMarchal's Theorem assures that,\nif $\\gamma$ is defined on $[a,b]$,\nthen $\\gamma(t)\\in\\Omega$ for all $t\\in(a,b)$.\nIn consequence, the restriction of $\\gamma$\nto $(a,b)$ must be a true motion.\n\nSuppose that there are no collisions at configurations\n$x$ and $y$.\nSince in this case $\\gamma$ is thus $C^1$ on $[a,b]$,\nwe can approximate it by sequence of piecewise affine curves\n$p_n\\in\\mathcal{C}(x,y)$,\nin such a way that $\\dot p_n(t)\\to\\dot\\gamma(t)$\nuniformly for $t$ over some full measure subset $D\\subset [a,b]$.\nIn order to be explicit, let us define for each $n>0$\nthe polygonal $p_n$ with vertices at configurations\n$\\gamma(a+k(b-a)n^{-1})$ for $k=0,\\dots,n$.\nThen $D$ can be taken as the complement in $[a,b]$\nof the countable set $a+\\mathbb{Q}(b-a)$. \nTherefore, we have\n$u(y)-u(x)\\leq \\mathcal{A}_{L+h}(p_n)$ for all $n\\geq 0$,\nas well as\n\\[\n\\lim_{n\\to \\infty}\\mathcal{A}_{L+h}(p_n)=\n\\mathcal{A}_{L+h}(\\gamma)=\\phi_h(x,y)\\,,\n\\]\nThis implies that $u(y)-u(x)\\leq \\phi_h(x,y)$.\nIf there are collisions at $x$ or $y$,\nthen we apply what we have proved\nto the configurations without collisions\n$x_\\epsilon=\\gamma(a+\\epsilon)$ and\n$y_\\epsilon=\\gamma(b-\\epsilon)$,\nand we get the same conclusion\ntaking the limit as $\\epsilon\\to 0$. \nThis proves that $u\\prec L+h$.\n\\end{proof}\n\n\\begin{remark}\nThe use of Marchal's Theorem in the last proof\nseems to be required by the argument.\nIn fact, the argument works well for non singular Hamiltonians\nfor which it is known \\emph{a priori} that the corresponding\nminimizers are of class $C^1$. \n\\end{remark}\n\n\\begin{notation}\nWe will denote $\\mathcal{S}_h$\nthe set of viscosity subsolutions of (\\ref{HJh}).\n\\end{notation}\n\nObserve that,\nnot only we have proved that $\\mathcal{S}_h$ is precisely the set\nof dominated functions $u\\prec L+h$,\nbut also that $\\mathcal{S}_h$ agrees with the set of functions\nsatisfying $H(x,d_xu)\\leq h$ almost everywhere in $E^N$. \n\n\\subsubsection{Estimates for the action potentials}\n\nWe give now an estimate for $\\phi_h$ which implies that\nthe viscosity subsolutions form an equicontinuous family\nof functions.\nTherefore, if we normalize subsolutions by imposing $u(0)=0$,\nthen according to the Ascoli's Theorem\nwe get to the compactness of the set of normalized subsolutions.\n\nThe estimate will be deduced from the basic estimates for\n$\\phi(x,y,\\tau)$ and $\\phi(x,y)$\nfound by the first author for homogeneous potentials\nand that we recall now.\nThey correspond in the reference\nto Theorems 1 \\& 2 and Proposition 9,\nconsidering that in the original formulation\nthe value $\\kappa=1\/2$ is for the Newtonian potential.\n\nWe will say that a given configuration $x=(r_1,\\dots,r_N)$\nis contained in a ball of radius $R>0$ if we have\n$\\norm{r_i-r_0}_E<R$ for all $1\\leq i \\leq N$\nand for some $r_0\\in E$.\n\n\\begin{theorem*}[\\cite{Mad1}]\nThere are positive constants $\\alpha_0$ and $\\beta_0$ such that,\nif $x$ and $y$ are two configurations contained\nin the same ball of radius $R>0$, then for any $\\tau>0$\n\\[\\phi(x,y,\\tau)\\leq \\;\n\\alpha_0\\; \\frac{\\;R^2}{\\tau}\\;+\\;\\beta_0\\;\\frac{\\;\\tau}{R}\\;.\\]\n\\end{theorem*}\n\nIf a configurations $y$ is close enough\nto a given configuration $x$,\nthe minimal radius of a ball containing both configurations\nis greater than $\\norm{x-y}$. \nHowever,\nthis result was successfully combined with an argument\nproviding suitable cluster partitions,\nin order to obtain the following theorem.\n\n\\begin{theorem*}[\\cite{Mad1}]\nThere are positive constants $\\alpha_1$ and $\\beta_1$ such that,\nif $x$ and $y$ are any two configurations, and $r>\\norm{x-y}$,\nthen for all $\\tau>0$\n\\begin{equation}\n\\tag{*}\n\\label{ineq-basic}\\phi(x,y,\\tau)\\leq \\;\n\\alpha_1\\; \\frac{\\;r^2}{\\tau}\\;+\\;\\beta_1\\;\\frac{\\tau}{r}\\;.\n\\end{equation}\n\\end{theorem*}\n\nNote that the right side of the inequality\nis continuous for $\\tau,\\rho>0$.\nTherefore,\nwe can replace $r$ by $\\norm{x-y}$ whenever $x\\neq y$.\n\n\\begin{remark}\n\\label{rmk-bound.phixxt}\nIf $x=y$ then the upper bound (\\ref{ineq-basic})\nholds for every $r>0$.\nChoosing $r=\\tau^{2\/3}$, we get to the upper bound\n$\\phi(x,x,\\tau)\\leq\\mu\\,\\tau^{1\/3}$ which holds for any $\\tau>0$,\nany $x\\in E^N$,\nand for the positive constant $\\mu=\\alpha_1+\\beta_1$.\n\\end{remark}\n \nTherefore we can now bound the critical potential.\nThe previous remark leads to $\\phi(x,x)=0$ for all $x\\in E^N$.\nOn the other hand,\nfor the case $x\\neq y$ we can bound $\\phi(x,y)$\nwith the bound for $\\phi(x,y,\\tau)$,\ntaking $r=\\norm{x-y}$ and $\\tau=\\norm{x-y}^{3\/2}$.\n\n\\begin{theorem*}\n[H\u00f6lder estimate for the critical action potential, \\cite{Mad1}]\nThere exist a positive constant $\\eta>0$\nsuch that for any pair of configurations\n$x,y \\in E^N$\n\\[\\phi(x,y)\\leq \\;\\eta\\;\\norm{x-y}^\\frac{1}{2}\\;.\\]\n\\end{theorem*}\n\nThese estimates for the action potentials have been used\nfirstly to prove the existence of parabolic motions\n\\cite{Mad1,MadVen} and were the starting point\nfor the study of free time minimizers \\cite{daLMad,Mad2},\nas well as their associated Busemann functions\nby Percino and S\u00e1nchez \\cite{Per, PerSan},\nand later by Moeckel, Montgomery and S\u00e1nchez \\cite{MoMoSa}\nin the planar three-body problem.\n \nFor our current purposes,\nwe need to generalize the H\u00f6lder estimate\nof the critical action potential\nin order to also include supercritical potentials.\nAs expected, the upper bound we found\nis of the form $\\xi(\\norm{x-y})$,\nwhere $\\xi:[0,+\\infty)\\to\\mathbb{R}^+$\nis such that $\\xi(r)\\approx r^\\frac{1}{2}$\nfor $r\\to 0$ and $\\xi(r)\\approx r$ for $r\\to +\\infty$.\n\n\\begin{theorem}\n\\label{thm-phih.estim}\nThere are positive constants $\\alpha$ and $\\beta$ such that,\nif $x$ and $y$ are any two configurations and $h\\geq 0$, then\n\\[\n\\phi_h(x,y)\\leq \\;\n\\left(\\alpha\\norm{x-y}+h\\;\\beta\\norm{x-y}^2\\right)^{1\/2}\\;.\n\\]\n\\end{theorem}\n\n\\begin{proof}\nWe have to bound\n$\\phi_h(x,y)=\n\\inf\\set{\\phi(x,y,t)+h\\tau\\mid\\tau>0}$.\nFix any two configurations $x$ and $y$ and let $r>\\norm{x-y}$.\nWe already know by (\\ref{ineq-basic})\nthat for any $\\tau>0$ we have\n\\begin{equation}\n\\tag{**}\n\\label{ineq-basic.h}\n\\phi(x,y,\\tau) + h\\tau\\;\\leq \\;\nA\\; \\frac{1}{\\tau}\\;+B\\;\\tau\n\\end{equation}\n\\[A=\\alpha_1\\,r^2\\quad\\text{ and }\\quad B=\\beta_1\\,r^{-1} + h\\,,\\]\n$\\alpha_1$ and $\\beta_1>0$ being two positive constants.\nSince the minimal value of the right side of inequality\n(\\ref{ineq-basic.h})\nas a function of $\\tau$ is $2(AB)^{1\/2}$ we conclude that\n\\begin{eqnarray*}\n\\phi_h(x,y)&=&\\inf\\set{\\phi(x,y,t)+h\\tau\\mid\\tau>0}\\\\\n&\\leq&\\left(\\alpha\\,r+h\\;\\beta\\,r^2\\right)^{1\/2}\n\\end{eqnarray*}\nfor\n$\\alpha=4\\,\\alpha_1\\beta_1$ and $\\beta=4\\,\\alpha_1$.\nBy continuity,\nwe have that the last inequality also holds for $r=\\norm{x-y}$\nas we wanted to prove.\n\\end{proof}\n\n\\begin{corollary} \\label{comp-visc-subsol}\n\\label{coro-visc.ssol.comp}\nThe set of viscosity subsolutions\n$\\mathcal{S}^0_h=\\set{u\\in\\mathcal{S}_h\\mid u(0)=0}$\nis compact for the topology of the uniform convergence\non compact sets.\n\\end{corollary}\n\n\\begin{proof}\nBy Propositions \\ref{prop-dom.are.visc.ssol} and\n\\ref{prop-visc.ssol.are.dom}\nwe know that $u\\in\\mathcal{S}_h$ if and only if $u\\prec L+h$.\nThus by Theorem \\ref{thm-phih.estim} we have that,\nfor any $u\\in\\mathcal{S}_h$, and for all $x,y\\in E^N$, \n\\[u(x)-u(y)\\leq \\phi_h(x,y)\\leq \\xi(\\norm{x-y})\\]\nwhere $\\xi:[0,+\\infty)\\to\\mathbb{R}^+$ is given by\n$\\xi(\\rho)=\\left(\\alpha\\,\\rho+h\\,\\beta\\,\\rho^2\\right)^{1\/2}$.\n\nSince $\\xi$ is uniformly continuous,\nwe conclude that the family of functions $\\mathcal{S}_h$\nis indeed equicontinuous.\nTherefore,\nthe compactness of $\\mathcal{S}^0_h$ is actually\na consequence of Ascoli's Theorem.\n\\end{proof}\n\n\n\n\\subsection{The Lax-Oleinik semigroup}\n\nWe recall that a solution of $H(x,d_xu)=h$\ncorresponds to a stationary solution\n$U(t,x)=u(x)-ht$ of the evolution equation\n\\[\\partial_tU+H(x,\\partial_xU)=0\\,,\\]\nfor which the Hopf-Lax formula reads\n\\[U(t,x)=\n\\inf\\set{u_0(y)+\\mathcal{A}_L(\\gamma)\\mid\ny\\in E^N,\\,\\gamma\\in\\mathcal{C}(y,x,t)}\\,.\\]\nIn a wide range of situations,\nthis formula provides the \\emph{unique}\nviscosity solution satisfying the initial condition $U(0,x)=u_0(x)$.\nUsing the action potential we can also write the formula as\n\\[U(t,x)=\\inf\\set{u_0(y)+\\phi(y,x,t)\\mid y\\in E^N}.\\]\nIf the initial data $u_0$ is bounded,\nthen $U(t,x)$ is clearly well defined and bounded.\nIn our case, we know that solutions will not be bounded,\nthus we need a condition ensuring that the function\n$y\\mapsto u_0(y)+\\phi(y,x,t)$ is bounded by below.\nAssuming $u_0\\prec L+h$ we have the lower bound\n\\[u_0(x)-ht \\leq u_0(y)+\\phi(y,x,t)\\]\nfor all $t>0$  and all $x\\in E^N$,\nbut this is in fact an equivalent formulation\nfor the domination condition\n$u_0\\prec L+h$, that is to say $u\\in\\mathcal{S}_h$.\n\n\\begin{definition}\n[Lax-Oleinik semigroup] The backward\\footnote{\nThe \\emph{forward} semigroup is defined in a similar way,\nsee \\cite{Eva2}.\nThis other semigroup gives the opposite solutions\nof the reversed Hamiltonian $\\tilde{H}(x,p)=H(x,-p)$.\nIn our case the Hamiltonian is reversible,\nmeaning that $\\tilde{H}=H$.}\nLax-Oleinik semigroup is the map\n$T:[0,+\\infty)\\times \\mathcal{S}_h\\to\\mathcal{S}_h$,\ngiven by $T(t,u)=T_tu$, where\n\\[\nT_tu(x)=\\inf\\set{u(y)+\\phi(y,x,t)\\mid y\\in E^N}\n\\]\nfor $t>0$, and $T_0u=u$.\n\\end{definition}\n\nObserve that $u\\prec L+h$ if and only if\n$u\\leq T_tu+ht$ for all $t>0$.\nAlso,\nwe note that $T_tu-u\\to 0$ as $t\\to 0$, uniformly in $E^N$.\nThis is clear since for all $x\\in E^N$ and $t>0$ we have\n$-ht\\leq T_tu(x)-u(x)\\leq \\phi(x,x,t)\\leq \\mu\\,t^{1\/3}$,\nwhere the last inequality is justified by Remark\n\\ref{rmk-bound.phixxt}.\n\nIt is not difficult to see that $T$ defines an action on $\\mathcal{S}_h$,\nthat is to say, that the semigroup property $T_t\\circ T_s=T_{t+s}$\nis always satisfied.\nThus the continuity at $t=0$ spreads throughout all the domain.\n\nOther important properties of this semigroup are the\n\\emph{monotonicity},\nthat is to say, that $u\\leq v$ implies $T_tu\\leq T_tv$,\nand the \\emph{commutation with constants},\nsaying that for every constant $k\\in\\mathbb{R}$,\nwe have $T_t(u+k)=T_tu+k$.\n\nThus,\nfor $u\\in\\mathcal{S}_h$ and $s,t>0$ we can write\n$T_su\\leq T_s(T_tu+ht)=T_t(T_su)+ht$,\nwhich implies that we have $T_su\\in\\mathcal{S}_h$ for all $s>0$.\n\n\\begin{definition}\n[Lax-Oleinik quotient semigroup]\nThe semigroup $(T_t)_{t\\geq 0}$\ndefines a semigroup $(\\hat{T}_t)_{t\\geq 0}$\non the quotient space $\\hat{\\mathcal{S}}_h=\\mathcal{S}_h\/\\mathbb{R}$,\ngiven by $\\hat{T}_t[u]=[T_tu]$.\n\\end{definition}\n\n\\begin{proposition}\n\\label{prop-LO.fixed.points}\nGiven $h\\geq 0$ and $u\\in\\mathcal{S}_h$ we have that,\n$[u]\\in\\hat{\\mathcal{S}}_h$ is a fixed point of $(\\hat{T}_t)_{t\\geq 0}$\nif and only if\nthere is $h'\\in [0,h]$ such that $T_tu=u-h't$ for all $t\\geq 0$.\n\\end{proposition}\n\n\\begin{proof}\nThe sufficiency of the condition is trivial.\nIt is enough then to prove that it is necessary.\nThat $[u]$ is a fixed point of $\\hat{T}$ means that we have\n$\\hat{T}_t[u]=[u]$ for all $t>0$.\nThat is to say, there is a function $c:\\mathbb{R}^+\\to\\mathbb{R}^+$ such that\n$T_tu=u+c(t)$ for each $t\\in\\mathbb{R}^+$.\nFrom the semigroup property, we can easily deduce that\nthe function $c(t)$ must be additive,\nmeaning that $c(t+s)=c(t)+c(s)$\nfor all $t,s\\geq 0$.\nMoreover,\nthe continuity of the semigroup implies the continuity of $c(t)$.\nAs it is well known,\na continuous and additive function from $\\mathbb{R}^+$ into itself is linear,\ntherefore we must have $c(t)=c(1)t$.\nNow, since $u\\leq T_tu+ht$ for all $t\\in \\mathbb{R}^+$,\nwe get $0\\leq c(1)+h$.\nOn the other hand, since $u\\prec L-c(1)$\nand $\\mathcal{S}_h=\\emptyset$ for $h<0$, hence $-c(1)\\geq 0$.\nWe conclude that $c(t)=-h't$ for some $h'\\in [0,h]$.\n\\end{proof}\n\n\n\\subsubsection{Calibrating curves and supersolutions}\n\nWe finish this section by relating the fixed points\nof the quotient Lax-Oleinik semigroup and\nthe viscosity supersolutions of (\\ref{HJh}).\nThis relationship is closely linked\nto the existence of certain minimizers,\nwhich will ultimately allow us to obtain\nthe hyperbolic motions we seek.\n\n\\begin{definition}\n[calibrating curves]\nLet $u\\in\\mathcal{S}_h$ be a given subsolution.\nWe say that a curve $\\gamma:[a,b]\\to E^N$\nis an \\emph{$h$-calibrating}\ncurve of $u$,\nif $u(\\gamma(b))-u(\\gamma(a))=\\mathcal{A}_{L+h}(\\gamma)$.\n\\end{definition}\n\n\\begin{definition}\n[h-minimizers]\nA curve $\\gamma:[a,b]\\to E^N$\nis said to be an \\emph{$h$-minimizer} if\nit verifies $A_{L+h}(\\gamma)=\\phi_h(\\gamma(a),\\gamma(b))$.\n\\end{definition}\n\n\\begin{remark}\n\\label{rmk-hcalib.hmin}\nAs we have see,\nthe fact that $u\\in\\mathcal{S}_h$ is characterized by $u\\prec L+h$.\nTherefore for all $x,y\\in E^N$ we have\n\\[\nu(x)-u(y)\\leq \\phi_h(x,y)\\leq \\mathcal{A}_{L+h}(\\gamma)\n\\]\nfor any $\\gamma\\in\\mathcal{C}(x,y)$.\nIt follows that every $h$-calibrating curve of $u$\nis an $h$-minimizer.\n\\end{remark}\n\nIt is easy to prove that restrictions of $h$-calibrating curves\nof a given subsolution $u\\in\\mathcal{S}_h$\nare themselves $h$-calibrating curves of $u$.\nThis is also true, and even more easy to see, for $h$-minimizers.\nBut nevertheless,\nthere is a property valid for the calibrating curves\nof a given subsolution but which is not satisfied in general\nby the minimizing curves.\nThe concatenation of two calibrating curves is again calibrating.\n\n\\begin{lemma}\n\\label{lema-concat.calib}\nLet $u\\in\\mathcal{S}_h$.\nIf $\\gamma_1\\in\\mathcal{C}(x,y)$ and $\\gamma_2\\in\\mathcal{C}(y,z)$\nare both $h$-calibrating curves of $u$,\nand $\\gamma\\in\\mathcal{C}(x,z)$ is a concatenation of\n$\\gamma_1$ and $\\gamma_2$,\nthen $\\gamma$ is also an $h$-calibrating curve of $u$.\n\\end{lemma}\n\n\\begin{proof}\nWe have $u(y)-u(x)=\\mathcal{A}_{L+h}(\\gamma_1)$,\nand $u(z)-u(y)=\\mathcal{A}_{L+h}(\\gamma_2)$.\nAdding both equations we get $u(z)-u(x)=\\mathcal{A}_{L+h}(\\gamma)$.\n\\end{proof}\n\nWe give now a criterion for a subsolution to be a viscosity solution.\nFrom here on, a curve defined on a noncompact interval will be said\n$h$-calibrating if all its restrictions to compact intervals are too.\nIn the same way we define $h$-minimizers\nover noncompact intervals.\n\nWe start by proving a lemma on calibrating curves of subsolutions.\n\\begin{lemma}\n\\label{lema-no.test.col}\nLet $u\\in\\mathcal{S}_h$, and let $\\gamma:[a,b]\\to E^N$ be an\n$h$-calibrating curve of $u$.\nIf $x_0=\\gamma(b)$ is a configuration with collisions,\nthen there is no Lipschitz function\n$\\psi$ defined on a neighbourhood of $x_0$\nsuch that $\\psi\\le u$ and $\\psi(x_0)=u(x_0)$.\n\\end{lemma}\n\n\\begin{proof}\nSince our system is autonomous,\nwe can assume without loss of generality that $b=0$.\nThus the $h$-calibrating property of $\\gamma$ says that\nfor every $t\\in [a,0]$\n\\[\n\\int_t^0 \\tfrac{1}{2}\\norm{\\dot\\gamma}^2\\,dt\\,+\n\\int_t^0 U(\\gamma)\\,dt\\,+ \\,h\\abs{t}=\n\\mathcal{A}_{L+h}(\\gamma\\mid_{[t,0]})=u(x_0)-u(\\gamma(t))\\,.\n\\]\nOn the other hand, if $\\psi\\leq u$ is a $k$-Lipschitz function\non a neighbourhood of $x_0$ such that $\\psi(x_0)=u(x_0)$\nthen we also have, for $t$ close enough to $0$,\n\\[\nu(x_0)-u(\\gamma(t))\\leq\n\\psi(x_0)-\\psi(\\gamma(t))\\leq\nk\\norm{\\gamma(t)-x_0}.\n\\]\nTherefore we also have\n\\[\n\\int_{t}^0\\norm{\\dot\\gamma}^2\\,dt\\leq\\,2k\\norm{\\gamma(t)-x_0}.\n\\]\nNow, applying Cauchy-Schwarz we can write\n\\[\n\\int_{t}^0\\norm{\\dot\\gamma}\\,dt\\leq\n\\abs{t}^{1\/2}\\left(\\int_{t}^0\\norm{\\dot\\gamma}^2\\,dt\\right)^{1\/2}\\]\nand thus we deduce that\n\\[\n\\norm{\\gamma(t)-x_0}^2\\leq\n\\left(\\int_{t}^0\\norm{\\dot\\gamma}\\,dt\\right)^2\\leq \n\\,2k\\norm{\\gamma(t)-x_0}\\,\\abs{t}\n\\]\nhence that\n\\[\n\\norm{\\gamma(t)-x_0}\\leq\n\\,2k\\abs{t}.\n\\]\nFinally, since\n\\[\n\\int_{t}^0U(\\gamma)\\,dt\\leq u(x_0)-u(\\gamma(t))\\leq\n\\,k\\norm{\\gamma(t)-x_0}\n\\]\nwe conclude that\n\\[\n\\int_{t}^0U(\\gamma)\\,dt\\leq\n\\,2k^2\\abs{t}.\n\\]\nTherefore, dividing by $\\abs{t}$ and taking the limit for $t\\to 0$\nwe get $U(x_0)\\leq 2k^2$.\nThis proves that $x_0$ has no collisions.\n\\end{proof}\n\n\\begin{proposition}\n\\label{prop-criterion.visc.sol}\nIf $u\\in\\mathcal{S}_h$ is a viscosity subsolution of (\\ref{HJh}), and\nfor each $x\\in E^N$ there is at least one $h$-calibrating curve\n$\\gamma:(-\\delta,0]\\to E^N$  with $\\gamma(0)=x$,\nthen $u$ is in fact a viscosity solution.\n\\end{proposition}\n\n\\begin{proof}\nWe only have to prove that $u$ is a viscosity supersolution.\nThus we assume that $\\psi\\in C^1(E^N)$ and $x_0\\in E^N$\nare such that $u-\\psi$ has a local minimum in $x_0$.\nWe must prove that $H(x_0,d_{x_0}\\psi)\\geq h$.\nFirst of all, we exclude the possibility that $x_0$\nis a configuration with collisions.\nTo do this, it suffices to apply Lemma \\ref{lema-no.test.col},\ntaking the locally Lipschitz function $\\psi+u(x_0)-\\psi(x_0)$.\n\nLet now $\\gamma:(-\\delta,0]\\to E^N$ with $\\gamma(0)=x_0$\nand $h$-calibrating.\nThus for $t\\in(-\\delta,0]$\n\\[\n\\int_t^0L(\\gamma,\\dot\\gamma)\\,dt\\,-\\,ht\n=u(x_0)-u(\\gamma(t))\n\\]\nand also, given that $x_0$ is a local minimum of $u-\\psi$,\nfor $t$ close enough to $0$\n\\[\nu(x_0)-u(\\gamma(t))\\leq\n\\psi(x_0)-\\psi(\\gamma(t))\\,.\n\\]\nSince $x_0\\in\\Omega$ and $\\gamma$ is a minimizer,\nwe know that $\\gamma$ can be extended beyond $t=0$\nas solution of Newton's equation.\nIn particular $v=\\dot\\gamma(0)$ is well defined,\nand moreover, using the previous inequality we find\n\\[\nd_{x_0}\\psi(v)=\n\\;\\lim_{t\\to 0^-}\\,\\frac{\\psi(x_0)-\\psi(\\gamma(t))}{-t}\\geq\nL(x_0,v)+h\n\\]\nwhich implies, by Fenchel's inequality,\nthat $H(x_0,d_{x_0}\\psi)\\geq h$.\n\\end{proof}\n\nThe following proposition complements the previous one.\nIt states that under a stronger condition,\nthe viscosity solution is in addition a fixed point\nof the quotient Lax-Oleinik semigroup.\n\n\\begin{proposition}\n\\label{prop-fixedLO.if.calib}\nLet $u\\in\\mathcal{S}_h$ be a viscosity subsolution of (\\ref{HJh}).\nIf for each $x\\in E^N$ there is\nan $h$-calibrating curve of $u$, say \n$\\gamma_x:(-\\infty,0]\\to E^N$,\nsuch that $\\gamma_x(0)=x$,\nthen $T_tu=u-ht$ for all $t\\geq 0$.\n\\end{proposition}\n\n\\begin{proof}\nFor each $x\\in E^N$, for $t\\geq 0$ we have\n\\[\nT_tu(x)-u(x)=\\inf\\set{u(y)-u(x)+\\phi(y,x,t)\\mid y\\in E^N} \n\\]\nthus it is clear that $T_tu(x)-u(x)\\geq -ht$\nsince we know that $u\\prec L+h$.\nOn the other hand,\ngiven that $\\gamma_x$ is  an $h$-calibrating curve of $u$,\n\\[\nu(x)-u(\\gamma_x(-t))=\\phi(\\gamma_x(-t),x,t)+ht.\n\\]\nWriting $y_t=\\gamma_x(-t)$ we have that\n$u(y_t)-u(x)+\\phi(y_t,x,t)=-ht$\nand we conclude that $T_tu(x)-u(x)\\leq -ht$.\nWe have proved that $T_tu=u-ht$ for all $t\\geq 0$.\n\\end{proof}\n\n\\begin{remark}\n\\label{rmk-inverse.sens.lamin}\nThe formulation of the previous condition can confuse a little,\nsince the calibrating curves are parametrized on negative intervals.\nHere the Lagrangian is symmetric,\nthus reversing the time of a curve always preserves the action.\nMore precisely, \ngiven an absolutely continuous curve $\\gamma:[a,b]\\to E^N$,\nif we define $\\tilde{\\gamma}$ on $[-b,-a]$\nby $\\tilde{\\gamma}(t)=\\gamma(-t)$,\nthen $\\mathcal{A}_L(\\tilde{\\gamma})=\\mathcal{A}_L(\\gamma)$.\n\nWe can reformulate the calibrating condition of the previous\nproposition in this equivalent way:\n\\emph{For each $x\\in E^N$,\nthere is a curve $\\gamma_x:[0,+\\infty)\\to E^N$ such that\n$\\gamma_x(0)=x$, and such that\n$u(x)-u(\\gamma_x(t))=\\mathcal{A}_{L+h}(\\gamma_x\\mid_{[0,t]})$\nfor all $t>0$}.\n\\end{remark}\n\\begin{remark}\nThe hypothesis of\nProposition \\ref{prop-criterion.visc.sol}\nimplies the hypothesis of\nProposition \\ref{prop-fixedLO.if.calib}.\nThis is exactly what we do in the proof of\nTheorem \\ref{thm-horofuns.have.lamin} below.\n\\end{remark}\n\n\n\n\\section{Ideal boundary of a positive energy level}\n\n\nThis section is devoted to the construction of global viscosity\nsolutions for the  Hamilton-Jacobi equations (\\ref{HJh}).\nThe method is quite similar to that developed by Gromov\nin \\cite{Gro} to compactify locally compact metric spaces\n(see also \\cite{BaGrSch}, chpt. 3).\n\n\\subsection{Horofunctions as viscosity solutions}\n\nThe underlying idea giving rise to the construction of horofunctions\nis that each point in a metric space $(X,d)$ can be identified \nwith the distance function to that point.\nMore precisely,\nthe map $X\\to C(X)$ which associates to each point $x\\in X$\nthe function $d_x(y)=d(y,x)$\nis an embedding such that for all $x_0,x_1\\in X$\nwe have $\\max\\abs{d_{x_0}(y)-d_{x_1}(y)}=d(x_0,x_1)$.\n\nIt is clear that\nany sequence of functions $d_{x_n}$ diverges if $x_n\\to\\infty$,\nthat is to say,\nif the sequence $x_n$ escapes from any compact subset of $X$. \nHowever, for a noncompact space $X$,\nthe induced embedding of $X$ into the quotient space\n$C(X)\/\\mathbb{R}$ has in general an image with a non trivial boundary.\nThis boundary can thus be considered\nas an ideal boundary of $X$.\n\nHere the metric space will be $(E^N,\\phi_h)$ with $h>0$,\nand the set of continuous functions $C^0(E^N)$\nwill be endowed with\nthe topology of the uniform convergence on compact sets.\nInstead of looking at equivalence classes of functions,\nwe will take as the representative of each class\nthe only one vanishing at $0\\in E^N$. \n\n\\begin{definition}\n[Ideal boundary]\nWe say that a function $u\\in C^0(E^N)$ is in the ideal boundary\nof level $h$ if there is a sequence of configurations $p_n$,\nwith $\\norm{p_n}\\to +\\infty$ and such that for all $x\\in E^N$\n\\[\nu(x)=\\lim_{n\\to\\infty}\\phi_h(x,p_n)-\\phi_h(0,p_n).\n\\]\nWe will denote $\\mathcal{B}_h$ the set of all these functions,\nthat we will also call horofunctions.\n\\end{definition}\n\nThe first observation is that $\\mathcal{B}_h\\neq\\emptyset$\nfor any value of $h\\geq 0$.\nThis can be seen as a consequence of the estimate for the\npotential $\\phi_h$ we proved,\nsee Theorem \\ref{thm-phih.estim}.\n\nActually for any $p\\in E^N$,\nthe function $x\\to \\phi_h(x,p)-\\phi_h(0,p)$ is in $\\mathcal{S}^0_h$,\nthe set of viscosity subsolutions vanishing at $x=0$.\nSince by Corollary \\ref{coro-visc.ssol.comp}\nwe know that $\\mathcal{S}^0_h$ is compact,\nfor any sequence of configurations $p_n$\nsuch that $\\norm{p_n}\\to +\\infty$\nthere is a subsequence\nwhich defines a function in $\\mathcal{B}_h$ as above.\n\nIt is also clear that $\\mathcal{B}_h\\subset\\mathcal{S}_h$.\nFunctions in $\\mathcal{B}_h$ are limits of functions in $\\mathcal{S}_h$,\nand this set is closed in $E^N$\neven for the topology of pointwise convergence.\nBut, since we already know that\nthe family $\\mathcal{S}_h$ is equicontinuous,\nthe convergence is indeed uniform on compact sets.\n\n\\begin{notation}\nWhen the value of $h$ is understood,\nwe will denote $u_p$ the function\ndefined by $u_p(x)=\\phi_h(x,p)$\nwhere $p$ is a given configuration.\n\\end{notation}\n\nOne fact that should be clarifying is that for any $p\\in E^N$,\nthe subsolution given by $u_p$ fails to be a viscosity solution\nprecisely at $x=p$.\nIf $x\\neq p$, then there is a minimizing curve of $\\mathcal{A}_{L+h}$\nin $\\mathcal{C}(p,x)$\n(see Lemma \\ref{lema-JM.geod.complet} below),\nand clearly this curve is $h$-calibrating of $u_p$.\nOn the other hand, there are no $h$-calibrating curves of $u_p$\ndefined over an interval $(-\\delta,0]$\nand ending at $x=p$.\nThis is because $u_p\\geq 0$, $u_p(p)=0$,\nand $h$-calibrating curves, as $h$-minimizers,\nhave strictly increasing action.\nActually, this property of the $u_p$ functions occurs\nfor all energy levels greater than or equal to the critical one,\nin a wide class of Lagrangian systems.\nThe simplest case to visualize is surely\nthe case of absence of potential energy in an Euclidean space,\nin which we have $u_p(x)=h\\,\\norm{x-p}$ and\nhis $h$-calibrating curves are segments of the half-lines\nemanating from $p$ with a constant speed (gradient curves).\n\nThis suggest that the horofunctions must be viscosity solutions,\nwhich is what we will prove now.\n\n\\begin{theorem}\n\\label{thm-horofuns.are.viscsol}\nGiven $u\\in\\mathcal{B}_h$ and $r>0$ there is,\nfor each $x\\in E^N$, some $y\\in E^N$ with $\\norm{y-x}=r$,\nand a curve $\\gamma_x\\in\\mathcal{C}(y,x)$ such that\n$u(x)-u(y)=\\mathcal{A}_{L+h}(\\gamma_x)$.\nIn particular, every function $u\\in\\mathcal{B}_h$\nis a global viscosity solution of (\\ref{HJh}).\n\\end{theorem}\n\n\\begin{proof}\nLet $u\\in\\mathcal{B}_h$, that is to say\n$u=\\lim_n(u_{p_n}-u_{p_n}(0))$\nfor some sequence of configurations $p_n$ such that\n$\\norm{p_n}\\to +\\infty$, and $u_{p_n}(x)=\\phi_h(x,p_n)$.\n\nLet $x\\in E^N$ be any configuration, and fix $r>0$.\nUsing Lemma \\ref{lema-JM.geod.complet} we get,\nfor each $n>0$, a curve $\\gamma_n\\in\\mathcal{C}(p_n,x)$\nsuch that $\\mathcal{A}_{L+h}(\\gamma_n)=\\phi_h(p_n,x)$.\nEach curve $\\gamma_n$ is thus\nan $h$-calibrating curve of $u_{p_n}$.\n\nIf $\\norm{p_n-x}>r$,\nthen the curve $\\gamma_n$ must pass through a configuration\n$y_n$ with $\\norm{y_n-x}=r$.\nExtracting a subsequence if necessary,\nwe may assume that this is the case for all $n>0$,\nand that $y_n\\to y$, with $\\norm{y-x}=r$.\nSince the arc of $\\gamma_n$ joining\n$y_n$ to $x$ also $h$-calibrates $u_{p_n}$ we can write\n\\[\nu_{p_n}(x)-u_{p_n}(y_n)=\\phi_h(y_n,x)\n\\]\nfor all $n$ big enough. We conclude that\n\\[\nu(x)-u(y)=\\lim_{n\\to\\infty}u_{p_n}(x)-u_{p_n}(y)=\\phi_h(y,x)\n\\]\nwhich proves the first statement.\nThe second one follows now from the criterion for\nviscosity solutions given in Proposition\n\\ref{prop-criterion.visc.sol}.\t\n\\end{proof}\nOur next goal is to prove that horofunctions are actually\nfixed points of the quotient Lax-Oleinik semigroup.\nWe will achieve this goal by showing the existence\nof calibrating curves allowing the use of\nProposition \\ref{prop-fixedLO.if.calib}.\nThese calibrating curves will be the key to the proof of\nthe existence of hyperbolic motions.\n\nThanks to the previous theorem\nwe can build maximal calibrating curves.\nThen, Marchal's Theorem will allow us to assert that\nthese curves are in fact true motions of the $N$-body problem.\nNext we have to prove\nthat these motions\nare defined over unbounded above time intervals,\nthat is to say,\nwe must exclude the possibility of\ncollisions or pseudocollisions.\nIt is for this reason that we will also invoke\nthe famous von Zeipel's theorem\\footnote{\nThis theorem had no major impact on the theory\nuntil it was rediscovered after at least half a century later,\nand proved to be essential for the understanding\nof pseudocollision singularities, see for instance Chenciner's\nBourbaki seminar \\cite{Che2}.\nAmong other proofs, there is a modern version due to McGehee \n \\cite{McG} of the proof originally outlined by von Zeipel.}\n that we recall now.\n\n\\begin{theorem*}\n[1908, von Zeipel \\cite{Zei}]\nLet $x:(a,t^*)\\to E^N$ be a maximal solution of the\nNewton's equations of the $N$-body problem with $t^*<+\\infty$.\nIf $\\norm{x(t)}$ is bounded in some neighbourhood of $t^*$, then\nthe limit $\\,x_c=\\lim_{t\\to t^*}x(t)$\nexists and the singularity is therefore due to collisions. \n\\end{theorem*}\n\n\n\\begin{theorem}\n\\label{thm-horofuns.have.lamin}\nIf $u\\in\\mathcal{B}_h$ then for each $x\\in E^N$ there is a curve\n$\\gamma_x:[0,+\\infty)\\to E^N$ with $\\gamma_x(0)=x$,\nand such that for all $t>0$\n\\[\nu(x)-u(\\gamma_x(t))=\\mathcal{A}_{L+h}(\\gamma_x\\mid_{[0,t]}).\n\\]\nIn particular,\nevery function $u\\in\\mathcal{B}_h$ satisfies $T_tu=u-ht$ for all $t>0$.\n\\end{theorem}\n\n\\begin{proof}\nLet us fix a configuration $x\\in E^N$.\nBy Theorem \\ref{thm-horofuns.are.viscsol} we know that\n$u$ has at least one $h$-calibrating curve\n$\\gamma:(-\\delta,0]\\to E^N$ such that $\\gamma(0)=x$.\nBy application of Zorn's Lemma\nwe get a maximal $h$-calibrating curve\nof the form $\\gamma:(t^*,0]\\to E^N$ with $\\gamma(0)=x$.\nWe will prove that $t^*=-\\infty$,\nand thus the required curve can be defined on $[0,+\\infty)$ by\n$\\gamma_x(t)=\\gamma(-t)$.\n\nSuppose by contradiction that $t^*>-\\infty$.\nSince $\\gamma$ is an $h$-minimizing curve, we know that its\nrestriction to $(t^*,0)$ is a true motion with energy constant $h$.\nEither the curve can be extended as a motion for values\nless than $t^*$, or it presents a singularity at $t=t^*$.\nIn the case of singularity, we have at $t=t^*$ either a collision,\nor a pseudocollision.\nAccording to von Zeipel's Theorem,\nin the pseudocollision case we must have\n$\\sup\\set{\\norm{\\gamma(t)}\\mid t\\in (t^*,0]}=+\\infty$.\n\nSuppose that the limit $y=\\lim_{t\\to t^*}\\gamma(t)$ exists.\nThen by Theorem \\ref{thm-horofuns.are.viscsol} we can choose\na calibrating curve $\\tilde{\\gamma}$ defined on $(-\\delta,0]$\nand such that $\\tilde{\\gamma}(0)=y$.\nThus the concatenation of $\\tilde{\\gamma}$ with $\\gamma$\ndefines a calibrating curve $\\gamma^+$ defined on\n$(t^*-\\delta,0]$ and such that $\\gamma^+(0)=x$.\nBut this contradicts the maximality of $\\gamma$.\n\nOn the other hand, if we suppose that $\\norm{\\gamma(t)}$\nis unbounded, we can choose a sequence $y_n=\\gamma(t_n)$\nsuch that $\\norm{y_n-x}\\to +\\infty$.\nLet us define $A_n=\\mathcal{A}_L(\\gamma\\mid_{[t_n,0]})$.\n\nA standard way to obtain a lower bound for $A_n$\nis by neglecting the potential term which is positive.\nThen by using  the Cauchy-Schwarz inequality we obtain that\nfor all $n>0$ we have $2\\abs{t_n}A_n\\geq \\norm{y_n-n}^2$.\nSince $\\gamma$ is $h$-minimizing we deduce that\n\\[\n\\phi_h(y_n,x)\\geq\n\\frac{\\norm{y_n-x}^2}{2\\abs{t_n}}+h\\abs{t_n}\n\\]\nfor all $n>0$.\nSince $\\norm{y_n-x}\\to +\\infty$ and $t_n\\to t^*>-\\infty$\nwe get a contradiction with the upper estimate given by Theorem\n\\ref{thm-phih.estim}.\nIndeed that theorem implies that\n$\\phi_h (y_n,x)$ is bounded above by a function which is\nof order $O(\\norm{y_n - x})$ as $\\norm{y_n-x} \\to +\\infty$,  \nwhich contradicts the displayed inequality.\n\nThe last assertion is a consequence of\nProposition \\ref{prop-fixedLO.if.calib} and\nRemark \\ref{rmk-inverse.sens.lamin}.\n\\end{proof}\n\n\n\n\\subsection{Busemann functions}\n\\label{s-busemann}\n\nWe recall that a length space $(X,d)$ is say to be a\n\\emph{geodesic space}\nif the distance between any two points is realized as the length\nof a curve joining them.\nA \\emph{ray} in $X$ is an isometric embedding\n$\\gamma:[0,+\\infty)\\to X$.\nAs we already say in Sect. \\ref{s-geom.view},\nthe Gromov boundary of a geodesic space is defined as\nthe quotient space of the set of rays of $X$ under the\nequivalence relation: $\\gamma\\sim\\gamma'$ if and only if the\nfunction given by $d(\\gamma(t),\\gamma'(t))$ on $[0,+\\infty)$\nis bounded.\n\nThere is a natural way to associate a horofunction to each ray.\nLet us write $d_p$ for the function measuring the distance to\nthe point $p\\in X$ that is, $d_p(x)=d(x,p)$.\nOnce $\\gamma$ is fixed, we define\n\\[\nu_t(x)=d_{\\gamma(t)}(x)-d_{\\gamma(t)}(\\gamma(0))\\,,\n\\quad\\text{ and }\\quad\nu_\\gamma=\\lim_{t\\to\\infty}u_t\\,.\n\\]\n\nThese horofunctions $u_\\gamma$ are called\n\\emph{Busemann functions}\nand are well defined because of\nthe geodesic characteristic property of rays.\nMore precisely, for any ray $\\gamma$ and for all $0\\leq s\\leq t$,\nwe have $d(\\gamma(t),\\gamma(s))=t-s$,\nhence that $u_t\\leq u_s$.\nMoreover, \nit is also clear that $u_t\\geq -d_{\\gamma(0)}$,\nwhich implies that $u_\\gamma\\ge -d_{\\gamma(0)}$.\nWe also note that $u_\\gamma=\\lim_n u_{t_n}$ whenever\n$(t_n)_{n>0}$ is a sequence such that $t_n\\to\\infty$.\n\nIt is well known that under some hypothesis on $X$ we have that,\nfor any two equivalent rays $\\gamma\\sim\\gamma'$,\nthe corresponding Busemann functions are the same\nup to a constant, that is $[u_\\gamma]=[u_{\\gamma'}]$.\nTherefore in these cases a map is defined\nfrom the Gromov boundary into the ideal boundary,\nand it is thus natural to ask about the injectivity and the surjectivity\nof this map.\nHowever, the following simple and enlightening example\nshows a geodesic space in which there are equivalent rays\n$\\gamma\\sim\\gamma'$ for which\n$[u_\\gamma]\\neq [u_{\\gamma'}]$.\n\n\\begin{example}\n[The infinite ladder]\nWe define $X\\subset\\mathbb{R}^2$ as the union of the two straight lines\n$\\mathbb{R}\\times\\set{-1,1}$ with the segments $\\mathbb{Z}\\times [-1,1]$,\nsee figure \\ref{ladder}. \n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=1]{ladder.pdf}\n\\caption{The infinite ladder.} \n\\label{ladder}\n\\end{figure}\n\nWe endow $X$ with the length distance induced by the standard\nmetric in $\\mathbb{R}^2$.\nIt is not difficult to see that every ray in $X$\nis eventually of the form\n$x(t)=(\\pm t+c, \\pm 1)$.\nEach possibility for the two signs determines one of the four\ndifferent Busemann functions which indeed compose the\nideal boundary.\nTherefore,\n there are four points in the ideal boundary of $X$,\nwhile there is only two classes of rays\ncomposing the Gromov boundary of $X$.\n\\end{example}\n\nLet us return to the context of the $N$-body problem,\nthat is to say,\nlet us take as metric space the set of configurations $E^N$,\nwith the action potential $\\phi_h$ as the distance function.\nActually $(E^N,\\phi_h)$ becomes a length space, and $\\phi_h$\ncoincides with the length distance of the Jacobi-Maupertuis\nmetric when restricted to $\\Omega$.\nProofs of all these facts are given in Sect. \\ref{s-jm.dist}.\nWe are interested in the study of the ideal and Gromov\nboundaries of this space,\nin particular we need to understand the rays in\nthis space having prescribed asymptotic direction.\nAs we will see, they will be found as calibrating curves\nof horofunctions in a special class.\n\n\\begin{definition}\n[Directed horofunctions]\nGiven a configuration $a\\neq 0$ we define the set\nof horofunctions directed by $a$ as the set\n\\[\n\\mathcal{B}_h(a)=\n\\set{u\\in\\mathcal{B}_h\\mid\nu=\\lim_n(u_{p_n}-u_{p_n}(0))\\,,\\;\np_n=\\lambda_na+o(\\lambda_n),\\;\n\\lambda_n\\to +\\infty}.\n\\]\n\\end{definition}\n\\begin{remark}\nTheorem \\ref{thm-phih.estim} implies,\nin a manner identical to the proof of\nCorollary \\ref{comp-visc-subsol},\nthat $\\mathcal{B}_h(a)\\neq\\emptyset$.\n\\end{remark}\n  \n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=1.1]{HyperKepler2.pdf}\n\\caption{Calibrating curves of a hyperbolic Busemann function\n$u(x)=\\lim_n (\\phi_h(x,na)-\\phi_h(0,na))$ in the Kepler problem.} \n\\label{HyperKepler2}\n\\end{figure}\n\nThe following theorem is the key\nfor the proof of Theorem \\ref{thm-princ}\nand its proof is given in Sect. \\ref{s-proofs.main}.\n\n\\begin{theorem}\n\\label{thm-calib.direct.horo}\nLet $a\\in\\Omega$ and $u\\in\\mathcal{B}_h(a)$.\nIf $\\gamma:[0,+\\infty)\\to E^N$ satisfies\n\\[\nu(\\gamma(0))-u(\\gamma(t))=\\mathcal{A}_{L+h}(\\gamma\\mid_{[0,t]})\n\\]\nfor all $t>0$,\nthen $\\gamma$ is a hyperbolic motion of energy $h$\nwith asymptotic direction $a$.\n\\end{theorem}\n\nWe can thus deduce the following corollary,\nwhose proof is a very easy application of the Chazy's Theorem on\nhyperbolic motions, see Remark \\ref{rmk-Chazy.implic}.\n\\begin{corollary}\n\\label{coro-calib.bus.equiv}\nIf $a\\in\\Omega$ and $u\\in \\mathcal{B}_h(a)$ then\nthe distance between any two $h$-calibrating curves for $u$\nis bounded on their common domain.\n\\end{corollary}\n\nWe can also apply Theorem \\ref{thm-calib.direct.horo} to deduce\nthat calibrating curves of a hyperbolic Busemann function are\nmutually asymptotic hyperbolic motions.\n\\begin{corollary}\n\\label{coro-calib.of.busemann}\nIf $\\gamma$ is an hyperbolic $h$-minimizer,\nand $u_\\gamma$ its associated Busemann function,\nthen all the calibrating curves of $u_\\gamma$ are hyperbolic\nmotions with the same limit shape and direction as $\\gamma$.\n\\end{corollary}\n\n\\begin{proof}\nSince $\\gamma$ is hyperbolic, we know that\nthere is a configuration without collisions $a\\in\\Omega$\nsuch that $\\gamma(t)=ta+o(t)$ as $t\\to +\\infty$.\nTaking the sequence \n$p_n=\\gamma(n)$ we have that $p_n=na+o(n)$,\nand also that\n\\[\nu_\\gamma-u_\\gamma(0)=\n\\lim_{n\\to +\\infty}[u_{p_n}-u_{p_n}(0)].\n\\]\nThis implies that $u_\\gamma-u_\\gamma(0)\\in\\mathcal{B}_h(a)$,\nhence that $u_\\gamma$ is a viscosity solution and\nmoreover, Theorem \\ref{thm-calib.direct.horo} says that\nthe calibrating curves of $u_\\gamma$ all of the form $ta+o(t)$.\nOn the other hand, clearly $\\gamma$ calibrates $u_\\gamma$\nsince for any $0\\leq s \\leq t$ we have that\n\\[\nu_{\\gamma(t)}(\\gamma(s))-u_{\\gamma(t)}(\\gamma(0))=\n-\\phi_h(\\gamma(0),\\gamma(s)),\n\\]\nwhich in turn implies, taking the limit for $t\\to +\\infty$, that\n\\[\nu_\\gamma(\\gamma(0))-u_\\gamma(\\gamma(s))=\n-u_\\gamma(\\gamma(s))=\n\\phi_h(\\gamma(0),\\gamma(s)).\\]\n\\end{proof}\n\n\n\n\\section{Proof of the main results on hyperbolic motions}\n\n\n\nThis part of the paper contains the proofs that so far it has been\npostponed for different reasons.\nIn the first part we deal with several lemmas and technical results,\nafter which we complete the proof of the main results in Sect.\n\\ref{s-proofs.main}.\n\n\n\\subsection{Chazy's Lemma}\n\\label{s-Chazy.lema}\n\nThe first lemma that we will prove states that the set\n$\\mathcal{H}^+\\subset T\\Omega$ of initial conditions in the\nphase space given rise to hyperbolic motions is an open set.\nMoreover,\nit also says that the map defined in this set\nwhich gives the asymptotic velocity in the future\nis continuous. \nThis is precisely what in Chazy's work appears as\n\\emph{continuit\u00e9 de l'instabilit\u00e9}.\nWe give a slightly more general version for homogeneous\n potentials of degree $-1$,\nbut the proof works the same for potentials\nof negative degree in any Banach space.\n\nIntuitively what happens is that,\nif an orbit is sufficiently close to some given hyperbolic motion,\nthen after some time the bodies will be so far away each other,\nthat the action of the gravitational forces\nwill not be able to perturb their velocities too much.\n\n\\begin{lemma}\n\\label{lema-cont.limitshape}\nLet $U:E^N\\to\\mathbb{R}\\cup\\set{+\\infty}$ be a homogeneous potential\nof degree $-1$ of class $C^2$ on the open set\n$\\Omega=\\set{x\\in E^N\\mid U(x)<+\\infty}$.\nLet $x:[0,+\\infty)\\to\\Omega$ be a given solution of\n$\\ddot x=\\nabla U(x)$ satisfying $x(t)=ta+o(t)$\nas $t\\to +\\infty$ with $a\\in\\Omega$.\n\nThen we have:\n\\begin{enumerate}\n\\item[(1)] The solution $x$ has asymptotic velocity $a$,\nmeaning that\n\\[\n\\lim_{t\\to+\\infty}\\dot x(t)=a\\,.\n\\]\n\\item[(2)] (Chazy's continuity of the limit shape)\nGiven $\\epsilon>0$,\nthere are constants $t_1>0$ and $\\delta>0$ such that,\nfor any maximal solution $y:[0,T)\\to\\Omega$ satisfying\n$\\norm{y(0)-x(0)}<\\delta$ and\n$\\norm{\\dot y(0)-\\dot x(0)}<\\delta$,\nwe have:\n\\begin{enumerate}\n\\item[(i)] $T=+\\infty$, $\\norm{y(t)-ta}<t\\epsilon$ for all $t>t_1$,\nand moreover\n\\item[(ii)] there is $b\\in\\Omega$ with $\\norm{b-a}<\\epsilon$ \nfor which $y(t)=tb+o(t)$.\n\\end{enumerate}\n\\end{enumerate}\n\\end{lemma}\n\n\\begin{proof}\nLet $0<\\rho<\\epsilon$ such that the closed ball\n$B=\\overline B(a,\\rho)$ is contained in $\\Omega$.\nLet $k=\\max \\set{\\norm{\\nabla U(z)}\\mid z\\in B}$, and choose\n$t_0>0$ in such a way that for any $t\\geq t_0$ we have\n$\\norm{x(t)-ta}<t\\rho$. Therefore, since $\\nabla U$ is\nhomogeneous of degree $-2$, for each $t\\geq t_0$ we have\n$t^{-1}x(t)\\in B$ and\n\\[\n\\norm{\\nabla U(x(t))} \\leq\nt^{-2}\\norm{\\nabla U(t^{-1}x(t))} \\leq\nkt^{-2}\\,.\n\\]\nThus, for $t_0<t_1<t_2$ we can write\n\\[\n\\norm{\\dot x(t_2)-\\dot x(t_1)} \\leq\n\\int_{t_1}^{t_2}\\norm{\\nabla U(x(s))}ds \\leq\n\\int_{t_1}^{+\\infty}ks^{-2}\\,ds =\n\\frac{k}{t_1}\n\\]\nfrom which we deduce that $\\dot x(t)$ has a limit for $t\\to +\\infty$.\nThis limit can not be other than $\\lim \\dot x= a$,\nsince otherwise we would have that the\nderivative of $x(t)-ta$ has a non null limit contradicting\nthe hypothesis $x(t)-ta=o(t)$.\n\nWriting $x_1=x(t_1)$ and $\\dot x_1=\\dot x(t_1)$, we see that\nwe can fix $t_1>t_0$ large enough such that\n\\[\n\\norm{x_1-t_1a}<t_1\\,\\frac{\\rho}{3}\\,.\n\\]\nIf in addition $t_1>3k\/\\rho$ we also have\n\\[\n\\norm{\\dot x_1-a}\\leq \\frac{k}{t_1}<\\frac{\\rho}{3}\\,.\n\\]\n\nOn the other hand, since the vector field $X(x,v)=(v,\\nabla U(x))$\nis of class $C^1$, it defines a local flow on $T\\Omega$.\nLet us denote by $(x_0,\\dot x_0)$ the initial condition\n$(x(0),\\dot x(0))$ of $x(t)$.\nWe can choose $\\delta>0$ such that, for any choice of\n$(y_0,\\dot y_0)\\in T\\Omega$ verifying\n$\\norm{y_0-x_0}<\\delta$ and $\\norm{\\dot y_0-\\dot x_0}<\\delta$,\nthe maximal solution $y:[0,T)\\to\\Omega$\nwith $y(0)=y_0$  and $\\dot y(0)=\\dot y_0$\nsatisfies the following two conditions: $T>t_1$, and\n\\[\n\\norm{y_1-t_1a}<t_1\\,\\frac{\\rho}{3},\n\\;\\textrm{ and }\\;\n\\norm{\\dot y_1-a}<\\frac{\\rho}{3}\n\\]\nwhere $y_1=y(t_1)$ and $\\dot y_1=\\dot y(t_1)$.\n\nNow, assume that $t\\in[t_1,T)$ is such that $y(s)\\in sB$\nfor all $s\\in[t_1,t]$.\nAs before we have $\\norm{\\dot y(s)-\\dot y_1}\\leq k\/t_1<\\rho\/3$,\nand thus $\\norm{\\dot y(s)-a}<2\\rho\/3$.\nTherefore we can deduce that\n\\begin{eqnarray*}\n\\norm{y(t)-ta}&\\leq& \\norm{y_1-t_1a}\n                              +\\int_{t_1}^t\\norm{\\dot y(s)-a}\\,ds\\\\\n &<& t_1\\,\\frac{\\rho}{3} +(t-t_1)\\frac{2\\rho}{3}<t\\rho\n\\end{eqnarray*}\nSince the last inequality is strict, in fact we have proved that\n$y(s)\\in s\\interior{B}$ for all $s\\in [t_1,t]$,\nwhere $\\interior{B}$ denotes the open ball $B(a,\\rho)$.\nThus, the set of $t\\in[t_1,T)$ such that $y(s)\\in sB$\nfor all $s\\in[t_1,t]$ is an open subset, and easily we conclude\nthat we must have $y(t)\\in t\\interior{B}$ for all $t\\in[t_1,T)$.\n\n$T=+\\infty$.\nOtherwise $K=\\cup_{t\\in[0,T]}\\,tB$ would be compact and\n$(y(t),\\dot y(t))\\in K\\times B$ for all $t\\in[t_1,T)$,\nwhich is impossible for a maximal solution.\nBy the same argument used for the motion $x$,\nwe have that $\\dot y(t)$ has a limit $b\\in B$.\nIn particular $\\norm{b-a}<\\epsilon$ and $y(t)=tb+o(t)$.\n\\end{proof}\n\n\n\n\\subsection{Existence and properties of h-minimizers}\n\nThe following lemma ensures that for $h>0$,\nthe length space $(E^N,\\phi_h)$ is indeed geodesically convex.\n\nActually the lemma give us minimizing curves\nfor any pair of configurations, even with collisions,\nand it follows from Marchal's Theorem that\nsuch curves avoid collisions at intermediary times.\nThe proof is a well-known argument based on the\nTonelli's Theorem for convex Lagrangians,\ncombined with Fatou's Lemma\nfor dealing with the singularities of the potential.\n\n\\begin{lemma}[Existence of minimizers for $\\phi_h$]\n\\label{lema-JM.geod.complet}\nGiven $h>0$ and $x\\neq y\\in E^N$ there is a curve\n$\\gamma\\in\\mathcal{C}(x,y)$  such that\n$\\mathcal{A}_{L+h}(\\gamma)=\\phi_h(x,y)$.\n\\end{lemma}\n\nWe need to introduce before some notation\nand make a simple remark that we will use several times.\nIt is worth noting that the remark applies whenever we consider\na system defined by a potential $U>0$.\n\n\\begin{notation}\nGiven $h\\geq 0$, for $x,y\\in E^N$ and $\\tau>0$ we will write\n\\[\n\\Phi_{x,y}(\\tau)=\\tfrac{1}{2}\\norm{x-y}^2\\tau^{-1}+h\\,\\tau\\,.\n\\]\n\\end{notation}\n\n\\begin{remark}\n\\label{rmk-usual.bound}\nGiven $h\\geq 0$ we have, for any pair of configurations\n$x,y\\in E^N$ and any $\\tau>0$\n\\[\n\\phi(x,y,\\tau)+ h \\tau \\;\\geq\\; \\Phi_{x,y}(\\tau).\n\\]\nIndeed, given any pair of configurations\n$x,y\\in E^N$ and for any $\\sigma\\in\\mathcal{C}(x,y,\\tau)$,\nthe Cauchy-Schwarz inequality implies\n\\[\n\\norm{x-y}^2\\leq\n(\\;\\int_a^b\\norm{\\dot \\sigma}\\,dt\\;)^2\\leq\n\\;\\tau\\,\\int_a^b\\norm{\\dot \\sigma}^2\\,dt\\,,\n\\]\nthus, since $U>0$,\n\\[\n\\mathcal{A}_L(\\sigma)>\n\\tfrac{1}{2}\\int_a^b\\norm{\\dot \\sigma}^2\\,dt \\geq\n\\tfrac{1}{2}\\,\\norm{x-y}^2\\tau^{-1}.\n\\]\nThis justifies the assertion,\nsince this lower bound does not depend on the curve $\\sigma$.\n\\end{remark}\n\n\n\\begin{proof}\n[Proof of Lemma \\ref{lema-JM.geod.complet}]\nLet $x,y\\in E^N$ be two given configurations, with $x\\neq y$.\nWe start by taking a minimizing sequence of\n$\\mathcal{A}_{L+h}$ in $\\mathcal{C}(x,y)$, that is to say,\na sequence of curves $(\\sigma_n)_{n> 0}$ such that\n\\[\n\\lim_{n\\to\\infty}\\mathcal{A}_{L+h}(\\sigma_n)=\\phi_h(x,y)\\,.\n\\]\nThen from this minimizing sequence we build a new one,\nbut this time composed by curves with the same domain.\nTo do this, we first observe that,\nif each $\\sigma_n$ is defined on an interval $[0,\\tau_n]$,\nthen by the previous remark we know that\n\\[\n\\mathcal{A}_{L+h}(\\sigma_n)\\geq\n\\phi(x,y,\\tau_n)+h\\tau_n \\geq\n\\Phi_{x,y}(\\tau_n)\n\\]\nwhere $\\Phi_{x,y}$ is the above defined function.\nSince clearly $\\Phi_{x,y}$ is a proper function on $\\mathbb{R}^+$,\nwe deduce that\n$0<\\liminf \\tau_n\\leq \\limsup \\tau_n<+\\infty$,\nand therefore we can suppose without loss of generality\nthat $\\tau_n\\to\\tau_0$ as $n\\to\\infty$.\nIt is not difficult to see that reparametrizing linearly\neach curve $\\sigma_n$ over the\ninterval $[0,\\tau_0]$ we get a new minimizing sequence.\nMore precisely, for each $n>0$ the reparametrization is\nthe curve\n$\\gamma_n:[0,\\tau_0]\\to E^N$ defined by\n$\\gamma_n(t)=\\sigma_n(\\tau_n\\tau_0^{-1}\\, t)$.\nComputing the action of the curves $\\gamma_n$ we get\n\\[\n\\int_0^{\\tau_0}\\tfrac{1}{2}\\norm{\\dot\\gamma_n}^2\\,dt=\n\\tau_n\\tau_0^{-1}\n\\int_0^{\\tau_n}\\tfrac{1}{2}\\norm{\\dot\\sigma_n}^2\\,dt\n\\]\nand\n\\[\n\\int_0^{\\tau_0} U(\\gamma)\\,dt=\n\\tau_0\\tau_n^{-1}\n\\int_0^{\\tau_n} U(\\sigma)\\,dt\n\\]\nthus we have that\n\\[\n\\lim_{n\\to\\infty}\\mathcal{A}_{L+h}(\\gamma)=\n\\lim_{n\\to\\infty}\\mathcal{A}_{L+h}(\\sigma)=\n\\phi_h(x,y).\n\\]\n\nOn the other hand, It is easy to see that a uniform bound\nfor the action of the family of curves $\\gamma_n$\nimplies the equicontinuity of the family.\nMore precisely,\nif the bound $\\mathcal{A}_L(\\gamma_n)\\leq \\tfrac{1}{2}\\,M^2$\nholds for all $n>0$,\nthen using Cauchy-Schwarz inequality as in Remark\n\\ref{rmk-usual.bound} we have\n\\[\n\\norm{\\gamma_n(t)-\\gamma_n(s)}\\leq\nM\\abs{t-s}^\\frac{1}{2}\n\\]\nfor all $t,s\\in [0,t_0]$ and for all $n>0$.\nThus by Ascoli's Theorem we can assume that\nthe sequence $(\\gamma_n)$ converges uniformly to\na curve $\\gamma\\in\\mathcal{C}(x,y,\\tau_0)$.\nFinally, we apply Tonelli's Theorem for convex Lagrangians to get\n\\[\n\\int_0^{\\tau_0}\\tfrac{1}{2}\\norm{\\dot\\gamma}^2\\,dt\\;\\leq\\;\n\\liminf_{n\\to\\infty}\n\\int_0^{\\tau_0}\\tfrac{1}{2}\\norm{\\dot\\gamma_n}^2\\,dt\n\\]\nand Fatou's Lemma to obtain that\n\\[\n\\int_0^{\\tau_0} U(\\gamma)\\,dt\\;\\leq\\;\n\\liminf_{n\\to\\infty}\n\\int_0^{\\tau_0} U(\\gamma_n)\\,dt.\n\\]\nTherefore $\\mathcal{A}_L(\\gamma)\\leq \\phi(x,y,\\tau_0)$,\nwhich is only possible if the equality holds,\nand thus we deduce that $\\mathcal{A}_{L+h}(\\gamma)=\\phi_h(x,y)$.\n\\end{proof}\n\nThe next lemma is quite elementary and provides a\nrough lower bound for $\\phi_h$.\nHowever it has an interesting consequence, namely that\nreparametrizations of the $h$-minimizers by arc length\nof the metric $\\phi_h$ are Lipschitz\nwith the same Lipschitz constant.\nWe point out that this lower bound only depends\non the positivity of the Newtonian potential.\n\n\\begin{lemma}\\label{lema-geod.are.lipschitz}\nLet $h>0$.\nFor any pair of configurations $x,y\\in E^N$ we have\n\\[\n\\phi_h(x,y)\\geq \\sqrt{2h}\\norm{x-y}.\n\\]\n\\end{lemma}\n\n\\begin{proof}\nWe note that\n\\[\n\\phi_h(x,y)=\n\\min\\set{\\phi(x,y,\\tau)+\\tau h\\mid \\tau>0}\\geq\n\\min\\set{\\Phi_{x,y}(\\tau)\\mid\\tau>0},\n\\]\nand that\n\\[\n\\min\\set{\\Phi_{x,y}(\\tau)\\mid \\tau>0}=\n\\sqrt{2h}\\norm{x-y}.\n\\]\n\\end{proof}\n\n\\begin{remark}\n\\label{rmk-reparam.are.Lip}\nIf $\\gamma(s)$ is a reparametrization of an $h$-minimizer\nand the parameter is the arc length for the metric $\\phi_h$, \nthen we have\n\\[\n\\sqrt{2h}\\,\\norm{\\gamma(s_2)-\\gamma(s_1)}\\leq\n\\phi_h(\\gamma(s_1),\\gamma(s_2))=\\abs{s_2-s_1}.\n\\]\nTherefore all these reparametrizations are Lipschitz\nwith Lipschitz constant $1\/\\sqrt{2h}$. \n\\end{remark}\n\nFinally, the following and last lemma will be used to estimate\nthe time needed by an $h$-minimizer to join two given\nconfigurations.\n\n\\begin{lemma}\n\\label{lema-time.estim}\nLet $h>0$, $x,y\\in E^N$ two given configurations,\nand let $\\sigma\\in\\mathcal{C}(x,y,\\tau)$ be an $h$-minimizer.\nThen we have\n\\[\n\\tau_-(x,y)\\leq \\tau \\leq \\tau_+(x,y)\n\\]\nwhere $\\tau_-(x,y)$ and $\\tau_+(x,y)$\nare the roots of the polynomial\n\\[\nP(\\tau)=2h\\,\\tau^2-2\\phi_h(x,y)\\,\\tau+\\norm{x-y}^2.\n\\] \n\\end{lemma}\n\n\\begin{proof}\nSince $\\sigma$ minimizes $A_{L+h}$,\nin view of Remark \\ref{rmk-usual.bound} we have\n\\[\n\\phi_h(x,y)=\n\\phi(x,y,\\tau)+\\tau h\\geq\n\\Phi_{x,y}(\\tau)\n\\]\nthat is,\n\\[\\phi_h(x,y)\\geq \\frac{\\norm{x-y}^2}{2\\tau}+\\tau h\\,,\\]\nwhich is equivalent to say that $P(\\tau)<0$.\n\\end{proof}\n\n\n\\subsection{Proof of Theorems \\ref{thm-princ} and \\ref{thm-calib.direct.horo} }\n\\label{s-proofs.main}\n\n\n\\begin{proof}[Proof of Theorem \\ref{thm-princ}]\nGiven $h>0$, $a\\in\\Omega$ and $x_0\\in E^N$ we proceed as\nfollows.\nFirst, we define the sequence of functions\n\\[\nu_n(x)=\n\\phi_h(x,na)-\\phi_h(0,na)\\,,\\qquad x\\in E^N.\n\\]\nEach one of this functions is a viscosity subsolution\nof the Hamilton-Jacobi equation $H(x,d_xu)=h$,\nthat is to say, we have $u_n\\prec L+h$ for all $n>0$.\nSince the estimate for the action potential $\\phi_h$\ngiven by Theorem \\ref{thm-phih.estim} implies that\nthe set of such subsolutions is an equicontinuous family,\nand since we have $u_n(0)=0$ for all $n>0$,\nwe can extract a subsequence converging to a function\n\\[\n\\mathfrak{u} (x)=\\lim_{k\\to +\\infty}u_{n_k}(x),\n\\]\nand the convergence is uniform on compact subsets of $E^N$.\nActually the limit is a directed horofunction\n$\\mathfrak{u}\\in\\mathcal{B}_h(a)$.\n\nBy Theorem \\ref{thm-horofuns.have.lamin}\nwe know that there is at least one curve $x:[0,+\\infty)\\to E^N$,\nsuch that\n\\[\n\\phi_h(x_0,x(t))=\n\\mathcal{A}_L(x\\mid_{[0,t]})+ht=\n\\mathfrak{u} (x_0)-\\mathfrak{u} (x(t)).\n\\]\nfor any $t>0$, and such that $x(0)=x_0$.\nProposition \\ref{prop-criterion.visc.sol} now implies\nthat $\\mathfrak{u}$ is a viscosity solution of\nthe Hamilton-Jacobi equation $H(x,d_xu)=h$, and moreover,\nthat $\\mathfrak{u}$ is a fixed point of the quotient Lax-Oleinik semigroup.\n\nFinally, by Theorem \\ref{thm-calib.direct.horo} we have that\nthe curve $x(t)$ is a hyperbolic motion, with energy constant $h$,\nand whose asymptotic direction is given by the configuration $a$.\nMore precisely, we have that\n\\[\nx(t)=t\\;\\frac{\\sqrt{2h}}{\\norm{a}}\\;a \\,+\\,o(t)\n\\]\nas $t\\to +\\infty$, as we wanted to prove.\n\\end{proof}\n\n\\begin{proof}[Proof of Theorem \\ref{thm-calib.direct.horo}]\nFor $h>0$ and $a\\in\\Omega$,\nlet $u\\in\\mathcal{B}_h(a)$ be a given horofunction directed by $a$.\nThis means that there is a sequence of configurations\n$(p_n)_{n>0}$, such that $p_n=\\lambda_na+o(\\lambda_n)$\nwith $\\lambda_n\\to+\\infty$ as $n\\to\\infty$, and such that\n\\[\nu(x)=\\lim_{n\\to\\infty}(u_{p_n}(x)-u_{p_n}(0))\n\\]\nwhere $u_p$ denotes the function $u_p(x)=\\phi_h(x,p)$.\nLet also $\\gamma:[0,+\\infty)\\to E^N$ be the curve\ngiven by the hypothesis and satisfying\n\\[\nu(\\gamma(0))-u(\\gamma(t))=\\mathcal{A}_{L+h}(\\gamma\\mid_{[0,t]})\n\\]\nfor all $t>0$.\nIn particular $\\gamma$ is an $h$-minimizer.\nWe recall that this means that the restrictions of\n$\\gamma$ to compact intervals are global\nminimizers of $\\mathcal{A}_{L+h}$.\nThus the restriction of $\\gamma$ to $(0,+\\infty)$ is\na genuine motion of the $N$-body problem,\nwith energy constant $h$,\nand it is a maximal solution if and only if\n$\\gamma(0)$ has collisions,\notherwise the motion defined by $\\gamma$\ncan be extended as a motion \nto some interval $(-\\epsilon, +\\infty)$.\n\nThe proof is divided into three steps.\nThe first one will be to prove that the curve $\\gamma$\nis not a superhyperbolic motion. This will be deduced from\nthe minimization property of $\\gamma$.\nThen we will apply the Marchal-Saari theorem to conclude\nthat there is a configuration $b\\neq 0$ such that\n$\\gamma(t)=tb+O(t^{2\/3})$.\nThe second and most sophisticated step will be to\nexclude the possibility of having collisions in $b$,\nthat is to say, in the limit shape of the motion $\\gamma$.\nFinally, once it is known that $\\gamma$ is a hyperbolic motion,\nan easy application of the Chazy's Lemma\n\\ref{lema-cont.limitshape} will allow us to conclude\nthat we must have $b=\\lambda a$ for some $\\lambda>0$.\nThen the proof will be achieved by observing that, since\n$\\norm{b}=\\sqrt{2h}$,\nwe must also have $\\lambda=\\sqrt{2h}\\norm{a}^{-1}$.\n\nWe start now by proving that $\\gamma$ is not superhyperbolic.\nWe will give a proof by contradiction.\nSupposing that $\\gamma$ is superhyperbolic\nwe can choose $t_n\\to +\\infty$ such\nthat $R(t_n)\/t_n\\to +\\infty$.\nWe recall that $R(t)=\\max\\set{ r_{ij}(t)\\mid i<j}$\ndenotes the maximal distance between the bodies at time $t$,\nand that $R(t)=O(\\norm{\\gamma(t)})$.\nThus we can assume that\n$\\norm{\\gamma(t_n)-\\gamma(0)}\/t_n\\to +\\infty$.\nGiven that the calibrating property implies that the curve\n$\\gamma$ is an $h$-minimizer,\nfor each $n>0$ we have\n\\[\n\\mathcal{A}_L(\\gamma\\mid_{[0,t_n]})+ht_n=\n\\phi_h(\\gamma(0),\\gamma(t_n)).\n\\]\nLet us write for short $r_n=\\norm{\\gamma(0)-\\gamma(t_n)}$.\nIn view of the observation we made in\nRemark \\ref{rmk-usual.bound},\nand using Theorem \\ref{thm-phih.estim},\n we have the lower and upper bounds\n\\[\n\\tfrac{1}{2}\\,r_n^2\\;t_n^{-1} +ht_n\\;\\leq\\;\n\\phi_h(\\gamma(0),\\gamma(t_n))\\;\\leq\\;\n\\left(\\alpha\\;r_n+h\\beta\\; r_n^2\\right)^{1\/2}\n\\]\nfor some constants $\\alpha,\\beta >0$ and for any $n>0$.\nIt is not difficult to see that this is impossible for $n$ large\nenough using the fact that $r_n\\,t_n^{-1}\\to +\\infty$.\nThus by the Marchal-Saari theorem there is a configuration\n$b\\in E^N$ such that $\\gamma(t)=tb+O(t^{2\/3})$.\nSince by the Lagrange-Jacobi identity $b=0$ forces $h=0$,\nwe know that $b\\neq 0$.\n\nWe prove now that $b$ has no collisions, that is to say,\nthat $b\\in\\Omega$. This is our second step in the proof.\nLet us write $p=\\gamma(0)$, $q_0=\\gamma(1)$\nand let us also define $\\sigma_0\\in\\mathcal{C}(q_0,p,1)$\nby reversing the parametrization of\n$\\gamma_0=\\gamma\\mid_{[0,1]}$.\nThus $\\sigma_0$ calibrates the function $u$,\nthat is to say, we have\n$u(p)-u(q_0)=\\mathcal{A}_{L+h}(\\sigma_0)$.\n\nNow, using Lemma \\ref{lema-JM.geod.complet} we can define\na sequence of curves $\\sigma'_n\\in\\mathcal{C}(p_n,q_0)$,\nsuch that $\\mathcal{A}_{L+h}(\\sigma'_n)=\\phi_h(p_n,q_0)$ for all $n>0$.\nThus each curve $\\sigma'_n$\nis an $h$-calibrating curve of the function\n$u_{p_n}(x)=\\phi_h(x,p_n)$.\nIt will be convenient to also consider the curves $\\gamma'_n$\nobtained by reversing the parametrizations of\nthe curves $\\sigma'_n$.\nIf for each $n>0$ the curve $\\sigma'_n$ is defined over\nan interval $[-s_n,0]$, then we get a sequence of curves\n$\\gamma'_n\\in\\mathcal{C}(q_0,p_n,s_n)$,\nrespectively defined over the intervals $[0,s_n]$. \n\nSince $q_0$ is an interior point of $\\gamma$,\nMarchal's Theorem implies that $q_0\\in\\Omega$.\nThus for each curve $\\gamma'_n$ the velocity\n$w_n=\\dot\\gamma'_n(0)$ is well defined.\nSince $h$-minimizers have energy constant $h$,\nwe also have $\\norm{w_n}^2=2(h+U(q_0))$ for all $n>0$.\nThis allow us to choose a subsequence $n_k$ such that\n$w_{n_k}\\to v_0$ as $k\\to\\infty$.\nAt this point we need to prove\nthat $\\lim s_n=+\\infty$.\nThis can be done by application of Lemma \\ref{lema-time.estim}\nto the $h$-minimizers $\\gamma'_n$ as follows.\nGiven two configurations $x,y\\in E^N$,\nthe polynomial given by the lemma satisfies\n$P(\\tau)\\geq \\norm{x-y}^2-2\\phi_h(x,y)\\tau$ for all $\\tau>0$.\nTherefore,\nwhen $x\\neq y$ its roots can be bounded below by\n$\\norm{x-y}^2\/2\\phi_h(x,y)$.\nUsing this fact, we have that for all $n>0$,\n\\[\ns_n>\\frac{\\norm{q_0-p_n}^2}{2\\,\\phi(q_0,p_n)}.\n\\]\nThen the upper bound for $\\phi_h$ given by\nTheorem \\ref{thm-phih.estim} implies that $\\lim s_n=+\\infty$. \n\nLet us summarize what we have built so far.\nFrom now on, let us write for short $q_k=p_{n_k}$, $t_k=s_{n_k}$,\n$v_k=w_{n_k}$, and also $\\gamma_k=\\gamma'_{n_k}$ and\n$\\sigma_k=\\sigma'_{n_k}$.\nFirst, there is a sequence of configurations $(q_k)_{k>0}$,\nsuch that, for some increasing sequence $n_k$\nof positive integers, we have\n$q_k=\\lambda_{n_k}a+o(\\lambda_{n_k})$ as $k\\to\\infty$.\nAssociated to each $q_k$ there is an $h$-minimizer\n$\\gamma_k:[0,t_k]\\to E^N$, with $t_k\\to +\\infty$,\nsuch that $\\gamma_k\\in\\mathcal{C}(q_0,q_k)$.\nMoreover, $v_k=\\dot\\gamma_k(0)$ and we have\n$v_k\\to v_0$ as $k\\to\\infty$.\nIn addition, each reversed curve $\\sigma_k\\in\\mathcal{C}(q_k,q_0)$\nis an $h$-calibrating curve of the function\n$u_{q_k}(x)=\\phi_h(x,q_k)$.\n\nWe will prove that $v_0=\\dot\\gamma(1)$. \nTo do this, we start by considering the maximal solution\nof Newton's equations with initial conditions $(q_0,v_0)$\nand by calling $\\zeta$ its restriction to positive times,\nlet us say for $t\\in [0,t^*)$.\nNext, we choose $\\tau\\in (0,t^*)$ and we observe that\nwe have $t_k>\\tau$ for any $k$ big enough.\nThus, for these values of $k$, we have that\n$\\gamma_k(t)$ and $\\dot\\gamma_k(t)$ converge respectively\nto $\\zeta(t)$ and $\\dot\\zeta(t)$, and the convergence is uniform\nfor $t\\in[0,\\tau]$.\nTherefore,\n\\[\n\\lim_{k\\to\\infty}\\mathcal{A}_{L+h}(\\gamma_k\\mid_{[0,\\tau]})=\n\\mathcal{A}_{L+h}(\\zeta\\mid_{[0,\\tau]}).\n\\]\nOn the other hand, since on each compact set our function\n$u(x)$ is the uniform limit of the functions\n$u_k(x)=u_{q_k}(x)-u_{q_k}(0)$, we can also write\n\\[\nu(q_0)-u(\\zeta(\\tau))=\n\\lim_{k\\to\\infty}\\,(\\,u_k(q_0)-u_k(\\gamma_k(\\tau))\\,).\n\\]\nWe use now the fact that for each one of these values of $k$\nwe have, by the calibration property, that\n\\[\nu_k(q_0)-u_k(\\gamma_k(\\tau))=\n\\mathcal{A}_{L+h}(\\gamma_k\\mid_{[0,\\tau]}),\n\\]\nto conclude then that\n\\[\nu(q_0)-u(\\zeta(\\tau))=\\mathcal{A}_{L+h}(\\zeta\\mid_{[0,\\tau]}).\n\\]\nNotice that what we have proved is that the reversed curve\n$\\zeta(-t)$ defined on $[-\\tau,0]$\nis indeed an $h$-calibrating curve of $u$.\nThe concatenation of this calibrating curve with the\ncalibrating curve $\\sigma_0$\nresults, according to Lemma \\ref{lema-concat.calib},\nin a new calibrating curve,\ndefined on $[-\\tau,1]$ and passing by $q_0$ at $t=0$.\nTherefore this concatenation of curves is an $h$-minimizer,\nwhich implies that it is smooth at $t=0$.\nWe have proved that $\\dot\\zeta(0)=v_0=\\dot\\gamma(1)$.\nThis also implies that $t^*=+\\infty$ and that\n$\\zeta(t)=\\gamma(t+1)$ for all $t\\geq 0$.\n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=1.1]{proof33a.pdf}\n\\caption{The $C^1$ approximation of the curve $\\gamma$ by\n$h$-minimizers from $q_0$ to $q_k=p_{n_k}$.\nHere $\\lambda=\\lambda_{n_k}$ and\n$\\norm{q_k-\\lambda a}<r=o(\\lambda)$.} \n\\label{Proof33a}\n\\end{figure}\n\nFor simplicity,\nin the rest of the proof we will call $\\gamma$ the curve $\\zeta$,\nassuming then that the original curve $\\gamma$ was\nreparametrized to be defined on the interval $[-1,+\\infty)$.\nMaking this abuse of notation we can then write\n$\\gamma_k(t)\\to\\gamma(t)$,\nand $\\dot\\gamma_k(t)\\to\\dot\\gamma(t)$,\nuniformly on any compact interval $[0,T]$.\n\nWe continue now with the proof that the limit shape $b$\nof $\\gamma $ has no collisions.\nWe will make use of the function $\\mu$ that we have mentioned\nin Remark \\ref{rmk-configur.measure} which is\ncalled the configurational measure.\nIt is defined as the homogeneous function of degree zero\n$\\mu:E^N\\setminus\\set{0}\\to\\mathbb{R}^+$ given by\n$\\mu(x)=\\norm{x}U(x)=U(\\norm{x}^{-1}x)$,\nthat is to say, $\\mu=UI^{1\/2}$. \nNotice that $\\mu(x)<+\\infty$ if and only if $x\\in\\Omega$.\n\nUnder the assumption that $b$ has collisions,\nwe will construct a new sequence of curves\n$\\eta_k\\in\\mathcal{C}(q_0,q_k)$ in such a way that\n$\\mathcal{A}_{L+h}(\\eta_k)<\\mathcal{A}_{L+h}(\\gamma_k)$\nfor all $k$ big enough.\nSince this contradicts the minimality of the curves $\\gamma_k$\nwe will conclude that $b\\in\\Omega$.\nThe construction of the curves $\\eta_k$ will be done in terms\nof the polar components of the curves $\\gamma_k$.\nMore precisely, for each $k>1$ we define the functions\n\\[\n\\rho_k:[0,t_k]\\to\\mathbb{R}^+,\n\\quad\n\\rho_k(t)=\\norm{\\gamma_k(t)}\n\\]\n\\[\n\\theta_k:[0,t_k]\\to\\mathbb{S},\n\\quad\n\\theta_k(t)=\\norm{\\gamma_k(t)}^{-1}\\gamma_k(t)\n\\]\nwhere $\\mathbb{S}=\\set{x\\in E^N\\mid \\inner{x}{x}=1}$ is the unit sphere\nfor the mass inner product. \nThus, for each $k>0$ we can write $\\gamma_k=\\rho_k\\theta_k$,\nand the Lagrangian action in polar coordinates writes\n\\[\n\\mathcal{A}_{L+h}(\\gamma_k)=\n\\int_0^{t_k}\\tfrac{1}{2}\\;\\dot\\rho_k^{\\,2}\\,dt\\,+\n\\int_0^{t_k}\\tfrac{1}{2}\\;\\rho_k\\,\\dot\\theta_k^{\\,2}\\,dt\\,+\n\\int_0^{t_k}\\rho_k^{-1}\\,\\mu(\\gamma_k)\\,dt\\;+\nht_k.\n\\]\nAssuming that $\\mu(b)=+\\infty$, we can find $\\epsilon>0$\nsuch that, if $\\norm{x-b}<\\epsilon$,\nthen $\\mu(x)>3\\mu(a)$.\nOn the other hand, since we have that $\\gamma(t)=tb+o(t)$,\nthere is $T_0>0$ such that\n$\\norm{\\gamma(t)t^{-1}-b}<\\epsilon\/2$ for all $t\\geq T_0$.\n\nWe use now the approximation of $\\gamma$ by the curves\n$\\gamma_k$. For each $T\\geq T_0$ there is a positive integer\n$k_T$ such that, if $k>k_T$,\nthen $t_k>T$ and\n$\\norm{\\gamma_k(t)-\\gamma(t)}<T_0\\epsilon\/2$\nfor all $t\\in[T_0,T]$.\nIt follows that, for $k>k_T$ and for any $t\\in[T_0,T]$\nwe have\n\\[\n\\norm{\\frac{\\gamma_k(t)}{t}-\\frac{\\gamma(t)}{t}}<\n\\frac{\\epsilon}{2},\n\\]\nand then $\\norm{\\gamma_k(t)t^{-1}-b}<\\epsilon$.\nIn turn, since $\\mu$ is homogeneous, this implies that\n\\[\n\\mu(\\gamma_k(t))=\n\\mu(\\gamma_k(t)t^{-1})>3\\mu(a).\n\\]\n\nNow we are almost able to define the sequence of curves\n$\\eta_k\\in\\mathcal{C}(q_0,q_n)$.\nLet us write $k_0$ for $k_{T_0}$.\nFor $k\\geq k_0$ we know that\n$\\mu(\\gamma_k(T_0))>3\\mu(a)$.\nMoreover, since the extreme $p_k$ of the\ncurve $\\gamma_k$ lies in a ball $B_r(\\lambda a)$ with\n$r=o(\\lambda)$, we can assume that $k_0$ is big enough\nin order to have $\\mu(p_k)<2\\mu(a)$ for all $k\\geq k_0$.\nThen we define\n\\[\nT_k=\n\\max\\set{T\\geq T_0\\mid\n\\mu(\\gamma_k(t))\\geq 2\\mu(a)\n\\text{ for all } t\\in [T_0,T]},\n\\]\nand $c_k=\\theta_k(T_k)$.\nGiven $T>T_0$,\nby the previous considerations we have that\n$k>k_T$ implies $T_k>T$.\nThus,\nwe can take $T_k$ as large as we want\nby choosing $k$ large enough.\nThe last ingredient for building the curve $\\eta_k$\nis a minimizer $\\delta_k$ of $\\mathcal{A}_{L+h}$ in\n$\\mathcal{C}(\\gamma_k(T_0),\\rho_k(T_0)c_k)$\nwhose existence is guaranteed by Theorem\n\\ref{lema-JM.geod.complet}.\nThen we define $\\eta_k$ as follows.\nFor $k<k_0$ we set $\\eta_k=\\gamma_k$.\nFor $k\\geq k_0$ the curve $\\eta_k$ is the concatenation\nof the following four curves: (i) the restriction of $\\gamma_k$\nto $[0,T_0]$, (ii) the minimizer $\\delta_k$ above defined,\n(iii) the homothetic curve $\\rho_k(t)c_k$ for $t\\in [T_0,T_k]$,\nand (iv) the restriction of $\\gamma_k$ to $[T_k,t_k]$\n(see Figure \\ref{Proof33b}).\n\nWe will show that\n$\\Delta_k=\\mathcal{A}_{L+h}(\\gamma_k)-\\mathcal{A}_{L+h}(\\eta_k)>0$\nfor $k$ large enough.\n\nWe start by observing that the first and the last components\nof $\\eta_k$ are also segments of $\\gamma_k$ so that\ntheir contributions to $\\Delta_k$ cancel each other out.\n\nAlso we have\n\\[\n\\mathcal{A}_{L+h}(\\gamma_k\\mid_{[T_0,T_k]}) = \n\\int_{T_0}^{T_k}\\,\\tfrac{1}{2}\\,\\dot\\rho_k^{\\,2}\\,dt +\n\\int_{T_0}^{T_k}\\,\\tfrac{1}{2}\\,\\rho_k\\dot\\theta^{\\,2}\\,dt +\n\\int_{T_0}^{T_k}\\,\\rho_k^{-1}\\mu(\\gamma_k)\\,dt +\nh(T_k-T_0),\n\\]\nand\n\\[\n\\mathcal{A}_{L+h}(\\,\\rho_kc_k\\mid_{[T_0,T_k]}) =\n\\int_{T_0}^{T_k}\\,\\tfrac{1}{2}\\,\\dot\\rho_k^{\\,2}\\,dt +\n\\int_{T_0}^{T_k}\\,\\rho_k^{-1}\\,2\\mu(a)\\,dt +\nh(T_k-T_0).\n\\]\nWe recall that\n$\\mu(\\gamma_k(t))\\geq 2\\mu(a)$ for all\n$t\\in [T_0,T_k]$.\nTherefore, so far we can say that\n\\[\n\\Delta_k>\n\\int_{T_0}^{T_k}\\rho_k^{-1}\\,\n\\left(\\mu(\\gamma_k(t))-2\\mu(a)\\right)\\,dt\\;-\\;\n\\mathcal{A}_{L+h}(\\delta_k).\n\\]\nThis part of the proof is essentially done.\nTo conclude we only need to establish estimates\nfor the two terms on the right side of the previous inequality.\nMore precisely,\nwe will prove that the the integral diverges as $k\\to\\infty$,\nand that the second term is bounded as a function of $k$.\n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=1.1]{proof33b.pdf}\n\\caption{For $k$ large enough, the $\\mathcal{A}_{L+h}$ action\nof the green curve $\\eta_k$\nis less than that of the curve $\\gamma_k$.\nThe intermediate points are \n$b_k=\\gamma_k(T_0)$,\n$d_k=\\rho_k(T_0)c_k$,\nand $e_k=\\rho_k(T_k)c_k=\\gamma_k(T_k)$.} \n\\label{Proof33b}\n\\end{figure}\n\n\\begin{claim}\nThe sequence $\\mathcal{A}_{L+h}(\\delta_k)$ is bounded.\n\\end{claim}\n\\begin{proof}\nIndeed, the curve $\\delta_k$ is a minimizer of $\\mathcal{A}_{L+h}$\nbetween curves binding two configurations of size\n$\\rho_k(T_0)$, and\n\\[\n\\rho_k(T_0)\\to\\rho(T_0)=\\norm{\\gamma(T_0)}\n\\]\nas $k\\to\\infty$. Therefore there is $R>0$ such that\nthe endpoints of the curves $\\delta_k$ are all contained\nin the compact ball $B_R(0)\\subset E^N$.\nOn the other hand, \nsince by Theorem \\ref{thm-phih.estim} we know that\nthe action potential $\\phi_h$ is continuous, we can conclude that\n$\\sup \\mathcal{A}_{L+h}(\\delta_k)<+\\infty$.\n\\end{proof}\n\n\\begin{claim}\nThe sequence\n$\\int_{T_0}^{T_k}\\rho_k^{-1}\\,\n\\left(\\mu(\\gamma_k(t))-2\\mu(a)\\right)\\,dt$\ndiverges as $k\\to\\infty$.\n\\end{claim}\n\\begin{proof}\nIn order to get a lower bound for the integral of $\\rho_k^{-1}$,\nwe make the following considerations.\nWe note first that $\\rho(t)=\\norm{\\gamma(t)}< \\alpha t+\\beta$\nfor some constants $\\alpha, \\beta>0$.\nThis is because we know that\n$\\gamma(t)=tb+o(t)$ as $t\\to +\\infty$.\nThus we have that for any $T>T_0$\n\\[\n\\int_{T_0}^T\\rho^{-1}dt \\;\\geq\\;\n\\log(\\alpha T+\\beta)-\\log(\\alpha T_0 +\\beta).\n\\]\nTherefore, for any choice of $K>0$ there is $T>0$ such that\nthe integral at the left side is bigger than\n$\\mu(a)^{-1}K$.\n\nOn the other hand,\nsince for $k>k_T$ we have that $T_k>T$, and since\n$\\gamma_k(t)$ uniformly converges to $\\gamma(t)$\non $[T_0,T]$, we can assume that we have\n$\\mu(\\gamma_k(t))>3\\mu(a)$ for all $t\\in [T_0,T]$\nand then,\nneglecting the part of the integral between $T$ and $T_k$\nwhich is positive, to conclude that\n\\[\n\\int_{T_0}^{T_k}\\rho_k^{-1}dt\\,\n\\left(\\mu(\\gamma_k(t))-2\\mu(a)\\right)\\,dt \\;>\n\\;\\mu(a)\\int_{T_0}^{T}\\rho_k^{-1}dt \\;>\\;K\n\\]\nfor every $k$ sufficiently large.\n\\end{proof}\nIt follows that for large values of $k$ the difference $\\Delta_k$ is\npositive, meaning that the corresponding curves $\\gamma_k$\nare not $h$-minimizers because the curves $\\eta_k$ have\nsmaller action.\nTherefore we have proved by contradiction that $b\\in\\Omega$.\n\nThe last step to finish the proof is to show that $b=\\lambda a$\nfor some $\\lambda >0$.\nIf not, we can choose two disjoint cones $C_a$ and $C_b$\nin $E^N$, centered at the origin and with axes directed by\nthe configurations $a$ and $b$ respectively.\nSince we know that $b\\in\\Omega$,\nwe can apply Chazy's Lemma to get that for $k$ large enough\nthe curves $\\gamma_k$ are defined for all $t>0$, and that there\nis $T^*>0$ for which we must have $\\gamma_k(t)\\in C_b$\nfor all $t>T^*$ and any $k$ large enough.\nBut this produces a contradiction, because we know that\n$q_k=\\gamma_k(t_k)=\\lambda_{n_k}a+o(\\lambda_{n_k})$\nas $k\\to\\infty$, which\nforces to have $q_k\\in C_a$ for $k$ large enough.\n\\end{proof}\n\n\n\n\\section{The Jacobi-Maupertuis distance for nonnegative energy}\n\\label{s-jm.dist}\n\nIn this section we develop the geometric viewpoint\nand we show, for $h\\geq 0$, that when restricted to $\\Omega$\nthe action potential $\\phi_h$ is exactly the Riemannian distance\nassociated to the Jacobi-Maupertuis metric $j_h=2(h+U)g_m$,\nwhere $g_m$ is the mass scalar product.\nMoreover,\nwe will see that the metric space $(E^N,\\phi_h)$\nis the completion of $(\\Omega,j_h)$.\nThe fact that $\\phi_h$ is a distance over $E^N$ is a\nstraightforward consequence of the definition and of\nLemma \\ref{lema-geod.are.lipschitz} or\nLemma \\ref{lema-compar.pot.action.kepler}\ndepending on whether $h>0$ or $h=0$.  \nIt is also immediate to see that $(E^N,\\phi_h)$ is a length space,\nthat is to say $\\phi_h$ coincides with the induced length distance.\nFrom now on,\nwe denote by $\\mathcal{L}_h(\\gamma)$ the Riemannian length\nof a $C^1$ curve $\\gamma$,\nand we denote by $d_h$ the Riemannian distance on $\\Omega$.\n \n\\begin{proposition}\nFor all $h\\geq 0$,\nthe space $(E^N,\\phi_h)$ is the completion of $(\\Omega,d_h)$.    \n\\end{proposition}\n\n\\begin{proof}\nIn the case $h>0$,\nthe fact that $(E^N,\\phi_h)$ is a complete length space\ncomes directly from the definition of $\\phi_h$\nand from Lemma \\ref{lema-geod.are.lipschitz}\nand Theorem \\ref{thm-phih.estim}.\nMoreover, we have that $\\phi_h$ generates the topology of $E^N$\nand that $\\Omega$ is thus a dense subset.\n\nFor the case $h=0$ the argument is exactly the same,\nbut instead of Lemma \\ref{lema-geod.are.lipschitz},\nwhich becomes meaningless,\nwe have to use Lemma \\ref{lema-compar.pot.action.kepler} below.\n\nThe proof will be achieved now by showing that\nthe inclusion of $\\Omega$ into  $E^N$ is an isometry,\nthat is to say,\nthat $\\phi_h$ coincides with $d_h$ when restricted to $\\Omega$.\nGiven $(x,v)\\in \\Omega\\times E^N$,\nwe have\n\\[\n\\norm{v}_h=j_h(x)(v,v)^{1\/2}\\leq L(x,v)+h\n\\]\nwith equality if and only if $\\mathcal{E}(x,v)=h$,\nwhere $\\mathcal{E}(x,v)=\\frac{1}{2}\\norm{v}^2-U(x)$\nis the energy function in $T\\Omega$.\nIt follows that if $\\gamma$ is an absolutely continuous curve in\n$\\Omega$ it holds $\\mathcal{L}_h(\\gamma)\\leq A_{L+h}(\\gamma)$,\nwith equality if and only if\n$\\mathcal{E}(\\gamma(t),\\dot{\\gamma}(t))=h$  for almost all $t$.\nGiven now $x,y\\in\\Omega$,\nby Marchal's Theorem any $h$-minimizer joining $x$ to $y$\nis a genuine motion,\nin particular it is a $C^1$ curve.\nSince $d_h$ is defined as the infimum of $\\mathcal{L}_h(\\gamma)$\nover all $\\mathcal{C}^1$ curves in $\\Omega$ joining $x$ to $y$,\nwe have that $d_h(x,y)\\leq\\phi_h(x,y)$.\n\nIn order to prove the converse inequality,\nlet $\\epsilon>0$ and $\\gamma:[0,1]\\to \\Omega$\nbe a $\\mathcal{C}^1$ curve joining $x$ to $y$ such that\n$\\mathcal{L}_h(\\gamma)\\leq d_h(x,y)+\\epsilon$.\nWe can now find a finite sequence $0=t_0<...<t_N=1$\nsuch that for any $i=1,...,N$ the points\n$\\gamma(t_{i-1})$ and $\\gamma(t_i)$ can be joined by a\nminimizing geodesic in $\\Omega$, here denoted $\\sigma_i$.\nWe will assume that each $\\sigma_i$ is parametrized by arclength,\nthus $\\dot{\\sigma}_i(t)\\neq 0$ for all $t$.\nLet us reparametrize now each $\\sigma_i$ so that,\ndenoting $\\delta_i$ the reparametrization,\nwe have $\\mathcal{E}(\\delta_i(t),\\dot\\delta_i(t))=h$ for all $t$,\nand let $\\delta$ be the concatenation of all $\\delta_i$. \nBy construction\n\\[\n\\phi_h(x,y)\\leq A_{L+h}(\\delta)=\n\\mathcal{L}_h(\\delta)\\leq\n\\mathcal{L}_h(\\gamma)\\leq\nd_h(x,y)+\\epsilon,\n\\]  \nand by arbitrariness of $\\epsilon$ we conclude that\n$\\phi_h(x,y)\\leq d_h(x,y)$.\n\\end{proof}  \n\n\\begin{lemma}\n\\label{lema-compar.pot.action.kepler}\nThere exist a constant $\\mu_0>0$ such that\nfor all $x,y\\in E^N$ satisfying $x\\neq y$, we have\n\\[\n\\phi_0(x,y)\\geq \\frac{\\mu_0}{\\rho}\\norm{x-y}\n\\]\nwhere\n$\\rho=\\max\\set{\\norm{x},\\norm{y}}^\\frac{1}{2}$.\n\\end{lemma}\n\n\\begin{proof}\nThe main idea of the proof is to estimate $\\phi_0$\nby comparing it with the action of some Kepler problem in $E^N$.\nSince $U$ is a continuous function with values in $(0,+\\infty]$,\nthe minimum of $U$ on the unit sphere of $E^N$,\nhere denoted $U_0$, is strictly positive.\nThus, by homogeneity of the potential,\nif $x$ is any nonzero configuration we have\n\\[\nU(x)=\\frac{1}{\\norm{x}}\\,U\\left(\\frac{x}{\\norm{x}}\\right)\n\\geq \\frac{U_0}{\\norm{x}}.\n\\]\nLet us consider now the Lagrangian function\nassociated to the Kepler problem in $E^N$\nwith potential $U_0\/\\norm{x}$, that is to say \n\\[\nL_{\\kappa}(x,v)=\n\\frac{1}{2}\\norm{v}^2+\\frac{U_0}{\\norm{x}}\\;.\n\\]\nBy the previous inequality we know that $L_\\kappa(x,v) \\le L(x,v)$.\nThe critical action potential associated to $L_\\kappa$\nis defined on $E^N\\times E^N$ by\n\\[\n\\Phi_0(x,y)=\n\\min\\set{\\mathcal{A}_{L_\\kappa}(\\gamma)\\mid \\gamma\\in\\mathcal{C}(x,y)},\n\\]\nand it follows immediately from the definition that\n$\\Phi_0(x,y)\\le \\phi_0(x,y)$.\nAssume now $x\\neq y$, and let\n$\\gamma : [0,\\tau]\\rightarrow E^N$ be a free-time minimizer for\n$\\mathcal{A}_{L_\\kappa}$ in $\\mathcal{C}(x,y)$.\nThus $\\gamma$ is an absolutely continuous curve satisfying\n$\\mathcal{A}_{L_\\kappa}(\\gamma)=\\Phi_0(x,y)$.\nAs a zero energy motion of the Kepler problem,\nwe know that $\\gamma$ is an arc of Keplerian parabola,\nand in particular we know that\n\\[\n\\max_{t\\in[0,\\tau]}\\norm{\\gamma(t)}=\n\\max\\set{\\norm{x},\\norm{y}}\n\\]\nwhich in turn implies that\n\\[\n\\frac{U_0}{\\norm{\\gamma(t)}}\\,\\geq\\,\n\\frac{U_0}{\\rho^2}\n\\]\nfor all $t\\in[0,\\tau]$. \nThus, using this lower bound and Cauchy-Schwarz inequality\nfor the kinetic part of the action of $\\gamma$ we deduce that \n$\\Phi_0(x,y)\\geq g(\\tau)$,\nwhere $g:\\mathbb{R}^+\\to\\mathbb{R}$ is the function defined by \n\\[\ng(s)=\n\\frac{\\norm{x-y}^2}{2s}+\\frac{U_0}{\\rho^2}\\,s.\n\\]\nObserving now that $g$ is convex and proper,\nand replacing $g(\\tau)$ in the previous inequality\nby the minimum of $g(s)$ for $s>0$, we obtain\n\\[\n\\phi_0(x,y)\\geq\n\\Phi_0(x,y)\\geq\n\\frac{\\mu_0}{\\rho}\\,\\norm{x-y}.\n\\]\nfor $\\mu_0=\\sqrt{2U_0}$.\n\\end{proof} \n\nNow we have all the necessary elements to give\nthe proof of the corollary stated in Sect. \\ref{s-geom.view}.\nWe have to prove that if two geodesic rays have the same\nasymptotic limit, then they are equivalent in the sense of\nhaving bounded difference.\n\n\\begin{proof}\n[Proof of Corollary \\ref{cor-Gr.boundary}]\nLet $\\gamma:[0,+\\infty)\\to E^N$ be a geodesic ray \nof the distance $\\phi_h$, with $h>0$.\nWe assume that $\\gamma(s)=sa+o(s)$\nas $s\\to +\\infty$ for some $a\\in\\Omega$.\nThus, we know that $\\gamma(s)$ is without collisions\nfor all $s$ sufficiently big. \nBy performing a time translation we can assume that\n$\\gamma(s)\\in \\Omega$ for all $s\\geq 0$, hence that\n$\\gamma$ is a geodesic ray of the\nJacobi-Maupertuis metric $j_h$ in $\\Omega$.\nNow we know that $\\gamma$ admits a factorization\n$\\gamma(s)=x(t_\\gamma(s))$ where\n$x(t)$ is a motion of energy $h$.\nMore precisely,\nthe inverse of the new parameter $t_\\gamma$\nis a function $s_x$ satisfying $x(t)=\\gamma(s_x(t))$.\nSince $\\gamma$ is arclength parametrized,\nwe have $\\norm{\\dot\\gamma(s)}_h=1$ for all $s\\geq 0$,\nand we deduce that $s_x$ is the solution\nof the differential equation \n\\begin{equation}\\tag{$\\star$}\\label{eq-edo.reparam}\n\\dot s_x(t)=2h+2U(\\gamma(s_x(t)))\n\\end{equation}\nwith intial condition $s_x(0)=0$.\nThis implies that $s_x(t)\\to +\\infty$ and $\\dot s_x(t)\\to 2h$\nas $t\\to +\\infty$,\nhence we also have $s_x(t)=2ht+o(t)$\nand $x(t)=2ht\\,a+o(t)$ as $t\\to +\\infty$.\nIn particular $x(t)$ is a hyperbolic motion.\nWe claim now that\n\\[\ns_x(t)=2ht+\\frac{U(a)}{h}\\log t+O(1).\n\\]\nand the proof is as follows.\nFrom (\\ref{eq-edo.reparam}) we have, for $t>1$,\n\\begin{equation}\\tag{$\\star\\star$}\\label{eq-sx.asymptotic}\ns_x(t)=2ht+\\int_0^1 2U(x(\\nu))\\,d\\nu+\\int_1^t 2U(x(\\nu))\\,d\\nu.\n\\end{equation}\nOn the other hand, by Chazy's Theorem we have that\n\\[\nx(t)=\n2ht\\,a-\\frac{\\log t}{4h^2}\\,\\nabla U(a)+O(1).\n\\]\nWe observe then that\n\\begin{eqnarray*}\nU(x(\\nu))&=&\n\\frac{1}{2h\\,\\nu}\\,U\\left(a +O\\left(\\frac{\\log \\nu}{\\nu}\\right)\\right)\\\\\n& &\\\\\n&=&\\frac{U(a)}{2h}\\,\\frac{1}{\\nu}+\nO\\left(\\frac{\\log \\nu}{\\nu^2}\\right)\n\\end{eqnarray*}\nNow the claim can be verified by replacing this last expression of\n$U(x(\\nu))$ in the last term of (\\ref{eq-sx.asymptotic}).\n\nGiven now another gedodesic ray\n$\\sigma : [0,+\\infty)\\to E^N$,\ndenoting $\\sigma(s)=y(t_\\sigma(s))$\nthe reparametrization such that $y(t)$ is a motion\nof energy constant $h$,\nand denoting $s_y$ the inverse of $t_\\sigma$,\nit is clear from the previous asymptotic estimates that the\ndifference $s_x(t)-s_y(t)$ is bounded.\nSince the derivative of $s_x$ and $s_y$\nare both bounded below by the same positive constant,\nwe easily conclude that\n$t_\\gamma(s)-t_\\sigma(s)$ is also bounded.\nBy replacing in the asymptotic expansion of $x(t)$ and $y(t)$\nwe find that $\\gamma(s)-\\sigma(s)$ is bounded. \n\\end{proof}\n\n\n\n\n\n\\section{Open questions on bi-hyperbolic motions}\n\\label{s-bi.hyp}\n\nWe finish with some general open questions.\nThey are closely related to the recent advances made by\nDuignan {\\it et al.} \\cite{DuMoMoYu}\nin which the authors show in particular that\nthe limit shape map $(x,v)\\mapsto (a^-,a^+)$\ndefined below is actually real analytic.\n\nWe define bi-hyperbolic motions\nas those which are defined for all $t\\in\\mathbb{R}$,\nand are hyperbolic both in the past and in the future.\nThe orbits of these entire solutions\ndefine a non-empty open set in the phase space,\nnamely the intersection of the two open set\n\\[\\mathcal{H}=\\mathcal{H}^ +\\cap\\mathcal{H}^-\\]\nwhere\n$\\mathcal{H}^+\\subset T\\Omega=\\Omega\\times E^N$\nis the set of the initial conditions giving rise\nto hyperbolic motions in the future, and\n$\\mathcal{H}^-=\\set{(x,v)\\in T\\Omega\\mid (x,-v)\\in\\mathcal{H}^+}$\nis the set of the initial conditions\ngiving rise to hyperbolic motions in the past.\nNewton's equations define a complete vector field\nin the open set $\\mathcal{H}\\subset\\Omega\\times E^N$.\nWe will denote by $\\varphi^t$ the corresponding flow\nand $\\pi:\\Omega\\times E^N\\to\\Omega$\nthe projection onto the first factor.\n \nWe also note that this open and completely invariant set\nhas a natural global section,\ngiven by the section of \\emph{perihelia}:\n\\[\\mathcal{P}=\\mathcal{H}\\cap\\set{(x,v)\\in T\\Omega\\mid \\inner{x}{v}=0}\\,.\\]\n\n\\begin{proposition}\nThe flow $\\varphi^t$ in $\\mathcal{H}$\nis conjugated to the shift in $\\mathcal{P}\\times\\mathbb{R}$.\n\\end{proposition}\n\n\\begin{proof}\nGiven $(x_0,v_0)\\in\\mathcal{H}$,\nlet $x(t)=\\pi(\\varphi^t(x_0,v_0))$ be\nthe generated bi-hyperbolic motion.\nSince $I=\\inner{x}{x}$,\nit follows from the Lagrange-Jacobi identity $\\ddot I=4h+2U$,\nthat $I$ is a proper and strictly convex function.\nThus, there is a unique $t_p\\in\\mathbb{R}$ such that \n$\\varphi^{t_p}(x_0,v_0)\\in\\mathcal{P}$.\nMoreover,\nthe sign of $\\dot I=\\inner{x}{\\dot x}$ is the sign of $t-t_p$\nand $\\norm{x(t)}$ reaches its minimal value at $t=t_p$.\nThe conjugacy is thus given by the map\n$(x_0,v_0)\\mapsto (p(x_0,v_0),-t_p)$,\nwhere $p:\\mathcal{H}\\to\\mathcal{P}$ gives the phase point at perihelion\n$p(x_0,v_0)=(x(t_p),\\dot x(t_p))$.\n\\end{proof}\n\nNaturally associated with each bi-hyperbolic motion,\nthere is the pair of limit shapes that it produces\nboth in the past and in the future.\nMore precisely, we can define the \\emph{limit shape map}\n$S:\\mathcal{H}\\to\\Omega\\times\\Omega$ by\n\\[S(x,v)=(a^-(x,v),a^+(x,v))\\]\n\\[a^\\pm(x,v)=\\lim_{t\\to\\pm\\infty} \\;\\abs{t}^{-1}\\pi(\\varphi^t(x,v))\\,.\\]\nAs a consequence of Chazy's \\emph{continuity of the instability}\n(Lemma \\ref{lema-cont.limitshape}) we have that\nthe limit shape map is actually a continuous map.\nIt is also clear that\n\\[\\norm{a^-(x,v)}=\\norm{a^+(x,v)}\\] for all $(x,v)\\in\\mathcal{H}$.\nIn fact, we have\n\\[\\norm{a^\\pm(x,v)}^2=2h=\\norm{v}^2-2U(x)\\]\nwhere $h>0$ is the energy constant\nof the generated bi-hyperbolic motion.\nHence the image of $S$ is contained in the manifold\n\\[\n\\mathcal{S}=\n\\set{(a,b)\\in\\Omega\\times\\Omega\\mid \\norm{a}=\n\\norm{b}}\\,.\n\\]\nClearly, we have $S\\circ\\varphi^t=S$ for all $t\\in\\mathbb{R}$.\nTherefore the study of the limit shape map can be restricted\nto the section of perihelia $\\mathcal{P}$.\nCounting dimensions we get\n\\[\\dim\\mathcal{P}=2dN-1=\\dim\\mathcal{S}\\]\nwhere $d=\\dim E$.\n\nWe will see now that the center of mass\ncan be reduced to the origin.\nLet us call $G:E^N\\to E$ the linear map that associates\nto each configuration its center of mass.\nMore precisely,\nif $M=m_1+\\dots+m_N$ is the total mass of the system,\nthen the center of mass $G(x)$ of $x=(r_1,\\dots,r_N)\\in E^ N$\nis well defined by the condition\n$MG(x)=m_1r_1+\\dots+m_Nr_N$.\nJust as we did for the quantities U and I,\nwe will write $G(t)$ instead of $G(x(t))$ when\nthe motion $x(t)$ is understood.\nWe observe now that if $x(t)=ta^++o(t)$ as $t\\to+\\infty$,\nthen $G(t)=tG(a^+)+o(t)$.\nMoreover, since $\\ddot G(t)=0$ for all $t\\in\\mathbb{R}$ we know that\nthe velocity of the center of mass $\\dot G(t)=v_G$ is constant,\nhence $G(t)=tv_G+G(0)$.\nTherefore we must have $G(a^+)=v_G$.\nIf in addition $x(t)=-ta^-+o(t)$ as $t\\to-\\infty$,\nthen we also have $G(a^-)=-v_G$.\nWe conclude that\n\\[G(a^-(x,v))=-\\;G(a^+(x,v))\\]\nfor all $(x,v)\\in\\mathcal{H}$.\nThis allows to reduce in $d$ dimensions\nthe codomain of the limit shape map.\nOn the other hand,\na constant translation of a bi-hyperbolic motion\ngives a new bi-hyperbolic motion with the same limit shapes.\nThus the domain can also be reduced of $d$ dimensions\nby imposing the condition $G(x(0))=0$.\n\nFinally,\nwe note that bi-hyperbolic motions are preserved\nby addition of uniform translations.\nLet $\\Delta\\subset E^N$ be the diagonal subspace,\nthat is the set of configurations of total collision. \nFor any bi-hyperbolic motion $x(t)$\nwith limit shapes $a^-$ and $a^+$, \nand any $v\\in\\Delta$,\nwe get a new bi-hyperbolic motion $x_v(t)=x(t)+tv$,\nwhose limit shapes are precisely $a^--v$ and $a^++v$.\nIn particular these configurations without collisions\nhave opposite center of mass and the same norm.\nThe equality of the norms can also be deduced\nfrom the orthogonal decomposition\n$E^N=\\Delta\\oplus \\ker G$ and using the fact that\n$G(a^+-a^-)=0$.\n\nIn sum,\nwe can perform the total reduction of the center of mass\nby setting $G(x(0))=G(\\dot x(0))$,\nwhich leads to $G(a^-)=G(a^+)=0$.\nWe define\n\\[\\mathcal{P}_0=\\set{(x,v)\\in\\mathcal{H}\\mid\\;\nG(x)=G(v)=0\\text{ and }\\inner{x}{v}=0}\\]\n\\[\\mathcal{S}_0=\\set{(a,b)\\in\\Omega\\times\\Omega\\mid\\;\nG(a)=G(b)=0\\text{ and }\\norm{a}=\\norm{b}}\\]\nand we maintain the balance of dimensions.\n\n\\begin{question}\nIs the limit shape map $S:\\mathcal{P}_0\\to\\mathcal{S}_0$\na local diffeomorphism?\n\\end{question}\n\nThe answer is yes in the Kepler case\n(see Figure \\ref{HyperKepler1}).\nBut in the general case,\nthis property must depend on the potential $U$.\nFor instance,\nin the extremal case of $U=0$,\nin which motions are thus straight lines,\nwe get the restriction $a^-=-a^+$ for all hyperbolic motion.\nIn this case the shape map loses half of the dimensions.\n\nIt is therefore natural to ask, for the general $N$-body problem,\nwhether or not\nthere is some relationship between these two functions.\n\n\\begin{question}\nHow big is the image of the limit shape map?\n\\end{question}\n\nIn the Kepler case, only the pairs $(a,b)$ such that\n$\\norm{a}=\\norm{b}$ and $a\\neq\\pm\\, b$\nare realized as asymptotic velocities of some hyperbolic trajectory.\nThis can be generalized for $N\\geq 3$.\nIf $a\\in\\Omega$ is a planar central configuration\nand $R\\in SO(E)$ keeps invariant the plane containing $a$,\nthe pair $(a,Ra)$ is realized as the limit shapes\nof a unique homographic hyperbolic motion,\nexcept in the cases $R=\\pm\\,Id$.\n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=1.1]{HyperKepler1.pdf}\n\\caption{Hyperbolic motions of the Kepler problem\nwith fixed value of the energy constant $h>0$\nand asymptotic velocity $a$ in the future.\nAll but one of these motions are bi-hyperbolic.\nThe blue curve $\\mathcal{P}$ is composed of the\ncorresponding perihelia.} \n\\label{HyperKepler1}\n\\end{figure}\n\nWe now devote attention to the effect of homogeneity.\nRecall that\nif $x(t)$ is a bi-hyperbolic motion of energy constant $h$,\nthen  for every $\\lambda>0$ the solution given by\n$x_\\lambda(t)=\\lambda\\,x(\\lambda^{-3\/2}t)$\nis still bi-hyperbolic with energy constant $\\lambda^{-1}h$.\nMoreover,\nif we note $x_0=x(0)$ and $v_0=\\dot x(0)$ then we have\n\\[\n(x_\\lambda(t),\\dot x_\\lambda(t))=\n\\varphi^t(\\lambda\\, x_0,\\lambda^{-1\/2}\\,v_0)\n\\]\nfor all $t\\in\\mathbb{R}$.\nThese considerations prove the following remark.\n\n\\begin{remark}\nFor any $(x,v)\\in\\mathcal{H}$ and for any $\\lambda>0$, we have\n\\[S(\\lambda\\, x,\\lambda^{-1\/2}\\,v)=\\lambda^{-1\/2}\\,S(x,v)\\,.\\]\n\\end{remark}\n\nLet us introduce the following question with an example.\nConsider the planar three-body problem with equal masses.\nThat is, $E=\\mathbb{R}^2\\simeq\\mathbb{C}$, $N=3$ and $m_i=1$ for $i=1,2,3$.\nFor $h>0$, define the equilateral and collinear configurations\n\\[a_h=\\sqrt\\frac{2h}{3}\\,(1,z,z^2)\\qquad b_h=\\sqrt h\\,(-1,0,1)\\]\nwhere $z$ is a primitive root of $z^3-1$.\nThus we have $\\norm{a_h}=\\norm{b_h}=\\sqrt{2h}$ and also\n$G(a_h)=G(b_h)=0$ for all $h>0$.\n\n\\begin{question}\nIs the pair $(a_h,b_h)$ in the image of the limit shape map?\n\\end{question}\n\nIn other words,\nis there a bi-hyperbolic motion whose dynamics originates\nin the past with a contraction from a big equilateral triangle,\nand then, after a period of strong interaction between the particles,\nthe evolution ends with an almost collinear expansion?\n\nIn our view, the method of viscosity solutions\ncould be useful to answer this question. \nIn particular, we consider it necessary to push forward\nthe understanding of the regions of differentiability\nof these weak solutions.\nIt seems reasonable that an orbit like this\ncan be found by looking for critical points\nof a sum of two Busemann functions (see Sect. \\ref{s-busemann}).\n\n\\begin{question}\nIf the answer to Question 3 is yes,\nwhat is the infimum of the norm of the perihelia\nof the bi-hyperbolic motions having these limit shapes? \n\\end{question}\n\nObserve that once we have a bi-hyperbolic motion which is\nequilateral in the past and collinear in the future,\nwe can play with the homogeneity in order to obtain a new one,\nbut having a perihelion contained in an arbitrarily small ball.\nThat is to say, it would be possible to make, at some point,\nall bodies pass as close as we want from a total collision.\nOf course, to do this\nwe must increase the value of the energy constant indefinitely.\nThus we preserve the limit shapes in the weak sense,\nbut not the size of the asymptotic velocities.\n In the family of motions $(x_\\lambda)$ described above,\nthe product of the energy constant $h$\nand the norm of the perihelion is constant.\nIn the Kepler case,\nonce we fix the value of $h>0$\nthere is only one bi-hyperbolic motion\nconnecting a given pair $(a,b)$ (see \\cite{Alb}).\nTherefore we can see the norm of the perihelion\nas a function of the limit shapes.\nWe can see that the norm of the perihelion\ntends to $0$ for $a\\to b$,\nand tends to $+\\infty$ for $a\\to -b$.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection*{Acknowledgements}\nThe authors would like to express\na very special thank to Albert Fathi,\nwho suggested the use of the method\nof viscosity solutions, as well as the way\nto construct the maximal calibrating curves\nof the horofunctions. \nThe first author is also grateful to\nAlain Albouy, Alain Chenciner and Andreas Knauf\nfor several helpful conversations at the IMCCE.\nFinally, we would like to thank the referee\nfor his accurate and helpful comments,\nand Juan Manuel Burgos\nfor pointing out a subtle mistake in one of the proofs.\n\n\n\n\n\n\n \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nUnderstanding open system dynamics and decoherence is important in several areas of quantum physics~\\cite{BreuerBook_2002,RivasBook_2012}. During the last ten years, there have been significant developments in both understanding the role of non-Markovian memory-effects~\\cite{Rivas_2014, Breuer_2016, Hall_2018, Li_2019,Li_2019_EPL2} and in developing improved tools and techniques to treat open system \ndynamics~\\cite{Vega_2017}.\nHere, one of the common themes is the role that various types of correlations play in open system dynamics. In particular, understanding\n initial correlations between composite environments~\\cite{Laine_2012,Liu_2013,Laine_2014,Xiang_2014,Liu_2016,HamedaniRaja_2017} and the role of initial system-environment correlations~\\cite{pechukas94,Alicki_1995,pechukas95,jordan04,shaji05a,Linta-Shaji,Wiseman_2019,Lyyra_2018,Alipour_2019}  have led to fundamental insights as well as practical knowledge regarding open systems.\n\nPhotons  provide a common and  highly controllable system where the influence of correlations can be studied both conceptually and practically~\\cite{Laine_2012,Liu_2013,Laine_2014,Xiang_2014,Liu_2016,HamedaniRaja_2017,Lyyra_2018}. Here, the polarization state of the photon is the open system and its frequency is the environment. Polarization and  frequency are coupled via birefringence leading to dephasing of a polarization state of the photon(s). The control of initial frequency distribution allows for the engineering of the decoherence and it is also possible to exploit various correlations for single photon or composite two-photon systems~\\cite{ElsiNature2011,ElsiPRL2012,Lyyra_2018}.\n\nOn the one hand, dephasing dynamics of photons has often been described using the concept of decoherence functions and subsequent family of completely positive (CP) dynamical maps, in the past. On the other hand, master equations are one of the most common tools to treat open system dynamics~\\cite{BreuerBook_2002}. However, master equations have not been used extensively when considering multipartite photonic systems and dephasing.\nWe consider first a bipartite two-photon system where the initial system-enviroment state is factorized whilst there exist initial correlations between the environmental states. \nIt has been shown earlier that this induces non-local memory effects in open system dynamics~\\cite{ElsiPRL2012,Liu_2013}. However,  the role of these types of initial correlations and non-local memory effects have not been considered on the level of master equations before, to the best of our knowledge. We derive generic master equations which display explicitly the role of initial correlations both on the dephasing rates and on the operator form of the master equation.  This allows also to reveal how even quite straightforward changes in the initial environmental state change drastically the description of photonic dephasing and increases the number of jump operators in the master equation. \n\nContinuing within the framework of correlations and open systems, we also study another long-standing problem in this context.\nThis is the role that initial system-environment correlations play in open system dynamics. Here, our interest is to see, what kind of insight the recently developed\n\\textit{bath positive decomposition} method~\\cite{Wiseman_2019} allows when studying the open dynamics of the polarization states. This very general method is based on decomposing initial arbitrary system-environment \nstate to a number of terms where each term can be treated with its individual CP-map. We show that for single-photon dephasing, this decomposition allows to describe, in a insightful way, how initial correlations influence the dynamics beyond the contribution arising from the factorized part.\n\nThe structure of the paper is the following. In the next section we describe briefly the basics of photonic dephasing.\nIn Section \\ref{sec3} we focus on the correlations within the composite environment and derive various master equations in this context and discuss the insight they provide.\nSection \\ref{sec4}, in turn, describes the initially correlated system-environment case for single photon and Sec.~\\ref{sec5} concludes the paper.\n\n\\section{Preliminaries with single photon dephasing dynamics}\n\nWe start with a brief recall of the single-photon dephasing model~\\cite{ElsiNature2011}.\nPolarization degree of freedom and frequency degree of freedom of a photon correspond to the open system and its environment, respectively. To begin with, we consider initially factorized joint polarization-frequency state \n\\begin{equation}\n\\hat{\\rho}_{SE}(0)=\\hat{\\rho}_S(0)\\otimes \\ket{\\Omega}\\bra{\\Omega}.\n\\end{equation}\nHere,  $\\hat{\\rho}_S(0)$ is the density operator of the initial polarization state and \n\\begin{equation}\n\\ket{\\Omega}= \\int d \\omega \\; g(\\omega)\\ket{\\omega},\n\\end{equation}\nis the initial  frequency state where $g(\\omega)$ is the probability amplitude that the photon has frequency $\\omega$. \nThe polarization Hilbert space is discrete and spanned by the horizontal-vertical polarization basis $\\{\\ket{h},\\ket{v}\\}$, while the Hilbert space of the frequency degree of freedom is spanned by the continuous frequency basis $\\{\\ket{\\omega}\\}$. \n\nThe system-environment -- or polarization-frequency -- interaction is provided by the Hamiltonian ($\\hbar=1$)\n\\begin{equation}\\label{eq:Hamiltonian}\n\\hat{H}=(n_h\\ket{h}\\bra{h}+n_v\\ket{v}\\bra{v})\\otimes\\int d \\omega \\; \\omega \\; \\ket{\\omega}\\bra{\\omega} ,\n\\end{equation}\nwhere $n_h$ ($n_v$) is the refraction index for polarization component $h$ ($v$).\nFor interaction time $t$, and tracing over the frequency, the reduced polarization state is\n\\begin{equation}\\label{eq:MapSinglePhoton}\n\\hat{\\rho}_S(t)=\\begin{pmatrix}\n\\bra{ h} \\rho_S(0)\\ket{h} & \\kappa(t)\\bra{ h} \\rho_S(0)\\ket{v} \\\\\n\\kappa(t)^{*}\\bra{ v} \\rho_S(0)\\ket{h} & \\bra{ v} \\rho_S(0)\\ket{v}.\n\\end{pmatrix},\n\\end{equation}\nHere, the dephasing dynamics is given by the decoherence function\n\\begin{equation}\n\\label{eq:kappa}\n \\kappa(t)=\\int d\\omega \\; \\vert g(\\omega)\\vert^2 \\mathrm{e}^{-i \\Delta n \\omega t},\n \\end{equation}\nwhere $\\Delta n \\equiv n_v-n_h$. Note that $0\\leq \\vert \\kappa(t) \\vert \\leq 1 $ for all times $t\\geq 0$ and $\\vert \\kappa(0) \\vert=1$. \n\nEquation \\eqref{eq:MapSinglePhoton} describes a $t$-parametrized completely positive (CP) map $\\hat{\\Phi}_t$, such that $\\hat{\\rho}_S(t)=\\hat{\\Phi}_t[\\hat{\\rho}_S(0)]$, and its corresponding master equation takes the form\n \\begin{equation}\\label{eq:MasterEq}\n\\frac{d}{dt}\\hat{\\rho}_S(t)=-i\\frac{\\nu(t)}{2}[\\hat{\\sigma}_z,\\hat{\\rho}_S(t)]+\\frac{\\gamma(t)}{2}[\\hat{\\sigma}_z \\hat{\\rho}_S(t) \\hat{\\sigma}_z-\\hat{\\rho}_S(t)].\n\\end{equation}\nHere,  $\\hat{\\sigma}_z$ is the Pauli $z$ operator and the rates $\\nu(t)$ and $\\gamma(t)$ can be expressed in terms of the decoherence function $\\kappa(t)$ as\n\\begin{equation}\\label{eq:Rates}\n\\gamma(t)=-\\Re \\bigg[\\frac{1}{\\kappa(t)} \\frac{d\\kappa(t)}{dt}\\bigg], \\quad \\nu(t)=-\\Im \\bigg[\\frac{1}{\\kappa(t)} \\frac{d\\kappa(t)}{dt}\\bigg],\n\\end{equation}\nwhere, $\\Re[\\cdot]$ and $\\Im[\\cdot]$ indicate the real and imaginary parts, respectively. \n\nEquation~\\eqref{eq:Rates} shows that once the decoherence function $\\kappa(t)$ is obtained from Eq.~\\eqref{eq:kappa}, then we can derive the corresponding rates in master equation ~\\eqref{eq:MasterEq}. Indeed,  the decoherence function $\\kappa(t)$ in Eq.~\\eqref{eq:kappa} is the Fourier transformation of the initial frequency \nprobability distribution $P(\\omega) =|g(\\omega)|^2$, and therefore the control of this distribution allows to study various types of dephasing maps and to engineer  the form and time dependence of the dephasing rate $\\gamma(t)$ in master equation ~\\eqref{eq:MasterEq}.\n\nFor example, a Gaussian frequency distribution with variance $\\sigma^2$ and mean value $\\bar{\\omega}$, i.e., \n\\[P(\\omega)=\\frac{\\mathrm{exp}[-(\\omega-\\bar{\\omega})^2\/2\\sigma^2]}{\\sqrt{2\\pi}\\sigma},\\]\nleads to a positive and time dependent dephasing rate $\\gamma(t)= \\Delta n ^2 \\sigma^2 t$ which presents a time-dependent Markovian dynamics. On the other hand, a Lorentzian distribution \n\\[P(\\omega)=\\frac{\\lambda}{\\pi[(\\omega-\\omega_0)^2+\\lambda^2]},\\]\nresults in a constant decay rate $\\gamma=\\lambda \\Delta n $, corresponding to dynamical semi-group and Lindbad-Gorini-Kossakowski-Sudarshan (LGKS) dynamics~\\cite{GoriniJmathPhys1976,LindbladCommun1976}. We note that the latter case has been also reported in \\cite{Smirne2014, Smirne2018}. \nThe transition from Markovian to non-Markovian regime, in turn,  is observed with further modifications of the frequency distribution~\\cite{ElsiNature2011}.\n\nIn the following, we generalize the master equation~in Eq.\\eqref{eq:MasterEq} to two-photon case. In particular, we are interested in how the initial correlations between the frequencies of the two photons influence the various dephasing rates and the operator form of the corresponding master equation for a bipartite open system. \n\n\\section{Master equation for two-photon dephasing dynamics: role of initially correlated joint frequency distribution} \\label{sec3}\n\nConsider a pair of photons, labeled $a$ and $b$, whose total polarization-frequency initial state is again in a factorized form\n\\begin{equation}\n\\hat{\\rho}_{SE}(0)=\\hat{\\rho}_S(0)\\otimes \\ket{\\Omega}\\bra{\\Omega},\n\\end{equation}\nwhere now\n\\begin{equation}\n\\ket{\\Omega}=\\int d \\omega_a \\int  d \\omega_b \\; g(\\omega_a,\\omega_b)\\ket{\\omega_a,\\omega_b},\n\\end{equation}\nis the initial state of the two-photon frequency degree of freedom and the corresponding joint probability distribution is $P(\\omega_a,\\omega_b)=\\vert g(\\omega_a,\\omega_b)\\vert ^2$. Initial polarization state is $\\hat{\\rho}_S(0)$, whose Hilbert space is spanned by the bipartite basis $\\{\\ket{hh},\\ket{hv},\\ket{vh},\\ket{vv}\\}$. \n\nThe polarization of each photon interacts locally with its own frequency and therefore system-environment interaction Hamiltonian for the two photons is a sum of the two local contributions~\\cite{ElsiPRL2012}\n\\begin{equation}\\label{eq:HamiltonianTwoPhoton}\n\\hat{H}=\\hat{H}_a \\otimes \\hat{I}_b +  \\hat{I}_a \\otimes \\hat{H}_b.\n\\end{equation}\nHere, each local term is given by Eq.~\\eqref{eq:Hamiltonian} and $\\hat{I}_a$ ($\\hat{I}_b$) is the identity operator for photon a (b).\n\nWe write initial bipartite polarization state $\\hat{\\rho}_S(0)$ as\n\\[\\hat{\\rho}_S(0)=\\sum_{\\alpha,\\beta}\\sum_{\\alpha',\\beta'}p_{\\alpha\\beta,\\alpha'\\beta'}\\ket{\\alpha \\beta}\\bra{\\alpha' \\beta'},\\]\nwith sums over $h$ and $v$. After interaction time $t$, the polarization state is \\citep{ElsiPRL2012}\n\\begin{flalign}\\label{eq:MapTwoPhotoon}\n&\\hat{\\rho}_S(t)=\n\\\\ \n&\\begin{pmatrix} \\nonumber\np_{hh,hh} & \\kappa_b(t)p_{hh,hv} & \\kappa_a(t)p_{hh,vh} & \\kappa_{ab}(t)p_{hh,vv} \\\\\n\\kappa_b^{*}(t) p_{hv,hh} & p_{hv,hv} & \\Lambda_{ab}(t)p_{hv,vh} & \\kappa_a(t)p_{hv,vv} \\\\\n\\kappa_a^{*}(t) p_{vh,hh} & \\Lambda_{ab}^{*}(t)p_{vh,hv} & p_{vh,vh} & \\kappa_b(t)p_{vh,vv} \\\\\n\\kappa_{ab}^{*}(t) p_{vv,hh} & \\kappa_a^{*}(t)p_{vv,hv} & \\kappa_b(t)^{*} p_{vv,vh} & p_{vv,vv}\n\\end{pmatrix}.\n\\end{flalign}\nHere, the local decoherence functions for photon $j=a,b$ are given by\n\\begin{equation}\n\\label{k-loc}\n\\kappa_j(t)=\\int d\\omega_a  \\int \\;d\\omega_b \\; \\vert g(\\omega_a, \\omega_b)\\vert^2 \\mathrm{e}^{-i \\Delta n \\omega_j t},\n\\end{equation}\nand the non-local ones by\n\\begin{equation}\n\\label{k1-nloc}\n\\kappa_{ab}(t)=\\int d\\omega_a \\int \\; d\\omega_b \\; \\vert g(\\omega_a, \\omega_b)\\vert^2 \\mathrm{e}^{-i \\Delta n(\\omega_a+\\omega_b)t},\n\\end{equation}\nand \n\\begin{equation}\n\\label{k2-nloc}\n\\Lambda_{ab}(t)=\\int d\\omega_a \\int \\; d\\omega_b \\;\\vert g(\\omega_a, \\omega_b)\\vert^2 \\mathrm{e}^{-i \\Delta n(\\omega_a-\\omega_b)t}.\n\\end{equation}\nThe density matrix evolution given by Eqs.~(\\ref{eq:MapTwoPhotoon}-\\ref{k2-nloc})\ncan also be described by a $t$-parametrized completely positive dynamical map $\\hat{\\Phi}_t$, such that \n\\begin{equation}\\label{eq:DynMap}\n\\hat{\\rho}_S(t)=\\hat{\\Phi}_t[\\hat{\\rho}_S(0)].\n\\end{equation} It is important to note that when the initial joint frequency distribution factorizes,  $P(\\omega_a,\\omega_b)=P_a(\\omega_a)\\times P_b(\\omega_b)$, then the global decoherence functions are products of the local ones, i.e.,\n$\\kappa_{ab} (t) = \\kappa_a (t)  \\kappa_b (t)$ and $\\Lambda_{ab} (t)=  \\kappa_a (t)  \\kappa^{\\ast}_b (t)$. Subsequently, the map for the bipartite photon system is tensor product of the local CP maps $\\hat{\\Phi}_t=\\hat{\\Phi}_t^{(a)} \\otimes \\hat{\\Phi}_t^{(b)}$. However, when the initial frequency distribution does not factorize, $P(\\omega_a,\\omega_b)\\neq P_a(\\omega_a)\\times P_b(\\omega_b)$, and contains correlations, then the map for the bipartite system is not anymore product of the local maps, $\\hat{\\Phi}_t\\neq\n\\hat{\\Phi}_t^{(a)} \\otimes \\hat{\\Phi}_t^{(b)}$~\\cite{ElsiPRL2012}. Now, we are interested in how to derive the generator of the corresponding non-local bipartite dynamical map and  what are the modifications in the corresponding  dephasing master equations when the amount of initial frequency correlations change.\n\nWe begin our derivation by writing the dynamical map formally as\n\\begin{equation}\\label{eq:dynMap}\n\\hat{\\Phi}_t = \\exp \\Big[\\int_0^t d\\tau \\hat{\\mathcal{L}}_{\\tau}\\Big],\n\\end{equation}\nwhere $\\hat{\\mathcal{L}}_t$ is the generator of the dynamics. Finding an expression for the generator then provides us the master equation we want to construct as\n\\begin{equation}\\label{eq:formalME}\n\\frac{d}{dt}\\hat{\\rho}_S(t)=\\hat{\\mathcal{L}}_t [\\hat{\\rho_S}(t)].\n\\end{equation}\nProvided that the map in Eq.~\\eqref{eq:dynMap} is invertible and its derivative is well-defined, one can obtain the generator as\n\\begin{equation}\\label{eq:genMapInvMap}\n\\mathcal{\\hat{L}}_t=\\frac{d}{dt}\\hat{\\Phi}_t \\circ \\hat{\\Phi}^{-1}_t.\n\\end{equation}\nTo find the generator in Eq.~\\eqref{eq:genMapInvMap} we need a suitable representation for the dynamical map $\\hat{\\Phi}_t$. With this in mind, we expand the two-photon density matrix $\\hat{\\rho}_S(t)$ in terms of a complete and orthonormal operator basis $\\{\\hat{F_{\\alpha}}\\}$. Specifically, we choose here fifteen generators of $\\mathrm{SU}(4)$, whose exact  expressions can be found in~\\cite{Alicki1987}, plus $\\hat{F}_1=\\hat{I}\/\\sqrt{4}$, such that $\\mathrm{Tr}[\\hat{F}_i^{\\dagger} \\hat{F}_j]=\\delta_{i j}$. It is worth mentioning that one can alternatively use the basis constructed by the tensor product of Pauli matrices plus the identity.  Fixing the basis for the representation, then the two-photon polarization state at time $t$ is\n\\begin{equation}\\label{eq:BlochVec1}\n\\hat{\\rho}_S(t)=\\sum_{\\alpha=1}^{16} r_{\\alpha} (t)\\hat{F}_{\\alpha}, \\qquad r_{\\alpha}(t)= \\mathrm{Tr}[\\hat{F}_{\\alpha}\\hat{\\rho}_S(t)],\n\\end{equation}\nwhere coefficients $\\{r_{\\alpha}\\}$ form the generalized Bloch vector corresponding to the state $\\hat{\\rho}_S(t)$ as\n\\begin{equation}\\label{eq:BlochVec2}\n\\vec{r}(t)=(1\/2,r_2(t),...,r_{16}(t))^{\\mathrm{T}}.\n\\end{equation} \nBy using Eq.~\\eqref{eq:BlochVec1} for both $\\hat{\\rho}_S(t)$ and $\\hat{\\rho}_S(0)$, we can write Eq.~\\eqref{eq:DynMap} as\n\\begin{equation}\\label{eq:MapBlochRep}\nr_{\\alpha}(t)=\\sum_{\\beta}[\\hat{\\Phi}_t]_{\\alpha \\beta} r_{\\beta}(0),\n\\end{equation}\nwhere $[\\hat{\\Phi}_t]$ is the transformation matrix corresponding to the map $\\hat{\\Phi}_t$ represented in the basis $\\{\\hat{F_{\\alpha}}\\}$. Elements of this matrix depend on the decoherence functions given in \nEqs.~(\\ref{k-loc}-\\ref{k2-nloc}) and each column can be systematically calculated by using a proper pair of initial and evolved states (c.f.~Eq.~\\eqref{eq:MapTwoPhotoon}). One can proceed to find the matrix representation of the generator by calculating the derivative and inverse of $[\\hat{\\Phi}_t]$ and using them in Eq.\\eqref{eq:genMapInvMap}, such that\n\\begin{equation}\\label{eq:genMat}\n[\\hat{\\mathcal{L}}_t]=\\frac{d}{dt}[\\hat{\\Phi}_t].[\\hat{\\Phi}_t]^{-1},\n\\end{equation}\nwhere we have replaced operator multiplication by matrix multiplication.\n\nLet us now consider the generator in a Lindblad operator form\n\\begin{eqnarray}\\label{eq:LindbladGen}\n\\hat{\\mathcal{L}}_t[\\hat{\\rho}_S(t)]&&=-i[\\hat{H}(t),\\hat{\\rho}_S(t)]+\n\\\\\n&&\\sum_{\\alpha=2}^{16}\\sum_{\\beta=2}^{16} R_{\\alpha \\beta}(t)\\Big(\\hat{F}_{\\alpha}\\hat{\\rho}_S(t) \\hat{F}_{\\beta}^{\\dagger}-\\frac{1}{2}\\{\\hat{F}_{\\beta}^{\\dagger}\\hat{F}_{\\alpha},\\hat{\\rho}_S(t)\\}\\Big), \\nonumber\n\\end{eqnarray}\nwhere \n\\begin{equation}\n\\hat{H}(t)=\\frac{-1}{2i}\\sum_{\\alpha=2}^{16}\\Big[R_{\\alpha1}(t)\\hat{F}_{\\alpha}-R_{1\\alpha}(t)^{*}\\hat{F}^{\\dagger}_{\\alpha}\\Big],\n\\end{equation}\ncaptures the environment induced coherent dynamics and $R_{\\alpha \\beta}(t)$ with $\\alpha, \\beta =2,3,...,16$ are elements of a $15\\times 15$ matrix providing the decay rates. Each element in the matrix representation of the generator then reads\n\\begin{equation}\\label{eq:equality}\n[\\hat{\\mathcal{L}}_t]_{\\alpha\\beta}=\\mathrm{Tr}[\\hat{F}_{\\alpha}^{\\dagger} \\hat{\\mathcal{L}}_t[\\hat{F}_{\\beta}]].\n\\end{equation}\nHere we use Eq.~\\eqref{eq:LindbladGen} in the right hand side. Finally, by elementwise comparison of Eq.~\\eqref{eq:equality} with Eq.~\\eqref{eq:genMat} we find the decay rates of the Lindblad master equation in Eq.~\\eqref{eq:LindbladGen} in terms of the decoherence functions in Eqs.~(\\ref{k-loc}-\\ref{k2-nloc}).\nBefore proceeding further, let us note that generator of a CP-divisible map always has a Linblad form \\cite{Alicki1987,GoriniJmathPhys1976,LindbladCommun1976,RivasBook_2012}. A map $\\hat{\\Phi}_t$ is CP-divisible  if it can be decomposed as $\\hat{\\Phi}_t=\\hat{\\Phi}_{t,s}\\hat{\\Phi}_s$ where the intermediate map $\\hat{\\Phi}_{t,s}$ is also a legitimate CP-map for all $t \\geqslant s \\geqslant0 $ \\cite{RivasPRL2010}. In this paper, however, we do not restrict ourselves to the CP-divisible maps and as we show later we also take non-Markovian dynamics into account.\n\nAfter finding the general expression for the decay rate matrix, it turns out that it is quite sparse and can be reduced to a $3\\times3$ matrix, which we denote by $R(t)$. The corresponding subspace is spanned by only three generators of $\\mathrm{SU}(4)$, which are linearly dependent on the operators $\\hat{I}_2 \\otimes \\hat{\\sigma}_z$, $\\hat{\\sigma}_z \\otimes \\hat{I}_2$, and $\\hat{\\sigma}_z \\otimes \\hat{\\sigma}_z$. This is indeed intuitive because population elements of the density matrix are invariant upon a dephasing channel, so those terms that couple the levels must be absent. \nThe explicit expression for the matrix $R(t)$, corresponding to a general frequency distribution, is provided in the Appendix. Considering this general result, we diagonalize it to rewrite the second term on r.h.s of Eq.~\\eqref{eq:LindbladGen} in the form\n\\begin{equation}\\label{eq:NormalizedME}\n\\hat{\\mathcal{D}}[\\hat{\\rho}_S(t)]=\\sum_{\\alpha=1}^{3} \\gamma_{\\alpha}(t)\\Big[\\hat{J}_{\\alpha}\\hat{\\rho}_S(t)\\hat{J}_{\\alpha}^{\\dagger}-\\frac{1}{2}\\{\\hat{J}_{\\alpha}^{\\dagger}\\hat{J}_{\\alpha},\\hat{\\rho}_S(t)\\}\\Big],\n\\end{equation}\nwhere \n\\begin{equation}\n\\begin{pmatrix}\n\\gamma_1(t) & 0 & 0 \\\\\n0 & \\gamma_2(t) & 0 \\\\\n0 & 0 & \\gamma_3(t)\n\\end{pmatrix}=U R(t) U^{\\dagger}, \\quad \\quad \\hat{J}_{\\alpha}=\\sum_j U_{\\alpha j}\\hat{F}_j,\n\\end{equation}\nand $U$ is the orthogonal transformation which diagonalizes the matrix $R(t)$. It is worth stressing that if the dynamical map in hand is CP-divisible, then all decay rates will be non-negative, i.e. $\\gamma_i(t)\\geq 0$ for all interaction times $t\\geq 0$. \n\nAbove general results hold for arbitrary initial frequency distributions.\nIn the following, we discuss explicitly initially correlated joint frequency distributions for bivariate single- and double-peak Gaussian cases.\nThese choices are motivated by their use in recent theoretical and experimental works, see e.g.~\\cite{ElsiNature2011,ElsiPRL2012,HamedaniRaja_2017}, and due to their ability to account for the explicit influence of frequency correlations in the dephasing dynamics.\n\n\\subsection{Single-peak bivariate Gaussian distribution}\n\nConsider the joint bivariate  Gaussian frequency distribution $P_{ab}(\\omega_a, \\omega_b)$\nand its covariance matrix $C$, such that $C_{ij}=\\langle \\omega_i \\omega_j\\rangle-\\langle\\omega_i\\rangle\\langle \\omega_j \\rangle$ for $i,j=a,b$ \\citep{ElsiPRL2012}.\nThe correlation coefficient is now given by $ K=C_{ab}\/\\sqrt{C_{aa}C_{bb}}$, such that $-1\\leq K \\leq 1$. A fully anti-correlated initial frequency distribution has $K=-1$, which dictates that for any pair of $\\omega_a$ and $\\omega_b$ we have $\\omega_a+\\omega_b\\equiv \\omega_0$, with some constant frequency $\\omega_0$.\nThe means of the local single photon frequency distributions are given by $(\\bar{\\omega}_a,\\bar{\\omega}_b)^{\\mathrm{T}}$ and we denote the difference between the local means as $\\bar{\\omega}_a-\\bar{\\omega}_b =\\Delta\\omega$ and their sum as $\\bar{\\omega}_a+\\bar{\\omega}_b =\\omega_0$. \nUsing Eqs.~(\\ref{k-loc}-\\ref{k2-nloc}) and denoting the variance of the distribution by $\\sigma^2$,  the decoherence functions become\n\\begin{flalign}\n&\\kappa_a(t)=\\mathrm{exp}\\Big[\\frac{-\\sigma^2 \\Delta n^2 t^2-i \\Delta n t (\\omega_0+\\Delta\\omega)}{2}\\Big],\n\\\\\n&\\kappa_b(t)=\\mathrm{exp}\\Big[\\frac{-\\sigma^2 \\Delta n^2 t^2-i \\Delta n t (\\omega_0-\\Delta\\omega)}{2}\\Big],\n\\\\\n&\\kappa_{ab}(t)=\\mathrm{exp}\\big[-\\sigma^2 \\Delta n^2 t^2(1+K)-i \\Delta n t \\omega_0\\big],\n\\\\\n&\\Lambda_{ab}(t)=\\mathrm{exp}\\big[-\\sigma^2 \\Delta n^2 t^2(1-K)-i \\Delta n t \\Delta\\omega\\big].\n\\end{flalign}\nIt is straightforward to check that the corresponding transformation matrix $[\\hat{\\Phi}_t]$ for the generalized Bloch vector is always invertible when time $t$ is finite. \nAfter inserting the above expressions for the decay rate matrix $R(t)$, see the Appendix, and followed by diagonalization, we obtain the rates  appearing in the master equation~\\eqref{eq:NormalizedME} as follows\n\\begin{flalign}\n&\\gamma_1(t)=2(1-K)\\sigma^2 \\Delta n^2 t,\\label{eq:gamma1}\n\\\\\n&\\gamma_2(t)=2(1+K)\\sigma^2 \\Delta n^2 t,\\label{eq:gamma2}\n\\\\\n&\\gamma_3(t)=0,\\label{eq:gamma3}\n\\end{flalign}\nand the corresponding jump operators \n\\begin{flalign}\n&\\hat{J}_1=\\frac{1}{2\\sqrt{2}}(\\hat{I}_2\\otimes \\hat{\\sigma}_z + \\hat{\\sigma}_z \\otimes \\hat{I}_2),\\label{eq:J1}\n\\\\\n&\\hat{J}_2=\\frac{1}{2\\sqrt{2}}(\\hat{I}_2\\otimes \\hat{\\sigma}_z - \\hat{\\sigma}_z \\otimes \\hat{I}_2),\\label{eq:J2}\n\\\\\n&\\hat{J}_3=\\frac{1}{2}\\hat{\\sigma}_z \\otimes \\hat{\\sigma}_z.\\label{eq:J3}\n\\end{flalign}\n\nDephasing rates $\\gamma_1$ and $\\gamma_2$ are linear functions of time and their slopes depend on the correlation coefficient $K$. Figure~\\ref{fig1} displays the rates for  $K=-1,0,1$. Since all the rates are non-negative and the first two are time dependent, this leads to CP-divisible dynamics which, however, does not fulfil the LGKS semigroup property. It is also interesting to note here the absence of the jump operator $\\hat{\\sigma}_z \\otimes \\hat{\\sigma}_z$ since the corresponding rate $\\gamma_3$ is always equal to zero. \nMoreover, the role of the environmental correlation coefficient $K$ of the initial joint frequency distribution is now explicit in expressions~(\\ref{eq:gamma1}-\\ref{eq:gamma3}). When $K=1$ ($K=-1$) the rate $\\gamma_1=0$ ($\\gamma_2=0$) and we are left with only one dephasing channel given by $\\hat{J}_2$ ($\\hat{J}_1$).  When there are no initial correlations between the two environments, $K=0$, then \n$\\gamma_1(t)=\\gamma_2(t)$. Subsequently, the corresponding generator and master equation contain equally weighted contributions of \n the two local jump operators $\\hat{J}_1$ and $\\hat{J}_2$. Changing the value of  the initial correlations $K$ allows then to tune the dynamics between the above mentioned extreme cases.\n\nIt is also worth discussing similarities and differences between our photonic model and the two-qubit model interacting with a common environment\n \\cite{PalmaPROC1996, ReinaPRA2002, CironeNEWJPhys2009, AddisPRA2013}. In the latter model two qubits are spatially separated by  a distance $D$, while they both interact with same physical and common bosonic environment. It is interesting that the master equation describing this model has the exact same operator form and jump operators \\cite{AddisPRA2013} obtained in equations \\eqref{eq:J1} to \\eqref{eq:J3}. In addition, decay rates derived in \\cite{AddisPRA2013} exhibit similar dependence on the distance $D$, as our decay rates here depend on the correlation coefficient $K$. Moreover, when $D \\rightarrow \\infty$, the dynamical map will be factorized to $\\hat{\\Phi}_t=\\hat{\\Phi}_t^{(a)} \\otimes  \\hat{\\Phi}_t^{(b)}$, with the superscripts corresponding to each qubit. The same behavior is also captured here when $K \\rightarrow 0$.\n However, it is worth keeping in mind that in our case the two environments are distinct physical entities and the tuning of the generator -- or form of the master equation -- is obtained by changing the initial bipartite environmental state. Furthermore, we can tune the generator continuously between the fully correlated and anti-correlated cases.\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.95 \\columnwidth, height = 1.5 cm]{gamma1SP.pdf}\n\\includegraphics[width=0.95 \\columnwidth, height = 1.5 cm]{gamma2.pdf}\n\\includegraphics[width=0.95 \\columnwidth ,height = 2.4 cm]{gamma3SP.pdf}\n\\caption{(Color online) Decay rates as a function of normalized interaction time in the case of single-peak Gaussian frequency distribution. Large-dashed green when $K=-1$, solid black when $K=0$, and small-dashed red when $K=-1$. Here we set $\\Delta \\omega \/\\sigma=2$.}\n\\label{fig1}\n\\end{figure} \n\n\n\\subsection{Double-peak bivariate Gaussian distribution}\n\nWe consider a double-peak frequency distribution as sum of two single-peak bivariate Gaussian distributions, already used in \\cite{HamedaniRaja_2017}, such that \n\\begin{equation}\nP(\\omega_a,\\omega_b)=[P_1(\\omega_a, \\omega_b)+ P_2(\\omega_a, \\omega_b)]\/2.\n\\end{equation}\nWe assume that both single-peak terms have the same correlation coefficient $K$ and standard deviation $\\sigma$, but their means are located at $(\\omega_0\/2-\\Delta \\omega\/2,\\omega_0\/2+\\Delta \\omega\/2)^{\\mathrm{T}}$ and $(\\omega_0\/2+\\Delta \\omega\/2,\\omega_0\/2-\\Delta \\omega\/2)^{\\mathrm{T}}$, respectively. Please note that the correlation coefficient $K$ of each single-peak distribution $P_1(P_2)$ does not equal to the actual correlation coefficient of the bivariate distribution $P$, obtained by its covariance matrix. In more detail, whenever we have nonzero $K$ for each single-peak, we have non-zero correlation in $P$. But note that if $K=0$, then we still have correlation in $P$ as long as we have non-zero peak separation, $\\Delta \\omega \\neq 0$.\n\nThe decoherence functions calculated from Eqs.~(\\ref{k-loc}-\\ref{k2-nloc}) become\n\\begin{flalign}\n&\\kappa_a(t)=\\mathrm{exp}\\bigg[\\frac{-\\sigma^2 \\Delta n^2 t^2-i t \\Delta n \\omega_0}{2}\\bigg]\\cos\\bigg(\\frac{t \\Delta n \\Delta \\omega}{2}\\bigg),\n\\\\\n&\\kappa_b(t)=\\kappa_a(t),\n\\\\\n&\\kappa_{ab}(t)=\\mathrm{exp}\\big[-\\sigma^2 \\Delta n^2 t^2 (1+K)-i t \\Delta n \\omega_0\\big],\n\\\\\n&\\Lambda_{ab}(t)=\\mathrm{exp}\\big[-\\sigma^2 \\Delta n^2 t^2 (1-K)\\big]\\cos(t \\Delta n \\Delta \\omega).\n\\end{flalign}\nBy using the earlier obtained general results, in a similar manner compared to single-peak case, we obtain the dephasing\nrates\n\\begin{flalign}\n&\\gamma_1(t)=2(1-K)\\sigma^2 \\Delta n^2 t+ \\tan(t \\Delta n  \\Delta \\omega )\\Delta n \\Delta \\omega ,\\label{eq:gamma1Two}\n\\\\\n&\\gamma_2(t)=2(1+K)\\sigma^2 \\Delta n^2 t,\\label{eq:gamma2Two}\n\\\\\n&\\gamma_3(t)= \\frac{1}{2} \\tan \\bigg(\\frac{t \\Delta n \\Delta \\omega}{2} \\bigg)\\big[1-\\sec (t \\Delta n \\Delta \\omega)\\big]\\Delta n \\Delta \\omega.\\label{eq:gamma3Two}\n\\end{flalign}\nThe corresponding jump operators $\\{\\hat{J}_1, \\hat{J}_2, \\hat{J}_3\\}$ are the same as in the single-peak case, see Eqs.~(\\ref{eq:J1}-\\ref{eq:J3}).\nIn the limit $\\Delta \\omega \\rightarrow 0$ corresponding to single peak case, the rates~(\\ref{eq:gamma1Two}-\\ref{eq:gamma3Two}) reduce to those given by\n Eqs.~(\\ref{eq:gamma1}-\\ref{eq:gamma3}).\n\nFigure~\\ref{fig2} displays the rates for $K=-1,0,1$.\nDephasing rate $\\gamma_2$ remains the same as in the single peak case. However, rate $\\gamma_1$ -- corresponding to $\\hat{J}_1$ including the sum of the local jump operators -- changes. The rate includes now an extra term, coming from the peak separation $\\Delta \\omega$,  \nand an oscillatory part displaying negative values of the rate as a function of time. This also leads to non-Markovian dephasing dynamics which is not CP-divisible. It is even more striking that introducing the double-peak frequency structure, opens now an additional dephasing channel since the rate $\\gamma_3$ is non-zero. Here, the corresponding jump operator $\\hat{J}_3=\\frac{1}{2}\\hat{\\sigma}_z \\otimes \\hat{\\sigma}_z$ displays a joint bipartite structure, in contrast to local features of $\\hat{J}_1$ and $\\hat{J}_2$. This is an interesting observation since the system-environment interaction Hamiltonian is the same as before having only local interactions, see Eq.~(\\ref{eq:HamiltonianTwoPhoton}), whilst the only change introduced was going from single- to double-peak structure of the initial bipartite environmental state. It is also worth noting that even though $\\gamma_3$ is independent \nof $K$, its functional form is non-trivial since it contains the peak separation $\\Delta \\omega$ and trigonometric functions. \n\nThere is a somewhat subtle mathematical point related to the behavior of rates $\\gamma_1$ [Eq.~\\eqref{eq:gamma1Two}] and $\\gamma_3$ [Eq.~\\eqref{eq:gamma3Two}] which needs an attention. Indeed, $\\gamma_1(t)$ and $\\gamma_3(t)$ diverge at isolated points of times. Subsequently, the corresponding dynamical maps are non-invertible at these points. According to the Eq.~\\eqref{eq:MapBlochRep}, the generalized Bloch vector of the two-photon polarization state at time $t$ reads\n\n\\begin{equation}\n\\vec{r}(t)=\\left(\n\\begin{array}{c}\n \\frac{1}{2} \\\\\n  \\Gamma_0\\cos(t\\Delta\\Omega\/2)[\\cos(t\\Omega_0\/2)r_2-\\sin(t\\Omega_0\/2)r_3] \\\\\n   \\Gamma_0\\cos(t\\Delta\\Omega\/2)[\\cos(t\\Omega_0\/2)r_3+\\sin(t\\Omega_0\/2)r_2] \\\\\n r_4 \\\\\n   \\Gamma_0\\cos(t\\Delta\\Omega\/2)[\\cos(t\\Omega_0\/2)r_5-\\sin(t\\Omega_0\/2)r_6] \\\\\n   \\Gamma_0\\cos(t\\Delta\\Omega\/2)[\\cos(t\\Omega_0\/2)r_6+\\sin(t\\Omega_0\/2)r_5] \\\\\n  \\Gamma_-\\cos(t\\Delta \\Omega)r_7 \\\\\n  \\Gamma_-\\cos(t\\Delta \\Omega)r_8 \\\\\n r_9 \\\\\n  \\Gamma_+[\\cos(t\\Omega_0)r_{10}-\\sin(t\\Omega_0)r_{11}] \\\\\n  \\Gamma_+[\\cos(t\\Omega_0)r_{11}+\\sin(t\\Omega_0)r_{10}] \\\\\n  \\Gamma_0\\cos(t\\Delta\\Omega\/2)[\\cos(t\\Omega_0\/2)r_{12}-\\sin(t\\Omega_0\/2)r_{13}] \\\\\n   \\Gamma_0\\cos(t\\Delta\\Omega\/2)[\\cos(t\\Omega_0\/2)r_{13}+\\sin(t\\Omega_0\/2)r_{12}] \\\\\n   \\Gamma_0\\cos(t\\Delta\\Omega\/2)[\\cos(t\\Omega_0\/2)r_{14}-\\sin(t\\Omega_0\/2)r_{15}] \\\\\n   \\Gamma_0\\cos(t\\Delta\\Omega\/2)[\\cos(t\\Omega_0\/2)r_{15}+\\sin(t\\Omega_0\/2)r_{14}] \\\\\n r_{16} \\\\\n\\end{array}\n\\right),\n\\end{equation}\nwhere we have defined $\\Gamma_0=\\exp[-\\sigma^2 \\Delta n^2 t^2\/2]$, $\\Gamma_{\\pm}=\\exp[-\\sigma^2 \\Delta n^2 t^2(1\\pm K)]$, $ \\Delta\\Omega= \\Delta n \\Delta \\omega$, $\\Omega_0=\\Delta n \\omega_0$, and $\\vec{r}(0)=(1\/2,r_2,r_3,...,r_{16})^T$ is the initial Bloch vector. One can check that all of the different initial vectors (states) that share the same values of $r_4,r_7,r_8,r_9,r_{10},r_{11}$, and $r_{16}$ are mapped to the same vector (state) at $t=\\pi \/\\Delta \\Omega$. This many to one nature of the map --  at these isolated times -- makes it non-invertible. Although all the trajectories corresponding to the aforementioned initial vectors end up together at the isolated points, it is evident that they continue their different paths immediately after this. This can be seen in the following way. Consider the generator of the master equation in matrix form and its action on the generalized Bloch vector.\nWe see that while some rates diverge at certain points in time, it is precisely at these points that the generalized Bloch vector components -- with which the rates get multiplied -- all go to zero. In more detail, we have\n\\begin{equation}\n\\frac{d}{dt} r_{\\alpha}(t)=\\sum_{\\beta}[\\hat{\\mathcal{L}}_t]_{\\alpha \\beta} \\, r_{\\beta}(t),\n\\end{equation}\ntherefore, the product of the divergent rate with the zero value component leads to a finite rate of change of the Bloch vector which allows us to continue propagation of each state forward in time. Accordingly, following the trajectories immediately before they unite at a single point, lets us identify each one of them immediately after that, when they separate again. We see therefore that in spite of the divergences in the rates, the master equation we have obtained describes the dephasing evolution of the two-photon polarization state in meaningful way.\nIt is also worth noting that the divergent decoherence rates in master equations have appeared in earlier literature many times, e.g., in the prominent resonant Jaynes-Cummings model~\\cite{BreuerBook_2002}.\n \n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.95 \\columnwidth, height = 1.5 cm]{gamma1DP.pdf}\n\\includegraphics[width=0.95 \\columnwidth, height = 1.5 cm]{gamma2.pdf}\n\\includegraphics[width=0.95 \\columnwidth ,height = 2.4 cm]{gamma3DP.pdf}\n\\caption{(Color online) Decay rates as a function of normalized interaction time in the case of double-peak Gaussian frequency distribution. Dashed green when $K=-1$, solid black when $K=0$, and dot-dashed when $K=-1$. Here we set $\\Delta \\omega \/\\sigma=2$.}\n\\label{fig2}\n\\end{figure} \n\\section{Single-photon dephasing with initial polarization-frequency correlations} \\label{sec4}\n\nWe described above how initial correlations between the composite environmental states influence the generator of the dynamical map and the corresponding master equation for photonic dephasing. In this section we continue with initial correlations but \ntake a different perspective by considering non-factorized initial system-evironmental state for single qubit.\nThis is motivated by the recent observation that initial system-environment correlations can be exploited for arbitrary control of single qubit dephasing~\\cite{Lyyra_2018}. We revisit this problem and obtain new insight by exploiting the very recently developed general method of \\textit{bath positive decomposition} ($\\mathrm{B+}$ decomposition) ~\\cite{Wiseman_2019}. \nIn general,  presence of initial system-environment correlations implies that the open system evolution is not described by a CP dynamical map   \\cite{pechukas94,Alicki_1995,pechukas95,jordan04,shaji05a,Linta-Shaji}. However, $\\mathrm{B+}$ decomposition method allows to treat this case with a set of CP maps, where each term of the decomposition is evolved over time with its individual CP map~\\cite{Wiseman_2019}. \n\n\\subsection{Preliminaries on $\\mathrm{B+}$ decomposition for initially correlated system-environment state}\nFollowing~\\cite{Wiseman_2019} we begin by considering arbitrary system-environment state -- in the corresponding Hilbert space $\\mathcal{H}=\\mathcal{H}_S\\otimes \\mathcal{H}_E$ -- and write it as \n\\begin{equation}\\label{eq:BplusDecom}\n\\hat{\\rho}_{SE}(0)=\\sum_{\\alpha}w_{\\alpha}\\hat{Q}_{\\alpha}\\otimes \\hat{\\rho}_{\\alpha}.\n\\end{equation} \nHere, $\\{\\hat{Q}_{\\alpha}\\}$ forms a basis (possibly overcomplete) for operators on $\\mathcal{H}_S$ and $\\{\\hat{\\rho}_{\\alpha}\\}$ are valid environmental density operators on $\\mathcal{H}_E$. Note that $\\hat{Q}_{\\alpha}$ need not be positive or trace orthogonal, so they may not constitute proper density matrices on the system Hilbert space. However when the initial state is factorized, this summation reduces to a single term $\\hat{\\rho}_{SE}(0)=\\hat{\\rho}_S(0)\\otimes \\hat{\\rho}_E(0)$ corresponding to reduced states of the open system and environment, respectively. In general, number of terms in this summation is restricted by $1\\leq N\\leq d^2$ where $d$ is the dimension of the system Hilbert space \\cite{Wiseman_2019}. All the information about initial state of the open system is incorporated in the weights $w_{\\alpha}$, such that $\\hat{\\rho}_S(0)=\\mathrm{Tr}_E[\\hat{\\rho}_{SE}(0)]=\\sum w_{\\alpha}\\hat{Q}_{\\alpha}$. Although $\\hat{Q}_{\\alpha}$ may not be legitimate density operators for the open system, those expressed by $\\hat{\\rho}_{\\alpha}$ are valid density operators for the environment. This means that the factorized form of the terms in \\eqref{eq:BplusDecom} allows to write the dynamics of the open system state as the weighted sum of legitimate CP-maps acting on $\\hat{Q}_{\\alpha}$. In more detail, if the total system-environment evolves due to a unitary operator $\\hat{U}(t)$, one has\n\\begin{eqnarray}\n\\hat{\\rho}_S(t)&&=\\sum_{\\alpha}w_{\\alpha}\\mathrm{Tr}_E[\\hat{U}(t)(\\hat{Q}_{\\alpha} \\otimes \\hat{\\rho}_{\\alpha})\\hat{U}(t)^{\\dagger}] \\nonumber\n\\\\\n&&=\\sum_{\\alpha}w_{\\alpha}\\hat{\\Phi}^{(\\alpha)}_t[\\hat{Q}_{\\alpha}],\n\\end{eqnarray}\nwhere\n\\begin{equation}\\label{eq:BPlusDecMap}\n\\hat{\\Phi}_t^{(\\alpha)}[\\cdot]:=\\mathrm{Tr}_E[\\hat{U}(t)(\\cdot\\otimes\\hat{\\rho}_{\\alpha})\\hat{U}(t)^{\\dagger}].\n\\end{equation}\nSince all maps of the form given in Eq.\\eqref{eq:BPlusDecMap} are CP, all previous tools for studying CP-maps are applicable here. In particular, one can investigate properties of each CP-map $\\Phi^{(\\alpha)}_t$ and see how they are connected to the presence of initial correlations.\n\nFor example, consider single qubit dynamics in the presence of initial system-environment correlations~\\cite{Wiseman_2019} . Using completeness of Pauli sigma basis $\\{I_2,\\hat{\\sigma}_x,\\hat{\\sigma}_y,\\hat{\\sigma}_z\\}$, we have \n\\begin{equation}\\label{eq:BplusDecQubit}\n\\hat{\\rho}_{SE}(0)=\\sum_{\\alpha=0,x,y,z} w_{\\alpha} \\hat{Q}_{\\alpha}\\otimes \\hat{\\rho}_{\\alpha},\n\\end{equation}\nin which\n\\begin{eqnarray}\n&&\\hat{Q}_0=\\frac{1}{2}(\\hat{I}_2 - \\hat{\\sigma}_x - \\hat{\\sigma}_y - \\hat{\\sigma}_z),\\label{eq:Q0}\\\\\n&&\\hat{Q}_{\\alpha}=\\frac{1}{2}\\hat{\\sigma}_{\\alpha} \\quad for \\; \\alpha = x,y,z,\\label{eq:Qalpha}\n\\end{eqnarray}\nand\n\\begin{eqnarray}\n&&\\hat{\\rho}_0=\\mathrm{Tr}_S[\\hat{\\rho}_{SE}(0)]=\\hat{\\rho}_E(0),\\label{rho1}\n\\\\\n&&\\hat{\\rho}_{\\alpha}=\\frac{\\mathrm{Tr}_S[((\\hat{I}_2+\\hat{\\sigma}_{\\alpha})\\otimes \\hat{I}_E)\\hat{\\rho}_{SE}(0)]}{w_{\\alpha}},\\label{rho2}\n\\end{eqnarray}\nwith $w_0=1$, and $w_{\\alpha}=\\mathrm{Tr}[((\\hat{I}_2+\\hat{\\sigma}_{\\alpha})\\otimes \\hat{I}_E)\\hat{\\rho}_{SE}(0)]$ for ${\\alpha}=x,y,z$.\nWe exploit these generic expressions below.\n\n\\subsection{Initial polarization-frequency correlation and $\\mathrm{B+}$ decomposition for single photon}\n\nWe consider initial polarization-frequency correlations by following the recent results and experimental work on generating, in principle, arbitrary single-photon dephasing dynamics~\\cite{Lyyra_2018}. Generic initial polarization-frequency state can be written as\n\\begin{eqnarray}\\label{eq:InStateCorrelated}\n\\ket{\\psi(0)}_{SE}=&& C_v\\ket{v}\\otimes\\int d \\omega g(\\omega)\\ket{\\omega}\\nonumber\n\\\\\n&&\\quad+C_h\\ket{h}\\otimes\\int d \\omega g(\\omega)\\mathrm{e}^{i \\theta(\\omega)}\\ket{\\omega},\n\\end{eqnarray}\nwhere $\\vert C_h \\vert ^2+\\vert C_v \\vert ^2=1$ and $\\int d \\omega \\vert g(\\omega ) \\vert ^2=1$.\nAbove, the crucial ingredient is the frequency dependent initial phase $\\theta(\\omega)$ for the component including the polarization $h$.\nIf $\\theta(\\omega)$ is a constant function, then there are no initial system-environment correlations. However, controlling the non-constant functional form of $\\theta(\\omega)$\nallows to control the initial correlations and their amount.\n  \nWhen the initial state evolves according to the interaction Hamiltonian in Eg.~\\eqref{eq:Hamiltonian}, the reduced polarization state at time $t$ is\n\\begin{equation}\\label{eq:MapInCorrel}\n\\hat{\\rho}(t)=\\begin{pmatrix}\n\\vert C_h \\vert ^2 & \\kappa(t)C_h C_v^{*} \\\\\n\\kappa(t)^{*}C_h^{*} C_v & \\vert C_v \\vert ^2\n\\end{pmatrix},\n\\end{equation}\nwhere the decoherence function is \n\\begin{equation}\\label{eq:decFuncCorrel}\n\\kappa(t)=\\int d \\omega \\vert g(\\omega) \\vert ^2  \\mathrm{e}^{i \\theta(\\omega)}\\mathrm{e}^{-i \\Delta n \\omega t}.\n\\end{equation}\nNote that in addition to the frequency probability distribution $|g(\\omega)|^2$, one can now use also $\\theta(\\omega)$, and subsequent initial correlations, to control the dephasing dynamics.\n\nThe dynamics given by Eqs.~(\\ref{eq:MapInCorrel}-\\ref{eq:decFuncCorrel}) can be equivalently formulated by using the $\\mathrm{B}+$ decomposition. \nConsidering the initial total state in Eq.~\\eqref{eq:InStateCorrelated}, and applying the $\\mathrm{B}+$ decomposition along Eq.~\\eqref{eq:BplusDecQubit} and  Eq.~\\eqref{rho1}-\\eqref{rho2}, we obtain environmental terms\n\\begin{widetext}\n\\begin{eqnarray}\n&&\\hat{\\rho}_0=\\int d\\omega \\int d\\omega'\\; g(\\omega)g(\\omega')^{*}\\;\\big(\\vert C_h\\vert ^2 \\mathrm{e}^{i[\\theta(\\omega)-\\theta(\\omega')]}+\\vert C_v\\vert ^2\\big)\\ket{\\omega}\\bra{\\omega'},\n\\\\\n&&\\hat{\\rho}_x=\\frac{1}{w_x}\\int d\\omega \\int d\\omega'\\; g(\\omega)g(\\omega')^{*}\\;\\big(\\vert C_h\\vert ^2 \\mathrm{e}^{i[\\theta(\\omega)-\\theta(\\omega')]}+\\vert C_v\\vert ^2+C_h C_v^{*}\\mathrm{e}^{i\\theta(\\omega')}+C_v C_h^{*}\\mathrm{e}^{-i\\theta(\\omega)}\\big)\\ket{\\omega}\\bra{\\omega'},\n\\\\\n&&\\hat{\\rho}_y=\\frac{1}{w_y}\\int d\\omega \\int d\\omega' \\;g(\\omega)g(\\omega')^{*}\\;\\big(\\vert C_h\\vert ^2 \\mathrm{e}^{i[\\theta(\\omega)-\\theta(\\omega')]}+\\vert C_v\\vert ^2+i C_h C_v^{*}\\mathrm{e}^{i\\theta(\\omega')}- i C_v C_h^{*}\\mathrm{e}^{-i\\theta(\\omega)}\\big)\\ket{\\omega}\\bra{\\omega'},\n\\\\\n&&\\hat{\\rho}_z=\\int d\\omega \\int d\\omega'\\; g(\\omega)g(\\omega')^{*}\\;\\ket{\\omega}\\bra{\\omega'},\n\\end{eqnarray}\n\\end{widetext}\nwith weights\n\\begin{eqnarray}\n&&w_x=1+2\\int d\\omega \\vert g(\\omega)\\vert ^2 \\Re{[C_v C_h^{*}\\mathrm{e}^{-i\\theta(\\omega)}]},\n\\\\\n&&w_y=1+2\\int d\\omega \\vert g(\\omega)\\vert ^2 \\Im{[C_v C_h^{*}\\mathrm{e}^{-i\\theta(\\omega)}]},\n\\\\\n&&w_z=2\\vert C_h\\vert ^2.\n\\end{eqnarray}\nEach specific term of the $\\mathrm{B}+$ decomposition is related to a frequency state ($\\hat{\\rho}_{\\alpha}$) above, and acts on its own input system operator $\\hat{Q}_{\\alpha}$, see Eqs~(\\ref{eq:Q0}-\\ref{eq:Qalpha}). In the current case, we can combine the contributions of $\\hat{\\rho}_0$ and $\\hat{\\rho}_z$ to simplify the decomposition into only three terms. Subsequently, polarization density matrix at time $t$ is given by  \n\\begin{eqnarray}\\label{eq:MapInCorrThreeTerms}\n\\hat{\\rho}(t)&=&\\frac{1}{2}\\begin{pmatrix} \\nonumber\nw_z & \\kappa_0(t)(i-1) \\\\\n\\kappa_0(t)^{*}(-i-1) & 2-w_z\n\\end{pmatrix}\n\\\\\n&&+\\frac{1}{2} w_x\\begin{pmatrix} \\nonumber\n0 & \\kappa_x(t) \\\\\n\\kappa_x(t)^{*} & 0\n\\end{pmatrix}\n\\\\\n&&+\\frac{1}{2} w_y\\begin{pmatrix}\n0 & -i \\kappa_y(t) \\\\\ni \\kappa_y(t)^{*} & 0\n\\end{pmatrix},\n\\end{eqnarray}\nwhere the three different decoherence functions are given by\n\\begin{flalign}\n&\\kappa_0(t)=\\int d \\omega \\vert g(\\omega)\\vert ^2 \\mathrm{e}^{-i \\Delta n \\omega t}, \\label{d1}\n\\\\\n&\\kappa_x(t)=\\frac{\\int d \\omega \\vert g(\\omega)\\vert ^2 (1+2 \\Re{[C_v C_h^{*}\\mathrm{e}^{-i\\theta(\\omega)}]})\\mathrm{e}^{-i \\Delta n \\omega t}}{w_x}, \\label{d2}\n\\\\\n&\\kappa_y(t)=\\frac{\\int d \\omega \\vert g(\\omega)\\vert ^2 (1+2 \\Im{[C_v C_h^{*}\\mathrm{e}^{-i\\theta(\\omega)}]})\\mathrm{e}^{-i \\Delta n \\omega t}}{w_y}.\\label{d3}\n\\end{flalign}\nIt is interesting to note here that the decoherence function $\\kappa_0$ is independent of $\\theta(\\omega)$ and actually corresponds directly to the case when there are no initial polarization-frequency correlations.\nThe other two functions, $\\kappa_x$ and $\\kappa_y$, depend also on $\\theta(\\omega)$ and describe in detail how the initial correlations change the dephasing dynamics.\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{kSimDAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{k0DAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{kxDAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth ,height = 2 cm]{kyDAbs.pdf}\n\\caption{(Color online) Non-positive map decoherence functions. Magnitudes of the original decoherence function ($\\kappa$) and $\\mathrm{B}+$ decomposition decoherence functions ($\\kappa_0, \\kappa_x, \\kappa_y$) as a function of time. We set $C_h=C_v=1\/\\sqrt{2}$.}\\label{fig3}\n\\end{figure}\n\n\nIt is also interesting to compare Eq.~\\eqref{eq:MapInCorrThreeTerms} with the $\\mathrm{B+}$ decomposition for generic dephasing dynamics of a qubit coupled to a Bosonic bath, when qubit and bath are initially correlated \\citep{Wiseman_2019}. The total Hamiltonian of the qubit and the Bosonic bath reads\n\\begin{equation}\n\\hat{H}=\\omega_q \\; \\hat{\\sigma}_z+\\sum_i \\; \\omega_i \\hat{b}^{\\dagger}_i \\hat{b}_i+\\hat{\\sigma}_z\\otimes \\sum_i g_i (\\hat{b}^{\\dagger}_i+\\hat{b}_i),\n\\end{equation}\nwhere $\\omega_q$ is the qubit's energy level separation (in $\\ket{0}$, $\\ket{1}$ basis), $\\hat{b}^{\\dagger}_i$ and $\\hat{b}_i$ are bath mode creation and annihilation operators respectively, and $g_i$ is the coupling strength. Employing the $\\mathrm{B+}$ decomposition, dynamics of the off-diagonal element of the qubit's density matrix in the interaction picture reads \\citep{Wiseman_2019}\n\\begin{equation}\\label{eq:dephasScale}\n\\bra{0}\\rho_S(t)\\ket{1}=\\sum_{\\alpha}\\;w_{\\alpha} \\bra{0}\\hat{Q}_{\\alpha}\\ket{1}\\chi_{\\hat{\\rho}_{\\alpha}}(\\vec{\\xi}_t),\n\\end{equation}\nwhere $\\chi_{\\hat{\\rho}_{\\alpha}}(\\vec{\\xi}_t)=\\mathrm{Tr}_B[\\hat{\\rho}_{\\alpha}\\hat{D}(\\vec{\\xi}_t)]$ is the Wigner characteristic function of the bath state $\\hat{\\rho}_{\\alpha}$. Above $\\vec{\\xi}_t=(\\xi_1(t),\\xi_2(t),...)$ with\n\\[\\xi_j(t)=2g_j \\bigg(\\frac{1-\\mathrm{e}^{i\\omega_j t}}{\\omega_j}\\bigg) ,\\]\nand $\\hat{D}(\\vec{\\xi}_t)=\\exp(\\sum_i \\xi_i \\hat{b}^{\\dagger}_i+\\xi^{*}\\hat{b}_i)$ is the Glauber displacement operator. The comparison between \nEqs.~\\eqref{eq:MapInCorrThreeTerms} and \\eqref{eq:dephasScale} reveals that the decoherence functions in our photonic model -- corresponding to integral transformations of the frequency probability distribution and frequency dependent phase $\\theta(\\omega)$ --   play the exact same role as the characteristic functions in the dephasing dynamics of a qubit coupled to Bosonic bath.\n\nLet us go back to the photonic model and see in detail, for some examples, what is the relation between the orginal decoherence function \\eqref{eq:decFuncCorrel} and those appearing in the $\\mathrm{B}+$ decomposition in Eqs.~(\\ref{d1}-\\ref{d3}). In particular, we consider the similar cases as used in~\\citep{Lyyra_2018} to demonstrate arbitrary control of dephasing dynamics. These include a non-positive map, Markovian, non-Markovian, and coherence trapping dynamics.\nIn all of the cases below, the frequency distributions used and the values for $\\theta(\\omega)$ are similar to those considered in Ref.~\\citep{Lyyra_2018}, respectively.\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.83 \\columnwidth, height = 1.5 cm]{k0DReIm.pdf}\n\\includegraphics[width=0.83 \\columnwidth, height = 1.5 cm]{kxDReIm.pdf}\n\\includegraphics[width=0.83 \\columnwidth, height = 2 cm]{kyDReIm.pdf}\n\\caption{(Color online) Non-positive map decoherence functions. Real and imaginary parts of the original decoherence function ($\\kappa$) and $\\mathrm{B}+$ decomposition decoherence functions ($\\kappa_0, \\kappa_x, \\kappa_y$) as a function of time. We set $C_h=C_v=1\/\\sqrt{2}$.}\n\\label{fig4}\n\\end{figure} \n\n\nFigure \\ref{fig3} shows the magnitude of various decoherence functions for the case of a non-positive (NP) map, i.e., $\\kappa (t) > \\kappa(0)$. \n It is easy to check that the off-diagonal term of the density matrix is obtained from $\\rho_{hv}(t)=(\\kappa_0(t)(i-1)+w_x \\kappa_x(t)-iw_y \\kappa_y(t))\/2$, and equivalently from $\\rho_{hv}(t)=\\kappa(t)C_h C_v^{*}$. Thereby, it is evident  that if $\\kappa_0(t)=\\kappa_x(t)=\\kappa_y(t)=0$, for some $t>0$, then $\\kappa(t)=0$. However, the reverse statement does not always hold. Instead, one can show that whenever $w_x=w_y=1$, then having identical decoherence functions, $\\kappa_0(t)=\\kappa_x(t)=\\kappa_y(t)$, is sufficient to have zero coherence, i.e., $\\kappa(t)=0$. This is an interesting result making a link between properties of the CP-maps obtained in $\\mathrm{B+}$ decomposition and  the original non-positive map. In fact, the case discussed in Fig. \\ref{fig3} demonstrates this situation.\nThis is even more evident when considering the real and imaginary parts of the decoherence functions explicitly, see Fig.~\\ref{fig4}. \nOne can see that the three decoherence functions $\\kappa_0$, $\\kappa_x$, and $\\kappa_y$ are identical when the interaction time is short. Therefore, since we also have $w_x = w_y = 1$, the decoherence function $\\kappa(t)$ has zero value in this regime.\n\nThe non-Markovian, Markovian, and coherence trapping cases are plotted respectively in Figs.~\\ref{fig5}, \\ref{fig6}, and \\ref{fig7}. Looking at the Fig.~\\ref{fig5}, one finds that $\\vert \\kappa(t) \\vert$ first decays to zero and then it revives again. This situation displays non-Markovian features, where coherence can revive after a period of disappearance. The Markovian case however illustrates a monotonically decaying  $\\vert \\kappa (t) \\vert$, see Fig.~\\ref{fig6}. Finally in the coherence trapping case we observe that $\\vert \\kappa(t) \\vert$ decays at first but mostly maintains its value later. \nMagnitudes of the other three decoherence \nfunctions, used in the $\\mathrm{B+}$ decomposition, are also plotted in the corresponding figures. We observe that these decoherence functions behave similarly, in contrast to the case of non-positive map. Again, whenever $\\kappa_0$, $\\kappa_x$, and $\\kappa_y$ are all zero, one has $\\kappa(t)=0$. However since $w_x$ and $w_y$ are not equal, we get a non-zero $\\kappa$, even though, $\\kappa_0$, $\\kappa_x$, and $\\kappa_y$ seem to be identical in some regions.\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{kSimAAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{k0AAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{kxAAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth ,height = 2 cm]{kyAAbs.pdf}\n\\caption{(Color online) Non-Markovian dynamics. Magnitudes of the original decoherence function ($\\kappa$) and $\\mathrm{B}+$ decomposition decoherence functions ($\\kappa_0, \\kappa_x, \\kappa_y$) as a function of time. We set $C_h=C_v=1\/\\sqrt{2}$.}\\label{fig5}\n\\end{figure} \n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{kSimBAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{k0BAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{kxBAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth ,height = 2 cm]{kyBAbs.pdf}\n\\caption{(Color online) Markovian dynamics. Magnitudes of the original decoherence function ($\\kappa$) and $\\mathrm{B}+$ decomposition decoherence functions ($\\kappa_0, \\kappa_x, \\kappa_y$) as a function of time. We set $C_h=C_v=1\/\\sqrt{2}$.}\\label{fig6}\n\\end{figure} \n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{kSimCAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{k0CAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth, height = 1.5 cm]{kxCAbs.pdf}\n\\includegraphics[width=0.8 \\columnwidth ,height = 2 cm]{kyCAbs.pdf}\n\\caption{(Color online) Coherence trapping dynamics. Magnitudes of the original decoherence function ($\\kappa$) and $\\mathrm{B}+$ decomposition decoherence functions ($\\kappa_0, \\kappa_x, \\kappa_y$) as a function of time. We set $C_h=C_v=1\/\\sqrt{2}$.}\n\\label{fig7}\n\\end{figure}\n\n\n\\section{Discussion} \\label{sec5}\nWe have studied the influence of initial correlations on open system dynamics from two perspectives corresponding to master equation descriptions and recently introduced $\\mathrm{B+}$ decomposition method. By using a common two-photon dephasing scenario with local polarization-frequency interaction, our results show explicitly how initial correlations -- between the composite environments (frequencies) -- influence the decoherence rates and operator form of the master equation for the polarization state.  When the environment has a single-peak gaussian structure, the master equation contains two sets of jump operators, corresponding to sum and difference between the local interactions, and  whose weights can be controlled by changing the amount of initial environmental correlations. Here, the dephasing rates are non-negative and depend linearly on time for the considered case. Having a double-peak bivariate structure, the situation changes drastically. This opens an additional dephasing path with a non-local form for the corresponding operator, and the associated rate also has divergences. Moreover, the rates for the other two dephasing operators have distinctive functional forms.\n\n $\\mathrm{B+}$ decomposition method, in turn, allows to study such cases where the system and environment are initially correlated, preventing the use of conventional CP-maps.  We have used this decomposition to study dephasing, when polarization and frequency of a single photon are initially correlated.\nThe results display in detail how the initial correlations change the dephasing contribution arising solely on initial factorized state.\nIndeed, instead of having one decoherence function associated to dephasing, we have now three different decoherence functions corresponding to the elements of the \n $\\mathrm{B+}$  decomposition. Here, one of the functions arises due to initially factorized part and additional two decoherence functions include also contributions from initial polarization-frequency correlations. In general, our results shed light and help in understanding how different types of correlations influence the dephasing dynamics within the commonly used photonic framework. \n \n\n\n\\section*{Acknowledgments}\nSina Hamedani Raja acknowledges finical support from Finnish Cultural Foundation. Anil Shaji acknowledges the support of the EU through the Erasmus+ program and support of the Science and Engineering Research Board, Government of India through EMR grant No. EMR\/2016\/007221.\n\\section*{Appendix}\nGeneral expressions for the elements of the nonzero subspace of the decay rate matrix, denoted by $R(t)$, are\n\\begin{widetext}\n\\begin{eqnarray}\n&&R_{11}(t)=-\\Re{[\\bold{k}_b(t)]},\n\\\\\n&&R_{12}(t)=\\frac{1}{\\sqrt{3}}\\Big(i\\Im{[\\bold{k}_b(t)]}-i\\Im{[\\bold{k}_a(t)]}+i\\Im{[\\bold{\\Gamma}_{ab}(t)]}+\\Re{[\\bold{\\Gamma}_{ab}(t)]}-\\Re{[\\bold{k}_{a}(t)]}\\Big),\n\\\\\n&&R_{13}(t)=\\frac{1}{2\\sqrt{6}}\\Big(4i\\Im{[\\bold{k}_a(t)]}+2i\\Im{[\\bold{k}_b(t)]}-3i\\Im{[\\bold{k}_{ab}(t)]}-i\\Im{[\\bold{\\Gamma}_{ab}(t)]}+4\\Re{[\\bold{k}_{a}(t)]}-3\\Re{[\\bold{k}_{ab}(t)]}-\\Re{[\\bold{\\Gamma}_{ab}(t)]}\\Big),\n\\\\\n&&R_{21}(t)=R_{12}(t)^{*},\n\\\\\n&&R_{22}(t)=\\frac{1}{3}\\Big(-2\\Re{[\\bold{k}_a(t)]}+\\Re{[\\bold{k}_b(t)]}-2\\Re{[\\bold{\\Gamma}_{ab}(t)]}\\Big),\n\\\\\n&&R_{23}(t)=\\frac{1}{6\\sqrt{2}}\\Big(-3i\\Im{[\\bold{k}_{ab}(t)]}+6i\\Im{[\\bold{k}_b(t)]}+3i\\Im{[\\bold{\\Gamma}_{ab}(t)]}-4\\Re{[\\bold{k}_{a}(t)]}-3\\Re{[\\bold{k}_{ab}(t)]}+8\\Re{[\\bold{k}_{b}(t)]}-\\Re{[\\bold{\\Gamma}_{ab}(t)]}\\Big),\n\\\\\n&&R_{31}(t)=R_{13}(t)^{*},\n\\\\\n&&R_{32}(t)=R_{23}(t)^{*},\n\\\\\n&&R_{33}(t)=\\frac{1}{6}\\Big(-2\\Re{[\\bold{k}_a(t)]}-3\\Re{[\\bold{k}_{ab}(t)]}-2\\Re{[\\bold{k}_b(t)]}+\\Re{[\\bold{\\Gamma}_{ab}(t)]}\\Big),\n\\end{eqnarray}\nwhere we have defined $\\bold{k}_i(t)=\\frac{1}{\\kappa_i(t)}\\frac{d}{dt}\\kappa_i(t)$, $\\bold{\\Gamma}_{ab}(t)=\\frac{1}{\\Lambda_{ab}(t)}\\frac{d}{dt}\\Lambda_{ab}(t)$ and $\\bold{k}_{ab}(t)=\\frac{1}{\\kappa_{ab}(t)}\\frac{d}{dt}\\kappa_{ab}(t)$.\n\\end{widetext}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzjuni b/data_all_eng_slimpj/shuffled/split2/finalzzjuni
new file mode 100644
index 0000000000000000000000000000000000000000..f47e41aec0fbd5a8fc82fdb51ced4755424fcd63
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzjuni
@@ -0,0 +1,5 @@
+{"text":"\\section{The SU(N+1) Schwarzschild-like Solution}\n\nIn a previous paper \\cite{sing} we exploited the connection between\ngeneral relativity and Yang-Mills theory to find an exact\nSchwarzschild-like solution for an SU(2) gauge theory coupled to\na massless scalar field. In the present paper we wish to show that\na similiar solution can be found for the general group SU(N+1).\nInstead of using the Euler-Lagrange formalism which leads to coupled\nsecond-order, nonlinear equations, we will use the Bogomolny\napproach \\cite{bogo} to derive our field equations.\nBogomolny  obtained his first-order version of the Yang-Mills\nfield equations by requiring that the gauge and scalar fields\nproduce an extremum of the canonical Hamiltonian. The field equations\nobtained in this way are first-order, but their solutions are\nalso solutions to the second-order Euler-Lagrange equations.\n\nThe model which we consider here is an SU(N+1) gauge field coupled\nto a massless scalar field in the adjoint representation. The\nLagrangian for this theory is\n\\begin{equation}\n\\label{lagran}\n{\\cal L} = -{1 \\over 4} F^{\\mu \\nu a} F_{\\mu \\nu} ^a + {1 \\over 2}\nD^{\\mu} ( \\Phi ^a ) D_{\\mu} ( \\Phi ^a)\n\\end{equation}\nwhere\n\\begin{equation}\nF_{\\mu \\nu} ^a = \\partial _{\\mu} W_{\\nu} ^a - \\partial _{\\nu}\nW_{\\mu} ^a + g f ^{abc} W_{\\mu} ^b W_{\\nu} ^c\n\\end{equation}\nand\n\\begin{equation}\nD_{\\mu} \\Phi ^a = \\partial _{\\mu} \\Phi ^a + g f ^{abc}\nW_{\\mu} ^b \\Phi ^c\n\\end{equation}\nwhere $f^{abc}$ are the structure constants of the gauge group\nand $a, b, c = 1, 2, \\dots , N, N+1$.\nThe canonical Hamiltonian obtained from Eq. (\\ref{lagran}) is\n\\begin{equation}\n\\label{hamo}\n{\\cal H} = \\int d^3 x \\left[{1 \\over 4} F_{ij} ^a F^{aij} - {1 \\over 2}\nF_{0i} ^a F^{a0i} + {1 \\over 2} D_i \\Phi ^a D^i \\Phi ^a\n- {1 \\over 2} D_0 \\Phi ^a D^0 \\Phi ^a \\right]\n\\end{equation}\nWe wish to find gauge and scalar fields which produce\nan extremum of ${\\cal H}$.\nFirst we rescale the scalar field ({\\it i.e.} $\\Phi ^a \\rightarrow\nA \\Phi ^a$). This is done so that later on it will be simple to examine\nthe pure gauge case by setting $A=0$.\nNext we specify that all the fields are time independent, and that\nthe time component of the gauge fields are proportional to the\nscalar fields ({\\it i.e} $W_0 ^a = C \\Phi ^a$, where $\\Phi ^a$ is\nthe rescaled scalar field). The time component of the gauge fields\nact like an additional Higgs field except its kinetic term appears\nwith the opposite sign in the Lagrangian \\cite{zee}. Using these two\nrequirements and the antisymmetry of $f^{abc}$ we find that\n$D_0 \\Phi ^a = 0$ and $F_{0i} ^a = C (D_i \\Phi ^a)$, so that the\nHamiltonian becomes\n\\begin{eqnarray}\n\\label{ham}\n{\\cal H} = \\int d^3 x \\Big[&&{1 \\over 4} \\left(F_{ij} ^a - \\epsilon_{ijk}\n\\sqrt{A^2 - C^2} D^k \\Phi ^a \\right) \\left(F^{aij} - \\epsilon_{ijl}\n\\sqrt{A^2 - C^2} D^l \\Phi ^a \\right) \\nonumber \\\\\n+ && {1 \\over 2} \\epsilon_{ijk} \\sqrt{A^2 - C^2}\nF^{aij} D^k \\Phi ^a \\Big]\n\\end{eqnarray}\nUsing the fact that\n\\begin{equation}\n{1 \\over 2} \\epsilon_{ijk} F^{aij} D^k \\Phi ^a = \\partial ^i\n\\left({1 \\over 2} \\epsilon_{ijk} F^{ajk} \\Phi ^a \\right)\n\\end{equation}\nand the requirement that the solutions we are looking for are\nonly functions of $r$ we find\n\\begin{eqnarray}\n\\label{ham1}\n{\\cal H} &=& \\sqrt{A^2 - C^2} \\int _S (\\Phi^a B^a _i)\ndS ^i \\nonumber \\\\\n&+& \\int d^3 x \\left[{1 \\over 4} \\left(F_{ij} ^a -\n\\epsilon_{ijk} \\sqrt{A^2 - C^2} D^k \\Phi ^a \\right)\n\\left(F^{aij} - \\epsilon_{ijl} \\sqrt{A^2 - C^2}\nD^l \\Phi ^a \\right) \\right]\n\\end{eqnarray}\nFor the total divergence term we\nhave used the definition of the non-Abelian\nmagnetic field in terms of the field strength tensor ({\\it i.e}\n$B^a _i = {1 \\over 2} \\epsilon_{ijk} F^{ajk}$), and used\nGauss's Law to turn the volume integral into a surface\nintegral. The lower limit of this Hamiltonian can be found by\nrequiring\n\\begin{eqnarray}\n\\label{fbogo}\nF_{ij} ^a &=& \\epsilon _{ijk} \\sqrt{ A^2 - C^2}\nD^k \\Phi ^a \\nonumber \\\\\nor \\nonumber \\\\\nB_i ^a &=& \\sqrt{A^2 - C^2} D_i \\Phi ^a\n\\end{eqnarray}\nTo get the second expression we have again used the definition of\nthe non-Abelian magnetic field. These are the Bogomolny equations\n\\cite{bogo}. Wilkinson and Goldhaber \\cite{gold} have given a\ngeneralized ansatz for the gauge and scalar fields\n\\begin{eqnarray}\n\\label{ansatz}\n{\\bf W}_i &=& {\\epsilon_{ijb} r^j ({\\bf T}^b - {\\bf M}^b (r)) \\over g r^2}\n\\nonumber \\\\\n\\Phi ^a &=& {{\\bf \\Phi} (r) \\over g}\n\\end{eqnarray}\n${\\bf W} _i$ are three $(N+1) \\times (N+1)$ matrices of the gauge\nfields. ${\\bf M}_b (r)$ and ${\\bf \\Phi} (r)$ are four $(N+1) \\times\n(N+1)$ matrices whose elements are functions of $r$, and in terms of\nwhich the Bogomolny equations will be written. ${\\bf T}_b$ are three\n$(N+1) \\times (N+1)$ matrices which generate the maximal embedding\nof SU(2) in SU(N+1). Because of the spherical symmetry requirement\none can look at Eq. (\\ref{fbogo}) along any axis \\cite{bais}\n\\cite{wilk}. Taking the positive $\\hat {z}$ axis the Bogomolny\nequations become $\\sqrt{ A^2 - C^2} (D_3 \\Phi ^a) = B _3 ^a$ and\n$\\sqrt{A^2 - C^2} (D_{\\pm} \\Phi ^a) = B_{\\pm} ^a$, or in terms of the\nansatz of Eq. (\\ref{ansatz})\n\\begin{eqnarray}\n\\label{fbogo1}\nr^2 \\sqrt{A^2 - C^2} {d {\\bf \\Phi} \\over dr} &=&\n[{\\bf M}_+  , {\\bf M}_- ] - {\\bf T}_3  \\nonumber \\\\\n{d {\\bf M}_{\\pm} \\over dr} &=& \\mp \\sqrt{A^2 - C^2}\n[{\\bf M}_{\\pm} , {\\bf \\Phi} ]\n\\end{eqnarray}\nTaking the third ``component'' of the maximal SU(2) embbedding into\nSU(N+1) as\n\\begin{equation}\n{\\bf T}_3 = diag \\left[{1 \\over 2}N, {1\\over 2}N -1, \\dots ,\n-{1 \\over 2} N +1, -{1 \\over 2} N \\right]\n\\end{equation}\nit has been shown \\cite{gold} that the matrix functions, ${\\bf M}_+ (r)$\nand ${\\bf \\Phi} (r)$, can be taken as\n\\begin{eqnarray}\n\\label{mat1}\n{\\bf \\Phi} = {1 \\over 2}\n\\left(\n\\begin{array}{ccccc}\n\\phi_1 &\\space &\\space &\\space &\\space \\\\\n\\space &\\phi_2 - \\phi_1 &\\space &\\space &\\space \\\\\n\\space &\\space &\\ddots &\\space &\\space \\\\\n\\space &\\space &\\space &\\phi_N -\\phi_{N-1} &\\space \\\\\n\\space &\\space &\\space &\\space &- \\phi _N \\\\\n\\end{array}\n\\right)\n\\end{eqnarray}\n\\begin{eqnarray}\n\\label{mat2}\n{\\bf M}_+ = {1 \\over \\sqrt{ 2}}\n\\left(\n\\begin{array}{ccccc}\n0 &a_1 &\\space &\\space &\\space \\\\\n\\space &0 &a_2 &\\space &\\space \\\\\n\\space &\\space &\\ddots &\\space &\\space \\\\\n\\space &\\space &\\space &0 &a_N \\\\\n\\space &\\space &\\space &\\space &0 \\\\\n\\end{array}\n\\right)\n\\end{eqnarray}\nwhere $\\phi _m$ and $a_m$ are real functions of $r$ and ${\\bf M}_- =\n({\\bf M} _+) ^T$. Substituting Eqs. (\\ref{mat1}), (\\ref{mat2}) into\nthe first order field equations of Eq. (\\ref{fbogo1}) the field\nequations become \\cite{bais} \\cite{wilk}\n\\begin{eqnarray}\n\\label{deqn}\nr^2  {d \\phi _m \\over dr} &=& {1 \\over \\sqrt{A^2 - C^2}}\n\\left[ (a_m)^2 - m{\\bar m} \\right] \\nonumber \\\\\n{d a_m \\over dr} &=& \\sqrt{A^2 - C^2} \\left(-{1 \\over 2} \\phi_{m-1}\n+\\phi_m - {1 \\over 2} \\phi _{m+1} \\right) a_m\n\\end{eqnarray}\nwhere $1 \\le m \\le N$, ${\\bar m} = N +1 - m$ and $\\phi_0 = \\phi_{N+1} =0$.\nExact solutions have been found to Eq. (\\ref{deqn}) \\cite{bais}\n\\cite{wilk} which are generalizations of the well known\nPrasad-Sommerfield solution \\cite{prasad} for SU(2). The\nPrasad-Sommerfield solution and their generalizations satisfy\nthe boundary condition that the gauge and scalar fields are\nfinite at the origin. If one does not require that the fields\nbe finite at the origin then the coupled equations for $\\phi _m (r)$\nand $a_m (r)$ can be solved by\n\\begin{eqnarray}\n\\label{soln}\n\\phi _m (r) &=& {1 \\over \\sqrt{A^2 - C^2}}\n{K m {\\bar m} \\over r (K - r)} \\nonumber \\\\\na_m (r) &=& {r \\sqrt{m {\\bar m}} \\over K - r}\n\\end{eqnarray}\n$K$ is an arbitrary constant with the dimensions\nof distance. This is the generalization of a similiar\nsolution which we found for SU(2) using the second-order\nEuler-Lagrange formalism \\cite{sing}. The reason for wanting to\ngeneralize our solution to SU(N+1) is to give a possible explanation for\nthe confinement mechanism in QCD whose gauge group is SU(3). Inserting\nthe functions $\\phi _m (r)$ and $a_m (r)$ of Eq. (\\ref{soln}) into\nthe fields of Eq. (\\ref{ansatz}) we find that these fields become\ninfinite at a finite radius of\n\\begin{equation}\nr_0 = K\n\\end{equation}\nThe non-Abelian ``electric'' ($E_i ^a = F_{0i} ^a$) and ``magnetic''\nfields ($B_i ^a = {1 \\over 2} \\epsilon_{ijk} F^{jka}$) calculated for\nthis solution also become infinite at $r_0$. Thus any particle which\ncarries an SU(N+1) charge would either never be able to penetrate beyond\n$r_0$ (when the SU(N+1) charges are replusive) or once it passed into\nthe region $r < r_0$ it would  never be able to escape  back to the\nregion $r > r_0$. One has in a sense a color charge black hole.\n\nBoth the present solution and our SU(2) solution were found by\nusing the connection between Yang-Mills theory and general relativity\n\\cite{utiyama}, and trying to find the Yang-Mills equivalent of the\nSchwarzschild solution. The objects in general relativity which correspond\nto the gauge fields are the Christoffel coefficients, $\\Gamma^{\\alpha}\n_{\\beta \\gamma}$. Examining a few of the Christoffel symbols of the\nSchwarzschild solution we find\n\\begin{eqnarray}\n\\Gamma ^t _{r t} &=& {2GM  \\over 2r ( r - 2GM )} \\nonumber \\\\\n\\Gamma ^r _{r r} &=& -{2GM  \\over 2r ( r - 2GM )}\n\\end{eqnarray}\nwhere $2GM$ the equivalent of the constant $K$ from the Yang-Mills\nsolution. The similarity between these Christoffel coefficients and the\ngauge and scalar fields that result from the solutions, $\\phi _m (r)$\nand $a_m (r)$ of Eq. (\\ref{soln}), is striking. The most important\nsimilarity from the point of explaining confinement is the existence\nin both solutions of an event horizon, from which particles which carry\nthe appropriate charge can not escape once they pass into the region\n$r < r_0$. For general relativity the appropriate ``charge'' is\nmass-energy so that nothing can climb back out of the Schwarzschild\nhorizon, while in the Yang-Mills case only particles carrying an SU(N+1)\ncharge will become confined.\n\nOne slightly disturbing feature of these Schwarzschild-like SU(N+1)\nsolutions is that they have an infinite energy due to the\nsingularity at $r = 0$.\nWhen quantities such as the energy of this field configuration\nare calculated the integral must be cutoff at some\narbitrary radius, $r_c$. The singularity at\n$r_0$ does not give an infinite energy unless one sets\n$r_c = K$. This singular behaviour at the origin is shared\nby several other classical field theory solutions. Both the\nSchwarzschild solution of general relativity, and the Coulomb solution\nin electromagnetism have similiar singularities.  The Wu-Yang\nsolution \\cite{wu} for static SU(2) gauge fields with no time component\nalso blows up at the origin, leading to an infinite energy if one\nintegrates the energy density down to $r=0$. Just as these classical\nsolutions are not expected to hold down to $r=0$ so the present solution\nwill certainly be modified by quantum corrections as $r$ approaches\nzero. Phenomenologically we know that the present solutions can not\nbe correct for very small $r$, since they do not exhibit the asymptotic\nfreedom behaviour that is a desirable consequences of the quantum\ncorrections to QCD. It would be interesting to see if the behaviour of\nthe fields at the origin could be modified by introducing a mass\nterm (${m^2 \\over 2} \\Phi ^a \\Phi ^a$) and a self interaction term\n(${\\lambda \\over 4} (\\Phi ^a \\Phi ^a) ^2$) to the scalar field part of\nthe Lagrangian, while still retaining the color event horizon feature of\nthe present solution. This smoothing of the fields at the origin does\nhappen when one compares the Prasad-Sommerfield exact solution (where\nthere are no mass or self interaction terms for the scalar field) with\nthe the numerical results of 't Hooft \\cite{thooft} or Julia and Zee\n\\cite{zee} (where mass and self interaction terms are included).\nThe numerical results lead to monopoles and dyons with a\nfinite core, while the exact Prasad-Sommerfield solution leads to a\npoint monopole (despite this their exact solution still has finite\nenergy when the energy density is integrated down to zero, unlike our\npresent solution). As in the case of the Prasad-Sommerfield solution,\nintroducing mass and self interaction terms for the scalar fields\nwould require solving the equations numerically, since we have\nnot been able to find an analytical solution under these conditions.\n\nTo calculate the energy of the field configuration of our solution it is\nnecessary to integrate the $T_{00}$ component of the energy-momentum\ntensor  over all space, excluding the origin. The  $T_{00}$\ncomponent of the energy-momentum tensor\nis similiar to the Hamiltonian density of Eq. (\\ref{ham}) except that\nall the terms have positive signs\n\\begin{equation}\nT_{00} = {1 \\over 4} F_{ij} ^a F^{aij} + {1 \\over 2} F_{0i} ^a\nF^{a0i} + {A^2 \\over 2} D_i \\Phi ^a D^i \\Phi ^a  + {A^2 \\over 2}\nD_0 \\Phi ^a D^0 \\Phi ^a\n\\end{equation}\nThe energy in the fields of our solution is the integral over all\nspace of $T_{00}$. Using the field equations of Eq. (\\ref{fbogo}),\nand the fact that $F_{0i} = C(D_i \\Phi ^a)$ the energy of the fields\nis\n\\begin{eqnarray}\nE &=& \\int T_{00} d^3 x \\nonumber \\\\\n&=& A^2 \\int d^3 x D_i \\Phi ^a D^i \\Phi ^a\n\\end{eqnarray}\nSince the fields only have a radial dependence the angular part\nof the integration can be easily done. Futher using the radial\nsymmetry to evaluate the integrand along the positive $\\hat{ z}$\naxis, and using the matrix expression for $\\Phi ^a$ as well as the\nfield equations, Eq. (\\ref{fbogo1}), we find that the energy\nbecomes \\cite{gold}\n\\begin{equation}\n\\label{energy1}\nE = {8 \\pi A^2 \\over g^2} \\int _{r_c} ^{\\infty} r^2 dr \\left(\nTr \\left( \\left[{d {\\bf \\Phi } \\over dr} \\right] ^2 \\right)\n+ {2 \\over \\ A^2 - C^2} Tr \\left( r^{-2} {d {\\bf M_+} \\over dr}\n{d {\\bf M_-} \\over dr} \\right) \\right)\n\\end{equation}\nUsing the solutions for the elements of the matrices,\n$\\bf{ \\Phi}$ and $\\bf{ M}_{\\pm}$ of Eq. (\\ref{soln}) we find\n\\begin{eqnarray}\n\\label{phim}\nTr \\left( \\left[ {d {\\bf \\Phi } \\over dr} \\right]^2 \\right)\n&=& {K^2 (2r - K)^2 \\over 4 r^4 (A^2 - C^2)\n(K - r)^4} \\sum _{n=0} ^N (N - 2n)^2 \\nonumber \\\\\nTr \\left( r^{-2} {d {\\bf M_+} \\over dr} {d {\\bf M_-} \\over dr} \\right)\n&=& {K^2 \\over r^2 (K-r)^4} \\sum _{n=0} ^N n(N+1-n)\n\\end{eqnarray}\nUsing this in Eq. (\\ref{energy1}) and carrying through the integration\nthe energy in the field configuration of this Schwarzschild-like\nsolution is\n\\begin{equation}\n\\label{energy2}\nE = {2 \\pi A^2 K^2 N(N+1)(N+2) \\over 3 g^2 (A^2 - C^2)}\n\\left[ {K  - 2 r_c \\over r_c (K -r_c)^3} \\right]\n\\end{equation}\nwhere the sums from Eq. (\\ref{phim}) have been done explicitly.\nThis result can be checked against the SU(2) result \\cite{sing}\nby taking  $N=1$ in Eq. (\\ref{energy2}), and the expressions for\nthe energy do indeed agree (In Ref. \\cite{sing} we required that\n$A^2 - C^2 =1$ whereas here this factor is divided out). As it\nstands there are two arbitrary constants that enter the solution\n({\\it i.e.} $K$ and $r_c$) which would have to be specified\nbefore any connection between this Schwarzschild-like solution\nand the real world could be carried out. As has already been\nmentioned $K$ is the Yang-Mills equivalent of $2GM$ in general\nrelativity. Thus it could be conjectured that $K$ is related\nto the strength of the gauge interaction\n($G$ in general relativity), and the\nmagnitude of the central charge which produces the gauge field\nconfiguration ($M$ in general relativity).\n\nOne interesting feature which this general SU(N+1) Schwarzschild-like\nsolution shares with our previous SU(2) solution is that scalar\nfields are apparently required in order to get a physically\nnon-trivial solution. If there where no scalar fields in the original\nLagrangian ({\\it i.e.} $A = 0$), then the field energy of Eq.\n(\\ref{energy2}) would be zero, and the $W_0 ^a$ component of the\ngauge fields would be pure imaginary. Although the pure gauge\ncase with no scalar fields is a solution mathematically, its\nphysical significance is dubious. Requiring that the\nsolutions are pure real, or that the energy in the fields\nbe non-zero would exclude the pure gauge case solution. Under either\nof these requirements on the solution, it can be seen that scalar\nfields must be present.\n\n\\section{Conclusions}\n\nIn this paper we have generalized our previous exact,\nSchwarzshild-like solution for SU(2) Yang-Mills theory\nto SU(N+1) by using an embedding of SU(2) into SU(N+1) \\cite{gold}.\nThis exact SU(N+1) solution was found by using the connection\nbetween general relativity and Yang-Mills theories. It was found that\nthe Schwarzschild solution of general relativity carries over\nwith only a little modification into an equivalent solution for an\nSU(N+1) gauge theory coupled to massless scalar fields. Just as the\nSchwarzschild solution possesses an event horizon which permanently\nconfines any particle which carries the ``charge'' of the  gravitational\ninteraction ({\\it i.e} mass-energy), so the present solution also\nhas a ``color'' event horizon which permanently confines any particle\nwhich carries the SU(N+1) gauge charge. This may be the confinement\nmechanism which has long been sought for the SU(3) gauge theory of\nthe strong interaction, QCD. Before this claim can be made there\nare several important questions which must be resolved. First, under\nsome reasonable physical assumptions about the nature of our solution\nit is found that scalar fields are required for a solution to\nexist. Normally scalar fields are not thought to play a significant role\nin confinement, so the physical importance of these scalar fields\nwould need to be addressed. Second, there are several arbitrary constants\nwhich crop up in the solution ($K$ and $r_c$). In order to make a\nconnection with the real world these constants would have to be given.\nTheoretically $K$ should be related to the strength of the gauge\ninteraction as well as the magnitude of the gauge charge which produces\nthe Schwarzschild-like gauge fields. Experimentally $K$ should be\nrelated to the radius of the various QCD bound states ({\\it e.g.}\nprotons, pions, etc.). The other constant, $r_c$, was\nintroduced chiefly to avoid the\nsingularity at $r=0$, but also because our solution does not\npossess the property of asymptotic freedom as $r \\rightarrow 0$.\nThis should not be too surprising since our solution is\nfor classical Yang-Mills fields, but as $r \\rightarrow 0$ quantum\neffects should become increasingly important.\nThus $r_c$ can be thought of roughly, as marking the boundary between\nthe classical, confining solution of this paper, and the quantum\ndominated asymptotic freedom regime. All this strongly suggests\na bag-like structure for QCD bound states : As a particle approaches\n$r = K$ from $r < K$, it feels a progressively  stronger color force\nwhich confines it to remain inside the bound state. As the particle\napproaches $r \\rightarrow 0$ it enters the asymptotic freedom\nregime, where it moves as if it were free.\n\nAn interesting extension of this work would be to see if other\nexact solutions from general relativity have Yang-Mills counterparts.\nIn particular if a Yang-Mills equivalent of the Kerr solution\ncould be found it might give some insight into the nature of\nthe spin of fermions.\n\n\\section{Acknowledgements}  I would like to acknowledge the help\nand suggestions of David Singleton and Hannelore Roscher.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nStarting with the original Great Dark Spot (GDS-89) observed by {\\it Voyager 2}, roughly a half-dozen large geophysical vortices have been observed on the Ice Giants. In 2015-2017, a feature was observed on Neptune in the southern hemisphere (SDS-2015) \\citep{Wong2016,Wong2018}. A recent observation as part of the Hubble Outer Planet Atmosphere Legacy (OPAL) program revealed a new dark spot with bright companion clouds in Neptune's northern hemisphere, NDS-2018 \\citep{Simon2019}. The structure is the most recent of large scale geophysical features\nto be observed on the ice giants. Although these Dark Spots have similar features to large vortices on Jupiter, such as the Great Red Spot, they exhibit dynamical motions such as shape oscillations and latitudinal drift. Neptune anticyclones evolve on a time scale of months \\citep{hsu2019} as opposed to large vortices on Jupiter, which evolve over many decades \\citep{Ingersoll2004}.  During the {\\it Voyager 2} encounter with Neptune beginning in January of 1989, GDS-89 was drifting towards the equator at an approximate rate of 1.3\\degree \/month \\citep{Sromovsky2002}. Post-{\\it Voyager 2} observations using the Hubble Space Telescope (HST) revealed that the vortex had dissipated as it approached the equator \\citep{HammelLockwood1997}. Many of the observed characteristics have been matched previously by numerical models\n(e.g., shape oscillation by \\citet{Polvani1990}, drift rate by \\citet{LeBeauDowling_Neptune} and companion cloud formation by \\citet{Stratman2001}). However, reproducing all of these features simultaneously has remained elusive.\n\nThese vortices exhibit surprising variability in terms of evolution, shape, drift, cloud distribution, and shape oscillations, so an explicit calculation of the environmental parameters is required for each vortex observed. However, this is beneficial because more diagnostic information can be obtained from each case than if the spot occurrences were repetitive in terms of their characteristics. For example, in the case of GDS-89, equatorial drift was observed \\citep{Smith1989,LeBeauDowling_Neptune} as opposed to the poleward drift of dark spot SDS-2015 \\citep{Wong2016,Wong2018}. In addition, GDS-89 had an accompanying cloud feature external to the dark spot, presumably condensed methane, whereas some vortices have centered bright companions such as D2 \\citep{Smith1989} and SDS-2015 \\citep{Wong2018}. \n\n\\citet{Stratman2001} demonstrated that orographic upwelling could be the cause of companion clouds. An analysis of these overlying orographic cloud features shows promising insight into the dynamics of clouds on Neptune, as the features are directly impacted by the underlying atmospheric structure and the deep methane abundance. To that end, it is necessary to apply a cloud microphysical model to make a more complete representation of dark spots. We use an updated microphysics calculation implemented in the Explicit Planetary Isentropic Coordinate General Circulation Model (EPIC GCM) \\citep{Dowling_EPICmodel1998,Dowling2006,Palotai2008} to account for methane cloud microphysics (see Section~\\ref{clouds}). We investigate the dynamics of vapor and subsequent persistent cloud formation on Neptune by modelling large scale vortices. \n \nClouds have been modelled explicitly in recent works to study the effect of convection \\citep[e.g.,][]{Sugiyama2011,Li2019} and the GRS \\citep{Palotai2014} on Jupiter, but not for Neptune. \n\n\nWe seek to answer the following questions: \n\\begin{enumerate}\n    \\item How does the addition of a methane cloud microphysical model affect the evolution of the vortex? \n    \\item How do various methane deep abundance (mole fraction) values affect the vortex? \n\\end{enumerate}\n\nTo investigate these questions, we use an increased horizontal grid resolution and increased number of vertical layers in the column compared to previous studies. \nAdditionally, we use methane vapor to track the vortex drift rate and shape oscillations whereas in previous studies, potential vorticity (PV) was used as the primary parameter to determine the features of the vortex.\n\n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/neptune_voyager.jpg}\n    \\caption{An image of the GDS-89 (dark feature near the center) taken by {\\it Voyager 2} in 1989. The high altitude white companion clouds around the GDS are visible. To the South, the Scooter, which is another dark spot observed by {\\it Voyager 2} is visible with its distinct centered cloud. Courtesy NASA\/JPL-Caltech.}\n    \\label{fig:GDS-89}\n\\end{figure}\n\n\\section{Methods}\n\\subsection{EPIC model}\nTo investigate persistent cloud formation on Neptune, we use the EPIC-GCM with an active hydrological cycle for methane.\nEPIC uses a hybrid vertical coordinate, $\\zeta$, described by \\citet{Dowling2006}. The top of the model uses potential temperature, $\\theta$, as a vertical coordinate while the bottom uses a scaled pressure variable, $\\sigma$. The transition between the two functions occurs at 10 hPa (see Figure \\ref{fig:TP}). Indeed, this transition allows for the use of EPIC on planets without a solid, terrestrial surface (i.e. gas giants) and increased vertical resolution at deeper layers where $\\theta$ is nearly constant. \n\n\\subsection{Cloud microphysics} \\label{clouds}\nWe use the active cloud microphysical model from \\cite{Palotai2008} which incorporates the condensation of methane in the EPIC model, with the revisions to precipitation given in \\cite{Palotai2016DPS}. \n\nThis scheme deals with bulk mass transfer between five explicit phases: vapor, cloud ice, liquid cloud droplet, snow and rain. The last two correspond to precipitation in the model and are subject to sedimentation at the terminal velocity.\n\nCloud particle sizes are diagnosed using the Gunn-Marshall distribution \\citep{GunnMarshall} for snow and the Marshall-Palmer distribution \\citep{MarshallPalmer} for rain. Both are log-normal with two free parameters describing the mean and standard-deviation of the particle-size distribution. We apply these distributions due to the low number of parameters (2) and the computational efficiency they provide compared to other, more recently retrieved parameterizations. Furthermore, most Earth-based literature use empirically derived distributions which are accurate for localised conditions, making them a poor choice for porting to gas-giant atmospheres \\citep{Palotai2008}.\n\n\\subsection{Fall Speed of Particles}\n\n\nTo speed up computation, we parameterize the terminal velocity snow particles of different diameters ($D$) using a power law:\n\\begin{equation}\\label{eq:fall_speed}\n    V_t = x D^y \\left( \\dfrac{p_0}{p}\\right)^{\\gamma}\n\\end{equation}\nwhere $x$, $y$ and $\\gamma$ are determined by fitting the terminal velocity calculated using  theoretical hydrodynamical principles  \\citep{PruppacherKlettBookFallSpeed}. $p_0=1$ bar is the reference pressure. Similarly to \\citet{Palotai2008}, we assume that snow is graupellike with a hexagonal shape and follow their formulation for calculating sedimentation velocity as a function of particle size. \n\nA plot of the terminal velocity of CH$_4$ and H$_2$S snow at a pressure of 1 bar is shown in Figure~\\ref{fig:termvel}, and the fit parameters for CH$_4$ and H$_2$S on Neptune are given in Table \\ref{tab:fall_speed}.\n\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/neptune_snow.png}\n    \\caption{Snow terminal velocity fits for CH$_4$ (solid) and H$_2$S (dashed) at 1 bar on Neptune.}\n    \\label{fig:termvel}\n\\end{figure}\n\nUsing the particle size distributions, the net sedimentation rate for a grid cell is calculated by weighting the terminal velocities by the mass of particles in each radius bin. Currently, only snow particles undergo sedimentation since the terminal velocity for cloud ice on Neptune is on the order of a few $\\mu$m\/s and thus fall only a few meters over the duration of our simulations.\n\n\\begin{table}\n\\begin{tabular}{|c|c|c|}\n\\hline\n\\centering\n  & CH$_4$ snow & H$_2$S snow  \\\\ \\hline \\hline\n$x$         & 14.5   & 22.2    \\\\ \\hline\n$y$         & 0.458  & 0.504   \\\\ \\hline\n$\\gamma$    & 0.320  & 0.320   \\\\ \\hline\n\\end{tabular}\n\\caption{These constants are determined from Eq. \\ref{eq:fall_speed} when $D$ is in meters and $V_t$ is in m\/s.}\n\\label{tab:fall_speed}\n\\end{table}\n\n\n\n\\subsection{Model setup} \\label{Environmental Initialization}\n\nWe run 3-dimensional simulations that span $-90\\degree$ to $0\\degree$ latitude and $-120\\degree$ to $120\\degree$ longitude with 256 points each resulting in horizontal boxes that are $0.5\\degree\\times1\\degree$ (lat$\\times$lon). These limits are sufficient to minimize the effects of the lateral boundaries on the simulated vortex and its associated clouds and prevent the vortex from interacting with itself \\citep{LeBeauDowling_Neptune}. The model covers 35 unequally spaced vertical layers between $1$ hPa and $14$ bar (see Figure \\ref{fig:TP}), which provides significantly higher resolution than previous studies of the GDS.\n\n\nThe pressure-temperature profile used in this study is shown in Figure \\ref{fig:TP}, which is an idealized curve taken from \\citet{LeBeauDowling_Neptune}. The black curve is from previous refinements of {\\it Voyager 2} radio-occultation T(P) data from \\citet{Conrath1991} and \\citet{Stratman2001} took helium at a 19\\% mole fraction. This profile is used as the initial input into the model at the equator. The temperature profile throughout the rest of the model is calculated using the thermal wind equation. The layers, shown on Figure \\ref{fig:TP} as horizontal lines on the right, were chosen in order to increase the resolution around the initial location of the spot (approximately 1 bar) in the vertical column and the methane cloud deck.  \nIn addition, since the model reaches up to 1 hPa, we can set the $\\sigma-\\theta$\ntransition at 10 hPa, or between $k = 2$ and $k = 3$ indicated by the intersection of the horizontal red line and the potential temperature profile in blue. We initialize equilibrium simulation using the idealized zonal wind profile $Q_y = \\frac{1}{3}$ from \\citet{LeBeauDowling_Neptune}\n, which closely matches the drift rate of the GDS-89 as opposed to other idealized curves (see Fig. \\ref{fig:zonal_wind} and Section \\ref{Drift_rate}). We run 130 day simulations to investigate stability, drift rate, and companion clouds throughout the model, with the ultimate goal of achieving similarities to the observations of GDS-89 and other vortices. Given that the observed periodicity in the oscillation of the GDS-89 was about 8 days \\citep{Sromovsky1993}, the model should be able to capture several periods of wobble in the vortex.\n\nInitially, the geopotential heights are determined in the model by integrating the hydrostatic equation. Due to numerical errors, the model is initially slightly unstable, so we run the model for 5 days to let the winds stabilize. During this time, cloud microphysics is turned off so as to not have spurious cloud growth. The spot is added to the model at the end of this equilibrium phase. \n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/tp_profile5.png}\n    \\caption{(a) shows the temperature and pressure profile of Neptune used in the EPIC model. (b) shows the potential temperature profile ($\\theta$) of Neptune (shown in blue). The horizontal black lines indicate the position of vertical layers used in the model. The GDS-89 extends from approximately 200 hPa to  3.5 bars (shown in the shaded region). The sigma-theta transition is also shown in red at 10 hPa.}\n    \\label{fig:TP}\n\\end{figure}\n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/zonal_wind.png}\n    \\caption{Mean zonal wind profile as a function of latitude using the pseudo PV gradient, $Q_y=\\frac{1}{3}$. The vortex is induced at roughly $32\\degree$ S latitude. }\n    \\label{fig:zonal_wind}\n\\end{figure}\n\n\n\\subsection{Methane abundance}\nThe primary goal of this work is to analyse the effect of methane on the dynamics and stability of the GDS-89. To that end, we vary the deep abundance (mole fraction) of carbon and initial ambient humidity in our test cases. \n\nIn the nominal case, we take the standard value of $40\\times$ the solar [C\/H] fraction for Neptune \\citep{Baines1995}, or an approximate CH$_4$ mole fraction of $\\textit{f}_{\\text{CH}_4} = 0.022^{+0.005}_{-0.006}$. The vertical methane abundance profile is initialized by a ``cold-trap\" model, where the mole fraction at the deepest layer is defined by a constant value (the deep abundance). Successive layers are limited by the minimum of the saturation mole fraction and the mixing ratio of the layer below. In our model, we take the initial relative humidity for all ``wet\" cases to be 95\\% to prevent spurious cloud growth in the first timestep. In a 3-dimensional model, advection of methane vapor and cooling produce localized supersaturation, which leads to cloud formation.\n\nWe run 5 cases which are shown in Table~\\ref{Cases}. Three include active cloud microphysics at different methane deep abundances. In the passive case, methane vapor is added to the model but does not condense. We also include a dry (H\/He atmosphere) case. These different parameters test both the effect of the additional mass from methane vapor and the latent heat release from cloud formation on the dynamics of the GDS. \n\n\\begin{table}\n\\centering\n\\begin{tabular}{ccc}\n\\hline\n\nCase    & Cloud microphysics & [C\/H] relative to solar \\\\ \\hline\\hline\n1       & On                 & $20$                                    \\\\ \\hline\n2       & On                 & $40$                                    \\\\ \\hline\n3       & On                 & $80$                                    \\\\ \\hline\n4       & Off                & $40$                                    \\\\ \\hline\n5       & Off                & -                                       \\\\ \\hline\n\\end{tabular}\n\\caption{A summary of cases tested in this study. For case 4, methane was added but cloud microphysical processes were turned off (i.e. methane vapor was subject only to advection). Case 5 is a dry model which has no added methane.}\n\\label{Cases}\n\\end{table}\n\n\\subsection{Addition of the Vortex} \\label{sec:addvort}\n\nWe utilize the vortex initialization as detailed in \\citet{LeBeauDowling_Neptune}, who use a Kida vortex model.\nThe vortex begins at a latitude of $32\\degree$ S at a pressure level of 1000 hPa ($k = 24$). The vortex extends roughly a scale height vertically in both directions (see Fig. \\ref{fig:TP}). The initial vortex adjustment period is about $6-8$ model days during which the shape of the spot changes drastically. As such, we begin our analysis after this adjustment period; $10$ days into the model. \n\nThe induction of the vortex creates a region of anomalous potential vorticity (PV) compared to the ambient zonal wind shear, defined as the difference in PV between the test case and the corresponding equilibrium simulation. PV has been used in previous modelling works \\citep[e.g.][]{LeBeauDowling_Neptune, Stratman2001} to study the GDS and is a useful tracer in dry models to track the vortex. We can define the extent of the GDS by a contour of constant anomalous PV at a pressure level of $1$ bar or $500$ hPa (the centre of initialized vortex). The shape and location of the vortex are then quantified by fitting an ellipse to these contours using the method of \\citet{HalirFlusser1998}. \n\n\nHowever, the PV of the simulated vortex is difficult to compare with {\\it Voyager 2} observations due to the lack of precise wind speed measurements. The change in the atmospheric structure by the addition of the vortex leads to a distinct variation in methane abundance inside the GDS, which can be used to track the dynamics of the spot in a similar way to PV and can also be compared with the observed spot opacity. By integrating the methane vapor density with depth, we obtain the column density (CD), which is analogous to optical depth in the upper troposphere. We then take the ratio of the CD to the equilibrium (see Section \\ref{Environmental Initialization}) and proceed similarly, by fitting an ellipse to a contour of constant CD. Hereafter, references to CD implies this ratio, unless otherwise specified.\n\n\n\n\n\\section{Results}\n\n\\subsection{1D Simulations}\nWe first run a 1-dimensional case with methane cloud formation enabled to test the microphysical processes and input parameters. We initialize the atmosphere with 150 layers between 1 hPa and 14 bar. We use a nominal value of $40\\times$ the solar [C\/H] fraction, and the model is initially saturated at 100\\% relative humidity everywhere. \n\nFrom equilibrium cloud condensation models (ECCM) \\citep[e.g.,][]{AtreyaWong2005}, methane ice clouds are predicted to form at around 15 bar. Figure~\\ref{fig:1dsim} shows the cloud as a function of time. The base of the clouds in the model are at about 1050 hPa. Snow is shown with the black contours and is precipitated out in a few hours. Cloud ice is most dense near the base and has a typical density of $\\sim 10^{-5}$ kg\/m$^3$. \n\n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/cloud_dens.png}\n    \\caption{Results from 1D simulations. Methane ice cloud is plotted in light blue and snow is plotted in black dashed contours. Colorbar corresponds to the base-10 log of the cloud density in kg\/m$^3$. }\n    \\label{fig:1dsim}\n\\end{figure}\n\n\\subsection{Potential vorticity} \\label{vorticity_dynamics}\nTo fit the vortex, we use the anomalous potential vorticity as a tracer. We also tracked the evolution of the anomalous PV within the vortex, as shown in Figure~\\ref{fig:pv_evolution}. As the vortex drifted equatorward, the background wind shear and the background potential vorticity increased. Consequently, although the total PV of the vortex itself was conserved, the anomalous potential vorticity of the vortex decreased with time, making it difficult to consistently track the vortex. Thus, we are limited to only the first 100 days of tracking the vortex with this method, after which the anomalous PV of the vortex was comparable to ambient noise. \n\n\nWe fit the anomalous PV at two levels: 1000 hPa and 500 hPa (Figure~\\ref{fig:cd_pv}), corresponding roughly to the vertical extent of the vortex. Below roughly 2000 hPa, the vortex is very weak and the anomalous PV is almost negligible. We find that the vortex is fairly uniform between the two layers, as the vortex is mostly equal in size and at the same position. The 1000 hPa anomalous PV decreases faster than the 500 hPa layer, and thus for all further analysis we report values from the vortex tracked using the 500 hPa anomalous PV.\n\n\n\\begin{figure*}\n    \\centering\n    \\includegraphics[width=1\\textwidth]{Figures\/panels5.png}\n    \\caption{Snapshots of the $40\\times$ solar methane abundance simulation showing CD fit (black), PV fit at 1 bar (red), and PV fit at 500 hPa (green) to the vortex, along with their respective centres ($\\times$). Methane column density is plotted in the background in blue, with the darker regions corresponding to lower CD (less vapour) with a lower limit of $-0.015$ kg\/m$^2$ and an upper limit of $0.4$ kg\/m$^2$ . The PV is shifted by about $1.5\\degree$ to the north east from the CD centre and decreases over time.}  \n    \\label{fig:cd_pv}\n\\end{figure*}\n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/pv_center_final.png}\n    \\caption{Temporal variation PV and anomalous PV\n    (both in units of m$^2$ K s$^{-1}$ kg$^{-1}$)\n    at 500 hPa inside the simulated GDS in our test cases using CD to track the vortex. In the dry case, only anomalous PV at 500 hPa was used to track the simulated GDS due to the lack of methane. } \n    \\label{fig:pv_evolution}\n\\end{figure}\n\n\\subsection{Drift Rate}\\label{Drift_rate}\n\\citet{LeBeauDowling_Neptune} investigated the equatorial drift of GDS-89 by using constant-vorticity gradient zonal wind profiles (Fig. \\ref{fig:zonal_wind}) and found that the value of the mid-latitude pseudo PV gradient, $Q_y$ is the primary influencer on meridionial drift. Using $Q_y=\\frac{1}{3}$, our experiments match the observed drift rate of the GDS-89 of $1.3\\degree$ per month \\citep{Sromovsky1993}.\n\nFigure \\ref{fig:drift_rate} shows the different cases investigated in this study and their latitudinal drift relative to the approximate observed drift rate of the GDS. Two lines per case are depicted, one for the PV at 500 hPa (dashed) and one for the methane column density (solid). Table \\ref{drift_rate_table} summarizes the average drift rate for each case investigated.\n\nCase 2 achieves the closest drift to the observed value of GDS-89, followed by Case 1. The  passive and dry cases (Cases 4 and 5 respectively) have the slowest drift. The $80\\times$ (Case 3) struggles to maintain dynamic stability throughout the simulation. We could not fit an ellipse around the vortex since it did not have a uniform shape and it dissipated after approximately 60 days. \n\n\\begin{table}\n\\centering\n\\begin{tabular}{ccc}\n\\hline\n\nCase    & CD Drift Rate [$\\degree$\/month] & PV Drift Rate [$\\degree$\/month]\\\\ \\hline\\hline\n1       & $0.82$   & $0.90$                                                   \\\\ \\hline\n2       & $1.36$ & $1.26$                                                     \\\\ \\hline\n3       & -        & -                                            \\\\ \\hline\n4       & $0.27$ & $0.31$                                                    \\\\ \\hline\n5       & - & $0.46$                                                   \\\\ \\hline\n\\end{tabular}\n\\caption{A summary of the approximate drift rate using either CD or PV at 500 hPa for each case. For case 3($80\\times$), we were unable to generate a fit. Case 5 is a dry model so PV alone was used to track the vortex.}\n\\label{drift_rate_table}\n\\end{table}\n\n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/drift_rate_final.png}\n    \\caption{Drift rate of the simulated GDS in our test cases. We used both methane column density (solid) and potential vorticity (dashed) at 500 hPa to fit the ellipse.  In the dry case, only PV at 500 hPa was used to track the simulated GDS due to the lack of methane. he dashed grey lines are the average meridional drift rate of the GDS-89 observed by {\\it Voyager 2} \\citep{Sromovsky1993}. }\n    \\label{fig:drift_rate}\n\\end{figure}\n\n\\subsection{Shape Oscillations}\\label{shape_oscillations}\nAlong with meridionial drift, time dependent oscillations in the shape of the vortex are of interest. Figure \\ref{fig:shape_oscillation} shows the inverted aspect ratio ($b\/a$) of the fitted ellipse for CD (Cases 1-4) and the PV at 1 bar (Case 5). In all cases, we correct for geometric effects by converting the extents to physical lengths using an equatorial radius of $24,760$ km and polar radius of $24,343$ km.  Clearly, these simulations exhibit complex dynamical variability in shape. The passive (Case 4) and dry (Case 5) cases have a lower inverted aspect ratio than the active cases (1-3) at around 0.3 as opposed to 0.4. Additionally, for the active cases, there does not appear to be a predictable frequency of oscillation and a Fourier power spectrum did not reveal any strong periodicity. The semi-major axis of the active cases are increasing without a corresponding increase in the minor axis resulting in a more elliptic vortex with time. Conversely, the passive and dry cases have the opposite occurring (more circular). \n\nThe GDS-89 was observed to increase in its semi-minor axis ($b$) at a rate of $3.8 \\times 10^{-5}$ h$^{-1}$ \\citep{Sromovsky1993} as it drifted northward, while the semi-major axis ($a$) was roughly constant, resulting a more circular vortex with time. This is in contradiction to our cloudy simulations where we see the vortex getting more elliptic by stretching along the zonal axis as it drifts northward while maintaining a nearly constant meridional height (Figure~\\ref{fig:cd_pv}). In the passive and dry case, there is very little change in the aspect ratio throughout the run, and they are much closer to the observed aspect ratio trend observed by {\\it Voyager 2}. \n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/shape_oscillation_final.png}\n    \\caption{The inverted aspect ratio of the ellipse (semi-major divided by semi-minor) for the different test cases using methane column density to fit the simulated GDS. The solid black line is the average increase in the inverted aspect ratio of the GDS-89 observed by {\\it Voyager 2} \\citep{Sromovsky1993}. The period nature of the vortex (i.e. the `rolling motion') is evident in all cases, but at different time scales. }\n    \\label{fig:shape_oscillation}\n\\end{figure}\n\n\\subsection{Companion Clouds}\n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/comp_cloud.png}\n    \\caption{Model output at day 44. (a) shows the top-down view of methane column density (blue) and cloud (white). (b) shows the vertical wind with upwelling in red and downwelling in blue, with wind vectors in the comoving frame. (c) and (d) are longitudinal slices showing methane relative humidity, with brighter corresponding to saturated regions and darker being drier. Wind vectors show the local circulation within the vortex and the black contours are ice cloud densities. The location of the slices are shown in (a) in red. }\n    \\label{fig:comp_cloud}\n\\end{figure}\n\nFigure~\\ref{fig:comp_cloud} (a) shows a snapshot of the model output with the methane column density in blue and companion clouds in white. There are two distinct types of clouds that interact with the vortex: those that are interior (within the horizontal extents of the vortex) and that are exterior to the vortex (Figure~\\ref{fig:comp_cloud} a). The exterior clouds form a thin layer at roughly 1 bar (Fig~\\ref{fig:comp_cloud} c, d), while the interior clouds form much higher and are extended vertically.  \n\nThe interior clouds form at two discrete levels: one close to the tropopause at $\\sim100$ hPa and the other further down around $400-500$ hPa. The upper level cloud particles are small due to being in a thinner environment and do not reach the critical diameter of $500\\mu$m to precipitate. The humid environment where the clouds form (bright in Fig~\\ref{fig:comp_cloud} c, d) are retained throughout the vortex lifetime due to the thermal structure of the vortex. \n\nThe deeper cloud is denser and precipitates immediately. However, both clouds are long lived and last about 30 days after the initial adjustment period before dissipating. The particle sizes in both clouds, which are diagnosed from the cloud water content \\citep{Palotai2008}, are on the order of $300-500\\mu$m with the larger particles forming in the lower cloud. These sizes are comparable to cold cirrus clouds on Earth \\citep{Heymsfield2017}, which is a similar habit to the interior clouds in the GDS. \n\n\\begin{figure}\n    \\includegraphics[width=\\columnwidth]{Figures\/drift_rate_nds_final.png}\n    \\caption{Drift rate (blue) and aspect ratio (red) of NDS-2018 from model output. }\n    \\label{fig:NDS_drift}\n\\end{figure}\n\\subsection{NDS-2018}\n\nIn 2018, Hubble Space Telescope visible wavelength imaging revealed the presence of a dark spot in the northern hemisphere (labelled NDS-2018) \\citep{Simon2019}. OPAL observations showed that there was increase in active cloud formation in the regions for 1-2 years leading up to the development of the spot. The NDS-2018 is similar in size and shape to the GDS-89 \\citep{Simon2019}. Consequently, in order to constrain the dynamics of this feature, we run simulations with identical vortex initialization, domain, and resolution as the GDS cases. We run 100 day simulations of this feature using an active cloud microphysical model. The vortex was initialized at $32\\degree$ N latitude with a \n$40\\times$ solar [C\/H] fraction and an initial relative humidity of 95\\%. Fig. \\ref{fig:nds} shows select timesteps of this NDS simulation. \n\nDue to the symmetrical nature of the zonal wind profile used in this study (Fig \\ref{fig:zonal_wind}), equatorial drift was observed in the simulated NDS case similar to the simulated GDS cases (Fig. \\ref{fig:NDS_drift}). The average approximate drift rate found in this study for the NDS-2018 was roughly $3.2\\degree$ per month. In contrast to the surprisingly consistent latitudinal wobble observed in the southern hemisphere for the GDS cases, the NDS case has inconsistent oscillations in latitude. This simulation also saw a decrease in inverted aspect ratio throughout the 100 day simulation with an average value of around 0.4 consistent with the value of $b\/a=0.45$ observed by \\citet{Simon2019} for the NDS-2018.\n\n\nThe cloud formation in the NDS simulations were also similar to the GDS cases, with a set of interior and exterior clouds, although the interior clouds were not perfectly centered like the GDS simulations. These are likely a result of the much more irregular dynamics of the NDS vortex in our simulations. \n\n\n\\begin{figure*}\n    \\centering\n    \\includegraphics[width=1\\textwidth]{Figures\/40x_shape_oscillation_nds.png}\n    \\caption{Select timesteps from a 100 day simulation of Neptune's NDS-2018 using the EPIC model with active microphysics for methane and $40\\times$ solar methane abundance. The blue is integrated column density of methane vapor with darker regions indicating areas of low density. The solid line is the fitted ellipse using dashed line, which is the vapor field contour.}\n    \\label{fig:nds}\n\\end{figure*}\n\n\\section{Discussion}\nLarge scale vortices that have been observed on Neptune exhibit surprising variability in terms of shape, drift, and lifetime. Consequently, they are some of the most dynamic features in the Solar System. Due to these variations, a variety of vortex characteristics can be examined at short timescales. Although we are constrained by limited observational data, recent developments in the accuracy of models using active microphysics can help us investigate the dynamics of these features. \n\n\\subsection{Methane deep abundance} \n\nThe various cases discussed here exhibit a wide range in both the meridionial drift and the dynamic time-dependent variations in shape of the GDS-89. \n\nWe tracked the vortex using both anomalous PV and methane column density (Figure~\\ref{fig:cd_pv}), and found that using the CD allows us to track the vortex for much longer due to the anomalous PV decreasing as the vortex moves through different shear environments. These cases differ significantly in the rate of latitudinal drift, the change in aspect ratio and the periodicity of the oscillations. Cases 1 and 2 ($20\\times$ and $40\\times$ solar methane abundance with active microphysics) are best matches for the drift rate (with Case 2 reproducing the drift almost perfectly), but do not show the observed decrease in ellipticity of the GDS-89. The passive and dry (Cases 4 and 5) are poor matches for the drift rate but are better at reproducing the observed slow change in the aspect ratio. Surprisingly, the $80\\times$ simulation failed to achieve a stable feature, and dissipates after 60 days. It should be noted that the high fidelity observations of the GDS started above $\\sim-26\\degree$ latitude \\citep{Sromovsky1993}, which is further north compared to where most of our simulations reach, and it is likely that we were probing an earlier part of the GDS-89's trajectory. A study of starting the vortex further north will need to be done to investigate this. Ultimately, the stability of Cases 1 and 2 and their consistency with {\\it Voyager 2} observations reinforces the measurements of a roughly $20-40\\times$ solar [C\/H] ratio on Neptune. \n\n\\subsection{Cloud microphysics}\n\nCloud microphysics has a much more drastic effect on the dynamics of the vortex compared to simply the addition of methane, as the passive case behaves similarly to the dry case. It is, however, much more difficult to trace the process(es) responsible for these effects. Due to the low density of the methane clouds, coupled with the low latent heat release of methane, it is unlikely to be just latent heating that drives this difference. \n\n\n\nClouds were present throughout the simulation and interacted strongly with the vortex. Similar to \\citet{Stratman2001}, we observed multi-layered clouds both within and without the vortex in our simulations (Figure~\\ref{fig:comp_cloud}). Their eastward cloud forms much higher than ours. However, this may be a function of vertical resolution and interpolation between the layers. In general, both results agree with the humid environment within the vortex and a region of dry air directly below. We are unable to reproduce the persistent poleward cloud. \n\\citet{Stratman2001} showed that vertical location of the vortex strongly influences the formation of clouds and indeed observed the poleward cloud only in certain configurations. The vertical extent and location of the spot in our simulations is held constant to reduce the number of free parameters, and we will investigate the effect of changing them in future simulations.\n\nThe deep cloud within the vortex formed snow and had cloud particles exceeded $300\\mu$m in diameter based on the assumption of hexagonal plate-like particles. Using {\\it Voyager 2} IRIS spectra, \\citet{Conrath1991} obtained particle sizes between $0.3-30\\mu$m, assuming Mie scattering by spherical particles. In our model, we assume ice and snow to be hexagonal plates (as determined for Earth clouds) resulting in much larger diameters than the equivalent spheres for the same particle masses. The equivalent radii for the spherical cloud particles in our simulations is about $50-70\\mu$m, for the same particle mass (i.e. the ``wetted radius\"). \\citet{Kinne1989} noted that using spherical ice crystals underestimates the albedo by up to $15\\%$ due to greater forward scattering, depending on the shape of the ice particle. Therefore, the discrepancy in cloud particle sizes on Neptune requires further study in the avenue of experimentally determining methane nucleation in a H\/He environment and scattering for non-spherical geometries. Both of these would further refine the microphysical parameters in our model to better represent gas-giant atmospheres. \n\n\n\\subsection{Optical depth}\n\nStrong methane absorption in Neptune's atmosphere largely correlates with a higher optical depth \\citep{Hueso2017}. In our simulations, we find that the vortex exists as an area of low methane vapor density compared to the surrounding atmosphere. This is due to the modified thermal structure of the atmosphere as a consequence of introducing the vortex (Figure~\\ref{fig:cd_pv}). All cases (except for Case 5 - which contains no methane vapor) reciprocate this phenomenon and decreased methane column density persist throughout the simulation. The reduced column density results in a decreased optical depth over the vortex compared to the ambient background atmosphere. We interpret this as being able to see deeper into the atmosphere, producing the ``darkness\" of the GDS-89. This is, indeed, an `apples-to-oranges' comparison, and applying a forward radiative transfer (RT) model to simulation outputs would lend additional insight into this discussion. We are working on an RT model that will address this in future studies. \n\n\n\\subsection{Applications to the NDS-2018}\n\nThe NDS-2018 simulation has surprising differences from our GDS test cases. There is much more irregularity in the equatorward drift of the vortex and a higher drift rate. The shape oscillation was similar to our wet GDS cases, with the vortex becoming more elliptic with time. \n\n\nThese differences could be due to the {\\it Voyager}-era zonal wind profile we use in our models. Recent OPAL observations have provided new zonal wind data and even shown evidence of weak vertical wind shear \\citep{Tollefson2018}. \\citet{Simon2019} suggest that a zonal wind gradient of $\\sim4\\times$ that of the \\citet{Sromovsky1993} fit is required to match the observed aspect ratio of the NDS-2018, or $du\/dy\\sim5.4\\times10^{-5}$ s$^{-1}$. The Q$_y=1\/3$ zonal wind profile we use has a value of $du\/dy\\sim 3\\times10^{-5}$ s$^{-1}$ around $30\\degree$ latitude. Testing different zonal wind gradients is not part of this study however, and will be introduced into future sims. Furthermore, without additional observations, it is difficult to verify the accuracy of the drift rate and shape oscillations we measured in the model. It is unknown whether the spot is still present because Hubble observations are limited. \n\n\n\\section{Conclusion}\n\nIn this study, we have analysed the effect of methane abundance and cloud formation on the dynamics of the vortex. While the addition of active microphysics improves the meridional drift rate of the vortex, there are other observations which are difficult to reproduce, such as the consistent periodicity of the shape oscillation or the increase in inverse aspect ratio. A further study of the parameter space that describes the spot is required, such as changing the initial vortex location and size (both vertically and horizontally). Additionally, \\citet{Tollefson2018} assumes a $\\times 2$ or an $\\times 4$ depletion of methane at the mid-latitudes and towards the poles and an increase in mixing ratio near the equator based on idealized equations. These recent observations would be beneficial in the study of the newer spots such as the NDS-2018, and indeed are likely required to explain their dynamics. \n\nThe active microphysics package implemented in this study has a clear effect on the dynamical motions of the vortex, such as meridional drift and shape oscillations. Using a $40\\times$ or $20\\times$ methane deep abundance, we achieve a stable simulation for over 120 days. We also see persistent bright companion cloud formation throughout the simulation. Additionally, the vortex exists as an area of low density which may be correlated to a decrease in optical depth. Finally, we found a possible scenario for the dynamical evolution of the NDS-2018 including its equatorial drift and the vortex becoming more elliptic with time. However, additional observations are needed to constrain these simulations. \n\n\\section*{Acknowledgements}\nThis research was supported in part by the NASA Solar System Workings Program grant NNX16A203G and the DPS Hartmann Student Travel Grant Program. N.H. thanks the Astronaut Scholarship Foundation for their support. We also thank Noah Nodolski for his help and the anonymous reviewer for their input.\n\n\\vspace{-1em}\n\\section*{Data Availability}\nThe data underlying this article will be shared on reasonable request to the corresponding author.\n\n\n\n\n\n\n\\vspace{-2em}\n\\bibliographystyle{mnras}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{intro}\nGame theory was originally developed in the field of economics to study strategic interactions amongst humans \\citep{neumann:1944ef,flood:1952aa}. \nThe ``agents\" who play against each other have a set of ``strategies\" to choose from.\nThe payoff which an agent gets depends on its own strategy and the strategy of the opponent.\nA player can decide which strategy to play against an opponent of a given strategy.\n\nIn evolutionary game theory players are born with fixed strategies instead, \\citep{maynard-smith:1982to}\nwhich are  considered to be inherited traits.\nAs usual, we assume a population game in which every player effectively plays against the average opponent.\nThe success of a strategy depends on the number of players of that strategy and also the number of players with other strategies.\nA classical example is the Lotka-Volterra equation \\citep{lotka:1910aa,volterra:1928aa,hofbauer:1998mm}.\nIf the number of wolves increases then the number of hares will decrease in turn leading to a decrease in the number of wolves.\nEvolutionary game dynamics studies the change in the frequencies of the strategies \\citep{nowak:2006bo}, which depends on mutation, selection and drift.\n\nA recurrent and obvious question asked in the study of games is which is the best strategy?\nAssuming an infinitely large population we can approach this question by the traditional replicator dynamics \\citep{hofbauer:1998mm}.\nThe frequency of a strategy will increase if its average payoff is greater than the average payoff of the whole population.\nThat is, if the individuals of a particular strategy are doing better on average than the individuals of other strategies then that strategy spreads.\nThe average payoff of a strategy is also dependent on the frequency of the strategy.\nFor finite populations one must resort to stochastic descriptions \\citep{ficici:2000aa,schreiber:2001aa,nowak:2004pw}.\nOne important quantity is the fixation probability.\nConsider two strategies $A$ and $B$ in a population of size $N$.\nLet the population be almost homogenous for $B$ with only a single $A$.\nIf there is no fitness difference amongst the strategies, i.e. selection is neutral, then the probability that the $A$ individual will take over the entire population is $1\/N$.\nIf this probability is greater than $1\/N$ we say that strategy $A$ is favoured by selection.\nWhen there are multiple strategies in the population, then a pair-wise comparison between the fixation probabilities of all the strategies will reveal which is the most abundant strategy \n\\citep{fudenberg:2006ee,hauert:2007aa,hauert:2008bb,van-segbroeck:2009mi,sigmund:2010aa}.\nThis analysis requires the assumption of low mutation rates.\n\nWhen mutations become more frequent then the concept of fixation itself is problematic and hence also that of fixation probability.\nIn such a case we resort to the average frequency of a strategy which is maintained at the mutation-selection balance.\nThis has been termed as the abundance of a strategy \\citep{antal:2009hc}.\n\nConsider $n$ strategies which are effectively neutral against each other.\nIn such a case the abundance of all the strategies in the stationary state will be just $1\/n$.\nUsually there are fitness differences between the strategies.\nIf the abundance of a strategy is greater than that of all the other strategies then we can say it is favoured under the effects of mutation, selection and drift.\nHence for $n$ strategies, the $k^{th}$ strategy will be favoured if the abundance of $k$ is greater than $1\/n$.\nCalculating the abundance of a strategy is a non-trivial exercise even when assuming weak selection.\n\\cite{antal:2009hc} have developed such an approach based on coalescence theory for the case of two-player games and $n$ strategies.\nUnder certain conditions and weak selection, one can calculate the most abundant strategy for arbitrary mutation rates even in structured populations \\citep{antal:2009aa,tarnita:2009df,tarnita:2009jx} and bimatrix games \\citep{ohtsuki:2010aa}.\n\nUsually two-player interactions are studied in evolutionary game theory.\nThe analysis of Antal et al. is also for two-player games.\nThe interactions which we usually use as examples in evolutionary game theory are in general multi-player interactions making the systems nonlinear \\citep{nowak:2010na}.\nA classical example where a certain minimum number of individuals are required to complete a task is group hunting.\n\\cite{stander:1992aa} studied cooperative hunting in lions.\nA typical hunting strategy is to approach the prey from at least three sides to cutoff  possible escape paths.\nThis hunting approach is impossible with only two hunters, i.e.\\ a two-player game theoretic approach would be insufficient to capture the dynamics.\nAlthough evolutionary dynamics of multi-player games has received growing interest in the recent years, the main focus has been the Public Goods Game and its variants \\citep{hauert:2002te,milinski:2006aa,rockenbach:2006aa,hauert:2007aa,santos:2008xr,pacheco:2009aa,souza:2009aa,veelen:2009ma,archetti:2011aa}.\nOnly few authors consider general evolutionary many person games  \n \\citep{hauert:2006fd,kurokawa:2009aa,gokhale:2010pn}.\nWe extend the approach developed by \\cite{antal:2009hc} for two-player games and multiple strategies to multi-player games.\nWe show that in the limit of weak selection it is possible to calculate analytical results for $n$ strategies and $d$ players for arbitrary mutation rates.\nFor a three-player game the mathematical analysis is described in detail.\nIt is followed by an example with simulations supporting the analytical result.\nLastly we discuss how the methodology can be extended for $d$-player games and argue that a general approach is possible, but tedious.\n\n\\section{Abundances in the stationary state for three-player games}\n\\label{model}\n\n\\cite{antal:2009hc} have developed an approach to find the abundances of $n$ strategies in a two-player game ($d=2$).\nFor a two-player game even with $n$ strategies, the payoff values can be represented in the usual payoff matrix form.\nThey can be represented as quantities with two indices, $a_{k,h}$.\nWe increase the complexity first by adding one more player ($d=3$).\nThis adds another index for the third player's strategy set, $a_{k,h,i}$.\nTo calculate the average change in the frequency of a strategy we thus need to take into account this payoff `tensor'.\n\nWe calculate the abundance of a strategy at the mutation-selection equilibrium.\nWe begin by checking if there is a change in the frequency of a strategy, say $k$ on average, due to selection.\nThe average change under weak selection is given by\n\\begin{eqnarray}\n\\label{replike}\n\\langle \\Delta x_k^{sel} \\rangle_\\delta = \\frac{\\delta}{N} \\left(\\sum_{h,i} a_{k,h,i}\\langle x_k x_h x_i\\rangle - \\sum_{h,i,j} a_{h,i,j}\\langle x_k x_h x_i x_j\\rangle \\right),\\nonumber \\\\\n\\end{eqnarray}\nwhere the angular brackets denote the average in the neutral stationary state.\nThe $\\delta$ (selection intensity) as a lower index on the left hand side, however, denotes that the average is obtained under (weak) selection.\nIf we pick three individuals in the neutral stationary state, then the probability of the first one to have strategy $k$, the next one $h$ and the last $i$, is given by the angular brackets in the first sum, $\\langle x_k x_h x_i\\rangle$.\nFurthermore, $a_{k,h,i}$ denotes the payoff values obtained by a strategy $k$ player when pitted against two other players of strategy $h$ and $i$.\nFor $n$ strategies the sums run from $1$ to $n$.\nThis equation is the special case of a $d=3$ player game.\nThe derivation for arbitrary $d$ is given in \\ref{eq1app}.\nThe above equation is similar to the replicator equation, which is also based on the difference between the average payoff of a strategy and the average payoff of the population, but as we will see below, here the averages on the right hand side also include mutations.\n\nTo incorporate mutations in the process, we write the total expected change due to mutation and selection as\n\\begin{eqnarray}\n\\label{xtot}\n\\Delta x ^{tot}_k = \\Delta x^{sel}_k (1-u)+ \\frac{u}{N}\\left(\\frac{1}{n} - x_k\\right).\n\\end{eqnarray}\nThe first term is the change in the frequency in the absence of mutation.\nIn presence of mutations, the second term shows that the frequency can increase by $1\/(nN)$ by random mutation and decrease by $x_k\/N$ due to random death.\nA mutation means that with a certain probability $u$, the strategy $k$ can mutate to any of the $n$ strategies.\n\nWe are interested in the abundance of a strategy in the stationary state.\nIn the stationary state, the average change in frequency is zero, $\\langle \\Delta x ^{tot}_k \\rangle_\\delta = 0$, as the mutations are balanced by selection.\nAveraging Eq.\\ \\ref{xtot} under weak selection thus gives us\n\\begin{eqnarray}\n\\label{abundeq}\n\\langle x_k \\rangle_\\delta = \\frac{1}{n} + N \\frac{1-u}{u} \\langle \\Delta x^{sel}_k \\rangle_\\delta.\n\\end{eqnarray}\nThis is our quantity of interest, the abundance of a strategy when the system has reached the stationary state.\nFor $d=2$ player games, this quantity is given by \\cite{antal:2009hc}.\nFor the abundance of a strategy to be greater than neutral, $\\langle x_k \\rangle_\\delta > \\frac{1}{n}$, the change in frequency in the stationary state due to selection must be greater than zero, $\\langle \\Delta x^{sel}_k \\rangle_\\delta >0$.\n\nThus, we need to resolve the right hand side of Equation \\ \\ref{replike}.\nConsider the first term in the brackets.\nIn the neutral stationary state the number of combinations in the sums reduces due to symmetry, e.g. $\\langle x_i x_j x_j \\rangle = \\langle x_j x_i x_j \\rangle = \\langle x_j x_j x_i \\rangle$.\nHence, we need to calculate only three different terms, $ \\langle x_1 x_1 x_1 \\rangle $, $ \\langle x_1 x_2 x_2 \\rangle $ and $ \\langle x_1 x_2 x_3 \\rangle $.\nAlso for $d$ player games, the terms in the sums are reduced.\nFor the second term in the brackets we need to calculate five different types of averages, $\\langle x_1 x_1 x_1 x_1\\rangle$, $\\langle x_1 x_2 x_2 x_2\\rangle$, $\\langle x_1 x_1 x_2 x_2\\rangle$, $\\langle x_1 x_1 x_2 x_3\\rangle$ and $\\langle x_1 x_2 x_3 x_4\\rangle$.\nThese averages are derived in the \\ref{averagesapp}.\nUsing an approach from coalescence theory, we derive $s_i$, the probability that $i$ individuals chosen from the stationary state all have the same strategy.\nHence $s_4$ is the probability that four individuals chosen in the stationary state all have the same strategy.\nIf there are in all $n$ strategies, then the probability that all have exactly strategy $1$ is $s_4\/n$.\nHence, $\\langle x_1 x_1 x_1 x_1 \\rangle = \\langle x_2 x_2 x_2 x_2 \\rangle = \\ldots = \\langle x_n x_n x_n x_n \\rangle = s_4\/n$.\nConversely, $\\bar{s}_i$ is the probability that if we choose $i$ individuals in the stationary state, each has a unique strategy.\nKnowing these averages helps us resolve Eq.\\ \\eqref{replike},\n\\begin{eqnarray}\n\\langle \\Delta x_k^{sel} \\rangle_\\delta\n= \\frac{\\delta \\mu (L_k + M_k \\mu + H_k \\mu^2)}{N n (1+\\mu) (2+\\mu) (3+\\mu)} \n\\end{eqnarray}\nwhere $\\mu = N u$ and $L_k$, $M_k$ and $H_k$ are functions consisting only of the number of  strategies $n$ and the payoff values $a_{k,h,i}$ (see \\ref{averagesapp}).\nUsing this and evaluating Eq.\\ \\eqref{abundeq} gives us the abundance of the $k^{th}$ strategy.\n\\begin{eqnarray}\n\\label{finalres}\n\\langle x_k \\rangle_\\delta = \\frac{1}{n}\\left[ 1 + \\frac{ \\delta (N- \\mu) (L_k + M_k \\mu + H_k \\mu^2) }{ (1+ \\mu) (2+ \\mu) (3+ \\mu)}\\right].\n\\end{eqnarray}\nThis expression is valid for large population sizes, $N\\delta \\ll 1$ and any $\\mu =N u$.\nSince we have $0\\leq u \\leq 1$, $\\mu$ is bounded by $0\\leq \\mu \\leq N$.\n\n\nWe arrive at the result with an implicit assumption that there are at least four strategies.\nFor $n \\leq d$, each player cannot have a unique strategy and hence we need to set the corresponding terms to zero (see \\ref{averagesapp}).\nIf there are less than $n=4$ strategies then $\\bar{s}_4$ vanishes.\nThis does not affect our general result as the affected terms in $L_k$, $M_k$ and $H_k$ simply vanish.\n\n\n\\section{An example for three-player games with three strategies}\n\\label{example}\n\nTo illustrate the analytical approach we explore an evolutionary three-player game with three strategies $A$, $B$ and $C$.\nLet our focal individual play strategy $A$.\nThe other two players can play any of the three strategies.\nThis can lead to a potential complication.\nConsider the combinations $AAB$ or $ABA$.\nIf the order of players does not matter, then both these configurations give the same payoffs but if they do matter then we need to consider them separately.\nHere we assume random matching, and hence the order drops out (e.g. $AAB$ and $ABA$ are equally likely).\nWe consider an arbitrary game as denoted in Table \\ref{paytab}.\n\nWe need to calculate the average change in the frequency of strategy $A$ due to selection, i.e. Eq.\\ \\eqref{replike}.\nWe denote the co-efficients of the averages in the first sum by $\\alpha_1$, $\\alpha_2$ and $\\alpha_3$.\nHence for example, $\\alpha_3 = a_{A,B,C} + a_{A,C,B}$.\nSimilarly for the second sum we have $\\beta_1$ to $\\beta_4$ (Note that $\\beta_1 = \\alpha_1 = a_{A,A,A}$).\nThus we have,\n\\begin{eqnarray}\n\\sum_{h,i} a_{A,h,i}  \\langle x_A x_h x_i\\rangle &=& \\alpha_1 \\langle x_A x_A x_A \\rangle + \\alpha_2  \\langle x_A x_B x_B \\rangle \\nonumber \\\\\n&&+ \\alpha_3 \\langle x_A x_B x_C \\rangle\n\\end{eqnarray}\nand\n\\begin{eqnarray}\n\\sum_{h,i,j} a_{h,i,j}\\langle x_A x_h x_i x_j\\rangle  &=& \\beta_1 \\langle x_A x_A x_A x_A\\rangle + \\beta_2 \\langle x_A x_B x_B x_B\\rangle \\nonumber \\\\\n&&+ \\beta_3 \\langle x_A x_A x_B x_B\\rangle + \\beta_4 \\langle x_A x_A x_B x_C\\rangle.\\nonumber \\\\\n\\end{eqnarray}\nNote that the term $\\langle x_A x_B x_C x_D\\rangle$ which would appear with a factor $\\beta_5$, does not appear, as we have only three strategies and thus $\\bar{s}_4 = 0$.\nThis also alters the definition of  $\\langle x_A x_A x_B x_C\\rangle$ and $\\langle x_A x_A x_B x_B\\rangle$ (see Figure \\ref{fig:1}, all terms dependent on $\\bar{s}_4$ are affected).\n\n\n\\begin{figure}\n\\includegraphics[width=\\columnwidth]{figure_1.pdf}\n\\caption{The average change in the frequency of strategy $k$ due to selection, $\\langle \\Delta x_k^{sel} \\rangle_\\delta$ for a three-player game.\nNotice first the similarity to the replicator equation where also we look at how a strategy is faring compared to the population.\nThe first term in the bracket is analogous to the average fitness of strategy $k$.\nIf we pick three individuals in the stationary state, then the probability that the first one has strategy $k$, second $h$ and the third $i$ is given by $\\langle x_k x_h x_i\\rangle$  (dashed box).\nEven for $n$ strategies there are only three possible combinations, either all can have the same strategy, a pair has the same strategy or all three have different strategies.\nThese probabilities were calculated by \\cite{antal:2009hc}.\nThe $s_i$'s appearing in the averages are the probabilities that if we choose $i$ individuals from the stationary distribution then they all have the same strategy.\nThe second term in the bracket is analogous to the average fitness of the population in the stationary state.\nFor this we need to pick four individuals and look for all the different combinations (solid box).\nFor $n$ strategies, five combinations can explain all the different configurations.\nThese range from all the individuals having the same strategy $\\langle x_1 x_1 x_1 x_1 \\rangle$ to all having a different strategy $\\langle x_1 x_2 x_3 x_4 \\rangle$ (\\ref{averagesapp}).\nFor the latter, we calculate $\\bar{s}_i$, the probability that we choose $i$  individuals from the stationary distribution and each of them has a unique strategy.\nFor a general $d$-player game we need to pick $d$ individuals for the first term and $d+1$ for the second.}\n\\label{fig:1}\n\\end{figure}\n\n\n\nWe know the form of $L_k$, $M_k$ and $H_k$ from \\ref{averagesapp} as,\n\\begin{eqnarray}\nL_k  &=& \\tfrac{1}{n} \\left[2 \\alpha_1 (n-1) + 3 \\alpha_2 - 2 \\beta_2 - \\beta_3\\right] \\\\\nM_k &=& \\tfrac{1}{n^2} \\left[\\left(3 n-3\\right) \\alpha_1 +\\left(n+3\\right) \\alpha_2 +3 \\alpha_3 - 3 \\beta_2 - 2 \\beta_3 - \\beta_4\\right] \\nonumber \\\\\n\\\\\nH_k &=& \\tfrac{1}{n^3} \\left[n (\\alpha_1 + \\alpha_2 + \\alpha_3) - (\\beta_1 + \\beta_2  + \\beta_3  + \\beta_4  + \\beta_5)\\right]\n\\end{eqnarray}\nWith $L_k$, $M_k$ and $H_k$ as above, Eq.\\ \\eqref{finalres} for $n=3$ reduces to,\n\\begin{eqnarray}\n\\langle x_A \\rangle_\\delta = \\frac{1}{3}\\left[ 1 + \\frac{\\delta (N- \\mu) (L_k + M_k \\mu + H_k \\mu^2) }{ (1+ \\mu) (2+ \\mu) (3+ \\mu)}\\right].\n\\end{eqnarray}\nThis gives us the abundance of strategy $A$ at the mutation selection equilibrium.\nRepeating the same procedure for strategies $B$ and $C$ gives the analytical lines in \nFigure \\ref{fig:2}.\nAlthough the analytical solutions are valid for large population sizes only, we still see a good agreement between the simulation and theory results, even for a population size as small as $30$.\n\n\n\\begin{figure}\n\\includegraphics[width=\\columnwidth]{figure_2.pdf}\n\\caption{\nFor a three-player game with three strategies ($d=3;n=3$) we plot the average abundances of the three strategies as a function of the mutation probability $u$.\nThe payoff table from Table \\ref{paytab} is used.\nThe lines are the solutions of Eq.\\ \\eqref{abundeq} and the symbols are the simulation results for the three strategies.\nAlthough the calculations are valid for large populations we see a good agreement even for a population size of  $N=30$\n(selection intensity $\\delta=0.003$, simulation points are obtained \naveraging over $20000$ independent runs, each over $2 \\times 10^6$ time steps after a transient phase of $N$ time steps).\n}\n\\label{fig:2}\n\\end{figure}\n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{ccccccc}\n\\hline\\hline\n\\hspace{0.2cm}\n\\begin{minipage}[c]{2cm}\n\\begin{center}\n\\vspace{0.1cm}\nWeights\n \\\\ \n( Total 9 )\n\\vspace{.2cm}\n\\end{center}\n\\end{minipage} & 1\t& 2 & 2 & 1 & 2 & 1\t\\\\\n\\hline\n & AA & AB & AC & BB & BC & CC\t\\\\\n \\hline\n A \t& 2 & 2  & 3 & 1 & 3 & 4\t\\\\\n B \t& 2 & 1 & 2 & 3\t& 0 & 2\\\\\n C \t& 2 & 12 & 2 & 0 & 1 & 3\t\\\\\n\\hline\\hline\n\\end{tabular}\n\\caption{An example payoff table for $d = 3$ and $n=3$.\nConsider a three-player game with three strategies $A$, $B$ and $C$.\nThe strategy of the focal individual is in the column on the left.\nFor example the payoff received by a $C$ individual when playing in a configuration of $CAB$ is  $12$.\nFrom the focal individual's point of view there are two ways of this configuration $CAB$ and $CBA$ as it is twice as likely as compared to e.g. $CAA$.\nHence we weight that payoff value by $2$ when calculating the average payoff of strategy $C$.}\n\\label{paytab}\n\\end{center}\n\\end{table}\n\n\\section{Abundances in $\\mathbf{d>3}$ player games.}\n\nWe can repeat the whole procedure for $d=4$ player games with $n$ strategies.\nThe formula for the abundance remains the same, Eq.\\ \\eqref{abundeq}, but the average change due to selection, Eq.\\ \\eqref{replike}, becomes more complicated.\nWe need to add an index in the sums,\n\\begin{eqnarray}\n\\langle \\Delta x_k^{sel} \\rangle_\\delta &=& \\frac{\\delta}{N} \\Big(\\sum_{l,m,n} a_{k,l,m,n}\\langle x_k x_l x_m x_n\\rangle \\nonumber \\\\\n&&- \\sum_{l,m,n,o} a_{l,m,n,o} \\langle x_k x_l x_m x_n x_o\\rangle \\Big)\n\\end{eqnarray}\nThe first term is comparatively simple as we already know all the different ways of picking four individuals.\nFor the second term we need to know the different possible combinations of strategies when picking five individuals from the neutral stationary state.\n\nFor $d$ players and $n$ strategies we can construct an expression analogous to Eq.\\ \\ref{replike}.\nConsider for example the strategies played by $d$ individuals denoted by, $r_1, r_2, r_3 \\ldots r_d$.\nNote that each of these can be a strategy from the strategy set $1,2,3 \\ldots n$.\nLet $k$ be our strategy of interest.\nThen the expression for the change of strategy $k$ due to selection is given by,\n\\begin{eqnarray}\n\\label{dplayers}\n\\langle \\Delta x_{k}^{sel} \\rangle_\\delta &=& \\frac{\\delta}{N}  \\Bigg( \\sum_{r_2,\\ldots r_d} a_{k,r_2,\\ldots r_d } \\langle x_k x_{r_2} x_{r_3} \\ldots x_{r_d} \\rangle  \\nonumber \\\\\n\\!\\!\\!\\! &&- \\sum_{r_2,\\ldots r_{d+1}} a_{r_2,\\ldots r_{d+1} } \\langle x_k x_{r_2} x_{r_3} \\ldots x_{r_{d+1}} \\rangle \\Bigg) \\nonumber \\\\\n\\end{eqnarray}\nwhere the sums range as usual from $1$ to $n$ (\\ref{eq1app}).\nSolving this and plugging it in Eq.\\ \\eqref{abundeq} gives the generalized expression for the abundance of strategy $k$ for an $n$ strategy, $d$-player game.\nWe see that in the first sum the averages are for choosing $d$ players but for the second it is $d+1$.\nHence we need to calculate the probabilities of the form $s_{d+1}$, but $s_{d+1}$ depends on $s_d$.\nThus we have to solve the expression recursively e.g.\nfor $d=6$, we will need to pick $7$ players at most and we must solve the expression for $d = 2,3,4,5,6$ before ($d=2$ has been solved by \\cite{antal:2009hc} and $d=3$ in this paper).\nAs $d$ increases calculating $s_{d+1}$ is not enough and we will also need to calculate terms such as $\\bar{s}_{d+1}$ which is already the case for $d=3$.\n\n\\section{Special case: Two strategies, $\\mathbf{n=2}$}\n\nGames with two strategies have been very well studied.\nIn two-player games with two strategies, one strategy can replace another with a higher probability if the sum of its payoff values is greater than the sum of the payoff values of the other strategy.\nThis is valid under small mutation rates for deterministic evolutionary dynamics \\citep{kandori:1993aa}.\nThe result also holds for for different dynamical regimes under specific limits of selection intensity and mutation rates \\citep{fudenberg:1992bv,nowak:2004pw,antal:2009th}.\nRecently it has been shown that this result can be generalized for $d$-player games with two strategies \\citep{kurokawa:2009aa,gokhale:2010pn}.\n\nHence the condition which we find for $d$-player games should be identical to $L_k > 0$ derived in this paper for $d$ players.\nWe check this for $d=3$,\n\\begin{eqnarray}\nL_k  &=& \\tfrac{1}{2} \\left[2 \\alpha_1 (2-1) + 3 \\alpha_2 - 2 \\beta_2 - \\beta_3 \\right]\n\\\\\n\\nonumber \n&=&\\tfrac{1}{2}  [ 2 a_{1,1,1} + 3 ( a_{1,1,2} + a_{1,2,1} + a_{1,2,2} )\\nonumber \\\\ \n&& - 2 ( a_{1,1,2} + a_{1,2,1} + a_{2,1,1} + a_{2,2,2} ) - a_{1,2,2} - a_{2,1,2} - a_{2,2,1} ] \\nonumber \\\\\n\\end{eqnarray}\nThus $L_k > 0$ is equivalent to,\n\\begin{eqnarray}\n2 a_{1,1,1} +&&   a_{1,1,2} + a_{1,2,1} +  2 a_{1,2,2} \\nonumber \\\\\n&&> 2 a_{2,1,1} +   a_{2,1,2} + a_{2,2,1} +  2 a_{2,2,2} \\nonumber \\\\\n\\end{eqnarray}\nIf we assume that the order of players does not matter then we have $a_{1,1,2} = a_{1,2,1}$ and $a_{2,1,2} = a_{2,2,1}$.\nThis yields\n\\begin{eqnarray}\na_{1,1,1} +   a_{1,1,2} +  a_{1,2,2} >  a_{2,1,1} +   a_{2,1,2} +  a_{2,2,2},\n\\end{eqnarray}\nwhich is exactly the condition that has been obtained previously using different methods and different notation by \\cite{kurokawa:2009aa} and \\citep{gokhale:2010pn}.\n\\section{Application to a task allocation problem}\nTo demonstrate the power of the approach we are motivated by \\cite{wahl:2002aa} who studies the problem of task allocation and of the evolution of division of labour.\n\\cite{wahl:2002aa} studied a two-player game between task $1$ specialists ($T_1$), task $2$ specialists ($T_2$) and generalists. \nInstead, we have $T_1$, $T_2$ and freeloaders $F$.\nWe can think of this problem  in context of bacteria that need two types of enzymes to obtain resources from the environment.\nOne strain produces one type of enzyme at a cost $c_1$ and \nanother strain produces the second type of enzyme at a cost of $c_2$.\nWe also have the freeloading strain which does not produce any enzyme but can get resources by the help of the other two strains.\nThe benefit of getting \nthe resources is given by $b$.\nWe have the condition that the total cost is less than the benefit accrued i.e. $b> c_1 + c_2$.\nFurther assume that our contenders are conservative in the enzyme production.\nSensing who they are pitted against, the strains share the costs of producing the enzyme.\nThus a two-player payoff matrix for such a setting can be written down as in Table \\ref{2plpaytabex}.\nIt is hard to imagine though that the bacteria interact only in a pair-wise fashion.\nAlthough it is hard to judge how many players are interacting, we can at least increase the complexity by one more player and study what effect this has on the abundances of the strains.\nTherefore, we study the system\nin a three-player setting.\nIn this case the payoff table will look like \\ref{3plpaytabex}.\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{ccccccc}\n\\hline\\hline\n & $T_1$ & $T_2$ & $F$ \t\\\\\n \\hline\n$T_1$ & $\\frac{-c_1}{2}$ & $b-c_1$  & $-c_1$ \t\\\\\n$T_2$& $b-c_2$ & $\\frac{-c_2}{2}$ & $-c_2$ \\\\\n$F$ \t& 0 & 0 & 0 \\\\\n\\hline\\hline\n\\end{tabular}\n\\caption{\nPayoff table for a two-player game with three strategies, $T_1$ i.e. specialising in task $1$ or $T_2$ i.e. specialising in task $2$.\n$T_1$ produces\nenzyme $1$ and \n$T_2$ produces \nenzyme $2$.\nWhen both the enzymes are present then a benefit $b$ is obtained.\nThe cost of producing enzyme $1$ is $c_1$ and the cost to produce enzyme $2$ is $c_2$.\nIf the partner in the game is of the same strategy then the cost is shared.\nThe freeloading strategy $F$ does not pay any cost and so the benefits of the resource are unavailable to it.}\n\\label{2plpaytabex}\n\\end{center}\n\\end{table}\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{ccccccc}\n\\hline\\hline\n\\hspace{0.2cm}\n\\begin{minipage}[c]{2cm}\n\\begin{center}\n\\vspace{0.1cm}\nWeights\n \\\\ \n( Total 9 )\n\\vspace{.2cm}\n\\end{center}\n\\end{minipage} & 1\t& 2 & 2 & 1 & 2 & 1\t\\\\\n\\hline\n & $T_1 T_1$ & $T_1 T_2$ & $T_1 F$ & $T_2 T_2$ & $T_2 F$ & $F F$\t\\\\\n \\hline\n $T_1$ \t& $\\frac{-c_1}{3}$ & $b-\\frac{c_1}{2}$  & $\\frac{-c_1}{2}$ & $b-c_1$ & $b-c_1$ & $-c_1$\t\\\\\n $T_2$ \t& $b-c_2$ & $b-\\frac{c_2}{2}$ & $b-c_2$ & $\\frac{-c_2}{3}$\t& $\\frac{-c_2}{2}$ & $-c_2$\\\\\n $F$ \t& 0 & b & 0 & 0 & 0 & 0\t\\\\\n\\hline\\hline\n\\end{tabular}\n\\caption{\nPayoff table for the same game as discussed in Table \\ref{2plpaytabex}.\n$T_1$ and $T_2$ refer to specialising in task $1$ and $2$ namely producing enzyme $1$ and $2$.\nNote the costs can also be shared if at least one of the game partners is of the same strategy.\nIn this case the freeloaders can get the benefit when the other two players produce both enzymes.\n}\n\\label{3plpaytabex}\n\\end{center}\n\\end{table}\n\nWe calculate the abundances of the strains in these different settings, cf.\\ Figure \\ref{fig:3}. \nEven when there are almost no mutations there is a quantitative difference between the average frequencies of the strains.\nFor a higher mutation probability the difference is also qualitative.\nWhile the freeloaders never pay a cost they have the highest abundance in the two-player setting for any mutation probability.\nFor the same reasoning but in three-player games we see that the abundance of the freeloaders falls below that of $T_2$ for a certain range of mutation probability.\n\n\n\\begin{figure*}\n\\includegraphics[width=2.0\\columnwidth]{figure_3.pdf}\n\\caption{\nThe strains of a bacteria $T_1$ and $T_2$ produce the enzymes $1$ and $2$ which when present together provide a benefit $b$.\nWhen more than one individual of the same strain is present then the production costs for the enzymes, $c_1$ and $c_2$ are shared.\nA third strain $F$ does not produce any enzyme and thus avoids the costs and cannot obtain the benefit on its own.\nWe can analyse the interactions by assuming them to be pair-wise (two-player game, Table \\ref{2plpaytabex}) or in triplets (three-player game, \\ref{3plpaytabex}).\nWe notice that the abundances of the three strains are qualitatively and quantitatively different in the two settings even though the underlying rules defining the interactions are the same.\nUnder neutrality the abundance of all the strains would be given by the dashed line.\nThe full lines are the analytical results obtained by solving Eq.\\ \\eqref{abundeq}, assuming $b=1.0$, $c_1 = 0.6$, $c_2 = 0.2$ and a population size of $N=30$ with selection intensity $\\delta =0.003$.\n}\n\\label{fig:3}\n\\end{figure*}\n\n\n\\section{Discussion}\n\nPublic goods games are often used as examples of multi-player games.\nIn the beginning there were the cooperators and defectors.\nThen came the punishers and then the loners \\citep{hauert:2002te,szabo:2002te}.\nNow we talk about second order punishers, pool and peer punishers \\citep{sigmund:2010aa} and more.\nStudying these systems for small mutation rates and arbitrary selection intensity is almost becoming standard \\citep{fudenberg:2006ee,hauert:2007aa,hauert:2008bb,van-segbroeck:2009mi,sigmund:2010aa}.\nIn the limit of weak selection our method allows to find out which strategy is most abundant for arbitrary mutation rates.\n\nYet, another important aspect of most social dilemmas and many other biological examples is that they involve multiple players \\citep{stander:1992aa,broom:2003aa,milinski:2008lr,levin:2009aa}.\n\\cite{antal:2009aa,antal:2009hc} have made use of the coalescence approach to characterize the mutation process under neutrality and then apply it under weak selection to two-player games with $n$ strategies ($n \\times n$).\nHere we extend the approach to $d$-player games with $n$ strategies.\n\n\nWe give an example for an $n \\times n \\times n$ game and derive the analogous expressions for abundances of the strategies for arbitrary mutation rates.\nWhen we increase the number of players to $d$, the payoff matrix becomes a $d$ dimensional object.\nWe run into the problem of whether the order of players matters or not.\nEither way this does not influence our results but notation-wise it is easier if the order of players does not matter.\nAdding a new player adds a new index to the payoff values.\nFor calculating the abundance we need to assess Eq.\\ \\eqref{dplayers}.\nFor solving the two sums in Eq.\\ \\eqref{dplayers} we need to know the different combinations of choosing $d$ players and $d+1$ players from the neutral coalescent stationary state.\n\nTo illustrate the complexity of the situation take for example $s_4$.\nThis is the probability that four chosen individuals have the same strategy.\nIn \\ref{coalescentapp} we have shown that deriving $s_4$ depends on $s_3$ which depends on $s_2$ in turn.\nHence in general to derive $s_{d+1}$, we need to know $s_{d}, s_{d-1}, s_{d-2} \\ldots , s_2$.\nIn addition, for general $d$-player games we need quantities such as $\\bar{s}_{d+1}$, probability that $d+1$ individuals chosen in the stationary state all have different strategies.\nIn the absence of mutations such probabilities as $\\bar{s}_{d+1}$ vanish and we are left with only $s_{d+1}$, as mentioned in \\cite{ohtsuki:2010bb}.\nIf $n<d$ then $\\bar{s}_{d+1}$ is zero and hence the terms dependent on it need to be recalculated.\nAfter recalculation the terms which are affected either vanish or are automatically adjusted such that the result can be written again in the form for $L_k$'s, $M_k$'s and $H_k$'s.\nHowever, for a $d$ player game, $d-2$ intermediate terms such as $M_k$ appear.\n\nFor two strategies, $L_k$ reduces to the general condition derived in \\citep{kurokawa:2009aa,gokhale:2010pn} and again holds for arbitrary $d$.\nFor $H_k$ for any number of strategies we conjecture that it will always be of the form $\\frac{1}{n^{d}}\\left[n \\left(\\sum_{r_2,\\ldots r_d} a_{k,r_2,\\ldots r_d } \\right)-\\left(\\sum_{r_2,\\ldots r_{d+1}} a_{r_2,\\ldots r_{d+1} } \\right)\\right]$ from Eq.\\ \\eqref{dplayers}.\nAddressing a generalization for $d$-player games is not a fundamental problem of the approach but requires a tedious \nrecursive effort and poses a notational challenge.\nAt the coalescence level the problem rests on permutations and combinations.\n\nArbitrary mutation rates can be interpreted in different ways.\nIn the social learning context \\citep{traulsen:2009aa} it can be thought of as the exploration rate where the players experiment with different strategies.\nA recent behavioral experiment  suggests that humans change their strategies with a probability much higher than usually considered in theoretical models \\citep{traulsen:2010pn}.\nAnalytical results for such high mutation rates can now be provided utilising the approach outlined herein.\nSmall mutation rates are most relevant in population genetic contexts where the strategies can be thought of as alleles.\nWhile most people think of  evolutionary game theory as a phenotypic approach, \none can as well consider evolutionary games on the level of genes \\citep{hofbauer:1982mm,sigmund:1987aa,rowe:1987aa,rowe:1988aa,cressman:1992aa,hofbauer:1984mm,hofbauer:1998mm}.\nA long standing problem in theoretical biology is to explain the maintenance of polymorphisms.\nSo far, the corresponding models typically assumed small mutation rates, but our approach provides a way to calculate the abundances for arbitrary mutation rates.\nHowever, our aim is not to calculate abundances, but to depict a way to derive them.\nA two-player interaction can capture the effect of one allele on another, but the epistatic interaction of many loci\ncalls for a theory of many-player interactions.\n\n\nMaking use of our approach we can precisely determine the composition of a population with any finite number of different types under weak selection for arbitrary mutation rates.\nAnother convenient way of finding the strategy which performs the best is the limit of small mutation rates.\nFor small mutation rates, the system spends most of its time in a monomorphic state.\nWe can approximate the system by just looking at fixation probabilities of the different types.\nOur approach illustrates that the interaction of $d$ players is significantly more complex than the usual two-player games.\nGeneral multi-player games pose exciting challenges way beyond the usual intricacies of public goods games.\\\\\n\n\\textbf{Acknowledgements}. The authors would like to thank Bin Wu for helpful discussions and suggestions throughout the preparation of the manuscript.\nThe suggestions of two anonymous referees are highly appreciated.\nC.S.G. and A.T. acknowledge support from the Emmy-Noether program of the Deutsche Forschungsgemeinschaft and from the Max-Planck Society.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nThe large sieve was an idea originated by J. V. Linnik \\cite{JVL1} in 1941 while studying the distribution of quadratic non-residues.  Refinements and extensions in various directions of this idea were made by many \\cites{Ba1, Ba2, PrRa, SBLZ, SBLZ3, BD1, Da, DH1, DRHB, Cla, B&Y, PXG, JVL1, Lem, HM2, MVa, Wol, Zha, Zha2, Zha3, Zha4}.  Large sieve results for Dirichlet characters with a fixed order\nare particularly useful in analytic number theory. We refer the readers to\n\\cite{Elliott}, Section 7, for some early large sieve-type results\non general $r$-th order characters.\n Let $(a_n)_{n\\in \\mathbb{N}}$ be an arbitrary sequence of complex numbers, D. R. Heath-Brown's quadratic large sieve \\cite[Theorem 1]{DRHB} states\n that for any $\\varepsilon>0$,\n\\begin{equation}\n\\label{realfinal}\n   \\sideset{}{^*}\\sum_{m \\leq M} \\left| \\sideset{}{^*}\\sum_{n \\leq N} a_n \\Big (\\frac {n}{m} \\Big ) \\right|^2 \\ll_{\\varepsilon} (MN)^{\\varepsilon}(M+N)\n   \\sideset{}{^*}\\sum_{n \\leq N} |a_n|^2,\n\\end{equation}\n   where the asterisks indicate that $m,n$ run over positive odd square-free\n   integers and $(\\frac {\\cdot}{m})$ is the Jacobi symbol. \\newline\n\n   Similar to \\eqref{realfinal}, Heath-Brown also established the following large sieve inequality involving the cubic symbols \\cite[Theorem\n   2]{DRHB1}:\n\\begin{equation}\n\\label{eq:HBcubic}\n \\sideset{}{^*}\\sum_{\\substack{m \\in \\ensuremath{\\mathbb Z}[\\omega] \\\\\\mathcal{N}(m) \\leq M}} \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[\\omega] \\\\\\mathcal{N}(n) \\leq N}} a_n \\leg{n}{m}_3 \\right|^2\n \\ll \\left( M + N + (MN)^{2\/3} \\right)(MN)^{\\varepsilon} \\sum_{\\mathcal{N}(n) \\leq N} |a_n|^2,\n\\end{equation}\nwhere the asterisks indicate that $m,n$ run over square-free elements\nof $\\ensuremath{\\mathbb Z}[\\omega], \\omega=\\exp(2 \\pi i\/3)$ that are congruent to $1$ modulo 3 and $(\\frac {\\cdot}{m})_3$ is the cubic residue symbol.  Moreover, here and after, we use $\\mathcal{N}(m)$ to denote the norm of $m$. \\newline\n\n   Using \\eqref{eq:HBcubic}, S. Baier and M. P. Young \\cite[Theorem 1.4]{B&Y} proved the following large sieve inequality for cubic Dirichlet characters:\n\\begin{equation*}\n\\begin{split}\n& \\sum\\limits_{\\substack{Q<q\\le 2Q}} \\\n\\sideset{}{^\\star}\\sum\\limits_{\\substack{\\chi \\bmod q\\\\ \\chi^3=\\chi_0}}\n\\left| \\ \\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M}} a_m\n\\chi(m)\\right|^2\\\\\n&\\ll\n(QM)^{\\varepsilon}\\min\\left\\{Q^{5\/3}+M,Q^{4\/3}+Q^{1\/2}M,Q^{11\/9}+Q^{2\/3}M,\nQ+Q^{1\/3}M^{5\/3}+M^{12\/5}\\right\\}\n\\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M}}\\left| a_m \\right|^2,\n\\end{split}\n\\end{equation*}\nwhere the star on the sum over $\\chi$ restricts the sum to\nprimitive characters and the asterisks attached to the sum over $m$\nindicates that $m$ runs over square-free integers. \\newline\n\nIt is our goal in this paper to prove a large sieve inequality for quartic\nDirichlet characters.  First we prove the following theorem involving the quartic symbols.\n\\begin{theorem} \\label{mainthm}\nLet $M,N$ be positive integers, and let $(a_n)_{n\\in \\mathbb{N}}$ be an arbitrary\nsequence of complex numbers, where $n$ runs over $\\ensuremath{\\mathbb Z}[i]$. Then we\nhave\n\\begin{equation} \\label{eq:quartic}\n \\sideset{}{^*}\\sum_{\\substack{m \\in \\ensuremath{\\mathbb Z}[i] \\\\\\mathcal{N}(m) \\leq M}} \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\\\mathcal{N}(n) \\leq N}} a_n \\leg{n}{m}_4 \\right|^2\n \\ll_{\\varepsilon} \\left( M + N + (MN)^{3\/4} \\right)(MN)^{\\varepsilon} \\sum_{\\mathcal{N}(n) \\leq N} |a_n|^2,\n\\end{equation}\n   for any $\\varepsilon > 0$,where the asterisks indicate that $m$ and $n$ run over square-free elements of $\\ensuremath{\\mathbb Z}[i]$ that are congruent to $1$ modulo $(1+i)^3$ and $(\\frac\n{\\cdot}{m})_4$ is the quartic residue symbol.\n\\end{theorem}\n\n   Next we shall establish the following large sieve inequality for quartic Dirichlet characters.\n\\begin{theorem}\n\\label{quarticlargesieve} Let $(a_m)_{m\\in \\mathbb{N}}$ be an\narbitrary sequence of complex numbers. Then\n\\begin{equation} \\label{final}\n\\begin{split}\n&  \\sum\\limits_{\\substack{Q<q\\le 2Q}}  \\\n\\sideset{}{^\\star}\\sum\\limits_{\\substack{\\chi \\bmod q\\\\ \\chi^4=\\chi_0,\n\\chi^2 \\neq \\chi_0}} \\left| \\ \\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M}}\na_m \\chi(m)\\right|^2\\\\ &\\ll\n(QM)^{\\varepsilon}\\min\\left\\{Q^{7\/4}+M,Q^{11\/8}+Q^{1\/2}M, Q^{5\/4}+Q^{2\/3}M,\nQ+Q^{1\/2}M+M^{17\/7}\\right\\} \\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M}}\\left| a_m\n\\right|^2,\n\\end{split}\n\\end{equation}\nwhere the star on the sum over $\\chi$ restricts the sum to\nprimitive characters and the asterisks attached to the sum over $m$\nindicates that $m$ runs over square-free integers.\n\\end{theorem}\n\nFollowing the techniques of \\cites{DRHB, DRHB1}, Theorem~\\ref{mainthm} is proved via recursive uses of the Poisson summation formula.   Theorem~\\ref{quarticlargesieve} follows, after some transformations, from Theorem~\\ref{mainthm}.   We note that \\eqref{eq:quartic} is used in \\eqref{square}.   Mark that the characters involved in the second line of \\eqref{square} are actually quadratic, since they are squares of the quartic symbol.  Therefore, it is conceivable that the bounds in \\eqref{final} can be improved if a large sieve inequality for quadratic characters in $\\mathbb{Z}[i]$ is available. \\newline\n\nFinally, we wish to mention that it is highly conceivable that these theorems will find applications in the study of families of $L$-functions involving quartic characters, analogous to those results in \\cite{B&Y} and \\cite{Luo}.\n\n\\subsection{Notations} The following notations and conventions are used throughout the paper.\\\\\n\\noindent $e(z) = \\exp (2 \\pi i z) = e^{2 \\pi i z}$. \\newline\n$\\widetilde{e} (z) = \\exp \\left( 2 \\pi i ( z + \\overline{z} ) \\right)$. \\newline\n$f = O(g)$ or $f \\ll g$ means $|f| \\leq cg$ for some unspecified\npositive constant $c$. \\newline\n\n\\section{Preliminaries}\n\\label{sec 2}\n\\subsection{Quartic symbol and the quartic Gauss sum}\n\\label{sec2.4}\n   The symbol $(\\frac{\\cdot}{n})_4$ is the quartic\nresidue symbol in the ring $\\ensuremath{\\mathbb Z}[i]$.  For a prime $\\pi \\in \\ensuremath{\\mathbb Z}[i]$\nwith $\\mathcal{N}(\\pi) \\neq 2$, the quartic character is defined for $a \\in\n\\ensuremath{\\mathbb Z}[i]$, $(a, \\pi)=1$ by $\\leg{a}{\\pi}_4 \\equiv\na^{(\\mathcal{N}(\\pi)-1)\/4} \\bmod{\\pi}$, with $\\leg{a}{\\pi}_4 \\in \\{\n\\pm 1, \\pm i \\}$. When $\\pi | a$, it is defined that\n$\\leg{a}{\\pi}_4 =0$.  Then the quartic character can be extended\nto composite $n$ with $(\\mathcal{N}(n), 2)=1$ multiplicatively. \\newline\n\n Note that in $\\mathbb{Z}[i]$, the ring of cosets modulo $(1+i)^3$ can be represented by $\\{0, \\pm 1, \\pm i, 1+i, 2, 2i \\}$ and every ideal coprime to $2$ has a unique\ngenerator congruent to 1 modulo $(1+i)^3$ (\\cite[Lemma 7, page\n121]{I&R}). Such a generator is called primary. Recall that the\nquartic reciprocity law states that for two primary primes  $m, n\n\\in \\ensuremath{\\mathbb Z}[i]$,\n\\begin{equation*}\n \\leg{m}{n}_4 = \\leg{n}{m}_4(-1)^{((\\mathcal{N}(n)-1)\/4)((\\mathcal{N}(m)-1)\/4)}.\n\\end{equation*}\n   Observe that a non-unit\n$n=a+bi$ in $\\ensuremath{\\mathbb Z}[i]$ with $a, b \\in \\ensuremath{\\mathbb Z}$ is congruent to 1 modulo $(1+i)^3$ if and only if $a \\equiv 1\n\\bmod{4}, b \\equiv 0 \\bmod{4}$ or $a \\equiv 3 \\bmod{4}, b \\equiv 2\n\\bmod{4}$ by Lemma 6 on page 121 of \\cite{I&R}. \\newline\n\nBelow, we briefly discuss some properties of Gauss sums.  These are dealt with in grater generality in Section 1 of \\cite{Patt}.  For $n , r \\in \\ensuremath{\\mathbb Z}[i]$, $n \\equiv 1 \\bmod {(1+i)^3}$, we set\n\\begin{equation*}\n g(r,n) = \\sum_{x \\bmod{n}} \\leg{x}{n}_4 \\widetilde{e}\\left( \\frac{rx}{n} \\right),\n\\end{equation*}\nwhere here and after\n\\begin{equation} \\label{etildedef}\n\\widetilde{e} (z) = \\exp \\left( 2 \\pi i ( z + \\overline{z} ) \\right).\n\\end{equation}\n   The quartic Gauss sum $g(n)$ is then defined to be $g(n)=g(1,n)$. \\newline\n\n   For $(s,n)=1$, we have\n\\begin{equation*}\n g(rs,n) = \\overline{\\leg{s}{n}_4} g(r,n).\n\\end{equation*}\n    It's easy to see that the above equality in fact holds for any $s$ when\n    $\\leg{\\cdot}{n}_4$ is a primitive character. \\newline\n\n   It's well-known that for square-free $n$'s,\n\\[ |g(n)|=\\sqrt{\\mathcal{N}(n)}. \\]\n\nSuppose $n \\equiv \\pm 1 \\bmod{{(1+i)^3}}$ with no\nrational prime divisor, so $(n, \\bar{n}) = 1$. Let $\\chi_n$ be a\nmultiplicative character on $\\ensuremath{\\mathbb Z}[i]\/(n)$, we define\n\\begin{equation}\n\\label{tau}\n \\tau(\\chi_n) =  \\sum_{1 \\leq x \\leq \\mathcal{N}(n)} \\chi_n(x) e \\left( \\frac{x}{\\mathcal{N}(n)} \\right).\n\\end{equation}\n   Now we specify $\\chi_n$ to be $\\left(\\frac{\\cdot}{n}\\right)_4$. On writing $x = y \\bar{n} + \\bar{y} n$, where $y$ varies over a set\nof representatives in $\\ensuremath{\\mathbb Z}[i] \\bmod{n}$, with $\\bar{n}$ being the\ncomplex conjugate of $n$, it's easy to see that\n\\begin{equation*}\n \\tau(\\chi_n) =  \\sum_{y \\bmod{n}} \\left(\\frac{y \\bar{n}}{n}\\right)_4 e \\left( \\frac{y}{n} + \\frac{\\bar{y}}{\\bar{n}} \\right) =\n \\left(\\frac{\\bar{n}}{n}\\right)_4g(n).\n\\end{equation*}\n   It follows that for $(n_1, n_2)=1$,\n\\begin{align*}\n    \\tau(\\chi_{n_1n_2})=\\left(\\frac{\\mathcal{N}(n_2)}{n_1}\\right)_4\\left(\\frac{\\mathcal{N}(n_1)}{n_2}\\right)_4\\tau(\\chi_{n_1})\\tau(\\chi_{n_2}),\n\\end{align*}\n    and that if $n$ is square-free\n\\begin{align*}\n  |\\tau(\\chi_n)|=\\sqrt{\\mathcal{N}(n)}.\n\\end{align*}\n  Similarly, we have for $n$ square-free\n\\begin{align*}\n  |\\tau(\\chi^2_n)|=\\sqrt{\\mathcal{N}(n)}.\n\\end{align*}\n\n\n\\subsection{Primitive quartic Dirichlet characters}\n\\label{sec2.5}\n   The classification of all the primitive cubic characters of conductor $q$ coprime to $3$ is given in\n   \\cite{B&Y}.\nSimilarly, one can give a classification of all the primitive\nquartic characters of conductor $q$ coprime to\n    $2$.  Every such character is of the form $m \\rightarrow\n(\\frac{m}{n})_4$ for some $n \\in \\ensuremath{\\mathbb Z}[i]$, with $n \\equiv 1\n\\bmod{(1+i)^3}$, $n$ square-free and not divisible by any rational\nprimes and $\\mathcal{N}(n) = q$.\n\n\n\n\\section{Strategy for the proof of Theorem \\ref{mainthm}}\n\n   Our proof of Theorem \\ref{mainthm} uses the ideas in \\cites{DRHB, DRHB1}. We first\n   estimate\n\\begin{equation*}\n   {\\sum}_1=\\sideset{}{^*}\\sum_{\\substack{m \\in \\ensuremath{\\mathbb Z}[i] \\\\M < \\mathcal{N}(m) \\leq 2M}} \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} a_n \\leg{n}{m}_4\n   \\right|^2.\n\\end{equation*}\n   We further simplify notation by supposing that\nthe coefficients $a_n$ are supported on such integers $n \\in\n\\ensuremath{\\mathbb Z}[i]$ satisfying $N < \\mathcal{N}(n)  \\leq 2N$.\n   We begin by defining the norm\n\\begin{equation*}\n   \\mathcal{B}_1(M,N)=\\sup \\left\\{ {\\sum}_1: \\sum_n|a_n|^2=1 \\right\\}.\n\\end{equation*}\nTherefore, we need to show\n\\begin{equation*}\n   \\mathcal{B}_1(M,N) \\ll_{\\varepsilon} (MN)^{\\varepsilon} \\left( M + N + (MN)^{3\/4} \\right).\n\\end{equation*}\nIntroducing a smooth weight function, we have\n\\begin{equation*}\n   {\\sum}_1 \\ll \\sum_m \\exp \\left (-2\\pi \\frac{\\mathcal{N}(m)}{M} \\right) \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\ N <\\mathcal{N}(n) \\leq 2N}} a_n \\leg{n}{m}_4\n   \\right|^2,\n\\end{equation*}\n   the sum being over all $m \\in \\ensuremath{\\mathbb Z}[i]$ for which $m \\equiv 1 \\bmod {(1+i)^3}$. If we now expand\nthe above expression we obtain sums of the form\n\\begin{equation} \\label{2.1}\n   \\sum_m \\exp \\left( -2\\pi \\frac{\\mathcal{N}(m)}{M} \\right) \\leg{n_1}{m}_4\\overline{\\leg{n_2}{m}}_4.\n\\end{equation}\n   We note the following analogue of Lemma 2 of Heath-Brown and Patterson\n   \\cite{H&P}.  As the proof is similar, we omit it here.\n\\begin{lemma}\n\\label{lem1} Let $\\chi$ be a character of modulus $f \\neq 1$, not\nnecessarily primitive. Then, for $w \\leq 1, \\varepsilon>0$,\n\\begin{equation*}\n  \\theta(w, \\chi)=\\sum_{\\substack{ a \\equiv 1 \\bmod{ (1+i)^3} \\\\ (a,f)=1}} \\chi(a)e^{-2\\pi \\mathcal{N}(a)w} \\ll E(\\chi)w^{-1}+\\mathcal{N}(f)^{1\/2+\\varepsilon},\n\\end{equation*}\n  where $E(\\chi)=1$ if $\\chi$ is principal, $0$ otherwise. The\n  implied constant depends only on $\\varepsilon$.\n\\end{lemma}\n\nLemma \\ref{lem1} implies that each of these sums in \\eqref{2.1}\nare $O\\left( \\mathcal{N}(n_1n_2)^{1\/2+\\varepsilon} \\right)$, provided that the\ncharacter involved is non-principal. Since $n_1$ and $n_2$ are\nsquare-free, $\\leg{n_1}{m}_4\\overline{\\leg{n_2}{m}_4}$ is principle only if  $n_1 = n_2$.\nIt follows that\n\\[ {\\sum}_1 \\ll_{\\varepsilon}\n   N^{\\varepsilon} \\left( M\\sum_n|a_n|^2+N\\sum_{n_1,n_2}|a_{n_1}a_{n_2}| \\right)  \\ll_{\\varepsilon}\n   N^{\\varepsilon} \\left( M+N^2 \\right)\\sum_n|a_n|^2. \\]\n We therefore have\n\\begin{equation}\n\\label{initialest}\n   \\mathcal{B}_1(M,N) \\ll_{\\varepsilon} N^{\\varepsilon}\\left( M+N^2 \\right).\n\\end{equation}\n    This will be the starting point for an iterative bound for\n    $\\mathcal{B}_1(M,N)$. \\newline\n\n   Similar to the proof of \\cite[Lemma 1]{DRHB}, using the duality\n   principle (see for example, \\cite[Chap. 9]{HM}) and the quartic\n   reciprocity law by considering the case for $n=a+bi$ with\n   $a \\equiv 1 \\bmod{4}, b \\equiv 0 \\bmod{4}$ or $a\n\\equiv 3 \\bmod{4}, b \\equiv 2 \\bmod{4}$ (and similarly for $m$),\nwe can establish the following lemma.\n\\begin{lemma}\n\\label{lem2} We have $\\mathcal{B}_1(M,N) \\leq 2\n\\mathcal{B}_1(N,M)$. Moreover, there exist coefficients $a'_n,\na''_n$ with $|a'_n|=|a''_n|=|a_n|$ such that\n\\begin{equation*}\n\\begin{split}\n\\sideset{}{^*}\\sum_{\\substack{m \\in \\ensuremath{\\mathbb Z}[i] \\\\M <\\mathcal{N}(m) \\leq 2M}} \\left| \\\n\\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} a_n\n\\leg{n}{m}_4\n   \\right|^2  & \\leq 2 \\sideset{}{^*}\\sum_{\\substack{m \\in \\ensuremath{\\mathbb Z}[i] \\\\M< \\mathcal{N}(m) \\leq 2M}} \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} a'_n \\leg{m}{n}_4\n   \\right|^2 \\\\\n   & \\leq 4 \\sideset{}{^*}\\sum_{\\substack{m \\in \\ensuremath{\\mathbb Z}[i] \\\\M< \\mathcal{N}(m) \\leq 2M}} \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} a''_n \\leg{n}{m}_4\n   \\right|^2.\n\\end{split}\n\\end{equation*}\n\\end{lemma}\n\n\n    Our next lemma is a trivial modification of Lemma 9 of \\cite{DRHB}, which shows that the norm $\\mathcal{B}_1(M,N)$ is essentially\n    increasing.\n\\begin{lemma}\n\\label{lem3} There is an absolute constant $C > 0$ as follows.\nLet $M_1, N \\geq 1$ and $M_2 \\geq CM_1\\log(2M_1N)$. Then\n\\begin{equation*}\n   \\mathcal{B}_1(M_1,N)\\leq C \\mathcal{B}_1(M_2,N).\n\\end{equation*}\n   Similarly, if $M, N_1 \\geq 1$ and $N_2 \\geq CN_1\\log(2N_1M)$. Then\n\\begin{equation*}\n   \\mathcal{B}_1(M,N_1)\\leq C \\mathcal{B}_1(M,N_2).\n\\end{equation*}\n\\end{lemma}\n\nNext, we define\n\\begin{equation*}\n   \\mathcal{B}_2(M,N)=\\sup \\left\\{ {\\sum}_2: \\sum_n|a_n|^2=1 \\right\\},\n\\end{equation*}\n    where\n\\begin{equation}\n\\label{sum2}\n   {\\sum}_2=\\sum_{\\substack{m \\in \\ensuremath{\\mathbb Z}[i] \\\\M < \\mathcal{N}(m) \\leq 2M}} \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} a_n \\leg{m}{n}_4\n   \\right|^2,\n\\end{equation}\n   the summation over $m$ running over all integers of $\\ensuremath{\\mathbb Z}[i]$ in the relevant range. \\newline\n\n   It follows directly from Lemma \\ref{lem2} that\n\\begin{equation}\n\\label{12comparison}\n  \\mathcal{B}_1(M,N) \\leq 2\\mathcal{B}_2(M,N).\n\\end{equation}\nFor the other direction, we have the following.\n\\begin{lemma}\n\\label{lem4} There exist $X, Y \\gg 1$ such that $XY^3 \\ll M$ and\n\\begin{equation*}\n   \\mathcal{B}_2(M,N) \\ll (\\log M)^3M^{1\/2}X^{-1\/2}Y^{-3\/2}\\min(Y\\mathcal{B}_1(X,N), X\\mathcal{B}_1(Y,N)).\n\\end{equation*}\n\\end{lemma}\n\\begin{proof}\n   To handle $\\sum_2$ we write each of the integers $m$ occurring in the outer summation\nof \\eqref{sum2} in the form $m = ab^2c^3d$, where $a, b, c\\equiv 1\n\\bmod {(1+i)^3}$ are square-free, and $d$ is a product of a unit,\na power of $1+i$, and a fourth power (so that $d$ can be written\nas $d=u(1+i)^je^4$ where $u$ is a unit, $0 \\leq j \\leq 3$ and $e\n\\in \\ensuremath{\\mathbb Z}[i]$). We split the available ranges for $a, b, c$ and $d$\ninto sets $X < \\mathcal{N}(a) \\leq 2X, Y < \\mathcal{N}(b) \\leq 2Y, Z < \\mathcal{N}(c) \\leq 2Z$\nand $W < \\mathcal{N}(d) \\leq 2W$, where $X, Y, Z$ and $W$ are powers of $2$.\nThere will therefore be $O(\\log^3M)$ possible quadruples $X, Y,Z,\nW$. We may now write\n\\begin{equation*}\n   {\\sum}_2 \\ll \\sum_{X,Y,Z, W}{\\sum}_2(X,Y,Z,W)\n\\end{equation*}\n  accordingly, so that\n\\begin{equation*}\n   {\\sum}_2 \\ll (\\log^3M){\\sum}_2(X,Y,Z,W)\n\\end{equation*}\n   for some quadruple $X,Y,Z, W$. However,\n\\begin{equation*}\n   {\\sum}_2(X,Y,Z,W) \\leq \\sum_{b,c,d}\\sideset{}{^*}\\sum_{\\substack{a  \\in \\ensuremath{\\mathbb Z}[i] \\\\X'<\\mathcal{N}(a) \\leq 2X'}}\n   \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} a_n \\leg{b^2c^3d}{n}_4 \\leg{a}{n}_4\n   \\right|^2,\n\\end{equation*}\n   where $X'=X'(b,c, d)=M\/\\mathcal{N}(b^2c^3d)$. It is easy to see that $X\/2 \\leq X' \\leq\n   2X$, and hence by Lemma \\ref{lem2}\n\\[ {\\sum}_2(X,Y,Z, W) \\ll \\sum_{b,c,d}\\mathcal{B}_1(X',N)\\sum_{n}\n   |a_n|^2 \\ll YZW^{1\/4}\\max \\left\\{ \\mathcal{B}_1(X',N): X\/2 \\leq X' \\leq 2X \\right\\} \\sum_{n}\n   |a_n|^2, \\]\n since there are $O(W^{1\/4})$ possible integers $d$. \\newline\n\n   In the same way we have\n\\begin{align*}\n   {\\sum}_2(X,Y,Z, W) &\\leq \\sum_{a, b, d}\\sideset{}{^*}\\sum_{\\substack{c  \\in \\ensuremath{\\mathbb Z}[i] \\\\Z'<\\mathcal{N}(c) \\leq 2Z'}}\n   \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} a_n \\leg {ab^2d}{n}_4 \\leg {c^3}{n}_4\n   \\right|^2 \\\\\n   &= \\sum_{a,b, d}\\sideset{}{^*}\\sum_{\\substack{c  \\in \\ensuremath{\\mathbb Z}[i] \\\\Z'<\\mathcal{N}(c) \\leq 2Z'}}\n   \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} \\overline{a}_n \\overline{\\leg {ab^2d}{n}}_4 \\overline{\\leg {c^3}{n}}_4\n   \\right|^2 \\\\\n   &= \\sum_{a,b,d}\\sideset{}{^*}\\sum_{\\substack{c  \\in \\ensuremath{\\mathbb Z}[i] \\\\Z'<\\mathcal{N}(c) \\leq 2Z'}}\n   \\left| \\ \\sideset{}{^*}\\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} \\overline{a}_n \\overline{\\leg {ab^2d}{n}}_4 \\leg {c}{n}_4\n   \\right|^2 \\\\\n   & \\ll \\ \\sum_{a,b,d}\\mathcal{B}_1(Z',N)\\sum_{n}\n   |a_n|^2 \\\\\n   & \\ll XYW^{1\/4}\\max \\left\\{ \\mathcal{B}_1(Z',N): Z \\ll Z' \\ll Z \\right\\} \\sum_{n}\n   |a_n|^2,\n\\end{align*}\n   where $Z'=Z'(a,b,d)=M\/\\mathcal{N}(ab^2d)$. As $Y \\ll M^{1\/2}X^{-1\/2}Z^{-3\/2}W^{-1\/2}$, we see that\n\\begin{equation*}\n   \\mathcal{B}_2(M,N) \\ll (\\log M)^3M^{1\/2}X^{-1\/2}Z^{-3\/2}W^{-1\/4}\\min(Z\\mathcal{B}_1(X,N), X\\mathcal{B}_1(Z,N)).\n\\end{equation*}\n   The assertion of the lemma now follows on replacing $Z$ by $Y$ above.\n\\end{proof}\n\n   As in \\cite{DRHB}, we introduce an infinitely differentiable weight function $W: \\ensuremath{\\mathbb R} \\rightarrow \\ensuremath{\\mathbb R}$, defined by\n\\begin{equation}\n\\label{W}\nW(x)= \\begin{cases} \\exp\\left(\\frac{-1}{(2x-1)(5-2x)}\\right),\n\\qquad & \\text{if }  \\frac{1}{2}<x<\\frac{5}{2},\\\\  0, \\qquad  &\n\\text{otherwise}. \\end{cases}\n\\end{equation}\nWe now have\n\\begin{equation}\n\\label{3.7}\n   {\\sum}_2 \\ll \\sum_{m \\in \\ensuremath{\\mathbb Z}[i]}W\\left( \\frac {\\mathcal{N}(m)}{M}\\right) \\left| \\sum_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i] \\\\N < \\mathcal{N}(n) \\leq 2N}} a_n \\leg {m}{n}_4\n   \\right|^2,\n\\end{equation}\n   where we recall that we can drop the conditions on $a_n$ on the inner sum above of the right-hand side expression by supposing that\nthe coefficients $a_n$ are supported on square-free integers $n\n\\equiv 1 \\bmod {(1+i)^3} \\in \\ensuremath{\\mathbb Z}[i]$ lying in the range $N < \\mathcal{N}(n)\n\\leq 2N$. \\newline\n\nExpanding the sum on the right-hand side of \\eqref{3.7}, we obtain\n\\begin{equation*}\n   {\\sum}_2 \\ll \\sum_{n_1,n_2}a_{n_1}\\overline{a}_{n_2}\\sum_{m \\in \\ensuremath{\\mathbb Z}[i]}\n   W\\left(\\frac {\\mathcal{N}(m)}{M}\\right)\n   \\leg{m}{n_1}_4\\overline{\\leg{m}{n_2}}_4.\n\\end{equation*}\n   We set\n\\begin{equation*}\n   {\\sum}_3={\\sum}_3(M,N)= \\sum_{(n_1,n_2)=1}a_{n_1}\\overline{a}_{n_2}\\sum_{m \\in \\ensuremath{\\mathbb Z}[i]}\n   W\\left(\\frac {\\mathcal{N}(m)}{M}\\right)\n   \\leg{m}{n_1}_4\\overline{\\leg{m}{n_2}}_4\n\\end{equation*}\n   and define\n\\begin{equation} \\label{B3def}\n   \\mathcal{B}_3(M,N)=\\sup \\left\\{ {\\sum}_3: \\sum_n|a_n|^2=1 \\right\\}.\n\\end{equation}\n    Similar to \\cite[Lemma 7]{DRHB, DRHB1}, we have the\n    following\n\\begin{lemma}\n\\label{lem5} Let $\\varepsilon > 0$ be given. Then there exist\npositive integers $\\Delta_2 \\geq \\Delta_1$ such that\n\\begin{equation*}\n   \\mathcal{B}_2(M,N) \\ll_{\\varepsilon} N^{\\varepsilon} \\mathcal{B}_3 \\left(\\frac {M}{\\Delta_1}, \\frac {N}{\\Delta_2}\\right).\n\\end{equation*}\n\\end{lemma}\n\n\n   We complete the chain of relations amongst the various norms by giving the following estimate for $\\mathcal{B}_3(M,N)$ in terms of\n   $\\mathcal{B}_2(M,N)$.\n\\begin{lemma}\n\\label{lem6} Let $N \\geq 1$. Then for any $\\varepsilon>0$ we have\n\\begin{equation*}\n   \\mathcal{B}_3(M,N) \\ll_{\\varepsilon} MN^{4\\varepsilon-1}\\max \\left\\{ \\mathcal{B}_2(K,\n   N): K \\leq N^2\/M\n   \\right\\}+M^{-1}N^{3+4\\varepsilon}\\sum_{K>N^2\/M}K^{-2-\\varepsilon}\\mathcal{B}_2(K,\n   N),\n\\end{equation*}\n   where $K$ runs over powers of $2$.\n\\end{lemma}\nThis bound uses the Poisson summation formula and is the key\nin the proof of Theorem \\ref{mainthm}.  Note that it does not cover the case in which $N =1\/2$, say, for which we have the trivial bound\n\\begin{equation}\n\\label{trivialbound}\n   \\mathcal{B}_3(M,N) \\ll_{\\varepsilon} M, \\hspace{0.1in} (N \\leq 1).\n\\end{equation}\nSection \\ref{sec4} will be devoted to the proof of Lemma~\\ref{lem6}.\n\n\\section{Proof of Lemma \\ref{lem6}} \\label{sec4}\n\nOur proof of Lemma \\ref{lem6} requires the application of the Poisson\nsummation formula. We shall write\n\\begin{equation*}\n   \\chi(m)=\\leg{m}{n_1}_4\\overline{\\leg{m}{n_2}}_4,\n\\end{equation*}\nwhich is a primitive character (on the group\n$(\\ensuremath{\\mathbb Z}[i]\/(n_1n_2))^{\\times}$) to modulus $q = n_1n_2$, provided\nthat $n_1$, $n_2$ and 2 are pair-wise coprime and that $n_1$ and $n_2$ are\nsquare-free.\n\\begin{lemma}\n\\label{lem7} With the above notations we have\n\\begin{equation*}\n   \\sum_{m \\in \\ensuremath{\\mathbb Z}[i]}W\\left(\\frac {\\mathcal{N}(m)}{M}\\right)\\chi(m)=\\frac {\\chi(-2i)g(n_1)\\overline{g(n_2)}M}{\\mathcal{N}(q)}\\leg{n_2}{n_1}_4\\overline{\\leg{n_1}{n_2}}_4\\leg{-1}{n_2}_4\n   \\sum_{m \\in \\ensuremath{\\mathbb Z}[i]}\\widetilde{W}\\left(\\sqrt{\\frac {\\mathcal{N}(k)M}{\\mathcal{N}(q)}}\\right)\\overline{\\chi}(k),\n\\end{equation*}\n   where\n\\begin{equation*}\n   \\widetilde{W}(t)=\\int\\limits^{\\infty}_{-\\infty}\\int\\limits^{\\infty}_{-\\infty}W(\\mathcal{N}(x+yi))\\widetilde{e}\\left( \\frac{t(x+yi)}{2i}\\right)\\mathrm{d} x  \\mathrm{d} y,\n\\end{equation*}\n   for non-negative $t$. Here $\\widetilde{e}(z)$ is defined in \\eqref{etildedef} and $g(n)$ is the Gauss sums defined in Section \\ref{sec2.4}.\n\\end{lemma}\n\\begin{proof}\nThis lemma is analogous to Lemma 10 in \\cite{DRHB1} and the proof is very similar.  The differences include we need to start with the Poisson summation formula for\n   $\\ensuremath{\\mathbb Z}[i]$, which takes the form.\n\\begin{equation*}\n   \\sum_{j \\in \\ensuremath{\\mathbb Z}[i]}f(j)=\\sum_{k \\in\n   \\ensuremath{\\mathbb Z}[i]}\\int\\limits^{\\infty}_{-\\infty}\\int\\limits^{\\infty}_{-\\infty}f(x+yi)\\widetilde{e}\\left( \\frac {k(x+yi)}{2i} \\right)\\mathrm{d} x  \\mathrm{d} y.\n\\end{equation*}\nWe omit the details of the rest of proof as it simply goes along the same lines as the proof of Lemma 10 in \\cite{DRHB1}.\n\\end{proof}\n\n    Our next result will be used to separate the variables in a function of a\nproduct, which is Lemma 12 of \\cite{DRHB}.\n\\begin{lemma}\n\\label{lem8} Let $\\rho: \\ensuremath{\\mathbb R} \\rightarrow \\ensuremath{\\mathbb R}$ be an infinitely\ndifferentiable function whose derivatives satisfy the bound\n\\[ \\rho{(k)}(x) \\ll_{k,A}|x|^{-A} \\]\nfor $|x| \\geq 1$, for any positive constant\n$A$. Let\n\\begin{equation*}\n   \\rho_{+}(s)=\\int\\limits^{\\infty}_{0}\\rho(x)x^{s-1} \\mathrm{d} x,\n   \\hspace{0.1in} \\rho_{-}(s)=\\int\\limits^{\\infty}_{0}\\rho(-x)x^{s-1} \\mathrm{d}\n   x.\n\\end{equation*}\n   Then $\\rho_{+}(s)$ and $\\rho_{-}(s)$ are holomorphic in $\\Re(s) = \\sigma > 0$, and\n   satisfy\n\\begin{equation*}\n   \\rho_{+}(s), \\ \\rho_{-}(s) \\ll_{A, \\sigma} |s|^{-A},\n\\end{equation*}\nin that same domain, for any positive constant $A$. Moreover if $\\sigma> 0$ we have\n\\begin{equation*}\n   \\rho(x)=\\frac {1}{2\\pi\n   i}\\int\\limits^{\\sigma+i\\infty}_{\\sigma-i\\infty}\\rho_{+}(s)x^{-s} \\mathrm{d} s \\; \\; \\; \\mbox{and} \\; \\; \\;\n   \\rho(-x)=\\frac {1}{2\\pi\n   i}\\int\\limits^{\\sigma+i\\infty}_{\\sigma-i\\infty}\\rho_{-}(s)x^{-s} \\mathrm{d} s\n\\end{equation*}\n   for any positive $x$.\n\\end{lemma}\n\nWe are now ready to prove Lemma~\\ref{lem6}.\n\n\\begin{proof} [Proof of Lemma~\\ref{lem6}]\n   In the notation of Lemma \\ref{lem7} we have\n\\begin{equation*}\n   {\\sum}_3(M,N)=\\sum_{(n_1,n_2)=1}a_{n_1}\\overline{a}_{n_2}\\sum_{m \\in \\ensuremath{\\mathbb Z}[i]}W\\left(\\frac {\\mathcal{N}(m)}{M}\\right)\\chi(m).\n\\end{equation*}\n   We proceed to evaluate the inner sum using Lemma \\ref{lem7}, whence\n\\begin{equation}\n\\label{5.1}\n   {\\sum}_3(M,N)=M\\sum_{k \\in \\ensuremath{\\mathbb Z}[i]}\\sum_{(n_1,n_2)=1}c_{n_1}\\overline{c}_{n_2}\\leg{n_2}{n_1}_4\\overline{\\leg{n_1}{n_2}}_4\\leg{-1}{n_2}_4\\widetilde{W}\\left(\\sqrt{\\frac {\\mathcal{N}(k)M}{\\mathcal{N}(n_1n_2)}}\\right)\\overline{\\chi}(k),\n\\end{equation}\n   where\n\\begin{equation*}\n    c_n=a_n\\leg{-2i}{n}_4\\frac {g(n)}{\\mathcal{N}(n)}.\n\\end{equation*}\n   Note by the law of quartic reciprocity, we have\n\\begin{equation*}\n   \\leg{n_2}{n_1}_4\\overline{\\leg{n_1}{n_2}}_4=(-1)^{((\\mathcal{N}(n_1)-1)\/4)((\\mathcal{N}(n_2)-1)\/4)}.\n\\end{equation*}\n    Now we let\n\\[ S_1 =\\{n \\in \\ensuremath{\\mathbb Z}[i]: N<\\mathcal{N}(n)\\leq 2N, n \\hspace{0.05in} \\text{square-free}, n=a+bi, a, b \\in \\ensuremath{\\mathbb Z}, a \\equiv 1 \\bmod{4}, b \\equiv 0 \\bmod{4} \\},  \\]\nand\n\\[ S_2 =\\{n \\in \\ensuremath{\\mathbb Z}[i]: N<\\mathcal{N}(n)\\leq 2N, n \\hspace{0.05in} \\text{square-free}, n=a+bi, a, b \\in \\ensuremath{\\mathbb Z}, a \\equiv 3 \\bmod{4}, b \\equiv 2 \\bmod{4} \\}. \\]\n   We can then recast the inner sum in \\eqref{5.1} as\n\\begin{align*}\n   &\\sum_{(n_1,n_2)=1} \\cdots \\\\\n   =& \\sum_{\\substack{(n_1,n_2)=1 \\\\ n_1 \\in S_1, n_2 \\in S_1}} \\cdots\n   \\; \\; +\\sum_{\\substack{(n_1,n_2)=1 \\\\ n_1 \\in S_1, n_2 \\in S_2}} \\cdots \\; \\; +\\sum_{\\substack{(n_1,n_2)=1 \\\\ n_1 \\in S_2, n_2 \\in S_1}} \\cdots \\; \\;\n   +\\sum_{\\substack{(n_1,n_2)=1 \\\\ n_1 \\in S_2, n_2 \\in S_2}} \\cdots \\; \\; -2\\sum_{\\substack{(n_1,n_2)=1 \\\\ n_1 \\in S_2, n_2 \\in S_2}} \\cdots \\\\\n   =& \\sum_{(n_1,n_2)=1}c_{n_1}\\overline{c}_{n_2}\\leg{-1}{n_2}_4\\widetilde{W}\\left(\\sqrt{\\frac {\\mathcal{N}(k)M}{\\mathcal{N}(n_1n_2)}}\\right)\\overline{\\chi}(k)-2\\sum_{(n_1,n_2)=1}c'_{n_1}\\overline{c'}_{n_2}\\leg{-1}{n_2}_4\\widetilde{W}\\left(\\sqrt{\\frac {\\mathcal{N}(k)M}{\\mathcal{N}(n_1n_2)}}\\right)\\overline{\\chi}(k),\n\\end{align*}\n   where we let $c'_n=c_n$ if $n \\in S_2$ and $0$ otherwise. Due\n   to similarities, it suffices to estimate\n\\begin{equation*}\n   M\\sum_{k \\in\n\\ensuremath{\\mathbb Z}[i]}\\sum_{(n_1,n_2)=1}c_{n_1}\\overline{c}_{n_2}\\leg{-1}{n_2}_4\\widetilde{W}\\left(\\sqrt{\\frac\n{\\mathcal{N}(k)M}{\\mathcal{N}(n_1n_2)}}\\right)\\overline{\\chi}(k),\n\\end{equation*}\n   Note that $k = 0$ may be omitted if $N \\geq 1$, since then $\\mathcal{N}(n_1n_2) > 1$ and $\\chi(0) = 0$,\nthe character being non-trivial. We may now apply Lemma \\ref{lem8}\nto the function $\\rho(x) = \\widetilde{W}(x)$, which satisfies the necessary conditions of the lemma, as one sees by repeated\nintegration by parts. We decompose the available $k$ into sets for\nwhich $K < \\mathcal{N}(k) \\leq 2K$, where $K$ runs over powers of $2$, and\nuse\n\\begin{equation} \\label{sigmadef}\n\\sigma = \\left\\{ \\begin{array}{ll} \\varepsilon , &  \\mbox{for} \\;  K \\leq N^2\/M, \\\\  4 +\n\\varepsilon , &  \\mbox{otherwise}.\n\\end{array} \\right.\n\\end{equation}\nThis gives\n\\begin{align*}\n    {\\sum}_3 & \\ll_{\\varepsilon} M\n    \\sum_{K}(KM)^{-\\sigma\/2}\\int\\limits^{\\infty}_{-\\infty}|\\rho_{+}(\\sigma+it)||S(\\sigma+it)| \\mathrm{d} t,\n\\end{align*}\n  where\n\\[\n   S(s)=\\sum_{K < \\mathcal{N}(k) \\leq 2K}\\left| \\sum_{(n_1,n_2)=1}b_{n_1}b'_{n_2}\\leg{-1}{n_2}_4\\overline{\\chi}(k)\\right|, \\; \\; \\;  \\mbox{with} \\; \\; \\;\n    b_n=c_n\\mathcal{N}(n)^{s\/2} \\; \\; \\mbox{and} \\; \\; b'_n=\\overline{c}_n\\mathcal{N}(n)^{s\/2} .\n\\]\nWe use the M\\\"obius function to detect the coprimality condition in the inner sum of $S(s)$, giving\n\\begin{align*}\n S(s)  &\\ll \\sum_{d}\\sum_{K < \\mathcal{N}(k) \\leq 2K}\\left| \\sum_{d|(n_1,n_2)}b_{n_1}b'_{n_2}\\leg{-1}{n_2}_4\\overline{\\chi}(k)\\right| \\\\\n&= \\sum_{d}\\sum_{K < \\mathcal{N}(k) \\leq 2K}\\left|\n\\sum_{d|n}b_{n}\\overline{\\leg{k}{n}}_4\\right| \\left|\n\\sum_{d|n}b'_{n}\\leg{-k}{n}_4\\right| \\leq S^{1\/2}_1S^{1\/2}_2,\n\\end{align*}\n   by Cauchy's inequality, where\n\\[  S_1 = \\sum_{d}\\sum_{K < \\mathcal{N}(k) \\leq 2K}\\left| \\sum_{d|n}b_{n}\\overline{\\leg{k}{n}}_4\\right|^2 \\]\nand satisfies the bound\n\\[  S_1 \\leq \\sum_{d}\\mathcal{B}_2(K,N)\\sum_{d|n}|b_n|^2  \\leq \\mathcal{B}_2(K,N)\\sum_{n}d(n)|a_n|^2\\mathcal{N}(n)^{\\sigma-1} \\ll_{\\varepsilon} N^{\\varepsilon+\\sigma-1}\\mathcal{B}_2(K,N). \\]\n$S_2$ can be treated similarly. It follows then that\n\\begin{equation*}\n   S(s) \\ll_{\\varepsilon} N^{\\varepsilon+\\sigma-1}\\mathcal{B}_2(K,N),\n\\end{equation*}\n   and since\n\\begin{align*}\n     \\int\\limits^{\\infty}_{-\\infty}|\\rho_{+}(\\sigma+it)| \\mathrm{d} t \\ll_{\\varepsilon} 1,\n\\end{align*}\nwe infer, mindful of our choices of $\\sigma$ in \\eqref{sigmadef}, that\n\\begin{align*}\n    {\\sum}_3 & \\ll_{\\varepsilon}  MN^{4\\varepsilon-1}\\max \\left\\{ \\mathcal{B}_2(K,\n   N): K \\leq N^2\/M\n   \\right\\}+M^{-1}N^{3+4\\varepsilon}\\sum_{K>N^2\/M}K^{-2-\\varepsilon}\\mathcal{B}_2(K,\n   N),\n\\end{align*}\nRecalling the definition of $\\mathcal{B}_3(M,N)$ in \\eqref{B3def}, we have completed the proof of Lemma \\ref{lem6}.\n   \\end{proof}\n\n\\section{The Recursive Estimate and the Proof of Theorem~\\ref{mainthm}}\n\n    Lemmas \\ref{lem4}, \\ref{lem5} and \\ref{lem6} allow us to estimate $\\mathcal{B}_1(M,N)$ recursively, as follows.\n\\begin{lemma}\n\\label{lem9} Suppose that $3\/2 < \\xi \\leq 2$, and that\n\\begin{equation}\n\\label{6.1}\n   \\mathcal{B}_1(M,N)\\ll_{\\varepsilon} (MN)^{\\varepsilon} \\left( M+N^{\\xi} + (MN)^{3\/4} \\right).\n\\end{equation}\n   for any $\\varepsilon > 0$. Then\n\\begin{equation*}\n   \\mathcal{B}_1(M,N)\\ll_{\\varepsilon} (MN)^{\\varepsilon} \\left( M+N^{(9\\xi-6)\/(4\\xi-1)} + (MN)^{3\/4} \\right).\n\\end{equation*}\n   for any $\\varepsilon > 0$.\n\\end{lemma}\n\\begin{proof}\n  By the symmetry expressed in Lemma \\ref{lem2} the hypothesis\n\\eqref{6.1} yields\n\\begin{align*}\n     \\mathcal{B}_1(M,N)\\ll_{\\varepsilon} \\left( M^{\\xi} + N + (MN)^{3\/4}\\right) (MN)^{\\varepsilon}.\n\\end{align*}\n    It follows from \\eqref{initialest} that the above estimation is valid with\n    $\\xi=2$. We now feed this into Lemma \\ref{lem4}, whence\n\\begin{equation} \\label{eqwithmin}\n   \\mathcal{B}_2(M,N) \\ll_{\\varepsilon} (MN)^{2\\varepsilon}M^{1\/2}X^{-1\/2}Y^{-3\/2}\\min(Yf(X,N),\n   Xf(Y,N)),\n\\end{equation}\n   where\n\\begin{equation*}\n     f(Z,N)=Z^{\\xi} + N + (ZN)^{3\/4}.\n\\end{equation*}\n   If $X \\geq Y$ we bound the minimum in \\eqref{eqwithmin} by $Yf(X,N)$, whence\n\\begin{equation*}\n   \\mathcal{B}_2(M,N) \\ll_{\\varepsilon} (MN)^{2\\varepsilon}M^{1\/2}X^{-1\/2}Y^{-3\/2}\\left( YX^{\\xi} + YN +\n   Y(XN)^{3\/4} \\right).\n\\end{equation*}\n   Here we have\n\\begin{equation*}\n   M^{1\/2}X^{-1\/2}Y^{-3\/2}YX^{\\xi} \\ll M^{\\xi}Y^{1-3\\xi}\n\\end{equation*}\n   since $X \\ll MY^{-3}$. On recalling that $\\xi > 3\/2 >1\/3$ and $Y \\gg 1$ we see that\nthis is $O(M^{\\xi})$. Moreover\n\\begin{equation*}\n   M^{1\/2}X^{-1\/2}Y^{-3\/2}YN=M^{1\/2}X^{-1\/2}Y^{-1\/2}N \\ll\n   M^{1\/2}N.\n\\end{equation*}\n   Finally\n\\[  M^{1\/2}X^{-1\/2}Y^{-3\/2}Y(XN)^{3\/4}=M^{1\/2}X^{1\/4}Y^{-1\/2}N^{3\/4}\n   \\ll M^{3\/4}N^{3\/4}\n   \\ll M^{1\/2}N+M^{3\/2} \\leq\n   M^{1\/2}N+M^{\\xi}, \\]\n   since $\\xi > 3\/2$. It follows that\n\\begin{equation}\n\\label{B2bound}\n   \\mathcal{B}_2(M,N) \\ll_{\\varepsilon}\n   (MN)^{2\\varepsilon} \\left( M^{1\/2}N+M^{\\xi} \\right)\n\\end{equation}\n   when $X \\geq Y$. \\newline\n\n   In the alternative case we bound the minimum in \\eqref{eqwithmin} by $Xf(Y,N)$, whence\n\\begin{equation*}\n   \\mathcal{B}_2(M,N) \\ll_{\\varepsilon} (MN)^{2\\varepsilon}M^{1\/2}X^{-1\/2}Y^{-3\/2} \\left( XY^{\\xi} + XN + X(YN)^{3\/4} \\right).\n\\end{equation*}\n   Here\n\\begin{equation*}\n   M^{1\/2}X^{-1\/2}Y^{-3\/2}XY^{\\xi} \\ll M^{1\/2}X^{1\/2}Y^{1\/2} \\ll M\n   \\ll M^{\\xi}\n\\end{equation*}\n   since $\\xi \\leq 2$ and $XY \\ll M$. Moreover\n\\begin{equation*}\n   M^{1\/2}X^{-1\/2}Y^{-3\/2}XN  = M^{1\/2}X^{1\/2}Y^{-3\/2}N \\ll\n   M^{1\/2}N\n\\end{equation*}\n  since we are now supposing that $Y \\geq X$.\n  Finally\n\\[ M^{1\/2}X^{-1\/2}Y^{-3\/2}X(YN)^{3\/4}=M^{1\/2}X^{1\/2}Y^{-3\/4}N^{3\/4} \\ll\n   M^{1\/2}Y^{-1\/4}N^{3\/4} \\ll  M^{1\/2}N^{3\/4} \\ll M^{1\/2}N+M^{\\xi}, \\]\n   as before. It follows that \\eqref{B2bound} holds when $Y \\geq X$ too. It will be convenient to\nobserve that \\eqref{B2bound} still holds when $M < 1\/2$ , since\nthen $\\mathcal{B}_2(M,N)= 0$. \\newline\n\n   We are now ready to use \\eqref{B2bound} (with a new value for $\\varepsilon$) in Lemma \\ref{lem6}, to obtain\na bound for $\\mathcal{B}_3(M,N)$. We readily see that\n\\begin{equation*}\n   \\max\\left\\{ \\mathcal{B}_2(K,\n   N): K \\leq N^2\/M\n   \\right\\} \\ll_{\\varepsilon} N^{\\varepsilon}\\left( M^{-1\/2}N^2+M^{-\\xi}N^{2\\xi} \\right)\n\\end{equation*}\n   and\n\\begin{equation*}\n   \\sum_{K>N^2\/M}K^{-2-\\varepsilon}\\mathcal{B}_2(K,\n   N) \\ll_{\\varepsilon}\n   N^{\\varepsilon}\\left( M^{3\/2}N^{-2}+M^{2-\\xi}N^{2\\xi-4} \\right).\n\\end{equation*}\n   Thus, if $N \\geq 1$, we will have\n\\begin{equation*}\n    \\mathcal{B}_3(M,\n   N) \\ll_{\\varepsilon}\n   N^{5\\varepsilon}\\left( M^{1\/2}N+M^{1-\\xi}N^{2\\xi-1} \\right).\n\\end{equation*}\n   When this is used in Lemma \\ref{lem5} we find that when $N\/\\Delta_2 \\geq\n   1$,\n\\begin{align*}\n    \\mathcal{B}_3\\left( \\frac {M}{\\Delta_1}, \\frac {N}{\\Delta_2} \\right) &\\ll_{\\varepsilon}\n   N^{5\\varepsilon}\\left( M^{1\/2}N+M^{1-\\xi}N^{2\\xi-1}\\Delta^{\\xi-1}_1\\Delta^{1-2\\xi}_2 \\right) \\leq N^{5\\varepsilon} \\left( M^{1\/2}N+M^{1-\\xi}N^{2\\xi-1}\\Delta^{-\\xi}_2 \\right) \\\\\n   & \\leq N^{5\\varepsilon}\\left( M^{1\/2}N+M^{1-\\xi}N^{2\\xi-1} \\right).\n\\end{align*}\n   Note that when $M \\geq N$, we have $M^{1\/2}N \\leq (MN)^{3\/4}$\n   and when $M \\leq N$, we have $(MN)^{3\/4} \\leq\n   M^{1-\\xi}N^{2\\xi-1}$ since $\\xi > 3\/2$. Thus we conclude that\n\\begin{equation*}\n    \\mathcal{B}_2(M,\n   N) \\ll_{\\varepsilon}\n   N^{6\\varepsilon}\\left( (MN)^{3\/4}+M^{1-\\xi}N^{2\\xi-1} \\right),\n\\end{equation*}\n   provided that $N\/\\Delta_2 \\geq 1$. In the alternative case \\eqref{trivialbound} applies, whence\n\\begin{equation*}\n    \\mathcal{B}_2(M,\n   N) \\ll_{\\varepsilon}\n   (MN)^{6\\varepsilon}\\left( M+(MN)^{3\/4}+M^{1-\\xi}N^{2\\xi-1} \\right),\n\\end{equation*}\n   In view of Lemma \\ref{lem3} and \\eqref{12comparison} we may now deduce that\n\\begin{align*}\n    \\mathcal{B}_1(M,\n   N)  \\leq \\mathcal{B}_1(M',\n   N) \\ll \\mathcal{B}_2(M',\n   N) \\ll_{\\varepsilon}\n   (M'N)^{6\\varepsilon}\\left( M'+(M'N)^{3\/4}+{M'}^{1-\\xi}N^{2\\xi-1} \\right) ,\n\\end{align*}\n  for any $M' \\geq CM \\log(2MN)$. Note that when ${M}^{4\\xi-1}\n  \\leq N^{8\\xi-7}$, we have\n\\begin{align*}\n    (MN)^{3\/4} \\leq {M}^{1-\\xi}N^{2\\xi-1}.\n\\end{align*}\n   We shall now choose\n\\begin{align*}\n    M'=C\\max \\left\\{ M, N^{(8\\xi-7)\/(4\\xi-1)} \\right\\} \\log(2MN) ,\n\\end{align*}\n   so that when $M \\geq N^{(8\\xi-7)\/(4\\xi-1)}$, we have\n\\begin{align*}\n     M'+(M'N)^{3\/4}+{M'}^{1-\\xi}N^{2\\xi-1} \\ll (MN)^{\\varepsilon} \\left( M+(MN)^{3\/4} \\right) ,\n\\end{align*}\n  while when $M \\leq N^{(8\\xi-7)\/(4\\xi-1)}$, we have\n\\begin{align*}\n    M'+(M'N)^{3\/4}+{M'}^{1-\\xi}N^{2\\xi-1} &\n     \\ll (MN)^{\\varepsilon} \\left( N^{(8\\xi-7)\/(4\\xi-1)}+N^{(8\\xi-7)(1-\\xi)\/(4\\xi-1)}N^{2\\xi-1} \\right) \\\\\n     & \\ll\n     (MN)^{\\varepsilon}N^{(9\\xi-6)\/(4\\xi-1)}.\n\\end{align*}\n   We then deduce that\n\\begin{align*}\n    \\mathcal{B}_1(M,\n   N)   \\ll_{\\varepsilon}\n   (MN)^{20\\varepsilon} \\left( M+(MN)^{3\/4}+N^{(9\\xi-6)\/(4\\xi-1)} \\right).\n\\end{align*}\n  Lemma \\ref{lem9} now follows.\n\\end{proof}\n\nWe now proceed to prove Theorem \\ref{mainthm}.\n\n\\begin{proof}[Proof of Theorem~\\ref{mainthm}] Note that it follows from \\eqref{initialest} that the estimation given in Lemma \\ref{lem9} is valid with\n    $\\xi=2$.  We further observe that\n\\begin{align*}\n   \\frac{3}{2} <  \\frac {9\\xi-6}{4\\xi-1} < \\xi,\n\\end{align*}\n  for $\\xi > 3\/2$ and in the iterative applications of Lemma~\\ref{lem9} the exponent of $N$ in the bound for $\\mathcal{B}_1(M,N)$ decreases and tends to $3\/2$.  We therefore\narrive at the following bound\n\\begin{align*}\n    \\mathcal{B}_1(M,\n   N)   \\ll_{\\varepsilon}\n   (MN)^{\\varepsilon}\\left( M+N^{3\/2}+(MN)^{3\/4} \\right),\n\\end{align*}\n   for any $\\varepsilon>0$.  Using Lemma \\ref{lem2} we then have\n\\begin{equation*}\n\\begin{split}\n    \\mathcal{B}_1(M,\n   N)  &  \\ll_{\\varepsilon}\n   (MN)^{\\varepsilon}\\min \\left\\{ M+N^{3\/2}+(MN)^{3\/4},\n   N+M^{3\/2}+(MN)^{3\/4} \\right\\} \\\\\n   & \\ll_{\\varepsilon} (MN)^{\\varepsilon} \\left(M+N+(MN)^{3\/4} \\right),\n   \\end{split}\n   \\end{equation*}\n   where the last estimation follows since when $N \\leq M, N^{3\/2}=N^{3\/4}N^{3\/4} \\leq (MN)^{3\/4}$ and similarly when $N \\geq M, M^{3\/2} \\leq (MN)^{3\/4}$.\n   This establishes Theorem \\ref{mainthm}.\n   \\end{proof}\n\n\n\\section{The Quartic large sieve for Dirichlet Characters}\n\\label{sec8}\n\nWe now proceed to prove Theorem~\\ref{quarticlargesieve}.  It is easy to reduce the expression on the left-hand side of\n\\eqref{final} to a sum of similar expressions with the additional\nsummation conditions $(q,2)=1$ and $(m,2)=1$ included. Thus it\nsuffices to estimate\n\\begin{equation} \\label{trans}\n\\begin{split}\n\\sum\\limits_{\\substack{Q<q\\le 2Q\\\\ (q,2)=1}}\\\n\\sideset{}{^\\star}\\sum\\limits_{\\substack{\\chi \\bmod q\\\\ \\chi^4=\\chi_0,\n\\chi^2 \\neq \\chi_0}} \\left| \\ \\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M\\\\\n(m,2)=1}} a_m \\chi(m)\\right|^2 &=\n\\sideset{}{'}\\sum\\limits_{\\substack{n\\in \\ensuremath{\\mathbb Z}[i]\\\\ Q<\\mathcal{N}(n)\\le 2Q\\\\\nn\\equiv 1 \\bmod {(1+i)^3}}} \\left| \\\n\\sideset{}{^*}\\sum\\limits_{\\substack{M< m\\le 2M\\\\ (m,2)=1}} a_m \\chi_n(m)\\right|^2\\\\\n&= \\frac{1}{2}\\sideset{}{'}\\sum\\limits_{\\substack{n\\in \\ensuremath{\\mathbb Z}[i]\\\\\nQ<\\mathcal{N}(n)\\le 2Q\\\\ n\\equiv \\pm 1 \\bmod {(1+i)^3}}} \\left| \\\n\\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M\\\\ (m,2)=1}} a_m\\chi_n(m)\n\\right|^2,\n\\end{split}\n\\end{equation}\nwhere the apostrophe indicates that $n$ is square-free and has no\nrational prime divisor and $\\chi_n(m)=\\left(\\frac{m}{n}\\right)_4$\nis the quartic residue symbol. We shall use this notation for all\n$n\\in \\ensuremath{\\mathbb Z}[i]$ and $m\\in \\ensuremath{\\mathbb Z}$.\n\n\\subsection{Definition of certain norms}\n  In the following, we shall estimate the expression in the last\nline of \\eqref{trans}. We begin by defining a norm corresponding\nto the double sum in the last line of \\eqref{trans} by\n\\begin{equation*}\nB_1(Q,M):=\\sup\\limits_{(a_m)} \\| a_m \\|^{-2}\n\\sideset{}{'}\\sum\\limits_{\\substack{n \\in \\ensuremath{\\mathbb Z}[i]\\\\ Q<\\mathcal{N}(n)\\le 2Q\\\\\nn\\equiv \\pm 1 \\bmod {(1+i)^3}}} \\left| \\\n\\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M\\\\ (m,2)=1}} a_m\n\\chi_m(n)\\right|^2,\n\\end{equation*}\nwhere\n\\begin{equation*}\n\\|a_m \\|^2 = \\sum_{m} |a_m|^2,\n\\end{equation*}\nand where by convention we suppose that $(a_m)$ is not identically\nzero. \\newline\n\nWe further define a norm $B_2(Q,M)$ in the same way as $B_1(Q,M)$\nexcept removing the condition that $n$ has no rational prime\ndivisor. Similarly, we define a norm $B_3(Q,M)$ by further\nremoving the condition that $n$ is square-free. \\newline\n\n  We now use the function $W(x)$ defined in \\eqref{W} to see that\n\\begin{equation*}\n  B_3(Q,M) \\ll \\sup\\limits_{(a_m)} \\| a_m \\|^{-2} \\sum\\limits_{n\\in \\ensuremath{\\mathbb Z}[i]}\nW\\left(\\frac{\\mathcal{N}(n)}{Q}\\right) \\left| \\\n\\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M\\\\ (m,2)=1}} a_m\n\\chi_m(n)\\right|^2.\n\\end{equation*}\nExpanding the sum on the right-hand side, we obtain\n\\begin{equation} \\label{db3bound}\n\\sideset{}{^*}\\sum\\limits_{\\substack{M<m_1\\le 2M\\\\ M<m_2\\le 2M\\\\\n(m_1m_2,2)=1}} a_{m_1}\\overline{a}_{m_2} \\sum\\limits_{n\\in \\ensuremath{\\mathbb Z}[i]}\nW\\left(\\frac{\\mathcal{N}(n)}{Q}\\right)\n\\chi_{m_1}(n)\\overline{\\chi}_{m_2}(n).\n\\end{equation}\n\nAs in  \\cite{DRHB}, it turns out that it suffices to restrict our attention to\nthe case in which $m_1$ and $m_2$ are coprime.  To see this, we sort the terms\nin \\eqref{db3bound} according to $\\delta = (m_1,m_2)$, and\ndetecting the condition $(n,\\delta)=1$ by the M\\\"obius function\nfor $\\ensuremath{\\mathbb Z}[i]$, we obtain that the expression in \\eqref{db3bound}\nequals\n\\begin{equation*}\n\\begin{split}\n\\sideset{}{^*}\\sum_{(\\delta,2)=1} \\sum\\limits_{d|\\delta} \\mu_{[i]}(d)\n\\sum\\limits_{s\\in \\ensuremath{\\mathbb Z}[i]}\nW\\left(\\frac{\\mathcal{N}(s)}{Q\/\\mathcal{N}(d)}\\right) & \\sideset{}{^*}\\sum\\limits_{\\substack{M\/\\delta<r_1\\le\n2M\/\\delta \\\\ M\/\\delta<r_2\\le 2M\/\\delta\\\\ (r_1r_2,2\\delta)=1\\\\\n(r_1,r_2)=1}} a_{r_1}^*\\overline{a_{r_2}^*}\n\\chi_{r_1}(s)\\overline{\\chi_{r_2}}(s) \\\\\n& \\ll  \\sideset{}{^*}\\sum_{(\\delta,2)=1} \\sum\\limits_{d|\\delta}\nB_4\\left(\\frac{Q}{\\mathcal{N}(d)},\\frac{M}{\\delta}\\right)\n\\sideset{}{^*}\\sum\\limits_{\\substack{M\/\\delta<r\\le 2M\/\\delta \\\\\n(r,2\\delta)=1}} |a_{r\\delta}|^2,\n\\end{split}\n\\end{equation*}\nwhere $d$ runs over non-associate divisors of $\\delta$ in\n$\\ensuremath{\\mathbb Z}[i]$,\n\\[  a_r^*:=a_{r\\delta}\\chi_r(d), \\]\nand\n\\begin{equation*}\nB_4(Q,M):=\\sup\\limits_{(a_m)} \\|a_m \\|^{-2}\n\\sideset{}{^*}\\sum\\limits_{\\substack{M<m_1, m_2\\le 2M\\\\ (m_1m_2,2)=1 \\\\\n(m_1,m_2)=1}} a_{m_1}\\overline{a}_{m_2} \\sum\\limits_{n\\in \\ensuremath{\\mathbb Z}[i]}\nW\\left(\\frac{\\mathcal{N}(n)}{Q}\\right)\n\\chi_{m_1}(n)\\overline{\\chi}_{m_2}(n).\n\\end{equation*}\n\nMoreover, we define a norm $C_1(M,Q)$ dual to $B_1(Q,M)$ by\n\\begin{equation*}\nC_1(M,Q):=\\sup\\limits_{(b_{n})} \\| b_n \\|^{-2}\n\\sideset{}{^*}\\sum\\limits_{\\substack{M<m\\le 2M\\\\ (m,2)=1}} \\left|\n\\sideset{}{'}\\sum\\limits_{\\substack{n\\in \\ensuremath{\\mathbb Z}[i]\\\\ Q<\\mathcal{N}(n)\\le 2Q\\\\\nn\\equiv \\pm 1 \\bmod {(1+i)^3}}} b_{n} \\chi_n(m)\\right|^2.\n\\end{equation*}\nBy the duality principle, we have\n\\begin{equation} \\label{B1C1}\nB_1(Q,M)=C_1(M,Q).\n\\end{equation}\nFurthermore, we define a norm $C_2(M,Q)$ by extending the\nsummation over $m$ in the definition of $C_1(M,Q)$ to all integers\n$m$ with $M < m \\leq 2M$. Trivially, we have\n\\begin{equation} \\label{C12}\nC_1(M,Q)\\le C_2(M,Q).\n\\end{equation}\n\n\\subsection{Comparison of the norms} \\label{section:comparison}\n\nFor the proof of our Theorem \\ref{quarticlargesieve}, we need the\nfollowing lemma on the norms defined in the previous section.\n\n\\begin{lemma} \\label{normlemma} Let $Q,M\\ge 1$ and $C$ be a sufficiently large positive constant. Then we have the following inequalities:\n\\begin{equation}\n\\label{C2e1} C_2(M,Q) \\ll (QM)^{\\varepsilon}\\left(M +\nQ^{7\/4}\\right);\n\\end{equation}\n\\begin{equation} \\label{C22}\nC_2(M,Q)\\ll\nM^{\\varepsilon}Q^{1-1\/v}\\sum\\limits_{j=0}^{v-1}C_2(2^jM^v,Q)^{1\/v},\n\\quad \\text{ for each fixed positive integer $v$};\n\\end{equation}\n\\begin{equation} \\label{B11'}\nB_1(Q_1,M)\\ll B_1(Q_2,M), \\quad \\text{ if $Q_1,M\\ge 1$ and $Q_2\\ge\nCQ_1\\log (2Q_1M)$};\n\\end{equation}\n\\begin{equation} \\label{B21}\nB_2(Q,M) \\ll (\\log{2Q})^3 Q^{1\/2}X^{-1\/2} B_1(XQ^{\\varepsilon},M),\n\\quad \\text{for some $X$ with $1\\le X\\le Q$};\n\\end{equation}\n\\begin{equation} \\label{B32}\nB_3(Q,M) \\ll (\\log 2Q)^3 Q^{1\/2}X^{-1\/2} B_2(XQ^{\\varepsilon},M),\n\\quad \\text{for some $X$ with $1\\le X\\le Q$};\n\\end{equation}\n\\begin{equation} \\label{B34}\nB_3(Q,M)\\ll M^{\\varepsilon}\nB_4\\left(\\frac{Q}{\\Delta_1},\\frac{M}{\\Delta_2}\\right), \\quad\n\\text{for some $\\Delta_1,\\Delta_2\\in \\mathbb{N}$ with\n$\\Delta_2^2\\ge \\Delta_1$};\n\\end{equation}\n\\begin{equation} \\label{B43}\nB_4(Q,M)\\ll Q+QM^{\\varepsilon-2} \\max\\left\\{B_3(K,M) : K\\le\nM^4Q^{-1}\\right\\} + Q^{-1}M^{6+\\varepsilon} \\sum\\limits_{K> M^4\/Q}\nK^{-2-\\varepsilon} B_3(K,M),\n\\end{equation}\nwhere the sum over $K$ in \\eqref{B43} runs over powers of $2$.\n\\end{lemma}\n\nSince the proofs of \\eqref{C22}-\\eqref{B43} are essentially the\nsame as those of (31)-(36) of Lemma 4.1 in \\cite{B&Y}, we omit\nthe proofs here. \\newline\n\nWe note that it follows from \\eqref{B1C1}-\\eqref{C22}, that we have\n\\begin{equation} \\label{C2egen}\nB_1(Q,M) \\ll (QM)^{\\varepsilon}\\left(Q^{1-1\/v} M +\nQ^{1+3\/(4v)}\\right)\n\\end{equation}\nfor any $v\\in \\ensuremath{\\mathbb N}$.\n\n\n\\subsection{Estimating $C_2$} \\label{section:C2}\n\n  In this section we prove \\eqref{C2e1}. Recall $C_2(M,Q)$\nis the norm of the sum\n\\begin{equation}\n\\label{eq:C2def} \\sum\\limits_{M<m\\le 2M} \\left|\n\\sideset{}{'}\\sum\\limits_{\\substack{n\\in \\ensuremath{\\mathbb Z}[i]\\\\ Q<\\mathcal{N}(n)\\le 2Q\\\\\nn\\equiv \\pm 1 \\bmod {(1+i)^3}}}\n b_{n} \\chi_n(m)\\right|^2,\n\\end{equation}\nwhere the apostrophe indicates that $n$ is square-free and has no\nrational prime divisor. \\newline\n\nThe sum in \\eqref{eq:C2def} is obviously bounded by\n\\begin{equation}\n\\label{eq:C2defW}\n \\ll \\sum\\limits_{m\\in \\ensuremath{\\mathbb Z}}\nW\\left(\\frac{m}{M}\\right) \\left| \\sideset{}{'}\\sum\\limits_{n} b_{n}\n\\chi_n(m)\\right|^2,\n\\end{equation}\nwhere the weight function $W$ is defined as in \\eqref{W}.\nExpanding out the sum in \\eqref{eq:C2defW} we get\n\\begin{equation*}\n\\sideset{}{'}\\sum \\limits_{\\substack{n_1,n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\nQ<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le 2Q\\\\ n_1,n_2\\equiv \\pm 1 \\bmod {(1+i)^3}}}\nb_{n_1}\\overline{b}_{n_2} \\sum\\limits_{m\\in \\ensuremath{\\mathbb Z}}\nW\\left(\\frac{m}{M}\\right) \\chi_{n_1}\\overline{\\chi}_{n_2}(m).\n\\end{equation*}\nNow we extract the greatest common divisor $\\Delta$ of $n_1$ and\n$n_2$, getting\n\\begin{equation*}\n\\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\Delta) \\leq 2Q \\\\ \\Delta \\equiv 1\n\\bmod{{(1+i)^3}}}}\\ \\sideset{}{'}\\sum \\limits_{\\substack{n_1,n_2\\in\n\\ensuremath{\\mathbb Z}[i]\\\\ \\frac{Q}{\\mathcal{N}(\\Delta)}<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le\n\\frac{2Q}{\\mathcal{N}(\\Delta)} \\\\ n_1,n_2\\equiv 1 \\bmod {(1+i)^3} \\\\\n(n_1,n_2)=1 \\\\ (n_1 n_2, \\Delta \\overline{\\Delta}) = 1 }} b_{n_1\n\\Delta}\\overline{b}_{n_2 \\Delta} \\sum\\limits_{\\substack{m\\in \\ensuremath{\\mathbb Z}\n\\\\ (m, \\mathcal{N}(\\Delta)) = 1}} W\\left(\\frac{m}{M}\\right)\n\\chi_{n_1}\\overline{\\chi}_{n_2}(m).\n\\end{equation*}\nIt is easy to see that there is a one-to-one correspondence between the pairs $(n_1,n_2)$ and $(n'_1\\Delta,n'_2 \\Delta)$ with $\\Delta \\equiv 1$, $n_1 \\equiv n'_1$ and $n_2 \\equiv n'_2 \\bmod{(1+i)^3}$.  We write $\\delta = (n_1, \\bar{n}_2)$ and change variables\nvia $n_1 \\rightarrow \\delta n_1$, $n_2 \\rightarrow\n\\overline{\\delta} n_2$ to get\n\\begin{equation} \\label{eq:prePoisson}\n\\begin{split}\n\\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\Delta) \\leq 2Q \\\\\n\\Delta \\equiv 1 \\bmod{{(1+i)^3}}}}\\\n\\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\delta)\n\\leq \\frac{2Q}{\\mathcal{N}(\\Delta)} \\\\ \\delta \\equiv 1 \\bmod{{(1+i)^3}} \\\\\n(\\mathcal{N}(\\delta), \\mathcal{N}(\\Delta)) = 1}} & \\\n\\sideset{}{'}\\sum\\limits_{\\substack{n_1,n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(\\delta \\Delta)}<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le \\frac{2Q}{\\mathcal{N}(\\delta\n\\Delta)} \\\\ n_1,n_2\\equiv \\pm 1 \\bmod {(1+i)^3} \\\\ (\\mathcal{N}(n_1),\n\\mathcal{N}(n_2)) = 1 \\\\ (n_1 n_2, \\delta \\overline{\\delta} \\Delta\n\\overline{\\Delta}) = 1 } } b_{n_1 \\Delta \\delta}\\overline{b}_{n_2\n\\Delta \\overline{\\delta}}\n\\\\\n& \\times \\sum\\limits_{\\substack{m\\in \\ensuremath{\\mathbb Z} \\\\ (m, \\mathcal{N}(\\Delta)) = 1}}\nW\\left(\\frac{m}{M}\\right)\n\\chi_{n_1}\\overline{\\chi}_{n_2}\\overline{\\chi}_{\\delta}^2(m),\n\\end{split}\n\\end{equation}\nwhere we use that for $m \\in \\ensuremath{\\mathbb Z}$,\n$\\chi_{\\delta}\\overline{\\chi}_{\\overline{\\delta}}(m)=\\chi_{\\delta}^2(m)=\n\\overline{\\chi}_{\\delta}^2(m)$. Next we remove the coprimality\ncondition in the sum over $m$ by the M\\\"obius function, getting\n\\begin{equation*}\n\\sum\\limits_{\\substack{m\\in \\ensuremath{\\mathbb Z} \\\\ (m, \\mathcal{N}(\\Delta)) = 1}}\nW\\left(\\frac{m}{M}\\right)\n\\chi_{n_1}\\overline{\\chi}_{n_2}\\overline{\\chi}_{\\delta}^2(m) =\n\\sum_{\\ell | \\mathcal{N}(\\Delta)} \\mu(\\ell)\n\\chi_{n_1}\\overline{\\chi}_{n_2}\\overline{\\chi}_{\\delta}^2(\\ell)\n\\sum\\limits_{\\substack{m\\in \\ensuremath{\\mathbb Z} }} W\\left(\\frac{m}{M\/\\ell}\\right)\n\\chi_{n_1}\\overline{\\chi}_{n_2}\\overline{\\chi}_{\\delta}^2(m),\n\\end{equation*}\nwhich by the Poisson summation formula is\n\\begin{equation} \\label{afterpoisson}\n\\begin{split}\n\\sum_{\\ell | \\mathcal{N}(\\Delta)} \\mu(\\ell)\n\\chi_{n_1}\\overline{\\chi}_{n_2}\\overline{\\chi}_{\\delta}^2(\\ell)\n& \\frac{M}{\\ell \\mathcal{N}(n_1 n_2 \\delta)} \\sum\\limits_{\\substack{h\\in \\ensuremath{\\mathbb Z}}}\n\\widehat{W}\\left(\\frac{hM}{\\ell \\mathcal{N}(n_1 n_2 \\delta)}\\right)\n\\\\\n& \\times \\sum_{r \\bmod{\\mathcal{N}(n_1 n_2 \\delta)}}\n\\chi_{n_1}\\overline{\\chi}_{n_2}\\overline{\\chi}_{\\delta}^2(r)\ne\\left(\\frac{rh}{\\mathcal{N}(n_1 n_2 \\delta)}\\right),\n\\end{split}\n\\end{equation}\n  where\n\\begin{align*}\n  \\widehat{W}(x)=\\int\\limits^{\\infty}_{-\\infty}W(y)e(-xy)dy.\n\\end{align*}\n\nWhen $h=0$, the expression in \\eqref{afterpoisson} vanishes unless\n$n_1 = n_2 = \\delta =1$. Hence, the contribution of $h=0$ to\n\\eqref{eq:prePoisson} is\n\\begin{equation} \\label{h0cont}\n\\ll MQ^{\\varepsilon} \\sideset{}{'}\\sum_{\\substack{Q<\\mathcal{N}(\\Delta) \\leq 2Q \\\\\n\\Delta \\equiv 1 \\bmod{{(1+i)^3}}}} |b_{\\Delta}|^2 \\ll M\nQ^{\\varepsilon}\\| b_n \\|^2.\n\\end{equation}\n\nIn the sequel, we assume that $h\\not=0$. The sum over $r$ in\n\\eqref{afterpoisson} can be computed by writing $r = r_1 \\mathcal{N}(n_2\n\\delta) + r_2 \\mathcal{N}(n_1 \\delta) + r_3 \\mathcal{N}(n_1 n_2)$ to get\n\\begin{equation} \\label{gauss}\n\\begin{split}\n&\\sum_{r \\bmod{\\mathcal{N}(n_1n_2\\delta)}}  \\chi_{n_1}\\overline{\\chi}_{n_2}\\overline{\\chi}_{\\delta}^2(r) e\\left(\\frac{rh}{\\mathcal{N}(n_1 n_2 \\delta)}\\right)\\\\\n& = \\sum_{r_1 \\bmod{\\mathcal{N}(n_1)}} \\chi_{n_1}(r_1\\mathcal{N}(n_2\\delta))\ne\\left(\\frac{r_1h}{\\mathcal{N}(n_1)}\\right) \\sum_{r_2 \\bmod{\\mathcal{N}(n_2)}}\n\\overline{\\chi}_{n_2}(r_2\\mathcal{N}(n_1\\delta))\ne\\left(\\frac{r_2h}{\\mathcal{N}(n_2)}\\right) \\\\\n&  \\hspace*{3cm} \\times \\sum_{r_3\n\\bmod{\\mathcal{N}(\\delta)}}  \\overline{\\chi}_{\\delta}^2(r_3\\mathcal{N}(n_1n_2))\ne\\left(\\frac{r_3h}{\\mathcal{N}(\\delta)}\\right) \\\\\n&= \\overline{\\chi}_{n_1}(h) \\chi_{n_2}\\chi^2_{\\delta}(-h)\n\\chi_{n_1}(\\mathcal{N}(n_2 \\delta)) \\overline{\\chi}_{n_2}(\\mathcal{N}(n_1 \\delta))\n\\overline{\\chi}_{\\delta}^2(\\mathcal{N}(n_1n_2)) \\tau(\\chi_{n_1})\n\\overline{\\tau(\\chi_{n_2})\\tau(\\chi^2_{\\delta})},\n\\end{split}\n\\end{equation}\n   where $\\tau (\\chi)$ is defined as in \\eqref{tau}. \\newline\n\nUsing quartic reciprocity and the identity\n\\begin{equation*}\n\\left(\\frac{m}{n}\\right)_4 =\n\\overline{\\left(\\frac{\\overline{m}}{\\overline{n}}\\right)}_4\n\\end{equation*}\nfollowing from the definition of the quartic residue symbol, we\nget the identities\n\\begin{align*}\n\\chi_{n}(\\mathcal{N}(m))\\overline{\\chi}_{m}(\\mathcal{N}(n))&=\\left(\\frac{\\mathcal{N}(m)}{n}\\right)_4\n\\overline{\\left(\\frac{\\mathcal{N}(n)}{m}\\right)}_4 =\n\\left(\\frac{m}{\\overline{n}}\\right)^2_4 = \\chi^2_{\\overline{n}}(m)\n\\\\\n\\chi_{n}(\\mathcal{N}(m))\\overline{\\chi}_{m}^2(\\mathcal{N}(n))&=\\left(\\frac{\\mathcal{N}(m)}{n}\\right)_4\n\\left(\\frac{\\mathcal{N}(n)}{m}\\right)^2_4 =\n\\left(\\frac{\\mathcal{N}(m)}{\\overline{n}}\\right)_4 =\n\\chi_{\\overline{n}}(\\mathcal{N}(m))\n\\end{align*}\nand\n\\begin{equation*}\n\\overline{\\chi}_{n}(\\mathcal{N}(m))\\overline{\\chi}_{m}^2(\\mathcal{N}(n))=\n\\overline{\\left(\\frac{\\mathcal{N}(m)}{n}\\right)}_4\n\\overline{\\left(\\frac{\\mathcal{N}(n)}{m}\\right)}^2_4 =\n\\left(\\frac{\\mathcal{N}(m)}{n}\\right)_4 = \\chi_{n}(\\mathcal{N}(m)),\n\\end{equation*}\nvalid for all $m,n\\in \\ensuremath{\\mathbb Z}[i]$ with $m, n \\equiv \\pm 1\n\\bmod{{(1+i)^3}}$. We use them to simplify the last line of\n\\eqref{gauss}, obtaining\n\\begin{equation*}\n  \\overline{\\chi}_{n_1}(h)\n\\chi_{n_2}\\chi^2_{\\delta}(-h)  \\left(\\frac{n^2_2\n\\mathcal{N}(\\delta)}{\\overline{n_1}}\\right)_4\n\\left(\\frac{\\mathcal{N}(\\delta)}{n_2}\\right)_4 \\tau(\\chi_{n_1})\n\\overline{\\tau(\\chi_{n_2})\\tau(\\chi^2_{\\delta})}.\n\\end{equation*}\n\nNow, changing $n_2\\rightarrow \\overline{n}_2$, the contribution of\n$h\\not=0$ to the sum in \\eqref{afterpoisson} takes the form\n\\begin{multline}\nS_W(M,Q)=M \\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\Delta) \\leq 2Q \\\\ \\Delta \\equiv 1 \\bmod{{(1+i)^3}}}}\\ \\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\delta) \\leq\n\\frac{2Q}{\\mathcal{N}(\\Delta)} \\\\ \\delta \\equiv 1 \\bmod{{(1+i)^3}} \\\\\n(\\mathcal{N}(\\delta), \\mathcal{N}(\\Delta)) =\n1}}\\frac{\\overline{\\tau(\\chi_{\\delta})}}{\\mathcal{N}(\\delta)} \\sum_{\\ell |\n\\mathcal{N}(\\Delta)} \\frac{\\mu(\\ell)}{\\ell} \\overline{\\chi}_{\\delta}^2(\\ell)\n\\sum_{h\\not=0}  \\chi^2_{\\delta}(h)\n\\\\\n\\times \\sideset{}{'}\\sum\\limits_{\\substack{n_1,n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(\\delta \\Delta)}<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le \\frac{2Q}{\\mathcal{N}(\\delta\n\\Delta)} \\\\ n_1,n_2\\equiv \\pm 1 \\bmod {(1+i)^3} \\\\ (\\mathcal{N}(n_1),\n\\mathcal{N}(n_2)) = 1 \\\\ (n_1 n_2, \\delta \\overline{\\delta} \\Delta\n\\overline{\\Delta}) = 1 } } \\widehat{W}\\left(\\frac{hM}{\\ell \\mathcal{N}(n_1 n_2\n\\delta)}\\right) c_{\\Delta,\\delta,\\ell,h,n_1}\nc_{\\Delta,\\delta,\\ell,h,n_2}'\n\\left(\\frac{n_1}{n_2}\\right)^2_4,\\nonumber\n\\end{multline}\nwhere\n\\[\nc_{\\Delta,\\delta,\\ell,h,n}:=\\chi_{n}(\\ell)\\overline{\\chi}_n(h)\n\\left(\\frac{\\mathcal{N}(\\delta)}{\\overline{n}}\\right)_4\\frac{\\tau(\\chi_n)}{\\mathcal{N}(n)}\nb_{n\\Delta\\delta} \\; \\; \\; \\mbox{and} \\; \\; \\;\nc_{\\Delta,\\delta,\\ell,h,n}':= \\chi_{n}(\\ell)\\overline{\\chi}_n(h)\n\\left(\\frac{\\mathcal{N}(\\delta)}{\\overline{n}}\\right)_4\\frac{\\tau(\\chi_n)}{\\mathcal{N}(n)}\n\\overline{b}_{\\overline{n}\\Delta\\overline{\\delta}}.\n\\]\n We now estimate the sum over $n_1$ and $n_2$ directly using\n\\eqref{eq:quartic}. We denote the inner sum in the definition of\n$S_W(M,Q)$ above to be $U(\\Delta, \\delta, \\ell, h)$ so that\n\\begin{align*}\n  U(\\Delta, \\delta, \\ell,\nh)= \\sideset{}{'}\\sum\\limits_{\\substack{n_1,n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(\\delta \\Delta)}<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le \\frac{2Q}{\\mathcal{N}(\\delta\n\\Delta)} \\\\ n_1,n_2\\equiv \\pm 1 \\bmod {(1+i)^3} \\\\ (\\mathcal{N}(n_1),\n\\mathcal{N}(n_2)) = 1 \\\\ (n_1 n_2, \\delta \\overline{\\delta} \\Delta\n\\overline{\\Delta}) = 1 } } \\widehat{W}\\left(\\frac{hM}{\\ell \\mathcal{N}(n_1 n_2\n\\delta)}\\right) c_{\\Delta,\\delta,\\ell,h,n_1}\nc_{\\Delta,\\delta,\\ell,h,n_2}' \\left(\\frac{n_1}{n_2}\\right)^2_4.\n\\end{align*}\n  To separate the variables $n_1,n_2$, we remove the coprimality\ncondition $(\\mathcal{N}(n_1),\\mathcal{N}(n_2))=1$. Because of the\npresence of $(\\frac{n_1}{n_2})_4$, we may assume that $n_1$ and\n$n_2$ are coprime.  Thus $\\mathcal{N}(n_1)$ and $\\mathcal{N}(n_2)$\nmust also be coprime unless $n_1$ has a factor in common with\n$\\overline{n}_2$. We proceed to detect this latter condition using\nthe Mobius function in the standard way to obtain\n\n\\begin{align*}\n  U(\\Delta, \\delta, \\ell,\nh)&= \\sideset{}{'}\\sum_{\\substack{e \\in \\ensuremath{\\mathbb Z}[i] \\\\ e \\equiv 1 \\bmod {(1+i)^3} \\\\ (\\mathcal{N}(e), \\mathcal{N}(\\delta\\Delta))=1 }} \\mu_{[i]}(e) \\sideset{}{'}\\sum\\limits_{\\substack{n_1,n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(\\delta\n\\Delta)}<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le\n\\frac{2Q}{\\mathcal{N}(\\delta \\Delta)} \\\\ n_1,n_2\\equiv \\pm 1 \\bmod\n{(1+i)^3} \\\\ e|n_1, \\overline{e}| n_2 \\\\ (n_1 n_2, \\delta\n\\overline{\\delta} \\Delta \\overline{\\Delta}) = 1 } }\n\\widehat{W}\\left(\\frac{hM}{\\ell \\mathcal{N}(n_1 n_2\n\\delta)}\\right) c_{\\Delta,\\delta,\\ell,h,n_1}\nc_{\\Delta,\\delta,\\ell,h,n_2}' \\left(\\frac{n_1}{n_2}\\right)^2_4 \\\\\n&= \\sideset{}{'}\\sum_{\\substack{e \\in \\ensuremath{\\mathbb Z}[i] \\\\ e \\equiv 1 \\bmod {(1+i)^3}\n\\\\ \\mathcal{N}(e) \\leq \\frac{2Q}{\\mathcal{N}(\\delta \\Delta)} \\\\\n(\\mathcal{N}(e), \\mathcal{N}(\\delta\\Delta))=1  }}\n\\mu_{[i]}(e)\\chi_{\\mathcal{N}(e)}(\\ell)\\overline{\\chi}_{\\mathcal{N}(e)}(h)\\left(\\frac{\\mathcal{N}(\\delta)}{\\mathcal{N}(e)}\\right)_4\\frac{\\tau(\\chi_e)}{\\mathcal{N}(e)}\n\\frac{\\tau(\\chi_{\\overline{e}})}{\\mathcal{N}(\\overline{e})}\\left(\\frac{e}{\\overline{e}}\\right)^2_4 \\\\\n& \\hspace*{2cm} \\times \\sideset{}{'}\\sum\\limits_{\\substack{n_1,n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(e\\delta \\Delta)}<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le \\frac{2Q}{\\mathcal{N}(e\\delta\n\\Delta)} \\\\ n_1,n_2\\equiv \\pm 1 \\bmod {(1+i)^3} \\\\  (n_1 n_2,\ne \\overline{e}\\delta \\overline{\\delta} \\Delta \\overline{\\Delta}) =\n1 } } \\widehat{W}\\left(\\frac{hM}{\\ell \\mathcal{N}(n_1 n_2 e\n\\overline{e}\\delta)}\\right) c_{\\Delta,\\delta,\\ell,h,e,n_1}\nc'_{\\Delta,\\delta,\\ell,h,e, n_2} \\left(\\frac{n_1}{n_2}\\right)^2_4 .\n\\end{align*}\n   where\n\\[ c_{\\Delta,\\delta,\\ell,h,e,n} :=\\chi_{n}(\\ell)\\overline{\\chi}_n(h)\n\\left(\\frac{\\mathcal{N}(\\delta)}{\\overline{n}}\\right)_4\\left(\\frac{\\mathcal{N}(e)}{n}\\right)_4\\left(\\frac{\\mathcal{N}(n)}{e}\\right)_4\n\\left(\\frac{n_1}{\\overline{e}}\\right)^2_4\\frac{\\tau(\\chi_n)}{\\mathcal{N}(n)}\nb_{ne\\Delta\\delta} \\]\nand\n\\[ c'_{\\Delta,\\delta,\\ell,h,e,n} :=\\chi_{n}(\\ell)\\overline{\\chi}_n(h)\n\\left(\\frac{\\mathcal{N}(\\delta)}{\\overline{n}}\\right)_4\\left(\\frac{\\mathcal{N}(e)}{n}\\right)_4\\left(\\frac{\\mathcal{N}(n)}{\\overline{e}}\\right)_4\\left(\\frac{e}{n_2}\\right)^2_4\\frac{\\tau(\\chi_n)}{\\mathcal{N}(n)}\n\\overline{b}_{\\overline{n}e\\Delta\\overline{\\delta}}. \\]\n Next observe that we may freely truncate the sum over $h$ for\n\\begin{equation*}\n|h| \\le \\frac{Q^2 \\ell}{\\mathcal{N}(\\delta)\\mathcal{N}(\\Delta)^2M} (QM)^{\\varepsilon}=:H\n\\end{equation*}\nsince $\\widehat{W}$ has rapid decay. More precisely, if we let $S_W\n(M,Q) = S'_W(M,Q) + E$ where $S'_W(M,Q)$ is the contribution to\n$S_W(M,Q)$ from $0 < |h| \\leq H$, then $E \\ll\n(MQ)^{-100} \\| b \\|^2$. \\newline\n\n  It remains to bound $S'_W(M,Q)$ and we have\n\\begin{equation*}\n\\begin{split}\nS'_W(M,Q) \\ll M \\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\Delta) \\leq 2Q \\\\ \\Delta\n\\equiv 1 \\bmod{{(1+i)^3}}}}\\\n\\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\delta) \\leq\n\\frac{2Q}{\\mathcal{N}(\\Delta)} \\\\ \\delta \\equiv 1 \\bmod{{(1+i)^3}} \\\\\n(\\mathcal{N}(\\delta), \\mathcal{N}(\\Delta)) = 1}} & \\frac{1}{(\\mathcal{N}(\\delta))^{1\/2}} \\sum_{\\ell |\n\\mathcal{N}(\\Delta)} \\frac{1}{\\ell} \\\\\n& \\times \\sideset{}{'}\\sum_{\\substack{e \\in \\ensuremath{\\mathbb Z}[i] \\\\ e\n\\equiv 1 \\bmod {(1+i)^3}  \\\\ \\mathcal{N}(e) \\leq \\frac{2Q}{\\mathcal{N}(\\delta\n\\Delta)}\\\\ (\\mathcal{N}(e), \\mathcal{N}(\\delta\\Delta))=1  }}\\frac {1}{\\mathcal{N}(e)} \\sum_{0<\n|h| \\leq H} \\left| U'(\\Delta, \\delta, \\ell, e, h) \\right|,\n\\end{split}\n\\end{equation*}\n  where\n\\begin{align*}\n  U'(\\Delta, \\delta, \\ell, e,\nh)=  \\sideset{}{'}\\sum\\limits_{\\substack{n_1,n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(e\\delta \\Delta)}<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le \\frac{2Q}{\\mathcal{N}(e\\delta\n\\Delta)} \\\\ n_1,n_2\\equiv \\pm 1 \\bmod {(1+i)^3} \\\\  (n_1 n_2,\ne \\overline{e}\\delta \\overline{\\delta} \\Delta \\overline{\\Delta}) =\n1 } } \\widehat{W}\\left(\\frac{hM}{\\ell \\mathcal{N}(n_1 n_2 e\n\\overline{e}\\delta)}\\right) c_{\\Delta,\\delta,\\ell,h,e,n_1}\nc'_{\\Delta,\\delta,\\ell,h,e, n_2} \\left(\\frac{n_1}{n_2}\\right)^2_4 .\n\\end{align*}\n    We  now remove the weight $\\widehat{W}$ in $U'(\\Delta, \\delta, \\ell, e,\nh)$ by applying Lemma \\ref{lem8} to the function $\\rho(x) =\n\\widehat{W}(x)$, which satisfies the conditions of that lemma, as one sees by repeated integration by parts.  We may assume $h>0$ here, since the contribution of the negative $h$'s can be treated similarly and satisfies the same bound.  We use $\\sigma = \\varepsilon$\nto see that\n\\begin{align*}\n    U'(\\Delta, \\delta, \\ell, e,\nh) & \\ll_{\\varepsilon}\n\\left(\\frac{\\ell \\mathcal{N}(e\\overline{e}\\Delta)}{hM}\\right)^{\\varepsilon}\\int\\limits^{\\infty}_{-\\infty}|\\rho_{+}(\\varepsilon+it)||V(\\varepsilon+it)|\n\\mathrm{d} t,\n\\end{align*}\n  where\n\\begin{align*}\n   V(s)= \\sideset{}{'}\\sum\\limits_{\\substack{n_1,n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(e\\delta \\Delta)}<\\mathcal{N}(n_1),\\mathcal{N}(n_2)\\le \\frac{2Q}{\\mathcal{N}(e\\delta\n\\Delta)} \\\\ n_1,n_2\\equiv \\pm 1 \\bmod {(1+i)^3} \\\\  (n_1 n_2,\ne \\overline{e}\\delta \\overline{\\delta} \\Delta \\overline{\\Delta}) =\n1 } } d_{n_1}d'_{n_2}\\left(\\frac{n_1}{n_2}\\right)^2_4,\n\\end{align*}\n   with\n\\begin{equation*}\n    d_n=c_{\\Delta,\\delta,\\ell,h,e,n}\\mathcal{N}(n)^{s} \\; \\; \\;  \\mbox{and} \\; \\; \\; d'_n=c'_{\\Delta,\\delta,\\ell,h,e,n}\\mathcal{N}(n)^{s} .\n\\end{equation*}\n   Note that $d_{n_1}$ and $d_{n_2}'$ depend on\n$\\Delta,\\delta, \\ell, h, e, n$ and $s$, and\n\\begin{equation*}\n|d_n| \\ll \\left(\\frac{\\mathcal{N}(e\\delta\\Delta)}{Q}\\right)^{1\/2-\\varepsilon}\n\\left| b_{ne\\Delta\\delta} \\right|, \\quad |d_n'| \\ll\n\\left(\\frac{\\mathcal{N}(e\\delta\\Delta)}{Q}\\right)^{1\/2-\\varepsilon}\n\\left| b_{\\overline{n}e\\Delta\\overline{\\delta}} \\right|.\n\\end{equation*}\n Now, using the Cauchy-Schwarz inequality and the estimate\n\\eqref{eq:quartic} upon noting that this estimate remains valid if\nthe summation conditions $m,n\\equiv 1 \\bmod {(1+i)^3}$ therein are\nreplaced by $m,n \\equiv \\pm 1 \\bmod {(1+i)^3}$ and\n$\\left(\\frac{n}{m}\\right)_4$ replaced by\n$\\left(\\frac{n_1}{n_2}\\right)^2_4$, we bound $V(\\varepsilon+it)$ by\n\\begin{equation} \\label{square}\n\\begin{split}\n& \\left| V(\\varepsilon+it) \\right|^2 \\\\\n&\\ll \\sideset{}{'}\\sum\\limits_{\\substack{n_1\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(e\\delta \\Delta)}<\\mathcal{N}(n_1)\\le \\frac{2Q}{\\mathcal{N}(e\\delta \\Delta)}\n\\\\ n_1 \\equiv \\pm 1 \\bmod {(1+i)^3} \\\\  (n_1, e\n\\overline{e}\\delta \\overline{\\delta} \\Delta \\overline{\\Delta}) = 1\n} } |d_{n_1}|^2 \\;\\;\\;\\; \\times\n\\sideset{}{'}\\sum\\limits_{\\substack{n_1\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(e\\delta \\Delta)}<\\mathcal{N}(n_1)\\le \\frac{2Q}{\\mathcal{N}(e\\delta \\Delta)}\n\\\\ n_1 \\equiv \\pm 1 \\bmod {(1+i)^3} \\\\  (n_1, e\n\\overline{e}\\delta \\overline{\\delta} \\Delta \\overline{\\Delta}) = 1\n} } \\left|\\sideset{}{'}\\sum\\limits_{\\substack{n_2\\in \\ensuremath{\\mathbb Z}[i]\\\\\n\\frac{Q}{\\mathcal{N}(e\\delta \\Delta)}<\\mathcal{N}(n_2)\\le \\frac{2Q}{\\mathcal{N}(e\\delta \\Delta)}\n\\\\ n_2 \\equiv \\pm 1 \\bmod {(1+i)^3} \\\\  (n_2, e\n\\overline{e}\\delta \\overline{\\delta} \\Delta \\overline{\\Delta}) = 1\n} } d_{n_2}'\n\\left(\\frac{n_1}{n_2}\\right)^2_4 \\right|^2 \\\\\n&\\ll (QM)^{8\\varepsilon}\\left(\\frac{\\mathcal{N}(e\\delta\n\\Delta)}{Q}\\right)^{1\/4 -4\\varepsilon} \\left( \\sideset{}{'}\\sum_{\\substack{Q\/\\mathcal{N}(e)< \\mathcal{N}(n)\\leq 2Q\/\\mathcal{N}(e)\\\\\nn \\equiv \\pm 1 \\bmod {(1+i)^3}\\\\ (\\mathcal{N}(n), \\mathcal{N}(e))=1 }} |b_{en}|^2 \\right)^2.\n\\end{split}\n\\end{equation}\n   Since\n\\begin{align*}\n     \\int\\limits^{\\infty}_{-\\infty}|\\rho_{+}(\\sigma+it)| \\mathrm{d} t \\ll_{\\varepsilon} 1,\n\\end{align*}\n    we deduce that\n\\begin{equation} \\label{cont}\n\\begin{split}\nS'_W(M,Q) & \\ll  M(QM)^{7\\varepsilon}\n\\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\Delta) \\leq 2Q \\\\ \\Delta \\equiv 1\n\\bmod{{(1+i)^3}}}}\\ \\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\delta) \\leq\n\\frac{2Q}{\\mathcal{N}(\\Delta)} \\\\ \\delta \\equiv 1 \\bmod{{(1+i)^3}} \\\\\n(\\mathcal{N}(\\delta), \\mathcal{N}(\\Delta)) = 1}}\\frac{1}{(\\mathcal{N}(\\delta))^{1\/2}} \\sum_{\\ell |\n\\mathcal{N}(\\Delta)} \\frac{1}{\\ell} \\sideset{}{'}\\sum_{\\substack{e \\in \\ensuremath{\\mathbb Z}[i] \\\\ e\n\\equiv 1 \\bmod {(1+i)^3}  \\\\ \\mathcal{N}(e) \\leq \\frac{2Q}{\\mathcal{N}(\\delta\n\\Delta)}\\\\ (\\mathcal{N}(e), \\mathcal{N}(\\delta\\Delta))=1  }}\\frac {1}{\\mathcal{N}(e)}\n\\\\\n& \\hspace*{2cm} \\times \\sum_{0< |h| \\leq H} \\left(\\frac{\\mathcal{N}(e\\delta\n\\Delta)}{Q}\\right)^{\\frac14 -2\\varepsilon}\\sideset{}{'}\\sum_{\\substack{Q\/\\mathcal{N}(e)< \\mathcal{N}(n)\\leq 2Q\/\\mathcal{N}(e)\\\\\nn \\equiv \\pm 1 \\bmod {(1+i)^3}\\\\ (\\mathcal{N}(n), \\mathcal{N}(e))=1 }} |b_{en}|^2 \\\\\n& \\ll Q^{7\/4+2\\varepsilon}(QM)^{8\\varepsilon}\n\\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\Delta) \\leq 2Q \\\\ \\Delta \\equiv 1\n\\bmod{{(1+i)^3}}}}\\frac {1}{\\mathcal{N}(\\Delta)^{7\/4+2\\varepsilon}}\n\\sideset{}{'}\\sum_{\\substack{\\mathcal{N}(\\delta) \\leq\n\\frac{2Q}{\\mathcal{N}(\\Delta)} \\\\ \\delta \\equiv 1 \\bmod{{(1+i)^3}} \\\\\n(\\mathcal{N}(\\delta), \\mathcal{N}(\\Delta)) = 1}}\\frac{1}{(\\mathcal{N}(\\delta))^{5\/4+2\\varepsilon}}\n\\sum_{\\ell | \\mathcal{N}(\\Delta)}1 \\\\\n& \\hspace*{2cm} \\times \\sideset{}{'}\\sum_{\\substack{e \\in \\ensuremath{\\mathbb Z}[i]\n\\\\ e \\equiv 1 \\bmod {(1+i)^3}  \\\\ \\mathcal{N}(e) \\leq \\frac{2Q}{\\mathcal{N}(\\delta\n\\Delta)}\\\\ (\\mathcal{N}(e), \\mathcal{N}(\\delta\\Delta))=1  }}\\frac\n{1}{\\mathcal{N}(e)^{3\/4+2\\varepsilon}}\n\\sideset{}{'}\\sum_{\\substack{Q\/\\mathcal{N}(e)< \\mathcal{N}(n)\\leq 2Q\/\\mathcal{N}(e)\\\\\nn \\equiv \\pm 1 \\bmod {(1+i)^3}\\\\ (\\mathcal{N}(n), \\mathcal{N}(e))=1 }} |b_{en}|^2 \\\\\n& \\ll Q^{7\/4+2\\varepsilon}(QM)^{8\\varepsilon}\\sideset{}{'}\\sum_{\\substack{Q< \\mathcal{N}(n)\\leq 2Q\\\\\nn \\equiv \\pm 1 \\bmod {(1+i)^3}}} |b_{n}|^2\n\\sideset{}{'}\\sum_{\\substack{e \\in \\ensuremath{\\mathbb Z}[i]\n\\\\ e \\equiv 1 \\bmod {(1+i)^3}  \\\\  e|n  }}\\frac\n{1}{\\mathcal{N}(e)^{3\/4+2\\varepsilon}} \\\\\n& \\ll Q^{7\/4+2\\varepsilon}(QM)^{9\\varepsilon}\\sideset{}{'}\\sum_{\\substack{Q< \\mathcal{N}(n)\\leq 2Q\\\\\nn \\equiv \\pm 1 \\bmod {(1+i)^3}}} |b_{n}|^2 .\n\\end{split}\n\\end{equation}\n\n  Combining \\eqref{h0cont} and \\eqref{cont}, we deduce that\n\\eqref{eq:prePoisson} and hence \\eqref{eq:C2def} is bounded by\n\\begin{equation*}\n\\ll (QM)^{\\varepsilon} \\left(M+Q^{7\/4}\\right) \\| b_{n} \\|^2\n\\end{equation*}\nwhich implies the desired bound \\eqref{C2e1}.\n\n\\section{Completion of the proof of Theorem \\ref{quarticlargesieve}}\nWe start with \\eqref{C2egen} with any $v\\ge 2$ (as one checks\neasily that $v=1$ does not lead to any improvement) as an initial\nestimate. From \\eqref{B21} and \\eqref{C2egen}, it follows that\n\\begin{equation*}\nB_2(Q,M) \\ll (QM)^{\\varepsilon} Q^{1\/2}X^{-1\/2}\n(X^{1+3\/(4v)}+X^{1-1\/v}M)\n\\end{equation*}\n   for a suitable $X$ with $1\\ll X\\ll Q$. The worst case is $X = Q$ which shows $B_2(Q,M)$ also satisfies\n   \\eqref{C2egen}. Repeating the argument, we have\n\\begin{equation*}\nB_3(Q,M)\\ll\n(QM)^{\\varepsilon}\\left(Q^{1+3\/(4v)}+Q^{1-1\/v}M\\right).\n\\end{equation*}\nCombining this with \\eqref{B43}, we obtain\n\\begin{eqnarray*}\nB_4(Q,M)&\\ll& Q+(QM)^{9\\varepsilon}QM^{-2} \\max\\left\\{K^{1+3\/(4v)}+K^{1-1\/v}M \\ :\\ K\\le M^4Q^{-1}\\right\\}\n\\\\ & & \\hspace*{1cm}+ (QM)^{9\\varepsilon}M^{6}Q^{-1} \\sum\\limits_{K\\ge M^4\/Q} K^{-2-\\varepsilon}(K^{1+3\/(4v)}+K^{1-1\/v}M)\\nonumber\\\\\n&\\ll&\nQ+(QM)^{10\\varepsilon}(Q^{-3\/(4v)}M^{2+3\/v}+Q^{1\/v}M^{3-4\/v}),\n\\end{eqnarray*}\nwhere the sum over $K$ runs over powers of $2$. From this and\n\\eqref{B34}, we deduce that\n\\begin{equation*}\nB_3(Q,M)\\ll \\frac{Q}{\\Delta_1}+(QM)^{\\varepsilon}\\left(\n\\left(\\frac{Q}{\\Delta_1}\\right)^{-3\/(4v)}\n\\left(\\frac{M}{\\Delta_2}\\right)^{2+3\/v}+\n\\left(\\frac{Q}{\\Delta_1}\\right)^{1\/v}\n\\left(\\frac{M}{\\Delta_2}\\right)^{3-4\/v}\\right)\n\\end{equation*}\nfor some positive integers $\\Delta_1$, $\\Delta_2$ with\n$\\Delta_2^2\\ge \\Delta_1$. From this and the trivial bound\n\\begin{equation*}\nB_1(Q,M)\\ll B_3(Q,M),\n\\end{equation*}\n we deduce that\n\\begin{equation}\n\\label{tem1} B_1(Q,M)\\ll\nQ+(QM)^{\\varepsilon}\\left(Q^{-3\/(4v)}M^{2+3\/v}+Q^{1\/v}M^{3-4\/v}\\right).\n\\end{equation}\nCombining \\eqref{tem1} with \\eqref{B11'}, we deduce that\n\\begin{equation} \\label{Re1}\nB_1(Q,M)\\ll\n(\\tilde{Q}M)^{\\varepsilon}\\left(\\tilde{Q}+\\tilde{Q}^{-3\/(4v)}M^{2+3\/v}+\\tilde{Q}^{1\/v}M^{3-4\/v}\\right)\n\\end{equation}\nif $\\tilde{Q}\\ge CQ\\log(2QM)$. We choose $\\tilde{Q}:=\\max\n(Q^{1+\\varepsilon}, M^{4-4v\/7}). $ Then \\eqref{Re1} implies that\n\\begin{equation} \\label{Re2}\nB_1(Q,M)\\ll (QM)^{\\varepsilon}\n\\left(Q+Q^{1\/v}M^{3-4\/v}+M^{17\/7}\\right).\n\\end{equation}\n\n  It's easy to see that the choice $v=2$ is optimal and a further cycle in the above process does not lead to an improvement of\nour result. Combining \\eqref{C2egen} with $v=1,2,3$ and\n\\eqref{Re2} with $v=2$, we obtain our final estimate\n\\begin{equation}\n\\label{final0} B_1(Q,M)\\ll\n(QM)^{\\varepsilon}\\min\\left\\{Q^{7\/4}+M, \\; Q^{11\/8}+Q^{1\/2}M, \\; Q^{5\/4}+Q^{2\/3}M,\\;\nQ+Q^{1\/2}M+M^{17\/7}\\right\\}.\n\\end{equation}\nwhich together with \\eqref{trans} (noting that the last expression in \\eqref{trans} is $\\ll B_1(Q,M)$ by the law of quartic reciprocity) implies Theorem \\ref{quarticlargesieve}. \\hfill $\\Box$ \\\\\n\nCalculating the right-hand side of \\eqref{final} for various\nranges of $Q$ and $M$, we obtain that it is bounded by\n\\begin{equation*}\n\\ll (QM)^{\\varepsilon} \\| a_m \\|^2\n\\cdot \\left\\{ \\begin{array}{llll} M &\\mbox{ if } Q\\le M^{4\/7},\\\\ \\\\ Q^{7\/4} &\\mbox{ if } M^{4\/7}<Q\\le M^{4\/5}, \\\\ \\\\\nQ^{1\/2}M &\\mbox{ if } M^{4\/5}<Q\\le M^{8\/7}, \\\\ \\\\\nQ^{11\/8} &\\mbox{ if } M^{8\/7}<Q\\le M^{24\/17}, \\\\ \\\\\nQ^{2\/3}M &\\mbox{ if } M^{24\/17}<Q\\le M^{12\/7}, \\\\ \\\\\nQ^{5\/4} &\\mbox{ if } M^{12\/7} <Q\\le M^{68\/35}, \\\\ \\\\\nM^{17\/7} &\\mbox{ if } M^{68\/35} <Q\\le M^{17\/7}, \\\\ \\\\\nQ & \\mbox{ if } M^{17\/7}<Q.\n\\end{array} \\right.\n\\end{equation*}\n  For convenience, we enclose a table displaying the estimates for $B_1(Q,M)$ that we get\nfor various ranges. This table should be read as follows. If the\nfractions $\\alpha$ and $\\beta$ are the $(n-1)$-th and $n$-th\nentries, respectively, in the first row, and the term $T$ is the\n$n$-th entry in the second row, then the estimate $B_1(Q,M) \\ll\n(QM)^{\\varepsilon}T$ holds in the range $M^{\\alpha} < Q \\leq\nM^{\\beta}$.\n\n\\begin{tabular}{|l||l|l|l|l|l|l|l|l|l|}\n\\hline Range & 4\/7 & 4\/5 & 8\/7 & 24\/17 & 12\/7 & 68\/35 & 17\/7 &  $\\infty$ \\\\\n\\hline\nBounds & $M$ & $Q^{7\/4}$ & $Q^{1\/2}$ & $Q^{11\/8}$ & $Q^{2\/3}$ & $Q^{5\/4}$ & $M^{17\/7}$ & $Q$  \\\\\n\\hline\n\\end{tabular} \\\\\n\nIt can be easily checked that \\eqref{C2egen} with $v\\ge 3$ does\nnot lead to an improvement of \\eqref{final0}. \\newline\n\n\\noindent{\\bf Acknowledgments.} During this work, P. G. was\nsupported by postdoctoral research fellowships at Nanyang\nTechnological University (NTU) and L. Z. by an AcRF Tier I Grant at NTU.  Moreover, L. Z. was on a visiting stay at {\\it Max-Planck-Institut f\\\"ur Mathematik} (MPIM) in Bonn and he wishes to thank MPIM for its financial support and hospitality during that pleasant and enjoyable period.  Finally, we thank the anonymous referee for his\/her many comments and suggestions.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction:}\n\nEarly universe (standard big-bang) nucleosynthesis [SBBN] is\nregarded as a major success for the \nStandard Big Bang [SBB] Model. As presented, SBBN results look \nrather good indeed. The observed light element abundances are \ntaken to severely constrain cosmological and particle physics \nparameters. Deuterium, in particular, is regarded as\nan ideal ``baryometer'' for determining the baryon content of the \nuniverse \\cite{olive}. \nThis follows from the fact that deuterium is burned away whenever\nit is cycled through stars, and a belief, that there are no \nastrophysical sites (other than SBBN), capable of producing it \nin its observed abundance \\cite{eps}.\nThe  purpose of this  article is to admit caution in adhering to \nthis belief and to explore nucleosynthesis in an environment  \nradically different from the Standard.\n\n\tWhat would be the point of such an exercise ? \n\nIndeed, at the outset, drastic variations from SBBN may sound \npreposterous at this time. Confidence in SBBN stems primarily \nfrom $D$, $^7Li$ and $^4He$ measurements.  $D$ abundance is \nmeasured  in the solar wind, in interstellar clouds  and, more \nrecently, in the inter-galactic medium \\cite{geiss,hogan}. \nThe belief  that no realistic astrophysical process other than \nthe Big Bang  can  produce sufficient $D$ lends \nsupport to its primordial origin. Further, \n$^7Li$ measurement [$^7Li\/H \\sim 10^{-10}$] in Pop II stars \n\\cite{spite}  and the consensus \\cite{yang} over the primordial \nvalue for the $^4He$ ratio $Y_p \\ge 23.4 \\%$ \n(by mass) suggest that\nlight element abundances are consistent with SBBN over nine \norders of magnitude. This is  achieved by adjusting just\none parameter,  the baryon entropy ratio $\\eta$. Alternative \nmechanisms for $^7Li$ production that are \naccompanied by a co-production of $^6Li$ with a later depletion \nof $^7Li$ have fallen out of favour. The debate on depletion\nof $^7Li$ has been put to rest by the observation of $^6Li$ in a \nPop II star \\cite{smith}. Any depletion of $^7Li$ would have to \nbe accompanied by a  complete destruction of the much more \nfragile $^6Li$. Within the SBBN scenario therefore, one seeks to \naccount for the abundances of $^4He$, $D$, $^3He$ and $^7Li$ \ncosmologically, while $Be$, $B$ and $^6Li$ are generated  by \nspallation processes \\cite{olive1}.\n\n\nThese results, however, do meet with occasional skepticism\n[see eg. \\cite{primak} for problems with BBN]. \nObservation of $^6Li$, for example, requires unreasonable \nsuppression of astrophysical destruction of $^7Li$. On the \nother hand, the production of $^6Li$ would be accompanied by a \nsimultaneous production of $^7Li$ comparable to observed levels \n\\cite{rees}. This raises doubts about using observed $^7Li$ \nlevels as a benchmark to evaluate SBBN. \n\nFurther the best value of $^4He$ mass fraction, \nstatistically averaged and extrapolated\nto zero heavy element abundances, \nhovers around $.216 \\pm .006$ for Pop II objects \\cite{rana}.\nSuch low $^4He$ levels have also been reported     \nin several metal poor HII galaxies \\cite{pagel}. For example \nfor  SBS 0335-052 the reported value is $Y_p = 0.21 \\pm 0.01$ \n\\cite{ter}. Such small values for $^4He$ would not\nlead to any concordant value for $\\eta$ consistent with bounds on\n$^7Li$ and $D$. Of course, one could still explore a \nmulti-parameter non-minimal  SBBN instead of the minimal model \nthat just uses $\\eta$ for a single parameter fit. Non-vanishing \nneutrino chemical potentials have been proposed to be ``natural'' \nparameters for such a venture. These conclusions have been \ncriticized in \\cite{yang,ter} on grounds of reliance on statistical \nover-emphasis on a few metal-poor objects with a high enough \n$^4He$ abundance to save minimal SBBN. On the other hand, there \nare objects reported with abysmally low $^4He$ levels. This is \nalarming for  minimal SBBN. For example, levels of $^4He$ \ninferred for $\\mu$ Cassiopeiae A \\cite{ter} and from the emission\nlines of several quasars \\cite{peim} are as low as 5\\% and \n10 - 15\\% respectively. Such low levels would most definitely \nrule out SBBN. At present one excludes such objects from SBBN \nconsiderations on grounds of ``our lack of understanding''of the \nenvironments local to these objects. As a matter\nof fact,  one has to resort to specially contrived explanations to\naccount for low $Y_p$ values in quasars. Considering that a host \nof mechanisms for light element synthesis are discarded on grounds\nof requirement of special ``unnatural'' circumstances \\cite{eps}, \nit does not augur to have to resort to special explanations to \ncontend with low $^4He$ emission spectra. This comment ought to \nbe considered in the light of much emphasis that is \nlaid on emission lines from nebulae with low metal content \n\\cite{yang}. Quasars most certainly qualify for such candidates. \nInstead, one merely seems to  concentrate on classes of Pop II \nobjects and HII galaxies\nthat would oblige SBBN. Until the dependence of light \nelement abundance on sample and statistics is gotten rid  of and \n\/ or fully understood, one must not close one's eyes to \nalternatives.\n\n\nWe end our overview of the status of SBBN  with a few comments.\nFirstly the low metallicity that one sees in type II stars and \ninterstellar clouds poses a problem in SBBN. There is\nno object in the universe that has low abundance \n[metallicity] of heavier elements as is produced \nin SBB. One relies on some kind of re-processing, much later in \nthe history of the universe, to get the low observed  \nmetallicity in,  for example, old clusters and \ninter-stellar clouds. This could be in the form of a generation \nof very short-lived type III stars. Such a generation of stars\nmay also be necessary to ionize the intergalactic medium. \nThe extrapolation of $^4He$ \nabundance in type II objects and low metal (HII) galaxies, \nto its zero heavy metal abundance \nlimit, presupposes that reprocessing and production of heavy\nelements in type III stars is not accompanied by a significant \nchange in the $^4He$ levels. A violation of this assumption,\ni.e. a minute increase in $^4He$ during reprocessing (even as low\nas 1 - 2 \\%) would rule out the minimal SBBN. As a matter of fact, \nit is possible to account for the entire pre-galactic $^4He$ \nby such objects \\cite{wagoner}. \n\n\nFinally, of late \\cite{lem}, the need for a careful scrutiny and \na possible revision of the status of SBBN has also been suggested \nfrom  the reported high abundance of $D$ in several $Ly_\\alpha$ \nsystems. It may be difficult to accommodate such high abundances\nwithin the minimal SBBN. Though the status of these observations \nis still a matter of debate, and (assuming their confirmation) \nattempts to reconcile the cosmological abundance of deuterium \nand the number of \nneutrino generations within the framework of SBB are still on, \na reconsideration of alternate routes to deuterium in a slow\nexpanding universe as described in this article\ncould well be worth the effort. This is specially in consideration\nof the stranglehold that Deuterium has on SBB in constraining the \nbaryon density upper limit to not more than some 3 to 4 \\% . This\nconstraint has been used in SBB to make out a strong case for non -\nbaryonic dark matter to make up the mass estimates at galactic and\ncluster scales. Relying on Deuterium that is so local environment\nsensitive, to predict the nature of CDM runs the risk of ``building\na colossus on a few feet of clay''\\cite{borner}.\n\nThis article reports our study of nucleosynthesis in a universe \nin which the scale factor evolves linearly with time independent \nof the equation of state of matter. A strictly linear evolution \nof the cosmological scale factor\nis surprisingly an excellent fit to a host of cosmological \nobservations. Any model that can support such a coasting presents \nitself as a falsifiable model as far as classical cosmological \ntests are concerned as it exhibits distinguishable and verifiable \nfeatures. \n\nLarge scale homogeneity and isotropy observed in the universe is\nincorporated in the Friedman-Robertson-Walker (FRW) metric:\n\\begin{equation}\n\\label{1}\nds^2 = dt^2 - a(t)^2[{dr^2\\over {1 - Kr^2}} + r^2(d\\theta^2 \n+ sin^2\\theta d\\phi^2)]\n\\end{equation}\nHere $K = \\pm 1, 0$ is the curvature constant. In the following \nsection, we summarize the \nconcordance of observations in a $K = -1$ FRW cosmology in which \nthe scale factor evolves linearly \nwith time: $a(t) \\propto t$, right from the creation event itself. \nThe motivation for such an endeavor has been discussed at \nlength in a series of earlier articles \\cite{meetu,annu}. \nFor the purpose of this article, we shall take as a conjecture\nthat a strictly homogeneous background FRW model coasts \nlinearly with time. This can be achieved in a large class of \nnon-minimally coupled theories of gravity. However, perturbations\naround the homogeneous background are asumed to satisfy the \nperturbed Einstein equations. \nSection 3 describes concordant nucleosynthesis in such a model.\n\n\\section{Concordance of a linear coasting cosmology:}\n\n{\\bf \\noindent Classical Cosmology tests}\n\\begin{itemize}\n\\item{\\it\\bf \\noindent n(z), a(z):} Data on Galaxy number counts \nas a function of red-shift  along with data angular diameter \ndistance as a function of red-shift do not rule out a linearly \ncoasting cosmology \\cite{kolb1}. However, as these tests are \nmarred by evolutionary effects (and mergers), they have fallen \ninto disfavour as reliable tests of a viable model.\n\n\n\\item{\\it\\bf \\noindent Hubble Diagram:} With the discovery of \nSupernovae type Ia [SNe Ia] as reliable standard candles, the \nstatus of the Hubble test has been elevated to that of a precision\nmeasurement. The Hubble plot relates the magnitude of a standard \ncandle to its redshift in an expanding FRW universe. In \n\\cite{meetu} we demonstrated how linear coasting is as \naccommodating for high red-shift objects as the standard \nnon--minimal model with a small cosmological constant. \nThe concordance of linear coasting with SNe1a data\nfinds a passing mention in the analysis of Perlmutter \\cite{perl}\nwho noted that the Hubble plot for $\\Omega_\\Lambda = \\Omega_M = 0$\n(for which the scale factor would have a linear evolution in \nstandard cosmology) is ``practically identical to the \n$\\bf{best fit}$ plot for an unconstrained cosmology''. The \nconcordance of this Hubble plot continues even for \nthe  more recent data on SNe1a with redshifts $z \\ge 1$. \nThe plot almost coincides with the Hubble plot for  \n$\\Omega_\\Lambda \\approx 0.72,~ \\Omega_M = 0.28$.\n\n\\item{\\it\\bf \\noindent Age of the Universe} The age estimate of \nan ($a(t) \\propto t$) universe, deduced from a measurement of the \nHubble parameter, is given by $t_o = (H_o)^{-1}$.  The low \nred-shift SNe1a give the best value of \n$65~{\\rm km~ sec^{-1}~ Mpc^{-1}}$ for the Hubble parameter.\nThe age of the universe turns out to be $15\\times 10^9$ years.\nSuch an age estimate is comfortably concordant with age estimates \nof old clusters. \n\n\\item{\\it\\bf \\noindent Lensing Statistics:} Consistency and\nconcordance of linear \ncoasting with gravitational lensing statistics was reported in \n\\cite{abha}. \n\n\\item{\\it \\bf \\noindent  Density Perturbations }\n\\vspace{.2cm}\n\nIn \\cite{pranav} we explored a conjecture that the background\nuniverse coasts linearly with perturbations around this \nbackground being described by\n\\begin{equation}\n-8\\pi G \\delta T^M_{\\mu\\nu} = \\delta G_{\\mu\\nu}\n\\end{equation}\nIt turns out that small perturbations can \nevolve to a non-linear regime and therefore be expected to lead \nto structures at large scales. This can be seen by \nexpressing the metric as\n$ g_{\\mu\\nu} = ^{(o)} g_{\\mu\\nu} + \\delta g_{\\mu\\nu}$, \nthe $\\delta g_{\\mu\\nu}$ being the perturbations. Scalar\nperturbations can be decomposed in terms of eigenmodes of\nthe laplacian on the constant $\\bar{\\eta}$ surface \n(here $d\\bar{\\eta} = a^{-1}dt$) with eigenvalues $-k^2$\nIn terms of matter gauge invariant variable  $D_g$\n(see eg. \\cite{mukh,ruth}) and a density parameter\n$$\nC \\equiv 4\\pi G \\rho_b^o a_0^2 = {3\\over 2}{{8\\pi G}\\over {3H_o^2}}\\rho_b^o \n= {3\\over 2}\\Omega_b  \n$$\nthe density perturbation equation simply reduces to \\cite{pranav}:\n\\begin{equation}\n[(k^2 + 3){{e^{\\bar{\\eta}}}\\over C} + 3]\\ddot D_g +\n[(k^2 + 3){{e^{\\bar{\\eta}}}\\over C} + 2]\\dot D_g\n- D_gk^2  = 0.\n\\end{equation}\n$k = 1$ corresponds to the Hubble scale which is the same as \nthe curvature scale in this model. At a redshift $\\approx 1000$, \na sphere of Hubble radius subtends an\nangle roughly .25 degrees. Using constraints from microwave \nbackground anisotropy at these angles gives $D_g \\approx 10^{-5}$ \nat these scales at the last scattering surface. It is easy to see \nthat modes \n$k \\le 1$ do not grow. At smaller angular scales ($k >> 1$),  \nthe observed anisotropy is expected to fall to much lower values \n\\cite{savthes}. Photon diffusion dampens anisotropies at angular \nscales smaller than about one minute. However, for such large \nvalues of $k$, $D_g$ has rapidly growing solutions. The \nperturbation equation becomes  \n\\begin{equation}\n\\ddot D_g + \\dot D_g - Ce^{-\\bar{\\eta}}D_g = 0  \n\\end{equation}\nThis has exact solutions in terms of modified first and second \ntype bessel functions $I_1,~K_1$:\n\\begin{equation}\nD_g = C_1(Ce^{-\\bar{\\eta}})^{1\\over 2}I_1((4Ce^{-\\bar{\\eta}})^{1\\over 2})\n       + C_2(Ce^{-\\bar{\\eta}})^{1\\over 2}K_1((4Ce^{-\\bar{\\eta}})^{1\\over 2})\n\\end{equation}\nFor large arguments, these functions have their asymptotic forms:\n\\begin{equation}\nI_1 \\longrightarrow {(Ce^{-\\bar{\\eta}})^{-{1\\over 4}}\\over {2\\sqrt{\\pi}}}\nexp[2(Ce^{-\\bar{\\eta}})^{1\\over 2}];~~\nK_1 \\longrightarrow {(Ce^{-\\bar{\\eta}})^{-{1\\over 4}}\\over {2\\sqrt{\\pi}}}\nexp[- 2(Ce^{-\\bar{\\eta}})^{1\\over 2}]\n\\end{equation}\nEven if diffusion damping were to reduce the baryon density contrast to \nvalues as low as some $10^{-15}$, a straight forward numerical integration\nof eqn(4) demonstrates that for $k \\ge 3000$ the density contrast becomes \nnon linear around redshift of the order 50. \n\nIn contrast to the above, in the radiation dominated epoch,\nthe adiabatic approximation perturbation equations imply \n\\cite{pranav}:\n\\begin{equation}\n[(k^2 + 3){3\\over {4k^2}} + {3\\tilde C\\over {2k^2e^{2\\bar{\\eta}}}}]\\ddot D_g +\n{3\\tilde C\\over {k^2e^{2\\bar{\\eta}}}}\\dot D_g\n+[{{k^2 + 3}\\over 8} - {\\tilde C\\over {2e^{2\\bar{\\eta}}}}]D_g  = 0 \n\\end{equation}\nFor $\\bar{\\eta}$ large and negative, small $k$ pertubation equation \nreduces to \n\\begin{equation}\n3\\ddot D_g + 6\\dot D_g -k^2D_g = 0\n\\end{equation}\nEqns(7-8) imply that \nperturbations bounded for large negative $\\eta$ damp out for \nsmall $k$ while large $k$ modes are oscillatory.\n\nWe conclude that fluctuations do not grow in the radiation \ndominated era, small $k$ (large scale) fluctuations do not grow \nin the matter dominated era as well. However, \neven tiny residual baryonic fluctuations $O(10^{-15})$ \nat the last scattering surface for large values of $k \\ge 3000$ \nin the matter dominated era, grow to the non linear regime. \nSuch a growth would be a necessary condition for structure \nformation and is not satisfied in the standard model. In the \nstandard model, cold dark matter is absolutely essential \nfor structure formation. \n\n\n\\vspace{.2cm}\n\\item{\\it \\bf \\noindent The recombination epoch}\n\\vspace{.2cm}\n\n        Salient features of the plasma era in a linear coasting \ncosmology have been described in \\cite{astroph,savitaI,savthes}. \nHere we reproduce some of\nthe peculiarities of the recombination epoch. These\nare deduced by making a simplifying assumption of thermodynamic \nequilibrium just before recombination. \n\nThe probability that a photon was last scattered in the interval \n$(z,z + dz)$ can be expressed in terms of optical depth,and turns out to be:\n\\begin{equation}\nP(z) = e^{-\\tau_\\gamma}{{d\\tau_\\gamma}\\over {dz}} \\approx 7.85\\times 10^{-3}\n({z\\over {1000}})^{13.25}exp[-0.55({z\\over {1000}})^{14.25}]\n\\end{equation}\nThis $P(z)$ is sharply peaked and well fitted by a gaussian of mean redshift\n$z \\approx 1037$ and standard deviation in redshift $\\Delta z \\approx 67.88$.\nThus in a linearly coasting cosmology, the last scattering surface locates at\nredshift $z^* = 1037$ with thickness \n$\\Delta z \\approx 68$. Corresponding values in \nstandard cosmology are $ z = 1065$ and $\\Delta z \\approx 80$.\n\n   An important scale that determines the nature of CMBR anisotropy is the \nHubble scale which is the same as the curvature scale for linear coasting. \nThe angle subtended today, by a sphere of Hubble radius at $z^* = 1037$, \nturns out to be $\\theta_H \\approx 15.5$ minutes. The Hubble length determines the scale \nover which physical processes can occur coherently. Thus one expects all \nacoustic signals to be contained within an angle $\n\\theta_H \\approx 15.5$ minutes.\n\nWe expect the nature of CMB anisotropy to follow from the above \nresults. The details are still under study and shall be reported \nseparately.\n\n\\vspace{.5cm}\n\\item{\\it \\bf \\noindent Summary}\n\\vspace{.5cm}\n\nIn spite of a significantly different evolution, a linear \ncoasting cosmology can not be ruled out by all the tests we have \nsubjected it to so far. Linear coasting being extremely\nfalsifiable, it is encouraging to observe its\nconcordance !! In standard cosmology, falsifiability has taken \na backstage - one just constrains the values of cosmological \nparameters subjecting the data to Bayesian statistics. Ideally, \none would have been very content with a cosmology based on physics\ntested in the laboratory. Clearly, standard cosmology does not \npass such a test. One needs a mixture of hot and cold dark \nmatter, together with (now) some form of \\emph{dark energy} to \nact as a cosmological constant, to \nfind any concordance with observations. In other words, one uses \nobservations to parametrize theory in Standard Cosmology. \nIn contrast, a universe that is born and evolves as a curvature \ndominated model has a tremendous concordance, it does not need any form of dark matter and there are \nsufficient grounds to explore models that support such a coasting.\n\n\\end{itemize}\n\\section{The Nucleosynthesis Constraint:}\n\nWhat makes linear coasting particularly appealing is a \nstraightforward adaptation of standard nucleosynthesis codes to\ndemonstrate that primordial nucleosynthesis is not an impediment \nfor a linear coasting cosmology \\cite{kapl,annu}. A linear \nevolution of the scale factor radically effects nucleosynthesis\nin the early universe. With the present age of the universe some \n$15\\times 10^9$ years and the $effective$ CMB temperature 2.73 K, \nthe universe turns out to be some 45 years old at $10^9$ K.  \nWith the universe expanding at such low rates, weak interactions \nremain in equillibrium for temperature as low as $\\approx 10^8$ K.\nThe neutron to proton ratio is determined by the n-p\nmass difference and is approximately $n\/p\\sim exp[-15\/T_9]$.\nThis falls to abysmally low values at temperatures below $10^9$ K.\nSignificant nucleosynthesis leading to helium formation commences \nonly near temperatures below $\\sim 5\\times 10^9$K. The low n\/p\nratio is not an impediment to adequate helium production. This\nis because once nucleosynthesis commences, inverse beta decay \nreplenishes neutrons by converting protons into neutrons and \npumping them into the nucleosynthesis network. For baryon entropy \nratio $\\eta\\approx 7.8\\times 10^{-9}$, the standard \nnucleosynthesis network can be modified for linear coasting and gives $\\approx 23.9\\% $ Helium.\nThe temperatures are high enough to cause helium to burn.\nEven in SBBN the temperatures are high enough for helium to burn.\nHowever, the universe expands very rapidly in SBBN. In comparison,\nthe linear evolution gives enough time for successive burning \nof helium, carbon and oxygen. The metallicity yield is some $10^8$ times the metallicity \nproduced in the early universe in the SBBN. The metallicity \nis expected to get distributed amongst nucleii with maximum \nbinding energies per nucleon. These are nuclei with atomic \nmasses between 50 and 60. This metallicity is close to\nthat seen in lowest metallicity objects. Figure(1) \\& (2) describe \nnuclesynthesis as a function of the Baryon entropy ratio. The \nmetallicity concommitantly produced with $\\approx 23.9\\%$ \nHelium is roughly $10^{-5}$ solar. \n\nThe only problem that one has to contend with is the significantly\nlow residual deuterium in such an evolution. The desired amount\nwould have to be produced by the spallation processes much later \nin the history of the universe as described below.\n\nInterestingly, the baryon entropy ratio required for the right \namount of helium corresponds to $\\Omega_b \\equiv \\rho_b\/\\rho_c = \n8\\pi G \\rho_b\/3H_o^2 \\approx 0.69$ . This closes dynamic mass \nestimates of large galaxies and clusters [see eg \n\\cite{tully}]. In standard cosmology this closure is \nsought by taking recourse to non-baryonic cold dark matter. \nThere is hardly any budget for non - baryonic CDM in linear \ncoasting cosmology.\n\n\n\n{\\bf Deuterium Production:}\n\nTo get the observed abundances of light elements besides $^4He$,\nwe recall spallation mechanisms that were explored in the \npre - 1976 days \\cite{eps}. Deuterium can indeed be produced by \nthe following spallation reactions:\n$$\np + ^4He \\longrightarrow D + ^3He; ~~ 2p \\longrightarrow D + \\pi^+;\n$$\n$$\n2p \\longrightarrow 2p + \\pi^o,~ \\pi^o \\longrightarrow 2\\gamma,~\n\\gamma +^4He \\longrightarrow 2D.\n$$There is no problem in producing Deuterium all the way \nto observed levels. The trouble is that under most conditions \nthere is a concomitant over - production of $Li$ nuclei and \n$\\gamma$ rays at unacceptable levels. Any later destruction of \nlithium in turn completely destroys $D$. As described in \n\\cite{eps}, figure (3) exhibits relative production of $^7Li$  \nand $D$ by spallation. It is apparent that the production of \nthese nuclei to observed levels and without a collateral \ngamma ray flux is possible only if the incident (cosmic ray or any\nother) beam is energized to an almost mono energetic value of \naround 400 MeV. A model that requires nearly mono energetic \nparticles would be rightly considered \n$ad~hoc$ and would be hard to physically justify.\n\nHowever, lithium production occurs by spallation of protons over \nheavy nuclei as well as spallation of helium over helium:\n$$\np,\\alpha ~+ ~C,N,O \\longrightarrow Li~+~X;~~ \np,\\alpha ~+ ~Mg,Si,Fe \\longrightarrow Li~+~X;~~\n$$\n$$\n2\\alpha \\longrightarrow ^7Li ~+~p; ~~ \\alpha ~+~D \\longrightarrow p ~+~^6Li;\n$$\n$$\n^7Be + \\gamma \\longrightarrow p + ^6Li; ~~ ^9Be + p \\longrightarrow\n\\alpha +^6Li.\n$$\nThe absence or deficiency of heavy nuclei in a target cloud and \ndeficiency of alpha particles in the incident beam would clearly \nsuppress lithium production. Such conditions could well have \nexisted in the environments of incipient Pop II stars. \n\nEssential aspects of evolution of a collapsing cloud to form a low\nmass Pop II star is believed to be fairly well understood \n\\cite{feig,hart}. The formation\nand early evolution of such stars can be discussed in terms of\ngravitational and hydrodynamical processes. A protostar would \nemerge from the collapse of a molecular cloud core and would be \nsurrounded by high angular momentum material forming a \ncircumstellar accretion disk with bipolar outflows.\nSuch a star contracts slowly while the magnetic fields play a \nvery important role in regulating collapse of the accretion disk \nand transferring the disk orbital angular motion to collimated \noutflows. A substantial fraction of the accreting matter is \nejected out to contribute to the inter - stellar medium.\n\nEmpirical studies of star forming regions over the last twenty \nyears have now provided direct and ample evidence for MeV \nparticles produced within protostellar and T Tauri systems \n\\cite{Terekhov,Torsti}. The source of such accelerated \nparticle beaming is understood to be violent magnetohydrodynamic \n(MHD) reconnection events. These are analogous to solar magnetic\nflaring but elevated by factors of $10^1$ to $10^6$ above levels \nseen on the contemporary sun besides being up to some 100 times \nmore frequent. Accounting for characteristics in the meteoritic \nrecord of solar nebula from integrated effects of particle \nirradiation of the incipient sun's flaring has assumed the status \nof an industry. Protons are the primary component of particles \nbeaming out from the sun in gradual flares while $^4He$ are \nsuppressed by factors of ten in rapid flares to factors of a \nhundred in gradual flares\\cite{Terekhov,Torsti}. Models of young \nsun visualizes it as a much larger protostar with a cooler \nsurface temperature and with a very highly elevated level of \nmagnetic activity in comparison to the contemporary sun. It is \nreasonable to suppose that magnetic reconnection events would \nlead to abundant release of MeV nuclei and strong shocks that \npropagate into the circumstellar matter. Considerable evidence \nfor such processes in the early solar nebula has been found in \nthe meteoric record. It would be fair to say that the \nhydrodynamical paradigms for understanding the earliest stages of \nstellar evolution is still not complete. However, it seems \nreasonable to conjecture that several features of collapse of a \ncentral core and its subsequent growth from acreting material \nwould hold for low metallicity Pop II stars. Strong magnetic \nfields may well provide for a link between a central star, its \ncircumstellar envelope and the acreting disk. Acceleration of \njets of charged particles from the surface of such stars could \nwell have suppressed levels of $^4He$. Such a suppression \ncould be naturally expected if the particles are picked up from \nan environment cool enough to suppress ionized $^4He$ in \ncomparison to ionized hydrogen. Ionized helium to hydrogen number \nratio in a cool sunspot temperature of $\\approx 3000~K$ can be \ncalculated  by the Saha's ionization formula and the \nionization energies of helium and hydrogen. This turns out to be \n$\\approx~ exp(-40)$ and increases rapidly with temperature. Any \nelectrodynamic process that accelerates charged particles from \nsuch a cool environment would yield a beam deficient in alpha \nparticles. With $^4He$ content in an accelerated particle beam \nsuppressed in the incident beam and with the incipient cloud \nforming a Pop II star having low metallicity in the \ntarget, the ``no - go'' concern of (Epstein et.al. \\cite{eps}) \nis effectively circumvented. The ``no-go'' used \n$Y_\\alpha \/Y_p \\approx .07$ in both the energetic particle\nflux as well as the ambient medium besides the canonical solar \nheavy element mass fraction. Incipient Pop II environments may \ntypically have heavy element fraction suppressed by more than \nfive orders of magnitude while, as described above, magnetic \nfield acceleration could accelerate beams of particles deficient \nin $^4He$.\n\nOne can thus have a broad energy band - all the way from a few \nMeV up to some 500 MeV per nucleon as described in the Figure (3), \nin which acceptable levels of deuterium could be ``naturally'' \nproduced. The higher energy end of the band may also\nnot be an impediment. There are several astrophysical processes \nassociated with gamma ray bursts that could produce $D$ at high \nbeam energies with the surplus gamma ray flux a natural by product.\n\n\n\nCircumventing the ``no-go'' concern of Epstein et al would be\nof interest for any cosmology having an early universe \nexpansion rate significantly lower than corresponding rates\nfor the same temperatures in early universe SBB.\n\n{\\bf Conclusions:}\n\nOur understanding of star formation has considerably evolved \nsince 1976. SBBN constraints need to be reconsidered in view of \nempirical evidence from young star forming regions. These models \nclearly imply that spallation mechanism can lead to viable and \nnatural production of Deuterium and Lithium in the incipient \nenvironment of Pop II stars. One can conceive of cosmological \nmodels in which early universe nucleosynthesis produces the \ndesired primordial levels of $^4He$ but virtually no $D$. Such a \nsituation can arise in SBBN itself with a high baryon entropy \nratio $\\eta$. In such a universe, in principle,\nDeuterium and Lithium  can be synthesized up to acceptable levels \nin the environment of incipient Pop II stars.\n\n\nIn SBB, hardly any metallicity is produced in the very early \nuniverse. Metal enrichment is supposed to be facilitated by a \ngeneration of Pop III stars. Pop III star formation from a \npristine material is not well understood till date in spite of a \nlot of effort that has been expanded to that effect recently \n\\cite{sneider}. It is believed that with metallicity below a \ncritical transition metallicity \n($Z_{cr} \\approx 10^{-4} Z_\\odot$), masses of Pop III stars would \nbe biased towards very high masses. Metal content higher than \n$Z_{cr}$ facilitates cooling and a formation of lower mass Pop II \nstars. In SBB, the route to Deuterium by spallation discussed in \nthis article would have to follow a low metal contamination by a \ngeneration of Pop III stars.\n\n\nDeuterium production by spallation discussed in this article \nwould be good news for a host of slowly evolving cosmological \nmodels \\cite{kapl,annu}. An FRW model with a linearly evolving \nscale factor enjoys concordance with constraints on age of the \nuniverse and with the Hubble data on SNe1A. Such a linear coasting\nis consistent with the right amount of helium\nobserved in the universe and metallicity yields close to the \nlowest observed metallicities. The only problem that one has to \ncontend with is the significantly low yields of deuterium in such \na cosmology. In such a model, the first generation of stars would \nbe the low mass Pop II stars and the above analysis would \nfacilitate the desired deuterium yields.\n\n\nIn SBB, large-scale production and recycling of metals through \nexploding early generation Pop III stars leads to verifiable \nobservational constraints. Such stars would be visible as \n27 - 29 magnitude stars appearing any time in every square \narc-minute of the sky. Serious doubts have been expressed on the \nexistence and detection of such signals \\cite{escude}. The linear \ncoasting cosmology would do away with the requirement of such \nPop III stars altogether.\n\n\\begin{center}\n\\begin{figure}\n\\resizebox{.8\\columnwidth}{!}\n{\\includegraphics[angle=270]{fig1a.ps}}\\\\\n\\title{Fig1(a). The figure shows abundance of He4 as a function of temperature for $\\eta\\approx 7.8\\times 10^{-9}$. The final abundance of He4 is approximately 23 \\%. It reaches this value around $T \\approx T_9$ and stays same thereafter.}\\\\\n\\resizebox{.8\\columnwidth}{!}\n{\\includegraphics[angle=270]{fig1b.ps}}\\\\\n\\title{Fig1(b). The figure shows metalicity as a function of temperature for $\\eta\\approx 7.8\\times 10^{-9}$. The metallicity for a linaer coasting model is nearly equal to $ 10^{-5}$  times solar metallicity. }\\\\ \n\\end{figure}\n\\end{center}\n\\begin{center}\n\\begin{figure}\n\\resizebox{.8\\columnwidth}{!}\n{\\includegraphics[angle=270]{fig2a.ps}}\\\\\n\\title{Fig2(a). The figure shows He4 abundance as a function of $\\eta$.}\\\\\n\\resizebox{.8\\columnwidth}{!}\n{\\includegraphics[angle=270]{fig2b.ps}}\\\\\n\\title{Fig2(b). The figure shows metallicity as a function of $\\eta$.}\\\\\n\\end{figure}\n\\end{center}\n\\eject\n\\begin{center}\n\\begin{figure}\n\\resizebox{.8\\columnwidth}{!}\n{\\includegraphics{fig3.ps}}\\\\\n\\title{ Fig3. The rates at which abundances approach their present values as a function of the energy per nucleon of the incident particle.} \\cite{eps}\\\\\n\\end{figure}\n\\end{center}\n\\vskip 1cm\n\n\n\n\\vfil\\eject\n{\\bf Acknowledgment.} \\\\ Daksh Lohiya and Sanjay Pandey acknowledge IUCAA for support under \nthe IUCAA Associate Program. Geetanjali and Pranav ackowledge C.S.I.R for financial support. \\\\\n\\vspace{0.5cm}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzkcua b/data_all_eng_slimpj/shuffled/split2/finalzzkcua
new file mode 100644
index 0000000000000000000000000000000000000000..c83eed7642df73a712b5621e9ce45c9fbeda81d1
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzkcua
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction} \n\nRecent observations with the Submillimetre Common-User Bolometer Array \n(SCUBA; Holland et al.\\ 1999) on the James Clerk Maxwell Telescope have \nhighlighted the presence of a number of submillimetre-luminous galaxies \n(Smail, Ivison \\& Blain 1997; Holland et al.\\ 1998; Barger et al.\\ 1998a; \nHughes et al.\\ 1998; Eales et al.\\ 1998). To date about forty \nsources have been found. These measurements confirm earlier suggestions \n(Blain \\& Longair 1993; Eales \\& Edmunds 1996, 1997) that submillimetre-wave \nobservations will provide an important probe of cosmology.\n\nThe optical counterparts of these SCUBA sources are faint, most with $I > 20$ \n(Smail et al. 1998). They are presumably not low-redshift sources: the best \nstudied is SMM\\,J02399$-$0136 (Ivison et al.\\ 1998), a dust-enshrouded AGN at \n$z=2.8$, perhaps similar to IRAS F10214+4724 (Rowan-Robinson et al.\\ 1991; \nLacy et al.\\ 1998).  The recent detection of molecular gas in SMM\\,J02399$-$0136 \n(Frayer et al.\\ 1998) also suggests that these galaxies are similar.\n \nWhat is the nature of these SCUBA-selected sources? In particular are they \nsimilar to the ultraluminous infrared galaxies (ULIRGs) observed locally (e.g. \nSanders \\& Mirabel 1996)? They have the same submillimetre-wave flux densities \nas would have local ULIRGs seen at high redshift (Barger et al.\\ 1998a). They also have \nsimilar optical colours (Smail et al.\\ 1998) to two of the three local ULIRGs\nstudied at ultraviolet wavelengths by Trentham, Kormendy \\& Sanders\n(1998), were those galaxies to be seen at high redshift. If this interpretation is \ncorrect, then we might hope to be able to use the wealth of observational \ninformation available for local ULIRGs to help to understand the properties of the \nSCUBA sources and their relevance to cosmology.  \n\nWhether the SCUBA sources are dust-enshrouded AGNs, like Markarian 231, or \ndust-enshrouded starbursts, like Arp 220, is an important question. \nThis is difficult to determine for even local ULIRGs, because there are up to \nseveral hundred magnitudes of extinction along our lines of sight to the galaxy \ncores at optical wavelengths. For local ULIRGs, simple conclusions can be \ndrawn based on the general form of the spectral energy distributions (SEDs) \n(e.g.~Sanders et al.\\ 1988a); however, this information is not available for the \nSCUBA sources. Recently, new more detailed methods based on mid-infrared \nspectroscopic diagnostics (Lutz et al.\\ 1996, Genzel et al.\\ 1998) have been used \nto resolve this question for the most local ULIRGs. \n \nWe construct redshift-dependent luminosity functions that are consistent with\nall the counts and backgrounds from a number of recent surveys at far-infrared \nand millimetre\/submillimetre wavelengths. We use non-evolving \nGaussian luminosity functions over specified redshift ranges.  These are the \nsimplest luminosity functions that we could adopt, without the results \nbeing dependent on the properties of low-luminosity galaxies that are not \nprobed by the SCUBA observations. Contributions from these low-luminosity \ngalaxies are important when computing backgrounds, although they contribute \ninsignificantly to the counts. The parameterization used to compare models \nwith observations reflects this fact. Imposing all the \nconstraints simultaneously does limit the possible form of the luminosity \nfunction and we identify three plausible models.\n\nGiven the redshift-dependent luminosity functions of these models, we \ninvestigate the properties to the individual sources using observations of their \nlocal ultraluminous counterparts, and derive the cosmological implications of \nthe SCUBA galaxies under both the starburst and AGN interpretation.\n\nWe first investigate the possibility that the SCUBA sources are high-redshift \nstar-forming galaxies. The starburst models of Leitherer \\& \nHeckman (1995) are used to convert far-infrared luminosities to star-formation \nrates; a transformation that is uncertain by more than an order of magnitude.\nWe then place the SCUBA galaxies on the Madau plot, which relates the \ncosmic star formation rate to the cosmic epoch (Madau et al.\\ 1996; Madau, \nDella Valle \\& Panagia 1998), \nand predict the total density of local stars produced in such \nobjects. Most of the star formation in the SCUBA sources is observed through\nhuge amounts of internal extinction, and so will not be included in global\nstar-formation rates that are computed using the optically selected samples that \nare normally used to construct the Madau plot.  Indeed Hughes et al.\\ (1998) \nshow that deriving a star-formation rate from a rest-frame ultraviolet flux \nresults in a value that is more than an order of magnitude too low.\nThe SCUBA sources are thus not accounted for in the existing samples that are \nused to construct the Madau plot.\n\nWe then investigate the possibility that the SCUBA sources are high-redshift\ndust-enshrouded AGN, as discussed by Haehnelt, Natarajan \\& Rees (1998) \nand Almaini, Lawrence \\& Boyle (1999). The three distant \nsubmillimetre-luminous galaxies that have been studied in detail -- \nAPM\\,08279+5255 (Irwin et al. 1998; Lewis et al. 1998; Downes et al. submitted), \nSMM\\,J02399$-$0136 and IRAS F10214+4724 -- all contain powerful AGN. If all \nthe sources derive their bolometric luminosity from AGN that heat their dust \nshrouds radiatively by accretion onto a massive black hole, then we can use our \nredshift-dependent luminosity functions to\ncompute the comoving integrated mass density of these black holes.\n\nWe find plausible (although not unique) scenarios that are consistent with all \nthe observations and present their cosmological implications. Finally, we \nhighlight future work which may help to distinguish between the various \nscenarios. Throughout this paper we assume an Einstein--de Sitter world model \nwith $H_0 = 50$\\,km\\,s$^{-1}$\\,Mpc$^{-1}$.\n\n\\section{Far-infrared\/submillimetre-wave counts and backgrounds\nand the ULIRG luminosity function}\n\nThere have been many recent measurements of the far-infrared and\nsubmillimetre source counts and backgrounds at a number of wavelengths:\nsee Table 1.  This has been a recent field of substantial activity \nbecause of new instrumentation, both SCUBA and {\\it ISO}. If we assume that\nthe SED at far-infrared and submillimeter\nwavelengths is known for all the sources,\nwe can then use all these measurements in conjunction to constrain the\nbivariate far-infrared luminosity--redshift function of these sources.\n\n\\begin{table*}\n\\caption{Far-infrared and submillimetre-wave surveys.\nLagache et al.~(1998) and Kawara et al.~(1997, 1998) obtain a different\ncalibration for the ISO 175-$\\mu$m counts.  A discussion of calibration is\ngiven in Lagache et al.~(1998). The detection limit in the 850-$\\mu$m \nsurvey by Hughes et al. (1998) is about 2\\,mJy: the count at 1\\,mJy is \nderived from a source confusion analysis. See Blain et al.~(1999b) and \nSmail et al. (1999) for a \ndirect sub-mJy 850-$\\mu$m count. For complementary \nfar-infrared\/submillimetre-wave background measurements the reader \nis referred to Puget et al.~(1996), Guiderdoni et al.~(1997), Dwek et al.~(1998) \nand Fixsen et al.~(1998).}\n{\\vskip 0.75mm}\n{$$\\vbox{\n\\halign {\\hfil #\\hfil && \\quad \\hfil #\\hfil \\cr\n\\noalign{\\hrule \\medskip} \nWavelength  & Counts \/     & Flux Limit \/& Background \/         & \nTelescope\/Instrument & Reference &\\cr\n            & deg$^{-2}$  & mJy        & nW m$^{-2}$ sr$^{-1}$  &\n       &           &\\cr \n\\noalign{\\smallskip \\hrule \\smallskip} \n\\cr \n2.8\\,mm & $<162$ & 3.55 & $-$ &  BIMA          & Wilner \\& Wright (1997) &\\cr \n\\noalign{\\smallskip}\n850\\,$\\mu$m &  $2500\\pm1400$ & 4  & $-$ &  JCMT\/SCUBA & \nSmail et al.~(1997)&\\cr\n\t    &  $1100\\pm600$ & 8 & $-$ & & Holland et al.~(1998)&\\cr \n\t    &  $800^{+1100}_{-500}$ & 3 & $-$ & & Barger et al.~(1998a) & \\cr\n            &  $7000\\pm3000$ & 1 & $-$ & & Hughes et al.~(1998) & \\cr \n\t    &  $1800\\pm600$ & 2.8 & $-$ & & Eales et al.~(1998) &\\cr \n\\noalign{\\smallskip}\n850\\,$\\mu$m & $-$ & $-$ & $0.55 \\pm 0.15$ & {\\it COBE}\/FIRAS & \nFixsen et al.~(1998)\n&\\cr\n\\noalign{\\smallskip}\n450\\,$\\mu$m &  $< 1000$ & 80 & $-$ & JCMT\/SCUBA & Smail et al.~(1997) &\\cr\n\t    &  $<360$ & 75 & $-$ & & Barger et al.~(1998a) &\\cr \n\\noalign{\\smallskip}\n240\\,$\\mu$m & $-$ & $-$ & $17 \\pm 4$ &  {\\it COBE}\/DIRBE + {\\it IRAS}\/ISSA & \nSchlegel et al.~(1998) &\\cr \n            & $-$ & $-$ & $14 \\pm 4$ & & Hauser et al.~(1998) &\\cr \n\\noalign{\\smallskip}\n175 $\\mu$m &  $41 \\pm 6$ & 150 & $-$ & {\\it ISO}\/ISOPHOT & Kawara et\nal.~(1998) \n&\\cr\n\t    & $98 \\pm 15$ & 100 & $-$ & \t    & \nLagache et al.~(1998) &\\cr\n\\noalign{\\smallskip}\n140 $\\mu$m & $-$ & $-$ & $32 \\pm 13$ & {\\it COBE}\/DIRBE + {\\it IRAS}\/ISSA & \nSchlegel et al.~(1998) &\\cr\n\t   & $-$ & $-$ & $24 \\pm 12$ & & Hauser et al. (1998) &\\cr\n\\noalign{\\smallskip \\hrule} \n\\noalign{\\smallskip}\\cr}}$$}\n\\end{table*} \n\nWe assume that the galaxies have the thermal SEDs of \nwarm dust that is heated by an enshrouded starburst or AGN, and adopt a \nsimple analytic form for the luminosity function between a minimum and \nmaximum redshift. All the observational constraints on the model are imposed \nthrough integral functions, and so do not require unique solutions.  \nNevertheless, it is interesting to see which general classes of \nluminosity--redshift distributions are ruled out and why.\n\nTo ensure consistent definitions are used when matching models to\nobservations, first we present all the details of our computations.  Much of this \nwill be familiar to many readers, but different authors define parameters in slightly \ndifferent ways. Secondly, we point out some generic features of the comparison \nbetween our models and observations, in particular the results of requiring the \nmodels to be consistent with source counts at one wavelength and with the \ninfrared background at another simultaneously. Finally, we isolate some \nplausible luminosity functions that are consistent with all the observations for \nfurther investigation.\n\nWe define a bivariate 60-$\\mu$m luminosity-redshift function \n$\\phi_z (L_{\\rm 60})$, with units Mpc$^{-3}$\\,${\\rm L}_{\\odot}^{-1}$, such that \n$\\phi_z (L_{\\rm 60}) \\, {\\rm d} L_{\\rm 60}\\, {\\rm d}z$ is the total number density of \ngalaxies with 60-$\\mu$m luminosity between $L_{\\rm 60}$ and \n$L_{\\rm 60} + {\\rm d} L_{\\rm 60}$ with redshifts between $z$ and $z + {\\rm d}z$. \nSome familiar analytic examples of this function are a \nGaussian in $\\log_{10} L_{\\rm 60}$ with no luminosity or density evolution, \n\\begin{equation} \n\\phi_z (L_{\\rm 60}) = C (1+z)^3 \\exp \\left[ - {1\\over{2 \\sigma^2}}  \n\\log_{10}^2 \\left( {{L_{\\rm 60}} \\over {L_{\\rm 60}^*}}\\right) \\right]   \n{1\\over{L_{\\rm 60} \\, \\rm{ln} 10}},\n\\end{equation} \nor a Saunders et al.\\ (1990) function, which is a power-law in $L_{\\rm 60}$\nwith index $\\alpha$ at the faint end and a Gaussian in $\\log_{10} L_{\\rm 60}$ at \nthe bright end, and allows for density and luminosity\nevolution,\n\\begin{eqnarray} \n\\lefteqn{\\nonumber \n\\phi_z (L_{\\rm 60}) = C(z)\\, (1+z)^{3} \n\\left( {{L_{\\rm 60}} \\over {L_{\\rm 60}^* (z)}} \\right)^{1 - \\alpha} \\times } \\\\ \n& & \\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\n \\exp \\left[ - {1\\over{2 \\sigma^2}}\n\\log_{10}^2 \\left( 1 + {{L_{\\rm 60}} \\over {L_{\\rm 60}^* (z)}}\\right) \\right]\n{1\\over{L_{\\rm 60} \\, \\rm{ln} 10}}.\n\\end{eqnarray} \nImplicit in both equations (1) and (2) above  \nare a normalization constant $C$ (units Mpc$^{-3}$, which depends on\n$z$ if there is density evolution), a characteristic\nluminosity $L_{\\rm 60}^{*}$ (which depends on $z$ if there is\nluminosity evolution), and a Gaussian width $\\sigma$.\n\nOnce we have specified $\\phi_z (L_{\\rm 60})$ for some\npopulation of galaxies, we can compute their contribution to the \ncosmic infrared background at some frequency $\\nu$:\n\\begin{equation} \n\\nu {\\rm I}_{\\nu} = {{1}\\over{4 \\pi}} \\int_{0}^{\\infty} \\int_{0}^{\\infty}\n{ {l_{\\nu} (z,L_{\\rm 60})}\\over{4 \\pi d_{\\rm L} (z)^2}} \\,\\, \\phi_z (L_{\\rm 60})\n\\, \\, {\\rm d} L_{\\rm 60}  \\, \\, { {{\\rm d} V}\\over{{\\rm d} z}} \\, \\, {\\rm d} z \n,\n\\end{equation}\nin units of W\\,m$^{-2}$\\,sr$^{-1}$, where, \n\\begin{equation} \nl_{\\nu} (z,L_{\\rm 60}) = \\left[ { {\\nu (1+z)} \\over {\\nu_{60}}}\\right]^4\n\\!\\! L_{\\rm 60} \n{ {k_{\\nu (1+z)}}\\over{k_{\\nu_{60}}}} \\,\n{ {\\exp \\left({{h \\nu_{60}}\\over{kT}} \\right) - 1 }\\over\n{\\exp \\left[{{h \\nu(1+z)}\\over{k T}} \\right] - 1 } },  \n\\end{equation}\nand $\\nu_{60}$ \nis the frequency corresponding to a wavelength of 60\\,$\\mu$m. \n$k_{{\\nu}}$ is the\nemissivity function of dust.  We follow Hughes (1996) and \nBlain et al.\\ (1999a) in \nassuming a power law $k_{\\nu} \\sim {\\nu^{1.5}}$, and so the dust emission \nspectrum at long wavelengths is a Raleigh--Jeans power-law with spectral \nindex 3.5. We can also compute the number density of sources with flux density \nabove some threshold $S_{\\rm lim}$, which is measured in units of\nW\\,m$^{-2}$\\,Hz$^{-1}$ (or Jy), \n\\begin{equation} \nn(S_{\\rm lim}) \n= {{1}\\over{4 \\pi}} \\int_{0}^{\\infty} \\int_{L_{\\rm lim} \n[S_{\\rm lim}]}^{\\infty} \\>  \n\\phi_z (L_{\\rm 60})\n\\, \\, {\\rm d} L_{\\rm 60}  \\, \\, { {{\\rm d} V}\\over{{\\rm d} z}} \\, \\, {\\rm d} z\n,\n\\end{equation}\nin units of sr$^{-1}$ (or deg$^{-2}$), where, \n\\begin{eqnarray} \n\\lefteqn{\\nonumber \nL_{\\rm lim} [S_{\\rm lim}] = \n4 \\pi d_{\\rm L} (z)^2 \\, \\, S_{\\rm lim} \\, \\nu_{60} \n\\left[ { {\\nu_{60}} \\over {\\nu (1+z)} } \\right]^{3} \\times } \\\\\n& & \\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\\>\n\\>\\>\\>\\>\\>\\>\n\\, { {k_{\\nu_{60}}} \\over {k_{\\nu(1+z)}} } \\,\n{ {\\exp \\left[{{h \\nu (1+z)}\\over{k T}} \\right] - 1} \\over\n {\\exp \\left({{h \\nu_{60}}\\over{kT}} \\right) - 1 }}\n.\n\\end{eqnarray} \nThe quantities,\n\\begin{equation} \nd_{\\rm L} (z) = \n{ {2 c}\\over{H_0}} \\left( 1 - {{1}\\over{\\sqrt{1+z}}} \\right) (1+z), \n\\end{equation} \nand,\n\\begin{equation} \n{ {{\\rm d} V}\\over{{\\rm d} z}} =\n16 \\pi \\, \\left({ { c}\\over{H_0}} \\right)^3\n\\, (1+z)^{-{{3}\\over {2}}} \\, \n\\left( 1 - {{1}\\over{\\sqrt{1+z}}} \\right)^2,\n\\end{equation} \nare the luminosity distance and the\nredshift-derivative of the volume element respectively (assuming\n$\\Omega_0 = 1$).\n\nA few features of the comparison between observation and theory\nare immediately apparent. Source counts constrain the integral of \n$\\phi_z(L_{60})$ over redshift and luminosity above some redshift-dependent \nlimit. However, measurements of the background light\nconstrain the integral of the product of luminosity $L_{60}$ and\n$\\phi_z(L_{60})$ over redshift and all luminosities. For a Saunders luminosity \nfunction with pure density evolution, we compare in Fig.\\,1 the ratio\nof the predicted 850-$\\mu$m source count and 240-$\\mu$m background \nas compared with the observed values listed in Table\\,1 as a function of the \ncharacteristic luminosity $L_{*} \\equiv L_{60}^{*}$. \nThe minimum is produced by the different constraints on the integral of \n$\\phi_z(L_{60})$ imposed by the source counts and the background \nmeasurement. \n\nVery low luminosity galaxies make a negligible contribution to the source counts, \nbut a substantial one to the infrared background if $L_*$ is low in the \nSaunders function. Hence, a low normalization is required to explain the \nbackground data, but a high one is required to explain the source count data,\nand so the ratio plotted in Fig.\\,1 is very high at low $L_*$. Increasing $L_*$\nincreases the fraction of high-luminosity galaxies, and so lowers the ratio of the\nnormalizations required in the figure.  At very high $L_*$, the source counts are \nproduced by a very small number of extremely luminous sources, which cause \nthe background to be extremely high based on their luminosities alone. Hence, \nthe ratio of the normalization begins to increase again, producing the minimum\nin Fig.\\,1.  If the flux threshold (lower limit) in the luminosity integral in\nequation (5) is reduced, then the turn-up of the ratio at high luminosities is less \nmarked, and disappears as the lower limit tends to zero.\n\nIt is intriguing that this minimum in the ratio occurs at a very high characteristic \nluminosity  $L_{*} = 10^{12}$\\,L$_\\odot$. Locally $L_{*} \\sim 10^{9}$\\,L$_\\odot$, \nand so if the luminosity function of the SCUBA sources has a Saunders form, \nhuge amounts of luminosity evolution are required to match the data. This was \nessentially one of the main conclusions of Blain et al.\\ (1999a).\n\n\\begin{figure} \n\\begin{center}\n\\vskip-2mm\n\\epsfig{file=fig1.ps, width=8.65cm}\n\\end{center}\n\\vskip-4mm\n\\caption{ \nThe normalization obtained by fitting a Saunders function \n(equation 2) with density evolution parameterized by $\\gamma$ to the \nCOBE 240-$\\mu$m background (Schlegel et al.\\ 1998), relative to the \nnormalization obtained by fitting a similar function to the SCUBA \n850-$\\mu$m counts of Smail et al.\\ (1997). A value of $\\sigma = 0.724$, \nderived by Saunders et al.\\ (1990), is assumed.  A dust emissivity index \nof 1.5 is assumed when converting luminosities measured at different \nwavelengths to restframe 60-$\\mu$m luminosities. The four line styles \nrepresent the following parameter values: solid ($T=70$\\,K, $\\gamma = 0$),\nshort-dashed ($T=40$\\,K, $\\gamma = 0$), long-dashed ($T=70$\\,K, \n$\\gamma = 6$), and dot-dashed ($T=40$\\,K, $\\gamma = 6$). Locally,  \n$L^{*}_{60} = 1.1 \\times 10^9$\\,L$_{\\odot}$.\n}\n\\end{figure} \n\n\\begin{figure*}\n\\begin{minipage}{170mm}\n{\\vskip-3.5cm} \n\\begin{center}\n\\epsfig{file=fig2.ps, width=18.65cm}\n\\end{center}\n{\\vskip-7.2cm} \n\\caption{\nCombinations of the normalization constant $C$ and the width $\\sigma$ for \nGaussian luminosity functions with no density evolution that are consistent \nwith the 850-$\\mu$m counts.  The units of $C$ are Mpc$^{-3}$. All galaxies \nare assumed to have a temperature $T = 70$\\,K. The comoving galaxy \ndensity $C$ is assumed to be constant between redshifts $z_1 = 3$ and \n$z_2 = 5$ and zero outside this range, (that is the upper and lower limits to \nthe redshift integral in equation (5) are $z_1$ and $z_2$). The solid lines show \nfits to the mean value quoted by Smail et al.\\ (1997). \nThe  dotted-dashed lines are fitted to the +1$\\sigma$ values. The dashed \nlines are fitted to the $-\\sigma$ values: see Table 1. The four panels are \nplotted for different values of $L_{*}$.\n}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{minipage}{170mm}\n{\\vskip-3.5cm}\n\\begin{center}\n\\epsfig{file=fig3.ps, width=18.65cm}\n\\end{center}\n{\\vskip-7.2cm}\n\\caption{As Figure 2, but for $z_1=2$ and $z_2=4$.}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{minipage}{170mm}\n{\\vskip-3.5cm}\n\\begin{center}\n\\epsfig{file=fig4.ps, width=18.65cm}\n\\end{center}\n{\\vskip-7.2cm}\n\\caption{As Figure 2, but for $z_1=1$ and $z_2=3$.}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{minipage}{170mm}\n{\\vskip-3.5cm}\n\\begin{center}\n\\epsfig{file=fig5.ps, width=18.65cm}\n\\end{center}\n{\\vskip-7.2cm}\n\\caption{As Figure 2, but for $T=40$K.}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{minipage}{170mm}\n{\\vskip-3.5cm}\n\\begin{center}\n\\epsfig{file=fig6.ps, width=18.65cm}\n\\end{center}\n{\\vskip-7.2cm}\n\\caption{As Figure 3, but for $T=40$K.}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{minipage}{170mm}\n{\\vskip-3.5cm}\n\\begin{center}\n\\epsfig{file=fig7.ps, width=18.65cm}\n\\end{center}\n{\\vskip-7.2cm}\n\\caption{As Figure 4, but for $T=40$K.} \n\\end{minipage}\n\\end{figure*} \n\nHigher temperature sources systematically produce greater background fluxes\nand counts at shorter wavelengths, because their dust spectra peak at shorter \nwavelengths. Hence, lower normalizations are required in Fig.\\,1 in order to \nexplain the data for 40-K sources as compared with 70-K sources. The 40-K \ncurve is consistent with a ratio of one over a range of luminosities, suggesting\nthat if a Saunders luminosity function describes the SCUBA sources, then they \nmust have temperatures of about 40\\,K. This was another conclusion of \nBlain et al.\\ (1999a): see their Figure 4 -- in their favoured scenarios most of the \nSCUBA sources are at $z>2$ and have luminosities \n$\\sim 10^{12} {\\rm L}_{\\odot}$ and dust temperatures $\\sim 40$\\,K. \n\nFinally, note that the results in Fig.\\,1 are only weakly dependent on the\nform of density evolution parameterized by $\\gamma$.\n\n\\subsection{Comparison with the 850-$\\mu$m source counts}\n\nWe now compute the normalizations $C$ required to fit the 850-$\\mu$m source \ncount data for a number of Gaussian luminosity functions (equation 1) with no \ndensity or luminosity evolution. $C$ is constant between redshifts \n$z_1$ and $z_2$ and is zero elsewhere. This is the simplest possible form of the \nluminosity function; at present the observations do not justify a more rigorous \ntreatment. This parametrization is motivated in part by the\nfact that the local 60-$\\mu$m luminosity function (Saunders et al.\\ 1990) is \napproximately Gaussian at the bright end. The local elliptical galaxy luminosity \nfunction (Binggeli, Sandage \\& Tammann 1988, Ferguson \\& Sandage 1991) is \nalso Gaussian, which is relevant if the SCUBA sources evolve into elliptical \ngalaxies: see Section 3. One important feature of the Gaussian function is that it \nis only valid for high-luminosity galaxies.  Large numbers of galaxies with low \nfar-infrared luminosities will also exist between $z_1$ and $z_2$. Although these \nwill not contribute to the source counts, they may contribute significantly to the \ninfrared backgrounds if they are very numerous.  Hence, when we match our \nluminosity functions to counts (equation 5), we require the model prediction to\nequal the observed values, but when we match our luminosity functions\nto background fluxes (equation 3), we require the model prediction to be less \nthan or equal to the observed values. Our approach is fundamentally different \nfrom that of Blain et al.\\ (1999a). We are not evolving the local 60-$\\mu$m \nluminosity function to high redshift.  Indeed, in Section 3, we argue that the\nsystems which have the highest far-infrared luminosities for redshifts \n$z_1 < z < z_2$ probably evolve into elliptical galaxies, \nwhich are not the most \nluminous systems at far-infrared wavelengths in the local Universe. \n\nIn Figs\\,2 to 7 we present the required normalization constants for\na Gaussian luminosity function to fit the 850-$\\mu$m data of Smail\net al.\\ (1997) for various values of $\\sigma$ and $L_{*}$ given\na constant dust temperature $T$.  The uncertainties are large (see Table\\,1),  \nand so the range of acceptable normalizations is large, with a peak-to-peak \nspread of about a factor of 4. Given these large uncertainties, all the \n850-$\\mu$m counts by different authors listed in\nTable 1 are fully consistent.\nSome general \nfeatures of Figs\\,2 to 7 are worth highlighting:\n\\begin{enumerate} \n\\item $\\sigma = 0$ (a $\\delta$-function) never appears to fit the data well;  \n\\item lower normalizations are required for higher characteristic luminosities;\n\\item the absolute values of the normalizations depend primarily on where the \ndust spectrum peak is shifted in wavelength space. It is shifted closer to\n850\\,$\\mu$m for a source at higher redshift at either 40 or 70\\,K, and so a lower \nnormalization is required at higher $z$;\n\\item lower temperatures require lower normalizations for a given 60-$\\mu$m \nluminosity, since 850\\,$\\mu$m is closer to the blackbody peak. \n\\end{enumerate} \n\n\\subsection{Comparison with counts at other wavelengths}\n\nHaving isolated various models that are consistent with the 850-$\\mu$m \ncounts, we now consider the constraints from measurements at other\nwavelengths. We select a number of models with various values of \n$\\sigma$, $L_{*}$, $C$, and $T$, each represented by a point \non the curves in Figs\\,2 to 7, and thus consistent with the 850-$\\mu$m count. \nFor each model, we consider three separate scenarios: scenario ``0'', in which \nthe 850-$\\mu$m source counts are the mean Smail et al.\\ (1997) values;\nscenario ``+'', in which they are 1$\\sigma$ larger; and scenario ``$-$'', in which \nthey are 1$\\sigma$ smaller.   The counts in the ``$-$'' scenario are very close to \nthe lowest published counts (Barger et al.\\ 1998a).  In all, a total of 45 models, \neach of which generates three scenarios, are considered.\n\nIn Table 2, we show how well the models defined by these parameters account \nfor the measurements at other wavelengths.  The numbers in that table \nrepresent the model prediction relative to the observed counts or background \nfluxes listed in Table 1, assuming scenario ``0''. The fractional uncertainties in \nthe numbers in Table 2 are given in Table 3. \n\nOther measurements exist in the literature that we do not use while\nmaking this comparison.  For example, measurements of 15-$\\mu$m source \ncounts with {\\it ISO} have recently been made (Rowan-Robinson \net al.\\ 1997, Aussel et al.~1998). \nHowever, these measurements probe far down the Wien tail of \nthe dust spectrum, and are of very limited use in constraining the high-redshift \nluminosity function. Furthermore we would need to account for \ncontamination in the 15-$\\mu$m samples by nearby (unobscured) galaxies and \nAGN. Similarly the IRAS 60-$\\mu$m source counts (Saunders et al.\\ 1990)\nare dominated by nearby ($z < 0.1$) sources. Measurements at 1.25\\,mm offer a \npromising probe in the future, but to date measurements have only been made \nfor IRAS-selected galaxies (Franceschini, Andreani \\& Danese 1998). Unbiased \nsamples are not yet available at this wavelength.\n\nSome of the more notable general trends shown in Table 2 are:\n\\begin{enumerate}\n\\item models in which the sources are at higher redshift tend to\nproduce higher source counts or backgrounds at longer \nwavelengths, because the peak of the dust spectrum is shifted\nto longer wavelengths;\n\\item models in which the sources are at higher redshift tend to\nproduce higher backgrounds for a given source count\n{\\it at the same wavelength}. The counts probe only part of the total range of \ngalaxy luminosities, and there are a larger number\nof low-luminosity sources that contribute to the backgrounds but\nnot to the counts;\n\\item on decreasing the temperature from 70 to 40\\,K, the predicted 2.8-mm \ncounts increase, but the predicted 175-$\\mu$m counts and 140- and \n240-$\\mu$m backgrounds decrease, because the peak in the dust emission \nspectrum shifts to longer wavelengths;\n\\item Changing the temperature has a substantial effect on the relative value \nof the source counts and backgrounds at the same wavelength. Decreasing the \ntemperature has a greater relative effect on the counts, because the lower limit\nin the integral in equation 5 is decreased: see Fig.\\,8. \n\\end{enumerate} \n\nSeven of the models that we investigate are consistent with all the\nobservations: see the last column of Table 2 for details. These all have a high \ncharacteristic luminosity greater than $10^{11} {\\rm L}_{\\odot}$.  \nUsing a different parametrization, Blain et al.\\ (1999a) also found that most of the\nSCUBA sources are distant galaxies with similarly high luminosities.\nThese seven models are:\n12\/40\/3\/5\/0.9``0'' (hereafter Model A);\n13\/40\/3\/5\/0.9``$-$'' (hereafter Model B);\n11\/40\/2\/4\/0.9``$-$'' (hereafter Model C);\n12\/40\/2\/4\/0.9``$-$'' (hereafter Model D);\n13\/40\/2\/4\/0.5``0'' (hereafter Model E);\n13\/40\/2\/4\/0.5``$-$'' (hereafter Model F);\n13\/40\/1\/3\/0.1``$-$'' (hereafter Model G).\nIn general, the tables suggest that models with $T = 70$\\,K overproduce the \n175-$\\mu$m counts and the 140- and 240-$\\mu$m backgrounds, given \nthe normalization from the 850-$\\mu$m source counts.  Models in which the \ngalaxies are nearby, that is where $z_1 = 1$, tend to have similar problems. \nConversely, models with very low temperatures $ T < 40$\\, K would overproduce\nthe 2.8-mm counts, but such low-temperature sources are ruled out by the\nconsistency arguments of Blain et al.~(1999a --- see Section 4 of that paper).\n\n\\subsection{Comparison with the FIRAS background}\n\nFixsen et al.\\ (1998) derived the cosmic submillimetre background from \n{\\it COBE} FIRAS data.  Although the background at these wavelengths is \ndominated by emission from the Galaxy and the cosmic microwave background, \nthey used three independent techniques to subtract out these signals. The \nresulting residual 850-$\\mu$m extragalactic background radiation intensity \n$\\nu I_\\nu$=$0.55 \\pm 0.15$\\,nW\\,m$^{-2}$\\,sr$^{-1}$.   \n\nWe can predict 850-$\\mu$m backgrounds in our models using\nequation (3). The results are presented in Table 4.  As in the previous\nsection, we require that our models do not overproduce the background. Model \nG achieves this convincingly, and models B and F are consistent within \n2$\\sigma$. \nWe select these three models for further\nstudy. In general, models with $z_1 = 3$ overpredict the 850-$\\mu$m \nbackground if the 240-$\\mu$m background is predicted correctly, because the \nobserved spectra at a temperature of 40\\,K are shifted to too long a \nwavelength. The surviving models have $z_1 = 2$ (B and F) or $z_1$ = 1 (G).\nAll these models also have $L_* = 10^{13}$\\,L$_{\\odot}$, meaning\nthat most of the far-infrared luminosity from this population comes\nfrom galaxies with 60-$\\mu$m luminosities in excess of 10$^{12}$\\,L$_{\\odot}$.  \nAs discussed in Section\\,2, models with lower characteristic luminosities tend \nto overpredict the 850-$\\mu$m background if they match the 850-$\\mu$m \ncounts. \n\nNote that in the three surviving models (B, F and G) the normalization of the \n850-$\\mu$m counts is consistent with all the observations. In the best-fitting \nmodel (G), the mean redshift of the sources $z_{\\rm s} \\sim 2$, as argued by Lilly \net al.\\ (1998). One half (F,G) or more (B) of the 240-$\\mu$m background, but \nconsiderably less of the 140-$\\mu$m background, comes from the \nhigh-luminosity galaxies described by our Gaussian luminosity function. In \nmodels B and F, about half of the 175-$\\mu$m sources are the same sources \nthat contribute to the 850-$\\mu$m source counts; in model G, the two \npopulations are practically the same. In Model B, the predicted 2.8-mm \ncount is close to the observed limit (Wilner \\& Wright 1997); for the other models\nthe predicted count is much smaller. The 450-$\\mu$m source count limit\n(Barger et al.\\ 1998a) is larger than the predicted values by a factor of about 3 \nfor Model B, and by a much larger factor for the other models.\n\nThree models appear to fit all the data. Even within our simple parametrization \nwe do not find a unique best-fitting model. Furthermore, there are presumably \nmany other (non-Gaussian) models that fit all the data, for example the \nmodels of Blain et al.\\ (1999a).  Nevertheless most of our models seem to be ruled \nout when we consider all the observations in conjunction. That a relatively \nnarrow region of parameter space is consistent with observation \n($L_{*} \\sim 10^{13}$\\,L$_{\\odot}$, $T \\simeq 40$\\,K, $z_{\\rm s} \\sim 2$) is \nencouraging and suggests that it will be productive to investigate these models \nin further detail. \n\n\\section{Properties of the SCUBA sources} \n\nWe have isolated three models of the redshift-dependent luminosity\nfunction of ULIRGs that are consistent with observation, and now\ninvestigate the cosmological implications. \nIn Section 3.1 we investigate the possibility that these are dusty star-forming\ngalaxies. We use the star-formation models of Leitherer \\& Heckman (1995) to\nplace the galaxies on the Madau Plot, and then examine the consequences\nof this interpretation in the context of the wider galaxy formation\npicture. In Section 3.2 we investigate the alternative possibility that the \nsources are dust-enshrouded AGNs. \n\n\\subsection{The SCUBA sources as star-forming galaxies}\n\nThe majority of local ULIRGs appear to be star-forming galaxies and not \ndust-enshrouded AGN (Sanders et al.\\ 1988a, Genzel et al.\\ 1988). Furthermore, \nthe temperatures of the SCUBA sources inferred in Section 2 ($T \\sim 40$\\,K) \nare close to, although systematically slightly cooler than, those of local \nstar-forming ULIRGs.  Locally, dust-enshrouded AGN like Mrk 231 tend to have \nhigher dust temperatures than dust-enshrouded starbursts like Arp 220 \n(Sanders et at.\\ 1988a); however, note that some dusty high-redshift quasars \nappear to be fairly cold: see Benford et al.\\ (1998). Hence, it seems \nreasonable to investigate the possibility that the SCUBA sources are\nhigh-redshift star-forming galaxies.\n\n\\subsubsection{Leitherer-Heckman models}\n\nIn order to compute the cosmological star-formation rate associated with the \nSCUBA sources at high redshift, we need a recipe to convert far-infrared \nluminosities to star-formation rates for individual sources.\n\nThe transformation between these two quantities is not straightforward to \ndetermine observationally even for local ULIRGs because of the high internal \nextinction along our lines to the galaxy centers. For example, \neven the near-infrared 2.2-$\\mu$m Br$\\gamma$ line strength--far-infrared\nluminosity correlation (Goldader et al.\\ 1997a,b), which is usually very \nreliable, breaks down in ULIRGs at very high luminosities, presumably due to \ninternal extinction. We therefore need to compute this transformation using \nmodels (Leitherer \\& Heckman 1995).\n\n\\begin{table*} \n\\caption{Comparison between observations and models. All the numbers \nrepresent the predicted source counts or background flux for\nmodel ``0'' that are appropriate to the luminosity function defined by\nthe parameters $L_{*}$, $T$, $\\sigma$, $z_1$, and $z_2$, relative to the \nobserved counts and background intensities listed in Table\\,1.\nThe model parameters are listed in condensed form in the model name, which\ntakes the general form log$_{10}$($L^*_{60}$)\/$T$\/$z_1$\/$z_2$\/$\\sigma$. The \nfigure panel in which the constraints for each model are imposed are \nlisted in the second column.  \nA value less than $10^{-10}$ is listed as $\\sim 0$ in the Table.\nThe errors in these quantities are listed in Table\\,3. \nAll the models have been selected {\\it a priori} to give the correct \n850-$\\mu$m counts. The comments refer to the selection or rejection of \nmodels based on the listed values. The range of acceptable values and a \ndescription of the numerical code values are given in Table\\,3. The \n140-$\\mu$m and 240-$\\mu$m background values of \nSchlegel et al.\\ (1998), the 175-$\\mu$m counts of Lagache\net al.~(1998), and the 450-$\\mu$m counts of Smail et al.~(1997)\nare fitted. \n} \n{\\vskip -2.75mm}\n{$$\\vbox{\n\\halign {\\hfil #\\hfil && \\quad \\hfil #\\hfil \\cr\n\\noalign{\\hrule \\medskip}\nModel & Figure \n         & 2.8-mm & 450-$\\mu$m & 175-$\\mu$m\n         & 240-$\\mu$m & 140-$\\mu$m & comments &\\cr\n       &  & counts & counts & counts & background & background & (See\nTable\\,3)&\\cr\n\\noalign{\\smallskip \\hrule \\smallskip}\n\\cr\n\n10\/70\/3\/5\/0.5 & 2a & $\\sim 0$\n        & $7.2 \\times 10^{-5}$ \n        & $0.18$  \n        & $1.5 \\times 10^{10}$ & $7.5 \\times 10^9$ & (4$^{-}$56) &\\cr  \n10.70\/3\/5\/0.9 & 2a & $0.0019$\n        & $0.082$\n        & $2.5$  \n        & $110$ & $55$ & (3$^{0+}$56) &\\cr\n11\/70\/3\/5\/0.5 & 2b & $3.2 \\times 10^{-9}$\n        & $8.1 \\times 10^{-4}$\n        & $0.40$  \n        & $2.3 \\times 10^{5}$ & $1.1 \\times 10^{5}$ & (56) &\\cr\n11\/70\/3\/5\/0.9 & 2b & $0.011$\n        & $0.17$\n        & $3.9$ \n        & $15$ & $7.4$ & (356) &\\cr\n12\/70\/3\/5\/0.5 & 2c & $1.3 \\times 10^{-6}$\n        & 0.0090 \n        & $1.0$ \n        & $178$ & $87$ & (3$^{+}$56) &\\cr\n12\/70\/3\/5\/0.9 & 2c & $0.067$\n        & $0.36$\n        & $6.0$ \n        & $6.3$ & $3.1$ & (356$^{0+}$) &\\cr\n13\/70\/3\/5\/0.1 & 2d & $\\sim 0$\n        & $\\sim 0$\n        & $3.2 \\times 10^{-6}$ \n        & $2.9 \\times 10^{13}$ & $1.9 \\times 10^{13}$ & (456) &\\cr\n13\/70\/3\/5\/0.5 & 2d & $4.4 \\times 10^{-4}$\n        & $0.094$\n        & $3.0$ \n        & $5.8$ & $2.8$ & (356$^{0+}$) &\\cr\n13\/70\/3\/5\/0.9 & 2d & $0.35$\n        & $0.71$\n        & $9.6$ \n        & $7.2$ & $3.5$ & (2$^{+}$356) &\\cr\n10\/70\/2\/4\/0.5 & 3a & $\\sim 0$\n        & $2.3 \\times 10^{-4}$\n        & $32$ \n        & $1.9 \\times 10^{10}$ & $1.6 \\times 10^{10}$ & (356) &\\cr\n10\/70\/2\/4\/0.9 & 3a & $0.0014$\n        & $0.12$\n        & $14$  \n        & $150$ & $120$ & (356) &\\cr\n11\/70\/2\/4\/0.5 & 3b & $1.5 \\times 10^{-9}$\n        & $0.0021$\n        & $20$ \n        & $3.0 \\times 10^{5}$ & $2.5 \\times 10^{5}$ & (356) &\\cr\n11\/70\/2\/4\/0.9 & 3b & $0.0090$\n        & $0.23$\n        & $14$ \n        & $20$ & $17$ & (356) &\\cr\n12\/70\/2\/4\/0.5 & 3c & $7.2 \\times 10^{-7}$\n        & $0.017$\n        & $14$ \n        & $230$ & $190$ & (356) &\\cr\n12\/70\/2\/4\/0.9 & 3c & $0.055$ \n        & $0.45$\n        & $16$ \n        & $8.3$ & $7.0$ & (356) &\\cr\n13\/70\/2\/4\/0.1 & 3d & $\\sim 0$\n        & $\\sim 0$\n        & $5.6 \\times 10^{5}$ \n        & $2.4 \\times 10^{13}$ & $2.1 \\times 10^{13}$ & (356) &\\cr\n13\/70\/2\/4\/0.5 & 3d & $3.0 \\times 10^{-4}$\n        & $0.15$\n        & $14$ \n        & $7.5$ & $6.4$ & (356) &\\cr\n13\/70\/2\/4\/0.9 & 3d & $0.3$\n        & $0.82$\n        & $18$ \n        & $9.5$ & $8.0$ & (356) &\\cr\n10\/70\/1\/3\/0.5 & 4a & $ \\sim 0$\n        & $8.8 \\times 10^{-4}$\n        & $3600$ \n        & $1.7 \\times 10^{10}$ & $2.4 \\times 10^{10}$ & (356) &\\cr\n10\/70\/1\/3\/0.9 & 4a & $0.0011$\n        & $0.17$\n        & $60$ \n        & $170$ & $230$ & (356) &\\cr\n11\/70\/1\/3\/0.5 & 4b & $7.6 \\times 10^{10}$\n        & $0.0054$\n        & $560$ \n        & $3.0 \\times 10^5$ & $4.0 \\times 10^5$ & (356) &\\cr\n11\/70\/1\/3\/0.9 & 4b & $0.0073$\n        & $0.31$\n        & $44$ \n        & $23$ & $32$ & (356) &\\cr\n12\/70\/1\/3\/0.5 & 4c & $4.5 \\times 10^{-7}$\n        & $0.034$\n        & $120$ \n        & $250$ & $350$ & (356) &\\cr\n12\/70\/1\/3\/0.9 & 4c & $0.047$\n        & $0.55$\n        & $34$ \n        & $10$ & $14$ & (356) &\\cr\n13\/70\/1\/3\/0.1 & 4d & $ \\sim 0 $\n        & $ \\sim 0$ \n        & $3.1 \\times 10^{10}$ \n        & $3.0 \\times 10^{11}$ & $4.3 \\times 10^{11}$ & (356) &\\cr\n13\/70\/1\/3\/0.5 & 4d & $2.2 \\times 10^{-4}$\n        & $0.21$\n        & $41$ \n        & $8.8$ & $12$ & (356) &\\cr\n13\/70\/1\/3\/0.9 & 4d & $0.27$\n        & $0.94$\n        & $29$ \n        & $12$ & $16$ & (2$^{+}$356) &\\cr\n10\/40\/3\/5\/0.5 & 5a & $1.0 \\times 10^{-8}$             \n        & $9.2 \\times 10^{-6}$\n        & $1.1 \\times 10^{-8}$ \n        & $1.1 \\times 10^{6}$ & $7.1 \\times 10^{5}$ & (456) &\\cr \n10\/40\/3\/5\/0.9 & 5a & $0.018$\n        & $0.033$\n        & $0.0067$ \n        & $3.6$ & $0.23$ & (45) &\\cr\n11\/40\/3\/5\/0.5 & 5b & $2.1 \\times 10^{-6}$\n        & $2.1 \\times 10^{-4}$\n        & $1.4 \\times 10^{-6}$ \n        & $200$ & $14$ & (456) &\\cr\n11\/40\/3\/5\/0.9 & 5b & $0.087$\n        & $0.092$\n        & $0.034$ \n        & $0.99$ & $0.067$ & (45$^{+}$) &\\cr\n12\/40\/3\/5\/0.5 & 5c & $3.9 \\times 10^{-4}$\n        & $0.0050$\n        & $1.8 \\times 10^{-4}$ \n        & $1.7$ & $0.12$ & (45$^{0+}$) &\\cr\n12\/40\/3\/5\/0.9 & 5c & $0.40$\n        & $0.25$\n        & $0.17$ \n        & $0.84$ & $0.056$ & (4$^{-}$5$^{+}$) &\\cr\n13\/40\/3\/5\/0.1 & 5d & $\\sim 0$\n        & $3.3 \\times 10^{-18}$\n        & $\\sim 0$ \n        & $1.14$ & $0.076$ & (45$^{+}$) &\\cr\n13\/40\/3\/5\/0.5 & 5d & $0.053$\n        & $0.11$\n        & $0.019$ \n        & $0.50$ & $0.034$ & (4) &\\cr\n13\/40\/3\/5\/0.9 & 5d & $1.6$\n        & $0.63$\n        & $0.82$ \n        & $1.8$ & $0.12$ & (1$^{0+}$3$^{+}$5$^{0+}$) &\\cr\n10\/40\/2\/4\/0.5 & 6a & $2.96 \\times 10^{-9}$\n        & $8.6 \\times 10^{-5}$\n        & $5.7 \\times 10^{-4}$ \n        & $1.1 \\times 10^{6}$ & $2.1 \\times 10^{5}$ & (456) &\\cr\n10\/40\/2\/4\/0.9 & 6a & $0.012$\n        & $0.068$\n        & $0.22$ \n        & $6.6$ & $1.2$ & (56$^{+}$) &\\cr\n11\/40\/2\/4\/0.5 & 6b & $8.7 \\times 10^{-7}$\n        & $0.0012$\n        & $0.0058$ \n        & $280$ & $51$ & (4$^{0-}$56) &\\cr\n11\/40\/2\/4\/0.9 & 6b & $0.065$\n        & $0.16$\n        & $0.54$ \n        & $2.0$ & $0.36$ & (5$^{0+}$) &\\cr\n12\/40\/2\/4\/0.5 & 6c & $2.2 \\times 10^{-4}$\n        & $0.017$\n        & $0.062$ \n        & $3.0$ & $0.54$ & (4$^{0-}$5$^{0+}$) &\\cr\n12\/40\/2\/4\/0.9 & 6c & $0.33$\n        & $0.38$\n        & $1.4$ \n        & $1.77$ & $0.32$ & (3$^{0+}$5$^{0+}$) &\\cr\n13\/40\/2\/4\/0.1 & 6d & $\\sim 0$\n        & $\\sim 0$\n        & $2.0 \\times 10^{-9}$ \n        & $1.1$ & $0.020$ & (45$^{+}$) &\\cr\n13\/40\/2\/4\/0.5 & 6d & $0.040$\n        & $0.22$\n        & $0.70$ \n        & $1.1$ & $0.19$ & (5$^{+}$) &\\cr\n13\/40\/2\/4\/0.9 & 6d & $1.4$\n        & $0.84$\n        & $3.7$ \n        & $4.0$ & $0.72$ & (1$^{0+}$2$^{+}$35) &\\cr\n10\/40\/1\/3\/0.5 & 7a & $9.4 \\times 10^{-10}$\n        & $8.0 \\times 10^{-4}$\n        & $3.7$ \n        & $9.6 \\times 10^{5}$ & $4.3 \\times 10^{5}$ & (356) &\\cr\n10\/40\/1\/3\/0.9 & 7a & $0.0086$\n        & $0.13$\n        & $3.6$ \n        & $11$ & $4.8$ & (356) &\\cr\n11\/40\/1\/3\/0.5 & 7b & $4.0 \\times 10^{-7}$\n        & $0.0062$\n        & $3.0$ \n        & $323$ & $147$ & (356) &\\cr\n11\/40\/1\/3\/0.5 & 7b & $0.051$\n        & $0.28$\n        & $4.5$ \n        & $3.5$ & $1.6$ & (356$^{0+}$) &\\cr\n12\/40\/1\/3\/0.1 & 7c & $ \\sim 0$\n        & $\\sim 0$\n        & $140$ \n        & $2.8 \\times 10^{17}$ & $1.3 \\times 10^{17}$ & (356) &\\cr\n12\/40\/1\/3\/0.5 & 7c & $1.4 \\times 10^{-4}$\n        & $0.52$\n        & $3.0$ \n        & $4.6$ & $2.1$ & (356$^{0+}$) &\\cr\n12\/40\/1\/3\/0.9 & 7c & $0.28$\n        & $0.56$\n        & $6.5$ \n        & $3.3$ & $1.5$ & (356$^{0+}$) &\\cr\n13\/40\/1\/3\/0.1 & 7d & $\\sim 0$\n        & $6.1 \\times 10^{-6}$\n        & $2.2$ \n        & $1.2$ & $0.54$ & (3$^{0+}$5$^{+}$) &\\cr\n13\/40\/1\/3\/0.5 & 7d & $0.033$\n        & $0.42$\n        & $5.4$ \n        & $2.0$ & $0.92$ & (35$^{0+}$6$^{+}$) &\\cr\n13\/40\/1\/3\/0.9 & 7d & $1.3$\n        & $1.1$\n        & $10$ \n        & $8.0$ & $3.6$ & (356) &\\cr\n\\noalign{\\smallskip \\hrule}\n\\noalign{\\smallskip}\\cr}}$$}\n\\end{table*}\n\n\\begin{table*}\n\\caption{Fractional uncertainties in the background and source counts \nvalues used to accept or reject the models listed in Table\\,2. The acceptable \nranges of values are used to make the selection, and the relevant cases are \ndescribed by numerical codes in the last column of Table\\,2. A code is \nshown if the model is rejected on the grounds of: (1) overproduction of \nthe 2.8-mm count; (2) overprediction of the 450-$\\mu$m count; (3) \noverproduction of the 175-$\\mu$m count; (4) underprediction of the \n175-$\\mu$m count; (5) overprediction of the {\\it COBE} 240-$\\mu$m background; \nand (6) overprediction of the {\\it COBE} 140-$\\mu$m background. Although \na model that underpredicts the 175-$\\mu$m count is not formally excluded, \nsuch a model requires that the 175-$\\mu$m counts and 850-$\\mu$m counts come\nfrom entirely different populations of galaxies. This is not impossible, but we \nregard it as unlikely; we choose a factor of ten discrepancy as the cutoff\nbetween a model being acceptable and unacceptable.   \nIn the last column of Table\\,2, superscripts 0, + or $-$ indicate that \nthe exclusion applies only in that scenario, corresponding to the \nvalues listed below. The absence of a superscript implies that the \nmodel is rejected in all three scenarios.} \n{\\vskip -0.75mm}\n{$$\\vbox{\n\\halign {\\hfil #\\hfil && \\quad \\hfil #\\hfil \\cr\n\\noalign{\\hrule \\medskip}\nModel & 2.8-mm\n          & 450-$\\mu$m\n         & 175-$\\mu$m  & 240-$\\mu$m & 140-$\\mu$m &\\cr\n       & counts & counts & counts & background & background & &\\cr\n\\noalign{\\smallskip \\hrule \\smallskip}\n\\cr\nFractional Error in ratio & $-$ & $-$ & 0.15 & 0.24 & 0.41 &\\cr\n & & & & & & & &\\cr\nRange of Acceptability (``0'' models) &\n$<1.0$ & $<1.0$ &   [0.85,1.2] &  $<1.2$ & $<1.4$ &\\cr\nRange of Acceptability (``$-$'' models) &\n$<2.4$ & $<2.4$ &   [2.0,2.8] &  $<3.0$ & $<3.4$ &\\cr\nRange of Acceptability (``+'' models) &\n$<0.63$ & $<0.63$ & [0.54,0.73] &  $<0.78$ & $<0.89$ &\\cr\n & & & & & & & &\\cr\n\\noalign{\\smallskip \\hrule}\n\\noalign{\\smallskip}\\cr}}$$}\n\\end{table*}\n\nIn Table 5 we list a number of star-formation models that we investigate in \nfurther detail. Note that we use capital letters to represent galaxy formation \nmodels (Section 2) and roman numerals to represent the different star-formation \nmodels. There is insufficient information to determine accurately the appropriate \nset of input parameters to the star-formation models for the SCUBA sources, \nand even for local ULIRGs in many cases. The more important parameters are:\n\\begin{enumerate}\n\\item the mode of star formation.  For example, the star formation may occur\ncontinuously, as an instantaneous burst, or with a more complex time\ndependence, for example an exponential decay. We investigate both the \ninstantaneous (Models I and II) and continuous (models III through X) cases.\nObservations of the core of Arp 220 (Mouri \\& Taniguchi 1992;\nPrestwich, Joseph, \\& Wright 1994; Armus et al.\\ 1995; Larkin et al.\\ 1995,\nScoville et al.\\ 1998), combined with the inferred presence of ionizing sources \nthere (Larkin et al.\\ 1995; Kim et al.\\ 1995; Goldader et al.\\ 1995), indicate that \nthe continuous models offer a more plausible description of the star formation \nin this well studied ULIRG;\n\\item the stellar initial mass function (IMF). The precise form of the IMF in \nstarburst galaxies is very much an open question: see Leitherer (1998) for a \nreview. It appears that the IMF of the most luminous star clusters in the Milky \nWay and the Magellanic Clouds follows closely the Salpeter form (Hunter et al.\\ \n1995; Hunter et al.\\ 1997; Massey et al.\\ 1995a). However, the field-star IMF may \nbe significantly steeper than the cluster IMF (Massey et al.\\ 1995b),\nand there is some evidence (Meurer et al.\\ 1995) that the most massive stars\nin starbursts form in environments that are more similar to the field than to \nthe cores of the luminous star clusters studied above. There are \nhence few direct observations to guide us to the correct IMF in starburst \ngalaxies, and we therefore consider four different scenarios in Models III to X.\nLeitherer \\& Heckman (1995) consider power-law IMFs, and \nwe investigate various possible combinations of\nthe upper and lower mass cutoffs and the slope of this power law.\nNote that if the SCUBA sources end up as elliptical galaxies (Section 3.1.3; \nBlain et al. 1999a; Lilly et al.\\ 1998), a lower limit to the IMF at \n$M_{\\rm l}$ = 3\\,M${_\\odot}$ is suggested, in agreement with the value suggested \nby Zepf \\& Silk (1996).\n\\item the inital gas metallicity.  We assume a metallicity of twice solar.\nThis is close to the metallicities of the most luminous elliptical\ngalaxies (e.g.~Faber 1973, Vader 1986); \n\\item the age at which we observe the star clusters.  We investigate the\ncases where we observe the galaxies at between 10$^8$ and 10$^{8.5}$\nyears after the onset of star formation.  Fortunately, most of the\nproperties of the starburst, like the total bolometric luminosity, reach\na plateau soon after the onset of star formation, and so our results do not \ndepend strongly on this parameter.  The median total amount\nof gas consumed by a $L_{*}$ galaxy 10$^{8.5}$ years after the onset\nof star-formation is 7 $\\times 10^{10}$\\,M$_\\odot$ in our models.  This is \nconsistent with the progenitor galaxies to the SCUBA sources being gas-rich \nnormal galaxies; \n\\item the effects of extinction.  Since we are only attempting to model\nthe far-infrared and submillimetre properties of the starburst, we\ncan assume that the galaxies are optically thin and do not need to\nmake any corrections for extinction. We assume that the dust absorbs\nand reradiates all the energy produced by the starburst.\n\\end{enumerate} \n\nFrom the seventh column of Table 5 it is immediately apparent that there is \nmore than an order of magnitude of uncertainty in the transformation from \nfar-infrared luminosity to star-formation rate, due to the uncertainty in the\nstar-formation parameters.  The constant conversion factor of 2.2 $\\times$\n10$^9$\\,L$_{\\odot}$\\,M$_{\\odot}^{-1}$\\,yr (Rowan-Robinson et al.\\ 1997), \nused by Blain et al.\\ (1999a), corresponding to 0.22 in the seventh column of\nTable 5, is bracketed by our results.\n\n\\subsubsection{The Madau plot}\n\nWe combine our redshift-dependent luminosity functions (Models B, F and G) \nwith the star-formation parameters for the models listed in Table 5 \n(Models I to X) to compute the comoving star formation rate in the SCUBA \nsources. The results are listed in Table 6.  We can then put the SCUBA \nsources on the the Madau plot: see Figs\\,9, 10 and 11. The other points on the \nMadau plot all come from optically-selected samples. As there is no luminosity \nevolution in the models between $z_1$ and $z_2$, the comoving star-formation \nrate is constant between these redshifts, and so the lines on the Madau plot are \nhorizontal. \n\nThe figures show that the uncertainty in determining where the SCUBA \nsources lie on the Madau plot is huge, more than an order of magnitude, \neven if we have specified the correct luminosity--redshift distribution model B, \nF or G. This uncertainty is solely due to our lack of knowledge regarding the \nstar-formation parameters, as discussed in Section 3.1.1. For Model B, and \npossibly Model F, if the true cosmic star-formation rate in the SCUBA sources\nis towards the higher end of our permitted range, then they dominate the \nstar-formation rate of the Universe: this is essentially the scenario proposed\nby Blain et al.\\ (1999a) and Hughes et al.\\ (1998). If the true cosmic star-formation \nrate in the SCUBA sources is towards the lower end of our range, then\nthey do not contribute significantly to the star-formation rate of the Universe \nat any redshift. In general, the instantaneous models \npredict higher star-formation rates.  This is because more stars\nneed to be formed to produce a given bolometric luminosity we observe\nmore than 10$^8$ years after the starburst.\n\nIt is interesting to note that the IMF proposed by Zepf \\& Silk (1996) for \nelliptical galaxies, if valid for the SCUBA sources, results in them being at \nthe extreme low end of our proposed range.  This is because these models \nunderproduce low-mass stars, and so result in a low star-formation rate for \na given amount of bolometric luminosity: the low-mass stars, when young, \ndo not contribute significantly to the bolometric luminosity. The implication \nhere is that if SCUBA sources evolve into elliptical galaxies, then they do \nnot contribute significantly to the star-formation rate of the Universe at \nany redshift given our models of the luminosity function. \n \n\\begin{figure}\n\\begin{center}\n\\epsfig{file=fig8.ps, width=8.65cm}\n\\end{center}\n\\caption{The lower limit on the integral in equation (5) as a function of the \ngalaxy dust temperature $T$, normalized to its value for $T=38$\\,K, predicted \nfrom {\\it IRAS} and {\\it ISO} counts by Blain et al.\\ (1999a).} \n\\end{figure} \n\nThe broadband optical colours of the SCUBA sources are not significantly \ndifferent from those of normal field galaxies (Smail et al.\\ 1998). Furthermore, \ntwo of the three local ULIRGs studied at ultraviolet wavelengths with {\\it HST} \nby Trentham, Kormendy \\& Sanders (1998) would also have broadband colours \nsimilar to normal field galaxes if they were placed at high redshift. Therefore,\nSCUBA sources cannot be identified as submillimetre-luminous galaxies \nbased on broadband optical colours alone. The star-formation rates given \nin Table 5 are far higher than the rates in normal galaxies. Therefore we need \nto treat the SCUBA sources as a separate population on the Madau plot. This \nis particularly important if the SCUBA sources contribute significantly to the\nstar-formation rate of the Universe at any redshift. \n\n\\begin{table}\n\\caption{Predicted 850-$\\mu$m background intensities. The observed\n850-$\\mu$m background intensity is $0.55 \\pm 0.15$\\,nW\\,m$^{-2}$\\,sr$^{-1}$ \n(Fixsen et al. 1998).} \n{$$\\vbox{\n\\halign {\\hfil #\\hfil && \\quad \\hfil #\\hfil \\cr\n\\noalign{\\hrule \\medskip}\nModel  & Background \/ & Model  & Background \/\\cr\n       & nW\\,m$^{-2}$\\,sr$^{-1}$  &  & nW\\,m$^{-2}$\\,sr$^{-1}$\\cr\n\\noalign{\\smallskip \\hrule \\smallskip}\n\\cr\nA & 3.40 & E & 1.71 \\cr\nB & 0.85 & F & 0.71 \\cr\nC & 1.32 & G & 0.34 \\cr\nD & 1.19 & & \\cr\n\\noalign{\\smallskip \\hrule}\n\\noalign{\\smallskip}\\cr}}$$}\n\\end{table}\n\n\\begin{table*}\n\\caption{Properties of star-formation models. \n$\\alpha$ is the slope of the stellar IMF and $M_{\\rm u}$ and  $M_{\\rm l}$\nare the lower and upper mass cutoffs.\nThe final two columns are derived from the results of Leitherer \\& Heckman\n(1995).  The star-formation\nrates (SFR) as a function of 60-$\\mu$m luminosity come from Figs\\,7 and 8,\nassuming a temperature of 70\\,K.  The metal masses $M_Z$ come from \nFigs\\,53 and 54 of Leitherer \\& Heckman (1995), assuming that the mass of \nmetals produced is equal to the mass returned by winds and supernovae.\nAll models assume an initial metallicity of twice solar.\n} \n{$$\\vbox{\n\\halign {\\hfil #\\hfil && \\quad \\hfil #\\hfil \\cr\n\\noalign{\\hrule \\medskip}\nModel & SF profile & log$_{10}$(age\/yr) &\n      $\\alpha$ & $M_{\\rm u}$ \/ M$_\\odot$ & $M_{\\rm l}$ \/ M$_\\odot$ & \nSFR \/ ($L_{60} \/ 10^{9} {\\rm L}_{\\odot}$) M$_\\odot$\\,yr$^{-1}$ \n& $M_Z$ \/ ($L_{60} \/ 10^{9} {\\rm L}_{\\odot}$) M$_\\odot$ &\\cr\n\\noalign{\\smallskip \\hrule \\smallskip}\n\\cr\nSF I    & Instantaneous & 8.0 & 2.35 & 100 & 1 & 1.0 & $4.0 \\times 10^7$ &\\cr\nSF II   & Instantaneous & 8.5 & 2.35 & 100 & 1 & 0.81 & $1.0 \\times 10^8$ &\\cr\nSF III  & Continuous    & 8.0 & 2.35 & 100 & 1 & 0.11 & $3.5 \\times 10^6$ &\\cr\nSF IV   & Continuous    & 8.5 & 2.35 & 100 & 1 & 0.072 & $7.2 \\times 10^6$ &\\cr\nSF V    & Continuous    & 8.0 & 2.35 &  30 & 1 & 0.15 & $4.1 \\times 10^6$ &\\cr\nSF VI   & Continuous    & 8.5 & 2.35 &  30 & 1 & 0.12 & $1.0 \\times 10^7$ &\\cr\nSF VII  & Continuous    & 8.0 & 3.3  & 100 & 1 & 0.34 & $8.0 \\times 10^5$ &\\cr\nSF VIII & Continuous    & 8.5 & 3.3  & 100 & 1 & 0.25 & $1.6 \\times 10^6$ &\\cr\nSF IX   & Continuous    & 8.0 & 2.35 & 100 & 3 & 0.056 & $3.5 \\times 10^6$ &\\cr\nSF X    & Continuous    & 8.5 & 2.35 & 100 & 3 & 0.043 & $7.2 \\times 10^6$ &\\cr\n\\noalign{\\medskip \\hrule}\n\\noalign{\\smallskip}\\cr}}$$}\n\\end{table*}\n\n\\subsubsection{Why do the result differ from those of other authors} \n\nBoth Blain et al.~(1999a) and Hughes et al.~(1998) derive global star-formation rates\nat least an order of magnitude higher than we derive in the current paper.\nThere are two sources of discrepancy.\n\\vskip 1pt\n\\noindent (i) differences in star-formation rates. \nFor example Blain et al.~(1999a) use a value of $M_{\\rm l}$ below 1 M$_\\odot$ and\nconsequently assume star-formation rates that are towards the upper end of our\nconsidered range.\n\\vskip 1pt\n\\noindent (ii) differences in the assumed luminosity-redshift distribution, which can \nbe broadly split further into (a) differences in the characteristic luminosity of the\nsources who dominate the contribution to the SCUBA counts , and (b) difference in the\nnormalization of the luminosity function at a given redshift.  Effect (iia) is not a\nmajor source of discrepancy between our results and those of Blain et al.~(1999a) --- in\nboth cases, most of the star formation occurs in very luminous sources\nwith $L_{60} > 10^{11}$\\,L$_{\\odot}$.  Effect (iib) is a much more substantial source\nof discrepancy.  Blain et al.~(1999a) assume a redshift-dependent Saunders luminosity function at\nhigh redshift which is related to the local 60-$\\mu$m luminosity function by simple luminosity\nevolution.  We assume a Gaussian luminosity function with no evolution over some specified\nredshift range.  Our objects, when evolved to, $z=0$ are early-type stellar populations, \nquite unrelated to the objects which dominate the local 60-$\\mu$m luminosity function.  \nWe consequently derive a far lower\nnormalization to our luminosity functions than do Blain et al.~(1999a).\nThe present observations do not permit us to distinguish \nbetween these models, but this should be a straightforward exercise when a \nsignificantly complete redshift distribution for the SCUBA sources is known. \n\nIn addition, Eales et al.~(1998) argue that at least 10 percent\nof the stars in the Universe\nformed in SCUBA sources since they produce about\n10 percent \nof the extragalactic background light.  This number is much closer to the\nnumbers presented in this paper.  Nevertheless, the assumption that the SCUBA sources\ncontribute the same fraction of the submillimeter background at all wavelengths, on which\nthe Eales et al.~calculation is based, appears to be inconsistent with the formulation that\nwe use, when the BIMA 2.8-mm counts, \nISO 175-$\\mu$m counts, and COBE 850-$\\mu$m background\nare all considered in conjuction.  Furthermore, it is unclear how we should relate\nstar-formation rates derived from optical or ultraviolet luminosities of normal field\ngalaxies to star-formation rates derived from submillimetre fluxes of the SCUBA sources.  \n\n\\begin{figure}\n\\begin{center}\n\\vskip -2mm\n\\epsfig{file=fig9.ps, width=8.65cm}\n\\end{center}\n\\vskip -5mm\n\\caption{The comoving star-formation density of\nthe Universe contained in the SCUBA sources when their\nluminosity-redshift distribution is as in Model B.\nThe eight dashed lines represent the SFR histories for models\n(in ascending order) X, IX, IV, III, VI, V, VIII, VII, II and I.\nThe other points come from:\nfilled triangle -- Gallego et al.~(1996);\nopen triangle -- Treyer et al.~(1998);\nopen circle -- Tresse \\& Maddox (1998);\nstars -- Lilly et al.~(1996);\nopen hexagons -- Hammer \\& Flores (1998);\nfilled squares - Connolly et al.~(1997);\nfilled circles - Madau et al.~(1996);\nopen squares - Pettini et al.~(1998; these include a global correction\nfor dust extinction).  The recent work of Glazebrook et al.~(1999) \nsuggests a SFR almost coincident with the $z=0.85$ point of Hammer\n\\& Flores (1998).} \n\\end{figure} \n\n\\begin{figure}\n\\begin{center}\n\\vskip -2mm\n\\epsfig{file=fig10.ps, width=8.65cm}\n\\end{center}\n\\vskip-5mm\n\\caption{\nAs Figure 9, but for model F.  The symbols\nhave the same meanings and the lines are in the same order.\n}\n\\end{figure} \n\n\\begin{figure}\n\\begin{center}\n\\vskip-2mm\n\\epsfig{file=fig11.ps, width=8.65cm}\n\\end{center}\n\\vskip-5mm\n\\caption{\nAs Figure 9, but for model G.  The symbols\nhave the same meanings and the lines are in the same order.\n}\n\\end{figure} \n\n\\subsubsection{The fate of the star-forming galaxies}\n\nWe have hinted that the SCUBA sources could evolve into elliptical galaxies.\nLocal ULIRGs have gas densities that are similar to the core stellar densities \nin elliptical galaxies (Kormendy \\& Sanders 1992, Doyon et al.\\ 1994).\nIf the SCUBA sources have similar morphologies to local ULIRGs, we \nmight then expect them to evolve into elliptical galaxies.   \n\nIn Table 7 we present the density parameter in stars produced by the SCUBA \nsources, in our luminosity-function and star-formation models. For most models, \nparticularly those with IMFs appropriate to elliptical galaxies (models IX and\nX), these numbers are very small as compared with the stellar density \ncontained in the local spheroid stellar population $\\Omega_{\\rm sph}$,\nthat is elliptical galaxies and bulges: $\\Omega_{\\rm sph} = 0.0036$ \n(Fukugita, Hogan \\& Peebles 1998). \nIn Models IX and X, between 1 and 4\\,per cent of $\\Omega_{\\rm sph}$\nformed in the luminous high-redshift SCUBA sources, and slightly more if a \nsolar-neighbourhood IMF (Models III and IV) is assumed. These numbers are \nsufficiently low that a scenario in which all the SCUBA sources evolve into \nelliptical galaxies is consistent with galaxy formation models that predict\nlow-redshift elliptical formation (Kauffmann 1996; Kauffmann, Charlot \\& White \n1996; Kauffmann \\& Charlot 1998).  They are also low enough to be\nconsistent with the observed paucity of red galaxies in the Hubble Deep Field \nand the consequent interpretation that less than 30\\,per cent of field ellipticals\nformed at high redshift (Zepf 1997; Barger et al.\\ 1998b).  \n\nVarious lines of argument suggest that the elliptical galaxies in clusters are \nvery old. Not only did the stars form a long time ago (Ellis et al.\\ 1997; \nStanford et al.\\ 1998; Kodama et al.\\ 1998), but it appears that in the richest \nclusters the most luminous elliptical galaxies themselves were assembled by \n$z \\sim 1$ (Trentham \\& Mobasher 1998). It is further possible that most 3C radio \ngalaxies are cluster ellipticals in the process of formation (Best, Longair \\& \nRottgering 1998). This leads to a natural question: are the SCUBA galaxies \nforming cluster ellipticals?  Low-redshift cluster ellipticals are\nhighly clustered, with a bias of about 4, and an even greater bias at high redshifts\n(Fry 1996; Mo \\& White 1996). In comparison, the reasonably uniform detection\nrate of SCUBA galaxies in the fields studied by Smail et al.\\ (1998) suggests \nthat this is unlikely. \nThese fields contained low-redshift clusters (which magnify the background\nSCUBA sources through gravitational lensing), but these low-redshift\nclusters are unrelated to the hypothesized ellipticals in formation that\nwe are discussing here. \nInstead, we propose that the SCUBA sources are a \nforming trace population of field ellipticals.  This is consistent with the \nconstraints outlined in the previous paragraph.  This is not to say that if we \nhappened to point SCUBA at a cluster in formation we would not detect a large \nnumber of galaxies.\n\n\\begin{table*} \n\\caption{Comoving star-formation rates in units of \nM$_\\odot$\\,yr$^{-1}$\\,Mpc$^{-3}$ in the three well fitting models of  \ndistant ULIRGs.\n}\n{$$\\vbox{\n\\halign {\\hfil #\\hfil && \\quad \\hfil #\\hfil \\cr\n\\noalign{\\hrule \\medskip}\nLF Model & SF I & SF II & SF III & SF IV & SF V & SF VI & SF VII & SF VIII & SF\nIX & SF X &\\cr\n\\noalign{\\medskip \\hrule \\smallskip}\n\\cr\nB & 0.097 & 0.078  & 0.011  & 0.0069 & 0.014  & 0.012  & 0.039 & 0.025 & 0.0064\n& 0.0041 &\\cr\nF & 0.042 & 0.034  & 0.0046 & 0.0030 & 0.0060 & 0.0050 & 0.017 & 0.010 & 0.0027\n& 0.0018 &\\cr\nG & 0.045 & 0.037 & 0.0050  & 0.0032 & 0.017 & 0.0054 & 0.018 & 0.011 & 0.0030 &\n 0.0019 &\\cr\n\\noalign{\\medskip \\hrule}\n\\noalign{\\smallskip}\\cr}}$$}\n\\end{table*}\n \n\\begin{table*} \n\\caption{The present-day values of the density parameter in stars $\\Omega_{*}$ \nproduced by each well fitting \nluminosity function (LF) model, in each star-formation model.} \n{$$\\vbox{\n\\halign {\\hfil #\\hfil && \\quad \\hfil #\\hfil \\cr\n\\noalign{\\hrule \\medskip}\nLF Model & SF I & SF II & SF III & SF IV & SF V & SF VI & SF VII & SF VIII & SF\nIX & SF X &\\cr\n\\noalign{\\medskip \\hrule \\smallskip}\n\\cr\nB & 0.0010 & 0.00082 & 0.00012 & 7.3 $\\times$ 10$^{-5}$  & 0.00015  & 0.00013 &\n0.00041 & 0.00026 & 6.7 $\\times$ 10$^{-5}$ & 4.3 $\\times$ 10$^{-5}$ &\\cr\nF & 0.00080 & 0.00064 & 8.7 $\\times$ 10$^{-5}$ & 5.7 $\\times$ 10$^{-5}$ & \n0.00011\n& 9.5 $\\times$ 10$^{-5}$  & 0.00032  & 0.00019 & 5.1 $\\times$ 10$^{-5}$ & 3.4\n$\\times$ 10$^{-5}$ &\\cr\nG & 0.0019 & 0.0016 & 0.00021 & 0.00014 & 0.00072  & 0.00023  & 0.00077 & 0.00047 \n& 0.00013 & 8.0 $\\times$ 10$^{-5}$ &\\cr\n\\noalign{\\medskip \\hrule}\n\\noalign{\\smallskip}\\cr}}$$}\n\\end{table*}\n\n\\begin{table*} \n\\caption{Cosmic enrichment from each well fitting model. The results are \nin units of the solar metallicity, assumed to be 0.0189 (Anders\n\\& Grevesse 1989). The redshift range is specified in the luminosity function \nmodel: see Table\\,2. All the enrichment due to distant ULIRGs is \ncompleted by the lower limit to this redshift range.} \n{$$\\vbox{\n\\halign {\\hfil #\\hfil && \\quad \\hfil #\\hfil \\cr\n\\noalign{\\hrule \\medskip}\nLF Model & $z$ range & SF I & SF II & SF III & SF IV & SF V & SF VI &\nSF VII & SF  VIII & SF IX & SF X &\\cr\n\\noalign{\\medskip \\hrule \\smallskip}\n\\cr\nB & $3<z<5$ & 0.12 & 0.29 & 0.010 & 0.021 & 0.012 & 0.030  & 0.0023 & 0.0047 & 0\n.010 & 0.021 &\\cr\nF & $2<z<4$ & 0.050 & 0.13 & 0.0044 & 0.0090 & 0.0051 & 0.012  & 0.0010 & 0.0020\n & 0.0044 & 0.0090 &\\cr\nG & $1<z<3$ & 0.055 & 0.14 & 0.0048 & 0.0098 & 0.0056 & 0.014  & 0.0011 & 0.0022\n & 0.0048 & 0.0097 &\\cr\n\\noalign{\\medskip \\hrule}\n\\noalign{\\smallskip}\\cr}}$$}\n\\end{table*}\n\nIt has been recently recognized that lyman-break galaxies are highly\nclustered at high redshift (Pettini et al.~1998), and so it is worth\ninvestigating a possible link between these objects and the SCUBA sources.\nLooking at the spectra of the two kinds of galaxies, we see that \nthat lyman-break galaxies and the SCUBA sources are very likely two completely\nseparate populations of objects (for example compare the 0.5 $\\mu$m\nspectrum of the lyman-break galaxy 1512-cB58 \nat $z=2.7$ taken by Pettini et al.~1998\nusing LRIS on Keck II with the 0.5 $\\mu$m spectrum of the SCUBA source\nSMM\\,J02399$-$0136 at $z=2.8$\ntaken by Ivison et al.~1998 using the MOS spectrograph\non the CFHT).\nHowever, while this observation is interesting, it does not rule out a\nhypothetical link since\nit is possible that one type of galaxy evolves into the other on\nshort timescales.\nMeasuring correlation functions would be the\nbest way of testing such a hypothetical link.  Unfortunately, the forty or\nso SCUBA sources found so far \ndo not have redshift measurements, so such an analysis is not\npossible at present.  Such a calculation will, however, be possible once\na large sample of SCUBA sources with measured redshifts is available.\n\nIf the elliptical galaxies that went through a submillimetre-luminous\nphase represent a sub-population, then their star-formation history \nmust be similar to that of the rest of the remaining field\nelliptical population. Otherwise a huge scatter in the stellar mass-to-light\nversus light correlation (Oegerle \\& Hoessel 1991) would be produced.\n\nA few ellipticals (e.g. Stockton et al.\\ 1995, Dunlop et al.\\ 1996) must have formed\nat high redshift and do not lie in very rich X-ray clusters. It is not obvious \nthat these galaxies will evolve into cluster ellipticals.  The existence of such \nobjects lends additional support to a scenario in which the SCUBA sources \nevolve into a trace sub-population of field elliptical galaxies. Furthermore, \nmany high-redshift quasars are surrounded by heavily enriched gas, and so there \nmust have been considerable star formation in their host galaxies at high \nredshift (Matteucci \\& Padovani 1993). \n \n\\subsubsection{Metal production}\n\nIn Table 8, we present the total amount of metals produced by the SCUBA \nsources for our models. The average metallicity of the Universe at $z=0$ is \npoorly known, but is probably about half solar -- see for example Section 5 of \nFukugita et al.\\ (1998) -- if the solar metallicity is 0.0189 (Anders \\& Grevesse \n1989), and is much larger than the values listed in Table 8. Hence, it appears \nthat a sufficiently small fraction of cosmic star-formation activity occurs in the \nSCUBA sources that they still may be a sub-population of elliptical galaxies \nundergoing a monolithic collapse at high redshift, without significantly \noverproducing the metal mass density of the Universe. \nOn the other hand,\nif {\\it all} elliptical galaxies formed via monolithic collapse\nat high redshift, then this would result in a metal mass density of the\nUniverse that is higher than that observed \n-- the ``cluster-field analogy'' of \nMadau 1997: see also Mushotzky \\& Loewenstein (1997) and Renzini (1997).\n\nFor comparison, if the enrichment of the Ly$\\alpha$ forest is regarded as a \nsignature of cosmic enrichment, then the metallicity of the intergalactic \nmedium at $z \\sim 3$ is about 10$^{-2.5}$ to 10$^{-2}$ solar (Cowie et al.\\ 1995;\nSongalia \\& Cowie 1996; Songaila 1997; Cowie \\& Songaila 1998), and may be \nhigher at lower redshift. \nThis value is close to the metallicities in Table 8. \nBut this similarity is perhaps not too meaningful because one would expect that\nmost of the metals produced in the SCUBA \ngalaxies would remain bound within the galaxies.  This is\nbecause ellipticals have deep \ngravitational potential wells and thus low ejection efficiencies (Nath \\& Chiba \n1995); based on their gas consumption alone, the SCUBA sources must have \nmasses in excess of 10$^{10}$\\,M$_{\\odot}$.  Hence, only a small fraction of the \nmetals should leak out into the intergalactic medium, and so the values \nlisted in Table 8 are best interpreted as\nupper limits when comparing with the intergalactic\nmedium metallicity, if the SCUBA sources are all at redshifts greater than\nthree. \nWe also note that most low-redshift elliptical galaxies have metal-poor \ninterstellar media: this is not what we would expect if the metals produced in the\nearly history of these galaxies remained bound to the galaxy, as we argue above. \nOne possible explanation of this apparent discrepancy is that \nthe elliptical galaxies accumulate substantial X-ray halos (e.g.~Forman, Jones \\& \nTucker 1985), which then strip the metals out of the centres of galaxies.  Another \npossible explanation is that the SCUBA sources evolve into the few local \nellipticals that {\\it do} have metal-rich interstellar media, for example \nCentaurus A.    \n \n\\subsection{The SCUBA sources as AGN}\n\nAn alternative interpretation is that the SCUBA sources derive their bolometric \nluminosities from dust-enshrouded AGN and not from star formation at all.  \nA number of lines of argument suggest that this may well be a plausible scenario.\n\nFirst, the one SCUBA-selected source that has been studied in detail \n(SMM\\,J02399$-$0136; Ivison et al.~1998) contains a powerful dust-enshrouded \nAGN. Note however that it is still possible for most of its bolometric luminosity \nto be produced in a starburst. The hyperluminous gravitationally lensed \ngalaxy IRAS F10214+4724 at $z=2.29$ (Rowan-Robinson et al.~1991; Lacy \net al.~1998 and references therein) also contains a dust-enshrouded AGN. \nThe other two known ultraluminous high-redshift dusty galaxies H\\,1413+117 \n(Barvainis et al.\\ 1995) and APM\\,08279+5255 (Irwin et al.\\ 1998; Lewis et al. 1998) \nalso contain powerful AGN. If these objects are at all typical of \nhigh-redshift submillimetre-luminous sources, then it may well be plausible \nthat a signficant fraction of their bolometric luminosities are powered by AGN as \nopposed to starbursts. \n \nA second line of argument is based on the observation that in local Universe, \nmassive dark objects (MDOs) -- probably supermassive black holes -- are \ninferred to reside in the centers of most nearby galaxies (Magorrian et al.\\ 1997), \nbased on gas- and stellar-dynamical measurements (Kormendy \\& Richstone \n1995). These MDOs are plausibly dead quasar engines that have run out of fuel.\n\nMagorrian et al.\\ (1997) show that the mass of the inferred MDO is well \ncorrelated with the luminosity of the spheroid stellar population in the host\ngalaxy. The total mass density in MDOs in the local Universe is about \n1.7 $\\times$ 10$^6$\\,M$_{\\odot}$\\,Mpc$^{-3}$ (Haehnelt et al.\\ 1998), about an \norder of magnitude greater than the inferred mass density of black holes that is \nrequired to explain the blue light of quasars (Phinney 1998, Haehnelt et al.\\\n1998), unless the accretion efficiency in quasars is much less than 1\\,per cent. \n\nOne interesting idea suggested by Haehnelt et al.\\ (1998) is that most \naccretion onto supermassive black holes in the centres of galaxies is obscured \nby dust.  If this is the case, then the presence of a population of dust-obscured \nAGN can explain the above discrepancy. The SCUBA sources would be \nnatural candidates for this population.  We use our luminosity functions to \ncalculate the comoving mass density of MDOs, $\\rho_{\\rm MDO}$ required to \ngenerate the observed bolometric luminosity of the SCUBA sources, assuming \naccretion at some efficiency $\\epsilon$ -- this is the accretion luminosity \ndivided by the Eddington luminosity:\n\\begin{equation} \n\\rho_{\\rm MDO} =  10^4 \\alpha \n          \\left( { {\\epsilon} \\over {0.1}}\\right)^{-1}\n          {\\rm M}_{\\odot} {\\rm Mpc}^{-3}. \n\\end{equation}\n$\\alpha = 3.8$, 1.6 and 1.8 in Models B, F and G respectively. \nThese numbers are all below the local mass density of MDOs.  \nTherefore it is plausible that all the SCUBA sources are AGN, but \nthey may only help to explain the discrepancy between the local density\nof MDOs and the inferred density of black holes required to explain the\nblue light of quasars if their accretion luminosity is significantly\nlower than 1\\,per cent of the Eddington value. Recent work by Almaini, \nLawrence \\& Boyle (submitted), based on the X-ray luminosity function and \nbackground confirms that a large fraction of the SCUBA sources could be \ndust-enshrouded AGN. \n\nA third, but weaker, line of reasoning is based on the analogy with the \nultraluminous $z=0.44$ cD galaxy IRAS\\,P09104$-$4109 (Kleinmann et al.\\ 1988), \nwhich with a bolometric luminosity of about $3 \\times 10^{13}$\\,L$_{\\odot}$ is \nby far the most luminous object detected at mid-infrared wavelengths at  \n$z<0.5$. It is at the centre of a very substantial cooling flow (Fabian \\& Crawford \n1995). Two of the cD galaxies in the lensing clusters studied by Smail et al.\\ \n(1998) were detected at 850\\,$\\mu$m (Edge et al. submitted), although they \nare not included in the counts presented by Smail et al.\\ (1997;\n1999). If the physical \nprocesses that make IRAS\\,P09104$-$4109 into a hyperluminous galaxy are \nrelated to its being in the center of a cluster, then we might expect the same \nprocesses in the cDs detected by SCUBA.  The bolometric luminosity of \nIRAS P09104$-$4109 appears to come from a powerful dust-enshrouded AGN \n(Kleinmann et al.\\ 1988), and an analogous mechanism could plausibly be \npowering the high-redshift SCUBA sources.\n\n\\section{Limitations of the present work and future prospects} \n\nThe main limitations of the present work are that: \n\\begin{enumerate}\n\\item we cannot determine whether the SCUBA sources are star-forming \ngalaxies or AGN. Clearly the implications for cosmology would be very \ndifferent for these two scenarios; \n\\item we cannot determine uniquely the redshift-dependent luminosity function \nof the SCUBA sources, either to tell which of Models B, F and G or a \ndifferent kind of model (Blain et al.\\ 1999a) are most correct; \n\\item we cannot determine the conversion factor to transform the far-infrared \nluminosity into a star-formation rate for the SCUBA sources to within one \norder of magnitude, even if all the far-infrared luminosity is assumed to be \ngenerated by star formation.\n\\end{enumerate} \n\nGiven these limitations, we suggest the following future studies to address \neach of the problems listed above: \n\\begin{enumerate}\n\\item Optical spectroscopic observations of SCUBA galaxies should be made to \nsearch for AGN, for example to determine the line ratios of hydrogen \nrecombination to forbidden lines (Sanders 1998b; Veilleux et al.\\ 1995; \nEvans 1996) and carry out spectral polarimetry (e.g.~Hines \\& Wills 1993,\nJanuzzi et al.\\ 1994). Note, however, that these measurements are extremely \ndifficult to carry out for very distant galaxies, and cannot be used to determine \nunambiguously whether most of the bolometric luminosity comes from a \nstarburst or an AGN, because of the huge amount of internal extinction\ntowards the galaxy centres at optical wavelengths. Genzel et al.\\ (1998) used \nthe ratio of high- to low-excitation mid-infrared emission lines in combination \nwith the strength of a 7.7-$\\mu$m PAH feature to search for AGN in local ULIRGs, \nbut it will be quite some time before such measurements become available for the \ndistant SCUBA sources. Crude interpretations can be made on the basis of \nsource temperatures and SEDs (Sanders et al.\\ 1998a), \nfor example compare the SEDs of Arp 220 and Mrk 231.\nPerhaps the best we can hope for in the near future is to match the\nSED of each SCUBA source to that of a plausible\nlow-redshift counterpart, for which mid-infrared observations have\nbeen used to determine a power source, and assume the high-redshift source \nis powered in the same way; \n\\item an accurate determination of the redshift-dependent luminosity function \nwill become available once redshifts for a significant number of SCUBA sources \nare obtained.  In addition, further surveys with SCUBA and other \nmillimetre\/submillimetre-wave detectors (Glenn et al.\\ 1998) should \nallow the luminosity function to be determined accurately (Blain 1998).\nFor many of our models (Table 8), the total star-formation rate in high-redshift \nULIRGs is greater than at low redshifts; a measurement of the redshift distribution \nwould allow this statement to be quantified far more accurately.\n\\item selecting star-formation parameters to use in the Leitherer \\& Heckman \nmodels is a difficult exercise.  This is a particular problem for the distant\nSCUBA galaxies, for which only very limited information about\ntheir global properties is available. Progress in this area would be possible if\nthe low-redshift remnants of the SCUBA galaxies were identified, and \ntheir stellar populations studied in detail in order to investigate their IMF.\nSome clues are given in Section 3.1, but the conclusions there are far\nfrom rigorous at this stage. \n\\end{enumerate} \n\nMore generally, placing the SCUBA galaxies in the context of the\ngalaxy-formation problem is clearly an important exercise. Measurements of the \nredshift distribution will be an crucial part of this.  For example, these \nmeasurements will let us see where the comoving bolometric luminosity density \nof the SCUBA sources peaks, relative to the peak in the comoving \nstar-formation rate in other galaxies (Madau et al.\\ 1996, Madau et al.\\ 1998, \nPettini et al.\\ 1998) and to the peak in the comoving AGN luminosity density at \nultraviolet (Boyle \\& Terlevich 1998) or radio (Dunlop 1998) wavelengths. \n\n\\section{Conclusions}\n\n\\begin{enumerate}\n\\item We identify various redshift-dependent luminosity functions that are \nconsistent with the 850-$\\mu$m SCUBA source counts and observations \nat other far-infrared and submillimetre wavelengths. Consistency can only be \nachieved if the 850-$\\mu$m SCUBA source counts are towards the lower end \nof the range suggested by Smail et al.\\ (1997).\nIn all of the consistent models, the SCUBA sources have high bolometric \nluminosities in excess of \n$10^{12}$\\,L$_{\\odot}$.\n\\item At present we cannot identify whether the power sources in the SCUBA\ngalaxies are predominantly starbursts or AGN. \n\\item If the SCUBA sources are dusty ultraluminous star-forming galaxies, then \nthey need not dominate the star-formation rate of the Universe at any redshift.  \nIn particular,\nif they evolve into elliptical galaxies, our models suggest that they only \ncontribute a few percent of the local spheroidal stellar population. \nThis result is consistent with a scenario in which most elliptical\ngalaxies formed at low redshift, as is implied by the paucity of red\ngalaxies in wide-field $K$-band surveys. \n\\item The alternative scenario in which the SCUBA sources are powerful \ndust-enshrouded AGN is also possible.  If the AGN are powered by accretion \nonto a black hole with a luminosity that is about one per cent of the Eddington \nvalue, then they may help to explain away the discrepancy of a factor of ten \nbetween the observed mass density of supermassive black holes in the local \nUniverse and that required to produce the blue light of high-redshift quasars.\n\\item Tight constraints on the redshift-dependent luminosity function of\nsubmillimetre-luminous galaxies at high redshift will follow from spectroscopic \nmeasurements of a large sample of SCUBA sources (Barger et al. in preparation). \nObtaining accurate star-formation rates for the galaxies and identifying the \nnature of the power source will be more difficult. Matching the SEDs of \nthe SCUBA sources to those of local ULIRGs, for which power sources have \nbeen determined using mid-infrared spectroscopy, offers one way to make \nprogress in this regard. \n\\end{enumerate} \n\n\\section*{Acknowledgments} \n\nWe thank our colleagues in Cambridge and Hawaii for many helpful \ndiscussions and the PPARC for financial support. We thank an \nanonymous referee for his\/her prompt and helpful comments.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction and Summary}\n\nThe mirror Thermodynamic Bethe Ansatz (TBA) is an efficient tool to analyze \nenergies of the light-cone  ${\\rm  AdS}_5\\times {\\rm S}^5$ string states, and \nthrough  the AdS\/CFT correspondence \\cite{M}, \nscaling dimensions of dual primary operators in planar ${\\cal N}=4$ SYM. \nThe mirror TBA originally proposed to determine the finite-size spectrum of two-dimensional relativistic integrable models \\cite{Zamolodchikov90,DT96,BLZe}\nreformulates the spectral problem in terms of \nthermodynamics of a so-called mirror theory\n\\cite{AF07} related to the original model by a double-Wick rotation.  The  ${\\rm  AdS}_5\\times {\\rm S}^5$  mirror model was studied in detail in \\cite{AF07} where, in particular, the bound state spectrum and the mirror form of the Bethe-Yang (BY) equations of \\cite{BS}, necessary to formulate the string hypothesis for the ${\\rm  AdS}_5\\times {\\rm S}^5$ mirror model  \\cite{AF09a},  were determined. This  opened a way to derive the ground state TBA equations \\cite{AF09b,BFT}, \nand to construct  excited state equations\nfor string states with real  \\cite{GKKV09}-\\cite{Sfondrini:2011rr} and complex momenta \\cite{AFT11}. This was done  by using the contour deformation trick,\na procedure inspired by \\cite{DT96,BLZe,KP},  and further developed in \\cite{AFS09,Arutyunov:2011uz}. The TBA equations were used to analyze various aspects of the finite-size spectrum. \nIt was shown in   \\cite{Gromov09a} that at the large  't Hooft coupling $\\lambda$ energies of  semi-classical string states found by using the mirror TBA agree with explicit string theory calculations. The scaling dimension of the Konishi operator was determined up to five loops and shown\n\\cite{AFS10,BH10a,BH10b} to agree with L\\\"uscher's corrections \\cite{BJ08}-\\cite{Janik:2010kd}\nand at four loops with explicit field-theoretic computations \\cite{Sieg,Velizhanin:2008jd}.\nThe TBA equations for  the Konishi operator  were also solved numerically for intermediate values of the\ncoupling \\cite{GKV09b,F10} and the results obtained agree  with various string theory considerations\n  \\cite {Gromov:2011de}-\\cite{Beccaria:2011uz}. \n\n\\medskip\n\n\nIn this paper  the mirror TBA equations of \\cite{AFS09} are solved numerically for several two-particle states dual to ${\\cal N}=4$ SYM operators  from the $\\sl(2)$ sector with various values of the charge $J$ and mode number $n$. \n For operators with $n\\ge 2$ the scaling dimensions  are found \nup to $\\lambda\\approx 2340$. The same code as in  \\cite{F10} is used here with minor modifications for the $J=4,n=1$ state beyond its (sub)critical value.\nThe mode number $n$ of a primary operator coincides with the string level of the dual string state \\cite{AFS},\nand at \nlarge values of  $\\lambda$ one can expand the energy of the state in an asymptotic series in powers of $1\/ \\sqrt[4]{n^2{\\lambda}} $\n\\begin{equation}\n\\label{asexp0}\nE_{(J,n)}(\\lambda)=c_{-1}\\sqrt[4]{n^2{\\lambda}}+c_0+\\frac{c_1}{\n   \\sqrt[4]{n^2{\\lambda}}}+\\frac{c_2}{\\sqrt{n^2{\\lambda}}}+\\frac{c_3}{(n^2\\lambda)^{3\/4}}+\\frac{c_4}{n^2\\lambda}+\\frac{c_5}{(n^2\\lambda)^{5\/4}}+ \\cdots\\,,\n   \\end{equation}\nwhere the coefficients $c_i$ are in general nontrivial functions of $J$ and $n$.\nThe coefficient $c_{-1}$ of the leading term  should be in fact equal to 2 as follows from the spectrum of string theory in flat space \\cite{GKV02} and asymptotic Bethe ansatz considerations \\cite{AFS}.  The constant term $c_0$ is believed to vanish for two-particle states because it does in the free fermion model \\cite{AF05}  describing the $\\alg{su}(1|1)$ sector in the semi-classical approximation and one does not expect getting quantum corrections to $c_0$ \\cite{Plefka}.  \nThe subleading coefficients $c_{2k-1}$ are supposed to have the following structure \\cite{AF05}\n\\begin{equation}\n\\label{c2km1}\nc_{2k-1}=-\\frac{\\left(-\\frac{1}{4}\\right)^k \\Gamma \\left(k-\\frac{1}{2}\\right)}{\\sqrt{\\pi } k!}J^{2k} + b_{2k-1}(J,n)\\,,\n\\end{equation}\nwhere the $J^{2k}$ term is fixed by the flat space spectrum, and $b_{2k-1}$ is a polynomial of degree $2k-1$ (or less) in $J$ with $n$ dependent coefficients. \nIn particular the first nonvanishing subleading coefficient $c_1$ is  of the form $c_1=J^2\/4 + b_1(J,n)$ where $b_1$ may be a linear function of $J$. \nThe mirror TBA prediction for the Konishi state with $J=2, n=1$ is $b_1(2,1)=1$  \\cite{GKV09b}, and it agrees  with (incompletely justified) string  computations\n  \\cite {Gromov:2011de}-\\cite{Beccaria:2011uz}. \nIn addition\nin the free fermion model one finds that $b_1$ is independent of both $J$ and $n$ and equal to $1\/2$ \\cite{AF05}. The formulae derived in the framework of the free fermion model definitely get quantum corrections but assuming that the $J$ dependence of $b_1$ remains unchanged one immediately concludes that for any $J$ one should have $b_1(J,1)=1$. Our data for the $J=3,n=1$ and $J=4,n=1$ states indeed confirms the conclusion. Fitting the data for the $J=4,n=2$ and $J=5,n=2$ states we find that the formula also works fine: $b_1(J,2)=1$. It is tempting to assume that the same formula might be valid for any $(J,n)$ state. The analysis of the $J=6,n=3$ and $J=7,n=3$ states shows however that for $n=3$ the formula is different:\n$b_1(J,3)=0$. Thus, the coefficient $c_1$ has a nontrivial $n$ dependence. \nAssuming that $b_1(J,n)$ is independent of $J$ and fitting the data for the $J=8,n=4$ state we find $b_1(J,4)=-2$. All these values of $b_1$ can be obtained from one simple formula $b_1(J,n)=n(3-n)\/2$, and therefore \n\\begin{equation}\n\\label{c1}\nc_{1}={J^{2}\\over 4} + {n(3-n)\\over 2}\\,,\\quad n=1,2,3,4\\,.\n\\end{equation}\nIt is clear that only an analytic derivation of $c_1$ can determine if this formula is valid for any $J$ and $n$. \n\nComing back to the series \\eqref{asexp0}, it was argued in \\cite{RT} that the coefficient $c_2$ should vanish due to the high degree of supersymmetry of the model, and our data supports this.   Recently by using a conjecture from \\cite{Basso}  a formula for the coefficient $c_3$ was proposed in \\cite{Gr11}. Our data for $n=1$ and $n=2$ states agrees with the formula.  It would be interesting to see if there is a simple modification of the formula for higher  values of $n$. Nothing is known about other coefficients in \\eqref{asexp0}. \nIt is even unclear if the series expansion  is in powers of $1\/\\sqrt[4]{{\\lambda}}$ as follows from the free fermion model  \\cite{AF05},  or up to an overall factor of $\\sqrt[4]{{\\lambda}}$ it is in powers of $1\/\\sqrt{{\\lambda}}$, that is $c_{2k}=0$, as was assumed in \\cite{GKV09b}. \nIf it is in powers of $1\/\\sqrt{{\\lambda}}$ then this would imply that quantum corrections to the free fermion model expressions \ndrastically change the structure of the strong coupling expansion. The precision of our computation is insufficient to come to a definite conclusion.  Nevertheless using the formula of \\cite{Gr11} and our data we find some evidence in favor of vanishing  $c_4$ for the $n=1$ states.\n\n\\medskip\n\n\n\nIt is known \\cite{AFS09} that two-particle states  from the $\\sl(2)$ sector are divided into infinitely-many classes which differ by analytic properties of exact Y-functions and therefore by driving terms in the TBA equations.  The analytic properties of Y-functions depend on the coupling and at critical values of $\\lambda$ a state moves from \none class to another one.\nAt weak coupling all the states we analyzed belong to the simplest Konishi-like class. \nThe states with $n\\ge2$ remain in the class up to the largest value of $\\lambda$ the TBA equations were solved. \nThe $J=3,n=1$ and $J=4,n=1$ states however have first critical values at $\\lambda\\approx 950$ and $\\lambda\\approx 133$, respectively. The values were obtained by interpolating the data because\nthe iterations stopped to converge for $\\lambda$'s close to the critical values.\nFor the  $J=3,n=1$  state we could solve the equations only up to  $\\lambda\\approx 540$ which is pretty far from its critical value. For the  $J=4,n=1$  state the equations were solved up to $\\lambda\\approx 105$, and then  in accordance with \\cite{AFS09} we changed the TBA equations,  jumped beyond the subcritical value to $\\lambda\\approx 191$ and resumed the iterations. The  iterations however stopped to converge at $\\lambda\\approx 483$, and we do not really understand a reason. \n\n\\medskip\n\nThe paper is organized as follows. In the next section we present\nthe analysis of the results of the numerical solution of the TBA equations for the states.  In section 3 our data for the states is collected.\n\n\n\\section{Fitting the numerical data}\n\n\\subsection{$J=3,n=1$ operator}\n\nIn the table \\eqref{E31data} we present the data for the $J=3,n=1$ state. Since we could solve the TBA equations only up to $g=3.7$ to fit the data we should make assumptions about the structure of the strong coupling expansion. Assuming that \n$c_{-1}=2$ and $c_0=0$ and fitting the data in the interval $g\\in [g_0, 3.7]$ we get \n{\\smaller \n\\begin{eqnarray}\\label{FitEJ3n1a}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n1.2 & 56.8489 & 2 \\sqrt[4]{\\lambda }+\\frac{3.1943}{\\sqrt[4]{\\lambda }}+\\frac{0.831811}{\\sqrt{\\lambda\n   }}-\\frac{6.99044}{\\lambda ^{3\/4}}+\\frac{13.106}{\\lambda }-\\frac{2.08406}{\\lambda ^{5\/4}} \\\\\n 1.3 & 66.7185 & 2 \\sqrt[4]{\\lambda }+\\frac{3.21575}{\\sqrt[4]{\\lambda }}+\\frac{0.508957}{\\sqrt{\\lambda\n   }}-\\frac{5.18593}{\\lambda ^{3\/4}}+\\frac{8.66792}{\\lambda }+\\frac{1.96869}{\\lambda ^{5\/4}} \\\\\n 1.4 & 77.3777 & 2 \\sqrt[4]{\\lambda }+\\frac{3.21158}{\\sqrt[4]{\\lambda }}+\\frac{0.572881}{\\sqrt{\\lambda\n   }}-\\frac{5.55021}{\\lambda ^{3\/4}}+\\frac{9.58264}{\\lambda }+\\frac{1.11474}{\\lambda ^{5\/4}} \\\\\n 1.5 & 88.8264 & 2 \\sqrt[4]{\\lambda }+\\frac{3.16939}{\\sqrt[4]{\\lambda }}+\\frac{1.23048}{\\sqrt{\\lambda\n   }}-\\frac{9.36522}{\\lambda ^{3\/4}}+\\frac{19.3462}{\\lambda }-\\frac{8.1862}{\\lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}For the $J=3,n=1$ state we expect $c_1=J^2\/4 + 1 = 3.25$ and indeed the values we get from the fitting are very close to it. Fixing then  $c_1= 3.25$ one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ3n1b}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 1.2 & 56.8489 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}+\\frac{0.0297414}{\\sqrt{\\lambda\n   }}-\\frac{2.71216}{\\lambda ^{3\/4}}+\\frac{3.08535}{\\lambda }+\\frac{6.61514}{\\lambda ^{5\/4}} \\\\\n 1.3 & 66.7185 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}+\\frac{0.00509108}{\\sqrt{\\lambda\n   }}-\\frac{2.43564}{\\lambda ^{3\/4}}+\\frac{2.06532}{\\lambda }+\\frac{7.85264}{\\lambda ^{5\/4}} \\\\\n 1.4 & 77.3777 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{0.00358391}{\\sqrt{\\lambda\n   }}-\\frac{2.33641}{\\lambda ^{3\/4}}+\\frac{1.6914}{\\lambda }+\\frac{8.31688}{\\lambda ^{5\/4}} \\\\\n 1.5 & 88.8264 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{0.00135757}{\\sqrt{\\lambda\n   }}-\\frac{2.36233}{\\lambda ^{3\/4}}+\\frac{1.79102}{\\lambda }+\\frac{8.19057}{\\lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}We see that the coefficient $c_2$ becomes very small and we set it to 0: $c_2=0$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ3n1c}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 1.2 & 56.8489 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{2.39691}{\\lambda\n   ^{3\/4}}+\\frac{1.99012}{\\lambda }+\\frac{7.86361}{\\lambda ^{5\/4}} \\\\\n 1.3 & 66.7185 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{2.38036}{\\lambda\n   ^{3\/4}}+\\frac{1.8682}{\\lambda }+\\frac{8.08376}{\\lambda ^{5\/4}} \\\\\n 1.4 & 77.3777 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{2.37618}{\\lambda\n   ^{3\/4}}+\\frac{1.83666}{\\lambda }+\\frac{8.14215}{\\lambda ^{5\/4}} \\\\\n 1.5 & 88.8264 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{2.37771}{\\lambda\n   ^{3\/4}}+\\frac{1.8484}{\\lambda }+\\frac{8.11991}{\\lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}According to the conjecture of \\cite{Gr11} the coefficient $c_3$ for the states with $n=1$ is equal to\n\\begin{equation}\\label{c3}\nc_3=-\\frac{J^4}{64}+\\frac{3 J^2}{8}-3 \\zeta (3)-\\frac{3}{4}\\,,\n\\end{equation}\nand therefore for $J=3$, $c_3\\approx -2.2468$. We see that the number is indeed very close to the one we get from the fit. Fixing the coefficient to this value and adding more terms to the expansion, one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ3n1d}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 1.2 & 56.8489 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{2.2468}{\\lambda\n   ^{3\/4}}+\\frac{0.363256}{\\lambda }+\\frac{13.8122}{\\lambda ^{5\/4}}-\\frac{7.89879}{\\lambda ^{3\/2}}+\\frac{1.96167}{\\lambda\n   ^{7\/4}} \\\\\n 1.3 & 66.7185 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{2.2468}{\\lambda\n   ^{3\/4}}+\\frac{0.0493902}{\\lambda }+\\frac{17.2428}{\\lambda ^{5\/4}}-\\frac{20.231}{\\lambda ^{3\/2}}+\\frac{16.5518}{\\lambda\n   ^{7\/4}} \\\\\n 1.4 & 77.3777 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{2.2468}{\\lambda\n   ^{3\/4}}-\\frac{0.0985827}{\\lambda }+\\frac{18.8979}{\\lambda ^{5\/4}}-\\frac{26.3304}{\\lambda\n   ^{3\/2}}+\\frac{23.9612}{\\lambda ^{7\/4}} \\\\\n 1.5 & 88.8264 & 2 \\sqrt[4]{\\lambda }+\\frac{3.25}{\\sqrt[4]{\\lambda }}-\\frac{2.2468}{\\lambda\n   ^{3\/4}}-\\frac{0.0771042}{\\lambda }+\\frac{18.6526}{\\lambda ^{5\/4}}-\\frac{25.4057}{\\lambda\n   ^{3\/2}}+\\frac{22.8107}{\\lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}\\begin{figure}[t]\n\\begin{center}\n\\includegraphics*[width=0.5\\textwidth]{EJ3n1a}\\qquad \\includegraphics*[width=0.42\\textwidth]{EJ3n1b}\n\\end{center}\n\\caption{\\smaller \nBlack dots represent the difference between the numerical solution and conjectured \nasymptotic expansions.\n}\n\\label{figJ3n1}\n\\end{figure}The outcome of this fitting is very interesting because the coefficient $c_4$ becomes very small and this implies that up to the overall $\\sqrt[4]\\lambda$  the expansion may indeed be in powers of $1\/\\sqrt\\lambda$.\\footnote{ One can check by using the data from \\cite{F10} that a similar phenomenon also happens for the Konishi operator.\nFor example fitting the data in the interval $g\\in [1.8,5.]$ with $c_{-1}=c_1=2,c_0=c_2=0,c_3=\\frac{1}{2}-3 \\zeta (3)\\approx 3.10617$, one gets\n$$\nE_K=2 \\sqrt[4]{\\lambda }+\\frac{2}{\\sqrt[4]{\\lambda }}-\\frac{3.10617}{\\lambda ^{3\/4}}+\\frac{0.0175158}{\\lambda }+\\frac{19.2403}{\\lambda ^{5\/4}}-\\frac{39.3787}{\\lambda\n   ^{3\/2}}+\\frac{36.5992}{\\lambda ^{7\/4}}\\,,\n$$\nwhich gives additional evidence in favor of the $1\/\\sqrt\\lambda$ expansion at least for the $n=1$ operators. } Finally setting $c_{2k}=0$ one gets the following fitting for the $J=3,n=1$ state\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ3n1e}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n1.2 & 56.8489 & 1.99982 \\sqrt[4]{\\lambda }+\\frac{3.25805}{\\sqrt[4]{\\lambda }}-\\frac{2.30759}{\\lambda\n   ^{3\/4}}+\\frac{13.7801}{\\lambda ^{5\/4}}-\\frac{11.3876}{\\lambda ^{7\/4}} \\\\\n 1.3 & 66.7185 & 1.9999 \\sqrt[4]{\\lambda }+\\frac{3.25325}{\\sqrt[4]{\\lambda }}-\\frac{2.20648}{\\lambda\n   ^{3\/4}}+\\frac{12.8714}{\\lambda ^{5\/4}}-\\frac{8.44329}{\\lambda ^{7\/4}} \\\\\n 1.4 & 77.3777 & 1.99988 \\sqrt[4]{\\lambda }+\\frac{3.25475}{\\sqrt[4]{\\lambda }}-\\frac{2.23931}{\\lambda\n   ^{3\/4}}+\\frac{13.1794}{\\lambda ^{5\/4}}-\\frac{9.49031}{\\lambda ^{7\/4}} \\\\\n 1.5 & 88.8264 & 1.9997 \\sqrt[4]{\\lambda }+\\frac{3.2658}{\\sqrt[4]{\\lambda }}-\\frac{2.48916}{\\lambda\n   ^{3\/4}}+\\frac{15.6166}{\\lambda ^{5\/4}}-\\frac{18.1459}{\\lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}In Figure \\ref{figJ3n1} we plot the difference between the numerical solution and its large $\\lambda$ asymptotics \n$2\\lambda^{1\/4}+{3.25\\over\\lambda^{1\/4}}$ and $2\\lambda^{1\/4}+{3.25\\over\\lambda^{1\/4}}-{2.2468\\over\\lambda^{3\/4}}$. \n\n\n\\subsection{$J=4,n=1$ operator}\n\nIn the table \\eqref{E41data} we present the data for the $J=4,n=1$ state.\nFor this operator the data is known only up to $g=3.4$ with a gap between $g=1.63$ and $g=2.2$. The operator has a critical point at $g\\approx 1.83$ and a subcritical one at $g\\approx 2.19$ and our iterations did not converge for $g\\in[1.64,2.1]$.\nBy this reason we fit the data  in the interval $g\\in [g_0, 3.4]$  with the assumption that $c_{2k}=0$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ4n1a}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 0.9 & 31.9775 & 2.00114 \\sqrt[4]{\\lambda }+\\frac{4.96572}{\\sqrt[4]{\\lambda }}-\\frac{2.24203}{\\lambda\n   ^{3\/4}}+\\frac{21.2561}{\\lambda ^{5\/4}}-\\frac{52.8464}{\\lambda ^{7\/4}} \\\\\n 1. & 39.4784 & 2.00071 \\sqrt[4]{\\lambda }+\\frac{4.98755}{\\sqrt[4]{\\lambda }}-\\frac{2.63256}{\\lambda\n   ^{3\/4}}+\\frac{24.1832}{\\lambda ^{5\/4}}-\\frac{60.6194}{\\lambda ^{7\/4}} \\\\\n 1.1 & 47.7689 & 1.9995 \\sqrt[4]{\\lambda }+\\frac{5.05089}{\\sqrt[4]{\\lambda }}-\\frac{3.81607}{\\lambda\n   ^{3\/4}}+\\frac{33.5122}{\\lambda ^{5\/4}}-\\frac{86.8559}{\\lambda ^{7\/4}} \\\\\n 1.2 & 56.8489 & 1.99575 \\sqrt[4]{\\lambda }+\\frac{5.25258}{\\sqrt[4]{\\lambda }}-\\frac{7.71075}{\\lambda\n   ^{3\/4}}+\\frac{65.4442}{\\lambda ^{5\/4}}-\\frac{180.907}{\\lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}We see that $c_{-1}$ is indeed close to $2$, and $c_1\\approx 5$ as expected for the $J=4,n=1$ state. Let us then fix $c_{-1}=2, c_1= 5$ \n\\begin{figure}[t]\n\\begin{center}\n\\includegraphics*[width=0.5\\textwidth]{EJ4n1a}\\qquad \\includegraphics*[width=0.42\\textwidth]{EJ4n1b}\n\\end{center}\n\\caption{\\smaller \nBlack dots represent the difference between the numerical solution and conjectured \nasymptotic expansions.\n}\n\\label{figJ4n1}\n\\end{figure}\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ4n1b}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 0.9 & 31.9775 & 2 \\sqrt[4]{\\lambda }+\\frac{5}{\\sqrt[4]{\\lambda }}-\\frac{2.51332}{\\lambda\n   ^{3\/4}}+\\frac{21.4871}{\\lambda ^{5\/4}}-\\frac{50.4063}{\\lambda ^{7\/4}} \\\\\n 1. & 39.4784 & 2 \\sqrt[4]{\\lambda }+\\frac{5}{\\sqrt[4]{\\lambda }}-\\frac{2.49341}{\\lambda\n   ^{3\/4}}+\\frac{21.0556}{\\lambda ^{5\/4}}-\\frac{48.2863}{\\lambda ^{7\/4}} \\\\\n 1.1 & 47.7689 & 2 \\sqrt[4]{\\lambda }+\\frac{5}{\\sqrt[4]{\\lambda }}-\\frac{2.47161}{\\lambda\n   ^{3\/4}}+\\frac{20.5437}{\\lambda ^{5\/4}}-\\frac{45.5455}{\\lambda ^{7\/4}} \\\\\n 1.2 & 56.8489 & 2 \\sqrt[4]{\\lambda }+\\frac{5}{\\sqrt[4]{\\lambda }}-\\frac{2.44817}{\\lambda\n   ^{3\/4}}+\\frac{19.9559}{\\lambda ^{5\/4}}-\\frac{42.1681}{\\lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}According to \\cite{Gr11} the coefficient $c_3$ for the $J=4,n=1$ state should be equal to  $c_3=\\frac{5}{4}-3 \\zeta (3)\\approx -2.35617$, and it indeed agrees well with  the one we get from the fit. \nIn Figure \\ref{figJ4n1} we plot the difference between the numerical solution and its large $\\lambda$ asymptotics \n$2\\lambda^{1\/4}+{5\\over\\lambda^{1\/4}}$ and $2\\lambda^{1\/4}+{5\\over\\lambda^{1\/4}}-{2.35617\\over\\lambda^{3\/4}}$. \n\n\\begin{figure}[t]\n\\begin{center}\n\\includegraphics*[width=0.49\\textwidth]{gr2Im}\\qquad \\includegraphics*[width=0.45\\textwidth]{gr2Re}\n\\end{center}\n\\caption{\\smaller  On the left and right figures the graphs of the imaginary and real parts of the rescaled root $r_2$ together with the fitting function (blue curves) $-1.25844\\, i\\, \\sqrt{g(2.17804-g)}$ are shown.\n}\n\\label{r2graph}\n\\end{figure}\n\nTo determine the values of the critical $g_{cr}$ and subcritical $\\bar g_{cr}$ points we found the solutions to the equation $Y_{1|vw}(r_2 +{i\\over g})=-1$, where $r_2$ is also a root of $Y_{2|vw}$. The results are collected in Table \\ref{r2data} and shown in Figure \\ref{r2graph}.\n{\\smaller \\begin{eqnarray}\\label{r2data}\n\\begin{array}{|c|c||}\n\\hline\ng& r_2\n\\\\\n\\hline\n 0.1 & -10.562 i \\\\\n 0.2 & -5.34994 i \\\\\n 0.3 & -3.63868 i \\\\\n 0.4 & -2.7981 i \\\\\n 0.5 & -2.30147 i \\\\\n 0.6 & -1.97299 i \\\\\n 0.7 & -1.73166 i \n \\\\\\hline\n\\end{array}\\begin{array}{|c|c||}\n\\hline\ng& r_2\n\\\\\n\\hline\n 0.8 & -1.55116 i \\\\\n 0.9 & -1.40522 i \\\\\n 1. & -1.29021 i \\\\\n 1.1 & -1.18521 i \\\\\n 1.2 & -1.09082 i \\\\\n 1.3 & -1.00062 i \\\\\n 1.4 & -0.91655 i \n \\\\\\hline\n\\end{array}\n\\begin{array}{|c|c||}\n\\hline\ng& r_2\n\\\\\n\\hline\n 1.5 & -0.84559 i\\\\\n 1.6 & -0.75899 i \\\\\n 1.61 & -0.74687 i \\\\\n 1.62 & -0.739759 i \\\\\n 1.63 & -0.727045 i \\\\\n&\\\\\n&\n  \\\\\\hline\n\\end{array}\n\\begin{array}{|c|c||}\n\\hline\ng& r_2\n\\\\\n\\hline\n 2.2 & 0.0087264 \\\\\n 2.3 & 0.199508 \\\\\n 2.4 & 0.314217 \\\\\n 2.5 & 0.397187 \\\\\n 2.6 & 0.463024 \\\\\n 2.7 & 0.519 \\\\\n 2.8 & 0.565948 \n \\\\\\hline\n\\end{array}\n\\begin{array}{|c|c||}\n\\hline\ng& r_2\n\\\\\n\\hline\n 2.9 & 0.608164 \\\\\n 3. & 0.646168 \\\\\n 3.1 & 0.679729 \\\\\n 3.2 & 0.711265 \\\\\n 3.3 & 0.740638 \\\\\n 3.4 & 0.767281\\\\\n &\n \\\\\\hline\n\\end{array}\n\\end{eqnarray}\n}\nThe root $r_2$ is purely imaginary for $g\\le 2.1$ and real for $g\\ge 2.2$. It vanishes at $g=\\bar{g}_{cr}$ \nFitting our data  in the interval $[1.5,16.3]$ to the function $c\\sqrt{g-\\bar{g}_{cr}\\over g}$, we get\n\\begin{equation}\nr_2(g)\\sim -1.25844\\, i\\, \\sqrt{2.17804-g\\over g}\\,.\n\\end{equation}\nThe subcritical value obtained from this fitting agrees very well with the data in Table \\ref{r2data} which shows that it should be $\\bar{g}_{cr}\\approx 2.19$.  \nTo find the critical value we use the fitting function and solve the equation $r_2(g)=-i\/g$. This gives ${g}_{cr}\\approx 1.83$. \n\n\n\n\\subsection{$J=4,n=2$ operator}\n\nIn the table \\eqref{E42data} we present the results of the computation of the energy of the $J=4,n=2$ state.\nFitting the data in the interval $g\\in [g_0, 7.7]$ we get \n{\\smaller \n\\begin{eqnarray}\\label{FitEJ4n2a}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 1.6 & 101.065 & 2.01324 \\sqrt[4]{\\Lambda }-0.599655+\\frac{16.0334}{\\sqrt[4]{\\Lambda }}-\\frac{106.352}{\\sqrt{\\Lambda\n   }}+\\frac{535.582}{\\Lambda ^{3\/4}}-\\frac{1548.42}{\\Lambda }+\\frac{1884.37}{\\Lambda ^{5\/4}} \\\\\n 1.7 & 114.093 & 2.00765 \\sqrt[4]{\\Lambda }-0.364641+\\frac{11.9675}{\\sqrt[4]{\\Lambda }}-\\frac{69.3126}{\\sqrt{\\Lambda\n   }}+\\frac{348.21}{\\Lambda ^{3\/4}}-\\frac{1049.34}{\\Lambda }+\\frac{1337.51}{\\Lambda ^{5\/4}} \\\\\n 1.8 & 127.91 & 2.00248 \\sqrt[4]{\\Lambda }-0.144622+\\frac{8.11028}{\\sqrt[4]{\\Lambda }}-\\frac{33.6705}{\\sqrt{\\Lambda\n   }}+\\frac{165.145}{\\Lambda ^{3\/4}}-\\frac{553.8}{\\Lambda }+\\frac{785.161}{\\Lambda ^{5\/4}} \\\\\n 1.9 & 142.517 & 1.99906 \\sqrt[4]{\\Lambda }+0.00296822+\\frac{5.49016}{\\sqrt[4]{\\Lambda }}-\\frac{9.13276}{\\sqrt{\\Lambda\n   }}+\\frac{37.2992}{\\Lambda ^{3\/4}}-\\frac{202.443}{\\Lambda }+\\frac{387.196}{\\Lambda ^{5\/4}}    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}where the expansion parameter $\\Lambda = n^2\\lambda = 4\\lambda$ is introduced.\nOne sees that $c_{-1}$ is very close to 2 as expected, and \nfixing  $c_{-1}= 2$ one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ4n2b}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n1.6 & 101.065 & 2 \\sqrt[4]{\\Lambda }-0.0636918+\\frac{7.12558}{\\sqrt[4]{\\Lambda }}-\\frac{28.5421}{\\sqrt{\\Lambda\n   }}+\\frac{158.802}{\\Lambda ^{3\/4}}-\\frac{589.219}{\\Lambda }+\\frac{881.06}{\\Lambda ^{5\/4}} \\\\\n 1.7 & 114.093 & 2 \\sqrt[4]{\\Lambda }-0.0505662+\\frac{6.66846}{\\sqrt[4]{\\Lambda }}-\\frac{22.2713}{\\sqrt{\\Lambda\n   }}+\\frac{116.455}{\\Lambda ^{3\/4}}-\\frac{448.43}{\\Lambda }+\\frac{696.68}{\\Lambda ^{5\/4}} \\\\\n 1.8 & 127.91 & 2 \\sqrt[4]{\\Lambda }-0.0413324+\\frac{6.34268}{\\sqrt[4]{\\Lambda }}-\\frac{17.7387}{\\sqrt{\\Lambda\n   }}+\\frac{85.3727}{\\Lambda ^{3\/4}}-\\frac{343.379}{\\Lambda }+\\frac{556.661}{\\Lambda ^{5\/4}} \\\\\n 1.9 & 142.517 & 2 \\sqrt[4]{\\Lambda }-0.0367516+\\frac{6.17907}{\\sqrt[4]{\\Lambda }}-\\frac{15.4318}{\\sqrt{\\Lambda\n   }}+\\frac{69.3241}{\\Lambda ^{3\/4}}-\\frac{288.293}{\\Lambda }+\\frac{482.019}{\\Lambda ^{5\/4}}\n  \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}We see that the coefficient $c_0$ becomes small and we set it to 0: $c_0=0$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ4n2c}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n  1.6 & 101.065 & 2 \\sqrt[4]{\\Lambda }+\\frac{5.0046}{\\sqrt[4]{\\Lambda }}-\\frac{0.795942}{\\sqrt{\\Lambda\n   }}-\\frac{19.4612}{\\Lambda ^{3\/4}}-\\frac{26.4872}{\\Lambda }+\\frac{182.368}{\\Lambda ^{5\/4}} \\\\\n 1.7 & 114.093 & 2 \\sqrt[4]{\\Lambda }+\\frac{4.95929}{\\sqrt[4]{\\Lambda }}+\\frac{0.454694}{\\sqrt{\\Lambda\n   }}-\\frac{32.1551}{\\Lambda ^{3\/4}}+\\frac{29.665}{\\Lambda }+\\frac{90.9888}{\\Lambda ^{5\/4}} \\\\\n 1.8 & 127.91 & 2 \\sqrt[4]{\\Lambda }+\\frac{4.92584}{\\sqrt[4]{\\Lambda }}+\\frac{1.39108}{\\sqrt{\\Lambda\n   }}-\\frac{41.8075}{\\Lambda ^{3\/4}}+\\frac{73.0916}{\\Lambda }+\\frac{19.0113}{\\Lambda ^{5\/4}} \\\\\n 1.9 & 142.517 & 2 \\sqrt[4]{\\Lambda }+\\frac{4.90238}{\\sqrt[4]{\\Lambda }}+\\frac{2.05656}{\\sqrt{\\Lambda\n   }}-\\frac{48.7676}{\\Lambda ^{3\/4}}+\\frac{104.906}{\\Lambda }-\\frac{34.6303}{\\Lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}This fitting shows that $c_1\\approx 5$, and assuming that $b_1$ is independent of $J$ one concludes that  for any two-particle $n=2$ state we should expect the same formula as for the $n=1$ states: $c_1(J,2)=J^2\/4 + 1$.\nSetting $c_1 = 5$, one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ4n2d}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 1.6 & 101.065 & 2 \\sqrt[4]{\\Lambda }+\\frac{5}{\\sqrt[4]{\\Lambda }}-\\frac{0.675854}{\\sqrt{\\Lambda\n   }}-\\frac{20.6105}{\\Lambda ^{3\/4}}-\\frac{21.7064}{\\Lambda }+\\frac{175.066}{\\Lambda ^{5\/4}} \\\\\n 1.7 & 114.093 & 2 \\sqrt[4]{\\Lambda }+\\frac{5}{\\sqrt[4]{\\Lambda }}-\\frac{0.626357}{\\sqrt{\\Lambda\n   }}-\\frac{21.6187}{\\Lambda ^{3\/4}}-\\frac{15.0422}{\\Lambda }+\\frac{160.75}{\\Lambda ^{5\/4}} \\\\\n 1.8 & 127.91 & 2 \\sqrt[4]{\\Lambda }+\\frac{5}{\\sqrt[4]{\\Lambda }}-\\frac{0.608926}{\\sqrt{\\Lambda\n   }}-\\frac{21.9793}{\\Lambda ^{3\/4}}-\\frac{12.6155}{\\Lambda }+\\frac{155.435}{\\Lambda ^{5\/4}} \\\\\n 1.9 & 142.517 & 2 \\sqrt[4]{\\Lambda }+\\frac{5}{\\sqrt[4]{\\Lambda }}-\\frac{0.614803}{\\sqrt{\\Lambda\n   }}-\\frac{21.856}{\\Lambda ^{3\/4}}-\\frac{13.4596}{\\Lambda }+\\frac{157.318}{\\Lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}The coefficient $c_2$ is not really small and we cannot reliably conclude that it vanishes.  The contribution of the corresponding term is however smaller than the contribution of the next term and we believe that increasing the precision of the computation one would show that  $c_2=0$. \n\n\\begin{figure}[t]\n\\begin{center}\n\\includegraphics*[width=0.475\\textwidth]{EJ4n2a}\\qquad \\includegraphics*[width=0.45\\textwidth]{EJ4n2b}\n\\end{center}\n\\caption{\\smaller \nBlack dots represent the difference between the numerical solution and conjectured \nasymptotic expansions.\n}\n\\label{figJ4n2}\n\\end{figure}\n\n\nAssuming that $c_{2k}=0$ one gets the following fitting\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ4n2e}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 1.6 & 101.065 & 2.00005 \\sqrt[4]{\\Lambda }+\\frac{4.96322}{\\sqrt[4]{\\Lambda }}-\\frac{26.0062}{\\Lambda\n   ^{3\/4}}+\\frac{136.487}{\\Lambda ^{5\/4}}+\\frac{65.3371}{\\Lambda ^{7\/4}} \\\\\n 1.7 & 114.093 & 1.99999 \\sqrt[4]{\\Lambda }+\\frac{4.97512}{\\sqrt[4]{\\Lambda }}-\\frac{26.8411}{\\Lambda\n   ^{3\/4}}+\\frac{160.533}{\\Lambda ^{5\/4}}-\\frac{175.699}{\\Lambda ^{7\/4}} \\\\\n 1.8 & 127.91 & 1.99995 \\sqrt[4]{\\Lambda }+\\frac{4.98407}{\\sqrt[4]{\\Lambda }}-\\frac{27.4881}{\\Lambda\n   ^{3\/4}}+\\frac{179.837}{\\Lambda ^{5\/4}}-\\frac{377.218}{\\Lambda ^{7\/4}} \\\\\n 1.9 & 142.517 & 1.99992 \\sqrt[4]{\\Lambda }+\\frac{4.99048}{\\sqrt[4]{\\Lambda }}-\\frac{27.9635}{\\Lambda\n   ^{3\/4}}+\\frac{194.497}{\\Lambda ^{5\/4}}-\\frac{536.145}{\\Lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}\\,,~~~~\n\\end{eqnarray}\n}which also agrees very well with $c_1=5$. The coefficient $c_3$ for the states with $n=2$ is conjectured \\cite{Gr11}\n to be equal to \n\\begin{equation}\\label{c3n2}\nc_3=-\\frac{J^4}{64}+\\frac{3 J^2}{8}-24 \\zeta (3)-\\frac{11}{4}\\,,\n\\end{equation}\nand for $J=4$, $c_3\\approx -29.5994$. We see that the number is indeed close to the one we get from the fit. The agreement with the conjectured value of $c_3$ becomes even more evident if one sets $c_{-1}=2, c_1=5$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ4n2f}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 1.6 & 101.065 & 2 \\sqrt[4]{\\Lambda }+\\frac{5}{\\sqrt[4]{\\Lambda\n   }}-\\frac{29.8997}{\\Lambda ^{3\/4}}+\\frac{269.391}{\\Lambda\n   ^{5\/4}}-\\frac{1346.11}{\\Lambda ^{7\/4}} \\\\\n 1.7 & 114.093 & 2 \\sqrt[4]{\\Lambda }+\\frac{5}{\\sqrt[4]{\\Lambda\n   }}-\\frac{30.0467}{\\Lambda ^{3\/4}}+\\frac{281.386}{\\Lambda\n   ^{5\/4}}-\\frac{1561.66}{\\Lambda ^{7\/4}} \\\\\n 1.8 & 127.91 & 2 \\sqrt[4]{\\Lambda }+\\frac{5}{\\sqrt[4]{\\Lambda\n   }}-\\frac{30.1745}{\\Lambda ^{3\/4}}+\\frac{292.273}{\\Lambda\n   ^{5\/4}}-\\frac{1767.33}{\\Lambda ^{7\/4}} \\\\\n 1.9 & 142.517 & 2 \\sqrt[4]{\\Lambda }+\\frac{5}{\\sqrt[4]{\\Lambda\n   }}-\\frac{30.2888}{\\Lambda ^{3\/4}}+\\frac{302.41}{\\Lambda\n   ^{5\/4}}-\\frac{1967.94}{\\Lambda ^{7\/4}}    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}In Figure \\ref{figJ4n2} we plot the difference between the numerical solution and its large $\\lambda$ asymptotics \n$2(4\\lambda)^{1\/4}+{5\\over(4\\lambda)^{1\/4}}$ and $2(4\\lambda)^{1\/4}+{5\\over(4\\lambda)^{1\/4}}-{29.6\\over (4\\lambda)^{3\/4}}$. \n\n\n\\subsection{$J=5,n=2$ operator}\n\nIn the table \\eqref{E52data} we present the results of the computation of the energy of the $J=5,n=2$ state.\nFitting the data in the interval $g\\in [g_0, 7.7]$ we get \n{\\smaller \n\\begin{eqnarray}\\label{FitEJ5n2a}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n1.6 & 101.065 & 2.00445 \\sqrt[4]{\\Lambda }-0.20912+\\frac{11.1966}{\\sqrt[4]{\\Lambda }}-\\frac{38.8728}{\\sqrt{\\Lambda\n   }}+\\frac{178.449}{\\Lambda ^{3\/4}}-\\frac{577.756}{\\Lambda }+\\frac{881.1}{\\Lambda ^{5\/4}} \\\\\n 1.7 & 114.093 & 2.00546 \\sqrt[4]{\\Lambda }-0.251818+\\frac{11.9353}{\\sqrt[4]{\\Lambda }}-\\frac{45.6022}{\\sqrt{\\Lambda\n   }}+\\frac{212.492}{\\Lambda ^{3\/4}}-\\frac{668.43}{\\Lambda }+\\frac{980.454}{\\Lambda ^{5\/4}} \\\\\n 1.8 & 127.91 & 2.00297 \\sqrt[4]{\\Lambda }-0.145733+\\frac{10.0755}{\\sqrt[4]{\\Lambda }}-\\frac{28.4169}{\\sqrt{\\Lambda\n   }}+\\frac{124.224}{\\Lambda ^{3\/4}}-\\frac{429.497}{\\Lambda }+\\frac{714.13}{\\Lambda ^{5\/4}} \\\\\n 1.9 & 142.517 & 1.99987 \\sqrt[4]{\\Lambda }-0.0122334+\\frac{7.70547}{\\sqrt[4]{\\Lambda }}-\\frac{6.22177}{\\sqrt{\\Lambda\n   }}+\\frac{8.58421}{\\Lambda ^{3\/4}}-\\frac{111.684}{\\Lambda }+\\frac{354.159}{\\Lambda ^{5\/4}}\n   \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}where $\\Lambda = n^2\\lambda = 4\\lambda$ is the same expansion parameter as for the $J=4,n=2$ state.\nOne sees that $c_{-1}$ is very close to 2 as expected, and \nfixing  $c_{-1}= 2$ one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ5n2b}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 1.6 & 101.065 & 2 \\sqrt[4]{\\Lambda }-0.0290362+\\frac{8.20356}{\\sqrt[4]{\\Lambda }}-\\frac{12.7288}{\\sqrt{\\Lambda\n   }}+\\frac{51.8515}{\\Lambda ^{3\/4}}-\\frac{255.467}{\\Lambda }+\\frac{543.99}{\\Lambda ^{5\/4}} \\\\\n 1.7 & 114.093 & 2 \\sqrt[4]{\\Lambda }-0.0275291+\\frac{8.15107}{\\sqrt[4]{\\Lambda }}-\\frac{12.0088}{\\sqrt{\\Lambda\n   }}+\\frac{46.9889}{\\Lambda ^{3\/4}}-\\frac{239.301}{\\Lambda }+\\frac{522.818}{\\Lambda ^{5\/4}} \\\\\n 1.8 & 127.91 & 2 \\sqrt[4]{\\Lambda }-0.0221103+\\frac{7.95989}{\\sqrt[4]{\\Lambda }}-\\frac{9.34883}{\\sqrt{\\Lambda\n   }}+\\frac{28.7486}{\\Lambda ^{3\/4}}-\\frac{177.652}{\\Lambda }+\\frac{440.648}{\\Lambda ^{5\/4}} \\\\\n 1.9 & 142.517 & 2 \\sqrt[4]{\\Lambda }-0.0175866+\\frac{7.79832}{\\sqrt[4]{\\Lambda }}-\\frac{7.07073}{\\sqrt{\\Lambda\n   }}+\\frac{12.9004}{\\Lambda ^{3\/4}}-\\frac{123.254}{\\Lambda }+\\frac{366.939}{\\Lambda ^{5\/4}}\n     \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}We see that the coefficient $c_0$ is even smaller than it was for  the $J=4,n=2$ state, and setting it to 0 one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ5n2c}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n1.6 & 101.065 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.23663}{\\sqrt[4]{\\Lambda }}-\\frac{0.0797212}{\\sqrt{\\Lambda\n   }}-\\frac{29.4165}{\\Lambda ^{3\/4}}+\\frac{1.07508}{\\Lambda }+\\frac{225.465}{\\Lambda ^{5\/4}} \\\\\n 1.7 & 114.093 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.22057}{\\sqrt[4]{\\Lambda }}+\\frac{0.363655}{\\sqrt{\\Lambda\n   }}-\\frac{33.9167}{\\Lambda ^{3\/4}}+\\frac{20.9822}{\\Lambda }+\\frac{193.07}{\\Lambda ^{5\/4}} \\\\\n 1.8 & 127.91 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.20197}{\\sqrt[4]{\\Lambda }}+\\frac{0.884427}{\\sqrt{\\Lambda\n   }}-\\frac{39.2849}{\\Lambda ^{3\/4}}+\\frac{45.134}{\\Lambda }+\\frac{153.039}{\\Lambda ^{5\/4}} \\\\\n 1.9 & 142.517 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.18739}{\\sqrt[4]{\\Lambda }}+\\frac{1.29794}{\\sqrt{\\Lambda\n   }}-\\frac{43.6097}{\\Lambda ^{3\/4}}+\\frac{64.9025}{\\Lambda }+\\frac{119.708}{\\Lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}This fitting shows that $c_1$ agrees with $c_1(J,2)=J^2\/4 + 1$.\nSetting $c_1 = 7.25$, one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ5n2d}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n1.6 & 101.065 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.25}{\\sqrt[4]{\\Lambda }}-\\frac{0.428891}{\\sqrt{\\Lambda\n   }}-\\frac{26.0747}{\\Lambda ^{3\/4}}-\\frac{12.8258}{\\Lambda }+\\frac{246.699}{\\Lambda ^{5\/4}} \\\\\n 1.7 & 114.093 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.25}{\\sqrt[4]{\\Lambda }}-\\frac{0.417828}{\\sqrt{\\Lambda }}-\\frac{26.3}{\\Lambda\n   ^{3\/4}}-\\frac{11.3363}{\\Lambda }+\\frac{243.5}{\\Lambda ^{5\/4}} \\\\\n 1.8 & 127.91 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.25}{\\sqrt[4]{\\Lambda }}-\\frac{0.410937}{\\sqrt{\\Lambda\n   }}-\\frac{26.4426}{\\Lambda ^{3\/4}}-\\frac{10.3768}{\\Lambda }+\\frac{241.398}{\\Lambda ^{5\/4}} \\\\\n 1.9 & 142.517 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.25}{\\sqrt[4]{\\Lambda }}-\\frac{0.415359}{\\sqrt{\\Lambda\n   }}-\\frac{26.3498}{\\Lambda ^{3\/4}}-\\frac{11.0121}{\\Lambda }+\\frac{242.815}{\\Lambda ^{5\/4}}\n  \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}The coefficient $c_2$ is again smaller than the one for the $J=4,n=2$ case, and moreover the contribution of the corresponding term is much smaller than the contribution of the next one. It is possible that one cannot see that $c_2$ vanishes because of the exponentially suppressed corrections  at large $\\lambda$. These corrections decrease with $J$ increasing and this  would explain why for the $J=5,n=2$ case the coefficients $c_0$ and $c_2$ are closer to 0 than the ones for the $J=4,n=2$ state.\n\n\\begin{figure}[t]\n\\begin{center}\n\\includegraphics*[width=0.475\\textwidth]{EJ5n2a}\\qquad \\includegraphics*[width=0.465\\textwidth]{EJ5n2b}\n\\end{center}\n\\caption{\\smaller \nBlack dots represent the difference between the numerical solution and conjectured \nasymptotic expansions.\n}\n\\label{figJ5n2}\n\\end{figure}\n\nNext setting $c_{2k}=0$ one gets the following fitting\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ5n2e}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n1.6 & 101.065 & 2.00001 \\sqrt[4]{\\Lambda }+\\frac{7.23042}{\\sqrt[4]{\\Lambda }}-\\frac{29.6628}{\\Lambda\n   ^{3\/4}}+\\frac{231.828}{\\Lambda ^{5\/4}}-\\frac{27.3344}{\\Lambda ^{7\/4}} \\\\\n 1.7 & 114.093 & 1.99999 \\sqrt[4]{\\Lambda }+\\frac{7.23469}{\\sqrt[4]{\\Lambda }}-\\frac{29.9624}{\\Lambda\n   ^{3\/4}}+\\frac{240.459}{\\Lambda ^{5\/4}}-\\frac{113.852}{\\Lambda ^{7\/4}} \\\\\n 1.8 & 127.91 & 1.99997 \\sqrt[4]{\\Lambda }+\\frac{7.23966}{\\sqrt[4]{\\Lambda }}-\\frac{30.3219}{\\Lambda\n   ^{3\/4}}+\\frac{251.185}{\\Lambda ^{5\/4}}-\\frac{225.82}{\\Lambda ^{7\/4}} \\\\\n 1.9 & 142.517 & 1.99995 \\sqrt[4]{\\Lambda }+\\frac{7.24362}{\\sqrt[4]{\\Lambda }}-\\frac{30.6156}{\\Lambda\n   ^{3\/4}}+\\frac{260.241}{\\Lambda ^{5\/4}}-\\frac{323.995}{\\Lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}\\,,~~~~\n\\end{eqnarray}\n}which agrees very well with $c_1=7.25$\nand shows that the coefficient $c_3$ is close to the conjectured value\n$c_3=-\\frac{201}{64}-24 \\zeta (3)\\approx -31.99$.\nSetting $c_{-1}=2, c_1=7.25$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ5n2f}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n  1.6 & 101.065 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.25}{\\sqrt[4]{\\Lambda }}-\\frac{31.9121}{\\Lambda\n   ^{3\/4}}+\\frac{310.838}{\\Lambda ^{5\/4}}-\\frac{878.22}{\\Lambda ^{7\/4}} \\\\\n 1.7 & 114.093 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.25}{\\sqrt[4]{\\Lambda }}-\\frac{32.}{\\Lambda ^{3\/4}}+\\frac{318.014}{\\Lambda\n   ^{5\/4}}-\\frac{1007.16}{\\Lambda ^{7\/4}} \\\\\n 1.8 & 127.91 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.25}{\\sqrt[4]{\\Lambda }}-\\frac{32.0823}{\\Lambda ^{3\/4}}+\\frac{325.019}{\\Lambda\n   ^{5\/4}}-\\frac{1139.5}{\\Lambda ^{7\/4}} \\\\\n 1.9 & 142.517 & 2 \\sqrt[4]{\\Lambda }+\\frac{7.25}{\\sqrt[4]{\\Lambda }}-\\frac{32.1572}{\\Lambda\n   ^{3\/4}}+\\frac{331.669}{\\Lambda ^{5\/4}}-\\frac{1271.1}{\\Lambda ^{7\/4}}\n   \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}makes the agreement even more impressive. \n\nIn Figure \\ref{figJ5n2} we plot the difference between the numerical solution and its large $\\lambda$ asymptotics \n $2(4\\lambda)^{1\/4}+{7.25\\over(4\\lambda)^{1\/4}}$ and $2(4\\lambda)^{1\/4}+{7.25\\over(4\\lambda)^{1\/4}}-{31.99\\over(4\\lambda)^{3\/4}}$ . \n\n\n\\subsection{$J=6,n=3$ operator}\n\nIn the table \\eqref{E63data} we present the results of the computation of the energy of the $J=6,n=3$ state.\nFitting the data in the interval $g\\in [g_0, 7.7]$ we get \n{\\smaller \n\\begin{eqnarray}\\label{FitEJ6n3a}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n2.2 & 191.076 & 2.02122 \\sqrt[4]{\\Lambda }-1.1605+\\frac{35.1776}{\\sqrt[4]{\\Lambda }}-\\frac{312.4}{\\sqrt{\\Lambda\n   }}+\\frac{1974.72}{\\Lambda ^{3\/4}}-\\frac{7098.66}{\\Lambda }+\\frac{10856.1}{\\Lambda ^{5\/4}} \\\\\n 2.3 & 208.841 & 2.01305 \\sqrt[4]{\\Lambda }-0.711293+\\frac{24.9684}{\\sqrt[4]{\\Lambda }}-\\frac{189.655}{\\sqrt{\\Lambda\n   }}+\\frac{1151.37}{\\Lambda ^{3\/4}}-\\frac{4177.2}{\\Lambda }+\\frac{6572.03}{\\Lambda ^{5\/4}} \\\\\n 2.4 & 227.396 & 2.00352 \\sqrt[4]{\\Lambda }-0.182115+\\frac{12.8223}{\\sqrt[4]{\\Lambda }}-\\frac{42.0904}{\\sqrt{\\Lambda\n   }}+\\frac{150.596}{\\Lambda ^{3\/4}}-\\frac{584.867}{\\Lambda }+\\frac{1239.93}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 1.99454 \\sqrt[4]{\\Lambda }+0.320466+\\frac{1.17703}{\\sqrt[4]{\\Lambda }}+\\frac{100.809}{\\sqrt{\\Lambda\n   }}-\\frac{828.784}{\\Lambda ^{3\/4}}+\\frac{2969.68}{\\Lambda }-\\frac{4097.42}{\\Lambda ^{5\/4}} \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}where the expansion parameter $\\Lambda = n^2\\lambda = 9\\lambda$ is introduced.\nOne sees that  as expected $c_{-1}$ is close to 2, and \nfixing  $c_{-1}= 2$ one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ6n3b}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n2.2 & 191.076 & 2 \\sqrt[4]{\\Lambda }-0.0280675+\\frac{10.2297}{\\sqrt[4]{\\Lambda }}-\\frac{21.9871}{\\sqrt{\\Lambda\n   }}+\\frac{90.6627}{\\Lambda ^{3\/4}}-\\frac{639.338}{\\Lambda }+\\frac{1711.89}{\\Lambda ^{5\/4}} \\\\\n 2.3 & 208.841 & 2 \\sqrt[4]{\\Lambda }-0.00754532+\\frac{9.29219}{\\sqrt[4]{\\Lambda }}-\\frac{5.02319}{\\sqrt{\\Lambda\n   }}-\\frac{61.3087}{\\Lambda ^{3\/4}}+\\frac{34.676}{\\Lambda }+\\frac{527.865}{\\Lambda ^{5\/4}} \\\\\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+0.00938827+\\frac{8.51111}{\\sqrt[4]{\\Lambda }}+\\frac{9.25714}{\\sqrt{\\Lambda\n   }}-\\frac{190.658}{\\Lambda ^{3\/4}}+\\frac{615.119}{\\Lambda }-\\frac{504.505}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+0.0202856+\\frac{8.00379}{\\sqrt[4]{\\Lambda }}+\\frac{18.6248}{\\sqrt{\\Lambda\n   }}-\\frac{276.408}{\\Lambda ^{3\/4}}+\\frac{1004.23}{\\Lambda }-\\frac{1204.79}{\\Lambda ^{5\/4}}\n  \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}We see that the coefficient $c_0$ becomes small and we set it to 0: $c_0=0$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ6n3c}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.2 & 191.076 & 2 \\sqrt[4]{\\Lambda }+\\frac{8.99159}{\\sqrt[4]{\\Lambda }}-\\frac{0.390111}{\\sqrt{\\Lambda\n   }}-\\frac{95.5746}{\\Lambda ^{3\/4}}+\\frac{154.709}{\\Lambda }+\\frac{372.41}{\\Lambda ^{5\/4}} \\\\\n 2.3 & 208.841 & 2 \\sqrt[4]{\\Lambda }+\\frac{8.95568}{\\sqrt[4]{\\Lambda }}+\\frac{0.91621}{\\sqrt{\\Lambda\n   }}-\\frac{113.173}{\\Lambda ^{3\/4}}+\\frac{258.775}{\\Lambda }+\\frac{144.476}{\\Lambda ^{5\/4}} \\\\\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{8.93423}{\\sqrt[4]{\\Lambda }}+\\frac{1.70451}{\\sqrt{\\Lambda\n   }}-\\frac{123.911}{\\Lambda ^{3\/4}}+\\frac{323.035}{\\Lambda }+\\frac{1.91857}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{8.9273}{\\sqrt[4]{\\Lambda }}+\\frac{1.96172}{\\sqrt{\\Lambda\n   }}-\\frac{127.452}{\\Lambda ^{3\/4}}+\\frac{344.466}{\\Lambda }-\\frac{46.2066}{\\Lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}This fitting shows that $c_1\\approx 9$, and assuming that $b_1$ is independent of $J$ one concludes that  for any two-particle $n=3$ state we should expect the  formula: $c_1(J,3)=J^2\/4$. This is different from the $n=1$ and $n=2$ cases and therefore $c_1$ shows a nontrivial dependence of the string level $n$.\n\\begin{figure}[t]\n\\begin{center}\n\\includegraphics*[width=0.475\\textwidth]{EJ6n3a}\\qquad \\includegraphics*[width=0.465\\textwidth]{EJ6n3b}\n\\end{center}\n\\caption{\\smaller \nBlack dots represent the difference between the numerical solution and conjectured \nasymptotic expansions.\n}\n\\label{figJ6n3}\n\\end{figure}\nThen setting $c_1 = 9$, one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ6n3d}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.2 & 191.076 & 2 \\sqrt[4]{\\Lambda }+\\frac{9}{\\sqrt[4]{\\Lambda }}-\\frac{0.683102}{\\sqrt{\\Lambda }}-\\frac{91.8011}{\\Lambda\n   ^{3\/4}}+\\frac{133.416}{\\Lambda }+\\frac{416.847}{\\Lambda ^{5\/4}} \\\\\n 2.3 & 208.841 & 2 \\sqrt[4]{\\Lambda }+\\frac{9}{\\sqrt[4]{\\Lambda }}-\\frac{0.646888}{\\sqrt{\\Lambda }}-\\frac{92.7809}{\\Lambda\n   ^{3\/4}}+\\frac{142.105}{\\Lambda }+\\frac{391.588}{\\Lambda ^{5\/4}} \\\\\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{9}{\\sqrt[4]{\\Lambda }}-\\frac{0.641557}{\\sqrt{\\Lambda }}-\\frac{92.9268}{\\Lambda\n   ^{3\/4}}+\\frac{143.414}{\\Lambda }+\\frac{387.73}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{9}{\\sqrt[4]{\\Lambda }}-\\frac{0.659812}{\\sqrt{\\Lambda }}-\\frac{92.422}{\\Lambda\n   ^{3\/4}}+\\frac{138.829}{\\Lambda }+\\frac{401.412}{\\Lambda ^{5\/4}}    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}Even though the coefficient $c_2$ is not really small  the contribution of the corresponding term is much smaller than the contribution of the next term, and we believe that this supports $c_2=0$. \nSetting $c_{2k}=0$ one gets the following fitting\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ6n3e}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n2.2 & 191.076 & 2.00009 \\sqrt[4]{\\Lambda }+\\frac{8.93337}{\\sqrt[4]{\\Lambda }}-\\frac{85.2279}{\\Lambda\n   ^{3\/4}}+\\frac{1023.82}{\\Lambda ^{5\/4}}-\\frac{3934.94}{\\Lambda ^{7\/4}} \\\\\n 2.3 & 208.841 & 2.00006 \\sqrt[4]{\\Lambda }+\\frac{8.94417}{\\sqrt[4]{\\Lambda }}-\\frac{86.5518}{\\Lambda\n   ^{3\/4}}+\\frac{1092.42}{\\Lambda ^{5\/4}}-\\frac{5204.87}{\\Lambda ^{7\/4}} \\\\\n 2.4 & 227.396 & 2.00004 \\sqrt[4]{\\Lambda }+\\frac{8.95121}{\\sqrt[4]{\\Lambda }}-\\frac{87.4341}{\\Lambda\n   ^{3\/4}}+\\frac{1139.29}{\\Lambda ^{5\/4}}-\\frac{6097.}{\\Lambda ^{7\/4}} \\\\\n 2.5 & 246.74 & 2.00003 \\sqrt[4]{\\Lambda }+\\frac{8.95445}{\\sqrt[4]{\\Lambda }}-\\frac{87.8483}{\\Lambda\n   ^{3\/4}}+\\frac{1161.82}{\\Lambda ^{5\/4}}-\\frac{6537.3}{\\Lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}which agrees very well with $c_1=9$\nbut it shows that the coefficient $c_3$ is different from  the conjectured value\n$c_3=-\\frac{87}{8}-81 \\zeta (3)\\approx -108.242$.\nSetting $c_{-1}=2, c_1=9$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ6n3f}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n2.2 & 191.076 & 2 \\sqrt[4]{\\Lambda }+\\frac{9}{\\sqrt[4]{\\Lambda }}-\\frac{96.7473}{\\Lambda ^{3\/4}}+\\frac{1737.24}{\\Lambda\n   ^{5\/4}}-\\frac{18361.}{\\Lambda ^{7\/4}} \\\\\n 2.3 & 208.841 & 2 \\sqrt[4]{\\Lambda }+\\frac{9}{\\sqrt[4]{\\Lambda }}-\\frac{96.9946}{\\Lambda ^{3\/4}}+\\frac{1774.91}{\\Lambda\n   ^{5\/4}}-\\frac{19670.4}{\\Lambda ^{7\/4}} \\\\\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{9}{\\sqrt[4]{\\Lambda }}-\\frac{97.2184}{\\Lambda ^{3\/4}}+\\frac{1809.99}{\\Lambda\n   ^{5\/4}}-\\frac{20931.5}{\\Lambda ^{7\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{9}{\\sqrt[4]{\\Lambda }}-\\frac{97.4245}{\\Lambda ^{3\/4}}+\\frac{1843.16}{\\Lambda\n   ^{5\/4}}-\\frac{22163.}{\\Lambda ^{7\/4}}\n   \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}does not help and one has to conclude that the formula conjectured in  \\cite{Gr11} is correct only for the $n=1$ and $n=2$ operators. It is not really surprising because \\cite{Gr11} used $c_1=10$ while the mirror TBA predicts $c_1=9$.  \n\nIn Figure \\ref{figJ6n3} we plot the difference between the numerical solution and its large $\\lambda$ asymptotics \n$2(9\\lambda)^{1\/4}$ and $2(9\\lambda)^{1\/4}+{9\\over(9\\lambda)^{1\/4}}$. \n\n\n\n\n\\subsection{$J=7,n=3$ operator}\n\nIn the table \\eqref{E73data} we present the results of the computation of the energy of the $J=7,n=3$ state.\nFitting the data in the interval $g\\in [g_0, 7.7]$ we get \n{\\smaller \n\\begin{eqnarray}\\label{FitEJ7n3a}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.2 & 191.076 & 2.02727 \\sqrt[4]{\\Lambda }-1.46037+\\frac{44.517}{\\sqrt[4]{\\Lambda }}-\\frac{377.119}{\\sqrt{\\Lambda\n   }}+\\frac{2352.97}{\\Lambda ^{3\/4}}-\\frac{8336.68}{\\Lambda }+\\frac{12906.3}{\\Lambda ^{5\/4}} \\\\\n 2.3 & 208.841 & 2.03163 \\sqrt[4]{\\Lambda }-1.70019+\\frac{49.9676}{\\sqrt[4]{\\Lambda }}-\\frac{442.652}{\\sqrt{\\Lambda\n   }}+\\frac{2792.56}{\\Lambda ^{3\/4}}-\\frac{9896.42}{\\Lambda }+\\frac{15193.5}{\\Lambda ^{5\/4}} \\\\\n 2.4 & 227.396 & 2.03791 \\sqrt[4]{\\Lambda }-2.04842+\\frac{57.9602}{\\sqrt[4]{\\Lambda }}-\\frac{539.755}{\\sqrt{\\Lambda\n   }}+\\frac{3451.11}{\\Lambda ^{3\/4}}-\\frac{12260.3}{\\Lambda }+\\frac{18702.2}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2.04761 \\sqrt[4]{\\Lambda }-2.59153+\\frac{70.5447}{\\sqrt[4]{\\Lambda }}-\\frac{694.179}{\\sqrt{\\Lambda\n   }}+\\frac{4509.47}{\\Lambda ^{3\/4}}-\\frac{16101.5}{\\Lambda }+\\frac{24470.}{\\Lambda ^{5\/4}} \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}where $\\Lambda = n^2\\lambda = 9\\lambda$.\nOne sees that $c_{-1}$ is close to 2, and \nfixing  $c_{-1}= 2$ one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ7n3b}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.2 & 191.076 & 2 \\sqrt[4]{\\Lambda }-0.00494946+\\frac{12.4534}{\\sqrt[4]{\\Lambda }}-\\frac{3.87439}{\\sqrt{\\Lambda\n   }}-\\frac{68.4585}{\\Lambda ^{3\/4}}-\\frac{35.0256}{\\Lambda }+\\frac{1153.99}{\\Lambda ^{5\/4}} \\\\\n 2.3 & 208.841 & 2 \\sqrt[4]{\\Lambda }+0.00564328+\\frac{11.9695}{\\sqrt[4]{\\Lambda }}+\\frac{4.88171}{\\sqrt{\\Lambda\n   }}-\\frac{146.9}{\\Lambda ^{3\/4}}+\\frac{312.873}{\\Lambda }+\\frac{542.839}{\\Lambda ^{5\/4}} \\\\\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+0.0162742+\\frac{11.4791}{\\sqrt[4]{\\Lambda }}+\\frac{13.8469}{\\sqrt{\\Lambda\n   }}-\\frac{228.106}{\\Lambda ^{3\/4}}+\\frac{677.277}{\\Lambda }-\\frac{105.285}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+0.0264211+\\frac{11.0067}{\\sqrt[4]{\\Lambda }}+\\frac{22.5695}{\\sqrt{\\Lambda\n   }}-\\frac{307.95}{\\Lambda ^{3\/4}}+\\frac{1039.59}{\\Lambda }-\\frac{757.345}{\\Lambda ^{5\/4}}\n  \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}Since the coefficient $c_0$ becomes small we set it to 0: $c_0=0$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ7n3c}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n2.2 & 191.076 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.2351}{\\sqrt[4]{\\Lambda }}-\\frac{0.065948}{\\sqrt{\\Lambda\n   }}-\\frac{101.3}{\\Lambda ^{3\/4}}+\\frac{104.997}{\\Lambda }+\\frac{917.781}{\\Lambda ^{5\/4}} \\\\\n 2.3 & 208.841 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.2212}{\\sqrt[4]{\\Lambda }}+\\frac{0.439529}{\\sqrt{\\Lambda\n   }}-\\frac{108.11}{\\Lambda ^{3\/4}}+\\frac{145.265}{\\Lambda }+\\frac{829.583}{\\Lambda ^{5\/4}} \\\\\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.2126}{\\sqrt[4]{\\Lambda }}+\\frac{0.754727}{\\sqrt{\\Lambda\n   }}-\\frac{112.403}{\\Lambda ^{3\/4}}+\\frac{170.959}{\\Lambda }+\\frac{772.582}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.2096}{\\sqrt[4]{\\Lambda }}+\\frac{0.866542}{\\sqrt{\\Lambda\n   }}-\\frac{113.942}{\\Lambda ^{3\/4}}+\\frac{180.276}{\\Lambda }+\\frac{751.66}{\\Lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}\\begin{figure}[t]\n\\begin{center}\n\\includegraphics*[width=0.475\\textwidth]{EJ7n3a}\\qquad \\includegraphics*[width=0.465\\textwidth]{EJ7n3b}\n\\end{center}\n\\caption{\\smaller \nBlack dots represent the difference between the numerical solution and conjectured \nasymptotic expansions.\n}\n\\label{figJ7n3}\n\\end{figure}This fitting shows that $c_1\\approx 12.25$ in agreement with the  formula $c_1(J,2)=J^2\/4$ we obtained analyzing  the $J=6,n=3$ state. \nThen setting $c_1 = 12.25$, one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ7n3d}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.2 & 191.076 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.25}{\\sqrt[4]{\\Lambda }}-\\frac{0.586725}{\\sqrt{\\Lambda\n   }}-\\frac{94.5925}{\\Lambda ^{3\/4}}+\\frac{67.1513}{\\Lambda }+\\frac{996.766}{\\Lambda ^{5\/4}} \\\\\n 2.3 & 208.841 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.25}{\\sqrt[4]{\\Lambda }}-\\frac{0.577563}{\\sqrt{\\Lambda\n   }}-\\frac{94.8404}{\\Lambda ^{3\/4}}+\\frac{69.3494}{\\Lambda }+\\frac{990.376}{\\Lambda ^{5\/4}} \\\\\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.25}{\\sqrt[4]{\\Lambda }}-\\frac{0.57989}{\\sqrt{\\Lambda\n   }}-\\frac{94.7767}{\\Lambda ^{3\/4}}+\\frac{68.7779}{\\Lambda }+\\frac{992.06}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.25}{\\sqrt[4]{\\Lambda }}-\\frac{0.59125}{\\sqrt{\\Lambda\n   }}-\\frac{94.4626}{\\Lambda ^{3\/4}}+\\frac{65.9249}{\\Lambda }+\\frac{1000.57}{\\Lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}Since the contribution of the $c_2$  term is much smaller than the contribution of the next term the fitting supports $c_2=0$. \nSetting $c_{2k}=0$ one gets the following fitting\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ7n3e}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n2.2 & 191.076 & 2.00005 \\sqrt[4]{\\Lambda }+\\frac{12.2061}{\\sqrt[4]{\\Lambda }}-\\frac{93.0595}{\\Lambda\n   ^{3\/4}}+\\frac{1340.05}{\\Lambda ^{5\/4}}-\\frac{2462.57}{\\Lambda ^{7\/4}} \\\\\n 2.3 & 208.841 & 2.00004 \\sqrt[4]{\\Lambda }+\\frac{12.2106}{\\sqrt[4]{\\Lambda }}-\\frac{93.6089}{\\Lambda\n   ^{3\/4}}+\\frac{1368.52}{\\Lambda ^{5\/4}}-\\frac{2989.6}{\\Lambda ^{7\/4}} \\\\\n 2.4 & 227.396 & 2.00003 \\sqrt[4]{\\Lambda }+\\frac{12.2136}{\\sqrt[4]{\\Lambda }}-\\frac{93.9924}{\\Lambda\n   ^{3\/4}}+\\frac{1388.89}{\\Lambda ^{5\/4}}-\\frac{3377.36}{\\Lambda ^{7\/4}} \\\\\n 2.5 & 246.74 & 2.00003 \\sqrt[4]{\\Lambda }+\\frac{12.2152}{\\sqrt[4]{\\Lambda }}-\\frac{94.1927}{\\Lambda\n   ^{3\/4}}+\\frac{1399.79}{\\Lambda ^{5\/4}}-\\frac{3590.34}{\\Lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}which agrees with $c_1=12.25$\nbut disagrees with the conjectured value of $c_3$: \n\n\\noindent $c_3=-\\frac{1489}{64}-81 \\zeta (3)\\approx -120.632$.\nFinally setting $c_{-1}=2, c_1=12.25$ one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ7n3f}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n2.2 & 191.076 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.25}{\\sqrt[4]{\\Lambda }}-\\frac{100.961}{\\Lambda\n   ^{3\/4}}+\\frac{1838.01}{\\Lambda ^{5\/4}}-\\frac{12626.6}{\\Lambda ^{7\/4}} \\\\\n 2.3 & 208.841 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.25}{\\sqrt[4]{\\Lambda }}-\\frac{101.136}{\\Lambda\n   ^{3\/4}}+\\frac{1864.62}{\\Lambda ^{5\/4}}-\\frac{13551.4}{\\Lambda ^{7\/4}} \\\\\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.25}{\\sqrt[4]{\\Lambda }}-\\frac{101.298}{\\Lambda\n   ^{3\/4}}+\\frac{1890.13}{\\Lambda ^{5\/4}}-\\frac{14468.5}{\\Lambda ^{7\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{12.25}{\\sqrt[4]{\\Lambda }}-\\frac{101.452}{\\Lambda\n   ^{3\/4}}+\\frac{1914.79}{\\Lambda ^{5\/4}}-\\frac{15384.2}{\\Lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}In Figure \\ref{figJ7n3} we plot the difference between the numerical solution and its large $\\lambda$ asymptotics \n$2(9\\lambda)^{1\/4}$ and $2(9\\lambda)^{1\/4}+{12.25\\over(9\\lambda)^{1\/4}}$. \n\n\n\\subsection{$J=8,n=4$ operator}\n\nIn the table \\eqref{E84data} we present the results of the computation of the energy of the $J=8,n=4$ state. The precision for this operator is higher than for the other operators and should be about $0.00002$. \nFitting the data in the interval $g\\in [g_0, 7.7]$ we get \n{\\smaller \n\\begin{eqnarray}\\label{FitEJ8n4a}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.4 & 227.396 & 2.02587 \\sqrt[4]{\\Lambda }-1.71713+\\frac{61.1202}{\\sqrt[4]{\\Lambda }}-\\frac{685.038}{\\sqrt{\\Lambda\n   }}+\\frac{5322.77}{\\Lambda ^{3\/4}}-\\frac{23175.3}{\\Lambda }+\\frac{43004.2}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2.0207 \\sqrt[4]{\\Lambda }-1.38273+\\frac{52.1731}{\\sqrt[4]{\\Lambda }}-\\frac{558.265}{\\sqrt{\\Lambda\n   }}+\\frac{4319.5}{\\Lambda ^{3\/4}}-\\frac{18970.8}{\\Lambda }+\\frac{35714.1}{\\Lambda ^{5\/4}} \\\\\n 2.6 & 266.874 & 2.02039 \\sqrt[4]{\\Lambda }-1.36242+\\frac{51.6249}{\\sqrt[4]{\\Lambda }}-\\frac{550.422}{\\sqrt{\\Lambda\n   }}+\\frac{4256.81}{\\Lambda ^{3\/4}}-\\frac{18705.2}{\\Lambda }+\\frac{35248.6}{\\Lambda ^{5\/4}} \\\\\n 2.7 & 287.798 & 2.0272 \\sqrt[4]{\\Lambda }-1.81055+\\frac{63.8305}{\\sqrt[4]{\\Lambda }}-\\frac{726.645}{\\sqrt{\\Lambda\n   }}+\\frac{5679.17}{\\Lambda ^{3\/4}}-\\frac{24790.5}{\\Lambda }+\\frac{46029.7}{\\Lambda ^{5\/4}}\\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}where $\\Lambda = n^2\\lambda = 16\\lambda$.\nOne sees that $c_{-1}$ is close to 2, and \nfixing  $c_{-1}= 2$ one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ8n4b}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }-0.0901497+\\frac{18.8267}{\\sqrt[4]{\\Lambda }}-\\frac{103.386}{\\sqrt{\\Lambda\n   }}+\\frac{859.119}{\\Lambda ^{3\/4}}-\\frac{5051.13}{\\Lambda }+\\frac{12580.9}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }-0.0684271+\\frac{17.659}{\\sqrt[4]{\\Lambda }}-\\frac{78.4877}{\\sqrt{\\Lambda\n   }}+\\frac{595.952}{\\Lambda ^{3\/4}}-\\frac{3672.19}{\\Lambda }+\\frac{9715.32}{\\Lambda ^{5\/4}} \\\\\n 2.6 & 266.874 & 2 \\sqrt[4]{\\Lambda }-0.0558615+\\frac{16.9775}{\\sqrt[4]{\\Lambda }}-\\frac{63.8179}{\\sqrt{\\Lambda\n   }}+\\frac{439.324}{\\Lambda ^{3\/4}}-\\frac{2842.69}{\\Lambda }+\\frac{7972.04}{\\Lambda ^{5\/4}} \\\\\n 2.7 & 287.798 & 2 \\sqrt[4]{\\Lambda }-0.0516738+\\frac{16.7484}{\\sqrt[4]{\\Lambda }}-\\frac{58.8418}{\\sqrt{\\Lambda\n   }}+\\frac{385.679}{\\Lambda ^{3\/4}}-\\frac{2555.67}{\\Lambda }+\\frac{7362.33}{\\Lambda ^{5\/4}}\n  \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}Since the coefficient $c_0$ becomes small we set it to 0: $c_0=0$\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ8n4c}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{14.1353}{\\sqrt[4]{\\Lambda }}-\\frac{6.68802}{\\sqrt{\\Lambda\n   }}-\\frac{127.649}{\\Lambda ^{3\/4}}-\\frac{64.996}{\\Lambda }+\\frac{2598.41}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{14.0619}{\\sqrt[4]{\\Lambda }}-\\frac{3.54403}{\\sqrt{\\Lambda\n   }}-\\frac{177.626}{\\Lambda ^{3\/4}}+\\frac{284.294}{\\Lambda }+\\frac{1692.72}{\\Lambda ^{5\/4}} \\\\\n 2.6 & 266.874 & 2 \\sqrt[4]{\\Lambda }+\\frac{14.0123}{\\sqrt[4]{\\Lambda }}-\\frac{1.39941}{\\sqrt{\\Lambda\n   }}-\\frac{212.063}{\\Lambda ^{3\/4}}+\\frac{527.596}{\\Lambda }+\\frac{1054.52}{\\Lambda ^{5\/4}} \\\\\n 2.7 & 287.798 & 2 \\sqrt[4]{\\Lambda }+\\frac{13.9798}{\\sqrt[4]{\\Lambda }}+\\frac{0.0198075}{\\sqrt{\\Lambda\n   }}-\\frac{235.074}{\\Lambda ^{3\/4}}+\\frac{691.858}{\\Lambda }+\\frac{618.868}{\\Lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}\\begin{figure}[t]\n\\begin{center}\n\\includegraphics*[width=0.475\\textwidth]{EJ8n4a}\\qquad \\includegraphics*[width=0.45\\textwidth]{EJ8n4b}\n\\end{center}\n\\caption{\\smaller \nBlack dots represent the difference between the numerical solution and conjectured \nasymptotic expansions.\n}\n\\label{figJ8n4}\n\\end{figure}This fitting shows that $c_1\\approx 14$ which suggests the  formula $c_1(J,2)=J^2\/4-2$. \nThen setting $c_1 = 14$, one gets\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ8n4d}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{14}{\\sqrt[4]{\\Lambda }}-\\frac{1.11641}{\\sqrt{\\Lambda\n   }}-\\frac{212.617}{\\Lambda ^{3\/4}}+\\frac{503.771}{\\Lambda }+\\frac{1187.75}{\\Lambda ^{5\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{14}{\\sqrt[4]{\\Lambda }}-\\frac{0.966912}{\\sqrt{\\Lambda\n   }}-\\frac{217.391}{\\Lambda ^{3\/4}}+\\frac{553.832}{\\Lambda }+\\frac{1015.24}{\\Lambda ^{5\/4}} \\\\\n 2.6 & 266.874 & 2 \\sqrt[4]{\\Lambda }+\\frac{14}{\\sqrt[4]{\\Lambda }}-\\frac{0.881553}{\\sqrt{\\Lambda\n   }}-\\frac{220.144}{\\Lambda ^{3\/4}}+\\frac{583.027}{\\Lambda }+\\frac{913.412}{\\Lambda ^{5\/4}} \\\\\n 2.7 & 287.798 & 2 \\sqrt[4]{\\Lambda }+\\frac{14}{\\sqrt[4]{\\Lambda }}-\\frac{0.839038}{\\sqrt{\\Lambda\n   }}-\\frac{221.528}{\\Lambda ^{3\/4}}+\\frac{597.866}{\\Lambda }+\\frac{861.055}{\\Lambda ^{5\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}Since the contribution of the $c_2$  term is much smaller than the contribution of the next term the fitting supports $c_2=0$. \nSetting $c_{2k}=0$ one gets the following fitting\n{\\smaller \n\\begin{eqnarray}\\label{FitEJ8n4e}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.4 & 227.396 & 2.00022 \\sqrt[4]{\\Lambda }+\\frac{13.8411}{\\sqrt[4]{\\Lambda }}-\\frac{180.225}{\\Lambda\n   ^{3\/4}}+\\frac{3375.94}{\\Lambda ^{5\/4}}-\\frac{13371.7}{\\Lambda ^{7\/4}} \\\\\n 2.5 & 246.74 & 2.00017 \\sqrt[4]{\\Lambda }+\\frac{13.8627}{\\sqrt[4]{\\Lambda }}-\\frac{183.91}{\\Lambda\n   ^{3\/4}}+\\frac{3643.1}{\\Lambda ^{5\/4}}-\\frac{20334.4}{\\Lambda ^{7\/4}} \\\\\n 2.6 & 266.874 & 2.00014 \\sqrt[4]{\\Lambda }+\\frac{13.8782}{\\sqrt[4]{\\Lambda }}-\\frac{186.603}{\\Lambda\n   ^{3\/4}}+\\frac{3842.8}{\\Lambda ^{5\/4}}-\\frac{25671.9}{\\Lambda ^{7\/4}} \\\\\n 2.7 & 287.798 & 2.00012 \\sqrt[4]{\\Lambda }+\\frac{13.8893}{\\sqrt[4]{\\Lambda }}-\\frac{188.555}{\\Lambda\n   ^{3\/4}}+\\frac{3990.66}{\\Lambda ^{5\/4}}-\\frac{29719.7}{\\Lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}which agrees with $c_1=14$.\nThe agreement becomes even better if one sets $c_{-1}=2$ \n{\\smaller \n\\begin{eqnarray}\\label{FitEJ8n4f}\n\\begin{array}{|c|c|c|}\n\\hline\ng_0&\\lambda_0& {\\rm Fit} \\\\\\hline\n 2.4 & 227.396 & 2 \\sqrt[4]{\\Lambda }+\\frac{13.9364}{\\sqrt[4]{\\Lambda }}-\\frac{195.091}{\\Lambda\n   ^{3\/4}}+\\frac{4356.69}{\\Lambda ^{5\/4}}-\\frac{36551.8}{\\Lambda ^{7\/4}} \\\\\n 2.5 & 246.74 & 2 \\sqrt[4]{\\Lambda }+\\frac{13.9395}{\\sqrt[4]{\\Lambda }}-\\frac{196.166}{\\Lambda\n   ^{3\/4}}+\\frac{4473.31}{\\Lambda ^{5\/4}}-\\frac{40538.4}{\\Lambda ^{7\/4}} \\\\\n 2.6 & 266.874 & 2 \\sqrt[4]{\\Lambda }+\\frac{13.9418}{\\sqrt[4]{\\Lambda }}-\\frac{196.979}{\\Lambda\n   ^{3\/4}}+\\frac{4563.51}{\\Lambda ^{5\/4}}-\\frac{43705.8}{\\Lambda ^{7\/4}} \\\\\n 2.7 & 287.798 & 2 \\sqrt[4]{\\Lambda }+\\frac{13.9435}{\\sqrt[4]{\\Lambda }}-\\frac{197.604}{\\Lambda\n   ^{3\/4}}+\\frac{4634.52}{\\Lambda ^{5\/4}}-\\frac{46263.4}{\\Lambda ^{7\/4}}\n    \\\\\\hline\n   \\end{array}~~~~\n\\end{eqnarray}\n}In Figure \\ref{figJ8n4} we plot the difference between the numerical solution and its large $\\lambda$ asymptotics \n$2(16\\lambda)^{1\/4}$ and $2(16\\lambda)^{1\/4}+{14\\over(16\\lambda)^{1\/4}}$. \n\n\n\\section*{Acknowledgements}\nThe author thanks Gleb Arutyunov for interesting\ndiscussions and Dmitri Grigoriev for computer help.  This work \nwas supported in part by the Science Foundation Ireland under\nGrant No.  09\/RFP\/PHY2142. \n\n\n\n\\section{Numerical data}\n\nHere we collect our numerical data for the energy of the two-paticle states or, equivalently, the conformal dimension of the dual ${\\cal N}=4$ SYM operators\nas a function of the effective string tension $g$ related to 't Hooft's coupling $\\lambda$ as $\\lambda=4\\pi^2g^2$.  \n\nAn interested reader can download a Mathematica file with this data and the data for Bethe roots from the Arxiv page of this paper:  http:\/\/arXiv.org\/abs\/arXiv:12??.????\n\n\\subsection*{ $J=3,n=1$ operator}\n{\\smaller \\begin{eqnarray}\\label{E31data}\n\\begin{array}{|c|c||}\n\\hline\ng& {\\rm E}_{(3,1)}\\\\\\hline\n0 & 5 \\\\\n0.1 & 5.01985 \\\\\n 0.2 & 5.07773 \\\\\n 0.3 & 5.16917 \\\\\n 0.4 & 5.28828 \\\\\n 0.5 & 5.42891 \\\\\n 0.6 & 5.5854 \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(3,1)}\\\\\\hline\n 0.7 & 5.75288 \\\\\n 0.8 & 5.92734 \\\\\n 0.9 & 6.10559 \\\\\n 1. & 6.2862 \\\\\n 1.1 & 6.46621 \\\\\n 1.2 & 6.64492 \\\\\n 1.3 & 6.82157 \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(3,1)}\\\\\\hline\n 1.4 & 6.9957 \\\\\n 1.5 & 7.16701 \\\\\n 1.6 & 7.33539 \\\\\n 1.7 & 7.50075 \\\\\n 1.8 & 7.66321 \\\\\n 1.9 & 7.82271 \\\\\n 2. & 7.97949 \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(3,1)}\\\\\\hline\n 2.1 & 8.13347 \\\\\n 2.2 & 8.28485 \\\\\n 2.3 & 8.4337 \\\\\n 2.4 & 8.58018 \\\\\n 2.5 & 8.72423 \\\\\n 2.6 & 8.86614 \\\\\n 2.7 & 9.00592 \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(3,1)}\\\\\\hline\n 2.8 & 9.14362 \\\\\n 2.9 & 9.27936 \\\\\n 3. & 9.41322 \\\\\n 3.1 & 9.54522 \\\\\n 3.2 & 9.67549 \\\\\n 3.3 & 9.80404 \\\\\n 3.4 & 9.93099 \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c|}\n\\hline\ng& {\\rm E}_{(3,1)}\\\\\\hline\n 3.5 & 10.0564 \\\\\n 3.6 & 10.1802 \\\\\n 3.7 & 10.3025\\\\\n &\\\\\n &\\\\\n &\\\\\n &\n \\\\\\hline\n\\end{array}\n\\end{eqnarray}\n}\n\n\n\\subsection*{$J=4,n=1$ operator}\n{\\smaller \\begin{eqnarray}\\label{E41data}\n\\begin{array}{|c|c||}\n\\hline\ng& {\\rm E}_{(4,1)}\\\\\\hline\n0 & 6 \\\\\n0.1 & 6.01375 \\\\\n 0.2 & 6.05416 \\\\\n 0.3 & 6.11897 \\\\\n 0.4 & 6.20502 \\\\\n 0.5 & 6.30878 \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(4,1)}\\\\\\hline\n 0.6 & 6.42681\\\\\n 0.7 & 6.55594 \\\\\n 0.8 & 6.6934 \\\\\n 0.9 & 6.83685 \\\\\n 1. & 6.98458 \\\\\n 1.1 & 7.13475 \n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(4,1)}\\\\\\hline\n 1.2 & 7.28623 \\\\\n 1.3 & 7.43822 \\\\\n 1.4 & 7.58999 \\\\\n 1.5 & 7.74085 \\\\\n 1.6 & 7.89072 \\\\\n 1.61 & 7.90572  \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(4,1)}\\\\\\hline\n1.62 & 7.92062 \\\\\n 1.63 & 7.93556 \\\\\n 2.2 & 8.75551\\\\\n 2.3 & 8.89485 \\\\\n 2.4 & 9.03165 \\\\\n 2.5 & 9.16659 \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(4,1)}\\\\\\hline\n 2.6 & 9.29982 \\\\\n 2.7 & 9.43134 \\\\\n 2.8 & 9.56136 \\\\\n 2.9 & 9.68974 \\\\\n 3. & 9.81658 \\\\\n 3.1 & 9.94203 \n \\\\\\hline\n\\end{array}\n\\begin{array}{c|c|}\n\\hline\ng& {\\rm E}_{(4,1)}\\\\\\hline\n 3.2 & 10.0659 \\\\\n 3.3 & 10.1884 \\\\\n 3.4 & 10.3096\\\\\n &\\\\\n &\\\\\n &\n \\\\\\hline\n\\end{array}\n\\end{eqnarray}\n}\n\n\n\\subsection*{$J=4,n=2$ operator}\n\n{\\smaller \\begin{eqnarray}\\label{E42data}\n\\begin{array}{|c|c||}\n\\hline\ng& {\\rm E}_{(4,2)} \\\\\\hline\n0 & 6 \\\\\n 0.1 & 6.03583 \\\\\n 0.2 & 6.13947 \\\\\n 0.3 & 6.30103 \\\\\n 0.4 & 6.50828 \\\\\n 0.5 & 6.74951 \\\\\n 0.6 & 7.01484 \\\\\n 0.7 & 7.29635 \\\\\n 0.8 & 7.58773 \\\\\n 0.9 & 7.88397 \\\\\n 1. & 8.18112 \\\\\n 1.1 & 8.47607 \\\\\n 1.2 & 8.7666 \n   \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(4,2)} \\\\\\hline\n 1.3 & 9.05125 \\\\\n 1.4 & 9.32919 \\\\\n 1.5 & 9.60001 \\\\\n 1.6 & 9.8638 \\\\\n 1.7 & 10.1208 \\\\\n 1.8 & 10.3713 \\\\\n 1.9 & 10.6157 \\\\\n 2. & 10.8543 \\\\\n 2.1 & 11.0876 \\\\\n 2.2 & 11.3158 \\\\\n 2.3 & 11.5393 \\\\\n 2.4 & 11.7583 \\\\\n 2.5 & 11.9732 \n   \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(4,2)} \\\\\\hline\n 2.6 & 12.1841 \\\\\n 2.7 & 12.3912 \\\\\n 2.8 & 12.5948 \\\\\n 2.9 & 12.795 \\\\\n 3. & 12.9921 \\\\\n 3.1 & 13.1861 \\\\\n 3.2 & 13.3771 \\\\\n 3.3 & 13.5654 \\\\\n 3.4 & 13.7511 \\\\\n 3.5 & 13.9342 \\\\\n 3.6 & 14.1148 \\\\\n 3.7 & 14.2931 \\\\\n 3.8 & 14.4691 \n    \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(4,2)} \\\\\\hline\n 3.9 & 14.643 \\\\\n 4. & 14.8147 \\\\\n 4.1 & 14.9845 \\\\\n 4.2 & 15.1523 \\\\\n 4.3 & 15.3182 \\\\\n 4.4 & 15.4824 \\\\\n 4.5 & 15.6447 \\\\\n 4.6 & 15.8054 \\\\\n 4.7 & 15.9644 \\\\\n 4.8 & 16.1218 \\\\\n 4.9 & 16.2777 \\\\\n 5. & 16.4321 \\\\\n 5.1 & 16.585 \n   \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(4,2)} \\\\\\hline\n 5.2 & 16.7364 \\\\\n 5.3 & 16.8865 \\\\\n 5.4 & 17.0353 \\\\\n 5.5 & 17.1828 \\\\\n 5.6 & 17.3289 \\\\\n 5.7 & 17.4739 \\\\\n 5.8 & 17.6176 \\\\\n 5.9 & 17.7601 \\\\\n 6. & 17.9016 \\\\\n 6.1 & 18.0418 \\\\\n 6.2 & 18.181 \\\\\n 6.3 & 18.3191 \\\\\n 6.4 & 18.4562\n   \\\\\\hline\n\\end{array}\n\\begin{array}{c|c|}\n\\hline\ng& {\\rm E}_{(4,2)} \\\\\\hline\n 6.5 & 18.5923 \\\\\n 6.6 & 18.7273 \\\\\n 6.7 & 18.8614 \\\\\n 6.8 & 18.9945 \\\\\n 6.9 & 19.1267 \\\\\n 7. & 19.258 \\\\\n 7.1 & 19.3883 \\\\\n 7.2 & 19.5177 \\\\\n 7.3 & 19.6464 \\\\\n 7.4 & 19.7742 \\\\\n 7.5 & 19.9012 \\\\\n 7.6 & 20.0273 \\\\\n 7.7 & 20.1526\n   \\\\\\hline\n\\end{array}\n\\end{eqnarray}\n}\n\n\n\\subsection*{$J=5,n=2$ operator}\n{\\smaller \\begin{eqnarray}\\label{E52data}\n\\begin{array}{|c|c||}\n\\hline\ng& {\\rm E}_{(5,2)}\\\\\n\\hline\n  0 & 7\\\\\n  0.1 & 7.02974 \\\\\n 0.2 & 7.11606 \\\\\n 0.3 & 7.25139 \\\\\n 0.4 & 7.42611 \\\\\n 0.5 & 7.63068 \\\\\n 0.6 & 7.85687 \\\\\n 0.7 & 8.09799 \\\\\n 0.8 & 8.3488 \\\\\n 0.9 & 8.60527 \\\\\n 1. & 8.86434 \\\\\n 1.1 & 9.12364 \\\\\n 1.2 & 9.38146 \n   \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(5,2)}\\\\\n\\hline\n 1.3 & 9.63657 \\\\\n 1.4 & 9.88812 \\\\\n 1.5 & 10.1356 \\\\\n 1.6 & 10.3787 \\\\\n 1.7 & 10.6173 \\\\\n 1.8 & 10.8513 \\\\\n 1.9 & 11.081 \\\\\n 2. & 11.3063 \\\\\n 2.1 & 11.5274 \\\\\n 2.2 & 11.7445 \\\\\n 2.3 & 11.9577 \\\\\n 2.4 & 12.1673 \\\\\n 2.5 & 12.3734 \n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(5,2)}\\\\\n\\hline\n 2.6 & 12.576 \\\\\n 2.7 & 12.7755 \\\\\n 2.8 & 12.9719 \\\\\n 2.9 & 13.1653 \\\\\n 3. & 13.3559 \\\\\n 3.1 & 13.5438 \\\\\n 3.2 & 13.7291 \\\\\n 3.3 & 13.912 \\\\\n 3.4 & 14.0924 \\\\\n 3.5 & 14.2705 \\\\\n 3.6 & 14.4464 \\\\\n 3.7 & 14.6201 \\\\\n 3.8 & 14.7918  \n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(5,2)}\\\\\n\\hline\n 3.9 & 14.9615 \\\\\n 4. & 15.1292 \\\\\n 4.1 & 15.2951 \\\\\n 4.2 & 15.4592 \\\\\n 4.3 & 15.6215 \\\\\n 4.4 & 15.7822 \\\\\n 4.5 & 15.9412 \\\\\n 4.6 & 16.0986 \\\\\n 4.7 & 16.2545 \\\\\n 4.8 & 16.4089 \\\\\n 4.9 & 16.5619 \\\\\n 5. & 16.7134 \\\\\n 5.1 & 16.8636\n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(5,2)}\\\\\n\\hline\n 5.2 & 17.0124 \\\\\n 5.3 & 17.1599 \\\\\n 5.4 & 17.3061 \\\\\n 5.5 & 17.4511 \\\\\n 5.6 & 17.5949 \\\\\n 5.7 & 17.7375 \\\\\n 5.8 & 17.879 \\\\\n 5.9 & 18.0194 \\\\\n 6. & 18.1586 \\\\\n 6.1 & 18.2968 \\\\\n 6.2 & 18.434 \\\\\n 6.3 & 18.5701 \\\\\n 6.4 & 18.7052\n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c|}\n\\hline\ng& {\\rm E}_{(5,2)}\\\\\n\\hline\n 6.5 & 18.8393 \\\\\n 6.6 & 18.9725 \\\\\n 6.7 & 19.1048 \\\\\n 6.8 & 19.2361 \\\\\n 6.9 & 19.3666 \\\\\n 7. & 19.4962 \\\\\n 7.1 & 19.6249 \\\\\n 7.2 & 19.7527 \\\\\n 7.3 & 19.8798 \\\\\n 7.4 & 20.006 \\\\\n 7.5 & 20.1314 \\\\\n 7.6 & 20.2561 \\\\\n 7.7 & 20.3799 \n  \\\\\\hline\n\\end{array}\n\\end{eqnarray}\n}\n\n\n\n\\subsection*{$J=6,n=3$ operator}\n\n{\\smaller \\begin{eqnarray}\\label{E63data}\n\\begin{array}{|c|c||}\n\\hline\ng& {\\rm E}_{(6,3)}\\\\\\hline\n0&8\\\\\n0.1 & 8.03765 \\\\\n 0.2 & 8.14655 \\\\\n 0.3 & 8.31636 \\\\\n 0.4 & 8.53443 \\\\\n 0.5 & 8.78889 \\\\\n 0.6 & 9.06998 \\\\\n 0.7 & 9.37014 \\\\\n 0.8 & 9.68362 \\\\\n 0.9 & 10.006 \\\\\n 1. & 10.3337 \\\\\n 1.1 & 10.6639 \\\\\n 1.2 & 10.9941 \n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(6,3)}\\\\\\hline\n 1.3 & 11.3223 \\\\\n 1.4 & 11.6469 \\\\\n 1.5 & 11.9667 \\\\\n 1.6 & 12.2807 \\\\\n 1.7 & 12.5884 \\\\\n 1.8 & 12.8897 \\\\\n 1.9 & 13.1845 \\\\\n 2. & 13.4729 \\\\\n 2.1 & 13.7553 \\\\\n 2.2 & 14.0319 \\\\\n 2.3 & 14.3029 \\\\\n 2.4 & 14.5687 \\\\\n 2.5 & 14.8296\n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(6,3)}\\\\\\hline\n 2.6 & 15.0857 \\\\\n 2.7 & 15.3374 \\\\\n 2.8 & 15.5848 \\\\\n 2.9 & 15.8282 \\\\\n 3. & 16.0677 \\\\\n 3.1 & 16.3036 \\\\\n 3.2 & 16.536 \\\\\n 3.3 & 16.765 \\\\\n 3.4 & 16.9909 \\\\\n 3.5 & 17.2136 \\\\\n 3.6 & 17.4335 \\\\\n 3.7 & 17.6505 \\\\\n 3.8 & 17.8647 \n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(6,3)}\\\\\\hline\n 3.9 & 18.0764 \\\\\n 4. & 18.2855 \\\\\n 4.1 & 18.4922 \\\\\n 4.2 & 18.6966 \\\\\n 4.3 & 18.8987 \\\\\n 4.4 & 19.0986 \\\\\n 4.5 & 19.2964 \\\\\n 4.6 & 19.4921 \\\\\n 4.7 & 19.6858 \\\\\n 4.8 & 19.8776 \\\\\n 4.9 & 20.0675 \\\\\n 5. & 20.2556 \\\\\n 5.1 & 20.4419 \n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(6,3)}\\\\\\hline\n 5.2 & 20.6266 \\\\\n 5.3 & 20.8094 \\\\\n 5.4 & 20.9908 \\\\\n 5.5 & 21.1705 \\\\\n 5.6 & 21.3487 \\\\\n 5.7 & 21.5254 \\\\\n 5.8 & 21.7007 \\\\\n 5.9 & 21.8745 \\\\\n 6. & 22.0469 \\\\\n 6.1 & 22.2179 \\\\\n 6.2 & 22.3876 \\\\\n 6.3 & 22.5561 \\\\\n 6.4 & 22.7232\n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c|}\n\\hline\ng& {\\rm E}_{(6,3)}\\\\\\hline\n 6.5 & 22.8892 \\\\\n 6.6 & 23.0539 \\\\\n 6.7 & 23.2174 \\\\\n 6.8 & 23.3798 \\\\\n 6.9 & 23.541 \\\\\n 7. & 23.7011 \\\\\n 7.1 & 23.8602 \\\\\n 7.2 & 24.0182 \\\\\n 7.3 & 24.1751 \\\\\n 7.4 & 24.331 \\\\\n 7.5 & 24.4859 \\\\\n 7.6 & 24.6398 \\\\\n 7.7 & 24.7927\n  \\\\\\hline\n\\end{array}\n\\end{eqnarray}\n}\n\n\n\\subsection*{$J=7,n=3$ operator}\n\n{\\smaller \\begin{eqnarray}\\label{E73data}\n\\begin{array}{|c|c||}\n\\hline\ng& {\\rm E}_{(7,3)}\\\\\\hline\n0&9\\\\\n 0.1 & 9.03383 \\\\\n 0.2 & 9.13189 \\\\\n 0.3 & 9.28531 \\\\\n 0.4 & 9.483 \\\\\n 0.5 & 9.71427 \\\\\n 0.6 & 9.97009 \\\\\n 0.7 & 10.2434 \\\\\n 0.8 & 10.5286 \\\\\n 0.9 & 10.8216 \\\\\n 1. & 11.1193 \\\\\n 1.1 & 11.4192 \\\\\n 1.2 & 11.7193 \n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(7,3)}\\\\\\hline\n 1.3 & 12.0182 \\\\\n 1.4 & 12.3149 \\\\\n 1.5 & 12.6083 \\\\\n 1.6 & 12.8979 \\\\\n 1.7 & 13.1833 \\\\\n 1.8 & 13.4643 \\\\\n 1.9 & 13.7407 \\\\\n 2. & 14.0124 \\\\\n 2.1 & 14.2796 \\\\\n 2.2 & 14.5423 \\\\\n 2.3 & 14.8006 \\\\\n 2.4 & 15.0546 \\\\\n 2.5 & 15.3046\n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(7,3)}\\\\\\hline\n 2.6 & 15.5507 \\\\\n 2.7 & 15.7929 \\\\\n 2.8 & 16.0315 \\\\\n 2.9 & 16.2667 \\\\\n 3. & 16.4984 \\\\\n 3.1 & 16.727 \\\\\n 3.2 & 16.9524 \\\\\n 3.3 & 17.1748 \\\\\n 3.4 & 17.3944 \\\\\n 3.5 & 17.6112 \\\\\n 3.6 & 17.8253 \\\\\n 3.7 & 18.0369 \\\\\n 3.8 & 18.2459\n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(7,3)}\\\\\\hline\n 3.9 & 18.4526 \\\\\n 4. & 18.6569 \\\\\n 4.1 & 18.859 \\\\\n 4.2 & 19.059 \\\\\n 4.3 & 19.2568 \\\\\n 4.4 & 19.4525 \\\\\n 4.5 & 19.6463 \\\\\n 4.6 & 19.8382 \\\\\n 4.7 & 20.0282 \\\\\n 4.8 & 20.2164 \\\\\n 4.9 & 20.4029 \\\\\n 5. & 20.5876 \\\\\n 5.1 & 20.7707\n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(7,3)}\\\\\\hline\n 5.2 & 20.9521 \\\\\n 5.3 & 21.132 \\\\\n 5.4 & 21.3103 \\\\\n 5.5 & 21.4871 \\\\\n 5.6 & 21.6625 \\\\\n 5.7 & 21.8365 \\\\\n 5.8 & 22.009 \\\\\n 5.9 & 22.1802 \\\\\n 6. & 22.3501 \\\\\n 6.1 & 22.5187 \\\\\n 6.2 & 22.686 \\\\\n 6.3 & 22.852 \\\\\n 6.4 & 23.0169\n  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c|}\n\\hline\ng& {\\rm E}_{(7,3)}\\\\\\hline\n 6.5 & 23.1806 \\\\\n 6.6 & 23.3431 \\\\\n 6.7 & 23.5045 \\\\\n 6.8 & 23.6647 \\\\\n 6.9 & 23.8239 \\\\\n 7. & 23.9821 \\\\\n 7.1 & 24.1391 \\\\\n 7.2 & 24.2952 \\\\\n 7.3 & 24.4502 \\\\\n 7.4 & 24.6043 \\\\\n 7.5 & 24.7574 \\\\\n 7.6 & 24.9095 \\\\\n 7.7 & 25.0607\n  \\\\\\hline\n\\end{array}\n\\end{eqnarray}\n}\n\n\n\\subsection*{$J=8,n=4$ operator}\n\n{\\smaller \\begin{eqnarray}\\label{E84data}\n\\begin{array}{|c|c||}\n\\hline\ng& {\\rm E}_{(8,4)} \\\\\\hline\n0& 10 \\\\\n0.1 & 10.0384 \\\\\n 0.2 & 10.1495 \\\\\n 0.3 & 10.3227 \\\\\n 0.4 & 10.5452 \\\\\n 0.5 & 10.8049 \\\\\n 0.6 & 11.0922 \\\\\n 0.7 & 11.3996 \\\\\n 0.8 & 11.7217 \\\\\n 0.9 & 12.0542 \\\\\n 1. & 12.3942 \\\\\n 1.1 & 12.739 \\\\\n 1.2 & 13.0867  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(8,4)} \\\\\\hline\n 1.3 & 13.4355 \\\\\n 1.4 & 13.7839 \\\\\n 1.5 & 14.1306 \\\\\n 1.6 & 14.4743 \\\\\n 1.7 & 14.814 \\\\\n 1.8 & 15.1491 \\\\\n 1.9 & 15.4789 \\\\\n 2. & 15.8032 \\\\\n 2.1 & 16.1218 \\\\\n 2.2 & 16.4347 \\\\\n 2.3 & 16.742 \\\\\n 2.4 & 17.0438 \\\\\n 2.5 & 17.3404  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(8,4)} \\\\\\hline\n 2.6 & 17.6319 \\\\\n 2.7 & 17.9186 \\\\\n 2.8 & 18.2007 \\\\\n 2.9 & 18.4784 \\\\\n 3. & 18.7518 \\\\\n 3.1 & 19.0213 \\\\\n 3.2 & 19.2868 \\\\\n 3.3 & 19.5486 \\\\\n 3.4 & 19.8068 \\\\\n 3.5 & 20.0617 \\\\\n 3.6 & 20.3132 \\\\\n 3.7 & 20.5616 \\\\\n 3.8 & 20.8069  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(8,4)} \\\\\\hline\n 3.9 & 21.0493 \\\\\n 4. & 21.2889 \\\\\n 4.1 & 21.5257 \\\\\n 4.2 & 21.7598 \\\\\n 4.3 & 21.9915 \\\\\n 4.4 & 22.2206 \\\\\n 4.5 & 22.4474 \\\\\n 4.6 & 22.6718 \\\\\n 4.7 & 22.894 \\\\\n 4.8 & 23.114 \\\\\n 4.9 & 23.3318 \\\\\n 5. & 23.5476 \\\\\n 5.1 & 23.7615  \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(8,4)} \\\\\\hline\n 5.2 & 23.9733 \\\\\n 5.3 & 24.1833 \\\\\n 5.4 & 24.3914 \\\\\n 5.5 & 24.5978 \\\\\n 5.6 & 24.8024 \\\\\n 5.7 & 25.0053 \\\\\n 5.8 & 25.2065 \\\\\n 5.9 & 25.4061 \\\\\n 6. & 25.6041 \\\\\n 6.1 & 25.8006 \\\\\n 6.2 & 25.9955 \\\\\n 6.3 & 26.189 \\\\\n 6.4 & 26.3811 \\\\\\hline\n\\end{array}\n\\begin{array}{c|c||}\n\\hline\ng& {\\rm E}_{(8,4)} \\\\\\hline\n 6.5 & 26.5717 \\\\\n 6.6 & 26.761 \\\\\n 6.7 & 26.9489 \\\\\n 6.8 & 27.1355 \\\\\n 6.9 & 27.3208 \\\\\n 7. & 27.5049 \\\\\n 7.1 & 27.6877 \\\\\n 7.2 & 27.8693 \\\\\n 7.3 & 28.0497 \\\\\n 7.4 & 28.2289 \\\\\n 7.5 & 28.407 \\\\\n 7.6 & 28.584 \\\\\n 7.7 & 28.7598  \\\\\\hline\n\\end{array}\n\\end{eqnarray}\n}\n\n \n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nLocal times for Gaussian processes or fields are important in the probability theory. Recently, their derivatives received much attention, see, for example, \\cite{jnp, hx} and references therein. In \\cite{hx},  we consider derivatives of local time for a $(2,d)$-Gaussian field\n\\[\nZ=\\big\\{ Z(t,s)= X^{H_1}_t -\\widetilde{X}^{H_2}_s, s,t \\ge 0\\big\\},\n\\]\nwhere $X^{H_1}$ and $\\widetilde{X}^{H_2}$ are independent processes from a class of $d$-dimensional centered Gaussian processes satisfying certain local nondeterminism property.  A sufficient condition for existence of derivatives of the local time of $Z$ was given. Then, under the condition, derivatives of the local time are shown to be H\\\"{o}lder continuous in both time and space variables. Moreover, under some mild assumption, the sufficient condition is necessary for existence of derivatives of the local time at the origin. However, when the location is not  the origin, the necessity of the condition is still open. To the best of our knowledge, for local times of Gaussian processes or fields, in most cases, one just gave sufficient conditions for existence of local times and their derivatives. Only in the case where the location is the origin, there are a few papers showing the necessity of the sufficient condition, see, \\cite{no, wx} for local times, \\cite{jnp} for the first derivative of local time and \\cite{ghx, hx} for both local times and their derivatives. Moreover, the Gaussian processes in \\cite{hx} can be Bifractional Brownian motions and Subfractional Brownian motions, which are more general than the fractional Brownian motions in \\cite{no,wx,ghx,jnp}.\n\nIn this paper, when the location is not the origin, we will show that,  if the Gaussian processes in \\cite{hx} satisfying some additional properties,  then the sufficient condition $\\frac{H_1H_2}{H_1+H_2}(2|\\mathbf{k}|+d)<1$ is necessary. Moreover, when the location is the origin and under certain additional assumption, we could give a shorter proof for the necessity of the sufficient condition $\\frac{H_1H_2}{H_1+H_2}(2|\\mathbf{k}|+d)<1$. To make our results as general as possible, we only consider the necessary condition for existence of derivatives of local times here and would pose less restrictions on the Gaussian processes.  For $H\\in (0,1)$,  let $X^H= \\{ X^H_t:\\, t\\geq 0\\} $ be a $d$-dimensional centered Gaussian stochastic process whose components $X^{H,\\ell} (1\\le \\ell \\le d)$ are independent and identically distributed, and satisfy the following property:\n\n{\\bf (P1)}    {\\it Bounds on the second moment of increments}: for any $T>0$, there exist two positive constants $\\kappa_{T,1,H}\\leq \\kappa_{T,2,H}$ depending only on $T$ and $H$, such that for any $0\\leq s<t<T$,\n\\begin{align*}\n\\kappa_{T,1,H}(t-s)^{2H}\\leq {{\\mathbb E}\\,}\\Big[(X^{H,\\ell}_{t} -X^{H,\\ell}_{s})^2\\Big]\\leq \\kappa_{T,2,H}(t-s)^{2H}.\n\\end{align*}\nLet $G^d_{1}$ be the class of all such $d$-dimensional centered Gaussian processes and $G^d_{1,2}$ the class of $d$-dimensional centered Gaussian processes in $G^d_{1}$ possessing the additional property:\n\n{\\bf (P2)}    {\\it Bounds on the covariance of increments on disjoint intervals}:   there exists a nonnegative decreasing function $\\beta(\\gamma): (1,\\infty) \\rightarrow \\mathbb{R}$ with $\\lim\\limits_{\\gamma\\to\\infty}\\beta(\\gamma)=0$, such that, for any $0<s<t<T$ with $\\frac{t-s}{s}\\leq \\frac{1}{\\gamma}$,\n \\[\n\\Big|{{\\mathbb E}\\,}\\big[(X^{H,\\ell}_{t}-X^{H,\\ell}_{s})X^{H,\\ell}_{s}\\big]\\Big|\\leq  \\beta(\\gamma)\\, \\Big[{{\\mathbb E}\\,}\\big(X^{H,\\ell}_{t}-X^{H,\\ell}_{s}\\big)^2\\Big]^{\\frac{1}{2}}\\Big[{{\\mathbb E}\\,}\\big(X^{H,\\ell}_{s}\\big)^2 \\Big]^{\\frac{1}{2}}.\n\\]\nAccording to results in \\cite{bgt, hv, sxy}, we can easily see that the following $d$-dimensional Gaussian processes are in $G^d_{1,2}$.\n\n\\noindent\n(i) {\\it Bifractional Brownian motion (bi-fBm)}. The covariance function for components of this process is given by\n\\[\n{{\\mathbb E}\\,}(X^{H,\\ell}_t X^{H,\\ell}_s)=2^{-K_0}\\big[(t^{2H_0}+s^{2H_0})^{K_0}-|t-s|^{2H_0K_0}\\big],\n\\]\nwhere $H_0\\in(0,1)$ and $K_0\\in(0,1]$.  Here $K_0=1$ gives the fractional Brownian motion (fBm) with Hurst parameter $H=H_0$.\n\n\\noindent\n(ii) {\\it Subfractional Brownian motion (sub-fBm)}.  The covariance function for components of this process  is given by\n\\[\n{{\\mathbb E}\\,}(X^{H,\\ell}_t X^{H,\\ell}_s)=t^{2H}+s^{2H}-\\frac{1}{2}\\big[(t+s)^{2H}+|t-s|^{2H}\\big],\n\\]\nwhere $H\\in(0,1)$.\n\n\nLet $X^{H_1}$ and $\\widetilde{X}^{H_2}$ be independent Gaussian processes in $G^d_1$ with parameters $H_1, H_2\\in (0,1)$, respectively. Then\n\\begin{align}\nZ=\\big\\{Z(t,s)= X^{H_1}_t -\\widetilde{X}^{H_2}_s, s,t \\ge 0\\big\\}  \\label{gf}\n\\end{align}\nis a $(2,d)$-Gaussian field.\n\nFor any $\\varepsilon>0$ and the multi-index $\\mathbf{k}=(k_1,\\cdots, k_d)$ with all $k_i$ being nonnegative integers, let\n\\[\np^{(\\mathbf{k})}_{\\varepsilon}(x)=\\frac{\\partial^\\mathbf{k}}{\\partial x^{k_1}_1\\cdots \\partial x^{k_d}_d}p_{\\varepsilon}(x) =\\frac{\\iota^{|\\mathbf{k}|}}{(2\\pi)^d}\\int_{{\\mathbb R}^d} \\Big(\\prod^d_{i=1}y^{k_i}_i\\Big)\\, e^{\\iota y\\cdot x}e^{-\\frac{\\varepsilon|y|^2}{2}}\\, dy,\n\\]\nwhere $p_{\\varepsilon}(x)=\\frac{1}{(2\\pi \\varepsilon)^{\\frac{d}{2}}} e^{-\\frac{|x|^2}{2\\varepsilon}}$ and $|\\mathbf{k}|=\\sum\\limits^d_{i=1}k_i$.\n\nFor any $T>0$ and $x\\in{\\mathbb R}^d$, if\n\\begin{align}\\label{epsilon}\nL^{(\\mathbf{k})}_{\\varepsilon}(T,x):=\\int^T_0\\int^T_0 p^{(\\mathbf{k})}_{\\varepsilon}(X^{H_1}_t-\\widetilde{X}^{H_2}_s+x)\\, ds\\, dt\n\\end{align}\nconverges to some random variable in $L^2$  when $\\varepsilon\\downarrow 0$, we denote the limit by $L^{(\\mathbf{k})}(T,x)$ and call it  the $\\mathbf{k}$-th derivative of local time for the $(2,d)$-Gaussian field $Z$.  If it exists,  $L^{(\\mathbf{k})}(T,x)$ admits the following $L^2$-representation\n\\begin{align} \\label{dlt}\nL^{(\\mathbf{k})}(T,x)=\\int^T_0\\int^T_0 \\delta^{({\\bf k})}(X^{H_1}_t-\\widetilde{X}^{H_2}_s+x)\\, ds\\, dt.\n\\end{align}\n\nThe following are main results of this paper.\n\\begin{theorem}\\label{thm1}\nAssume that $X^{H_1}=\\{X^{H_1}_t:\\, t\\geq 0\\}$ and $\\widetilde{X}^{H_2}=\\{\\widetilde{X}^{H_2}_t:\\, t\\geq 0\\}$ are two independent Gaussian processes in $G^d_{1,2}$ with parameters $H_1, H_2\\in(0,1)$, respectively.  For any $x\\neq 0$, if $\\frac{H_1H_2}{H_1+H_2}(2|\\mathbf{k}|+d)\\geq 1$, then there exist positive constants $c_1$ and $c_2$ such that\n\\begin{align*}\n\\liminf_{\\varepsilon\\downarrow 0}\\frac{{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{\\varepsilon}(T,x)|^2]}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\geq c_1e^{-c_2|x|^2},\n\\end{align*}\nwhere\n\\begin{align} \\label{rate}\nh^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)=\n\\left\\{\\begin{array}{ll}\n\\varepsilon^{\\frac{H_1+H_2}{2H_1H_2}-\\frac{d}{2}-|\\mathbf{k}|} &   \\text{if}\\; \\frac{H_1H_2}{H_1+H_2}(2|\\mathbf{k}|+d)>1\\\\  \\\\\n\\ln(1+\\varepsilon^{-\\frac{1}{2}}) &   \\text{if}\\; \\frac{H_1H_2}{H_1+H_2}(2|\\mathbf{k}|+d)=1.\n\\end{array} \\right.\n\\end{align}\n\\end{theorem}\n\n\\begin{theorem}\\label{thm2}\nAssume that $X^{H_1}=\\{X^{H_1}_t:\\, t\\geq 0\\}$ and $\\widetilde{X}^{H_2}=\\{\\widetilde{X}^{H_2}_t:\\, t\\geq 0\\}$ are two independent Gaussian processes in $G^d_{1}$ with parameters $H_1, H_2\\in(0,1)$, respectively. We further assume that  (i) $|\\mathbf{k}|$ is even or  (ii) ${{\\mathbb E}\\,}[X^{H_1,1}_{t}X^{H_1,1}_{s}]\\geq 0$ and  ${{\\mathbb E}\\,}[\\widetilde{X}^{H_2,1}_{t}\\widetilde{X}^{H_2,1}_{s}]\\geq 0$ for any  $0<s,t<T$. Then, if $\\frac{H_1H_2}{H_1+H_2}(2|\\mathbf{k}|+d)\\geq 1$, there exists a positive constant $c_3$ such that\n\\[\n\\liminf\\limits_{\\varepsilon\\downarrow 0}\\frac{{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{\\varepsilon}(T,0)|^2]}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\geq c_3.\n\\]\n\\end{theorem}\n\n\\begin{remark} For independent Gaussian processes $X^{H_1}$ and $\\widetilde{X}^{H_2}$ in $G^d_{L}$ as defined in \\cite{hx}, if they are also in $G^d_{1,2}$,  then, for $x\\neq 0$, $L^{(\\mathbf{k})}(T,x)$ exists in $L^2$ if and only if $\\frac{H_1H_2}{H_1+H_2}(2|\\mathbf{k}|+d)<1$.\n\\end{remark}\n\n\\begin{remark} For independent Gaussian processes $X^{H_1}$ and $\\widetilde{X}^{H_2}$ in $G^d_{L}$ as defined in \\cite{hx}, if they also satisfy the assumptions in Theorem \\ref{thm2},  then $L^{(\\mathbf{k})}(T,0)$ exists in $L^2$ if and only if $\\frac{H_1H_2}{H_1+H_2}(2|\\mathbf{k}|+d)<1$. Moreover, the definition of $d$-dimensional bi-fBm implies that its components have nonnegative covariance function. The non-negativity of covariance function for components of sub-fBm follows from \\cite{bgt}.\n\\end{remark}\n\n\\begin{remark}\nFor each $N\\in{\\mathbb N}$, define the $(N, d)$-Gaussian field\n\\[\n Z^{N}=\\Big\\{\\sum^{N}_{j=1} X^{j,H_j}_{t_j}:\\; t_j\\geq 0,\\, j=1,\\dots,N\\Big\\},\n\\]\nwhere $X^{j,H_j}_{t_j}$ are independent $d$-dimensional Gaussian processes in $G^d_{1}$. Replace $Z$ in $L^{(\\mathbf{k})}_{\\varepsilon}(T,x)$ and $L^{(\\mathbf{k})}(T,x)$ by $Z^{N}$ and denote the new terms by $L^{(\\mathbf{k})}_{N, \\varepsilon}(T,x)$ and $L^{(\\mathbf{k})}_{N}(T,x)$, respectively. Using the methodologies developed here, we could obtain similar results for the existence of $L^{(\\mathbf{k})}_{N}(T,x)$ in $L^2$. That is,\n\\begin{enumerate}\n\\item[(i)] Assume that $X^{j,H_j}_{t_j} (j=1,\\dots,N)$ are independent $d$-dimensional Gaussian processes in $G^d_{1,2}$, $x\\neq 0$ and $2|\\mathbf{k}|+d\\geq \\sum\\limits^N_{j=1} \\frac{1}{H_j}$.  Then there exist positive constants $c_4$ and $c_5$ such that\n    \\[\n\\liminf\\limits_{\\varepsilon\\downarrow 0}\\frac{{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{N,\\varepsilon}(T,x)|^2]}{h^{d,|{\\bf k}|}_{H_1,H_2,\\dots, H_N}(\\varepsilon)}\\geq c_4e^{-c_5|x|^2},\n\\] where $h^{d,|{\\bf k}|}_{H_1,H_2,\\dots, H_N}(\\varepsilon)=\n\\left\\{\\begin{array}{ll}\n\\varepsilon^{\\sum\\limits^N_{j=1}\\frac{1}{2H_j}-\\frac{d}{2}-|\\mathbf{k}|} &   \\text{if}\\;\\; 2|\\mathbf{k}|+d>\\sum\\limits^N_{j=1} \\frac{1}{H_j}\\\\\n\\ln(1+\\varepsilon^{-\\frac{1}{2}}) &   \\text{if}\\;\\; 2|\\mathbf{k}|+d=\\sum\\limits^N_{j=1} \\frac{1}{H_j}.\n\\end{array} \\right.$\n\n\\item[(ii)] Assume that $X^{j,H_j}_{t_j} (j=1,\\dots,N)$ are independent $d$-dimensional Gaussian processes in $G^d_{1}$, $|\\mathbf{k}|$ is even or all $X^{j,H_j}$ have nonnegative covariance functions, and $2|\\mathbf{k}|+d\\geq \\sum\\limits^N_{j=1} \\frac{1}{H_j}$. Then there exists a positive constant $c_6$ such that $\n\\liminf\\limits_{\\varepsilon\\downarrow 0}\\frac{{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{N,\\varepsilon}(T,0)|^2]}{h^{d,|{\\bf k}|}_{H_1,H_2,\\dots, H_N}(\\varepsilon)}\\geq c_6.$\n\\end{enumerate}\nThe case $N=1$ is easy. It follows from simplified proofs of Theorems \\ref{thm1} and \\ref{thm2}.  Moreover, our methodologies also work for derivatives of local times of L\\'{e}vy processes or fields.\n\\end{remark}\n\nAfter some preliminaries in Section 2, Sections 3 and 4 are devoted to the proofs of Theorems \\ref{thm1} and \\ref{thm2}, respectively. Throughout this paper, if not mentioned otherwise, the letter $c$, with or without a subscript, denotes a generic positive finite constant whose exact value may change from line to line.  For any $x,y\\in{\\mathbb R}^d$, we use $x\\cdot y$ to denote the usual inner product  and $|x|=(\\sum\\limits^d_{i=1}|x_i|^2)^{1\/2}$.  Moreover, we use $\\iota$ to denote $\\sqrt{-1}$.\n\n\n\\section{Preliminaries}\n\nIn this section, we give three lemmas. The first two will be used in the proof of Theorem \\ref{thm1} and the last one in the proof of Theorem \\ref{thm2}.\n\\begin{lemma} \\label{lma1} Assume that $k\\in{\\mathbb N}\\cup\\{0\\}$ and $\\varepsilon>0$. Then, for any $a,b,c, x\\in{\\mathbb R}$ with $a>0$, $c>0$ and $\\Delta=c+\\varepsilon-\\frac{(b-\\varepsilon)^2}{a+2\\varepsilon}>0$, we have\n\\begin{align} \\label{integral}\n&\\frac{(-1)^k}{2\\pi}\\int_{{\\mathbb R}^2} \\exp\\Big\\{-\\frac{1}{2}(y_2^2a+2y_2 y_1b+y_1^2c)-\\frac{\\varepsilon}{2}((y_1-y_2)^2+y_2^2)+\\iota y_1x\\Big\\}  y^{k}_2 (y_1-y_2)^{k} \\, dy \\nonumber \\\\\n&=\\sum^k_{\\ell=0}\\sum^{k+\\ell}_{m=0:\\text{even}}\\sum^{2k-m}_{n=0:\\text{even}} c_{k,\\ell,m,n}  (a+2\\varepsilon)^{-\\frac{m+1}{2}} (\\frac{\\varepsilon-b}{a+2\\varepsilon})^{k+\\ell-m}\\Delta^{-(2k-m)-\\frac{1-n}{2}} x^{2k-m-n}e^{-\\frac{x^2}{2\\Delta}},\n\\end{align}\nwhere\n\\[\nc_{k,\\ell,m,n}=(-1)^{\\ell-\\frac{m+n}{2}} \\binom{k}{\\ell}  \\binom{k+\\ell} {m}\\binom{2k-m} {n}(m-1)!! (n-1)!!\n\\]\nand we use the convention $0^0=1$ for the case $x=0\\in{\\mathbb R}$.\n\\end{lemma}\n\\begin{proof}  Let $L$ be the left hand side of the equality \\eref{integral}. It is easy to show that\n\\begin{align*}\nL&=\\frac{(-1)^k}{2\\pi}\\int_{{\\mathbb R}^2} \\exp\\Big\\{-\\frac{1}{2}y_2^2(a+2\\varepsilon)-y_2 y_1(b-\\varepsilon)-\\frac{1}{2}y_1^2(c+\\varepsilon)+\\iota y_1  x\\Big\\}  y^{k}_2 (y_1-y_2)^{k} \\, dy\\\\\n&=\\sum^k_{\\ell=0}\\frac{(-1)^{k+\\ell}}{2\\pi} \\binom{k}{\\ell}\\int_{{\\mathbb R}^2} \\exp\\Big\\{-\\frac{1}{2}y_2^2(a+2\\varepsilon)-y_2 y_1(b-\\varepsilon)-\\frac{1}{2}y_1^2(c+\\varepsilon)+\\iota y_1  x\\Big\\}  y^{k+\\ell}_2 y_1^{k-\\ell} \\, dy\\\\\n&=\\sum^k_{\\ell=0}\\sum^{k+\\ell}_{m=0:\\, \\text{even}}  \\frac{(-1)^{k+\\ell}}{\\sqrt{2\\pi}}\\binom{k}{\\ell}  \\binom{k+\\ell} {m}(m-1)!! (a+2\\varepsilon)^{-k-\\ell-\\frac{1-m}{2}} (\\varepsilon-b)^{k+\\ell-m} \\int_{{\\mathbb R}} y_1^{2k-m}e^{-\\frac{1}{2} y_1^2\\Delta+\\iota y_1 x}   \\, dy_1\\\\\n&=\\sum^k_{\\ell=0}\\sum^{k+\\ell}_{m=0:\\, \\text{even}}\\sum^{2k-m}_{n=0:\\, \\text{even}} c_{k,\\ell,m,n} (a+2\\varepsilon)^{-\\frac{m+1}{2}} (\\frac{\\varepsilon-b}{a+2\\varepsilon})^{k+\\ell-m}\\Delta^{-(2k-m)-\\frac{1-n}{2}} x^{2k-m-n}e^{-\\frac{x^2}{2\\Delta}}.\n\\end{align*}\n\\end{proof}\n\n\n\\begin{lemma} \\label{lma2}  Assume that $k\\in{\\mathbb N}\\cup\\{0\\}$ and $\\varepsilon>0$. Then, for any $a_1,b_1,c_1, a_2,b_2,c_2, x\\in{\\mathbb R}$ with $a_1, a_2, c_1, c_2>0$ and $\\Delta'=c_1+c_2+a_2+2b_2+\\varepsilon-\\frac{(b_1-b_2-a_2-\\varepsilon)^2}{a_1+a_2+2\\varepsilon}>0$, we have\n\\begin{align*}\n&\\frac{(-1)^k}{2\\pi}\\int_{{\\mathbb R}^2} \\exp\\left\\{-\\frac{1}{2}\\big([y_2^2a_1+2y_2 y_1b_1+y_1^2c_1]+[(y_1-y_2)^2a_2+2(y_1-y_2)y_1b_2+y^2_1c_2]\\big)\\right\\}\\\\\n&\\qquad\\qquad\\times \\exp\\Big\\{-\\frac{\\varepsilon}{2}((y_1-y_2)^2+y_2^2)+\\iota y_1x\\Big\\}  y^{k}_2 (y_1-y_2)^{k} \\, dy\\\\\n&=\\sum^k_{\\ell=0}\\sum^{k+\\ell}_{m=0:\\text{even}}\\sum^{2k-m}_{n=0:\\text{even}} c_{k,\\ell,m,n} (a_1+a_2+2\\varepsilon)^{-\\frac{m+1}{2}} (\\frac{\\varepsilon+b_2+a_2-b_1}{a_1+a_2+2\\varepsilon})^{k+\\ell-m}(\\Delta')^{-(2k-m)-\\frac{1-n}{2}} x^{2k-m-n}e^{-\\frac{x^2}{2\\Delta'}},\n\\end{align*}\nwhere\n\\[\nc_{k,\\ell,m,n}=(-1)^{\\ell-\\frac{m+n}{2}} \\binom{k}{\\ell}  \\binom{k+\\ell} {m}\\binom{2k-m} {n}(m-1)!! (n-1)!!\n\\]\nand we use the convention $0^0=1$ for the case $x=0\\in{\\mathbb R}$.\n\\end{lemma}\n\\begin{proof}  Note that the integral in the above statement can be written as\n\\begin{align*}\n\\int_{{\\mathbb R}^2} \\exp\\Big\\{-\\frac{1}{2}y_2^2(a_1+a_2+2\\varepsilon)-y_2 y_1(b_1-a_2-b_2-\\varepsilon)-\\frac{1}{2}y_1^2(c_1+c_2+a_2+2b_2+\\varepsilon)+\\iota y_1  x\\Big\\}  y^{k}_2 (y_1-y_2)^{k} \\, dy.\n\\end{align*}\nThen the desired result follows from Lemma \\ref{lma1}.\n\\end{proof}\n\n\\begin{lemma} \\label{lma3}   Assume that $k\\in{\\mathbb N}\\cup\\{0\\}$ and $\\varepsilon>0$. Then, for any $a,b,c\\in{\\mathbb R}$ with $a,c>0$ and $(a+\\varepsilon)(c+\\varepsilon)-b^2>0$, we have\n\\begin{align*}\n&\\frac{(-1)^k}{2\\pi}\\int_{{\\mathbb R}^2} \\exp\\Big\\{-\\frac{1}{2}(y_2^2a+2y_2 y_1b+y_1^2c)-\\frac{\\varepsilon}{2}(y_2^2+y_1^2)\\Big\\}  y^{k}_2 y_1^{k} \\, dy\\\\\n&\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad=\\sum^k_{\\ell=0, \\text{even}}    \\frac{c_{k,\\ell} \\,b^{k-\\ell}}{((a+\\varepsilon)(c+\\varepsilon)-b^2)^{\\frac{2k-\\ell+1}{2}}},\n\\end{align*}\nwhere $c_{k,\\ell}=(\\ell-1)!!  \\binom{k}{\\ell} (2k-\\ell-1)!!$.\n\\end{lemma}\n\\begin{proof} This follows from similar arguments as in the proof of Lemma \\ref{lma1}.\n\\end{proof}\n\n\n\\section{Proof of Theorem \\ref{thm1}}\n\nIn this section, we give the proof of Theorem \\ref{thm1}.\n\n\\begin{proof} We divide the proof into several steps.\n\n\n\\noindent\n{\\bf Step 1.}\nRecall the definition of $L^{(\\mathbf{k})}_{\\varepsilon}(T,x)$ in (\\ref{epsilon}). Using Fourier transform,\n\\begin{align*}\nL^{(\\mathbf{k})}_{\\varepsilon}(T,x)\n&=\\frac{\\iota^{|\\mathbf{k}|}}{(2\\pi)^d} \\int^T_0\\int^T_0\\int_{{\\mathbb R}^d} e^{\\iota z\\cdot (X^{H_1}_u-\\widetilde{X}^{H_2}_v+x)}e^{-\\frac{\\varepsilon|z|^2}{2}}  \\prod^d_{i=1}z^{k_i}_i\\, dz\\, du\\, dv.\n\\end{align*}\nHence\n\\begin{align*}\n{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{\\varepsilon}(T,x)|^2]\n&=\\frac{(-1)^{|\\mathbf{k}|}}{(2\\pi)^{2d}}\\int_{[0,T]^4}\\int_{{\\mathbb R}^{2d}} e^{-\\frac{1}{2}\\big[{{\\mathbb E}\\,}(z_2\\cdot X^{H_1}_{t_2}+z_1\\cdot X^{H_1}_{t_1})^2+{{\\mathbb E}\\,}(z_2\\cdot \\widetilde{X}^{H_2}_{s_2}+z_1\\cdot \\widetilde{X}^{H_2}_{s_1})^2\\big]}\\\\\n&\\qquad\\qquad \\times e^{-\\frac{\\varepsilon}{2}(|z_2|^2+|z_1|^2)+\\iota(z_1+z_2)\\cdot x} \\prod\\limits^d_{i=1}z^{k_i}_{2,i} \\prod\\limits^d_{i=1}z^{k_i}_{1,i}\\, dz_2\\, dz_1\\, dt\\, ds,\n\\end{align*}\nwhere $z_1=(z_{1,1},\\cdots,z_{1,d})$ and $z_2=(z_{2,1},\\cdots,z_{2,d})$.\n\nFor $i=1,\\cdots, d$, we first introduce the following notations\n\\begin{align*}\nI_i(H,t_2,t_1,z_2,z_1)&=e^{-\\frac{1}{2} {{\\mathbb E}\\,}[z_{2,i}\\cdot (X^{H,i}_{t_2}-X^{H,i}_{t_1})+z_{1,i}\\cdot X^{H,i}_{t_1}]^2}\\\\\n\\widetilde{I}_i(H,t_2,t_1,z_2,z_1)&=e^{-\\frac{1}{2} {{\\mathbb E}\\,}[z_{2,i}\\cdot (\\widetilde{X}^{H,i}_{t_2}-\\widetilde{X}^{H,i}_{t_1})+z_{1,i}\\cdot \\widetilde{X}^{H,i}_{t_1}]^2}\\\\\nK_i(\\varepsilon,z_2, z_1)&=e^{-\\frac{\\varepsilon}{2}(z^2_{2,i}+z^2_{1,i})+\\iota(z_{1,i}+z_{2,i})x_i}z^{k_i}_{2,i}z^{k_i}_{1,i}.\n\\end{align*}\nThen we define\n\\begin{align*}\nF_1(t_2,t_1, s_2,s_1, x_i)&=\\frac{(-1)^{k_i}}{2\\pi}\\int_{{\\mathbb R}^2}I_i(H_1,t_2,t_1,z_2,z_1+z_2)\\widetilde{I}_i(H_2,s_2,s_1,z_2,z_1+z_2)K_i(\\varepsilon,z_2, z_1) \\, dz_{2,i}\\, dz_{1,i}\\\\\nF_2(t_2,t_1, s_2,s_1, x_i)&=\\frac{(-1)^{k_i}}{2\\pi}\\int_{{\\mathbb R}^2}I_i(H_1,t_2,t_1,z_2,z_1+z_2)\\widetilde{I}_i(H_2,s_2,s_1,z_1,z_1+z_2)K_i(\\varepsilon,z_2, z_1)\\, dz_{2,i}\\, dz_{1,i}.\n\\end{align*}\nNow we can obtain that\n\\begin{align}  \\label{e1}\n{{\\mathbb E}\\,}\\Big[ |L^{(\\mathbf{k})}_{\\varepsilon}(T,x)|^2\\Big]&=\\frac{2}{(2\\pi)^d}\\left[\\int_{D}\\prod^d_{i=1}F_1(t_2,t_1, s_2,s_1, x_i)\\, dt\\, ds+\\int_{D}\\prod^d_{i=1}F_2(t_2,t_1, s_2,s_1, x_i)\\, dt\\, ds\\right] \\nonumber \\\\\n&=:\\frac{2}{(2\\pi)^d}(I_1(\\varepsilon)+I_2(\\varepsilon)),\n\\end{align}\nwhere $D=\\{0<s_1<t_1<T, 0<s_2<t_2<T\\}$.\n\n\\noindent\n{\\bf Step 2.}  We estimate $\\liminf\\limits_{\\varepsilon\\downarrow 0}\\frac{I_1(\\varepsilon)}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}$. Note that\n\\[\nI_1(\\varepsilon)=\\int_{D}\\prod\\limits^d_{i=1}F_1(t_2,t_1, s_2,s_1, x_i)\\, dt\\, ds.\n\\]\nMaking the change of variables $y_{2}=z_{2}$ and $y_1=z_1+z_2$ gives\n\\begin{align*}\nF_1(t_2,t_1, s_2,s_1, x_i)&=\\frac{(-1)^{k_i}}{2\\pi}\\int_{{\\mathbb R}^2}I_i(H_1,t_2,t_1,y_2,y_1)\\widetilde{I}_i(H_2,s_2,s_1,y_2,y_1)K_i(\\varepsilon, y_2, y_1-y_2) \\, dy_{2,i}\\, dy_{1,i}.\n\\end{align*}\nIn order to calculate the above integral,  we set\n\\begin{align*}\na&={{\\mathbb E}\\,}[(X^{H_1,1}_{t_2}-X^{H_1,1}_{t_1})^2]+{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2}-\\widetilde{X}^{H_2,1}_{s_1})^2]\\\\\nb&={{\\mathbb E}\\,}[(X^{H_1,1}_{t_2}-X^{H_1,1}_{t_1})X^{H_1,1}_{t_1}]+{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2}-\\widetilde{X}^{H_2,1}_{s_1})\\widetilde{X}^{H_2,1}_{s_1}]\\\\\nc&={{\\mathbb E}\\,}[(X^{H_1,1}_{t_1})^2]+{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_1})^2]\\\\\n\\Delta&=c+\\varepsilon-\\frac{(b-\\varepsilon)^2}{a+2\\varepsilon}.\n\\end{align*}\n\n\n\nFor any $(t_2,t_1,s_2,s_1)\\in D$, it is easy to see that $a,b,c>0$ and\n\\begin{align*}\n\\Delta=\\frac{ac+a\\varepsilon+2c\\varepsilon+\\varepsilon^2-b^2+2b\\varepsilon}{a+2\\varepsilon}\\geq \\frac{c\\varepsilon+\\varepsilon^2}{a+2\\varepsilon}>0,\n\\end{align*}\nwhere we use $|b|\\leq \\sqrt{ac}\\leq \\frac{a+c}{2}$ in the first inequality.\n\nBy Lemma \\ref{lma1}, $F_1(t_2,t_1, s_2,s_1, x_i)$ equals\n\\begin{align*}\n\\sum^{k_i}_{\\ell=0}\\sum^{k_i+\\ell}_{m=0:\\text{even}}\\sum^{2k_i-m}_{n=0:\\text{even}} c_{k_i,\\ell,m,n}  (a+2\\varepsilon)^{-\\frac{m+1}{2}} (\\frac{\\varepsilon-b}{a+2\\varepsilon})^{k_i+\\ell-m}\\Delta^{-(2k_i-m)-\\frac{1-n}{2}} x^{2k_i-m-n}_ie^{-\\frac{x^2_i}{2\\Delta}},\n\\end{align*}\nwhere $c_{k_i,\\ell,m,n}=(-1)^{\\ell-\\frac{m+n}{2}} \\binom{k_i}{\\ell}  \\binom{k_i+\\ell} {m}\\binom{2k_i-m} {n}(m-1)!! (n-1)!!$.\n\n\nFor any $\\gamma>1$ and $(t_2,t_1,s_2,s_1)\\in D$,  using the Cauchy-Schwartz inequality and properties {\\bf (P1)} and {\\bf (P2)}, we can show that\n\\begin{align*}\n\\big|{{\\mathbb E}\\,}[(X^{H_1,1}_{t_2}-X^{H_1,1}_{t_1})X^{H_1,1}_{t_1}]\\big|\\leq c_1\\big[(\\gamma^{H_1}+\\gamma^{-H_1})a+\\beta(\\gamma)a^{\\frac{1}{2}}\\big],\n\\end{align*}\nwhere $\\gamma^{H_1}a$ comes from the case $\\frac{1}{\\gamma}<\\frac{t_2-t_1}{t_1}<\\gamma$,  $\\gamma^{-H_1}a$ from the case $\\frac{t_2-t_1}{t_1}\\geq \\gamma$, and $\\beta(\\gamma)a^{\\frac{1}{2}}$ from the case $\\frac{t_2-t_1}{t_1}\\leq \\frac{1}{\\gamma}$. Similarly,\n\\begin{align*}\n\\big|{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2}-\\widetilde{X}^{H_2,1}_{s_1})\\widetilde{X}^{H_2,1}_{s_1}]\\big|\\leq c_2\\big[(\\gamma^{H_1}+\\gamma^{-H_1})a+\\beta(\\gamma)a^{\\frac{1}{2}}\\big].\n\\end{align*}\nHence\n\\begin{align*}\n\\Big|\\frac{\\varepsilon-b}{a+2\\varepsilon}\\Big|\n&\\leq \\frac{1}{2}+c_3\\frac{(\\gamma^{H_1}+\\gamma^{-H_1}+\\gamma^{H_2}+\\gamma^{-H_2})a+\\beta(\\gamma)a^{\\frac{1}{2}}}{a+2\\varepsilon}\\leq c_4\\Big(\\gamma^{H_1}+\\gamma^{H_2}+\\frac{\\beta(\\gamma)}{(a+2\\varepsilon)^{\\frac{1}{2}}}\\Big).\n\\end{align*}\n\nLet \\begin{align} \\label{dg}\nD_{\\gamma}=D\\cap\\Big\\{0<\\frac{t_2-t_1}{t_1}<\\frac{T\\wedge 1}{2\\gamma}, \\frac{T}{4}<t_1<\\frac{T}{2}, 0<\\frac{s_2-s_1}{s_1}<\\frac{T\\wedge 1}{2\\gamma}, \\frac{T}{4}<s_1<\\frac{T}{2} \\Big\\}.\n\\end{align}\nFor any $(t_2,t_1,s_2,s_1)\\in D_{\\gamma}$, using the property {\\bf (P2)}, we can show that\n\\begin{align} \\label{det}\nc_5(T^{2H_1}+T^{2H_2})\\leq \\Delta\\leq c_6(T^{2H_1}+T^{2H_2})\n\\end{align}\nprovided that $\\gamma$ is very large and $\\varepsilon$ is very small.\n\nNote that for any $\\alpha>0$, the function $h(w)=\\frac{1}{w^{\\alpha}}e^{-\\frac{1}{w}}\\in(0,\\alpha^{\\alpha}e^{-\\alpha}]$ when $w\\in(0,+\\infty)$. Choosing $\\gamma$ large enough gives\n\\begin{align*}\n\\liminf_{\\varepsilon\\downarrow 0}\\frac{I_1(\\varepsilon)}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\n&\\geq \\liminf_{\\varepsilon\\downarrow 0} \\frac{(1-c_4\\beta(\\gamma))^d}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\int_{D} (a+2\\varepsilon)^{-|{\\bf k}|-\\frac{d}{2}}\\, \\Delta^{-\\frac{d}{2}}e^{-\\frac{|x|^2}{2\\Delta}}dt\\, ds,\n\\end{align*}\nwhere $0<c_4\\beta(\\gamma)<1$.\n\nUsing the inequality (\\ref{det}), we can obtain that\n\\begin{align} \\label{e2}\n&\\liminf_{\\varepsilon\\downarrow 0}\\frac{I_1(\\varepsilon)}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)} \\nonumber \\\\\n&\\geq c_7\\liminf_{\\varepsilon\\downarrow 0} \\frac{(1-c_4\\beta(\\gamma))^d}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\int_{D_{\\gamma}} (a+2\\varepsilon)^{-|{\\bf k}|-\\frac{d}{2}}\\, (T^{2H_1}+T^{2H_2})^{-\\frac{d}{2}}e^{-\\frac{|x|^2}{2c_5(T^{2H_1}+T^{2H_2})}}dt\\, ds \\nonumber \\\\\n&\\geq c_8e^{-\\frac{|x|^2}{2c_5(T^{2H_1}+T^{2H_2})}} \\liminf_{\\varepsilon\\downarrow 0} \\frac{(1-c_4\\beta(\\gamma))^d}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\int_{D_{\\gamma}} ((t_2-t_1)^{2H_1}+(s_2-s_1)^{2H_2}+2\\varepsilon)^{-|{\\bf k}|-\\frac{d}{2}}dt\\, ds \\nonumber \\\\\n&\\geq c_9e^{-\\frac{|x|^2}{2c_5(T^{2H_1}+T^{2H_2})}},\n\\end{align}\nwhere in the last inequality we use Lemma {\\bf A.3.} in \\cite{hx} and the property {\\bf (P1)}.\n\n\\noindent\n{\\bf Step 3.}  We estimate $\\liminf\\limits_{\\varepsilon\\downarrow 0}\\frac{I_2(\\varepsilon)}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}$. Note that\n\\[\nI_2(\\varepsilon)=\\int_{D}\\prod\\limits^d_{i=1}F_2(t_2,t_1, s_2,s_1, x_i)\\, dt\\, ds.\n\\]\nMaking the change of variables $y_{2}=z_{2}$ and $y_1=z_1+z_2$ gives\n\\begin{align*}\nF_2(t_2,t_1, s_2,s_1, x_i)&=\\frac{(-1)^{k_i}}{2\\pi}\\int_{{\\mathbb R}^2}I_i(H_1,t_2,t_1,y_2,y_1)\\widetilde{I}_i(H_2,s_2,s_1,y_1-y_2,y_1)K_i(\\varepsilon, y_2, y_1-y_2) \\, dy_{2,i}\\, dy_{1,i}.\n\\end{align*}\nIn order to calculate the above integral,  we set\n\\begin{align*}\na_1&={{\\mathbb E}\\,}[(X^{H_1,1}_{t_2}-X^{H_1,1}_{t_1})^2],\\; a_2={{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2}-\\widetilde{X}^{H_2,1}_{s_1})^2],\\\\\nb_1&={{\\mathbb E}\\,}[(X^{H_1,1}_{t_2}-X^{H_1,1}_{t_1})X^{H_1,1}_{t_1}],\\; b_2={{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2}-\\widetilde{X}^{H_2,1}_{s_1})\\widetilde{X}^{H_2,1}_{s_1}]\\\\\ne_1&={{\\mathbb E}\\,}[(X^{H_1,1}_{t_1})^2],\\; e_2={{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_1})^2]\\\\\n\\Delta'&=e_1+e_2+a_2+2b_2+\\varepsilon-\\frac{(b_1-b_2-a_2-\\varepsilon)^2}{a_1+a_2+2\\varepsilon}.\n\\end{align*}\nIt is easy to see that, for any $(t_2,t_1,s_2,s_1)\\in D$, $a_1, a_2, e_1,e_2>0$ and\n\\begin{align*}\n\\Delta'&\\geq \\frac{a_1e_2+a_1a_2+a_2e_1+2a_1b_2+2a_2b_1+2b_1b_2+\\varepsilon(e_1+e_2)+\\varepsilon^2}{a_1+a_2+2\\varepsilon}\\geq \\frac{\\varepsilon(e_1+e_2)+\\varepsilon^2}{a_1+a_2+2\\varepsilon}>0,\n\\end{align*}\nwhere we use $|b_1|\\leq \\sqrt{a_1e_1}\\leq \\frac{a_1+e_1}{2}$ and $|b_2|\\leq \\sqrt{a_2e_2}\\leq \\frac{a_2+e_2}{2}$ in the first two inequalities.\n\n\n\n\nBy Lemma \\ref{lma1}, $F_2(t_2,t_1, s_2,s_1, x_i)$ equals\n\\begin{align*}\n\\sum^{k_i}_{\\ell=0}\\sum^{k_i+\\ell}_{m=0:\\text{even}}\\sum^{2k_i-m}_{n=0:\\text{even}} c_{k_i,\\ell,m,n} (a_1+a_2+2\\varepsilon)^{-\\frac{m+1}{2}} (\\frac{\\varepsilon+b_2+a_2-b_1}{a_1+a_2+2\\varepsilon})^{k_i+\\ell-m}(\\Delta')^{-(2k_i-m)-\\frac{1-n}{2}} x^{2k_i-m-n}e^{-\\frac{x^2}{2\\Delta'}},\n\\end{align*}\nwhere $c_{k_i,\\ell,m,n}=(-1)^{\\ell-\\frac{m+n}{2}} \\binom{k_i}{\\ell}  \\binom{k_i+\\ell} {m}\\binom{2k_i-m} {n}(m-1)!! (n-1)!!$.\n\nFor any $(t_2,t_1,s_2,s_1)\\in D$, using the Cauchy-Schwartz inequality and properties {\\bf (P1)} and {\\bf (P2)}, we can show that\n\\begin{align*}\n\\Big|\\frac{\\varepsilon+b_2+a_2-b_1}{a_1+a_2+2\\varepsilon}\\Big|\n&\\leq 1+\\frac{|b_2-b_1|}{a_1+a_2+2\\varepsilon}\\leq c_{10}\\Big(\\gamma^{H_1}+\\gamma^{H_2}+\\frac{\\beta(\\gamma)}{(a_1+a_2+2\\varepsilon)^{\\frac{1}{2}}}\\Big).\n\\end{align*}\nTherefore,\n\\begin{align*}\n\\liminf_{\\varepsilon\\downarrow 0}\\frac{I_2(\\varepsilon)}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\n&\\geq \\liminf_{\\varepsilon\\downarrow 0} \\frac{1}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\int_{D} (a_1+a_2+2\\varepsilon)^{-|{\\bf k}|-\\frac{d}{2}}\\, \\Delta^{-\\frac{d}{2}}e^{-\\frac{|x|^2}{2\\Delta}}dt\\, ds\\\\\n&\\qquad\\qquad-c_{11}\\beta(\\gamma)\\limsup_{\\varepsilon\\downarrow 0} \\frac{1}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\int_{D} (a_1+a_2+2\\varepsilon)^{-|{\\bf k}|-\\frac{d}{2}}\\, dt\\, ds\\\\\n&\\geq -c_{12}\\beta(\\gamma)\\limsup_{\\varepsilon\\downarrow 0} \\frac{1}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\int_{D} ((t_2-t_1)^{2H_1}+(s_2-s_1)^{2H_2}+2\\varepsilon)^{-|{\\bf k}|-\\frac{d}{2}}\\,dt\\, ds\\\\\n&\\geq -c_{13}\\beta(\\gamma).\n\\end{align*}\nLetting $\\gamma\\uparrow+\\infty$ gives\n\\begin{align} \\label{e3}\n\\liminf_{\\varepsilon\\downarrow 0}\\frac{I_2(\\varepsilon)}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\geq 0.\n\\end{align}\n\n\\noindent\n{\\bf Step 3.}  Combining \\eref{e1}, \\eref{e2} and \\eref{e3} gives\n\\begin{align*}\n\\liminf_{\\varepsilon\\downarrow 0}\\frac{{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{\\varepsilon}(T,x)|^2]}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\n&\\geq \\liminf_{\\varepsilon\\downarrow 0}\\frac{I_1(\\varepsilon)}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}+\\liminf_{\\varepsilon\\downarrow 0}\\frac{I_2(\\varepsilon)}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\geq c_{14}e^{-\\frac{|x|^2}{2c_{5}(T^{2H_1}+T^{2H_2})}}.\n\\end{align*}\nThis completes the proof.\n\\end{proof}\n\n\n\\section{Proof of Theorem \\ref{thm2}}\n\nIn this section, we give the proof of Theorem \\ref{thm2}.\n\n\\begin{proof}\nBy Lemma \\ref{lma3},\n\\begin{align*}\n{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{\\varepsilon}(T,0)|^2]\n&=\\frac{(-1)^{|\\mathbf{k}|}}{(2\\pi)^{2d}}\\int_{[0,T]^4}\\int_{{\\mathbb R}^{2d}} e^{-\\frac{1}{2}\\big[{{\\mathbb E}\\,}(z_2\\cdot X^{H_1}_{t_2}+z_1\\cdot X^{H_1}_{t_1})^2+{{\\mathbb E}\\,}(z_2\\cdot \\widetilde{X}^{H_2}_{s_2}+z_1\\cdot \\widetilde{X}^{H_2}_{s_1})^2\\big]}\\\\\n&\\qquad\\qquad \\times e^{-\\frac{\\varepsilon}{2}(|z_2|^2+|z_1|^2)} \\prod\\limits^d_{i=1}z^{k_i}_{2,i} \\prod\\limits^d_{i=1}z^{k_i}_{1,i}\\, dz_2\\, dz_1\\, dt\\, ds\\\\\n&=\\frac{1}{(2\\pi)^d}\\int_{[0,T]^4} \\prod^d_{i=1}\\Big(\\sum^{k_i}_{\\ell=0, \\text{even}}    \\frac{c_{k_i,\\ell} \\,b^{k_i-\\ell}}{((a+\\varepsilon)(c+\\varepsilon)-b^2)^{\\frac{2k_i-\\ell+1}{2}}}\n\\Big)dt\\, ds,\n\\end{align*}\nwhere $a={{\\mathbb E}\\,}[(X^{H_1,1}_{t_2})^2]+{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2})^2]$, $b={{\\mathbb E}\\,}[X^{H_1,1}_{t_2}X^{H_1,1}_{t_1}]+{{\\mathbb E}\\,}[\\widetilde{X}^{H_2,1}_{s_2}\\widetilde{X}^{H_2,1}_{s_1}]$ and $c={{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_1})^2]+{{\\mathbb E}\\,}[(X^{H_1,1}_{t_1})^2]$. According to the assumption (i) $|\\mathbf{k}|$ is even or  (ii) ${{\\mathbb E}\\,}[X^{H_1,1}_{t}X^{H_1,1}_{s}]\\geq 0$ and  ${{\\mathbb E}\\,}[\\widetilde{X}^{H_2,1}_{t}\\widetilde{X}^{H_2,1}_{s}]\\geq 0$ for any  $0<s,t<T$,\n\\begin{align*}\n{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{\\varepsilon}(T,0)|^2]\n&\\geq \\frac{1}{(2\\pi)^d}\\prod^d_{i=1} c_{k_i,0}\\int_{[0,T]^4} \\frac{b^{|\\mathbf{k}|}}{\\Big((a+\\varepsilon)(c+\\varepsilon)-b^2\\big)^{\\frac{2|\\mathbf{k}|+d}{2}}}\\, dt\\, ds.\n\\end{align*}\n\nRecall the definition of $D_{\\gamma}$ in \\eref{dg}. For any $(t_2,t_1,s_2,s_1)\\in D_{\\gamma}$ with $\\gamma$ large enough, by the property {\\bf (P1)}  and the Cauchy Schwartz inequality,\n\\begin{align*}\nb&={{\\mathbb E}\\,}[(X^{H_1,1}_{t_1})^2]+{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_1})^2]+{{\\mathbb E}\\,}[(X^{H_1,1}_{t_2}-X^{H_1,1}_{t_1})X^{H_1,1}_{t_1}]+{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2}-\\widetilde{X}^{H_2,1}_{s_1})\\widetilde{X}^{H_2,1}_{s_1}]\\\\\n&\\geq c_1(t^{2H_1}_1+s^{2H_2}_1-\\frac{t^{2H_1}_1}{\\gamma^{H_1}}-\\frac{s^{2H_1}_1}{\\gamma^{H_2}})\\\\\n&\\geq c_2(t^{2H_1}_1+s^{2H_2}_1).\n\\end{align*}\nLet $a_{22}={{\\mathbb E}\\,}[(X^{H_1,1}_{t_2}-X^{H_1,1}_{t_1})^2]+{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2}-\\widetilde{X}^{H_2,1}_{s_1})^2]$, $a_{11}={{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_1})^2]+{{\\mathbb E}\\,}[(X^{H_1,1}_{t_1})^2]$ and $a_{12}={{\\mathbb E}\\,}[(X^{H_1,1}_{t_2}-X^{H_1,1}_{t_1})X^{H_1,1}_{t_1}]+{{\\mathbb E}\\,}[(\\widetilde{X}^{H_2,1}_{s_2}-\\widetilde{X}^{H_2,1}_{s_1})\\widetilde{X}^{H_2,1}_{s_1}]$. Then\n\\begin{align*}\n0<(a+\\varepsilon)(c+\\varepsilon)-b^2\n&=(a_{22}+2a_{12}+a_{11}+\\varepsilon)(a_{11}+\\varepsilon)-(a_{12}+a_{11})^2\\leq 2(a_{22}+\\varepsilon)(a_{11}+\\varepsilon).\n\\end{align*}\nTherefore, for $\\gamma$ large enough,\n\\begin{align*}\n&\\liminf_{\\varepsilon\\downarrow 0}\\frac{{{\\mathbb E}\\,}[|L^{(\\mathbf{k})}_{\\varepsilon}(T,0)|^2]}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}\\\\\n&\\geq \\liminf_{\\varepsilon\\downarrow 0}\\frac{c_3}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}  \\int_{[0,T]^4} \\frac{b^{|\\mathbf{k}|}}{\\Big((a+\\varepsilon)(c+\\varepsilon)-b^2\\big)^{\\frac{2|\\mathbf{k}|+d}{2}}}\\, dt\\, ds\\\\\n&\\geq \\liminf_{\\varepsilon\\downarrow 0}\\frac{c_4}{h^{d,|{\\bf k}|}_{H_1,H_2}(\\varepsilon)}  \\int_{D_{\\gamma}} \\frac{(t^{2H_1}_1+s^{2H_2}_1)^{|\\mathbf{k}|}}{((t_2-t_1)^{2H_1}+(s_2-s_1)^{2H_2}+\\varepsilon)^{|\\mathbf{k}|+\\frac{d}{2}}(t^{2H_1}_1+s^{2H_2}_1+\\varepsilon)^{|\\mathbf{k}|+\\frac{d}{2}}}\\, dt\\, ds\\\\\n&\\geq c_5,\n\\end{align*}\nwhere in the last inequality we use Lemma {\\bf A.3.} in \\cite{hx} and the property {\\bf (P1)}.\n\\end{proof}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{Sec:introduction} \n\nStudies based on data from the Sloan Digital Sky Survey (SDSS) have revealed the existence of a color bimodality in the mass distribution of local galaxies \\citep{2001AJ....122.1861S,2003MNRAS.341...33K,2004ApJ...600..681B}. The most massive systems (basically spheroids) accumulate into a well-defined Red Sequence in color-magnitude diagrams, while the less massive blue ones (mostly disks) reside into a more spread Blue Galaxy Cloud  \\citep{2001AJ....122.1861S,2003MNRAS.341...54K,2004ApJ...600..681B}. Although this color-mass bimodality is observed up to $z\\sim 1$, observational data evidences a strong evolution in it for both field and cluster environments \\citep{1998ApJ...497..188C,2000ApJ...541...95V,2001ApJ...553...90V,2004ApJ...608..752B}. In fact, the mass limit isolating the Red Sequence from the Blue Cloud rises as the redshift increases and the stellar mass harbored by the former has nearly doubled since $z\\sim 1$ \\citep[whereas that of the Blue Cloud has remained nearly constant, see][]{2007A&A...476..137A,2008ApJ...672..177L,2008ApJ...677..828S,2009ApJ...694.1171T}. This points to a progressive buildup of the Red Sequence during the last $\\sim 9$\\,Gyr, associated with the migration of disks from the Blue Cloud to the Red Sequence through mechanisms that are still poorly understood, but that must be responsible of their star formation quenching and morphological transformation \\citep[][F07 hereafter]{2000ApJ...536L..77B,2007ApJ...665..265F}.\n\nAccording to hierarchical models of galaxy formation, the mechanism governing this evolution in the most massive systems have been major mergers \\citep[i.e., with mass ratios from 1:1 to 1:4, see][]{1999MNRAS.310.1087S,2002NewA....7..155S}. Present-day massive spheroids (E-S0's) are expected to be the result of the most massive and violent merging sequences in the Universe, also being the latest systems to be completely in place into the cosmic scenario  \\citep[at $z\\lesssim 0.5$, see][]{2006MNRAS.366..499D,2008ApJS..175..356H,2010ApJ...725.2312O}. However, this prediction conflicts directly with recent data indicating that massive galaxies seem to have been in place before their less-massive counterparts \\citep[a phenomenon known as downsizing, see][]{2006ApJ...651..120B,2006A&A...453L..29C,2008ApJ...675..234P,2011arXiv1101.2867M}. \n\nAlso, this assembly epoch seems to depend strongly on the galaxy mass and its environment \\citep[][]{2005ApJ...621..673T,2005A&A...442..125D,2006ApJ...652L.145D,2006ApJ...647L..99D,2008ApJ...687...50P,2010MNRAS.402.1942C,2010MNRAS.405..477N,2010MNRAS.401L..39V}. The wide range of ages found for E-S0's ($\\sim 2$-15\\,Gyr) and the disagreement between optical and NIR age estimators (sometimes, of up to $\\sim 6$\\,Gyr for a given galaxy) indicate that E-S0's have been built up at different epochs and through different mechanisms, basically depending on their masses \\citep[][]{2000AJ....119.1645T,2006ApJ...647..265B,2010AJ....139..540L}. It is generally accepted that the time period at $1<z<2$ is a transition era in which an increasing fraction of galaxies end their star formation activity and move onto the Red Sequence (\\citealt{2007A&A...476..137A}, but see also \\citealt{1997ARA&A..35..389E, 2003ApJ...595...71C, 2006ApJ...639..644E,2009ApJ...694.1171T,2011arXiv1104.2595B,2011MNRAS.417..900D}). Nevertheless, there are conflicting views on the number evolution experienced by massive E-S0's at $z\\lesssim 1$, with studies reporting from a negligible evolution to an increase by a factor of up to $\\sim 3$ in these systems \\citep[][]{2006A&A...453..809I,2007ApJ...665..265F,2007ApJS..172..406S,2008ApJ...682..919C,2011ApJ...727...51N}. \n\nMoreover, the Red Sequence is not made of a homogeneous galaxy population, but of a mixing of different galaxy types that has evolved strongly with redshift \\citep[][]{2002A&A...381L..68C,2003ApJ...586..765Y,2003MNRAS.346.1125G,2004ApJ...600L.131M,2007A&A...465..711F,2011MNRAS.414.2246H}. In the last years, different studies have analysed the number evolution of the Red Sequence from color- and morphologically-selected samples, but the conclusions derived from the former do not apply to the latter ones in general \\citep{2007A&A...465..711F,2010ApJ...719.1969B,2011MNRAS.414.2246H}. Recently, \\citet{2010ApJ...709..644I} have considered simultaneously both the morphological and star-formation properties of red galaxies to analyse their buildup. These authors confirm that the bulk of massive quiescent galaxies is rapidly created at $1\\lesssim z\\lesssim 2$, this mass assembly becoming negligible at later epochs. As in many previous studies, they also propose major mergers as drivers of this buildup. \n\nSeveral estimates assuming that most of the mass growth in quiescent galaxies is due to mergers indicate that this mechanism is capable of explaining at least 50\\% of the number density evolution of massive galaxies \\citep[see, e.g.,][]{2010A&A...519A..55E,2010arXiv1003.0686E,2011ApJ...739...24B}. However, no direct observational evidence has been found up to the date on the existence of a cause-and-effect link between major mergers and the definitive assembly of massive quiescent galaxies \\citep[][]{2007ApJ...665..265F,2009MNRAS.398...75S,2011MNRAS.411..675S,2010MNRAS.tmpL.176B,2011MNRAS.tmp...90B,2010ApJ...718.1158L,2011MNRAS.413.1678C}. \n\nThe present study tries to advance in the understanding of the formation and evolution of massive galaxies by analysing the physical properties of red galaxies at $0.3<z<1.5$ with stellar masses $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$. The novelty of our study over previous ones is two-fold. First, we include information about the structural distortion of each galaxy to trace merger remnants (besides considering morphology and star formation properties). And secondly, as most objects in their evolution towards the Red Sequence must have gone over nearby Green Valley locations transitorily (F07), we have analysed the red galaxies both lying on the Red Sequence and at close positions on the Green Valley. Therefore, red galaxies in the context of this paper include both the galaxies on the Red Sequence and at its neighbourhood. The galaxy classes resulting from the combination of morphological, structural, and star-formation activity properties allow us to trace the evolution of intermediate stages of major mergers and of their final remnants since $z\\sim 1.5$. Finally, the observed number density evolution experienced by each galaxy type is used to carry out a set of novel observational tests defined on the basis of the expectations of hierarchical models, which provide observationally and for the first time  main evolutionary paths among the different red galaxy types that have occurred in the last $\\sim 9$\\,Gyr. \n\nThe paper is organized as follows. In \\S\\ref{Sec:sample}, we provide a brief description of the survey. Section \\S\\ref{Sec:RGSelection} is devoted to the definition of the mass-limited red galaxy sample. In \\S\\ref{Sec:classification}, we define the galaxy classes according to the global morphology, structural distortion level, and star formation enhancement of the red galaxies. In \\S\\ref{Sec:Error}, we comment on the sources of errors and uncertainties. Section \\S\\ref{Sec:Tests} presents three novel tests to check the existence of any evolutionary links between the different red galaxy types, based on the expectations of hierarchical models of galaxy formation. The results of the study are presented in \\S\\ref{Sec:Results}. In particular, the results of the three tests proposed for the hierarchical scenario of E-S0 formation can be found in \\S\\ref{Sec:TestsResults}. The discussion and the main conclusions of the study are finally exposed in \\S\\S\\ref{Sec:Discussion} and \\ref{Sec:Conclusions}, respectively. Magnitudes are provided in the Vega system throughout the paper. We assume the concordance cosmology \\citep[$\\Omega_\\mathrm{m} = 0.3$, $\\Omega_\\Lambda = 0.7$, and $H_0 = 70$\\,km s$^{-1}$ Mpc$^{-1}$, see][]{2007ApJS..170..377S}. \n\n\n\\begin{figure}\n\\includegraphics[width=0.5\\textwidth,angle=0]{star_galaxy_separation.eps}\n\\caption{Color-color diagram for distinguishing stars from galaxies  ($I-K_{s}$ vs.~$V-I$). \\emph{Dots}: Data from the original $K$-band selected catalogue. \\emph{Solid line}: Color cut defined to isolate stars (i.e., the sequence of data located below the line) from galaxies (data lying above it). \\emph{Circles}: Objects classified as \"stars\" or \"compact\" visually (see \\S\\ref{Sec:Morphology}). All objects identified as \"stars\" visually are located in the stellar region of this diagram. }\\label{Fig:star-galaxy}\n\\end{figure}\n\n\n\\begin{figure}\n\\includegraphics[width=0.5\\textwidth,angle=0]{zspecRainbow_vs_zpRainbow_GRs_mag.eps}\n\\caption{Spectroscopic redshifts vs. photometric redshifts for the red galaxies in the sample having spectroscopic confirmation in the DEEP2 catalog \\citep{2003SPIE.4834..161D,2007ApJ...660L...1D}. Bright and faint galaxies in each one of the three wide redshift bins under consideration in the study are plotted with different symbols. The typical photometric redshift uncertainty for the red galaxy sample is below $\\Delta(z) \/ (1+z) <0.03$ at all redshifts for both bright and faint sources (see the estimates in the figure).}\\label{Fig:zspec-zphot}\n\\end{figure}\n\n\\section{The sample}\n\\label{Sec:sample}\n\nWe have combined multiwavelength data from the Rainbow Extragalactic Database\\footnote{Rainbow Extragalactic Database:\\\\https:\/\/rainbowx.fis.ucm.es\/\\-Rainbow\\_Database\/\\-Home.html} \\citep{2011ApJS..193...13B,2011ApJS..193...30B} and the GOYA photometric survey\\footnote{GOYA project (Galaxy Origins and Young Assembly):\\\\ http:\/\/www.astro.ufl.edu\/GOYA\/home.html} \\citep[see][]{2002INGN....6...11B} over an area of $\\sim 155$\\,arcmin$^{2}$ in the Groth Strip \\citep[$\\alpha=14^h 16^m 38.8^s$ and $\\delta=52^o 16' 52''$, see][]{1994AAS...185.5309G,1999AJ....118...86R,2002ApJS..142....1S}. The Rainbow Extragalactic Database compiles multi-wavelength photometric data from the UV to the FIR (and, in particular, in Spitzer\/MIPS 24$\\mu m$ band) over this sky area, providing analysis of spectral energy distributions of nearly 80,000 IRAC 3.6$+$4.5 $\\mu m$ selected galaxies. This study considers the photometric redshifts available in the Rainbow Database, which have a typical photometric redshift accuracy of $<\\Delta z\/(1+z)> = 0.03$ \\citep{2011ApJS..193...30B}, as derived for the sources with spectroscopic redshifts available in the DEEP2 Galaxy Redshift Survey \\citep{2003SPIE.4834..161D,2007ApJ...660L...1D}. The GOYA Survey is a survey covering the Groth Strip compiling photometry in four optical bands ($U$, $B$, $F606W$, and $F814W$) and in two near infrared ones ($J$ and $K_{s}$) with visual classifications available, reaching similar depths to the Rainbow data in similar bands \\citep[$U\\sim 25$, $B\\sim 25.5$, $K\\sim 21$ mag, see][]{2003ApJ...595...71C,2006ApJ...639..644E,2007RMxAC..29..165A,2008A&A...488.1167D}.\n\nWe have performed the sample selection starting from a $K$-band selected catalog in the field, reaching a limiting magnitude for 50\\% detection efficiency at $K\\sim 21$\\,mag. Several cuts have been performed to the original catalogue to obtain a mass-limited red galaxy sample. Firstly, red galaxies are selected as detailed in \\S\\ref{Sec:RGSelection}. This selection determines the redshift interval of the study, as it is restricted to the redshifts where the obtained number of red galaxies is statistically significant (i.e., to $0.3\\lesssim z\\lesssim 1.5$, see \\S\\ref{Sec:ClassificationSED}). \n\nAccording to the $M_{K}$-$z$ distribution of the red galaxies sample, the faintest absolute magnitude for which the catalogue is complete in luminosity up to $z\\sim 1.5$ corresponds to $M_{K,\\mathrm{lim}}\\sim -24$\\,mag. According to the redshift evolution of the mass-to-light relation (assuming a Salpeter IMF) derived by \\citet{2007A&A...476..137A} for a sample of quiescent bright galaxies, a red passive galaxy with this $K$-band absolute magnitude at $z\\sim 1.5$ has a stellar mass of $M_{*,\\mathrm{lim}}\\sim 5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$. Therefore, we have selected red galaxies with masses higher than $M_{*}\\sim 5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at each $z$ just considering all galaxies with $M_{K,\\mathrm{cut}} (z) =  -23.3 - 0.45 z$ to account for their luminosity evolution. This luminosity cut is very similar to the one obtained by \\citet{2007MNRAS.380..585C}. Analogously, the equivalent luminosity cut to obtain a complete red galaxy sample for $M_{*,\\mathrm{lim}}=10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ would be: $M_K = -24-0.45 z$ (we will use this selection for comparing our results with those reported in other studies, see \\S\\ref{Sec:RGSelection}). The detection efficiency in the $K$-band drops below 0.9 for $m_K >20.5$\\,mag \\citep{2003ApJ...595...71C}, so we have checked that all galaxies in our mass-limited red sample exhibit apparent magnitudes brighter than this limit. \n\nWe have used the color-color diagram shown in Fig.\\,\\ref{Fig:star-galaxy} to remove stars from the sample. It represents the $I-K_{s}$ vs.~$V-I$ distribution for all the sources in the mass-limited red galaxy sample. Stars typically exhibit NIR colors bluer than galaxies, so they populate the lower region in the diagram. Attending to this bimodality of star-galaxy colors, we have defined a color-color cut to isolate galaxies from stars (see the solid line in the figure). The marked points include the stars and compact objects in the sample. We have checked that the stars identified according to it include all the objects at lower redshifts that have been classified as \"stars\" in the morphological classification performed in \\S\\ref{Sec:Morphology} (they are marked in Fig.\\,\\ref{Fig:star-galaxy}). \nAs the number of compact objects found in the sample is not statistically significant (see \\S\\ref{Sec:Morphology}), they have been excluded from this study. From an initial sample of 1809 sources from the original $K$-band selected catalogue, we finally have a mass-limited red galaxy sample of 257 systems at $0.3<z<1.5$.\n\nFigure\\,\\ref{Fig:zspec-zphot} compares the photometric and the spectroscopic redshifts for the red galaxies in our mass-limited sample with spectroscopic redshift determinations from the DEEP2 survey \\citep{2007ApJ...660L...1D}.  The average redshift uncertainties are similar for both bright and faint sources at all redshifts, being below $\\Delta(z)\/(1+z) \\sim 0.03$ in the whole redshift interval under study.\n\n\\begin{figure*}\n\\begin{center}\n\\includegraphics[width=\\textwidth,angle=0]{colors.eps}\n\\includegraphics[width=\\textwidth,angle=0]{UBrestframe_hist.eps}\n\\caption{Color histograms of all galaxies in the $K$-band selected catalogue in the three wide redshift bins under consideration ($0.3<z<0.7$,  $0.7<z<1.1$, and $1.1<z<1.5$). \\emph{Top panels}: Histograms of the apparent color nearest to the rest-frame $U-B$ at each redshift interval. \\emph{Red and blue solid lines}: Gaussian functions fitted to match the bimodal color distributions at each redshift. \\emph{Vertical dashed lines in top panels}: Color cuts used to isolate red from blue galaxies in each redshift bin (see the text). \\emph{Bottom panels}: Histograms of the rest-frame $U-B$ in the same redshift bins. The horizontal bar in the upper left corner of each frame represents the average color error of one galaxy in the sample in each case. Dashed red and dotted blue histograms in these panels show the distributions of red and blue galaxies, respectively, selected according to the criteria based on the apparent colors of the top panels. Red galaxies are selected on the basis of apparent colors just attending to the low uncertainties associated to them compared to the typical errors of the rest-frame $U-B$ colors at all redshifts.}\n\\label{Fig:simul}\n\\end{center}\\end{figure*}\n\n\\section{Red galaxies selection}\n\\label{Sec:RGSelection}\n\nPrevious studies on red galaxies have been traditionally centered on the galaxies lying on top of the Red Sequence \\citep[see, e.g.,][]{2000ApJ...541...95V,2006ApJ...647..853W,2007MNRAS.380..585C}. These studies derive a linear fit to the rest-frame $(U-B)_\\mathrm{rest-frame}$-$M_B$ relation and consider all the objects within 1$\\sigma$ scatter of this relation as red galaxies. Nevertheless, the majority of the galaxies that have migrated to the Red Sequence is expected to have spent part of their lives at nearby locations on the Green Valley, undergoing transitory stages of $\\sim 1$\\,Gyr in their evolution towards typical E-S0's (F07). Many observational and computational studies confirm that advanced stages of major mergers usually lay on the Red Sequence or at nearby locations on the Green Valley, because gas-rich encounters experience noticeable dust extinction due to the starbursts induced by the encounter \\citep[see][]{1995AJ....110..129K,2001ApJ...550..212B,2003MNRAS.341...54K,2006MNRAS.370...74R,2008MNRAS.384..386C,2007MNRAS.380..585C,2009ApJ...693..112P,2010A&A...518A..61C,2008MNRAS.391.1137L,2010MNRAS.404..590L,2010MNRAS.404..575L}. Therefore, in this study we have included the systems both lying on the Red Sequence and on nearby positions on the Green Valley into our red galaxy sample, to also trace these transitory evolutionary stages towards the Red Sequence \\citep[see more references in][]{2010A&A...519A..55E}.\n\n\n\\subsection{Color cuts for red galaxies selection}\n\\label{Sec:Colorcuts}\n\nFollowing previous studies, we have selected red galaxies according to their rest-frame $U-B$ color \\citep[see, e.g., F07;][]{2008ApJ...682..896K}. This color traces the 4000\\,\\AA\\ break up, a spectral feature characteristic of evolved stellar populations. However, the rest-frame $U-B$ estimates derived from the present dataset exhibit so high uncertainties due to photometry and redshift-determination errors that we have used instead the observed color that samples the rest-frame $U-B$ more closely at the center of the three wide redshift bins covering the complete redshift range ($0.3<z<0.7$, $0.7<z<1.1$, and $1.1<z<1.5$).\n\nThe top panels of Fig.\\,\\ref{Fig:simul} show the color distribution of all galaxies in our $K$-band selected catalogue in the colors that sample more closely the rest-frame $U-B$ at these three redshift bins ($U-V$, $B-I$, and $V-K$ for the low, middle, and high  redshift intervals, respectively). Typical color errors of the galaxy sample are indicated with a horizontal bar at the left top corner of each frame. The figure shows the well-known bimodal distribution of galaxies into red and blue populations at all redshifts up to $z\\sim 2$ (see references in \\S\\ref{Sec:introduction}). These bimodal distributions have been modelled as the addition of two Gaussian functions (also plotted in the figure). \n\nIn order to include the galaxies located at nearby positions on the Red Sequence in the red sample (and not just the galaxies lying within 1$\\sigma$ scatter of the red peak), we have adopted the colors at which both Gaussian distributions cross as the color cuts for isolating red from blue galaxies at each redshift bin. The resulting cuts are $(U-V)=1.4$\\,mag for $0.3<z<0.7$, $(B-I)=2.7$\\,mag for $0.7<z<1.1$, and $(V-K)=4.5$\\,mag for $1.1<z<1.5$. \n\nIn the bottom panels of Fig.\\,\\ref{Fig:simul}, we show the histograms of the rest-frame $U-B$ color in the same redshift bins. The dashed red and dotted blue histograms show the distribution of red and blue galaxies selected according to the criteria based on the apparent colors commented above. In $1.1<z<1.5$ redshift range, the red and blue galaxy distributions appear quite mixed, probably due to the high errors associated to rest-frame $U-B$ colors (see the horizontal bar in the upper left corner of each frame). These high errors in the rest-frame $U-B$ color inhibited us to perform the red galaxies selection on the basis of rest-frame $U-B$ colors. \n\nPrevious studies report a negligible dependence of the rest-frame $U-B$ color cut isolating the Red Sequence from the Blue Cloud with the galaxy mass for both the mass and redshift range considered in this study \\citep[the $U-B$ color cut varies $\\sim 0.3$\\,mag at most, see][]{2009ApJ...694.1171T,2011ApJ...727...51N}. Therefore,  any dependence of our color cuts with mass (or, equivalently, with luminosity) has been overridden.\n\n\\begin{table*}\n \\begin{minipage}{140mm}\n  \\caption{Simulated star formation histories characteristic of different galaxy types.\\label{Tab:SFH}}\n\\begin{center}\n  \\begin{tabular}{llrcl}\n  \\hline\n\\multicolumn{1}{c}{Galaxy Type} & \\multicolumn{1}{c}{SFR law} & \\multicolumn{1}{c}{Metallicity} & \\multicolumn{1}{c}{$\\tau_{*, V}$ (mag)\\footnote{$\\tau_{*, V}$: Optical depth of the stellar population in the $V$-band due to dust extinction.}} & \\multicolumn{1}{c}{$z_\\mathrm{f}$}\\\\\n\\multicolumn{1}{c}{(1)} & \\multicolumn{1}{c}{(2)} & \\multicolumn{1}{c}{(3)} & \\multicolumn{1}{c}{(4)}& \\multicolumn{1}{c}{(5)}\\\\  \\hline\n\\multicolumn{1}{l}{Elliptical} & Finite burst ($\\tau =0.7$\\,Gyr) &  0.02& 0.6 & 0.8,1.0,1.3,1.5,2.0,2.5,3.0 \\\\[0.1cm]\n \\multirow{2}{*}{S0 and spirals} & Exponentially declining with& \\multirow{2}{*}{0.02} & \\multirow{2}{*}{0.6}   & \\multirow{2}{*}{1.2,1.3,1.5,2.0,3.0}\\\\\n & $e_f=1$, 2, 3, 5, and 7\\,Gyr\\footnote{$e_f$: Star formation e-folding timescales in exponentially declining SFRs.}& &   & \\\\[0.1cm]\n\\multicolumn{1}{l}{Irregular} & Constant&  0.008& 0.0& Present at all z\\\\[0.1cm]\n\\multicolumn{1}{l}{Dust-reddened}  & \\multirow{2}{*}{Constant} & \\multirow{2}{*}{0.008} & \\multirow{2}{*}{3.0} & \\multirow{2}{*}{Present at all z}  \\\\\n\\multicolumn{1}{l}{star-forming galaxy} &  &  &  &  \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\vspace{-0.5cm}\n\\end{minipage}\n\\end{table*}\n\n\\begin{figure*}\n\\includegraphics*[width=0.33\\textwidth]{UV_z_Szfdiff_v2.eps}\n\\includegraphics*[width=0.33\\textwidth]{BI_z_Szfdiff_v2.eps}\n\\includegraphics*[width=0.33\\textwidth]{VK_z_Szfdiff_v2.eps}\n\\caption{Color-redshift distributions for all galaxies in the $K$-band selected catalogue, in the observed colors closest to the rest-frame $U-B$ color in the three wide redshift bins of the study. \\emph{Panel a}: $U-V$ color (used for red galaxy selection at $0.3<z<0.7$). \\emph{Panel b}: $B-I$ color (used for red galaxy selection at $0.7<z<1.1$). \\emph{Panel c}: $V-K$ color (used for red galaxy selection at $1.1<z<1.5$). \\emph{Dots}: Observational data. \\emph{Lines}: Theoretical trends in the color-$z$ space for different galaxy types according to standard SFHs and physical properties of different galaxy types (more details in the text). \\emph{Red}: Ellipticals with different $z_\\mathrm{f}$. \\emph{Magenta}: S0 galaxy with $z_\\mathrm{f}=3$. \\emph{Yellow}: Spirals with different $z_\\mathrm{f}$. \\emph{Blue}: Star-forming irregular. \\emph{Green}: Dust-reddened star-forming galaxy with $\\tau_{*, V}=3$. \\emph{Horizontal black lines}: Color cuts defined to isolate red from blue galaxies, according to Fig.\\,\\ref{Fig:simul}. \\emph{Vertical solid lines}: Limits of the redshift interval associated to the color plotted in each panel. Red galaxies in each redshift bin are those enclosed between the vertical lines and above the horizontal line marking the color cut.}\n\\label{Fig:colorvsz}\n\\end{figure*}\n\n\n\\subsection{Galaxy populations in the red galaxy sample}\n\\label{Sec:GalaxyPopulations}\n\nWe have analysed the kind of galaxy populations selected at each redshift interval with the color cuts defined in \\S\\ref{Sec:Colorcuts} to find out if the selection is homogeneous at each redshift bin. In Fig.\\,\\ref{Fig:colorvsz} we show the color-redshift distributions of all the galaxies in the $K$-band selected catalogue, for the color indices nearest to the rest-frame $U-B$ color in the three wide redshift bins considered in the study ($0.3<z<0.7$, $0.7<z<1.1$, and $1.1<z<1.5$). The color cuts to distinguish between red and blue galaxies at each redshift bin are marked in their corresponding panels with horizontal lines. The red galaxies selected at each redshift bin are those above the color cut and enclosed between the redshift limits associated to the color index in each panel. \n\nWe have overplotted the theoretical evolution followed in each color-redshift plane by different galaxy types. These trends have been modelled using the IRAF package {\\tt COSMOPACK\\\/} \\citep{2003RMxAC..16..259B}, which uses the spectral energy distributions (SEDs) predicted by the stellar population synthesis models by \\citet[]{2003MNRAS.344.1000B} to obtain the evolution of color indices with $z$. The galaxy types plotted in the figure include E's and spirals formed at different redshifts, a S0, a star-forming irregular, and a dust-reddened star-forming galaxy. Standard star-formation histories (SFHs), metallicities, and dust extinction values are assigned to each galaxy type, accordingly to observations  \\citep{1989ApJ...344..685K,2005MNRAS.362...41G,2009ApJ...701.1965M}. The modelling parameters assumed for each simulated galaxy type are listed in Table\\,\\ref{Tab:SFH}. We must remark that we have adopted for the ellipticals a finite burst instead of the traditional single stellar population model. Although both SFRs provide similar colors and magnitudes evolution, the finite burst model can account for the short initial phases of star formation observed in these systems \\citep{2009AJ....138..579K,2010A&A...515A...3H}.\n\nDifferent formation redshifts have been considered for all the types. Nevertheless, as the redshift evolution of colors for S0's and their values were quite independent of $z_\\mathrm{f}$, we have just plotted the S0 track for $z_\\mathrm{f}=3$ in Fig.\\,\\ref{Fig:colorvsz} in benefit of clarity. As Irr's with different $z_\\mathrm{f}$ are basically located below the spirals region in the plots, we only plot the case with $z_\\mathrm{f}=3$ for the same reason. We have also simulated several cases of dust-reddened star-forming galaxies with different dust extinction levels. Their tracks basically overlap with those of the ellipticals in the plots, so we only show the model with $\\tau_{*, V}=3$\\,mag. \n\n Although we have assumed different $z_\\mathrm{f}$ for the formation of spirals, to assume the same epoch for their formation have a negligible effect on both their color evolution and location in the color-$z$ plane. They differ basically in their e-folding timescales, metallicities, and gas and dust contents. However, a similar conclusion cannot be derived for ellipticals. If we assume that all ellipticals have formed at an early epoch (e.g., $z_\\mathrm{f}\\geq 2$, as supported by some studies, see \\S\\ref{Sec:introduction}), the observed color-$z$ space of real red galaxies cannot be reproduced with the tracks modelled for $z_\\mathrm{f}>2.0$, unless there is a large population of dust-reddened star-forming objects at all redshifts at $0.4<z<2$ \\citep[][]{2006MNRAS.366..858K,2010A&A...519A..55E}. A wide range of values for the formation redshift of ellipticals reproduces more properly the observed color-$z$ distribution of red galaxies (see the mesh of red lines in each panel of the figure), a fact that does not exclude the existence of relevant populations of dust-reddened objects at different redshifts. \n\nThe models for E's, S0's, and dust-reddened star-forming galaxies lie all above the color cuts in the three panels and that no spiral track enters the region of red galaxies in Fig.\\,\\ref{Fig:colorvsz}. This proves that the color cuts used in this study select quite homogeneous samples of galaxy populations in the whole redshift interval, basically galaxy types earlier than Sa and dust-reddened star-forming galaxies.\n\n\\begin{figure*}\\begin{center}\n\\includegraphics[width=0.33\\textwidth]{comp_autores_I.eps}\n\\includegraphics[width=0.33\\textwidth]{comp_autores_II.eps}\n\\includegraphics[width=0.33\\textwidth]{comp_autores_III.eps}\n\\caption{Comparison of the redshift evolution of the number density of red galaxies obtained in this study with results from the literature for different mass and color selection criteria (see the text for details). Panels a and b plot the results for red galaxies with $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, but for different mass-to-light transformation relations. Panel c presents the results obtained with the same selection criteria as panel b, but for red galaxies with $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$. All data plotted in the same panel use equivalent color and mass selection criteria. \\emph{Filled black circles}: Results for our $K$-band selected data for each selection. \\emph{Rest of symbols}: Results obtained by \\citet{2007A&A...476..137A}, \\citet{2007MNRAS.380..585C}, F07, \\citet{2009ApJ...694.1171T}, \\citet{2010ApJ...709..644I}, \\citet{2010MNRAS.405..100M}, and \\citet{2011ApJ...727...51N}. Plotted data assume $h\\equiv H_0\/100 = 0.7$ and a Salpeter initial mass function. Cosmic variance and sample incompleteness contribute to the large dispersion found among different studies at $z<0.4$.\n\\label{Fig:comparacion}}\n\\end{center}\n\\end{figure*}\n\n\n\\subsection{Comparison with other studies}\n\\label{Sec:Comparison}\n\nThe red galaxy selection made in this study cannot be directly compared to the red galaxy samples obtained by most studies in the literature because, first, we have included red galaxies adjacent to the Red Sequence to study objects at transitory stages of their evolution towards it (which is not usual, see \\S\\ref{Sec:introduction}), and secondly, we have estimated masses using the $\\mathrm{M}_*\/L_K$-z relation derived by \\citet{2007A&A...476..137A} for different redshifts, whereas most authors use the $\\mathrm{M}_*\/L_V$-color relation derived by \\citet{2001ApJ...550..212B} or an equivalent relation. Moreover, most studies report the number evolution of red galaxies for masses $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, instead of for masses $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ (as our case). In order to check out our results, we have made alternative red galaxy selections for $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, adopting the color cuts and\/or the mass-to-light relation used by other authors.\n\nThe three panels of Fig.\\,\\ref{Fig:comparacion} compare the redshift evolution of the number density of red galaxies derived from our data with the results of different authors, for analogous mass and color selections in each case. In panel a, we have assumed the $U-B$ color evolution derived by \\citet{2001ApJ...553...90V} to select red galaxies (following F07), and the masses are estimated using the $\\mathrm{M}_*\/L_V$-color relation by \\citeauthor[][]{2001ApJ...550..212B}. Only red galaxies with $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at each redshift are considered in this panel. Panel b of the figure also assumes the color cut by \\citeauthor{2001ApJ...553...90V} for selecting red galaxies, but the mass estimates assume the $\\mathrm{M}_*\/L_K$ relation by \\citeauthor{2007A&A...476..137A}, which includes evolutive corrections \\citep[it is equivalent to the one derived by][]{2007MNRAS.380..585C}. The number densities of red galaxies shown in panel b are also for galaxies with  $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at each redshift. Finally, panel c of the figure use the same selection criteria as panel b, but the number densities of red galaxies have been computed for $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$. Note that the results of our color selection (including galaxies on the Red Sequence and at nearby locations) are not plotted in this figure (see \\S\\ref{Sec:Results} and Table\\,\\ref{Tab:densities}).\n\nThe data from \\citet{2007A&A...476..137A}, \\citet{2007MNRAS.380..585C}, and F07 have been obtained by integrating their red galaxy luminosity functions at each redshift for $\\log(\\mathcal{M}_*\/\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi)>11$. In this case, the absolute magnitudes have been transformed into stellar masses using the expression derived for local E-S0's by \\citet{2006A&A...453L..29C}, considering the L-evolution of red galaxies derived by F07 and the redshift evolution of the $(B-K)$ color expected for E-S0's \\citep[]{1998ApJ...501..578S,2003A&A...404..831D,2007A&A...476..137A}. AB magnitudes have been transformed to the Vega system in the $B$ and $K$ bands according to \\citet{2007AJ....133..734B} transformations and considering galaxy colors derived for E-S0's by \\citet{1995PASP..107..945F}.\n\nThe good agreement between our results and those from independent studies for similar selection criteria supports the reliability of our methodology and completeness of our nominal red sample (compare the black filled circles with the rest of studies in all panels of Fig.\\,\\ref{Fig:comparacion}). However, although our first data point in panels b and c in the figure is inside the cloud of points within errors, it does not follow the trend of the other authors. So, our data at this redshift are probably affected by volume and cosmic variance effects.\n\n\\section{Classification of red galaxy types}\n\\label{Sec:classification}\n\nThe hierarchical picture of galaxy formation predicts that massive E-S0's are the result of the most violent and massive merging histories in the Universe (see references in \\S1 in EM10). To test this scenario, we need to distinguish between galaxies undergoing a major merger and normal E-S0's (see \\S\\ref{Sec:Tests}). Normal relaxed galaxies and major mergers differ basically in their structural distortion level. Major mergers also exhibit different global morphology and star formation enhancement depending on the gas content of the progenitors and the evolutionary stage of the encounter.\n\nA gas-rich major merger is expected to turn into a dust-reddened star-forming disk with noticeable structural distortions at intermediate and advanced stages of the encounter, basically since the coalesce of the two galaxies into an unique galaxy body (this stage is known as the merging-nuclei phase). In earlier phases of the merger, the two galaxies can develop noticeable tidal tails and asymmetric structures, but the two bodies can still be distinguished and are not expected to suffer from enough dust reddening to lie nearby or on top of the Red Sequence. During the latest phase of the encounter (post-merger), the star formation is quenched and the remnant gets a more relaxed spheroidal structure until it transforms into a typical E-S0 \\citep[see][]{2008MNRAS.384..386C,2008MNRAS.391.1137L,2010MNRAS.404..590L,2010MNRAS.404..575L}. Intermediate-to-late stages of gas-poor major mergers present a distorted spheroidal morphology and negligible levels of star formation, thus being quite red too \\citep{2005AJ....130.2647V}. By the contrary, typical E-S0's present a spheroidal-dominated relaxed morphology, although they are also expected to be quite red due to their negligible star formation. Therefore, a gas-rich major merger is expected to be quite red from its merging-nuclei phase until its transformation into a typical E-S0, so we have traced major mergers once the two merging galaxies have merged into a unique remnant, because they are expected to be quite red in any case. Accounting for this, we have classified the galaxies in our red sample attending to their global morphology, structural distortion level, and star formation enhancement to distinguish among normal galaxies and intermediate-to-advanced phases of major mergers.\n\n\n\\begin{figure*}\n\\begin{center}\n\\includegraphics[width=\\textwidth,angle=0]{stamps2.eps}\n\\caption{False-color postage stamps of some red galaxies in our sample, obtained using the $V$ and $I$ bands. One example representative of each type is shown for each wide redshift bin used in the present study ($0.3<z<0.7$, $0.7<z<1.1$, and $1.1<z<1.5$). North is up, East is left. The frames correspond to a $5\\arcsec\\times 5\\arcsec$ field-of-view, except for the irregular spheroid at $0.3<z<0.7$ (141618.91+521352.3), where a $10\\arcsec\\times 10\\arcsec$ view is used to emphasize the interacting group to which this galaxy belongs (the galaxies at the North and at the Southern-East of the central object are located at the same redshift as the central object). No compact or unclassified objects are found at $0.3<z<0.7$. }\n\\label{Fig:stamps}\n\\end{center}\\end{figure*}\n\n\\begin{figure*}\n\\begin{center}\n\\includegraphics[width=\\textwidth,angle=0]{stampssurf2.eps}\n\\caption{$I$-band contour maps and surface plots of some red galaxies in Fig.\\,\\ref{Fig:stamps}. One galaxy representative of each type is shown (\"C\", \"RS\", \"RD\", \"IS\", \"ID\", \"NC\"). The axes in both the contour and surface maps are in CCD pixels.}\n\\label{Fig:stampscon}\n\\end{center}\\end{figure*}\n\n\\subsection{Classification according to global morphology and distortion level}\n\\label{Sec:Morphology}\n\nDespite the definition of very efficient quantitative morphological indices \\citep{2008ApJ...672..177L}, visual inspection is still the most trustworthy method to classify galaxies morphologically \\citep{2007MNRAS.382.1415S,2009ApJ...697.1971J,2010MNRAS.401.1043D}. The red galaxies in our sample have been thus classified visually by three co-authors. The comparison of the visual results with those obtained through quantitative classification methods has proven the reliability and robustness of the visual classification (see \\S\\ref{Sec:Robustness}).\n\nNo preconceived or classical morphological types have been used for the visual classification, as the emergence of the classical Hubble types seems to occur at $z\\sim 1.0$-1.5 \\citep{1996ApJ...472L..13O,2005ApJ...631..101P,2006ApJ...652..963R}. The visual types of red galaxies have been defined attending to the global characteristics exhibited by these galaxies in the sample. We find that red galaxies in our sample can be grouped morphologically attending to two aspects: 1) their structural distortion, and 2) its disk- or spheroid-dominated morphology. Six major exclusive classes have been identified according to the previous two criteria (see Fig.\\,\\ref{Fig:stamps}):\n\n\\begin{enumerate}\n\\item Compact galaxies (C).- Galaxies exhibiting compact morphologies, according to the seeing of the $I$-band images. No spatial information is available for them. The number of these objects in the sample is negligible, so we will not consider them henceforth.\n\\item Regular Spheroids (RS).- Galaxies with regular isophotes and dominated by a central spheroidal component. We remark that our RS's do not correspond to the spheroidal type defined by \\citet{2012ApJS..198....2K}. This class basically groups E-S0 galaxies.\n\\item Regular Disks (RD).- Galaxies with regular isophotes and dominated by a disk component. Dust-reddened, typical spiral Hubble types correspond to this class.\n\\item Irregular Spheroids (IS).- Galaxies with irregular isophotes in the whole galaxy body but dominated by an spheroidal component.\n\\item Irregular Disks (ID).- Galaxies with irregular isophotes in the whole galaxy body and dominated by a disk.\n\\item Non-Classified or unclassified objects (NC).- Galaxies that cannot be classified into any one of the previous classes, because of their faintness or noise. The number of these objects is also negligible, so we will not consider them from now on.\n\\end{enumerate}\n\nWe have used surface brightness isophotes and surface maps to identify structural or morphological features that are more noticeable in these maps than in normal images (see Fig.\\,\\ref{Fig:stampscon}). We have also adopted the following additional classification rules. As commented above, we have traced exclusively advanced stages of major mergers, i.e., once both galaxies have merged into a unique body. Therefore, we have assigned a certain type to a red galaxy regardless of its environment, i.e., independently of whether it has close neighbours or not. We have considered as irregular galaxies only those systems that exhibit a noticeable distortion level in its \\emph{whole} body. This implies that a galaxy in an interacting pair is identified as an independent regular galaxy, because its central body does not exhibit noticeable distortions yet, despite of the existence of significant tidal features in its outskirts. We remark that we are excluding from the irregular class the early phases of mergers in which the interacting galaxies have not merged into one body yet. The reason is because the tests for the hierarchical scenario of E-S0 formation described in \\S\\ref{Sec:Tests} are based in the tracing of these specific advanced stages of major mergers (and not of earlier phases). \n\nMinor mergers imprint less significant distortions than major mergers \\citep{2006A&A...457...91E,2011A&A...533A.104E,2008MNRAS.391.1137L}, but they can also redden the galaxy enough to locate it at neighbouring regions of the Red Sequence temporarily \\citep{2010MNRAS.404..590L,2010MNRAS.404..575L}. We have avoided the inclusion of minor mergers into the irregular class by considering exclusively morphological features typical of major mergers to classify a system as irregular, following \\citet{2009ApJ...697.1971J}, such as the existence of multiple nuclei of similar luminosity in the body, the existence of equal-length tidal tails, or \"train-wreck\" morphologies. So, our red galaxy sample contain some minor mergers, but they are included into the regular class.\n\nOur classification criteria try to minimize the effects of the spatial resolution loss and cosmological dimming inherent to the rise of redshift, which soften the luminosity distribution of galaxies, losing the physical regions of fainter surface brightness. Therefore, we have defined our galaxy types attending to features that affect to the whole galaxy body and that are poorly affected by these effects for the considered redshifts. Moreover, the classification has been done in the reddest visual band available with the best spatial resolution ($I$-band from HST\/WFPC2). This band samples the rest-frame visual spectrum in the whole redshift range under study (from $I$ at low redshifts to $B$ at $z\\sim 1.5$). Galaxies usually exhibit more distorted and clumpy morphologies in the rest-frame UV than in optical or NIR bands, but the morphology of a system is very similar in all rest-frame optical bands \\citep{2000ApJS..131..441K,2009ApJ...697.1971J}, so we expect our visual classifications to not be biased towards irregular types at any redshift in our study. Simulations of the cosmological effects in the apparent $I$-band morphology of our systems have demonstrated the robustness of our visual classification against this effect (see \\S\\ref{Sec:TestVisual2}). In general, the three independent classifiers agreed in $\\sim90$\\% of the classifications at each redshift bin, a fact that strongly supports the robustness of the visual classification.\n \n\n\\begin{figure*}\n\\begin{center}\n\\includegraphics[width=0.32\\textwidth,angle=0]{comparison_classifications_03z07.eps}\n\\includegraphics[width=0.32\\textwidth,angle=0]{comparison_classifications_07z11.eps}\n\\includegraphics[width=0.32\\textwidth,angle=0]{comparison_classifications_11z15.eps}\n\\caption{Comparison of visual and quantitative morphological classifications into regular\/irregular classes. The histograms of the galaxies corresponding to a given visual class are shown as a function of the quantitative irregularity parameter $C_\\mathrm{irr,isoph}$ defined in \\S\\ref{Sec:TestVisual1}, for the three wide redshift bins of the study. \\emph{Left panels}: For $0.3<z<0.7$. \\emph{Middle panels}: For $0.7<z<1.1$. \\emph{Right panels}: For $1.1<z<1.5$. Visual regulars, irregulars, and stars or unclassified objects are plotted from the top to the bottom panels of each column, respectively. The galaxies classified as regular\/irregular according to the quantitative method are indicated in each panel. \\emph{Vertical dashed lines}: Limiting values of $C_\\mathrm{irr,isoph}$ to classify a galaxy as regular ($|C_\\mathrm{irr,isoph}|=0.05$). Galaxies with $|C_\\mathrm{irr,isoph}|<0.05$ are regular. However, $|C_\\mathrm{irr,isoph}|$ values above this limit do not necessarily imply irregular morphology (see the cases in the text). Visual and quantitative classifications of irregularity agree in $\\sim 75$\\% of the cases at all redshifts on average, supporting the robustness of the visual method.}\n\\label{Fig:IrregularClassification}\n\\end{center}\\end{figure*}\n\n\n\\subsection{Tests to the robustness of the visual morphological classification}\n\\label{Sec:Robustness}\n\nWe have carried out two kind of quantitative tests to check the robustness of the visual classifications:\n\n\\begin{enumerate}\n \\item Tests on the reliability of the visual distinction of spheroid\/disk-dominated and irregular\/regular classes, based on the quantification of the light concentrations and the deviations of the isophotes from perfect ellipses in the whole galaxy body. \n\n \\item Tests on the cosmological effects on the visual morphology in the observed $I$-band (resolution loss, \ncosmological dimming, and change of the observed rest-frame band with redshift). \n\\end{enumerate}\n\n\\subsubsection{Reliability of the visual classifications}\n\\label{Sec:TestVisual1}\n\nIn order to check our visual classification, we have computed concentration and asymmetry indices as defined by \\citet{2003ApJS..147....1C}, which are quantitative indices closely related to our visual classes by definition (irregular galaxies should exhibit high asymmetries, while spheroid-dominated galaxies must have high concentrations). We find that galaxies visually classified as RS's show high concentration indices in general ($\\sim 90$\\%). The irregulars (IS's and ID's) present a wide spread of concentration values, consistently with their merger-related nature. \n\nNevertheless, we also find that the galaxies classified visually as irregulars do not exhibit any correlations with the asymmetry index, contrary to expectations. This is probably because the asymmetry index estimates are extremely affected by background substructures, thus requiring high signal-to-noise data to be reliable \\citep[$S\/N>100$, see][]{2000ApJ...529..886C,2003ApJS..147....1C,2009MNRAS.394.1956C}. But the galaxies in our red sample have $S\/N \\sim 40-50$ at most (as $I$-band magnitude errors are $\\sim 0.02-0.03$\\,mag typically), making our asymmetry estimates quite uncertain. Moreover, asymmetry indices are sensitive to environmental influences in the galaxy outskirts. This means that some galaxies identified as regulars according to our criteria (because they do not exhibit noticeable distortions in its whole body) may have a high asymmetry index because of tidal features in the outer parts. This obviously smudges the correlation between visual irregularity and computed asymmetries. \n\nWe have adapted the method by \\citet{1993ApJ...418...72Z} to quantify the irregularity level of galaxy morphology. These authors developed a procedure to classify an elliptical galaxy as regular or irregular, attending to the distortion level of their isophotes with respect to perfect ellipses. They fitted ellipses to the isophotes of each elliptical to obtain the radial profiles of the coefficients $a_3$, $b_3$, $a_4$, and $b_4$ of their Fourier expansion series. The peak value of each Fourier coefficient was identified along the radial profile. These authors considered the following criteria to distinguish among regular and irregular galaxies:\n\n\n\\begin{enumerate}\n \\item If all the peaks of the coefficients were small, this meant that the isophotes exhibited small deviations \n   from perfect ellipses. Therefore, these galaxies could be considered as regulars.\n \\item If one of them was not small, then they differentiated between two possible cases:\n    \\begin{itemize}\n     \\item If the maximum value of the peaks of all coefficients did not correspond to $b_4$, then the isophotes deviated noticeably from ellipses, meaning that the galaxy was irregular.\n     \\item If the peak of $b_4$ was the maximum among all the peaks, its classification depended on its trend with the radial position in the galaxy. If the profile of this coefficient changed from one type to another within 1.5 effective radius of the galaxy, then the galaxy was irregular. If not, it just implied that the galaxy was boxy or disky (depending on the sign of $b_4$), but the galaxy morphology could be considered as regular.\n    \\end{itemize}\n\\end{enumerate}\n\nWe can adopt this method for our galaxies, as we are considering irregularities that must affect to the galaxy as a whole. We have limited the analysis in each red galaxy to the isophotes with a mean signal higher than 1.5 times the standard deviation of the sky signal per pixel. We have used the IRAF task \\texttt{ellipse} for fitting ellipses to the isophotes and for getting the third and fourth order coefficients of their Fourier expansion series. We have identified the peaks of each coefficient in the galaxy radial profile. \n\nThe task \\texttt{ellipse} uses a normalization to the surface brightness of the isophote that directly measure the deviations of the isophote from perfect ellipticity. According to de \\citet{1990AJ....100.1091P}, these deviations can be considered negligible if they are $< 5$\\%, a value that can be translated directly to a value of 0.05 in these coefficients. Therefore, we have adopted this limit as the critical value to distinguish between small and high values. We have defined the irregularity index $C_\\mathrm{irr,isoph}$ as the peak value of maximum absolute value among the peaks of the four Fourier coefficients. Therefore, according to \\citet{1993ApJ...418...72Z}, any galaxy that has $|C_\\mathrm{irr,isoph}|<0.05$ is regular. If not, it is irregular, except if $C_\\mathrm{irr,isoph}$ corresponds to the $b_4$ coefficient and this coefficient does not change between $|b_4|>0.5$ and $|b_4|<0.5$ values or viceversa along its radial profile. \n\nWe compare the results of the visual and quantitative classifications concerning the irregularity level of our red galaxies in Fig.\\,\\ref{Fig:IrregularClassification} for each wide redshift bin. The percentage of agreement between the visual and quantitative classifications into the regular type is $\\sim 77$\\% (decreasing from 83\\% to 70\\% from low to high redshifts). This percentage is slightly lower in the irregular type: $\\sim $66\\% (rising from 58\\% to 74\\% from low to high redshifts). The miss-classifications between both methods are $\\sim $23\\% for visually-identified regular galaxies (rising the confussion percentage from 17\\% to 30\\% from low to high z), and $\\sim $34\\% for visual irregulars (dropping from 42\\% at low z to 26\\% at high z). In general, both procedures coincide in $\\sim 78$\\% of the galaxy classifications at $0.3<z<0.7$, in $\\sim 68$\\% of the classifications at $0.7<z<1.$1, and in $\\sim 73$\\% at $1.1<z<1.5$. \n\nIt is important to remark that only isophotal data above 1.5 times the sky standard deviation have been considered to quantify the irregularity of the galaxy in the quantitative method, i.e., it analyses isophotes of $S\/N> 1.5$ at all redshifts. This implies that the quantitative method is not biased towards more irregular types at high redshifts, as it is limited to the isophotes with enough $S\/N$ at all redshifts. Obviously, $C_\\mathrm{irr,isoph}$ is derived from an intrinsic physical region in the galaxies smaller at high redshift than at low redshift, just because of cosmological effects. But, as commented above, we consider as irregular galaxies only the stages of advanced major mergers, which imply a noticeable distortion level in its whole body. The effects of cosmological dimming and resolution loss on the classification are analysed in \\S\\ref{Sec:TestVisual2}.\n\nIn conclusion, this test proves the robustness of the visual classifications into regular and irregular types at all redshifts.\n\n\\subsubsection{Robustness of the observed morphology against cosmological effects}\n\\label{Sec:TestVisual2}\n\nIn order to find out how the loss of spatial resolution, the cosmological dimming, and the change of rest-frame band with redshift are affecting to our classification, we have simulated images of galaxies at different redshifts in the observed $I$-band. We have used \\texttt{COSMOPACK} \\citep{2003RMxAC..16..259B}, an IRAF package that transforms images of real galaxies to depict their appearance at a given redshift as observed with a given telescope, camera, and filter. The transformation includes K-corrections, change of observing band, repixelation to the scale of the observing system, convolution by the seeing, and noise from sky, detector, and dark current. \n\nStarting from the $I$-band image of a galaxy representative of one type at the lowest wide redshift bin ($0.3<z<0.7$), we have simulated the observed $I$-band image of the same object at the middle of the other two redshift bins ($z= 0.9$ and $z=1.3$), in order to check if its morphological classification changes as the object is placed at higher redshifts. We have assumed a typical SFH, metallicity, and formation redshift for the galaxy to assign a characteristic SED  at its original redshift. Once we obtain the simulated image at $z=0.9$ and $z=1.3$, we have classified them visually following the same procedure as with the original image. \n\nThe surface maps at different redshifts show that the distinction between the spheroid\/disk-dominated morphology is quite robust in the whole redshift interval under consideration. In general, we can distinguish the winged surfaces of disks in the surface maps at all redshifts (see Figs.\\,\\ref{Fig:stamps}-\\ref{Fig:stampscon}). This means that the visual classification into spheroid\/disk-dominated systems is quite robust against cosmological effects for the redshifts and magnitudes studied here.\n\nConcerning the irregularity, the contour plots support the expected trend of external isophotes to appear more irregular as we move towards higher redshifts. But this effect should not affect strongly our results, as we derive our visual classification into regular\/irregular classes having into account the morphology of the isophotes over the whole galaxy body, discarding the most external ones. This qualitative test indicates that cosmological effects are not expected to affect noticeably the classification into regular\/irregular types either.\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=0.5\\textwidth,angle=0]{fluxcut.eps}\n\\caption{SFR cuts selected to define the red galaxies with enhanced SFRs compared to the average SFR of the galaxy population, as a function of redshift. \\emph{Red squares}: Redshift evolution of the SFR of galaxies with $\\log(\\mathcal{M}_*\/\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi) >11.1$ derived by \\citet{2011ApJ...730...61K}. \\emph{Yellow circles}: Redshift evolution of the SFR of galaxies with $10.8 < \\log (\\mathcal{M}_*\/\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi) < 11.1$ derived by the same authors. \\emph{Grey stars}: Galaxy data from \\citet{2005ApJ...630...82P} with $F(24\\mu m)> 85$\\,$\\mu$J. \\emph{Black stars}: Galaxy data from the same authors with $F(24\\mu m)< 85$\\,$\\mu$J. This limiting flux in 24\\,$\\mu$m naturally isolates galaxies with high (enhanced) SFR compared to the average value of the whole galaxy population at each redshift from those with low SFR, for the mass range considered here.} \n\\end{center}\n\\label{Fig:ksfr}\n\\end{figure}\n\n\\subsection{Classification according to star formation activity}\n\\label{Sec:ClassificationSED}\n\nA typical problem of studies based on red galaxy samples is to disentangle dust-reddened star-forming galaxies from quiescent ones \\citep[][]{2000MNRAS.317L..17P,2004ApJ...617..746D,2007ApJ...665..265F,2011MNRAS.412..591P}, because both galaxy populations are indistinguishable using only broad-band photometry at wavelengths $\\lesssim 10$\\,$\\mu$m \\citep{2006AJ....132.1405S}. In particular, the rest-frame $U-B$ color cannot differentiate between both red galaxy types adequately at $z>0.8$ (F07). Therefore, different selection techniques based on color indices, mid-IR data, or SED fitting have been developed to isolate both populations in red galaxy samples \\citep{1999ApJ...518..533L,2003A&A...401...73W,2006A&A...455..879Z,2009ApJ...691.1879W}.\n\nThe mid-IR emission and the SFR of a galaxy are known to be tightly correlated \\citep[][]{1998ARA&A..36..189K,2005ApJ...630...82P}. The higher sensitivities and spatial resolutions achieved by IR instruments in the last years have allowed the development of SFR indicators based on the emission of a galaxy in a single mid-IR band  \\citep[]{2005ApJ...633..871C,2007ApJ...666..870C,2006ApJ...648..987P}. In particular, the 24\\,$\\mu$m band of the Multiband Imaging Photometer in the \\emph{Spitzer} Space Telescope (MIPS) is found to be a good tracer of the infrared emission coming from the dust heated by star-forming stellar populations \\citep{2006ApJ...650..835A}. \n\nIn this study, we have identified galaxies with noticeable star formation compared to the average SFR exhibited by the galaxies with similar masses at the same redshift, because this is an evidence of that mechanisms different to passive evolution are triggering it (such as tidal interactions, mergers, gas infall, or stripping). The SFR of a galaxy changes noticeably with redshift due to the natural evolution of their stellar populations. The specific SFR has decayed with cosmic time as $\\sim (1+z)^{n}$ since $z=3$, being $n=4.3$ for all galaxies and $n=3.5$ for star-forming sources \\citep{2011ApJ...730...61K}. This means that we must have into account the intrinsic rise of SFR with redshift to define when a galaxy is forming stars more efficiently than the average of the whole galaxy population at each redshift. Therefore, we have used {\\it Spitzer}\/MIPS 24~$\\mu$m data to discriminate between red galaxies with enhanced SFRs from those that have lower SFRs compared to the average SFR of the whole galaxy population at each redshift \\citep[see also][]{2009ApJ...691.1879W}. A limiting flux in 24\\,$\\mu$m of $\\sim 60$\\,$\\mu$Jy corresponds to the 5-$\\sigma$ detection level on our MIPS 24~$\\mu$m data \\citep[][]{2011ApJS..193...13B}.\n\nIn Fig.\\,\\ref{Fig:ksfr}, we plot the $z$-evolution of the average SFR of galaxy populations with different mass ranges overlapping with ours (which is $\\log (\\mathcal{M}_*\/\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi)>10.7$), as derived by \\citet{2011ApJ...730...61K} from a deep 3.6\\,$\\mu$m-selected sample in the COSMOS field. We have overplotted the location of the galaxies from \\citet{2005ApJ...630...82P} in the diagram, differentiating those with emission fluxes in MIPS 24~$\\mu$m above 85\\,$\\mu$J from those below it. Note that this limiting flux follows pretty well the redshift evolution of the average SFR of the whole galaxy population for our mass range, being a straightforward way for distinguishing galaxies with enhanced SFRs from those with low SFRs, compared to the average value of the galaxy population at each redshift. Therefore, we have considered red galaxies with a 24~$\\mu$m MIPS flux above $85$\\,$\\mu$Jy as systems with enhanced star formation compared to the global galaxy population at the same redshift (High Star-Forming galaxies or HSF, hereafter), whereas the galaxies with a 24~$\\mu$m flux below this limit are not substantially star-forming compared to it (so, they are Low Star-Forming ones or LSF, henceforth). \n\n\\begin{table}\n\\begin{minipage}{0.5\\textwidth}\n\\caption{Percentages of AGN contamination in the subsample of HSF red galaxies by morphological types.\\label{Tab:agns}}\n\\begin{center}\n\\begin{tabular}{lcccccccc}\n\\hline\n \\multirow{2}{*}{HSF}   & \\multicolumn{2}{c}{$0.3<z<0.7$}   & & \\multicolumn{2}{c}{$0.7<z<1.1$} & &  \\multicolumn{2}{c}{$1.1<z<1.5$}  \n\\vspace{0.05cm}\\\\\\cline{2-3}\\cline{5-6}\\cline{8-9}\\vspace{-0.2cm}\\\\\ntype &\\multicolumn{1}{c}{Pure$^\\mathrm{a}$} & \\multicolumn{1}{c}{Total$^\\mathrm{b}$} \n& &\\multicolumn{1}{c}{Pure} & \\multicolumn{1}{c}{Total} & &\\multicolumn{1}{c}{Pure} & \\multicolumn{1}{c}{Total}  \\\\\n & (\\%) & (\\%) & & (\\%) & (\\%) & & (\\%) & (\\%) \\\\\n\\multicolumn{1}{c}{(1)} & \\multicolumn{1}{c}{(2)} & \\multicolumn{1}{c}{(3)} & & \\multicolumn{1}{c}{(4)} & \\multicolumn{1}{c}{(5)}& & \\multicolumn{1}{c}{(6)} & \\multicolumn{1}{c}{(7)}\\\\\\hline\nRS  &  0 & 0 & & 22 & 22 & & 0 & 0\\\\\nRD  &  0 & 0 & & 0 & 0 & & 0 & 0\\\\\nIS   &  0 & 0 & & 13 & 38 & & 0 & 13\\\\\nID   &  0 & 0 & & 0 & 0 & & 0 & 0\\vspace{0.12cm}\\\\\nAll  &  0 & 0 & & 7 & 13 & & 0 & 4\\vspace{-0.1cm}\\\\\n\\hline\n\\end{tabular}\\\\\n\\end{center}\n$^ \\mathrm{a}$Columns labelled as \"Pure\" represent the contribution of pure AGNs (Type 1 and 2) to each HSF galaxy type (i.e., without starburst connection).\\\\\n$^\\mathrm{b}$Columns labelled as \"Total\" provide the total contribution of AGNs to each type, including pure AGNs (Type 1 and 2) and mixed types (starburst-dominated AGNs, starburst-contaminated AGNs, and normal galaxies hosting AGNs). \n\\end{minipage}\n\\end{table}\n\nActive Galactic Nuclei (AGN) emission can coexist with star formation in galaxies, i.e., both phenomena are not mutually exclusive. Moreover, AGN activity is expected to be induced and enhanced in gas-rich mergers \\citep{2008ApJS..175..390H,2008ApJS..175..356H}, so we should expect to find AGNs in our red galaxy sample, especially associated to our irregular class. Galaxies with an AGN are expected to be bright in the mid-to-far IR (and, in particular, in 24 $\\mu m$) due to the emission of the hot dust surrounding the central engine \\citep[see references in][]{2005ApJ...630...82P}. Therefore, pure or dominant AGN emitters can be confused with HSF galaxies according to the criterion used in this study to identify HSF galaxies. \n\nTherefore, we have cross-correlated our red galaxy sample with the AGN catalogue over the Extended Groth Strip by \\citet{2009AJ....137..179R} to estimate the contamination of our HSF class by pure or dominant AGNs. These authors use a reliable technique of classification of active galactic nuclei (AGNs) based on fits of the UV-to-FIR SEDs of the galaxies with a complete set of AGN and starburst galaxy templates, in such a way that they are capable of distinguishing between pure and host-dominated AGNs up to $z\\sim 2$ . The contribution of AGNs of any type and of pure AGNs (i.e., with no contribution of starbursts) to our HSF red galaxy sample at each redshift bin is tabulated in Table\\,\\ref{Tab:agns}. We also list the contribution of AGNs to HSF red galaxies at each redshift bin by morphological types. \n\nThe results in Table\\,\\ref{Tab:agns} show that the contamination by any type of AGNs to our HSFs is negligible (below 13\\% at all redshifts), the contribution of pure AGNs being even smaller ($<7$\\% at all redshifts). Therefore, we can conclude that AGN contamination does not affect our results concerning the classification into HSF galaxies significantly. \n\n\\section{Errors and uncertainties}\n\\label{Sec:Error}\n\nThe errors in the estimates of the number density of each red galaxy type are derived considering the following sources of errors: statistical and classification errors, photometric redshift errors, and cosmic variance uncertainties. \n\nStatistical counting errors have been estimated for the number densities derived by each classifier for each galaxy type and at each redshift \\citep[][]{1986ApJ...303..336G}. The final number density of each morphological type at each redshift bin is estimated as the mean of the number densities resulting from the three independent classifiers. We have estimated the error of this mean \nas the quadratic propagation of the statistical error of each classifier \\citep[consult][]{2009ApJ...697.1971J}. \n\nConcerning to redshift errors, we have used the redshift estimates from the Rainbow Extragalactic Database \\citep{2011ApJS..193...30B}. As commented in \\S\\ref{Sec:sample}, uncertainties in the redshifts are $\\Delta z \/ (1+z) \\lesssim 0.03$ for the whole redshift interval under consideration, for both bright and faint red sources. \n\nWe have included estimates of the uncertainties introduced in the number densities of each red galaxy type by the redshift errors. These estimates have been derived using Monte-Carlo simulations. We have made 100 simulated catalogues of the (mass-limited) red galaxy sample, adopting a photometric redshift value for each source between $[z_\\mathrm{phot} - \\Delta(z_\\mathrm{phot}), z_\\mathrm{phot} + \\Delta(z_\\mathrm{phot})]$ at random, being $z_\\mathrm{phot}$ the nominal photometric redshift of the source and $\\Delta(z_\\mathrm{phot})$ the typical dispersion of the photometric redshifts compared to the spectroscopic ones. This dispersion is estimated as: $\\Delta(z_\\mathrm{phot}) = < \\Delta(z)\/(1+z)> \\cdot (1+z_\\mathrm{phot}$), where $<\\Delta(z)\/(1+z)>$ is the average value obtained for this normalized dispersion at the redshift bin of the galaxy (see Fig.\\,\\ref{Fig:zspec-zphot}). Then, we have obtained the number densities corresponding to each simulated catalogue for each galaxy type and at each redshift bin, accounting for the different redshifts of each catalogue. The dispersion of the 100 values obtained for the number density at each redshift bin and galaxy type represents an estimate of the error associated to the photometric redshift uncertainties. \n\nStatistics of massive red galaxies can be dramatically affected by cosmic variance due to their high clustering \\citep{2004ApJ...600L.171S}. We have estimated cosmic variance using the model by \\citet{2011ApJ...731..113M}, which provides estimates of cosmic variance for a given galaxy population using predictions from cold dark matter theory and the galaxy bias. They have developed a simple recipe to compute cosmic variance for a survey as a function of the angular dimensions of the field and its geometry, the mean redshift and the width of the considered redshift interval, and the stellar mass of the galaxy population. We have considered the geometry and angular dimensions of our field, as well as the different redshift bins analysed in each case to estimate the cosmic variance. \\citeauthor{2011ApJ...731..113M} software provides these estimates in two mass ranges overlapping with ours: $10.5<\\log (\\mathcal{M}_*\/\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi)<11$ and $11<\\log (\\mathcal{M}_*\/\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi)<11.5$. Therefore, we have considered the mean cosmic variance of both mass ranges as a representative value of the cosmic variance of our mass-limited sample at each redshift bin. Cosmic variance depends on the redshift. At $0.3<z<1.5$ and for our mass range, cosmic variance decreases from $0.3<z<0.5$ to $0.7<z<0.9$ approximately, and then starts rising again towards higher redshifts. This behaviour is observed for all used redshift bins ($\\Delta z = 0.1$, 0.2, and 0.4). For $\\Delta z = 0.1$, the root cosmic variance acquires minimum and maximum values equal to 34\\% and 40\\%, respectively. For $\\Delta z = 0.2$, it changes between 24\\% and 28\\%, and between 17\\% and 19\\% for $\\Delta z=0.4$. All our results include these uncertainties quadratically added to the other error sources (statistical and classification errors, and redshift uncertainties).\n\nThe predictions of the cosmic variance obtained with the model by \\citet{2011ApJ...731..113M} are in good agreement with the rough estimates that can be derived from panel a of Fig.\\,\\ref{Fig:comparacion}. At $0.7<z<1.1$, the dispersion of the different studies is $\\sim 30$\\%, most of which can be attributed to cosmic variance. This value is quite similar to the estimate obtained with \\citeauthor{2011ApJ...731..113M} model at these redshifts for $\\Delta z = 0.2$ ($\\sim 27$\\%). At lower and higher redshifts, the dispersion among different authors may arise also in  completeness problems and higher observational errors, so a direct comparison cannot be done.\n\nThe redshift errors have been added quadratically to the statistical and classification errors and to the uncertainties associated to cosmic variance to obtain the final error of the number density at each $z$ interval and for each galaxy type. In general, for regular red galaxies, the statistical and classification errors contribute to $\\sim 30$\\% to the total error of their number density for both low and high redshifts, the redshift errors represent $\\sim 10$\\% of the total error, and the cosmic variance contributes to $\\sim 60$\\% of the total error at all redshifts. For irregular galaxies, the contribution of the statistical and morphological classification errors represents $\\sim 35$\\% at all redshifts, the redshift errors are $\\sim 25$\\% (being $\\sim 30$\\% at low z, and decreasing down to $\\sim 23$\\% at high z), and the cosmic variance contributes to $\\sim 37$\\% (being $\\sim 35$\\% at low z, and rising to $\\sim 40$\\% at high z).\n\n\\begin{table*}\n\\begin{minipage}{\\textwidth}\n\\caption{Correspondence between different galaxy evolutionary stages and our red galaxy types.\\label{Tab:correspondence}}\n\\begin{center}\n\\begin{tabular}{llll}\n\\hline\n\\multicolumn{1}{c}{Galaxy Type} & \\multicolumn{1}{c}{Global morphology} & \\multicolumn{1}{c}{Structural distortion$^\\mathrm{a}$} & \\multicolumn{1}{c}{Star formation$^\\mathrm{b}$} \\\\\n\\multicolumn{1}{c}{(1)} & \\multicolumn{1}{c}{(2)} &\\multicolumn{1}{c}{(3)} &\\multicolumn{1}{c}{(4)} \\\\\\hline \nE-S0 & Spheroid-dominated &  Regular & LSF \\\\\nSpiral & Disk-dominated       &  Regular   & HSF\/LSF \\\\\n\\hline\\vspace{-0.2cm}\\\\\nGas-rich major mergers (merging-nuclei phase)& Disk-dominated      & Irregular  & HSF\/LSF \\\\\nGas-rich major mergers (post-merger phase)   & Spheroid-dominated  & Irregular  & HSF\/LSF \\\\\nGas-poor major mergers & Spheroid-dominated  & Irregular  & LSF \\\\\\hline\n\\end{tabular}\\\\\n\\end{center}\n$^ \\mathrm{a}$Non-distorted morphologies are noted as regular, and merger-like distorted ones as irregulars.\\\\\n$^ \\mathrm{b}$HSF: objects with enhanced star formation compared to the average of the whole galaxy population; LSF: objects with star formation lower than this average SFR.\\\\\n$^ \\mathrm{c}$Only major mergers already merged into one body are traced by this study. Galaxy pairs are considered as two still-independent galaxies.\\\\\n\\end{minipage}\n\\end{table*}\n\n\n\\section{Observational tests to the hierarchical origin of massive E-S0's}\n\\label{Sec:Tests}\n\nAs commented in \\S\\ref{Sec:introduction}, no observational evidence on the existence of a evolutionary link between major mergers and the rise of the present-day massive E-S0's exists up to the date. In order to test the major-merger origin of massive E-S0's observationally, we must be capable of providing evidence supporting or rejecting the existence of such a link. However, the transitory stages and end products of these evolutionary tracks coexist at each redshift, making this task difficult. Here we define three tests to observational data based on the predictions of hierarchical models to check if data are coherent with the existence of this link, that can be done thanks to the classification performed in this study.\n\n\\subsection{Equivalence between our galaxy types and the different evolutionary stages of red galaxies}\n\\label{Sec:Equivalence}\n\nThe morphological and structural properties of a galaxy can be combined with information about its star formation enhancement to establish correspondences between its galaxy type in our classification and the evolutionary stage of the galaxy. Once a galaxy is identified as a major merger on the basis of its noticeable structural distortion, both its star formation level and its global morphology may be pointing either to the gas-content of its progenitors or to the merger phase \\citep{2008MNRAS.384..386C,2008MNRAS.391.1137L,2010MNRAS.404..590L,2010MNRAS.404..575L}. \n\nGalaxies involved in a gas-rich major merger are expected to be disk-dominated during the merging-nuclei phase. During the initial moments of this phase, these mergers experience strong starbursts that last less than $\\sim 0.5$\\,Gyr. Therefore, depending on the evolutionary stage of these mergers, they might appear either as HSF or LSF. Post-merger stages of these events will still exhibit noticeable distortion, but its morphology is expected to be spheroidal-dominated. Depending on the efficiency of the star formation quenching in the merger, late phases of gas-rich major mergers may be HSF or LSF. Additionally, gas-poor mergers are expected to be irregular, spheroidal-dominated, and mostly LSF since their merging-nuclei phase. Normal disks and E-S0's exhibit a regular disk or spheroidal-dominated morphology, respectively. Most E-S0's are quiescent, meaning that they must be LSF.\n\nOur classification thus allows us to distinguish among these evolutionary stages of red galaxies just attending to their types, except between gas-poor mergers and post-merger stages of wet mergers. In Table\\,\\ref{Tab:correspondence} we list the correspondence between a galaxy evolutionary stage and its characteristics in our classification.\n\n\\subsection{Hierarchical evolutionary paths among red galaxy types}\n\\label{Sec:F07}\n\nHere, we describe three tests based on the expectations of hierarchical models of galaxy formation to check whether data is coherent with the existence of an evolutionary link between major mergers and the E-S0's appearing on the Red Sequence since $z\\sim 1.5$ or not.\n\nF07 proposed a hierarchical mixed evolutionary scenario for explaining the observed mass migration from the massive end of the Blue Galaxy Cloud to that of the Red Sequence since $z\\sim 2$, in which \"quenched galaxies enter the Red Sequence via gas-rich mergers\", and can be \"followed by a limited number of gas-poor, stellar mergers along the sequence\". The semi-analytical model by \\citet[EM10 hereafter]{2010A&A...519A..55E} proved the feasibility of the F07 scenario for explaining the buildup of E-S0's that end up with $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $z=0$, just accounting for the effects of the major mergers strictly reported by observations since $z\\sim 1.2$ \\citep{2009ApJ...694..643L}. This model reproduces the observed evolution of the massive end of the galaxy luminosity function by color and morphological types. The evolutionary track described by F07 appears naturally in the model, as it considers the relative contribution of gas-poor and gas-rich mergers at each redshift reported by \\citet{2008ApJ...681..232L} and their different effects on galaxy evolution. \n\nThe advantage of this model is that its predictions are in excellent agreement with cosmological hierarchical models (despite being based on observational major merger fractions), reproducing observational data at the same time \\citep[see EM10;][]{2010arXiv1003.0686E}. Based on these predictions, we have defined some tests that observational data must fulfill if most massive E-S0's have really derived from major mergers occurred at relatively late epochs in the cosmic history. These predictions are the following ones:\n\n\\begin{enumerate}\n \\item Most present-day E-S0's with $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ are the result of at least one gas-rich major merger that place them on the Red Sequence since $z\\sim 1.2$.\n \\item In addition, $\\sim 75$\\% of the remnants resulting from these gas-rich events have been involved in a subsequent gas-poor major merger, occurred quite immediately. The remaining $\\sim 25$\\% have thus continued their evolution towards an E-S0 passing through a quiet post-merger phase. \n \\item The bulk of these major mergers are at intermediate-to-late stages during the $\\sim 2$\\,Gyr period elapsed at $0.7<z<1.2$, which means that the gas-rich ones must have started at $1<z<1.5$, accouting for the typical timescales of these events. The gas-poor ones are later, but must take place earlier than $z\\sim 0.7$ in any case, as the resulting massive E-S0's have been in place since that epoch. \n\\end{enumerate}\n\nTherefore, according to the EM10 model, the appearance of the bulk of massive E-S0's takes place at $0.7<z<1.2$, and nearly all have evolved according to the following path: \n\n\\begin{center}\n {\\small\n \\framebox[0.26\\textwidth][c]{\n  \\begin{minipage}[c]{0.25\\textwidth}\n  \\begin{center}\n {\\bf Gas-rich major merger\\\/} \\\\  \n  \\end{center}\n  \\end{minipage}\n }\n\n\\vspace{0.2cm}\n$\\Downarrow$\n\\vspace{0.2cm}\n\n\\begin{tabular}{lr}\n\n\\framebox[0.22\\textwidth][c]{\n  \\begin{minipage}[c]{0.21\\textwidth}\n   \\begin{center}\n{\\bf Post-merger stage\\\/}\\\\\n$[$ $\\sim 25$\\% $]$\\\\\n  \\end{center}\n  \\end{minipage}\n }\n& \n\n\n\\framebox[0.22\\textwidth][c]{\n  \\begin{minipage}[c]{0.21\\textwidth}\n   \\begin{center}\n{\\bf Gas-poor major merger\\\/}\\\\\n$[$ $\\sim 75$\\% $]$\\\\\n  \\end{center}\n  \\end{minipage}\n }\n\n \\\\\n\\end{tabular}\n\n \\vspace{0.2cm}\n$\\Downarrow$\n\\vspace{0.2cm}\n\n\\framebox[0.2\\textwidth][c]{\n  \\begin{minipage}[c]{0.18\\textwidth}\n   \\begin{center}\n{\\bf Massive E-S0a\\\/} \n  \\end{center}\n  \\end{minipage}\n }. \\vspace{-0.5cm}\n\\begin{equation}\\label{eq:track}\n\\end{equation}\n}\n\\end{center}\n \n\\noindent Note that this evolutionary track implies the existence of a nearly 1:1:1 numerical relation at $0.7<z<1.2$ between gas-rich major mergers at merging-nuclei stages, gas-poor events and post-mergers stages of gas-rich ones, and the massive E-S0's assembled at those epochs. Accounting for the correspondence of these evolutionary stages and the red galaxy types defined in this study (see Table\\,\\ref{Tab:correspondence}), the evolutionary path schematized in eq.\\,\\ref{eq:track} can be re-written as follows:\n\n\n\\begin{center}\n {\\small\n \\framebox[0.12\\textwidth][c]{\n  \\begin{minipage}[c]{0.11\\textwidth}\n  \\begin{center}\n {\\bf ID (HSF\/LSF)\\\/} \\\\  \n  \\end{center}\n  \\end{minipage}\n }\n\n\\vspace{0.2cm}\n$\\Downarrow$\n\\vspace{0.2cm}\n\n\\begin{tabular}{lr}\n\n\\framebox[0.15\\textwidth][c]{\n  \\begin{minipage}[c]{0.14\\textwidth}\n   \\begin{center}\n{\\bf IS (HSF\/LSF)\\\/}\\\\\n$[$ $\\sim 25$\\% $]$\\\\\n  \\end{center}\n  \\end{minipage}\n }\n& \n\n\n\\framebox[0.15\\textwidth][c]{\n  \\begin{minipage}[c]{0.3\\textwidth}\n   \\begin{center}\n{\\bf IS (mostly LSF)\\\/}\\\\\n$[$ $\\sim 75$\\% $]$\\\\\n  \\end{center}\n  \\end{minipage}\n }\n\n \\\\\n\\end{tabular}\n\n \\vspace{0.2cm}\n$\\Downarrow$\n\\vspace{0.2cm}\n\n\\framebox[0.18\\textwidth][c]{\n  \\begin{minipage}[c]{0.17\\textwidth}\n   \\begin{center}\n{\\bf RS (mostly LSF)\\\/} \n  \\end{center}\n  \\end{minipage}\n }. \\vspace{-0.5cm}\n\\begin{equation}\\label{eq:track2}\n\\end{equation}\n}\n\\end{center}\n\n\\noindent Then, the previous 1:1:1 relation between the different stages of these galaxies in their evolution towards the Red Sequence can be translated into an equivalent 1:1:1 relation between the following red galaxy types, according to Table\\,\\ref{Tab:correspondence}: \n\n\n\\begin{equation}\\label{eq:track3}\n \\mathrm{\\textbf{ID}} \\rightarrow \\mathrm{\\textbf{IS}} \\rightarrow \\mathrm{\\textbf{RS}}.  \n\\end{equation}\n\n\\noindent If most massive E-S0's have really evolved according to the hierarchical scenario proposed by the EM10 model, then the data must fulfill this evolutionary path among massive red galaxy types at $0.7<z<1.2$. This imposes the following three observational tests or constraints to observations:\n\n\\begin{itemize}\n\\item[1.] The accumulated number density of ID's (gas-rich major mergers) on our red sample since $z\\sim 1.2$ down to a lower redshift $z$ must reproduce the net numerical increment of RS's (E-S0's) observed between the two redshifts. \n\n\\item[2.] An analogous relation must be fulfilled by the accumulated number density of IS's (gas-poor major mergers and post-merger stages of gas-rich events).\n\n\\item[3.] The bulk of RS's (E-S0's) with stellar masses $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $z=0$ must have been definitely built up during the $\\sim 2.2$\\,Gyr time period elapsed at $0.7<z<1.2$.\n\\end{itemize}\n\nOur data is complete for galaxy masses $\\mathrm{M}_*>5\\times10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at each redshift. This means that we can ensure that we are in a position to trace back in time the potential progenitors of the present-day E-S0's with $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $z\\sim 0$ that could have merged to create them during the last $\\sim 9$\\,Gyr (see \\S\\ref{Sec:sample}).\n\nTherefore, we have estimated the cumulative distribution of ID's and of IS's, and we have compared them with the redshift evolution of the number density of RS's since $z\\sim 1.5$. In the case that major mergers have not driven the assembly of the massive E-S0's as proposed by the EM10 model, the previous three tests must fail. On the contrary, if these three distributions agree pretty well, these tests will support strongly the existence of an evolutionary link between major mergers and the appearance of massive E-S0's, as expected by hierarchical scenarios of galaxy formation. The results of these tests are presented in \\S\\ref{Sec:TestsResults}. \n\nWe must remark that the EM10 model exclusively quantifies the effects of major mergers on galaxy evolution at $z<1.2$. Hence, it does not discard the contribution of different evolutionary processes to the definitive assembly of massive E-S0's, although it predicts that it must have been low, as most of their number density evolution can be explained just accounting for the effects of the major mergers. This seems to be confirmed by observations, as other evolutionary mechanisms (such as minor mergers, ram pressure stripping, or bars) seem to have been significant for the formation of the Red Sequence only for low and intermediate masses, but not for high masses \\citep[][]{2004ARA&A..42..603K,2007ApJ...660.1151D,2008A&A...489.1003D,2009ApJ...697.1369B,2009A&A...508.1141S,2010MNRAS.409..346C,2011MNRAS.411.2148K}. Moreover, the model does not exclude disk rebuilding after the major merger either. On the contrary, it is probably required for giving rise to a S0 instead of an elliptical, as indicated by observations \\citep{2005A&A...430..115H,2009A&A...507.1313H,2009A&A...496..381H,2009A&A...501..437Y}.\n\nMoreover, the EM10 model assumes that intermediate-to-late stages of major mergers are red and will produce an E-S0, on the basis of many observational and computational studies \\citep[see references in EM10 and][]{2002A&A...381L..68C,2007MNRAS.382.1415S,2010ApJ...714L.108S,2010A&A...518A..61C}. These assumptions are crucial for the model, as they are necessary to reproduce the redshift evolution of the luminosity functions selected by color and morphological type. Therefore, testing if our data is coherent with the existence of an evolutionary link between the advanced stages of major mergers in our red sample and the definitive buildup of massive E-S0's, we are also indirectly testing these assumptions of the EM10 model.\n\n\n\\subsection{Observational considerations for the tests}\n\\label{Sec:RSEvolution}\n\nAccording to \\citet{2006ApJ...652..270B}, the average number density of major mergers at a given redshift centered at $z$, $n _\\mathrm{m}(z)$, is related to the number density of the major mergers detected at certain intermediate phase of the encounter in that redshift bin, $<n_\\mathrm{m,phase}(z)>$, as follows:\n\n\\begin{equation}\\label{eq:density}\nn_\\mathrm{m}(z) = <n_\\mathrm{m,phase}(z)>  \\frac{t([z_1,z_2])}{\\tau _\\mathrm{det}},\n\\end{equation}\n\n\\noindent with $t([z_1,z_2])$ being the time elapsed in the redshift bin, and $\\tau _\\mathrm{det}$ representing the  detectability time of the intermediate merger stage under consideration. We have used this equation in our tests.\n\nWe find that the number densities of ID's and IS's remain quite constant with redshift (see \\S\\ref{Sec:Results}). As ID's and IS's correspond to intermediate merger stages, this means that the major merger rate must evolve smoothly with redshift, in good agreement with observational estimates of merger rates  \\citep{2008ApJ...681..232L,2011ApJ...739...24B,2011ApJ...742..103L}. This also indicates that the net flux of irregular galaxies appearing on the Red Sequence or at nearby locations on the Green Valley (i.e., the number of red irregulars created and destroyed per unit time in the red sample) must have been nearly constant at $0.3<z<1.5$ for our mass range. Together with the evolutionary track stated in eq.~\\ref{eq:track3}, this implies that the accumulated number of ID's observed in a redshift bin must be equal to the accumulated number of IS's in the same bin, and also to the number of RS's assembled at the end of the redshift bin. As we also find that the number of RS's is negligible at $z=1.5$ (see \\S\\ref{Sec:Results}), it is also justified to start accumulating ID's and IS's since this redshift down to $z\\sim 0.3$.\n\nIn order to estimate $n_\\mathrm{m}(z)$, we have adopted the merger timescales derived by \\citet{2010MNRAS.404..590L}. These authors report typical detectability timescales through CAS indices of simulated major mergers, as a function of the baryonic gas fraction and the mass ratio of the encounter. For gas fractions representative of gas-rich mergers up to $z\\sim 1$ \\citep[$\\sim 30-50\\%$, see][]{2009A&A...507.1313H} and mass ratios typical of major mergers (1:1 to 1:4), they find an average detectability timescale $\\tau _\\mathrm{det,gas-rich}\\sim 1.0\\pm 0.3$\\,Gyr of merging-nuclei phases. For gas fractions representative of gas-poor major mergers ($\\lesssim 30$\\%), we estimated from these author and from \\citet{2005AJ....130.2647V} an average timescale of $\\tau _\\mathrm{det,gas-poor}\\sim 0.5\\pm 0.2$\\,Gyr of their merging-nuclei phase. The timescales for post-merger stages are similar to those of their merging-nuclei phases for both gas-rich  and gas-poor mergers\n \\citep{2007AJ....133.2132S,2010MNRAS.404..590L}. The errors in these timescales account for small changes of these representative values with redshift, accordingly to \\citet{2010ApJ...718.1158L}. \n\n\\begin{table*}\n\\begin{minipage}{\\textwidth}\n\\caption{Comoving number densities of the different red galaxy types in units of $\\times 10^{-4}$ Mpc$^{-3}$.\\label{Tab:densities}}\n\\begin{center}\n\\begin{tabular}{lcrrcrrcrrcrrcr}\n\\hline\n\n\\multicolumn{1}{c}{\\multirow{2}{*}{Redshift}} & \\multicolumn{1}{c}{\\multirow{2}{*}{Number$^ \\mathrm{a}$}} &\\multicolumn{2}{c}{N(RS)$^\\mathrm{b}$} && \\multicolumn{2}{c}{N(RD)}  &&  \\multicolumn{2}{c}{N(IS)} && \\multicolumn{2}{c}{N(ID)}  && \\multicolumn{1}{c}{\\multirow{2}{*}{N(Total)}}  \\vspace{0.2cm}\\\\ \\cline{3-4}\\cline{6-7}\\cline{9-10}\\cline{12-13}\n\\multicolumn{1}{c}{} & \\multicolumn{1}{c}{} &\\multicolumn{1}{c}{LSF$^\\mathrm{c}$} & \\multicolumn{1}{c}{HSF} && \\multicolumn{1}{c}{LSF} & \\multicolumn{1}{c}{HSF} &&  \\multicolumn{1}{c}{LSF} & \\multicolumn{1}{c}{HSF} && \\multicolumn{1}{c}{LSF} & \\multicolumn{1}{c}{HSF}  && \\multicolumn{1}{c}{}  \\\\\n\\multicolumn{1}{c}{(1)} & \\multicolumn{1}{c}{(2)} & \\multicolumn{1}{c}{(3)} & \\multicolumn{1}{c}{(4)} &&   \\multicolumn{1}{c}{(5)}& \\multicolumn{1}{c}{(6)} && \\multicolumn{1}{c}{(7)} & \\multicolumn{1}{c}{(8)} && \\multicolumn{1}{c}{(9)} & \\multicolumn{1}{c}{(10)}  && \\multicolumn{1}{c}{(11)}\\\\\\hline\n$0.3<z<0.5$ & 18& 5.2$^{+2.1}_{-1.8}$ & 1.2$^{+1.0}_{-0.6}$ && 0.6$^{+0.9}_{-0.9}$ & 2.3$^{+1.3}_{-0.9}$ && 0.0 & 0.8$^{+1.5}_{-1.5}$ && 0.0 & 1.9$^{+1.2}_{-0.8}$ &&  11.0$^{+3.4}_{-2.7}$ \\\\[0.2cm]\n$0.5<z<0.7$ & 48&10.2$^{+2.9}_{-2.8}$ & 1.7$^{+0.8}_{-0.6}$ && 1.7$^{+0.8}_{-0.6}$ & 1.2$^{+0.7}_{-0.5}$ && 0.8$^{+0.7}_{-0.5}$ & 0.2$^{+0.8}_{-0.8}$ && 1.0$^{+0.6}_{-0.4}$ & 0.1$^{+0.4}_{-0.4}$ && 16.6$^{+3.4}_{-3.2}$ \\\\[0.2cm]\n$0.7<z<0.9$ & 61& 6.5$^{+1.8}_{-1.7}$ & 1.6$^{+0.9}_{-0.8}$ && 1.6$^{+0.7}_{-0.5}$ & 0.3$^{+0.3}_{-0.3}$  &&0.9$^{+0.6}_{-0.6}$ & 1.6$^{+1.1}_{-0.9}$ && 0.3$^{+0.3}_{-0.3}$\t  & 2.8$^{+0.9}_{-0.8}$ && 15.0$^{+2.7}_{-2.4}$\\\\[0.2cm]\n$0.9<z<1.1$ &54 & 3.4$^{+1.0}_{-1.0}$ & 0.3$^{+0.3}_{-0.2}$ && 0.3$^{+0.3}_{-0.2}$ & 0.2$^{+0.3}_{-0.3}$\t &&2.2$^{+0.8}_{-0.7}$ & 0.9$^{+0.7}_{-0.5}$ && 0.9$^{+0.4}_{-0.3}$\t  & 2.3$^{+0.8}_{-0.7}$ && 10.6$^{+1.8}_{-1.6}$\\\\[0.2cm]\n$1.1<z<1.3$ & 31&1.0 $^{+0.4}_{-0.3}$ & 0.2$^{+0.2}_{-0.1}$ && 0.1$^{+0.2}_{-0.2}$ & 0.0  &&1.2$^{+0.5}_{-0.4}$ & 0.9$^{+0.7}_{-0.5}$ && 0.8$^{+0.4}_{-0.3}$\t  & 1.1$^{+0.5}_{-0.4}$ && 5.3$^{+1.2}_{-0.9}$\\\\[0.2cm]\n$1.3<z<1.5$ & 24&0.2$^{+0.2}_{-0.1}$ & 0.0 && 0.0 & 0.0  &&1.0$^{+0.5}_{-0.5}$ & 0.7$^{+0.6}_{-0.5}$ && 0.4$^{+0.3}_{-0.2}$\t  & 1.5$^{+0.6}_{-0.5}$ && 3.7$^{+1.1}_{-0.9}$\\\\\n\\hline\n\\end{tabular}\\\\\n\\end{center}\n$^\\mathrm{a}$Net number of galaxies in the final sample in a sky area of $\\sim 155$\\,arcmin$^{2}$.\\\\\n$^\\mathrm{b}$Galaxy types according to morphology: Regular Spheroid-dominated (RS), Regular Disk-dominated (RD), Irregular Spheroid-dominated (IS), Irregular Disk-dominated (ID).\\\\\n$^\\mathrm{c}$Galaxy types according to star formation activity: High Star-Forming (HSF), Low Star-Forming (LSF).\n\\end{minipage}\n\\end{table*}\n\n\\begin{figure*}\n\\begin{center}\n\\includegraphics[width=\\textwidth,angle=0]{fraction_density_types_media_v2.eps} \n\\caption{Redshift evolution of the number density and fraction of red galaxies with $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, according to their morphology and structural distortion level, for the three wide redshift bins considered in the study ($0.3<z<0.7$, $0.7<z<1.1$, and $1.1<z<1.5$). \\emph{Top panels}: Redshift evolution of the fraction of each type with respect to the whole red galaxy population at each redshift bin. \\emph{Bottom panels}: Redshift evolution of the number density of each morphological type in the same redshift bins. \n}\\label{Fig:fractypes}\n\\end{center}\n\\end{figure*}\n\n\\section{Results}\n\\label{Sec:Results}\n\nIn Table\\,\\ref{Tab:densities} we show the number densities of red galaxies with $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ per redshift bins at $0.3<z<1.5$ obtained from our data, according to the classification resulting from the morphological\/distortion level of the galaxy (\\S\\ref{Sec:Morphology}) and from its star formation level (\\S\\ref{Sec:ClassificationSED}). Therefore, the galaxies are classified as regulars or irregulars (according to their structural distortion level), as spheroid\/disk-dominated (according to their global morphology), and as HSF\/LSF (according to their star formation enhancement). Errors in the results listed in this table and in all the figures of the present section account for the statistical and classification errors, the redshift errors, and the cosmic variance uncertainties, as described in \\S\\ref{Sec:Error}. \n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=0.5\\textwidth,angle=0]{ES0as_DSFs_v2.eps}\n\\caption{Redshift evolution of the number density and fraction of all regular and irregular (i.e., major mergers) red galaxies with $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $0.3<z<1.5$, in the three wide redshift bins under consideration ($0.3<z<0.7$, $0.7<z<1.1$, and $1.1<z<1.5$). \\emph{Top panel}: Redshift evolution of the fraction of red massive regular and irregular galaxies with respect to the total red galaxy population. \\emph{Bottom panel}: Redshift evolution of the number density of regular and irregular massive red galaxies in the same redshift bins.} \\label{Fig:E_D}\n\\end{center}\n\\end{figure}\n\n\n\\subsection{Morphological evolution of red galaxies since $z\\sim 1.5$}\n\\label{Sec:MorphologyEvolution}\n\nFigure\\,\\ref{Fig:fractypes} shows the redshift evolution of the fraction and the comoving number density of massive red galaxies by galaxy types considering their global morphology and structural distortion level. The fractions and number densities of red regular galaxies rise with cosmic time, with the fraction of spheroids being higher than that of disks at the same redshift. Therefore, we are tracing the progressive settlement of regular galaxies on the massive end of the Red Sequence at $0.3< z<1.5$, made primarily of spheroids but also containing some regular disks (mainly at $z<0.7$). We also find significant populations of irregular galaxies at all redshifts up to $z\\sim 1.5$, with number densities $> 10^ {-4}$\\,Mpc$^{-3}$. Although the fractions of red irregular spheroids and disks decrease with cosmic time, their densities remain quite constant at $0.3<z<1.5$. This fact clearly points to the transitory nature of red irregular galaxies at any redshift, as indicated by previous studies \\citep{2008ApJ...672..177L}. \n\nFigure\\,\\ref{Fig:E_D} shows the redshift evolution of the number density and fractions of red regular galaxies (RS $+$ RD) and irregulars (IS $+$ ID) at $0.3<z<1.5$, for the three wide redshift bins under consideration. The fraction of regular galaxies increases by a factor of $\\sim 6$ since $z\\sim 1.3$ down to $z\\sim 0.5$, whereas the fraction of irregulars decreases  by the same amount (top panel in the figure). Moreover, the number density of regulars has risen by a factor of $\\sim 12$ during this time period (bottom panel in the figure), while that of the irregulars keeps constant until $z\\sim 0.9$, decreasing by a factor of $\\sim 3$ at $z\\lesssim0.6$ \\citep[in excellent agreement with the results by][]{2010ApJ...709..644I}.\n\nAt $z\\sim 1.3$, irregular galaxies (i.e., major mergers) represent nearly 80\\% of the red galaxy population. Their fraction decreases down to $\\sim 50$\\% at $z\\sim 0.9$, and reaches $\\lesssim 15$\\% at $z\\sim 0.5$. Considering that $\\sim 70$\\% of these irregular galaxies are dust-reddened due to intense star formation (see \\S\\ref{Sec:SFandMorphology}), these results are in good agreement with previous estimates of the fraction of dust-reddened star-forming galaxies on the Red Sequence at different redshifts \\citep{2002A&A...381L..68C,2003ApJ...586..765Y,2003MNRAS.346.1125G,2004ApJ...600L..11B,2004ApJ...600L.131M,2005ApJ...620..595W,2007MNRAS.380..585C,2007A&A...465..711F,2011ApJ...726..110Z}. \n\n\n\\begin{figure}\n\\includegraphics[width=0.5\\textwidth,angle=0]{histogram_RG_v4.eps}\n\\caption{Redshift evolution of the number density of red regulars and irregulars with $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $0.3<z<1.5$, using narrow redshift bins of $\\Delta z = 0.1$.} \\label{Fig:hist}\n\\end{figure}\n\n\nWe have derived the redshift evolution of the number density of regular and irregular massive red galaxies in narrower redshift bins, to delimit more accurately the epoch at which the bulk of the red regular galaxies appears into the cosmic scenario (see Fig.\\,\\ref{Fig:hist}). The large uncertainties of our results in these narrow redshift bins prevent us of deriving quantitative conclusions based on this figure. However, we can conclude from it that the number density of red irregulars (i.e., major mergers) has remained nearly constant at $0.7\\lesssim z\\lesssim 1.5$ within errors. This indicates that these systems must have been forming and disappearing at similar rates during this time period. Therefore, the decrease of the fraction of irregular systems with cosmic time is exclusively relative, i.e., it is just due to the rise of the population of regular galaxies, but not to a net drop in their number density down to $z\\sim 0.6$. The figure also shows that the redshift-evolution of the number densities of regulars and irregulars on the Red Sequence cross at $z=0.9$ for $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$. \n\nAs commented in \\S\\ref{Sec:introduction}, the rise of the number density of red regular types with cosmic time and the constancy of that of irregular ones has been interpreted as a sign pointing to the conversion of irregulars into regulars with time. We provide observational evidence supporting the existence of this evolutionary link in \\S\\ref{Sec:TestsResults}. \n\n\\begin{figure*}\n\\begin{center}\n\\includegraphics*[width=0.24\\textwidth,angle=0]{mip_RS_v2.eps}\n\\includegraphics*[width=0.24\\textwidth,angle=0]{mip_RD_v2.eps}\n\\includegraphics*[width=0.24\\textwidth,angle=0]{mip_IS_v2.eps}\n\\includegraphics*[width=0.24\\textwidth,angle=0]{mip_ID_v2.eps}\n\\caption{Redshift evolution of the comoving number density of red galaxies with $\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, according to their morphological, structural, and star formation activity properties. \\emph{Solid lines}: Number densities for LSF galaxies of each type. \\emph{Dashed lines}: Number densities of HSF galaxies of each morphological type. \\emph{Panel a)}: Regular spheroids (RS's). \\emph{Panel b)}: Regular disks (RD's). \\emph{Panel c)}: Irregular spheroids (IS's). \\emph{Panel d)}: Irregular disks (ID's). }\\label{Fig:mip_p_classification}\n\\end{center}\n\\end{figure*}\n\n\\subsection{Star formation activity according to red galaxy types since $z\\sim 1.5$}\n\\label{Sec:SFandMorphology}\n\nIn Fig.\\,\\ref{Fig:mip_p_classification} we show the redshift evolution  of the number density of massive red galaxies for each morphological type defined in this study, attending to its star formation activity. We remark that HSF's are galaxies that show enhanced SFRs compared to the average SFR of the galaxy population at each redshift (\\S\\ref{Sec:ClassificationSED}). All types, except RS's, host a significant number of HSF galaxies, with percentages varying depending on type and redshift. Red regular spheroids are the galaxy types hosting the lowest fractions of HSF systems at all redshifts since $z\\sim 1.5$, as expected. Curiously, red RD's exhibit a noticeable increase of the HSF systems fraction at $z<0.7$ (panel b). Irregular types harbour enhanced SFRs typically (both spheroidal and disk systems), coherently with their merger-related nature (panels c and d in the figure). The percentage of HSF objects in these types has not changed at $0.3<z<1.5$ within errors, the fraction of HSF objects in ID's being much higher than in IS's at all redshifts ($\\sim 80$\\% for ID's and $\\sim 50$\\% for IS's). This is normal if we consider that the former ones correspond to intermediate stages of gas-rich mergers, while the later ones group gas-poor major mergers and post-merger phases of the gas-rich ones. \n\nFigure\\,\\ref{Fig:mip_p_classification} implies that, at $0.7<z<1.5$, the enhanced star formation in red galaxies is mostly hosted by major mergers; mostly by gas-rich merger remnants at intermediate phases (ID's, which represents $\\sim 30$\\% of all red galaxies at these redshifts, see Fig.\\,\\ref{Fig:fractypes}) and by $\\sim 50$\\% of spheroidal remnants (IS's, which represent $\\sim 30$\\%).  At $z<0.7$, enhanced SFRs can be found still in most red major mergers (which represent $\\sim 25$\\% of the whole red population, see Fig.\\,\\ref{Fig:fractypes}) and in nearly all red RD's ($\\sim 15$\\% of it). RS's are the types that host the lowest levels of SFR enhancement at all redshifts, hosting $\\sim 20$\\% at most at $z<0.7$ (despite being $\\sim 60$\\% of the whole red population at $z<0.7$). \n\nConsidering that our detectability timescale for gas-rich mergers is $\\tau \\sim 1$\\,Gyr (\\S\\ref{Sec:RSEvolution}), the merger rate derived from our data for ID's at $0.3 < z < 0.7$ is $\\sim 2.5\\times 10^{-4}$ Gyr$^{-1}$ Mpc$^{-3}$ (considering their number density from Fig.\\,\\ref{Fig:mip_p_classification}), which is an estimate that is in good agreement with the one reported by \n\\citet{2011AJ....141...87C} for gas-rich mergers using a different methodology (see their Figure\\,6). This strongly supports the identification of our ID's with intermediate stages of gas-rich major mergers.\n\n\\begin{figure*}\n\\begin{center}\n\\includegraphics*[width=0.33\\textwidth,angle=0]{arti_acumID.eps}\n\\includegraphics*[width=0.33\\textwidth,angle=0]{arti_acumIS.eps}\n\\includegraphics*[width=0.33\\textwidth,angle=0]{modelo.eps}\n\\caption{Observational tests to the data of red galaxies for testing the hierarchical buildup of massive E-S0's, on the basis of the expectations of the EM10 model.  {\\bf Panel a) Test 1\\\/}: Cumulative redshift distribution of red ID's (intermediate-to-late stages of gas-rich major mergers) since $z=1.5$ down to $z=0.3$, compared to the buildup of massive RS's (E-S0's) during the same time period. {\\bf Panel b) Test 2\\\/}: Cumulative redshift distribution of red IS's (intermediate-to-late stages of gas-poor major mergers and late stages of gas-rich ones) since $z=1.5$ down to $z=0.3$, compared to the buildup of massive RS's (E-S0's) during the same time period. {\\bf Panel c) Test 3\\\/}: Comparison of the redshift evolution of the number density of RS's (E-S0's) for two different mass ranges ($\\mathrm{M}_*\\gtrsim 5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ and $\\mathrm{M}_*\\gtrsim 10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$) and the predictions of the EM10 model for E-S0's that end up with $\\mathrm{M}_*\\gtrsim 10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $z=0$. \\emph{Vertical solid line}: Epoch at which the E-S0's with $\\mathrm{M}_*\\gtrsim 10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $z=0$ can be considered as definitively assembled according to the EM10 model. \\emph{Blue circle}: Local number density of red galaxies with $\\mathrm{M}_*\\gtrsim 10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ derived by\n\\citet{2003ApJ...599..997M} from 2dF survey. \nThe filled areas around the cumulative data points in panels a and b correspond to the uncertainties in the merger detectability timescales, while in panel c indicates the model uncertainties. The lowest redshift bin probably suffers from incompleteness.\n}\\label{Fig:acumIDSF}\n\\end{center}\n\\end{figure*}\n\n\\subsection{Tests to the definitive buildup of massive E-S0's through major mergers}\n\\label{Sec:TestsResults}\n\nThis section presents the results of the three observational tests commented in \\S\\ref{Sec:TestsResults} to test the hierarchical formation scenario of massive E-S0's.\n\n\\subsubsection{Test 1: Cumulative redshift distributions of red irregular disks since $z\\sim 1.5$}\n\\label{Sec:Test1}\n\nThe first panel of Fig.\\,\\ref{Fig:acumIDSF} shows the result of the first test proposed in \\S\\ref{Sec:F07}. We plot the cumulative number density distributions of red ID's (intermediate stages of gas-rich major mergers, see Table\\,\\ref{Tab:correspondence}) since $z\\sim 1.5$ down to redshift $z$ as obtained from eq.\\,\\ref{eq:density}, and compare it with the redshift evolution of the number density of red RS's (E-S0's, see the same table).  The detectability timescale considered for the ID's is that commented in \\S\\ref{Sec:RSEvolution}. The filled area around the cumulative data points accounts for the uncertainties in this timescale. The number densities at the lowest redshift bin are probably affected by volume and selection effects as suggested by this figure and as indicated in \\S\\ref{Sec:Comparison}, so we will override this redshift bin in all our results and comments henceforth.\n\nThe cumulative distribution of ID's reproduces pretty well both the redshift evolution of all RS's (E-S0's) and that of exclusively the LSF RS's (quiescent E-S0's) at $0.6<z<1.5$ within errors (most E-S0's at these redshifts are LSF's, see Fig.\\,\\ref{Fig:mip_p_classification}). This is compatible with that the bulk of red gas-rich major mergers at intermediate stages of their evolution at these redshifts evolve into the E-S0's that start to populate the Red Sequence at later cosmic times. Therefore, panel a in Fig.\\,\\ref{Fig:acumIDSF} supports the existence of the following evolutionary link among these two massive red galaxy types at $0.6<z<1.5$: \n\n\\begin{equation}\\label{eq:IDtoRS}\n \\mathrm{\\textbf{ID}} \\rightarrow  \\mathrm{\\textbf{RS}}.  \n\\end{equation}\n\nPanel a of Fig.\\,\\ref{Fig:acumIDSF} provides observational support to many aspects concerning the buildup of massive red galaxies expected by hierarchical models of galaxy formation:\n\n\\begin{enumerate}\n \n\\item At $0.6<z<1.5$ all irregular disks populating the massive end of the Red Sequence and nearby locations have evolved into the regular spheroids that appear on it some time later. \n\n\\item This implies that the bulk of red massive E-S0's at $z\\sim 0.6$ derive from disk galaxies that have migrated from the Blue Cloud to the Red Sequence during the time period enclosed at $0.6<z<1.2$.\n\n\\item It also supports that the dominant mechanism after this evolution has been major merging, as data is compatible with the fact that most massive E-S0's that have appeared on the Red Sequence since $z\\sim 1.2$ seem to have undergone a previous phase of gas-rich major merger (i.e., a previous evolutionary stage as a red ID). \n\\end{enumerate}\n\nWe remark that the major mergers detected at their phases as ID's by $z\\sim 1.2$ in this study must have started $\\sim 0.5$-0.7\\,Gyr before, i.e., they were at their approaching (pre-merger) phases by $z\\sim 1.5$. Therefore, the first generation of E-S0's that should result from these mergers according to the hierarchical scenario have appeared after $z\\sim 1.2$. Accounting for this and for the fact that the EM10 model traces the evolution of massive E-S0's back-in-time up to $z=1.2$, a comparison between our data and this model is feasible only up to this redshift.\n\nIn conclusion, the panel a of Fig.\\,\\ref{Fig:acumIDSF} indicates that the data fulfill the first observational constraint imposed by the EM10 model (\\S\\ref{Sec:F07}), supporting the evolutionary track indicated in eq.~\\ref{eq:track} (see also eqs.\\ref{eq:track2} and \\ref{eq:track3}). \n\n\\subsubsection{Test 2: Cumulative redshift distributions of red irregular spheroids since $z\\sim 1.5$}\n\\label{Sec:Test2}\n\nPanel b of Fig.\\,\\ref{Fig:acumIDSF} now compares the accumulated redshift distribution of all IS's (gas-poor mergers plus post-merger stages of gas-rich ones, see Table\\,\\ref{Tab:correspondence}) with the redshift evolution of the number density of massive E-S0's (RS's) since $z\\sim 1.5$. The detectability timescales considered for the IS's are those commented in \\S\\ref{Sec:RSEvolution}. The filled area around the cumulative data points accounts for the uncertainties in this timescale. Again, the accumulated distribution of IS's reproduces quite nearly the buildup of massive E-S0's at $0.6<z<1.5$ within errors. Therefore, this figure supports the existence of an additional evolutionary link at $0.6<z<1.5$ among the following red galaxy types: \n\n\\begin{equation}\\label{eq:IStoRS}\n \\mathrm{\\textbf{IS}} \\rightarrow  \\mathrm{\\textbf{RS}}.  \n\\end{equation}\n\nThis panel of Fig.\\,\\ref{Fig:acumIDSF} also shows that data is compatible with the fact that most massive red E-S0's at $z\\sim 0.6$ have also experienced a previous transitory phase as a red IS at $0.6<z<1.5$. The evolutionary links shown in eqs.\\,\\ref{eq:IDtoRS} and \\ref{eq:IStoRS} can be summarized into the following evolutionary track:\n\n\\begin{equation}\\label{eq:otro}\n \\mathrm{\\textbf{ID}} \\rightarrow   \\mathrm{\\textbf{IS}} \\rightarrow \\mathrm{\\textbf{RS}},\n\\end{equation}\n\n\\noindent which is the evolutionary path between red galaxy types expected by the hierarchical scenario of the EM10 model for the buildup of massive E-S0's (see eq.\\,\\ref{eq:track3}). Therefore, the panel b of Fig.\\,\\ref{Fig:acumIDSF} shows that the data also fulfill the second constraint imposed by the hierarchical evolutionary scenario proposed in the EM10 model (\\S\\ref{Sec:F07}), supporting the evolutionary track indicated in eq.~\\ref{eq:track}.\n\n\\subsubsection{Test 3: Epoch of definitive assembly of massive E-S0's}\n\\label{Sec:Test3}\n\nIn the last panel of Fig.\\,\\ref{Fig:acumIDSF}, we compare the redshift evolution of the number density of E-S0's predicted by the EM10 model with the one obtained from our data for two different mass selections: for our nominal one ($\\mathrm{M}_*>5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$), and for an alternative one which is identical to our nominal one in all aspects, except in the mass range ($\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$).\n\nThe EM10 model traces back in time the evolution of the E-S0's that have $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $z=0$ (\\S\\ref{Sec:F07}). According to the model, these galaxies have been mostly assembled through major mergers at $0.7<z<1.2$, their buildup being frozen since then. Therefore, the model starts to trace the progenitors of these E-S0's at $z>0.7$, which have masses lower by a factor of $\\sim 2$ compared to the E-S0's resulting from the merger. Consequently, the model predictions on the number density of E-S0's at $z>0.9$ can be compared with our results for $\\mathrm{M}_*\\gtrsim 5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ (as both studies trace similar mass ranges globally). But at lower redshifts, the EM10 model traces E-S0's that already have $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, so it is comparable to the results with a mass selection $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$.  \n\nAs Fig.\\,\\ref{Fig:acumIDSF} c shows, at $z>0.7$, the model reproduces much better the settlement of the RS's with $\\mathrm{M}_*\\gtrsim 5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, whereas at $z<0.7$ it clearly follows the trend of RS's with $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, as expected from the arguments given above. However, our data seem to have completeness problems at $z<0.5$, so we cannot assure that the number density of E-S0's with $\\mathrm{M}_*> 10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ has remained constant since $z\\sim 0.7$. \n\nNevertheless, the number density of E-S0's with $\\mathrm{M}_*>10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $z\\sim 0.6$ estimated with our data is\nquite similar to the one estimated for these galaxies at $z=0$ \\citep{2003ApJ...599..997M}, as shown in panel c of  Fig.\\,\\ref{Fig:acumIDSF}. This means that the number density of these objects has remained nearly constant since $z\\sim 0.6$, in good agreement with the predictions of the EM10 model.\n\nAlthough better data at $z<0.6$ are required to directly confirm this result, our data are coherent with the fact that E-S0's with $\\mathrm{M}_*> 10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ have been definitively assembled since $z\\sim 0.6$, supporting that the bulk of the assembly of red massive E-S0's has occurred during the $\\sim 2.2$\\,Gyr period elapsed at $0.7<z<1.2$, as predicted by the EM10 model. Therefore, we can conclude that our data fulfill the third constraint imposed by the hierarchical evolutionary scenario proposed in the EM10 model (\\S\\ref{Sec:F07}), supporting again the evolutionary track indicated in eq.~\\ref{eq:track}. \n\nSummarizing, the three observational tests to the hierarchical evolutionary framework proposed by the EM10 model strongly supports this scenario, pointing to major mergers as the main mechanism for the buildup of massive E-S0's.\n\n\\section{Discusion}\n\\label{Sec:Discussion}\n\nIn general, our results strongly support a late definitive formation redshift for massive E-S0 ($z\\lesssim1.5$), in agreement with hierarchical scenarios of galaxy formation (see references in \\S\\ref{Sec:introduction}). \\citet{2010ApJ...709..644I} already claimed for the freezing in the assembly of massive E-S0's at $z\\lesssim0.7$, proposing that a sudden drop of the gas-rich major merger rate must take place at $z\\lesssim0.8$ to explain it. This fact was proven to be observationally feasible by the EM10 model, just accounting for the major merger fractions reported by observations \\citep{2010arXiv1003.0686E}. The present study supports it observationally. \n\nApart from the major mergers that seem to have been the main responsible mechanisms to place the massive E-S0's on the Red Sequence at $0.6<z<1.5$, other evolutionary processes must have contributed to the evolution of massive E-S0's down to the present (and even coeval with them). But, as commented above, they must not have risen their masses noticeably or changed their morphology noticeably, as E-S0's with $\\log (M_*\/\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi)> 11$ seem to have been in place since $z\\sim 0.6$ (see \\S\\ref{Sec:TestsResults}). This is supported by the fact that many of these processes are observed to be relevant only for the evolution of galaxies with lower masses \\citep[in particular, the fading of stellar populations, see]{2002ApJ...577..651B,1998ApJ...496L..93D,2006A&A...458..101A}. \n\nWe must also remark that our red galaxy sample does not trace the evolution of S0's observed in the clusters, which seems to have been relevant since $z\\sim 0.4$-0.5 due to the environmental star-formation quenching of the spirals that fall into the clusters \\citep{2007ApJ...660.1151D,2009ApJ...697L.137P,2009A&A...508.1141S,2011MNRAS.412..246V}. Cluster S0's have typical masses lower than those selected here \\citep[$\\mathrm{M}_*\\lesssim 5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$, see][]{1999ApJS..122...51D,2006MNRAS.373.1125B}, and hence, our results do not apply to them in general. Moreover, some studies indicate that the fraction of S0's in groups is similar to that of clusters at $z < 0.5$ \\citep{2009ApJ...692..298W}. Considering that most galaxies reside in groups \\citep[$\\sim 70$\\%, see][]{2006ApJS..167....1B,2007ApJ...655..790C}, this means that the majority of S0's in the Universe are located in groups (not in clusters). Nevertheless, note that this evolution in clusters does not contradict the EM10 model at all, because this model exclusively analyses the effects of the major mergers on galaxy evolution since $z\\sim 1.2$, independently on the relevance of other evolutionary processes. \n\nTo summarize, our study supports that major mergers have been the main drivers of the evolution of the massive end of the Red Sequence since $z\\sim 1.5$, although other processes can also have contributed to it significantly at intermediate-to-low masses (especially, since $z\\sim 0.6$). Our tests support observationally a late definitive buildup of the massive E-S0's through major mergers (mostly at $0.6<z<1.2$), in agreement with the expectations of hierarchical models of galaxy formation. \n\n\\section{Conclusions}\n\\label{Sec:Conclusions} \n\nWe study the buildup of the Red Sequence by analysing the structure, morphology, and star formation properties of a sample of red galaxies with stellar masses $\\mathrm{M}_*\\gtrsim 5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $0.3<z<1.5$. The novelty of this study is two-fold: first, our red galaxy sample includes galaxies both on the Red Sequence and at nearby locations on the Green Valley to trace transitory evolutionary stages towards it, and secondly, we have simultaneously considered structural (regular\/irregular), morphological (disks\/spheroids), and star formation enhancement (HSF\/LSF) to define galaxy classes that can be directly associated with intermediate-to-late stages of major mergers, as well as with normal E-S0's and red regular disks. The redshift evolution of the fractions and number densities of each red galaxy type have been derived. Finally, these data are used to carry out a set of novel observational tests defined on the basis of the expectations of hierarchical models, to test the hierarchical origin of massive E-S0's. \n\nBoth the number densities and fractions of regular galaxies increase with cosmic time at $0.3<z<1.5$, tracing the progressive buildup of massive normal early-type galaxies during the last $\\sim 9$\\,Gyr (mostly E-S0's, but also some red disks). The fractions of red regular spheroids (E-S0's) plus red disks increase by a factor of $\\sim 6$ since $z\\sim 1.3$ down to $z\\sim 0.5$, whereas the fraction of irregulars (major mergers) decreases by the same factor. However, the number density of red irregulars (major mergers) is constant down to $z\\sim 0.7$, decreasing at lower redshifts. This means that the fraction of red irregulars decreases only relatively to that of regulars, pointing to their transitory nature, as already claimed in previous studies. We find that the number density distributions of regular spheroids (E-S0's) and of irregulars (major mergers) cross at $z\\sim 0.9$ for $\\mathrm{M}_*\\gtrsim 5\\times 10^{10}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$.\n\nEnhanced SFRs compared to the average SFR of the global galaxy population at each redshift at $0.3 < z < 1.5$ are hosted by most irregular disks in our red sample and by nearly half of the irregular spheroids (in agreement with the major merger-related nature of both types). At $z\\lesssim 0.7$, enhanced SF can also be found in nearly all red regular disks. On the other hand, only $\\sim 25$\\% of red regular spheroids (E-S0's) harbour enhanced star formation at all redshifts. \n\nThe main result of this study is that we provide observational evidence pointing to the existence of a main evolutionary path among red galaxy types at $0.6<z<1.5$, being:\\\\[-0.1cm]\n\n\\noindent  {\\bf Irregular disk $\\rightarrow$ irregular spheroid $\\rightarrow$  regular spheroid}. \\\\[-0.3cm]\n\nThis track traces the conversion of blue disks into passive E-S0's through major mergers and dominates the buildup of the Red Sequence at $z\\gtrsim 0.6$, in excellent agreement with the expectations of the EM10 model. Our data are coherent with the prediction of this model about that the bulk of massive E-S0's with $\\mathrm{M}_*\\gtrsim 10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ have been definitively assembled through major mergers during the $\\sim 2.2$\\,Gyr period elapsed $0.6<z<1.2$, as also proposed by \\citet{2010ApJ...709..644I}. \n\nOur results support observationally several expectations of hierarchical theories of galaxy formation concerning the buildup of massive red galaxies: \n\n\\begin{enumerate}\n \\item Data is compatible with the fact that the massive red regular galaxies at low redshifts derive from the irregular ones populating the Red Sequence and its neighbourhood at earlier epochs up to $z\\sim 1.5$.\n\n \\item The progenitors of the bulk of present-day massive red regular galaxies seem to have been disks that have migrated to the Red Sequence mostly through major mergers at $0.6<z<1.2$ (these mergers thus starting at $z\\lesssim 1.5$).\n\n \\item The formation of E-S0's that end up with $\\mathrm{M}_* \\gtrsim  10^{11}\\ifmmode{\\mathrm M_\\odot}\\else{M$_\\odot$}\\fi$ at $z=0$ through gas-rich major mergers seems to have frozen since $z\\sim 0.6$.\n\\end{enumerate}\n\n\\section*{Acknowledgments}\nThe authors thank the anonymous referee for the provided input that helped to improve this publication significantly. We also thank M.~Bernardi, N.~Deveraux, S.~di Serego Alighieri, B.~Rothberg, and D.~Sobral for interesting and useful discussion on the topic. Supported by the Spanish Ministry of Science and Innovation (MICINN) under projects AYA2009-10368, AYA2006-12955, and AYA2009-11137, and by the Madrid Regional Government through the AstroMadrid Project (CAM S2009\/ESP-1496, http:\/\/www.laeff.cab.inta-csic.es\/\\-projects\/\\-astromadrid\/\\-main\/ index.php). Funded by the Spanish MICINN under the Consolider-Ingenio 2010 Program grant CSD2006-00070: \"First Science with the GTC\" (http:\/\/www.iac.es\/\\-consolider-ingenio-gtc\/).  Based on observations made with the Isaac Newton and Willian Herschel Telescope operated on the island of La Palma by the Isaac Newton Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof\\'{\\i}sica de Canarias. Some of the data presented herein are part of the DEEP2 survey, funded by NSF grants AST95-09298, AST-0071048, AST-0071198, AST-0507428, and AST-0507483, as well as NASA LTSA grant NNG04GC89G. This work is based in part on services provided by the GAVO data center. S.D.H. \\& G.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nProtons and carbon ion beams are presently used to treat many different solid cancers \\cite{Jakel2008,Durante2010} and several new centers based on hadron accelerators are operational or under construction \\cite{Amaldi2005,Schardt2010}.\nThe main advantage of this technique, in comparison to the standard radiotherapy with X-ray beams, is the better localization of the irradiation dose in the tumor affected region sparing healthy tissues and possible surrounding organs at risk. This feature can be achieved because the heavy charged particles loose most of the energy at end of their range, the Bragg peak (hereafter BP), in comparison to the exponentially decreasing energy release of the X-ray beam. Up to now most of the patients have been treated at centers with proton beams, but routinary use of carbon beams has now started. There are also proposals for future use of $^{4}He$, $^{7}Li$ or $^{16}O$ beams \\cite{Brahme1986}.\\\\\nNew dose monitoring techniques need to be developed and introduced into clinical use, to meet the improved capability of hadrontherapy to match the dose release with the cancer position. The R\\&D effort should be then focused to develop novel imaging methods to monitor, preferably in real time, the 3-dimensional distribution of the radiation dose effectively delivered during hadrontherapy. \\\\\n This holds true especially for treatments using carbon ion beams since the dose profile is very sensitive to anatomical changes and minor patients' positioning uncertainties.  \\\\\nConventional methods for the assessment of patients' positioning used in all X-ray based radiation therapy, where a non-negligible fraction of the treatment beam is transmitted through the patient, cannot be used to pursue this task due to the different physics underlying.\nAll the proposed methods exploit the information provided by the secondary particles produced by the hadron beam along its path to the tumour, inside the patient's body. In particular it has been already shown that the peak of the dose released by the hadron beam can be correlated with the emission pattern of the flux of secondary particles created by the beam interaction, namely: i) prompt photons within the 1-10 MeV energy range~\\cite{Min2006,Testa2008,Testa2009} and ii) pairs of back-to-back photons produced by the annihilation of positrons coming from $\\beta^+$ emitters, mainly $^{11}C$ and $^{15}O$~\\cite{Pawelke1997,Parodi2002,Enghardt2004,Fiedler2008,Vecchio2009,Attanasi2009}.\\\\\nIn this paper we suggest the possibility to correlate the position of the BP in the patient with the emission region of charged secondary particles, mainly protons with kinetic energy E$_{\\rm kin}$<150 MeV.\nWe report the study of the charged secondary particles produced from the irradiation of a Poly-methyl methacrylate (PMMA) with the 80 MeV\/u fully stripped carbon ion beam of the INFN Laboratori Nazionali del Sud (LNS). Section~\\ref{setup} is devoted to the description of the experimental setup;\nthe event selection and the spectra of the charged secondary particles are presented in Section~\\ref{datasel}. The analysis of the production region of charged secondary particles is described in Section~\\ref{region}, and the measurement of their differential production rate is reported in Section~\\ref{flux}.\n\\section{Experimental setup}\n\\label{setup}\n\n\\begin{figure}[!ht]\n\\begin{center}\n\\centerline{\n\\includegraphics [width = 1 \\textwidth] {Fig1.pdf}}\n\\caption{\\small{Experimental setup: picture and schematic view. The acquisition is triggered by the coincidence of the Start Counter and the LYSO detector.}}\n\\label{fig:Schema}\n\\end{center}\n\\end{figure}\nFigure~\\ref{fig:Schema} shows the experimental setup.\nA 4x4x4 cm$^3$ PMMA target is placed on a 80 MeV\/u, fully stripped $^{12}C$ ion beam. The beam rate, ranging from hundreds of kHz to $\\sim 2$ MHz, is monitored with a 1.1 mm thick scintillator placed at 17 cm from the PMMA on the beam line and read-out by two photomultiplier tubes (PMTs) Hamamatsu 10583 put in coincidence (Start Counter). \\\\\nAn array of 4 LYSO crystals, each measuring 1.5x1.5x12 cm$^3$, is placed at 90$\\degree$ with respect to the beam line, at 74 cm from the PMMA center. The scintillation light of the crystals is detected with a PMT EMI 9814B triggered in coincidence with the Start Counter.\n\n\\noindent\nA 21 cm long drift chamber~\\cite{Abou-Haidar2012} is placed at 51 cm from the PMMA center, along the flight line connecting the PMMA to the LYSO crystals. \nWe have chosen the configuration at 90$\\degree$ with respect to the beam line to maximize the sensitivity to the Bragg peak position along the beam.\nIn the following the coordinate system is defined (Figure~\\ref{fig:Schema}) with the x-axis along the beam line toward the Start Counter, the z-axis along the line connecting the centers of PMMA, drift chamber and LYSO crystals detector and the y-axis oriented according to the right-hand rule, and origin at the drift chamber center. The PMMA center in the vertical axis was at y = -4 mm.\nThe drift chamber provides a 2-dimensional reconstruction of the space point by alternated horizontal (x-z plane V-view) and vertical (y-z plane U-view) layers of wires.  Each layer is composed of three 16x10 mm$^2$ rectangular cells for a total of 36 sense wires (Figure~\\ref{fig:Camera}). The twelve layers, six on each view, provide tracking redundancy and ensure high tracking efficiency and excellent spatial resolution. In order to minimize tracking ambiguities, the consecutive layers of each view are staggered by half a cell. \nCustom front-end electronics boards, designed and realized at the INFN Laboratori Nazionali di Frascati (LNF) electronics workshop, are embedded in the detector and provide single wire signal amplification by a factor of 10. The drift chamber has been operated with 1.8 kV sense wire voltage, Ar\/CO$_2$ (80\/20) gas mixture and 30 mV discriminating threshold for the signals, achieving  $\\leq 200~\\mu$m single cell spatial resolution and $\\simeq 96\\%$ single cell efficiency~\\cite{Abou-Haidar2012}.\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics [width = 1\\textwidth] {Fig2.pdf}\n\\caption{\\small{Mechanical drawing of the drift chamber.}}\n\\label{fig:Camera}\n\\end{center}\n\\end{figure}\n\n\\noindent\nThe signals from the Start Counter and the LYSO crystals are split and fed into a 12-bit QDC (Caen V792N) and a 19-bit TDC (Caen V1190B), after discrimination, to provide the measurements of both the particles' energy and arrival time. The signals from the 36 cells of the drift chamber are fed, after discrimination, into the same TDC providing the drift time measurements.  The front-end electronics has been read-out by a VME system using a MOTOROLA 5100 CPU board.\n\n\\noindent The energy and time calibration of the LYSO crystals and the determination of the drift chamber space-time relations have been described in \\cite{Agodi2012a,Agodi2012} and \\cite{Abou-Haidar2012} respectively. A custom tracking algorithm, based on a least squares iterative fitting method, has been also developed to reconstruct the direction of the charged secondary particles. A first track reconstruction is performed using very clean topologies asking for at least three layers with a single fired cell (hit), on both the V- and U-views. Then a hit addition algorithm improves the tracking performance by using the information from all the other layers.\n\n\\section{Data selection}\n\\label{datasel}\nThe trigger signal is provided by the coincidence of the Start Counter and LYSO crystals signals, within 80 ns. \n\\begin{figure}[!htb]\n\\includegraphics [width = \\textwidth] {Fig3.pdf}\n\\caption{\\small{Distribution of the number of fired cells in the drift chamber $N_{\\rm Hits}$ for events with detected energy in the LYSO crystals $E_{ \\rm LYSO} >$ 1 MeV.}}\n\\label{fig:Nhits}\n\\end{figure}\nFigure~\\ref{fig:Nhits} shows the distribution of the number of hits  in the drift chamber ( $N_{\\rm Hits}$ ) obtained for events with detected energy in the LYSO crystals $E_{\\rm LYSO} > $  1 MeV. Events with $N_{\\rm Hits} >$ 9 are selected for the analysis of the charged secondary particles.\n\n\\noindent\nIn order to evaluate the setup acceptance and efficiency, and to optimize the particle identification analysis a detailed simulation has been developed using the FLUKA software release 2011.2~\\cite{Fasso'2003,Ferrari2005}. The detailed geometry description with the setup materials (air included) together with the trigger logic, the time resolution of the scintillator as well as the experimental space resolution of the drift chamber have been considered. The quenching effect in the scintillator has also been introduced in the Monte Carlo according to \\cite{Koba2011}.\nThe interaction of a sample of $10^9$ carbon ions with 80 MeV\/u, equivalent to $10^3$ s of data taking at the typical 1 MHz rate of beam, has been simulated. To identify the charged particles reconstructed in the drift chamber, we exploit the distribution of the detected energy in the LYSO detector $E_{\\rm LYSO}$  as a function of Time of Flight (ToF), Figure~\\ref{fig:Etof}. \nIn the data sample (left panel) a fast low-energy component due to electrons\nis clearly visible for ToF values around zero, in the area delimited by the first dashed line. These electrons are produced by Compton scattering of the de-excitation photon induced by beam interactions in the PMMA material. \nThe central most populated band, delimited by the two dashed lines, is made by protons with detected energy within a very wide range, originating also the clearly visible saturation of the LYSO crystals QDC for $E_{\\rm LYSO} >$ 24 MeV. The FLUKA simulation (right panel) shows similar populations in the (ToF , $E_{\\rm LYSO}$) plane with an additional component of deuterons, above the second dashed line, which is not present in data.\n\n\\begin{figure}[!h]\n\\begin{center}\n\\includegraphics [width = 1\\textwidth] {Fig4ab.pdf}\n\\caption{\\small{ Distribution of the detected energy in the LYSO crystals as a function of the Time of Flight: Data (Left) and FLUKA Simulation (Right).\n}}\n\\label{fig:Etof}\n\\end{center}\n\\end{figure}\n\\noindent\nWe have then identified as proton a charged secondary particle with ToF and $E_{\\rm LYSO}$ values inside the area delimited by the two dashed lines in Figure~\\ref{fig:Etof}. \nThe systematic uncertainty on the proton\/deuteron identification has been estimated using the data events in the deuterons area of the (ToF , $E_{\\rm LYSO}$) plane.\nFigure~\\ref{fig:beta} shows the distributions of $\\beta = \\frac{v}{c}$ and the corresponding detected kinetic energy $E_{\\rm kin}$ for the identified protons, obtained using the ToF measurement together with the distance between LYSO crystals and PMMA.\nThis detected kinetic energy can be related to the proton kinetic energy at emission time, $E^{\\rm Prod}_{\\rm kin}$, considering the energy loss in the PMMA and the quenching effect of the scintillating light for low energy protons. The minimum required energy to detect a proton in the LYSO crystals is $E^{\\rm Prod}_{\\rm kin} = 7.0\\pm 0.5$ MeV, evaluated using the FLUKA simulation, and a proton with an average detected kinetic energy $E_{\\rm kin}$ = 60 MeV has been emitted with $E_{\\rm kin}^{\\rm Prod} 83\\pm 5$ MeV. The uncertainty is mainly due to the finite size of both the beam spot $\\mathcal{O}$(1 cm) and profile.\n\\begin{figure}[!htb]\n\\begin{center}\n\\includegraphics [width = \\textwidth] {Fig5ab.pdf}\n\\caption{\\small{Distribution of $\\beta = \\frac{v}{c}$ (left) and kinetic energy (right) of charged secondary particles identified as protons.}}\n\\label{fig:beta}\n\\end{center}\n\\end{figure}\n\n\\noindent\nIn order to use the secondary protons for monitoring purposes, the crossing of some centimeters of patient's tissue has to be considered and therefore the range  $E_{\\rm kin} > $ 60 MeV of the detected kinetic energy distribution is the most interesting for the above-mentioned application.\nIn the following the proton kinetic energy detected in the LYSO crystals will be referred to as the kinetic energy.\n\\section{Production region of charged secondary particles}\n\\label{region}\nTracks reconstructed in the drift chamber are backward extrapolated to the PMMA position, to find the production region of charged secondary particles along the path of the carbon ion beam. The PMMA is mounted on a single axis movement stage allowing position scans along the x-axis to be performed with a 0.2 mm accuracy (Figure~\\ref{fig:Schema}). In the configuration with the centers of PMMA, drift chamber and LYSO crystals aligned along the z-axis, the PMMA position in the stage reference frame is taken as 0 and will be referred to as the reference configuration. \n\n\\noindent From each track reconstructed in the drift chamber and backward extrapolated to the beam axis we can measure the x and y coordinates of the estimated emission point of the charged secondary particle, named $x_{\\rm PMMA}$ and $y_{\\rm PMMA}$. The expected position of the Bragg peak obtained with the FLUKA simulation \\cite{Fasso'2003} is located at $(11.0 \\pm 0.5)$ mm from the beam entrance face of the PMMA. With the setup in the reference configuration, the expected position of the Bragg peak in our coordinate system is $x_{\\rm Bragg}|^{\\rm Ref} = (9.0 \\pm 0.5)$ mm. \nFigure~\\ref{fig:peak} shows the distribution of the reconstructed $x_{\\rm PMMA}$, compared to the expected distribution of the dose deposition in the PMMA, both obtained with the setup in the reference configuration. \n\\begin{figure}[!htb]\n\\begin{center}\n\\includegraphics [width = 0.8\\textwidth] {Fig6.pdf}\n\\caption{\\small{Expected dose deposition in the PMMA  evaluated with FLUKA (hatched) compared to the distribution of $x_{\\rm PMMA}$ (solid), the emission point of charged secondary particles along the x-axis. The beam entrance and exit faces of the PMMA are at $x_{\\rm PMMA}$ = 2 cm and $x_{\\rm PMMA}$ = -2 cm, respectively.}}\n\\label{fig:peak}\n\\end{center}\n\\end{figure}\nThe mean of the gaussian fit to the distribution is $ \\bar{x}_{\\rm PMMA} = 17.1\\pm0.2$ mm, and consequently the separation between the BP and the peak from secondary proton emission is $\\Delta_{\\rm ProtonBragg} = 8.1 \\pm 0.5$ mm.\n Figure~\\ref{fig:reso_ekin} shows the distribution of the reconstructed $x_{\\rm PMMA}$ and $y_{\\rm PMMA}$ for all identified protons (solid line), for protons with $E_{\\rm kin} > $ 60 MeV (hatched) and for protons with $E_{\\rm kin} >$ 100 MeV (grey). The beam entrance and exit faces of the PMMA are at $x_{\\rm PMMA}$ = 2 cm and $x_{\\rm PMMA}$ = -2 cm, and $y_{\\rm PMMA}$ = 1.6 cm and $y_{\\rm PMMA}$ = -2.4 cm. The $x_{\\rm PMMA}$ distribution is related to the range of the beam while the $y_{\\rm PMMA}$ to its transversal profile. \nQuite remarkably the shape of the distribution of the emission point is approximately the same for protons emitted with different kinetic energies, e.g. the resolution on $x_{\\rm PMMA}$ does not depend critically on the $E_{\\rm kin}$ variable.%\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics [width = 1 \\textwidth] {Fig7ab.pdf}\n\\caption{\\small{Distribution of $x_{\\rm PMMA}$ (Left) and $y_{\\rm PMMA}$ (Right) obtained for all charged particles identified as protons (black solid line), for protons with $E_{\\rm kin} > $ 60 MeV (dashed line) and with $E_{\\rm kin} > $ 100 MeV (grey).  The beam entrance and exit faces of the PMMA are at $x_{\\rm PMMA}$ = 2 cm and $x_{\\rm PMMA}$ = -2 cm, and $y_{\\rm PMMA}$ = 1.6 cm and $y_{\\rm PMMA}$ = -2.4 cm.}}\n\\label{fig:reso_ekin}\n\\end{center}\n\\end{figure}\n\n\\noindent\nThe existence of a relationship between the expected BP position and the peak of the $x_{\\rm PMMA}$ distribution, as a function of the PMMA position, in principle could allow us to follow the BP position using the $x_{\\rm PMMA}$ measurements.  To estimate the accuracy of this method\n, a position scan has been performed acquiring several data runs moving the PMMA by means of the translation stage.\n\n\\noindent\nFor each run with different PMMA position, the production region of the protons have been monitored using the mean values of the gaussian fit to $x_{\\rm PMMA}$ and $y_{\\rm PMMA}$ distributions, $\\bar{x}_{\\rm PMMA}$ and $\\bar{y}_{\\rm PMMA}$. \nSince $\\bar{y}_{\\rm PMMA}$ is the coordinate of the proton emission point along the vertical axis, and is related to the fixed beam profile in the transverse plane, its behaviour as a function of the PMMA position provides an estimate of the method's systematic uncertainty.\n\n\\noindent\nEach PMMA position in the stage reference frame can be translated into the expected Bragg peak position $x_{\\rm Bragg}$ for that given PMMA position.\nFigure~\\ref{fig:ADD} shows the results obtained for $\\bar{x}_{\\rm PMMA}$ and $\\bar{y}_{\\rm PMMA}$ as a function of $x_{\\rm Bragg}$, with $E_{\\rm kin} >$ 60 MeV protons. A clear linear relationship  is observed between $\\bar{x}_{\\rm PMMA}$ and $x_{\\rm Bragg}$, indicating that the charged secondary particles emission reconstructed with the drift chamber follows accurately the BP movement.\nNo dependence of the $\\bar{y}_{\\rm PMMA}$ values on the Bragg peak position is observed, as expected from a translation of the PMMA along the x-axis only.  \nSimilar results can be obtained using protons with different $E_{\\rm kin}$ selection, as it can be inferred from Figure~\\ref{fig:reso_ekin}.\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics [width = 1 \\textwidth] {Fig8.pdf}\n\\caption{\\small{Reconstructed peak position of the secondary proton emission distribution $\\bar{x}_{\\rm PMMA}$,$\\bar{y}_{\\rm PMMA}$ as a function of the expected Bragg Peak position $x_{\\rm Bragg}$, with $E_{\\rm kin} >$ 60 MeV.}}\n\\label{fig:ADD}\n\\end{center}\n\\end{figure} \n\n\\noindent\nTo estimate the achievable accuracy on the BP determination several contributions need to be considered.\nWe evaluated the difference $\\Delta_{\\rm ProtonBragg} = \\bar{x}_{\\rm PMMA} - x_{\\rm Bragg}$ for all identified protons and for the proton sample with $E_{\\rm kin} >$ 60 MeV.  The $\\Delta_{\\rm ProtonBragg}$ root mean square is $\\sigma_{\\rm \\Delta_{\\rm ProtonBragg}}\\simeq$ 0.9 mm for both samples.\nThis can be explained as follows: in the sample with all identified protons the contribution to the total uncertainty due to the scattering is partially compensated by the larger statistics with respect to the sample with $E_{\\rm kin} >$ 60 MeV. Table \\ref{TAB:NPStat} reports the number of identified protons with $E_{\\rm kin} >$ 60 MeV obtained with the position scan data.\n\\begin{table}[!hbt]\n\\caption{Statistics of identified protons with $E_{\\rm kin} >$ 60 MeV, obtained with the position scan data.}\n\\begin{center}\n\\begin{tabular}{cccccccccccc}\n\\hline\n\\bs\n$x_{\\rm Bragg}$ (mm) & -19 & -15 & -11 & -9 &  -5 &  -3 &  1 &    5&    9&    11 &  13 \\\\\n\\bs\n\\hline\n\\bs\n$N^{\\rm 60~MeV}_{\\rm Protons}$ & 67& 77& 88& 61& 92& 75& 113& 154& 1223& 130& 83 \\\\\n\\bs\n\\hline\n\\end{tabular}\n\\label{TAB:NPStat}\n\\end{center}\n\\end{table}\n\n\\noindent\nThe uncertainty $\\sigma_{\\rm Extrapol}$ due to the backward extrapolation of the track from the drift chamber to the beam line can be estimated from the root mean square of the $\\bar{y}_{\\rm PMMA}$ values, $\\sigma_{\\bar{y}_{\\rm PMMA}} = \\sigma_{\\rm Extrapol}$ = 0.5 mm. The latter contributes to the $\\Delta_{\\rm ProtonBragg}$ distribution, together with $\\sigma_{\\rm Stage}$ = 0.2 mm from the uncertainty on the PMMA positioning. \nWe can then estimate the contribution to the total uncertainty coming from the shape of the distribution of the emission point of charged secondary particles as: \n\\begin{equation}\n\\sigma_{\\rm Emission} = \\sqrt{\\sigma_{\\rm \\Delta_{\\rm ProtonBragg}}^2  - \\sigma_{\\rm Extrapol}^2 - \\sigma_{\\rm Stage}^2} \\sim 0.7 \\text{mm}\n\\end{equation}\n\n\\noindent It must be stressed that this value represents only an indication of the precision achievable in the BP determination using secondary protons, due to the target thickness and homogeneity in the present setup, with respect to a possible clinical application.\n\\section{Flux of charged secondary particles}\n\\label{flux}\nThe flux of the secondary protons emitted from the beam interaction with the PMMA has been measured at 90$\\degree$ with respect to the beam direction and in the geometrical acceptance of the triggering LYSO crystals, configuration maximizing the sensitivity to the Bragg peak position. The surface of the LYSO is 3x3 cm$^2$, corresponding to a solid angle $\\Omega_{\\rm LYSO} = 1.3\\times 10^{-4}$ sr at a distance of 74 cm. The proton's kinetic energy spectrum measured with data has been inserted in the FLUKA simulation to evaluate the detection efficiency in the LYSO crystals for protons with $E_{\\rm LYSO} >$ 1 MeV: $\\epsilon_{\\rm LYSO}= (98.5\\pm 1.5)\\%$, with the uncertainty mainly due to the Monte Carlo statistics. To properly evaluate the rate of charged secondary particles reaching the LYSO crystals, the number of carbon ions reaching the PMMA target ($N_{\\rm C}$) has been computed according to \\cite{Agodi2012a}: counting the number of signals in the Start Counter ($N_{\\rm SC}$) within randomly-triggered time-windows of $T_w=2\\ \\micro\\second$, corrected for the Start Counter efficiency $\\epsilon_{\\rm SC} = (96 \\pm 1)\\%$, and the acquisition dead time. \nThe number of emitted secondary protons $N_{\\rm P}$ has been measured with the $x_{\\rm PMMA}$ distribution counts, corrected for $\\epsilon_{\\rm SC}$, $\\epsilon_{\\rm LYSO}$, the tracking efficiency $\\epsilon_{\\rm Track} = (98 \\pm 1)\\%$~\\cite{Abou-Haidar2012} and the acquisition dead time.\n\n\\noindent\nThe double differential production rate of secondary protons emitted at 90$\\degree$ with respect to the beam line is estimated as:\n\\begin{equation}\n\\frac{d^2N_{\\rm P}}{dN_{\\rm C}d\\Omega}(\\theta=90\\degree)=\\frac{N_{\\rm P}}{N_{\\rm C}~~\\Omega_{\\rm LYSO}}.\n\\end{equation}\nFigure~\\ref{fig:flusso} shows the double differential production rate of secondary protons, emitted at 90$\\degree$ with respect to the beam line, as a function of the rate of the carbon ions $R_{\\rm C}$ reaching the PMMA: all identified protons and protons with $E_{kin} >$ 60 MeV.\n\\begin{figure}[!ht]\n\\begin{center}\n\\includegraphics [width = 1\\textwidth] {Fig9.pdf}\n\\caption{\\small{Double differential production rate for secondary particles emitted at 90$\\degree$ with respect to the beam line, as a function of the rate of the carbon ions $R_{\\rm C}$ reaching the PMMA target: all identified protons (triangles) and protons with $E_{\\rm kin} >$ 60 MeV (circles).\n}}\n\\label{fig:flusso}\n\\end{center}\n\\end{figure}\n\n\\noindent Expressing these results in terms of the secondary proton's kinetic energy at emission $E^{\\rm Prod}_{\\rm kin}$, we obtain:\n\\begin{eqnarray}\n\\fl\n\\frac{dN_{\\rm P}}{dN_{\\rm C}d\\Omega}(E^{\\rm Prod}_{\\rm kin} > 7 {\\rm ~MeV}, \\theta=90\\degree) =  (9.56\\pm 0.18_{\\rm stat} \\pm 0.40_{\\rm sys})\\times 10^{-4} sr^{-1} \\\\\n\\fl\n \\frac{dN_{\\rm P}}{dN_{\\rm C}d\\Omega}(E^{\\rm Prod}_{\\rm kin} > 83 {\\rm ~MeV}, \\theta=90\\degree) =  (2.69\\pm 0.08_{\\rm stat} \\pm 0.12_{\\rm sys})\\times 10^{-4} sr^{-1}\n\\end{eqnarray}\nwith the systematic contribution mainly due to proton identification and to the uncertainty on the production kinetic energy related to the beam's transversal profile uncertainty. \n\n\\noindent\nThe same experimental setup described in Section \\ref{setup} has been used to measure the differential production rate for prompt photons, with energy $E_{\\rm LYSO} >$ 2 MeV and emitted at 90$\\degree$ with respect to the beam line: $dN_{\\rm \\gamma}\/(dN_{\\rm C}d\\Omega)(E_{\\rm LYSO} > 2 {\\rm ~MeV} , \\theta=90\\degree) = (2.92 \\pm 0.19)\\times 10^{-4} sr^{-1}$~\\cite{Agodi2012a}.\n\n\\section{Discussion and conclusions}\nWe reported the study of secondary charged particles produced by the interaction of 80 MeV\/u fully stripped carbon ion beam of INFN-LNS laboratory in Catania with a PMMA target. \nProtons have been identified exploiting the energy and time of flight measured with a plastic scintillator together with LYSO crystals, and their direction has been reconstructed with a drift chamber. A detailed simulation of the setup based on the FLUKA package has been done to evaluate its acceptance and efficiency, and to optimize secondary particle's identification.\n\\\\\n\\noindent\nIt has been shown that the backtracking of secondary protons allows their emission region in the target to be reconstructed. Moreover the existence of a correlation between the reconstructed production region of secondary protons and the Bragg peak position has been observed, performing a position scan of the target.\nThe achievable accuracy on the Bragg peak determination exploting this procedure has been estimated to be in the submillimeter range, using the described setup and selecting secondary protons with kinetic energy at emission $E^{\\rm Prod}_{\\rm kin} >$ 83 MeV. \n\\\\\n\\noindent\nThe obtained accuracy on the position of the released dose should be regarded as an indication of the achievable accuracy for possible applications of this technique  to monitor the BP position in hadrontherapy treatment. In fact in clinical application the secondary particles should cross a larger amount of material (patient tissue) resulting in an increased multiple scattering contribution worsening the BP resolution by, at most, a factor 2-3. On the other hand an optimized device allowing a closer positioning to the patient could greatly improve the collected statistics of protons produced with $E^{\\rm  Prod}_{\\rm kin} >$ 80 MeV, reducing multiple scattering effects. Furthermore the intrinsic good tracking resolution and high detection efficiency easily achievable in charged particles detectors, make this monitoring option worthwhile of further investigations.\n\n\\noindent\nThe measured differential production rate for protons with $E^{\\rm Prod}_{\\rm kin} >$ 83 MeV and emitted at 90$\\degree$ with respect to the beam line is: $dN_{\\rm P}\/(dN_{\\rm C}d\\Omega)(E^{\\rm Prod}_{\\rm kin} > 83 MeV , \\theta=90\\degree) = (2.69\\pm 0.08_{\\rm stat} \\pm 0.12_{\\rm sys})\\times 10^{-4} sr^{-1}$.\n\n\\ack\nWe would like to thank the precious cooperation of the  staff of the INFN-LNS (Catania, Italy) accelerator group. The authors would like to thank Dr. M.~Pillon and Dr. M.~Angelone (ENEA-Fra\\-scati, Italy) for allowing us to validate the response of our detector to neutrons on the Frascati Neutron Generator; C.~Piscitelli (INFN-Roma, Italy) for the realization of the mechanical support; M.~Anelli (INFN-LNF, Frascati) for the drift chamber construction. \n\n\\noindent\nThis work has been supported by the ``Museo storico della fisica  e Centro di studi e ricerche Enrico Fermi''. \n\\section*{References}\n\\bibliographystyle{jphysicsBforPMB}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzkvxu b/data_all_eng_slimpj/shuffled/split2/finalzzkvxu
new file mode 100644
index 0000000000000000000000000000000000000000..19ed20fa2a1c1d51c2411714c2de6d50088430db
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzkvxu
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\nEvery particle accelerator needs a vacuum system to transport its particle beams with low losses. With a~certain probability beam particles interact with residual gas molecules. The scattering leads to immediate particle losses from the beam, or to a deterioration of the beam quality. Both effects are not wanted and the beam losses can even lead to a problematic activation of accelerator components. For different situations, i.e. beam particle species and beam energies, the requirements for the quality of acceptable vacuum conditions can differ significantly. For example in a hadron accelerator with a section that is passed by the beam only once, a pressure of $10^{-5}\\,$mbar might be sufficient. On the other hand an~electron storage ring might need a base pressure of $10^{-10}\\,$mbar in the absence of beam. Consequently the~technology and physics of vacuum systems covers a broad range of effects and concepts, depending on the application. Vacuum systems for electron and proton storage rings are discussed for example in Ref. \\cite{benvenuti}, and a dedicated CERN school on accelerator vacuum is documented under Ref. \\cite{CERN}. Fundamentals of vacuum physics are discussed in Ref. \\cite{redhead}. \nFigure\\,\\ref{fig:p_overview} shows the range of pressure levels from ambient conditions down to the lowest pressures in accelerators. The pressure ranges for typical applications, the volume density of molecules and the mean free path of nitrogen molecules are indicated. The pressure range for beam vacuum is in technical language referred to as Ultra-High-Vacuum (UHV). One often speaks about dynamic vacuum, when the presence of an intense beam affects the residual gas pressure.\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.85\\textwidth]{Fig_01_Vac.png}\n\\caption{Gas pressures ranging from ambient conditions down to cold accelerator vacuum cover 13 orders of magnitude.}\n\\label{fig:p_overview}\n\\end{figure}\n\n\n\\section{Pressure and Gas Equation}\nPressure is basically a force that gas molecules apply to a surface by mechanical momentum transfer, averaged over a huge number of collisions during a macrosopic time interval. Pressure is measured as a~force per area. A common unit is Pascal, 1\\,Pa~=~1\\,N\/m$^2$. Another common unit is 1\\,mbar~=~$100$\\,Pa. The~average velocity of molecules depends on the square root of the temperature as shown in Eq. (\\ref{eq:velo}). Using the molecule density $n_v$ the average velocity can be related to the rate of molecules impinging on the wall of a vessel per area and per time.\n\n\\begin{equation}\n\\overline{v} = \\sqrt{ \\frac{8 k_b}{\\pi m_0} ~ T },~~ \\d{N}{A\\,dt} = \\frac{1}{4} n_v \\overline{v}\n\\label{eq:velo}\n\\end{equation}\n\nHere $k_b = 1.38\\times 10^{-23}\\,$J\/K is the Boltzmann constant. The gas equation is a fundamental law relating pressure, volume, temperature and amount of a gas:\n\n\\begin{equation}\nPV = N k_b T = nRT.\n\\label{eq:pv}\n\\end{equation}\n\n$R = 8.314\\,$N\\,m\\,\/\\,mole\\,K is the gas constant. The majority of vacuum systems operate at room temperature and we can consider the temperature as being constant. Consequently the product of pressure and volume is a measure of the amount of gas, related to the number of molecules $N$ or the number of moles $n$. In practice a leak rate is often given in terms of mbar\\,l\/s, which is the amount of gas that is entering the considered recipient per unit of time.\nVacuum systems are equipped with pumps, devices that absorb gas molecules. A vacuum pump is characterised by its pumping speed $S = Q\/P$, quantified in l\/s at its interface. Here $Q$ is the gas load at the interface of the pump. The pumping speed varies for different gas species. Some chemically inactive gases like the inert gases He, Ar, and for example methane (CH$_4$), are pumped less efficiently by several types of pumps like Titanium sublimation pumps and NEG pumps. Turbo pumps and cryo pumps are not based on chemical binding reactions and are suited for all gas types. \nIn vacuum systems we can discriminate two types of flow regimes - viscous flow and molecular flow. Viscous flow occurs for higher gas densities. The higher the density of a gas the~shorter is the mean free path between two collisions of a gas molecule with others. The Knudsen number is the ratio between the mean free path and a typical dimension of the vacuum recipient. If the~mean free path is much larger than a typical dimension, we have molecular flow. With the cross section $\\sigma$ for collissions the mean free path $\\lambda$ is calculated as follows:\n\n\\begin{equation}\n\\lambda = \\frac{k_b T}{\\sqrt{2} \\sigma P}.\n\\end{equation}\n\nFor example Nitrogen residual gas at room temperature and a pressure of 10$^{-6}$\\,mbar has a mean free path of 60\\,m, which is much larger than the diameter of a typical vacuum pipe. Thus for particle accelerators we normally deal with molecular flow from a source of residual gas to a pump. We define the conductance of a vacuum component, e.g. an orifice or a piece of vacuum tube, as the ratio of the~molecular flow and the pressure drop across the element: \n\n\\begin{equation}\nC = \\frac{Q}{\\Delta P} . \n\\label{eq:cond}\n\\end{equation}\n\nThe conductance of an orifice of cross section $A$ can be estimated by:\n\\begin{equation}\nC = \\sqrt{\\frac{k_b T}{2\\pi M}} A\\, , ~~~\nC_\\mathrm{air} = 11.6 \\mathrm{[l\/s]} ~\nA \\mathrm{[cm^2]}.\n\\end{equation}\n\nOrifices may be used to realise a defined pumping speed for outgassing measurements. The conductance of a circular tube with diameter $d$ and length $l$ is given by:\n\\begin{equation}\nC = \\sqrt{\\frac{2 \\pi k_b T}{M}} \\frac{d^3}{l} \\, , ~\nC_\\mathrm{air} = 12.1 \\mathrm{[l\/s]} \\,\n\\frac{d^3 \\mathrm{[cm]}}{l \\mathrm{[cm]}}.\n\\end{equation}\n\nConductance varies with the type of gas, and in both formulas $M$ denotes the molecular mass of the~considered gas species. If two components are connected, the resulting conductance can be calculated from the individual conductances $C_1, C_2$. For a concatenation in series the resulting conductance is obtained by inverse addition: \n\n\\begin{equation}\nC_\\mathrm{total} = \\left( \\frac{1}{C_1} + \\frac{1}{C_2} \\right) ^{-1}.\n\\end{equation}\n\nAnd for a combination in parallel, simple addition has to be applied: \n\n\\begin{equation}\nC_\\mathrm{total} = C_1 + C_2. \n\\end{equation}\n\nIn a practical example an ion sputter pump of $400\\,$l\/s is connected to a recipient by a 30\\,cm long, $d=8\\,$cm tube. This results in an effective reduction of the pumping speed to $136\\,$l\/s. \n\nIn an accelerator vacuum system the operating pressure is established as a balance between release rate of free gas molecules and the removal rate that results from conductance and pumping. Gas molecules are released by different effects, such as thermal desorption from surfaces, beam induced desorption, diffusion of gas molecules from the bulk of material, permeation from ambient conditions through material, but also from leak rates through sealed connections between components. Among those effects thermal desorption is typically a significant contribution. Because of thermal energy, physical and chemical bindings of gas molecules to the material of the wall can be broken up and molecules are released. The sojourn time of a molecule at the wall is an exponential function of the temperature: $\\tau \\propto \\exp{\\left( E_d\\,\/\\,k_b T \\right) }$. For example a binding energy of 1\\,eV at room temperature leads to a sojourn time of 5 hours. The qualitative behaviour of the pressure in a recipient during pump-down, that results from the mentioned outgassing mechanisms, is shown in Fig.\\,\\ref{fig:pdown}. In the first phase of the pumpdown the~amount of gas removed from the recipient per unit time is proportional to the pressure, and thus one observes an exponential pressure decay. At some point a balance is reached between pumping speed and release of gas molecules from the surface of the walls into the volume of the recipient. In this phase the pressure decays inversely with time until the surface is emptied. Afterwards the outgassing is dominated by molecules that are transported in the bulk material to the surface by thermal diffusion. According to the~nature of diffusion this process scales as $1\/\\sqrt{t}$. It is possible to reduce this contribution to outgassing by a heat treatment of the material under vacuum conditions, thereby enhancing diffusion speed \\cite{calder}. Finally an equilibrium is reached when the remaining pressure is dominated by gas that permeates from the outside through the wall of the vacuum vessel. Naturally the permeation rate is very small in typical situations, and diffusion coefficients in metals are relevant only for light molecules like hydrogen.  \n\n\\begin{figure}\n\\centering\\includegraphics[width=0.90\\textwidth]{Fig_02_Vac.png}\n\\caption{Qualitative pump down behaviour of a recipient. Note the large logarithmic time scale on which $10^8$\\,s corresponds to three years.}\n\\label{fig:pdown}\n\\end{figure}\n\nSo far we have considered thermal outgassing of materials as the main source of gas load in a~vacuum recipient. In the presence of an intense particle beam the release of gas molecules from the~chamber walls can be drastically enhanced, by orders of magnitude, and those effects must be taken into account and quantified. A prominent effect is photo-desorption due to synchrotron radiation (SR), emitted by an electron or positron beam \\cite{fischer}. When a photon is absorbed on a metallic surface, the~photo effect may lead to the emission of a free electron. Absorption of the electron may then result in the~release of a gas molecule that was bound on the surface of the vacuum chamber. In a dipole magnet with bending radius $\\rho$ the number of photons emitted per unit length and time is given by:\n\n\\begin{equation}\n\\frac {dN_\\gamma}{dtds} = 1.28 \\cdot 10^{17} \\frac{I\\,[\\RM{mA}]\\,E\\,[\\RM{GeV}]}{\\rho\\,[\\RM{m}]}\\,.\n\\end{equation}\nHere $E$ is the beam energy and $I$ the beam current. The photons exhibit a statistical distribution of their energies and the given formula delivers the total number. More details on the properties of synchrotron radiation are given for example in Ref. \\cite{vacuumelectronic}. The SR induced desorption results in a specific outgassing rate per unit length of:\n\n\\begin{equation}\nq = \\eta \\, k_b\\, T\\, \\frac {dN_\\gamma}{dt\\,ds}\\,.\n\\end{equation}\n\nThe desorption yield $\\eta$ equals the number of gas molecules released per absorbed photon. It depends on the material of the chamber wall, the preparation of the material and foremost the conditioning of the surface under the bombardment with photons. For a surface cleaned with standard procedures one observes a decrease of the desorption yield inversely proportional to the total number of absorbed photons, e.g. Ref.\\,\\cite{billy}. The pressure obtained in a storage ring as a balance between beam induced desorption and installed pumping speed is called dynamic pressure as it depends on the beam intensity. In Fig.\\,\\ref{fig:petra} the~conditioning process of a NEG pumped vacuum chamber for the synchrotron light source PETRA-III is shown. The pressure rise per beam current is reduced by several orders of magnitude over the course of the conditioning process. In a well conditioned vacuum system the desorption yield $\\eta$ may reach values of $10^{-6}$ or lower. Rings with high intensity beams exhibit a high photon flux and one might be tempted to expect also high dynamic pressure for those. However, in this situation also the conditioning process advances faster and so the achieved pressure after a certain operating time is often similar for different storage rings. The typical gas composition is dominated by H$_2$ and a $\\sfrac{1}{4}$ fraction of CO.\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.85\\textwidth]{Fig_03_Vac.png}\n\\caption{The pressure rise per beam current is called dynamic pressure. It is shown here for a test chamber of the~PETRA-III storage ring as a function of integrated beam current.}\n\\label{fig:petra}\n\\end{figure}\n\nBesides the discussed mechanism of photo desorption there are other mechanisms causing beam induced desorption. If ion beams are accelerated, small losses of energetic ions may lead to high desorption rates. For example there are situations where a single ion, impinging on the wall of the vacuum chamber, may release of the order of $10^5$ gas molecules \\cite{sen}. Ion induced desorption cannot easily be reduced by conditioning. \n\nAnother important effect is the electron cloud instability \\cite{ecloud}. A free electron is accelerated in the~electromagnetic field of the beam and releases more than one secondary electron when absorbed on the chamber wall. Due to the multiplicative behavior of the process, the intensity of these electrons grows exponentially, resulting in a proportional growth of gas release in the vacuum chamber. A key factor for this process is the secondary emission yield, that is the number of electrons released after the~absorption of one electron. It depends on the type of material and can be reduced by coating of the~surface, for example with TiN or C. Another countermeasure is the application of a small longitudinal magnetic field, by winding a coil around the beampipe, to force the low energy free electrons on spiral paths.\n\n\\section{Pressure Computation for One-Dimensional Systems}\n\nAccelerator vacuum systems are build for beam transport and are typically lengthy, that is the longitudinal dimension is much larger than the transverse dimensions. For a calculation of the pressure profile a one-dimensional calculation is then sufficient. We start the derivation of the corresponding diffusion equation from the previously discussed relation between gas flow $Q$ and conductance $C$ in Eq. (\\ref{eq:cond}). Note that we have to introduce at this point a minus sign that ensures positive gas flow towards smaller pressure. In the~limit of small differences we obtain a differential equation for the gas flow. Here a specific conductance $\\mathcal{C} = C \\Delta s$ is introduced, which is a property of the vacuum vessel cross section. \n\n\\begin{eqnarray}\nQ & \\propto & - \\d{P(s)}{s} \\nonumber \\\\\nQ(s) & = & -\\mathcal{C}\\cdot \\d{P(s)}{s} \n\\label{eq:flow}\n\\end{eqnarray}\n\nA second equation is the continuity equation for the gas flow, which expresses that the change in the amount of transported gas is given by the sum of outgassing from the wall minus the pumped gas of a considered section with infinitesimal length. Here we use the specific pumping speed $\\mathcal{S} = S\/\\Delta s$ and the specific outgassing rate $q$ per unit length in mbar\\,l\/m\\,s.\n\n\\begin{equation}\n\\d{Q(s)}{s} = q - \\mathcal{S}\\,P(s)\n\\label{eq:continuity}\n\\end{equation}\n\nThese two Eqs. (\\ref{eq:flow}) and (\\ref{eq:continuity}) can now be combined into a~second order diffusion equation for a~one-dimensional vacuum system with the independent coordinate $s$.\n\n\\begin{equation}\n\\d{}{s}\\,\\mathcal{C}\\,\\d{}{s}\\,P(s)-\\mathcal{S}P(s) + q = 0\n\\label{eq:diffeq}\n\\end{equation}\n\nDepending on the nature of the pumps two different types of solutions are obtained for Eq. (\\ref{eq:diffeq}). In the most common situation of systems with lumped pumps the pumping speed $\\mathcal{S}$ is non-zero only for short sections of the system. In-between these pumps the pressure distribution follows a quadratic function with a maximum half-way between a pair of pumps that are installed at a distance $l$:\n\n\\begin{equation}\nP(s) = \\frac{ql}{S}+ \\frac{q}{8\\mathcal{C}} \\left(l^2-4s^2\\right).\n\\label{eq:qprofile}\n\\end{equation}\n\nPeak pressure and average pressure for this situation are given by:\n\n\\begin{equation}\nP_\\RM{avg} = ql\\,\\left(\\frac{1}{S}+\\frac{l}{12\\,\\mathcal{C}}\\right), \\quad\nP_\\RM{max} = ql\\,\\left(\\frac{1}{S}+\\frac{l}{8\\,\\mathcal{C}}\\right).\n\\label{eq:aprofile}\n\\end{equation}\n\nThese functions have two terms. Even with infinite pumping speed (left term) the pressure is still limited by the conduction of the vacuum vessel. The economy of a technical solution is thus to be optimized w.r.t. density and size of the vacuum pumps, and the transverse dimensions of the vacuum vessel that determine the specific conductance.\nBesides lumped pumps, also distributed pumps are used in accelerator vacuum systems. Distributed pumps can be realised by NEG strips or NEG coating, and by distributed ion sputter pumps that utilize the magnetic field of accelerator magnets. For the case of non-zero pumping speed we obtain an exponential solution of Eq. (\\ref{eq:diffeq}). At some distance from neighboured sections the pressure in a long section with distributed pumps approaches a value of $P=q\/\\mathcal{S}$. Figure\\,\\ref{fig:v2} shows an exemplary calculation of a pressure distribution with lumped pumps in the right part and a long distributed pump in the left part of the graph.\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.925\\textwidth]{Fig_04_Vac.png}\n\\caption{Simulated pressure profile in the upper part of the image. The lower part shows the pumping speed along the beamline. A $d=10\\,$cm beam pipe is assumed for this demonstration. While the left section contains a 20m long distributed pump, the  right section has 5 lumped pumps installed.}\n\\label{fig:v2}\n\\end{figure}\n\nPressure profiles can also be calculated in a numerical approach using matrix multiplications \\cite{ziemann}: \n\n\\begin{eqnarray}\n\\left(\\begin{array}{c} P(l) \\\\ Q(l) \\end{array} \\right) & = &\n\\left( \\begin{array}{cc}\n\\cosh(\\alpha l) & -\\frac{1}{c\\alpha} \\sinh(\\alpha l) \\\\\n-\\alpha c \\sinh( \\alpha l) & \\cosh(\\alpha l) \\end{array} \\right)\n\\left( \\begin{array}{c} P(0) \\\\ Q(0) \\end{array} \\right)\n+ \\frac{q}{\\alpha} \\left(\n\\begin{array}{c} \\frac{1-\\cosh(\\alpha l)}{\\alpha c} \\\\\n\\sinh(\\alpha l)  \\end{array} \\right). \\hphantom{8888} \n\\label{eq:matrix}\n\\end{eqnarray}\n\nHere the variable $\\alpha = \\sqrt{\\mathcal{S}\/\\mathcal{C}}$ was introduced. For sections without pumping, $\\mathcal{S}=0$, the elements containing $\\alpha$ in Eq. (\\ref{eq:matrix}) have to be taken in the limit $\\alpha\\rightarrow 0$, leading to the quadratic profile Eq. (\\ref{eq:qprofile}). So far we have considered the static situation of equilibrium pressure profiles. This is a special case of the general time dependent diffusion equation: \n\n\\begin{equation}\n\\mathcal{V} \\d{}{t} P(s,t) = \\d{}{s}\\,\\mathcal{C}\\,\\d{}{s}\\,P(s,t)\n-\\mathcal{S}P(s,t) + q.\n\\label{eq:timediff}\n\\end{equation}\n\nThe specific volume $\\mathcal{V}$ denotes the volume of the vessel per unit length. This equation describes also dynamic evolutions of the pressure profile, for example when He gas is injected for reasons of leak search. By comparison with a classical diffusion equation $\\d{}{t} f(x,t) = \\d{}{x}\\,\\mathcal{D}\\,\\d{}{x} f(x,t)$ that is known from the literature, we identify the~diffusion coefficient of our problem as:\n\n\\begin{equation}\n\\mathcal{D} = \\frac{<\\Delta x^2>}{<\\Delta t>} = \\frac{\\mathcal{C}}{\\mathcal{V}}.\n\\label{eq:diffcoeff}\n\\end{equation}\n\nUsing this parameter one can estimate that it takes 3 seconds for He gas to travel a 5\\,m distance in a 2\\,cm pipe. Figure\\,\\ref{fig:diff_He} shows the time evolution of the pressure distribution for a Delta-function like inlet of He gas in such a pipe.\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.85\\textwidth]{Fig_05_Vac.png}\n\\caption{A pressure bump of He in this example diffuses in a 2\\,cm diameter tube at limited speed.}\n\\label{fig:diff_He}\n\\end{figure}\n\nThe shown analytic calculations allow one to estimate the pressure in vacuum systems and to calculate the required number of pumps and their distance. For complex geometries Monte Carlo methods for pressure calculations might be more accurate. The code MolFlow \\cite{molflow} follows individual gas molecules on their scattered path through a vacuum system, including sticking probabilities and sojourn times. Pressure and other variables are then calculated as statistical averages. For lepton storage rings the~code may be augmented by another code, SynRad \\cite{synrad}, which allows to simulated the photo desorption process.\n\n\\section{Requirements for Accelerator Vacuum Quality}\n\nIn order to assess the required vacuum quality in terms of pressure or density it is necessary to study the~different mechanisms of beam gas interaction. Scattering of beam particles may lead to immediate loss of beam particles, or to a degradation of the beam properties. The number of lost particles $\\Delta N_b$ from a beam passing through a section of length $\\Delta l$ can be estimated in the following way:\n\n\n\\begin{eqnarray}\n\\Delta N_b & = & -N_b \\times \\frac{\\mathrm{area\\,of\\,molecules}}{\\mathrm{total\\,area}} \\nonumber \\\\\n& = & -N_b \\times \\frac{n_v V \\sigma}{V\/\\Delta l} \\nonumber \\\\\n& = & -N_b n_v \\sigma \\Delta l \\nonumber \\\\\n& = & -N_b n_v \\sigma \\beta c \\Delta t \\, . \\nonumber\n\\label{eq:cross}\n\\end{eqnarray}\n\nHere $\\sigma$ is the cross section of a generic interaction process, $N_b$ is the number of beam particles and $n_v$ is the volume density of the residual gas. In case the considered scattering mechanism leads to the loss of the particle, and by converting this relation into a differential equation, the solution is given by an exponential decay of the beam intensity:\n\n\\begin{equation}\nN_b(t) = N_0 \\exp \\left( - \\sigma \\beta c n_v \\, t \\right), \n~\\tau = \\frac{1}{\\beta c \\, \\sigma \\, n_v}.\n\\label{eq:diffcoeff}\n\\end{equation}\n\nThe beam lifetime $\\tau$ is deduced from the exponential solution, and for most situations we can safely assume $\\beta=1$. In the following we consider the effect of different scattering mechanisms for electrons and protons.\\hfill\\\\\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.85\\textwidth]{Fig_06_Vac.png}\n\\caption{A beam with $N_b$ particles passes through a volume with residual gas density $n_v$. The gas molecules exhibit an effective cross section $\\sigma$ that describes the interaction probability with the beam for specific processes.}\n\\label{fig:beam_gas}\n\\end{figure}\n\n\\subsection{Coulomb Scattering for Electrons}\n\n\\noindent\nThis process is described by the well known formula for Rutherford Scattering, which gives the differential cross section for the occurrence of a scattering angle $\\theta$:\n\n\\begin{equation}\n\\frac{d\\sigma_i}{d\\Omega} = \\frac{Z_i^2\\,r_e^2}{4\\gamma^2}~\n\\frac{1}{\\sin^4(\\theta\/2)}.\n\\label{eq:rutherford}\n\\end{equation}\n\nThe charge of the residual gas atom is $Z_i$ and $r_e=2.8\\,$fm the classical electron radius. If we integrate this differential cross section from the angle $\\theta_0$ above which particles are lost to $\\pi$ and use $\\theta_0 \\ll 1$, the total elastic scattering cross section for particle loss is:\n\n\\begin{equation}\n\\sigma_{i, \\RM{el}} = \\frac{2\\pi\\,Z^2_i\\,r_e^2}{\\gamma^2}~\n\\frac{1}{\\theta_0^2}.\n\\label{eq:elastic}\n\\end{equation}\n\nThe limiting angle $\\theta_0$ can be estimated from a typical value for the $\\beta$-function $\\overline{\\beta_y}$ and the minimum aperture $A_y$ of the accelerator: $\\theta_0 = A_y\/\\overline{\\beta_y}$. Using the parameters for the vertical plane is sufficient since the vertical aperture is usually smaller than the horizontal one in electron storage rings. Average values of the $\\beta$ functions at the locations of particle scattering and particle loss have to be used. Combining the~above relations and carrying out the sum over different atom species we obtain the following formula for the beam lifetime due to elastic scattering:\n\n\\begin{equation}\n\\tau^{-1}_\\RM{el} = \\frac{2\\pi r_e^2 c}{\\gamma^2}~\n\\frac{\\overline{\\beta_y}^2}{A_y^2} \\sum_i n_i \\sum_j k_{ij} Z_j^2.\n\\label{eq:telastic}\n\\end{equation}\n\nHere $k_{ij}$ is the number of atoms of type $j$ within the molecule of type $i$. By inserting numbers for the fundamental constants and expressing the gas density in terms of pressure at room temperature we obtain the following formula for the beam lifetime in electron rings due to elastic scattering:\n\n\\begin{equation}\n\\tau_\\RM{el}\\,[\\RM{h}] = 2839~\\frac{E^2\\,[\\RM{GeV}^2]\\,\\,A_y^2\\,[\\RM{mm}^2]}\n{\\overline{\\beta_y}^2\\,[\\RM{m}^2]}~\n\\left( \\sum_i P_i\\,[\\RM{pbar}] \\sum_j k_{ij} Z^2_j \\right)^{-1}.\n\\label{eq:handy}\n\\end{equation}\n\nNote that the quadratic function of $Z$ causes a sensitive dependence of the beam lifetime on the~presence of heavy gas species in the gas composition.\\hfill\\\\\n\n\\subsection{Bremsstrahlung} \\noindent\nDue to deceleration of a beam particle in the Coulomb field of a residual gas atom and the emission of a high energy photon, the particle may leave the energy acceptance of the accelerator. The important parameter in this context is the largest allowed relative energy deviation for the particles to stay confined within the beam: $\\delta_E = \\Delta E\/E_0$.  The cross section for the inelastic process is\n\n\\begin{equation}\n\\sigma_\\RM{inel} \\approx -\\frac{4}{3}\\,\\, \\frac{V_n}{N_A}\\,\\,\\frac{1}{X_0}\\,\\ln\\,\\delta_E.\n\\label{eq:inelastic}\n\\end{equation}\n\nFrom this the following lifetime $\\tau_\\RM{brems}$ is computed. For a gas mixture one has to sum up contributions of gas species with their partial pressures $P_i$ and corresponding radiation lengths $X_{0,i}$. \n\n\\begin{eqnarray}\n\\frac{1}{\\tau_\\RM{brems}} & = & -\\frac{4}{3}~\\frac{c}{P_n}\\ln(\\delta_E)~ \\sum_i \\frac{P_i}{X_{0,i}} \\nonumber \\\\\n\\tau_\\RM{brems}\\,[\\RM{h}] & = & \\frac{-0.695}{\\ln(\\delta_E)}\\,\\left(\\sum_i \\frac{P_i\\,[\\RM{pbar}]}{X_{0, i}\\,[\\RM{m}]}\\right)^{-1}.\n\\label{eq:brems}\n\\end{eqnarray}\n\n$N_A$ is the Avogadro constant and $V_n=22.4\\,$l\/mol, $P_n$ the molar volume and the pressure under standard conditions. The \\emph{radiation length} $X_0$ is the length over which a particles energy has dropped by a factor $1\/e$. $X_0$ scales roughly inversely proportional to the square of the nuclear charge of the~residual gas, and also inversely proportional to its density.  Radiation length values for common gases under normal conditions are tabulated for example in Ref. \\cite{pd}. In Table \\ref{tab:radlength} we list $X_0$ for the important gases of accelerator vacuum systems. With common energy acceptance and transverse acceptance of storage rings, the mechanism of Bremsstrahlung is the more severe mechanism for loss of particles from the~beam. \n\n\n\\subsection{Emittance Growth for Hadrons} \\noindent\nFor a proton or ion beam already the degradation of the beam emittance from elastic gas scattering at small angles is harmful. Due to the absence of radiation damping any decrease of the beam density over the storage time cannot be recovered. For the beam emittance a growth time can be defined:\n\n\\begin{equation}\n\\frac{1}{\\tau_\\varepsilon} = \\frac{1}{\\varepsilon_x}~\\frac{d\\varepsilon_x} {dt}.\n\\label{eq:emmlife}\n\\end{equation}\n\nThe scattering causes a diffusive growth of the mean squared angular deviation of the particles momentum vector which is linear in time.  The emittance growth is related to this angle as follows ($\\theta_0$ is the rms scattering angle projected on a transverse plane):\n\n\\begin{equation}\n\\frac{d\\varepsilon}{dt} = \\frac{1}{2}~\\overline{\\beta_y}~\\frac{d(\\theta_0^2)}{dt} = \n\\frac{1}{2}~\\overline{\\beta_y}~\\frac{(13.6)^2}{(cp)^2\\,[\\RM{MeV}^2]}~\\frac{c}{P_0}~\n\\sum_i \\frac{P_i}{X_{0,i}}.\n\\label{eq:emmgrowth}\n\\end{equation}\n\nUsing Eq. (\\ref{eq:emmlife}) the resulting emittance growth time for protons is:\n\n\\begin{equation}\n\\tau_\\varepsilon\\,[\\RM{h}] \\approx 34.2~\\frac{\\varepsilon_y\\,[\\RM{m\\,rad}]\\,\nE^2\\,[\\RM{GeV}^2]\\,T\\,[\\RM{K}]}{\\overline{\\beta_y}\\,[\\RM{m}]}~\\left(\n\\sum_i \\frac{P_i\\,[\\RM{pbar}]}{X_{0, i}\\,[\\RM{m}]}\\right)^{-1}.\n\\end{equation}\n\nThe temperature $T$ has been included since proton accelerators often use superconducting magnets and cold beam pipes. The described mechanism ignores other elastic scatting mechanisms besides Coulomb scattering. \\hfill\\\\\n\n\\subsection{Inelastic Scattering for Hadrons}\n\nAnother process is the complete removal of particles from the beam by an inelastic reaction. The beam lifetime for this effect can be computed using the inelastic interaction length $\\lambda_\\RM{inel}$ which is also tabulated in Table\\,\\ref{tab:radlength}:\n\n\\begin{equation}\n\\frac{1}{\\tau_\\RM{inel}} = \\frac{\\beta c}{P_0}~\n\\sum_i \\frac{P_i}{\\lambda_{\\RM{inel},i}}.\n\\label{eq:tauinel}\n\\end{equation}\n\nThe inelastic interaction length is related to the corresponding nuclear cross section via $\\lambda_\\RM{inel} = A\/\\rho\\,N_A\\,\\sigma_\\RM{inel}$, where $A$ is the molar mass and $\\rho$ the density. If we again include the gas temperature and take out all constants we obtain the following formula for the inelastic beam-gas lifetime:\n\n\\begin{equation}\n\\tau_\\RM{inel}\\,[\\RM{h}] = 3.2\\cdot10^{-3}~T\\,[\\RM{K}]\\,\\left(\n\\sum_i \\frac{P_i\\,[\\RM{pbar}]}{\\lambda_{\\RM{inel}, i}\\,[\\RM{m}]}\\right)^{-1}.\n\\end{equation}\n\n\\begin{table}\n\\begin{center}\n\\caption{Radiation length $X_0$ and inelastic interaction length $\\lambda_i$ \nfor different gases under atmospheric pressure and 20\\,$^\\circ$C \\cite{pd}.}\n\\label{tab:radlength}\n\\begin{tabular}{|l|cc|cc|cc|cc|cc|cc|cc|cc|cc|c|}\n\\hline\\hline\n&& \\textbf{H}$_\\textbf{2}$ && \\textbf{He} && \\textbf{CH}$_\\textbf{4}$ && \\textbf{H}$_\\textbf{2}$\\textbf{O} &&\\textbf{CO}&&\\textbf{N}$_\\textbf{2}$&&\\textbf{Ar}&&\\textbf{CO}$_\\textbf{2}$&&\\textbf{air} \\\\\n\\hline\nA && 2   && 4  && 16     && 18     &&28&& 28  &&40&&44    &&     \\\\\n$X_0$\\,[m] && 7530 && 5670 && 696 && 477 && 321&&326&&117&&196&& 304    \\\\\n$\\lambda_\\RM{inel}$\\,[m]&&6107&&3912&&1103&&1116&&763&&753&&704&&490&&747 \\\\\n\\hline\\hline\n\\end{tabular} \\end{center}\n\\end{table}\n\n\\section{Vacuum Technology for Accelerators}\n\\subsection{Pumping}\n\\label{pumping}\n\nAs discussed in the previous sections the average pressures required for accelerators range from $10^{-6}\\,$mbar down to $10^{-11}\\,$mbar. For facilities of large size, containing a huge number of components, reliability of the overall system becomes a critical aspect. Pumps without moving mechanical parts are thus advantageous. Figure\\,\\ref{fig:pumps} shows an overview of the most commonly used types of pumps in large accelerator systems. Initial pumpdown of accelerator vacuum systems is often done by turbo-molecular pumps in combination with rotary pumps that are installed on mobile pump carts. During normal operation these are disconnected while the required vacuum conditions are maintained by sputter ion pumps, titanium sublimation pumps (TSP) and non-evaporable getter (NEG) pumps. These types of pumps are almost exclusively used for routine operation in storage rings and large linear accelerators. \n\n\\begin{figure}\n\\centerline{\\includegraphics[width=0.9\\textwidth]{Fig_07_Vac.png}}\n\\caption{Overview of the most commonly used types of pumps and gauges in large accelerator vacuum systems including their operating range.} \n\\label{fig:pumps}\n\\end{figure} \n\n\\emph{Turbo-molecular pumps} are fully mechanical pumps, based on a mechanism to transfer physical momentum to residual gas molecules in a preferred direction. The momentum transfer is achieved through fast moving blades with rotation frequencies of $30\\dots60\\cdot 10^3\\,$ RPM (rounds per minute). At these rotation frequencies the blades reach a speed of $300\\dots600\\,$m\/s, which is to be compared with the speed of the residual gas molecules that should ideally not escape the blades. At room temperature heavier molecules like CO have a speed of $470\\,$m\/s, while hydrogen moves at $1800\\,$m\/s. Consequently the compression ratio (gas density ratio) achieved with a turbo-molecular pump may vary by several orders of magnitude for these gas species. Turbo-molecular pumps are always combined with mechanical roughing pumps that provide an intermittent vacuum level between UHV conditions and the normal atmospheric pressure.\n\n\\emph{Sputter ion pumps} are capable of pumping all gases and they can be operated at relatively high pressure. These pumps use penning cells with an applied high voltage of 3\\dots7\\,kV and a superimposed magnetic field. Permanent magnet blocks are used to generate the magnetic field. Residual gas molecules are ionized and accelerated in the electric field. The current drawn from the high voltage power supply is thus proportional to the residual gas pressure. This synergy is often used to measure the pressure in accelerators in a cost effective way. Hydrogen is pumped by diffusion into the bulk of the cathodes. All other reactive gases are chemisorbed by the cathode material. A commonly used material is titanium, which is sputtered onto the walls and anodes by the ions upon incident on the cathodes. Noble gases are physically buried by the sputtered cathode atoms. The pumping speed for noble gases is small, but it can be increased to values of $25-30\\,$\\% of that for N$_2$ replacing the cathode plate by heavy material such as tantalum. Such \\emph{noble diodes} are often used in systems with enhanced risk of helium leaks as in accelerator sections \nusing superconducting magnets or resonators cooled with liquid helium.\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.75\\textwidth]{Fig_08_Vac.png}\n\\caption{Penning cells are elements in ion sputter pumps to ionize residual gas molecules. In a combined electric and magnetic field electrons are accelerated on spiral paths, thereby enhancing their efficiency to ionize neutral gas molecules. Ions are then also accelerated and implanted in the cathod material or burried under sputtered metal on the anodes.}\n\\label{fig:penning}\n\\end{figure}\n\nA cost effective solution are so-called integrated sputter ion pumps inserted linearly into a channel parallel to the beam channel \\cite{cummings}, \\cite{koupt}. These pumps utilize the magnetic field of the bending magnets of the accelerator. This solution has been adopted at the electron ring of HERA, PETRA, PEP and TRISTAN reaching typical pump speeds of $25\\,$l\/s\/m. On the downside this couples the functions of the accelerator magnets and the vacuum system. Magnets must be powered to maintain pumping. In-between ramp cycles of storage rings these pumps are not active. Furthermore the magnetic field intensity is decreased when the particles are injected at lower energies, resulting in a reduced pumping speed. This becomes crucial for accelerators where the injection energy and thus the corresponding magnetic field are much lower than the nominal beam energy, such that the discharge in the sputter ion pumps extinguishes. Thus additional pumps are required to ensure good vacuum conditions. \n\n\\emph{Titanium sublimation pumps} are sorption pumps. In a metallic vessel titanium\nis evaporated by temporary electrical heating and deposited on the walls, forming a getter surface. These pumps exhibit a~high pumping speed for active gases but have limited pumping capacity since the thin titanium film saturates quickly. The pumping surface is renewed\nby deposition of fresh titanium from a heated filament by sublimation. A pump with $1000\\,$l\/s pumping speed is saturated after one hour at a pressure of $10^{-7}\\,$mbar. Titanium sublimation pumps cannot pump noble gases and are therefore used in combination with a low pumping speed ion sputter pump. Often a chicane is incorporated in the pumping port, to avoid that titanium atoms enter the beam chamber or contaminate surfaces, e.g. mirrors, ceramic insulators or instrumentation.  \n\n\\emph{Non-evaporable getter (NEG) pumps} are sorption pumps as well. The NEG material is made of special alloys which forms stable chemical compounds with the majority of active gas molecules. The~sorption of hydrogen is reversible by heating of the material. Also NEG pumps have a limited pumping capacity. The NEG material is activated by heating for times below one hour. Activation temperatures depend on the NEG material and range from $180^\\circ$C to $400^\\circ$C. During heating the gas molecules are not evaporated from the NEG material, but the molecules diffuse into the bulk material. Hydrogen is an exception, which is released again into the gas phase, thus requiring other pumps during the process of activation and reactivation. The heating produces fresh surface sites for further adsorption of active gases. The NEG material is a compound of different metals, for example Zircon, Vanadium, Iron, and is typically sintered in the form of a powder onto flexible strips. Such strips can be integrated in a side channel of the vacuum chamber design. The initial specific pumping speed provided by such schemes may exceed 1000\\,l\\,s$^{-1}$\\,m$^{-1}$. This technique has been developed for LEP \\cite{ben-NEG} and is now applied in many accelerators. At LEP about 24 km of the beam pipe have been equipped with 30\\,mm wide and 0.2\\,mm thick constantan ribbons coated with 0.1 mm thin NEG material on both sides. A newer application for the synchrotron light source PETRA-III is shown in Fig.\\,\\ref{fig:chamber}. The strips are installed onto a~rigid stainless steel carriage via insulating ceramics inside a separate pump channel. For electric heating the pumps are connected to current feedthroughs. NEG pumps are also available commercially as lumped pumps, cartridge units that can be connected to recipients by standard flange connections.\n\nAnother approach to the NEG pumping concept is the deposition of thin film coatings of TiZrV, sputtered onto a vacuum chamber. The activation temperature of these coatings is relatively low, a fact that is important to limit the thermal stress on the vacuum system during activation \\cite{Benvenuti-coating-1}, \\cite{Benvenuti-coating-2}. If the~design of the vacuum chamber allows that, the coating may cover the complete inner surface of the~beam vacuum system and thus the outgassing of the vacuum vessel itself is drastically reduced. It should be emphasised that even with low activation temperature the need for baking the entire vacuum system to ca. $200\\,^\\circ$C implies severe restrictions for the design of vacuum chambers, support structures and magnets. For accelerators in which the vacuum conditions are dominated by beam induced desorption, it is possible to reduce outgassing with NEG coated surfaces in the vicinity of the particle beam. In particular for light sources NEG coated surfaces are advantageous to reach good vacuum conditions without long conditioning times \\cite{chiggiato}. Modern light sources use complex multi-bend achromat lattice cells to achieve extremely small horizontal emittances. As a result the apertures of vacuum chambers are small, and the achievable pressure is conductance limited. Lumped pumping concepts are less efficient in this situation since a large number of pumps had to be installed per unit length. Today it is common for such light sources to use NEG coating for efficient pumping of the narrow beam chambers. Also hadron accelerators benefit from NEG coated chambers through the reduction of the secondary emission yield of electrons \\cite{wfischer}.\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.85\\textwidth]{Fig_09_Vac.png}\n\\caption{Concept view of a vacuum chamber with integrated NEG pump for an electron beam storage ring. The~aluminum profile is extruded with integrated cooling channels. The synchrotron radiation is absorbed on the left side of the chamber, while the right side contains the NEG strip (blue) in a side channel, which is shielded from direct view to the beam to suppress capture of dust particles (courtesy DESY).}\n\\label{fig:chamber}\n\\end{figure}\n\n\\emph{Cryo pumps} use the effect of cryosorption to bind gas molecules on cold surfaces inside the pump vessel. With sufficiently low temperature these pumps can remove all gas species and they provide high pumping speed and capacitance. On the downside cryo pumps must be regenerated by regular warm-up cycles, for which the accelerator operation must be interrupted. During the regeneration cycle all pumped gases are released again, and are typically removed from the vacuum system by turbo molecular pumps. A concept sketch of a cryo pump is shown in Fig.\\,\\ref{fig:cryo}.\n\nFor performance reasons many accelerators make use of superconducting magnets or superconducting accelerating structures. With the beam pipe being integrated into the cryostat this leads to a \\emph{cold bore} vacuum system, which takes on the characteristics of a huge cryopump. Design and operation of such cold bore vacuum systems have many specific implications \\cite{grobner}.\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.575\\textwidth]{Fig_10_Vac.png}\n\\caption{Concept view of a cryo pump with a large aperture flange connection on the top side (courtesy Lothar Schulz, PSI).}\n\\label{fig:cryo}\n\\end{figure}\n\n\\subsection{Instrumentation} \\label{instrumentation}\n\nAccelerator based research infrastructures are expensive installations, they use a lot of grid energy and their operation should be efficient and reliable. Also for vacuum systems it is therefore important that the integrity of the system is continuously monitored and problems like leaks or regions of unusual high pressure resulting from beam impact can be identified quickly to allow fast and targeted intervention. Using gate valves the beam vacuum system of accelerators is divided into several sections. In this way it is possible to exchange components without venting the entire facility. Fast shutters, capable to stop shock waves in milliseconds, are commonly used to avoid contamination of sensitive sections caused by a sudden break of the vacuum system.\n\nEach of the segments of a larger vacuum system should have at least one gauge to monitor the~integrated residual gas pressure. Total pressure gauges are included in Fig.\\,\\ref{fig:pumps} with their operating range. For practical operation it is usually not necessary to obtain precise absolute measurements, but to be able to diagnose relative changes over time and to compare sections with each other. Cold cathode gauges or Bayard-Alpert gauges are frequently used at low pressures. Current monitoring of sputter ion pumps is a~cost effective method, particularly for large facilities to monitor the residual gas pressure down to levels of $10^{-9}\\,$mbar. \n\nUsing quadrupole mass spectrometers the residual gas composition in a vacuum system can be analysed. The relative occurrence of molecule masses is determined, which allows to diagnose problems in an accelerator vacuum system. For example it can be determined whether a leak or a contamination is the reason for unusually high pressure. Such residual gas analysers (RGA) are typically not part of a standard installation, but these are temporarily connected to the recipient. Often the sensitive electronics is not compatible with the radiation environment of the stray magnetic fields of an accelerator in operation. \n\n\\subsection{Materials and Technology Choices for Accelerator Vacuum Systems}\n\nFor large facilities production cost can be optimized by a careful design and by utilization of industrial manufacturing processes. For example extrusion processes serve as a cost effective method to produce large lengths of beam pipe profiles. Over time a wide variety of best practices have been developed for accelerator vacuum systems and more details may be found for example in Ref. \\cite{CERN}.\n\nMaterials for the manufacturing of beam chambers and other beam vacuum components have to be selected carefully according to the specific requirements of each accelerator. A significant number of aspects must be addressed in parallel. The air pressure under normal conditions on a surface area of $10\\times10\\,\\RM{cm}^2$ results in a force equivalent to the weight of 100\\,kg. Consequently mechanical robustness is already one important criterion for a vacuum chamber, while the costly aperture of accelerator magnets might favour a thin wall solution. Vacuum chambers should be bake-able and thus stability must be guaranteed also at elevated temperatures. The magnetic guide field for the beam should not be disturbed by magnetic properties of the beam chamber. If synchrotron radiation is deposited on the chamber wall a high thermal conductivity is desirable. And the transport of beam image currents in the chamber walls requires good surface conductivity and smooth electrical connections across components. For machines susceptible to electron cloud instabilities the secondary electron emission yield of the material should be low. Last but not least the compatibility with UHV vacuum conditions and low outgassing rates are important. The requirement of UHV class pressure in combination with resistance to radiation and corrosive atmospheres demands all metal solutions for beam vacuum system.  \n\nStainless steel, copper or aluminum are the most common vacuum chamber materials. Electrical and thermal conductivity are by factors better for copper and aluminum surfaces compared to steel. On the other hand the mechanical strength of steel is outstanding. Copper and aluminum alloys exhibit better mechanical strength than the pure metals, at the expense of somewhat lower conductivity. A~few properties for common materials are listed in Table\\,\\ref{tab:materials}. Joining techniques for materials of vacuum systems include inert gas shielded arc welding, electron-beam welding, laser beam welding as well as brazing in a~furnace. Laser and electron beam welding can deposit large amounts of heating power to a~small volume in a short time. These technologies can be used advantageously for welding of sensitive components that allow only local heating while another part of the component must be kept at moderate temperature.\n\n\\begin{table}\n\\begin{center}\n\\caption{Properties of materials that are utilized for accelerator vacuum components.} \n\\label{tab:materials}\n\\begin{tabular}{|l|cc|cc|cc|cc|} \n\\hline\\hline\n                      && \\textbf{density}    && \\textbf{thermal}      && \\textbf{electrical}         && \\textbf{yield}      \\\\   \n                      &&            && \\textbf{conductivity} && \\textbf{conductivity}       && \\textbf{strength}   \\\\   \n\t                  && \\textbf{[g\/cm}$^3$] && \\textbf{[W\/K\/m]}      && \\textbf{[10}$^6\/ \\Omega$\\textbf{\/m]} && \\textbf{[N\/mm}$^2$] \\\\ \\hline \nstainless steel 316LN && 8.00  \t    && 16     \t    && 1.35 \t\t      && 205        \\\\ \naluminum pure         && 2.70\t    && 235     \t    && 37  \t\t          && 35         \\\\  \nAlMgSi0.5             && 2.70       && 200          && 30  \t\t          && 70-150     \\\\  \ncopper pure           && 8.95       && 394          && 58  \t\t          && 40-80      \\\\ \nCu\\,Sn$_2$            && 8.90       && 140          && 25  \t\t          && 150        \\\\ \n\\hline\\hline\n\\end{tabular} \\end{center}\n\\end{table}\n\nAluminum or copper are favoured for electron facilities due to their high thermal conductivity. The synchrotron radiation can be absorbed directly by the vacuum chamber if the power line-density is not exceeding values of $\\approx 100\\,$W\/m. With appropriate water cooling of the chamber a power load of several 10\\,kW\/m can be accepted. For intense synchrotron radiation fans with a shallow height the temperature profile should be simulated. The often quite elaborate beam pipe cross sections in combination with pumping and cooling ducts can be economically produced by continuous extrusion as shown in the example of Fig.\\,\\ref{fig:chamber}. More complex chambers are produced from solid blocks, which is associated with higher manufacturing cost. Neighboured chambers may be connected by aluminum flanges in combination with Helicoflex$^\\RM{TM}$ gaskets. Alternatively aluminum\/stainless steel transitions, for example made by explosion bonding, allow the usage of standard stainless steel Conflat$^\\RM{TM}$ flanges. Overall the sealing of aluminum systems is not as reliable as the standard stainless steel system with copper gaskets. \n\nIn some cases copper or copper alloy chambers are used to benefit from the even higher conductivity compared to Al. Examples include the accelerator facilities HERA-e, KEK-B and PEP. Brazing techniques are typically applied to join copper components and to connect stainless steel flanges. Massive water cooled copper blocks are often used as collimators or absorbers for synchrotron radiation at locations of high power density.   \n\nFor proton accelerators austenitic stainless steel has become the most widely used material. Beam pipes are often fabricated from seamless tubes with discrete pumps attached every few meters. For sealing usually welded stainless steel flanges and copper Conflat$^\\RM{TM}$ gaskets are used. Only metal sealed flange connections allow to achieve leak rates compatible with UHV conditions and radiation resistance at the same time. A concept sketch of the Conflat system is shown in Fig.\\,\\ref{fig:conflat}.\n\n\\begin{figure}\n\\centerline{\\includegraphics[width=1.0\\textwidth]{Fig_11_Vac.png}}\n\\caption{In a Conflat$^\\RM{TM}$ metal sealed flange connection the copper seal is clamped between two stainless steel flanges that contain a knife edge.} \n\\label{fig:conflat}\n\\end{figure} \n\nFor accelerators with superconducting magnets the vacuum chamber is often also operated at low temperature, since there is no room for thermal insulation in the tight space between the magnet coils. Examples include the proton ring of HERA\/DESY, RHIC at Brookhaven and LHC at CERN. The~cool down over a large temperature range from room temperature to an operating temperature of, for example, $4.5\\,$K presents another challenge for the beam vacuum system. A system of bellows and space for expansion must be foreseen to handle the mechanical contraction. Usually the beam pipes are made from a type of stainless steel with the inner surface coated by copper to enhance the thermal conductivity. \n\nFor electrical feedthroughs into vacuum ceramics are used as insulators. In some cases ceramics are used for entire vacuum chambers. This is necessary if the chamber is to be placed in rapidly changing magnetic fields, and in a metallic chamber strong eddy currents would be induced. Applications include for example kicker magnets and rapid cycling synchrotrons \\cite{csns}. Beam chambers inside particle physics detectors should influence particles generated at the interaction point as less as possible. For this purpose very thin wall tubes are used, made from low Z material, such as aluminum, beryllium or carbon fiber materials. For exit windows of beams similar solutions are common.\n\nThe beam chamber carries an image current that acts back on the beam and may deteriorate beam quality properties like emittance or energy spread. To minimize such effects the chamber should carry the~image current with low resistance, avoiding geometric discontinuities. Variations of the vacuum chamber cross section should be applied gradually using tapered sections. Bellows and openings for pumping ports must be electrically shielded. In bellows often a set of flexible, sliding spring contacts of copper-beryllium alloys is installed around their circumference. Perforated electric screens with circular holes of some millimeters diameter or longitudinal slits are used for pump ports. Of course such electrical shielding measures result in a reduction of the effective pumping speed. Also for gate valves in the open state, gaps have to be covered by spring contacts that move with the gate mechanism. Inappropriate shielding of transverse openings will not only affect the beam quality, but may  also result in the excitation of trapped RF modes, leading to a strong heating effect for vacuum components.\n\nAccelerator components installed in the vicinity of the beam pipe should be radiation resistant and must withstand corrosive atmospheres produced by the primary radiation. This includes cables and electronics, which must either be properly chosen or shielded. For high energy electron\/positron storage rings and synchrotron radiation facilities the generated X-rays may cause problems, and often the beam chamber is wrapped into a lead shield to absorb as much radiation as possible. Figure\\,\\ref{fig:att} shows the~attenuation of X-rays in various materials as function of the photon energy. Using beam energy and bending radius the critical photon energy may be estimated with the expression: \n\n\\begin{equation}\nE_c [\\RM{keV}] \\approx 2.218 ~ \\frac{E^3 [\\RM{GeV}^3]}{\\rho [\\RM{m}]}.\n\\label{crit}\n\\end{equation}\n\n\\begin{figure}\n\\centering\\includegraphics[width=0.85\\textwidth]{Fig_12_Vac.png}\n\\caption{Attenuation length for X-rays of commonly used materials for vacuum vessels and shielding as a function of photon energy.}\n\\label{fig:att}\n\\end{figure}\n\n\\section{Summary}\nThe vacuum system presents a challenging technical aspect of each particle accelerator. To achieve required beam lifetimes and beam quality, and to minimize unwanted losses of high energy particles associated with radio-activation and damage to components, vacuum systems must be carefully designed to provide the adequate low gas densities.\n\nSteps for designing an accelerator vacuum system can be roughly categorized into three groups. The first step involves an evaluation of the {\\bf gas sources} in an accelerator. This includes outgassing rates for surfaces and beam induced outgassing dynamics, such as synchrotron radiation, electron cloud, heavy ion bombardment to name a few. Certain accelerator designs require quick handling of activated components thus involving relatively leaky inflating seals. In such cases leak rates must be considered. In practice a clean and baked stainless steel surface might exhibit an outgassing rate of $q_0 = 10^{-11}\\,$mbar\\,l\\,s$^{-1}$\\,cm$^{-2}$. In the presence of synchrotron radiation and after a reasonable time of conditioning the outgassing is still dominated by releasing at least $\\eta = 10^{-6}$ gas molecules per photon incident on the chamber wall.\n\nThe second step covers the definition of the {\\bf target residual gas pressure and composition} (more precisely the gas density). Physics effects of beam gas interaction and the resulting performance degradation must be considered for this purpose. To give a couple of examples the acceptable dynamic gas pressure in an electron storage ring is in the order of $10^{-8}\\,$mbar with a typical composition of $\\sfrac{3}{4}$ H$_2$ and $\\sfrac{1}{4}$ CO. A proton cyclotron as a single pass accelerator is more forgiving and a pressure of $10^{-6}$\\,mbar is sufficient.\n\nThe third step involves then to lay out the vacuum system in terms of geometry, installed {\\bf pumping speed} and perhaps more complex technical measures like surface coating to achieve the required vacuum quality under operating conditions. Types of pumps may include turbo pumps, ion sputter pumps, NEG coating or cryo pumps for large recipients. A typical electron storage ring may be equipped with $S = 100$\\,l\/s ion sputter pumps at a distance of 5\\,m. Today software can be used to compute the pressure profile using Monte Carlo methods or numerical solutions of the diffusing Eq. (\\ref{eq:diffeq}). \nIn addition to such conceptual considerations the design of vacuum systems requires a lot of engineering. Keywords include: UHV compatible materials and materials preparation, mechanical stability, thermo-mechanical problems under heat load, pumps, gauges, flange systems and valves.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}%\n\n\\par A vast range of space and astrophysical scenarios are driven by the rapid expansion of plasmas through space. Such examples include interplanetary coronal fast ejecta~\\cite{Burlaga2001}, the expansion of the stellar material from supernova remnants~\\cite{1990ApJ...356..549S}, and artificial magnetospheric releases of tracer ions~\\cite{Krimigis1982}. When these expanding plasmas encounter obstacles of magnetic nature, the resultant interaction leads to highly nonlinear and complex dynamics. In the solar system, the interaction between the plasma flow (\\textit{i.e.} the solar wind) and planetary-sized magnetic obstacles leads to the formation of magnetospheres~\\cite{Russell1991}.%\n\n\\par The effective size of the magnetic obstacles is determined by the equilibrium position between the kinetic pressure of the solar wind and the magnetic pressure exerted by the planetary magnetic fields~\\cite{Schield1969}. The region of equilibrium, called the magnetopause, can be described using the pressure balance derived from magnetohydrodynamics (MHD)%\n\\begin{equation}\n    n_dm_{i,d}v_0^2 = \\frac{B^2}{8\\pi} \\ ,\n    \\label{eq:pressure-equilibrium}\n\\end{equation}\nwhere $n_d$ is the density of the solar wind, $v_0$ is its flow velocity, $m_{i,d}$ is the mass of its ions, and $B$ is the total magnetic field at the magnetopause. The total magnetic field can be written as $B = B_0 + B_\\textrm{dip}$, where $B_0$ is the collective magnetic field and $B_\\textrm{dip} = M \/ L_0^3$ is the magnetic field of the obstacle, often well described by a dipolar profile of magnetic moment $M$. The distance $L_0$ between the center of the dipole and the magnetopause, often referred to as the plasma standoff distance, measures the effective size of the magnetic obstacle.%\n\n\\par For planetary-sized magnetospheres, the obstacle size is typically tens of thousands of kilometers. However, magnetospheres with a few hundreds of kilometers are also observed in space environments such as the lunar surface. When the magnetic obstacle size is smaller or of the order of the ion kinetic scales of the plasma, \\textit{i.e.} the ion skin depth or the ion gyroradius, the interaction with the solar wind results in ion-scale magnetospheres, or mini-magnetospheres.%\n\n\\par The study of mini-magnetospheres in past years was mainly motivated by the observation of crustal magnetic anomalies on the lunar surface~\\cite{Lin1998,Halekas2008,Kato2010,Wieser2010,Kramer2021}. Although the Moon does not have a global magnetic field like Earth, it does have small localized regions of crustal magnetic field, of 10-100 nT over distances of 100-1000 km~\\cite{Lin1998}, which are of the same order as the gyroradius of solar wind ions near the Moon's surface. As a result, when these regions of the lunar surface are exposed to the solar wind, mini-magnetospheres are formed. The deflection of charged particles off of lunar mini-magnetospheres commonly leads to the formation of ``lunar swirl'' structures~\\cite{Bamford2012}. Similar interactions between the solar wind and small-sized patches of magnetic field also occur in other planets and natural satellites without a planetary magnetosphere, such as Mars~\\cite{Lillis2013}, Mercury~\\cite{doi:10.1126\/science.1211001}, Ganymede~\\cite{https:\/\/doi.org\/10.1029\/97GL02201}, and comets and asteroids~\\cite{https:\/\/doi.org\/10.1029\/GL011i010p01022}.%\n\n\\par Multiple experiments have been performed in laboratory environments that replicate the interaction between plasma flows and magnetic obstacles. With a proper re-scaling of parameters~\\cite{Ryutov_2002}, these experiments represent highly controlled configurations where a large variety of diagnostics can be used to obtain more accurate measurements than those obtained from the direct probing of astrophysical events. In experimental studies, fast-moving plasma flows are usually driven resorting to high-intensity lasers focused onto solid targets of plastic or metal composition~\\cite{ablated,ablated2}. These laser-ablated plasmas can be mildly collisional or collisionless, replicating astrophysical conditions~\\cite{Niemann2014a,Bondarenko2017}. By adding dipole field sources against the plasma flow, previous experiments of mini magnetospheres studied possible applications for spacecrafts~\\cite{Winglee2007,Bamford2008,Bamford2014}, the formation of lunar swirls~\\cite{Bamford2012}, and the conditions for the formation of magnetosphere features~\\cite{Brady2009,Shaikhislamov2013, Shaikhislamov2014,Rigby2018}. Although these experiments achieved important breakthroughs in the study of ion-scale magnetospheric physics, they were limited to i) 1D measurements of the magnetic field and plasma density profiles and ii) fixed properties of the obstacle and plasma flow.%\n\n\\par Numerical simulations play a key role in interpreting and designing experiments. Early MHD simulations attempted to explain the formation and characteristics of lunar mini-magnetospheres and validate experimental and analytical models~\\cite{Harnett2000,Harnett2002,Shaikhislamov2013}. Hybrid simulations were used to study the role of ion kinetic effects, and obtain conditions for the formation of magnetospheres~\\cite{Blanco-Cano2004} and replicate previous experimental results~\\cite{Gargate2008}. However, these simulations do not resolve the electron scales and do not capture important kinetic effects on the magnetosphere's boundary, \\textit{e.g.} charge separation effects and nonthermal particle distributions. Particle-in-cell (PIC) simulations were used to fully resolve the micro-physics of these systems and study its role in the formation of lunar mini-magnetospheres~\\cite{Kallio2012,Deca2014,Deca2015,Zimmerman2015,Bamford2016}, the scaling of their properties with solar wind speed and magnetic field orientation~\\cite{Deca2021} and the conditions for the formation of collisionless shocks~\\cite{Cruz2017}.%\n\n\\par In this work, we use PIC simulations of ion-scale magnetospheres to interpret the results of recent experiments~\\cite{Schaeffer2021} performed at the LArge Plasma Device (LAPD), University of California, Los Angeles. In these experiments, fast collisionless plasma flows generated by high-repetition-rate lasers were collided with the magnetized ambient plasma provided by the LAPD and with a dipolar magnetic field obstacle, leading to the formation of ion-scale magnetospheres. Using motorized probes, high spatial and temporal resolution measurements of the magnetic field allowed characterization of 2D magnetic field and current density structures. Apart from validating the experimental results, the simulations presented in this work explore a set of upstream and magnetic parameter scans and configurations not accessible in the laboratory to determine the importance of each system parameter on the magnetospheric properties. The simulations show that the background ions, and then the driver ions, are responsible for the formation of the magnetopause observed in the experiments. They also show that a reflection of the downstream magnetic compression is observed for certain parameters of the driver plasma, and that the distance between the main current features is dependent on the dipolar and driver plasma parameters. \n\n\\par This paper is organized as follows. In Sec.~\\ref{sec:experiments}, we briefly review the LAPD experiments and their main results. In Sec.~\\ref{sec:simulations}, we present PIC simulations of ion-scale magnetospheres. In Sec.~\\ref{sec:numerical-methods}, we outline the standard configuration and parameters used for the simulations. In Sec.~\\ref{sec:additional}, we provide an overview of the temporal evolution of these systems and show that the simulations agree with the results of the LAPD experiments. We discuss the origin of the structures observed in current density and magnetic field synthetic diagnostics and use particle phase spaces to interpret them. In Sec.~\\ref{sec:length}, we present the results for different lengths of the plasma flow and define the conditions required to reproduce the features observed experimentally. The coupling between the laser-ablated driver and background plasmas is characterized in Sec.~\\ref{sec:density} with simulations with different driver densities. In Sec.~\\ref{sec:momentum}, different magnetic moments are considered, and we show that the main current density features are highlighted and more easily visible for weaker magnetic obstacles.\nIn Secs.~\\ref{sec:realistic} and~\\ref{sec:finite}, we discuss and illustrate the validity of the key simplifications and approximations used for the parameter scans presented in Secs.~\\ref{sec:additional}-\\ref{sec:momentum}. Finally, we outline the conclusions of this work in Sec.~\\ref{sec:conclusions}.%\n\n\\par This paper is the second part of a two part series. Detailed experimental results are presented in Part I~\\cite{Schaeffer2021}. \n\n\\section{LAPD Experiment}\n\\label{sec:experiments}\n\n\\par A new experimental platform has been developed on the LAPD to study mini-magnetospheres. The platform combines the large-scale magnetized ambient plasma generated by the LAPD, a fast laser-driven plasma, and a pulsed dipole magnet, all operating at high-repetition-rate ($\\sim1$ Hz). In the experiments, a supersonic plasma is ablated from a plastic target and then expands into the dipole magnetic field embedded in the ambient magnetized plasma. By measuring 2D planes of the magnetic field over thousands of shots, detailed maps of the magnetic field evolution are constructed.  Additional details on the platform and results can be found in Part I.\n\n\\par Example results are shown in Fig.~\\ref{fig:experiment} for the measured change in magnetic field $\\Delta B_z = B_{z}-B_{z,\\textrm{initial}}$ and the current density $J_x = \\partial \\Delta B_z\/\\partial y$.  Here, $B_{z}$ is the total magnetic field, $B_{z,\\textrm{initial}}=B_0 + B_\\textrm{dip}$ is the total initial magnetic field, $B_0$ is the background LAPD field, and $B_\\textrm{dip}$ is the dipole magnetic field.  These results are taken along $y$ at $x=0$ from the $z=0$ plane probed experimentally. In the experiments, the dipole is centered at $(x,y,z)=(0,0,0)$ and has a magnetic moment $M=475$ Am$^2$.\n\n\\par As seen in Fig.~\\ref{fig:experiment}(a), the expanding laser-driven plasma creates a leading magnetic field compression followed by a magnetic cavity.  The cavity reaches a peak position of $y\\approx-13$ cm, while the compression propagates closer to the dipole before being reflected back towards the target.  The current density in Fig.~\\ref{fig:experiment}(b) shows two prominent structures.  Following the expansion of the magnetic cavity is a diamagnetic current, which reaches a peak position of $y\\approx-15$ cm before stagnating for approximately 1 $\\mu$s and then dissipating.  Ahead of the diamagnetic current is the magnetopause current near $y\\approx-13.5$ cm, which lasts for about 0.5 $\\mu$s.\n\n\\par Here, we aim to qualitatively model these experiments in order to address key questions that aid in the interpretation of the experimental results. In particular, simulations can explain the role of each system component in the features observed, address which plasma component (ambient or laser-driven) is responsible for the features observed and which pressure balances are most relevant. \n\n\\par For convenience, the notations used in this paper are different for the ones used in Part I. Here, we use the CGS system, and the axis system is rotated from the used in Part I.\n\n\\begin{figure}[ht]\n    \\includegraphics[width=0.85\\linewidth]{plots\/experiment.pdf}\n    \\caption{\\label{fig:experiment} LAPD experimental results for the temporal evolution of a) the variation of the magnetic field $\\Delta B_z$ and b) the current density $J_x$ at $x=z=0$. The experimental results are discussed with more detail in Part I.}\n\\end{figure}\n\n\\section{PIC simulations}\n\\label{sec:simulations}\n\n\\subsection{Configuration of the simulations} \\label{sec:numerical-methods}\n\n\\par Motivated by the results of experiments described in Sec.~\\ref{sec:experiments}, we performed 2D simulations with OSIRIS, a massively parallel and fully relativistic PIC code~\\cite{Fonseca2002,Fonseca2013}. With PIC simulations, we can accurately resolve the plasma kinetic scales characteristic of mini-magnetospheres dynamics.%\n\n\\par The numerical simulations presented in this work stem from a simplified description of the LAPD experimental setup, represented in Fig.~\\ref{fig:config}. In these simulations, a driver plasma moves against a background plasma permeated by a uniform magnetic field $\\mathbf{B_0}$ and a dipolar magnetic field $\\mathbf{B_{dip}}$. $\\mathbf{B_0}$ and $\\mathbf{B_{dip}}$ are oriented along the $z$ direction and are transverse to the driver plasma flow. Since the most relevant dynamics of the simulations occurs at the ion kinetic scales, all the spatial scales are normalized to the ion skin depth of the background plasma $d_i=c\/\\omega_{pi}=\\sqrt{m_{i,0}c^2\/4\\pi n_0e^2}$, where $c$ is the speed of light in vacuum, $\\omega_{pi}$ is the ion plasma frequency, $m_{i,0}$ is the mass of the background plasma ions, $n_0$ is the background density, and $e$ is the electron charge. In turn, the temporal scales are normalized to $1\/\\omega_{ci}$, where $\\omega_{ci} = eB_0\/m_{i,0}c$ is the ion cyclotron frequency of the background. The simulation box is a 12 $d_i$ $\\times$ 12 $d_i$ area with open and periodic boundary conditions in the $x$ and $y$ directions, respectively. The flow is in the $x$ direction and the size of the simulation domain in the $y$ direction is large enough to avoid re-circulation of the particles through the whole interaction. The simulations considered 25 particles per cell per species. To resolve the dynamics of the electron kinetic scales, we used 10 grid cells per electron skin depth $d_e=d_i\\sqrt{m_e\/m_{i,0}}$ in both $x$ and $y$ directions, where $m_e$ is the electron mass.\n\n\\begin{figure}[ht]\n    \\includegraphics[width=0.85\\columnwidth]{plots\/config.pdf}\n    \\caption{\\label{fig:config} Schematic illustration of the initial setup of the 2D PIC simulations performed. The system considers a vacuum region at the left, a driver plasma (I) of density $n_d$ and length $L_x$, travelling to the right with flow velocity $v_0$, and a background plasma (II) with constant density $n_0$ and with an internal magnetic field $B_0$. A dipole is included at the center of the background region. Both the uniform and the dipolar magnetic fields are oriented in the $z$ direction. An illustration of the effective magnetic obstacle created by the dipole and of the magnetic field profile at $y=0$ are also shown in a dashed circumference and in a solid black line, respectively.}%\n\\end{figure}\n\n\\par The driver plasma, shown in region I in Fig.~\\ref{fig:config}, represents ideally the plasma ablated from the plastic target in the experiments. We assume that this driver has a length $L_x$ that is typically 2 $d_i$, and a width $L_y$ that is typically infinite. It has a constant density $n_{d}$, and it is initialized moving to the right side with initial flow velocity $v_0$. The driver is composed of an electron species and a single ion species, with ion mass $m_{i,d}$. Because the driver plasma is reflected during the interaction with the background, an empty region at the left of the driver was added to accommodate the reflecting particles.%\n\n\\par The background plasma is represented in region II. It is an 8 $d_i$ length and infinite width plasma and it has uniform density $n_0$. The initial interface between the driver and background plasma is located at $x_B=-4\\ d_i$. Like the driver plasma, it has an electron species and a single ion species, of mass $m_{i,0}$. The background plasma is magnetized with an internal uniform magnetic field $\\mathbf{B_0} = B_0 \\mathbf{\\hat{z}}$, and its magnitude is defined such that the Alfv\u00e9nic Mach number of the flow, $M_A \\equiv v_0\/v_A = v_0\\sqrt{4\\pi n_0m_{i,0}}\/B_0$ matches the peak experimental value $M_A=1.5$, where $v_A$ is the Alfv\u00e9n velocity.%\n\n\\par A dipolar magnetic field is externally imposed in our simulations (\\textit{i.e.}, it is added to the plasma self-consistent electromagnetic fields to advance particle momenta but is not included in Maxwell's equations to advance the fields). The dipole is centered at $(x,y)=(0,0)$ and its associated magnetic field is $\\mathbf{B_{dip}} = B_\\mathrm{dip} \\mathbf{\\hat{z}}$, with $B_\\mathrm{dip} = M \/ r^3$, where $M$ is the dipolar magnetic moment, $r = \\sqrt{x^2 + y^2+\\delta^2}$ is the distance to the origin of the dipole and $\\delta=0.25\\ d_i$ is a regularization parameter. For most simulations, the magnetic moment $M$ was chosen such that the expected standoff, obtained from Eq.~\\eqref{eq:pressure-equilibrium}, is similar to the experimental value $L_0=1.8\\ d_i$. For this particular magnetic moment, the total initial magnetic field $B_0+B_\\mathrm{dip}$ is $\\approx 3.0~B_0$ at the standoff distance. Near the interface between the driver and background plasmas, the magnetic field of the dipole is relatively small and the initial magnetic field is $\\approx 1.2~B_0$.%\n\n\\par In this work, we present simulations with different drivers and magnetic dipole moments. All the simulations presented here, and their respective parameter sets, are listed in Table~\\ref{tab:runs}. Simulations B-G are discussed through Sec.~\\ref{sec:simulations} on equally labeled subsections. Simulation B is used to discuss the overall dynamics of the system, while simulations C, D, and E illustrate the role of the driver length, the density ratio, and the magnetic moment, respectively. Simulations F show the results for more realistic choices of parameters and simulation G for a more realistic driver shape. The physical parameters of the simulations (\\textit{e.g.} $M_A$, $L_0\/d_i$) were adjusted to be similar to the LAPD experiments, whereas other parameters (\\textit{e.g.} $m_i\/m_e$, $v_0$, $v_{the}$) were chosen to make simulations computationally feasible. The experimental and numerical parameters are presented in Table~\\ref{tab:parameters} and compared with lunar mini-magnetospheres.%\n\n\\begin{table*}\n    \\caption{\\label{tab:runs} List of simulations performed and their parameters. $v_{the,x}$ and $v_{thi,x}$ represent the $x$ component of the electron and ion thermal velocities, respectively. All the runs considered $v_{th,x}=v_{th,y}=v_{th,z}$ for the electrons and ions.}%\n    \\begin{ruledtabular}\n        \\begin{tabular}{cccccccccc}\n            \\textrm{Name} & $v_{the,x}\/v_0$ & $v_{thi,x}\/v_0$ & $n_d\/n_0$ & $m_{i}\/m_e$ & $m_{i,0}\/m_e$ & $L_x\/d_i$ & $L_y\/d_i$ & $L_0\/d_i$\\\\ \\colrule\n            \\textrm{B\/D2\/E2} & 0.1 & 0.01 & 2 & 100 & 100 & 2 & $+\\infty$ & 1.8 \\\\\n            \\textrm{C1} & 0.1 & 0.01 & 2 & 100 & 100 & 1 & $+\\infty$ & 1.8 \\\\\n            \\textrm{C2} & 0.1 & 0.01 & 2 & 100 & 100 & 4 & $+\\infty$ & 1.8 \\\\\n            \\textrm{C3} & 0.1 & 0.01 & 2 & 100 & 100 & $+\\infty$ & $+\\infty$ & 1.8 \\\\\n            \\textrm{D1} & 0.1 & 0.01 & 1 & 100 & 100 & 2 & $+\\infty$ & 1.8 \\\\\n            \\textrm{D3} & 0.1 & 0.01 & 4 & 100 & 100 & 2 & $+\\infty$ & 1.8 \\\\\n            \\textrm{E1} & 0.1 & 0.01 & 2 & 100 & 100 & 2 & $+\\infty$ & 2.3 \\\\ \n            \\textrm{E3} & 0.1 & 0.01 & 2 & 100 & 100 & 2 & $+\\infty$ & 1.4 \\\\ \\colrule\n            \\textrm{F1} & 0.1 & 0.002 & 2 & 1836 & 1836 & 2 & $+\\infty$ & 1.8 \\\\\n            \\textrm{F2} & 2.5 & 0.033 & 2 & 1836 & 1836 & 2 & $+\\infty$ & 1.8 \\\\\n            \\textrm{F3} & 2.5 & 0.033 & 2 & 100 & 100 & 2 & $+\\infty$ & 1.8 \\\\\n            \\textrm{G} & 0.1 & 0.01 & 2 & 100 & 100 & 2 & 6 & 1.8 \\\\\n        \\end{tabular}\n    \\end{ruledtabular}\n\\end{table*}\n\n\\par In most simulations, we considered a reduced mass ratio $m_i \/ m_e = 100$, a flow velocity $v_0 \/ c = 0.1$, and cold plasmas to reduce the required computational resources, allow extended scans over the different parameters of the system, and simplify our analysis. The thermal effects are negligible for the main results, and the chosen ion-to-electron mass ratio is high enough to ensure sufficient separation between electron and ion spatial and temporal scales. We confirm the validity of our assumptions in Sec.\\ref{sec:realistic}.%\n\n\\par In most of the simulations presented in this work, we have assumed that ions and electrons are initially in thermal equilibrium, and thus used the electron thermal velocities $v_{the}$ shown in Table~\\ref{tab:runs}, to compute the ion thermal velocities $v_{thi}$. Because we aim to study the role of the hydrogen ions of the experimental driver in the interaction with the background plasma, these simulations considered equal ion masses for the driver and background plasmas, \\textit{i.e.} $m_{i,d}=m_{i,0}$.%\n\n\\begin{table*}\n    \\caption{\\label{tab:parameters} Typical parameters associated with lunar mini-magnetospheres~\\cite{Russell1991,Bamford2012,Lin1998}, the range of parameters of LAPD~\\cite{Schaeffer2021} and the canonical simulation B. The parameters are written in both physical and normalized units to facilitate the comparison between the space, the laboratory environments and the PIC simulations. The experimental parameters are presented in ranges of values computed with the possible LAPD values for the flow velocity $v_0$, the density $n_0$ and the temperature $T$. The plasma parameters shown for lunar mini-magnetospheres are relative to the solar wind, while for the experiments and the simulations, they are relative to the background plasma. The ion data shown corresponds to Hydrogen ions. The magnetic field $B_{\\textrm{std}}$ is calculated at the standoff position, \\textit{i.e.}, at a distance $L_0$ from the center of the obstacle.}%\n    \\begin{ruledtabular}\n        \\begin{tabular}{cccccc}\n            \\multirow{2}{*}{\\textrm{Parameters}} & \\multicolumn{2}{c}{Lunar mini-magnetospheres} & \\multicolumn{2}{c}{LAPD experiments} & PIC simulations \\\\ \n            & Physical units & Normalized units & Physical units & Normalized units & Normalized units\\\\ \\colrule \\\\ [-9 pt]\n            Flow velocity, $v_0$ & $400$ km\/s & $10^{-3}$ $c$ & 200-300 km\/s & 0.7-1.0$\\times10^{-3}$ $c$ & 0.1 $c$ \\\\\n            Density, $n_0$ & 5 cm$^{-3}$ & --- & $10^{12}$-$10^{13}$ cm$^{-3}$ & --- & ---\\\\\n            Mass ratio, $m_i\/m_e$ & --- & 1836 & --- & 1836 & 100 \\\\\n            Ion skin depth, $d_i$ & 100 km & --- & 7-23 cm & --- & --- \\\\\n            Electron skin depth, $d_e$ & 2 km & 2$\\times10^{-2}$ $d_i$ & 0.2-0.5 cm & 0.7-7.0$\\times10^{-2}$ $d_i$ & 0.1 $d_i$ \\\\\n            Magnetic obstacle size, $L_0$ & 300 km & 3 $d_i$ & 14-18 cm & 0.6-2.5 $d_i$ & 1.8 $d_i$\\\\\n            Internal magnetic field, $B_{0}$ & $10^{-4}$ G & $10^{-2}$ $m_ec^2\/ed_e$ & 300 G & 3-9$\\times10^{-2}$ $m_ec^2\/ed_e$ & 0.67 $m_ec^2\/ed_e$ \\\\\n            Ion gyroradius, $\\rho_i$ & 500 km & 5 $d_i$ & 7-10 cm & 0.3-1.5 $d_i$ & 1.5 $d_i$ \\\\\n            Electron gyroradius, $\\rho_e$ & 800 m & $8\\times10^{-3}$ $d_i$ & 4-6$\\times10^{-3}$ cm & 2-8$\\times10^{-4}$ $d_i$ & 0.15 $d_i$ \\\\\n            Ion gyroperiod, $\\omega_{ci}^{-1}$ & 1 s & --- & 230-520 ns & --- & --- \\\\\n            Alfv\u00e9n velocity, $v_A$ & 80 km\/s & $3\\times10^{-4}$ $c$ & 140-980 km\/s & 0.5-3.3$\\times10^{-3}$ $c$ & 0.067 $c$ \\\\\n            Alfv\u00e9nic Mach number, $M_A$ & --- & 5 & --- & 0.3-1.5 & 1.5 \\\\\n            Temperature, $T$ & 5 eV & --- & 1-10 eV & --- & --- \\\\\n            Electron thermal velocity, $v_{the}$ & 1500 km\/s & 4 $v_0$ & 730-2300 km\/s & 2.4-11.5 $v_0$ & 0.1 $v_0$ \\\\\n            Ram pressure, $n_0m_iv_0^2$ & 1 nPa & --- & 70-1500 Pa & --- & --- \\\\\n            Standoff magnetic field, $B_{\\textrm{std}}$ & $5\\times10^{-4}$ G & 0.07 $m_ec^2\/ed_e$ & 100-600 G & 0.02-0.2 $m_ec^2\/ed_e$ & 2.0 $m_ec^2\/ed_e$ \\\\\n        \\end{tabular}\n    \\end{ruledtabular}\n\\end{table*}\n\n\\subsection{\\label{sec:additional} Evolution and main features of the system}\n\n\\par To identify the main magnetospheric and kinetic-scale structures that arise from the initial configuration, simulation \\textrm{B} was performed. It considered a driver with length $L_x=2\\ d_i$ and density $n_d=2\\ n_0$ (twice the background density). Figs.~\\ref{fig:movie} a1-3) represent the total ion density $n_i=n_{i,d}+n_{i,0}$, for three different times, and Figs.~\\ref{fig:movie} b1-3) show the variation of the $z$ component of the magnetic field, from its initial value, $\\Delta B_z=B_z-B_{z,\\textrm{initial}}$.%\n\n\\begin{figure*}[t]\n    \\includegraphics[width=0.98\\linewidth]{plots\/movie.pdf\n    \\caption{\\label{fig:movie} Spatiotemporal evolution of a) the total ion density and b) the variation of the $z$ component of the magnetic field in simulation \\textrm{B} (see Table~\\ref{tab:runs} for a list of parameters). Columns 1-3 correspond to three different times in the simulation. The vertical and circular dashed lines mark the initial border between the driver and background plasma and the dipolar magnetic obstacle with radius $L_0$, respectively.}%\n\\end{figure*}\n\n\\par In Fig.~\\ref{fig:movie} a1), we see the total ion density for an early time ($t\\omega_{ci}=1.5$). Given the small distance propagated by the driver plasma at this time, the dipolar magnetic field does not significantly affect the interaction between the plasmas. For this reason, we can express the early system as a driver flowing against a uniform magnetized background plasma. \nIn Fig.~\\ref{fig:movie} b1), we observe that this interaction creates a region of compressed magnetic field in the downstream region, where the background plasma is located, and expels the magnetic field in the region of the driver, leading to a magnetic cavity in the upstream region with approximately null magnetic field~\\cite{Bondarenko2017}.%\n\n\\par In Figs.~\\ref{fig:movie} a2) and b2), we start to observe the effects of the dipolar magnetic field for a later time ($t\\omega_{ci}=3.0$). As the magnetic pressure exerted against the plasmas increases, a region of compressed background plasma forms in front of the dipole, as Fig.~\\ref{fig:movie} a2) shows. After the interaction between the background and the dipole, the magnetic field pressure becomes large enough to counterbalance the kinetic pressure of the driver, reflecting it upstream. This can be seen seen in Fig.~\\ref{fig:movie} a3) for a subsequent time ($t\\omega_{ci}=4.5$). After the reflection, there is no longer a plasma flow pushing the magnetic compression forward or holding the decompression by the left side of the background region, and as a result, the region near the dipole quickly decompresses --- see Fig.~\\ref{fig:movie} b3).%\n\n\\par To compare the numerical results with the experimental data shown in Fig.~\\ref{fig:experiment}, synthetic diagnostics were obtained from the simulations. In Fig.~\\ref{fig:standard}, the variation of the magnetic field $\\Delta B_z$ and the density current $J_y$ measured at the axis of symmetry $y=0$ and as a function of time are plotted for simulation \\textrm{B}. These diagnostics are important to comprehend the system dynamics, due to the importance of the $z$ direction of the magnetic field in the motion of the particles.%\n\n\\begin{figure}[ht]\n    \\includegraphics[width=0.85\\columnwidth]{plots\/standard.pdf}\n    \\caption{\\label{fig:standard} Temporal evolution of a) the variation of the magnetic field $B_z$ and b) current density $J_y$ at $y=0$ for the simulation \\textrm{B}. The driver has a 2 $d_i$ length and a density $n_d = 2\\ n_0$. The dashed lines have slopes that match the flow velocity $v_0$, the coupling velocity $v_c$ and the reflection velocity $v_r$.}%\n\\end{figure}\n\n\\par The main features of Fig.~\\ref{fig:standard} are consistent with the experimental results. In the magnetic field plot of Fig.~\\ref{fig:standard} a), both the upstream magnetic cavity and the downstream magnetic compression are present. Between $t\\omega_{ci}=0$ and $t\\omega_{ci}\\approx1.5$, the system behaves approximately as a driver piston moving against a uniform magnetized plasma. As the driver pushes the background plasma and magnetic field, the discontinuity that separates these two media travels at constant coupling velocity $v_c < v_0$, measured as $v_c\\approx0.49\\ v_0$ for this simulation. The leading edge of the compression of the magnetic field travels with a velocity close to $v_0$ for the runs considered.%\n\n\\par The driver experiences increasingly higher magnetic fields until the magnetic pressure is enough to reflect the driver near the expected standoff $x_0 = -L_0$, at $t\\omega_{ci}\\approx3$. The magnetic cavity and magnetic compression are also reflected, and the boundary between these two regions travels with a velocity $v_r$ after reflection. The background magnetic decompression is seen after $t\\omega_{ci}=5$.%\n\n\\par In the current density plot of Fig.~\\ref{fig:standard} b), we can observe the diamagnetic current that supports the magnetic field gradient between the driver and background plasmas and that identifies the leading edge of the magnetic cavity. During the driver reflection, this current branches into multiple components due to the multi-stream velocity distributions developed in the driver and background plasmas. We can also verify that this structure is reflected near the expected standoff $x_0 =-L_0$. Between $t\\omega_{ci}\\approx2$ and $t\\omega_{ci}\\approx3$, a second current structure is present in the background region. It is associated with the magnetopause of the system and the small decompressed field region that we see in Fig.~\\ref{fig:standard} a), and it arises from the interaction of the accelerated background ions with the dipole, as we show in Sec.~\\ref{sec:momentum}. The presence of these two current structures is consistent with the experimental results.%\n\n\\par In Fig.~\\ref{fig:standard} b) we can also see the formation of waves in the background plasma, near the dipole region. These waves are excited in regions of highly non-uniform density and magnetic field, and have periods and wavelengths between the ion and electron kinetic scales. We have verified that their properties change significantly for different ion thermal velocities. In particular, we have found these waves to be more clearly excited for lower ion temperatures, which may explain why these waves have not been observed in the experiments performed at the LAPD. A detailed characterization of these waves and the conditions for their formation is out of the scope of this paper, and shall be addressed in a future work.%\n\n\\par To better understand the particle motion during the events described, we show in Fig.~\\ref{fig:phase-space} the phase spaces of ions and electrons located near $y=0$. For the ions, the $x$ component of the velocity of the particles is presented, to illustrate their reflection and accumulation, while for the electrons, the $y$ component is shown instead, to show the formation of the currents. The magnetic field $B_z$ and the current density $J_y$ profiles for $y=0$ are also represented. Once again, we used the parameter set \\textrm{B} of Table~\\ref{tab:runs}.%\n\n\\begin{figure*}[t]\n    \\includegraphics[width=0.95\\linewidth]{plots\/phase-scan-standard.pdf\n    \\caption{\\label{fig:phase-space} Ion (a) and electron (b) phase spaces, and magnetic field $B_z$ and current density $J_y$ profiles at $y=0$, for simulation \\textrm{B} and for three different times (1-3). The particles shown were randomly selected in the region $-0.2\\ d_i < y < 0.2\\ d_i$. The frames labeled a1) to a3) show the $v_x$ velocity of the ions, while the frames labeled b1) to b3) show the $v_y$ velocity of the electrons. Blue\/orange markers correspond to background\/driver plasma particles. The green and purple lines correspond to the magnetic field $B_z$ and current density $J_y$, respectively. The left dashed line marks the initial border between the driver and the background plasmas, and the right dashed line marks the expected standoff $x_0=-L_0$.}%\n\\end{figure*}\n\n\\par Fig.~\\ref{fig:phase-space} a1) shows the $v_x$ velocity of the ions when the dipole field is still negligible. The ions initially move upstream with velocity $v_0$ until they interact with the background field. After reaching the background, they are mostly decelerated and reflected by electric field in the interface between the plasmas~\\cite{Bondarenko2017}, and end up with a flow velocity that is close to zero for the simulation considered. The reflection occurs near the boundary of the magnetic cavity, which moves with velocity $v_c$ through the background, as mentioned above. During this stage, the background ions accelerate from rest to velocities of average close to $v_c$.%\n\n\\par The driver and the accelerated background ions continue to approach the dipole until they are reflected. This can be seen in Fig.~\\ref{fig:phase-space} a2). During this interaction, two main current structures are visible in the $J_y$ profile. The first one (from the left) corresponds to the typical diamagnetic current, while the second one corresponds to the magnetopause. To the right of these two main current structures, we can see the background waves observed in Fig.~\\ref{fig:standard} b). In Fig.~\\ref{fig:phase-space} a3), the driver ions are totally reflected. The ions reflected by the dipole obtain a velocity close to $-v_0$, while the magnetic cavity moves back with velocity $v_r$.%\n\n\\par Because the simulation considers a cold plasma approximation, the ion thermal velocities remain small most of the time, except for the boundary between the two plasmas, where the velocity of the ions changes abruptly. The same does not occur for the electrons. We can see in the $v_y$ velocity of the electrons, represented in Figs.~\\ref{fig:phase-space} b1) to b3) that, although the electron thermal velocities are initially small, they rapidly increase considerably. At the boundary, the electrons can reach thermal velocities of $6\\ v_0$, much higher than the ion velocities. Because the electron and ion density profiles are very similar during the entire evolution of the system, the current density $J_y = e(n_iv_{iy}-n_ev_{ey})$ is then mainly transported by the electrons, where $n_j$ is the density and $v_{jy}$ the $y$ component of the velocity of the ions and electrons ($j=i,e$, respectively). This is also consistent with the observed spatial distribution of electrons during the reflection, which shows an excess of fast electrons around the standoff position.\n\n\\subsection{Driver length} \\label{sec:length}\n\n\\par To choose a driver length that best reproduces the experimental results shown in Fig.~\\ref{fig:experiment} and to understand its role on the magnetic field and current density structures, we performed simulations \\textrm{C1} to \\textrm{C3} (see Table~\\ref{tab:runs}) with varying driver length $L_x$. In Fig.~\\ref{fig:scan-length}, we show $\\Delta B_z$ and $J_y$ at $y=0$ for $L_x=1\\ d_i$ (C1), $L_x=4\\ d_i$ (C2) and for an infinite driver (C3). For these simulations, the properties of the background plasma and the width of the driver $L_y$ were kept unchanged. The density of the driver was $n_d=2\\ n_0$.%\n\n\\par In Figs.~\\ref{fig:scan-length} a1) and b1), we see the magnetic field and current density plots for the short driver length $L_x=1\\ d_i$. We observe most of the features of Fig.~\\ref{fig:standard}, namely the reflection of the compressed magnetic field in a1) and the diamagnetic and magnetopause currents in b1). For this length, however, the driver never fully interacts with the dipole. The closest that the diamagnetic current structure gets to the dipole is $x_r\\approx-3.0\\ d_i$, \\textit{i.e.}, much farther than the expected standoff $x_0 = -L_0=-1.8\\ d_i$. To replicate the experimental results and ensure that the driver can reach the dipole, we should thus use a sufficiently long driver such that $x_r>x_0$. Additionally, short drivers risk entering in a decoupling regime between the two plasmas~\\cite{Hewett2011}, which can compromise the observation of a magnetopause. The coupling effects on the results are discussed in detail in Sec.~\\ref{sec:density}.%\n\n\n\\par The position where the driver is fully reflected by the background can be estimated as $x_r\\approx x_B+L_xv_c\/(v_0-v_c)$, where $x_B$ is the initial boundary position between the two plasmas. This estimate is obtained by computing the volume of the background plasma required for the driver plasma to deposit its kinetic energy, \\textit{i.e.} $x_r - x_B$ corresponds to the magnetic stopping radius of the system~\\cite{rb}.\n\n\n\\par In the simulation with $L_x=4\\ d_i$, represented in Figs.~\\ref{fig:scan-length} a2) and b2), we observe once more the main features identified in Fig.~\\ref{fig:standard}, but unlike the $L_x=1\\ d_i$ case, the driver is long enough and ends up reflected by the dipole. We observe that the diamagnetic current reaches the expected standoff and has enough plasma to maintain it near the dipole for a time period ($t\\omega_{ci}\\approx3$ to $t\\omega_{ci}\\approx5$) longer than the $2\\ d_i$ case shown in Fig.~\\ref{fig:standard}. As a result, the magnetic decompression in the background region is delayed for longer drivers. However, because the full driver reflection also occurs later, longer drivers will result in short-lived reflections of the compression of the magnetic field.%\n\n\\par In Figs.~\\ref{fig:scan-length} a3) and b3), we show the results for a driver with infinite length ($L_x=+\\infty$). In this simulation, the driver plasma is only partially initialized inside the simulation domain, and a flow is continuously injected from the lower $x$ boundary. An infinite driver configuration allows us to understand the dynamics of the system in an asymptotic regime in which the driver plasma stays close to the dipole. As expected, until $t\\omega_{ci}=3$, the features observed are very similar to $L_x=2\\ d_i$ and $L_x=4\\ d_i$. After this time, the magnetic and the driver kinetic pressures balance each other near $x_0$, so the diamagnetic current remains stationary. Because the driver can hold for longer near the dipole, the decompression in the background region is much slower and is not visible for the time range of the plot. We can also observe that the background waves are only visible during a transient.%\n\n\\par In all the three simulations, the coupling velocity measured was always $v_c \\approx 0.49\\ v_0$. Given the results shown in Fig.~\\ref{fig:scan-length}, we chose a driver length of $2\\ d_i$ to reproduce the experimental results. This driven length is large enough to ensure that the driver arrives at the dipole and small enough to observe a significant reflection of the compression of the magnetic field as we see in the experiments.%\n\n\\begin{figure*}[t]\n    \\includegraphics[width=\\linewidth]{plots\/different-lengths-plot.pdf\n    \\caption{\\label{fig:scan-length} Temporal evolution of the variations of the magnetic field $\\Delta B_z$ and current density $J_y$ at $y=0$, for driver lengths of a) 1 $d_i$, b) 4 $d_i$ and for c) an infinite driver length (see Table~\\ref{tab:runs} for a full list of the parameters). The dashed lines represent the slopes of the flow velocity $v_0$, the coupling velocity $v_c$, and the reflection velocity $v_r$.}%\n\\end{figure*}\n\n\\subsection{Plasma coupling with density ratio} \\label{sec:density}\n\n\\par As expected from previous works, increasing the ratio between the driver and background plasma densities should improve the coupling between the two plasmas~\\cite{Bondarenko2017, Hewett2011}, meaning that, for denser drivers, the transfer of momentum and energy from the driver to the background plasma is more efficient. To better understand the role of the coupling mechanism, we performed simulations with different values of the driver density, namely $n_d=n_0$ (\\textrm{D1}), $n_d=2\\ n_0$ (\\textrm{D2}) and $n_d=4\\ n_0$ (\\textrm{D3}), while keeping a constant background density $n_0$ and a driver length $L_x = 2\\ d_i$. For each run, the magnetic moment was chosen such that the expected standoff obtained from Eq.~\\eqref{eq:pressure-equilibrium} was always $L_0=1.8\\ d_i$. The synthetic magnetic field and current density diagnostics were obtained for these simulations and are shown in Fig.~\\ref{fig:scan-density}.%\n\n\\begin{figure*}[t]\n    \\includegraphics[width=\\linewidth]{plots\/different-densities-plot.pdf\n    \\caption{\\label{fig:scan-density} Temporal evolution of the variations of the magnetic field $\\Delta B_z$ and current density $J_y$ at $y=0$, for different ratios between the driver and background densities $n_d \/ n_0$. The magnetic moment was chosen so that the expected standoff distance $L_0$, calculated from Eq.~\\eqref{eq:pressure-equilibrium}, was kept as 1.8 $d_i$ for all the simulations. Panels a-c) show results for $n_d = n_0$,  $n_d = 2\\ n_0$ and $n_d=4\\ n_0$, respectively.}%\n\\end{figure*}\n\n\\par In Figs.~\\ref{fig:scan-density} a1) and b1) we can see $\\Delta B_z$ and $J_y$ for the lowest driver density considered, $n_d = n_0$ (\\textit{i.e.}, background and driver with the same initial density). In this regime, the coupling is less efficient and, as a result, the coupling velocity $v_c \\approx 0.38\\ v_0$ is lower than obtained in the higher densities cases represented in Figs.~\\ref{fig:scan-density} b) and c). Due to the low coupling velocity, the driver plasma is reflected more quickly by the background than for denser drivers, and the expected position $x_r$ for the total reflection on the background is farther from the dipole than the expected standoff $x_0$, meaning $x_r<x_0$. As a result, Fig.~\\ref{fig:scan-density} a) shows similarities with the short driver length represented in Fig.~\\ref{fig:scan-length} a), because, in both simulations, the driver parameters do not ensure that the driver arrives near the dipole.%\n\n\\par In Figs.~\\ref{fig:scan-density} a2) and b2), we show the results for $n_d = 2\\ n_0$, which is the same run represented in Fig.~\\ref{fig:standard}. For this density, the coupling velocity, measured as $v_c\\approx0.49\\ v_0$, is high enough to secure a reflection of the driver by the dipole, as we observe at $t\\omega_{ci}\\approx3$. In Figs.~\\ref{fig:scan-density} a3) and b3) we show the case with the highest driver density $n_d=4\\ n_0$, which is similar to the $n_d=2\\ n_0$ case, because the measured coupling velocity for Fig.~\\ref{fig:scan-density} c) was $v_c \\approx 0.56\\ v_0$, \\textit{i.e.}, only slightly larger than the $v_c$ measured for Fig.~\\ref{fig:scan-density} b). In the high density case, we also see that the current density structures during the plasma reflection are filamented, due to analogous multi-stream velocity distributions discussed for Fig.~\\ref{fig:scan-length} b).%\n\n\\par To guarantee that the driver reaches the expected standoff, we thus require that $x_r>x_0$. In fact, the position where the driver is reflected $x_r$, for no dipole cases, increases with the driver length $L_x$ and the velocity ratio $v_c\/v_0$, and thus, both quantities must be large enough to guarantee that $x_r>x_0$. In turn, the ratio $v_c\/v_0$ increases with increasing driver density ratio $n_d\/n_0$, and so, the driver should be sufficiently long and dense to effectively couple to the background plasma. Our results (in particular Sec.~\\ref{sec:additional}) show that a driver with $L_x=2\\ d_i$ and $n_d=2\\ n_0$ qualitatively reproduces the experimental results.%\n\n\\par A separate study was also performed to analytically determine the properties of the driver-background plasma coupling. The results of this study will be presented in a future paper.\n\n\\subsection{Dependency of the magnetopause position with the magnetic moment} \\label{sec:momentum}\n\n\\par To confirm that the features previously associated with the magnetopause location change according with its expected position, we performed simulations with a 2 $d_i$ long driver with density $n_d = 2\\ n_0$ for three different magnetic moments. Considering the magnetic moment that results in the expected standoff $L_0=1.8\\ d_i$ as $M_0$ (simulation \\textrm{B\/E2} on Table~\\ref{tab:runs}), simulations with the magnetic moments $2\\ M_0$ (\\textrm{E1}) and $M_0\/2$ (\\textrm{E3}) were also performed, corresponding respectively to the expected standoffs $L_0\\approx2.3\\ d_i$ and $L_0\\approx1.4\\ d_i$. Fig.~\\ref{fig:scan-momentum} shows the $\\Delta B_z$ and $J_y$ synthetic diagnostics at $y=0$ for the three simulations.%\n\n\\begin{figure*}[t]\n    \\includegraphics[width=\\linewidth]{plots\/different-momentums-plot.pdf\n    \\caption{\\label{fig:scan-momentum} Temporal evolution of the variation of the magnetic field $\\Delta B_z$ and current density $J_y$ at $y=0$, for three different magnetic moments. The magnetic moments $M$ considered were a) $M=2\\ M_0$, b) $M=M_0$ and c) $M=M_0\/2$, where $M_0$ represents the magnetic moment that corresponds to a standoff $L_0=1.8\\ d_i$ for a driver density $n_d=2\\ n_0$. The corresponding standoffs for these simulations are a) $L_0\\approx2.3\\ d_i$, b) $L_0 = 1.8\\ d_i$ and c) $L_0 \\approx 1.4 \\ d_i$.}%\n\\end{figure*}\n\n\\par Figs.~\\ref{fig:scan-momentum} a1) and b1) show the results for the highest magnetic moment $M=2\\ M_0$. We see that the current structures associated with the magnetopause and the background waves are less evident than for the lower magnetic moments, as they are formed farther from the dipole. Figs.~\\ref{fig:scan-momentum} a2) and b2) correspond to the magnetic moment $M_0$ that leads to $L_0=1.8\\ d_i$ and are the same results shown in Fig.~\\ref{fig:standard}. As previously mentioned, there are two main observable current structure standoffs. The first one is associated to the diamagnetic current, which is reflected around $t\\omega_{ci}\\approx3$ near the expected value $x_0=-L_0=-1.8\\ d_i$. This standoff is related to the interaction between the driver ions and the dipole. The second standoff occurs between $t\\omega_{ci}\\approx2$ and $t\\omega_{ci}\\approx3$ and it is located in the background plasma region. This standoff also occurs near $x=-1.8\\ d_i$.%\n\n\\par In Figs.~\\ref{fig:scan-momentum} a3) and b3), we show the results obtained for the half magnetic moment $M=M_0\/2$. In this case, the magnetic pressure exerted by the dipole is lower, leading to a smaller $L_0$, and consequently, the diamagnetic current feature visible in b3) is closer to the dipole than in Figs.~\\ref{fig:scan-momentum} b1) and b2). The main changes, however, occur in the magnetopause current. Unlike what we observe for the other magnetic moments, the magnetopause current, pinpointed in the current density plot, lasts for a longer time (until $t\\omega_{ci}\\approx4$). This current is also more separated from the diamagnetic current standoff and is easier to identify. This is consistent with the experimental observations.%\n\n\\par To identify the pressure balances associated with the two observed standoffs, and because the magnetic and kinetic pressures vary over time, we studied the temporal evolution of the different plasma and magnetic pressure components of the system. In particular, we calculated the spatial profiles of the magnetic pressure $B^2\/8\\pi$, the ram pressure $n_jm_jv_{flj}^2$ and the thermal pressure $n_jm_jv_{thj}^2$ as a function of time for $y = 0$. In these expressions, $n_j$, $m_j$, $v_{flj}$ and $v_{thj}$ refer to the density, mass and flow and thermal velocities, respectively, of the ions ($j=i$) and electrons ($j=e$). The magnetic pressure was calculated from the magnetic field measured in each PIC grid cell located at $y=0$. The flow and thermal pressures, were calculated from averaged particle data. To ensure that the calculation of each kinetic pressure considered a sufficiently large number of particles, all the particles between $-0.1\\ d_i<y<0.1\\ d_i$ were binned into equal-sized bins of width $0.05\\ d_i$ over the $x$ direction. For each bin we computed: i) the average density of each species, ii) the flow velocity, corresponding to the average of the velocity of the particles, and iii) the thermal velocity, corresponding to the standard deviation of the velocity of the particles~\\cite{Liboff2003}. With these averaged quantities, the ram and thermal pressures were calculated in each bin for each species of ions and electrons and each component of the velocity $x$, $y$, and $z$. The $y$ and $z$ components of the pressures, however, are negligible.\n\n\\par These pressure profiles were obtained for simulation E3 with magnetic moment $M=M_0\/2$ and are plotted in Fig.~\\ref{fig:pressures} for times where a) the magnetopause and b) the diamagnetic current standoff can be observed. The kinetic pressures represented were calculated by adding all the components of the ram and thermal pressures of the ions and electrons for the background ($P_0$) and the driver ($P_\\mathrm{d}$) plasmas. The magnetic pressures represented were calculated by considering the total and the relative magnetic field pressures ($P_\\mathrm{mag} = B_z^2\/8\\pi$ and $P_\\mathrm{rel} = P_\\mathrm{mag}-B_0^2\/8\\pi$, respectively). The pressures were normalized to the initial ram pressure of the driver ions.%\n\n\\begin{figure*}[t]\n\\includegraphics[width=\\linewidth]{plots\/pressures_and_energy3.pdf\n\\caption{\\label{fig:pressures} Pressures profiles calculated for simulation \\textrm{E3} with a magnetic moment $M=M_0\/2$ (shown in Fig.~\\ref{fig:scan-momentum} c)), during the occurrence of a) the magnetopause and b) the standoff of the diamagnetic current. The magnetic pressures are $P_\\mathrm{mag} = B_z^2\/8\\pi$ and $P_\\mathrm{rel} = P_\\mathrm{mag}-B_0^2\/8\\pi$. The kinetic pressures $P_\\mathrm{d}$ and $P_0$, corresponding to the driver and background plasmas, respectively, consider both the ions and electrons and the flow and thermal components of the velocity. c) Temporal evolution of the variation of the total kinetic energies of the driver $\\Delta W_{\\mathrm{kin,d}}$ and background $\\Delta W_{\\mathrm{kin,0}}$ plasmas, the magnetic energy $\\Delta W_{\\mathrm{mag}}$, and the total energy of the simulation box $\\Delta W_{\\mathrm{tot}}$. The total energy is calculated by adding all the kinetic energies and the electric and magnetic energies. Since the background plasma is magnetized, the electric energy term is many orders of magnitude smaller than the magnetic energy term. The energies were normalized to the initial total energy of the driver ions $W_{\\textrm{d,ini}}$. The loss of energy conservation near $t\\omega_{ci}\\approx 4$ is caused by the escape of background plasma particles and magnetic field through the right hand side of the simulation box.}%\n\\end{figure*}\n\n\\par Fig.~\\ref{fig:pressures} a) shows the magnetic and kinetic pressures at time $t\\omega_{ci}\\approx2.33$ where we observed the magnetopause in Fig.~\\ref{fig:scan-momentum} b3). When the driver starts pushing the background, the pressure of the driver at the interface between the plasmas increases because the driver density and thermal velocities also increase. During the flow, the driver transfers energy and momentum to the background plasma, and as a result, the background develops a strong kinetic pressure. At the time represented in Fig.~\\ref{fig:pressures} a), the background plasma pressure equals the total and the dipolar magnetic pressures in $x \\approx -1.4\\ d_i$, near the location of the magnetopause current of Fig.~\\ref{fig:scan-momentum} b3). This observation supports the hypothesis that this current emerges from the standoff between the background and magnetic pressures. Fig.~\\ref{fig:pressures} b) shows the pressures for $t\\omega_{ci}=3$ where we see the beginning of the reflection of the driver. The driver pressure equals the magnetic and dipolar pressures near $x_0=-L_0\\approx-1.4\\ d_i$. After this time, the driver is incapable of moving any further into the background because the magnetic pressure exceeds its kinetic pressure.%\n\n\\par The energy variations integrated over the entire simulation domain can also help us understand the system dynamics. Fig.~\\ref{fig:pressures} c) shows the variation of the total driver and background kinetic energies, $\\Delta W_{\\mathrm{kin,d}}$ and $\\Delta W_{\\mathrm{kin,0}}$, respectively, as well as the variation of the magnetic energy $\\Delta W_{\\mathrm{mag}}$, and of the total energy $\\Delta W_{\\mathrm{tot}}$. The kinetic energies of the background and driver plasmas consider all ions and electrons. In early times $t\\omega_{ci}<3$, as the driver and background plasmas interact, the driver transfers its energy to the background plasma and the magnetic field. The total energy, given by the sum of the electromagnetic energy and the kinetic energies, remains constant during this period. After the driver is fully reflected by the dipole for $t\\omega_{ci}>3$, the magnetic field loses most of its energy to the background and driver plasmas leading to a drop of the magnetic energy. After $t\\omega_{ci}\\approx4$, the background ions start to leave the simulation box, and the total energy is no longer conserved. The background kinetic energy remains approximately constant because the background plasma loses energy to the sink at the right boundary of the simulation but gains energy from the magnetic field. For both driver and background plasma, the ions carry most of the energy.%\n\n\\par From Fig.~\\ref{fig:pressures}, we can identify the positions where multiple pressure balances occur, and therefore, develop an insight into the pressure equilibria that are behind the structures of the current density synthetic diagnostics. Using the previously calculated pressures, we obtained the equilibrium positions where certain pressure balances manifested and plotted them in Fig.~\\ref{fig:equilibrium} alongside $J_y$.%\n\n\\begin{figure}[ht]\n\\includegraphics[width=\\columnwidth]{plots\/pressure-equilibrium3.pdf}\n\\caption{\\label{fig:equilibrium} Temporal evolution of the current density $J_y$ at $y=0$, with the closest locations to the dipole of different pressure balances for multiple times. The represented locations of pressure balances are the equilibria between the driver kinetic pressure $P_{\\mathrm{d}}$ with the total magnetic field pressure $P_{\\mathrm{mag}}=B_z^2\/8\\pi$, represented by the solid line; the background kinetic pressure $P_0$ with the pressure exerted by the relative magnetic field $P_{\\mathrm{rel}}=P_{\\mathrm{mag}}-B_0^2\/8\\pi$, by the dotted line, and $P_{\\mathrm{d}}=P_{\\mathrm{rel}}$, by the dashed line. The results correspond to simulation \\textrm{E3} (see Table~\\ref{tab:runs}).}%\n\\end{figure}\n\n\\par This analysis shows that the system has, in general, two magnetopause structures: one driven by the background, and one by the driver plasma. The former structure is defined by the balance $P_{\\mathrm{0}}=P_{\\mathrm{rel}}$. For the latter structure to form, the driver needs to have almost enough energy to push the diamagnetic current up to the magnetopause, defined by Eq.~\\ref{eq:pressure-equilibrium}. This is illustrated in Fig.~\\ref{fig:equilibrium}, where we show the location of the pressure equilibrium between the driver kinetic pressure and the total magnetic pressure, $P_\\mathrm{d} = P_\\mathrm{mag}$. \n\n\\par As shown in Fig.~\\ref{fig:pressures}, the current associated with the background magnetopause seems to overlap with the region of background and magnetic pressure balance. Unlike the driver, the background plasma is magnetized. If we neglect the compression of the magnetic field in the downstream region, the pressure balance that describes this magnetopause can then be estimated by the equilibrium of the kinetic pressure of the background plasma with the relative magnetic pressure, $P_0 = P_\\mathrm{rel}$. In Fig.~\\ref{fig:equilibrium}, we show that this pressure balance, represented by the dotted line, describes well the position of the current feature identified as the magnetopause between times $t\\omega_{ci}\\approx2$ and $t\\omega_{ci}\\approx3$. \n\n\n\\par After $t\\omega_{ci} \\approx 3$, the magnetopause current is well described by the pressure balance $P_\\mathrm{d} = P_\\mathrm{rel}$, as illustrated by the dashed line in Fig.~\\ref{fig:equilibrium}. In fact, after inspecting the phase spaces in Figs.~\\ref{fig:phase-space} a3) and b3), we can observe that a combination of driver plasma particles (separated from the bulk distribution) and background ions pushes the dipolar field and sets the position of the magnetopause.\n\n\n\n\\par We stress that, because we are determining equilibria via MHD pressure balances but are checking the intersection between pressure curves with kinetic resolution, some caution must be made to ensure that we are observing the equilibrium between pressures and not merely the interface between the different regions of interest. To ensure that the pressure equilibria were correctly obtained, the corresponding pressure profiles were always carefully inspected with additional diagnostics.%\n\n\\subsection{Realistic parameters}\\label{sec:realistic}\n\n\\par Due to the need for more extensive scans (and thus using physically equivalent but computationally feasible parameters), the simulations shown so far considered reduced ion mass ratios, cold plasmas, and higher velocities than the ones used in the LAPD experiments - see Table~\\ref{tab:parameters}. To ensure that the main results presented in the previous sections are also valid with realistic parameters, we have performed a set of simulations with parameters similar to those expected experimentally. \n\n\\par Three simulations were performed, labeled as runs F1 to F3. Run F1 employs realistic mass ratios $m_{i,d}\/{m_e} = m_{i,0}\/{m_e} = 1836$. Additionally, run F2 also considers a ratio between the electron thermal and flow velocities close to the ones expected for the LAPD experiments, namely $v_{the,x}\/v_0=2.5$ and $v_{thi,x}\/v_0=0.033$, leading to higher temperatures than in the previous simulations, and thus allowing possible thermal effects on the system. Finally, run F3 considers the same electron thermal velocity ratios of F2 but the standard reduced mass ratios. \n\n\\par The $\\Delta B_z$ and $J_y$ plots for these simulations are shown in Fig.~\\ref{fig:realistic}. Note that, due to changes in $m_i\/m_e$, the spatial and temporal scales were recalculated for the new parameters. Once again, the magnetic dipole moment for the three simulations was adjusted to ensure that $L_0=1.8\\ d_i$.%\n\n\\begin{figure*}[t]\n    \\includegraphics[width=\\linewidth]{plots\/realistic2.pdf\n    \\caption{\\label{fig:realistic} Temporal evolution of a) the variation of the magnetic field $\\Delta B_z$ and b) the current density $J_y$ at $y=0$, for the simulations with similar parameters to the experiments. Run F1 considers realistic mass ratios for the driver and background plasmas and low ratios between the thermal and flow velocities; run F2 uses realistic mass ratios and thermal velocity ratios close to the ones expected in the experiments; run F3 uses the realistic thermal velocity ratios but reduced mass ratios.}%\n\\end{figure*}\n\n\\par As expected, these simulations show the same main structures discussed in the previous sections. We observe the typical reflection of the compression of the magnetic field and the current structures of the magnetopause and diamagnetic cavity. However, some differences are also visible. In Figs.~\\ref{fig:realistic} a1) and b1), \\textit{i.e.} for the realistic mass ratios but cold plasmas simulation, we observe a stronger filamentation of the plasma flow reflected off the dipole and a thinner diamagnetic current. This is because $d_e$ is the characteristic length scale of the current layer and we have lower $d_e\/d_i$ values for larger $m_i\/m_e$. Figs.~\\ref{fig:realistic} a2) and b2), for the simulation with higher temperatures, show no major differences with Figs.~\\ref{fig:realistic} a1) and b1), even though there is a significant increase in the thermal velocities. \n\n\\par In Figs.~\\ref{fig:realistic} a3) and b3), however, we observe significant differences for reduced mass ratios with realistic thermal velocity ratios. In particular, we observe in the current density plot smoother magnetic and current structures and less defined background waves between the magnetopause and the dipole. We also observed for increased ion thermal velocities, for example, $v_{thi}\/v_0 \\approx 0.25$, that the background waves are no longer visible. \n\n\\par Additionally, other simulations were performed to look for possible changes with realistic parameters. A simulation with a lower flow velocity $v_0=0.01\\ c$ and realistic thermal velocity ratios lead to no significant features observed, and the obtained synthetic diagnostics were very similar to the ones in Figs.~\\ref{fig:realistic} a3) and b3), meaning that the system scales well with $v_0$. Another simulation was performed to observe if the shape of the initial density profiles of the plasmas would affect the main results. Namely, the constant density profiles used on both the driver and background plasmas were replaced by Gaussian density profiles with a typical gradient scale $\\sigma=1\\ d_i$ on the edges of the plasmas. This simulation did not show meaningful differences, in agreement with previous plasma coupling works, which observed that the leading edge of the plasmas evolves similarly for different initial density profiles~\\cite{doi:10.1063\/1.1694472}.%\n\n\\subsection{Finite transverse size}\\label{sec:finite}\n\n\\par For simplicity, and because we were more interested in studying the system along the axis of symmetry $y=0$, the previous simulations only considered a driver with infinite width $L_y$ and a length of $L_x=2\\ d_i$. In the experiments, however, the drivers had a width comparable to their lengths and did not have the sharp boundaries used in the simulations. To investigate if and how our results are modified with a more complex-shaped driver, we performed a simulation with a finite width, semi-circular-shaped driver plasma. This driver is initially defined with the conditions $(x+7.25\\ d_i)^2+y^2<(3.25\\ d_i)^2$ and $x>-6\\ d_i$ and has length $L_x=2\\ d_i$ and width $L_y=6\\ d_i$. Fig.~\\ref{fig:finite} shows the results of this simulation and includes the initial shape of the driver in Fig.~\\ref{fig:finite} a).%\n\n\\begin{figure*}[t]\n    \\includegraphics[width=\\linewidth]{plots\/finite-driver.pdf}\n    \\caption{\\label{fig:finite} a) Total ion density at time $t\\omega_{ci}=3.0$, and temporal evolution of b) the variation of the magnetic field $\\Delta B_z$ and c) the current density $J_y$ at $y=0$, for simulation G with a finite width driver with a circular segment shape. The dashed lines at a) represent the initial position of the driver and the left border of the background plasma.}%\n\\end{figure*}\n\n\\par Due to the finite width of the new driver and its particular shape, we should expect to see significant differences in the regions of the simulation plane far from $y=0$. In the total ion density plot of Fig.~\\ref{fig:finite} a) for a time $t\\omega_{ci}=3$, when there is a strong interaction of the driver with the dipolar magnetic field, we observe the propagation of waves at the lower and upper sides of the dipole caused by the finite width of the driver, that was not present for infinite width drivers.%\n\n\\par In Figs.~\\ref{fig:finite} b) and c), we see the usual magnetic and current density plots at $y=0$ for this simulation. By shortening the driver plasma width, the background particles escape from the bottom and top regions of the simulation box, and the driver has more difficulty holding the magnetic decompression in the background region. The decompression, therefore, occurs quicker for finite drivers, as seen in Fig.~\\ref{fig:finite} b), leading to short reflections of the magnetic compression.\n\n\\par Although this complex-shaped driver gets us closer to the experimental configuration, the simulations did not include all the properties of the experimental driver, as for example, the non-uniform density, velocity profiles of the plasmas and the flow divergence. Additionally, 3D effects should also be considered. Future simulations are planned to study the effect of these properties in the results. However, we expect that these features will not change the main results of the simulations.%\n\n\\section{Conclusions} \n\\label{sec:conclusions}\n\n\\par In this work, we have performed PIC simulations of mini-magnetospheres in the interaction between a plasma flow and a magnetized background plasma. In particular, we have successfully reproduced results from recent experiments performed at the LAPD, validating the experimental platform to study mini-magnetospheres in the laboratory. We have also explored an extensive parameter space defining the interaction, allowing us to i) determine how the main properties of the system change with the parameters and ii) identify the required conditions for the creation of a mini-magnetosphere.%\n\n\\par Our simulations have shown that some system features are present across multiple regimes. The initial flow of the driver expels the magnetic field in the upstream region, leading to a magnetic cavity, and compresses the downstream magnetic field. The driver travels through the background until the magnetic field pressure is large enough to counterbalance the driver plasma pressure. A fast decompression of the background magnetic field then follows. If the background decompression occurs after the total reflection of the driver plasma, then we can observe the reflection of the compression of the magnetic field. To see this feature, the driver needs to be short enough to anticipate the driver reflection relative to the decompression but sufficiently long to ensure that it can get close to the dipole.%\n\n\\par For the super-Alfv\u00e9nic flows considered, the driver particles are reflected upstream during the interaction with the background plasma and the magnetic field. The coupling velocity (\\textit{i.e.}, the velocity at which the leading end of the driver travels through the background) is lower than the flow velocity and increases with the increase of the ratio between the driver and background densities. The coupling velocity and the length of the driver determine how far the driver can go through the background region without a dipole, for a uniform driver plasma. \n\n\\par The interaction of the plasmas with the dipole results in two magnetopauses. The first describes the balance between the kinetic pressure of the propelled background plasma plus the pressure of the plasma internal magnetic field and the total magnetic pressure. The seconds describes approximately the balance between the kinetic pressure of the driver plasma separated from the bulk distribution and the relative magnetic pressure. Using simulations with different dipole moments, we have shown that, for lower magnetic moments, the driver and background standoffs are closer to the center of the dipole, and the magnetopause current is more clearly identified than for higher magnetic moments. Furthermore, it is also easier to separate the magnetopause and diamagnetic currents for lower magnetic moments, consistent with experimental observations.%\n\n\\par In the simulations performed, we also observed the formation of waves in the background plasma region, between the magnetopause and the center of the dipole, where the magnetic field gradient was significant. These waves result from the excitation that always followed the formation of the magnetopause and were only observed for background plasmas with relative low ion thermal velocities. This condition may explain the absence of these waves in the experimental plots.%\n\n\\par Most of the simulations presented in this work were performed in idealized configurations. In particular, we used reduced ion-to-electron mass ratios, unrealistically high flow velocities, a simple flat-top driver density profile, and neglected thermal effects. In Sec.~\\ref{sec:realistic} and~\\ref{sec:finite}, we presented simulations that drop some of these simplifications. Replacing reduced ion mass ratios with realistic ones and considering high thermal velocities ratios close to the obtained in the experiments did not lead to significant changes in the results. The same occurred when considering smoothed density profiles. It was also possible to conclude that the main features of the system scaled as expected with the absolute value of the driver flow velocity. We also presented a simulation to study possible effects associated with the complexity of the experimental laser-ablated driver. A simple circular segment-shaped driver was considered and led to similar results in the axis of symmetry as the infinite width driver simulations. However, wave-like structures were observed on both the bottom and upper sides of the dipole. For future studies on the regions outside the axis of symmetry, the driver shape and complexity must be considered.%\n\n\\par Additionally, we also performed other parameter scans related to the complexity of the driver. For instance, we performed simulations where the driver ions were heavier than the background ions to simulate the small role of the carbon ions in the experimental driver. These studies showed no significant differences to the lighter ions simulations.\n\n\\par In conclusion, the simulations were consistent with the LAPD experimental results, and the multiple parameter scans performed dictated the formation conditions of the main features of mini-magnetospheres. For future works, we intend to exploit the features present in the sides of the dipole, exploit anti-parallel magnetic field configurations, perform 3D simulations, and consider even more realistic properties of the driver.\n\n\\begin{acknowledgments}\n\n\\par We acknowledge the support of the European Research Council (InPairs ERC-2015-AdG 695088), FCT (PD\/BD\/114307\/2016 and APPLAuSE PD\/00505\/2012), the NSF\/DOE Partnership in Basic Plasma Science and Engineering (Award Number PHY-2010248), and PRACE for awarding access to MareNostrum (Barcelona Supercomputing Center, Spain). The simulations presented in this work were performed at the IST cluster (Lisbon, Portugal) and at MareNostrum.\n\n\\end{acknowledgments}\n\n\\nocite{*}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nRadio continuum emission traces star formation on timescales of up to\n100 Myr \\citep{C92}. Two physical processes resulting from massive\nstar formation produce most of the radio continuum emission between 1\nand 100 GHz in star-forming galaxies: (1) nonthermal synchrotron\nemission from relativistic electrons accelerated by magnetic fields as\na result of recent supernovae and (2) thermal free-free emission from\ngas ionized by young massive stars \\citep{C92}. The nonthermal\nemission is closely tied to the number of supernova-generating massive\nstars produced in recent episodes of star formation, while the thermal\nemission gives a nearly direct measure of the current equivalent\nnumber of O stars via the ionizing flux in the sampled area. Since\neach component traces a physical process with a well-known timescale,\nwe can use measurements of the radio continuum to determine star\nformation rates and constrain the ages of recent episodes of star\nformation.\n\nRecent studies of nearby star-forming galaxies with interferometers\nhave emphasized resolving individual star-forming regions\n\\citep*[e.g.][]{B00,J03,JK03,J04,T06,R08a,J09,A11}. Since radio\ncontinuum emission is not affected by extinction, it can be used to\nobserve deeply embedded regions of current star formation that have\nnot yet shed their surrounding material and are thus invisible at\nshorter wavelengths. These studies have taken advantage of\ninterferometers' exceptional spatial resolution to probe very young\nstarbursts whose optical emission is obscured by dust. While these\nstudies have been invaluable for determining star formation properties\nin galaxies outside of our own, the high angular resolution and\nmissing short-spacing data of interferometers, especially at higher\nfrequencies, ``resolves out'' the diffuse radio continuum emission\noutside of compact star-forming regions. This effect disproportionally\nimpacts synchrotron emission, which tends to be much more diffuse than\nthe primarily thermal emission surrounding areas of ongoing massive\nstar formation \\citep{J09}. Unlike interferometers, single dish\ntelescopes are not plagued by missing short spacings. Therefore, these\ntelescopes provide a way to simultaneously measure the compact thermal\nand diffuse non-thermal components of a galaxy's radio continuum\nemission in order to characterize its \\emph{global} star formation\nproperties.\n\nDetermining the relative contributions of the thermal and nonthermal\ncomponents of the measured flux of entire galaxies can be challenging.\nFortunately, each component has a distinct behavior with respect to\nfrequency, and therefore we can model radio continuum emission with a\nsimple two-component fit. Radio continuum flux follows a power law\nrelation such that $S_{\\nu} \\propto \\nu^{\\alpha}$, where $\\alpha$ is\nthe spectral index that is characteristic of a source's\nemission. Optically thin thermal emission exhibits $\\alpha =$ -0.1,\nand nonthermal emission exhibits $\\alpha \\approx$ -0.8 \\citep{C92}. To\ndetermine a reliable fit to these parameters, observations sampling\nthe same physical area at multiple, widely-spaced frequencies are\nrequired. If only one frequency is observed, it is impossible to\ndetermine the relative contributions of each emission process without\nprevious knowledge of the source. Since single dish telescopes are\nsensitive to both compact thermal and diffuse nonthermal emission over\nlarge spatial extents, they are useful for constraining the\nlarge-scale properties of multiple components of a galaxy's radio\ncontinuum emission, and are thus powerful probes of star formation.\n\n\nThe goal of this paper is to characterize the \\emph{global} star\nformation properties of local galaxies. Our observations were taken in\nfour independent channels continuous in frequency across the full\n26-40 GHz span of Ka band. This range in frequencies is where a\ntypical star-forming galaxy's global radio continuum emission would be\nexpected to contain relatively equal amounts of flux from\nsteep-spectrum synchrotron and flat-spectrum thermal sources\n\\citep{C92}. Our observations are thus ideal for approximating the\nrelative contributions of each type of emission at this ``lever arm''\nfrequency range. Using new radio continuum observations centered at\n27.75 GHz, 31.25 GHz, 34.75 GHz, and 38.25 GHz, as well as archival\nNVSS 1.4 GHz and IRAS 60 $\\rm \\mu m$ and 100 $\\rm \\mu m$ data, we have\ndetermined these galaxies' thermal fractions and star formation\nrates. We have also explored the radio-far-infrared correlation in\nthese galaxies and its implications for their star formation\ntimescales. We will describe the galaxy sample and our observations\nand data reduction in Section 2, present our results and address the\nprocess of fitting spectral energy distributions to our data in\nSection 3, and finally conclude in Section 4.\n\n\\section{Data}\n\n\\subsection{Sample Selection}\n\nWe selected a heterogeneous group of 27 local (D $<$ 70 Mpc),\nwell-studied star-forming galaxies with known thermal radio continuum\nemission. Our sample contains galaxies spanning a variety of shapes,\nsizes, and environments, from blue compact dwarfs to grand-design\nspirals, including major and minor mergers, with members of compact\ngroups as well as more isolated galaxies (see Table\n\\ref{fig:obssummary} for galaxy types). The intention was to observe\nas many types of star-forming galaxies as possible to probe star\nformation in a diverse range of environments. See Table\n\\ref{fig:obssummary} and Figure \\ref{fig:sampleproperties} for sample\nproperties. For more information on each galaxy's previous radio\ncontinuum observations and discussions of their properties, see the\npapers named in Table \\ref{fig:obssummary}.\n\n\nThe galaxies in our sample span a range of distances (1-70 Mpc) and\nproperties. They all have previously detected radio emission and\nongoing star formation that covers three orders of magnitude in star\nformation rate. Thus, they are strong targets for a study of global\nradio continuum properties at a frequency range that probes both\nthermal free-free and nonthermal synchrotron star formation\nindicators. As seen in Figure \\ref{fig:sampleproperties}, these\ngalaxies are largely less massive and have higher star formation rates\nthan the Milky Way, and have subsolar metallicities. However, their\nproperties are not so similar that they can be considered as a single\nclass. It would not be surprising if their radio continuum properties\nalso encompassed a range of values. Our analysis is best understood as\nreflecting properties of nearby star-forming galaxies, though it is\nbeyond the scope of this paper to perform detailed analysis on each\ngalaxy individually.\n\n\\subsection{Observations and Data Reduction}\nWe observed the galaxies in our sample with the Caltech Continuum\nBackend (CCB) on the Robert C. Byrd Green Bank Telescope\n(GBT)\\footnotemark{} using single pointings. The CCB is designed for\nthe GBT's dual-beam Ka band receiver spanning the entire range of\nfrequencies from 26-40 GHz. The primary observing mode of the CCB is a\n70 second ``nod'', where each beam takes a turn as the on-source beam\nwhile the other beam is off-source. We observed 24 of the galaxies\nusing a single nod each, while we observed eight galaxies using\nmultiple nods, which we then averaged. Five galaxies in our sample\nwere observed on two different nights with both of these methods; we\ntreated these on a case-by-case basis and chose the observation(s)\nwith the best weather and elevation conditions. We used the standard\nNRAO primary flux calibrators 3C 147 and 3C 48 for flux calibration,\nas well as nearby pointing calibrators to ensure accurate\npointing. See Table \\ref{fig:obssummary} for a summary of the\nobservations.\n\n\\footnotetext{The National Radio Astronomy Observatory is a facility\n  of the National Science Foundation operated under cooperative\n  agreement by Associated Universities, Inc.}\n\n\nWe reduced our data using IDL reduction routines developed by B.\nMason \\citep[for details on the data reduction process,\n  see][]{M09}. Data with wind speeds over 5 $\\rm m \\ s^{-1}$ were\nexcluded due to the possibility of large pointing errors. We detected\n22 galaxies in all four channels. When a galaxy's flux was lower than\nthe 2$\\sigma$ level in one or more of the four channels, we combined\nthe channels' fluxes to produce one average flux across the entire\nband, centered at 33 GHz. One galaxy, Pox 4, was detected at the\n$5\\sigma$ level after averaging the four channels. Three additional\ngalaxies were marginally detected (between 2$\\sigma$ and 3$\\sigma$)\nusing this method. We report an upper limit 33 GHz flux for one\ngalaxy, Tol 35. The galaxies' observed fluxes are reported in Table\n\\ref{fig:uncorrectedflux}.\n\nSince the angular size of a telescope's beam is inversely proportional\nto the frequency observed, the beam size of the GBT varies appreciably\nacross the 26-40 GHz range of our observations ($\\sim27\\arcsec$ in the\nlowest-frequency sub-band versus $\\sim19\\arcsec$ in the\nhighest-frequency sub-band, see Figure ~\\ref{fig:beamsizes} for an\nillustration). We followed the procedure of \\citet{M10} to correct for\ndiffering beam sizes in each of the four sub-bands. First, we imaged\nan archival VLA radio continuum map of each galaxy (typically at\nfrequencies of 4-10 GHz) using the AIPS task IMAGR. For these maps, we\nselected the archival UV data from the NRAO science data\narchive\\footnotemark{} with the closest beamsize to our Ka-band\ndata. We explicitly imposed each of the four CCB beam sizes on these\nimages using BMIN and BMAJ (assuming a circular beam). We determined\ncorrection factors for each beam by normalizing the flux contained in\neach beam area in the archival map to the flux in the 34.75 GHz port's\n$\\sim21\\arcsec$ beam. This procedure partially adjusts for more flux\nbeing observed at lower frequencies due to these frequencies'\nintrinsically larger beam sizes. We then could approximate\n``beam-matched'' flux measurements to determine spectral indices\nbetween 26-40 GHz (see Figure \\ref{fig:histogram} for an illustration\nof the galaxies' spectral indices before and after applying the\ncorrections). NGC 1222 did not have available archival data, so we\napplied to it the average correction factors of all of the other\ngalaxies. We emphasize that these correction factors are only\napproximate. In many cases, they are based on resolved archival images\nthat may not contain all of the galaxies' radio flux. In particular,\nthese resolved images may contain most of the thermal emission, which\ntends to be compact, but underestimate the galaxies' nonthermal\nemission, which tends to be diffuse. This could bias the correction\nfactors to be closer to 1.0 than should be the case, especially in the\nhighest-frequency (and thus highest-resolution) channel. See Table\n\\ref{fig:beamcorrections} for the beam correction factors for each\ngalaxy. \n\nThe dominant sources of uncertainty in our beam corrections are\nsystematic errors due to the geometries of our sources. The smallest\ncorrections possible are for a galaxy whose most diffuse, extended\nflux is still contained within the smallest beam and is unresolved by\nthe lower-frequency interferometric observations. This type of source\nwould look identical to all four of the GBT beam sizes. In this case,\nthe correction factors would be 1.0 for each sub-band. For a source\nmuch more extended than the beam sizes, the maximum deviations from no\nbeam corrections in each sub-band are -36$\\%$, -19$\\%$, 0$\\%$, and\n+21$\\%$. Pointing offsets from the peak of radio emission can also be\nsources of systematic error, though the errors depend on whether the\nsource is compact or extended, and the magnitude of the pointing\noffset from the central peak of radio emission. These errors are\ntypically smaller than the maximum deviations discussed above. Since\nwe do not know how much diffuse emission is missing in the archival\ndata, we do not have enough information to quantify uncertainties in\nthe beam correction factors for each galaxy.\n\n\\footnotetext{https:\/\/archive.nrao.edu}\n\nMany of the galaxies that we observed were more extended than the\n$\\sim 23\\arcsec$ beam size of the GBT at 33 GHz. In these cases, radio\ncontinuum fluxes and star formation rates should only be interpreted\nas covering the inner $\\sim 23\\arcsec$ of the galaxies. The galaxies\nwith resolved lower-frequency archival data that was more extended\nthan the beam size are flagged with a ``1'' in Table\n\\ref{fig:correctedflux}.\n\nThe CCB has a beam separation of $78\\arcsec$ between the ``on'' and\n``off'' beams. M 51 and M 101 are more extended than that separation\nin both optical images (see Figure \\ref{fig:beamseparation}) and in\nmaps of their lower-frequency radio continuum emission\n\\citep{K84,G90}. In these cases, our flux measurements may be lower\nthan the true amount of flux contained within the beam. There is\nlikely to be radio continuum emission at the ``off'' positions, which\nwould cause an oversubtraction of flux in the reduction process.\n\n\\section{Results and Discussion}\n\n\\subsection{Fluxes}\nFor 22 of the 27 galaxies that we observed, the fluxes we report are\nthe first detections (either in all four sub-bands or averaged) at\n$\\sim$33 GHz. Four of the galaxies in our sample were previously\nobserved with the CCB by \\citet{M12}, three of which were detected (M\n101 was reported as an upper limit by \\citet{M12} and is a $2.6\\sigma$\nmarginal detection when the four sub-bands were averaged in our\nobservations). Only one galaxy in our sample, Tol 35, was not detected\nwhen averaging four sub-bands' fluxes. Its $3\\sigma$ upper-limit flux\nis 0.87 mJy. This galaxy was observed at a very low elevation\n($7.9^{\\circ}$), so it was observed with large atmospheric\nextinction. See Table \\ref{fig:uncorrectedflux} for the uncorrected\nfluxes, and Table \\ref{fig:correctedflux} for the fluxes corrected for\nthe differing beam sizes of each frequency.\n\n\\subsection{Spectral energy distribution fitting}\nWe fit a spectral energy distribution (SED) for each galaxy that was\ndetected in all four sub-bands using the four CCB fluxes and archival\nNRAO VLA Sky Survey (NVSS) 1.4 GHz fluxes (measured with a 45$\\arcsec$\naperture). We assumed a two-component fit of nonthermal emission with\na spectral index $\\alpha_{N}$ = -0.8 and thermal emission with a\nspectral index $\\alpha_{T}$ = -0.1. These fits are plotted in Figure\n\\ref{fig:sedpanel}. Though the spectral index of nonthermal emission\ncan vary (this phenomenon is described further in Section 3.2.1), we\nused this simple model because we only fit to five data points for\neach galaxy; our model did not include enough data to justify\nadditional free parameters. We do not see evidence of anomalous dust\nemission in the observed regions of these galaxies \\citep[for\n  explanations of anomalous dust, see][]{D98,M10}. Our observations\nare also at frequencies low enough to have negligible contributions\nfrom the low-frequency tail of the dust blackbody. Therefore, we did\nnot include any thermal dust emission in our fits. Our spectra also do\nnot show the inverted structure characteristic of self-absorption or\noptically thick thermal emission, so we did not include either of\nthese components. From these fits, we determined each galaxy's thermal\nand nonthermal fluxes at 33 GHz.\n\nNone of the galaxies have globally flat spectra indicative of purely\nthermal emission, nor the inverted spectra seen in some resolved\nobservations of very young, obscured thermal sources. Thermal emission\nwas the primary component at 33 GHz in some galaxies, while others had\nless prominent or even negligible thermal components in the observed\nregions. In contrast to radio continuum studies done at high spatial\nresolution, our single dish observations detect the diffuse\nsynchrotron emission produced by past supernovae in addition to the\nstrong compact thermal emission from H II regions, so the spectral\nindices that we derive are typically much steeper than those derived\nonly from detections of compact radio sources. Since our observations\ndo not spatially separate regions of thermal and nonthermal emission,\nwe cannot further distinguish the two components in that way.\n\n\\subsubsection{Galaxies with steep radio spectra}\nThe fitted spectra for eight of the 27 galaxies (Arp 217, NGC 4449,\nNGC 2903, Maffei II, NGC 4038, M 51, NGC 4490, and NGC 1741) are\nsignificantly steeper than can be fit by a combination of thermal\n($\\alpha_{T}$ = -0.1) and nonthermal ($\\alpha_{N}$ = -0.8) components\n(see Figure \\ref{fig:sedpanel}). When we could not fit a galaxy's SED\nwith both the thermal and nonthermal components at the $2\\sigma$\nlevel, we used only a single-component fit that assumed no thermal\nflux and a fixed nonthermal spectral index of $\\alpha_{N}$ = -0.8 for\nconsistency. The thermal fluxes and associated properties of this\ngroup of galaxies are reported as upper limits. We used the total flux\nin the 34.75 GHz channel plus 3$\\sigma$ as a conservative upper limit\nto the thermal flux in these cases.\n\nThere are two possible explanations for the steep spectra that we see\nin some galaxies. There could be technical considerations due to\nimperfect beam-matching in our data, or there could be physical\nprocesses taking place within these galaxies causing their spectra to\nsteepen at high frequencies. In order to have more accurate SED\nfits---and more precise star formation rates---we would need to have\nbeam-matched observations of the same regions at many different\nfrequencies. \n\nThe correction factors for differing beam sizes that are given in\nTable \\ref{fig:beamcorrections} are limited by being calculated using\nhigher-resolution data that could be missing extended emission. If\nextended emission is missing in the archival data, the correction\nfactors in Table \\ref{fig:beamcorrections} could be closer to 1.0 than\nis actually the case. While all of the correction factors calculated\nact to flatten the SED between 26 GHz and 40 GHz with respect to the\nuncorrected data, it is possible that they do not flatten the SED\nenough if they do not reflect contributions from extended emission (as\ndiscussed in Section 2.2). In addition, we did not correct for\nmismatched beams between the $\\sim 45\\arcsec$ NVSS data and the $\\sim\n23\\arcsec$ CCB data. This beam difference only affects resolved\ngalaxies (those marked with a ``1'' in Table \\ref{fig:correctedflux}),\nwhich comprise $33\\%$ of our sample. It is possible that synchrotron\nemission is more adversely affected by the differences in beam sizes\nthan thermal emission. More diffuse synchrotron emission could be\nundetected at higher frequencies (and thus smaller beam sizes) than\nwould be expected for a smooth flux distribution observed with two\napertures of different sizes. If this is the case in our observed\nregions, it could explain why some of our galaxies' spectra steepen at\nthe frequencies we observed. It is also possible that the choice of\nwhere the GBT beams were pointed within a galaxy could affect its\nfluxes in different beam sizes. If the beam is not centered on the\ngalaxy (in the case of unresolved galaxies) or is not centered on a\nbright knot of emission (in the case of resolved galaxies), the\nsmaller beams could contain even less flux than would be expected\nafter corretions for the beams' areas. NGC 1741 and NGC 4490 are\nlikely affected by pointing offsets, as seen by comparing the GBT\npointing in Table \\ref{fig:obssummary} to previous radio continuum\nmaps in Figure 2 of \\citet{B00} and Figure 4 of \\citet{A11}. As\ndescribed in Section 2.2, pointing offsets from the peak of radio\ncontinuum emission result in the need for larger beam correction\nfactors than derived from the archival radio continuum data, the lack\nof which result in steep spectra at the observed frequencies.\n\n\nIn addition to the technical issue of mismatched beam sizes, there are\npossible physical explanations for steep spectra in star-forming\ngalaxies. It is difficult to distinguish between a spectrum with a\nnonthermal component having $\\alpha_{N} \\approx -0.8$ coupled with a\nlow thermal fraction from a spectrum with a steeper nonthermal\ncomponent coupled with a relatively high thermal fraction\n\\citep{C92}. Though the spectral indices that we used are typical\nvalues \\citep{C92}, they can vary depending on the physical parameters\nof the observed regions. Thermal emission can have a positive spectral\nindex if the emission regions are optically thick, though we do not\nsee any evidence that this is occuring on the angular scale of our\nobservations. Nonthermal spectral indices can be positive at low\nfrequencies due to synchrotron self-absorption (which we do not\nobserve), or become more negative with increasing frequency and\nincreasing scale height from the disk due to aging cosmic ray\nelectrons losing energy as they propagate outward from their parent\nsupernovae \\citep{S85,CK91,H09}. \\citet{K11b} calculated the timescale\nfor synchrotron losses for cosmic ray electrons in NGC 4214 to be 44\nMyr at 1.4 GHz and 18 Myr at 8.5 GHz. There is also some evidence of\nsteepening spectra at higher frequencies ($\\gtrsim$ 10 GHz) for\nluminous and ultra-luminous infrared galaxies, as well as in the\npost-starburst galaxy NGC 1569 \\citep{I88,L04,C08,C10,L11}. These\nauthors hypothesize that winds or outflows may disperse synchrotron\nemission from its parent source more quickly than would be expected\nfor simple diffusion. This rapid dispersal could cause a dearth of\nsynchrotron emission at higher frequencies on shorter timescales than\nwould be predicted from the timescale of energy loss. \\citet{L11} also\nhypothesize that there could be a modified injection spectrum in\ngalaxies where this is the case. Our sample of galaxies does not\ncontain any LIRGs or ULIRGs, and we do not see steepening in our\nmeasurements of NGC 1569. We are only observing the inner region of\nNGC 1569, while the dispersed synchrotron emission resides in its\nouter halo, so it is not surprising that we do not observe a\nsteepening spectrum in this galaxy.\n\nWe suspect that the steep spectra seen in our sample are primarily a\nresult of imperfect beam matching as discussed above. This is\nespecially likely to be the case for the galaxies resolved by the GBT\nat 33 GHz, since these galaxies will have emission that is outside of\nthe view of the GBT beam but is included in the NVSS flux. As\ndiscussed earlier, the galaxies that appear unresolved in archival\nmaps could still have diffuse synchrotron emission that was not\ndetected in the archival data but that is more extended than the\n$23\\arcsec$ beam at 33 GHz. Five of the eight resolved galaxies that\nwere detected in all sub-bands had steep spectra (four out of those\nfive are classified as spiral galaxies), while only three of the\nfourteen unresolved galaxies had this feature. Two of these three are\nclassified as SABbc galaxies, while the third is classified as\npeculiar. It is possible that these steep-spectrum galaxies contain\nemission in their spiral arms that is extended with respect to the\nGBT's smaller beam but is observed in the NVSS data. In Figure\n\\ref{fig:sedpanel}, most of the galaxies with steep spectra (and thus\nsingle component fits) also showed the NVSS 1.4 GHz data point being\nlocated above the best-fit line expected for purely nonthermal\nemission. This could be a consequence of the larger beam at 1.4 GHz\nsampling a larger physical area of emission. Even so, the alternative\nphysical explanations merit consideration, especially in the case of\nthe unresolved galaxies. In Figure \\ref{fig:rad-IR}, which will be\ndiscussed further in Section 4.6, the three unresolved galaxies with\nsteep spectra (NGC 1741, NGC 2903, and Arp 217) have elevated 1.4 GHz\nfluxes with respect to what would be expected from the radio-far\ninfrared correlation. Since the 33 GHz fluxes of these galaxies are\nnot similarly elevated with respect to their far-infrared fluxes in\nFigure \\ref{fig:rad-IR}, their steep radio spectra may indicate an\ninternal physical process that strongly increases the amount of\nsynchrotron emission.\n\n\\subsection{Thermal fractions}\nThe average thermal fraction fit by two-component models at 33 GHz was\n54$\\%$, with a $1\\sigma$ scatter of 24$\\%$ and a range of\n10$\\%$-90$\\%$. The average is consistent, albeit with large scatter,\nwith the average global thermal fraction at 33 GHz in star-forming\ngalaxies without active galactic nuclei following the relation\n\\begin{equation}\n\\frac{S}{S_{T}} \\sim 1 + 10\\left(\\frac{\\nu}{GHz}\\right)^{0.1+\\alpha_{N}}\n\\end{equation}\n where $\\alpha_{N} = -0.8$ is the nonthermal spectral index, $S_{T}$\n is the thermal flux at a given frequency, and S is the total flux at\n that frequency \\citep{CY90}. When a two-component fit was not\n possible, we report the thermal flux as the corrected flux at 34.75\n GHz plus $3\\sigma$, which gives a very conservative upper limit. We\n expect from the galaxies' SEDs that their true thermal fractions are\n very low at 33 GHz, which we assume in the rest of our analysis.\n\n\\subsubsection{Implications for star formation timescales}\nThe large scatter in the thermal fraction is likely a consequence of\nour heterogeneous galaxy sample; these galaxies are at different\nstages of evolution and have different star formation rates, stellar\npopulations, and physical properties \\citep{B00}. Some of them may\nhave a very recent ($<$ 10 Myr) burst of star formation that produces\na large amount of free-free emission that dominates their spectra from\n1-100 GHz. Others may be in between episodes of very active star\nformation and instead be experiencing a more quiescent phase, which\nwould result in a relatively low thermal fraction and steepening\nnonthermal component at 33 GHz due to synchrotron energy losses at\nhigh frequencies.\n\nThermal emission traces very recent star formation, since it comes\nfrom ionized regions around short-lived, massive stars. For a single\nstarburst, a spectrum showing solely thermal emission requires that\ntoo few supernovae have yet occurred to detect their emission. This\nwould constrain the starburst to be less than $\\sim$ 6 Myr old (or\neven younger, depending on the mass and lifetime of the most massive O\nstars in the starburst; \\citet{M89} find the lifetime of a 120\n$M_{\\sun}$ star to be 3.4 Myr). A complete absence of thermal flux\nimplies the absence of enough massive O stars to have detectable\nfree-free emission for a long enough period of time that the emission\nhas dissipated from its parent region. If this was the case, the\nstarburst is likely at least 30 Myr old (the lifetime of the least\nmassive supernova progenitors). On the other hand, nonthermal emission\nprobes star formation on longer timescales (30 Myr $< \\tau <$ 100\nMyr). It is produced by recent supernovae of stars that can be less\nmassive and have longer lifetimes than the O stars that produce\nthermal emission \\citep[see Figure 9 of][]{C92}. The presence of\nnonthermal emission implies that the starburst is at least 6 Myr old\nbut younger than the timescale dictated by synchrotron energy loss for\nthe galaxy's magnetic field ($\\sim$ 100 Myr) \\citep{C92}.\n\nWe note that there are limits to the amount of each component that we\ncan detect, so the timescales quoted in the previous paragraph are\nonly approximate. To constrain how much nonthermal emission could be\npresent in a spectrum that appears purely thermal, we generated\nspectra with varying thermal fractions with fluxes at the same five\nfrequencies as those in our data set (1.4 GHz, 27.75 GHz, 31.25 GHz,\n34.75 GHz, and 38.25 GHz) and 10$\\%$ errors on the fluxes. When these\nspectra are fit with a two-component model assuming $\\alpha_{T} =\n-0.1$ and $\\alpha_{N} = -0.8$, nonthermal emission can only be\ndetected in the spectra for thermal fractions less than 97$\\%$. This\nmeans that the galaxy could have some nonthermal emission (up to $3\\%$\nfor $10\\%$ errors on the fluxes), but the emission would be\nundetectable and thus the starburst would appear younger than it\nis. Similarly, a spectrum could look like it contains no thermal\nemission while actually containing quite a bit. For the same spectra\nwith $10\\%$ errors on the fluxes, thermal fractions of up to $20\\%$\nresulted in undetectable thermal components. This means that a galaxy\ncould look like its massive star formation has ceased while still\nhaving a small thermal component.\n\nFor the galaxies in our sample, this picture could be more\ncomplicated. The quoted timescales in this section are for an isolated\nsingle starburst. Since our observations measure star formation\nproperties on large angular scales, the galaxies may have multiple\noverlapping generations of star formation that are not easily\nseparated in time. We are also sampling different structures and\nphysical scales in each galaxy. For some galaxies, we are only\nobserving the most central region. For these galaxies, we may be\nmissing the majority of the ongoing star formation happening in outer\nregions and spiral arms. For the more compact galaxies, however, we\nare likely measuring the entirety of the galaxy's star formation\nwithin the GBT beam, so our measurements characterize their global\nstar formation properties.\n\n\\subsection{O stars producing ionizing photons}\nFor those galaxies whose SEDs were fit with thermal components, we\nused their fluxes at 33 GHz to calculate their thermal\nluminosities. We then used those luminosities to calculate the number\nof ionizing photons responsible for the thermal fluxes seen within the\nGBT beam following Equation 2 in \\citet{C92}:\n\\begin{equation}\n\\left(\\frac{Q_{Lyc}}{s^{-1}}\\right) \\geq 6.3 \\times 10^{52}\n  \\left(\\frac{T_{e}}{10^{4}K}\\right)^{-0.45} \\left(\\frac{\\nu}{GHz}\\right)^{0.1}\n  \\left(\\frac{L_{T}}{10^{20}W Hz^{-1}}\\right),\n\\end{equation}\nwhere $Q_{Lyc}$ is the number of Lyman continuum photons emitted by\nthe region on thermal emission, $T_{e}$ is the electron temperature,\nand $L_{T}$ is the thermal luminosity. The resulting values are\ndetailed in Table \\ref{fig:sfrfractableunres} (unresolved galaxies)\nand Table \\ref{fig:sfrfractableres} (resolved galaxies). We used an\nelectron temperature of $10^{4}$K, as is typical for star-forming\nregions \\citep{C92}, and used $Q_{0} = 10^{49} s^{-1}$ as the number\nof Lyman continuum photons emitted by an O7.5V star from Table 5 in\n\\citet{Vacca96}. We report the total number of O7.5V stars in the\ngalaxies that are unresolved by the GBT at 33 GHz, and the number of\nO7.5V stars per square kiloparsec for the resolved galaxies in Tables\n\\ref{fig:sfrfractableunres} and \\ref{fig:sfrfractableres}. As seen in\nTable \\ref{fig:sfrfractableunres}, the number of O7.5V stars in each\nunresolved galaxy varies widely (log $\\#$ O7.5V stars is between 2.42\nand 4.66). This is likely due to the wide range in the unresolved\ngalaxies' overall star formation rates and physical areas observed.\n\n\\subsection{Supernova rates}\nSince we were able to fit nonthermal components for all of our\ngalaxies, we calculated supernova rates ($\\nu_{SN}$) for each of them\nfollowing Equation 18 in \\citet{C92}:\n\\begin{equation}\n\\left(\\frac{L_{N}}{10^{22}W Hz^{-1}}\\right) \\sim 13\\left(\\frac{\\nu}{GHz}\\right)^{-0.8} \\left(\\frac{\\nu_{SN}}{yr^{-1}}\\right),\n\\end{equation}\nwhere $L_{N}$ is the nonthermal luminosity. We report the total\nsupernova rate of the unresolved galaxies in Table\n\\ref{fig:sfrfractableunres}, while for the resolved galaxies we\nreport the supernova rate per square kiloparsec in Table\n\\ref{fig:sfrfractableres}. The supernova rates of the unresolved\ngalaxies vary by three orders of magnitude (log SNe rate between -3.72\nand -0.71), which is not surprising given the differences in star\nformation rates and physical areas sampled.\n\n\\subsection{Star formation rates}\nWe calculated massive star formation rates (SFRs) from thermal fluxes\nfor each galaxy whose SEDs have a thermal component and from\nnonthermal fluxes for all of our galaxies following Equations 21 and\n23 of \\citet{C92}:\n\\begin{equation}\n\\left(\\frac{L_{N}}{W Hz^{-1}}\\right) \\sim 5.3 \\times 10^{21}\n  \\left(\\frac{\\nu}{GHz}\\right)^{-0.8} \\left(\\frac{SFR_{N}\\left(M \\geq 5M_{\\sun}\\right)}{M_{\\sun} yr^{-1}}\\right)\n\\end{equation}\n\\begin{equation}\n\\left(\\frac{L_{T}}{W Hz^{-1}}\\right) \\sim 5.5 \\times 10^{20}\n  \\left(\\frac{\\nu}{GHz}\\right)^{-0.1} \\left(\\frac{SFR_{T}\\left(M \\geq 5M_{\\sun}\\right)}{M_{\\sun}yr^{-1}}\\right)\n\\end{equation}\nwhere $L_{T}$ and $L_{N}$ are thermal and nonthermal luminosities,\nrespectively, calculated from each galaxy's thermal and nonthermal\nfluxes, and $\\nu = 33$ GHz. These equations are derived from Equations\n2 and 18 of \\citet{C92} (reproduced as Equations 2 and 3 in this\npaper). Those equations were derived assuming (1) an extended\nMiller-Scalo IMF \\citep{MS79} with an exponent of $-2.5$, (2) that all\nstars with masses greater than $8 \\rm M_{\\sun}$ become supernovae, and\n(3) that dust absorption is negligible \\citep{C92}. We then scaled the\nmassive SFRs generated by each equation by a factor of 5.6 to\ntransform them to total SFRs (M $\\geq$ 0.1$M_{\\sun}$) calculated with\na Kroupa IMF \\citep{K01}. The galaxies' SFRs calculated from their\nthermal and nonthermal fluxes are shown in Table\n\\ref{fig:sfrfractableunres} (unresolved galaxies) and Table\n\\ref{fig:sfrfractableres} (resolved galaxies). We report the total\nmassive SFRs of the unresolved galaxies, while we report the massive\nSFR per square kiloparsec of the resolved galaxies. All of the\ngalaxies for which we calculated both thermal and nonthermal SFRs\nshowed agreement between the two to within an order of magnitude, but\nnot necessarily to within their margins of uncertainty. The\ndisagreement correlates with the thermal fractions of each galaxy:\ngalaxies with high thermal fractions were likely to have higher\nthermal SFRs than nonthermal SFRs, while galaxies with low thermal\nfractions showed the opposite relation. Like the differences in\nthermal fractions between galaxies in our sample, disagreement could\nbe due to the different star formation timescales traced by the\nthermal and nonthermal fluxes. Since these two emission components are\ncaused by physical processes that operate over differing lengths of\ntime (as discussed in Section 3.3.1), it is possible that the\ndiscrepancies between the star formation rates could be used to infer\nthe recent star formation histories of the observed regions.\n\nWe compared the radio continuum SFRs to monochromatic SFRs from 24$\\mu\nm$ fluxes as described in \\citet{Cal10}. The galaxies' SFRs (for the\nunresolved galaxies) and SFR densities (for the resolved galaxies)\nderived from 24$\\mu m$ fluxes are listed in Table\n\\ref{fig:sfrfractableunres} and Table \\ref{fig:sfrfractableres}. In\nFigure~\\ref{fig:comparesfrs}, we compare the SFRs derived from thermal\nand nonthermal radio continuum fluxes of the unresolved galaxies for\nwhich we fit two-component SEDs to SFRs derived from 24$\\mu m$\nfluxes. We find that most of the galaxies in our sample have higher\nradio continuum SFRs (both from thermal and nonthermal fluxes) than\nSFRs from 24$\\mu m$ data. One possible explanation for this is that\nextinction is lower at radio wavelengths than it is at 24$\\mu\nm$. Another possible explanation is that since radio continuum\nemission traces very young star formation while 24$\\mu m$ emission\ntraces less recent star formation, higher SFRs calculated from radio\ncontinuum observations than from 24$\\mu m$ data could be another\nindication that our sample of galaxies is undergoing recent star\nformation.\n\n\\subsection{Radio-far-infrared correlation}\nThere is a well-established tight correlation between far-infrared\n(FIR) and radio flux in star-forming galaxies\n\\citep[e.g.][]{H85,M06,M12}. When plotted on a log-log scale, the\nrelationship between radio continuum and FIR flux for star-forming\ngalaxies appears linear. This correlation has been well-studied at low\nfrequencies ($\\sim$ 1.4 GHz) where synchrotron emission is the\ndominant component of radio emission in a star-forming galaxy. We\ninvestigated whether this correlation could also be found on a global\nscale at 33 GHz, where synchrotron emission is weaker than it is at\n1.4 GHz and the relative contribution from thermal emission is more\nsignificant.\n\nWe limited our study of the radio-FIR correlation to the galaxies in\nour sample that are unresolved with the GBT beam at 33 GHz (as\ndiscussed in Section 2.2). We chose this limit to ensure that we were\nobserving both the total area of radio emission and total area of\nfar-infrared emission in each galaxy. This minimizes issues related to\nthe different beam sizes of the GBT and IRAS (objects are considered\npoint sources to IRAS if they are more compact than 1$\\arcmin$ at 60\n$\\rm \\mu m$ and 2$\\arcmin$ at 100 $\\rm \\mu m$). \n\nWe fit a power law to our 33 GHz flux as a function of total FIR\nflux. The total FIR flux was determined by a combination of archival\nIRAS 100 $\\rm \\mu m$ and 60 $\\rm \\mu m$ fluxes as described in\n\\citet{H88} ($S_{FIR} = 2.58 S_{60\\mu m} + S_{100 \\mu m}$). We chose\nto compute each galaxy's 33 GHz flux by taking the average of its\nfluxes in the four sub-bands. We used this measure (rather than the\nflux at 33 GHz inferred from the galaxies' SEDs) in order to eliminate\npossible uncertainties in the flux due to using assumed spectral\nindices in our fits. We found that the fluxes were related by $\\rm log\n\\ S_{33} = (0.88 \\pm 0.01) log \\ S_{FIR} + log \\ (5.3\\times 10^{-4}\n\\pm 6\\times 10^{-5})$. This correlation is relatively well-fit (the\nfractional errors of both fit parameters are small) even though our\nsample contains a wide range of thermal fractions. \\citet{M12} found a\nsimilar correlation between 33 GHz and $24 \\rm \\mu m$ fluxes for\nresolved nuclei and individual star-forming regions of galaxies. We\nfind that the radio-FIR correlation at 33 GHz can be extended to\nglobal measurements of galaxies' fluxes.\n\nAs a control of the tightness of the radio-FIR correlation in our\nsample, we also fit a relationship between the galaxies' NVSS 1.4 GHz\nfluxes and their total FIR fluxes. This relationship for the\nunresolved galaxies in our sample is $\\rm log \\ S_{1.4} = (0.85 \\pm\n0.01) log \\ S_{FIR} + log \\ (0.0047 \\pm 0.0006)$. The fractional\nuncertainties on the fit parameters are similar to those of the fit at\n33 GHz. We plot both correlations in Figure \\ref{fig:rad-IR}.\n\nAs discussed in Section 3.2, we have determined thermal fractions from\nSED fits assuming fixed thermal and nonthermal spectral indices. Due\nto the limited number of radio data points we have for each galaxy, we\ncannot more accurately constrain the thermal fractions at 33 GHz of\nthe galaxies in our sample at this time. Therefore, we do not have\nenough information to definitively isolate thermal and nonthermal\ncomponents to explore whether the radio-FIR correlation is equally\ntight for each. As an estimate, we have coded approximate thermal\nfractions in the plot. Even given these limitations, we are confident\nthat a correlation exists between the unresolved galaxies' total radio\nflux at 33 GHz and total FIR flux. \\citet{M12} found a similar\ncorrelation at 33 GHz for resolved nuclei and star-forming regions of\ngalaxies.\n\nTo further constrain the radio-FIR correlation at 33 GHz in our\nsample, we calculated $q_{\\nu}$ for each galaxy. $q_{\\nu}$ is a\nlogarithmic measure of the ratio of total far-infrared flux ($S_{FIR}$\nin Janskys) to radio continuum flux ($S_{\\nu}$) in units of $\\rm W\nm^{-2} Hz^{-1}$ at a given frequency.  It is defined in \\citet{H85} as\n\\begin{equation}\nq_{\\nu} = log\\left(\\frac{S_{FIR} \\cdot 1.26 \\times 10^{-14} W\n  m^{-2}}{3.75 \\times 10^{12} W m^{-2}}\\right) -\nlog\\left(\\frac{S_{\\nu}}{W m^{-2} Hz^{-1}}\\right).\n\\end{equation}\nThe average $q_{33}$ for our sample is $q_{33}=3.3$, with a 1$\\sigma$\nscatter of 0.3. \\citet{C92} reported that at 1.4 GHz, the average\nvalue of $q_{1.4}$ from a large sample of galaxies is $q_{1.4}=2.3 \\pm\n0.2$. The average value of $q_{\\nu}$ at 1.4 GHz for this set of\ngalaxies is $q_{1.4} = 2.4 \\pm 0.2$, consistent with the \\citet{C92}\nvalue. Since $q_{\\nu}$ is a function of the ratio of FIR flux to radio\nflux at a given frequency, it makes sense that $q_{\\nu}$ is larger\nusing 33 GHz fluxes than it is using 1.4 GHz fluxes (star-forming\ngalaxies are generally much brighter at 1.4 GHz than at 33 GHz). The\nscatter on $q_{\\nu}$ at 33 GHz is larger than that at 1.4 GHZ, which\nindicates that the radio-FIR correlation is not as tight at 33 GHz as\nat 1.4 GHz. This may be due to contamination from increased thermal\nflux at 33 GHz. If the correlation is solely between synchrotron and\nFIR emission, thermal flux at 33 GHz will increase the scatter in the\ncorrelation. However, due to our small sample size, we cannot rule out\nthe possibility that the correlation is just as strong at 33 GHz,\nwhere thermal fractions are higher, as it is at 1.4 GHz, where\nnonthermal emission is typically much stronger. We note that the\ngalaxies with the highest thermal fractions lie above the fitted\ncorrelation at 33 GHz, while the same is not true at 1.4 GHz, which\nsupports thermal emission being the cause of increased scatter.\n\nIn addition to plotting the radio-FIR correlation, we also plot the\nratio of 33 GHz flux to FIR flux, $q_{33}^{-1}$, against\n$\\alpha_{1.4-33}$ for our unresolved galaxies in Figure\n\\ref{fig:inverseqvsalpha}, similar to \\citet{M12}. The plot shows an\nincreasing $q_{33}^{-1}$ for flatter values of\n$\\alpha_{1.4-33}$. Flatter $\\alpha_{1.4-33}$ values are presumably\nindicative of a higher proportion of thermal flux to nonthermal flux,\nwhich is reflected in the highest thermal fractions in our sample also\nhaving the flattest $\\alpha_{1.4-33}$. A correlation between an\nelevated $q_{33}^{-1}$ and flat values of $\\alpha_{1.4-33}$ is not\nsurprising if the radio-FIR correlation is solely dependent on\nsynchrotron emission. If the radio-FIR correlation was independent of\nthe type of radio emission, $q_{33}^{-1}$ should be relatively\nconstant between galaxies and should not be affected by different\nspectral indices or thermal fractions. Our data support that the\nradio-FIR correlation is independent of a galaxy's thermal emission\nsince the addition of thermal emission results in elevated ratios of\n33 GHz flux to FIR flux.\n\n\\subsubsection{Implications for star formation timescales}\n\nWhen the timescales of the emission mechanisms for thermal,\nnonthermal, and FIR fluxes are taken into account, the observed\nrelationship between the ratio of 33 GHz and FIR fluxes and\n$\\alpha_{1.4-33}$ may be a way to age-date an episode of star\nformation. Since thermal flux is only produced by the shortest-lived\n($\\tau<10$ Myr) massive stars, its presence in large quantities\nrelative to synchrotron emission is indicative of very young star\nformation. Since in addition to massive stars, infrared emission also\ntraces less massive stars ($\\rm M > 5M_{\\sun}$) that live longer than\nthe $\\rm M > 8M_{\\sun}$ stars that produce thermal and nonthermal\nradio emission \\citep{D90}, FIR emission is a tracer of star formation\non longer timescales. Stars with these masses can live up to $\\sim$100\nMyr, while nonthermal radio emission traces stars with lifetimes of up\nto $\\sim$30 Myr and whose emission is detectable for up to 100 Myr\n\\citep[for an illustrative plot of stellar lifetimes, see Figure 3\n  of][]{R05}. In addition, infrared emission also contains a component\nfrom diffuse dust that is heated by lower-mass stars with lifetimes\nlonger than 100 Myr. These timescales could mean that the galaxies\nthat show both flat spectral indices and enhanced $q_{33}^{-1}$ also\nhost the youngest areas of ongoing star formation. This correlation\ncould then be a method of determining approximate ages for galaxies'\nglobal star formation. As a simple test, we used a Starburst 99 model\nof a single instantaneous burst using default inputs (solar\nmetallicity, a 2-component Kroupa IMF, and no effects of cosmic ray\naging, escape, or absorption taken into account) run for 100 Myr\n\\citep{L99,V05,L10}. This model, depicted in Figure \\ref{fig:sb99},\nshows the flattest spectral indices and highest thermal fractions at\nthe earliest times of the starburst. Similarly, the steepest spectral\nindices and lowest thermal fractions were seen as the lowest-mass\nstars that produce supernovae were dying (at $\\sim$40 Myr). The\nstarburst's ratio of 33 GHz luminosity to FIR luminosity was also high\nat early times (between 3 Myr and 40 Myr) while the lowest ratios of\n33 GHz luminosity to FIR luminosity were seen even later (after 40\nMyr). While modeling a more robust quantitative relationship between\nthis observed correlation and the age of each galaxy's star-forming\nepisode is beyond the scope of this work (the simple model we used\ndoes not take into account multiple co-existing generations of star\nformation), the apparent relationship between enhanced 33 GHz flux,\nflat spectral indices, and high thermal fractions is a promising\nmetric for future global radio and far-infrared photometric studies of\nstar-forming galaxies. Our simple model is not robust enough to\nconstrain the timescales' uncertainties, but is only meant to be\nillustrative of a correlation visible in our data.\n\n\n\\section{Conclusions}\n\nWe have observed 27 local, well-studied, star-forming galaxies between\n26-40 GHz with the GBT and obtained the first detections at this\nfrequency range for 22 of the galaxies. We determined the\ncontributions of thermal free-free and nonthermal synchrotron emission\nto the galaxies' total radio emission. We have used these measures to\nderive the number of massive, short-lived O stars and the number of\nrecent supernovae in the observed regions of each galaxy. In addition,\nwe have calculated SFRs for each galaxy using thermal and nonthermal\nfluxes and explored the radio-FIR correlation for the unresolved\ngalaxies. We found that\n\\begin{itemize}\n\\item None of the galaxies have spectral incides indicative of purely\n  thermal emission; eight galaxies show spectra that are too\n    steep to fit thermal components,\n\\item Thermal fractions range from 10$\\%$ to 90$\\%$, with a\n  median of $55\\%$,\n\\item The radio-far infrared correlation holds for the unresolved\n  galaxies at 1.4 GHz and 33 GHz, though the scatter at 33 GHz is\n  larger due to the increased influence of thermal emission at higher\n  frequencies, and\n\\item Galaxies with flat $\\alpha_{1.4-33}$ and high thermal fractions\n  have enhanced radio flux at 33 GHz with respect to far-infrared\n  flux, which identifies them as galaxies with recent star\n  formation. This is consistent with a simple model of a single\n  starburst.\n\\end{itemize}\n\nWe found that the observed regions of our galaxies had a diverse mix\nof radio continuum characteristics, with some galaxies' SEDs being\ndominated at 33 GHz by the thermal emission indicative of ongoing\nmassive star formation, while others have little or no detectable\nthermal emission. Even with this spread in the relative contributions\nof thermal and nonthermal emission, we saw that there is still a\ncorrelation between the global 33 GHz and far-infrared flux in the\nunresolved galaxies. The scatter in the correlation is larger than\nthat at 1.4 GHz, likely due to the increased influence of thermal\nemission at 33 GHz. We cannot, however, rule out that the radio-FIR\ncorrelation is not solely dependent on synchrotron emission. We also\nfound that higher ratios of 33 GHz emission to FIR emission correlated\nwith flatter spectral indices (and higher thermal fractions) for\nunresolved galaxies, which is consistent with younger ages in simple\nstarburst models. This correlation may be useful as a rough indicator\nof the age of the most recent episode of star formation. Future global\nstudies of more homogeneous galaxy populations or resolved studies of\nindividual star-forming regions will enable better modeling of star\nformation timescales using this metric.\n\nIn giving a broad measure of nearby galaxies' radio continuum\nemission, our observations complement previous studies done with\ninterferometers in which individual star-forming regions in local\ngalaxies were highly resolved. With the GBT, we can simultaneously\nobserve compact and diffuse thermal and nonthermal emission and\ndetermine their relative intensities, and in doing so estimate the\ntimescale for the current episode of star formation. Unfortunately, we\ncannot make stricter timescale estimates than those discussed in\nSection 3.3 at this time, as we do not have enough radio data points\nto robustly fit thermal and nonthermal flux components with varying\nspectral indices. Obtaining more unresolved radio fluxes at lower and\nhigher frequencies would help this effort.\n\nThis research has made use of the NASA\/IPAC Extragalactic Database\n(NED) which is operated by the Jet Propulsion Laboratory, California\nInstitute of Technology, under contract with the National Aeronautics\nand Space Administration. We acknowledge the use of NASA's SkyView\nfacility (http:\/\/skyview.gsfc.nasa.gov) located at NASA Goddard Space\nFlight Center. We thank the telescope operators and support staff at\nthe GBT for assistance with this project. K.R. acknowledges support\nfrom an NRAO student observing support award (GSSP10-0002). K.R. also\nthanks Brian Mason for his help with understanding the CCB observation\nand data reduction process.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section*{Appendix A. <some heading here>}\n\n\\widetext\n\\section*{\\large Supplemental material for stacking-induced Chern insulator}\n\n\\section{I. Haldane model in bilayer honeycomb lattice}\n\nWe consider a HM bilayer with AB and AA stackings where the layers are assumed to have complex NNN phases $\\Phi_1=-\\Phi_2=\\frac{\\pi}2$, to drop the global energy shift ($a^0_{\\mathbf{k}}=0$ (Eq.~\\ref{al})) which does not affect the topology of the system.\nIn the basis of the four orbitals forming the unit cell ($A_1,B_1,A_2,B_2$) the corresponding Hamiltonians can be written as\n\\begin{eqnarray}\n H_\\text{AA-HM}(\\mathbf{k})=\n\\begin{pmatrix}\na_{\\mathbf{k}} +M_1 & f_{\\mathbf{k}} &2t_{\\perp}&0 \\\\\nf^{\\ast}_{\\mathbf{k}} & -a_{\\mathbf{k}} -M_1&0&2t_{\\perp}\\\\\n2t_{\\perp}&0&-a_{\\mathbf{k}} +M_2 & f_{\\mathbf{k}}\\\\\n0&2t_{\\perp}&f^{\\ast}_{\\mathbf{k}} & a_{\\mathbf{k} -M2}.\n\\end{pmatrix}\n\\end{eqnarray}\n\n\\begin{eqnarray}\n H_\\text{AB-HM}(\\mathbf{k})=\n\\begin{pmatrix}\na_{\\mathbf{k}} +M_1 & f_{\\mathbf{k}} &0 &2t_{\\perp} \\\\\nf^{\\ast}_{\\mathbf{k}} & -a_{\\mathbf{k}} -M_1&0&0\\\\\n0&0&-a_{\\mathbf{k}} +M_2 & f_{\\mathbf{k}}\\\\\n2t_{\\perp}&0&f^{\\ast}_{\\mathbf{k}} & a_{\\mathbf{k} -M2}.\n\\end{pmatrix}\n\\end{eqnarray}\n\nThese Hamiltonians can be expressed, using the layer and the sublattice pseudospin matrices $\\boldsymbol{\\sigma}$ and $\\boldsymbol{\\tau}$, as\n\\begin{eqnarray}\nH_\\text{AA-HM}(\\mathbf{k})&=&\\left( b_{\\mathbf{k}}\\sigma_x+c_{\\mathbf{k}}\\sigma_y\\right)\\tau_0\n+2t_{\\perp}\\sigma0\\tau_x+ a_{\\mathbf{k}}\\sigma_z\\tau_z\n+\\frac 12 \\left(M_1+M_2\\right)\\sigma_z\\tau_0+\\frac 12 \\left(M_1-M_2\\right)\\sigma_z\\tau_z,\\\\\nH_\\text{AB-HM}(\\mathbf{k})&=&\\left( b_{\\mathbf{k}}\\sigma_x+c_{\\mathbf{k}}\\sigma_y\\right)\\tau_0\n+t_{\\perp}\\left(\\sigma_x\\tau_x-\\sigma_y\\tau_y\\right)+ a_{\\mathbf{k}}\\sigma_z\\tau_z\n+\\frac 12 \\left(M_1+M_2\\right)\\sigma_z\\tau_0+\\frac 12 \\left(M_1-M_2\\right)\\sigma_z\\tau_z.\n\\label{AB-HM-mass}\n\\end{eqnarray}\nwhere $a_{\\mathbf{k}}$ is given by Eq.~\\ref{al} in the main text.\\\n\n$H_\\text{AA-HM}$ ($H_\\text{AB-HM}$) breaks TRS $\\mathcal{T}=K$, the charge conjugation, represented by $\\mathcal{C}=\\sigma_z\\tau_zK$ ($\\mathcal{C}=\\sigma_z\\tau_0K$) with $\\mathcal{C}^2=\\mathds{1}$, and the chirality $\\mathcal{S}=\\tau_z\\sigma_z$ ($\\mathcal{S}=\\tau_0\\sigma_z$).\\\n\nIn the following, we will show based on numerical band structure calculations on bilayer ribbons, that coupling two HM with opposite chiralities ($C_1=-C_2$), resulting from oppositely broken TRS ($\\Phi_1=-\\Phi_2$), gives rise, as expected, to a trivial Chern insulator with $C=C_1+C_2=0$.\\\nWe will discuss the stacking order, the nature of the ribbon edges (zigzag or armchair) and the effect of the intralayer Semenoff masses $M_l$, where $l=1,2$ is the layer index. The case of AA stacking was discussed in Ref.~\\onlinecite{Dutta} for a fixed value of the mass term $M_l$.\\\n\nFigure~\\ref{band-HM-ZZ} shows the band structure of the AB bilayer HM on zigzag ribbons for $\\Phi_1=\\Phi_2= \\frac{\\pi}2$, $M_1=M_2=0$ and at different values of the interlayer hopping $t_{\\perp}$ . Starting from uncoupled ($t_{\\perp}=0$) chiral layers, with equal Chern number $C_1=C_2=\\pm 1$, the system turns, under the interlayer coupling, into a Chern insulator with a Chern number $C=\\pm 2$ characterized by a pair of chiral edge states propagating at the boundaries of each layer as shown in Fig.~\\ref{table-res} of the main text.\n \n\\begin{figure}[hpbt] \n\\begin{center}\n$\n\\begin{array}{ccc}\n\\includegraphics[width=0.3\\columnwidth]{HM-AB-ZZ-a.eps}\n\\includegraphics[width=0.3\\columnwidth]{HM-AB-ZZ-b.eps}\n\\includegraphics[width=0.3\\columnwidth]{HM-AB-ZZ-c.eps}\n\\end{array}\n$\n\\end{center}\n\\caption{Tight binding calculations of the electronic band structure of an AB bilayer HM on zigzag nanoribbons of a width $W = 60$ atoms. The interlayer hopping is (a) $t_{\\perp}=0$, \n(b) $t_{\\perp}=0.5t$ and (c) $t_{\\perp}=0.8t$.\nCalculations are done for $\\Phi_1=\\Phi_2= \\frac{\\pi}2$, $M_1=M_2=0$ and $t_2 = 0.1t$, where $t$ is the NN hopping integral.}\n\\label{band-HM-ZZ}\n\\end{figure}\nThe $C=\\pm 2$ Chern insulating phase occurs as far as the Semenoff mass $|M_l|<|M_{lc}|$, where\n\\begin{eqnarray}\nM_{lc}=3\\sqrt{3}t_2\\sin \\Phi_l.\n\\label{Mlc}\n\\end{eqnarray}\n$M_{lc}$ is the critical mass at which the transition from a topological phase ($C_l=\\pm 1$) to a trivial gapped phase ($C_l=0$), takes place in the monolayer HM~\\cite{Haldane}.\\\n\nThis feature is depicted in Fig.~\\ref{band-HM-mass}, showing that the pair of chiral edge states appears at the boundaries of the bilayer ribbons only if both layers have the same chirality~\\cite{Haldane}.\\\n\n\\begin{figure}[hpbt] \n$\n\\begin{array}{ccc}\n\\includegraphics[width=0.3\\columnwidth]{HM_AB_mass_a.eps}\n\\includegraphics[width=0.3\\columnwidth]{HM_AB_mass_b.eps}&\\includegraphics[width=0.3\\columnwidth]{HM_AB_mass_c.eps}\\\\\n\\includegraphics[width=0.3\\columnwidth]{HM_AB_mass_d.eps}\n\\includegraphics[width=0.3\\columnwidth]{HM_AB_mass_e.eps}&\n\\includegraphics[width=0.3\\columnwidth]{HM_AB_mass_f.eps}&\n\\end{array}\n$\n\\begin{center}\n\n\\end{center}\n\\caption{Electronic band structure of an AB bilayer HM on zigzag\nnanoribbons of a width $W = 60$ atoms. Calculations are done for $t_2 = 0.1t$, $\\Phi_1=\\Phi_2= \\frac{\\pi}2$, $t_{\\perp}=0.5t$ and for (a) $M_1=M_2=0$, (b) $M_1=M_2=\\sqrt{3}t_2$, (c) $M_1=-M_2=\\sqrt{3}t_2$,\n(d) $M_1=0, M_2=3\\sqrt{3}t_2$, (e) $M_1=0, M_2=5\\sqrt{3}t_2$, (f) $M_1=5\\sqrt{3}t_2, M_2=5\\sqrt{3}t_2$.}\n\\label{band-HM-mass}\n\\end{figure}\n\nThis behavior is independent of the nature (zigzag or armchair) of the ribbon boundaries as shown in Fig.~\\ref{band-HM-AC}.\n\n\\begin{figure}[hpbt] \n\\begin{center}\n$\n\\begin{array}{cc}\n\\includegraphics[width=0.3\\columnwidth]{HM-AB-ZZ-b.eps}\n\\includegraphics[width=0.3\\columnwidth]{HM_AC_AB_b.eps}\n\\end{array}\n$\n\\end{center}\n\\caption{Electronic band structure of an AB bilayer HM on (a) zigzag and (b) armchair nanoribbons of a width $W = 60$ atoms. \nCalculations are done for $t_2 = 0.1t$, $t_{\\perp} = 0.5t$, $\\Phi_1=\\Phi_2=\\frac{\\pi}2$ and\n$M_1=M_2=0$.}\n\\label{band-HM-AC}\n\\end{figure}\n\nRegardless of the stacking type (AB or AA), the bilayer HM is~\\cite{Dutta}:\n$(i)$ a trivial insulator, if the layers have opposite Chern numbers $C_1=-C_2$,\n$(ii)$ a topological chiral insulator with $C=\\pm 2$, if the layers have the same chirality ($C_1=C_2$),\n$(iii)$ and a Chern insulator with $C=\\pm1$ if one layer has a non-vanishing Chern number $C_1=\\pm 1$ and the other layer is a trivial insulator $C_2=0$, as depicted in Fig.~\\ref{band-HM-AA} showing the band structure of an AA bilayer HM on zigzag ribbons.\n\\begin{figure}[hpbt] \n\\begin{center}\n$\n\\begin{array}{cc}\n\\includegraphics[width=0.3\\columnwidth]{HM-AA-a.eps}\n\\includegraphics[width=0.3\\columnwidth]{HM-AA-b.eps}\\\\\n\\includegraphics[width=0.3\\columnwidth]{HM-AA-c.eps}\n\\includegraphics[width=0.3\\columnwidth]{HM-AA-d.eps}\n\\end{array}\n$\n\\end{center}\n\\caption{Electronic band structure of an AA Bilayer HM on zigzag\nnanoribbons of a width $W = 60$ atoms for $t_{\\perp} = 0.5t$,\n(a) $\\Phi_1=\\Phi_2=\\frac{\\pi}2$, $M_1=M_2=0$, (b) $\\Phi_1=\\Phi_2=-\\frac{\\pi}2$, $M_1=M_2=0$, (c) $\\Phi_1=\\Phi_2=\\frac{\\pi}2$, $M_1=0$, $M_2=5\\sqrt{3}t_2$ and\n(d) $\\Phi_1=\\frac{\\pi}2, \\Phi_2=0$,  $M_1=\\sqrt{3}t_2$, $M_2=0$. Calculations are done for\n$t_2=0.1t$ in (a), (b) and (d) and $t_2=0.2t$ in (c).}\n\\label{band-HM-AA}\n\\end{figure}\n\n\n\\section{ II. Modified Haldane model in AB stacked layers}\n\nTo derive the low energy Hamiltonian given by Eq.~\\ref{Heff} in the main text, we use the \nL\\\"owdin partitioning method~\\cite{Lowdin,McCann} in the case of bilayer graphene. \nFor simplicity, we consider the case $\\Phi_1=-\\Phi_2=\\frac{\\pi}2$ to remove the energy-shift terms $a^0_{l,\\mathbf{k}}$ (Eq.~\\ref{al}). We rewrite the full Hamiltonian (Eq.~\\ref{HBL}), in the basis ($A_2,B_1,A_1,B_2$) as\n\\begin{eqnarray}\n H_{B}(\\mathbf{k})=\n\\begin{pmatrix}\nH_{\\alpha\\alpha} & H_{\\alpha\\beta} \\\\\nH_{\\beta\\alpha} & H_{\\beta\\beta}\n\\end{pmatrix},\n\\end{eqnarray}\nwhere\n\\begin{eqnarray}\nH_{\\alpha\\alpha}=\n\\begin{pmatrix}\n -a_{\\mathbf{k}}+M_2& 0 \\\\\n0 & a_{\\mathbf{k}}-M1\n\\end{pmatrix},\\,\nH_{\\alpha\\beta}=H_{\\beta\\alpha}\n\\begin{pmatrix}\n0&f_{\\mathbf{k}} \\\\\nf^{\\ast}_{\\mathbf{k}} & 0\n\\end{pmatrix},\\,\nH_{\\beta\\beta}=\n\\begin{pmatrix}\n a_{\\mathbf{k}}+M_1& t_{\\perp} \\\\\n t_{\\perp}& -a_{\\mathbf{k}}-M_2\n\\end{pmatrix}.\n\\end{eqnarray}\nThe corresponding effective Hamiltonian is~\\cite{McCann}\n\n\\begin{eqnarray}\n H_\\text{eff}({\\mathbf{k}},E)=H_{\\alpha\\alpha}+H_{\\alpha\\beta}\\left( E-H_{\\beta\\beta}\\right)^{-1} H_{\\beta\\alpha},\n\\end{eqnarray}\nwhich reduces in the limit $M_l\\sim t_2\\ll t_{\\perp}$ ($l=1,2$), and for $E\\sim 0$ to\n\\begin{eqnarray}\nH_\\text{eff}({\\mathbf{k}},E=0)\\equiv H_\\text{eff}({\\mathbf{k}})\\sim H_{\\alpha\\alpha}-\\frac 1{X^2}H_{\\alpha\\beta}H_{\\beta\\beta} H_{\\beta\\alpha},\n\\end{eqnarray}\nwhere $X^2=\\left(a_{\\mathbf{k}}+M_1\\right)\\left(a_{\\mathbf{k}}+M_2\\right)+4t^2_{\\perp}$.\\\n\nAssuming $M_l\\frac{|f_{\\mathbf{k}}|^2}{X^2}\\ll M_{l^{\\prime}}\\sim t_2 \\, (l,l^{\\prime}=1,2)$, the corresponding effective Hamiltonian gives rise to Eq.~\\ref{Heff} of the main text.\n\n\\section{III. Modified Haldane model in AA stacked layers}\n\n\\begin{figure}[hpbt] \n$\n\\begin{array}{cc}\n\\includegraphics[width=0.3\\columnwidth]{mHM-AA-ZZ-a.eps}\n\\includegraphics[width=0.3\\columnwidth]{mHM-AA-AC-b.eps}\\\\\n\\includegraphics[width=0.3\\columnwidth]{mHM-AA-ZZ-c.eps}\n\\includegraphics[width=0.3\\columnwidth]{mHM-AA-ZZ-d.eps}\n\\end{array}\n$\n\\begin{center}\n\\end{center}\n\\caption{Band structure of the mHM on AA nanoribbons of a width of $W=60$ atoms with  (a,c,d) zigzag and (b) armchair boundaries. Calculations are done for $t_2 = 0.1t$, $t_{\\perp}=0.5t$, (a) and (b) $\\Phi_1=-\\Phi_2= \\frac{\\pi}2$, $M_1=M_2=0$, while in (c)  $\\Phi_1=-\\Phi_2= \\frac{\\pi}2$, $M_1=-M_2=\\sqrt{3}t_2$ and (d) $\\Phi_1=-\\Phi_2= \\frac{\\pi}2$, $M_1=0$, $M_2=\\sqrt{3}t_2$. }\n\\label{AA}\n\\end{figure}\nFigure~\\ref{AA} shows the band structure of the mHM in AA stacked ribbons with zigzag and armchair boundaries in the case of opposite complex phases $\\Phi_1=-\\Phi_2$.\nIn the absence of the Semenoff masses ($M_1=M_2=0$), the system remains gapless under the interlayer coupling. However, it turns to a trivial insulator if the layers have Semenoff mass terms. \\\n\nTherefore, in the absence of the Semenoff masses, the Fermi surface (Fig.~\\ref{Fig-intro}) of the mHM in AA stacked bilayer is,\ncontrary to the AB stacking, stable against the interlayer hopping which cannot induce a gap opening.\\\n\nTo understand the Fermi surface stability, we start by writing the corresponding Hamiltonian in the basis of the four orbitals forming the unit cell ($A_1,B_1,A_2,B_2$) and we consider, for simplicity, the case of opposite complex NNN phases $\\Phi_1=-\\Phi_2=\\frac{\\pi}2$ to have a vanishing global energy shift ($a^0_{\\mathbf{k}}=0$ (Eq.~\\ref{al}))\n\\begin{eqnarray}\n H_{AA-mHM}(\\mathbf{k})=\n\\begin{pmatrix}\na_{\\mathbf{k}} & f_{\\mathbf{k}} &2t_{\\perp}&0 \\\\\nf^{\\ast}_{\\mathbf{k}} & a_{\\mathbf{k}} &0&2t_{\\perp}\\\\\n2t_{\\perp}&0&-a_{\\mathbf{k}} & f_{\\mathbf{k}}\\\\\n0&2t_{\\perp}&f^{\\ast}_{\\mathbf{k}} & -a_{\\mathbf{k}}\n\\end{pmatrix}.\n\\label{AA-mHM}\n\\end{eqnarray}\nThis Hamiltonian can be written, using the layer and the sublattice pseudospin matrices $\\boldsymbol{\\sigma}$ and $\\boldsymbol{\\tau}$, as\n\\begin{eqnarray}\nH_\\text{AA-mHM}(\\mathbf{k})&=&\\left( b_{\\mathbf{k}}\\sigma_x+c_{\\mathbf{k}}\\sigma_y\\right)\\tau_0\n+2t_{\\perp}\\sigma_0\\tau_x+ a_{\\mathbf{k}}\\sigma_0\\tau_z,\n\\label{HBLAA}\n\\end{eqnarray}\nwhere $a_{\\mathbf{k}}$ is given by Eq.~\\ref{al} in the main text.\\\n\nThe Hamiltonian of Eq.~\\ref{HBLAA} breaks TRS, $\\mathcal{T}=K\\tau_x$, the charge conjugation, represented by $\\mathcal{C}=\\sigma_z\\tau_zK$ with $\\mathcal{C}^2=\\mathds{1}$, and the chirality $\\mathcal{S}=\\tau_z\\sigma_z$.\\\n\nThe gap separating the two bands, $E_{-,-}(\\mathbf{k})$ and $E_{+,-}(\\mathbf{k})$, around the zero energy is $\\Delta=\\mathrm{min}_{\\mathbf{k}}\\left(\\Delta_{\\mathbf{k}}\\right)$, where \n\\begin{eqnarray}\n \\Delta_{\\mathbf{k}}=2\\sqrt{A_{\\mathbf{k}}-B_{\\mathbf{k}}},\\;\n A_{\\mathbf{k}}=a^2_{\\mathbf{k}}+|f_{\\mathbf{k}}|^2+4t^2_{\\perp},\\; B_{\\mathbf{k}}=2|f_{\\mathbf{k}}|\\sqrt{a^2_{\\mathbf{k}}+4t^2_{\\perp}}\n\\end{eqnarray}\n$\\Delta_{\\mathbf{k}}=0$ leads to\n\\begin{eqnarray}\n|f_{\\mathbf{k}}|^2=a^2_{\\mathbf{k}}+4t^2_{\\perp},\n\\label{FL}\n\\end{eqnarray}\nwhich defines a closed Fermi line. \\\n\nFor $a_{\\mathbf{k}}=0$, Eq.~\\ref{FL} corresponds to the Fermi line of the AA graphene bilayer in the absence of NNN hopping terms. \\\n\nFor $t_{\\perp}=0$, Eq.~\\ref{FL} describes the mHM in AA bilayer with a particle-hole Fermi line obeying to $|f_{\\mathbf{k}}|=|a_{\\mathbf{k}}|$.\\\n\nBy turning on $t_{\\perp}$, this Fermi line is, simply, shifted but cannot be gapped (Eq.~\\ref{FL}).\nThe mHM on AA bilayer remains, then, metallic for vanishing Semenoff masses.\\\n\n\n\\section{IV. Modified Haldane model in AB stacked layers: effect of Semenoff masses}\n\nThe effect of Semenoff mass on the mHM in monolayer graphene nanoribbon is represented in Fig.~ \\ref{supp-mass-ML} showing that the mass term lifts the degeneracy of the antichiral edge modes which\nsurvive as far as $M<M_c\\equiv 3\\sqrt{3}t_2\\sin \\Phi$.\n\n\\begin{figure}[hpbt] \n\\begin{center}\n$\\begin{array}{cccc}\n\\includegraphics[width=0.2\\columnwidth]{mHM-ML-mass-a.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-ML-mass-b.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-ML-mass-c.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-ML-mass-d.eps}\n\\end{array}$\n\\end{center}\n\\caption{Band structure of the mHM in monolayer graphene nanoribbon with zigzag boundaries and a width $W=60$ atoms. Calculations are done for $t_2=0.1t$, $\\Phi=\\frac{\\pi}2$, (a) $M=0$, (b) $M=0.1t_2$, (c) $M=M_c\\equiv 3\\sqrt{3}t_2$, and (d) $M_2=4\\sqrt{3}t_2$.}\n\\label{supp-mass-ML}\n\\end{figure}\n\nIn Fig.~\\ref{mass}, we plot the band structure of the mHM on AB bilayer honeycomb lattices with different choices of intralayer Semenoff masses.\n\n\\begin{figure}[hpbt] \n\\begin{center}\n$\\begin{array}{cccc}\n\\includegraphics[width=0.2\\columnwidth]{mHM-supp-mass-a.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-supp-mass-b.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-supp-mass-c.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-supp-mass-d.eps}\\\\\n\\includegraphics[width=0.2\\columnwidth]{mHM-supp-mass-e.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-supp-mass-f.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-supp-mass-g.eps}\n\\includegraphics[width=0.2\\columnwidth]{mHM-supp-mass-h.eps}\n\\end{array}$\n\\end{center}\n\\caption{Band structure of the mHM in AB stacked bilayer zigzag ribbons of a width $W=60$ atoms with $t_2=0.1t$, $t_{\\perp}=0.5 t$, $\\Phi_1=-\\Phi_2=\\frac{\\pi}2$, (a) $M_1=M_2=0$, (b) $M_1=0$, $M_2=t_2$, (c) $M_1=0$, $M_2=3\\sqrt{3}t_2$ (d) $M_1=0$, $M_2=6\\sqrt{3}t_2$, (e) $M_1=M_2=\\sqrt{3}t_2$, (f) $M_1=-M_2=\\sqrt{3}t_2$, (g) $M_1=M_2=3\\sqrt{3}t_2$, (h) $M_1=M_2=4\\sqrt{3}t_2$.}\n\\label{mass}\n\\end{figure}\n\nFigure \\ref{mass} shows that, in AB bilayer mHM, the chiral edge states emerge as far as $M_l<M_{lc}$ (Eq.~\\ref{Mlc}), for which the nodal lines, originating from the overlap of the two layer bands, can occur, as discussed in the main text \\ref{Fig-intro}.\n\n\\section{ V. Modified Haldane model in AB stacked layers: effect of the NNN hopping complex phase}\n\nIt is noteworthy that the  induced Chern insulator in the AB bilayer mHM occurs as far as $\\Phi_1$ and $\\Phi_2$ have opposite signs and not only in the case where $\\Phi_1=-\\Phi_2=\\frac{\\pi}2$, which we considered to obtain simple analytical expressions. This feature is shown in Fig.~\\ref{phi}.\n\\begin{figure}[hpbt] \n\\begin{center}\n$\\begin{array}{c}\n\\includegraphics[width=0.3\\columnwidth]{mHM-phi-a.eps}\n\\includegraphics[width=0.3\\columnwidth]{mHM-phi-b.eps}\n\\includegraphics[width=0.3\\columnwidth]{mHM-phi-c.eps}\n\\end{array}$\n\\end{center}\n\\caption{Band structure of the mHM in AB stacked bilayer ribbons of a width $W=60$ atoms, for $t_2=0.1t$, $t_{\\perp}=0.5 t$, $M_1=M_2=0$ and (a) $\\Phi_1=-\\Phi_2=\\frac{\\pi}3$, $\\Phi_1=\\frac{\\pi}3$, $\\Phi_2=-\\frac{\\pi}4$ and (c) $\\Phi_1=0,\\Phi_2=-\\frac{\\pi}2$.}\n\\label{phi}\n\\end{figure}\n\\section{VI. Modified Haldane model in bilayer graphene: from AB to BA stacking \\label{AB-BA}}\n\nWe consider a generic Hamiltonian that, continuously, interpolates between AB $(\\theta=0)$ and BA $(\\theta=\\pi\/2)$ stacking of two single graphene layers described by the mHM. The interlayer hopping terms, for a given value of $\\theta$ between these limits, does not represent physical couplings.\nWe take, for simplicity, vanishing Semenoff masses and inplane complex phases $\\Phi_1=-\\Phi_2=\\frac{\\pi}2$. The Bloch Hamiltonian written in the basis ($A_1,B_1,A_2,B_2$) is\n\\begin{eqnarray}\n H_{B}(\\mathbf{k},\\theta)=\n\\begin{pmatrix}\na_{\\mathbf{k}}& f_{\\mathbf{k}} &0& 2t_{\\perp} c_{\\theta}\\\\\nf^{\\ast}_{\\mathbf{k}} & a_{\\mathbf{k}} & 2t_{\\perp} s_{\\theta} &0\\\\\n0&2t_{\\perp} s_{\\theta}&-a_{\\mathbf{k}}& f_{\\mathbf{k}}\\\\\n2t_{\\perp} c_{\\theta}&0&f^{\\ast}_{\\mathbf{k}} & -a_{\\mathbf{k}}\n\\end{pmatrix}\n\\label{HBLtheta}\n\\end{eqnarray}\nwhere $f_{\\mathbf{k}}=t\\sum_{i=1}^3 e^{i\\mathbf{k}\\cdot\\boldsymbol{\\delta}_i}$ and $a_{\\mathbf{k}}=-2t_2\\sum_{i=1}^3  \\sin\\left(\\mathbf{k}\\cdot\\mathbf{a}_i\\right)$. \\\n\nThe AB (BA) stacking corresponds to $c_{\\theta}\\equiv\\cos\\theta=1$ and $s_{\\theta}\\equiv\\sin\\theta=0$ ($c_{\\theta}=0$, $s_{\\theta}=1$). \\\n\nBy varying $\\theta$, the system can be interpolated between the two stacking configurations, without going through the AA stacking.\\\nUsing the intralayer and interlayer pseudo-spin matrices $\\boldsymbol{\\sigma}$ and $\\boldsymbol{\\tau}$, the Bloch Hamiltonian of Eq.~\\ref{HBLtheta} becomes\n\n\\begin{eqnarray}\nH_{B}(\\mathbf{k},\\theta)=\\left( b_{\\mathbf{k}}\\sigma_x+c_{\\mathbf{k}}\\sigma_y\\right)\\tau_0\n+2t_{\\perp}\\left[\\left(c_{\\theta}\\sigma_++s_{\\theta}\\sigma_-\\right)\\tau_+\n+2t_{\\perp}\\left(c_{\\theta}\\sigma_-+s_{\\theta}\\sigma_+\\right)\\tau_-\\right],\n\\label{HBL2theta}\n\\end{eqnarray}\nwhere $b_{\\mathbf{k}}$, $c_{\\mathbf{k}}$, $\\sigma_{\\pm}$ and $\\tau_{\\pm}$ are given in the main text.\\\n\nThe Hamiltonian of Eq.~\\ref{HBL2theta} breaks TRS, chirality but is invariant under charge-conjugation and inversion since $M_l=0$ and $\\Phi_1=-\\Phi_2=\\frac{\\pi}2$.\\\nThe corresponding energy spectrum is expressed, as in Eq.~\\ref{E+-} of the main text with\n\\begin{eqnarray}\n A_{\\mathbf{k}}&=&a^2_{\\mathbf{k}}+|f_{\\mathbf{k}}|^2+2t_{\\perp}^2,\\nonumber\\\\\n B_{\\mathbf{k}}&=&2\\sqrt{|f_{\\mathbf{k}}|^2\\left(a^2_{\\mathbf{k}}+t_{\\perp}^2\\right)+c^2_{2\\theta}t_{\\perp}^4+s_{2\\theta}t_{\\perp}^2\\left( b^2_{\\mathbf{k}}-c^2_{\\mathbf{k}}\\right)}\\nonumber\\\\\n \\label{ABktheta}\n\\end{eqnarray}\nThe gap separating the lowest energy band around zero energy is $\\Delta=\\min_{\\mathbf{k}}\\left(\\Delta_{\\mathbf{k}}\\right)=2\\sqrt{A_{\\mathbf{k}}-B_{\\mathbf{k}}}$. \\\n\n$\\Delta_{\\mathbf{k}}$ closes, for uncoupled layers ($t_{\\perp}=0$), for $A_{\\mathbf{k}}=B_{\\mathbf{k}}$ which defines, as we have seen in the main text, two non-intersecting closed Fermi lines.\nFor a non vanishing interlayer hopping $t_{\\perp}$, $\\Delta_{\\mathbf{k}}$ can be expressed as\n\n\\begin{eqnarray}\n\\Delta_{\\mathbf{k}}=2\\frac{\\sqrt{A^2_{\\mathbf{k}}-B^2_{\\mathbf{k}}}}{A_{\\mathbf{k}}+B_{\\mathbf{k}}}\n\\sim \\frac{2t_{\\perp}}{|f_{\\mathbf{k}}|}\\sqrt{\\left(1-s_{2\\theta}\\right)b^2_{\\mathbf{k}}+\\left(\\lambda^2_{\\mathbf{k}}-c^2_{2\\theta} \\right)t_{\\perp}^2},\n\\label{Delta}\n\\end{eqnarray} \nwhere we introduced the parameter $\\lambda_{\\mathbf{k}}$ defined as \n\\begin{eqnarray}\na^2_{\\mathbf{k}}=|f_{\\mathbf{k}}|^2+\\left(2\\lambda_{\\mathbf{k}}-1\\right)t_{\\perp}^2\n\\label{lambda}\n\\end{eqnarray}\nIn Eq.~\\ref{Delta}, the numerator is given by its exact expression, whereas the denominator has been approximated to the zeroth order in $t_{\\perp}$.\n\nAccording to Eq.~\\ref{Delta}, $\\Delta_{\\mathbf{k}}$ cannot vanish for $\\theta\\neq \\pi\/4,3\\pi\/4$. \\\n\nFor $\\theta=\\pi\/4 $, $\\Delta_{\\mathbf{k}}=0$ if $\\lambda_{\\mathbf{k}}=0$, which give rise, according to Eq.~\\ref{lambda}, to a closed loop defined by $a^2_{\\mathbf{k}}+t_{\\perp}^2=|f_{\\mathbf{k}}|^2$.\\\n\nFor $\\theta=3\\pi\/4$, the closing of the gap $\\Delta_{\\mathbf{k}}$ requiers $\\lambda_{\\mathbf{k}}=0$ and $b_{\\mathbf{k}}=0$.\\\n\nThe critical values $\\theta=\\pi\/4,3\\pi\/4 $ correspond to the semimetallic phase marking the transition from the topological Chern insulator phase $C=2$, occurring for $0\\le\\theta<\\pi\/4 $ to the Chern insulator phase $C=-2$, associated to $3\\pi\/4<\\theta\\le\\pi $.\nAt this topological phase transition, the gap closes at the four Dirac points of the bilayer system where, right after the transition, the signs of the gap flip, inducing a variation $\\Delta C=-4$ of the Chern number.\n\nThe flipping of the Chern number sign, at the crossing form the AB to BA stacking, could be understood from Fig.~\\ref{AB-AA}. Such crossing can be regarded as a sign change of the complex phases: since the inplane sublattices have opposite fluxes, the AB stacking corresponds to the dimer ($A_1$,$B_2$) for which the complex phases are $\\Phi_1=-\\Phi_2=\\pi\/2$ while the BA stacking is ascribed to the dimer ($B_1$,$A_2$) with $\\Phi_1=-\\Phi_2=-\\pi\/2$ (Fig.~\\ref{AB-AA} of the main text).\n\n\n\\end{document}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction} \nHigh energy heavy ion collisions at RHIC and the LHC have created a new form of nuclear matter comprised of deconfined, yet strongly interacting quarks and gluons. This matter exhibits strong collective and anisotropic flow in the transverse plane, which is well described by relativistic hydrodynamics~\\cite{Alver:2010dn,Gale:2012in,Heinz:2013th}. The magnitude of the anisotropic flow has been to found to be sensitive to the transport properties, as well as the space-momentum profile in the initial state. A central goal of current research is to understand the nature of various fluctuations in the initial state and how these fluctuations influence the hydrodynamic evolution of the matter in the final state.\n\nIn heavy ion collisions, the anisotropy of the particle distribution in azimuthal angle $\\phi$ is customarily characterized by a Fourier series:\n\\begin{equation}\n\\label{eq:flow0}\n\\frac{dN}{d\\phi}\\propto1+2\\sum_{n=1}^{\\infty}v_{n}\\cos n(\\phi-\\Phi_{n})\\;,\n\\end{equation}\nwhere $v_n$ and $\\Phi_n$ (event plane or EP) represent the magnitude and phase of the $n^{\\mathrm{th}}$-order harmonic flow. These flow harmonics have been associated to various shape components of the created matter~\\cite{Alver:2010gr}. The magnitude and direction of each shape component can be estimated via a simple Glauber model from the transverse positions (r, $\\phi$) of the participating nucleons~\\cite{Qin:2010pf,Teaney:2010vd}:\n\\begin{eqnarray}\n\\label{eq:ena}\n\\epsilon_n &=& \\frac{\\sqrt{\\langle r^m\\cos n\\phi\\rangle^2+\\langle r^m\\sin n\\phi\\rangle^2}}{\\langle r^m\\rangle},\\\\\\label{eq:glau} \n\\tan (n\\Phi_n^*+\\pi)&=&\\frac{\\langle r^m\\sin n\\phi\\rangle}{\\langle r^m\\cos n\\phi\\rangle},\\\\\\nonumber\n&&m=3\\; {\\rm if}\\; n=1, m=n\\; \\rm{ for}\\; n>1\n\\end{eqnarray} \nwith $\\epsilon_n$ and $\\Phi^*_n$ referred to as the eccentricity and participant plane (PP), respectively. Model calculations suggest that hydrodynamic response to the shape component is linear for the first few flow harmonics, i.e. $\\Phi_n\\approx \\Phi_n^*$ and $v_n\\propto \\epsilon_n$ for $n=$1--3~\\cite{Teaney:2010vd,Qiu:2011iv}. But these simple relations are violated for higher-order harmonics, due to strong mode-mixing effects intrinsic in the collective expansion~\\cite{Qiu:2011iv,Gardim:2011xv,Teaney:2012ke}.\n\nThe presence of large event-by-event (EbyE) fluctuations of the initial geometry suggests a general set of observables that involve correlations between $v_n$ and $\\Phi_n$:\n\\begin{equation}\n\\label{eq:flow}\np(v_n,v_m,...., \\Phi_n, \\Phi_m, ....)=\\frac{1}{N_{\\mathrm{evts}}}\\frac{dN_{\\mathrm{evts}}}{dv_ndv_m...d\\Phi_{n}d\\Phi_{m}...},\n\\end{equation}\nwith each variable being a function of $\\pT$, $\\eta$ etc~\\cite{Gardim:2012im}. Among these, the joint probability distribution of the EP angles:\n\\small{\n\\begin{eqnarray}\n\\nonumber\n\\frac{dN_{\\mathrm{evts}}}{d\\Phi_{1}d\\Phi_{2}...d\\Phi_{l}} &\\propto& \\sum_{c_n=-\\infty}^{\\infty} a_{c_1,c_2,...,c_l} \\cos(c_1\\Phi_1+c_2\\Phi_2...+c_l\\Phi_l),\\\\\\label{eq:ep}\na_{c_1,c_2,...,c_l}&=&\\left\\langle\\cos(c_1\\Phi_1+c_2\\Phi_2+...+c_l\\Phi_l)\\right\\rangle\n\\end{eqnarray}}\\normalsize\ncan be reduced to the following event-plane correlators required by symmetry~\\cite{Bhalerao:2011yg,Qin:2011uw,Jia:2012ma}:\n\\begin{eqnarray}\n\\label{eq:ep2}\n\\left\\langle\\cos(c_1\\Phi_1+2c_2\\Phi_2...+lc_l\\Phi_l)\\right\\rangle, c_1+2c_2...+lc_l=0.\n\\end{eqnarray}\nThese observables are sensitive to the fluctuations in the initial density profile and the final state hydrodynamics response~\\cite{Teaney:2012ke}.\n\n\nEarlier flow measurements were aimed at studying the individual $v_n$ coefficients for $n=$1--6 averaged over many events~\\cite{Adare:2011tg,star:2013wf,Aamodt:2011by,Aad:2012bu,CMS:2012wg}. Recently, the LHC experiments exploited the EbyE observables defined in Eq.~\\ref{eq:flow} by performing the first measurement of $p(v_n)$~\\cite{Aad:2013xma} for $n=2-4$ and fourteen correlators involving two or three event planes~\\cite{Jia:2012sa,ALICE:2011ab}. The measured event-plane correlators are reproduced by EbyE hydrodynamics~\\cite{Qiu:2012uy,Teaney:2012gu} and AMPT transport model~\\cite{Bhalerao:2013ina} calculations. The EP correlation measurement provides detailed insights on the non-linear hydrodynamic response, for example the correlators $\\left\\langle\\cos 4(\\Phi_{2}-\\Phi_{4})\\right\\rangle$ and $\\left\\langle\\cos 6(\\Phi_{3}-\\Phi_{6})\\right\\rangle$ mainly arise from the non-linear effects, which couple $v_4$ to $(v_2)^2$ and $v_6$ to $(v_3)^2$. Similarly, the correlator $\\left\\langle\\cos (2\\Phi_{2}+3\\Phi_{3}-5\\Phi_5)\\right\\rangle$ is driven by the coupling between $v_5$ and $v_2v_3$~\\cite{Gardim:2011xv,Teaney:2012ke}. \n\n\nThis paper focuses on two subsets of the observables defined by Eq.~\\ref{eq:flow}: $p(v_n,v_m)$ and $p(v_n, \\Phi_m, \\Phi_l, ....)$, which can provide further insights on the linear and non-linear effects in the hydrodynamics response. The correlation $p(v_n,v_m)$  quantifies directly the coupling between $v_m$ and $v_n$, while $p(v_n, \\Phi_m, \\Phi_l, ...)$ allows us to study how the event-plane correlations couples to a specific flow harmonics $v_n$. The probability distributions of these correlations are difficult to measure directly, instead we explore them systematically using the recently proposed event shape selection method~\\cite{Schukraft:2012ah} (also investigated in Ref.~\\cite{Petersen:2013vca,Lacey:2013eia}): Events in a given centrality interval are first classified according to the observed $v_n$ signal in certain $\\eta$ range, and the $p(v_m)$ and $p(\\Phi_m, \\Phi_l, ...)$ are then measured in other $\\eta$ range for each class. The event shape observables should be those that correlate well with the $\\epsilon_n$ of the initial geometry, such as the observed $v_1$ (dipolar flow), $v_2$ and $v_3$. The roles of these selection variables are similar to the event centrality, except that they further divide events within the same centrality class.\n\nThe event shape selection method also provides a unique opportunity to investigate the longitudinal dynamics of the collective flow. For example, events selected with large $v_2$ in one pseudorapidity window, in addition to having bigger $\\epsilon_2$, may also have stronger density fluctuations, larger initial flow or smaller viscous correction~\\cite{Pang:2012he}. Studying how the $v_n$ values or EP correlations vary with the $\\eta$ separation from the selection window may provide better insights on the longitudinal dynamics in the initial and the final states. Earlier efforts in this front can be found in Refs.~\\cite{Petersen:2011fp,Pang:2012he,Xiao:2012uw}.\n\nIn this paper, we apply the event shape selection technique to events generated by the AMPT model, to investigate the $p(v_n,v_m)$, $p(v_n, \\Phi_m, \\Phi_l, ....)$, and the longitudinal flow fluctuations. These correlations are studied for events binned according to the observed $v_2\/v_3$ signal, which are then compared with results for events binned directly in $\\epsilon_2\/\\epsilon_3$. This comparison helps to elucidate whether the changes in the correlation are driven mostly by the selection of the initial geometry or due to additional dynamics in the final state. This study also help to develop and validate the analysis method to be used in the actual data analysis.\n\nThe structure of the paper is as follows: Section~\\ref{sec:1} introduces the observables and method of the event shape selection in the AMPT model. Section~\\ref{sec:2} studies how the correlations among the eccentricities and PP angles vary with event shape selection. Section~\\ref{sec:3} presents a study of the rapidity fluctuations of flow. Section~\\ref{sec:4} studies how the correlations among the $v_n$'s and $\\Phi_n$'s vary with event shape selection. Section~\\ref{sec:5} gives a discussion and summary of the results.\n\n\n\n\\section{The method}\n\\label{sec:1}\nA Muti-Phase Transport model (AMPT)~\\cite{Lin:2004en} has been used frequently to study the higher-order $v_n$ associated with $\\epsilon_n$ in the initial geometry~\\cite{Xu:2011jm,Xu:2011fe,Ma:2010dv}. It combines the initial fluctuating geometry based on Glauber model from HIJING with the final state interaction via a parton and hadron transport model. The collective flow in this model is driven mainly by the parton transport. The AMPT simulation in this paper is performed with string-melting mode with a total partonic cross-section of 1.5 mb and strong coupling constant of $\\alpha_s=0.33$~\\cite{Xu:2011fe}, which has been shown to reproduce reasonably the $\\pT$ spectra and $v_n$ data at RHIC and LHC~\\cite{Xu:2011fe,Xu:2011fi}. The initial condition of the AMPT model with string melting has been shown to contain significant longitudinal fluctuations that can influence the collective dynamics~\\cite{Pang:2012he,Pang:2012uw}.\n\nThe AMPT sample used in this study is generated for $b=8$~fm Pb+Pb collisions at LHC energy of $\\sqrt{s_{NN}}=2.76$ TeV, corresponding to $\\sim 30\\%$ centrality. The particles in each event are divided into various subevents along $\\eta$, one example division scheme is shown in Fig.~\\ref{fig:m1}. Four subevents labelled as S, A, B, C, with at least 1 unit $\\eta$ gap between any pair except between S and A, are used in the analysis. Note that particles in $-6<\\eta<-2$ are divided randomly into two equal halves, labelled as S and A, respectively. The particles in subevent S are used only for the event shape selection purpose, and they are excluded for $v_n$ and event-plane correlation analysis. This choice of subevents and analysis scheme ensure that the event shape selection does not introduce non-physical correlations between S and A, B or C.\n\n\nThe flow vector in each subevent is calculated as:\n\\begin{eqnarray}\n\\nonumber\n&&\\overrightharp{q}_n =(q_{x,n},q_{y,n}) = \\frac{1}{\\Sigma_i w_i}\\left(\\textstyle\\Sigma_i (w_i\\cos n\\phi_i), \\Sigma_i (w_i\\sin n\\phi_i)\\right)\\;, \\\\\\label{eq:me1}\n&&\\tan n\\Psi_n = \\frac{q_{y,n}}{q_{x,n}}\\;,\n\\end{eqnarray}\nwhere the weight $w_i$ is chosen as the $\\pT$ of $i$-th particle and $\\Psi_n$ is the measured event plane. Due to finite number effects, $\\Psi_n$  smears around the true event-plane angle $\\Phi_n$. Hence $q_n$ represents the weighted raw flow coefficients $v_n^{\\mathrm{obs}}$, $q_n=\\Sigma_i \\left(w_i (v_n^{\\mathrm{obs}})_i\\right)\/\\Sigma_i w_i$. In this study, each subevent in Fig.~\\ref{fig:m1} has 1400-3000 particles, so $q_n$ is expected to follow closely the true $v_n$.\n\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.8\\linewidth]{dets}\n\\caption{\\label{fig:m1} (Color online) The $\\eta$ range of the subevent for the event shape selection (S) and three other subevents for correlation analysis (A, B and C). Note that the particles in $-6<\\eta<-2$ are divided randomly and equally into subevents A and S.}\n\\end{figure}\n\nFor each generated event, the following quantities are calculated for $n=$1--6: $(\\epsilon_n, \\Phi^*_n)$ from initial state, $(q_n^{\\mathrm{A}}, \\Psi^{\\mathrm{A}}_n)$ for subevent A, $(q_n^{\\mathrm{B}}, \\Psi^{\\mathrm{B}}_n)$ for subevent B, $(q_n^{\\mathrm{C}}, \\Psi^{\\mathrm{C}}_n)$ for subevent C, and $(q_n^{\\mathrm{S}}, \\Psi^{\\mathrm{S}}_n)$ for subevent S, a total of 60 quantities. The event shape selection is performed by dividing the generated events into 10 bins in $q_2^{\\mathrm{S}}$ or $q_3^{\\mathrm{S}}$ with equal statistics. Similar event shape selection procedure is also performed by slicing the values of $\\epsilon_2$ or $\\epsilon_3$ directly, with the aim of studying how well the physics for events selected in the final state correlates with those selected purely on the initial geometry.\n\nFigure~\\ref{fig:m2} shows the performance of the event shape selection on $q_2^{\\mathrm{S}}$ and $q_3^{\\mathrm{S}}$. Strong positive correlations between $\\epsilon_n$ and $q_n^{\\mathrm{S}}$ seen in the top panels reflect the fact that collective response is linear for $n=2$ and 3~\\cite{Qiu:2012uy}. The bottom panels show that events selected with top 10\\% of the $q_2^{\\mathrm{S}}$ have a $\\left\\langle\\epsilon_2\\right\\rangle$ value that is nearly 3 times that for events with the lower 10\\% of $q_2^{\\mathrm{S}}$. For $n=3$ the difference in $\\epsilon_3$ in the two event classes is about a factor of 2. These results suggest that the ellipticity and triangularity of the initial geometry can be selected precisely by slicing the flow vector in the final state. \n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=1\\linewidth]{cqe3paper_cent8_m1}\n\\caption{\\label{fig:m2} (Color online) Correlations between $\\epsilon_n$ and magnitude of flow vector $q_n^{\\mathrm{S}}$ calculated using half of the particles in $-6<\\eta<-2$ (top panels), the 10 bins in $q_n^{\\mathrm{S}}$ with equal statistics (middle panels) and the corresponding distributions of $\\epsilon_n$ for events in the top 10\\%, bottom 10\\% and total of $q_n^{\\mathrm{S}}$ (bottom panels). The results are calculated for $b=8$~fm for $n=2$ and $n=3$, and are shown in the left and right column, respectively.}\n\\end{figure}\n\nIn the event shape selection method, $p(v_m,v_n)$ is not directly calculated. Instead, the calculated correlation is:\n\\begin{eqnarray}\n\\label{eq:m2}\np(q_m^{\\mathrm{S}},v_n^{\\mathrm{obs}}) =  p(q_m^{\\mathrm{S}})\\times p(v_n^{\\mathrm{obs}})_{q_m^{\\mathrm{S}}},\\;\\; m=2,3\n\\end{eqnarray}\nwhere conditional probability $p(v_n^{\\mathrm{obs}})_{q_m^{\\mathrm{S}}}$ represents the distribution of $v_n^{\\mathrm{obs}}$ for events selected with given $q_m^{\\mathrm{S}}$ value. To minimize non-flow effects, the $v_n^{\\mathrm{obs}}$ is calculated for particles separated in $\\eta$ from the subevent that provides the event plane. To minimize non-flow effects, a $\\eta$ gap from the corresponding event plane in each case is required. The probability $p(v_n)_{q_m^{\\mathrm{S}}}$ can be obtained from $p(v_n^{\\mathrm{obs}})_{q_m^{\\mathrm{S}}}$ via the unfolding technique~\\cite{Aad:2013xma,Jia:2013tja}, or if one is interested in the event-averaged $v_n$ values, the standard method~\\cite{Poskanzer:1998yz} can be applied for each $q_m^{\\mathrm{S}}$ bin:\n\\begin{eqnarray}\n\\label{eq:m3}\nv_n(\\pT,\\eta)_{q_m^{\\mathrm{S}}} = \\left[\\frac{v_n^{\\mathrm{obs}}(\\pT,\\eta)}{\\mathrm{Res}\\{ n\\Psi_n \\} }\\right]_{q_m^{\\mathrm{S}}},\n\\end{eqnarray}\nwhere the event-plane resolution factor $\\mathrm{Res}\\{ n\\Psi_n \\}$ is calculated separately for A, B, and C via the three-subevent method, providing three independent $v_n$ estimates~\\cite{Poskanzer:1998yz}. Since the magnitude and direction of the flow vector are uncorrelated, the event shape selection is not expected to introduce biases to the resolution correction. One special case of Eq.~\\ref{eq:m3} is $n=m$, which probes into the rapidity fluctuation of the $v_n$ itself (see Section~\\ref{sec:3}).\n\nTo calculate the event-plane correlation for each $q_m^{\\mathrm{S}}$ bin, the standard method introduced by the ATLAS collaboration based on event-plane correlation~\\cite{Jia:2012sa,Jia:2012ma}, and the method based on scalar products in Refs.~\\cite{Luzum:2012da,Bhalerao:2013ina} are adopted:\n\\begin{eqnarray} \n\\nonumber\n\\langle\\cos (\\Sigma \\Phi)\\rangle &=& \\frac{\\langle\\cos (\\Sigma \\Psi)\\rangle} {\\mathrm{Res}\\{c_1\\Psi_1\\}\\mathrm{Res}\\{c_22\\Psi_2\\}...\\mathrm{Res}\\{c_ll\\Psi_l\\}}\\\\\\label{eq:m4a}\n\\\\\\nonumber\n\\langle\\cos (\\Sigma \\Phi)\\rangle_w &=& \\frac{\\langle q_1^{c_1} q_2^{c_2}... q_l^{c_l}\\cos (\\Sigma \\Psi)\\rangle} {\\mathrm{Res}\\{c_1\\Psi_1\\}_w\\mathrm{Res}\\{c_22\\Psi_2\\}_w...\\mathrm{Res}\\{c_ll\\Psi_l\\}_w}\\\\\\label{eq:m4}\n\\end{eqnarray}\nwhere shorthand notions $\\Sigma \\Phi = c_1\\Phi_{1}+2c_2\\Phi_{2}+...+lc_l\\Phi_{l}$ and $\\Sigma \\Psi = c_1\\Psi_{1}+2c_2\\Psi_{2}+...+lc_l\\Psi_{l}$ are used. They are referred to as the EP method (Eq.~\\ref{eq:m4a}) and the SP method (Eq.~\\ref{eq:m4}) for the rest of this paper. The resolution factors $\\mathrm{Res}\\{c_nn\\Psi_n\\}$ and $\\mathrm{Res}\\{c_nn\\Psi_n\\}_w$ are calculated via three-subevent method involving subevents A, B and C:\n\\small{\n \\begin{eqnarray}\n \\label{eq:m5a}\n &&{\\mathrm{Res}}\\{jn\\Psi^{\\mathrm A}_{n}\\}=\\sqrt{\\frac{\\left\\langle {\\cos\\Delta\\Psi^{AB}_n} \\right\\rangle\\left\\langle {\\cos \\Delta\\Psi^{AC}_n}\\right\\rangle}{\\left\\langle {\\cos \\Delta\\Psi^{BC}_n} \\right\\rangle}}.\\\\\\nonumber\n&&{\\mathrm{Res}}\\{jn\\Psi^{\\mathrm A}_{n}\\}_w= \\sqrt{\\frac{\\left\\langle { (q_n^{\\mathrm A}q_n^{\\mathrm B})^j \\cos \\Delta\\Psi^{AB}_n} \\right\\rangle \\left\\langle { (q_n^{\\mathrm A}q_n^{\\mathrm C})^j\\cos \\Delta\\Psi^{AC}_n }\\right\\rangle}{\\left\\langle { (q_n^{\\mathrm B}q_n^{\\mathrm C})^j\\cos \\Delta\\Psi^{BC}_n} \\right\\rangle}}.\\\\\\label{eq:m5}\n \\end{eqnarray}}\\normalsize\nwhere $\\Delta\\Psi^{AB}_n = jn \\left(\\Psi_n^{\\mathrm A} - \\Psi_n^{\\mathrm B}\\right)$ etc. Each $\\Psi_n$ angle in Eq.~\\ref{eq:m4} is calculated in a separate subevent to avoid auto-correlations. The two subevents involved in two-plane correlation are chosen as A and C in Fig.~\\ref{fig:m1}, while the three subevents in three-plane correlation are chosen as A, B, and C in Fig.~\\ref{fig:m1}. Note that selecting on $q_n^{\\mathrm{S}}$ explicitly breaks the symmetry between subevents A and C even though they still have symmetric $\\eta$ acceptance. Thus their resolution factors are different and need to be calculated separately.\n\n\\section{Correlations in the initial state}\n\\label{sec:2}\nBefore discussing correlations in the final state, it is instructive to look first at how the initial geometry variables $\\epsilon_n, \\Phi^*_n$ and their correlations vary with the event shape selection. Figure~\\ref{fig:i1} shows the correlations between pairs of $\\epsilon_n$ for $n\\leq4$ for the generated AMPT events. Significant correlations are observed between $\\epsilon_2$ and $\\epsilon_3$~\\cite{Lacey:2013eia,ATLAS2014-022}, $\\epsilon_1$ and $\\epsilon_3$. The correlations between $\\epsilon_1$ and $\\epsilon_2$ are weak for this impact parameter but become more significant for $b=10$~fm (see Appendix~\\ref{sec:7}). Since the hydrodynamic response is nearly linear for $n=1-3$~\\cite{Qiu:2011iv}, these correlations are expected to survive into correlations between $v_n$ of respective order. The $\\epsilon_2$ and $\\epsilon_4$ correlation is also significant, especially for large $\\epsilon_2$ values, this correlation may survive to the final state but it competes with non-linear effects expected for $v_4$~\\cite{Gardim:2011xv}. \n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.9\\linewidth]{ceepaperb_cent8}\n\\caption{\\label{fig:i1} (Color online)  Selected correlations between $\\epsilon_n$ of different order for Pb+Pb events at $b=8$~fm. More examples are given in Appendix~\\ref{sec:7}. The $x$- and $y$-profiles of the 2D correlations are represented by the solid symbols.}\n\\end{figure}\n\nFigure~\\ref{fig:i2} shows selected correlations between $\\Phi_n^*$ of different order for events binned in $\\epsilon_2$ (boxes) or $q_2^{\\mathrm{S}}$ (circles)~\\cite{Jia:2012ma,Jia:2012ju}. It is clear that the correlation signal varies dramatically with $\\epsilon_2$, implying that the correlations between $\\Phi_n^*$'s can vary a lot for events with the same impact parameter. Figure~\\ref{fig:i2} also shows that events with different correlations in the initial geometry can be selected with nearly the same precision between using $q_2^{\\mathrm{S}}$ and using $\\epsilon_2$.\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.9\\linewidth]{cephilonga_cent8}\n\\caption{\\label{fig:i2} (Color online) Dependence of the participant-plane correlations on $\\epsilon_2$ (boxes) or $q_2^{\\mathrm{S}}$ (circles), calculated for Pb+Pb events with $b=8$~fm. Results for three two-plane, three three-plane and two four-plane correlators proposed in Refs.~\\cite{Jia:2012ma,Jia:2012ju} are shown.}\n\\end{figure}\n\n\n\n\\section{The correlation between $v_n$ and $v_m$ and longitudinal fluctuations}\n\\label{sec:3}\nFigure~\\ref{fig:eta1} shows the $v_2(\\eta)$ values for events selected for lower 10\\% (top panels) and upper 10\\% (bottom panels) of the values of either $q_2^{\\mathrm{S}}$ (left panels) or $\\epsilon_2$ (right panels). They are calculated via Eqs.~\\ref{eq:m3} and \\ref{eq:m5a} using all final state particles with $0.1<\\pT<5$ GeV, excluding those particles used in the event shape selection (i.e. subevent S). The event-plane angles are calculated separately for the three subevents A, B, and C, and a minimum 1--2 unit of $\\eta$ gap is required between $v_n(\\eta)$ and the subevent used to calculate the event plane. Specifically, the $v_2$ values in $-6<\\eta<0$ are obtained using the EP angle in subevent C covering $2<\\eta<6$ (open boxes), the $v_2$ values in $0<\\eta<6$ are obtained using the EP angle in subevent A covering $-6<\\eta<-2$ (open circles), and the $v_2$ values in $|\\eta|>2$ are also obtained using the EP angle in subevent B covering $|\\eta|<1$ (solid circles).\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=1\\linewidth]{cvnbpaper_cent8_pt0_har1_m1}\n\\caption{\\label{fig:eta1} (Color online) $v_2(\\eta)$ for events selected with lower 10\\% (top panels) and upper 10\\% (bottom panels) of the values of either $q_2^{\\mathrm{S}}$ (left panels) or $\\epsilon_2$ (right panels) for AMPT Pb+Pb events with $b=8$~fm. In each case, the integral $v_2$ calculated for particles in $0.1<\\pT<5$ GeV relative to the event plane of subevent A, B and C (Their $\\eta$ coverages are indicated in the legend) with a minimum $\\eta$ gap of 1 unit are shown.}\n\\end{figure}\n\\begin{figure*}[!t]\n\\centering\n\\includegraphics[width=1\\linewidth]{cvncombpaper_cent8_pt0_m1}\n\\caption{\\label{fig:eta2} (Color online) $v_n(\\eta)$ for events selected with lower 10\\% (open symbols) and upper 10\\% (solid symbols) of the values of $q_2^{\\mathrm{S}}$ for AMPT Pb+Pb events with $b=8$~fm. Results are shown for $v_2(\\eta)$, $v_3(\\eta)$,..., and $v_6(\\eta)$ from left panel to the right panel. The ratios of $v_n(\\eta)$ between events with $q_2^{\\mathrm{S}}$ selection to the inclusive events are shown in the bottom panels.}\n\\end{figure*}\n\\begin{figure*}[!t]\n\\centering\n\\includegraphics[width=1\\linewidth]{cvnQdeppaper_cent8_pt0_eta1_m1}\n\\caption{\\label{fig:eta3} (Color online)  Dependence of the $v_n$ on $q_2^{\\mathrm{S}}$ in a forward ($-5<\\eta<-4$) and a backward ($4<\\eta<5$) pseudorapidity ranges.}\n\\end{figure*}\n\nThere are several interesting features in the observed $\\eta$ dependence of $v_2$. The $v_2(\\eta)$ values for events selected with lower 10\\% values of $q_2^{\\mathrm{S}}$ or $\\epsilon_2$ are significantly lower (by a factor of 3) than for events selected with upper 10\\%, indicating that the $v_2$ signal correlates well with both the $q_2^{\\mathrm{S}}$ and the $\\epsilon_2$. Furthermore, a significant forward\/backward asymmetry of $v_2(\\eta)$ is observed for events selected on $q_2^{\\mathrm{S}}$ but not $\\epsilon_2$. This asymmetry is already observed outside the $\\eta$ range covered by subevent S, but is bigger towards larger $|\\eta|$. This asymmetry may reflect the dynamical fluctuations exposed by the $q_2^{\\mathrm{S}}$ selection. Additional cross-checks performed by choosing subevent S in a more restricted $\\eta$ range show similar asymmetry (see Fig.~\\ref{fig:a0} in the Appendix).\n\n\nBased on the good agreement between the three $v_2$ estimations in Fig.~\\ref{fig:eta1}, they are combined into a single $v_2(\\eta)$ result. Good agreement is also observed for higher harmonics, hence they are combined in the same way. The resulting $v_2(\\eta)$--$v_6(\\eta)$ are shown in Fig.~\\ref{fig:eta2} for events with lower 10\\% and upper 10\\% of the values of $q_2^{\\mathrm{S}}$. The asymmetry of $v_n$ in $\\eta$ is much weaker for the higher-order harmonics. The values of $v_n(\\eta)$ for $n>3$ are also seen to be positively correlated with $v_2$, $i.e.$ events with large $q_2^{\\mathrm{S}}$ also have bigger $v_n(\\eta)$. On the other hand, $v_3$ values are observed to decrease with increasing $q_2^{\\mathrm{S}}$. This decrease reflects the anti-correlation between $\\epsilon_2$ and $\\epsilon_3$ in Fig.~\\ref{fig:i1} (also confirm by ATLAS data~\\cite{ATLAS2014-022}). Figure~\\ref{fig:eta3} quantifies the forward\/backward asymmetry of $v_2$--$v_6$ in two $\\eta$ ranges: $-5<\\eta<-4$ and $4<\\eta<5$. Clear asymmetry can be seen for $v_2$, $v_4$ and $v_5$, but not for $v_3$. This behavior re-enforces our earlier conclusion that the correlation between $v_2$ and $v_3$ in the AMPT model is mostly geometrical, $i.e.$ reflecting correlation between $\\epsilon_2$ and $\\epsilon_3$.\n\nAn identical analysis is also performed for events selected on $q_3^{\\mathrm{S}}$ or $\\epsilon_3$. The $v_n(\\eta)$ for events with the upper 10\\% and lower 10\\% values of $q_3^{\\mathrm{S}}$ or $\\epsilon_3$ are shown in Fig.~\\ref{fig:eta1b}. A strong $\\eta$ asymmetry is observed as a result of $q_3^{\\mathrm{S}}$ selection, but not for $\\epsilon_3$ selection. Nevertheless, the overall magnitude of the $v_3$ is similar between the two selections. In the $-6<\\eta<-2$ range where $q_3^{\\mathrm{S}}$ is calculated, $v_3(\\eta)$ values for events with the lower 10\\% of $q_3^{\\mathrm{S}}$ drop to below zero. This implies that the $\\Phi_3$ angle for large negative $\\eta$ region become out of phase with the $\\Phi_3$ angle in the large positive range. This $\\Phi_3$ angle decorrelation is also observed for events selected with lower 10\\% of $\\epsilon_3$ values as shown in the top-right panel of Fig.~\\ref{fig:eta1b}. This behavior suggests that in the AMPT model, rapidity decorrelation of $v_3$ is stronger for events with small $\\epsilon_3$ and grows towards large $|\\eta|$ (negative $v_3$ implies its phase is opposite to that in the $\\eta$ region used to obtain the event plane). An earlier study~\\cite{Xiao:2012uw} has show evidences of $\\eta$ decorrelation of $v_3$ in the AMPT; Our later studies published in separate papers trace this decorrelation to the independent fluctuations of the $\\epsilon_n$ for the projectile nucleus and the $\\epsilon_n$ for the target nucleus~\\cite{Jia:2014vja,Jia:2014ysa}.\n\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=1\\linewidth]{Q3cvnbpaper_cent8_pt0_har2_m1}\n\\caption{\\label{fig:eta1b} (Color online) The $v_3(\\eta)$ for events selected for lower 10\\% (top panels) and upper 10\\% (bottom panels) of the values of either $q_3^{\\mathrm{S}}$ (left panels) or $\\epsilon_3$ (right panels) for AMPT Pb+Pb events with $b=8$~fm. In each case, the integral $v_3$ calculated for particles in $0.1<\\pT<5$ GeV relative to the event plane of subevent A, B and C (Their $\\eta$ coverages are indicated in the legend) with a minimum $\\eta$ gap of 1 unit are shown. }\n\\end{figure}\n\n Figure~\\ref{fig:eta3b} quantifies the rapidity asymmetry of $v_n$ between $-5<\\eta<-4$ and  $4<\\eta<5$ as a function of $q_3^{\\mathrm{S}}$ and $\\epsilon_3$. The even harmonics $v_2$ and $v_4$ show little asymmetry and are nearly independent of $q_3^{\\mathrm{S}}$. In contrast, the $v_5$ values show a strong $\\eta$-asymmetry similar to that for $v_3$. \n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=1\\linewidth]{Q3cvnQdeppaperb_cent8_pt0_eta1_m1}\n\\caption{\\label{fig:eta3b} (Color online)  Dependence of the $v_n$ on $q_3^{\\mathrm{S}}$ in a forward ($-5<\\eta<-4$) and a backward ($4<\\eta<5$) pseudorapidity ranges.}\n\\end{figure}\n\nFigure~\\ref{fig:eta5} shows the particle multiplicity distributions $dN\/d\\eta$ for events selected on $q_2^{\\mathrm{S}}$ (left) or $q_3^{\\mathrm{S}}$ (right). The distributions remain largely symmetric in $\\eta$ and the overall magnitude is nearly independent of the event selection. We also verified explicitly that the number of participating nucleons for the projectile and target are nearly equal for all $q_2^{\\mathrm{S}}$ or $q_3^{\\mathrm{S}}$ bins. This suggests that the underlying mechanism is not due to the EbyE fluctuations of the $dN\/d\\eta$ distribution.\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=0.5\\linewidth]{cvnNpaper_cent8_pt0_m0}\\includegraphics[width=0.5\\linewidth]{Q3cvnNpaper_cent8_pt0_m0}\n\\caption{\\label{fig:eta5} (Color online) The $dN\/d\\eta$ distributions of all particles for events selected on $q_2^{\\mathrm{S}}$ (left) and $q_3^{\\mathrm{S}}$ (right).}\n\\end{figure}\n\n\n\\section{event-plane correlations}\n\\label{sec:4}\nThe AMPT model has been shown to reproduce~\\cite{Bhalerao:2013ina} the centrality dependence of various two-plane and three-plane correlations measured by the ATLAS Collaboration~\\cite{Jia:2012sa}. Here we use AMPT model to study how these correlators change with $q_n^{\\mathrm{S}}$ or $\\epsilon_n$. In this analysis, the two-plane correlators $\\langle\\cos k(\\Phi_{n}-\\Phi_{m})\\rangle$ are calculated by correlating the EP angles from subevent A and subevent C. Each subevent provides its own estimation of the EPs, leading to two statistically independent estimates of the correlator: Type1 $\\langle\\cos k(\\Phi_{n}^{\\mathrm{A}}-\\Phi_{m}^{\\mathrm{C}})\\rangle$ and Type2 $\\langle\\cos k(\\Phi_{n}^{\\mathrm{C}}-\\Phi_{m}^{\\mathrm{A}})\\rangle$. The two estimates are identical for events selected on $\\epsilon_2$, and hence they are averaged to obtain the final result. But for events selected based on $q_2^{\\mathrm{S}}$, the two estimates can differ quite significantly. \n\nFigure~\\ref{fig:ep1} shows the values of four two-plane correlators in bins of $q_2^{\\mathrm{S}}$ or $\\epsilon_2$. The values of the correlators are observed to increase strongly with increasing $q_2^{\\mathrm{S}}$ or $\\epsilon_2$. The two estimates based on $q_2^{\\mathrm{S}}$ selection differ significantly, reflecting the influence of longitudinal flow fluctuations exposed by the $q_2^{\\mathrm{S}}$ selection. Interestingly, the correlators whose $\\Phi_2$ angle is calculated in subevent C agree very well with those based on $\\epsilon_2$ event shape selection, such as $\\langle\\cos 4(\\Phi_{2}^{\\mathrm{C}}-\\Phi_{4}^{\\mathrm{A}})\\rangle$. This is because $\\Phi_{2}^{\\mathrm{C}}$ is expected to be less dependent on the $q_2^{\\mathrm{S}}$ selection than $\\Phi_{2}^{\\mathrm{A}}$ (see Fig.~\\ref{fig:eta3}(a)). These observations suggest that the dependence of $\\langle\\cos 4(\\Phi_{2}^{\\mathrm{C}}-\\Phi_{4}^{\\mathrm{A}})\\rangle$ and $\\langle\\cos 6(\\Phi_{2}^{\\mathrm{C}}-\\Phi_{6}^{\\mathrm{A}})\\rangle$ on $q_2^{\\mathrm{S}}$ reflects mainly the change in the initial geometry and the ensuing non-linear effects in the final state. Note that the last bin in each panel represents the value obtained without event shape selection, which agrees between the three calculations by construction.\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=1\\linewidth]{c2pcomp2paperw_cent8_type_m1}\n\\caption{\\label{fig:ep1} (Color online) The four two-plane correlations as a function of bins of $q_2^{\\mathrm{S}}$ or $\\epsilon_2$ for AMPT Pb+Pb events with $b=8$~fm. The two event planes $\\Phi_n$ and $\\Phi_m$ are measured by subevent A and subevent C. The $q_2^{\\mathrm{S}}$-binned results are presented separately for the two combinations: $\\langle\\cos k(\\Phi_{n}^{\\mathrm{A}}-\\Phi_{m}^{\\mathrm{C}})\\rangle$ (open circles) and $\\langle\\cos k(\\Phi_{n}^{\\mathrm{C}}-\\Phi_{m}^{\\mathrm{A}})\\rangle$ (solid circles).}\n\\end{figure}\n\nFigure~\\ref{fig:ep2} compares various two-plane correlators calculated via the EP method and the SP method given by Eqs.~\\ref{eq:m4a}-\\ref{eq:m5}. The SP method is observed to give systematically higher values for Type1 correlators where the first angle is measured by subevent A, while it gives consistent or slightly lower values for Type2 correlators. The last bin in each panel shows the result obtained without event shape selection, where the values from the SP method are always higher, as expected~\\cite{Bhalerao:2013ina}. \n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=1\\linewidth]{c2pcomp3paper_cent8_type_m1}\n\\caption{\\label{fig:ep2} (Color online) The four two-plane correlators in bins of $q_2^{\\mathrm{S}}$ for AMPT Pb+Pb events with $b=8$~fm, shown for two different combinations of the event-plane angles (solid symbols), and compared with the correlations calculated via the scalar product method (open symbols).}\n\\end{figure}\n\nFigure~\\ref{fig:ep1b} shows $\\langle\\cos 6(\\Phi_{2}-\\Phi_{3})\\rangle$ and $\\langle\\cos 6(\\Phi_{3}-\\Phi_{6})\\rangle$ in bins of $q_3^{\\mathrm{S}}$ or $\\epsilon_3$. The first correlator shows little dependence on $q_3^{\\mathrm{S}}$ or $\\epsilon_3$, while the second correlator does. This is in sharp contrast to the results seen in Fig.~\\ref{fig:ep1}, where both correlators show strong but opposite dependence on $q_2^{\\mathrm{S}}$ or $\\epsilon_2$. This behavior is consistent with a strong coupling between $v_6$ and $v_2$, $v_6$ and $v_3$, but weak coupling between $v_2$ and $v_3$.\n\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[width=1\\linewidth]{Q3c2pcomp2paperw_cent8_type_m1}\n\\caption{\\label{fig:ep1b} (Color online) Two two-plane correlators as a function of either $q_3^{\\mathrm{S}}$ or $\\epsilon_3$ for AMPT Pb+Pb events with $b=8$~fm. The event planes $\\Phi_n$ and $\\Phi_m$ are measured by subevent A and subevent C. The $q_3^{\\mathrm{S}}$-binned results are presented separately for the two estimates: $\\langle\\cos k(\\Phi_{n}^{\\mathrm{A}}-\\Phi_{m}^{\\mathrm{C}})\\rangle$ (open circles) and $\\langle\\cos k(\\Phi_{n}^{\\mathrm{C}}-\\Phi_{m}^{\\mathrm{A}})\\rangle$ (solid circles).}\n\\end{figure}\n\nTo calculate three-plane correlations, subevents A, B and C are used. Each subevent provides its own estimation of the three EP angles, and hence there are $3!=6$ independent ways of estimating a given three-plane correlator. For $c_nn\\Phi_{n}+c_mm\\Phi_{m}+c_ll\\Phi_{l}$ with $n<m<l$, these six estimates are labelled as the following:\n\\begin{itemize}\n\\item Type 1a: $c_nn\\Phi_{n}^{\\mathrm{B}}+c_mm\\Phi_{m}^{\\mathrm{A}}+c_ll\\Phi_{l}^{\\mathrm{C}}$\n\\item Type 1b: $c_nn\\Phi_{n}^{\\mathrm{B}}+c_mm\\Phi_{m}^{\\mathrm{C}}+c_ll\\Phi_{l}^{\\mathrm{A}}$\n\\item Type 2a: $c_nn\\Phi_{n}^{\\mathrm{A}}+c_mm\\Phi_{m}^{\\mathrm{B}}+c_ll\\Phi_{l}^{\\mathrm{C}}$\n\\item Type 2b: $c_nn\\Phi_{n}^{\\mathrm{C}}+c_mm\\Phi_{m}^{\\mathrm{B}}+c_ll\\Phi_{l}^{\\mathrm{A}}$\n\\item Type 3a: $c_nn\\Phi_{n}^{\\mathrm{A}}+c_mm\\Phi_{m}^{\\mathrm{C}}+c_ll\\Phi_{l}^{\\mathrm{B}}$\n\\item Type 3b: $c_nn\\Phi_{n}^{\\mathrm{C}}+c_mm\\Phi_{m}^{\\mathrm{A}}+c_ll\\Phi_{l}^{\\mathrm{B}}$\n\\end{itemize}\nFor events selected on $\\epsilon_n$, the symmetry of the $\\eta$-coverage between A and C reduces them into three equivalent pairs of estimates. However for events selected on $q_n^{\\mathrm{S}}$, all six estimates can be different.\n\nFigure~\\ref{fig:ep3} summarizes the results for five three-plane correlators, one for each column, calculated for events classified by $q_2^{\\mathrm{S}}$ or $\\epsilon_2$~\\footnote{We also calculate these correlators using the SP method (a.la. $q_n$-weights), the dependences on $q_2^{\\mathrm{S}}$ are found to be qualitatively the same, though the overall magnitudes may differ (see Fig.~\\ref{fig:a3}).}, including a previously unnoticed strong correlator $\\left\\langle\\cos (2\\Phi_{2}-8\\Phi_{4}+6\\Phi_6)\\right\\rangle$. The six estimates of each correlator are grouped into three pairs and are shown in the three rows. Many of these correlators exhibit a breaking of the symmetry between subevent A and C, see for example the Type1 and Type2 for the first two correlators, as well as the Type1 and Type3 for the third and fourth correlators. Some correlators even show opposite dependence on $q_2^{\\mathrm{S}}$, such as the Type1 and Type3 for the fourth correlator ($\\left\\langle\\cos (2\\Phi_{2}-6\\Phi_{3}+4\\Phi_4)\\right\\rangle$). In most cases, however, the overall dependences on $\\epsilon_2$ bin (open circles) are reasonably captured by the dependence on $q_2^{\\mathrm{S}}$ (open boxes), implying that these correlations reflect mainly the intrinsic hydrodynamic response to the change in the selected initial geometry. \n\n\\begin{figure*}[t!]\n\\centering\n\\includegraphics[width=1\\linewidth]{c3pcomp2paperw_cent8_m1}\n\\caption{\\label{fig:ep3} (Color online) \nThe five three-plane correlators (from left to right) as a function of either $q_2^{\\mathrm{S}}$ (solid symbols) or $\\epsilon_2$ (open symbols) for AMPT Pb+Pb events with $b=8$~fm. The results for the three type groups are shown in different row: Type1a and Type1b (top row), Type2a and Type2b (middle row), Type2a and Type2b (bottom row). The last bin in each panel shows the inclusive result.}\n\\end{figure*}\n\\begin{figure*}[!t]\n\\centering\n\\includegraphics[width=1\\linewidth]{Q3c3pcomp2paperw_cent8_m1}\n\\caption{\\label{fig:ep3b} (Color online) \nThe five three-plane correlators (from left to right) as a function of either $q_3^{\\mathrm{S}}$ (solid symbols) or $\\epsilon_3$ (open symbols) for AMPT Pb+Pb events with $b=8$~fm. The results for the three type groups are shown in different row: Type1a and Type1b (top row), Type2a and Type2b (middle row), Type2a and Type2b (bottom row). The last bin in each panel shows the inclusive result.}\n\\end{figure*}\n\nFigure~\\ref{fig:ep3b} summarizes the results for the same five three-plane correlators, but calculated for events classified by $q_3^{\\mathrm{S}}$ or $\\epsilon_3$. Comparing with Fig.~\\ref{fig:ep3}, we find that the values of $\\left\\langle\\cos (2\\Phi_{2}-3\\Phi_{3}+5\\Phi_5)\\right\\rangle$ are more sensitive to $q_3^{\\mathrm{S}}$ or $\\epsilon_3$ than to $q_2^{\\mathrm{S}}$ or $\\epsilon_2$ for small bin numbers, possibly reflecting stronger rapidity decorrelation effects associated with $\\Phi_3$ seen for small $q_3^{\\mathrm{S}}$ or $\\epsilon_3$ in Fig.~\\ref{fig:eta1b}. The correlators $\\left\\langle\\cos (2\\Phi_{2}-6\\Phi_{3}+4\\Phi_4)\\right\\rangle$ and $\\left\\langle\\cos (2\\Phi_{2}+6\\Phi_{3}-8\\Phi_4)\\right\\rangle$ show better agreement between the six types than when they are selected by $q_2^{\\mathrm{S}}$ or $\\epsilon_2$ as shown in Fig.~\\ref{fig:ep3}, again reflecting the weak correlation between $v_3$ and $v_2$, and between $v_3$ and $v_4$.\n\n\n\n\n\n\\section{Discussion and Summary}\n\\label{sec:5}\n\nThis paper studies two sets of flow observables involving correlations between harmonic flow coefficients $v_n$ and their phases $\\Phi_n$, utilizing the recently proposed event shape selection technique~\\cite{Schukraft:2012ah}. The shape of the collision geometry is selected by cutting on $q_n$ (the magnitude of the flow vector in a subevent) and eccentricity $\\epsilon_n$. The $p(v_m)$ or the differential distribution of event-averaged $v_m$, and the event-plane correlations $p(\\Phi_m, \\Phi_l, ....)$ are then be studied in each $q_n$ or $\\epsilon_n$ bin. A special case of interest is the $v_n(\\eta)$ for events selected on $q_n$, which is sensitive to rapidity fluctuations of collective flow. The feasibility of measuring these new observables is investigated using the AMPT model. This model combines the Glauber initial fluctuating geometry with collective flow generated by partonic transport, and hence allows one to correlate the initial geometry information, $e.g.$ ($\\epsilon_n$, $\\Phi_n^*$), with ($v_n$,$\\Phi_n$) on a EbyE basis. Since the AMPT model describes reasonably the experimentally measured $\\pT$ spectra, $v_n$~\\cite{Xu:2011fe,Xu:2011fi}, and event-plane correlations~\\cite{Bhalerao:2013ina}, it should provide a good benchmark for the performance of event shape selection, as well as provide qualitative understanding of the physics behind these new observables.\n\n\nTo summarize, our study has been performed for Pb+Pb collisions at $\\sqrt{s_{NN}}=2.76$ TeV with fixed impact parameter $b=8$~fm, which corresponds to $\\sim30\\%$ centrality. The event shape selection is performed on the $q_2^{\\mathrm{S}}$ and $q_3^{\\mathrm{S}}$ calculated using half of the particles in $-6<\\eta<-2$, as well as on $\\epsilon_2$ and $\\epsilon_3$. The EP angles used to calculate the EP correlators are calculated in subevent A (the other half particles in $-6<\\eta<-2$), subevent B covering $-1<\\eta<1$ and subevent C covering $2<\\eta<6$. Our main findings can be summarized below:\n\\begin{itemize}\n\\item\nThe eccentricity $\\epsilon_n$ distribution is very broad for events with fixed impact parameter and correlates well with $q_n$ for $n=2$ and $3$, hence events with different ellipticity or triangularity can be selected precisely using $q_2$ and $q_3$, respectively.\n\\item\nThe participant plane correlations, such as $\\langle\\cos4(\\Phi_{2}^*-\\Phi_{4}^*)\\rangle$, $\\langle\\cos6(\\Phi_{2}^*-\\Phi_{6}^*)\\rangle$ and $\\langle\\cos6(\\Phi_{3}^*-\\Phi_{6}^*)\\rangle$, are observed to vary strongly with $\\epsilon_2$ or $\\epsilon_3$, and much of these dependences are preserved when selecting on $q_2$ or $q_3$. \n\\item\nSignificant correlations or anti-correlations are observed among the $\\epsilon_n$, such as $p(\\epsilon_2, \\epsilon_3)$, $p(\\epsilon_1, \\epsilon_3)$ and $p(\\epsilon_2, \\epsilon_4)$. These correlations can be easily probed by the event shape selection technique, some of these correlations, $e.g.$ $p(\\epsilon_1, \\epsilon_3)$ and $p(\\epsilon_2, \\epsilon_3)$, are expected to survive to the final state. Indeed, the correlation between $\\epsilon_2$ and $\\epsilon_3$ seems to be captured by the observed correlation between $v_2$ and $v_3$ in the AMPT model. \n\\item\nThe overall $v_n$ values in each $q_n^{\\mathrm{S}}$ bin are similar to that in the corresponding $\\epsilon_n$ bin ($n=2$ and 3). However a strong forward\/backward asymmetry of $v_n(\\eta)$ is observed in $q_n^{\\mathrm{S}}$ selected events (also $v_4$, $v_5$ for $q_2^{\\mathrm{S}}$ and $v_5$ for $q_3^{\\mathrm{S}}$), reflecting the dynamical fluctuations either in the initial state~\\cite{Pang:2012he,Pang:2013pma} or during the collective expansion present in the AMPT model. These dynamical fluctuations are exposed by the $q_n^{\\mathrm{S}}$ selection, probably because they are either short range in $\\eta$ or have strong $\\eta$ dependence. These dynamical effects also contribute strongly to event-plane decorrelations. We also observe that the $dN\/d\\eta$ distribution is not affected much by the event shape selection.\n\\item\nThe $v_n$ values are always positively correlated with $q_n^{\\mathrm{S}}$, however other harmonics $v_m$ for $m\\neq n$ show non-trivial dependence on $q_n^{\\mathrm{S}}$. For $q_2^{\\mathrm{S}}$ selection, $v_4$, $v_5$ and $v_6$ show positive correlation, while $v_3$ shows negative correlation consistent with the behavior of $p(\\epsilon_2, \\epsilon_3)$. For $q_3^{\\mathrm{S}}$ selection, $v_5$ shows positive correlation, while the $v_2$ and $v_4$ show slight negative correlation. These correlations are qualitatively consistent with couplings between different harmonics expected for collective flow~\\cite{Teaney:2012ke}.\n\\item\nThe strengths of several event-plane correlators vary strongly with $q_n^{\\mathrm{S}}$ and $\\epsilon_n$. These variations are observed to be similar between the EP method and the SP method. In many cases, they are also found to be similar between $q_n^{\\mathrm{S}}$ selection and $\\epsilon_n$ selection, namely the $\\langle\\cos 4(\\Phi_{2}^{\\mathrm{C}}-\\Phi_{4}^{\\mathrm{A}})\\rangle$, $\\langle\\cos 6(\\Phi_{2}^{\\mathrm{C}}-\\Phi_{6}^{\\mathrm{A}})\\rangle$, and many of $\\langle\\cos (2\\Phi_{2}+3\\Phi_3-5\\Phi_{5})\\rangle$, $\\langle\\cos (2\\Phi_{2}+4\\Phi_4-6\\Phi_{6})\\rangle$ and $\\langle\\cos (2\\Phi_{2}-8\\Phi_4+6\\Phi_{6})\\rangle$. For these correlators, the change of signal reflects mainly the selection on the collision geometry. In some other cases, results differ significant between $q_n^{\\mathrm{S}}$ and $\\epsilon_n$ selections, such as $\\langle\\cos 4(\\Phi_{2}^{\\mathrm{A}}-\\Phi_{4}^{\\mathrm{C}})\\rangle$, $\\langle\\cos 6(\\Phi_{2}^{\\mathrm{A}}-\\Phi_{6}^{\\mathrm{C}})\\rangle$ and $\\langle\\cos (2\\Phi_{2}^{\\mathrm{B}}+3\\Phi_3^{\\mathrm{A}}-5\\Phi_{5}^{\\mathrm{C}})\\rangle$ between $q_2^{\\mathrm{S}}$ and $\\epsilon_2$, and $\\langle\\cos (2\\Phi_{2}^{\\mathrm{B}}+3\\Phi_3^{\\mathrm{A}}-5\\Phi_{5}^{\\mathrm{C}})\\rangle$ and $\\langle\\cos (2\\Phi_{2}^{\\mathrm{A}}+3\\Phi_3^{\\mathrm{B}}-5\\Phi_{5}^{\\mathrm{C}})\\rangle$ between $q_3^{\\mathrm{S}}$ and $\\epsilon_3$. For these correlators, the change of signal is probably also affected by the dynamical fluctuations present in the AMPT model.\n\\item\nFor some event-plane correlators, the signal for different types show very different dependence on $q_2^{\\mathrm{S}}$. For example $\\langle\\cos (2\\Phi_{2}^{\\mathrm{A}}-6\\Phi_3^{\\mathrm{C}}+4\\Phi_{4}^{\\mathrm{B}})\\rangle$ and $\\langle\\cos (2\\Phi_{2}^{\\mathrm{C}}-6\\Phi_3^{\\mathrm{A}}+4\\Phi_{4}^{\\mathrm{B}})\\rangle$ have opposite dependence, and both differ from the dependence on $\\epsilon_2$. This may be a result of the rapidity fluctuations of $v_3(\\eta)$, as shown in Fig.~\\ref{fig:eta1b}.\n\\end{itemize}\n\n\n\n\nHeavy ion collisions at RHIC and LHC are a finite number system. A typical Pb+Pb collision involves a few hundred colliding nucleons and produces on the order of 10,000 particles in the final state. Both the collision geometry defined by the nucleons and the collective expansion of produced particles can fluctuate strongly event-by-event. It remains a challenge to disentangle the fluctuations at the initial state and dynamical fluctuations generated in the collective expansion, a prerequisite for understanding the physics behind these fluctuations. Future progress requires a detailed and systematic study of the correlations between all $v_n$ and their phases $\\Phi_n$: $p(v_n,v_m,..., \\Phi_n, \\Phi_m,...)$, in order to disentangle different sources of fluctuations. The study presented in this paper attempts to establish the methodology for accessing these correlations and provides the initial guidance on how these correlations are connected to the initial geometry and dynamics in the collective expansion. Much more theoretical efforts, especially those based on the application of event shape selection technique in EbyE hydrodynamics, will provide more realistic and detailed insights on the nature of the fluctuations and non-linear dynamics in various stages of the heavy ion collisions.\n\nThis research is supported by NSF under grant number PHY-1305037 and by DOE through BNL under grant number DE-AC02-98CH10886.\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzovib b/data_all_eng_slimpj/shuffled/split2/finalzzovib
new file mode 100644
index 0000000000000000000000000000000000000000..fddab64ab118b25d5fa4b0516c83d9e4721e979d
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzovib
@@ -0,0 +1,5 @@
+{"text":"\\section{Introduction}\n\\label{intro}\nHuman action recognition \\cite{AggarwalR11,TuragaCSU08} has become an important area in computer vision research, whose aim is to automatically classify the  action ongoing in a video. It is one of the challenging problems in computer vision for serval reasons. Firstly, there are large intra-class variations in the same action class, caused by various motion speeds, viewpoint changes, and background clutter. Secondly, the identification of an action class is related to many other high-level visual clues, such as human pose, interacting objects, and scene class. These related problems are very difficult themselves. Furthermore, the determination of temporal extent for an actions is more subjective than a static object, which means there is no precise definition about when an action starts and finishes. Finally, the high dimension and low quality of video data usually add difficulty to developing robust and efficient recognition algorithm.\n\nEarly approaches interpret an action as a set of space-time trajectories of 2-dimensional or 3-dimensional points of human joints \\cite{Webb81,NiyogiA94,CampbellB95,YacoobB99}. These methods usually need dedicate techniques to detect body parts or track them at each frame. However, the detection and tracking of body part is still an unsolved problem in realistic videos. Recently, recognition methods using local spatiotemporal features \\cite{Laptev05,LaptevMSR08,WangKSL13,WangQT14} have become the main stream and obtained the state-of-the-art performance on many datasets \\cite{WangS13a}. These methods do not require algorithms to detect human body, which treat the action volume as a rigid 3D-object and extract appropriate features to describe the patterns of each 3D volume. They are robust to background clutter, illumination changes, and noise.\n\nBag of Visual Words (BoVW) framework with local features and its variants \\cite{Wang13,Wu13,Karaman13,Murthy13,PengWCQP13} have dominated the research work of action recognition and showed their effectiveness in the recent THUMOS'13 Action Recognition Challenge \\cite{THUMOS13}. As shown in Figure \\ref{fig:flowchart}, the pipeline of BoVW for video based action recognition consists of five steps: (i) feature extraction, (ii) feature pre-processing, (iii) codebook generation, (iv) feature encoding, and (v) pooling and normalization. In each step, many efforts have been made and several progress has been obtained. Regarding local features, many successful feature extractors (e.g. STIPs \\cite{Laptev05}, Dense Trajectories \\cite{WangKSL13}) and descriptors (e.g. HOG \\cite{LaptevMSR08}, HOF \\cite{LaptevMSR08}, MBH \\cite{WangKSL13}) have been designed for representing the visual patterns of cuboid. Feature pre-processing technique mainly de-correlates these descriptors to make the following representation learning more stable. For codebook generation, it aims to describe the local feature space and provide a partition (e.g. $k$-means \\cite{Bishop06}) or generative process (e.g. GMMs \\cite{Bishop06}) for local descriptor.  Feature encoding is a hot topic in image classification and many alternatives have been developed for effective representation and efficient implementation (see good surveys \\cite{ChatfieldLVZ11,HuangWWT14}). Max pooling \\cite{YangYGH09} and sum pooling \\cite{ZhangMLS07} are usually used to aggregate information from a spatiotemporal region. For normalization methods, typical choices include $\\ell_1$-normalization \\cite{ZhangMLS07}, $\\ell_2$-normalization \\cite{WangYYLHG10}, power normalization \\cite{PerronninSM10}, and intra normalization \\cite{ArandjelovicZ13}. \\emph{How to make decision in each step to obtain the best pipeline of BoVW for action recognition} still remains unknown and needs to be extensively explored.\n\nMeanwhile, unlike static image, video data exhibits different views of visual pattern, such as appearance, motion, and motion boundary, and all of them play important roles in action recognition. Therefore, multiple descriptors are usually extracted from a cuboid and each descriptor corresponds to the specific aspect of the visual data \\cite{WangKSL13,LaptevMSR08}. BoVW is mainly designed for a single descriptor and ignores the problem of fusing multiple descriptors. Many research works have been devoted to fusing multiple descriptor for boosting performance  \\cite{GehlerN09,VedaldiGVZ09,TangYLK13,WangS13a,CaiWPQ14}. Typical fusion methods include descriptor level fusion \\cite{LaptevMSR08,WangWQ12}, representation level fusion \\cite{Wang13,WangKSL13}, and score level fusion \\cite{TangYLK13,MyersNHPNSHKSSS14}. For descriptor level fusion, multiple descriptors from the same cuboid are concatenated as a whole one and fed into BoVW framework. For representation level fusion, the fusion is conducted in the video level, where each descriptor is firstly fed into BoVW framework independently and the resulting global representations are then concatenated to train a final classifier. For score level fusion, each descriptor is separately input into BoVW framework and used to train a recognition classifier. Then the scores from multiple classifiers are fused using arithmetic mean or geometric mean. In general, these fusion methods are developed in different scenarios and adapted for action recognition by different works. \\emph{How these fusion methods influence the final recognition of BoVW framework and whether there exists a best one for action recognition} is an interesting question and well worth of a detailed investigation.\n\nSeveral related study works have been performed about encoding methods for image classification \\cite{ChatfieldLVZ11,HuangWWT14} and action recognition \\cite{WangWQ12}. But these study works are with image classification task or lacking full exploration of all steps in BoVW framework. Meanwhile, the study work of action recognition \\cite{WangWQ12} is limited regarding the evaluation dataset and ignores the influence of fusion methods. This article aims to \\emph{provide a comprehensive study of all steps in BoVW and different fusion methods, and uncover some good practice to produce a state-of-the-art action recognition system}. Our work is mainly composed of three parts:\n\n\\textbf{Exploration of BoVW.} We place an emphasis on extensively explorations about all components in BoVW pipeline and discovery of useful practice tips. Specifically, we investigate two widely-used local features, namely Space Time Interest Points (STIPs) with HOG, HOF \\cite{Laptev05}, and Improved Dense Trajectories (iDTs) with HOG, HOF, MBH \\cite{WangS13a}. For feature encoding methods, the current approaches can be roughly classified into three categories: (i) voting based encoding methods, (ii) reconstruction based encoding methods, (iii) super vector based encoding methods. For each type of encoding methods, we choose several representative approaches and totally analyze ten encoding methods. Meanwhile, we explore the relations among these different encoding methods and provide an unified and generative perspective over these encoding methods. We fully explored eight pooling and normalization strategies for each encoding method. From our extensive study of different components in BoVW, server good practice can be concluded:\n\\begin{itemize}\n  \\item Dense features with more descriptors are more informative in capturing the content of video data and suitable for action recognition. Meanwhile, dense features may exhibit different properties with sparse features with respect to variations of BoVW such as codebook size and encoding methods.\n  \\item Data pre-processing is an important step in BoVW pipeline and able to greatly improve the final recognition performance.\n  \\item Basically, high dimensional representation of super vector is more effective and efficient than the other two types of encoding methods.\n  \\item Pooling and normalization is a crucial step in BoVW, whose importance may not be highlighted in previous studies. Sum pooling with power $\\ell_2$-normalization is the best choice during all the possible combinations.\n  \\item In above, every step is crucial for contributing to the final recognition rate. Improper choice in one of the steps may counteract the performance improvement of other steps.\n\\end{itemize}\n\n\\textbf{Investigation of Fusion Methods.} As combination of multiple descriptors is very crucial for performance improvement, we also investigate the influence of different fusion methods inour designed action recognition system. Specifically, we study three kinds of fusion methods, namely descriptor level fusion, representation level fusion, and descriptor level fusion. We find that the way different descriptors correlate with each other determines the effectiveness of fusion methods. The performance gain obtained from fusing multiple descriptors mainly owns to their complementarity. We observe that this complementarity is not only with multiple descriptors, but also with multiple BoVW models. Based on this view, we propose a new representation, called \\emph{hybrid representation}, combining the outputs of multiple BoVW models of different descriptors. This representation utilizes the benefit of each BoVW and fully considers the complementarity among them. In spite of its simplicity, this representation turns out to be effective for improving final recognition rate.\n\n\\textbf{Comparison with the State of the Art.} Guided by the practice tips concluded from our insightful analysis of BoVW variants and feature fusion methods, we design an effective action recognition system using our proposed hybrid representation, and demonstrates its performance on three challenging datasets: HMDB51 \\cite{KuehneJGPS11}, UCF50 \\cite{ReddyS13}, and UCF101 \\cite{SOOMRO12}. Specifically, we leverage the richness and effectiveness of low-level features, design a hybrid super vector, a combination of Fisher vector \\cite{PerronninSM10} and SVC-$k$, and resort to representation level fusion to boost final recognition performance. From comparison with other methods, we conclude that our recognition system reaches the state-of-the-art performance on the three datasets, and our hybrid representation acts as a new baseline for further research of action recognition.\n\nThe rest of this paper is organized as follows. In Section \\ref{sec:method}, we give an detailed description of each step in BoVW framework of action recognition system. Meanwhile, we uncover several useful techniques commonly adopted in these encoding methods, and provide a unified generative perspective over these encoding methods. Then, several fusion methods and a new representation are introduced in Section \\ref{sec:fusion}. Finally, we empirically evaluate the BoVW frameworks and fusion methods on three challenging datasets. We analyze these experiment results and uncover good practice for constructing a state-of-the-art action recognition system. We conclude the paper in Section \\ref{sec:conclusion}.\n\n\n\\section{Framework of Bag of Visual Words}\n\\label{sec:method}\nAs shown in Figure \\ref{fig:flowchart}, the pipeline of Bag of Visual Words (BoVWs) framework consists of five steps: (i) feature extraction, (ii) feature pre-processing, (iii) codebook generation, (iv) feature encoding, and (v) pooling and normalization. Then the global representation is fed into a classifier such as linear SVM for action recognition. In this section, we will give detailed descriptions of the popular technical choices in each step, which are very important for constructing a state-of-the-art recognition system. Furthermore, we summarize several use techniques in these encoding methods and provide a unified generative perspective over these different encoding methods.\n\\begin{figure*}\n  \\centerline{\\includegraphics[width=\\textwidth]{pipeline.eps}}\n  \\caption{The pipeline of obtaining Bag of Visual Words (BoVWs) representation for action recognition. It is mainly composed of five steps: (i) feature extraction, (ii) feature pre-processing, (iii) codebook generation, (iv) feature encoding, and (v) pooling and normalization.}\n  \\label{fig:flowchart}\n\\end{figure*}\n\n\\begin{table*}[!htb]\n\\caption{List of encoding methods and their formulations. The detailed descriptions of these encoding methods can be found in the text.}\n\\centering\n\\begin{tabular}{|c|l|l|c|}\\hline\nType & Method & Formulation & Dim.\\\\ \\hline\n\\multirow{5}{*}[-1cm]{\\rotatebox{90}{Voting based}} &1. Vector Quantization (VQ) \/ Hard Voting (HV) & \\tabincell{l}{$\\mathbf{s}(i) = 1, \\ \\textrm{if} \\ \\ i=\\textrm{arg}\\min_{j}||\\mathbf{x} - \\mathbf{d}_j||_2^2, $\\\\$ \\textrm{s.t.} \\ ||\\mathbf{s}||_{0} = 1$ } & $K$\\\\\n\\cline{2-4}\n& 2. Soft-assignment (SA) \/ Kernel Codebook Coding (KCB) & $\\mathbf{s}(i) = \\frac{\\exp(-\\beta||\\mathbf{x}-\\mathbf{d}_i||_2^{2})}{\\sum_{i=1}^K \\exp(-\\beta||\\mathbf{x} - \\mathbf{d}_i||_2^{2})} $ & $K$\\\\\n\\cline{2-4}\n& 3. Localized Soft Assignment (SA-k) & \\tabincell{l}{$ \\mathbf{s}(i) = \\frac{\\exp(-\\beta||\\mathbf{x}-\\mathbf{d}_i||_2^{2})}{\\sum_{i=1}^k \\exp(-\\beta||\\mathbf{x} - \\mathbf{d}_i||_2^{2})},\\ \\textrm{if} \\ \\mathbf{d}_i\\in N_{k}(\\mathbf{x})$,\\\\ $ \\textrm{s.t.} \\ ||\\mathbf{s}||_{0} = k $} & $K$ \\\\\n\\cline{2-4}\n& 4. Salient Coding (SC) & \\tabincell{l}{$ \\mathbf{s}(i) = \\sum_{j=2}^k(\\frac{||\\mathbf{x}-\\mathbf{d}_j||_2-||\\mathbf{x}-\\mathbf{d}_1||_2}{||\\mathbf{x}-\\mathbf{d}_j||_2}),\\mathbf{d}_j\\in N_{k}(\\mathbf{x})$,\\\\$ \\textrm{if} \\quad i=\\textrm{arg}\\min_{j}||\\mathbf{x} - \\mathbf{d}_j||_2^2, \\quad \\textrm{s.t.} \\ ||\\mathbf{s}||_{0} = 1$} & $K$\\\\\n\\cline{2-4}\n& 5. Group Salient Coding (GSC) & \\tabincell{l}{$ \\mathbf{s}(i) = \\max\\{\\mathbf{v}^k(i)\\}, \\ \\textrm{group size } k=1,...,M$,\\\\$ \\mathbf{v}^k(i)=\\sum_{j=1}^{M+1-k}||\\mathbf{x}-\\mathbf{d}_{k+j}||_2-||\\mathbf{x}-\\mathbf{d}_k||_2$,\\\\$ \\textrm{if} \\ \\mathbf{d}_i\\in N_{k}(\\mathbf{x})$, \\ \\textrm{s.t.} \\ $\\|\\mathbf{s}\\|_0 = 1$ }  & $K$ \\\\\n\\hline\\hline\n\\multirow{4}{*}[-0.2cm]{\\rotatebox{90}{Reconstruction based}}& 6. Orthogonal Matching Pursuit (OMP) & $\\min_{\\mathbf{s}}||\\mathbf{x}-\\mathbf{D} \\mathbf{s}||_2^2, \\ \\textrm{s.t.} \\ ||\\mathbf{s}||_{0}\\le k $ & $K$ \\\\\n\\cline{2-4}\n& 7. Sparse Coding (SPC) & $ \\mathbf{s} = \\textrm{arg}\\min_{\\mathbf{s}}||\\mathbf{x-Ds}||_2^2+\\lambda ||\\mathbf{s}||_1$ & $K$\\\\\n\\cline{2-4}\n& 8. Locality-constrained Linear Coding (LLC) & \\tabincell{l}{$\\mathbf{s} = \\textrm{arg}\\min_{\\mathbf{s}}||\\mathbf{x-Ds}||_2^2+\\lambda||\\mathbf{e}\\odot\\mathbf{s}||_2^2,$\\\\\n$ \\textrm{s.t.} \\quad \\mathbf{1^{\\top}s} = 1$} & $K$ \\\\\n\\cline{2-4}\n& 9. Local Coordinate Coding (LCC) & $\\mathbf{s} = \\textrm{arg}\\min_{\\mathbf{s}}||\\mathbf{x-Ds}||_2^2+\\lambda ||\\mathbf{\\hat e}\\odot|\\mathbf{s}|||_1$ & $K$ \\\\\n\\hline\\hline\n\\multirow{4}{*}[-1cm]{\\rotatebox{90}{Super vector based}}& 10. Local Tangent-based Coding (LTC) & \\tabincell{l}{$\\mathcal{S}=[\\mathbf{s}(i),\\mathbf{s}(i)(\\mathbf{x}-\\mathbf{d}_i)^T\\mathbf{U}_i]_{i=1}^K,$ \\\\\n$ \\mathbf{U}_i \\in \\mathbb{R}^{D \\times C} \\ \\textrm{is a projection matrix} $} & $K(1+C)$ \\\\\n\\cline{2-4}\n& 11. Super Vector Coding (SVC) &  \\tabincell{l}{$ \\mathcal{S}=[0,\\mathbf{0},\\cdots,\\frac{\\alpha\\mathbf{s}(i)}{N\\sqrt{p_i}},\\frac{\\mathbf{s}(i)}{N\\sqrt{p_i}}(\\mathbf{x}-\\mathbf{d}_i),\\cdots,0,\\mathbf{0}]$, \\\\ $\\textrm{where} \\ i=\\textrm{arg}\\min_{j}||\\mathbf{x} - \\mathbf{d}_j||_2^2$ }& $K(1+D)$\\\\\n\\cline{2-4}\n& 12. Fisher Vector (FV) & \\tabincell{l}{$\\mathcal{S} = [\\mathcal{G}_{\\mu,1}^\\mathbf{x},...,\\mathcal{G}_{\\mu,K}^\\mathbf{x},\\mathcal{G}_{\\sigma,1}^\\mathbf{x},...,\\mathcal{G}_{\\sigma,K}^\\mathbf{x}], \\textrm{where}$\\\\\n$\\mathcal{G}_{\\mu,i}^\\mathbf{x}=\\frac{1}{\\sqrt{\\pi_i}}\\gamma_i(\\frac{\\mathbf{x}-\\mathbf{\\mu}_i}{\\sigma_i})$,\\\\\n$\\mathcal{G}_{\\sigma,i}^\\mathbf{x}=\\frac{1}{\\sqrt{2\\pi_i}}\\gamma_i[\\frac{(\\mathbf{x}-\\mathbf{\\mu}_i)^2}{\\sigma_i^2}-1]$,\\\\\n$\\gamma(i)=\\frac{\\pi_i \\mathcal{N}(\\mathbf{x};\\mu_i,\\Sigma_i)}{\\sum_{j=1}^K \\pi_j \\mathcal{N}(\\mathbf{x};\\mu_j,\\Sigma_j)}$} & $2KD$\\\\\n\\cline{2-4}\n& 13. Vector of Locally Aggregated Descriptors (VLAD) &  \\tabincell{l}{$ \\mathcal{S}=[\\mathbf{0},\\cdots,(\\mathbf{x}-\\mathbf{d}_i),\\cdots,\\mathbf{0}]$, \\\\ $\\textrm{where} \\ i=\\textrm{arg}\\min_{j}||\\mathbf{x} - \\mathbf{d}_j||_2^2$ } & $KD$\\\\\n\\hline\n\\end{tabular}\n\\label{tab:list}\n\\end{table*}\n\n\\subsection{Feature Extraction}\nLow-level local features have become popular in action recognition due to their robustness to background clutter and independence on detection and tracking techniques. These local features are typically divided into two parts: detecting a local region (detector) and describing the detected region (descriptor) \\cite{WangUKLS09}. Many feature detectors have been developed such as 3D-Harris \\cite{Laptev05}, 3D-Hessian \\cite{WillemsTG08}, Cuboid \\cite{DollarRCB05}, Dense Trajectories \\cite{WangKSL13}, and Improved Dense Trajectories \\cite{WangS13a}. These detectors try to select locations and scales in video by maximizing certain kind of function or using dense sampling strategy. To describe the extracted region, several hand-crafted features have been designed such as Histogram of Oriented Gradients (HOG) \\cite{LaptevMSR08,WangKSL13}, Histogram of Oriented Flow (HOF) \\cite{LaptevMSR08,WangKSL13}, and Motion Boundary Histogram (MBH) \\cite{WangKSL13,WangS13a}. Multiple descriptors are usually adopted to represent the local region, each of which corresponds to a certain aspect of visual pattern such as static appearance, motion, and motion boundary.\n\nAmong these local features, Space Time Interest Points (STIPs) \\cite{Laptev05} and Improved Dense Trajectories (iDTs) \\cite{WangKSL13} are widely used due to their easy usages and good performance. STIPs resort to 3D-Harris to extract regions of high motion salience, which resulting a set of sparse interest points. For each interest point, STIPs extracted two kinds of descriptors, namely HOG and HOF. iDTs features are an improved version from Dense Trajectories (DTs), where a set of dense trajectories are firstly obtained by tracking pixels with median filter, and five kinds of descriptors are extracted, namely trajectory shape, HOG, HOF, MBHx, and MBHy. iDTs improve the performance of DTs by taking into account camera motion correction. Generally speaking, iDTs resort to more sophisticated engineering skills and integrate much richer low-level visual cues compared with STIPs. Therefore, they represent two different kinds of low level features, namely sparse features and dense features, and may exhibit different properties with respect to variants of BoVWs.\n\n\\subsection{Feature Pre-processing}\nThe low-level local descriptors are usually high dimensional and strong correlated, which results in great challenges in the subsequent unsupervised learning such as $k$-means clustering and GMM training. Principal component analysis (PCA) \\cite{Bishop06} is a statistical procedure to pre-process these features, which uses orthogonal transform to map feature into a set of linearly uncorrelated variables called principal components. Typically, the number of used principal components is less than the number of original variables, thus resulting in dimension reduction. Whitening technique usually follows the PCA, which aims to ensure the feature have the same variance through different dimensions. The transform formula of pre-processing is as followings:\n\\begin{equation}\n  \\mathbf{x} = \\Lambda U^\\top \\mathbf{f},\n\\end{equation}\nwhere $\\mathbf{f}\\in R^M$ is the original feature, $\\mathbf{x} \\in R^N$ is the PCA-whitened result, $U \\in R^{M \\times N}$ is the dimension reduction matrix from PCA, $\\Lambda$ is the diagonal whitening matrix $diag(\\Lambda) = [1\/\\sqrt{\\lambda_1},\\cdots,1\/\\sqrt{\\lambda_N}]$, and $\\lambda_i$ is the $i^{th}$ largest eigenvalue of covariance matrix.\n\nIt is worth noting that this step is not necessary and many previous encoding approaches skip this step, such as Vector Quantization \\cite{SivicZ03}, Sparse Coding \\cite{YangYGH09}, and Vector of Locally Aggregated Descriptor \\cite{JegouPDSPS12}. However, in our evaluation, we found this step is of great importance to improve the recognition performance.\n\n\\subsection{Codebook Generation}\nIn this section, we present the codebook generation algorithms used for the following feature encoding methods. Generally there are two kinds of approaches: (i) partitioning the feature space into regions, each of which is represented by its center, called codeword, and (ii) using generative model to capture the probability distribution of features. $k$-mean \\cite{Bishop06} is a typical method for the first type, and Gaussian Mixture Model (GMM) \\cite{Bishop06} is widely used for the second.\n\n\\textbf{$k$-means.} There are many vector quantization methods  such as $k$-means clustering \\cite{Bishop06}, hierarchical clustering \\cite{Johnson67}, and spectral clustering \\cite{NgJW01}. Among them, $k$-means is probably the most popular way to construct codebook. Given a set of local features $\\{\\mathbf{x}_1,\\cdots,\\mathbf{x}_M\\}$, where $\\mathbf{x}_m \\in \\mathbb{R}^D$. Our goal is to partition the feature set into $K$ clusters $\\{\\mathbf{d}_1,\\cdots,\\mathbf{d}_K\\}$, where $\\mathbf{d}_k \\in \\mathbb{R}^D$ is a prototype associated with the $k^{th}$ cluster. Suppose for each feature $\\mathbf{x}_m$, we introduce a corresponding set of binary indicator variables $r_{mk} \\in \\{0,1\\}$. If descriptor $\\mathbf{x}_m$ is assigned to cluster $k$, then $r_{mk}=1$ and $r_{mj} = 0$ for $j \\neq k$. We can then define an objective function:\n\\begin{equation}\n  \\min \\mathcal{J}(\\{r_{mk}, \\mathbf{d}_k\\}) = \\sum_{m=1}^M \\sum_{k=1}^K r_{mk} \\| \\mathbf{x}_m - \\mathbf{d}_k \\|_{2}^2.\n  \\label{equ:kmeans}\n\\end{equation}\nThe problem is to find values for $\\{r_{mk}\\}$ and $\\{\\mathbf{d}_k\\}$ to minimize the objective function $\\mathcal{J}$. Usually,  we can optimize it in an iterative procedure where each iteration involves two successive steps corresponding to optimization with respect to the $r_{nk}$ and $\\mathbf{d}_k$. The details can be found in \\cite{Bishop06}.\n\n\\textbf{GMM.} Gaussian Mixture Model is a generative model to describe the distribution over feature space:\n\\begin{equation}\n  p(\\mathbf{x}; \\theta) = \\sum_{k=1}^K \\pi_k \\mathcal{N}(\\mathbf{x} ; \\mu_k, \\Sigma_{k}),\n  \\label{equ:gmm}\n\\end{equation}\nwhere $K$ is mixture number, and $\\theta=\\{\\pi_1,\\mu_1,\\Sigma_1,\\cdots,$ $\\pi_K,\\mu_K,\\Sigma_K\\}$ are model parameters. $\\mathcal{N}(\\mathbf{x}; \\mu_k, \\Sigma_k)$ is $D$-dimensional Gaussian distribution.\n\nGiven the feature set $\\mathbf{X} = \\{\\mathbf{x}_1,\\cdots,\\mathbf{x}_M\\}$, the optimal parameters of GMM are learned through maximum likelihood estimation $\\mathrm{arg}\\max_{\\theta} \\ln p(\\mathbf{X}; \\theta)$. We use the iterative EM algorithm \\cite{Bishop06} to solve this problem.\n\n$k$-means algorithm performs a \\emph{hard} assignment of feature descriptor to codeword, while the EM algorithm of GMM makes \\emph{soft} assignment of feature to each mixture component based on  posterior probabilities $p(k|x)$. But unlike $k$-means, GMM delivers not only the mean information of code words, but also the shape of their distribution.\n\n\\subsection{Encoding Methods}\nIn this section, we provide a detailed description of thirteen feature encoding methods. According to the characteristics of encoding methods, they can be roughly classified into three groups, namely (i) voting based encoding method, (ii) reconstruction based encoding method, and (iv) super vector encoding method, as shown in Table \\ref{tab:list}.\n\nLet $\\mathbf{X}$ be a set of $D$-dimensional local descriptors extracted from a video, $\\mathbf{X}= [\\mathbf{x}_1, \\mathbf{x}_2,\\cdots,\\mathbf{x}_N] \\in \\mathbb{R}^{D \\times N}$. Given a codebook with $K$ codewords, $\\mathbf{D} = \\left[\\mathbf{d}_1, \\mathbf{d}_2, \\cdots, \\mathbf{d}_K \\right] \\in \\mathbb{R}^{D \\times K}$. The objective of encoding is to compute a code $\\mathbf{s}$ (or $\\mathcal{S}$) \\footnote{We use $\\mathbf{s}$ to denote the code of voting and reconstruction based encoding methods, and $\\mathcal{S}$ to represent the one of super vector based encoding methods.} for input $\\mathbf{x}$ with $\\mathbf{D}$. Table \\ref{tab:list} lists all the formulations and dimension of encoding methods, where $\\mathbf{s}(i)$ denotes the $i^{th}$ element of $\\mathbf{s}$.\n\n\\subsubsection{Voting based encoding methods}\nVoting based encoding methods \\cite{SivicZ03,GemertVSG10,LiuWL11,HuangHYT11,WuHWT12} are designed from the perspective of encoding process and each descriptor directly votes for the codeword using a specific strategy. A $K$-dimensional ($K$ is the size of codebook) code $\\mathbf{s}$ is constructed for each single descriptor to represent the votes of the whole codebook. Methods along this line include Vector Quantization(or Hard Voting) \\cite{SivicZ03}, Soft Assignment (or Kernel Codebook Coding) \\cite{GemertVSG10}, Localized Soft Assignment \\cite{LiuWL11}, Salient Coding \\cite{HuangHYT11}, and Group Salient Coding \\cite{WuHWT12}, as shown in Figure \\ref{fig:encVote}.\n\n\\begin{figure*}[htb]\n  \\centering\n  \\subfigure[VQ]{\\includegraphics[width=0.24\\linewidth]{vq}}\n  \\subfigure[SA]{\\includegraphics[width=0.24\\linewidth]{sa}}\n  \\subfigure[SA-$k$]{\\includegraphics[width=0.24\\linewidth]{sa-k}}\n  \\subfigure[SC\/GSC]{\\includegraphics[width=0.24\\linewidth]{sc-gsc}}\n  \\caption{Comparison among all the voting based encoding methods.}\n  \\label{fig:encVote}\n\\end{figure*}\n\nFor each descriptor $\\mathbf{x}$, the voting value for the codeword $\\mathbf{d}_i$ can be viewed as a function of $\\mathbf{x}$, namely $\\mathbf{s}(i)=\\phi(\\mathbf{x})$. Different encoding methods differ in the formulation of $\\phi(\\mathbf{x})$. For encoding of Vector Quantization (VQ):\n\\begin{equation}\n\\textrm{VQ:} \\quad \\phi(\\mathbf{x}) = \\left\\{\n \\begin{array}{l}\n 1, \\ \\textrm{if} \\ \\ i=\\textrm{arg}\\min_{j}||\\mathbf{x} - \\mathbf{d}_j||_{2}, \\\\\n 0,\\ \\ \\textrm{otherwise,}\n \\end{array} \\right.\n  \\label{equ:vq}\n\\end{equation}\nwhere each descriptor $\\mathbf{x}$ only votes for its nearest codeword. The VQ encoding method can be viewed as a hard quantization and may cause much information loss. To encounter this problem, Soft Assignment (SA) encoding method votes for all the codewords:\n\\begin{equation}\n\\textrm{SA:} \\quad \\phi(\\mathbf{x}) = \\omega_i,\n  \\label{equ:sa}\n\\end{equation}\nwhere $\\omega_i$ is the normalized weight of descriptor $\\mathbf{x}$ with respect to codeword $\\mathbf{d}_i$:\n\\begin{equation}\n\\omega_i = \\frac{\\exp(-\\beta\\|\\mathbf{x} - \\mathbf{d}_i\\|_2^2)}{\\sum_{j=1}^K \\exp(-\\beta \\|\\mathbf{x} - \\mathbf{d}_j\\|_2^2)},\n\\label{equ:weight1}\n\\end{equation}\nwhere $\\beta$ is a smoothing factor controlling the softness of the assignment. Considering the manifold structure in the descriptor space, localized Soft Assignment (SA-$k$) votes for its $k$-nearest codewords:\n\\begin{equation}\n\\textrm{SA-}k: \\quad \\phi(\\mathbf{x}) = \\omega'_i = \\frac{I(\\mathbf{x},\\mathbf{d}_i)\\exp(-\\beta\\|\\mathbf{x} - \\mathbf{d}_i\\|_2^2)}{\\sum_{j=1}^K I(\\mathbf{x},\\mathbf{d}_j) \\exp(-\\beta \\|\\mathbf{x} - \\mathbf{d}_j\\|_2^2)},\n\\label{equ:weight2}\n\\end{equation}\nwhere $I(\\mathbf{x},\\mathbf{d}_i)$ is the indicator function to identify whether $\\mathbf{d}_i$ belongs to the $k$ nearest neighbor of $\\mathbf{x}$:\n\\begin{equation}\n    I(\\mathbf{x},\\mathbf{d}_i) = \\left\\{ \\begin{array}{cl}\n                                         1 & \\ \\ \\mathrm{if} \\ \\ \\mathbf{d}_i \\in NN_k(\\mathbf{x}), \\\\\n                                         0 & \\ \\ \\mathrm{otherwise.}\n                                       \\end{array}\n                                       \\right.\n\\end{equation}\nNote that VQ can be viewed as a special case of SA-$k$ when $k$ is set as $1$.\n\nFigure \\ref{fig:encVote} illustrates the difference of these voting based encoding methods. VQ, Salient coding, and Group salient coding are all hard assignment strategies. Unlike VQ, the Salient coding employs the difference between the closest visual word and the other $k-1$ closest ones to obtain the voted weight but not 1. The detailed formulations of Salient coding and Group salient coding can be found in Table \\ref{tab:list}.\n\n\\subsubsection{Reconstruction based encoding methods}\nReconstruction based encoding methods \\cite{YangYGH09,WangYYLHG10,YuZG09,TroppG07} are designed from the perspective of decoding process, where the codes $\\mathbf{s}$ are enforced to reconstruct the input descriptor $\\mathbf{x}$. This kind of algorithm includes Orthogonal Matching Pursuit (OMP) \\cite{TroppG07}, Sparse Coding (SPC) \\cite{YangYGH09}, Local Coordinate Coding(LCC) \\cite{YuZG09}, and Locality-constrained Linear Coding (LLC) \\cite{WangYYLHG10}. Typically, these encoding methods are formulated in a least square framework with a regularization term:\n\\begin{equation}\n\\textrm{arg}\\min_{\\mathbf{s}}||\\mathbf{x}-\\mathbf{Ds}||^2_2 + \\lambda\\psi(\\mathbf{s}),\n\\label{equ:reconEnc}\n\\end{equation}\nwhere the least square term enforce the small reconstruction error, $\\psi(\\mathbf{s})$ encourages some properties of codes $\\mathbf{s}$, $\\lambda$ is a weight factor to balance this two terms.\n\nAmong these methods, OMP and SPC pursue a sparse representation. As for OMP, this constraint is conducted by $\\ell_0$-norm:\n\\begin{equation}\n\\textrm{OMP:} \\quad \\psi(\\mathbf{s})=||\\mathbf{s}||_{0}\n\\end{equation}\nwhere $\\ell_0$-norm means the number of non-zero elements in $\\mathbf{s}$. However, due to the non-convexity of $\\ell_0$-norm, solution to this problem usually needs some heuristic strategy and obtains an approximate optimal solution. SPC relaxes this non-convex $\\ell_0$-norm with $\\ell_1$-norm:\n\\begin{equation}\n\\textrm{SPC:} \\quad \\psi(\\mathbf{s})=||\\mathbf{s}||_{1}\n\\end{equation}\nwhere $\\ell_1$-norm can also encourage the sparsity in code $\\mathbf{s}$, and the solution is equal to the solution of $\\ell_0$-norm under some conditions \\cite{BrucksteinDE09}. The\n$\\ell_1$-norm relaxation allows for more efficient optimization algorithm \\cite{LeeBRN06} and obtaining the global optimal solution.\n\nOMP and SPC is empirically observed to tend to be local, \\emph{i.e.} nonzero coefficients are often assigned to bases nearby to the encoded data \\cite{YuZG09}. But this locality can not be ensured theoretically and they suggested a modification to SPC, called Local Coordinate Coding (LCC). This encoding method explicitly encourages the coding to be local, and they theoretically pointed out that under certain assumptions locality is more essential than sparsity, for successful nonlinear function learning using the obtained codes. Specifically, the LCC is defined as follows:\n\\begin{equation}\n\\textrm{LCC:} \\qquad \\psi(\\mathbf{s}) = \\| \\mathbf{\\hat e} \\odot |\\mathbf{s}| \\|_{1}, \\ \\\n\\mathrm{s. t.} \\ \\ \\mathbf{1}^T \\mathbf{s} =1,\n\\label{equ:lcc}\n\\end{equation}\nwhere $\\odot$ denotes the element-wise multiplication, $\\mathbf{\\hat e}$ is the locality adaptor that give weights for each basis vector proportional to its similarity to the input descriptor $\\mathbf{x}$:\n\\begin{equation}\n\\mathbf{\\hat e} = \\left[\\mathrm{dist}(\\mathbf{x},\\mathbf{d}_1), \\cdots, \\mathrm{dist}(\\mathbf{x},\\mathbf{d}_K) \\right]^\\top,\n\\end{equation}\nwhere $\\mathrm{dist}(\\mathbf{x},\\mathbf{d}_k)$ is the Euclidean distance between $\\mathbf{x}$ and $\\mathbf{d}_k$. Due to the problem of $\\ell_1$-norm optimization in both SPC and LCC, it is computationally expensive and hard to apply to large scale problem. Then, a practical coding scheme called Locality-constrained Linear Coding (LLC) \\cite{WangYYLHG10} is designed, which can be viewed as a fast implementation of LCC that utilizes the locality constraint to project each descriptor into its local-coordinate system:\n\\begin{equation}\n\\textrm{LLC:} \\qquad \\psi(\\mathbf{s}) = \\| \\mathbf{e} \\odot \\mathbf{s} \\|^2_2, \\ \\\n\\mathrm{s. t.} \\ \\ \\mathbf{1}^T \\mathbf{s} =1,\n  \\label{equ:llc}\n\\end{equation}\nwhere $\\mathbf{e}$ is the exponentiation of $\\mathbf{\\hat e}$:\n\\begin{equation}\n  \\mathbf{e} =  \\exp \\left( \\frac{\\mathrm{dist}(\\mathbf{x}, \\mathbf{D})}{\\sigma} \\right),\n\\end{equation}\nwhere $\\sigma$ is used for adjusting the weighted decay speed for the locality adaptor. The constraint $\\mathbf{1}^T \\mathbf{s} =1$ follows the shift-invariant requirements of the final code vector. In practice, an approximate solution can be used to improve the computational efficiency of LLC. It directly selects the $k$ nearest basis vectors of $\\mathbf{x}$ to minimize the first term in Equation (\\ref{equ:reconEnc}) by solving a much smaller linear system. This gives the code coefficients for the selected $k$ basis vectors and other code coefficients are simply set to be zero.\n\n\\subsubsection{Super vector based encoding methods}\nSuper vector based encoding methods yield a very high dimensional representation by aggregating high order statistics. Typical methods include Local Tangent-based Coding (LTC) \\cite{YuZ10}, Super Vector Coding (SVC) \\cite{ZhouYZH10}, Vector of Locally Aggregated Descriptors (VLAD) \\cite{JegouPDSPS12}, and Fisher Vector (FV) \\cite{PerronninSM10} .\n\nLocal Tangent-based Coding \\cite{YuZ10} assumes that codebook and descriptors are embedded in a smooth manifold. The main contents of LTC are manifold approximation and intrinsic dimensionality estimation. Under the Lipschitz smooth condition, the nonlinear function $f(\\mathbf{x})$ can be approximated by a local linear function as:\n\\begin{equation}\n  f(\\mathbf{x}) \\approx \\sum^K_{i=1} \\mathbf{s}(i)\\left[f(\\mathbf{d}_i)+0.5\\nabla f(\\mathbf{d}_i)^T(\\mathbf{x} - \\mathbf{d}_i)\\right],\n\\end{equation}\nwhere $\\mathbf{s}(i)$ is obtained by LCC \\cite{YuZG09}. Then, this approximate function can be viewed as a linear function of a coding vector $[\\mathbf{s}(i),\\mathbf{s}(i)(\\mathbf{x}-\\mathbf{d}_i)]_{i=1}^K \\in \\mathbb{R}^{K \\times (1+D)}$. LTC argues that there is lower intrinsic dimensionality in the feature manifold. To obtain it, Principal Component Analysis (PCA) is applied to the term of $\\mathbf{s}(i)(\\mathbf{x}-\\mathbf{d}_i)$ using a projection matrix $\\mathbf{U}_i = [\\mathbf{u}_1^i,\\cdots, \\mathbf{u}_C^i]\\in \\mathbb{R}^{D \\times C}$ trained from training data, i.e., the local tangent directions of the manifold. Therefore, the final coding vector for LTC is written as follows:\n\\begin{equation}\n\\textrm{LTC:} \\qquad  \\mathcal{S} = \\left[\\alpha \\mathbf{s}(i),\\mathbf{s}(i)(\\mathbf{x}-\\mathbf{d}_i)^T\\mathbf{U}_i \\right]_{i=1}^K,\n\\end{equation}\nwhere $\\alpha$ is a positive scaling factor to balance the two types of codes. Super Vector Coding (SVC) \\cite{ZhouYZH10} is a simple version of LTC. Unlike LTC, SVC yields the $\\mathbf{s}(i)$ via VQ and does not apply PCA to the term of $\\mathbf{s}(i)(\\mathbf{x}-\\mathbf{d}_i)$. Consequently, the coding vector of SVC is defined as follows:\n\\begin{equation}\n  \\textrm{SVC:} \\ \\mathcal{S} = [0,\\mathbf{0},\\cdots,\\frac{\\alpha\\mathbf{s}(i)}{N\\sqrt{p_i}},\\frac{\\mathbf{s}(i)}{N\\sqrt{p_i}}(\\mathbf{x}-\\mathbf{d}_i),\\cdots,0,\\mathbf{0}],\n\\end{equation}\nwhere $\\mathbf{s}(i)=1$, $\\mathbf{d}_i$ is the closest visual word to $\\mathbf{x}$, and $\\alpha$ is a positive constant.\n\nFisher vector is another super vector based encoding method derived from fisher kernel \\cite{JaakkolaH98} and is introduced for large-scale image categorization \\cite{PerronninSM10}. The fisher kernel is a generic framework which combines the benefits of generative and discriminative approaches. As it is known, the gradient of the log-likelihood with respect to a parameter can describe how that parameter contributes to the process of generating a particular example. Then the video can be described by the gradient vector of log likelihood with respect to the model parameters \\cite{JaakkolaH98}:\n\\begin{equation}\n  G_{\\theta}^\\mathbf{x} = \\nabla_{\\theta} \\log p(\\mathbf{x};\\theta).\n\\end{equation}\nNote that the dimensionality of this vector depends on the number of parameters in $\\theta$. Perronnin \\emph{et al}. \\cite{PerronninSM10} developed an improved fisher vector which is as follows,\n\\begin{equation}\n  \\mathcal{G}_{\\mu,k}^\\mathbf{x} = \\frac{1}{\\sqrt{\\pi_k}}  \\gamma_k \\left( \\frac{\\mathbf{x} - \\mu_k}{\\sigma_k}\\right),\n\\end{equation}\n\\begin{equation}\n  \\mathcal{G}_{\\sigma,k}^\\mathbf{x} = \\frac{1}{\\sqrt{2\\pi_k}} \\gamma_k \\left[ \\frac{(\\mathbf{x} - \\mu_k)^2}{\\sigma_k^2} - 1\\right],\n\\end{equation}\nwhere $\\gamma_k$ is the weight of local descriptor $\\mathbf{x}$ to $k^{th}$ Gaussian Mixture:\n\\begin{equation}\n  \\gamma_k = \\frac{\\pi_k \\mathcal{N}(\\mathbf{x}; \\mu_k, \\Sigma_k)}{\\sum_{i=1}^K \\pi_i \\mathcal{N}(\\mathbf{x}; \\mu_i, \\Sigma_i)}.\n\\end{equation}\nThe final fisher vector is the concatenation this two gradients:\n\\begin{equation}\n  \\mathrm{FV:} \\qquad \\mathcal{S} = [\\mathcal{G}_{\\mu,1}^{\\mathbf{x}},\\mathcal{G}_{\\sigma,1}^\\mathbf{x},\\cdots,\\mathcal{G}_{\\mu,K}^{\\mathbf{x}},\\mathcal{G}_{\\sigma,K}^\\mathbf{x}].\n\\end{equation}\nVector of Locally Aggregated Descriptors (VLAD) \\cite{JegouPDSPS12} can be viewed as a hard version of FV and only keeps the $1^{st}$ order statistics:\n\\begin{equation}\n   \\textrm{VLAD:} \\qquad  \\mathcal{S} = [\\mathbf{0},\\cdots,\\mathbf{s}(i)(\\mathbf{x}-\\mathbf{d}_i),\\cdots,\\mathbf{0}],\n\\end{equation}\nwhere $\\mathbf{s}(i)=1$, $\\mathbf{d}_i$ is the closest visual word to $\\mathbf{x}$.\n\n\\subsubsection{Relations of Encoding Methods}\n\\label{sec:relation}\nIn this section, we summarize several practical techniques widely used in these encoding methods, and give a unified generative perspective of these encoding methods. This analysis will uncover the underline relations between these methods and provide insights for developing new encoding methods.\n\n\\textbf{From ``hard'' to ``soft''.} These encoding methods transform local features from descriptor space to codeword space. There are two typical transformation rules in these methods, namely \\emph{hard assignment} and \\emph{soft assignment}. Hard assignment quantizes the feature descriptor into a single codeword, while soft assignment enables the feature descriptor to vote for multiple codewords. In general, soft assignment accounts for the codeword uncertainty and plausibility \\cite{GemertVSG10}, and reduces the information loss during encoding. This technical skill of soft assignment can be found in several encoding algorithms, such as SA-$all$ vs. VQ, and VLAD vs. Fisher Vector. By the same techniques, we can extend the VLAD to VLAD-$all$, SVC to SVC-$all$:\n\\begin{equation}\n\\mathrm{VLAD-}all: \\ \\mathcal{S} = [\\omega_1(\\mathbf{x}-\\mathbf{d}_1),\\cdots,\\omega_K(\\mathbf{x}-\\mathbf{d}_K)],\n\\label{equ:vladall}\n\\end{equation}\n\\begin{equation}\n\\begin{split}\n\\mathrm{SVC-}all: \\  \\mathcal{S} & = \\left[\\frac{\\alpha\\omega_1}{N\\sqrt{p_1}},\\frac{\\alpha\\omega_1}{N\\sqrt{p_1}}(\\mathbf{x}-\\mathbf{d}_1),\\cdots, \\right.  \\\\\n& \\left. \\frac{\\alpha\\omega_K}{N\\sqrt{p_K}},\\frac{\\alpha\\omega_K}{N\\sqrt{p_K}}(\\mathbf{x}-\\mathbf{d}_K) \\right],\n\\end{split}\n\\label{equ:svcall}\n\\end{equation}\nwhere $\\omega_i$ is the normalized weight of feature descriptor $\\mathbf{x}$ with respect to codeword $\\mathbf{d}_i$ defined in Equation (\\ref{equ:weight1}).\n\n\\textbf{From  ``global'' to ``local''.} In several encoding methods, the manifold structure in descriptor space is captured to improve the stability of encoding algorithms. In the traditional soft assignment, each descriptor is assigned with all the codewords, which is called \\emph{global assignment}. However, in the high dimensional space of feature descriptor, Euclidian distance may be not reliable especially when the codeword is outside the neighborhood of feature descriptor. Therefore, in the encoding methods such as SA-$k$ and LLC, each descriptor is enforced to only vote for these codewords belonging to its $k$-nearest neighbors, called \\emph{local assignment}. In general, the incorporation of local structure in encoding methods is able to improve the stability and reduce the sensitivity to noise in descriptor. Using the same techniques, we can also extend the VLAD-$all$ to VLAD-$k$, SVC-$all$ to SVC-$k$ by replacing the $\\omega_i$ in Equation (\\ref{equ:vladall}), (\\ref{equ:svcall}) with localized $\\omega_i'$ defined in Equation (\\ref{equ:weight2}):\n\\begin{equation}\n\\mathrm{VLAD-}k: \\qquad \\mathcal{S} = [\\omega'_1(\\mathbf{x}-\\mathbf{d}_1),\\cdots,\\omega'_K(\\mathbf{x}-\\mathbf{d}_K)],\n\\end{equation}\n\\begin{equation}\n\\begin{split}\n\\mathrm{SVC-}k: \\qquad  \\mathcal{S} & = \\left[\\frac{\\alpha\\omega'_1}{N\\sqrt{p_1}},\\frac{\\alpha\\omega'_1}{N\\sqrt{p_1}}(\\mathbf{x}-\\mathbf{d}_1),\\cdots, \\right.  \\\\\n& \\left. \\frac{\\alpha\\omega'_K}{N\\sqrt{p_K}},\\frac{\\alpha\\omega'_K}{N\\sqrt{p_K}}(\\mathbf{x}-\\mathbf{d}_K) \\right],\n\\end{split}\n\\end{equation}\n\n\\textbf{From ``zero order statistics'' to ``high order statistics''.}  In these super vector based encoding methods, they preserve not only the affiliations of descriptors to codewords (zero order statistics), but also the high order information such as the difference between descriptors mean and codeword, thus resulting a high-dimensional super vector representation. As these super vectors keep much richer information for each codeword, the codebook size is usually much smaller than that of voting and reconstruction based encoding methods. Above all, these super vector is with high dimension, storing more information, and is proved to outperform the other two kinds of encoding methods in Section \\ref{sec:experiment}. The high dimensional super vector will be a promising representation and designing effective dimension reduction algorithms for super vector will be an interesting problem.\n\n\\textbf{Generative perspective of encoding methods.} Although these encoding methods are developed in different scenarios, a unified generative probabilistic model can be used to uncover the underline relations among them. These encoding methods can be interpreted in a latent generative model:\n\\begin{equation}\n  \\begin{split}\n    p(\\mathbf{h}) & \\in \\mathbb{P}, \\\\\n    p(\\mathbf{x}|\\mathbf{h})&  = \\mathcal{N}(\\mathbf{x};W\\mathbf{h} + \\mu_\\mathbf{x},\\Sigma),\n  \\end{split}\n\\end{equation}\nwhere $\\mathbf{x} \\in R^{D}$ represents the descriptor, $\\mathbf{h} \\in R^{K}$ denotes the latent factor, $\\mathcal{N}(\\mathbf{x};W\\mathbf{h} + \\mu_\\mathbf{x},\\Sigma)$ is multivariate Gaussian distribution. Different encoding methods mainly different in two aspects: \\emph{How to model the prior distribution $\\mathbb{P}$ of latent factor $\\mathbf{h}$} and \\emph{How to use the probabilistic model to transform the descriptor into codeword space.}\n\nFor encoding methods such as VQ, SA-$all$, VLAD-$all$, and Fisher vector, they choose the prior distribution $p(\\mathbf{h})$ as follows:\n\\begin{equation}\n  p(\\mathbf{h}) = \\prod_{i=1}^K \\pi_i^{h_i},\n\\end{equation}\nwhere $\\mathbf{h}\\in\\{0,1\\}^K$ is discrete random variable, and the prior distribution is a Multinomial distribution. For SA-$all$, this Mutinomial distribution is specified by uniform distribution, i.e. $\\pi_1 = \\cdots = \\pi_K = \\frac{1}{K}$, where for Fisher vector, this Multinomial distribution is learned during GMM training. Meanwhile the SA-$all$ choose the latent variable embedding to encodes the descriptor by computing conditional expectation, i.e. $\\mathbf{s(x)} = \\mathbb{E}(\\mathbf{h}|\\mathbf{x})$, while the Fisher vector choose the gradient embedding \\cite{JaakkolaH98}, i.e.  $\\mathcal{S}(\\mathbf{x}) = \\nabla_{\\theta} \\log p(\\mathbf{x};\\theta)$. The VQ encoding can be viewed an extreme case of Soft-$all$, when:\n\\begin{equation}\n   p(\\mathbf{x}|\\mathbf{s})  = \\mathcal{N}(\\mathbf{x};W\\mathbf{s} + \\mu_\\mathbf{x},\\epsilon I), \\ \\ \\epsilon \\rightarrow 0.\n\\end{equation}\nVLAD-$all$ and SVC-$all$ can be viewed as the gradient embedding in this extreme case.\n\nFor encoding methods such as sparse coding, the latent variable $\\mathbf{h}$ is continuous and its corresponding prior distribution is specified as:\n\\begin{equation}\n  p(\\mathbf{h}) = \\prod_{i=1}^K \\frac{\\lambda}{2} \\exp(-\\lambda|h_i|).\n\\end{equation}\nThis prior distribution is called Laplace prior and sparse coding can be viewed as the latent variable embedding of this generative model using the maximum a posteriori value (MAP), i.e. $\\mathbf{s(x)} = \\arg\\max_{\\mathbf{h}} p(\\mathbf{h} | \\mathbf{x})$.\n\n\\subsection{Pooling and Normalization Methods}\n\\begin{figure*}[!htb]\n  \\centering\n  \\includegraphics[width = \\linewidth]{fusion.eps}\n  \\caption{Feature fusion is performed in different levels: descriptor level, representation level, and score level. The complementary effect of varied BoVW models can also be taken into account and a hybrid representation is obtained by fusing outputs from different BoVW models.}\n  \\label{fig:fusion}\n\\end{figure*}\n\nGiven the code coefficients of all local descriptors in a video, a pooling operation is often used to obtain a global representation $\\mathbf{p}$ for the video. Specifically, there are two common pooling strategies:\n\\begin{itemize}\n\\item \\textbf{Sum Pooling.} With sum pooling scheme \\cite{LazebnikSP06}, the $k^{th}$ component of $\\mathbf{p}$ is $p_k = \\sum_{n=1}^N \\mathbf{s}_n(k)$.\n\\item \\textbf{Max Pooling.} With max pooling scheme \\cite{YangYGH09}, the $k^{th}$ component of $\\mathbf{p}$ is $p_k = \\max (\\mathbf{s}_1(k),  \\cdots, \\mathbf{s}_N(k))$, where $N$ is the number of extracted local descriptors, $\\mathbf{s}_n$ denotes the code of descriptor $\\mathbf{x}_n$.\n\\end{itemize}\nIn \\cite{BoureauPL10}, the authors presented a theoretical analysis of average pooling and max pooling. Their results indicate sparse features may prefer max pooling.\\\\\n\nTo make this representation invariant to the number of extracted local descriptors, the pooling result $\\mathbf{p}$  is further normalized by some methods. Generally, there are three common normalization techniques:\n\\begin{itemize}\n\\item \\textbf{$\\ell_1$-Normalization.} In $\\ell_1$ normalization \\cite{YangYGH09}, the feature $\\mathbf{p}$ is divided by its $\\ell_1$-norm: $\\mathbf{p} = \\mathbf{p} \/ \\| \\mathbf{p}\\|_{1}$.\n\\item \\textbf{$\\ell_2$-Normalization.} In $\\ell_2$ normalization \\cite{PerronninSM10}, the feature $\\mathbf{p}$ is divided by its $\\ell_2$-norm: $\\mathbf{p} = \\mathbf{p} \/ \\| \\mathbf{p}\\|_{2}$.\n\\item \\textbf{Power Normalization.} In power normalization \\cite{PerronninSM10}, we apply in each dimension the following function:\n\\begin{displaymath}\n  f (p_k) = \\mathrm{sign}(p_k) | p_k |^\\alpha.\n\\end{displaymath}\nwhere $0 \\leq \\alpha \\leq 1$ is a parameter for normalization. We can combine power normalization with $\\ell_1$-normalization or  $\\ell_2$-normalization.\n\\end{itemize}\n\nRecently, a special normalization strategy is proposed for the VLAD, called \\textbf{intra-normalization} \\cite{ArandjelovicZ13}. In this paper, we extend it to all the super vector based encoding algorithms. This method carries out normalization operation in a block by block manner, where each block denotes the vector related to one codeword. Generally, the intra-normalization can be formulated as follows:\n\\begin{equation}\n\\mathbf{p} = \\left[\\frac{\\mathbf{p}^1}{\\| \\mathbf{p}^1 \\|},\\cdots,\\frac{\\mathbf{p}^k}{\\| \\mathbf{p}^k \\|},\\cdots,\\frac{\\mathbf{p}^K}{\\| \\mathbf{p}^K \\|}\\right],\n\\end{equation}\nwhere $\\mathbf{p}^k$ denotes a vector related to codeword $\\mathbf{d}_k$ (or the $k^{th}$ Gaussian), $\\|\\cdot\\|$ may be $\\ell_1$-norm or $\\ell_2$-norm.\n\n\n\\section{Feature Fusion}\n\\label{sec:fusion}\nFusing multiple local features has turned out to be an effective method to boost the performance of recognition system in computer vision community \\cite{GehlerN09,VedaldiGVZ09,TangYLK13,WangS13a,CaiWPQ14}. The video data is usually characterized in multiple views, such as static appearance, motion pattern, and motion boundary. The essence of multi-view data requires fusing different features for action recognition. In this section, we present several feature fusion methods for action recognition, and analyze its corresponding properties. Meanwhile, based on the analysis of fusion methods, we propose a simple yet effective representation, called \\emph{hybrid representation}.\n\nAs shown in Figure \\ref{fig:fusion}, the fusion methods are usually conducted in different levels, typically including: descriptor level, representation level, and score level. For descriptor level fusion, it is performed in the cuboid level, where multiple descriptors from the same cuboid are concatenated into a single one, and then it is fed into the BoVW to obtain the global representation. For representation-level fusion, it is performed in the video level, where different descriptors are input into BoVW separately and the resulting global representations are fused as a single one, which is further fed into classifier for recognition. For score-level fusion, it is also performed in the video level, but the representations of different descriptors are used independently for classifier training. The final recognition score is obtained by fusing the scores from multiple classifiers. For fusing the scores, arithmetical mean or geometrical mean is often used.\n\nIn general, these fusion methods at different levels owns their pros and cons, and the choice of fusion method should be guided by the dependence of descriptors. If these multiple descriptors from the same cuboid are highly correlated, it will be better to resort to descriptor level feature fusion. Otherwise, the choice of descriptor level fusion is not a good one, as descriptor level fusion usually results in a higher dimension and adds the difficulty for unsupervised feature learning such as $k$-means and sparse coding. For the case where different views of features are less correlated in cuboid level but highly correlated in video level, representation level fusion is usually a good choice. When these different features are independently with each other, it will be appropriate to choose score level fusion, as this fusion reduce the dimension for classifier training and make the learning faster and more stable.\n\nThe performance boosting of fusing multiple features mainly owns the complementarity of these features. However, the complementarity can be explored not only for different features, but also for different types of BoVW methods. As shown in Figure \\ref{fig:fusion}, we propose a simple yet effective representation, called hybrid representation, which combines the outputs from multiple variants of BoVW and multiple descriptors. The resulting hybrid representation effectively explores the complementarity of different encoding methods and greatly enhances the descriptive power for action recognition. As we shall see in Section \\ref{sec:stoa}, this representation will improve the recognition rate of a single BoVW model and obtain the state-of-the-art results on the three challenging datasets.\n\n\\section{Empirical Study}\n\\begin{figure*}[!htb]\n  \\centering\n   \\subfigure[HMDB51]{\\includegraphics[width=0.48\\linewidth]{hmdb}}\n  \\subfigure[UCF 50 and UCF101]{\\includegraphics[width=0.48\\linewidth]{ucf}}\n    \\caption{Sample frames from the HMDB51, UCF50 and UCF101 datasets. Note that UCF50 is a subset of UCF101.}\n  \\label{fig:dataset}\n\\end{figure*}\n\n\\label{sec:experiment}\nIn this section, we describe the detailed experimental settings and the empirical study of variants of BoVW and different fusion methods. We first introduce the datasets used for evaluation and their corresponding experimental setup. We then extensively study different aspects of BoVW, including pre-processing techniques, encoding methods, pooling strategies, and normalization approaches. After that, we explore the different choices of fusion methods for multiple features. Finally, we compare the performance of our hybrid representation with that of the state-of-the-art methods on three challenging datasets.\n\n\\subsection{Datasets and Evaluation Protocols}\nWe conduct experiments on three public datasets: HMDB51 \\cite{KuehneJGPS11}, UCF50 \\cite{ReddyS13}, and UCF101 \\cite{SOOMRO12}. Some examples of video frames are illustrated in Figure \\ref{fig:dataset}. Totally, we work with 26,704 videos in this paper.\n\nThe \\textbf{HMDB51 dataset} has 51 action classes with total 6,766 videos and each class has more than 100 videos \\footnote{http:\/\/serre-lab.clps.brown.edu\/resources\/HMDB\/index.htm}. All the videos are obtained from real world scenarios such as: movies, youtube. The intra-class variation is very high due to many factors, such as viewpoint, scale, background, illumination etc. Thus, HMDB51 is a very difficult benchmark for action recognition. There are three training and testing splits released on the website of this dataset. We conduct experiments based on these splits and report average accuracy for evaluation.\n\nThe \\textbf{UCF50 dataset} has 50 action classes with total 6,618 videos, and each action class is divided into 25 groups with at least 100 videos for each class. The video clips in the same group are usually with similar background. We choose the suggested evaluation protocols of Leave One Group Out cross validation (LOGO) and report the average accuracy \\cite{ReddyS13}.\n\nThe \\textbf{UCF101 dataset} is an extension of the UCF50 dataset and has 101 action classes. The action classes can be divided into five types: human-object interaction, body-motion only, human-human interaction, playing musical instruments, and sports. Totally, it has 13,320 video clips, with fixed frame rate and resolution 25 FPS and 320 $\\times$ 240 respectively. To our best knowledge, this dataset has been the largest dataset so far. We perform evaluation according to the three train\/test splits released in Thumos'13 challenge \\footnote{http:\/\/crcv.ucf.edu\/ICCV13-Action-Workshop\/} and report the mean average accuracy of these splits.\n\nIn our evaluation experiment, we choose linear Support Vector Machine (SVM) as our recognition classifier. Specifically, we use the implementation of LIBSVM \\cite{ChangL11}. For multiclass classification, we adopt one-vs-all training scheme and choose the prediction with highest score as our predicted label.\n\n\\subsection{Local Features and Codebook Generation}\nIn our evaluation, we choose two widely-used local features, namely Space Time Interest Points (STIPs) \\cite{Laptev05} with HOG, HOF descriptors \\cite{LaptevMSR08}, and improved Dense Trajectories (iDTs) with HOG, HOF, MBHx, MBHy descriptors \\cite{WangKSL13}. Specifically, we use the implementation released on the website of Laptev \\footnote{http:\/\/www.di.ens.fr\/~laptev\/download.html} for STIPs and Wang \\footnote{https:\/\/lear.inrialpes.fr\/people\/wang\/improved\\_trajectories} for iDTs. We choose the default parameter settings for both local features. STIPs and iDTs represent two types of local features: sparse interest points and densely-sampled trajectories. They may exhibit different properties with varying BoVW settings, and thus it is well worth exploring both STIPs and iDTs.\n\nRegarding codebook generation, we randomly sample $100,000$ features to conduct $k$-means, where codebook size range from 1,000 to 10,000 for STIPs, and from 1,000 to 20,000 for iDTs. For GMM training, we randomly sample 256,000 features to learn GMMs with mixture number ranging from 16 to 512 for both STIPs and iDTs.\n\n\\subsection{Importance of Pre-processing}\n\\begin{figure}\n  \\centering\n  \\includegraphics[width=\\linewidth,height=0.6\\linewidth]{pca.eps}\n  \\caption{Comparison the results with PCA+Whiten and without PCA-Whiten of different encoding methods on the UCF101 dataset, where STIPs are chosen as the local features.}\n  \\label{fig:pca}\n\\end{figure}\nIn this section, we explore the importance of pre-processing in BoVW framework. Specifically, we use STIPs as local features and choose a representative method for each type of encoding, namely FV, LLC, and VQ . For pooling and normalization strategy, we use sum pooling and power $\\ell_2$-normalization. We use the descriptor-level fusion method to combine HOG and HOF descriptors.\n\nWe conduct experiments on the UCF101 dataset and investigate the importance of pre-processing for these encoding methods. With pre-processing step, the descriptors of STIPs are firstly reduced to $100$-dimension and then whitened to have unit variance. The results are shown in Figure \\ref{fig:pca}. We observe that the pre-processing technique of PCA-Whiten is very important to boost the performance of encoding methods. Surprisingly, the performance of FV (state-of-the-art) without PCA-Whiten is lower than or comparable to VQ and LLC with PCA-Whiten. In previous research work, PCA-Whiten is often done for FV encoding methods but seldom used for other encoding methods. Our study suggests that using PCA-Whiten techniques enable us to greatly improve final recognition rate for all encoding methods. We obtain the recognition rate $56.1\\%$ for VQ, which significantly outperform over the result $43.9\\%$ reported in \\cite{SOOMRO12}, where the same local feature and encoding method is used.\n\nIn the remaining part of evaluation, we will use PCA-Whiten to de-correlate the descriptor, reduce the dimension, and normalize the variance. For descriptor level fusion of STIP, the dimension of concatenated descriptor is reduced from $162$ to $100$. For HOG and HOF, the dimension is reduced from $72$ to $40$, and from $90$ to $60$, respectively. For descriptor level fusion of iDT, the dimension of concatenated descriptor is reduced from $396$ to $200$. For separate descriptor, the dimensions of HOG, MBHx, and MBHy are all reduced from $96$ to $48$. HOF descriptor is reduced from $108$ to $54$.\n\n\\subsection{Exploration of Encoding Methods}\n\\label{sec:ex_encoding}\n\\begin{figure*}\n  \\centering\n  \\subfigure[HMDB51 with STIPs]{\\includegraphics[width=0.49\\linewidth,height=0.3\\linewidth]{EncSTIPonHMDB51}}\n  \\subfigure[HMDB51 with iDTs]{\\includegraphics[width=0.49\\linewidth,height=0.3\\linewidth]{EncIDTonHMDB51}}\\\\\n  \\subfigure[UCF50 with STIPs]{\\includegraphics[width=0.49\\linewidth,height=0.3\\linewidth]{EncSTIPonUCF50}}\n  \\subfigure[UCF50 with iDTs]{\\includegraphics[width=0.49\\linewidth,height=0.3\\linewidth]{EncIDTonUCF50}}\\\\\n  \\subfigure[UCF101 with STIPs]{\\includegraphics[width=0.49\\linewidth,height=0.3\\linewidth]{EncSTIPonUCF101}}\n  \\subfigure[UCF101 with iDTs]{\\includegraphics[width=0.49\\linewidth,height=0.3\\linewidth]{EncIDTonUCF101}}\n  \\caption{Performance of different encoding methods with varying codebook (GMM) sizes on the HMDB51, UCF50, and UCF101 datasets for STIPs and iDTs features using descriptor-level fusion.}\n  \\label{fig:encIDT}\n\\end{figure*}\n\\begin{figure*}\n  \\centering\n  \\subfigure[Time of STIPs]{\\includegraphics[width=0.49\\linewidth,height=0.3\\linewidth]{CostSTIP}}\n  \\subfigure[Time of iDTs]{\\includegraphics[width=0.49\\linewidth,height=0.3\\linewidth]{CostIDT}}\\\\\n  \\caption{Average time of different encoding methods with varying codebook (GMM) sizes on the UCF101 datasets for STIPs and iDTs features using descriptor-level fusion.}\n  \\label{fig:time}\n\\end{figure*}\nIn this section, we compare and analyze the performance of different encoding methods. For each encoding method, we fix other settings, such as parameter setting, pooling and normalization strategy, the same with previous papers. We explore these encoding methods with descriptor level fusion, for both STIPs and iDTs. The influence of different pooling and normalization strategy, and fusion methods will be investigated in the following sections.\n\n\\textbf{Encoding methods selection and setting}. We select six popular encoding methods according to categorization in Table \\ref{tab:list}. For voting based encoding methods, we choose VQ as a baseline and SA-$k$ as a representative method. LLC is selected as the representative of reconstruction-based encoding methods due to its computational efficiency and performance \\cite{WangWQ12}. Super vector based encoding methods have shown the state-of-the-art performance on several datasets \\cite{WangS13a} . We choose three super vector based encoding methods for evaluation, namely FV, VLAD, and SVC.\n\n\\emph{Baseline: Vector Quantization Encoding (VQ).} In the baseline method, each descriptor is quantized into a single codeword. Following the suggested settings in object recognition \\cite{ZhangMLS07}, the final histogram is obtained by sum pooling and normalized with $\\ell_1$ norm.\n\n\\emph{Localized Soft Assignment Encoding (SA-$k$).} In the localized soft assignment, each descriptor is assigned to its corresponding $k$ nearest neighborhood. It requires a single parameter $\\beta$, which is the smoothing factor controlling the softness. According to \\cite{LiuWL11}, we set $\\beta$ as $1$ and $k$ as 5 in our evaluation. We use max pooling and $\\ell_2$-normalization.\n\n\\emph{Locality-constrained Linear Encoding (LLC).} Following \\cite{WangYYLHG10}, we use approximated LLC for fast encoding, where we simply use $k$ nearest neighborhood of descriptor as the local bases. The parameter of $k$ is set as $5$, and we choose max pooling and $\\ell_2$-normalization strategy.\n\n\\emph{Fisher Vector (FV).} For GMM training, we use the $k$-means result to initialize iteration and the covariance matrix of each mixture is set as a diagonal one. Following \\cite{PerronninSM10}, we use sum pooling and power $\\ell_2$-normalization.\n\n\\emph{Vector of Locally Aggregated Vector (VLAD).} VLAD was originally designed for image retrieval in \\cite{JegouPDSPS12} and can be viewed as a simplified version FV for fast implementation. Just like FV, we choose sum pooling and power $\\ell_2$-normalization.\n\n\\emph{Super Vector Coding (SVC).} From the view of statistics, SVC can be viewed as a combination of VQ and VLAD. It contains the zeros and first-order statistics, and the parameter $\\alpha$ keep balance between these two components. Following \\cite{ZhouYZH10}, we set $\\alpha$ as $0.1$. Like other super vector based encoding methods, we choose sum pooling and power $\\ell_2$-normalization.\n\n\\textbf{Results and analysis.} The experimental results of STIPs and iDTs on the three datasets are shown in Figure \\ref{fig:encIDT}. Several rules can be found from these experimental results:\n\\begin{itemize}\n  \\item Basically, the recognition performance of all selected encoding methods increases as the size of codebook (GMM) becomes larger and will reach a plateau when the size exceeds a threshold. For super vector based encoding methods, the performances reach a saturation when size of codebook (GMM) becomes $256$ for both STIPs and iDTs. There is a slight change of the recognition rate when GMM size grows from $256$ to $512$. For the other two types of encoding methods, the performances are saturated as the size of codebook reaches $8,000$. We also notice that these encoding methods using iDTs have slight improvements when the codebook size varies from 8,000 to 20,000 , while the performances using STIPs start shaking when the codebook size becomes larger than 8,000 due to the over-fitting effect. This difference may be ascribed to the dimension of local descriptors and sampling strategy. The descriptors dimension of iDTs is twice of STIPs and requires more codewords to divide the feature space. Meanwhile, STIPs is a set of interest points and the extracted descriptors distribute sparsely in the feature space. The codebook with large size will result in an over-partition of feature space, which means for a specific video, there may be no descriptors falling into the corresponding regions for some codewords. iDTs are more densely sampled features and codebook with large size is more suitable to divide the space of dense features. \\textbf{Above all, for a good balance between performance and efficiency, sizes of $256$ and $8,000$ are good choices for super vector based encoding and other encoding respectively}.\n  \\item For local features of both SITPs and iDTs, super vector based encoding methods outperform the other types of encoding methods on the three datasets. According to previous introduction, these super vector encoding methods not only preserve the affiliations of descriptors to codewords, but also keep high order information such as the difference of means and variances. These high order information enables the encoding methods to better capture the distribution shape of descriptor in feature space. In these super vector based methods, FV is typically better than VLAD and SVC, whose performance is quite similar. This can be own to two facts: (i) FV keeps both $1^{st}$ and $2^{nd}$ statistics, which is more informative than VLAD (only $1^{st}$ statistics) and SVC ($0^{th}$ statistics and $1^{st}$ statistics). (ii) FV is based on GMM and each descriptor is softly assigned to codewords using posterior probability, while VLAD and SVC are based on $k$-means results and use hard assignment. We also notice that the difference between FV and the other two methods (VLAD, SVC) for iDTs seems smaller than STIPs. The more dense descriptors may make the learned codebook more stable for SVC and VLAD, and reduce the influence of soft assignment in FV. Meanwhile, the information contained in $2^{nd}$ statistics may be less complementary to $1^{st}$ statistics for iDTs. \\textbf{In conclusion, super vector based representation, aggregating high order information, is a more suitable choice for good performance, when the high dimension of representation is acceptable}.\n  \\item For reconstruction based and voting based encoding methods, VQ reaches the lowest recognition rate for STIPs and iDTs on the three datasets. This can be ascribed to the hard assignment and descriptor ambiguity in the VQ method. In essence, the LLC and SA-$k$ are quite similar in spirt, for that they both consider locality when mapping descriptor into codeword. The performance of LLC is better than SA-$k$ for STIPs, while the performances of them are almost the same for iDTs. This can be explained by the mapping strategy in LLC and SA-$k$. The mappings of descriptor to the nearest codewords in LLC are determined jointly according to their effect in minimizing the reconstruction error, while the mappings in SA-$k$ are calculated independently for each individual codeword according to the Euclidean distance. The mapping method in LLC may be more effective to deal with manifold structure than just considering Euclidean distance in SA-$k$. For sparse features such as STIPs, the descriptors distribute sparsely around each codeword, and using Euclidean distance may introduce noise and instability for SA-$k$. For dense features such as iDTs, the descriptors are usually sampled densely and more compact around codewords, reducing the influence caused by the usage of Euclidean distance. \\textbf{In a word, compared with hard assignment, locality and soft assignment is an effective strategy to improve the performance of encoding methods}.\n  \\item STIPs and iDTs represents two types of local features, namely sparsely-sampled and densely-sampled features. In general, they exhibit consistent performance trends for different encoding methods, for example, super vector encoding methods outperforms others, soft-assignment is better than hard-assignment. However, there is a slight difference between them in some aspects, such as sensitivity to codebook size and encoding methods, performance gaps among super vector based methods, difference between LLC and SA-$k$, as previously observed. From the perspective of data manifold, the more densely-sampled features can help us more accurately describe the data structure in the feature space. We can obtain a more compact clustering result using $k$-means, and the local Euclidean distance is more stable. \\textbf{Thus, when choosing codebook size and encoding method, the type of local feature can be a factor needed to be considered}.\n\\end{itemize}\n\n\\textbf{Computational costs.} We also compare the efficiency of different encoding methods and the running time is shown in Figure \\ref{fig:time}. Our codes are all implemented in Matlab, and running on a workstation with 2x Intel Xeon 5560 2.8GHz CPU and 32G RAM. We randomly sample 50 videos from the UCF101 dataset and report the total time for these videos. For super vector based methods, FV is much slower due to the calculation of posterior probability during encoding, and the time of VLAD and SVC is almost the same. For the other types of encoding methods, LLC is less efficient as it solves a least square problem. The computational cost of super vector encoding methods are usually lower than that of the other types of encoding methods, due to their smaller codebook sizes.\n\nBased on the above analysis, super vector based encoding methods are more promising for high performance and fast implementation, especially for SVC, VLAD. However, the feature dimension of super vector methods is much higher than the other two kinds of encoding methods, for example, when the codebook size is 256, the dimension of FV and VLAD is 102,400 and 51,200 respectively for iDT features. The effective dimension reduction may be a future research direction for super vector encoding methods.\n\n\\subsection{Exploration of Pooling and Normalization}\n\\label{sec:poolingnorm}\n\\begin{figure*}\n  \\center\n\\includegraphics[width=0.3\\linewidth,height=0.3\\linewidth]{PNorm2STIPonUCF101}\n\\includegraphics[width=0.68\\linewidth,height=0.3\\linewidth]{PNorm1STIPonUCF101}\n  \\caption{Comparison of different pooling-normalization strategies with \\textbf{STIPs} features using descriptor level fusion on the UCF101 dataset. Note that there is only max pooling for voting and reconstruction based encoding methods, and there is only intra normalization for super vector based encoding methods.}\n  \\label{fig:PoolNorm1}\n\\end{figure*}\n\\begin{figure*}\n  \\center\n\\includegraphics[width=0.3\\linewidth,height=0.3\\linewidth]{PNorm2IDTonUCF101}\n\\includegraphics[width=0.68\\linewidth,height=0.3\\linewidth]{PNorm1IDTonUCF101}\n  \\caption{Comparison of different pooling-normalization strategies with \\textbf{iDTs} features using descriptor level fusion on the UCF101 dataset. Note that there is only max pooling for voting and reconstruction based encoding methods, and there is only intra normalization for super vector based encoding methods.}\n  \\label{fig:PoolNorm2}\n\\end{figure*}\n\nIn this section, we mainly investigate the influence on recognition rate for different pooling and normalization strategies on the UCF101 dataset. Based on the performances of different encoding methods on the UCF101 dataset in previous section, we choose the codebook (GMM) size as $512$ for super vector based methods and codebook size as $8,000$ for the other two types of encoding approaches. Meanwhile, according to our conclusion that super vector based encoding is a promising method and soft assignment is an effective way to improve the encoding methods, we extend VLAD to VLAD-$k$ and VLAD-$all$, SVC to SVC-$k$ and SVC-$all$ as described in Section \\ref{sec:relation}. Thus, there are totally $10$ kinds of encoding methods.\n\nFor super vector based encoding methods, we evaluate eight normalization methods, specified by with or without intra-normalization, with or without power operation, final $\\ell_1$ or $\\ell_2$ normalization. For the other two types of encoding methods, we choose two pooling methods, namely max pooling and sum pooling, and four normalization methods, namely $\\ell_1$-normalization, $\\ell_2$-normalization, power $\\ell_1$-normalization, and power $\\ell_2$-normalization. In our evaluation, the parameter $\\alpha$ in power normalization is set as $0.5$.\n\nThe experimental results are shown in Figure \\ref{fig:PoolNorm1} and Figure \\ref{fig:PoolNorm2}. Several observation can be concluded from these results:\n\\begin{itemize}\n  \\item For super vector based encoding methods, intra-normalization is an effective way to balance the weight of different codewords and suppress the burst of features corresponding to background. We found this technique works very well when dense features are chosen. A large number of features in iDTs are irrelevant with the action class and intra-normalization can suppress this influence. However, for sparse features, the effect of intra normalization is not so evident, and even cause performance degradation in the case of hard assignment such as VLAD, SVC. We ascribe  this phenomenon to the fact that the STIPs features are usually located in the moving foreground and related with action class. Thus, these descriptors only vote for a subset of codewords, that are highly related with action class. In this case, intra-normalization can decrease the discriminative power of action-related codewords and increase the influence of irrelevant codewords. \\textbf{In conclusion, intra-normalization is effective in handling burst of irrelevant features in the case of dense-sampling strategy}.\n  \\item For different encoding methods and local features, we observe that the final $\\ell_2$-normalization outperforms $\\ell_1$-normalization. In fact, the normalization method is related to kernel used in final classifier. In our case of linear SVM, the kernel is $k(\\mathbf{x},\\mathbf{y}) = \\mathbf{x}^\\top\\mathbf{y}$. The choice of $\\ell_2$-normalization can ensure two things: (i) $k(\\mathbf{x},\\mathbf{x}) = \\mathrm{const.}$; (ii) $k(\\mathbf{x},\\mathbf{x}) \\geq k(\\mathbf{x},\\mathbf{y})$. This can guarantee a simple consistency criterion: by interpreting $k(\\mathbf{x},\\mathbf{y})$ as a similarity score, $\\mathbf{x}$ should be the most similar point to itself \\cite{VedaldiZ12}. However, the choice of $\\ell_1$-normalization can not make sure that the point is most similar to self and may cause the instability during SVM training. \\textbf{Above all, $\\ell_2$-normalization generally outperforms $\\ell_1$-normalization when using linear SVM}.\n  \\item The influence of power operation in normalization is highly related with pooling method. We observe that power normalization is an effective approach to boost the performance of representation obtained from sum pooling, such as super vector based representation, LLC, SA-$k$ with sum pooling. However, power normalization have little effect for max pooling and sometimes even cause the performance degradation for LLC, SA-$k$. The operation of power usually reduces the difference between different codewords, which means smoothing the histogram. This smooth effect can reduce the influence of high frequent codeword on the kernel calculation and improve the influence of less frequent codeword. For sum pooling, the resulting histogram is usually very sharp and unbalanced due to feature burst, and the smooth operation has a positive effect for suppress the high frequent codeword. However, for max pooling, the histogram is itself not so sharp as sum pooling, and thus the power normalization may have a side effect. \\textbf{In above, power operation is an effective strategy to smooth the resulting histogram and can greatly improve the performance of sum pooling representation}.\n  \\item Among different choices of pooling operations and normalization methods, we conclude that sum pooling and power $\\ell_2$-normalization is the best combination. For dense features, intra normalization is an extra bonus for performance boosting. For sparse features, intra normalization sometimes may have a negative effect. The success of sum pooling and power $\\ell_2$-normalization can be explained by the Hellinger's kernel \\cite{VedaldiZ12}, which has turned out to be an effective kernel to calculate the similarity between two histograms. The linear kernel calculation in the feature space resulting from power $\\ell_2$-normalization is equivalent to the Hellinger's kernel calculation in the original space just using $\\ell_1$ normalization:\n      \\begin{equation}\n        <\\frac{\\sqrt{\\mathbf{x}}}{\\|\\sqrt{\\mathbf{x}}\\|_2},\\frac{\\sqrt{\\mathbf{y}}}{\\|\\sqrt{\\mathbf{y}}\\|_2}> = <\\sqrt{\\frac{\\mathbf{x}}{\\|\\mathbf{x}\\|_1}},\\sqrt{\\frac{\\mathbf{y}}{\\|\\mathbf{y}\\|_1}}>\n      \\end{equation}which means power $\\ell_2$-normalization explicitly introduces non-linear kernel in the final classifier. \\textbf{In a word, sum pooling and power $\\ell_2$-normalization is effective and efficient way to enable linear SVM to have the power of non-linear classifier and boost final recognition rate}.\n\\end{itemize}\n\nIn conclusion, pooling and normalization is a crucial step in the pipeline of BoVW framework, whose importance may not be highlighted in previous research work. Proper choice of pooling and normalization strategy may largely reduce the performance gap of different encoding methods. For sum pooling and power $\\ell_2$-normalization, which is the best combination in all these possible choices, the performances of LLC, SA-$k$, and VQ are comparable to each other for iDT features. Thus, in the remaining evaluation for fusion methods, we fix the pooling and normalization strategy as sum pooling and power $\\ell_2$-normalization.\n\n\\subsection{Exploration of Fusion Methods}\n\\begin{table*}\n  \\caption{Comparison of different fusion methods for the encoding methods on the \\textbf{HMDB51} dataset.}\n  \\label{tbl:hmdb}\n  \\centering\n  \\begin{tabular}{lcccccccccc}\n  \\hline\n  \\hline\n  Methods & ~~~FV~~~ & ~~SVC~~ & ~SVC-$k$~ & ~SVC-$all$~ & ~VLAD~ & VLAD-$k$ & VLAD-$all$ & ~~LLC~~ & SA-$k$ & ~~~VQ~~~ \\\\\n  \\hline\n  \\hline\n  \\multicolumn{11}{l}{\\textbf{Space Time Interest Points (STIPs)}} \\\\\n  ~HOG & 22.81 & 17.76 & 21.09 & 21.87 & 18.13 & 19.87 & 20.04 & 20.46 & 18.39 & 16.10 \\\\\n  ~HOF & 31.96 & 30.44 & 32.68 & 33.36 & 30.46 & 31.53 & 31.55 & 27.19 & 26.27 & 24.49\\\\\n  ~d-Fusion & \\textbf{38.82} & \\textbf{35.12} & 36.64 & \\textbf{37.19} & \\textbf{34.81} & \\textbf{36.18} & \\textbf{36.23} & 29.87 & 28.13 & 25.66 \\\\\n  ~r-Fusion & 37.32 & 34.36 & \\textbf{36.73} & \\textbf{37.19} & 34.23 & 35.84 & 35.88 & \\textbf{33.44} & \\textbf{32.59} & \\textbf{30.35} \\\\\n  ~s-Fusion & 36.71 & 32.14 & 34.51 & 34.99 & 32.11 & 33.90 & 34.01 & 32.52 & 30.96 & 27.54 \\\\\n  \\hline\n  \\multicolumn{11}{l}{\\textbf{Improved Dense Trajectories (iDTs)}} \\\\\n  ~HOG & 45.12 & 36.93 & 39.32 & 38.10 & 36.93 & 39.30 & 37.08 & 37.08 & 35.45 & 34.81 \\\\\n  ~HOF & 50.70 & 47.70 & 49.00 & 48.00 & 47.70 & 49.00 & 45.80 & 42.20 & 42.70 & 42.10 \\\\\n  ~MBHx & 44.14 & 39.35 & 43.01 & 41.68 & 39.43 & 43.03 & 41.55 & 35.51 & 35.51 & 34.6 \\\\\n  ~MBHy & 50.04 & 44.25 & 47.02 & 46.51 & 44.27 & 47.02 & 44.68 & 40.39 & 40.35 & 39.78 \\\\\n  ~d-Fusion & 58.37 & 54.12 & 56.82 & 56.86 & 54.2 & 56.88 & 54.73 & 48.25 & 48.58 & 47.93 \\\\\n  ~r-Fusion & \\textbf{60.22} & \\textbf{58.19} & \\textbf{60.09} & \\textbf{60.07} & \\textbf{58.26} & \\textbf{60.09} & \\textbf{58.58} & \\textbf{55.45} & \\textbf{55.8} & \\textbf{55.27} \\\\\n  ~s-Fusion &  59.62 & 57.27 & 59.11 & 58.78 & 57.14 & 59.17 &  57.54 & 53.68 & 53.94 & 53.27 \\\\\n  \\hline\n  \\hline\n  \\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n  \\caption{Comparison of different fusion methods for the encoding methods on the \\textbf{UCF50} dataset.}\n  \\label{tbl:ucf50}\n  \\centering\n  \\begin{tabular}{lcccccccccc}\n  \\hline\n  \\hline\n  Methods & ~~~FV~~~ & ~~SVC~~ & ~SVC-$k$~ & ~SVC-$all$~ & ~VLAD~ & VLAD-$k$ & VLAD-$all$ & ~~LLC~~ & SA-$k$ & ~~~VQ~~~ \\\\\n  \\hline\n  \\hline\n  \\multicolumn{11}{l}{\\textbf{Space Time Interest Points (STIPs)}} \\\\\n  ~HOG & 66.20 & 60.76 & 63.98 & 63.94 & 60.22 & 62.32 & 62.22 & 60.42 & 59.11 & 56.21 \\\\\n  ~HOF & 73.10 & 71.93 & 74.14 & 74.56 & 71.30 & 72.36 & 72.51 & 64.72 & 63.80 & 61.55\\\\\n  ~d-Fusion & \\textbf{78.32} & \\textbf{76.33} & 77.60 & 77.59 & \\textbf{75.57} & \\textbf{76.06} & \\textbf{76.13} & 70.13 & 68.66 & 67.16 \\\\\n  ~r-Fusion & 77.21 & 76.07 & \\textbf{78.42} & \\textbf{78.91} & 75.36 & 75.95 & 75.99 & \\textbf{74.05} & \\textbf{73.67} & \\textbf{71.95} \\\\\n  ~s-Fusion & 76.33 & 76.19 & 77.76 & 77.25 & 73.79 & 74.91 & 74.98 & 72.95 & 71.66 & 69.16 \\\\\n  \\hline\n  \\multicolumn{11}{l}{\\textbf{Improved Dense Trajectories (iDTs)}} \\\\\n  ~HOG & 84.39 & 78.22 & 80.29 & 79.97 & 78.19 & 80.20 & 78.33 & 72.73 & 73.76 & 74.27 \\\\\n  ~HOF & 86.33 & 85.18 & 85.92 & 84.94 & 85.15 & 85.87 & 83.48 & 80.23 & 80.58 & 80.29 \\\\\n  ~MBHx & 84.03 & 81.33 & 83.19 & 82.46 & 81.28 & 83.12 & 81.16 & 77.77 & 77.91 & 77.04 \\\\\n  ~MBHy & 87.02 & 84.64 & 86.38 & 85.29 & 84.60 & 86.32 & 84.04 & 80.36 & 80.6 & 80.3 \\\\\n  ~d-Fusion & 90.84 & 89.39 & 90.72 & 90.62 & 89.43 & 90.64 & 90.18 & 84.18 & 84.76 & 84.67 \\\\\n  ~r-Fusion & \\textbf{92.07} & \\textbf{90.87} & \\textbf{91.89} & \\textbf{91.50} & \\textbf{90.82} & \\textbf{91.80} & \\textbf{90.56} & \\textbf{87.56} & \\textbf{87.92}  & \\textbf{88.12} \\\\\n  ~s-Fusion &  91.03 &  90.08 & 90.71 & 90.36 & 90.11 & 90.63 &  89.67 &   87.37 & 87.86 & 87.41 \\\\\n  \\hline\n  \\hline\n  \\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n  \\caption{Comparison of different fusion methods for the encoding methods on the \\textbf{UCF101} dataset.}\n  \\label{tbl:ucf101}\n  \\centering\n  \\begin{tabular}{lcccccccccc}\n  \\hline\n  \\hline\n  Methods & ~~~FV~~~ & ~~SVC~~ & ~SVC-$k$~ & ~SVC-$all$~ & ~VLAD~ & VLAD-$k$ & VLAD-$all$ & ~~LLC~~ & SA-$k$ & ~~~VQ~~~ \\\\\n  \\hline\n  \\hline\n  \\multicolumn{11}{l}{\\textbf{Space Time Interest Points (STIPs)}} \\\\\n  ~HOG & 53.74 & 47.56 &  50.07 &  50.31 & 47.15 & 49.21 & 49.35 & 46.70 & 45.79 & 42.85 \\\\\n  ~HOF & 62.89 & 60.57 &  63.81 &  64.02 & 60.04 & 61.73 & 61.60 & 54.16 & 52.78 & 50.04\\\\\n  ~d-Fusion & \\textbf{69.90} & \\textbf{66.43} & 68.22 &  68.40 & \\textbf{65.42} & \\textbf{66.42} & \\textbf{66.46} & 59.52 & 57.83 & 56.09 \\\\\n  ~r-Fusion & 68.21 & 65.39 & \\textbf{69.00} & \\textbf{69.18} & 65.39& 66.13 & 66.19 & \\textbf{63.04} & \\textbf{62.13} & \\textbf{59.31} \\\\\n  ~s-Fusion & 66.77 & 62.50 & 65.81 & 65.98 & 62.17 & 63.97 & 64.15 & 60.94 & 59.48 & 56.69 \\\\\n  \\hline\n  \\multicolumn{11}{l}{\\textbf{Improved Dense Trajectories (iDTs)}} \\\\\n  ~HOG & 74.79 & 69.74 & 72.14 & 72.36 & 69.66 & 71.65 & 71.39 & 65.46 & 65.81 & 65.40 \\\\\n  ~HOF & 78.63 & 76.26 & 77.70 & 77.12 & 76.28 & 77.76 & 76.35 & 71.03 & 71.14 & 70.57 \\\\\n  ~MBHx & 76.82 & 71.63 & 74.24 & 73.92 & 71.62 & 74.11 & 71.84 & 67.00 & 67.55 & 66.43 \\\\\n  ~MBHy & 79.15 & 74.53 & 77.46 & 76.82 & 74.54 & 76.78 & 74.21 & 69.6 & 69.67 & 68.50 \\\\\n  ~d-Fusion & 85.32 & 83.36 & 85.19 & 85.17 & 83.39 & 85.14 & 85.45 & 77.65 & 77.96 & 76.76 \\\\\n  ~r-Fusion & \\textbf{87.11} & \\textbf{84.87} & \\textbf{86.54} & \\textbf{86.19 }& \\textbf{84.90} & \\textbf{86.16} & \\textbf{85.59} & \\textbf{81.43} & \\textbf{81.65} & \\textbf{81.37} \\\\\n  ~s-Fusion &  85.49 & 83.34 & 84.84 & 84.57 & 83.29 &  85.04 & 83.83 &  80.11 &  80.39 & 79.81 \\\\\n  \\hline\n  \\hline\n  \\end{tabular}\n\\end{table*}\n\nThe local features usually have multiple descriptors, such as HOG, HOF, MBHx, and MBHy, each of which corresponds to a specific view of video data. For the empirical study in previous section, we choose a simple method to combine these multiple descriptors, where we just concatenate them into a single one, namely descriptor level fusion. In this section, we mainly analyze the influence of different fusion methods on final recognition performance.\n\nFor encoding methods, we choose the same ten approaches as in previous section. The codebook size of super vector based methods is set as $512$ and the one of other encoding methods is set as $8,000$. For pooling and normalization methods, we use sum pooling and power $\\ell_2$-normalization, according to the observations in Section \\ref{sec:poolingnorm}. We also use intra normalization for super vector based encoding methods of iDTs features. For fusion methods, we evaluate three kinds of methods, namely descriptor level fusion, representation level fusion, and score level fusion, as described in Section \\ref{sec:fusion}. For score level fusion, we use the geometrical mean to combine the scores from multiple SVMs.\n\n\\begin{table*}\n  \\caption{Comparison our hybrid representation with the sate-of-the-art methods.}\n  \\label{tbl:cmp}\n  \\centering\n  \\begin{tabular}{lcc|lcc|lcc}\n  \\hline\n  \\hline\n  HMDB51 & ~Year~ & \\% & ~UCF50 & ~Year~ & \\% & ~UCF101 & ~Year~ &\\% \\\\\n  \\hline\n  \\hline\n  Kuehne \\emph{et al.} \\cite {KuehneJGPS11} & 2011 & 23.0 &  Sadanand \\emph{et al.} \\cite{SadanandC12} & 2012 & 57.9 & Soomro \\emph{et al.} \\cite{SOOMRO12} & ~2012~ & 43.9 \\\\\n  Sadanand \\emph{et al.} \\cite{SadanandC12} & 2012 & 26.9 & Kliper-Gross \\emph{et al.} \\cite{Kliper-GrossGHW12} & 2012 & 72.7 & Karpthy \\emph{et al.} \\cite{Karpathy14} & 2014 & 63.3 \\\\\n  Kliper-Gross \\emph{et al.} \\cite{Kliper-GrossGHW12} & 2012 & 29.2 & Solmaz \\emph{et al.} \\cite{SolmazAS13} &  2012 & 73.7  &  Cai \\emph{et al.} \\cite{CaiWPQ14} & 2014 & 83.5  \\\\\n  Jiang \\emph{et al.} \\cite{JiangDXLN12} & 2012 & 40.7 & Reddy \\emph{et al.} \\cite{ReddyS13} & 2012 & 76.9  & Wu \\emph{et al.} \\cite{WuZL14} & 2014 & 84.2 \\\\\n  Wang \\emph{et al.} \\cite{WangQT13} & 2013 & 42.1  & Wang \\emph{et al.} \\cite{WangQT13} & 2013 & 78.4 &  Peng \\emph{et al.} \\cite{PengWCQP13} & 2013 & 84.2  \\\\\n  Wang \\emph{et al.} \\cite{WangKSL13} & 2013 & 46.6 &  Wang \\emph{et al.} \\cite{WangKSL13}  & 2013 & 84.5 & Murthy \\emph{et al.} \\cite{Murthy13} & 2013 & 85.4   \\\\\n  Peng \\emph{et al.} \\cite{PengQPQ13}& 2013 & 49.2 & Wang \\emph{et al.} \\cite{WangQT13b}  & 2013 & 85.7  & Karaman \\emph{et al.} \\cite{Karaman13} & 2013 & 85.7 \\\\\n  Wang \\emph{et al.} \\cite{WangS13a} & 2013 & 57.2 & Wang \\emph{et al.} \\cite{WangS13a} & 2013 & 91.1 & Wang \\emph{et al.} \\cite{Wang13} & 2013 & 85.9 \\\\\n  \\hline\n  Hybrid representation & - & \\textbf{61.1} & Hybrid representation & - & \\textbf{92.3} & Hybrid representation & - & \\textbf{87.9} \\\\\n  \\hline\n  \\hline\n  \\end{tabular}\n\\end{table*}\n\nThe experimental results on three datasets are shown in Table \\ref{tbl:hmdb}, Table \\ref{tbl:ucf50}, and Table \\ref{tbl:ucf101}. From these results, we observe serval trends:\n\\begin{itemize}\n  \\item \\textbf{For iDTs features, representation level fusion is the best choice for all of the selected encoding methods on the three datasets}. This result indicates that these multiple descriptors are most correlated in the video level. Descriptor level fusion emphasizes the dependance in cuboid and results in high dimension features for codebook training and encoding. This may make these unsupervised learning algorithm unstable.\n  \\item \\textbf{For STIPs features, representation level fusion is more effective for reconstruction based and voting based encoding methods}. For super vector based encoding methods, the performance of representative level fusion is comparable to that of descriptor level fusion. This trend is consistent with the finds with iDTs features.\n  \\item \\textbf{For both features, SA-$k$, LLC, and VQ encoding methods are much sensitive to fusion methods than those super vector based encoding methods}. Great improvement can be obtained for SA-$k$, LLC, and VQ when using representation level fusion, but slight improvements happen to those super vector methods. We analyze this is due to two facts. Firstly, for reconstruction and voting based encoding methods, the final dimension of representation level fusion is $M$ (the number of descriptors) times of the dimension of descriptor level fusion. However, for super vector based encoding methods, the dimension of descriptor level fusion is the same with representation level fusion. The higher dimension of final representation may enable SVM to classify more easily. Secondly, the codebook size $K$ of super vector methods is much smaller than that of other types of encoding methods, where clustering algorithm may be more stable for high dimensionality in descriptor level fusion method.\n\\end{itemize}\n\nBased on the observation and analysis above, we conclude that fusion method is a very important component for handling combination of multiple descriptors in the action recognition system. Representation level fusion method is a suitable choice for different kinds of encoding methods due to its good performance. From our analysis, we know that the performance boosting of fusing multiple features mainly owns the complementarity of these features. This complementarity may be not limited to the exploration of different descriptors, but also can be extended to the different BoVWs. From the perspective of statistics, FV aggregates information using $1^{st}$ and $2^{nd}$ order statistics, while SVC is about zero and $1^{st}$ order statistics. Intuitively, these two kinds of super vector encoding methods are complementary to each other. Thus, we present a new feature representation, called hybrid representation, combining the outputs FV and soft version SVC of multiple descriptors, including HOG, HOF, MBHx, and MBHy. This representation is simple but proved to be effective in next section.\n\n\\subsection{Comparison to the State-of-the-Art Results}\n\\label{sec:stoa}\nIn this section, we demonstrate the effectiveness of our proposed hybrid representation according to our previous insightful analysis. Specifically, we choose two super vector based encoding methods, namely SVC-$k$ and FV, for iDTs features. We use the power operation and then intra $\\ell_2$-normalization. For feature fusion, we adopt the representation level fusion method.\n\nTable \\ref{tbl:cmp} shows our final recognition rates and compare our results to that of state-of-the-art approaches. For the HMDB51 dataset, we obtain a recognition rate of $61.1\\%$, which is superior to the best result \\cite{WangS13a} by $3.9\\%$. Our system reaches classification accuracy of $92.3\\%$ on the dataset of UCF50 and $87.9\\%$ on the dataset of UCF101, which outperform the best results by $1.2\\%$ and $2.0\\%$ respectively. It is worth noting that UCF101 is newest and largest dataset, so few published papers have reported results on this dataset. We mainly compare with those top performers in the Thumos'13 Action Recognition Challenge \\cite{THUMOS13}. We also compare with three latest papers in CVPR 2014. Karpathy \\emph{et al.} \\cite{Karpathy14} resorts to a large deep Convolutional Neural Network trained with an extra 1-M training dataset. Cai \\emph{et al.} \\cite{CaiWPQ14} propose a complex and less efficient encoding method by considering the correlation of different descriptors. Wu \\emph{et al.} \\cite{WuZL14} propose a simple, lightweight, but powerful bimodal encoding method. Our results outperform these top performer and latest papers on the UCF101. From these comparisons, our hybrid representation is an efficient and effective method and obtains the state-of-the-art performance on the three challenging datasets.\n\n\\section{Conclusion}\n\\label{sec:conclusion}\nIn this paper, we have comprehensively studied each step in the BoVW pipeline and tried to uncover good practice to build a more accurate and efficient action recognition system. Specifically, we mainly explore five aspects, namely local features, pre-processing techniques, encoding methods, pooling and normalization strategy, fusion methods. We conclude that every step is crucial for contributing to the final recognition rate and improper choice in one of the steps may counteract the performance improvement of other steps. Meanwhile, based on the insights from our comprehensive study, we propose a simple yet effective representation, called \\emph{hybrid representation}. Using this representation, our action recognition system obtains the state-of-the-art performance on the three challenging datasets.\n\n\n\n\n\\bibliographystyle{spmpsci}     \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\\label{S0}\nFrobenius theory for completely positive maps on von Neumann\nalgebras was developed in \\cite{A-H} (further contributions to\nthis subject can be found in \\cite{Gr} and \\cite{Wa}). This theory\nstates, in paticular, that for an ergodic semigroup of completely\npositive (or, in fact, even Schwarz) maps on a von Neumann algebra\nits point spectrum forms a group, and the corresponding\neigenspaces are one-dimensional and spanned by a unitary operator.\nThe aim of this paper is to show that neither of these is true for a\nsemigroup of merely positive maps. Namely, we first prove that the\neigenvectors are either multiples of a partial isometry or linear\ncombinations of two partial isometries or multiples of a unitary\noperator, and then show by means of examples, that there is a whole\nclass of semigroups of positive maps on a von Neumann algebra such\nthat their point spectra are not groups and the corresponding\neigenspaces have dimensions greater than one.\n\\section{Preliminaries and notation}\\label{S1}\nLet $M$ be a von Neumann algebra, and let $(\\varPhi_g\\colon\ng\\in\\mathbb{G})$ be a semigroup of linear normal positive unital maps on\n$M$. We shall be concerned with two cases: $\\mathbb{G}=\\mathbb{N}_0$\n--- all nonnegative integers, and $\\mathbb{G}=\\mathbb{R}_+$ --- all\nnonnegative reals (notice that in the first case the semigroup has\nthe form $(\\varPhi^n\\colon n=0,1,\\dots)$, where $\\varPhi$ is a\nlinear normal positive unital map on $M$).\n\nA complex number $\\lambda$ of modulus one is called an\n\\emph{eigenvalue} of the semigroup, if there is a nonzero $x\\in M$\nsuch that for each $g\\in\\mathbb{G}$\n\\begin{equation}\\label{e0}\n \\varPhi_g(x) = \\lambda^g x.\n\\end{equation}\nThe collection of all $x's$ such that \\eqref{e0} holds is called\nthe \\emph{eigenspace} corresponding to the eigenvalue $\\lambda$,\nand denoted by $M_{\\lambda}$. In particular, $M_1$ is the\nfixed-point space of the semigroup, and the semigroup is called\n\\emph{ergodic} if $M_1$ consists of multiples of the identity. The\nset of all eigenvalues of the semigroup is called its \\emph{point\nspectrum}, and denoted by $\\sigma((\\varPhi_g))$. Let $\\omega$ be a\nnormal faithful state on $M$ such that for each \\linebreak\n$g\\in\\mathbb{G},\\ \\omega\\circ\\varPhi_g = \\omega$. The part of Frobenius\ntheory developed in \\cite{A-H} which is of interest to us, states\nthat in this case, if we assume that \\linebreak $(\\varPhi_g\\colon g\\in\\mathbb{G})$\nis ergodic and the maps $\\varPhi_g$ are two-positive, the\npoint spectrum is a group, and the corresponding eigenspaces are\none-dimensional and spanned by a unitary operator. A natural question\nis if the same is true under the assumption of mere positivity of the\nmaps $\\varPhi_g$. We shall show that this is not the case neither\nfor the group structure nor for the dimension of the eigenspaces.\n\nLet $N$ be the $\\sigma$-weak closure of the linear span of\n$\\bigcup_{\\lambda}M_{\\lambda}$, where the sum is taken over all\neigenvalues of $(\\varPhi_g)$. Then according to \\linebreak \\cite[Theorem\n1]{Lu} $N$ is a $JW^*$-algebra, by which is meant that $N$ is\n\\linebreak a $\\sigma$-weakly closed linear space, closed with respect\nto the Jordan product\n\\[\n x\\circ y = \\frac{1}{2}(xy + yx);\n\\]\nmoreover, $\\varPhi_g|N$ are Jordan $^*$-automorphisms.\nConsequently, if $x\\in M_{\\lambda}$, then\n\\[\n \\varPhi_g(x^*) = \\varPhi_g(x)^* = \\bar{\\lambda}^g x^*,\n\\]\nmeaning that $x^*\\in M_{\\bar{\\lambda}}$, and for $x\\in\nM_{\\lambda_1},\\ y\\in M_{\\lambda_2}$ we have\n\\[\n \\varPhi_g(x\\circ y) = \\varPhi_g(x)\\circ\\varPhi_g(y) = \\lambda_1^g\n x\\circ\\lambda_2^g y = (\\lambda_1\\lambda_2)^g x\\circ y,\n\\]\nmeaning that $x\\circ y\\in M_{\\lambda_1\\lambda_2}$. In particular,\nfor an eigenvector $x$ we have $x\\circ x^*\\in M_1$.\n\\section{Eigenvectors}\\label{S2}\nIn the following theorem we shall describe the eigenvectors of\n$(\\varPhi_g)$.\n\\begin{theorem}\nAssume that $(\\varPhi_g)$ is ergodic, and let $x\\in M_{\\lambda}$\nbe an eigenvector of $(\\varPhi_g)$. Then one\nof the following possibilities holds:\n\\begin{enumerate}\n\\item[(i)] $x=\\alpha v$, where $\\alpha\\in\\mathbb{C}$, and $v$ is a\npartial isometry in $M_{\\lambda}$ such that\n\\[\n v^*v=e, \\qquad vv^*=e^{\\bot}\n\\]\nfor some nonzero projection $e$, $e\\neq\\boldsymbol{1}$;\n\\item[(ii)] $x=\\alpha_1v_1+\\alpha_2v_2$, where\n$\\alpha_1,\\alpha_2\\in\\mathbb{C},\\,\\alpha_1\\neq\\alpha_2$, and\n$v_1,v_2$ are partial isometries in $M_{\\lambda}$ such that for\nsome nonzero projection $e,\\ e\\neq\\boldsymbol{1}$,\n\\[\n v^*_1v_1=e, \\quad v_1v^*_1=e^{\\bot}, \\quad v^*_2v_2=e^{\\bot}, \\quad\n v_2v^*_2=e;\n\\]\n\\item[(iii)] $x=\\alpha u$, where $\\alpha\\in\\mathbb{C}$, and $u$ is\na unitary operator in $M_{\\lambda}$.\n\\end{enumerate}\n\\end{theorem}\n\\begin{proof}\nWe have $x\\circ x^*\\in M_1$, so renorming $x$, if\nnecessary, we may assume that\n\\begin{equation}\\label{E1}\n x^*x+xx^*=\\boldsymbol{1}.\n\\end{equation}\nMultiplying both sides of the above equality by $x$ on the left\nand on the right, respectively, we obtain\n\\begin{equation}\\label{E2}\n xx^*x+x^2x^*=x=x^*x^2+xx^*x,\n\\end{equation}\nso in particular $x^*$ commutes with $x^2$. Multiplying again both\nsides of the second part of the above equality by $x^*$, we obtain\n\\begin{equation}\\label{E3}\n x^*xx^*x+x^{*2}x^2=x^*x.\n\\end{equation}\n\n(i) Assume that $x^2=0$. Then \\eqref{E3} gives\n\\[\n (x^*x)^2=x^*x,\n\\]\nso $x^*x$ is a projection $e$, and by \\eqref{E1} $xx^*=e^{\\bot}$,\nthus $x$ is a partial isometry with initial projection $e$ and\nfinal projection $e^{\\bot}$, hence part (i) of the conclusion of\nthe theorem follows.\n\n(ii) and (iii) Assume that $x^2\\neq 0$. Then $x^2\\in\nM_{\\lambda^{2}},\\,x^{*2}\\in M_{\\bar{\\lambda}^2}$, so $x^2\\circ\nx^{*2}\\in M_1$, and since $x^2$ and $x^{*2}$ commute, we get\n\\[\n x^2x^{*2}=x^2\\circ x^{*2}=\\theta\\boldsymbol{1}\n\\]\nfor some $\\theta>0$, by the assumed ergodicity of $(\\varPhi_g)$.\nDenote $z=x^*x$. Then the above equality and \\eqref{E3} give\n\\[\n z^2-z+\\theta\\boldsymbol{1}=0,\n\\]\nthat is\n\\[\n \\left(z-\\frac{1-\\sqrt{1-4\\theta}}{2}\\,\\boldsymbol{1}\\right)\n \\left(z-\\frac{1+\\sqrt{1-4\\theta}}{2}\\,\\boldsymbol{1}\\right)=0.\n\\]\nIt follows that $\\theta\\leq 1\/4$, and we have two\npossibilities for the spectrum of $z$: either $\\theta=1\/4$\nin which case $\\text{sp}\\,z=\\left\\{1\/2\\right\\}$, or $\\theta\n< 1\/4$ in which case\n$\\text{sp}\\,z=\\left\\{\\frac{1-\\sqrt{1-4\\theta}}{2},\n\\,\\frac{1+\\sqrt{1-4\\theta}}{2}\\right\\}$. The first possibility\ngives at once\n\\[\n x^*x=\\frac{1}{2}\\,\\boldsymbol{1}, \\qquad\n xx^*=\\frac{1}{2}\\,\\boldsymbol{1},\n\\]\nand part (iii) of the conclusion of the theorem follows.\n\nFor the second possibility we have\n\\[\n x^*x=\\frac{1-\\sqrt{1-4\\theta}}{2}\\,e +\n \\frac{1+\\sqrt{1-4\\theta}}{2}\\,e^{\\bot}\n\\]\nwhere $e$ and $e^{\\bot}$ are the spectral projections of $x^*x$.\nFrom \\eqref{E1} we get\n\\[\n xx^*=\\frac{1+\\sqrt{1-4\\theta}}{2}\\,e +\n \\frac{1+\\sqrt{1-4\\theta}}{2}\\,\n e^{\\bot},\n\\]\nand denoting\n\\[\n \\alpha_1=\\left(\\frac{1-\\sqrt{1-4\\theta}}{2}\\right)^{1\/2}, \\qquad\n \\alpha_2=\\left(\\frac{1+\\sqrt{1-4\\theta}}{2}\\right)^{1\/2},\n\\]\nwe obtain\n\\begin{equation}\\label{E4}\n \\begin{aligned}\n |x|&=\\alpha_1e + \\alpha_2e^{\\bot}\\\\\n |x^*|&=\\alpha_2e + \\alpha_1e^{\\bot}.\n \\end{aligned}\n\\end{equation}\nLet\n\\[\n x=u|x|\n\\]\nbe the polar decomposition of $x$. Then\n\\[\n x^*=u^*|x^*|\n\\]\nis the polar decomposition of $x^*$, and since $|x|$ and $|x^*|$ are\ninvertible the operator $u$ is unitary. Moreover,\n\\[\n |x^*|=u|x|u^*,\n\\]\nwhich gives the equality\n\\[\n \\alpha_2e + \\alpha_1e^{\\bot}=\\alpha_1ueu^* + \\alpha_2ue^{\\bot}u^*,\n\\]\nyielding\n\\[\n \\alpha_1\\boldsymbol{1} +\n (\\alpha_2-\\alpha_1)e=\\alpha_2\\boldsymbol{1} +\n (\\alpha_1-\\alpha_2)ueu^*.\n\\]\nThus\n\\[\n (\\alpha_1-\\alpha_2)\\boldsymbol{1}=(\\alpha_1-\\alpha_2)(e + ueu^*),\n\\]\nshowing that\n\\[\n ueu^*=e^{\\bot},\n\\]\nand consequently,\n\\[\n e=\\boldsymbol{1}-ueu^*=ue^{\\bot}u^*.\n\\]\nFrom the polar decomposition and formula \\eqref{E4} we obtain\n\\begin{equation}\\label{E4'}\n x=\\alpha_1ue + \\alpha_2ue^{\\bot}=\\alpha_1v_1 + \\alpha_2v_2,\n\\end{equation}\nwhere\n\\[\n v_1=ue, \\qquad v_2=ue^{\\bot}.\n\\]\nWe have\n\\[\n v^*_1v_1=e,\\quad v_1v^*_1=ueu^*=e^{\\bot},\\quad\n v^*_2v_2=e^{\\bot},\\quad v_2v^*_2=ue^{\\bot}u^*=e,\n\\]\nso \\eqref{E4'} is the representation of $x$ as in part (ii) of the\nconclusion of the theorem. It remains to show that $v_1,v_2\\in\nM_{\\lambda}$. Equality \\eqref{E2} gives\n\\[\n xx^*x=x-x^2x^*=x-x^2\\circ x^*\n\\]\nbecause $x^2$ and $x^*$ commute. Since $x^2\\in M_{{\\lambda}^2}$ and\n$x^*\\in M_{\\bar{\\lambda}}$, we get $x^2\\circ x^*\\in M_{\\lambda}$, so\n$xx^*x\\in M_{\\lambda}$. We have\n\\[\n xx^*x=(\\alpha_1v_1 + \\alpha_2v_2)(\\alpha^2_1e + \\alpha^2_2e^{\\bot})\n =\\alpha^3_1v_1 + \\alpha^3_2v_2,\n\\]\nand the equality\n\\[\n \\varPhi_g(xx^*x)=\\lambda^g xx^*x\n\\]\nyields\n\\begin{equation}\\label{E5}\n \\alpha^3_1\\varPhi_g(v_1) +\\alpha^3_2\\varPhi_g(v_2)\n =\\lambda^g\\alpha^3_1v_1 + \\lambda^g\\alpha^3_2v_2.\n\\end{equation}\nOn the other hand $\\varPhi_g(x)=\\lambda^g x$, which gives\n\\begin{equation}\\label{E6}\n \\alpha_1\\varPhi_g(v_1) + \\alpha_2\\varPhi_g(v_2) = \\lambda^g\\alpha_1v_1\n + \\lambda^g\\alpha_2v_2.\n\\end{equation}\nMultiplying both sides of equality \\eqref{E6} by $\\alpha^2_2$ and\nsubstracting \\eqref{E6} from \\eqref{E5} we obtain\n\\[\n \\alpha_1(\\alpha^2_1-\\alpha^2_2)\\varPhi_g(v_1) =\n \\lambda^g\\alpha_1(\\alpha^2_1-\\alpha^2_2)v_1,\n\\]\nwhich gives $\\varPhi_g(v_1)=\\lambda^g v_1$,\nand analogously $\\varPhi_g(v_2)=\\lambda^g v_2$.\n\\end{proof}\n\\section{Positivity of elements from $\\textbf{Mat}_2(M)$}\\label{S3}\nIn what follows we shall need a number of properties concerning\npositivity of matrices with elements in a von Neumann algebra.\nThey will be exploited in examples in a particular case of an\nabelian von Neumann algebra, but as these properties seem to be\ninteresting in their own right, we prove them here in slightly\ngreater generality. For more information on positivity of such\nmatrices the reader is referred to \\cite[Chapter IV.3]{Ta} and\n\\cite{Wo}. It should be added that some of the facts obtained\nbelow can be given alternative proofs based on methods used in\n\\cite{Ta,Wo}.\n\nLet $M$ be a von Neumann algebra, and let\n$\\widetilde{M}=\\textbf{Mat}_2(M)$ be the algebra of\n$2\\times2$-matrices with elements from $M$. Assuming that $M$ acts\non a Hilbert space $\\mathcal{H}$, we can consider $\\widetilde{M}$\nas acting on the Hilbert space $\\widetilde{\\mathcal{H}} =\n\\mathcal{H}\\oplus\\mathcal{H}$.\n\n\\begin{proposition}\\label{P1}\nLet $A=\\left[\\begin{smallmatrix}a & b\\\\ c &\nd\\end{smallmatrix}\\right]\\in\\widetilde{M}$.\n\\begin{enumerate}\n\\item[(i)]$A\\geq 0$ if and only if $a,d\\geq 0,\\,c=b^*$, and for\neach $\\varepsilon > 0 \\linebreak d\\geq\nb^*(a+\\varepsilon\\boldsymbol{1})^{-1}b$.\n\\item[(ii)] Assume that $a,b\\text{ and }c$ commute. Then\n$A\\geq 0$ if and only if $a,d\\geq 0,\\,c=b^*$, and $ad\\geq b^*b$.\n\\end{enumerate}\n\\end{proposition}\n\\begin{proof}\nCalculate first the quadratic form of $A$. For\n$\\tilde{\\xi}=\\left(\\begin{smallmatrix}\\xi_1 \\\\\n\\xi_2\\end{smallmatrix}\\right)$,\\linebreak\n$\\xi_1,\\xi_2\\in\\mathcal{H}$, we have\n\\begin{equation}\\label{e1}\n \\begin{aligned}\n \\langle\n A\\tilde{\\xi},\\tilde{\\xi}\\rangle_{\\widetilde{\\mathcal{H}}}&=\\langle\\begin{pmatrix}\n a\\xi_1+b\\xi_2 \\\\ c\\xi_1+d\\xi_2\\end{pmatrix},\\begin{pmatrix}\\xi_1\n \\\\ \\xi_2\\end{pmatrix}\\rangle_{\\widetilde{\\mathcal{H}}} \\\\\n &=\\langle a\\xi_1,\\xi_1\\rangle_{\\mathcal{H}}+\\langle\n b\\xi_2,\\xi_1\\rangle_{\\mathcal{H}}+\\langle\n c\\xi_1,\\xi_2\\rangle_{\\mathcal{H}}+\\langle d\\xi_2,\\xi_2\\rangle_{\\mathcal{H}}.\n \\end{aligned}\n\\end{equation}\n\nIt is clear that in order that $A$ be positive we must have\n$a,d\\geq 0$ and $c=b^*$, so we restrict attention to matrices $A$\nof the form $A=\\left[\\begin{smallmatrix}a & b \\\\ b^* & d\n\\end{smallmatrix}\\right]$ with $a,d \\geq 0$. Then \\eqref{e1}\nbecomes\n\\begin{equation}\\label{e2}\n \\langle A\\tilde{\\xi},\\tilde{\\xi}\\rangle_{\\widetilde{\\mathcal{H}}}=\\langle\n a\\xi_1,\\xi_1\\rangle_{\\mathcal{H}}+\\langle b\\xi_2,\\xi_1\\rangle_{\\mathcal{H}}\n +\\langle\\xi_1,b\\xi_2\\rangle_{\\mathcal{H}} + \\langle\n d\\xi_2,\\xi_2\\rangle_{\\mathcal{H}}.\n\\end{equation}\n\n(i) \\emph{Step 1}. First we shall show that for $A$ of the form\n$A=\\left[\\begin{smallmatrix}\\boldsymbol{1} & b \\\\ b^* & z\n\\end{smallmatrix}\\right]$, $A\\geq 0$ if and only if $z\\geq b^*b$.\nThis is virtually proved in\\\\ \\cite[Lemma 3.1]{Wo}. For the sake of\ncompleteness we give a simple proof below.\n\nFor the quadratic form of $A$ we have\n\\begin{equation}\\label{e3}\n \\langle\n A\\tilde{\\xi},\\tilde{\\xi}\\rangle_{\\widetilde{\\mathcal{H}}}=\n \\langle\\xi_1,\\xi_1\\rangle_{\\mathcal{H}}+\\langle\n b\\xi_2,\\xi_1\\rangle_{\\mathcal{H}}+\\langle\\xi_1,b\\xi_2\\rangle_{\\mathcal{H}}+\n \\langle z\\xi_2,\\xi_2\\rangle_{\\mathcal{H}}.\n\\end{equation}\n\nLet $b^*b\\leq z$. Then\n\\begin{align*}\n \\langle A\\tilde{\\xi},\\tilde{\\xi}\\rangle_{\\widetilde{\\mathcal{H}}}&\\geq\n \\langle\\xi_1,\\xi_1\\rangle_{\\mathcal{H}}+\\langle b\\xi_2,\\xi_1\\rangle_{\\mathcal{H}}\n +\\langle\\xi_1,b\\xi_2\\rangle_{\\mathcal{H}}+\\langle\n b\\xi_2,b\\xi_2\\rangle_{\\mathcal{H}}\\\\&=\\langle\\xi_1+b\\xi_2,\\xi_1+b\\xi_2\\rangle_{\\mathcal{H}}\n \\geq 0,\n\\end{align*}\nshowing that $A\\geq 0$.\n\nConversely, if $A\\geq 0$ then substituting $-\\xi_1$ for $\\xi_1$ in\n\\eqref{e3}, we obtain\n\\[\n 0\\leq \\langle\\xi_1,\\xi_1\\rangle_{\\mathcal{H}}-\\langle\n b\\xi_2,\\xi_1\\rangle_{\\mathcal{H}}\n -\\langle\\xi_1,b\\xi_2\\rangle_{\\mathcal{H}}+\\langle\n z\\xi_2,\\xi_2\\rangle_{\\mathcal{H}},\n\\]\nthat is\n\\[\n\\langle b\\xi_2,\\xi_1\\rangle_{\\mathcal{H}}+\\langle\\xi_1,b\\xi_2\\rangle_{\\mathcal{H}}\n-\\langle \\xi_1,\\xi_1\\rangle_{\\mathcal{H}}\\leq\\langle\nz\\xi_2,\\xi_2\\rangle_{\\mathcal{H}}.\n\\]\n\nNow putting $\\xi_1=b\\xi_2$ in the above inequality, we get\n\\[\n \\langle b\\xi_2,b\\xi_2\\rangle_{\\mathcal{H}}\\leq\\langle\n z\\xi_2,\\xi_2\\rangle_{\\mathcal{H}},\n\\]\nwhich shows that $b^*b\\leq z$.\n\n\\emph{Step 2}. Let now $A=\\left[\\begin{smallmatrix}a & b \\\\ b^* &\nd\\end{smallmatrix}\\right]$ be arbitrary. $A\\geq 0$ if and only if\nfor each $\\varepsilon > 0, \\quad\nA_{\\varepsilon}=\\left[\\begin{smallmatrix}a+\\varepsilon\\boldsymbol{1}&\nb \\\\ b^*& d \\end{smallmatrix}\\right]\\geq 0$, and denoting\n$a_\\varepsilon = a + \\varepsilon\\boldsymbol{1}$, we obtain\n\\[\n \\langle\n A_{\\varepsilon}\\tilde{\\xi},\\tilde{\\xi}\\rangle_{\\widetilde{\\mathcal{H}}}=\n \\langle a_{\\varepsilon}\\xi_1,\\xi_1\\rangle_{\\mathcal{H}}+\\langle b\\xi_2,\\xi_1\n \\rangle_{\\mathcal{H}}+\\langle\\xi_1,b\\xi_2\\rangle_{\\mathcal{H}}+\\langle\n d\\xi_2,\\xi_2\\rangle_{\\mathcal{H}}.\n\\]\n\nPutting $\\eta_1=a_{\\varepsilon}^{1\/2}\\xi_1$, we get\n\\[\n \\begin{aligned}\n \\langle\n A_{\\varepsilon}\\tilde{\\xi},\\tilde{\\xi}\\rangle_{\\widetilde{\\mathcal{H}}}&=\n \\langle \\eta_1,\\eta_1\\rangle_{\\mathcal{H}}+\\langle\n a_{\\varepsilon}^{-1\/2}b\\xi_2,\\eta_1\\rangle_{\\mathcal{H}}\n +\\langle\\eta_1,a_{\\varepsilon}^{-1\/2}b\\xi_2\\rangle_{\\mathcal{H}}+\\langle\n d\\xi_2,\\xi_2\\rangle_{\\mathcal{H}}\\\\\n &=\\langle\\begin{bmatrix}\\boldsymbol{1}& a_{\\varepsilon}^{-1\/2}b \\\\\n b^* a_{\\varepsilon}^{-1\/2} & d \\end{bmatrix}\\begin{pmatrix}\\eta_1\\\\\n \\xi_2\\end{pmatrix},\\begin{pmatrix}\\eta_1 \\\\\n \\xi_2\\end{pmatrix}\\rangle_{\\widetilde{\\mathcal{H}}}.\n \\end{aligned}\n\\]\n\nSince $a_{\\varepsilon}^{1\/2}$ maps $\\mathcal{H}$ onto\n$\\mathcal{H}$ in a 1--1 way, we see that $A_{\\varepsilon}\\geq 0$\nif and only if $\\left[\\begin{smallmatrix}\\boldsymbol{1} &\na_{\\varepsilon}^{-1\/2}b \\\\ b^* a_{\\varepsilon}^{-1\/2} & d\n\\end{smallmatrix}\\right]\\geq 0$, which by \\emph{Step 1} is\nequivalent to the condition\n\\[\n d \\geq\n b^*a_{\\varepsilon}^{-1}b=b^*(a+\\varepsilon\\boldsymbol{1})^{-1}b,\n\\]\nand the proof of (i) is complete.\n\n(ii) The reasoning is similar to that in part (i) using the simple\n\\linebreak $\\varepsilon$-trick. Namely, the inequality $ad\\geq\nb^*b$ is equivalent to $(a+\\varepsilon\\boldsymbol{1})d \\geq b^*b$\nfor each $\\varepsilon >0$, which in turn, by the assumed\ncommutation property, is equivalent to $d\\geq\nb^*(a+\\varepsilon\\boldsymbol{1})^{-1}b$. Applying part (i)\nfinishes the proof.\n\\end{proof}\n\\begin{remark}\nIn virtually the same way we obtain the following variant of (i):\n\\begin{enumerate}\n\\item[(i${}'$)] $A\\geq 0$ if and only if $a,d\\geq 0,\\quad c=b^*$,\nand for each $\\varepsilon > 0 \\linebreak a\\geq\nb(d+\\varepsilon\\boldsymbol{1})^{-1}b^*$.\n\\end{enumerate}\n\\end{remark}\n\\begin{lemma}\\label{L2}\nLet $\\left[\\begin{smallmatrix}a & b \\\\ b^* & d\n\\end{smallmatrix}\\right]\\geq 0$. Then\n\\begin{enumerate}\n\\item[(i)]$\\left[\\begin{smallmatrix}d & b^* \\\\ b & a\n\\end{smallmatrix}\\right]\\geq 0$.\n\\item[(ii)] For each $x,y\\in M \\quad\n\\left[\\begin{smallmatrix}xax^* & xby^* \\\\ yb^*x^* & ydy^*\n\\end{smallmatrix}\\right]\\geq 0$.\n\\end{enumerate}\n\\end{lemma}\n\\begin{proof}\n(i) follows from the equality\n\\[\n \\begin{bmatrix}d & b^* \\\\ b & a \\end{bmatrix} = \\begin{bmatrix}0\n & \\boldsymbol{1} \\\\ \\boldsymbol{1} & 0\n \\end{bmatrix}\\begin{bmatrix}a & b \\\\ b^* & d \\end{bmatrix}\n \\begin{bmatrix}0 & \\boldsymbol{1} \\\\ \\boldsymbol{1} & 0\n \\end{bmatrix},\n\\]\nand (ii) from the equality\n\\[\n \\begin{bmatrix}xax^* & xby^* \\\\ yb^*x^* & ydy^* \\end{bmatrix}=\n \\begin{bmatrix}x & 0 \\\\ 0 & y \\end{bmatrix}\\begin{bmatrix}a & b\n \\\\ b^* & d \\end{bmatrix}\\begin{bmatrix}x^* & 0 \\\\ 0 & y^*\n \\end{bmatrix}.\n\\]\n\\end{proof}\n\\begin{lemma}\\label{L3}\nLet $a$ commute with $b$, and assume further that either $b$ is\nnormal or that $b$ commutes with $d$. If\n$\\left[\\begin{smallmatrix}a & b \\\\ b^* & d\n\\end{smallmatrix}\\right]\\geq 0$, then $\\left[\\begin{smallmatrix}a\n& b^* \\\\ b & d \\end{smallmatrix}\\right]\\geq 0$.\n\\end{lemma}\n\\begin{proof}\nLet $\\left[\\begin{smallmatrix}a & b \\\\ b^* & d\n\\end{smallmatrix}\\right]\\geq 0$, and assume first that $b$ is\nnormal. Then by Proposition \\ref{P1} (i) we have for each\n$\\varepsilon > 0$\n\\[\n d \\geq b^*(a+\\varepsilon\\boldsymbol{1})^{-1}b =\n b^*b(a+\\varepsilon\\boldsymbol{1})^{-1} =\n b(a+\\varepsilon\\boldsymbol{1})^{-1}b^*,\n\\]\nwhich again by Proposition \\ref{P1} (i) means that\n$\\left[\\begin{smallmatrix}a & b^* \\\\ b & d\n\\end{smallmatrix}\\right]\\geq 0$.\n\nNow let $b$ commute with $d$. Then for each $\\varepsilon > 0$,\n\\[\n d \\geq b^*(a+\\varepsilon\\boldsymbol{1})^{-1}b =\n |b|^2(a+\\varepsilon\\boldsymbol{1})^{-1} =\n |b|(a+\\varepsilon\\boldsymbol{1})^{-1}|b|,\n\\]\nso $\\left[\\begin{smallmatrix}a & |b| \\\\ |b| & d\n\\end{smallmatrix}\\right]\\geq 0$. By Lemma \\ref{L2} (i) it follows\nthat $\\left[\\begin{smallmatrix}d & |b| \\\\ |b| & a\n\\end{smallmatrix}\\right]\\geq 0$, and thus, on account of\nProposition \\ref{P1} (i), for each $\\varepsilon > 0$,\n\\[\n a \\geq |b|(d+\\varepsilon\\boldsymbol{1})^{-1}|b| =\n b^*b(d+\\varepsilon\\boldsymbol{1})^{-1} =\n b^*(d+\\varepsilon\\boldsymbol{1})^{-1}b,\n\\]\nwhich means that $\\left[\\begin{smallmatrix}d & b \\\\ b^* & a\n\\end{smallmatrix}\\right]\\geq 0$. Applying again Lemma \\ref{L2} (i)\nwe obtain $\\left[\\begin{smallmatrix}a & b^* \\\\ b & d\n\\end{smallmatrix}\\right]\\geq 0$.\n\\end{proof}\n\\section{Examples}\\label{S4}\nLet us begin with a simple example.\n\\begin{example}\\label{Ex1}\nKeeping the notation of Section \\ref{S3}, put\n$\\widetilde{M}=\\mathbb{B}(\\mathbb{C}^2)$ (i.e. $M=\\mathbb{C}$),\n$\\omega=\\frac{1}{2}tr$, and let $\\lambda_0\\in\\mathbb{C}$ be such\nthat $|\\lambda_0|=1,\\ \\lambda_0\\ne1$. Define\n$\\varPhi:\\widetilde{M}\\to\\widetilde{M}$ as\n\\[\n \\varPhi\\left(\\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\\right) =\n \\begin{bmatrix}\\frac{a+d}{2}&\\lambda_0b\\\\\n \\bar{\\lambda}_0c&\\frac{a+d}{2}\\end{bmatrix}.\n\\]\nIt is clear that $\\varPhi$ is linear normal unital, and that\n$\\omega\\circ\\varPhi=\\omega$. Moreover, for $\\left[\\begin{smallmatrix}a&b\\\\c&d\\end{smallmatrix}\\right]\\geq 0$, we have\n$a,d \\geq 0,\\ c=\\bar{b}$, and $\\left[\\begin{smallmatrix}d & b \\\\\n\\bar{b} & a \\end{smallmatrix}\\right]\\geq 0$, thus \\linebreak\n$\\left[\\begin{smallmatrix}a+d & 2b \\\\ 2\\bar{b} & a+d\n\\end{smallmatrix}\\right]\\geq 0$, so\n$\\left[\\begin{smallmatrix}\\frac{a+d}{2} & b \\\\ \\bar{b} &\n\\frac{a+d}{2} \\end{smallmatrix}\\right]\\geq 0$, and consequently\n$\\left[\\begin{smallmatrix}\\frac{a+d}{2} & \\lambda_0b \\\\\n\\bar{\\lambda}_0\\bar{b} & \\frac{a+d}{2}\n\\end{smallmatrix}\\right]\\geq 0$, showing that $\\varPhi$ is\npositive.\n\nThe equality\n\\[\n \\varPhi\\left(\\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\\right) = \\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\n\\]\nyields\n\\[\n \\frac{a+d}{2} = a = d,\\qquad \\lambda_0b = b,\\qquad\n \\bar{\\lambda}_0c = c,\n\\]\nhence $b=c=0$, and the fixed-points have the form\n$\\left[\\begin{smallmatrix}a & 0 \\\\ 0 & a \\end{smallmatrix}\\right]\n= a\\left[\\begin{smallmatrix}1 & 0 \\\\ 0 & 1\n\\end{smallmatrix}\\right]$, which means that $(\\varPhi^n)$ is\nergodic.\n\n(i) Let $\\lambda_0$ be such that $\\lambda_0\\ne-1,\\\n\\lambda_0^3\\ne1$, and let $\\lambda\\ne1$ be an eigenvalue of\n$(\\varPhi^n)$. Then\n\\[\n \\frac{a+d}{2} = \\lambda a = \\lambda d,\\qquad \\lambda_0b = \\lambda\n b,\\qquad \\bar{\\lambda}_0c = \\lambda c,\n\\]\nwhich yields\n\\[\n a = d = 0,\\qquad \\bar{\\lambda}\\lambda_0b = b,\\qquad\n \\bar{\\lambda}\\bar{\\lambda}_0c = c.\n\\]\nThus either $\\lambda = \\lambda_0,\\ c = 0$ or $\\lambda =\n\\bar{\\lambda}_0,\\ b = 0$, so $\\lambda_0 \\text{ and }\n\\bar{\\lambda}_0$ are the only eigenvalues of $(\\varPhi^n)$\ndifferent from $1$, with the eigenspaces\n\\[\n \\widetilde{M}_{\\lambda_0} = \\left\\{\\begin{bmatrix}0 & b \\\\ 0 & 0\n \\end{bmatrix}\\colon b\\in\\mathbb{C}\\right\\}, \\qquad\n \\widetilde{M}_{\\bar{\\lambda}_0} = \\left\\{\\begin{bmatrix}0 & 0 \\\\\n c & 0 \\end{bmatrix}\\colon c\\in\\mathbb{C}\\right\\}.\n\\]\nConsequently, $\\sigma((\\varPhi^n)) =\n\\{1,\\lambda_0,\\bar{\\lambda}_0\\}$, which is not a group if\n\\linebreak $\\lambda_0\\ne-1,\\ \\lambda_0^3\\ne1$.\n\n(ii) Now let $\\lambda_0 = -1$. The above calculations give\n$\\sigma((\\varPhi^n)) = \\{1,-1\\}$, and\n\\[\n \\widetilde{M}_{-1} = \\left\\{\\begin{bmatrix} 0 & b \\\\ c & 0\n \\end{bmatrix}\\colon b,c\\in\\mathbb{C}\\right\\},\n\\]\nso the eigenspace is not one-dimensional.\\hfill\\qedsymbol\n\\end{example}\n\nLet us observe that the reasoning above may be repeated with\nvirtually no change for the semigroup $(\\varPhi_t\\colon t\\geq 0)$\ndefined as\n\\[\n \\varPhi_t\\left(\\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\\right) = \\begin{bmatrix} \\frac{a+d}{2} &\n \\lambda_0^t b \\\\ \\bar{\\lambda}_0^t c & \\frac{a+d}{2}\n \\end{bmatrix},\n\\]\nthus giving a corresponding example in the continuous case.\n\\begin{remark}\nThe triple $(\\mathbb{B}(\\mathbb{C}^2),(\\varPhi_t),\\omega)$ from\nthe above example constitutes what in \\cite{Gr} is called an\nirreducible $W^*$-dynamical system. In \\linebreak\\cite[Theorem\n3.8]{Gr} it is proved that under the assumption that the\n$\\varPhi_t$'s are Schwarz maps every such a system on a full\nalgebra has trivial point spectrum (i.e. consisting only of $1$).\nAs we see this is not the case if we assume only positivity of the\nmaps $\\varPhi_t$'s.\n\\end{remark}\nNow we construct a more involved\nexample (in fact, a class of examples) in which we shall see that\nall the possibilities for the eigenvectors given in Theorem may\noccur.\n\\begin{example}\\label{Ex2}\nLet $M$ be abelian, let $\\omega$ be a normal faithful state on\n$M$, and let $\\varPsi$ be a positive normal unital map on $M$ such\nthat $\\omega\\circ\\varPsi = \\omega,\\ (\\varPsi^n)$ is ergodic, and\n$\\sigma((\\varPsi^n)) = \\{-1,1\\}$. The abelianess of $M$ implies\nthat $\\varPsi$ is completely positive (cf. \\cite[Chapter IV.3]{Ta}),\nthus according to \\cite{A-H} the eigenspace corresponding to $-1$\nis one-dimensional and spanned by a unitary operator $u$, i.e.\n\\[\n \\varPsi(x) = -x\n\\]\nif and only if $x$ is a multiple of $u$.\n\nPut $\\widetilde{M} = \\textbf{Mat}_2(M)$,\n\\[\n \\tilde\\omega\\left(\\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\\right) = \\frac{1}{2}[\\omega(a) +\n \\omega(d)],\n\\]\nand let $\\lambda_0\\in\\mathbb{C}$ be such that $|\\lambda_0|=1,\\\n\\lambda_0\\notin\\{-1,1\\}$. Define\n$\\varPhi:\\widetilde{M}\\to\\widetilde{M}$ as\n\\[\n \\varPhi\\left(\\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\\right) =\n \\begin{bmatrix}\\varPsi\\left(\\frac{a+d}{2}\\right) & \\lambda_0\\varPsi(b) \\\\\n \\bar{\\lambda}_0\\varPsi(c) & \\varPsi\\left(\\frac{a+d}{2}\\right)\\end{bmatrix}.\n\\]\n$\\varPhi$ is a linear normal unital map on $\\widetilde{M}$ such\nthat $\\tilde\\omega\\circ\\varPhi = \\tilde\\omega$. Arguing as in\nExample \\ref{Ex1}, and using Lemma \\ref{L2} with $x =\n\\lambda_0\\boldsymbol{1},\\ y = \\boldsymbol{1}$, and Lemma \\ref{L3}, we see\nthat if $\\left[\\begin{smallmatrix}a&b\\\\c&d\\end{smallmatrix}\\right]\\geq 0$, then\n$\\left[\\begin{smallmatrix}\\frac{a+d}{2} & \\lambda_0 b \\\\ \\bar{\\lambda}_0 c &\n\\frac{a+d}{2}\\end{smallmatrix}\\right]\\geq 0$, so $\\varPhi$ is\npositive by virtue of the complete positivity of $\\varPsi$.\n\nThe equality\n\\[\n \\varPhi\\left(\\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\\right) = \\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\n\\]\nyields\n\\[\n \\varPsi\\left(\\frac{a+d}{2}\\right) = a = d,\\qquad \\lambda_0\\varPsi(b) =\n b,\\qquad \\bar{\\lambda}_0\\varPsi(c) = c,\n\\]\nhence $b = c = 0$ and $\\varPsi(a) = a$. From the ergodicity of\n$\\varPsi$ it follows that $a$ is a multiple of $\\boldsymbol{1}$, so\nthe fixed-points of $(\\varPhi^n)$ have the form\n$\\left[\\begin{smallmatrix}\\theta\\boldsymbol{1} & 0 \\\\ 0 &\n\\theta\\boldsymbol{1}\\end{smallmatrix}\\right]$ with\n$\\theta\\in\\mathbb{C}$, which means that $(\\varPhi^n)$ is ergodic.\nLet $\\lambda\\ne1$ be an eigenvalue of $(\\varPhi^n)$. Then\n\\[\n \\varPsi\\left(\\frac{a+d}{2}\\right) = \\lambda a = \\lambda d,\\qquad\n \\lambda_0\\varPsi(b) = \\lambda b,\\qquad \\bar{\\lambda}_0\\varPsi(c)\n = \\lambda c,\n\\]\nwhich yields\n\\begin{equation}\\label{e4}\n \\varPsi(a) = \\lambda a,\\qquad \\varPsi(b) = \\bar{\\lambda}_0\\lambda b,\n \\qquad \\varPsi(c) = \\bar{\\lambda}_0\\lambda c.\n\\end{equation}\n\n(i) Take $\\lambda_0$ such that $\\lambda_0\\neq i,\\\n\\lambda_0\\neq-i,\\ \\lambda^3_0\\neq1,\\ \\lambda^3_0\\neq-1$.\nEqualities \\eqref{e4} yield the following possibilities:\n\n(i.1) $\\lambda=-1$. Then $a=d$ is a multiple of $u,\\\nb=c=0$, and\n\\[\n \\widetilde{M}_{-1}=\\left\\{\\alpha\\begin{bmatrix}u & 0\\\\ 0 & u\n \\end{bmatrix}\\colon \\alpha\\in\\mathbb{C}\\right\\},\n\\]\nso the eigenvector corresponding to the eigenvalue $-1$ is as in\npart (iii) of Theorem.\n\n(i.2) $\\lambda\\neq-1$. Then $a=d=0$, and one of the four\nsituations must occur:\n\n(i.2.1) $\\lambda=\\lambda_0$. Then $b$ is a multiple of\n$\\boldsymbol{1},\\ c=0$, and\n\\[\n \\widetilde{M}_{\\lambda_0}=\\left\\{\\alpha\\begin{bmatrix}0 &\n \\boldsymbol{1}\\\\ 0 & 0\n \\end{bmatrix}\\colon\\alpha\\in\\mathbb{C}\\right\\},\n\\]\nso the eigenvector corresponding to the eigenvalue $\\lambda_0$ is\nas in part (i) of Theorem.\n\n(i.2.2) $\\lambda=-\\lambda_0$. Then $b$ is a multiple of $u,\\ c=0$, and\n\\[\n \\widetilde{M}_{-\\lambda_0}=\\left\\{\\alpha\\begin{bmatrix}0 & u\\\\\n 0 & 0\\end{bmatrix}\\colon\\alpha\\in\\mathbb{C}\\right\\}.\n\\]\n\n(i.2.3) $\\lambda=\\bar{\\lambda}_0$. Then $b=0,\\ c$ is a multiple of\n$\\boldsymbol{1}$, and\n\\[\n \\widetilde{M}_{\\bar{\\lambda}_0}=\\left\\{\\alpha\\begin{bmatrix}0 &\n 0\\\\ \\boldsymbol{1} & 0\n \\end{bmatrix}\\colon\\alpha\\in\\mathbb{C}\\right\\}.\n\\]\n\n(i.2.4) $\\lambda=-\\bar{\\lambda}_0$. Then $b=0,\\ c$ is a multiple\nof $u$, and\n\\[\n \\widetilde{M}_{-\\bar{\\lambda}_0}=\\left\\{\\alpha\\begin{bmatrix}0 &\n 0\\\\u & 0 \\end{bmatrix}\\colon\\alpha\\in\\mathbb{C}\\right\\}.\n\\]\n\nMoreover, we have\n\\[\n \\sigma((\\varPhi^n))=\\{1,-1,\\lambda_0,\\bar{\\lambda}_0,-\\lambda_0,\n -\\bar{\\lambda}_0\\},\n\\]\nwhich is not a group under our assumptions on $\\lambda_0$.\n\nNow take $\\lambda_0=i$. Equations \\eqref{e4} become then\n\\[\n \\varPsi(a)=\\lambda a,\\qquad \\varPsi(b)=-i\\lambda b,\\qquad\n \\varPsi(c)=i\\lambda c.\n\\]\nAs in part (i) we have the possibilities:\n\n(ii.1) $\\lambda=-1$, in which case $a=d$ is a multiple of\n$\\boldsymbol{1}$, and $b=c=0$.\n\n(ii.2) $\\lambda\\neq-1$, in which case $a=d=0$, and we may only\nhave either $\\lambda=i$ or $\\lambda=-i$. In the first case $b$ is\na multiple of $\\boldsymbol{1},\\ c$ is a multiple of $u$, and\n\\[\n \\widetilde{M}_i=\\left\\{\\alpha_1\\begin{bmatrix}0 &\n \\boldsymbol{1}\\\\ 0 & 0\\end{bmatrix}+ \\alpha_2\\begin{bmatrix}0 &\n 0\\\\ u &\n 0\\end{bmatrix}\\colon\\alpha_1,\\alpha_2\\in\\mathbb{C}\\right\\},\n\\]\nso the situation is as in part (ii) of Theorem with\n\\[\n v_1=\\begin{bmatrix}0 & \\boldsymbol{1}\\\\ 0 & 0\\end{bmatrix},\\\n v_2=\\begin{bmatrix}0 & 0\\\\ u & 0\\end{bmatrix},\\\n e=\\begin{bmatrix}0 & 0\\\\ 0 & \\boldsymbol{1}\\end{bmatrix},\\\n e^{\\bot}=\\begin{bmatrix}\\boldsymbol{1} & 0\\\\ 0 & 0\\end{bmatrix}.\n\\]\nIn the second case $b$ is a multiple of $u,\\ c$ is a multiple of\n$\\boldsymbol{1}$, and\n\\[\n \\widetilde{M}_{-i}=\\left\\{\\alpha_1\\begin{bmatrix}0 & u\\\\ 0 &\n 0\\end{bmatrix}+ \\alpha_2\\begin{bmatrix}0 & 0\\\\ \\boldsymbol{1} &\n 0\\end{bmatrix}\\colon\\alpha_1,\\alpha_2\\in\\mathbb{C}\\right\\},\n\\]\nso again part (ii) of Theorem occurs with\n\\[\n v_1=\\begin{bmatrix}0 & u\\\\ 0 & 0\\end{bmatrix},\\\n v_2=\\begin{bmatrix}0 & 0\\\\ \\boldsymbol{1} & 0\\end{bmatrix},\\\n e=\\begin{bmatrix}\\boldsymbol{1} & 0\\\\ 0 & 0\\end{bmatrix},\\\n e^{\\bot}=\\begin{bmatrix}0 & 0\\\\ 0 & \\boldsymbol{1}\\end{bmatrix}.\n\\]\n\\hfill\\qedsymbol\n\\end{example}\nAs in Example \\ref{Ex1}, we observe that taking $(\\varPsi_t\\colon\nt\\geq 0)$ --- an ergodic semigroup of positive maps on $M$ with\n$\\sigma((\\varPsi_t)) = \\{1,-1\\}$, and defining\n\\[\n \\varPhi_t\\left(\\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}\\right) =\n \\begin{bmatrix}\\varPsi_t\\left(\\frac{a+d}{2}\\right) &\n \\lambda_0^t\\varPsi_t(b) \\\\ \\bar{\\lambda}_0^t\\varPsi_t(c) &\n \\varPsi_t\\left(\\frac{a+d}{2}\\right)\\end{bmatrix},\\qquad t\\geq 0,\n\\]\nwe obtain a continuous counterpart of Example \\ref{Ex2}.\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nThere are a number of reasons why metrics are believed to be useful\nfor studying spike trains. It can be argued that it is the most\ngeneral, useful, mathematical framework for spike trains\n\\cite{VictorPurpura1997a}, it may be possible to find a manifold of\nspike trains using local linear methods and, of most relevance to the\npresent discussion, it is possible that studying spike train metrics\nis a useful approach to understanding how content is coded in spike\ntrains.\n\nThe Victor-Purpura metric is an edit distance metric on the space of\nspike trains. The distance between two spike trains is, in effect,\ncalculated as the cost of changing one spike train into the other by\nadding, deleting, or moving spikes, with an individual cost for each\ntype of elementary moves. In particular, a cost of one is associated\nwith adding or deleting a spike and a cost of $q\\delta t$ with moving\na spike a time $\\delta t$: the distance is\n\\begin{equation}\nd({\\bf u},{\\bf v};q)=\\mbox{min}_\\gamma c_{\\gamma;q}({\\bf u},{\\bf v})\n\\end{equation}\nwhere $c_\\gamma({\\bf u},{\\bf v})$ is the cost of a sequence of\nelementary moves $\\gamma$ and is calculated by adding the cost of all\nthe elementary moves in the sequence. The minimum is taken over all\nsequences $\\gamma$ changing ${\\bf u}$ to ${\\bf v}$. The parameter\n$2\/q$ gives an important timescale for the metric: it is never\nworthwhile to move a spike more than $2\/q$ since it would be cheaper\nto delete the spike from one temporal location and to add it to the\nother. This gives a timescale that, roughly speaking, separates jitter\nfrom unreliability in comparing spikes in the spike trains. However,\nthe Victor-Purpura metric does more than this; it explicitly pairs up\nthose spikes that can be thought of as being related by jitter.\n\nThe Victor-Purpura metric has an $l^1$ character: the cost $c_\\gamma$\nis a simple linear sum of the individual costs of the individual\nmoves. The generalization proposed in \\cite{DubbsSeilerMagnasco2009a}\nchanges this to an $l^p$-like sum. For notational convenience, from\nnow on the set of sequences will be restricted: the minimum sequence\nwill never involve moving a spike after it has been added, it would\nalways be cheaper to add the spike in the correct location, similarly,\nspikes are never moved before they are deleted. It is also specified\nthat spikes can only be moved once. With these restrictions, the\nsequence $\\gamma$ can be considered to be an unordered set made up of\ndeletions, additions and moves. Let\n\\begin{equation}\n\\gamma=\\alpha\\cup\\mu\n\\end{equation}\nwhere $\\alpha$ is the set of additions and deletions and $\\mu$ is the\nset of moves. The elements of $\\mu$ are pairs of spikes $(u,v)$, with\n$u\\in {\\bf u}$ and $v\\in {\\bf v}$, that are related by jitter.\n\nNow,\n\\begin{equation}\nc_{\\gamma;q}({\\bf u},{\\bf v})=|\\alpha|+\\sum_{(u,v)\\in\\mu} q|u-v|\n\\end{equation}\nThis is generalized in \\cite{DubbsSeilerMagnasco2009a} to\n\\begin{equation}\nc_{\\gamma;q,p}({\\bf u},{\\bf v})=\\left(|\\alpha|+\\sum_{(u,v)\\in\\mu} q^p|u-v|^p\\right)^{1\/p}\n\\end{equation}\nwith $p\\ge 1$, to give the $\\mathcal{L}_p$ Victor-Purpura metric\n\\begin{equation}\nd({\\bf u},{\\bf v};q,p)=\\mbox{min}_\\gamma c_{\\gamma;q,p}({\\bf u},{\\bf v})\n\\end{equation}\nwhere the minimum is taken over sequences $\\gamma$ changing ${\\bf u}$\nto ${\\bf v}$ and satisfying the restrictions specified above. An\nalgorithm for calculating this quantity is given in\n\\cite{DubbsSeilerMagnasco2009a}; the existing algorithms used to\ncalculate the Victor-Purpura metric,\n\\cite{VictorGoldbergGardner2007a}, for example, could also be adapted\nto $p>1$.\n\n\\section{Evaluating the metric using clustering}\n\nIn the data that will be considered here, spike trains were recorded\nfrom field L of the auditory fore-brain of anesthetized zebra finch\nduring playback of 20 con-specific songs with each song repeated ten\ntimes, to give a total of 200 spike trains. These spike trains, and\nthe experimental conditions used to produce them, are described in\n\\cite{NarayanEtAl2006b,WangEtAl2007a} and they have previously been\nused to compare metrics in\n\\cite{Houghton2007a,HoughtonVictor2009a}. The key point, in this\ncontext, is that a good metric, one which depends on the content\nencoded in the spike train, should measure a smaller distance between\nspiking responses to the same song than between responses to different\nsongs. One motivation for looking at spike train metrics is that\nscoring metrics in this way, and examining how good metrics measure\ndistance, might reveal details about how content is encoded.\n\nThe usual method for evaluating how well a metric succeeds in this way\nis to calculate the transmitted information\n\\cite{VictorPurpura1996a}. There are two ways to cluster the spike\ntrains: a true clustering, based on the identity of the song that\nelicited the response and an estimated clustering, based on the metric\ndistances between the responses. Roughly speaking, the transmitted\ninformation quantifies the amount of information about the true\nclustering given by the estimated clustering.\n\nCalculating the transmitted information relies on the calculation of a\nconfusion matrix $N$. This is described in detail in\n\\cite{VictorPurpura1996a}, described specifically for the data\nconsidered here, $N$ is a $20\\times 20$ matrix of integers where the\nentry $N_{ij}$ counts how many of the spike trains from the $i$th true\ncluster is closest, on average, to the spike trains in the $j$th true\ncluster. As in \\cite{VictorPurpura1996a} this averaging is carried out\nas a root-mean-square averaging to under-weigh outliers. If the metric\nclustering is close to the true clustering, $N$ will be nearly\ndiagonal. The transmitted information gives a measure of this, it is\n\\begin{equation}\n\\tilde{h}=\\frac{1}{n\\ln{20}}\\sum_{ij}N_{ij}\\left(\\ln{N_{ij}}-\\ln{\\sum_k{N_{kj}}}-\\ln{\\sum_k{N_{ik}}}+\\ln {n}\\right).\n\\end{equation}\nwhere $n=\\sum_i\\sum_jN_{ij}$. All sums are from one to 20: the number\nof clusters. The factor of $\\ln{20}$ normalizes $\\tilde{h}$ and so\nthat it takes values between zero and one; a low value corresponds to\npoor clustering and a value near one corresponds to a near-diagonal\nconfusion matrix.\n\n\\begin{figure}\n\n\\begin{center}\n\\setlength{\\unitlength}{0.01575pt}\n\\framebox{\n\\begin{picture}(20999,10500)(0,0)\n\\put(0,700){{0}}\n\\put(10499,25){{$\\tilde{h}$}}\n\\put(20499,700){{1}}\n\\put(500,850){\\line(1,0){4924}}\n\\put(5574,850){\\line(1,0){4849}}\n\\put(10574,850){\\line(1,0){4849}}\n\\put(15574,850){\\line(1,0){4924}}\n\\put(6030,2500){\\line(0,1){300}}\n\\put(6945,2500){\\line(0,1){300}}\n\\put(8182,2500){\\line(0,1){300}}\n\\put(9926,2500){\\line(0,1){300}}\n\\put(9934,2500){\\line(0,1){300}}\n\\put(11429,2500){\\line(0,1){300}}\n\\put(12395,2500){\\line(0,1){300}}\n\\put(13853,2500){\\line(0,1){300}}\n\\put(14254,2500){\\line(0,1){300}}\n\\put(14439,2500){\\line(0,1){300}}\n\\put(14686,2500){\\line(0,1){300}}\n\\put(14946,2500){\\line(0,1){300}}\n\\put(16081,2500){\\line(0,1){300}}\n\\put(16128,2500){\\line(0,1){300}}\n\\put(16837,2500){\\line(0,1){300}}\n\\put(17302,2500){\\line(0,1){300}}\n\\put(17577,2500){\\line(0,1){300}}\n\\put(18511,2500){\\line(0,1){300}}\n\\put(18663,2500){\\line(0,1){300}}\n\\put(19278,2500){\\line(0,1){300}}\n\\put(19838,2500){\\line(0,1){300}}\n\\put(20274,2500){\\line(0,1){300}}\n\\put(20388,2500){\\line(0,1){300}}\n\\put(20496,2500){\\line(0,1){300}}\n\\put(0,2800){{\\bf F}}\n\\put(500,2650){\\line(1,0){4924}}\n\\put(5574,2650){\\line(1,0){4849}}\n\\put(10574,2650){\\line(1,0){4849}}\n\\put(15574,2650){\\line(1,0){4924}}\n\\put(14933,2650){\\line(0,1){450}}\n\\put(14933,2650){\\line(0,-1){450}}\n\\put(7203,3800){\\line(0,1){300}}\n\\put(9090,3800){\\line(0,1){300}}\n\\put(9568,3800){\\line(0,1){300}}\n\\put(12104,3800){\\line(0,1){300}}\n\\put(12860,3800){\\line(0,1){300}}\n\\put(13432,3800){\\line(0,1){300}}\n\\put(14572,3800){\\line(0,1){300}}\n\\put(16247,3800){\\line(0,1){300}}\n\\put(16365,3800){\\line(0,1){300}}\n\\put(16796,3800){\\line(0,1){300}}\n\\put(17102,3800){\\line(0,1){300}}\n\\put(17495,3800){\\line(0,1){300}}\n\\put(18349,3800){\\line(0,1){300}}\n\\put(18843,3800){\\line(0,1){300}}\n\\put(18945,3800){\\line(0,1){300}}\n\\put(19353,3800){\\line(0,1){300}}\n\\put(19497,3800){\\line(0,1){300}}\n\\put(19599,3800){\\line(0,1){300}}\n\\put(19763,3800){\\line(0,1){300}}\n\\put(19947,3800){\\line(0,1){300}}\n\\put(20052,3800){\\line(0,1){300}}\n\\put(20161,3800){\\line(0,1){300}}\n\\put(20496,3800){\\line(0,1){300}}\n\\put(20499,3800){\\line(0,1){300}}\n\\put(0,4100){{\\bf E}}\n\\put(500,3950){\\line(1,0){4924}}\n\\put(5574,3950){\\line(1,0){4849}}\n\\put(10574,3950){\\line(1,0){4849}}\n\\put(15574,3950){\\line(1,0){4924}}\n\\put(16597,3950){\\line(0,1){450}}\n\\put(16597,3950){\\line(0,-1){450}}\n\\put(6049,5100){\\line(0,1){300}}\n\\put(6951,5100){\\line(0,1){300}}\n\\put(7649,5100){\\line(0,1){300}}\n\\put(8878,5100){\\line(0,1){300}}\n\\put(10424,5100){\\line(0,1){300}}\n\\put(12478,5100){\\line(0,1){300}}\n\\put(12600,5100){\\line(0,1){300}}\n\\put(13347,5100){\\line(0,1){300}}\n\\put(14025,5100){\\line(0,1){300}}\n\\put(14745,5100){\\line(0,1){300}}\n\\put(14857,5100){\\line(0,1){300}}\n\\put(15047,5100){\\line(0,1){300}}\n\\put(15980,5100){\\line(0,1){300}}\n\\put(16024,5100){\\line(0,1){300}}\n\\put(16921,5100){\\line(0,1){300}}\n\\put(17125,5100){\\line(0,1){300}}\n\\put(17379,5100){\\line(0,1){300}}\n\\put(18440,5100){\\line(0,1){300}}\n\\put(18663,5100){\\line(0,1){300}}\n\\put(19170,5100){\\line(0,1){300}}\n\\put(19730,5100){\\line(0,1){300}}\n\\put(20161,5100){\\line(0,1){300}}\n\\put(20388,5100){\\line(0,1){300}}\n\\put(20496,5100){\\line(0,1){300}}\n\\put(0,5400){{\\bf D}}\n\\put(500,5250){\\line(1,0){4924}}\n\\put(5574,5250){\\line(1,0){4849}}\n\\put(10574,5250){\\line(1,0){4849}}\n\\put(15574,5250){\\line(1,0){4924}}\n\\put(14897,5250){\\line(0,1){450}}\n\\put(14897,5250){\\line(0,-1){450}}\n\\put(6810,6900){\\line(0,1){300}}\n\\put(7705,6900){\\line(0,1){300}}\n\\put(8680,6900){\\line(0,1){300}}\n\\put(10738,6900){\\line(0,1){300}}\n\\put(11557,6900){\\line(0,1){300}}\n\\put(11812,6900){\\line(0,1){300}}\n\\put(13248,6900){\\line(0,1){300}}\n\\put(14872,6900){\\line(0,1){300}}\n\\put(15103,6900){\\line(0,1){300}}\n\\put(15458,6900){\\line(0,1){300}}\n\\put(15810,6900){\\line(0,1){300}}\n\\put(15952,6900){\\line(0,1){300}}\n\\put(17369,6900){\\line(0,1){300}}\n\\put(17589,6900){\\line(0,1){300}}\n\\put(18284,6900){\\line(0,1){300}}\n\\put(18313,6900){\\line(0,1){300}}\n\\put(18547,6900){\\line(0,1){300}}\n\\put(18935,6900){\\line(0,1){300}}\n\\put(19267,6900){\\line(0,1){300}}\n\\put(19931,6900){\\line(0,1){300}}\n\\put(20055,6900){\\line(0,1){300}}\n\\put(20274,6900){\\line(0,1){300}}\n\\put(20496,6900){\\line(0,1){300}}\n\\put(20499,6900){\\line(0,1){300}}\n\\put(0,7200){{\\bf C}}\n\\put(500,7050){\\line(1,0){4924}}\n\\put(5574,7050){\\line(1,0){4849}}\n\\put(10574,7050){\\line(1,0){4849}}\n\\put(15574,7050){\\line(1,0){4924}}\n\\put(15721,7050){\\line(0,1){450}}\n\\put(15721,7050){\\line(0,-1){450}}\n\\put(6248,8200){\\line(0,1){300}}\n\\put(7545,8200){\\line(0,1){300}}\n\\put(8476,8200){\\line(0,1){300}}\n\\put(10738,8200){\\line(0,1){300}}\n\\put(11095,8200){\\line(0,1){300}}\n\\put(11812,8200){\\line(0,1){300}}\n\\put(13105,8200){\\line(0,1){300}}\n\\put(14587,8200){\\line(0,1){300}}\n\\put(14885,8200){\\line(0,1){300}}\n\\put(15004,8200){\\line(0,1){300}}\n\\put(15578,8200){\\line(0,1){300}}\n\\put(15651,8200){\\line(0,1){300}}\n\\put(17276,8200){\\line(0,1){300}}\n\\put(17369,8200){\\line(0,1){300}}\n\\put(18090,8200){\\line(0,1){300}}\n\\put(18120,8200){\\line(0,1){300}}\n\\put(18293,8200){\\line(0,1){300}}\n\\put(18568,8200){\\line(0,1){300}}\n\\put(18935,8200){\\line(0,1){300}}\n\\put(19838,8200){\\line(0,1){300}}\n\\put(19857,8200){\\line(0,1){300}}\n\\put(20274,8200){\\line(0,1){300}}\n\\put(20496,8200){\\line(0,1){300}}\n\\put(20499,8200){\\line(0,1){300}}\n\\put(0,8500){{\\bf B}}\n\\put(500,8350){\\line(1,0){4924}}\n\\put(5574,8350){\\line(1,0){4849}}\n\\put(10574,8350){\\line(1,0){4849}}\n\\put(15574,8350){\\line(1,0){4924}}\n\\put(15514,8350){\\line(0,1){450}}\n\\put(15514,8350){\\line(0,-1){450}}\n\\put(6218,9500){\\line(0,1){300}}\n\\put(7242,9500){\\line(0,1){300}}\n\\put(8200,9500){\\line(0,1){300}}\n\\put(9985,9500){\\line(0,1){300}}\n\\put(10102,9500){\\line(0,1){300}}\n\\put(11812,9500){\\line(0,1){300}}\n\\put(12659,9500){\\line(0,1){300}}\n\\put(14064,9500){\\line(0,1){300}}\n\\put(14141,9500){\\line(0,1){300}}\n\\put(14812,9500){\\line(0,1){300}}\n\\put(14850,9500){\\line(0,1){300}}\n\\put(15196,9500){\\line(0,1){300}}\n\\put(16686,9500){\\line(0,1){300}}\n\\put(16925,9500){\\line(0,1){300}}\n\\put(17279,9500){\\line(0,1){300}}\n\\put(17515,9500){\\line(0,1){300}}\n\\put(17908,9500){\\line(0,1){300}}\n\\put(17965,9500){\\line(0,1){300}}\n\\put(18935,9500){\\line(0,1){300}}\n\\put(19745,9500){\\line(0,1){300}}\n\\put(19832,9500){\\line(0,1){300}}\n\\put(20274,9500){\\line(0,1){300}}\n\\put(20496,9500){\\line(0,1){300}}\n\\put(20499,9500){\\line(0,1){300}}\n\\put(0,9800){{\\bf A}}\n\\put(500,9650){\\line(1,0){4924}}\n\\put(5574,9650){\\line(1,0){4849}}\n\\put(10574,9650){\\line(1,0){4849}}\n\\put(15574,9650){\\line(1,0){4924}}\n\\put(15139,9650){\\line(0,1){450}}\n\\put(15139,9650){\\line(0,-1){450}}\n\\end{picture}\n}\n\\end{center}\n\n\\caption{Performance as $p$ changes. {\\bf A}, {\\bf B} and {\\bf C}\n  correspond to $p=1$, $p=2$ and $p=10$. Each horizontal line runs\n  from zero to one. For clarity, there are tiny gaps at 0.25, 0.5 and\n  0.75. Each small vertical dash marks the $\\tilde{h}$ value for one\n  site where for each site the optimal value of $q$ is used. The large\n  vertical dash marks the average, 0.732, 0.751 and 0.761\n  respectively. To indicate the range over which $\\tilde{h}$ values\n  vary, two other metrics are plotted for comparison. ${\\bf D}$\n  corresponds to the van Rossum metric \\cite{vanRossum2001a}, with\n  each site using its optimal value of $\\tau$. ${\\bf E}$ corresponds\n  to the synapse metric, with each site using its optimal value of\n  $\\tau$ and $\\mu$ \\cite{Houghton2007a}. Finally, ${\\bf F}$\n  corresponds to the $L^1$ van Rossum metric, with a boxcar filter;\n  this metric measures a very similar distance to the $p=1$ metric\n  \\cite{HoughtonSen2006a}.\\label{Results}}\n\\end{figure}\n\n\nThe main purpose of this comment is to evaluate the $\\mathcal{L}_p$\nVictor-Purpura metric by calculating $\\tilde{h}$ for the zebra finch\ndata previous used to evaluate other spike train metrics\n\\cite{Houghton2007a,HoughtonVictor2009a}. The data set contains 24\nsets of spike trains, corresponding to 24 recording sites from\nmultiple birds. Although the songs themselves are of different\nlengths, all of the songs are at least a second long and, in each\ncase, the spike train is truncated to one second, starting at song\nonset.\n\n\\begin{figure}\n\\begin{center}\n\n\\setlength{\\unitlength}{0.240900pt}\n\\ifx\\plotpoint\\undefined\\newsavebox{\\plotpoint}\\fi\n\\sbox{\\plotpoint}{\\rule[-0.200pt]{0.400pt}{0.400pt}}%\n\\begin{picture}(900,540)(0,0)\n\\sbox{\\plotpoint}{\\rule[-0.200pt]{0.400pt}{0.400pt}}%\n\\put(140,197){\\makebox(0,0)[r]{ 0.74}}\n\\put(160.0,197.0){\\rule[-0.200pt]{4.818pt}{0.400pt}}\n\\put(140,341){\\makebox(0,0)[r]{ 0.75}}\n\\put(160.0,341.0){\\rule[-0.200pt]{4.818pt}{0.400pt}}\n\\put(140,485){\\makebox(0,0)[r]{ 0.76}}\n\\put(160.0,485.0){\\rule[-0.200pt]{4.818pt}{0.400pt}}\n\\put(160,41){\\makebox(0,0){ 1}}\n\\put(160.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(235,41){\\makebox(0,0){ 2}}\n\\put(235.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(311,41){\\makebox(0,0){ 3}}\n\\put(311.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(386,41){\\makebox(0,0){ 4}}\n\\put(386.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(462,41){\\makebox(0,0){ 5}}\n\\put(462.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(537,41){\\makebox(0,0){ 6}}\n\\put(537.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(613,41){\\makebox(0,0){ 7}}\n\\put(613.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(688,41){\\makebox(0,0){ 8}}\n\\put(688.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(764,41){\\makebox(0,0){ 9}}\n\\put(764.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(839,41){\\makebox(0,0){ 10}}\n\\put(839.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(160.0,82.0){\\rule[-0.200pt]{0.400pt}{100.696pt}}\n\\put(160.0,82.0){\\rule[-0.200pt]{163.571pt}{0.400pt}}\n\\put(160,82){\\usebox{\\plotpoint}}\n\\multiput(160.58,82.00)(0.498,2.412){73}{\\rule{0.120pt}{2.016pt}}\n\\multiput(159.17,82.00)(38.000,177.816){2}{\\rule{0.400pt}{1.008pt}}\n\\multiput(198.58,264.00)(0.498,1.181){71}{\\rule{0.120pt}{1.041pt}}\n\\multiput(197.17,264.00)(37.000,84.840){2}{\\rule{0.400pt}{0.520pt}}\n\\multiput(235.58,351.00)(0.498,0.565){73}{\\rule{0.120pt}{0.553pt}}\n\\multiput(234.17,351.00)(38.000,41.853){2}{\\rule{0.400pt}{0.276pt}}\n\\multiput(273.58,394.00)(0.498,0.565){73}{\\rule{0.120pt}{0.553pt}}\n\\multiput(272.17,394.00)(38.000,41.853){2}{\\rule{0.400pt}{0.276pt}}\n\\multiput(311.00,437.59)(4.161,0.477){7}{\\rule{3.140pt}{0.115pt}}\n\\multiput(311.00,436.17)(31.483,5.000){2}{\\rule{1.570pt}{0.400pt}}\n\\multiput(349.00,442.58)(0.560,0.497){63}{\\rule{0.548pt}{0.120pt}}\n\\multiput(349.00,441.17)(35.862,33.000){2}{\\rule{0.274pt}{0.400pt}}\n\\multiput(386.00,475.58)(3.935,0.491){17}{\\rule{3.140pt}{0.118pt}}\n\\multiput(386.00,474.17)(69.483,10.000){2}{\\rule{1.570pt}{0.400pt}}\n\\multiput(462.00,485.59)(4.918,0.488){13}{\\rule{3.850pt}{0.117pt}}\n\\multiput(462.00,484.17)(67.009,8.000){2}{\\rule{1.925pt}{0.400pt}}\n\\multiput(537.00,493.59)(6.819,0.482){9}{\\rule{5.167pt}{0.116pt}}\n\\multiput(537.00,492.17)(65.276,6.000){2}{\\rule{2.583pt}{0.400pt}}\n\\put(613,498.67){\\rule{18.067pt}{0.400pt}}\n\\multiput(613.00,498.17)(37.500,1.000){2}{\\rule{9.034pt}{0.400pt}}\n\\put(688.0,500.0){\\rule[-0.200pt]{36.376pt}{0.400pt}}\n\\put(160.0,82.0){\\rule[-0.200pt]{0.400pt}{100.696pt}}\n\\put(160.0,82.0){\\rule[-0.200pt]{163.571pt}{0.400pt}}\n\\end{picture}\n\n\n\\end{center}\n\\caption{The average performance plotted against $p$.\n  $\\tilde{h}$ has been calculated for a range of $p$ values using the\n  optimal value of $q$ for each site and the average value of\n  $\\tilde{h}$ is plotted against $p$.\\label{p}}\n\\end{figure}\n\nThe performance of the $\\mathcal{L}_p$ Victor-Purpura metric is\nillustrated in Fig.~\\ref{Results}. A remarkable feature is that\n$\\tilde{h}$ rarely decreases as $p$ is increased. Other\nmulti-parameter metrics show a mixed effect; although changing a\nparameter might increase the average $\\tilde{h}$ across the sites,\nthere will typically be many individual sites where $\\tilde{h}$\ndecreases. In the case of $p$, while the average improvement as $p$\nincreases is modest and a small number of sites show no change; there\nis no site where the clustering is negatively affected when $p$ is\nchanged from one to two, three do show a tiny decrease between $p=1$\nand $p=1.5$. $\\tilde{h}$ increases for 19 sites between $p=1$ and\n$p=2$ and for 15 between $p=2$ and $p=3$, the improvement gets less\nand less and appears to have plateaued by $p=10$. The average\nperformance is plotted against $p$ in Fig.~{p}. The optimal value of\n$q$ does not vary significantly as $p$ changes; however, the range of\n$q$ that produces the optimal performance does get wider.\n\n\\section{Discussion}\n\n\nIt is interesting to compare this metric to another generalization of\nthe Victor-Purpura metric\n\\cite{VictorPurpura1996a,VictorPurpura1997a}. The linear distance\nfunction $q\\delta t$ can be replaced by any convex function,\n$f(|\\delta t|)$, of distance:\n\\begin{equation}\nc_{\\gamma;f(\\cdot)}({\\bf u},{\\bf v})=|\\alpha|+\\sum_{(u,v)\\in\\mu} f(|u-v|).\n\\end{equation}\nThe distance function $f(|\\delta t|)$ must be convex to ensure that\nthe triangular inequality is satisfied. Now, the function $q^p\\delta\nt^p$ in $c_{\\gamma;q,p}$ above is concave for $p>1$. However, because\nof the $1\/p$ exponent in $d({\\bf u},{\\bf v};q,p)$, this does not cause\nthe same difficulty with the triangular inequality: an interesting\nproperty of the ${\\mathcal L}_p$ metrics is that they satisfy the\ntriangular inequality despite having a concave distance function.\n\nAs $p$ is increased, $q^p|\\delta t|^p$ becomes increasingly concave\nand spikes located at similar times contribute less and less to the\ntotal cost and this cost is predominately made up of the cost of\nadding and deleting spikes that are not related by jitter. This means\nthat the metric performs more and more as a windowed coincidence\ndetector as $p$ increases. The fact that it is always beneficial to\nincrease $p$ appears to imply that, for these data, coincidence and\ncoincidence detection has a role in the encoding and decoding of\ncontent in spike trains.\n\n\\begin{figure}\n\\begin{center}\n\\setlength{\\unitlength}{0.24pt}\n\\ifx\\plotpoint\\undefined\\newsavebox{\\plotpoint}\\fi\n\\begin{picture}(1200,720)(0,0)\n\\sbox{\\plotpoint}{\\rule[-0.200pt]{0.400pt}{0.400pt}}%\n\\put(330,232){\\makebox(0,0)[r]{ 0.25}}\n\\put(350.0,232.0){\\rule[-0.200pt]{4.818pt}{0.400pt}}\n\\put(330,381){\\makebox(0,0)[r]{ 0.5}}\n\\put(350.0,381.0){\\rule[-0.200pt]{4.818pt}{0.400pt}}\n\\put(330,531){\\makebox(0,0)[r]{ 0.75}}\n\\put(350.0,531.0){\\rule[-0.200pt]{4.818pt}{0.400pt}}\n\\put(330,680){\\makebox(0,0)[r]{ 1}}\n\\put(350.0,680.0){\\rule[-0.200pt]{4.818pt}{0.400pt}}\n\\put(500,41){\\makebox(0,0){ 0.25}}\n\\put(500.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(649,41){\\makebox(0,0){ 0.5}}\n\\put(649.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(799,41){\\makebox(0,0){ 0.75}}\n\\put(799.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(948,41){\\makebox(0,0){ 1}}\n\\put(948.0,82.0){\\rule[-0.200pt]{0.400pt}{4.818pt}}\n\\put(350.0,82.0){\\rule[-0.200pt]{0.400pt}{144.058pt}}\n\\put(350.0,82.0){\\rule[-0.200pt]{144.058pt}{0.400pt}}\n\n\\put(889,633){\\line(1,0){8}}\n\\put(816,566){\\line(1,0){8}}\n\\put(911,657){\\line(1,0){8}}\n\\put(632,366){\\line(1,0){8}}\n\\put(945,680){\\line(1,0){8}}\n\\put(817,573){\\line(1,0){8}}\n\\put(893,604){\\line(1,0){8}}\n\\put(838,603){\\line(1,0){8}}\n\\put(774,511){\\line(1,0){8}}\n\\put(782,510){\\line(1,0){8}}\n\\put(861,584){\\line(1,0){8}}\n\\put(632,369){\\line(1,0){8}}\n\\put(749,488){\\line(1,0){8}}\n\\put(580,312){\\line(1,0){8}}\n\\put(515,253){\\line(1,0){8}}\n\\put(852,591){\\line(1,0){8}}\n\\put(761,521){\\line(1,0){8}}\n\\put(948,680){\\line(1,0){8}}\n\\put(706,420){\\line(1,0){8}}\n\\put(941,673){\\line(1,0){8}}\n\\put(928,660){\\line(1,0){8}}\n\\put(543,284){\\line(1,0){8}}\n\\put(767,490){\\line(1,0){8}}\n\\put(677,446){\\line(1,0){8}}\n\n\\put(889,633){\\line(-1,0){8}}\n\\put(816,566){\\line(-1,0){8}}\n\\put(911,657){\\line(-1,0){8}}\n\\put(632,366){\\line(-1,0){8}}\n\\put(945,680){\\line(-1,0){8}}\n\\put(817,573){\\line(-1,0){8}}\n\\put(893,604){\\line(-1,0){8}}\n\\put(838,603){\\line(-1,0){8}}\n\\put(774,511){\\line(-1,0){8}}\n\\put(782,510){\\line(-1,0){8}}\n\\put(861,584){\\line(-1,0){8}}\n\\put(632,369){\\line(-1,0){8}}\n\\put(749,488){\\line(-1,0){8}}\n\\put(580,312){\\line(-1,0){8}}\n\\put(515,253){\\line(-1,0){8}}\n\\put(852,591){\\line(-1,0){8}}\n\\put(761,521){\\line(-1,0){8}}\n\\put(948,680){\\line(-1,0){8}}\n\\put(706,420){\\line(-1,0){8}}\n\\put(941,673){\\line(-1,0){8}}\n\\put(928,660){\\line(-1,0){8}}\n\\put(543,284){\\line(-1,0){8}}\n\\put(767,490){\\line(-1,0){8}}\n\\put(677,446){\\line(-1,0){8}}\n\n\\put(889,633){\\line(1,0){8}}\n\\put(816,593){\\line(1,0){8}}\n\\put(911,663){\\line(1,0){8}}\n\\put(632,413){\\line(1,0){8}}\n\\put(945,680){\\line(1,0){8}}\n\\put(817,586){\\line(1,0){8}}\n\\put(893,643){\\line(1,0){8}}\n\\put(838,615){\\line(1,0){8}}\n\\put(774,519){\\line(1,0){8}}\n\\put(782,544){\\line(1,0){8}}\n\\put(861,614){\\line(1,0){8}}\n\\put(632,388){\\line(1,0){8}}\n\\put(749,512){\\line(1,0){8}}\n\\put(580,327){\\line(1,0){8}}\n\\put(515,271){\\line(1,0){8}}\n\\put(852,622){\\line(1,0){8}}\n\\put(761,540){\\line(1,0){8}}\n\\put(948,680){\\line(1,0){8}}\n\\put(706,420){\\line(1,0){8}}\n\\put(941,673){\\line(1,0){8}}\n\\put(928,667){\\line(1,0){8}}\n\\put(543,297){\\line(1,0){8}}\n\\put(767,529){\\line(1,0){8}}\n\\put(677,463){\\line(1,0){8}}\n\n\\put(889,633){\\line(-1,0){8}}\n\\put(816,593){\\line(-1,0){8}}\n\\put(911,663){\\line(-1,0){8}}\n\\put(632,413){\\line(-1,0){8}}\n\\put(945,680){\\line(-1,0){8}}\n\\put(817,586){\\line(-1,0){8}}\n\\put(893,643){\\line(-1,0){8}}\n\\put(838,615){\\line(-1,0){8}}\n\\put(774,519){\\line(-1,0){8}}\n\\put(782,544){\\line(-1,0){8}}\n\\put(861,614){\\line(-1,0){8}}\n\\put(632,388){\\line(-1,0){8}}\n\\put(749,512){\\line(-1,0){8}}\n\\put(580,327){\\line(-1,0){8}}\n\\put(515,271){\\line(-1,0){8}}\n\\put(852,622){\\line(-1,0){8}}\n\\put(761,540){\\line(-1,0){8}}\n\\put(948,680){\\line(-1,0){8}}\n\\put(706,420){\\line(-1,0){8}}\n\\put(941,673){\\line(-1,0){8}}\n\\put(928,667){\\line(-1,0){8}}\n\\put(543,297){\\line(-1,0){8}}\n\\put(767,529){\\line(-1,0){8}}\n\\put(677,463){\\line(-1,0){8}}\n\n\n\n\\put(889,633){\\line(0,1){4}}\n\\put(816,593){\\line(0,1){4}}\n\\put(911,663){\\line(0,1){4}}\n\\put(632,413){\\line(0,1){4}}\n\\put(945,680){\\line(0,1){4}}\n\\put(817,586){\\line(0,1){4}}\n\\put(893,643){\\line(0,1){4}}\n\\put(838,615){\\line(0,1){4}}\n\\put(774,519){\\line(0,1){4}}\n\\put(782,544){\\line(0,1){4}}\n\\put(861,614){\\line(0,1){4}}\n\\put(632,388){\\line(0,1){4}}\n\\put(749,512){\\line(0,1){4}}\n\\put(580,327){\\line(0,1){4}}\n\\put(515,271){\\line(0,1){4}}\n\\put(852,622){\\line(0,1){4}}\n\\put(761,540){\\line(0,1){4}}\n\\put(948,680){\\line(0,1){4}}\n\\put(706,420){\\line(0,1){4}}\n\\put(941,673){\\line(0,1){4}}\n\\put(928,667){\\line(0,1){4}}\n\\put(543,297){\\line(0,1){4}}\n\\put(767,529){\\line(0,1){4}}\n\\put(677,463){\\line(0,1){4}}\n\n\n\\put(889,633){\\line(0,-1){4}}\n\\put(816,566){\\line(0,-1){4}}\n\\put(911,657){\\line(0,-1){4}}\n\\put(632,366){\\line(0,-1){4}}\n\\put(945,680){\\line(0,-1){4}}\n\\put(817,573){\\line(0,-1){4}}\n\\put(893,604){\\line(0,-1){4}}\n\\put(838,603){\\line(0,-1){4}}\n\\put(774,511){\\line(0,-1){4}}\n\\put(782,510){\\line(0,-1){4}}\n\\put(861,584){\\line(0,-1){4}}\n\\put(632,369){\\line(0,-1){4}}\n\\put(749,488){\\line(0,-1){4}}\n\\put(580,312){\\line(0,-1){4}}\n\\put(515,253){\\line(0,-1){4}}\n\\put(852,591){\\line(0,-1){4}}\n\\put(761,521){\\line(0,-1){4}}\n\\put(948,680){\\line(0,-1){4}}\n\\put(706,420){\\line(0,-1){4}}\n\\put(941,673){\\line(0,-1){4}}\n\\put(928,660){\\line(0,-1){4}}\n\\put(543,284){\\line(0,-1){4}}\n\\put(767,490){\\line(0,-1){4}}\n\\put(677,446){\\line(0,-1){4}}\n\n\n\n\n\n\n\\sbox{\\plotpoint}{\\rule[-0.400pt]{0.800pt}{0.800pt}}%\n\\put(350,82){\\usebox{\\plotpoint}}\n\\put(352,82){\\line(1,1){600}}\n\n\\put(677,446){\\line(0,1){17}}\n\\put(767,490){\\line(0,1){39}}\n\\put(543,284){\\line(0,1){13}}\n\\put(706,420){\\line(0,1){1}}\n\\put(928,660){\\line(0,1){7}}\n\\put(941,673){\\line(0,1){1}}\n\\put(948,680){\\line(0,1){1}}\n\\put(761,521){\\line(0,1){19}}\n\\put(852,591){\\line(0,1){31}}\n\\put(515,253){\\line(0,1){18}}\n\\put(580,312){\\line(0,1){15}}\n\\put(749,488){\\line(0,1){24}}\n\\put(632,369){\\line(0,1){19}}\n\\put(861,584){\\line(0,1){30}}\n\\put(782,510){\\line(0,1){34}}\n\\put(774,511){\\line(0,1){8}}\n\\put(838,603){\\line(0,1){12}}\n\\put(893,604){\\line(0,1){39}}\n\\put(817,573){\\line(0,1){13}}\n\\put(945,680){\\line(0,1){1}}\n\\put(632,366){\\line(0,1){47}}\n\\put(911,657){\\line(0,1){6}}\n\\put(816,566){\\line(0,1){27}}\n\\put(889,633){\\line(0,1){1}}\n\n\\sbox{\\plotpoint}{\\rule[-0.200pt]{0.400pt}{0.400pt}}%\n\\put(350.0,82.0){\\rule[-0.200pt]{0.400pt}{144.058pt}}\n\\put(350.0,82.0){\\rule[-0.200pt]{144.058pt}{0.400pt}}\n\\end{picture}\n\n\n\\end{center}\n\\caption{Comparing the $L^1$ boxcar van Rossum metric with the $p=1$\n  and $p=10$ ${\\mathcal L}_p$ metrics. Here $\\tilde{h}$ values for the\n  $p=1$ and $p=10$ metrics are graphed against the values for the\n  $L^1$ van Rossum metric with a boxcar filter with optimal values of\n  the $q$ or $\\tau$ parameter has been used for each site. The $p=1$\n  and $p=10$ values are marked by a horizontal line, the two values\n  for a given site are joined by a vertical line. Since increasing $p$\n  never decreases $\\tilde{h}$ between $p=1$ and $p=10$, the topmost of\n  the two horizontal lines corresponds to $p=10$. The \\lq{}x=y\\rq{}\n  line is also plotted for clarity.\\label{Compare}}\n\\end{figure}\n\nThe pairing of near coincident spikes is the key distinction between\nthe Victor-Purpura metrics and the van Rossum metrics, a family of\nspike train metrics which are calculated by comparing reconstructed\nrate functions. In fact, computationally, an $L^1$ van Rossum metric\nwith a boxcar filter measures a very similar distance to the\nVictor-Purpura metric \\cite{HoughtonSen2006a} and, as seen in\nFig.~\\ref{Compare}, has a very similar performance. The way in which\n${\\mathcal L}_p$ Victor-Purpura metric performance increased with $p$\nseems to indicate that the significant temporal structure of spikes is\nnot fully accounted for by the temporal structure of a spike rate.\n\n\\section*{Acknowledgments}\nC.H. is supported by Science Foundation Ireland grant\n08\/RFP\/MTH1280. He thanks Kamal Sen for the use of the zebra finch\ndata analyzed here and Jonathan Victor for comments on an early draft\nof this comment.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\\section{Introduction}\n\n\n\\par Unsupervised learning has long been an intriguing field in artificial intelligence. Human and animal learning is largely unsupervised: we discover the structure of the world mostly by observing it, not by being told the name of every object, which would correspond to supervised learning \\cite{lecun15nature}. \nA system capable of predicting what is going to happen by just watching large collections of unlabeled video data needs to build an internal representation of the world and its dynamics \\cite{mathieu2015deep}. When considering the vast amount of unlabeled data generated every day, unsupervised learning becomes one of the key challenges to solve in the road towards general artificial intelligence.\n\nBased on how a human would provide a high level summary of a video, we hypothesize that there are three key components to understand such content: namely \\textit{foreground}, \\textit{motion} and \\textit{background}. These three elements would tell us, respectively, what the main objects in the video are, what they are doing and where their location. We propose a framework that explicitly disentangles these three components in order to build strong features for action recognition, where the supervision signals can be generated without requiring from expensive and time consuming human annotations.\nThe proposal is inspired by how infants who have no prior visual knowledge tend to group things that move as connected wholes and also move separately from one another \\cite{elizabeth90cognitivemotion}. Based on this intuition, we can build a similar unsupervised pipeline to segment foreground and background with global motion, i.e. the rough moving directions of objects. Such segmented foregrounds across the video can be used to model both the global motion (e.g.~transition or stretch) and local motion (i.e.~transformation of detailed appearance) from a pair of foregrounds at different time steps. \nSince background motion is mostly given by camera movements, we restrict the use of motion to the foreground and rely on appearance to model the former.\n\nThe contributions of this work are two-fold: (1) disentangling motion, foreground and background features in videos by human alike motion aware mechanism and (2) learning strong video features that improve the performance of action recognition task. \n\n\n\n\\section{Related Work}\n\n\n\n\n\n\n\nLeveraging large collections of unlabeled videos has proven beneficial for unsupervised training of image models thanks to the implicit properties they exhibit in the temporal domain, e.g. visual similarity between patches in consecutive frames \\cite{wang2015unsupervised} and temporal coherence and order \\cite{misra2016shuffle}. Since learning to predict future frames forces the model to construct an internal representation of the world dynamics, several works have addressed such task by predicting global features of future frames with Recurrent Neural Networks (RNN) \\cite{srivastava2015unsupervised} or pixel level predictions by means of multi-scale Convolutional Neural Networks (CNN) trained with an adversarial loss \\cite{mathieu2015deep}. The key role played by motion has been exploited for future frame prediction tasks by explicitly decomposing content and motion \\cite{villegas2017decomposing} and for unsupervised training of video-level models \\cite{luo2017motionprediction}. Similarly in spirit, separate foreground and background streams have been found to increase the quality of generative video models \\cite{vondrick2016generating}.\n\nTechniques exploiting explicit foreground and background segmentations in video generally require from expensive annotation methods, limiting their application to labeled data. However, the findings by Pathak et al. \\cite{pathak2017learning} show how models trained on noisy annotations learn to generalize and perform well when finetuned for other tasks. Such noisy annotations can be generated by unsupervised methods, thus alleviating the cost of annotating data for the target task. In this work we study our proposed method by using manual annotations, whereas evaluating the performance drop when replacing such annotations with segmentations generated in an unsupervised manner remains as future work.\n\n\n\n\n\n\n\\section{Methodology}\n\n\\begin{figure*}[ht]\n\\centering\n\\includegraphics[width=\\linewidth]{.\/figs\/architecture.pdf}\\\\\n\\caption{System architecture. Please note that in this work, the masks used to generate ground truth are from manual annotations while uNLC will be utilized in our future work.}\n\\label{fig:architecture}\n\\end{figure*}\n\n\nWe adopt an autoencoder-styled architecture to learn features in an unsupervised manner.  The encoder maps input clips \nto feature tensors \nby applying a series of 3D convolutions and max-pooling operations \\cite{du2015c3d}. Unlike traditional autoencoder architectures, the bottleneck features are partitioned into three splits which are then used as input for three different reconstruction tasks, as depicted in Figure \\ref{fig:architecture}.\n\n\\textbf{Disentangling of foreground and background:} depending on the nature of the training data, reconstruction of frames may become dominated either by the foreground or background.  We explicitly split the reconstruction task to guarantee that none of the parts dominates over the other. Partitioned foreground and background features will be passed into two different decoders for reconstruction. While segmentation masks are often obtained by manual labeling, it is worth noting they can be obtained without supervision as well, e.g. by using methods based on motion perceptual grouping such as uNLC \\cite{pathak2017learning}. The latter approach has proven beneficial for unsupervised pre-training of CNNs \\cite{pathak2017learning}.\n\n\\textbf{Disentangling of foreground motion:} leveraging motion information can provide a boost in action recognition performance when paired with appearance models \\cite{simonyan2014two}. We encourage the model to learn motion-related representations by solving a predictive learning task where the foreground in the last frame needs to be reconstructed from the foreground in the first frame. Given a pair of foregrounds at timesteps $t_1$ and $t_2$, namely $\\left(f_{t_{1}}, f_{t_{2}} \\right)$, we aim to estimate a function $M$ from motion features $m_{t_1\\rightarrow t_2}$ throughout $t_1$ and $t_2$ that maps $f_{t_{_1}}$ to $f_{t_{2}}$ in deep feature space $G$: \n\n\\begin{equation}\nG \\left( f_{t_{2}} \\right) = M \\left( G(f_{t_{1}}), m_{t_1 \\rightarrow t_2} \\right)\n\\end{equation}\n\nThroughout this work, the space of encoded features is used for $G$, and $M$ is parametrized by a deterministic version of cross convolution \\cite{visualdynamics16}. The foreground decoder weights are shared among all foreground reconstruction task. Gradients coming from the reconstruction of $f_{t_{2}}$ are blocked from backpropagating through $G( f_{t_{1}})$ during training to prevent $G( f_{t_{1}})$ from storing information about $f_{t_{2}}$.\n\n\n\\textbf{Frame selection:} assuming that the background semantics stay close throughout the short clips, only the background in the first frame is reconstructed. First and last frames are chosen to perform foreground reconstruction, since they represent the most challenging pair in the clip.\n\n\\textbf{Loss function:} the model is optimized to minimize the L1 loss between the original frames and their reconstruction. In particular, the loss function is defined from a decomposition of the input video volume $x$ of $T$ frames into the foreground $x_{fg}$ and background $x_{bg}$ volumes:\n\n\\begin{equation}\n\\begin{split}\nx_{fg} = x \\cdot b_{fg} \\\\\nx_{bg} = x \\cdot (1- b_{fg})\n\\end{split}\n\\end{equation}\n\nwhere $b_{fg}$ corresponds to a volume of binary values, so that $1$ correspond to foreground pixels and $0$ to the background ones.\n\nThis decomposition allows defining the reconstruction loss $L_{rec}(x)$ over the video volume $x$ as the sum of three terms:\n\n\\begin{equation}\n\\label{eq:loss}\nL_{rec}(x) = L^{1}_{fg}(x) + L^{1}_{bg}(x) + L^{T}_{fg}(x)\n\\end{equation}\n\nwhere the components $L^{1}_{fg}$, $L^{1}_{bg}$ and $L^{T}_{fg}$ represent the reconstruction loss for the first foreground and first background , and last foreground , respectively. These three terms are particularizations at the first ($t=1$) and last ($t=T$) frames of the generic foreground $L^{t}_{fg}(x)$ and background $L^{t}_{bg}(x)$ reconstructions losses:\n\n\\begin{equation}\nL^{t}_{fg}(x) = \\frac{1}{A^t}\\sum_{i,j}{W^t[i,j] \\cdot \\left|\\hat{x}^{t}_{fg}[i,j] - x_{fg}[i,j,t]\\right|}\n\\end{equation}\n\\begin{equation}\nL^{t}_{bg}(x) = \\frac{1}{A^t}\\sum_{i,j}{\\left|\\hat{x}^t_{bg}[i,j] - x_{bg}[i,j,t]\\right|}\n\\end{equation}\n\nwhere $\\hat{x}^t$ denotes a reconstructed foreground\/ background at time $t$, $A^t$ is the area of the reconstructed frame at time $t$, and $W^t$ is an element-wise weighting mask at time $t$ designed to leverage the focus between the foreground and background pixels:\n\n\\begin{equation}\nW^{t}[i,j]= \n\\begin{cases}\n1 & \\text{if } (i,j) \\in \\text{background}\\\\\n\\max\\left[ 1, \\frac{A^t_{bg}}{A^t_{fg}} \\right] & \\text{if } (i,j) \\in \\text{foreground}\n\\end{cases}\n\\end{equation}\n\n\n\n\n\n\n\n\n\n\n\n\nDuring preliminary experiments, we observed that the reconstruction of the first foreground always outperformed the reconstruction of the last one by a large margin, given the increased difficulty of the latter task. In order to get finer reconstruction of the last foreground, we introduce an L2 loss $L_{feat}$ on $G(f{t_{2}})$. The pseudo ground truth for this task is obtained by getting first foreground features from the encoder fed with the temporally reversed clip. The final loss to optimize is the following:\n\n\\begin{equation}\nL_{total}(x) = L_{rec}(x) + L_{feat}(x) \n\\end{equation}\n\n\n\\section{Experimental setup}\nPlease note again we are showing results trained with ground truth masks to check the feasibility of our proposal and the pure unsupervised framework generating masks from uNLC \\cite{pathak2017learning} remains as future work.\n\n\\textbf{Dataset:} there are 24 classes out of 101 in UCF-101 with localization annotations \\cite{UCF101,THUMOS15}. Following \\cite{pathak2017learning}, we first evaluate the proposed framework with supervised annotations and use the bounding boxes in the subset of UCF-101 for such purpose. Evaluating the proposal in weak annotations collected by means of unsupervised methods remains as future work. We follow the original splits of training and test set and also split 10\\% videos out of the training set as validation set in order to perform early stopping and prevent the network from overfitting the training data.\n\n\\textbf{Training details:} videos are split into clips of 16 frames each. These clips are then resized to $128\\times128$ and their pixel values are scaled and shift to $[ -1, 1]$. The clips are randomly temporally or horizontally flipped for data augmentation. Weight decay with rate of $10^{-3}$ is added as regularization. The network is trained for 125 epochs with Adam optimizer and a learning rate of $10^{-4}$ on batches of 40 clips.\n\n\\section{Results}\n\n\\begin{figure*}[ht]\n\\centering\n\\includegraphics[width=\\linewidth]{.\/figs\/results.pdf}\\\\\n\\caption{Reconstruction results on the test set. For each example, the top row shows the reconstruction while the bottom one contains the ground truth. Each column shows the segmentation of foreground in first frame, background in first frame and foreground in last frame, respectively.}\n\\label{fig:recon_results}\n\\end{figure*}\n\nWe tested our model on test set for reconstruction task. For better demonstrating the efficiency of our proposed pretraining pipeline, we also trained the network to do action recognition with pretrained features.\n\n\\textbf{Reconstruction task:} reconstruction results on test set are shown in Figure \\ref{fig:recon_results}. From these results, we can clearly see that the network already can predict similar foreground segmentation as ground truth. However, the image reconstructions are still blurry. We argue that this is due to the properties of the L1 loss we are adopting \\cite{mathieu2015deep}. One interesting fact is that the network has learned to generalize foreground to some other moving objects in the scene even though they are not included in the annotations. For example, the result shown in the top-right corner: instead of only segmenting the person, the dog walking beside the person is also included. This fact suggests that the network has successfully learned to identify foreground from motion cues.\n\nBesides from foreground and background features, these results also demonstrate a good extraction of motion features. The learned motion features contain both global motions, e.g.~transition of foreground, and local motions, e.g.~change of human pose. In the bottom-center result, the generated kernels from motion feature successfully shift the object from right to the middle and change its gesture.\n\n\\textbf{Action recognition:} a good pretraining pipeline should show better performance on some typical discriminative tasks than random initialization, especially when training data is scarce \\cite{misra2016shuffle,luo2017motionprediction,pathak2017learning,vondrick2016generating,wang2015unsupervised}. We also conducted comparative experiments on the task of action recognition. By discarding the decoders in our framework and training a linear softmax layer on top of the disentangled features, we can obtain a simple network for action recognition. For the first experiment, we first pretrain our encoder on the subset of UCF-101 with the settings discussed above and then fine-tune the whole action recognition network with added softmax layer on the same subset. As baselines, we trained another two action recognition networks, one with all weights initialized randomly and another one pretrained with an unsupervised autoencoder architecture. This autoencoder shared the same 3D convolutional encoder architecture with ours, while its decoder was the mirrored version of the encoder but replacing the pooling operations with convolutions.\n\nDuring training, we observed that our pretrained model reached 90\\% accuracy on training set immediately after one epoch while the randomly initialized network took 130 epochs to achieve it. All three models reached around 96\\% accuracy at the end of training and encountered severe overfitting problems. The accuracy of different methods on the validation set during training time is shown in Figure \\ref{fig:val_results}. The best accuracy obtained on the test set with our pretrained model is 62.5\\%, while it drops to 52.2\\% and 56.8\\% respectively when using a random initialization and autoencoder as pretraining scheme, as shown in Table \\ref{tab:test_acc}. We observe a margin of more than 10\\% on accuracy between our proposed method and random initialization on both validation set and test set. This further demonstrates that with our proposal, the network can learn features that generalize better. These results are specially promising given the small amount of data used during pretraining, which is just a fraction of UCF-101. While this demonstrates the efficiency of the approach, using a larger dataset for pretraining should provide additional gains and better generalization capabilities. \n\n\n\n\\begin{table}\n  \\centering\n  \\caption{Action recognition accuracy of different methods on the test subset of UCF-101.}\n  \\label{tab:test_acc}\n  \\resizebox{0.6\\linewidth}{!}{\n    \\begin{tabular}{cc}\n      \\toprule\n      \\textbf{Method}  & \\textbf{Accuracy}  \\\\ \n      \\midrule\n      Random initialization & 52.2\\%  \\\\ \n      \\midrule\n      Pretrained (autoencoder) & 56.8\\%  \\\\ \n      \\midrule\n      Pretrained (ours)  & \\textbf{62.5\\%}  \\\\\n      \\bottomrule\n    \\end{tabular}\n  }\n\\end{table}\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=\\linewidth]{.\/figs\/val_figure.png}\\\\\n\\caption{Action recognition results on validation set. This figure shows the accuracy of each method on validation set during the training time.}\n\\label{fig:val_results}\n\\end{figure}\n\n\n\n\\section{Conclusions}\n\nThis work has proposed a novel framework towards an unsupervised learning of video features capable of disentangling of motion, foreground and background.\nOur method mostly exploits motion in videos and is inspired by human perceptual grouping with motion cues. \nOur experiments using ground truth boxes render convincing results on both frame reconstruction and action recognition, showing the potential of the proposed architecture.\n\nHowever, multiple aspects still need to be explored in our work. As our plans for the future work, we decide to (1) introduce unsupervised learning for foreground segmentation as well, as proposed in uNLC \\cite{pathak2017learning}; (2) train with a larger amount of unlabeled data; (3) introduce adversarial loss to improve the sharpness of the reconstructed frames \\cite{mathieu2015deep}; and (4) fill the gap of absent motion features between the first frame and the last frame by reconstructing any random frame in the clip.\n\nOur model and source code are publicly available at \\url{https:\/\/imatge-upc.github.io\/unsupervised-2017-cvprw\/} .\n\\section*{Acknowledgments}\nThe Image Processing Group at UPC is supported by the project TEC2013-43935-R and TEC2016-75976-R, funded by the Spanish Ministerio de Economia y Competitividad and the European Regional Development Fund (ERDF). The Image Processing Group at UPC is a SGR14 Consolidated Research Group recognized and sponsored by the Catalan Government (Generalitat de Catalunya) through its AGAUR office. \nThe contribution from the Barcelona Supercomputing Center has been supported by project TIN2015-65316 by the Spanish Ministry of Science and Innovation contracts 2014-SGR-1051 by Generalitat de Catalunya.\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nBroad emission lines are a hallmark feature of type 1 active galactic nuclei \n(AGNs) and quasars \\citep{osterbrock1986}.  As pervasive as they are, \nmany basic properties of the broad-line region (BLR), such as its basic \ngeometry, dynamics, and physical connection to the accretion disk around the \nsupermassive black hole (BH), remain ill-defined.  AGN spectra exhibit both \ntremendous diversity as well as discernable patterns of systematic \nregularity.  Principal component analysis has isolated several dominant \nrelationships among emission-line properties \\citep{boroson1992, sulentic2000}. \nThe main varying trend of those properties, which is so-called Eigenvector \n1 (EV1), has been demonstrated to be driven by Eddington ratios, \n$L_{\\rm bol}\/L_{\\rm Edd}$, where $L_{\\rm bol}$ is the bolometric luminosity and \nthe Eddington luminosity $L_{\\rm Edd} = 1.5 \\times 10^{38}\\, (M_{\\bullet}\/M_{\\odot})$ \n\\citep{boroson1992, sulentic2000, shen2014}. As one of the most prominent \nvariables in EV1, the relative strength of broad optical Fe {\\sc ii}\\ emission, expressed as \n\n\\begin{equation}\n{\\cal R}_{\\rm Fe}=\\frac{F_{\\rm FeII}}{F_{\\rm H\\beta}}, \n\\end{equation}\nmay correlate with $L_{\\rm bol}\/L_{\\rm Edd}$. \nSources with high Eddington ratios (accretion \nrates), for instance so-called narrow-line Seyfert 1 galaxies \\citep{osterbrock1985}, \nemit exceptionally strong Fe {\\sc ii}\\ lines compared with the normal ones\n\\citep{boroson1992, hu2008, dong2011}. \nHowever, the underlying physical mechanism that controls ${\\cal R}_{\\rm Fe}$ remains unclear, \nas the formation of Fe {\\sc ii}\\ is very complex (e.g., \\citealt{baldwin2004}). \nIt may be influenced by different hydrogen density of BLR gas \\citep{verner2004}, \nor diverse contribution from microturbulence \\citep{baldwin2004}.\nIn addition, Fe {\\sc ii}\\, lags are generally longer by a factor of a few than H$\\beta$ \nin broad-line Seyfert 1 galaxies \\citep{barth2013, chelouche2014} and roughly\nequal to H$\\beta$ lags in narrow-line Seyfert 1s \\citep{hu2015},  \nimplying the potential connection of ${\\cal R}_{\\rm Fe}$ with the distribution or structure of \nline-emitting gas. The ${\\cal R}_{\\rm Fe}-L_{\\rm bol}\/L_{\\rm Edd}$ correlation indicates that \nEddington ratios probably regulate all above mentioned properties of BLR. It should \nbe noted that ${\\cal R}_{\\rm Fe}$ also correlates with some other properties like \nX-ray spectral slopes (e.g., \\citealt{wang1996, laor1997, sulentic2000}), \nbut it likely originates from relation of those properties and Eddington ratios \n(e.g., \\citealt{wang2004, risaliti2009, shemmer2006, brightman2013}).\n\n\n\n\nThe overall breadth of the broad emission lines, notably H$\\beta$, reflects \nboth the virial velocity and inclination of the BLR \\citep{kollatschny2011, shen2014}. \nThe shape of the line profile may encode more \ninformation on the detailed dynamics of the BLR (e.g., \\citealt{collin2006, kollatschny2011}), \nwhich itself may depend on fundamental properties \nsuch as the accretion or outflow rate.  The broad H$\\beta$ lines of NLS1s \ntend to have more sharply peaked ($\\sim$Lorentzian) profiles compared to \ntype 1 AGNs with more normal Eddington ratios \\citep{veron2001, zamfir2010}. \nAs a non-parametric description of the line profile, one can define\n\\begin{equation}\n{\\cal D}_{_{\\rm H\\beta}}=\\frac{\\rm FWHM}{\\sigma_{_{\\rm H\\beta}}},\n\\end{equation}\nwhere $\\sigma_{_{\\rm H\\beta}}$ is the dispersion (second moment) of the H$\\beta$ line. \nThe value of ${\\cal D}_{_{\\rm H\\beta}}$ is 2.35, 3.46, 2.45, 2.83 and 0 for a Gaussian, a \nrectangular, a triangular, an edge-on rotating ring, and a Lorentzian \nprofiles (for a pure Lorentzian profile $\\sigma_{_{\\rm H\\beta}}\\rightarrow \\infty$ and thus \n${\\cal D}_{_{\\rm H\\beta}}=0$), respectively (e.g., \\citealt{collin2006}). The quantity ${\\cal D}_{_{\\rm H\\beta}}$\ncorrelates loosely with Eddington ratio \\citep{collin2006} and, as the ratio \nof the rotational and turbulent components of the line-emitting clouds \n\\citep{kollatschny2011}, gives a simple, convenient parameter that may be \nrelated to the dynamics of the BLR.\n\nWhile ${\\cal R}_{\\rm Fe}$ and ${\\cal D}_{_{\\rm H\\beta}}$ each correlates separately with Eddington ratio, we \ndemonstrate that both ${\\cal R}_{\\rm Fe}$ and ${\\cal D}_{_{\\rm H\\beta}}$ {\\it combined}\\ correlate even \nmore tightly with Eddington ratio (and dimensionless accretion rate).  This \nbivariate relation, which we call the ``fundamental plane''\\footnote{Borrowing \nthe terminology from galaxy formation (e.g., \\citealt{djorgovski1987}) and \naccreting BHs (e.g., \\citealt{merloni2003})} of the BLR links two direct \nobservables, plausibly related to the structure and dynamics of the BLR, with \nthe dimensionless accretion rate.  Applying the BLR fundamental plane to a \nlarge sample of Sloan Digital Sky Survey (SDSS) quasars, we find that a \nlarge fraction of quasars at $z < 0.8$ have super-Eddington accretion rates.\n\n\n\\renewcommand{\\arraystretch}{1.2}\n\\begin{deluxetable*}{lcccccccl}[!t]\n\\tablecolumns{9}\n\\setlength{\\tabcolsep}{3pt}\n\\tablewidth{0pc}\n\\tablecaption{The Sample of Reverberation-mapped AGNs}\n\\tabletypesize{\\footnotesize\n\\tablehead{\n   \\colhead{Objects}                       &\n   \\colhead{$\\log L_{5100}$}               &\n   \\colhead{$\\log\\left(M_{\\bullet}\/M_{\\odot}\\right)$} &\n   \\colhead{$\\log\\dot{\\mathscr{M}}$}               &\n   \\colhead{FWHM}                          &\n   \\colhead{$\\sigma_{\\rm line}$}           &\n   \\colhead{${\\cal D}_{_{\\rm H\\beta}}$}                    &\n   \\colhead{$\\cal{R}_{\\rm Fe}$}            &\n   \\colhead{Ref.}                          \\\\ \\cline{2-9}\n   \\colhead{}                              &\n   \\colhead{(${\\rm erg~s^{-1}})$}                     &\n   \\colhead{}                              &\n   \\colhead{}                              &\n   \\colhead{($\\rm km~s^{-1}$)}                      &\n   \\colhead{($\\rm km~s^{-1}$)}                      &\n   \\colhead{}                              &\n   \\colhead{}                              &\n   \\colhead{}\n}\n\\startdata\nMrk 335     & $    43.69\\pm0.06 $ & $    6.87_{-0.14}^{+0.10} $ & $     1.17_{-0.30}^{+0.31} $ & $2096\\pm170$ & $1470\\pm 50$ & $    1.43\\pm0.13 $ & $    0.39 $ & 1, 2, 3, 4 \\\\\n           & $    43.76\\pm0.06 $ & $    7.02_{-0.12}^{+0.11} $ & $     1.28_{-0.29}^{+0.30} $ & $1792\\pm  3$ & $1380\\pm 6$ & $    1.30\\pm0.01 $ & $    0.77 $ & 4, 5, 6$^a$ \\\\\n           & $    43.84\\pm0.06 $ & $    6.84_{-0.25}^{+0.18} $ & $     1.39_{-0.29}^{+0.30} $ & $1679\\pm  2$ & $1371\\pm 8$ & $    1.23\\pm0.01 $ & $    0.77 $ & 4, 5, 6$^a$ \\\\\n           & $    43.74\\pm0.06 $ & $    6.92_{-0.14}^{+0.11} $ & $     1.25_{-0.29}^{+0.30} $ & $1724\\pm236$ & $1542\\pm 66$ & $    1.12\\pm0.16 $ & $    0.69 $ & 4, 7$^a$ \\\\\n           & $\\bm{43.76\\pm0.07}$ & $\\bm{6.93_{-0.11}^{+0.10}}$ & $\\bm{ 1.27_{-0.17}^{+0.18}}$ & ...          & ...          & $\\bm{1.27\\pm0.05}$ & $\\bm{0.62}$ & 4 \\\\\nPG 0026+129 & $    44.97\\pm0.02 $ & $    8.15_{-0.13}^{+0.09} $ & $     0.65_{-0.20}^{+0.28} $ & $2544\\pm 56$ & $1738\\pm100$ & $    1.46\\pm0.09 $ & $    0.33 $ & 4, 5, 8$^a$ \\\\\nPG 0052+251 & $    44.81\\pm0.03 $ & $    8.64_{-0.14}^{+0.11} $ & $    -0.59_{-0.25}^{+0.31} $ & $5008\\pm 73$ & $2167\\pm 30$ & $    2.31\\pm0.05 $ & $    0.12 $ & 4, 5, 8$^a$ \\\\\n\\enddata\n\\vspace{-0.2cm}\n\\tablecomments{All the values of \n $\\log L_{5100}$, $\\log (M_{\\bullet}\/M_{\\odot})$ and $\\log \\mathscr{\\dot{M}}$ are compiled from Du et al. (2015).\nValues in boldface are the weighted averages of all the measurements for this object. \\\\ \\vglue 0.15cm\n\\vspace{-0.30cm}\n\\hspace{0.1in}\nRef.:\n (1) \\citealt{du2014}; \n (2) \\citealt{wang2014}; \n (3) \\citealt{hu2015}; \n (4) \\citealt{du2015}; \n (5) \\citealt{collin2006}; \n (6) \\citealt{peterson1998}; \n (7) \\citealt{grier2012}; \n (8) \\citealt{kaspi2000}. \n \\\\ \\vglue 0.02cm\n\\vspace{-0.2cm}\n %\n \\hspace{0.1in} \nThe superscript $a$ for references indicates that ${\\cal R}_{\\rm Fe}$ is measured in this \npaper; $b$ indicates that FWHM and $\\sigma_{_{\\rm H\\beta}}$ are measured from SDSS spectra (the \nH$\\beta$ width of SEAMBHs is significantly broadened by the 5$^{\\prime\\prime}$ \nlongslit of our campaign; see details in Ref. 4); $c$ means the MCMC BH mass \nis used (see Section 2.2); $d$ means that ${\\cal D}_{_{\\rm H\\beta}}$ is taken from the latest \nmeasurements in \\cite{kollatschny2011}. NGC 5548 marked with $e$ is measured from its mean \nannual spectra in the AGN watch database; the average value is provided here.  \nWe first calculate ${\\cal D}_{_{\\rm H\\beta}}$ for each measurement, and then average. In the \nmain text, we use these averaged numbers for the objects with multiple RM \nmeasurements (treated as one point in all figures). For NGC 7469, which was\nmapped twice \\cite{collier1998} and \\cite{peterson2014}, the H$\\beta$ lags are not very \ndifferent but the H$\\beta$ FWHM is very different; take the values of FWHM \nmeasured by \\cite{kollatschny2011}.  NGC 4051 and PG 1700+518 have very small values of \n${\\cal D}_{_{\\rm H\\beta}}$ in Ref. 5, but \\cite{kollatschny2011} provides new measurements, which are used \nhere.\\\\ \\vglue 0.02cm\n\\vspace{-0.2cm}\n\\hspace{0.1in}  This table is available in its entirety in a machine-readable \nform in the online journal. A portion is shown here for guidance regarding its \nform and content.\n}\n\\end{deluxetable*}\n\n\n\n\n\n\n\\section{Measurements}\n\\subsection{The Reverberation-mapped AGN sample}\nWe select all AGNs with reverberation mapping (RM) data (here only broad H$\\beta$ \nline), which yield robust BH \nmass estimates needed for our analysis.  All RM AGNs before 2013 are summarized\nby \\cite{bentz2013}. We took all of 41 AGNs from \\cite{bentz2013}.  \nThree additional sources (Mrk 1511, NGC 5273, \nKA1858+4850) were subsequently published.  Our project to search for \nsuper-Eddington accreting massive black holes (SEAMBHs) has monitored about 25 \ncandidates and successfully measured H$\\beta$ lags ($\\tau_{_{\\rm H\\beta}}$) in 14 AGNs to \ndate \\citep{du2015} and other five objects monitored between 2014-2015\n(to be submitted).  We measure Fe {\\sc ii}\\, using the same approach as \\cite{hu2008}\nand \\cite{hu2015}.\nFor reverberation-mapped AGNs without published measurements of Fe {\\sc ii}\\ and \nH$\\beta$ flux, we fit the mean spectra from the monitoring campaigns, using \nthe fitting scheme described in \n\\cite{hu2015}. In short, the spectrum is fitted with several components simultaneously: \n(1) a power law for continuum, (2) Fe {\\sc ii} template from \\cite{boroson1992}, \n(3) host galaxy template if necessary, (4) broad H$\\beta$, (5) broad He {\\sc ii} \n$\\lambda 4686$ emission line, and (6) several Gaussians for narrow lines such as [O {\\sc iii}] \n$\\lambda\\lambda$4959, 5007.  The \nflux of broad optical Fe {\\sc ii} is measured by integration from 4434 \\AA\\ to 4684 \\AA.\nTable 1 lists the 63 RM AGNs we consider, along with \nthe BH mass, 5100 \\AA\\, luminosity, dimensionless accretion rate, FWHM, \n$\\sigma_{_{\\rm H\\beta}}$, ${\\cal R}_{\\rm Fe}$ and data sources. \n\nThe sample covers a wide range of accretion rates, $\\dot{\\mathscr{M}} \\approx 10^{-3} \n- 10^3$, from the regime of a \\cite{shakura1973} standard disk to a \nslim disk \\citep{abramowicz1988}.  We take ${\\cal R}_{\\rm Fe}$ from the published \nliterature if available; otherwise, we measure it from the averaged spectra \nfollowing the spectral fitting scheme of \\cite{hu2008, hu2015}.  As the \nvariability of H$\\beta$ is unusually much larger than that of Fe {\\sc ii}\\ in \nsub-Eddington AGNs, the uncertainties of ${\\cal R}_{\\rm Fe}$ are mainly governed by \nH$\\beta$ variability, which on average is $\\sim 20$\\%.  \n \nWe estimate the BH mass as $M_{\\bullet}=f_{_{\\rm BLR}} V_{\\rm FWHM}^2 c\\tau_{_{\\rm H\\beta}}\/G$, where \n$f_{_{\\rm BLR}}$ is the virial factor, $V_{\\rm FWHM}$ is H$\\beta$ FWHM, and $G$ is the \ngravitational constant.  In practice, the factor $f_{_{\\rm BLR}}$ is calibrated against\nthe $M_{\\bullet}-\\sigma$ relation of inactive galaxies \\citep{onken2004, ho2014}. \nFor consistency with our earlier series of papers, we adopt $f_{_{\\rm BLR}}=1$.\n\n\n\\subsection{Accretion rates and Eddington ratios}\nWe derived accretion rates from the disk model of \\cite{shakura1973},\nwhich has been extensively applied to fit the spectra of quasars and Seyfert 1 \ngalaxies \\citep{czerny1987, sun1989, laor1989, collin2002, brocksopp2006, kishimoto2008, \ndavis2011, capellupo2015}. The effective temperature distribution is \ngiven by $T_{\\rm eff}=6.2\\times 10^{4}\\,\\dot{m}_{\\bullet,0.1}^{1\/4}m_7^{1\/4}\nR_{14}^{-3\/4}$\\,K, where $\\dot{m}_{\\bullet,0.1}=\\dot{M}_{\\bullet}\/0.1M_{\\odot}\\,\n{\\rm yr^{-1}}$, $\\dot{M}_{\\bullet}$ is mass accretion rates, $m_7=M_{\\bullet}\/10^7\nM_{\\odot}$, and $R_{14}=R\/10^{14}$cm \\citep{frank2002}.  Here the effect of the \ninner boundary is neglected because the region emitting optical radiation is \nfar from the boundary. Introducing $x=h\\nu\/kT_{\\rm eff}$, we have the spectral \nluminosity by integrating over the entire disk,\n\\begin{equation}\nL_{\\nu}=1.58\\times 10^{28}\\,\\dot{m}_{\\bullet,0.1}^{2\/3}m_7^{2\/3}\\nu_{14}^{1\/3}\\cos i \n        \\int_{x_{\\rm in}}^{\\infty}\\frac{x^{5\/3}}{e^x-1}dx\\,\\,\\,\\,{\\rm erg\\,s^{-1}\\,Hz^{-1}},\n\\end{equation}\nwhere $i$ is the disk inclination relative to the observer and \n$\\nu_{14}=\\nu\/10^{14}$Hz. Since long-wavelength photons are radiated from \nlarge disk radii, the integral term in Equation (3) can be well approximated \nby 1.93 for $x_{\\rm in}=0$ \\citep{davis2011}. We thus have\n$\\dot{M}_{\\bullet}=0.53\\left(\\ell_{44}\/\\cos i\\right)^{3\/2}m_7^{-1}~M_{\\odot}~{\\rm yr^{-1}}$,\nand the dimensionless accretion rate\\footnote{The applicability of Eq. (4) \nto SEAMBHs can be justified by the self-similar solution of slim disks \\citep{wang1999a, wang1999b}. \nThe solution shows that the 5100 \\AA\\,\nphotons are emitted from $R_{5100}\/R_{\\rm Sch}\\approx 4.3\\times 10^3\nm_7^{-1\/2}$, and the photon trapping radius $R_{\\rm trap}\/R_{\\rm Sch}\\approx \n144\\dot{\\mathscr{M}}_{100}$, where $R_{\\rm Sch}$ is the Schwartzschild radius. Eq. (4) \nholds provided that $R_{5100}\\gtrsim R_{\\rm trap}$, or $\\dot{\\mathscr{M}}\\lesssim \n3\\times 10^3m_7^{-1\/2}$. No SEAMBH so far has exceeded this limit.}\n\\begin{equation}\n\\dot{\\mathscr{M}}=20.1\\left(\\frac{\\ell_{44}}{\\cos i}\\right)^{3\/2}m_7^{-2},\n\\end{equation}\nwhere  $\\ell_{44}$ is the 5100 \\AA\\, luminosity in units of $10^{44}\\,{\\rm erg~s^{-1}}$. \nThis convenient expression can easily convert luminosity and BH mass into \ndimensionless accretion rates. In this paper, we take an average value of \n$\\cos i = 0.75$, which corresponds to the opening angle of the dusty torus \n(e.g., \\citealt{davis2011, du2015}). The uncertainties of $\\dot{\\mathscr{M}}$ due to \n$i$ ($\\in[0,45^{\\circ}]$) are\n$\\Delta\\log\\dot{\\mathscr{M}}=1.5\\Delta\\log\\cos i\\lesssim 0.15$ from Equation (4),\nwhere we took $\\Delta \\log \\cos i\\lesssim0.1$. This uncertainty is significantly\nsmaller than the average error bars of $\\log \\dot{\\mathscr{M}}$ ($\\sim 0.35$), and is \nthus neglected.\n\nThe dimensionless accretion rate is related to the more widely used Eddington \nratio via $L_{\\rm bol}\/L_{\\rm Edd}=\\eta\\dot{\\mathscr{M}}$, where $\\eta$ is the radiative \nefficiency, and $L_{\\rm bol} \\approx 10 L_{5100}$ \\citep{kaspi2000}. \nThe uncertainties of Eddington ratios result from the fact that the bolometric\ncorrection depends on both accretion rates and BH mass \\citep{jin2012}.  In \nour following discussion, we will use both $\\dot{\\mathscr{M}}$ and $L_{\\rm bol}\/L_{\\rm Edd}$.\n\n\n\\begin{figure*}[t!]\n\\begin{center}\n\\includegraphics[angle=0,width=0.82\\textwidth]{fig1.eps}\n\\end{center}\n\\vglue -0.5cm\n\\caption{\\footnotesize Correlations between ({\\it a}) ${\\cal R}_{\\rm Fe}-\\dot{\\mathscr{M}}$ and \n({\\it b}) ${\\cal D}_{_{\\rm H\\beta}}-\\dot{\\mathscr{M}}$.  The Pearson's coefficient, null-probability, \nand scatter of the $X-\\dot{\\mathscr{M}}$ correlation are given by ($r,p,\\Delta_X$). \nIn panel ({\\it a}), the SDSS quasars overlap with the RM AGNs quite well, \nexcept for AGNs with ${\\cal R}_{\\rm Fe}\\gtrsim 1.4$. This could be because these objects \nare super-Eddington accretors, in which the normal $R-L$ relation \\citep{bentz2013} \noverestimates $R_{_{\\rm H\\beta}}$ as well as BH mass \\citep{du2015}, and \nhence $\\dot{\\mathscr{M}}$ is greatly underestimated (see details in the text). In \npanel ({\\it b}), the SDSS sample also overlaps well with the RM AGNs, but the \nlow$-\\dot{\\mathscr{M}}$ AGNs lie beyond the locus of the SDSS sample. There are some \nSDSS quasars with extremely high accretion rates, $\\dot{\\mathscr{M}}\\gtrsim 10^2$, \nsuggesting that we should monitor them in the future of SEAMBH project. The \nhistograms indicate the distributions of ${\\cal R}_{\\rm Fe}$, ${\\cal D}_{_{\\rm H\\beta}}$ and $\\dot{\\mathscr{M}}$ on \na normalized scale. We note that there is no significant correlation between\n${\\cal R}_{\\rm Fe}$ and ${\\cal D}_{_{\\rm H\\beta}}$, either in the RM AGN or SDSS sample, indicating that \n${\\cal D}_{_{\\rm H\\beta}}$ and ${\\cal R}_{\\rm Fe}$ are independent from each other, although both correlate \nwith $\\dot{\\mathscr{M}}$. Panels ({\\it c}) and ({\\it d}) are the same as ({\\it a}) and \n({\\it b}), but for Eddington ratios. \n}\n\\end{figure*}\n\n\n\n\n\n\\section{Fundamental plane of the BLR}\n\\subsection{Correlations}\nFigure 1{\\it a} and 1{\\it c} show the ${\\cal R}_{\\rm Fe}-(\\dot{\\mathscr{M}},L_{\\rm bol}\/L_{\\rm Edd})$ \nplots and yield the following correlations:\n\\begin{equation}\n{\\cal R}_{\\rm Fe}=\\left\\{\\begin{array}{l}\n     (0.66\\pm 0.04)+(0.30\\pm 0.03)\\log \\dot{\\mathscr{M}},\\\\[0.8em] \n     (1.20\\pm 0.07)+(0.55\\pm 0.06)\\log \\left(L_{\\rm bol}\/L_{\\rm Edd}\\right).\n     \\end{array}\\right.\n\\end{equation}\nWe define the scatter of a correlation as \n$\\Delta_{X}=\\sqrt{\\sum_{i=1}^N(X-X_i)^2\/N}$, where $N$ is the number of \nobjects, and $X$ represents ${\\cal R}_{\\rm Fe}$, ${\\cal D}_{_{\\rm H\\beta}}$, $\\dot{\\mathscr{M}}$, or $L_{\\rm bol}\/L_{\\rm Edd}$.  \nThe Pearson's correlation coefficient ($r$), null-probability ($p$), and \nscatters are indicated in the plots. By comparing $(r,p,\\Delta_{\\rm {\\cal R}_{\\rm Fe}})$ in \npanels ({\\it a}) and ({\\it c}), we find that the ${\\cal R}_{\\rm Fe}-\\dot{\\mathscr{M}}$ correlation \nis slightly stronger than that of ${\\cal R}_{\\rm Fe}-L_{\\rm bol}\/L_{\\rm Edd}$.  In \nhigh-$\\dot{\\mathscr{M}}$ AGNs, both H$\\beta$ and continuum variability are \nsignificantly smaller than those in sub-Eddington AGNs. On the other hand, \nFe {\\sc ii}\\, reverberates in a very similarly fashion to H$\\beta$ with respect to \nthe continuum \\citep{hu2015}. Indeed, it can be seen that the scatter of the \ncorrelation gets larger with decreasing $\\dot{\\mathscr{M}}$ or \n$L_{\\rm bol}\/L_{\\rm Edd}$. The ${\\cal R}_{\\rm Fe}-(\\dot{\\mathscr{M}}, L_{\\rm bol}\/L_{\\rm Edd})$ correlations \nsupports the idea that Fe {\\sc ii}\\, strength is not governed by metallicity \nbut by the ionizing flux and hydrogen density \\citep{verner2004}. \n\nWe plot the ${\\cal D}_{_{\\rm H\\beta}}-(\\dot{\\mathscr{M}}, L_{\\rm bol}\/L_{\\rm Edd})$ relations in Figure 1{\\it b} and \n1{\\it d} and find\n\\begin{equation}\n{\\cal D}_{_{\\rm H\\beta}} =\\left\\{\\begin{array}{l}\n           (2.01\\pm 0.05)-(0.39\\pm 0.04)\\log \\dot{\\mathscr{M}},\\\\[0.8em]\n            (1.28\\pm0.09)-(0.72\\pm0.08)\\log\\left(L_{\\rm bol}\/L_{\\rm Edd}\\right).\n           \\end{array}\\right.\n\\end{equation}                   \nThe above two correlations are similar, but the former is slightly stronger \nthan the latter. \\cite{collin2006} also found a correlation between \n${\\cal D}_{_{\\rm H\\beta}}$ and $L_{\\rm bol}\/L_{\\rm Edd}$ (see their Figure 6), but their results are much \nweaker than ours. This is mainly due to the lack of high$-\\dot{\\mathscr{M}}$ AGNs in\ntheir sample. We would like to emphasize that the \n${\\cal D}_{_{\\rm H\\beta}}-(\\dot{\\mathscr{M}},L_{\\rm bol}\/L_{\\rm Edd})$ correlations cannot be an artifact of the \ninclusion of FWHM in $\\dot{\\mathscr{M}}$.  For a constant $\\sigma_{_{\\rm H\\beta}}$ of RM AGNs, the \naccretion rates span over about 5 dex whereas luminosities span over 4.5;\nhowever, the ${\\cal D}_{_{\\rm H\\beta}}-\\dot{\\mathscr{M}}$ relation has a scatter of only\n$\\Delta_{_{\\cal D}}=0.3-0.4$. The correlations are intrinsic. \n\nFigure 1 also shows, as background, the SDSS DR5 sample of \\cite{hu2008}. \nThe sample comprises 4037 $z\\lesssim 0.8$ \nquasars with criteria of S\/N$\\ge 10$ and EW(Fe {\\sc ii})$\\ge 25$ \\AA\\, (this excludes Fe {\\sc ii}-weak \nquasars). BH masses assume $f_{\\rm BLR} = 1$ and a standard $R-L$ relation\\footnote{ \nThis is an empirical relation between the BLR size and the continuum.  From the recent work \nof Bentz et al. (2013), it has the form  $R_{\\rm BLR}=33.65\\,\\ell_{44}^{0.53}$ltd. However, \n\\cite{du2015} found that it only applies to sub-Eddington AGNs; it depends on $\\dot{\\mathscr{M}}$ \nfor super-Eddington AGNs. We do not consider \nthe dependence of the $R-L$ relation on $\\dot{\\mathscr{M}}$ for the SDSS sample in this paper.}.  \nThe RM AGNs overlap very well with the SDSS sample, on both the \n${\\cal R}_{\\rm Fe}-(\\dot{\\mathscr{M}},L_{\\rm bol}\/L_{\\rm Edd})$ and the ${\\cal D}_{_{\\rm H\\beta}}-(\\dot{\\mathscr{M}},L_{\\rm bol}\/L_{\\rm Edd})$ plots. \nWe note that among the mapped AGNs there is a small population ($\\lesssim 9\\%$; Figure \n1{\\it a} and {\\it c}) of AGNs with ${\\cal R}_{\\rm Fe}>1.4$ of what appear to be super-Eddington sources.  \nTheir values of $\\dot{\\mathscr{M}}$ are likely underestimated because their black hole masses were \nestimated using the standard $R-L$ relation.\n\n\n\\begin{figure*}[!t]\n\\begin{center}\n\\includegraphics[angle=0,width=0.45\\textwidth]{fig2a.eps}\n\\includegraphics[angle=0,width=0.45\\textwidth]{fig2b.eps}\n\\end{center}\n\\vglue -0.5cm\n\\caption{\\footnotesize The fundamental plane of AGN BLRs, showing a physical \nconnection between accretion disks and BLRs. \nThe dependent variable is ({\\it left}) $\\dot{\\mathscr{M}}$ and ({\\it right}) \nEddington ratio. The two observables of ${\\cal R}_{\\rm Fe}$ and ${\\cal D}_{_{\\rm H\\beta}}$ can be readily \nmeasured from single-epoch spectra, allowing us to constrain the accretion \nstatus of the central engine. }\n\\end{figure*}\n\n\n\n\\subsection{Fundamental Plane}\nThe $({\\cal R}_{\\rm Fe},{\\cal D}_{_{\\rm H\\beta}})-(\\dot{\\mathscr{M}},L_{\\rm bol}\/L_{\\rm Edd})$ relations reflect \nconnections between the BLR structure and dynamics with BH accretion.  We \ninvestigate whether these two univariate correlations can be unified into a \nsingle bivariate correlation of the form\n\\begin{equation}\n\\log (\\dot{\\mathscr{M}}, L_{\\rm bol}\/L_{\\rm Edd})=\\alpha_k + \\beta_k{\\cal D}_{_{\\rm H\\beta}}+\\gamma_k{\\cal R}_{\\rm Fe},\n\\end{equation}\nwhere $(\\alpha_k,\\beta_k,\\gamma_k)$ are coefficients to be determined by \ndata ($k=1,2$).  We define\n\\begin{equation}\n\\chi_k^2=\\frac{1}{N}\\sum_{i=1}^N\n       \\frac{\\left(\\log {\\cal A}_k^i-\\alpha_k-\\beta_k{\\cal D}_{_{\\rm H\\beta}}^i-\\gamma_k{\\cal R}_{\\rm Fe}^i\\right)^2}\n            {\\sigma_{\\scriptscriptstyle{{\\cal A}_i}}^2+\n            \\beta_k\\sigma_{\\scriptscriptstyle{{\\cal D}_{_{\\rm H\\beta}}^i}}^2+\\gamma_k\\sigma_{\\scriptscriptstyle{{\\cal R}_{\\rm Fe}^i}}^2},\n\\end{equation}\nwhere ${\\cal A}_k=(\\dot{\\mathscr{M}},L_{\\rm bol}\/L_{\\rm Edd})$, \n$\\sigma_{\\scriptscriptstyle{{\\cal A}_i}},\\sigma_{\\scriptscriptstyle{{\\cal D}_{_{\\rm H\\beta}}^i}}$ \nand $\\sigma_{\\scriptscriptstyle{{\\cal R}_{\\rm Fe}^i}}$ are the error bars of $\\log{\\cal A}$, \n${\\cal D}_{_{\\rm H\\beta}}$, and ${\\cal R}_{\\rm Fe}$ of the $i-$th object, respectively. Minimizing $\\chi_k^2$,\nwe obtain \n$$\n\\alpha_1=2.47\\pm 0.34;~~~\\beta_1=-1.59\\pm 0.14;~~~{\\rm and}~~\\gamma_1=1.34\\pm 0.20,\n$$\n$$\n\\alpha_2=0.31\\pm 0.30;~~~\\beta_2=-0.82\\pm 0.11;~~~{\\rm and}~~\\gamma_2=0.80\\pm 0.20.\n$$\nThe error bars of $(\\alpha_k,\\beta_k,\\gamma_k)$ are derived from bootstrap \nsimulations.  The bivariate correlations, plotted in Figure 2, are much \nstronger than individual corrections of Figure 1 (see the correlation \ncoefficients and null-probability).  We call these new correlations as the \nfundamental plane of the BLR.\n\nThe implications of Equation (7) are exciting.   From two simple measurements \nof a single-epoch spectrum of a quasar---strength of Fe {\\sc ii}\\ and shape of broad \nH$\\beta$---we can deduce the status of its accretion flow.  This can be very \nuseful when applied to large samples of quasars to investigate the cosmological \ngrowth of BHs.  Our method can be usefully applied to quasars with suitable \nspectroscopy in the rest-frame H$\\beta$ region, for which the strength of Fe {\\sc ii}\\ \ncan be measured or constrained.\n\n\\subsection{Application to SDSS sample}\nWe apply the $\\dot{\\mathscr{M}}-$plane (Equation 7) to a sample of \n4037 objects \\cite{hu2008}, which were selected from the\nSDSS DR5 sample composed of $N_{\\rm tot}\\approx 15,000$ quasars with $z\\lesssim 0.8$.  \nWe calculate fractions of quasars with $\\dot{\\mathscr{M}}\\ge \\dot{\\mathscr{M}}_c$,\n$\\delta=N_{{\\dot{\\mathscr{M}}_c}}\/N_{\\rm tot}$, where $N_{{\\dot{\\mathscr{M}}_c}}$ \nis the number of quasars and\n$\\dot{\\mathscr{M}}_c$ is the critical accretion rate in question. For objects with $\\dot{\\mathscr{M}}\\ge 3$, we \nfind $\\delta_3=N_3\/N_{\\rm tot}\\approx 0.18$. Similarly,\nwe have $\\delta_{10}=N_{10}\/N_{\\rm tot}\\approx 0.12$ and \n$\\delta_{100}=N_{100}\/N_{\\rm tot}\\approx 0.02$.\nThese numbers show that\nsuper-Eddington accreting AGNs are quite common in the Universe at $z<0.8$. We should note \nthat these fractions are lower limits, as a result of the selection criteria imposed by \nHu et al.  Detailed results of the application of our technique to the latest sample of SDSS \nquasars will be carried out in a separate paper.\n\n\\section{Conclusions}\nThis paper studies correlations among three dimensionless AGN parameters: \naccretion rate (or Eddington ratio), shape of the broad H$\\beta$ line, and \nflux ratio of optical Fe {\\sc ii}\\, to H$\\beta$.  A strong correlation among them is \nfound, which we denote as the fundamental plane of AGN BLRs (Equation 7). \nThe BLR fundamental plane enables us to conveniently explore the accretion \nstatus of the AGN central engine using single-epoch spectra, opening up many \ninteresting avenues for exploring AGNs, including their cosmological evolution.\nA simple application of the BLR fundamental plane shows that super-Eddington \naccreting AGNs are quite common in among low-redshift quasars.\n\n\\acknowledgements{ This research \nis supported by the Strategic Priority Research Program - The Emergence of Cosmological Structures \nof the Chinese Academy of Sciences, Grant No. XDB09000000, by NSFC grants NSFC-11173023, -11133006, \n-11373024, -11233003 and -11473002, and a NSFC-CAS joint key grant of U1431228.}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzpipv b/data_all_eng_slimpj/shuffled/split2/finalzzpipv
new file mode 100644
index 0000000000000000000000000000000000000000..6a3b73fffe814f9b59f4122d4ee3af948d5bc15c
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzpipv
@@ -0,0 +1,5 @@
+{"text":"\\section{Motion of a point charge in a Coulomb potential well}\n\nThe behavior of a point charge in a Coulomb potential well was studied well\n enough (see, e.g., \\cite{1}). By contrast, the behavior of {\\itshape\\bfseries a distributed} charge in a Coulomb potential well reveals some\n specific features. And it is the specific features arising in the behavior of {\\itshape\\bfseries a distributed} charge that we are going to address in the present paper. \n\nWe start by assuming a negative distributed charge with a density \n$\\rho(\\mathbf{r})$ to be placed into the field of a point positive charge $e$ of infinite mass at the origin of a coordinate system. For the sake of conveniency, we shall call this charge a nucleus. Our goal will be to reveal the specific features in the behavior of the distributed charge \n$\\rho(\\mathbf{r})$ in a Coulomb potential well.\nWe shall look for the solution of this problem in the framework of the approach that was employed, for instance, in monograph \\cite{1}, i.e., in the nonrelativistic approximation. This condition is reliably substantiated.\nFor instance, in an atom any element of charge located at a distance of the Bohr radius from the nucleus has a velocity on the order of $\\alpha c$, where $\\alpha$ is the fine structure constant, and $c$ is the velocity of light. Because in the nonrelativistic approximation the velocities of motion of individual charge elements are small, we will disregard in what follows the generation of magnetic field induced by charge motion. Said otherwise, we are going to neglect the vector potential $\\mathbf{A}(\\mathbf{r})$ induced by charge motion and assume the elements of a distributed charge to feel only the field of the scalar potential $\\Phi(\\mathbf{r})$.\n\nWe shall address in this paper the case where the density of the distributed charge is small. This licenses us to neglect the potential of the distributed charge $\\rho(\\mathbf{r})$ itself compared with that of the nucleus, and assume each element of the distributed charge to move only in the field of a point charge $e$ with the spherical potential $\\Phi(r)=e\/r$.\n\nNext we choose in the distributed charge a constant element of charge $dq$ with a mass $dm$ and, assuming this element to be a point charge, recall some features in the behavior of a point charge $dq$ in a Coulomb potential well, which we are going to use later on. (We shall denote this element sometimes by $dq$, and sometimes by $dm$, bearing in mind that in all cases we will deal with an element of charge $dq$ and mass $dm$). A comment is here, however, in order.\n\nAn element of charge $dq$ moving with acceleration must radiate energy. Our analysis of the motion of this element in the field of the nucleus will, however, be conducted under the assumption that the element does not radiate. Indeed, the element under consideration, rather than being a single isolated element of charge, has been selected by us out of the total distributed charge. As this will be demonstrated later on, there exist such states of a distributed charge which do not radiate. It is only such states that will be studied in this paper. Therefore in consideration of the motion of a charge element isolated from the total charge we also shall assume that this element does not radiate. Note that each given separate element of charge must radiate.\n\n\\medskip\n\nThe most convenient approach to identifying the significant details in the behavior of a point charge $dq$ in a Coulomb potential well is to resort to monograph \\cite{1}, \\$~15. It describes the behavior of a point particle in a field inversely proportional to $r^2$. Among such fields are Newton's gravitational and Coulomb's electrostatic fields.\nThe gravitational forces being weak, we are going to neglect them. The only force we will take account of is the Coulomb interaction of a negative element of charge $dq$ with the positively charged nucleus. Because the element $dq$ separated out from the total charge does not radiate (a point to be substantiated later on), one can invoke here all the conclusions drawn in \\cite{1}, \\$~15.\n\nConsider now the specific features in the behavior of an element of charge we shall treat in the discussion to follow.\n\nIn a Coulomb potential well, a constant element of charge \n$dq$ with a mass $dm$ can move in a circle or an ellipse, \nand the ellipse can degenerate into a straight line. The \nenergy of an element of charge depends on the semimajor axis \nof the ellipse (or on the radius of the circle). The actual \nshape of the ellipse (i.e., its semiminor axis) depends on \nthe angular momentum of the particle. Thus, all ellipses with \nthe same semimajor axis but different semiminor axes have the \nsame energies but different angular momenta, down to the zero \nmomentum (in which case the ellipse degenerates into a straight \nline). Said otherwise,  elements of the same energy \ncan move in a Coulomb potential well along trajectories which \ndiffer in the value of the angular momentum.\n\n\nLet us analyze the various trajectories along which an \nelement of charge $dq$ with a mass $dm$ can move in the \ncase where the total energy of the element in each trajectory \nis the same. \n\n\\begin{figure}\n\\label{F1}\n\\begin{center}\n\\includegraphics[scale=1]{Figure1.eps}\n\\caption{}\n\\end{center}\n\\end{figure}\n\n\nFigure~1 for an element $dm$ located at some point\n$\\mathbf r$ illustrates several such orbits of all possible \nones: a circular orbit $a$,  eight elliptical orbits \n$(b-k)$ with different eccentricities (and, hence, different \nangular momenta), and a linear orbit $l$ into which the \nellipse degenerates at an eccentricity of unity. This orbit \npasses through the nucleus. All the orbits are \ncharacterized by identical semimajor axes (if the energies \nof the elements are equal, the semimajor axes of the ellipses \nshould likewise be equal). All orbits lie in the same plane. \nThe elements of charge in all orbits rotate in the same \nsense.\n\nAll orbits focus at the same point. In this focus (in our \nfigure, this is the center $O$ of the circle) the nucleus \nis located. Using the focal properties of \nellipses, one can readily show that each elliptic trajectory \nintersects a circular orbit at the point where this ellipse \nintersects its semiminor axis. The dashed lines confine the \nregion of allowed trajectories along which an element $dm$\ncan move.\n\nSignificantly, the extended trajectories with an eccentricity close to unity pass not far from the nucleus. Therefore, within a small region in the vicinity of the nucleus the condition of the smallness of the element motion velocities does not hold. This region, however, is not large.\n\nBecause the energy of an element in each trajectory is the same, element $dm$ can move over {\\itshape\\bfseries any} of the trajectories specified. As follows from Fig.~1 and an analysis of the trajectories along which element  $dm$ can propagate, all possible directions of motion of the element at a given point are strictly confined to the angle $\\pi$ (a few words on a semicircle located above orbit $l$---if the elements rotated in their orbits in the opposite direction, this semicircle would lie below orbit $l$).\n\nAn element residing in a Coulomb potential well moves in one plane. Note, however, that the number of planes which can be passed through the line connecting the element under consideration with the nucleus is infinite. Any of these planes can confine the trajectory of the given element, because the Coulomb field possesses spherical symmetry. In this case, all possible directions of the velocities of element motion at a given point lie inside the solid angle $2\\pi$ (a hemisphere).\nIn Fig.~1, this hemisphere extends above the plane passed through orbit $l$ perpendicular to the drawing. If elements in their orbits rotated in the opposite sense, the hemisphere would be located below this plane. Additional conditions related with the position of this plane will be specified below (in Sections 4 and 5).\n\nConsider now the magnitude of the velocities with which \nelements of charge having equal energies move in different \ndirections. The Reader can be conveniently referred to monograph \n\\cite{1}, \\$~14. The energy \n$d\\mathcal E$  of an element of charge $dq$ with a mass $dm$ \nmoving in a central field is preserved. Recalling the standard \nexpression for energy\n\n\\begin{equation}\n\\label{1}\nd\\mathcal E=d\\mathcal E_{Kin}+d\\mathcal E_{Pot}=\n\\frac{dm\\upsilon^2}{2}+d\\mathcal E_{Pot},\n\\end{equation}\nwhere $d\\mathcal E_{Kin}$ is the kinetic, and $d\\mathcal E_{Pot}$, \nthe potential energy of the element, and $\\upsilon$ is its \nvelocity, we obtain\n\n\\begin{equation}\n\\label{2}\n\\upsilon=\\sqrt{\\frac{2}{dm}(d\\mathcal E-d\\mathcal E_{Pot})}.\n\\end{equation}\n\nThis means that the magnitude of the velocity of an element \nwith a given energy $d\\mathcal E$ depends only on the potential \nenergy of this element $d\\mathcal E_{Pot}$. Equation (\\ref{2}) \ndoes not contain any other parameters, in particular, of \nparameters which would suggest the dependence of the magnitude \nof the velocity on its direction. As for the potential energy \nof this element, it depends only on the position of this element, \n$d\\mathcal E_{Pot}=edq\/r$. \nOne comes inevitably to the conclusion that the {\\itshape\\bfseries\n{magnitude of the velocity}} of an element at a given point \n{\\itshape\\bfseries{does not depend on \nthe direction}} of motion of this element.\n\nIt is a very significant statement, and, hence, it has to be \ncorroborated in more detail and in a more revealing way. \nRewrite Eq. (\\ref{1}) in the form\n\n\\begin{equation}\n\\label{3}\nd\\mathcal E=\\frac{dm}{2}(\\dot r^2+r^2\\dot\\zeta^2)+d\\mathcal E_{Pot}\n=\\frac{dm\\dot r^2}{2}+\\frac{dM^2}{2dmr^2}+d\\mathcal E_{Pot}.\n\\end{equation}\nHere $\\zeta$ is the angular coordinate in the plane in which \nthe element $dm$ rotates, and $dM$ is the angular momentum of \nthis element. Whence we come to \n\n\\begin{equation}\n\\label{4}\n\\dot r^2=\\frac{2}{dm}(d\\mathcal E-d\\mathcal E_{Pot})-\n\\frac{dM^2}{dm^2r^2}\n\\end{equation}\nThe term $r^2\\dot\\zeta^2$ can be derived from the expression \nfor the angular momentum $dM=dmr^2\\dot\\zeta$. Substituting it \ninto the expression for the velocity, we come to\n\n\\begin{equation}\n\\label{5}\n\\upsilon=\\sqrt{\\dot r^2+r^2\\dot\\zeta^2}=\\sqrt{\\frac{2}{dm}\n(d\\mathcal E-d\\mathcal E_{Pot})-\\frac{dM^2}{dm^2r^2}+\n\\frac{dM^2}{dm^2r^2}}.\n\\end{equation}\n\nAs seen from Eq.~(\\ref{5}), terms containing the angular \nmomentum cancel. Said otherwise, the magnitude of the \nvelocity does not depend on the angular momentum. Figure~1 \nshows, however, that it is different angular momenta of an \nelement of a given energy residing at a point that account \nfor the different directions of the elements velocity. \n\nThis brings us to the conclusion  that the magnitude of the velocity \n{\\itshape\\bfseries at a given point} (i.e., at point $\\mathbf r$ where element $dm$ resides) does not depend on the trajectory on which element $dm$ moves. At a given point, the element $dm$ has the same velocity, no matter what trajectory is involved.\n\nOne more comment is here in order. A separate element of charge $dq$ rotating in a {\\itshape\\bfseries circular} trajectory radiates an ac field with the frequency of rotation. If, however, elements of the charge fill completely the circular trajectory, this charge distribution will not radiate ac fields, because this state is the steady-state which does not depend on time. The trajectory of such a state is closed and is actually an analog of a circular current. And circular current, as is well known, does not radiate ac fields while generating constant electric and magnetic fields.\n\n\n\\section{Motion of a distributed charge in a Coulomb potential well}\n\n\nNow recall that we are considering motion not of a point but ruther  \nof a distributed charge.\n\nBecause in all trajectories which are shown in Fig.~1\nthe element of charge $dq$ has \nthe same energy, it can move \n{\\itshape\\bfseries along any} trajectory. Moreover, \nthis element of charge can move {\\itshape\\bfseries in all \ntrajectories at the same time}. This \ncan be visualized in the following way. Divide element   \nof charge $dq$ in $k$ parts. Then one element of charge \n$dq'=dq\/k$ with mass $dm'=dm\/k$ can move along one elliptical \ntrajectory, another \ncharge $dq'$, along another trajectory, and so on. As $k$ \ntends to infinity, all the trajectories will criss-cross \nall of the allowed region containing trajectories of the \nelements of charge $dq'$ of the same energy but with \ndifferent angular momenta. Generally speaking, this \nprocess may be considered not as motion of elements of \ncharge along trajectories but rather as motion of a \ncontinuous medium, of a {\\itshape\\bfseries charge wave}. \n\nConsider now the velocity with which elements of a distributed charge move. As already shown, elements of a distributed charge can propagate from a given point along all trajectories simultaneously. In Section~1 it was demonstrated that elements of charge have at a specific point the same velocity in any trajectory. At this specific point, these trajectories are characterized by different directions (within a solid angle $2\\pi$, see Fig.~1). Hence, when a charge propagates over all trajectories simultaneously, the directions of velocities of different elements at a given point are confined within the solid angle $2\\pi$, while their magnitude is the same.\n\nThis motion {\\itshape\\bfseries of a charge wave} may be treated from two angles, to wit, either as motion of different elements of charge on all trajectories at the same time, or as motion of a wave. In the first case, the behavior of each element is described by equations of mechanics (allowing for the potentials in which these elements move; but for the description of the overall picture to be complete, one will have to take into account that the number of these elements is infinite). In the second case, one will have to resort to equations in partial derivatives. For description of the behavior of any continuous medium, and, in particular, of a distributed charge the second model appears to be simpler and, thus, preferable. For the present, however, we are going to adhere to the first approach -- it appears more graphic (while certainly more cumbersome). \n\nTurning now to Fig.~1, we see immediately that different trajectories (i.e., trajectories characterized by the same energy but different momenta) cross one another. Said otherwise, it turns out that the charges moving along all trajectories simultaneously {\\itshape\\bfseries can \"interpenetrate\"} one another without  changing their trajectories.\n\nThis would seem at first glance to be in contradiction with the well known statement that like charges repel. Therefore the assumption that likely charged elements can penetrate into one another may sound surprising, to say the least. But point charges considered usually in science have an infinite density at the point of charge. Therefore like point charges cannot penetrate into one another  and, moreover, cannot even approach one another to a short enough distance. The distributed charges considered by us have a specific finite charge density. We are going to show now that charges can penetrate into one another, depending on what external forces act on these charges and what relevant forces are generated by the charges themselves.\n\nThe force $d\\mathbf F=\\mathbf Edq$ acting on any element of charge \n$dq=\\rho dV$ is defined by the magnitude of the electric field \n$\\mathbf E$ at this point. The field $\\mathbf E(\\mathbf r)$ at a given point  $\\mathbf r$ is a sum of the field $\\mathbf E_N(\\mathbf r)$ generated by the nucleus and the field $\\mathbf E_{\\rho}(\\mathbf r)$ created by all the charges surrounding the given charge:\n\n\\begin{equation}\n\\label{6}\n\\mathbf E(\\mathbf{r})=\\mathbf E_N(\\mathbf{r})+\\mathbf E_{\\rho}(\\mathbf{r})=\n\\frac{e\\mathbf r}{r^3}+\\int{\\frac{\\rho(\\mathbf r')(\\mathbf r-\\mathbf r')dV'}\n{|\\mathbf r-\\mathbf r'|^3}}.\n\\end{equation}\n\nThe presence of expression $|\\mathbf r-\\mathbf r'|^3$ in the denominator of the second term in equality (\\ref{6}) might cause an erroneous idea that the field $\\mathbf E_{\\rho}(\\mathbf{r})$ at point $\\mathbf r$ is large. In this case the element of charge located at point $\\mathbf r''$, near point\n $\\mathbf r$, will not be able to approach in its motion point \n$\\mathbf r$, because both these elements of charge have like signs.\n One can readily show that this is not so: indeed, the field \n$\\mathbf E_{\\rho}(\\mathbf{r})$ is finite at point $\\mathbf r$, and the difference between the fields at the two neighboring points $\\mathbf r$ and   $\\mathbf r''$ tends to zero as the magnitude of \n$|\\mathbf r-\\mathbf r''|$ approaches zero. \n\nTo prove this, we use the approach employed in monograph \\cite{2}, $\\$44$. Circumscribe a sphere of radius $R_0$ around point $\\mathbf r$. The field generated by the charges outside the sphere $R_0$ is finite, because these charges are at a finite distance larger than $R_0$ from point $\\mathbf r$. We have now to verify that the field $\\hat\\mathbf E(\\mathbf r)$ generated by charges confined inside the sphere $R_0$, i.e., in the immediate vicinity of point $\\mathbf r$, is also finite. Denoting  $|\\mathbf r-\\mathbf r'|=R$, and \n$(\\mathbf r-\\mathbf r')=\\mathbf R$, we can write for this part of the field:\n\n\\begin{equation}\n\\label{7}\n| \\hat \\mathbf E(\\mathbf r)|\\le\\int{\\frac{|\\rho(\\mathbf r')\\mathbf R|d\\hat V}\n{R^3}},\n\\end{equation}\nwhere integration of $d\\hat V$ is performed over the volume of the sphere \n$R_0$. But\n$$\n|\\rho(\\mathbf r')\\mathbf R|\\le |\\rho_{max}|R,\n$$          \nwhere $|\\rho_{max}|$ is the absolute value of the maximum density of charge inside sphere $R_0$.\n\nWe finally come to \n$$\n| \\hat \\mathbf E(\\mathbf r)|\\le|\\rho_{max}|\\int{\\frac{d\\hat V}\n{R^2}}.\n$$    \n\nIntroducing spherical coordinates  $R, \\vartheta, \\varphi$ with the center at point $\\mathbf r$, with $d\\hat V=R^2sin\\vartheta d\\vartheta d\\varphi dR$,\nand integrating with respect to $R$ from $0$ to $R_0$, we obtain\n\n\\begin{equation}\n\\label{8}\n|\\hat \\mathbf E(\\mathbf r)|\\le 4\\pi|\\rho_{max}|R_0.\n\\end{equation}\n\nThus $\\hat \\mathbf E(\\mathbf r)$ is a finite quantity tending to zero with decreasing radius of the sphere $R_0$. Moreover, this immediately suggests a conclusion that the difference between the values of vector $\\mathbf E$ \nat two adjacent points, for instance, $\\mathbf r$ and $\\mathbf r''$, tends to zero with the distance between these points approaches zero too. Suppose that these two points are located inside the sphere $R_0$. The field created by charges outside the sphere $R_0$ is continuous, because these charges are at finite distances from points $\\mathbf r$ and $\\mathbf r''$.\n As for the field $\\hat \\mathbf E$ generated by charges confined inside the sphere $R_0$, the strength of this field in absolute magnitude, as proved above, cannot be larger than the value of $4\\pi|\\rho_{max}|R_0$. As the magnitude of $R_0$ is going to zero, we see that this part of the field also changes continuously and tends to zero as $R_0$ approaches zero.\n\nThus the electric field $\\mathbf E$ surrounding any element of the distributed charge $dq=\\rho dV$ is finite and varies continuously. And this is why the force $d\\mathbf F=\\mathbf Edq$ acting on this element of charge is finite and varies continuously. The element of distributed charge will be driven by this force to move in the direction of the total force acting at this point.  \n\nIn actual fact, the statement that charges can pass through \none another does not carry anything supernatural in it. For \ninstance, electromagnetic fields can penetrate one into or \nthrough the other without at the same time affecting one \nanother---this is nothing but the standard principle of \nsuperposition. Two radar beams can cross without interaction; \nthis is just penetration of ac fields through one another. \nSuperposition of one dc field on another (the principle of  \nsuperposition) may be regarded as penetration of one field \ninto another. Significantly, in this process the fields do \nnot act in any way on one another.\n\nAs for the charges, no statements concerning passage of one \ncharge through another without direct action on one another \n(interaction of charges is taken into account through the \nfields created by these charges) have thus far been made, \nalthough the principle of superposition is valid for charges \nas well. This statement should, however, be made. \n\nThis paper was intended to address the case of small density of the distributed charge. This means that we shall neglect the second term in expression (\\ref{6}) compared to the first one. In this case, any element of charge $dq$ with mass $dm$ moves only in the field of charge of the nucleus \n$e$, and for this element all the conditions specified in Section~1 are fully met, and the motion of this element will be subject to the laws described in the above monograph \\cite{1}, \\$~15.\n\nWe have considered earlier a set of trajectories, both elliptical and circular, which are characterized by the same energy. In a Coulomb potential well, however, elements moving along different, including circular, trajectories may have different energies. The potential energy of an element in a circular trajectory is constant and depends only on the distance of this element from the nucleus, $d\\mathcal E_{Pot}=edq\/r$. Each element in any circular trajectory can be identified by a set of elliptical trajectories with the same energy (see Fig.~1). This makes the total set of all trajectories extremely complex.\n\n\n\\section{Distributed charge has no spherical symmetry}\n\nConsider the shape which can have a charge in a Coulomb potential well.\n\nIn a spherical coordinate system $r, \\vartheta, \\varphi$ the angular part of any distribution of charges can be presented in the form of an expansion in spherical functions $Y_{lm}(\\vartheta, \\varphi)$. Let us see what spherical functions can be employed in description of a distributed charge in a Coulomb potential well.\n\nThe simplest spherical function is the spherically symmetric function \n$Y_{00}(\\vartheta, \\varphi)$. This function should be present in an expansion always (except for the cases where the total charge of the distribution is zero). This has the following natural explanation. The integral over all space of a charge expanded in spherical functions $Y_{lm}(\\vartheta, \\varphi)$ yields the total charge $Q$. But the only angular function whose integration yields a nonzero result is $Y_{00}(\\vartheta, \\varphi)$. Integration of all other functions will yield zero. \nTherefore only the function $Y_{00}(\\vartheta, \\varphi)$ can describe the presence itself of a charge in a volume. All the other angular functions participating in the expansion can only change the shape of the charge distribution, while not being capable of removing or adding a charge.\n\nOn the other hand, a distributed charge cannot be characterized with the use of one angular function $Y_{00}(\\vartheta, \\varphi)$ only. This becomes evident from the following consideration. A Coulomb potential well is spherically symmetric. Therefore, an elliptical trajectory of propagation of an element of charge may lie in any plane passing through the nucleus (i.e., through the origin of coordinates).\n\nAn analysis of all elements of a distributed charge reveals that their trajectories lie {\\itshape\\bfseries in all planes simultaneously}. Consider now different planes in which the elliptical trajectories of elements may lie. We choose for this purpose one of such planes, rotate it successively and follow several trajectories of motion of an element. The continuity of the distributed charge allows this operation.\n\n\\begin{figure}\n\\label{F2}\n\\begin{center}\n\\includegraphics[scale=1]{Figure2.eps}\n\\caption{}\n\\end{center}\n\\end{figure}\n\nThis situation is visualized in Fig.~2. It shows three planes which may confine the trajectories of motion $A$, $B$ and $C$. The nucleus is located at point $O$. A $K-K$ line passing through the nucleus is drawn in plane $A$. One can see three trajectories in plane $A$: a circular trajectory $a1$, an elliptical trajectory $a2$, and another elliptical trajectory $a3$, which is symmetric to $a2$ about the $K-K$ line.\nIt is shown that all elements lying in plane $A$ rotate in the same sense. We shall turn plane $A$ about the $K-K$ line in angle $\\eta$ starting from an initial direction. Because the Coulomb potential is spherically symmetric, and the charge continuous, it can be expected that on turning plane $A$ about the $K-K$ line through angle $\\pi$, we shall come to the state in which all trajectories will coincide with the ones that had been there before the turn of the plane.\n\nLet us perform this operation of the turn. Figure~2 shows two positions of the plane after a turn by $\\pi\/2$ and by an angle $\\pi$. By turning plane $A$ about the $K-K$ axis in angle $\\eta$ by an angle $\\pi\/2$, we come to plane \n$B$ with trajectories $b1$, $b2$, $b3$, and by angle $\\pi$, to plane $C$ with trajectories  $c1$, $c2$, $c3$. \nSignificantly, trajectory $c1$ in plane  $C$ will exactly coincide with trajectory $a1$ in plane $A$. Similarly, trajectory  $a2$ will merge with trajectory $c3$, and trajectory  $a3$, with $c2$. Thus for each elliptical trajectory in plane $A$ there will be always the corresponding trajectory in plane $C$. After the turn of the plane, these trajectories will coincide.\n\nIt will turn out, however, that motion along all these trajectories after completion of the turn of the plane (i.e., in position $C$) will occur in the sense opposite to that in which the elements moved in the plane before its turn (that is, in position $A$). The + sign on planes $A$, $B$, $C$ is put for the sake of convenience in following the effect of plane rotation.\n\nSince we are considering a {\\itshape\\bfseries distributed charge}, its elements should move simultaneously in all planes, including planes $A$ and $C$. As showed, however, our analysis, motion over the latter should occur in opposite directions. All elements just cannot rotate simultaneously in opposite directions (this would involve loss of energy).\n\nIt thus turns out that motion over these trajectories is impossible altogether. Hence, there should exist a direction in which trajectories for motion of charges do not exist at all. In the spherically symmetric potential well of the nucleus one cannot, however, isolate a specified direction (for instance, the direction from which we reckoned the angle  $\\eta$ in Fig.~2). Hence, a distributed charge must have a specified direction, a direction in which the distributed charge does not exist. In this case, with no charge in this direction, one cannot expect existence of trajectories along which propagation could occur in opposite directions.\n\nIn other words, although the Coulomb potential is spherically symmetric, distributed charge loses spherical symmetry.\n\nThis appears only natural, because the angular momentums  in plane $A$ (i.e., before the turn of the plane) do not coincide with those in plane $C$ (i.e., after the turn of the plane) and, moreover, have opposite orientation.\n\nTo sum up, in a spherically symmetric Coulomb potential well a spherically symmetric charge distribution just cannot exist; there must therefore exist a specified direction. An additional comment concerning a specified direction in which there is no distributed charge will be proposed in Section 5.\n\n\n\\section{Description of a charge with spherical functions}\n\nAs follows from previous considerations, description of a distributed charge has to be made with a spherically symmetric angular function \n$Y_{00}(\\vartheta, \\varphi)$ (this function specifies the presence itself  of a charge in the given potential well). This function alone is not sufficient, however, because the $Y_{00}(\\vartheta, \\varphi)$ function does not have any specified direction (a specified direction appears as a result of the circular motion of the elements of charge around the nucleus). Therefore, description of a charge requires, even in the simplest case, invoking some other $Y_{lm}(\\vartheta, \\varphi)$ functions as well. Let us see what functions could be employed in description of a distributed charge.\n\nWe start by assuming that the specified direction discussed above coincides with the $\\vartheta=0$ direction of the spherical coordinate system. We shall call this direction the $Z$ axis. Then total rotation of the elements of charge will occur about the $Z$ axis, i.e., along the $\\varphi$ coordinate. We understand under total rotation here not the rotation of any one element but rather that of the totality of the elements, of the distributed charge as a whole. We discussed in Section 1 a plane with respect to which an element   $dq$ (or $dm$) propagates as a wave in a solid angle $2\\pi$. In the present case this plane passes through the axis $Z$ and the position of the element at the given moment, i.e., perpendicular to the $\\varphi$ coordinate.\n\nIntroduce an additional condition; to wit, we are going to consider only stationary, i.e., time-independent, states of the charge. States of charge which do not depend on time, do not produce radiation of variable fields, while generating constant electric and magnetic fields. Because stationary states of a distributed charge do not vary with time, no need appears in proving that such states do not generate variable fields, i.e., fields depending on time. If total rotation of the charge occurs about the $Z$ axis, i.e., along the $\\varphi$ coordinate, absence  of radiation can be described by using for description  only functions which are axially symmetric about the $Z$ axis. This restricts the allowable set of functions to those of the $Y_{l0}(\\vartheta, \\varphi)$ group. Indeed, only \n$Y_{l0}(\\vartheta, \\varphi)$ functions do not depend on the coordinate \n$\\varphi$, i.e., have axial symmetry with respect to the $Z$ axis.\n\nIf we impose one more constraint, namely, that the distributed charge is symmetric with respect to the coordinate $\\vartheta=\\pi\/2$, i.e., about the equator (which is a more frequent situation), index $l$ of the spherical function $Y_{l0}$ can be only even.\n\nThere are no other proper functions for description of a charge which does not generate radiation. Indeed, $Y_{lm}(\\vartheta, \\varphi)$ functions contain a factor $exp(\\pm im\\varphi)$. Motion of such a charge along the coordinate $\\varphi$ will initiate dependence on time (a factor of the kind of $exp(\\pm im\\varphi-i\\omega t)$ will appear, where $\\omega$ is the frequency of the moving wave). The appearance of the dependence on time will inevitably give rise to radiation of variable fields. We disregard here such states involving radiation and focus our interest on stationary states only, which do not generate radiation.\n\nThe simplest function satisfying the above requirements is $Y_{20}$. We write therefore the angular part of the relation for a distributed charge in the form\n\n\\begin{equation}\n\\label{9}\nL=D(Y_{00}+D_{20}Y_{20}),\n\\end{equation}\n$$\n\\mbox{where  }Y_{00}=\\frac{1}{\\sqrt{4\\pi}},\\quad Y_{20}\n=\\sqrt{\\frac{5}{4\\pi}}\\left(\\frac{3}{2}\\cos^2\\vartheta-\\frac{1}\n{2}\\right),\\quad \\mbox{(see, e.g., \\cite{3}).}\n$$\n\nThe coefficient $D_{20}$ can be determined from the condition that at \n$\\vartheta=0$ and $\\vartheta=\\pi$ (i.e., on the $Z$ axis) the function $L$ be zero. Coefficient  $D$ can be found from the condition that at \n$\\vartheta=\\pi\/2$ (i.e., at the equator) function $L$ is unity. These conditions bring us to\n\n\n\n$$\nD=\\frac{2\\sqrt{4\\pi}}{3},\\qquad D_{20}=-\\frac{1}{\\sqrt{5}}.\n$$\nNow function L acquires the final form\n$$\nL=\\frac{2\\sqrt{4\\pi}}{3}\\left[\\frac{1}{\\sqrt{4\\pi}}-\\frac{1}\n{\\sqrt5}\\cdot\\sqrt{\\frac{5}{4\\pi}}\\left(\\frac{3}{2}\\cos^2\n\\vartheta-\\frac{1}{2}\\right)\\right].\n$$\nOne can readily verify that this function simply coincides with the function \n$\\sin^2\\vartheta$. This means that in this case the angular part of the density of distributed charge can be written in one of two ways:\n\n\\begin{equation}\n\\label{10}\nL=\\sin^2\\vartheta, \\quad \\mbox{or} \\quad L=D(Y_{00}+D_{20}Y_{20}),\n\\end{equation}\nand the density of distributed charge corresponding to this angular distribution will read\n\\begin{equation}\n\\label{11}\n\\rho(r,\\vartheta)=AR(r)\\sin^2\\vartheta, \\quad \\mbox{or} \\quad\n\\rho(r,\\vartheta)=AR(r)D(Y_{00}+D_{20}Y_{20}),\n\\end{equation}\nwhere $R(r)$ is the radial part of the distribution. The coefficient $A$ is derived from normalization of the distributed charge against the total charge $Q$.\n\nOne may choose any form that would seem appropriate in a given situation.\n\nThus, in describing a charge with spherical functions one obtains for the charge distribution in a Coulomb potential well in the simplest case a figure resembling a torus. All elliptical and circular trajectories of an elements of the charge (of any energy) should be confined to this torus. We note that at the $Z$ axis the charge is zero.\n\nA comment will be appropriate here. As shown earlier, at a given point the element $dm$ propagates in all directions (within a solid angle $2\\pi$) with the same velocity. It would seem that this is in direct contradiction with the statement that a distributed charge has a specified direction in which there is no charge. In particular, in the above example with a torus-shaped charge, it would seem that the trajectories lying on the equator must differ from those confined to a perpendicular plane, because these trajectories cross the $Z$ axis, where the charge is zero. \n\nThe following point may be in order here. The trajectories of the element $dm$ in Fig.~1 were considered by us under the tacit assumption that this element will continue to move along its original trajectory. (This assumption derives from the concept of the motion of a solid body.) This is, however, not necessarily so. An analysis of Fig.~1 shows that {\\itshape\\bfseries each point} is a center from which elements of charge propagate in all directions (within a solid angle $2\\pi$). Said otherwise, element $dm$ does not move along this trajectory all the time. At each point it breaks up into many elements $dm'$ which continue to move subsequently, but now along other trajectories.\n At the next point the situation repeats, with breakup into many elements, at the next point -- again into countless elements, and so on. Thus, the element $dm$, in starting its motion at a point on a trajectory, should not necessarily terminate it at the same trajectory. Actually, this is motion not of individual elements but rather that of a wave. This is why a mass (and a charge) may have different densities at different points in space.\n\nThis is an allowed process, because in each trajectory the corresponding element has the same energy. But {\\itshape\\bfseries at each given point} the velocity of the elements remains, as before, the same in all directions, irrespective of the density of charge or mass at the given point.\n\n \n\\section{Differences in the velocity of motion between a charge wave and individual elements}\n\nAs already pointed out, it appears more appropriate to consider the motion of elements of equal energy along different elliptical trajectories as that of a charge wave. It appears pertinent to compare now different parameters of motion of this wave with those of an individual element.\n\nThe total energy of all elements making up a charge wave is equal to the energy of one combined element lying at the point of crossing of all elliptical trajectories and moving along one of the circular trajectories. Considered in the context of equality of energies, the motion of a charge wave may be correlated with that of one point element, with the sum of the energies of all elements in this wave equal to the energy of one combined element moving in a circle. This energy can be readily determined.\n\nAn element moving along a circular trajectory retains both its total and the potential and kinetic energies. By the virial theorem (see, e.g. \\cite{1}, \n\\$~10), in this case the potential energy of an element is twice its total energy, and its total energy is equal to the kinetic energy taken with the opposite sign, \n$2d\\mathcal E=d\\mathcal E_{Pot}$, $d\\mathcal E=-d\\mathcal E_{Kin}$. No averaging is needed here, because the energies are constant. As for the potential energy of an element in a circular orbit, it can be derived simply from the radius $R$ of the circular orbit: $d\\mathcal E_{Pot}=edq\/R$. \n\nThe situation is different with the velocities of motion of a wave and of individual elements.\n \nAn analysis of Fig.~1 suggests that {\\itshape\\bfseries each point} of a charge is a center from which elements of charge propagate in all directions (within a solid angle $2\\pi$). One might say that the motion of a distributed charge at a given point represents a kind of \"a velocity fan\"\\ for all directions (within a solid angle $2\\pi$); note that, as shown in Section~1, in any direction the velocity has the same magnitude. \n\nThe velocity of an element being a vector, the velocity must \nretain its vector properties even in the case of the element \npropagating (in the form of a wave) within a solid angle of \n$2\\pi$. This, however, will be not the velocity of a single \nelement but rather that of motion of a wave, of propagation \nof a wave process. It turns out that the velocity of propagation \nof a wave process does not coincide with that of motion of \nelements of mass or charge. The momentum of an element $dm$ \npropagating as a wave likewise does not coincide with that \nof an element moving as a whole in one direction.\n\nDenote the velocity of motion of a charge wave by $\\mathbf \nv_w(\\mathbf r)$ (the subscript $w$ standing for wave), and \nthe magnitude of this velocity, by $\\upsilon_w(\\mathbf r)$, \nto discriminate this velocity from the velocity \n$\\mathbf v(\\mathbf r)$ and $\\upsilon(\\mathbf r)$ of motion \nof an element of charge. The momentum of an element $dm$ \npropagating as a wave will be denoted, accordingly, by \n$\\mathbf p_w(\\mathbf r)$.\n\nConsider this situation in more detail.\n\nIsolate an element of mass $dm$ at a point in space. If this \nelement moves as a whole with a velocity $\\mathbf{v}_l$ along \na trajectory $l$, the momentum $d\\mathbf{p}_l$ of this element \nwill be\n\\begin{equation}\n\\label{12}\nd\\mathbf{p}_l=dm\\mathbf{v}_l,\\qquad\\mbox{and the magnitude of \nthe momentum }\\qquad dp_l=dm\\upsilon.\n\\end{equation}\n\nTo describe the motion of this element of mass as that of a wave \nin the solid angle of $2\\pi$, divide the mass $dm$ into many parts \n$dm'$. Each part $dm'$ will propagate within a solid angle $d\\Omega$. \nIn this case, we can write $dm'=dm\\cdot\\frac{d\\Omega}{2\\pi}$. \nAs was shown in Section~1\nthe velocity of motion of each element $dm'$ is the same, equal \nin magnitude to the velocity $\\upsilon$ of motion of the whole \nelement $dm$. \n The direction of this velocity \n$\\mathbf{v'}$ is determined by the solid angle $d\\Omega$. \nFor the momentum of element $dm'$ in this case we can write\n\\begin{equation}\n\\label{13}\nd\\mathbf p'=dm'\\mathbf v'=dm\\frac{d\\Omega}{2\\pi}\n\\mathbf v',\\quad\\mbox{and for its magnitude}\\quad\ndp'=dm\\frac{d\\Omega}{2\\pi}\\upsilon.\n\\end{equation}\n\nIt might come up as a surprise that sometimes we discuss motion \nalong an elliptical trajectory (for instance, trajectory $l$) \nto stress that the element $dm$ moving in this trajectory obeys \nall laws of theoretical mechanics, while in other cases we prefer \nto identify the motion of the same element in a solid angle as \nthat of a wave.\n\nIn actual fact, we are speaking in these cases about different \nthings. When discussing the motion along a trajectory, we follow \nthe motion of {\\itshape\\bfseries{one}} specific element, be it \nelement $dm$ or $dm'$. It appears only natural that the motion \nof this element obeys all laws of theoretical mechanics.\n\nWhen, however, we discuss the motion of an element as a wave in \na solid angle, we have in mind rather the motion of \n{\\itshape\\bfseries{many}} elements crossing at a point \n$\\mathbf r$. This is shown in a revealing way in Fig.~1. \nThis set off elements could be formed of one element $dm$ as well. \nIt is for this purpose that we broke up element $dm$ into a set \nof elements $dm'$, which thereafter moved along {\\bfseries\\itshape\n{different}} trajectories.\n\n\\medskip\n\nWe chose to orient a spherical coordinate system such that the \ndirection $\\vartheta=0$ coincides with that of the angular momentum \nof the charge, and denoted this axis by $Z$. All elements of a \ndistributed charge rotate in the same sense (overall rotation \nis around the $Z$ axis). That all elements rotate in one sense only \nimplies that there are no velocity components along the negative \ndirection of the $\\varphi$ axis. In other words, on passing a \nplane through the $Z$ axis and the position of element $dm$, we end \nup with the following situation: element $dm$ propagates (as a wave) \ninto a solid angle of $2\\pi$, i.e., into the hemisphere located \non one side of this plane.\n\n\\begin{figure}\n\\label{F3}\n\\begin{center}\n\\includegraphics[scale=1]{Figure3.eps}\n\\caption{}\n\\end{center}\n\\end{figure}\n\nThis situation is illustrated by Fig.~3. In Fig.~3, the $Z$ axis is \ndirected at us (i.e., it is actually a top view). The nucleus  \nis at point O. Dashed lines are lines of equal mass density. \nElement $dm$ propagates into a solid angle of $2\\pi$, i.e., into the \nhemisphere. We see a fanlike distribution of velocities $\\mathbf v'$ \nof the elements of mass $dm'$. The velocity of motion of element \n$dm'$ in any direction is the same. In Fig.~3, this is shown by all \nvelocity vectors $\\mathbf v'$ being of equal length.\n\nTo find the resultant momentum of an element $dm$ in the case where \nit propagates (as a wave) into a hemisphere, we have to sum all the \nmomentum vectors $d\\mathbf p'=dm'\\mathbf v'$. This can be done by \nintroducing a local spherical system of coordinates centered on the \nlocation of element $dm$, with angles $\\eta$ and $\\xi$. We orient \nthe coordinate system such that the $\\eta=0$ direction is \nperpendicular to the above-mentioned plane and denote this direction \nby $Z'$. In this particular case, $Z'$ coincides with the direction \nof the $\\varphi$ axis of the common coordinate system. Next we \nresolve the momentum into a component along the $Z'$ axis, and another,\nperpendicular to it. By virtue of the symmetry relative to \nthe $Z'$ axis, the perpendicular component will vanish after the \nsummation, leaving only the component along the $Z'$ axis, i.e., \nalong the $\\varphi$ axis. Thus, the resultant momentum of an element \nmoving in all directions simultaneously (into a solid angle of $2\\pi$, \ni.e., into the hemisphere) is aligned with the $\\varphi$ axis. \nCalculate now $dp_{w,\\varphi}$, i.e., the projection of the momentum \non the $\\varphi$ axis. To do this, we sum all $dp'_\\varphi$ components. \nUsing Eq. (\\ref{13}), we come to $dp'_\\varphi=dp'\\cos\\eta=\ndm'\\upsilon\\cos\\eta=dm\\frac{d\\Omega}{2\\pi}\\upsilon\\cos\\eta$, whence:\n\\begin{equation}\n\\label{14}\ndp_{w,\\varphi}=\\int{dm\\frac{d\\Omega}{2\\pi}\\upsilon\\cos\\eta}=\n\\frac{dm}{2\\pi}\\upsilon\\int\\limits_0^{\\pi\/2}\\cos\\eta\n\\sin\\eta d\\eta\\int\\limits_0^{2\\pi}d\\xi=\n\\frac{1}{2}dm\\upsilon=\\frac{1}{2}dp_l,\n\\end{equation}\nor\n\\begin{equation}\n\\label{15}\nd\\mathbf p_w=\\frac{1}{2}dm\\upsilon \\mathbf n_\\varphi ,\n\\end{equation}\nwhere $\\mathbf n_\\varphi$ is the unit vector along the $\\varphi$ axis.\n\nComparing now Eqs. (\\ref{14}) and (\\ref{15}) with relations (\\ref{12}), \nwe see that the momentum of an element propagating into a hemisphere \nis one half that in magnitude of an identical element moving in one \ndirection. Also, while the momentum of an element moving as a whole \nin one direction coincides in direction with its velocity, the \nmomentum of an element propagating into a hemisphere is directed \n{\\itshape\\bfseries {only along the}} $\\varphi$ {\\itshape\\bfseries \n{axis}}. {\\itshape\\bfseries {This momentum has no other components}}.\n\nThe above reasoning and the conclusions were conducted for a momentum. \nTo obtain a diverging  wave, the element $dm$ was broken up \ninto smaller elements $dm'$, with all $dm'$ elements having the same \nvelocity $\\upsilon$, and each element of mass $dm'$ propagating in \nits solid angle $d\\Omega$. This is a rigorous treatment. It can be \nmade more convenient, however, by considering not the momentum but \nrather directly the velocity. To do this, we denote conventionally \n $d\\upsilon=\\upsilon d\\Omega$, understanding by $d\\upsilon$  a set \n of velocities with directions confined to the solid angle $d\\Omega$. \n Then in place of Eq. (\\ref{15}) and taking into account (\\ref{12})\n we come to\n\\begin{equation}\n\\label{16}\n\\mathbf v_w=\\frac{1}{2}\\upsilon\\mathbf n_\\varphi.\n\\end{equation}\n\nHere $\\mathbf v_w$ is no longer the velocity of a single element \n$dm$ moving in its trajectory; it is now the remaining vector part \nof the velocity of the element $dm$ propagating into the hemisphere, \nand $\\upsilon$ is, as before, the magnitude of the velocity of the \nelement moving in its trajectory.  \n(Equation (\\ref{16}) can be also derived \ndirectly from Eq. (\\ref{15}) by canceling $dm$).\n\nThus, the velocity $\\mathbf v_w(\\mathbf r)$ is the velocity of \npropagation of a wave process, and the modulus of \n$\\mathbf v_w(\\mathbf r)$ is the magnitude of the velocity of the \nwave process $\\upsilon_w(\\mathbf r)$. The magnitude of the velocity \nof a wave process does not coincide with that of propagation of \nelements of charge. Indeed, taking the modulus of $\\mathbf v_w$ \n(using Eq. (\\ref{16}) and recalling that vector $\\mathbf v_w$ has \nonly one component, and it is directed along the $\\varphi$ axis), \nwe obtain only one half of the real velocity of an element $\\upsilon$. \nIndeed, some of the vector components vanish in propagation of \nthe element as a wave into the hemisphere. \nActually, these components do not disappear without trace, so that, \nfor instance, they have to be taken into account in calculation of \nthe energy, because in actual fact elements move along elliptical \ntrajectories with a velocity $\\upsilon$.\nSpecifically, for calculation of the kinetic energy one must use\nthe $\\upsilon$ quantity that is the real velocity of an element.\nFor calculation of the angular momentum (vector quantity) \nof the distributed charge one must use $\\mathbf v_w$ quantity.\n\n\n\\addcontentsline{toc}{chapter}{\u041b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\\label{sec:intro}\nGiven an integer $k > 0$ and a set $P$ of $n$ weighted points in the plane,\nour objective is to fit a $k$-step function to them so that the maximum weighted\nvertical distance of the points to the step function is minimized.\nWe call this problem the {\\em $k$-step function problem}.\nIt has applications in areas such as geographic information systems, \ndigital image analysis, data mining, facility locations, and\ndata representation (histogram), etc.\n\nIn the unweighted case, if the points are presorted,\nFournier and Vigneron \\cite{fournier2011} showed that\nthe problem can be solved in linear time using the results of \n\\cite{frederickson1991a,frederickson1984,gabow1984}.\nLater they showed that the weighted version of the problem can also be solved\nin $O(n\\log n)$ time~\\cite{fournier2013},\nusing Megiddo's parametric search technique \\cite{megiddo1983a}.\nPrior to these results, the problem had been discussed by several researchers\n\\cite{chen2009,diazbanez2001,liu2010,lopez2008,wang2002}. \n\nGuha and Shim \\cite{guha2007} considered this problem in the context of {\\em histogram construction}.\nIn database research, it is known as the {\\em maximum error histogram} problem.\nIn the weighted case,\n this problem is to partition the given points into $k$ buckets based on their $x$-coordinates,\nsuch that the maximum $y$-spread in each bucket is minimized.\nThis problem is of interest to the data mining community as well (see \\cite{guha2007} for references).\nGuha and Shim \\cite{guha2007} computed the optimum histogram of size $k$,\nminimizing the maximum error.\nThey present algorithms which run in linear time when the points are unweighted,\nand in $O(n\\log n + k^2\\log^6n)$ time and $O(n\\log n)$ space when the points are weighted.\n\nOur objective is to improve the above result to $O(n)$ time when $k$ is a constant.\nWe show that we can optimally fit a $k$-step function to unsorted weighted points in linear time.\nWe earlier suggested a possible approach to this problem at an OR workshop~\\cite{bhattacharya2013b}.\nHere we flesh it out, presenting a complete and rigorous algorithm and proofs.\nOur algorithm exploits the well-known properties of prune-and-search along the lines in \\cite{bhattacharya2007}.\n\n\nThis paper is organized as follows.\nSection \\ref{sec:prelim} introduces the notations used in the rest of this paper.\nIt also briefly discusses how the prune-and-search technique can be used\nto optimally fit a $1$-step function (one horizontal line) to a given set of weighted points.\nWe then consider in Section~\\ref{sec:cond2step} a variant of the 2-step function problem,\ncalled the anchored 2-step function problem.\nWe discuss a ``big partition'' in the context of the $k$-partition of a point set\ncorresponding to a $k$-step function in Section \\ref{sec:kstep}.\nSection \\ref{sec:algorithm} presents our algorithm for the optimal $k$-step function problem.\nSection \\ref{sec:conclusion} concludes the paper,\nmentioning some applications of our results.\n\n\n\n\\section{Preliminaries}\\label{sec:prelim}\n\\subsection{Model}\\label{sec:model}\nLet $P=\\{p_1,p_2,\\ldots, p_n\\}$ be a set of $n$ weighted points in the plane.\nFor $1\\leq i\\leq n$ let $p_i.x$ (resp. $p_i.y$) denote the $x$-coordinate (resp. $y$-coordinate)\nof point $p_i$, and let $w(p_i)$ denote its weight.\nThe points in $P$ are not sorted,\nexcept that $p_1.x\\leq p_i.x\\leq p_n.x$ holds for any $i=1, \\ldots, n$.\\footnote{For the sake\nof simplicity we assume that no two points have the same $x$ or $y$ coordinate.\nBut the results are valid if this assumption is removed.\n}\nLet $F_k(x)$ denote a generic $k$-step function,\nwhose $j^{th}$ segment (=step) is denoted by $s_j$.\nFor $1\\leq j \\leq k-1$, segment $s_j$ represents a half-open horizontal interval $[s_j^{(l)}, s_j^{(r)})$\nbetween two points $s_j^{(l)}$ and $s_j^{(r)}$.\nThe last segment $s_k$ represents a closed horizontal interval $[s_k^{(l)}, s_k^{(r)}]$.\nNote that $s_j^{(l)}.y= s_j^{(r)}.y$,\nwhich we denote by $s_j.y$.\nWe assume that for any $k$-step function $F_k(x)$,\n segments $s_1$ and $s_k$ satisfy $s_1^{(l)}.x = p_1.x$ and $s_k^{(r)}.x = p_n.x$,\nrespectively.\nSegment $s_j$ is said to {\\em span} a set of points $Q\\subseteq P$,\nif $s_j^{(l)}.x \\leq p.x <s_j^{(r)}.x$ holds for each $p\\in Q$.\nA $k$-step function $F_k(x)$ gives rise to a {\\em $k$-partition} of $P$, \n${\\cal P}= \\{P_j \\mid j = 1, 2, \\ldots, k\\}$,\n such that segment $s_i$ spans $P_i$.\n It satisfies the {\\em contiguity condition} in the sense that for each partition $P_j$,\nif $a.x \\leq b.x$ for $a,b\\in P_j$,\nthen every point $p$ with $a.x \\leq p.x \\leq b.x$ also belongs to $P_j$.\nIn the rest of this paper, we\nconsider only partitions that satisfy the contiguity condition.\nFig.~\\ref{fig:4steps} shows an example of fitting a 4-step function $F_4(x)$.\n\\begin{figure}[ht]\n\\centering\n\\includegraphics[height=2.8cm]{figs\/4steps.pdf}\n\\hspace{2mm}\n\\caption{Fitting a 4-step function.\n}\n\\label{fig:4steps}\n\\end{figure}\n\nGiven a step function $F(x)$, \ndefined over an $x$-range that contains $p.x$,\nlet $d(p, F(x))$ denote the vertical distance of $p$ from $F(x)$.\nWe define the {\\em cost} of $p$ with respect to $F(x)$\nby the weighted distance\n\\begin{equation}\\label{eqn:pointCost}\nD(p, F(x))\\triangleq d(p, F(x))w(p).\n\\end{equation}\nWe generalize the cost definition for a set $Q \\subseteq P$ of points by\n\\begin{equation}\\label{eqn:setCost}\nD(Q, F(x)) \\triangleq \\max_{p \\in Q} \\{D(p, F(x))\\}.\n\\end{equation}\nPoint $p_h$ is said to be {\\em critical} with respect to $F(x)$ if\n\\begin{equation}\nD(p_h, F(x)) = D(P, F(x)).\n\\end{equation}\nNote that there can be more than one critical point with respect to a given step function.\nWe similarly define a critical point with respect to a single segment of $F(x)$\nas a point that has the maximum vertical weighted distance to it.\n\nFor a set of weighted points in the plane or on a line,\nthe point that minimizes the maximum weighted distance to\nthem is called the {\\em weighted 1-center}~\\cite{bhattacharya2007}.\nGiven a {\\em $k$-partition} of $P$, \n${\\cal P}= \\{P_j \\mid j = 1, 2, \\ldots, k\\}$,\nit is clear that $\\exists P_i \\in {\\cal P}$ such that $|P_i| \\geq \\lfloor n\/k\\rfloor$.\nWe call any such partition a {\\em big partition}.\nA big partition spanned by a segment in an optimal solution plays an important role.\n(See Procedure {\\tt Big$({\\cal P}, k)$} in Sec.~\\ref{sec:findBig}.)\n\n\n\\subsection{Bisector}\\label{sec:bisector}\nIf we map each point $p_i\\in P$ onto the $y$-axis,\nthe {\\em cost} of (or the weighted distance from) $p_i$\ngrows linearly from 0 at $p_i.y$ in each direction as a function of $y$.\nConsider arbitrary two points $p$ and $q$.\nTheir costs intersect at either one or two points,\none of which always lies between $p.y$ and $q.y$.\nIf there are two intersections,\nthe other intersection lies outside interval $[p.y,q.y]$ on the $y$-axis.\nIf $p.y\\not=q.y$ and $w(p)=w(q)$ hold\nthen there is only one intersection.\\footnote{If $p.y=q.y$,\nwe can ignore one of the points with the smaller weight.\n}\nLet $a$ (resp. $b$) be the $y$-coordinate of the upper (resp. lower) intersection point,\nwhere $b\\leq a$.\nWe call the horizontal line $y=a$ (resp. $y=b$)\nthe {\\em upper} (resp. {\\em lower}) {\\em bisector} of $p$ and $q$.\nIf there are only one intersection,\nwe pretend that there were two at $b=a$, which lies between $p.y$ and $q.y$.\n(Note that the $y$-axis is shown horizontally in Figs.~\\ref{fig:2points1} and \\ref{fig:2points3} below,\nwhere $y$ increases to the right.)\n\nLet $\\wp$ denote the $\\lceil n\/2\\rceil$ pairs,\nformed by pairing up the points in $P$ arbitrarily.\nThe cost lines of the points in each pair $(p,q)$ intersect\nas shown in Figs.~\\ref{fig:2points1}.\n\\begin{figure}[h]\n\\centering\n\\subfigure[]{\\includegraphics[height=1.5cm]{figs\/2points1.pdf}}\n\\hspace{2mm}\n\\subfigure[]{\\includegraphics[height=1.5cm]{figs\/2points2.pdf}}\n\\caption{1\/3 of upper intersections are at $y<U$:\n(a) $p$ can be ignored at $y>U$; (b) $q$ can be ignored at $y>U$.\n}\n\\label{fig:2points1}\n\\end{figure}\nLet $y=U$ be the line at or above which at least 2\/3 of the upper bisectors lie,\nand at or below which at least 1\/3 of the upper bisectors lie.\nWe use $\\wp^U_{2\/3}$ and $\\wp^U_{1\/3}$ to name the subsets of\n $\\wp$ that have these two sets of bisectors, respectively.\n Note that $|\\wp^U_{2\/3}|\\geq n\/2\\times 2\/3 = n\/3$ and $|\\wp^U_{1\/3}|\\geq n\/2\\times 1\/3 = n\/6$.\nSimilarly, let  $y=L$ be the line at or below which at least 2\/3 of the  \nlower bisectors lie,\nand  at or above which at least 1\/3 of the bisectors lie.\\footnote{{We define $U$ and $L$ this way,\nbecause many points could lie on them.}}\nWe use $\\wp^L_{2\/3}$ and $\\wp^L_{1\/3}$ to name the subsets of\n$\\wp$ that have these two sets of bisectors, respectively.\n Note that $|\\wp^L_{2\/3}|\\geq n\/2\\times 2\/3 = n\/3$ and $|\\wp^L_{1\/3}|\\geq n\/2\\times 1\/3 = n\/6$.\n\\begin{lemma} \\label{lem:one6th}\nWe can identify $n\/6$ points that can be removed without affecting the weighted 1-center\n for the values\nof their $y$-coordinates.\n\\end{lemma}\n\\begin{proof}\nConsider the following three possibilities.\n\\begin{enumerate}\n\\item[(i)]\nThe weighted 1-center lies above $U$.\n\\item[(ii)]\nThe weighted 1-center lies below $L$.\n\\item[(iii)]\nThe weighted 1-center lies between $U$ and $L$,\nincluding $U$ and $L$.\n\\end{enumerate}\n\nIn case (i), there are two subcases,\nwhich are shown in Fig.~\\ref{fig:2points1}(a) and (b), respectively.\nSince the center lies above $U$, \nwe are interested in the upper envelope of the costs in the \n$y$-region given by $y > U$.\nIn the case shown in Fig.~\\ref{fig:2points1}(a),\nthe costs of points $p$ and $q$ satisfy $d(y,p.y)w(p) <  d(y,q.y)w(q)$ for $y > U$.\nThus we can ignore $p$.\nIn the case shown in Fig.~\\ref{fig:2points1}(b),\n the costs of points $p$ and $q$ satisfy\n$d(y,p.y)w(p) >  d(y,q.y)w(q)$ for $y > U$.\nThus we can ignore $q$.\nSince $|\\wp^U_{1\/3}|\\geq n\/6$,\nin either case, one point from each such pair can be ignored,\ni.e., 1\/6 of the points in $P$ can be eliminated, because it cannot affect the weighted 1-center.\nIn case (ii) a symmetric argument proves that 1\/6 of the points in $P$ can be discarded.\n\n\\begin{figure}[ht]\n\\centering\n\\subfigure[]{\\includegraphics[height=1.5cm]{figs\/2points3.pdf}}\n\\hspace{2mm}\n\\subfigure[]{\\includegraphics[height=1.5cm]{figs\/2points4.pdf}}\n\\caption{2\/3 of upper bisectors are at $y> U$.}\n\\label{fig:2points3}\n\\end{figure}\n\nIn case (iii) see Fig.~\\ref{fig:2points3}.\nThe costs of each pair in $\\wp^U_{2\/3}$ (of the $2n\/3$ pairs) as functions of $y$ intersect at most once at $y<U$.\nThe cost functions of each pair in $\\wp^L_{2\/3}$ ($2n\/3$ pairs) intersect at most once at $y>L$.\nTherefore, $\\wp^U_{2\/3}\\cap \\wp^L_{2\/3}$  ($n\/3$ pairs must be common to both,)\ni.e., both intersections of each such pair occur outside of the $y$-interval $[L,U]$.\n$|\\wp^U_{2\/3}\\cap \\wp^L_{2\/3}| = n\/2 \\times 1\/3 = n\/6$.\nThis implies that their cost functions do not intersect within in $[L,U]$,\ni.e., one of each pair lies above that of the other in $[L,U]$,\nand can be discarded.\n\\end{proof}\n\n\n\\subsection{Optimal 1-step function}\\label{sec:1step}\nThis problem is equivalent to finding the weighted center for $n$ points on a line.\nWe pretend that all the points had the same $x$-coordinate.\nThen the problem becomes that of finding a weighted 1-center on a line,\ni.e., on the $y$-axis.\nThis can be solved in linear time using Megiddo's {\\em prune-and-search} method \\cite{bhattacharya2007,chen2015a,megiddo1983a}.\nIn \\cite{megiddo1983b} Megiddo presents a linear time algorithm in the case where the\npoints are unweighted. \nFor the weighted case we now present a more technical algorithm that we can apply\nlater to solve other related problems.\nThe following algorithm uses a parameter $c$ which is a small integer constant.\n\n\\begin{algorithm}{\\rm :} {\\tt 1-Step}$(P)$\n\\begin{enumerate}\n\\item\nPair up the points of $P$ arbitrarily.\n\\item\nFor each such pair $(p,q)$ determine their horizontal bisector lines. \n\\item\nDetermine a horizontal line, $y=U$ such that $|\\wp^U_{2\/3}|\\geq  n\/3$\nand $|\\wp^U_{1\/3}|\\geq n\/6$ hold.\n\\item\nDetermine a horizontal line, $y=L$ such that $L$ $|\\wp^L_{2\/3}|\\geq  n\/3$ and\n$|\\wp^L_{1\/3}|\\geq n\/6$ hold.\n\\item\nDetermine the critical points for $U$ and $L$.\n\\item\nIf there exist critical points for $U$ on both sides of (above and below) $U$, \nthen $y=U$ defines an optimal 1-step function, $F^*_1(x)$; Stop. \nOtherwise, let $s_U$ (higher or lower than $U$) be the side of $U$ on which the critical point\nlies.\n\\item\nIf there exist critical points for $L$ on both sides of $L$,\n$y=L$ defines $F^*_1(x)$; Stop.\nOtherwise, let $s_L$ (higher or lower than $L$) be the side of $L$ on which the critical point\nlies.\n\\item\nBased on $s_U$ and $s_L$, discard 1\/6 of the points from $P$,\nbased on Lemma~\\ref{lem:one6th}.\n\\item\nIf the size of the reduced set $P$ is greater than constant $c$, \nrepeat this algorithm from the beginning with the reduced set $P$.\nOtherwise, determine $F^*_1(x)$ using any known method\n(which runs in constant time).\n\\end{enumerate}\n\\end{algorithm}\n\n\\begin{lemma}\\label{lem:1step}\nAn optimal 1-step function $F^*_1(x)$ can be found in linear time.\n\\end{lemma}\n\\begin{proof}\nThe recurrence relation for the running time $T(n)$ of {\\tt 1-Step}$(P)$ for general $n$ is \n$T(n) \\leq T(n-n\/6) + O(n)$,\nwhich yields $T(n) = O(n)$.\n\\end{proof}\n\n\\section{Anchored $2$-step function problem}\\label{sec:cond2step}\nIn general, we denote an optimal $k$-step function by $F^*_k(x)$\nand its $i^{th}$ segment by $s^*_i$. \nLater, we need to constrain the first and\/or the last step of a step function to be\nat a specified height.\nA $k$-step function is said to be {\\em left-anchored} (resp. {\\em right-anchored}),\nif $s_1.y$ (resp.  $s_k.y$) is assigned a specified value,\nand is denoted by $^{\\downarrow}\\!F_k(x)$ (resp. $F_k^{\\downarrow}(x)$).\nThe {\\em anchored $k$-step function} problem is defined as follows.\nGiven a set $P$ of points and two $y$-values $a$ and $b$,\ndetermine the optimal $k$-step function $^{\\downarrow}\\!F^*_k(x)$  (resp. $F_k^{\\downarrow *}(x)$)\nthat is left-anchored (resp. right-anchored) at \n$a$ (resp. $b$) such that cost $D(P, ^{\\downarrow}\\!\\!F^*_k(x))$ (resp. $D(P, F_k^{\\downarrow *}(x))$)\n is the smallest possible.\nIf a $k$-step function is both left- and right-anchored, \nit is said to be {\\em doubly anchored} and is\ndenoted by $^{\\downarrow}\\!F_k^{\\downarrow}(x)$.\n\n\n\\subsection{Doubly anchored 2-step function}\nSuppose that segment $s_1$ (resp. $s_2$) is anchored at $a$ (resp. $b$).\nSee Fig.~\\ref{fig:anchored2}(a).\n\\begin{figure}[ht]\n\\centering\n\\subfigure[]{\\includegraphics[height=3cm]{figs\/conditional2.pdf}}\n\\hspace{4mm}\n\\subfigure[]{\\includegraphics[height=3cm]{figs\/goftNhoft.pdf}}\n\\caption{(a) $s_1.y=a$ and $s_2.y=b$;\n(b) Monotone functions $g(x)$ (in blue) and $h(x)$ (in red).\n}\n\\label{fig:anchored2}\n\\end{figure}\nLet us define two functions $g(x)$ and $h(x)$ by\n\\begin{eqnarray}\ng(x) &=& \\max_{p.x\\leq x} \\{w(p)\\cdot|p.y - a|~\\mid p\\in P\\},\\label{eqn:g}\\\\\nh(x) &=&\\max_{p.x>x} \\{w(p)\\cdot |p.y - b|~\\mid p\\in P\\},\\label{eqn:h}\n\\end{eqnarray}\nwhere $g(x) =0$ for $x <p_1.x$ and $h(x) =0$ for $x >p_n.x$.\nIntuitively, if we divide the points of $P$ at $x$ into two partitions $P_1$ and $P_2$,\nthen $g(x)$ (resp. $h(x)$) gives the cost of partition $P_1$ (resp. $P_2$).\nSee Fig.~\\ref{fig:anchored2}(b).\nClearly the global cost for the entire $P$ is minimized for any $x$\nat the lowest point in the upper envelope of $g(x)$ and $h(x)$,\nwhich is named $\\overline{x}$.\nSince the points in $P$ are not sorted,\n$g(x)$ and $h(x)$ are not available explicitly,\nbut we can compute $\\overline{x}$ in linear time using the {\\em prune-and-search} method,\ntaking advantage of the fact that $\\max\\{g(x),h(x)\\}$ is unimodal.\n\n\\begin{algorithm}{\\rm :} {\\tt Doubly-Anch-2-Step}$(P,a,b)$\\label{alg:double}\n\\begin{enumerate}\n\\item\nInitialize $P'=P$.\n\\item\nFind the point in $P'$ that has the median $x$-coordinate, $x_m$.\n\\item\nEvaluate $g(x_m)$ (resp. $h(x_m)$) using (\\ref{eqn:g}) (resp. (\\ref{eqn:h})).\n\\item\nIf $g(x_m) = h(x_m)$ then $\\overline{x}=x_m$. Stop.\n\\item\nIf $g(x_m) < h(x_m)$ (resp. $g(x_m) > h(x_m)$), \ni.e., $\\overline{x}< x_m$ (resp. $\\overline{x}< x_m$),\nprune all the points $p$ with $p.x < x_m$ (resp. $p.x > x_m$),\n from $P'$,\nremembering just the maximum cost.\n\\item\nStop when $|P'|=2$, and find the lowest point $\\overline{x}$.\nOtherwise, go to Step~2.\n\\end{enumerate}\n\\end{algorithm}\n\nWe have the following lemma.\n\\begin{lemma}\\label{lem:doublyAnchored}\nAn optimal doubly anchored 2-step function\ncan be found in linear time.\n\\end{lemma}\n\\begin{proof}\nSteps~2 and 3 of Algorithm {\\tt Doubly-Anch-2-Step}$(P,a,b)$ can be carried out in linear time.\nSince Step~4 cuts the size of $P'$ in half every time, Step~2 is entered $O(\\log n)$ times.\nTherefore the total time is $O(n)$.\n\\end{proof}\n\n\\subsection{Left- or right-anchored 2-step function}\nWithout loss of generality, we discuss only a left-anchored 2-step function. \nGiven an anchor value $a$,\nwe want to determine the optimal 2-step function with the constraint\nthat $s^*_1.y=a$, denoted by $^{\\downarrow}\\!F^*_2(x)$.\nSee Fig.~\\ref{fig:anchored2}(a).\nIn this case, $b$ in (\\ref{eqn:h}) is not given; \nwe need to find the optimal value for it.\nBut assume for now that $b$ is also given,\nand execute {\\tt Doubly-Anch-2-Step}$(P,a,b)$.\nFrom the solution that it yields,\ncan we find the direction in which to move $b$ to find the optimal\nleft-anchored 2-step function?\n\\begin{lemma}\nLet $P_1$ (resp. $P_2$) be the left (resp right) partition of $P$ generated by {\\tt Doubly-Anch-2-Step}$(P,a,b)$\nsuch that  $s_1.y=a$ (resp. $s_2.y=b$), where $a<b$ without loss of generality.\nAssume that $P_1$ is maximal in the sense that the boundary between $P_1$ and $P_2$\ncannot be moved to the right without increasing the cost of the solution.\n\\begin{enumerate}\n\\item[(a)]\nIf $D(P_1, s_1) \\geq D(P_2, s_2)$ then the optimal right-anchor cannot lie above $y=b$.\n\\item[(b)]\nIf $D(P_1, s_1) < D(P_2, s_2)$ and there is a critical point in $P_2$ for $s_2.y=b$ above $y=b$,\nthen the optimal right-anchor cannot lie below $y=b$.\n\\item[(c)]\nIf $D(P_1, s_1) < D(P_2, s_2)$ and there is a critical point in $P_2$ for $s_2.y=b$ below $y=b$,\nthen the optimal right-anchor cannot lie above $y=b$.\n\\end{enumerate}\n\\end{lemma}\n\\begin{proof}\n(a) Assume first that the critical point $p_1$ for $s_1$ lies below $s_1$ ($y=a$).\nThen we cannot reduce the cost by changing the value of $b$.\nTherefore, assume that $p_1$ lies above $s_1$.\nBy the definition of $\\{P_1,P_2\\}$, the leftmost point in $P_2$ lies above $y=b$,\nand moving the boundary between $P_1$ and $P_2$ to the right increases the cost,\nwhich is due to the weighted distance between $s_1$ and the new point in $P_1$,\nand this increase is independent of the value of $b$.\nMoving this boundary to the left cannot decrease the cost,\nuntil $p_1$ becomes a part of $P_2$,\nand even then a decrease is not possible unless $b$ is made smaller.\nOtherwise, $\\{P_1,P_2\\}$ wouldn't be optimal with the current $b$.\n\n(b) We know that moving the boundary between $P_1$ and $P_2$ to the right increases the cost\n if $b$ is kept at the same value.\nThe cost increases if $b$ is made smaller.\n\n(c) Symmetric to Case (b).\n\\end{proof}\n\n\\begin{figure}[ht]\n\\centering\n\\includegraphics[height=4cm]{figs\/leftAnc1.pdf}\n\\hspace{2mm}\n\\caption{An example for {\\tt $l$-Anch-2-Step}$(P,a)$.\n}\n\\label{fig:leftAnc}\n\\end{figure}\n\\begin{example}\nIn Fig.~\\ref{fig:leftAnc},\nassume that $d_2$ is slightly larger than $d_1$.\nWe have a doubly anchored solution with the minimum cost (weighted distance)\nequal to $d_2$.\nWhen the boundary between $P_1$ and $P_2$ is at $A$,\nwe can reduce the cost of the optimal solution by moving $b$ up.\nWe cannot do so if the boundary is at $B$,\nbecause $D(p_3, s_2)$ would increase.\nThis is why we maximize $P_1$ in Step 5(b) of Algorithm~\\ref{alg:cond2}\npresented below.\n\\hfill$\\qed$\n\\end{example}\n\n\n\nTo make use of the prune-and-search method,\nwe want to find the big partition (defined in Sec.~\\ref{sec:model}),\n$P_1$ or $P_2$, that is spanned by one segment of $^{\\downarrow}\\!F^*_2(x)$.\n\\hide\n\\begin{procedure} {\\tt Big2-$l$-Anc}$(P,a)$\\label{proc:big2}\n\\begin{enumerate}\n\\item\nDivide $P$ into left partition $P_1$ and right partition $P_2$,\nwhose sizes differ by at most one.\\footnote{As before,\nwe assume that the points have different $y$-coordinates.\n}\n\\item\nLet $s_1$ be the segment with $s_1.y=a$ spanning $P_1$,\nand let $s_2$ be the 1-step (optimal) solution for $P_2$.\n\\item\nIf $D(P_1, s_1) \\leq D(P_2, s_2)$ (resp. $D(P_1, s_1) > D(P_2, s_2)$)\nthen $P_1$ (resp. $P_2$) is the big partition.\n\\end{enumerate}\n\\end{procedure}\n\nIf $P_1$ is the big partition, we can eliminate all the points belonging to it,\nwithout affecting $^{\\downarrow}\\!F^*_2(x)$ that we will find.\nSee Step~4 of the Algorithm~\\ref{alg:cond2} given below.\nWe then repeat the process with the reduced set $P$.\nIf $P_2$ is the big partition, on the other hand, we need to do more work,\nsimilar to what we did to find an optimal 1-step function.\nNamely,\nwe determine values $U$ and $L$ for $P_2$ by executing Algorithm {\\tt 1-Step}$(P_2)$.\nWe then find a doubly anchored 2-step solution for $P$ with left anchor $a$\nand right anchor $U$.\n\n\n\\begin{algorithm}{\\rm :} {\\tt $l$-Anch-2-Step}$(P,a)$\\label{alg:cond2}\n\\begin{enumerate}\n\\item\nDivide $P$ into left partition $P_1$ and right partition $P_2$,\nwhose sizes differ by at most one.\\footnote{As before,\nwe assume that the points have different $y$-coordinates.\n}\n\\item\nLet $s_1$ be the segment with $s_1.y=a$ spanning $P_1$,\nand let $s_2$ be the 1-step (optimal) solution for $P_2$.\\footnote{\nSegment $s_2$ can be found in $O(|P_2|)$ time by Lemma~\\ref{lem:1step}.}\n\\item\nIf $D(P_1, s_1) = D(P_2, s_2)$ then\noutput $\\{s_1,s_2\\}$, which defines $^{\\downarrow}\\!F^*_2(x)$.\nStop.\n\\item\nIf $D(P_1, s_1) < D(P_2, s_2)$, remove from $P$ the points of $P_1$,\nexcept the critical point for $s_1$.\nGo to Step~6.\n\\item\nIf $D(P_1, s_1) > D(P_2, s_2)$ then carry out the following steps.\n\\begin{enumerate}\n\\item\nDetermine points $U$ and $L$ for $P_2$ as described in Algorithm {\\tt 1-Step}$(P)$.\n\\item\nExecute {\\tt Doubly-Anch-2-Step}$(P,a,U)$,\nand find the solution whose left partition is maximal.\nRepeat it with right anchor $L$.\n\\item\nEliminate 1\/6 of the points of $P_2$ from $P$, based on the two solutions\n(as in Steps 6--8 of Algorithm {\\tt 1-Step}$(P)$.)\n\\end{enumerate}\n\\item\nIf $|P| > c$ (a small constant),\nrepeat Steps~1 to 4.\nOtherwise, optimally solve the problem in constant time, using a known method.\n\\end{enumerate}\n\\end{algorithm}\nIn the example in Fig.~\\ref{fig:leftAnc}, \nassume that $b$ is not given,\nand $s_2$ is determined by Step~2.\nThen we have $D(P_1, s_1) > D(P_2, s_2)$,\nand Step~5 applies.\nAccording to Step~5(a), we determine $U$.\nWe then find the doubly anchored solution with the right anchor set to $b=U$.\n\n\n\\begin{lemma}\nAlgorithm {\\tt $l$-Anch-2-Step}$(P,a)$ computes $^{\\downarrow}\\!F^*_2(x)$ correctly,\nand runs in linear time.\n\\end{lemma}\n\\begin{proof}\nStep~3 is obviously correct.\nIf $D(P_1, s_1) < D(P_2, s_2)$ holds in Step~4,\nthen the first partition of $^{\\downarrow}\\!F^*_2(x)$ contains $P_1$.\nWe need to keep the critical point for $a$,\nbut all other points of $P_1$ can be ignored from now on\nbecause $P_1$ will expand.\nIf $D(P_1, s_1) > D(P_2, s_2)$ holds in Step~5,\nthen the first partition of $^{\\downarrow}\\!F^*_2(x)$ is contained in $P_1$.\n\nEach iteration of Steps 3 and 4 will eliminate at least $1\/2\\times1\/6=1\/12$ of the points of $P$.\nSuch an iteration takes linear time in the input size. \nThe total time needed for all the iterations is therefore linear.\n\\end{proof}\n\n\\section{$k$-step function}\\label{sec:kstep}\n\\subsection{Approach}\nTo design a recursive algorithm, assume that for any set of points $Q\\subset P$,\nwe can find the optimal $(j-1)$-step function and the optimal left- and right-anchored $j$-step function \nfor any $2\\leq j < k$ in $O(|Q|)$ time,\nwhere $k$ is a constant .\nWe have shown that this is true for $k=2$ in the previous two sections.\nSo the basis of induction holds.\n\nGiven an optimal $k$-step function $F^*_k(x)$, for each $i~(1\\leq i \\leq k)$,\nlet $P^*_i$ be the set of points vertically closest to segment $s^*_i$.\nBy definition, the partition\n$\\{P^*_i \\mid i = 1, 2, \\ldots, k\\}$ satisfies the contiguity condition.\nIt is easy to see that\nfor each segment $s^*_i$, there are (local) critical points with respect to $s^*_i$,\nlying on the opposite sides of $s^*_i$.\n\nIn finding an optimal $k$-step function,\nwe first identify a big partition that will be spanned by a segment in\nan optimal solution.\nBy Lemma~\\ref{lem:big},\nsuch a big partition always exists.\nOur objective is to eliminate a constant fraction of the points in a big partition.\nThis will guarantee that a constant fraction of the input set is eliminated when $k$ is a fixed constant.\nThe points in the big partition other than two critical points are ``useless''\nand can be eliminated from further considerations.\\footnote{Note that there may\nbe more than two critical points in which case all but two are ``useless.''}\nThis elimination process is repeated until the problem size gets small enough\nto be solved by an exhaustive method in constant time.\n\n\\subsection{Feasibility test}\\label{sec:feasibility}\nGiven a weighted distance (=cost) $D$,\na point set $P$ is said to be $D$-{\\em feasible} if there exists a $k$-step function\n$F_k(x)$ such that $D(P,F_k(x)) \\leq D$. \nTo test $D$-feasibility\nwe first try to identify the first segment $s_1$ of a possible $k$-step function $F_k(x)$.\nTo this end we compute the median $m$ of $\\{p_i.x\\mid i = 1, 2,\\ldots, n\\}$ in $O(n)$ time,\nand divide $P$ into two parts $P_1 = \\{p_i \\mid p_i.x \\leq m\\}$ and $P_2 = \\{p_i \\mid p_i.x > m\\}$,\nwhich also takes $O(n)$ time.\nNote that $|P_1| \\leq \\lceil |P|\/2\\rceil$ and $|P_2| \\leq \\lceil |P|\/2\\rceil$ hold.\nWe then find the intersection $I$ of the $y$-intervals in $\\{|p_i.y-y| \\leq D \\mid p_i \\in P_1\\}$.\nAssuming that $P$ is $D$-feasible,\nthen we have two cases.\n\nCase (a): [$|I|=\\emptyset$] $s_1$ ends at some point $p_j \\in P_1$.\nThrow away all the points in $P_2$ and look for the longest $s_1$ limited by cost $D$,\nconsidering only the points in $P_1$ from the left.\n\n\n\nCase (b): [$|I|\\not=\\emptyset$] $s_1$ may end at some point $p_j \\in P_2$.\nThrow away all the points in $P_1$\nand look for the longest $s_1$, using $I$ and the points in $P_2$ from the left.\n\nClearly,\nwe can find the longest $s_1$ in $O(n)$ time.\nRemove the points spanned by $s_1$ from $P$,\nand find $s_2$ in $O(n)$ time, and so on.\nSince we are done after finding $k$ steps $\\{s_1, \\ldots, s_k\\}$,\nit takes $O(kn)$ time.\n\n\\begin{lemma}\\label{lem:feasibility}\nWe can test $D$-feasibility in $O(kn)$ time.\n\\hfill$\\qed$\n\\end{lemma}\n\n\\subsection{Identifying a big partition}\\label{sec:findBig}\n\\begin{lemma}\\label{lem:big}\nLet ${\\cal P}=\\{P_i\\mid i=1,\\ldots,k\\}$ be any $k$-partition of $P$,\nsatisfying the contiguity condition,\nsuch that the sizes of the partitions differ by no more than 1,\nand let $\\{P^*_i\\mid i=1,\\ldots,k\\}$ be an optimal $k$-partition.\nThen there exists an index $j$ such that $P_j$ is a big partition spanned by $s^*_j$.\n\\end{lemma}\n\\begin{proof} \nLet $j$ be the smallest index such that $s^{(r)}_j.x \\leq s^{*(r)}_j.x$.\nSuch an index must exists, because if $s^{(r)}_j.x > s^{*(r)}_j.x$\nfor all $1\\leq j \\leq k-1$ then $s^{(r)}_k.x = s^{*(r)}_j.x$.\nWe clearly have $s_j\\subset s^*_j$,\nwhich implies that $s^*_j$ spans $P_j$.\n\\end{proof}\n\nGiven a point set $P$ in the $x$-$y$ plane,\nlet ${\\cal P}=\\{P_i\\mid i=1,\\ldots,k\\}$ be any $k$-partition of $P$,\nsatisfying the contiguity condition,\nsuch that the sizes of the partitions differ by no more than 1.\nThe following procedure returns a big partition $P_j$ spanned by $s^*_j$,\nwhose existence was proved by Lemma~\\ref{lem:big}.\nSince $P=\\cup\\{P_i \\mid P_i \\in {\\cal P}\\}$,\n$P$ is implicit in the input to the next procedure.\n\n\\begin{procedure}{\\rm :} {\\tt Big$({\\cal P}, k)$}\\label{proc:bigk}\n\n\\noindent\n\\begin{enumerate}\n\\item\nUsing Algorithm~{\\tt 1-Step}$(P)$, compute the optimal 1-step function for $P_1$\nand let $D_1$ be its cost for $P_1$.\nIf $P$ is not $D_1$-feasible (i.e., $D(P,F^*_{k}(x))>D_1$),\nthen return $P_1$ and stop.\\footnote{There exists an optimal solution for $P$\n in which $s^*_1$ spans $P_1$.}\n\\item\nUsing Algorithm~{\\tt 1-Step}$(P)$, compute the optimal 1-step function for $P_k$\nand let $D'_k$ be its cost for $P_k$.\nIf $P$ is not $D'_k$-feasible (i.e., $D(P,F^*_{k}(x))>D'_k$),\nthen return $P_k$ and stop.\n\\item\nFind an index $j~ (1 < j < k)$ such that for $D_{j-1}=D(\\cup_{i=1}^{j-1} P_i, F^*_{j-1}(x))$\n$P$ is $D_{j-1}$-feasible, \nand for $D_j=D(\\cup_{i=1}^{j} P_i, F^*_j(x))$ $P$ is not $D_{j}$-feasible.\\footnote{This means\nthat $D_{j-1}\\geq D^*$ and $D_{j}< D^*$,\nwhere $D^*$ is the cost of the optimal solution for $P$.\nUnless $P^*_i =P_i$ for all $i$, such an index $j$ always exists.\n[We should indicate why.]}\nReturn $P_j$ and stop.\n\\end{enumerate}\n\\end{procedure}\n\n\\begin{lemma}\\label{lem:Bigiscorrect}\nProcedure {\\tt Big$({\\cal P},k)$} is correct.\n\\end{lemma}\n\\begin{proof}\nIt is clear that Steps~1 and 2 are correct.\nTo show that Step~3 is also correct, \nwe {\\em stretch} a step $s$ of an optimal step function\nby making it as long as possible as follows.\nMove $s^{(l)}.x$ (resp. $s^{(r)}.x$) to the left (resp. right) as far as possible without changing the cost\nof the step function.\nThe step that has been stretched is called a {\\em stretched step.} \nLet us assume without loss of generality that $s^*_j$ corresponding to $P_j$ returned by Step~3 is stretched.\nSince $D_{j-1}\\geq D^*$,\nwe must have $s^{*(l)}_j.x \\leq s^{(l)}_j.x$.\n\nThe optimal solution $F^*_j(x)$ for $\\cup_{i=1}^j P_i$ has cost $D_j$,\nwhich is too small for $P$ to be $D_j$-feasible.\nRegarding the remaining points $\\cup_{i=j+1}^k P_i$,\nlet $G^*_j(x)$ denote the optimal $(k-j)$-step function for this point set.\nIf $D(\\cup_{i=j+1}^k P_i, G^*_j(x)) \\leq D_j$,\nthe $P$ would be $D_j$-feasible.\nSince it is not,\n $s^{(r)}_j.x$ would be stretched to the right under the optimal solution $F^*_k(x)$,\ni.e., $s^{*(r)}_j.x \\geq s^{(r)}_j.x$.\nTogether with $s^{*(l)}_j.x \\leq s^{(l)}_j.x$,\nit follows that $P_j$ is spanned by $s^*_j$.\n\\end{proof}\n\n\\begin{lemma}\\label{lem:Bigislinear}\nProcedure {\\tt Big$({\\cal P},k)$} runs in linear time in $n$.\n\\end{lemma}\n\\begin{proof}\nIn Step~1, the optimal 1-step function for $P_1$ can be found in $O(|P_1|)$ time by Lemma~\\ref{lem:1step},\nand it takes $O(kn)$ time to test if $P$ is not $D_1$-feasible by Lemma~\\ref{lem:feasibility}.\nSimilarly, Step~2 can be carried out in $O(n)$ time.\nTo carry out Step~3,\nwe compute, using binary search, $\\lceil \\log n\\rceil$ values out of $\\{D_i\\mid 1\\leq i \\leq k-1\\}$,\nwhich takes $O(f(k)n)$ time for some function $f(k)$,\nunder the assumption that any $i$-step function problem, $i < k$,\nis solvable in time linear in the size of the input point set.\n\\end{proof}\n\n\n\\section{Algorithm}\\label{sec:algorithm}\n\\subsection{Optimal $k$-step function}\nIn this section we are assuming that we can solve any $(j-1)$-step and anchored\n$j$-step function problems for any $2\\le j <k$.\nWe have shown that this is true for $k=2$ in the previous section.\nSo the basis of recursion holds. \n\nLet us find an optimal doubly anchored $k$-step function, $^{\\downarrow}\\!F_k^{\\downarrow *}(x)$,\nwhich consists of $k$ horizontal segments,\n$s_i^*, i=1,2, \\ldots, k$,\nsatisfying $s_1^{*(l)}.x=p_1.x$,  $s_1^*.y=a$,   $s_k^{*(r)}.x = p_n.x$,  and $s_k.y=b$,\nwhere $a$ and $b$ are given constants.\nLet $P_i^*$  {be}  the set of points of $P$ vertically closest to $s_i^*$. For each segment $s_i^*$, there are critical points with respect to $s_i^*$, lying on the opposite sides of $s_i^*$.\nIn order to find $^{\\downarrow}\\!F_k^{\\downarrow *}(x)$, \nwe first execute {\\tt Big$({\\cal P}, k)$}\nand identify a big partition containing at least $\\lfloor n\/k\\rfloor$ points,\nwhich are vertically closest to the same segment in some optimal solution.\n\n\nOnce a big partition, say $P_j$, is identified,\nWe first determine $U$ and $L$ for $P_j$ as described in Algorithm {\\tt 1-Step}$(P)$.\nTo illustrate the idea,\nlet us consider a special case where $j=1$ and $k=2$.\nWe execute {\\tt $l$-Anch-2-Step}$(P,U)$ and  {\\tt $l$-Anch-2-Step}$(P,L)$\nand determine $s_U$ and $s_L$ as in  Algorithm {\\tt 1-Step}$(P)$.\nWe can thus eliminated 1\/6 of the points in $P_1$.\nWe repeat this with the reduced $P$.\nIt may turn out that the right partition is the big partition in the next round.\nThen we can repeat the above process symmetrically.\nEventually, the size of $P$ gets small enough,\nso that we can find the solution using an exhaustive method.\n\nFor a general $k$ and $j>1$,\nwe need to find the left- and right-anchored solution for $U$ and $L$,\nand prune $1\/6$ of the points in $P_j$ using {\\tt Prune-Big$(k,P_j)$}, given below,\nwhich is very similar to Algorithm {\\tt 1-Step}$(P)$.\nLet $P_j$ be a big partition spanned by $s^*_j$,\nwhich is an input to the following procedure.\n\\begin{procedure}{\\rm :} {\\tt Prune-Big$(k,P_j)$}\n\n\\noindent\n{\\bf Output:} 1\/6 of points in $P_j$ removed.\n\n\n\\begin{enumerate}\n\\item\nDetermine $U$ and $L$ for $P_j$ as in Algorithm {\\tt 1-Step}$(P)$. \n\\item \nIf $j>1$, find two right-anchored $j$-step functions $F_j^{\\downarrow *}(x)$ for $\\cup_{i=1}^{j} P_i$,\none anchored by $L$ and the other anchored by $U$.\n\\item\nIf $j< k$, find two left-anchored $(k-j+1)$-step functions\n $^{\\downarrow}\\!F^*_{k-j+1}(x)$ for $\\cup_{i=j}^k P_i$,\none anchored by $L$ and the other anchored by $U$.\n\\item\nIdentify 1\/6 of the points in $P_j$ with respect to $L$ and $U$,\nwhich are ``useless''\\footnote{See Step~8 of Algorithm~{\\tt 1-Step}$(P)$.}\nbased on $F_j^{\\downarrow *}\\!(x)$\nand $^{\\downarrow}\\!F^*_{k-j+1}(x)$ found above,\nand remove them from $P$. \n\\end{enumerate}\n\\end{procedure}\n\n\n\n\\begin{lemma}\\label{lem:anchored}\n{\\tt Prune-Big$(k,P_j)$} runs in linear time when $k$ is a constant..\n\\hfill$\\qed$\n\\end{lemma}\n\nWe can now describe our algorithm formally as follows.\n\n\\begin{algorithm}{\\rm :} {\\tt $k$-Step}$(P)$. \n\n\\noindent\n{\\bf Output:}  Optimal $k$-step function $F^*_k(x)$\n\\begin{enumerate}\n\\item \nDivide $P$ into partitions $\\{P_i \\mid i = 1, 2, \\ldots, k\\}$,\nsatisfying the contiguous condition,\nsuch that their sizes differ by no more than one.\n\\item \nExecute Procedure {\\tt Big$({\\cal P},k)$} to find a big partition $P_j$\nspanned by $s^*_j$. \n\\item\nExecute Procedure {\\tt Prune-Big$(k,P_j)$}.\n\\item\nIf $|P| > c$ for some fixed $c$, \nrepeat Steps~1 to 3 with the reduced $P$.\n\\end{enumerate}\n\\end{algorithm}\n\n\n\\subsection{Analysis of algorithm}\nTo carry out Step 1 of Algorithm {\\tt $k$-Step}$(P)$, \nwe first find the $(hn\/k)^{th}$ smallest among $\\{p_i.x \\mid 1\\leq i \\leq n\\}$,\nfor $h=1, 2, \\ldots, k-1$.\nWe then place each point in $P$ into $k$ partitions delineated by these\n$k-1$ values.\nIt is clear that this can be done in $O(kn)$ time.\\footnote{This could be done in $O(n\\log k)$ time.}\nAs for Step~2,\nwe showed in Sec.~\\ref{sec:findBig} that finding a big partition spanned by an optimal step\n$s_j^*$ takes $O(n)$ time, since $k$ is a constant.\nStep~3 also runs in $O(n)$ time by Lemma~\\ref{lem:anchored}.\nSince Steps 1 to 3 are repeated $O(\\log n)$ times,\neach time with a point set whose size is at most a constant fraction of the size of the previous set,\nthe total time is also $O(n)$, when $k$ is a constant.\nBy solving a recurrence relation for the running time of Algorithm~{\\tt $k$-Step}$(P)$,\nwe can show that it runs in $O(2^{2k\\log k}n)=O(k^{2k}n)$ time.\n\n\\begin{theorem}\nGiven a set of $n$ points in the plane $P=\\{p_1,p_2,\\ldots, p_n\\}$,\nwe can find the optimal $k$-step function that minimizes the maximum distance\nto the $n$ points in $O(k^{2k} n)$ time.\n\\hfill$\\qed$\n\\end{theorem}\nThus the algorithm is optimal for a fixed $k$.\n\n\n\\section{Conclusion and Discussion}\\label{sec:conclusion}\nWe have presented a linear time algorithm to solve the optimal $k$-step function problem,\nwhen $k$ a constant.\nMost of the effort is spent on identifying a ``big partition.''\nIt is desirable to reduce the constant of proportionality. \n\nThe {\\em size-$k$ histogram construction problem}~\\cite{guha2007},\nwhere the points are not weighted, \nis similar to the problem we addressed in this paper.\nIts generalized version,\nwhere the points are weighted,\nis equivalent to our problem, and thus can be solved in optimal linear time when $k$ is a constant.\nThe {\\em line-constrained $k$ center problem} is defined by:\nGiven a set $P$ of weighted points in the plane and a horizontal line $L$,\ndetermine $k$ centers on $L$\nsuch that the maximum weighted distance of the points to their closest centers is minimized.\nThis problem was solved in optimal $O(n\\log n)$ time for arbitrary $k$ even if the points\nare sorted~\\cite{karmakar2013,wang2014a}.\nOur algorithm presented here can be applied to solve this problem \nin $O(n)$ time if $k$ is a constant.\n\nA possible extension of our work reported here is to use a cost other than the weighted vertical distance.\nThere is a nice discussion in \\cite{guha2007} on the various measures one can use. \nOur complexity results are valid\nif the cost is more general than (\\ref{eqn:pointCost}),\nin particular, $D(p, F(x))\\triangleq d(p, F(x))^2 w(p)$,\nwhich is often used as an error measure.\n\\section*{Acknowledgement}\\label{sec:ack}\nThis work was supported in part by Discovery Grant \\#13883 from\nthe Natural Science and Engineering Research Council (NSERC) of Canada and in part by MITACS,\nboth awarded to Bhattacharya.\n\n\n\\section*{Reference}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{\\bf Introduction}\nOne of the most interesting new developments in hadron physics is\nthe application of the AdS\/CFT correspondence~\\cite{Maldacena} to\nnonperturbative QCD\nproblems~\\cite{Polchinski,Janik,Erlich,Karch,Brodsky1,Teramond1,Teramond2}.\nIt is well know that AdS\/CFT  gives an important insight into the\nviscosity and other global properties of the hadronic system\nformed in heavy ion collisions~\\cite{Kovtun}. The essential ansatz\nfor the application of AdS\/CFT to hadron physics is the indication\nthat the QCD coupling $\\alpha_s(Q^2)$ becomes large. Therefore\nconformal symmetry can be applied to, for example solutions of the\nQCD Dyson Schwinger equations  and phenomenological studies of QCD\ncouplings based on physical observables such as $\\tau$ decay and\nthe Bjorken sum rule show that the QCD $\\beta$ function vanishes\nand $\\alpha_s(Q^2)$ become constant at small virtuality; i.e.,\neffective charges develop an infrared fixed point. Fully\nexploiting the gauge\/gravity correspondence to produce a model for\nreal strong interaction physics- a method called \" holographic\nQCD\" or \"AdS\/QCD\"-may be attempted either through a top-dawn\napproach starting with a particular string theory and choosing a\nbackground that naturally produces QCD-like properties, or a\nbottom-up approach starting with real QCD properties and using\nthem to obtain constraints on viable dual gravity theories.\n\nThe first attempts have been made for constructing phenomenological\nholographic models of QCD~\\cite{Erlich}. Surprisingly simple models\nconsisting of gauge theory in an anti-de-Sitter space interval have\nturned out to provide a remarkably good description of the meson\nsector of QCD. Therefore, it will be interesting that the\ncalculation of the higher twist effects within holographic QCD in\nproton-proton collisions in the running coupling approach.\n\nThe large-order behavior of a perturbative expansion in gauge\ntheories is inevitably dominated by the factorial growth of\nrenormalon diagrams~\\cite{Hooft,Mueller,Zakharov,Beneke}. In the\ncase of quantum chromodynamics (QCD), the coefficients of\nperturbative expansions in the QCD coupling $\\alpha_{s}$ can\nincrease dramatically even at low orders. This fact, together with\nthe apparent freedom in the choice of renormalization scheme and\nrenormalization scales, limits the predictive power of perturbative\ncalculations, even in applications involving large momentum\ntransfer, where $\\alpha_{s}$ is effectively small.\n\nIn this work we apply the running coupling approach~\\cite{Agaev}\nin order to compute the effects of the infrared renormalons on the\npion production in proton-proton collisions within holographic\nQCD. This approach was also employed\npreviously~\\cite{Ahmadov3,Ahmadov4,Ahmadov5,Ahmadov6} to calculate\nthe inclusive meson production in proton-proton and photon-photon\ncollisions.\n\nFor the calculations of the higher-twist cross sections on the\ndependence of wave functions of pion, we used the holographic QCD\nprediction $\\Phi_{hol}(x)$~\\cite{Brodsky2,Brodsky3,Vega} and pion\nasymptotic wave functions $\\Phi_{asy}(x)$~\\cite{Lepage1} from the\nperturbative QCD evolution. Theoretically obtained predicted\nresults within holographic QCD were compared with results of the\nperturbative QCD which obtained by the running coupling and frozen\ncoupling constants approaches.\n\nThe frozen coupling constant approach in\nRefs.~\\cite{Bagger,Baier,Ahmadov1,Ahmadov2} was used for calculation\nof integrals, such as\n\\begin{equation}\nI\\sim \\int\\frac{\\alpha_{s}({Q}^2)\\Phi(x,{Q}^2)}{1-x}dx.\n\\end{equation}\nIt should be noted  that, in pQCD calculations, the argument of the\nQCD coupling constant (or the renormalization and factorization\nscale) ${Q}^2$ should be taken equal to the square of the momentum\ntransfer of a hard gluon in a corresponding Feynman diagram. But\ndefinition of $\\alpha_{s}(\\hat{Q}^2)$ suffers from infrared\nsingularities. Therefore, in the soft regions as $x_{1}\\rightarrow\n0$, and  $x_{2}\\rightarrow 0$, integrals (1.1) diverge and for their\ncalculation some regularization methods are needed for\n$\\alpha_{s}(Q^2)$ in these regions. Investigation of the infrared\nrenormalon effects in various inclusive and exclusive processes is\none of the most important and interesting problem in the\nperturbative QCD. It is known that infrared renormalons are\nresponsible for factorial growth of coefficients in perturbative\nseries for the physical quantities. But, these divergent  series can\nbe resummed by means of the Borel transformation ~\\cite{Hooft} and\nthe principal value prescription ~\\cite{Contopanagos}. Studies of\nhigher-twist and renormalon effects also opened  new prospects for\nevaluation of power suppressed corrections to processes\ncharacteristics.\n\nWe organize the  paper as the follows. In Section \\ref{ht}, we\nprovide some formulas for the calculation of the contributions of\nthe higher twist  and leading twist diagrams. In Section \\ref{ir},\nwe present the formulas and analysis of the higher-twist effects\non the dependence of the pion wave function by the running\ncoupling constant approach, and in Section \\ref{results}, the\nnumerical results for the cross section and discuss the dependence\nof the cross section on the pion wave functions are presented.\nFinally, some concluding remark are stated in Section \\ref{conc}.\n\n\\section{HIGHER TWIST AND LEADING TWIST CONTRIBUTIONS TO INCLUSIVE REACTIONS}\n\\label{ht} The higher-twist Feynman diagrams, which describe the\nsubprocess $q_1+\\bar{q}_{2} \\to \\pi^{+}(\\pi^{-})+\\gamma$ for the\npion production in the proton-proton collision are shown in Fig.1.\nThe amplitude for this subprocess can be found by means of the\nBrodsky-Lepage formula ~\\cite{Lepage2}\n\\begin{equation}\nM(\\hat s,\\hat\nt)=\\int_{0}^{1}{dx_1}\\int_{0}^{1}dx_2\\delta(1-x_1-x_2)\\Phi_{\\pi}(x_1,x_2,Q^2)T_{H}(\\hat\ns,\\hat t;x_1,x_2).\n\\end{equation}\nIn Eq.(2.1), $T_H$ is  the sum of the graphs contributing to the\nhard-scattering part of the subprocess.\n\nThe Mandelstam invariant variables for subprocesses $q_1+\\bar{q}_{2}\n\\to \\pi^{+}(\\pi^{-})+\\gamma$ are defined as\n\\begin{equation}\n\\hat s=(p_1+p_2)^2,\\quad \\hat t=(p_1-p_{\\pi})^2,\\quad \\hat\nu=(p_1-p_{\\gamma})^2.\n\\end{equation}\nThe pion wave functions predicted by\nAdS\/QCD~\\cite{Brodsky2,Brodsky3,Vega} and the PQCD evolution\n~\\cite{Lepage1} has the form:\n$$\n\\Phi_{asy}^{hol}(x)=\\frac{4}{\\sqrt{3}\\pi}f_{\\pi}\\sqrt{x(1-x)},\n$$\n\\begin{equation}\n\\Phi_{VSBGL}^{hol}(x)=\\frac{A_1k_1}{2\\pi}\\sqrt{x(1-x)}exp\\left(-\\frac{m^2}{2k_{1}^2x(1-x)}\\right),\\quad\n\\Phi_{asy}^{p}(x)=\\sqrt{3}f_{\\pi}x(1-x)\n\\end{equation}\nwhere $f_{\\pi}$ is the pion decay constant.\n\nThe cross section for the higher-twist subprocess $q_1\\bar{q}_{2}\n\\to \\pi^{+}(\\pi^{-})\\gamma$ is given by the expression\n\\begin{equation}\n\\frac{d\\sigma}{d\\hat t}(\\hat s,\\hat t,\\hat u)=\\frac\n{8\\pi^2\\alpha_{E} C_F}{27}\\frac{\\left[D(\\hat t,\\hat\nu)\\right]^2}{{\\hat s}^3}\\left[\\frac{1}{{\\hat u}^2}+\\frac{1}{{\\hat\nt}^2}\\right]\n\\end{equation}\nwhere\n\\begin{equation}\nD(\\hat t,\\hat u)=e_1\\hat\nt\\int_{0}^{1}dx\\left[\\frac{\\alpha_{s}(Q_1^2)\\Phi_{\\pi}(x,Q_1^2)}{1-x}\\right]+e_2\\hat\nu\\int_{0}^{1}dx\\left[\\frac{\\alpha_{s}(Q_2^2)\\Phi_{\\pi}(x,Q_2^2)}{1-x}\\right].\n\\end{equation}\nIn the Eq.(2.5) $Q_{1}^2=(x-1)\\hat u \\,\\,\\,\\,$and $Q_{2}^2=-x\\hat\nt$ \\,\\, represent the momentum squared carried by the hard gluon\nin Fig.1, $e_1(e_2)$ is the charge of $q_1(\\overline{q}_2)$ and\n$C_F=\\frac{4}{3}$. The higher-twist contribution to the\nlarge-$p_{T}$ pion production cross section in the process\n$pp\\to\\pi^{+}(\\pi^{-})+\\gamma+X$ is ~\\cite{Owens,Greiner}\n\\begin{equation}\n\\Sigma_{M}^{HT}\\equiv E\\frac{d\\sigma}{d^3p}=\\int_{0}^{1}\\int_{0}^{1}\ndx_1 dx_2 G_{{q_{1}}\/{h_{1}}}(x_{1})\nG_{{q_{2}}\/{h_{2}}}(x_{2})\\frac{\\hat s}{\\pi} \\frac{d\\sigma}{d\\hat\nt}(q\\overline{q}\\to \\pi\\gamma)\\delta(\\hat s+\\hat t+\\hat u).\n\\end{equation}\nWe denote the higher-twist cross section obtained using the frozen\ncoupling constant approach by $(\\Sigma_{\\pi}^{HT})^0$.\n\nRegarding the higher-twist corrections to the pion production\ncross section, a comparison of our results with leading-twist\ncontributions is crucial. We take two leading-twist subprocesses\nfor the pion production:(1) quark-antiquark annihilation $q\\bar{q}\n\\to g\\gamma$, in which the  $g \\to \\pi^{+}(\\pi^{-})$ and (2)\nquark-gluon fusion, $qg \\to q\\gamma $, with subsequent\nfragmentation of the final quark into a meson, $q \\to\n\\pi^{+}(\\pi^{-})$ ~\\cite{Ahmadov3,Ahmadov5}.\n\n\\section{THE HIGHER TWIST MECHANISM IN HOLOGRAPHIC QCD AND INFRARED RENORMALONS}\\label{ir}\n\nThe main problem in our investigation is the calculation of integral\nin (2.5) by the running coupling constant approach within\nholographic QCD and also discussion of the problem of normalization\nof the higher twist process cross section in the context of the same\napproach. Therefore, it is worth noting that, the renormalization\nscale (argument of $\\alpha_s$) according to Fig.1 should be chosen\nequal to $Q_{1}^2=(x-1)\\hat u$, $Q_{2}^2=-x\\hat t$. The integral in\nEq.(2.5) in the framework of the running coupling approach takes the\nform\n\\begin{equation}\nI(\\mu_{R_{0}}^2)=\\int_{0}^{1}\\frac{\\alpha_{s}(\\lambda\n\\mu_{R_0}^2)\\Phi_{M}(x,\\mu_{F}^2)dx}{1-x}.\n\\end{equation}\nThe $\\alpha_{s}(\\lambda \\mu_{R_0}^2)$ has the infrared singularity\nat $x\\rightarrow1$, for $\\lambda=1-x$  or $x\\rightarrow0$, for\n$\\lambda=x$ and so the integral $(3.1)$ diverges. For the\nregularization of the integral, we express the running coupling at\nscaling variable $\\alpha_{s}(\\lambda \\mu_{R_0}^2)$ with the aid of\nthe renormalization group equation in terms of the fixed one\n$\\alpha_{s}(Q^2)$. The solution of renormalization group equation\nfor the running coupling $\\alpha\\equiv\\alpha_{s}\/\\pi$ has the form\n~\\cite{Contopanagos}\n\\begin{equation}\n\\frac{\\alpha(\\lambda)}{\\alpha}=\\left[1+\\alpha\n\\frac{\\beta_{0}}{4}\\ln{\\lambda}\\right]^{-1}.\n\\end{equation}\nThen, for $\\alpha_{s}(\\lambda Q^2)$, we get\n\\begin{equation}\n\\alpha(\\lambda Q^2)=\\frac{\\alpha_{s}}{1+\\ln{\\lambda\/t}}\n\\end{equation}\nwhere $t=4\\pi\/\\alpha_{s}(Q^2)\\beta_{0}=4\/\\alpha\\beta_{0}$.\n\nHaving inserted  Eq.(3.3) into Eq.(2.5) we obtain\n$$\nD(\\hat t,\\hat u)=e_{1}\\hat t\\int_{0}^{1}dx\\frac{\\alpha_{s}(\\lambda\n\\mu_{R_0}^2)\\Phi_{M}(x,Q_{1}^2)}{1-x}+ e_{2}\\hat\nu\\int_{0}^{1}dx\\frac{\\alpha_{s}(\\lambda\n\\mu_{R_0}^2)\\Phi_{M}(x,Q_{2}^2)}{1-x}\n$$\n\\begin{equation}\n=e_{1}\\hat t\\alpha_{s}(-\\hat u)t_{1}\\int_{0}^{1}dx\n\\frac{\\Phi_{M}(x,Q_{1}^2)}{(1-x)(t_{1}+\\ln\\lambda)} + e_{2}\\hat\nu\\alpha_{s}(-\\hat t)t_{2}\\int_{0}^{1}dx\n\\frac{\\Phi_{M}(x,Q_{2}^2)}{(1-x)(t_{2}+\\ln\\lambda)}\n\\end{equation}\nwhere $t_1=4\\pi\/\\alpha_{s}(-\\hat u)\\beta_{0}$ and\n$t_2=4\\pi\/\\alpha_{s}(-\\hat t)\\beta_{0}$.\n\nAlthough the integral (3.4) is still divergent, it is recast into a\nsuitable  form for calculation. Making the change of variable as\n$z=\\ln\\lambda$, we obtain\n\\begin{equation}\nD(\\hat t,\\hat u)=e_{1}\\hat t \\alpha_{s}(-\\hat u) t_1\\int_{0}^{1}dx\n\\frac{\\Phi_{M}(x,Q_{1}^2)}{(1-x)(t_1+z)}+ e_{2}\\hat u\n\\alpha_{s}(-\\hat t) t_2 \\int_{0}^{1} dx\n\\frac{\\Phi_{M}(x,Q_{2}^2)}{(1-x)(t_2+z)}\n\\end{equation}\nIn order to calculate (3.5) we will apply the integral\nrepresentation of $1\/(t+z)$ ~\\cite{Zinn-Justin,Erdelyi}.\n\\begin{equation}\n\\frac{1}{(t+z)}=\\int_{0}^{\\infty}e^{-(t+z)u}du,\n\\end{equation}\ngives\n\\begin{equation}\nD(\\hat t,\\hat u)=e_{1} \\hat{t} \\alpha_{s}(-\\hat u) t_1 \\int_{0}^{1}\n\\int_{0}^{\\infty} \\frac{\\Phi_{\\pi}(x,Q_{1}^2)e^{-(t_1+z)u}du\ndx}{(1-x)}+ e_{2} \\hat{u} \\alpha_{s}(-\\hat t) t_2 \\int_{0}^{1}\n\\int_{0}^{\\infty} \\frac{\\Phi_{\\pi}(x,Q_{2}^2)e^{-(t_2+z)u}du\ndx}{(1-x)}\n\\end{equation}\nIn the case $\\Phi_{asy}^{hol}(x)$ for the $D(\\hat t,\\hat u)$ it is\nwritten as\n\\begin{equation}\nD(\\hat t,\\hat u)=\\frac{16 f_{\\pi} e_{1} \\hat t}{\\sqrt{3}\\beta_{0}}\n\\int_{0}^{\\infty} du\ne^{-t_{1}u}B\\left(\\frac{3}{2},\\frac{1}{2}-u\\right)+  \\frac{16\nf_{\\pi} e_{2} \\hat u}{\\sqrt{3}\\beta_{0}} \\int_{0}^{\\infty} du\ne^{-t_{2}u}B\\left(\\frac{3}{2},\\frac{1}{2}-u\\right)\n\\end{equation}\nand for $\\Phi_{asy}^{p}(x)$ wave function\n\\begin{equation}\nD(\\hat t,\\hat u)=\\frac{4\\sqrt{3}\\pi f_{\\pi}e_{1}\\hat t}{\\beta_{0}}\n\\int_{0}^{\\infty}du e^{-t_{1}u}\n\\left[\\frac{1}{1-u}-\\frac{1}{2-u}\\right] +\\frac{4\\sqrt{3}\\pi\nf_{\\pi}e_{2}\\hat u}{\\beta_{0}} \\int_{0}^{\\infty}du e^{-t_{2}u}\n\\left[\\frac{1}{1-u}-\\frac{1}{2-u}\\right].\n\\end{equation}\nwhere $B(\\alpha,\\beta)$ is Beta function.  The structure of the\ninfrared renormalon poles in Eq.(3.8) and Eq.(3.9) strongly depend\non the wave functions of the pion. To remove them from Eq.(3.8) and\nEq.(3.9) we adopt the principal value prescription. We denote the\nhigher-twist cross section obtained using the running coupling\nconstant approach by $(\\Sigma_{\\pi}^{HT})^{res}$.\n\n\\section{NUMERICAL RESULTS AND DISCUSSION}\\label{results}\n\nIn this section, we discuss the higher-twist contributions\ncalculated in the context of the running and frozen coupling\nconstant approaches on the dependence of the chosen pion wave\nfunctions in the process $pp \\to \\pi^{+}(or\\,\\, \\pi^{-})\\gamma+X$.\nIn numerical calculations for the quark distribution function\ninside the proton, the MSTW distribution function ~\\cite{Martin},\nand the gluon and quark fragmentation ~\\cite{Albino} functions\ninto a pion have been used. The results of our numerical\ncalculations are displayed in Figs.2-14. Firstly, it is very\ninteresting comparing the higher-twist cross sections obtained\nwithin  holographic QCD with the ones obtained within perturbative\nQCD. In Fig.2 and Fig.3 we show the dependence of higher-twist\ncross sections $(\\Sigma_{\\pi^{+}}^{HT})^{0}$,\n$(\\Sigma_{\\pi^{+}}^{HT})^{res}$ calculated in the context of the\nfrozen and  running coupling constant approaches as a function of\nthe pion transverse momentum $p_{T}$ for different pion wave\nfunctions at $y=0$. It is seen from Fig.2 and Fig.3 that the\nhigher-twist cross section is monotonically decreasing with an\nincrease in the transverse momentum of the pion. In Fig.4-Fig.7,\nwe show the dependence of the ratios\n$(\\Sigma_{HT}^{hol})$\/$(\\Sigma_{HT}^p)$,\n$(\\Sigma_{\\pi}^{HT})^{res}$\/$(\\Sigma_{\\pi^{+}}^{HT})^{0}$,\n$(\\Sigma_{\\pi^{+}}^{HT})^{0}$\/$(\\Sigma_{\\pi^{+}}^{LT})$ and\n$(\\Sigma_{\\pi^{+}}^{HT})^{res}$\/$(\\Sigma_{\\pi^{+}}^{LT})$ as a\nfunction of the pion transverse momentum $p_{T}$ for\n$\\Phi_{\\pi}^{hol}(x)$, $\\Phi_{\\pi}^{p}(x)$ and\n$\\Phi_{VSBGL}^{hol}(x)$ pion wave functions. Here\n$\\Sigma_{\\pi^{+}}^{LT}$ is the leading-twist cross section,\nrespectively. As shown in Fig.4, in the region\n$2\\,\\,GeV\/c<p_T<30\\,\\,GeV\/c$ resummed higher-twist cross section\nfor $\\Phi_{\\pi}^{hol}(x)$ is suppress by about half orders of\nmagnitude relative to the resummed higher-twist cross section for\n$\\Phi_{\\pi}^{p}(x)$ also higher-twist cross section for\n$\\Phi_{\\pi}^{p}(x)$ is suppress by about half orders of magnitude\nrelative to the  higher-twist cross section for\n$\\Phi_{VSBGL}^{hol}(x)$ . In Fig.5 and Fig.6, we show the\ndependence of the ratios\n$(\\Sigma_{\\pi}^{HT})^{res}$\/$(\\Sigma_{\\pi^{+}}^{HT})^{0}$, and\n$(\\Sigma_{\\pi^{+}}^{HT})^{0}$\/$(\\Sigma_{\\pi^{+}}^{LT})$ as a\nfunction of the meson transverse momentum $p_{T}$ for the\n$\\Phi_{\\pi}^{hol}(x)$,  $\\Phi_{\\pi}^{p}(x)$ and\n$\\Phi_{VSBGL}^{hol}(x)$ pion wave functions. It is observed from\nFig.5 that, the ratios  for all wave functions decrase with an\nincrease in the transverse momentum of pion, but in the region\n$2\\,\\,GeV\/c<p_T<8\\,\\,GeV\/c$ resummed higher-twist cross section\nfor $\\Phi_{\\pi}^{hol}(x)$ is suppress by about 2-3 and 2-4 orders\nof magnitude relative to the higher-twist cross sections\ncalculated in the context of the frozen coupling method for\n$\\Phi_{\\pi}^{p}(x)$ and $\\Phi_{VSBGL}^{hol}(x)$, respectively.\nAlso, resummed higher-twist cross section for $\\Phi_{\\pi}^{p}(x)$\nis suppress by about 1-3 orders of magnitude relative to the\nhigher-twist cross sections calculated in the context of the\nfrozen coupling method for $\\Phi_{VSBGL}^{hol}(x)$. But, as shown\nin Fig.6, the ratios decrease with increasing in the $p_{T}$\ntransverse momentum of the pion and has a minimum approximately at\nthe point $p_{T}=13 GeV\/c$, then the ratios increase with\nincreasing in the $p_{T}$ transverse momentum of the pion. In\nFig.7 is similar to Fig.6 with an exception that there in a\nminimum approximately at the point $p_{T}=25 GeV\/c$. In Fig.8 -\nFig.10, we have depicted higher-twist cross sections\n$(\\Sigma_{\\pi^{+}}^{HT})$, and ratio\n$(\\Sigma_{HT}^{hol})\/(\\Sigma_{HT}^{p})$,\\, as a function of the\nrapidity $y$ of the pion at $\\sqrt s=62.4\\,\\,GeV$ and\n$p_T=4.9\\,\\,GeV\/c$. Figures show that higher-twist cross section\nand ratios have a different distinctive. The resummed higher-twist\ncross section for $\\Phi_{\\pi}^{hol}(x)$ has a maximum\napproximately at the point $y=-1.92$. However in this point\nhigher-twist cross section for $\\Phi_{VSBGL}^{hol}(x)$ has a\nminimum. As shown in Fig.9 in the region ($-2.52\\leq y\\leq -1.92$)\nthe ratios $(\\Sigma_{HT}^{hol})^{0}\/(\\Sigma_{HT}^{p})^{0}$ and\n$(\\Sigma_{VSBGL}^{hol})^{0}\/(\\Sigma_{HT}^{p})^{0}$ increase with\nan increase of the $y$ rapidity of the pion and has a maximum\napproximately at the point $y=1.22$, but ratio\n$(\\Sigma_{HT}^{hol})^{0}\/(\\Sigma_{VSBGL}^{hol})^{0}$ has a minimum\nin this point. As is seen from Fig.10 ratios\n$R=(\\Sigma_{\\pi^{+}}^{HT})^{res}\/(\\Sigma_{\\pi^{+}}^{HT})^{0}$,\\,\nfor all wave functions increase with an increase of the $y$\nrapidity of the pion and has a maximum approximately at the point\n$y=-1.92$. In the region  $-2.52<y<-1.92$ resummed higher-twist\ncross section is suppress by about half order of magnitude\nrelative to the higher-twist cross section calculated in the\nframework of the frozen coupling approach. Besides that, the ratio\ndecreases with an increase in the $y$ rapidity of the pion. As is\nseen from Fig.10, the ratio $R$  depends on the choice of the pion\nwave function. Analysis of our calculations shows that\n$(\\Sigma_{\\pi^{+}}^{HT})^{0}$, $(\\Sigma_{\\pi^{+}}^{HT})^{res}$\nhigher-twist cross sections and ratio sensitive to pion wave\nfunctions predicted holographic and perturbative QCD.\n\nWe have also carried out comparative calculations in the\ncenter-of-mass energy $\\sqrt s=200\\,\\,GeV$ and obtained results\nare displayed in Fig.11-Fig.14.  Analysis of our calculations at\nthe center-of-mass energies $\\sqrt s=62.4\\,\\,GeV$ and $\\sqrt\ns=200\\,\\,GeV$, show that with increasing in the beam energy\ncontributions of higher-twist effects  to the cross section\ndecrease by about one-two order. As is seen from Fig.5, Fig.7,\nFig.10 and Fig.13 that infrared renormalon effects enhance the\nperturbative predictions for the pion production cross section in\nthe proton-proton collisions about 2-3 order. This feature of\ninfrared renormalons  may help the explain theoretical\ninterpretations with future experimental  data for the pion\nproduction cross section in the proton-proton collisions. In our\ncalculations, the higher-twist cross section of the process the\ndependence of the transverse momentum of pion appears in the range\nof $(10^{-8}\\div10^{-26})mb\/GeV^2$. Therefore, higher-twist cross\nsection obtained in our work should be observable at RHIC.\n\n\\section{CONCLUSIONS}\\label{conc}\n\nProton-proton collisions are known  are known to be the most\nelementary interactions and form the very basis of our knowledge\nabout the nature of high energy collisions in general. Physicists,\nby and large, hold the view quite firmly that the perturbative\nquantum-chromodynamics  provides a general framework for the\nstudies on high energy particle-particle collisions. Obviously,\nthe unprecedented high energies attained at Large Hadron Collider\noffer new window and opportunities to test the proposed QCD\ndynamics with its pros and cons. However, we should remember that\nLHC opens a new kinematical regime ah high energy, where several\nquestions related to the description of the high-energy regime of\nthe QCD. Consequently, studies of proton-proton interactions at\nthe RHIC  and LHC could provide valuable  information on the QCD\ndynamics at high energies. In this work the single meson inclusive\nproduction via higher twist mechanism within holographic QCD are\ncalculated . For calculation of the cross section, the running\ncoupling constant approach is applied and infrared renormalon\npoles in the cross section expression are revealed. Infrared\nrenormalon induced divergences is regularized by means of the\nprincipal value prescripton and the resummed expression (the Borel\nsum) for the higher-twist cross section is found. It is observed\nthat, the resummed higher-twist cross section differs considerably\nfrom that found using the frozen coupling approximation, in some\nregion. The following results can be concluded from the\nexperiments; the higher-twist contributions to single meson\nproduction cross section in the proton-proton collisions have\nimportant phenomenological consequences, the higher-twist pion\nproduction cross section in the proton-proton collisions depends\non the form of the pion model wave functions and may be used for\ntheir study. Also the contributions of renormalons effects within\nholograpich QCD in this process are essential and may help to\nanalyse experimental results. Further investigations are needed in\norder to clarify the role of higher-twist effects  in QCD.\nEspecially, the forthcoming RHIC and LHC measurements will provide\nfurther tests of the dynamics of large-$p_T$ hadron production\nbeyond the leading twist.\n\n\\section*{Acknowledgments}\nOne of author A.I.Ahmadov is grateful to all members of the\nDepartment of Physics of Karadeniz Technical University for\nappreciates hospitality extended to him in Trabzon. Financial\nsupport by TUBITAK under grant number 2221(Turkey) is also\ngratefully acknowledged.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Lighting and LiFi}\nAmong the major innovations in the energy sector, the development of LED lighting has been nothing less than earth shattering over the last 10 years, largely thanks to the virtuous conjunction of technology development and policies and measures in support of energy efficiency and renewable energy. Common LED bulbs today consume 85\\% less energy than their incandescent counterparts and their deployment is poised to have a massive impact on the energy mix, with lighting accounting currently for as much as 15\\% of global electricity consumption and 5\\% of worldwide greenhouse gas emissions. \n\nCosts have been slashed down through improvements in manufacturing and higher wall-plug efficiency for a given optic illumination. Costs per LED bulb remain higher than for incandescent and fluorescent technologies but a much longer lifespan up to 25,000 hours and energy savings make the cost per lumen \u2013 a measure of the total quantity of visible light emitted by a source \u2013 much more competitive. \nAs a consequence, the LED lighting market share is already 40-50\\% (depending on the geography) and 70\\% of a global \\$100bn general lighting market will stem from LED shipments (lamps and luminaires) as early as 2020. In the US alone, LED installed stock is expected to grow from 6\\% in 2016 to close to 60\\% in 2025 and 90\\% in 2035 \\cite{NAS2}. \n\nWhile the lighting industry has been traditionally slow to adapt and move, with product cycles longer than 10 years, LED lighting is providing the opportunity, at an accelerated pace, to improve existing business operations on the one hand, and create new business opportunities on the other hand. With the Solid-State Lighting (SSL) technologies - including LED, Organic LED (OLED) and Laser Diode technologies - come lighting control and communication systems that bring intelligence at the level of the AC-to-DC driver. These are greatly expanding the functions that can be performed by a luminaire, making it a central part of the Smart Building and Smart City concepts. \n\n\\begin{figure}\n  \\includegraphics[width=\\linewidth]{weo2.jpg}\n  \\caption{Recent cost trends for selected energy technologies. The LED sector has outperformed over the last 10 years all energy technologies, including solar\nphotovoltaic. Source: World Energy Outlook 2016, IEA}\n  \\label{fig:weo}\n\\end{figure}\n\nLucibel has been since 2008 at the forefront of the LED revolution, manufacturing and distributing luminaires and offering innovative indoor lighting solutions for its Commercial and Industrial customers. While downward trending prices and commoditization are happening and re-shaping the industry, Lucibel is always looking for ways to provide groundbreaking value-adding features to its customers. Control systems, connected or not, act only on one of the two components of light, its intensity, in a conventional, quasi-static way. Lucibel builds on these systems and adds new functionalities to address two pressing needs of our society: well-being and high-speed communications.\n\nThe first development is to program or adjust on demand the spectral content of a LED luminaire ({\\it i.e.} its color) to follow circadian rhythms in the course of the day in a biologically and emotionally effective way. The second concept is to modulate the intensity at a flicker-free high frequency to code information into light and create a very high-speed wireless data exchange channel between a luminaire and a receiver.  This technology is termed as Visible Light Communication (VLC) and complete wireless networking using VLC is called LiFi, a term coined by Professor Haas \u2013 also co-founder of Lucibel's technology partner PureLiFi - at his 2011 TED Global Talk \\cite{haasted2011} where he introduced the idea of \"wireless data from every light\". \n\nOptical communications are nothing new. First developed in the 1970s, fiber-optics have revolutionized the telecommunications industry and have been a major enabler of the current Information Age. The internet runs mostly on optical fibers and last-mile fibers are more and more common. LiFi extends the optical communication revolution closer to the final customer, to the last meter, transforming indoor lighting into a backbone for information. \n\n\\section{Light Communications}\n\nThere are multiple ways to encode information into light, and they all involve some combination of amplitude, frequency and phase modulation (or keying in the language of the digital signals community). The ultimate goal of the signal processing is to achieve reliable wireless communications with a minimal bit-error ratio between any two nodes in the network, {\\it i.e.} a given ratio of bits in error relative to the total number of transmitted bits, as a function of the signal to noise ratio of the modulated signal. Bit errors occur over a communication channel because of noise, interference, distortion or synchronization issues.\n\n\n\\begin{figure}[h]\n  \\includegraphics[width=\\linewidth]{aphp.jpg}\n  \\caption{Short term applications for LiFi are in places where high-speed wireless connectivity has to be guaranteed and secured or where RF communications are hampered or prohibited, for example in hospitals. Source: APHP}\n  \\label{fig:hopital}\n\\end{figure}\n\nIn the context of VLC, light is emitted by a LED and detected either by a single photodetector (a photodiode or an avalanche photodiode in case of low irradiation) or an imaging sensor, for example the camera of a consumer electronic device. In this last case, one talks about Optical Camera Communication (OCC). With such a pair of front end components, VLC poses a tricky challenge: contrary to what's happening in the Radio Frequency (RF) domain, the amplitude and phase of the electromagnetic field emitted by LEDs can't be separately modulated and detected because of the absence of a reference local oscillator at the detection point, and data transmission is only doable as an intensity modulation and direct detection scheme. This imposes a constraint on the signal that can be used to modulate the LED through the current driver: it has to be real valued and strictly positive to be successfully mapped into the light intensity and that limits the typology of eligible modulation schemes with respect to the RF domain.  \n\n\n\\begin{figure}[t!]\n  \\includegraphics[width=\\linewidth]{frequencychart.jpg}\n  \\caption{US frequency allocation chart (logarithmic scale). The RF spectrum spans the 3kHz-300GHz range of the electromagnetic spectrum and is heavily regulated and used. The most common bands for consumer electronics and IoT are shown on the graph. By contrast the visible light and near infrared spectrum from 250 THz to 800 THz, more usually expressed in wavelength from 400 nm to 1.2 \\selectlanguage{greek}u\\selectlanguage{english}m, is not regulated and can be used for light communications over a much larger range of frequencies. Sources: US Department of Commerce \\cite{freq}, Lucibel}\n  \\label{fig:frequencychart}\n\\end{figure}\n\n\nOn the flipside, the LiFi domain, which is the near IR and visible light frequency range, is not regulated and is orders a magnitude larger than the RF range, suffering from the \"spectrum crunch\" due to the exponentially increasing need for bandwidth. \n\n\nFinally, the modulation scheme must be designed with the characteristics of the luminaire in mind: dimming must be possible, no flickering should be perceived (achieved with a switching rate faster than 2kHz), the LED visual appearance characterized by the Color Rendering Index (CRI) and Correlated Color Temperature (CCT) shouldn't be impacted, power loss and heat should be minimized. \n\nIndeed, LiFi systems must be designed as illumination systems with communications capabilities, not the reverse.\n\n\\section{LED Modulation Techniques}\n\nSingle Carrier Modulation (SCM) techniques are relatively straightforward to implement in Light Communications. Illumination control can be supported by adjusting the light intensities of the \"on\" and \"off\" states at typically +\/- 10\\% of dimming level, without affecting the system performance. Different kinds of pulses (symbols) are used, such as Non-Return-to-Zero or Manchester codes. \n\n\nOn-Off Keying (OOK) is the technology of choice for OCC and applications such as location based marketing where a limited amount of contextual information is pushed to a mobile device. But, for high speed communiactions, performances deteriorate as the bit rates increase. Sophisticated equalization techniques with different degrees of performance and computational complexity, as well as significant power consumption, are required for SCM techniques to be effective at high data rates which makes them unattractive. The IEEE Standards Association has developed the 802.15.7 standard \\cite{ieee15} for this kind of short-range and low data rate communication using visible light.\n\n\\begin{figure}[h]\n  \\includegraphics[width=\\linewidth]{ofdm.jpg}\n  \\caption{Block Diagram of a high speed LiFi device. Through the allocation of signal bits among sub-carriers, OFDM is a technique that allows to pack much more signal in a given frequency carrier than Single Carrier Modulation techniques. The subcarrier frequencies are chosen so that the signals are mathematically orthogonal over one symbol period. Pre-distortion is used to linearize the dynamic range of the LED. Adapted from \\cite{hass2012li}}\n  \\label{fig:ofdm}\n\\end{figure}\n\nFor high-speed optical wireless communication, Multi-Carrier Modulation (MCM) is preferred. For example, PureLiFi's technology incorporated into Lucibel's devices relies on Orthogonal Frequency Division Multiplexing (OFDM) \\cite{armstrong2009ofdm}\\cite{afgani2006visible}, where parallel data streams are transmitted simultaneously through a collection of orthogonal subcarriers. The spectra of individual subcarriers overlap, but because of the orthogonality property the subcarriers can be demodulated without interference. The subcarrier spacing is the inverse of the symbol duration and the subcarrier bandwidth is designed so that it is smaller than the channel coherence bandwidth in order to omit complex equalizer circuitry.  \n\n\nAt the level of the LED, Quadrature Amplitude Modulation (QAM) is used to encode data into symbols loaded afterwards into the subcarriers. QAM introduces complexity but is more robust to noise than alternative schemes at high speeds. The parallel symbols can then be multiplexed into a serial time domain output using Inverse Fast Fourier Transformation (IFFT) and then de-multiplexed after using FFT at the receiver. A so called Cyclic Prefix is added to the start of each time domain OFDM symbol before transmission, this way eliminating both inter-symbol and inter-channel interference from the received signal. \n\nOFDM is a well-known technique used in RF communication protocols for WiFi, powerline and 4G communications and its implementation for light communication is almost equivalent but for one important characteristic: RF OFDM generates complex-valued negative and positive (bipolar) signals, incompatible with LED intensity modulation. With a proper symmetry operation, the time domain signal is forced into the real domain but at the detriment of a reduction of the system bandwidth by a half. A simple way to make a bipolar signal strictly positive is to introduce a direct current (DC) bias around which the original bipolar signal can vary. This scheme is known as DC-biased Optical OFDM (DCO-OFDM). Numerous variant OFDM techniques have been developed over the last 10 years to provide energy efficient alternatives without the sacrifice of spectral efficiency. This is still a subject of intense research \\cite{islim2016modulation}\\cite{noshad2016hadamard}. \n\nAs well as its many advantages, OFDM has a number of disadvantages, such as the high peak-to-average power ratio which imposes a wide dynamic range in many of the components of the transmitter and the receiver. Very fast Digital Signal Processing implementation is required to perform Fourier Transforms and the design of the Digital-Analog converters is critical because of the complexity of the signal and the required accuracy of the conversion. All these requirements entail a cost but this technology scales up quickly, in a similar way to WiFi components.\n\n\n\\section{LiFi as a Communication Solution }\n\nLiFi is not only a photonic virtual cord, it is a complete wireless networking system, offering bi-directional multi-user communication, within a wireless network of very small optical cells,  therefore a very high spatial connection density, and with seamless handover. Each LiFi luminaire is an Access Point (AP) \\cite{dimitrov2015principles}.\n\nOptical OFDM provides natively a multiple access technique called OFDMA, also the method of access for the new WiFiax standard, where users of data broadcasted by a given luminaire are separated by a number of orthogonal subcarriers. Other multi-user access technologies can also be used such as Time Division Multiple Access (TDMA).  \n\nFor a complete LiFi communication system, duplex communication is required, {\\it i.e.} an uplink connection from the mobile terminals to the optical AP should be provided. RF duplex techniques where the downlink and the uplink are separated by different time slots, or different frequency bands, could be used. However, emitting intense white light by the receiver terminal is not acceptable in practice. A solution, implemented by Lucibel and PureLiFi, is to use Wavelength Division Duplexing (WDD), using visible light modulation for the downlink and the modulation of an IR LED for the uplink communication channel. Using RF communication for the uplink is also an option in certain configurations since there is often a traffic imbalance in current wireless communication systems that makes the uplink channel considerably less congested.\n\nIn RF wireless communications, the network is distributed over areas called cells, each served by at least one fixed-location base station. In 4G LTE, in order to improve user access, the network is densified by the addition of cells of different sizes referred to as macro-, micro-, pico- and femto-cells in order of decreasing base station power. Inter- and intra-cell interference avoidance is one of the most critical challenges for the concurrent operation of these cells. 5G wireless network should see the incorporation of unlicensed networks such as WiFi into so called heterogeneous networks. \n\nThe concept of cell is easily transposed to LiFi and the optical AP associated to a LiFi luminaire is frequently called an \"attocell\" because of its small size. Because of the density of luminaires and the nearly uniform illuminance, optical attocells can drastically improve coverage and data density. In an hybrid LiFi\/WiFi deployment \\cite{ayyash2016coexistence}, LiFi offloads some of the traffic from WiFi to maintain the broadband user experience. \n\nWith LiFi, each user benefits from the bandwidth available under each luminaire, without sharing it with users under other luminaires. This idea of \"connection densification\" is a key point in favor of LiFi with respect to WiFi, as much as the high data rate.\n\nMoreover, whereas complex beamforming techniques are developed for next generation RF wireless systems to increase capacity, beamforming is native for light based communications. It is worth noting that, similar to conventional RF based communication systems, Multiple Input-Multiple Output (MIMO) schemes in LiFi and more generally VLC are capable of bringing data transmission speed enhancements \\cite{zhang2017localisation}. \n\nAll these characteristics make LiFi a crucial enabler of mobility indoor with as yet unmatched quality of service, improving substantially the user experience.\n\nA Study Group of the IEEE Standards Association is exploring adding light communication protocols to the 802.11 WiFi standards for communications \\cite{ieeelcsg}\\cite{burchardt2014vlc}. This standardisation effort is an important factor towards large scale deployments of LiFi and Lucibel is a contributor to the work being performed.\n\n\\begin{figure}[b!]\n  \\includegraphics[width=\\linewidth]{lucibel.jpg}\n  \\caption{The first commercial LiFi downlight, manufactured by Lucibel and PureLiFi and brought to the market in September 2016. Rated performance is 42 Mbps downlink and uplink in a standard lighting geometry at a height of 2.5 m. 8 users can be served data simultaneously by a luminaire. The uplink channel is in the near infrared band to avoid glare from the USB receiver connected to a laptop or tablet}\n  \\label{fig:lucibel}\n\\end{figure}\n\n\\section{Performances and Outlook}\n\nLucibel has developed with its partner PureLiFi a fully functional commercial LiFi luminaire for enterprise applications, commercialized in its current version in September 2016. This is the first LiFi luminaire on the market.\n\nThe dimmable Lucibel Ores LiFi downlight \\cite{oreslifi} implements proprietary technologies to perform energy and spectrum efficient modulation of a standard white light LED for the downlink, and an IR LED for the uplink. The bidirectional link is rated up to 42 Mbps (megabits per second) and up to 8 users can connect per AP, within a very a cell of diameter 3 m for a ceiling height of 2.5 m. Whereas a WiFi acces point covers a much larger area, many users have to share the bandwidth and end up with a lower speed. \n\nDimming is possible while a user is communicating through an AP and communications are encrypted with standard WPA2 authentication protocols. \n\nCharacteristics such as the receiver's form factor and the handover protocol from AP to AP will be improved in the second generation to be released in 2018, with a new energy efficient electronic architecture.  Other configurations such as 2 ft x 2 ft panels and floor lamps will be put on the market to broaden the range of installations and use cases. An updated LiFi API will improve network configuration and management and make the LiFi system a part of Lucibel's cloud based lighting management system.\n\nThe LiFi luminaire is compatible with Power over Ethernet (PoE) technology. This key characteristic permits to transmit through a single RJ45 cable at the same time data and power, thus minimizing the necessary wiring for the deployment of a LiFi network infrastructure and ultimately reducing the installation costs. PoE architectures are also more energy efficient.   \n\nAll components of the LiFi system have an impact on the performance in terms of data rate and energy consumption but, once the best available modulation technology is implemented and interferences and spatial effects are controlled in laboratory conditions, the most important contributor to performance is the modulation response of the LED. A lower modulation frequency translates into a lower data rate, although the relation is not straightforward and published data are not easily comparable. Equalization, for one, improves the LED 3dB cutoff frequency but at the detriment of energy efficiency. Various advanced processing methods can boost the throughput but they are not necessarily easily implemented in a compact and cost effective device.\n\n\\begin{table}[h]\n\\begin{center} {\n\\begin{tabular}{lllll}\n\\hline\n & \\multicolumn{1}{l}{Technology} & \\multicolumn{1}{l}{Bit Rate} & \\multicolumn{1}{l}{Reference}\\\\\n\\hline\n& Phosphor coated blue LED & 1.1 Gbps & \\cite{khalid20121} \\\\\n& Color converted blue \\selectlanguage{greek}m\\selectlanguage{english}LED & 1.7 Gbps & \\cite{chun2014visible} \\\\\n& Multicolor R(Y)GB LED and \\selectlanguage{greek}m\\selectlanguage{english}LED & 2 -- 11.3 Gbps & \\cite{cossu20123} \\cite{chun2016led} \\cite{wang20158} \\\\\n& Color Converted Laser Diodes & 1 - 4 Gbps & \\cite{lee2017gigabit} \\cite{chi2017violet} \\\\\n\\hline\n\\end{tabular} }\n\\end{center}\n\\caption{Data transmission speeds reported for various white light solid-state lighting technologies. With the exception of phosphor coated blue LEDs which constitute the building block of current commercial LED luminaires, the other technologies are in the demonstration phase for lighting applications.}\n\\label{turns}\n\\end{table}\n\nCommercial blue LEDs coated with a yellow phosphor to produce white light have modulation bandwidths limited to a few MHz due to the long photoluminescence lifetimes of the phosphors. The application of a blue filter at the receiver removes the slow component from the signal and enables modulation frequencies of up to 20 MHz \\cite{ayyash2016coexistence}.  This is the standard technology that is used in Lucibel's Ores LiFi luminaire. Several strategies are being pursued to overcome this limitation.\n\nMicro-LEDs can offer optical modulation bandwidths in excess of 600 MHz thanks to their small active areas enabling high current density injection \\cite{islim2017towards}. They can be positioned in arrays to enable parallel communication, which is of interest for communication with displays.\n\nAnother way to create white light is to mix optically the emissions of three Red, Green and Blue LEDs or micro-LEDs. For LiFi, this has two main advantages: there is no bandwidth limiting color converter coating and the three LEDs can be modulated separately, thus allowing for the transmission of three parallel independent information streams \\cite{cossu20123}.\n\nBut the best way to improve the modulation response is to use GaN Laser Diodes, because their modulation speed is controlled by the photon lifetime, on the order of ps, instead of the carrier lifetime for LEDs, several orders of magnitude higher. A 2.6 GHz modulation frequency has been reported \\cite{lee20154} and 15 Gbps (gigabits per second) data rate over a single blue channel \\cite{viola201715}. While Laser Diodes are as of today an expensive option for indoor lighting, their cost is expected to decrease exponentially over the next five years because of mass market demand for applications such as automotive lighting, projectors and LIDAR for autonomous vehicle.\n\n\nAll these technologies have been rated in the laboratory for white light emission, intensity modulation and data transfer to a photodiode. The feasibility of over Gbps LiFi data transmission is established, auguring well for transition to product development and commercialization shortly. With Laser Diodes, data rates in excess of 100 Gbps are hypothesized \\cite{tsonev2015towards}. Constant new developments in the fields of design and manufacturing of LEDs \\cite{li2017localization}\\cite{lozano2016metallic}, Laser Diodes \\cite{lee2016dynamic}, photon converters \\cite{leitao2017gb} and optical sensors \\cite{lestoquoy2014multimaterial}\\cite{fink2017lifi}, as well as in the field of signal processing \\cite{zhang2017localisation}, are monitored closely by Lucibel's teams to identify and update the best available technology for its LiFi devices.\n\n\\section{Use Cases: Towards Large Scale Deployments}\n\nVLC has been a subject of intense research \\& development for more than 15 years with steady improvements in performance, cost, reliability and components' compactness. While many applications have been imagined, such as vehicle to vehicle communications or underwater data transmission, the exponential development of Solid State Lighting has directed the short-term developments towards the best defined and most valuable use cases. \n\n\\begin{figure}[!h]\n  \\includegraphics[width=\\linewidth]{usecases.jpg}\n  \\caption{Projected data access demands of RF and LiFi technologies. Intrinsic low latency and the potential for a very large bandwidth make LiFi a technology of reference for video streaming and cloud based office as well as for emerging use cases such as Virtual Reality and applications of robotics in the industry, in the office or in public spaces. Sources: AT\\&T \\cite{att5G}, Lucibel}\n  \\label{fig:usecases}\n\\end{figure}\n\nLucibel has installed LiFi luminaires for more than 50 customers and has engaged extensively with them and communities, thus gaining a unique experience of the key value propositions for its first generation of products. Lucibel's customers are implementing LiFi as a powerful complement or alternative to WiFi and 4G, in environments where data exchange should be perfectly secure (banks, R\\&D centers, defense, \u2026), radio waves are not permitted or restricted (hospitals, pre-K schools, EMI sensitive industrial facilities such as natural gas compression stations) or connectivity should be guaranteed (conference rooms, hotels).  Train to train communications are also being explored. \n\nThe selection of use cases is driven by the facts that, on the one hand, the light frequency range is interference free and not regulated and, on the other hand, Light Communications happen in the cone of light. In contrast to WiFi which suffers intrinsically from radiation leakage, the directionnality of light drastically limits the risk of eavesdropping and hacking of the network \\cite{mostafa2015physical} \\cite{chen2017physical}. Moreover, a key generation mechanism specific to OFDM can improve the internal communication security \\cite{al2017secret}. \n\nObvious limitations of the technology, such as the fact that the light has to be switched on with a minimum level of illumination, have to be acknowledged and constitute simple boundary conditions in the immense space of the indoor wireless use cases. \n\nThere is no commercial deployment in the residential space yet. This relies on further cost reductions, miniaturization and integration of the receivers' components in consumer electronics devices, expected to happen around 2020.\n\nThe data transmission speed of LiFi by Lucibel in the 10-50 Mbps range and the densification of Access Points position LiFi to be an enabler for the digital transformation of companies and infrastructures. Three numbers by Cisco explicit the global ever-accelerating need for bandwidth and wireless \\cite{ciscovni2017}: by 2021 more than half of 17 billion connected devices will be mobile, 65\\% of the IP traffic will be from mobile devices, 80\\% of the internet traffic will be video requiring high speed wireless and the average RF wireless speed will be 20 Mbps. Mobile video streaming and personal cloud access are where LiFi excels and, with people in industrialized nations spending more than 90\\% of their time indoors, lighting is poised to become a communications infrastructure of choice.\n\nFrom an energy efficiency promotion perspective, with LiFi, lighting technologies offer enough value to customers for them to switch from incandescent and fluorescent lights to the much more energy efficient and cost competitive LEDs. This could be a considerable driver to increase LED adoption in existing buildings where first generation smart lighting's reception has been so far tepid. The strong appetite for high quality and high speed internet access could push to make lighting infrastructure retrofits at the considerably quicker pace of IT infrastructure retrofits.\n\nBut what makes LiFi an even more exciting technology is the possibility to reach, with a next generation of LiFi by Lucibel devices, transmission and reception speeds in the 1 to 10 Gbps range with a very low latency inherent to optical technologies. New use cases will emerge.\n\nOffice robotic telepresence is a perfect example of synergy between the lighting and communication functions of Lucibel's LiFi solution. In the workspace, lighting is ubiquitous and LiFi has a guaranteed coverage over the whole floor with a high minimum bandwidth, without interference and disconnection, perfectly adapted to the video streaming. Moreover LiFi, and more generally VLC technologies, have the inherent capacity to localize devices at the level of a luminaire, but even better, with a cm level precision thanks to signal processing \\cite{do2016depth}\\cite{lin2017experimental}. This is of tremendous value for many applications because indoor RF technologies are by far not as precise \\cite{hu2016demonstration}. \n\n\\begin{figure}[h]\n  \\includegraphics[width=\\linewidth]{newuse.jpg}\n  \\caption{Emerging use cases for LiFi: warehouse robot, robotic telepresence, augmented reality. Pictures are for illustration purpose only. Sources: 6 River Systems, Suitable Technologies, Diota}\n  \\label{fig:newuse}\n\\end{figure}\n\n\nLiFi's data transmission speed is beyond what's needed to connect IoT devices such as thermostats and presence detectors requiring at most 100 kbps. But the density of potential connections under a LiFi light spot is such that many devices can connect to a single AP and aggregate their bandwidth requirements. These devices can even harvest energy from the LED or Laser Diodes through the communication channel \\cite{sandalidis2017illumination}\\cite{passivevlc}, potentially solving the critical power supply issue for the IoT. Light communication directly between devices is also possible.\n\nLiFi as a high-speed communication solution is extremely well positioned to be a solution of choice for the Industrial IoT, for example to feed and collect 3D data to and from AR devices at the service of workers on a manufacturing floor. Existing IoT architectures are highly centralized and heavily rely on a back-end core network for all decision-making processes. With LiFi, a large amount of data can be gathered in a secure way from multiple devices and processed at the edge by a local processor with the benefit of lower latency and reduced bandwidth requirements to communicate with the cloud \\cite{bader2016front}. In the same spirit of decentralization, LiFi could be a crucial enabler for trusted transactions between IoT devices mediated by blockchains \\cite{danzi2017analysis}.  \n\nLucibel is building with its partners, startups and other innovation driven companies, an ecosystem to bring progressively to the market the products that will fuel the large scale penetration of LiFi for these use cases and certainly many others. The first steps are to create awareness about the technology, to make its potential and also its limits known, to implement quickly the lessons learnt from early deployments and to train the workforce with the skills to build projects at the confluence of lighting and communication technologies. \n\n\\hfill \n\\break\n\\break\n{\\it Dr. C. Jurczak is Lucibel's Chief Scientific Officer, in Palo Alto, CA (USA).}\n\n\\medskip\n\n\\bibliographystyle{ieeetr\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\n\\IEEEPARstart{R}{einforcement} Learning (RL) using neural networks as parametric functions, a.k.a. deep RL, has been successfully applied to a variety of reward-oriented tasks, ranging from pixel-based video games \\cite{mnih2015human, mnih2016asynchronous, wang2016sample, kapturowski2018recurrent} to robotic control applications \\cite{wang2016sample, lillicrap2015continuous, haarnoja2018soft}. One main advantage of RL is that it enables agents to learn highly adaptive control skills through self-exploration. However, most successes have been achieved in relatively simple, idealized environments. To advance deep RL in real-world applications, such as those potentially encountered by robots, there are still a number of difficulties that must be overcome.\n\nOne major challenge is the trade-off between exploration and exploitation, a long-standing dilemma in RL. Many tasks only provide sparse rewards, i.e., a single reward obtained only after a specific set of actions is completed. This often causes significant difficulties in real-life robotic tasks, as interactions between the agent and the environment cannot be accelerated by software; thus, the agent spends an intolerable amount of time engaging in exploration before discovering a reward to improve its policy. A typical state-of-the-art RL algorithm usually executes millions of interaction steps to train an agent player to play an Atari 2600 game or to teach an insect-like robot to walk \\cite{mnih2015human, mnih2016asynchronous, wang2016sample, kapturowski2018recurrent, lillicrap2015continuous, haarnoja2018soft}, which is an extremely impractical for real-world applications. The exploration problem appears to be inherent in autonomous agents, and is almost impossible to resolve perfectly using a pure RL scheme. \\textit{Reward shaping} is a method that smoothes sparse rewards to hand-coded dense rewards, indicating the distance to the goal state. It is useful to reduce exploration overhead in tasks with sparse rewards. However, in practice, it requires a considerable amount of engineering and experimentation. Otherwise, the local minima trap or unexpected behavior may be introduced by the shaping function \\cite{ng1999policy, vevcerik2017leveraging}.\n\nHumans can learn much by imitating demonstrations by others. However, imitation is also misleading when demonstrator behaviors are not optimal, or when imitators lack the ability to replicate demonstrator behaviors \\cite{price2003accelerating}. If we examine professional video game players, we observe that they improve their skills not only by learning from how other players play, but also by exploring more effective strategies by themselves \\cite{kim2015stage}. Extra cost can be given to the agent if it follows the demonstrator's trajectory, forcing it to rely more on its own exploration \\cite{duminy2019learning}. It is also possible to balance imitation and exploration by using imitation to accelerate RL, either with homogeneous actions, in which the agent can replicate demonstrator behavior \\cite{price1999implicit}, or with heterogenous actions, in which the agent lacks the ability to follow the demonstrator's action \\cite{price2001imitation}.\nIt is also practical to use imitation with RL even when the demonstrator's performance cannot be evaluated \\cite{ho2016generative}. \n\nRecent studies have focused on integrating imitation throughout the RL process, when demonstration samples can be used not only to help agents learn a naive strategy for achieving a goal, but also to improve adaptability through further self-exploration in different circumstances. This way, it is possible for agents to acquire adaptive skills with a reasonably small number of demonstration samples, even if they are not optimal. This approach, known as \\textit{RL from demonstrations} (RLfD), has recently been employed in video games \\cite{hester2018deep} and robot control \\cite{vevcerik2017leveraging}, and is significantly more efficient than RL without demonstrations. \n\nPrevious studies of RLfD assumed that crucial information necessary for making a decision is fully observable \\cite{vevcerik2017leveraging, hester2018deep}. However, this assumption does not hold in real-world environments where unobservable information always exists. A step toward real-world applications must still be developed by exploring new schemes that do not require such an assumption. Decision-making should not be based solely on current observations, but also on memory, and unobservable information should be inferred from historical observations. In deep RL, although it is theoretically possible to combine all historical and current observations, the cost becomes unacceptable due to hardware capacities and the curse of dimensionality \\cite{friedman1997bias}. A representation of fixed size is expected to enable practical policy learning. Recurrent neural networks (RNNs) have proven effective at solving partially observable tasks in RL \\cite{utsunomiya2008contextual, shibata2015reinforcement,  heess2015memory, vezhnevets2017feudal, al2017continuous, kapturowski2018recurrent}. Well-trained RNNs are able to encode useful historical information by its hidden states, which can be used to make optimal decisions. Although RNNs appear to be practical solutions to challenges in partially observable environments, some outstanding issues remain, such as representational drift and long-term memory dependencies \\cite{kapturowski2018recurrent}, despite the fact that training an RNN is usually harder than training a feed-forward neural network \\cite{pascanu2013difficulty}. Evidently, it is not sufficient to simply embed an RNN in a deep RL agent.\n\nIn this study, we consider applying RLfD to more challenging, partially observable continuous control tasks by proposing a novel algorithm called Recurrent Actor-Critic with Demonstration and Experience Replay (READER). READER does not require demonstrations that follow an optimal strategy. Instead, imperfect demonstrations can be used, and an agent can conduct self-exploration to learn strategies that are more efficient than the demonstrated strategies. The proposed algorithm was tested in three different types of continuous control tasks, in which learning optimal control requires (1) a large amount of exploration due to sparse rewards; (2) inference of hidden information from a trajectory of observations; and\/or (3) long-term memorization of previous experiences. Experimental results show that performance can be significantly improved even using imperfect demonstrations by humans. The algorithm is also tested against Recurrent Deterministic Policy Gradient from Demonstrations (RDPGfD), an extension of Recurrent Deterministic Policy Gradient (RDPG) \\cite{heess2015memory} to RLfD. The comparison shows that READER has better sample efficiency in all experiments, and better learning capabilities in some RL tasks.\n\n\n\\section{Background}\n\\label{sec:background}\n\\subsection{Reinforcement Learning in Partially Observable Environments}\nSolving memory-dependent control tasks can be formulated into a \\textit{Partially Observable Markov Decision Process} (POMDP) \\cite{aastrom1965optimal} framework. A POMDP can be used to define interactions between an agent and the environment into discrete time steps. In a POMDP, $\\mathcal{S}$ defines the set of possible environment states. $\\mathcal{A}$ is the set of actions the agent can perform at each time step. An initial state $s_0$ is sampled at the beginning by the distribution $p_0(s_0)$, and the environment reacts to the action following a Markovian dynamic $p(s_{t+1}|s_t, a_t)$. A reward function, $r(s_t, a_t)$, defines the immediate reward given to the agent at each time step ($t$). In contrast to MDP, in a POMDP, the agent cannot observe the exact environmental state, $s_t$. Instead it can receive an observation $x_t$ from the observation set $\\mathcal{X}$, conditioned on the underlying state through $p(x_t|s_t)$. The current paper assumes that unobservable information can be inferred from historical observations.  \n\n\nUsing RNNs as function approximators to estimate the current true state is a common way to overcome these difficulties and has been utilized effectively in many studies \\cite{utsunomiya2008contextual, heess2015memory, vezhnevets2017feudal, kapturowski2018recurrent}. In general, RNNs encode the history of observations, $x_{0:t}$, into a vector representation $h_t$ known as the hidden state. At each time step $t$, the new hidden state is calculated using $h_t = f(h_{t-1}, x_t)$ and the output is calculated using $o_t = g(h_t)$. An RNN can be trained by backpropagation through time (BPTT) \\cite{werbos1990backpropagation}. In keeping with \\cite{heess2015memory, kapturowski2018recurrent}, we use long-short term memory (LSTM) \\cite{hochreiter1997long} architecture as the RNN for encoding historical observations in our algorithm.\n\n    \\subsection{Reinforcement Learning from Demonstrations (RLfD) }\n        \\label{sec:related}\n        RLfD has been studied in many different cases. Some algorithms have explored the use of an extra action \\cite{taylor2011integrating, wang2017improving} to follow the demonstrator. These methods usually require a knowledge of the demonstrator's policy, and work well only if the action space is discrete. \\cite{subramanian2016exploration} introduced an exploration policy to enable both self-exploration and exploration from demonstrations. Behavior cloning has also been used to learn from accurate demonstrations \\cite{nair2018overcoming, rajeswaran2017learning}. Another set of algorithms has been introduced to enable an agent to learn from demonstrations by putting the state transition samples ($x_t, x_{t+1}, a_t, r_t$) from the demonstrator into a replay buffer, known as \\textit{demonstration replay}, and using them to assist policy evaluation and optimization with off-policy RL. Some widely used off-policy RL algorithms, such as deep deterministic policy gradient (DDPG) \\cite{lillicrap2015continuous} and deep Q-networks (DQN) \\cite{mnih2013playing}, have been extended with this concept of demonstration replay in DDPGfD \\cite{vevcerik2017leveraging} and DQfD \\cite{hester2018deep}. These methods use a demonstration replay buffer to learn a state-action value $Q$ function, and to train the policy network (as in DDPGfD) or to derive the policy directly (as in DQfD) from the $Q$ function. \n        \n        These RLfD studies were all conducted in the framework of MDPs, whereas RLfD for memory-dependent tasks has not been investigated. In this paper, we introduce this same concept of demonstration replay into an RL algorithm, \\textit{Sample Efficient Actor-Critic with Experience Replay} (ACER) \\cite{wang2016sample} by proposing several modifications to the original algorithm, and we extend it to the POMDP framework by employing an RNN.  In the following section, we describe the application of policy evaluation and policy optimization using a demonstration buffer.\n        \n\\section{Recurrent Actor-Critic with Demonstration and Experience Replay}\n\\label{sec:method}\n\n\n    To solve POMDPs where exploration is crucial, we propose an RL algorithm, READER. We demonstrate it by building upon the existing ACER algorithm. Compared to other RLfD algorithms, such as DDPGfD \\cite{vevcerik2017leveraging} and DQfD \\cite{hester2018deep}, READER learns a memory-dependent policy that can solve POMDPs. READER also uses policy optimization on demonstration samples, making better use of multi-step returns in demonstrations to improve the policy. In this section, we introduce the components of READER and how READER exploits them to solve exploration-crucial POMDPs.\n    \\subsection{Recurrent Actor-Critic}\n        ACER \\cite{wang2016sample} is a state-of-the-art actor-critic algorithm that can learn in both discrete and continuous action cases. We focus on continuous action space in this work. To extend ACER for use in POMDPs, we use RNNs to approximate value and policy functions. As in ACER, we use two networks parameterized by $\\theta$ and $\\theta_v$ called the policy network and the value network. The policy network does not learn a parameterized distribution, $\\pi_\\theta (\\cdot|x_t)$, conditioned on the current state. Instead, it learns a policy conditioned on a full history of observations from the beginning of the episode, $\\pi_\\theta (\\cdot|X_t)$, where $X_t = x_{0:t}$. We will use the notation $X_t = x_{0:t}$ hereafter, and any function with this notation is expected to be computed recursively using an RNN. RNNs are employed to encode the history of observations $x_{0:t}$ into a vector representation $h_t$. $h_{-1}$ is set to a fixed value, and $h_t$ is recursively computed through the following equation: $h_t = f(h_{t-1}, x_t)$. The policy at time $t$ can be computed as a distribution conditioned $h_t$. Similarly, the value network takes the trajectory of observations, $X_t$, as input and then outputs $V_{\\theta_v}(X_t)$ and $Q_{\\theta_v}(X_t, a_t)$.\n        \n        To better estimate value functions, we propose an architecture for the value network: the \\textit{stochastic recurrent dueling network} (SRDN), which is a recurrent version of the stochastic dueling network \\cite{wang2016sample}. Instead of estimating $Q^\\pi(X_t, a_t)$ directly, in SRDN, we calculate $A_{\\theta_v} (X_t, a_t)$ as an estimate of the \\textit{advantage} $A^\\pi(X_t, a_t) = Q^\\pi(X_t, a_t) - V^\\pi(X_t)$, and correct the bias by random sampling $n$ from the policy $\\pi_\\theta$, leading to the following stochastic estimate of $Q^\\pi$: \n        \\begin{equation}\n        \\begin{split}\n            \\tilde{Q}_{\\theta_v}(X_t, a_t)\n              = & V_{\\theta_v}(X_t) + A_{\\theta_v} (X_t, a_t) - \\frac{1}{n} \n              \\sum_{i=1}^{n}A_{\\theta_v} (X_t, u_i), \\\\\n              & \\mathrm{where} \\: \\: u_i \\sim \\pi_\\theta(\\cdot| X_t).\n        \\end{split}\n        \\end{equation}\n        $A_{\\theta_v}$ shares the same recurrent layer with $V_{\\theta_v}$ in SRDN. This equation will maintain a consistency between $\\tilde{Q}_{\\theta_v}$ and $V_{\\theta_v}$ such that\n        $\n            \\mathbb{E}_{a, u_{1:n} \\sim \\pi(\\cdot, X_t)} \\left(\n                    \\tilde{Q}_{\\theta_v}(X_t, a)\n                \\right) = V_{\\theta_v}(X_t).\n        $\n        \n    \\subsection{Prioritized Episodic Demonstration and Experience Replay}\n        Experience replay has been widely used in reinforcement learning to improve sample efficiency \\cite{mnih2013playing, wang2016sample, lillicrap2015continuous} by storing past interactions with the environment into a replay buffer. Past interactions are randomly sampled from the replay buffer and used as training samples, breaking the temporal correlation among samples. Prioritized experience replay (PER) \\cite{schaul2015prioritized} is an improvement on experience replay that samples potentially useful interactions with high priority. \n        \n        In memory-dependent control, a continuous trajectory of time steps should be sampled as RNN input rather than as independent time steps. \\cite{kapturowski2018recurrent, hausknecht2015deep} discussed several ways of sampling a trajectory, including sampling the whole episode. The tasks used in our experiments are relatively short (no more than 200 time steps in length), so we sample and replay the whole episode trajectory. High sample variance is caused by correlation within samples in the same episode \\cite{kapturowski2018recurrent}. To prevent this, we sample several times at each learning step and form a batch from the sampled episodes to introduce uncorrelated samples from other episodes. \n        \n        We follow \\cite{kapturowski2018recurrent} in defining the priority of the $i$th episode, $p_i$, through a mixture of max and mean absolute n-step TD-errors, $\\delta_i$, over the episode: \n        \\begin{equation}\n            p_i = \\eta \\max_i \\delta_i + (1 - \\eta) \\bar{\\delta} .\n        \\end{equation}\n        TD-errors are also recorded in the replay buffer. However, TD-errors change when the policy is updated, and we cannot afford the cost of recomputing TD-errors for all episodes after each learning step. Instead, TD-errors of an episode are only updated after being replayed. The probability of sampling the $i$th episode is then calculated using the following equation: $P(i) = \\frac{p_i^\\alpha}{\\sum_i p_i^\\alpha}$. To correct bias introduced by non-uniform sampling, updates to the neural networks are scaled by the following importance sampling weight: \n           \n            $\\frac{L(i)}{N} \\cdot \\frac{1}{P(i)}$.\n        $L(i)$ is the length of the $i$th episode, and $N$ is the sum of the lengths of all episodes stored in the replay buffer. To keep a uniform update on each environmental step in the replay buffer, the importance sampling weight is also scaled down by the length of episode $L(i)$, and the resulting weight is used to scale the update of both the policy and value networks:\n        \\begin{equation}\n            \\label{equ:weight}\n            w_i = \\frac{1}{N} \\cdot \\frac{1}{P(i)} .\n        \\end{equation}\n        \n        As in DDPGfD, we store demonstration episodes in a separate prioritized replay buffer called the \\textit{demonstration buffer}. The replay buffer containing past experiences is then called the \\textit{experience buffer}. In each learning step, sampling is performed by putting the demonstration and experience buffers together in a combined buffer, using the same definition of priority and update rule of TD-errors mentioned above. Probabilities and important sampling weights are calculated with respect to the combined buffer.\n\n    \n    \\subsection{Policy Evaluation}\n        Policy evaluation is a necessary part of ACER. We extend it using the RNNs mentioned above. The goal is to learn an optimal policy $\\pi^{*}(\\cdot|X_t)$, which is a distribution of actions conditioned on the history of observations. During the process of improving the current policy $\\pi$, the state-action value function $Q^\\pi(X_t,a)$ and the state value function $V^\\pi(X_t)$ are learned simultaneously. Learning these two value functions is termed policy evaluation. \n        \n        Retrace($\\lambda$) \\cite{munos2016safe} is the policy evaluation method used in ACER. In experience replay, the policy used to generate previous episodes, also known as the \\textit{behavior policy} $\\mu$, is not the same as the current policy ($\\pi$). A set of trajectories sampled from $\\mu$ is given to estimate $Q^\\pi(X_t,a)$ and $V^\\pi(X_t)$. Consider the general operator of return-based policy evaluation used for updating $Q$: \n        \\begin{equation}\n        \\begin{split}\n             & \\mathcal{R}Q(X_{t_0},a) = Q(X_{t_0},a)+ \\\\ & \\mathbb{E}_\\mu \n                            \\left[\n                                \\sum_{t \\geq t_0} \\gamma^{t-t_0} \\left( \n                                    \\prod_{s=t_0+1}^t c_s\n                                \\right)\n                                (r_t + \\gamma \\mathbb{E}_\\pi Q(X_{t+1}, \\cdot) - Q(X_t, a_t))\n                            \\right].\n        \\end{split}\n        \\end{equation}\n        The coefficient $c_s$ is called \\textit{traces} of the operator. $\\prod_{s=t_0+1}^t c_s$ is defined as $1$ when $t=t_0$. Different $c_s$ choices lead to different policy evaluation algorithms \\cite{munos2016safe, harutyunyan2016q, precup2000eligibility, precup2001off}. Retrace($\\lambda$) is a policy evaluation algorithm that can be applied to arbitrary behavior policy $\\mu$, when $c_s=\\lambda \\min\\left(1, \\frac{\\pi(a_s|X_s)}{\\mu(a_s|X_s)}\\right)$ for $0 \\leq \\lambda \\leq 1$. Retrace($\\lambda$) has several advantages. It can utilize full returns in near on-policy cases, and does not suffer from high variance in off-policy cases. We can derive a bootstrap equation of Retrace($\\lambda$) from one trajectory sampled from $\\mu$ to estimate $Q^\\pi(X_t, a_t)$: \n        \\begin{equation}\n        \\begin{split}\n            & Q^{ret}(X_t, a_t) = r_t + \\\\ & \\gamma \\bar{\\rho}_{t+1} \\left[ \n                Q^{ret}(X_{t+1}, a_{t+1}) - \\tilde{Q}_{\\theta_v}(X_{t+1}, a_{t+1})\n            \\right] + \\gamma V_{\\theta_v}(X_{t+1}).\n        \\end{split}\n        \\end{equation}\n        \n        Retrace($\\lambda$) assumes that the behavior policy is known to the algorithm. However, this does not hold in demonstration samples. Demonstration samples, generated by a human demonstrator, do not necessarily follow a parameterized policy. Hence, we cannot use Retrace($\\lambda$) to evaluate the policy $\\pi$ from demonstrations because $\\mu(a|X)$ is intractable. To solve this issue, a one-step estimator $Q^{0}$ \\cite{precup2000eligibility} is used to evaluate the policy $\\pi$ from demonstrations, by setting the trace $c_s=0$:\n        \\begin{equation}\n            \\label{equ:policy_op}\n            Q^{0}(X_t, a_t) = r_t + \\gamma V_{\\theta_v}(X_{t+1}).\n        \\end{equation}\n        Although this does not utilize the full return from the demonstration samples, it does guarantee the convergence of policy evaluation. For experience samples generated by a past policy $\\mu$ of the agent, we record $\\mu(a_t|X_t)$ and use Retrace($\\lambda$) to evaluate the current policy $\\pi$. \n        \n        $V^\\pi(s)$ is also trained with the target \n        \\begin{equation}\n        \\begin{split}\n            & V^{target}(X_t) = \\\\ & \\min\\left(1, \\frac{\\pi(a_t|X_t)}{\\mu(a_t|X_t)}\\right) \n                    \\left( Q^{ret} (X_t, a_t) - \\tilde{Q}_{\\theta_v}(X_t, a_t) \\right) + V_{\\theta_v}(X_t).\n        \\end{split}\n        \\end{equation}\n        This is only trained on experience samples, for the same reason that $\\mu(a_t|X_t)$ is intractable in demonstration samples.\n        \n    \\subsection{Policy Optimization}\n        We follow the use of policy gradient with truncated importance sampling weights in ACER to update the policy network, but without trust region policy optimization \\cite{schulman2015trust} and bias correction \\cite{wang2016sample} for simplicity. The gradient of network parameter $\\theta$ is:\n        \\begin{equation}\n            \\hat{g}_t(\\theta) = \\bar{\\rho}_t \n                \\nabla_\\theta \\log \\pi_\\theta (a_t|X_t) [Q^{target}(X_t, a_t) - V_{\\theta_v}(X_t)],\n        \\end{equation}\n        where $\\bar{\\rho}_t = \\min(c, \\rho_t)$, and $c$ is a hyperparameter used to truncate the update to the policy network. In experience buffer, $\\rho_t = \\frac{\\pi(a_t|X_t)}{\\mu(a_t|X_t)}$, while in demonstration buffer, $\\rho_t = \\pi(a_t|X_t)$. \n        \n        We use $Q^{ret}$ as $Q^{target}$ when replaying the experience buffer, as in ACER, and $Q^{0}$ in Equation (\\ref{equ:policy_op}) as $Q^{target}$ when replaying demonstration buffer in order to make use of full returns of the episodes.\n\n    \\subsection{Pre-trained Policy Network}\n    As an optional step, we use behavior cloning\\cite{nair2018overcoming} to pre-train the policy network. Instead of being randomly initialized, the policy network is trained from demonstrations before interacting with the environment, by maximizing the likelihood of following the demonstrations. In our case, the policy network outputs the mean of a Gaussian with fixed variance; thus, it is equivalent to minimizing the squared error between network outputs and recorded actions.\n    \n    Since environments used in our experiments are randomly initialized, we need enough samples in the demonstrations to generalize different initializations in order to benefit from pre-training. A pre-trained policy network provides a better start for reinforcement learning than random initialization and it improves learning efficiency. \n        \n    \\subsection{The READER Algorithm}\n        Algorithm \\ref{algo} summarizes these ideas; thus, the agent is able to learn a policy in a model-free setting from both demonstrations and from its own past experiences. The algorithm also utilizes a separate target network for the value network, which has been used to stabilize the value estimations in several RL algorithms \\cite{mnih2013playing, mnih2016asynchronous, lillicrap2015continuous}. Before RL starts, the algorithm trains the policy network by behavior cloning for $e_{Pretrain}$ epochs. $e_{Pretrain}$ can be $0$, which disables pre-training. Then the algorithm interacts with the environment for $e_{Start}$ episodes before starting to learn. At each learning step, the policy network and value network are updated, and a soft update of the target network is also done. \n        \\begin{algorithm*}\n        \\SetAlgoLined\n             Initialize demonstration buffer with collected demonstrations $\\mathcal{D}$\\;\n             Initialize an empty experience buffer $\\mathcal{E}$\\;\n             Initialize the policy network $\\pi_\\theta$\\;\n             Initialize the SRDN $(V_{\\theta_{v}}, \\tilde{Q}_{\\theta_{v}})$\\ and the target Network $(V_{\\theta'_{v}}, \\tilde{Q}_{\\theta'_{v}})$ with $\\theta'_{v} = \\theta_v$\\;\n             Pretrain the policy network for $e_{Pretrain}$ epochs\\;\n             \\For{$k \\in \\{ 1 .. maxEpisode \\}$}{\n                Interact with the environment using the policy network, generate an episode $e$\\;\n                Append $e$ to $\\mathcal{E}$\\;\n                \\If{$k > e_{Start}$}{\n                    \\For{$z \\in \\{1..learningSteps\\}$}{\n                        Sample a batch of $b$ episodes from the joint buffer $\\mathcal{E} \\cup \\mathcal{D}$\\;\n                        Update $\\theta$ by Equation (\\ref{equ:policy_op}) wrt. $w_i$ in Equation (\\ref{equ:weight})\\;\n                        Set $g(\\theta) = 0$ and $g(\\theta_v) = 0$ \\;\n                        \\For{Episode $i$ in the batch}{\n                            Compute $w_i$ by Equation (\\ref{equ:weight})\\;\n                        \\eIf{Episode $i$ is from $\\mathcal{E}$}{\n                                $g(\\theta_v) \\leftarrow  g(\\theta_v) + w_i \\nabla_{\\theta_v} \\sum_{0 \\leq t < L(i)} (Q^{ret}(X_t, a_t)-\\tilde{Q}_{\\theta_v}(X_t, a_t))^2 $ \\;\n                                $g(\\theta_v) \\leftarrow  g(\\theta_v) + w_i \\nabla_{\\theta_v}\\sum_{0 \\leq t < L(i)} (V^{target}(X_t)-V(X_t))^2$ \\;\n                                $g(\\theta) \\leftarrow g(\\theta) + w_i \\sum_{0 \\leq t < L(i)} \\hat{g}_t(\\theta)$\\;\n                            }{\n                                $g(\\theta_v) \\leftarrow  g(\\theta_v) + w_i \\nabla_{\\theta_v}\\sum_{0 \\leq t < L(i)}(Q^{TB}(X_t, a_t)-\\tilde{Q}_{\\theta_v}(X_t, a_t))^2 $ \\;\n                                $g(\\theta) \\leftarrow g(\\theta) + w_i \\sum_{0 \\leq t < L(i)} \\hat{g}_t(\\theta)$\\;\n                            }\n                        }\n                        Update $\\theta$ and $\\theta_v$ with gradient $g(\\theta)$  and $g(\\theta_v)$, respectively \\; \n                        Update the target network: $\\theta'_v \\leftarrow \\beta \\theta'_v + (1 - \\beta) \\theta_v$ \\;\n                    }\n                }\n             }\n             \\caption{READER}\n            \\label{algo}\n        \\end{algorithm*}\n\n\\section{Experimental Results}\n\\label{sec:experiments}\n    We tested READER in three different simulated control tasks. We show the learning curve of each experimental setting through the average success percentage or the average \\textit{return} during the progress of learning. The \\textit{return} is defined as the discounted sum of the reward $R=\\sum_{t=0}^{t_{max}} \\gamma^t r_t$, where $\\gamma$ is the discount factor used in READER. To demonstrate the performance of READER against other RLfD methods, we tested RDPGfD, a method based on RDPG that can also use demonstration samples for memory-dependent continuous control. Details of the RDPGfD algorithm can be found in the Appendix. RDPGfD is tested with the maximum number of demonstration samples available in each task, and comparisons are made between READER and RDPGfD with the same number of demonstration samples.\n    \n   We chose three tasks where we could test READER on different action dimensions, observation dimensions and difficulty in explorations. Mountain Car is a widely used RL task that requires a large amount of exploration. The sequential target-reaching task used in \\cite{han2019remaster} divides the task into 3 sequential stages. Each stage requires the agent to complete a sub-goal. This task requires the agent to infer the current stage from historical observations. Finally, to demonstrate the application of our algorithm in robot control, we also performed a simulation experiment on the robot simulator V-REP \\cite{vrep2013}. \n   \n   While these tasks may be difficult for an RL agent to learn, they are easily grasped by humans after only a few minutes of training. Videos on how human demonstrations were collected can be found in the supplementary materials. However, humans do not react as quickly or as accurately as robots, so we expect robots to learn better policies than humans through RL. Results show that a reasonable number of demonstrations can reduce required interactions with the environment so as to achieve the same level of performance. The number of demonstrations required for each task depends on the difficulty and complexity of the task. \n   \nHyperparameters used in READER are listed in Table~\\ref{table:hyperparameters}. \n        \\begin{table*}[!t]\n\n          \\centering\n        \n          \\begin{tabular}{lll}\n        \n           \\hline\n                    \\textbf{Hyperparameter} & \\textbf{Description} & \\textbf{Value}   \\\\ \n        \n            \\hline\n            \n                $\\sigma^2$ & Variance of the action distribution & 0.1  \\\\ \\hline\n                $H$ & Number of neurons in fully connected layers & 64  \\\\ \\hline\n                $HR$ & Number of LSTM units & 64   \\\\ \\hline\n                $n$ & Number of sampled actions for SRDN & 16 \\\\ \\hline\n                batch size & Number of episodes in one batch & 32 \\\\ \\hline\n                optimizer & Optimization algorithm & Adam \\\\ \\hline\n                lr\\_actor & Learning rate of the policy network & 1e-4 \\\\ \\hline\n                lr\\_critic & Learning rate of the value network & 1e-3 \\\\ \\hline\n                target update ratio & Linear coefficient of updating target network & 0.99 \\\\ \\hline\n                $e_{start}$ & Number of episodes before training started & 10\\\\ \\hline\n                learning steps & Number of training steps after each episode & \\makecell[l]{160 (in POMountainCar) \\\\ 40 (in SequentialReach) \\\\ 100  (in SequentialTouch)}\\\\ \\hline\n                $\\gamma$ & Discount factor  & \\makecell[l]{0.995 (in SequentialReach) \\\\ 0.99 (in others)}    \\\\ \\hline\n                $\\lambda$ & Discount of trace in Retrace($\\lambda$) & 1.0 \\\\ \\hline\n                $c$ & Policy update truncation & 1.0 \\\\ \\hline\n                $\\alpha$ & Scale factor of episode priority & 0.3 \\\\ \\hline\n                buffer size & \\makecell[l]{Maximum number of episodes\\\\ in  the experience buffer} & 1000 \\\\\n            \\hline\n  \\end{tabular}\n\n\\caption{Values of hyperparameters}\n\\label{table:hyperparameters}\n\\end{table*}\n    \n    \\subsection{The Partially Observable Continuous Mountain Car Task}\n        The mountain car task (Figure~\\ref{fig:mountaincar}a) was introduced in \\cite{moore1990efficient} as a benchmarking problem of exploration in RL and control. In this task, a car is required to reach a goal site at the top of the mountain on the right. However, it lacks sufficient power to drive straight up the mountain. The only solution is to drive back and forth to build up mechanical energy before ascending to the goal. The agent does not receive any reward until it reaches the goal, making it extremely difficult to find the goal with only autonomous random exploration.\n        \n        In our setting, the speed of the car is hidden from the agent, and the agent can only observe its own coordinates. We denote this task as \\textit{POMountainCarContinuous}. A human is trained to control the car with a joystick, and the environment is displayed as feedback to the human demonstrator. We assume that the agent observes the sensory input in its own view instead of the rendered view that the human demonstrator observes. \n        \n        We implemented this task based on the \\textit{MountainCarContinous} implementation in OpenAI Gym \\cite{brockman2016openai}.\n       \n        The time limit is set to 200 time steps. The only change we made to the task is removing speed information from the observations. After this change, the observation is one-dimensional with its horizontal coordinate in the range $[-1.2, 0.6]$. The car starts every episode at a random position from $-0.6$ to $-0.4$ with zero velocity. The action space is $[-1, 1]$. A negative action means pushing the car to the left, while a positive action means pushing the car to the right. The reward is 100 when the car reaches the target of the hill, along with the squared sum of action as a negative reward at every time step.\n        \n        We collected 4 sets of demonstrations containing 1 episode, 8 episodes, 16 episodes and 64 episodes, respectively. \n        \n        Figure \\ref{fig:mountaincar}b shows the average return and its standard error over five repeated experiments. The result shows that all 3 sets of demonstrations can lead to near-optimal policies, while learning without demonstrations mostly converges to a local optimum of $0$ return to avoid a negative reward. None of the five agents that learned without demonstrations ever reached the goal, with the consequence that they could never improve their policies. In contrast, even with only 1 episode of demonstration, an agent always quickly improved its policy to reach the goal. \n        \n        To test whether the algorithm can learn from sub-optimal demonstrations, we collected another demonstration of 1 episode, during which we asked the demonstrator to circle around the starting position a few times before powering up to the goal. The results (Figure \\ref{fig:mountaincar}c) show that the agent learned a better policy than that of the demonstration. The algorithm can work even with sub-optimal demonstrations because it does not directly clone the behavior of the demonstrator. Rather, it extracts reward-related information from demonstration samples to reduce unnecessary exploration. \n\n\\begin{figure*}[!t]\n\\centering\n\\subfloat[An illustration of the mountain car task.]{\\includegraphics[width=1.7in]{MC.png}%\n\\label{fig:MCA}}\n\\hfil\n\\subfloat[Learning curves of POMountainCarContinuous with different numbers of demonstrations.]{\\includegraphics[width=2.3in]{RL2021\/mc1.png}%\n\\label{fig:MCB}}\n\\hfil\n\\subfloat[Learning curves of POMountainCarContinuous when learning from a sub-optimal demonstration, compared to the return of the sub-optimal demonstration.]{\\includegraphics[width=2.3in]{PDF\/MC0814Sub.pdf}%\n\\label{fig:MCC}}\n\\caption{Experiments on POMountainCarContinuous. Error bands in the plots represent the standard errors of the average success percentages at each episode.}\n\\label{fig:mountaincar}\n\\end{figure*}\n\n        \n    \\subsection{The Sequential Target-Reaching Task}\n        To test our algorithm in memory-crucial environments, we also conducted experiments on the Sequential Target-Reaching task (Figure \\ref{fig:taskt3}a) introduced in \\cite{han2019remaster}. We denote this task as \\textit{SequentialReach}. A two-wheeled robot in a two-dimensional field with a square boundary is required to reach the three randomly sampled target positions in the correct sequence. The robot is rewarded every time it reaches a target in the required sequence (Figure \\ref{fig:taskt3}a). The action space is 2-dimensional, representing the rotation speeds of both wheels respectively. The robot can detect distances and angles to the three targets, as well as distances to the field boundary. This task is of interest because there is no clue regarding the current target in the current sensory input, but the agent needs to develop cognitive ability to infer which target to pursue, based on the history of observations.\n        \n        Our implementation is based on the original example in \\cite{han2019remaster}, with modified initial target positions. The robot is placed into a 15 unit $\\times$ 15 unit square area, and each of the 3 targets is randomly placed 3 units to 7 units from the center. There is a further restriction that any two targets should be at least $\\sqrt{2}$ units away from each other.\n        \n        As in the previous experiment, a human demonstrator is asked to demonstrate using a joystick. Feedback to the demonstrators is given via a rendered image (Figure \\ref{fig:taskt3}b) at each time step. \n        \n        The results (Figure \\ref{fig:taskt3}c) show that improvements can be achieved in 64 episodes of demonstrations, but even 16 episodes of demonstration do not improve the result significantly. This can be explained by the fact that the configurations of each episodes, such as coordinates of the three targets, are random. The environment cannot be generalized without an adequate number of demonstrations. \n\n\\begin{figure*}[!t]\n\\centering\n\\subfloat[An illustration of the SequentialReach task.]{\\includegraphics[width=2in]{TaskT3Pic2}%\n\\label{fig:T3A}}\n\\hfil\n\\subfloat[The rendered view for the demonstrator. The pink triangle with a black tail is the car controlled by the demonstrator. ]{\\includegraphics[width=1.7in]{T3Display2.png}%\n\\label{fig:T3B}}\n\\hfil\n\\subfloat[Learning curves of SequentialReach.]{\\includegraphics[width=2.3in]{RL2021\/Tri1.png}%\n\\label{fig:T3C}}\n\\caption{Experiments on SequentialReach. Error bands in the plots represent standard errors of average success percentages at each episode.}\n\\label{fig:taskt3}\n\\end{figure*}\n\n        \n    \\subsection{The Robot Sequential Target-Touching Task}\n        To demonstrate the efficiency of our algorithm in robot control applications, we introduced a robot simulation experiment on the robot simulator V-REP. We use the simulation model of the humanoid robot OP2 (Figure \\ref{fig:OP2}a). We allow the robot to control the 6 motor joints on both arms. However, it is difficult to control a humanoid-like OP2 using joysticks. We used a controlling device (Figure \\ref{fig:OP2}a) to control both arms of OP2. We record the joint angles of the 3 joints on the right arm and 3 joints on the left arm, and convert the joint angles to action signals in order to move the simulated robot.\n        \n        Three spherical targets (one red, one green and one blue) are placed in front of the robot. We introduce some randomness when initializing each episode by sampling the targets at arbitrary positions within a certain range. The robot is required to touch the red ball first, then the green ball, and finally the blue ball with either of both arms. We denote this task as \\textit{SequentialTouch}. The robot has sensory input from its 6 joint angles, which it controls, as well as the relative coordinates of each target to the front ends of both arms. The rewards are given when each target is touched in the correct sequence. A reward of 0.5, 2.0 and 1000.0 is given when the robot touches the first target, second target and third target respectively in the correct order. Each time step is 0.2 seconds in real time. The task has a time limit of 50 time steps, which equals 10 seconds in real time.\n        \n        The results (Figure \\ref{fig:OP2}c) show significant improvements using 1, 8, 16 or 64 demonstrations. Results with 8, 16 and 64 demonstrations have similar performance, and are better than result with 1 demonstration. \n        \n\n\\begin{figure*}[!t]\n\\centering\n\\subfloat[A picture of an OP2 and its controlling device.]{\\includegraphics[width=1.5in]{OP2-2}%\n\\label{fig:OP2A}}\n\\hfil\n\\subfloat[A screenshot of the V-REP simulator with the setting of this task. ]{\\includegraphics[width=1.43in]{OP2T3.png}%\n\\label{fig:OP2B}}\n\\hfil\n\\subfloat[Learning curves of SequentialTouch with different numbers of demonstrations. ]{\\includegraphics[width=2.0in]{RL2021\/OP21.png}%\n\\label{fig:OP2C}}\n\\caption{Simulated humanoid experiment. Error bands in the plots represent standard errors of the average success percentages at each episode.}\n\\label{fig:OP2}\n\\end{figure*}        \n                        \n\n        \n\\begin{figure*}[!t]\n\\centering\n\\subfloat[READER compared to RDPGfD in PoMountainCar Continuous]{\\includegraphics[width=1.5in]{RL2021\/mc2.png}%\n\\label{fig:fDA}}\n\\hfil\n\\subfloat[READER compared to RDPGfD in Sequential Reach]{\\includegraphics[width=1.43in]{RL2021\/Tri2.png}%\n\\label{fig:fDB}}\n\\hfil\n\\subfloat[READER compared to RDPGfD, READER+Pretrain and supervised learning in Sequential Touch]{\\includegraphics[width=2.0in]{RL2021\/OP22.png}%\n\\label{fig:fDC}}\n\\caption{READER compared to RDPGfD and other experiment settings.}\n\\label{fig:RDPGfD}\n\\end{figure*} \n    \n    \\subsection{Comparison to RDPGfD}\n    Besides testing READER on the selected environment, we tested RDPGfD in comparison with READER. All tests are done with 64 episodes of demonstrations. In Figure \\ref{fig:RDPGfD}, we can see in all three tasks, READER outperforms RDPGfD, either by requiring less explorations or by learning a better policy. \n    \n    \\subsection{The Effects of Pre-training}\n    We also tested a pre-trained policy network using 64 demonstrations. The horizontal line \\textbf{Supervised} (Figure \\ref{fig:RDPGfD}c) marks the performance of the policy network after pre-training, while the line \\textbf{READER+Pre-train} shows the learning curve using the pre-trained policy network. Compared to the pre-trained policy network, RL is necessary after pre-training to achieve better performance on the task. The result with a pre-trained policy network also outperforms the result without a pre-trained policy network in both sample efficiency and convergent success percentage.\n    \n\t\\subsection{The Effects of Prioritized Replay}\n        In order to examine the effects of prioritized episodic demonstration and experience replay (PER), we ran another experiment on SequentialTouch without PER. The results in Figure \\ref{fig:OP2PER} show PER contributes significantly to the overall performance. To show how PER affects the attentions of the agents, in Figure \\ref{fig:OP2Priority}, we plot the values of average demonstrations priority and average experience priority collected from one run of READER with 64 demonstrations on SequentialTouch. In the beginning 200 episodes of the learning process, average demonstration priority is significantly higher than average experience priority, allowing the agent to learn more from demonstrations. After this period, average demonstration priority and average experience priority converge to close values, while average demonstration priority keeps slightly higher than average experience priority. \n        \n\\begin{figure}[!t]\n\\includegraphics[width=3.2in]{PDF\/PERablation.pdf}\n\\caption{The learning curve of READER without prioritized replay compared to READER with prioritized replay and learning with no demonstrations.}\n\\label{fig:OP2PER}\n\\end{figure}  \n\n\\begin{figure}[!t]\n\\includegraphics[width=3.2in]{PDF\/priority.pdf}\n\\caption{Average demonstration priority and experience priority in the first 2000 episodes of SequentialTouch using READER with 64 demonstrations.}\n\\label{fig:OP2Priority}\n\\end{figure} \n\\section{Conclusion}\n\\label{sec:conclusion}\n\n\tIn this paper, we presented READER, a model-free RL algorithm that uses demonstrations to accelerate learning and to reduce unnecessary exploration. This is crucial for real-world robotic applications because exploration consumes much more time than simulation. READER can be used in memory-dependent POMDPs with continuous action spaces. PER and demonstration replay are used to balance learning with demonstrations and experiences. It also employs RNNs to learn memory-dependent policies. We propose using different update methods of policy evaluation and optimization when using demonstrations and experiences, due to differences between the two sets of trajectories. Our results show that reasonably small numbers of demonstrations significantly improve learning efficiency and reduce the number of episodes required to achieve the same performance. Compared to RDPGfD, another RLfD method for memory-dependent control, READER is more sample efficient and can also solve some tasks that RDPGfD is unable to solve. We also note that the number of demonstrations required to produce a significant performance improvement depends on the difficulty and complexity of the environment. If a task is simple to explore, demonstrations will not improve the sample efficiency significantly since the agent can gather enough successful trials easily through self exploration. Randomness of the environment is a determining factor of required number of demonstrations. If the agent can always follow the same path to finish the task, like in POMountainCarContinuous, then it is expected one episode of demonstration can lead to a significant difference. On the other hand, when the environment is initialized randomly, a larger number of demonstrations should be chosen. A strategy to choose the number of demonstrations is that the demonstrations should cover the major variations of the task, while allowing small differences to be learned further by RL. Furthermore, even when the demonstrations are far from optimal, the agent is still able to outperform the demonstrators by interacting with the environment. Finally, as an optional step, a pre-training policy network from demonstrations can further improve learning efficiency when there are enough demonstration samples to generalize the task.\n\t\n\tThe main idea of READER is to utilize demonstration samples to achieve more efficient exploration; thus, demonstrations can be sub-optimal. This is especially useful in real-world robot learning tasks because exploration using physical robots can be slow and dangerous. In this sense, our algorithm can be considered as one type of human-robot interaction for developing robot intelligence \\cite{aly2016towards, goodrich2008human}. However, it is possible that an agent learns a local-optimal policy if the demonstrator provides a similar one. Efforts to avoid such a predicament will be made in our future work.\n\t\n\tFurthermore, future studies may investigate possible performance gains by introducing a model-based approach \\cite{igl2018deep, ha2018recurrent} to the current scheme. Such enhanced schemes can allow agents to perform mental simulation while predicting sensory outcomes of their own actions using the learned internal model of the environment. Therefore, agents can explore the environment not only through on-line physical interaction, but also through offline mental simulation. We anticipate that mental simulation along with demonstration will improve sampling efficiency drastically.\n\t\n\n\n\n\n\n\n\n\n\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzqtcc b/data_all_eng_slimpj/shuffled/split2/finalzzqtcc
new file mode 100644
index 0000000000000000000000000000000000000000..ecd4b639988d1cc8ca7faf8d0f2498c569bab1b7
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzqtcc
@@ -0,0 +1,5 @@
+{"text":" \nThe authors and publisher have provided this e-book to you without Digital Rights Management software (DRM) applied so that you can enjoy reading it on your personal devices. This e-book is for your personal use only. You may not print or post this e-book, or make this e-book publicly available in any way. You may not copy, reproduce, or upload this e-book, other than to read it on one of your personal devices.\n\nCopyright infringement is against the law. If you believe the copy of this e-book you are reading infringes on the authors' copyright, please notify the publisher at: us.macmillanusa.com\/piracy.\nThis book is for John Varley, Arthur C. Clarke, Bob Shaw, Paul McAuley, Alastair Reynolds, Iain M. Banks, Robert Reed, and others of the Big Object Society. On to larger things!\nACKNOWLEDGMENTS\n\nWe conferred on scientific and literary matters with many helpful people. Erik Max Francis, Joe Miller, and David Hartwell gave detailed comments on the manuscript. And of course Olaf Stapledon and Freeman Dyson were first.\nCAST OF CHARACTERS, COMMON TERMS\n\nSUNSEEKER CREW AND TERMS\n\nCaptain Redwing\n\nCliff Kammash\u2014biologist\n\nMayra Wickramsingh\u2014pilot, with Beth team\n\nAbduss Wickramsingh\u2014engineer, with Beth team\n\nGlory\u2014the planet of destination\n\nSunSeeker\u2014the ramship\n\nBeth Marble\u2014biologist\n\nEros\u2014the first drop ship\n\nFred Ojama\u2014geologist, with Beth team\n\nAybe\u2014general engineer officer, with Cliff team\n\nHoward Blaire\u2014systems engineer, with Cliff team\n\nTerrence Gould\u2014with Cliff team\n\nIrma Michaelson\u2014plant biologist, with Cliff team\n\nTananareve Bailey\u2014with Beth team\n\nLau Pin\u2014engineer, with Beth team\n\nJampudvipa (shortened to Jam)\u2014an Indian petty officer\n\nAyaan Ali\u2014Arab woman navigator\/pilot\n\nClare Conway\u2014copilot\n\nKarl Lebanon\u2014general technology officer\n\nASTRONOMER FOLK\n\nMemor\u2014Attendant Astute Astronomer\n\nBemor\u2014Contriver and Intimate Emissary to the Ice Minds\n\nAsenath\u2014Chief of Wisdom\n\nIkahaja\u2014Ecosystem Savant\n\nOmanah\u2014Ecosystem Packmistress\n\nRamanuji\u2014Biology Savant\n\nKanamatha\u2014Biology Packmistress\n\nThaji\u2014Judge Savant\n\nUnajiuhanah\u2014Senior Mistress, Keeper of the Vault Library\n\nOTHER PHYLA\n\nfinger snakes\u2014Thisther, male; Phoshtha, female; Shtirk, female\n\nIce Minds\u2014cold life of great antiquity\n\nthe Adopted\u2014those aliens already encountered and integrated into the Bowl\n\nthe Diaphanous\n\nFOLK TERMS\n\nAnalyticals\u2014artificial minds that monitor Bowl data on local scales\n\nTransLanguage\n\nLong Records\n\nLate Invaders\n\nUndermind\n\nSerf-Ones\n\nthe Builders\u2014the mix of species that built the Bowl\n\nThird Variety\u2014Astronomer variety\n\nAstronauts\u2014Astronomer variety\n\nQuicklands\n\nKahalla\nCONTENTS\n\nTitle Page\n\nCopyright Notice\n\nDedication\n\nAcknowledgments\n\nCast of Characters, Common Terms\n\nPart I: Essential Error\n\nChapter 1\n\nChapter 2\n\nChapter 3\n\nChapter 4\n\nChapter 5\n\nChapter 6\n\nChapter 7\n\nChapter 8\n\nIllustration 1\n\nPart II: Sunny Slaughterhouse\n\nChapter 9\n\nChapter 10\n\nChapter 11\n\nPart III: Status Opera\n\nChapter 12\n\nChapter 13\n\nChapter 14\n\nPart IV: Sending Superman\n\nChapter 15\n\nChapter 16\n\nPart V: Mirror Flowers\n\nChapter 17\n\nChapter 18\n\nPart VI: The Deep\n\nChapter 19\n\nChapter 20\n\nChapter 21\n\nPart VII: Crunchy Insects\n\nChapter 22\n\nChapter 23\n\nPart VIII: Counterthreat\n\nChapter 24\n\nChapter 25\n\nChapter 26\n\nPart IX: On the Run\n\nChapter 27\n\nChapter 28\n\nIllustration 2\n\nIllustration 3\n\nIllustration 4\n\nChapter 29\n\nPart X: Stone Mind\n\nChapter 30\n\nChapter 31\n\nIllustration 5\n\nChapter 32\n\nPart XI: Double-Edged Sword, No Handle\n\nChapter 33\n\nIllustration 6\n\nIllustration 7\n\nIllustration 8\n\nChapter 34\n\nChapter 35\n\nPart XII: The Word of Cambronne\n\nChapter 36\n\nChapter 37\n\nChapter 38\n\nPart XIII: The Diaphanous\n\nChapter 39\n\nChapter 40\n\nChapter 41\n\nIllustration 9\n\nChapter 42\n\nChapter 43\n\nChapter 44\n\nChapter 45\n\nChapter 46\n\nChapter 47\n\nChapter 48\n\nChapter 49\n\nPart XIV: Memory's Flickering Light\n\nChapter 50\n\nChapter 51\n\nChapter 52\n\nAfterword: Big Smart Objects\n\nI. How We Built the Books\n\nII. Fun with High Tech\n\nIII. Bowl Design\n\nBooks by Gregory Benford and Larry Niven\n\nAbout the Authors\n\nCopyright\nPART I\n\nESSENTIAL ERROR\n\nIt is better to be wrong than to be vague. In trial and error, the error is the true essential.\n\n\u2014FREEMAN DYSON\nONE\n\nMemor glimpsed the fleeing primates, a narrow view seen through the camera on one of the little mobile probes. Simian shapes cavorted and capered among the understory of the Mirror Zone, making their way to\u2014what? Apparently, to the local express station of mag-rail. Very well. She had them now, then. Memor clashed her teeth in celebration, and tossed a squirming small creature into her mouth, crunching it with relish.\n\nThese somewhat comic Late Invaders were scrambling about, anxious. They seemed dreadfully confused, too. One would have expected more of ones who had arrived via a starship, with an interstellar ram of intriguing design. But as well, they had escaped in their scampering swift way. And, alas, the other gang of them had somehow evaded Memor's attempt to kill them, when they made contact with a servant species, the Sil. So they had a certain small cleverness, true.\n\nEnough of these irritants! She would have to concentrate and act quickly to bring them to heel. \"Vector to intercept,\" Memor ordered her pilot. Their ship surged with a thrumming roar. Memor sat back and gave a brief clacking flurry of fan-signals expressing relief.\n\nMemor called up a situation graphic to see if anything had changed elsewhere. Apparently not. The Late Invader ramship was still maneuvering near the Bowl, keeping beneath the defensive weapons along the rim. From their electromagnetic emissions, clearly they monitored their two small groups of Late Invaders that were running about the Bowl. But their ship made no move to directly assist them. Good. They were wisely cautious. It would be interesting to take their ship apart, in good time, and see how the primates had engineered its adroit aspects.\n\nMemor counted herself fortunate that the seeking probe had now found this one group, running through the interstices behind the mirror section. She watched vague orange blobs that seemed to be several simians and something more, as well: tentacular shapes, just barely glimpsed. These shapes must be some variety of underspecies, wiry and quick. Snakes?\n\nThe ship vibrated under her as Memor felt a summoning signal\u2014Asenath called, her irritating chime sounding in Memor's mind. She had to take the call, since the Wisdom Chief was Memor's superior. Never a friend, regrettably. Something about Asenath kept it that way.\n\nAsenath was life-sized on the viewing wall, giving a brilliant display of multicolored feathers set in purple urgency and florid, rainbow rage. \"Memor! Have you caught the Late Invaders?\"\n\n\"Almost.\" Memor kept her own feather-display submissive, though with a fringe of fluttering orange jubilance. \"Very nearly. I can see them now. The primate named 'Beth' has a group, including the one I've trained to talk. I'm closing on them. They have somehow mustered some allies, but I am well armed.\"\n\nAsenath made a rebuke display, slow and sardonic. \"This group you let escape, yes?\"\n\n\"Well, yes, they made off while I was attending to\u2014\"\n\n\"So they are the escaped, I take it. I cannot attend to every detail, but this was a plain failure, Attendant Astute Astronomer. They eluded you.\"\n\nMemor suppressed her irritation. Asenath always used full titles to intimidate and assert superiority\u2014usually, as now, with a fan-rattle. \"Only for a short while, Wisdom Chief. I had also to contend with the other escaped primates, you may recall, Your Justness.\"\n\n\"Give up everything else and get us that primate who can talk! We need it. Don't fire on them. If they die, you die.\"\n\nMemor had to control her visible reaction. No feather-display, head motionless. \"Wisdom Chief? What has changed?\"\n\nNo answer. Asenath's feather-display flickered with a reflexive blush of fear, just before she faded.\n\nShe was hiding something... but what? Memor would have to learn, but not now. She glanced at the detection screen, ignoring her pilot. Beth's group had disappeared into a maze of machinery. There were heat traces in several spots, leading... toward the docks. Yes! Toward another escape.\n\nThere had been six of these Late Invaders when they escaped. Now the heat traces found only five, plus some slithering profiles of another species. Had one died or gone astray? These were a social species, on the diffuse hierarchy model, so it was unlikely they had simply abandoned one of their kind.\n\n\"Veest Blad,\" she said to the pilot, \"make for the docks. We'll intercept them there. Fast.\"\nTWO\n\nTananareve Bailey looked back, face lined, sweat dripping from her nose. Nobody behind her now. She was the last, almost keeping up. Her injuries had healed moderately well and she no longer limped, but gnawing fatigue had set in. She was slowing. Her breath rasped and her throat burned and she was nearly out of water.\n\nIt had been a wearing, sweaty trip through the maze she thought of as \"backstage.\" The labyrinth that formed the back of the Bowl's mirror shell was intricate and plainly never intended for anybody but workers to move through. No comforts such as passageways. Poor lighting. Twisty lanes a human could barely crawl through. This layer underpinning the Bowl was the bigger part of the whole vast structure, nearly an astronomical unit across\u2014but only a few meters thick. It was all machinery, stanchions, and cables. Control of the mirrors on the surface above demanded layers of intricate wiring and mechanical buffers. Plus, the route twisted in three dimensions.\n\nTananareve was sweating and her arms ached. She couldn't match the jumping style of her companions in 18 percent gravity without a painful clicking in her hip and ribs. Her pace was a gliding run, sometimes bounding off an obstructing wall, sometimes taking it on her butt\u2014all assisted by her hands. It demanded a kind of slithering grace she lacked.\n\nBeth, Lau Pin, Mayra, and Fred were ahead of her. She paused, clinging to a buttress shaft. She needed rest, time, but there was none of that here. For a moment she let the whole world slide away and just relaxed, as well as she could. These moments came seldom but she longed for them. She sighed and... let go....\n\nEarth came to her then... the quiet leafy air of her childhood, in evergreen forests where she hiked with her mother and father, her careless laughter sinking into the vastness of the lofty trees. Her heart was still back there in the rich loam of deep forests, fragrant and solemn in the cathedral redwoods and spruce. Even in recalling it all, she knew it had vanished on the tides of time. Her parents were dead for centuries now, surely, despite the longevity treatments. But the memories swarmed up into her as she relaxed for just a long, lingering moment.\n\nHer moment of peace drained away. She had to get back to running.\n\nIn the dim light, she could barely make out the finger snakes flickering ahead of the long-striding humans. They had an amazingly quick wriggle. Probably they'd been adapted through evolution to do repairs in the Bowl's understory. Beth had gotten fragments of their history out of the snakes, but the translation was shaky. They'd been here on the Bowl so long, their own origins were legends about a strange, mythical place where a round white sun could set to reveal black night.\n\n\"Beth,\" Tananareve sent over short-range comm, \"I'm kinda... I... need a rest.\"\n\n\"We all do,\" came the crisp reply. Beth turned up ahead and looked back at her, too far away to read an expression. \"Next break is five minutes.\"\n\n\"Here I come.\" She clamped down her jaw and took a ragged breath.\n\nTheir target was an automated cargo drone. The snakes had told of these, and now the bulkheads and struts they passed were pitched forward, suggested they were getting close. Up ahead, as she labored on, she could see it emerge, one in a line of identical flat-bellied cylinders. Tananareve could see the outline of a great oyster-colored curved hatch in its side, and\u2014was that? Yes!\u2014stars beyond a window wall. She felt elation slice through her fatigue. But now the hip injury had slowed her to a limping walk.\n\nWithout the finger snakes, this plan would have been impossible.\n\nShe limped up to the rest of them, her mouth already puckering at the imagined taste of water. The three snakes were decorated in camouflage colors, browns and mottled blacks, the patterns almost the same, but Tananareve had learned to tell them apart. They massed a bit more than any of the humans, and looked like snakes whose tails had split into four arms, each tipped with a claw. Meaty things, muscular, slick-skinned. They wore long cloth tubes as backpacks, anchored on their ridged hides.\n\nBeth's team had first seen finger snakes while escaping from the garden of their imprisonment. Tananareve surprised a nest of them and they fled down into deep jungle, carrying some cargo in a sling. The snakes were a passing oddity, apparently intelligent to a degree. Her photos of them were intriguing.\n\nNow it was clear the finger snakes must have tracked and observed their party ever since. When Fred led the humans to an alien computer facility, they were not in evidence. Fred had found a way to make the computer teach them the Bird Folk language. Among his many talents, Fred was a language speed-learner. He got the quasilinear logic and syntax down in less than a day. Once he had built a vocabulary, his learning rate increased. A few more days and he was fluent. The whole team carried sleep-learning, so they used a slip-transfer from Fred's. By then he had been somehow practicing by himself, so it was best that he got to talk to the snakes first.\n\nThey just showed up, no diplomacy or signposting. Typical snake character\u2014do, don't retreat into symbols or talk. When the finger snakes crawled through the door, somehow defeating Lau Pin's lock, Fred said hello and no more. He wasn't exactly talkative either\u2014except, as he often rejoined, when he actually had something important to say.\n\nSo after his hello, and a spurt of Snake in reply, Tananareve was able to yell at them. \"Give you honor! We are lost!\"\n\nFive snakes formed a hoop, which turned out to be a sign of \"fruitful endeavor commencing.\" Tananareve made a hand-gesture she had somehow gotten from the slip-transfer. This provoked another symbol, plus talk. Formal snake protocol moved from gestures and signs into the denser thicket of language. Luckily, the highest form of Snakespeech was a modified Bird Folk structure that stressed lean and of sinew as virtues, so their knotted phrases did convey meaning in transparent, staccato rhythms.\n\nThe finger snakes were rebels or something like it, as nearly as Tananareve could untangle from the cross-associations that slithered through Snakespeech. Curious, also. Humans were obviously new to their world, and therefore they began tracking the human band in an orderly, quiet way shaped by tradition. The snakes worked for others, but retained a fierce independence. Knowledge was their strong suit\u2014plus the ability to use tools of adroit shape and use. They went everywhere in the Bowl, they said, on engineering jobs. Especially they maintained the meters-thick layers between the lifezone and the hard hull. In a sense, they maintained the boundary that separated the uncountable living billions from the killing vacuum that waited a short distance away.\n\nThe snakes wanted to know everything they could not discover by their intricate tracking and watching. They knew the basic primate architecture, for their tapering \"arms\" used a cantilevered frame that bore a warped resemblance to the human shoulder. This, plus a million more matters, flew through their darting conversations. Snakes thought oddly. Culture, biology, singing, and food all seemed bound up in a big ball of context hard to unravel. But when something important struck them, they acted while humans were still talking.\n\nWhen it was clear that humans would die if they stayed at low gravity for too long, the finger snakes led them here: to a garage for magnetically driven space vehicles. Snake teams did the repairs here.\n\n* * *\n\nOne of the finger snakes\u2014Thisther, she thought\u2014clicked open a recessed panel in the drone, so the ceramic cowling eased down. Thisther set to work, curling head to tail so his eyes could watch his nail-tipped fingers work. The wiry body flexed like cable. Phoshtha turned away from him, on guard.\n\nTananareve was still guessing at genders, but there were behavior cues. The male always seemed to have a tool in hand, and the females were wary in new surroundings. Thisther was male; Phoshtha and Shtirk were female.\n\nPhoshtha's head dipped and curled as she turned around, seeking danger. Shtirk wasn't visible; she must be on guard. Tananareve sensed no obvious threats, barring, perhaps, a whistling just at the edge of her hearing.\n\nPhoshtha wriggled to meet her. \"Thisther knows computers-speak,\" she said. \"King of computers = persons. Will write thrust program for us quick, person-comp-adept, she is. Are you sick?\"\n\n\"Was injured,\" Tananareve said. \"Not sick. Am healing.\" Both spoke in Bird talk, its trills and rolled vowels chiming like a song.\n\n\"Is well we know.\"\n\nThe curved side of the cargo drone slid up with a high metallic whine. Green verdant wealth. The drone was filled, jammed with vegetation\u2014live plants standing forth in trays, rich hanging streamers. Lights in the curved ceiling glared like suns. Thisther continued to work, and suddenly trays were sliding out and falling. Half the trays had piled up on the deck when it stopped.\n\n\"Keep some plants. Air for us while we travel,\" Phoshtha said. She wriggled away.\n\nLau Pin jog-hopped in the light grav, springing over to help Tananareve. \"You okay? Shall I carry you?\"\n\n\"I'm fine. What's that whistling?\" It was loud and now had a low rumble to it.\n\n\"We need to get aboard,\" Lau Pin said, glancing around at the snake teams at work. \"Quick.\" He tried pulling her along by her belt, desisted when he saw her pain.\n\nTananareve walked over to a copper-hued wall, leaning against its warmth. The finger snakes chattered in their jittering bursts and oozed across the platforms with wriggling grace. She studied them amid the noise, and... let herself go.\n\nShe was back in the leafy wealth she had grown up in and, yes, knew she would never see again. She allowed her head to tilt back and felt her spine kink and lapse as it straightened and eased. Amid metal and ceramics, she thought of green. This odd construction they were moving through, a weird place bigger than planets, had its own version of green paradise... and was the only reason she had survived in it. The vast, strange canopies with their chittering airborne creatures; the stretching grasslands and zigzag trees; animals so odd, they threw her back into her basic biology\u2014they were all natural in some way, yet... not. Someone had designed their setting, if not their species.\n\nThose sprawling lands of the Bowl had been tolerable. These mechanical labyrinths below the Bowl's lifesphere were... not. She had seen quite enough, thank you, of the motorized majesty that made such a vast, rotating artifact. Rest, that was her need now. She had to descend into blissful sleep, consign to her unconscious the labors of processing so much strangeness.\n\nShe let go slowly, head lapsing back. Easing was not easy, but she let herself descend into it, for just a moment before she would get up again and stride off, full of purpose and letting no soft moments play through her... Just for a while...\n\n\"Looks like the male is finished playing with the controls,\" Lau Pin called.\n\nDimly she sensed the snakes moving by her. Thisther wriggled into the hold... then Phoshtha and Shtirk.\n\nTananareve came out of her blissful retreat slowly. Voices echoed odd and hollow around her. Lead infected her legs; they would not move without great strain. She made herself get unsteadily up onto two uncertain feet. Clouds in her mind dispelled slowly\u2014something about green wealth, forests of quiet majesty, her parents...\n\nShe made her chin snap up, eyes fluttering, back on duty... and slowly turned to survey the area. Where's Beth?\n\nClouds still grasped at her. Breathe deeply, keep it up.\n\nTananareve strode off to check around some angular buttress supports. No human about.\n\nThe snakes had crawled into the ship, fitting somehow into open spaces. Lau Pin jogged to join them. He glanced back at her, waved a hand, turned, went away....\n\nStill there were clouds. She listened intently as she tried to put one small foot in front of the other. Remarkably difficult, it was.\n\nRumbling, sharp whistling, chatter. Tananareve walked a bit unsteadily back toward the ship. Her vision was blurred, sweat trickling into her eyes and stinging.\n\nThe great curved door closed in Tananareve's face.\n\n\"Hey,\" Tananareve said. She stopped, blinked. Clouds swept away on a sudden adrenaline shock\u2014\n\n\"Wait!\"\n\nThe drone slid out of line and away, slow at first, then faster and faster.\n\n\"Dammit!\" she shouted. \"Damn\u2014\" She couldn't hear herself over a whistling roar. Hot air blasted her back.\n\n* * *\n\n\"Wait!\" Beth Marble shouted. She could feel the acceleration building. The finger snakes were wrapped around support pillars, and her crew were grabbing for tie-downs. She found handholds and footholds while thrust pulled massively at her.\n\nShe wailed, \"Tananareve!\"\n\n\"She was sick,\" Phoshtha said, recessed eyes glittering. \"Thrust would have killed her. She would have slowed us.\"\n\n\"What? You let\u2014\" Beth stopped. It was done; handle the debriefing later, in calmer moments. The snakes were useful but strange.\n\nThey were accelerating quickly and she found a wedge-shaped seat. Not ideal for humans, but manageable. There was little noise from the magnetics, but the entire length of the drone popped and ponged as stresses adjusted.\n\nLau Pin said, \"I have SunSeeker online.\"\n\n\"Send Redwing our course. Talk to him.\" Beth couldn't move; she was barely hanging on to a tie-down bar. \"Use our best previous coordinates.\"\n\n\"Okay. I'm having it compute from the present force vectors.\" Lau Pin turned up the volume so others could hear. \"Lau Pin here.\"\n\n\"Jampudvipa here, bridge petty officer. Captain Redwing's got some kind of cold, and Ayaan Ali is bridge pilot. What's your situation?\"\n\n\"We're on our way. It went pretty much as we'd planned. Hardly anything around on the way but finger snakes. We've got three with us. Uh... We lost Tananareve Bailey.\"\n\n\"Drown it,\" the officer said. \"All right. But you're en route? Hello, I see your course... yeah. Wow. You're right up against the back of the mirror shell.\"\n\n\"Jampudvipa, this drone is driven by magnets in the back of the Bowl. Most of their ships and trains operate that way, we think. It must save reaction fuel. We don't have much choice.\"\n\nSome microwave noise blurred the signal, then, \"Call me Jam. And you don't have pressure suits?\"\n\n\"No, and there's no air lock. No way to mate the ships.\"\n\nA pause. \"Well, Ayaan says she can get SunSeeker to the rendezvous in ten hours. After that... what? Stet. Stet. Lau Pin, we can maybe fit you into the bay that held Eros before we lost it. If not... mmm.\"\n\nLau Pin said, \"The finger snakes don't keep time our way. I think it's longer for us. I'll make regular checks and send them.\"\n\n\"We'll be there. And you all need medical assistance? Four months in low gravity, out in the field\u2014yeah. We'll have Captain Redwing out of the infirmary by then, but it only holds two. Pick your sickest.\"\n\n\"Would have been Tananareve.\"\n\n* * *\n\nThe drone was gone. The system's magnetic safety grapplers released with a hiss. Tananareve stood in the sudden silence, stunned.\n\nA high hiss sounded from a nearby track. She turned to find a snake to stop the drone, call it somehow\u2014and saw no snakes at all. All three had boarded the drone. Now the shrill hiss was worse. She stepped back from the rising noise, and an alien ship came rushing toward the platform from a descending tube. It was not magnetic; it moved on jets.\n\nTananareve looked around, wondering where to run. The ship had a narrow transparent face and through it she could see the pilot, a spindly brown-skinned creature in a uniform. It looked not much bigger than she was and the tubular ship it guided was enormous, flaring out behind the pilot's cabin. The ship eased in alongside the main platform, jetting cottony steam. Tananareve wondered what she should do: hide, flee, try to talk to\u2014?\n\nThen, behind huge windows in the ship's flank, she saw a tremendous feathered shape peering out at her, and recognized it. Quick flashing eyes, the great head swiveling to take in all around it, with a twisted cant to its heavy neck. She gasped. Memor.\nTHREE\n\nRedwing looked out across the yawning distances, frowning.\n\nFar down, there were all the artful graces of land and sea, suspended before a warming sun like a rich, steaming dish offered on a steel-hard plate. Everything was larger, grander, and strange.\n\nThe Bowl seas were light blue expanses larger than Jupiter, bounded by shallow brown edges. Across those ran arcs of grand wave trains, immense ripples that must roll on for years before finding a shore. At finer resolution, sediment plumes of tan and chocolate spread across shallow seabeds, feeding kelp straits of festering ripe green. Rumpled hill ranges were larger than Asia. Never driven by continental drift, these crosshatched the vast lands, carved by rivers that could cut no farther than the Bowl's hull. Indeed, he could see places where wind or water had worn away the living zone, leaving patches of rusting metal. Under close-up, he and Karl watched teams repairing such erosions.\n\nThe deserts were huge, too. Tan lands of grass went on over distances greater than the Moon was from Earth, with only dots of green beckoning where an oasis sprouted. Sprawling dry lands ended where water found its way to make moist forests. Storms spiraling in immense white-bright pinwheels churned with ponderous energies, raking across deserts larger than planets, and over forests so deep, no one could ever walk out of them.\n\nHow did anyone design a thing like this? A vast trapped atmosphere, oceans the size of planets, lakes like continents, yet no real mountains\u2014maybe that was a clue. Of course, putting an Everest on the Bowl would make it lopsided and complicate dynamics. There could be no plate tectonics and so no volcanoes, but how did this biosphere circulate carbon and water? On Earth, a complex cycle a hundred million years long did the job. As well, Earth's tectonic ranges forced air over and around them, generating the moving chaos humans called weather. The Bowl's dwellers did not suffer from mountain wind shadow, or the combing winds that raced through narrow passages. Mountains made for stormy trouble on Earth. The Bowl was a milder place than planets could be.\n\nBut why build a whole contraption like this, when you could just move to Florida?\n\nThe question wasn't just rhetorical. If he could fathom what built such a thing, and why, he might have a clue about how to deal with them.\n\nPing. His autosec reminded him of lunch.\n\nHe thought of it as the mess, very old school, but Fleet said it was a Starship Wardroom. He sat as usual for Meal 47, his current choice: classic turkey dinner, rich cream sauce and cranberries. He made himself not think about the simple fact that it was all made of ingredients centuries old; after all; so was he.\n\nHe had kept mistaking what Mayra Wickramsingh said at every meal: Nosh for me, it sounded like. After she and her husband, Abduss, went down in the disastrous descent to the Bowl, he had looked it up. The Linguist AI had a transform function, so it learned even through his mushy pronunciation; the AI found it was an Indian phrase, naush faramaiye, meaning \"please accept the pleasure of savoring this meal,\" which seemed like bon app\u00e9tit to Redwing. Suitable. \"Naush faramaiye to you all,\" Redwing said, bowing his head. The crew bowed back. Clare looked puzzled.\n\n\"Cap'n, I'm having trouble with the Artilect coherence,\" Jampudvipa said.\n\nRedwing still used AI as a shorthand for the shipboard systems that patiently oversaw operations, since that's what everybody called them when he was growing up. But Artilect was the actual Fleet term, since integrated artificial minds constituted a collective intellect. It was useful to think of the systems as different people, engaged in a constant congress, discussing the ship's current state. \"What's their problem?\"\n\n\"They want to go back into full scoop mode.\"\n\n\"In a solar system? We can't get the necessary plasma densities.\"\n\n\"I know.\" Jampudvipa shrugged. \"I think they're showing mission fatigue.\"\n\n\"Have you tried to give them some shut-eye time, one by one?\"\n\n\"They resist it.\"\n\n\"Enforce it. Tell them they need a psych reboot, only make the language prettier.\"\n\nThis got rueful laughs around the wardroom table. \"Diplomacy\u2014not our strong suit,\" Clare Conway said. She was more personable than most pilots, one of the reasons she had made the crew. Redwing had gone through her file while making his selection of whom to revive.\n\nAyaan Ali frowned. \"It is serious problem, Artilect coherence. They start to disagree, to have their own ideas\u2014trouble.\"\n\n\"They want what's impossible,\" Karl Lebanon said. He folded his hands and leaned back against a bulkhead. As general technology officer, he shepherded Artilects through daily problems, plus a dozen other jobs. \"We can't go back to interstellar mode.\"\n\nClare sipped her coffee. \"They have to adjust our ramscoop intake in ten-second intervals, to optimize. That burns their attention reservoir, makes their duty cycles long. Stresses them pretty hard.\"\n\n\"We're getting system clash in our magnetic scoop system,\" Karl said. \"It'll tire the Artilects and we'll start getting torques, surges, inductive effects that wear down our gear.\"\n\n\"Same small-scale coil problem?\"\n\n\"Yeah. The system's pretty stressed. Never made for this kind of low-velocity maneuvering. We can't get into the magneto components to adjust them.\"\n\nClare said, \"A mechanical problem, fixable\u2014but only if we could get a bot in the inductive chamber. Those we could maybe make, but present bot complement can't do it. That choice set is not even in the partition menu.\"\n\n\"We can't downtime them?\" Redwing knew the answer but if he let people talk, they felt better. All three chimed in with their versions of the same hard fact: A ship designed to work at interstellar speeds was a bitch to control in planetary orbit, and have any actual maneuvering capability. The Artilects were taking the brunt of it.\n\nRedwing nodded as each spoke but ran his own inventory as well.\n\nBy this time his knees were sending angry messages that they wanted a trial separation. His weight workout this morning had pushed the limit too far, again. A warning sign: When he overexerted, he was working out unconscious worries. So he concentrated on Clare's detailed tech talk and focused outward, nodding and keeping his gaze on her while thinking about all the crew. They worked well together, as the Psych Artilect Adept predicted, before Redwing had wakened the new members. How well would they do when Beth's team came aboard? Only four left out of six, but\u2014the ship would get more crowded and irritations would begin to build. He had a time window before he would have to decide whether to get out of this entire situation and cast off into interstellar flight again or\u2014what? Go down onto the Bowl in enough numbers to accomplish a resupply and... what? Too many unknowns.\n\nHe let the crew run on for a while, noting that their uniforms were getting a tad messy, hair uncombed, beards a few days old. He would have to sharpen them up a bit, and now might be the time.\n\nAt least this crew would look better then, when and if they got Beth's team aboard. They'd have to double on berths. Working spirit and order would be more difficult. A clock would start ticking.\n\nHe said mildly, \"Officer Jampudvipa, with the Artilects going moody, should we be letting them run the bridge alone while we have lunch?\"\n\nBlinks, nods. Jampudvipa looked rueful, mouth turning down, and got up hurriedly. \"Yes, sir. They're in collective agreement mode but\u2014yes.\"\n\nThat let him focus on the others. \"Beth's team will be aboard in a few hours. That's if we're lucky and solve the problem we have to focus on now. Still, I want everybody spruced up\u2014clean, shaven, bright eyed.\" Nods all around, some repentant. He turned to Karl. \"But the major problem is, how do we get them aboard?\"\n\n\"I've got her photos of the vehicle they're in\u2014basically, a magnetic train car with locks facing outward, to vacuum,\" Karl said. \"But they don't have their suits. The aliens, these 'Folk,' took those at capture.\"\n\n\"So...\" Redwing let them think a moment. \"Can we match velocities and run a pressured conduit?\"\n\n\"Not easily.\" Karl's mouth fretted as he thought. \"We've got EVA gear, sure, but it's one-man, for repairs.\"\n\n\"How about the Bernal?\" Clare asked. \"It's for freight transfer, but we could maybe refit it for a fix-up flexi passage.\"\n\n\"I don't trust anything flexi to stand up to torques and stretches,\" Karl said. \"If we try it, yes, Bernal is the best craft.\"\n\nRedwing had used the repair bots to inspect SunSeeker's hull soon after entering the Bowl system, and he privately agreed with Karl. In interstellar mode, their strong magnetic fields had kept the ship from the blizzard of neutral atoms and dust. SunSeeker was less effective dealing with erosions while it maneuvered at low thrust around the Bowl. The externals looked pitted and scarred now, and he wondered about whether the repair bots could spot flaws that could prove fatal in a personnel transfer. Or if the flexi would sustain pitting from random debris. A thousand questions nagged at him.\n\nRedwing said, \"We could try a fit with our dorsal hatch. We'd have to rig some kind of docking collar.\"\n\nThis they liked. Redwing let them toss ideas around for a while as he tried to envision exactly how that configuration might work. Ayaan Ali had little to say, but he saw a quick widening of her eyes and nodded at her, holding up a hand to draw attention.\n\n\"I... have an idea,\" she said quietly. \"But we must work quickly.\"\nFOUR\n\nBeth watched the Bowl's outer hull, a fast-forward world flittering by below the hard black of space. Even protrusions the size of skyscrapers were just passing gray blurs. In contrast, though the Bowl itself had a surface rotation speed in the range of many kilometers a second, the array of gas clouds and nearby suns hung still. Even high speeds on the interplanetary scale meant nothing to the solemn stars.\n\nTheir tubular craft traveled down the outside of the Bowl, hovering close on magnetically secured trap-rails. She watched enormous plains of gray steel and off-white ceramic flash by. Images jittered so fast, she could not tell what was important. A wall with crawling maggot robots, doing unknown labors. A sliding cascade of liquid metal fuming in high vacuum as it slid into jet-black chunks, then ivory cylinders, then shapely gray teardrops\u2014all to descend into intricate new works, objects meant for mysterious use. All that went by in a stretched display she processed in a few seconds\u2014an entire industrial process carried out in cold vacuum, far from the Bowl star's intrusions. It seethed with robot motion. Fumes danced, billowed, and evaporated away in lacy blue streamers.\n\nNow enormous tangled structures the size of mountains flowed by them. She could see lattice works and cup-shaped constructs but not what they did. It was difficult to keep perspective and their speed seemed to increase still, pressing her at an angle. She was sitting in a chair designed for some other being, one wider and taller. Windows on all sides showed landscapes flitting by, lit by starlight and occasional bright flares amid the odd buildings. From above her head came occasional clanking noises and whispery whistles\u2014sounds of the mag-rail.\n\n\"All this industrial infrastructure,\" Fred said quietly beside her. \"Kept out of their living zone.\"\n\n\"Ah, yes,\" Beth said, not taking her eyes from the images flashing by in the big board window. \"We hardly saw any cities before, either.\"\n\n\"Sure, the Bowl's land area is enormous, but then you realize that their whole mechanistic civilization is clinging to the outer skin. So they have twice the area we thought.\"\n\nBeth glanced upward into the \"sky,\" where the hull's burnished metal gleamed beneath fitful lights. \"And anyone who lives here, does so wrong way up. Centrifugal gravity pushes them away from the hull, so the Bowl is always over their heads. The stars are at their feet.\" Beth laughed softly. \"An upside-down world of its own.\"\n\n\"Smart, really.\" Fred was watching, too, his eyes darting at the spacious spectacle zooming past. \"You can do your manufacturing and then throw your waste away in high vacuum.\"\n\nBeth shook herself; enough gawking. \"Look, we're in a cargo drone. We have to be ready in case we stop and get new passengers.\"\n\n\"Relax. We'll feel the deceleration, get ready.\"\n\n\"At least we should search for food dispensers. This passenger compartment is for whoever's accompanying the cargo\u2014\"\n\n\"Plants, yeah,\" Fred said distantly, still distracted by the view. \"Those finger snakes arranged to escort the plants, fit us in. Neat.\"\n\nBeth smiled. Fred had summed up days of negotiations. Their halting efforts had been beset by translation errors and mistakes. Even sharing a sort-of common language, a mix of Bird and Anglish, there were ambiguities that came from how different minds saw the universe. The snakes used wriggles and tiny movements of their outsized faces to convey meaning, and it took a while to even notice that. Words meant different things if a right-wriggle came with it, versus a left-wriggle. The snakes had similar troubles reading \"primate face gestures\" as they termed it.\n\nFred turned to her. \"You're worried about Tananareve.\"\n\n\"I... yes.\"\n\n\"You're surprised I noticed.\"\n\n\"Not really, I\u2014\"\n\n\"Look, I know what's in my personnel file. I'm classic Asperger's, yep. But I hope I make up for it by, well, my quirky ability to see how things work. Or that's what the file says.\"\n\nTo stall for time she asked, \"How did you see your file?\"\n\nFred was honestly surprised. She realized he did not actually know how to be dishonest, or at least without detection. \"An easy hack.\"\n\n\"Well... yes. I read everybody's file before we left SunSeeker. Standard field-prep method.\"\n\n\"So I should overlook how you fret about us, especially Tananareve.\"\n\n\"She's not really recovered, and I should've noticed she didn't get in here with us.\"\n\nFred gave her an awkward smile. \"Look, the place was confusing and we didn't have any time. She wandered off. There were the finger snakes making a racket and shooting questions at us.\" A sigh. \"Anyway, put it aside. We've got the boarding problem coming up.\"\n\nShe sighed. \"Right, of course.\" So much for Asperger's patients not picking up on social signals. What had that training program said? \"Cognitive behavioral therapy can improve stress management relating to anxiety.\" Yet Fred seems calmer than the rest of us....\n\nFred pressed on. \"The snakes say we're due for a stop about where SunSeeker could rendezvous with us. But we have to come out at high speed, so they have to match us. But\u2014\"\n\n\"Nothing like pressure suits aboard,\" Lau Pin said. \"The snakes say they can't make anything like that, not in time.\"\n\nHe and Mayra had come up, carrying a bowl of what looked like gruel. Mayra scooped some out with a spoon, tasted it. \"Bland, but no harm on my bioregister. This comes out of a dispenser in the next car.\"\n\nSo they all fell to eating. Beth was hungry, so the lack of taste in the muddy mixture of carbs and sugars didn't stop her. She was thinking, anyway. Silence, except when two snakes came by and chattered in their high, fluting voices. Beth ignored them while Mayra carried on a halting conversation with the aliens. Intelligent aliens, the goal of centuries of searching, and I don't have time for them....\n\nHer hand stopped with her spoon in midair as she stared into the distance. Slowly she turned to Mayra. \"Ask them if we can disconnect this car from the track,\" she said.\n\n* * *\n\nThe big problem was hard to sense when you were blithely standing in fractional gravity and not paying attention to the sky. Here on the mag-train, that sky was filled with stars, and it took an hour or two to notice that they were moving. As she thought, Beth watched a bright star move off the window where she sat. The Bowl rotated in thirty-two hours, so the night sky seemed to move a bit slower than it did on Earth. She recalled how, in elementary school, she had been amazed that while sitting at her desk she was really whizzing around at well over a thousand kilometers an hour. The Earth's rotation did that, and its orbit moved her at thirty kilometers a second, too. Now she was sitting in a fast train car and also moving with the Bowl's rotation, hundreds of kilometers a second. Leaving the Bowl meant launching into space at that huge velocity.\n\nMayra said, \"They're scared. Why would you want to\u2014?\"\n\n\"Can they do it?\"\n\n\"Yes, at the next stop. There's a launch facility they use for traveling off the Bowl, but\u2014\"\n\n\"How do we shed the velocity?\" Fred said.\n\nBeth said, \"Carefully, I bet. If they can launch, they must fire us off against the Bowl's rotation, to bring the exit speed down to a manageable level.\"\n\n\"SunSeeker must be moving at a few tens of klicks a second,\" Fred said. \"To lose half a thousand klicks a second...\" His voice trailed off into a croak, apparently at the magnitude of it. \"... that's not the way to do it, though.\"\n\nBeth watched the landscape zoom by outside. Were they slowing?\n\nMayra said, \"They call it the Jumper.\"\n\n\"A launch facility?\" Beth asked. \"Fred, what did you mean?\"\n\n\"The obvious way to get off the Bowl is to go near the axis, where there's nearly no centrifugal grav, so not a high speed. Then leap off into vacuum.\"\n\n\"We're headed that way, but\u2014\" Beth stopped. \"Where is this Jumper?\"\n\nMayra chattered to the snakes, and then said, \"The next stop, if we take the right shunt. They say.\" She looked doubtful, as if this was all moving too fast. Which it is, Beth thought, in more ways than one.\n\nThe finger snakes rattled their \"shells,\" which seemed to work like fingernails. She had seen them use those with lightning-quick skill, to manipulate the intricate tools carried in their side pouches. Now they made a noise like castanets\u2014or, she noticed, like a rattlesnake about to strike. Each snake had four of them on their four fingers. Beth saw Mayra drawing back, her face a mask of alarm. \"What's\u2014?\"\n\n\"They sense great risk,\" Mayra said slowly, \"in taking a Jump in this hauler.\"\n\n\"Not space rated?\"\n\n\"No, a lack of 'life caring'\u2014habitat gear, I think. That noise, though... Ewww.\"\n\n\"Yeah, kinda hard to take,\" Beth said. The snakes were weaving now, standing on leathery, strong \"arms\" and straining up into the air. Their bodies seemed all ribbed muscle, eyes glittering as they glanced at each other.\n\nFred said, \"Maybe they're deciding whether the risk is worth it.\"\n\n\"Worth what?\" Mayra asked, her face still tight with alarm.\n\n\"Worth going with us,\" Fred said. \"That's what you meant, right, Beth?\"\n\n\"I figured there had to be a way to launch into raw space without going to the pole, the Knothole, to get the speed down. I guess there is.\"\n\nMayra said, \"That's what the finger snakes imply. They're working out whether to help us do that... I think.\" A wry shrug. \"Not really sure.\"\n\nBeth leaned forward, eyes still on the scenery flashing by above the perpetual night sky below. Yes, they were moving slower. Definitely. And was the grav here lighter? So they were moving toward the Knothole? \"They can handle the tech for a Jump?\"\n\n\"Yes, they say. But... they say it will be hard on us. A lot of acceleration, and\u2014\"\n\nThe snakes chattered and rattled and Mayra bowed her head, listening. \"The seats will self-contour, so we will... survive.\"\n\n\"It's that hard?\" Fred asked.\n\n\"High. We don't have suits that baffle us against sudden surges.\" Mayra shrugged. \"It is not as though we could have carried them with us, all these months.\" A slow sad smile.\n\nBeth saw she was recalling her husband, who had died when they broke out of confinement, crushed by a hideous spiderlike thing. \"What else?\"\n\n\"They say there is little time to do it. As soon as we reach the next station stop, they must gain control of the shunting system. They say they can, the attendants there\u2014mostly finger snakes\u2014are old friends. Then they must move us into a cache that will ratchet us into a 'departure slot' as they call it. Then we move into line and get dispatched by an electromagnetic system. It seizes us, in a manner independent of the precise shape of this hauler... and flings us into space, along a vector counter to the Bowl's spin.\"\n\nMayra had not spoken so much in a long while. Beth chose to take that as a positive sign. She was right about gear; they had little and would be forced to use whatever came to hand. The seats here were oddly shaped and not designed for humans. The finger snakes had couches to strap into. Not so the bare benches she was sitting on. Still less so for the latrine, which turned out to be a narrow cabin with holes in the floor, some of them small, others disturbingly large.\n\nShe signed. \"I know it may be uncomfortable. But it's the only way.\"\n\nSilence. Even the snakes had gone quiet.\n\nLau Pin said, \"We're dead if we stay down here. They'll catch us again. We escaped once; that trick won't work again.\"\n\nMayra and Fred nodded. Collective decision, great.\n\nBeth noted the snakes watching her. They had somehow deduced that she was the nominal leader of these odd primates who strode into their lives. Maybe all smart species had some hierarchy?\n\n\"Okay, we do it. Notice we're slowing down?\"\n\nFred nodded. \"Yeah, felt it.\"\n\nLau Pin said, \"We don't have much time. Got to hit the ground and move fast. The snakes will tell us what to do.\"\n\n\"Right, good,\" Beth said. She glanced at Mayra. \"And... what else?\"\n\n\"Well...\" Mayra hesitated. \"It's the finger snakes. They want to come with us.\"\nFIVE\n\nRedwing plucked a banana that grew in a weird toroid, peeled and ate it, its aroma bringing back memories of tropical nights and the lapping of waves. Cap'n's privilege.\n\nHis comm buzzed and Clare Conway said, \"We'll need you on the bridge presently.\"\n\n\"On the way.\"\n\nYet he hesitated. Something fretted at the back of his mind.\n\nRedwing had read somewhere that one of his favorite writers, Ernest Hemingway, had been asked what was the best training for a novelist. He had said \"an unhappy childhood.\" Redwing had enjoyed a fine time growing up, but he wondered if this whole expedition was unfolding more like a novel, and would be blamed on one person, one character, the guy in charge: him. Maybe you got a happy childhood and then an unhappy adulthood, and that's how novels worked.\n\nHis mother had made it happy. His father was away at one war or another while he grew up, and when he was home seemed absorbed by sports and alcohol. But that didn't include playing catch with Redwing or coming to his football games. His mother had given him a birthday gift of a telescope and microscope, and a big chemistry set. He bought chemical supplies by selling gunpowder and other pyrotechnics to the local kids. So science had been in his bones from the time he could read. But there were other currents in the mix. He bought a bicycle and a better telescope with gambling cash. His mother, who was a bridge Grand Master, always played penny-ante poker with Redwing while they waited in the car for his music lessons to start. He then applied what she had taught him to the neighborhood kids. They didn't know how to count cards or compute probabilities from that. They also paid to see him blow something up or dissect some poor animal as a bio experiment. He was without principle but soon had enough principal to advance. A university career and PhD led to space, where he really wanted to go. But this far?...\n\nMaybe, considering a \"fault tree\" analysis of his life, having a father who never gave him much time, Redwing figured he was socially unhappy enough to satisfy Hemingway. But finding fault wasn't like solving a problem, was it?\n\nHe had been gaining belly weight in these long months skimming along the Bowl structure. Onboard physio analysis said cortisol was the culprit, a steroid hormone prompted by the body's \"fight or flight\" response to stress. It had bloated him, listening to the plight of his teams fleeing aliens, and damn near nothing he could do to help.\n\nHe paused outside the bridge, straightened his uniform, and went in with his shoulders straight.\n\n\"Cap'n on bridge,\" Ayaan Ali said crisply. Unnecessary, but it set the tone. Going into battle, if that's what this was, had a way of quickening the heart.\n\n\"We're skimming as close as we can to the Bowl rim,\" Ayaan Ali said. \"Having thruster problems.\"\n\nRedwing made a show of staying on his feet, taking in the screens, not pacing. \"Seems like cutting it pretty near.\"\n\nKarl Lebanon, neatly turned out with his general technology officer uniform cleaned and creases stiff, said, \"That magneto grip problem is back, big-time. Sir.\"\n\nRedwing gave him a nod. \"Hand-manage it. Stay with the scoop Artilect all the time, ride it.\"\n\n\"Yes, sir. It knows what's up, is running full complement.\"\n\n\"Stations,\" Redwing said quietly. Old trick: speak softly, make them stay sharp to hear.\n\nHe didn't want to call out of the cold sleep enough people to crew this any better, much less to populate some kind of a big landing expedition. Defrosting and training them would burn time and labor. Even after the reawakened came up to speed, at Glory system in some far future, the whole crew would all have to triple up on a hot hammock schedule, skimpy rations, and shower once a week. Under such stress, how could they perform? He didn't want to find out. Not yet, anyway.\n\nSunSeeker had five crew defrosted, including Captain Redwing. Beth's remaining four would make nine. If he had the chance to rescue Cliff's team, they'd be fourteen aboard. A bit crowded, but they could do it.\n\n\"Coming up, sir.\" Ayaan Ali stared intently at the screens. \"Rim looks the same, but that big cannon thing is swiveling to track us.\"\n\n\"We're in that slot?\"\n\n\"See those walls?\" Below he saw where the atmosphere screen was tied down. There was a rim zone with big constructions dotted across it, out in the vacuum. Ayaan had found a slot between two of them that kept below the cannon declination and now they were gliding through it, a few kilometers above the edge zone. Complex webs of buildings and immense, articulating machinery slid by below.\n\nThe Bowl's outer edge loomed before them, bristling with knobs and bumps the size of nations back on Earth. Looking at the rear screens, he saw the thin, smart film that held in the Bowl atmosphere shimmering in slanting sunlight, blue white. This was the closest they had coasted in to that atmosphere blanket. He hoped they wouldn't take ground fire, though the Bowl's Great Plain was a thousand kilometers away, and any projectile fire would puncture their filmy cover. But yes, Karl was probably right, just from elementary geometry.\n\nStill... \"We're low enough?\"\n\n\"Yes, sir. They can't depress that snout to aim into the Bowl structure.\"\n\n\"Smart sociology. If there are wars here, at least nobody can blow a hole in their life support.\"\n\nWe keep below their firing horizon, so we're safe. Or so went the theory. So many theories had gotten blown away, ever since they sighted this huge, spinning contrivance. But if this one failed, they'd be in easy range of what looked like, Karl said, a gamma ray laser.\n\n\"Karl, what's the emission gain?\"\n\n\"They're running something that gives off a lot of microwaves. Chargers, probably. Running up capacitor banks, I'd guess.\"\n\n\"To discharge against us, through some plasma implosion, giving them the gammas?\"\n\n\"That's my estimate, sir.\"\n\n\"What do you make of our situation?\"\n\n\"I had the usual basic training in remote warfare. The find-fix-track-target-engage-assess decision tree, with Artilects providing the live data. That's all I know.\"\n\n\"No course in alien strategy and tactics?\" This got him a round of chuckles around the bridge, as he had planned. Let them get a little steam out.\n\n\"Uh\u2014no, sir. Not on the curriculum, couple centuries back.\"\n\nA quiet jab, well delivered. Redwing nodded and smiled in tribute. \"Then full speed ahead.\" In a tribute to ancient naval traditions, he added, \"Give us some steam.\"\n\n\"I don't like to flex our magnetic scoop system any more, uh, sir,\" Karl said.\n\n\"Same small-scale problem?\"\n\n\"Yeah. The system's pretty compressed. We can't get into the magneto components to adjust them. It's a mechanical problem, not just some digital e-management thing.\"\n\n\"Do your best.\" Not the time for more technospeak. Though that was all that kept them alive, of course. \"Belay any repairs until we get Beth aboard. How's the flexi gear straightening?\"\n\n\"Programmed on the printer,\" Jampudvipa said. \"Fold points and tension web seem sturdy enough to compile at pickup.\"\n\n\"Excellent. Clare?\"\n\n\"Look at the screen. The laser pods are above us now.\"\n\nWhat's the old saying? \"Come in under their radar\" means something else. This is running in under the guns of a fortress that cannot fire down into the Bowl lifezone. \"Um. Can we skim that close to the atmosphere?\"\n\nKarl pointed to the blue sheen cast off by the boundary film of the atmosphere. This close in, it spread like an ocean landscape, yet the eye saw through it to lands and seas below. These stretched away in infinite perspective, intricate layers basking in unending solar radiance, free of night. The eggshell sheen of the boundary tricked the eye into seeing it as an ocean, with lands on the floor below. There were even long rolling waves to the boundary, flexing in slow, marching rows.\n\nRedwing had to admit the design features here were clever beyond easy measure. Rather than fading off in the familiar exponential, like planets, the Bowl's air ran up and into a hard boundary. The air was thin there, hundreds of kilometers high\u2014but the multilayer smart film kept the errant wind streams and vortices at bay, spreading the energies across vast distances, smoothing them out. No molecules leaked away forever, as they had for poor Mars. The Bowl's own magnetic field gave a spiderweb defense against cosmic rays and angry storms flailing out from the persecuted star that powered all this. Its fields were like spaghetti strands wrapped around the atmosphere, layers of argument against intruding particles wanting to plow into innocent gases.\n\nRedwing said, \"What other weapons does this place have?\"\n\n\"More than we do,\" Clare said mildly.\n\n\"Look,\" Jampudvipa said with an irked twist to her mouth, \"this thing's unknowably old. Ancient! Beyond ancient. On Earth a century was a huge time for weapons to evolve. I read up on this in preoutbreak history, back when we were on one world. Amazing stuff. In the same century as the first nuke got used, we also killed each other with bayonets and one-shot rifles. So how can we think about\u2014this?\"\n\nThis outbreak of consternation made them all sit back, think.\n\nKarl said solemnly, \"The laws of physics constrain everybody\u2014even the Bowl Folk, whoever they are. Or whatever.\"\n\n\"Tech has its own evolution,\" Clare said. \"What's in those big domes at the Bowl rim?\"\n\n\"No way to know. Fly low, is all we can do,\" Redwing said. Taking my ship into uncharted waters... It was liberating to be simply honest.\n\nThey slid on a blithe arc over the quickly spinning lip of the Bowl. Sensors set on the big domes and their enormous snouts registered no change.\n\nCruising over the Bowl's lip and down the swiftly rushing hull brought quick instructive views. SunSeeker had come at the Bowl from the side and below, along the axis of revolution and through the Knothole. Now Redwing could see the detailed and intricate lattice that framed the hull's support structures, threaded by long ribbed structures that looked like enormous subways and elevators, some with spiky turrets protruding at the junctions. But here and there were sections clearly retrofitted, yellow and green splotches of newer joints and fix-up ornamentations of mysterious use.\n\nAdditions and afterthoughts, he judged. Some reminded him of accumulated grime, touch-up attempts and insertions. Like the yellowing varnish on a Renaissance masterpiece, he thought. Strip away the accretions, and beneath is the original brilliance. Interstellar archaeology.\nSIX\n\nKarl deployed the smart flexi with an electric shock. Under a kilovolt surge the velvet blue shroud billowed out\u2014so thin, he could see the gyrating hull grinding past in the distance. Starlight lit its eternal churn. A certain serenity enveloped the view, for the background was the eternal spread of stars. The approaching dot was for the moment nothing.\n\nHe had static-fixed the flexi to the Bernal's hull. Its sensors would follow inbuilt commands he could activate. Well, here goes...\n\nThe flexi popped open at the electro-command. Yet the micro sensors at the far end remained live and ready, he saw from his wrist monitor. The flexi bubble furled out as liquidly as a cape cast off a shoulder, though all this was in high vacuum, no gravity or atmosphere to command its dynamics. Such a thin fabric of layered smart carbon could be made and trained in the ship printers, but he had never tried anything this complex before. Now they had to use it to rescue Beth's team from the big train car that came swarming up at them, the dot assuming a velocity a bit too high. Problems, yes. Perhaps not fatal, entirely. Yet.\n\nKarl had not been thawed when SunSeeker shot through the Knothole, so all this gigantic architecture was new to him. He stared, momentarily lost in detail.\n\n\"Coming up on rendezvous prompt,\" Jam sent on comm. \"Bogie on vector grid.\"\n\n\"Got it.\" He eased the flexi controls, using both hands. For ease of manual operations, there were no left-handed crew on SunSeeker. Karl had made the crew cut because he was genuinely ambidextrous. In college he had made extra cash as a juggler.\n\n\"It's coming up too fast,\" Jam said urgently.\n\n\"I've got mag fields on, maybe I can push it off.\" Karl ran the mag amplitude to the max. That was a stressor in a thick-hulled freighter like the Bernal; he could hear tinny pings.\n\nHe was looking out a true port, not a screen. Living inside a starship with only screen views felt disconnected. There was something about capturing the actual starlight photons bouncing off the Bowl that made it more real. This huge thing had to have incredible strength to hold it together, he realized. SunSeeker had a support structure made of nuclear tensile strength materials, able to take the stresses of the ramjet scoop at the ship core. Maybe the Bowl material was similar. So he scanned the Bowl's wraparound struts, the foundational matter, on the long-range telescopes on his bridge board. It was only a few tens of meters thick, pretty heavily encrusted with evident add-on machinery and cowlings. Which meant the Bowl stress-support material had to be better than SunSeeker's. What engineers they were....\n\nJam said, \"It's braking. Must have some maneuvering ability.\"\n\n\"I can see them,\" Kurt said quietly. He ran his scopes to the max. There were windows in part of the hauler and human heads peering out at him. He had to admire them. They had made it through captivity, struck out across unknown alien territory, stolen transport, liberated themselves\u2014and were coming back to the ship to report.\n\nJam said, \"Ease them in. Careful.\"\n\n\"I read their roll at near zero, yaw zero point three five, but correcting\u2014and pitch seven point five degrees.\" Kurt rattled off the numbers just to be saying something while he used hand controls to turn Bernal into a plausible alignment.\n\n\"Bearing in,\" Jam said. \"Just got confirming signal. Ha! As if anybody else were meeting us out here.\"\n\n\"Aligned. Now's the hard part.\"\n\nCenter ball was smack on, horizontal bar of the crosshatch dead center with vertical bar, and the bulky burnished train car that looked like a shoe box came to rest in the Bernal rest frame. With both hands he triggered the flexi with an electrostatic burst.\n\nThe flexi skirted across the gap like an unfolding velvet blue scarf. It unfolded and clamped on to the boxcar metal around the simple air lock. It anchored and popped him a message: PRESSURE SEAL SECURED.\n\n\"Got it.\" Kurt palmed the pressure valves, and air rushed into the flexi corridor between the ships. Of course, the craft weren't perfectly matched. But the flexi compensated, extruding further lengths of itself to accommodate the vagrant torques and thrusts as the two spacecraft wobbled and rocked in the magnetic grasp. Pressured. Secure.\n\n\"The flexi's working!\" Jam's words came compressed, excited. \"Ayaan was right. Programming them to double-seal solved the pressure problem, straightened them out.\"\n\nThe boxcar's lock popped and he saw the first head appear, looking around. Beth he recognized from her photo.\n\n\"Tag 'em through.\" It happened fast and he had to keep them aligned with the mag grapple. Kurt watched the people come out through the boxcar air lock. The flexi was so transparent, he could see them kick against the sides for momentum and glide through the channel into the Bernal. He counted them. But\u2014\n\n\"What's that with you?\"\n\n\"Snakes,\" Jam sent the audio through a direct link.\n\nIt was Beth. \"Smart snakes. They helped us.\"\n\n\"Trouble,\" Kurt said to himself.\nSEVEN\n\nIt was a rough ride, irritating for Memor. She was cramped in the rattling hot cabin, subjected to rude accelerations. Her pilot seemed to take relish in throwing them into wrenching swoops and pivots. Magnetic ships moved more smoothly, of course, but Memor had chosen a rocket vehicle: it would not have to hover so close to the outer hull of the World. Memor braced against the surge and wondered if her pilot could be among the disaffected. This might be a small way of expressing smoldering anger. Best make a note for future use?\n\nSurely not. Veest Blad was of an Adapted species, but he had been with her for years, back before Memor became female. Veest was too smart not to be loyal.\n\n\"Ah!\" And there, her prey were in sight. That limping one was Tananareve. And those ropy things the probes had seen, now wriggling into one of the cargo cars in a magnetic train, were finger snakes.\n\nTreason! They must be assisting the escaping bipeds. Finger snakes were a useful species, but their adaptation to civilization had always been chancy.\n\nThe car's side closed. The whole train lifted, eased away from the docks, and moved into star-spattered space.\n\nMemor considered. She had the acceleration to catch the train. Could she shoot out the magnetic locking plates without harming those inside? But Asenath had forbidden that\u2014and the primate Tananareve, Memor saw abruptly, was still standing on the dock.\n\nTananareve had been the language adept of this band, with many sleeps spent acquiring the Folk language. Thus, the most important, for Asenath wanted a speaking primate, for reasons unknown. But... the creature seemed ready to fall over. How far could she get before Memor claimed the rest of them and came back for her? Perhaps she would not even be needed... but wait\u2014\n\n\"Veest Blad, land near the biped. Not too near. We don't want her fried.\"\n\n\"Yes, lady.\"\n\nSo what was that about? Memor had countermanded her own decision. A moment's brief look into her Undermind told her why. The abandoned female looked to be dying, and she was the one whom Memor had inspected, had trained, had grown to know. The others\u2014perhaps they could be caught, perhaps they might all be killed by Memor's overbuilt weapons, true\u2014but they weren't needed while Tananareve was here.\n\n* * *\n\nTananareve wiped sweat away and watched the bulbous vehicle settle a good distance away, engines throbbing. Still teetering a bit, feeling woozy, she stood in the hot moist wash of rocket exhaust, waiting. Running wouldn't help her. She'd seen the tremendous creature's speed.\n\nMemor opened the great target-shaped window and rolled out. It looked painful: the rocket vehicle was cramped for her. Memor walked to Tananareve, huffed, and bent low, her eye to the woman's eyes. In her own tongue she asked, \"Where have they gone?\"\n\nTananareve groped for a lie, and it was there. Beth's team had discussed destinations, and rejected\u2014\"They've gone to join Cliff.\"\n\n\"The other fugitives? The killers?\"\n\n\"Cliff's team, yes.\"\n\n\"Where?\"\n\nShe said, \"I don't know. The aliens knew.\"\n\n\"The limbless ones? They are Adopted, but often rebellious. We must take action against them. Tananareve, how goes your adventure?\"\n\n\"We were dying for lack of weight,\" she said. \"Lost bone and muscle. What choice did we have?\"\n\nMemor seemed to restrain herself. \"No choice now. Come. Or shall I carry you?\"\n\nTananareve took two steps, wobbled, and fell over.\n\nShe woke to a vague sensation, a hard surface with big ribs under it: Memor's hands. She flexed her fists and shook her head, trying to get her mind to work. Now they were in the ship, her face close against a wall dotted with icons for controls. Something rumbled, vibrated. Language? And now the wall took on the appearance of a distant forest of plants grown in low gravity, like the place she'd escaped from. A creature like Memor stepped into view and flexed a million multicolored feathers.\n\nNo way could Tananareve follow a conversation that was largely the flexing of feathers and silent subsonic tremors that shook her bones. Memor was holding Tananareve like a prize, and the other was snarling....\n\n* * *\n\nAsenath the Wisdom Chief was not of a mind to be placated. \"One! You have one, and it is dying!\"\n\n\"I will save it,\" Memor said. \"I will take it... her... down to the Quicklands, where spin gravity can restore her muscle and strengthen her bones. I know what she eats and I will procure it. This female is the one who understands me best. Gifted, though in many ways simple. She knows Rank One of the TransLanguage. Wisdom Chief, will you question her now?\"\n\n\"What would I ask?\" Asenath's feathers showed rage, but that was a plumage lie. Memor's undermind had caught the truth: She was in despair.\n\nMemor found that revealing. Earlier the Wisdom Chief had been trying to bring about Memor's disgrace and death. What had changed? Memor decided to wait her out.\n\nAsenath broke first. \"There comes a message from the Target Star, from our destination.\"\n\nAll Memor's feathers flared like a puffball. The human, engulfed, tried to wriggle free. Memor said, \"That is wonderful! And dangerous, yes? Can you interpret\u2014?\"\n\n\"There are visuals. Complex ones. The message seems aimed at these creatures. At your Late Invaders!\"\n\nMemor's feathers went to chaos: a riot of laughter. \"That is... endlessly interesting.\"\n\n\"You must care for your talking simian. We will try to make sense of this message. It is still flowing in. If I call, answer at once, and have the human at hand.\"\n\n* * *\n\nTananareve had caught little of that. She was nibbling at a melon slice now, slipped to her by Memor. She was enraged\u2014tight-lipped, squinting in the strange glow\u2014that she'd been caught again, but grudgingly grateful that Memor had brought provisions. The huge thing did not seem to mind carrying on conversation in front of a human, either.\n\nWhat was that about? Hard to follow. Was Glory inhabited? And had someone there sent a message? Surely not to Earth; that would be foolish, when the Bowl was straight between Earth and Glory, and so much more powerful.\n\nThe captain should be told. He and his crew would figure it out.\n\nRockets fired, accelerations gripped her\u2014and Memor's ship was in flight. Tananareve sagged into the pull. The hard clamp was too strong to allow movement. She relaxed against the floor and tried to get into savasana pose, letting her muscles ease, hoping that her dinosaur-sized captor wouldn't step on her.\nEIGHT\n\nThey couldn't all get into SunSeeker's infirmary. Beth and Fred and Captain Redwing hovered around the door, watching as Mayra and Lau Pin were led to elaborate tables. Tubes and sensors snaked out to mate with them. Jam, acting as medic now, watched, tested, then asked, \"Are you comfortable?\"\n\nMayra and Lau Pin mumbled something.\n\n\"I'm sedating you. Also, you're being recorded. Mayra Wickramsingh, I understand you lost your husband during the expedition?\"\n\n\"Expedition, my arse. We were expi... expiment... animals for testing. Big birds had us\u2014\"\n\nRedwing said, \"Come with me. You'll both be on those tables soon enough, but for now we'll give you gravity and normal food.\"\n\nBeth resisted. \"You're testing her while she talks about Abduss? He was slaughtered by one of those monstrous spider-things.\"\n\n\"We'll need to know how badly that traumatized her. The rest of you, too. How are you feeling now?\"\n\nFred said, \"Hungry.\" He lurched up the corridor toward the ship's mess, then sagged against the bulkhead. \"Feeble.\"\n\nBeth asked, \"How is Cliff? Where is he?\"\n\nRedwing allowed a vexed expression to flit across his face, then went back to the usual stern, calm mask. \"Holed up with some intelligent natives, Cliff's last message said. The Folk tried to kill them all. They were shooting down from some living blimp\u2014sounds bizarre, but what doesn't here? The locals helped Cliff's people get away. Aybe sends us stuff when he can. We have pictures of a thing that looks a lot like a dinosaur, plus some evolved apes. I sent those to you; did you get them?\"\n\nFred spoke over his shoulder. \"We got them, Cap'n. The Bowl must've stopped in Sol system at least twice. Once for the dinosaurs, once for the apes, I figure. And we found a map in that museum globe.\"\n\n\"You sent us the map,\" Redwing said, ushering them along the corridor. A pleasant aroma of warm food drew them. \"How did that strike you?\"\n\n\"Strange. Might be history, might be propaganda for the masses.\"\n\n\"There's a difference?\"\n\nShe smiled. \"It was in a big park, elaborate buildings, the works.\"\n\nFred wobbled into the mess. Beth was feeling frail, too; there were handholds everywhere, and she used them. Surely she'd been longing for foods of Earth? There had been almost no red meat in the parts of the Bowl she'd seen. Beef curry? Its tang enticed. The mess was neat, clean, like a strict diner. Already Fred had picked a five-bean salad and a cheese sandwich.\n\nRedwing dialed up a chef's salad. \"We're recording everything we can get in electromagnetics from the Bowl surface, but there's not much,\" he said.\n\nBeth asked, \"What are you doing with our allies? I mean the\u2014\"\n\n\"Snakes? They kind of give me the willies, but they seem benign. We're helping the finger snakes unload that ship you hijacked. Those plants will do more for them than for us, don't you think? Shall we house them in the garden? We'll have to work out what to give them in the way of sunlight and dirt and water. Want to watch?\" Redwing finger-danced before a sensor.\n\nThe wall wavered, and yes, on the visual wall there were finger snakes and humans moving trays out of the magnetic car. Beth saw these were new crew. Ayaan Ali, pilot; Claire Conway, copilot; and Karl Lebanon, the general technology officer. The ship's population was growing. They moved dexterously among the three snakes, struggling with the language problem.\n\nBeth muted the sound and watched while she ate. Silence as she forked in flavors she had dreamed of down on the Bowl. No talk, only the clinking of silverware. Then Fred said, \"The map in the big globe? It looked alien, but it's blue and white like an Earthlike planet.\"\n\n\"Could that have been Earth in the deep past?\"\n\n\"Yeah. A hundred million years ago?\"\n\nRedwing said, \"Ayaan says no. She pegs that clump of migrating continents to the middle Jurassic. Your picture was upside down, south pole up. Argue with her if you don't agree.\"\n\nFred shook his head. \"I can recall it, but look\u2014I sent Ayaan my photo file, so\u2014\"\n\nRedwing called up a wall display. \"There is a lot of spiky emission from that jet. Seems like message-style stuff, but we can't decipher it. Anyway, it fuzzed up your pictures and Ayaan had a tedious job getting it compiled. She compiled, processed, and flattened the image store. Piled it into a global map, stitching together your flat-on views\u2014here.\"\n\nFred read the notes. \"Of course... All those transforms have blurred out the details, sure. So now, look at South America. Just shows what looking at things upside down and only one side, will do. Now, rightside up and complete, I can see it. How could I have missed it?\"\n\nBeth said kindly, \"You didn't, not really. We were on the run, remember? And this doesn't look a lot like Earth, all the continents squeezed together. But you were right about the Bowl having some link to Earth. Tell the cap'n your ideas.\"\n\nFred glanced at Redwing, eyes wary. \"I was tired then, just thinking out loud\u2014\"\n\n\"And you were right.\" Beth opened her hands across the table. \"Spot on. Sorry I didn't pay enough attention. So, tell the cap'n.\"\n\nFred gazed off into space, speaking to nobody. \"Okay, I thought... wow, Jurassic. A hundred seventy-five million years back? That's when the dinosaurs got big. Damn. Could they have got intelligent, too? Captain, I've been thinking that intelligent dinosaurs built the Bowl and then evolved into all the varieties of Bird Folk we found here. Gene tampering, too, we saw that in some species\u2014you don't evolve extra legs by accident. They keep coming back to Sol system because it's their home.\" Fred remembered his hunger and bit into his cheese sandwich.\n\nA smile played around Redwing's lips. \"If they picked up the apes a few hundred thousand years ago, then they could have been en route to Glory for that long. They're definitely aimed at Glory, just like we were. Beth?\" Beth's mouth was full, so Redwing went on. \"All that brain sweat we spent wondering why our motors weren't putting out enough thrust? The motors are fine. We were plowing through the backwash from the Bowl's jet, picking up backflowing gases all across a thousand kilometers of our ramjet scoop, for all the last hundred years of our flight.\"\n\nBeth nodded. \"We could have gone around it. Too late now, right? We'll still be short.\"\n\n\"Short of everything. Fuel. Water. Air. Food. It gets worse the more people we thaw, but what the hell, we still can't make it unless we can get supplies from the Bowl. And we're at war.\"\n\n\"Cliff killed Bird Folk?\"\n\n\"Yeah. And they tried to repay the favor.\"\n\n* * *\n\nBeth had expected some shipboard protocols, since Redwing liked to keep discipline. But the first thing Redwing said when they got to his cramped office was, \"What was it like down there?\"\n\nAcross Beth's face emotions flickered. \"Imagine you can see land in the sky. You can tell it's far away because even the highest clouds are brighter, and you can't see stars at all. The sun blots them out. It gives you a queasy feeling at first, land hanging in the distance, no night, hard to sleep...\" She took a deep breath, wheezing a bit, her respiratory system adjusting to the ship after so long in alien air. \"The... the rest of the Bowl looks like brown land and white stretches of cloud\u2014imagine, being able to see a hurricane no bigger than your thumbnail. It's dim, because the sun's always there. The jet casts separate shadows, too. It's always slow-twisting in the sky. The clouds go far, far up\u2014their atmosphere's much higher than ours.\"\n\n\"You can't see the molecular skin they have keeping their air in?\"\n\n\"Not a chance. Clouds, stacking up as far as you can see. The trees are different, too\u2014some zigzag and send long feelers down to the ground. I never did figure out why. Maybe a low-grav effect. Anyway, there's this faint land up in the sky. You can see whole patches of land like continents just hanging there. Plus seas, but mostly you see the mirror zone. The reflectors aren't casting sunlight into your eyes\u2014\"\n\n\"They're pointed back at the star, sure.\"\n\n\"\u2014so they're gray, with brighter streaks here and there. The Knothole is up there, too, not easy to see, because it's got the jet shooting through it all the time. It narrows down and gets brighter right at the Knothole. You can watch big twisting strands moving in the jet, if you look long enough. It's always changing.\"\n\n\"And the ground, the animals\u2014\"\n\n\"Impossible to count how many differences there are. Strange things that fly\u2014the air's full of birds and flapping reptile things, too, because in low grav everything takes to the sky if there's an advantage. We got dive-bombed by birds thinking maybe our hair was something they could make off with\u2014food, I guess.\"\n\nRedwing laughed with a sad smile and she saw he was sorry he had to be stuck up here, flying a marginal ramscoop to make velocity changes against the vagrant forces around the Bowl. He didn't want to sail; he wanted to land.\n\nShe sipped some coffee and saw it was best that she not say how she had gotten a certain dreadful, electric zest while fleeing across the Bowl. Redwing asked questions and she did not want to say it was like an unending marathon. A big slice of the strange, a zap to the synaptic net, the shock of unending Otherness moistened with meaning, special stinks, grace notes, blaring daylight that illuminated without instructing. A marathon that addicted.\n\nTo wake up from cold sleep and go into that, fresh from the gewgaws and flashy bubble gum of techno-Earth, was\u2014well, a consummation requiring digestion.\n\nShe could see that Redwing worried at this, could not let it go. Neither could she. Vexing thoughts came, flying strange and fragrant through her mind, but they were not problems, no. They were the shrapnel you carried, buried deep, wounds from meeting the strange.\nPART II\n\nSUNNY SLAUGHTERHOUSE\n\nAfter the game, the King and the pawn go into the same box.\n\n\u2014ITALIAN PROVERB\nNINE\n\nCliff stood at the edge of the ruined city and tried to get his eyes to work right.\n\nThis world looked... strange. Shimmering green and blue halos hovered around the edges of every burned tree and smashed building. The jet scratched across the sky had its usual twisting helical strands around its hard, ivory-bright core... but there, too, an orange halo framed it, winking with vagrant lights.\n\nOkay... shake the head, blink. Repeat. The colored halos dimmed. He made himself breathe long and slow and deep. Acrid smoke tainted the dry air.\n\nIn the second Folk attack, he had gotten hit again. Irma had stitched the wound in his right shoulder and then... he slept. It was strange to sleep for days and nights\u2014though those words meant nothing here, where the ruddy star hung forever in the same spot in the sky. Yet he had slept long, his irked back and aching bones told him.\n\nHe had come out of it, stiff and dry and jerky. A bit foggy, he watched the Sil deal with their wounded and put out the widespread fires. He had just woken up and now, after a breakfast of odd foods and stale water, felt pretty well. The halos ebbed, faded. With Irma he stood watching the Sil work. Their lithe bodies slumped and sagged. They were naturally limber, dexterous creatures, but not now.\n\nIrma said, \"The skyfish came over this part while you and I were trying to help carry that heavy ammo the Sil use. Blasted everything.\"\n\nHe nodded, dimly recalling the fevered hours of carrying heavy cargo on rolling flatcars. Their wooden frame carriers held long cylinders of shaped shells with elementary fuses on the underside. It paid to be careful with them. Hard, dumb, sweaty work it was, while they heard hollow hammer blows rain down like a distant drumming wrath of sky gods. The concussions rolled over them and he had learned pretty quickly not to look up or back too much, because the occasional orange-hot fragment or buzzing shrapnel came that way. Once he had seen a zigzag tree burst into flame after a sizzling meteor slammed into it. He had helped throw water on it, then dirt when they had to. The burning city took all the reservoir water, and then that ran out, too.\n\nAfter they got it put out, the humans went back to hauling ammo. The Sil guns hammered hard, trying to take down the skyfish. The brown and green football blimps churned across the sky and aimed lasers, antennas, and some kind of fire weapon down on the city.\n\nHe distracted himself by thinking how the skyfish could work at all. Its elaborate fins could flare out, capturing wind like a sail, and driving the gasbag forward. He guessed the huge creature could trim on this by shifting mass inside itself, getting a torque about its center of mass to navigate. This can be somewhat like a ship sailing at angles to the wind, tacking with its big side fan-fins spread out. It had big eyes and blister pods, maybe evolved from some balloonlike species. A bioengineered creature used to slowly patrol the air above the Bowl.\n\nHe had watched the battle and recalled how this place had been only a short while before. The Sil had their pride, of course. Their first full awake time in this large Sil city, the five visiting humans had to be led around, shown the town. They saw ancient majestic buildings of stacked stone, gleaming shiny statues to great dead savants, beautiful swooping curves and ramps and towers, then spindly ceramic bridges over moist green gardens and sprawled homes. They exhausted their reserves of oohs and ahhs. It was indeed a fine city of untold ancient origin.\n\nNot now.\n\nDuring the battle, at least five of the living skyfish had circled, covering each other against any Sil artillery. When the guns barked up at them, a shower of beams and missiles cascaded down, silencing the crews. The pain beam was terrifying. When it struck, Cliff could see the shocked fear come into the Sil faces. They turned and ran, some snatching at their skins as though they were on fire. At the sensory level, they were.\n\nThe pain gun was a microwave beam that excited Sil nerves with agonies that made them fall, writhe, scream. It deranged some, who howled and jerked and ran in chaotic bursts. Others had the sense to run steadily out of the beam, if they could. The effect was intense, immediate, and ended Sil resistance where the beams struck. The pain projectors were soundless, which made them even more horrifying. These were the standard Folk weapon to panic opponents, and they worked their silent terror well.\n\nBut humans did not feel it at all. Some difference in the neural wiring made them immune. So Cliff, Aybe, Terry, Howard, and Irma hauled ammo and tried to stay alive. The skyfish wallowed across the air above the Sil city and brought flame spouts to bear. Some forked down green rays that seared buildings and people alike. The enormous living sky creatures systematically burned along geometric paths, and whole blocks of homes and factories burst into yellow flame.\n\nThe Sil brought their archaic weaponry to bear and blew shredding blasts into the skyfish underbodies. Once Cliff heard an enormous hollow whoosh that thundered down like a bass note. He and Irma looked up and saw a skyfish belly explode. A huge yellow ball licked around the green skin and trailed up the sides.\n\n\"Hydrogen,\" Irma said brightly. \"That's their buoyancy gas.\"\n\nHoward said, \"Helium must not give them enough lift. Tricky.\"\n\n\"Oh, come on, where would they get helium?\"\n\nAnother skyfish was floundering now, spewing fluids from multiple wounds, losing altitude, veering erratically. The city below it boiled with flame. The great beast slid down the sky through realms of smoke. Its crash was like a green egg crumbling in slow motion as it burned.\n\nThe destruction lumbered on amid roars and bangs and the sour stench of flame. Not long after, a nearby explosion Cliff never saw caught him. He took hot fragments in his left side and arm and went down. Then it all got fuzzy, the licking flames filmed over by a gray screen of pain.\n\nHe recalled seeing the skyfish turn and begin their ascent. They rose quickly, buoyed by the spreading fires below. Someone said the huge blimps would mend and rearm at higher altitude and might come back... and then it all went vague and he fell away into troubled sleep.\n\nSo now, getting his eyes to see this place right again, it seemed odd to have the big world go rolling along without him. Sils labored nearby and gave the humans no notice whatever. There was a gray silence to their movements, but they kept on stolidly.\n\nJust like it will keep on after you're dead, Cliff thought. The wide busy world of muscle work, weather changing, window washing, future judging, fast joyous dancing, racing heart in great passion, nose picking, fun talking, and bug swatting\u2014all that will go merrily yea merrily along. If these aliens were never aware of your presence, they won't be overwhelmed by your absence. But the same is true of the people you know, too. The world picks up the pace and moves on. Eternally.\n\nThey were standing apart from the men\u2014Terry, Aybe, Howard\u2014at the city's edge. The humans had all slept in a makeshift cave in the surrounding hills, to avoid the constant light. Here there were scraps of the lush greenery on the slopes amid the rocky landscape, with some odd trees and big-leafed plants rich in fruit. They were eating some of these, rather bland with lots of pale blue juice. Irma said, \"Quert looks worn down.\"\n\nCliff turned to see the slim alien approach, its usually light-footed stride slow and lame. Quert's voice was grainy, flat. \"Onto here I-we came to speak\"\u2014a jerky hand gesture\u2014\"and wish share help.\"\n\nQuert's Anglish was still improving, and quite a few of the other Sil had managed to share the language upload and integrator AI. Cliff still found it striking that the Astronomer Folk had widely distributed\u2014\"among the hunters,\" Quert had said\u2014a software that taught Anglish with a few immersion sleeps. He had seen the squat little machine that \"learn us\" as Quert said, but had no idea how it really worked.\n\nIrma said, \"We can labor beside you.\"\n\nQuert's large yellow eyes studied them all in turn. \"Medical we are now at. The dead rot.\"\n\n\"They be many,\" Irma said. The Sil had the most trouble with the irregular forms of to be, so they tried to use simple forms.\n\n\"I sad be for our acts.\"\n\n\"You could not know the Folk would exact such a price,\" Terry said, coming up to the group.\n\n\"Many dead. Have not known before, fire on our city.\"\n\n\"You have lost the city, too,\" Terry said.\n\n\"No. Do not hurt for the city. We build again fast.\" Quert paused for a moment, eyes distant, then said, \"The city speaks what has happened to us. Everywhere on the Bowl, the wounds, they show.\"\n\n\"Sure,\" Irma said.\n\n\"When we have more to say, we rebuild, the city speaks again,\" Quert said. Irma didn't understand, then.\n\nThe Astronomer Folk had apparently hoped the varying species of this area would rally to the Folk cause, and use the Anglish to somehow ensnare Cliff and the others. For the Sil it had worked in reverse. The Sil had been festering under Folk rule for a long time, and had seized the opportunity of uniting with their small human band. Now they suffered for it repeatedly, as the Folk tried to find the humans.\n\nHow long will they bear up? Cliff wondered. We've caused them huge losses...\n\n\"How we help?\" Aybe asked.\n\nQuert stood silent as its large eyes elongated up and down, rhythmically. The yellow eyes closed and the eyelids vibrated, as if shaken from behind. These expressions had no human parallel. Cliff had thought before that this must mean surprise or puzzlement, but now the alien made a curious squatting motion, its sinewy arms knotted in front of it. With the large Sil pancake hands and thick fingers it shaped a twisting architecture in the air.\n\nThen its eyes jerked open and it stood. Cliff was cautious in inferring emotions from facial signatures in the Sil, but this case at least seemed clear. The constricted face oozed sad resolve.\n\n\"Dead are many. Have time now little.\"\n\nIrma said softly, \"You wish help with the dead?\"\n\n\"We may share violence. Share our ends also.\"\n\n* * *\n\nThe finely tended Sil city was now a chaos of jagged building shells, of splintered statues to great Sils now shattered into lumpy gray shards, of cratered streets, of angular trees sheared off at their roots or burned to cinders, of vehicles sitting gnarled and toasted, and the only sounds those of stones falling from half-crumpled walls. No groans, anymore. A city of dead.\n\nA grim procession clogged the few cleared routes. Sil shuffled along with blackened faces and torn skins, mournful angular faces with eyes that saw little before them. Some of them bore wounded; others bore their dead. None spoke. None needed to.\n\nThe stench came to Cliff as they strode down from the surrounding hills. It rose as they entered the ruined precincts. Terry made masks for them all that proved essential as they labored through the endless day.\n\nThere was a code for burying the dead, something to do with recycling their substance into the Bowl's sealed ecology. Especially here, water seemed scarce and the bodies went into a kind of pit that had a flexible blue cover and drains at the bottom.\n\nCliff hated going into the buildings and avoided them. He came upon a big Sil body that had a family gathered around it. They were rolling it in a pale green sheet. They stepped back and looked at Cliff. They were short, thin, and probably could not easily carry the body. He nodded and squatted to pick up the stiff fragrant mass. He got it standing on the rigid legs, then tipped the body onto his shoulder. As he stood up, the pressure forced gas through the voice box and a ragged croak rattled out. It sent shivers down his back. For a long second he wondered if the alien was protesting. He made himself look into the contorted Sil face, gone rigid. A purple tongue stuck out between the small knobby Sil teeth. The eyes had burst and goo ran down the angular cheeks.\n\nCliff looked away, stopped breathing. He took short jolting steps and the family followed him silently, all the way to the pit. He was sweating when he edged the body gently into the opening flap. The family just stared at the green sheet as it slid in, murmured to each other, then turned and walked slowly away. No sayings over the body, no ceremony. There was something dignified in the utter lack of ritual.\n\nNone of the Sil had looked him in the eye. He wondered what that meant.\n\nThe first day was hardest. After that, a numb resignation set in. The bodies got loaded on wagons and taken to parks\u2014the only large, open areas in the city not filled with rubble. Some places the Sil got funeral pyres going, burning the bodies to keep them from stinking and from spreading disease. \"Dirt takes not all,\" Quert said. Cliff supposed that meant the soil processors were overloaded by such massive numbers.\n\nMany corpses were underground. The job became an elaborate Easter egg hunt, Irma remarked sourly. They would bust into a shelter where often Sil had taken refuge, sitting in orderly rows. The humans were just helpers beside the Sil who would gather up valuables from the Sil laps, where often the dead had held what they felt was most dear. The Sil did not attempt identification anymore. They just turned the valuables over to an escort team. Then Sil would come in with a tubular flamethrower and stand in the door and cremate those sitting rigid inside. Get the precious metals and jewelry out, Cliff supposed, and then burn everybody inside. An alien Belsen, he thought, and in the end, our fault.\n\nThe first bodies the human team had carried out, they treated with care and respect, loading them onto stretchers provided to give some semblance of funeral dignity. But after the first day of working on the piles and acres of wrecked bodies, humans and Sil alike became more casual. Bodies got stacked and carried for convenience. After that, a rank callousness descended and they used racks to group the bodies, then drag them with electrical haulers like sleds of dead.\n\nThe Sil called this entire bleak spectacle, the elegant stonework buildings smashed and seared brown and hard black, something that sounded like scleelachrhoft. But they all spoke little. In answer to questions, Quert mostly had an eye-move that meant \"yes\" or a side-nod that meant \"no.\"\n\nThen came the patient patrols through the gray stone rubble. Here a leg, there an arm. Just pickings at first, parts to bag, but then they hit a treasure vault of tragedy. A reeking hash of a hundred had assembled in a basement. Cliff stepped in and found the tiled floor was awash in a still-warm broth of rank water and viscera. When the burst water mains had erupted, Cliff deduced, some of them had tried to escape through a narrow exit in the back. Their bodies were packed in a tight passageway. The dead did not bear burns. From their stiff, bloated condition, he gathered they had died of the smoke or oxygen loss as the firestorm sucked it all away.\n\nTheir leader had made it halfway up a ramp, only to be buried halfway up to her neck in a plaster goo and stone chips. She looked delicately young, smooth of skin still, though it was swollen and had begun to pucker with brown and blue welts. He carried her out himself.\n\nHumans were bigger and stronger and came from a higher-grav world, so they got assigned the harder jobs. When they went into a typical shelter, usually an ordinary basement, it looked to Cliff like a streetcar full of Sil who'd simultaneously had heart failure. Just sitting there in their chairs, all dead. A firestorm may occur naturally in forests, but in cities becomes a conflagration attaining such intensity that it creates and sustains its own wind system. Cliff had watched the first stages of it from a distance, as wind whirls darted among buildings like dust devils of pure yellow and burnt orange flame. Those danced among tall apartment buildings like eerie flame children having fun.\n\nCliff became used to the hovering ruddy heat that seeped through the clouds still overhead. Smells came rising from the dead and made all the work gangs speed up their work. The bodies were not alike but strangely specific. Some clutched purses, others wore jewelry, and a few who had prepared for what they thought the worst wore rucksacks full of food. Some of the Sil work teams took these, and Cliff just looked away, not knowing what to say or do or whether to care at all. A young boy Sil had a pet, a four-legged furry thing Cliff had never seen the likes of\u2014still leashed to the boy, eyes still gleaming.\n\nThey were at their work, doggedly going from apartment to apartment, when a Sil woman suddenly appeared and hurled herself at Cliff. She shouted incoherent abuse and battered at him with tight fists. Another Sil rushed over and pulled her off him. She broke down sobbing, chanting, and was led away. He stood stolidly for a long while, emotions churning.\n\nOnce some Sil work partners found a small cellar of what seemed to be a winelike drink. When Cliff passed by them a while later, carrying a Sil body, they seemed to be roaring drunk. He saw them later, too, and unlike those teams nearby were working energetically and maybe even enjoying it. So whatever they drank, it seemed a blessing.\n\nIt went on and Cliff stopped even estimating the dead. The number was beyond thousands and probably in the tens of thousands and he did not want to think about it anymore. The fiery death penalty applied to all who happened to be in the undefended city\u2014babies, old people, the zoo animals....\n\nThe teams talked less and less and the work days seemed to go on infinitely, down a dwindling pipe. A day toward the end, when they could see there were few streets left to cover, they were combing the shattered shells of the last buildings. With scarcely a whisper, a flittering craft came over and dropped filmy oval leaflets that drifted down from the sky. The curious script meant nothing to the humans, of course, but a Sil read it in broken Anglish:\n\nWe destroyed you because you harbored the Late Invaders. They will damage our fragile eternal paradise and bring disease, unease, and horror to your lot, and to all who dwell beneath the Perpetual Sun in warm mutual company. We struck at the known location of Late Invaders and those helping them to elude our capture. Destruction of other than targets of high security value was unintended and an unavoidable consequence of the fortunes of safekeeping of our eternal Bowl.\n\nThe Sil became angry when reading these notes. They hurled them to the ground, stomped on them. Then others gathered them up and marched off with piles of the filmy sheets. Cliff wondered at this and so followed. The Sil went to their collective lavatory. Since he was in need, he went in and found the propaganda stacked for use in wiping asses.\n\nHe understood all this emotionally. Gathering up body parts in bushel baskets, helping a sorrowed male Sil dig with hands and shovels where he thought his wife might be... the events blended, endlessly.\nTEN\n\nIrma said, \"You have a flat affect.\"\n\n\"Um, what's that?\" Cliff had just awakened from another long sleep. He looked out the narrow opening of the cave they called home. Beyond lay the same stark sunlit landscape of despair he had become accustomed to. He yawned. At least the halo effect in his vision had gone away. Not much else had.\n\n\"It's a failure to express feelings either verbally or nonverbally\u2014that would be, just using your usual grunts and shrugs.\"\n\nHe kept watching the view out the cave opening and shifted uneasily on the inflatable bedding the Sil had given them. It was a bit small. \"Can't say much after what we've been through.\"\n\n\"I learned this in crew training. They gave it to us because we could go through traumas if we get to Glory\u2014\"\n\n\"When we get there. This Bowl, this is an... interlude.\"\n\n\"Okay, when. There might be pretty heavy events to get through on Glory, our trainers said. So we trained to deal with shock, combat fatigue, stress disorders. Recognize the symptoms, apply a range of therapies. You've had low affect for days now.\"\n\nHe could not claim he didn't feel differently, so he said nothing. That was always easier.\n\n\"Look me in the eye.\"\n\nReluctantly, he did. Somehow it was easier to peer out at the blasted and sunny landscape... though now that he thought of that, it made no real sense. Still\u2014\n\nIrma leaned forward, took his head in both hands, and looked fiercely into his eyes, shaking his head to get him to focus on her. \"Good! Trust me, this is a problem and we both need to work on it. They told us to expect it especially when a subject\u2014\"\n\n\"Now I'm a subject?\"\n\n\"Okay, a fellow crew member. It's when people talk about issues without engaging their emotions.\"\n\n\"I'm... sorting things out.\"\n\n\"Another symptom is lack of expressive gestures, little animation in the face, not much vocal inflection.\"\n\n\"Um. Ah. So?\"\n\n\"Do you split your feelings away from events?\"\n\n\"Not... by design. I'm just trying to hold it together here.\"\n\n\"Taking pleasure in real things can help that.\"\n\n\"Um.\"\n\nPleasure. Good idea, quite distant from here...\n\nHe looked out at the ever-bright sunshine that was beginning to weigh on him. The stellar jet cut across the sky, adding its neon glow to the hammering sunlight. They had experienced some darkness here and there on this long \"expedition\" through the strange, incomprehensibly large Bowl... and in his dreams now, he longed for more darkness. He dreamed of diving into deep waters, where a murky cool leafy world wrapped itself around him. He was always sorry to wake up.\n\nHe was thinking of this when he realized she was deftly pushing his buttons. Her voice turned furry, intimate. Hands stroked, caressed. Pretty clearly she wasn't being made wanton and reckless by his fabulous magnetism.\n\nThis was therapy. Not that the fact mattered.\n\nIt became a matter of silky moments and building readiness. Then a gliding delight, sweetly enclasped, and a long exultant shudder for both of them. The artful ease lasted him into a sliding sleep....\n\nWhen he woke she took him through some softly worded moments he only later saw were exercises. Irma asked him in her soft, insistent voice to report the lurid dark nightmares he had. She walked him through those, tracing out moments like the rattling wheeze of corpses, the leaden weight of stiff bodies, the sharp acrid stench of rot... and then she asked him to watch her hand weave, left to right to left... a sway of motion that somehow called up calming spirits in him, let him lapse into a silent, quiet place where he could rest and feel and not swirl back down into those tormented whirlpools. She sighed and stayed with him while he sobbed silently, yet at least not alone. And slept again.\n\nHe woke while Irma slept and reflected on good ol' plain human sex among all this strangeness. Making love worked just fine here. He knew that aliens would have other such modes and they would be odd indeed. Earthside, male honeybee genitals exploded after sex; wasps turned cockroaches into zombie incubators; male scorpion flies produced wads of saliva to feed their mates\u2014a nuptial gift that distracted her front end while her hind end mated. He had learned a basic lesson here: Expect the unexpected.\n\nMore dozing. A lot later, it seemed, he asked vaguely, \"We should go... somewhere....\"\n\n\"The mass funeral festival of the Sil. We must go.\"\n\n\"When?\"\n\n\"Get dressed.\"\n\n* * *\n\nShe had gotten him into a halfway presentable mood with the most direct possible method. Smart, with talents he could not anticipate. He had always tried to work with people who were smarter, quicker, and more naturally adept than he was, plus those who had talents he could not even anticipate. Irma was all of that. In this incredible mess of an interstellar expedition, she kept her wits.\n\nHe realized that he, on the other hand, had exceeded his limits. He had no combat experience and yet had somehow gotten through the first Folk assault with just a wound. That had nearly healed when the Folk came back with not one skyfish but six\u2014to kill so many Sil that nobody could count them. No doubt the Folk hoped to catch the humans and burn them, too, but that could not have been the reason for the hours of unrelenting flame war.\n\nThe Folk wanted discipline, and knew how to get it. Discipline meant punishment meant order meant stability meant this giant spinning contraption could go on its ancient trajectory, bound for Glory and stars beyond.\n\nLearn to think the way the Folk do, he thought. That was the only way to survive this bizarre, strange, and wonderful-but place.\n\nHe slowly got from Quert a way to deal with all the violence. After all, loss was everywhere. Everyone on SunSeeker knew when they departed Earthside that they would never see family or friends again. Cliff tried to phrase what seemed to work. You will lose someone you can't live without, and your heart will be badly broken, and the bad news is that you never completely get over the loss of your beloved. But this is also the good news. They live forever in your broken heart, a wound that doesn't seal back up. And you come through. It's like having a broken leg that never heals perfectly\u2014that still hurts when the weather gets cold, but you learn to dance with the limp.\nELEVEN\n\nCliff listened to the deep rolling music of the Sil dirge. This was an honor, he realized\u2014to witness the public mourning of these lithe aliens, their voices soaring in a long, rolling symphony he could understand, at least emotionally. It was truly so\u2014music had fundamentals common here. Their flowing melodic line had tricky interior cadences, subthemes, and as it gathered force, these merged to become a high, howling remorse laced through with beautiful, somber notes. In the carved rock amphitheater, the Sil stood as they sang, sat when they did not, their angular heads lifted up to show faces twisted with grief.\n\nThey had lost many in the assault by the remorseless, hydrogen-fueled sky beasts. Those vast creatures had killed so many Sil almost as an afterthought, punishment for hiding humans. Apparently firing into crowds was permissible, and the Sil seemed unsurprised by these events.\n\nCliff sat and thought of that as the music wrapped around him. It immersed them all\u2014he could see this strong music had its effects on those beside him. The Sil had many subtle eye-gestures and the odd elongation of the flesh around the eyes apparently meant mourning. All because of the humans...\n\nHis small band had been on the run for a long time, and now had met the sobering fact that those Folk who ran this huge, spinning machine would kill others just to stop a few humans. But... why were they important? It puzzled him and gave the slow, solemn proceedings of public mourning a gravitas he respected.\n\nTheir song rose and fell; their long bass notes reverberating from elaborately carved walls. The Sil leader Quert stood tall and splayed arms to the sky as the large wind instruments among them\u2014not separated, as in a human orchestra\u2014joined in the deep notes, pealing forth as the longer wavelengths resonated with those reflecting from the walled basin. It was eerie and moving and Cliff let himself be drawn into it. Grief made its same choices for the Sil as among humans\u2014gliding, graceful themes, deepening as the growing amplitude plowed into more somber courses. Then, suddenly, that ended in a stunning trill the voices held for a long while, as their instruments boomed forth.\n\nThe silence. No applause. Just grief.\n\nThey all\u2014Howard, Irma, Terry, and Aybe\u2014sat respectfully until told to move, as they had learned was considered polite here. Howard was nursing a bad cut and a bum knee, Terry and Aybe had burns and bound-up wounds, but altogether the humans had minimal damage. They kept their heads down, perhaps from politeness, but Cliff lowered his eyes because he did not want to look into the eyes of the Sil more than he had to. The Sil filed out, their slanted faces seeming even longer now, no one speaking. Their instruments caught Cliff's eye. The laws of physics set design constraints for woodwinds and stringed players\u2014long tubes, resonant cavities, holes for tuning\u2014but the music that bloomed from these oddly shaped chambers and strings was both eerie and yet familiar. It had an artful use of counterpoint, moments of harmonic convergence, repeating details of melodic lines. There were side commentaries in other keys, too. Was music somehow universal?\n\nAs they emerged from the stone bowl, he looked back at the now-empty crescents where the seats each had a slight rounded depression for sitting. Once in Sicily he had seen an ancient open theater that looked much like this. But here the stones were pale conglomerate, not limestone, and far older. Yet the same design emerged.\n\nStill obeying the code of silence, they walked into the sprawling community. This part of the Sil cityscape had escaped the fire bombing. It was a vast relief to be away from the charred precincts where he and the others had worked for... he could not even recall the count. At least a week, though now it seemed a boundary between a past where he had felt in control of his world, and now... this....\n\nHe pulled his mind away from the memories. Focus. His crew training made this possible, but not easy.\n\nThe Sil chose habitats, he noticed, the way a seasoned soldier instinctively chooses cover. Here a wall gave an angled exposure to the star. Another wall stood oblique to that, to allow the jet's glow to have its say with redder luminosities, so each shadow had different colors at play. One wall gave protection from the prevailing wind, with an apartment perched to take advantage of the cooler prospect, big open windows facing away from the field of bright, fine sands that bounded the Sil town. There was a lake nearby, not deep but enough to fetch a tranquil blue from the hovering sky. Sils lounged in shadows for delicious rest, on a spongy plane, their bodies prone on the soft jade green. Sil crowds gathered there, their trilling speech low and reflective. A moist breeze blew through the crowd, and streamers of fog danced among the zigzag trees.\n\nAll eyes followed the humans. They had all agreed to affect a casual disregard of this. \"Think of it as like being a movie star,\" Irma had said.\n\nAnd it was. The Sil at least hid their sliding gaze by turning heads a bit away, but Cliff felt the pressure of their regard.\n\n\"They wonder what to make of us,\" Howard whispered.\n\nAybe said, \"We're enough like them\u2014two arms, two legs, one head. Maybe that's an optimal smart alien design? Makes us sorta simpatico. Better than the Bird Folk, anyway.\"\n\n\"And the Sil know to keep a distance, give us some room to take them in, too,\" Terry added. \"It's kinda fun. Here are real, smart aliens who aren't chasing us.\"\n\n\"Or killing us,\" Irma said sardonically. \"Beth's team wasn't so lucky.\"\n\nThis memory sobered them as they passed by a truly ancient-looking stone edifice, erect on its bare site, the huge blocks sweating with every gush of mists from the lowlands. Cliff savored the moist breath. The winds here stirred with minds of their own, sinewy and musical as they hummed through the Sil streets. The homes somehow generated music from the wind, hollow woodwind notes in lilting harmonies that seemed to spill from the shifting air.\n\nThe sky was clear, a flight of huge lenticular clouds sliding past like a parade of ivory spaceships. The sky creature had been of that size, moving with ponderous poise. Beautiful in its way, and lethal. These clouds poured rain onto distant hills, and the fragrant breeze brought the flavor to them.\n\nAs they often did, the humans watched the strange landscapes around them and tried to figure out how it all worked. Aybe and Terry maintained that there had to be tubes moving water around the Bowl, since otherwise all fluids would end up in the low-grav regions near the poles. Irma pointed out that some photos of the Bowl, taken when SunSeeker was approaching, showed just what Aybe and Terry thought\u2014huge pipes running along the outside of the Bowl. Cliff listened to all this and sorted through his photographs. He had nearly filled his comm-camera's digital storage with photos of plants and animals and had to edit out some to free up space. Already he had decided to ignore algae, bacteria, Protoctista, fungi, and much else. He kept snaps of purple-skinned animals loping on stick legs across a sandy plain. He had captured flapping, flying carpets with big yellow eyes, massive ruddy blobs moving like boulders on tracks of slime, spindly trees that walked, birds like big-eyed blue fish. A library of alien life.\n\nCliff knew he had missed a lot of creatures because they had quick and good camouflage to conceal themselves. They discovered this by stepping on what looked like limbs or lichen or dirt and turned out to be small animals that knew the arts of disguise. He sucked in the moist air and recalled that on Earth, desert plants defended against losing moisture by keeping their stomata closed in the day. They opened at night to take in carbon dioxide without evaporating too much water away. On the Bowl, though, without night, the air had to hold enough moisture to let plants respire, venting oxygen. That meant a lot of water. It explained the heavy rainstorms and thick, flavored air, the sprawling rivers they had to work around, the mists that shrouded even small depressions in the land.\n\nYet some aspects here were like an Earth that had vanished long ago. Standing nearby was an enormous version of something he had seen Earthside, embedded in coal beds: horsetails. These resembled a first draft of bamboo\u2014thick walled, segmented grass, tan and tall. The trunks popped as they swayed in the wind, eternally fighting for space and sun and soil just as did all the others. He had seen creatures that excreted through pores in their feet\u2014surely not from Earth. Their speech sounded like whistling and farting at the same time. Both used flowing gases through a pinched exit, but...\n\nQuert broke off from a murmuring crowd. Moving with efficient grace, it came up to them, its big yellow eyes heavily lidded, and said, \"Thank delivered in kind. We now speak, want.\"\n\nIts language ability came in simple stutters of words. Cliff could usually guess the content. Quert moved with rippling muscles. Like brilliant gazelles, Cliff thought. The Sil were limber, dexterous creatures that worked on the Bowl's understructure. They lived in small towns, mostly, so this now-ruined city was unusual. Quert said Sil were peppered through the immense lands of the Bowl. They seldom met other Sil groups larger than the few thousand here, since distance isolated them. They received instructions from the Folk and carried out their labors. Otherwise, they governed themselves. Populations were stable, by social conventions handed down for countless generations. This was a standard Folk method, apparently. Divide and rule, Cliff thought.\n\nThrongs of Sil followed their mourning with festival. The humans stood aside as the lithe forms began to move, sway, sing. All around them spontaneous movement broke out. The warm sun and lancing jet stung their skins and they danced until a kind of glow spread on their skins. \"Maybe the exercise changes their surface circulation?\" Irma wondered as the pumping music swelled, bodies glided and kicked, and the golden richness of Sil skins seemed to give off its own moist radiance.\n\nQuert led them to a low building, its walls slanted sheets of ivory rock. Beneath their feet was blond gravel that as they entered a small room turned green, each pebble wrapped in a translucent skin of slime. Quert bent and carefully unhinged from some sculpted seats small blobs that seemed to be slugs that had adhered. They sat and the seats adjusted to their bodies with a slithery grace.\n\nThere was a long wait, but as protocol required, the alien spoke first. \"We need know goal Astronomers.\"\n\n\"They want to catch us,\" Terry said. \"Or kill us.\"\n\n\"Whichever is easier,\" Aybe added.\n\n\"Capture best for them. Folk want know what you know.\" Quert said this flatly.\n\n\"About what?\" Irma asked.\n\n\"Ship you ride, plants you carry, bodies you have, songs. Possible is.\" The swift slippery slide of Quert's words belied a calm the feline alien wore like a mantle. Plainly Quert was a leader.\n\nThe talk went on, speculating on why the Folk had fired into a Sil crowd. Yes, humans were among them, but why did that matter? Cliff watched the alien and reflected on what could come next. In his experience people centered their lives around money or status or community or service to some cause, but the Sil seemed to live learning-centered lives. Here little bits of practical knowledge were the daily currency\u2014Howard had given them a M\u00f6bius strip to amuse the children\u2014and their main vocation was to be preoccupied with some exciting little project or maybe a dozen. As one Sil had told him, it was quicker to list the jobs he didn't hold than the ones he did.\n\nThere were teams completing a pit to turn manure into electricity, plans to build a micro-hydroelectric generator in a local stream. They devised and built their own lathes and saws, tough enough to carve into the hard wood of the big trees that ringed their sprawling village. The Sil seemed shaped by what Cliff saw as a frontierlike culture. Here they drilled into trees to make body lotion or designed cement hives for swarming insects, as if to foil a creature that sounded to Cliff like honey badgers. They're isolated, Cliff thought, no other Sil for great distances, or other intelligent species... out here in the bush, lost in their experiments.\n\nHis attention had wandered. Aybe had been peppering Quert with questions, and nobody understood its answers. Then the alien leaned back, yawned to show big teeth, and held up its hands. \"Not right thing, you speak for. Folk want all Adopted to obey. I-we, you\u2014\" A liquid pointing gesture. \"\u2014not made in Bowl. Danger badness comes from us, say Folk.\"\n\nThis came out as hard, clipped words, not the sliding sibilants Quert usually used. It was tricky inferring emotions from alien facial signatures, Cliff's judgment warned him, but the narrowing eyes and tensed lips made a constricted face that oozed resentment. Cliff said, \"You came before us.\"\n\nA quick blinking, which seemed to convey agreement among the Sil. \"Not Adopted over long time. We move, live, work. Folk give us things. We do their commands.\"\n\nIrma said, \"You said earlier that you move often?\"\n\nQuert looked puzzled, as it always did by the human habit of conveying a question by a rising note at the end of a sentence. \"Our kind rove.\"\n\n\"But you have buildings.\"\n\n\"Young must learn by doing. This I-we know. Costs to know. Must pay. No such thing as free education. And buildings, cities used to talk.\"\n\n\"Talk?\"\n\n\"Adopted can see our work from everywhere in the Bowl. We shape our cities to make messages. Small messages. Big shapes for streets, parks, buildings. When we know, they know, too. What Folk want from you.\"\n\nThe Sil had a way of leading you toward what they meant, then letting you go the rest of the way. Maddening, at times. Asking them again, or in a different way, got nowhere, banging on a door that wouldn't open.\n\nThe Sil preferred to show them. Quert took them to a site where the ground seethed with a tan, stretching substance. It came out of the Bowl when the Sil triggered it, Quert said. Then they tuned it somehow. Cliff inspected one of their handheld devices but could make nothing of the ribbed and fissured face of it. The Sil apparently took in information and gave instructions by feel, not visually. This seemed odd for ones who had so many eye-moves to express themselves. Cliff was still wondering at this when the slick tan surface began to ease upward. It became grainy as it rose, wedges emerging from the big bubble that blossomed above them. It firmed up into walls and crossbeams as windows opened like sleepy eyes along the edge. A thick cloying scent like drying cement filled the air and Cliff stepped back with the others, not able to follow the complex moves the \"constructors,\" as Quert termed them, made to shape the thing, through signals he could not fathom.\n\nAfter an hour or two, a fresh building stood two stories tall. The floors were rough and there was no clue how the inhabitants could get water or electricity, but the oval curves of its walls and sloping floors of the interior were elegantly simple. The roof sported an odd array of sculptures that imitated Sil body shapes and cups pointed at the horizon.\n\nIn the entire growth of the home, Cliff felt a tension between order, as seen in the room gridiron pattern, and a spontaneous, discontinuous rhythm to the wrinkled walls and oblong windows. It had just enough strangeness to be expressive, though he did not know what the Sil made of it. They seemed to think it played a role in reconciling them to their lost friends and shattered city.\n\nNomadic, Cliff guessed. Each generation set up shop in a new area, hunted and gathered, devised their own kind of town. A species with a wandering curiosity, alighting on interesting parts of their environment. The Bowl was big enough to accommodate that style. But buildings as messages? \"Do the Bird Folk read your building messages?\"\n\n\"Think not.\" Quert made a rustling sound in its big chest and said quietly, \"I-we lost many. Sil like you, many parts, all lost.\"\n\nThere was a sadness in the long, sliding words. The self-forming building seemed to play a role in their reconciling what had happened. Yet none cast glares or stares at the humans. He could imagine no reason why the Sil should forgive the humans for bringing all this upon them. But then he was yet again seeing them as thinking like humans, and they did not.\n\nThe talk continued for a while as Cliff listened intently, trying to judge how Quert saw the world. Having an alien who had already learned Anglish was an immense advantage, but Quert's short, punchy sentences gave only a surface view of the mind beneath.\n\n\"If I were a lizard, I'd be a belt by now,\" Irma said at one point, and for the first time they saw Quert laugh. Or something like it\u2014barks that could just as well have been a summons, but accompanied by eye-blinks and sideways jerks of the head. As Quert did this, the eyes watched the humans, and there came a moment of\u2014Cliff grasped for the right word\u2014yes, communion. A meeting of minds. This cheered him up a great deal.\n\nThen Quert said there were meetings to go to, clearly meaning to end on a high, light note. They broke up and returned to the cavelike place the Sil had given over to the humans. It was a rude warren built of rocks rolled together to form corridors and rooms. A thick tentlike sheet drawn over the top of the whole sprawl of rock made a roof. At certain places detachable patches let in sun for the rooms, and were easily pegged back in place for sleep. Utilitarian and, Cliff realized, quite portable\u2014just roll up the sheet and find another field of boulders. The Sil apparently used whole gangs to move the rocks, a communal effort.\n\nThe whole team was tired and somehow the Sil dirge had quieted them. They went to their rooms. Cliff took a side corridor to his own small cubbyhole; Irma gave him a smile he could feel in his hip pocket.\n\nCliff had never fancied himself much of a lover, but since they had been taken under the protection of the Sil, they were at it every sleep period. This was no exception. They slept awhile then, and when he woke up she was looking at him. With a lazy smile she said, \"When the chemistry is right, all the experiments work.\"\n\n\"I'm more of a biology type.\"\n\n\"That, too. Y'know, you've learned how to keep this pack of people together, too. I watch you do it. You've learned how to pull their strings.\"\n\n\"Um\u2014yours, too?\"\n\n\"Not so much. Learning to pull men's strings is one of a woman's major skills, of course. I can see you do it in your own guy way.\" She softened this, though, with a grin.\n\nHe felt uneasy thinking about being manipulative, but\u2014 \"I learned on the job.\"\n\n\"You let everybody have their say, then let them do the calculation. Who's with them, who's not. Most of the time that solves the problem.\"\n\n\"Well, they think I have your vote already.\"\n\nShe laughed. \"Touch\u00e9! But not because of fun in the sack.\"\n\nThey were indeed in a sack, of sorts. The open, braced hammock fiber somehow stayed flat though it hung from straps, a smart carbon sheet. He didn't like discussing how to manage their little team, though. He now trusted his intuition and was relieved not to think about it. He leaned over, kissed her. \"What do you think we should do next?\"\n\n\"If you keep caressing my leg, I'll tell you.\"\n\nCliff laughed and kept up a smooth, steady stroking of her tawny leg. He hadn't noticed he was doing it. \"I don't see how we can find Beth or stay away from the Folk, much less figure out this place.\"\n\nIrma shrugged. \"I don't either. Yet.\"\n\n\"What makes you think we can?\"\n\n\"Well, for one thing, it's us. And we have smarts.\"\n\n\"Smarter than what built this contraption?\"\n\n\"Well, there's street smarts on Earth\u2014remember that phrase? Means you can get around on your own. Maybe here we have planet smarts.\"\n\n\"Which means?\" A pretty obvious way not to give away what he thought, but people didn't seem to notice it.\n\n\"This place seems to be deeply conservative. You have to be, to keep a contrivance like this running. Hell, even at first glance, I knew it wasn't stable. If the Bowl gets closer to the star, the biosphere heats up and starts to fall toward the star. To correct that, I'd guess the locals have to fire up the jet stronger, propel the star away, and get back to the right distance for heating. Then there's the problem of what to do if I stamp my foot and the Bowl starts to wobble. It must be they have correction mechanisms in place. On a planet, inertia alone, and Newton's laws, keep you going if you do nothing. Not here.\"\n\n\"Ah, the spirit of an engineer. You didn't answer my question.\"\n\nShe chuckled. \"You noticed! I'd say stay here, try to get back in touch with SunSeeker. Let Redwing figure a way to help us.\"\n\n\"He doesn't seem to have a clue. Unless you're down here, it's hard to get a grip on the quiet, odd ways this place is so different from a planet.\"\n\n\"Such as?\"\n\n\"It's impossibly big, but it's mostly vacant. Why?\"\n\n\"It suits the Folk mentality, must be. Lots of natural landscape\u2014okay, not natural, but it's shaped to feel natural. It's a park, really. The Sil fit in here, too.\"\n\n\"Nomad habits of mind, right. And the Bowl is a nomad, too. Wanderers living on a wandering artifact. A big, smart object.\"\n\nShe pursed her lips. \"Smart? Because it has to be managed all the time, kept from falling into its star?\"\n\n\"It moves forward in a dangerous way, just like us. Any two-legged creature has to fall forward and catch itself. Aside from birds, there aren't many Earthside animals that do that. The most common two-legged one is us.\"\n\nShe considered this. \"The Bird Folk are two-legged, in a way. Though I saw them move on all fours, too, since the forearms can help them for stability. Maybe they're concerned about not falling, because they're massive.\"\n\n\"So they have the same gut instinct\u2014move forward, even if it's tricky. I\u2014\"\n\nShouting in the distance. Irma got up and pulled on her rather tattered uniform, stuck a head out through the curtain of her chamber. \"Quert? What's\u2014?\"\n\nThe alien came into the room in the quick, sliding way the Sil made look so liquidly graceful.\n\n\"Come... they.\"\n\nCliff hauled out of the hammock, feeling his joints ache and eyes sticky. His fingers fumbled as he got dressed. Irma went with Quert. By the time he got to the entrance, they were all staring up at something humming in the sky. Not the balloon creature that had fired on them all, something smaller, faster. It skimmed low, wings purring. A slim, winged thing of feathers and a big crusty head that scanned the land below systematically. Its big glittering eyes saw the Sil settlement and turned toward them.\n\n\"Like a huge dragonfly,\" Irma whispered.\n\nQuert said, \"Scout. Smart one. High value, so Folk must\u2014\"\n\nThe thing surged as it turned toward them. Cliff said, \"Inside!\"\n\nThe nearest building was ceramic coated with crusty, bronzed metal. He ran toward it as he looked back. Howard was watching with binoculars the slim body as it canted in the air, wings furious. \"Howard!\"\n\nQuert was faster than the humans and got into the building entrance. It caught the big hinged door and swung it nearly closed as people ran under its arch. \"Howard!\" Cliff called, and then went in.\n\n\"We must be inside,\" Quert said. \"Scout smart with\u2014\"\n\nA humming in the air washed over them. Cliff saw Howard jerk and grab with frenzied fingers at his head. A startled yelp from him turned to a high, shrill scream. Howard fell and was snatching at his legs, head, chest. His jaw yawned wide with a colossal cry. His eyes bulged white.\n\nQuert slammed the heavy metal door closed and drove a latch into place, cutting off Howard's shriek like a knife.\n\nCliff stood blinking at the big door, unable to push away the sharp image of Howard frantically slapping at invisible demons.\n\nThe humans looked around at the crowds, dazed. There were many Sil already inside, providing a chorus of their sliding speech, feet shuffling, eyes shifting uneasily at this latest attack. Others, though, slumped against walls and let their heads rest back, eyes closed, as if resigned to absorbing yet one more disaster.\n\n\"They get to shelter fast,\" Irma noted. \"Seem to be riding it out, pacing themselves.\"\n\nThere were no windows in this place. Phosphors lit the narrow rooms. Cliff went through the Sil crowds, their eyes tracking him, and down a corridor, searching for a way to see out. The air hung thick and carried an odd, sour flavor.\n\nHe turned back and found Quert following him, who said, \"Hurt come through glass.\"\n\n\"You come here to get away from the Folk microwave weapon?\"\n\nQuert made the odd, waggling sign of assent. \"They Folk change to do your kind.\"\n\nIrma had followed Quert through the claustro-corridors. \"This time it hit Howard. The Folk must've found the right frequency or power levels.\"\n\n\"Folk know technologies well. Adjust fast. Always have.\"\n\n\"And sent it on that scout?\" Cliff wanted to see how Howard was doing. \"If I could get a look\u2014\"\n\n\"No window this place.\" Quert made a hand gesture that they had learned, during the long days of burying the Sil dead, meant \"rest peacefully, no cares.\"\n\nThe Sil would not let Cliff find a way to look out. One of them came down a chute and, speaking quickly in the sibilant squirts the Sil used, through Quert reported that the fast-flying scout with the big gleaming eyes had circled until it tired, fired down randomly at some Sil, then flew away.\n\nIrma said, \"It's come before?\"\n\n\"Only metal stops hurt.\" Quert looked weary, long lines running down its pale face and leathery neck. \"Keep tight.\"\n\nCliff knew that microwaves in the spectral region that plucked at the human nervous system were about three millimeters in wavelength. The Sil must be vulnerable to a different wavelength, since humans had not felt the pain gun used in earlier assaults. So the Folk must have developed something that hurt Howard a great deal, and done it within a short while. Something around a hundred gigahertz. Impressive.\n\nIrma said, \"So they must know you Sil very well\u2014\"\n\n\"The aquladatorpa knows us. It look for you.\"\n\n\"You've been living a long time with the Folk. Under them, I should say. How do you bear it?\"\n\nQuert thought awhile and Cliff let him, not interrupting. Humans had a nervous, intrusive way of interrupting each other, a social gaffe of some consequence among the Sil. Then Quert sighed and said slowly, \"You have word, 'enchant,' means our ochig. Or like it. Enchant comes from light, from sun and jet. Living essence, is enchant. Ochig comes down streaming. Plants, animals, Sil, and now human grow and learn and think from ochig. Bowl turns to keep us here so ochig can bring enchant passing through us. Sil in world, human in world, Folk more in the ochig, thick in ochig. Moving through world, ochig makes pattern. Folk see pattern. Get pattern wrong and Folk do wrong.\"\n\n\"They don't seem any better than you Sil.\"\n\n\"Not better. But in right place.\"\n\n\"They're in the right place when they slaughter you?\"\n\n\"Right will come. Ochig endures.\"\n\nThis was the longest Quert had ever talked about anything, indeed the longest speech he had ever overheard among any of the Sil. They had an air of paying attention to the passing moment. He envied that.\n\nCliff wandered aimlessly, still seeing in his mind's eye Howard slapping at himself and shrieking. He came upon Irma, who had found a little cranny and was sitting on the bare cold stone floor, sobbing. He sat beside her and took her shoulders in his hands and drew her close. Soon enough he was murmuring and clutching her, letting out emotions he did not wish to name. Just holding her helped. He kneaded the tight muscles in her neck and shoulders. She did the same for him and in the long dim time between them some comfort stole over their bodies and then deeper. He could not cry but she could, letting the soft sobs out one at a time. Time eased around them.\n\nThey spent more hours inside before the Sil unwrapped the shelter. They coiled up shiny sheets that they had triggered to cover all the door hinges. Intense electromagnetic waves with millimeter wavelengths can leak around slim edges, even those less than a millimeter wide.\n\nCliff looked out a small window and saw Howard curled up on the ground with no Sil within view. They came out a side door and surveyed the empty sky. Aybe rushed forward, unhooking the first-aid kit... and they all stopped where Howard sprawled.\n\nHoward did not resemble a man now nearly so much as a twisted, red, roasted chicken. Lips blue and bloodless, arms a blotchy purple. His eyes peered up at them as though asking what had happened.\n\nCliff stared at the face a long time. This man had been under his leadership since they left the ship, since they went through the lock at their landing, and then across long weary paths and through sudden panics. Howard had a habit of getting hurt, missing jumps and landing wrong, some scrapes and sprains, despite his physical stats. The ground truth, as their training had told them, was the final fact, and no tests or training could tell you what happened when plans met reality in a usually brutal collision. Swift came reality, and it took no prisoners. Cliff had not seen this coming and Howard had lagged a step or two behind and so was now forever gone. On his watch.\n\nQuert said quietly, \"Is quick. Hurt is where beam hits.\"\n\nThey buried Howard with the other Sil in the collective grave site. Cliff said little and they were walking back from the site when a faint hum filled the air. Heads turned. Sil nearby rustled with alarm.\n\nThe slim shape skimmed low, wings whirring in the sky. Sil began running. Their yellow eyes raced with jittery panic.\n\n\"Go time,\" Quert said. They went.\nPART III\n\nSTATUS OPERA\n\nScientists study the world as it is; engineers create the world that has never been.\n\n\u2014THEODORE VON K\u00c1RM\u00c1N\nTWELVE\n\nMemor watched the primate scream. She tried to lunge out of the beam and tripped. Sprawled. Gasped. The armaments team dutifully tracked her as the poor dim creature scrambled to crawl away. She kept up the sobbing little shrieks as the weapons crew tuned their large antennas further. It went on until Memor waved an impatient fan-display and the team cut off the pain beam.\n\nThe team was pleased, their feathers fluttering with joy, though they kept discipline and said nothing. They had correctly adjusted their weaponry and hit the right resonance for nerve stimulation in the alien.\n\n\"Tananareve,\" Memor in her best learned accent, trying to address the primate by name in its own awkward tongue, \"you can survive this level of agony for, you would say, how long?\"\n\nFree of agony, the primate leaped to her feet. Eyes narrow, mouth tight, voice high. \"You torture me like a lab animal!\"\n\n\"A legitimate use,\" Memor said mildly, \"in warfare.\"\n\n\"War? We landed on your world-thing, tried to open negotiations\u2014\"\n\n\"No use to revisit the past, little one. We are on to other matters, and this experiment was useful to us.\"\n\n\"How?\" The primate sagged to her knees, than sat, wiping sweat from her forehead. \"How can slamming me with that damn fire-beam help?\"\n\n\"We need to know how to... negotiate... with those of your kind.\"\n\n\"You mean fight them.\"\n\n\"The opening struggle comes first, of course.\"\n\nTananareve's face took on an expression Memor had learned to interpret: cautious calculation. These primates managed to convey emotion through small moves of mouth, eyes, chin. They had evolved on some flat plain, apparently, without benefit of the wide range of expression that feathers conferred. Tananareve said slowly, \"I'm very glad they're still free. It means you don't know how to deal with them.\"\n\nMemor disliked the sliding logic of this creature, but knew she had to get around it. \"We need the means to bring them to order. Inflicting pain is much more... virtuous... than simply killing them, I think you will agree?\"\n\nTananareve shot back, \"Do you have anything you would die for? Your freedom to make your own way, for example?\"\n\n\"No, dying seems pointless. If you die, you cannot make use of the outcome of the act.\"\n\n\"Die to save others? Or for a belief?\"\n\n\"I certainly would not die for my beliefs. I could be wrong.\"\n\nTananareve shook her head, which seemed to be how these creatures implied rejection. \"So you experiment on me, to see what power level of your beam works best?\"\n\n\"That, and tunable frequency. How else are we to know?\"\n\nThin lips, narrowed eyes. Anger, yes; Memor was getting used to their ways. \"Don't do it again.\"\n\n\"I see no need to. You obviously felt a great terrible agony. That will suffice.\"\n\n\"I need... sleep.\"\n\n\"That I can grant.\" In truth, Memor was tired of this exercise. She did not like to inflict stinging hurt. Yet her superior, Asenath, had commanded that a fresh weapon be developed, capable of delivering sudden sharp pain. The customary such radiator, which worked well on the Sil, had failed in the first, clumsy battle. Memor did not like to think of that engagement, which had killed the skyfish she rode in. Her escape pod had lingered long enough to witness the giant, buoyant beast writhe in air, its hydrogen chambers breached by rattling shots from the ground cannon below. Then the hydrogen ignited in angry orange fireballs and the skyfish gave a long, rolling bass note of agony. The mournful cry did not end until its huge cylindrical body crumpled, crackling with flames, against a hillside. What a fiasco!\n\nNow Memor had to redeem herself. She could do so by developing and delivering quickly a pain projector, one that could damage the primates without overloading their nervous systems, and thus killing them. And now she had. Further, at the insistence of the weapons shops, Memor's stroke of insight had been to carry out earlier testing on small tree-dweller primates, gathered from the Citadel Gardens for the purpose. They seemed to have similar neurological systems and vulnerabilities, and so were the optimal path to this success.\n\nMemor swelled with pride. The trials on the Sil city had been preliminary, and it was difficult from the skyfish to discern if humans had been affected at all. But these tunings made that probable. The Sil had needed discipline, and the possibility of death-stinging the humans hiding among them was a bonus, of course.\n\n\"We will speak later,\" she told the primate. \"I have more interesting experiments in mind for us to work upon together.\"\n\nThe primate made a noise of deep tones\u2014nothing more than grunts, really\u2014perhaps some symptom of a residual pain. Memor thought it best not to notice this as she departed, her small attendants and the weapons team following dutifully.\nTHIRTEEN\n\nMemor hated when her insides wanted to be her outsides.\n\nShe did not like the testing of new weapons upon her charge, the primate. To do so made her nauseated, her acids run sour. Yet Asenath had ordered quick results quite clearly, and to preserve her position Memor had to comply. She accepted the logic, however distasteful the experience.\n\nLooked at another way, the slap of pain did not merely withhold: the slap imparted. It conveyed precisely the knowledge of greater power withheld. In that knowledge lay the genius of using, the deep humiliation it imposed. It invited the victim to accept a punishment in pursuit of a larger purpose, one that might have been worse\u2014that would in fact be worse if the use wasn't accepted. The pain-slap required that the higher goal be understood.\n\nOf course, the primates could not understand this, but in time with their Adoption that would come. If they could not be so opened, then they would have to be extinguished, well before their vagrant abilities could be a threat.\n\nMemor relaxed a bit by regarding the aged wonders nearby as she passed down corridors and through yawning archways. The teeth of time wore long on the Bowl. By its nature it must run steadily. Engineer species must fix problems without the luxury of trial and error experimenting. That meant engineer teams relied on memory, not ingenuity. Intelligence was less vital than ready response to situations that had occurred before, and so were lodged in cultural recollection. Species had their mental abilities shaped to do this. It was the Way.\n\nMemor thought on this as she watched some mutants being culled. They were small variants on the repair snakes, long ago acquired from a world with rapid tectonics. They had evolved swift, acute responses to those treacherous lands, a driver of their crafty intelligence. Memor had witnessed the underground cities this kind built, when allowed, in the underskin of the Bowl\u2014labyrinths of elegance and deft taste she had been much impressed by. Memor remained surprised that these snakes had subsections of their genome that made them resist the nirvana of the Bowl. Surely here they should be endlessly joyful, for they were free of the frightening ground-quakes, foul volcanoes, and hammering ocean waves that often dashed their hopes and their subsurface homes to oblivion?\n\nThese, however, had a touch too much of their crafty independence. They were in a nearby chamber with transparent walls, where another research team had tried to correct the mental errors in the snakes. Apparently, this corrective experiment had failed. The researchers were exterminating them by gas, and Memor paused to watch the agonies of these smart serpents, who under duress flung themselves into twisting knots. It was revolting, writhing bodies and pain-stretched mouths. At least she could not hear them, as she had Tananareve's shrieks. Gazing through the wall at this, she could not help but reflect upon the fate of the primates, should they continue to provoke.\n\nThey would face the fate of the Sil, whose rebellion had united with the renegade primates and brought down Memor's skyfish. That had made the reprisal destruction of the Sil city inevitable\u2014though it came first as an idea sprung from the slim though weighty head of Asenath, the reigning Chief of Wisdom.\n\nMemor sighed and trudged on, putting the image of the snake agonies behind her. Now she must go to Asenath and confer, though she sorely disliked and feared the Chief of Wisdom, who was known to be capricious.\n\nAn oddity of long history had placed the confinement and punishment chambers together with ancient honoring sites. They were all now encased in a great Citadel that loomed above the lush green landscapes here. She lumbered past large, luxuriant stone structures of vast age, moss clinging to the doorways of crypts polished by time. Some bore blemishes of tomb raiders, but even those harsh, jagged edges had smoothed. These chambers held ancient dead who had been allowed burial, in a far-distant time when that was possible, and before the realization that all mass and vital elements must be reprocessed. Surely that was the highest honor, to be part of life eternally, not a mere oxidized relic. The bodies inside had long returned to the air, of course, with only shriveled bones remaining as a small, unharvested calcium deposit. No doubt the grave goods\u2014ornaments and valuable family remembrance-coffers that some added to the sepulchers of that age\u2014had disappeared long ago, at the hands of vagrant intruders. The past was the easiest venue to rob, after all.\n\nThough not to fathom, came a vagrant sliver of thought. Memor stopped, shocked. Her attendants rustled, unsure what to do. With a feather rattle Memor bade them stand away. The sudden thrust of not to fathom carried guilt and fear wrapped around it. Memor felt the thought-voice and knew it had come lancing up from her Undermind. Something had festered there, and now propelled out, calling to her. She would have to deal with the unruly, understand what this shaft of emotion meant. But not now. She forced herself to resume her stroll, not letting her aides see her vexed condition. Best to rattle her feathers, sigh, casually move on.\n\nShe noted there were pointless messages for the unknowable future, here: TO BE READ UPON YOUR WAKING, from some lost age when minds stored in silica or cryo could, they hoped, work forth from their decay into some future with vaster, smarter resources. None awoke, for there was no shortage of minds in the Bowl. Nor of bodies, for the number of walking, talking minds was a matter of stability, not wealth. Minds were not the point of the Bowl, but the long-run destiny of the Folk was... and of course, of those lucky species who came onboard through countless Annuals of time, to help make the Bowl sail on, sail on, to witness and grasp the great prospect offered by the whole galaxy's own vast, strange, ponderous assets. Whoever or, indeed, whatever wrote TO BE READ UPON YOUR WAKING lived in some illusion of past times. They now drifted as fragrant dust beneath Memor's great slapping feet.\n\nShe looked around, savoring. Some mausoleums carried chiseled epitaphs noted for their charm, which may have preserved the blocky tombs' hard carbo-concentrated walls in their revered sanctity. Here one referred to\n\nI, THE FAMOUS WIT, PLONEJURE,\n\nSOOTHED PAIN WITH COMEDY AND LAUGHTER.\n\nA PERFORMER OF PARTS, SURE I OFTEN DIED...\n\nBUT NEVER QUITE LIKE THIS.\n\nAnother was more dry:\n\nDIUREAUS SAW THE OTHER FOLK BESIDE HIM,\n\nGUILTY, TRUE, AND SQUARE, AND WORSE,\n\nHUNG UP ON A HIGHER CROSS THAN SHE,\n\nDIUREAUS DIED HERE OF FURIOUS ENVY.\n\nPleasant, to think that wit was ancient. She wished that the Chief of Wisdom Asenath had a touch of wit in her genes. One more tomb inscription caught well Asenath's melancholy spirit:\n\nTHEY TOLD ME, HERADOLIS; THEY TOLD ME YOU WERE DEAD.\n\nTHEY BROUGHT ME BITTER NEWS TO HEAR, AND BITTER TEARS TO SHED.\n\nI WEPT WHEN I REMEMBERED HOW OFTEN YOU AND I\n\nHAD TIRED THE SUN WITH TALKING, AND SAW A JET-CURL CARVE THE SKY.\n\nSince this passage was carved, Memor noted, whole worlds had evolved to harbor life, and others had been scorched of life by ancient brutalities. Yet the image saw a jet-curl carve the sky endured.\n\nAh! Here was the entrance; no more time for rumination. Step proud and high\u2014\n\nMemor marched in grandly, head held high with casual grace, her attendants trailing beneath the grand arches of this Citadel of Remembrance. Herald music rumbled and sang to greet her. Pungent mists fell in tribute and out of duty she sniffed, bowed, fluttered a quick ruby tail display. Skin-caressing life fell in curling display around her, caressing her head leathers, whispering faint blessings and salacious compliments. Invitations whispered in her ears, promising succulent delights, then fluttered away. Aromas of heady prospect swarmed up her nostrils and tainted the air with ruddy promise.\n\nImpatient, she shook these off and looked around for the right portal to find Asenath. From the court rabble here dawdling came much sensory babble, greetings, aromas, electric skin-jolts, high hails, a murmur of veiled gossip\u2014all usefully ignored, for now, to show that she was above the insolent fray.\n\nHigh ramparts trimmed in grace notes of colorful mega-flowers loomed like cliffs over the noisy gathering crowd, most of them come for the extermination ceremonies. They knew the ancient rules against recording in any medium, sight or sound or scene\u2014a ritual death\u2014and so came for the immediate experience. They did carry magnifier scopes and had an anxious, eager air. Skittering voices surged with a hunger that had no proper name. All these she avoided.\n\nAdministrative high offices were disguised from those unwelcome, which meant of course the crowd schooled in mere sensation\u2014and the even greater number of the unknowing, unschooled, blunt of mind\u2014all got shielded away by pale luminances that misled the unwary, sending them down dank corridors to their elemental raw pleasures. In such holes the halt and lame of mind would find some passing delights, and forget why they came, forget for their short vexed time the whole point of the Folk. Good enough.\n\nYet the dancing sheaves of prickly glow were smart sensors, and the walls knew well whom to admit. Those embedded intelligences, ever circumspect in their ways, sent fraying brilliant amber fingers to direct Memor down somber, ancient corridors. Crusty, glistening rock winked her forward past a sensor net of embedded eyes. She drew in the soft moist airs. There were always fresh changes in the Citadel, yet the Ancient Zone captured best the colossal powers lodged here. The rough stones held much elegant and courtly wisdom of ages past, canny knowledge set in stone. Memor heaved a sigh. She belonged here.\n\nA quiet, delicious blend of dread and strangeness flowed in her Undermind; she sensed it with a tingle of relish. She forgave it the sudden lance that had jarred her, and concentrated on the immediate. That strumming presence knew that this primordial, welcoming Citadel could well be her place of execution. Should she not perform well, and fail with the primates that were fully her charge now, she would receive little mercy.\n\nYet this did not fully overcome her awe at the majesty here. Of course, her Undermind often used its trickster mode, slipping words and even phrases into her speech, in its keen, eager way. Jokes about Underminds escaping control were a staple of classic literature and current japes. She could feel its hopeful spikes of muted zeal and would have to keep it carefully controlled now. Though not to fathom, indeed.\n\nDrama entered seldom in an Astronomer's life, and for that she was grateful.\n\nAh! The correct portal. She entered into a small knot of Astronomers, to be greeted by feather-riffs in orange and emerald, then small trill songs that echoed complimentary status-signals. Heads turned. Eyes widened. Bass calls of friendship resounded. A shield, of course, for what all knew: Memor had been summoned and they were looking forward to the show. Anticipation danced in their eyes and neck-feather-flutters.\n\nShe had to wait while a Revealing ceremony concluded. It had been a passage of legendary ardor and travail. The recent male, unsteady and weak-eyed, now advanced toward the welcoming cadre, where she knelt with gravid solemnity. The new She looked around in a many-wrinkled face full of bewildered puzzlement. She blinked with surprise, her feather-fan awash in ripples of wonder and flourishes of muted purple hope. Memor recalled this stage, when the male dwindled away into memory and a new She emerged, dewy-eyed.\n\nFrom this fresh female's Revealing she would, through the difficult next Annuals, acquire the long views of a She, yet retain the robust memories of prancing, exploring thrill that had marked her vivid He era. Memor could not help joining in with her deep soprano the rising fulsome joy-song, full of deep welcoming tones, and from above, the high, tenor resonances\u2014all celebrating the conferred judgment and sympathy-from-experience that the Revealing summoned forth. This new She would in time, and with much further study of the essential astrophysics and the Vast History, join the Order of Astronomers. From this essential balance\u2014more a sure dance, truly\u2014between the He and She, wisdom could and thus would come.\n\nStriding forward, clumping with big solemn feet, Memor took note of this new Her-name: Zetasa. In time this new She could, and so might, bring a new, vital stabilizing element to their colloquy\u2014a wise method evolved by the Folk over many, many twelve-millennia in the truly ancient past. This was the essential, time-honored, and stabilizing truth. She relished it.\n\n\"Memor!\" came Asenath's solemn, deep bass voice. \"We have not greeted in longtimes, I do say.\"\n\nUntrue, but perhaps useful. \"I greet in tribute, and wish to confer on present problems,\" Memor said in long sliding tones, with a penumbral, light-yellow feather display. This drew an attendant twitter of speculation. As tradition demanded, Memor ignored the light trilling soprano chorus of conjecture.\n\n\"Which have multiplied, I gather.\"\n\n\"I captured one of the primates and am learning much from her,\" Memor said. \"As we speak, skyfish descend upon the Sil lands, to either capture the primates remaining on the Bowl, or else kill them.\"\n\n\"Ah! As Governors, we must attend to the dismay of the Bowlcrafters, who do not relish such punishments.\" Asenath made a flutter-rush of red and gold to signal concern, but Memor thought it was only a pretense. Something else was in play.\n\n\"Please lead me,\" Memor said to place the conversation in the right ranking order. Asenath had to take the lead.\n\n\"You showed us results of your neural net and brain interrogations of these primates, I recall. Eukaryotic multicellular bilaterians, they are, with unexposed Underminds\u2014fascinating, I am sure. You then estimated their capacities as well below we Folk, and perhaps somewhat above others of the Adopted. Yet they continue to elude us, and now half of them have fled the Bowl.\"\n\nThe attendant minor figures drew in their collective breath at this. To escape! was their clear, unspoken message. Memor made a half turn to block most of them from Asenath's piercing gaze. She was saying, \"Now they have returned to their plasma scoop starship. Do you still feel they can be integrated into our Way?\"\n\nMaking a ritual humble-flush, Memor said, \"Apologies most firm indeed, for my failure to retain or recapture these strange primates. I believe their curious gait\u2014a continual, controlled toppling upon those hind feet that have thick, artificial coverings\u2014must be a key clue to their ability to improvise. They can hop to new ideas far more readily than we anticipated. Their ability to form a quick bond-alliance with the Sil is an example\u2014another two-footed species, I remark, which perhaps helps explains their rebellion. The primates arrived on train transport, and immediately engaged with the Sil in a battle against our skyfish. How this came about with such speed is a puzzle. Perhaps there is a species-signal here that may explain it in part.\"\n\n\"I would think their two-legged forms were adaptive on a more aggressive and quick-fighting world.\"\n\n\"So... you would urge extermination.\"\n\nAsenath saw she had been maneuvered into a hasty conclusion, always a mistake. \"Perhaps not immediately. Their ship has interesting features of magnetic control I and others feel would be useful to examine.\"\n\n\"Ah, wise. Perhaps a consultation, then?\" Memor motioned Asenath into a speaking cloister. She took the feather-flush hint. They made it seem they were merely strolling as they spoke. Memor dropped the shimmering, electric-blue sonic cloak behind them once in the narrow confines, where luminous walls gave a warm green glow.\n\n\"I did not want to refer to our continuing trouble with the jet flare guidance,\" Memor said.\n\n\"You venture that primates could help somehow?\" Asenath's neck fringe fluttered with skepticism.\n\n\"They are inventive\u2014\"\n\n\"Surely you do not imagine that we could allow them to touch what is most sacred and vital to the Bowl!\"\n\n\"I was trying to\u2014\"\n\n\"The very idea would be transparent heresy to some of the Folk.\" A slow, studied gaze, no feather signals at all. \"Perhaps... including me.\"\n\nThere was surely danger here. Asenath's feather tones shifted from bright attentive colors of rose-purple and olive into hues tending toward pewters and subdued solemn blues. They rustled, too, with an air of menace. Betrayal by Asenath could take several avenues, all hard for Memor to counter. So\u2014admit failure, and do so quickly and first.\n\n\"I mention that possibility only because my own narrow escape\u2014when they and the Sil attacked my starfish\u2014was essential. I had learned that the primates could quickly use the chemically driven Sil weaponry. Our assault teams needed to hear that. The primates are swift, original, unpredictable. I wished to report this firsthand\u2014\"\n\n\"Your death at their hands would have carried the same message,\" Asenath said dryly.\n\nWithout hesitation at this sally, Memor said, \"I brought recordings, Wisdom Chief, to analyze\u2014\"\n\n\"Which show that these Late Invaders are erratic, impulsive, volatile, capricious\u2014yes, all qualities we Folk have suppressed, in order to preserve the Bowl of Heaven. Yet these very same Late Invaders you now propose to use, to harvest, to\u2014\"\n\n\"No, no! I think they could show us new technologies, aid us\u2014and perhaps bring word of a world we do not know, have never visited.\"\n\n\"And then?\"\n\n\"Of course, if they cannot be Adopted into our society, then they and their odd ship must be erased.\"\n\nAsenath gave a subtle fan-salute, undercut with a skeptical throat-wash of dubious red. \"I must say, Attendant Astute Astronomer, that you maneuver well here in chambers, though alas, not on the battlefield.\"\n\n\"I was not commanding the skyfish!\"\n\n\"I hear otherwise....\"\n\nToo late, Memor recalled giving orders to the skyfish Captain. She had been unnerved while the simple Sil artillery hammered loud and strong at the great beast's walls. There was some panic then, before the hydrogen vaults were breached. Only her own quick commands had gotten her into her pod. Her parting sally to the doomed Captain had been, Soon we shall have no further disputes. I will have my pod now. The Captain had of course not appreciated the ironic tone. Memor had not looked back as she quickly departed. The Captain had gone to his proper reward.\n\nMemor had been a bare short distance from the lumbering gray-skinned beast when a Sil shot struck a girder-bone and ricocheted into a hydrogen vault, then through the outer wall. Surely that had been a lucky shot, which Memor witnessed at a distressingly close distance. The hard slam of the exploding hydrogen had very nearly thrown her fleeing pod into a fatal yaw and tumble. She had shuddered as the skyfish bellowed a long, hoarse cry, realizing its imminent death.\n\nMemor sensed she had been silent too long, reflecting on the sudden memory welling up. Her Undermind had not processed those harrowing moments then. But now was not the time to dally over the past. \"I made a few suggestions to the Captain, all in the heat of the moment.\"\n\n\"It became even more heated as you escaped,\" Asenath said with brittle brevity, eyes narrowed.\n\n\"Had I not, you would know little of the engagement.\"\n\n\"You are aware that you are already in disfavor?\"\n\n\"I know that my efforts have not been widely recognized. These primates are difficult to reason with, for their mental structures suffer primitive modes we have not dealt with for a great while.\"\n\n\"At least you recaptured one of those who escaped in the original party. Yet the others now divide into two groups: those ones we have never captured, somewhere among the Sil, and as well a party of four, who escaped the Bowl entirely, and now return to their ship. This last is most infuriating. Their ship somehow glides just below the firing field of view of our gamma ray lasers on the Rim.\"\n\n\"Yes, most regrettable.\" Memor made an apologetic display of amber and blue gray, rippling her feathers to convey remorse. \"I did note that our defenses are deliberately unable to be aimed downward at our Bowl, and this decision was made by Elders long ago, after the Maxer Rebellion.\"\n\n\"Your history is correct. Alas, the Maxer Movement is not completely extinguished, and I fear this flaw in our defenses can be laid at their door.\"\n\n\"I did not know!\" Memor did not have to pretend; this was indeed bad news, a defense flaw coming at the worst time, with Late Invaders at large.\n\n\"It is not your matter, Memor. Concentrate upon the Late Invaders.\"\n\n\"You mean, capture and kill?\" That would be easiest, and would get Memor out of the spotlight. Though she would regret their loss, for they were intriguing in their odd mysteries.\n\n\"No! I felt that way before, but there are now new issues. To understand, and keep these discussions secure, we must visit the Vaults.\"\n\nMemor felt a tremor of unease ripple up from her Undermind. Grave matters came to those who had to consult the Vaults. \"But why?\"\n\n\"That you must ask Unajiuhanah, Keeper of the Vault Library.\"\n\nThe idea itself was puzzling, and filled Memor with dread.\nFOURTEEN\n\nAbout Unajiuhanah there was a timeworn joke, that she loved to sing the ancient songs at public events, even at funerals. Asked if she had performed at a recent high burial, Unajiuhanah answered no, and the riposte was, \"Then it was a merciful death indeed.\"\n\n\"Compliments to you, Asenath,\" Unajiuhanah began with a ritual rippling feather salute in gray and violet. This achieved the feat of representing the Great Seal of the Vaults in an actual fluttering picture, a striking image on Unajiuhanah's high fan display. Memor could even see a jittering vague white patch that stood for the formal writing of ancient times, indecipherable now but signifying the weight of vast history. It shimmered like a mute reminder of the long purpose of the Bowl and thus of the Vault.\n\nAsenath introduced Memor, which proved unnecessary as Unajiuhanah brushed aside a summary of Memor's life details and turned to address her directly.\n\n\"Memor, I will entertain your notions because I knew your great ancestors and feel I owe them some indulgence. Indeed, I live because a certain fine SheFolk many generations ago stood and fought against an insurrection that very nearly toppled all order in this Vault. That ForeFolk stands before me now, represented by a minute genetic fraction\u2014in you, Memor.\"\n\n\"I am most grateful,\" Memor said with a simple mild flourish of ruby, embarrassed neck-fringe.\n\n\"Now I have a surprise of sorts for you, to bring you into our deliberations. Here is your other self.\"\n\nUnajiuhanah paused, her voice rising to call, \"Bemor, come forth.\"\n\n\"Be More\" Memor heard, the very name plunging her backwards into her young days\u2014while her eyes fixed on the big, somewhat ungainly senior male that was... she saw, breathing hard... herself. At least, genetically. Bemor! Lost brother! They had been separated long before Memor went through the Revealing. Now with \"Bemor\" she heard again the joke between the two of them. It had been funny then while young but had turned sour many twelve-cubed Annuals ago... Be More. More than Memor. Be smarter, swifter, know more, exert power, fathom more deeply, stand taller, command power. Be More.\n\n\"Brother!\" Memor called, for Bemor had not suffered the Revealing's agonies and transformations\u2014all done in their youth, by high design. Be more... be male.\n\n\"I thought this meeting should best come as a surprise, or else one or the other or even both of you would surely dodge it.\" Unajiuhanah gave a mirthful display, fluttering ruby breast-feathers discreetly. Clearly she was enjoying this.\n\n\"Your great turbine of a mind reports you well,\" Bemor said as overture. \"I've sensed your reports. Quite complex and deep.\"\n\n\"Sensed?\" Memor realized her own whole-mind scans, carried out routinely to monitor performance, were not private. Usually they were, but of course not in matters of high security.\n\n\"They are also quite entertaining,\" Bemor said. \"You remember well, and your Undermind is a source of insight. The facts you confronted alone are high drama. I could scarcely imagine such odd aliens as these Late Invaders. What zest!\"\n\n\"You mean, how did I let them escape?\"\n\n\"No, I mean they have a crafty nature we could use.\"\n\nMemor was sure Your great turbine of a mind was an ironic salute, but best not to draw Unajiuhanah's attention to it. \"If we can Adopt them, perhaps\u2014\"\n\n\"I think not. Too unstable, as species go. They can be better used to carry out our larger cruising agenda.\"\n\nThis was new, beyond the time-honored precepts of the Astronomers, and indeed, of all other castes. Larger cruising agenda? Memor should be shocked, she knew, but had no time for that now. \"I acted to constrain their actions, under Asenath's direction.\"\n\nBemor waved this aside with a cluster-flourish in green and sea blue. \"Those orders now vanish. There is new wisdom, falling upon us from the stars.\"\n\nMemor contented herself with a fan-feather gesture and let Asenath carry the conversation. She was still staggering mentally from the sudden meeting of her near-self: the path not taken, if somehow she could have stayed a male. Bemor had a quick, brusque way of saying things that swept away the niceties of diplomacy and polite evasion. Quite male. Best to change direction.\n\n\"I was discussing how I was forced to carry forward the reconnaissance of the Sil, who had sheltered the primates. They proved better at bringing down our skyfish with their simple chemical cannon, admittedly. I\u2014\"\n\n\"Fled, as you should.\" Bemore spoke kindly, shuffling his large feet in a faint echo-dance of welcome\u2014to soften what was to come? \"The primate ingenuity combined nonlinearly with that of the Sil, who were always an irksome and crafty kind.\"\n\n\"Destabilizing,\" Asenath added, \"still.\" But then she backed away, as if to let the twins negotiate their own newfound equilibrium. So did Unajiuhanah, with a muted bow. Memor saw this meeting was arranged to divulge information, in a way slanted to make best use of the perpetual jockeying for position in the Astronomer hierarchy\u2014and of course, in the status of the Vaulted, who tended the most ancient records, integrating them with the emerging new.\n\nSo, take the momentum away from them. \"What new wisdom intrudes?\" Memor chose to use an ancient saying, said to come from the Builders, though across the sum of Bowl eras, no one truly knew.\n\n\"We fathom more of the gravitational waves, and their true origin,\" Bemor said.\n\n\"As I recall, they come from Glory, or from some source well beyond,\" Memor said, for this had been the received wisdom from before she was born.\n\n\"Not so,\" Bemor said. \"Not beyond. The source is in the immediate Glorian system.\"\n\n\"There is no plausibility, as some argued, that the gravitational waves came from a chance coincidence in the sky? From some cosmological source far away?\"\n\n\"Not even close. I see your early education has been a waste of time.\"\n\nMemor knew this gibe, a lancing shot at her earlier ranking in the rigorous status queue of the elect, pre-Astronomer examinations. Quadlineal calculus had always eluded her somehow, and Bemor had never let her forget it.... She now had to get back some position in this conversation playing out before their elders.\n\n\"But surely there cannot be heavy masses moving near a planetary system. That would render unstable the orbits of any planet nearby\u2014\"\n\n\"No, that must now be considered untrue. Facts say otherwise. We have heard from our Web trading partners.\"\n\n\"What can they\u2014?\"\n\nBemor beamed, yet kept to his clear, factual mask. \"You may recall some long Annuals ago we asked them to erect gravitational wave antennas to concentrate upon Glory. They have so done, and with felicitous trading strategies, we have secured their data.\"\n\nVery well, play for time. And think. \"I did not know that. Expensive, I suppose?\"\n\nBemor was enough similar that Memor could easily read the quick, darting expressions in feather-flutter\u2014quill rattle, spines flexing so hues slid from steel blue to indigo sheen\u2014that bespoke anticipation of an opportunity to make a veiled boast.\n\nAsenath raised some pink neck-rustle as a deft, ironic signal. Memor realized this was what some intimates of the court termed Status Opera, the only true game when the social structure must remain static, for the sake of Bowl stability. Maneuver for position, yes, but carefully, deftly, for the system must always endure, above all.\n\nBemor was in his element, and so took his fulsome time. \"I engaged three other Galactic Web partners, one of whom knew nothing of gravitational waves whatever, and how to detect them. As expected, those who did know had technologies smaller and less sensitive than ours.\"\n\nBemor delivered this in a flat, factual way, almost offhand, and with a subtle wing-shrug\u2014a good precursor to a revelation. Memor appreciated the method, as it was hers as well. They were twins, after all.... Though Bemor seemed to do it with more verve, as if knowing their audience would approve verve.\n\n\"I had to trade valuable arts and science to induce their cooperation,\" Bemor said. \"We barter and gain, delayed for many Annuals, of course. I employed a rich trading language to describe our wants, and used the artificial, intelligent agents we had installed in those societies long in the past.\"\n\nMemor was at a disadvantage here, since she had learned little of such distant diplomacies. She did know that the Ancients had seen value in establishing agents, transferred as sealed minds in code, to distant worlds. Interstellar commerce over huge distances made sense only if exchange of knowledge\u2014arts, science, engineering, the equivalent of patents\u2014could be traded for some return value. Such a market occurred, mediated among artificial intelligences run solely inside mutually agreed upon containment: the Mind Province established among alien societies. Elaborate protocols ensured that no artificial intelligences could run outside the Mind Province. They were safe there, too, to run their code without corruption. This protected Bowl secrets from the alien locals, and in turn, the local infosphere from the agent.\n\n\"I chose truly distant worlds for two reasons,\" Bemor said. \"They had to be displaced from our trajectory, so that we could gain triangulation on Glory. I then\u2014\"\n\n\"You transmitted double-encrypted?\" Asenath demanded. \"You are sure the gravitational wave signatures were unwrapped in secrecy by our sequestered agent?\"\n\n\"I received the coded instant return notice, yes. I got it back many Annuals before the official trading partner even acknowledged receipt.\"\n\n\"Meaning? That they pondered it long before even notifying us?\"\n\nBemor was not disturbed by these thrusts; he seemed bemused. \"Caution is admirable, do you not think so? The first reply came from an insectoid civilization, apparently hungry for further astronomical knowledge. They trade such wares eagerly and built the needed detectors with speed.\"\n\n\"How distant are they?\"\n\n\"Over a twelve-squared light-Annuals, at a high angle with respect to our trajectory. The second reply came from a similar distance and a different, large angle. We paid them with techno-lore, methods our prior history implied would interest them. These were duly lodged in the host species' banking system. Credits not spent locally may be transmitted, securely encrypted, between solar systems, of course. Then came a third reply, also willing.\"\n\nBemor made to condense around them a shimmering shell display of the realm around the Bowl. The three agreeable trader stars shone bright yellow, all at considerable angles away. One lay very nearly parallel to the Bowl, along the trajectory axis they followed, ending in Glory. The simulation showed message flags denoting ongoing info-commerce transporting among all three, as well as their links to the Bowl.\n\n\"So they set to work, these trade partners\u2014\"\n\n\"Ran their gravitational wave detectors. Learned our skills. And nailed firm the site of the waves. It is in our destination system\u2014Glory.\"\n\nMemor said slowly, \"Agents do amass more and more knowledge about their host species. They report back. Do these worlds have any opinion about the cause of the waves?\"\n\nBemor looked pleased, with a body-flutter of magenta flush. To Memor this was a giveaway: a salute, really, as if to say, I recognize!\u2014you can leap ahead, see what's coming. \"They could not resist diagnosing the long wavelengths and their resonances. And... there are messages within.\"\n\nAsenath gasped and could not resist: \"Saying what?\"\n\nBemor's elation collapsed, his neck wattles compressing to thin red layers. \"We do not know. These, too, are apparently deeply encrypted.\"\n\nMemor felt a tremor of awe, that emotion mingling fear and wonder, so seldom sensed in a calm, regular life. It swept her like a tidal slap. \"Sending coded messages, by oscillating huge masses to make waves of gravity itself?\u2014in organized ways? That is...\" She was about to say, impossible\u2014but caution ruled. \"... improbable, in the extreme.\"\n\nAsenath added wryly, \"We are approaching something strange and perhaps quite dangerous. Glory seems innocuous, but they send gravitational messages\u2014somehow. The escaped primates are headed that way, too\u2014or were, until they decided to land upon the Bowl of Heaven. They seem\u2014\" She preened with an oddly insulting fan-gesture, ominous and foreboding. \"\u2014ambitious.\"\n\nMemor decided not to rise to the bait. \"They are able and may be of use.\"\n\nUnajiuhanah came in then with a gentle, sad wing-shrug. \"I enjoy your sparring, but there are larger issues, you twins.\" A nod to Asenath, to proceed. \"Our larger cruising agenda, recall?\"\n\nAsenath said, \"The Glorians, as we term them, have sent an electromagnetic signal.\"\n\n\"Directed at us?\" Unajiuhanah prompted.\n\n\"I... suppose.\" Asenath looked puzzled.\n\n\"There is no distinction in spatial coordinates between the Bowl and the primate star rammer,\" Bemor said. \"That may explain the content.\"\n\n\"Which is?\" Memor asked, impatient with this parrying.\n\n\"Cartoons,\" Unajiuhanah said. \"Such as primitive cultures employ. They might as well be painted on cave walls, but for the fact that they move. Showing violence, often physically improbable.\"\n\nSilence. \"I would truly like to know some way to discover if these abject signals are insulting, from a culture that has devolved so deeply that it thinks these are useful, or even amusing.\"\n\nBemor said, \"Beings who can hurl huge masses to make messages would not be so. All our knowledge of cultural evolution, gathered in your archives, Unajiuhanah, says so.\"\n\n\"I would so believe,\" Unajiuhanah said simply.\n\n\"Or else...\" Memor hesitated. \"We are mistaken in our assumptions.\"\n\n\"Whatever can you mean?\" Asenath said with a nasty rebuke-rustle.\n\n\"Suppose they are not sent to intersect us, or the star rammer.\" Memor envisioned the line of sight\u2014Glory, the Bowl, and upon it the alien ship, orbiting above... and beyond, at an unknown distance, farther from Glory... \"The Glorians may be transmitting to hail and instruct, and so to warn... the primate home world.\"\n\n\"But then\u2014\" Bemor hesitated. Fevered rattles came from his wing, a note of harried distress at what he glimpsed.\n\nImagination helps, Memor realized. The insight had come from her Undermind, direct and unsaid until now.... She felt a rumble of discontent from deep within her\u2014of knowledge pent up, unexpressed, and so vagrant and wild. Fear surged in her, but she suppressed it, focused on the moment. She had been in a duel with Bemor here, and now there was a sally she could use, at last, an advantage coming from within, uninspected, yet sure, she felt, sure.\n\nMemor said, not without some pleasure, \"They are afraid not of us, but of the humans.\"\nPART IV\n\nSENDING SUPERMAN\n\nNothing fails like success, because we do not learn anything from it. The only thing we ever learn from is failure. Success only confirms our superstitions.\n\n\u2014KENNETH BOULDING\nFIFTEEN\n\nIt was possible to exercise at Earth gravity on SunSeeker, just by jogging six-minute kilometers in the direction the deck was rotating. Beth sweated but didn't make that speed, running on the spongy turf and sucking down the chilly ship air that always seemed to taste faintly of oil. An hour into her slogging, choppy run she felt better in the odd way that returning to good gravs did\u2014a sensation of solidity, of the body's chugging machinery settling back into its groove. If she ran fast in the same direction the deck rotated, she increased her speed of rotation, and so increased her weight. She reversed for her hard-pounding finish. Going fast against the rotation, she nearly floated like some sticky angel on air, her bare feet barely skimming the soft fabric. She sped around the outer habitat circumference in her shorts and sopping T-shirt and lurched into the showers, gasping and happy.\n\nThe shower next to her went on. She leaned around the corner and saw a finger snake wriggling in the spray.\n\n\"Phoshtha?\"\n\n\"Hello, Beth. This device is delight.\" The thin, sliding voice somehow fit the dancing eyes.\n\n\"Yes, but do not use it too often. We can't recycle the water very fast.\" Beth stepped back in and turned the shower on, a giggle tickling her lips. The finger snakes had no sense of privacy.\n\nShe got herself in order, feeling much better. Exercise calmed, made her world brighter. Ready for Redwing. Maybe.\n\nTen minutes later she rapped on his door. He was wedged behind his desk, leaving her more room in the narrow captain's cabin. His wall display showed the slowly passing infinities of Bowl landscapes\u2014at the moment, low mountain ranges in a low-grav region, with cottony cloud masses stacked above them. She had seen such clouds from below while swinging through the spindly trees on vines of thin, flexing strength. The clouds were nearly as tall as Earth's entire atmosphere, and from the ground looked like an ivory cliff that tapered away to a speck.\n\n\"Hope you're feeling better,\" Redwing, rising\u2014unusual for him, indeed\u2014to shake her hand. \"Admirable performance down there. I'd like to get some background from you, away from the others.\"\n\n\"I think if we met as a group and\u2014\"\n\n\"A unit commander always reports first.\" Redwing's crusty face wrinkled into a grin, but she knew beneath the wry, leathery look he was absolutely serious.\n\n\"Oh.\" Back in the navy we are, yessiree.\n\n\"Before we get to specifics, bring you up to speed, I want to know what it was like down there.\"\n\nShe was prepared for this, because the shipboard crew all asked the same thing. They had spent months eating canned food and breathing desiccated air, gazing down at a whole vast thing gliding by, like having a terrific top view and no way out of your cramped apartment.\n\nStill, she struggled to put the experience into words. Wonder, terror, hunger, spurts of fear, aching weariness fringed with a lacing anxiety that every time you closed your sticky eyes and fell into sweaty sleep, you could wake to find yourself about to die... \"A tailored wilderness. For days you forget you're not on an alien planet but on the skin of a furiously rotating machine. The star is always there and after a while, even after you've learned to sleep in shade and heat, you hate it. Darkness\u2014I can't tell you what a luxury it is to turn out the light. There's weather, for sure, lightning that seems to be sheeting yellow all around you, and the jet\u2014like a golden snake twisting across the sky. Always on the run, looking to see if something's coming up on your tail to eat you, going for days without a bath, running without water even, feeling your steps get lighter because you've lost weight without even noticing it, hunger being sometimes the only thing you can think about\u2014\"\n\nShe made herself stop. With the crew she had been able to hold back but here, with Redwing, she couldn't... and realized that something in the smile, his head nodding as she spoke on and on, the eyes dancing with interest, had made it happen. How did he do that? Maybe it was something you had to learn, from commanding ships all over the solar system.\n\n\"I know some of that,\" he said, face now open and eyes far away. \"You don't get to pick the nightmare that wakes you up at four A.M.\u2014it comes looking for you, again and again.\"\n\nThis was a startling moment, taking her unaware. He was a man in a hard place to be, and she read in his gentle downturned smile a rueful regret that he could not possibly, as captain, go down there.\n\nShe made herself sit up straight, regain some composure. Keep your smile in the upright and locked position. \"My mom used to say, a truly happy person is one who can enjoy the scenery on a detour.\"\n\nHe laughed, a hearty, full-throated roar in the metal echo chamber of his cabin. \"Good one! Damn true, this whole thing is a detour.\"\n\nThis last sentence came out of nowhere, with baritone notes of regret. He sat back and took a moment to see the mountain range far below slide away on the wall, a huge glimmering eggshell blue sea lapping against the mountains' slate gray slopes along a narrow beach.\n\nHe knows how to pace this conversation, let it breathe.\n\nHe swiveled back to gaze at her with deep blue, penetrating eyes. \"Tell me about... the food.\"\n\nShe held her breath for a long moment, comparing the bland, warm forgettable dishes she had wolfed down in ship's mess, realizing that while she ate eagerly it left no trace of memory. \"I... there was something we could shoot out of the trees, when we were desperate. A fat primate thing, in the low-grav region. Stringy meat, yellow fat, looked like a big roasted monkey, but when you'd gone two days without anything but a kind of thick-leaved grass, it was... heavenly.\"\n\n\"Taste human?\"\n\n\"How the hell would I know?\" Then she saw he was grinning, and laughed. \"Not that I would've cared.\"\n\n\"You could digest it?\"\n\n\"Surprisingly, yes. Of course, we had all the biotech compatibility injections and a handful of pills. I had all of us start taking them as soon as the aliens\u2014they call themselves the Folk, just like primitives on Earth\u2014gave us food. We held out on our own rations for a while, then I had us cook the live game they gave us\u2014\"\n\n\"Live?\"\n\n\"Yes. They were smart enough to let us prepare it our way, which they watched closely. We dispatched them with our lasers. Simmered some, with some herbs tossed in, it stayed down pretty well. But once, when we were hiding near somebody\u2014something\u2014searching for us in the tall tree region, we ate fish, raw. In fact, I had to be still and not give us away, afraid to get out my knife or laser, so I ate it while it was... alive.\"\n\n\"Not for long, I bet. Sashimi still moving.\"\n\n\"Unpleasant... for me and for the fish.\"\n\n\"You all lost weight.\"\n\n\"Even after eating yummy dried worms, very ripe, like sticky Jell-O. Live antlike things, as big as dogs in the low-grav zone. Crunchy embryos in the shell, tasted good but I felt horrid after it, dunno why. A fried scorpion-like thing, two tails. The head was bitter but I ate it anyway.\" She paused; it came back so easily.... \"Trying to forget that one. Bizarre, memorable.\"\n\nRedwing smiled fondly. \"Hey, I ate haggis once in Edinburgh. So... uh, thanks.\"\n\nShe blinked. Thanks for what? Then she saw; the yucky food made him yearn to go down there a little less. And he had gotten her to unload some, too, get some of it behind her. A ship's captain is always about moving on.\n\n\"So I wondered\u2014what kind of weaponry can they have down there? Gray goo bombs? Nerve flatteners? Old-style shaped charge with spinning flechettes?\"\n\n\"I didn't really see weapons.\"\n\n\"Um. Cliff did\u2014I'll get to that in a moment.\"\n\nCliff! The crew had been evasive about him and his team, but they did say the \"Cliff team\" seemed healthy and still free\u2014quite a tribute, they said, considering. She had thought to shooting back, Considering how we got snapped up right away?\u2014but didn't.\n\n\"Point is, what can we expect from them?\"\n\n\"I think they want to control this, keep us around\u2014preferably, in a nice, spacious prison like the low-grav one we were stuck in\u2014while they figure out who we are, and if they can use us.\"\n\n\"Use us? For what?\n\n\"Maybe make their big whirling machine work better? New tech?\u2014though it's hard to believe we could tell them anything. They built this\u2014\"\n\n\"You're sure?\"\n\n\"Well, they run it, anyway. It must be really old. Maybe somebody else built it? The big one who interrogated us, Memor, was evasive on that.\"\n\nHe frowned. \"Hiding something they don't want outsiders to know?\"\n\n\"Yes, it's a puzzle. Or maybe a really ancient mystery. I wonder if even the Folk don't know where the Bowl really comes from. They do know the terrain, though. There are life-forms that dazzle any biologist, some I couldn't figure out at all. Cliff must be in heaven\u2014he likes taxonomy. I filled up my digital photo files keeping track of the plants and weird animals. Some are bizarre, and others are kind of like Earthside, but changed. Larger, for one thing.\"\n\n\"Because the grav is less, point eight?\"\n\nShe nodded. \"That, yes. Could also be the island effect.\"\n\n\"Which is?...\"\n\n\"We see it Earthside. Small islands have smaller animals. The last mammoths lived on Siberian islands, the smallest of their kind because the resource base is less.\"\n\n\"So... continents here are sure bigger. Some are larger than Earth. So are oceans\u2014seas, I guess we should call them, they're shallow. I've studied them in close-up scan while you were down there.\" Redwing brightened. Here was something he knew and Beth didn't. He flashed pictures on the wall and she realized he had cooked up a slide show. He went through it eagerly, describing how and where he had found the images. He and Karl had worked up a Bowl version of longitude and latitude. Numbers marked each slide.\n\n\"So much open territory! Forests as big as North America, not a town anywhere. But cities the size of countries back home\u2014hell, bigger than our continents. I'd sure as hell like to know who made it, and how.\"\n\nBeth nodded. It had been an impressive show. \"The Folk may have built it, or know who did. They're unlike anything I've ever seen\u2014think of elephant-sized, two feet and a heavy tail, big eyes and mouths\u2014and feathers they flutter around all the time, like it's some kind of coded fan dance.\"\n\nHe grunted and frowned, which she took as encouragement. She knew she had to write a report, but telling it helped shape the story. Enthusiasm began to steal into her voice. \"They examined Tananareve for long times in a big machine that seemed, she said, to read everything in her body. Plus her mind, somehow. She could feel tingling all over her, sensations like quiet little sparks, she said. There were plenty of other smart aliens around, most with handlike things that Earth never evolved\u2014a sort of wriggly tentacle that split out into feelers, like you might see on an octopus that could make tools. They worked for the honcho\u2014the big Folk creature in charge, named Memor. Terrifying thing, when it loomed over you, huffing hot smelly air in your face. Memor was in charge, all right. Once I saw it\u2014her, whatever\u2014eat something that was still alive, a kind of crunchy armadillo the size of a pony. It bellowed as she chewed it up. Disgusting! But sights like that were just getting started\u2014\"\n\nRedwing gave her a concerned look. \"Um, if you could...\"\n\n\"Sorry, once I get started\u2014okay. It'll be in my report.\"\n\n\"Everything you recall. Anything could be vital; we just don't know enough.\"\n\nBeth nodded. It had all come rushing out, the pent-up emotions and thoughts of months on the ground, every day tense and wearing.... She took a deep breath. \"Anyway. This Memor seemed to read Tananareve and ask questions about how her mind worked, what she thought of, how it felt to think\u2014odd stuff.\"\n\nRedwing pursed his lips and looked down at the vast clouds coasting by far below. His wall screen amped the image to the max, so they both watched huge purple cloud-anvils towering over a seemingly endless sea. There were sand bars the size of the Rockies lounging in the sea's green shallows, like tan punctuation marks. Vegetation dotted them, and one dot she judged to be the size of Texas.\n\nShe had learned to let him have his silences, as he let her experience settle in with all the rest of what he knew. Beth sucked in the dry ship air and tried to recall the cloying thick, aromatic atmosphere they had wondered about, alien air they called it because of the syrupy way it filled your lungs with a heavy, cloying sweetness unlike any flower she had ever known. The smell was still on some of her carry-gear. Up here, in dry antiseptic rooms, she sniffed it and liked the aroma and body. Breathing it in, she felt something like nostalgia.\n\nRedwing nodded as if making a decision. \"You can review Cliff's messages\u2014some text, some voice. Short, to the point. Don't be alarmed by them. He had not much time to report in. Reception is bad, we should have sent you down with more robust comm.\"\n\n\"Our good comm gear was in the landers.\"\n\n\"Of course. That's how the Folk found out our operating frequencies, broadband patterns, encryption. For the landers and for the hand comms, too, damn it. So he and you could get through only a short while, then the Folk autoscreens went up and it was all fuzz.\"\n\n\"Look, Cap'n, we had no way of knowing\u2014\"\n\n\"I should've been more cautious.\" He shook his head abruptly, face pinched. \"I used the landing protocols we rehearsed Earthside\u2014simple stuff for an uninhabited planet. No defensive measures. I went by rote, when I should have been wary of anything like this\u2014an impossible machine churning through space, managing its own star to\u2014\"\n\nHe broke off, she saw, knowing he shouldn't vent his inner doubts to officers or crew. Yet it helped him, she was sure, and he needed it. A man like Redwing had spent his life wanting authority, getting some, then some more, all the time finding out how to make it work, how to move up a ladder everybody wanted to climb. Nobody had a captaincy forced on them. Nobody told them it meant keeping yourself to yourself for long years and decades and, for starships, the rest of your life.\n\nHe swiveled his chair away from the constant landscape sliding by and looked at her with an expression made rigid by force of will. \"Cliff described a mass slaughter. He was hurt\u2014not too bad, but he took days to even be able to call in. Wounds, fever, the cruds.\"\n\n\"We had the cruds a lot of the time,\" she said to be saying something, keep him from lapsing into a monologue again. This captain needs help. But then we all do.\n\n\"I got reports just this watch. From Cliff, pretty noisy. The Folk killed a whole damn city. Some kind of living blimp\u2014he sent two pictures, hard to believe even then. And Howard... died.\"\n\n\"Oh no. He was\u2014\"\n\n\"Always thought he was a little too inquisitive, couldn't move fast\u2014I down-wrote him in an operations report during crew training, but Command ignored me. He didn't come into a shelter fast enough, Cliff said. Got burned with a weapon tuned to our nervous system. Heats up the skin some, overloads the neurological system\u2014fries it, really. Pain like he'd never felt before, Cliff said.\"\n\nIt was Beth's turn to look away. \"We had it easy.\"\n\n\"But these 'ally aliens' as Cliff calls them, the Sil\u2014they had scavenged around in the blimp thing. Got some Folk comm gear they'd never seen before. Those Sil are smart. They got it running, broke the encryption barriers on the Folk message center, pried out all sorts of stuff they can use\u2014and something bigger than that. Lots bigger, that we can use. The Folk had a message, just came in recently, the tags said\u2014\" Redwing leaned across the desk, laced his hands together on it, spoke directly at her. \"\u2014from Glory.\"\n\nBeth had been in sympathetic mode, trying not to think about Cliff's wounds, Howard being fried, and all the rest\u2014but this made her snap out of it. \"Earthside never picked up a peep from Glory. No leakage, no ordinary surface EM traffic\u2014\"\n\n\"I know. This is plainly different, directed at Earth.\"\n\n\"How do you know?\"\n\n\"Here.\" He thumped his desk, and the wall turned from sliding perspectives of a tan grassland swept by waves the size of continents\u2014and became... a cartoon.\n\nLine drawings, vibrant color. Purple background. Traceries of yellow on the edges, twisting like snakes. A strange red-skinned asymmetric being with what looked like three arms stood alone, facing the viewer. It began a rhythmic move, arms rotating in their sockets in big, broad sweeps\u2014except the third, which somehow lashed up and down, then made a wide circular arc with a sharp snap at the end. Athletics? Beth thought. Or some diplomatic pose? Ritual? Kabuki theater among the stars?\n\nThe thing wore tight blue green sheath-clothes that showed muscles everywhere, bulging and pulsing. The covering seemed sprayed on, showing a big cluster of tubular\u2014genitalia? If so, male\u2014not between the legs but above them, where a human's belly button would be. They, too, bulged as she watched.\n\nThe skintight covering ran all over the body, including the wide gripping feet. But the arms and its head were exposed; the head was triangular and oddly ribbed. Two large black eyes. No discernible nose, but three big holes in the middle of the face, echoing the face's triangle, with big hairy black coronas around each hole like a weird round mustache. A large mouth with two rows of evenly spaced gray teeth.\n\nFor a moment the viewpoint closed in on the head, which looked like an Egyptian pyramid upside down\u2014ferocious, with mouth twisting, thin lips rippling with intricate fine muscles around the gray teeth, which kept clashing together. The front three teeth in both rows were pointed\u2014evil-looking things\u2014and the mouth had puffed-out lips to accommodate them.\n\n\"So far, just an introductory picture, looks like,\" Redwing said. \"No sound. But then we get action.\"\n\nBeth was still blinking in pure astonishment. Her father had centuries ago called this a whatthehell moment.... She had met uncountable aliens, fled from some, killed some, eaten many\u2014but this...\n\nThe viewing angle expanded, and walking in from the right was a... human. Beth gasped.\n\nThe man wore a blue skintight suit with a red cape, big head, black hair\u2014clearly a man, yes. Muscled, striding forward proudly\u2014and the alien third arm struck out, caught the human in the face. A nasty slap. The man staggered back. The alien made a half turn and thrashed the man, slamming him away and then grabbing him by his right shoulder, twisting him into full view. There was a large red S on the man's deep blue chest.\n\n\"Superman!\" Beth did not know whether to laugh or just gape. She did both.\n\nThe alien leaped, twisting in air, kicking Superman in the gut. He went down hard on the rocky ground. The graphics were good\u2014Beth could see Superman's shock, surprise, pain. Dust puffed up where he fell. Vigorously the alien leaped high, paused while it made more mouth-gestures directly toward the viewer\u2014and came down hard on top of Superman with obvious relish, slamming down with both big feet. Superman's mouth opened in shock and surprise, eyes bulging, showing white. The alien fanned its two arms, whipped the third one that seemed slim and sharp\u2014and brought it down on Superman's head. The lash brought blood streaming from Superman's left ear and\u2014incredibly, splashed big red gobbets on an imaginary window between the scene and the viewer. The blood ran down in rivulets while the alien raised all three arms into the air, head back.\n\nThe effect made Beth rock back, as if the blood had flown in her face. She gasped.\n\nPrancing, whip arm twirling, the alien proceeded to dance on Superman. It sent more kicks to the head and gut as the opportunity arose. The alien looked full at the viewer as it pranced, eyes even bigger. Its image swelled to fill the screen, and the eyes glowered at the viewer.\n\nStop.\n\nA long silence.\n\n\"Pretty clear message, I'd say,\" Redwing clasped hands across his belt and leaned back in his flex chair.\n\nBeth could not take her eyes from the alien head, its threatening expression frozen. \"They eavesdropped on something, TV I guess, or...\"\n\n\"And chose to send a message a child could understand: Stay away.\"\nSIXTEEN\n\nCliff had handed him a problem from hell. How to stop the Folk from killing a lot more of an alien species, to intervene with big things Redwing had never seen, minds unknown... or else do nothing. \"Nothing\" looked like the right answer, but he didn't have to like it.\n\nHe had the shipmind call up readings on this from the ancients available on the ship's database of all human cultures. These long-dead voices had never confronted any remotely similar problem, but came as close as humans could: Saint Augustine, Spinoza, Churchill, Lao Tzu, Kant, Aristotle, Niebuhr, Gandhi, King, Singh. Interesting, thick reading\u2014but it made him think about his life in perspective. Maybe he could use that if he survived this whole huge thing. But for now, alas... No help there.\n\nThe best solution was to get Cliff's team out of that place. Then the Folk would stop trying to capture or kill them. Bargaining could begin.\n\nThe brief comm burst Cliff had managed to get through to SunSeeker, fighting through the electromagnetic haze-screen the Folk had put up, gave the cartoon files and some optical spectral data that fit Glory exactly. No question where it came from.\n\nIt couldn't be a coincidence. The Glorians were sending the Bowl a threat. But it used imagery of Superman, of all things\u2014an antique \"superhero\" (he had to look the term up) from the expansionist phase of the Anglo-Saxon era. Technically, of course, that era was not over. It had merged with the larger economic unification of Earthside. English was the obvious unifying language\u2014larger, richer, with simple introductory grammar. Irregular verbs galore, of course, but by the time the interplanetary phase of economic expansion was well under way, there was no competition. Mandarin, Cantonese\u2014they came from a productive society, as did Hindi\u2014but nobody could write them well, and they didn't work simply with digital culture anyway. Plus the Chinese culture didn't have the flexibility of the Anglo structure. The other Asian cultures did a bit better, but English was as set into the world culture as the qwerty keyboard. History ruled.\n\nSo a comic book figure like Superman, his Pedia base said, fit with the modern social structure, too. Other archetypes like Dracula, Sherlock Holmes, Frankenstein had clear roles, but fit uncomfortably with the world culture. The other superheroes of the twencen were modeled on men like animals\u2014bats, spiders, apes. Superman, tellingly, was an alien. Yet he fit into human society seamlessly.\n\nSuperman's key assumption was that his disguise was just to put on glasses and business clothes and be an everyman. Then nobody, even Lois Lane\u2014a character that reminded Redwing of his ex-wife\u2014could spot him. Every man a Superman. What could be more obvious? Do your job, toe the line, the daily grind\u2014but all the time you are free to imagine yourself leaping over buildings, flying through the air, flattening the baddies. Maybe even getting a date with Lois.\n\nRedwing shook his head. Cultures could best be understood in the rearview mirror. Superman might work among the multitudes of Earthside, but such guiding archetypes were not what you needed in deep space. The interplanetary culture spawned Smoke, Ellipso, Whitethighs, and others. Such larger-than-life figures helped cultures understand themselves, turn their lives into stories.\n\nSo... Here among the worlds and stars, this was a frontier. Earthside hadn't had one in centuries.\n\nBut the aliens spoke in that antique visual language. They must have used big antennas to pick up all sorts of popular media, broadcast over hundreds of years. Then, apparently, they finally saw the Bowl headed toward them. So they sent a brush-off message, using the cartoons that swerved around language and slammed home the point. Aliens stomping on Superman, beating him up, kicks to his head and gut, the finishing glower straight into the viewer's face\u2014classic, in its way. Any chimpanzee would get that right away. Even a smart one with a starship.\n\nThere were intelligent, technological Glorians who knew something about images with power\u2014and they didn't want the Bowl to appear in their skies.\n\nWell, who would? It had immense mass and its own star in tow. It couldn't approach a planetary system without scrambling up planetary orbits. Coming to call meant the bull comes into your china shop and is in no hurry to leave.\n\nA warning was understandable. Threats, comic book or not, might work.\n\nBut... no curiosity? No desire to embrace the strange, the alien, the obviously huge technology the Bowl implied? What kind of aliens were these Glorians, anyway?\n\nBeth had said shakily, \"I need to think about this,\" and departed.\n\nA sharp rap startled Redwing. He glanced at his desk, which pulsed with a reminder color.\n\nKarl had knocked smartly on the door, right on time. Redwing got up and met him, shaking hands as he did sometimes with crew to show this conversation was more than ordinary. After all, the close quarters and endless waiting led, in classic fashion, to rumors, imaginary problems, and endless speculation.\n\n\"I carried forward those points you brought up,\" Karl began.\n\n\"You're done integrating the new crew?\"\n\n\"Nearly. They're slow, dazed. Some sleep pods didn't work just right, it seems.\"\n\n\"Anything serious medically?\"\n\n\"No, just slow recovery rates.\" Karl looked tired.\n\nRedwing knew that rumor-mongering went double for the newbies. Some of the freshly revived had the checked-my-actual-personality-at-the-door look of people absorbing and not able to react. It was a surprise, yes. Not Glory on the viewscreens, but an immense, whirling landscape. Redwing had decided to let them get into the work cycle, then get to know them, see what teams he could shape from them. Dealing with the Bowl to get what Redwing wanted was going to be a complex game.\n\nThey needed supplies of volatiles and fusion fuel catalysts, just to depart and head for Glory. That was only the beginning, though.\n\nBest to get things back on firm ground. He leaned forward, hands clasped on the desk. \"You and I need to have a clear understanding of how the dynamics of this Bowl and star system work. It may be the only leverage we have over the Folk.\"\n\n\"They've been running this place for a very long time,\" Karl said. \"I doubt it has any vulnerabilities.\"\n\n\"Start with that jet. You'd think they'd have reached cruising speed and been able to shut off the plasma jet by now, but never mind that\u2014\"\n\n\"They can't!\"\n\nRedwing looked skeptical. He liked playing this role, letting crew \"educate him\" and tumble out their ideas. While a lower-rank officer dealing with the myriad specialists a ship needed, he had learned that you could get to the point much faster this way. These were tech types first and crew members a distant second. \"Ummm... Maybe they can't.\"\n\nKarl rose to the bait. \"Look, a grad student can show that the Bowl isn't statically stable. I know, I checked with a shipmind nonlinear analysis, and I'm just an engineer.\"\n\n\"Why not?\"\n\n\"The Bowl's not in orbit around the star. Turn off the jet, the star draws it in by gravity. It hits the star.\"\n\n\"So the jet has to stay on.\"\n\n\"This whole thing is dynamically stable, not static\u2014same as we are when we walk. We take a step, fall forward, catch ourselves\u2014only way to get anywhere.\"\n\n\"So what makes the whole star-and-Bowl scheme work?\" Redwing had a hunch, but he liked to check it against somebody who really knew. It helped the intuition. Karl was just the type he needed.\n\n\"The jet comes off that glaring hot spot. The Bowl reflects a lot of the star's own sunlight on that spot, making the corona far hotter than you ever see on the surface of a star. Somehow\u2014here's the real magic trick\u2014the star's own magnetic field gets wound up in that spot. Notice the star's spinning\u2014so it generates magnetic fields deep in its core, a dynamo. That leaks out, forms the whole region dominated by the fields\u2014the magnetosphere\u2014and that hot spot draws field lines in, wraps them around the jet as it forms. Then the field takes off with the incredibly hot plasma, trapping that pressure in a wraparound like rubber bands\u2014and it all escapes the star. The magnetic field lines wrap around the plasma like tight invisible fingers, squeeze it, make it spurt out. The jet carries forward, slim as you like, straight for the Knothole\u2014and passes through. The jet thrust makes the whole damned thing move forward, star and Bowl and all.\"\n\n\"So?\" Redwing knew he could appear incisive by just asking the obvious next question, interrupting the headlong spinning out of a whole complex story.\n\nIt worked. Karl blinked, seemed to come out of his techno-daze. \"So... the magnetic fields hit the Bowl's fields\u2014\"\n\n\"What fields?\"\n\n\"The Bowl's a huge conductor, spinning fast, with electrical currents running in it. It makes its own magnetic fields. I checked the lander data from when the teams went down. Strong fields, even at the top of that deep atmosphere. Keeps cosmic rays away, sure, but its real reason is\u2014\"\n\nKarl blinked again and sensed he was going into lecture mode. Redwing just nodded. Keep 'em anxious but focused, his old cycle-ship commander had said. They never really notice you're leading them.\n\nKarl slowed. \"The Bowl mag fields, they catch the fields from the jet. I've got plenty of mag-depth photos of this. The Bowl shapes the jet and binds to it, both. That links the Bowl to the star. Of course, gravity's making the Bowl want to fall toward the star\u2014after all, it's not in orbit or anything, just spinning around. But it can't fall into the star\u2014there's a sort of dance between them. The star's running away, thanks to the steady push it gets from the jet. So the Bowl is chasing it. To make the ride less bumpy, the system has those nice magnetic fields, acting like rubber bands you can't break. See, magnetic fields always form closed loops.\"\n\n\"Why?\" Even Redwing knew this, but it was best to throw the occasional bone.\n\n\"Old Doc Maxwell. It's the law.\"\n\n\"So\u2014\"\n\nKarl jumped right in, as Redwing had known he would. \"The fields massage the Bowl, cushion minor excursions, smooth out the ride.\"\n\n\"So the Folk can't turn it off. Ever.\"\n\n\"Do that, the Bowl crashes. I estimate it'll take about a year to fall into the star. I'd love to see it\u2014gotta be spectacular.\"\n\n\"But it can't happen. Because of the jet. So\u2014how do we screw around with it?\"\n\nKarl blinked yet again, twice. \"But... why...\"\n\n\"We have people down there. Must be billions of smart aliens on the Bowl, too. We have to make a deal to get our people back. To get on to Glory.\"\n\nKarl looked at the Bowl view sliding by on the wall\u2014forestland now, dotted with twinkling small seas, whitecaps outlining some where a strong wind blew down from somber gray mountains. \"They've been safe for millions of years. Longer.\"\n\n\"How long?\"\n\n\"I don't know. But to make something like this\u2014you have to have some large-scale ambition in mind.\"\n\nRedwing looked skeptical. \"Touring the galaxy?\"\n\n\"While you get a permanent suntan, yes.\" Karl grinned. \"And never get cold.\"\n\nRedwing nodded. \"Never get cold\u2014maybe a motive? Not just a small thing like going interstellar, but never leaving your home?\"\n\nKarl thought awhile and Redwing let him. When Karl spoke, it was a whisper. \"Taking a whole culture, a world, so many species... on a ride that could last forever. Not just colonizing some planet. An eternal voyage. That's got to be it.\"\n\nRedwing shrugged. \"Over millions of years, your own species has got to change\u2014maybe go extinct.\"\n\n\"The whole thing will go unstable if you don't have somebody to do the tweaks, keep watch, fix accidents.\"\n\n\"For sure. Then there's cultural change. But you can't let the society decide the whole Bowl experiment is a bad idea. Then you die!\"\n\nKarl hadn't thought this way. Engineers don't, he mused, and then recalled that his three degrees were in electrical, mechanical, and astroengineering. Okay, usually. \"Look, Karl. A few hundred years ago, we called people savages because they pierced their ears, ballooned their lips, wore trinkets in their nose, cut their hair so it looked wild or had no hair at all. They did weird stuff, had strange noisy dances and rites, and tattooed their bodies. Then, when I was growing up, everybody called that stuff hip and fashionable.\"\n\n\"Uh, so?\"\n\nThe lands below were back to mountains and seas\u2014beautiful expanses, larger than the whole Earth\u2013Moon system. Redwing never tired of it all.... \"We can take cultural change, even stuff that comes back from our ancestors and looks odd. But we're expanding, moving out into the stars.\"\n\n\"Well, sure.\"\n\n\"And so are the Folk. I guess they can take tattoos. It's fashion, which means it's over by the time people like us even hear about it. But I doubt they can take big new religions or political mobs that want to, say, take over piloting this contraption. They can't allow that.\"\n\nKarl got it. He nodded eagerly. \"And we thought we knew what conservative meant.\"\n\n\"They can't risk the wrong kind of change. And that's exactly what we new-kid-on-the-block humans represent.\"\nPART V\n\nMIRROR FLOWERS\n\nA man who carries a cat by the tail learns something he can learn in no other way.\n\n\u2014MARK TWAIN\nSEVENTEEN\n\nCliff and his party followed Quert at an easy, loping pace. The lower gravity made long strides easy, but the humans could not match the ease of the Sil's fluid grace. There was no ground transport except the Sil city subway, but that had been damaged, too. Quert said it was intermittent and unreliable, \"Smoke go in there. And... some say... be worse things.\"\n\nThey made their way beyond the ruined Sil city and broke into open woodlands. It was a relief to suck in soft, moist air and just move, escape. No one looked back.\n\nThey paused on a short hill and Cliff could not resist a last perspective on the blasted landscape. Its once-proud ramparts and arches, its residential precincts, its lofty spires of what might have been elegant churches\u2014all burned or hammered down to rubble. The Folk had no mercy. Yet he could see rising from rubble the tan buildings they had watched self-forming with a quiet, eternal energy. Seen at a distance, the fresh shoots of new life moved like stop-motion videos, eager plants rising to begin anew a city that surely, in the immense history of the Bowl, had been rebuilt myriad times. Cliff sighed and clasped Irma to his side. \"It's coming back. Slow but steady.\"\n\n\"This place was made to replace itself. A technology that counts on having to regenerate. I wonder what it runs on.\"\n\n\"Solar energy, reprocessed waste\u2014did you see that molecular printer Quert used to make us your new carry-pack?\"\n\nShe nodded and shrugged the new pack, easing the straps. \"Great, some kind of light composite stuff. Made a molecule at a time, Quert said. It's built exactly like the old busted one. Minus the broken frame, from when I fell down.\"\n\nCliff shrugged. \"If you hadn't been down, that flame beam would've burned you.\"\n\n\"Yeah, lucky break.\" She puffed her overhanging hair back from her eyes, a classic gesture of bemused frustration. \"Dumb luck. Poor old Howard ran out of luck.\"\n\n\"Damn shame. He was always getting hurt, breaking something, even getting lost to go pee.\"\n\n\"Some people are like that. Crew selection was by Fleet merits, y'know\u2014not backpack experience. R\u00e9sum\u00e9s don't account for plain old bad luck that keeps coming back.\"\n\n\"Sure 'nuff\u2014a big mistake. Next starship I'm on, I'll remember that.\"\n\nShe laughed and punched him in the arm, which drew sidelong glances from Terry and Aybe. Even Quert noticed. Well, let 'em, Cliff thought. Not like it's been a lot of fun lately.\n\nThen they pressed on, turning their backs on the burgeoning city that would live again.\n\nQuert led the way, with other Sil flanking them. They all carried weapons, long slim tube launchers. Their faces were grim, focused, and they did not seem to tire.\n\nRelentless sunlight streamed down through the symphonic play of ivory clouds. Tall and cottony, they were so vast that parts of them were laced through with blue tinges of moist anvils. Clouds as anthologies: the anvils hanging in the soft mist of larger puffballs, lightning sheeting across denser, purple knots, all of it like separate cities of the sky, tapering away into the far heights. Here and there clots condensed out, their understories fading into rainfalls\u2014sheets of pale blue falling great distances, then absorbed back into the air before ever striking the Bowl.\n\nCliff said to Irma and Aybe, \"Relax into tourist mode,\" and they all chuckled, not because it was funny but because everyone needed an excuse to smile. They came into a flash of green, almost pornographically abundant in the smoky, almost rotting aroma of turned black earth, rains sweating down from passing squalls, air thickened with rich purpose. A vehicle purred past and from its big tailpipe a lush pale blue cloud gushed. Irma drew in a breath of it and said, \"You can almost smell dinosaurs in that. It smells like a fossil fuel.\"\n\nAybe sniffed. \"Probably ethanol, but it sure smells rich.\"\n\nNone of them had actually ever smelled the exhaust of a true oil burner, on an Earthside that was scrupulous about emissions. Only jet airplanes using turbines rated fossil fuel use, back when SunSeeker left the solar system. Cliff wondered if by now Earthside biotech had engineered anything like the skyfish here, living beasts that could float and fight.\n\nHe doubted it. What biological substrate could they start with to develop such bizarre forms? That made him consider how the Folk had ever engineered their skyfish. From some airborne floaters, found on some planet where thick air and light gravity made that an optimal path? Big, slow, made invulnerable by its size, like elephants or whales or a brontosaurus? This place is like a museum of other life-forms, he thought, but one that keeps evolving. Maybe that was part of the point of building the Bowl itself? An ongoing, moving experiment with more room than a million planets?\n\nThey entered a broad plain of short grass, and there was a trampled, much-traveled track stretching into the hazy distance. Straight up in the air, though, momentary openings between the towering clouds gave a dim vision of the Bowl hanging in a pale eggshell blue sky. Cliff watched the watery vision of huge lands shimmer, a vision from all the way across this solar system. Only it's not any solar system we ever envisioned, he thought. More like a huge contraption made of a system's parts. Back on SunSeeker before they came down, Fred the engineer type had estimated the Bowl's mass, and got more than Jupiter, more probably than there was in the Kuiper belt or the Oort cloud. Somebody had scavenged an entire expanse of space, maybe all the worlds that circled Wickramsingh's Star, to make this thing.\n\nAlong the trampled path, occasional Sil held out strings of fish, stringy rootlike vegetables, a gauzy plant like a haze of wire. He realized these were for sale, but of course, the humans had nothing like Sil cash. Passing these hawkers, making poor imitations of the Sil no no no eye-gestures, they went by. Here and there a Sil stepped forward, lowered its head, and held goods up, waving them toward the humans\u2014an offering. This struck Irma as an eye-widening surprise. Cliff knew enough to take some food, with eye-moves of thanks, and then wondered how to cook the food that began accumulating. All this occurred silently, for the Sil seemed to relish a gentle, still presence. It was usually hard to get them to talk at all, and when they did, they were terse.\n\nAcross the plain came small, darting vehicles sheathed in shiny silver metal. Some moved toward the humans, though most went their own way. A knot of about a dozen Sil cars eased up in the purring machines and shut them down. With proper greetings they got out to address Quert. They had a conversation taking at least twenty minutes.\n\nThat was long enough for the humans to sit near the cars and find out which of the gift foods they could eat raw. \"Hand meal\" the Sil called this. Sil talked while they ate. When Irma asked about that, Quert had consulted an electronic aid he sometimes used to translate, and said, \"Sportive verse.\" This apparently meant creating poetry, a ritual perhaps parallel to humans drinking alcohol and singing together.\n\nThey were hungry. There was a pleasant nutty spiral fruit that left a peppery taste. They ate it all and had moved on to a nearly rhomboid-shaped bittersweet fruit. Quert and three other Sil came over to the humans, doing the head-moves and eye-signals that always came before an important discussion. Cliff reflected on how much they had learned about Sil culture by simply watching their social cadences. Humans talked all the time, Quert had noted with genuine wonder, as though that were uncommon on the Bowl.\n\nQuert said, \"They gift movers to us.\"\n\n\"We are gift happy,\" Irma said, smiling and nodding. She was better at ferreting out the meanings of the clipped Sil sentences and echoing their manner. She kept track of the myriad eye- and head-gestures and tried to imitate them, though not always with much success. There had been some amusing errors, such as when she had inadvertently asked Quert if sex was part of their diet, or where the beds were to be, and then walked into the rather primitive male toilets. She could not then tell male from female Sil and had to be told, with furious elbow signals.\n\nThe small, squat vehicles were actually simple to drive. They used hands and feet, just as Earthside cars did, and ran on an auto-gear system with adjustable constraints, mostly apparently magnetic. Indeed, its propulsion seemed magnetic, but it never rose more than a meter above the broad plain. Everything here, even the homes, seemed powered by electromagnetic induction, through the Bowl's substructure. There were solar collectors everywhere, befitting a land where the sun always shone, and the self-shaping buildings were driven that way, too. Cliff could tell by the occasional tingling of electrical discharge that ran over his skin when he stood near the walls, as they surged up and formed elegant cusps and arches.\n\nQuert showed Cliff how to drive the magcar, seeming to insist it was a guest's privilege. That let him take the little thing out onto the broad plain, Quert in the copilot seat, and Irma and Aybe in the rather cramped rear seats. Their backpacks and gear went in racks on the roof, secured by a curious self-wrapping lattice that figured out its own way to secure the arrangement, tripped by a tiny tapping from Quert.\n\nThey headed on toward distant mountains, cloud-shrouded and mysterious. Quert then went into comm mode, using the inbuilt dash system to get in touch with other Sil, using a system Quert said the Folk could not intercept. Quert apparently had embedded acoustic receivers, for it peered ahead intently and subvocalized, face giving nothing away. Irma sat in the back, and the others were in another car, following close on the right side. Cliff took the odd magcar up to its highest speed as other car traffic thinned out. They were moving away from the Sil concentrations, but Cliff had no idea of their destination.\n\nHe did not notice nearby cars or anyone following until abruptly one drew up alongside them. It deftly came in and blocked them from the other human car. The two Sil inside did not look at him, but they matched exactly his velocity. Then the magcar started coming in closer. He thought nothing of it until they were only a car-length away. He slowed. They slowed. He sped up. So did they. Another magcar came in from his left, moving fast. Its driver also didn't even seem to notice the three cars moving now together. They all peered straight ahead. Maybe they're a guard party? he wondered.\n\nCloser, closer... Cliff had time to say, \"Quert\u2014Quert?\" interrupting the alien's concentration, its eyes slowly coming fully open, as if it had been in a trance. \"I think something's\u2014\"\n\nA third car came over fast from the left, slightly ahead. It slewed hard and set itself up exactly in front of their car.\n\nIrma said, \"Are these\u2014?\"\n\nThe lead car slowed, its big tail signal sliding in ruby red pulses across the back. Cliff had to step on the mag brakes, and the car hummed loudly. He tried to maneuver to the left, then right, but there was no room now, and then the car ahead braked harder.\n\nCliff slammed on the brakes. The three that had boxed him in hit theirs a few seconds later. The brake howl was a high skkkrrreeeee, all of them losing speed as fast as they could. The cars were identical, so they hardly separated at all as the howling deceleration threw Cliff forward. They all wore odd net belts that stopped Cliff from being heaved onto the windshield. His few seconds' lead in decelerating meant he was now about ten meters behind them all as they slid to a stop, throwing gray dust and the humming loud and shrill.\n\nIrma was saying something and Quert, too, but Cliff focused on the six Sil who jumped out of the magcars. They called short crisp orders to each other and reached into their workbelts. Going for weapons, Cliff thought. Not guards.\n\nThe Sil ran around their cars and formed an orderly bunch, intent on Cliff's car, shouting now. Quert gave its gravel growl and took off its web-belt. Irma gave an alarmed cry.\n\nThe only weapon we have, we're inside.\n\nCliff saw what he must do. He slammed on the acceleration and shot forward. The car shook as he hit the Sil. Impact scattered them across the blunt shiny hood. Bodies struck their windshield and rolled up it, tumbling over the roof\u2014dull thumps\u2014and Cliff kept his foot on the accelerator until just before they hit the forward car.\n\nThey slammed in hard and the magnetic bumper pushed them back, lessening the impact. Their magcar's hood crumpled. Alarms blared an odd hooting call in Cliff's ears. Quert cried out in surprise and Irma went silent.\n\n\"Okay?\" Cliff said, surprised at how mildly he said it. \"Irma? Quert?\"\n\n\"O-okay,\" Irma said. Coughed, gasped. Aybe said, \"What the\u2014?\"\n\nQuert caught Cliff's eye and gave the assent signal. Its mouth sagged open.\n\nHe had scooped up all the Sil. Some had rolled off to the side and others over the cabin. They had all absorbed the full hard impact of the car, giving off sharp, surprised cries. He watched where they had hit the plain. None bounced back up.\n\nThey wanted to grab us, maybe kill us. No negotiation. Went for their weapons.\n\nSome of them had gotten their odd little guns free and lay stretched out, guns in hand but arms not moving.\n\nCliff backed out, turning to his left so the car glided over the bodies on that side. They crunched beneath the magcar. He got ten meters behind the bodies and shifted. He moved forward very deliberately and ran over the ones sprawled on the right. Moving fast, he slewed to ride over the two in front. Each body nudged the car up, no more, but that brought the full pressure of the magcar down on them.\n\nHe knew the bumps meant smashed bones, organs, spurting gouts of fluids lost into the soil. Agony, screams, the light fading behind terrified eyes.\n\nNone of them moved as Cliff then backed all the way out and drove around the whole mess. No point in checking to see if anyone survived.\n\nIrma said, \"The other car's gotten free, too. Looks like they have a Sil driving.\"\n\n\"My mate,\" Quert said quietly. \"She fine. Drive hard.\" Cliff glanced at the alien, who seemed as quiet and calm as ever.\n\nTerry was in the other car and waved at them, holding thumbs-up. \"They must've done something similar,\" Aybe said quietly. \"Wasn't watching...\"\n\nCliff amped the acceleration and had them up to max speed by the time the cars and bodies were just a dot in his side rearview screen. He was surprised that he did not need to think much at all about what had happened. The three-car team had tried to grab those he cared about and were willing to use force to do it. That meant they had crossed a line.\n\nCliff had spent endless days stacking and processing bodies, and now knew he was not the same man. He had done what he had to and had not taken any time to think it through. Before he came down to the Bowl, he had been another sort of man entirely. This place had taught him a lot, and most of it he could not say but perhaps comprehended it better that way. It was in his nervous system now, experience digested and made part of himself.\n\nMaybe that was what Quert had. Indeed, maybe the Sil had it without having to learn. In the silence of the magcar he felt himself relax. The mountains ahead loomed large now beneath their mantle of anvil clouds, bellies ripe with purple richness, ready to rain as they climbed the slopes. Already he looked forward to that. He would get out of the car and let the falling big drops hammer him with their wealth and feel each moment for what it was, for the joy of it entire.\n\n\"Those wanted capture,\" Quert said.\n\n\"I figured that,\" Irma said. \"Killing us is easier.\"\n\n\"Our chances would be not good in their tender care,\" Cliff said.\n\n\"Give us to the Folk, show loyalty.\" Quert made a head-shrug.\n\n\"So... you killed them,\" Irma said.\n\nCliff nodded. \"Probably so.\"\n\nIrma let that ride and then said, \"They would have gotten in their cars and come after us.\"\n\nCliff thought that was obvious and kept his attention on their rearviews and the mountains ahead. No visible pursuit. He reminded himself that attack could easily come from above. A skyfish could be hovering a kilometer up and\u2014he glanced out the window\u2014not obvious until it was too late. Worrying isn't thinking, he thought, using a saying he had honed in the long, unending days of pursuit when they were first on the run across the Bowl. Perpetual alert could degenerate into a floating anxiety that robbed the mind of concentration, sent it skittering into pointless knots. Not returning to the same damn subject was a learned skill, he saw.\n\n\"Where do we go now?\" he said directly to Quert.\n\n\"Into cold.\"\nEIGHTEEN\n\nThey went under the mountains, not up them.\n\nBefore entering the underground maze, Cliff looked down through a short pass at the lands beyond the lofty mountains. Beyond lay the first mirror zone he had ever seen. Big hexagonal patterns gave some sparkling side-scatter of sunlight. They filled a valley and dotted the hills above. Lush vegetation filled the spaces between, but clearly most of the sunlight reflected back at the star. This was how the Bowl fueled the jet that boiled up from the hot arc light inferno at the center of the stellar disk. Expanses of mirrors, incomprehensible in scale, focused on the central fury. Somehow, the SunSeeker engineers said, magnetic fields got drawn into the perpetual hellhole. These fed outward with the jet as it escaped the focal point. The brilliant plasma billowed out at its base, and then the magnetic fields gripping it in rubbery embrace disciplined the flow, narrowing it. By the time the luminous jet reached the Bowl's Knothole, it passed through easily without brushing the heavily armored walls.\n\nAs he watched the enormous sheets of reflecting metal in the distance, Cliff mused that this was how the star provided its own thrust, from sunlight that first bounced off the hexagonal mirrors, returned to its parent source, and propelled the jet. Riding on light, he thought, and held his phone up to the star itself, letting the device consider it. In a moment, the back panel said\n\nK2 STAR. SIMILAR TO EPSILON ERIDANI (K2 V). INTERMEDIATE IN SIZE BETWEEN RED M-TYPE MAIN-SEQUENCE STARS AND YELLOW G-TYPE MAIN-SEQUENCE STARS.\n\nYet he recalled the watch officer who revived him had said it was an F star. It had turned out later that the spectrograph was saturated by the hot spot glare, and got its signatures wrong. Classic field error.\n\nAnd indeed the star seen through the phone's polarizer was a troubled disk, speckled by dark blots that circled the base where the jet blossomed. The whole star rotated around the jet base, which meant the builders had started their mammoth final touch there, perching the Bowl as a cup high above the original star's pole. Fascinating to consider\u2014\n\n\"Come!\" Cliff noticed Quert glance back at him with irritation, eyes jouncing in the Sil way. He rushed to catch up with the others.\n\nTheir party neared the underground labyrinth and found they were not alone. There were zigzag trees in dense blue green forests near the entrance. Sil moved under the canopy, bands trotting with deft speed. They kept to well-defined bunches, entering the weaving corridors under the stony flanks. The corridor's external locks yawned. Even in the rock hallways, yellow orange plants hung, emitting light to guide the constant line of Sils and humans. The Sil barely glanced at the humans. Quert and mate moved together in the swift shuffle Sil used, like loping in light gravity, as easy as swimming in air. All in silence.\n\nCliff saw as they fled that many Sils had small, betraying injuries. Parts missing\u2014splayed knobby fingers with one gone, just a blank space of gnarled red skin. A conical Sil ear half sheared away. Marvelous purple-irised eyes clouded by some past collision with life. Mottled skin; scars adorning slim legs, feet, inflamed two-step joints that served as elbows in their arms; faces sporting red scars that wrapped around as though some enemy had used a curved blade. Cliff felt oddly embarrassed at the humans' smooth clear skins, unmarked by a life of labor and hardship, or battle and disaster. Without even thinking about it, the humans paraded around with skins and sturdy limbs that spoke of city comforts, the easy life away from fear and pain, a softness not earned.\n\nThe unseen Sil damage was perhaps more lasting.\n\nHe watched Irma as they sped down internal corridors of the Bowl, following Quert and its team along the gradual downward slope. She was changed, subdued and reflective. Her eyes peered ahead but were focused on some internal scene. He recognized the symptoms because he had known them, back there amid the wholesale slaughter of the Sil. She had announced his own blunted responses to him, using her jargon\u2014diminished affect, emotional isolation, a thousand-meter stare, a general emotional numbness, stress disorder.\n\nNow it visited her. Maybe Howard's death had done it, tipped her over the edge. Or the fast way Cliff had crushed the Sil who wanted to grab them.\n\nHe thought of this as they kept their steady pace, moving away from the big thick doors of what seemed to be the occasional air lock. Since he and Irma started having sex\u2014neither of them called it lovemaking, and in a fundamental way, it wasn't\u2014they had drawn closer. The other team members had seen that, and aside from a few wry references, nobody said much about it, or seemed to let it irk them. They were a field team, not a social circle. Howard's death had made that clear enough.\n\nHe watched Irma's concentrated expression, ever alert to what lay ahead, but clearly introspective. He cared about her now and had to understand what she was going through. They had lost Howard in a way nobody saw coming, and for Cliff there were no afterthoughts, because he knew he could have done nothing different. In the sudden deadly moments, everyone was truly on their own.\n\nMaybe Irma didn't see that yet. Something would have broken her sooner or later. She would have come up against some hammering event that changed how she saw the world. If she had stayed Earthside, she might have gone into late old age before it happened. The ones with no give, the ones with the carefully guarded, clear-skinned little porcelain selves, shatter in the end. Some chips and splinters get lost, so that when mended, little fracture lines show. Nobody gets through life immune to the hard collisions. The blackness always follows a step or two behind you, hand raised to touch you on the shoulder. That tap, when it comes, shakes you and hastens your step. When the indifferent world breaks your illusions, that shattering takes something out of your own inner cosmos. Something dies within. Irma will never fit together quite so well again. Neither will I, of course.\n\nThey came through another of the bulky air locks, and when the intermediate chamber closed, Cliff saw that their escort Sil were the only ones left with the four humans. The fleeing Sil had gone elsewhere.\n\nAt the other side, the cool, clammy corridor sloped steeper still, and now they passed into a different kind of passageway. The flooring became transparent and then the walls. The orange glow of luminous plants dimmed because there were few of them on the ceiling. Through the floor he could see nothing but black and then abruptly, as they passed a ribbed steel seam\u2014stars. Wheeling slowly across their view through walls and floor, red and blue and yellow.\n\n\"Ah!\" Aybe said. Irma sighed. Quert made the gesture of approval and eye-bulge.\n\n\"We're on the outside of the Bowl,\" Cliff said needlessly, hearing the joy in his voice at the same moment he noticed the air before him fog with his breath.\n\nThe wheeling sky lit a twilight world.\n\nThey all stood and took it in. The whispering drone of the airflow masked any sounds that might come from the outside world. They stood on a pathway looking up at the Bowl skin, visible in starlight through cylindrical walls transparent in all directions. Their passage stretched into the distance, below a flat plane above them that even looked cold, a land showing silver ice and black ribbed lines that marched away like longitudes and latitudes.\n\n\"Ice and iron,\" Irma said.\n\nBetween the black support struts was a rumpled terrain of dirty ice. The stars moved in lazy arcs above. A few craters pocked the ice, broken by strands of black rock and\u2014\n\nGlimmers on the plain. Cliff turned and looked behind them, where the long shadows of a quick dawn stretched. And sharp diamonds sparkled white and hard.\n\n\"Reading 152 K in starlight from that surface,\" Aybe said, peering at his all-purpose detector\/phone\/computer.\n\n\"Nearly as cold as the Oort cloud,\" Terry said. \"But why is there a tube to take people\u2014well, Sil\u2014up above the Bowl skin?\"\n\nQuert said nothing.\n\nIrma pointed to bright points of light winking on and, after a few seconds, off. \"It's always dark here, just starlight. Maybe that's mica reflecting from rock?\"\n\n\"Too bright,\" Terry said.\n\nA flash came from nearby. They turned and looked at a pinnacle that forked up from the silvery plain below. \"A... flower,\" Terry whispered.\n\nFronds spread up from a gnarled base, which itself sat firmly on the icy crust. Light green leaves speared up, tilted toward them. \"A paraboloid plant,\" Aybe said.\n\nThe thing was at least five meters long and curved upward to shape a graceful cup made of glossy, polished segments. The plant turned steadily as they watched, and as the direct focus of it swept over them, the reflected beam was like a blue-tinged spotlight.\n\nIrma looked over her shoulder and said, \"It's tracking that big blue star.\"\n\nThe plant turned steadily away and Aybe said, \"Look down at the focus point.\" Where the glassy frond skins narrowed down, they became translucent, tight, and stretched. The starlight collected all along the parabolic curve, about a meter on a side.\n\nCliff close-upped it in his binocs and made out an intricate tan-colored pattern of lacy veins. \"Chloroplasts working in this cold? Impossible.\"\n\n\"It's not so cold at the focus, I bet. That's the point of concentrating starlight,\" Irma said. She gestured at the horizon, which seemed sharp even though it must have been thousands of kilometers away. \"A whole damn biosphere in vacuum.\"\n\n\"Running on just starshine?\" Terry asked. \"Not much energy there.\"\n\n\"So this plant evolved to work like an antenna,\" Aybe said. \"They live here, hanging upside down on the outer edge of the Bowl.\"\n\n\"Where did a star flower evolve?\" Irma asked wistfully. They saw now the thick dark stalk that supported and held the flower, swiveling it as the Bowl's fast rotation swept stars across the sky. \"To track starlight and digest it.\"\n\nAybe snorted. \"Life evolving in vacuum?\"\n\nCliff noticed that Quert was letting them work through this.\n\n\"Doing its chemistry by... starlight?\" Disbelief made Aybe grimace. \"How's that happen?\"\n\n\"Folk bring,\" Quert said.\n\n\"From were?\" Terry asked. \"Why?\"\n\nQuert paused and struggled with the language problem, eyes jittery and trying to convey nuances, Cliff thought, that were simply beyond human capacities. \"Light life we term them. Here when we came. Learned to get out... live from ice... find star.\"\n\nIrma said, \"Maybe they started in a warm core of an asteroid? Or iceteriod? Got to the surface and used sunlight? Far out from its star, maybe no star at all nearby. Survived. Made leaves to be sunlight concentrators. So then parabola flowers just evolved, out in the dark.\"\n\n\"Long time,\" Quert said.\n\nIrma shrugged. \"Maybe a long way from a star, too. So the Bowl comes by, grabs some? But... why?\"\n\nCliff watched across the flat plain and, yes, glimmers came from everywhere as\u2014he glanced back\u2014stars rose and the light-seeking flowers tracked them. Or one of them. The slow steady sway of the focusing plants swept the sky, selected the brightest, fixed on it. The big flowers locked on a bright blue-white star. Light vampires, Cliff thought.\n\nHe judged the humans and Sil stood perhaps a kilometer or two above the Bowl's outer shell, looking down at a wonderland of deep cold night. Yet it lived. He watched a forest of strange, attentive life-forms that tracked across the moving sky, clinging to the outer skin of this whirling top. All this cold empire\u2014stretching far away, perhaps around the entire Bowl\u2014worked on, as it moved through starfields and brought heat to kindle their own chemistry. An entire vast ecology lurked here. SunSeeker had flown by it and seen none of this, Cliff recalled. The whole Bowl was so striking, nobody registered details. They had taken the huge ribbed outer structures to be the mechanical substructure it seemed. Nobody noticed icefields or plants; they were on too small a scale.\n\nHe close-upped some of the points of light and saw shiny emerald sheets moving all together, following the brightest star visible. They never saw the star that drove the Bowl, of course, only the eternal spinning night. There were translucent football cores at their central focus. In a nearby parabolic flower, he could make out how the filmy football frothed with activity at the focus\u2014bubbles streaming, glinting flashes tracing out veins of flowing fluids. Momentary Earthly levels of warmth and chemistry, from hard bright dots that crept across a cold black sky. Flowers rooted in ice, hanging under the centrifugal grav. Driven by evolution that didn't mind operating without an atmosphere, in deep cold and somber dark. Always, everywhere, evolution never slept.\n\nIrma said as they moved along the transparent tube corridor, \"Y'know, we've found piezophiles that thrive under extreme ocean pressure, and halophiles grow in high salt concentrations. This isn't all that much stranger.\"\n\nAybe said, \"I wonder if they cover the whole outer surface. They could be the most common form of life in the Bowl.\"\n\nTerry pointed. \"Maybe even more than we thought.\"\n\nThey gaped. Terry said, \"Like a... cobweb. Stretching up.\" The thing hung on several stringy tendons that sprouted from an icefield in the distance. Their eyes had adjusted so even in starlight they could make out five sturdy arms of interlaced strands. It climbed away from the Bowl and into the inky sky, and all across it were more of the flowers, their heads slowly turning to track the brightest blue-white point of light above. It narrowed as it extended and cross struts met branches to frame the huge array of emerald flowers. These were larger than the ones on the ground. The colossal tree tapered as it reached out.\n\n\"A cold ecology,\" Terry said. \"The flip side of the Bowl's constant sunlight. A steady night.\"\n\nIrma asked Quert, \"Why do the Folk need this?\"\n\n\"Soft fur, sharp claws. Same animal.\"\n\nThis seemed enigmatic to Cliff, so he said, \"They get something from it\u2014what?\"\n\n\"Their past.\" Quert's slim face struggled for the right translation. In the dim starlight, the alien face showed its seams, its lines drawn by tragedy. He reached for his mate, a willowy Sil who seldom uttered a word, but whose eyes slid and danced expressively. She clasped Quert to her, they embraced, and there was much eye movement between them. Apparently such signals were more intimate and effective among Sil\u2014and certainly so, compared to the talky humans.\n\nCliff had learned to look away at such moments; Sil had a different code for privacy and display, and apparently did not mind expressing emotional intimacy in view of others. Cliff was not used to it, and wondered if he ever would be. Quert turned from its mate and nodded toward the cold fields of paraboloid flowers. \"Soft fur of Folk.\"\n\nQuert turned back to the humans and visibly made itself stand firmly, looking at them all. Speaking slowly, to let its inboard translation training give it the human words, Quert said, \"The plants are always here. Stars power them. They store. Always Bowl skin is cold. This be\u2014\" Quert gave a sweeping gesture, eye-moves, and said in a whispery tone, \"sacred memory.\"\n\nIrma said, \"You mean their... data store?\"\n\n\"History,\" Quert said. \"Big history. Sil want to read it. You can help?\"\nPART VI\n\nTHE DEEP\n\nThe Mind, that Ocean where each kind\n\nDoes streight its own resemblance find;\n\nYet it creates, transcending these,\n\nFar other Worlds, and other Seas.\n\n\u2014ANDREW MARVELL\nNINETEEN\n\nAs soon as Memor sat down, she noted that the Late Invader Tananareve was carefully watching the bulk of Contriver Bemor settle into place. Bulging eyes, lips tight-pressed and white, body tensed as if ready to flee\u2014Tananareve showed the classic primate fear signals.\n\nFair enough; being the smallest creature in the ample cavern, more slight even than Serf-Ones, must draw up primordial dreads of being trampled. Memor tossed Tananareve some glossy sweatfruit to ease her trembling. She took it, bit, considered the taste. Gave a small smile. No sign of gratitude, however.\n\nIntelligence generally emerged on worlds only after earlier forms exploited the advantages of being large, slow, and stupid. Size was a ready defense inspiring no selection pressure toward more complex neuro systems and forward-seeing capability. Indeed, Memor had learned about such creatures as Tananareve in her study immersions. They were among the class that built models of their external world, all the better to predict where food might lie, or what predators would do, and still later, what others of their kind would think of them. Somewhere along that axis of change their internal models learned that other creatures also had models running behind their anxious eyes. Thus emerged advanced societies.\n\n\"We merely wish to question you about aspects of your species,\" Memor said as a preliminary.\n\n\"That last session\u2014where you 'slapped' me with that pain gun? Was that asking questions?\"\n\n\"You understand, we were developing\u2014quite successfully, I must remark\u2014a tool to use in making contact with the others of your kind.\"\n\n\"They're still alive?\" The primate seemed to honestly doubt.\n\n\"Of course. They are taking their pleasure with travel about our vast lands.\"\n\n\"You haven't caught them, have you?\"\n\nOne of Tananareve's least attractive qualities, as a medium-level intelligence, was her way of leaping ahead in a discussion.\n\n\"We have not exerted sufficient effort to capture them, if that is what you mean. They did elude us at the very moment we took custody of you Late Visitors. We decided to let them remain at large, as experience of our wonders is the best lesson we can give.\"\n\n\"Do you understand our word 'smug'?\"\n\n\"I do. Our reading of your entire dictionary\u2014both active that you use, and passive that you merely recognize\u2014shows you have levels of nuance.\"\n\nMemor had meant this as a compliment, but Tananareve gave a dry little cackle that meant derision.\n\n\"I think you should consider our relative status before invoking your 'smug' word.\"\n\n\"Ummm. Smug is as smug does.\"\n\nThis elliptical remark brought a dismissive rumble from Bemor. Memor's twin, though still held at the male First Life, let his words sprawl forward, languid, as if he wished the small audience to savor them. \"We desire your counsel, little smart monkey. Your fellows have done harm to several castes, from Serf Prime to even a few at the lower rungs of the Folk. All this\u2014\" Abruptly Bemor belched out a bass snarl. \"\u2014because they would not submit to diplomatic engagements.\"\n\nTananareve laughed again. \"Loud bluster is still just bluster.\"\n\nMemor admired how Bemor did not allow emotion to flare further in his speech. This was evidence of an Undermind fully and well integrated, unlike the turmoil Memor felt bubbling up from her own. His voice and feather display suddenly smoothed, becoming a cool refrain. \"I wish you all now to focus upon our slow, steady response to the Glorian crisis. This goal we have long sought, for it is the plentiful world long observed but never understood\u2014and so we pursue it.\"\n\n\"Because we seek the origin of the gravitational messages,\" Asenath interjected. \"And now, the electromagnetic sendings from Glory are so simple, we can at least decipher those. Yet they do not speak to us.\"\n\nBemor allowed this interruption, though only marginally within conversation protocols, and gave a feather-rush of agreement. \"Indeed. As we approach, suddenly these Late Invaders appear in our skies. So arrive the primates in their adroitly engineered magnetic funnel fusion rammer\u2014and we receive a message from our destination. The simple drawings carried in electromagnetic codings are of the primates, not of the Bowl. These two events are not coincidences. They come so very close together in the great abyss of galactic time.\" Bemor reclined in his chute, easing his bulk. \"The Glorians convey a strange warning message. As Memor noted, they warn away these smart monkeys, but not we of the Bowl. So we must act. The vectors of our circumstance demand so.\"\n\nMemor turned to Tananareve. \"Your expedition knew none of this?\"\n\n\"Right,\" Tananareve said, eyeing them both warily. \"Your\u2014what do you call it?\u2014Bowl, that was enough.\"\n\nMemor began, \"Their story is that they did not suspect our presence or trajectory. As well, their ship lacked supplies\u2014\"\n\n\"I know all that.\" Bemor gave a feather-fan shrug. \"And their star ramship rode a prow of ionization that absorbed the microwave emissions we saw, so they could not have received them in flight. Their own communications are simple digital amplitude-modulated laser beams\u2014and those are directed back toward their star, not ahead.\"\n\nHe waved an arm-fan at Tananareve. \"You have said your ship did not receive messages from your home world for a long time, then did. Why?\"\n\n\"Political instability, we think. We did send reports, but apparently our people went through a phase of no interest in the interstellar expeditions.\" She sat stiffly, Memor noted, as though reluctant to admit this.\n\nBemor looked skeptical, his eyes turned upward derisively\u2014though Memor knew Tananareve could not interpret this. \"Why this lack of concern?\"\n\nBemor saw this primate was unable to follow their discourse, and so waxed prolific in his remarks. Memor cocked a scarlet at him in ironic interest, for this was unusual for him. Bemor said, \"We have only a few long-flight expeditions, such as this one. Most are from stars we pass nearby, who see us in their night sky. Those mount an expedition, those who have interplanetary abilities. In that sense, we inspire progress among slumbering civilizations, simply by appearing to them in passing. Those that have arrived had great trouble living in the biospheres they found. Microbial mismatches, food-production difficulties, and some unknown health problems.\"\n\n\"But we did receive a message about the time we discovered your... Bowl.\"\n\nTananareve was still edgy, and yielded this information only, Memor saw, because she feared Bemor. Something about an inherent caution with males? Bemor's rank musk was a bit overpowering. Or had the earlier pain gun incident made this primate more willing to cooperate? If so, it had been a good move.\n\n\"Ah. The primates did not expect to receive signals from Glory, suggesting that this is their first attempt to reach that star. So\u2014\" Bemor turned to Tananareve and whispered in her tongue. \"\u2014I hope you are telling true?\"\n\nShe returned his gaze. \"Right, we're the first expedition. Your Bowl... We knew none of this.\"\n\n\"You had no plan when you invaded our paradise?\"\n\nTananareve snorted. \"The team I was in, Beth Marble's team\u2014until we escaped, we had as much control over what happened as a kitten does in a clothes dryer. Cliff's team is showing you what we can do, I hear.\"\n\nBemor gave a bemused eye-flutter with his delicate purple fringe. \"I saw in your vessel a high level of ingenuity, more than expected of First Stage intelligences.\"\n\n\"Which is...?\n\n\"Curiosity, as you display in that admirably simple phrase. Artifice in magnetic engineering, particularly the ingenious flux conservation mechanism in your scoop. We have studied it, following the fluorescence of decaying ions, and so mapped your magnetic artifice. Your configuration can navigate on the skimpy ion density gathered from our star. Admirable!\"\n\nTananareve blinked, unsure how to respond. Memor began, \"I, too, am surprised that you manage to\u2014\"\n\n\"Moving on,\" Bemor said, turning away from Tananareve and Memor alike, \"I believe you, Asenath, have questions for the primate?\"\n\nAsenath fluttered forward\u2014glad of some attention, finally, Memor guessed. She questioned Tananareve, with Memor supervising occasionally, and learned nothing new. Bemor became bored. They were still close enough in manner\u2014since, after all, they shared the same genetics\u2014for Memor to know that Bemor was remaining politely present, but in fact was importing signals from elsewhere in the Citadel. Perhaps from superiors?\n\n\"This Late Invader is most useful for studies of the structure of her mind,\" Memor said, trying to introduce what was for her the most original Late Invader trait, their submerged and unreachable unconscious.\n\nBut Asenath went on, her agenda becoming apparent. \"The message from Glory is aimed at primates. The Glorians think primates are running the Bowl!\"\n\nCackles, hoots, coughs, and murmurs. General hilarity, even among the assistants, who normally suppressed any show. \"Good!\" Asenath said. \"Let them keep that misapprehension. Make the true rulers, ourselves, unpredictable.\"\n\n\"We surely are that,\" Bemor said sardonically. Yet something in his tone conveyed ironic skepticism.\n\nAsenath made a submission-display flutter, but it was unconvincing. \"Ideal setting for an entire suite of deception-maneuvers, yes. We will need cooperation of the primates to bring this off.\"\n\nBemor turned to the primate and said in its tongue, \"You follow this?\"\n\nMemor was surprised that Bemor articulated the alien fricative consonants quite well, directing breath with his tongue over the sharp edge of the teeth and into the capture hollows of his cheeks. It gave Bemor a solemn, echoing way of pronouncing the rather simple constructions the primates could manage. Memor had taken several sleep-times to master that, and her words still came out reedy and thin. Worse, the primate understood Bemor immediately, saying, \"I don't know your language.\"\n\nSo Bemor gave a guarded version of their conversation, keeping it minimal, giving away nothing, omitting of course anything the primate could use. Artfully done, Memor had to admit.\n\nTananareve's first comment was a question. \"What about the light-speed problem?\"\n\nBemor said, \"We think long. Perhaps few of us will live to arrive near Glory.\"\n\n\"So you want to reply to their signal? Deceive them?\"\n\nMemor felt the primate showed insufficient respect for their company, but Asenath chose that moment to recover some role in the conversation. \"My team is putting together a response for Glory. No great hurry, but there may be a time limit.\"\n\nTananareve shot back, \"What if the Glorians send out an exploring expedition of their own?\"\n\n\"We can surely see it well in advance and defend properly,\" Asenath said with a fan-flutter in ivory that said, Such is obvious.\n\n\"You know about the gravity waves, right?\"\n\nBemor said, \"You imply, we should be wary of what weapons might they have?\"\n\nTananareve stood, stretched, plucked some sweatfruit from an ample bowl. A show of indifference? Perhaps this was all the primate could do, since it could not give feather displays or more subtle signals. With a mouth partly full of the fruit\u2014a grave social error for the Folk\u2014she said, \"Well, I sure would be.\"\n\n\"I believe,\" Asenath said, \"and Contriver Bemor may amend this, that the Lambda Spear can be revived?\"\n\nBemor made a ring-show of blue and green, meaning \"yes,\" for he knew the primate could not grasp this.\n\n\"What's that?\" Tananareve said.\n\n\"It is a truly terrible device, able to alter the fundamental constants of a small region of space-time, upon command,\" Memor put in.\n\nHer eyes widened. \"You use this... how?\"\n\n\"With great care, obviously,\" Bemor said. \"We can project such an effect only over long distances, so to avoid being in the realm affected. It is appropriate for defense on a system-wide scale.\"\n\n\"It comes to us,\" Memor added, \"from the Time of Terror.\"\n\n\"I'd love to hear the story,\" Tananareve said.\n\n\"I can show you a worked example of how we avoid such dark times, soon enough,\" Asenath said with a mild feather-rustle. \"I have an appointment at a Justice Rendering. Duty summons.\"\nTWENTY\n\nCliff and the others were glad to get back into the warmer precincts of the Bowl underground. They rested in a large view space that gave them warmth, yet through a broad portal gave a closer view of the \"vacuum flowers,\" as Irma termed them. They ate the food they carried, and the Sil leading them brought water from a small delivery system lodged in the hard rock walls. The Bowl's outer hull was intricately woven through with passages, rooms, narrow little living quarters, and shops for what looked like repairs. As well, they passed by warrens that seemed to be where the finger snakes lived and worked. In some of the shops, snakes wearing harnesses labored at rack arrays, doing metal and electronics work. They were intense little creatures of glistening, gunmetal blue skin, beady eyes focused at close range on implements usually smaller than a finger\u2014a human finger, not the bigger boneless ones the snakes used.\n\n\"Y'know,\" Aybe said, \"it's kind of reassuring that in this incredible place, they're making flanges and hex joints, pressure sleeves and shafts with ball joints.\"\n\n\"Engineering,\" Terry said, \"is a universal.\"\n\nSome of the snake teams were working now on a large, intricate wall. They worked with a fevered energy, clacking and hissing to each other and slithering adroitly over copper arrays. This wall lay behind where the humans watched the dim landscape of the hull. Hull ice was thick here, and vacuum flowers lapped against the transparent portal. Cliff touched the window and had to snatch his hand away at a sudden sharp pain. He feared it was so cold, his fingers would freeze to it. Quert had said there were multiple vacuum layers in these transparent walls, but the cutting cold came through.\n\n\"That's it,\" Aybe said, \"these corridors are below the mirror zone. We're at the edge of a big mirror area, too. This whole section of the Bowl must be chilly.\"\n\nIt seemed so. So the land beyond was extremely cold, dotted with rock that formed roofs over areas of gray ice steeped in dark. Following Quert's advice, Irma played her laser beam, set on dispersed mode, into those dark spaces. In this flashlight mode, they were surprised to see odd, ivory-colored things moving with agonizing slowness.\n\nAybe asked what these were. \"On our way here we saw bizarre life-forms feeding on ice, but those\u2014\"\n\nIrma said, \"Those slow creatures with mandibles and eyestalks, yes\u2014like lobsters, but living in high vacuum and low temperatures.\"\n\nTerry eyed the moving gray things. \"These shapes are amorphous. More like moving fluids.\"\n\n\"Ice life,\" Quert said. \"Kin to ice minds.\"\n\nIrma said, \"So, ah... You brought us here to...\"\n\nQuert let the silence lengthen, then said, \"Sil want speak.\"\n\n\"To...?\"\n\n\"Ice minds.\"\n\n\"What can we do?\" Irma asked.\n\n\"Ice minds speak to you.\" Quert made eye-moves that might imply hope or expectation; it was still hard to tell.\n\n\"Won't they speak to you?\" Terry asked.\n\n\"Not speak Adopted.\"\n\nIrma said, \"You mean, species brought onboard the Bowl? Why not?\"\n\n\"Ice minds old. Want only new.\"\n\n\"Y'know, those blobs in the shadows are moving, together. Toward us,\" Aybe said.\n\n\"Watchers,\" Quert said. \"Allied with ice minds.\"\n\nCliff said, \"So you were ignored before\u2014,\" and saw that now the vacuum flowers were opening and turning. \"Why... why are those doing\u2014?\"\n\nQuert gestured at the vacuum flowers that abandoned their slow sweep of the sky, dutifully tracking nearby stars for their starlight. They rotated on their pivot roots toward this transparent wall.\n\nThe company fell silent as the flowers began to open fully, from their tight paraboloid shapes that focused sunlight on their inner chemistry. Slowly they nosed toward the wall where humans and Sil watched. As they did so, they blossomed into broad white expanses, each several meters across.\n\n\"They're really large,\" Irma said. \"Still hard to imagine, plants that can live in vacuum, and bring in starlight from over a large area. To feed... Quert, did you mean these flowers provide energy for the whole biosphere living out there, on the hull?\n\nQuert simply gave eye-signals, apparently a \"yes.\" Then the Sil said, \"Commanded by cold minds,\" and would say no more.\n\nThe thin glow of the jet brimmed above the horizon here, and some flowers seemed focused permanently on that. It seemed an unlikely source of much energy, for the plasma was recombining and emitting soft tones in blue and red. On the other hand, that was steady though weak and some flowers had perhaps evolved to harvest even such dim energies.\n\nThey were all transfixed as the radiators spread open and completed their pivot toward the humans. There was silence broken only by the faint sound of air circulating, as the field of flowers\u2014Cliff swung his head around to count over a hundred within view\u2014then began to pulse with a gray glow. Behind the flower field the stars still wheeled, cutting arcs in the black. The humans stood mutely watching, their heads tilted up to see the spreading flowers, who in turn clung to the rotating hull. The gray glow built slowly, the whole flower display assuming a shape like a giant circle flecked with light, staring at them. Cliff felt a chill wash over his skin that was not from the temperature. This is truly alien....\n\nA pattern began to emerge. In the dim light their eyes had adjusted, and so the brighter flower circles made blotchy spots while the darker flowers accented a contrast... and the entire array began to form a speckled image....\n\nA picture came into view. Irma gasped. \"It's Beth's face\u2014again!\"\n\nThe picture was crude because there were fewer pixels to be had from the flowers, but still Cliff found it unsettling. He gazed at the cartoon of Beth Marble while others talked on. Finally he said, \"Reasonably close, too. Whoever commands these vacuum flowers knows the method they used with the mirror zones. They're using this to get our attention.\"\n\nQuert gave a rustle of agreement. \"Ice minds.\"\n\n\"At least her lips aren't moving,\" Terry said. \"That gave me the creeps.\"\n\n\"So... no message,\" Aybe said. \"Just a calling card.\"\n\nQuert looked around and pointed to the wall behind them. The snake team was still working, this time with some armatures like waldoes. They had somehow extruded a flat tank from the wall, and snakelike machine arms were completing it. This was not repair but construction. They worked by coaxing features from a substrate that simmered with flashes of orange light. The whole working team was laboring with new members. A big lizardlike thing of crusted hide had four tentacles, each of which alone was larger than a finger snake, fissioning into more small ones that snakes did not have. Cliff watched one use fingernails, too, that deformed into helical screwdrivers, snub pliers, a small hammer. It was trimming away and adjusting features freshly drawn from the wall. Cliff glanced back at the Beth portrait, still frozen in a smile. When he turned, the work team was slithering away across the wall, as the central oval they left brimmed with orange glows.\n\nLetters and then words seemed to drift to the surface of the wall, as if bubbling up from deep ocean water.\n\n\"It's Anglish,\" Terry said. \"How do they know?\"\n\n\"Ice minds,\" Quert said. Across the Sil's face\u2014and across those of the other Sil with them, who had been quiet all along\u2014the skin stretched and warped, framing the eyes. Did this mean joy? Fear? Impossible to tell. But there were no other signs of concern in the body, which remained still.\n\nThe script ran slowly.\n\nWe have ranged the Deep and kept history near.\n\nWe are not of you carbon-children of thermonuclear heat and light.\n\nWe ride here to preserve the greatness you have found now.\n\nLong ago we shaped this traveling structure, when the warm folk came to us from deep within the whirlpools that girdled our suns. The warm folk gave us tools to build large. Some of us stayed among the comets, but we here have clung to the Bowl. We live through eons of time, and so have seen the many thousands of faces intelligence can assume. We dealt with them in turn. We are the Bowl memory.\n\nIrma said, \"This looks like a prepared lecture.\"\n\nAybe nodded. \"Must be. They've used it before. I guess if there are thousands of years between passes nearby other stars, you work up an all-purpose greeting.\"\n\nTerry smiled. \"Boilerplate, huh? This doesn't look like a greeting, though. More of an announcement, I'd say.\"\n\n\"Intended to awe, yep,\" Cliff said.\n\n\"As if this place didn't impress us enough? Their Anglish is good,\" Irma said. \"They must have access to the Folk's experience. But are we missing a point? These\u2014Ice Minds\u2014claim they built the Bowl.\"\n\n\"Shaped it. Designed it, maybe,\" Terry corrected her. \"After intelligent warm life found them. After they ranged through the solar system and then the planets of this other little companion sun, after they worked their way into... would you say a mutual Oort cloud? And found these forests of supercold life. And the Ice Minds used them for engineering.\"\n\n\"Or they could be bragging,\" Cliff said. Nobody laughed.\n\nThey watched as the words faded and a long series of still pictures followed. Each came in at an easy pace, as though there were all the time in the world to show images of planets\u2014crisp and dry, cloudy and cool, cratered yet with shimmering blue atmospheres\u2014and stars, sometimes in crowded clusters, at times seen close-up and going nova in bright, virulent streamers, or in tight orbits around unseen companions that might be neutron stars or black holes. Wonders the Bowl had seen while driven forward by its jet. Portraits of the early Bowl years, Cliff gathered\u2014the jet flaring and trembling in tangled knots of ruby and sharp yellow as the vast cup got under way.\n\nFor these ones that Quert termed Ice Minds there was indeed all the time in the world. The screen visions streamed on and the humans sat with backs against the rough walls to watch them. Strange landscapes loomed.\n\n\"They call us warmlife,\" Quert added as the screen showed an iceworld. Against a black sky odd lumps moved, in a lake lit by a smoldering red light. There were dune fields, ponds, channels. The lake sat in a convoluted region of hills cut by valleys and chasms.\n\nAybe said, \"I'd say that looks kind of like Titan, Saturn's moon.\"\n\n\"There was small life there,\" Irma said. \"Microbial, some pond scum, nothing more.\"\n\n\"There're moving forms on that screen,\" Terry said. For this view the screen showed sequential shots. The lumps seemed like knots of fluid, assisted by sticks that crossed through the globular bodies. Blobs that somehow used tools like rods? These coherent colloids moved across bleak fluid that might be hydrocarbons like ethane. On the beach the lumps moved ashore with viscous grace, pulling themselves forward with extruded feelers that managed the sticks. \"They're clustering around that domed thing that looks like a termite mound,\" Irma said. \"Even blobs can build.\"\n\n\"Those forms we saw in the shadows out there\u2014\" Terry gestured to the ice plains beyond. \"\u2014might have some connection to these. Except these are on a planet.\"\n\n\"Life adapts,\" Irma said. \"A big leap, from a Titan-like cold around a hundred degrees Kelvin, with high atmospheric pressure, to those vacuum flowers and the rest of it, all holding on to the outside hull.\"\n\n\"A big jump,\" Terry said. \"But there must have been incremental steps, and they had billions of years to do it.\"\n\nBy this time the image had faded, replaced by a view of a dense jungle. This one, though, had spiral trees, whipped by high winds against a purple sky of shredded clouds. The stilled storm had a big beast in the foreground, something like a dirty brown groundhog, its head tucked in against the wind.\n\nThe show went on and then on some more. After a while even exotic alien landscapes became repetitious: blue green mountain ranges scoured by deep gray rivers, placid oceans brimming with green scum, arid tan desert worlds ground down under heavy brooding brown atmospheres\u2014\n\n\"All planets,\" Terry said. \"They're not showing us comets. Not showing us themselves.\"\n\n\u2014iceworlds aplenty beneath starry skies, grasslands with four-footed herds roaming as volcanoes belched red streamers in the distance, oceans with huge beasts wallowing in enormous crashing waves, places hard to identify in the swirling pink mists. Life adapts, indeed.\n\nAfter a while, the slide show was over and more Anglish words appeared.\n\nYou warmlife now learn to journey from star to star.\n\nWe have seen your kind before.\n\nYou expand outward at great cost to you, for fleeting quicklife reasons.\n\nMost warmlife comes in small ships, as do you.\n\nThe dream of this Bowl enticed us with its capacity. Its slow progress fits our minds, our style. Over eons we have seen little need to change its design.\n\nThrough voyages we gain passengers warm and cold. This is only part of us. Other ice minds live elsewhere in the Bowl's shadow.\n\nWe deeplife are one in fluidity.\n\nWe address you now because this is an unusual time. This Bowl approaches a fresh world. As do you.\n\nWe have no reason to intervene in warmlife affairs. We act when the Bowl faces threats to its stability and endurance.\n\nYou will help us.\n\n\"We will?\" Aybe said.\n\n\"They're probably listening in some way, y'know,\" Cliff said sternly.\n\nAybe blinked and said loudly, \"Ah, yes, we will. If we know how.\"\n\nIrma stood and gazed out at the dim icelands where the vacuum flowers still held Beth's image. She fanned her laser and said, \"Those blobs, they're moving, all right.\"\n\n\"Maybe these Cold Minds keep those forms around because they're related by mutual evolution?\" Terry asked. \"Hard to know. If these Cold Minds are as old as they say, there's not much that can be new to them.\"\n\nCliff said, \"And even less that's interesting.\"\n\nLiquid life-forms? he thought. Trying to think on huge time scales was hard. Maybe warmlife is just a buzzing, frantic irritant to them. And there is something in their manner, dealing with us warmlife, that suggests immense distance. These things had probably evolved in the outer fringes of solar systems. They could travel on comets, maybe, bouncing from star to star. So maybe they freely roamed the galaxy while the most advanced warmlife consisted of single-celled pond scum.\n\nNone of this was reassuring.\n\n\"What did you have in mind?\" Irma addressed the screen.\nTWENTY-ONE\n\nMemor watched Tananareve carefully as their party entered the chamber for the Justice Rendering. The primate studied the walls and ornamental traces with a quick and ready eye, as though cataloging all she saw. Quite natural for an explorer, who expected to report back to her superiors. That might well not happen, but no need to give the primate a hint of that.\n\nThey sat in high rows above the steeply inclined vault. Above them hovered ancient tapestries of gold and ivory, while the funnel at the vault's floor was an ominous jet black. Bemor sat higher than Asenath, Memor, and the primate, as fitted his rank. He spoke with the Highers, even the Ice Minds. Memor knew\u2014and envied, of course. Though Bemor was her twin genetically, but for those genes that expressed sex, he had been reared to deal with long-term thinking and abstractions at a level Memor had not. Perhaps that explained, Memor thought, the tenor of irritation that crept into his sentences when discussions flagged or failed to reach a sharp point of usefulness. Male traits indeed, she recalled.\n\nA clarion call sounded deep and long in the vault. It comprised some high trills, playing against long strumming bass notes that Memor knew were resonant with the body size of Folk, and so would be felt rather than heard. Such musics instilled an uneasy impression of immensity and whole-body involvement, a tool persuasive yet hard to recognize. It instilled an apprehensive awe.\n\nTananareve watched and listened, saying nothing. Her eyes darted with quick intelligence. Only her tight pale lips told of some inner tension.\n\nResonant chords came from the music walls. At a signal, a team of brawny Folk strode from the witnesses gathered on the lower level. With prods, these forced each of the Maxer Cult members forward... closer to the edge... their legs slipping in the slime... then at the teetering brink... as a deep voice extolled their violations of the Great Pact. At a second hooting call, the Folk thrust the Maxers into the pit. Some flailed in resistance. Others turned with resigned shrugs and jumped. Cries, shouts, shrieks.\n\n\"This is a most useful spectacle,\" Asenath said mildly. \"Well done, too.\"\n\nThe music rose to a triumphant chorus, high notes rejoicing. Barely audible beneath the sound was a chanting\u2014\n\n\"Live in this moment. Give in this moment.\"\n\n\"Ritual reprocessing is too good for those who undermine stability,\" Asenath said, spitting out the words. \"They endanger us all.\"\n\n\"So may we,\" Memor said, and at once regretted it.\n\nAsenath shot back, \"Not if we exterminate the humans as we have these!\"\n\nThey had apparently forgotten that the primate sat among them, Memor saw. Tananareve's head jerked up for a moment; then she bowed it... which meant, Memor knew, that the primate had learned some of their speech. Had understood Asenath's remark. These creatures were smarter than she knew.\n\nThere was a long silence after the ceremony, hanging in the heavy air.\n\nBemor said softly, \"We Folk must conquer our own festering anxieties, as well. These reprocessings are necessary for stability and for life itself. We Folk in our own wide variety, along with the multitudes of Adopted, should accept the hard, simple fact that we ourselves and all we encounter are transitory, ephemeral, beings of the moment. We matter little. We should embrace the beauty and pleasure of the world, knowing it will cease for us, inevitably. We are not the Ice Minds. Such is the Order of Life.\"\n\nMemor added her agreeing fan-display to that of Asenath and other Folk within range of Bemor's deep bass voice. For her it was a satisfying moment. Bemor could make these matters far more resonant and inspiring than she; just another sign of his ability range. When they were both young, cared for by their long dead Principal Mother, he had early on shown his ability to handle higher-level abstractions and find the nugget of wisdom in passing moments. She admired him.\n\nBut Asenath would not let it be. She said, \"These primates do not see such wisdom. They are an expansionist species, such as has been seldom seen in the Bowl for great ages. Their ship has maneuvered below range of our defense gamma ray lasers. Their parties afoot elude us. It is time to marshal efforts to eliminate them.\" A pause and vigorous fan-rattle. \"Obviously.\"\n\nBemor gave an agreeable rainbow flourish with mingled eye-frets, but then said soberly, \"There have been, down through the vast generations, uncounted acts to restore stability. All these carried a penumbra of drownings, starvation, sad sickness, massacre, looting, ethnic scourges, laser conflagrations, air-cutting slaughters, assisted group suicides, expulsions into vacuum\u2014the list trudges on.\"\n\n\"You seem saddened by this,\" Memor said\u2014a bit presumptively, but after all, she was his identical.\n\nBemor yielded on this with an embarrassed flutter. \"I recall when young\u2014you were spared this, my twin\u2014assisting the more militant among us. We walked on corpses, sat on wrecked bodies to rest, stacked them as they stiffened to provide us a momentary table to eat upon. The delay in recycling them into the Great Soil meant they had to be assembled and even defended, against predators both feral and intelligent. But it had to be done.\"\n\nMemor said kindly, in mellow tones, \"Brother, I do not follow\u2014\"\n\n\"The Bowl grows errant beliefs like mutant species. There were obscure faiths and ethical theories that held the body was some kind of holy vessel, whose owners had not yet departed. Or else such spirits would require the body, even though rendered into dust, to be made animate again. So they resisted return to the Great Soil, a true sin.\"\n\nHe looked around at nearby Folk, who regarded him with varying displays of doubt. \"You flutter your fan-feathers with disbelief, yes\u2014but I have seen this in historical records, and even in person. Sad sights I regret witnessing now.\" Bemor sagged a bit as if borne down by history, his feathery jaws swaying. \"Alas, my memory is long and I cannot erase those laid down with such feeling.\"\n\nCrowds come to witness now shuffled out of the Vault. Other Folk dispersed until it was Asenath, Bemor, and Memor, plus of course the primate.\n\nAsenath said, \"Your report is due, Memor. Your hunt for the bandit crew still loose among the Sil continues?\"\n\nMemor duly reported finding the Late Invaders among the Sil. With a quick air display of images, she told of the attack upon the Sil city, the vast destruction.\n\n\"Approved by upper echelons?\" Asenath asked severely.\n\n\"I ushered it through,\" Bemor said mildly, eyeing Asenath but making no feather-display at all. Lack of fan-signal was a subtle sign of coolness, but Asenath missed this and rushed ahead, eager with a point to make.\n\n\"And they are dead?\"\n\nMemor suppressed her usual feather-rainbow to convey irked response and said, \"No. I had surveillance auto-eyes study the Sil buildings. While they are rebuilding themselves, they involuntarily shape new messages in their forms. This is not a language but a gesture-speak. The influence of building style plainly shows a vagrant presence among the Sil, and I deduce that the humans survived the assault.\"\n\nAsenath pressed forward with full fan-clatter. \"So. You failed.\"\n\n\"I did not command the skyfish. Those who did not achieve their goals were demoted. But recently one fast-fly craft caught this.\" Memor flicked an image into the air surrounding them. A down view showed a primate running between recently shaped buildings. A pain beam rippled over it, and the figure crumpled. The beam stayed on and the writhing thing kicked and thrashed and then lay still.\n\n\"A single kill?\" Asenath said with downcast tones.\n\n\"We now know we can hurt them at will over distance. My primate here\"\u2014a gesture at Tananareve\u2014\"was our test subject. But I found also that the Sil have secured access to my own surveillance.\"\n\nBemor said, \"So the Sil are watching you, too?\"\n\n\"I withdrew immediately, of course. In that interval the primates made their way toward a nearby mirror zone.\"\n\nAsenath brushed this aside, pressing on. \"Memor, we have not heard your report on this primate of yours. I take it she has been well fed and often exercised?\"\n\nMemor puzzled at Asenath's apparently friendly tone, suspecting something. \"Of course. I brought her here to higher gravities, for her health. Her species was clearly not made for lightness\u2014indeed, their bone and joint structures suggest a world of heavier gravitation than even the Great Plain.\"\n\nBemor asked, \"You have read her mind structures enough? Your reports mentioned this odd character, inability to see her own Undermind.\"\n\n\"Yes, obviously an early evolutionary step. Imagine building a large, coherent society of individuals who could not know their own impulses, their inner thoughts! Touring her mind was instructive. I got most of what I need.\"\n\nAsenath fluttered with appreciation. \"I shall depend upon your ability to monitor this primate. We will need her cooperation to convey our response to their ship's attempts at contact.\"\n\nMemor hid her surprise. \"Now?\"\n\nAsenath said sternly, \"We must deceive the Glorians about who commands the Bowl. Your primates can do this for us, if properly handled.\"\nPART VII\n\nCRUNCHY INSECTS\n\nIt is a common experience that a problem difficult at night is resolved in the morning after the committee of sleep has worked on it.\n\n\u2014JOHN STEINBECK\nTWENTY-TWO\n\n\"These snakes are incredible,\" Beth said to Karl. It was pleasant to have time to relax and just watch without feeling endlessly responsible. She had gotten used to that on the Bowl.\n\n\"If you'd asked me before I saw them, I'd have said more like improbable.\" Karl could not take his eyes from the screen. \"Hard to see how evolution worked out skills like this.\"\n\nThey were watching some aft zone electronic repairs carried out in the narrow spaces near the magnetic drive modules. The snakes wriggled into spaces that would have taken her and Kurt hours to unsheath, disconnect, monitor, diagnose, and fix.\n\nKarl called to them, \"Go left at the condenser bank. They're cylindrical drums with oil valves on the upper side, colored yellow. Then spin open the double diode\u2014they're the blue plates.\"\n\nThe Maintenance Artilect took this from Karl's mike and translated it into the sliding vowels and clipped sharp notes that made up the finger snake language. On the screen they both watched the snakes make the right moves. They each had a tool harness that they plucked small instruments from. With these they deftly inserted, turned, levered, and adjusted their way through one task after another, with speeds almost impossible to follow. The interior cameras were tiny light pipes and gave barely enough definition to make this work. All the while, the ship hummed on and occasional thumps and surges hampered the work. SunSeeker's magscoop was operating close to its shutdown threshold already, and repairs while operating were the bane of all ships\u2014but it had to be done.\n\nBeth was out of her depth here\u2014hell, I'm a field biologist!\u2014but regs said nobody worked alone on ship maintenance, ever. Flight deck officers were full up, conning SunSeeker as close in to the Bowl's atmosphere levels as they could, while still grabbing enough plasma from the star as they could. Just maintaining flight trajectories while watching for bogies was burning up all their attention.\n\nBeyond tending to the hydroponics, certifying the air content, and helping turn algae into edible insects and porridge, Beth had nothing more to do. She helped a little with the preliminary \"fault tree\" analysis of this maintenance run, but that meant mostly giving instructions to the Artilect, which plainly knew far more than she did about what she was supposed to be doing. So she used a wise saying she'd learned from Cliff: Never pass up a chance to shut up.\n\nWhich was harder to do than she had thought. \"Uh, can I help?\" she asked for maybe the eighteenth time.\n\n\"No, I got it.\" Kurt never took his eyes from the screens, and his headphones whispered constantly with updates from the Artilect. \"Going well.\"\n\nMan of few words, bless him. At least Karl didn't ask her over and over about living on the Bowl, like the rest of the watch crew.\n\nThe snakes wriggled some more, did scrub procedures on some parts, and with surprising speed got a discharge capacitor line back up to specs\u2014part of the booster system that allowed them to amp their magscoop when needed. \"Okay,\" Kurt said, \"come on back out. You guys need a break.\"\n\nThe snakes dutifully turned and started on their tortured way back out of the engine labyrinths. \"Amazing what they can do,\" Kurt said, nodding his head. \"Makes me wonder how we got by without them.\"\n\n\"Barely,\" Beth said.\n\n\"You're bio, how did smart snakes ever evolve? They sure didn't Earthside.\"\n\n\"Something about their home world, one of them said. It had plate tectonics gone wild, crazy surface weather, storms that would take the paint off metal. So smart life stayed underground.\"\n\n\"How about earthquakes? Volcanoes?\"\n\n\"Their world had 'bands of furious turmoil,' they said\u2014their language has considerable poetic power. Their landmasses butt against each other, kind of like Earth, with its baseball seam wrapping around the globe. Stay away from those, and life underground is somewhat easier, they learned. Where are you from?\"\n\n\"Gross Deutschland. You?\"\n\n\"Everyplace, mostly away from California\u2014after the Collapse, we had plenty of migrants from there.\"\n\n\"Okay, snakes got smart, but mein Gott they are wonders at handling mechanics.\"\n\nBeth grinned. \"Look, we don't even know why we're relatively hairless, compared with the other apes. Why we walk on two legs and can outrun anything over distance. Why we're so damn good at mathematics, at music\u2014you name it. So understanding where an alien species came from is hopeless.\"\n\nThe finger snakes came wriggling out of the narrow cap passage into the drive's innards. Ordinarily she and Kurt would've used smart cables to get in there, running them with a control panel. To her astonishment, the snakes broke into a high, wailing song\u2014chip chip, duooo, rang rang, chip, duoo duoo. Not entirely unpleasant, either. At least it did not last long. Then they formed a \"wriggle dance\" as Redwing called it, arcing over each other and forming intricate curves that included bobbing in and out of the circle, rolling over and doubling up to make O's, then back into the throng\u2014still singing, though less shrill. They finally ended up standing halfway erect on their muscular tails, their fingers wriggling at the dumbstruck humans in comradeship\u2014or so whispered the Artilect in Karl's ear.\n\nThen, with good-bye hails, they went off to eat in the algae pits, where a repast cooked up by Beth earlier awaited.\n\nKarl said, \"They're so coordinated. As if it was completely natural for them.\"\n\n\"You mean instead of how humans do it\u2014drill, train, discipline, drill some more?\"\n\n\"Pretty much. The snakes\u2014look at them, off to their home in the biospace. All together, chattering... Some species are better at collaboration than we are. How come?\"\n\n\"We're pretty new at it. About two hundred fifty thousand years ago Earthside, group hunting became more successful than individual hunting. That started the logic of shared profits and risks. Penalties kept alpha males from dominating. There emerged a kind of inverted eugenics: elimination of the strong, if they abuse power. And the cooperators won out.\"\n\n\"Wow, you know this stuff. It'll be fun seeing you work out all the aliens on the Bowl.\"\n\nBeth opened her mouth to say something modest but... he'd brought up what she'd already missed. Back onboard, but dreaming at nights of the Bowl. \"Uh, yes. Look, it's time for that self-cook in the mess,\" she said.\n\n* * *\n\nFred was talking while he pounded a wad of bread dough. Physical work opened him as well as anyone could, so Beth tried to pay attention. \"I kept wondering, y'know. The Bowl map shows Earth as of the Jurassic period, when all of the biggest dinosaurs emerged. Y'know, apatosaurs and so forth. I think I finally have the sequence right.\"\n\nBeth nodded while she did her own kitchen work. He slammed the dough down and punched it for punctuation. \"A variety of intelligent dinosaurs emerged first. Oof! They must have been carnivores. They invented herding. Uh! For millions of years they must have been breeding meat animals for size. Ahh!\"\n\nHe looked around and realized that nobody was listening except Beth. \"You mean all those theories about dino evolution are wrong?\" This was interesting to her but apparently not to the others. The crowded kitchen buzzed with low conversation as they worked on aspects of dinner. Fred's jaw closed with a snap. She knew the pattern\u2014if people didn't listen, he didn't talk.\n\nKarl handed Beth a handful of roasted crickets that reeked of garlic. \"Try these. Crunchy.\" He had pitched in with the cooking before she even got to the ship's mess.\n\n\"Yum,\" she said. Next came a basket of aromatic wax worms ready to cook. She tossed aside black ones: that meant necrosis. \"They go bad fast; hell, I harvested them two hours ago,\" she apologized. \"The rest are pupating\u2014just right.\" Deftly she peeled back their cocoons and tossed them into the electric wok.\n\nCaptain Redwing came in and watched, standing straight and tall, smacking his lips slightly. \"Wax moth larvae, a gourmet favorite.\" The crew laughed, because he always pretended to like the food in the mess, no matter how implausible that was. Or else he ate alone in his cabin. After their last culinary disaster, a motley mashed-up dish everyone disliked and called Stew in Hell, he went on dry rations alone.\n\nKarl turned and swept brown roasted crickets up, salted them\u2014salt was easy to extract from the recycler\u2014and with head tilted back, trickled them into his mouth. \"How come when you have less to eat, it tastes better?\"\n\n\"Less is more,\" Redwing said. Everyone around him raised eyebrows. \"Look, we're in a tough spot, carrying forward maneuvers nobody trained for\u2014\" He nodded at Karl, Beth, Ayaan Ali. \"\u2014and exploring a big thing nobody even imagined. We've got to do with less until we see our way out of this.\"\n\nEveryone nodded. Redwing finished with, \"So on to Glory\u2014and let's eat.\"\n\nThe moth larvae weren't all done. The crew watched the chubby white larvae sway and wriggle in delirious fits as the heat took them. Insect protein was simple to raise on algae and, if well cooked, had a zest that the rest of the menu lacked. Fresh from a skillet, they had a kind of fried fritter some called \"pond scum patties\" to go with them. The ship couldn't afford the room or resources to raise muscle and sinew. Some crew came from the North American Republic and weren't used to insect food, or else from experience regarded it as beneath their standards. A few weeks' exposure to the stored rations usually fixed that. Some things, like the trays of gray longworms, few could bear to look at. Those Beth thought it best to grind into a paste for a fake pancake.\n\nBeth spread the larvae into a frying pan, where they fell into a fragrant, fatty goo Ayaan Ali had made. They squirmed as they sizzled and then went still. She stirred them, thinking Amazing what you'll eat when you have to... and then recalled things she had gratefully ingested when she had to on the Bowl. Sometimes, admittedly, while deliberately not looking at them...\n\nA zesty aroma rose from the crusty larvae and as soon as she set them out, crew descended on them.\n\nRedwing had saved a morsel for this moment, and now trotted out from his personal stock a bowl of\u2014\"Honey!\"\n\nThat made the dish work. Everyone dug in. \"As insect vomit goes,\" Karl said, \"not at all bad.\"\n\nAyaan Ali asked Karl, \"Done with that flight analysis?\"\n\nKarl barely slowed his eating to say, \"Realigned the simulation, yes. Fitted it to isotope data from the scoop over the last century.\"\n\nBeth asked, \"Meaning?\"\n\nAyaan Ali said, \"We're still trying to understand why the scoop underperformed. It might help us fly it now in this low-plasma-density regime.\"\n\nRedwing said casually, \"How's the detector mote net working?\"\n\nBeth knew this was one way Redwing liked to turn social occasions into a loose staff report meeting. Certainly his approach made hearing tech stuff flung about a tad more appetizing.\n\nAyaan Ali gave herself an extra helping of sauce\u2014much needed, since to Beth the woman seemed rail thin and low energy\u2014and crunched up some more insect delicacies before saying softly to the others, \"Karl and I deployed, on the captain's direction, the diagnostic fliers we'd planned to use when we came into the Glory system. They would give us a good three-D map of the mag fields and solar wind when we came in.\"\n\nRedwing said, \"So I decided we could send them out on a short leash. They can tell us details about the plasma turbulence, density ridges, things that we can't get a good reading on inside SunSeeker's mag cocoon.\"\n\nThis, too, was a Redwing method\u2014let the crew know there was logic behind his orders, but do so ex post facto. Playing along, Beth asked, \"Short leash?\"\n\nKarl said, \"I'm pretty sure we can reel them back in. They're marvels, really, size of a coin but able to propel themselves by using tiny electric fields that let them sail on magnetic energy, to sense plasma and measure waves, and report back in gigahertz band. We've got them spread over a big fraction of an astronomical unit, sniffing out ion masses and densities, picking up plasma waves, the whole lot.\"\n\nBeth was impressed with SunSeeker's abilities and kept quiet while the others kicked around their lingo. They loved their gadgets the way ordinary people cherish their pets. The thousands of \"smart coins\" sending back data were working well. That they could be fetched back, told to return home for reuse\u2014amazing stuff. Plus they had useful results right now.\n\nAyaan Ali waved one of her augmented fingers, and a 3-D vision snapped into view, sharp and clear above their table. Hanging in air, it showed schematics of the Bowl in green, with SunSeeker a tiny orange dot swimming above it. The ship had to stay below the rim of the Bowl to avoid the defensive weapons there. But it also had to skate above the upper membrane that held in the Bowl's atmosphere. That left a narrow disk of vacuum for SunSeeker to navigate, riding the plasma winds that came direct from the star. But more important, they got plasma spurts from the traceries and streamers that purled off the yellow-colored jet. The churning jet was big in the 3-D view, a slowly twisting nest of luminous threads that drove forward. As the crew watched the display, it shifted smoothly, since the Bridge Artilect tracked human eye movements to display what interested people. They witnessed the jet narrowing further as it flowed out, then piercing the Bowl cleanly at the back, through the Knothole and out into interstellar space.\n\nDeftly Ayaan Ali pointed to the safety zone disk where SunSeeker flew and the 3-D dutifully expanded until they could see bright blue dots swimming in a grid formation all across the huge expanse. They were sprinkled over a distance of about an astronomical unit and when Ayaan Ali waved her hand, they answered with momentary violet flares, a ripple slowly expanding away from the ship's position.\n\n\"They report in steadily, each staying a good distance from the others. We get plasma signatures in ample arrays. The coins feed on the plasma itself and change momentum by electrodynamic steering.\" She could not restrain herself, beaming. \"Beautiful!\"\n\nKarl nodded. \"And they got good news, in a way. Remember, before we sighted the Bowl, our scoop underperforming? Turned out it was eating a lot more helium and molecular hydrogen than ordinary interstellar space has. Some of it got ionized by our bow shock and then sucked into the main feeder.\"\n\n\"Ah, but it doesn't fuse\u2014got it,\" Fred said. This was the first time he had spoken during the entire meal, and everyone looked at him. \"Hard to tell from inside the ship that it wasn't getting the right food.\"\n\nBeth didn't see, but wasn't afraid to ask, \"So?\"\n\n\"Those useless ions slowed us down, just pointless extra mass\u2014and not fuel.\" Fred dipped his head, as if apologizing. \"Sorry if I get too technical. My obsessions don't translate well.\"\n\nEveryone around the table laughed, including Redwing's rolling bark. \"Don't put down your assets, Fred,\" Redwing said. \"Even that dinosaur idea.\"\n\nBeth appreciated Redwing's methods but wanted to move this along, so she asked, \"So our drive's okay? We're managing to keep it flying in interplanetary conditions, after all\u2014which it was never designed to do.\"\n\n\"That's what the smart coins tell us. We're actually getting more plasma than we would if we were in near-Earth space,\" Karl said. \"The jet snarls up some, so we get a bit more blowoff plasma from it.\"\n\n\"That star isn't behaving like a main-sequence one, either,\" Redwing said. \"I had the Astro Artilect look into it. It says we got the spectral class wrong at first because of the hot spot\u2014it swamped some spectral lines. But as well, the whole jet formation active zone makes the star act funny.\"\n\nAyaan Ali asked, \"You mean those big solar arches we keep seeing? Big billowing loops. They dance around the hot spot, and every week or two they blow up in huge, nasty flares.\"\n\n\"Right,\" Karl said. \"Those help build the jet, somehow\u2014I really don't see how to build so stable a pillar of plasma from the storm at its feet. Those storms give the jet its power and blow off other plasma, too. The jet's base storms also spatter out a big, highly ionized solar wind\u2014which helps us scoop up more fusion fuel, too.\"\n\nBeth nodded, feeling more than a bit out of it. \"Pleasant to have some good news for once.\"\n\nRedwing said quietly, \"So the smart coins tell us we have some room to maneuver. Good indeed.\"\n\nSmiles all round. Fred nodded enthusiastically.\n\nA new flight deck officer Beth didn't know well, one of the recent revivals, came into the mess. \"Captain, we're getting a tightbeam laser signal from the Bowl. Did a translation in digital format. It's in Anglish. Visual's cutting in and out. But we can tell who it is\u2014it's Tananareve.\"\nTWENTY-THREE\n\nAs he sat waiting for the signal to stabilize, Redwing recalled the hammering noise that worked through the ship's plates in the trial run, as acoustics bled from the ramscoop magnetic fields into the marrow of their bones. At the departure reception, a president of one of the major ship builders said lightly of the din, \"To me, it's the sound of the cash register.\" It had been a major achievement not to deck him right there.\n\nAnd even better later, when the medical teams were putting him under, to reflect that when he next opened his eyes, the ship builder would be dust.\n\nNow the background rattles and pops and long rolling strums were second nature. He listened all the same, as a captain should. Now he heard a crackling and a carrier hum. Then \"\u2014hope this gets through.\"\n\nTo Redwing, Tananareve's smoke-and-whiskey voice said she had been through a lot, but the timbre of it spoke of her resolution. The screen was blank, but audio came with little pips and murmurs in the background, perhaps static, perhaps the background noise of some alien place.\n\n\"How goes it?\" he said.\n\nAfter a delay of only five or six seconds, her shaky voice answered carefully, \"It goes.\"\n\nThen she coughed. \"They... they here want me to talk to you about cooperating on a message. You've seen the feed from Glory, right?\"\n\nHe saw a bottom-screen crawl line from the bridge comm system say they had picked up the full feed. The screen flickered, and then suddenly an image of Tananareve snapped into full color view. Against a black rock background, she looked haggard and pale but her eyes flashed with flinty energy. Nothing more in view. Her clothes were the field-issue pants, shirt, and jacket she had gone down in, looking beat up and patched. She also wore an odd gray shawl around neck and shoulders. There was dirt on the left side of her jaw and scratches along the neck. Overall she looked worn down.\n\n\"Yes, we have. Very odd,\" Redwing said. Best to be guarded. He knew her captors were listening and wished one would step into view. He hungered for a feel of what these aliens were like.\n\n\"The Folk, these aliens call themselves, they want to work, to, uh, collaborate with us\u2014with you, Captain\u2014on making a message. Something to send to Glory.\" Her eyebrows rose on you, and Redwing wondered what that meant.\n\nSomething in her voice had roughened, maybe from being in the field so long. It was Anglish with the corners knocked off. She laughed suddenly. \"The civilization at Glory, they seem to think we're running the Bowl. My, um, mentors, they want to leave it that way. Keep themselves in the shadows, at least until they know something about Glory. But they need our help for that.\"\n\n\"Outstanding. What do they want to say to the Glory Hounds?\"\n\n\"Captain, they're still fighting about that. They'll have to talk to us first.\"\n\n\"That's it? What about Cliff's team?\"\n\nHe could see conflict flicker in her face. So could Beth and Karl, sitting behind him, judging from the way they stirred in their seats. They were in Redwing's cabin because he wanted to keep this first transmission from the aliens, after months of silence, from the rest of the crew. It was always a bad idea to let crew see policy being made, especially if it was on the fly, as this might have to be. \"I... don't know anything... about that.\"\n\nHer hesitations told more than the words. She was probably trying not to let the Folk know how much she knew. Then, to confirm his hunch, she very carefully gave him a wink with her left eye. Left: something wrong. A common code in visual reporting, all across the Fleet. Right meant things were right but more was to be said.\n\n\"So why don't they let Cliff's team go? And you?\"\n\nHesitation, a side glance at whatever was directing her. \"They need me as translator....\"\n\n\"And Cliff's team?\"\n\n\"And as for Cliff, they don't know where he is.\" A right-eye wink this time. What could that mean? That the Folk knew something but not enough to use?\n\n\"So if we work with them on a Glory message, what do we get?\" It was time, he judged, to put something on the table. Let them go first.\n\n\"You are all welcome down here. There is plenty for us.\" She said this straight, no inflection, staring straight at the camera as if this were a rehearsed line.\n\n\"Thanks, but mostly we want supplies for the ship. And information.\"\n\n\"I believe they want to help with ship repairs.\" Again the straight stare, no eye movement.\n\n\"We don't need repair. We figured out that we'd been fighting their jet backwash for a century. Once we're full up on ship stores, we'll be on our way.\"\n\nFor the first time, she showed a darting, skeptical squint of the eyes. \"That isn't what they have in mind.\"\n\n\"Tell them we will exchange delegates, perhaps. We can't house more than one or two\u2014\"\n\n\"They want you, Captain, for negotiations in person.\"\n\n\"Not until they release you and Cliff's people. They've been in the field a long time, need medical and some R and R. You, too, Tananareve.\"\n\n\"I believe they have something more... lasting... in mind.\"\n\n\"Such as?\"\n\n\"They mentioned a generation or two. Enough time. They say, for species to get to know each other.\"\n\n\"I'm a ship officer with orders to carry out. I'm conveying colonists to Glory and cannot change mission.\"\n\nHesitation, side look, pursed lips. \"I... gather they like to sort of collect species, to live here, to work with them.\"\n\n\"I can't spare people. Colonizing a whole planet takes teams, and they're barely big enough as it is. Cut our numbers and then downstream both halves\u2014those we left with you, and those we took\u2014would get inbred.\"\n\nA pause, her eyes dancing, looking off to the side. \"They... they say they find us very interesting.\" The flat way she said it told him that she was also not saying a lot, and he would have to guess it. But what?\n\nThere came a sudden voice, swift chippering sounds underlaid by deep notes, as if someone was speaking in two tones at once. Redwing thought it was the first truly alien thing in this transmission\u2014speech built like a symphony, with several elements rendering part of the message in different sliding tones, sometimes highs and lows scampering over each other. Some notes rang hollow, others full. Yet all this was also oddly resonant, as if the play of words\u2014if the screeches, grunts, trills, and mutters were that at all\u2014made a larger work of greater scale.\n\nHe really wanted to see who made that voice. The six-second delay was driving him nuts.\n\nShe considered for a moment, looking off camera, and then said slowly, \"They welcome us with... total hospitality. We can live here. They will assign a huge territory to us and help us set up a civilization comparable to\u2014\" She paused. \"\u2014well, what we had Earthside.\"\n\n\"Um,\" Redwing said, keeping his face blank.\n\n\"And... from what I've seen, there are rules to keep this whole big habitat working. They impose... order. They're very, uh, firm about that. Make a mistake here, and you could endanger the whole place.\"\n\n\"Like any spaceship,\" Redwing said. \"Open a hatch the wrong way, and you die. Maybe everybody in crew dies.\"\n\nShe nodded and her eyes slid briefly to her left, then back. \"I think so. They do say we should know for the long run that there are generous upper limits on population. We could have territory bigger than Earth itself. Really, we could choose what part of this whole huge thing we wanted. I'd guess we'd probably want to be on the Great Plain, where it's point eight gravs and pretty calm, I gather.\"\n\n\"You make it sound pretty fine,\" Redwing said in a flat voice, no inflection at all.\n\nHer tongue darted out, and she looked uncertain. \"It is, in its way.\"\n\n\"We all have to come down? Leave the ship in some orbit?\"\n\nShe paused. Redwing now sensed a presence near her, the target of her glances. Somehow from the small sounds of muffled movement, shuffles, and long slow breaths, he felt something nearby. The source of that strange voice, yes. Maybe more of them, several aliens watching, listening, no doubt knowing through their technology what he meant as soon as he said it. And what else would they get from this conversation?\n\n\"I... suppose so. They do want to study SunSeeker, they say. There are some aspects of the magnetic throat and drive they might be able to use. One of the Folk\u2014a big one who seems in command, though it's hard to tell, really\u2014says the techniques we use may have been known a long time ago, and lost. So they're interested.\"\n\n\"Lost? How old is this Bowl?\"\n\n\"They won't say.\" She frowned. \"Maybe they don't know.\"\n\nBeth and the others kept quiet as Redwing's face furrowed with thought.\n\n\"And if we don't like to stay long? And give over a lot of our people?\"\n\n\"They say this aspect of our interactions is not negotiable. They must acquire some of us.\"\n\n\"No deal,\" Redwing said sharply.\n\n\"Then... there will be... suffering, they say.\"\n\n\"We've come to threats pretty quick, haven't we?\" Redwing said with lifted eyebrows.\n\nShe gave him a quick nod. Then the screen went blank.\n\nThey sat in Redwing's cabin a long time, watching to see if the signal came back on. It didn't.\nPART VIII\n\nCOUNTERTHREAT\n\nThe possession of knowledge does not kill the sense of wonder and mystery. There is always more mystery.\n\n\u2014ANA\u00cfS NIN\nTWENTY-FOUR\n\n\"They seem as recalcitrant as you implied,\" Asenath said, leaning toward Memor and fluttering irked yellows about her neck. Her harsh warm breath rippled Memor's ruff feathers, an unpleasant sensation.\n\nBemor added, \"More so.\"\n\nThey were ensconced in a shadowy side chamber after the transmission to the alien ship. The dark rock walls were of truly ancient times, furrowed with past attempts at adornment\u2014panoramas that once depicted vast sagas of civilizations, long vanished. These had nearly worn away, leaving the striations and sparkles of the original grit-soil substance from which the Bowl was first built. The air of great, chilly expanses of time clung to them.\n\nTananareve, the last remaining Late Invader prisoner, was bending, flexing, pulling her foot to her forehead, sitting up and lying down over and over with a weight on her straightened hind limbs. The motion was distracting. They were flexible creatures, indeed. Memor told herself that the primate was doing it for her health and tried to ignore it.\n\nAsenath restlessly gave an agree-flutter. \"I do not enjoy negotiating with those who can see so little of their true position.\"\n\nMemor gave a fan-salute of agreement but said, \"They are new to all this. No doubt they wish to take their best possible outcome as a beginning position.\"\n\nBemor gave no feather-signals at all, but let his voice range down into low registers. \"They are not negotiating from strength.\"\n\n\"I think they imagine they are,\" Memor said.\n\n\"I could not diagnose that from their speech,\" Bemor said with a casual, superior sniff.\n\nMemor still felt uncomfortable around Bemor, and tried to tell herself that his dismissive murmurs and small feather-displays were not meant to offend her. Perhaps they were mannerisms he had evolved to deal with staff and lower workers? Stiffening her resolve with this thought, she allowed herself some of what the Folk termed \"lubrications\" on what she had learned, using images of the primate cast on a shimmering wall projection. \"I have studied their 'tells,' their limited visible methods of adding meaning beyond their words. They communicate, process, and fully feel emotions by mimicking the facial expressions of others nearby. So I studied the subtle shifts in their Captain's eyes, mouth, even the slight expansions and contractions of his nostrils. Apparently they have no ability to signal with their ears.\"\n\n\"Ah, their Captain is male? Unusual.\" Bemor looked skeptical.\n\n\"Bemor, there have been other Invaders who had male hierarchy leadership, yes?\" Memor felt this appeal to his greater range of knowledge would mollify her brother. And give a nod to the very idea of male leadership, too\u2014though he knew well that his prominence at high levels was a planned aberration in Folk social structures.\n\n\"Of course, though we managed them throughout their Adoption to cleanse them of that destabilizing structure. They are now all proper matriarchies.\"\n\n\"But not the Sil,\" Asenath said.\n\n\"They are young, not fully formed,\" Bemor countered.\n\nAsenath gestured outside the Citadel, toward where the primate was hanging from a tree limb, her legs raised to form a V. She remained in that position as the moments passed, but her eyes were on her captors. Distracting. \"And that one\u2014you watched her during the talk with Captain Redwing? She gave some facials.\"\n\n\"Of course. Tananareve is under therapy: well fed, often exercised. This local gravity is closer to her home world, too. A fairly simple creature, she is. And she used no unusual signals, as I could see.\" The Late Invader was still watching her, but surely Tananareve could not follow the swift, layered Folk speech. Simple commands, yes, but nothing sophisticated. She might overhear a word or two, but never the feather-nuances.\n\n\"The eyes,\" Bemor said. \"What does a slow wink mean to them?\"\n\n\"Puzzlement, I believe,\" Memor said.\n\n\"Nothing more?\"\n\n\"Uh, I believe not.\"\n\n\"She used a long slow wink when questioned by that male Captain about the whereabouts of their other party.\"\n\n\"I noticed, but how much can a single small gesture convey?\"\n\n\"Could it be a sexual signal?\"\n\nThey all found this amusing, since sex among the Folk involved ritual feather-displays lasting through several mealtimes, classic dancing and cadences, song-trills of expectation and mutual agreed definition, then the ultimate mounting, all with urging songs and the completing union\u2014not a matter to be taken lightly or often.\n\nMemor was pleased that this remark drew amusement; she was known for her humor. \"They are storytelling creatures, transferring useful knowledge from short-term into long-term memory, with assigned significance, all by telling a narrative to themselves.\"\n\nAsenath said, \"They constantly update this?\"\n\n\"Without complete fidelity to the original, yes. Remembering a narrative alters it.\"\n\nBemor said mildly, \"So they know their inner selves as fictional characters, written by themselves? Then rewritten?\"\n\nAfter more agreeable and incredulous laughter, and then a timely arrival of small tasty animals served on sticks by the attendants, Asenath said, \"I fear that adds to their lack of realism. We should remind them of it.\"\n\nBemor looked skeptical, with purple rushes at his neck. \"That would be...?\"\n\n\"Memor, fetch forth your primate.\"\n\nWhen Tananareve came hesitantly through the arch, the contrast of her spindly, pale skin and dull-toned clothes with the three large full-feathered Folk was striking. Her feet slapped the bare cold stones in her frayed boots and her breath wheezed as she got used to the moist, salty scents of life within a Citadel. She was only a bit larger than the attendants who sat dutifully near Asenath, Bemor, and Memor, their faces always tilted upward hopefully in the ivory light, watching to see what their superiors might need.\n\n\"How do you think, little one?\" Bemor addressed the primate with his rumbling voice.\n\nMemor was shocked. Somehow in a mere few sleep-times, Bemor had mastered the Late Invader tongue, solely from Memor's reports and recordings. His pronunciation was accurate, too, strong on the clunky primate vowels. She felt a wash of cold anxiety and not a little fear. My brother truly is quicker, sharper. Can it be because he links so much with the Ice Minds?\n\n\"Clearly,\" Tananareve said. \"Quietly.\"\n\nBemor gave an amused rustle that no doubt the primate did not fathom. \"Quite well put,\" he said in Anglish. \"Do you think your Captain will cooperate with us?\"\n\n\"If you let go of our people, he will.\"\n\n\"We will compromise on that. We might very well let many of you go on to Glory.\"\n\n\"Nope, we all go.\"\n\n\"That is unreasonable.\"\n\nBemor turned to Memor and in Folk said, \"This is normal?\"\n\n\"They sail before the thousand breezes that blow through their opaque unconscious Underminds,\" Memor said. She noted the primate was looking at them, but did not worry that this creature could fathom their speech. After all, Folk had layered grammars and conditional tenses the primates totally lacked.\n\nBemor huffed skeptically. In formal Folkspeak he said, \"Very pretty. What do we do?\"\n\n\"They do learn by experience,\" Asenath said. \"Memor herself says so. They are in a wholly strange place and may relapse into patterns from their past, fearing to face their future here.\"\n\n\"To face their fate,\" Bemor said.\n\nAsenath said, \"In them there is an undercurrent of strong neurological response to social life. In their neural patterns I read connecting elements, plainly honed by long natural selection. They evolved as hunter-gatherers within a socioeconomy where sharing and justice were critical to long-term survival. Yet these fail when extended to larger groups\u2014a major problem of theirs, even now. Judging from the encased memories I read, even their stable societies oscillated between banquets and barbarism.\"\n\nBemor said formally, \"Our long voyages have revealed much poignant wisdom. I have often viewed from the hull observatories, the vibrant stars glaring in their perpetual dark. That star swarm marks not so much a mystery but a morgue, brimming with once glorious and now dead civilizations. This I learned from the Ice Minds.\"\n\nMemor rustled at this. Here at last Bemor played his strong card, the slow intelligences of great antiquity. They dozed through the Bowl's long voyages, else they might try too many experiments. In this way they were a reserve of long-term wisdom, not of mere passing expertise. They had been present at the Bowl's construction, even participating in its design, or so legend had it. How such cold creatures could know mechanics was an ancient puzzle.\n\nBemor used the rolling cadences of formal speech to stress his different status. Infuriating, but she could do nothing overt about it. And she was his sister twin, too. Asenath would falsely assume they worked together. Perhaps, Memor saw, she could use that in her own favor.\n\n\"You believe they wish to play a role in this Glory matter already?\" Asenath asked intently.\n\nBemor fan-marked yellow agreement tones. \"They must. The Glorians have technologies we need to ascend to a higher level of communications, with minds that have ignored us until now. The Ice Minds also surely wonder if these primates could ever fit in on the Bowl. They have implied such.\"\n\nAsenath said, \"The primates will have to.\"\n\nBemor said with casual superiority, \"If they are able. We live among the long history of spaces and species. We encourage local groupings and discourage long travels across the Bowl. These adventurers may not fit in well. They seem obsessed with pushing beyond their horizons.\"\n\nAsenath said, \"Most of our Adopted give their names as 'the people'\u2014whom they of course assume to be blessed. Others are, well, not so blessed. Each likes to see itself as central and important even among the vast tracts of the Bowl. Many live within a history of faces\u2014bosses and chiefs, matrons and managers on high. As they adapt, these Adopted, to the majesty that is the Bowl, their history becomes simple. It is about who wore their own species' crown and then who wore it next.\"\n\nBemor fluttered agreeably. \"Of course, as planned long ago. The Adopted do not any longer reflect upon great matters, beneath our eternal sun, untroubled by the universe around them. They dwell in comfort, without the horrors of unsteady sunlight, of seasons and slantwise sun. The Ice Minds see nothing but the entire universe, all around them. They are of the constant dark.\"\n\nMemor thought this a bit much, attaching Ice Mind majesty to his own agenda. But she said nothing. She thought, though, upon her own past roles in this. Species grew in number until the Folk had to shepherd them to their equilibrium value. Belligerence and slaughter ran their bloody course. Borders brought a fretwork of scars, a long scrawl of history made legible on ground. With borders of sand or forest or water, Astronomer Folk shaped place to match species. Boundaries defined. When warring muddles arose, they examined yet again why territory caused them. Often this came from inept borders drawn by yawning bureaucrats far in the past.\n\nSo Memor and others thrust themselves into the ground truth of locales, letting time brew wisdom from raw rubs and strife. Such lands were often the equivalent of cluttered attics, stuffed by history with soiled rags, dented cans, and old, oily wood: a single spark could ignite them. Such running sores where species war raged unchecked, the Folk could only cleanse with great diebacks. Quite commonly, the packing fraction of religious passions in too little space was the deep cause, and had to be corrected. Folk molded the Adopted so none sprawled in an unending tide. Conversations and genetics shaped better and longer than mountains and monsoons could. Tribal beliefs in a tyrannical God figure running an imaginary, celestial dictatorship were often easier to manage. They understood hierarchy.\n\nSuch was the aged truth the Folk learned either from the Cold Minds or from hard experience. Memor had climbed up with a chilly indifference to necessity, and so now had merited the honor of dealing with the Late Invaders. I hope I can capture the renegades and win approval, Memor thought, suppressing her Undermind's qualms. Or else there will come... execution. She felt a shudder from her Undermind\u2014something she could not see, a secret of great implication... it slipped away.\n\nHer reverie done, Memor snapped back to attention. Asenath ventured, \"So... we should not consider these primates good Adoption candidates?\"\n\nBemor gestured at the primate, who narrowed her eyes and looked intently at him. \"No, I believe they can be broken to the rule of reason, in time. But their Adoption should not be assumed to be an important value to us. We need them to help negotiate with the Glory system, true. But we can then cast them aside like a sucked carcass, if we wish, at little loss.\"\n\n\"What habitat would suit these creatures, then?\" Asenath asked.\n\nMemor said, \"I have plumbed the mind of this primate, Tananareve. I gather they want to be on a height looking down, they prefer open savanna-like terrain with scattered trees and copses, and they want to be close to a body of water, such as a river, lake, or ocean. They prefer to live in those environments in which their species evolved over millions of years. Instinctively, they gravitate toward parklands and transitional forest, looking out safely over a distance toward reliable sources of food and water. They can flee predators from land to water, or back, or to forest, where their kind once lived in trees.\"\n\n\"What a primitive mode!\" Asenath seemed repulsed.\n\n\"Is this opinion, that the primates are mostly useful for dealing with Glory, the sole wisdom the Ice Minds wish to convey to us at this point?\" Memor asked, turning to Bemor.\n\n\"I think that is quite enough indeed,\" Bemor said\u2014rather haughtily, Memor thought. \"But...\" Bemor moved uneasily, feathers rustling. \"The Ice Minds do not always reveal their thinking. They seem unusually interested in these primates. Still, they wish us to secure the help of these Late Invaders.\"\n\nAsenath rushed to send an assent-flutter toward Bemor and turned a subtle angle toward him, and so away from Memor. \"So, Contriver, I propose that we give the primate ship a reminder of their true position.\"\n\n\"Um,\" Bemor said with a skeptical eye-cant. \"How?\"\n\n\"They are inspecting the magnetic configurations around their ship, probably to better guide their own craft. But it could be they will use it to disturb our magnetic mechanics, as well. Their technique is to spread a wide array of sensors.\"\n\n\"Adeptly so?\" Bemor said.\n\n\"These are craftily done, hundreds of disks the size of my toenail. I suggest we wipe our skies free of them.\"\n\n\"Destroy them?\" Memor asked.\n\n\"It will serve as a calling card,\" Aseneth said with a smirk-flutter.\n\n\"I'm sure it will,\" Bemor said, sending an assent corona of yellow and blue. He leaned forward eagerly. \"We will at least learn something from their response.\"\n\n\"I shall see it is done,\" Asenath said happily. \"I believe these Late Invaders will be put in their proper place, and soon realize it.\"\n\nMemor wondered if she had been outmaneuvered here. Caution would have been her policy, but Bemor seemed bemused by the idea of overt action. \"I hope you enjoy it as well, Asenath,\" Memor said with what she hoped was just the right tone of sardonic agreement. It was always difficult to get these things right.\nTWENTY-FIVE\n\nBlessed night, Cliff thought. The soothing qualities of pure deep darkness washed over them all. After months of relentless sun, they had all they wished of sweet shadow. It fell like a club upon their minds, sucking them into sleep.\n\nHe swam up to blurred consciousness after another long sleep, wrapped in a fuzzy warm blanket the Sil had found for them all. His team lay around like sacks of sand, feasting on the festival of dark that released their need, after so long in the field, for rest.\n\nHe was still groggy. Something had sent a twinge, awakened him. He got up, pulled on pants and boots, and left their little room carved from brown rock. His boots were getting worn down and he wondered how he could get something serviceable. As usual, the right answer was, ask the Sil.\n\nSmall soft sounds were coming from where they viewed the Ice Minds messages. He came in carefully, watching the two Sil speaking in their curious way. There was more eye and head movement than there was talk. And as usual, the most active one was Quert\u2014who noticed Cliff and beckoned him over with an eye-shrug.\n\n\"Ask for wisdom of past,\" Quert said. \"This got now.\"\n\nOn the screen were phrases that might have been answers to Sil questions.\n\nOver long times there is no lack of energy or materials, only of imagination.\n\nNot having resources makes species resourceful.\n\nAnger dwells long only in the bosom of fools.\n\n\"Thanks for having them do this in Anglish.\"\n\n\"Did not ask. They spoke first to us. Now to you.\"\n\n\"What is this all about?\"\n\n\"Want to deal with Folk. You can help. Ice Minds care not for us. Care for you.\"\n\n\"Why?\"\n\n\"New Invaders know new things.\"\n\n\"So they brush you off with 'Anger dwells long only in the bosom of fools.' And you are supposed to forget how the Folk killed so many of you?\"\n\nQuert gave only a tightening around the eyes, and his words were in a cool whisper. \"Ice Minds say we are unquiet in soul.\"\n\n\"You're handling those deaths better than I have done with my friend Howard.\"\n\n\"There is more worry to come.\"\n\nQuert beckoned him toward the large portal that gave a view of the sprawling icefields. To the side the stars wheeled and on the dim icy outer crust of the Bowl the vacuum flowers slowly tracked the brightest stars in the moving sky. This was for Cliff still a magical vision. He watched it with Quert, who after a moment made a simple hand gesture and the portal flickered. The view jerked and though the stars still swept across the jet-black sky, now there was a bright object moving counter to the Bowl's rotation, skating across the blackness. When it was nearly overhead, a sudden beam flashed into view and Cliff realized the craft was using a spotlight. A powerful green laser beam fanned out to a ten-meter circle, sweeping. The beam flared briefly as it shone directly into the portal and then moved on. The bright point of the surveying ship tracked on, away and over the horizon. The stars wheeled on.\n\n\"That was a recording?\"\n\nAn assent-rachet of Quert's eyes. \"They not see your kind. Saw us.\"\n\n\"Some Sil? If they were looking for us, then we're safe\u2014\"\n\n\"Folk say Sil not come here.\"\n\n\"I thought\u2014\" He stopped, realizing that he had not thought at all whether the Sil were trespassing here. Apparently they were. Once the thought occurred, it seemed reasonable. You don't want riffraff intruding into the provinces of beings who dwell in deep cold. Their mere body heat could cause damage.\n\n\"No one is to come talk to the Ice Minds?\"\n\n\"Not allowed by Folk.\"\n\n\"So they'll come after you?\"\n\n\"Soon. We move.\"\n\nCliff realized he had thought of this cool dark refuge in rock as a resting place. They were all tired of moving across strange landscapes. But now they would lose that, too.\n\n\"Where to?\"\n\n\"Warm and hot.\"\nTWENTY-SIX\n\nRedwing woke from a blurred dream of swimming in a warm ocean, lazily drifting... to a melodious call from the bridge. He hated buzzers in his cabin, and so the strains of Beethoven's Fifth drew him up with their four hammering notes. If he didn't answer within ten seconds, it would double in volume. He got to it in nine. \"Um, yeah.\"\n\n\"Captain, the smart coins aren't reporting in,\" Ayaan Ali said in a tight, clipped voice. In task rotation, this was her week on the skeleton watch. It was 4:07 ship time.\n\n\"How many?\" He was still groggy.\n\n\"All of them. Their hail marks just winked out. I had them up on the big board along with full stereo visuals in optical. Their hails started disappearing at angle two eighty-seven, and a wave of them swept across the real space coordinate representation. It took, let's see, one hundred forty-nine seconds to sweep over all of them. I can't get a response hail from a single one.\"\n\n\"Sounds like an in-system malf.\"\n\n\"I checked that. The Insys Artilect says nothing wrong.\"\n\n\"You called on the other two?\"\n\n\"I brought them up into partial mode to save time. With just their diagnostic subset running, I got them to review whole-system stats for the last hour. They say there's nothing wrong.\"\n\n\"The full Artilect is right, then.\" His mind scrambled over the problem, got nothing. \"Run it again. And direct for an all-spectrum search. Plus look at all the particle count indexes. Everything we've got.\"\n\n\"Yes, sir. Shall I call\u2014?\"\n\n\"Right, Karl. And Fred.\"\n\n\"Yes, sir.\"\n\n\"I'll be there pronto.\"\n\nHe made it in under two minutes. His onboard coverall slipped on easily\u2014he had been losing weight lately, working the weights and doing pace running\u2014and he used Velcro shoes. Ayaan Ali's brow was creased with lines he had never seen before. Worry, not fatigue.\n\n\"Nothing unusual in the all-spectrum,\" she said, voice high and tight. \"Particle fluxes normal. The magnetosonic and ion cyclotron spectrum is as usual, pretty much. But the Alfv\u00e9n wave spectrum power is up nearly an order of magnitude.\"\n\nThe Insys Artilect visualized this spectrum, cast over the schematic of their near-space environment. It presented as a green front of waves rolling over the zone of the smart coins, silencing each as it swamped them. With an on-screen slider bar, Ayaan Ali moved this map backwards and forward in time. \"I wonder how these magnetic waves could turn off our coins.\"\n\n\"Tumbling them, I would think,\" Karl said. He had come in quietly with Fred just behind. \"Alfv\u00e9n waves can nonlinearly decay into waves short enough to be of the same size as the coins. That tumbles them and can kill their navigation.\"\n\n\"And maybe turn them off, too,\" Fred added.\n\nKarl pointed to the wave sequences. \"They spread out from the jet, notice. An example of what my language has a single word for\u2014Vernichtungswille: the desire to annihilate.\"\n\n\"So this is the Folk reply to our first negotiation?\" Ayaan Ali asked.\n\n\"Looks like,\" Fred said. \"Say, what's that?\" The back-time display ran into earlier hours, and Fred reached over to freeze it, march it forward. As he did, a blue wave rushed across the entire display space. He backtracked it, shifting out to larger frames. \"Look, it traces back to the jet. What's blue mean?\"\n\n\"High-energy ions.\" Ayaan Ali thumbed the resolution until they could make out a snarl in the jet itself. It was a knot of magnetic stresses that tightened, fed by smaller curls of magnetic flux that rushed outward along the jet.\n\n\"Look,\" Fred said. \"Kinks came purling along the jet, moving fast. They converged in that knot, and\u2014here comes the blue.\"\n\nKarl nodded. \"From that we get the Alfv\u00e9n waves. Very neat, really. They can control the magnetic fields in their jet, focus them.\"\n\n\"To kill our coins.\" Redwing looked around at them. \"To show us what they can do.\"\n\nA silence as they looked at him, as if to say, What do we do?\n\n\"Officers of the bridge, I want you to fly a small satellite over the rim of the Bowl. We haven't got any recon of the outside of this thing, and Ayaan Ali reports that we got a stray signal from Cliff's team just hours ago. It was text only, said they were under the mirror zone. If we can put a relay sat within range of them, on the outside, maybe we can make a stable link.\"\n\nFred looked at Redwing for a long moment. \"You want to risk a satellite?\"\n\n\"I think we need to know how far these Folk will go,\" Redwing said. He kept his tone mild and his face blank.\n\n\"As for further measures, I have a brief from Karl\"\u2014giving him a nod\u2014\"and we will meet in the mess at eight hundred hours to discuss it.\" A pause to let this sink in. Time to go public, he figured. \"Dismissed.\"\n\n* * *\n\nHe started the meeting with news. Ayaan Ali delivered it, standing beside an image that flickered onto their wall screen. All exec crew were arrayed around the biggest table on the starship, coffees smartly set in front of them, uniforms fresh pressed from the steamer presser, everybody aware that this was not just another damn crew meet.\n\nGrimly she said, \"We launched our satellite toward the nearest Bowl rim. It is a microsat with ion drive, so it accelerated fast. I took it over a mountain range that neighbors the rim edge. See the picture sequence.\"\n\nA set of stills ran, in time jumps that made the craggy mountains below zoom past. Their peaks were in permanent snow despite the constant sunlight. Redwing supposed this meant that the atmosphere was thin there and the outer skin, which they now knew was quite cold, was only a short distance away. The chill of space kept water frozen out.\n\nNow the scene stuttered forward to show the Bowl rim approaching. The sat probe scanned forward, aft, both sides. At the far left edge, the atmospheric film shimmered, keeping air confined. On the left a small bright light appeared.\n\n\"I stop it here,\" Ayaan Ali said. \"Note the near-UV burst on this view. It appeared within a microsecond frame, apparently a precursor.\"\n\n\"To...?\" Karl wondered.\n\n\"This. Next frame.\" Ayaan Ali pointed to a bigger white blotch at the same location to the sat probe's left. Her smile had a sardonic curve. \"And that is it.\"\n\nKarl asked, \"What happened? Where's the next frame?\"\n\nAyaan Ali gave them a cold smile. \"There are no more. It stopped transmitting. Here is an X-ray image of that region. I had it running all during the fly-out, just in case.\"\n\nThey could make out the dim X-ray images of mountains and Bowl rim. Apparently this came from minor particle impacts of the solar wind. At the very edge of the rim was a hard bright dot. \"That's our probe dying. From spectra and side-scatter analysis, I believe the killing pulse, which we saw the UV precursor of, was a gamma ray beam.\"\n\n\"From where?\" Redwing knew the answer, but he liked to let Ayaan Ali keep the stage.\n\n\"That big cannonlike thing farther along the Bowl rim, sir.\"\n\n\"It's an X-ray laser?\"\n\nAyaan Ali shook her head. \"This image comes from secondary emissions. I can tell by looking at the spectrum. Also, I had a gamma ray detector taking a broader picture. It gave this.\"\n\nAnother bright dot. This time there was no background at all, just a point in a black field. \"The power in this image is five orders of magnitude higher than the X-ray fluence.\"\n\nHe said flatly. \"So we were right. It's a gamma ray laser.\"\n\nRedwing looked at Beth. Ever since she returned, he had asked her to attend tech meetings, reasoning that she might have insights called forth by new events. \"As far as I know, we never found a way to go that high in photon energy. Did you see any signs the Folk had tech like that?\"\n\nNow Beth shook her head. \"Weapons weren't really around us. Or maybe we didn't even recognize them as weapons. They didn't need them, I guess. We were trapped.\"\n\nAyaan Ali said, \"Weapons of this class would be very dangerous on a rotating shell world. Blow a hole in the ground and you're dead.\"\n\nKarl said, \"There was an Earthside program to develop high-frequency lasers long ago\u2014I mean even before we left\u2014and it never got lasing to gamma energies. At those tiny wavelengths, a laser could focus to very small areas, so you wouldn't need very much power to blow something to pieces.\"\n\nFred said, \"This is bad news. Now we can't fly a probe over the rim. They can kill any sensors we send out. We're bottled up.\"\n\n\"No doubt they expect us to come back to them and ask for a negotiation,\" Ayaan Ali said.\n\n\"Which we won't do,\" Redwing said. Nobody said anything. Time to change direction. Sometimes that jarred loose a fresh insight. He leaned forward, fingers knitted together. \"Beth, do you think that the Folk would ever let us go forward to Glory?\"\n\nBeth sighed and looked at the screen, where the explosion of their probe was frozen in time. \"They have a very hierarchical society. The big one who interrogated us, Memor, acted as if she owned the world. It's hard to think they'll let us go and reach Glory first.\"\n\nAyaan Ali said, \"Which we certainly could do, since we won't be facing their jet backwash.\"\n\nRedwing remembered a lecture on alien biospheres during flight training in which someone said, \"Humans and animals regard each other across a gulf of mutual incomprehension. With aliens, that has to go double.\" Yet here he was trying to figure out the negotiating strategy of an alien mind, immersed in a civilization uncountably old. He let them toss ideas around for a while to get them used to their situation. Sending the probe out to get destroyed had given the right edge to this, he decided. And it had laid to rest any notion that the Folk were bluffing.\n\n\"So...\" He let the pause grow; they were so quiet, he could hear the whisper of the air circulation. \"Let's send a reply.\"\n\nKarl got up to speak and flicked on the wall display. It showed the jet in an extreme view\u2014magnetic field lines in ruby, the tubes of bright plasma they contained glowing orange, the Bowl itself sketched in nearby as abstract lines. \"We can fire a shot across their bow. The jet is pretty narrow as it approaches the Knothole. Notice the helical mag fields that funnel and contain the plasma. Very neat.\"\n\nBeth said, \"So the idea is...?\"\n\n\"Fly into it. Disturb the jet. Let it flicker around in the Knothole.\"\n\nThey just gaped at Karl. He had a chance to check their teeth and noted that Beth had an incisor with some ragged damage and stains. Beth let out a breath. \"I flew us up the jet, remember? Remember? It was like taking a sailing ship through a hurricane. Do that again?\"\n\nFor a long moment Redwing watched the naked fear play across her face. He recalled the long hours of strain and sweat as the ship popped and creaked, the racking uncertainty Beth had showed as she stayed with it through surges and awful wrenching turns. All the crew had worked to the limits of their endurance. That had been their only real choice. Through it all he showed no uncertainty. That was his job. And in the end he did not regret it.\n\nBut this was not a necessity. They could coast here and play for time. But they could not leave. And they were eating their provisions while Cliff's team was in constant danger.\n\nHe said slowly, \"I think we need to show them that we are not going along with their agenda. That we will not be docile members of their big club.\"\n\nA long silence. Their faces tightened and mouths compressed to thin white lines: startled fright, worry, puzzlement. Karl then said, \"I wasn't thawed when you danced through the Knothole, Beth, but I checked this out with Fred. The physics is fairly straightforward. It won't last long, maybe ten hours.\"\n\nRedwing could see they were too stunned to take it in.\n\n\"We'll leave the technical aspects for later. There will be three crew rated to pilot on the bridge at all times. In fact, all crew present. Warn the finger snakes to anchor themselves.\"\n\nKarl said formally, \"I want you all to know I have done calculations and simulations. There is a broad parameter range of what we might face. The Navigation Artilects have been working full bore to study trajectories, the back-reaction of the jet plasma flow on our mag throat. It compresses our prow fields and alters our uptake\u2014but that's mostly good news, because we get more thrust from the plasma. There'll be plenty of ions to fuel our fusion burn. I think\u2014\"\n\n\"Yes, technical aspects come later.\" Redwing smiled and tried to look confident. \"Thanks, Karl.\"\n\nBeth looked him straight in the eye. \"We don't understand the Folk worth a damn, sir.\"\n\n\"Indeed.\"\n\n\"I have no idea how they'll respond.\" Beth looked worried, and her eyes jerked around the table, looking for support.\n\n\"They understand negotiation, that's clear from our conversation through Tananareve. They've killed our coins and now our probe. Let's show them we know tit for tat, too.\"\n\nThey looked hard at him. Ayaan Ali still had her slightly wide-eyed, shocked gaze. Fred wore his usual expectant fixed stare. Karl was trying to look confident. Beth's face was pale and strained, eyes fixed on him.\n\nHe stood. \"I want you all to know we'll reply to the Folk. But while doing so, we'll navigate toward the jet and make preparations.\"\n\nThey left quietly. None of them looked back at him except Beth. She waited until the others were gone and closed the door. \"I have to admit it feels good to be doing something. I didn't like being in their prison. Even when we got out, it was into a bigger prison.\"\n\nRedwing blinked. \"One the size of a whole damn solar system?\"\n\nShe laughed, gave him the high sign, and left.\nPART IX\n\nON THE RUN\n\nSome folks are wise and some are otherwise.\n\n\u2014TOBIAS SMOLLETT\nTWENTY-SEVEN\n\nCliff was tired of traveling. The immense distances of the Bowl took a steady toll that could not be erased by dozing in uncomfortable seats designed for another species, or indifferent food gotten from dispensers along the way, or headphones that tuned out the drones and rattles of endless long transport. The Bowl was built on the scale of solar systems, but humans were built to smaller perspectives.\n\nQuert and the other Sils had brought Cliff's team through a twisting labyrinth of tunnels, moving away from the hull where the Ice Minds dwelled. Then a mag-train. More tunnels. Occasional glimpses of odd landscapes seen through huge quartz sheets that glided by as they took barely curved speed ramps at planetary velocities.\n\nHe had felt the surges and high speeds, but after a while they did not register as distinct events, just a long symphony of lurches. At times he felt he knew where they were in an astronomical sense\u2014alignments of star and jet and horizon, glimpsed through flickering windows. But those got confused as soon as he looked again, hours later, after being pummeled and spun.\n\nNow they ventured out, on foot, into a terrain that reminded him of California deserts\u2014low scrub brush, gullied tan terrain, hazy sky, occasional zigzag trees. Those seemed to grow everywhere on the Bowl. Gravity was different here, a lot less. He felt a slight tilt to his weight, too. They were closer to the Knothole, had to be.\n\nCurious blocky buildings visible through some dust haze in the distance, maybe ten kilometers away, a tapered tower at its center. Cliff drew in hot dry air with a crisp, nose-tingling flavor and basked in the raw sunlight. It was good to be still and on your feet in sunlight. Always sunlight.\n\nQuert beckoned the others out of the well-disguised hatch that led into the hull system. For many hours they had crawled through some conduits and once had to wade through a sewer to get onto a fast-moving slideway. Then a train. The Bowl's constant daylight threw off their sleep cycles. He'd measured this, and found that the team had shifted to a thirty-hour waking cycle. The welcome dark of the night-side hull had helped fix that. But they were worn down.\n\n\"Think we're okay here?\" Irma asked Quert.\n\n\"Need go farther,\" Quert said, looking around. \"Not safe here.\" The other Sil shifted uneasily and looked at the zigzag trees.\n\n\"What's the danger? At least it's warm.\" Irma had not liked the cold and had hugged one or the other of the men in the night, seeking warmth. Nobody thought anything of it; they were all in a pile most of the time, dead to the world.\n\n\"The Kahalla. In shape they are more like you than we. An old kind of Adopted. Loyal to Folk.\"\n\nIrma frowned. \"So what do we do?\"\n\n\"Find...\" Quert paused, as if translating from his language. \"Tadfish. You would say. Maybe.\"\n\n\"There's shelter over there.\" Terry pointed at the low hills to their left. He seemed more alert and energetic now, Cliff noted.\n\n\"We go past that,\" Quert said, but the other Sil around him rustled with unease. This was the first sign Cliff had seen that they all could understand Anglish. Plainly they were worried, their legs shifting and heads jerking around as if looking for threats.\n\n\"So let's do this fast,\" Aybe said. He, too, looked refreshed. They all had skins worn from constant sun but not deeply tanned. There wasn't a lot of UV in this star's spectrum.\n\nThey set off at a long lope made graceful by the lower gravity. Cliff got into his stride easily, enjoying the sensation of hanging a second or two longer at the apex while his legs stretched out. As much as he had liked the dark of the hull labyrinth, the sunlit open was more his style.\n\n\"Kahalla!\" one of the Sil cried. Quert stopped and turned and so did they all. Some fast shapes flitted through a distant stand of zigzags and heavy brush.\n\nAt first Cliff thought these were four-legged creatures, but as one of them sped across a gap in the rust-colored brush, he saw they had two legs. Their gait leaned forward and hinged oddly. Big angular heads.\n\n\"Here Kahalla live,\" Quert said.\n\n\"What should we do? Deal with them?\"\n\n\"Do not know.\" Quert and the other Sil looked carefully at the Kahalla. There were many of them.\n\nThey all began to run again. Quert waved them away from the zigzag trees where the moving figures were and toward the buildings several kilometers away across a dusty plain. It seemed to Cliff they were needlessly exposed there but then Quert, who was in the lead, took them behind a rise and into a slight gully that was enough to shield them from direct fire. Dust from their running stung his nose. They were all running flat out. His team had their lasers and Quert their own weaponry, but they were vastly outnumbered. Until now he had not thought much about how lightly armed Bowl natives were. That seemed to imply little overt conflict despite the vast and horrible damage the Folk had dealt out to the Sil. There was an odd Zen-like grace to them in the face of horror.\n\nAs if sensing that something was up, big birds flapped suddenly from the surrounding brush and zigzags. They swarmed and turned together and made off with loud keening squawks. In the lower grav, the big wings could use the slight wind to escape. Obviously to these odd four-winged birds, the running figures meant trouble.\n\nThe dust swarmed up into his nostrils and stung. The acrid nip also snapped him into focus. He looked up at the big birds stroking themselves up into the air and he recalled his sense of relish when he saw his first Baltimore oriole. They were nearly extinct then. The Great Crash had passed but many birds were teetering on the edge, and the sight of the deep flaming orange against the rest of its black plumage thrilled him. He knew the Baltimore oriole's name came from some ancient coat of arms royalty, but that mattered nothing compared with the small fragile beauty of it. These alien birds sweeping and cawing above had none of that, yet they still stirred him. So why had this structure, vast in size and time, kept so much rich wildlife when Earth had not? Humanity had overrun itself in vast sullen cities long ago. Its soiled vapors ruled the sky, still, despite earnest geoengineering.\n\nThat question swarmed up, awakened by this wealth of life flapping around him. Stinging sweat trickled into his eyes and he was glad of it.\n\nHe remembered the bleak gray landscapes he had seen across the American West following the Great Dry. The denuded skeleton forests of the High Sierras, where fires consumed the last needles of the demolished pine forests and layered the Owens Valley with black shrouds for weeks. The dead dry prospects of deserted suburban streets lined by abandoned cars already stripped of their paint by the hissing sands borne on constant hot winds.\n\nHis legs burned with fatigue. Cliff shook his head to throw the sweat aside. He checked that his team was staying together, and panted, and felt the ache slicing in his lungs, and ran on.\n\nSometimes he could abstract himself out of the moment with thoughts, memories, dreams, anything. Anything but the terrible fear that once again they were the prey. His team. Being run down again. His responsibility.\n\nSo... how did this enormous artifact preserve such diversity of life? It was like some goddamned Central Park in Old Manhattan, before the rising seas washed all that away. A natural place that life sought refuge in, yet it was an artifact, a managed simulacrum of the natural world. A jewel in a concrete setting.\n\nBut this place was not a dead park. It lived and maintained itself and went on. He had to concede that to the Folk who ran this place. They had evaded the excess that had nearly ruined Earth.\n\nHe ran on. The others panted and strained around him. The Sil took their long strides with easy grace and were always ahead. The humans labored in sweat and stink and gathering sour fatigue as the building complex loomed.\n\nIn the zigzag trees around them, Cliff felt the presence of the running humanoids though he could not see them. It seemed stupid to be pursued on foot like Homo sapiens sapiens of a hundred thousand years before. Here amid a fantastic construction they were reduced to\u2014\n\nThen he saw it. The Bowl, a huge facsimile of a real planet, kept itself running and stable by being larger than worlds could be. Giving life enough room to find its own way.\n\nBut how did they stop the myriad intelligent species here from expanding beyond their province? A puzzle.\n\nAnd now there was no more time for idle thought. The distant buildings were close. And his legs were made of lead.\n\nQuick is the word and sharp's the action. Where had he heard that?\n\nThey came upon the towering great gray slabs through an outer maze of silvery metal sculptures. These depicted heavyset humanoids in various poses, mostly in combat with assorted knives, shields, lances, and the like. The nude bodies were squat and sturdy, big muscled chunks above short legs and fat feet. Their ribs seemed to wrap around the whole body and their arms turned both ways, double-jointed and elbowed. Some statues were of standing figures and in the air around these gleamed some unintelligible script that flashed brighter as Cliff looked at them. A smart system that registered his gaze and amped the label? They reached a large bladelike tower that seemed solid, standing at the center of a hexagonal open spot. Flagstones of intricate angular designs led toward this tower and up its flanks in elongated perspectives. There was a solemn air to the place as its design soared up the flat tower face, ornamented with bumps and knobs that tapered away into the sky.\n\nThey paused to drink water and Cliff stood looking at the big stonework. Slowly, about fifty meters up, an eye opened.\n\nHe knew it was an eye though it was of the same burnished tan as the rest of the tower. It had a green center like an iris. Slowly the entire oval, several meters across, turned downward to look at them. One eye.\n\n\"What...\" Cliff could not take his eyes off the single enormous pupil at the thing's center. It seemed to be looking straight at him. A pupil in rock? An eye with lens and retinas?\n\n\"Stone mind,\" Quert said simply. Then he turned quickly and peered into the distance.\n\nCliff looked to his left and saw several of the stumpy humanoids flitting among the sculptures. There were a lot of them, moving with surprising speed. They huffed and squatted and made ready. Their brown clothes seemed to have endless pockets and they fished among those to bring out things, affixing them to the long tubes.\n\n\"Chem guns,\" Aybe said. \"In all this high tech, the old stuff still makes sense.\"\n\n\"Or maybe they haven't been allowed any more advanced tech?\" Terry wondered.\n\n\"We saw a humanoid like this, remember?\" Irma said. \"It opened a door leading down into some entrance, back there on an open plain. When it saw us, it just walked away.\"\n\nAybe said, \"Yeah, maybe we should've looked into that entrance. We were getting pretty ragged, maybe it would've been good shelter.\"\n\nCliff knew this was a way of calling up an unspoken grudge. He had argued to push on and they had. \"That means these humanoids are maybe maintenance workers,\" he said mildly. \"They're working for the Folk, keeping the Bowl fit.\"\n\nThey broke off talk as the creatures moved. Without a word the entire party of Sil and humans turned and watched the humanoids go to each flank, surrounding them. Nobody spoke.\n\n\"Kahalla,\" Quert said. \"They hold us for Folk. Send message.\"\n\nTerry whispered, \"How can we get away?\"\n\nBefore Quert could speak, a long droning note washed over the area. It seemed to come from everywhere and was more like a sensation in Cliff's body than a sound. The tone shifted and a long rolling vowel played out, aaahhhhmmmm.\n\nQuert said, \"Sit. Listen. The stone mind wakes.\"\n\nCliff sized up their situation. There were at least a few hundred of the humanoids around them. They didn't look friendly. Many wore jackets and carried long tubes that looked like some sort of launch weapon. They were swarthy and their heads never turned away from watching the humans near the tower. They bristled with suppressed energy. Cliff wondered how he knew this and saw it was something about reading body postures. Maybe that was a universal, across species? Or else the whole primate suite of abilities converged\u2014driven by the urgent need to communicate, no matter what world your abilities came from\u2014on myriad subtle signs that told stories from a mere glance.\n\nIrma said quietly, \"They're dangerous. We can't fight them. Are we waiting for this song to end or what?\"\n\n\"They hear the long voice,\" Quert said.\n\nAybe said, \"So? How long does this last?\"\n\n\"The rock being speaks of its many deaths,\" Quert said, its head dipping low and eye darting up and down, a gesture Cliff did not know.\n\nTones now shifted higher, into shrees, kinnnes, awiiihs, and oooeeeiiinneees. The pressing power in it seemed to hammer the air around them. Cliff felt these as warring long-wavelength notes that made his muscles dance, his body arch and flex and stretch in resonance with the powerful sounds rolling through the dry air around them.\n\n\"It's... it's playing us,\" he managed to get out. \"This sound...\"\n\n\"It tells of its great death,\" Quert said. \"Takes far time.\"\n\nThe Sil had formed a crescent facing outward against the solemn threatening silence of the humanoids. Together with Quert, the Sil flexed their arms, turning their inner elbows up to the sun. Cliff saw slender black fibers extend in the pits of their elbows. Their tips gleamed in the hard sunlight. He had never been able to tell males from females in the Sil, but it did not matter. They all had done some physiological magic and made these black lances poke out of their inner elbows. One of them abruptly jerked an arm down and the lance arced fast and sure out in a long parabola. The elegance of it struck Cliff as it watched it skewer a small wood emblem atop a hunkering stone sculpture of a big-chested humanoid. It hit the dry dark wood exactly in its center, and the black arrow flapped with energy not yet dissipated. As sure a challenge as he could imagine.\n\nThe humanoids did not respond. Their feet shuffled, their heads waggled a bit, but no sounds came. The big notes had fallen silent, and Cliff thought the song or whatever it was had come to an end. Dead silence. The Sil glowered at the humanoids and flexed their black arrows. He wondered how that had evolved. Gene tampering? An onboard defense, obviously. You didn't have to carry anything, and the black rods with their gleaming pointed tips waited for the downward yank of the arm. Their hands could be free, so they could have other weapons there, too. But... the Sil held no other weapons in their hands. No pistols or guns of any sort. Unlike the humanoids, who now sent forth barking calls, high and shrill.\n\nA taunt? A rebuke? It was impossible to tell. The calls stopped and Cliff felt himself tensing, pulse fast and hard. The two bands of aliens glared at each other in what seemed another universal signal\u2014narrowed eyes. Grunts and hisses and heavy panting. Feet stirred in the dust. Arms and chests bunched and flexed. A fevered bristly aroma came drifting on the still air, the heat of bodies exuding aromas that, he supposed, carried signals evolved long ago on planets far from this stark scene. Time stood crisp and still. Eyes darted and judged.\n\nBut then came long drawing notes from the stone tower. Echoing tones of kinnnes awrrrragh yoouuiunggg arrrafff...\n\nHe panted and watched the aliens move into position around them. Shuffling in the dust. Huffing with energy.\n\n\"We haven't got a chance, do we?\" he said in a casual way.\n\nIrma said wryly, \"Looks like.\"\n\nBoonnnug wrappppennnu faaaaliiiooong...\n\nThe humanoids lifted their heads. Their shuffling ceased. As the long solemn notes washed over them, they slowly buckled. Sat. Folded their armaments and their arms, down and low.\n\nThe long, loud notes rolled on. Cliff did not know this speech. Neither did the Sil, he gathered. But the humanoids did and they wilted before the slow steady sway of the music that poured over them. The words became a soothing song that washed over the entire stonework, itself laid out some vast time long ago, an era beyond knowing.\n\nThe warmth lulled Cliff as well. \"Take a break,\" he said to the others. \"Sit. Wait them out.\"\n\nHe felt the flowing wall of sound as it called, yoouuiunggg kinnnes awrrrragh yoouuiunggg.... He felt his knees go weak.\n\nQuert was having none of this. It said, \"Let them sit. You do not.\"\n\n\"Huh? Why?\" Cliff straightened up.\n\n\"The slow song will reach them. Resist it.\"\n\n\"Resist? I don't\u2014\"\n\nQuert gave him an eye-goggle he could not read.\n\n\"Let it go,\" Irma said. \"There's more going on here than we know.\"\n\nTerry and Aybe agreed, heads nodding, eyes drifting, going drowsy and vague. Greee habbbiiitaaa loohgeree...\n\nStrange fat pauses drifted by in the warm air. Hums and echoes. Like corpses on an ocean, Cliff thought, and jerked awake. What an odd repellent metaphor of the vaguely meaningful. His unconscious was seeping through as he got drowsy. Or was it something the words called forth? The low booming voice called... biiitha ablorgh quartehor biiilannaa...\n\nTo keep himself awake and not weaken and sit down, Cliff asked Quert, \"This is a sculpture? With a recording? Why is it so important?\"\n\nQuert looked at him with an expression Cliff had learned to read as puzzlement. \"It is alive. It awakes to speak.\"\n\nCliff glanced up at the huge eye, which was still staring down at them. Gradually Quert's indirect way of saying things unfurled the story of this place. What Cliff saw as a sculpture was actually a living thing. Alien to the Bowl, rugged and slow, it had come long ago from a world that died. \"It lives to tell. It awakes when audience approaches.\"\n\nIrma said, \"This is a smart rock?\"\n\nQuert said, \"Sunlight powered. From world very hot.\"\n\n\"It can't move, right?\" Aybe asked. \"How'd it get here?\"\n\nQuert found all this unremarkable. \"Bowl passing by. Explored that hot world. These Kahalla asked the Bowl to take one of them to keep themselves. To speak for them.\"\n\nTerry asked, \"To carry their culture?\"\n\nQuert turned to them and made a gesture they now knew meant \"stay steady\" among the Sil. \"It sings. The Kahalla decide to send one of them. Their sun swelled. They would soon melt.\"\n\nTerry said, \"I thought those humanoids\u2014\" He gestured at the ring surrounding them. \"\u2014were the Kahalla.\"\n\n\"They take name of living stone.\" Quert seemed to find this completely natural.\n\n\"We triggered the monument? The Kahalla stone?\" Aybe asked, his eyes wandering over the landscape.\n\nCliff understood; it was so ordinary in a dry fashion, but there were plenty of ways to get everything wrong here. Stones and primitives, all beneath a luminous sky, elements of ancient human history and still so easy to see as simple, a tailoring of Earth history. It was nothing like that. The strange kept trying not to be strange.\n\nQuert's eyes meant \"yes.\" \"I-us took here. Knew song was only way.\" The alien's eyes told more than its words, but then words were tight little symbol lines. They could easily deceive the mind.\n\nOnly way? To not get caught? Cliff studied the stern stonework that soared over a hundred meters above them. A single creature, something he would have bet plenty could never evolve: smart rock. On a hot dry world, there must have been some sort of competition. Among rocks? He could not grasp how they contended. Against weathering? To gain mass and so defend themselves against abrasive winds and tides? How could information flow in a stone? How could it gain intelligence, to control its fate?\n\nThis went beyond biology into geology\u2014and yet evolution had to explain such a thing. He recalled how dumbfounded he had been when he first saw the Bowl from SunSeeker. This made him feel the same way.\n\nIt was harder to remain standing, but Quert insisted. The resonant voice boomed on and the Sil listened intently. Long droning notes rode the hot dry air.\n\n\"Each time, different information,\" Quert said.\n\nLong song pealing on. In the next hour, Quert gave Cliff, in halting detail, some of the Kahalla's slow evolution. Planets that condensed out early near their stars necessarily must seethe and surge. Liquid metals and decaying radioactives spit energy into crystalline lattices. Order came from oblique condensations. The essentials geological were much like essentials biological: Life began from metabolism wedded with reproduction.\n\nThe first sentient Kahallans used their world's temperature and metallic difference between the core and the upper mantle as their thermodynamic driver. Along slithering seams of flowing lava, moving with aching slowness, they learned to track the shifting heat patterns. Predicting these was even better. Among the metal ions in their crystalline rhomboids, variations made their own order. Slow, slow and strange, reproduction of patterns followed. Some worked and so persisted. When shifting crystalline lattices held the basic data of early sentience, evolution's hammer could find its anvil\u2014much like bits encoded in silicon by humans' computing chips, fresh intelligences arose without benefit of the bio world.\n\nSize conferred advantages in energy harvesting, so the Kahalla grew ever larger, over working agonies of billions of years. They learned to communicate through acoustic waves amid the strata. Social evolution drove the geological, just as they had driven the biological.\n\nTime stretched on. There was plenty of it.\n\nAs their world's core cooled, the Kahalla migrated from near the core and toward the surface, for their planet was slowly spiraling toward its sun, its barren rocky surface cracking with the warming\u2014a new source of nourishment. Geological energy was like the biological\u2014diffuse, persistent. Driven by gradients, not logic. Yet it sifted through patterns and choices.\n\nAges passed. Finally the early Kahalla extruded themselves onto the plains festering with swarming heat, simmering beneath a glowering orange sky that was mostly now the skin of their star. Bio life had never arisen here, but now persistently the Kahalla colonized the stark black fields graced by rivers of smoldering lava. Great strange sagas of conquest and failure played out across smoldering landscapes. Songs worthy of immortality sang across blistered lands and blighted great monuments.\n\nCivilizations faded as tidal forces forced the planet nearer its star, ever nearer beneath a flowering culture\u2014and soon the Kahalla saw their fatal trap.\n\nWith their gravid slow slides of silicate, they could not migrate away from the surface fast enough to evade the heat. It lanced down from a star that swept the Kahalla with furious particle storms and bristling plasma. They retreated. Not fast enough. And ahead, their silicate minds knew, lay a great brutal force. They would soon enough reach the limit where tidal stretching could wrench and wrest apart their entire world.\n\nTheir society, ponderous and unimaginative, began to disintegrate. Their muted culture was largely a society of songs\u2014purling out through the stacked geological layers, soaring operas of driven love and inevitable death. Like all life in its long run, it strove to understand itself and so perhaps its universe.\n\nYet some had fashioned instruments to survey their lands, their swarming sultry skies\u2014and caught a glimmer of the Bowl in a momentarily clear sky. The Bowl had ventured in without fear of disrupting life-bearing worlds, for there were none\u2014it thought. It coasted clear and sure in a long hyperbolic orbit. The Bowl was a sudden beckoning promise to those slow and solid and doomed.\n\nSomehow the Kahalla sent a signal to the Bowl. It was of long wavelength and thus carried low meaning, A slow song. Yet over time their signal persisted, and was heard.\n\nAn expedition of robots answered\u2014the spawn of a crafter species that stubbornly managed the near-Bowl transport and mass harvesting. Much conversation came and went and came again. It became with gravid grace a slow sliding talk across barriers of time and mind and much else.\n\nYet still. These robots retrieved the essence of the Kahalla intelligence\u2014slabs of silicate, laced with evolved strands of impurities, all serving as a computational matrix.\n\nSo the robots brought the Kahalla mind to the Bowl in crystalline crucibles. It was a great act of graceful tribute, ordered by the least likely magistrates of all\u2014the Ice Minds. So did the very cold save the very hot from utter extinction.\n\n\"And this is the only one?\" Cliff asked Quert. The droning long chant was still pealing on. And on. Bass thuds and hollow tones spoke wruuunggg laddduuutt eeeillooonnnggghh.\n\n\"It alone stands for all the Kahalla now.\"\n\nCliff could sense the majesty of it as he watched the great vibrating rock, framed against cottony clouds that rushed across the sky. \"How does it live?\"\n\n\"The sun lights those\"\u2014an eye-shrug toward the hills\u2014\"and tech condenses the heat, feeds the Kahalla crystals.\"\n\n\"So it's like an enormous, living museum exhibit,\" Irma said.\n\n\"Bowl preserves. Without, life-forms die.\"\n\n\"All life-forms?\" she asked.\n\n\"Must be.\"\n\nCliff turned to watch the humanoids who had taken the name of this mournful singing stone and saw that the Kahalla's long hours of chant had done its work. The humanoids lay sprawled in deep slumber.\n\n\"Song goes to their souls,\" Quert said.\n\n\"You knew it would?\" Aybe whispered.\n\n\"Heard it did. Only chance.\" Quert turned and gave them a comical eye-shrug. Then Quert bowed and gestured to them all. \"Silent go.\"\n\nThe long aaahhhhmmmm loohgeree oojahhaaa habbbiiitaaa pealed on. It was great and strange and still impossible to fathom.\n\nThey left quietly. They were tired, but the long notes drove them forward. Somehow the place now smelled ancient and timeworn without question. The very scented air told them this without instruction.\n\nCliff and Irma and Aybe and Terry\u2014they were all that was left now, and they had to move. The constant sun slanted pale yellow through high sheets as they trundled on with the Sil forming a crescent escort around them. He saw rainbow clouds hovering in the vapor over their laboring heads. Their crescents spoke bold colors shimmering through the sky's firm radiance.\n\nHis team was shambling on now, sweaty and confused, truly tired in the way he had learned to recognize. Heads sagged, feet dragged, words slurred. The alien song droning on from far behind them would never end, he saw, down through however many corridors of ruin and turbulence that song needed. They were beautiful stretched songs telling of sad histories that no one would ever quite know. There would be scholars of it somehow in the long run, but they would carve off only a sheet of it and not know it entire. Cliff looked back once as they neared a stand of zigzag trees, a whole sweeping forest waving in the moment's breeze, and saw that the round eye was still watching them.\n\nIt never blinked. They went on.\nTWENTY-EIGHT\n\nCaptain Redwing started crisp and sharp, fresh from coffee, with the same questions he always used when taking staff through the planning stages of a new, untried operation. Standard questions, but always able to surprise.\n\nThey had walked through Karl's simulations and Ayaan Ali's trajectory analysis. The Specialty Artilects had put their own stamp upon the general plan, though as always they did not make judgments beyond a probability analysis. Their deep problem, Redwing thought, was that they were so much like human reason with far better data\u2014and yet so forever uncertain.\n\nThe worst way of reviewing options was to let people make speeches. Questions shook them up, made them come forth.\n\nHe looked at the entire assembled crew around the main deck table. \"First question: What could we be missing?\"\n\nKarl Lebanon answered. \"Their defenses.\"\n\nFred Ojama said, \"Ayaan Ali and I did a depth scan for those. Nothing obvious, like the gamma ray laser.\"\n\nBeth Marble set her mouth at a skeptical slant. \"They could launch craft against you from anywhere.\"\n\nPetty Officer Jam scowled. \"I've seen curiously few flights above their atmosphere envelope. They don't seem to launch into space often.\"\n\nClare Conway said, \"Speaking as copilot, the obvious way to launch is to just pop a craft out on the hull side. It's moving at hundreds of klicks a second right away, so you zoom around the rim. Come at us from that angle.\"\n\nAyaan Ali nodded. She was wearing a metallic blue scarf over her hair and resisting the urge to toy with it, Redwing noticed. This crew was good at suppressing tension and not allowing it to change the group mood. That had been a high selection criterion. She spoke slowly. \"We would have time to deal with that. I am able to turn the ship quickly now. We've learned how to use the magnetic torque technique to gain angular momentum from the fields above their atmosphere. And we may be difficult to spot, since we will be in the jet.\"\n\nKarl nodded. Redwing saw they had now mentally stacked up the unknowns, which was a good moment to hit them with more. \"Second big question: How will this not work?\"\n\nSilence. Beth said quietly, \"If they have something to prevent tipping the jet awry. Something we can't guess at now.\"\n\n\"They've surprised us plenty before,\" Ayaan Ali added.\n\nKarl added, \"Right. They've had lots of time to think about this.\"\n\nClare said, \"What maybe won't work? Me. I may overestimate my ability to pilot through the jet. Beth, how bad was it?\"\n\n\"An endurance test, mostly. I was driving straight up the bore, staying near the middle. Had to stay on the helm every second of the way. The big problem was keeping SunSeeker stable in the plasma turbulence. The jet is far denser than anything this ship and its magscoop were designed for. I had to max everything we had.\"\n\nRedwing wanted to add, And we nearly overheated, too, but he said instead, \"Sounds hard. But we're thinking of a fast flight through, yes?\"\n\n\"I think so,\" Beth said, looking at Redwing, who nodded. \"Put it this way\u2014staying alive on the Bowl was hard, too, but lots more fun.\"\n\nTheir faces had grown more somber already. Most of them hadn't been revived when SunSeeker flew up the jet and through the Knothole, but they had heard about the long hours of a creaking, groaning ship, and the dizzy swirls when they yawed and nearly tumbled. Their eyes turned introspective. He decided to loosen them up.\n\n\"Y'know, way back when I was in nav school, I asked an instructor, 'Why do people take such an instant dislike to me?' At first the woman didn't want to answer. But I nagged her and finally she said, 'It saves them time.'\"\n\nWhen their laughter died down\u2014he could read their tensions by that measure, too\u2014he said, \"Point is, I'm a bug about details. Made me pretty damn obnoxious in nav school and ever since.\" He gave them a smile. \"I learned that in nav and tactics and all the rest. Space doesn't forgive anybody. So we have to simulate all the troubles we can see coming.\"\n\nKarl said, \"And then?\"\n\n\"I'll throw some unknowns you hadn't thought of into the simulation, the training pod, all the rest. I want you to expect the unexpected.\"\n\nThey nodded and for half an hour they tossed around possible unknowns. Then he said, \"Question three: Will you please shoot as many holes as possible into my thinking on this?\"\n\nThis led to more scattershot thinking, more debate. The jet was the big problem, and there were many ways to look at it. Redwing waved his hand in a programmed way, and the bridge wall lit up with a photo of the Bowl made when they were on the approach from the side. This was when Redwing and the small watch crew, plus Cliff and Beth, were just trying to grasp the concept of the Bowl. That now seemed so long ago, but it was less than a year.\n\nSome of them must not have seen it before, because it brought gasps.\n\n\"I'd forgotten how beautiful it is,\" Beth said.\n\nClare said wistfully, \"Some of us have only seen it up close. We missed a lot.\"\n\nFred pointed. \"Notice how it flares out from its star, then narrows down a lot. That's the magnetic stresses working. Wish I knew how they do it.\"\n\nKarl said, \"I've fished around in the thousands of images SunSeeker's Omni-survey Artilect made on our approach. That's when we got far enough ahead, while we were making our long turn to rendezvous. By the way\"\u2014a nod to Beth\u2014\"that was brilliant navigation. Hitting a moving target on an interstellar scale.\"\n\n\"This was all-spectra?\" Fred asked.\n\n\"Exactly. Here is a view of the other side of their star. Away from the jet. It's in spectral lines specified to bring out the magnetic structures visible in their solar corona.\"\n\nAyaan Ali said, \"Star acne,\" one of her rare jokes. She even blushed when everyone laughed.\n\nBeth said hesitantly, \"Those are all... magnetic storms?\"\n\n\"Not storms, though on our sun, they would eventually blow open and make storms. Those loop structures are anchored in the star's plasma. Think of the magnetic fields as rubber bands. The plasma holds them down, and when they get free they stretch away from their feet. They're stable, at least for a while. Lots of magnetic field energy in those things. They move, just like the ones on our sun. But in the long run they move toward the edge we see and migrate. Over to the other side.\"\n\nBefore Karl could go on, Fred said, \"To the jet.\"\n\nKarl chuckled. \"I should know somebody'd steal my thunder. Fred's good at that.\"\n\n\"So the other side of their star, which we can't see\u2014\"\n\n\"Is a magnetic farm, sort of?\" Clare said skeptically.\n\nKarl chuckled again. \"You guys are too fast. Yep, Clare, that's where the star builds big magnetic loops and swirls. Then they drift over to our side of the star. They gang up around the foot of the jet. Then they merge\u2014don't ask me how. That feeds magnetic energy into the jet\u2014builds it, I guess.\" He shrugged. \"I don't have a clue about how this gets done.\"\n\nAll but Karl had blank, big-eyed stares. Redwing watched them digest the scale of the whole thing for a long moment. Star engineering, he thought. Somehow we missed that in school....\n\n\"There's a real problem here,\" Ayaan Ali said. \"These Folk aliens you talked to, Captain\u2014did they seem like beings who could command a star?\"\n\nRedwing pursed his lips. He liked to let things speak for themselves, and so had not kept the recording of his talk with Tananareve away from the crew. The more heads working these problems, the better. They had intuitions about the Folk, too, and now was the right time to let them come out. So he just nodded to Beth with raised eyebrows.\n\nBeth said, \"You've all seen my pictures of the one who interrogated us, Memor. Plus all the assistants\u2014so much smaller, they seem like another species entirely. Probably they are, but they work together in what looked to us like a steep hierarchy. Impressive, that Memor\u2014especially in bulk. But a creature that could manage a star?\" She arched a skeptical eyebrow and let her mouth turn down in a comic show of doubt.\n\nThis brought smiles all round the table. \"My point exactly,\" Ayaan Ali said. \"How would anything our size\u2014hell, any size\u2014made out of ordinary matter, control solar magnetic loops?\"\n\n\"Good point,\" Fred said. \"There's something else going on.\"\n\n\"But what?\" Redwing said.\n\nNo answers. They were all thinking, and he saw it was time to get back to work. He flicked another image on the view wall. \"Here's a later view as we came around in advance of their star.\"\n\nThis brought more quiet ooohs and aahhhs.\n\n\"Here's where we see the point about those magnetic loops,\" Karl said. Fred was already nodding. \"See how the jet seems to curl around? Those are\u2014\"\n\n\"Magnetic helices,\" Fred cut in. \"The corkscrew threads are brighter, because the field strength is stronger there, and so is the plasma density. Classic stuff. Way back a century or two ago, we saw all that in the big jets that come out of disks around black holes. Astronomers know plenty about these.\"\n\n\"Uh, thanks.\"\n\nRedwing could tell Karl was getting irked with Fred's butting in. But Karl was holding himself back with admirable restraint. And Fred's point was well taken. Redwing said mildly, \"So to get the idea for this, whoever built it had only to look into the night sky. At other galaxies, same as we did back in the\u2014what, twenty-first century?\"\n\nKurt nodded. \"As Fred said, yes. My point is, the jet gets all that magnetic field strength from the loop structures. So those magnetic fields migrate around to the jet base and get sucked up into it somehow.\"\n\nFred said, \"Ah! Then those fields do the crucial job of confining the jet, straightening it out into the lance that spears through the Knothole.\"\n\n\"Right. Because the star spins, its magnetic field gets twisted and wrinkled, kind of like a ballerina's skirt. That gets swept into the base of the jet, hangs up in it. The intense pressures at the base throw the jet out. It swells at first. Then the magnetic fields sort themselves out. Because field lines have to eat their tail\u2014they can't break\u2014they weave themselves. We've known a long while that you can twist a magnetic field so it crosses itself\u2014but then it just springs back as two loops, almost like reproduction. So the field self-organizes in the flow and takes the jet through the Knothole.\" Karl finished with a flourish, getting the picture of the Bowl to make the threads in the jet fluoresce like neon signs.\n\nBeth caught on to this. \"I get it\u2014hell, I experienced it. Waves of hard turbulence, coming at us at speeds SunSeeker was never designed for.\"\n\nKarl smiled, happy to see his theory confirmed by raw experience. \"You came in on the jet at first in the exhaust, right? Backwash. That's where the folds of the skirt bunch up\u2014\"\n\nKarl went on with some more technical stuff, but Redwing didn't listen. He watched them all to see how they took it in. Teams had to feel they had some understanding of what they were about to get into. If you were lucky, you even got a dividend, a fresh idea or two.\n\n\"It's self-organizing,\" Ayaan Ali said, gazing at the intricate luminous lines that laced through the jet. \"That's why it all works.\"\n\nPlainly this surprised everyone. Ayaan Ali's crew slot was navigator\/pilot, not astrophysics.\n\nShe paid no attention to their puzzled expressions and went on, \"Our fusion drive is the same. It confines plasma long enough to fuse it for energy, heats the incoming plasma that way. Then we blow it out the back. It's a hot plasma shaped by magnetic fields all along the way. That jet that makes the Bowl work\u2014it's just like our exhaust jet.\"\n\nA few jaws dropped. Redwing had always enjoyed moments like this. Get a smart crew together and let them Ping-Pong ideas back and forth. Add new information. Stir. Turn up the heat a notch. Simmer. Amazing, how often good fresh notions came out.\n\nA rustle of astonishment. \"Good point,\" Karl said. \"The same basic idea in our ship and... theirs.\"\n\n\"Their shipstar,\" Redwing said.\n\nThe melody of the conversation had shifted. The immensity of what they faced simmered below everything they said, and their faces showed this. Tight mouths, chins stiff, eyes dancing or else narrowed. Time to get them back into focus.\n\n\"Even if it's technically sound,\" Redwing said, leaning forward with hands clamped together on the table. \"There's the big question\u2014is this maneuver understandable enough for the ship Artilects to operate, to troubleshoot, and to extend what they've learned?\"\n\nBeth said, \"Our flight in, up the jet\u2014the Nav Artilect group certainly learned from that.\"\n\nAyaan Ali's face became veiled, remembering. \"You're right. When I came on duty, I was amazed at how much they could do. Remember when we had trouble with the scoop getting enough mass to fuse it in our core chamber? They adjusted the field structure before I could even grasp what was wrong. They'd never done that in our field trials out in the Oort cloud.\"\n\nThe talk got technical. They all ran with it. The deep silent secret of SunSeeker was the collaboration between mere mortal humans and the crystal Artilects who knew much that the vagrant human mind could not hold in ready use. The Artilects managed innumerable details at a speed and accuracy far beyond the blunt comprehension of their fragile cargo. They were integrated artificial minds, merged into a collective intellect. A society of minds, furiously engaged. Redwing always thought of them as crew who rarely talked back. They kept track of innumerable daily problems and never complained. The Insys Artilect, especially; he spoke with it several times every watch. On the other hand, they never had really original ideas.\n\nClare said sternly, \"Their attention reservoirs can take only so much\u2014\"\n\n\"Let's leave that to experience,\" Redwing cut in. \"Officer Conway,\" with a nod to Clare, \"consult the Artilects themselves. Give them your simulations; ask them to appraise their own capabilities. Regard them as crew members who couldn't make it to this meeting, if you will.\" And since the interior systems no doubt can hear us in their acoustic monitors, they actually are here. Not that the Insys Artilect would ever bring it up; strategy was not its province. But he suppressed that thought, for now.\n\n\"Yes, sir,\" she said, and sipped her coffee. Always the caffeinated, he recalled\u2014she used it to drive herself harder. Several others around the table did the same, an amusing social echo.\n\n\"Then we are resolved on this course?\" Redwing said with a light and conversational air.\n\nOnly Beth failed to get the message. Probably, he thought, because she had been down on the Bowl so long and had forgotten shipboard's unspoken signals. She said, \"I don't know if we've resolved anything, Cap'n.\"\n\n\"We're going to give the Folk a nudge,\" Redwing said. \"Their reply was quite clear\u2014they killed our coin array. They don't want us knowing the local conditions well, to navigate by. If we were Earthside, that would be an act of war.\"\n\nBeth wouldn't stand down. \"A 'nudge'? Despite all these problems? Unknowns? Risks?\"\n\nHe leaned forward, extending his clasped hands. \"There are always problems. My orders are to get us to Glory and see if we can colonize it. Extracting us from this strange... place... this shipstar... I see as my duty. To do so, I must impress on these aliens that we will not join the\u2014what was their term? The one Beth reported?\"\n\nRedwing looked down the table at Beth, whose open O of a mouth told him she had not expected this. Maybe the ground truth of the Bowl had told her something he did not know? \"Beth?\"\n\n\"The... the Adopted.\"\n\n\"Right. We're not a damn bunch of orphans from Earth. We're not going to get Adopted.\"\n\nBeth said, \"In their eyes...,\" and stopped.\n\n\"Yes?\"\n\n\"We've been gone from Earth so long, all our relatives dead, who knows what has happened...\" She looked forlorn for a moment, grasping for words, head down. \"We might as well be orphans.\"\n\nHe had not expected this. What had the Bowl done to her? \"We're officers of a ship, Science Officer Beth Marble. Humanity's farthest excursion. We have a goal and we shall reach it. This Bowl interlude, however amazing, will be useful, but we shall go on. Is that understood?\"\n\nLong silence. Karl started to say something, his lips half-forming a word, but thought better of it. Fred was quite obviously biting his tongue, eyes studying the table as if it were a brilliant new discovery. Their faces closed up into pale masks with eyes looking everywhere but not at Beth or at him. Very well. \"This was an exploratory discussion, folks. I appreciate a free airing of views, as always.\"\n\nFred said, \"Outcome pretty obvious. When we came in.\"\n\nRedwing let nothing show in his face. \"I'm sorry, Officer Ojama? Your special area is geology, as I recall. And ship systems. You said...?\"\n\n\"It was pretty obvious you had decided to fly into the jet. You wanted to get us used to it.\" Only after saying this did Fred's eyes jerk away from the table's smooth obsidian finish and dart a look at Redwing.\n\nRedwing did not let his feelings show, much less his surprise at Fred's suddenly becoming a talker on something other than tech details. Always remember that these people are damned smart. And odd. Not predictable. \"Quite so. It's useful to hear how hard this is going to be. Also to know the purpose.\"\n\n\"Which is?\" Beth was still softly defiant. Her eyes glowed.\n\n\"Getting to Glory. Those are our mission orders. We're carrying humanity to the stars. Beginning a process that ensures our species immortality.\" They had all heard these terms, but maybe they needed to be reminded.\n\n\"We haven't discussed other options,\" Fred said, his eyes still holding firm on Redwing.\n\n\"I haven't heard any proposed,\" Redwing said, deliberately settling his cheek on his right palm, as if settling in to listen.\n\n\"We could\u2014should\u2014continue our conversation with the Folk. Edge them toward our point of view.\" Beth said this stiffly, eyes on Redwing. \"They have Tananareve and Cliff's team, yes. But we have so many sleeping souls with us\u2014\"\n\n\"We have given them days already,\" Clare Conway said. \"And they attacked our coins. In a few more days, what else might they do?\"\n\nRedwing was happy with this support and decided to let them talk awhile, let the idea sink in.\n\nFred said, \"Think about us as orphans. This thing, the Bowl, is so old\u2014they must be used to expeditions from some nearby star coming out to look. So whatever alien species arrived, they were on a one-way trip. Just like us. That's the Folk history. So they think of us the same way.\"\n\n\"Makes sense,\" Karl said. \"They think the Bowl is so wonderful, of course smart species want to come and see it. Tourists who came and stayed.\"\n\nFred grinned, a rare event. \"Not like us, passersby.\"\n\nRedwing did not like the way this was going. He kept his tone measured and precise. \"In the end, a ship is not a democracy. It's a ship and there's only one captain. I'm it. I have to decide.\" This came out of him as a formula, but he had to say it.\n\n\"The Bowl teaches us a lot, Captain.\" Beth spoke quietly, slowly, but firm and steady. \"We should study it awhile before we just go on. Before we leave it behind. There's so much to learn!\"\n\n\"They could be just waiting us out,\" Clare said. \"They know our general flight plan. It demands that we have only a few crew up and consuming food while we're on full-bore flight. Here, we're in a solar system, of sorts. We're catching their solar wind, what there is of it, and barely maintaining good sailing conditions. They know us. We don't know them.\"\n\nFred said, \"They must have seen our magscoop flexing, struggling, trying out new patterns.\" He nodded to Clare. \"And we kept running, but barely.\"\n\n\"It's pretty obvious, now that I think about it, from their point of view,\" Karl said. \"They know this system intimately\u2014hell, we don't even know how they manage to run it!\"\n\n\"So it's likely they want to wait us out. Run low on supplies.\" Clare looked around at the whole table. \"Gives them more time to hunt down Cliff's team, too.\"\n\nRedwing was glad to get some support without saying a word. \"Y'know,\" he said casually, \"Magellan lost most of his crew when he sailed around the world.\"\n\n\"Magellan didn't make it home either,\" Fred said. \"And we have over a thousand souls sleeping aboard who count on us.\"\n\nWell, that backfired. \"They're always in my calculations, Fred,\" he said as warmly as he could.\n\n\"I still think\u2014,\" Beth began.\n\n\"That's not a crew officer issue,\" Redwing said firmly. \"Not at all.\"\n\nSilence as it sank in. To his surprise, Karl said with a deliberate mild voice, \"We do not know what we face.\"\n\nRedwing felt the tension rising in the room. At least the Artilects don't argue.... \"The human race has never known what it faced. We came out of Africa not knowing that deserts and glaciers lay ahead. Same here. If we have no respect from these Folk, we will be captives. Humanity will become zoo animals.\"\n\nThis shocked them. Their eyes widened, blinked, mouths opened and closed with a snap. Maybe they'll remember their obligations. Where they came from.\n\nThey all looked at him long and hard. But Beth looked away\u2014and in that moment he knew that he had them.\nTWENTY-NINE\n\nTananareve was a useful test subject. Memor enjoyed experimenting with the primate.\n\nMemor listened to the rumble of the fast train and ignored Bemor, who was working on his portable communicator. The primate was irked, eyes narrowed, after she heard some of Memor's remarks about the difficulty of negotiating with their Captain. Tananareve did not know she carried embedded sensors that reported regularly to Memor's diagnostic systems. When she got angry, her heart rate, arterial tension, and testosterone production increased. Quite interestingly, her stress hormones decreased.\n\nMemor turned out of the line of sight and flourished a flat display of the primate response.\n\n\"Bemor, note this, please.\"\n\nBemor idly cast a distracted glance. Memor sent the data set to him and he glanced at the curves on his comm. \"How odd, that anger relieves stress in these primates.\"\n\nHe sniffed. \"With bad social effects, I would wager.\"\n\n\"Why? It must have evolved in the wild\u2014\"\n\n\"Exactly. They feel the stress-lowering as a kind of pleasure. So to relieve anxieties, they fight. This is not good for a peaceful society. It may explain why they are out here, far from home, exploring.\"\n\nMemor paused. She differed with her brother over this area, which was, after all, her own realm of research. But... \"You could be right. It seems an unlikely feature in a species we would make docile.\"\n\n\"I note her left brain hemisphere becomes more stimulated as well. This may confer some aggressive abilities.\"\n\nMemor let this ride. The strumming metallic rhythms of the fast train were comforting, considering that they were moving with truly astronomical speeds down magnetically pulsing tubes, over elegant curve trajectories, arcing across and within the Bowl's long slopes. They had voyaged now for several slumbers. The fast tubes were cramped, and their outer metal skins at times heated to smarting temperatures through inductive losses. Tight, unamusing quarters even for Folk. Uninspired edibles, with little live game at all. Memor passed the last wriggling forkfish to Bemor; it flapped weakly and gave a soft cry of despair. He took it with relish and crunched happily, snapping the bones. The heady, acid flavor of the forkfish filled the cabin. Tananareve made a clenched face and covered her mouth and nose with a cloth.\n\nAll this travel to rendezvous with the proximate locus the autoprobes had found\u2014among the icefields of the hull, in ready range of the Ice Minds\u2014for the vagrant primates.\n\nThe renegade primates had tripped detectors among the renegade Sil first. Now this. Memor's attempts to keep a distant trace on the primates was well enough, Bemor thought, but \"Given to excess,\" he had remarked, \"when not well policed.\"\n\nSeveral ready examples had happened a short while ago.\n\nFirst came the incident in which Sil hirelings had patrolled the precincts outside the recently bombed Sil city. There were minor traces of the primates in the area, but the bombardment had eliminated most of the sites where identification would have been simple. Instead there were vague sightings and some detector probables. Bemor had disliked Memor's delegation of patrolling to a band of Sil unloyal to the central Sil hierarchy. They attempted a poorly thought-through maneuver to block the primates' movements across a plain. The Sil accompanying the Late Invaders managed to kill and badly injure several of their blockers. There was one report that a car of Late Invaders had taken part in the action. Since Memor knew this same party had killed a local party in a magcar before, and taken part in an insurrection from which Memor herself narrowly escaped, this latest incident was no surprise.\n\nThe second incident was more troubling. The same Sil and Late Invaders party had been glimpsed by a routine patrol skirting the hull territories. Only one clear identification, but enough. Yet by the time automatic patrols had arrived, the party was gone.\n\nNow a third report, in a region housing old intelligences. The portal near the Kahalla shrine had triggered an abnormality alert. This signal came to the attention of resident monitors for the Zone. Since Memor had a tag on such genetic identifiers, she heard of this just a short while ago, when already in the long magnetic train tube network with Bemor.\n\n\"They move in crafty fashion,\" Bemor had observed. \"Doubtless this is not a signature of Late Invader cleverness. They do not know our territories. They must be guided by the Sil.\"\n\nMemor sent a fan-array in a flutter of subtle, doubting yellows. \"I doubt the Sil have such abilities either. We have contained them in their urge to expand for a great long time now. Many generations have passed since Sil could roam in exploring parties.\"\n\nBemor considered this. \"They are also a rambunctious species, still. Some longlives ago, they sought access to the strictly nonsentient Zones.\"\n\n\"I do recall.\" Memor quickly accessed her Undermind, and the memory unfolded for her quick review. \"Outright demands for territory, claiming that their species had spread quickly over their homeworld due to a mixed genetic and social imperative.\"\n\n\"Quite. Note that seems, from your own work, to be a signature heritage of your Late Invaders.\"\n\nThe implications of this struck Memor only now. But her Undermind quickly sent a link that showed she had been mulling over these Late Invader\u2013Sil resonances. But only vaguely. Bemor, on the other hand, had seen it immediately.\n\nMemor turned to Tananareve. \"Your origins are how far back in your own measure?\"\n\nThe primate took her time. Her eyes swept from Memor to her brother as she kept her mouth stiff. Then, \"Several hundred thousand orbitals.\"\n\nBemor had not ingested Memor's concept-map of her studies of the Late Invaders, for he said, \"She must not know the correct sum.\"\n\n\"No, this fits with her supporting frame-referencing knowledge. I read it directly from her long-term memory.\"\n\n\"Unreliable. We do not know the topology of her Undermind.\"\n\n\"We will. But more important, I asked her. She gave a detailed history of their species traumas. Detailed and odd, but plausible. They were several times forced into small surviving parties, due to climate shifts. At one point they were barely above levels to avoid inbreeding in a cold place near an ocean. This built in a desire to expand\u2014almost an assumption, I would say, that the lands far beyond the hills they saw could be better.\"\n\nBemor huffed and shifted his bulk uneasily. In close quarters, his musk flavored the air and rankled her nose. She sniffed as a rebuke. \"It is rare to proceed up through the stages of mental layering you describe. I cannot believe it would occur in so few orbitals of an ordinary star.\"\n\n\"As I recall, the Sil also evolved high intelligence and tool use in a short while.\" Memor fished up the details and sent them to Bemor.\n\nA long moment of brooding inspection, a rumbling in his chest, wheeze of slowly expelled breath. \"So they did. This explains their intuitive alliance with the Late Invaders.\"\n\nMemor said, \"We have new data that the Sil have been privy to our general messages about the Late Invaders. They may have sensed this as their opportunity.\"\n\nBemor turned to Tananareve. \"You know of the Sil?\" he asked in something resembling Anglish.\n\n\"Only what you have said of them,\" she said.\n\n\"They are with the other escaped Late Invaders.\"\n\n\"We were not invaders at all!\" This animated the primate. \"We came as peaceful explorers.\"\n\nHe rumbled with mirth at this, but a quick startled expression on Tananareve's face showed she thought it an aggressive sound. \"Your peacefulness is surely moot, is it not? You of course we retained, but some others of you escaped.\"\n\n\"We do not like being unfree.\"\n\n\"And we\u2014who of course did not fear any warlike abilities such as your kind might have\u2014do not savor intrusion. We avoid having new influences introduced into our Bowl without adequate wise supervision.\" Bemor said this slowly, as if speaking to a child, or to some of the slower Adopteds.\n\n\"I think by now all of 'our kind' would like to just get away from this place. We have another destination.\"\n\n\"As well we know,\" Memor said, flashing a humor her fan-signal to Bemor. \"But that is also why we cannot allow you to arrive there first.\"\n\nA nod. \"That's how I figured it.\"\n\n\"Can you also give an opinion of why your companions are allied with the Sil?\"\n\nTananareve smiled. \"They need help.\"\n\n\"And why together a band of these is moving through the Bowl, using fast transport and undersurface methods?\" Bemor huffed, drawing nearer the primate\u2014who then shrank back, nose wrinkling.\n\n\"They're on the run. Been running so long, maybe it's a habit.\"\n\nMemor suspected this was a gibe but said nothing. Bemor persisted, his sour and salty male odor rising in their compartment. \"Nothing more?\"\n\nShe looked up at them both with a level, assessing gaze. \"How about curiosity?\"\n\n\"That is not a plausible motive,\" Memor said, but saw that Bemor gave off flurry-fan-signals of disagreement.\n\n\"I fear it is,\" Bemor said. \"We try not to allow such facets of a species' character to rule their behavior.\"\n\nTananareve smiled again. \"That's what becoming Adopted means?\n\n\"In part,\" Bemor conceded.\n\n\"Then you will savor our destination,\" Memor said. \"It will show you creatures you have never seen and quite probably cannot imagine.\" No point in not using a touch of anticipation, was there? Some species appreciated that.\n\nThe primate said, \"Try me.\"\nPART X\n\nSTONE MIND\n\nIt's not the size of the dog in the fight, it's the size of the fight in the dog.\n\n\u2014MARK TWAIN\nTHIRTY\n\nCliff watched the sleeting, tarnished-silver rain slam down from an angry, growling purple cloud. This was like a more ferocious form of the cool autumnal storms he had waited out while hiking in the high Sierra Nevada, with crackling platinum lightning electrifying half the sky's dark pewter. Crack and boom, all louder and larger than in the Sierra, maybe because it came from an atmosphere deeper and more driven, sprawling across scales far larger than planets. This violence was casually enormous, with clouds stacked like purple sandwiches up the silvered sky until they faded in the haze. The stench of wet wood mingled with a zesty tang of ozone, sharp in his nose and sinuses. He tasted iron in the drops that splashed on his outstretched tongue, and salt in the rough leaves they'd just eaten, plus a citrus burn in the vegetables they'd managed to scrounge from some trees nearby, before the hammering rainstorm arrived. Tastes of the alien lands.\n\n\"Rain near done,\" Quert said. \"Need go. Soon.\"\n\nCliff could scarcely believe this prediction. \"Why?\"\n\n\"Folk find us.\"\n\n\"You're sure?\"\n\n\"They know much. Even stones\u2014\" A gesture to distant sharp peaks, emerging from cottony clouds as the storm ebbed. \"\u2014speak to them. Always know.\" A grave nod of Quert's bare head said much.\n\nCliff nodded. Rain pattered down and smoke stained the air and it was hard to think. Quert made sense. The whole Bowl was deeply wired in some way. Its lands were vast but not stupid; there had to be a smart network that wove all this together. Still, most of the Bowl had to run on its own. No one or no thing could manage so huge a space unless the default options were stable, ordinary, and would work without incessant managing. Still...\n\nNo security from prying eyes would last for long. Their only advantage was that the Bowl was, while well integrated, still so vast. Even light took a while to cross it\u2014up to twelve minutes, from the edge of the rim to the other edge. The delays sending text or faint voices across it, to Redwing on SunSeeker, were irritating. Especially when you could lose contact at any second.\n\nThe sky roiled with restless smoldering energy. Sudden gusts of howling wind drove the cold hard rain into their rock shelter. The pewter sky slid endlessly across them. But Quert had made them stop here in a long shaped-stone space, angular and ancient seeming, cut back into a hillside. They got in just before the slamming storm descended. Then after hours of huddling, the sky calmed. By the time they ate some of their food, heating it with burning twigs, a black slate wedge had slid overhead and the first hard drops spattered down.\n\nNow it suddenly ended. Cliff turned to the others and said, \"Pack up, gang.\"\n\nSil and humans, they all grunted a bit with the effort of getting moving and splashed water on their fire. Cliff could still taste the sweet meat they had roasted there. It had made him wish for a robust California zinfandel, though perhaps those didn't even exist anymore now. Maybe there wasn't a place called California anymore back Earthside, he mused.\n\nThe succulent aromatic filets came from a big fat meaty doglike creature that had rushed at them hours before. When it came fast out of some big-leafed rustling bushes, they first noticed the curved yellow horns it carried on a broad, bony head. Then the bared teeth. It snarled and leaped, with an expression Cliff thought looked as greedy as a weasel in a henhouse. Most of them froze, for it was a true surprise\u2014not even Quert and the Sils had seen it coming. But Aybe had caught it in midair with a laser shot that drilled through its surprisingly large brain cage and the thing fell limp and sprawling at their feet. It died with a shudder and a long, gut-deep gasp.\n\nThey ate the dark rich meat eagerly. It had a strong muscular frame that gutted easily. The Sil cracked its bones and sucked out the marrow. Cliff considered doing it\u2014fat hunger!\u2014but the rank, oily smell put him off. So he offered his bone around.\n\n\"Sure,\" Aybe said, taking it. He sliced a line in it with his serrated blade and snapped the bone open over his knee. \"Yum.\"\n\nIrma and Terry shook their heads, no. \"Ugh,\" Terry said. \"I grew up on a low-fat diet. That was gospel for a half century, before we had nano blood policing.\"\n\n\"Me, too,\" Irma added, wrinkling her nose. \"Our generation hated that fat smell.\"\n\n\"I like it plenty,\" Aybe said. \"Must be\u2014hey, what generation are you?\"\n\nTerry, Cliff, and Irma looked at each other. \"We're in our seventies,\" Irma said.\n\n\"Gee, I'm forty-four,\" Aybe said.\n\n\"Just a kid,\" Terry said. \"Surprised you made the grade. The rumor around Fleet was, nobody has enough experience before they're in their fifties.\"\n\nAybe smirked. \"You old guys always say that.\"\n\nIrma chuckled. \"The first forty years are for sex and reproduction. You used yours amassing a lot of tech abilities?\"\n\n\"Sure did.\" Aybe shrugged. \"I wanted more than anything to get on a starship. Reproduction is overrated.\"\n\nThey all laughed. \"Women routinely stored eggs and you guys are never quite out of business,\" Irma said. \"Childbirth's just easier below sixty.\"\n\n\"How old do you think Redwing is?\" Terry asked, finishing a slab of meat he had traded with Aybe in return for another bone.\n\n\"Gotta be a hundred,\" Terry said.\n\n\"Older, I'd say. Went through the tail end of the Age of Appetite, he told me once. Pretty nasty time.\"\n\n\"He's a pretty nasty guy,\" Aybe said, and then sucked loudly on a long bone until they could hear him drawing air all the way through it, a hollow slurp.\n\n\"Look,\" Cliff said mildly, \"plenty of people live to well over a hundred and fifty now. Redwing's not what I'd call old.\"\n\n\"By 'now' you mean 'when we were Earthside,' right?\" Terry said. \"God knows how old people live there now.\"\n\nThat made everyone think of the abyss of time separating them from everyone they knew, Cliff saw. He let that ride for a while. Quert nodded to him, seeming to understand. Then it was time to move on.\n\nThey hiked away from their latest rough stone shelter into a clearing sky. There were local horizons here, but now the stray clouds skated over those near horizons and the sweet blue air above cleared further. Cliff had not seen before this sharp, sure atmosphere that he knew was deeper than anything on Earth. Yet now few clouds intruded into a shimmering sharp air. The piercing point star of the Bowl's governing sky still hung above them, of course. But he and his team had moved along the slope of the Bowl for many days at high speeds, one way or the other, and now the star\u2014Cliff had named it Wickramsingh's Star, he recalled\u2014shone not at the absolute center of this sky, but at a slight angle. Its jet seemed now to plunge more deeply toward them. Its streamers turned with elegant grace, pale orange filaments laced across the gauzy firmament. He watched its slow swirls as they slogged across a broad hill. The humans hung back from the Sil advance point men\u2014though some of their Sil party, he had finally realized, were women. He still could not tell their sexes apart with assurance. The Sil didn't seem to have strong binary distinctions between sexes in looks, dress, or behavior. Their occasional puzzled glances at Irma might come from that. Maybe, Cliff realized, humans were just more sexually restless than these Sil.\n\nShapes darted around in the forest. Cliff had seen that with constant sunlight, creatures had to be on guard all the time. Prey had eyes that looked broadly, like rabbits' bulging eyes, or insects' compound eyes\u2014all designed to see at wide angles. Predators, as on Earth, had good depth of field, with eyes looking mostly forward, and wide-spaced for maximal 3-D perception.\n\nIrma walked beside him, shouldering her pack where it wore on her, and said brightly, \"Ever think, how come we're seeing so many bipeds?\"\n\nCliff tried to remember that he actually was a biologist. \"Um. Hadn't thought. But look, as I recall from lectures, anyway, Earthside bipedalism was really nothing more than an oddball vertebrate artifact.\"\n\nShe adjusted her hat against the sunlight. \"Those back there, the Kahalla, they couldn't pass for us, not even in a dim room. Humanoids, though, for sure. Same basic design. But they're from a tide-locked world, not like Earth at all. Odd.\"\n\nHe kept watching the forest slipping by as they marched on. But theory was fun, too. He bit off a bit of a sweet root they'd pried up from the ground, under Quert's instruction, and said, \"Convergent evolution, must be. Those Kahalla prob'ly had four-limbed ancestors, just like us. Back Earthside, the arthropods always had limbs to spare, but not poor old mammals like us. We're bipeds because we started with four limbs, and developed climbing skills, then tool use. That left two limbs for walking, so that pressure forced us to stand up.\"\n\nIrma took some of the sweet root, ate through all the rest of it, and smiled. She, too, endlessly scanned the passing trees and vines, and searched the skies. You learned to stay alert after so long in the field. \"Yeah, Earthside, bipeds are really rare. Except for birds, who've got 'em because they invest so much in wings. For invertebrates, the closest thing to that vertical posture is something like a praying mantis.\"\n\nCliff thought on that as he slapped a fat bug that wanted to use his hair for a nest. \"A mantis has four legs.\"\n\nIrma's voice always went up in pitch when she had an idea. \"You're skipping my point. We saw one biped far back, right? Big lumbering thing that ignored us, dunno why. Then the Sil. Now these Kahalla. All had heads with faces, two forward-looking eyes and jaws and a nose.\"\n\nCliff saw her point. \"Not a necessary arrangement, right. Just look at arthropod faces. Scary, because they're just close enough to ours to look threatening, horrible.\"\n\n\"Those Kahalla though, had pointy faces, eyes more on the side.\"\n\n\"That's a prey signature. I remember from high school, 'Eyes front, likes to hunt; eyes on side, likes to hide.' Seems to be a universal.\"\n\n\"Plus they had fur,\" Irma said. \"We don't, because we overheated when we ran long distances\u2014so we lost the fur.\"\n\nCliff nodded, recalling how lumbering those Kahalla figures had been. Bulky, ponderous, more like bears than people. And not a word had been spoken between them and the humans and Sil. Just glowers and postures, like the signals animals give. \"Um, okay. So the Kahalla aren't runners. Or talkers.\"\n\nIrma said, voice rising more, \"The Bowl is telling us that smart aliens converge to a humanoid form.\"\n\nCliff thought on that, never ceasing his scan of the forest around them. Or could be, somebody designed them....\n\nQuert was ahead of them and now turned. \"Not the Folk. Not like, your word, humanoid. We say, Sil Shape. Same thing.\"\n\n\"Um, yeah,\" Irma said. \"I wonder why?\"\n\n\"Come from self design, for Folk,\" Quert said. \"Ancient.\"\n\n\"So they have\u2014what?\u2014two arms and four legs?\" Cliff asked.\n\n\"Some do. Many others, two legs. Still all Folk.\"\n\nIrma asked, \"The Folk, do they really run things here?\"\n\nQuert gave a downward eye-gesture, which Cliff now knew expressed polite doubt. \"Ice Minds, they above Folk.\"\n\n\"How's that work?\" Cliff pressed.\n\n\"That changes now. Since you came. We Sil work for Ice Minds too, now.\" Quert brandished his small communicator, a pyramidal solid that could deform into a flat screen. Cliff had yet to figure out how that worked.\n\nIrma said, \"What do you do for them?\"\n\n\"Brought you to them.\"\n\n\"That's it?\" Irma asked. \"Why us?\"\n\n\"You disturb. Folk call you 'Late Invader' because you new. Ice Minds want to see you. Know you. So we bring.\"\n\n\"We're just a small ship, passing by,\" Irma said.\n\n\"Something about Glory, I hear from Ice Minds. They want to know what you are, going to Glory.\" Quert gave a head-shrug. \"Not sure what Glory be.\"\n\n\"It's a star right ahead of you,\" Cliff said. \"We can't see it\u2014your star's too bright.\"\n\n\"Star ahead?\" Quert's face went blank, which meant the alien was thinking, giving nothing away.\n\nIrma said, \"It's a star a lot like yours, still so far away that it's only a dot. Its planet has a biosphere with oxygen and nitrogen and the usual. We want to go there, live there.\"\n\nQuert kept the blank look, but the eyes jittered up, down, around. The alien was undergoing an entire conceptual shift.\n\nSuddenly Cliff saw it. The Sil had been ushered into the view from the Bowl hull\u2014the deep dark abyss of glinting stars\u2014only lately. The Ice Minds had beckoned to them somehow, sent signals, and propelled forward the events Cliff's team had then intersected. So Quert and the others had never seen the stars at all, until they brought Cliff's team through the underground labyrinth and to where they could see the sliding panorama of the galaxy in full.\n\nThe Sil had been like people trapped in a cave, never shown the sky. Their world, the world of all who lived on the Bowl, was an endless warm paradise in steady daylight. Their sun and jet obliterated perspective. The ordinary denizens never saw the stars, or the great plane of the galaxy hanging in a black firmament, dark and strange and sprinkled with twinkling jewel stars.\n\nThat revelation had come to the Sil when they were restless and angry. The Folk had suppressed them for ageless times, but now they knew where they were, who they were. All that had exploded into their world only lately. Cliff's team had confirmed new truths, and so had made many tragedies come to pass\u2014the battle with the skyfish, the bombing and firestorms of the Sil cities, so much else.\n\nCliff started to say some of this to Quert. The alien still had the stiff fixed face, giving nothing away while it thought. But then movements caught their attention.\n\nThe point Sil stopped, gestured, and muttered something in a low whisper. Head and arm gestures: something ahead, spread out.\n\nThey all followed their standard tactic, moving off to both sides and seeking cover, then moving carefully forward. The humans had learned this in training, fire-and-maneuver. Each member of the Sil and human team moved only when others could cover with fire from lasers, arm-arrows.\n\nAhead, a faint repeating clatter came through the trees and vines.\n\nBeyond, the land cleared. Cautiously they worked their way to a vantage point on a small hill. A strip of neatly arranged, emerald green agricultural fields stretched into the distance to their left and right. Simple farm machinery worked in them, making whack-whack-whack noises. Directly ahead, the forest resumed several kilometers away. The crop was yellow and purple shoots that seemed to spray out like arrows from a thick brown trunk. These were three or four meters tall, Cliff judged, like trees with spokes flying out. The spokes were fat and had wide, fanlike flowers along their lengths. The air carried a fine mist of\u2014what? Pollen?\n\n\"We can cross that at a run,\" Aybe said.\n\nQuert pointed to figures working in the field. They had trucks and a robot harvester that worked away, chopping off the shoots and dropping them into the trucks. The machinery worked with a regular whump whump whump. A breeze brought a heady sweet scent like orange blossoms with a cutting undertang. Everything moved with a slow rhythm, and the scene reminded Cliff of a monotonous summer he had spent on a farm in California's Central Valley. He close-upped them and said, \"They're the same kind we left behind, those humanoids mesmerized by that ancient rock life. Kahalla.\"\n\n\"These special Kahalla evolve for farm work,\" Quert said. \"They stay here always on farm. Birthing and dying, all done here.\"\n\nIrma asked, \"They live in a village all their lives?\"\n\n\"Content. In balance.\" Quert conferred with the other Sil in quick, scattershot bursts of unintelligible talk. They all looked wary to Cliff, as nearly as he could judge. The Sil had complex suites of expressions that darted across their faces, mostly coded in their eye-moves and the light-browed ridgelines above. Quert turned to the humans. \"This Aybe right. Run fast across. See there?\"\n\nNearly directly across from them was a complex of low buildings the tan color of dried mud. \"Their hatchery. Few Kahalla there most times. We cross, the Kahalla not see.\"\n\nCliff tried to take this in. A special form of Kahalla just for the grunt labor of farming? Had the Folk specially bred for that? And... hatchery?\n\nThey moved through the cover of a long winding grove of zigzag trees. He and Irma thought the zigzag strategy was to get more sunlight under a constant sun, which meant more exposed foliage turned to the direction of the star, a reddish dot fixed firmly in the sky. The jet's filmy light they ignored. Bristly branches and coiling vines sprawled along the thick zigzag trunks to harvest the constant sunlight. That made them useful cover, because the branches were thin at the top and thicker at the tree base. Easy to slip among and elude any watching eyes.\n\nWarily they stopped within easy view of the tannin brick buildings. As a Californian, Cliff seldom saw ceramic slabs stacked to great heights; his instinct said they were earthquake vulnerable. But there were no quakes here at all. He saw through binocs furry figures moving with lumbering, swaying bodies on two legs, moving slowly among the brick walls. He pointed to them.\n\n\"Friends not,\" Quert said with narrowed eyes and edgy eye-clicks.\n\n\"These Kahalla will turn us over to the Folk?\" Terry asked.\n\nQuert said, \"Must,\" and gave a downturned eye-move.\n\nThe other Sil shuffled and eye-clicked in what seemed agreement, their feet shuffling, impatient. They seemed to feel there was no time to waste in pondering this problem. No point in trying to go around the long farming strip that faded away into the light tan color of the distance, which came from simple dust haze. No telling how long this farm was. An odd way to cultivate; why not in squared-off plots so you minimized the travel distance?\n\n\"No time to think much,\" Aybe said. \"Ready to run?\"\n\nThey set off at a good pace. The Sil got out in front right away with their long graceful strides, taking long slow deep breaths as their feet came down. They seemed to have evolved for running. Humans had, too, but not this well. Cliff wondered if their home world, with somewhat lower gravity, had better shaped them for this part of the Bowl. Again he wondered, as sweat collected in his eyebrows and trickled down, stinging his eyes, what the Sil's agenda was. Getting out from under the Folk, yes. But those big birds ran this place, and a few puny humans surely could not make much difference. A puzzle. But without the Sil, they'd have been nabbed by the Folk long ago. He let it pass.\n\nThey made a good fast run across the fields, running close to the curious trees. The Kahalla were upwind of their crossing route, too, so that might be an advantage. Cliff was surprised at how easily he ran. He was in better physical condition now from so long on the run, and the local grav seemed lower here, too. But Quert's head turned, surveying the whole area, as did all the Sil. They were worried.\n\nThe rough rectangular buildings Quert called a hatchery loomed up, two stories high and no windows. They entered the complex, panting and sweaty, and made their way down the main corridor between the buildings. There were no Kahalla around at all. A few zigzag trees lined this main street of the place, their wood worn and gray. The Sil went down side passages, doing reconn, and in a few moments came running back fast. They shouted a word in Sil language and formed a defensive arc facing two passageways. Automatically the humans gathered in behind them, drawing weapons, looking anxiously around.\n\nOnly when a Sil launched one of its arm-arrows did they look up.\n\nThings like meter-wide spiders came over the lip of the roof. They were white and clacked as they moved, surging down the wall on flexing black palps. Their legs were bristly and black; big angry red eyes glared at the sides of a squashed face.\n\nThe first Sil arm-arrow lanced through one that was halfway over the edge of the roof. It scrabbled at the wall and fell with a smack at their feet. The Sil who had nailed it stepped forward, shot at another of the attackers, hit it at dead center of its circular body\u2014then bent and plucked the arrow out, inserting it quickly back in the air sheath.\n\nThe Sil were shooting at the things now, and the humans used their lasers. But there were plenty of the things, and they kept coming.\n\nThey move more like crabs than like spiders, Cliff thought as the Sil fell back. He aimed at one of the things and hit it, but it just kept climbing down the wall toward them. His shot had gone through it near its edge, but that was not enough, apparently.\n\nThey made small, shrill chippering sounds. They moved sideways with quick sure moves.\n\nNow Cliff recalled a relayed message from Beth when they had broken out of their captivity. \"Spidows,\" he said.\n\nIrma got the reference. \"Those were huge, they said. These aren't.\"\n\n\"Local adaptation,\" Aybe said. \"Our lasers blow through them but don't kill, most of the time.\"\n\nFive of the things took on a Sil. They crawled up its legs and bit deep with claws. The Sil howled. It batted at them and lurched away. That unnerved the other Sil as rivers of the midget spidows rushed down from other roofs and through the lanes nearby. Their high, shrill cries became a shriek. The humans huddled behind a thin line of Sils who were running out of their arm-arrows.\n\nQuert was driving arm-arrows into the spidows but then shouted in Sil and then in Anglish, \"Back through!\"\n\nCliff turned and saw a Sil had found, down a side corridor, a big frame door that opened. They all turned and rushed there. The spidows' shrill cries rose as they came after the running Sil and humans. Several Sil tore branches off the zigzag trees along the way, snapping them off. They got through the doorway and into a big high room. The door slammed. Sil secured it.\n\nIllumination streamed down from a ceiling that simmered with ivory light. The place reeked of some sullen odor. It was damp and warm here, and the humans looked at each other, eyes wide, still surprised by the sudden ferocity of the spidow attack. The Sil muttered to each other. They were all standing under the heat beating down from above, panting in moist air flavored with an odd stinging taste.\n\n\"Were... were those spiders?\" Aybe asked.\n\n\"More like crabs,\" Cliff said.\n\n\"They have a shell and move with a sideways crawl, lots of legs,\" Irma said.\n\n\"If there weren't so many, we could just tromp on them,\" Terry said.\n\n\"But there are!\" Aybe was scared and covered it with anger.\n\nThe Sil stirred and murmured and Quert listened to them intently. The humans talked but no ideas emerged. The high keening cries of the spidows came through the walls. They all knew they were trapped, and the shock of it was sinking in, Cliff saw.\n\n\"Let's see what there is here. What this place is,\" Cliff said. It was good to get them focused on something beyond their fears. They murmured, shuffled, and started to look around.\n\nAround them stood cylindrical towers with big fat orange spheres arrayed in a matrix. There were some kind of ceramic tubes laced through the crude baked brick frame, and those felt warm to the touch.\n\n\"What are these things? A whole room full,\" Irma said.\n\nQuert said, \"Kahalla eggs. Hatch here,\" and took two other Sil to prowl the room. Cliff followed down the line of Kahalla egg cylinder holders. The warm damp air was cloying. Heads jerked toward a scraping noise. They all saw a white carapace of a spidow scuttling away. It left behind a ripped-open Kahalla egg that dripped brown fluids on the red clay floor. The spidow had been eating it. A Sil stabbed it with a shaft of wood it had yanked off a zigzag tree outside. The spidow writhed, worked its claws against the shaft, and died with a faint squealing gasp.\n\nThey found another a few moments later. Some had gotten in here, Cliff supposed, and were eating Kahalla eggs. \"Food source,\" Irma said.\n\nSeveral of the big orange spheres were already spattered over the ceramic floor, their insides gone. Cliff followed, still dazed by the speed of events. He shook his head, rattled. As the Sil searched the aisles of egg-holding cylinders Cliff kept up, feeling pretty useless, and then asked Quert, \"The Kahalla look kind of like us\u2014two legs, same body shape. But they lay eggs?\"\n\n\"Kahalla way,\" Quert said. Its eyes were wary, searching the whole room. \"Stack their eggs here. Let hatch. Safe so they can work their fields.\"\n\n\"Uh, but the spidows\u2014that's what we call them\u2014they come and eat?\"\n\nAn eye-click of agreement. \"Been so, long time. We call those things upanafiki. Pests, are.\"\n\n\"They're smart enough to get into these hatcheries.\"\n\nQuert sniffed and gave soft barking sounds with a head-jerk, which seemed to be the Sil equivalent of laughter. All the Sil joined in. Some alien inside joke, Cliff suspected. Or was Sil humor a category outside human comprehension? Quert stopped the quiet barking laugh and said, \"Kahalla not smart.\"\n\n\"Egg layers...\" Cliff tried to get his head around all this.\n\nIrma said, \"Earthside we have monotremes, mammal egg-layers. They're very old, Triassic maybe.\"\n\nCliff shook his head. \"Forget about parallels to Earth. So: smart egg-layers who are humanoid tool-users. What the hell, with evolution on the Bowl, all bets are off.\"\n\nQuert said, \"Upanafiki many. Kahalla crave land. Upanafiki keep Kahalla numbers down. Kahalla and upanafiki\u2014\" Quert thrust its bony hands together. \"Always. Fight. Dance.\"\n\nAybe said, \"Where did these Kahalla come from? What world?\"\n\nQuert said, \"Kahalla means in your tongue One Face Folk.\"\n\nTerry got it. \"So they come from a planet tidally locked to its star? On their side it was always sunny. They had an adaptation advantage when they arrived at the Bowl, over people like us who need night. Makes sense.\"\n\nQuert gave an eye-click of agreement. \"Spread widely. They are conservative. Folk use them. Not good allies for us.\"\n\nCliff frowned. Evolutionary theory in the middle of a fight...\n\n\"Come see this,\" Irma called. She was at the other end of the room. They followed her up some crudely fashioned stairs of gray clay ceramic. The dusty second floor was like the first but Irma pointed to a hole in its ceiling. \"Looks like they dug down through.\"\n\nCliff crouched, jumped, and caught the edge of the hole. Some of it crumbled away, but he held on and pulled his head through the meter-wide opening. This might be risky, but he was curious\u2014and hanging there, he saw the roof now deserted. A nearby piece of wood caught his eye. He held on with one hand and shuffled a slim shaft nearby into the hole, letting it drop. Then he followed it, landing neatly. Low grav had its uses.\n\nIrma picked up the slender piece of wood. \"It has a tip like flint. Those small spidows\u2014they're tool-users.\"\n\n\"Keep Kahalla stable,\" Quert said, glancing upward. \"They outside on ground. We go this way.\"\n\nCliff and Irma looked askance at the alien. Quert went to the stairwell and shouted orders in the slippery Sil speech. Terry and Aybe came up with them. \"Those spidows,\" Terry said, \"they're chipping at the door with something.\"\n\nIrma needed help, but in surprisingly short order their entire team, humans and Sil alike, made the leap to the ceiling hole. Those already on the roof grabbed their hands and hauled them out, onto the flat roof. It was made of tan triangular bricks. Now Cliff could see Quert's plan. The hatchery buildings were close together, and the Sil could leap from one roof to the next. So could the humans. The Sil were remarkably calm; they had met this foe before. They started leaping across. Cliff looked down as he took a running jump across. The spidows were clustered around the door to the building they had just left. Several of them held bigger wood shafts, also with blackened hard tips that seemed to have been turned on a fire.\n\nIrma came next. She landed with one foot halfway onto the next roof lip. Cliff grabbed her and tugged her in. Terry and Aybe followed. By that time, most of the Sil were across to the next building, looking unhurried but quick.\n\nThey all ran and leaped, ran and leaped, and soon were at the far end of the hatchery buildings. There the Sil slung a thin wire around nearby trees, throwing it with a kind of boomerang hook that wrapped around a tree trunk. Then a Sil attached the wire to its backpack solar panel source, made some adjustments, hit a command switch\u2014and the wire expanded, puffing up into a thick rope that hands could grab. Cliff blinked; a useful trick he had never seen.\n\nThey descended on that rope, belaying a bit to break their sliding descent. Cliff and Irma leaned over the side of the building to glimpse the spidows while others took the rope down. Spidows were still working on the door, chipping with crude spikes. But then some Kahalla came in from a side corridor, shouting. The spidows turned, and a battle began.\n\nThe spidow's bristly palps moved in a jerky blur. The Kahalla had simple hoes or similar farm tools. They struck down hard on the spidows and pinned them. But there were a lot, and some Kahalla got overwhelmed.\n\nThis was nature red in tooth and claw in a way he'd never seen. There were over a hundred spidows and maybe a dozen Kahalla\u2014a melee. As they watched, Irma said, \"A fight over reproduction? Nasty.\"\n\nQuert had come over to them and looked down, unsurprised. \"Folk set rules. Keep Kahalla from farming more and more. Use upanafiki to keep not many Kahalla eggs to hatch. These upanafiki pests for us. Their war with Kahalla never end.\"\n\n\"The Folk don't stop this?\" Irma asked.\n\n\"Folk want this.\" Quert paused, searching for the right Anglish words. \"Equilibrium. Stasis.\"\n\nAs Cliff watched five spidows swarm fast over a struggling Kahalla humanoid, he thought, Nightmare spiders on a caffeine high. The Kahalla toppled and vanished beneath the swarming spidows. He recalled a remark heard long ago, Flattery isn't the highest compliment\u2014parasitism is.\n\n\"Damn!\" Irma's shrill shout jerked him out of his thoughts.\n\nHe saw several spidows, their legs grappling for purchase over the lip of the roof, twenty meters away. They had come up the wall. They made a sharp hissing, their legs clicking with darting moves.\n\nHe and Irma had been distracted and now with Quert were the only ones left on the roof. Quert was already ahead of them and took the rope with an easy grace. Down Quert slid, shouting back \"Come fast!\" Irma went next, and Cliff turned to take a laser shot at the mass of spidows surging across the tan brick roof. The bolts punched holes easily enough, but the spidows did not stop. A bolt to the center did work, and one of the things flopped down. But now they were five meters away. Cliff leaned down and plucked the securing anchor of the rope. No time to slide down it now. He couldn't be sure the spidows couldn't use it. The black rope was firmly fixed in the trees thirty meters away, so he just grabbed it and ran off the edge of the roof. He dropped, then swung.\n\nHis breath rasped and he ignored a snap in his shoulder. He tumbled on the descent and tried to pull himself up the rope as it carried him toward the trees. His swing brought him boot-forward, so when he hit the branches of a zigzag tree the leaves lashed him. One limb caught him smack in the face. He hit another, and a sharp pain lanced into his ribs. He gasped and slid down the rope, a nearly vertical drop now. The zigzag tree trunk smacked his thigh, but he managed to get his boots under him. He sprawled when he hit.\n\nAs he was rolling away, his ribs sent him a lance of pain and his vision blurred for a moment. He lay there gasping and hands grabbed him. They heaved him up and Terry shouted, \"Gotta run!\" So he did. Not very well.\n\nThe spidows were running through the trees already, lots of them. Their chippering calls were loud now. But the spidows were small and if humans were good at anything, he thought, it was sure as hell good old running.\n\nFor a while, though, until they no longer saw the spidows behind them, it was more like limping for him. He was worn out.\nTHIRTY-ONE\n\nRedwing watched the Bowl landscape slide by below, distracting himself for a moment of relaxation with the splendid view. Getting back to work, he switched to interior ship views. In the garden, on screens left and right, two finger snakes were slithering through plants, picking here, planting seeds there, while the third\u2014the male, Thisther, darker and a bit bigger than the others\u2014was playing with two pigs, all three having hissing and oinking fun. A laugh bubbled in Redwing's throat\u2014and still the big first question was there. What could I be missing?\n\nBeth was due in a moment and he let the Bowl feed play on his display wall. He took out a tattered, yellowing paper. As part of his several-kilogram weight allowance it was nothing, but in his memories it was everything. His father had written it to him when in the Huntsville hospital from which he would not return. When he was ten, it had meant a great deal and now it meant more.\n\nLIVE FULLY. TAKE RISKS. THINK CAREFULLY BUT ACT, TOO. SPEAK UP. KEEP MIND OPEN AND HEART WARM. DON'T JUST PASS THE TIME. LIVE LIVE LIVE!\u2014FOR SOMEDAY YOU WILL NOT.\n\nHe recalled the man at his best: sawdust sprinkled in black hair, deftly pushing a Douglas fir two-by-four through the buzzing blade of a circular saw, then trimming it and taking a quick measure of the work by holding it against the studs, nodding in the damp fragrant sawdust air, plucking a nail from where he stored it in his front teeth, fetching a ball-peen hammer from its loop on his belt, two quick whaps and a finishing tap, a bright grin, then on to the next.\n\nHe stared at the paper scrap and then put it away, for perhaps the thousandth time. It was centuries old but still true.\n\nBeth tapped on his door. He stood to slide the door aside and nodded with a greeting. They got right to it.\n\nShe sat across from him in his narrow cabin and he made a show of finishing a log entry. It was not entirely show. He had to keep on top of how SunSeeker sailed on the vagrant winds of plasma and magnetic fields. Plus preparations for the jet interception. And an anxious, overworked crew.\n\nBut Beth was the hardest. She had been down there for long months and managed to get back aboard, a striking feat. She had prestige with the rest of the crew. She regaled them with stories of aliens and exploits and weird doings down on the Bowl. She'd taken casualties and escaped from a prison. Figured out the alien landscape and made her team get across it. And fly back home in an alien craft. So he had promoted her two grades in the science officer ladder. When she got to Glory\u2014and we will do that, by damn!\u2014she would command the first landing. Still, her tight face promised trouble.\n\n\"We're in an existential position here, sir,\" she began.\n\n\"Right. We don't have enough supplies to get to Glory. Our logistics were marginal when we sighted the Bowl. Now it's hopeless. We've burned food and essentials hovering over this enormous thing. Plus time.\"\n\nBeth said with deliberation, \"I mean, if we commit an overt hostile act, that sure does change the game.\"\n\nHe nodded. Always concede the rhetorical stuff. \"We have to start a clock running. Otherwise they'll wait us out.\"\n\n\"But their jet is the key to their Bowl. Damaging it is a mortal threat.\"\n\n\"Sure it is. We don't mean to shove a dagger in. We want to show that we can.\"\n\nBeth twisted her mouth into a wry grimace. \"A pinprick, then?\"\n\n\"That's all.\"\n\n\"These are aliens, Cap'n. Their civilization is older than anything we know. Hell, maybe than we can know. This maneuver, this provocation, is a huge gamble.\"\n\n\"That it is.\" He sat back and folded his hands on his desk. \"One we've got to take.\"\n\n\"Look, we don't know how that damn jet operates. How the Folk run it. How unstable it is.\"\n\n\"Right. Isn't that how science works?\" Redwing grinned. \"If you don't understand, do an experiment.\"\n\nBeth shook her head. \"Plus we don't understand the Glory message, or how the Folk really feel about it. I just... I worry.\"\n\n\"So do I.\" What could I be missing?\n\n\"There are risks to every choice. Maybe the right question is, do we want to play Russian roulette with two bullets or one?\"\n\nShe sighed and got up. She was a bit wobbly. He wondered if she was truly fit for service as their backup pilot. On impulse, he got up and gave her a firm warm hug. With a sigh, too.\n\n* * *\n\nKarl showed him the external views of SunSeeker, freshly gathered by their small auto-cam bots that had flown around the entire ship. \"She's centuries old now, but holding up,\" he said with a hint of pride. Karl was a bit stiff and formal, but he could not conceal his feelings completely.\n\nThe ship's sleek after section hid behind the torus of the life zone. The shuttle cradles along the central boom were yawning yellow and orange cups for craft docking and vacuum maintenance bots. Micrometeorites had pitted the hull, and radiation burns splashed black filigrees along the flanks. The entire sleek design focused on the demands of starflight. Now their planetary-scale orbits made it hard to get adequate plasma into the magnetic funnel, and the ship barely ran. Fitful spasms sometimes passed through her, the coughs and sputters of a system hovering on the brink of shutting down entirely. The fusion fires in her belly ran soft, then hard, then not at all\u2014until Karl and the crew could get them burning full and furious again. It reminded him of a fine ship built for the high seas, rotting beside a wharf.\n\nRedwing nodded. \"Fair enough. The mag systems, they can handle the jet?\"\n\nAyaan Ali said, with a tired and exasperated sigh, \"Our upgrades are basically fine-tuning. They seem to work. I'm pretty sure, from records and Artilect memories of Beth's flight up the jet, that we can deal with the turbulence levels.\"\n\n\"And if we can't?\" Redwing persisted.\n\nKarl said, \"The more plasma we get into our magscoop, the better. So we steer for the density ridges, held in by the helical mag field.\"\n\nAyaan Ali pursed her full lips, and her long eyelashes flickered. Redwing recalled this was the closest she came to showing that she was irked. \"The jet's mag pressure is high. It and those fast-changing plasma pressures can punch our scoop around, too. They're two orders of magnitude beyond our optimal design.\"\n\nRedwing saw himself as referee when crew disagreed on the tech issues, but in the end he knew he had to decide who was right. \"How bad can it be if we lose our magscoop shape?\"\n\n\"We'll tumble,\" Ayaan Ali said.\n\n\"And we can recover,\" Karl said evenly.\n\nThey had the reliable Bear Down leptonic drive, the first to use the dark energy substrate as an energy stabilizer. Redwing did not pretend to understand its complex mechanisms that somehow drew power from the substrate of the very universe. Fundamentals were not his concern; its operation was. Karl pointed out endless details but in the end they had to play the hand they were dealt\u2014a drive running on empty, unless they could grab enough plasma.\n\nAyaan Ali laid out the geometry on the big display screen that dominated the bridge. SunSeeker had to stay below the Bowl rim, or else come within the sighting angle of the domed gamma ray lasers sited there. Their \"experiment\" with flying a small package over the rim\u2014and watching it disappear in a furious instant\u2014proved that the Folk sense of diplomacy did not include letting them get out of the narrow cage SunSeeker now occupied. They could navigate in the space below the rim, down to the upper reaches of the Bowl's air zones. Spread out as the Bowl was over hundreds of millions of kilometers, it exerted a small but steady grav pull on them. Thrusting with the thin plasma here offset that. And through the center of that volume the jet spiked like a living, writhing yellow lance.\n\nAyaan Ali's 3-D display showed in detail the atmosphere's partitions far below them. It was not continuous, or else pressure differences between the low-grav sections would cause the air to gather there to a stifling degree. Instead, firm walls isolated wedges of the Bowl, cutting off circulations to high latitudes. Yet the air zones allowed gas to flow throughout the entire circumference of the annular regions. This meant that the air could flow over zones covering the size of the entire solar system, creating weather patterns unknown on mere planets. But the air could not ascend to the higher latitudes\u2014the \"bottom\" of the Bowl, toward the Knothole.\n\n\"Those partitions are a wonder,\" Ayaan Ali said. \"Made of some layered stuff that is flexible enough to have some give to it. But it's hundreds of kilometers on a side!\"\n\nRedwing nodded, thinking again, What could I be missing? This thing was built by engineers who thought like gods. They must have methods we can't see, can't yet imagine.\n\nYet the Folk who ran this place had let Beth's team escape. First from their low-grav Garden prison, then from the Bowl itself. Beth is quick, ingenious, a real leader, but still... They're not all that smarter than we are. Bigger, though, Beth says. So how do they run this contraption?\n\nAyaan Ali pointed to the roughly conical section, shaded blue, that was their allowed flight volume. She said, \"So we can cruise around in here, and zip across the jet when we want to. So far we've just circled it, mostly.\"\n\nKarl pointed at her simulation, which showed the bright jet purling down from the star, tightening as it neared the Knothole, then\u2014as the display moved down, its smart eyes following his finger-point\u2014beyond, where it expanded again, losing luminosity. That made the fast wind that SunSeeker had been swimming upriver against for a century, slowing them, costing them time and supplies. Coasting on the vagrant tendrils of plasma fraying off the jet had been a constant piloting problem, running Ayaan Ali ragged. Beth's return had taken some of the burden from her, and together they would take on the reverse problem\u2014flying into the jet's thick, turbulent, moving cauldron of ionized particles and mag fields.\n\n\"I've calculated how to tip in near the top\u2014that's our sign convention, right? Top is as high as we dare get, just below the deflection ability of the gamma ray lasers. We turn and plunge down, toward the Knothole. We sway back and forth across the jet while we drive down. Thrust hard in a helix winding path.\"\n\nHe had painted a red line in her simulation, standing for SunSeeker's calculated path. Its helix widened as it got nearer the Knothole and the magnetic field lines\u2014blue swirls embedded in the yellow and orange showing plasma\u2014bulged outward in response. \"See? We make the jet sway a little. A kink in the flow.\"\n\nRedwing thought he followed this, but decided to play dumb. \"Which are?\"\n\n\"I'm sure you went through the basic plasma-instabilities material, Cap'n. It was in your briefing run-up.\"\n\nThe right word may be effective, but no word was ever as effective as a rightly timed pause. He let it simmer a bit. \"Karl, you will always answer a direct technical question and skip your idea of what I know. Assume I know nothing.\"\n\n\"Sorry, um, Cap'n. Of course. Certainly. I meant that...\" His voice trailed off, uncertain of anything.\n\nRedwing bailed him out. \"Like a fire hose?\"\n\n\"Right! Fast water going through a fire hose, if it swerves a little, the centrifugal force of it forces the hose even more to the side. It corkscrews, makes a kink.\"\n\n\"So it will lash the side of the Knothole? You're sure?\"\n\nKarl paused, nodded. \"More of a brush, I'd say.\"\n\nRedwing nodded. Ayaan Ali said, \"I have some good news. We got a short signal from Cliff's team\u2014from Aybe.\"\n\nRedwing brightened. \"Where are they? What\u2014?\"\n\n\"Here. They passed under the edge of the mirror zone and got out onto the hull. Found ice there. Then they had to take off. They got led to a place where there were something like, well, talking stones.\"\n\nRedwing leaned forward. \"And those said...?\"\n\nA shrug. \"We got cut off. See down there? They were in lands between that zone of hexagonal mirrors. The icelands, with some life in them, those are on the outer hull under the mirrors, which keep it cold. Then Cliff's team and those Sil got to the drylands between the mirrors and this huge ocean.\"\n\nRedwing stared at the view. Even when Ayaan Ali brought up a max resolution image, there was nothing to show more than occasional towns and roads. Again it struck him how much of this place was endless forests and seas and ranges of tan hills. Very few large cities and plenty of room for wildlife. Why? Hard to evaluate a thing as big as this Bowl. Earth alone had plenty of habitats that a few thousand years back were places where the crown of creation would be a tasty breakfast.\n\nKarl asked, \"Those are\u2014what, hurricanes on that ocean?\"\n\n\"Seems so.\" Ayaan Ali pointed to a few. \"The big winds have lots more room to play out, too. Huge storms. Cyclones the size of planets.\"\n\nRedwing stood to end the meeting. \"We'll hit the jet in a few days, right? Keep doing your simulations and drills. Get some rest, too,\" with a nod to Ayaan Ali.\n\nNow that the die was cast, he needed some alone time. SunSeeker's steady rumble always told you that you were in a big metal tube, only meters away from other people. And meters away from both a furious fusion burn and, not far from that, high vacuum. First he quietly made his way through the biozones, sniffing and savoring air that came fresh from the oxy-making plants, and avoiding the finger snakes in their happy labors. They were fun, but he was not in a fun mood.\n\nGecko slippers let him walk the far reaches of the ship, out of the centri-grav torus. They were like weak glue on your soles, following the sticky patches on the walls. The zero-grav plants were matted tangles of beans and peas, with carrots that grew like twisted orange baseballs and green bananas that made weird toroids. A finger snake tunnel ran underneath. The snakes weren't showing.\n\nHe went on into the hibernation modules, where what he thought of as the biostasis crew lay. Just sleeping, sort of, though hard to wake up. His footsteps rang as he walked the aluminum web corridor beside the solemn gray capsules. He didn't want to call out of cold sleep enough people to crew a big landing expedition, not for the Bowl anyway. In the defrosting and training they would all have to triple up on a hot hammock, and shower once a week. As it was now, even the small present crew\u2014nine plus Redwing plus three finger snakes\u2014got two showers a week and didn't like it.\n\nNow that they were headed for a battle, of sorts, he realized how far from its expected role this expedition had come. This was not a craft built for war and neither were the crew. They had been carefully tuned for exploration and centuries of confinement. They were living in a constantly running machine where opening a hatch without proper precautions could kill you dead in seconds flat.\n\nWith that happy thought, he turned back. You're worrying, not thinking. He could use some time with the finger snakes.\n\n* * *\n\nRich garden smells slapped him in the face. He looked around him, seeing miniature sheep and full-sized pigs and chickens, clucking and grunting\u2014and no finger snakes. Their tunnel was big enough, he could peer into it... but he went to the screens. If they weren't in the tunnel, he'd still find them easily enough.\n\nNow, what had the finger snakes left on-screen? They'd been watching the Bowl slide past, even as he had. No, they hadn't: this view was following a cityscape as it rolled below SunSeeker. If Redwing understood rightly, that was a Sil city, newly rebuilt after an attack from the Folk. It looked quite strange. Streets and peaks like hieroglyphs, or wispy Arab writing.\n\nHe jumped when a flat head poked his elbow. \"This they did hide,\" said\u2014Shtirk? Marked near the tail with a bent black hourglass. \"Hide no more. A great shame.\"\n\n\"Wait. Is this writing? So big?\"\n\nIts voice had a sliding, flat tone, faint. \"Can see such writing from everywhere on the Bowl. This says the Bird Folk stamped their own world flat. A mistake in steering ended their bloodline. This was in a message... a message from the stars. Captain, yes please, how does a star send a message?\"\n\nRedwing dithered for a moment about how much to reveal; but he wanted to know what Shtirk knew. \"You know what a star is? It's like your sun, that sun, but much farther away. Stars have worlds, not Bowls but spinning balls. We have a message from one of those, from Glory. We haven't been able to read it all, and it's still coming in.\"\n\n\"The Sil read,\" Shtirk said. \"Your bandits learn find the message from you, the Sil from them, then the Sil read. Now they tell us. Thisther goes to tell you all in command deck. Is it true? Bird Folk did smash their own world?\"\n\nRedwing laughed. \"And they think they're the Lords of Creation! Yeah, I believe it. I'll put it to the others, and we'll look through the message from Glory. But I believe it.\"\n\n* * *\n\nFred Ojama and a giant snake were hard at work at the control screens when Redwing found them. Thisther's head and the fingernails on its tiny quick tail were close up against the controls, typing. Fred was saying, \"Yup, yup, yup...\"\n\n\"Fred?\"\n\n\"Sir.\" Fred didn't turn. \"If you'll look past me... see the starscape? And the blue dot? The dot is the Bowl. The stars move, too. I've run this twice already. The Bowl left Sol system in Jurassic times, then tootled around to several other stars\u2014not moving as fast as it does now. Then they came back between the Cretaceous and Tertiary. If the times hold, then the mass of the Bowl ruined some comet orbits that second time, and that was it.\"\n\n\"It?\"\n\n\"The timeline checks. They caused the Dinosaur Killer impact.\"\n\nThisther said, \"Great shame. They hid this for lifetimes of worlds.\"\n\n\"My God,\" Redwing said.\n\nThisther said in his quiet way, \"But no more. All will know. They killed their own genetic line. Sil will tell all.\"\nTHIRTY-TWO\n\nTananareve realized she should agree with the big, ponderous beast that was Memor. She had come to think of the alien as a kind of smart elephant, with a sense of humor equally heavy. \"Yes, that was a clever saying,\" Tananareve made herself say.\n\n\"I am happy you have discovered the nuances of our nature,\" Memor said. Apparently sarcasm is unknown here, never mind irony, Tananareve thought. She knew Memor thought what she'd said was amusing, from the way her body shook, but it went right by human ears.\n\n\"The wonder of all this is what impresses me most,\" Tananareve said to move on to better things. Memor and Bemor were huge and strange, but they liked her to play the awed-primate role. The hard case was Asenath, who mostly ignored Tananareve except for the occasional glower. Plus deliberately aimed stale exhaled breaths and well-timed, acid farts.\n\nThey stood among a crowd of hundreds of squat, humanoid creatures who formed neat, obedient circles around the Folk party. She watched these, the first human-shaped aliens she had seen, trying to understand the blank expressions on their hairy faces, to figure out what was going on. Beyond the crowd was a tall pinnacle with a single round thing in it that she had just now realized was an eye or camera, watching all this.\n\nAsenath was holding forth to the rapt assembly in a booming voice that had made Tananareve flinch when she first heard it. Study of the Folk conversations had given her some hints of meaning, but the long phrases Asenath used seemed more like chanting. Tananareve asked Memor, \"Is this some kind of ritual?\"\n\n\"Quite observant of you. She is reassuring the Kahalla that the Sil and humans who escaped their capture will be taken in hand soon. No damage shall follow from this Kahalla failure.\"\n\n\"What's that about their... children?\"\n\n\"Nothing important. The Kahalla are losing many eggs to the appetites of scavengers. They seek us to somehow ward off their predators.\"\n\n\"Will you?\"\n\n\"We do not intervene in natural matters. Nature runs itself well.\"\n\n\"You told me earlier that you Folk ran Nature.\"\n\nMemor gave a fan-flutter of amber and blue, which seemed to mean pleasant amusement. \"And so we do. At a remove, of course. Long ago the Folk set up this dynamic equilibrium, a predator\u2013prey oscillation that will not go too far.\"\n\n\"So these... Kahalla?... won't get wiped out?\"\n\n\"No, they are sufficiently intelligent and wary to deal with their predators\u2014a nasty little vermin species. Both predator and prey have a low mental level and can adapt to changes in the other species, as they occur over long times. Evolution is thus contained. Populations do not sprawl out, consuming natural lands. There are several such interlacing balances in this zone.\"\n\nTananareve pondered this as Asenath's long bellow went on.\n\nThen a new droning cry came\u2014shree, kinnne, warrickk, awiiiha...\n\nMemor said, \"Ah, they have awakened the memory box.\"\n\nAsenath paused, then went on, trying to boom over these new deep tones with their extended cadences. Tananareve saw that the laboring sounds came from the tower with the eye. \"What is it?\"\n\n\"A form of consciousness prison. From a hotworld it came and we are its stewards. Or rather these Kahalla are its attendants.\"\n\n\"A... rock mind?\"\n\n\"We have several strewn about the Bowl. They are slow but sure and alert us to long-term trends that otherwise might elude our quick eyes. You are, for example, a somewhat old-fashioned individual intelligence, organic. This is an inorganic one, and the Kahalla are a sort of hybrid mind who attend the stone lattice mind. They are nothing like the vast collective intelligences\u2014but never mind, we have had enough of this slow-thought place. And our escape approaches.\"\n\nawrrrragh yoouuiunggg arrraff kinnne yuuf...\n\nTananareve had not noticed the huge wall of scaly flesh settling down from the sky, beyond the talking tower. Across its rough brown skin silvery fins fanned as the bulk waltzed lazily into place. It spread slender tentacles grasping for ground. They played across the land. Kahalla ran to secure these to boulders, looking in perspective like ants bringing down a sea fish. The tentacles wrapped around catch points and pulled the great thing snug to ground.\n\nAsenath finished and the Kahalla bowed deeply, on their knees with a low, sonorous moan that grew in volume until it washed over Tananareve. Asenath returned the bow, gave a vibrant trill salute and a four-color fan-flurry of farewell. Memor scooped up Tananareve and made short work of the journey to the immense thing\u2014a bag inflated to fly, she guessed. But alive.\n\nBy now she knew that Memor enjoyed the open land, and spoke, too, of \"the serene voyaging our living craft affords.\" They entered by a flap that opened like a mouth. A huge tongue unfurled and Memor walked up it, carrying the primate on her shoulder. It felt to Tananareve unpleasantly like being eaten. Memor said in her booming Anglish, \"The mucus of this great beast had been engineered to carry a delicate fragrance unlike anything else. Its scent is a luxury and settles the mind, a necessary aid in air travel. Chaos may come to rage all about us, but we shall be mild.\"\n\nTananareve sucked in a lingering taste. Like flowers, though with an oily undertaste. Bemor, too, sighed, though he said, \"We must make haste,\" and bellowed an order to small scampering things that had come to greet them.\n\nThey were in a wet cavern. This \"skyfish\" as Memor called it was like a cave of moist membranes lit by phosphorescent swirls embedded behind translucent tissues. They reminded Tananareve of illuminated art back Earthside.\n\nA deep bass note rang, ending in a whoosh that made it seem like an immense sigh. Grav momentarily rose, and Tananareve knew they had lifted off. Ruddy wall membranes fluttered. Warm air eased by them as they entered a large bowl-shaped area. Sunshine lanced through membranes so clear, Tananareve thought at first they were open to the air. But the sweet breeze swept first one way, then reversed, and she realized that it was the breathing of this great beast. The tower that had seemed so tall outside now dwindled away and the skyfish turned, so the sweep of a plain came into view. Clouds stacked like fat blue plates loomed on the shimmering distance. She could see the long arc of Bowl curving up into a pale sky; she was looking across a distance the size of planetary orbits. The eggshell blue of seas dominated the somewhat washed-out greens and browns of landmasses, and made pale the sheet grays of mirror zones. Across that flapped big-winged angular birds with long snouts and crests atop their bony heads.\n\nMemor met the captain of this gasbag being. The whole idea of a captain was odd until Tananareve realized they were like people riding a larger animal, as she had ridden horses. Memor spoke quickly, with booming comments from Bemor, all too fast for her to fathom.\n\nThe captain listened for a while, big eyes watery and anxious. This creature was somewhat like some of the Folk\u2014a big thing, four-legged and solemn and slow, mouth wide and salmon-pink and lipless. Bursts of words rattled from the mouth. Its narrow nostrils were veined pink, with fleshy flaps beneath. Large round black eyes watched them, yellow irises flashing in the slanting sunlight. From the top of the captain's head sprouted a vibrant blue crest, serrated and trimmed with yellow fat, reminding Tananareve of a cock's comb.\n\nThe captain took them on a walk through the ramparts, view balconies, and residential segments of the great living volume. A narrow hissing hydrogen arc heated its eating levels and lit the translucent furniture in blue light, where workers of four and six and even eight legs labored to bring forth live dishes for Folk delight. Pressed, Tananareve cracked a carapace and slurped out the warm white flesh of some sea creature. The next dish was a kicking big insect basted in creamy sauce. Memor said something about how keeping it alive through the cooking added savor to the proteins, but Tananareve decided that it was best to know less about Folk gustatory tastes. She tried to break the thick legs with her hands and snap off the tasty eyestalks. Crunchy but with a peppery flavor that stung her lips and sent a scent like stale meat into her sinuses. A green pudding turned out to be a slime mold that thrust probes out into her mouth as she tried to chew it. The flavor wasn't nearly worth it.\n\nStill, it was useful food. Folk ate meats and veggies she found mostly dull or repulsive, with little in between. She sat in the steady warm breeze of the skyfish's sweet internal breath\u2014were they essentially sitting in its trachea?\u2014and listened as Memor rattled on to other Folk sitting nearby about matters political and somehow always urgent. Or so her limited translation abilities told her. Finally Memor turned and said to her\u2014whom she described to the other Folk as \"the small Invader primate\"\u2014\"You must surely admire our craft. We took the early forms of this creature from the upper atmosphere of a gas giant world, long ago. Their ancestors found our deep atmosphere a similar paradise, to cruise on soft moist winds, and mate in their battering fashion, and wallow in our air, to turn falling water into their life fluid, hydrogen.\"\n\n\"I doubt the primate can follow your description,\" Asenath said, coming into view.\n\nTananareve warily backed away from the lumbering thing. She could smell the malice oozing from Asenath. \"Still, she could be of some use in capturing the renegades of her kind, whom we shall soon intersect.\"\n\nAsenath ushered them all over to the broad window in the skyfish's side. Elaborate orange-colored fins flexed near the back of the beast. They flared out, capturing winds like a sail, driving the bag forward. Tananareve felt a lurch and a dull thump. She had the sense of rumbling movement under her feet and in the living walls. Memor explained that the bag was \"trimming\" in flight by shifting weight inside itself. Asenath said, \"Our admirable skyfish can torque about its center of mass, and thus navigate.\" Tananareve watched the flexible yet controlled fan-fins spread out, at least a hundred meters long. Its gravid majesty seemed somewhat like a ship sailing at angles to the wind, tacking above the lush forest below.\n\nAsenath said, \"We are precisely on course to intersect the renegades. They are sailing on this same gathering wind.\"\n\nTananareve watched the opalescent walls shimmer with hot perspiration. Memor remarked that these were \"anxiety dewdrops,\" brought out by the laboring muscles of the great fish. The shimmering moist jewels hung like gaudy chandeliers, lit by the blue glow of hydrogen flares and phosphorescent yellow bands that ran across the high ceiling. One of the drops, bigger than Tananareve's head, fell from high up and spattered at her feet with cutting acid odor.\n\nBemor shifted his bulk and remarked, \"The new signal from Glory is coded in a different manner. We are having difficulties decoding it, except for a few images.\"\n\nMemor shifted into Folkspeech. \"Best not to let the primate know. Show what images you have.\"\n\nTananareve felt her pulse speed up but kept her face blank and made a show of turning to gaze out at the view. A huge bird was flapping by below, eyeing the skyfish. Casually she stepped away to the spot where, leaning forward, she could see reflected in the transparent window the projection Bemor was showing Memor. It was an animated series of images. A man in a white robe advanced into view and something leaped at him. It was an alien with ruddy skin and three arms. It jumped at the man, and huge feet kicked him to the ground. The alien wore tight blue clothes that showed muscles bulging as the view drew closer. The alien head was like a pyramid with sharp chin and bones like ribs under tight, ruddy skin. Two large black eyes glinted at the man, who was getting up, his smiling face mild and his long blond hair flowing. He was holding forward an object\u2014a wooden cross\u2014to the alien. Tananareve saw suddenly that the man was Jesus. The alien leaped on the man, hammering him with feet and two fists. Its third arm was bony and sharp, with nasty nails tapering to points. The alien slammed this into the head of Jesus, shattering the skull into pieces. Blood flew into the air and Jesus collapsed. His body lay still. The black alien eyes looked straight out from the screen Bemor held and thick lips pulsed, swelling and narrowing in what must have been some kind of victory gesture.\n\nThe sudden raw images startled her. A surge of anger tightened her throat. She made herself keep still and watched the bird flap out of view on its four wings.\n\n\"Ah,\" Memor said, \"similar to the earlier one. But look\u2014we are intersecting the tadfish, as we had hoped to. Now we can deal with these primates, brought together.\"\n\nTananareve saw swimming in the filmy air below them a gossamer tube shape. Fins stroked all along the barrel body as it rose from the forest below. Somehow, she realized, the Folk had found Cliff's team, and now had them cornered.\nPART XI\n\nDOUBLE-EDGED SWORD, NO HANDLE\n\nIt is not because things are difficult that we dare not venture. It is because we dare not venture that they are difficult.\n\n\u2014SENECA\nTHIRTY-THREE\n\n\"What's that?\" Irma pointed.\n\nHanging among cottony clouds, near to the woody horizon, was a thing that struck him as a silvery, flapping blimp. Coming toward them.\n\n\"What's that?\" Cliff echoed to Quert\u2014who scowled.\n\n\"Escape,\" Quert said. \"So you say?\"\n\n\"From what?\"\n\n\"Folk know where we are. Track us.\"\n\n\"They can?\" Terry asked.\n\n\"Makes sense,\" Irma said. \"They must have sensors embedded in the original frame that holds the Bowl together. Any smart building does. The trick would be managing such a torrent of data.\"\n\nQuert gave an assenting eye-click and fell silent. The Sil took their orders from Quert and studiously let Quert alone speak for them. Cliff wondered about this but did not want to bring up or question an arrangement that was at least keeping his small party out of the hands of the Folk.\n\nWhen the spidows gave up the chase, the tired party of Sil and humans had moved on awhile, crossed a stream that Quert said spidows could not, and then stopped without a word. Cliff could feel the adrenaline collapse; he had gotten used to it after so many scares and flights. He wondered how the Sil managed crises. The same play of hormones?\n\nSome cold food with water from the convenient spring made them all feel better. Cliff had little storage left in the electronics he had carried all this time. He had chronicled all the places he had been and enjoyed looking back over the images. One from a good while back he liked, a clear day when the great sweep of the Bowl and its jet was sharp and clear. Too often the deep atmosphere blocked long views with enormous stacks of cloud. He had caught some of the team in the foreground, slogging along near a zigzag tree.\n\n\"You're keeping notes?\" Irma asked. \"I filled my data storage a long time ago.\"\n\nCliff shrugged. \"I'm either lazy or just plain picky. After the first week, when I was taking shots of every flower, tree, animal, insect, bird\u2014well, harder to be a scientist when you're on the run.\"\n\n\"One thing you're not is lazy.\" She looked at his small working screen. \"Notes for each shot, even.\"\n\n\"I do them at our rest stops, like this.\"\n\nBut there was no real resting, as the Sil made clear.\n\nQuert eyed the humans. \"We not go under now. Best not.\"\n\n\"Into the tunnels?\" Aybe asked. \"The trains? They'll catch us there?\"\n\nSlow steady eye-shifts. \"Soon. Yes. Best not go in tunnels.\"\n\n\"I kind of liked those fast tunnels,\" Aybe said.\n\n\"Folk hold them now.\"\n\n\"So... what do we do?\" Terry persisted.\n\n\"See there.\" Quert's slim arm pointed. The small silvery thing hung in the distance above a dense forest ridgeline. It moved slowly and the sun reflected winking spots of yellow and blue from it. \"Tadfish.\" The Sil around him shuffled uneasily but as usual said nothing.\n\n\"We're getting away in that?\" Irma frowned doubtfully.\n\n\"Best way,\" Quert said, and they moved forward steadily. \"Hide in sky.\"\n\nCliff wondered at the Sil social conventions, and their psychology. They were all in mortal danger but the Sil showed little jittery nervousness. Quert ruled absolutely. In contrast, he had to deal with ongoing questions and doubt from Aybe, Terry, and Irma. Only the need to move on, endlessly on, kept him in shaky control.\n\nThe tadfish was coming this way and as they entered the nearby forest of vine-rich trees and brush, Cliff could see it had a deft grace to its movement, though he could not see how it did so. Tendrils of vines yearned for the sun, though some turned at another angle, apparently partial to the jet's rosy rays\u2014specialization at work. The woods had a thick cloying stink, but were so thick overhead that the tadfish crew could not possibly see them below. Animals scampered away in their path, but there were plenty more concealed. From endless movement, Cliff had picked up ways to sense the life around them. Some animals here were superb at hiding, skinnying up into dense trees, or burrowing in hidden pits like trapdoor spiders. Others just flew away on quick stubby wings, fluttering fast enough to discourage pursuit.\n\nAybe and Irma walked with him, and Sils were both point and rear guards. The Sil somehow kept themselves in good order, Cliff saw, while the humans in their worn cargo pants with big flap pockets were drab and saggy. The Sil had patched those up for the bedraggled humans, back in the all-too-brief rest period following the battle with the skyfish. All that now seemed a long time ago. More wear had made their clothes ragged and rough. In contrast, the Sil had loose-fitting, lightweight tan and dusty white jumpsuits that never looked the worse for wear. They could be cleaned by just dipping them in water and connecting them to the Sil onboard and solar-powered back-batteries. Apparently some electrical method rejected ions the cloth disliked and knitted up broken fibers. The humans marveled at this.\n\nCliff let himself relax for a moment and enjoy the one sure thing he knew here\u2014life: wild flocks of strange things wheeling and crying high overhead; guttural lowings and crisp cacklings from the forest around them; a smelly cloying carpet underfoot, springy, more like moss than grass, starred with bright stalks like flowers; zigzag trees silvery and ripe with flapping life, big coppery-winged things that shrieked and dived at humans when they could. Somehow the big things knew not to go after the Sil, who used their arm-arrows to slice them from the sky. Cliff hit a few with his laser and so did the others and they sank to the ground after that, going for cover.\n\nThey managed to get some sleep. Cliff woke up several times, slapping and swearing at bugs that got into his clothes. Terry kept warily watching the trees and shrubs. The spidow encounter and the bird attack had made them jumpy. There were a lot of ropy vines, and gibbering small things rushed among them, sometimes hurling down oblong red fruit as if to drive the intruders away. A Sil caught one fruit and bit into it, made a twisted face, and tossed it aside. Cliff saw a long vine move on its own and pointed. \"A snake. Adapted to trees, probably disguises itself as a vine.\"\n\nQuert heard and nodded. \"We call sky pirates.\"\n\nIrma chuckled. \"Why?\"\n\n\"Intelligent. In a way.\"\n\n\"Really? What do they do with intelligence?\"\n\n\"Save food for hard times.\"\n\nShe stared up at the muscular, glistening snake that hung ten meters above their heads and seemed at least that long. It curled itself and leveraged onto another branch of a tall, spindly tree. Above it were cocoons of pale gray suspended among bare branches. \"Like those?\"\n\nQuert gave an assenting eye-click. \"Call them\u2014\" He paused, searching for the right Anglish term. \"\u2014mummies. Smart snakes store so many. Sometimes mummies we use for fertilizer.\"\n\nAybe gaped at this and as they moved on, he said, \"Mummies for... I don't get it.\"\n\n\"Closed ecology, see?\" Irma shrugged. \"They have to keep everything moving.\"\n\n\"So does the Earth,\" Aybe said. \"At least, until we started industrializing space. Then we did metal smelting and manufacture in vacuum, where we could throw the wastes into the solar wind, and clean up the planet a bit.\"\n\n\"But this ground ecology is just a few tens of meters deep,\" Cliff said. \"Has no plate tectonics. Can't hide carbon from its air. Can't bring fresh elements up from far below, vomit it out from volcanoes.\"\n\nIrma finished, \"So you do that artificially. Plus you save resources. You might not get any more for a while. Or ever again.\"\n\nHe nodded at this elementary wisdom that could always bear repeating, especially on the Bowl. They were still trying to figure out the greater scheme here, as a long-term investment. A negotiation might come up ahead, and Redwing would need to know something about those on the other side of the table.\n\nThat suited Cliff for now: seeing the Bowl as a puzzle. He had always been a problem-solver, a man who reflexively reacted to the unknown by breaking it into understandable pieces. Then Cliff would carefully solve each small puzzle, confident that the sum of such micro-problems would finally resolve the larger confusions. Irma thought the same way, one reason he liked her so much. On this endless trek through strange lands, they had grown to need each other. Every day was unnerving and wonderful at the same time, and for the same reasons. His whole team had gone into cold biostasis\u2014always a risk\u2014so they could reach an alien planet they knew very little about. Now they were immersed in that, multiplied by orders of magnitude. And they knew even less about this huge strange thing, the Bowl. It was daunting and thrilling, every day\u2014in a place where there were not really days at all.\n\nNow that they had a clear destination, the team of Sil and humans moved on with renewed energy. As they mounted a low hill, they saw the tadfish was closer. \"It lands there,\" Quert said, gesturing toward the next hill.\n\nThe slowly drifting football-shaped creature was maneuvering under tendrils of rain. Cliff remembered the one that had ravaged the Sil city and looked at its blister pods, wondering if the skyfish carried weapons there.\n\n\"Virga,\" Aybe said. \"That's the name for when water evaporates away before hitting the ground. See? It's falling from clumps of altocumulus clouds up there.\" Among towering, steepled clouds rain fell, to be absorbed by lower, dryer layers.\n\n\"Tadfish drinking,\" Quert said. \"Hurry.\"\n\nThey came up on the strange creature through a cluster of zigzag trees thickly wreathed in green vines. The silvery tadfish settled down in a clearing near some ceramic buildings. Quert picked up the pace. Cliff watched the complex sheen of skin as it flexed and stroked its translucent fins. Some attendants clustered at its base as it settled down. Quert was taking them in a flanking approach through the zigzag and vine maze. The ground crew was Kahalla in bright, creamy clothes. They took a small party of passengers off, and Cliff could not see who or what they were as they went into the dun-colored buildings. The Sil did not slow down.\n\nWith the humans struggling in the rear, the whole band sprinted from the last of the zigzags into the open pale dirt field and quickly across to the tadfish. They approached its face as its big green oval eyes peered down at them.\n\nSeveral Sil peeled off and took up positions between the tadfish and the buildings. Cliff came out of the trees and saw some of the Kahalla ground crew turn back. They started running toward the tadfish, and the Sil moved to block them. A Kahalla drew a weapon and one Sil flexed his arm. The Kahalla went down instantly. The other Kahalla backed off and the Sil advanced.\n\nQuert said, \"They stay. Tadfish small. Not carry all of us.\"\n\n\"Ah.\"\n\nThe tadfish mouth was still open. Quert ducked and ran directly into the mouth. This looked to Cliff like a very bad idea. He slowed as they approached the ruby red lip of the mouth and saw the floor of the mouth was a hardened cartilage, lime green and ribbed. He tromped in, boots rapping on the cartilage. A musky smell seemed to wrap around his face. He edged down a narrow passage to the left, dimly lit by amber phosphors in the fleshy walls. The walls pulsed with heat and he emerged into a long room devoted to the view out a transparent wall in the tadfish side. The humans were there but no Sil. As he crossed the room, he felt a surge and the tadfish took off, angling over the zigzags. It turned to bask in the wind and accelerated. Everyone caught their balance, bracing against the softly resistant, fleshy walls. Below he saw Kahalla figures running vainly toward some tow lines that had held the tadfish in place. They retracted, and a Kahalla raised a tube weapon toward the humans looking down. It sighted\u2014then lowered the weapon and shook its arms in frustration.\n\nIrma said, \"The Sil stole this thing.\"\n\nThey all laughed a bit in appreciation, relieved, and Quert came into the room. In its staccato manner, it confirmed that the Sil had kept track of when the tadfish would set down on its regular route and had rushed to get there just in time to seize the tadfish when the flight crews changed shift. \"Good timing,\" Terry said, and Quert gave a hand-pass that meant assent.\n\nCliff did not remark that the Sil had not bothered to tell the humans what was up. Quert didn't like debating policy; indeed, the Sil did not share the human appetite for endless talk and at times made fun of it.\n\n\"So now we'll 'hide in the sky' as you said.\" Aybe scowled. \"From what?\"\n\n\"Folk trace us. Saw at Ice Minds. Kahalla alert them.\"\n\nThey were rising fast above the spreading plain. The atmosphere became supersaturated, the air suddenly full of mist. Cliff looked out along the axis of his shadow and there it was forming, a huge round luminous rainbow. The circular rainbow popped into the halo air. It formed near the top of a mountain, aslant from the constant star hanging at his back. He could see five separate colors; the red was intense. Slowly the mist dissolved and the spectral promise faded away. Yet it moved him with its beauty and its quick demise.\n\nThe tadfish walls popped and creaked. Irma said, \"What's that?\" They rose faster. The fins outside beat in synchronous rhythm, and they heard a heavy thudding through the walls. \"Is that its heart?\"\n\nAybe looked out the transparent wall. \"Maybe the body is expanding. It must be making more hydrogen from water, filling itself out.\"\n\nCliff put his head against the oddly warm transparent window and only then noticed a separate transparent bulge farther along the curving skin. It promised a better viewing angle. But the wall nearby had no opening. He saw no way to reach that bulge but ran his hands along the wall and felt a crease in the warm flesh. He pried at it, and with a rasping purr a sheet came free along a seam. A pressure seal, apparently. He peeled it back and saw a narrow footway lit by blue phosphors. A few steps took him to the transparent blister. From here he could see farther around the curve of the great flying balloon, and the stately ranks of flapping translucent fins.\n\nThe view now was majestic and vast. The deep Bowl atmosphere fell off slowly with height, so a living balloon with a fishlike shape could rise a long way before the slackening pressure outside made it bulge. He looked down through many kilometers at the clouds flowing over the low mountains that only a short while ago, while they were running, had loomed in the distance. Refracted glows of the jet and star danced and coiled in deep clouds. Except for the slow thump of the tadfish heart, he felt as though he were hanging in air, seeing the Bowl as did the great birds he had seen far up the towering sky.\n\nHe turned to rejoin the others and saw to his side another pressure seal. He felt it for a seam. Then Irma came into the cramped blister. \"What's going on?\"\n\n\"Look, we're just passengers, can't do anything but wait. Let's see how this thing works. Might be useful up ahead.\"\n\nIrma twisted her mouth in a skeptical curve. \"I could use a rest.\"\n\n\"The more we know, the better.\"\n\nIrma leaned against the warm wall and gazed out on the spectacular view. \"Um, maybe. Me, I've got strangeness overload. Every day there's more to digest. And on the run, too.\"\n\nHe smiled. \"We're in the belly of a beast already. Let's not get digested.\"\n\nShe shrugged. \"These passages are claustrophobic. Let's leave Aybe and Terry back there\u2014Quert's brought some gloppy food for them and they're wolfing it down. Tastes like a chicken-flavored milk shake. Hard bits in it, too, tasted like bitter snails. I can wait.\"\n\nThey went through the narrow tunnels along the tadfish's streamlined form. It had a torpedo shape, and the occasional viewing blister was flanked by big slabs of sinewy brown muscle. These flexed as it propelled forward and Cliff sniffed; their close, moist air took on a sweaty, salty tinge.\n\n\"Fishoids, torpedo-shaped predators,\" Irma said when they looked out a blister and saw a swarm of long tubular birds flocking below. They swerved and scooped in the air, catching something that vented from the tadfish. \"Feeding on waste?\" Irma asked.\n\n\"One species' waste is another's food,\" Cliff said.\n\nAround the long curve of the tadfish body came big gliding shapes in convoy, more like manta rays than like birds. They were flying in a V formation and had slick, matted gray skins. Diving and banking in concert through the thick air, big eyes intent on the feeding tubular birds. Their shapes, Cliff saw, reflected the demands of curvature, flow, and tension as they lazily slid down the air. Meaty triangular wings led back to rudderlike fins and a long spike at the tail. Cliff pointed. \"The killing instrument.\" A pair of eyes protruded in knobs at either side of their wedgelike heads, above the long slit mouth. Another pair of bigger, yellow eyes sat close together and peered forward. The flying tubes moved with stately grace through the glassy air. Fleshy, oarlike appendages flanked the heads, as the manta snapped up the smaller tubular birds. Through the window, Cliff and Irma could hear cries and shrieks as the pillage cut through the flock.\n\nIt was a strange sight and over in a moment. The mantas dove under the tadfish, while a few survivors scattered in frantic haste. Irma put an arm around Cliff's waist and he felt a rush of contentment. In all this strangeness, the small comforts mattered most. They stood that way awhile, until warm air drew their attention to an inward-leading passage. He was trying to analyze all they were seeing, but the dimly lit passage drew them onward. Squishing sounds came from ahead. They worked along a throbbing wall and came upon a translucent interior layer, where they could see dark bones working in a sheath. Low murmurs and hums came through the transparent wall, and they could see gray fluids running down the bulky flesh everywhere. Lubricants?\n\n\"This is its internal skeleton?\" Cliff wondered. The sliding parallel bones worked through thick green collars, coiling like a flexible spring. But their attention focused on two moving stick-figure creatures that seemingly tended this living machinery. They were about a meter tall, with six limbs that moved quickly, clambering everywhere, adjusting the mechanical supports of the bony spine. These creatures used their flexing limbs as either arms or legs, depending on where they scampered over the big moving apparatus. Irma pointed\u2014they had long, two-petaled tails that folded to protect sexual organs that occasionally came into view as they worked. They seemed like slender, pink skeletons, with brains carried in a bump between the pair of limbs at the top of the spinal cord. Three eyes worked on stalks, making an equilateral triangle around a broad red slit of a mouth.\n\n\"They can see us,\" Irma said, \"but they're ignoring us.\"\n\n\"Not so peculiar, really. Think what it's like to work on a public conveyance,\" Cliff said. \"They've seen plenty odder than we are.\"\n\nThey moved along the transparent wall and saw two thick, muscular creatures wearing what seemed to be equipment belts. They were working on a panel pulled open, revealing some complex piping throbbing with amber liquids. They moved with deft small fingers, using tools too small to make out. \"Those look like the ones we saw before,\" Irma said. \"Remember? We were\u2014\"\n\n\"Screwing, yes. And one of them fell on us.\"\n\n\"Turns out they're smart tool-users. I wonder what they thought of us.\"\n\n\"These are ignoring us, same as before. We're pretty ordinary, I guess.\"\n\n\"Here, sophisticated means, I guess, not impressed to run into just another funny alien.\"\n\nCliff chuckled. \"Puts us in our place, doesn't it?\"\n\nAs they neared the tail, there were sudden orange flares jetting from tubes below the viewing blisters. \"Must be fueled by hydrocarbons,\" Cliff said, \"brewed into burnable fuels.\"\n\n\"We're moving fast,\" Irma said as a surge rippled through the body around them. The floor also rolled a bit, like a ship. \"The burn helps.\"\n\n\"Quert said they're artificially bred forms of an original balloon-birdlike species,\" Cliff said. \"So their energy source got engineered, too.\"\n\n\"We'd better get back,\" Irma said. They were moving quickly now, diving out over a sheet of green water that seemed a continent wide, beneath the waving fields of grass. Dotting this grass sea were bumps shaped like tadpoles, with a crust of trees ornamenting them. The thick end pointed upstream, while the water swept debris past and then dropped it in the eddy behind the hummock. This made the tadpole tail grow, building slim islands where animals lived among the dense amber and green trees. All this simmered beneath the reddish light of the star and orange filigrees cast by the slowly churning helices in the jet. As they descended, gaining speed, packs of large fishlike life became clear. They breached the shallow sea in great leaps, hanging in air, then crashing down in great sprays of white.\n\nIrma said, \"Those look a lot like dolphins.\"\n\n\"The basic fish shape, as you say.\" Cliff pointed at the width of the moving school. \"Thousands of them. What a great way to see Bowl life.\"\n\nIrma said, \"I always thought, we believe dolphins are not as smart as we because they never built cars or refrigerators or New York or had wars. All they do is spend every day swimming in warm oceans, chasing and eating fish, mating and having fun. The dolphins think they are smarter than us, for the very same reasons.\"\n\nAgain, Cliff chuckled. \"I always thought, on a statistical argument about time scales, that if we ran across intelligent aliens at Glory, they'd be overwhelmingly likely to be far more intelligent than us.\"\n\nIrma nodded. \"And therefore wouldn't care at all about us\u2014if they even noticed us.\"\n\n\"Me, too. But we've been able to stay out of the hands of the Folk for a long time now. On their own turf!\"\n\n\"Could be the aliens who built this place were super-minds, but their descendants have gotten stupid.\"\n\n\"So both the skeptics about smart aliens were wrong, and so were the optimists?\" Cliff liked the idea. \"Wonder what that means\u2014\"\n\nShe and Cliff were so caught up in the sight, they only noticed the huge thing hanging above when it blotted out the star.\n\nThe skyfish was firing hydrogen jets behind it and slewing swiftly through the filmy air. Headed toward them. Some strange angular birds were flocking out of the skyfish. They were lean and had long jaws with\u2014 \"Are those teeth?\" Irma asked.\n\n\"Looks like. Not friendly, no.\"\nTHIRTY-FOUR\n\nThey had been running hot and hard now for many hours, and it was starting to show in his crew.\n\nRedwing sat on the bridge because if he paced for hours, as he already had, everybody got edgy. Fair enough; he sat and twitched, mostly by moving his feet, in their gecko shoes, where nobody could see. He had used up his weekly shower ration in two days of this.\n\nThey had entered the jet days ago, not that there was any clear sign of it. The mag field values started to climb a day ago and the plasma density followed it. Only by amping certain spectral lines of yellow and green could the wall screens show the filmy curtains of sliding ion flow in the jet. Those weren't plasma, really\u2014the light came from ions, as electrons found them at last and cascaded down the energy levels to emit a photon. The light showed where plasma eased into little deaths.\n\nNow Ayaan Ali had taken over as lead pilot and Clare Conway sat in the copilot deck chair. Beth Marble had gone to get some sleep. They all watched the blue and green lines work on the large screens, mapping pressures and flux changes at the perimeter of their magscoop fields.\n\n\"How's the scoop impedance looking?\" Redwing asked.\n\n\"Down to three meg-ohms, sir.\" From her sideways glance, he knew Ayaan Ali understood that he could have read it from the screens, but that they needed to have some talk on the bridge, just to diffuse tensions.\n\nA rumble and a rolling shock came rippling through the ship. \"Ride's interesting,\" Redwing said mildly.\n\nAyaan Ali smiled and nodded, eyes never leaving the screens, hands on the e-helm at all times. \"We took a shock front from forty-two degrees starboard, seventeen degrees south. Plasma still rising.\"\n\n\"This fits the model Karl worked up?\"\n\n\"Um, sort of.\" A skeptical arching of eyebrows.\n\nRedwing picked up something more in her body language. Karl and Ayaan Ali always kept a wary distance in crew meetings and were crisply correct around him... which led him to wonder if something was going on between them. They were in a dangerous place, and tensions needed release. He decided to put it away for later, if ever. The mission was the point here. \"Okay. Nobody expects models to work well here. I don't, anyway. Let's see the aft scoop and plume.\" Redwing always felt a bit jumpy about anything sneaking up behind them, though with the Artilects on constant duty, that was extremely unlikely.\n\nThe rumbling aft faded. Eerie popping noises came through the support beams and hollow creakings sounded. A sour stench of something scorched\u2014probably just overheating in a forward tank. The display space before them showed flurries of plasma, highlighted in violet, slamming into the scoop.\n\n\"Those knots again,\" Ayaan Ali said.\n\n\"Let's see long-range radar,\" Redwing said.\n\nThey studied the yawning space around the jet, looking from multiple dishes. \"Nothing near us, nothing in near space, nothing farther out,\" Ayaan Ali said. \"I've always wondered why we saw so few spacecraft. You'd think they would be sending ships out to monitor the whole system.\"\n\nRedwing nodded. \"This system has no planets, or asteroids, no comets coming in. Nothing bigger than a school bus. But there were some small craft, remember? They came over the Bowl rim, flew along the top of their atmosphere manifolds, ducked into a hole in the upper atmosphere layer.\"\n\n\"But very few, very little craft.\" Clare shrugged. \"And we know the gravitational instabilities that the Bowl risks all the time. If they get too close to the star, they have to fire up the jet and push the stellar mass away, while they grab the rising jet flux and let it push them back. Reverse if they start falling behind. Then there's the spinning Bowl, same instabilities as a spinning top. But I guess they can run this whole wacky system without many spacecraft.\"\n\nKarl came onto the bridge, back from checking inductance coils along the ship. He had heard Ayaan Ali. \"It's all maintained with magnetic fields and jet pressure,\" he said. \"Plus the reflected sunlight, to heat the hot spot. Tricky stuff.\"\n\n\"Those inductance coils getting worked hard?\" Redwing asked.\n\n\"Running high, but within margin.\" Karl got into his chair and belted up, casting a side look at Redwing, as if to say, Why don't you sit?\n\nRedwing never explained that he liked to move through the ship when it was having trouble. He could tell more with his feet and ears than the screens could say.\n\nThey had taken three days to cross the jet with the fusion chambers running at full bore, driving them to nearly two hundred kilometers per second. That was far higher than an orbital velocity, though still far under the ship's coasting specs. SunSeeker now was turning in the helix Karl had calculated, cutting in an arc near the jet's boundary, its magscoop facing the star at a steep angle and swallowing its heated plasma. They had faced such a headwind coming in and survived. But now the navigation was tougher. This time they had to remain lower than the Bowl's rim, or else come within the firing field of the gamma ray lasers there.\n\n\"How do we know this is the optimal path?\" Redwing asked Karl.\n\n\"Calculations\u2014\"\n\n\"I mean from what we've learned these last few days.\"\n\n\"It's working.\" Karl's lean face tightened, ending in his skewed, tight mouth above a pointed chin where he had begun to grow a goatee. \"We're brushing the mag pressures outward. Our sideways thrust drives the magnetic kink mode, feeding off the jet's own forward momentum. We're stimulating the flow patterns at the right wavelength to make the jet slew.\"\n\n\"We'll see sideways jet movement before it shoots through the Knothole?\"\n\n\"It should.\" Karl's gaze was steady, intent. He had a lot riding on this.\n\n\"Let's look aft. Have we got better directionals this time?\" Redwing asked Ayaan Ali.\n\n\"Somewhat,\" she said. \"I rotated some aft antennas to get a look, the sideband controllers, too.\"\n\nShe changed the color view, and Redwing watched brilliant yellow knots twist around the prow of their magscoop like neon tropical storms. \"These curlers push us sideways a lot.\"\n\nA rumble ran down the axis and Redwing hung on to Ayaan Ali's deck chair. Clare showed the acoustic monitors display in red lines on a side screen. The strains worked all down the ship axis.\n\n\"We're getting side shear,\" Redwing said mildly. He took care not to give direct piloting instructions; no backseat driving.\n\n\"I'll fire a small side jet, let some plasma vent from the side of the magscoop, rotate on the other axis, and take our aft around some.\"\n\nHer hands traced a command in the space before her. A faint rumbling began, then a surge. The ship slid sideways and Redwing hung on to a deck chair. Multiple-axis accelerations had never been his strong point. His stomach lurched.\n\nShe worked on getting the aft view aligned. SunSeeker's core was no mere pod sitting atop the big fuel tank that held the fusion catalysis ions. Gouts of those ions had to merge with the incoming plasma, fresh from the magscoop. In turn, the mated streams fed into the reactor. Of course, the parts had to line up that way along the axis, no matter how ornate the subsections got, hanging on the main axis, because the water reserves tank shielded the biozone and crew up front, far from the fusion reactor, and the plasma plume in the magnetic nozzle.\n\nRedwing knew every rivet and corner of the ship and liked to prowl through all its sections. The whole stack was in zero gee, except the thick rotating toroid at the top, which the crew seldom left. A hundred and sixteen meters in diameter, looking like a dirty, scarred angel food cake, it spun lazily around to provide a full Earth g at the outside. There the walls were two meters thick and filled with water for radiation shielding. So were the bow walls, shaped into a Chinese hat with its point forward, bristling with viewing sensors. From inside, nobody could eyeball the outside except through electronic feeds. Yet they had big wall displays at high resolution and smart optics to tell them far more than a window ever could.\n\nAyaan Ali's work brought the multiple camera views into alignment with some jitter. They were looking back at the Bowl and she had to tease the jet out of all the brighter oceans and lands slowly turning in the background, a complicated problem.\n\n\"Let's get a clear look-down of the jet,\" Redwing said.\n\nTo see and diagnose the plume, they had a rearview polished aluminum mirror floating out forty meters to the side. They didn't dare risk a survey bot in the roiling plasma streams that skirted around the magscoop, with occasional dense plasma fingers jutting in.\n\nThe image tuned through different spectral lines, picking out regions where densities were high and glows twisted. On the screen, a blue-white flare tapered away for a thousand kilometers before fraying into streamers. Plasma fumed and blared along the exhaust length, ions and electrons finding each other at last and reuniting into atoms, spitting out an actinic glare. The blue pencil pointed dead astern. He was used to seeing it against the black of space, but now all around their jet was a view of the Bowl. The gray-white mirror zones glinted with occasional sparkles from the innumerable mirrors that reflected light back on the star.\n\nSeen slightly to the side of the jet, the Knothole was a patch of dark beneath the filmy yellow and orange filigrees of the jet. Redwing supposed that at the right angle, the whole jet looked like a filmy exclamation point, with Wickramsingh's Star as the searing bright dot.\n\nKarl said, \"See that bulge to the left? That's the kink working toward the Knothole.\"\n\nAyaan Ali nodded. \"Wow. To think we can kick this thing around!\"\n\n\"Trick is, we're using the jet's energy to do the work.\" Karl smiled, a thin pale line. \"It's snaking like a fire hose held in by magnetic fields.\"\n\nAyaan Ali frowned. \"When it hits the Knothole, how close to the edge does it get?\"\n\n\"Not too close, I think.\"\n\n\"You think?\"\n\n\"The calculations and simulations I've run, they say so.\"\n\n\"Hope they're right,\" Ayaan Ali said softly.\n\nThey continued on the calculated trajectory as the ship sang with the torque. The helix gave them a side acceleration of about a tenth of a grav, so Redwing kept pacing the deck on a slight slant, inspecting the screens in the operating bays.\n\nHe also watched how everyone was holding up. His crew had been refined so they fit together like carefully crafted puzzles, each skill set reinforcing another's. That meant excluding even personal habits, like \"mineralarians,\" a faction who insisted that eating animals or even plants, which both cling to life, was a moral failing. Instead, they choked down an awful mix of sugars, amino and fatty acids, minerals and vitamins, all made from rocks, air, and water. That could never work while pioneering a planet, so the mineralarians got cut from the candidate list immediately. Same for genetic fashions. Homo evolutis were automatically excluded from the expedition as too untested, though of course no one ever said so in public. That would be speciesism, a sin when SunSeeker was being built, and in Redwing's opinion, one of the ugliest words ever devised.\n\nBut with all the years of screening, there were still wild cards in his deck. Smart people always had a trick or two you never saw until pressure brought it out. Managing people was not remotely like ordering from a menu.\n\nAs he watched an internal status board Fred was manning, Redwing felt a hard jar run down the axis. Ayaan Ali quickly corrected for a slew to their port side. The fusion chamber's low rumble rose. It sounded, Redwing thought, a lot like the lower notes on an organ playing in a cathedral.\n\n\"Exhaust flow is pulsing,\" she said. \"External pressure is rising behind us.\"\n\n\"Funny.\" Redwing watched the screens intently. \"Makes no sense.\"\n\n\"We're getting back pressure.\" Her hands flew over the command board. A long, wrenching wave ran through the ship. Redwing sat at last in a deck chair\u2014just in time, as a rumbling sound built in the walls and surges of acceleration shook the ship.\n\nThe aft picture worsened. They saw from two angles looking aft that the plume was bunching up, as if rippling around some unseen obstacle. The logjam thickened as they watched. Rolling waves came through the deck, all the way from hundreds of meters down the long stack.\n\n\"Getting a lot of strange jitter,\" Beth said. She was in uniform, crisply turned out.\n\nRedwing looked around. \"It's your sleep time.\"\n\n\"Who could sleep through this? Captain, it's building up.\"\n\n\"You're to take the chief pilot's chair in three hours\u2014\"\n\n\"Aft ram pressure is inverting profile,\" Ayaan Ali said crisply. \"Never happens, this. Not even in simulations.\"\n\n\"I can feel it,\" Beth said. \"This much vibration, the whole config must be\u2014\"\n\n\"Too much plasma jamming back into the throat.\" Ayaan Ali gestured to the screen profiling the engine, its blue magnetic hourglass-shaped throat. Its pinch-and-release flaring geometry was made of fields, so could adjust at the speed of light to the furious ion pressures that rushed down it, fresh from their fusion burn. But it could only take so much variation before snarling, choking\u2014and blowing a hole in the entire field geometry. That would direct hot plasma on the ship wall itself, a cutting blowtorch.\n\nAs they watched, the orange flow in its blue field-line cage curled and snarled. \"It's under pressures from outside the ship,\" Ayaan Ali said, voice tight and high.\n\n\"If it gets close to critical pressures, shut down,\" Redwing said. He was surprised his own voice sounded calm.\n\nBeth said, \"But we'll\u2014\"\n\n\"Go to reserve power if we have to,\" Clare said.\n\n\"That won't last long,\" Karl said. \"And this external pressure on our magscoop could crumple it.\"\n\nA long, low note rang through the ship\u2014a full system warning. No one had heard that sound since training. The drive had not been off since they left Earthside.\n\n\"I'm going to spin us,\" Ayaan Ali said. \"Outrace the pressure.\"\n\nShe ran the helm hard over and the magscoop responded, canting its mouth. Next she flared the magnetic nozzle at the very aft end of the ship, clearing it of knotted plasma. That took two seconds. Then she flexed the field back down and ran the fusion chamber to its max. Redwing could follow this, but her speed and agility were what made her a standout. They were all hanging on as the entire ship spun about its radial axis. Redwing closed his eyes and let the swirl go away from him, listening to the ship. The pops and groans recalled the drastic maneuvers they'd run SunSeeker through, during the years-long Oort cloud trials. He trusted his ears more than the screen displays of magnetic stresses.\n\nThe rumbles ebbed away. When the spin slowed, he opened his eyes again. The screens showed milder conditions around the ship. \"I broke us out of that magnetic pinch,\" Ayaan Ali said. \"We got caught in a sausage instability. Had to flex our scoop pretty hard.\"\n\nRedwing recalled that meant the radial squeezing the jet sometimes displayed. Karl had said the jet narrowing looked like some sort of sausage mode, which took it through the Knothole and made it flare out once it was well beyond. But they weren't that close to the Knothole. That was the point\u2014the kink instability took a while to develop while the jet was arrowing in toward the Bowl.\n\nRedwing thought it strange that the pinch effect had been so strong. He asked Karl if the magnetic pressures on their magnetic nozzle could be so strong, but before Karl could answer he felt a prickly sensation play fretfully across his skin. Everyone looked around, sensing it also.\n\nAbruptly a yellow arc cut through the air above the deck. It crackled and snaked as it moved, but turned aside whenever it met a metal barrier. They all bailed out of their couches. Redwing lay flat on the deck as the snapping, curling discharge twisted in the air above him. The crackling thing snarled around itself. Sparks hissed into the air. Yellow coils flexed, spitting light. The discharge arched and twisted and abruptly split, shaped into an extended cup shape that spun.\n\n\"It's shaping the... the Bowl,\" Beth said.\n\nThe yellow arc made a bad cartoon, snapping and writhing, never holding true for long.\n\nRedwing felt his heart thump. \"Something is out there. Making trouble for us.\"\n\nBeth said, \"Something we can't see.\"\n\nRedwing recalled that in their discussions he had asked, What could I be missing? Well, here it was.\n\nBeth had once said that flying into the jet could give them an edge, all right\u2014but there were huge unknowns. Unknown unknowns were like a double-edged sword, she had said, with no handle. You didn't know which way the edge would cut.\nTHIRTY-FIVE\n\nAsenath made a show of her entrance. She gave the assembled crew and servants a traditional bronze-golden chest display, then unfurled side arrow lances, ending in brilliant purple fan crescents. Her cycle-shaped tail laces coiled out with a snap, their flourish attracting attention first to tail, then with a flurry, to breast. Even the sub-Folk knew this strategy, though without nuance or passion. Crowds of them in the big bay of the skyfish clustered and tittered as Asenath presented. Memor watched with glazed eyes, Bemor at her side and the primate crouched nearby.\n\nThe grand bang and rattle caught many eyes, so she followed with a sharp pop. Yellow patch flares then ignited their tips, flavoring the already fragrant air. Quills rattled at incessant pace, rolls and frissons, japes and jars. All this was a part of the eternal status-flurry that kept order across the great stretches of the Bowl.\n\n\"What's all this for?\" the primate said.\n\nThe impudence of this question, coming at the climax of Asenath's display, angered both Memor and, she could see, Bemor. The primate was about to become very useful, so Memor decided to discipline her in full view of all. As she turned, Bemor clasped her shoulder in a restraining grasp. \"Do not. It will disturb this creature more than you know.\"\n\n\"I have spent more time with her than\u2014\"\n\n\"Than I have, yes. But indulge me this once.\"\n\nMemor explained to the primate that such social rituals shored up the hierarchy needed to manage the entire Bowl society. Whenever the Folk visited a local venue of use, such as this skyfish, they reminded all of how the vast world worked, by showing ancient rituals. \"Making the past come into their present, and so reside for their futures.\"\n\n\"It's just a dance with feathers, incense, songs, and whatever drug is floating in this air,\" Tananareve Bailey said. \"I can sense it creeping in through my pores.\"\n\n\"I will be most surprised if it affects your chemistry. It is tuned for these Kahalla and their minions, plus adjacent evolved subspecies.\"\n\nTananareve coughed. \"Stinks, too.\"\n\nMemor rankled at this but said, \"The destiny of our species is shaped by the imperatives of survival, operating on six distinct time scales. To survive means to compete successfully, but the unit of survival is different at each of the six time ranges. On intervals of what you would term years, or orbital periods, the unit surviving is the individual. On a time scale of decades of orbitals, the unit is the family. On a scale of centuries, the unit is the tribe or nation\u2014such as this district of the Kahalla. On a time range of millennia, the unit is the culture. The Kahalla culture is widespread. So they may lend that gracious stability to vagrant districts. On a time scale of tens or more of millennia, the surviving unit is the species. Some cultures do survive that long, and we encourage that. On the range of eons, the unit is the whole web of life on our Bowl.\" Memor made a signifying fan-rattle to conclude and for punctuation gave a sweet aroma-belch from her neck.\n\nBemor added, \"That is the scale we now confront with you Late Invaders.\"\n\n\"Huh? We're just stopping by.\"\n\nBemor huffed in amusement. \"Not so. You are important at this juncture as we approach Glory.\"\n\n\"Who says?\"\n\n\"The Ice Minds,\" Memor injected, though she knew the primate did not know the term, much less the substance.\n\nAsenath finished and resumed command of this skyfish with quick, darting orders. Squads rushed off to prepare for battle, a rolling bass note summoned crew to stations, and an electric intensity shot through the air\u2014a zippy ion augmentation to stimulate. A wall flushed from its solemn gray to a stunning view of the region the skyfish commanded.\n\nNeedles of spiral rock forked up, moss-covered and home to many flapping species. The skyfish had recently fed there, from server species that brought arrays of food to be easily ingested as the skyfish moored on the peaks. These erections stood beside bays and lagoons, where waves reflecting the jet and star winked up at them. Here and there in the complex landscape, white snakes curved, highways like lines drawn on a lush green paper.\n\nTo the side, fluttering fast, was a silvery mote. Their target, just as the Kahalla had said.\n\n\"What's the battle?\" Tananareve asked, watching the many minions scurry around.\n\n\"We expect little fighting,\" Memor said. \"We are to capture the rest of you.\"\n\n\"Be careful,\" Tananareve said. \"They've been on the run here a long time. And they bite.\"\n\nMemor found this amusing and sent a subtle fan-display of this to Bemor. \"As if we had cause to fear them!\" she said in Folk.\n\n\"Yes, perhaps this primate has a sense of humor,\" Bemor said, distracted, his big eyes looking into the distance.\n\nSuddenly Memor felt a tremor from her Undermind. It was a cool trickle of apprehension, not of actual fear, yet its icy fingers crept into her thinking. She paused a moment to do her inward-turning, letting the Undermind gradually open. She found a swamp. Fresh, gaudy notions and worries laced through fetid dark pools of ancient fears, all beneath a sullen sky. Trepidations wrapped around a locus, like tendrils of gray fog settling on a hill. The darting slips of anxiety seemed to orbit that hill. What was in it? Under it? She did not recall ever seeing this rising bulge before. Yet she knew it was not new, but old. She knew the bodies of congested uneasiness might be thrust down for a while, into the recesses of the Undermind. But this was a large bolus of somber dark emotions, and it drove fresh fears into her conscious layers.\n\nYet she had no time for this now. Action drew near. \"Asenath, how might we assist?\"\n\n\"Keep your Late Invader close. We will need her to interpret nuance and the other Invaders' nonverbal signaling.\"\n\nBemor seemed uneasy. Memor gave him a flurry of feathers that bespoke concern, but he shook it off with a rustle. She saw from his distant gaze that he was tapped into his comm and studying information.\n\nHe breathed quicker, a low rumble of thought. Memor respected Bemor's ability to go beyond the Bowl's constant data flood, mediated through its incessantly collecting local Analyticals. Those artificial minds monitored Bowl data on local scales, then sent it upward through an ascending pyramid of minds both wholly artificial and natural\u2014though, of course, all minds had been bred and engineered for optimal performance, far long ago. Then the smoothed product of much mastication came to such as Bemor, to make sense nuanced of mind-numbingly complex situations. Digested data could help compensate for Folk overconfidence in their own intuitions, thus reducing the distortion of perception by desire. Natural minds were unable to deal with avalanches of data and mathematics, but were excellent at social cognition. Bemor could draw from his deep knowledge of history and the higher intellects. He was good at mirroring others' emotional states, such as detecting uncooperative behavior, and at assigning value to things through emotion. Was he dealing with new ideas from the Ice Minds now? Something in his posture told Memor that he was deeply concerned about some matter far distant from their pursuit of these Late Invaders.\n\nAbruptly Bemor broke off and spat at Asenath, \"We need those Late Invaders captured immediately. No delay! But handle them carefully. Loss of even one of their lives could endanger us all.\"\n\nAsenath knew enough to take this command without question. She turned and ordered a nearby Kahalla, \"Do not chance a glancing shot.\"\n\n\"But we planned\u2014,\" the Kahalla began.\n\n\"Ignore all that came before. A shot to compel them might do damage to the tadfish. Especially if you miss by even a fraction.\"\n\n\"Madam, we have already dispatched the sharpwings,\" the Kahalla said, going into a bowing posture of apology.\n\n\"I did not so order!\"\n\n\"It was explicit in your attack plan, timed to occur as we first sighted the tadfish.\"\n\nMemor could see that Asenath had no ready reply to this, so she turned away with a rebuking ruffle-display of red with scarlet fringes.\n\nThey all moved close to the observation wall. The tadfish drew nearer and now a school of angular birds came forking in toward the silvery shape. They were big in wing and head. Memor knew these sharpwings as pack birds who could harry and bring down far larger prey.\n\nBemor was alarmed enough to be distracted from his comm. \"Stop them. Now.\"\n\nAsenath obeyed. Memor knew that here, nearer to the Knothole, craft such as tadfish had a natural utility. Great circulating cells of warm air cycled across the zones and life used these free rides. Skyfish were a transport business in the long voyages and tadfish had been bred from them, long ago, to traverse the shorter routes. In its constant restless way, evolution had spawned species of sharpwings to prey on tadfish. Most often they swarmed the prey, as Memor now watched them do.\n\nAsenath shouted, \"I said to turn them back!\" to the Kahalla who backed away from her, head bent deep in contrition.\n\n\"They do not respond,\" the Kahalla whispered. \"They are hirelings, and hard to deflect once engaged in their ancient battle rites.\"\n\n\"So they make for the meaty passengers,\" Memor said dryly.\n\n\"Their spirits are up,\" the Kahalla said. \"Difficult to countermand.\"\n\nNow the sharpwings circled the tadfish. The great fish fired its hydrogen jets at them. Great plumes of ignited gas forked out and burned sharpwings black in an instant. Bodies tumbled away but more sharpwings came arrowing in. Their long jaws with razor teeth sliced at the working fins to disable navigation. The orange tongues licked more sharpwings.\n\nThey were drawing nearer, and Asenath ordered external ears to pick up the battle sounds. Memor could make out the anguish cries of those being burned. Sharpwing song-calls also laced the air, vibrant and shrill. Beneath that came the deep bass roll of the tadfish's agony. It echoed across the diminishing distance.\n\nNow sharpwings dove along the tadfish flanks, going for the gut. Their spiked wings ripped along and into the scaly flesh. It was, Memor reflected, as though the attackers were writing on the lustrous flesh their own messages, in long lines that soon brimmed red. These species had evolved to a stable predator\u2013prey balancing, now governed by their betters\u2014but only when their passions could be blunted.\n\n\"Bring your lancing shots to bear,\" Asenath ordered.\n\n\"Please note, we cannot be so accurate at this range,\" the Kahalla said. \"I fear\u2014\"\n\n\"Do it.\" Asenath was stern. \"Otherwise they will bring down the tadfish and devour its passengers.\"\n\nThe Kahalla did not attempt to argue. It turned and gave orders. Over the amplified booming, shrieks, and cries, Memor could scarcely hear the sharp psssstt! of the pellet guns. These hit the sharpwings with shattering blows. Next came the rattling laser batteries, picking off the great birds with quick stabs of green brilliance. All these weapons had to hit the sharpwings as they banked away from the tadfish, to avoid wounding it, so those sharpwings already close in on the attack escaped for a while. Orange jets from the tadfish belly licked at flights of the sharpwings. Squawks and screeches rose in an anguished crescendo. The thuds of pellets firing slowed as targets became scarce. A rain of blackened and shattered bodies tumbled, turning slowly in the long descent toward the green forests and glinting lakes below.\n\nThe remaining few sharpwings broke off the attack and flapped away, sending mournful long songs forth. \"Very good,\" Asenath said.\n\n\"Let us escort the tadfish down, then,\" Memor said. \"We can land and take possession.\"\n\nAsenath conferred with the Kahalla, then turned to address Bemor, ignoring Memor. \"We can swallow such a small tadfish. No need to land. We can continue to higher altitudes and catch the fast winds toward the upper Mirror Zone.\"\n\nBemor sent approval-displays, but his eyes did not move from his comm plate. \"Good. Do so. We need the other Late Invaders.\"\n\nMemor felt shunted aside. She had been pursuing these vagrant primates for a great while, and now Bemor\u2014and even worse, Asenath\u2014would get credit for their apprehension. But at least it was done. \"Why are they so useful? I am happy to have them in hand, of course, but\u2014\"\n\nBemor gave a low, bass growl. \"The Ice Minds command it. Events proceed elsewhere. A crisis threatens. We must get the primates.\"\n\n\"We have this one here\u2014\" A gesture at Tananareve.\n\n\"We may need more. The Ice Minds want to use them to converse in an immersion mode.\"\n\nMemor stirred with misgivings. Her Undermind was fevered and demanded to be heard, but there was no time now. \"Immersion? That can be destructive.\"\n\nTananareve seemed to be following this, but wisely said nothing.\n\n\"That is why we need several pathways. The connection may be too much for them, and we will need replacements.\"\n\nMemor said softly, feeling a tremor from her Undermind, \"What crisis?\"\n\n\"It goes badly in the jet.\"\nPART XII\n\nTHE WORD OF CAMBRONNE\n\nIt was at Waterloo that General Cambronne, when called on to surrender, was supposed to have said, \"The Old Guard dies but never surrenders!\" What Cambronne actually said was, \"Merde!\" which the French, when they do not wish to pronounce it, still refer to as, \"the word of Cambronne.\" It corresponds to our four-letter word for manure. All the difference between the noble and the earthy accounts of war is contained in the variance between these two quotations.\n\n\u2014ERNEST HEMINGWAY, MEN AT WAR\nTHIRTY-SIX\n\nThe first sight of the Folk commanding the big skyfish was daunting. Cliff had seen these Folk aliens when his team came through the lock, in what seemed a very long time ago. Later he had heard fragments about the Folk from the scattered SunSeeker transmissions.\n\nBut now these before him seemed different\u2014larger, with big heads on a leathery stalk neck. Their feathers made the body shape hard to make out. The Folk back at the air lock had feathers, but not nearly so large, colorful, and vibrant. As Cliff's team and Quert's Sil entered, the three big Folk rattled their displays, forking out neck arrays that flashed quick variations in magenta, rose, and ivory. Their lower bodies flourished downy wreaths of brown and contrasting violet.\n\n\"They're... giant peacocks,\" Irma whispered.\n\nCliff nodded. Back Earthside, peacocks used their outrageously large feathers to woo females. But these rustling, constantly shifting feather-shows had far more signaling capacity. Beneath the layers, he could glimpse ropy pelvic muscles. Loose-jointed shoulders gave intricate control to the feathers. \"More like, those flaunt unspoken messages, I'd guess.\"\n\nQuert gestured and said, \"Quill feather gives mood. Tail fan on neck cups sound to ears. Fan-signals are many. Rattle and flap for more signal. Color choice gives messages, too.\"\n\nAybe said, \"Structural coloration, I'd say. Microfibers, fine enough to interfere with the incoming light, reflect back the color the creature wants.\"\n\nCliff watched the beautiful iridescent blue green or green-colored plumage shimmer and change with viewing angle. \"Reflections from fibers, could be.\"\n\nThey all stood bunched together, humans and Sil, as the Folk came slowly into the big room, passing nearby with a gliding walk before settling on a place. The big things loomed over them and rattled out a long, ordered set of clattering sounds. \"What's that sound say?\" Terry whispered.\n\n\"Greet to visitor. But visitors inferior and should say so.\"\n\n\"Say so?\" Irma whispered. \"How?\"\n\nQuert gave the other Sil quick sliding words, a question. They all responded with a few other short, soft words. Quert's face took on a wrinkled, wry cast. \"Sil not say, you not either.\"\n\n\"Good,\" Aybe said, and the others nodded. No tribute, no submission.\n\nCliff regarded the Folk's unmistakable piercing eyes, big though now slitted and slanted beneath heavy, crusted eyelids. Their pupils were big and black, set in bright yellow irises. There was something going on behind those eyes. Cliff had an impression of a brooding intelligence measuring the small band of humans and Sil. The tall, feathered Folk held the gaze of humans and Sil as they settled back on their huge legs and tails and gestured, murmuring to each other while still peering down at the humans. Cliff felt a prickly, primitive sensation, an awareness of a special danger. His nostrils flared and he automatically spread his stance, fists on his hips, facing the three aliens fore square.\n\nThe three Folk settled into the high room bounded by pink, fleshy walls. Attendants flanked the three, and others scurried off to unknown tasks. There were small forms with six legs and plumed heads, carrying burdens and arranging the flesh-pink walls with quick energy. Constant motion surrounded the Folk, who went slowly, almost gliding. It was like watching an eerie parade with three big, frightening floats.\n\n\"Irma! Cliff!\" Suddenly Tananareve Bailey appeared from behind one of the Folk. She ran toward them.\n\nMeeting any friend in this bizarre place was wonderful. They all embraced Tananareve as she rushed into their arms. To Cliff, she was as lean and steely as a piece of gym equipment; you saw the skull beneath the skin. Irma said, laughing, \"At last! Some woman company.\" And they all laughed long and hard. Giddy jokes, ample smiles.\n\nA long loud sentence from the largest of the Folk broke them out of their happy chatter. They looked up into big yellow eyes.\n\n\"They said they needed you,\" Tananareve translated, \"but I never know if they're telling me true.\"\n\n\"This skyfish just swallowed our tadfish,\" Irma said. \"I thought we were goners.\"\n\n\"Better than a fight,\" Terry said. \"But... we're captured.\"\n\nThe enormity of this last hurried and harried hour came to Cliff. He had kept his team free for so long now, barely escaping in one scrape after another... only to fail so quickly, swallowed, a slap in the face with cold water. He opened his mouth but could think of nothing to say. The others were still happy just to have Tananareve, but the implications were stunning.\n\n\"Maybe they want to negotiate,\" Cliff said, not really believing it.\n\nTananareve said, \"They got orders from someone to grab you, pronto. They've been tracking you ever since you saw something called the Ice Minds. It took this long to catch up with you. They're big and can't crawl through the Bowl understructure. They kept complaining about having to take the other transports that can handle their size.\"\n\n\"What's up?\" Aybe asked.\n\n\"They're under pressure. I don't know why.\" Tananareve stood near the Folk and introduced Asenath, Memor, and Bemor. It took a while to explain that Memor and Bemor had nearly the same genetics, were something like fraternal twins of different sexes, but that Bemor was somehow enhanced and held a higher-status position. \"He can speak to the Ice Minds. Whereas Asenath\"\u2014a nod to the tall, densely feathered creature, sharp-eyed and rustling with impatience\u2014\"is a Wisdom Chief.\" A shrug. \"As near as I can tell, that's kind of like an operations officer.\"\n\nThere followed some back and forth translating as Memor insisted on a full introduction using her complete title, Attendant Astute Astronomer. Bemor then managed to get his \"Contriver and Intimate Emissary to the Ice Minds\" into the discussion. Tananareve whispered, \"Slip those titles into your remarks now and then; they like that.\"\n\nCliff watched the huge aliens as the light of the jet and star, at these higher altitudes, poured down on the fleshy floor like glistening yellow-white oil. Asenath thundered, \"We have you indeed, at last. The first issue is our need of you, to prepare a message for those whom you term the 'Glorians'\u2014to continue the artifice.\"\n\nThe others looked to Cliff. He faced the big skull Asenath lowered, as if to listen more closely. Cliff suspected this was just intimidation\u2014and decided to ignore it, the only strategy that might work. \"Artifice?\"\n\n\"Glorians believe you primates are the rulers and pilots of our Bowl,\" Asenath thundered. \"They confuse our mutual trajectories as meaning that the Bowl comes from your world.\"\n\n\"Weird. So?\" It seemed to Cliff better to play dumb for a while. There was too much going on to make sense of this. He needed time to talk to Tananareve and get his bearings. These Folk had talked to Redwing, using Tananareve, but what were the nuances of that?\n\nAsenath gave a purple and rose display and her head descended still closer. Her Anglish was clipped and brusque, perhaps because she had only recently imbibed the language, or because she meant it that way. \"Of course we converge on Glory. Over time scales of many thousands of orbitals, similar goals emerge. The only puzzle to us is why you, with your simple though ingenious and craftily made ship, desire to attain the status the Glorian technologies imply.\"\n\nCliff shrugged, glanced at Tananareve\u2014who shrugged. \"Imply?\"\n\n\"The gravitational signals. Surely this lures you.\"\n\n\"Not really. We're bound for Glory because it's a biosphere a lot like our own. The right oxygen levels, water vapor, a hydrogen cycle with oceans. Plus no signs of technology. No signatures of odd elements in its air. No electromagnetic emissions. No signals at all. Kind of like our world thousands of years\u2014I guess you call them orbitals\u2014ago.\" Cliff spread his hands, hoping this was a signal of admitting the obvious.\n\nAsenath gave a rustling flurry of feather displays, crimson and violet. \"Your ship has received the Glorian signals, yet you do not know?\"\n\n\"Know what?\"\n\n\"The Glorians, as you term them, are of the August.\"\n\n\"Meaning...?\"\n\n\"They do not deign, over many megaorbitals, to answer our electromagnetic signals. No matter of what frequencies. The Aloof and August.\"\n\n\"The same might be said of any rock.\"\n\n\"The advanced societies of this galaxy deliver their August messages only by means that young societies, such as yours, cannot detect.\" Asenath gave a rattling side-display in eggshell blue. \"Most important, signals of great information density, to which young worlds cannot reply.\"\n\n\"We picked up the gravity waves, around the time our ship left Earthside,\" Cliff said. \"There didn't seem to be a signal, just noise.\"\n\n\"So young societies would think,\" Bemor said from beside Asenath. \"We do\u2014\"\n\nSuddenly something made the three Folk pause, Bemor with his mouth partly open. Silence. Their yellow eyes were distant.\n\nQuert appeared at Cliff's side and whispered, \"They hear other voices.\"\n\n\"They've done this before, getting signals somehow,\" Tananareve said. \"Let's use the time. What's our strategy here?\"\n\n\"These Folk have something in mind, using us somehow, I'll bet,\" Aybe said. \"Wish I knew what they're hearing right now.\"\n\nQuert said, \"They now listen to what we Sil brought forth. Told to. We showed old truth.\"\n\n\"How?\" Tananareve asked.\n\n\"Folk control electromagnetic pathways in Bowl. So Sil make signs buildings.\" The swift slippery slide of Quert's words belied the content.\n\nCliff said, \"Those deforming houses we saw you building?\" He recalled how the Sil had deftly rebuilt their ruined city. He had seen a growing arch inching out into a parabolic curve, the scaffolding of tan walls rising from what seemed to be a sticky, plastic dirt. Wrinkled bulks had surged up as oblong windows popped into shape from a crude substrate, all driven by electrical panels. The Sil were working their entire city into fresh structures like spun glass, growing them into artful loops and bridges and elegant spires.\n\n\"You make signals with your cities?\" Irma asked. \"How?\"\n\n\"City, all can see all across Bowl. Others know to look to us. To get message.\" Quert had now a calm the feline alien wore like a cloak.\n\n\"What was the message?\"\n\nQuert looked at them all slowly, as if unburdening at last. He wagged his head and said, \"Bowl pass by your sun. Go too close. Shower down mass. Damage world biosphere.\"\n\nIrma said, \"What? When?\"\n\n\"Long ago. Folk call it Great Shame.\"\n\nTerry said, \"You got this how?\"\n\nQuert looked puzzled, as it always did by the human habit of conveying a question by a rising note at the end of a sentence. \"Your ship told you. You told us.\"\n\n\"What?\" Terry turned to Cliff. \"You got this from Redwing?\"\n\n\"Yup. I tried it out on Quert. I didn't believe it, really.\"\n\n\"You didn't tell us!\" Aybe said.\n\n\"Saw no need to.\" Cliff's face stiffened. \"I still don't know if it's true.\"\n\n\"We got more from... others,\" Quert said. \"Come.\"\n\nQuert led them to a small room that puckered into the ribbed, pink slabs that formed the great hall. Cliff looked back. The Folk were still rigid, eyes focused on infinity, taking in some transmission from... where? Their bodies were clenched, feet grasping at the floor. He turned and went into a narrow chamber where a bright screen fluoresced into pale blue light. \"We have map sent. History.\"\n\nIt was a 3-D starscape. Across it scratched a ruby line. \"Bowl went there. Time go backward.\"\n\nA dot started at the Bowl, shown as a small cup embracing a red star. The ruby line stretched as it moved backwards, away, into the reaches of stars. Cliff and the others muttered to each other, watching the constellations slip by as time ran in reverse, accelerating. The line looped near many dots that were stars\u2014yellow, red, some bright blue\u2014and went on, faster, until the perspective became confusing. It wound along the Orion arm of the slowly churning galaxy. They could see the stars moving now in their gyres. The ruby line ventured out toward the Perseus arm, which was festering with light, then looped near some to pick off glimmering sites apparently of interest. The Bowl's method, Cliff could see, was to dive into the distant, shallow slope of the grav well of a star, slowing somehow, and skate by. A close-up view near a yellow dot showed bright sparks departing the Bowl, to descend deeper into the gravity potential well of the destination star. These soon returned, apparently bearing whatever they found on the circling worlds down in the grav well. This happened several times as they watched.\n\nThen the Bowl cruised through what Cliff recognized as the Local Fluff inside the Local Bubble, terms he recalled from some distant lecture for the spaces around Sol. Then the Bowl surged a bit, building speed, bound for the next target brimming ahead.\n\nCliff and the Sil had to interpret in this way the backward-running line, for what they saw was the reverse. Then the Bowl-star pair descended on a yellow star.\n\nThey watched the entire encounter and talked about it, piecing the story together in backward fashion. After the encounter, the Bowl came soaring out of a system racked and ruined. Comets flared in the yellow star glow, and it was clear why. The Bowl had swept through the prickly small motes of light that swarmed far from the star. It had left a roiling path through those tiny lights, giving them small nudges, and so some had plunged inward. Only one was needed.\n\nOne. It slid down the slow slope of gravity and arced on its long hyperbola toward a pale blue dot. And hit.\n\n\"They brushed along in our Oort cloud,\" Aybe said. \"That's it. They, they tipped that rock into\u2014\"\n\n\"An accident. Killed the dinosaurs,\" Terry said, \"who were descendants of their own kind. Can't check the time axis on this thing\u2014what the hell would the units be anyway?\u2014but there's a reason it shows this way. Somebody's making a point. The Bird Folk were clumsy, careless.\"\n\n\"Yeah...\" Irma stared at the screen. \"Who?\"\n\nCliff said nothing, just tried to take it all in. He felt Quert's presence strongly as a kind of intense energy, as though this were the crucial moment in some plan the alien had. Yet there was no overt sign of it he could detect.\n\nHe said, \"Terry, I think the Glorians' point is, 'See, we know all about you.'\"\n\nQuert seemed unperturbed, his face calm. The other Sil had not come into this room, but they clustered at the entrance, watching silently. \"Folk go to other stars after yours. But yours special for other reason.\"\n\n\"Why's that?\" Irma asked.\n\n\"They come from your sun.\"\n\n\"Who?\" Irma's mouth gave a skeptical twist. \"The Folk?\"\n\n\"See.\" Quert moved his hand near the screen and the ruby line seemed to accelerate, slipping smoothly from star to star in the Orion Arm. The speed now barely showed a slowing as the Bowl dived near a star, sent expeditions down, then moved on. Cliff lost count of how many the Bowl visited. Then the trajectory took a long swooping arc, still sampling stars and worlds. The curve turned back along the sprinkle of slowly moving stars.\n\n\"These are the even earlier eras for the Bowl?\" Irma said. \"Must be a really long time ago.\"\n\n\"Notice how the Bowl is going now from one star to the next, pausing near each one,\" Aybe said. \"That fits\u2014they were exploring for the first time. Sizing up what solar systems around other stars are like.\"\n\n\"Then we're headed back to\u2014look, there's the Local Bubble,\" Terry said. In an overlay, a thin ivory blob approached probably an image of the low-density shell that surrounded Sol. \"But... Sol's not there.\"\n\n\"Stars move,\" Irma said. \"See, the Bowl is moving on past that, not stopping.\"\n\nAybe said, \"It's slowing down a lot, seems to be approaching this yellow star\u2014hey, is that us?\"\n\nThey watched, stunned, as the Bowl and its reddish star slowed more and more, edging up to the yellow star.\n\n\"Can't be, see?\" Terry pointed. \"The Bowl's going into orbit, making\u2014\"\n\nThe image froze.\n\nIrma whispered, \"The Bowl came from... a binary.\"\n\n\"They built it around a binary star,\" Cliff said, \"and one of those stars was Sol.\"\n\n\"Didn't we hear a little from Redwing about Beth's team, pretty far back?\" Terry said. \"They went to some kind of museum and saw a show about how the Bowl got built.\"\n\nAybe said, \"After all, they had to start with a smaller star than Sol. They grabbed big masses from the swarm around that star, and\u2014who knows?\u2014maybe some of Sol's Oort cloud.\"\n\nIrma snorted. \"Are you saying they came from Earth?\"\n\nAybe shrugged. \"Looks like it. I mean, Mars had an early warm era, so maybe\u2014\"\n\n\"That was in the first billion years or so after Sol formed,\" Terry said. \"The end of this Bowl voyage show we just saw, it can't be that far back. Makes no sense! You'd have to get an intelligent species up to full industrial ability in just a billion years.\"\n\n\"Okay, then whoever built the Bowl had to come from Earth,\" Irma said, hands on hips. \"I'm discounting smart creatures from the Jovian moons or Venus or someplace.\"\n\n\"Fair enough,\" Aybe said. \"So, Earth. These Folk out there, you're saying they had to come from some time\u2014\"\n\n\"We're all thinking the same thing? They were dinosaurs,\" Cliff said. \"The feathers make it hard to see, though. Asenath looks more like a monster Easter chick than a Tyrannosaurus rex.\"\n\n\"Damn!\" Aybe said. \"Remember when we were on the run, when we hid under a bridge? We saw\u2014\"\n\n\"Right,\" Terry burst in. \"Big plant-eater reptile. We ran away, pretty damn scared.\"\n\n\"So...\" Cliff's training as a biologist was taking a beating. \"That thing comes from maybe the Jurassic, one hundred and forty-five million years ago. Maybe the Bowl builders took along the current flora and fauna?\"\n\n\"Because they came from then?\" Irma scoffed. \"We would've seen their ruins. A whole industrial civilization, and we missed it? This whole idea is impossible!\"\n\n\"Maybe it was very short-lived, lasted say about ten thousand years,\" Terry said. \"Just a tiny sliver of the geological record.\"\n\nAybe said, \"Consider what alien explorers might discover if they arrived on Earth one hundred million years from now. Their scientists would find evidence of vast tectonic movements, ice ages, and the movement of oceans, a geological history sprinkled with life. Maybe an occasional catastrophic collapse.\"\n\n\"Exactly,\" Terry talked right over Aybe. \"They might also find, in a single layer of rock, signs of cities and the creatures who built them. But that layer had been crushed, subducted, oxidized. Hell, tens of thousands of years\u2014that'll be smashed flat, only a centimeter thick when it comes out from the subduction. In dozens of million years, there's nothing.\"\n\nCliff was warming to the idea. \"Easy to miss, especially if you aren't looking for it.\"\n\n\"Explains why the Folk are interested in us,\" Irma said. \"We're relatives!\"\n\nCliff saw Quert give the eye-moves of disagreement. \"Not so?\"\n\n\"Folk want to know of ship you ride. Plants you carry. Bodies you have, songs, lore.\"\n\n\"Then they don't know where we're from?\" Aybe demanded.\n\n\"They know. Do not care.\" Quert looked uneasy, a change from the pensive calm of only minutes before. Cliff wondered if the alien and other Sil knew all the implications of this backward history of the Bowl. Had they recognized the home star as Sol?\n\nA loud, rolling boom came from the large area outside. At first Cliff thought it was an explosion, but then it took on other notes and held, lingering with a mournful long strumming cadence. Like someone crying, he thought. Or some thing.\n\n\"It's the Folk,\" Aybe said. Quert gave an agreeing eye-click. \"They... something's wrong.\"\nTHIRTY-SEVEN\n\nRedwing stepped into the garden and inhaled through his nose. Good moist green smells. Take a moment, just a breather. The animals\u2014\n\nThe animals had been tied down, netted, and they were not happy. He hadn't ordered that. He should have, of course, the way SunSeeker was lurching about. Had the finger snakes done that?\n\nThe finger snakes. Redwing tended to forget that they were part of what he was trying to save. Were they in their tunnel? No, he could see all three of them wrapped around three thick-bole apple trees.\n\nA smartbot prowled the rows of plants, testing soil and injecting fluids where needed. Just growing plants hydroponically wasn't enough. Humans needed micronutrients, vitamins, minerals\u2014but so did the plants and animals they ate. So all organisms in the looping food chains had to provide the right micronutrients needed by others, without them getting locked up in insoluble forms or running out. Selenium had gone missing a century back, he had learned from the log. Only with sophisticated biochem types woken up for the task did they get the food chain running right again.\n\nRedwing savored the leafy comfort lacing the air and staggered as SunSeeker surged. Redwing caught himself on a stanchion. The snakes didn't seem to notice. Phoshtha and Shtirk were watching a screen, a view of lands showing murkily through the jet, while they worked on small things with their darting, intricate hands. Thisther was watching the captain.\n\nRedwing asked, \"Thisther, did you secure the pigs and sheep and such?\"\n\n\"Yes. Was well done?\" A thin, reedy command of Anglish.\n\n\"Yes, thank you. Are you comfortable?\"\n\n\"Better. What a ride!\"\n\nRedwing left the garden feeling better. Now what? There was nothing like cramped quarters to concentrate the mind. So he went to his cabin as the deck creaked and rolled with the jet storms that whipped by it. He watched the Bowl view crawl past on his wall and did a few standing exercises, adjusted against the tilt local grav had, due to the helix SunSeeker was following. He had learned to disappear within himself, walling out a ship's routine humming and stale smells and dead air, to create a still, silent space where he could live, rest, think. In the continual noise of the ship he had learned to hear well, picking telltale murmurs out of SunSeeker's constant vibrations.\n\nA call buzzed in his ear. \"Cap'n, got something to see on the bridge. The jet's really snaking now. Flares like sausages running down it, too.\"\n\nHe started back, still listening to the pops and creaks of his ship. With his crew he also knew how to listen carefully, or to deliberately not hear. An essential skill, taking only a lifetime of daily practice to master.\n\nBeth's voice had been strained, and she had just replaced Ayaan Ali in the lead pilot's chair, with Clare Conway in the second chair. They all looked pale, their eyes never leaving the wall screens and operations boards. SunSeeker's long helix within the jet had worn them all down, and now the pace was picking up. He hadn't been resting well, and neither had the others. Coffee could only do so much.\n\nAs he entered the bridge, he noted that everyone had coffee ready at the elbow. Should he tell them to switch to decaf? No, too much meddling.\n\nKarl said as Redwing came onto the bridge, \"It's whipping around in the Knothole, just as the simulation said.\"\n\nOn the biggest screen, the jet was now lit up in yellow. They were looking straight down it and could see the flexed jet now bulging very close to the Knothole edge. \"See, the Knothole has big mag fields to stop it.\"\n\n\"Are we driving the jet just enough to give them a scare?\" Redwing leaned over the panel and switched to a flank camera view. \"And what's that secondary bump?\"\n\nKarl studied it. Redwing noted that Beth was working a different telescoping camera, focused far away from the jet, on the mirror zone. Karl said, \"That's a nonlinear effect\u2014a backflow.\"\n\n\"You mean there's a shock wave working back toward us?\" Redwing watched the small sideways oscillation evolve, working around the rim of the jet. \"It's from the big kink?\"\n\nSunSeeker could run for weeks in the jet without climbing into view of the gamma ray lasers on the Bowl rim. They were already fairly deep in the Bowl and getting a closer view of the zones near the Knothole, where centrifugal gravity was less. The mirror zone, a vast annulus, was behind their forward-looking views, and ahead loomed the forested regions just in from the Knothole. Beth had been kept somewhere in all that.\n\n\"Looks like the kink went nonlinear and launched this shock back at us,\" Karl said. \"I don't understand\u2014\"\n\n\"Here's a better view,\" Beth said. \"I asked the Bridge Artilect to find any part of the mirror zone that could give us an angled reflection, and it found this.\"\n\nShe smiled, and Redwing saw she was enjoying this. She always seized fresh opportunity with relish, one of her best qualities. The wobbly, somewhat blurred image gave them a view from far away to the side. He watched the kink bulge warping as it met the higher mag fields at the Knothole rim, and a countershock race away up the jet. That played among the boundary mag fields of the jet, pushing out farther to the side\u2014\n\n\"It's going to hit the atmospheric membrane in the closest-in zone,\" Beth said. \"Moving at high speed\u2014over a hundred klicks a second in sideways motion.\"\n\n\"This wasn't in the simulation, as I recall.\" Redwing let his statement hang there, without a tone of sarcasm. Flat facts spoke for themselves.\n\nKarl nodded, said nothing. Beth watched the fast-moving side shock as it plowed toward the atmosphere's envelope, a layer sketched in by a graphic; it wasn't truly visible in these narrow line widths. \"Is there enough mass in that to do damage?\"\n\n\"Plenty,\" Karl said, \"and the magnetic energy density, too, can hammer the envelope.\" He looked worried and said no more.\n\n\"What about the structure itself?\" Redwing said. He knew this huge thing had to have incredible strength to hold it together. SunSeeker had a support structure made of nuclear tensile strength materials, able to take the stresses of the ramjet scoop at the ship's axial core. Maybe the Bowl material was similar.\n\nKarl said in a distant tone, almost automatically, \"I scanned the Bowl wraparound struts, the foundational matter, on the long-range telescopes. Had the Artilects do a spectral study. It was only a few tens of meters thick, mostly carbon composite looks like, at least on the outside. That's pretty heavily encrusted with evident add-on machinery and cowlings. Calculated the stress.\"\n\n\"Which means...?\" Redwing persisted.\n\n\"The Bowl stress-support material has to be better than SunSeeker's. Maybe lots better.\"\n\n\"Should we alter our planned trajectory?\" Beth asked, eyes moving among the screens.\n\n\"Not yet.\" He was thinking fast but getting nothing. So many factors at play... \"That display we got before, the lightning here on the bridge, it must be some kind of message.\"\n\n\"I noticed something here before,\" Karl said. \"Look.\" He thumped his command pad and brought up a recorded scene on a side screen. \"See that?\"\n\nThe vector locator was focused on the zone nearest the Knothole. They could see the massive mag field coils at the rim, then the boundary of the atmospheric envelope, shiny in orange, reflected jet light. There were verdant forests sprawling away from the bulky Knothole structures.\n\n\"That's the same sort of area we were in,\" Beth said. \"Low gravs, huge tall trees, big spider things. And I saw some of that orange light shimmering up high, from far off, bounced off the upper boundary layer, I guess. Jet light.\"\n\nPartway into the large band of forest was a burnt brown and black slash among the lush greens, now mostly faded. Something had left a fresher black burn on the metal and ceramic portion near the Knothole, where the jet passed through.\n\nKarl said slowly, \"So instability was a major problem here. It's damaged the Bowl before.\"\n\n\"But shouldn't forest have covered over damage pretty quickly?\" Beth asked.\n\n\"Maybe it was damage to the understructure,\" Karl said. \"It broke systems that deliver water and nutrients. Not repaired yet.\"\n\n\"That means they're neglecting upkeep,\" Redwing said. \"The usual first sign of a system sliding downhill.\"\n\n\"So why don't they have defenses against the occasional jet malf?\" Beth asked.\n\nA long silence. They recalled the crackling image of the Bowl dancing in air above the bridge, sent by some mysterious agency. Karl had explained it in terms of some inductive electromagnetic fields, playing along the outside of the ceramic walls nearby. Redwing was skeptical of that mechanism but certain that the event had been a crude attempt at getting their attention. Then nothing more happened. \"A trial run, maybe,\" Karl had said. Redwing decided to keep to their planned helical trajectory.\n\nClare Conway said, rising from the copilot chair, \"Cap'n, I see three small ships coming up behind us. They popped into view of long-range microwave radar minutes ago.\"\n\nRedwing flicked the radar display on the biggest screen. \"Where'd they come from?\"\n\n\"From the Knothole rim, looks like,\" Clare said.\n\nKarl said, \"Maybe this answers Beth's question. They're sending out something to attack us.\"\n\n\"What's their ETA on current trajectory?\" Redwing asked, keeping his voice calm.\n\n\"Two hours, approx,\" Clare said.\n\n\"Get me an image.\" Redwing considered what they could do. SunSeeker had no substantial defenses against projectile or high-intensity laser weapons. He had learned a simple rule back in the brief, enormously destructive Asteroid War: that any mass hitting at three kilometers per second delivers kinetic energy equal to its mass in TNT. And SunSeeker was moving well above 100 km\/sec now. Add to that any incoming kinetic energy of an attacker. Square it. Any interesting space drive was a weapon of mass destruction, even to itself.\n\nThat was why the ship had auto-laser batteries run by the Artilects, designed for interstellar travel. They could hammer a rock the size of your fist or smaller into ionized atoms in a microsecond. But above that mass level, not much. They might deflect it a bit, which could be useful. That's all. Throw a living room couch at SunSeeker at these speeds and they would suffer a hull breach.\n\n\"They're small, can maneuver faster than we can,\" Clare said. \"Accelerating at three gravs, too.\"\n\n\"So maybe robotic,\" Redwing said. This was not looking good. \"How do they navigate in the jet? Can we tell?\"\n\n\"Looks like magscoops, same as us. Smaller, of course.\"\n\nClare brought up the same telescope Beth had used and sought out the small moving dots. \"Less than a hundred meters across,\" she said. \"Cylindrical, with an ionized propulsion signature.\"\n\nRedwing said, \"Maybe they didn't take us seriously before. Slow reflexes.\"\n\n\"No,\" Karl said flatly. \"We're missing something here.\"\n\nThe ship strummed with long rolling waves and sharp pops and snaps. No one spoke, and Redwing listened to his ship while all around him his crew worked to find out more about the roiling jet that streamed by, into the magscoop and their fusion chambers. The shipboard Artilects were working as well, but seldom spoke or called attention to themselves. They were built and trained for their talents to sustain, not for imagination and quick responses to the wholly new.\n\nInto the long uncomfortable silence Beth said quietly, watching the screens, \"That shock wave pushing out the jet in the Knothole\u2014it's hit the membrane. At high velocity.\"\n\nThey all turned and saw it on max amplification. Beth had used the overlay yellow and orange to signify plasma and lag fields, and strands of these showed the jet striking the boundary of the Bowl biosphere. Filmy gases escaped into space, pearly strands they saw in the visible. Redwing knew what this meant. The plasma's high-energy particles, encased in the sheath of magnetic fields, would deliver prickly energies. This would fry away the long-chain organic molecules that made the gossamer boundaries. Those separated the Bowl's many compartments, holding the great vaults of air above the living zones. So it would all go to smash and scatteration in a blizzard of unleashed furies.\n\nHe tried to imagine what that meant to those living there. Then he made himself stop.\n\nA booming roll came through the deck, all the way from hundreds of meters down the long stack.\n\n\"Plasma densities nearby are rising. Our exhaust is getting blocked again,\" Beth said.\n\n\"This is how it started before,\" Karl said. \"To break down air, the voltage is\u2014\"\n\n\"Megavolts,\" Clare snapped. \"Got it. If that happens, stay flat. Stick your head up, it'll draw current, fry you.\"\n\n\"You think they\u2014it\u2014is trying to kill us?\" Beth said. \"This could be communication.\"\n\n\"Strange way to do it,\" Redwing said.\n\n\"Retaliation for thrashing the jet, I'd think,\" Fred said. He had come onto the board so quietly no one noticed him.\n\n\"I'm getting rising inductive effects close to our skin,\" Beth said. \"Must be Alfv\u00e9n waves rippling in on the scoop fields. Higher electric fields\u2014\"\n\nRedwing felt his hair stand on end. He hit the deck.\n\nSparks snapped. Everyone flopped onto the deck and lay flat. A bright yellow-white line scratched across the air. More lines sputtered. They arched and twisted. Some split, and yellow green strands shaped a tight shape\u2014\n\n\"Human form!\" Fred said from the deck. \"They're making our image. They know what we are.\"\n\nThe shape wobbled and throbbed in the fevered air. Carved in shifting, crackling yellow lines, it was like a bad cartoon. Stretched legs, arms flapping, wobbly head, hands first spread then balled into fists, the whole body flailing. Then it was gone in a sizzle and a flicker.\n\nBeth said, \"Can they see us?\"\n\n\"Who's 'they' anyway?\" Clare said. Her face was flushed, lips compressed. \"They're trying to jam our fusion burn, get us to stop, I suppose. So they're sending us an echo, an image of us to\u2014make some kind of communication?\"\n\nThe shape popped up again. Outlined in crackling yellow and orange, the figure wriggled and sputtered.\n\n\"Let me try...\" Clare raised a hand slightly into the singed air. A long moment. Then slowly, twisting and shuddering, losing definition in the legs, the figure moved, too. It raised its left hand, mirror image to Clare's right. Air snapped around the dancing yellow image. The hand flexed, worked, wriggled itself into... fingers. A thumb grew, extended, turned red, and contracted. Now the crackling image filled itself in, a skin spreading yellow-bright and warped and seething. The body grew a head, and it struggled to make a mouth and eyes of pale ivory. The electrical fog flickered, as if barely able to sustain the sizzling voltage.\n\nClare slowly flexed her fingers. The fingers twitched, too, suffused in a waxy, saffron glow. The body hovered in the air unsteadily, holding pattern, all the defining bright yellow lines focused on the shimmering, burnt-yellow hand.\n\n\"Let's try to signal\u2014,\" Redwing began.\n\nThe arc snapped off with a pop. There was nothing in the air but a harsh, nose-stinging stench.\n\nClare sobbed softly. Fred jumped up and turned in all directions, but could see nothing to do. The only sound was the rumbling fusion engines.\n\n\"Let's get back to stations,\" Redwing said.\n\nClare laughed with a high, nervous edge. She got up and resumed the copilot chair. Everyone got back into bridge position, unsteady and pensive.\n\nFred said, \"The low-frequency spectrum has changed.\"\n\n\"Which means?\" Redwing asked.\n\n\"It's got a lot more signal strength. Let me run the Fourier\u2014\" His fingers and hands gave the board complex signals through its optical viewers. \"Yep, got some FM modulation, pretty coherent.\"\n\n\"Someone sending? Now?\" Beth said. \"Maybe they want to talk?\"\n\n\"This is really low-frequency stuff,\" Fred said. \"The antennas we use to monitor interstellar Alfv\u00e9n waves, to keep watch on perturbations in the magscoop. Never thought we'd get a coherent message on those!\" Fred brightened, always happy to see a new unknown.\n\nKarl had gotten up and now stood behind Fred's chair. He said, \"That fifteen kilohertz upper frequency\u2014look at the spike. Amazing. Antennas radiate best if they're at least as large as a wavelength, so... that means that the radiator is at least thirty kilometers across!\"\n\nRedwing tried to imagine what big structure could send such signals. \"Is there anything on radar of that size in the jet?\"\n\nThe answer came quickly: no.\n\n\"How can we decode it?\" Clare asked. She stood and walked over to see Fred's Fourier display.\n\nFred said, \"I can look for correlates, but\u2014hell!\u2014we're starting from knowing nothing about who the hell is\u2014\"\n\nThis time Redwing barely had time to register the prickly feeling on his hands and head before a crackling burnt-yellow discharge surged all along the bridge, snarling. The air snapped as they again dived for the deck. Redwing hit and flattened and saw Clare choose to stand against the nearest wall. A tendril shot forth and caught her. She twitched and crackled as the ampere violence surged through her. Her mouth opened impossibly wide, and a guttural gasp escaped\u2014and then the mouth locked open, frozen. Smoke fumed from her hair. Her legs jumped and her arms jerked and she fell.\n\nHer red coverall sparked at the belt. Tiny fires forked from her fingers as she struck the deck. Her hair seethed with smoke. She shuddered, twitched\u2014was still.\n\nRedwing did not move, but he noticed the tension had left the air. A seared silence came as acrid air stung the nostrils.\n\nIn the silence he could hear a last long sigh ease out of Clare, whistling between broken teeth.\n\nBeth sobbed as they gingerly gathered around the singed body. Redwing wondered what he could do in the short time before the cylindrical alien ships arrived, climbing up the jet toward them.\nTHIRTY-EIGHT\n\nMemor was roaring out of control. The two other Folk restrained her as she twisted and clawed at them. Their howls and wails blended together, even to Tananareve Bailey's ears as she ran toward the enormous, thrashing things.\n\nHer Folk attendants had scattered, not knowing what to do. They were backed against the walls, stunned into silence by Memor's deep growls. Tananareve could tell they were too afraid to leave and too afraid to do anything. She saw that a figure among them lurked under a cowl, a humanoid with a gray metallic head, carrying three ruby red eyes that peered out from the cowl's shadows. A cyborg, she guessed\u2014mind downloaded into a metal body. Such things had begun to manifest Earthside in the era when they had departed, so perhaps it was natural that an alien form of embodied Artilects should have manifested here in a Bowl that was millions of years old. The cyborg had a crystal silicon carbide assembly, four arms, and sturdy legs. She had seen no artificial bodies in the Bowl but now here was one, an attendant to the Folk, cowering like the rest, against the pink living wall.\n\nTananareve glanced at all those pressed against the walls and now could tell they were all far too afraid, too devoted to the entire Bowl system, ever to see any other future. A stasis state where nothing changed.\n\nThen there came a move, from the Folk.\n\nBemor acted. He held his genetic sister in a firm embrace while Asenath did something at the back of Memor's head. Her great shape stopped writhing and shuddering and then slowly eased, her arms going slack. Memor's eyes were distant, her face blank, breath long and heavy, a whuff whuff Tananareve had not heard before. Her big, nimble four-fingered hands twitched but did nothing.\n\nBemor turned from Memor, chuffing and labored, his face troubled. Blinking, he saw the humans and Sil. \"We now know what you Sil have been spreading.\" His voice came from the barrel chest, low and threatening.\n\nQuert stepped forward, mild and calm, seeming utterly unafraid. Tananareve had met the alien Sil only moments before and was still trying to understand them. They were humanoid and walked with a fluid grace, their tan clothing adjusting itself to their movements. Quert said, \"Glorian message came to human ship, the SunSeeker.\"\n\nBemor huffed, stamped around, clearly calling on outside Artilects, and thinking on what they said, and finally himself said, \"I am, yes, aware that our forward stations, orbiting from ahead of us, did not register the Glorian signals well and bring them to the proper level of attention. A bureaucratic error, alas. These stations have had no true news for many kilo-orbitals. They suffer from a sclerotic inability to adapt, to remain fresh.\"\n\nQuert said softly, \"We know so. Sire.\"\n\nBemor ignored this status salute. \"These humans managed to get the Glorian mischief to you, the vagrant and difficult Sil.\"\n\n\"It was important, surely you can see so, Sire. We spread such message through city-speak.\" Quert spoke mildly but with eyes steady. \"Then came more. Diagram of Bowl's path. Much long history, strange tales the Glorians know.\"\n\nBemor said, \"Annoying! You had no need to be familiar with such.\"\n\nQuert did not blink. \"Sil think opposite.\"\n\nThen they got into a hot discussion Tananareve could not follow, so she stepped back a few paces, into the comforting circle of humans. She had not realized, living so long among aliens whose social signals were strange and hard to register, what a simple warmth came from her own kind. After so long, it felt like a profound blessing. As the Folk chatter waxed on around them\u2014Bemor booming, Quert's small voice in sliding syllables\u2014she considered her fellow humans. This was so strange in itself that the mere phrase fellow humans said it all as she thought of it. She had competed for, and then signed on to SunSeeker, all for one solid purpose\u2014to go to a distant star and begin a new civilization. Straight out, true enough\u2014a species imperative, some had said, and so she had supposed. She did feel that, then. She had stored her eggs and planned to find a man who deserved them, and to do what she could, in some distant land among the stars, to bring humanity to a greater destiny.\n\nYet... now these fellow humans in their nervous chatting selves looked... strange to her. Their rambling, whispered words, their ill-concealed yet clearly frightened eyeball-jittering glances... all these seemed both familiar and yet edged in strangeness.\n\nCliff, for example, looked worn down. Skinny. Standard uniform but patched here and there, knees and elbows replaced, and tattered beyond easy recognition. Rough-cut beard, hair chopped into blunt wedges, a true wild man from many wearing days. Yet his eyes were watchful and quick, listening to his team and also sizing up the alien discussion going on a few paces away. He seemed somehow telescoped down a long range, so she could see him in a perspective she had never known. As a member of his species, he talked less than others and never stopped studying his surroundings. Watching him was to her now refreshment, consolation, peace.\n\nBest to leave that for later, though. You met the alien on your own terms and what you took away might be unexpected. She had to use whatever perspective worked.\n\nSo Tananareve turned to Irma, smiled, and did the ritual girl thing, and got the whole story in a few minutes.\n\nThe Glorians had sent their own history of the Bowl's long trajectory, plus some cartoon threats to stay away from Glory. Apparently they had been surveying all their galactic neighborhood for a great long time, while keeping electromagnetic silence. But now that the Bowl was steadily approaching, they resorted to a simple microwave signal train. And it told a truly ancient tale.\n\nAn event the Folk called the Great Shame was marked in the Bowl's path. The Sil wrote it in their architectural messages. Their new city rapidly rebuilt after the Bird Folk smashed it. The new Sil array of parks, plazas, streets, and structures held an agreed code. This conveyed a message other societies ringed around the great expanses of the Bowl could see and use. Now everyone knew of the Great Shame.\n\nTananareve asked, \"And why's that important?\"\n\n\"Because the Folk destroyed their own home world,\" Cliff said. \"As we saw. Earth. It looks like they blundered into the Oort cloud, and their gravitational impulse nudged the Dinosaur Killer comet, sixty-five million years ago.\"\n\n\"So life changed directions,\" Tananareve said, eyes distant. \"Doomed the dinosaurs, but made us possible.\"\n\n\"Must be more,\" Irma said. \"Must be.\"\n\nMemor thrashed and called in long strident shrieks. She raised her huge, thick-lipped mouth and made a warbling, keening sound. Bemor sheltered his sister twin through this and gathered himself, a big hulking presence, and said to them all, \"The Sil did not truly know what they were doing. This is the Great Shame, yes. Now that it is known, the task of us all is to make clear that it came from an earlier species, and so does not imply that the Folk are responsible.\"\n\nTananareve's eyes flared, eyebrows arched. \"Huh? C'mon\u2014this 'does not imply that the Folk are responsible'\u2014but you caused it! And why's Memor so distressed?\"\n\nBemor shuddered a bit and in low bass tones said, \"She is in conversation with her... Undermind. The Great Shame was merely a phrase to her. Now she has discovered that her Undermind concealed its meaning, to preserve her balance.\"\n\n\"I thought you Folk could view all your unconscious,\" Tananareve said.\n\n\"Not always.\" Bemor hesitated, then with a rustle of feathers that she now knew meant he had made a decision, went on. \"The proto-Folk of that ancient era, who committed the Great Shame, were unwise. They returned to their home system, flush with triumphant contacts with scores of nearby worlds. The dynamics of their parent system were well known to them, but wrong. Their data was gathered when the second sun\u2014our star, now\u2014was still in place. And perhaps they ventured too deeply into the large cloud of iceteroids.\"\n\nTananareve was digesting this when Cliff frowned and said, \"The Bowl has one great commandment\u2014stability is all. Right? Having this Great Shame is a contradiction you don't want to face\u2014is that what's making that one\"\u2014a nod to Memor\u2014\"so crazy?\"\n\nAn awkward silence. Then Asenath said, \"We Folk differ from those who built the Bowl. Those could not view their Underminds. The vagrant forces that arise in Underminds can be managed, if the sunshine of the Overmind shines upon them.\"\n\nTananareve said, \"You think of your unconscious as like, say, bacteria? Sanitize it, problem solved?\"\n\nBemor and Asenath looked at each other and exchanged fast, complex fan-signals with clacking and rustling. Bemor had Memor in a restraining hold and the big creature was slowly becoming less restive.\n\n\"Not knowing your desires renders them more potent,\" Bemor said. \"They then emerge in strange ways, at unexpected moments. Your greatest drives lie concealed from your fore-minds. So the running agents and subsystems of your immediate, thinking persona can be invaded, without knowing it, by your Underminds. Quite primitive.\"\n\n\"Which defeats control, right?\" Cliff said.\n\n\"And so stability,\" Tananareve added.\n\nAsenath said, \"You mean, Late Invaders, that notions simply appear in your Overminds?\"\n\n\"You mean do we have ideas?\" Tananareve considered. \"Sure.\"\n\n\"But you have no clue where the ideas came from,\" Asenath said.\n\nBemor added, \"Worse, they cannot go find where their ideas were manufactured. Much of their minds is barred to them.\"\n\n\"Astounding!\" Asenath said. \"Yet... it works in a way. They did get here on their own starship.\"\n\n\"There are many subtle aspects,\" Bemor began, and then paused. \"We must keep to task.\" He turned and gestured. Attendants rolled forward a large machine.\n\n\"I don't like the look of that,\" Tananareve said. \"Is this the same machine you put me in before? That Memor used to study my mind?\"\n\n\"No,\" Bemor said. \"This enables you to communicate with other minds, specifically those who need you to serve as an intermediary.\"\n\n\"Who?\" Tananareve turned to Irma and Cliff. \"I hated that suffocating box with its foul smell. And the feeling\u2014like snakes swarming over my skull. Then fingers in my head. I'd think something, then it slipped away, as if something was... running greasy hands over it.\"\n\n\"We require you to enter this device,\" Asenath said. She turned to Bemor and said in Folk\u2014but not so fast that Tananareve could not translate it\u2014\"Do we need the others? They are trouble.\"\n\nBemor rattled suppressing signals with his hind feathers. Not now.\n\nCliff and Irma had caught none of this. She said, \"Look, I can't square that Great Shame history of yours. You came back from star-voyaging to see the old place, Earth. So why haven't we found Folk artifacts on other planets in the solar system?\"\n\n\"There were stages. There was the era, after the Great Shame, that earlier Folk forms called the Dusting. It was a rain of small fragments into the solar system. An aftereffect of the Shame, in ways known to orbital specialists, arising from multiple iceteroid collisions far out from Sol. A sad era. Mere high-velocity dust destroyed much space-based technology. It etched whole cities out of existence on worlds not protected by atmospheres.\n\n\"But enough of this!\" Bemor said. \"Into this device you go now, Late Invader. We are ordered to send you thus, for reasons opaque to me. The Ice Minds would have it so. Welcome to this\"\u2014a broad sweeping gesture with a final feathered flourish\u2014\"a singular machine which we term a Reader.\"\n\nShe had no choice. The assistants looked nasty and they moved swiftly, closing in on her. She turned and embraced the people near her. \"Damn, we've just reunited and, and\u2014\"\n\n\"We'll still be here when you come out.\"\n\nThe others gave murmuring reassurances. She turned to follow the assistant, some nervous little form of robot, and suddenly a loud thunderclap hammered through the room. The fleshy walls of the skyfish rippled with it, and the floor lurched beneath her. She staggered, caught herself on Irma's shoulder, stayed standing. \"Damn!\"\n\n\"A shock wave,\" Cliff said. He turned to the Folk. \"From what?\"\n\nBemor looked out the transparent wall. \"Disaster.\"\nPART XIII\n\nTHE DIAPHANOUS\n\nIt appears that the radical element responsible for the continuing thread of cosmic unrest is the magnetic field. What, then, is a magnetic field... that, like a biological form, is able to reproduce itself and carry on an active life in the general outflow of starlight, and from there alter the behavior of stars and galaxies?\n\n\u2014EUGENE PARKER,  \nCOSMICAL MAGNETIC FIELDS\nTHIRTY-NINE\n\nKarl said, \"It's a standing kink.\"\n\nBeth looked at the screen showing the jet, its plasma and magnetic densities highlighted in color. \"This is a snap of it?\"\n\n\"No, it's real-time. The sideways movement of the jet in the Knothole region is hung up, lashing against the mag bumpers meant to keep it away.\" A side excursion had forked over against one of the life zones, penetrating the atmospheric envelope of a pie-shaped wedge.\n\n\"How in hell did that happen?\" Redwing asked from over Beth's shoulder.\n\nKarl grimaced. \"We've been driving our fusion burn pretty hard, trying to get some distance from the fliers that are coming up at us in the jet\u2014\"\n\n\"And failing,\" Redwing added.\n\n\"\u2014so that added our plume to the plasma already forcing the kink instability. Nonlinear mechanics at work. The kink has gotten into some mode where it snags against the mag defenses and just stays there.\" Karl shrugged, as if to say, Don't blame me, it's nonlinear.\n\n\"So it's getting worse down there,\" Beth said. Her eyes were always on the shifting screens as they powered away from their pursuers. In the howling maelstrom of the jet, there were always vagrant pressures, sudden snarling knots of turbulence, shifts in SunSeeker's magscoop configuration. Now SunSeeker had Mayra Wickramsingh and Ayaan Ali as backup navigator\/pilot, since Clare Conway had died in an instant's sudden lightning flash through the excited air above the bridge deck.\n\nThat had been only an hour ago, but the sharp terror of it was already fading in memory. There was too much to do now, to think of what had happened. Beth had helped carry away the charred corpse, holding Clare by the arms, seeing the face that was swollen and already darkening. Only hours ago, she had seen that mouth smiling, laughing.\n\nBeth heard her own voice rattling out, \"Those flitters, as you call 'em, Cap'n, are coming up fast.\" Her eyes studied the slim, quick shapes, just barely defined in size by their microwave radars. They had spread into a triangle, centered on SunSeeker's wake.\n\nRedwing stood in the middle of the bridge and said to everyone, \"We're plainly about to go into battle. Those flitters are fast. We can't outrun them. So we've got to engage them with a ship not designed to do battle at all.\"\n\nSilence. Jampudvipa usually said little, but now she said quietly, \"Is there any advantage in leaving the jet?\"\n\nBeth knew Redwing should answer that, but she seethed with anger now and could not stop herself. \"I don't want to maneuver against craft that fast, with our only fuel the star's solar wind. Or what's left of it\u2014the jet gets over ninety percent of the plasma that leaves the star. I can't fly hard with no mass coming through the scoop.\"\n\nKarl Lebanon asked, head bowed, \"What do the flitters fly on?\"\n\n\"Not plasma, right?\" Redwing turned to Beth.\n\n\"Their plume shows fusion burners, but they're running on boron-proton. They carry their fuel and reaction mass.\"\n\n\"They're flying upstream, which costs them in momentum,\" Karl said. \"For us, it's gain. We get more charged mass down the magscoop gullet. So\u2014\"\n\n\"What do we do when we get to gunplay?\" Redwing asked. \"We got no guns aboard, Dr. Lebanon.\"\n\nBeth said, \"You've got the big gun, Cap'n\u2014the torch.\"\n\nRedwing nodded somberly. \"You think it can make that much difference?\"\n\nKarl said, \"Whatever's flying the flitters, Artilects or aliens, it has to be vulnerable to the jet. They have magnetic screens for sure. They must've been engineered to take care of problems in the jet.\"\n\nBeth turned her back on Karl, irritated that he had jumped in when Redwing clearly addressed his question to her. \"So\u2014if we push them harder, give 'em some twist, maybe we can keep them at a distance, dodge them. Not like there's not room to play out here in the jet.\"\n\nRedwing scowled, his face more lined than she had ever seen. \"It's ten light-seconds across. Room to dodge, but\u2014can we keep them far enough away?\"\n\n\"Depends on what their weaponry is.\" Karl wore a dispassionate expression, staring into space. \"Nuclear, sure, we can see hardware coming and hit it with our scoop-policing lasers. But if they have gamma ray lasers, like those big domes on the Bowl rim, we're done.\"\n\nBeth sat back and watched the flitters edge up from behind. She bit her lip, adjusted for a vortex plasma knot, felt it surge them to starboard, and said, even and controlled, \"Cap'n, we don't have much choice.\"\n\nRedwing was silent, pacing, frowning. More silence. And suddenly Beth found herself on her feet, speaking in a flat, hard voice. \"You ordered us into the jet, you wanted to press the Folk, Clare got killed right here, and you now have no idea what to do?\"\n\nRedwing spun on his heel. \"I have over a thousand souls aboard who signed on to go to Glory. I took an oath to deliver them. I didn't agree to turn them over to aliens riding along in a big contraption.\"\n\n\"I don't think\u2014\"\n\n\"Point is, your job is to not think beyond your rank!\"\n\n\"We all just saw Clare killed by something we don't understand, that's got us all terrified, and you\u2014\"\n\n\"Quiet!\" Jam said, rising to her height on the deck, her dark face severe. \"The captain commands. We do not question, especially under combat conditions.\"\n\nBeth stared at Jam, whom she recalled was a mere petty officer. But... she had to admit, Jam was right. \"I...\" Beth's throat filled, choking off her words. \"Clare...\"\n\n\"Enough,\" Redwing said, addressing all the bridge crew. \"We're all jumpy. Forget this happened. We are committed and we shall engage.\" He turned to Beth. \"But you're lead pilot. You are carrying this ship into a battle we cannot master without you. Do it.\"\n\nSo she did.\nFORTY\n\nWe have need of your skills with your own kind, the cool voice said inside her mind. Tananareve felt around her, but no one had entered the narrow, warm envelope that had closed in on her as soon as the Folk sealed up this device. It smelled of dense, fleshy tissues, and indeed, the walls were softly springy, like the skyfish.\n\n\"I am certainly willing,\" Tananareve said, and waited. She could see nothing and heard no sounds. Yet the voice in her head seemed to be spoken.\n\nWe desire you to be quiet of soul.\n\n\"I don't know what that means.\"\n\nWe can see you churn with emotion. This is to be expected. But calm will come with concentration.\n\n\"Uh, who are you?\"\n\nThe Folk term us Ice Minds. They see us, as shall you, as those of slow thoughts, as our barred spiral galaxy turned upon its axis dozens of times. We have of late examined your species and believe you can be of use to avert the gathering catastrophe that awaits in short time.\n\n\"You know us? From Cliff's team, I suppose?\"\n\nThose who stand now outside this reading realm.\n\n\"Reading? You're inside my mind somehow.\"\n\nFrom the Folk termed Memor, we inherited her inspections of your mind. From those primates outside, we learned, again with Memor's excursions in your selfhood, to convey meaning in your Anglish. Now the Folk at our command immerse you in this fashion, so we can use you.\n\nShe didn't like the sound of this. \"To do what?\"\n\nTo prevent damage to us all. Unite so that the destination we all share can be made coherent with the purposes of the Bowl. To let life call out to life in depths and ranges greater still.\n\nTananareve had never liked sermons, and this sounded like one. Or maybe sanctimony varied with species. \"Why are you Ice Minds? I mean, what do you look like?\"\n\nThere flashed before her images that somehow blended with knowing at the same instant\u2014vision and insight coupled, so that in a few shifting seconds she felt herself understand in a way that simple explanations did not convey. It was less a sense of learning something than of understanding it, gaining an intuitive ground in the flicker of a moment, without apparent effort.\n\nA rumpled night terrain under steady dim stars. Dirty gray ice pocked with a few craters, black teeth of black rock, grainy tan sandbars... and fluids moving in gliding grace across this.\n\n\"You're the ivory stuff sliding on the rocks and ice?\"\n\nAnd you are death to us. We remain a mystery to you myriad warmlife races. To you bustling carbon-children of thermonuclear heat and searing light. We are of the Deep and knew, shortly after the stars formed, of the beauty stark and subtle, and old to you beyond measure. Our kind came before you, in dark geometries beneath the diamond glitter of distant starlight on time-stained ices. Metabolism brims in the thin fog breath of flowing helium, sliding in intricate, coded motion, far from the ravages of any sun.\n\n\"And you live here?\" Still too much like a sermon, but it had an odd feeling of being true.\n\nThe Bowl rushed at her, sharp and clear, the rotating great bright wok beneath the hard little red star, its orange jet\u2014and then the point of view swept around, to the hull. It plunged along the metalware\u2014humps and rhomboids and spindly stretching tubes of the outer skin\u2014until it swept still closer and she saw endless fields of parabolic plants, all swaying with the Bowl's rotation, focused up at the passing stars... while among them flowed that pearly fluid, lapping against odd hemispheres that might\u2014she knew, without thinking about it\u2014be dwellings, of a sort.\n\n\"Never thought of that. Shielded from the star, it's kind of like being on the far outside of our solar system, in what we call the cometary sphere.\"\n\nWe exploit the heat engine of leaked warmth from the Bowl's sunswept side to our realm, so we bask in beautiful cold-dark while harvesting waste energy from below. Our minds organize as complex interactive eddies of superconductive liquids.\n\nThe view skated across huge curved fields of icy hummocks and hills, with sliding strange rivers of ivory glowing beneath the dim stars. There came to her a creeping sensation of a vast crowd on this stretching plain, a landscape of minds that lived by flowing into each other, and somehow teasing out meaning, thought... more.\n\n\"Why do you care about us? We\u2014\"\n\nWarmlife, you are. In our primordial form, we traded knowledge collected over vast eras, useful for chemicals, coldworld facilities, or astronomy. We were shrewd traders and negotiators, having lived through eons, and having dealt with the many faces intelligence can assume. Our cold realm has existed relatively unchanged since the galaxy was freshly forged in the fires of the strong nuclear force.\n\nTananareve was startled by the linguistic sophistication of their speech, resounding in her head exactly like real sounds, in a flat accent\u2014no, wait, they were speaking to her with her accent. Even more impressive. Not many could ape her honey-toned Mississippi vowels.\n\n\"Against all that, why bother with me?\" Maybe not a smart question, but she was wondering, and here were the minds that seemed to rule this place.\n\nTo us little is new. Even less is interesting. We have watched great clouds of dust and simple molecules as they were pruned away, collapsing into suns, and so left the interstellar reaches thinner, easier for our kind to negotiate, and for the ion churn of plasmas to form and self-organize. But these were slow shifts. We are as near to eternal as warmlife can imagine. But you are quite the opposite. You are swift and new.\n\nInto her mind came an image of their bulblike bodies and weaving tentacles, all gracefully flowing, a sliding ivory cryogenic liquid. Something like an upturned cat-o'-nine-tails whip appearance.\n\nWe stand at an immense distance from such as you, yet at times arouse when the Bowl, our transport, is under threat. As it is now\u2014from you.\n\n\"Look, I don't know what Redwing is doing\u2014\"\n\nYet you are also vital to the Bowl's survival when we arrive at the target star, one you term Glory. So you are both friend and foe.\n\n\"Why me? I\u2014\"\n\nMemor integrated your neural levels to enough detail that we can access them. So we choose you to speak for us to your nominal leader, the Redwing, and to the Diaphanous.\n\n\"I don't know what's going on!\"\n\nOur long views are essential to the Bowl's longevity. At this moment some 123,675 of us are engaged in this collective conversation with you. The number shifted even while the Ice Minds spoke.\n\nWe are individually slow, but together we can think far quicker than you. We are eternal and you are like the flickerings of a candle flame\u2014that which combusts dies, as must all warmlife. When we evolved, the most advanced warmlife creatures on hotlife worlds were single-celled pond scum.\n\n\"Why are you on the Bowl at all, then?\" She was getting irked with all this bragging. But trapped in a smelly box, probed by who-knows-what kinds of technologies, it seemed best not to be obnoxious. And she would hate to meet whatever these things needed help with. If these Ice Minds just wanted her to talk to Redwing, fine. But somehow she knew it couldn't just be that.\n\nWe bring a wisdom of long memory. We alone speak with and for the Diaphanous. We wish to explore and to meet the Superiors who seem to be at Glory.\n\nThen she felt a surge, as though the entire machine containing her was moving. It lurched a bit and she poked an elbow against a soft wall. Hoarse calls came from outside. What now?\nFORTY-ONE\n\nCliff looked down at what the Folk called their mooring mountain. They said it held a shelter for this skyfish, but it was far beneath them, barely visible through stacked gray cumulus clouds.\n\nThe ship crew had leaped into action after the big long boom pressed through the skyfish. They had all rushed to the big transparent wall, mouths gaping, not heeding the shouted orders of Bemor. The male Folk stamped his feet in an accelerating rhythm, big hard thuds. That snapped the crew out of their funk and they followed his barking orders.\n\nThe humans and Sil did not know what was going on, so they moved to the wall, now deserted, to look out. Cliff saw far overhead an upside-down tornado. In profile, it looked like a funnel. Within it, huge clouds churned in an ever-tightening upward spiral, turning somber purple as moisture condensed within them. The lower levels of the air were clear, so Cliff knew he was seeing far up into the atmosphere. The conical cloud was fat and white at the bottom and tapered upward into a narrow purple-dark neck. Even at this great distance, Cliff could see flashes of blue and orange lightning between immense clouds. Across the sky, other high decks of stratocumulus were edging toward the inverted hurricane. He was looking at a puncture in the high envelope.\n\n\"They're trying to ground the skyfish in this storm,\" Irma said.\n\nThe skyfish dove deeper and shuddered with the racking winds. Irma and the others watched the high vortex churn as if it could change, but Cliff knew with a wry sinking feeling that it could only worsen. A huge deep atmosphere would take a long time to empty out into space, but the pressure drop would drive weather hard. He wondered if the Folk could patch a big rip in the high shimmering envelope from the way Bemor was lumbering around and barking at the crew, he doubted it. He looked down and saw they were headed for the nearest clear ground they could find within quick reach, the mooring mountain.\n\nAybe pointed. \"The crew\u2014they're taking that machine away, with Tananareve in it. Damn! We get her back, and then right away she's goddamn gone.\"\n\n\"We're all gone, really,\" Terry said. \"No chance of getting out of this living blimp that I can see.\"\n\nIrma was talking to Quert and reported back. \"That's a kind of Folk redoubt we're approaching. They can shelter there.\"\n\nQuert came over. \"Wind hard. Anchor skyfish, it hard.\"\n\nAs if to demonstrate, the skyfish lurched and they all fell to the deck. Cliff tucked in and rolled, coming up to look out the transparent wall just in time to see a brilliant yellow lightning strike descend from a high cloud. Unlike on Earth, this one snaked down, shooting side bolts as it kept going. The distance was so much, Cliff could see the entire brilliant streamer, the vibrant, bristling conducting path for electrons seeking the ground. Like a lazy snake, it slid sideways in a long twist. Then it hit the mountain below and snapped off, just vanished in an instant. The thunderclap shook the entire skyfish, and Terry, who had already gotten back up, came crashing down again.\n\nSomething rumbled in the pink walls nearby. The skyfish went into a steep descent. \"It fears,\" Quert said.\n\n\"Me, too,\" Irma added. Everybody stayed down, hugging the deck that reeked with some slimy fluid. The skyfish tilted and turned violently. More lightning scratched across a lead sky.\n\nThe skyfish hit like a fat balloon. It squashed and flexed, the walls of their big chamber collapsing down, then wheezing with the effort to rebound. The walls thumped with the slow, massive heartbeat of the skyfish. Cliff heard bones snap and the soft rip of tissues deep in the walls. Blood ran across the deck.\n\n\"Let us go fast, my friends,\" Quert said. They fled.\n\nAs Cliff followed the Sil down fleshy corridors that reeked of fluids he did not want to think about, sloshing boot-deep through it, he recalled something his army uncle had said once. Try to get all your posthumous medals in advance.\nFORTY-TWO\n\nWith her fellows, Memor watched a high view of their Zone, sent from a craft dispatched to survey.\n\nSomething had hit the great sea at the center of the Zone, not far from where their skyfish labored. An enormous tsunami rushed across the dappled gray surface. The sea was shallow, so the wave was already at great height and as they watched, it broke, white foam curling forward. This towering monster broke across the land. Forests and towns disappeared.\n\nThe skyfish rolled to port and then back, with an alarming twist running down the great beast's spine as well. Their compartment twisted as the skyfish fought to right itself. In this very low gravity zone, the air density fell off slowly and there was less acceleration to gain from venting hydrogen. The floor tilted as they accelerated downward at a steep angle. Memor staggered, then abruptly sat. The capsule where Tananareve was in immersion with someone\u2014could it be Bemor was right, and she spoke now with the Ice Minds? Surely that was impossible. The mismatch of mind states was surely too much for that. Memor herself had encountered difficulties with the primate. The Ice Minds were scarcely reachable without considerable training, such as Bemor had endured.\n\nThe deck heaved sickeningly, but Memor forced herself to her feet. Bemor was gone on a task he said came from the Ice Minds, and Asenath lay whimpering in a slung rack. It was one of the water-clasping type, so she now floated in a sleeve, only her head visible. Her eyes wandered, and Memor judged Asenath would be paying no attention to Memor. Good.\n\nEach step she took came freighted with fear. The deck rolled with flesh waves. The body around them groaned and sloshed. The hydrogen exhaust was roaring and she felt its dull tone through her legs. Memor had made herself put away the terrifying\u2014and, she now realized, quite embarrassing\u2014storm within her. Suppressed truths had overwhelmed her. She realized that her Undermind had sheltered much of the Bowl's long history from her and she had never suspected. The Undermind somehow knew she could not bear facts that clashed with her deepest beliefs in the role, status, and glory of the Folk.\n\nThen, in shocking moments that she never wanted to relive, all the tensions and layered lies of her entire lifetime came welling up. Spewing as from a volcano, it burst through her.\n\nNow she made herself put all that aside. She sealed layers over her Undermind. She confronted a problem demanding all her ability now. Put a foot forward. Brace against the rumbling, twisted flooring. Take another step. Each demanded labor and focus, and it seemed to take a long while to reach the external panel of the capsule.\n\nThe harness fit her head, and the connections self-aligned. She sank into the inner discourse, but only as an observer. She could affect nothing inside.\n\nShe felt Tananareve's mind as a skittering, quick bright thing. Few images, but thoughts of the Ice Minds played through the strata of the primate mind. They seemed to fragment and go into separate channels, streams fracturing as they flowed.\n\nMemor struggled to make sense of the hot-eyed fervor of these flows. Revelation dawned along axes of the primate Undermind. New data flowed into Memor and she could flick back and forth between her own mental understory and the primate's. These laced with the shadowy strangeness of linear minds. Hereditary neural equipment governed these divided minds\u2014straight down the middle, a clear cleft. Such was common in the Bowl's explored region of the galaxy.\n\nShe saw Tananareve's mind taking in the Ice Minds' conversation and hammering that on the twin forges of reason and intuition, with great speed. So the Ice Minds wished to enlist her! Astounding, but perhaps it was only to speak to that Captain Redwing. Still, Bemor was the proper pathway for such diplomacy.\n\nThe deck lurched. Memor barely kept her purchase. Shouts and cries echoed.\n\nThe conversations and images seemed to condense in Memor's mind like a vapor forming a shape. The precise words shifted and changed as the translations moved restlessly. Memor had to cling to nuance, not precision. Something about Redwing the Captain and the jet, yes, and how much humans could help in dealing with the Glorians. A need to intervene between Redwing and\u2014\n\nA hard jerk knocked her over. Memor struggled up to her feet and grasped for the harness, which had come unfastened. She just got it positioned when another twisting roll came through the ship and Asenath collided with her. \"We are down!\" she cried. \"Get out!\"\n\n\"But the primate\u2014\"\n\n\"Bemor is in charge, and he says we should go out and seek the central shelter. Come!\" Asenath turned and fled.\n\nMemor hesitated. She wanted to know what the Ice Minds said. She started to settle in, restarting the harness configuration, when a voice bellowed at her, \"Go! I will care for this.\"\n\nShe turned, and joy flooded through her at the sight of Bemor. The ship trembled, and a great wheezing came rattling down through the corridor outside. She hurried away.\n\nWithin a few moments, Memor lost her footing in the dim light outside. She curled up and slammed to ground. Screams, shouts, crashes. The mountain's firm rock snapped and cracked, heaved and buckled. The path to the shelter now had a great pit crossing it. Sound came from everywhere, and the ground seemed to be grinding against itself, sending gray dust plumes shooting up.\n\nA black curtain boiled across the sky. Within its churn, flashes snapped like eyes in a great beast. Ozone stung the howling breeze. With it came rain.\n\nNot rain\u2014mud. Pellets of it, hard and dry on their skins, soft at their centers. They splatted down, rapping Memor's skull. \"From some body of water,\" she said wonderingly, \"thrown up by something hitting\u2014\"\n\nShe extended her long tongue and tasted the warm rain, like water from a bath, and\u2014salt. The great sea was pelting even this high fortress mountain. Memor folded her feathers close and tight, a raincoat of sorts.\n\nA pool of ink poured across the sky, layers of cloud sliding over each other as if liquid. The reassuring steady day had now turned to a dim night, one filled with sky fireworks far brighter now than the star and jet. Her view flashed in blue-white light and then vanished into the murk. \"Bemor!\" No answer. She got up and walked on legs like pillows through strobes of lightning.\n\nThe flashes showed ahead a new problem\u2014a crevasse yawned. It was a split in the crowning rock slab itself, showing fresh sharp edges. She could barely glimpse the far side in the lightning flashes. Far away. Even in this low gravity, nothing could leap it, certainly none of the bulky Folk. It blocked their way to the station.\n\nMemor looked around in anxious despair. Various staff and crew milled at the edge of this gap, looking desperate. She sniffed their acrid fears. Asenath was nowhere among them. Another blue-white flash allowed her to survey the gathering jam all along the broken path, jostling and shouting strident calls.\n\nMemor saw a new problem. Where were the Sil? And the primates?\nFORTY-THREE\n\nRedwing paced the bridge and watched the approaching shapes, flitting close now among the roiling turbulent knots. Moments ticked by, and the bridge was silent. Beth was ready to focus their exhaust as much as the tunable scoop mag fields allowed. And now there was something new and strange as well.\n\nTheir hull resounded with a strange strumming symphony. The long notes were just at the edge of hearing but clear and distinct. Haunting low notes came like the beating of a giant heart, or of grand booming waves crashing with slow majesty upon a crystal beach, ceramic resonating instrument. Redwing felt the notes with his whole body, recalling a time when as a boy he stood in a cathedral and heard Bach on a massive pipe organ. The pipes sent resounding wavelengths longer than the human body. He did not so much hear notes as feel them as his body vibrated in sympathy. A feeling like being shaken by something invisible conveyed grandeur in a way beyond words.\n\nBeth said, \"Whatever's outside\u2014and I can't see a thing on these screens, just plasma and magnetic signatures\u2014is trying to say something.\"\n\nKarl said, \"Their last attempt killed Clare.\"\n\n\"Yes, a horrible way to die. I... I wonder how whatever is outside makes sounds?\" Beth said. \"Oh\u2014Cap'n, there's a dense plasma knot headed for us.\"\n\n\"Focus it in on the prow fields,\" Redwing said. \"Can we snag it and narrow the exhaust, then aim at the first of those fliers?\"\n\n\"I... think... so.\" Beth and the entire bridge crew were concentrated on their work, belted in tight, eyes following screens, hands hitting key commands. \"The workaround on that digital algorithm block is coming up, running right. The Artilects are all over this problem, but they don't like it.\"\n\n\"They don't have to,\" Redwing said.\n\nThe strange deep notes running through the ship's hull ceased. \"They're leaving us alone, maybe,\" Beth muttered.\n\nThe roiling knot of hot ions clamped within a nest of rubbery magnetic fields came slamming at them at over seven hundred kilometers a second. \"Added to our speed, the impact will be well over a thousand kilometers a second,\" Karl said. \"Is the magscoop cinched in?\"\n\n\"As much as we can,\" Beth said, voice high and lips tight.\n\nThey watched the large blob come straight at them. It was far bigger than SunSeeker's scoop, and they felt the surge, their heads snug against their chair braces. The ship groaned.\n\nTheir internal diagnostics tracked the flow of dense plasma through the magnetic funnel out front, through the tapered neck that flushed it into the reaction chambers. There lived the steadily maintained, self-shaping field geometries that further compressed the plasma, added catalysts, and\u2014the screens showed the pulsing glow in coiled doughnuts of prickly yellow\u2014burned with fusion fire. This got expelled at the max temperature, into an opening throat that sent this starfire into the classic magnetic nozzle facing aft.\n\nBut not exactly dead aft. Beth's fingers flew over the complex command web. The fields slanted slightly, clamping down on the flow, shunting it sideways. The bridge surged again under this momentum change. The Ship Stability Artilect kept them from tumbling with extruded counterfields. Virulent plasma jetted out in a starboard cant. Beth altered the fusion geometry's exit profile to include more shaping magnetic fields in the exhaust. The emerging bolt of hot plasma was like a finger scratching across the wave behind them.\n\n\"With a little bit of windage...,\" Beth mused, intent on the screens.\n\nA flier lay dead at the center of the bolt. When the exhaust struck it, the image wobbled, refracted by the complex play of forces, then sharpened. Fragments swirled where the flier had been.\n\n\"Got it,\" Beth said quietly.\n\n\"Brilliant,\" Redwing said. \"The others\u2014\"\n\n\"The second one is taking an evasive trajectory,\" Karl said. \"Moving away laterally.\"\n\nBeth angled their exhaust and caught it before the flier could get away. Nobody cheered.\n\n\"The third is dropping back,\" Karl said.\n\n\"We can't fly much farther up the jet,\" Redwing said. \"They know that. We'll reverse, make our turn.\"\n\n\"And that third one will be waiting for us,\" Beth finished for him. \"And it'll be ahead of us.\"\nFORTY-FOUR\n\nTananareve was grateful the walls of her confinement were soft but firm. Whatever was carrying her along did not trouble to make the trip pleasant. Jerks and jostles made it hard to keep focused on the sliding, cool voice of the Ice Minds in her mind, overlayered with their images of the lands where they lived.\n\nStarlight cast stretched pale fingers across the plain of rock and ice, where vacuum flowers dutifully pointed their parabolic eyes at the slow sweep of target suns. Around the base of the light-harvesters flowed the pearly fluids that were the commingled selves of the Ice Minds. How these blended thought and became coherent, she could not imagine.\n\nThe moment hastens. We decided to revive ourselves wholly, to deal with this pressing problem.\n\n\"What problem?\"\n\nYour species. The Folk believed they could deal with you as a young and largely incompetent species, but we came to see this is not so.\n\nShe thought of saying, Gee, thanks! but sarcasm might not translate in dealing with aliens. \"Look, we have been imprisoned or chased ever since we got here.\"\n\nThe Folk are our\u2014 A pause. \u2014our police. They also maintain at equilibrium. We are not at equilibrium now. They have failed to understand your kind. Now disruption proceeds.\n\n\"What? Why? How?\"\n\nYour ship has disturbed our jet. The Folk have ordered attacks on your ship. This is against our wishes. We cannot well communicate with your kind in your ship, as some of the Folk have prevented that. We wish you to speak directly to your ship through channels we shall soon open.\n\n\"That's a lot to take in. SunSeeker is in your jet? Wow.\"\n\nInto her mind came an image of a small dark mote plowing upstream against a torrent of coiling plasma. The view backed away and she could see the jet slide sideways as it approached the Knothole. It surged over the Knothole restraining fields and into several life zones. Atmosphere belched out. Some thin girders holding the atmosphere zones apart fractured and fell. She was startled.\n\nYour mind we can approach. The Folk Attendant Astute Astronomer Memor made deep soundings of your neural labyrinths. These we use now. We wish you to speak with your own kind and then to serve to reassure the Diaphanous.\n\nAnother alien? \"Who are\u2014?\"\n\nInto her mind came images of fluid fluxes merging in eddies and turning in fat toroids, all in intricate yellow lines against a pale blue background. Somehow she knew these were larger than continents and fuzzy at their edges, where flow was more important than barriers. Intricate coils bigger than worlds, shattering explosions\u2014all testified to the recombining energy of the fields.\n\n\"These... live in the jet?\" She could not imagine this, but lack of imagination had ceased to be a good argument here.\n\nThey evolved in the magnetic structures that dot the skin of stars. These could knot off, twist, and so make a new coil of field. Embedding information in those fields led to reproduction of traits. From that sprang intelligence, or at least awareness.\n\n\"But they don't have bodies. How can they\u2014?\" Her grasp faltered.\n\nYou and we do not witness the chaotic tumble of great plasma clouds between the stars. We all see nothing hanging between the hard points of incandescent light, and so falsely assume that space is somehow nothing. But evolution works there against the constant forces of dissolution.\n\nTananareve knew a bit of general life theory. Brute forces seemed bound, inevitably, to yield forth systems that evolution drove to construct some awareness of their surroundings. It took billions of years to construct such mind-views. Those models of the external world could become more complex. Some models worked better if they had a model of... well, models. Of themselves. So came the sense of self in advanced animals. But in plasma and magnetic fields?\n\nThe Diaphanous migrated on solar storms into the greater voids where we evolved. When the building of the Bowl began, it became essential to include them, as managers of the jet and of the star itself. Only by shaping the magnetic fields of star and jet can we move the Bowl, with constant attention to momentum and stability. Who else to govern magnetic machinery than magnetic beings?\n\nThe Ice Minds sounded so reasonable, their conclusions seemed obvious. Before her inner eye played scenes of magnetic arches rising from stars, twisting and kinking to cut off and therefore give birth to new self-stabilized beings. She could sense, not merely see, waves lashing among the complex magnetic nets that surged in her mind\u2014speech of a sort, maybe. Now the view in her mind shifted to the jet and the plight of SunSeeker, pursued by small ships of destructive intent.\n\n\"You want to\u2014what? Broker a deal? After hounding us across\u2014\"\n\nThe Folk have failed us. Their defenses of the jet are ancient and many failed. Your ship did not even notice these, we are certain. The loosened jet now lashes across Life Zones and wreaks much ill. Yet those who bear down upon that ship now may well have to resort to a weapon we have vowed never to use. It could bring far more evil.\n\nThat, at least, was a familiar concept. Calamity stacking up. \"Okay, what do I do?\"\n\nLet us override the Folk pathways. We shall connect you to your Captain Redwing.\n\nA ripple ran through her mind, a floating airy sensation that somehow mixed with colors flashing in what she felt as her eyes. Yet at the same time, she knew her eyes were open in the complete blackness of the cramped machine. Her eyes saw black, but her mind saw shifting bands of orange and purple, and on top of that\u2014bursting yellow foam ran over an eggshell blue plain. Speckled green things moved on it in staccato rhythm. Twisting lines meshed there and wove into triangles where frantic energy pulsed. A shrill grating sound came with flashes of crimson.\n\nThen she saw Redwing. His image wobbled and she wondered how they could put that into her mind. \"What are you?\" His voice echoed as though he were in a chamber.\n\n\"Captain, this is Tananareve. I'm in some device that, well, wants to speak with you. They are\u2014let's skip that, okay? The Bowl has a lot stranger aliens than we thought.\"\n\n\"How do I know you're really Tananareve at all?\"\n\nThis question hadn't occurred to her. \"Recall that party we had before we went down to land? Feels like a long time ago.\"\n\n\"Yes, I suppose I do.\" He was standing on the bridge, and she could see Beth and others in the background, all looking at what had to be a\u2014what? She tried to remember the bridge but failed. Maybe a camera? How did these aliens tap into internal ship systems?\n\nInto her head came the Ice Minds' sliding, calm voice. We have dealt with what you term your Artilects. They are most agreeable.\n\n\"You brought out a bottle of champagne, remember? You said it was for our first landfall at Glory, but what the hell, this was a landfall and so here it was.\"\n\n\"Damn!\" Redwing's face broadened into a grin. \"It really is you. No video, but\u2014welcome aboard, sort of.\"\n\n\"Captain, I'm conveying messages from, well, some aliens we didn't know were here. They want you to stop fooling with the jet.\"\n\nThat comes later. For now tell your commander that they are in grave danger.\n\nShe said that, but Redwing's face turned away to look at a screen she could partially see. On it some flecks moved against a yellow weave of lines that she knew represented magnetic field contours.\n\n\"You mean these guys coming up on us?\"\n\nYour ship has permission to destroy them. But a weapon aboard one of them can erase your ship.\n\n\"Captain, try to kill them right away. They have something\u2014\" She paused, not knowing what to say.\n\nIt is the Lambda Gun, and will disrupt space-time near them.\n\n\"It's some sort of ultimate weapon,\" she said.\n\nRedwing looked tired. He nodded. \"Okay, stay on the line. We'll try that\u2014\"\n\nThe connection broke. His image dwindled and she was in darkness. Somebody was still carrying her around, and she felt a sudden drop. Thump. She heard distant shouts in a language she did not know and felt all at once very tired.\nFORTY-FIVE\n\nCliff crouched with the others and watched the big blimp skyfish wallow on the mountaintop. Scampering crews had secured the huge thing at both ends and now were lashing the sides down with big cables. A heavy rain ate most of the light from the skyfish itself, dim glows of ivory that got drowned in the brilliant lightning flashes. Hammering raindrops scattered even the crashes of lightning into a blurred white murk.\n\n\"Where'd the Folk go?\" Irma shouted against the wind.\n\n\"Into that big entrance!\" Aybe pointed. \"They had that thing they put Tananareve into with them.\"\n\nTerry said, \"Remember what threw us around, back in the skyfish? To make a shock like that, and blow sheets of rock off this mountain\u2014that takes a lot of quake energy. But there aren't quakes here\u2014no plate tectonics.\"\n\nAybe swept rain from his eyes and jutted his chin out. \"Look, the Bowl has a light, elastic underpinning, with not much simple mass loading. So an impact, from something thrown down here, that has a lot of energy. Real quick it moves through the support structure. It came here, to this big slab of rock, a whole mountain\u2014and knocked the bejeezus out of it.\"\n\n\"Just as we landed. What luck.\" Irma huddled down. Cliff read her body language: the rain was warm, at least. It smacked down hard.\n\nTerry sniffed and said, \"I'd like to get out of this damned rain.\"\n\nAs if on cue, white specks began smacking down on the flat rock plain around them. \"Hail!\" Aybe said.\n\nA dirty white ball the size of his fist hit Cliff in the side. He thought he felt a rib crack. The weather here was bigger and harder than he could deal with. Plus the darkness of the storm kept making him feel like sleeping.\n\n\"Let's get inside, out of this storm,\" Cliff said. \"Not the skyfish\u2014who knows what'll happen in there?\"\n\nTo his surprise, the others just nodded. They looked tired, and that made them compliant. He turned to Quert. \"How can we get into their station?\"\n\nQuert had been dealing with his Sil, who were doing what they usually did at a delay\u2014resting. They were squatting and eating something they had gotten on the skyfish. The more anxious humans just milled around. \"Let us lead,\" Quert said.\n\nThe Sil set off at an angle to the crack that had formed in the slab rock. In the confusion of abandoning the skyfish, they had all managed to slip away from the Folk and their many, panicked attendants. The darkness from huge black clouds that slid endlessly across their sky had sent the crew into jittery, nervous states, their legs jerking as they moved, eyes cast fearfully skyward. They had never known night, and this vast storm could not be common here.\n\nThe crack finally ended several hundred meters away from the skyfish. The Sil simply walked around the end of it with complete confidence, and headed back toward a raised bump near the larger mound of the Folk station. As they all cautiously approached, the lightning came less often. Cliff looked back in the darkness and saw the skyfish dimly lit from inside, like some enormous orange Halloween lantern on its side. There was no one in the tube passageway that led downward. \"Why?\" Cliff asked Quert.\n\n\"All fear,\" Quert said. \"Folk, others, all hide inside.\"\n\nAnd so it was. They padded carefully down corridors and across large rooms bristling with gear whose function Cliff could not even guess. It seemed to be working, there were some small lights on the faces, but no clue as to what they did.\n\n\"Folk not know how to work when big change comes,\" Quert said laconically. He relayed this to the Sil and they all made the yawning, hacking sound of Sil laughter.\n\nThey came into a large room that looked down on an even larger area. Quietly they crept up to the edge of a parapet and saw below a milling crowd. The attendants and servants, a throng including alien shapes Cliff had never seen before, and robotic ones as well, held back toward the walls. At the center were the three large Folk and the machine holding Tananareve. The far walls were large oval screens showing views of the Knothole region. One smaller screen was a view from far above, where a long tear in the atmospheric envelope had drawn clouds streaming in, moisture condensing and lightning forking along the flanks of immense purple storms.\n\n\"That's the top of the typhoon we're under,\" Terry said. \"Judging the scale, I'd say those cloud banks are the size of Earthside continents\u2014and look at that lightning flash! You can see it coiling around. As big as the Mississippi, easy.\"\n\n\"Look,\" Irma said, pointing at the shifting view as it tilted toward the Knothole. \"There's the jet\u2014and my God!\u2014SunSeeker.\"\n\nThe screens showed swift small motes dodging and banking in the center of the luminous swirling plasma jet. A quick close-up of their own starship showed it plowing through knots of turbulence and making a tight helix, aiming its pencil exhaust in a tight hot luminous finger at the\u2014\n\n\"Damn, they hit it!\" Aybe said, eyes jumping. \"Blew that flier to pieces.\"\n\n\"Damn right!\" Terry said, pumping his fist.\n\nThey didn't know what was going on, but excitement rippled through humans and Sil alike as they watched something like a dogfight going on. Cliff watched the ballet of ships moving at many hundreds of kilometers a second, seen on scales that had to be zoomed six or seven orders of magnitudes. Nothing but machines could handle this, and even they seemed strained from the sudden turns and swerves they saw.\n\nThe crowd below gazed upward at the screens, and the Folk were at the center, managing machines. The odd curved box that held Tananareve was with them. He wondered what they were making of this confusing mess. He grasped Irma and held her close. They kissed, not caring if anyone saw. Then the guards arrived.\nFORTY-SIX\n\nThey were drenched and cold, Folk and Serfs alike, but the hour demanded attention. Memor slumped down to rest, sitting back a bit on her haunches.\n\nTheir flight from the poor agonized and wounded skyfish had been rowdy, noisy, swept by rain beneath inky clouds flashing with electrical anger. Their ragged party had slipped and stumbled their way across great slabs of rock, with Memor trying to keep order in their flight. A team from the station had come out to erect, with swift competence, a bridge over the jagged chasm that had split open. The station's deputy commander said a flying hard-carbon flange had fallen on the mountain, apparently freed of its support structure high up in the envelope's stanchions, and plunged deep into the mountain's firm mass. The shock wave had rocked the skyfish sideways and blown several of its compartments, spilling crew onto the rock. That knife-sharp girder had also split a crevasse at the worst possible moment, spraying fragments into the skyfish and killing some local staff. The great skyfish bellowed and writhed against the crews attempting to moor it, killing several. Its flailing fins were sharp and deadly.\n\nConsidering this, it was a wonder anything worked.\n\nMemor sagged with exhaustion. She watched Asenath stand proudly at the prow of the command center in their mountain shelter, in full authority. She listened to the panicked signals from the fliers, displayed on screens and sounding shrill even in this large command room. The fliers were guided by robot minds, high level and capable of what seemed like emotions. The voices were brittle, sharp, edged with urgency. The swift ships tumbled and gyred, blown about by the ramscoop thrust. That made evasive navigation and aiming nearly impossible.\n\n\"We could use the Lambda Gun, as you said before, Wisdom Chief,\" a small lieutenant said softly. \"One of the fliers bears only the gun. It is bulky and makes maneuver difficult in the jet. That flier hangs back, away from the pencil exhaust the primates are using against us.\"\n\n\"Under whose orders was this done?\" Memor said.\n\n\"Mine,\" Asenath said firmly.\n\n\"Have the Ice Minds agreed? They have\u2014\"\n\n\"Bemor is not here, so we cannot readily consult with the Ice Minds. He is off managing their discourse, if that is the proper word, with your talking primate. So I shall have to assume command.\"\n\nMemor felt compelled to say, \"Separated command? This is not proper use of the hierarchy\u2014\"\n\n\"Ah, but then, this is a clear emergency. Communications are fragmented and time ticks on. I order the Lambda Gun unfolded.\"\n\nMemor felt a sudden spike of fear. \"That, that will take time\u2014\"\n\n\"Get to it,\" Asenath ordered the lieutenant. Various officers, gathered around the two Folk in a crescent, rustled with unease. Nobody moved. The silence stretched.\n\nMemor said, \"You had the Lambda Gun prepared before, didn't you?\"\n\nAsenath gave an irritated fan-rebuke to her underlings. \"Now!\" They scurried off to their many tasks.\n\nAlmost casually, in a way that told Memor this had been long planned, Asenath turned and gave a gray green feather rush of haughty disregard. \"I felt it necessary. Events now prove me correct.\"\n\nMemor felt icy fatigue run through her but summoned up reserves, rustled her feathers, and turned inward. She had heard of the Lambda Gun long ago as a historical curiosity, and now had to call up its history to have any hope of dealing with Asenath. Her Undermind held this lore, and was sore abused. She felt this as she unveiled portions, stripping back layers of youthful memory, gazing inward past the trauma suffered after the revelation of the Great Shame. She felt it now in its full ghastly panorama\u2014the images of a long cometary tail, pointing directly at Earth in the final moments, like an accusatory finger, and the spreading circle of destruction that annihilated the ancient civilization of smart, warm-blooded reptiles. Their majesty lay not in vast edifices, culminating in the Bowl. Instead, they were heirs to the fraction of that great species which relished their natural planet and did not want to take part in the Bowl, or its technical prowess, or the alliance with strange minds in the cometary halo. They had kept Earth green and fertile, restricting their own numbers so the natural luxuriant world was not paved over with artifice. In a way, Memor recalled, the Bowl became a tribute to their deep instincts. Its huge expanses enabled many species to live intelligently in Zones dominated by leafy wealth, though built upon a substrate of spinning metal and carbon fiber intricacies. A natural world built upon a machine...\n\nShe had become lost in her introspection, a common liability of voyages into the Undermind's shadowy labyrinths. Memor revived an old image of the Lambda Gun, a fearsome projector of gray spherical bulk, tapering into a belligerent snout. It could project a disturbance in the vacuum energy of space-time, throwing this knot of chaos out in a beam. Suitably tuned, it would cause, when it struck solid matter, a catastrophic expansion of a small volume of space. The inflation field increased the cosmological constant in a very restricted region for a brief snap of time. Whatever contained this howling monstrosity, reborn from the first instant of this universe, would be ripped into particles far smaller than nuclei.\n\nMemor recoiled from this appalling vision. With a hasty withdrawal salute, she slammed her Undermind shut. \"This is grisly! This is a planet buster, capable of delivering enormous energies\u2014\"\n\n\"So well I do know,\" Asenath replied. \"I have studied this ancient device and its history. The true Ancients invented it as a last resort against balky species. Some hurled relativistic masses at the Bowl to drive it away. The Lambda Gun put a quick end to their mischief.\"\n\n\"Surely we have shields that would be useful\u2014\"\n\n\"Not against a vagrant craft with powerful magnetic scoops. We enjoyed great magnetic craftsmanship in Ancient ages, but our Bowl does not muster such intensities. Nor do the Diaphanous have ready responses. Meanwhile, the jet stands in a nonlinear kink mode and deals us terrible destruction.\"\n\nAsenath said this with a reasonable air and somber fan-display. Memor knew she could not deflect Asenath in an area where her expertise and rank prevailed. She gave it one last try. \"The Ice Minds and the Diaphanous are in charge of jet dynamics!\"\n\n\"And they have failed. Prepare to fire,\" Asenath said to a lieutenant, and turned her back on Memor.\nFORTY-SEVEN\n\nBeth felt the hairs on her neck rise, prickly and trembling as the electrical charge built again. But this time she was getting irked and instead of flattening herself yet again on the deck, she hit a hard thruster in the magscoop. Fields vented plasma and the ship lurched. The others were hitting the deck but Beth discharged a brace of capacitors in the magscoop's leading magnetic fields. This gave a powerful burst of electrons at the far end of the scoop, moving at the speed of light. Instantly her neck hairs stopped tingling.\n\n\"Cap'n, looks like I've found a way to offset the charge buildup these things are using against us,\" she said with a deliberately casual air.\n\nRedwing looked up from the deck, where he had sprawled. \"Brilliant!\"\n\n\"And she nailed that flier flat on, too,\" Karl said with one of his seldom-seen grins. \"There's only one flier left, and it's hanging back pretty far.\"\n\n\"Good,\" Redwing said, getting up and straightening his uniform. He was always meticulous when on the bridge. \"But we're near the top of our mission profile, right?\"\n\nBeth checked. \"Yes, sir, got to turn around soon and head back down, run with the jet.\"\n\n\"That will lower our plasma influx pretty far,\" Karl said. \"We'll have a reduced exhaust.\"\n\n\"So the exhaust will be less useful as a weapon, certainly,\" Redwing said. \"Let's try to hover near our top limit, then. Can you do that, Officer Marble?\"\n\nRedwing also liked to get formal in tight situations. She had often wondered if in such moments he saw himself as fearless admiral at the helm of a battleship on tossing gray seas. Well, this was about as close to that as he was going to get, and as close as she ever wanted to be.\n\n\"Keep an eye on that flier as we make our turn.\" Redwing settled into his deck chair. He looked tired and gray to Beth, but so did they all now. Hours of dodging among the jet knots, harvesting them with split-second timing and then blowing the excess post-fusion plasma out the flexing nozzle as a weapon\u2014well, it added up fast.\n\nThe ship rumbled as she took it on a slow tipping angle. She was concentrating so didn't notice the beeping of the comm.\n\nKarl picked it up for her. His body went rigid and he glanced at his shocked face. \"It's... Tananareve, Cap'n. For you.\"\n\nHe grabbed it. \"Redwing here. How in\u2014?\" Redwing's face showed nothing as he listened. Then his mouth slowly opened and he stared into space. \"How did\u2014?\" More silence. \"So they'll let us go?\"\n\nBeth suddenly realized that this was a negotiation that could end all this madness. She kept SunSeeker in a tight helical turn, with a wary eye on the flier below, now approaching. Something told her that she should make some quick dodgy movements to make them a less predictable target. While hanging on Redwing's every word, of course.\n\n\"Okay, details later. Right.\" Redwing's entire body was tense now, on his feet, spine ramrod straight. He gripped his chair so hard, she saw his hand turn pale. \"What?\" The silence seemed long and unbearable, but she noticed the seconds on her situation screen were going by slowly. \"Roger. More later.\"\n\nRedwing turned to her and said, \"That flier behind us, take all the evasion you can. They're trying to shut down a weapon that's in armed and aiming mode right now.\"\n\nShe slammed the helm over hard and teased the fusion burn to its max. Then she released the bolus of searing plasma and wrenched the helm again, putting them into a flat spin, then a dive. Pops and creaks came echoing down the bridge from the connecting corridors. Karl's tablet escaped from the ridged worktable and smacked into the bulkhead.\n\nRedwing said, \"There's an electromagnetic precursor maybe two seconds before discharge. Look for that. Say again, Tananareve\u2014\"\n\nKarl flicked their EM antennas into one overlay, frequencies color-coded. Beth could see the flier as a dark point among hills and valleys of Technicolor richness. \"It's buried in all this plasma emission,\" Karl said.\n\n\"Integrate the whole spectral emission,\" Beth said. \"I don't know what frequency it will come out in, but if we\u2014\"\n\n\"Got it.\" A smooth topological surface appeared now in auburn colors, brown for valleys and nearly yellow at the peaks. The sky flexed like an ocean rolling with colliding wave fronts.\n\nShe fought the helm around again and let their speed drop a bit. This let her fill reserve chambers with incoming plasma and build to the max density they could carry. The jet wind was coming in at velocities over a thousand kilometers a second, and she could vary the inflow rate simply by moving the magscoop to angle it more fully into the stream. SunSeeker was working far from its optimal performance peak, which had been designed to run steady and smooth on interstellar plasma, orders of magnitude below the sleeting hail of knotty ionized matter rushing at them. Now she used, without thinking about it, the skills she had won from their flight up the jet when they arrived here. Through long hours she had fought violent currents, swimming upstream against conditions SunSeeker had never seen.\n\nNow she just let her instincts rule. Her hands and eyes moved restlessly, shaping plasma and bunching it. When she saw the holding chambers were full, she began to trickle more into the fusion chambers. The boost took them up jetward and to starboard as she waited for something strange to come at them.\n\nIt wasn't subtle. The maroon tones around the flier profile suddenly blossomed with a hard bright yellow peak. She fed the stored plasma into the chambers and goosed the drive. The helm slammed over, and she had time to shout \"Incoming!\"\n\nThe bridge shuddered and then wrinkled. She looked down the deck line and saw the bulwark ripple and flex. Pops and groans rose. Karl dove for the deck. She felt a tight pressure run through her like a slow, sinuous wave. Her stomach lurched. A deep bass tone rolled along the ship axis and\u2014\n\n\u2014it was gone. The bridge snapped back into straight lines and firm walls. The hail of small stressed sounds fell away.\n\n\"They missed us,\" Karl said.\n\nRedwing nodded. \"But what missed us? The deck got rubbery\u2014\"\n\n\"A space-time wrinkle, maybe,\" Karl said. \"I dunno how in hell anybody could make one, but\u2014\"\n\n\"Let me concentrate,\" Beth said. \"They could shoot at us again.\"\n\nShe dodged and swerved and dove and soared and plunged, and time stretched the way space had moments before. She heard nothing, saw nothing but the feeds that told her what the flier was doing. It cut her off on a side curve and flared more exhaust to draw closer. She countered with her own moves. All this she did with hands incessantly moving as her eyes looked for another of the hard bright yellow peaks. But it didn't come.\n\nThe comm beeped. Redwing answered. \"Oh. Good. What? Say again. Good. Great. You're sure. Okay. Terms come later, sure. Soon, yes.\"\n\nHe hung up and turned to Beth. She allowed her eyes to stray to him and she was shocked at how old he looked.\n\n\"They're standing down. No more pulses like that. Something called the Lambda Gun.\"\n\nShe opened her mouth to say something, and the comm beeped again.\n\nRedwing answered. \"What? Look at the star?\"\n\n\"Got it,\" Karl said. He and Fred, who had come onto the bridge, peered at the big screen.\n\nGeysers. The curve of the red star worked with furious energies. Flares and huge arches broke into space. Currents swept across the troubled crescent. Beth saw there was a dent in the perfect circle. Something had chewed it.\n\nKarl said, \"Look at these vectors.\" He had told the Kinematic Artilect to project an acceptance cone on the thing that had missed them. He had set the basic width to be a few times the jittering pattern Beth had followed to evade whatever the flier threw at them. Within the error bars, the cone snipped a bit off the star.\n\nRedwing frowned. \"Tananareve says the Folk call it a Lambda Gun. It does something with space-time, so if it just projected on\u2014\" He stopped. Facts trump words.\n\nThey watched the star adjust gravity against its internal pressures. Huge fissures opened and closed like snapping mouths. Fountains of restless plasma worked up in slender, vibrant yellow tendrils before curving and dying. The star flooded simmering masses into the gap, and waves spread from that. Fluids shaped by strong magnetic fields moved in complex eddies. Storms peeled off this and spread, tornadoes the size of planets.\n\nBeth let out a long slow breath, trying to get herself back into somewhat normal condition. She was tired and worn and completely confused. Coffee no longer helped. She needed a bath, too.\n\nShe stood, wobbling a little. \"Tananareve said more, Cap'n. I could tell. What?\"\n\n\"We've got a deal. They'll resupply us.\"\n\nGasps. Redwing shrugged and smiled, bobbing his head when the entire bridge burst into applause. \"Uh, yes. There's more. They want some of us, maybe enough to avoid inbreeding, to stay on the Bowl. The ones who actually run this place aren't those Folk at all. Those are like the local police on the beat, or middle managers in a bureaucracy. This thing is so old, something needs to live long enough to run it.\"\n\n\"Some aliens we didn't see down there?\" Beth asked, her vision bleary, bones aching now. \"Some kind of\u2014\"\n\nRedwing shrugged, as though he should have known all along. \"Ice Minds move slowly because they're cold. They keep the memories and experience, Tananareve said. They work with something called the Diaphanous, who manage the jet and the star.\"\n\n\"Plasma stuff?\" Karl said. \"Those were what made those sounds, that created those discharge arcs, that\u2014\"\n\n\"Killed Clare,\" Beth said. \"Trying to stop us from kinking the jet.\"\n\n\"The cold works with the hot, then,\" Karl said. \"The Folk are just local managers.\"\n\n\"They sure don't think so. They imagine they're the whole show,\" Beth said. \"Funny, really.\"\n\n\"So why did the Ice Minds, or whatever, let us live at all?\" Fred said. He had been silent the whole time but now seemed happy, smiling, eyes dancing.\n\n\"They need help with Glory,\" Redwing said. \"We can get there first, going full blast. We can reconnoiter. And talk to the Glorians, who think we humans are running the Bowl. They got our radio and TV, and since they were along the same line of sight, thought the Bowl was ours.\"\n\nBeth frowned. \"We have to?\"\n\n\"Part of the deal.\" Redwing smiled. \"Tananareve said it's pretty much take it or leave it.\"\n\nKarl laughed. \"No question, I'd say. We take it.\"\n\n\"They do want us to straighten out that standing kink. It's rubbing against the Knothole and it's gonna stay that way. But if we fly through it the right way, maybe we can bust it loose.\"\n\nKarl said dryly, \"There are better ways to put that, more precise. But I think with the fluences we have, and Beth as pilot, we can.\"\n\nBeth laughed, a bit dry. \"Beth the perfect pilot thinks she needs sleep. Lots of it. Then more coffee.\"\n\nRedwing smiled and finally sat down in his deck chair, more relaxed than she had seen him in a long while. He looked at the walls showing their situation and said, \"If we run down the jet, fix the Knothole plasma stall, then out\u2014well, we can loop around and come back into simple orbit.\"\n\nBeth scowled. \"Back into the cold sleep vaults?\"\n\n\"Some stay here,\" Redwing said. \"The Ice Minds want some new species to give the Bowl some stability. The Folk couldn't handle us, so they're out of the policing business. We get that.\"\n\nBeth nodded, knowing her piloting days were very nearly over.\nFORTY-EIGHT\n\nTananareve was tired when the incessant images and thoughts finally started to taper away. The Ice Minds had much to convey in their cool, gliding manner, but it was all so big and strange, she could not really think what to say. Mostly she just digested. Which was exhausting in itself. But one thing did puzzle her, and she asked about it.\n\n\"Why was your jet open to attack? I mean, it and the star and the Bowl\u2014it's an unstable system, has to be adjusted all the time or it falls apart. Anybody wants to do you harm, the jet is an open target, the heart of the system.\"\n\nSome confusion and delay. Soft pictures floated into her mind. The jet's filmy twisting strands working out from the star. Sometimes it snarled a bit, but the plasma clots called the Diaphanous adjusted that. They made the jet smooth out and glide tight and sure through the Knothole. All was well. Nominally.\n\n\"What's the idea of letting it be so vulnerable? I mean, we just came alongside you and slipped in, rode up the jet. We could've damaged it then, even by accident. But other kinds, other aliens, they might want to bring you down.\"\n\nSome did.\n\n\"What was your strategy then?\" She was tired, but what she learned could be useful. Redwing would want to know every damn detail.\n\nImagine a simple army's task, under imminent attack. They must find the part of their landscape best suited to strengthen their position when fighting in open battle. The answer is to fight on the edge of a sharp cliff. This gives their soldiers just two choices\u2014to fight or retreat, and in retreating to go over the cliff and die. Their enemy has different options\u2014to fight or flee. That option to flee makes the enemy's attack less likely to persevere. Placing yourself in peril makes you appear fearless. It gives your opponent cause to consider breaking off the battle.\n\nShe found this strange. \"So you put your backs to the wall and that's a defense?\"\n\nWe prefer to dissuade. We regret that the Folk, or rather one of them, used our final defense. Our Lambda Gun is immensely powerful. Luckily it was ineptly used. We have stopped its use and will punish those who erred so grievously.\n\nTananareve said nothing. She felt a rising, apprehensive note strike through her mind, and realized it was coming from the Ice Minds. They said, The Diaphanous now speak to those who caused this deep error. You should hear as well. A somber, rolling voice came then, not so much spoken as unfurled.\n\nWho is this that wrecks our province without knowledge?\n\nDo you know the sliding laws of blithe fluids?\n\nWere you here when the great curve of the Bowl shaped true?\n\nCan you raise your voice to the clouds of stars?\n\nDo fields unseen report to you?\n\nCan your bodies shape the fires of thrusting suns?\n\nHave you ever given orders to the passing stars or shown the dawn its place?\n\nCan you seize the Bowl by the edges to shake the wicked out of it?\n\nHave you journeyed to the springs of fusion or walked in the recesses of the brittle night?\n\nHave you entered the storehouses of the Ice Minds and found there tales of your long past?\n\nCan you father events in times beyond all seeing?\n\nYour answer to all these cannot justify your brute hands upon machines of black wonder.\n\nNor shall you ever chance to be so able again, for you shall be no more.\n\nThe space and time you sought to dissolve shall reckon without you hence.\n\nTananareve knew somehow this came from the invisible ones who dwelled in the jet. She did not understand any of this. She just sighed and put such troubles away as she gratefully slipped into sleep.\nFORTY-NINE\n\nMemor watched the great floods sweep across lands that had held towns and forests and would now be swamps. Great constructions from far antiquity were undermined and slumped. Under great magnification, from this satellite view, she studied the rooftops of homes and city centers. There were no survivors awaiting rescue. A few boats bobbed here and there, but not many.\n\n\"It is a tragedy, indeed,\" Bemor said. He looked tired, surely from the work of keeping the Ice Minds in touch with the primates, funneled through the mind of the poor Tananareve. \"But we are demanded at the leaving ceremony. Come.\"\n\n\"Who demands this? I do not wish to witness such.\"\n\n\"The Ice Minds command. Their attitude has changed substantially. I do not sense their goodwill toward us any longer.\"\n\nMemor bristled and gave quick fan-signals of rebuke and mild anger. \"The crisis faded away, yes? And we surely played a role.\"\n\n\"Of a kind.\" Bemor gave a feathered signature of drab purple resignation, and wheezed a bit. \"Come. And bring your primates. The Ice Minds wish them to see this.\"\n\n\"They have rested and eaten,\" Memor said. \"Perhaps they will profit from witnessing.\"\n\nThey entered the Citadel of the Dishonored to see Asenath's end. She would be churned into the great matrix of dead plants and animals, so the dishonored could enhance topsoil. Memor and Bemor plodded into the high, arched atrium, where subtly hidden machinery murmured, managing the bacterial content, acidity, and trace elements of the slowly roiling mud-fluid below the Pit. First the Pit, then the Garden: the fate of all.\n\n\"I disliked Asenath,\" Memor whispered. \"But she did have talent.\"\n\nBemor said, \"Insults are best not remembered. She was sure of herself and had no thought of consequence.\"\n\nStill, Memor needed to consult her Undermind to help her get through this. Calling the extinction of one she had worked with \"a just recycling\" did little good.\n\nThe primates followed, and the Sil. Bemor remarked, \"They show few signs of the early stages of Adoption. Perhaps we'd best be rid of them.\"\n\n\"I believe the Ice Minds will not allow any executions or harm to them,\" Memor said. \"Or the Sil, though we could build a case against them.\"\n\nBemor flashed vigorous objection. \"The Ice Minds were behind the Sil actions. They wished the humans brought to them, without our knowing such intent.\"\n\n\"Ah, so the Sil are invulnerable, as are the primates. I dislike profoundly having our command of these creatures revoked for the sake of a passing problem\u2014\"\n\n\"It is not passing. Asenath's Lambda Gun pulse passed along the jet for a considerable distance. It intersected portions of several of the Diaphanous. One was killed, the others injured. These could self-repair, with help of others who could lend portions of their own anatomy. To damage the Diaphanous is to endanger the jet and thus the Bowl.\" Bemor's grave voice boomed. \"An example must be made.\"\n\nMemor saw Asenath being led to the Pit and recalled when she herself had faced the prospect of oblivion. Asenath had been disappointed at Memor's being spared, and had allowed a pitch of reluctance into her later comments. Now Asenath faced the yawning black Pit at the center of the Vault. The sentence was read and Asenath gave no reply, or any mournful yips and drones. Her feathers were a muted gray and hung lifeless. Her fate spread before her in the green slime before the final descent. Deep long chords sounded.\n\nVarious religious figures were there, clad in ancient Folk grandcloth. They urged Asenath to convert to their faiths, here in her last moments. Memor recalled that through its history the Bowl had passed by worlds where creatures shaped like ribbons or pancakes held sway. These the ancients had termed Philosophers, for they had little tool-using ability. Such fauna were deeply social and spun great theories of their world, verging into the theological. To Memor philosophy was like a blind being searching a dark room for an unknown, black beast. When philosophy verged into theology, it was like that same predicament, but the black beast did not even exist, yet the search went on. Asenath waved the religious Folk away, giving a fan-flutter of rejection.\n\nAsenath declined a final statement; then her feather-crown altered to deep gray. She raised her head and said, \"We die containing a richness of lovers, and characters we have climbed into, as if trees. I have marked these on my body for my death. Then I go into the Great Soil.\"\n\nMemor wondered at this. No one would see such inscriptions. Perhaps it was a declaration Asenath hoped would somehow make its way into Folk-lore?\n\nHead held high, with a resigned shrug, she simply stepped off the edge and slid down into the disposal hole. She had never looked at the crowd of witnesses.\n\nMemor could smell a fear among the primates; she had nearly forgotten them. She reassured them that this was to educate them in the ways of the Bowl and the Great Soil to which all must return.\n\nA primate vomited at the sight and smell of the execution, spattering vile acid. Memor saw it was Tananareve, who she recalled had learned some of Folk speech. These creatures were smarter than she had supposed, as recent events revealed.\n\nThere was a long silence after the ceremony. Bemor said to the primates, \"We have strict justice for all here.\"\n\nTananareve said, \"It looks like you're ruled by those Ice Minds. They can order executions?\"\n\nBemor said, \"The Bowl would fail if there were not an authority who could override the passing opinions of individuals. Or of species. Your own ship has a Captain.\"\n\n\"I never thought it would be a pleasure to see Redwing again,\" Tananareve said. \"But life is full of surprises.\"\n\nThey all\u2014Cliff, Irma, Terry, Aybe\u2014laughed hard and long at this. Memor saw that this eruption came from great internal pressures, now released.\n\n\"We shall have to be careful with these primates,\" Bemor whispered in Folk speech. \"They are few and we are merely many trillions.\"\n\nHe and Memor laughed with deep, rolling tones of relieving tensions. In not too long a time, they would remember Bemor's joke with little humor.\nPART XIV\n\nMEMORY'S FLICKERING LIGHT\n\nThe natural world does not optimize, it merely exists.\n\n\u2014KEN CALDEIRA\nFIFTY\n\nBeth yawned and stretched and looked at the big foaming breakers curling onto a beach, splashing with a churning roar out to the edge of her wall. Relaxing lapping ocean sounds were a pleasant wake-up call. She had surfed there once a century or so ago and very nearly drowned. Her wrenched back had taken a while to stop complaining.\n\nNow her muscles ached and spoke to her of her many hours in the lead pilot's chair on the flight deck. They hadn't enjoyed it, and neither had she. More fun to get worked over in a wave, she thought fuzzily. I wonder if there are surf-worthy waves somewhere on the Bowl? Maybe when a hurricane's running somewhere, safely far away...\n\nShe got up and trooped down to the head and spent three days' allotment of water on a hot shower. It helped ease her back muscles, and she could think again, too. About how to deal with Redwing and Cliff and all the open doors she was about to slam shut.\n\nShe slumped through the mess in her bathrobe, ignoring Fred, who was reading his tablet anyway, and scored a big coffee hit in her extra-size cup. Then back in bed and the wall now running a restful English village, with enough background sounds of breeze and birds to let her forget the ghastly silence aboard SunSeeker.\n\nIt wasn't easy for SunSeeker's chief pilot to ignore the quiet. SunSeeker was at rest, motors down, shields down. Only a pattern in the Bowl's magnetic fields protected her from a flood of interstellar radiation. And an alien magnetic pattern, the Diaphanous, was shaping that.\n\nThe silence was eerie, after she had spent so long under its background working rumble. Now came a massive, heavy thump. A tanker, she thought. Tankers and cargo craft were a cloud around SunSeeker, and there were thumps and scraping as one or another mated to the ship and masses moved through air locks. Some robots dispatched by the Folk clumped and clanked across the hull on magnetic graspers.\n\nShe took a sip and shut out the fevered world.\n\nE-mail first, to get up to speed after ten hours in the sack. She plunged in. The very first was a slab of homework from Tananareve. She had craftily recorded nearly all her interactions with the Ice Minds, at least those rendered in speech within the machine they had her trapped in. She had asked them to use audio rather than somehow making a voice resound in her mind. In the middle of the transcript, captured on her phone and patched up by a shipboard Artilect, was a nugget.\n\nYou must realize that Glory is not a true planet but rather a shell world. Many different species of intelligent Glorians live on concentric spheres, with considerable atmosphere spaces between them. Many pillars support this system, and powerful energy sources provide light and heat. Entirely different life-forms inhabit the differing spheres. The innermost shells support life without oxygen. These kinds come from deep within ordinary worlds, creatures of darkness and great heat. Some species have made their spheres into imitations of whatever their best-loved environments are. At the very top is a re-creation of a primitive oxygen world, flush with forests and seas. This outer shell your astronomers have studied. You conclude that Glory is a succulent target for a colony. That upper layer is deceiving, perhaps deliberately so\u2014we do not know. Certainly Glory is not a simple prospect for your kind.\n\nThe Glorians who constructed this shell paradise of theirs also communicate on scales of the galaxy itself. They do not use simple electromagnetics, as you do. There are many worlds, many of them ruled by machine intelligences, who use electromagnetics over stellar scales. Emitting in these ways reveals an emergent society capable of beginner technologies. Most keep silent, their radiated power low, fearing unknown perils. We often found such silent planets. We were drawn to worlds we knew by distant examination were life-bearing, yet electromagnetically quiet.\n\nThe Glorians disdain such societies. They wish to speak, over many long eras, with greater minds\u2014those who can blare forth using gravitational waves. Those waves are far harder to detect and stupendously more difficult to emit in coherent fashion, to carry messages. Here again, to radiate at all is a show of power.\n\nThese signals you primates have detected but cannot translate. That is unsurprising. So thus have many minds discovered, over many millions of your years. Some of these who hear but cannot understand gravitational waves, the Bowl encountered long ago. The gravitational message landscape is an intricate puzzle few solve.\n\nWe Ice Minds have unraveled the Glorian waves, with the help of the Diaphanous. It was a lengthy labor. They are strange, intriguing, and imply much more than they say. We now wish to know the Glorian Masters ourselves, to join in their company. That is why the Bowl now feels itself ready to approach. Before, we did not dare.\n\nFor you primates to dare is surely folly.\n\nBeth took a deep breath and watched people from another century\u2014when she grew up, of course\u2014walk down the streets of the English village, the sea breeze sighing, birds all atwitter. So the Ice Minds were making their case for some of SunSeeker's passengers to stay. Fair enough. The problem was going to be Redwing.\n\nNext came data and text from Tananareve and ship Artilects, dissecting the events with the Diaphanous.\n\nKarl and the Theory Artilect had worked out some ideas about what the hell the Diaphanous beings who had killed Clare could be. Self-organizing magnetic fields, smart bellies full of plasma, harvesting energy from the jet? And bigger than planets? Well, the jet was a puzzle, and managing it seemed beyond the Folk. She and the others had ignored that problem, now pretty obvious once you thought of it. Who mustered solar storms to the jet base? Who got the mag fields aligned so the jet was under steady control?\n\nSomething big. Beth tried to envision what would radiate waves kilometers long. That could induce enormous electric fields inside SunSeeker, and sound waves, too. To such creatures, humans might be as inconsequential as the lice that pestered the skin of a blue whale.\n\nWithout the Diaphanous, the whole Bowl system was impossible. Want someone to manage a star? Take the children born in stellar magnetic arches, evolved there. Hire the locals.\n\nEnough. She left off the reading to get ready for her appointment with Redwing. Time to don the battle uniform, gal.\nFIFTY-ONE\n\nThe worst part about the free-bounding exercise he did in zero grav was the sweat. Sweat didn't run. Redwing clung to a stanchion and mopped some from his eyes, but it was hard to get it all. Some covered his eyes in lenses. Blinking only made his image of the big craft bay wobble. Then his belt rang, reminding him of his appointments with Karl and then Beth.\n\nKarl was waiting. Redwing hated showing up late for a crew appointment, but he had needed the exercise to clear his mind. As they went into his cabin, he saw his wall was running their real-time view. He was glad to see they had rounded the Bowl lip and so could see the Knothole region again. Radiation remained near zero as the Diaphanous sun dwellers' mag shield followed their orbit. Redwing could not imagine magnetic stresses that could grasp and guide a starship of a thousand tons, but he was getting used to the apparently impossible.\n\nKarl grinned. \"It's been a hell of ride. The way Beth drove us down into the cinch point of the Knothole, and then stood us here, blasting plasma out the back and pushing the standing kink over toward center, into a straight line\u2014wow. Just, wow.\"\n\nRedwing nodded. \"The finger snakes loved it, too. They're bright, seemed to know a lot about how the jet works. I've seen piloting but never like that. We owe her one.\"\n\n\"Maybe more than one,\" Karl said, but Redwing let it pass.\n\nKarl studied the hurricanes visible on long-range scopes. They were beyond spectacular, when you adjusted for scale. In the fractured zones near the knothole, the seas were giving up their moisture to the lowered atmospheric pressure. An enormous hurricane fed on the air pressure drop, a quickening drift toward the ruptured atmospheric envelope.\n\n\"Maybe we need a new term,\" Karl said. He stood and pointed on the wall. \"See, those eddies form in the big churning spiral, then spin off into hurricanes. It's a fractal fluid turbulence.\" He increased screen resolution. \"So those too fling out smaller hurricanes, and so on down to some scale more like Earth's puny varieties.\"\n\n\"So more and more of them dance out their fury on the life below,\" Redwing said, musing.\n\n\"They'll take a while to patch the tears.\" Karl turned away, shaking his head. \"We really went too far.\"\n\nThere was business to do, but he asked instead, \"A celebration seems in order\u2014the old eat, drink, and be merry. Plus we're all tired. Let's let the Artilects take over, say two hours from now, and muster the crew.\"\n\nKarl nodded, distracted. Redwing reflected that at tonight's party, the entr\u00e9e steak would not be meat, the wine would be water plus a grape extract and alcohol, and the water was fashioned from their collective piss. After all the deaths, maybe being merry was the hard part.\n\n\"Cap'n, this blizzard of info we're getting from Tananareve and the Folk\u2014it's hard to digest. We're getting their point of view, and I try to cock it around to our line of sight.\"\n\n\"They're old, we're young. To be expected.\"\n\nKarl gave a wry smile. \"Some of these messages, I sort of feel that they should have a space for 'fill in name, address, and solar system'\u2014it's hard to grasp their assumptions.\"\n\n\"And so, hard to know how to negotiate with them?\"\n\n\"Damn right. Look, the Bowl is on a journey that takes it all over a chunk of the available galaxy. They should've settled most of the local arm by now. But these Bird Folk, they're deeply conservative. They don't seem to leave colonies.\"\n\nRedwing pursed his lips, sat back, and watched the super-hurricane grinding on. He tried not to think about what was happening below them. His work...\n\n\"Um. They say that's because the Bowl is perfect, suited for the smart dinosaurs that built it. Warm, stable, predictable weather. They don't want to leave it. So?\"\n\n\"Then who's doing the exploring? The Folk don't want to advertise this, but it's pretty clear. They tried colonies and failed. After millions of years in this nice, steady place\u2014heaven, right?\u2014they don't work out well on planets.\"\n\n\"But they say they keep track of every star they've visited. That's how they knew what was going on, the Great Shame, all that.\"\n\nKarl leaned forward with a thin smile. \"It's the Ice Minds. They think slow, they live slow, but there's still room for boredom. They've left some of themselves in the local Oort clouds, all over this galactic arm. Plus Earth's. They like it, there's no weather there. Stable, gives them lots of data, propagates the species, too.\"\n\n\"And the Folk?\"\n\n\"They're the caretakers. They pick up some new species every million years or so, but mostly they just lord it over all the other species on the Bowl\u2014the Adopted, they call them.\"\n\n\"And we're the new kids on the block?\"\n\n\"Wait'll you see this.\" Karl clicked his tablet and flashed a picture on the opposite wall. A view of two spheres orbiting each other, black and white. A simulation, too clean to be real.\n\n\"The Ice Minds think the Glorians have a binary-charged black hole system, Tananareve says. It looks like this, they say. Since the black holes are basically very large charged particles, you could control their orbits with very large electromagnetic containment fields. That avoids collision of the black holes. But then they swerve them a little, so the near misses generate intense gravitational waves. That's the Glorians' communication link with other big-time civilizations in the galaxy.\"\n\n\"And the Ice Minds want in on the conversation?\" This was getting stranger than he liked.\n\n\"Social climbers, yes. They want to meet the adults, looks like.\"\n\nRedwing frowned. \"But they can't have black holes around the Bowl. Too dangerous.\"\n\n\"Maybe so, but\u2014these black holes are small, maybe a few meters across.\"\n\n\"That small? It's still massive.\"\n\n\"Right, around a hundred times more massive than Earth. Oh, and\u2014the Glorians made the holes, too.\"\n\n\"What!\"\n\n\"The Ice Minds want to find out how.\"\n\n\"And we're headed there....\" Redwing wanted to think this through, but a polite knock told him it was time for Beth.\n\nKarl said, \"I was talking to Fred just now and he made an interesting point. Remember when we all were approaching the Bowl? Flabbergasted, sure. But now, Fred says to him it's been like a twisted encounter with the eventual human future.\"\n\n\"That makes no sense.\"\n\n\"In a tilted way\u2014in Fred's style of thinking, anyway\u2014SunSeeker left an Earth already pretty well worked over by the human hand. Remember? Sunlight reflected by sulfur dioxide particles shimmering in its stratosphere, so at the right angle we could see it from space. Clouds of seawater mist billowing up from those small sail ships, to shield oceans from sunlight. Big carbon collector towers, stretching out across continents. Farm waste rounded up and consigned to the deep ocean, where it'll keep for a thousand years. Throwing fine-ground chalk into those oceans every year, remember that?\u2014in masses equal to the white cliffs of Dover.\"\n\nRedwing nodded, recalling the furiously working fretwork of corrections. \"Right, to offset the acid from absorbed CO2. I was in deep space for decades, running hot nukes. Made no difference to us.\"\n\n\"Me, too, mostly. Somebody else's problem, and we had plenty of our own, running closed biospheres.\" Karl gave a wry shrug.\n\n\"That was pretty much taking on an infinite career, endlessly shaping habitat. So I see Fred's point\u2014why didn't he come with you to lay it out?\"\n\nKarl gave Redwing a skeptical arched eyebrow. \"You don't know he's scared of you?\"\n\n\"He does seem a bit quiet.\"\n\n\"He's not when you're absent. His point is, someone or some thing faced those same problems long ago. They built the Bowl to be a better place. Got tired of planets, probably. Wanted to venture into the night sky, but in no hurry. So they took a big fraction of the species with them. Left behind the stay-at-homes.\"\n\nRedwing liked this. \"You and Fred are saying they wanted managed landscapes that seemed natural. All nice and dinosaur-friendly warm, under a constant reddish sun. Plus its amigo, the jolly jet.\"\n\nKarl chuckled. \"God knows what Earth looks like now, centuries into running its biosphere.\"\n\n\"Is this a way of saying you and Fred want to stay on the Bowl?\"\n\n\"Not at all!\"\n\n\"Um. So what do I do with this new input?\" He disliked asking advice from crew, but at least they were alone. \"How does it affect going to Glory?\"\n\n\"I thought you should hear what the crew thinks. Time's up, I know.\" Karl stood and saluted. \"I want to go see the show at Glory, sir. Sail on.\" He left.\n\nWhen Beth came in, he could see her jaw set at a determined angle. She had looked that way through the long hard hours straightening the standing knot. When it was done, she had barely made it to her quarters.\n\n\"Captain, I formally request transfer to the colony on the Bowl.\"\n\n\"Colony?\" Things were moving too damn fast.\n\n\"The Folk\u2014okay, they're just speaking for the Ice Minds now\u2014they say Cliff's team all want to stay. I want to join them.\"\n\n\"Look, I can't have crew leaving. We need a sharp pilot\u2014\"\n\n\"Warm one up. I'm a biologist first, just a backup pilot, really.\"\n\n\"You're our best! The way you flew us\u2014\"\n\n\"Then it's payback time, Captain. You made the deal with the Folk, right?\"\n\n\"Not the Folk, no. The Ice Minds and the Diaphanous, actually, seems like.\"\n\n\"You have to leave some of us on the Bowl, then. So leave enough to reproduce without inbreeding.\"\n\n\"The genetic stores\u2014\"\n\n\"Need enough founding population to reduce risk, even with the genetic augmentations from the database. That's at least a hundred people, no, several hundred. Defrost them while we're resupplying.\"\n\n\"You want a\u2014\"\n\n\"Colony. That's what we were sent for.\"\n\nRedwing told himself to stay steady, calm, but his heart thumped harder. \"I'll have to do that anyway, Beth. The finger snakes want to ride with us. Just the three, a male and two females; they don't seem to have an inbreeding problem. But fifty Sil have already been picked. There are other species who might want to board. The Artilects say they can rework the freezer capsules, but some of our passengers will have to stay awake longer than optimal.\"\n\n\"You've got room for a bigger live crew, don't you? You're launching fully provisioned, yes? We're already near relativistic speed.\"\n\n\"Faster than that. We'll fly up the Jet and get a boost from rounding the sun. Sure you want to miss that?\"\n\n\"I'm sure. I'm the one who wants to stay, Captain. Cliff is going along with that.\"\n\nRedwing sighed. \"Then there's no room for Bird Folk, of course, except as fertilized eggs and an artificial womb\u2014but they want that, and it's a big volume.\"\n\nBeth's mouth twisted. \"After all they did to us?\"\n\n\"It's part of our deal. Those Folk don't run the Bowl, they're more like the cop on the beat\u2014\"\n\n\"Corrupt cops. They kill other species to keep some equilibrium of theirs running. It's a murderous regime. They chased us, imprisoned us\u2014\"\n\n\"We'll be carrying them because we could hardly carry Ice Minds. Though we will have a Diaphanous\u2014more on that later, when it's worked out.\"\n\n\"But your charge Earthside wasn't to pick up aliens and carry them\u2014\"\n\n\"You have to adjust your initial launch orders to the situation. Beth, I'll have to download nearly half our passengers, and how do I pick them? It isn't as if I could thaw them and let them choose. They get no more vote than the unborn.\"\n\nBeth said, \"Pick mated couples. Pick the ones who wanted to colonize rather than explore. We were tested for attitudes.\"\n\n\"We were all picked for adaptability. Even so...\"\n\nShe leaned forward, smiling. He sat back, a little mouth twitch telling her he found that a bit strange. \"Look at our larger aim\u2014to get humanity out into the galaxy. Play the big game. This way we have two colonies.\"\n\n\"Glory's a bigger game,\" he said. She hadn't heard Karl go on about the black hole radiator theory, but no doubt she would in the mess, later, when the reconstituted booze started flowing.\n\n\"Glory's not our kind of game, I'd guess. Not yet.\" She shrugged ruefully. \"It's maybe a league up from what we can handle. The Bowl was tough enough.\"\n\nRedwing knew enough to wait. Her voice became soft, almost sympathetic. \"But we'll get there. The Bowl will get our first human colony to Glory. Long after I'm dead, sure\u2014and I'm hoping to reach two hundred. Hell, more! But we humans, we'll get there. And be waiting to meet up with you.\"\n\nRedwing frowned. \"I have orders.\"\n\n\"And crew. You'll have nearly a thousand left in cold sleep. Plus, y'know, not all our people on the ground down there want to stay. Tananareve doesn't! She's had enough of the Folk, thank you.\"\n\n\"Okay, I heard that. You want to reunite with Cliff, too. So you'll join this Bowl colony you want.\"\n\n\"Right. But not because of Cliff, especially. He's important to me, sure, but\u2014oh, that's right. You probably know from the field reports\u2014somebody must've blabbed, though it's obvious\u2014 He's been screwing Irma.\"\n\n\"Well, I'm not prepared to reveal\u2014\"\n\n\"You don't have to. Put people under dire threat for many months, and the prospect of death makes them set about being sure there's going to be a replacement. Plus it feels good when the world threatens you. Hey, I'm a biologist.\"\n\n\"I know. And Irma's coming with us. So is her husband. You don't\u2014?\"\n\n\"I don't mind. Irma, Cliff\u2014that was a 'field event,' as we used to call it. Whatever works in a pinch, I say. And... isn't that party you talked about earlier about to start?\"\n\nA big sunny smile. And she gave him, unmistakably, a wink.\nFIFTY-TWO\n\nHe got back to his cabin only a bit squiffed. Odd term, squiffed. He had inherited it from his grandfather, who had never given a definition. It was pretty clear, though. Pleasantly inebriated but in control. As a captain should be.\n\nRedwing also recalled a parting remark from his commanding officer, just before he took the shuttle out to SunSeeker for his last transfer. Remember that people break down, too, not just machinery. You had to give them room.\n\nThere was plenty more to being a captain than bulldog stubbornness. Beth was good at giving him a different angle on events. It had been fun seeing her play with the finger snakes tonight. Who knew that they liked alcohol, too? There had been a lot of laughter, the pure long gasps that meant pressures were easing somewhere deep inside.\n\nBeth was good, quite so. But she hadn't seen that the Ice Minds wanted Tananareve to go forward to Glory on SunSeeker, as part of their exploratory advance party. Tananareve would be able to report back to the Folk\u2014or maybe directly to the Ice Minds?\u2014in an intuitive way. Better than the rest of the rude invader primates, since now they knew how her mind worked.\n\nHe still hadn't told Beth all of it.\n\nThe ship would run up the jet, gulping plasma, boosting hard, and as it flew past the sun, SunSeeker would gain one more passenger. A Diaphanous would ride the motor. The Diaphanous thought that was a fresh opportunity, helping shape the magnetic geometry and exhaust parameters, while clinging to the ship and its scoop geometry. They'd never tried such a lark before. And maybe they wanted to meet up with the Diaphanous species on yet another star? Redwing suspected he would never truly know their motives.\n\nSunSeeker's Artilects had already been brought up to speed on that. Would a magnetic pattern obey a ship's captain?\n\nThat problem could wait. He shrugged off his uniform and decided to shower in the morning. He brushed his teeth and dropped the plastic glass as he tried to dump the waste rinse water into the tiny bowl his cabin alone had. Was he losing his ability to process alcohol? Well, so be it. After all, he was somewhere in his eighties.\n\nHe stared into the Bowl. They had called this huge artifact Wokworld when they first found it, but names were just pigeonholes. The feeling he had gotten, at first glance, seeing the vast spinning machine at a distance, was of some parasite grasping a star, sucking life from it. And charging forward, too, using that raw energy to move, forever restless, onward into the great night.\n\nBeth had been a quick, sharp slap in the face today. She had made him see the bigger view of what they were here for. He owed her for that. And he would miss her, he just now realized.\n\nShould he just stay here, dock SunSeeker somehow, and join the happy guys down on the Bowl? No. He had a clear duty and he would carry it out, even if all those who had ordered him were dead.\n\nThe biggest mistake is being too afraid of making one, he had heard somewhere in his Fleet training. Somehow in this evening, with Beth's help, he had made a lot of them.\n\nOn his wall he called up the real-time view of the landscape passing below them. They were headed for a good place to rendezvous with the lander they had sent down. The Folk would put Tananareve on board\u2014and Aybe, who had just changed his mind; tech types often did. The Folk would send up supplies, and it shouldn't take long to mate their comm gear with SunSeeker's, so they could stay in close touch with the Bowl, and get going again. Bound for Glory.\n\nYes\u2014squiffed he was. Indeed, sir. Onward.\n\nThis Bowl was not so strange, after all. Maybe it meant that really advanced societies overshot their agenda, gliding for a while in the enameled perfection of their way of life, following habits deep-grained and evolved long before. So they correct and modify and engineer and correct again. Build big and think big and think again. The Bowl was the first big strange idea humanity had really met\u2014terrifying and intriguing. And among many yet to come. Of that he was sure. Terrors can be mirrors, too.\n\nDetails. The tortured landscapes below passed before his eyes like an unending scroll. He thought of how the decisions that seem momentous in the moment, or even over a lifetime, were flickering instants in the life of the Bowl. These matters were too small to be observed by the Ice Minds, just single passing lives.\n\nThe Bowl had made them look back across a gulf of not mere centuries or millennia, but on the grand scale of evolution itself. Maybe that was the true deep purpose of coming out here among the stars. To see times that glowed and shimmered in memory's flickering light.\n\nHe had a thought. Was there more than one Bowl, coasting around the galaxy? Maybe such things were a technological niche that others thought of and inhabited\u2014very-long-view things, hard to quite grasp for humans. Maybe if alien species had the right precursor society\u2014that of those smart dinosaurs, who loved warmth and sun and stillness\u2014then their love of a forever summer would make them build such contraptions. If so, the blunt hammer of evolution gave another strategy to gain the stars, one different from smart, talky primates.\n\nWhatever waited at Glory, in its stacked levels, there was a biosphere on top, a place to love beneath a star that had a sunset every day. Beings who lived in layers would be strange indeed, and humanity would have to adapt. Redwing smiled. If the Bowl had taught him anything, it was about human versatility. He would be alert when he reached Glory after a long sleep, and he liked his odds.\n\nIt couldn't be stupid to voyage out in small vessels, to distant worlds where beauty and happiness would get redefined again and again. Even if Earth became a distant and perhaps wistful memory\u2014as all his crew and himself would inevitably be, for sure\u2014the expansion of human horizons was an ultimate good. Whatever built the Bowl had believed that, too. There was something comforting in that thought alone.\n\nTime for bed.\nAFTERWORD\n\nBIG SMART OBJECTS\n\nI. HOW WE BUILT THE BOOKS\n\nGregory Benford's take\u2014\n\nIn science fiction, a Big Dumb Object is any immense mysterious object that generates an intense sense of wonder just by being there. \"The Diamond as Big as the Ritz\" by F. Scott Fitzgerald is a non-SF example. They don't have to be inert constructs, so perhaps the \"dumb\" aspect also expresses the sensation of being struck dumb by the scale of them.\n\nLarry said to me at a party, \"Big dumb objects are so much easier. Collapsed civilizations are so much easier. Yeah, let's bring them up to speed.\"\n\nSo we wrote Bowl of Heaven, deciding that we needed two volumes to do justice to a Big Smart Object. The Bowl has to be controlled, because it's not neutrally stable. His Ringworld is a Big Dumb Object since it's passively stable, as we are when we stand still. (Or the ringworld would be except for nudges that can make it fall into the sun. Those are fairly easy to catch in time. Larry put active stabilizers into the second Ringworld novel.)\n\nA Smart Object is statically unstable but dynamically stable, as we are when we walk. We fall forward on one leg, then catch ourselves with the other. That takes a lot of fast signal processing and coordination. (We're the only large animal without a tail that's mastered this. Two legs are dangerous without a big brain or a stabilizing tail.) There've been several Big Dumb Objects in SF, but as far as I know, no smart ones. Our Big Smart Object is larger than Ringworld and is going somewhere, using an entire star as its engine.\n\nOur Bowl is a shell more than a hundred million miles across, held to a star by gravity and some electrodynamic forces. The star produces a long jet of hot gas, which is magnetically confined so well, it spears through a hole at the crown of the cup-shaped shell. This jet propels the entire system forward\u2014literally, a star turned into the engine of a \"ship\" that is the shell, the Bowl. On the shell's inner face, a sprawling civilization dwells. The novel's structure doesn't resemble Larry's Ringworld much, because the big problem is dealing with the natives.\n\nThe virtues of any Big Object, whether dumb or smart, are energy and space. The collected solar energy is immense, and the living space lies beyond comprehension except in numerical terms. While we were planning this, my friend Freeman Dyson remarked, \"I like to use a figure of demerit for habitats, namely the ratio R of total mass to the supply of available energy. The bigger R is, the poorer the habitat. If we calculate R for the Earth, using total incident sunlight as the available energy, the result is about twelve thousand tons per watt. If we calculate R for a cometary object with optical concentrators, traveling anywhere in the galaxy where a zero magnitude star is visible, the result is one hundred tons per watt. A cometary object, almost anywhere in the galaxy, is 120 times better than planet Earth as a home for life. The basic problem with planets is that they have too little area and too much mass. Life needs area, not only to collect incident energy but also to dispose of waste heat. In the long run, life will spread to the places where mass can be used most efficiently, far away from planets, to comet clouds or to dust clouds not too far from a friendly star. If the friendly star happens to be our Sun, we have a chance to detect any wandering life-form that may have settled here.\"\n\nThis insight helped me think through the Bowl, which has an R of about 10\u221210! The local centrifugal gravity avoids entirely the piling up of mass to get a grip on objects, and just uses rotary mechanics. So of course, that shifts the engineering problem to the Bowl's structural demands.\n\nBig human-built objects, whether pyramids, cathedrals, or skyscrapers, can always be criticized as criminal wastes of a civilization's resources, particularly when they seem tacky or tasteless. But not if they extend living spaces and semi-natural habitat. This idea goes back to Olaf Stapledon's Star Maker:\n\nNot only was every solar system now surrounded by a gauze of light traps, which focused the escaping solar energy for intelligent use, so that the whole galaxy was dimmed, but many stars that were not suited to be suns were disintegrated, and rifled of their prodigious stores of sub-atomic energy.\n\nOur smart Bowl craft is also going somewhere, not just sitting around, waiting for visitors like Ringworld\u2014and its tenders live aboard.\n\nWe started with the obvious: Where are they going, and why?\n\nAnswering that question generated the entire frame of the two novels. That's the fun of smart objects\u2014they don't just awe, they also intrigue.\n\nMy grandfather used to say, as we headed out into the Gulf of Mexico on a shrimping run, A boat is just looking for a place to sink.\n\nSo heading out to design a new, shiny Big Smart Object, I said, An artificial world is just looking for a seam to pop.\n\nYou're living just meters away from a high vacuum that's moving fast, because of the Bowl's spin (to supply centrifugal gravity). That makes it easy to launch ships, since they have the rotational velocity with respect to the Bowl or Ringworld... but that also means high seam-popping stresses have to be compensated. Living creatures on the sunny side will want to tinker, try new things....\n\n\"Y'know, Fred, I think I can fix this plumbing problem with just a drill-through right here. Uh\u2014oops!\"\n\nThe vacuum can suck you right through. Suddenly you're moving off on a tangent at a thousand kilometers a second\u2014far larger than the 50 km\/sec needed to escape the star. This makes exploring passing nearby stars on flyby missions easy.\n\nBut that easy exit is a hazard, indeed. To live on a Big Smart Object, you'd better be pretty smart yourself.\n\nLarry Niven's take\u2014\n\n\"The Enormous Big Thing\" was my friend David Gerrold's description of a plotline that flowered after the publication of Ringworld. Stories like Orbitsville, Ring, Newton's Wake, John Varley's Titan trilogy and Rendezvous with Rama depend on the sense of wonder evoked by huge, ambitious endeavors. Ringworld wasn't the first; there had been stories that built, and destroyed, whole universes. These objects often become icons of larger issues implying unknowable reaches and perspectives. Their governing question is usually, \"Who built this thing? And why?\" They had fallen out of favor.\n\nI wasn't the first to notice that a fallen civilization is easier to describe than a working one. Your characters can sort through the artifacts without hindrance until they've built a picture of the whole vast structure. Conan the Barbarian, and countless barbarians to follow, found fallen civilizations everywhere. I took this route quite deliberately with Ringworld. I was young and untrained, and I knew it.\n\nA fully working civilization, doomed if they ever lose their grasp on their tools, is quite another thing. I wouldn't have tried it alone. Jerry Pournelle and I have described working civilizations several times, in Footfall, Lucifer's Hammer, and The Burning City.\n\nWith Greg Benford, I was willing to take a whack at a Dyson-level civilization. Greg shaped the Bowl in its first design. It had a gaudy simplicity that grabbed me from the start. It was easy to work with: essentially a Ringworld with a lid, and a star for a motor. We got Don Davis involved in working some dynamite paintings.\n\nGreg kept seeing implications. The Bowl's history grew more and more elaborate. Ultimately I knew we'd need at least two volumes to cover everything we'd need to show. That gave us time and room.\n\nII. FUN WITH HIGH TECH\n\nWarning: some plot spoilers lurk here.\n\nOur first book, Bowl of Heaven, set up reader expectations and introduced the Folk who ran the place\u2014or thought so. That let us wrap up storylines in the sequel, Shipstar, in part by undermining the expectations built up in Bowl of Heaven. We chose to write all this in two volumes because it took time to figure out. The longer time also let us process what many readers thought of Bowl of Heaven, its problems and processes.\n\nMuch of this comes from the intricacies of how the Bowl came to be built. Plus its origins.\n\nWe supposed the founders made its understory frame with something like scrith\u2014a Ringworld term, grayish translucent material with strength on the order of the nuclear binding energy, stuff from the same level of physics as held Ringworld from flying apart. This stuff is the only outright physical miracle needed to make Ringworld or the Bowl work mechanically. Rendering Ringworld stable is a simple problem\u2014just counteract small sidewise nudges. Making the Bowl work in dynamic terms is far harder; the big problem is the jet and its magnetic fields. This was Benford's department, since he published many research papers in The Astrophysical Journal and the like on jets from the accretion disks around black holes, some of which are far bigger than galaxies. But who manages the jet? And how, since it's larger than worlds? This is how you get plot moves from the underlying physics.\n\nOne way to think of the strength needed to hold the Bowl together is by envisioning what would hold up a tower a hundred thousand kilometers high on Earth. The tallest building we now have is the 829.8 m (2,722 ft) tall, Burj Khalifa in Dubai, United Arab Emirates. So for Ringworld or for the Bowl, we're imagining a scrith-like substance 100,000 times stronger than the best steel and carbon composites can do now. Even under static conditions, though, buildings have a tendency to buckle under varying stresses. Really bad weather can blow over very strong buildings. So this is mega-engineering by master engineers indeed. Neutron stars can cope with such stresses, we know, and smart aliens or even ordinary humans might do well, too. So: let engineers at Caltech (where Larry was an undergraduate) or Georgia Tech (where Benford nearly went) or MIT (where Benford did a sabbatical) take a crack at it, then wait a century or two\u2014who knows what they might invent? This is a premise and still better, a promise\u2014the essence of modern science fiction.\n\nOur own inner solar system contains enough usable material for a classic Dyson sphere. The planets and vast cold swarms of ice and rock, like our Kuiper belt and Oort clouds\u2014all that, orbiting around another star, can plausibly give enough mass to build the Bowl. For alien minds, this could be a beckoning temptation. Put it together from freely orbiting substructures, stick it into bigger masses, use molecular glues. Then stabilize such sheet masses into plates that can get nudged inward. This lets the Builders lock them together into a shell\u2014for example, from spherical triangles. The work of generations, even for beings with very long life spans. We humans have done such, as seen in Chartres cathedral, the Great Wall, and much else.\n\nStill: Who did this? Maybe the Bowl was first made for just living beneath constant sunshine. So at first the Builders may have basked in the glow of their smaller sun, developing and colonizing the Bowl with ambitions to have a huge surface area with room for immense natural expanses. But then the Bowl natives began dreaming of colonizing the galaxy. They hit on the jet idea, and already had the Knothole as an exit for it. Building the Mirror Zone took a while, but then the jet allowed them to voyage. It didn't work as well as they thought, and demanded control, which they did by using large magnetic fields.\n\nThe system had virtues for space flight, too. Once in space, you're in free fall; the Bowl mass is fairly large, but you exit on the outer hull at high velocity, so the faint attraction of the Bowl is no issue. Anyone can scoot around the solar system, and it's cleared of all large masses. (The Bowl atmosphere serves to burn any meteorites that punch through the monolayer.)\n\nThe key idea is that a big fraction of the Bowl is mirrored, directing reflected sunlight onto a small spot on the star, the foot of the jet line. From this spot the enhanced sunlight excites a standing \"flare\" that makes a jet. This jet drives the star forward, pulling the Bowl with it through gravitation.\n\nThe jet passes through a Knothole at the \"bottom\" of the Bowl, out into space, as exhaust. Magnetic fields, entrained on the star surface, wrap around the outgoing jet plasma and confine it, so it does not flare out and paint the interior face of the Bowl\u2014where a whole living ecology thrives, immensely larger than Earth's area. So it's a huge moving object, the largest we could envision, since we wanted to write a novel about something beyond Niven's Ringworld.\n\nFor plausible stellar parameters, the jet can drive the system roughly a light-year in a few centuries. Slow but inexorable, with steering a delicate problem, the Bowl glides through the interstellar reaches. The star acts as a shield, stopping random iceteroids that may lie in the Bowl's path. There is friction from the interstellar plasma and dust density acting against the huge solar magnetosphere of the star, essentially a sphere 100 astronomical units in radius.\n\nSo the jet can be managed to adjust acceleration, if needed. If the jet becomes unstable, the most plausible destructive mode is the kink\u2014a snarling knot in the flow that moves outward. This could lash sideways and hammer the zones near the Knothole with virulent plasma, a dense solar wind. The first mode of defense, if the jet seems to be developing a kink, would be to turn the mirrors aside, not illuminating the jet foot. But that might not be enough to prevent a destructive kink. This has happened in the past, we decided, and lives in Bowl legend.\n\nThe reflecting zone of mirrors is defined by an inner angle, \u0398, and the outer angle, \u03a9. Reflecting sunlight back onto the star, focused to a point, then generates a jet which blows off. This carries most of what would be the star's solar wind, trapped in magnetic fields and heading straight along the system axis. The incoming reflected sunlight also heats the star, which struggles to find an equilibrium. The net opening angle, \u03a9 minus \u0398, then defines how much the star heats up. We set \u03a9 = 30 degrees, and \u0398 = 5 degrees, so the mirrors subtend that 25-degree band in the Bowl. The Bowl rim can be 45 degrees, or larger.\n\nThe K2 star is now running in a warmer regime, heated by the mirrors, thus making its spectrum nearer that of Sol. This explains how the star can have a spectral class somewhat different from that predicted by its mass. It looks oddly colored, more yellow than its mass would indicate.\n\nFor that matter, that little sun used to be a little bigger. It's been blowing off a jet for many millions of years. Still, it should last a long time. The Bowl could circle the galaxy itself several times.\n\nIII. BOWL DESIGN\n\nAs the book says, the Bowl star is\n\nK2 STAR. SIMILAR TO EPSILON ERIDANI (K2 V). INTERMEDIATE IN SIZE BETWEEN RED M-TYPE MAIN-SEQUENCE STARS AND YELLOW G-TYPE MAIN-SEQUENCE STARS.\n\nSo its light is reddish and a tad less bright than Sol. There is a broad, cylindrical segment of the Bowl at its outer edge, the Great Plain. This is huge, roughly the scale of Ringworld, with centrifugal gravity Earth normal times 0.8, so humans can walk easily there. Beyond that is the bowl curve, a hemisphere that arcs inward toward the Knothole. On the hemisphere, the Wok, the centrifugal gravity varies with latitude, and is not perpendicular to the local ground. To make a level walking surface, the Bowl has to have many platforms that are parallel to the jet axis, so gravity points straight down.\n\nThe local apparent centrifugal gravity has two vector components:\n\nA: Centrifugal gravity that is perpendicular to the local level surface on the bowl, vs angle \u03a8 (in radians). Here \u03a8 is measured away from the polar bowl axis\u2014that is, the jet axis. The curve peaks at 90 degrees, where the Great Plain has a local g of 1 in this plot. (It's 0.8 of Earth's.)\n\nB: Below shows the magnitude of centrifugal gravity that is parallel to the local level surface on the bowl, vs angle \u03a8\u2014thus, it's the felt force pushing away from the pole where the Knothole lies, along the local level.\n\nSo the pushing-away force is largest at the mid-latitudes, then falls away because the total force is small at the poles. This component also vanishes on the Great Plain.\n\nLocal Gravity versus Angle from the Jet Axis\n\nThe Builders designed it this way so that some of the lands are hard to walk upon in the direction of the Knothole. This discourages others from simply traveling to the Knothole by a slog across the entire Bowl; it takes a lot of work, working against a slanted local \"gravity\"\u2014especially near the Mirror Zones, which are in the mid-latitudes. Remember also that you must pump fluids around, since local forces drive rivers to flow and either they return through clouds and rain, or you must pump them when the weather doesn't perform well. There's a tendency for fluids to wind up in the lower gravity regions, too.\n\nWe did other such calculations, and many such didn't get into the final book. But they lurked in our minds. This may be an example of Ernest Hemingway's dictum that the more you know about a story's background, the more you can then leave out, and the detail will still make the story stronger because of the confident way you write it.\n\nThis odd centrifugal gravity also presents the Builders with a big stress problem. Holding together this whirling, forward-driving system demands nuclear-force levels of strength.\n\nThe atmosphere is quite deep, more than two hundred kilometers. This soaks up solar wind and cosmic rays. Also, the pressure is higher than Earth normal by about 50 percent, depending on location in the Bowl. It is also a reservoir to absorb the occasional big, unintended hit to the ecology. Compress Earth's entire atmosphere down to the density of water, and it would only be thirty feet deep. Everything we're dumping into our air goes into just thirty feet of water. The Bowl has much more, over a hundred yards deep in equivalent water. Too much carbon dioxide? It gets more diluted.\n\nSideways \"Gravity\" versus Angle from the Jet Axis\n\nThis deeper atmosphere explains why in low-grav areas, surprisingly large things can fly\u2014big aliens and even humans. We humans Earthside enjoy a partial pressure of 0.21 bars of oxygen, and we can do quite nicely in a two-bar atmosphere of almost pure oxygen (but be careful about fire). The Bowl has a bit less than we like: 0.18 bar, but the higher pressure compensates. This depresses fire risk, someone figures out later.\n\nStarting out, we wrote a background history of where the Builders came from, which we didn't insert into the novel. It lays out a version of that distant history that isn't necessarily what we ended up implying and partially describing:\n\nLong before 65 million years ago, there were dinosaurs who maintained internal temperatures through feathers, in a largely warmer world. But they ventured out with rockets into a solar system chilly and hostile. Still, they needed metals and did not want to destroy their biosphere with the pollutants from smelting, fast energy use, excess carbon dioxide, and the like. So the Bird Folk split into two factions:\n\n\u2022 the Gobacks who wanted to return to simple habits compatible with the world they once knew, using only minimal technology, and\n\n\u2022 the Forwards, who wanted to re-create around the Minor Star (which became the Bowl's) a fresh paradise that fulfilled the warm, comfortable paradise the Folk had once known. That could send the Forwards out into the galaxy that beckoned, full of living worlds ripe for the spread of the evolving Folk and all they stood for.\n\nSome of the Forwards were impatient to see what worlds lay millennia away. Many had themselves put in stasis to await a planetary rendezvous. Some faiths arose, hoping to commune somehow with the Godminds whose SETI signals told of great feats of engineering... but these turned out to be funeral pyre signals, of greatness departed long before. By that time, Earth was far behind the Bowl and shrouded in nostalgic legend.\n\nSo came the Separation, with the warmth-loving Forwards leaving and the Gobacks remaining on Earth. There they returned to the free life available in the ancestral lands. They kept their numbers low and gradually came to dislike the technologies they had inherited from the Forwards and the earlier civilizations. They reverted to a quiet, calm, agricultural culture. And they prospered, until a bright, flaring tail appeared in their skies....\n\nAfter all, by then, the dinosaurs didn't have a space program.\n\n\u2014April 2013\nBOOKS BY GREGORY BENFORD AND LARRY NIVEN\n\nBowl of Heaven\n\nTOR BOOKS BY GREGORY BENFORD\n\nJupiter Project\n\nThe Stars in Shroud\n\nShiva Descending\n\nArtifact\n\nIn Alien Flesh\n\nFar Futures\n\nBeyond Human\n\nTOR BOOKS BY LARRY NIVEN\n\nN-Space\n\nDestiny's Road\n\nRainbow Mars\n\nScatterbrain\n\nRingworld's Children\n\nThe Draco Tavern\n\nStars and Gods\n\nPlaygrounds of the Mind\nABOUT THE AUTHORS\n\nGREGORY BENFORD is a professor of physics at the University of California, Irvine, and lives in Irvine. He is a winner of the United Nations Medal for Literature, and the Nebula Award for his classic novel Timescape. Visit him at www.gregorybenford.com.\n\nLARRY NIVEN is the author of the Ringworld series and many other science fiction masterpieces. His Beowulf's Children, coauthored with Jerry Pournelle and Steven Barnes, was a New York Times bestseller. He lives in Chatsworth, California. Visit him at www.larryniven.net.\nThis is a work of fiction. All of the characters, organizations, and events portrayed in this novel are either products of the authors' imaginations or are used fictitiously.\n\nSHIPSTAR\n\nCopyright \u00a9 2014 by Gregory Benford and Larry Niven\n\nAll rights reserved.\n\nCover photograph of Galaxy 4499 by NASA, ESA, A. Aloisi (STSCI\/ESA), and The Hubble Heritage (STSCI\/AURA)\u2014ESA\/Hubble Collaboration\n\nA Tor Book\n\nPublished by Tom Doherty Associates, LLC\n\n175 Fifth Avenue\n\nNew York, NY 10010\n\nwww.tor-forge.com\n\nTor\u00ae is a registered trademark of Tom Doherty Associates, LLC.\n\nThe Library of Congress Cataloging-in-Publication Data is available upon request.\n\nISBN 978-0-7653-2870-0 (hardcover)\n\nISBN 978-1-4299-4968-2 (e-book)\n\ne-ISBN 9781429949682\n\nFirst Edition: April 2014\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\nFor Florence Freeman, with love\n\nContents\n\nOne: Princess Frida and the Mourning Curtain\n\nTwo: King Alberto's Bad Decision\n\nThree: The Secret\n\nFour: A Dance and a Doughnut\n\nFive: King Alberto's Second Bad Decision\n\nSix: Delilah and the Dormidon\n\nSeven: A Coronation\n\nEight: Peacocks and Paw Prints\n\nOne\n\nPrincess Frida and the Mourning Curtain\n\nNot far from where you're sitting right now, there exists a country called Kalia. It's a beautiful place, well worth visiting if you have the time. The capital is an ancient city named Lago Puera, and sailors and visitors usually enter through its port. They are greeted by the sight of the palace domes, sparkling in the sun, painted like the Kalian sea, whose waves foam silver, whose depths shade the eye with unending blues. The shore shimmers gold, the land opens like an emerald quilt, and the Kalian mountains rise up as giants to greet the sky.\n\nYou'd think that for the princesses in this story, who were born in Kalia, who grew up in that palace, who were destined to survey the waters of the Kalian sea, this would be a happy place to live.\n\nIn fact, it was the opposite.\n\n\u22c7\n\nThere were twelve of them, and the eldest was called Frida. Frida was very clever, and she had many ambitions, but most persistent was her desire to fly a plane.\n\nThen came Polina, and she could read the stars.\n\nNext was Lorna, the kindest, and thus the wisest, of them all.\n\nAfter her was Ariosta, a talented painter, who cut off all her hair without permission when she was ten. (She had the same style ten years on: it still suited her.)\n\nChessa came next, a girl who sang to break your heart in twenty pieces, then put it back together with a jazzy aria.\n\nThen came Bellina, who'd taught herself five languages.\n\nVita was the seventh daughter, a happy spirit, whose laugh was like a tonic. She was the luckiest, and the quickest at jokes.\n\nMariella came next, and she loved to do sums, numbers dancing in her mind like obedient bears.\n\nThen there was Delilah, who had such green fingers that even the stubbornest plant grew at her touch.\n\nNext was Flora, always reading a book, a newspaper or the side of a biscuit box.\n\nAfter her came Emelia, who wanted to be a vet.\n\nAnd the youngest was Agnes, the most watchful of the sisters. She was going to be a writer when she grew up.\n\nAnd their parents?\n\nWell. This was the problem, as parents often are.\n\nQueen Laurelia was their mother, dead before this story starts, but in her end is this beginning. Laurelia had been a woman of many words and the driver of a racing car \u2013 open top, leather seats, a craving for speed and a fatal crash that was the bitterest unfairness her daughters ever tasted.\n\nWhen they were very little, the princesses had never understood why it made their mother so happy to speed off down the road, goggles on, hair flying, metal gleaming, the engine roaring to a buzz and then to silence as she disappeared over the hill. Sometimes, at night, after Laurelia had died, Agnes thought she could feel the vibration of her mother's engine revving in her ribcage. Then she woke up and realised it was Emelia's snores. Agnes discovered that both the imagined and the real worlds could be equally comforting, and that sometimes it was very hard to tell the difference.\n\nNever mind jewels and diadems, the words they'd heard from Laurelia were the princesses' inheritance: her songs down the corridors, her bedtime stories of other worlds. Her words roosted like birds in the girls' imaginations. In the days, weeks and months after Laurelia's death, they took flight from her daughters' mouths and became their own.\n\nTheir father was called Alberto, and Alberto was king of Kalia. In the scheme of the story, this is a fact both important and irrelevant, like most things are, depending on the time of day you're looking at them. It was Alberto being king that made his daughters princesses. Now, between you and me, I don't think any of them liked being princesses very much. It might _seem_ fun to wear a jewelled crown and have people do everything for you \u2013 but it quickly becomes tiresome, to the point that boiling an egg for yourself feels like a holiday.\n\nAfter Queen Laurelia's death, King Alberto became the sort of person who ate a whole cake without offering anyone else a slice, and who punished his girls for things that weren't their fault at all. The girls weren't alone in this: the world is full of children picking up their parents' crumbs. Alberto and Laurelia had no sons, and I think this was part of the problem, because after Laurelia died, Alberto didn't know what to do with _one_ daughter, let alone twelve of them. Laurelia had been the one watching them, nurturing their imaginations, their educations.\n\nAnd now she was gone.\n\nGrowing up, Alberto had never learned a thing about girls; as a prince, all his friends were boys, and then as king, all his advisers were men. Girls in Kalia, whether they were princesses or not, had never been considered very important. Most important were the subjects of horse riding, hawking, killing small animals, sitting on thrones and gathering taxes. When she was alive, Queen Laurelia had done her best to encourage her daughters to look forward to their adulthood, but it's hard when you're just one queen racing your motor against a long line of history trying to squash you down. No one had done such a thing for her when _she_ was a little girl \u2013 they hadn't even thought it necessary to teach her how to read.\n\nEvery girl in Kalia was the same, and the people in charge of them clumped their individual hopes and dreams together like one big ball of moss. It didn't matter how well a girl could play the trumpet, or grow a sunflower, or write a poem, or solve a quadratic equation. _None_ of that mattered. The best a girl could hope for was a marriage where the money was good and her husband didn't hog all of life's fun. A girl might as well have been a sunflower or a trumpet herself for all that her feelings were taken into consideration.\n\nIn the first week of mourning after Queen Laurelia's death, King Alberto dispensed with the girls' music lessons. He couldn't bear the sound of Chessa singing, he said, because she sounded too much like her mother. Chessa didn't open her mouth for days, not even to speak.\n\nThen, in the second week of mourning, their mathematics tutor was dismissed, because princesses didn't need numbers. Mariella took to lying on her bed, tapping out times tables on her forearm.\n\nBy the third week of mourning, their botany classes were taken away from them. No longer were they allowed to take trips to the majestic Kalian mountains to collect plant samples for the palace laboratory. It wasn't just Delilah who had loved the clear air \u2013 all the girls enjoyed the mountains, where birds of extraordinary plumage called to each other from high trees, and the wildest flowers flourished.\n\nBack at the palace, life was a tomb. The bright walls that Queen Laurelia had decorated were now shrouded in black velvet. No electric light was allowed, only candles were permitted \u2013 and their flames barely lit the corners of the huge, dark rooms.\n\nThe maids and cooks and butlers scurried along the walls, their shadows long and looming, heads down towards carpets that gathered dust because no one could see to clean them.\n\nThe sun, the gorgeous spanning sea beyond the windows, the sky such a blue, were shut out. Only melancholy was allowed to illuminate the girls' days.\n\nThe telephones \u2013 so recently installed, and such a thrill to Laurelia that she could speak to her sisters, who had married kings in other lands \u2013 were disconnected. The girls ached for that cheery metallic ring, which had always excited them, to know which far-off aunt was calling by the touch of her finger.\n\nNow all was silence.\n\nIn the fourth week of mourning for the queen, King Alberto took away:\n\nAriosta's painting supplies\n\nAll the girls' novels, poetry, dictionaries, encyclopedias, maps, comics and newspapers\n\nMariella's chemistry set\n\nEmelia's guide to looking after sick tigers\n\nAgnes's typewriter\n\nPolina's telescope\n\nDelilah's key to the greenhouse (the plants were left untended and began to die)...\n\nAnd their mother's gramophone and all her jazz records.\n\nFrida, who I told you was the cleverest, hid her aeroplane manuals in her knicker drawer. But regardless of this personal ingenuity, the girls were more miserable than they had ever been in their lives.\n\nThe king explained to the girls that they were now no longer allowed to go beyond the palace walls.\n\n'But why?' asked Frida, surrounded as usual by the others. 'You can't keep us locked in.'\n\n'I'm king and I can,' Alberto said. He sighed, scratching the top of his balding head through the circle of his crown. 'I'm doing it because I love you,' he went on. 'I couldn't bear it if anything happened to you. It's so dangerous outside the palace walls.'\n\n'It's dangerous inside them too,' Frida muttered, as their father hurried off. He almost ran away from them, as if each of his daughters carried within her the spark of his dead wife, and their faces might pin him to the floor with grief.\n\nBy now, not even their eyes felt like the princesses' own, not even their hands and feet. Their hearts were gloomy; the palace guards watched them everywhere. Everything they saw and touched belonged to their father.\n\nA yearning for their mother spread through the princesses' bodies like mould. It grew and grew, inside and over them, a creeping, seeping crust of pain swallowing them up \u2013 and the only things that might have kept them breathing, might have pushed back the mould a little bit, might have reminded them that they were still alive, and deserved a chance to _enjoy_ this fact, Alberto had taken away. The girls felt as dead as their mother.\n\nFrida's sorrow over this turned to confusion, and finally to clarity and anger. She understood what that motor car had meant to Laurelia \u2013 it wasn't the car itself so much as what it had given her: a sense of movement, of direction. 'You see, my darlings,' Frida said to her younger sisters, 'it made her feel _free_. And I'll tell you something else. The time for muttering is done.'\n\nFrida was true to her word, as she always was.\n\nOne fateful afternoon, after the princesses had endured yet another morning cooped up like twelve chickens with no promise of an egg, she stormed the corridors looking for their father. Polina and Lorna ran after her, trying to keep up. The other nine sisters scattered behind, a confusion of sad butterflies.\n\nKing Alberto was in the throne room as usual, the curtains closed. His advisers were standing in the shadows, unsure of what to do with their increasingly difficult monarch.\n\n'Your Majesty,' said Frida, coming towards him. 'This isn't fair, and you know it. You cannot tell us how to grieve.'\n\n'Please go away,' he said. 'I can't bear to look at you.'\n\n'Father,' Frida persisted. 'We know you're sad, but we're sad too. Why take away our lessons, our music, our books and our paints? They make us feel as if Mother is still here.'\n\n'Your mother is not here!' the king cried. 'She's gone! Dead, by her own stupidity \u2013 and mine, for ever allowing her to drive that blasted racing car in the first place!'\n\n'She loved that racing car,' said Frida.\n\n'Well, it didn't love her back,' the king replied, screwing his face up like a horrible turnip. 'I'm having it crushed.'\n\n'You can't!'\n\n'Frida,' said Alberto, 'I'm the king. I can do what I want.'\n\nFrida pretended she hadn't heard. 'Let me fix it with the help of the palace mechanic,' she said.\n\n'You'll do no such thing!' King Alberto snapped, losing his patience. 'No man will marry a girl who fixes cars!'\n\n'What does Mother's motor car have to do with getting married?' asked Frida.\n\n(Frida, you may have noticed, never gave up.)\n\nKing Alberto's round cheeks turned tomato red, and he looked at his other eleven daughters, who had gathered behind Frida as she faced their father.\n\n'Every one of you is a stick of dynamite!' he bellowed. 'You'll explode me, and this kingdom \u2013 BOOM! Your mother was ridiculous about you, and now no one will touch you. Girls aren't supposed to do even a tiny _bit_ of what you got up to. And look at what happened to her. Dead. _Dead!_ I won't have it, I won't!' He slammed his hand on the arm of his throne, and his crown knocked slightly sideways.\n\n'We're not sticks of dynamite,' said Frida. 'We're simply excellent girls.'\n\nKing Alberto ignored her, throwing his hands up in the air. 'Oh, why, why, _why_ were we not blessed with a boy? Just one boy, one incy-wincy little boy, just one! That's all I ever asked for! I'm getting old, I feel a hundred \u2013 I look _two_ hundred \u2013 and still no heir!'\n\n'But you have twelve heirs,' Frida said.\n\nAlberto was used to these conversations with Frida. They'd been having them since she could talk, and he too would rarely give up. (In fact, I think that sometimes he rather enjoyed them.) 'I have twelve girls,' he said. 'And what use are you? No woman can inherit my kingdom.'\n\n'Says who?' said Frida.\n\nAlberto jumped from the throne as if his eldest daughter had slapped him in the face with a Kalian trout, and a large one at that. 'It's the law!' he cried.\n\n'Your Majesty,' said Frida patiently. ' _You_ are the law.'\n\nHis advisers shuffled on their feet like a group of perturbed pigeons. King Alberto was silent as he sat back into his throne, stroking his chin. For an agonising, ecstatic moment, he actually seemed to be considering Frida's point. Agnes felt her heart lift, and the energy between her sisters' bodies shifted with hopeful anticipation. _Good old Frida_ , she thought. _Quick as ever._\n\nBut then their father stared down at them in horror, as if he was looking at his dead wife's image, a woman's lost face reflected in twelve young mirrors of fear. 'None of you has the faintest idea what it takes to run a kingdom,' he said.\n\nFrida fell on her knees towards him, her arms open wide. 'Because no one has ever taught us! But we'd learn. And have we not lived with your advisers our whole lives? I could lead a kingdom, I know I could. And if I couldn't, Polina could, and then there's \u2013'\n\nAlberto snorted. ' _Polina?_ Polina, who spends her life with one eye glued to a telescope?'\n\n'But, Father,' said Polina. 'There is so much in the sky we've yet to learn \u2013'\n\n'No,' interrupted Alberto, pointing at the floor. 'Down _here_ is what matters, not twinkling stars.' He readjusted his crown.\n\n'Father,' said Frida, jumping to her feet and pacing back and forth in front of the throne. 'I want you to imagine something for me. Can you do that?' She looked at her father with a doubtful expression, as if it was unlikely he had any imagination left. 'Imagine not being able to do anything, except _sit_.'\n\n'Sounds good to me.'\n\n'Except sit, and think about getting married. That's it, nothing else. Married to a man who doesn't even _exist_ yet. And you can't even sit at a window with a view, because they're all covered over with black cloth.'\n\n'It'll do you good to calm down,' he said. 'Respect your mother's memory.'\n\n'We will respect her by carrying on as we did when she was alive.'\n\n'Your Majesty,' Agnes piped up, encouraged by her sister's fire, 'imagine... imagine that our hearts are lions, needing to jump and play, and feed and drink, and grow.'\n\nFrida laughed with joy. 'Oh yes, Agnes!' she said. 'Our hearts are lions!'\n\n'Your hearts are _what_?' spluttered Alberto. 'You're not lions! You and your ridiculous ideas, Agnes. Grow up.'\n\nHe turned from his youngest daughter back to his eldest. 'Frida. Be an example to the others, _please_. Think of your marriages, and accept that no girl, no woman, could ever be smart enough for my job.'\n\nFrida narrowed her eyes. 'You wish me to be an example to the others?' she said.\n\nAlberto folded his arms and stared at his defiant daughter. 'Frida, it's my dearest wish.'\n\n'Very well, Your Majesty,' she said.\n\nThe king sighed with relief; but everyone else in the room knew Princess Frida better. There was a beat. The room was silent, waiting to see what she would do next.\n\nFrida walked, head held high, towards the curtain covering one of the windows.\n\nWhen they realised what she was about to do, the advisers cried in unison for her to stop.\n\nBut Frida did not stop.\n\nWith one sharp heave, she pulled the curtain back, and a golden vengeance poured into the room.\n\n'Insolence!' screamed the king, and in that moment it was hard to tell whether he was blinded by the light of the sun or his daughter.\n\nFrida was moving like a spirit, curtain to curtain, pulling down the black drapes, advisers and maids cringing with their eyes closed, the dust swirling like gold motes around the throne as velvet and taffeta tumbled to the floor. Ariosta rushed to help her, and Bellina followed, then Chessa and Delilah and Mariella, then Polina and Emelia, then Flora and Vita, and finally Lorna and Agnes, twelve princessly pairs of hands making portal after portal of sunshine to flood the room.\n\nNo one could stop them,\n\nno one dared go near them,\n\nand thus their father's throne was nothing,\n\na chair bleached white by the light of grief.\n\nTwo\n\nKing Alberto's Bad Decision\n\nI don't think it's exactly right to say Frida _regretted_ her performance in the throne room \u2013 for who could ever regret a slice of sunshine? \u2013 but the consequences for her and her eleven sisters were dire. As I've mentioned: it was a fateful afternoon.\n\nTrue, Alberto didn't crush Laurelia's racing car to pieces, despite his threats. He had it renovated and sealed up inside the palace garage, where it started to gather dust, and a family of mice took up residence in the passenger seat.\n\nBut just when the girls thought life couldn't get any worse, it got worse.\n\nThree days after the curtain incident, King Alberto, flanked by his advisers, summoned his daughters to a room in the palace they'd never seen before.\n\n'You'll be perfectly safe in here,' he said.\n\nBy now, the girls had barely enough energy to lift their heads and peer in, but when they did, they stared in horror at their new surroundings.\n\nIt was a room with no windows.\n\nIt contained twelve beds, in two facing rows of six. Off to the side was one small bathroom. On the far wall, hanging between the ends of the rows of beds, was a truly enormous portrait of Queen Laurelia in her motor-racing gear, as if to remind the girls what might happen if they ever tried to go faster than was appropriate.\n\n'Good _lord_ ,' said Ariosta, staring up at the painting. The other girls could barely look at it.\n\n'You can't do this to us,' said Frida, turning to her father and the advisers, several of whom were looking puffed up and pleased with themselves. 'We used to play in Lago Puera and the mountains beyond. We used to make chemistry experiments in the royal laboratory. We used to play music in our own little band! Now this is what you do to us?'\n\n'It's for your own good,' replied the king. His expression was horribly blank, which was worse than him being angry.\n\n'No,' said Frida. 'We were destined to survey the waters of the Kalian sea. Everyone told us that. You always said it yourself.'\n\n'I did. But in happier days.'\n\n'We deserve happier days again. Instead, you would put us in a cell, where we cannot even hear the waves? You would shrink our lives to this small room, and a frozen picture of our mother's face \u2013'\n\n'Frida, stop!' said Alberto. 'One of these days you will go too far.'\n\n'No,' she replied. 'I fear I won't go far enough.' She took up Agnes's hand, which had begun to tremble.\n\n'You can't be serious about this, Father,' said Polina, attempting reason, wishing to thaw the air of hostility.\n\n'I'm most serious,' he replied. 'One hour a day out in the palace grounds to stretch your legs.'\n\nFrida still hadn't given up. She turned to the king's advisers. 'Gentlemen. Surely, for the good of Kalia, we should have our telescopes and typewriters back. Surely, instead of worrying about whether your princesses are going to explode, you should be concerning yourselves with your harvests, and your relations with the borderlands?' There was a slight panic in her voice now, and it scared the other princesses. They huddled behind her, hugging one another tight.\n\nThe advisers looked away, but Frida was right. (Frida was often right when it came to matters of state, although no one ever listened to her.) The kingdom of Kalia was falling apart, but Alberto was more obsessed with keeping his daughters locked safely away than doing his kingly duty.\n\nNone of the advisers wanted to lose his job, so they said nothing. Frida turned up her chin in disgust. 'Cowards,' she said. One of them, at least \u2013 her father's youngest adviser, a whippety-thin man called Clarence \u2013 looked shamefaced.\n\n'You've all gone mad,' said Ariosta.\n\n'Not mad, just sensible,' said the king. He brandished a heavy iron key at Frida. 'Inside,' he said. ' _Now_. And please,' he pleaded, 'just go to sleep.'\n\nThe advisers ushered them in, and each princess found a bed. They heard the key turn in the lock, a horrid grating sound that plunged their hearts into their feet.\n\nThere was no natural light, no privacy, no place for them to hide away with their thoughts. All Agnes wanted to hear was Emelia's little snores, to remind her that once they'd had a mother who loved a motor's engine. But instead the room hummed with the nervous energy of twelve young minds, crawling up the walls with no way out.\n\nThat day, the princesses learned that the line between mad and sensible is a very fine line indeed.\n\n\u22c7\n\nIt went on like this for weeks. The girls were kept in the room, allowed one hour a day for a walk, and their mother's painted face greeted them on their return. The maids brought their meals to the door, and the girls ate on their beds. King Alberto had ordered that they should be given a plain diet of porridge and toast, morning and night, with the occasional satsuma, but the girls barely noticed what was passing their lips.\n\nThey slept very badly. Frida said it felt as if they were getting older as their mother stayed young. And, of course, the painting's expression did indeed stay the same, friendly but distant, Queen Laurelia's mouth slightly open on a word they would never hear. 'Oh, if only she would walk out of the frame and take us to the mountain!' Frida cried, tossing the skin of yet another satsuma to the floor.\n\nIt was such a sad sight, these wilting girls, that I can hardly bear to type it. But I've since learned that sadness comes and goes, and typewriters win out.\n\nYou see, the king could control the paths his daughters trod; he could take away their pleasures and their views and lock them up. He could make sure that the princesses didn't have anything in that room except their toothbrushes and tiaras, pyjamas and dressing gowns. But king or no king, there was one thing they possessed that he could never own: their imaginations.\n\nHave _you_ ever tried getting into someone else's imagination? It's practically impossible. Our inability to do so has caused headache and heartache since time began. Even your own imagination can be a slippery thing \u2013 you can't see it, you can't hold it, but you can certainly _feel_ it. It can fill your day with sunshine or with storm. It will conjure worlds from nowhere and make them real. It will open doors you didn't even know existed; it will show you secrets that are yours alone. And the strange thing about imagination is that it can fly absolutely anywhere, even when your body stays in one place. I've seen it happen.\n\nImagination was the greatest weapon those girls had.\n\nAnd one night, sitting up in their beds, telling stories as they always did, the princesses did indeed discover a secret.\n\nIt was the most perfect, timely secret, like moonlight on a pillow in a windowless room. It changed their lives forever.\n\nAnd what was the secret?\n\nOh, go on then. Seeing as it's you.\n\nThree\n\nThe Secret\n\nThat night \u2013 that particular night when everything changed \u2013 it was Frida's turn to tell a story. The others had climbed out of their own beds and were gathered on hers \u2013 quite a squeeze, as you might imagine. They always liked it when it was Frida's turn because, as the eldest, she had the most memories of Queen Laurelia. But sometimes Frida told stories that were only half a memory, and the other half was made up \u2013 'because really,' she would say, 'who can tell the difference?'\n\nThe lamps were lit as usual \u2013 twelve glowing orbs around the room. The princesses felt as if they were living in a jewel box, their hair and silk pyjamas golden in the light.\n\nFrida was just about to start her story, when she lifted her lamp towards the portrait of their mother. 'Has someone moved the painting?' she asked. 'It's crooked.'\n\nThe other princesses looked over at the painting. It was true: Queen Laurelia was looking back at her daughters at a slight angle.\n\n'I haven't touched it,' said Flora.\n\n'She never said you did, dearest,' said Delilah.\n\n'Maybe Vita knocked it by mistake,' said Chessa. 'You can't swing a cat in here.'\n\n'Tell us a story, Frida. _Please_ ,' said Lorna, sensing that everyone was a bit crotchety.\n\nBut Frida had slipped off the bed and was standing close to her mother's painting. 'I'll tell you a story in a minute,' she said. 'But don't you think her eyes are inviting us in?'\n\n'Inviting us in where?' asked Polina.\n\nFrida touched the edge of the frame in an attempt to straighten it, and her hand froze. ' _No_ ,' she said. 'That's _impossible_.'\n\n'What? What is it, Frida?' whispered Agnes as her skin turned to goosebumps, her hairs on end.\n\nFrida turned to her sisters, her face pale. 'Can you come and help me lift the painting off?' she said. The sisters rushed over and did as they were asked, staggering with the weight of their mother's portrait. All twelve of them shuffled between the beds with the frame, propping Queen Laurelia to one side.\n\nFrida held up her lamp to the wall. 'By all the stars of Kalia,' she breathed. 'I wondered, but I hardly dared hope.'\n\nIn the flickering light of her lamp, the others could see what Frida had thought was impossible, but which, in fact, was true.\n\n'Is that... a _door_?' whispered Emelia.\n\nEmelia was quite right. It was a thin outline of a door, a panel embedded in the wall. Frida reached out. Her hand could touch it, feel it! It was _real_.\n\n'How did we never notice this before?' she asked her sisters, but none of them could answer.\n\nThe door was made of the same material as the wall, and there was no handle. Frida pushed the panel, and under her touch it swung back easily. The other girls joined her and stood around the threshold. All they could see was pitch black, as if they were standing on the edge of a deep pit. Cold air hit their cheeks and knocked the breath out of them. In the silence, from somewhere deep and far away, Agnes thought she could hear music, the sweet jazzy waft of a clarinet. A strange smell she'd never tasted before rose up: heady, heavy, a little smoky, like a raspberry dipped in black amber. A tinkling of bells, the lap of a wave. It was most unsettling.\n\nAnd most exciting.\n\nFor a moment, no one said anything. It felt as if they were teetering between an old life and a new.\n\n'Where does this lead?' asked Mariella.\n\n'Good question. Who knows? But I'm going to find out,' replied Frida.\n\n'I'm coming with you,' said Vita.\n\n'Me too,' said Ariosta.\n\n'We'll _all_ go,' said Frida. 'No one should be left behind.'\n\n'But it could be dangerous,' Bellina cried, leaping to Frida's side and hanging on her sleeve. 'It might be a trap.'\n\n'A trap?' said Frida, laughing. 'I think we've been trapped long enough, don't you?'\n\n'I don't want something bad to happen. What would Father say \u2013?'\n\n'He's not going to say anything, my sweet, because we're not going to tell him,' said Frida. 'And, Bellina, _think_. What could be worse than being holed up here for another night?'\n\nBellina bit her lip.\n\n'Darling Bell,' said Lorna. 'What Frida's saying is true. And if I have to spend one more evening in this tiny room with nothing to do except count sheep and polish my tiara, I might go mad.'\n\n'I'm surprised I'm not mad already,' said Emelia. 'We have to go.'\n\n'Well said, both of you,' said Frida. 'This door is exactly what we need. Hurry!' she went on, shooing her sisters. 'Dressing gowns and shoes. Fetch your lamps. Voices down. Father's guards may be on the other side of the walls, wherever it is we're going.'\n\nThe princesses found their lamps, put on their shoes and followed their eldest sister to the edge of the strange door.\n\nFrida held her lamp over the threshold, and the light opened up the darkness like a dancer cast from orange flame, jumping and jutting, finding its way. The others waited with bated breath for her to tell them what she could see.\n\n'A staircase!' she whispered. 'Oh, it goes down and down and down! I can't imagine how many steps there are. It's so _dark_.'\n\nNevertheless, one by one, the princesses began to follow her down,\n\nand down,\n\nand down,\n\nand down,\n\ntheir lamps held high,\n\ntheir soles echoing\n\nand echoing\n\non the stone steps.\n\nThe staircase did not appear to have been used for years. Cobwebs clung to their faces and stuck to their hair. There was a new smell of mould and damp, and the air was still horribly cold.\n\n'Do you think Mother went down this staircase?' asked Mariella. 'Did she ever mention one to you, Frida?'\n\nFrida was silent for a moment. 'Do you know, Mari, I think she might have. But only when I was tiny.'\n\n'I don't like it,' Polina whispered over Frida's shoulder. 'We're going underground. What if there are spiders?'\n\n'The stars will be waiting for you when we come back, Pol. And as for spiders, they'll be more frightened of you. Keep walking,' Frida whispered back. 'I'm sure this is something important.'\n\nAfter about fifteen minutes, the girls, made dizzy from the continual spiralling downwards and the fluff of cobweb in their eyes, finally reached a flat level. They held up their lamps again. They could see nothing beyond them but darkness. All they could hear was their own blood beating in their bodies, and their breath on the cool air.\n\n'That was five hundred and three steps,' whispered Mariella. 'I counted.'\n\n'I think we're deep beneath the palace,' said Flora. She held her lamp higher. 'And look \u2013 there's the mouth of the sea!'\n\nBut it was not the mouth of the sea. Beyond was a lagoon \u2013 a wide, deep, dark underground pool \u2013 lit around its edges and in the crannies of its rocks by tiny lights that blinked from the darkness like stars.\n\nWhen Polina looked at it, she wondered why she'd ever been worried. It felt as if they'd travelled upwards into a firmament of celestial wonder, not deep beneath the surface of their father's land. It was a breathtaking vision.\n\nAgnes ran to the lagoon's edge.\n\n'Don't touch it!' said Flora, for she had read many stories of tempting and beautiful sights that would only lead a princess to her doom.\n\n'I'm not going to touch it,' said Agnes. 'I'm just trying to work out how we're going to cross it.'\n\nThe others joined her, and stared at the water. It was as deep as a dream from which you might never wake. They shivered; for all its beauty, they felt that perhaps they shouldn't hang around. And then came the noise of the music again, that sweet melodious sound of a single clarinet, from somewhere across the lagoon, and it felt to the girls as if it was calling them to join it.\n\n'Maybe we should swim across?' said Ariosta, beginning to roll up her pyjama legs. 'It's been ages since I had a dip.'\n\n'I \u2013 Ari \u2013 really?' said Bellina.\n\n'Let her,' said Frida. 'Ariosta's the best swimmer out of all of us, and sometimes a dolphin just has to swim.'\n\n'But what if there's something in the water?' whispered Flora.\n\n'There's always something in the water,' said Ariosta, grinning, and she sat by the side of the lagoon and plunged in one leg and then the other. The girls held their breath, but nothing bad happened to their sister. Ariosta splashed her legs around, the drops illuminated by the twinkling lights. 'Oooh! It's _freezing_!' she said, which made them laugh for the first time since their mother died.\n\nEmboldened by her intrepid sister, Bellina dipped her hand into the water. 'It feels like Mother's shirts,' she said. 'So satiny!'\n\n'Don't drink it,' warned Lorna. 'It's bad enough that one of us is swimming in it.'\n\n'I don't want to drink it, I just want to swim in it. I'll be back,' said Ariosta.\n\n'It'll be all right, Lorn,' said Frida. 'Trust me.'\n\n'Oh, Ari,' said Delilah proudly. 'You really are a fantastic fish.' They waited in silence, holding their lamps up as high as they could to illuminate Ariosta's swim. The minutes ticked.\n\n'I've found something!' Ariosta called, and her sisters breathed a sigh of relief.\n\n'What is it?' Polina shouted back. 'Ari, be careful!'\n\n'Hold on \u2013 it's so dark,' Ariosta replied. And then \u2013 'Oh! I've found... some boats!'\n\nThe sisters cheered and clapped as Ariosta swam back and forth six times, bringing six boats to their side of the lagoon, six boats that turned out to fit two princesses apiece. When Ariosta was finished and had pulled herself out of the water, her sisters hugged her so tightly, and covered her with so many of their dressing gowns until her teeth stopped chattering, that she looked happier than she had in over a year.\n\nTwo by two, the girls lowered themselves into the bobbing vessels and set off across the water. Chessa splashed her oars into the dark, her eyes on the bank ahead. She hummed a quiet tune, gently testing the acoustics of the rocks above.\n\nThe others, who loved to hear her sing, and who had missed it terribly since King Alberto had stopped their music lessons, kept their own oars as quiet as they could, hoping they might hear again the glorious sound of their childhood.\n\nThey were in luck. After what had felt to them a lifetime, Chessa took a deep breath, closed her eyes, opened her mouth and began to sing:\n\n' _The girls rowed on a dark lagoon_\n\n_In the cave's imaginary night._\n\n_They didn't know why_\n\n_But still in the sky \u2013_\n\n_There burned a beautiful light!_ '\n\nChessa's voice reverberated across the water and round the rocks in a magical echo. 'Oh, Chess,' Frida called from the boat she was sharing with Agnes. 'You always pop my heart like a champagne cork.' The others laughed at the truth of Frida's words, for Chessa's singing did fizz their blood like the finest bubbles. Then far off came the clarinet again, as if it was replying to the power of Chessa's voice, waiting impatiently for her to give it more music.\n\n'Mother used to sing that to me at bath time,' said Chessa after she stopped, now dipping her fingers in the lagoon.\n\n'Well, Mother was right,' said Flora. ' _Look!_ '\n\nThe girls turned towards the bank. It was as if the words of Chessa's song had conjured the sight before them. Where minutes before all had been darkness, now, through a crack in the rock beyond, narrow enough for one princess at a time, there was indeed a light.\n\nThis light sparkled more than any knife or fork the girls had used at their parents' banquets. This light seemed to burn brighter than the moon, as its shining rays beckoned them in. This light was extraordinary.\n\n'What _is_ it?' said Emelia, as the girls jumped out of the boats and tied them to various rocks lining the new side of the lagoon.\n\n'We won't know until we go a little closer,' said Agnes. 'Frida, wise to pursue?'\n\nAll the sisters turned to Frida. Frida looked first at the moored boats, secondly at Agnes's hopeful little face, and then towards the lagoon, darker than a thought that never ends.\n\n'It would be a shame,' she said, 'given how enterprising Ariosta has been with getting us over the water, and how observant Chessa has been about this light, _not_ to carry on. To do anything else feels wrong. Agnes, you shall lead the way.'\n\nAgnes's small body puffed up with pride and pleasure at such responsibility, and the older sisters hid their affectionate smiles at their little walking popcorn. With Agnes at the fore, princess after princess slipped through the crack in the rock. Once they were all safely through, they abandoned their lamps and approached the glowing magnificence.\n\nAny fear they might have been holding in their hearts was forgotten. The light made their cheeks pale, their eyes shining coins, their hair a moving field of silver wheat. As they kept on, the princesses soon realised they were walking through the most beautiful forest. They trod a delicate path lined by tall and slender birch trees, each leaf on the branches a glorious, shimmering pocket of light. Silver birds sang to each other, glimpsed through the foliage like falling stars.\n\n'I can't believe it,' whispered Polina. 'I'm sure I dreamed of such a place when I was a little girl!'\n\n'Me too,' said Frida, turning up her face in wonder.\n\n'Me three,' breathed Lorna.\n\nThe eldest three sisters agreed that the silver forest, for all its surprise, also had the air of familiarity \u2013 as if, once upon a time, someone had told them about it, as if it had always been there, waiting for them to return. Frida scrunched up her face, trying to remember where, how, _why_ this place felt like a second home. But it was no use \u2013 and Frida knew when it was best to accept a mystery and not pull its wings off, like a brute might to a butterfly.\n\nAfter a while, the birches started to thin out, and the calls of the silver birds fell silent. The light that had cloaked them faded away, and everything went dark. Polina looked up, in case there were any stars she could use to guide their way \u2013 but she couldn't see a thing. The girls stopped walking and formed a circle, holding hands, palm against damp palm as they looked outwards on the endless night.\n\n'I wish we still had our lamps,' whispered Bellina.\n\n'What do we do now?' asked Delilah.\n\n'We could retrace our steps,' Mariella suggested.\n\n'We don't know where those steps _are_ , it's so dark,' replied Vita.\n\nIt was true. They'd lost their bearings. They were surrounded by a nothingness, a looming absence of landscape and dimension, depth and time. A strange feeling of uncertainty crept up the backs of their legs and spines, into their stomachs, their throats, their eyes. It was as if the silver forest, the lagoon, the staircase \u2013 even the palace upstairs \u2013 had never existed.\n\nWithout warning, Emelia broke the circle and dropped down on to all fours. 'Shh!' she said. 'Can you hear that?'\n\n'Hear what?' said Flora.\n\n' _That_ ,' replied Emelia. 'Where are you?' she called. 'I can hear you!'\n\n'Who is she talking to? Has she gone mad?' said Vita.\n\nBut then the other sisters began to hear it too, a faint sound of dried leaves swishing, a thrum of movement on the air.\n\n'Maybe it's one of Father's advisers, come to punish us,' said Ariosta. The girls huddled closer together against this new fear.\n\n'Never,' said Frida. 'They're not brave enough to come down here.'\n\nEmelia carried on crawling around in the dark, and called gently, 'Don't be scared, I'll help you.'\n\nAs she said this, a small fox crawled into view.\n\nNow, you probably know what a fox looks like.\n\nPerhaps you picture a proud red coat, neat and springy black legs, intelligent eyes the colour of an orange stone?\n\nWell, this fox didn't look like that. _This_ fox had green eyes and fur like tarnished gold, a weak star fallen in the girls' circle. He was dragging one of his back legs. It was broken, and little whimpers were coming from his damaged body. Suddenly, the girls forgot their own worry, and turned instead to this beautiful, suffering creature, so fantastical he could have climbed out of a treasure chest.\n\nEmelia got to her feet and went over to Mariella. Without warning, she dug deep in her sister's dressing gown pocket. 'Aha!' she said, pulling out Mariella's favourite wooden ruler. 'I _knew_ you still had it. Perfect for a splint.'\n\n'Hold on \u2013'\n\nBut Emelia was down again, facing the fox. She put out a hand, and he turned his muzzle, sniffing the scent of her welcome on the air. He approached her \u2013 slowly, timidly \u2013 his emerald eyes fixed on her in the hope that she would remove his pain.\n\n'But that's my best ruler!' said Mariella.\n\n'We'll make sure you have a new one, sweetheart,' Frida replied. 'By the looks of it, right now that little creature needs it more than you.'\n\nEmelia whipped off her dressing gown cord and fashioned it into a bandage against the fox's leg. The fox didn't flinch under her ministrations. He kept quite still, as if he trusted her. The other eleven girls admired their sister, her deftness, her confidence, her gentle handling of such a frightened being.\n\nEmelia finished securing the fox's bad leg into a splint.\n\n'I'm sure it's glowing brighter,' said Agnes, and it did seem as if the fox had absorbed Emelia's expertise. His golden fur was shining; his body beamed like a living lantern. Nudging Emelia's hand as if to say _thank you_ , he trotted out of the circle, three good legs padding on the ground, his healing leg treading lighter. The girls followed the fox's glow, happy that Emelia's skill had led them from that place of doubt.\n\nAs they followed the fox, the princesses noticed that the air had warmed, its texture thicker. A forest of oaks began to appear, trees with bark so shining the sisters were dazzled by their light. Delilah patted one of the trunks. 'These must be made of gold!' she said. When the others touched it too, it certainly felt to them like something precious.\n\nThe forest where the fox had led them became a glowing goblet. In the canopy that beamed above, every leaf on every tree turned honey, amber, topaz, ruby. It was as if the world was on fire, and they were standing in the centre of their father's crown. Delighted, they spun round and round until the forest was nothing but a bright blur.\n\nBut by the time they steadied themselves, the little fox had vanished.\n\n'We must keep walking,' said Frida. 'This adventure isn't over yet.' She looked round at her sisters. Their eyes were bright; they were chatting amongst themselves. 'We have to keep going.'\n\n'Can't we just stay here?' said Flora. 'It's so beautiful.'\n\n'We could. But I think something even more special is waiting for us at the end,' said Frida.\n\nAnd as she uttered these words, just as the forest of silver had done, the forest of gold began to disappear. The darkness grew around them once more. But this time the princesses were not frightened. They knew now that the dark was simply the beginning of new things. The dark was necessary. The dark might bring you a golden fox. The dark could be kind to twelve girls simply looking for their next path.\n\nAnd soon enough, they could hear the tinkling of bells, the same they had heard standing in their bedroom at the top of the staircase.\n\nAs they kept on through the dark, following this sound, a forest of diamonds appeared, diamonds hanging everywhere in heavy vines of brilliance, a splendour that outshone even the forests of silver and gold. Nature itself was a jewel. Beholding this sight, the girls felt themselves to be as powerful as the glittering stones draping every inch of the underground world they had discovered.\n\nDelilah approached the shining vines, her eyes wide in wonder. 'It can't be!' she whispered. She stood before the sinewy, silvery ropes, not daring to touch them.\n\n'What is it, Delly?' Chessa asked.\n\n'It's a dormidon plant,' said Delilah. 'The diamonds are growing on its vines.'\n\n'My goodness!' said Bellina.\n\n'I'd read that they existed,' Delilah went on, the excitement growing in her voice, 'but no one's ever seen one in the flesh. It's such a powerful plant, and that's why diamonds choose to grow on it.'\n\n'How beautiful it is!' said Agnes.\n\nAs the other girls ran over to join Delilah and Agnes, to take in the twisting, twinkling, intoxicating strings of stones, they realised the source of those tinkling bells: it was the diamonds themselves, moving against each other on the vines.\n\n'The seeds live inside the vine,' Delilah said. She turned to her eldest sister. 'Do you... do you think I could take some back with me, Frida? Just to see if I could grow one in the palace gardens, if Father ever lets me?'\n\nFrida put her hands on her hips and stood back to survey the thick, swaying curtain of dormidon vines. From somewhere very near came the sound of that clarinet, except now there was something else \u2013 a beating drum \u2013 and was that a trumpet, so fast and lively and exciting? The other sisters looked at each other: they could hear it too.\n\n'I promise you, Delilah,' Frida said, 'that one day you will return to those gardens. So you'd better take some dormidon with you, for when the moment comes.'\n\nDelilah stepped in amongst the vines and gently tugged one. It came away in her hands like a girl's cut plait. She tucked it into her dressing gown pocket and began to wander further in.\n\n'Let me help you, Delly,' said Frida, reaching towards the cool plant, feeling the icy touch of the diamonds as they tumbled from the vine on to the forest floor. 'You're going to need a bit more.'\n\n'How can you possibly know that?' asked Mariella.\n\nFrida shrugged. 'Just a feeling. Sometimes a feeling can be as true as fact.'\n\nMariella laughed at this, but she helped her sisters with the vines regardless. Bellina joined in too, and then all the princesses, and as several hands touched the swaying ropes, something astonishing happened.\n\nWith a _whoosh_ , a whole sheet of vines and diamonds fell to the forest floor, revealing the most incredible sight any of the princesses had ever seen.\n\nNone of them could speak. They simply stood there in their dressing gowns. All they could do was stare at the scene beyond them, as the dormidon vines snaked silverly around their feet.\n\nAnd what did they see? It's not easy to describe. But seeing as you've come this far with me, I will most definitely try.\n\nIt was a gigantic tree, probably the biggest tree they'd ever seen, and bigger even than that. At the front of this gigantic tree, the twists of its own roots \u2013 the thickest, strongest, highest roots imaginable \u2013 made an arch wide enough, and tall enough, for a three-storey house to fit beneath with room to spare.\n\n'I can see lights in there!' said Agnes.\n\n'And can you hear that wonderful music?' said Chessa.\n\nThey looked closer: under that soaring arch of roots, deep into its heart, a hollowed entrance hall spanned out in shining tiles of black and white. Around the hall, lights of every colour bobbed like fireflies, whilst above, hanging in the ceiling, clear chandeliers glittered like illuminated raindrops.\n\nIt felt wonderful to be near. In a funny way, it was just as they imagined it would be, even though they didn't know they were coming and they'd never seen it before. It felt like, in this place, the girls might have nothing to worry about, nothing to fear.\n\n'Wise to pursue?' Agnes whispered to her eldest sister.\n\n'Wise to pursue,' replied Frida, and Agnes was sure that Frida had quickly wiped away a tear.\n\nFour\n\nA Dance and a Doughnut\n\nThe girls moved as if in a living dream. Never in their lives had they desired something as much as they desired to enter that tree.\n\nBut _just_ as they had walked under the soaring tree roots and were about to set foot on that black and white floor, they heard a voice.\n\nA blustering, slightly squeaky, indignant voice.\n\n'Do you have the right to come in here?' asked the voice. 'Oh, goodness me. There's _twelve_ of you?'\n\nThey looked down. To their surprise, a peacock had appeared before them, his tail feathers spread. He wore a red velvet waistcoat that could not meet across the plump brilliance of his turquoise chest. His wings clutched a huge leather book, gold letters across it spelling out the words: _Necessary Guests_. The feathers on the crown of his head quivered in a way that was strangely familiar to the twelve sisters.\n\n'I beg your pardon?' said Lorna, who could not abide rudeness.\n\n'You can't just _walk_ in here, you know,' said the peacock. 'You have to _be expected_.'\n\n'Saleem,' said another voice. 'Please calm down.'\n\nFrom across the black and white floor came a lioness. Her voice was very different: smooth and deep, a little smoky, warm as a rug on a cold winter night. She was big, and the girls shrank away a little in fear. Her fur shone under the multicoloured lights, changing rainbow shades as she strode towards them. Her paws were huge, the size of dinner plates, and her eyes burned with an intelligence that intimidated the girls.\n\nThe lioness sat up straight before them. 'Page thirty-five, Saleem,' she said patiently.\n\nSaleem riffled through the pages of his book, even as his own feathers ruffled with indignation. 'Ah!' he squeaked. 'The _princesses_. I see. Yes, yes.' He cleared his throat. 'Item: found door to staircase, and descended despite spiders. Item: sourced boats and crossed lagoon. Item: walked the three forests, and endured doubt. Item: befriended, tended and mended the fox. Item: identified the dormidon amongst the diamonds. Item: discovered the tree palace.'\n\nThe lioness examined her claws. 'Brave, resourceful, clever and kind. And terribly imaginative. Just how I like princesses to be.' She grinned, retracting the claws. The girls still felt a little unsure. The lioness extended her front right paw. 'I wasn't sure you were ever going to find us,' she said. 'But I'm glad you did.'\n\nFrida was the first to shake the lioness's paw. 'Perhaps you've been expecting us,' she said. 'I believe we have a reservation.'\n\nLioness and princess eyed each other, and each seemed satisfied by what they could see. 'You have indeed,' replied the lioness. She swished her majestic tail. 'Welcome to the tree palace.'\n\n'The what?' said Agnes, forgetting her manners in a moment of curiosity.\n\n'The tree palace. You're a little late, but Saleem and I appreciate that sometimes one's delays are not one's fault,' the lioness went on. 'Moreover, of course, certain guests never know they're coming to the tree palace until they find it.'\n\n'Very true,' said Saleem. 'I call it the reverse search.' He peered at the girls. 'Often happens with the likes of you. Down here, you don't find what you're looking for, but you will find what you need.'\n\nOne by one, the other girls lined up to shake the lioness's paw. And a strange thing happened when human palm met feline pad: each of the princesses felt a touch of power. It was as if they had drunk a mug of hot chocolate and it was coursing through their bodies, with a little kick of chilli at the end. It felt, quite frankly, _marvellous_.\n\n'We could hear music,' said Chessa.\n\n'Ah, _that's_ how you did it. Of course!' said the lioness. 'Well, I expected you girls to have excellent taste. I do love jazz.' She swept a paw back to welcome the girls in.\n\n'My goodness,' said Emelia. 'Can you smell the food?'\n\nThe princesses were starving; they hadn't eaten a morsel since the cook's thin porridge many hours ago. And indeed, on the air, there was a mixture of the most delicious cooking aromas the girls had ever smelt.\n\n'I can smell lamb chops,' said Lorna.\n\n'Juicy ones!' said Vita.\n\n'Sprigged with rosemary,' said Flora.\n\n' _Look_ ,' said Polina, and she pointed to a trestle table at the back of the dance floor.\n\nOn this trestle table there were indeed lamb chops, and next to these the princesses could also see doughnut pyramids \u2013 and next to _these_ , glistening pavlovas and roast chickens. Oh, how they wanted to touch the tiny caraway seed rolls and curls of the creamiest butter! There were peppercorn biscuits piled high like a pastry chef's counting house. Fountains of elderflower champagne, fizzing and frothing into the finest glasses they'd ever seen. They wanted to dip their fingers in the tureens of bubbling chocolate sauce and the ice creams to pour it on, flavours of cinnamon, satsuma, vanilla and coconut all mingling in the air. They wanted it all.\n\nRound the edges of the dance floor, small circular tables had been arranged, with tasselled, pristine tablecloths. And in the near distance, a band of musicians was playing jazz \u2013 the jazz they'd been hearing so far away, for so long \u2013 now here, before them, sweet and clear, free and joyous! The girls felt a happiness they had never dared hope could be theirs again.\n\nThe lioness gazed at their pyjamas and dressing gowns. 'I _adore_ your evening attire. A little louche, yes, but inimitably stylish.'\n\n'Hold on,' said Mariella. 'Are they... bears?'\n\n'Oh yes,' replied the lioness. 'Dancing bears.'\n\nTwo bears were shimmying in sequin skirts whilst a leopard played the clarinet. A tiger was playing the piano, a monkey was on the sax, a tabby cat was on the trumpet, an ostrich in a red beret was shaking her tail feathers, and three tortoises were working together, one on top of the other, to strum the double bass. The music they were making was perfect to the girls' ears: lively, happy and quick. It was dizzying to watch them.\n\n'I'm _starving_ ,' said Ariosta, her eye on the teetering trestle table.\n\n'Then you shall eat,' said the lioness. 'You've done so well to get here, it's the least we can do.' She grinned indulgently. 'We're a bit off the beaten track, so take your table and the waiters will be with you.'\n\nThe girls did as she said, and the lioness clicked her claws. A toucan flew over, depositing a perfect jam doughnut on Ariosta's plate. In fact, all the waiters were toucans, flying from girl to girl with menus in their beaks.\n\n'Try that doughnut for starters,' said the lioness. 'Then take your fill.'\n\nAriosta took a bite, and rolled her eyes in amazement. ' _Unf_. This is the best jam doughnut I've ever tasted.'\n\nThe girls ordered from the toucan waiters, who obligingly flew hither and thither, fetching lamb chops and chicken legs, squishy cheeses and hot buttered toast, sausage and mash, glasses of champagne, strawberries dipped in chocolate, and cups of smoky black tea that seemed to contain within it all the spices of the world.\n\n'How do you like the place so far?' the lioness asked Frida.\n\nFrida sat back in her chair, holding a glass of elderflower champagne as she surveyed the inside of the tree palace: the dance floor, the glittering chandelier, her sisters' delighted, happy faces at the food and music surrounding them. 'It's funny,' she said, 'but it's just like the forests of silver, gold and diamonds.'\n\n'What do you mean?'\n\n'I mean that this tree palace seems to have been waiting for us particularly.'\n\nThe lioness nodded. 'Tree palaces are a bit like that.'\n\n'It feels like home,' said Frida.\n\nThe lioness shook her large head, her whiskers glinting in the lights. 'Oh, no. The tree palace isn't your home. You mustn't think it is.'\n\n'But it's so much nicer than what we've got upstairs!'\n\n'Well. It does belong to you, Frida, but it isn't your home. There's a difference. You mustn't forget that.' She pinned Frida with a thoughtful look. 'You girls can't stay here, you know.'\n\n'But why ever not? We were in the book of necessary guests!'\n\nThe lioness smiled. 'Exactly, Frida. You're _guests_. And good guests always leave in the end \u2013 however much we might want them to stay. But you must never forget your way here. Palaces like this won't survive without guests like you.'\n\nThe lioness was almost talking in riddles. Frida tried to understand, but before she could find out anything more, Saleem had strutted over to the table. 'Do take your fill, my ladies,' he said. 'But leave some time for dancing. Princess Frida, will you do me the honour?'\n\n'Dancing?' said Frida. She felt inexplicably sad after her conversation with the lioness. 'Oh, I don't dance. I can't.'\n\nSaleem readjusted his waistcoat. 'You can't dance? Don't believe it for a minute.'\n\n'None of us has ever really danced before.'\n\n' _Ever?_ '\n\n'Oh, well, there were the courtly dances we were taught as little girls: a step here, a heel there.' Frida looked over to the dance floor. 'But shimmying and stomping like those bears? Never.'\n\nSaleem extended his wing, and it flashed iridescent in the light. 'So brave to come here, but she won't dance! Fear not, Princess Frida! I will take the utmost care of you. Michel the monkey is playing a solo on the saxophone and it is not something I care to miss.'\n\n'Oh, go on, Frida,' said Polina. 'You need to let your hair down. You've looked after us so well. Go and have some fun.'\n\n'She's right!' said the others. 'Please, Frida. Please dance with Saleem!'\n\nOnly for her sisters did she accept Saleem's invitation, but it was a dance that stayed inside her feet for the rest of Frida's life.\n\nAs soon as the peacock and the princess took to the floor, it was clear that Saleem was an excellent dancer \u2013 wings neat, toes tidy, feathers adding the flair.\n\nBut it wasn't that.\n\nIt was the freedom Frida had talked of but never known for herself, until now, until the endless music and movement, round in circles, hand in wing \u2013 sometimes on her own, her feet moving and stamping, arms in the air, body jumping and swirling, whirling and twirling, in and out of the multicoloured lights. She felt as if her feet were flying on Saleem's wings, as if every soul on that dance floor with her \u2013 her eleven sisters, the lioness too, even a couple of the toucan waiters \u2013 had truly understood what it meant to be alive. And Frida said to herself, _What more could I ask from life than a monkey playing the sax, a stomach full of doughnuts, my sisters close and a dance floor made for us inside the roots of a gigantic tree?_\n\nBut in that moment, the lioness came up and whispered hot breath into Frida's ear: 'Even necessary guests must leave, my dear \u2013 and nothing in this palace comes for free.'\n\nFive\n\nKing Alberto's Second Bad Decision\n\nIt was the best time the sisters had ever known. Every night, their father would lock them in with his heavy iron key, and after the palace had fallen quiet, they would take it in turns to push open the secret door behind their mother's portrait,\n\nand down they would go,\n\nall five hundred and three steps of the dark staircase,\n\nacross the lagoon,\n\nthrough the three beauteous forests,\n\nuntil finally they reached their tree palace, where the lioness would greet them at the arch, Saleem would show them to their regular table, and the toucan waiters would attend to their every happiness.\n\nWhatever the girls had dreamed of eating, that exact dish was always on the menu. Baked beans on toast, spaghetti with clams, fresh fish fingers in buttery buns? No matter what they'd been dreaming about on the way there, the lioness's kitchen was ready. She would sit with them, and they would talk to her about their dreams for the future, or they would tell silly jokes, and she would tell them stories about princesses locked in rooms. And then the girls would dance in rapture to the jazz music until they could barely feel their feet, and their shoes were worn through.\n\nAnd every morning in the upstairs palace, King Alberto would unlock their bedroom door to find his twelve lovely daughters fast asleep in their rows of beds. All the king had ever wanted was for his girls to go to sleep, because he believed that only in their dreams could they be safe. (That, and they were easier to manage than when they were awake.) As he watched them snoring, he was delighted that they were finally so obedient.\n\nThe girls hated their daytime hours doing nothing. But although the king and his advisers continued to deny them any tasks or pleasures, the existence of their tree palace made everything bearable. The sisters knew that, come the night, they would have a chance once more to feel free.\n\nThey would whisper about new dance steps, what tiara might look best with their pyjamas. Ariosta looked forward to a swim in the lagoon. Delilah had discovered that the forests contained other plants for her to examine. Emelia always kept her eyes peeled for the little golden fox, but I am sad to say she never saw him again. Instead, she busied herself making sure the jazz musicians had sleek fur and clean claws, in order to play their instruments to the best of their abilities. Chessa, who had been promised an invitation by the lioness to sing onstage with the band, would practise in her mind which numbers she was going to perform.\n\nIn short, the girls started to feel alive. They were in possession of the most brilliant secret, and they hid it so very well that neither King Alberto nor any of his advisers had the faintest clue.\n\n'It feels like _home_!' Bellina declared happily one breaking dawn, all of them sinking gratefully (but not particularly gracefully) into their beds after a night of dancing.\n\nBut Frida was worried. She'd never been able to put out of her mind what the lioness had told her on their first visit. The lioness had said that the tree palace _belonged_ to the princesses, but they could never call it home. Was that because someone was going to steal it from them? Why was she so insistent on reminding Frida that they must leave the tree palace, when it seemed expressly designed for them? And if nothing in the tree palace came for free, what was the price they were going to have to pay for spending so much time there?\n\nShe almost felt anger at the lioness \u2013 for showing them such a wonderful place and making them feel as if it was theirs, only to suggest they couldn't stay. They'd explained to her how miserable their life upstairs had become! It wasn't as if the lioness was unaware of their horrid situation.\n\nFrida sighed to herself. Her mother's death had taught her well that the world doesn't always skip along to your wishes. But then again, wisdom didn't always make this fact any easier to accept.\n\nSo one night, after coming back up the staircase at dawn, closing the secret door quietly, adjusting her mother's portrait and making sure every princess was accounted for, Frida said they should make a pact. 'We must swear to each other that we will protect this tree palace,' she said, kicking off her worn-out shoes and rubbing the balls of her feet.\n\n'But why? We're not going to tell anyone,' said Ariosta, snuggling under her duvet.\n\n'Of course we're not. But that might not stop Father's advisers \u2013 or Father himself \u2013 from asking questions.'\n\n'Father's none the wiser,' said Flora. 'We've been doing this for weeks!'\n\nFrida frowned like a military general. 'True, but we cannot be complacent. What would we do if we could never dance in the tree palace again? If we were trapped in this bedroom without even the promise of the music down below to cheer us up?'\n\n'Imagine never seeing the lioness again!' said Delilah.\n\n'Or Saleem,' said Mariella.\n\n'Ugh,' said Vita, burying her face in her pillow. 'I couldn't bear it.'\n\n'Exactly,' said Frida. 'We must plan. We found the tree palace together, and if anything happens we will defend it together. Whatever it takes, we'll do it. Agreed?' She put her hand out.\n\n'Agreed,' said the eleven others, without hesitation, piling their hands on top of Frida's.\n\nBut as it happened, there was just one tiny detail the girls hadn't thought through. Not even clever Frida.\n\nIt caught them out, as you might say, royally.\n\n\u22c7\n\nOne morning, King Alberto opened their bedroom door as usual. And, as usual, his daughters' twelve pairs of shoes were lined up neatly against the wall. Except this time (why this time? Who knows \u2013 kings are unreliable characters) he bent down and lifted one shoe in order to admire the craftsmanship.\n\nThe king was in for a shock.\n\nHe stood there in the soft morning light, shaking his grey head as his girls slumbered away. 'These are not the shoes of a princess,' he said to himself. 'They're completely ruined!'\n\nAnd he was right. The sole of this particular shoe \u2013 belonging, in this case, to Polina \u2013 was utterly destroyed. The king reached down and picked up another shoe, then another and another \u2013 until he'd turned all twenty-four shoes upside down.\n\nAll of them had more holes than a fine Swiss cheese.\n\nHe tiptoed away and ordered the royal shoemaker to make the girls some better ones.\n\n'But I never stop making shoes for your daughters, Your Majesty,' said the shoemaker.\n\n'I beg your pardon?' said King Alberto.\n\nThe shoemaker gestured mournfully towards his dwindling leather supplies. 'I've made more pairs of shoes for them than my wife makes me hot dinners.'\n\n'What on earth is going on?' King Alberto asked himself, for the shoemaker was a talented man and had been making sturdy footwear since the king was a boy.\n\nThe next morning, the king opened the girls' bedroom door and discovered that the shoes he'd ordered for his daughters but one day previously were again worn through.\n\nHe sent for even more shoes. And yet again, the morning after their delivery, whilst his daughters slept unawares, he found that every shoe was ruined.\n\nKing Alberto hated not knowing answers generally, but this particular mystery enraged him. You'd think a king had bigger fish to fry, but no! He summoned each daughter, one by one, and asked them to explain the reason behind the unending pairs of holey shoes. The girls were frightened, but Frida had prepared them for disaster. Remembering the pact they had made to each other, the princesses held their nerve.\n\n'The guard dogs bite them,' said Frida.\n\n'I walk a great deal,' said Polina.\n\n'I stood on a nail,' said Lorna.\n\n'The shoemaker's no good,' said Ariosta.\n\n'My feet get hot, so I let the air in,' said Chessa.\n\n'I find mice in them,' said Bellina. 'We need to get a palace cat.'\n\n'It's my fault,' laughed Vita. 'I scuff my feet all day.'\n\n'I have no idea,' said Mariella, with a shrug.\n\n'I ripped them on a tree root in the garden,' said Delilah.\n\n'I held them too long over a candle when I was warming them up,' said Flora.\n\n'They're my favourite pair, so I've worn them through,' said Emelia.\n\n'Maybe they're supposed to have holes?' said Agnes, staring at the floor.\n\nKing Alberto was sure they weren't telling the truth. He felt it in his royal gut. His daughters had such innocent faces, but it was too bizarre that they were going through so many pairs of shoes at such a rapid rate! The shoemaker, who had made thousands of pairs of shoes and whose fingers were worn to the bone, begged for early retirement. The king dismissed him, and raged that his daughters were out of control.\n\n'They're just shoes, Your Majesty!' his advisers pleaded with him, knowing that there were much more important things to be worrying about, like gathering the harvests, and the uprisings in the west of the kingdom.\n\nThe king couldn't agree. They weren't just shoes. They were his _daughters'_ shoes, and they had holes in them when they shouldn't. It felt like his girls were going somewhere beyond his reach, and he didn't like it.\n\nOne morning, he summoned Frida to his throne.\n\nFrida came, feeling a nervousness in her stomach which she tried to push away. As usual, the black drapes were up, but Frida could just make out the dust gathering in small grey balls around the legs of her father's ornate throne. _Really, someone should do a spring clean in here_ , she thought.\n\nHer father's advisers were huddled in the corner like a group of worried penguins, the candlelight throwing their shadows into grotesque shapes. She sighed, thinking about the beautiful multicoloured lights of the tree palace, the fluttering wings of the toucan waiters, how pleased the lioness always was to see the princesses and how they danced and danced with Saleem \u2013\n\n'So, my girl,' the king said, interrupting her daydream. 'Are you going to tell me your secret?'\n\nFrida flicked her eyes towards the king. Something in her father's voice chilled her. The memories of the previous night's dancing melted like ice under a flame.\n\n'My secret?' she echoed.\n\n'Come on, Frida. You're slyer than a fox. You're the eldest. You're the ringleader. You should be setting an example. I've asked you why your shoes are worn out and not one of you has told me the truth. Why are your sisters all so disobedient?'\n\nFrida thought about her younger sisters. They were so much happier since the discovery of the tree palace: it made their life in this upstairs mausoleum tolerable. She thought of the pact she'd asked them to make. In a way, her father was right. She _was_ responsible. She had been the one to find the door behind the painting, after all. She had been the first to shake the lioness's paw. She had been the one who encouraged her sisters to lie. 'Father,' she replied, 'They are not disobedient. They are loyal and true.'\n\n'True to what?' asked her father. 'To _whom_?'\n\nFrida remained silent.\n\n'You are the most disobedient of all,' he said. 'Just like your mother.'\n\nFrida closed her eyes. 'I beg you, Father, attend to your kingship.'\n\n'Outrageous cheek! I will know your secret,' Alberto raged, 'and you will tell me or face the consequence!'\n\nFrida took a deep breath. _The consequence_. She knew silence was no longer an option, that she must speak and suffer. 'Father,' she said quietly, 'it is not your secret to know.'\n\nAt this, the king leapt out of his throne, the hair on the top of his head quivering. The advisers rushed forward, worried that he might trip on his robes. 'Get out!' he screamed at his daughter. 'But don't think this is the end. I'll get the truth out of you if it's the last thing I do!'\n\nFor the first time in her life, Frida was truly frightened. Suddenly, the lioness's voice filled her ears: _Nothing in this palace comes for free_.\n\nShe looked at her father's advisers, who did nothing to help her, and she stumbled away, running through the gloom of the corridors to find her sisters. _You think I'm slyer than a fox?_ she thought, her mind racing. She remembered the golden fox that Emelia had saved, down in the darkness. _Well, Father_ , she thought. _And you too, lioness._ You haven't seen anything yet.\n\nBy the time Frida returned to the bedroom, she had composed herself.\n\n'What did he say?' asked Vita, looking nervous.\n\n'Nothing he hasn't said already,' said Frida, smiling. 'Don't worry. We'll go down to the tree palace tonight and have a marvellous time. Although \u2013 listen, my darlings. Look after the soles of your shoes. Less dancing, if possible.'\n\nShe was met with a chorus of protest.\n\n'I know, I know. But we need to be even cleverer than we already are.'\n\nFrida never wanted to be the one to tell her sisters to dance less. But what could she do? Their father was so suspicious, so dangerous! His face in anger these days was redder than a lobster. She feared that their time in the tree palace was running out, but she wasn't going to let her sisters worry too. She racked her brains to think of some way to put King Alberto off the scent, whilst ensuring her sisters could still go to the tree palace. Yet all the time, the lioness's words went round in her head: _Even necessary guests must leave_.\n\n\u22c7\n\nThat night, as they rowed across the lagoon, Frida draped her fingers in the dark water. She felt its cool quality, how its very touch cleansed her father's anger and strengthened her resolve. They walked through the forest of silver, with Frida bringing up the rear. Making sure none of the others saw her, Frida quietly picked up a shining fallen leaf and slipped it into the pocket of her dressing gown. When they reached the forest of gold, Frida did the same again, scooping up a glowing twig, adding it to the silver leaf. And in the forest of diamonds, ensuring that she was the last to leave, she plucked one of the precious stones and dropped it in her pocket. It rested with the silver leaf and gold tree limb, cold and hard through the fabric of her gown.\n\nNone of the other girls noticed a thing.\n\nThat night in the tree palace, the lioness decided the time had come for Chessa to step up to the stage and take her moment.\n\n'Chessa,' she announced, 'you are our starriest singer, on this starriest night!'\n\nThe other girls clapped and cheered, delighted that the lioness was finally going to hear their sister's magical voice. Chessa, who had been waiting for this for weeks, bounded up, standing before the microphone as if it was the most comfortable place in the world.\n\nEven the shimmying bears in their sequin skirts \u2013 even the toucan waiters \u2013 stopped what they were doing to listen. A hush fell, and Chessa began to sing. Into the silence, her beautiful, entrancing voice rose up, spreading through the roots of the tree. It wove like invisible smoke into the ear, filling their hearts, bringing tears to eyes and smiles to whiskers.\n\nOh, it was an evening none of them would ever forget. Chessa started with a song called 'Laurelia, My Love', a sad number which nevertheless had some strains of happiness to be heard in its major shifts, but her next number was a jumpy, jivey, madcap extravaganza with Michel the monkey on the saxophone that had everyone whooping out of their chairs on to the dance floor.\n\nVita even taught the bears how to pirouette three times in a row without falling over. And every time Chessa thought her set was finished, trying to step away from the microphone in order to slug back a glass of elderflower fizz and reunite with her sisters, the leopard with his clarinet and the tabby cat on her trumpet would shout, 'Come back and sing another!' \u2013 and the ostrich threw her feathers at Chessa's feet in adoration.\n\nThe lioness, who had noticed Frida looking a little sad despite all this fun, sat down next to her.\n\n'Have you been thinking about what I said, Princess Frida?' she asked in her low, warm voice. 'Have you been thinking how to say goodbye?'\n\n'I never stop thinking about it,' said Frida a little coldly. She felt the remnants she had taken from the three forests lodged inside the pocket of her dressing gown.\n\n'You're angry with me,' said the lioness.\n\nFrida didn't dare admit it, but she could not help but speak a little of her mind. 'But it's so _lovely_ down here, you see?' she said. 'My sisters are happy. Look at them dancing!'\n\nThe lioness twisted her whiskers together and let them spring apart again. 'Tree palace or no tree palace, you and your sisters have a capacity to be happy wherever you are, which is a very fortunate thing indeed.'\n\n'Our father \u2013' Frida began.\n\n'From what you've told me about your father,' said the lioness, 'he does not sound like a bad man. But he is a lost one. Parents can be tricky creatures.' She smiled at Frida. 'Or so I've heard.'\n\n'Here is the only place we can feel happy,' said Frida, feeling stubborn.\n\nThe lioness turned away from the chaos on the dance floor and placed a dinner-plate paw on Frida's heart. 'No, Frida, that's not true,' she said. 'Look closer.'\n\n'He wants to know what we're doing every night to make our shoes so worn out. He keeps summoning me, talking about _the consequence_. I'm scared what he'll do if he finds out \u2013'\n\n' _Frida_.' The lioness pressed a little harder with her paw, and Frida felt suffused with such serene power, such warmth and contentment, such a sense of coming home.\n\n'I promise you, I understand,' the lioness said. 'But listen to me. Frida, trust yourself. You know exactly what you have to do.'\n\n\u22c7\n\nThe next morning, King Alberto summoned his eldest daughter yet again.\n\nHe looked crazed. His hair was even more stuck out through the top of his crown, and he was waving a pair of Frida's shoes on his hands. 'Do these look like the shoes of a princess?' he shouted.\n\nFrida had felt completely calm since her conversation with the lioness at the end of the previous evening. Her whispered words made circles in her head: _Frida, trust yourself_.\n\n'They look like the shoes of a woman with places to go,' she said to her father.\n\n'Argh!' King Alberto hurled the shoes across the room, where they struck the side of an adviser's head with a leathery slap. 'You have _nowhere_ to go,' her father cried. 'And I made it so in order to protect you!'\n\n'You have let us rot inside this palace,' she replied. 'You've been so scared that we will die, as your queen has died, that you've tried to stop us living. You're mad with grief and blind to your madness. It has been outrageous and unfair.'\n\nHe narrowed his eyes. 'Then tell me your secret, and maybe I'll give you some freedom.'\n\nShe looked him in the eye. 'I fear your idea of freedom is not the same as mine.'\n\n'Frida, as your king, I demand the secret.'\n\nShe took a deep breath. 'Then, as your subject, I deny you.'\n\n'Then you give me no choice,' her father roared.\n\nFrida knew that _the consequence_ was coming.\n\n'Frida, I banish you!'\n\nShe bowed her head. The air sang with a strange electricity. _I banish you_. Her father's words washed over her, they drenched her skin with pain, but they did not unsteady her. She did not move, she did not speak. _Banished_ : the word like a magic spell! Out of the corner of her eye, Frida could see the advisers, frozen in fear. From far off, she was certain she heard a lion's cry.\n\n'Sire,' said one of the advisers, stepping out of the shadows, clutching the hurled shoes. He cleared his throat. It was Clarence, the youngest of Alberto's staff, a pair of shrewd eyes in that whippety-thin face. Despite his youth, Clarence looked exhausted, as if dealing with Alberto over the past weeks had done him in.\n\n'Princess Frida is \u2013 um, a great _asset_ to Kalia, Your Majesty. Are you quite sure that this is a \u2013 er, a sensible thing to do?'\n\n'Be quiet!' screamed Alberto. 'Only weaklings change their minds! Frida, did you hear me? You're _banished_!'\n\nStill Frida did not speak. The king stopped, catching his breath. 'And hear this too,' he went on, clambering out of his throne and pacing up and down. 'Whosoever can solve the riddle of your sisters' shoes shall inherit my kingdom, and choose any remaining girl for a wife.'\n\n'Sire!' cried Clarence.\n\nBut King Alberto was past listening to counsel. He pointed to the circle of gold resting on his hair. 'And I shall place this crown on their head myself.'\n\nAgain, Frida said nothing, her eyes fixed on the balls of dust around her father's throne. The king's own eyes widened as he circled round her. 'Oh, you've nothing to say now, Frida? Thought not \u2013 it's a miracle \u2013 Frida has nothing to say! This is my royal decree,' he spat. 'And once done, it cannot be undone. Didn't you say I was the law?'\n\nAt this, Frida looked up. She could feel the chill of the silver forest running through her veins and how the heat of the gold forest was turning the inside of her head to flames. She looked at her father, and her eyes flashed as hard as a pair of diamonds. Clarence shrank from her, and King Alberto looked frightened.\n\n'See how he would give away a daughter so thoughtlessly?' she said. Her voice was strong and clear. 'Never mind the kingdom. Of _course_ it's not sensible, Clarence. But when has my father ever done anything sensible?' She drew herself up. 'Father, you can banish me, but to marry one of my sisters to a man she does not love \u2013 that is beyond cruelty.'\n\n'My word is final!' said King Alberto.\n\nFrida looked at him with a thoughtful expression she had borrowed from the lioness. 'I see that you will never change the way you treat your daughters. It pains me. Perhaps you will live to regret it. But even after this, for as long as you call me daughter, I will never tell you the secret of our shoes.'\n\nAlberto climbed back up into his throne and thumped his fist on the arm. 'Then I shall never call you daughter again!'\n\nFrida took her shoes from Clarence's thin and trembling hands. 'Then so it shall be,' she said, and walked from the throne room without another word.\n\n\u22c7\n\nFrida's sisters were enjoying their hour in the palace grounds, still unaware of her predicament. She took a pouch of Kalian coins from the royal mint, and packed the meagre contents of her drawers into a suitcase as quickly as she could. She added the silver leaf, glittering with light, the gold branch that glowed like the sun, and the single diamond, hard and cold in her palm, plucked from her last visit to the underground world.\n\nWhen her sisters came back, they found a pale-faced Frida sitting on the edge of her bed, in a plain brown dress and the sort of coat that no one would ever suppose belonged to a princess.\n\n'Where on earth did you find that coat?' asked Delilah.\n\n'And why do you have a suitcase?' asked Mariella.\n\n'It's Father, isn't it?' Agnes said.\n\n'It's always Father,' said Ariosta.\n\nFrida smiled sadly. 'He's realised that there's another reason why our shoes are wearing out so quickly, and he wants to know what it is, of course. He wants to know about Saleem and the lioness, and the toucan waiters. He wants to know it all. But I won't tell him any of it. So here's the thing, my loves. He's banished me.'\n\nA cry came up from the others, a sound of rage and sadness.\n\n' _Banished?_ ' said Bellina, falling to the floor, wrapping her arms round Frida's knees. 'No, no, you can't leave us, you _can't_.'\n\n'You'll be perfectly fine without me,' said Frida.\n\n'We won't,' said Polina.\n\n'Where will you go?' said Lorna.\n\n'How are you going to _survive_?' asked Flora.\n\n'I was born to do more than survive. And so were you.' Frida rummaged in her coat pocket and pulled out a key. 'And guess what I've got.'\n\n' _No_. It can't be,' said Vita. 'You naughty thing!'\n\n'The key to Mother's motor car.' Frida grinned. 'If Father thinks I'm walking out of here, or riding a _horse_ , he's in for a surprise.'\n\n'I think you're lucky,' said Emelia. 'You get to leave. You get true freedom, whilst the rest of us stay here.'\n\nThe others were quiet at this, and Frida looked sombre. She thought about the terrible decree her father was going to make, how he would give one of his daughters away, and his kingdom too, to whichever man \u2013 it didn't even matter who he was! \u2013 as long as he was first to uncover the secret. Emelia was right in that respect, Frida thought. By being banished from Kalia, a random marriage against her will was one fate she was definitely going to avoid. King Alberto was indeed a law unto himself; look at the way he treated even clever Clarence. Her sisters were going to have to be strong.\n\nFrida stood up. 'I'm lucky in some ways, Emmy,' she said. 'But you'll still have the tree palace. It will be there for as long as you need it. More importantly, you still have each other. And anyway, I've a suspicion that freedom is a bit of a slippery fish.' She placed her hand on each of their hearts, one after the other, just as the lioness had done to her. 'I swear to you, as I love each and every one of you, I _will_ come back.'\n\nShe scooped her suitcase off the bed. 'I don't know where I'm going, but I promise that I will work out how to free us all. In the meantime, you must never stop going down to the tree palace. Do you promise? You have to keep going, otherwise... well, otherwise it might just disappear.'\n\n'Disappear? How?' asked Chessa.\n\n'If a tree palace doesn't have its necessary guests, it might get forgotten. If you want to keep something alive, you have to turn up.'\n\n'We will,' said Agnes. 'We promise.'\n\n'There are going to be difficult times ahead,' said Frida. 'So cry if you feel like crying. Never hold in tears, it's pointless. Then dry your eyes, look around you, think \u2013 think a bit _more_ \u2013 then act. It's time to stand on your own twenty-two feet, my loves, whether your shoes have holes in them or not. And if you can cross lagoons and heal foxes and find tree palaces, then you're halfway there already.'\n\nShe hugged each of her sisters tightly. 'Will you tell the lioness that I understand now, and that I said goodbye?'\n\nBefore the princesses could ask Frida what she meant, she had gripped her suitcase handle and walked out of the bedroom with her head held high. She took a left, then a right towards the staircase that led to the palace garages.\n\nThe royal mechanic, who'd heard about the banishment and assumed she was there under her father's orders, opened the garage door for her. Frida revved her mother's engine so loudly that the mice that had been happily nesting in the passenger seat, for several generations by now, squeaked in terror, jumped out en masse and dived inside an empty petrol can.\n\nHer sisters, who, as you will recall, had no window in their room, couldn't even watch her go.\n\nFrida drove along the coastal road out of Lago Puera, the salt wind billowing her loose hair, the sun on her back, both palaces diminishing with every revolution of Laurelia's wheels. Who knew that standing up to her father would give her the freedom she'd so desired? That part had been easy in the end, but it didn't make it any easier to leave.\n\nThe truth was, Frida's feelings were complicated.\n\nLook at this sunshine \u2013 this should have been a glorious moment, something she'd longed for, for years! But how could she be happy knowing her sisters were at the mercy of their father's ridiculous decree?\n\nFrida sighed, set her eyes on the road and knew that she would never dance in the tree palace again. The lioness had known this day would come well before Frida had. But the tree palace had not completely disappeared. It was inside Frida now, a paw print pressure, a hot coal memory stoking her fire. And her sisters would still go dancing. They must; it was all they had. They would think of something to protect their secret, and so would she.\n\nA few more turns of the wheels, and the motor car dipped over the brow of a hill.\n\nFrida honked her horn at the last of the Kalian seagulls,\n\nand with that, the eldest princess crossed the city border,\n\nand was gone.\n\nSix\n\nDelilah and the Dormidon\n\nMeanwhile, back at the palace, King Alberto printed his ridiculous decree one thousand times. It looked like this:\n\nROYAL DECREE\n\nATTENTION, SUBJECTS:\n\nBE THE MAN WHO SOLVES THE SECRET OF THE SHOES!\n\nINHERIT THE KINGDOM OF KALIA AND MARRY A PRINCESS\n\n(I'VE GOT ELEVEN: YOU CAN CHOOSE)\n\nInterested candidates: please register at the main palace door by Tuesday morning\n\nBy order of HRH King Alberto of the Kingly Kingdom of Kalia\n\nSigned: Alberto Rex\n\nOne thousand decrees were glued fast to shop windows and caf\u00e9 doors, and further afield, on farmers' gates. The kingdom and its princesses were up for grabs, and King Alberto wanted everyone to know. Some of the decrees came unstuck, and I like to think of them being blown by the sea winds far beyond the city, along the coast road, up over the hills and on to the mountain passes. I also like to think that one found its way into Frida's hands. One can only imagine her feelings on seeing her father's stupidity, proved in print.\n\nBy Tuesday, a long line of applicants appeared outside the palace door. Men of all ages and abilities came to try their luck in solving the mystery of the princesses' shoes. They arrived from every corner of the kingdom, far beyond the city of Lago Puera, from the borderlands, from the mountains, from the sand dune towns. Some women came too, but to their intense annoyance, the palace guards told them to leave.\n\nThe men formed an orderly queue, flexing their muscles at each other and boasting about which girl they'd pick out of the remaining eleven. They set up tents, and market traders came to sell them lunch, and street entertainers came to take their money. None of these men had much idea what was actually going to be asked of them once they were inside the palace walls. They just knew it was something about shoes, so it was going to be easy.\n\nClarence, the whippety-thin adviser, slipped behind one of the black drapes over the throne room window and watched the circus gather. He thought King Alberto had lost his mind. Princess Frida had been right \u2013 what sort of method was this to find the future king of Kalia? Alberto had ordered that a camp bed be set up outside the girls' room for a man to sleep on. Rightly anticipating a high level of interest, he'd decreed that each man would be allowed one night only to solve the mystery.\n\nClarence put his face in his hands and hoped for a miracle.\n\nThe eleven remaining sisters, who had been allowed into the throne room as these events unfolded, watched miserably from another window. Bellina threw a walnut and snickered as it bounced off a man's head.\n\n'I don't care if these men are princes or paupers; I don't want any of them,' said Ariosta.\n\n'This is _awful_ ,' said Lorna. 'I feel sick. I miss Frida so much.'\n\n'Frida said she'd come back and save us, and I believe her,' said Agnes.\n\nBut the other girls could not share their youngest sister's hope. Vita's usually happy face was pale. 'Well, she isn't here now, and we're going to have to be very, very clever,' she said.\n\n'You're right. All sorts of idiots are going to try to uncover our secret,' said Delilah. 'We have to make sure none of them succeeds, but we are _not_ going to throw walnuts.' She gave Bellina a stern look.\n\n'Frida was banished for refusing to reveal our secret,' Chessa whispered. 'She sacrificed her happiness for ours. So we must never stop \u2013' here, she mouthed the word \u2013 ' _dancing_.'\n\n'That would make Frida's banishment twice as bad,' agreed Ariosta. 'The tree palace is all we have now. I wonder where she is. Will she write to us, do you think?'\n\nMariella was sobbing quietly. 'I don't want to get married,' she said.\n\n'I certainly don't want to marry anyone so intent on spoiling our fun,' said Polina, looking out of the window at the line of preening men.\n\n'Exactly \u2013 someone who's going to peer through the keyhole and creep behind us, watching everything we do,' said Agnes with a shudder. 'Anyway, I'm too young to be married. Surely if I'm ever picked, Father will say no?'\n\nLorna bit her lip. 'I don't know, Aggie. That is why we have to be careful.'\n\n'But, girls,' said Flora. 'Whichever man comes to sit outside our door, he'll know we're not in there. We can't block up the keyhole, because he'll get suspicious. What are we going to _do_?'\n\nThe princesses looked forlornly at one another, as outside the line of men grew and grew. Their situation felt impossible. It seemed inevitable that one of them \u2013 someday soon \u2013 would be taken as a reluctant bride, and the rest of them forbidden to dance ever again.\n\nSuddenly, Delilah's eyes widened in excitement. 'Oh, boy. I've got it,' she said. 'Why didn't I think of this before? Bedroom. Now, before the first man gets in.'\n\nAs princessly as they could, the eleven girls walked back to their room. They could almost see the excitement fizzing around Delilah's head.\n\nOnce they were all inside, and the bedroom door closed, Delilah rushed over to her dressing gown. From down below, they could hear the palace door being opened, and the sound of tramping feet as the men lined up to be registered to sleep outside the princesses' room.\n\n'It's got to be here somewhere,' Delilah said, throwing leaves and soil and even a woodlouse across her bed. 'Aha!' She brandished her treasure at her sisters. It didn't look very promising: a limp, dried vine of brownish colour, dangling from her hands like a worm.\n\n'That's supposed to help us?' said Bellina, tears welling in her eyes.\n\n'Yes, it is,' said Delilah proudly. 'Don't you remember the first time we went to the tree palace?' Her sisters looked at her blankly. 'The _dormidon_!' she whispered. 'All right,' she said, hoiking herself up on to her bed and looking round at her sisters. 'I know it doesn't look like much. But we haven't much time, and we need to discuss this. Tell me what you know about the dormidon plant.'\n\nNo one said anything. Delilah sighed. Voices could be heard coming up the corridor.\n\n'Delilah, _hurry_ ,' said Agnes.\n\n'Girls, we _are_ going to go dancing,' Delilah said. She held the vine up. 'And this is how: If you drop a dormidon vine in hot water and drain off the liquid, it will make you a tasteless sleeping draught so powerful that just one drop of it in a goblet of wine or cup of tea is enough to knock a grown man out for twelve hours.' Her voice dropped to a whisper. 'But you have to be very, very careful with the dormidon, because too much of it will kill someone. Only experienced botanists should handle such a powerful little plant.'\n\n'An experienced botanist like you, say?' said Agnes, grinning.\n\nDelilah grinned back. 'You know exactly where this is going, don't you, Aggie. I've got enough in this bedroom for a hundred men.'\n\n'But what if you make a mistake and knock them out... forever?' said Emelia.\n\n'Well, it's their own damned fault for coming here to ruin our lives in the first place,' said Ariosta. 'Spying on us, trying to marry us without our permission.'\n\n'I'd put three dormidons in their drink if I could,' said Vita.\n\nLorna put up her hands. 'All right, all right. We don't want dead men on our hands. We just want them to leave us alone.'\n\n'Wise to pursue?' Delilah asked her sisters.\n\n'Wise to pursue,' they whispered back.\n\n\u22c7\n\nThe first man to be admitted was \u2013 how can I put this tactfully? \u2013 a buffoon. He didn't walk into the palace, he _swaggered_. He practically _rolled_ in, as if grabbing the kingdom for himself and picking a daughter \u2013 or grabbing a daughter and picking the kingdom \u2013 was as easy as brushing his teeth.\n\nI forget his name. It doesn't matter.\n\nIt was Agnes, the most innocent-looking, the sweetest, the most childlike, who smiled and handed him a goodnight cup of milky hot chocolate as he sat on the edge of the camp bed. The man took it greedily, not even bothering to say thank you before he swigged it down. The girls were locked in their room immediately after.\n\nSettling in for a night of vigilance, he was asleep in five minutes.\n\n\u22c7\n\nThat night in the tree palace, every one of the princesses danced that little bit longer, taking extra pleasure in every whirl and jig they made, in case it was the last time they might ever be allowed. Agnes told the lioness that Frida wanted her to know that she understood, and passed on her message of goodbye. The youngest princess was surprised by the look of pride in the lioness's eyes, where Agnes thought there might at least have been sadness.\n\nThe next morning, Delilah's plan had worked.\n\nThe first man was late to his meeting with the king and had no evidence to present him as to the girls' activity. He could barely string a sentence together and was booted out of the first floor window, and \u2013 if I recall correctly, from Emelia's account of it \u2013 he landed slap bang in a pile of horse manure.\n\nThe second man was given a goblet of delicious Kalian wine to drink. Again, Agnes, the saintly darling little angel that she was, was given the job of handing over the drink. He sloshed it down, and through their door the girls could hear his teeth clanking against the soft gold of the cup, followed by loud snoring. They moved aside their mother's portrait and vanished in silence.\n\nThat night down in the tree palace, they told Saleem and the lioness the news. Delilah was made guest of honour, and the toucans brought her a special doughnut filled with wild blueberry jam, with a diamond on top.\n\n\u22c7\n\n'It's all right,' said King Alberto to himself, after the third, the fourth, the fifth, the sixth man entered the palace, full of confidence, only to be dismissed as unsuccessful, unable to recall a jot of what he might have seen or heard. 'There are enough men out there. One of them will crack it, I'm sure.'\n\nBy the failure of the eightieth man, King Alberto was nearly bursting with fury.\n\nOver the next four months, the line outside the palace shrank as, one by one, the men attempted to uncover the secret of the shoes and, one by one, they failed. Their tents were packed up, the smell of street food evaporated, and the entertainers left to find bigger audiences in other kingdoms. Inside the palace, King Alberto bounced up and down on his throne until his backside split a cushion. 'Does every man in Kalia have a radish for a brain?' he ranted, spluttering on the feathers.\n\nHis advisers, particularly Clarence, were delighted that Alberto's scheme was failing, but the girls didn't know how much longer they could get away with drugging a man with dormidon every night. Delilah's supply of the plant was running perilously low. The last time they'd gone to the forest of diamonds, they realised they'd plucked all the ripe plants, and the saplings were still growing.\n\nBut whilst they still had the last of the dormidon to help them, the eleven sisters descended the five hundred and three steps of the staircase, crossed the lagoon in their boats, walked through the three sparkling forests, and danced in their tree palace until their shoes had lost their soles. Saleem and the lioness were always happy to see them, but they always asked them if they had news of Frida, and the sisters always had to say no. The telephone lines were still disconnected, and they hadn't even received a letter.\n\nAnd were they happy?\n\nWell, that's a good question. Their happiness these days was of a strange kind. They were outsmarting those who wanted to ruin their fun, but it was a happiness that lasted in the whirl of a dance and died within a breath. It was _tiring_ having to attend to these men every day. And it wasn't just that. Going to bed in the early hours of morning, they felt as if an anchor of sadness was plunging through them, pinning them to their mattresses. The dancing had stopped being enough. They dearly missed their sister. They wanted her stories, her strength. They wanted to stand on their twenty-four feet together, not their twenty-two.\n\nEventually, the last man turned his back on the palace, thwarted in his attempt to unmask the princesses' secret. The king was exhausted, regretting deeply that he'd ever agreed to such a ridiculous scheme. He blamed his advisers for suggesting it, and they duly apologised.\n\nFor the girls, never had a victory tasted so bittersweet. A bit like pre-boiled dormidon, in fact.\n\nThe palace was quiet. None of the girls felt like dancing. Not even a tiny jig.\n\nAnd then, just like that, everything in Kalia changed forever.\n\nSeven\n\nA Coronation\n\nIt was Vita who heard it first: a faint buzzing in the sky. It was coming, she suspected, from across the sea.\n\nIt was their hour of recreation, and the eleven girls were in the palace garden, wandering aimlessly amongst the palms and hothouse flowers, whose bright pinks no longer cheered them. The high walls that surrounded them cut most of the sunshine at this time of day, and the garden had no view.\n\nBut Vita heard it, all the same. She looked up, and saw only the bright rectangle of cloudless blue above her. Yet the buzzing was getting louder. 'Ariosta,' she said to her sister, 'give me a leg-up against that wall.'\n\n'I beg your pardon?'\n\n' _Listen_. Can't you hear that?'\n\n'It's just an angry bee.'\n\n'Don't be ridiculous. No bee is ever that angry. I want to see!'\n\nIn the end, it took Emelia standing on Flora, standing on Delilah, standing on Mariella, standing on Vita, standing on Bellina, standing on Chessa, standing on Ariosta, standing on Lorna, standing on Polina \u2013 with Agnes, who was the smallest, at the top on Emelia's shoulders \u2013 even to be able to _peer_ over the top of the wall, taking a few precious seconds before the guards came back and all of them tumbled to the ground.\n\n'What is it?' hissed Polina. 'Please hurry up \u2013 my shoulders are killing me!'\n\n'Oh my, oh _my_ ,' said Agnes. 'It's an aeroplane.'\n\n'Is that all? I think I'd rather it was an angry bee.'\n\n'No you wouldn't, Pol \u2013 this one's about to land on the beach!'\n\nAgnes scaled down her sisters' arms and legs, and ran out of the garden to find a better view. The others followed, the plane's engines reverberating deep in their bodies. No one stopped them, because by now everyone had heard that a plane was trying to land on the royal beach, and the palace was in uproar, maids running hither and thither, advisers reaching for their robes, the guards trying to find their weapons. Nothing this exciting had happened in Kalia for _ages_.\n\nFrom a high balcony, the princesses looked down and saw a small biplane circling above the turquoise surf. Whoever was flying it was an expert pilot, making circles and ovals, dipping down and soaring up into the sky. It was as if the pilot wanted to make sure that everyone in Lago Puera had seen this display, and the eleven princesses in particular, seeing as this was happening directly outside the palace. Eventually, it was time for the plane to land properly, and the girls watched its tail scud away before it turned round and came down upon the vast, empty stretch of royal sand that ribboned round the palace. The pilot landed effortlessly with a single bump, and cut the engines.\n\nThe sisters watched with an exquisite mixture of excitement and dread as the palace guards rushed towards the aircraft, their revolvers at the ready. A group of advisers, led by Clarence, hurried after them. The cockpit window opened, and a tall, slender young man pushed his arms up, then his body, then his legs, before jumping down easily on to the sand. He was wearing a pilot's jumpsuit, a flying jacket, a white scarf, a leather cap and a pair of goggles, but even with these covering his face, the princesses could see he was handsome.\n\nThey strained their ears to hear the conversation taking place on the beach. The pilot had pushed his goggles up on to his forehead and was now shading his eyes against the punishing sun as he admired the sea. 'What a beautiful beach,' he said. 'Is this the kingdom of Kalia?'\n\n'It might be,' said Clarence. 'Why do you want to know?'\n\nThe pilot fumbled in his jacket pocket and produced a piece of paper, which fluttered in the breeze. He steadied himself against the wing. 'I'm here to see the king,' he said. 'King Alberto, I believe?'\n\n'Oh, _no_ ,' said Polina. 'He's holding one of Father's decrees!'\n\nBellina groaned. 'I thought we'd seen the last of those silly men.'\n\n'But he's so handsome,' said Chessa. 'And he's got a _plane_.'\n\n'I don't care if he's handsome! I don't care if he's got twenty planes! We still have to make him drink the dormidon!' said Ariosta, crossing her arms. 'Turning up here with one of those dratted pieces of paper \u2013'\n\n'Of course, sweetest,' said Polina, but she also found it rather hard to draw her eyes from the youth, who was by now walking in the centre of the guards, striding up the beach, leaving nimble boot prints in the sand.\n\n'Imagine dancing with _him_ ,' breathed Agnes. 'Oof, I bet he's an excellent dancer.'\n\n\u22c7\n\nThe sisters hid behind a curtain and listened as the pilot spoke with their father.\n\n'And where are you from?' King Alberto asked him.\n\n'From across the sea,' the pilot replied. Now that they were closer to him, the girls could hear his voice properly. It was low and calm, and ever so slightly musical.\n\n'You've got a nice, um... aeroplane,' said King Alberto. He sounded very un-king-like. (He'd given up hope, you understand \u2013 and it's not often you see someone so fine-looking, so confident, someone who looks so perfectly like your future heir.) Alberto felt as if he was looking at one of his heroes from the fairytales he'd read as a little boy. And a pilot, no less. How modern, how daring, to live up in the air!\n\n'Thank you,' said the youth, smiling. 'In my kingdom, we guard our vehicles well \u2013 for battle, mainly.'\n\n'Been in any battles, have you?'\n\n'Of sorts. My people fight a particular type of war.'\n\n'Excellent. And d'you hunt?'\n\n'I have chased illusions, Your Majesty.'\n\nKing Alberto nodded, pretending that he'd understood. He'd never met such an impressive fellow. 'Of course,' he replied. 'And I assume you're here to see if you can uncover the secret of my daughters' shoes?'\n\nThe youth handed over the crumpled decree. 'I am.'\n\n'It'll take a miracle. My daughters have cleared this town of men.'\n\n'Well, miracles happen. And is it still true, sire, that you will crown me if I am successful?'\n\nThe king spread his hands. 'But of course! A king never goes back on his word. Moreover, it's time for my retirement. And you would do perfectly, a good strapping lad like you. You're not... a prince, by any chance?'\n\nThe man bowed. 'A royal since birth, Your Majesty.'\n\nThe king clapped with joy. 'Oh, marvellous, marvellous!' he cried. Clarence craned his neck with new interest towards the young man. King Alberto patted the pilot on the back and went off humming, thinking about the hobbies he would take up once he was no longer king.\n\n\u22c7\n\nThat night, Delilah prepared the last of the dormidon in the girls' little bathroom. And, as usual, Agnes was the one to offer it to the young pilot, this time in a glass of sweet mint tea. The pilot was sitting upright on the camp bed, his back against the wall. He looked thoughtful, and a little sad, his gaze cast towards the floor as he turned the glass of tea round and round in his hands. He wouldn't look at her, but Agnes was used to this by now \u2013 so few of the men who'd come to find their secret had bothered to acknowledge her. But this one hadn't looked at any of the princesses as they'd filed past him; instead, he'd kept his chin down, half his face tucked in his scarf, deep in thought, eyes averted.\n\nAgnes stood in front of him. 'It's very good tea,' she said. 'You should drink it.'\n\n'Thank you,' he mumbled into the scarf.\n\n'Well, go on then. Drink it up.'\n\n'You seem very keen for me to drink this tea, Princess Agnes,' he said, looking into the glass. Fragrant steam rose off the top of the liquid.\n\n'I \u2013' said Agnes.\n\n'Do you like it here, Agnes?' the pilot asked.\n\n'I... used to.'\n\n'Why?'\n\n'Because we used to do experiments, and play music, and explore. Of course, we still have the \u2013' Agnes stopped herself just in time. She'd found it strangely easy to talk to this pilot, but if any of her sisters heard her nearly reveal the tree palace, they'd be furious.\n\n'You still have the secret,' the pilot said, attempting to finish her sentence. 'You've guarded it well. From what I've heard, I'm about the thousandth person to try to uncover it.' He laughed, and Agnes couldn't help grinning.\n\n'Maybe,' she said.\n\n'And do you like being a princess?' the pilot asked.\n\n'Bits of it.'\n\n'What bits?'\n\nAgnes shifted from foot to foot. None of the other men had ever asked her any questions, and she wasn't used to it. 'I like being with my sisters,' she said. 'But you want to take one of us away.'\n\n'Well, I would hope one day you'd leave this palace of your own will. There's a big world out there, Princess Agnes,' the pilot said. 'I've seen a bit of it. It wouldn't be so bad to go and take a look, you know.'\n\nAgnes was confused by this, and grateful that without another word, the young pilot put the glass to his lips and drank down the whole of the dormidon.\n\nIn a few minutes, the girls heard his light breathing. As they listened to the gentle slumber of the pilot on the other side of the door, they felt strangely peaceful. And after Agnes told them what the pilot had said to her, for the first time in ages, the princesses truly wanted to dance.\n\n\u22c7\n\nThe next morning, they agreed that although it was a relief the dormidon had worked, it was a shame the young man would be on his way. They went down to the throne room to watch him be dismissed. He was dressed in his pilot's outfit and goggles, and was holding a small sack at his side. Agnes noticed that his hands were trembling a little.\n\n'So, my boy,' King Alberto said. 'Are you going to tell me the secret?'\n\nAt these words, the young man seemed to hesitate, but then resolved himself. 'Yes, Your Majesty,' he said. 'I am.'\n\nThe girls gasped. They all turned to Delilah. The dormidon had _worked_ , hadn't it? Agnes said she'd watched him drink the whole thing! And they'd heard him snoring on the other side of the door! What on earth was going on? Delilah looked more boiled than the dormidon vine she'd prepared the night before.\n\nKing Alberto could hardly believe his ears. He leaned forward. 'You _are_? Go on then. Spill the magic beans!'\n\n'Your girls go dancing every night,' the young man said.\n\n' _What?_ '\n\nAgnes let out a cry, but the pilot carried on. 'They open a secret door that lies behind the portrait of your wife in their bedroom.'\n\nAlberto's eyes boggled. 'My wife's _portrait_?'\n\n'Indeed, sir. One might say that Queen Laurelia leads the way. They go down five hundred and three steps, through the gloom and the cobwebs, towards a wide lagoon. Your daughter Ariosta swims into the deep water to find six little boats that the girls row over to the other side. They walk through three forests that they found themselves: the first is a forest of silver, which your daughter Chessa discovered. The second is made of gold, which Emelia found when she helped a wounded fox, and the last is made of diamonds. In the forest of diamonds, you'll find the dormidon vine, which your botanist daughter, Delilah, has been using to drug all the suitors who have competed for your kingdom.'\n\nKing Alberto looked towards his daughters in astonishment. 'Ariosta?' he said dumbly. 'I didn't even know you could swim. Chessa? Delilah, have you been... drugging a potential _king_?'\n\nThe girls stared with hatred at the pilot, but the pilot wasn't finished. 'At the end of the forests, Your Majesty, they enter a tree palace.'\n\nAt these words, several of the princesses fell to their knees.\n\n'A _what_?' said King Alberto.\n\nOne of the older advisers, a man called Bernard, began to move forward. 'Sire,' he whispered in the king's ear, 'this is preposterous. Shall we remove the young man now?'\n\n'Your Majesty,' said Clarence, looking with great interest at the pilot. 'May I suggest it wiser to let him speak?'\n\nThe pilot carried on before the king could decide. 'The tree palace is a dance floor in the roots of a tree, where your daughters dance and dine and sing with a lioness and a peacock and all kinds of other animals. They dance to their hearts' content. Their happiness is unlike any I've ever seen. And if I could bottle that happiness up, Your Majesty, I reckon I could fly my plane on it.'\n\n'This is absurd,' said Bernard.\n\n'But is it true?' asked the king.\n\n'As true as I stand before you now. At the end of the evening, they return back the way they came. They fall into bed, and they leave their shoes in a neat row, worn to pieces. And that, Your Majesty, is the sum total of the secret you have been craving, all this time.'\n\nIn the silence that followed, the princesses looked at each other in deep sorrow. The advisers would find the secret door. Their lives would be over. Their father would seal up the staircase, and after this, they would never be allowed out of their bedroom, even for an hour. And who was the pilot going to pick for a wife? Nobody liked him now. Lorna began to weep.\n\nThe king looked stunned. 'A forest made of silver?' he said. 'A forest made of gold?'\n\n'He imagined it,' said Bernard.\n\nThe pilot laughed. 'Maybe I did. But it's real.'\n\n'Do you take His Majesty for a fool?' said Bernard. 'There is no such thing as a tree palace, or dancing with a lioness. A lioness would eat you.'\n\nThe pilot bowed. 'Forgive me, but this particular lioness would not. Although,' he added, looking Bernard up and down, 'she might have a go at you.'\n\n'Pilot,' said Clarence. 'Do you have any proof of these forests? Then at least the matter can be settled.'\n\nThe pilot bent down and opened the sack, and to the girls' horror he pulled out a single silver leaf, unmistakably from the forest. He pointed it at the king, and it shimmered in his hand like a small shield. King Alberto shrank back into the seat of his throne, a little frightened. The pilot put the silver leaf on the floor and pulled out a branch, made of gold. It glittered in the daylight, and he held it up to the king as if it were a ceremonial mace. The king swallowed nervously. And finally, the pilot rummaged in the sack and pulled out a large diamond. He handed it to Alberto, and it winked in his palm like an accusing eye.\n\n'My goodness,' breathed Alberto. 'I've never seen precious metals like it. Girls, do you deny this? Answer me!'\n\nPolina rose from the floor. Something in her looked broken. 'Oh, Father,' she said. 'We only liked a little dancing!'\n\n'Please, please, Father,' said Vita. ' _Please_ don't lock us up again!'\n\nThe king lurched to his feet. 'So it's true! Your insolence, your disobedience, your downright _outrageous_ rebellion makes me sad to call you my daughters! Every night, going down to a dark lagoon, strange forests, talking lionesses \u2013 after all I did to try to keep you safe!'\n\nThe princesses looked at the pilot, their faces portraits of pure distress. 'I understand it was precious to you, ladies,' said the pilot. 'Believe me. But the kingdom of Kalia needs a new ruler, so I really had no choice.'\n\n'How could you?' said Flora. 'We thought you were _nice_!'\n\nKing Alberto turned to the pilot. ' _Finally!_ ' he cried. 'I've found someone worthy to inherit my kingdom! So clever, so brave, so ingenious! Come here, boy. You are a true prince and you shall have your reward. Clarence, see to it that the coronation takes place tomorrow. A small affair. No fuss.'\n\nThe advisers looked at each other. Half of them, including Clarence, seemed to say, _Why not?_ Alberto had always been an impossible king to manage one way or another, and this young man had excellent potential. The other half, led by Bernard, did not look convinced. In fact, they looked very unhappy indeed, and stared at the boy with hostility.\n\n'Are you sure you wish to crown me, sire?' asked the youth.\n\n'I've never been surer of anything in my life!' replied the king. 'And which one of these girls do you want for a wife?'\n\nThe pilot faltered, turning to the eleven girls, who scowled at him in unison. Agnes thought she saw a look of dismay pass across his face, which he quickly tried to hide.\n\n'I'm not sure I'll ever know how to pick,' he said.\n\nAlberto beamed. 'Crown first, bride later?' he asked the pilot.\n\n'That couldn't be more perfect,' came the young man's reply.\n\n\u22c7\n\nClarence was an efficient organiser. The coronation was prepared for the next day, in the throne room. King Alberto even ordered the black drapes to be removed and the dust balls to be swept away from the legs of his throne. The maids had done a fabulous job in cleaning the place, and the crystal chandelier sparkled in the glorious light.\n\nThere was just one small problem.\n\nUnbeknownst to the pilot, or King Alberto and the eleven girls, Bernard, the most suspicious of the king's advisers, decided to check whether the pilot's story was true: namely that, behind Laurelia's portrait, he would find a door that led down five hundred and three steps to a wide lagoon, three forests and a tree palace. Once the princesses were in the throne room downstairs, Bernard snuck into the girls' cell and wrenched the portrait of Queen Laurelia from off the wall.\n\nThere was no sign of a door.\n\nBernard looked and looked. He tapped the wall; he ran his hands over its stone \u2013 but he couldn't find a thing.\n\nAll he could see was a solid wall.\n\nIt was a trick! To think the future of Kalia was to be handed over like this to a complete stranger, and a liar at that! About what else had the pilot deceived them? 'Never trust a man who arrives by plane,' Bernard muttered to himself as he scurried furiously out of the girls' bedroom and through the palace to tell King Alberto, before it was too late.\n\nThe eleven princesses were, by now, seated on gold chairs to the left of the throne, with the advisers in favour of the pilot's coronation standing behind them. Alberto was sitting in the throne, a seat in which he had sat for years, and which he was soon to vacate. The king had even woken up his old herald, who hadn't played his trumpet since the passing of Queen Laurelia. He stood at Alberto's side, his trumpet waiting. There was an atmosphere of intense expectation.\n\nWhen the pilot entered the throne room, hush descended. Alberto stood up and removed the crown from his own head.\n\nFrom far off, somewhere in the palace, came the sound of hurried footsteps.\n\nThe pilot approached the throne. As he knelt before Alberto, the girls could hardly breathe. The herald blew on his trumpet: a triumphant, trilling fanfare with suitably royal pomp.\n\nThe hurried footsteps were getting louder, reverberating along the corridor.\n\nAlberto lifted the crown high. 'With this, I name you King of Kalia,' he said to the pilot, and the old man encircled the young man's head with the heft of the crown.\n\n'Stop!' cried a voice, and Bernard burst into the throne room. Everyone turned to him. 'There isn't any door!'\n\nBut Bernard was seconds too late. Kalia had a new king. Clarence breathed an audible sigh, his thin face flushed with relief.\n\nAgnes turned to the windows. The sea wind was blowing freshly through, the curtains danced in joy, and the sunlight in the room had become, yes, _brighter_. She blinked. Was that \u2013 was that \u2013 a _toucan_ that just flew by? When she looked again, it was gone.\n\nThe adviser Bernard clung to the curtains, severely out of breath.\n\n'And once done, it cannot be undone,' said the pilot, rising to his feet and surveying the room. He looked very calm, and he smiled at the girls. For all their sorrow, they had to admit to themselves that the crown suited him very well; it shone as brightly on his pilot's cap as the circle of oaks in the forest of gold.\n\n'Sire, sire,' panted Bernard, letting go of the curtain and staggering towards Alberto. 'This is all a terrible mistake. There's been a trick. There isn't any door! I've looked! There isn't any tree palace. It's nonsense. This boy was lying to you. You've handed your crown to a liar!'\n\nAlberto blinked and shook his head. 'A liar?'\n\n'There _is_ a tree palace,' said the new king. 'I've been there, several times.'\n\nThe princesses stared at each other in confusion. _Several_ times? But this pilot had only been with them for one night.\n\n'I want to go there myself,' announced Alberto. 'If it _isn't_ there, I'll take my crown back.'\n\n'Ah. It isn't possible to enter the tree palace simply because you want to,' said the new king.\n\n'You see! You see!' said Bernard. 'Because it isn't there!'\n\n'Not at all,' said the new king. 'You have to be a necessary guest, that's all.'\n\nAgnes looked with curiosity at the pilot. Had he been a necessary guest too? 'It _is_ there,' she said, forgetting in her anger at Bernard that she was supposed to keep the tree palace secret. 'You just have to know where to look.'\n\n'Yes,' said Polina, drawing close to Agnes's side. 'You saw the gold branch, Father. The silver leaf, the diamond.'\n\nAlberto looked from daughter to daughter in confusion. 'I did,' he said. 'It's true.'\n\nBernard scoffed. 'He could have got those shining trinkets from any old market on his way here.'\n\nAlberto looked panicked. 'That's true too.'\n\n'Sire,' soothed Clarence. 'Think of your retirement plans.'\n\nAs if to settle the argument, the new king reached into his pockets to show a worn-out pair of shoes, with holes in their soles. 'If I have deceived you, sire,' he said to Alberto, 'it is over one thing only.' He held the shoes out towards the old king. 'Perhaps you will remember these?'\n\nAlberto peered at the bashed-up shoes, and turned pale. He started huffing and puffing. When Agnes saw the shoes for herself, and realised how the new king might have that particular pair in his possession, she gasped.\n\nThe new king dropped the worn-out shoes on the throne room floor.\n\nHe lifted off his crown, his pilot's cap and goggles, never once taking his eyes off Alberto. With a twist of his fingers, long locks of billowing hair fell to his shoulders, tumbling from their bindings \u2013 and Frida stood before them.\n\nFrida, their brand new king.\n\n'I suppose you'd better call me queen of Kalia, actually,' Frida said to the stunned gathering, as she twirled her pilot's goggles on her index finger, placing the crown back on her head with her free hand.\n\nBernard took one look at her and fainted to the floor.\n\n'I knew it!' cried Agnes.\n\nAlberto staggered away. 'Frida?' he uttered. 'But \u2013'\n\n'I knew you'd come back,' said Agnes. Lorna fell to her knees in tears, and the other sisters laughed and whooped around the room.\n\n'Queen Frida! Queen Frida!' Vita chanted.\n\n'I promised, didn't I?' said Frida \u2013 expert pilot, new queen of Kalia \u2013 as she opened her arm s. Her sisters ran towards her, each of them hugging her tight, sobbing into her shoulders, kissing her face, patting her flying jacket and trying on her goggles.\n\n'Where have you been?' Agnes said. 'How have you \u2013'\n\n'Didn't I say, Aggie? It's a big world out there,' said Frida, smiling. 'I'll tell you about it later.'\n\n'This is impossible,' said Alberto, stamping his foot. 'No daughter of mine knows how to fly a plane!'\n\n'Oh, Father. This one does. It took me a few weeks, but I managed it.'\n\n'Frida, give me back my crown!'\n\n'I'm afraid I won't be doing that, Father,' said Frida firmly. 'And as you once pointed out to me: with this crown, I am the law.'\n\n'But \u2013'\n\n'And Clarence is right. Thank you, Clarence. What about all those hobbies you wanted to take up in retirement?'\n\n'But \u2013!'\n\n'You may keep the diamond as a token of my appreciation.'\n\nAlberto stared at his daughter the queen. The princesses watched with fascination as their father seemed to wrestle with him self without actually moving. His mouth bobbed open and closed like a confused fish. His eyes boggled. He looked like a man having a tug of war with his own soul. And then he laughed \u2013 yes, Alberto, the man who had not laughed for months and months, began to shake, big belly hoots, wheezing squeals of what they dared to hope was joy. 'Oh my, oh my!' he said.\n\n'Are you quite well, sire?' said Clarence.\n\nThe old man stared at the adviser. 'Quite well!' he said. 'I think I may never have been better!' He opened his palm and looked at the diamond resting in the centre, glinting and winking at him like a promise of a future he'd never dared admit. Then, to their astonishment, he ran from the room, tripping over the figure of Bernard, who was still lying in shock on the floor.\n\nNo one could stop the old king; he couldn't get out of there fast enough. They could hear the patter of his footsteps down the corridor, interspersed with occasional hoots and whoops, noises he hadn't made since he was a boy.\n\n'Queen Frida,' said Clarence, his thin face alight with pleasure as he emerged from the cluster of astonished staff. He knelt. 'A great leader stands before us,' he said. 'It shall be an honour to serve you.'\n\nThe other advisers looked at each other, wondering whether to follow Clarence's lead.\n\n'A queen?' whispered one. 'This is a bit... new.'\n\n'How glad I am I didn't call the new monarch a liar. Poor, stupid Bernard!' whispered another.\n\n'But she isn't really new, is she?' said yet another. 'Queen Frida is still the same brave, clever, thoughtful person she's always been.'\n\n'Indeed. And who knows Kalia better? No one.'\n\nThey all fell to their knees before her.\n\n'Thank you, Clarence. Thank you, gentlemen,' said Frida. 'But, please, get up. And stop whispering. We've got so much to do.'\n\nEight\n\nPeacocks and Paw Prints\n\nKalia was a very different place after Frida became queen. Bernard and a few others who weren't in agreement with a queen being in charge, particularly one so talented, were dismissed. Frida, aided by Clarence, filled her palace with people from all sorts of backgrounds and experiences. She became an excellent leader, and a great favourite am ongst the Kalian citizens: fair, thoughtful, open-minded and patient, not without a little bit of spark to get her through the difficult times. She can still be seen occasionally, flying in her biplane over the city of Lago Puera, dipping and soaring over the famous Kalian sea.\n\nAbout a month into her reign, she built a dance floor in the palace. It has black and white tiles on the floor, and multicoloured lights which bob like fireflies, and every Friday all the people of Kalia are invited to come and dance. The food's pretty good too.\n\nAlberto eventually recovered from his fit of giggles. He'd realised two things: firstly, that his daughter had been cleverer than him all along, and secondly, that his time as king was indeed over, and he could have some fun. Laughter seemed the best solution to these two realisations, and he packed his own suitcase and went off for a year or two of sightseeing. He took the diamond.\n\nThat was several years ago, in fact, and the princesses are still wondering if he'll ever come back. They each secretly, bafflingly, miss him. That's parents for you. The lioness was right: Alberto wasn't bad. No one's entirely bad, but they do get a little lost. And perhaps \u2013 just like his eldest daughter \u2013 in leaving, Alberto has found him self. He sends postcards from every country that he visits, and the palace fridge is covered with his missives.\n\nPolina was appointed palace astronomer, and Delilah is head gardener; she still keeps a strong supply of dorm idon, just in case, and advises the citizens on their herbs and vegetables. Bellina is chief of foreign affairs, and since her appointment Kalia's wars with neighbouring kingdom shave ended. Emelia is a vet, and oversees the health of Kalia's livestock. Ariosta is a famous artist who shows her paintings around the world. Mariella keeps the kingdom's budget in order, and Chessa gives singing recitals and occasionally tours. When she's home in Lago Puera, the palace doors are open every afternoon for musicians to come and play. Lorna has established several schools for the people of the city, where lessons are available for all Kalian boys and girls. Vita runs a theatre on the beach, and every summer the famous Kalian festival lasts for weeks on end. If you time your trip well, you can see some excellent plays. Flora is the palace librarian, and people flock from miles around to come and find a cosy nook, where they while away the hours with her excellent choice of books.\n\nAnd Agnes? The one with the typewriter, who wanted to tell stories?\n\nLet's just say I managed it.\n\nAs for the tree palace, you may well be wondering whether it really existed. People often do. The old king's adviser Bernard claimed it didn't, but that was only because he couldn't find it.\n\nThe truth is, we were so tired the night after Frida's coronation that we completely forgot to check if the door was still there. And with Frida crowned queen, and so many things for us to do, we never looked for that particular door again. We got older, became women of the world, our energies directed to the lives we had made. Yes, often, we thought about the tree palace, about Saleem and the lioness, and the toucan waiters, and the fun of dancing. But we were so busy upstairs that I must confess our thoughts about it lessened as the years went on. I think it is also true to say that none of us particularly wanted to revisit that windowless room, where we'd been so unfairly cooped up for months on end.\n\nThat is, until yesterday, when a strange thing happened, and I had to write all this down.\n\nYesterday morning, a huge box was delivered to the palace door. I enquired as to who had delivered it, but the guard on duty had seen nobody. Neither was there any message. Except \u2013 next to the box, a feather had been laid, belonging to a peacock. And by its side, marked in the earth, was a paw print the size of a dinner plate. Gingerly, I opened the box. Inside was a pyramid of jam doughnuts.\n\nI stood there, looking at the doughnuts \u2013 suddenly so familiar! \u2013 and my heart was thumping hard. I rem embered the way Frida whirled and twirled under the multicoloured lights, the way Ariosta swam across the lagoon, the way Emelia saved that little fox. It felt so long ago, and yet it could have been last week. Was someone watching me? I turned around, scanning the horizon \u2013 the Kalian sea, the shore, the green hills \u2013 but there was no one to be seen.\n\nThat afternoon, I took the box to Frida, who had just finished a meeting in the throne room with Clarence. The other princesses were all out of the city on various missions. Queen Frida's eyes lit up when she saw the doughnuts, and I told her how they'd appeared earlier in the day with no explanation, but for a peacock feather and a paw print.\n\nFrida reached into the box and lifted one out. It was newly baked, and the sugar that dusted it glittered like tiny diamonds. 'You don't think... ?' She trailed off.\n\nI looked at her. 'That's exactly what I think,' I said.\n\nShe hesitated. 'Do you know, Agnes, there are times when I might be brushing my teeth, or about to hold a meeting, or writing a letter \u2013 and I swear, I swear, I can hear a lioness's roar.'\n\n'Me too!'\n\n'Oh, thank goodness. I thought I might be mad.'\n\n'It feels very far off, but strangely, I can feel it deep within me.'\n\nMy sister the queen looked at me. Time had barely aged her, and she still wore exquisite shoes. 'That's exactly how it is for me too,' she said. 'And I've been thinking about it, Aggie. I've no doubt that the tree palace is still there, that Saleem and the lioness and the toucan waiters and the jazz band are waiting for their next necessary guests. For although some things exist in places out of reach, that doesn't mean they cannot be.'\n\n(My sister really is a wise queen.)\n\n'I always thought I'd never be able to go back. But shall we... shall we go and look tonight?' she went on, nibbling the doughnut. 'Shall we go to that poky room and look behind Mother's portrait?'\n\nI thought of Bernard the old adviser, pushing aside the portrait of Queen Laurelia and finding nothing but a solid wall. I thought of the twelve of us when we were younger, finding the cold staircase and descending the five hundred and three steps to a world that gave us so much happiness. I was frightened to think of what we might find, but then I remembered the box of glittering doughnuts.\n\nI must have been silent a long while, for Frida looked at me with concern. 'Wise to pursue?' she asked me.\n\nI smiled. 'Wise to pursue,' I replied, and we agreed on a time when the rest of the palace would be fast asleep.\n\nAnd as I look at my clock, I see the hour has come. It's very dark and quiet outside in Kalia at this time of night; thanks to Bellina's international efforts, a peace has reigned for years. Frida's footsteps are coming up the corridor, and I see the golden glow of her lantern pooling. I can feel the old thrum of excitement in my heart. We'll walk the corridors of her palace together, my sister and I, hand in hand, the lioness's cry an echo in our ears. We'll find that old room and approach that portrait of our mother. We'll push it aside. And we will see.\n\nBLOOMSBURY CHILDREN'S BOOKS\n\nBloomsbury Publishing Plc\n\n50 Bedford Square, London WC1B 3DP, UK\n\nThis electronic edition published in 2018 by Bloomsbury Publishing Plc\n\nBLOOMSBURY, BLOOMSBURY CHILDREN'S BOOKS and the Diana logo are trademarks of Bloomsbury Publishing Plc\n\nFirst published in Great Britain in 2018 by Bloomsbury Publishing Plc\n\nText copyright \u00a9 Peebo & Pilgrim Ltd, 2018\n\nIllustrations copyright \u00a9 Angela Barrett, 2018\n\nJessie Burton and Angela Barrett have asserted their rights under the Copyright, Designs and Patents Act, 1988, to be identified as Author and lllustrator of this work\n\nAll rights reserved  \nYou may not copy, distribute, transmit, reproduce or otherwise make available this publication (or any part of it) in any form, or by any means (including without limitation electronic, digital, optical, mechanical, photocopying, printing, recording or otherwise), without the prior written permission of the publisher. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages.\n\nA catalogue record for this book is available from the British Library\n\nISBN: 978-1-4088-8691-5 (HB)   \nISBN: 978-1-4088-8690-8 (eBook)\n\nTo find out more about our authors and their books please visit www.bloomsbury.com where you will find extracts, author interviews and details of forthcoming events, and to be the first to hear about latest releases and special offers, sign up for our newsletter.\n\n#\n\n  1. Cover\n  2. Title Page\n  3. Dedication\n  4. Contents\n  5. One: Princess Frida and the Mourning Curtain\n  6. Two: King Alberto's Bad Decision\n  7. Three: The Secret\n  8. Four: A Dance and a Doughnut\n  9. Five: King Alberto's Second Bad Decision\n  10. Six: Delilah and the Dormidon\n  11. Seven: A Coronation\n  12. Eight: Peacocks and Paw Prints\n  13. eCopyright\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \nPRAISE FOR\n\nGEMINI CELL\n\n\"The best novel [Cole's] written so far . . . A military fantasy that combines intense personal anguish with elements of actual horror.\"\n\n\u2014Tor.com\n\n\"Myke Cole's novels are like crack: they're highly addictive, and this one is no exception.\"\n\n\u2014BuzzFeed\n\n\"Intense and explosive\u2014Cole tells a hell of a story.\"\n\n\u2014Mark Lawrence, international bestselling author of _The Liar's Key_\n\n\"The story is a powerful one . . . it takes some oft-maligned tropes of military adventure fiction and shows us how those things are supposed to be done.\"\n\n\u2014Howard Tayler, award-winning creator of the webcomic _Schlock Mercenary_\n\n\"Think Vince Flynn plus a whole lot of magic mixed in and baked in hellfire, and you've got the gist of how awesome Myke Cole's new series is shaping up to be.\"\n\n\u2014Michael Patrick Hicks, author of _Convergence_\n\n\"Cole's books are an intriguing mix of fantasy and military fiction . . . [ _Gemini Cell_ ] is outstanding.\"\n\n\u2014SFcrowsnest\n\n\"With each book, Myke Cole levels up, and _Gemini Cell_ is no exception. This is Cole's best work to date . . . A fast-moving, page-turning story that you'll read late into the night.\"\n\n\u2014Fantasy-Faction\n\n\"Myke Cole is a fantastic author who gets better with every book he writes.\"\n\n\u2014Whatchamacallit Reviews\n\n\"This is some really good, exciting military\/urban fantasy. Cole's style is fast-paced, immensely enjoyable, and delivers on both action and character in equal measure.\"\n\n\u2014SFRevu\n\nPRAISE FOR THE SHADOW OPS NOVELS\n\n\"It's not _just_ military . . . It's just a great book.\"\n\n\u2014Patrick Rothfuss, #1 _New York Times_ bestselling author of _The Slow Regard of Silent Things_\n\n\"Hands down, the best military fantasy I've ever read.\"\n\n\u2014Ann Aguirre, _New York Times_ bestselling author of _Breakout_\n\n\"Fast-paced and thrilling from start to finish . . . military fantasy like you've never seen it before.\"\n\n\u2014Peter V. Brett, international bestselling author of _The Skull Throne_\n\n\"Excellent, action-packed novels that combine elements of contemporary magic and superhero fiction with the type of atmosphere genre readers usually only get in military SF.\"\n\n\u2014Tor.com\n\n\"Arguably one of the definitive military fantasy novels.\"\n\n\u2014The Founding Fields\n\n\"[Cole] proves that an action blockbuster can have heart and emotional depth, while never skimping on the fireworks and explosions.\"\n\n\u2014Fantasy-Faction\n\n\"Myke Cole is an absolute gift to urban fantasy and military fantasy subgenres.\"\n\n\u2014Fantasy Book Critic\n\n# Ace Books by Myke Cole\n\nSHADOW OPS: CONTROL POINT\n\nSHADOW OPS: FORTRESS FRONTIER\n\nSHADOW OPS: BREACH ZONE\n\nGEMINI CELL\n\nJAVELIN RAIN\n\n** **\n\n**An imprint of Penguin Random House LLC**\n\n**375 Hudson Street, New York, New York 10014**\n\nJAVELIN RAIN\n\nAn Ace Book \/ published by arrangement with the author\n\nCopyright \u00a9 2016 by Myke Cole.\n\nPenguin supports copyright. Copyright fuels creativity, encourages diverse voices, promotes free speech, and creates a vibrant culture. Thank you for buying an authorized edition of this book and for complying with copyright laws by not reproducing, scanning, or distributing any part of it in any form without permission. You are supporting writers and allowing Penguin to continue to publish books for every reader.\n\nACE\u00ae is a registered trademark of Penguin Random House LLC.\n\nThe \"A\" design is a trademark of Penguin Random House LLC.\n\nFor more information, visit penguin.com.\n\neBook ISBN: 978-1-101-63676-3\n\nPUBLISHING HISTORY\n\nAce mass-market edition \/ April 2016\n\nCover illustration by Larry Rostant.\n\nCover design by Diana Kolsky.\n\nThis is a work of fiction. Names, characters, places, and incidents either are the product of the author's imagination or are used fictitiously, and any resemblance to actual persons, living or dead, business establishments, events, or locales is entirely coincidental.\n\nVersion_1\nFor Peat and Pete,   \nmy brother and my brother\n\n# ACKNOWLEDGMENTS\n\nWriting novel acknowledgments is always a fraught exercise. So many people other than the author are involved in making a successful book that it is inevitable you'll miss someone. Any omissions are my own, and I hope those slighted will accept my apology.\n\nI want to single out for praise my tireless teams at Ace\/Roc and Headline, and my agents at JABberwocky and Zeno. Thanks also to my audio publishers at Recorded Books and W. F. Howes, and extra-special thanks to GraphicAudio, whose gorgeous full-scale radio dramas have brought my books to life in a way I never imagined possible. Thanks also to Larry Rostant, who similarly evokes my world through imagery. I see my world because of you, and I am incredibly grateful.\n\nThanks are due to my beta readers, and in particular to Mallory O'Meara, who weathered the storms of my moods as she applied the same critical lens with which she brings incredible films to life. This book would not be worth reading if not for her.\n\nThanks also to my two tribes: the nerds and the military\/police, both separate and intersecting, simultaneously teaching me to fight and giving me something to fight for.\n\nAnd Peat, once more lighting the way and covering my six. Not a day goes by that I don't remember how very much I owe you.\n\n# CONTENTS\n\n_Praise for Myke Cole_\n\n_Ace Books by Myke Cole_\n\n_Title Page_\n\n_Copyright_\n\n_Dedication_\n\n_Acknowledgments_\n\n_Epigraph_\n\n_Author's Note_\n\nCHAPTER I: THE PLAN IS SOUTH\n\nCHAPTER II: HUNTING THE DEAD\n\nCHAPTER III: CALIFORNIA SUNSHINE\n\nCHAPTER IV: BRIEFING\n\nCHAPTER V: TOUCHING DOWN\n\nCHAPTER VI: MAMA DADOU\n\nCHAPTER VII: PATCHING UP\n\nCHAPTER VIII: WHAT IT'S LIKE\n\nCHAPTER IX: HONESTLY, OFFICER\n\nCHAPTER X: COLLATERAL DAMAGE\n\nCHAPTER XI: TOGETHER\n\nCHAPTER XII: PURE GOLD\n\nCHAPTER XIII: PROGRAM REVIEW\n\nCHAPTER XIV: ON TO THE LIVING\n\nCHAPTER XV: ALL THE DEAD CAN DO IS PROTECT\n\nCHAPTER XVI: DOESN'T ANYONE KNOCK ANYMORE?\n\nCHAPTER XVII: THE PLAN IS WEST\n\nCHAPTER XVIII: PUSHED TOO FAR\n\nCHAPTER XIX: THE THINGS WE DO FOR LOVE\n\nCHAPTER XX: WHY DID YOU GO?\n\nCHAPTER XXI: LAST RESORT\n\nCHAPTER XXII: NEW MANAGEMENT\n\nCHAPTER XXIII: RETURN\n\nCHAPTER XXIV: THE FLIGHT IN\n\nCHAPTER XXV: COMBINED\n\nCHAPTER XXVI: SO OTHERS MIGHT LIVE\n\nEPILOGUE: COASTLINE\n\n_Glossary of Military Acronyms and Slang_\nThe term \"Javelin\" denotes the seizure, theft, or loss of a national security asset with strategic impact. The term is followed by an explanatory code word indicating the severity of the incident and the nature of the response. Code word \"Dry\" indicates executive authorization of a diplomatic or clandestine response, with no action required from major commands. Code word \"Drizzle\" indicates a combined response involving assets from the State Department, the Office of the Director of National Intelligence, and the Joint Chiefs of Staff.\n\nCode word \"Rain\" indicates a crisis of existential proportions representing a direct and pressing threat to the continued security of the nation. Javelin Rain incidents authorize any and all means necessary to bring the matter to a resolution as quickly and completely as possible.\n\n\u2014CHAIRMAN JOINT CHIEFS OF STAFF MANUAL 3250.03B  \nJOINT REPORTING STRUCTURE EVENT AND INCIDENT REPORTING\n\nThe fear of death follows from the fear of life.\n\n\u2014MARK TWAIN\n\n# AUTHOR'S NOTE\n\nA glossary of military acronyms and slang can be found in the back of this book.\n\n# CHAPTER I\n\nTHE PLAN IS SOUTH\n\nJames Schweitzer's bare foot came down on a splintered root that punctured his sole, digging an inch-deep furrow in the gray flesh. His senses registered the cut, assessed the damage, dismissed it.\n\nHe felt no pain. The furrow in his flesh didn't bleed.\n\nSchweitzer knew he should be horrified by what he had become. What little clothing remained on him was shredded, filthy, and stinking. The body beneath was a landscape of puckered purple-white scars, dotted with darker gray rents, wounds that would never heal, revealing the yellowed articulation of the bone beneath. His face was a dark horror, a parody of his features stretched over a skull that was mostly metal.\n\nHis eyes were gone. In their place burned twin silver orbs, thimbles full of metal-colored fire.\n\nHe was a Hollywood zombie. No, movie zombies shambled. Schweitzer picked his way through the forest as nimble as a cat, his body instinctively low, hands up and bone claws extended, ready for the fight that might find him at any moment.\n\nHis wife came behind him, their son slung across her chest. Schweitzer had tried to carry him, but Patrick wouldn't have it. Sarah Schweitzer knew her husband despite what death had made of him, years of love bound up in the magic that linked their souls, but Patrick was just a boy. Maybe, one day, he would develop the arcane sympathy that connected Schweitzer and his wife, but he hadn't yet, and he squalled and fought whenever Schweitzer came near.\n\n_Keep them alive._ The words were a mantra, repeating in his mind. Over and over again, _Keep them alive._ His magically augmented hearing picked up the steady beating of Sarah's and Patrick's hearts, the rhythm keeping him from panic, reminding him that he hadn't lost them. Or had he? He listened to Sarah's panting breaths as she struggled to keep up. She was alive.\n\nHe wasn't. His embrace was cold, his skin hard from the glycerol they'd used to keep his veins inflated and resistant to wear. Even if they shook off the Gemini Cell, found a way to escape them forever, he couldn't stand at her side at art shows, laugh with her at parties, take her out to dinner. No matter how much he loved her, he couldn't be a husband to her anymore.\n\nHe glanced back over his shoulder, and his spiritual stomach seized as he realized how far behind him she was. Sarah was young and fit, but the monsters pursuing them were immortal, needing neither rest nor food. She stumbled, wheezed. Schweitzer forced himself to slow, to wait for her. The need to run was almost overwhelming; the dead muscles in his legs twitched with the desire to move on.\n\nFor the hundredth time since they'd fled together, he considered telling her to leave him, to take Patrick and find some place to lie low, to start over. He dismissed the idea as soon as it arose. He was the Gemini Cell's primary target, but they would never suffer someone knowing as much as Sarah did. As for Patrick, they'd either kill him or take him as their own, and Schweitzer wasn't going to let either of those things happen. The Gemini Cell had all the resources of a special operations regiment and intelligence service combined, but that paled in comparison to their Gold Operators, feral monsters, all as immortal and superpowered as Schweitzer himself.\n\nNo, Sarah and Patrick were safest with him. Only Schweitzer was strong enough to protect them. Grief for all he had lost ripped through him yet again, and yet again he quashed it. Grief was an emotion for the living. As was anger, or regret, or joy. He couldn't afford those luxuries now. He could take one thing from his former life: his oath as a Navy SEAL. _So others might live._\n\nHe'd died trying to protect Sarah and Patrick. He'd been fortunate enough to get a second crack at it, and by God, he'd take it.\n\n_So others might live._\n\nHe turned his focus to the woods around him, leaping over a fallen log, landing on a stone barely larger than his foot and balancing there. The magic that animated his corpse gave him heightened senses. He could see for miles in different spectrums. He could sniff out a rose petal buried in a garbage heap. Now, he dialed his hearing out, straining to catch the sounds of dirt-bike engines or helicopter rotors, anything that might indicate that the Cell's agents were closing in.\n\nNothing. His boosted senses brought him only the sounds of beetles foraging in the dead leaves beneath them, the wind rushing in the canopy over their heads. The only smells were leaf mold and wildflowers and fresh water a long way off. No trace of humanity.\n\nThey were deep in nearly two million acres of forest spanning three states. Years of running counterinsurgency ops in the rugged mountains of Afghanistan had taught Schweitzer firsthand how hard it was to locate a single man on the run, even one with a family. All the drone cameras and ground teams backed by largest defense budget in the world couldn't make the haystack any smaller, the needles any bigger. He nodded and pressed on.\n\n\"Jim!\" Sarah sounded winded and a lot farther behind him than he'd realized. He stopped, whirled.\n\nShe was bent at the waist, hands on her hips, breathing in labored gasps. Her pink hair was clotted with leaves and mud, her T-shirt ripped and filthy. Patrick flailed in his makeshift sling, all cried out but still struggling.\n\n\"Wait . . .\" she panted. \"Jesus . . . fucking . . . Christ . . . just wait . . . one . . . minute.\"\n\nHe had pushed her too hard, too fast. He had forgotten mortal limitations. It was a reminder of the chasm that separated them, and it tore his heart anew. \"Sorry.\"\n\n\"Patrick and I aren't like you.\" She straightened, spat a long streamer of mucus-flecked saliva, and suppressed a coughing fit. \"We can't keep going like this.\"\n\nHer skin was pale and waxy, her eyes fever bright. He was hurting her, as his frequent absences had in life, all the missed art shows, her long nights at home alone caring for Patrick while he was away on ops. And now she was condemned to run like an animal, hounded by the undead, all because of him.\n\n\"I'm sorry,\" he said again, hoping that his tone conveyed just how much. \"I'll slow down.\"\n\nBut he didn't want to slow down. The Gemini Cell wouldn't rest until it had them. He turned to go.\n\nSarah didn't move. \"Where are we going?\"\n\nSchweitzer realized that he didn't know. Since they'd won the battle at Drew's farm and fled into the forest, his only thought had been an animal litany of _get away get away get away_. He cursed himself. That was feral thinking, better suited to jinn like Ninip, the monster who'd shared his own corpse. At last, he'd figured out how to exorcise the jinn and take full control of his body, but he wondered if Ninip hadn't corrupted him, warped him with its predator lust.\n\n\"Away,\" Schweitzer said. \"We have to put miles between us and our last known position. They'll be launching from that old man's house.\" Drew and Martha, kindly old retirees who had taken Sarah in, and paid the ultimate price for it. More deaths laid at Schweitzer's door.\n\n\"Away?\" Sarah asked. \"That's the plan? We have to do better than that.\"\n\nShe was right, of course, but the feral side of him, the jinn side, as he was coming to think of it, snarled. She was slowing them down. \"We can't stop,\" he said.\n\n\"Your goal here is to protect Patrick and I, and you're not going to succeed at that if we both drop dead of exhaustion. We need to rest.\"\n\n\"Sarah, I . . .\"\n\n\"No, Jim. We are in this together. If you want to help me, that's fine. I accept your help, but I won't accept a leash. We need to come up with a plan.\"\n\nOne advantage to death was that Schweitzer had no trouble keeping his emotion off his face. He swallowed his anger and frustration, doubly intense because he knew she was right.\n\n\"Fine,\" he said, keeping his voice neutral. \"The plan is that we keep moving as fast as we can, but slow enough that you and Patrick can keep up.\"\n\n\"That's not a plan.\"\n\n\"Sarah, they're coming.\"\n\n\"How are they coming? On foot? By helicopter? On horseback? How many of them? More monsters or people this time?\"\n\nHe didn't answer, because the truth was that he didn't know. Death had given him superhuman physical capabilities, but it hadn't sharpened his mind. She was smarter than he was. Always had been. It was one of the many reasons he loved her.\n\nSarah sighed. \"Didn't you say they were the government?\"\n\nSchweitzer nodded.\n\n\"The government controls the entire country, Jim,\" she went on. \"That means that while we're getting away from them in one direction, we're heading toward them in another. This is _their_ country. If they're as powerful as you say they are, they'll be able to tap police in any town we come to. There isn't anywhere to run and we can't stay in the woods forever.\"\n\n\"Then we get out of the country. We slip across the border into Mexico, or make our way to Florida and stow away on a ship bound for Cuba or Haiti.\"\n\n\"How?\"\n\n\"I ran operations against drug cartels and human smuggling networks for years. I still know some of the players. I know how they operate. Let's get down there and then I can figure out a way to get us across the border.\"\n\n\"We need more specifics, Jim. How are we going to get across the border? I know you're trying to protect us, but we need a real plan.\"\n\n\"At least my plan comes with a direction. The plan is south. If you've got a better one, I'm all ears. For now, all we can do is keep moving. This forest is enormous, and that'll buy us some time at least.\"\n\n\"We can't keep moving unless we have somewhere to move.\"\n\n\"All right, then where do we move, Sarah? What place is safe for us now?\"\n\n\"No place, Jim. That's my whole point. We can't hide from this threat forever.\"\n\nSchweitzer swallowed his frustration, the need to keep going like an itch in his soul. \"Then what do you propose we do?\"\n\nSarah swallowed. Schweitzer could tell she was choking back tears. \"What do you do with a threat you can't escape?\"\n\nThe itch vanished. Schweitzer narrowed his eyes. \"You stop it.\"\n\n\"You stop it,\" Sarah repeated. \"We have to go on offense.\"\n\n\"Sarah, I spent months in that facility. I saw the guns, the people, the Gold Operators. We can't go up against that.\"\n\n\"You're right,\" Sarah said. \" _We_ can't.\"\n\nSchweitzer's dead stomach clenched. \"What the hell are you talking about?\"\n\nSarah was silent for a long time. When she finally spoke, the defeat in her voice made him cringe. \"Jim, you're dead. Patrick and I are alive.\"\n\n\"What's that supposed to mean?\" Schweitzer snarled, knowing exactly what she meant, knowing that she was right. He could feel the grief down the magical link between them, the desperation, but it didn't change the sinking feeling in his own soul. _She wants me to go._\n\n\"You know what it means,\" she said. \"It means that Patrick and I hunker down somewhere, and you find a way to make all this stop. You found me even though hell itself stood between us. You'll find me again.\"\n\n\"You saw what those things can do. You expect me to go up against an army of them by myself?\"\n\n\"I saw you take on four of them and win.\" Three. Sarah had destroyed one, but Schweitzer didn't correct her.\n\n\"There are more than four! And that doesn't even count the living enemy.\"\n\n\"I don't know what else to do, Jim. I don't know how else we can stop this. Please . . . I . . . I love you, but you're dead, Jim. Patrick is alive. Protecting him has to be our first priority.\"\n\nPatrick began to squall, pulling at his mother's shirt. Schweitzer searched his own mind desperately for a retort, for a way to make her stay with him, but the grief and anger clouded everything. \"You're safest with me.\"\n\n\"You can't honestly believe that. The Cell wants _you_ , Jim. If I go on TV, people can roll their eyes at a widow gone mad with grief, but nobody who sees you can deny what you are. Wherever you are, they will come. It's the government. They don't give up. They don't run out of money. You have to stop this threat.\"\n\n\"I won't leave you.\"\n\n\"Damn it, Jim,\" she shouted, tears glistening in her eyes. \"You think this is easy for me? What about Patrick? Are you going to drop him off at school? Are you going to help him with his math homework? Do you expect him to spend the rest of his life running?\"\n\nThe grief funneling down the link between them triggered his own. His dead body still possessed the phantom limbs of life: he felt the shade of a tightening throat, the pricking of phantom tears at the corners of his eyes. His voice came out as a strangled cry. \"Sarah, please. I fought so hard to get back to you. I can't lose you again.\"\n\nShe put her head in one hand, hugged Patrick tightly with the other, and wept.\n\n\"You're dead, Jim. We can't make love, we can't be together. You can't raise Patrick. We'll only slow you down. We're already slowing you down.\"\n\n\"I can keep you both safe.\"\n\n\"Jim, please. Please don't make this harder. If you push me, I'll just stay, and that's no life for either of us. Just . . . just . . . go and find a way to make them stop. Patrick and I are only human. We can't fight them. You can.\"\n\n\"I love you.\"\n\n\"I love you too. When this is over, you'll find me again, and we can . . . figure something out.\"\n\nWith that shred of a promise, thin as tissue, Schweitzer's SEAL side took control. _She's right. If you want to keep her, keep Patrick safe, you have to find a way to shut the Cell down._ \"Chang.\"\n\n\"What?\" Sarah asked.\n\n\"We can trust Steve Chang. He has the training. He has steel. He can keep you safe while I finish this. I wouldn't ask him to turn his coat, and I don't know that he ever would, but he loves you and Patrick as much as I do. He'll protect you.\"\n\n\"Jim,\" Sarah sobbed anew. The feelings along the link between them were tangled now, a riot of terror and love and grief and rage.\n\n\"What? What's wrong?\"\n\n\"Steve's dead.\"\n\nSchweitzer's mouth hadn't had saliva since the day he died, but he felt it had gone dry just the same. More phantom limbs, shades of the life he'd once had. \"No.\"\n\nSarah was too overcome with weeping to answer. She only nodded.\n\n\"Did you see a body?\"\n\n\"I don't need to.\"\n\n\"Then how do you know?\"\n\n\"I _know_ , Jim. The same way I knew that you were alive. I could feel it.\"\n\n\"Are you sure?\" Schweitzer could hear the anger in his voice, the desperation, couldn't stop either. \"Sarah, are you _sure_?\"\n\nShe wept again, nodded. \"Completely.\"\n\nSchweitzer was too crushed by his own loss to focus on the tangle of emotions coming down the link from her. Steve Chang, his best friend, his teammate, gone. He struggled for a long moment before he found his voice again.\n\n\"How did he die?\"\n\n\"I don't know. I just know that he did.\" Sarah's emotions became pinched, frightened. \"He came around a lot at first, when we thought you were dead, but then he just disappeared. Chief Ahmad said he'd been deployed.\"\n\n\"And then you just felt it? He was gone?\" Fear came flooding along the link from her. Schweitzer smelled the slightest hint of adrenaline in her bloodstream.\n\nShe nodded. \"He's gone, Jim. That's all I can tell you.\" _No, that's bullshit. There's more. Something between her and Steve._\n\n\"Sarah, there's something wrong here. What aren't you telling me?\"\n\nShe only shook her head and wept. \"I just . . . I just know he's gone, Jim. Please, just leave it at that.\"\n\nAnd now Schweitzer's grief came on him like a wave, so strong that his legs shook. He grit his spiritual teeth and pushed it down, swallowed it. The questions rioted, the urge to interrogate her so strong that he suppressed a growl. There was something wrong with the way she was feeling, something more complex than the simple grief of someone mourning a passed friend.\n\nEnough. Steve would have wanted him to be strong. He'd shown Sarah and Patrick enough of his underbelly for one day. When she was ready to tell him what she was thinking, she would. \"He was our best option.\"\n\n\"I know,\" Sarah said, mastering her tears, drawing strength from Jim, as she had when he was alive.\n\n\"There are no good options here, Sarah. We can't go to a family member, no matter how far removed. Family's the first thing a targeter diagrams out. Close friends will be next.\"\n\nHe would have trusted his brother, Peter, to protect Patrick. Peter the golden boy, the model SEAL Schweitzer had aspired to be. _Proud of you, bro._ But Peter was dead, his body shredded in the wreckage of the downed helo in Afghanistan. He'd died when Schweitzer was still alive, before he'd known that death wasn't the end. He supposed Peter twisted in the soul storm now, or maybe there was somewhere else beyond it. It didn't matter. There was no way to know, and knowing wouldn't help him now anyway.\n\nSarah swallowed, nodded. \"I'll think of something, but we're not going another step until we rest. That's not negotiable. You want to go on, you go ahead. Patrick and I are getting a few hours sleep.\"\n\n\"Sarah, I don't know that we have a few hours.\"\n\n\"Well, we damn well have to. We can't keep going. I can't see straight, Jim.\" She sat down where she was, not bothering to inspect the ground beneath her. She flopped over on her back, cradling Patrick against her chest. Her voice was already sluggish as fatigue wrenched her down into drowsiness. \"And we could use something to eat.\"\n\n\"Sarah, let me carry you. I can tote you and Patrick without breaking a sweat.\"\n\nShe shook her head faintly. \"We need to sleep, and Patrick is going to freak if you come near him. Can you get us some food?\" And then she was snoring softly, her breath lightly wheezing, thick in a way that troubled him.\n\n\"Sarah,\" he said. She didn't respond. He knelt at her side, reached out to touch her, thought better of it. Patrick's face was turned away from him, his cheek nestled against his mother's chest. Schweitzer could tell from his breathing that he had collapsed into sleep the moment he had stopped bouncing in the sling.\n\nSarah was right, they needed sleep, and they needed food. Schweitzer sat back, pushed his hearing out to its very limit. A hawk circled miles out, crying out warning to any who would seek to approach its hunting grounds. An aircraft droned miles overhead, likely a passenger airliner, moving steadily away from them. There were still no sounds of pursuit. He dialed his hearing in closer, pausing at intervals to assure himself that all he heard were the sounds of the natural world around him. When he finally heard the snuffling of a deer drinking at a stream less than a mile away, he made his decision.\n\n\"I'll give you a few hours,\" he whispered to his wife. He bent to kiss Patrick's head, pulled back. Better not to risk waking him. \"I love you,\" he whispered, then stood, turned, and took off running.\n\nThe wind was out of the south, blowing a steady two knots, bringing the sharp odor of the deer's hide to him, and more importantly, carrying his own scent away. He shifted his balance up into his midsection, slowing just enough to make his footfalls light. He brushed over the leaves, barely making a sound, the forest falling away to either side as the stream grew louder. At last, he saw an elbow of the water shining silver in the failing light, broken into glowing filaments by sharp rocks and jagged twigs. He heard the deer now, nosing in the water. It was breathing in deep pants, far apart. Gulping. It was thirsty then, winded from the climb to the stream.\n\nSchweitzer advanced at a crouch, letting his senses dial in on the deer's breathing, concerned that the focus on the animal took so much of his concentration that it left him vulnerable to attack from another direction. He examined the branches above him, looking for a way to get off the ground and make a safer approach.\n\n_No time. Every second you're away from Sarah and Patrick puts them in danger. Get it done._\n\nSchweitzer gave free rein to his jinn side, letting his magical reflexes take over. His crouch turned into a loping crawl, wickedly fast, shoulders pumping as he knuckled over the uneven terrain, bone spines beginning to protrude from his head and back. This was the form Ninip had favored, an appearance in better keeping with its nature. When he'd shared the body with Ninip, taking this form had clouded Schweitzer's mind, submerging it in a sea of predatory lust. But now the jinn was gone, and the form was just one of many tools at Schweitzer's disposal, like his training. He put on speed, heedless of noise now, crashing through the underbrush. He heard the deer stop drinking, the creaking of its neck as it raised its head, muscles tensing as it prepared to spring away.\n\nSchweitzer exploded from a patch of stunted trees, slamming into the animal before its eyes had so much as a chance to widen, locking his limbs around its thick body and sending it tumbling. The deer was strong, thrashing against him, the back of its skull hammering his face. It might as well have been a kitten compared to Schweitzer's magical strength. He locked his hands around the creature's chest, squeezing his arms together until its ribs snapped and blood fountained out its mouth and nose.\n\nThe coppery smell recalled the red joy he had known in Ninip's thrall. He had been able to forget himself, forget those who depended on him, forget the tasks left undone. There had been nothing but the feel of his body, his enemy, and the shrill joy of the kill.\n\nBut that had been before he knew his wife and son were alive.\n\nHe drove inward with his elbows, working the broken ribs until they pierced the heart and lungs, and the animal shuddered and lay still. He waited silently, listening. The forest had gone quiet around him. Still no sound of pursuers.\n\nHe rose, hefting the heavy deer easily over one shoulder, and sprinted back to where his wife and child lay. As he neared his back trail he could hear the faint patter of their heartbeats, the slow bellows of their breathing, each gust a moment apart. They were alive and still asleep.\n\nHe arrived at their side and slid the deer to the ground. He coaxed one of the bone spikes from his fingertips, skinning and gutting the animal, lost in the work until he heard the leaves rustle and turned to see his wife looking at him.\n\n\"Thanks, babe,\" she said. Patrick stirred weakly against her shoulder.\n\n\"Don't wake him,\" Schweitzer said. \"He needs all the sleep he can get.\"\n\nShe nodded as he held out a long strip of thick, red meat. \"Backstraps,\" Schweitzer said. \"Best part.\"\n\n\"We can't eat it raw, Jim,\" she said.\n\nHe looked down at the steaming strip of wet flesh. \"Right,\" he said, feeling farther from her than ever. \"I forgot, sorry.\"\n\n\"I don't have a lighter. I don't suppose you have heat vision or something?\"\n\n\"Something,\" Schweitzer said, scanning the ground until he'd located what he needed. He took a slab of bark and placed a stick against it, set his palms to either side. \"Watch this.\"\n\nHe rubbed his hands back and forth. His magical strength and speed soon had the stick twirling to a blur, smoke rising from the friction against the bark. Within moments, it was burning brightly, and he picked it up, carrying it to a pile of leaves.\n\n\"Baby,\" Sarah said, sitting up, eyes widening at the burning tinder against the meat of his hand. \"Doesn't that hurt?\"\n\nSchweitzer shook his head as the fire took, then set to clearing a ring around it. Sarah watched in silence as he built it, and the crackling flame sent embers sparking into the sky.\n\nSchweitzer looked up at the thick canopy of trees, branches interlocking to form a green carpet that barely admitted sunlight. Even a powerful drone with an infrared camera wasn't going to be able to spot such a small fire through that. He hoped.\n\nAs he wrestled for a way to ask her what was going on, Sarah sighed. \"Okay, champ. I can take it from here. Can you give us a little privacy while I get this cooked?\"\n\nSchweitzer's heart twisted. \"Why?\"\n\n\"Honey, I need Patrick to eat. He's not going to do that if he's . . . Please, Jim. Don't make this harder than it has to be. Patrick's had one hell of a shock. I just need him to have smooth sailing until we can figure this out.\"\n\nThe anger took him by surprise. _She doesn't trust me._ \"Damn it, I'm going to have to leave you anyway.\" Schweitzer snarled. \"Let me have another second with him. He's my son.\"\n\nSarah gave him a hard look. \"Then you'll want him to eat without shitting his pants. Jim, I am doing my level best to accept the new reality of . . . what you are. You can't expect that of a child. Work with me here.\"\n\n\"You _want_ me to leave.\" Her words made sense; his logical mind, the cold professional that was the Navy SEAL, accepted the calculus without batting an eyelash. But a deeper part of him didn't care. That part knew she was still hiding something from him. He could feel it in the sour edge of the emotions travelling down the link between them.\n\nSarah's expression softened at the hurt in his voice, and he cursed himself for letting it sound there loudly enough for her to recognize it for what it was. He couldn't control what she felt through the link between them, but he didn't have to make it harder on her by confirming it. Peter would have been disappointed. That wasn't the SEAL's way. \"No, Jim. I don't. I just want to take care of our son.\"\n\nSchweitzer could see that the exchange was hurting her too, that she was trying. _When she wants you to know whatever she knows about Steve, she'll tell you._ He could see himself through her eyes, a shambling horror, a walking corpse tied to her chest by the supernatural link their love had forged. There was no guile in the flow through that link now, only love, fear and exasperation. He knew he should say something, bow his head and tell he loved her, tell her that he understood.\n\nBut in the end, all he did was turn without a word, stalking off into the underbrush, letting his eyes roam the emerging heat signatures as they stood more starkly in the cooling air. Patrolling the perimeter gave the jinn part of Schweitzer his head, let the animal instinct to fight and defend take control. The sorrow and grief faded to a background buzz. Jinn Schweitzer didn't need to worry that his wife thought him a monster, that his son would likely grow up never knowing his father, fearing him as a thing that went bump in the night. Jinn Schweitzer was busy preparing to meet the enemy.\n\n# CHAPTER II\n\nHUNTING THE DEAD\n\nCold air billowed out of the open refrigerator doors, bathing Doctor Eldredge in chilly white clouds.\n\nEldredge wrinkled his nose at the chemical-vanilla smell of the coolant and pulled the gurney out into the bare white room. The walls were dotted with metal nozzles. Half of them flickered with tiny blue pilot lights, the other half crackled with chemical frost. At the touch of a button, the contents of the room could be burned or frozen solid in seconds.\n\nJawid Rahimi stood, hands clasped. His eyes were shadowed, dark curls unruly under his round, brimless cap. He looked sad, preoccupied. The same whipped puppy-dog look that made Eldredge want to both comfort and shake him. It had been this way ever since Schweitzer had escaped.\n\nJawid insisted on continuing to wear his traditional dress, a long and impractical shirt and ballooning trousers. He still prayed five times a day, a damned inconvenience when they were on an op and schedules were tight. Eldredge didn't have much patience for religion, but the psychiatrist assigned to Jawid had recommended he be allowed it, that any attempt to forbid it would only make him dig in deeper.\n\nEldredge put on a smile in spite of his frustration, hoping it put Jawid at ease. He might want to shake him, to fire him, but Eldredge couldn't afford to lose Jawid. The man's magic was the basis of the entire program.\n\nAnd Eldredge knew that being fired from Jawid's particular job was fatal. With what Jawid knew, with what he could do, there was no way the Director would ever just let him walk away.\n\nEldredge gestured at the corpse on the gurney, an Asian man, his body a network of scars. Tattoos were scrawled across his pale skin: a nautical star on his left pectoral, his blood type and serial number up his side just above the gaping hole where one of the Gold Operators had thrust its hand inside. A tattoo on his bicep showed his most important affiliation: an eagle perched on a trident crossing an anchor. In one set of sharp talons, it clutched the business end of a flintlock pistol.\n\n\"You recognize him?\" Eldredge asked.\n\nHe realized it was a silly question the moment he'd spoken. Of course Jawid recognized him. He'd tracked him, had helped run the op that took him down. His name was Steve Chang. His brother SEAL and best friend, James Schweitzer, was somewhere in the middle of the George Washington National Forest, a needle in a haystack nearly two million acres large.\n\nJawid nodded. \"You want me to put a jinn in him?\"\n\nEldredge sighed. \"It's been a few days since his death. Do you think his soul is still there to work with?\"\n\nJawid placed a hand on the corpse's forehead and closed his eyes. \"He's still in there.\" Jawid opened his eyes, but they focused on the middle distance.\n\n\"Jawid,\" Eldredge said.\n\nThe Sorcerer jumped, eyes snapping to him. \"Sorry.\"\n\n\"What's wrong?\"\n\n\"Nothing . . .\" Jawid looked down, face pained.\n\nEldredge swallowed his anger, took a moment to calm himself. The psychiatrist had warned him that the Sorcerer wouldn't respond to confrontation. He needed to be coddled. \"Jawid\"\u2014Eldredge forced a gentle tone, his knuckles white around the gurney handle\u2014\"I need you to focus here. It's all going to be all right.\"\n\n\"Schweitzer escaped because of me,\" Jawid whispered.\n\n\"That's not . . . entirely true.\" Except that it was. Schweitzer had plumbed Jawid's past, discovering that his own wife and son still lived. It had been a watershed moment for Schweitzer, the instant he discovered that he was a tool, and not a partner, of the Gemini Cell. Jawid had stared at the video monitors as Schweitzer wreaked carnage on the facility, carving a bloody path to freedom. Men and women, the closest Jawid had ever come to friends, lay in tatters in the corridors. His greatest failure splashed in red across the walls. And now Eldredge had to make him feel better about it. _Damn it, I am not trained for this. I don't know how to be a therapist._ \"You want to make this right? You have to help us catch him.\"\n\n\"What if we can't catch him?\"\n\n\"He's got his wife and toddler with him. They're not immortal. They have no magic. He's not going to abandon them. Trust me, we'll catch him.\"\n\nEldredge winced as he realized that he was trying to reassure himself. It wasn't just Jawid's failure. Schweitzer had escaped on Eldredge's watch too.\n\nJawid looked down at Chang again, his face wistful, eyes looking off into the middle distance again. God, dealing with his moods was exhausting.\n\n\"We need to get it right this time,\" Eldredge said. \"I need you to fight hard to preserve Chang's soul. I don't want the jinn pushing him out.\"\n\nJawid looked up. \"I never want the jinn to push the soul out. I always fight to keep it. It's just . . .\"\n\n\"I know it's hard, Jawid.\"\n\n\"You don't know. You've never worked magic.\"\n\n_Like a whining teenager._ Eldredge bit back his retort. \"I suppose you're right,\" he breathed, \"but Chang was Schweitzer's best friend; we need to interrogate him. He might know some of Schweitzer's connections. Family members or friends we may have missed. A clue to where he's headed.\"\n\n\"The jinn are not interrogators. They are . . .\"\n\n\"I _know_ what they are.\" Eldredge's impatience got the better of him. \"I know this is challenging and that's why I'm asking you to _try_. You need to push on this one. I need you focused; I need you to put the effort in.\"\n\n\"We have drones and reconnaissance teams. They can find him.\"\n\n\"Maybe they can and maybe they can't. That forest is enormous. We need every advantage we can get. If there's something that Chang knows that can help us, we can't afford to pass it up.\"\n\n\"I'm sorry, Doctor. I just . . . I have been sad for home lately.\"\n\n_Jawid's loyalty must be transferred to this institution,_ the psychiatrist's report read. _So long as it remains embedded in his tribal roots, he will never be truly reliable._ \"This is your home,\" Eldredge said, putting a hand on his shoulder. \"Schweitzer escaped because he was special. He escaped because there was . . . something in his spirit that let him beat the jinn. Chang was the closest man in the world to Schweitzer, and I can't shake the hope that that means they are _alike_ somehow. Maybe alike enough that Chang could be a Silver Operator, too. That may be what we need to find Schweitzer, to catch him.\"\n\n\"If Chang is the master of his own corpse, he will never hunt his best friend for you. Even if I could do it, it won't work.\"\n\n\"Try anyway.\"\n\nJawid paused, stalling. \"You can't blame Schweitzer for leaving. He only wanted to be with his family.\"\n\nThe truth was that Eldredge didn't blame Schweitzer. The Cell had lied to him about Patrick and Sarah, had kept him a virtual prisoner. But he wasn't going to indulge Jawid. The Sorcerer didn't need a friend to agree with him. He needed a boss to get him on task.\n\n\"Schweitzer is dead,\" Eldredge said. \"He can't be with anyone. At least we offer him a way to help keep the world safe so the rest of the living can be with their families. You need to remember that.\"\n\nJawid straightened, nodded. \"Okay. I will try.\" He placed his hand on Chang's face again, looked awkwardly at Eldredge. \"Do you think . . . you could leave me to do this alone? It is strange to be watched.\"\n\n\"I watch you every time you do a Summoning,\" Eldredge said. \"Does it matter whether it's through a camera or in person?\"\n\n\"No, I suppose not.\" Jawid turned his head away from Eldredge and closed his eyes. Eldredge watched as his breathing slowed, deepened. At last, his body gave a tiny shudder, and Eldredge knew that he was working his magic. The muscles in Jawid's jaw moved; his eyelids twitched. Eldredge would have thought him in the midst of a dream if he hadn't been standing. Jawid murmured words, so soft that Eldredge couldn't make them out, the mumbling of a sleep-talker.\n\nExcept that Eldredge knew Jawid wasn't talking in his sleep, that the words of his mouth mimicked those coming from his consciousness, communicating with the souls that drifted in some world that Eldredge couldn't see. At last, Jawid grunted and whispered. \"I have him.\"\n\nEldredge couldn't keep the excitement out of his voice. \"Can you save Chang? Can you keep him in there?\"\n\nJawid and the corpse opened their eyes at the same time.\n\nJawid's were dark and distant, red-rimmed from lack of sleep.\n\nChang's were gone. In their place burned two flames, deep gold shot through with tiny threads of silver. Jawid looked at the silver and sighed. _\"Allahu akhbar,\"_ he said over and over again. \"Thank you, Allah.\"\n\nAnd though he didn't believe in God, Eldredge echoed him. \"Thank you, Allah.\" The silver threads meant that Chang was holding on, that the jinn had not driven him out into the void and taken the corpse for itself.\n\n\"Who is it?\" Eldredge always asked this. The question was partly motivated by a search for patterns, something that could help him understand the nature of the spirits Jawid drew across the line and bound into the bodies of the dead. But more than that, it was simple curiosity. The jinn were always ancient, and Eldredge thrilled at the idea that somewhere in the depths of the corpse before him was the soul of someone who had died millennia ago.\n\n\"He calls himself Partolan,\" Jawid said. \"His hair was red, his skin tattooed in blue.\"\n\n\"Anything else?\"\n\nJawid shrugged. \"He is a lord of some kind. They always are.\"\n\n\"Can you talk to Chang directly?\"\n\n\"No. He is there, but he is not as strong as Schweitzer was.\" The silver threads in the eyes were thin. Schweitzer's had burned solid silver from the start.\n\n\"Maybe he will gain ground,\" Eldredge said.\n\n\"Maybe.\" Jawid didn't sound convinced. He sounded exhausted. \"Can you leave me alone with him, Doctor? It will . . . help me to focus.\"\n\nEldredge paused. He didn't want to take his eyes off Jawid, not for a moment. The man was unpredictable, in need of supervision. But a good supervisor knew when to back off and let things evolve. Standing here staring at Jawid accomplished nothing.\n\n\"All right.\"\n\n\"I will try harder,\" Jawid said. \"I will.\"\n\n\"I know you will,\" Eldredge said, turning to go. But the truth was that the Director was losing patience, and Eldredge wasn't sure at all.\n\nHe felt sick panic boiling in his belly as he returned to his office to punch up the video feed that would allow him to watch Jawid's progress from one of the thousands of hidden cameras throughout the facility. Jawid was right that they had every technical advantage in the hunt for Schweitzer. Feeds from half a dozen drones, Ranger teams on the ground, and spotters in the air. Local law enforcement prowling the edges of the forest. But Eldredge had run hundreds of ops in areas this large and remote. Single men, even burdened by their families, were hard to find, and that was when they weren't immortal supermen who could hear a pin drop a mile off.\n\nHe shook his head, dismissed the thought. A free Schweitzer could out the program, could confront the public with the truth that magic was real, that death wasn't the end, that the government didn't really know how it worked or how to control it. That couldn't be allowed to happen. Schweitzer had escaped on Eldredge's watch; the buck stopped with him.\n\n_There's more here,_ Eldredge knew. The risk Schweitzer presented to the program wasn't the only reason he wanted him back, but he couldn't think about that right now. To do so would be to lose focus as surely as Jawid had.\n\nEldredge needed his head in the game. He pulled up his laptop and called the Director's office, steeling himself to make his report. He'd promised progress and thus far had failed to deliver.\n\nIn the Gemini Cell, that kind of failure wouldn't go unpunished for long.\n\n# CHAPTER III\n\nCALIFORNIA SUNSHINE\n\nDadou Alva walked through the California sunshine, smiling. Californians were always smiling. Frowning would mark her as an outsider, drawing as much attention as openly wearing the compact pistol she had tucked into the small of her back. She carried the gun for contingencies but knew to save the last bullet for herself. Her boss had made it clear: discovery was tantamount to death.\n\nShe had spent most of her life underground and she basked in the sun's strange warmth, the feel of the air on her skin. She was used to taking pleasure in the small luxuries: breathing clearly, a full belly, a clean body, and a warm bed. The people around her had no such appreciation. Americans never ceased to amaze her. They bickered and complained about the silliest things: reception for their mobile phones, whining that they brought them the wealth of the world's knowledge in five seconds instead of three. They were the richest, most comfortable people in the world, and they still managed to be miserable. Nothing was ever enough for them.\n\nDadou shook her head and laughed. American luxury had lifted her up out of the broken asphalt and septic mud of Port-au-Prince and given her things she had only dreamed of all her life. Actually, that wasn't entirely true. American luxury provided the wealth that created the Scorpio Cell, the vast and sprawling secret infrastructure that supported her, but it was her magic that made them want her in the first place.\n\nShe followed the directions in the text message, turning down the narrow alley where it cut behind the pizza parlor. As she glanced in the open door to the kitchen, she surveyed the cooks. They were completely convincing to the average observer, slack-jawed, broad-shouldered men in white aprons stained with marinara sauce, working with the bored and distracted look of veterans of underpaid, menial jobs.\n\nDadou recognized one of them. His hair had grown out from the buzz cut he'd worn as he stood to attention outside a door of her office, his military uniform so clean that it looked as if dust dare not touch him.\n\nThe alley ended at a low cinder-block building, white paint flaking from the surface of a metal roll gate. A rusted sign hung over it, nearly covered in graffiti and stickers: CORONADO IRONWORKS. Clusters of weeds crowded the broken path leading to a single metal door. She glanced over her shoulder, careful to make a show as if she were inspecting her back pocket, as her countersurveillance instructors had taught her. She caught a glimpse of the men in the pizzeria kitchen, looking alertly out the open door. They were \"covering her six,\" as the American soldiers liked to say, a comfort to her as she faced the door and tried the handle.\n\nIt didn't move, but she felt it warm as the pulse reader the Cell's agents had connected to the handle scanned the signature in her blood. There was a click and the door swung open.\n\nThe interior matched the outside. A single fluorescent-tube light cast shadows over the pitted cinder-block walls. Trash clotted the corners along with the discarded needles and condoms where druggies and prostitutes had plied their trade. The whole place stank of desperation and stale piss. She smiled. It reminded her of home.\n\nA thick length of rope had been looped over the flaking iron remains of a long-unused sprinkler system, hanging down to a thicker knot. A man hung by his wrists from it, skin gray-white. He had thinning hair plastered across the clammy surface of his forehead. His head hung, body limp.\n\nA man stood to either side of him. They were dressed self-consciously to imitate homeless people, complete with stereotypical watch caps, threadbare overcoats, and fingerless gloves. Dadou could tell that the filth on their clothing had been recently applied, knew that the gloves were fingerless so as not to impede the smooth action of their trigger fingers. One of them turned alert, killer's eyes on her. \"You're late,\" he said.\n\n_\"Komik,\"_ Dadou snorted. \"A wizard is never late. She arrives precisely when she means to.\"\n\nIt was a quote from one of the endless films they showed in the Scorpio Cell's rec room, and both men smiled at the response, but she could feel them tense. They didn't like to be reminded of her magic; it frightened them. That was good. Dadou found that men were more likely to do what she asked them when they were frightened or aroused. Much of the time, one was linked to the other.\n\n\"He can still talk?\" she asked.\n\n\"So far,\" one of the men answered.\n\nDadou leaned forward and seized a hunk of the man's hair. \"Wake up, Rodriguez.\"\n\nHis head rolled back, his hair wet in her hands, eyes staying stubbornly shut. \" _Reveye, sak t\u00e8._ Wakey, wakey,\" she said. Nothing. \"It will go easier for you if you talk to me.\" Nothing.\n\nShe turned to one of the thugs. \"You said he could still talk.\"\n\nThe man cursed and jammed a thumb behind Rodriguez's jaw, working it back and forth until the prisoner screamed, eyes opening and glaring at Dadou with a hatred that made her take a step back.\n\nBut only a single step. She took another forward and seized his hair again. \"Your brother picks up the money you send him at Salto del \u00c1ngel. When is he coming next?\"\n\nRodriguez stared. His mouth worked silently.\n\n\"Clearly, he appreciates it, _non_?\" Dadou asked. \"I'm sure he'll break in here any second to rescue you.\"\n\n\"Fuck you. I'm not telling you shit.\"\n\nSo clich\u00e9d. Like a bad movie on Tele Jeunesse. She gripped his hair tighter. \"Why are you being an idiot, Rodriguez? What do you think you are accomplishing?\" She pulled down on his head, his wrists straining against the knotted ropes. \"You feel that? That's real. This isn't a movie. You're not an action hero. No one is coming to save you. This ends in one of two ways: you talk and you live, or you refuse and then we hurt you and you suffer and you talk anyway and afterwards, you die. You're not a hero, Rodriguez, and your brother is a murdering bastard.\"\n\nRodriguez found his feet at that, jerking toward her before being pulled back by the rope, shouting a stream of Spanish that she couldn't understand beyond knowing it was unkind.\n\nShe reached into her vest and took out a picture, waved it in his face. \"You see this helicopter? Nice and crispy, isn't it? Did you know there were kids on it? Let me hold it closer so you can see.\" She tapped the edges of the photograph with her thumb, pointing out the black lumps that had once been hostages.\n\n\"Your brother took them,\" Dadou said, \"and he burned up our helicopter rather than let us rescue them. That's where your money goes. To terrorists who kill babies. This is what your brother uses his magic for, to burn up rescue helicopters. You're no hero, and your brother isn't either.\"\n\n\"Fuck you,\" he spat blood, narrowly missing her face. \"You fucking bitch!\"\n\n_\"Raz,\"_ Dadou drawled. \"Last chance to do this nicely.\"\n\nRodriguez swallowed. \"If you're going to torture me, just get it over with. It won't work, anyway.\"\n\nDadou smiled. \"I would never torture you, _moun komik_. People say anything when you hurt them badly enough. You would scream and mix lies with truth and listen for what you thought I wanted and tell me that just as fast as you could. Anything, just to make the hurting stop. By the time we untangled the lies from the truth, we would have lost even more time. I want to find your brother quickly, before he can use his magic to do more damage.\"\n\n\"That's why you want him, for his _brujer\u00eda_. Not for hurting no fucking kids. So, you'd better torture me, because it's the only way you'll get me to even lie to you.\"\n\nDadou sat cross-legged on the dirty floor before him, relaxed her shoulders. The truth was that this was the answer she'd known he would give, that she'd wanted him to give. It gave her the excuse to do what she'd been planning to do anyway. \"I don't need lies, Rodriguez. I need truth. And I also have the _brujer\u00eda_. Which is why I don't need to torture you.\n\n\"I told you that you'd talk, and you will.\"\n\nDadou gathered the tide of her magic around her, closed the eyes of her physical body, and pushed her spirit outward. She reached out into the void, racing through the blackness. There was a time when the inky dark had felt thick as molasses to her, but she had been a _S\u00e8vit\u00e8_ since she was four years old, and the journey was second nature to her now. She reached the soul storm in moments, the light broadening across her vision, filling her ears with screaming.\n\nThe tangled mass of souls whirled about her, the distinct undertow lapping at her like the waters in the bay where she'd swum as a child. She kept her distance, sifting easily through the voices, discarding the half-mad shrieks of apology, dire promises of vengeance that would forever remain unfulfilled.\n\nDadou drifted on the edges of what she called the _gwo fant\u00f4mes_ , the cyclone where the dead churned. She listened patiently, pushing enough of her consciousness into the twisting hell to let those within know she was present. The strongest would make themselves known. Sooner or later, they always did.\n\nDadou became conscious of a quiet ferocity from deep within the storm. It emanated from a spirit just as hungry and violent as all the others, but not wasting its energy on words. Instead, it clawed its way steadily to the edge, relentlessly following the tide of Dadou's magic, until it was close enough for her to single it out.\n\nDadou reached out and touched the presence, letting it mingle with her magic. The experience was always heady when she first touched a soul. It was a sudden immersion in the sense of a person, a storm of emotion and experience coming on in a rush. Like all of the _mist\u00e8_ , this one was freezing cold, ravenously hungry, desperate to reach the beating hearts and flowing blood it knew were just beyond its reach. It wanted to know some shred of warmth, even if only for a moment.\n\nDadou's spiritual eyes pictured the _mist\u00e8_ as a young girl, barely older than twelve, a red plume flying from a bronze helmet covering her pin-straight black hair.\n\n_I am Hua Mulan,_ the spirit declared in a little girl's voice. _I am the flower of Wei, the lord commander of the three armies. Kneel before me._\n\nThe language was unfamiliar, but it didn't matter. Souls communicated at a level beyond speech, and Dadou had no more need to translate the creole of her home when she replied. _I am honored to meet you, Mulan. I am here to give you what you most desire, in exchange for a favor._\n\n_You do not bargain with the blood of Emperors,_ the _mist\u00e8_ said.\n\nDadou only smiled patiently. _Call it a gift, then, bestowed upon a faithful subject as reward for an act of devotion._\n\n_What devotion do you offer me?_\n\n_I will return you to the world of men. Living men. Men that breathe and bleed. Blood that can be yours, so much that you can bathe in it._\n\nMulan grinned in the blackness. _Go on._\n\nDadou could feel the _mist\u00e8_ 's eagerness. It attempted to hide its anticipation, failed. It practically shivered with excitement. Dadou smiled inwardly. _Take my hand._\n\nThe _mist\u00e8_ let Dadou coil her magic around it, flashing another image of a little girl in armor, bronze halberd over one shoulder. Doubtless it expected Dadou to recognize her and be cowed.\n\nDadou only drifted back, pulling the _mist\u00e8_ with her, down the magical link that brought her back to her physical body, the endless depths of the void slipping past her in an instant. Mulan struggled as they came closer, Dadou's magic intensified, and the _mist\u00e8_ felt itself beginning to be roped into the form Dadou intended, compressed into the flow of the _vodou_ that pulsed in her veins. But by then, it was too late and Mulan was within her, filling Dadou with such an intense sense of power that she doubled over. She opened her physical eyes back inside the filthy cinder-block walls and looked at Rodriguez.\n\n\"I warned you,\" she said through gritted teeth. \"I gave you a chance to do this another way.\"\n\nShe focused her magic and Bound the _mist\u00e8_ into his body.\n\nThe two thugs backed away as she moaned in relief, lips curling in disgust at the sexual sound. In truth, it was closer to pissing after holding it in for hours, the doubled tide of magic pouring out and into Rodriguez.\n\nDadou could feel Mulan driving hungrily at him, desperate for his warmth and blood and life. Dadou tried to follow Mulan in, to see the souls mixing, to understand what was happening now.\n\nThere was the brief moment where the _mist\u00e8_ and Rodriguez's soul were joined, and Dadou came to truly know both of them. Mulan had been a child general, taking the place of her ill father in the army of some ancient emperor, rising through the ranks to become his concubine. Rodriguez was a two-bit thug who had grown up in the Colombian ghetto, cutting his teeth first on shell games and pickpocketing before graduating to second-story work. He'd never amounted to much, even as a criminal, but his brother had.\n\nWith the dead, this next part was easy. The Binding was simple, and Dadou had only to concentrate on the silence within, pushing her magic out and letting the jinn do the rest.\n\nBut Rodriguez was alive.\n\nDadou could feel his heart pounding, a steady rhythm of hammerblows that shook both Mulan and her. The heat of his blood might as well have been a searing furnace after the endless cold of the void. Where the souls of the dead were silent, the living shouted their connection to the world. Dadou could hear the soul's link to everything in Rodriguez's body. His cells dividing. His nerves reporting the pain in his wrists. The sick panic in his gut as he felt Mulan tearing into him.\n\nDadou weathered it all, feeling her physical teeth clench as she focused her magic on Binding Mulan into Rodriguez's body. Rodriguez's soul recoiled at the invasion. Dadou could feel his body contracting, muscles going rock hard, veins dilating. Her physical ears could hear his strangled howl, could smell the stink as his bowels let go.\n\nYet still the heartbeat hammered. This was the closest she'd yet come to success. The living soul would tear the body to pieces resisting the incursion of the _mist\u00e8_. Mulan would have to be held back just enough to let the Binding finish before it was turned loose.\n\nThe _mist\u00e8_ howled, scrabbling toward Rodriguez's soul, enraged and enraptured by the nearness of life. _No,_ Dadou said to her, _not yet._\n\nMulan strained against the chains of Dadou's magic.\n\nRodriguez screamed, his soul spasmed, and Dadou heard the sound of bones grinding, muscle tearing away from tendon.\n\nDadou coiled her magic back, pulled with everything she had. _Just wait for a moment,_ she shouted to Mulan. _Just a moment and you'll have what you want._\n\nShe might as well have pulled against a mountain. Mulan's only answer was a strangled shout of its own. The _mist\u00e8_ redoubled its efforts, pulling toward Rodriguez. Dadou was overwhelmed by images of Mulan's swinging fists, bronze squares flashing. At last, the wild beating of Rodriguez's heart began to overwhelm her, and Dadou felt her magic slip as Mulan strained forward. The _mist\u00e8_ shouted, pulled and broke free, Rodriguez's vitality and Mulan's fury kicking Dadou back and into her own physical body, the link broken. She felt a moment's disorientation as her physical eyes opened. Reality always shocked her when she returned to it, the universe suddenly a warm, hard thing of sharp edges and foul smells.\n\nRodriguez breathed his last. Swathes of purple mottled his pale chest where the vessels beneath the skin had burst. One of his pectorals had detached, slid into his armpit. His eyes stared sightlessly, the sclera completely red. Blood bubbled out of his mouth with his death rattle.\n\nDadou cursed, stood. The thugs backed away. Dadou knew what they had seen, Dadou sitting, teeth gritted, frowning in concentration as Rodriguez's body slowly clenched, purpled, and died.\n\n_So close. Just another moment and I would have had it._ It was the same problem every time. She couldn't perform the Binding quickly enough, locking the jinn in place before the victim's body tore itself apart from the shock of the incursion.\n\nThe thugs stared at her, horrified. The luxury that Americans enjoyed went hand in hand with a mad insistence on the sanctity of human life. It was not so back home. You learned quickly that people die easily, saw firsthand that life rolled on regardless.\n\n\"I got what I needed. _M\u00e8si._ Clean up here. Bring the body back to base,\" Dadou said.\n\nShe tried to keep her voice casual, but even she could hear the resignation. Another failure. The Director would not be pleased. She turned to go.\n\n\"You're supposed to wait another hour before you leave,\" the thug said.\n\n\"The Director will want to hear about this immediately.\"\n\n\"I have my orders,\" the thug said.\n\n\"And I have mine,\" Dadou answered. \"I also have the _vodou_ if you'd care to try and stop me.\" She nodded at the Rodriguez's cooling remains. _\"Sa se pa vre?\"_\n\nThe man's jaw set and Dadou grunted in satisfaction. It was as close to fear as these hard-operator types ever came. She turned on her heel and left, her back itching as she waited for one of them to try to stop her.\n\nBut they let her go, and the copper stink of blood followed her for a block or so before the breeze from the Santa Monica Bay whisked it away.\n\n* * *\n\nBack in her cell underground, the bright azure of the California sky locked away by miles of earth, her laptop chimed.\n\nDadou was just emerging from the shower, and she wrapped the towel around the wet mass of her dreadlocks, glorying in the water still dripping off her muscular body. She didn't bother to cover her nudity. Only one person ever called on her laptop, and she could never tell if he was bothering to look at the camera or not. At forty, Dadou knew she looked better than many half her age. Most girls spent their days preening and waiting for a man to lift them out of want. Dadou spent hers training. The difference was as obvious as it was stark.\n\nShe went to the computer, tapped in her password to unlock it.\n\n\"Good afternoon, Miss Dadou.\" The voice coming through her laptop was a mechanical rasp, as if the speaker had a mouth full of buzzing hornets. Dadou knew that there was better software out there, programs that could hide the speaker's voice without adding this creepy element, but she also knew that the Director preferred horror-show theatrics. She supposed it was no different from how she cowed the men she worked with, and she respected it.\n\n\"Good afternoon, _Direkt\u00e8_ ,\" she said. \"How's the view from the top?\"\n\n\"Anxious,\" he replied, \"I have received some concerned reports from my element leader at the temporary wetworks we established for your latest foray.\"\n\nDadou laughed through the thick rage she felt sour her stomach. Frightened men were worse than old women, always filing reports and making complaints. \"You know how these 'pipe hitters' are, _Direkt\u00e8_. They run screaming at the first sign of the _vodou_. Everything is fine.\"\n\n\"I hear Rodriguez did not talk, and that your efforts to Bind a spirit with him ended his life.\"\n\n\" _Se sa, Direkt\u00e8._ Both true.\"\n\n\"Perhaps you do not appreciate the need for progress in this particular operation.\"\n\n\"I came close this time, _Direkt\u00e8_.\"\n\n\"How close?\"\n\n\"Very close. If I'd had another moment, we would have had it, a _mist\u00e8_ in a living body.\"\n\n\"You've been close before, Miss Dadou. It only counts for horseshoes and hand grenades.\"\n\n\"I'll get it. I'll get it soon.\"\n\n\"I'll be delighted when you do. In the meantime, Rodriguez is dead, and we are no closer to capturing his brother. That man's magic is too valuable to let go unchecked. We need to bring him in or bring him down.\"\n\n\"I know.\"\n\nThe silence on the other end of the line was as close as the Director ever came to an outward expression of anger. \"Miss Dadou, I am at the helm of a considerably well-resourced organization. Surely there is some insight you can provide me as to where the problem lies so I can find a way to help you?\"\n\n\"There's nothing, sir.\"\n\n\"Then, what is the problem? You said this would work.\"\n\n\"It _can_ work. I know it can. The problem is the Binding. It has to be done quickly, before the . . . shock of the Binding destroys the host body. It is so much easier with the dead; I don't know how to explain it.\"\n\n\"Yet you must try.\"\n\n\"It's the speed of the Binding. That's the problem.\"\n\n\"Is there anything we can do to make that happen faster?\"\n\n\"Not unless you've got another Sorcerer to help me.\"\n\nAgain the pause, and this time Dadou couldn't tell what emotion lay behind it. At last, he spoke again. \"Another Sorcerer.\"\n\nShe squinted at the laptop, as if she could look through the blank screen to see his expression. \"Not just any Sorcerer. Another _S\u00e8vit\u00e8_. One who speaks with the dead.\"\n\nSilence again; this time it dragged on.\n\n\"Sir? Are you still there?\"\n\n\"I'm thinking,\" the Director answered.\n\nDadou's gut clenched. \"Dare I ask what you are thinking about?\"\n\n\"I'm thinking about another problem I have, on the East Coast. You might be able to help me with it. In turn, I might be able to help you. Forget Rodriguez, turn everything over to the watch captain, and pack a bag.\n\n\"I want you in Virginia by tomorrow.\"\n\n# CHAPTER IV\n\nBRIEFING\n\nDoctor Eldredge sat at the cherrywood desk and stared into the video teleconference monitor. The light beside the camera was green, indicating that his image was being relayed to the person on the other end, but the move wasn't reciprocated. Eldredge had been working for the Director for most of his adult life now, and he still had yet to see the man. He didn't know his name or even what his voice sounded like. The deep rasping that came over the phone or video teleconference line had to be the work of a voice modifier.\n\nOf course, the Director didn't know Eldredge's name, either. Eldredge had worn his moniker so long that he thought of it as his own. There were days he couldn't remember his real name, a trio of foreign-sounding words that described a stranger he had known a lifetime ago.\n\n\"Doctor,\" came the Director's voice over the line. Eldredge had heard it at least a hundred times in his career, and it never failed to give him shivers. Eldredge could almost feel the man's satisfaction as the video conveyed the revulsion on Eldredge's face. \"It's good to see you.\"\n\n\"It's good to _see_ you too, sir,\" Eldredge answered, cocking an eyebrow.\n\nThe Director chuckled, distinguished from coughing only by cadence. \"The security of this operation is my chief responsibility. Given the recent breach, I think my concern is justified. Wouldn't you agree?\"\n\nEldredge felt his face color. The Director was referring to Schweitzer's escape. Schweitzer had been Eldredge's greatest achievement and his worst failure. He was the only Operator the program had ever produced whose own soul had triumphed over the jinn bound into his corpse. On Eldredge's watch, he had become the first Operator capable of ethics, of restraint, of anything other than the predator's instinct to kill. And on Eldredge's watch, he had escaped. He took the Director's meaning. Compartmentalization was a key part of keeping every aspect of the program secret. That meant that you didn't get to know what your own boss looked like. \"Of course, sir.\"\n\n\"I knew you'd agree. What's the SITREP?\"\n\nThe Director's insistence on military acronyms was the one clue Eldredge had to his identity. Civilians learned and used acronyms too, but only a former military man mingled them with everyday speech until it became a kind of creole.\n\n\"Jawid has succeeded, sir. Chang is paired with a jinn. From Jawid's description, he sounds like some ancient Celt or Norseman.\" Before Schweitzer had taken control of his own corpse, he had been paired with the soul of an ancient Akkadian god-king. All the jinn were older than dust, powerful, and hopelessly evil.\n\n\"And Chang?\"\n\n\"Jawid says he's in thrall to the jinn,\" Eldredge said. \"He's hoping we can learn something that will help us to locate Schweitzer.\"\n\n\"Outstanding. How soon until we send the teams?\"\n\n\"I'm certain Schweitzer and his family are in the George Washington National Forest, sir, but we've got nothing more than that. I already have Blue One, Two, and Six over the target. So far, they've got nothing.\"\n\n\"I thought those were your best direct-action teams.\"\n\n\"They are my best _regular_ teams, sir. Schweitzer has all the capabilities of a Gold Operator and the presence of mind to leverage years of training with the SEALs. That forest is over one point eight million acres.\"\n\n\"So, engage the Gold teams. You can add Chang to one of them. There would be a certain poetic justice to that, don't you think?\"\n\nEldredge's stomach clenched. The Director was all too quick to employ the Gold Operators, but the living dead monsters were ruled by their lust for blood. Any time they were put in the field, there was a risk of a massacre. Eldredge forced a shaking breath before he was calm enough to answer. \"Respectfully, sir, the Gold teams are unpredictable. Every time we use them in public, we run the risk of collateral damage with the potential to compromise this program. I'd rather engage them only when we're sure of the target.\"\n\n\"Get out there with the Blue elements and use your magic knife.\"\n\nEldredge's hand moved to his white coat, feeling the hard outline of the KA-BAR utility knife Jawid had ensorcelled for him. The blade was old and pitted from the sea salt that had scoured it during the Normandy landing when it had bounced along Eldredge's father's hip as the young marine had waded ashore.\n\nEldredge remembered handing it to Jawid when the Sorcerer had first been brought in, still covered in Band-Aids from healing cuts and taking a handful of antibiotics to drive out the parasites that had colonized his gut during years of hard living in the Afghan mountains. _Use this,_ Eldredge had said as Jawid's hand closed around the handle. _Show me what you can do._\n\nThe knife didn't look any different. It was hard to believe that the slim metal blade contained anything as mighty as a jinn, but Jawid had been ensorcelling talismans almost as long as he had been ensorcelling corpses, and Eldredge had seen the proof with his own eyes. _This jinn was mad in life, _Jawid said when he handed the blade back. _Death has not made him sane. He will not abide another soul near him._ Eldredge had kept the blade concealed in his waistband ever since. When one of the Golds had gone feral and leapt for him, he'd managed to rip the blade from its sheath and plunge it into the monster's calf. The thing had gone limp as the jinn inside was banished back into the void.\n\nAnd something else.\n\n_Why was it glowing?_ Eldredge had asked.\n\n_I do not know. Perhaps the jinn inside is angry enough to touch the metal._\n\nEldredge patted the knife, remembering a line from one of his favorite books. _My sword Sting. It glows when enemies are near._\n\nNot orcs but jinn. The closer they came, the brighter it glowed.\n\n\"That knife's effective range is less than two hundred yards, sir,\" Eldredge said. \"Until we have a better fix, I'd just be underfoot. Besides, I'm needed here to look after Jawid.\"\n\n\"How is he doing?\" the Director asked. He sounded bored.\n\n\"He's . . . shaken by Schweitzer's escape, sir. Doctor Empath is having a tough time getting the whole story out, but I've been having his food dosed with sodium amytal, and it's making him open up a bit more. It seems Schweitzer pillaged his memories, learned his wife and son were still alive, which was what predicated his escape. Jawid is . . . fragile. He lacked the strength of character to stand against Schweitzer. The experience left him shaken.\"\n\n\"Empath tells me Jawid is pining for a family.\"\n\n\"That's true, sir. He was apparently betrothed before we rescued him from the Taliban. He has remarked that he desires children.\"\n\n\"Will this be an obstacle?\"\n\n\"I'm not certain, sir. It's definitely a major distraction, even a preoccupation for him. He lacks the . . . patriotic motivations that drive the rest of us. This isn't his country. He's lonely, to be frank.\"\n\n\"Perhaps we can assign him a mate. A roll in the hay might put it to bed. No doubt one of the analysts would be willing to dive on that grenade for the sake of the mission.\"\n\n\"Respectfully, sir, I don't think it's sexual. I mean, that's part of it, but I think what he really wants is to feather a nest. He wants to make a home. You know the tribes in Waziristan, sir. Family is the only thing they hold more sacred than their faith.\" Eldredge thought of his own nights furtively masturbating on his cot, an efficient exercise designed to take the edge off a raw need that he would have surgically removed if he could. A part of him mourned the loss of the life he could have had, the woman he might have married, the children he might have raised. _That ship has sailed. You only have time for one life, and you chose this one._\n\n\"That's not possible,\" the Director's voice was flat. \"Magic has put him beyond that. Jawid must accept that he's not in the world as others are.\"\n\n\"I agree, sir, but that is precisely what he won't accept.\" Eldredge thought of Jawid's fearful eyes, the sad turn of his mouth. He had been a boy captured and abused by religious madmen when the army had found him. The Sorcerer had never had a chance to chart the course of his own life. _I wish there was some way to help you, but magic is like cancer. You don't ask for it, and it changes everything._ Eldredge was silently grateful that he'd been spared magical ability. His life wasn't that much different from Jawid's, but it was self-determined, and that made all the difference.\n\nThe Director was silent for a long time. \"Is he reliable?\" he finally asked.\n\n\"Honestly, sir? I can't say. There's something going on with what Schweitzer did to him that he's not telling us. Doctor Empath is sure of it. I spend a lot of time getting him over crying jags. He may need a vacation. Maybe we can send him somewhere, under guard, without freedom of movement, but some R and R, at least.\"\n\n\"There's no time for that, especially now.\"\n\n\"I know, sir, but if we lose our best asset, we're going to have bigger problems.\"\n\n\"Which is why I'm engaging a backup plan. Jawid isn't this program's best asset. I'm pulling Scorpio Cell's Sorcerer and bringing her here.\"\n\nEldredge managed to keep the surprise out of his voice. \"Understood, sir, and you know I'm grateful for the help. But won't that necessitate closing down Scorpio's operations? That's going to give China a big leg up.\"\n\n\"We'll have to worry about that later. Schweitzer is a loose nuke, which is how it's been presented to the President. He's declared this a Javelin Rain\u2013class incident. All options are on the table.\"\n\nEldredge swallowed. He knew the Director was being literal. The Javelin series of code words was generally used to describe nuclear incidents. The President had been lied to. He'd been told they'd lost a nuclear warhead, and not a magically reanimated, superpowered corpse. The power that lay in that level of secrecy terrified him.\n\n\"Understood, sir. Are you going to tap the reserve?\"\n\n\"You told me you don't have a lot of confidence in that Sorcerer's skill. Has your position changed?\"\n\n\"No, sir. It's just that you said that all options were on the table . . .\"\n\n\"All effective options. We're not desperate yet. Scorpio's Sorcerer is very, very good.\"\n\n\"Yes, sir. I'm excited to meet her.\"\n\n\"She'll be here tomorrow. Pair her up with Jawid and get them to work. I want Schweitzer found yesterday. Every second he's at large jeopardizes not only the safety of this program, but of the entire nation.\"\n\n\"Understood, sir.\"\n\nThe Director's voice took on an edge. \"I've been very lenient with you, Eldredge. I put you in charge of this program and gave you a free hand because I was confident in your ability to get the job done. Don't make me a liar. You blow up whatever you have to. You kill whomever you have to. You steal and lie and break every damn law in the world if that's what it takes to bring Schweitzer down.\n\n\"Destroyed. Not captured, Eldredge. You make sure there's no piece of Schweitzer left bigger than a softball. It's safe to assume that his wife and child are fully aware of our operations here?\"\n\nIt was a rhetorical question. Eldredge's throat went dry as he nodded.\n\n\"Unfortunate,\" the Director's modified voice rasped. \"Make sure you deal with them, too.\"\n\n# CHAPTER V\n\nTOUCHING DOWN\n\nHours passed. Twice, Schweitzer resisted the urge to stalk back to his wife and ask her what was going on. He put thoughts of Steve Chang out of his mind. He avoided pushing back into the emotional link between himself and Sarah. Sarah could feel it on her end too, and he knew what it would tell him anyway. He could hear Patrick murmuring to her, the sizzle of cooking meat, the slow smacking of their chewing. He began to tune his hearing to make out their conversation, then decided he didn't want to, and dialed further down to focus on their beating hearts. The twin pulses reminded him of what was important: they were alive. He had done what he said he would he would do, would continue to do it.\n\nAt last, he turned and slithered on his belly, keeping to the shadows of a low copse of trees that got him close enough to the tiny orange-red flower that was their dying cooking fire. The smell of venison was strong enough to bring predators, but those same noses detected the strange, chemical odor of the glycerol and pungent cocktail of humectants and cell conditioners that kept his dead flesh supple. Schweitzer could hear the padding of tiny feet, the soft rustle of wings far overhead, but the animals always steered clear the moment they drew close enough to smell him.\n\nSarah had kept the fire low and stamped it out the moment she no longer needed it, not drawing any more attention to their position than necessary. At last, Schweitzer's patience wore out. \"Babe,\" he said. \"We have to go.\"\n\nPatrick stiffened, and Sarah bundled their son against her chest, hiding his face in her armpit and stroking his hair. She sighed. \"I know.\"\n\n\"Can you manage now? Can he?\"\n\nShe nodded. \"We'll have to.\"\n\n\"I'm sorry. I'll be more careful with you. I'll try to remember that you're . . .\"\n\n\"Human.\" She looked up, eyes wet. \"And you're not anymore.\"\n\n\"I don't know what I am, baby. I know I still love you and Patrick. I know I'd do anything for you, and that I'll keep you safe no matter what. I know that I would never have stopped looking for you, not for a minute. They tricked me, Sarah.\" He knew she was right, knew he'd have to leave, but he needed to know that she understood before he did.\n\nShe cradled Patrick closer to her, reached out one hand.\n\nSchweitzer crawled from the shadows a little way, reaching toward her. His son squirmed, but Sarah pressed Patrick's face more tightly against her, shushing him. Schweitzer crept quietly toward them, straining until their hands met, fingers clasped. He could feel the warmth of her hand, the steady rhythm of her pulse below the skin. She looked away, and he could see her working to suppress a shudder. She raised his hand to her mouth, kissed it.\n\n\"Oh God, Jim,\" she said. Her tears pattered on his knuckles. \"I miss you.\"\n\n\"I'm still here.\"\n\n\"You smell like formaldehyde. You feel like cold rubber.\"\n\n\"Doesn't change anything.\"\n\n\"I know, baby; it's just going to be . . .\"\n\nThe sound of the birds overhead solidified, thickened. Schweitzer heard a sudden snap as a vast pair of wings unfurled, catching the air and slowing the bird's descent. But the sound was too loud, too sudden, pregnant with the vibrating ring of metal.\n\nNot birds.\n\nSchweitzer seized Sarah's hand and yanked on her arm. She cried out as her shoulder wrenched in its socket, but Schweitzer managed enough leverage to throw her away from him. He rolled into a crouch, but not before he saw a long line of rounds stitch the ground beneath where his wife's arm had just been.\n\nHe craned his neck, caught the faint outlines of angels settling into the canopy, metal-framed wings falling from their backs as they descended. _Gliders. They knew I'd pick up on helo rotors from too far away._ They must have jumped from high altitude and deployed their wings only at the last possible moment to get them as close as they could without alerting him. Gliders meant they had no way to run. They were in the fight to win or die.\n\nThem or him. Them or his family.\n\nSchweitzer launched himself to his feet, claws and horns extending fully, jaw unhinging. \"Run,\" he hissed to Sarah. \"I'll find you.\"\n\n\"And get caught out alone? Not a chance.\" She thrust Patrick against her chest and bent to lift a rock.\n\nThe men began to descend from the canopy, slowly floating toward the ground. Schweitzer narrowed his eyes. He could see no ropes, no means of support. They were kitted out as operators: tactical vests, helmets, modified carbines nestled in the crooks of their arms, sighting in at Schweitzer. The first round cracked, and Schweitzer felt an impact in his cheek as the bullet holed it and whisked out the other side. Schweitzer knew that the shooter was targeting a three-inch triangle over his face. Schweitzer had trained to put his rounds in the same spot for his entire career as a SEAL. It was the fastest way to put a living target down.\n\nBut Schweitzer was no living target.\n\nHe leapt, rocketing across the intervening distance, claws piercing one the enemy's throat before he had time to pull the trigger. His head lolled silently and he went limp, sliding off Schweitzer's claws, sinking slowly to the ground.\n\nThe other men finished their descent, boots touching gently on the forest floor as if they had been set there by an invisible hand. Schweitzer could feel the column of hot air rising up off the ground. He could feel a flow in the midst of the air, a shimmering energy that permeated his veins, resonating with the substance that kept his dead body moving. Magic. This was how the men had floated down from the high trees.\n\n\"Jim!\" a thick Afrikaner accent, one he recognized. A man blazed in the sky, floating eight feet above the ground, wreathed in crackling lightning.\n\nThe split-second distraction was all the floating man needed. He flicked his wrist and the wind rose, vaulting one of the operators over Schweitzer's head toward where Sarah crouched behind him.\n\nSchweitzer leapt straight up, catching the operator's ankle. The operator's leg snapped as Schweitzer swung him over his head. Schweitzer reached out with his other hand, grabbed the man's weapon, and broke it free from the sling with a single twist of his arm, sending his enemy sailing back toward the floating man, crying out in pain as he went. The floating man laughed and rose two feet, and the operator whipped under him and crashed into a tree, fell limp to the ground.\n\n\"The fuck are you doing here?\" Schweitzer grunted. He remembered the floating man now. Raees Gruenen, a South African mercenary who had been contracted to help Schweitzer's team with an op in Botswana a lifetime ago. The Gruenen he knew had never floated. Schweitzer pulled the carbine up into his shoulder. A light on the weapon's upper receiver flashed red and he felt the trigger seize. They'd been developing this tech right when he'd been killed. The weapon wouldn't fire without the operator's wristband close by.\n\n\"Guess I'm just talented,\" Gruenen said. \"Had some wild dreams and woke up in the air. Brave new world, eh?\" He opened a hand and lightning sprang from his palm, plowing into the ground and blowing Schweitzer off his feet. He tumbled through the air, shoulder slamming into his son, popping Patrick free of Sarah's grip. The three of them rolled over and over through the smoldering leaves.\n\n\"Sarah?!\" Schweitzer scrambled to his feet just in time to feel one of the operators' boots brush his head as he leapt over him, borne on the updraft of Gruenen's magic. Schweitzer flailed out a hand, brushing the man's calf. The enemy landed behind Schweitzer and stepped on Patrick's arm, making for the greater threat that was Sarah.\n\nShe roared and rose to meet him. The operator raised his weapon and squeezed off a round before she crashed into him, snarling, wrapping her limbs around him like a spider embracing prey.\n\nGruenen frowned. \"Aim needs work, though.\" He extended his hand again, and Schweitzer threw the useless carbine at him. It spun into the next burst of lightning, the metal sparking and the magazine exploding in a crackle of gunshots. Gruenen rolled in midair, dove low to escape the sudden detonation of rounds.\n\nSchweitzer turned back to his family. Patrick sprawled on his face, bawling. He was red-faced and terrified, but the immediate threat wasn't to him. Sarah held the operator too tightly to throw a punch, and the enemy raised his hand, hooking two fingers over her sternum, yanking down on the cluster of nerves and vulnerable windpipe behind it.\n\nThe pain must have been excruciating, but Sarah was already screaming, leaning forward, fastening her teeth on the man's face. He shrieked as his nose and upper lip shifted, blood squirting over Sarah, misting the ground beneath their feet.\n\nSchweitzer thrust his claws into the man's lower back. The enemy's upper body stiffened, his legs went suddenly limp, and Sarah let him go. He turned toward Schweitzer, his face a twisted red horror, nose and upper lip sloughing away below the semicircular tears left by Sarah's teeth.\n\nSchweitzer let him fall, grabbing his carbine, yanking his wrist up along with it.\n\nSarah spit out meat, blood trickling out of the corner of her mouth, and turned to Gruenen. \"Stay away from my son.\"\n\nGruenen got to one knee. \"You crazy fucking bitch,\" he said, raising a hand. Schweitzer could feel the current of Gruenen's magic coalescing, focusing. The sky above them darkened, and Schweitzer could smell ozone, feel the static charge gathering in the air.\n\n\"That's my wife you're talking to, asshole,\" Schweitzer said, sighting the carbine one-handed, raising the dying operator's wrist to the bottom of the handle. The light on the receiver went green, and Schweitzer fired.\n\nIn life, Schweitzer would never have had the control to aim a carbine one-handed. In death, he was as steady as a rock. A small, dark hole appeared in Gruenen's forehead. His eyes widened, then crossed. Twin trails of black blood leaked out of his nose, and he pitched forward on his face, his current suddenly gone, the forest going deathly silent.\n\nSchweitzer paused, listening. The animal sounds had vanished. Only those insects too small to get away from the fight quickly could be heard, burrowed as deep as they could go into the fallen leaves. Patrick's sniffling reminded Schweitzer that his boy was alive. Whether or not he was hurt was another matter.\n\nHe turned to go to him, stopped himself. The boy didn't need to be scared any more than he already was. \"Sarah, Patrick might be hurt. Can you . . .\"\n\nShe crouched, her face and shirt painted with the operator's blood, eyes still fixed on Gruenen's corpse. \"Was he flying, Jim?\"\n\n\"Yes, baby. He was.\"\n\n\"What the fuck?\"\n\n\"It's magic. Same stuff that is keeping me upright and walking. There are other kinds. I fought a man who could mold his own flesh. They called it Physiomancy.\"\n\n\"How are we supposed to run from these people? How can we fight them?\"\n\nSchweitzer could hear the edge of panic in her voice, forced his own to stay calm. \"Baby. Sarah. Look at me?\"\n\nShe didn't move, but her dark eyes flicked in their sockets, sliding to meet his own. His wife's eyes were slits, focused, locked into fight mode long after the threat had passed. This was hurting her, the kind of hurt that would last.\n\n\"Sarah,\" Schweitzer said. \"You're right. We can't beat them with technology, and we can't beat them with magic. So, we have to beat them with heart. We control the one thing we can control.\"\n\n\"What's that?\"\n\n\"We don't quit. We stay in the fight until they kill us. We don't break and we don't give up. Can you do that?\" He put steel in his voice, willing the words across the intervening distance, praying they stiffened her spine.\n\nSarah only stared at him, eyes still narrowed, as if she wasn't entirely certain whether or not he was a threat. He focused inward, retracted his horns, spines, and claws, heard the slight slurping sound as the tips slid below the skin.\n\n\"Sarah. Can you do that?\" he asked again.\n\nShe nodded.\n\n\"Say it.\"\n\n\"Say what?\" she asked.\n\n\"Say you won't quit.\"\n\n\"I won't quit.\" Robotic repetition. She didn't mean it, not like he needed her to. But it was a start.\n\nHe nodded. \"Okay. Patrick will freak if I pick him up. Will you please see to him?\"\n\nShe turned, took a step. Her leg didn't support her weight and she fell to her knees. Schweitzer reached her in a single stride, followed the scent of fresh blood to her hip. \"Fucker shot me,\" she mumbled.\n\nSchweitzer extended a claw and sliced into her waistband. The dirty fabric broke apart, peeling back from pale skin, slick with sweat and dusted with dirt and bits of leaves. The operator's round had clipped the meat over her hip, parting the skin neatly. Blood sheeted down below, soaking her thigh. Schweitzer could see the soft glint of exposed bone, going jagged where the bullet had tumbled, breaking off a small fragment.\n\nHer head lolled against his shoulder, and Patrick howled for his mother. Schweitzer looked up at his son, saw the boy facedown in a soft tangle of vines. Clusters of arrowhead-shaped leaves covered Patrick's face. He seemed whole enough, but Schweitzer knew that plant, knew that even now the oil covering it was working its way into his son's skin. Patrick would be an itching, screaming mess by nightfall.\n\nAnd they couldn't afford screaming. Because the Gemini Cell wouldn't have just sent Gruenen and a single fire team. They were a recon force, spotters deployed to locate Schweitzer and his family. And that meant the main thrust of the search couldn't be far behind.\n\nThey didn't have much time.\n\nSchweitzer took one more look at Sarah's wound and raced to Gruenen's corpse. \"Baby?\" He called to her as he rolled the body over onto its back, began checking the pouches in the tactical vest. \"Baby? Remember what you said. Don't give up, Sarah. Don't quit.\"\n\nBut Sarah didn't answer, her pale face settling in the crook of her arm, her mouth opening, her eyes shut against the gathering gloom.\n\n# CHAPTER VI\n\nMAMA DADOU\n\nJawid straightened, the stiffness in his back reminding him of his devotion. It was one of a series of small sacrifices that made his daily prayers cathartic. He raised his hands, softly whispering, _Allahu Akbar. Allah listens and responds to the one who praises Him._\n\n_Dear Allah, be with me. Help me to find Schweitzer. Protect me from Eldredge. Turn his anger from me. I will be patient. Bring me forth from here and send me home, where I can have a wife and children of my own, that I may spend the last of my days praising You and living as You intended._\n\nHe bent to roll his prayer rug, stowing it in the corner of his cell, the one flash of color in the otherwise bare expanse of white and stainless steel. It had seemed the height of luxury when he had first arrived, after years of sleeping out in the open on rock, root, and frozen mud. The hot showers, electricity, and endless food seemed the stuff of paradise. Now, just a few years later, Jawid saw it for what it was: the thing the _Talebs_ had warned against, a prison of comfort that was designed to keep him locked away from Allah's plan for mankind. He had no wife, no children, struggled against an enemy not his own, for ends that were valued only by the infidels. The sinking feeling that his life had gone wrong had solidified into a curdled horror, equaled only by the certainty that the Gemini Cell would kill him the moment they suspected he had real plans to leave.\n\nThe Qur'an counseled that there was no greater blessing than patience. He would watch; he would wait. He would find a way.\n\nUntil then, he had work to do.\n\nHe keyed in the code that slid open the door, no less a cell for the fact that he could leave it. He stepped out into the plain white corridor outside the ops center. They blindfolded him for the trips aboveground, so he had no idea how deep the complex went, but he imagined he could feel the great weight of the earth above him, the sun huge and bright over the false office complex that guarded the entrance.\n\nHe entered the elevator, waited through the silent descent, the flickering of digital numbers the only indicator that he'd moved at all. There were no signs in the facility. An interloper would be unable to find anything, but Jawid knew the way from memory. He made two sharp rights and found himself in a corridor that narrowed until only a single man could walk along it. Three-foot-thick seams appeared at regular intervals as he proceeded, home to massive metal barriers that could instantly seal it off.\n\nJawid struggled against claustrophobia, making his way toward the door at the far end. It was much thicker than the one to his room, the transparent palladium panel giving a distorted fishbowl view of the plain white interior.\n\nChang's corpse stood motionless in the middle of the room, back to the door. A Gold Operator had killed Chang with its claws, extending them up until they pierced his heart, leaving long rents in his side that extended halfway around his back. They were stitched shut now, crude purple-gray scars over raised welts an inch high. Chang's back was tattooed with angel wings, cresting his shoulder blades above a blotched scrawl that read ONLY GOD CAN JUDGE ME.\n\nJawid could feel the eddying current of magic pouring off the corpse, knew that for all his stillness, Partolan was hard at work within the dead vessel, warring with Chang's soul. Jawid pitied Chang. His own life was a twisting purgatory, an enslavement to the agenda of unbelievers. But even that was far, far better than an eternity of unlife chained to the side of a jinn leapt from the breast of the _Shaytan_ himself. The jinn were infinitely cunning, infinitely strong, infinitely evil. How Schweitzer had managed to best one was beyond him. He tried not to think about it. Because, if Schweitzer's soul was so honored by Allah, then what did that say about Jawid and what he had done? What he was still doing?\n\nChang-Partolan stood completely still. Jawid summoned his current, sent it rippling through the door, feeling it mingle with the eddying tide that whirled around the standing corpse. Jawid focused his magic, opened a channel, and spoke to the jinn and Chang at once. _Good morning, I have come to . . ._\n\nA surge of animal lust came pouring up the channel he had opened between them. Jawid felt his knees go weak. He stumbled a step back down the corridor, terror competing with his instinct to sever the link and roll his magic back. He regained control of his body just before the tipping point, saving himself from a nasty tumble to the hard, concrete floor. The red wave that had assaulted his senses had been pure, uncontaminated by the smallest trace of humanity. He hadn't felt Chang at all.\n\nHis vision came back into focus, his hearing registering a rhythmic pounding in time with the vibrating of the cell door. Tiny cracks were appearing in the surface of the palladium panel, white spider webs of breaks in the transparent metal extending with each successive blow.\n\nJawid could see Chang's corpse hammering itself against the barrier, desperately scrabbling to get at him. Bone claws emerged from the shredded stumps of its hands, fingers hanging rent and useless like the sepal leaves of some bladed flower.\n\nThe thing's eyes burned pure gold.\n\nJawid did fall now, panic stealing what little strength remained, sitting down hard on his bony backside, the pain of the impact not even registering in his shock.\n\nPartolan had pushed Chang back out into the void. There would be no insight into Schweitzer. There would be no repeat of Schweitzer's strange success, no new Operator with silver in his eyes who was something more than an animal. Jawid had failed again.\n\nAnd in the Gemini Cell, the price of failure was high.\n\nPartolan threw Chang's disfigured corpse against the door. The thick metal shuddered, squealed, and held. For now.\n\nBut that didn't mean it would hold forever. Jawid walked backward on his hands until he could get his feet under him, then jumped up, thumbing his commlink. \"I'm in access corridor three. My subject has gone gold. I need a lockdown.\"\n\nHe was already turning, running back the way he had come. He fought against the instinct to keep his eyes on the threat. It didn't make a difference; facing Partolan or running from him, he was just as dead.\n\nEldredge's voice sounded in his ear. \"Calm the hell down; stay where you are. We're right around the corner. We'll be right there.\"\n\nJawid knew that Eldredge wanted him to stay where he was, but the panic gripped him, and he felt that his heart would stop unless he moved his legs. The cell door shuddered behind him, and he could hear a faint whining, the mewling of a predator overwhelmed with desire by the nearness of its quarry.\n\nHe ran, the motion of his body burning off a tiny fraction of the terror, both of what lay behind him and what lay ahead.\n\nHe reached the end of the corridor, his sandaled feet slapping against the concrete, and slid out into the junction as he turned the corner toward the elevator.\n\nHe rebounded off of something soft but firm, staggered backward, his nose suddenly filled with the pleasant odor of clean sweat, soap, and a woody, dry smell that reminded him of roots stretching below the earth.\n\nEldredge's hands were thrust into the pockets of his long white coat, his shock of hair spraying in every direction at once. Jawid had never once seen the man with his hair combed.\n\nThe pleasant smell came from the woman standing beside him. She was at least four inches taller than Jawid, made more towering by the pile of dreadlocked hair atop her head, bound in leather thongs twined with beads and tiny shells. Her body was lean as a whip and so strong, Jawid could see the striations of her muscles sliding beneath her dark skin. She wore a tactical vest and cargo pants bloused into combat boots. A pistol nestled in a paddle holster tucked against one lean thigh. Her eyes were dark and crinkled with amusement, her full lips ghosting a smile.\n\nJawid's eyes swept across her powerful shoulders, graceful collarbones, lean neck. The analysts in the Gemini Cell never bared themselves so. The sight of her naked shoulders mesmerized him. Her eyes were hard, pitiless, but no less entrancing for all that.\n\n\"Whoa, there!\" She laughed, putting out a hand. \"Who's this?\"\n\n\"This,\" Eldredge sighed, \"is our Sorcerer, Jawid Rahimi, who cannot seem to follow simple instructions, I'm sad to say.\"\n\nJawid started. The magical current from Partolan had died off, only to be replaced with a new one, every bit as powerful, but darker, deeper, the edges of it mixing and probing at his own.\n\nIt came from the woman.\n\n\"Easy, now,\" the woman said. \"What's got you running like a chicken?\" Her accent was deep and drawling. Jawid could not place it.\n\n\"Jawid,\" Eldredge said, \"this is Dadou Alva.\"\n\nJawid's jaw dropped; he shut it forcibly, eliciting another laugh from Dadou before he could form words. \"She is . . . like me.\" The thought transfixed him as he studied the feel of her magical tide, the monster battering down the door behind him all but forgotten. Jawid knew there were other Sorcerers in the world, but always they were enemies, targets of the program he had helped to build. He had never known of another working for the American government.\n\nEldredge nodded as if this were obvious, as common as the grass. \"We pulled her from Scorpio Cell to assist you here.\"\n\n_\"Achante,\"_ Dadou said, extending a hand.\n\nThe thought of touching a woman who was not a relative both terrified and thrilled him, and Jawid felt the lust surging in his hips and belly, stiffening him beneath his robes. Dadou waited, her smile fading.\n\n_God forgive me,_ Jawid thought, then reached out and took her hand. Her skin was dry and calloused, and her grip strong enough to make him wince.\n\n\"Looks like our timing couldn't be better,\" Eldredge said. \"Can you tell me what the hell is going on?\"\n\nJawid tore his gaze away from Dadou, breathed deeply. \"Chang is gone. The jinn has the body.\"\n\nEldredge cursed and Dadou's smile vanished. \"You're certain?\" Eldredge asked.\n\nJawid nodded. \"I saw his eyes.\"\n\n\"Show me,\" she said.\n\nJawid froze. \"I . . . I don't know if the door will hold . . .\"\n\nEldredge cursed again. \"Then we don't have time to stand here discussing it, do we? Go!\"\n\nThe command jarred Jawid into motion, and his sandals slapped the concrete back the way he came, the soft padding of Dadou and Eldredge's feet coming behind him. The door still trembled in its frame, Chang's dead face pressed against the cracking pane of palladium, Partolan dancing behind the gold flames of his eyes.\n\nEldredge stared for a moment before cursing a third time. \"Seal access corridor to prime subject,\" he said into his commlink. \"Barrier one. Prime for freeze.\"\n\n\"Barrier one, section one is primed\" came the response, buzzing in Dr. Eldredge's commlink loud enough to be heard.\n\n\"Do it.\" Eldredge said.\n\nLiquid nitrogen burst from the nozzles in the walls as the thick steel partition slid out of its home in the ceiling, dropping to close off the cell and its rapidly failing door. Partolan let out a savage howl, echoing down the tight space before the barrier slid home, the seal so tight that it cut off all sound behind it. The flow of magic around the jinn dampened from the interference, but Jawid could still feel it whispering through the thickness of the metal.\n\nHe turned to Eldredge. The old man's eyes were hard as flint.\n\nJawid struggled, blinked, looked at the floor. But the terror had him now, and he knew he could not stop the tears from coming. He had failed. His elation at discovering that there were other Sorcerers like him working for the government was eclipsed by the realization that she was there to replace him.\n\nSchweitzer had escaped on his watch, and now, at long last, Eldredge had lost confidence. Jawid couldn't get the job done, so Eldredge had brought in someone who could.\n\nThis was the Gemini Cell. Jawid wouldn't be fired. They wouldn't simply let him go.\n\n\"Please.\" Jawid was disgusted by his own voice. His legs trembled and he sank to his knees. \"I'm sorry. I did what I could. I thought Partolan understood he had to keep him. I'm sorry. I will find a way to fix this. Please don't . . . don't . . .\"\n\nDadou frowned down at him, disgust flashing across her face in time with Eldredge's deepening scowl.\n\n\"Get up,\" Eldredge said. \"Stop being so dramatic.\"\n\n\"Please.\" Jawid reached for Eldredge's legs. \"I beg you . . .\"\n\nEldredge jerked away. \"That's enough!\"\n\nEldredge's hand disappeared inside his coat. _He's got a gun; he's going to shoot me._\n\nJawid briefly considered fighting, dismissed it. He was no warrior, as the _Talebs_ had told him so many times. He had made a mockery of so many things. He would make a mockery of this as well. Instead, he closed his eyes and turned his mind to Allah, to reflect on Him in his final moments. It would hurt, but not for long, then paradise would be his.\n\n_Allah, the merciful and compassionate. You know I am a coward and a weakling, but I hope You will judge me gently._\n\nA stirring of the air above his head, a hand descending. Jawid tensed for the blow, for the bullet to tear through him.\n\nInstead, there was the dry smell of roots below the earth. A hand settled on the back of his neck, warm, callused. It massaged the knotted muscles there, spreading warmth through his shoulders.\n\n\"It's okay,\" Dadou said. \"It's okay. Everything is going be all right, dahling.\" Her voice was like warm milk.\n\n\"I'm sorry,\" Jawid said.\n\n\"I know, dahling,\" Dadou said. \"But it's going to be okay. Mama Dadou is here to help.\"\n\nJawid still couldn't bring himself to open his eyes, though the softness of Dadou's voice made the fear begin to subside. \"You're going to replace me. You're the new Sorcerer.\"\n\n_\"Pas enkie twa, mon chouchou,\"_ Dadou said, the lilting of her voice approaching a song. _\"Men anpil, chay pa lou.\"_\n\nAnd Jawid did open his eyes now, her face filling his vision. Her skin was wrinkled about the eyes, her mouth lined, and deep creases walking from the corners of her mouth to the edge of her nose. She had seen hard use, this woman. She had known trials. He could not take his eyes from her.\n\n\"I don't understand,\" he whispered.\n\nShe smiled, and the world went warm around him. \"It means don't be ridiculous, dahling,\" she drawled. \"Together, you and I are going to do great things.\"\n\n# CHAPTER VII\n\nPATCHING UP\n\n\"Stay with me,\" Schweitzer said. He paused long enough to hear Sarah's response, a slurred murmur that couldn't be called a word.\n\nGruenen stared sightlessly up at the sky, the look of surprise frozen on his face. The bullet hole in his forehead was dime-sized, but the back of his head was completely missing, the shattered eggshell remains testifying to the bullet's force. Schweitzer dug through the pouches in Gruenen's tactical vest. He didn't have to look; his hands knew each item as soon as they touched them, could almost guess where they'd be located. There was the pistol in its chest holster, three loaded magazines tucked just below. There was the knife snapped in behind it, just outside the body armor's intercept plate. He made a mental note to check the handle later. His own had been hollow and packed with supplies. Down over Gruenen's gut he found water-cleaning tablets, a headlamp. Not what he needed. Not now, anyway. _Come on, come on, damn it._\n\nPatrick had gotten to his hands and knees, crawled to his mother's side.\n\n\"Don't touch her!\" Schweitzer yelled.\n\nPatrick shrieked, but he obeyed.\n\nThe sound tore at Schweitzer, but he couldn't afford to have Sarah getting poison ivy on top of her wound. He only knew what little casualty care was necessary to stabilize a patient until medevac could dust them off. But there was no helo coming here. It was on him. Being yelled at was the least of what his son had suffered over the past few days.\n\nHe abandoned the vest, moving to the drop pouch strapped to Gruenen's thigh. He dug past a smartphone and a small wad of papers before his fingers closed on what he sought. \"Sarah! You're going to be okay!\"\n\nIt was a bulging ziplock refrigerator bag. He'd carried one just like it for his entire career; every SEAL did. He cursed himself for not remembering where he'd kept it, losing precious seconds in the search. Schweitzer popped it open, turned it over as he raced back to Sarah's side.\n\nTourniquet, alcohol pads, roll after roll of sterile gauze.\n\nAnd the dark-green vacuum-sealed packet that he would know by touch alone. HEMOSTATIC AGENT was stenciled across the front. CAUTION: WILL CAUSE EXTREME BURNS.\n\nSchweitzer rolled Sarah onto her side and ripped the remainder of her bloody jeans away from the wound, trying to ignore the exposed striations of muscle, the steadily flowing blood. He tore open one of the alcohol pads, wiping his hands as clean as he could before putting on the thin rubber gloves. He then turned to the wound, rinsing it with the alcohol, trying to scrub away as much of the dirt, sweat, and burned residue as possible. There was no sign of the round, and he was sure the bullet had torn straight through. That was good. He wasn't equipped for surgery out here.\n\nSarah groaned. \"Ow. Fucking ow,\" she said weakly.\n\n\"This is just foreplay,\" Schweitzer said. \"Hard part comes next.\"\n\nShe looked up at him, eyes focused. \"Bring it.\"\n\nHe smiled as much as the skin stretched over the metal armature of his jaw would allow. \"That's my girl. Here we go.\"\n\nHe fished the black plastic bite stick out of the trauma kit and pressed it to her lips. She accepted it between her teeth and met Schweitzer's eyes, held them.\n\nSchweitzer felt Patrick's hand against his hip, glanced down to see his son, one hand on him, the other on his mother's boot. Schweitzer felt a surge of emotion at the sight of his boy voluntarily touching him, fought it down. _Keep the bubble. Focus._\n\n\"Lock it up, lock it on,\" he said to Sarah, then tore open the package of the agent and dumped it into the wound.\n\nThe yellow powder began to sizzle the instant it came into contact with Sarah's blood, turning a deep red-orange as it sank in, sending up thin puffs of ochre smoke that stank of chemicals and cooked meat. Schweitzer thrust his fingers into the mass, pressing the powder deeper in, pinching the edges of Sarah's flapped flesh closer together. He wasn't careful about where he put his hands, and he could feel the heat of the agent burning through the gloves, scalding the fingertips beneath. That was fine. He wasn't going to need to be fingerprinted anytime soon.\n\n\"Going to fuck up my manicure,\" Schweitzer said, as Sarah's hand snaked out and gripped the back of his neck, pulling him down until their foreheads touched.\n\nHer face had gone the color of rotten fish, her eyes burning. Her forehead was sweating so intensely that it ran down her temples. Her teeth ground against the bite stick audibly.\n\nBut she did not scream.\n\n\"You are a machine, you know that?\" Schweitzer asked her as the first wave of agony subsided and Sarah relaxed a fraction, gulping air.\n\n\"I don't know why you hate me so much,\" she said, spitting out the bite stick. \"I bore you a child, for Chrissake.\"\n\n\"Guy can't come back from the dead and be hunted by the government in peace,\" Schweitzer said, rocking back to examine his handiwork. \"It's always nag, nag, nag.\"\n\nThe wound sizzled, but there was no visible blood flow, and the edges seemed elastic enough to withstand some movement. It would dry over time, and that meant it would crack. There was also no way to tell if she wasn't bleeding internally. Sarah's life could be pouring out below the surface of her skin, and neither of them would know until she collapsed. She needed medical attention, and she needed it soon.\n\nHe would worry about that later. First, he had to see to the boy.\n\n\"Don't move,\" he said, turned to Patrick.\n\n\"No! No!\" his son said. \"Mommy! Want mommy!\"\n\n\"Shh, now,\" Schweitzer said, pulling the boy closer as gently as he could. \"Mommy's going to be okay. I have to fix you now.\"\n\nPatrick whined and called softly for his mother, but he submitted as Schweitzer tore open more alcohol pads, wiping down his face and hands, anywhere the exposed skin had touched the poison ivy.\n\nAt last Schweitzer released him, sitting back, letting his augmented vision dial down into the infrared spectrum. Red blotches covered Patrick's face, arms, and hands, the heat blazing out to Schweitzer's magically powered eyes as the skin below the surface became inflamed by the plant's oil.\n\nHe'd missed the window. Patrick was going to be in a bad way very soon.\n\nSarah was sitting up, gently touching the edge of the wound, hissing.\n\n\"Knock it off,\" Schweitzer called to her. \"You'll infect it.\"\n\n\"It's going to get infected either way,\" she said. \"We need something to keep it clean.\"\n\nSchweitzer pointed to the corpses of the operators. \"They'll each have trauma kits. Should be enough alcohol and sterile pads to handle that for a while. Anyway, we've got another problem. Patrick rolled in poison ivy.\"\n\nSarah winced. \"Maybe he's immune. Not everybody gets it.\"\n\n\"He's got it,\" Schweitzer said, \"and bad. He's going to be a mess very soon.\"\n\n\"Is there anything in the trauma . . .\"\n\nSchweitzer shook his head before she'd finished speaking. \"I must have packed a hundred of those things in my life. It's for handling gunshot wounds, not stuff like this. We need calamine, hydrocortisone, and some cold packs.\"\n\n\"Maybe he can ride it out.\"\n\n\"Do you think he'll ride it out?\"\n\nSarah cursed. \"No. He'll scream his head off. What's the worst-case scenario?\"\n\n\"For poison ivy in a kid? Anaphylactic shock. We can't have that, Sarah. We've got to fix this.\"\n\n\"We need a drugstore.\"\n\nSchweitzer nodded. \"There's one in every small town. I'll break in at night and get us what we need. Might be I can steal some antibiotics for you, too.\"\n\nSarah rolled onto her knees, and he raced to her side. \"Baby, you have to . . .\"\n\n\"Stop,\" she said. \"Get your head on straight. You want to risk breaking into an alarmed store in the middle of the night like some petty thief? You think that's going to make us safer?\"\n\nShe slowly got to her feet, wincing. Schweitzer winced with her, reaching out to support her elbow, backing off at a look from her. \"I'm fine,\" she said. \"I can stand.\n\n\"Jim, that team was coming for _you_. We have to split up. You have to go after them, and you have to do it now.\"\n\nSchweitzer swallowed the grief and rage, let it pass down into his spiritual gut to churn there. The SEAL was in charge again; he was focused. \"Okay. Just let me get you to a town and make sure that you have what you need. Then we'll come up with a plan.\"\n\n\"Jim . . . Please don't think this is easy for me. I just . . .\"\n\nHe raised a hand. \"Sarah, I'm with you on this. I just want to make sure there isn't another team inbound that might catch you out in the open. Once I'm certain we've got some breathing room, I'll leave. I swear I will.\"\n\nThe grief churned in him, rose up through his spine so that he felt it in the back of his throat. He knew it was riding the link to Sarah, that she could feel it too.\n\n\"I love you, Jim\" was all she said.\n\n\"I know you do,\" he said. \"It doesn't change anything. Let's get this done.\"\n\nShe looked down at herself. \"I'm a mess. I look like I've been through a battle.\"\n\nSchweitzer cocked an eyebrow. \"You have been through a battle.\"\n\nShe quirked a smile, the tiny motion a gut-punch reminder of how it felt to have things normal between them. \"Can you find me a river? I'll wash up.\" She pointed to Gruenen's corpse. \"Those are plain khaki cargo pants. No camouflage pattern. They're clean enough.\"\n\n\"Those are tactical pants. They're made for operators.\"\n\n\"You're telling me hikers never buy and wear that stuff?\"\n\nSchweitzer paused. She was right.\n\nShe looked down at her shirt and pullover. They were dirty, but not beyond salvage. \"We can wash these. If anyone asks, I can say we were camping.\"\n\n\"This is risky.\"\n\nPatrick ran to her, and she stripped off her pullover, bundling him in the cloth before picking him up, keeping the inflamed skin well covered. \"What's more likely to raise the alarm: a hiker wandering into town out of the woods and buying some common first aid supplies, or a break-in in the dead of night?\"\n\nShe had always been smarter than him. The elite reputation of the SEALs was a legend that even the SEALs themselves bought into after a while. There were precious few people who could pop that bubble, remind Schweitzer of his own limitations. Sarah was one.\n\nAnd in the face of her logic, he found himself telling the truth. \"If I lost you, I don't know what I'd do.\"\n\nShe smiled sadly at that, touched his hand. \"You're not going to lose me, Jim. Not if you leave the thinking to me, anyway. Now help me get these assholes stripped, and then let's get me cleaned up.\"\n\nSchweitzer was glad to get to the business of salvaging everything they could from the corpses. They took two of the carbines and their matching wristbands, Schweitzer equipping himself with every spare piece of medical equipment and ammunition he could fit on his body, carrying the load of three men. He put on gear more out of habit than need, and was surprised at the comfort of the tactical vest and thigh-strapped go-bag's familiar weight. Sarah rigged herself out as best she could, slinging the carbine like a pro, or at least a gifted amateur. Schweitzer silently thanked himself for the hundredth time for all the time he had spent forcing her to go to the range.\n\nThey left the corpses for the coyotes. As they picked their way through the woods back to the river where Schweitzer had killed the deer, he could hear the beetles already starting.\n\n\"Feels wrong.\" Schweitzer jerked his head in the direction of the bodies.\n\nSarah gestured to the black, clotted furrow in her hip. \"So does this.\"\n\nAt the river bend, Sarah stripped and waded fearlessly into the freezing water, Patrick propped on her hip. Schweitzer didn't even bother chastising her about catching his son's poison ivy, and instead crouched, alert for threats, watching the water sluice down Sarah's body.\n\nIt glittered on her pale skin, standing up in gooseflesh, making the colored surface of her tattooed arms ripple. Her hair slicked back behind her ears, sending the water running down the graceful curve of her spine. She set Patrick down on the bank and bent to scrub at her shirt and pullover, caught Schweitzer looking.\n\n\"What?\"\n\n\"You're beautiful,\" he rasped, suddenly aware of the distance between them. Sarah, still a young woman. Still beautiful and fertile, her body ready to carry the second child they'd started talking about before he'd been killed. He looked down between his knees, unable to meet her eyes, closing his own to avoid seeing the useless gray piece of meat that had once been his penis, nestled between the mass of hideous scar tissue and clumsy surgical stitching that was the body around it.\n\n\"I'm sorry,\" he mumbled before he had a chance to stop himself.\n\nSarah didn't answer, finishing in silence and lifting Patrick back onto her hip after she'd dressed. Her wet clothing wound up draped over Schweitzer's broad back as they travelled on, spread out and drying. The silence stayed with them for a long time. Schweitzer desperately wanted to bridge it, but there was simply nothing to say.\n\n\"So,\" Sarah said eventually, \"drugstore.\"\n\n\"I'll find a road.\" He paused, dialing his hearing out as far as he could, grateful for something else to think about. At first there was nothing but the trickle of the water, the soft scrabbling of squirrel claws as they raced through the trees. And finally, somewhere in the distance, so faint he could barely make it out, the low droning of a motorcycle engine, a Big Twin like the one he'd stolen to make his way back to Sarah. That meant roads, civilization.\n\n\"That way.\" He pointed.\n\nHis wife nodded and they pushed on, Patrick beginning to fidget, pawing at his face, sniffling as his skin turned red under the constant attention.\n\n# CHAPTER VIII\n\nWHAT IT'S LIKE\n\nThe door chime roused Jawid from his prayers.\n\nHe sat in the same position he used for his formal prayers, his left leg folded in so tightly that his thigh touched the ground. The cramped posture sent pins and needles through his hips, but he savored the sensation as a reminder of his devotion to God.\n\nHe stumbled to his feet, so surprised he forgot to answer, staring until whoever was outside lost patience and the door opened.\n\nDadou stood in the doorway, her eyes crinkled into a smile. She'd traded the tactical gear for a pair of slim-fitting jeans and a tank top that bared the slopes of her breasts and the strong muscles of her arms and shoulders. Jawid could count on one hand the number of times he'd seen a woman so revealed, and each time, he'd spent at least a week begging God's forgiveness for his sin. But standing here before Dadou, he found his mind far from repentance.\n\n_\"Bon apre-midi, chouchou,\"_ she said. _\"Ki jan ou ye?\"_\n\n\"I was praying,\" Jawid said, feigning irritation he did not feel.\n\nThe smile left Dadou's eyes. \"Yes. Eldredge told me you were a godly type. They don't listen, you know.\"\n\n\"God always listens.\" Jawid forced himself to relax. \"Whenever I am not working, I am here, praying.\"\n\nDadou entered without asking, surveyed the bare surroundings. \"And just think of everything you could be doing with that time, _non_? If you weren't spending it talking to something that isn't there.\"\n\n\"You think you're smart, but God will judge you.\"\n\n\"He has already judged me,\" Dadou laughed. \"God and I have been at odds for a long time now. As you can see\"\u2014she gestured to her own hard body, her clean clothes\u2014\"Mama Dadou isn't doing so bad.\"\n\nShe sat down beside him on the bed, her shoulder brushing his. Jawid felt the heat of her through the thin fabric of his robes.\n\n\"When I first learned that magic was real,\" Jawid said, \"I was not surprised. It was but one more example of the many ways in which God shows He can do anything.\"\n\n\"Or _Shaytan_ ,\" Dadou answered.\n\nJawid started at her use of the Arabic word for the devil. \"How do you know that word?\"\n\n\"Poor does not mean stupid, my friend,\" Dadou smiled. \"I've always been amazed at how godly men like you always assume the good things in the world are God's doing, when you have no evidence that it isn't the devil behind them.\"\n\nA sick ball formed in Jawid's stomach. The truth was that consorting with jinn was specifically forbidden in Islam, but Jawid wasn't sure that the things from the soul storm were truly the jinn described in the Qur'an. But there was no one to discuss it with. If there were other Muslims here, Eldredge had not introduced them to Jawid. The so-called chaplain wore a cross on his collar and spoke always of Jesus, and the doctor who Jawid was forced to constantly speak to only smiled silently when he spoke of his faith. There was no imam to advise him, no qaadi to judge him.\n\nJawid breathed deeply, letting his pride and anger go out on his breath, trying to expel the lust that rose in him at Dadou's nearness. \"Sometimes, I think this is my punishment, that I am trapped here for my sins.\"\n\nDadou nudged him with her shoulder. \"Back in Haiti, they raised us to be afraid of being women, to hide when we bled, to never want a man. They called those things sins, and I spent a lot of time hating myself for them. But you reach a point where you go over the edge, _non_? Might as well enjoy yourself. Plenty of time to repent while you're burning in hell.\"\n\n\"I am not going to hell,\" Jawid answered, but he wasn't so sure.\n\n\"No,\" Dadou breathed. \"I don't think you are.\"\n\n\"Magic is proof of God, but in the end you all continue to worship your science. You just assume there is an explanation, that if you just look hard enough, you will find it.\"\n\nHeat came into Dadou's voice. \"'You all'? I use magic, same as you.\"\n\n\"Yet you refuse to believe in God.\"\n\n\"I never said that I don't believe, _chouchou_ ,\" Dadou said. \"I believe with every bit as much passion as you. God exists, and He's a bastard, a mean little boy who pulls the legs off spiders.\"\n\nJawid knew he should grab her by her arm and throw her out. She was only a woman, after all. But he looked at the hard muscle of her arms and realized that throwing her out would not be so easy. And the truth was that he wanted the warmth of her shoulder touching his much more than he wanted her out of his cell.\n\nDadou placed her hand on his knee, just high enough to send shivering sparks up his leg. \"Let's not fight. I came here to help you.\"\n\nHe couldn't answer, unable to control his breathing, to tear his eyes from her hand.\n\n\"You're not the only one who's alone,\" she said. \"I have never met another person who can do what I do. Actually, that's not true. There was one, but I killed him.\"\n\nThe words broke the spell woven by her hand on his knee. Back home, no one could reach adulthood without seeing killing in abundance. Most of the men he had known were killers, but never the women. \"You've killed?\"\n\nDadou's face went serious. \"With my own hands, _chouchou_.\"\n\nThe dread certainty that she was telling the truth overwhelmed him.\n\nJawid blinked. It was strange, but the fear her words inspired only made him want her more.\n\n\"So, tell me what it's like for you?\" Dadou asked, as if they had just been talking of the weather.\n\n\"I have never killed.\" Jawid said. _That's not true. You've never killed with your own hands, but to say you haven't killed at all is a lie._ Another sin piled on the growing mountain.\n\nDadou laughed. \"Not that, _moun komik_! I meant what is it like for you to use the _vodou_?\"\n\n\"You mean the magic.\"\n\nShe nodded. \"I see a storm. All the people who ever lived and died are tangled in it.\"\n\n\"I see the same thing,\" Jawid answered. \"They are screaming. It is awful.\"\n\n\"It is hell,\" Dadou said, tears forming in the corners of her eyes. \"Do you have any idea how long I have been waiting to hear someone else say that they saw it too? That I am not crazy?\"\n\n\"Of course you're not crazy. Do you think the American government would deal with you if you were?\"\n\n\"The American government has a long history of doing very stupid things.\"\n\n\"In this, they are not stupid.\"\n\n\"I know that, but it is not the same thing as hearing it from someone else.\"\n\nJawid's heart swelled at the thought that he was helping her, that he was finally talking to someone who understood what magic did. \"I see bodies, but also through bodies. It is chaos. It is impossible to see where one ends and the next begins.\"\n\nDadou was nodding, tears tracking down her face. \"That's exactly right.\"\n\n\"It is terrible,\" Jawid said, \"and I fear that some day it is where I will wind up.\"\n\n\"And yet you still believe in God.\"\n\n\"I do, and I pray He will save me from it. He is the only one who can.\"\n\nDadou shook her head, cuffing the tears away with the back of her wrist. \"Then I will pray the same. _M'espere bondye rete av\u00e8k ou e gade ou._ \"\n\n\"This is what helps me think that maybe what we do isn't evil. Maybe this is God's plan, to have us reach out and pluck the souls of the worthy from hell, give them a second chance.\"\n\n\"Eldredge tells me you call them 'jinn.'\"\n\nJawid nodded.\n\n\"I call them _mist\u00e8_ , and I do not think for a second that they are worthy.\"\n\nJawid looked at his lap She was right, of course. The jinn were unspeakably evil.\n\nSave one. Save Schweitzer.\n\nDadou's voice was flat. \"Have you met a single one of them that was not a monster?\"\n\n\"No,\" Jawid lied.\n\n\"Make no mistake,\" Dadou said. \"What we do is not benediction for the deserving. We summon devils, and we put them to use.\"\n\n\"Yes.\" Jawid nodded. \"But without it, what would I be? A slave to stronger men. This has given me my life.\"\n\nDadou nodded. \"It is the same for me. I would be groveling in the gutter in Port-au-Prince if not for the Americans. I owe for that, and so do you.\"\n\n\"But . . . how much? When is the debt paid? And what comes after?\"\n\nDadou tilted her head, looked into his eyes. \"If you could have any after you wanted, what would you choose?\"\n\nJawid started to answer, looked down at his lap. Who was she? A stranger. \"It is . . . easy to talk to you.\"\n\nDadou laughed, touched his shoulder. \"Of course it is, _chouchou_. We are the same, you and I. You know what our magic controls?\"\n\n\"Devils.\"\n\n\"Communication. It is a way of talking. Have you ever tried it with a living person?\"\n\nJawid shook his head. \"It's impossible. Life is . . . too loud.\"\n\nDadou smiled. \" _Se sa_ , but see you said 'loud'? It's a sound to you. Summoning is really communication. And that is why you like talking with me. Because, deep down, our magic is already doing that.\"\n\nJawid smiled. \"That's . . . crazy.\"\n\n\"Is it any crazier than a man sitting in the sky and telling you to get on your knees five times a day?\"\n\nAgain, Jawid knew he should be angry, but it was so good to talk to someone. Not a doctor, not a superior, not even an American. Someone like him. The silence stretched and he realized he was staring at her.\n\nShe didn't seem to mind. \"So, if you could have any after, what would it be?\"\n\n\"A wife. A family. Isn't that what people do?\"\n\nDadou's face went hard for a moment, her eyes narrowed, the muscles on her neck tightening just a fraction. He sat up. \"I'm sorry; I've made you angry.\"\n\nBut as she turned back to him, her smile returned, only sad now, her eyes wide and mournful. \"No, _chouchou_. Don't be silly.\"\n\nRelief warmed his belly. Of course he was mistaken. \"You looked unhappy.\"\n\n\"I was only thinking that I had never let myself hope for such a thing. Our lives have been like the storm where the dead live. We are twirling this way and that. One day, we live in the mud and then we have the _vodou_ , and suddenly we are killers in another country. Who thinks of family then?\"\n\n_I do,_ Jawid thought, but he could not speak, because he felt like his stomach had shrunk into a tiny ball at the thought that this woman, this beautiful woman, might feel the same way. Was this magic too? Perhaps they really were communicating without words, like Dadou said.\n\nShe sighed. \"But this is misty-eyed talk. We are neither of us ready for an after. We must focus on the now.\"\n\nHer words were a bucket of cold water down his back. The warmth in his belly vanished, replaced with the knot that reminded him of his failure with Chang, his failure with Schweitzer.\n\nHe knew it made him seem weak, but he couldn't stop himself from asking. \"So, you are not here to replace me?\"\n\n\"Of course not,\" she said, \"but . . . I would be lying if I said the _Dokt\u00e8_ was happy with how things have gone.\"\n\nJawid looked up at her. \"What did he say to you?\"\n\nShe put her hand back on his knee, smiled, and some of the warmth returned. \"Don't worry about it, dahling. I can handle Eldredge. He just needs something to put you back in his good graces. Some success.\"\n\n\"How?\" Jawid asked.\n\nDadou moved her hand up his leg now, just a fraction of an inch, but enough to cause his head to spin.\n\nHer grin widened, her teeth gleaming under the fluorescent lights. \"Let me show you.\"\n\n* * *\n\nDadou sat up, rubbed the sore spot below her shoulder blades that had cramped as she hunched over the computer. In Port-au-Prince, people were nothing, scrabbling in wreckage like insects. There were a few, a very few, who had the money to be actual people, to have their lives count in any real way, to be loved, remembered. For most, living was much the same as dying, an involuntary function as random as the weather.\n\nIn America, it seemed that everyone mattered. Almost everyone, anyway. There were mountains of paper, computers full to bursting with legacy. Every doctor visit, every school grade, every idle thought on the Internet. She wondered how big the Gemini Cell's file on her was. She had been an actual person for only a few years now, but she didn't doubt that was more than enough time for the American government to put her in their endless databases, to note their speculations on her sanity, health, potential.\n\nThey'd certainly dredged enough up on Jawid Rahimi.\n\nHere was a digital photo, recovered from a Taliban laptop by a Special Forces team. Jawid was dressed in fabric so gauzy it billowed, perched on the knee of a hard-faced, bearded warrior. The man's skin was tanned like old leather, his eyes sharp in a way that spoke of a lifetime at war. One hand was curled around the barrel of an assault rifle. The other rested lightly on Jawid's hip, long fingers disappearing over the curve of his thigh.\n\nJawid was younger, his light scruff of a beard shaved away. He was made up like a woman, thick lines of black around his eyes, cheeks and lips rouged. His own eyes looked haunted. Distant. Dadou had seen that look many times before. Her sister's eyes had looked the same way. Dadou's might have too, if she hadn't killed the man who'd hurt her.\n\nDadou turned back to the case files and the notes of the psychologist assigned to profile Jawid, under the duplicitous title of HEALTH RISK ASSESSMENT. She had read them so many times that she knew them by heart, but let her eyes read over the words regardless.\n\nSubject's village was attacked by combined elements of the Taliban and Haqqani network, though subject believes the attack was not religious in nature but rather related to intertribal rivalry over access to grazing lands. Subject's grandfather, who he revered, was killed. Disposition of the rest of his family is unknown, but ground branch was unable to locate and they are assumed dead. Subject was taken as \"boy\" by band leader and subject to routine and repetitive sexual assault before rescue.\n\nAs a result of this experience, subject suffers from Post Traumatic Stress Disorder 309.81, with the following second-order effects: Generalized Anxiety Disorder 300.02, and Major Depressive Disorder, Recurrent (severe, no psychotic features)\u2014296.33. Symptoms include intensely low self-confidence and preoccupation with religious observance. Subject has lionized his family and childhood, and seeks to recreate that experience, preoccupied with marriage, children, and a return to his tribal roots.\n\nFear-Up, Pride-in-Belonging, and Hammer-of-Justice approaches yielded negative results. Subject responds dramatically to female influence, and has basis for a substantial Madonna-Whore Complex that will likely prevent him from forming meaningful romantic relationships without persistent therapy.\n\nRecommend increased SSRI as a bulwark against both depression and libido and mirtazapine to reduce anxiety and increase appetite (subject is eight pounds underweight). Appealing to subject's religiosity remains counterproductive, as subject's religious beliefs are strongly weighted against magic use and likely to focus subject even more firmly on his goals of marriage and family.\n\nIt is possible that appealing to subject's pathology may yield more positive results. A female honey trap operator may make inroads, but it is unlikely that subject will respond to someone who is not a religious Muslim, and Waziristani tribal courtship rituals are notoriously slow. This could be circumvented by a talented operator with a powerfully connecting common trait.\n\nDadou smiled. _My magic. That's the common trait._ They had underestimated his weakness to sighs and touches. Jawid was as horny as a schoolboy and would likely have responded to any pretty girl who seemed willing. But she had to admit the magic helped. She thought of the look in his eyes as he described the soul storm. _Do you have any idea how long I have been waiting to hear someone else say that they saw it too?_ She had told him, _That I am not crazy?_ That had been no lie.\n\nHe was like a little boy who had been given something too big for him. He was innocent and adrift, and it tugged at her heart. The world needed more boys. By the time they became men, more often than not, they were like the one who had hurt her sister, like the killers who'd flanked Rodriguez in that warehouse back in California.\n\n_Stupid. You are here to do a job, and you will do it._\n\nShe turned back to his file, read it again. So much concern, so much attention.\n\nHow many people back home wandered every day in a PTSD-induced fog? How many had minds broken by rape, torture, the horror of watching their own children die because they could not feed them? Nobody kept files on them. There were no smart doctors making careful notes, staying up late worrying how to fix them. They were not actual people, not people who mattered. If not for her magic, Dadou wouldn't matter either.\n\nThe door chime sounded, startling Dadou up from her chair. It would be Jawid again, tugging at his scraggle of black beard and staring at her chest. He was so nakedly obvious in his hungers, showing the world how best to manipulate him. She almost felt bad as she went to the door, letting a smile play across her face despite her irritation at being interrupted.\n\nAlmost.\n\nBut the smile died as she saw Eldredge standing in the corridor, glowering from under his bushy white eyebrows. Where Jawid was the very picture of naivet\u00e9, Eldredge was stone. \"We need to talk,\" he said.\n\nDadou sighed and stood aside, gesturing into the cell. \"Have a seat.\" She motioned toward the chair at her desk. Had it been Jawid, she would have motioned toward the bed.\n\nEldredge ignored her. \"We need progress.\"\n\n\"Progress in what, _Dokt\u00e8_?\"\n\n\"Don't play with me. I just had a rather . . . uncomfortable conversation with the Director. He's of the mind that you need to push Jawid harder.\"\n\n\"This won't come from pushing, _Dokt\u00e8_.\"\n\n\"I don't understand why you can't involve me in this operation. I have worked with Jawid longer than anyone else in this program. I know him. I can help.\"\n\nDadou laughed, cupped her breasts. \"I'm afraid you lack certain assets necessary for this work.\"\n\nEldredge swallowed his anger, breathed for a moment. When he spoke, his voice was even. \"Doctor Empath has told me about his levers. I understand that you are leaning on . . . particular ones. What I don't understand is how this is going to help find Schweitzer. We lost Chang. We don't have anyone else to hand that we could possibly mine for information, even if they were able to resist the jinn . . .\"\n\nDadou put up a hand. \"Do you ever wonder how Schweitzer found his wife?\"\n\nEldredge froze, mouth open. At last, he closed it. \"Of course. I wonder that every day. The prevailing theory is that he has some kind of link to her.\"\n\n\" _Se sa, Dokt\u00e8._ You must understand that what we do, at its heart, isn't summoning. It is . . . a kind of talking. We know so little about the _vodou_. Perhaps there is some way that Schweitzer can talk to his wife. His soul to hers. Very romantic, _non_?\"\n\n\"Are you sure this link exists?\"\n\nDadou spread her hands. \"This is the _vodou_ , _Dokt\u00e8_. I am not sure of anything. Except for this: I must be left alone to work with Jawid if I am to have any chance of finding your missing Operator. Jawid and I have a better chance if we work together, and we can only work together if you leave us to it.\"\n\n\"Have you made any progress at all?\"\n\n\"Tremendous progress, _Dokt\u00e8_. Jawid and I have gone into the void together; we are learning from one another. But these things take time.\"\n\nShe could hear the edge of excitement in Eldredge's voice. \"If you're right, the implications are staggering. The ability to . . . find an Operator? But you're talking about Sarah, and she's alive. So, it would be the ability to find a _person_.\"\n\nDadou patted the air with her palms. \"I don't want to over-promise. We are a long way from that. I am merely telling you what we are chasing. In the meantime, you must work on finding Schweitzer the old-fashioned way.\"\n\n\"We are gearing up the follow on to Gruenen's team. There are three towns nearby. We think Schweitzer will head for one of them. He will need supplies for his wife and child.\"\n\n\"If you can get us close enough for the Golds to feel his magic, we won't need to worry about links. It will be a fox hunt.\"\n\n\"I would rather not use the Golds if we can avoid it.\" Eldredge swallowed. \"How much more time do you need?\"\n\nDadou shrugged. \"Jawid's heart is not in this. He is . . . distracted. Unhappy. To do this right, he needs to focus. I am doing what I can, _Dokt\u00e8_.\"\n\n\"The Director is emphatic that this move quickly.\"\n\n\"Tell me something, _Dokt\u00e8_ ; when was the last time you had a woman?\"\n\nEldredge blanched, then turned red. \"I am not going to discuss that with . . .\"\n\nDadou laughed. \"I thought so. I am not surprised. You have been locked down here for so long, _non_? If you were not so rusty, you would remember that these kinds of things can't be rushed. That would be the fastest way to make him feel like it was . . . false, _ou konprann_? I have to let it roll until it boils.\"\n\n\"And how the hell will you know when he's . . . boiling?\"\n\nDadou tapped her temple. \"I will know.\"\n\n\"The Director doesn't think we can run this program with a single Sorcerer. We need Jawid's head in the game.\"\n\n\" _Pas enkie twa._ His head is in the game.\"\n\n\"Doctor Empath isn't so sure.\"\n\n_Doctor Empath doesn't have him staring at her tits all day._ \"I've got this.\"\n\n\"If there are any resources you need . . .\"\n\n\"Just time and a little patience,\" Dadou said, then, glancing meaningfully at the door, \"and some privacy.\"\n\nEldredge frowned. He opened his mouth to speak, closed it, left still shaking his head. Dadou let him hear her hiss of a chuckle as she slid the door shut.\n\nShe took a deep breath, let it go before returning to her computer. Jawid was easy. She had seen the way he looked at her, the way his breathing changed whenever she touched him. If his file was any indicator, he'd never even touched a woman who wasn't a relative. She already had him. Getting him to agree to help her Bind _mist\u00e8_ into a living subject would be much harder.\n\nShe thought of the lie she'd just told Eldredge. It was clumsy, to be sure, but the Director had been clear. Her orders came directly from him, and Eldredge was to be kept in the dark until the project was ready to be revealed.\n\nEldredge might look like a wise man with his white hair and his white coat, but in the end, he was a man. Dadou had met many, and most were, at their root, like Jawid. You started with sighs and glimpses of skin, then moved to guile and finished up with threats. Sooner or later, they did what you wanted.\n\nStill, she would tell the Director of their conversation. _Leave him to me,_ the man's modulated voice had rasped. _He will be of no help to you in this._\n\n_I understand,_ Dadou had said. _But will he be an obstacle?_\n\n_If he becomes one, you will let me know,_ the Director had said. _And I will deal with it personally._\n\nShe punched up her laptop and called the Director's line.\n\nHis rasping voice answered. \"You're calling about Eldredge.\"\n\nDadou smiled. She didn't doubt that the Director had her monitored. They'd taught her to sweep a room for recording devices when they'd brought her on, but she also didn't doubt that any device they used would be designed with her training in mind. \"However did you know?\"\n\n\"Because I spoke to him a little while ago, and I know him to be a man of action. You must understand, Miss Dadou, that he lacks certain pieces of information that are critical to his estimation of your progress.\"\n\n\"I gave him the story we agreed on. About the links. About how Jim Schweitzer found his wife.\"\n\n\"The best lies are mostly truth, Miss Dadou.\"\n\n\"Mostly.\"\n\n\"Anyway, when I deem Eldredge ready to handle it, I'll have him read on. I have some doubts about his ability to fully appreciate the criticality of what we're doing here.\"\n\n\"It's your show, _Direkt\u00e8_. I only work here.\"\n\n\"But Eldredge wasn't wrong about our need for progress. How is Jawid coming along?\"\n\nDadou was silent for a moment. \"I am almost there; he just needs a little push.\"\n\nThe Director didn't bother to keep the frustration out of his voice. \"You sound . . . reluctant.\"\n\n\"Your psychologist's assessment is correct, _Direkt\u00e8_. He wants a woman. That's the lever.\"\n\n\"If that is the lever, Miss Dadou, then you are to pull it, and with all expediency.\"\n\nAnger boiled in the back of her throat. She thought of her sister, of the long parade of men who had tried to tell her that she belonged to them. \"I . . .\"\n\n\"Listen to me carefully, Miss Dadou. I want to make sure I'm perfectly clear\"\u2014the Director's spoke slowly, enunciating each word\u2014\"that while you are a critical asset to this program, you are not so critical that I will tolerate shirking. I brought you here to do a job, and I need you to _do_ it.\"\n\nFear doused her anger. She knew the kind of power the Director wielded. She knew what he could do, what he would do. \"Sir,\" she said. \"It will be very tricky. The process of Binding a jinn into the living is . . . ugly . . . bloody. It may . . . frighten someone so delicate. I will have to bring him in at precisely the right moment. It's like pitching a source, _ou konnen_? You don't ask the question unless you already know the answer.\"\n\n\"Then make sure you know the answer. He wants a wife; he wants a family. Promise to marry him and have his babies.\"\n\nThe anger boiled in the back of her head, mixing with the terror in her gut. \"I'm not sure that . . .\"\n\n\"Let me tell you something about my leadership style, Miss Dadou. I don't get involved in the operational details of any of the programs I run. Instead, I recruit the most talented people I can find, and trust them to do whatever is necessary to get the job done. I trust them to do their jobs, Miss Dadou. I don't micromanage them. I am an executive. I _execute_.\"\n\nHe bit off the last word, raising his voice just enough to underscore the point. He waited for Dadou to reply, and when she didn't, spoke into the silence. \"Do we have an understanding, Miss Dadou?\"\n\nIt wasn't until she tried to answer that she discovered her mouth was dry. \"We do.\"\n\n\"Excellent,\" the Director said. \"I look forward to great progress in your next report.\"\n\nThen he cut the connection. Dadou stared at her laptop for a long time. Jawid was just a man. It was nothing that she hadn't done before.\n\nShe looked in the mirror and ignored the void in her gut, swallowing the pinpricks of tears forming in the corners of her eyes.\n\nAllergies. Everything in America was strange and new. She'd get used to it.\n\n# CHAPTER IX\n\nHONESTLY, OFFICER\n\nIt was the kind of Shenandoah town where Schweitzer had kept promising to take Sarah: old clapboard barns converted to antique shops and used bookstores, little caf\u00e9s hung with the work of local artists, the semipermanent stalls of a farmers market. As the years rolled by and they never visited, she didn't nag him about it. _I always thought there'd be time._\n\nThe corpse of her husband looked over at her. The face of the man she loved was only faintly visible on the gray-purple skin stretched over its mostly metal skull. Jim's beautiful gray eyes were gone. The silver balls that replaced them were chilling, their flickering dance a constant reminder of the strangeness of the new world she'd woken up to in the Sentara Princess Anne Hospital. This was not the man who had fathered her child. This was not the man who had made her feel so safe, not because he could protect her, but because he could help her to protect herself.\n\nBut the magic that linked them would not be denied. She could feel it dragging at her chest, a physical thing, a ship's line tying them together. The love in that channel was thick and solid, as if everything they'd shared when Jim had been alive had been distilled into it, something she could smell and taste and touch, but outside of her. A museum piece. It reminded her that she loved him but was not in love with him. It was obligation and legacy and the raw knowledge that only he could protect her son from the monsters that were just like him in every way, save the color of the flames that burned in the eye sockets of their skulls.\n\nThat same link had nearly betrayed her as she had betrayed her husband. _No, it was not betrayal._ When she'd slept with Steve Chang, she'd thought Jim was dead, would never have done it otherwise. _You shouldn't have done it, anyway._ She loved Steve, but not in that way, and their lovemaking had been more a desperate flailing for something other than panic and agony, grasping for anything that felt good, even for a moment.\n\nThere was nothing to be gained by telling Jim. He had lost enough. The link between them had tipped him off. He knew something was wrong, but he also knew her well enough not to press her, and the urgency of their situation didn't exactly lend itself to a deep conversation at the moment. Even in this, her hiding something from him, they were working together.\n\nBecause the truth was that the core of their marriage had been more than passion. It had been the yoke they'd worn together, harnessed and straining for common goals. She looked at Jim now, not as her lover and the father of her son but as the person she would be working with to get the mission accomplished. _Oh God, Jim. I miss you._\n\nJim stared back at her, his dead face expressionless, devoid of the slow movement that breathing provided. She could feel his own emotions pushing down the link to her: love, but also desperation, and a rising impatience with her all-too-human limitations.\n\nShe ruffled Patrick's hair. \"You'll have to find a way to keep him quiet.\"\n\n\"I'll figure it out.\"\n\n\"Don't hurt him.\" She wished she could take the words back as soon as she spoke.\n\nJim looked away, and Sarah felt the pulse of anger, humiliation, and pain along the link. \"He's my son. What the hell do you think I'm going to do?\"\n\nShe knew she should apologize, try to salve the hurt. But the truth was that Jim was dead now, and she worried that with each passing day he grew less and less in touch with the demands of the living. She grunted and turned back to the gorgeous scene unfolding below them.\n\n\"I'm not seeing a drugstore,\" he said.\n\n\"There's a drugstore. See that?\" She pointed to a road winding its way up a hill that had been cleared of anything taller than a blade of grass. The sign beside it was large enough to be read at this distance. BRYCE RESORT, BASYE, VA.\n\n\"Looks like a ski resort,\" he said.\n\n\"It is. Big enough for a hotel. No way they're not going to have a way for guests to buy aspirin.\"\n\n\"Doesn't mean they'll have what we need for Patrick.\" The boy stared sullenly down the hill, rubbing absently at the growing red welts on his arms.\n\n\"Itches,\" Patrick whined.\n\n\"I know it does, sweetheart,\" Jim said, \"but you can't scratch it. No matter what.\"\n\nPatrick ignored his father, looked up at Sarah instead, his eyes questioning. \"Do as Daddy says,\" Sarah said.\n\nPatrick was sullen, but he stopped rubbing his arms. She spoke quickly, before Jim could say anything, before she had to reckon with the pain filtering down the link between them.\n\n\"Ski resorts run year-round,\" Sarah said. \"Big ones do, anyway. There'll be a zip line and mountain bike trails and a conference center. They'll have what we need.\"\n\nJim grunted. \"Not too late to do this my way.\"\n\nSarah's answer was to stand, dusting off her pants. \"He's going to start screaming bloody murder the minute I walk away.\"\n\n\"I'll head back into the woods far enough that nobody will hear him. He'll cry himself to sleep eventually.\"\n\nShe bent, gave Patrick a long hug. \"I can't even begin to think how this all is hurting him,\" she said.\n\n\"Best not to,\" Jim answered.\n\nThey looked at one another then, and Sarah felt a tremor pass along the link connecting them. She suppressed a shudder at the sudden intrusive memory of Steve moving on top of her and inside her, watching him couple with her as if she hovered outside her own body, looking down at his pumping hips, her trembling shoulders. Could Jim tell? Did he know? She had thought she was certain he didn't, but the magic had power beyond anything she understood. It enabled her to know things that she shouldn't. She had been able to tell where Jim was and how far away. She knew that Steve was dead, had been certain of it the same way she'd been certain that Jim was alive.\n\nShe looked at the grinning skull of his face, the embalmed skin stretched across it. _Not alive. Not anymore._\n\nShe kissed the top of Patrick's head and tried to ignore his cries as Jim bundled him into his dead arms and turned for the woods. _Commit to the fight,_ Jim had taught her. _Go all in and stay in until one of you is down. Half measures are how you lose._\n\nShe walked down the hill, her clothes mostly clean, her stride mostly even, reciting her story, falling into character. Nobody would ask, but if they did, she was camping in the forest and had hiked in to grab some medical supplies. The ground sloped sharply, the sun warming her neck and shoulders. Birds shouted out competing claims to territory and roots crunched under her boot soles. For a moment, she could almost believe she was alone, walking in the sunshine toward some Shenandoah Valley art town, instead of on the run for her life from an army of the undead.\n\nShe took refuge in that thought, turned away from her anxiety over Patrick, the museum piece of her love for Jim heavy in her chest, and spared a glance for her surroundings. A low barn had been converted to an antiques showroom to her right. An ice cream parlor, closed for the winter, topped a trio of a barber, sandwich shop, and small motor repair store. Further along, the art galleries and coffee shops crowded the narrowing road as it wound its way toward the ski resort. There were few people on the main road between the ski resort and the town proper. A young couple with a baby in a sling smiled at her, another set of parents smiled sheepishly as they tailed screaming children. None gave her more than a second glance.\n\nShe passed the repair shop and angled toward the broken gravel road that began the long climb to the resort's top. She felt the aching in her hips and knees, the fatigue brought on by nights out in the open on hard ground. Too little sleep and far, far too much walking, Patrick's dead weight always on her shoulder. This entrance was designed for families coming from a long way off, driving cars that could carry them the miles up the hill to the main entrance. The view would be spectacular, but the climb would be punishing.\n\nSarah sighed, set her teeth, and headed off.\n\nAs she passed the corner, her eye caught a flash of white and red. A drugstore stood at the end of the row, sign bleached from long years in the sun. The glass door was propped open with an old brick. Rows of detergent bottles were on display in the dirty window.\n\nA brown car was parked in front, a five-pointed gold star emblazoned on the side. SHERIFF was written beneath it in angled letters, then SHENANDOAH COUNTY. The light bar on the roof glinted at her.\n\nSarah felt the sour panic boiling in her stomach. It was useless to fight it, Jim had taught her. Far better to acknowledge its presence and factor that into your decision-making. Grappling with fear honestly was the only way to mitigate its power over you. She kept walking, not looking at the cruiser again. For a normal person, it would just be part of the scenery, and Sarah was normal. Nothing to see here, folks. Move along.\n\nThe car wasn't idling. The windows were rolled up and the doors locked. It could be parked for a minute; it could be parked overnight. The sheriff might be inside the store or on vacation in Florida. _Make a decision. You either go up that hill and see if there's another store or you go inside this one. You do not wander around in circles, drawing attention to yourself while your son's poison ivy gets worse._\n\nHer hip. She felt the throbbing ache of the divot in her flesh, the steady heat that she prayed was the aftereffect of the clotting powder and not an infection. She looked at the winding road up to the ski resort again. Steep, long, the broken gravel would spin a tire, slip with each footstep.\n\nShe muttered a silent apology to the training Jim had given her and let pain and fatigue make the decision. She turned to the store's open door even as she told herself that it was time and not exhaustion driving her to this choice, knowing it was a lie.\n\nThe inside of the store was organized and warm. Posters advertising everything from whitening toothpaste to chest rubs were yellowed with age, but the shelves were neat and well stocked. The silver edges of an old-style black metal cash register glinted under fluorescent lights. Behind it, an older man stood chatting, his enormous belly spilling over the brown braided leather belt that held up his khaki trousers.\n\nA sheriff's deputy leaned in toward him, hard lines of her jaw creased in a smile. Her uniform was brown and gold to match the car outside, her hair wound into a long braid coiled into a bun that popped out just below the edge of her ball cap. The deep lines in her skin spoke of a life out in hard weather. Her hand, sporting a gold wedding ring, was tapping against the butt of her pistol. Her head swiveled as soon as Sarah walked in, smile never fading, eyes out of the conversation, fixed firmly on her.\n\nSarah suppressed the sudden urge to turn and leave. _No. That's what someone with something to hide would do. You're here shopping._\n\nSarah smiled and looked up at the white poster-board signs hanging from clear fishing line over each aisle. _Calamine._ She headed to the aisle marked SKIN CARE. She bent, heart hammering, making a great show of scanning the rows of white and yellow bottles, the panic rising until they were all a plastic blur, labels unreadable. She felt a sharp pain as the cauterized skin over her wound stretched taut, and worked to keep a grimace off her face.\n\n\"Help you find something, ma'am?\" The man behind the counter's voice drifted over to her.\n\n\"Got any calamine lotion?\" she asked, hearing the edge of fear in her voice, praying the deputy didn't notice.\n\n\"You're in the right aisle,\" the man answered. \"Should be two shelves from the bottom. Look for the pink.\"\n\n\"Pink, right,\" Sarah said, focusing. _Don't lose the bubble,_ Jim's voice echoed in her head. Where was he now? Could his magical senses tell him where she was? She felt for the link but was interrupted by footsteps coming toward her. \"It's okay,\" she said, looking up to the man, \"I can find . . .\"\n\nThe deputy stood there, eyes crawling over Sarah, looking for indicators. \"Let me show you,\" she said. \"I practically live here.\" Her voice was high, with a slight southern twang. Clusters of freckles dotted her cheeks and nose.\n\nSarah swallowed. She only noticed these kinds of details when she was truly panicked. She swallowed; it was an indicator, but she needed it to get her voice back. \"I've got it,\" she said, tapping a pink bottle that she hoped was calamine.\n\nThe deputy's eyes flicked to it, and Sarah could tell she'd missed her guess. \"What else are you looking for, ma'am? Might be I can help you.\"\n\n\"Sure,\" Sarah said, standing and working the kinks out of her spine, wincing at the pain in her hip. The deputy didn't appear to miss that one, either. _Engage her. That's what a normal person would do._ \"Need aspirin, hydrogen peroxide, and antibiotic ointment. An extra tent stake would be awesome if you sell that stuff.\"\n\nThe deputy relaxed a bit at that. \"You camping out here?\"\n\nSarah nodded, following the woman into the next aisle. \"Been a disaster so far. Tent blew over, my son cut himself 'trying to help.'\"\n\nThe deputy nodded, handing her a bottle of aspirin and moving farther along the aisle. \"Boys do that,\" she said. \"Got two of my own. Spend half my time putting Band-Aids on 'em. You need a doc? The ski lodge has an EMT on call.\"\n\n\"Nah, he's fine. Just scraped up. My husband's with him.\"\n\nThe deputy nodded as Sarah collected the rest of her things and headed to the counter. \"How long you in town?\"\n\n\"I'm not in town,\" Sarah smiled. \"Just discovered that we hadn't packed enough. We don't do this a lot.\"\n\n\"Where you from?\" The man behind the counter's voice was light, and his eyes easy and open compared to the deputy's.\n\n_Good lies are as close to the truth as possible._ If there was an APB out, then the information Sarah was providing would be giving the deputy what she needed to make a positive ID, but that was a risk she was simply going to have to take. \"Tidewater,\" she answered. \"Outside Norfolk. My man's in the Navy. You?\"\n\nThe man laughed and even the deputy seemed to relax. \"Been here my whole life.\" He handed her the purchases and her change. \"Now, you be sure to thank your husband for his service from us.\"\n\n\"I will,\" Sarah said, picturing Jim's dead face.\n\n\"Bye, now,\" said the deputy, as Sarah turned and left. She could feel their eyes on her back, following her out. She forced down the urge to hurry, keeping her stride even and casual. She strained her eyes, hoping against hope that the conversation would start up again, that she would hear the light strains of their chatter, showing they had turned from her and back to the life before she'd wandered into town.\n\nBut instead, she heard the crunching of shoes on the gravel behind her.\n\n\"Ma'am?\" The deputy's voice.\n\nSarah froze, thrust her hands into her pockets to stop them trembling, forced herself to turn, smile. \"What's up?\" _Please tell me that I forgot my receipt . . ._\n\nThe deputy had hooked her thumbs into her gun belt, took a few steps closer, looking at her feet. She stopped outside striking range, crossed her hands in front of her buckle, looked up. \"Ma'am, I've been in law enforcement all my life. I've got something of a sixth sense when it comes to trouble. There's trouble here. Is there anything you want to tell me?\"\n\nSarah rolled her eyes and tried to keep from bolting. \"Trust me, if there was something I needed police help with, I'd be asking.\"\n\n\"You running away from something, ma'am?\"\n\nSarah fought the urge to swallow again, put a little edge into her voice. \"I'm a thirty-three-year-old mother. I am a successful artist. I am married to an amazing man. What the hell would I be running away from?\"\n\nThe deputy looked sheepish. \"That's what I'm trying to figure out.\"\n\n\"Well, there's nothing to figure. I'm going back to my camp. We'll sharpen a stick or something for the stake.\"\n\n\"Ma'am, you look a little banged up. This amazing man of yours, he hitting you?\"\n\nAnd now Sarah did swallow, tamping down on the sick certainty that this woman wasn't going to let her go.\n\n\"They just keep doing it unless you stop them,\" the deputy said. \"I see it all the time. Happened to me once. No shame in admitting it.\"\n\n\"No, no,\" Sarah said. \"Jim would never do that. We're just lousy campers, is all.\"\n\nThere was a long silence, during which Sarah was suddenly very conscious of how empty the street felt, deserted save for her and the deputy, eyes narrowed and tracking Sarah's hands. _Commit to the fight,_ Jim's voice in her head. _Even long odds are still odds. Make a plan._\n\nSarah didn't want to hurt this woman who was, in all likelihood, trying to protect her. But she had driven a knife through the throat of a man who would have kept her from her son, had bitten the face off another. She would not hesitate if that's what it took to get her back to Patrick.\n\nAt last, the deputy sighed. \"All right, ma'am. I'll let you be on your way. If you change your mind, I eat my lunch in my car right here most days. Just come on down and we'll talk it over. No need for a report or anything. Just us girls.\"\n\nRelief flooded Sarah with such intensity her knees went weak, but she put a smile on her face. \"That won't be necessary, but thanks anyway. It's good to know that people like you are out here, keeping us safe.\"\n\nThe deputy smiled but said nothing, eyes kindly suspicious.\n\nJim had taught her this technique, how police and military interrogators had been trained to use the silent stare. Most people abhorred silence, and would fill it with anything, clues, even confession, if it went on long enough.\n\nBut Sarah was not most people. She turned on her heel and took a long and confident stride back toward the woods. It was the sort of purposeful step she imagined an innocent woman would take, the fast pace of a camper anxious to get back to her living husband and child, who were just out for a pleasure trip and not being hunted by the government. She felt the deputy's eyes on her back, but each step lifted her confidence. _Keep going. Long strides. You've got somewhere to be. Move quickly, but don't run._\n\nSarah felt a stinging in her hip, then a sudden warm wetness.\n\nToo fast. Too long. Too confident.\n\nThe wound had reopened.\n\nBefore she could stop herself, Sarah had clapped her hand to her hip. Her jeans were already soaked, the red stain easily seeping through the thick fabric to glisten wetly in the sun. Even a casual observer couldn't miss it.\n\nShe was already turning as she heard the deputy's shocked voice. \"Ma'am? My God, ma'am, are you okay?\"\n\nThe deputy's eyes were wide. She was already advancing on Sarah, eyes fixed on the spreading bloodstain on her hip.\n\n\"I'm fine,\" Sarah mumbled, backpedaling.\n\n\"Like hell you are! You sit down right now; we're going to get you help.\" The deputy thumbed the radio clipped to her shoulder. \"Don, I'm going to need your help over here, Fairway and Ridge. Ten fifty-four, uncontrolled bleeding. Over.\" Sarah's stomach turned over. She knew this type of cop. There was no way she would let her go now. They would take Sarah to a hospital. That meant identity checks. It meant radio chatter. It meant the Cell would find out.\n\n_Make a decision._ She had no doubt the deputy could draw and fire before she could close the distance between them.\n\nThe radio crackled a reply, but it was lost in the blood roaring to Sarah's ears. Her vision was graying at the edges, coming into crystal clarity as she focused on where the deputy was vulnerable, how she would disable her before she had a chance to draw her weapon.\n\n_No. Even if you could, you're not going to hurt her. She's done nothing wrong. She's trying to help._\n\nSarah backpedaled faster, her hip throbbing. \"I said I'm fine! Leave me alone.\"\n\n\"Ma'am, you are badly hurt. You are not going anywhere until an EMT tells me that you're not going to bleed out. I am trained in first aid. Just let me stop the bleeding until we can get an ambulance here.\"\n\nTires crunching on gravel, another police cruiser pulling up alongside.\n\nNow or never.\n\nSarah broke for the line of storefronts, her boots spraying dirt and making her feel as if she was wading through molasses. She heard the dull clunk as the deputy dropped the radio and it banged against the body armor beneath her shirt. \"Oh, shit. Ma'am! Stop right now! Go, Don, go!\"\n\nTires peeling as the driver of the other cruiser threw it in gear and picked up speed. Sarah ran with every ounce of will she possessed, feeling the seared wound in her hip tear wider, fresh blood soaking her waistband. The storefronts drew closer with dreamlike slowness. _Damn it, Jim. You were right. You should have just come in the dead of night and stolen this stuff._\n\nShe heard the sudden roar of an engine, the sound of crunching gravel, and the other cruiser leapt around the building corner, fishtailing to a stop between her and the door. The driver jumped out and took cover behind the engine block, pistol trained on Sarah's face. \"Police officer!\" He shouted through a thick accent. \"Stop right there! Let me see your hands!\"\n\nHe had a black flattop cut close enough for a Marine to envy. He was a caricature of a southern county cop: huge paunch and jowls, red pug nose, aviator glasses. His ball cap had flown off in his hurry to draw down on her.\n\nSarah slowed, stopped. She wouldn't do Patrick any good with a hole in her head. She looked left and right, saw only the female deputy slowly coming closer, eyes locked on her gun sights, staring down the barrel at Sarah.\n\n_There's no running now,_ she thought. _Only dying._\n\nAnother thought came close on its heels. _Maybe that's best. If they take you, they can use you to get Patrick, to get Jim._\n\nHer husband was a superpowered immortal. He might be able to rescue her, and she knew he wouldn't stop trying until he succeeded. And that was the problem. Because there were other superpowered immortals, and as soon as they had confirmation of where she was, they would be coming.\n\nShe swallowed. _I'm sorry, baby._ She felt the tremor of the communication pass along the link, could feel Jim tightening at the other end. He would be coming. Even now, he would be coming for her.\n\n\"On your knees,\" the male deputy said. \"One knee at a time, nice and slow. Right knee first.\"\n\nSarah hesitated. \"Ma'am, do it right now!\" the female deputy shouted.\n\n_Patrick._ She wasn't sure Jim could care for him. But then again, she wasn't doing such a great job either.\n\nShe heard gravel scuffling as the female circled around to triangulate her, keep both guns on her without the risk of shooting one another.\n\n\"Knees!\" the man shouted. \"Do it now!\"\n\n\"We're trying to help you!\" the woman called.\n\nSarah willed herself to run, but her legs refused to obey her. _Oh God, baby. I'm sorry._\n\n\"Fuck you,\" she said.\n\n\"Damn it.\" She heard the female stalking toward her, the loud _shick_ as she snapped open her metal baton. \"This is going to hurt you, ma'am. Watch it, Don.\"\n\n\"I've got her,\" the male said, angling his head to get a better sight on his weapon. \"I've go\u2014\"\n\nAnd then his head was gone, and the bright red of his arterial blood was spraying into the sky, mixing with the powdered glass of his cruiser's shattered windshield.\n\nSomething had landed on the cruiser's roof, its weight bowing the car inward, the windows exploding in sprays of shining dust. It crouched, slowly rising, gray-white body slashed across with the deputy's blood, as if it had been hit by an errant paint roller dipped in crimson.\n\nIt was one of the monsters she'd fought back on Drew's farm. It looked so much like Jim. It wore the same leering skull, the same Frankenstein stitching, the same haunting imprint of the living thing it had once been. Bone spikes projected from its elbows, hooked upward from its shoulders. Purple-black mottles showed where it had been grafted together, woven and stitched from the fabric of other corpses. It raised its head on a stub of a neck held to its torso by an armature of metal cables straining beneath thin scraps of dead flesh.\n\nIts eyes were twin flames.\n\nBright gold.\n\nGunshots. The female deputy was screaming now, her cop's sangfroid a memory. In its place was the sound of a little girl, hiccupping sobs as she poured on panicked fire, in no danger of hitting anything.\n\nSarah leapt back from the monster on the cruiser, looked over toward the deputy.\n\n\"Run!\" Sarah shouted to her.\n\nGray shapes loped along the blasted gravel path to the ski resort, at least ten. She could hear the distant growls, the sound of breaking glass. There were more of them in the town. She whirled, trying to pick a safe direction. The way she'd come looked clear.\n\n\"Run,\" Sarah breathed, shoved off the ground, started running.\n\n\"Wait!\" the deputy screamed.\n\nSarah didn't wait. Because she knew what these monsters were. Because just three of them had nearly been more than a match for her and Jim together. And now there were more than double that number, racing through the streets of Basye, crashing through the storefront windows, savaging the occupants. Sarah stumbled through a slick red pulp that had once been a person. She swallowed bile and ran as fast as she could, knowing it was useless. There was no way she could outrun these monsters, no way anyone could.\n\n\"Wait!\" the deputy shouted again, whether to her or to the Gold Operators, Sarah couldn't tell. Her world narrowed to the six inches in front of her face, the burning agony in her hip as she ran as fast as she could.\n\n\"Waaaaaaiiiiiit!!!\" The deputy dragged out the scream a third time, trilling on until it ended in a wet ripping that reached Sarah even across the wide distance she had opened up in her panicked run.\n\nShe could hear the pounding gallop of feet on the road behind her. If an animal had been pursuing her, she'd have heard the panting exertion of its breath as it put on speed. But the Gold Operators didn't breathe, and they came on silently, revealed only by the light touch of their clawed hands and feet on the ground. She could feel her back prickling at their nearness, heard the change in their gait as they went from four limbs to two, reaching toward her.\n\nShe threw herself to her right, crashing through a window. For a sickening moment, she felt the surface vibrate and hold, thought she would bounce off and into the arms of her pursuers, but then the glass gave way and she fell in, sprawling across the concrete floor.\n\nThe glass made a jagged carpet below her, and she left skin on it as she rolled to her hands and knees, lurched back into a run.\n\nShe was in a potter's studio, rows of tables, each with a wheel, fanning out before a central desk below a grease board. Cupboards lined the walls, bulging with bricks of clay.\n\nTwo women crouched behind the desk. They were both blonde and fortyish, hair in buns meant to keep it clear of clay. One was shouting frantically into a phone.\n\n\"Fucking run!\" Sarah shouted to them. She tore between tables, eyes roving frantically for a back door.\n\nThe woman stared at her and she ran past. \"Nobody is coming to help! Move!\" she called back over her shoulder.\n\nThey shouted something at her that she ignored, concentrating everything she had on running. She glimpsed them starting to run after her, knew they were too slow, too late.\n\nSarah tried to shut out the sounds, to focus instead on finding a back exit, to not hear the tinkling of the glass as the Gold Operators came through behind her, the slapping of their bare feet on the concrete floor.\n\nThe studio ended in a wall of metal shelves stacked with boxes; if there was a door hidden behind them, Sarah didn't have the time to search for it. She swallowed the sick panic that boiled in her stomach and turned to the side window. She tried to avoid looking at the central desk, but it was impossible.\n\nThe two women had bought her precious seconds. Three Gold Operators were crouched behind the central desk, up to their elbows in red. The screaming had stopped, replaced by growling and liquid gurgles. Blood had begun to spread out on the floor, as if a bucket had been upended. _I didn't know there was that much in a human body._\n\nSomething thick and wet flew out of the feast, struck her in the shoulder as she slammed into the window and crashed through. The metal frame groaned on its hinges and slammed open, spilling Sarah out into the side street. She rolled to her knees, oriented herself, and raced toward the ridge where she'd crouched with Jim.\n\nShe kept her eyes straight ahead, focused on her pumping legs, on ensuring the muscles were stretched to the limit, that she was putting on as much speed as possible. She knew that if one of the Gold Operators decided to pursue her, it could close the distance and overtake her in a matter of seconds.\n\nBut all around her, she could hear the ripping flesh, the shattering glass, could see the low gray shapes in her peripheral vision. There was enough living prey to keep the monsters busy. She didn't know how much time the unfortunate population of Basye had bought her, but she was determined to make the most of it. She poured her desperation, her fear into the channel that linked her to Jim. Jim could hear a twig breaking from a mile away; there was no way he could miss the screaming as Basye came apart around her. _Come on, baby. Get your ass over here._\n\nThe thought was followed by a stab of guilt. He couldn't leave Patrick in the woods, and bringing the boy would mean bringing him into danger. But _damn_ , now that she saw a chance to live, she realized how badly she wanted to.\n\nShe ran on, the solid road giving way to broken chunks of asphalt and then to the flat expanse of gently rising grass. Her hip screamed at her; she could feel the edges of the wound ripping wider with each long stride. The plastic bag full of the supplies she'd bought to clean it was lost in the wreckage somewhere behind her. _All that for nothing._\n\nIt seemed as if she ran through molasses. A soft fog was forming in the corners of her eyes, stubbornly staying in her vision after she blinked. She raised a wrist, rubbed hard at her eyes, let it drop. The fog remained. It might be infection or blood loss, but she was starting to come apart. Her vision became a stutter-flash of staccato images, like an old film reel running too slow.\n\nOne moment, she was running on open grass, and then the grass was suddenly interspersed with packed gravel, and Sarah vaulted something boxy and black. She heard a low hiss, smelled the dull scent of gas. She glanced down long enough to see that she was running through a small grill park, the white canisters of propane scattered among the half-cooked hot dogs and hamburgers, grills knocked on their sides as the Golds had lit among the families here. A woman lay on her side, cut in half, face pressed against the black bars of a hot grill. Sarah was grateful the corpse's head was turned away from her, so she couldn't see what the metal was doing to its face, but she could hear the sizzle and pop of the melting skin, could smell the cooked-meat stink mixing with the stench of the leaking gas. Her gorge rose and she focused on picking her way through the field of scattered propane canisters. The gravel thinned and Sarah gulped air, feeling her lungs inflate with hope with each passing stride. The Gold Operators may have come for her, but Jim had said they were driven by bloodlust, happy to slaughter whoever was closest. By the time they realized their original quarry had escaped, she would be in the woods and with the one person in the world who could protect her. _And what then? You're bleeding out and you know it._\n\nSomething heavy and hard hit the backs of her knees, sending her flying.\n\nSarah didn't even have time to land before she was snatched out of the air by her ankle and swung around. She felt the tendon cry out, the bone creaking against the strain. _If my ankle breaks, I can't run, and if I can't run, I can't get back to my son._\n\nAnd then the ground rushed up to meet her and she was tumbling across it, the sharp grass tearing at her face, a propane tank smacking into her gut, knocking the breath out of her, her vision going black. She skidded across the ground, flopped and rolled for a few feet, and finally slid to a stop on her back. She groaned, struggled to suck in air. _Get up get up get up get up._\n\nShe could hear a slow tamping in the grass, something stalking toward her.\n\nSarah scrambled with both hands, hoping to come across a rock, a stick, anything she could use as a weapon. But she didn't look away. When it made its move, she would be ready.\n\nThe Gold Operator looked like it had once been an Asian woman, slight and lean. Its body was remarkably well preserved, with only a long gash across its throat that had been lasered shut, the long burn scar puckering between holes where stitching had failed. There was even the stubble of hair clinging in patches to the skull. The mouth was drawn in a wide smile; the only spines were two short bone spikes protruding from the gray remains of small, high breasts. She couldn't have been more than twenty when she died.\n\nBut its eyes were the same hungry gold flames as the rest. It advanced like a stalking cat, shoulders hunched, clawed fingers spread, enjoying Sarah's distress. It whispered something in a voice like broken glass, a low, harsh string of language that sounded like Russian. The burning eyes flicked to Sarah's belly and she noticed that her shirt had hiked up during the tumble.\n\nAnd then Sarah's fear overpowered her, and she scrambled back on her hands, because she knew what the Gold Operator was thinking, could imagine those teeth and claws slicing into the taut skin of her stomach, digging out the soft organs behind. \"No,\" Sarah said in spite of herself. \"Nononononono.\"\n\nThe Gold bent at the waist, smile widening further, until the face threatened to rip open, cheeks stretching so thin, Sarah thought she could see daylight through them. Thin, articulating tusks slipped out of the corners, curling around below the mouth, sharp points clicking together.\n\nSarah scrambled back, trying to get her feet under her, succeeding only in tangling her ankles together and folding her legs painfully beneath her thighs.\n\nHer knuckles barked painfully on something hard and cool behind her. The propane canister that had knocked the wind out of her rolled away. She reached for its edge, felt her fingers close around the thick metal ring of the valve guard handle.\n\nThe Gold Operator shrieked and lunged.\n\nSarah shrieked back, throwing herself to the side and using her momentum to wrench her arm forward. The heavy tank swung so hard, she thought her arm would tear out of its socket. For a moment, she feared she'd missed and the tank would pass through empty air, turning her around so the Gold could savage her back instead of her front.\n\nBut then she was rewarded with a heavy thud that sent a satisfying tremor up her arm as the tank crashed into the Gold Operator's head, sending it stumbling back. She heard a soft crack as one of the thing's tusks snapped off.\n\nIt crouched, howling, bone spikes sliding out of its fingertips.\n\nThe tank settled back into her grasp, bottom thudding into the ground beneath her. She pushed herself up to her feet. For a moment, the world went gray and Sarah swayed. _No no no stay up stay up stay up._ She blinked, shook her head furiously, nearly sobbed in relief as her vision came clear and she found she was still up. She had a handle on it now; she was standing. She was fighting.\n\nShe heard a familiar hissing, close by now, followed by the faint rotten-egg stink of the gas. The valve had been jarred by the blow, the pressurized contents starting to leak out.\n\nSarah smiled, lifted the tank.\n\nShe couldn't outrun a Gold. This would either work, or it wouldn't.\n\nEither way, she was fighting, and in spite of the life slowly leaking out of her hip, in spite of all she had lost over the past months, it felt amazing.\n\nShe screamed defiance and hurled the tank at it.\n\nSarah didn't wait to see what Gold's reaction. She was already turning, already diving for the ground, throwing her arms up to shield her face, watching through slitted eyes.\n\nThe Operator grinned, raised its bone claws, and slashed the tank out of the air.\n\nSarah heard the metallic clang as the razor-sharp bones struck the tank, saw the sparks as they ripped it open. Only then did she allow herself to close her eyes.\n\nShe didn't hear the explosion. She was only conscious of sudden heat roaring over her, of a high ringing in her ears, of the feel of something sharp and hard cutting through her side, her cheek, her arm, her shoulder.\n\nShe lay for a moment, breathing. _Maybe I've lost too much blood; maybe the explosion got me too. Maybe the Operator survived and will cut into me any second . . ._\n\nBut a second passed, then two.\n\nSarah opened her eyes.\n\nThere was precious little left of the thing. Scraps of gray meat twitching in a black pit of ash dotted with smoldering grass. Sarah turned her attention to herself. The pain in her hip was worse than ever; the fog was still gathered in the periphery of her vision. She was weak as a kitten, but she wasn't going to die just yet. She sat up, passing her hands over her body, assessing the damage. If another Gold came, it wasn't as if she were in any condition to outrun it now, anyway.\n\nShe blinked; another dead thing stood there. Rage flooded her. She was so close. She was almost home free. She snarled, preparing herself to fight. She wouldn't make it easy.\n\nAnd then she saw its eyes. Burning silver.\n\nJim.\n\n\"Fucking . . . took you . . . long enough . . .\" Sarah breathed, unfolding her legs and staggering unsteadily to her feet.\n\nJim was looking over her shoulder into the town. \"Are you okay?\"\n\n\"Do I fucking look okay?\"\n\n\"Fair enough. You're standing, so that's something.\"\n\n\"I can walk. Come on.\" She turned back toward the town.\n\nHe stopped her with a hand on her shoulder. \"Sarah, this is bad; we have to go.\"\n\n\"I can't.\" Her lips were numb, her hands shaking. She tried to take a step, found she couldn't. \"I lost my bag. I have to go back and get my bag.\"\n\nShe saw it now, even as her vision grayed and the ground pitched unsteadily beneath her. She had come to town to get supplies. If she just left the bag behind, then it was all for nothing, and she couldn't have that. She had to go back.\n\nJim cocked his head to the side. \"Your bag? Oh God, baby. Your hip.\"\n\nHe reached for the sopping wound, and Sarah saw he was going to stop her. She had to get her bag. But she was so tired. She slapped his hand away. \"Don't touch me.\"\n\n\"Baby.\" The rictus face grimaced. \"We have to go; we have to get you some help. You're going to bleed out if we don't treat that.\"\n\n\"The bag!\" Sarah shouted. \"It has Patrick's calamine!\"\n\nJim cast a worried glance over his shoulder. She heard the howl of the Golds getting closer. \"We're going now.\" He reached out, scooped her up like she was a toy, threw her over his shoulder. His grip suffocated her. The press of his cold, dead skin was more than she could bear. She gagged on the faint smell of glycerol.\n\n\"Get off me!\" she screamed. \"I can walk!\" Though she wasn't sure that was true.\n\n\"Not this time,\" Jim whispered as he set off running so fast that the grass turned into a green blur beneath his feet. \"This time, I'm carrying you.\"\n\n# CHAPTER X\n\nCOLLATERAL DAMAGE\n\nEldredge sat in the swivel chair, facing the monitors. The huge screens dominated the ready-room wall, expensive liquid crystal displays framed in businesslike stainless steel.\n\nEvery one of them showed sickening carnage.\n\nHere was a trio of Gold Operators overturning a shuttle bus, dragging one of the passengers out through the driver-side window. There was a Gold Operator stalking out of a burning building, the crisped corpse of what Eldredge assumed had once been a person impaled on a single bone horn projecting from its forehead. As he watched, the propane tank on a parked RV exploded, the flames racing up the side of the vehicle to engulf the building beside it.\n\nThey moved like a flock of geese, the tip of their vaguely triangular formation led by the Gold Jawid had made of Chang's corpse. They forged deeper and deeper into the town, drawn by the promise of those they hadn't yet unburdened of their lives. There were too many still cowering in cellars and closets. It would be the devil's work convincing the Golds to give up the hunt and get on Schweitzer's trail.\n\nEldredge flicked his gaze to two screens set down and to the right of the rest. One was dark, reflecting his mop of white hair back at him. The other showed a pale green and orange palette of a map, flashing teardrops corresponding to each camera shot overhead, feeds from the drone cameras independently tracking the scene from ten thousand feet above. Right now, they were all clustered around a dot nestled in the broad green patch that took up most of West Virginia. BASYE, it read, or it had read before the feeds had engaged and the densely packed orange teardrops had blotted out the words.\n\n\"This is not good, sir,\" Eldredge whispered.\n\n\"No, it's not, but it's a price I'm willing to pay,\" the Director's voice replied from the speaker below the dark screen. \"The Gold teams are engaged because Schweitzer is nearby. It's just a matter of time until we find him.\"\n\n\"Sir, did Dadou . . . say anything to you?\" Eldredge's stomach tightened.\n\n\"You know she did. I brought Dadou here to find Schweitzer, and she's close to doing just that.\"\n\n\"Sir, I think her theory of an emotional link shows promise. It matches up with my thoughts about how Schweitzer located his wife and son so quickly. We need to give that angle a chance to work.\"\n\n\"Of course, but in the meantime, Gruenen's team has given us a location.\"\n\n\"An _approximate_ location, sir. Not specific enough to risk using a Gold team, let alone . . . Jesus, it looks like you used all of them. Schweitzer is west of there, and he's widening his lead every minute.\"\n\n\"I am done being played for a fool by a single Operator and his living wife and child. We should have caught them all long ago. Approximate is good enough. They have the scent now; they'll find him.\"\n\n\"Sir, they are not finding him. They are pillaging.\"\n\n\"Pillaging? How dramatic.\"\n\n\"Sir, are you not seeing what I'm seeing here?\" Eldredge swept his hand across the abattoir that had once been a Virginia resort town. \"Basye has over twelve hundred residents. Add in tourists and you're talking at least fifteen hundred.\"\n\n\"I understand this must shock you, but this is a Javelin Rain incident, Eldredge. We're authorized for whatever measures are necessary to bring things to a speedy resolution.\"\n\nEldredge bit down on his anger. The Gemini Cell had always killed. It was part of the job, what Eldredge had accepted when he'd come on board. But never in these numbers, and never at once. \"We're talking about an entire town. Of Americans.\"\n\n\"Have you been laboring under the delusion that we don't target Americans, Doctor?\"\n\n\"This isn't an American in another country. This is on American soil.\" But even as Eldredge spoke, he saw the holes in his own logic. They had targeted dozens of Americans on home soil over the years. _It's the scale. It's the scale that bothers you. It's the carelessness._\n\nThat thought was followed by another, even more chilling. _It's not the scale. Working with Schweitzer has broken something loose. The joint has come unglued for you._\n\n\"Schweitzer's last op was off the coast of Hampton Roads,\" the Director went on. \"Are you forgetting Operation Stable Hammer? That took out a city block in the most densely populated city in the country. We have to take lives so that we can save lives, Eldredge. This isn't your first day on the job. You know this.\"\n\nEldredge sucked in his breath, tried to gather his thoughts. He looked down at his lap, but the grisly scene unfolding on the screens still danced in his peripheral vision. He knew that even though he couldn't see the Director, the man was surely watching him. The thought kindled anger and resolve.\n\n\"We can't control them, sir,\" Eldredge said. \"They're animals. They go for whatever heartbeat is closest. Schweitzer's heart isn't beating. We have to do something.\"\n\n\"That's right,\" the Director said. \" _You_ do have to do something. Which is why you have Dadou Alva putting her head together with Jawid. It's your job to extract results from those two, Eldredge, and it's my job to extract results from you. The sooner we get Schweitzer, the sooner we can pull the Golds out. You seem so hell-bent on an exact location before the Gold teams are employed, so I'd like to hear your plan on getting one.\"\n\n\"Dadou is working on it, sir.\"\n\n\"How is she working on it? How exactly does this link theory of hers work?\"\n\n\"I'm not clear on that, sir. Right now I'm pretty much proceeding on a basis of 'trust me, I know what I'm doing.'\"\n\n\"I am not entirely comfortable with that basis.\"\n\n\"It's magic, sir. I'm open to ideas if you've got any.\"\n\nSilence.\n\n\"Well, you can chat with her about the collaterals after all this is over,\" the Director finally said. \"Talk to Dadou, have her and Jawid rein the Gold teams in, get them headed in the right direction.\"\n\n\"What do you plan to tell the press, sir? There's no way a massacre of this size is going to stay out of the public eye.\"\n\n\"Gas explosion. Happens all the time in these country towns.\"\n\nEldredge couldn't resist casting a glance up at the monitors, shuddered at the sight of the broken asphalt strewn with the corpses hewn beyond recognition. \"That doesn't look like a gas explosion, sir.\"\n\n\"Not yet.\" Eldredge could hear the Director's smile. \"Go talk to Dadou. Find Schweitzer. I am tired of how long this is taking.\"\n\n* * *\n\nEldredge caught himself running, forced himself to slow down.\n\nHe remembered standing outside Schweitzer's cell just a few days ago. The undead SEAL had been talking about a comic book, his telepathic projections translated through Jawid. _There was a scene where a prisoner passed a letter to another, _Schweitzer had said. _\"It is the very last inch of us,\" she said of integrity, \"but within that inch, we are free.\"_\n\nSchweitzer's last inch had been needless notions of his former life: nodding, sitting, scratching his head. Eldredge's last inch was not running to do to the Director's bidding. He breathed deeply, slowing himself to a walk and biting down on the voice in his head that told him delay was tantamount to suicide.\n\nJawid and Dadou were in the prep room, seated on one of the metal gurneys, eyes closed, thighs gently touching. Eldredge knew that for Jawid, touching a woman was a very big deal, and he doubted the Sorcerer was focused on the task at hand. It also meant that Dadou was making inroads on his affections, as ordered. _Progress._\n\nThe refrigerated units were closed, with the corpses inside. A monitor above them showed the carnage unfolding in Basye. Whatever Jawid and Dadou were doing, it wasn't focused on this world.\n\nEldredge thought of clearing his throat, stopped himself. They might be close to finding Schweitzer's exact location. He couldn't risk interrupting that. He leaned against a wall instead, thrust his hands into the pockets of his white lab coat. The coat was completely unnecessary, but the look helped calm the analysts and military members in the facility. It was better to project the image of a doddering scientist and not the brains behind a military program dedicated to developing weapons from beyond the grave.\n\nHe waited, feeling ridiculous, and finally sighed, cleared his throat loudly.\n\nDadou's eyes stayed closed, but the corner of her mouth quirked. \"We are working the _vodou_ , _Dokt\u00e8_ , but that doesn't mean we can't hear you.\"\n\nEldredge smiled, feeling his cheeks redden. \"I'm sorry.\"\n\nNeither Dadou nor Jawid moved. The bare, still room made Eldredge's skin crawl. He was at least used to seeing corpses arrayed on the gurneys. The two Sorcerers sitting silently was unnerving. \"No need to apologize, _Dokt\u00e8_. How can we help you?\"\n\n\"The Golds are rampaging through Basye, heading in every direction except the one Schweitzer ran in. I need them reined in. I need them going after him.\"\n\nJawid tensed at this, but Dadou's smile only widened. \"The Golds are not easy to convince, _Dokt\u00e8_.\"\n\nEldredge bit down on his frustration, struggled to keep his voice even. \"Convincing them is your job. This was the whole point of putting you two together.\"\n\nDadou smiled, as if at some private joke. \"We're very, very close to being able to do just that,\" she said.\n\n\"You are out of time,\" Eldredge said. \"The Golds are massacring that town. There's a pretty bad body count and it's only going to be higher by the time it's over.\"\n\nDadou shrugged. \"It is an addiction. Like rum or sleeping pills.\"\n\n\"What is?\" Eldredge asked.\n\n\"Slaughter,\" Dadou said. \"Do you like your beating heart? The warm blood in your veins?\"\n\nEldredge frowned. \"You're wasting time.\"\n\n\"Do you?\" Dadou's smile didn't waver.\n\n\"I've never really thought about it, to be honest. I guess I take it for granted.\"\n\n\"All those who do not touch the _vodou_ do, because we never have to live a single day without it. Our bodies are always warmed by blood. Our hearts always beat. When these things stop, so does our perception of them.\n\n\"But the jinn, as you call them, live thousands of years knowing the absence of both. And when they are returned, they want it more than anything. They want to bathe in blood, if only so they might enjoy the smallest reminder of life for even a moment. With time, it becomes compulsive. Like all compulsions, it eventually becomes all-encompassing.\"\n\n\"Not for Schweitzer.\"\n\nFor the first time, Dadou's smile faded. \"No, not for him. He is different.\"\n\n\"What makes him different?\"\n\nDadou's voice was cold. \"I have never touched him. But once we have him, I intend to.\"\n\n\"Well, I need you to get on that. I can't have the Gold teams ripping a hole in every human inhabitation they come across. I need you to influence them.\"\n\nDadou's smile returned. \"Your so-called jinn may be addicted to shedding blood, but that doesn't mean they don't have their own wills. I can't control them.\"\n\n\"Schweitzer could.\"\n\n\"Schweitzer is rare. Maybe even unique. And the only jinn he ever controlled was the one in his own corpse.\"\n\n\"Damn it, stop playing games. Can you get the Golds moving on him or can't you?\"\n\nDadou opened her eyes, glanced over at Jawid. Her smile faded. \"Yes,\" she said, confidence slowly dawning on her face. \"Yes, I think we are ready now.\"\n\nEldredge swallowed, found the courage to say the next words. \"Good. I'll leave you to it. I need you on this right away, and I'll need your report the moment you're done.\"\n\n\"All right, _Dokt\u00e8_. We'll get started immediately.\"\n\nEldredge paused, swallowed. \"One more thing. You're right about Schweitzer being unique. That's why I need him brought in alive.\"\n\nNow Jawid opened his eyes. \"Schweitzer is not alive,\" Dadou said.\n\n\"You know what I mean. I want his corpse returned intact and with his soul still in it.\"\n\nJawid's eyes shone with gratitude. Dadou was inscrutable. \"Those were not my orders when I was pulled from Scorpio Cell.\"\n\n\"New orders. We need him.\" Eldredge pictured the Director as a tall man in a black suit, pistol in his hand.\n\n\"Why do we need him?\" Dadou asked.\n\n\"Because we have to understand him,\" Jawid answered.\n\nEldredge nodded. \"If this program is ever going to be effective, we have to find a way to control the Gold Operators. Even trained dogs are more reliable.\" But Eldredge knew that wasn't the whole truth. _Schweitzer is a good man. Floating in that chaos for eternity is less than he deserves._\n\nDadou's face was stone, but her eyes smiled again. \"And I assume you have no objections to his wife and child being put down, also per my original orders?\"\n\nJawid turned to her, eyes widening. She put a hand on his knee, squeezed, and the Sorcerer stayed silent.\n\n\"No, they should be brought in alive as well.\" Eldredge tried to keep his voice calm.\n\n\"That will be a . . . challenging task. Some might say impossible,\" Dadou said.\n\n\"Can you do it?\"\n\n\"We can try, sir,\" Jawid answered for her.\n\n\"Try hard.\"\n\n\"Why do you care?\" Dadou asked.\n\n_Because if I have a way to keep Schweitzer united with his family, even as prisoners, I will do it. Because if I can do that, then maybe I'm not completely evil._ \"I'm working on a theory that living family members can be used as a means of control. Hostages are a crude method but often an effective one. You said yourself that love, if it's intense enough, is itself a magical bond.\"\n\nDadou didn't look convinced at all. \"I'm not certain you fully appreciate how it works, _Dokt\u00e8_.\"\n\n\"Oblige me.\"\n\n\"You're the boss.\" She shrugged. \"The Director may not be happy with this turn.\"\n\n\"I'll deal with the Director. This is my call.\"\n\nDadou nodded, and Eldredge turned and left. Eldredge knew he would have to explain his actions, but he doubted that even the Director would order Schweitzer or his family destroyed once they were in custody. Not if Eldredge could come up with a convincing-enough argument for keeping them. What he had was thin, but he would work on it. The Schweitzer family was dead either way; he had nothing to lose by trying.\n\nSave his life.\n\n# CHAPTER XI\n\nTOGETHER\n\nDadou and Jawid sat in front of the video monitor watching the pack of Golds race through Basye's burning wreckage. Chang's golden-eyed corpse ran in the lead, forming the tip of a long, narrow delta of gray flesh. Dadou had seen it before when Golds were deployed in groups. The pack followed the fastest and strongest one. She supposed it was because they thought it would lead them to the most abundant slaughter.\n\nOr maybe it was something else. She didn't know. She had never seen this many Golds in one place before.\n\n\"Well,\" Dadou said as Eldredge left. \"It seems we have a task before us.\"\n\n\"An impossible one.\" Jawid looked at his lap, eyes sad.\n\n\"Nothing is impossible.\" Dadou leaned toward him. \"We only need to try.\"\n\nHe looked up, lip trembling, eyes wide. The melodrama made her sick with anger and she drove her fists into her lap so he could not see them clenching.\n\nShe kept her voice gentle. \"Remember when I told you that magic is a conversation?\"\n\n\"Yes,\" he answered. She watched his eyes darting to the curve of her chest, back up to her face. His file said he came from a religious hinterland where they never saw a women unveiled. She had dressed accordingly, a tank top to bare her arms and shoulders, long trousers bloused into combat boots.\n\n\"We need to reach out to the _mist\u00e8_. To talk to them.\" _Keep raising the idea of conversation, of connection._\n\nIt was clearly working. Jawid's eyes were dewy with a mix of desire and admiration. \"There is no talking to them. They are beasts.\"\n\nDadou smiled, shrugged her shoulders, watching his eyes follow as her breasts rose and fell. \"Beasts can still be clever when it gets them prey or a mate. They can be devious. Do you think the _mist\u00e8_ answer our summons because they must? We _can_ force them, but it is so much harder. Better to convince them it is what they want.\"\n\n\"Yes.\" Jawid nodded. His face fell.\n\n\"Does that upset you?\" she asked.\n\n\"I promise them . . . I promise them blood if they will help me.\"\n\n\"So?\"\n\n\"It is the blood of men they want. I am promising them murder.\"\n\n\"Everyone does a thing because they want a reward. A dog will guard your house for a bone and a pat on the head. A soldier will fight for money or if you wave the right-colored flag in front of him. Is it any different to offer a _mist\u00e8_ the thing it prizes the most? You are only doing what you must, _chouchou_.\"\n\n\"They are hungry for blood.\"\n\n\"The _mist\u00e8_ are hungry for _life_. They have been dead so long that they have forgotten that living is about more than warm blood and a beating heart. With time and practice, we will teach them again.\"\n\n\"How?\" Jawid look doubtful and hopeful in equal measure.\n\n\"It is a conversation, as I said. You convinced them to follow you into the world of the living, to let themselves be Bound into a corpse. You can convince them to go after Schweitzer. This Partolan, the one you put in Chang, it is out front. It is the one we will talk to.\"\n\nJawid shook his head, a hint of flush behind his beard. _He doesn't want to fail in front me._ A good sign. \"It has what it wants. It is in the living world; it has the chance to kill. Why should it do anything I say?\"\n\n\"Because you won't be alone. Because we will go and speak to it _together_.\"\n\n\"We can do that?\" His eyes lit. \"Working magic beside one another isn't the same as working it together, truly sharing it.\"\n\nShe shrugged, tried to look bored. \"We can try.\" She forced the bored look to shift into shy uncertainty. \"That is, if you want to?\"\n\nJawid smiled. \"Of course I do. \"\n\nShe took his hand, brought it to her, careful to let the back rest on her thigh. She heard his breathing quicken, could feel his pulse racing in his hand. Too easy, really. He was like a little boy.\n\n\"I . . . I . . .\" He wouldn't admit that he didn't know what to do next. It was always this way with the deeply religious. They would rather run screaming off a cliff than confess ignorance of anything. If she didn't offer help, she would sit there, listening to his stammering forever.\n\n\"It's all right,\" she said. \"Just do what you usually do. Seek the void, and I will seek you.\"\n\nShe closed her eyes, Drew her magic about her, and sent it spiraling out into the fabric between the two worlds. The truth was that she'd never done this before either, was as nervous as he was. She didn't know if it would work, didn't know what she'd do if it didn't.\n\nBut she hadn't clawed her way out of the gutters of Port-au-Prince by shrinking from risks. Her eyes closed and the cold dark of the void settled around her, and for a moment, her stomach clenched in panic at the thought that she had lost him, that he was far away, seeing the soul storm from a different angle, and that he wouldn't be able to hear her.\n\nThen she felt his current, stronger here, more intense. It was his emotion distilled, nervousness and wonder and delight and overpowering lust. The void was as empty as ever, only the faint line of the soul storm breaking the black monotony. _Are you with me, Jawid?_\n\nHis presence beside her pulsed, invisible but as evident as if he'd been a glowing star. _I am. Allahu akhbar, I am!_\n\nShe suppressed her annoyance and laughed, trying to send him a pulse of delight. _I knew it would work. I knew it. I knew we could do it together._\n\n_Allahu akhbar._\n\n_Are you seeing what I see?_ she asked. She knew perfectly well he was, but the shared experience would help him feel a bond.\n\n_The storm,_ he answered, _in the distance._\n\nSe sa. _Can you find your jinn? The one you put in Chang?_\n\n_Of course I can. I have done this many times._ She felt his wounded pride, his need to impress, more lust.\n\nShe felt his magic concentrate, pull them forward together. She had always viewed her own connections cutting through the void as a blue lane, and she was shocked to see that Jawid's looked much the same, a ribbon of azure pushing through the uniformity and ending somewhere in the distance. She edged her presence toward the line, reaching out with her magic to dip into it.\n\nShe felt the presence at the other end instantly intensely enough to make her reel. Rage, lust like Jawid's, only darker and more urgent, and above all, a tautness, like a piano string tuned nearly to breaking, every straining atom tuned to the frequency of carnage. She pulled herself back from Jawid's connection, gasping. _That is the jinn?_\n\n_That is the one I put in Chang. It is called Partolan. It is . . ._\n\n_Strong,_ she finished for him. _But you are stronger._\n\n_You've felt it. How can you say that\u2014_\n\n_Stop it. You are a Sorcerer. You survived months with the warriors who defeated both the Russians and the Americans. You have run ops for the greatest military in the world. Whatever you need to move this Partolan, you have it._\n\nJawid hesitated. She could feel him trying to summon the courage to reach out to Partolan, failing.\n\nShe pushed her presence out toward him, pulsed an image of her hand taking his. _Go on; I am with you._\n\nHe sighed, pushed off into the channel, and Dadou went with him.\n\nInstantly, the rage and hunger slammed into her. This Partolan was powerful, both in strength and appetite. Jawid's terror was palpable. Dadou felt it instantly, could tell that Partolan felt it too.\n\n_I am the one who called you. I am the one who gave you life again,_ Jawid said to it. _You must do as I command._\n\nDadou nearly rolled her spiritual eyes. The _mist\u00e8_ were always proud, always haughty. It was exactly the wrong thing to say. She could feel Partolan's contempt come reverberating back up the link between them.\n\nIt sent an image of itself in life, a squat, naked man, so hairy that Dadou almost thought him an ape. His hair and beard were fiery red, thick and matted. Blue paint covered his skin, spiral patterns that interwove with crude pictures of men and animals. In one hand he held a primitive, copper-headed spear. The other was hidden behind a rudimentary shield, rawhide stretched over a wooden frame. _I am Partolan, father of nations. I kneel to no one._\n\nDadou had promised herself that she would let Jawid handle this, knew it would help him build confidence, but he was already putting them on the wrong footing. She had to step in. _Do not kneel,_ she sent to Partolan, _only follow._\n\nShe could feel Jawid stiffen at her intervention, but he composed himself and answered. _There is one who escaped. One like you. He flees to the west. You must go after him._\n\nDadou cursed inwardly at Jawid's use of the word \"must.\"\n\nPartolan only laughed. _Why? There is sport enough here. Why should I chase the dead when I am hip-deep in the living?_\n\n_We need him,_ Jawid said.\n\n_You need him,_ Partolan answered. _I need nothing save a spear in my hand and ground enough for my chariot to run._\n\nIf she let Jawid keep talking, Partolan would never obey them. Ancient lords respected only strength. It would do no good to hold back bargaining chips.\n\n_You will have all the spears and all the ground you require,_ she said, _but you will only have them if you help us._\n\n_And if I do not?_\n\nDadou sent an image of an American bomber flying low over the ruins of Basye, black metal cylinders plummeting earthward, a lake of fire that turned every Gold for miles into gently drifting clouds of ash.\n\nPartolan was quiet; the lust and rage were reeled back as it considered. This worried Dadou more than the rage. Thinking monsters were the worst kind.\n\n_So, then I will return to the void and wait for the next Summoner to call me forth._\n\n_You will not go back to the void if the body I put you in is destroyed,_ Jawid lied. His deception was plain in his heightened anxiety, the emotion flowing back down the link to Partolan, who only laughed.\n\n_I think you are a stupid thrall,_ Partolan sent back. _I will speak with the woman._\n\n_You will return to the void,_ Dadou answered, ignoring the humiliation emanating from Jawid, _but it may be that you will not be called again._\n\n_I will be,_ Partolan answered. _The strongest always are._\n\nHe had drifted in the soul storm long enough to know, and it didn't matter either way. Schweitzer was getting away. They needed him to move now. She had only one card to play, and now she had to play it. Dadou sighed. _Then I will give you something more, something greater._\n\n_What more could I possibly want? I am in the sunlit world. I am swimming in blood. I have rid this shell of the coward who believed he was a great warrior because he was given machines that let him strike blind men in the dark from a field away._\n\n_A dead shell,_ Dadou answered.\n\nShe could feel Jawid's emotions shift, humiliation giving way to confusion.\n\n_You can offer me a living one?_ Partolan asked.\n\n_No, she ca\u2014_ Jawid began.\n\n_I can_ \u2014Dadou cut him off\u2014 _but only if you go west and after the one we seek._\n\n_I think you are lying,_ Partolan said.\n\n_I am not lying,_ Dadou answered. _You can stay here and stop the hearts of others, or you can go west and have one beating for your very own._\n\n_And if you are lying?_\n\n_Then I am lying, and after you have taken your quarry, we will send you out to kill more, because as you have said, you are the strongest, and the strongest are always put where the fighting is thickest._\n\nPartolan was silent, considering. Jawid's emotions went sour. Shock and fear mingling with anger. Dadou ignored it. She would deal with him in a moment.\n\n_Well?_ she sent back to Partolan. _We don't have much time._\n\n_Very well,_ Partolan replied, though she could feel his excitement down the link Jawid had opened. _Where does this hunt take me?_\n\n_For now, only go west,_ Dadou replied. _We will guide you as you near him._\n\n_Make sure the . . . others . . . make sure they follow you,_ Jawid added.\n\nPartolan laughed again. _They always follow me, as the carrion crows follow an army. Because they know that is where the feast will be greatest._\n\nAnd then Jawid cut the link, the blue lane winking out, his presence pulling back from her. Dadou said nothing, only shunted her magic back and pulled herself back into her physical body, opening her eyes back in the room, the video monitor showing the delta of Golds turning, veering away from the ruins and streaming out of the town to the west.\n\n\"What . . .\" Jawid began, \"what was that? You lied to it. You can't put it in a living body.\"\n\nDadou shrugged. \" _Se sa, chouchou._ That's right.\"\n\n\"It will be angry that you lied. It will never do anything for us again.\"\n\nDadou laughed. Jawid's eyes were wide, his Adam's apple bobbing as he swallowed. \"No, dahling. Partolan will be in a living body and grateful to us for putting him there. It will be the beginning of a great partnership, just like yours and mine.\"\n\n\"But you can't . . .\"\n\n\"You're right, _chouchou_ , _I_ can't. But _we_ can.\"\n\nJawid sat in stunned silence, eyes as wide as dinner plates. Dadou suppressed a laugh, reached out, and took his hand again. \"I know this is a shock to you. I know about your work on the Virgo Cell. I know how it turned out.\"\n\nHe stammered, head shaking gently, and Dadou suddenly wished they were back in the void together so she could feel his emotions, know if she'd pushed too far, too fast.\n\n\"They were abominations. They were murders. It is one thing to put a jinn in the body of the dead, but putting one in the living\u2014\"\n\n\"\u2014is the greatest work two people can accomplish together. Look at what we just did! Partolan is a savage animal. We _turned_ it, Jawid. You and I. We went into the beyond together and we bent the monster there to our will. There is nothing, _nothing_ we can't do if we do it together. Can't you feel that?\"\n\nJawid snatched his hand back, shook his head. \"Not this. I will not do this.\"\n\nThe anger was a ball in her throat and she choked as she swallowed it down. He _would_ do it, and all of this posturing and pious angst were just wasting her time. Her hands twitched. She wanted to choke the life out of him, to shake him until his neck snapped.\n\nInstead, she took his hand again, and he let her guide it back to her thigh, rest it there. \"Very well, _chouchou_ ,\" she said. \"It doesn't matter. We have done what we set out to do; we have turned Partolan to our will.\"\n\nJawid glanced up at the monitor and Dadou saw the flicker of pride in his eyes, the twitch at the corner of his mouth. \"It was mostly you. You should call Doctor Eldredge and tell him,\" he said.\n\nShe squeezed his hand and he squeezed it back. \"We'll call him together.\"\n\nHe glanced sidelong at her, then at the floor, suddenly shy. But Dadou could tell the hook was in, and it was only a matter of reeling now.\n\nHe would help her, and soon.\n\n* * *\n\nDoctor Eldredge punched the cipher code into his office door and entered the closet-sized space, slumping in the rolling chair at his desk. The cheap wooden surface was cluttered only with papers and office supplies, the edges of his laptop monitor. There were no pictures of family, no Christmas cards stood on end. No knickknacks. _Is that why you want Schweitzer back? Because you felt a connection with him? Because he was something other than the work?_\n\nThe thought made Eldredge feel pathetic. It didn't matter anyway; whatever his motives, he had to get Schweitzer back, he had to find a way to corral the spiraling appetite of the Golds.\n\nHe reached into his waistband, pulling out the KA-BAR fighting utility knife. The weight of the weapon in his palm steadied him. He hadn't noticed his heart had been racing until he began to feel it slow. With this, he could defend himself. It wasn't much, but he wasn't completely helpless against the superhuman might of the Golds.\n\nIt also meant that, if he could just get close enough, he could find Schweitzer himself. Slim hope, but slim was better than none at all.\n\nThe chime sounded at his laptop. He winced as he pushed the button to connect, he wasn't ready to talk to the Director just yet.\n\nBut it was the ops boss on the other end. \"White, this is ops.\"\n\n\"Go ahead, ops,\" Eldredge said.\n\n\"Sir, we just got word from the eyes-on over Basye.\"\n\nEldredge sighed relief; even if the news was bad, at least ops didn't scare him. \"What's up?\"\n\n\"The Golds are surging en masse to the west. Observers report them in pursuit of one Operator, one woman, and one little boy. That's confirmed. We've got him.\"\n\nEldredge felt his stomach turn over. They didn't need links anymore. Dadou's fox hunt had begun.\n\n# CHAPTER XII\n\nPURE GOLD\n\nSchweitzer felt his wife go unconscious. He rolled her off his shoulder and into his cradling arms. Her head lolled, drool trailing from the corner of her mouth, but the pale sclera of her eyes rolled back and the pupils inside the deep brown irises fixed on him.\n\n\"It's okay, baby.\" He tried to keep the worry from his voice. \"We got out of there. We're safe.\"\n\nIt was a lie. His augmented hearing could make out the frantic padding of the Gold Operators as they hurried after him, fixed on the scent of Sarah's blood. He could feel the constricted flow as her veins dilated, her circulatory system responding to the loss of blood. Precious little was making its way to her brain He glanced down at her hip. The wound was completely open now, the flesh beneath burning hot.\n\n\"Baby?\" he asked again.\n\nShe blinked, made no response. Her eyes glowed with fever. He reached down the link that connected them, felt only confusion, exhaustion.\n\nPatrick had wandered out from the shelter of the rock where Schweitzer had left him. He'd known the boy would, had counted on him not being able to get far. He knew that racing up on his son would terrify him, but there was no time.\n\nPatrick was sobbing, walking downhill through a low thicket of berry bushes, slapping at the thorns. His face was a red mottle of poison ivy rash, the heat beneath the skin so intense that it glowed to Schweitzer's augmented eyes. The boy turned and screamed at the skull-faced gray monster bearing down on him. Schweitzer shifted Sarah back to his shoulder and scooped Patrick up, folding the boy into his mother's arms, switching Sarah back to his own. Sarah clutched Patrick tightly to her, repeating the same words Schweitzer had said to her just a moment ago. \"Oh, baby, it's okay. It's okay,\" she breathed. \"Mama's got you.\"\n\nSchweitzer tightened the muscles in his arms and chest, but his family flopped like rag dolls as he vaulted a downed log. Sarah and Patrick hunched closer as the tree branches tore at them.\n\nA whooshing sound to his right told him one of the Golds had leapt into the canopy, was pushing off a tree trunk in an effort to get ahead of them.\n\nSchweitzer came down, skidding on his heels as he tried to stay upright. The Gold Operator hit the ground in front of him, landing on its shoulder, rolling down the grade. It extended a hand, trying to stop its momentum and get onto its feet. In life, the thing must have been at least seven feet tall, with shoulders like a linebacker. Bone spikes jutted from the point of each. One of them dug into the ground as the thing began to rise, sending it into a tumble again. It stuck out a hand to change the direction, forcing it into Schweitzer's path.\n\nTo slow was to lose Sarah and Patrick, to lose everything.\n\nSchweitzer didn't break stride. He counted his steps, made sure that his right foot was swinging forward with everything he had.\n\nHe felt some of the small bones in the top of his foot snap as his instep slammed into the Gold Operator's ribs. But some of the crunching bones were not his own, and the monster launched into the air, flipping head over feet until it struck a trunk hard enough to crack it, Gold Operator and tree going over in a splintering crash.\n\nSchweitzer took long strides to keep himself upright, each one hammering Sarah as his arms shook. She screamed, and Patrick screamed with her, wrapping his arms around her neck.\n\nSchweitzer heard a snarl as another Operator galloped along behind them, reaching out to snatch at his heel, missing by inches. Rotor blades were sounding in the distance.\n\n\"Put me down,\" Sarah gasped.\n\n\"Are you fucking crazy?\" Schweitzer asked. \"They'll kill you.\"\n\n\" _You're_ going to kill me if we keep going.\"\n\nShe was right. They had to get that wound closed.\n\nA rock hammered into Schweitzer's shoulder, knocking him off-balance. He pitched into a roll, taking the impact on his head and neck, locking his core muscles to use his own bulk as a shield for Sarah and Patrick. He felt one of his cervical vertebrae snap.\n\nHe flung himself off of his wife and child, springing clear. The crack in his spine would have paralyzed a normal man, but for him it was just a footnote. The structural integrity of his back held, and that was all he needed for now. There was no time to turn to Sarah or Patrick. The thing that had thrown that rock was coming on fast, ignoring him to angle for the beating hearts of his wife and son.\n\nHis augmented hearing picked up racing wind and he knew the Gold Operator had leapt immediately after it had thrown the rock, was descending on him from above. It hit him just as he looked up, sending him rolling. Something hard and metal slapped against his thigh, spinning fast enough to burn his skin. For the living, the first thing adrenaline robbed you of was your fine motor skills. SEALs trained to compensate, emphasizing big and easy movements. They didn't waste time punching. The striking surface of a fist was tiny.\n\nThough Schweitzer no longer had adrenaline in his body, the training held, and he clubbed the Gold Operator's neck with his forearm, striking solid metal hard enough to crack his ulna and to throw his enemy off.\n\nSchweitzer rolled to his feet, clenching and unclenching his fist. The break was hairline thin; he could still use his arm. He turned to his enemy rising to its feet.\n\nHe could glimpse flashes of the slate-gray skin, the now familiar clumsy surgical stitching common to its kind, the flashes of burning gold he knew were its eyes. But most of it was covered by thick metal plate that looked bolted to the thing's skeleton, screw heads and lug nuts crowned with rust. Its left arm had been removed below the elbow, replaced with a metal armature clenched around a circular saw spinning madly, buzzing like an angry hornet.\n\n_That's for me. This thing was custom-built to cut me to pieces._\n\nBut whatever the machinery, the Operator lusted for beating hearts and warm blood. Schweitzer was cold and dead.\n\nSarah swayed on her feet, limping away, Patrick dragged along by one wrist, face chalk white.\n\nThe Gold turned from Schweitzer, the spinning blade missing Sarah by inches as Schweitzer tackled it to the ground. It bucked, snapped at him. Schweitzer held on, using his weight to pin it in place, wrist locked on the metal forearm, pushing the blade into the dirt. The buzzing muffled; dirt and rocks sprayed into the air.\n\nHe could hear the thudding of feet on earth, the speed of the intervals too rapid for living men. Other Golds, inbound. At least a klick out but closing fast.\n\nSchweitzer lifted his weight long enough to get both hands around the metal shaft that had replaced the Operator's arm. The metal bolted to the thing's body gave it the weight advantage, and it used it, pulling against him, trying to rip the spinning blade out of his hand. Schweitzer kneed it in the face, kneecap rebounding off the metal plate bolted to the skull.\n\nHe pulled with everything he had, bracing one foot against a root. There was no way to bring his training to bear now; this was a contest of raw strength against strength, and the monster beneath him had the advantage of an extra hundred pounds of metal.\n\nSchweitzer felt the saw slide an inch, another. He was losing his grip on it. The Gold Operator hissed.\n\nPatrick cried out, then Sarah.\n\nIt was unforgivable to break concentration now. Schweitzer knew he should keep his head in the fight, but he was powerless before the sound of his wife and son's voices raised in fear.\n\nHe looked up.\n\nGold Operators were cresting the rise behind them, gray shapes flashing between the tree trunks, coming closer. One was in the lead, not galloping on all fours but jogging steadily, gray-white fists clenched and pumping before its bare chest.\n\nSteve Chang.\n\nDeath hadn't changed Schweitzer's closest friend much. Bone claws emerged from the shredded remains of his hands. There was what had once been an ugly wound in Chang's side, three matching jagged holes in the opposite shoulder, all stitched shut with more care than Schweitzer was used to seeing in these monsters. Chang's head was down, the skull shaved. Schweitzer could see the top half of the eagle, flintlock, and trident Chang had tattooed on his arm the day after he'd pinned on. Schweitzer had sat in the chair next to him, waving the twenty-dollar bill he'd bet that Chang would wince before the two-hour job was over.\n\nSchweitzer couldn't remember the last time he'd been that happy to lose twenty dollars. Because it meant Chang could hack it. Because it meant they could stick together.\n\nHe knew the thing stalking toward him wasn't Chang, but he had come to know that face so well that he recognized it even though Chang's head was lowered.\n\n_Oh God, brother. They got you. They fucking got you._\n\nWas this what Sarah was hiding from him? That they had made Steve into a Gold? Steve was dead. His best friend, his brother. The closest person to him on the team. Sarah had told Schweitzer of the persistent, nagging belief that he was still alive. Had she told Steve? Had Steve gone looking for him? Had the Cell found out and . . . done this to him?\n\nThe thoughts drowned in sick sadness. Steve Chang, dead. He remembered watching the banner on the bottom of the TV screen as the news relayed Peter's death even before the Navy could send a chaplain to tell the family in person. U.S. NAVY HELICOPTER CRASHES IN AFGHANISTAN\u201417 DEAD. Peter, gone. And now Steve. A brother by birth and a brother by shared trials, both family.\n\nThe grief nearly overwhelmed him. Hope mingled with it, mad and fluttering. Because if Chang was an Operator, that meant that Schweitzer might still be able to reach him. Chang was a SEAL, as strong a man as any Schweitzer had ever known. Maybe he hadn't gone Gold? Maybe he was coming to save them.\n\n_Then why does it look like he's leading the charge? Why aren't the other Golds attacking him?_ He knew it made no sense, but his dead heart still surged at the sight of his best friend. He wanted to abandon everything, run for him, pull him into a hug.\n\n_No. That's not Steve. You are looking at a corpse._\n\nBut while Schweitzer had lost focus, the Gold Operator beneath him hadn't. With a jerk of its metal limb, it ripped the spinning saw free and lunged.\n\nFor Sarah.\n\nSchweitzer dropped his weight on the thing's arm, giving Sarah a moment to twist away, dragging her son with her, the saw swinging wide and digging into the tree trunk beside them. Schweitzer rolled off it, felt the Gold struggle to jump to its feet. Schweitzer grabbed its ankle, twisted his back and pulled. The Gold Operator spun off the ground, saw breaking free of the wood, the flat of the blade rebounding off Schweitzer's head, notching the top of his ear. The Gold Operator flew, spinning in a slow circle until it smacked into Chang and sent them both tumbling back into the pack of monsters ranging through the trees.\n\nThe shock over seeing Chang would have to keep. \"Hold on to Patrick!\" Schweitzer shouted, then scooped Sarah over one shoulder and leapt for the trees. The branches gave, but not before he was able to leap for the next one, Sarah folding herself over his back and shuddering as the sharp branches dug at her, Patrick wailing like a siren.\n\nSchweitzer's vision became a staccato of still images. Branches, tangled leaves, blue sky. He pulled them along as fast as he could, arms and legs pumping, wood splintering with each leap. The forest floor sped by beneath them, and Schweitzer lost all sense of where he was heading, focused only on the sound of his pursuers smashing through the wood behind him. Part of him railed against the lack of a plan, but SEALs also knew when it was time to throw planning to the wind, when it was time to fight like an animal. When it was time to run.\n\nMore images. Pulses of gray and pale blue. Skin taut over tight muscle. Flashes of flickering gold.\n\nSplintering from overhead.\n\nMore of them, in the trees.\n\nSchweitzer thudded into a landing on a thick bough strong enough to hold, overbalanced, let his momentum carry him forward to the ground.\n\nThe jarring landing forced a cry from his wife. \"Jim, stop.\"\n\nThere was no time to stop. He kept running, trying to lock her in place with his arm, unable to stop her bouncing regardless. He could feel Patrick crushed against his neck, the tightness in her arms as she held him there. \"Jim, I can't keep hold of him.\"\n\nHe raised a hand to Patrick, trying to pull the boy from Sarah so he could secure him under his arm. Patrick screamed and kicked, began to slip free.\n\nSchweitzer slowed to keep him from falling, and the first Gold Operator was upon them.\n\nSarah spasmed in his arms, dropping Patrick and pushing off Schweitzer's chest, breaking free as the Gold's gray tongue whipped over Schweitzer's shoulder, missing his wife by inches and wrapping around his neck instead. The Gold Operator lacked discipline and training. It squeezed, cutting off his windpipe, a futile tactic against a being that didn't need to breathe.\n\nSchweitzer reached back, pointing his fingers and punching into its mouth, feeling a long tooth scrape along his hand until the crux of his forefinger and thumb snapped it off. He grabbed the tongue at its root, yanked forward.\n\nThe thing came over his shoulder, biting down on his hand as he'd known it would. Schweitzer hooked his fingers through the golden flames, found the edges of the skull, pulled forward and down. The Gold turned in the air, slammed down on its back, ribs cracking. The sound of the pursuit drawing closer fueled a desperate strength. Schweitzer knew that the second best thing to cold professionalism was hot rage. Lukewarm was the zone where you lost the fight.\n\nHe channeled his despair into a stomp that collapsed the Gold's chest, crushing the sternum and revealing the gray edges of a heart pierced by its shattered ribs. He lifted the thing by its neck and hauled it over his head, slamming it on the ground again and again, stomping and wrenching.\n\nCrack. Crack. Crack. Bones crunching like gunshots. The thing writhed in his grip, but it was helpless to fight, first against his brutal strength and then its own steadily reducing armature, as its own bones broke into fragments. He threw the thing away, writhing as it rolled but powerless to rise. He thought briefly of the gun he'd taken from the operator on Gruenen's team, but the weapon was gone, the sling having snapped during his flight through the trees. It didn't matter. A gun would do no good against this enemy.\n\nSarah was on her knees. Her skin was chalk white, her hip a sheet of red. Her beautiful pink hair was streaked with blood, leaves, and the grime of the forest floor. _I'm losing her._\n\nCrashing, branches breaking. The Golds getting closer. Chang was somewhere at the front of the pack. Schweitzer turned back to Sarah, reaching for her. \"Get ahold of Patrick,\" he said.\n\nShe reached down with surprising strength, swatted his hand away. \"We can't. They're too many and too fast.\"\n\nShe got shaking to her feet, pushed Patrick roughly into his arms. The boy cried, reached for her, but Sarah's eyes were pitiless.\n\nSchweitzer's spiritual stomach turned over. He didn't bother keeping the panic out of his voice this time. \"Sarah, we don't have time. What the fu\u2014\"\n\n\"You're right\"\u2014her voice was calm\u2014\"we don't have time. I'm leading them away. Get Patrick out of here.\"\n\nShe took a shaking step away from him, got her legs under her, started to move more quickly.\n\nSchweitzer knew how much blood she'd lost, could feel her lowered body temperature, could hear her weakened heartbeat. He was amazed at how much strength she showed, but even Sarah at her fastest couldn't compare to his superhuman speed. He reached her in a single step, snaked an arm around her waist. \"Baby, I am not dealing with this martyr shit right now! They are going to . . .\"\n\nShe screamed, tore at his arm, flinging it off her. \"Save my son, damn it!\" He could feel the rage and desperation down the link they shared.\n\nSomething gray flashed in their peripheral vision. Schweitzer reacted instinctively, grabbing Patrick's wrist tightly with one hand and punching out with the other, snatching the incoming Gold's arm and swinging it around into a tree trunk with enough force to send the thing into the wood a half an inch. He followed with a knee hard enough to shatter its pelvis. It collapsed under its own weight, slumping to the ground, reaching out to stop its fall.\n\nPatrick yanked at Schweitzer, trying to twist away, but the boy may as well have struggled against a metal vise. Schweitzer turned his attention to the immediate threat, reaching over the Gold's head and yanking down on a thick bough, driving the splintering branch into the monster's shoulder, pushing the wood through its chest and down into its ravaged hips, until at last he felt the softer surface of the earth beneath, and the monster was staked in place. He kicked it in the ribs savagely, once, twice, until his toes passed into the hollow beyond.\n\n\"Sarah!\" He ran to her, hearing the rest of the Golds crash closer.\n\n\"Jim, for the last time, take Patrick and run! I'll get them to follow me!\"\n\n\"Sarah, no!\"\n\n\"Didn't you see Steve? He's with them.\"\n\n\"That's not Steve, Sarah. That's . . .\"\n\n\"Maybe he's like you, Jim. Maybe there's some of him left in there.\"\n\n\"You've lost too much blood; you're not thinking straight. Sarah, Steve is dead. That is something else wearing his corpse.\"\n\nHer eyes were fever bright; Schweitzer could see the dark circles under them fading to pale white from blood loss. \"He loves me!\"\n\nSchweitzer tucked Patrick against his side, reached for her waist. \"Fuck this. I am not wasting another sec\u2014\"\n\nSarah grabbed his wrist, gritted her teeth, and concentrated so hard that she screamed. The link that bound them throbbed, the dull pulse of emotions went from a thematic buzz to a sudden spike as Sarah desperately pushed her feelings for Steve Chang down the channel.\n\nSchweitzer froze, stunned.\n\nIt was the most intense burst of emotion from her yet, so strong that it evoked the link he'd been able to forge with Jawid, to plunder his memories, to learn that his wife and son were still alive. The link began to throb with memories, images.\n\nThe tangled burst surged out of Sarah: love, so strong it crackled, but not for him. Loss and need, despair so keen that it was a hole inside her, a yawning gulf opening below her, vast and black and endless, a living soul storm. The desire to feel warm and safe, desperate and heady, dull and addictive. Love, not romantic, not lustful, tangled now, lost in the fear of the void of loneliness. Tripping up her judgment, chewing away at caution, until the only thing she wanted was to not feel awful, just for a moment.\n\nSweat, moaning, flesh on flesh.\n\n_This._ This is what she had been hiding from him. Steve had come around after Schweitzer had been killed. Steve had done what a brother was supposed to do. He had taken care of Schweitzer's family.\n\n_Steve. We were supposed to be brothers; how could you?_\n\nA part of him knew he wasn't being fair. Both Sarah and Steve had every reason to believe that Schweitzer was dead. His best friend and his widow were trying to move on, build something new. If Schweitzer had been dead, he would have wanted her to find someone else, someone who could make her and Patrick happy.\n\nBut he wasn't dead, not really. Not in the way that would dull the pain of the revelation that his wife had slept with his best friend.\n\n\"I'm sorry, baby,\" Sarah whispered so softly that only his augmented hearing allowed him to make out the words.\n\nJames Schweitzer couldn't move. For all his magical might, he stood rooted to the spot, hurt burning in his silver eyes.\n\nSarah turned and ran.\n\nShe moved with incredible strength and speed for someone so badly wounded, a desperate tapping of her reserve to lead the chase away from her son. She ran with everything she had, arms and legs pumping, straight toward the pack of monsters that were finally emerging from the wood. She ran and Schweitzer stood, his spiritual nerves still paralyzed with the shock of realization.\n\nThe Golds reacted as Sarah predicted. They veered after her, ignoring Schweitzer's cold corpse and Patrick's smaller, fainter pulse. Steve Chang led them, though whether he was led by the nearness of blood, of a beating heart, or his love for Sarah, Schweitzer couldn't tell. The corpse of Schweitzer's best friend put on speed, dogging Sarah's heels, close enough to put a hand on her shoulder. And now Schweitzer found himself praying that Sarah was right, that it really was Steve Chang in there, that he was battling the jinn for supremacy of his own body, as Schweitzer had.\n\nBecause even as his paralysis broke, he realized there was no way he could reach her in time. Not now, not with Patrick in tow, not with so many enemies so close together.\n\nHe tried anyway. He crouched to leap toward her, tucking Patrick into his belly, locking him firmly in place with one arm. One of the Golds flagged behind the pack, a tall thing with impossibly long limbs, scrabbling along the ground like a spider. Bone spines sprouted from its back in looping lines that matched the curve of its ribs, covered with leaves and clods of dirt. It darted toward Sarah, saw the other Gold Operators would have made short work of her before it arrived, and turned for closer prey.\n\nIt leapt, catching the tops of Schweitzer's feet before he could clear it, sending him rolling.\n\nPatrick tumbled from his grip, got to his feet, and raced away from the fight into the woods behind them. Schweitzer rolled, came up on one knee.\n\nChang had caught Sarah, had turned her around. His hand was on the back of her neck, his head bent to look into her eyes. One of the other Gold Operators tried to surge around him, and Chang backhanded it into the brush. His other hand, the one on Sarah, looked gentle. Sarah raised her own to grip his wrist. They looked like lovers, leaning in for a kiss.\n\nMaybe she was right. Maybe Chang was as Schweitzer had been with Ninip. Maybe there was enough of him left in his own body to hold his humanity. Schweitzer's heart rejoiced, because it meant that Sarah might live.\n\nChang lifted his head.\n\nHis eyes were shining, shimmering gold. Untarnished, pure.\n\n\"Sarah!\" Schweitzer shouted. \"That's not Steve!\"\n\nBut the jinn wearing his best friend's dead skin had already started to squeeze.\n\n_No. Oh God. Sarah, no._\n\nSchweitzer screamed. A wordless, high cry. A ringing grief so keen, it cut the air. Schweitzer hadn't known he had such sounds in him. The SEAL was gone, leaving only the grieving husband, reeling in shock. The love of his life. The mother of his child. The woman he'd fought so hard to get back to.\n\nBlood shot out of Sarah's nose. Her hand on Chang's wrist pulled frantically, the backs of the knuckles purple. Her chalk-pale skin turned the same gray as the dead things pursuing her. She opened her mouth to scream, but only blood came out, thick and dark. Schweitzer heard the cracking of bones.\n\n_Oh God, Sarah._ He tensed to spring again, heard Patrick scream, the scuttling of the bug-like Gold racing over the cold ground after him.\n\nClear fluid sprayed out with the blood, Sarah's eyes glazed, and Schweitzer knew his wife was gone. The link between them buzzed, faltered, cut off. Rage and grief competed in his dead gut, his legs straining to push him after the body of his wife, to wreak useless revenge, to kill things that were already dead.\n\nThe SEAL bulled the impulse aside. _Sarah is dead. Patrick is alive. Grieve later._\n\nSarah's voice, panicked, feral. _Save my son, damn it!_\n\nThe Gold reached Patrick, grabbing ahold of his ankle. Patrick shouted, fell, twisting free of the Gold's grip, sprawling on his face.\n\nSchweitzer spun, flung himself after the insectile Gold. He grabbed the spines, hauled himself up onto the creature's back. The monster swatted at Schweitzer. Schweitzer snatched one flailing wrist, held it easily, then the other.\n\nSchweitzer slammed the Gold's wrists down, impaling both arms on its own spines. The thing flailed, rocking its shoulders, stuck fast. Schweitzer's mind chanted a ceaseless litany as he worked: _SarahGoneSarahGoneSarahGone._\n\nPatrick was up and running, heading blessedly deeper into the woods. Schweitzer made sure he had a fix on his son, then reached back, seizing one of the Gold Operator's flailing ankles. He bent it back, pulling on the leg until the knee snapped, spiking it on the spines as well. He grunted, placing one knee on the monster's head, driving it deeper into the dirt. \"Hold still, you fucker.\"\n\nWhen he was done, the Gold was bundled in a neat package, shuddering as it tried to untangle itself, broken limbs sagging under their own weight, impaled on its own spines.\n\nPatrick had disappeared into the woods, but Schweitzer could hear his son's footfalls and sobs. Schweitzer glanced over his shoulder to see if any of the Golds would follow.\n\nHe looked away before he could focus on the details, pick the lines out of the quivering red gray mass behind him. The shredded mess that had been Sarah.\n\nGrief and horror warred within him until his training locked them down. For now, he only needed to know one thing. He had a few minutes to find his son and widen the lead on the pursuit. They wouldn't be coming after him for a little while at least.\n\nThey were busy.\n\n# CHAPTER XIII\n\nPROGRAM REVIEW\n\nSenator Donald Hodges looked like he had stepped out of a library portrait. The effect was so pronounced that Eldredge half expected a gold-leaf frame to appear around the man's head. His jaw was chiseled, just beginning to run to distinguished jowls. His hair was a shellacked dollop of cream. His face was creased in a semipermanent expression of warmth.\n\nThe creases didn't reach his eyes. They were steel gray, never settling in one place for long. Now they were narrowed, watching the digital map on the monitors. Faint green lines sketched out the elevation of hills and the path of streams, dotted with dark blotches that were stands of trees. Layered over it were seven blinking gold triangles, floating as the Operators they designated moved. Four were still, covered with red _X_ 's.\n\n\"We can effect repairs on them, sir,\" Eldredge said. \"In some cases, Schweitzer broke the bones so completely that they'll need complete alloy armatures. Even then, they still may not be fully mission-capable, but we won't know until we fix them and put them back through trials.\"\n\nThere should, of course, have been a silver triangle marking Schweitzer's position, but there wasn't.\n\nThey'd lost him. All that damage, that bloody massacre, and they'd still lost him.\n\n\"Doctor Eldredge\"\u2014Hodges's voice had a slight New England aristocratic lilt\u2014\"the exact amount of the line item that funds this program is classified in channels known only to myself and the President.\"\n\n\"Yes, sir.\"\n\nThe Senator brushed some imagined dust from his lapel. \"But I want you to believe me when I tell you that it's an awful lot of money. I'd even go so far as to call it a staggering amount of money.\"\n\n\"I believe you, sir.\" _Now stop wasting my fucking time and get to the point._\n\n\"You should,\" Hodges said, not getting to the point at all. He gestured to the expensive liquid crystal screens, the ergonomic office chairs, the stainless steel and graphite furniture frames. \"We've spared no expense with your program.\"\n\nIt wasn't his program, but Eldredge figured it was best to let the overstatement pass. \"We're very grateful, sir.\"\n\nHodges looked down at him. \"Well, gratitude is always a good thing. It's nice to know one's contributions are appreciated.\"\n\n_They're the taxpayers' contributions, you self-important ass,_ Eldredge thought.\n\n\"But do you know what I like even more than gratitude?\" Senator Hodges went on, stabbing an angry finger at the screen. \"Results.\n\n\"So, perhaps you can explain to me why this . . . shall we just say more-than-adequately-funded program, is now responsible for the wholesale slaughter of a popular Shenandoah resort town, laying waste to several miles of countryside, all for the ultimate loss of a single man and his little boy?\"\n\n\"We got the wife, sir.\" The words made Eldredge's stomach twist.\n\n\"Do you think\"\u2014Hodges's mild voice slowed\u2014\"that I give a damn about the wife? Do you think we called Javelin Rain on some hippie artist from the ass end of Norfolk? Schweitzer. Where is Schweitzer?\"\n\nEldredge took a deep breath, repeated the same answer he'd been giving for over an hour. \"We don't know, sir.\"\n\n\"This is the biggest deployment of Gold Operators we've ever endeavored, supported by as many conventional operators as we can beg, borrow, or steal. He's a walking corpse burdened by a screaming child. He's in the continental United States in a specific national park. How the hell is it that your Golds can't find him?\"\n\n\"They're . . . they're animals, sir.\"\n\n\"What the hell is that supposed to mean?\"\n\nEldredge knew that he needed to pick his next words carefully, that the Director would be furious if Hodges lost faith in the program based on something Eldredge said. \"They are driven by their appetites,\" Eldredge said. \"Like dogs. They have some free will, but in the end, they go after what they want.\"\n\n\"And what is that?\"\n\n\"Blood, sir. They're addicted to the stuff.\"\n\nHodges pursed his lips. \"And Schweitzer doesn't have any blood.\"\n\nEldredge sighed, stood. \"Glycerol, sir. Keeps everything lubricated so he can move without seizing up. But if you're a Gold, that doesn't tickle your pickle, as my dad used to say.\"\n\n\"The boy . . .\"\n\n\"Is small. Fainter heartbeat, less of the stuff they're after.\"\n\n\"And you're sure of this?\"\n\nEldredge thrust his hands into the pockets of his white lab coat. \"No, sir. This is magic. Jawid's not even sure of it and he's the one using it every day. When we still had Schweitzer, he told me that the jinn were both addicted to blood as the stuff of life and angry at those who still lived for living. He said it was some kind of twisted mix of dependence and vengeance. But I don't think even he was sure, and he's not around to ask.\"\n\n\"Well, that's the crux of the matter. How the hell do you propose to get him back?\"\n\n\"More of the same, sir. We round up the Golds and have Jawid and Dadou parlay with them. We can trot out incentives to nudge them left or right.\"\n\n\"Incentives?\"\n\n\"Livestock, sir. Or convicts.\"\n\n\"Convicts?\" Hodges's lip curled. \"You mean people?\"\n\nDeath row inmates, but people all the same. The Director had only recently floated the idea. It didn't sit well with Eldredge, but he couldn't let that show. \"It's just to get their attention. We dust them off before the Golds catch up with them.\"\n\n\"Can you guarantee that?\"\n\nEldredge was quiet for a moment. \"No.\"\n\n\"I see.\"\n\nHodges folded his arms across his chest. \"Okay, so you do your human sacrifices and your Sorcerers send the remaining Golds out after him.\"\n\n\"No, sir. The Sorcerers round them up, and we lock them back down. We don't drop them in again until we're sure that we're right on top of the target. What happened at Basye has convinced me that we just don't have the control we need. I am not risking collateral like that again.\"\n\n\"Collateral happens in war,\" Hodges said.\n\n\"Respectfully, sir, this isn't a war. It's an experiment gone haywire. I have not yet looked in a mirror and faced what just happened out there. I'm putting it off until after I get Schweitzer back, because I don't want to lose focus. But sooner or later, I'm going to have to, and it's going to sting.\"\n\n\"You're not getting him back,\" Hodges said. \"You're destroying him.\"\n\n\"Sir, that is the wrong call. Schweitzer is unique. Throwing him away would be like turning your back on a gun because you prefer swords. The Golds are wild dogs. Schweitzer is a person. He is a rational, ethical, thinking person, and when you combine that with what magic has made of him, there is no limit to what he can do.\"\n\nHodges's eyes narrowed. \"Is he your friend?\"\n\n\"No, sir. He hates me too much for that. Even before he got away, he harbored resentment at not being in control of himself and his own fate. He never trusted me. But the truth is that he is a good man, probably better than either of us, and we did him wrong.\"\n\n\"We gave him a second chance.\"\n\n\"We lied to him about his family. We kept him prisoner here. Do you know what tipped the scales for him? The point when he finally pushed the jinn out and dominated his own body?\"\n\n\"Enlighten me.\"\n\n\"When he began asserting himself. When he began defying orders and saving people. When he acted less like Ninip and more like Jim Schweitzer. He's good, sir, and that's what makes him different. That's what makes him strong. I want this program to be good, so we're not going to destroy him. We're going to get him back and find out what makes him tick.\"\n\n\"You yourself have told me multiple times that Schweitzer is more powerful than any Gold Operator.\"\n\n\"Not more powerful, sir, as powerful. He combines this with a highly intelligent, rational mind that has the ability to discipline itself. He's also able to access his training and experience in a way that the Golds can't. He's not blinded by bloodlust. He can think.\"\n\nHodges waved the words impatiently away. \"Whatever, Doctor. You know what I mean. Schweitzer is more . . . dangerous than the Golds? He's a tougher adversary?\"\n\n\"Yes, sir. That's accurate.\"\n\n\"Doctor, every second Schweitzer eludes us, we run the risk of him deciding that he'd rather go in front of a TV camera than fight. He could grant interviews to bloggers, or decide to walk into the middle of Times Square. That would be a very bad day.\"\n\n\"Yes, sir. It would.\"\n\n\"I am this close, Doctor, _this_ close to just ordering that entire forest razed. Bomb it until no two stones are left atop one another.\"\n\n\"If your goal is to avoid press, sir, that might not be the best move.\"\n\nThe politician's mask fell away. \"Don't talk to me about what the best move is, Eldredge. You lost Schweitzer and now you've failed to recapture him. Even men more charitable than I might call your judgment into question at this stage of the game.\"\n\nEldredge had no answer to that.\n\n\"We are not capturing anyone,\" Hodges went on. \"We are going to pinpoint a location, we are going to cordon it off, and we are going to have a Spectre cover it with enough fire to shred every chipmunk, ant, and inchworm down there. Then we will bomb what's left. We'll chain the story to Basye, say it was another rupture farther down the same gas line.\"\n\n\"You might want to make sure there are actually gas lines running through there first.\" _Good lord. How does a man this stupid get elected?_\n\n\"Don't get cute with me. I need you to locate Schweitzer so that we can get this done.\"\n\n\"Sir, please. That's the wrong call.\"\n\n\"There is only one thing you need to know about this call, Eldredge,\" Hodges said, \"and that is that it isn't yours to make. I am done negotiating with you. I want to speak to the Director.\"\n\n\"Sir, he can be . . .\"\n\n\"SOCOM is making a power play and the Secretary of the Army is delivering a passionate argument for why his branch is the only one in the service capable of acting as the executive agent for what they're calling the 'Arcane Domain.' That means your precious program here would be dissolved. That means all your resources would be moved to MacDill. Maybe they'd let you stay on. Maybe not. You want to avoid that happening? Let me talk to your Director.\"\n\n\"The Director prefers me to handle these interactions, sir. He doesn't talk to anyone.\" _That's not true, though, is it? He talks to Jawid and Dadou now._\n\n\"That's fine,\" Hodges said. \"I'll just call my staffer and let her know that I'll be voting to give SOCOM control.\"\n\nEldredge sighed, nodded. \"Give me a minute, sir.\"\n\nHe walked down the hall to his office and took a moment to cool himself down. His desk was buried under stacks of paper, chaotic and sprawling: personnel files, budget spreadsheets, lists of equipment, and project schedules. The morning operations and intelligence briefing was still on his computer screen, half prepared for presentation to the Director the next morning. That briefing was the Director's main window on to the day-to-day operations of the Cell, the litany of tasks that, after all these years, it seemed only he knew how to do. Eldredge had lost count of how many times he'd prepared the document. The thought made him tired.\n\nHe double-clicked the shortcut labeled simply COMMS and waited. A moment later, the Director's voice whispered to him through the speaker under the monitor. \"Ah, Doctor. I'm glad you called. Did we work out the coolant contracts?\"\n\n\"Almost, sir. Entertech is negotiating the purchase, but we're having a tough time coming up with a justification for the bulk order. Entertech is well backstopped. They'll look legitimate to anyone investigating, but it's still not a good idea to make anyone suspicious.\"\n\n\"Surely there's some front technology we can claim to be using. Say it's for a nuclear plant.\"\n\n\"That's not liquid nitrogen, sir. That's helium, or molten salt, or just lots of water.\"\n\nThe Director made a strangled cough that Eldredge decided was meant to be a sigh. \"You'll figure it out, Eldredge. You always do.\"\n\n\"That's not why I called, sir.\"\n\n\"One more thing: I do want the reserve Sorcerer brought to this facility. I know he's not the best we have, but I want him on deck in case this situation with Schweitzer grows more complex. Might be we can find a way to put him to use.\"\n\n\"Understood, sir, I'll take care of it. That's still not why I called.\"\n\n\"Why, then?\"\n\n\"It's Senator Hodges, sir. He's here.\"\n\n\"I'm aware.\" The man's voice was distracted, tired. \"I trust you are handling him.\"\n\n\"He's not happy that we lost Schweitzer. He wants to talk to you.\"\n\nA pause, then: \"Find a way to put him off.\"\n\nA chill worked its way from Eldredge's balls up his spine to freeze the base of his skull. _Has he gone insane?_ \"Sir, did you hear me? It's Senator Hodges.\"\n\n\"I know perfectly well who he is, Eldredge.\"\n\n\"Then you know that he's the man who funds this program.\"\n\n\"I do. I'm not available right now. I need you to handle this.\"\n\n\"Sir. He can defund our line item. He can shut everything down. He's threatening to put us under the army, make us report to SOCOM at MacDill. In Tampa, sir. They'll make us tear everything down before we move.\"\n\n\"No, they won't.\"\n\n\"With all due respect, sir, how the hell can you know that?\"\n\n\"Trust me. Things are about to change. We're going to find Schweitzer.\"\n\nIt was a moment before Eldredge could speak. Scenarios raced through his mind. The Director was on drugs. The Director was insane. The Director was under duress. He forced himself to breathe evenly, spoke as if to a child. \"But we just lost him. Finding him means more teams out, more helos up. More gas and more bullets and more bribes to the press and police. More drones in the air and sources on the ground. All of that costs money, and Senator Hodges can make the money stop.\"\n\n\"What we're doing is more important than money.\"\n\n\"Sir, I . . .\"\n\n\"I said handle him, Eldredge. Don't make me tell you again.\"\n\nThe connection cut and Eldredge stood, balling his fists. The Director was insane if he thought he could snub Senator Hodges. _Maybe he knows something he's not telling you?_ That had to be it. Why else would he risk losing funding?\n\nEldredge was shocked to feel a sick swell of relief in his gut, mingling with the anger and frustration. An end to the program would mean he would be free of this place and this man, whose will he had served for years despite never having seen his face.\n\nIt wouldn't bring redemption, but it would bring change, time above ground, the voices of people whose names he could know, whose faces he could see somewhere other than at the office.\n\nThat wasn't redemption, but it was something.\n\nHe didn't realize how long he'd been sitting there until a knock sounded at his door. A soldier stuck his head in, face sheepish. \"Sorry, sir. The Senator said he'd been kept waiting long enough.\"\n\nEldredge spun in his chair. \"All right, I'm com\u2014\"\n\nHodges pushed past the soldier, stuck his immaculate coiffure into the room. \"Your response isn't exactly endearing me to the program, Eldredge.\"\n\n\"I'm sorry, sir. It's just that . . .\"\n\n\"I already told you that I was done talking with you. My business is with the Director; now, am I on his calendar or not?\"\n\nEldredge exhaled, looked down. \"I'm sorry, sir. He's unavailable.\"\n\n\"I see.\"\n\n\"Sir, I can assure you that . . .\"\n\n\"Spare me, Doctor. I appreciate your efforts, but I think I know everything I need to. My staff will be in touch.\"\n\n\"Sir!\" Eldredge stood and followed him out into the hall. Hodges didn't turn, didn't so much as acknowledge his presence, and Eldredge was not so stupid as to try and stop him, to do anything more than watching his receding back as he entered the elevator that would take him to the helo hangar, where his bird back to Washington was spun up and waiting.\n\n# CHAPTER XIV\n\nON TO THE LIVING\n\nDadou slid closer. The touch of her thigh against Jawid's own horrified and thrilled him in equal measure. He had grown used to voices inside his head. The magic brought them, the sorcerous link that conveyed both emotion and language between him and the souls of the dead. But there were other voices too, his grandfather Izat for one, who had been the ulema, the religious leader for the small cluster of huts that clung tenaciously to the slowly shifting rock face where Jawid had grown up. They had held on for generations until the _Talebs_ had fired their mortars into them. Thousands of years undone in an instant. Izat had lost his life then, but Jawid still heard his voice now.\n\n_And come not near unto fornication. Lo! it is an abomination and an evil way._ Jawid could hear the old man's voice as if it were he and not Dadou who sat beside him, leg brushing his own.\n\nThat village had seemed the whole world to him all those years ago. Jawid knew better now. All those huts, the goat paths and the mosque, the wells and even the trampled field where the men played _buzkashi_ could all fit in one corner of the squad bay where the Gemini Cell kept its helicopters. Jawid didn't know how many levels the underground complex had, but he knew he could have fit ten of his villages in just one of them.\n\nThe world was so big, and there was so much that his grandfather hadn't even imagined. _Do not let the infidels blind you. Follow the way of those on whom Allah has bestowed His grace, not of those who earned His anger, nor of those who went astray._ Jawid supposed Izat spun in the soul storm now, his admonitions mixing with the regrets and misdeeds of millions of others across time. All the prayers and all the studying and all the righteous living made no difference. Jawid had clung to the belief that only bad men went there, the sort of monsters that he called back into the corpses of the newly slain. Ninip, Partolan, an ancient archer who called herself Hippolita. A part of him, deep in his heart, knew this was wrong, but he had believed it with a stubborn faith that allowed him to do his work.\n\nUntil Schweitzer.\n\nAnd if Schweitzer had gone to the soul storm, then _all_ people must go to the soul storm, the Muslims and the unbelievers, the righteous and the wicked. Every last one.\n\nJawid inhaled Dadou's smell: soap and roots, clean and earthy. She was not a Muslim. He did not have his parents' permission. But the world was vast and complicated beyond anything the wisest men he had known had ever imagined. Surely, God would not judge him harshly for loving her.\n\n\"Look at those curls.\" Dadou hooked a long finger in a lock of Jawid's thick black hair, gave it a tug, laughed as it sprang back. \"Boink.\" She pulled again, released. \"Boink.\"\n\nJawid's head felt as if it were stuffed with cotton. He was stiff beneath his robes, worried she might see, wanted her to see. \"It's too long\" was all he could manage. He sounded like he was gasping. Because he was.\n\nShe laughed again. \"You're so cute.\"\n\n\"I like that you laugh.\" He almost never saw women back home, and when he did, they were shrouded in burqa. They could have been laughing uproariously or weeping fit to fill a valley and he would never have known. The women here had men's names and never even smiled.\n\n\"That's what you like? When a woman laughs?\" Dadou sounded surprised.\n\n\"There isn't a lot of laughing here.\"\n\n\"Plenty of cryin' to be done in our line of work, dahling,\" Dadou said. \"You make hay while the sun shines.\"\n\n\"Do you like our line of work?\" Jawid asked.\n\nDadou shrugged. \"You want to talk about work now? I thought we were talking about you.\"\n\nJawid's cell seemed close and dark, his bed impossibly small. But it was private enough, and Eldredge had been giving him more of a free hand lately.\n\n\"I don't understand this.\" He turned to her. \"You are a . . .\" He couldn't bring himself to compliment her beauty; he didn't understand how men did it. He knew he should recite poetry, compare her to a flower or a jewel, but his head was spinning with the nearness of her and he couldn't find the words. \"You are . . . different. I don't understand why you are touching me . . . talking to me. Because you like my hair?\"\n\nDadou laughed a long time. Jawid didn't like this laughter. It felt harder. It bled the softness, the quiet intimacy out of the air. He felt his cheeks flush, tried to smile along with the joke. Failed.\n\n\"Oh, _mon petit chouchou_ ,\" Dadou said. \"Don't be angry. I'm not laughing at you. No, it's not just the hair. Though it is pretty.\"\n\n\"What, then?\" Jawid had always believed that he would first see his wife on their wedding day. The look he'd stolen at Anoosheh had almost cost him his life. She would also be seeing him for the first time; whether he was beautiful or not would not be at issue. If he was, he wanted to know; he was hungry to know, to hear her say it.\n\nDadou paused, sighed. Her eyes were huge, the pupils blending with the dark irises, so big that the sclera drowned in them, tiny slivers of white in an ocean of black. \"Have you ever met another person with the _vodou_ , Jawid?\"\n\nThe loneliness in her voice evoked it in his own heart. \"No,\" Jawid answered, his voice thick.\n\n\" _Se sa._ I don't know how I knew there must be others out there who were like me, but I knew. Maybe it is because of the _mist\u00e8_ , how we link to them and they to us. It is a . . . community, _non_? But I never met anyone. You can feel it when it is real. The _vodou_ has a touch.\"\n\n\"Like standing in a river, only it flows through instead of around you.\"\n\n\" _Se sa_ ,\" Dadou said again, \"only the river comes from you, and you can feel it coming from others. But I never did. I always searched for it, but I never found it. After a while, I started to wonder if I would be alone forever.\"\n\nJawid only nodded. How could this be wrong? She _knew_ him.\n\n\"And then the Americans came and took me,\" Dadou went on. \"Do you remember when you first came here? Everyone is so rich! Then I finally did meet others with the _vodou_ , but it was only to kill them. Once, I ran an op on a _S\u00e8vit\u00e8_ who used a homeless shelter as a cover. Most of her charity cases were dead.\"\n\n\"She was like us? A Summoner?\"\n\n_\"Non.\"_ Dadou shook her head. \"This was different. She did not call the _mist\u00e8_ as we do. She did not venture into the beyond. She simply made the dead stand up and walk. They only moved by her will, not their own.\"\n\n\"A Necromancer, Doctor Eldredge calls them.\"\n\n\" _N\u00e9cromancien._ That's what we call them back home. Even then I was alone. I couldn't even find someone like me to fight.\"\n\n\"You killed her?\"\n\n\"I sent my _s\u00f2lda yo an l\u00f2_ , my 'Gold Operators,' to deal with her. Against them, her creatures had no chance. Even among the dead, it is better to be clever than stupid.\"\n\nShe paused, turned her head to look at him, and he could feel the current flowing from her, a liquid note of kinship. Here was someone to whom he need make no explanation. She would just understand. How could Allah oppose this? How could this be sin?\n\n\"All my life, I have never known someone who could understand,\" Dadou went on. \"I have never thought I could have a family of my own. Not a brother or sister, certainly not a husband. I didn't even know I could have a friend. Back home, everything was family. Now there is nothing. So, yes. I like your curls, and I like your eyes. I like how you are a grown man, but you shake and stutter like a little boy. But most of all, I like that you _know_ what it is to live like this. I think this is part of why the program has put us together. They are not stupid. They know what we want, and they think by giving it to us they can keep us loyal.\"\n\nJawid felt as if he were floating. He could feel bubbles in his blood, so heady and intoxicating that he could no longer distinguish between the magical current and the giddiness brought on by Dadou so close beside him. \"And what do you think?\" he husked.\n\n\"I think,\" Dadou answered, \"that in this one case, I am happy to be their puppet.\"\n\nShe leaned in. Jawid knew he was supposed to do something. He had seen enough infidel television and movies, but the truth was that no one had taught him, and it was one thing to know how people did a thing, and another to have practice.\n\nBut Dadou didn't mind. She giggled, whispered at his stiffness. \" _Se byen, chouchou._ Let me drive.\"\n\nJawid was glad, because he wasn't sure that he could move under his own power now, anyway; the bubbles in his blood had made him weak, and the floating sensation was now competing with terror. What if he was clumsy? What if it made her change her mind? Made her laugh at him? And there was Izat and Allah Himself, shaking their heads in disappointment. _An infidel,_ they said, _and you unmarried._\n\nDadou's lips met his, and they were soft, the smell of her blotting out his senses. He could feel her dreadlocks brush his nose, his chin, his chest. He tried to return her kisses, but pursing his lips didn't seem to be what she wanted. She kept pulling away, then darting back in, following some rhythm that he couldn't understand. He raised a hand tentatively to the small of her back. He desperately wanted to touch her legs and her breasts, to plunge his hands into her hair, but his arms would not obey him. He was so terrified to do it wrong. He could not bring himself to think of Dadou as a wanton, but she knew so much more than him. At last she reached down, grasped his wrist, brought his hand to her breast. She was so soft, so beautiful. Shocks ran up his arm, as if he had touched a live wire. He left his hand there as she dropped hers, not knowing what to do, afraid to ask.\n\nDadou paused. \"This is your first time?\"\n\nIt was a simple question, but Jawid could not bring himself to answer.\n\nShe lifted her hand to his again, squeezed. \"Like this,\" she said, her breath coming ragged. \"Not so hard.\"\n\nJawid felt his hand move under her own, the whole world vanishing save for the softness of her beneath his touch. \"I'm sorry,\" he said before he'd known that he'd spoken.\n\nDadou laughed, kissed him again. \"Don't you worry, dahling. Mama Dadou will teach you everything you need to know, and the first thing you need to know is never to say you're sorry.\" But he couldn't help himself. Jawid apologized again and again as they fumbled through the act, wincing internally each time.\n\nIzat's voice was clear in his mind. _When you enter upon your wife, you have first to perform two rak'ats and then hold your wife's head and say, \"O Allah! Bless my wife for me, bless me for my wife, give her bounty out of me, and give me bounty out of her!\" Then you can do what you want._ But Dadou was not his wife, and the moment they shared seemed to be made of spun glass, as though any interruption might shatter it.\n\n\"I'm sorry,\" he said again, cursing himself even as he said it. This time, it wasn't even for her. It was for Allah and Izat and Anoosheh. He was weak, and he was lonely, and he knew that he would be judged anyway.\n\nDadou stayed on top of him, his hand still crushed to her breast. His back had begun to ache, and he realized he was clenching his body so tightly that the muscles were hard as rock. He tried to relax, tried to stop his mouth from moving, but he failed and he failed, and in the end, he said \"I'm sorry\" again.\n\nDadou stopped him with a kiss, easing her hand down into his trousers, grabbing his flaccid penis, squeezing it, pumping it. \"It's all right, dahling,\" she breathed over and over, \"it's all right.\" Only now Jawid felt his face flush in humiliation. When he touched himself, when he thought of her, of nearly any woman, he had always been rock hard, but now the one time that it mattered, his manhood was as soft as the cushion of Dadou's breast. _Will she think I am unmanned? Am I unmanned? Will it never get hard again?_\n\nBut Dadou squeezed tirelessly, leaning down every so often to kiss him. He was getting a little better at that, parting his lips just enough to admit the tip of her tongue, bringing them gently together each time she pulled away. After what seemed like forever, his penis felt rubbed raw, but it was a little harder, at least.\n\nDadou stood, slid her trousers down to her knees. The curve of her was all hard muscle, only the faintest hint of the edge of her hip rippling over the bone beneath. A wicked scar, thick and badly healed, ran from the side of her buttock down her thigh before winding its way behind her knee and out of sight. The evidence of rushed, rough stitching made him think of the Golds, and then his penis was soft again, but by then Dadou had mounted him.\n\nShe spat in her hand, a harsh sound, massaged it into her cleft. She guided his limpness into her, but it was so dry that she winced, and spat again, and again, rubbing and rubbing until there was enough wetness to get him inside by dint of sheer pushing.\n\nAnd then the thought that he was doing it, actually making love to a woman who was not his wife, overwhelmed him. He had thought it would be the physical feeling, but it was something else. The knowledge that he defied Allah and his parents and the millennia of tradition that he had felt as heavy as the mountainside he'd grown up on, it was so incredibly, deliciously _wrong_. The thought set a fire in his loins, and before he knew it he was harder than he'd ever been.\n\nDadou grunted. She rocked back and forth, moving her hips like a saw. She closed her eyes tightly, concentration on her face. The workmanlike look diminished his own arousal, but the motion and the thought could not be denied, and within seconds, the pressure in him had built to a flood, and he slapped his palms on the bed, gripping the sheets tightly.\n\nHe cried out, feeling like the whole world, all his magic and all his soul and everything in him was letting go inside her. She was looking at him now, her movements slowed, satisfaction in her eyes. \"That's good, _chouchou_ ,\" she said. _\"Li bon.\"_\n\nAnd then it was over, and he lay flat on the bed, all his muscles unclenching. A voice was chanting, \"I'm sorry, I'm sorry, I'm sorry,\" over and over and over, and it took him a moment to realize that it was him. He closed his eyes, was amazed at how suddenly tired he was. All he wanted to do now was sleep.\n\n\"You don't have to be sorry,\" Dadou said. \"You've done nothing wrong.\" But he kept saying it, couldn't stop.\n\n_Will she get with child?_ he wondered, amazed at how the thought both delighted and terrified him. Surely Allah would judge him less harshly if a son came from all this?\n\nAnd suddenly his heart was full, swelling fit to burst out of his chest. He sat bolt upright, wrapping his arms around her, burying his face in her chest, breathing in her smell. He felt himself going soft inside her, fluid leaking out around him. It slid down his abdomen, soaking the sheets. He knew that seed staining his clothing made him impure in the sight of Allah, was fastidious about cleaning when need and weakness compelled him to touch himself. But now he didn't care. He loved this woman; they had joined. She would be his wife. He didn't care that she was an infidel; he didn't care that they had joined outside marriage. He didn't care about anything except for her.\n\nTears streamed down his cheeks and he pulled her close. Dadou's back went stiff. He could feel her pulling gently away. Perhaps she was frightened, but he would set her at ease. They could not have done what they had just done and not have love come of it. It was too wonderful, too magnificent. He gripped her more tightly.\n\n\"Gah,\" she gasped. \"Easy, _mon cheri_. You are going to break my ribs.\"\n\n\"I'm sorry,\" he gasped, releasing her to cuff away a tear, kissing the tops of her breasts. \" _Allahu akhbar._ That was wonderful.\"\n\n\"I'm glad,\" she said, touching his hair awkwardly. Of course. She was frightened. Loving someone was a frightening thing.\n\n\"I was betrothed,\" Jawid said, \"but now it is you. I love you, my Dadou.\"\n\nHe felt her ribcage hitch against his face, her belly spasming. She was crying too; it was too much for her to hear him say it. He strained his ears to hear her say the same things to him.\n\nA dry coughing, staccato barks from the back of her throat.\n\nLaughter.\n\nDadou disentangled Jawid's arms, putting a hand gently but firmly on his throat, pushing him back down to the bed and sliding off him. The thin mixture of her saliva and his seed ran down her thigh, ignored. She grinned at him, but the smile didn't reach her eyes.\n\n\"Love?\" she asked. \"You are too kind to me, Jawid.\"\n\nJawid tried to look stern. He was a man. It was not for her to deny how she felt. He opened his mouth to refute her, but the words felt childish even as they formed in his head, so instead what he said was, \"After what we have done . . . we must be married.\"\n\nDadou stared at him. \"Married.\"\n\n\"It is what is right,\" he said, aware of how petulant he sounded, at a loss as to how to sound any other way.\n\n\"Married.\" She swallowed. She was trying to contain something. She was struggling, too. It was so sudden, but it didn't matter. They didn't have the luxury of families to match them, of a common faith. Jawid had felt her magical tide flowing around and through him; he knew he would never feel that again with anyone else. \"What is right,\" she said, \"depends on where you stand.\"\n\nJawid's stomach felt as if it was packed with ice. The swelling in his heart reversed itself, became a violent contraction. \"You don't know what is right. People cannot do what we have done and then just . . . just . . . go on. This is God's will.\"\n\n\"God's. Will.\" She bit off each word, and the look in her eyes made Jawid suddenly afraid. He remembered their first private conversation together.\n\n_You've killed?_\n\n_With my own hands,_ chouchou _._\n\nWho knew what she could do? What she would do? _Don't be ridiculous. She is still only a woman, and now she is yours. She only needs time to understand._\n\nDadou drew a deep breath, closing her eyes. When she opened them again, the anger was gone. \"I am . . . not sure I am ready. This is . . . sudden.\"\n\nHe stood, took her hand. It felt hot, the muscles in her fingers stiff. She twitched, as if she meant to pull away from him, stopped herself. \"This is not a thing one waits for,\" he said. \"We are _joined_ ; don't you see? What if a child comes of this? Will we raise it like an animal? We must marry.\"\n\nAt the word \"child,\" Dadou's eyes snapped back to him, the simmering anger more intense than before. \"I will consider this,\" she said. \"I just need time.\"\n\n\"Time for what? What can I do to sway you, my love?\" His heart was suddenly full again, and he choked on his tears, throwing his arms around her neck. She was as hard as iron, unmoving. He didn't care; he loved her. \"Ask me whatever you need to be sure. I will do anything.\"\n\nShe reached up and broke his grip as easily as if he were a child, pushed him back until his legs hit the bed and he sat down hard. The anger in her eyes had been replaced by a coldness that frightened him more. \"Anything.\"\n\n\"Anything,\" he nodded, love and terror mixing in his gut.\n\n\"I need your help with . . . some work.\"\n\nSick relief washed through him, making Jawid's knees weak. Part of him was disgusted at himself for wanting this conversation to be over, for being frightened to push her on the matter. He was the man, and what they had done made Dadou his tilth, his fertile field. _Go to your tilth as you will,_ the Qur'an said. She was his now. She would come to see it; he would make her.\n\nBut not now. Maybe not just yet.\n\n\"What work?\" he asked, disgusted at the quaver in his own voice, hoping against hope that she wouldn't hear it.\n\nIf she noticed, she gave no sign. \"The most important aspect of our work,\" she said. \"This is big, bigger than anything we've done before.\"\n\nHe felt his eyes narrow. A part of him mourned the loss of the conversation about love and marriage, the other part of him was roused by curiosity. \"What do you mean?\"\n\n\"I'll show you,\" Dadou said, taking his hand and pulling him up, leading him to the door.\n\n\"No,\" Jawid said. \"We have . . . joined. We need to wash. We are unclean.\"\n\n\"We can do it later,\" she said. \"I know what you smell like.\"\n\n\"It's not the smell,\" he said, \"it is ritual impurity; the Qur'an says that . . .\"\n\nDadou stopped short, her shoulder suddenly immovable, so that he bounced off her and staggered back a step. \"I do not read your Qur'an. Do not mistake me for a Muslim. Back home, many people mistook me for a Catholic. These assumptions are . . . not helpful.\"\n\n\"We must,\" Jawid said, dropping her hand and heading to the bathroom. \"Come.\"\n\nHe saw the struggle behind Dadou's eyes, the two Dadous, one murderously angry and the other warmly smiling, doing war with one another. At long last, the smiling Dadou won and she sighed. \"All right.\"\n\nShe suffered through his prayers and even consented to wash herself. She let him lead her to the bed and draw her down next to him. \"I love you,\" he said, and she didn't answer, but she put one hand on his head and traced circles in his chest hair with the other. He floated on the tide of joy and contentment, feeling the sparks through his whole body at her touch, his eyelids slowly growing heavy. He snuggled his face into her chest and shut his eyes. Not to sleep, just to inhale her smell and feel her softness against him.\n\nBut he knew he had slept for hours when he finally opened them again. The softness of Dadou's breast had been replaced by the firm cushion of his pillow. She was standing, looking at him, as if she had been waiting for him to wake the whole time.\n\nJawid opened his mouth and the danger returned to Dadou's eyes. \"You said you would do anything,\" she said. \"Did you mean it?\"\n\nAnd then she was pulling him along again, and even though she frightened him, he was grateful, because the touch of her hand meant she still loved him, meant that he hadn't dreamed what had passed between them.\n\nShe led him into the stairwell and took him down several winding flights, down a bare corridor lined with doors. The facility was big, but Jawid had been here a long time, and while he had been down each corridor at least once, they all looked the same. White, sterile-looking cinder-block walls, stainless steel doors with keypad locks above each handle. At last, they came to a door with a red sign engraved with white lettering: RESTRICTED AREA WARNING: IN ACCORDANCE WITH THE PROVISIONS OF THE DIRECTIVE ISSUED BY THE SECRETARY OF DEFENSE ON 10 DECEMBER 2005.\n\nDadou turned to Jawid, put a hand on his shoulder. The touch felt intimate at first but soon tightened painfully. \"This task comes to us straight from the program director. It is not from Doctor Eldredge. He does not know about it and you must not tell him.\"\n\nJawid's mind filled with questions. She had talked to the Director? When? How? Jawid had heard Eldredge mention him, but never anything beyond that. Why couldn't they tell Doctor Eldredge? Eldredge was his jailor, but he had been kinder to him than anyone. But the dangerous look was in Dadou's eyes again, so all he did was nod, swallowing.\n\nDadou gestured back to the sign: UNAUTHORIZED ENTRY IS PROHIBITED. ALL PERSONS HEREIN ARE LIABLE TO SEARCH. PHOTOGRAPHY OF THE FACILITIES IS PROHIBITED WITHOUT SPECIFIC AUTHORIZATION FROM THE COMMANDER. _DEADLY_ _FORCE IS AUTHORIZED_ _._\n\nJawid felt the muscles in his back cramp, a chill rippling beneath them as a bead of sweat worked its way from the back of his neck to the top of his buttocks. Dadou keyed in the code, the lock beeping and clicking open. She turned the knob and dragged him inside.\n\nThe room was simple enough, an old freeze-burn cell of the sort they used with Operators. The scorch marks on the wall had been painted over sloppily, the smell of the drying paint still lingering in the air.\n\nA single recessed fluorescent light shone down on them from the ceiling, the plastic cover partially melted and streaked with cleaning fluid where some enterprising soul had tried to scrub off the soot before finally giving up.\n\nBelow it was a padded chair like the one the post dentist had Jawid lie in when he worked on his teeth. It had straps over the legs and arms, wide and strong-looking, with shining metal buckles.\n\nA man struggled against them. He mumbled around a ball gag, powerful muscles bulging as he pushed against the straps fruitlessly. One eye was blackened, a lump rising just below his forehead. Jawid had seen enough gunshot wounds to recognize the hole in his shoulder. It was dressed, gauze soaked with still-moist red going brown around the edges. Whoever this man was, they were trying to keep him alive.\n\nDread blossomed in Jawid's stomach. He knew what the work was now and why Dadou had brought him here.\n\n\"Our new work is the same as our old,\" Dadou said. \"Only the vessel is different. It should be easy.\"\n\nJawid stared, nausea rising up his throat. He looked at this woman that mere moments ago he had thought he would marry, and shuddered.\n\nA man. Not a corpse. A living man.\n\nThey were going to put a jinn in him.\n\n# CHAPTER XV\n\nALL THE DEAD CAN DO IS PROTECT\n\nSchweitzer ran.\n\nPatrick bounced in his arms, no longer screaming. The boy had tripped over the line of terror and sadness into a pale-faced silence, meekly accepting the rough ride of Schweitzer's panicked gait.\n\nSchweitzer was just as numb. _You turned and ran while monsters killed your wife._ From what little he'd seen, there hadn't been anything left bigger than a softball.\n\n_Oh God. Sarah._ He pushed the vision of the red ruin of her body aside, only to find it replaced with memories of their life together. Applauding from the audience as she'd stood to accept the Best New Artist award from the Tidewater Chamber of Commerce. They'd made love in his car that night, so blind with passion that one of them had kicked the window out.\n\nHe remembered kneeling on the deep pile of the kitchen throw rug, his head in Sarah's lap as he shook and cried, the phone swinging by its cord, sentenced to hang after delivering the news that cancer and grief over Peter's death had finally taken his mother's life. His brother and his mother, just months apart. _I can't be strong right now,_ he'd sobbed.\n\nShe'd run her fingers through his hair, letting her hand drop to the back of his neck. _You don't have to be, babe,_ she'd said. _I can carry us until you're ready again._\n\nIt was one of the rare times Schweitzer ever fully gave himself over to another human being. It had taken him the rest of the night to get it together, and he had never felt so safe. She had his six. She wouldn't let him fall.\n\nHad he told her how grateful he was? He couldn't remember.\n\n_You're a coward._\n\n_No. You ran because she told you to._ He'd run because she'd told him to save their son.\n\nHe slowed, dialed out his hearing, listening. He could hear the helo rotors still in the distance, vainly circling above the canopy where the fight had gone down with the Golds, no doubt searching for him. He'd opened up a good-enough lead on them while they were busy with Sarah.\n\nShe'd bought him the time he needed. He had to make good on that.\n\nHe looked down at Patrick, pale as death save for the puffy red blotches on his face and arms, his blond hair so streaked with dirt and gore that it looked black. The boy was terrified of him. He would only respond to his mother. He needed her.\n\nSchweitzer needed her too.\n\nSarah's body had been destroyed, which meant her soul would be in the void even now. His link to her had helped him find her in life, would it in death?\n\n_Just a quick second,_ he told himself, _just to see._ He had let her die. He had watched her die. He needed to tell her he was sorry. _You should have saved her. You should have found a way._\n\nSarah was the strength he'd drawn on to do the dangerous work of a SEAL, and the lifeline he'd followed out of the Gemini Cell's facility and back into the sunlit world. Their love was a thing so strong that it was a magic in and of itself, a bond that linked them through death and time and distance.\n\nA part of him, the cold professional who carefully weighed risk and outcome, stayed focused on the mission, knew there was no good reason for this. Schweitzer couldn't bring her back to life, had no way to comfort or even communicate with her in the chaos of twisting souls.\n\nBut that part of him was crushed under the heel of the other part, the husband and best friend, the man who had known and loved Sarah from the moment he'd met her. That part of him had to see her in the beyond, just to know, just to . . . _just to say goodbye. You didn't thank her enough. You didn't tell her what she meant to you. Not clearly enough. Not nearly often enough._\n\nSchweitzer had felt the pull of the link between them even when he'd thought her dead, and he still felt it now. It pointed into the darkness of the void, the place where Sarah now tumbled, sucked into the spinning chaos of the soul storm.\n\nSchweitzer turned his focus inside himself, felt the darkness at the edges of his physical form, pushed out into it. The cold of the void wrapped itself around him. He felt the edges of his own body slip past and recede.\n\nSchweitzer felt the undertow of the soul storm, slowly reeling him in, hungry and grasping. He pushed against it, holding his position, keeping a watchful inner eye on his own body in the distance. He concentrated, reaching out for Sarah's presence, trying to feel the link that joined them.\n\nThere it was, so faint he could almost miss it. Sarah's distilled soul, always coming to him in the same way: the touch of her rosewater perfume, a phantom scent he could follow to its source. He inhaled deeply, filling spiritual lungs with the fragrance. It grew stronger as he went, clearer, until he could almost see the edges of the stream, the smell leading arrow-straight into the storm.\n\nThis close, the screaming was deafening. Schweitzer's spiritual ears pulsed with the chorus of shouts beginning to move past mere hearing, speaking directly into his mind. A litany of battle cries, regrets, and last testaments. Schweitzer felt them chipping at the edges of his consciousness, trying to suck his identity into the tangle, desperate to turn it over and over until he didn't know who he was anymore.\n\nSarah was somewhere in there.\n\nSchweitzer pushed deeper, hauling himself up the trail of his wife's perfume, calling her name. He was forging too far, too deep. The undertow had seized him, was pulling him deeper and deeper into the throng.\n\nA part of him didn't care. He was desperate to reach Sarah, no matter what the cost. He snarled, pushed on. But the other part of him, Schweitzer the SEAL, forced him to slow, to push back. _You're no good to Sarah, to anyone, if you get lost in this morass. Withdraw for now. Come up with a plan. Come back when you're ready._\n\nThe thought of Sarah screaming and tumbling in the maelstrom almost made Schweitzer continue, but then his own voice put the hammer down. _No good to Sarah. No good to yourself. No good to Patrick._\n\nPatrick.\n\n_Save my son, damn it!_\n\nSchweitzer turned back, following his own sense of self back into the limits of his body, feeling the void shrug off and reality snap into place with a ringing that sounded in his ears.\n\nNot ringing, crying.\n\nPatrick was sprawled on his face, nose bleeding.\n\nHe'd dropped him. He'd been so focused on exploring the void that his body must have relaxed. He'd dropped Patrick on his face.\n\n\"Oh, my god. Oh, Patrick. I'm sorry,\" Schweitzer knelt and scooped up his son, dusting the dirt off his face, checking the scratches. \"You okay, little man? Daddy's sorry. Daddy's so sorry.\"\n\nHe'd had years to build a bond with Sarah, something that could sustain their relationship in times of trouble. He'd had far less time to build it with Patrick. Their relationship was truncated, stopped cold the moment the men who'd murdered Schweitzer had entered his home. His uncle Peter was dead. His uncle Steve was dead. Now his mother was dead. All the warm hearts and kind faces who were ready to teach Patrick how to be an adult, all snatched away before the boy was old enough to appreciate how much he needed them.\n\nPatrick sniffled, but the crying stopped. _He's getting used to me. He's starting to realize that just because I look like a monster doesn't mean I am one._\n\n\"Want Mommy,\" Patrick said, cuffed at the poison ivy rash on his face.\n\nSchweitzer folded him to his chest. \"Me too,\" he said, feeling tears that would never come, the rigidity of his tear ducts, dried and hardened. The grief threatened to swamp him. His chance to be a father to Patrick had been stopped before it really started. They had no relationship beyond Schweitzer's duty to keep him safe and alive. \"I want Mommy, too.\"\n\nHe looked back down at his son, filthy, scratched, and with a serious case of poison ivy. He'd lost Sarah. He wasn't going to lose Patrick, too.\n\nAnd the boy would never be safe at his father's side. Not now.\n\n\"Okay, pal,\" he said, scanning their surroundings, dialing his hearing out for the sound of a neighboring road, a town, even a group of hikers.\n\n\"Let's get you fixed up and then find some place safe for you.\"\n\nThough where that place was, Schweitzer didn't know.\n\n* * *\n\nIn the end, Schweitzer broke into a convenience store.\n\nHe waited for Patrick to fall asleep, then tucked the boy over his shoulder and moved silently down into the parking lot, where he made Patrick a bed of cardboard and plastic bags. \"Just for a sec,\" he whispered, more to himself than his sleeping son, and stood.\n\nPatrick huddled, ragged and filthy, in the nest he'd built. His Tiny Tim, his beggar boy. _Oh God, Patrick. I've failed you._ And now he was walking away, leaving his child alone in the dark like an after-school special.\n\n\"I don't know what else to do,\" Schweitzer whispered aloud as he jogged over to the drugstore loading dock, tried the handle of the rusted blue door. The SEAL in him had replaced Ninip as his partner in internal dialogue. _Parenting is for the living. All the dead can do is protect._\n\nThe door wasn't alarmed. The tight-knit relations of a small town were enough to deter most of the crime. It was hard enough to steal from a stranger, and in these little hamlets, everybody knew everybody. For those who could overcome the instinct to do right by one's fellow man, a stout lock did the job.\n\nBut Schweitzer didn't know anyone here, and his magical strength twisted the lock off its mounting like it was soft clay.\n\nInside, darkness shrouded the stainless steel racks of greeting cards, laundry detergent, and shampoo in orderly rows. He remembered corpses in the same orderly rows when he'd stormed a freighter off the Virginia coast. He'd had a beating heart then, had breathed sweet air. _Stop it. Focus._\n\nHe grabbed a child's backpack from a section of the store marked by a giant cardboard ladybug with the words BACK TO SCHOOL blazoned across her back. He filled it with rubbing alcohol, calamine lotion, hydrogen peroxide, sterilizing pads, gauze, medical tape, and two boxed first aid kits. To this he added a Coleman stove and plenty of fuel, cans of spam and beans, and bottles of water. He grabbed a child's elf costume. The tights and shirt were brown and green, at least, and they were clean. At last, he leapt the counter into the pharmacy, snatching up a double handful of orange plastic bottles of antibiotics.\n\nHe paused, listening. Hushed whispers in a house some distance away. Someone had heard some noise, was debating going to check it out, being talked down by a worried wife. Schweitzer heard the relief in their voice as they acquiesced. No one was coming.\n\nHe rummaged back through the bag, paused as the moonlight caught his hand. It was shredded, more bone than flesh now, the ragged gray striations of the muscle visible where the skin had been peeled back, or burned off, or simply rubbed away. He could only imagine what it must look like to Patrick, to anyone. Dirt packed the holes, bunched around the tendons.\n\nSchweitzer cursed and roved the aisles until he found a roll of duct tape. He spent fifteen minutes taping over the various gaps and rents, pausing every so often to listen for breathing, footsteps, any indicator that someone was drawing closer. No one was. He could still hear Patrick's breathing, slow and steady and even. The boy was where he left him, sleeping.\n\nSchweitzer surveyed his handiwork. Striped with duct tape, he looked . . . less horrible, but no more human. It would have to be enough. He shouldered the bag and headed back out the door.\n\nHe crouched beside Patrick, gently lifted the boy up and over his shoulder again. His son didn't struggle, didn't moan, gave no indicator he'd noticed at all. He was dead weight on Schweitzer's shoulder, his slow breaths the only indicator that he was alive. The events of the past few days had taken that much out of him, or it was simply safer in dreams than in the waking world.\n\nSchweitzer made sure they were a good distance into the woods, and that the only sounds near him were animals, before he bent to his task. He cleared the ground as best he could and lay Patrick down, then set to work cleaning himself with bottled water and alcohol before doing the same to the boy's face. Patrick didn't scream when he came awake, merely stared at his father sullenly as he submitted to being washed, cleaned, and then liberally smeared with the calamine. Schweitzer cleaned his cuts and bandaged them as best he could. It wasn't until he was mostly done that he realized he had been humming softly out of instinct, an old nonsense lullaby that he'd used to sing to his son at bathtime.\n\nPatrick looked up at his father, staring exhausted into his skull face, his burning silver eyes. \"Daddy,\" he said.\n\n\"Yes,\" Schweitzer choked the words out. \"I'm your daddy.\"\n\n\"Are you a monster?\" Patrick's eyes were wide.\n\nSchweitzer almost said no, stopped himself. Patrick had seen so much. It would do no good to lie to him now.\n\n\"Yes,\" Schweitzer said, \"but there are different kinds of monsters, sweetheart. Some are good monsters, and some are bad monsters. Daddy is one of the good ones.\"\n\n\"Good monster,\" Patrick said.\n\n\"Yes.\"\n\n\"Mommy. Want Mommy.\"\n\n\"I know, sweetheart,\" Schweitzer answered. What else could he say?\n\nThe imagery from the link between them flared in his mind; he fought the memory down, but not before it gave him a painful glimpse of what had transpired. Sarah had been with Steve. She had fucked him. She had loved him. She had belonged to him.\n\n_She thought you were dead. What the hell did you expect?_\n\nThere were so many questions he wanted to ask her, both wanting and not wanting to know the answers. _Were you sure I was dead? Did you try to see my body first? Was Patrick close enough to hear? Was it good? Did you come? Did you think of me?_ But above it all were two questions pulsing in alternating tandem, one blinking on as the other blinked off: _Why? How could you? Why? How could you?_\n\nHis mind was quick to provide him with a flood of cuckold's fantasies: Chang's sweating back, Sarah's nails drawing red lines across it. Schweitzer still remembered the soft moans she made, the dirty words she used, the way she said \"please\" when she was close to orgasm. He remembered them now in vivid detail, always with Chang in the foreground. His wife, his best friend, a clich\u00e9 out of a bad movie.\n\nThe vision was replaced by the blurry distance, Sarah as a red mound, pieces of her detaching, the gray shapes of the Golds fighting over them. Schweitzer inventoried each lump. That might have been her arm, or her elbow, or her foot. He hadn't focused enough to tell; he'd known he wouldn't be able to bear it.\n\nThe temptation to go after her, to quest into the void, was so strong he almost succumbed, but he forced himself to look back at his son. _Sarah is dead. Patrick is alive. Take care of your son._\n\n\"Come on, big man,\" he said, taking his son's hand, \"let's get you somewhere safe.\"\n\nPatrick held his hand, toddled along beside his father. Frightened, shaken, but starting to realize that the thing beside him wasn't going to hurt him. Maybe the duct tape over the wounds helped, but Schweitzer doubted it. Schweitzer had to stoop low to walk beside his son, knew he should scoop him up so they could move at a faster clip. _Not just yet,_ he thought. _Let the boy walk for a moment. A few minutes won't make a difference._ More likely that it would, but Schweitzer forced himself to match his son's fumbling gait anyway.\n\n\"Good monster,\" Patrick repeated.\n\nSchweitzer nodded. It hurt to hear it, but that didn't make it any less true. \"The best.\"\n\n\"Where we goin'?\" Patrick asked.\n\n\"Well, where would you like to go?\" Schweitzer asked. His own mind worked feverishly. Where could he take Patrick that was safe? The Gemini Cell was a classified program embedded deep in the intelligence community; that meant it likely had its hooks in all over the country, the ability to tap local law enforcement or the FBI. They clearly had mercenaries at their beck and call, if Gruenen was any indicator. Where could he go where they couldn't find him?\n\nPatrick tripped over a root, clung tightly to his father's finger to stay upright. Schweitzer began to swing him up into his arms, relented when Patrick squalled, \"Nooooooo,\" continued to let the boy toddle at the maddening, slow pace.\n\n_Sarah was right. They want you. They aren't after Patrick. They'll take him if they can get him, but that's a lot more likely if he stays with you._\n\n_No. He's dead if you leave him. You're the only one who can protect him._\n\n_Protect him to what end?_ What did he think would happen? He was a walking corpse, animated by magic. He was a horror to look at, an immortal being purpose-built for war. Did he think he could go back to life as a father? Drop Patrick at the school bus each day? Go to his high school football games? Teach him to ride a bike? All of that was lost to him. His focus had been too tactical. It was time to pull the camera back, time to ask the big question. Sarah was dead.\n\n_Why go on?_\n\nTo protect Patrick. That was the obvious, the only, answer. _What do you want for him? What could be salvaged from this mess? He's still young. He can heal. He will have a hard time with what he's seen, but he can get past it._\n\n_You can't have a normal life. He can._\n\nBut not while the Gemini Cell existed. Eldredge had seemed kindly, Jawid na\u00efve, but Schweitzer's tour through the Sorcerer's memories had shown him what he needed to know. They would do anything, absolutely anything to further their \"program.\" While they lived, Patrick would never be safe.\n\nWhile they lived.\n\nIn all his time with the Cell, Schweitzer had never seen another person who could do what Jawid could. Maybe killing him would stop things cold. Maybe by holding him hostage, Schweitzer could extract a promise of Patrick's safety. Maybe by surrendering himself, he could get them to forget the boy. All of those plans were paper-thin, all of them more likely to end up with both him and his son physically destroyed and sent to the soul storm, but Sarah was right that they were better than the current option: run senselessly, endlessly.\n\nAnd all had one thing in common: they were dangerous. Infiltration missions requiring a lone operator with powers like his. He couldn't do it with Patrick under his arm. He had to find somewhere safe for the boy.\n\nA hundred strategies rose in his mind and were instantly discarded. He could drop Patrick at an orphanage. He could find a kind and good adoptive family desperate for a child. All were ridiculous. All would put Patrick and whoever took him in at terrible risk. Families weren't experts in OPSEC; they wouldn't know how to keep his son's origin a secret. The Gemini Cell would find them.\n\nHis mother and brother were dead. Sarah's sister was a flake with a mild drug habit and a string of questionable boyfriends. Her father was gone, her mother in the early stages of Alzheimer's. He needed someone frosty, someone trained.\n\nHe needed SEALs.\n\nHis heart sped up as he thought of Chang. The man had been completely dedicated to Schweitzer, his family as an extension of himself. He would have risked anything, gone any distance, to keep Patrick safe. _Maybe that's why he fucked your wife. Because he loved her._\n\n_Stop it. This won't help._\n\nChief Ahmad was a company woman. Her first and sole loyalty was to the nation. She would never sell out a teammate, but her by-the-book attitude meant that if the government came knocking, she'd salute and do what she was asked. He couldn't ask her to take that risk. Ditto for Lieutenant Biggs. Martin was a religious fanatic who believed an invisible man in the sky had told him to hate gay people. Who the hell knew what he would get up to? What things he would ask Patrick to get up to?\n\nThat left Perretto.\n\nSchweitzer's heart quickened a little at the thought. As the lone Coast Guard assigned to the team, he was outside the decision-making circle. If any of Schweitzer's brother SEALs had been co-opted by the Gemini Cell, it likely wasn't him. Schweitzer knew he had two children of his own. Perretto had botched his takedown during their last mission together, nearly getting the whole team killed. He was still stinging over it, but that didn't change his heart. Schweitzer remembered his quick and irreverent sense of humor, the mischievous turn of his mouth. Was he the sort of man who would defy his own government? Who would take in a child with no questions asked? Schweitzer had no idea, but he did know the bond between operators was strong, and Perretto was the best chance he had.\n\nSchweitzer knew that after his botched job, he wouldn't stay with the team in Little Creek; he'd be \"reattached\" to his original unit, the Pacific Tactical Law Enforcement Team in San Diego, California.\n\nNearly three thousand miles away.\n\nSchweitzer nodded internally. The distance would do double duty. It was a place to run to; it was a direction to run in.\n\nAnd he knew just how to get there.\n\n# CHAPTER XVI\n\nDOESN'T ANYONE KNOCK ANYMORE?\n\nThe analyst did her level best to look nonchalant, but she was trained to crunch numbers, write software, and pull needles out of giant data haystacks. Working for a spy service didn't make her a spy. Eldredge could see all the classic tells, refusal to make eye contact, increased breathing, sweat sheening from the hollows of her neck where they showed through her thin green blouse.\n\n\"What do you mean, I can't see Jawid and Dadou?\" Eldredge racked his brain for this analyst's name. Joseph? Daniel? \"I am the lead scientist on this program.\"\n\n\"I'm sorry, sir,\" she said, trying to keep the quaver out of her voice and failing. He decided her name . . . her cover name, at least, was Matthew. \"They're cloistered right now.\"\n\n\"What the hell does that mean?\" It was times like this that the kindly Samuel Clemens look he'd worked so hard to cultivate backfired. On the one hand, it made others more likely to trust and open up to him; on the other, it made them less likely to obey him when he was trying to put the hammer down.\n\n\"It means they're unavailable, sir,\" the soldier behind her answered. \"It means you need to check back later.\"\n\nEldredge scanned the man's blouse for his rank, noticed there was none displayed. That meant he was assigned directly to the Cell. It meant he wasn't going to blink, but that wouldn't stop Eldredge from trying. \"I was here when they brought Jawid in. I have been with him every day since. I have never, not even once, been denied access to him.\"\n\nThe soldier shrugged. \"Guess there's a first time for everything.\"\n\nThe analyst frowned at the floor, looking pained.\n\n\"This is going to be bad,\" Eldredge seethed, hating himself for not having more self-control, \"for both of you.\"\n\nHe spun on his heel and stormed back to his office, feeling the soldier's smug grin burning against his back the entire way.\n\nEldredge slumped into his chair, crossing his arms over his chest, staring at the clutter on his desk. It soon became clear there was no answer there, so he pulled up the commlink and called the Director.\n\nHe heard the low buzz, saw the icon blink as the call went through.\n\nNothing.\n\n_What the fuck is going on?_ The Director had never failed to answer him before. Eldredge wracked his brain, going back the years since he'd come here. His secretary had at least answered. Eldredge had never had to wait more than fifteen minutes. He'd just assumed that the Director lived in his office, worked around the clock. _Like me._\n\nEldredge broke the connection and pulled up the overhead layout tracking the Golds. The triangles flashed. They were fanning out west, moving in a pack. Schweitzer had moved off along a ravine, and Eldredge was betting that he'd followed it. The mop-up team showed as a blue square, hovering over the last place they'd seen Schweitzer. They were busy cleaning all traces of the Golds' presence.\n\nThey were dealing with what was left of Sarah Schweitzer's corpse.\n\nEldredge had only glanced at the image before turning away. The Golds had been in a frenzy. They had been thorough. There wasn't much left. Eldredge swallowed his revulsion. Sarah was a threat to the program; he knew that. He knew what the price would be if she were allowed to leak details to the public. He knew how they would react. The Gemini Cell would be shut down, and repulsive as they might be, the alternative was worse. But it didn't change the fact that Schweitzer was a good man and Sarah a good woman. _What would you have done? Asked them nicely to come in? You know as well as anyone that Sarah Schweitzer wasn't going to allow herself to be captured._\n\nMore lives would have been lost if a human team had tried to engage Schweitzer. He'd watched the videos of Operations Jackrabbit and Nightshade over and over again. He knew what Schweitzer could do. Sarah had a good heart, but it was still just one heart weighed against the dozens or even hundreds that Schweitzer would stop beating if mortal humans tried to capture him. The Director had done what he had to.\n\nSo, why did it feel so wrong?\n\nHe looked back to the map, watched the blinking phalanx of Golds sweeping south and west, drawn by the promise of the heartbeat they had missed, Schweitzer's son, Patrick.\n\n_Sarah would have blown the whistle on the program._ He'd read her file. He knew how she'd fought like a cornered bear to save her son when her husband had first been killed. _She wouldn't have let it go. She would have found a way to have revenge._\n\nBut Patrick was a child. He was far too young to understand what he'd seen to be believed, even if he could communicate it.\n\nYet there were the Golds, running down his trail. Eldredge pulled the map out until the red rings representing the circling drones came into view. He toggled from camera to camera, trying to find one that had a clear shot through the dense forest canopy. He cycled through the feeds until he saw the flickers of gray shapes, then dialed in on the ground below.\n\nAnd froze.\n\nHe called up the commlink and dialed another number.\n\n\"Ops,\" came a woman's voice.\n\n\"This is White,\" Eldredge said. \"I'm punched into Eyes Seven, and I . . . I don't like what I'm seeing.\"\n\n\"Are you sure you have a clear view, sir?\" the ops boss asked. \"Might be you're not sure what you're seeing.\"\n\nEldredge fought the ball of rage threatening to make him shout. You never got anything done that way. \"I have a clear view. It looks like the action element has found . . . something.\"\n\nThe ops boss sighed on the other end. \"Yes, sir. That's a campsite. We're waiting for them to finish and then we'll send the mop-up team to their position.\"\n\n\"So, you knew what I was seeing.\" Now Eldredge couldn't keep the edge off his voice.\n\nThe ops boss sighed again. \"Just trying to make sure we're talking about the same thing, sir.\"\n\n\"How many?\"\n\n\"How many what, sir?\"\n\n\"How many did they kill this time?\"\n\n\"We won't be able to get a count until the mop-up team gets there, sir. The Golds aren't exactly great at math. From what I can see, it looks like somewhere around twelve.\"\n\nEldredge dialed in further, maximized the camera feed, squinted at his screen. \"Jesus . . . Are those . . . are those uniforms?\"\n\n\"Yes, sir.\" Ops sounded bored. \"Looks like Boy Scouts.\"\n\nIt was a long time before Eldredge could speak. \"We just massacred a scout troop.\"\n\n\"The Golds aren't responding to the incentives, sir. We were hoping you might be able to talk to the Ops Taskers.\" She meant Jawid and Dadou.\n\n\"Keep me posted,\" he said, and cut the connection.\n\n\"We will, sir,\" she lied just before the line went dead.\n\nEldredge stood, whirled, and stormed back to the lab entrance. The analyst had gone, but the same soldier was there, hands crossed behind the small of his back, eyes fixed on Eldredge's approach.\n\nAs Eldredge came within striking distance, the soldier put his hand out. \"Sir, please. Don't make me . . .\"\n\nBut Eldredge could tell that his narrow shoulders and white hair had already put the soldier at his ease. He didn't believe that this old man with his bushy moustache and white lab coat was any threat at all, wasn't prepared for any real resistance.\n\nEldredge knew he wasn't strong enough to fight him, was flying by his gut now, the strange feeling of working without a plan both exhilarating and terrifying. He needed to talk to Dadou and Jawid for just a moment. He had to find a way to bring the Golds under control. He'd figure the rest out as he went.\n\nThe soldier's expression went from smug and unafraid to shocked as Eldredge brought his hand up, spread his first two fingers and poked him in the eyes.\n\nThe soldier sputtered, seizing his wrist, bending double.\n\nEldredge reached smoothly under his elbow and grabbed the door handle. It was one of the newer ones, with an embedded palm reader, which was probably why they'd posted the guard in the first place. Eldredge felt it warm as it read the signature of his pulse and unlocked.\n\nThe soldier grabbed his elbow, blinked tears. \"What the hell do you think you're . . . ?\"\n\nEldredge smoothly switched hands, using his free one to turn the knob and open the door. He shook the other arm free from the guard's grip. \"What are you going to do? Beat up an old man?\"\n\n\"If I have to,\" the soldier said, seizing Eldredge's arm and jerking it back, locking his elbow, and bending his wrist painfully. \"You have lost your goddamn mind. Jesus, you little shit.\"\n\nEldredge struggled, unable to match the younger man's strength, knowing he was already beaten but refusing to give in. The soldier put more pressure on his arm, and Eldredge bent at the waist, desperately trying to give his shoulder some relief from the feeling that it might pop out of its socket.\n\nAnd then the soldier froze. Eldredge looked up from beneath his brows, and all thoughts of pain vanished.\n\nJawid and Dadou crouched over a chair, faces drooping in shock and guilt, like cheating lovers caught in the act by a husband who came home early. But Eldredge's mind only briefly acknowledged them, turning instead to the chair and the figure bound in it.\n\nIt was padded and fitted with buckled restraints, like some fetishist's dungeon prop, stuffed black faux leather with thick white stitches. Or, at least, he thought they were white. The entire assemblage dripped with blood, sheeting from the body of the man strapped into it. He looked like he'd bled from every orifice in his body. Thick crimson runnels streamed from his nose, his ears, his mouth, his genitals. Beads of the stuff had formed on his face and chest, as if he'd sweated it.\n\nEldredge looked at the purple blotches just beginning to form across the man's body. There were no visible lacerations, no bruising. This man hadn't been cut or beaten. He'd torn himself apart from the inside out.\n\n\"You shouldn't be here.\" Dadou sounded sheepish.\n\n\"What the fuck is this?\" Eldredge asked, the words choked off as the soldier hauled on his arm, dragging him back.\n\n\"Let him go.\" Dadou sounded tired. \"You've already failed to keep him out.\"\n\n\"Sorry, ma'am,\" the soldier said, sniffing and blinking, releasing Eldredge, who staggered forward a few steps before straightening.\n\n\"Get out and close the damn door,\" Dadou barked at the soldier. Eldredge had just enough time to glare at the soldier before he complied.\n\nJawid stammered, shot a terrified glance at Dadou. She gestured, a mere movement of her wrist, palm outward, and the Sorcerer instantly stilled, shoulders slumping. \"I'll handle this,\" she said.\n\n\"That\"\u2014Eldredge stabbed a shaking finger toward the man in the chair\u2014\"does not look like a corpse.\"\n\nDadou placed two fingers against the dark line of the man in the chair's carotid, slowly going an unhealthy shade of purple. The tips came away wet and crimson. \"He is dead.\"\n\n\"He is recently dead,\" Eldredge said. \"That is fresh blood.\"\n\n\"Dead is dead,\" Dadou said. Jawid swallowed.\n\n\"You killed him. Who was he? What the hell is going on here?\"\n\n\"What is going on here is not your concern, _Dokt\u00e8_.\"\n\nDadou was leaner than the solider he'd just evaded, but her body was all muscle, and there was something in the set of her mouth and eyes that made him think that she'd be more than happy to mete out those consequences herself. The soldier was a man in a uniform doing his job. Dadou had the look of a person who had a different relationship with the value of human life. The thought made his heart rate speed up, but he didn't let it show. \"I run this program, damn it. You do not tell me what is or is not my concern.\"\n\nDadou stepped closer. \"You do _not_ run this program, _Dokt\u00e8_. You are an employee, the same as I. This program is run by the taxpayers of the United States. You are just a public servant.\"\n\n\"I am the public servant from whom you take orders. There is a chain of command.\"\n\n\"Yes, there is, and you are bound by it just as I am. My orders come from a higher authority, and if you have concerns, you are welcome to take them up with him.\"\n\nEldredge's blood went cold. \"The Director ordered you to murder someone? Why?\"\n\n\"We are in the killing business,\" Dadou said. \"Or had you forgotten? The targets, the incentives, the collateral damage. Why is this one suddenly a problem?\"\n\nIt was a good question. Eldredge only knew that it was. _Because you met Schweitzer,_ he thought. _Because you got to know him. Because he made you realize that there is more going on behind those burning eyes. _He thought of the town of Basye, the offhanded casual manner in which the Director dismissed all those deaths.\n\n_That doesn't look like a gas explosion, sir._\n\n_Not yet._\n\nHe thought of the ragged remains of the scout troop, the ops boss's bored tone. _We won't be able to get a count until the mop-up team gets there, sir. The Golds aren't exactly great at math. From what I can see, it looks like somewhere around twelve._\n\nHe thought of the ruined pile of flesh scraps, all that remained of Sarah Schweitzer.\n\n\"Wait here,\" he said. \"Don't do another goddamn thing until you hear from me.\" He spun on his heel and stormed off, breezing through the door and past the soldier, who was chattering something into his radio. Dadou shouted something at his back, but Eldredge ignored it, the bit already between his teeth. A small part of him knew the truth, that he was leaning on momentum now, that if he stopped, the fear would take control, and he would lose the will to do what he was about to do.\n\n_This is what Schweitzer would do._\n\nHe stormed past his office and into the stairwell alongside the single elevator shaft at the end of the hallway. He took the steps two at a time, following the elevator shaft up one floor, two, then three. This was the subsurface level, the place he'd foolishly allowed Schweitzer to live on, never thinking he would try to make his break. _He played me. No, I don't think he was the type to play anyone. He wanted to be closer to the surface because it felt more like living. And that's what he wanted more than anything, to be alive._\n\nAt last, he crested the top flight, threw open the door, and marched across the hall to the opposite doors. They were big and metal, the only ones without cipher locks in the whole facility. That was because the Director's vestibule lay beyond, manned by his secretaries twenty-four hours a day. They were drawn from a pool of block-faced and broad-shouldered professionals, humorless, each one dedicated to protecting the Director's privacy. Eldredge had only met them the few times the Director had been unable to take his calls, or when he'd had to drop off a thumb drive for the Director's eyes only, a file too big or too sensitive to send over the network.\n\nThe fear pricked at the back of his neck, and he felt his knees wobble. _If you keep going, you might well be killed. But if you stop now, you'll live, and hate yourself for every second that you do._\n\nHe dropped his hand to the handle of the KA-BAR, tucked into its sheath in his waistband. The feel of the ridged leather handle steadied his nerves. He thought of his father, advancing under the withering fire of German guns. _This is just a conversation, and the Director is just a man. Grow a pair._\n\nHe drew the KA-BAR out. It was an antique weapon, but a weapon nonetheless, and the sharp edge against his thumb would remind him of that.\n\nHe froze, blinked.\n\nThe blade was glowing.\n\nA jinn was nearby. Eldredge stared at the blade, then looked around. Apart from the stairwell door and the doors to the Director's vestibule, there was nothing.\n\nHe paused, listening. The only sound was the static hiss of the climate control system blowing air through the vents overhead.\n\nWas the knife . . . broken somehow? Had the magic gone sour? _No, magic isn't machinery. It doesn't wear out. It has never been wrong before. A jinn is near._\n\nHe sheathed the knife, squared his shoulders, and with a final glance at the air vents, opened the double doors.\n\nThe secretary was already rising from behind the ebony desk, her reflection distorted by the stainless steel walls. \"Doctor Eldredge, you didn't call. How can I help you?\"\n\n\"Mark, good to see you.\" She could have been swapped with any of the other secretaries who manned the station and he would have been hard-pressed to spot the change. He hoped he'd gotten her cover name right.\n\n\"It's always a pleasure,\" she beamed, the polished presentation contrasting with the tension in her muscular arms. The welcoming smile didn't reach her eyes.\n\n\"Sorry for not calling in advance, but something's come up and I need to speak with the Director.\"\n\n\"Certainly, Doctor,\" Mark said, sitting down in front of her computer. \"I can block you out for a video conference right away.\"\n\n\"Thanks\"\u2014Eldredge tried to keep his tone casual\u2014\"but I think this time, I need to talk to him in person.\"\n\nMark's smile went from forced to pained. She snorted a quick laugh. \"Come on, now, Doctor. You know the Director doesn't see anyone.\"\n\n\"He sees you.\"\n\n\"Not very often. I'm afraid he values his privacy very highly, as I'm sure you understand. It's critical that we keep all aspects of this program, and identities in particular, as compartmentalized as possible.\"\n\nEldredge looked around for a chair, but there wasn't one. The office wasn't designed to accommodate those with a mind to wait around. Eldredge leaned on the corner of the desk, ignoring Mark's sour look. \"Well, this is really important. I need to speak to him right away.\"\n\nHis eyes drifted over the ebony desk's reflective surface. It was bare save for a phone and a computer, one of the upright models where the monitor housed the whole works. Sticking out of its side was her ID card, inserted to allow her access to the network.\n\nEldredge glanced to the door to the Director's office, noted the black contact pad beside it. He couldn't be sure that Mark's card would unlock it, but he bet it would.\n\n\"Certainly.\" Mark clicked her mouse and brought up the Director's calendar. \"Is this an emergency? I can . . .\"\n\n_Now or never._ Eldredge thought of the man in the chair, swollen and bleeding. He thought of his order to Dadou to bring Jim and Patrick in alive. He thought of the Director's drunken tone when he told Eldredge to handle Senator Hodges. He thought of the fires burning in Basye, the bodies in the streets. _Now. The Director has lost his mind. You have to talk to him now._\n\nEldredge wasn't as fast as he once was, but he was more than fast enough to reach out and yank the card out of its reader, turn, and reach the Director's office door in three strides. He slammed the card against the contact pad.\n\nNothing.\n\nMark spun in her swivel chair, leapt to her feet. \"God damn it . . .\"\n\nEldredge cursed, tapped the card against the contact reader again and again. Could he have been wrong?\n\nA sharp beep brought relief so strong that he nearly sagged against the door.\n\nMark's hand settled on his left wrist, clamped down painfully. \"This is going to hurt you a lot more than it's going to hurt me.\"\n\nEldredge drove for the door handle with his left hand, but Mark's grip was like iron, and he knew he wasn't going anywhere. His right reached back for the KA-BAR, whipped it out of its sheath, the blade glowing so brightly it nearly blinded him. _Idiot. What do you intend to do with that? You're going to stab her?_\n\nBut Mark let him go, leaping back at the sight of the raised blade. \"Fine. Let's do this the hard way,\" she said, pulling open one of the desk drawers, hand reaching inside.\n\nEldredge saw the black plastic of a pistol in her hand as he slid through the door and felt it click shut behind him.\n\nThe room beyond was freezing.\n\nA second click sounded as the door lock engaged, sealing him in darkness so total that he thought he had gone blind. He raised the knife, holding it up like a torch. The light slowly adjusted his eyes, casting dancing turquoise shadows around the small space, energy smoking in the refrigerated cold.\n\nEldredge slowly became aware of a high, clacking sound, traced it to himself. His teeth were chattering, breath coming in plumed clouds from his nose and mouth. The KA-BAR's light intensified, glowing so bright that he had to hold it at full arm's length away from his slitted eyes.\n\n\"I don't recall you having an appointment.\" In person, the Director's voice was a wheezing, high-pitched rasp. The sound of it stole the last of Eldredge's resolve, and fear and revulsion took the reins, forcing him back a step until his back pressed up against the door. He fumbled for the handle with his free hand, failed to find it.\n\nThe teal light finally found the corners of the room, showed the edges of a plain concrete floor. The ceiling stretched high above them, a pitch-black shaft leading who knew where, beyond the reaches of the brave light. The room was bare of furnishings. A wheeled computer stand stood in the center, a closed laptop resting on the single narrow shelf.\n\nThe Director stood behind it. His muscular frame was draped with an ill-fitting black suit, a tie askew at his throat. His hands hung at his sides, covered by thin leather gloves. A single piece of stretched white fabric covered his head and face, a reflective surface against which the light played. He looked like a store mannequin poorly dressed for display. Only the movement of his lips under the white cloth gave any indicator that he was the one speaking.\n\nBehind him, three Gold Operators stood along the featureless far wall.\n\nTheir bodies were withered, ancient, the old muscle looking hard and narrow as braided plastic, the skin stretched across it brittle and peeling. They were crowned in beaten gold and tin, stepped geometric patterns of plants and faces, animals and people, all surmounted by the blazing corona of a stylized sun. Their necks and chests were hidden beneath massive pectorals of the same metals, studded with rough-cut gems that refracted the KA-BAR's light. Their waists were draped in dirty linen, gone to dusty rags at the fringes of what had once been gorgeous metallic brocade. Their withered feet were tied into rotten leather sandals, hints of bone showing through where the toes had worn away. Their arms were drawn up in _X_ 's across their chests, hands resting over their collarbones.\n\nTheir eyes burned, tiny pinpoints of flickering light, staring straight ahead. Without pupils, he could never tell when a Gold was looking at him or not.\n\n\"I assume there is a reason for this downright suicidal intrusion, Eldredge,\" the Director said.\n\n\"Sir, I . . .\" He couldn't form words. Couldn't think. He could only stare at the Director's shrouded silhouette, at the gloriously arrayed living dead behind him. Why had he come here?\n\n\"Eldredge.\" The Director slowed his words. \"You barged into my office. Now, if you want to barge back out again, you had better tell me why.\"\n\nThe threat jarred Eldredge's nerves, brought some of his focus back. He became conscious of the cold again, realized that terror wasn't the only reason he was shivering. \"Sir, I've just come from Dadou and Jawid. They . . .\"\n\n\"Dadou and Jawid are cloistered, Eldredge. They're not supposed to see anyone until they have completed their latest project for me. I had them under guard for that very reason.\"\n\n\"You didn't discuss it with me, sir.\"\n\nThe lips under the white mask twitched, sliding against the cloth as the Director formed words. No other part of him moved. \"I am not in the habit of discussing things with you. And you should not be in the habit of having things discussed. We have a chain of command in this organization. We follow orders.\"\n\nEldredge fought the urge to fumble for the door handle again. \"Sir, they had a freshly killed subject in there.\"\n\n\"I know what they had in there, Doctor. I am the one who ordered them to have it.\"\n\n\"Has there been a change to the program? We don't\u2014\"\n\n\"We don't until we do, and we do when I say it is time. We are reviving the old program. Virgo Cell.\"\n\n\"Virgo? Sir, that failed for a reason. A living subject can't house a jinn; we have stacks of results that\u2014\"\n\n\"I have reason to believe that Dadou has had a breakthrough in this arena. Working with Jawid, she is making progress.\"\n\n\"Sir, I just came from the room, and that subject is dead. The manner of his death is consistent with the Virgo Cell failures.\"\n\n\" _That_ subject is dead, Doctor. Maybe the next one will be as well. We will keep trying until we get it right.\"\n\n\"How many? If we're continuing along the lines of the Virgo program, these are _service members_ we are killing.\"\n\n\"As many as it takes. Service members sign up to die. That is part of the oath they take when they enlist.\"\n\n\"And our oath as leaders is to only spend those lives when we must.\"\n\n\"Agreed. And we must. These are not good men, Doctor. We are using the ones who would be breaking rocks in Leavenworth, or on death row. This way, they serve their country even on their way out.\"\n\n\"Sir, this is out of control. The Gold Element just massacred a scout troop in the George Washington National Forest. This is right on the heels of Basye. We are going to out the program. We were set up to defend American lives, not slaughter them.\"\n\n\"We are defending American lives. Eggs to omelets, Doctor. You of all people know the threat we face. We are making the hard choice necessary to keep this nation stable.\"\n\nAnger competed with the fear and, for a split second, won the upper hand. \"Senator Hodges is furious. We can't keep being this careless. I need Jawid and Dadou full-time on getting the Golds wrangled back under control. We need to find Schweitzer and bring him back intact. We need to figure out what makes him tick. That's the only way, the _only_ way we're going to be able to save this program. That's the only way we're going to be able to do this right.\"\n\n\"There is no _we_ , Doctor. There is _me_ giving instructions, and there is _you_ carrying them out. I am fully aware of the disposition of the Gold Element. I am fully aware of the current operational taskers set before our magical assets. I am fully aware of the challenges this program faces in the Senate. I am fully aware of you contravening my orders and directing Jawid and Dadou to bring Schweitzer and his son in alive and intact. I appreciate you underscoring your concerns, and now I invite you to close your mouth and sit on them. I and not you will decide the best way forward. If you do not feel you can continue, please submit your resignation to Mark outside _after_ you have apologized for whatever means you used to gain entry here.\"\n\nEldredge's mouth went dry. \"Resign?\"\n\n\"I grow tired of you questioning the decisions of executives. The Gemini Cell is founded on decisive action in the face of a rapidly growing and existential threat to the nation. We do not have the luxury of ethical struggles here. I value your work, Doctor. You have been an essential building block, a piece of the foundation of all we've built here, but if you labor under the delusion that you are _indispensable_ , that we cannot proceed with what is arguably the most critical work in this nation's history without the earnest trembling of your most endearing mustache, then you are sadly mistaken.\n\n\"Do you know why you are still alive, Doctor?\"\n\n\"I . . .\" Eldredge felt his knees go weak.\n\n\"You know every line item in every contract we hold. You know the idiosyncrasies of every soldier and analyst we employ. This program is a tangled weave of a million different threads, and you know just where they are whenever I want them pulled. I will be honest with you. It would take me years to train someone up to the point where they could handle your duties with the efficiency and competence you show, even if I could find someone who wouldn't run screaming at the first mention of magic.\n\n\"But I will also be honest with you in that I will find a way to soldier on without you if all this doesn't work out. If, like Jawid, you suddenly decide that your heretofore singular dedication to the advancement of this program is wavering, that other priorities are coming to the fore, I will lose my patience. Because, unlike Jawid, you are not a Sorcerer, and that means you can be replaced.\n\n\"Now, I have suffered your uninvited entry into my _sanctum sanctorum_. I have _explained_ myself to you, something I have never done in the history of this program. I am willing to chalk this up to some feverish humor of your brain and let it go, provided that you walk out of here, forget this entire ugly incident, and get back to work, this time providing whatever assistance Miss Dadou Alva requires. Her project is to be your first priority. You are to do whatever she asks. That is the alternative to your . . . resignation, Doctor. That is the choice before you.\"\n\nThere was no resigning from the program, Eldredge knew. He'd known it from the moment he'd first signed his nondisclosure agreement. It would be difficult to out the program even with specific evidence, because no one would believe him, but he also knew that the Director, even Senator Hodges would never risk it. Eldredge could dream of retiring from the government someday, living a comfortable life in Arlington, Virginia, under the watchful eye of the FBI, but resigning? Pursuing work in the private sector? Being free to travel to a foreign country or talk to the press? No way.\n\nTo resign was to die. Which, he supposed, was the Director's point.\n\n\"Do you have anything else you would like to say?\" the Director asked. The wet, rasping voice. The completely motionless body, save for the lips rising and falling behind the white mask. No skin exposed at all, not a sliver.\n\nEldredge's hand finally settled on the door handle. He didn't realize that it had been questing for it all this time, the fear giving it a mind of its own. His head worked side to side, a refutation of a number of questions, none of which had been asked. _No, I don't think I can defeat you. No, I don't want to work for you anymore. No, I don't understand what's going on here._\n\n_No, I don't want to die._\n\nUnasked questions. The Director responded to the asked one. \"No? Excellent. Dismissed.\"\n\nThe handle turned and the door opened. The three Golds along the wall twitched in time, leaning toward him. Eldredge quickened his step, nearly falling over himself in his sudden hurry to escape. The Director spread his fingers, turning one of his hands out, palm toward the Golds. They stopped as if he'd flipped a switch.\n\n\"Close the door, Doctor. We wouldn't want to let all the cold air out.\"\n\nEldredge stood gaping, grateful that his bladder was empty. It was Mark who reached across him, slamming the door shut.\n\n* * *\n\nThe vision of the Director was seared on his brain. The dark room, the biting cold, the shabby suit pulled clumsily over the vaguely human frame, the head shrouded in white fabric, like a lamp bulb stripped of its shade. Every inch of skin covered.\n\n_I didn't see him breathe,_ Eldredge thought. _I didn't see his chest move at all._\n\nOnly the lips beneath the fabric. Only the hand to gesture the Golds to stop, and only after a few minutes.\n\nThe room must have been below freezing. No living man could have survived in there long, not in such thin clothing. The warm blood in his veins would have eventually filled with ice crystals, gone solid.\n\nBut the living-dead Operators had no such concern. Their veins were full of glycerol, their skin waxen. Their chief worry was to preserve dead flesh that could no longer heal, and for that, you needed cold that a living man couldn't abide for long.\n\nEldredge shivered, and not from cold this time. The jinn were intelligent but slaves to their appetites. He'd always thought of them as animals, a step above trained dogs or messenger pigeons. So long as the blood addiction ruled them, they could never be a threat to humanity. Animals couldn't think, couldn't plan, couldn't make grand strategies.\n\n_But Schweitzer did, didn't he?_\n\nEldredge's mouth went dry. His eyes focused on his desk. He was back in his office with no memory of how he'd gotten there. He'd been so focused on the positives of Schweitzer's breakthrough that he'd been blinded to the threat behind the idea. _You wanted an Operator that could think. But what happens when that Operator's agenda isn't in sync with your own?_ That made Schweitzer a threat.\n\n_And what if the Operator's agenda isn't in sync with humanity's?_ That made it a loose nuke.\n\nEldredge remembered his conversation with Senator Hodges, when he described the thing that Schweitzer was now. He'd told him that Schweitzer wasn't more powerful than a Gold Operator, but _as powerful_. _He combines this with a highly intelligent, rational mind that has the ability to discipline itself. He's also able to access his training and experience in a way that the Golds can't. He's not blinded by bloodlust. He can think._\n\nEldredge leaned forward in his chair. His chest felt tight, his breath coming in whooping gasps. Sweat broke out along his brow and ran down his temples, tracking behind his ears. He put his hand to his chest. His heart was hammering, but it was doing it regularly. Not a heart attack, then. A panic attack.\n\nHe tried to slow down his thinking, to focus. What was the right call here? He couldn't get back in the Director's office, and even if he could, there was nothing he could do. He couldn't kill a dead man. He could go to the press. No. They wouldn't believe him, and by the time anyone could verify his story, _if_ they could verify his story, he'd be finished.\n\nSenator Hodges. Again, no. He had no way to contact the Senator. His regular reports went through the Director's office. The man had only visited the facility twice in the past year, and then with no forewarning whatsoever. And even if he could get off campus to contact him, he had no guarantee the Senator would help. Maybe the Senator even knew? _No, he wanted to see the Director, and the Director refused._ And now Eldredge knew why, knew why the Director refused to see not only the Senator but _anyone_ all these years. Only his secretaries. Were there others?\n\nBut not Hodges. He remembered the man's curled lip, his threats to shut down the program. It would be one hell of a risk to reach out to him. Just because it would be news to him didn't mean that he wouldn't support it, or be angry at Eldredge for going outside his chain. Politicians served their own interests first and foremost.\n\n_Doesn't matter. You can't stay. Your boss is walking dead. You've got to get out of here._\n\nHe forced himself to stand, felt his knees wobble. He thought briefly of contacting Jawid, dismissed it. If the Director hadn't killed him where he stood when he'd stormed into the room and put two and two together, it was because he wanted to keep Eldredge on, felt he could still extract use from him even with his identity revealed.\n\n_That means you have time. They're not going to kill you. You can figure this out. Are you sure you want out?_\n\nIt was the only real life he'd ever known. He remembered brief flashes of his past. The University of Illinois at Urbana-Champaign, his brilliance as a fluid engineer leading to a career as a Navy scientist. That's where the Cell found him. It seemed so long ago that thinking on it was like watching a biographical film about a stranger. No, the Gemini Cell was his life.\n\nBut he thought of the ruins of Basye, of the overhead camera's view of Sarah's shredded remains. He thought of the Director snubbing Hodges, of his lack of concern with an end of funding for the Cell.\n\nHe thought of his father on D-Day, tried to recall the last photograph he'd seen of him standing in uniform, rifle slung over his shoulder. Eldredge imagined his strong jaw, his determined gaze. He pictured his father under the withering Nazi fire, churning the sands of Omaha Beach around him, advancing steadily regardless. He knew what his father would do in his situation. But Eldredge thought of the Director's chest, how utterly still it was, even as his mouth moved, telling Eldredge to close the door to keep the chill air from escaping. Eldredge thought of the crowned Golds surging toward him, stopping at a twitch from the Director's hand, and admitted that he wasn't his father, never had been.\n\nHe knew that now.\n\n# CHAPTER XVII\n\nTHE PLAN IS WEST\n\n\"You ready?\" Schweitzer asked his son. The metal wheels were thrumming on the rails, still a quarter mile out at least but as loud as pounding hammers to his magically enhanced hearing. He lifted Patrick up, tucking him tightly against his belly. Patrick hooked his hands into the ragged remains of his father's web belt. Even now he wouldn't suffer being close to the silver flames burning in Schweitzer's eye sockets.\n\nBut he wasn't crying, and the angry red welts on his face and arms were starting to recede under the medication's touch. Patrick still had his limits, but he was letting Schweitzer handle him more, responding to the sound of his voice. He was, with time, getting used to him. A part of Schweitzer grieved the development. He didn't want his son to live in a world where monsters, even good monsters, were a fact of life. He didn't want Patrick to understand that the walking dead came in varieties, that you could tell the tenor of their hearts by the color of the fire in their eyes. He could feel Patrick's youth warping under the pressure of what he'd been through, a plant permanently twisted by poisonous air. He turned away from the thought. He could no more dwell on it than he could on the thought of Chang's sweating back, hips pumping away at Sarah beneath him.\n\nSchweitzer set off at a run, keeping his center of gravity low, arms locked to hold Patrick in place, keep the boy from bouncing too much. Patrick's hands dug into Schweitzer's forearms as he picked up speed, sliding along the duct tape that held his wounds closed.\n\n\"We're going to see the train!\" Schweitzer said to him. \"Don't you want to see the train?\" The benefit of complete breath control meant that there was no panting, a weird even temper to his voice that defied the speed at which they were covering ground. \"See the tracks?\"\n\nHe spun Patrick in his arms, turning him outward as the ground rose alongside them, sloping gently up through a scramble of softball-sized stones until the surface suddenly flattened and twin metal lines cut across it, arrowing straight ahead and out of sight. The scent of creosote was cloying, interspersed with the thick smell of rust. The tracks began to vibrate, a high, metallic pinging sound as the train drew closer.\n\nPatrick squinted as the wind picked up his hair, but he pointed at the rails before Schweitzer spun him back around to shield his eyes.\n\nHe felt the ground shaking, heard the metal wheels rumbling louder and louder, until at last he turned and put on a burst of speed, Patrick's shriek drowned out by the noise of the train rocketing past them. Schweitzer watched the cars stutter-flash past, the locomotive well ahead, the freight containers flying by, corrugated sides painted in giant block letters. Schweitzer ignored them, looking instead for the sliding car doors, the huge padlocks that held them shut. A normal man might be able to run fast enough to grab hold of one of the speeding cars, but without a solid foothold, there was no way he'd be able to break the lock and open the door.\n\nA normal man.\n\nSchweitzer broke from the cover of the trees and pushed up the rise. The rocks slid under his feet, and for a sickening moment, he thought he might pitch under the spinning metal wheels, but he found his balance a moment later, picked up speed until he matched the car briefly. There was no keeping Patrick stable now. The boy jolted and bounced and cried as Schweitzer leapt, reached out, and hooked his fingers into the top of the lock, yanking downward. He felt the bones in his fingers tremble, and he sprang before they could give, providing him enough reach to clasp his entire hand around the piece of metal, shearing it away.\n\nAnd now he did stumble, his strides lengthening, feeling his balance pitching toward the train, the gravity of the spinning metal wheels pulling him, as if they were hungry, eager to chew up his dead body and his son's living one with equal gusto. He fumbled Patrick, staggered as he caught him, reaching out a hand to push off the train's side.\n\nHe missed the train's side, slipping under the car and into the undercarriage; the top of the spinning wheel blazed heat on his palm. He snatched the hand back, overbalanced, began to fall. Patrick slid in his grip, tumbled. Schweitzer growled, snatched him under his arm like a football, pushed off with his legs.\n\nHis shoulder collided with the train door, hard enough to dent the metal. His body rebounded, then fell back in toward the spinning wheels. He reached out, desperation welling in his throat as his hand slid down the flat surface.\n\nAnd settled on the handle, still trailing the remains of the broken lock.\n\nHis weight swung the clasp open, and the door hauled back, dragged by his body. He tucked Patrick in tighter, bracing himself for the door to slam into its terminus, the rubber stopper, making the whole structure shake. His arm straightened, taking his weight, and he grunted, pivoting his mass and pulling himself around, throwing them both into the car.\n\nThe door slid forward, Schweitzer's momentum momentarily stronger than the wind, and slammed shut, closing them in darkness as Schweitzer skidded into a pallet stacked with plastic pipes hard enough to shake them against the holding straps.\n\nThe train thrummed away beneath them, wheels pounding in time with Patrick's sobs.\n\nSchweitzer lay still for a moment. He'd shut his eyes out of instinct, and he kept them closed, letting his other senses paint the picture of the car's interior.\n\nA fresh breeze blew at them from the car's front end. A connecting door between cars, open. He could hear Patrick's little heart hammering away, just beginning to slow as his mind processed that he was safe, that they had stopped moving.\n\nA second heartbeat, rising as his son's fell. It was bigger, a man's heart. That man was crouched at the far end of the car, frozen by the sudden appearance of Schweitzer and Patrick. He wasn't trained for this. The scent of it was in his sweat, pores opening to exude adrenaline, the high stink of norepinephrine mixing with the sweet smell of a dramatic spike in blood sugar. A civilian, then. That was good.\n\nSchweitzer tucked Patrick against the stack of plastic pipes and rolled into a crouch, opening his eyes to let the silver flames dance for whatever audience they'd found.\n\nIt was a young man. He had risen to his knees on a dirty foam bedroll. A cloth knapsack was held together by patches and duct tape. His blond hair was formed into dreadlocks that trembled around his face. His chapped lips worked in his dirty beard as he said, \"Hang on, man; hang on, man,\" over and over. A hobo, a stowaway. He must have hidden himself somewhere as the train was loaded, before the locks went on.\n\n\"Shut up,\" Schweitzer rasped. The young man did.\n\nHe knew he should kill him. The man had seen him, seen Patrick. No good could come from letting him live to tell the tale willingly, or have it surface under questioning. The average cop, even a very good one, wouldn't believe him. But the Gemini Cell would.\n\nPatrick stirred against Schweitzer's thigh. \"Mommy,\" he sighed.\n\nSchweitzer cursed and slid the door open a fraction. \"Jump,\" he said to the hobo. \"Take the bedroll; leave everything else.\" The bag might contain food, or medicine, or camping supplies.\n\nThe young man started to speak.\n\n\"If you are not out of this car in the next five seconds,\" Schweitzer cut him off, \"you are meat.\"\n\nThe boy nodded, raced for the opening, hesitated at the prospect of drawing near Schweitzer.\n\nSchweitzer grunted and snapped out a hand, lightning-fast, tapping the boy's back. He squealed and jumped.\n\nSchweitzer didn't look to see where he landed. The fall might hurt him, but provided that he could still move, he would be able to find help if the Gold Operators didn't find him first. Schweitzer felt a twist in his gut like the one he'd felt when he'd slaughtered the guards keeping him in the underground Gemini Cell facility. But as with them, he shrugged it off. They had been keeping him from reuniting with his family. This boy's life and health were not going to take precedence over Patrick's. He didn't want to hurt anyone, but if he was going to be a monster, then he may as well be one to protect his own.\n\nHe knelt beside Patrick, checked him over for cuts or scrapes. The boy came to him, folding against his chest, crying into the ragged remnants of his tactical vest. Schweitzer held him apart just long enough to ensure he wasn't hurt, then brought him back in, conscious of his own chemical smell, of the chill, rubbery feel of his skin. His embrace couldn't convey warmth, which came from blood. He didn't have any of that, not anymore. At least the child's costume Patrick wore under his ragged clothes kept him warm.\n\n\"It's okay,\" he whispered.\n\n\"Hungry,\" Patrick said.\n\nThe word tore at Schweitzer, a reminder of how quickly his own humanity was slipping away. He didn't have to eat, so it was easy to forget that others needed food. He didn't have to sleep, so it was easy to forget that others needed rest. _You cannot protect him if you starve him to death._\n\nSchweitzer tucked Patrick against his side and went to rummage through the bag. The filthy leather buckle parted at a twitch of Schweitzer's fingers, spilling out the contents: a plastic bag that contained at least a pound of marijuana, a battered copy of a paperback novel, plastic bags stuffed with pills, and a dead smartphone wrapped in its charger. Deeper in the bag were things Schweitzer could actually use: a rusted pocketknife, a box of matches that looked like they'd been dropped in water but dried again. A ball of twine and a packet of wet wipes. A few unopened packages of chemlights.\n\nTwo old and dry-looking granola bars, mostly crumpled inside their bleached foil packaging. _How the hell did this kid eat?_\n\nIt wasn't like there was a caf\u00e9 car. The freight train had been heading west when Schweitzer had hauled himself and his son on board, and he slid the door open just wide enough to reckon the sun's position before shutting it again. Angling more south now, but still mostly west. He was trained as a maritime counterterrorism operator. If there had been a class on domestic rail lines, he'd missed it.\n\nSchweitzer pulled out a can of beef stew from the child's backpack he'd taken from the convenience store. He slid out a bone claw, punching easily through the thin metal and working around the can, peeling it back, then he handed it to Patrick. \"Here you go, little man.\"\n\nPatrick took the can tentatively, sat staring at it. He brought it to his face, frowned, his upper lip quivering.\n\nSchweitzer's dead stomach turned over. _It's cold, you moron. You need to warm it up for him._ If it had been mere stupidity, it wouldn't have caused his soul to contract in horror. But it wasn't. Schweitzer had forgotten that little children couldn't heat their own meals. He had forgotten that they needed help from their parents. He had forgotten how to be a father.\n\nAnd if he didn't remember, Patrick would die. _You're like a monkey playing with a gold watch. Just because you don't want to break it, doesn't mean you won't. _He would save Patrick from the Gold Operators only to lose him to his own new state of existence.\n\n_Oh God. Sarah. I need you. I don't know how to do this._\n\n_Stop. This doesn't help. Focus._\n\nSchweitzer set up the camping stove and set the can on it. Patrick stared at them doubtfully.\n\n\"Come on, little man,\" Schweitzer said. \"It'll just take a minute.\"\n\n\"No!\" Patrick said.\n\n\"Fine,\" Schweitzer proffered him the can again. \"You can eat it cold.\" _Idiot. He needs a spoon, at least._\n\n\"No!\" Patrick said, thrusting his hand into his armpit. \"No! No! No! No!\"\n\nSchweitzer winced.\n\n\"I don't want that!\" his son shouted. \"Hungry!\"\n\nBut all of Schweitzer's magical power couldn't conjure up a sandwich or a glass of milk. Anything to eat would be somewhere out in the countryside around them, rocketing past at one hundred and fifty miles per hour. If they jumped off, they wouldn't get getting back on. And the Gold Operators were somewhere behind them, sniffing out their trail.\n\n\"That's what there is,\" Schweitzer said. \"Sorry.\"\n\nHe held Patrick as the boy raged and sobbed, peeked his head out the door again to reckon the position of the sun once more. Still west.\n\nHe had no idea if they were on the same latitude as San Diego. He had no idea if the train kept on in this direction as it went. Maybe it would turn north. Maybe it would double back entirely. He had no idea how to find his former teammate.\n\nBut San Diego was west, and that's the direction that, for now, they were heading.\n\nIt was something.\n\n# CHAPTER XVIII\n\nPUSHED TOO FAR\n\nDadou came to Eldredge's office a few hours later.\n\nShe stood in the doorway, arms folded, shoulder casually resting against the jamb. \"I told you that you shouldn't have come in there.\"\n\nEldredge swallowed the ball of panic in his gut, resisted the temptation to reach for the KA-BAR. Dadou was at least twenty years younger than him and athletic. She'd take that knife away from him and stick it in his eye. \"Are you here to kill me?\"\n\nDadou laughed. \"No, _Dokt\u00e8_. I'm a Sorcerer. We have people who handle the wetwork; you know that. The _Direkt\u00e8_ wanted me to talk to you.\"\n\n\"You . . . you've seen him?\"\n\nShe laughed. \"No. That's an almost unique privilege you can lay claim to.\"\n\n_Should I tell her? Maybe she already knows. Would it make a difference to her?_ \"He's . . .\"\n\nDadou held up a hand. \"The less I know about him, _Dokt\u00e8_ , the better. All you need know is that he has been good to me, and where I come from, that kind of thing buys loyalty. _Eske ou konprann?_ \"\n\n\"I'm not going to try to talk you out of anything. Do I still run this program?\"\n\n\"No, _Dokt\u00e8_ , you don't. But there is still plenty of work to be done, and we can use your help in doing it.\"\n\n\"The Virgo project.\"\n\n\"That's right. You've seen it now.\"\n\n\"I saw the aftermath of a failure. A bleeding corpse tied to a chair. We've been down this road, Dadou. We know exactly where it leads. You can't Bind a jinn into a living man without killing him.\"\n\n\"You Americans are all so smart; you know that? The less you know about a thing, the more sure you are that you have nothing to learn.\"\n\n\"I know what I saw.\"\n\n\"Weren't you a scientist before you came here?\"\n\nEldredge thought of his lab at the university, whirlpools and model pipelines. Lab experiments to determine how fluid moved and why. \"I still am.\"\n\nDadou laughed. \"Really? You live in a world with a real afterlife. You live in a world where magic is real. How can you call yourself a scientist now?\"\n\n\"Magic isn't . . . it isn't magic. There's an explanation. Just because we don't know the science behind it doesn't mean we won't learn eventually. There just hasn't been time to test, to study. We've been too busy . . .\"\n\n\"Killing,\" Dadou finished for him.\n\n\"I was going to say 'protecting the country.' I still believe in science, Dadou. Magic hasn't changed that.\"\n\n\"Perhaps, but your analytical skills are poor. You lack a skeptic's natural ability to instinctively question. Just because you saw one corpse doesn't mean that they all end like that. Some people are stronger than others. Some resist the jinn with greater . . . enthusiasm.\"\n\n\"Are you saying that you've succeeded?\"\n\n\"Come with me, _Dokt\u00e8_. I want to show you something.\"\n\nHe stood, followed her down the corridor and into one of the cold storage units. \"I hope this one is still alive,\" she said. \"If he isn't, then you'll have to take my word that he . . . Oh, good.\"\n\nShe stepped up to one of the sealed access doors, thick steel with a panel of transparent palladium in the center. She gestured. \"Take a look.\"\n\nEldredge stepped closer, squinting through the clear metal, adjusting to the sudden sense of vertigo that came from the fishbowl effect it always had on the view beyond.\n\nA man stood in the center of the plain white room. His soldier's uniform was stained with fresh blood. He stood with his back to Eldredge, arms hanging loose at his side. His neck was crooked at what look like a painful angle, head rigid on his shoulder.\n\n\"Another Gold,\" Eldredge said.\n\nDadou laughed. \"Golds are gray, _Dokt\u00e8_. Does he look dead to you?\"\n\nEldredge squinted, then his eyes widened. The soldier's neck was the angry purple-red of a sunburned bruise. That meant blood. He glanced around the room, looking for the telltale misting of the Freon injectors that kept the room refrigerated. Nothing. Dadou had put the soldier in here to keep him contained, not to keep dead flesh cool.\n\n\"So?\" Eldredge tried to keep his voice even. \"He's newly dead.\"\n\n\"Is he?\" Dadou reached across Eldredge's face and rapped on the transparent pane.\n\nThe soldier jerked, pivoted on one foot, faced the door.\n\nEldredge stifled a scream as he recognized the soldier who'd failed to stop him from getting to Jawid and Dadou. His uniform was unbuttoned at the front, the angry purple flush extending all the way down to where his stretched T-shirt cut it off. Badly corded muscle stood out around the ugly bend in his neck, blotched in darker purple where veins had clearly burst. Fresh blood tracked from his nose and the corner of his mouth.\n\n\"Private First Class Welch felt so terrible about letting you invade our privacy,\" Dadou crooned, \"that he asked if there was anything he could do to make up for it. It turned out there was.\"\n\nWelch's face was screwed up in agony, lips drawn back in a fixed grimace, teeth gritted together so hard that Eldredge was surprised they didn't crack. Men in pain moved, their lips twitching and chins trembling, but Welch's face was frozen, as if he had begun to scream and suddenly stopped. His eyes were wide, and Eldredge felt his mouth go dry at the sight.\n\nPupil and iris were nearly a matched purple-black. The sclera was the bright red of burst capillaries.\n\nBut they were whole, human eyes. There were no flickering flames.\n\nEldredge could see Welch's chest rising and falling rapidly. Hyperventilating, a rabbit's super-rapid, super-shallow breaths. At the sight of them, Welch took a staggering step forward, arms coming up. Eldredge knew the man was still alive, but he looked more the zombie than any of the dead Operators.\n\nEldredge gave a strangled cry and backed away from the pane as Welch lurched against it, hammering his hands against the palladium, leaving sticky red handprints. He gibbered in a language Eldredge didn't understand, the angle of his neck straining his windpipe and forcing the words out in a bubbling, choked wheeze.\n\n\"Jesus,\" Eldredge breathed.\n\n\"As you can see, he's very much alive,\" Dadou said. \"I have done better, and I have also done worse, as you have seen. But I am improving, and with the right . . . preparation, I know I'll be able to get it right reliably in the near future.\"\n\n\"How . . .\" Eldredge fought against the rising sickness in his gut. He had seen horrors in his time with the Cell, but this exceeded all of them. \"How soon?\"\n\n\"At the rate I'm improving?\" Dadou asked. \"Very soon, _Dokt\u00e8_. Very soon. I suppose we should thank you for convincing Welch to volunteer.\"\n\nEldredge shuddered. He had gotten the drop on the soldier for a split second, and the man had paid for it with his life. \"Is this supposed to be a threat?\"\n\nDadou flashed a vulpine smile. \"The Director asked me to underscore the consequences of . . . how did he put it? Violating strict rules of need-to-know.\"\n\nEldredge's head spun. \"Will he live?\"\n\nDadou shook her head. \"You're not asking the right questions, _Dokt\u00e8_. Whether he lives or dies doesn't matter. What matters is what this means for the future of our program. We are on the brink of . . . expanding our capabilities beyond anything we ever dreamed of. I will be able to have one of our jinn wearing a living man's skin. I do less damage to the host each time, and eventually the jinn will live behind their eyes. Dominating only the spirit, the space inside.\"\n\n\"That's . . . possession.\"\n\n\" _Se sa, Dokt\u00e8._ That is what you call it. For us, it is, as the soldiers say, 'an overmatch capability.' Do you know what a possessed man says, _Dokt\u00e8_?\"\n\nEldredge looked at her.\n\n\"Whatever you tell him to.\" Dadou's smile grew wider.\n\n\"How the . . . How can you control the jinn?\" Eldredge asked.\n\n\"By giving them what they want more than anything else in the world. With the Gold Operators, we have created your horror-movie zombie. With Welch, we are creating your horror-movie vampire. They are in warm bodies with beating hearts. The frenzy is dampened. They can _think_.\"\n\nEldredge looked back at Welch, his frozen face pressed up against the transparent metal pane, smearing the bloodstains across his nose. \"He doesn't look like he's thinking.\"\n\nDadou shrugged. \"He is _much_ better than a Gold, and as I said, I am getting better at this. I promise you, with time, I will be able to make them perfect.\"\n\nEldredge took a step back, shaking his head. Dadou put a hand on his shoulder.\n\n\"When they are perfect, they will be able to go undetected anywhere we choose to deploy them. Think about it, _Dokt\u00e8_. No more devastation as there was at Basye. A single Operator who responds to commands. We won't need to keep on with the Gemini program in the futile hopes that we'll get another Schweitzer.\"\n\nEldredge still said nothing, his stomach doing somersaults.\n\n\"Think about it! With a Silver Operator, we are dependent on the subject being . . . as unique as Jim Schweitzer. With a Virgo Operator, we'll be able to repeat the process at will. It will be reliable, a known quantity. A game changer. Isn't this what you wanted?\"\n\nEldredge nodded agreement. _No,_ he thought. _This is absolutely not what I wanted at all._\n\nHis conversation with the Director came racing back to his mind with such force that he almost sat down on the floor.\n\n_Sir, did you hear me? It's Senator Hodges._\n\n_I know perfectly well who he is, Eldredge._\n\n_Then you know that he's the man who funds this program._\n\n_I do. I'm not available right now._\n\nIt explained Basye. It explained the Director's almost-insane willingness to deploy the Golds without a second thought. Because if the Director could turn a living person into a jinn answering to him, then he wouldn't have to worry about answering to anyone.\n\n\"How fast can you do it?\" Eldredge asked.\n\n\"How fast can I do what?\"\n\n\"How fast can you master this . . . putting a jinn in a living host?\"\n\nDadou shrugged, but she sounded troubled. \"It takes as long as it takes, but we have time.\"\n\nEldredge cocked an eyebrow. \"Do we?\"\n\nDadou grinned. \"You're talking about Senator Hodges, aren't you? His threats to shut the program down and put us all under the Army.\"\n\n\"You know about that?\"\n\nDadou waved a hand. \"Of course I do. The _Direkt\u00e8_ doesn't trust you anymore. That means that he has to trust me. And I am not worried. Hodges is like all politicians. He yells and screams, and in the end, he does nothing.\"\n\n\"I'm not so sure you're right.\"\n\n\"It doesn't matter what you're sure about.\"\n\n\"Then why keep me alive at all?\"\n\nDadou squeezed Eldredge's shoulder firmly, her fingertips digging in just below his collarbone. \"You transgressed, _Dokt\u00e8_. You violated compartmentalization protocols. But the Director has told me that in spite of what you've done, you're needed on this program, and he is giving you a chance. I need to know that you're with us, Eldredge. I understand that this may frighten you, but you of all people understand the benefit here? The Golds are like . . . _yon eksplozyon_ . . . an explosion, _non_? This will give us a laser. No more . . . collaterals; no more shotgun blasts. Eggs to omelets.\"\n\nEldredge nodded, desperately trying to work saliva into his mouth, to keep his knees steady. Welch had slid away from the panel, was wandering aimlessly inside the cold storage unit, blood dripping from his twisted nose. He wasn't hurling himself against the door, which was an improvement over the Golds, but not by much. Maybe Dadou could do what she promised; maybe she couldn't. It didn't matter to Eldredge either way.\n\nDadou's grip tightened further, and Eldredge winced. \"Are you on board, _Dokt\u00e8_? The Director is giving you this one chance. We need to know that you're with us.\"\n\nEldredge couldn't make himself give her the answer he wanted, so he stalled for time. \"What about Jawid?\"\n\nDadou's eyes narrowed, a simmering anger gathering behind them. He winced as her grip tightened further. \" _Sa se pa yon repons, Dokt\u00e8._ Jawid is Jawid. I am asking if _you_ are with us.\"\n\nEldredge shook off her arm. \"Yes.\"\n\nDadou advanced on him, hands twitching. \"You're absolutely certain?\"\n\nEldredge's belly was sour with fear. Dadou looked like she was itching to strike him. \"Yes, of course.\"\n\nThe anger vanished as quickly as it had come, and Dadou smiled again. \"That's good to hear. I knew we could rely on you.\"\n\nEldredge took a step back, trying desperately to keep the horror off his face. He briefly considered telling her that the Director giving her orders was a walking dead thing, a corpse like one of the Golds, or maybe even Schweitzer, but he looked at her false smile showing entirely too many teeth and thought better of it. She wouldn't care.\n\n\"I'll . . . I'll go back to my office,\" he said.\n\n\"You do that.\" She smiled wider. \"The Director would like you to pack it up.\"\n\nSick fear churned in his guts, made his chest tighten. It was a moment before he could stammer a response. \"Wha . . . what? Why?\"\n\nDadou waited, enjoying his discomfort. \"He'd like you to move up on to the first tier, in the annex adjacent to his office. He thinks that, as part of the executive team, it would be good to have you close by.\"\n\n\"Of course,\" Eldredge said. \"I'll go get on that right now.\"\n\nDadou said something to his back as he walked away, but Eldredge didn't hear and didn't ask her to repeat herself. It was time to go, as fast as he could and as far as he could. He'd figure the rest out from the road.\n\nThe moment he was back in his office, his knees went weak, the tightness in his chest worsened. He put out a hand to steady himself against his desk. He didn't have time. Even now Dadou was reporting the outcome of the meeting. He doubted he had convinced her, and it didn't matter if he had. He couldn't do this. Dadou was insane. If she achieved the desired outcome, she would be placing this power in the hands of a dead thing that had shown callous disregard for human life time and again. What would the Director do then? Would he put a jinn inside Eldredge?\n\nHe thought of the Director receiving Dadou's report, communing with the three monsters behind him, the things bedecked in ancient regalia, like kings ready to mount matched thrones. He shuddered at the thought. Maybe they were advising him to snuff out Eldredge even as he stood here wrestling with his own anxiety. It didn't matter. He was not working for a monster.\n\nAnother spasm hit him, a wave of nauseating weakness that almost took him down. More panic. The tightness in his chest solidified, welled upward, leaked out the corners of his eyes.\n\nNot panic. Grief.\n\nThe Gemini Cell was the closest thing he'd had to a home for as long as he could remember. At first, it was a cool job, then a calling, and over year after year, it simply was. He had accepted the threat that magic posed, his role in stopping it. The horizon stopped drawing nearer. Schweitzer had been the first nail in that coffin, the first tremor of the realization that what he was doing might not be good, that _he_ might not be good.\n\nAnd now . . . those thin lips, wriggling like worms behind the tight weave of the white fabric . . . Welch's canted neck, purple muscles bulging. Eldredge shuddered again.\n\n_Quit fucking around. If you're going, get on with it._\n\nHe was going. Eldredge thrust his hands deeper into his pockets, hunched his shoulders, and did his best to look preoccupied. _You always chew your moustache when you're really bothered._ He tucked the corner into his mouth and chewed on it, as if he were contemplating a problem that required great concentration, headed for the double doors that led to the main elevator bay.\n\n\"Sir.\" A male voice, commanding.\n\nEldredge kept walking. Boots tramped as the speaker ran to catch up. \"Sir! Sir! Doctor Eldredge!\"\n\nThere was no way to pretend he hadn't heard him now. _Act natural. You're in the middle of something; you'd be irritated._\n\nHe turned, frowned, faced a soldier he didn't recognize. \"You're wanted in the Director's office. In person. Not over the commlink, sir.\"\n\nEldredge's bowels turned to water. He had to pause for a moment, clenching his bladder to keep it from letting go. _They want to discuss things further, and by \"discuss,\" I mean they want to fucking kill you._\n\n\"I was just ordered to move my office up there. I'm getting started on that right now.\"\n\n\"I understand, sir, but apparently, he wants to talk to you first.\"\n\nThe Director had never wanted to speak to him face-to-face in all the days he'd been in the Cell. _Dadou told him she wasn't convinced. It's over for you._\n\n\"Director's elevator is this way, sir,\" the soldier said, gesturing behind him. \"It's been enabled for your use.\"\n\n\"I was actually on my way to the latrine,\" Eldredge said. \"Let me drain the vein, and then I'll head on over.\"\n\n\"He was real specific, sir. He wants you to come now.\"\n\nEldredge paused half a second too long for a man who had nothing to hide. _If you go back in that office, you are not coming out._ He pointed at his crotch, cocked his eyebrow. \"Sorry, man. When you gotta go, you gotta go.\"\n\nThen he turned on his heel and hurried toward the elevators. He could feel the soldier's eyes on his back, the thrumming of the blood in his ears drowning out the sound of him talking into his radio, no doubt calling Eldredge's reluctance upstairs. _Don't overthink it. Even angry spirits from beyond the grave understand that a guy has to go to the bathroom. They'll wait._\n\nAt the last minute, he veered away into the stairwell again, not wanting to risk being trapped in a metal box that could be shut down externally. He was slowly conscious of his excuse becoming painfully real. His bladder felt suddenly full, the need to vacate it overwhelming. _No way; you do not have time to stop for a bathroom break._\n\nHe took the stairs two at a time, his bladder jostling with each step, threatening to open up. If it opened, then it opened. He could die just as easily with piss running down his leg.\n\nOne floor, then two; the air in the stairwell was close and musty, trapped in the narrow space between the cinder-block walls and the metal staircase. The lights were low, dull fluorescents running on a separate, lower-powered generator to allow them to stay lit in an emergency. It had never bothered him before, but in his sudden panic, the space felt claustrophobic, the coiling shadows ready to congeal into a clutching threat. The tight space seemed to absorb sound, close as a womb, ready to birth him into the daylight if he could just climb fast enough. The only sound was his own breathing, labored and panting, the rubber soles of his shoes padding over the grip tape on the stairs.\n\nAnd something else.\n\nA dull scrape, something leathery whispering over the surface above, trying to keep quiet and very nearly succeeding.\n\nEldredge froze, and suddenly the light around him brightened, took on a faint teal cast.\n\nIt was coming from his waistband, the light so bright, it spilled the banks of his white coat, colored the air around him. He reached back, grasped the grooved metal of the hilt, drew it out.\n\nThe KA-BAR blazed, the jinn locked inside so agitated that it practically smoked, thick turquoise light filling the air. It chased the shadows from the corners, bounced off the white doors and their silver handles, the dimly lit EXIT sign one level up. The one he wanted. The way out.\n\nThe scrape again, and a whooshing sound. Something big and heavy falling toward him.\n\nEldredge stumbled back as something tall and lean fell onto the landing in front of him. It was an involuntary move, born of shock and fear, but it saved his life. The shadow swiped for him, bone claws ripping through his lab coat and the shirt beneath, digging bloody furrows in his chest. He felt them score his ribcage, but his heart, his precious lungs, were spared.\n\nThe light from the KA-BAR washed over the thing, reflecting off lines of rough-cut gems, playing across ridges of hammered tin and copper where they pushed through the layers of ancient dust.\n\nOne of the three crowned Golds from the Director's office. It must have been sent to ensure that he made his appointment. The striations of its gray muscles slid under skin gone thin as old cellophane. Its face was totally gone, any vestiges of humanity utterly wiped away. The bald skull was stretched taut with the old skin, peeling back in places to reveal the gray-yellow bone. The gold eyes flickered, brighter and larger than any others Eldredge had ever seen.\n\nIt said something in a language long dead, Eldredge guessed. What few jinn he'd heard described had been uniformly ancient. Its mouth folded into a tube, the jaw flexing and curling, until it was a lamprey tube ringed with sharp teeth. Its cheeks rose in a gross facsimile of a smile, and it lunged.\n\nEldredge shouted and leapt back, feeling his shoulders arc out over empty air. He tucked his chin, resisted the urge to flail with his arms. His one weapon was the KA-BAR, and he kept it tight against him as his shoulders slammed against the sharp lip of the stair. His head followed, stars exploding across his vision as he slid backward, each step cracking into his spine in steady, staccato rhythm, until his shoulder collided with the landing and darkness enveloped him.\n\nHe felt something heavy hit his stomach, knock the wind from him. His vision swapped places with his breath, air headed out, sight coming in. He was folded up around one sharp, bony knee, the ankle bent between his own legs, copper bangles sparkling with square-cut emeralds. A hand locked around his throat, the sharp edges of metal rings digging into the folds of his skin, drawing blood. Eldredge grabbed the wrist, pulled hard, desperately trying to swallow air. The wrist was so thin that his thumb and forefinger met with inches to spare, but it was stronger than iron and just as cold.\n\nIn the periphery of his vision, the crowned head reared back, the lamprey mouth flexed. Dust pattered against Eldredge's face.\n\nHe tried to stab it in the back with the KA-BAR, folding his arm down, bringing the monster into a tight embrace that drove its knee deeper into his gut. The monster put its weight on his throat, and he felt his windpipe collapse as it grabbed his bicep, pushing his arm down.\n\nEldredge coughed, the edges of his vision going as gray as the monster's skin. He pushed with all he had, but he may as well have pushed against a truck. The monster pushed on his bicep, and his arm went flying back down to the floor. Eldredge bent his elbow, let his forearm drop, stopping as the knife struck the monster's back. He tightened his grip, felt the blade's edge catch, bite.\n\nThe Gold screamed, a high-pitched sound like a bird of prey, and Eldredge felt the magic in the knife discharge. The monster shook as the jinn in the knife lunged for it, spiritually grappling it, pushing it out and back into the void from whence it came.\n\nThe teal light went sky-blue, then white, so bright that Eldredge had to shut his eyes.\n\nAnd then it was over.\n\nThe Gold King's body slumped against him, light as a bundle of dry sticks. He felt the crown slough off its head. It bounced down the stairs, clattering like a dropped pan.\n\nAnd then there was silence, broken only by the pinhole wheeze of Eldredge's breath whistling through the tiny hole left in his crushed trachea. He sat up, the Gold King rolling away, little more than a dusty mummy without the jinn to animate it. He dropped the KA-BAR in his lap and clawed at his neck, frantically trying to suck in air. _Stop. Think. Panic won't save you. You have to fix this._\n\nHe stiffened his thumbs, jamming them at angles in below his Adam's apple, pressing harder until he felt the edges of the airway, struggled against the nausea that threatened to swamp him. _Don't panic. You can breathe. That wheezing sound means you can breathe._ He pushed, massaging in and out, until at last he felt the airway spring open with an agony that blotted out his vision for the third time in as many moments.\n\nHe slumped against the floor, his neck searing agony, his tongue feeling several sizes too large for his mouth. _Get up. You can breathe, so get up! You bought yourself some time, but you don't know how much. You have to get out of here._\n\nHe staggered to his feet, his back singing out as his spine took the weight of his torso. _Slowly. Start with one foot._\n\nHe took a shaking step forward. A gleam of light caught his attention, brought his vision into focus. He slipped his hand around the KA-BAR's ridged leather handle. The jinn inside was sated with the banishment of its enemy, and the blade glowed so softly, he could barely make it out. He shook his head and winced as he swallowed involuntarily, slid the weapon back into its sheath in his waistband, and made his way topside again.\n\nHis tongue hung out of the corner of his mouth, the root of it thick and foreign in his mouth. His throat felt as if he'd swallowed a hot coal. His back and shoulders screamed with every step. Pins and needles in his butt and thighs.\n\nBut the pain was blotted out by the looming doorway, leading out of the stairwell and into the lobby beyond. Eldredge bit his lip, steadied himself, and checked his clothing.\n\nHis shirt was ripped and bloody where the Gold King's claws had sliced through. He pulled his coat tight, ensured that it covered him to the neck. It would have to do. He tucked his tongue back into his mouth and clamped his jaw shut. The movement caused him to swallow reflexively, the hot agony making his eyes water. He waited until the pain subsided to a manageable level, then opened the door, stepping out into the corridor beyond.\n\nIf there was an alarm, he couldn't hear it. To his right, the hallway ended at a door he knew led into the \"corporate\" foyer. This was the isolated facility's only cover, a manned receptionist desk that sported the Entertech logo, the corporate sponsor who'd lent their company name to the project, despite not knowing what it was used for. _Paid a pretty penny to get them to take that on._\n\nEldredge turned left, walking down the long hallway and badging his way through a door, which opened with a click and hiss of air. The elevator beyond required another swipe of his keycard. They hadn't disabled his accesses yet. _There was no need. Who would guess the Gold King would fail to do its job?_\n\nThe elevator opened on a short hallway that ended in another sealed door. There were no guards. There was no need for any. As far as Eldredge knew, the blast-proof doors would only open for the electronic IDs of Eldredge, Jawid, Dadou, and the Director himself. Each step down the hallway was two kinds of agony, the first physical, the second the dread certainty that at any moment, one of the other Gold Kings would settle a bony hand on his shoulder, claws sinking in, slowly turning him around . . .\n\n_Don't be stupid; it hasn't been a minute since you fought the other one. They can't know yet._ Still, he hurried the rest of the way and badged himself through the door marked simply CONTROL.\n\nIn the dark silence beyond, with his back to the door, he finally allowed himself to breathe. The small room featured a broad control board covered in buttons and blinking lights. The wall above was a series of monitors. This was the reason he had come here. The screens showed the inside of the facility from dozens of angles. There were other control rooms like it, manned by soldiers, but this was the only one that gave the full view: the cold storage chambers, the laboratories, the testing chambers dotted with burn-freeze nozzles. All the spaces where the true work of the Gemini Cell was performed. Even the Director's foyer was shown, the secretary's face bathed in the static glow of her computer monitor.\n\nEldredge saw no running guards, heard no alarm bells. He had a little time, at least. _Make it count._\n\nHe needed to get out of here, and fast. There was no hope of going on foot. The Cell's cover facility was an office park in northern Virginia. He would escape into a city crawling with police in the center of his nation's seat of government.\n\nHe looked longingly at the helo bay, the limbered helicopters crouching like huge insects. The duty pilots sat around a crate, playing cards. They knew him as the Cell's lead scientist and would follow his orders without question. If he went down there now, he had no doubt one of them would fire up one of the birds and fly him anywhere he wanted to go. _But what will happen when he radios flight control for clearance to take off? Or worse, what will happen when you're already in the air and he gets a call from base?_\n\nNo, the helos were out. He looked instead at the motor pool. The cars were specifically chosen to be discreet, a range of sedans and compacts common in suburbs across the country. No white vans, no black sedans with tinted windows. Eldredge could see license plates from thirty different states and knew each one of them was backstopped enough to stand up to scrutiny. Two guards stood near the shack beside the giant, rolling steel garage doors. Since there was a possibility of exposure to outside view, they wore jeans and pullovers, sunglasses propped on their ball caps. But Eldredge could see the thin bands wrapping the paddle holsters in the backs of their trousers, knew there were high-caliber pistols nestled inside. Two killers, dressed to look like a couple of manual laborers on a smoke break.\n\nSame problem there with the helos. They would let him check out a car, but they would also call it in. It also wouldn't take them long to chase him down even if he could get out of the garage. He needed them occupied. He needed the entire facility occupied, at least long enough for him to get a head start.\n\nHe checked the monitor in the arms locker. Claymore mines were stacked beside coils of det-cord, bricks of pre-casting Composition B. There was enough firepower in there to blow half the building sky-high, but he'd need to go several floors down to reach it, and unlike this control center, that _was_ guarded, and by people who would look askance at his presence there. Like everyone working for the Cell, Eldredge had received at least rudimentary explosives training, but that didn't mean guards wouldn't cock an eyebrow at him attempting to check any out.\n\nBesides, explosives weren't the Cell's real weapon. Those were the undead, immortal Operators, like the ancient, withered king he'd just dispatched. They were more powerful than any explosive. His throat throbbed as he thought of the creature's hand on it, slowly choking the life out of him while its gold eyes blazed into his.\n\nAnd suddenly, Eldredge knew. He couldn't fight his way out of here, but he didn't have to.\n\nSomeone else would do it for him.\n\nHe flicked his eyes between the cold storage chambers. The Golds stood like statues in the center of each one. With no blood nearby, all the heartbeats on the other side of doors and walls they couldn't break, they abandoned even the tiniest pretenses of the living: sitting or pacing, twitching or scratching. Eldredge had only seen one Operator continue going through these motions, a nod to a humanity he desperately clung to. Schweitzer.\n\nHe caught himself glancing between cells, trying to pick the best one. _Just do it. You don't have time._ He settled on Gold Eight, a thick-limbed Operator who had been short and stocky in life. It squatted on muscular thighs, sharp elbows perched on its knees, facing the back corner of the room, so still that it looked carved from stone.\n\nEldredge matched the number over the cell door to the button on the console, flipped the plastic cover up. He thought of the ruins of Basye, the tangled remains of the scout troop. The Gold King's knee in his gut, the window of his vision slowly narrowing, going gray as he struggled for air.\n\nThe Director had been willing to unleash the Golds on an innocent town, on a bunch of children, on anyone who got in his way. He had been willing to unleash one on him. He would do it again, Eldredge knew, the very moment he learned that the one he'd sent had failed.\n\nLet him learn what it was like to face one of them down.\n\nEldredge punched the button, watched through the flickering monitor as the cell door slid open. Gold Eight jerked upright immediately, head snapping toward the sound. It paused only to open its mouth in a silent howl, then crouched down on all fours, knuckle-walking out the door so quickly that it seemed to blink off the monitor.\n\nEldredge knew the run-books by heart for every emergency protocol affecting the facility. There was only one that called for every guard to leave their post. Only one that turned every eye inward. Its code word was _Sunspot_ , and it meant that a Gold had slipped its bonds, was loose in the facility.\n\nEldredge grabbed the radio that connected to the building-wide address system. He depressed the thumb switch, hearing the alarm sound in response. \"All personnel, all personnel,\" he said into the speaker, hearing his words echoing through the hallways, in every room. \"All personnel seal acc-points in East Wing, level two. East Wing, level two, is Sunspot. I say again, Sunspot, East Wing, level two.\"\n\nIt was, of course, the wrong information. The Gold was currently speeding its way down the open access tunnel on the level below, but it would take them a while to sort that out.\n\nEldredge wasted no more time, ignoring the pain in his back and throat, rushing out the door and back to the elevator, his impatience so great, he actually danced from foot to foot as the car rose and opened on the upper floor. He turned and raced toward the motor pool. He badged through the entryway just in time to nearly collide with the two guards shouting into their radios as they came on. \"Doctor Eldredge!\" said one. \"They called Sunspot; are we sur\u2014\"\n\nEldredge cut them off with a gesture. \"It's not a drill. Ruptured cold line put a crack in the door. There're three in East Wing. There's a flamethrower team there, but they could use someone at the junction acc-point. The duty roster isn't in the control room. I don't know where the axe team is, but I need one of you to check the rack room.\"\n\n\"Which\u2014\"\n\n\"Figure it out en route! Go right now!\"\n\nThe men exchanged a glance, and Eldredge felt his mouth go dry. It was thin, and he knew it. Hopefully, they didn't know it too.\n\nBut you didn't get assigned to guard the motor pool due to a surfeit of mental acuity. A moment later, the men were shouldering past Eldredge, guns drawn, the door clicking shut behind them.\n\nEldredge stood for a moment in the sudden relative quiet of the motor pool. The cars around him reflected the fluorescent tube lights stretching across the unadorned concrete ceiling. The alarm still sounded, faintly audible through the thickness of the door. A light swirled overhead, washing all in honey-colored waves.\n\nHe made his way over to the shack by the door, reached in through the window, and slapped the broad green button inside. With a groan followed by the rapid clicking of chains, the door began to rise. Eldredge blinked at the daylight flooding in.\n\nThe keys were kept in the ignition. Eldredge chose a small subcompact, the kind of car that an old man living alone might drive on his weekly trip to the grocery store. He almost signed the logbook checking the car out, as he had so many times before, before remembering his situation. He got behind the wheel and started the motor, his mind screaming at him to rev the engine and peel out of the lot.\n\nHe didn't. He drove slowly and deliberately, praying he wouldn't draw undue attention as the facility locked down, that by the time they had the situation contained, it would be too late to catch him. Again, thin.\n\nHe drove by rote and memory, letting his hands and feet guide the car out of the office parking lot, down the access road, and onto the entrance ramp for 66 West, out into the countryside, toward Basye and the forests where Schweitzer had last been seen. The route brought him closer to the deployed Gold team, but they had long since moved on from Basye, and he doubted the Director would have them double back if it meant taking the pressure off Schweitzer. If he was going to hide, the huge forest where they'd lost Schweitzer was his best chance.\n\nThe highway traffic was thick but moving, and Eldredge blinked in the sunshine, looking at the other drivers. None so much as glanced his way, just one more commuter in a throng. If he ignored the pain in his back, he could almost pretend that he was just another person. He had been outside many times before, overseeing ops, meeting with potential recruits, but this was the first time he'd ever truly left. In spite of the pain and terror, in spite of the pit in his stomach as he realized that he'd left without supplies, Eldredge found himself excited. The forest lay ahead of him, and all the cars in the motor pool were kept with a full tank. After he passed the first police cruiser and it didn't turn on its lights, Eldredge actually began to hope he would make it. As 66 snaked past Warrenton and the signs of civilization around him grew sparser, he was able to turn his mind to formulating a plan with more substance than simply putting the Cell facility behind him.\n\nWhat now? Would he run to the cops? Tell them that he was being chased by soldiers on the orders of a walking corpse in a bad suit and a white hood? They would hold him until they got direction from on high, and on high was precisely where the Gemini Cell was situated.\n\nThere was no one to tell who would believe him. He had lived in that bunker for so many years. He had no family with whom he was close. His room and his belongings were all back there, just a few floors below the crowned thing that had just tried to kill him.\n\nThe Gemini Cell was designed to take people in and keep them.\n\nThe only ones it let out into the world were dead. That had worked until Schweitzer.\n\nSchweitzer.\n\nThe man was still out there somewhere. Eldredge surprised himself by using the title, was more surprised to find it was true. Schweitzer might not be living, but he was still a man. More, he was the one man strong enough to oppose the Cell. He'd escaped, he'd eluded them, he'd shredded seven Operators, stopped the Cell's only living Aeromancer. He had been retreating ever since he'd run, but Eldredge didn't think it was because he was afraid. He was doing it to protect his family, and now just his son. Eldredge thought of the raw heap of meat that had once been Schweitzer's wife, and shuddered.\n\nNo, Schweitzer was protecting his family. It would be a long shot for him to oppose the Cell head on, but he was the only being in the world who had a shot at all.\n\nEldredge thought of the Director, the three kings behind him. Two now, thanks to Eldredge. He had seen them. He knew. They would never let him go.\n\nSchweitzer might be a thin hope, but it was the only one he had.\n\n# CHAPTER XIX\n\nTHE THINGS WE DO FOR LOVE\n\nJawid turned away from the ruined piles of flesh that had been the flamethrower team. They'd managed to catch Gold Eight on fire before it had reached them, but even burning brightly, it had still been able to rip them limb from limb before the axe men had arrived to cut it down.\n\nThe soldiers had finished with their axes and now knelt among the remains, working with their knives. Sunspot protocol said there should be nothing left larger than four inches square. Even with a burned corpse, that took time.\n\nThere was nothing for Jawid to do, but they'd called him down anyway, also according to protocol.\n\nAfter a minute, one of the soldiers looked up from his knife work and cocked an eyebrow. \"So, are we good here? No nasty surprises coming?\"\n\nJawid shook his head. \"Of course not. The body is destroyed. Even if the jinn were still inside, it couldn't harm anyone.\"\n\nThe soldier went back to slicing through a tough knot of bone. \"So, no chance of it all . . . coming back together and giving us a fight?\"\n\n\"None.\"\n\n\"Well, then . . . you're making me nervous standing there.\"\n\nJawid turned away, not knowing where he was walking, only that the burned-flesh stink of Gold Eight was growing fainter with each step. When at last he realized where he was, he stood outside a door, hand hovering over the only break in the otherwise reflective stainless steel surface. A black plastic plate had been slipped into two brackets, engraved in white letters. 202\u2014ALVA, DADOU. SCORPIO LNO.\n\nJawid realized with a shock that he was frightened, sickened. And so he had come here. Because he loved her. Still, his hand hung in the air.\n\n_Knock, you idiot! You love her. Tell her!_\n\nBut his hand wavered and would not move. He forced himself to think of her softly parted lips, her hips rocking against him, the earthy smell of her throat. But he had to force himself to recall, for when he didn't, a different vision took the fore: Dadou's curled lip, the rage simmering behind her eyes, the taut muscles in her arms and shoulders. Long, graceful fingers flexing. She had killed before. She could kill again. Magic had given Jawid many things. Strength was not among them.\n\n_Have some courage. She is your tilth now. What would you prefer? To stay here and put jinn in living men?_ He shuddered as he thought of corpse after corpse, of the men writhing in what Dadou called her _ch\u00e8z espesyal_ , her special chair. Their eyes bulging out of their heads, their arms straining against the straps, their death rattles sounding as Dadou threw up her hands in exasperation. _K\u00e8t! We are so close. The next one. It will work with the next one._\n\nJawid didn't doubt she was right. They were close. He could feel the living soul being pushed aside, making room for the dead one they were attempting to Bind in with it.\n\nBut he could still smell the smoking remains of Gold Eight, mixing with the copper tang of the soldiers' spilled blood. How had it gotten out? Had the door mechanism broken? Had someone been careless? Would he be blamed? It didn't matter; Jawid felt his guts roil, his breathing coming faster. He could suddenly feel the closeness of the corridor around him, the weight of the earth overhead. Wherever the jinn were concerned, there was always blood, one way or another.\n\nHe had to talk to Dadou. He had to take her away from this place. They had joined. They were one in the eyes of Allah now. The escape of Gold Eight was a sign. Allah was telling him it was time to take her and go.\n\nAnd soon as the thought occurred to him, Jawid knew it was right. _Allahu akhbar._ He had to talk to her now. Allah was with him. No matter how Dadou frightened him, he would tell her of his love.\n\n_You reached out to Schweitzer, and look what happened._ Jawid could remember himself opening to Schweitzer, and Schweitzer's sudden lunge into his own memories. _This is why he escaped._\n\nAnd now he was doing the same with Dadou, making himself vulnerable to her. The thought chilled him, stayed his hand as he tried to knock again.\n\n_What is your other choice? To stay here forever?_ _How else would a Gold have gotten out save by the will of Allah? He has sent you a sign. You wanted a family. She is your one chance._\n\nHis knuckles finally scraped against the metal. Once. Twice.\n\nJawid was about to turn away when he heard the soft click of the door opening.\n\nDadou's face in the crack of the doorway was the one he feared. Her eyes burned, narrowed slits sizing up targets. Her fingers curled around the doorjamb as if she were about to throttle it. Jawid froze as her eyes found him, simmered, unchanging, no recognition in them. He was just something close enough to hurt.\n\nAn instant later, the corners of her eyes turned up; her mouth followed. \" _Chouchou._ You lonely?\" She swung the door wide, stepped back so he could enter.\n\n\"The alarm . . .\"\n\n\"I heard. It's been handled.\"\n\n\"How did it get out?\"\n\nShe shrugged, the ease of the motion troubling him. \"Occupational hazard.\"\n\n\"They called me down to . . .\"\n\n\"I heard that too.\" She motioned him inside. \"Come in.\"\n\nHe had been in her cell once before. It was the opposite of his own. Clothing was heaped in the corner, mostly tactical gear, the sort he'd seen the soldiers wear when they weren't in uniform. There was one long dress of brown and gold laid out next to a pair of leather sandals beaded with seashells. They both looked very old. He had never seen her wear either one. Her bed was unmade, pillows lying on the floor.\n\nA shrine had been built in the corner opposite the clothing, a riot of objects surrounding a framed portrait of the Virgin Mary: a doll's head, a plastic Christmas tree, a string of beads and a bottle of rum, a plastic skull and a heart-shaped mirror. Just below the image of the Virgin was an unframed wallet photograph in black and white. It was curling at the edges, yellow cracks working their way through a smiling man holding two little girls.\n\nDadou noted his stare. \"That is my _vodou_ ,\" she said. \"It keeps my family close.\"\n\n\"You believe that?\"\n\nShe smiled sadly. \"Sometimes, it helps to try.\"\n\n\"But we know what happens to the dead. We know that doesn't make a difference.\"\n\n\"Do we now? You believe that a magic man in the sky gets angry when you make pictures of him.\" The anger returned to her eyes.\n\n\"I'm sorry.\" He cursed himself. She hated when he said that. _Tell her the truth._ Holy Qur'an said that Allah did not forgive the worship of idols.\n\nBut he saw the murder in her eyes and quailed. He had not come to fight with her on this. That was for another day. Once they were together and away from this place, he would ensure she built no more shrines to idols. He watched as she forced the anger down, covered it over with the smile.\n\n\"Anyway\"\u2014he tried to sound relaxed, but his voice came out terrified instead\u2014\"I didn't come here to fight.\"\n\nDadou sat on the bed, patted it. The action should have stirred him, filled his head with thoughts of love, but all he could think of was the risk he was taking, and his manhood wilted. Nobody left the Gemini Cell, certainly not a Sorcerer. _Do you believe in the power of Allah, or don't you?_\n\n\"I didn't come for love, either,\" he said.\n\nDadou leaned back on her arms, her breasts rising toward him, cocked her head to the side. _\"Tr\u00e8 kirye,\"_ she said. \"What did you come here for?\"\n\n\"The truth is . . .\" And now that the moment had arrived, he found he could not say it. \"The truth is . . .\" He stammered, his tongue suddenly too big for his mouth. _Just say it! Why is it so hard to speak the truth!_\n\nDadou's face went serious. \"Stop,\" she said. \" _Rete, chouchou._ Nothing good can come of what you will say next.\" She pushed herself to her feet, pointed her finger at him. \"Time for you to go. We will talk more tomorrow.\"\n\nBut by then, he'd found some sliver of strength. It was little more than an ember, barely enough for him to call himself a coward, but it was enough to speak. \"The truth is that I love you. We are joined. You and I are to be together. And if you will not see that on your own, I only ask that you give me the chance to show you. If you come away with me, we will make a beautiful thing together, as God intended when He joined us. I know we are different, but all people are from God, and God will smooth these differences until we go forward as one. We only need to give it a chance. I love you, Dadou. You must be my wife.\"\n\n\"We were doing so well,\" she said, her voice flat. \"We were making such progress. We were working. You had managed to keep your stupid mouth shut for _days_. I thought we were . . . how did the _Dokt\u00e8_ say it? Out of the woods.\"\n\n\"Please,\" Jawid said. \"I love you.\"\n\n\"Love.\" Jawid could hear the rage rising in her throat. \"Love,\" she said again. \"What the fuck do you know about love?\"\n\n\"I know that when a man and woman do what we've done, that means they love one another. And I know what the Holy Qur'an says, that those who love one another must marry. Love is a thing that comes from God, Dadou.\" Jawid was angry now, and it felt good to be angry, because it made him feel safe, because maybe if his anger could match hers, she could not hurt him. His father had told him that when spiders joined, the female ate the male. That would not happen here.\n\nDadou blinked. Predator eyes. Like a coiling snake. Or a spider. \"You think because you dip your wick a time or two that you are in love? You think your stupid god cares whether we stand at an altar and mumble some words?\"\n\nShe stabbed an angry finger at her shrine. \" _That_ is not magic. _That_ is not even god. I am a _S\u00e8vit\u00e8_. I _know_ what happens when you die. I have _seen_ the soul storm with my own eyes. That is to help me remember my home, my family, where I came from. That is _not_ because I believe an invisible man in the sky is looking at me and judging whether or not I build a pile of trinkets for him, and he certainly does not care who I fuck, or when, or why.\"\n\n\"Alva, this is wrong. Us being apart is wrong. What the Cell is doing is wrong. We are murdering people. We are making piles of bodies. And now a Gold has escaped. He killed some soldiers, not as many as when Schweitzer escaped, but still . . .\" He shuddered.\n\n\"They are soldiers. They are paid to be killed.\"\n\n\"You didn't see . . .\"\n\n\"I have seen plenty. More than you. It's the mission, Jawid.\"\n\n\"The mission? You sound like an American.\"\n\n\"I sound like someone who does their job.\"\n\n\"What is our job? Whatever the Director tells us. Why should we care what he wants or what he doesn't? America was never my home. I am from the mountains above Bibiyal and wherever the Baba Khel graze their herds. You are from Port-au-Prince. Americans helped us, maybe even saved us, but they didn't do it out of love. They didn't do it because they want us to be happy, or well, or right with God. They did it because they want what we can do. We are machines to them. We are . . . assets, they call it. I owe them nothing. And if I did owe them anything, it has been repaid. I want my own life now, and now that I have met you, I know what that life is supposed to be. It is to be us, together. I am going back to the Korengal.\"\n\n\"You are not going anywhere.\"\n\nHe ignored her. \"You should see the Pech River, Alva. It is like a silver ribbon. You will come back with me, and we will make a home there.\"\n\n\"You are not listening to me.\"\n\n\"You are not listening to me! I am telling you that I love you!\"\n\n\"You don't know what love is! You don't even know what a woman is!\"\n\n\"Then you will teach me. You cannot be happy here. You cannot be happy killing people.\"\n\nDadou took a step toward him, and this time, Jawid didn't flinch back, closed with her. \"I have never been happier,\" she growled.\n\n\"You are wrong. You don't want to leave because you feel you will not be safe. But you will be safe in the mountains with me. My family is there, and if you are my wife, they will protect you too. If we work together, we can escape. If we work together, we can survive. This is what the American army is always talking about, teamwork. We are a team. And together we can be gone and safe in my home.\"\n\n\"Now, you listen carefully.\" Dadou looked at him from below her brow, fists clenched. \"There is _nowhere_ you can run. There is _nowhere_ you can go where they can't find you.\"\n\n\"You are wrong. It took them over ten years to find bin Laden. They never found Mullah Omar. And neither of those men had magic. Maybe they will find us, and together, we will be ready. We beat the Soviets, we beat the Americans before. _Ooba chi thur sur wawooshte, se yawa naiza, se sul naize._ I love you. That comes from God. He will see it through.\"\n\nDadou's anger peaked, and she shrieked, an incoherent animal noise.\n\n\"God?! God?!\" She spat out the words. \"Where was God when I crawled the streets of Port-au-Prince, down in the dog shit on my knees, sucking the cocks of old men for enough food to see the next dawn? Where was God when my brothers were killed for a rooster, when my sister was raped to 'teach her not to be so high and mighty'? Where was God when I lost my first baby? My second? When the army doctor told me I would never have any more?\"\n\nThe fire of her anger burned his to ashes, and with it, his resolve. Suddenly, he was no longer angry. Suddenly, he was afraid. \"You will have more,\" he said, but his voice sounded very soft, as if it came from a long way away. \"We have magic. We can do anything.\"\n\n\"That is not how our magic works,\" Dadou answered. \"It is not magic for making children. It is not magic for hiding. It is magic for speaking with the dead. That is all.\"\n\nThere was something in her voice now, something in her face, darker and more solid than what he'd seen before. His love had been a white-hot thing when he entered the room; now he could scarcely believe he had come at all, wished that Allah would reach down from heaven and turn back time, take him back to the hallway when he'd been hesitant to knock, make him trust his instincts. _No, you will have faith. You will trust in Allah._\n\n\"I'm leaving,\" he said. \"Come with me.\" He looked at her eyes and thought of female spiders eating their mates. He didn't want her to come with him anymore, only insisted now because it was Allah's will.\n\nDadou circled, stood between him and the door. \"Don't be stupid. I am not coming with you, and you are not leaving.\"\n\n\"You are a woman. You cannot stop me from doing anything. I am done with this place and with this work.\"\n\nDadou said nothing. She crouched before the doorway, long fingers hooked. Her spider eyes looked eager.\n\n\"You are mine!\" Jawid shouted. It was an angry sound, though fear was in possession of his body, as if it were a jinn driving his limbs. He reached out and grabbed her wrist, pulled her toward the door. She was a woman; he was stronger than her. That was the will of Allah.\n\nExcept that he knew he wasn't stronger than her, could see it in her ready stance, in the taut ripples of muscle. _Allah protect me._\n\nShe dropped her arm, casually, gently, the look in her eyes never changing. He tried to yank his hand back, but she clamped his wrist to her side, as if she were made of solid iron. He pulled harder; she didn't move.\n\n\"Ah, _chouchou_ ,\" she whispered softly, not sounding angry at all. \"This is going to hurt you a lot more than it is going to hurt me.\"\n\nShe whipped her head forward.\n\nBy the time Jawid felt the impact, he was three steps back, his vision a gray tunnel. Something wet and sticky was running into his eyes. The fear had given way to nausea, and he felt his stomach hitch as if it would try to push the panic out of his mouth. He ran, and suddenly there was pain in his nose, and he was reeling back from her closet. He had run into it. How had he gotten here?\n\nPain in the back of his head. She had grabbed his hair, was pulling his head back. _\"Mwen regret sa,\"_ she said. \"You think you fucking own me? You think you are the first man who has told me that I belonged to him?\"\n\nHe grunted, the pain a fire in his scalp. It brought some of the anger he so desperately needed back. He pumped his arm, throwing his elbow back into something hard but yielding.\n\n\"Fuck,\" Dadou gasped, her grip on his hair loosening. He jerked his head forward and felt some of his hair rip out by the roots. Dadou whooped a breath, tightened her grasp on what remained, holding him fast. He threw the elbow again, but it found empty air this time.\n\nDadou was screaming, a litany of unintelligible Creole curses that finally descended into an animal growl. Jawid couldn't recognize her voice anymore; it scarcely sounded human.\n\nHis need to be free of her grip became desperate. He felt his lungs constrict, his heart hammering so fast and so hard, he thought it would leap from his chest. At that moment, he knew he would do anything to escape, suffer any indignity, anything if she would only stop hurting him. He had misread the sign. This wasn't Allah's will. Or, if it was, he lacked the bravery to see it through. \"I'll leave!\" he shouted. \"I'm sorry! I'll leave!\"\n\nDadou didn't hear him. \"Think. You. Own. Me.\" She bit off each word. Her knee collided skillfully with his hamstring, perfectly placed to make the entire leg go numb. He leaned, desperately shifting his weight to his good leg, but Dadou held his head fast, and the pain proved too much for him; with a groan, he swung back to the weak leg, overbalanced, dropped to his knees.\n\n\"Stop!\" he shouted, not even trying to elbow her now. There was no point in struggling against her. She was so much stronger than him, so much better at fighting.\n\n\"Now you want me to stop?\" Dadou asked. \"What happened to us belonging together? What happened to the will of your stupid fucking God?\"\n\nHer knee again, this time in the base of his spine. Jawid felt the vertebrae flex, strain, and finally give, a low _crunch_ that sent pins and needles shooting down his legs at first, finally vanishing into numbness. The reality of it hit home. He was defenseless. She was pitiless. He was going to die. He tried to scramble to his knees, to find the strength to fight for his life, but his legs would not answer him and his arms and shoulders felt heavy, as if his veins ran with lead.\n\nDadou knelt over him, lowering him gently down, until his chest lay on the floor. He swatted at her weakly until she knelt on his hand, grinding the bones into the stiff carpet.\n\n\"Please,\" he whispered. \"Please.\"\n\n\"You love me, eh?\" she said. \"I'll tell you a little story so you know the woman you wanted to marry.\n\n\"When I was little, we begged on the steps of a church. The nuns were good to us, but the mason who worked on the church wanted to wed my sister. He said some funny things. Things like what you said: 'I love you,' and 'God meant for us to be together.' And when she refused him, he raped her. Said it was a lesson, to teach her 'not to be so high and mighty.'\n\n\"My sister was a good girl. She never hurt anyone in her whole life. She was always smiling, always kind. Men see that in a woman and they think her weak. That's what you think of me, Jawid. That's what you mean when you say, 'I love you.'\n\n\"That mason was the first man I ever killed. I faced him in the church nave, in front of the altar of the God who said, 'Thou shalt not kill.' I didn't rush it, _chouchou_. I took my time.\n\n\"That is what happens to men who try to own me and mine, Jawid. You're a stupid animal, so I will let you live, but like all animals, you must be trained.\"\n\nShe reached down and grabbed his hand, bending his finger back until he felt the bones begin to creak. He screamed, thrashed, and the hand came away. Dadou cursed and flailed for it again, but Jawid punched out with a strength born of desperation, his thumb jamming into her eye.\n\nDadou shrieked, ripping his hand away and punching him hard enough to make his head bounce off the floor. \"You fucking bastard!\"\n\nHe tried to roll to his feet, but she grabbed his hair again, hammered his head down.\n\nIzat was there, and Anoosheh, and his father and mother as well. The river sparkled behind them. The old man had his arms folded around a walking stick, his forehead creased with worry. \"It will flood,\" he said. \"You must take the goats to high ground.\"\n\n\"Where are the goats, Grandfather?\" Jawid tried to ask, but he couldn't speak; his head hurt too much. The riverbank flashed red.\n\nHis mother's burqa shivered. Gold lights glinted behind the mesh veil. \"The Americans are coming.\"\n\nJawid heard the roar of helicopters and tried to turn his head to see them, but the pain was too great.\n\nHe opened his eyes and suddenly, his family was gone. The river had melted into the iron-gray carpet on Dadou's floor, soaked through with red. Bits of wet gray slime floated in the fluid, along with yellow-white fragments.\n\nHis head whipped forward.\n\nIt was just Anoosheh now, washing in the river, as she had been on the day he had seen her. Her skin was the color of the dry ground, her hair as thick and curled as sheep's wool. She looked over her smooth shoulder, her graceful neck arching, caught his eye, smiled.\n\n\"There you are.\" Izat, at his shoulder. Jawid's bowels turned to water. The old man had caught him looking at her. He would be furious.\n\n\"I'm sorry, Grandfather,\" Jawid said, eyes filling with hot tears.\n\nIzat put his hand on the back of Jawid's head, ruffled his hair. \"I do not judge. That is for Allah only.\" He smiled. \"He is merciful and compassionate.\"\n\nJawid felt relief so great that he sank to the dusty ground. \"Thank you, Grandfather.\"\n\nIzat kept his hand on the back of Jawid's head. \"Don't thank me; thank Allah.\"\n\nAnd then he whipped Jawid's head forward and threw him into darkness.\n\n# CHAPTER XX\n\nWHY DID YOU GO?\n\nEldredge squatted next to the pickup parked in the discount store lot, grateful its owner had parked it nose into the light. The shadows pooled behind the tailgate, giving Eldredge plenty of cover as he unscrewed the license plate using the screwdriver in his car's toolkit, swapping the plates out with his own. The front was dicier, but the lot was deserted at this late hour, and he made short work of it. The Cell had given him basic training they'd intended to be used if he had to roll out on ops with fire teams. They'd never meant it to be used to make good his escape, but it had taught him enough to remember to swap the plates. It would throw off law enforcement, but not for long.\n\nHis body still ached, but not as much as before, and each time he woke up and saw the sun rising outside the window of his car, he felt lighter.\n\nBecause he was still alive. He'd evaded the Cell another day. _Why bother? What is the point of staying alive?_ He was running nowhere; he had no idea where to find Schweitzer, the only weapon that stood a chance of bringing the Gemini Cell down. And then what?\n\nBut the truth was that he wanted to live. Even through the pain and the loneliness and the dislocation, he desperately wanted to live. Even in an old body, a damaged one. The strangers he passed on the road, families singing in SUVs, college students with their hatchbacks crammed with furniture, all occupied a different universe, one he could never set foot in. They didn't know that magic existed. They didn't know that the government had a hidden hand in it. They didn't know that hidden hand was attached to an arm no longer living, governed by a dead mind, cold and ancient, driven by an agenda they couldn't possibly understand.\n\nIt was isolating, but the isolation was followed by a fierce, animal need to protect them. These were the people he'd dedicated his life to keeping safe. These strangers. He'd sacrificed everything for them. He'd given up family and friends and future. Staying alive as long as he could wasn't so much more to ask.\n\nIn addition to the toolkit, the glove compartment had a tiny brown envelope with a hundred dollars in twenties, the petty cash included with each vehicle for road emergencies. Added to the forty in his own wallet, it was enough to buy a cheap T-shirt to replace his ripped and bloody one, keep the tank full, and eat at roadside diners for a few days, but the time was coming when he'd have to steal some more money to keep himself going.\n\nWhen he'd last been tracking Schweitzer, he'd been heading west with his son in tow. That was an incredibly vague set of directions, but it was all that Eldredge had to go on. Years of working targets for the Cell had taught him some of the basics. _Focus on the target's immediate needs._ Schweitzer didn't need to eat or sleep. He didn't need clothing or shelter. There was no one for him to check in with. The entire world thought he was dead. Hell, Schweitzer _was_ dead.\n\nBut Patrick wasn't.\n\nThe next morning, Eldredge bought a cheap scissor and disposable razor in a gas station. He shaved in the restroom and hacked his hair down. It looked wilder than ever, but it also looked different, and without his walrus mustache, he would be a little harder to recognize, at least.\n\nThirty minutes later, he pulled up outside the town's public library, little more than a couple of ramshackle trailers linked together and parked behind a church. Eldredge walked past its soaring white steeple and fresh-painted siding, and realized where the town fathers were putting their money. He'd been religious once, back in another life. He laughed to think of it now. Christians were always talking about the Rapture, a glorious day of the dead crawling out of their graves and walking the earth. They had the story of Jesus raising Lazarus, an example of shining hope, the benevolence of a kind and gracious God. For a time, Eldredge had even believed it. But that had been before he'd actually seen the dead walk, had learned firsthand that there was nothing kind or gracious about it.\n\nEldredge hauled the door open; it creaked on spring hinges and banged shut behind him. The library was as unimpressive inside as it was outside, just walls of beaten-looking pressboard shelves and stacked plastic milk crates jumbled with old and poorly used\u2013looking books. Yellowing posters extolling the virtues of reading adorned the water-stained walls.\n\nBut Eldredge didn't mind, because he saw the two things he'd most hoped for. The first was that the library was empty save for the receptionist, a teenager who sat behind a battered and peeling desk, eyes glued to his phone.\n\nThe second was a computer sitting below a battered plastic laminated sign, which read PUBLIC INTERNET.\n\n\"Just going to use the computer for a bit,\" Eldredge said. \"I'm afraid I forgot my library card.\"\n\nThe boy behind the desk waved at him, not looking up.\n\nEldredge sat down at the computer and woke it up, suppressing an almost violent need to run. He'd swapped out the plates, but it was still the same car. He'd cut off some hair, but he was still the same man. He was far from the Cell, but not far enough. They would find him, and every second he delayed made it more certain. _Focus; you can't run forever with no place to go. You have to do something._\n\nDoing something meant taking some risks. This would be his first. He knew the Gemini Cell could read his Internet browsing history, but he had to hope that either he wouldn't alert them, or if he did, that he would be gone before they found him here. He pulled up Google and searched for \"Burglary and Virginia,\" narrowing his search results to those articles posted in the last week.\n\nThe results were staggering, and he wrestled with them for more than an hour, dialing in on drugstores. The thieves always took the same things: cash, drugs from the pharmacy. But Eldredge kept looking. It was the best lead he had.\n\nBecause when the mop-up team had found the bag Sarah Schweitzer had dropped, it had been full of supplies necessary to treat a bad case of poison ivy: antibiotic ointment, calamine lotion.\n\nJim Schweitzer's dead skin wasn't reactant to anything. He didn't have living nerve endings to report itching sensations. That stuff was for Patrick. Dead men also had no use for money, and Schweitzer was that rarest of creatures, the Boy Scout who always did the right thing. He wouldn't steal money beyond what he needed to take care of his son.\n\nEven with Schweitzer's superhuman capabilities, he couldn't have gone far after escaping Basye. Not with a little boy cradled in his arms, crying and scratching at the swelling rash the plant's oil had set to burning beneath his skin. Eldredge narrowed his search. Robberies in and around Shenandoah County, focusing on the limits of what a man could do at a fast walk. Patrick would be nestled in his father's dead arms, but Eldredge knew Schweitzer's determination well enough to know that the man would never stop moving, no matter how much his son squalled.\n\nNothing. If there was a needle in the haystack, Eldredge couldn't see it. Judging by the pieces on blogs and local Virginia papers, all anyone did out here was steal. The kid had stepped outside for his third smoke break when Eldredge finally came across a searchable crime blotter from a tiny police department in Timberville. It was basic and old-looking, but the information was up-to-date and, more importantly, he was able to search robberies and burglaries by type. The drop-down menu had a few options: ARMED, RESIDENTIAL, BUSINESS LARGE (>10 EMP), BUSINESS SMALL (<10 EMP).\n\nEldredge arched an eyebrow. \"Here's hoping,\" he muttered to the empty room, and clicked through.\n\nIt was as he expected. \"BUSINESS SMALL\" burglaries were almost exclusively convenience stores and gas stations when this far out in the country. The blotter laid out inventories of the stolen property like all the other articles. Drugs and cash, always drugs and cash. Eldredge rubbed his eyes as the kid came back in, looking askance at the strange old man who'd been sitting at the public computer for over two hours.\n\n\"How's it going over there, sir? You need any help?\" the kid asked.\n\n\"I'm fine,\" Eldredge answered, barely noticing he had spoken.\n\nBecause he'd just clicked on a link, and there it was.\n\nA little town called Fulks Run, less than twenty miles southwest of Basye. A healthy man could have walked it in a full day. Schweitzer would have been able to make it by nightfall.\n\nThere were pharmaceuticals stolen, but they weren't the usual targets: sleep aids, painkillers, opiates, and narcotics. A few bottles of antibiotics were missing, and the rest of the aisles had been ransacked, leaving almost everything of value in place. The thief had packed a child's school pack with first aid and cooking supplies, what food was available.\n\nCalamine lotion was listed among the missing items, along with a child's Halloween costume.\n\nThere were a thousand possible explanations. Maybe it was a prank. Maybe the antibiotics were part of a homemade drug recipe. Maybe the thief was a crackpot with a penchant for dressing up his dog. It didn't have to be Schweitzer.\n\nBut somehow, Eldredge knew that it was.\n\nThere were no major highways leading to Fulks Run, and the drive seemed painfully slow, despite the fifty-five-mile-per-hour limit on most of the bigger roads. Eldredge kept it strictly at the limit; despite his impatience, he absolutely could not afford to get pulled over now.\n\nFulks Run itself was little more than a wide space in the road, a collection of vinyl-sided houses that were just a step above trailers. It was rustic and beautiful in the way that drew rich, urbane government contractors from DC on romantic-getaway weekends with their wives and mistresses. The convenience store was alongside a diner just off the main drag, sheltered in the shade of the thick Virginia pines that made up the edge of the National Forest.\n\nThe investigation was long since concluded, any broken windows repaired. The blotter had said the break-in occurred at night, when no one was working. It wasn't like he could interview the clerk. Why was he even here? He walked past the windows once, twice, drew a few stares before adjourning to the diner. _You need to figure this out fast or you are going to get caught._\n\n_Ah, hell. You're going to get caught anyway._ The Director would be angry. It would not be painless. It would not be quick.\n\nEldredge ordered a coffee and avoided making eye contact with the waitress, who acted like an old man wearing dirty clothes was an everyday occurrence. He ran his fingers through the tangles in his hair, feeling the grease that had settled in over the past day. It would get harder and harder to blend in, unless he was trying to appear homeless.\n\n_Think. This was the last place he was. Where would he have gone?_\n\nAway from the Cell; that meant south or west, or both. He could be in Arizona. He could be in Florida. He could be anywhere. _No. He has no transportation. Wait. If you can steal a car, so can he._\n\n\"Jesus.\" He couldn't stop the words from tumbling out of his mouth. He didn't even know if it was Schweitzer who'd robbed that store. He had nothing to go on. Any minute now, the local sheriff was going to come in and . . .\n\n\"Hey, can you turn the volume up on that?\" Eldredge pointed to the flat-screen TV hanging behind the counter, the only thing remotely modern-looking in the place. It was turned to the news, showed a young man in his twenties with a dirty yellow beard and matching dreadlocks. He looked like a privileged runaway, or one of those children of CEOs who decides to spend a year homeless on the streets of a big city. His face and body showed the signs of weather and rough living, but the set of his mouth and the hurt entitlement in his eyes told Eldredge that this was someone born into money. The kid had been worked over badly. One eye was swollen shut, and thick black stitches showed where a long gash had been sewn shut in his forehead. One ear was cauliflowered.\n\nThe news banner marquee rolled past too fast for Eldredge, but he could make out the words: CLAIMS TO HAVE BEEN THROWN FROM TRAIN BY ZOMBIE.\n\n\". . . had a kid with him; I think he kidnapped him,\" the man was saying.\n\nThe TV cut to a sheriff in a dark green uniform, gray moustache quivering on red jowls. \"Of course, we are taking Mister Colridge's story seriously, and will keep you updated as we have more information. However, given the outlandish nature of his claims, and the positive results of his drug test . . .\"\n\n\"That kid is crazy,\" the waitress said, drowning out the sheriff's next words. \"I used to know . . .\"\n\n\"Shhh!\" Eldredge jumped out of his chair, jamming a finger against his lips.\n\n\"No need to be a jerk,\" the waitress said, sauntering away with a wounded look.\n\nThe news had already cut to the next segment, a story about a car wreck on I-64. The young man's face was replaced with a burning segment of blacktop rolling through the verdant Shenandoah Valley.\n\nBut Eldredge was already digging through his pockets, fumbling for the money to pay the check.\n\nBecause he'd managed to hear the young man say one more thing in spite of the waitress's nattering, a burst of profanity the news station had only just managed to bleep out.\n\n\"His eyes, man. They were silver. They were on fucking fire.\"\n\n# CHAPTER XXI\n\nLAST RESORT\n\nThe need for supplies forced Schweitzer off the train somewhere in Kentucky. The magic that augmented his senses didn't come with a built-in map, and he was sure of their location only by virtue of a state border sign that whipped past while he peeked out a crack in the door.\n\nThe poison ivy was healing well, but Patrick's steady sobbing had been replaced by something far more troubling, a stone-faced silence, inscrutable eyes that looked shockingly wise in such a young face. Life in the SEALs had been a steady parceling-out of hell; Schweitzer's life had been spent wading through the depths of human depravity, the sewers peopled by human traffickers, narco-terrorists, and those organized-crime operators strong enough to threaten the power of states. It had offered him a glimpse of not only what was done in those depths but how it impacted those it was done to. He looked at his son again and shivered. He'd seen those eyes before. He knew what they meant.\n\nBut even a steady diet of traumatic terror couldn't dampen Patrick's need to eat and sleep, and so Schweitzer jogged his way along, his boy nestled against his shoulder now, cheek placid and accepting of the cold, dead skin beneath it. Patrick would grow up in a world where it was possible to trust a corpse. As far as Schweitzer knew, he was the only one who could be trusted. Anything else remotely like him would kill Patrick as soon as look at him. He thought on that, on the hard conversation that he was going to have to have, how he was going to explain all this to Perretto, if Perretto would even speak to him, or would just draw and fire when he saw what Schweitzer had become? He would worry about it when he got closer; for now, the only plan he had was to keep moving, to keep his son fed and alive and as far from the Golds as possible.\n\nSchweitzer kept returning to his augmented hearing, straining to hear a stealthy approach, a muffled hiss, anything that might indicate the approach of pursuit, but there was nothing. If the Gemini Cell had his trail, then they were not following it for some reason or had found a way to silence pursuit effectively enough to take him unawares. He doubted that, but he couldn't doubt the fact that Kentucky was disappearing under his feet, a steady drumbeat that took them west, moving through the woods just off the roads, ducking low whenever he heard a car approaching.\n\nAfter two days, he had become a petty thief. The routine of smash-and-grab robberies of boutiques and small shops was too easy, given his powers. _You are an immortal superman,_ he told himself, _and you use it to lift premade sandwiches and bottles of sports drink from gas stations._ It was for Patrick, he reminded himself; that had to make it okay.\n\nHe told himself this as he broke the lock off the freezer cabinet in a gift shop that was self-consciously rustic, lacquered rough wood garlanded with plastic ivy and flowers. Patrick was getting better about being alone, learning to sit tight and keep quiet, secure in the knowledge that this cold, dead thing that claimed to be his father would return eventually and would bring food with it when it did. He'd promised the boy ice cream, and he intended to deliver. The trick was to be quick enough that Patrick wouldn't lose patience and start wandering off. Schweitzer was confident that he would overhear anyone drawing near. He scanned the soggy cardboard dividers, the brightly colored packaging. What hadn't Patrick tried yet? Schweitzer remembered Peter passing him a tricolored rocket pop, blue eyes crinkling at the corners as Schweitzer's face lit in response to the sweet tang of it hitting his tongue. Would Patrick have a similar reaction? Had he ever tried a Creamsicle? Schweitzer felt another stab of grief as he realized that he didn't remember. He thought of Patrick's hard eyes, wondered why he was bothering. _You are dead. You are just trying to get him to a safe place. That doesn't require ice cream. There is no fathering left for you to do._\n\nBut he remembered his early days of unlife, navigating his dead body around the refrigerated cell they'd kept him in. He hadn't had to sit, but he had. He hadn't had to nod or shake his head when he \"spoke\" through Jawid to Eldredge.\n\nBut he had. Those tiny gestures had saved his humanity, and his humanity had cast out Ninip and given him himself.\n\nSitting for him, ice cream for Patrick. It was something.\n\nHe snatched a chocolate-dipped Popsicle out of the freezer. Best to go with the classic when he wasn't sure what Patrick's tastes were. He straightened, closed the lid as gently as he could, slipped the broken padlock back through the hasp. The longer the morning shift took to notice the break-in, the more time before they called it in. He turned to head back to the corner of the store, where Patrick sat among a pile of plush toy owls. He wouldn't play with them, Schweitzer knew. He would stare off into the distance, face pale and eyes blank. _What did you expect? For him to chatter, babble, and play nice while you rob the place?_\n\nSchweitzer paused, concentrating, dialed his hearing out, straining to pick out anything from the chorus of usual night sounds: insects chirruping, distant cars, and the stealthy padding of nocturnal mammals going about their routines.\n\nHeavy breathing, the thumping of running feet.\n\nMale, out of shape, hoofing it alone down the center of the main drag. Schweitzer sniffed the air. It was still too far out for him to smell the fear in the interloper's sweat, but he could hear it in the high edge of his labored breathing. The man was terrified. Wincing huffs. In pain, too.\n\nSchweitzer dropped the ice cream and hefted the bag of canned food as he raced to the back of the store. Patrick was standing, one toy owl in each hand. He was making low noises in his throat, flying them in circles over his head, one chasing the other. His eyes still had too much thousand-yard stare in them, and he was not smiling, but the small gesture of genuine childhood made Schweitzer's dead heart clench. He wanted nothing more than to stand there and watch his son just be his age.\n\nThe thumping steps, the heavy breathing. Closer now.\n\nThere was no time. _He can't be a kid. Not for five minutes. Not ever._\n\nHe raced to scoop up his son, saw the surprise on Patrick's face as he swooped in, shifting briefly to fear as he caught him around the waist and swung him up over his shoulder. Schweitzer knew he should say something, make it appear he was attempting to play, but all of his senses were focused on the sound of the breathing and the feet, the lone man running closer and closer. A tiny part of him registered the damage he was doing, that this was hurting Patrick, but the focus of the SEAL and the super senses of the magically augmented being bulled them aside. _Got to see what I'm dealing with here. Need high ground._\n\nThere was a staircase behind the register, but it was close to the storefront window, in the direction of whoever was coming. Schweitzer pushed open the back door to the building, but he still couldn't prevent it from squealing on the hinges he'd broken getting in.\n\nThe footsteps slowed to a jog, then stopped. Whoever it was held their breath as they tried to listen. _Damn it._ It didn't change anything. He still needed the ground. Patrick might have been frightened by the speed with which Schweitzer had appeared and scooped him up, but he was quiet for now, settling into the familiar rhythm of nestling into his father's shoulder.\n\nSchweitzer turned and looked up. The building could barely be called two stories, more like a single floor and an attic, but it was higher off the ground than anything else around. It would have to do. Schweitzer jumped. The strength in his legs with so great that he barely had to crouch to get the momentum he needed. Patrick pressed close as the wind swept over them and the weathered brick wall rushed past. For a brief moment, it was only the two of them, washed by the light of the moon and the cold blast of the passing air. Under other circumstances, it would have been wonderful.\n\nHe vaulted the lip of the roof and put his son down on the torn tar paper. Behind Patrick, Schweitzer could see the open door leading down into the storefront. \"Shh,\" he said, putting a finger to the gray smears that had been his lips, before making his way to the opposite edge.\n\nA man stood in the street, head sawing left and right, dirty white hair wild on his head. Schweitzer recognized him, not just his face and body, but the tenor of his winded breathing, his bouncing gait. _It can't be. Why the hell would they send him alone?_\n\nIt didn't matter. It would be good to kill him. Schweitzer conjured Sarah's mangled corpse in his mind and prepared himself to spring.\n\nThe man reached into his waistband, pulled out a long-bladed knife. Teal light spilled off the blade, so bright that it washed the street before him, chasing shadows into the gutter. He turned away from Schweitzer, and the light dimmed, he turned back toward him, and the light grew brighter. He took a step toward the building, lifted his eyes to the lip of the roof. \"Jim!\" he shouted.\n\nThere was no doubting the voice. It was Eldredge.\n\n\"I know you're there!\" Eldredge called. \"Please! I just want to talk! I need your help!\"\n\nScrabbling in the darkness behind him. Patrick was stirring, crawling on his hands and knees over to his father. Schweitzer put out a hand and he stopped, crouched, listening.\n\n\"Jim!\" Eldredge took a step closer, and now Schweitzer could feel the magic washing off the blade, the current eddying toward him, faint but powerful, the light brightening as it drew nearer.\n\nSchweitzer stood, head and shoulders rising above the roof's lip. His SEAL mind told him he presented a good target for a sniper, backlit against the moon. It was bad tactics, but there was something in Eldredge's voice, his ragged appearance, that let him take the chance. He heard no one else, and a sniper's round would do nothing more than punch a hole in him.\n\n\"You've got to be out of your fucking mind, Eldredge.\"\n\n\"Jim. Oh, thank God.\"\n\n\"You've got about thirty seconds before I rip your fucking head off.\" He was conscious of Patrick listening at his side. The boy had seen so much, curses and threats were nothing now.\n\n\"I know about Sarah, Jim. I'm sorry.\"\n\n\"Are you, now? I am too. Killing you might make me feel a little better about it.\"\n\n\"I'm dead anyway. I went against the Cell, Jim. I'm on the run. Sarah was the last straw.\"\n\nSchweitzer could hear the lie in his voice, the change in pulse and breathing, the rush of blood as his heart pumped faster. Sarah might be part of the reason he'd left, but not the whole.\n\n\"Is that why you're here? You want me to do it before they do?\"\n\n\"No. I want to live. I want you to help me to live.\"\n\n\"And why the hell would I do that?\"\n\nEldredge's eyes were wide, his cheeks tight, forehead lined. Schweitzer saw no guile in him. He was terrified. He was desperate. \"We both know the Cell will never stop hunting you. It's either you or them.\"\n\n\"I'm dead, Eldredge, in case you hadn't noticed. Now my wife is too. Let them come. I'll make a good fight of it.\"\n\n\"You have Patrick, Jim. He's with you.\"\n\n\"Patrick's dead.\" Schweitzer tried to put his hand on his son's shoulder, but Patrick had moved back from him. Schweitzer turned his head to look for his son as he spoke to Eldredge. \"Funny thing, but life on the run from a SOF unit that fields killer zombies isn't conducive to the health of small children.\"\n\n\"You're lying,\" Eldredge said. \"Patrick's alive, but he won't be much longer if you don't stop the Cell. You're the only one who can do it, Jim. Whatever you may think of me, I didn't have a hand in killing Sarah. Our interests are aligned here.\"\n\n\"What the fuck do you expect me to do? Go running back to Virginia with my son in my arms?\" The deep shadow on the roof forced Schweitzer to dial into the infrared spectrum to find his son. Patrick was standing now, walking toward the open door downstairs.\n\n\"I will stay with him,\" Eldredge said. \"I will keep him safe.\"\n\n\"Don't move,\" Schweitzer whispered to his son, then leapt. The movement and the emotion that drove it were so sudden that he didn't realize he intended to kill Eldredge until he was already in the air. Shades of Ninip, Schweitzer's jinn self, made manifest.\n\nHe landed on the broken asphalt in a crouch, bone claws slid out, spines and horns working their way through the rents in the skin along his back and head. Eldredge stumbled back a step, thrusting the knife out before him. Up close, Schweitzer felt the magic in it more strongly. It thrummed against his own, checking him, cooling his anger. He didn't want to go near that blade. He straightened instead, leaned in. \"You want me to give you my son?\"\n\n\"Even a small cut from this will destroy you,\" Eldredge said. \"Don't come near me.\"\n\nSchweitzer wasn't sure he believed him, but it didn't matter. It would be easy enough to move around the blade, rip the old man's arm off at the shoulder. The key would be to get close enough to the wrist to control the weapon's movement.\n\n\"Listen to me,\" Eldredge said. \"The Cell is everywhere. There is no place in this country where they can't reach you, probably no place in the world. Whoever you entrust with Patrick is going to be discovered, and that means they're going to be killed. Like it or not, Patrick is a death sentence.\"\n\nSchweitzer thought of Perretto. He'd known this, of course, that to entrust Patrick to him was to condemn his own children to lives without a father, if they lived at all, but he had been desperate for a direction, for some kind of _hope_ that Patrick could have something approaching a normal life. His rage surged as Eldredge spoke the words. Because once said, they couldn't be unsaid; because now he couldn't give Patrick to Perretto.\n\n\"You need someone who already has a death sentence.\" Eldredge spoke in a rush. \"Someone with nothing to lose. Someone who will believe stories about a secret magical military unit that marshals an army of superpowered corpses. As far as I know, I'm the only person in existence with that resume, Jim. We need one another.\"\n\nSchweitzer heard a rapping from behind him, turned to see Patrick banging on the locked glass door to the store. Schweitzer could hear the boy faintly through the barrier. \"Daddy!\" The same word he had cried when Schweitzer's enemies had broken into his home and ended his life.\n\nSchweitzer moved just as quickly as he had against Eldredge. Before he knew it, he had raced to the door and ripped it open, the shattered lock flying. He reached down for his son.\n\nPatrick paused, hand on Schweitzer's leg, stared shyly at Eldredge. Schweitzer ruffled his hair, only touching a few strands before his son detached from his leg, closed the distance to Eldredge, and froze, staring up into the old man's eyes. Eldredge lowered the knife, mouth crinkling into a smile. \"There you are,\" he said to Patrick, then looked up at Schweitzer. \"You're not a very good liar, Jim. You never were.\"\n\n\"Fuck you,\" Schweitzer said, heading toward his son. But Patrick had already closed the rest of the distance, grasped Eldredge's fingers. Schweitzer came closer, but didn't intervene as Eldredge bent down to the boy. _How long have you kept Patrick on the run?_ Schweitzer asked himself. _How long has it been since he touched another warm, living hand? Looked into eyes that aren't made of fire?_\n\nSchweitzer remembered when he had visited the Cell's command center before he'd escaped. He'd shaken hands with one of the analysts, thrilled to the warm pulse in her palm. He knew the power of that contact, knew what it meant to Patrick, young as he was.\n\n_You can never give him that. No matter what you do. Not ever._\n\n\"How the hell did you find us?\"\n\nEldredge looked up, the ghost of the smile he'd had for Patrick still playing on his lips. \"I got lucky. I caught a news segment on TV saying that you chucked a guy off a train.\"\n\n\"I didn't chuck anyone. I told him to jump. Is he okay?\"\n\n\"Banged up but fine. It gave me a positive location for you and told me how you were travelling. There's only one cargo line through here, Jim, and it goes in a straight line. From there, it was a question of calculating time and distance. Luckily, we're in the middle of nowhere, Kentucky. There aren't a lot of towns, and I figured you'd have to resupply. The rest\"\u2014he hefted the knife\u2014\"came down to this.\"\n\nPatrick stared up at Eldredge, and the old man ruffled his hair. \"Ah, Jim. All those years shut underground. You get bent on a task and you start to forget why you do it. The thing itself becomes its own reason. There is no end state.\"\n\n\"Patrick is my end state, Eldredge. There's nothing else.\"\n\n\"And this is the only way Patrick will ever be safe,\" Eldredge said. \"Take out the Cell, or sooner or later, they'll take out your son.\"\n\nHe was right, of course. Nothing would make Schweitzer happier than to see the program that had birthed him into this new life, that had kept him prisoner and lied to him about his family's survival, pay. He could see himself tearing through the hallways, the blood of his enemies, the soldiers, the analysts, painting the walls.\n\n_No. They are serving their country the best way they know how. They don't deserve this. Only the people at the top. You have the remember that. That is the difference between you and Ninip._\n\n\"Why did you run?\" Schweitzer asked.\n\n\"The Director, he . . .\"\n\n\"I thought you were the Director.\"\n\n\"No, Jim. I'm the 'Lead Scientist' in a program that involves no real science. I run things, but I took my orders from him.\"\n\n\"And he is?\"\n\n\"He's an Operator, Jim. All the years I worked there, and I never knew. But I know now. He's as dead as you are.\"\n\nSchweitzer looked at his face, smelled the chemicals in his bloodstream. He was telling the truth. \"How did you find out?\"\n\n\"We always communicated over video chat without the video. I finally went to see him.\"\n\n\"Why?\"\n\n\"Because it's out of control, Jim. He's killing indiscriminately; by the time we caught up with you and Sarah, the Golds had wiped out an entire town.\"\n\n\"I know; I saw.\"\n\n\"No, you didn't. Not the aftermath, the gutted buildings and corpses. It was . . . It's too much. They got a Boy Scout troop later. Boy Scouts, Jim!\"\n\nSchweitzer said nothing, his eyes fixed on his son, who clung to Eldredge's leg now, cheek pressed against his thigh.\n\n\"And there's more,\" Eldredge said. \"They brought in another Sorcerer to work with Jawid. She's . . . better than he is. They're Binding jinn into living subjects. We tried it before, years before you . . . before we got you. The subjects never lived through it, and eventually, we called it off. But this time, they've kept on trying, and they're having some success. They'll get it eventually.\"\n\n\"Why would they want to do that?\"\n\n\"I don't know, but it's not hard to guess. A Gold Operator can't walk in the daylight, can't attend board meetings or make speeches. They are monsters, Jim. A jinn in a living person? They could go hidden. They could do something other than kill.\"\n\n\"No, they couldn't. You didn't live with a jinn, didn't share your body with one. Killing is all they know how to do.\"\n\n\"Maybe it's different with a living soul. Maybe it's different in a living body. Maybe it isn't different, but they've figured out some other way.\"\n\n\"I can't believe you expect me to believe any of this. I may be the corpse, Eldredge, but you're the monster. You've murdered and you've lied and you've worked in the shadows for years, and you expect me to believe that you've suddenly found a conscience. You expect me to leave my son with you and race off to my own destruction. How convenient that would be for you, for the Cell.\"\n\nEldredge's face twisted in grief and anger, but his smell didn't change. Schweitzer's words were hurting him, but he still wasn't lying. \"You're right, Jim. I have done terrible things. I am the monster. Even dead, you're a better man than I am. But in this case, in this one case, we need one another. Everything I've done, I've done with the idea that it was better for the country, for humanity. I broke eggs to make an omelet. You mean to tell me that you never killed innocents on all your scores of operations?\"\n\nHe was right. Schweitzer had killed people to keep ops from being compromised. In a small Eastern European hamlet owned by the self-styled \"Amir of the Caucasus,\" he'd put a bullet in a girl in her early twenties for turning a corner too fast. She had just been a blur in his vision, and then she had been dead. His training had put her down; it helped him with the shock and grief, too, kept him focused on the op. It was within rules of engagement, but it still ate at him. He'd never discussed it with Sarah. Why bother? It wouldn't bring the girl back to life.\n\nHe didn't discuss it with Eldredge now, but he saw the man's point.\n\n\"It all went so fast,\" Eldredge said. \"By the time I realized it was too much, Basye was already gone. I always assumed that I was working toward a goal I could understand, could share in. I was taking on a burden so that others wouldn't have to.\"\n\n_So others might live._ Schweitzer knew the oath well, had almost sacrificed his own marriage on that altar.\n\n\"The Director is . . . maybe not a Gold. He's patient; he's smart. He has control of his appetites. I wonder if he's like you. He's definitely dead, Jim. Whatever he's got planned, it isn't part of the national agenda; it isn't event part of the _human_ agenda. This Binding into the living, I shudder to think of what he plans to do with that.\"\n\n\"Put himself in a living body.\" The thought lanced through Schweitzer. A living body. A beating heart again. Warm arms to hold his son. _There's no end state,_ Eldredge had just said, but if magic could put Schweitzer back in a living body, then maybe he was wrong. \"Someone important,\" Schweitzer went on, grateful that his unlife enabled him to keep emotion out of his voice.\n\nEldredge nodded. \"I don't want that to happen, Jim. I want to enjoy some of this freedom I've supposedly been fighting for. I want to live.\"\n\n\"Death's not so bad. You get used to it.\"\n\n\"Please, Jim. I'm not a SEAL. Nobody's going to bring me back.\"\n\nSchweitzer looked at Patrick, reached out a hand toward him. Patrick took it tentatively, but he didn't let go of Eldredge's leg. \"You are not taking my son.\"\n\n\"That's right,\" Eldredge said, detaching Patrick and gently pushing him back toward his father. \"I'm not. I'm sitting tight with him, wherever you tell me, giving you whatever reassurances you want, until you've killed the Director and whomever else you have to in order to make sure the program stays dead.\"\n\n\"That might be a lot of people.\"\n\nEldredge shrugged. \"However many it takes, Jim. It isn't much of a chance, but it's a better idea than running until Patrick really does expire.\"\n\n\"I can't protect you, Eldredge.\" The thought of Sarah materialized too fast for him to squash it or the spike of remorse that followed. \"I can't protect anyone.\"\n\n\"I don't want you to protect me. I want you to help me bring it all down. It's the only way I'll ever be safe. It's the only way your son will ever be safe.\"\n\n# CHAPTER XXII\n\nNEW MANAGEMENT\n\nDadou knelt over Jawid's corpse for a long, long time.\n\nHis head had come open at the top, the skull cracking along the forehead, spilling its contents onto the rug. His nose was broken, both eyes swollen shut. If she looked at him from the right angle, he looked like he'd passed out after being in a barroom brawl. She followed the procedures, checked his pulse, both carotid and radial. Nothing. He was gone.\n\nHer mind sorted through and discarded any number of excuses. He had turned traitor. He was going to run. He'd put his hands on her. But the truth made a cold and slow crawl up her spine until it seated, immovable, in her mind.\n\nThe fact was that she barely remembered the moments between Jawid telling her to come away with him and now. The rest was stuttering, red-tinted flashes, like glimpses of the countryside seen through the slats of a boxcar hurtling along the tracks, or when booze and _ariwana_ had begun to shut off her mind.\n\nShe had been so _angry_. But the anger that had propelled her through the killing vanished as soon as the deed was done, leaving her only the memories of Jawid that she liked. His sweet shyness. His earnest honesty. His bone-deep understanding of what she lived with every day. She blinked at the corpse before her, the one she had made.\n\nHe was a man, and the worst kind of man, a _religious_ man. All religions were built to subjugate women, to make them bend their knees and spread their legs for entitled children. She had seen what had become of that for her sister. Jawid wanted the same thing, no matter how sweet his sighs and protestations of love. She had tolerated them because they made him pliant in the short term at least, but combined with his desire to betray the program, they were past enduring.\n\nSo, why was she sorry he was gone?\n\nBecause the truth was this: the anger, the simmering rage, had made her another person. She had meant to hurt him, frighten him.\n\nNot to kill him.\n\nShe looked up at the shrine she'd built, the picture of her mother and sister. She wondered what her sister was doing now. Married, she assumed, or dead in a ditch. It didn't matter; there was no way Dadou could talk to her now, no way to explain what had become of her life.\n\nMaybe that was why she was sorry Jawid was gone. Because he was one of the few people who had known who she was now. Because that pool seemed to be forever shrinking.\n\nThe isolation gripped her, and she went mad for the second time that day. She sobbed, the tears turning into laughter. She grabbed the small, thin pillow off the bed, put it over his purple face, covered some of the blood and brain that pooled on the floor. He looked better that way, more peaceful. Dadou lay down, placed her head on his back, pulled the tight curls of his thick black hair. It was clotted with blood and tiny chips of bone, but it still had that delightful spring to it. \"Boink,\" she said, with each pop of the curl. \"Boink.\"\n\nHe was still warm. She nestled against him, felt some of the blood reach her shoulder. It was still warm too. She was two Dadous, one who knew that lying beside Jawid's corpse was sick and crazy, and another who reveled in his warmth, in the close contact, in the knowing that another person was nearby.\n\n\"Ah, _chouchou_ ,\" she breathed. \"I didn't mean to; I am sorry.\" It changed nothing, but it felt good to say it.\n\nDadou didn't realize she had fallen asleep until she was awakened by a low beeping. She had closed her laptop while she had touched herself before Jawid had come to her door, and she hadn't wanted the Director to be able to see. She was sure there were other cameras in the room, but she controlled what she could. Now the light on the side of the webcam flashed as the call came in.\n\nDadou shook sleep from her head. She was foggy, but her mind had returned to her. The blinding rage and crippling loneliness were gone, and she was Dadou again. Jawid's body had gone stiff and cool beneath her, his blood gelling to a thick paste that stuck to her neck and shoulders. She propped herself up on her elbows, blinked at the pallor in his skin, the dull copper smell rising from him. Too weak to be brought back as a Gold Operator, even though it was probably still soon enough to return his soul. She glanced at the laptop. It was likely the Director or his secretary. She would have to report what had happened here; it couldn't be hidden. Fear roiled in her belly. Her lack of control had cost the Cell one of its most valuable assets. The Director would be furious.\n\nShe calmed the fear with an effort, reminding herself that without Jawid, she was the Cell's _most_ valuable asset. _No, they may have others._ Dadou doubted it, but there was no way to know.\n\nThe laptop's chime sounded again. The Director knew her whereabouts at all times; hell, he had probably seen what she did to Jawid already.\n\nShe flipped up the laptop to see the Director's secretary, disingenuous smile already melting away as her eyes roved over Dadou's shoulder to take in Jawid's corpse. \"Miss Dadou . . . I. Are you all right? Is that Mister Rahimi?\"\n\n\" _That_ ,\" Dadou said, \"is none of your business. I will discuss it with the Director directly. Please put me through.\"\n\n\"No need.\" The secretary found her composure, smile springing back to her face, stretching her improbably bright lips. Dadou thought she looked like a circus clown. \"The Director wanted to see you personally. He should be . . .\"\n\nThe chime outside Dadou's door sounded and the transmission cut off. Dadou felt fear sinking in her belly, turned to face the door. Its stainless steel surface reflected a funhouse mirror image of herself, down to the knees where a spray of drying blood interrupted it.\n\nShe didn't have time to approach it before it clicked open, lock manipulated by the master electronic key. A man in a black suit entered, gun drawn, eyes roving the room, never alighting in one place. He ignored Jawid's corpse, gestured with the barrel at one corner. \"Ma'am, I need you to step over there and face the wall. Do not turn around, no matter what happens.\"\n\n\"Do\u2014\"\n\nThe barrel hovered over her heart. \"Ma'am, do not speak. Move to the corner and face it. Do it right now. I won't ask you again.\"\n\nDadou knew she should be angry, knew that if they already had decided to punish her for Jawid, that she was better served by going down fighting. _No. If he wanted you dead, he'd have shot you by now._ She stepped into the corner, so close that her nose almost touched the wall. She heard the man bustling around behind her, going through drawers, kneeling in front of the bed.\n\nHer back and shoulders itched, anticipating the bullet that could come at any moment. _If it's my time, then it's my time. It is no great loss if the world goes on without me._ She thought of the long years ahead of her, angry and alone, and wondered if she might not like it better that way herself.\n\nThe thought gave her some peace, and she focused on the ache in her heart and stomach that contemplating her own death brought.\n\nShe didn't know how long she'd been lost in thought when she finally noticed that all sound of movement had stopped. The room was silent. The air vents did not hiss. She shivered, cool air on her shoulders. She waited another moment before mustering the courage to speak. \"Sir? I'm sorry; can I turn . . .\"\n\nNo sound of movement, no breathing, no answer. Dadou risked a glance over her shoulder.\n\nThe door was closed; the man with the gun was gone. In his place was another man, tall and muscular. He also wore a suit, rumpled and threadbare, draped carelessly over his body. The chipped buttons were misaligned, the cuffs bagging around his black shoes. His hands were enclosed in black gloves, fake leather flaking off in patches. His head and neck were covered in stretched white fabric, giving only the vaguest outline of the depression of his eye sockets, stub of a nose, cut of a mouth. The cold air came from him. As if he had just been wheeled out of a refrigerator.\n\nHe was completely still. No rise and fall of his chest, no twitching of his fingers. For a moment, Dadou wondered if she was the victim of some prank, if the man had placed an eerily dressed mannequin behind her before he departed.\n\nBut then the thing in the suit spoke. \"Do you know who I am?\"\n\nIts lips slid against the constraining fabric, adding a whisper to the crooning, monster-movie voice. She'd never heard it before, not without the aid of a computer modulator, but she knew precisely who he was, had always known, really.\n\n\"You are the Director.\"\n\n\"It's nice to meet you in person, Miss Alva.\"\n\nDadou said nothing. It was not nice to meet this thing in front of her, this freezing thing that didn't breathe, didn't move, save for its lips behind their mask.\n\nOne finger on the gloved hand twitched toward Jawid's corpse. Otherwise, the thing was stone. \"I appreciate your work, Miss Alva, first for Scorpio Cell and now for our joint effort here. You've made stunning progress in a very short period of time, and I'm pleased to see the psychology reports indicating that Jawid had become more compliant thanks to your efforts to . . . convince him.\n\n\"So, you will forgive me,\" the Director went on, \"if I find the evidence before us\"\u2014the finger twitched again toward Jawid\u2014\"somewhat to the contrary.\"\n\n\"I'm sorry,\" Dadou echoed what had become Jawid's favorite words since they'd first made love. It was the truth. She was deeply and truly sorry. She hadn't meant to kill him. But the deeper truth was that her remorse was far outmatched by the possibility of incurring the wrath of the thing standing before her.\n\n\"I am too,\" the Director said. \"Mister Rahimi was an enormous asset to this program, and the most effective we ever employed. He'd have given you a run for your money in his early days, I'd wager. Would you mind telling me what happened?\"\n\n\"He told me he loved me,\" Dadou said. \"He wanted us to marry.\"\n\n\"Those were your orders, Miss Alva. To woo him. To win him. It sounds like you succeeded. Why, then, is he dead?\"\n\n\"He wanted to take me home with him. He was planning to escape. You ordered me to deal with him if he turned traitor.\"\n\n\"And you are certain he would have been successful in this enterprise? You could not have subdued him, bound him, waited for assistance?\"\n\nDadou swallowed. She didn't like being questioned. It made the anger burn behind her eyes, her throat tightening and her hands flexing. But she looked at the tall, thin figure, and the tension in her muscles went slack. She didn't think she could fight him. She didn't think she could win. \"I got angry,\" she said, her hands making useless circles at her side.\n\n\"You got angry,\" he repeated.\n\n\"You don't understand,\" she said. \"It was . . . like going crazy. There were some things that happened . . . to my sister, when we were little.\"\n\n\"You mean to tell me\"\u2014the Director cut her off\u2014\"that you murdered your coworker because you have unresolved issues from your childhood? You think that is an excuse?\"\n\n_Now is where the rubber meets the road,_ Dadou thought. If she was going to pay, it would be now.\n\nThere was a long pause.\n\n\"This is most unfortunate,\" the Director said. \"We cannot have team members inflicting violence on one another in the workplace, Miss Dadou. I'm afraid there will be consequences.\"\n\nDadou felt her fear reach a height where it finally lapped itself, leaving centered calm in its wake. She had seen the dead slaughter the living. Even in a world transformed by magic, dying was still dying. She was ready. When she answered, her voice was steady. \"What will you do to me? Arrest me? Feed me to the Golds?\"\n\nThe Director was silent.\n\nDadou laughed long and low. It was forced, but the action still felt good in the face of this thin, rumpled dead thing in her cell.\n\n\"I fail to see the humor,\" the Director said. \"You have cost me one of my most important assets.\"\n\n\"No, _Direkt\u00e8_ ,\" Dadou answered. \"I took out your garbage. I did you a favor.\"\n\n\"The work he was doing for the program . . .\"\n\n\"He was done working for the program. He was done working for you. It was time for him to go.\"\n\nHis horror-film voice sounded confused, frustrated. \"That is not your decision to make, Miss Dadou. Give me one good reason why I shouldn't kill you right now.\"\n\nShe laughed again. \"There isn't one, unless you've got another _S\u00e8vit\u00e8_ running around? Maybe there is another cell you can call for a replacement Sorcerer?\"\n\n\"There are others.\"\n\n\"Others who can do what I do?\"\n\nThe Director was silent. Dadou smiled wider. She had guessed right. \"I am going to take that as a no.\"\n\n\"But you should not take that to mean you can write your own ticket. I can and will find other Sorcerers if I must, and you should not labor under the delusion that I will hesitate to kill you if I feel you are too far off the reservation. Is that clear?\"\n\nDadou nodded. It was clear, but now that she knew she was the only resource the program had, the boundaries of the reservation had just become a whole lot wider. Dead or alive, all men were the same. Give them the illusion of control, and they were docile as sheep.\n\n\"Anyway\"\u2014the Director flicked a finger at Jawid's corpse again\u2014\"we now have a small problem.\"\n\n\"We have two problems,\" Dadou said, \"and neither of them are small.\"\n\n\"I assume neither of these problems have anything to do with the act of unspeakable violence you have visited on my dear friend and colleague, Mister Rahimi.\"\n\nDadou shook her head.\n\n\"Then\"\u2014the Director's voice took on a hint of exasperation that made him a sliver less frightening behind his masked immobility\u2014\"kindly enlighten me as to your insights into the problems faced by this program.\"\n\n\"Your problems are people. One is a powerful man who wants to shut this program down. The other is James Schweitzer.\"\n\n\"Schweitzer is dead. I would hardly call him a person,\" the Director said.\n\n\"Yet the solution is the same for both of them.\"\n\n\"And that is?\"\n\nDadou smiled. _\"Se de bon ki f\u00e9 bonbon.\"_\n\nThe Director was silent for a long time. \"I know the French, but your dialect is hard for me to follow.\"\n\n\"How do you like to say it here? Kill two birds with one stone.\"\n\n# CHAPTER XXIII\n\nRETURN\n\nEldredge shivered at the base of the tree. He'd seemed a big man when Schweitzer had been his prisoner, the perennial white lab coat giving him a heft that Schweitzer missed now that it was gone. He was all knees and elbows, white hair sprouting from his ears and nose, skin so pale and thin that Schweitzer could see the tracery of veins beneath. He looked like some crazy, homeless grandpa, and of course Patrick loved him.\n\nIt had been the same way with Steve, with the old man who took Sarah in just before Schweitzer came for her. It was always this way with men. Schweitzer tried to write it off as coincidence, a quirk of character baked into Patrick's DNA, but he was too smart to see it as anything other than the accusation it was, as bold and clear as a pointed finger. Without a real father figure at home, his son sought them out wherever he could. He sat on Eldredge's knee, tugging gently on the old man's ear. Eldredge smiled at him, the corners of his eyes crinkling with genuine joy. When he spoke, his voice was thick. \"Such a cutie. I can see why you love him so much.\"\n\nSchweitzer stifled the urge to snatch him away from Eldredge. He had done enough snatching of Patrick as of late. Let the boy experience something other than fear for five minutes. He could sense Eldredge's intentions in the speed of his heartbeat and the smell of his sweat. If he summoned the will to hurt Patrick, Schweitzer would be ready.\n\n\"I am sorry we kept you from him,\" Eldredge said, looking up. The remorse in his eyes was genuine. \"We didn't see how reuniting you would do any good.\"\n\n\"Bullshit,\" Schweitzer rasped. \"You thought separating us would help keep me under control.\"\n\nEldredge looked shamefacedly at the ground. \"That's true. Guess it didn't work.\"\n\n\"Might as well come clean now, Eldredge. Since we're on the same side.\" Schweitzer intended the words to be sarcastic but found that even with his increased control over his voice, he lacked the nuance to carry the tone. Eldredge looked up hopefully.\n\n\"Was it deliberate?\" Schweitzer asked. \"Did the Cell have me killed deliberately so they could use my body? Did you leak my identity to the Body Farm on purpose?\"\n\nEldredge was quiet for a long time. His increased heart rate and blood sugar told Schweitzer that the question rattled him but not why.\n\n\"If you'd asked on the day you escaped us, I'd have said absolutely not,\" Eldredge said. \"But now, I don't know. The Director isn't human, Jim. Who the hell knows why he does anything?\"\n\n\"Who is he working for? There has to be a human hand behind this.\"\n\n\"Does there? You don't work for anyone.\"\n\n\"I'm different. I'm . . .\"\n\n\"Good? That's what I thought too, that your essential sense of ethics was the thing that made you different. It certainly seemed that your 'good' acts were the thing that pushed Ninip out and kept you in. But the truth is that nobody has any idea of how this works except for Jawid and the Scorpio Sorcerer they brought in, and even they don't fully understand it.\n\n\"This Senator I was telling you about. He pulls the purse strings. He'd been threatening to shut us down over the . . . excesses of the Gold Elements we put in the field to find you.\"\n\nSchweitzer felt the lie in Eldredge's chemical cocktail. \"Don't fuck with me, Eldredge.\"\n\n\"He was going to shut us down for failing to find you.\"\n\n\"So? You want the Cell shut down. I don't want to be found. Everybody wins.\"\n\n\"He's going to replace it with something worse. Some new corps under SOCOM. It wouldn't be the end of the Cell, Jim. New boss, same as the old boss. I didn't entertain any illusions that they'd keep any of the old staff, though. We'd all get tossed in the trash or put under some asshole Army three-star who thinks magic is a satanic conspiracy.\"\n\n\"How was he going to do it?\"\n\n\"The same way government suits have done these things since they invented the red power tie. He was going to cut off our money.\"\n\n\"That got your Director's attention, I'll bet.\"\n\n\"It didn't. He didn't really care. Jim, you've been in government long enough to know that nobody ignores funding line items. _Nobody_ , no matter how self-interested, no matter how altruistic, no matter how cynical or idealistic, ignores threats to their funding. I know it seems crazy, but that was the scariest thing of all.\"\n\nIt was Schweitzer's turn to be quiet for a while. \"No, that makes sense.\"\n\n\"I don't know for sure, but I think that's the end game here. To put a jinn in him, to have the one man we answer to be our puppet.\"\n\n\"Our?\" Schweitzer asked. \"I thought you said you were done.\"\n\nPatrick grew impatient at the adult talk, tangled his hands in Eldredge's hair, pulling his head down toward him. \"Oh, hey, there! What have you found? Is there something on my head?\" Eldredge asked.\n\n\"Don't get too comfortable.\" Schweitzer couldn't keep the bitterness from his words. This bastard who had kept him from his son could give him something he never could, warm arms to fold him against a chest that housed a beating heart. \"You're not going to be with him long.\"\n\n\"I'll take what I can get,\" Eldredge said seriously. \"You weren't the only prisoner down there, Jim. I was locked underground for years. I came topside for ops, but that was it. I can't remember the last time I just sat and smelled the wind in the trees, or had a kid play on my lap.\"\n\n\"Do you expect me to feel bad for you?\"\n\n\"No, but I do expect you to understand that this isn't some sneak attack on your family. I am not lying to you, Jim. We are wasting time here. Every minute we delay is another minute for them to find us and make us fight them on ground of their choosing, pitted against the pawns instead of the king. We need to move east, Jim. They won't expect it.\"\n\nSchweitzer ignored him, dialing his hearing out into the wind-tossed tops of the trees behind the building. It was a trap. It had to be\u2014the Cell was desperate; both its regular and Gold teams had failed to bring Schweitzer to heel, so they'd set up this elaborate ruse to lure him in.\n\n_Come on. Ockham's Razor. What makes more sense? That Eldredge is on the run from his own leadership, or that you're being tricked?_\n\nSchweitzer laughed internally. This was the problem with the brave new world he now occupied. When the dead could walk and magic was real, all possibilities were equally unlikely. Logic wasn't going to work here.\n\n_Fine. What does your gut tell you?_\n\nHe studied Eldredge as the man returned his attention to Patrick, patiently enduring the boy's fingers up his nose.\n\nAnd then . . . something.\n\nThe stirring of something in his chest, like a wound reopening, a vein he'd thought severed and scabbed over pumping blood again. His dead heart clenched, his spiritual stomach turned over.\n\nWith Sarah's death, his sense of her, of the link that connected them, had gone dead. He'd been able to focus on it enough to confirm what he knew, that she twisted in the soul storm with the rest of the screaming dead, that she endured the torture that had turned Ninip into a monster over the course of millennia. He knew he would never find her in that morass, that trying would only pull him further from his son. He couldn't abandon the living for the sake of the dead. That was what the monsters did.\n\nSchweitzer didn't know much about magic or how it worked, but as far as he understood, dead was dead. The dead could be returned to the world of the living, but that wasn't the same thing as being returned to life.\n\nAnd with a thunderclap of sudden feeling, the instant resurgence of the link he shared with his wife, Schweitzer knew that was what had happened to Sarah. She wasn't alive. That was impossible. Much as he had tried to turn away from the sight, he couldn't. He had witnessed her horrible death. No, not alive.\n\nBut she was here. In the world of the living.\n\nThe link reported as it had when she lived: emotion and resonance, direction and distance. She was a long, long way away, battered and frightened.\n\nAnd not alone.\n\n\"Jim?\" Eldredge had been speaking, and Schweitzer stopped him now, raising a palm toward him. He concentrated again, wrestling with the strength of his certainty, matched only by the vagueness of the details he needed. She was northwest. Many, many miles. She needed him. He could feel her crushed in the grip of something, battered by it. His wife, pushed into a corner, fighting madly for . . . for herself.\n\nSchweitzer knew that feeling, could remember the sweet sense of corruption, Ninip constantly trying to slide his demonic filter over Schweitzer's perception of the world. Sarah was facing something like that now, save that, where Ninip had tried to slyly persuade, she was being battered.\n\n\"I have to go,\" Schweitzer heard himself say absently. He was already moving.\n\n\"Where? What's wrong?\" Eldredge stood, Patrick reached for Schweitzer, caught hold of his hand.\n\n\"It's Sarah; she's back.\"\n\n\"That's not . . .\" Eldredge paused. \"You're sure?\"\n\nSchweitzer nodded. He squeezed Patrick's hand, but the link yanked him in Sarah's direction as surely as if he were a fish on a line. The need to go to her was as overwhelming as it was instant. \"I have to find her, Eldredge. I have to do it now.\"\n\n\"It's a trap, Jim. It has to be. They wouldn't have brought her back without a very specific reason. They're probably hoping you'll come. They're going to be ready.\"\n\n\"Maybe she's alive . . . You said they were binding jinn into living bodies.\"\n\nEldredge shook his head. \"Not _her_ body, Jim. I saw what happened to Sarah's body. There's no way to put anything back in it.\"\n\n\"Maybe\u2014\"\n\n\"Jim,\" Eldredge cut him off. \"This is the _Cell_. They don't do things to be nice. If Sarah's spirit is back in this world, it's because it suits them to have it here.\"\n\nThe need burned in Schweitzer. Already it was blotting out his senses, the strength of the link so intense that he set his shoulders back to stop it from physically dragging him forward. He knew he had an obligation to Patrick, but it felt fuzzy. It was hard to focus on anything other than the blazing, white-hot sensation of Sarah's presence. She was in the same world. She was so _near_. \"I still have to go. I don't expect you to understand.\"\n\n\"I don't need to understand,\" Eldredge said. \"I ran that program for years without understanding a goddamn thing. Makes things simpler. Jim, this is not a good idea.\"\n\n\"She's _hurting_ , damn it!\" Schweitzer snarled. \"There's something . . . with her.\"\n\n\"They've paired her up with another soul, then.\"\n\n\"That doesn't make sense.\" The jinn had always been summoned into the body of the dead. \"This would mean . . . _she's_ the jinn. She's not a monster, Eldredge.\"\n\n\"This new Sorcerer is good,\" Eldredge said. \"Really good. Who the hell knows what she can do?\"\n\n\"You know.\" Jim was surprised at how angry he was. The link ran on emotion, and it fed his jinn side, crushing the cool professionalism of his training, making him itch to get underway and moving toward her, to _do_ something. \"You're the one who's supposed to know!\"\n\nPatrick shrank into Eldredge's side. Schweitzer knew he was scaring the boy, but he could feel Sarah again, backed into a corner, savaged. He could picture her in his mind, arms up, sheltering under a rain of blows. Eldredge leaned forward. \"I don't know what you're going to find when you reach her, Jim, but it won't be friendly.\"\n\n\"I have to help her.\" The link to her pulsed like an ache in his chest.\n\n\"I know you do,\" Eldredge said, \"and I also know that the only way to do that is to put her back in the void.\"\n\nSchweitzer nodded. \"If I have to,\" he said, not at all sure that he meant it. The maddening feeling of Sarah _alive_ and so close . . . _No. She's not alive. It's not the same._ But he couldn't think, couldn't focus. He had to get to Sarah. He would deal with the rest then.\n\n\"Jim, I\u2014\"\n\n\"I'm going, Eldredge.\" In the face of the emotional onslaught, all resistance to the thought of leaving Patrick with Eldredge crumbled. \"I can't . . . I just can't . . .\"\n\nEldredge sighed. \"Okay. You have to go to her. I've got it. Let me help you.\" He drew out the KA-BAR, teal light spilling over them both.\n\n\"Jim, look at me. I know this is hard for you, but you have to focus.\"\n\nThe light from the knife blazed in Schweitzer's vision. It was a weapon; it could hurt him. The thought distracted him from the tug of Sarah's presence, let the SEAL in him assert himself just enough. A few more moments wouldn't make a difference. If he went after Sarah, he had to do it right.\n\nSchweitzer forced his feet to stay where they were. \"You said that knife would destroy me. What's in it?\"\n\n\"A jinn. One that can't abide others. I've killed a Gold with it already. The Director had three . . . I don't know what they were. Gold Operators, but wearing ancient jewelry. They had crowns. They looked like mummified kings. One of them came for me. I killed it with this knife.\"\n\n\"You want me to take it.\"\n\nEldredge nodded. \"There are only two ways I know to send a jinn back to the void: complete destruction of the body, or what I have in my hand here. The first option would be . . . hard on you. You want to help Sarah, you're going to need this.\"\n\nSchweitzer stared at the knife. It was insane, but the thought of sending Sarah back into the void felt like killing her all over again. Which was, of course, what the Cell was counting on him to feel. _You'll do what needs to be done. You owe her that._\n\nSchweitzer felt the tug in his chest again, stumbled a step forward.\n\n\"We both know it's going to be one hell of a fight, Jim,\" Eldredge said, \"and we both know we can't just stash Patrick in an alley and go mix it up. Someone's got to look after him. You have a better chance with this knife than I do. Go find Sarah. Wherever she is, the Gemini Cell will be there too.\"\n\nSchweitzer put out his hand. Eldredge slapped the knife handle-first into it. It glowed so brightly that Schweitzer had to dial his vision back to take it in. \"Careful of that blade,\" Eldredge said. \"So far as I know, it works at a scratch. Keep it sheathed. You don't want to send this whole thing south because you accidentally cut yourself.\"\n\nSchweitzer slid the knife into its leather sheath, held it in his hand, adjusting his vision as the light winked out. \"Will it even work on me? Maybe it only affects Golds.\"\n\n\"I'd rather not risk finding out. It's sure as hell glowing brightly enough for you.\"\n\n\"If I cut Sarah with this . . .\"\n\n\"It'll send her back to the storm, Jim. I'm sorry.\"\n\nSchweitzer stared at the knife.\n\n\"Maybe she's not a jinn, Jim,\" Eldredge said, \"maybe they've found some other way to bring her back. You're certain she's in this world?\"\n\nSchweitzer reached inward, felt the unerring compass needle of his link to her. \"Absolutely.\"\n\n\"Magic is new,\" Eldredge sighed. \"There's more we don't know about it than we do. But I only know of one way a soul exits this world, and only one way it can reenter. Sarah definitely exited. If she's back, it's because the Cell brought her here for some reason and by some means you're not going to like.\"\n\n\"I don't know if I can kill her.\"\n\n\"She's dead, Jim. You can't kill her.\"\n\n\"You know what I mean.\"\n\nEldredge shrugged. \"Think of it as a mercy killing. Maybe you can find a way to . . . make her like you. Either way, you must destroy the Cell.\"\n\nSchweitzer looked up at him, held his eyes for a long time. Eldredge shrugged again. \"I'm not all bad, Jim. Wanting to live without fear isn't a crime. It doesn't mean I'm not trustworthy. The likes of you and Sarah are beyond me.\" He gave Patrick a squeeze. \"Now, this lad here, this lad I can look out for. We're going to have a fine time together, won't we?\"\n\nSchweitzer was silent for a long time, fighting against the pulling of the link. At long last, he felt himself regain some kind of balance. The insistent tug continued, but it wasn't yanking him off his feet now. He looked down at his son. Patrick looked back, and Schweitzer could see the trust in the boy's eyes. But Eldredge's leg was visible over his son's shoulder, the heat of his blood visible to Schweitzer's augmented vision. The warm pulse in Eldredge's femoral was in and of itself more fatherhood than Schweitzer could ever muster on his own. The boy would be better off with anyone other than him. Eldredge was right. If he was an agent of the Gemini Cell, Schweitzer would be destroyed and Patrick dead by now. And even life with the Gemini Cell was still more life than Schweitzer could give him. Living was beyond him.\n\n\"How will I find you?\" Schweitzer asked. And even though living was beyond him, Schweitzer felt a little piece of himself die with the question.\n\n\"Craigslist,\" Eldredge answered so quickly that Schweitzer knew he'd already thought it through. \"I'll put an ad in the personals once a week. I'll say I'm more Mark Twain than Bettie Page. You can find it in a Google search; whatever city it's posted under is where I'll be. Respond to the ad and we'll go from there.\"\n\nSchweitzer held up his mangled fingers. \"The fuck am I supposed to Google anything?\"\n\nEldredge rolled his eyes. \"You have to be the first zombie prima donna in history. You're a goddamn SEAL, Jim. You can figure out how to use a computer with no skin on your fingers.\"\n\nThey were quiet for a long time, Eldredge locking eyes with the flames in Schweitzer's sockets. He could smell the fear stink on the old man, but Schweitzer had to admit, he did a damn good job of not showing it. He was right, of course. Schweitzer was going after Sarah, and he was leaving Patrick with the good doctor, and he would break into a library and do a Google search if there was anything left of him bigger than a breadbox after it was all over.\n\nSchweitzer shook his head. \"I'll figure something out.\"\n\nEldredge nodded. \"This is likely certain death for both of us . . . well, death for me. Whatever passes for death for you. Can you give me anything?\"\n\nSchweitzer handed him the child's backpack that was all their supplies. \"I won't need it.\"\n\nEldredge took the pack, stared at it dangling from his hand. Schweitzer felt the pull of his link to Sarah. _Be patient. A few more minutes. For Patrick._\n\n\"I know it's not exactly Gucci,\" Schweitzer said, \"but it's what I've got.\"\n\nEldredge rolled his eyes, but he didn't return the pack. \"This is great, but that's not what I meant. I mean, is there anywhere for me to go? Do you have family who would take us in? Friends?\"\n\n\"I've only got one, and it's a long shot, but it's away from here. West.\"\n\n\"How far west?\"\n\n\"San Diego. Guy named Dan Perretto, Coast Guard Maritime Enforcement Specialist First Class. Assigned to PACTACLET. I don't know where he lives, but if you found me, you can sure as hell find him.\"\n\n\"And he'll help?\"\n\n\"Not sure, but I think so. Dan's a good man. Got kids of his own. We went through a lot together.\"\n\nEldredge paused. \"You know this could bring . . . scrutiny on your friend, Jim?\"\n\n\"Yeah,\" Schweitzer said. \"But I also don't have a lot of options here. And I'm not just dumping Patrick off with him. You're going to keep him with you, and you're going to find a way to keep this out of Perretto's living room.\"\n\n\"If he'll even talk to me.\"\n\n\"If. Anyway, whether you find Perretto or not, west is still a direction to move in.\"\n\n\"That's pretty thin, Jim.\"\n\n\"Whole fucking thing is pretty thin,\" Schweitzer answered. \"Entire world's turned on its head lately, or didn't you notice? If you've got a better idea, I'm all ears.\"\n\n\"How are you going to get there?\"\n\n\"I'll have to fly. Wherever she is, it's much too far to walk.\"\n\n\"You can tell that?\"\n\nSchweitzer nodded. \"We're joined; it's a kind of magic. Similar to what bound Ninip to me. I can tell direction, and distance more or less. She's a long way away, to the northwest. You got any idea what's there?\"\n\n\"Canada?\"\n\n\"That doesn't make sense. Why bring her back outside the country?\"\n\n\"Idaho? I don't fucking know. North of here is . . . Ohio, I think.\"\n\n\"What's in Ohio? Does the Cell have a facility there?\"\n\n\"Not that I know of. We had one in California, Scorpio Cell, but we shut that down and pulled the Sorcerer over to Virginia when you flew the coop.\"\n\n\"What's north? Think, Eldredge. This . . . makes it hard to concentrate.\" He gestured at his chest, as if Eldredge could see the magic link to Sarah.\n\n\"Jesus, Jim. I'm a doctor, not a cartographer.\" Schweitzer stared at him, stone-faced. \"Okay, fine. I-states. Indiana. Illinois. Iowa . . . Fuck, Jim. Iowa.\"\n\n\"What about Iowa?\"\n\n\"That's where Hodges is from.\"\n\n\"Hodges . . . Don Hodges?\"\n\nEldredge nodded. \"The Senator. He's the one I was telling you about. The one who knows about our budget and authorizes funding.\" He met Schweitzer's eyes. \"Someone important.\"\n\n\"Doesn't mean anything. Maybe they're taking Sarah to him for a demo.\"\n\n\"Maybe we're completely off base and she's in Nebraska. Or the Dakotas. Jesus, Jim. It's all a wing and a fucking prayer.\"\n\n\"You got any other details on Hodges? Where does he live?\"\n\nEldredge rolled his eyes again. \"How the hell should I know? He's a Senator. Start with the state house. Look him up on Goo\u2014 Oh, Jesus Christ.\"\n\nSchweitzer waved a hand. \"It doesn't matter. I can find Sarah. I can always find Sarah.\"\n\nHe knelt down before his son, wrestling with his impatience to be away. It would be so easy to just stand and go, leave Eldredge to make his excuses. Patrick was too young to understand. _No. That's bullshit and you know it. He's busted up enough by all of this. Do it right this time._\n\n\"Hey, little man.\" Patrick tucked himself against Eldredge's leg. Schweitzer winced. \"Daddy's got to go away for a little while, but I'll be back soon. Uncle . . .\" He realized with a start that he didn't know Eldredge's first name. He looked up at the older man.\n\n\"Julius,\" Eldredge said.\n\n\"Are you serious?\"\n\n\"I fail to see how that's any less of a decent name than James. And my last name isn't Eldredge. It's Whiting.\"\n\nSchweitzer stared, smelled the truth in him. \"You're serious.\"\n\nEldredge shrugged. \"They're just names. It's not like it matters now anyway.\"\n\n\"It matters to me.\"\n\nEldredge looked embarrassed. \"It's funny; I haven't used either name in so long. No, I think I'll stick with Eldredge. Julius Whiting died a long time ago.\"\n\n\"Eldredge it is,\" Schweitzer said.\n\n\"My middle name is Eustis. Glad to be shot of that.\"\n\nSchweitzer turned back to Patrick. \"Uncle Julius is going to take care of you until I come back. He's going to keep you safe until I can catch up to you\"\u2014he looked back up at Eldredge\u2014\"because Uncle Julius understands that if he doesn't, no matter what Hallmark moment we may just have shared, I will find him. Uncle Julius knows that if any harm should come to even a single hair on your head, then I will find him and I will make him pay.\"\n\n\"Uncle Julius is a coward,\" Eldredge said to Schweitzer, \"and you can always count on cowards acting in the interest of self-preservation.\"\n\nSchweitzer ignored him, reached out, touched his son's cheek. \"I'll come back for you.\"\n\nPatrick nodded, looked at the ground. His eyes were already somewhere else, taking him to the faraway place where none of this was happening, a world where dead men lay down and stayed dead. It was the best Schweitzer was going to get, and he took it.\n\nSchweitzer felt his spiritual stomach clench with grief. _This may be the last time you see him._ His son. _Oh, Patrick. We never had a chance._ He opened his mouth to say something more, but he didn't bother. What good would it do? In the end, all that came out was \"Take care of him, Eldredge. And don't forget to keep in touch.\"\n\nEldredge's hand tightened on Patrick's shoulder. \"Westward bound, Jim. We'll leave a light on for you.\"\n\nSchweitzer knew he should feel fear. He knew he should feel regret, disgust that he was leaving his son in the hands of a stranger.\n\nBut the truth was that as he turned to the northwest and began to move, as he gave himself over to the impulse to follow the link wherever it led, he felt his dead heart lift. His limbs felt light, his step longer. Every cell in his body vibrated with the pulse of the magic, every foot a foot closer to her. It was right. Going after her was right.\n\nSchweitzer broke into a run and the trees around him lengthened into brown and green blurs. He didn't know where he was going, but for now, it felt good just to run, away from Eldredge and his son, toward Sarah. He didn't have the details he needed: where she was, who she was with, what he could expect.\n\nHe'd played for higher stakes on less. No plan survived contact with the enemy, anyway. He put on speed and let the woods fall away behind him.\n\n# CHAPTER XXIV\n\nTHE FLIGHT IN\n\nAshland Regional Airport was a postage stamp, a tiny smudge of runway surrounded by poplars growing so thick that they blocked the breeze. A few planes dotted the flight line, two-seater private jobs for the most part, though he made out one small postal service cargo plane and an Air National Guard training jet.\n\nIt was too small for a control tower, just a collection of aluminum Quonset huts huddling together off the tarmac, beneath a ragged-looking wind sock and a fluttering American flag. There was no fence, no guards, nothing that marked the terror-addled culture of big-city airports, where he wouldn't have been able to get within half a klick of the runway without alerting a dozen armed guards.\n\nSchweitzer kept his ears tuned, heard the footsteps of someone down on the runway's far end, probably a night watchman, given the late hour. He heard the droning of the last flight to take off, the angry-insect sound he'd used to find the airport in the first place, homing in as the plane taxied and took off.\n\nHe sized up the tail numbers of the parked planes and then made for the largest of the white huts, a two-story building with a long bank of tinted windows facing the runway. If the flight controller had a desk, that's where it would be.\n\nThe door to the tarmac wasn't even locked, and Schweitzer made his way through the rows of desks and chairs unmolested, moving silently through the litter of real lives. Trophies, motivational posters, framed pictures of families. There was something about the small-town setting that tugged at him. Partly because it reminded him of his life back in Little Creek. Partly because, once again, it dangled the existence of families just outside of his grasp. But the tug was nothing compared to the tug he felt toward Sarah. It kept him focused, kept him moving.\n\nThe controller's desk was where he expected it. An old microphone stood beside a bank of dark equipment. Schweitzer could still smell the ozone from their being powered on to see the last flight off. He must have arrived just behind the departing shift.\n\nHe dug in drawers until he found what he sought, yellowed hanging folders, FLIGHT PLANS written in black marker across the top. He thumbed through them, checking the time and date against the huge red LED readout of the twenty-four-hour clock hanging above the desk. He paged back and through again, cursing under his breath. There was a flight due to leave tomorrow morning, ten hours from now. He had no choice. Unless he suddenly learned to fly a plane, he would have to wait.\n\nThe aircraft was also unlocked. It was a tiny, blue-striped single-engine plane, so clean that if Schweitzer hadn't just seen three logged flights for it in the past week, he'd have sworn it was brand-new. There was barely room for him behind the narrow seats, just enough to wedge himself into the tight space, lying on his back, knees drawn up to his chest. A blanket had been laid out there, loosely draped over a pile of towels, flip-flops, and bottles of sun block. Schweitzer huddled under it now, the odd plastic shapes digging into his back. As always, he was aware of the sensation of the discomfort, but it had no power to disturb him. Being dead had its advantages.\n\nIt grew hot in the back of the plane, long past the point where a living man would have been stifled, forced to throw the blanket aside to gasp for air, where the stink of his sweat would have filled the cockpit. It would have made him move, do any number of things that would have alerted others to Schweitzer's presence. But in death, he was completely still, the last hours of night finally shrugging off, the sun peeking above the treetops just as the rumble of engines announced the first members of the flight crew reporting for duty.\n\nThe pilot was late. Schweitzer didn't have a watch, but his augmented senses did give him a heightened sense of time passing, of the air heating by degrees as the sun rose. Before long, he heard a man making his way to the plane's side, whistling to himself tunelessly. He was overweight, the labored beating of his heart speaking of clogged arteries and old age. The door opened with a click, and Schweitzer felt the plane sag as the man lowered his weight into the pilot's chair.\n\nSchweitzer listened to the preflight checks, the man's deep southern twang as he went down the list, the dull scratching on the pen against the clipboard. Schweitzer would wait until they were airborne and away from the airport. He hadn't paid attention to the destination. It wouldn't matter. He just hoped the old man's ticker would hold out, given what was about to happen.\n\nAt last, the engine coughed into life, and the pilot spoke into his radio headset. \"Ashland Regional Unicom, five niner one niner for a radio check, over.\"\n\nThe response was muffled by the cups of his headphones, drowned out by the roar of the engines. Schweitzer dialed in his hearing, shutting out the engine noise and focusing on the buzzing crackle of the radio. \"Ashland Regional Unicom has you, Lima Charlie. Good morning, Frank.\"\n\nFrank smiled. \"Good morning, Paul. Five niner one niner is departing two-six.\"\n\n\"Roger that. Have fun and be safe.\"\n\nSchweitzer felt the plane begin to move slowly. It picked up speed, and Schweitzer watched the shadows play along the inside of the cockpit, racing faster and faster, until at last, Schweitzer felt the plane's nose come up, taking his weight as it pushed its way up into the sky.\n\nThe plane banked as Frank circled out from the pattern, and Schweitzer felt the airframe sag, shuddering. \"What the fuc . . .\" Frank muttered, looking over his instruments. He turned around and looked behind him, straight at Schweitzer's hiding place, then forward again as the plane banked once more.\n\n\"Ashland Regional, five niner one niner.\"\n\n\"Everything okay, Frank?\"\n\n\"Plane doesn't feel right. I'm dragging ass up here.\"\n\n\"Okay, how worried should I be right now?\"\n\nFrank looked at his instruments, shrugged. \"Not worried. Everything's responding; it just doesn't feel right. I'm going to set her back down. Is there anyone else on approach I didn't see?\"\n\n\"No, you're . . .\"\n\nNo time. Schweitzer slid out from under the blanket. Pushed his upper body into the passenger seat, never rising high enough to be seen over the canopy's edge. He lifted one skeletal hand, duct tape peeling away from the rents, and for the first time was grateful for his horrific appearance. He placed it on the pilot's chest. \"Don't say a goddamn thing into that radio. You speak and you're fucking dead.\"\n\nThe man, strictly speaking, obeyed him. He screamed, a high whining sound that made Schweitzer think of cats fucking, but Schweitzer didn't hear the rasping click that would have meant he'd toggled the radio. His meaty face went white, shook.\n\n\"You pass out, and I'll fucking kill you,\" Schweitzer rasped.\n\nThe man did not pass out; his chins quivered, tears leaked out the corners of his eyes, but he kept his grip on consciousness.\n\n\"You want to get through this alive, you do exactly as I say. I'm already dead, so you better fucking believe that crashing this aircraft is no big deal to me. I will walk away from it. You won't. You read me?\"\n\nThe man nodded.\n\n\"Radio back and tell them you figured it out. Tell them you're good to go.\"\n\n\"But I just told them that I'm dragging.\" The man's voice was high, whining. \"How do I explain\u2014\"\n\n\"You're the fucking pilot. You figure it out. And God as my witness, you'd better figure it out.\"\n\n\"I can't believe this. This isn't happening.\"\n\nSchweitzer let one bone claw extend far enough to pierce the man's shirt, brought it gently across his collarbone. _You bastard. This guy's done nothing wrong. He doesn't deserve this._\n\n_Fuck that. This guy is your chance to find Sarah. Mission first. Focus._\n\n\"You feel that?\" Schweitzer asked.\n\nThe man nodded. Whimpered.\n\n\"That's real blood coming out of you, pal. _Your_ blood. You better fucking believe this is happening, and you better start believing it right now.\"\n\n\"Okay.\"\n\n\"Good. Now use that radio and keep us in the air.\"\n\nThe buzzing click of the radio sounded as the pilot switched over. \"Ashland Regional, five niner one niner.\" His voice was halting, on the verge of a stutter.\n\n\"Lock it up,\" Schweitzer whispered. \"If they guess something's wrong, it's over.\"\n\nThe man's terrified eyes rolled over, his face asking the question: _A corpse just rolled out from behind me and is hijacking my plane. I'm fucking terrified. How do you expect me to sound like everything's normal?_\n\nSchweitzer bared his teeth. \"Find. A. Way.\"\n\nThe radio crackled as the tower replied. \"Frank, what's going on?\"\n\n\"It's me. I'm an idiot,\" the pilot said, still sounding rattled but better than before. \"I forgot my cooler from last time. Left it in the back. It's fine.\"\n\nThe voice on the other end of the radio sounded doubtful. \"You sure?\"\n\n\"Yeah, everything checks out. Everything responds. It must have been the cooler and a crosswind. I just got in a clear patch and the plane feels fine. Sorry about that.\"\n\nA long pause. \"Dude. Don't scare me like that.\"\n\n\"Yeah,\" Frank laughed nervously. \"Sorry about that.\"\n\n\"Well done,\" Schweitzer said. \"You just bought yourself another fifteen minutes. Now get us to cruising altitude.\"\n\n\"I have a wife,\" the man said. \"Children, grandchildren, please.\"\n\n\"You think I give a fuck about any of that?\" Schweitzer growled. But the truth was that he did care, that the words twisted in his spiritual gut. _Patrick was wrong. You are a bad monster. No better than the terrorists and human traffickers you operated against for years. It doesn't matter why you're doing this._ He remembered standing over the \"Amir of the Caucasus.\" The man had set fire to a school for daring to teach girls to read. Schweitzer had taken great pleasure in kicking down his door and putting a bullet in his gut.\n\nThe man had stared up at him from the floor, trying to keep the tangled mess of his guts from spilling up. There was pain in his eyes, but righteous fury too, and that had angered Schweitzer. He didn't want him to die feeling like he was in the right. \"How could you do that? You burned down a _school_ , you fucker. You killed dozens of little girls. Don't you have daughters of your own?\"\n\n\"I did,\" the Amir whispered, blood bubbling out with the words. \"Your drones killed them. Why should my children die and yours live?\"\n\nSchweitzer hadn't had an answer for him. He probably twisted in the soul storm now, there to while away the millennia until someone like Jawid brought him back. He'd make an excellent jinn.\n\n\"You're not going to kill me, are you?\" The pilot asked.\n\n\"Not if you do exactly as I say,\" Schweitzer answered. \"Get us up and where I want to go, and then I'll be out of your hair and you can fly on home to that family of yours. This isn't personal. I just need a ride.\"\n\n\"Are you dead?\"\n\nSchweitzer knew he should tell him to shut up, that revealing anything personal was a risk, but there was a limit to how much of a monster he could be. He waited until he saw the man gently pull on the yoke and the he felt the plane's nose lift.\n\n\"Yes, Frank,\" Schweitzer said, watching Frank's eyes widen as he discovered Schweitzer already knew his name. \"I am.\"\n\n\"Jesus,\" the man said.\n\n\"Magic is real, Frank. Sorry you had to find out this way.\"\n\n\"Where am I taking you?\"\n\n\"You have a smartphone?\"\n\nFrank nodded.\n\n\"Hand it to me.\"\n\nFrank dug in his pocket and handed it to Schweitzer. \"It's not locked.\" Schweitzer drew a finger across the virtual keyboard to open it up. No reaction. _You fucking idiot. These things work off the heat in your fingers._ He bit back on the spasm of grief that accompanied the reminder that he lacked even the body heat to work a phone.\n\n\"Looks like I'm going to need your help here, Frank.\" He handed the phone back. \"I need you to look something up for me.\"\n\n\"Okay.\" Frank took the phone, hovered his thumb over it.\n\n\"I need the Iowa offices for Senator Don Hodges.\"\n\n\"You mean the address? Why?\"\n\n\"Because you're going to fly me there.\"\n\n\"Why?\"\n\nThe cooling air told Schweitzer that they were well airborne now. He wouldn't be seen from the ground. He crawled up into the seat and turned to look at Frank. \"You have got to be out of your fucking mind, asking me questions like that, Frank. Did you miss the whole part of me walking away from a plane crash?\"\n\n\"You'll be too messed up in a plane crash to walk, even if you are dead. You'd be burned to a crisp or in pieces.\"\n\n\"You want to test that theory?\" Schweitzer reached out and nudged the control stick forward. The nose of the plane dipped sharply and Frank let out a terrified squeal.\n\n\"Okay! Okay! I'll look it up!\"\n\n\"Good boy.\"\n\nFrank tapped on his phone for a moment. \"I have the address. Des Moines.\"\n\n\"Outstanding. Take me there.\" Hodges likely wouldn't be at his Iowa office, but it didn't matter. He would feel it as they drew nearer to Sarah, and the closer they came, the better he would know where she was.\n\n\"Flight plan says Little Rock, man,\" Frank said. \"We don't have the fuel to make it there. We'll crash, and then neither of us gets what we want.\"\n\n\"Look at me, Frank.\" Schweitzer leaned toward him. His elbow brushed a bobblehead hula dancer Frank had suctioned to the dash. \"Look at me.\"\n\nFrank looked at him sidelong, head still facing forward. The effect was comical, and Schweitzer felt a phantom smile rise to his face, a ghost of the man he'd once been, a living man who could laugh and appreciate irony. But his face was a skull now, and skulls grinned all the time, whether the joke was funny or not. \"Do you think that, in life, I was a stupid man, Frank?\"\n\nNo answer. Frank looked back out the windshield.\n\n\"I said, fucking look at me!\"\n\nThe eyes jerked back over. \"I'm looking at you!\"\n\n\"Do you think I was stupid?\"\n\n\"How should I know? I didn't know you.\"\n\n\"I'm very smart, Frank. Dying hasn't changed that. Smart guys like me know that Little Rock isn't much farther than even the far side of Iowa. I used to drop from light aircraft like this. I knew a thing or two about reckoning fuel. You can make it, Frank. You can make it and to spare. And if you try to trick me again, I will kick your ass out of the cockpit and see if all that hot air can float you down slowly enough to land on your feet.\"\n\nFrank said nothing, the tears still leaking out of the corners of his eyes.\n\n\"You may look away now, Frank. Always want to keep your eyes on the road.\"\n\nFrank looked back out the windshield and Schweitzer quelled his rebel conscience yet again. The ground was a swath of green pasteboard beneath them, the clouds a flat line of white over their heads. Schweitzer had the weird sensation of buzzing through a layer of a landscape painting, the reality above and below him too perfectly rendered to be real.\n\nSchweitzer heard the light click of Frank engaging the radio, whipped a claw out to hover below his chin. \"Don't.\"\n\n\"I have to radio the course change, man. I can't just fly wherever the hell I want. It's not like driving a car,\" he said, and Schweitzer's augmented senses assured him that Frank believed it to be true. \"Please, I'm not lying. I'm not trying to trick you; don't hurt me.\"\n\nSchweitzer considered. The midair course change would require a reason, would set the authorities on alert. An unreported and unscheduled flight change would also raise alarms, but it would take more time for ground crews to figure out what the problem was and to coordinate a response. \"Just keep flying,\" he said.\n\n\"Even if you don't kill me, man, you're going to get me arrested as soon as I land.\"\n\n\"You can tell them there was a stowaway.\"\n\n\"A zombie stowaway.\" Frank rolled his eyes. \"Nobody is going to believe that. I don't even believe that.\"\n\n\"Believe it. And tell them that I had a gun on you if it helps.\"\n\n\"It won't.\"\n\nSchweitzer shrugged. \"I'm fucking dead, dude. You'll forgive me if I lack sympathy for your predicament. Just keep flying and you'll live through this. Keep it as low as you can without drawing attention.\"\n\nSchweitzer felt the plane slowly shed altitude as Frank obeyed. The man started to speak again and stopped at a shushing from Schweitzer. The next two hours were an odd silence, Frank with his eyes straight ahead, the plane engines droning, and the airframe shaking under the pressure of the currents of wind and Schweitzer's dead weight on the cockpit floor. Schweitzer could feel Sarah's signal getting stronger, the emotions passed along the link more intense. They were moving in the right direction. Schweitzer imagined the distance dropping away, stifled the urge to drum his fingers on his knees as the agitation at her growing nearness almost overwhelmed him.\n\nSchweitzer kept his bone claw extended and near Frank's throat, a reminder of what was at stake. Schweitzer could feel Frank's chemical scent change as he calmed, slowly realizing that he wasn't going to die, at least not yet. Schweitzer could hear his heart slowing, feel the pressure in him change as his veins dilated back to their regular diameter. Schweitzer thought of amping his fear up again with some menacing gesture but decided he didn't want to. It was exhausting being a monster. He had done it enough to Patrick. He wanted a break.\n\nSchweitzer knew Frank was going to speak before he opened his mouth. \"So . . . who were when you were alive?\"\n\n\"The fuck do you care about me?\"\n\nA spike in the fear, but not as high as before. \"Hey, man. It's a long flight. We might as well make conversation.\"\n\n\"I was a man.\"\n\nFrank actually smiled. \"Well, I figured.\"\n\nSchweitzer knew this wasn't good. There was no reason to connect with this man, no reason to communicate with him at all. He was the ride to Sarah, nothing more. Schweitzer's training tried to kick in, to dehumanize, to reduce Frank to his functional role, to keep Schweitzer's situational awareness. But the truth was that Schweitzer was exhausted. Since his death, Schweitzer's every conversation had been fraught. Cutting deals with Eldredge, getting briefed by Jawid, explaining the new lie of the world to Sarah. He had forgotten the gentle rhythms of easy, adult conversation, the micro-connections that small talk forged. And once he remembered, he realized that he wanted it, desperately.\n\n\"I had a family.\" Schweitzer said.\n\n\"They died too?\" Frank asked.\n\n\"Yes,\" Schweitzer answered. Best not to let the man know there were any levers on him.\n\n\"I'm really sorry to hear that. I don't know what I'd do if my kids died.\"\n\n\"You'd find a way to go on, same as everyone else.\"\n\n\"Not everybody finds a way. I know I couldn't.\"\n\n\"You'd be surprised at what you can do. You ever serve?\"\n\nFrank arched an eyebrow at that. The question itself gave him information Schweitzer knew the man probably shouldn't have, but he cared less and less. He'd lost his life. He'd lost Sarah. He could have this one thing. \"You were . . . in the military? When you were alive? I kinda guessed when you talked about dropping out of planes.\"\n\nSchweitzer nodded.\n\n\"What branch?\"\n\n\"None of your fucking business.\"\n\n\"Hey, man. That's fine. I was in the Army. I only did four years, though. You could do four and get out back then. I drove trucks.\"\n\n\"Then you remember what it was like. They take you in, they break you down, they build you back up. By the time they're done with you, you're capable of amazing things. Things you never thought you'd be able to do.\" He'd had this conversation with Sarah when they'd first dated. _I could never paint like that,_ he'd said. She'd fixed him with a serious look, and her voice had been stern, even scolding. _Yes, you could. If you were willing to put in the time, willing to give up your leisure and your freedom and your money, you could be the greatest painter that ever lived. The only difference between you and I is focus, commitment, and desire._\n\nHe wasn't sure of the exact moment when he figured out that he would love her and no other for the rest of his life, but that was certainly a candidate.\n\n_Oh God. Sarah. I miss you so much._\n\nFrank shrugged. \"All I learned to do was drive a truck, man. And stand in line a lot.\"\n\n\"You'd adapt to it,\" Schweitzer said, \"but I hope you never have to.\" Showing sympathy was a terrible idea, and it felt fantastic.\n\n\"Everybody's got to go sometime,\" Frank said. Schweitzer waited for him to say more, but he was content to fly on in silence, and eventually, Schweitzer settled into the lull of the throbbing engines and the whoosh of the air over the wings. He watched the clouds scud by above them. Frank was keeping the plane low per his orders, and Schweitzer watched the sun peek out between billowing white banks. The brightness was dazzling, but he had no eyes left to damage. For the first time in his existence, he stared directly into the center of the fiery ball, letting his vision play over the rippling plasma, seeing the sparking tendrils of heat even from this distance. It was amazing. Every moment he existed as a dead man, he found new ways to experience the world. In some ways, he was like a newborn baby.\n\n_I can look straight into the sun. For as long as I want._\n\nHe heard a dull click, felt the faint vibrations of the radio trembling through the headphones around Frank's ears. Schweitzer dialed his hearing up to pick up the frequency.\n\nA normal human ear wouldn't have been able to hear over the ambient noise of the moving plane, but Schweitzer wasn't a normal human.\n\n\"Cessna one seven two, tail number November five niner one niner, November five niner one niner, this is Air National Guard India Alpha three one two. You have entered restricted airspace. I say again you have entered restricted military airspace. Assume heading two seven zero and depart the area immediately.\"\n\nFrank stayed quiet, a bead of sweat slowly working its way from his forehead behind one of the earphones. His eyes flicked to Schweitzer, only for an instant, back to the windscreen. Schweitzer smelled the burned-sugar stink of his blood sugar spiking, the chemically sour odor of adrenaline, heard the hammering of his speeding heart.\n\nSchweitzer waited for Frank to turn the plane.\n\nHe didn't. It wasn't an accident.\n\nThe radio crackled again. \"November five niner one niner, this is India Alpha three one two. If you do not leave the airspace on heading two seven zero, we will engage you. If you are in distress and cannot respond, please toggle your radio three times in one-second intervals, over.\"\n\nSchweitzer sat bolt upright. \"What the fu . . .\"\n\nFrank kept his eyes straight ahead, his hand on the controls. With the other, he reached down and toggled his radio. _Click-click. Click-click . . ._\n\nFrank didn't get a chance to sound a third click before Schweitzer snatched his wrist, but the radio was already sounding again. \"November five niner one niner, this is India Alpha three one two. We are in receipt of your distress indicator and are inbound to intercept. Assume heading two seven zero and maintain speed and altitude. Toggle your radio twice in one-second intervals to indicate that you will comply, over.\"\n\nFrank clicked two more times as Schweitzer reached over to snatch his wrist. \"Roger that,\" the radio crackled. \"We're on our way. India Alpha three one two out.\"\n\n\"Are you a fucking idiot?\" Schweitzer asked.\n\n\"I don't know what you're talking about, man,\" Frank practically squeaked.\n\n\"I'm talking about you deliberately flying over a fucking Air National Guard base,\" Schweitzer hissed. \"What part of 'Do what I say and you'll live through this' didn't you understand?\"\n\n\"I didn't do anything!\" Frank screamed.\n\nSchweitzer sat up, his head and shoulders flattening against the canopy as he seized Frank's neck, the man's fat jowls spilling over his grip, eyes bugging out of his head. Schweitzer pointed at his throat with the other finger, letting the bone claw extend until it touched Frank's Adam's apple. \"You stupid motherfucker.\"\n\n\"You know, man,\" Frank gasped, \"I don't think you're going to hurt me. I don't think that's what you're going to do at all.\"\n\n_You idiot,_ Schweitzer screamed at himself. _Why did you fucking talk to him?_ Too much sympathy, too much humanity. Enough to give Frank the glimmer of hope that Schweitzer was too soft to do the deed. Schweitzer wasn't too soft to do the deed, but he would have to do it now. There was no intimidating Frank into anything, and the Air National Guard jets that were scrambling would be there soon.\n\nSchweitzer cursed, retracted the bone claw, and punched down on the controls. The plane's nose dipped sickeningly and Frank shrieked as it dove, engines roaring. Schweitzer saw the green paste of the Iowa plain below him, a flashing blue ribbon that he knew meant one of the rivers that crisscrossed the state. He'd always planned to travel there with Sarah, see the fields where the Indian Wars had been fought, the edges of the frontier where the nation had been born.\n\nThe ground rushed toward them; Frank grabbed the controls and pulled futilely against Schweitzer's strength. \"Please! Please!\"\n\nAbove them, a long way off but coming fast, Schweitzer could hear the high-pitched whine of a jet engine burning hard.\n\nThe Air National Guard jet, inbound at speed. An F-16, most likely. It wouldn't take them long to arrive, and he had to be gone by then.\n\n\"Please!\" Spit trailed out of the corners of Frank's mouth. \"Let me level her off! I have a family!\"\n\nThe green stretch of ground sped toward them; a thick swath of trees came and went. The bright, shining line of the river rushed closer. \"Keep us over the river,\" Schweitzer said, and Frank nodded enthusiastically, hauling back on the yoke as soon as Schweitzer released it.\n\nIt was a near thing. Frank pulled and the plane groaned, straining as if, now that it was committed to the dive, it didn't want to pull out of it, had its heart set on crashing straight into the river glinting silver-white now that the sun was behind them. Schweitzer heard the airframe groan as the metal strained against the wind, the high-wire twanging of the wings cutting through the rushing air. Frank couldn't hear those sounds, had no idea how close his tiny little airplane was coming to ripping itself apart. Better for him that way.\n\nThe radio crackled again. \"Five niner one niner, India Alpha three one two. I say again, maintain your current speed and altitude on bearing two seven zero or we will open fire.\"\n\n\"They might kill you,\" Schweitzer said. \"I definitely will. Get as low and slow as you can get us without stalling. Keep diving.\"\n\nFrank banked the plane until the electronic compass pointed to two seven zero but otherwise kept the aircraft steady. Schweitzer pressed the claw into his throat. \"Last chance, Frank. I'm done being nice.\"\n\nFrank swallowed and slowed the plane, pushing the nose gently down. Schweitzer watched the river grow beneath them until it filled the entire horizon. The whine of the jet engine came louder.\n\n\"Fuck,\" Frank whispered. \"They'll just fire a missile. We won't even see it coming.\"\n\nSchweitzer retracted the claw and squeezed Frank's shoulder. \"Then I'll get off. Thanks for the ride, man.\"\n\nSchweitzer forced the side door open, struggling briefly against the rush of wind that tried to hold it shut. He heard Frank curse as he leapt.\n\nThe plane must have slowed to little more than fifty knots, but the tail still swept over him so close that he could feel the rags of his clothing stirred by its passing. Then he was falling, letting his body stretch to keep himself stable, creating as much wind resistance as possible. The Iowa countryside was beautiful out here, the air sharp and clear, the river winking at him, breaking the sunlight into a shivering screen of diamonds. The whining of the jet engines became a roar as the river rushed upward and he arced into a graceful dive, tucking his chin, pointing his arms, and breaking the surface with little more than a splash.\n\nThe river wasn't deep down here. No sooner had the cold water admitted him than Schweitzer saw the sandy bottom racing upward, dotted with slimy rocks. He arched his back again, widening the angle of his descent and giving himself more time to shed speed. The resistance of the water continued to break his momentum, but not enough to keep him from colliding sharply with the bottom. He felt his ribs take the impact, flex enough to crush the lungs and heart of a living man but hold without more than a couple of minor breaks. He spun onto his back as he rebounded upward, swatting away a cloud of minnows and focusing his eyes up toward the surface.\n\nThe reflection of the sun and the wavering surface made it harder, but not impossible, for his magically augmented eyes to see out and into the open air, but it was still an oily and wave-washed image of Frank's little Cessna slowly gaining altitude below two gray streaks that were the F-16s finally arriving, overshooting at their higher airspeed, banking around for another pass. Schweitzer was certain that Frank was even now shouting into the radio, desperately telling them to wave off, that he'd been hijacked, that he was complying.\n\nThere was no fireball, no whoosh and roar of explosive ordnance being deployed. Schweitzer had gambled with Frank's life, to be sure, and there was a part of him that curdled at the thought, but it was a gamble that paid off as the Cessna motored on and out of sight.\n\nSchweitzer nodded in satisfaction. Sarah was close, the tug of her through the link dragging him along like a fish on a lure. He gave into it, turning on his belly and swimming down into the dark, sweeping up against the current to where he knew his wife awaited him.\n\n# CHAPTER XXV\n\nCOMBINED\n\nSchweitzer swam the river's oily length, pulling himself along the river bottom, ragged fingers digging into the silt and rock. He could feel the dark water pressing in on him from all sides, and the current worked furiously against him, desperately trying to sweep him down and out into the Mississippi, as if the water itself were trying to keep him from reaching his wife.\n\nIt could do as it liked. It couldn't stop him. Schweitzer pulled himself relentlessly along, so deep he knew he wasn't as much as a shadow to someone on the surface, even though the river was clear as glass and the day bright and sunny. He didn't need to rest, and his legs were strong enough to kick his way along upriver faster than a man could walk. With each yard, the maddening closeness of Sarah's presence grew, until he had to force himself to keep from scrabbling at the riverbed and take long, deliberate strokes. _Slow is smooth, smooth is fast. Focus._ Hand over hand, Schweitzer climbed the river bottom north and west.\n\nThe sun was setting, the rippling surface of the river blazing orange and red above him as he became aware of the shadows of buildings falling over the water's surface. He could hear the churning of motors, taste the rancid tang of garbage that told him he'd entered the dirtier water that carved its way through a major city. Sarah blazed like a coal forced down his throat and into his chest.\n\nThe sun sank farther as he pulled his way farther into the city, until the river bottom was shrouded in gloom, and Schweitzer had to adjust his vision to take advantage of the scarcer light. A few garbage bags had been sunk around him, old boots and crushed tin cans. Soggy fur and scattered bones. The detritus of a people living cheek by jowl. The river bent back on itself, and as he turned to follow it, he felt Sarah's presence growing farther. If he was going to find her, he'd have to go the rest of the way on land.\n\nSchweitzer rolled onto his back, let himself surface by inches, fighting against the impulse to race up and out of the water, to go after her. _Go ahead; come up in the middle of a bunch of couples out for a stroll, or in front of a cop car._ He knew what he looked like. He could pass for a man if he had a man's clothes and at least something to cover his face, but his leering, dripping skull wouldn't leave room for doubt, especially with his burning silver eyes.\n\nDes Moines was not New York, and while the water muted the sounds of those on the surface, Schweitzer could still hear the thrum of car wheels against the ground, the distant tread of footsteps. Nothing close. At night, it was a city of the dead.\n\nSchweitzer let the top of his head break the surface, felt the soft touch of the air on his scalp. A high wall of gray stone rose sheer to one side, a wide stretch of grass between it and the road that wound its way along the river. As he watched, a car sped past, headlights painting two white cones on the asphalt. They wouldn't be able to see him from there. Not at night. Not even if they were looking.\n\nHe swam to the wall, tested the stone. It was uneven, the tiny ledges between the bricks slick with river slime, but he swarmed his way up with ease, his magically augmented muscles making short work of the climb, his shredded fingers and toes as strong as a living man's arm or leg. He threw a hand over the top, holding himself flat against the side of the wall as another car rushed past.\n\nWhen he finally pulled himself up, he was greeted by a white stone building in classical style, flanked by bronze lamps and covered with sweeping arched windows. A wide stone staircase led up to the huge bronze double doors, closed and locked for the night. Some government building, full of the pompous grandeur that men used to deceive themselves into thinking the things they did had meaning, that they could protect anyone. That was fine. The architectural overstatement cast many shadows, offered an endless series of alcoves. It was perfect for a creature that wanted to shroud itself in darkness, to hide.\n\nSchweitzer squatted beneath a stone eave and scanned the city skyline, feeling Sarah pulse in his throat, a steady rhythm that he could nearly hear. If his heart still beat, he knew it would be surging. A modern-sculpture park sprawled on the river's far side. Schweitzer could hear someone snoring fitfully beneath one of the pieces, a gang of kids whispering around a can of something just a few feet away from him. Easy to avoid, easier to scare off if they got wind of him. Beyond the park, tall glass-sided buildings reared into the night, limned in neon that only set them more starkly against the plain black-gray of the Iowa night sky.\n\nThere. Sarah was there.\n\nSchweitzer bolted from cover, raced to the river's edge, leapt into the air. The river was at least fifty feet across. Schweitzer cleared it easily. A part of him knew that he should be amazed, filled with wonder at the fact that with a better running start, he could have jumped twice as far, but Schweitzer felt that part of him slipping away. This new creature, the one who could bend cold iron with its bare hands, the one that didn't need to eat, didn't need to sleep, didn't need to breathe, was more and more of who he was. That creature couldn't take care of a little boy, couldn't love a wife.\n\n_Lock it up. Patrick is with Eldredge now, for better or for worse. You can't do anything for him until you finish this._\n\nFor now, this creature was who he needed to be. All warriors needed to remember what they were fighting for, but it didn't change what the warrior had to do to win the fight. War was monstrous. To win, you had to be a monster.\n\nAnd he was.\n\nSchweitzer landed in a crouch on the far bank of the river, dropping into the shadows of the sculpture park. The kids stopped talking, swiveled their heads in his direction. There were whispers of \"Did you see that?\" But Schweitzer knew he had jumped too far and too fast. There would be too much for their minds to take in, and by the time they made sense of it, he'd be gone.\n\nHe took off at a sprint, sticking to the shadows of the office park, until he had to risk the streetlights along a broad avenue that wended its way toward the straight metal teeth of the skyline.\n\nAs the shadows of the buildings fell over him again, Sarah's signal grew focused, and Schweitzer fought against the edges of a tunnel vision threatening to settle on him. He had felt the same thing when he'd put down the kickstand on the stolen Harley-Davidson, stepping onto the front lawn of the farmhouse where Sarah had taken refuge while she'd still been alive.\n\nThe tallest of the buildings loomed closer, a modern, star-shaped tower with a beaten-copper roof that had failed to deliver the promised verdigris and instead turned a sick-looking dark brown. Schweitzer's powerful eyes could see the directory posted in the lobby, the prominent brass plaques posted below it, the guard behind the marble-topped desk. An office building, then. If Senator Hodges lived there, his was one of the very few residences.\n\nBut it didn't matter, because Sarah was in there. Schweitzer was sure of it. Schweitzer had thought that once he'd pushed Ninip out, he'd mastered his new self, was in complete control. He'd had no idea. The compulsion of his link to Sarah took hold of him now, batted all resistance aside. His years of training to be a SEAL, his gift for self-denial, his pridelessness, his endurance, all were swept away in an instant, replaced by an animal need to _get to her_ no matter what the cost.\n\nSchweitzer the SEAL wanted to case the target, to surveil the entrances, figure out the path of any guard patrols, to wait, to plan, to do things right. But Schweitzer the jinn just galloped across the road, vaulting over a parked BMW sports coupe and hammering through the front doors so quickly, he nearly took them off their hinges.\n\nThe one guard was already rising, eyes fixed on a monitor that no doubt showed Schweitzer's approach, so fast that he didn't have time to register what he was seeing. He winced as the doors banged open, turned to face Schweitzer, eyes widening, before one hand disappeared beneath the desk.\n\nSchweitzer smoothly vaulted the countertop, closing the distance between them and seizing the man's wrist. He ripped it away from the white button the guard had been reaching for, bent it painfully back. The guard drew breath to cry out and Schweitzer seized his throat. \"You can scream, or you can go on breathing, but you can't do both.\"\n\nThe guard was bald, in his thirties, his thick torso covered by a black cable-knit sweater. He stared at Schweitzer, slowly closing his mouth, raising his free hand. \"It's cool, man. Be cool.\"\n\n\"Cool is my middle fucking name,\" Schweitzer whispered, running his hands over the man's waist. There was a thick utility belt there. Ring of keys, flashlight, handcuffs, radio. No gun.\n\nSchweitzer did a quick once-over of the guard's armpits and ankles. No hidden holsters. He was unarmed. \"What's your name?\"\n\nThe guard was staring into Schweitzer's silver eyes. \"Are you for fucking real, man?\"\n\nSchweitzer shook him hard enough to make his head rock side to side. \"I ask the questions. What's your goddamn name?\"\n\nThe man coughed, sputtered. \"Raoul, man. Fucking Raoul.\"\n\n\"All right, Raoul. You're going to come with me, and you're going to be very quiet while you do, or I'm going to kill you.\"\n\n\"I'm going crazy. You're dead, man. You're dead.\"\n\n\"Yes, I am dead. But you're not, and you have a chance to keep it that way, but only if you do exactly as I say. Now, are you going to be good? Or are you going to be meat?\" With the last word, Schweitzer let a single bone claw slide from his fingertip.\n\nRaoul didn't answer, raised his hand instead. The terror in his face was evident, but he forced a weak smile.\n\nSchweitzer relaxed a hair. \"Good.\" He snatched the radio from Raoul's holster. \"How often do you check in?\"\n\n\"Every hour; due in another twenty minutes.\"\n\nSchweitzer disconnected the battery and put the two pieces beside one another under Raoul's metal chair. \"Stairs?\"\n\nRaoul pointed to a black door set in the reflective stainless steel of the lobby wall. A broad white sign glowed red above it, blaring the words EXIT to anyone looking. Schweitzer would have rolled his eyes had he had them to roll. His mouth reflexively stretched into a smile, failed as the taut skin met resistance from the metal armature beneath. But he was able to sound sheepish, at least. \"Should have seen that. There an alarm on that door?\"\n\nRaoul shook his head, and Schweitzer pulled them both through the door and into the white-painted stairwell beyond. Metal stairs wound their way up out of Schweitzer's sight, obscured by a series of concrete landings above. Schweitzer glanced to his right, found what he was looking for, a water pipe rising out of the concrete floor, disappearing into the landing above. Schweitzer snatched Raoul's handcuffs out of his belt, slapped the guard's wrist to the pipe. The man resisted, but Schweitzer overpowered him as easily if he were a child. He wisely didn't raise his other hand.\n\n\"You're not going to kill me, are you?\" Raoul asked.\n\n\"No,\" Schweitzer said, cuffing him to the pipe. \"So long as you don't make a lot of noise. All you have to do is sit here quietly, and I'll be done and out of here in about fifteen minutes. You can be quiet for fifteen minutes, can't you?\"\n\nRaoul nodded vigorously. \"Not a peep, man. I'm cool.\"\n\n\"You are cool,\" Schweitzer said, \"which is why I'm not going to kill you. But, unfortunately, I am going to have to hurt you, but I promise not any more than I absolutely have to.\"\n\n\"Wait . . .\" Raoul began, but Schweitzer had already lifted his shoulder, keeping his elbow hooked and raising his right hand in an uppercut that would have been the envy of a prizefighter. He planted it precisely on the point of Raoul's chin, snapping the guard's head back hard enough that his brain sloshed in the hard housing of his skull, the stem stretching and snapping back as the muscles and tendons engaged to keep his head from spinning all the way around. Raoul gave a brief groan, the light went out of his eyes, and he collapsed, hanging by his cuffed wrist.\n\nHe wouldn't be down long. He would scream when he came to. Schweitzer had to make sure that by then, it wouldn't matter.\n\nHe felt Sarah's signal, rising in his chest, pull him on and up. He surrendered to it, letting his legs and arms pump, taking the stairs two, then five, then entire flights at a time, pausing only to hook the railing with his arm to propel him around and up again at each landing. He lost count of how many floors he'd gone up, seeing only the flashing white of the cinder-block walls blurring along beside him. He could see the faint heat signatures of people on the floors, could hear hushed conversations, muted breathing, the sounds he'd expect to hear in a late-night office building. He ignored them all, listening only to the siren's call of Sarah growing more intense with each step.\n\nSchweitzer realized that he was suddenly in silence. The SEAL side of him began to curse his lack of caution, even as the jinn continued to plunge upward, listening only for the sound of his lost love. He slowly mastered himself, ripping his eyes from the dwindling pinnacle of the stairwell, turned to the thickness of the wall and its black steel door leading out to the floor beyond. The floor number, 38, was painted in white stencil beside it. Schweitzer squinted, just barely able to make out the outlines of five heat signatures. They were incredibly faint, far more than they should have been, but Schweitzer could make out men lined up beside the door, each with his hand on the shoulder of the man before him.\n\nSchweitzer knew the formation well, the snake formed behind the point man, stacked on the door. Trained professionals. Trouble.\n\nBarreling ahead was not the answer here. They were ready. But he could feel Sarah's soul screaming down the link between them. Whatever she was paired with was hurting her. There was no way he could slow-roll this. Not when she was so close.\n\nSchweitzer drove forward as the door slammed open, the first two operators buttonhooking into the stairwell, one mounting the stairs and the other moving to the corner of the landing. Cold came off them in waves, a light dusting of frost on their body armor and helmets. They had been hosed down with Freon, or stood in a refrigerator before being sent against him. He could smell the Composition B explosive in the oversized drums hanging beneath the barrels of their carbines. They'd been loaded out and prepared to fight against an enemy who could see into the infrared spectrum. The Comp B meant they knew that regular bullets weren't going to do the job. They were waiting for him. They were ready.\n\nSchweitzer growled and leapt as the first one fired. The round ripped through the air, narrowly missing his head.\n\nBut instead of thudding into the wall, Schweitzer saw a light on the operator's weapon flash red and heard a dull _whump_ behind him as the round exploded. A hot hand slapped his back, turning his leap into a spin. He crashed into the men, lowering his shoulder to catch one of them under the chin and slamming him into the wall. The operator's throat collapsed under the pressure, and he fell to the floor, clawing at his neck and rolling down the stairs into the boiling black smoke left by the round's detonation. Schweitzer didn't have time to fully assess the damage, but he could feel the backs of his ribs exposed where the shrapnel had torn the flesh away, the chips of concrete flaying the backs of his arms and thighs.\n\nThe other operator raised his weapon, cursed as he realized he was too close to fire the explosive round, and whipped the carbine off the sling. A long axe blade swung out of the stock with a loud click. He lifted the gun up by the barrel, stepping into the swing as another of the operators came through the doorway.\n\nSchweitzer rolled to his knees, got a hand up in time to intercept the axe blade, catching the operator's wrist and crushing it with a quick squeeze. The bones snapped, grinding together, the operator screaming. But the weapon already had the momentum, and the axe blade was heavy. It flew down, sinking deep into Schweitzer's shoulder. The scar left by the fight with Jackrabbit had left a divot in that shoulder, a relic of where the bone cleaver had cut in, nearly severing the arm. The Gemini Cell had spent hours repairing the damage, shoring it up with metal cables that held the arm in place, giving Schweitzer the freedom of movement he needed, strength he could rely on. In the days since the repair, it had been so reliable that he'd forgotten about the damage.\n\nBut the divot guided the blade in, the axe biting into the old wound, sharp metal cutting effortlessly through the soft flesh until it caught on the fibers of the metal cable at the joint. Schweitzer could feel a few of the precious threads part, springing back on their own tension with a metallic twanging sound muted by the dead meat around them.\n\nThese men were trained to fight him. They weren't wasting time with bullets. They would blow him apart or cut him to pieces.\n\nSchweitzer reached across his chest, grasping the back of the axe blade. The operator was well trained, and he released the weapon, dropping his hand to a hatchet hanging at his waist. He jerked it out by the head, letting its own momentum carry it upward before catching it by the handle.\n\nSchweitzer jerked the carbine-axe head up and out of his shoulder, spun it around so the blade faced his enemy. The operator's eyes widened briefly as he realized his mistake, and then Schweitzer plunged the axe head forward, punching it through the black Kevlar of his helmet, feeling it cut through his skull and into the soft brain behind. The enemy collapsed, sliding down the stairs, carbine bouncing against the metal as it trailed from the blade, still stuck in his head.\n\nThe other operator dropped his carbine to hang by its sling and already had his hatchet out. He swung it just as Schweitzer turned back to him, planting the head in the wound opened by the carbine-axe. The metal head cut deeper into the cable, more threads snapping, the arm going slack to hang by a slim line of gristle and metal wire. Glycerol squirted against the wall, dribbled down Schweitzer's side.\n\nSchweitzer reached out and grabbed the man's throat, expecting him to try to back away, but he should have reckoned that an operator would follow Schweitzer's own oath: _so others might live._ Schweitzer was an enemy, a monster. Of course the operator would be willing to sacrifice himself. He had been training to die his entire professional life.\n\nThe operator leaned in, letting Schweitzer's hand cut off his windpipe. Schweitzer was lightning-fast, but the operator still had precious seconds to react before Schweitzer's magical strength collapsed the flesh of his neck onto his vertebrae, began crushing the bone. He used those seconds well, grasping Schweitzer's wrist and yanking it with surprising strength, the strands finally parting, the arm ripping away even as Schweitzer snapped his neck and he collapsed.\n\nSchweitzer followed his corpse down, catching up the carbine with his remaining hand, leveling the weapon and firing even as the other operators tried to clear the doorway. The round sped so quickly that the contrail sucked the door in behind it, slamming it shut. The subsequent blast bent it, knocking it askew on its hinges, but it had been designed to hold back fire, the thick metal sagging but holding steady. The men beyond were not so lucky; Schweitzer could tell by the screams. His heat vision was suddenly alight as their warm remains were spattered by the explosive round, dripping off the walls and ceiling.\n\nThrough it all, Sarah's proximity, her agony, still vibrated through the link they shared. She was just a floor or two above, so close he couldn't concentrate. He stared down at his arm, looking tiny now that it was parted from him. The gray muscles were ragged, covered more by duct tape than skin, the metal cables trailing from the shoulder turned blue where the scraping of the hatchet and axe blades had heated them.\n\nHe left it where it lay. He was past sentiment, had no place for keepsakes. Only the Gemini Cell's technicians could fix it anyway, and they weren't exactly inclined to help him. He felt lighter as he bounded up the remaining stairs, compensating for the sudden change in his balance by leaning against the heavier pull of his remaining arm. At last, he could bear it no more and jumped straight up, cresting the metal railing and vaulting over to land at a crouch outside the landing doorway.\n\nThere were no heat signatures beyond it, but he could feel Sarah just a few feet away, separated from him only by the thick piece of metal on its well-oiled hinges. He reached for it instinctively with his missing arm, corrected himself, pulled it open with his real one. His senses screamed out in warning, the SEAL within him long since bludgeoned into silence by the jinn. This direct approach was idiocy, had already cost him an arm. That those operators had been cooled to dampen their heat signatures showed that the enemy was ready for him.\n\nBut the pull of the magic was far too strong. A wild, mad part of him truly believed that if he could only get close enough to Sarah, there wasn't a force in the world that could stop him. That love, contrary to everything he'd learned in a lifetime of running ops, really conquered all. The SEAL in him knew this was wrong, that he was running headlong into ambush, that he was down an arm. It didn't matter; the signal was all. Ninip had spoken of his addiction to the blood of the living, likened it to heroin. Schweitzer understood that now, as helpless as a rowboat on a storm-tossed sea. _Sarahsarahsarahsarahsarah._\n\nSchweitzer gave his jinn aspect free rein. The horns broke his scalp, the line of spikes punching through the open remains of his back, more vertebrae exposed than covered. His claws came out on his remaining hand, and he was surprised to feel a bone spike jut out from the stump of his shoulder, projecting out into the space where his arm used to be.\n\nHe reached out for the door handle, hesitated at a sudden strong sensation from just beyond the metal. Liquid power washed over and through him, as if he stood in the midst of a current, a tide that drowned and carried him up in the same moment. Magic. Sarah's terror and urgency, her love and anger, her need came roaring down the link that bound them, signal boosted by the presence of whatever magic was beyond the door.\n\nSchweitzer could see a heat signature now, faint but growing as the human behind it drew closer. If it was another operator, he was alone.\n\nAnd then the tide of magic and Sarah's nearness overwhelmed Schweitzer and he lost control, yanked the door handle so hard that it ripped free of the metal, sending slivers of metal sparkling through the air. Schweitzer stumbled back, victim to his own momentum, as the door shivered in its hinges and held fast.\n\nThen it exploded.\n\nThe door flew out of the jamb, corner striking Schweitzer on his sternum, crushing him into the railing so hard that the metal bent. The door spun away, clattering down the stairwell. Schweitzer reached out to stop himself, realized the arm he'd used was missing, and flipped over sideways, tumbling. His face struck the stairs and he rolled, flopping down the steps until he skidded to a stop on the landing below, beside the broken remains of the door, his arm, and the operators he'd killed just moments before. The feeling of the magic at his back grew stronger, followed by the sound of heavy tread crunching on the metal fragments left by the shattered door.\n\n\"Jim Schweitzer.\" A woman's voice, rich and low, with the slightest trace of an accent. \"You've lost an arm. _Pa bon._ That's government property, you know.\"\n\nSchweitzer got himself up on the right hand this time, flipped himself over.\n\nRaees Gruenen stood a few steps up, gray skin waxy under the fluorescent light.\n\nThe bullet hole Schweitzer had put in his forehead had been plugged and melted over, leaving a wet-looking round scar. The process of rebuilding his skull had stretched his face, as it had with Schweitzer, but with Raees, the Cell had been careless, favoring one side. The result was a leer, long and rising, his mouth lopsided as if mirth had dragged it too high and too hard, a dead man laughing out one side of his mouth. Long bone spines curved upward from his back, the frames of featherless wings. Others projected from his knees.\n\nOver his shoulder, Schweitzer could see a woman, lean and muscular, her dreadlocked hair gathered into a long braid tossed over one shoulder. She was kitted out as an operator and carried a pistol, which she didn't bother to point at him. The tide of her magic was so strong that Schweitzer felt his dead skin prickle in response.\n\n\"'Lo, Jim,\" Gruenen said from the corner of his canted mouth. Schweitzer could tell from the wheezing flexion of his chest that he was doing the same bellows-dance Schweitzer had done before he pushed Ninip out and took control of his own corpse.\n\nSchweitzer felt his link to Sarah vibrate, his wife's presence so close that she was almost on top of him. The edges of Schweitzer's vision narrowed again, the same sign he'd had when he'd first escaped the Cell and found Sarah, the surefire sign that the link they shared had reached its terminus.\n\nHe looked at the twisted smile with dawning horror. Gruenen took a step down, the link pulsed, and Schweitzer knew his wife was inside that mercenary's broken corpse.\n\n# CHAPTER XXVI\n\nSO OTHERS MIGHT LIVE\n\n_Jim,_ the link throbbed. Gruenen took another step, his fists began to crackle, blue arcs of electricity spanning the knuckles. He could feel Gruenen battering Sarah aside, slamming her against the walls of the body they shared. _Jim_. Sarah's voice. _Jim, run._\n\n_What did you expect,_ Schweitzer asked himself, _that she'd be walking and talking? Body whole and heart beating? That they'd truly brought her back to life?_ The truth was that he hadn't had any expectations, that he had only been drunk on the bond between them. _Enough. She's trapped in there and she's hurting. Use the knife; set her free._\n\n\"Jim.\" The Sorcerer's voice was soft, reasonable, but she was careful to keep Gruenen's corpse between her and Schweitzer. \"Can you feel your wife, Jim? She's in there, you know. The love of your life.\"\n\nThey had brought her soul back. They had paired it with the still-cooling corpse of that mercenary. Their souls were linked, her memories and experiences laid bare as his had been to Ninip. The thought filled him with rage and grief, propelling him to his feet, sending him flying forward, an insensate growl escaping his mouth, a howl not unlike the one Ninip had uttered when he'd been in thrall to his bloodlust, scenting beating hearts and the stench of fear.\n\nBut Gruenen was not afraid. His eyes narrowed, the gold threaded with thick lines of silver that showed he was in control. He raised his buzzing hand and lightning exploded, blue arcs sizzling across Schweitzer's chest. Schweitzer's dead muscles seized, and he felt as if a hammer struck his chest, launching him back down to the landing. Smoke rose from his shoulders, flame licking the earlobe of his remaining ear.\n\nDeath had not robbed Gruenen of the magic he had commanded in life. Schweitzer could feel Gruenen's magical current looping and coiling around him. It felt the same as the magic he'd felt around the Golds. All a single element. Was it linked to the dead mercenary's body? His soul? \"Stoo . . . pid,\" Gruenen managed, descended another step.\n\n_Jim._ Another burst of emotion along the link they shared, carrying the hints of Sarah's voice.\n\n\"Don't be stupid,\" the Sorcerer said. \"You're missing an arm, and what's left of you is held together by duct tape, literally. You want to be with your wife again, don't you? I can arrange that.\"\n\n\"That's not how it works,\" Schweitzer growled, struggling to get up.\n\n\"You don't know how it works,\" the Sorcerer answered. \"Nobody does. You have only ever worked with Jawid. You don't know what I can do. I brought your wife back, and I can put you two together. How would you like to share a body with her, Jim? How would you like to be linked to her, soul to soul, for the rest of eternity? I can make that happen.\"\n\nSchweitzer felt his dead heart jump at the thought. Eldredge had said that the Cell was learning how to put souls in living bodies. If there was a way . . . _No. If there is a way, it isn't this one._ \"I'm not working for you again.\"\n\n\"Nothing in life is free, Jim. You know that.\" She nodded to Gruenen's corpse.\n\nSchweitzer jumped onto his haunches, sprang aside as Gruenen extended his hand again, and Schweitzer felt the electrostatic charge building in the air around him. A thick cable of lightning arced into the landing, sizzling just behind Schweitzer's heel as he dove through the singed remains of the doorway, tumbling through the scattered bodies of the operators he'd fought before. There was precious little left to them, most of it spread across the blackened walls by the explosion of the airburst round. Schweitzer rolled in the ash and dust, putting out the fire Gruenen's lightning bolt had kindled on his back. The landing behind him burned brightly.\n\n\"Jim!\" the Sorcerer called. \"Stop playing games! What do you think is going to happen here? If by some miracle you beat this one, I'll bring your wife back in another body. And another. I am not Jawid. I can find anyone in the void. I can find your son after he is dead. I can even find you. Would you like a new body? A whole one? A strong one? I can make it happen for you.\n\n\"What do you plan to do, Jim? Kill Gruenen and Sarah goes back into the void. You lose her again.\"\n\nShe was right, of course. The link to his wife had dragged him all this way, and now all he could do was cut her free. \"You only want one thing, Jim, and I have it. Let me give it to you.\"\n\nThe Sorcerer made her way around Gruenen's corpse. The dead thing put out an arm to hold her back, but the Sorcerer pushed the hand aside as confidently and easily as it had been a living man. \"Jim, please.\" Her dark eyes were honest, sympathetic. Schweitzer tried to sniff out the scent of the chemicals in her bloodstream, listen to the beat of her heart, but the tide of her magic blotted out his senses. He couldn't focus, not with Sarah so near. \"We didn't bring you back here to destroy you. Eldredge was right about you. You're unique. Your country still needs you. I can reunite you with your wife. Is that so much worse than life on the run? You can't care for your son. You must know that.\"\n\nGruenen stood on the stairs, the tension in his muscles making him shiver, but holding his position for now.\n\n\"Eldredge told me about the Director,\" Schweitzer said. \"You work for a Gold.\"\n\nDadou smiled. \"I work for a soul. Dead or living, we all have them. The body means nothing, Jim. You, of all people, should know that.\"\n\nSchweitzer could feel her magic focusing, reaching out to him, probing and touching, tugging experimentally. \"Let me get you out of this pile of rag and bone. Let me set you free.\"\n\nSchweitzer thought of the feral madness of Ninip, of what he'd seen the Golds do to the old man and his wife when he'd fought to save Sarah at that Virginia farmhouse. He thought of the hours trapped in the clear white expanse of his underground cell.\n\nHe thought of the chance to be in a living body, to feel his heartbeat, to feel it in time with his son's, with his wife's.\n\nBut he felt the nearness of Sarah again, her agony pulsing along the link to him. Summoned back after death, it was stronger, clearer. He could hear her voice now. _No,_ she sent. _Don't._\n\nSchweitzer let his hand drop, scooping up one of the operator's fallen carbines, angling the barrel up toward the ceiling.\n\nThe Sorcerer bared her teeth, not bothering to cry out. She raised her pistol, and Schweitzer felt the forty-five-caliber round tear through his chest, exit his shoulder. He went tumbling backward, but not before he felt the carbine fire, the airburst round tearing into the concrete slab overhead. It detonated with a sharp kick, the shock wave driving him into the floor and knocking Gruenen from his feet. Schweitzer felt the concrete fracture, the huge chunks of masonry tumbling down around them. He'd hoped to catch both the Sorcerer and her creation in the sudden fall, but the round in his chest had thrown off his aim. Most of the debris fell harmlessly down the stairwell.\n\nAt last, the momentum of the explosion spent itself, and Schweitzer got to his feet.\n\nThe Sorcerer lay on the floor of the hallway, her leg twisted at an unnatural angle, blood pooling beneath her knee. The joint was flattened beneath a piece of fallen concrete, the rebar support disappearing into the flesh below. Her face was twisted in pain, her breathing coming in great gulps.\n\nGruenen sprang to his feet behind her, pointed a finger at Schweitzer, who dove aside as the lightning tore a hole in the landing, leaving a ring of flames around a black scar in the floor.\n\n\"Gah!\" the Sorcerer shouted to Gruenen. \"Just rip that fucker to pieces! I'm done talking to it.\"\n\nSchweitzer scrambled to his feet. He couldn't take Gruenen head to head, not if he hoped to win. But he could feel Eldredge's knife tucked into the waistband of his trousers, a cold firmness nestled into the small of his back. He reached for it now, drew it out, let the angry teal light wash over Gruenen's leering dead face.\n\n\"Come!\" Gruenen bellowed, leaping down to the landing and standing in the pool of flame. \"Come! Wife! Have!\" _Jim,_ Sarah sent along the link. _Run._ Then Gruenen bulled her aside and Schweitzer could feel the rage and pain along the link as she struggled against him.\n\n_No,_ Schweitzer sent back, not sure if she could hear him. _I'm going to set you free._\n\nSEALs trained for knife-fighting, and Schweitzer instinctively fell into his old stance, bringing the knife hand back, waving the free one forward as a visual distraction. It wasn't until Gruenen charged him that he realized that he'd once again forgotten his missing arm. He swung the blade crosswise, hoping Gruenen would be as careless as a Gold, let Schweitzer stab him in an effort to close.\n\nBut Gruenen wasn't a Gold. His burning eyes were threaded with silver, and they flicked to the glowing weapon, sensing the magic or guessing at it from the glow. He danced back, the knife tip missing him by inches, and then stepped in, grabbing Schweitzer's wrist and elbow carefully, pulling his arm across his chest.\n\nWith only one arm, Schweitzer had no leverage to grapple with him. He twisted his body violently away, and Gruenen slid his fingers up Schweitzer's wrist, pinching the KA-BAR by its metal hilt, yanking it from Schweitzer's grasp and tossing it down the stairwell.\n\nThe only real weapon he had. Gone. Schweitzer listened to the hollow-sounding clatter of the blade as it tumbled and finally came to a stop a floor below.\n\nGruenen laughed and punched Schweitzer in the face. The blow would have broken a bone jaw, but Schweitzer's was made of metal, and the shot only made his head spin as Gruenen threw him down the hallway.\n\n_Stupid move. He had me. He should have ripped me up._ But while Gruenen was a trained Operator, he was no SEAL. The dead mercenary howled again, thumping his fists against his chest. _He's enjoying this._ That was good. It would make him careless.\n\nPanic began to well in Schweitzer's spiritual gut at the thought of his disadvantage, but he pushed it aside. _Focus. He's got one up on you. You need to find another way to win._\n\nGoing after the knife would take him straight into Gruenen's arms, so Schweitzer ran the other way, pelting down the industrial carpeting, faux-wooden office doors a blur to either side. Plexiglas plaques proclaimed business names beside windows reinforced with wire. Sarah's signal came behind him, maddeningly close, calling him back to her.\n\nBut there was no Sarah. Her soul was bound into the corpse that shambled after him. She was there and not there. She was with him and lost to him. Grief blurred his senses, even as he felt the electrostatic charge rise as Gruenen readied himself for another burst of lightning. Schweitzer shot to his right, yanking a door open as the blast tore after him, the electricity exploding the cheap pressboard into splinters, the glass melting and running down the wall. The cloud of dust filled the hallway, and Schweitzer knew he couldn't keep on like this. The narrow space was a shooting gallery, giving Gruenen the range and tight quarters he needed to hem his target in. Schweitzer had to get out of there until he could close the distance.\n\n_And then what?_ To kill Gruenen was to kill Sarah. _No, Sarah's already dead._ He remembered Jawid's words. _The great death. The last one._ If he destroyed Gruenen, would that condemn Sarah to something beyond the void? It didn't matter. He couldn't leave her tangled with Gruenen's rotten soul.\n\n_Position first. You need out of this hallway._ It stretched out ahead of him for at least another thirty feet. He wouldn't make it before the dust cleared. Schweitzer veered left, throwing his shoulder into the next office door, smashing it open and sending himself hurtling into the darkness within.\n\nThe wall behind the reflective metal desk was made of the same cheap wood as the door, and Schweitzer caught his own reflection as he cleared the dust cloud and caught his hips against the desk, sending him flipping over and into the chair on the other side. A huge embossed seal dominated the wall, brass silhouette of a rifleman standing on farmland before an American flag. THE GREAT SEAL OF THE STATE OF IOWA.\n\nSchweitzer rolled off the chair, picking it up and flinging it through the door. It wouldn't take Gruenen long to clear it, but it would buy him a second to survey his surroundings. There was nothing; a door led to adjacent offices from their side of the desk, and a small hatch in the wall likely led to a trash chute below. Schweitzer dared to hope that there was an incinerator at the bottom of it, but he already knew there wasn't. He would have been able to see the heated air wafting up the shaft.\n\nA crash as Gruenen tore through the dust cloud and stumbled over the wreckage of the chair. He smashed through it, the bones rising from his shoulders tossing the twisted metal back down the hall, then pushed into the doorway, knuckle-walking like a gorilla. \"Jim!\"\n\n_Sarah._ Schweitzer tried to reach back down the link, fumbling to connect to his wife. He tried to push his love to her, to give her some comfort as she struggled against Gruenen's relentless battering of her soul. He moved upstream against a strong current, as he had when he'd reached out to Jawid, Gruenen forcing the tide against him. For a moment, he felt Sarah's presence, so near it was like a physical touch. With that touch, he again lost the bubble, his training knocked aside by a need so powerful that he could no more stand against it than he could against gravity.\n\nA professional never let grief or anger drive. A professional didn't believe in fair fights, let alone fights where they were at a disadvantage, down an arm, body slowly coming apart, skeletal integrity compromised by hundreds of breaks, flesh held together by duct tape. A professional chose their ground and their moment, made damn sure that they didn't take on fights they couldn't win.\n\nBut with Sarah so close, Schweitzer was a professional no longer. He stood, hurling the desk up and into Gruenen's face, following close behind. _No,_ Sarah passed along the link as Gruenen rose, driving his head forward into the desk, breaking it in half. He strode through to meet Schweitzer, hands blazing lightning. Schweitzer kicked at his knee, succeeded only in nearly impaling one foot on the bone spike before Gruenen extended a hand. Schweitzer leaned aside as a lightning bolt sizzled over his shoulder, striking the hatch to the trash chute and sending it spinning away, leaving a dark, smoking hole in the wall.\n\nSchweitzer swung back, head-butting Gruenen in the ribs and driving a bone horn into his side. He could feel it grate against the dead mercenary's ribs, locking in place between the two of them, taking Gruenen's weight. This close, Schweitzer could feel the tide of Gruenen's magic so strongly, it was nearly suffocating. He shouted, straightened, jerking his head back and feeling Gruenen's feet come off the ground.\n\nGruenen shouted, bringing his fists down against Schweitzer's lower back hard enough to make his whole skeleton vibrate. The impact set Schweitzer off-balance, and he fell backward a few steps. Gruenen's weight sagged forward, and he brought his knees down, driving the spikes into Schweitzer's chest, then ripped them free. Schweitzer could feel his dead flesh tearing as the bone projections pulled out, Gruenen's thighs tensing to drive them in again. He would not be able to hold against more of those blows. He had to get Gruenen off of him quickly.\n\nSchweitzer let Gruenen's weight carry them the rest of the way, toppling over, waiting for the body to slide off the horn, freeing him to turn and fight. There was a shuddering impact and Schweitzer's forward momentum was halted. Gruenen flailed, legs kicking before he remembered the knee spines and tried to drive them forward again. Schweitzer got his good arm up in time to intercept Gruenen's right leg, but his left cleared the empty space where Schweitzer's other arm should have been, driving into his chest again. Schweitzer howled and wrenched his neck, desperate to get free. Gruenen worked to the same purpose, trying to rip himself off Schweitzer's horn. There was a moment of strain, a loud crack, and at last, Schweitzer felt the horn rip away from his skull, cracking in half along with Gruenen's ribs. The weight dropped away from his neck, and he whirled.\n\nGruenen was getting his feet under him, hands planted against the wall. Schweitzer's fall had slammed his head and shoulders into the trash chute, and the spider-webbing of cracks through the white cinder-block wall testified to the force of the impact. It wouldn't hold him for long.\n\nSchweitzer didn't need long. He kicked Gruenen in his ass. The dead mercenary shuddered, shoulders breaking as he hammered forward into a chute designed to accommodate boxes of paper half his size. His hands ripped off the wall as his arms were pressed to his sides. His legs twitched. Schweitzer could feel the rise in his magical current as he gathered it to him.\n\nSchweitzer stepped back, ran forward, leaping into a final kick that drove Gruenen the rest of the way through the wall and down into the chute below, his body jerking as he flailed himself to a stop a few feet down, knee spikes digging into the thin metal of the chute sides, claws dragging rents through the bright surface. As he stopped, the metal's shriek was replaced by Gruenen's animal cry. \"Jiiiiiiimmmmm!\"\n\nSchweitzer thrust his head and shoulders into the chute top, looked down at Gruenen's tangled corpse. The chute was twice the width of the entryway, and the dead mercenary jerked his broken shoulders, ripping his arms free, pulling himself forward and up.\n\nGruenen's shoulders were broken but still broad enough to wedge him into the tight space. Schweitzer was one arm slimmer and had the high ground. If he was going to fight Gruenen head on, circumstances would never favor him more.\n\nSchweitzer came down the chute boot-first, planting his sole against Gruenen's forehead, snapping the dead mercenary's head back. Schweitzer heard a dull cracking of Gruenen's cervical vertebrae as they took on Schweitzer's full weight. Schweitzer jammed his fist against the chute side and pushed, wedging himself in and keeping himself from falling farther. He planted one foot on Gruenen's shoulder and lifted the other to stomp him again.\n\nBut Gruenen, for all the beating he had taken, was still more whole than Schweitzer, stability and skeletal integrity lending him speed. He swept a hand up, catching Schweitzer's ankle and yanking it down.\n\nSchweitzer came off-balance, shoulder slamming into the rent left by Gruenen's claws. Gruenen pulled harder, pinning Schweitzer's arm against his side. Schweitzer struggled to free it, but even his magical strength was useless against the feet of concrete wall behind the thin metal sheeting. Gruenen hauled on the leg, pulling it taut and hauling himself up. He flailed out with another hand and grasped Schweitzer's other foot. Schweitzer tried to kick his feet free, but Gruenen held him fast, slowly hauling himself up Schweitzer's body, hand over hand.\n\nSchweitzer swept a knee up as soon as Gruenen's hands left his ankles, but it was impossible to get enough leverage in the tight space, and he succeeded only in keeping Gruenen below him, pinned to the back of the chute. All the while, Sarah's nearness tore at him, a moth fluttering against the side of a glass jar.\n\n\"Got you,\" Gruenen whispered. \"Got you.\"\n\nThe dead mercenary reached up, claws sliding out from his finger tips, and plunged them into Schweitzer's stomach. Schweitzer flailed, pushed, kicked, all for naught. Gruenen's feet were braced against the chute sides now, his broad bulk solidly wedged into the tight space, stable as if he stood on firm ground. Schweitzer felt the claws digging in, tunneling up as Schweitzer had done so long ago, when he and Sarah had fought the Golds in a Virginia field. But where Schweitzer had grasped his enemy's spine, Gruenen's hands curled around Schweitzer's floating ribs.\n\n\"Got you,\" Gruenen repeated, and began to pull.\n\nSchweitzer felt the pressure torquing him in two directions, his spine quivering, sternum sliding off center. The tendons in his torso began to tear, ligaments straining, muscles starting to fray. Gruenen's leverage was unbreakable. He was going to tear Schweitzer in half.\n\n_Jim._ Sarah's voice. She was so close. Schweitzer looked back up the shaft to the hatchless opening. He couldn't reach it with his arm trapped against his side. He flailed, pushed, stayed firmly locked in place.\n\nHe felt the first tiny cracks shudder through his ribcage.\n\nHe wondered if his soul would stay attached to his body once Gruenen broke him. How destroyed would he have to be before he was freed to return to the churning of the soul storm? Maybe he would be able to find Sarah there. With no way to resist Gruenen physically, he instead channeled his energy into the link with Sarah, trying to get a last touch of her. Maybe if he could scent her, truly feel her one last time, he would be able to follow her in the void. Maybe they could find one another in that churning chaos. He didn't think it was possible, but just a short while before, he had thought that life after death was impossible too.\n\n_Sarah, I'm sorry._ He'd failed her; he'd failed the mission. Love didn't conquer all. Righteousness was not stronger than death, not when you were down an arm, not when you had more duct tape than skin holding you together. The SEAL never ascribed to idiot notions of failure not being an option. Failure was always an option, and understanding that was the first step to avoiding it. And understanding failure meant accepting it when it came.\n\nGruenen's focus was on breaking Schweitzer in two, and for the moment, Sarah swam back down the link to him, her love so intense and immediate that it made his senses buzz. He drowned in the sensation, the nearness of her, so close it felt as if the stuff that made them up was mingling.\n\nSince Schweitzer's death and reanimation, their bodies had separated them, a gulf riven by her warm blood and beating heart. Now, here in the link forged by the magic that connected them, they were truly together, for the first time since a gun barrel had been shoved under Schweitzer's chin. He felt Sarah's soul anchored in the dead mercenary's body, as if only a branch of her flowed out to him. Schweitzer wrapped himself around it, wove into it.\n\nAnd for a moment, it was as it had been in their apartment on the night he'd been killed, with the moonlight making hammered silver of their skin as they made love. As it had then, the line between the two of them blurred, until Schweitzer forgot where he left off and she began, and they were one thing, drowning in love.\n\n_Oh, baby. I'm so sorry,_ he whispered.\n\n_Patrick is . . ._\n\n_He's safe. I'm sorry; I had to try . . ._\n\n_It's okay. It's okay._\n\n_I can't leave you in here with him; I've got to get you out of here. I'll find a way. I'll come back._\n\nAnd now Schweitzer could feel Gruenen's presence turning, reaching back from its focus on making the dead hands pry Schweitzer apart, focusing instead on the rosewater tide that linked Jim and Sarah Schweitzer blazing like a flower in the midst of the dark inner space within the dead mercenary.\n\nSarah turned from Schweitzer, facing her enemy, ready for the next round.\n\nSchweitzer focused on the link, visualized Gruenen's presence, hulking and black, dwarfing the tiny silver light that was his wife. He could feel the mercenary's malevolence, his anger. Schweitzer had snuck into his spiritual backfield, and Sarah had helped. There would be plenty of time to tear Schweitzer's body apart. For now, Sarah would be made to pay for speaking to the enemy.\n\n_No! You fucker! I'll kill you!_ Schweitzer was vaguely aware of his physical mouth emitting a howl of rage that rebounded off the chute's reflective metal walls. He funneled his anger through the link, as if by the very heat of it, he could blast Gruenen back.\n\nBut the only person to hear his words, the only person to feel the heat of his anger, was Sarah. She squared herself against Gruenen, buzzing hate so strong that Schweitzer could feel it in the back of his throat. Schweitzer could see her spiritual form, the silver outline of her body glowing orange with the heat of Schweitzer's anger, growing.\n\nIt was impossible to tell in the darkness of Gruenen's inner space, in the confusion of emotions that buffeted him, but Schweitzer imagined that he saw Sarah look back down the link toward him, saw the silver-washed contours of her face. She smiled at him, turned away.\n\nShe launched herself against Gruenen, the rage making the dark space within him reverberate. Gruenen was driven back, his huge darkness staggering under the assault of Sarah's onslaught. He reeled, fell against the edges of himself. Sarah pressed forward, buffeting him, pushing him back.\n\nBut Gruenen was strong. It only took him a moment to find his spiritual footing, to begin pressing back. Schweitzer continued to scream, helpless to move, to aid her. Unable to do anything but feel what she felt through the link.\n\nAnd so it was that he saw the plan forming in her mind, knew what she was about to do.\n\nAnd even now, when he knew it would free her from pain, he didn't want her to do it. Because he had fought so hard and come so far. Because at last, he had found her, and even agony was agony _together_.\n\nOnce Bound, two souls shared one corpse. The stronger could control the body. A spoken word, a bent finger, a footstep.\n\nSarah was not stronger than Gruenen, but the dead mercenary was knocked back for the moment.\n\n_Don't,_ Schweitzer found himself sending to Sarah, even as she swept up, seizing control of Gruenen's magic.\n\n_So others might live._ Sarah's voice was faint, wracked with the agony of her constant struggle with Gruenen. Schweitzer felt her tap into the flow that Gruenen commanded, drawing it about them. Schweitzer's physical senses heard the crackle of electricity as it wreathed Gruenen's lower body, well clear of Schweitzer. He smelled the burned stink of ozone and metal.\n\n_So others might live,_ Sarah repeated.\n\nHis oath.\n\n_I lost you,_ Schweitzer said. No matter how badly he wanted her, there was no way to have her back, not now. Sarah was dead; there was no changing that. Patrick was still alive in the hands of a stranger. He had solved the mystery of Sarah's return. He had found as much as there was to find. Now he had to destroy the Cell so Patrick could go on living. The void wasn't going anywhere. It would be waiting for him when the tattered remnants of his body finally gave out. _But the longer she twists in the soul storm, the more insane she'll become._ He knew that Ninip had not always been the ravening monster who shared Schweitzer's corpse. He had been a man once, before the maelstrom had its way with him. Schweitzer couldn't bear the thought of Sarah being slowly warped into a creature like that. _No,_ Schweitzer thought. _Ninip had millennia. You'll end this one way or another in less than a month._\n\nThe emotion travelled down the link, resonating with Sarah's spirit on the other end. The bolt of love and loss that she sent back up staggered him. _I'll find a way back to you, Jim. I always do._\n\nGruenen growled, tore after her. Sarah gave him a final spiritual shove, sending Schweitzer one last message. _So others might live. I died, Jim. Help him._\n\nPatrick. Help Patrick.\n\nGruenen's presence slammed into Sarah, dragging her back from her control over his magic. His malice flowed down the link between them, so strong it threw Schweitzer back, knocking him into his own physical form, wedged into the chute, trapped between Gruenen and the concrete behind the thin reflective metal.\n\nBut not before he saw Sarah smile, release the magic she'd Drawn around them.\n\nBright blue lightning flashed down from Gruenen's waist. Arcs of electricity danced up the metal chute, the smell of smoke and ozone nearly overwhelming to Schweitzer's augmented senses. A sudden burst of heat engulfed his head and shoulders. He kicked off, pushing Gruenen away, launching himself up toward the chute entrance, throwing himself through.\n\nTongues of lightning chased him, the cool air of the office rising up to embrace him. The lightning storm inside the chute collapsed the wall, and Schweitzer could see it crackling, rebounding off the chute's reflective metal surface. Gruenen's corpse hung in the center, flesh smoking, tongues of flame rising as he was consumed by electricity of his own making. _Not his making. Sarah pulled that trigger._\n\nGruenen tried to roar, the cry reduced to an insect buzzing as his throat melted. The flames of his eyes vanished as his face sheeted down, a gray liquid mixing with the sizzling ruin of his chest. Schweitzer tried to reach out for Sarah, but the link was static noise now. He had a vague sense of struggle, of agony, but nothing close to the detail he had known before Sarah had triggered Gruenen's magic against himself.\n\n\"Sarah!\" Schweitzer shouted as the lightning reached a fever pitch, the blue arcs self-sustaining now, independent of the magic, the entire chute turned into a glittering column of fire. The heat forced Schweitzer to back away, throwing his arm across his face, but not before he saw Gruenen shiver and finally explode.\n\nThe dead mercenary's flesh pattered off Schweitzer's face and shoulders. The broken link with Sarah throbbed, her absence a punch in his gut. Smoke was rising from his head and shoulders, one of his eyes closing as the skin melted over it, fusing the socket shut until the silver flame burned back through a moment later. He stumbled back into the wreckage of the desk, his enhanced hearing picking up the splattering sound of the pieces of Gruenen pattering down into the Dumpster below.\n\nThe link with Sarah was silent, the emotional funnel gone dead. Gruenen's magical tide no longer eddied. Schweitzer tried to roll his shoulders, felt the melted ruin of his skin catching, inhibiting the movement. But in the confines of the chute, the damage had been magnified a hundredfold. Schweitzer didn't need to look back in the hole to know that Gruenen was gone, and with him, Sarah.\n\nHe went back out into the hallway. The Sorcerer had managed to drag herself most of the way toward a bigger office farther down, where Schweitzer could see the heat signatures of five men crouching by the cold, dark square of a window. One of them was bent, arms working to uncoil a rope ladder.\n\nThe Sorcerer looked hopefully over her shoulder, her expression turning sour as she realized that it was Schweitzer and not Gruenen who has returning for her. \"You fucking . . . With one arm. You beat him with one arm!\"\n\n\"Don't need it,\" Schweitzer managed, snatching her up by her collar. Her shattered legs dragged on the carpet and she cried out.\n\n\"Shut up,\" he said. He dragged her the rest of the way to the door, the loss of Sarah making him savage. Her eyes rolled back in her head, and he felt her magical tide reaching out into the distance, and he knew she was seeking the void as Jawid had. Her magic washed over him and he bulled it aside. It got easier with practice. Each time he felt another's magic, he got a little better at controlling his own.\n\n\"You think because you are winning that you are a hero,\" the Sorcerer snarled. \" _Salle bette_ , you're a walking dead man. My kind created you. I'm the hero!\"\n\n\"Uh-huh,\" Schweitzer said. \"How're your legs?\"\n\nThe Sorcerer twitched in his grasp. She flailed her fists, drumming them against the melted scar slurry of his hips. \"You don't fucking own me! You don't control me!\" she screamed.\n\n\"Not at all,\" Schweitzer said. \"You're your own woman. You chose to lock my wife in with a monster. You chose to stand by while he hurt her. You chose to work for the enemy. All your choices. All your responsibility.\"\n\n\"Listen to me! I can still help you. I can bring you together with your wife. I can protect your son.\"\n\nSchweitzer smiled his rictus grin. \"I've run against people like you all my life. You always bargain at the end.\"\n\n\"Please! I know how you won out against Ninip, Jim! You have to be good. You can't murder me.\"\n\nThe final door was thick; a cipher lock blinked red beside a shaded glass window. The state seal hung below the great seal of the United States, the eagle pronouncing that from the many, they had built one. Schweitzer planted his foot in the center of the seal.\n\nHis grief had tripped the scales, gone so far into the red that it lapped itself. It gave him a hideous focus, a strength beyond even what he'd known when he'd first pushed Ninip out and taken control of his corpse. The door folded in on itself, bending double, the doorknob popping off, the cipher panel sparking. The figures beyond froze, hands dropping to pistols. Two of them pushed down another, forcing him to shelter behind the desk. The last redoubled his efforts to get the rope ladder out.\n\nA second kick and the door flew inward. Schweitzer followed, the Sorcerer dragged in the wreckage, screaming as Schweitzer kicked the receptionist's desk out of the way and hauled her upright. The office was configured just as the last one, with doors at both sides of the room. Schweitzer went to the doorway where the red outlines of the figures ghosted the thickness of the walls. He heard the tension on trigger springs, the men around the Senator drawing down on the entrance. They would fire at the first thing to come through that door.\n\n\"I'm not going to murder you,\" he said.\n\n\"What the hell are you doing?\" the Sorcerer asked him as he swung her around to the doorway.\n\n\"You're the hero,\" Schweitzer said, \"prove it.\"\n\nHe shoved her forward, letting her go and sending her tumbling through the door.\n\nThe bullets tore into her even as she crumpled on her broken legs. She twitched in the air, spinning as she collapsed, her blood misting the far wall. Sarah had danced that way the last time Schweitzer had been alive, Patrick too. He supposed everyone looked like that when the gunfire came calling.\n\nHe felt her current wink out, saw her body sprawl, limp as a rag in a darkening pool. White dust settled slowly over her, broken away when the bullets had pierced her and torn divots in the wall.\n\nSchweitzer knew that the shooters would stay covered down on the entrance, scanning after their target had dropped. He had done the same thing a dozen times himself, and so he knew that a few moments later, they would relax just a fraction, their guard dropping as they slowly came to believe that nothing was coming in after them. They would begin to move toward the door, confusion sapping their focus.\n\nHe waited, heard their footsteps, heard the miniscule creak of the triggers as they let them out just a fraction, just enough to give him the time he needed.\n\nSchweitzer flowed around the door.\n\nHe immediately heard the trigger springs take on tension, could smell the adrenaline dumping into the gunmen's veins, wafting into the air from the sudden sheen of sweat that sprang out on their foreheads at the sight of him. They had just gunned down one of their own, flopping like a rag doll on broken legs; now they faced a one-armed monster, a shambling thing of ragged bone trailing scraps of meat.\n\nYet they still moved as if in slow motion. The operators in the stairwell had been prepped with cutting weapons, staged and ready to face him. These men had no such advantage. Schweitzer had been fighting the Golds for so long now that mere humans were no contest. The enemy closest to him swiveled his wrist to follow Schweitzer, loading the trigger, slapping it to the rear. Years on the range had taught Schweitzer that the rush would yank the pistol's muzzle low and to the left, and he leaned in the opposite direction, chopping out with his arm, expertly striking the man at the base of his neck, snapping it sideways. As the man fell forward, Schweitzer brought his knee up, cracking his ribs and sending him hurtling into the man with the rope ladder. He had just enough time to scream before the corpse of his comrade slammed into him, sending them both crashing through the window, his scream fading as they fell.\n\nThe next man got a shot off, and Schweitzer knew right away that his aim was true, could tell from the shooter's steady stance, his calm breathing. He also knew that the man was a professional, and professionals didn't shoot center mass. The bullet would be headed for the three-inch triangle that ran from the top of his mouth to the center of his forehead. Schweitzer tilted his head, bending his neck low enough to touch his ear to his shoulder, a move that would have given a living man whiplash.\n\nThe bullet skidded through the flesh, digging a furrow as it whined along the surface of his skull. Schweitzer felt the intense heat of its touch, and then it was gone again, flying on and through the wall behind him. The man had been so sure of his shot that he'd released the trigger, giving himself a split second to see that his target was down. It would have been a fatal mistake for a lesser shot, but this man was good and he knew it. His eyes widened in shock as the round missed and Schweitzer closed the rest of the distance, kicking straight up, catching the enemy on his chin and snapping his neck. He turned a twitching somersault, landing in a limp pile.\n\nThe final enemy reached down behind the desk, dragging an older man into view. His hair was immaculate despite sheltering in the midst of the fight, his kind features crunched with worry. He stayed low, crab-walking with his escort, clearly a man trained for protective security details.\n\n\"Senator Hodges,\" Schweitzer said as the last enemy leveled his gun at him.\n\n\"Stop right there!\" The man's voice was panicked; he knew he couldn't beat Schweitzer. He'd just watched him take out his three squadmates in as many seconds.\n\nHodges had more sangfroid. He shook off the man's hand, straightening. \"Hello, Jim.\"\n\nSchweitzer turned to the remaining man. \"Time for you to go,\" he said. \"I've had enough killing. You can tell your bosses that you blew it.\"\n\nThe man looked at the Senator, and Hodges put a hand on his shoulder. \"I'm glad you're being reasonable, Jim.\" Hodges's voice was a cartoon of New England gentry, and Schweitzer remembered it now from televised committee hearings.\n\n\"I'm not being reasonable,\" Schweitzer said. \"I'm being exhausted. Last chance.\" He nodded to the man.\n\n\"Now, Jim.\" Hodges patted the air with his palms. \"I understand that you're angry . . .\"\n\nSchweitzer heard the tension coming out of the trigger spring in the man's hand. He couldn't leave his charge. He was a professional. Schweitzer could respect that. He would have done the same thing, had taken the same oath. So others might live.\n\nHe punched the man's wrist, the gun going off, bullet discharging harmlessly into the ceiling. The pistol's hammer struck the man in the eye at the same time his wristbone snapped, and Schweitzer heard him groan as he dropped to the floor, hand clapped to the bleeding socket, desperately trying to hold the popped remains of his eye in his skull.\n\nHodges winced. \"Christ, Jim. It's hard to believe you used to be a good man.\"\n\n\"I'm not a man anymore,\" Schweitzer said, \"but good or bad, I just saved your life.\"\n\n\"You just took the lives of four service members, Jim. Men just doing their jobs. Men protecting me.\"\n\n\"They weren't protecting you,\" Schweitzer said. \"They were holding you hostage.\"\n\nThe man on the ground groaned, driving the heel of his hand into the ruined remains of his eye. His free hand held the broken wrist. He was definitely out of the fight. Schweitzer jerked his thumb at the Sorcerer. If she was like Jawid, there would probably be more. Who knew if they would all be able to do what Eldredge said she could have done? Hodges wouldn't be safe, not now.\n\n\"Why the hell would my own people hold me hostage?\" Hodges asked, but Schweitzer could hear the vibration in his throat, the tiny upward lilt at the end of his words. The seeds of doubt were already planted.\n\n\"That\"\u2014Schweitzer gestured to the Sorcerer again\u2014\"was going to do something terrible to you. I take it you know about the Gemini Cell?\"\n\n\"I'm not going to tell\u2014\"\n\n\"So, yes, you do. Eldredge had mentioned that there was only one person in the government who knew about it.\"\n\n\"Doctor Eldredge is a traitor. He is in the employ of a foreign\u2014\"\n\nSchweitzer waved the statement away. \"Maybe, but the truth is that I don't care. You know about the jinn. What you don't know is that that woman was going to put one in you. Because they wanted to keep the program going. Because they knew you would shut it down.\"\n\n\"You're lying,\" Hodges said, but Schweitzer could tell that the Senator believed him.\n\nSchweitzer shrugged, feeling the tension in his melted skin. \"Maybe, but you're out of choices, Senator. You can't fight me and I'm not letting you go.\"\n\n\"Where are you taking me?\"\n\n\"Away. There'll be more coming. There are always more. First, we're going get someplace safe, then you're going to call off the dogs and save my son. After that, we can work on taking this program apart.\"\n\n\"Just who do you think you are?\" Hodges's voice was full of wonder.\n\n\"I'm the monster who saved your life,\" Schweitzer answered. He took hold of Hodges's elbow, began to steer him toward the rope ladder. \"They had the right idea, at least. Makes more sense than going out through the lobby.\"\n\nHodges shook off Schweitzer's hand. He had courage. Schweitzer would credit him with that, but he knew it was always the way with people used to being in charge. \"What do you want?\" the Senator asked.\n\nSchweitzer thought about that for a moment before answering. \"I want my wife back.\"\n\nSchweitzer wasn't sure if Hodges was genuinely sympathetic or merely seeking leverage, but his voice sounded genuine enough, sorrowful. \"She's dead.\"\n\nSchweitzer gave Hodges a shove, steadying the Senator as he got his feet onto the rope ladder. The man refused to climb down, staring up into Schweitzer's face. \"I'm truly sorry, Jim, but she's dead.\"\n\nSchweitzer didn't bother trying to smile. He was too tired. The fatigue gave him strength, put an edge on his doggedness. This life after death had painted the whole world with a patina of despair, but it had turned everything he'd ever known about what it meant to be alive on its ear. That wasn't quite hope, but it was close. \"That never stopped her before,\" Schweitzer said. \"Come on, Senator. It's a long climb down.\"\n\nHodges went, and Schweitzer followed. The Iowa night was cool and still. A thick sheet of cloud had rolled out over the sky, blotting out the stars behind a wall of spun cotton. It pooled shadows around the base of the building, wrapping itself around an island of sodium street lights marching in orderly rows all the way to the river.\n\nHodges looked up at Schweitzer, and Schweitzer saw no fear in him, knew that if he listened for his heartbeat, he would find it steady and calm. \"You're not going to hurt me, are you?\"\n\nSchweitzer shook his head. \"Hurt enough in the world already.\"\n\nHodges nodded and started moving again, until his feet touched down on top of an access ledge that marked the rope ladder's end. From there, Schweitzer scooped him up over his shoulder and vaulted the rest of the way down. Hodges suffered the indignity until they reached the lake of shadows around the tower's base, and the darkness swallowed them whole.\n\n# EPILOGUE\n\nCOASTLINE\n\n\"You're late,\" Eldredge said, tapping his watch. \"If we're going to be in business together, we can't have that. I need to be able to trust you.\"\n\n\"This isn't exactly what I call a big purchase,\" the kid answered. \"You want to be treated like a high roller, you have to pay for it.\" A breeze blew in from San Diego Bay, ruffling the kid's hair. He couldn't have been older than sixteen. The thought of one so young making a living at crime twisted Eldredge's gut, but he quelled the sympathy before it had a chance to make him lose focus. He had one kid to take care of already.\n\n\"I only get a fifteen-minute break.\" Eldredge nodded at the night watchman's booth behind him. \"I'm gone too long, I can get in trouble.\" Knuckling under to his twentysomething manager for minimum wage stuck in his craw, but it was the only job Eldredge could find where they wouldn't ask questions.\n\n\"No way you can afford this from this bitch-ass job.\" The kid gestured at the booth. \"Where you get this kind of money?\"\n\n\"Let's just say I have some other skills. I moonlight.\"\n\n\"The fuck you do. You're like ninety, dude.\"\n\n\"I don't have time for this. Do you have it or not?\"\n\n\"Relax, man. I have it.\" The kid produced a manila envelope. Eldredge took it, but the kid held on. \"Dude. Money.\"\n\nEldredge passed him a wad of cash and the kid let go. Eldredge tore the envelope open, trying not to let his eagerness show. The birth certificate looked real enough, right down to the raised seal. \"Carlos?\" he asked.\n\nThe kid shrugged. \"I wrote a script that generates the names randomly. Trust me, a lot less likely to get caught that way.\"\n\n\"This backstopped?\"\n\n\"Yeah. I told you. I've got remote access to the citizens registry database. You want out of this job? I can get you a fucking doctor's license if you want. It'll check out.\"\n\n\"Thanks; if this works out, I will definitely be back for some more items.\"\n\n\"I always appreciate repeat customers, man.\"\n\nEldredge knew he should end it there, but he couldn't help himself. \"Look, kid. You need to get an interlocutor. You don't want to be meeting with your clients in person.\"\n\nThe kid looked up at him, eyes hard. \"The fuck you know about it?\"\n\n\"I was in a . . . similar business for a long time.\"\n\n\"Yeah? Well, then, you know that the more people involved, the more chance you're going to have a fucking rat.\"\n\n\"That's why you need someone you trust.\"\n\n\"You trying to get in on my business?\"\n\nEldredge laughed. \"No, no. I've got enough on my plate. I'm just saying that you're getting lucky here. Sooner or later, you're going to get burned. If you don't have someone you trust, you need to use a dead drop to drop off the goods and pick up the money.\"\n\n\"What the fuck is a dead drop?\"\n\nEldredge looked back down at his watch. \"Google it.\"\n\nHe turned to go. \"Hey,\" the kid said.\n\n\"Yeah?\" Eldredge turned.\n\n\"What do you need that for? You're not . . . like you're not . . .\" There was a glimmer there of the kid he'd been before whatever had happened to him had flipped the switch that made the difference between legitimate computer programmers and hackers.\n\n\"I'm not a kid-toucher,\" Eldredge said. \"He's my grandson. His dad's a violent drunk who also happens to be a cop. Court wouldn't give me custody, and his dad was about one bender away from killing him. I had to get him out of there.\"\n\nThe kid raised a skeptical eyebrow, but Eldredge knew the tells on his face. He'd wanted a story he could repeat to himself when his conscience came calling, and Eldredge had given him one. He wasn't dumb enough to go chasing the truth. Besides, what he wanted to know _was_ true. Eldredge wasn't exploiting Patrick.\n\n\"Okay,\" the kid finally said, turning to go.\n\n\"Oh, hey, one more thing,\" Eldredge said. \"You know Sector San Diego? That Coast Guard building near the . . .\"\n\n\"The museum, on Guadalcanal Avenue. Yeah, I know it.\"\n\n\"Do you know if they take Transport Workers Identity Cards to get on the pier near there?\"\n\n\"I don't know, but I can get you a TWIC. Email me at the same address.\"\n\n\"All right, I will. You remember what I told you about dead drops. Google brush passes while you're at it.\"\n\n\"Whatever. What do you want with the Coast Guard?\"\n\n\"Old friend,\" Eldredge said. \"Fan of my grandson. I figured he'd like to see me again.\"\n\nThe kid nodded and vanished into the gloom. Eldredge turned and headed back to the booth. He'd probably said more to the kid than he should have, but that was the trick with these sorts of things. Sooner or later, you had to stick your neck out if you wanted to get anything done. When he tried to think about the complexity of the way forward, how he was going to contact Schweitzer's old shipmate, how to approach him, how to keep himself and Patrick hidden until he was ready, what to do if Perretto wasn't sympathetic, it seemed overwhelming. Best to take baby steps, then. Eat the elephant one bite at a time.\n\nFirst, he would go back to the booth and call Patrick's babysitter, make sure everything was okay. Second, he would finish his shift doing research on schools where he could get Patrick enrolled with the forged birth certificate. That was enough for tonight.\n\nEldredge looked up at the pink streaks on the horizon. Tomorrow was coming on fast.\n\n# GLOSSARY OF MILITARY ACRONYMS AND SLANG\n\nABC'S\u2014Airway, breathing, circulation. First responders check these to ensure a patient's vitality. Direct-action teams check them to ensure a target has been neutralized.\n\nBIRD\u2014Aviation asset such as a helicopter or fixed-wing aircraft.\n\nBLEED OUT\u2014Die via blood loss.\n\nBMF\u2014Boat Maintenance Facility.\n\nBUD\/S\u2014Basic Underwater Demolition\/SEAL training. The six-month training course that all sailors must graduate to become US Navy SEALs. BUD\/S alone does not make one a SEAL, and additional training is required. BUD\/S is intensely grueling, with an 80 percent attrition rate.\n\nCARBINE\u2014A long gun with a shorter barrel than a rifle. Carbines are better suited to combat in close quarters than their longer cousins.\n\nCAS\u2014Close air support. Action taken by fixed or rotary-wing platforms to assist ground troops.\n\nCHEMLIGHT\u2014Also known as \"glow sticks.\" A short plastic tube filled with chemical compounds in separate compartments. When the stick is bent, the barrier between the compartments breaks, allowing the compounds to mix. The resultant chemical reaction causes the tube to emit a strong colored glow.\n\nCLEARED HOT\u2014Authorized to open fire.\n\nCO\u2014Commanding Officer.\n\nCONDITION BLACK\u2014A state of paralysis brought on by sudden, unanticipated violence.\n\nCONDITION YELLOW\u2014A state of hypervigilance where a person is constantly anticipating sudden violence.\n\nCONEX\u2014A type of intermodal shipping container.\n\nCOP\u2014Combat Outpost.\n\nCORPSMAN\u2014Job title for United States Navy personnel assigned to field medical duties.\n\nCQB\u2014Close quarters battle. Refers to the tactics of breaching and clearing confined spaces, such as a building or ship.\n\nDANGER CLOSE\u2014Indicates a friendly force in close proximity to a target of fire, usually from artillery or close air support.\n\nDFAC\u2014Dining facility.\n\nDUST OFF\u2014Evacuate via helicopter.\n\nDYNAMIC\u2014An operational state wherein the enemy is aware of the assault team's presence, rendering stealth unnecessary.\n\nEMBED\u2014Embedded or one who is embedded.\n\nEMT\u2014Emergency Medical Technician.\n\n\"EYES ON\"\u2014Indicates the speaker is observing the subject of the sentence. \"I have eyes on the door.\"\n\nFIRE TEAM\u2014The smallest operational military unit, usually composed of 4\u20135 members.\n\nFNG\u2014Fucking New Guy\/Girl. A person who is newly assigned to a military unit. This friendly pejorative is meant to indicate the likelihood that the described will make mistakes.\n\nGROM\u2014Grupa Reagowania Operacyjno-Manewrowego. Poland's elite counterterrorism unit.\n\nHAWK\u2014Armed aviation asset such as a helicopter or fixed-wing aircraft.\n\n\"HONEY TRAP\"\u2014A clandestine operation in which an agent sexually attractive to the target is used to entice the target into a compromised position. Honey traps are also used to elicit information from pliant targets.\n\nHVAC\u2014Heating, Ventilation, and Air-Conditioning.\n\nK-9\u2014Canine. A unit that employs working dogs for law enforcement or military operations. The term is also used to refer to the dogs themselves.\n\nKC\u2014Kill-Capture. A direct-action mission wherein the team's first goal is to capture a human target. If the team is unable to capture the target without risking harm to their own number, they will kill him\/her. A successful KC must conclude with the target either captured or dead.\n\nKLICK\u2014Slang for a kilometer.\n\nLNO\u2014Liaison Officer.\n\nMAM\u2014Military-aged male.\n\nMANPAD\u2014Man-portable air-defense system. A shoulder-mounted missile launcher.\n\nMCPO\u2014Master Chief Petty Officer.\n\nMEDEVAC\u2014Medical evacuation. An emergency retrieval and removal of a casualty from a crisis zone. The patient is stabilized and transferred as quickly as possible to a medical facility where adequate care can be provided.\n\nMGRS\u2014Military Grid Reference System.\n\n\"MIKES\"\u2014Minutes.\n\nMWR\u2014Morale, Welfare, and Recreation center.\n\nNODS\u2014Night Optical Devices. Mechanical devices that permit the user to see in the dark.\n\n\"OFF TO SEE THE WIZARD\"\u2014Slang used to indicate a visit to a mental health professional.\n\nOP\u2014Operation. Refers to any military undertaking with a discrete beginning and end.\n\nOPERATOR\u2014Members of Special Forces elements who engage in special operations. Term connotes members of direct-action elements whose primary tasking is breaching hardened targets and neutralizing a dug-in enemy.\n\nPAX\u2014Passenger or passengers.\n\n\"PINNING ON\" OR \"PINNED ON\"\u2014The act of physically attaching the insignia of a new rank or qualification to a uniform.\n\nPIPE HITTER\u2014A fighter. A person whose principal occupation is the use of force.\n\nPJ\u2014Pararescue Jumpers, also known as Pararescuemen. A special operations element within the United States Air Force.\n\nPLATOON\u2014A military organizational unit consisting of twenty-eight to sixty-four members.\n\nPTSD\u2014Post-Traumatic Stress Disorder.\n\nQRF\u2014Quick Reaction Force. A standby troop of warfighters positioned to respond rapidly to an emergency.\n\nR AND R\u2014Rest and Relaxation.\n\nROE\u2014Rules of Engagement.\n\nSEABEES\u2014CBs, the construction battalions of the United States Navy.\n\nSEAL\u2014\"Sea, Air, and Land.\" A special operations force of the United States Navy.\n\nSITREP\u2014Situation Report.\n\nSO2\u2014Special Warfare Operator 2nd Class.\n\nSOAR\u2014Special Operations Aviation Regiment. A special operations force of the United States Army that provides both general and specialized aviation support.\n\nSOC\u2014Supernatural Operations Corps.\n\nSOCOM\u2014Special Operations Command.\n\nSOF\u2014Special Operations Forces. Also referred to as \"SF,\" as an acronym for \"Special Forces.\"\n\nSPECTER\u2014A flying gunship.\n\nSQT\u2014SEAL Qualification Training.\n\nSQUIRTERS\u2014A colloquial term for those enemy who flee a targeted location.\n\nSSG\u2014Special Services Group. Pakistan's special operations forces.\n\nSSRI\u2014Selective Serotonin Reuptake Inhibitor. Medication typically used to treat anxiety and depression.\n\nSST\u2014Special Security Team. An elite counterterrorism unit in the Japanese Coast Guard.\n\nTCCC\u2014Tactical Combat Casualty Care. First-responder medical training given to operators. It is designed to allow nonmedical personnel to engage in triage under fire, and to stabilize casualties for medevac.\n\nTIC\u2014Troops in Contact. Indicates that the speaker is engaged and fighting with the enemy.\n\nVTC\u2014Video Teleconference.\n\nWIA\u2014Wounded in Action.\n\nYN1\u2014Yeoman First Class. A senior enlisted member of the US Navy or Coast Guard specializing in administration.\n**Looking for more?**\n\nVisit Penguin.com for more about this author and a complete list of their books.\n\n**Discover your next great read!**\n\n  1. Cover\n  2. Praise for Myke Cole\n  3. Ace Books by Myke Cole\n  4. Title Page\n  5. Copyright\n  6. Dedication\n  7. Acknowledgments\n  8. Contents\n  9. Epigraph\n  10. Author's Note\n  11. CHAPTER I: THE PLAN IS SOUTH\n  12. CHAPTER II: HUNTING THE DEAD\n  13. CHAPTER III: CALIFORNIA SUNSHINE\n  14. CHAPTER IV: BRIEFING\n  15. CHAPTER V: TOUCHING DOWN\n  16. CHAPTER VI: MAMA DADOU\n  17. CHAPTER VII: PATCHING UP\n  18. CHAPTER VIII: WHAT IT'S LIKE\n  19. CHAPTER IX: HONESTLY, OFFICER\n  20. CHAPTER X: COLLATERAL DAMAGE\n  21. CHAPTER XI: TOGETHER\n  22. CHAPTER XII: PURE GOLD\n  23. CHAPTER XIII: PROGRAM REVIEW\n  24. CHAPTER XIV: ON TO THE LIVING\n  25. CHAPTER XV: ALL THE DEAD CAN DO IS PROTECT\n  26. CHAPTER XVI: DOESN'T ANYONE KNOCK ANYMORE?\n  27. CHAPTER XVII: THE PLAN IS WEST\n  28. CHAPTER XVIII: PUSHED TOO FAR\n  29. CHAPTER XIX: THE THINGS WE DO FOR LOVE\n  30. CHAPTER XX: WHY DID YOU GO?\n  31. CHAPTER XXI: LAST RESORT\n  32. CHAPTER XXII: NEW MANAGEMENT\n  33. CHAPTER XXIII: RETURN\n  34. CHAPTER XXIV: THE FLIGHT IN\n  35. CHAPTER XXV: COMBINED\n  36. CHAPTER XXVI: SO OTHERS MIGHT LIVE\n  37. EPILOGUE: COASTLINE\n  38. Glossary of Military Acronyms and Slang\n\n  1. Contents\n  2. Cover\n  3. Start\n\n  1. i\n  2. ii\n  3. iii\n  4. iv\n  5. v\n  6. vi\n  7. vii\n  8. viii\n  9. ix\n  10. x\n  11. xi\n  12. xii\n  13. xiii\n  14. xiv\n  15. \n  16. \n  17. \n  18. \n  19. \n  20. \n  21. \n  22. \n  23. \n  24. \n  25. \n  26. \n  27. \n  28. \n  29. \n  30. \n  31. \n  32. \n  33. \n  34. \n  35. \n  36. \n  37. \n  38. \n  39. \n  40. \n  41. \n  42. \n  43. \n  44. \n  45. \n  46. \n  47. \n  48. \n  49. \n  50. \n  51. \n  52. \n  53. \n  54. \n  55. \n  56. \n  57. \n  58. \n  59. \n  60. \n  61. \n  62. \n  63. \n  64. \n  65. \n  66. \n  67. \n  68. \n  69. \n  70. \n  71. \n  72. \n  73. \n  74. \n  75. \n  76. \n  77. \n  78. \n  79. \n  80. \n  81. \n  82. \n  83. \n  84. \n  85. \n  86. \n  87. \n  88. \n  89. \n  90. \n  91. \n  92. \n  93. \n  94. \n  95. \n  96. \n  97. \n  98. \n  99. \n  100. \n  101. \n  102. \n  103. \n  104. \n  105. \n  106. \n  107. \n  108. \n  109. \n  110. \n  111. \n  112. \n  113. \n  114. \n  115. \n  116. \n  117. \n  118. \n  119. \n  120. \n  121. \n  122. \n  123. \n  124. \n  125. \n  126. \n  127. \n  128. \n  129. \n  130. \n  131. \n  132. \n  133. \n  134. \n  135. \n  136. \n  137. \n  138. \n  139. \n  140. \n  141. \n  142. \n  143. \n  144. \n  145. \n  146. \n  147. \n  148. \n  149. \n  150. \n  151. \n  152. \n  153. \n  154. \n  155. \n  156. \n  157. \n  158. \n  159. \n  160. \n  161. \n  162. \n  163. \n  164. \n  165. \n  166. \n  167. \n  168. \n  169. \n  170. \n  171. \n  172. \n  173. \n  174. \n  175. \n  176. \n  177. \n  178. \n  179. \n  180. \n  181. \n  182. \n  183. \n  184. \n  185. \n  186. \n  187. \n  188. \n  189. \n  190. \n  191. \n  192. \n  193. \n  194. \n  195. \n  196. \n  197. \n  198. \n  199. \n  200. \n  201. \n  202. \n  203. \n  204. \n  205. \n  206. \n  207. \n  208. \n  209. \n  210. \n  211. \n  212. \n  213. \n  214. \n  215. \n  216. \n  217. \n  218. \n  219. \n  220. \n  221. \n  222. \n  223. \n  224. \n  225. \n  226. \n  227. \n  228. \n  229. \n  230. \n  231. \n  232. \n  233. \n  234. \n  235. \n  236. \n  237. \n  238. \n  239. \n  240. \n  241. \n  242. \n  243. \n  244. \n  245. \n  246. \n  247. \n  248. \n  249. \n  250. \n  251. \n  252. \n  253. \n  254. \n  255. \n  256. \n  257. \n  258. \n  259. \n  260. \n  261. \n  262. \n  263. \n  264. \n  265. \n  266. \n  267. \n  268. \n  269. \n  270. \n  271. \n  272. \n  273. \n  274. \n  275. \n  276. \n  277. \n  278. \n  279. \n  280. \n  281. \n  282. \n  283. \n  284. \n  285. \n  286. \n  287. \n  288. \n  289. \n  290. \n  291. \n  292. \n  293. \n  294. \n  295. \n  296. \n  297. \n  298. \n  299. \n  300. \n  301. \n  302. \n  303. \n  304. \n  305. \n  306. \n  307. \n  308. \n  309. \n  310. \n  311. \n  312. \n  313. \n  314. \n  315. \n  316. \n  317. \n  318. \n  319. \n  320. \n  321. \n  322. \n  323. \n  324. \n  325. \n  326. \n  327. \n  328. \n  329. \n  330. \n  331. \n  332. \n  333. \n  334. \n  335. \n  336. \n  337. \n  338. \n  339. \n  340. \n  341. \n  342. \n  343. \n  344. \n  345. \n  346. \n  347. \n  348. \n  349. \n  350. \n  351. \n  352.\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \n# Landscape Painting Essentials\n\n## Lessons in Acrylic, Oil, Pastel and Watercolor\n\n## with Johannes Vloothuis\n\nCINCINNATI, OHIO\n\nartistsnetwork.com\n\n### Thank you for purchasing this _Artist Network_ eBook.\n\nSign up for our newsletter and receive special offers, access to free content, and information on the latest new releases and must-have art resources! Plus, receive a coupon code to use on your first purchase from NorthLightShop.com for signing up.\n\nor visit us online to sign up at\n\n<http:\/\/artistsnetwork.com\/ebook-promo>\n\n# Contents\n\nSpecial Offers\n\nIntroduction\n\nMaterials\n\n### Chapter 1\n\n## Paint How the Eye Sees\n\nVisual Perception vs. Photographic Perception\n\nReference Photos: Friend or Foe?\n\nThe Peripheral Area\n\nSimplifying Foregrounds\n\nBlurred Edges\n\nDemonstration: Paint a Landscape with a Simplified foreground\n\n### Chapter 2\n\n## Design With Abstract Shapes\n\nSymmetrical Brain vs. Artistic Brain\n\nLandscape Shapes\n\nTechniques for Promoting the Artistic Brain\n\nNegative Painting\n\nDemonstration: Use Negative Painting to Create Abstract Shapes\n\nComposition With Abstract Masses\n\nDemonstration: Paint With Abstract Shapes\n\n### Chapter 3\n\n## Vary and Enrich Colors\n\nControlling Monochromatic Color Schemes\n\nDemonstration: Color Matching\n\nColor Temperature\n\nEstablishing Color Harmony\n\nDemonstration: Variegate Color in a Painting\n\n### Chapter 4\n\n## Create Melodic Movement\n\nProblematic Implied Lines\n\nValuable Implied Lines\n\nLost-and-Found Lines\n\nSolving Problematic Implied Lines\n\nVisual Paths\n\nEstablishing Rhythm\n\nDemonstration: Create Melodic Movement in a Painting\n\n### Chapter 5\n\n## Simplify\n\nZoom In and Cut Out\n\nSimplifying Nature\n\nSimplifying Architecture\n\nDemonstration: Simplify Your Painting Composition\n\n### Chapter 6\n\n## Avoiding Clones\n\nIdentifying Clones\n\nOffsetting Clones\n\nAvoid a mirror effect\n\nDemonstration: Offset Clones in a Landscape Painting\n\n### Chapter 7\n\n## Accentuate Depth\n\nMethods for Accentuating Depth\n\nDemonstration: Accentuate Depth in A Background\n\nAbout the Author\n\nDedication\nTo my wife, Patty, who always supported me in my painting ventures and to my sons, Johannathan, Christopher and especially Kenny, who is also an artist and contributed some of his knowledge to this book.\n\n## Introduction\n\nI fell in love with landscape painting when I was in my thirties. I was thrilled with the idea that I could create my own worlds. As happens with all artists, my early attempts were to copy photographs exactly. I erroneously thought that if I could copy nature from a good photo, I would end up with a successful painting. I chose the most outstanding scenes, set my studio up and started to paint... but it just was not working. I said to myself, \"This doesn't look right. I don't like what I am painting. \"\n\nFor years, I battled to get the answers to what it took to paint successful landscapes. I went to several instructors, got a few tips here and there, but nothing that could really make a big enough impact in my artwork. I remember promising myself, \"If I ever get good at this, I will share everything so others won't have to go through the same frustration\".\n\nAfter reading countless books and carefully observing top artists' work, I started to see patterns that they all repeated in their artwork. So I back engineered their paintings and figured out the commonality in their compositions. This is when I began to apply a science to my process, and my paintings started to click. I won the top award in a nationwide contest in Mexico and began to sell many paintings.\n\nA few years later, I joined WetCanvas, an art focused social network where people share their paintings and tips. I remembered my promise and offered help and advice to other artists seeking answers. Eventually, I was recognized by the publishers of this book, who named me a Master Painter. They approached me to teach live online classes and workshops that would reach out to even more artists.\n\nSince then, I have taught over 15,000 artists, including professionals. These classes enabled me to verbalize in simple understandable terms the science of beauty in landscape painting, and much of it is now being revealed in this book. I part with this notion, I don't believe in ugly paintings because it is a human expression, but I do believe one should pursue venues to make them more beautiful.\n\nThe Teton\n\n**Open acrylics on linen glued to masonite board, 8\" \u00d7 10\" (20cm \u00d7 25cm)**\n\n## Materials\n\nThere are entire books devoted to the topic of how to choose the best supplies and tools for creating your artwork. Here is a brief overview of the materials I prefer to use when creating my paintings. Experiment with different brands and mediums to find the products that work best for you.\n\n#### Easels\n\nI use a Soltek easel. This is the diamond of all easels. Set up is fast and easy. There are no wing nuts to turn. It is all metal and light weight compared to many other easels. I have done over 500 plein air paintings with it.\n\n#### Brushes\n\nI prefer brights for all my mediums. The square heads help me design abstract shapes. Rigger brushes work well for thin lines. I use a pastry brush for grass in watercolor.\n\n#### Sponge Tools\n\nThese PanPastel washable applicators are made with a special sponge to apply the paint in a thin film.\n\n#### Palettes\n\nThis homemade palette has a glass panel with a mid-value gray sheet under it. The surface makes scraping off unwanted paint a breeze.\n\n#### Oil Paints\n\nI prefer Winsor and Newton Artist's Oil Paints. They cooperate very well without the need of a medium.\n\n#### Acrylic Paints\n\nAtelier acrylics are buttery and feel like oil paints.\n\n#### Pastels\n\nPanPastel is a marvelous pastel medium that is applied like paint. It feels like a cross between oils and watercolors, with the advantage that you can erase unwanted areas. You can also add stick pastels to it.\n\n#### Watercolors\n\nWinsor and Newton Artist's Watercolors are much better to work with than the lesser-quality pigments.\n\n# Chapter 1\n\n# Paint How the Eye Sees\n\nCrowfoot Glacier, banff\n\nOil on linen, 24\" \u00d7 20\" (61cm \u00d7 51cm)\n\nOne of the most common phrases art instructors use is, \"Paint what you see!\" This needs some clarification however, because many artists assume this means to copy what they see literally, rather than designing their paintings to be compatible with how the eye anatomically sees. This applies to both plein air and painting from reference photos. Once you understand the way the human eye perceives reality, you will be able to tailor your paintings to look the way the scene would appear as the information is processed in the brain.\n\nTry this: Look at the first word in this paragraph. Without moving your eyes from that word, read as many adjacent words as you can. You'll notice that you can only bring a few words into focus and will not be able to read the rest of the sentence unless you move your eyes. The same applies to nature scenes\u2014as long as you are looking at one specific area, definition elsewhere becomes lost. You will get better results if you keep this concept in mind: Paint how the eye sees, not what you see!\n\nIn this chapter you will learn:\n\n  * How to avoid distractions in the peripheral areas of a landscape scene.\n  * How to blur edges in the distance.\n  * How to simplify foregrounds.\n\n## Visual Perception vs. Photographic Perception\n\nOne of the most common mistakes beginning artists make is attempting to recreate exactly what appears in their reference photos\u2014everything in sharp focus, everything in detail\u2014but this is not the way the eye actually sees a given scene. The eyes have only a narrow range of sharp visual perception, and the camera does not capture an image in the same way that the eye sees it. In images captured by a camera, everything is in equal focus and all edges are well defined because all the light sensors are equally dispersed in the camera chip. So if an artist copies that photo exactly, the painting will seem \"off\" to viewers.\n\nTo illustrate this, imagine you are playing a game of pool. When focusing on the white cue ball several feet away from you, your eye will bring only that specific ball into sharp focus. All the surrounding balls, even the ones that are actually closer to you will appear to become blurred round objects with undefined edges. This is an important concept to keep in mind with your paintings.\n\n#### How Cameras Work\n\nA digital camera has millions of pixels. This picture shows the way they appear evenly spaced. Each pixel works like a sensor cell in our eyes, but in this case the cells don't become more dispersed towards the outer regions of the eye. That's why everything in a photo is in sharp focus, but with the human eye it is not.\n\n#### Peripheral Vision\n\nThis is the way sensor cells in the human eye look under a microscope. There is a much higher concentration of cells in the center of the eye. These cells become more spaced out the further away they get from the middle. This is why our peripheral vision is blurry and cannot see detail outside of the parameter we are looking at directly. Every cell receives visual input much like camera sensors. The closer the cells are together, the sharper the image becomes. The more space between the cells the blurrier the image becomes.\n\n#### Real Life Scenes Are Not Cropped\n\nBecause of the format of a canvas, paintings become cropped, which results in unnatural and abrupt interruption to eye flow and contradicts how we perceive the world. Therefore, we must rely on artistic techniques to offset this.\n\nIn the eye's peripheral vision:\n\n  * Darks become lighter.\n  * Color saturation is less pronounced.\n  * Details become blurrier.\n\n## Reference Photos: Friend or Foe?\n\nThe answer is both! Photographs can help or hinder us as artists. They can trick us into copying them exactly, yet provide excellent visual information to tell a story. When I first began painting, I relied heavily on photos. I copied exactly the values, colors, edges and every detail. Yet, no matter how good a reference photo I had, I could not produce a solid painting. I kept asking myself what I was missing. Finally it dawned on me\u2014you can rely on reference photos for details and shapes, but colors and values cannot be trusted.\n\nPhotos will show outdoor mid-dark objects as a colorless black. This will contradict daylight ambience. To make matters worse, once you print out a digital photo there is even further deterioration of colors, which end up being muddy. After this revelation, my artwork surged to a new level.\n\nTo understand this, it helps to understand a bit about how a camera works. The shutter opens and closes in a fraction of a second. The amount of time the shutter stays open relates to the degree of light allowed in, which results in more light in the photo. The auto setting of the light meter of the camera measures a specific area and shoots with a predetermined shutter speed. If the sensor sees a bright light such as in the sky, the values in the photo will be accurate only in that specific area. Everything outside of that center point will get darker. If the light meter registers a dark area such as a group of evergreen trees, the sky will appear overexposed. This is how it's possible to end up with two completely different photos of the same scene.\n\n#### Camera Exposure\n\nThe photo on the left is under exposed because the center of the camera was aimed at the bright waterfall. The photo on the right is overexposed because the camera measured the dark evergreen trees. The naked eye would never see masses of evergreen trees that dark during the daytime like in the second photo. Likewise, you wouldn't see a bleached out waterfall such as in the first photo. There were also far more colors in the rocks than could be seen in either photo.\n\nYou don't want your painting to end up with dull, flat dark or over-exposed areas\u2014so which photo should be used as reference? The answer is: both. The best thing to do is take several pictures of the same scene with variances in shutter speed. Even if the real scene does not have color variances, you as an artist should enhance monotonous colors to make the painting more interesting. Proficient artists basically use photos only for ideas and details, much like a movie director bases a film on a storyboard.\n\n## The Peripheral Area\n\nDo you remember the notebook paper you used in school that had blue lines and a red margin on the left? When I was a kid I constantly got scolded for writing in the margins because that was a forbidden area that was supposed to remain blank. You can apply this same principle to all four sides of your paintings\u2014the \"margins\" being in proportion to the scale of your painting surface. This area is also known as the peripheral area.\n\nInside the peripheral area, it's best to avoid:\n\n  * obvious value contrasts\n  * hard edges\n  * saturated colors\n  * intricate or outstanding details\n\nThe peripheral area will simulate how detail fades in the peripheral vision of the eye. Applying this will help the eye agree with how things are naturally seen. The objective is to encourage your viewers to visually wander within the center portion of your painting so they do not exit it easily and will not get distracted by too much interest being created near the edges.\n\n#### Conveying the Illusion of Daylight\n\nIn most art instruction, there is usually reference to a ten-value scale, but this would only apply if the artwork is inside a room. Outdoors in nature, you can see hundreds of values because of the sun's intensity. Trying to replicate this light in a painting is an impossible task. So here, _paint what you see_ , goes out the window. Again we need to implement ways to mimic reality.\n\nBefore the Cadmium pigments were invented to add a glow to colors, the Old Masters had real problems depicting sunlit areas. They had to purposely exaggerate the dark areas to compensate. This practice contradicted nature... until the Impressionists started using Cadmiums and became successful at mimicking sunlight.\n\n#### Reduce Interest in the Peripheral Area\n\nIn this painting of a small fishing town in Nova Scotia, distractions have been reduced in the section marked as peripheral area. There was a choice of placing the window where it was originally, on the right edge of the canvas. After applying these principles, the window was moved to a better location in the painting.\n\n#### Don't Usher the Viewer Out of the Painting\n\nThe white building is not in a suitable place. It should be removed or darkened in value. If painted as is, it will become an eye magnet luring the viewer to exit the painting at the right side.\n\n## Simplifying Foregrounds\n\nWhen painting the way the eye anatomically sees, it is a good policy to generally leave the foreground alone. Remove obstacles and details so your viewers look past this area and deep into the painting. You might be inclined to think that the things closest to you should have the most detail, but the reality is that nobody looks directly at the ground unless is they're looking for something they dropped.\n\nLikewise, a painting should resemble how the eye sees in accordance to where it is looking under normal circumstances. The logic of where things are situated in the various planes, even if it they are closer, does not apply. By keeping your foreground simple, that area will not compete for attention.\n\nThe general practice by most accomplished landscape artists is to compile the most attractive visual information in the middle ground, where the head would be level and the eyes looking straight ahead. Details and objects in sharp focus should appear where the eye is looking, even if they are further into the distance.\n\n#### Example of a Simplified Foreground\n\nThe immediate foreground in this photo was altered to be used as an analogy of how to handle foregrounds. You cannot clearly distinguish the wooden ties and grass. The steel rails are not sharp either. The area that comes into focus is about fifteen feet ahead. This is how the eye would function if you were walking down those train tracks. Apply this principle to your paintings, and your viewers will feel more encouraged to \"walk in.\"\n\n#### Invite Your Viewers in from the Foreground\n\nThe immediate foreground should have no strong value contrasts, no strong color saturation and no outstanding detail. The foreground just serves the purpose of inviting you in.\n\nAlso note that the other three borders of the painting do not have eye-catching visual information. The intent is to invite the eye to see the arbor and the flowers and hold the attention there.\n\n#### Reduce Clutter in Foregrounds\n\nMerge stones in the immediate foreground or avoid them altogether. If you must have objects in those areas, match their values so they don't stand out. The original scene was cluttered with rocks. They were removed from the painting.\n\n#### Foreground Grass\n\nIt is not necessary to indicate grass strands at the very bottom margin. Take a step into the painting then add grass strands, rocks, flowers, etc., if this is what you wish to do. Like many professional artists, leave out grass strands entirely in paintings smaller than 16\" \u00d7 20\" (41cm \u00d7 51cm).\n\n#### Plan Your Mid-Values to Convey Daylight\n\nTo convey the illusion of broad daylight, plan your paintings to have predominant mid-values in most areas.\n\n#### Avoid Vertical Objects in the Bottom of a Frame\n\nCompare these two versions of the same plein air painting. The distraction from the foreground was removed in the bottom painting so that you are looking into the distance without the vertical objects pulling your eye.\n\n## Blurred Edges\n\nIn reality, both background and foreground objects in a scene have hard edges on their contours. The background objects won't get any softer, no matter how far away they are. We never give this any thought because the brain has its own mechanism of determining that something is further back in comparison to another object. The field depth is never questioned. Three-dimensional perception in reality is never compromised.\n\nHowever, if you paint those contours exactly as they are in reality (with hard edges), this can result in flat, hard edges all over the painting and a scene that looks two-dimensional. The trick here is to convey a three-dimensional scene on a two-dimensional surface.\n\nBlurring edges, also known as softening edges, is an efficient method you can use to fool the viewer's brain into seeing background objects as further away, creating depth and the illusion of three dimensions in a painting.\n\nAnother advantage of softening edges is that it simulates the eye's peripheral vision, as well as detracting viewers from getting \"stuck\" in certain areas of a paintings.\n\nRemember\u2014the secret is to paint _the way the eye anatomically sees_ , not how the reference photo looks!\n\n#### Soften Edges in Backgrounds\n\nThe blurred edges in the furthest plane convey the illusion of depth. As a general recommendation, blur as many edges as you can in backgrounds, especially if they appear behind buildings.\n\nIn this piece, I decided that adding too many bulrushes in the foreground would be distracting, so I just indicated a few as visual pointers.\n\n#### Photos Always Have Sharp Edges\n\nIn reality, you could easily distinguish which parts of a tree recede and which parts are closer to you. As soon as a photo is taken, however, the three-dimensional perception is nullified because all the foliage ends up looking hard edged. If painted this way, the foliage will look pasted on. Instead, render trees like portraits, softening edges of leaves and branches the same way you would do when painting hair at the back of a subject's head.\n\n#### Photos Flatten Planes\n\nCan you distinguish the different planes of those trees? Truthfully, the tree on the left is in front of the other trees, separated by at least fifty yards. If you just paint what you see, you will lose field depth.\n\n#### Lost-and-Found Edges\n\nBecause of the play of soft edges vs. hard edges, the tree looks round and you can tell which parts are closer to you. This is referred to as lost-and-found edges. The foliage against the sky has soft edges as well as hard edges. The soft areas convey the leaves in that cluster are more distant, while the harder edged leaves indicate they are closer.\n\n#### Stay Away from Tree Tops\n\nAvoid unnecessary branches that are too distracting, especially at the top of trees. Your viewers are supposed to look in the middle area without feeling somebody is waving at them from another part of the painting. This helps to agree with the out-of-focus peripheral portion of the eye. The tree on the right has just enough tree trunks to avoid a \"cotton ball\" aspect.\n\n#### Manipulate Edges to Recede Foliage\n\nThe hard-edged tree conveys the idea it is closer than the soft-edged tree, which is situated in a more distant plane. Wet-on-wet watercolor application allows for great edge diffusion.\n\n#### Walls, Bricks and Roof Tops\n\nThe back wall has fewer grooves than the front portion. The roof tiles are reduced at the far top corner. (The naked eye would not see all the tiles at the same time.) The indentations in the adobe bricks become less distinct higher up.\n\n#### Pros and Cons of Plein Air Painting\n\nPros of Plein Air Painting\n\n  * Strong emotional response instills motivation to paint the scene.\n  * Atmospheric perspective is more evident.\n  * Subtle variations in color are more easily picked up.\n  * 3D reality is true and can be depicted better in a painting than working from photos.\n\nCons of Plein Air Painting\n\n  * Many colors are too garish, monotonous and monochromatic.\n  * The sky colors in an average blue sky don't work in a painting.\n  * Values are broken and scattered.\n  * Many shapes in nature are too symmetrical.\n  * The blue hue of mountains is too cool.\n  * There are hard edges everywhere.\n  * There are many cloned shapes.\n  * Capturing sunlight and translating it into pigment is challenging.\n\n### Creating the Illusion of Motion\n\nMaking people, animals and other landscape subjects appear as though they are moving in a painting and not just posing can be one of the greatest challenges for beginning artists. How do you create the illusion that water is falling, or that a horse is trotting?\n\nTry this experiment: Wave your hand in front of your face. Do you see that the crevices at the back of your hand are no longer noticeable? The same concept applies for creating the look of motion in a painting.\n\nFor example, when a photo is taken of falling water, the shutter stays open for a fraction of a second. This ends up \"freezing\" the water, making it appear it is suspended in midair. However, the brain does not take still photos, so water would never appear this way. It would be blurred. If an artist copied a waterfall exactly from a photo, then the viewer would sense something isn't right.\n\nThe best way to convey a sense of movement is to blur things like moving water so they lose definition. Likewise, smudge the legs of animals and people that are in motion. In the latter case, don't add any facial features and place the subjects well within the middle ground. Merge the bottom part of their figures into the wet paint more than the rest of the body. Just allow for a silhouette of the legs. Create the \"V\" shape of distant birds, then smudge their forms.\n\n#### Reference Photo\n\nThe camera shutter opened and closed in a fraction of a second. The water appears frozen in time. This is not a natural way we see water moving.\n\n#### Painting Water In Motion\n\nDo you get the impression the water is toppling over the cliff? The soft edges give the appearance of movement. Blurring foam in seascapes works great as well.\n\n#### Can These Concepts Be Applied to Portraits and Still Lifes?\n\nYes! Edge manipulation tactics come in handy with all kinds of subjects. Do not rely solely on diminishing the size of objects that are further back, but manipulate their edges to create depth as well. If a piece of fruit is behind another piece of fruit, soften the edge of the background fruit where the forms intersect. Also try to avoid distracting colors and strong edges in the peripheral area. Many artists cast shadows into these regions and only highlight a limited area in still lifes.\n\nYou can make the rump areas of animals recede by placing them at a 3\u20444 position and painting the back part with softer edges. Merging fur into the background is also effective. If you want your viewers to notice the animal's finer details, design the background so everything is out of focus.\n\nIn portraits, hard edges will be evident everywhere in photos as well as with real life subjects. If you do not manipulate these edges in a painting, the back part of the head and the ears will not recede. Instead of the portrait appearing 3D, it will look like a wall poster. Hyperrealism will not offset this. One solution is to take advantage of the subject's hair and clothes, blending and merging them into the background and allowing only a few defined edges. Ears should be depicted conceptually, not in detail. The lost-and-found edge technique works great for this.\n\n### Optical Hard Edges\n\nIn nature, hard edges are non-existent in objects that are motionless. If you can get away without diffusing edges and distorting a certain sense of reality, all the better. You can have a soft-edged shape in your painting that will still appear to be hard-edged, especially when seen from a distance, as long as there is a strong value shift between that shape and the area around it. This is referred to as an _optical hard edge_.\n\nOn the other hand, you may have a shape with hard edges within an area that has little to no value contrast. That shape will not appear hard edged anyhow, so it would be useless to soften it.\n\nA good rule of thumb is: Hard edges attract the eye, and blurred edges dissuade the eye from staring at an area for too long. Remember\u2014too many hard edges will make things look pasted on in paintings. Trick the eye into perceiving depth by:\n\nPurposely blurring edges in backgrounds. (Don't do this with rocky mountains or they lose their character.)\n\n  * Adding details such as individual leaves and tree branches to only the middle ground of a painting.\n  * Keeping foregrounds simple with the least visual information of all areas in the painting.\n  * Softening or blurring edges by blending some of the foliage into the sky or background.\n\n#### Optical Hard Edges vs. Physical Hard Edges\n\nCompare the tall evergreen tree on the left that appears in front of the white snow with the other tall evergreen in front of the blue area of the mountain. The left one appears more defined, even though it has been blurred. Yet that tree is optically hard edged due to its value contrast. The other trees are physically hard edged, but optically soft edged, because the value contrast is not outstanding.\n\n#### The Adjusted Painting\n\nThe sharpness of the evergreen tree has been corrected. The value contrast is reduced. Now we have a physical and an optical soft edge.\n\n#### Helpful Hints\n\n  * Blur everything except rocky mountains behind buildings. Allow for lost-and-found edges for variances.\n  * Don't paint under a very bright light source if this kind of light will not be present where the painting will hang.\n  * Placing mist where water is agitated helps create the illusion of movement.\n\n## Demonstration: Paint a Landscape with a Simplified foreground\n\nFollow the steps to create blurred edges and a simplified foreground in a landscape painting.\n\n#### Reference Photo\n\n#### MATERIALS\n\nSurface\n\nArches 300-lb. (640gsm) cold-pressed watercolor paper\n\n**Brushes**\n\n1\u20444\", 1\u20442\" and 3\u20444\" synthetic brights\n\n**Watercolor Pigments**\n\nBurnt Sienna, Cobalt Blue, Hooker's Green, Indian Red, Payne's Gray, Permanent Rose, Raw Sienna, Ultramarine Blue\n\n**Other**\n\nHB pencil\n\n#### STEP 1: Sketch the Composition and Lay In the Sky\n\nSketch the composition with an HB pencil. (Watercolor paintings need a good base drawing in order to create soft edges in the background.) Soak the paper up to the roofs of the buildings. You can never over-wet watercolor paper.\n\nLay in the sky wet-on-wet to create undefined edges while keeping the general forms distinguishable. Use Cobalt Blue for the sky and a mixture of Cobalt Blue and Indian Red for the clouds. The clouds at the top should be darker than the clouds at the bottom.\n\nAdd a hint of red for flavor and darken the corner to keep the viewer's eye in the painting a little longer. Allow time to dry.\n\n#### STEP 2: Begin the Middle Ground\n\nRewet from the top of the roofs upward. Paint the background trees. Use Payne's Gray, Indian Red and Ultramarine Blue. Paint the brick house with a mix of Indian Red and Burnt Sienna and a hint of blue to gray down the brick colors. Indicate only a few bricks. Concentrate them around the window to offset the symmetrical shape and to stay away from the edges. Use the same colors for the bricks as for the house, but a darker value. Negative paint out the form of the bougainvillea. Use Permanent Rose for the flowers. Paint the uneven stone wall. Use Cobalt Blue, Burnt Sienna and a touch of Raw Sienna. Place some shadows under the stones. Reduce the stones near the edge. Define the bottom part of the flowers and leave highlights at the top.\n\nDrybrush the fishing shack wall to create texture. Use warm colors to indicate sunlit wood. For the shingles, start dark in the closest corner and get lighter at the top. Make the roof line irregular and protruding, like some shingles are broken. Create an irregular pattern for the shadows. Make the wood look weathered by indicating a few hairline cracks in the boards.\n\n#### STEP 3: Paint the Remaining Buildings and the Grass\n\nPaint the remaining buildings, modifying the colors of each for interest. Lift out some individual boards with a thirsty brush. Tap in some broken boards, vertically, so they're opposite to the adjacent building. Use a drybrush technique when painting the tin roof, and skip the paint to indicate rust with Burnt Sienna. Hold back on texture closer to edges of painting.\n\nDrybrush in the grass with a mixture of Hooker's Green, Burnt Sienna and Raw Sienna. Leave room for the flat rocks that lay on the grass. Skip the brush to indicate stones and. Allow the grass to bleed right against the rocks. Vary the colors within each four square inches or so.\n\n#### STEP 4:Paint the Water and Finish with Details\n\nWet the entire water area. Lay in color from bottom up with Payne's Gray. While still wet, reflect the objects on dry land by dragging the brush vertically. Then at the end of the reflections, use choppy strokes. This will give the illusion that the water is moving lazily. Indicate the warm yellowish glow of the clouds in the furthest part of the water and the darker part in the foreground.\n\nOut Fishing in Glouster\n\nWatercolor on Arches 300-lb. (640gsm) cold-pressed watercolor paper, 9\" \u00d7 12\" (23cm \u00d7 30cm)\n\n# Chapter 2\n\n# Design With Abstract Shapes\n\n**The Storm Is breaking**\n\n**Watercolor and PanPastel on Fabriano cold-pressed watercolor paper, 12\" \u00d7 16\" (30cm \u00d7 41cm)**\n\nAbstract shapes are beautifully designed asymmetrical symbols. Understanding and applying abstract designs to your paintings will give you the backbone of successful renditions whether they be landscapes, portraits, figures or still lifes. The application of this concept is the most important key to all hand-painted works.\n\nIn this chapter you will learn:\n\n  * How to think in terms of pictorial symbols and then design them.\n  * How to see and paint not just forms, but the spaces surrounding those forms.\n  * How to prioritize when massing shapes.\n  * How to avoid problematic shapes.\n  * How to build a pictionary of attractive landscape symbols that will represent real objects so you can avoid directly copying them.\n\n## Symmetrical Brain vs. Artistic Brain\n\nIn the previous chapter you learned about the ways paintings cannot compare with the real macro scene as far as size and the three-dimensional aspects of nature.\n\nThere are many unattractive shapes present in natural settings. Artists can design objects in paintings to look better than they do in reality. Nature's canvas is much bigger than you could ever paint, but as an artist you have the ability to produce more beautiful shapes and lines than nature does, even if the forms are much smaller in scale.\n\nThe macro world will provide you with an abundance of visual information, and the left side of your brain (the symmetrical brain) will naturally want to document visual information in close detail for the viewer. This is one of the most common challenges beginning artists face, because many operate under the belief that the closer they get to realism the better the painting will be.\n\nThe real landscape world has little to do with the painting landscape world, and the right side of the brain (the artistic brain) prefers the poetic license aspect of artwork. Instead of imitating exact forms, you will depict symbols that represent trees, rocks, bushes, etc.\n\nContrary to photography, as a painter, you have the freedom and ability to relocate and resize the diverse landscape elements. A tree in your painting may be the size of a mere few inches, but that tiny size can be very attractive due to its abstract design, which should outdo its equivalent in a photo.\n\nWe won't go into right brain\/left brain theories in depth in this chapter, but rather focus on techniques to help you tap into your artistic brain in a more functional way so it becomes a useful tool to strengthen your landscape symbol designs.\n\nFrom the time we are babies and first open our eyes to the world, the first thing we see is the symmetrical interior of our homes. These images get imprinted into the subconscious mind and stored forever. From then on every time we produce a shape, we tap into our subconscious mind and feel compelled to create circles, ovals, squares, straight lines etc.\n\nWe practiced these shapes in our early elementary school drawings. We kept reinforcing by repetition the symmetry of these and developed habits. So when we paint or draw, the subconscious mind wants to continue on with the childish practice of drawing triangular Christmas trees and round trees that makes the abstract designs so much more difficult to depict. To make matters worse, nature has a strong tendency to produce visually implied symmetrical shapes, and we feel compelled to copy these because they are in sync with our symmetrical brain.\n\nWe will always war against symmetry from nature and symmetrical brain influence. Even artists with decades of experience still struggle from overstating details and depicting geometrical designs. The good news is you don't have to train the artistic brain. With the proper approach you will automatically tap into it more thoroughly by implementing certain techniques. You can double your artistic IQ!\n\nNow that you are aware of what may put the brakes on your paintings from escalating to new levels, you can overcome your own symmetrical brain's interference.\n\n#### Symmetrical Shapes in Nature Are not Pleasing\n\nNature produces many symmetrical shapes. They may look good outdoors but once scaled to mini sizes in your artwork they become painfully obvious. This takes a toll on the artistic beauty. Note the symmetrical triangle shapes of the pine trees to the left and the obvious round and almost perfect oval shapes in the foliage pictured above.\n\n#### Switching Between Your Artistic and Symmetrical Brains\n\nYears ago Betty Edwards, author of _Drawing on the Right Side of the Brain_ , did ground breaking research and proved that the opponent to producing attractive shapes is our own symmetrical brain, which fulfills the function in the level of logic to scientifically process and register data. In this hemisphere of the brain we store symmetrical shapes. On the other hand, the artistic brain is the area that functions for the production of artistic beauty. Edwards demonstrated that when novice artists focused on the surrounding air and the empty space between the legs of a chair instead of the object per se, they produced more accurate drawings. Your consciousness can switch back and forth between the two brain hemispheres and from that you can increase your artistic ability.\n\n#### Symmetrical Isn't Always Aesthetically Pleasing\n\nThe tree trunk has a cylindrical shape and the tree branches protrude like a fork equally on opposite sides. Frankly, this is an ugly tree.\n\n## Landscape Shapes\n\nNature will also give us very pleasing shapes. But these do not appear very commonly. Just like with a crowd of people\u2014you see the occasional impressive good looking human. In the same manner a modeling agency keeps files on beautiful people, an artist should be a shape collector and keep reference photos in a file from which to derive various landscape symbols. With time and practice, these will be stored in your mind. But first, let's identify the criteria a shape needs to meet to be part of your pictorial language.\n\n#### Which Shapes Are Most Appealing?\n\nYou probably voted for the oval because it has a different height than width. If a tree shape fits inside a circle, no matter how realistically you render it, the shape will not be attractive. Tree shapes look better if their foliage is oval in shape rather than circular.\n\nThe same applies to a square format vs. a rectangular format. If a waterfall or a rock fits inside a square, the abstract design is compromised. You would want to change the anatomy of a waterfall and stretch it to fit in a rectangle rather than in a square.\n\nIt's not what you do inside the shape that makes the symbol look good. It is the shape itself. The key is to make the overall shape appealing. Details within the boundaries of the shape are less important.\n\n### Determining Symmetrical and Abstract Shapes\n\nA handy method for determining whether a shape is abstract or not is to draw an imaginary line through the middle of it and compare both sides. If the two sides are similar, chances are you have a visually implied symmetrical shape. Redesign the shape to show different sides. Also make sure your symbol does not resemble a geometrical shape.\n\n#### Symmetrical Shape\n\nThis foliage is equally balanced on both sides, meaning it is a symmetrical shape and not ideal for painting in landscapes.\n\n#### Abstract Shape\n\nMuch better! Both sides of the tree are very different. This is an example of a nice shape seen in nature. Store these oddities in your landscape pictionary. You can use this shape in several paintings.\n\n#### Abstract vs. Non-Abstract Shapes\n\nThe first rock is a non-abstract shape. It looks like a loaf of bread. Try not to paint rocks such as these. The second rock is an abstract shape\u2014all four contour lines are different.\n\n#### Depicting Rocks\n\nAvoid concave semi-circles when depicting rocks. This weakens their character. A good way to practice rock shapes is to get some stones that have interesting shapes from a gardening center. Place them in alternate positions, even some grouped together and draw their shapes with a Sharpie marker.\n\n### Visualize Landscape Forms as Silhouettes\n\nThe black pictorial silhouettes resemble portions of the photos but they are not identical. They have been designed to be more appealing symbols. The drawings were done with a Sharpie Magnum marker, which is a great tool because it has a large blunt edge just like a brush. It is a crossover between a pen and a brush, so you will feel comfortable drawing with it. As a discipline and for practice, draw all kinds of abstract silhouettes.\n\nThe secret is to ensure each gap in between the trees is visually different from the others. Not one tree shape is repeated.\n\nThe waterfall in the photo is a visually implied rectangle. The two sides are not visually different. The silhouette shows a correction.\n\nThe mountain peak in the photo is too close to a triangle and the protrusions on both sides are cloned. The silhouette is an improvement.\n\nEven though the shape of the tree in the photo is not scientifically symmetrical, from an artistic standpoint it is implied to be symmetrical. The black tree silhouette is quite different on both sides and its contour is very interesting. The artistic version resembles the tree in the photo. It is not a copy.\n\nThe photo is displaying a rare case in which the rocks are abstract by themselves and needed very little tweaking. The silhouette was done almost to face value. Sometimes nature will cooperate with you. (This photo got added to my pictionary.)\n\nThe parallel sides are gone. The cylindrical shape is no longer present. The smaller branches are different from each other. This artistically designed tree trunk shape by far is better looking than what we see on that front lawn.\n\n## Techniques for Promoting the Artistic Brain\n\nKeeping aware that your strongest opponent to producing beautiful artistic designs is your own symmetrical brain will make you pay more attention during your painting process and break the spell of producing shapes that visually fall into implied triangles, squares, circles, rectangles and ovals. Here are some scenarios to help you identify the symmetrical brain interference more clearly.\n\n  1. **Think in pictorial symbols instead of real objects.** Avoid speaking to yourself in terms of painting trees, rocks, etc. Instead of saying, \"Now it's time to paint the evergreen trees,\" tell yourself, \"Now it's time to paint the shapes that symbolize evergreen trees.\" This awareness will keep you on track. Keep in mind that the landscape painting language is composed of symbols that _represent_ the real object, like than the word _orange_ represents the fruit. When I give workshops and someone asks me how to paint a green tree, I will reply jokingly, \"Buy a can of spray paint and spray graffiti on it.\" A skilled landscape artist will use attractive symbols that have been practiced many times, even repeating some of these in different paintings, just like using the same words in different sentences.\n  2. **Double your artistic intelligence by negative painting.** In the case of pastel, acrylics or oil painting, you can put the sky in afterwards and paint in a reverse format to carve out the contour of a tree from the sky point of view. The artistic brain will acknowledge how valuable this approach is.\n  3. **Draw an imaginary line down the middle of a shape.** Compare both sides. If they are visually mirrored, the attractiveness of the design is probably compromised.\n  4. **Pretend you are designing a puzzle.** This reduces the complexity of shapes when translating the pictorial information onto your painting surface. Imagine you shrink wrap things. The resulting contour is what you draw.\n  5. **Build your own personal pictionary.**\n\n#### Symmetrical Brain Intentions\n\n  * Build tree shapes with leaves.\n  * Indicate many separate rocks when grouped together.\n  * Single out deciduous or evergreen trees in a group.\n  * Painstakingly indicate many unnecessary branches.\n  * Make boxes out of rocks.\n  * Depict grass with strands rather than large clumps.\n\n#### Artistic Brain Intentions\n\n  * Build trees in designed clusters with a few brushstrokes that indicate thousands of leaves at once.\n  * Group rocks into one unit and only suggest a few.\n  * Join foliage together to read as one unit.\n  * Indicate the main tree branches and suggest just enough smaller branches to make the point.\n  * Ensure rocks appear unequal with each other in their shapes and look carved out.\n  * Only indicate a few grass strands to hint at the idea of grass, or leave them out completely.\n  * Group evergreens together into a mass.\n  * Think in landscape silhouettes instead of landscape objects.\n\n#### Think In Puzzle Pieces\n\nThis scene is quite complicated. If you apply a puzzle-piece technique to break things down and assemble those pieces to form the entire painting, it will not be too overwhelming to represent on the canvas. First decide on the major masses when you are doing the drawing outline. Next visualize the smaller portions inside those larger masses and convert them into your own version of mini abstract shapes until you assemble the entire puzzle. The painting should end up with a pleasing abstract design. By thinking in terms of puzzle pieces, you will require less effort from the artistic brain to construct this scene.\n\n#### Simplify Complex Details\n\nThere is a widespread movement in the art world called Representational Landscape Painting. Most professional landscape artists who are not hyperrealists apply this concept. As the names states, you represent scenes by reinterpreting everything into pleasing abstract-designed puzzle pieces that, when snapped together, make up the whole painting.\n\n#### Simplify Contours\n\nThese rocks have many bumpy protrusions which weakens the abstract shapes of the rocks. By putting these into a mental shrink wrap we will ignore all these unnecessary small protrusions. Once we file off those protrusions the design will improve.\n\nFrom this visualization technique we can derive the thumbnail sketch. The abstract designs are very clear now.\n\n#### Imagine Things are Shrink Wrapped\n\nDrawing nature's very complex contours onto your painting surface can be time consuming. To make it easier, pretend you shrink wrap the objects. Wherever the plastic molds itself around the form will be your contour drawing. This will enable you to catch deficiencies in shapes and find cloned objects. Simplify these contours to end up with the overall abstract design.\n\n#### Reference Photo\n\nThe rocks in this seascape have a vast amount of crevices. In the painting many protrusions were dramatically simplified and the whole painting was reduced to basic abstract designs. The left rock in the distance in the photo was visually symmetrical. In the painting it is edited so it would be asymmetrical. The technique mentioned earlier about dividing that shape in the middle with an imaginary line and comparing both sides was applied.\n\n#### Focus on Shape Contours, Not Inside Details\n\nThe more you work a painting, the more the viewer will have to work to put the visual information together. The viewer should be able to understand simple shapes effortlessly.\n\n## Negative Painting\n\nNegative painting is extremely important. It will become one of your most valuable assets. If you want to grow as an artist, you must acquire this tool.\n\nSimply defined, the negative space is the surrounding space or the air that is adjacent to an object as well as the in-between space. In the case of a portrait or still life, it will be the background. In landscapes, it is the sky when a tree shape is added. For objects such as chairs, it is the space between the legs. For any painting to hold together in a pleasing way, both the negative space and the positive space have to be abstract. For example, if your tree shape resembles an egg, you will have a poor positive shape. The deficiency will be doubled in the adjacent negative shape.\n\nEvery advanced artist works from his artistic right side of the brain as much as possible. In all the previous silhouettes, the white space was given as much importance as the black silhouette. Reverse painting will help you work from your abstract brain to correct unpleasant shapes. Let's get a better understanding about this before we see the direct application of negative painting.\n\n1. Positive Space in White\n\n2. Negative Space in Black\n\n#### Positive vs. Negative Space\n\nRubin's vase will appear as a vase or as two faces in profile. When you see the vase you are connected to the symmetrical brain. When you see the two profiles you are using the artistic brain. Do you feel how your brain switches back and forth between the forms? This will happen to you automatically when you learn to focus on the surrounding space when painting by the same token as you depict the positive shape. If you were to draw the object while solely looking at the positive (white) space, you would have a harder time replicating the form. If you only paid attention to the negative (black) space, then you would end up with a much better result. You would bypass the stored symmetrical influence coming from your left part of the brain. Try it!\n\n#### What Makes a Master?\n\nAndrew Loomis was a master at abstract shape design. To avoid symmetrical round heads in his portraits he depicted bumps on the hairlines to make them a bit wavy. Other expert portrait artists such as Anders Zorn will put hats and bandanas on their subjects to offset the helmet-head effect.\n\nStill life artists will change round fruits into attractive carved out angled forms as if the round convex protrusions were sliced with a knife, and both sides would be altered slightly. That way they don't end up being too circular or oval.\n\n## Demonstration: Use Negative Painting to Create Abstract Shapes\n\nFollow the steps to use negative painting to create abstract forms derived from symmetrical\/\/ shapes. Remember to check your negative and positive space simultaneously while painting.\n\n#### MATERIALS\n\npermanent marker\n\nliquid corrector with foam applicator\n\n**STEP 1:** Draw a black oval about 6\" \u00d7 4\" (15cm \u00d7 10cm).\n\n**STEP 2:** Using a liquid corrector applicator, \"carve out\" by reverse painting a tree shape. Use only the white liquid for the first stage. Work randomly to avoid cloning. Keep comparing both sides of your form. Pay equal attention to the white space, not just the black form.\n\n**STEP 3:** Do as much as you can only using the white liquid. Then you can go in with a black permanent marker and refine the shape from the positive point of view. If necessary, resort back to the corrector fluid to make further corrections until you are content with the tree symbol. Go back and forth from positive to negative painting. If you have not done this before, your brain has no preconceived stored input of this procedure, so you may feel confused and uncomfortable when starting. That is normal. After several attempts your artistic brain will kick in and you will probably come to enjoy this technique. (If you were to depict a tree in your painting, you could use the blue sky color and carve into the tree shape.)\n\n**STEP 4:** Apply the same process with other shapes.\n\n## Composition With Abstract Masses\n\nChapter 1 discussed how nature scenes never get abruptly cropped, but rather gradually fade into blurry forms in the peripheral vision of the human eye. Due to the limited space in a rectangular canvas format, we need to budget the space of pictorial areas, so whatever fits in the constricted area must be well planned.\n\nWhen approaching a subject, the best thing is to first decide what the painting's main setting will be. Just like with movies, they are categorized into action, drama, suspense, etc., and the movie director emphasizes one of those to be the general theme.\n\nLandscapes can be sorted into the following categories:\n\n  * Sky\n  * Mountain or cliffs\n  * Lake, river or waterfalls\n  * Terrain\n  * Foliage\n\nTo simplify even more, you must determine whether the sky, the vertical plane or the horizontal plane takes up the most space. They should not be similar in size to each other. A well planned composition will show one of these areas (here on referred to as a mass) to be the predominant one in size, and the masses will be designed into abstract masses. When possible that mass should take up roughly two-thirds of the space in your painting. A common mistaken procedure is to try to show several masses competing in sizes in one painting, which will result in those areas competing for attention. For example, if your theme is a skyscape, then everything else should shrink in size. The mountain peak should not be higher than one-third of the way up from the bottom.\n\nIf you decide to make your main theme about a rocky mountain, then the peak of that mountain should be close to the top of the painting in order to stretch its mass as far as possible to gain square inches and reduce the sky. The surrounding trees should get a \"haircut\" and diminish in size. The horizon line of the lake should be just a few inches up from the bottom.\n\nWhen you decide which mass will be predominant in size, there should be sufficient interest to make it attractive for the viewer. For example, if you have a clear blue sky and decide to make the painting about the sky showing it to be the largest mass, you will end up with lots of dead square inches because you won't have enough variances. On the other hand, a sunset or a cloudy sky with weather effects may merit dedicating a large percentage to that mass and make everything subordinate to that. The same will apply to a lake mass. If there are no reflections or boats to fill the void, a lake mass can be quite boring if most square inches are just showing flat water. If a lake does have reflections and boats, however, then it may merit being the main mass of your composition and dominate in size.\n\n#### Reference Photo\n\nThis is a good reference photo to work from for creating a thumbnail sketch (about the size of a playing card) to plan the sizes of the masses and make them abstract. If the masses were painted as they are in the photo, the mountain would be minimized.\n\n#### Thumbnail Sketch\u2014Budget Your Space\n\nThumbnail sketches will help you catch weak lines and shapes. They do not have to be detailed. They are great for working out the bugs in your composition so you don't hit obstacles during the painting process and can anticipate them early in your painting strategy. It is not necessary to indicate the smaller shapes within the masses. The purpose is to visualize the masses as abstract puzzle pieces and check the predominance or subordination of the surrounding masses.\n\nIn the reference photo, all the masses are competing for attention. The lake is void of visual richness because too many square inches are equal and take up most of the space. This will work better as a mountain scene. The evergreen trees can be reduced in height. The sky does not need to take up so much space either.\n\n#### The Finished Painting\n\nYour eye is now wandering around the mountain and it appears to be large and majestic due to its predominant mass. The lake, trees and sky are just supporting actors.\n\n### Cropping\n\nIt is very easy to fall into the trap of taking a photo at face value. However, if you apply the concepts of mass planning, you will be able to crop out the other competing masses.\n\n#### Poor\n\n#### Improving On the Reference Image\n\nAn example of a poor cropping and mass design is the photo on the left. The terrain and sky are both demanding the same attention. One of the two masses should be obviously smaller. This photo on the right will make an interesting skyscape. There are interesting lines and forms because of the rain clouds. You may even want to add rain pouring down. The sky mass takes up about 70% of the space which definitely establishes predominance.\n\n#### Better\n\n#### Helpful Hints\n\n  * Avoid boughs that protrude equally on both sides of evergreen trees. They take on an airplane wing effect. Make sure evergreens vary in width and height from each other.\n  * Avoid equal slants on rocks even if they are opposite.\n  * Make round rocks more angular with straight lines with some convex protrusions for variety.\n  * When trees are adjacent to each other, paint them together as one unit by merging the foliage into one mass. The highlights can somewhat show their individuality.\n  * To help search and destroy implied symmetrical shapes, turn the photo upside down before working out the drawing.\n  * Vary negative space gaps between trees.\n  * Check the negative space between your bare tree branches and mountains for negative-shaped triangles.\n  * Another effective way to determine if a shape is well designed is to pretend you cut it out of context with a utility knife.\n\n#### Focus on One Mass\n\nAvoid the temptation to say everything in one image. It may be better to do two or three paintings of the same reference, each emphasizing a different mass.\n\n#### Photo Editing\n\nYou can use a graphics program to edit your photo to get a better idea how it will look. In this example, the mountain was trimmed and the sky was reduced as much as possible without suffocating the painting. After the cropping, do a thumbnail sketch to correct things. The most important mass would be the river in this case.\n\n#### Alternate View\n\nHere is an alternate take on the same photo. The mountain becomes the main mass and this time the river is subordinate in size. A painting based on either of the last two photos would work.\n\n#### Stretch Masses\n\nTo favor the composition, you will often need to stretch or reduce the size of masses. This is a good reference photo but even if we crop out some of the water, the mountain will still seem tiny because of the sky mass and the size of the evergreens. This gets solved in the thumbnail sketch.\n\nBow River\n\nOil on canvas, 24\" \u00d7 30\" (61cm \u00d7 76cm)\n\n#### Alternate Version 1\n\nYou can completely ignore the mountain and make the evergreen trees the main actors in a foliage scene.\n\nBow River (Alternate 1)\n\nOil on canvas, 24\" \u00d7 30\" (61cm \u00d7 76cm)\n\n#### Alternate Version 2\n\nYou can completely ignore the mountain, downplay the sizes of the trees and make the river the main mass.\n\nBow River (Alternate 2)\n\nOil on canvas, 24\" \u00d7 30\" (61cm \u00d7 76cm)\n\n### One Scene, Several Compositions\n\nHow many paintings can you make out of this scene? I have travelled all over North America in my RV and when I hit a gold mine like this, I tend to stay in that one spot and do several paintings from the same location.\n\nYou could do three different successful paintings derived from this photo, and they would all give a different yet effective message. The point is to try not to say too much in one painting and to focus on just one important mass. Feel free to alter your landscapes even if they are well known areas. Viewers do not memorize how things look in real life. The beauty of your painting with its shapes should always trump the precise anatomy of mountains, buildings and trees. There are resident artists that live in the Teton National Park area. They know all too well that the Teton peaks are very symmetrical and will alter them to end up with a better design. Buyers of these scenes do not return paintings because they are not exact copies of the mountains.\n\nAll three thumbnails emphasize a different mass and all the paintings derived will work. The water, the foliage, the sky and the buildings do not compete with each other in the different settings.\n\n## Demonstration: Paint With Abstract Shapes\n\nI selected this scene because rocks and cliffs tend to create their own beautiful abstract designs. I was also drawn to the beautiful warm colors of the rocks in Acadia National Park.\n\n#### Reference Photo\n\n#### MATERIALS\n\n**Surface**\n\nArches 300-lb. (640gsm) cold-pressed watercolor paper\n\n**Brushes**\n\nsynthetic brights\n\n**Watercolor Pigments**\n\nBurnt Sienna, Cobalt Blue, Hooker's Green, Indian Red, Payne's Gray, Raw Sienna, Ultramarine Blue, Winsor Violet\n\n**Other**\n\nHB pencil, pastel chalks, sandpaper\n\n#### STEP 1: Sketch the Composition and Lay In the Sky\n\nSketch the composition with an HB pencil. Wet the sky past the distant evergreen trees and past the horizon line, where the ocean meets the sky. Use Raw Sienna, Winsor Violet and Indian Red to paint the clouds. Fill in the sky with Cobalt Blue and Hooker's Green. Make a swooping motion with the brush. Take care not to create an exact balance between the blue sky and clouds\u2014you want them to compete with each other. The sky should be darker tone at the top.\n\n#### STEP 2: Paint the Trees\n\nRewet the sky and go past the distant cliff area. Carefully avoid wetting the rock\/cliff area\u2014 wet only the evergreen trees. Using the wet-on-wet technique, begin to paint the first row of trees using Payne's Gray, Hooker's Green and a touch of Burnt Sienna. Move the brush in a zigzag motion to create the distant trees. Try to avoid too many zigzag areas though\u2014just indicate a few and allow the rest near the top to bleed into the sky. Keep the greens cool. Paint the second row of trees in a slightly darker tone. Negative paint out the silhouettes of the brighter trees. Do not heavily define any of them at this point\u2014 show only hints of the trees within that grouping. Glaze on top of the sunlit trees to bring them into the sunlight.\n\n#### STEP 3: Paint the Distant Cliffs\n\nPaint the farthest cliff Cobalt Blue with touches of Burnt Sienna and a touch of Winsor Violet. Leave a tiny white spot at top for highlights. Apply Burnt Sienna at the bottom of the cliffs to pick up reflected light from the water. Gradually get darker as the planes get closer.\n\n#### STEP 4: Paint the Foreground Rocks and Water\n\nBegin to define some of the flatter foreground rocks using Raw Sienna, Burnt Sienna, Winsor Violet and Cobalt Blue. Avoid subdividing too many times and avoid cloning the subdivisions. Think in terms of abstract designs. Do not darken the vertical planes too much. Feel free to exaggerate the warm color on the rocks. Then add the water with Ultramarine Blue allowing it to be hazier at the horizon. Gradually get darker in the middle ground. Add Hooker's Green to your water mixture as you get closer to the rocks. Drybrush the foam in the middle ground.\n\n#### STEP 5: Build Up and Define the Rocks and Cliffs\n\nAdd more definition to the vertical planes of the rocks by suggesting indentations. Add thin lines to suggest cracks. Using Cobalt Blue, glaze over the rocks where the cast shadow is. Create a darker flat rock where the water has made it wet.\n\n#### STEP 6: Add Details to Finish\n\nCarve out the rock indentations. Lightly drybrush on the rocks to add texture. Use a medium-coarse sandpaper to indicate the foam in the foreground. Negative paint into the sunlit evergreens to establish depth and roundness. If necessary, you can make corrections with pastels.\n\n_Otter Cliffs, Acadia National Park_\n\n_Watercolor on Arches 300-lb. (640gsm) cold-pressed watercolor paper, 9\" \u00d7 12\" (23cm \u00d7 30cm)_\n\n# Chapter 3\n\n# Vary and Enrich Colors\n\nSunrise Over Rockport\n\nOil on linen, 12\" \u00d7 16\" (30cm \u00d7 41cm)\n\nYou have probably noticed by now that I keep comparing nature against landscape paintings. This is because most artists believe they can use nature as a foundation for their paintings. While this is true for ideas and inspiration, we need to compensate where nature falls short.\n\nIn the previous chapter, you learned that one of the flaws of nature is the symmetrical, and in many instances unattractive, shapes it produces. Another drawback of nature is that much of the color you see is monochromatic, meaning it consists of various tones of only one color. It is our ability to vary and enhance colors that gives us artists the upper hand. Color variety is the flavor of your painting.\n\nIn this chapter you will learn:\n\n  * How to avoid the common pitfalls of monochromatic color schemes.\n  * How to establish color harmony.\n  * How to simplify the value scale.\n  * How to mix and match colors.\n  * How to attain more pictorial beauty through subtle color variance.\n\n## Controlling Monochromatic Color Schemes\n\nDirectly copying the colors you see outdoors or in photos will only result in a flat dull painting. You may ask, \"Why can't I just mirror the colors I see in nature? They work just fine!\" The reason is the macro world compensates for the monochromatic colors with intense sunlight that dramatically increases the range of values. (Value is the degree of how dark or light something is.)\n\nIn addition, the enormous size of real landscapes creates a huge impression of beauty. These conditions can never be replicated in a studio, especially because the value range you can work with in the studio is very reduced. However, once you become aware of the pitfalls of the monochromatic color schemes found in nature, half of your problems will already be solved.\n\nThe key to making monochromatic color schemes work is to add touches and hints of other colors, even though they are not present in the real scene or the reference photo. For example, in a scene with monochromatic greens, you would add yellow-oranges such as Yellow Ochre Pale and Burnt Sienna, with the purpose of variegating the greens with other hues to break the monotony.\n\n#### Summer Greens\n\nThe scene that inspired this plein air painting was all green. Hints of Yellow Ochre Pale and Burnt Sienna were added to those greens to add light and break the monotony. The red-orange bushes also give relief.\n\n#### Example of Monochromatic Greens in Nature\n\n#### Consider Eliminating Greens\n\nThis pastel painting has no green in it. Leaving green out of paintings completely will result in instant color harmony.\n\n#### Variegate, Variegate, Variegate!\n\nThis zoomed in version shows subtle variations of greens. Many artists mute the \"neon\" greens we see in nature and add more of a red-orange hue. If your foliage ends up being the same color as a martini olive, your greens will be quite pleasing.\n\n#### Don't Paint Solid Gray Tree Trunks\n\nIn reality, you would never see this many colors in a tree trunk. You can justify the presence of the blue light on the shadow side of the tree as reflected sky light. Artists look for justifiable reasons to exaggerate color variegation.\n\n#### Example of Monochromatic Grays in Nature\n\n#### Paint Like a Hollywood Animator\n\nThe painting below has so much more life than the photo. There are more variations of color. If your painting ends up with a somewhat cartoonish aspect, you are on the right track. Because you need to reduce real life objects to just a mere few inches, the best thing to do is design shapes in an abstract way and liven them with variegation of color inside those shapes to compensate for the micro size, then convince the viewers to accept them as a representation of a real landscape objects.\n\nThe point is not to be concerned to make things look real in a painting, rather make them look good. The secret is to improve nature by enhancing colors where they would be otherwise dull.\n\n#### Advantages of Pre-Toned Canvas\n\nMany artists pre-tone their canvases with Burnt Sienna. They scumble the darks very thinly and allow some of the undertone to glow through. This can bring relief to greens and add warmth to snow scenes.\n\n#### Handling Whites\n\nFor anything white in a painting, such as snow, water foam or clouds, do not use white right out of the tube. Always warm it with a touch of yellow-orange, or orange or pink.\n\nWhite water can be a problem when there is too much of it because it is a note of silence due to lack of color. It's like a pause in a song. If you limit white in waterfalls, snow scenes and seascapes the smaller portion of it will stand out more. An analogy to remember is that three candles on a table look romantic. One hundred candles will make it look like a funeral. Too much white and your painting will die!\n\n#### Snow In Shadows\n\nI never paint blue skies, blue lakes, blue mountains or blue snow as far as hue is concerned. Why? Blue is considered the coolest hue in the color wheel. As such, it is unpleasant for the viewer so we artists find ways around it. Snow or water in shadows does not have color of its own. The snow in shadow in this photo will seem just blue at first glance, but a careful look will show it has more colors. It will be a compilation of the surrounding colors from the rest of the painting. In the zoomed-in version, you can see hints of red, green and violet in mainly a blue overall setting, which picks up the sky color.\n\n#### Detail View\n\n## Demonstration: Color Matching\n\nThere are already countless books on the color wheel and color mixing, so we won't cover that in great detail in this book. However, I will share an easy color-matching method with you. Once you learn to match your colors with this system, you will not need to resort to color recipes with pigment names. (Keep in mind that all those names that appear on paint tubes are the result of intermixing the three primaries.) Now, instead of the color wheel, imagine a clock\u2014with each hour on the clock representing a different hue. (To differentiate the terms hue and color: Hue is the raw blue, red or yellow and the combination of any two of the latter. Color is the result of adding a third hue to the mixture.)\n\n#### STEP 1: Identify the Hues You Want to Match\n\nIdentify which of the twelve hues corresponds to the one you want to match. The twelve hues are derived from only three: yellow, red and blue, known as primaries. Pinpointing a hue is done by elimination process. Ignore how dark or grayed it is for the first stage. Just locate the raw hue. The minutes on the clock would represent all the in-between color mixtures.\n\n#### STEP 2: Determine Value\n\nDetermine how dark or how light a color is on a gray value scale. You can guess the value easier if you squint your eyes. (This scale does not show white.)\n\n#### STEP 3: Judge the Hue Saturation\n\nIf you do not add a third primary you will have pure color by only mixing two hues. Once a third hue is added to a mixture, you have desaturation as well as a tendency to gray down. When you add the direct opposite of a hue, it becomes desaturated. For example, when you add blue (4 o'clock) to orange (10 o'clock) the color intensity diminishes until you end up with gray.\n\n## Color Temperature\n\nMost people prefer warm hues like yellow-orange over cooler palettes of greens or blues. I never paint an absolute blue sky, a blue mountain or a blue lake that would be at 4 o'clock on the color clock. Instead, I would add Viridian to a Cobalt Blue mixture for my sky. For a lake, I would lean towards a gray-blue violet so the hue increases slightly in color temperature because of the addition of red. The viewer would still see it is blue though. When it comes to mountains, I will bend the color temperature towards a blue-violet The red in the violet helps offset the garish primary blue and warm it up a bit. Even if a mountain in a plein air setting is a neutral blue, I will not match its color.\n\nIt may surprise you to learn then that winter scene paintings, if handled skillfully, can end up being warmer as far as color temperature than a summer painting with greens. This is where your artistic instinct will help balance this out. It is commonly understood that all hues from green to blue-violet on the color wheel are considered cool colors, the rest are warm.\n\n#### Cool vs. Warm Painting\n\nWhich do you prefer? Most people prefer warm hues like yellow-orange to cooler palettes of greens or blues.\n\n#### Avoid an Equal Balance of Warm and Cool Colors\n\nThis winter scene predominantly has orange and yellow-orange. As such, it is classified as a warm painting, which is pleasing to the majority of people. As a word of caution: Paintings can be too warm or too cool. The cool gray-blue water and shadows on the snow help soothe the hot oranges. Pictorial temperature balance includes the correct ratio of warm vs. cool temperature. Only one should predominate.\n\n#### Don't Give Your Paintings the Blues\n\nI did this plein air painting at the Teton National Park. The mountains were much bluer, but I had to distort reality and turned them more towards a blue-violet. The sky is a turquoise blue. Adding green, because it has yellow, warms the blue. Even the left cloud has some Ochre in it to avoid a cool gray.\n\n#### Judging Local Color\n\nJudging a precise color can be difficult when it is in context with surrounding colors. If you close your hand and leave just a small tunnel to peek thru, the local color will be more faithful.\n\n#### Reduce Value Ranges\n\nWhen dealing with mixing color, it is easiest to reduce the ten main values on the gray scale down to only four grays. (In this specified scale, we leave out most white and black since they are easy to determine.) An almost white would only be used for clouds, water foam, buildings and sunlit snow. The key is to distinguish each value between those four grays only when mixing and applying color by thinking how they would appear if you took a black-and-white photo.\n\n#### General Values\n\nWhen it comes to the major shapes, simplify by thinking in light, mid-light, mid-dark and dark when mixing paint for daylight scenes. Make a clear separation between them. After all the mixing, the final painting will inadvertently end up with the ten values anyway. On a side note, I tend to stay away from the dark value if I can help it and work with only three main gray values and will resort to the darker gray if only needed to separate planes. The idea is to work with predominately mid values for daylight scenes. In most cases, skies tend to be a mid-light value, horizontal planes will be a mid value and vertical planes will be mid-dark values. The general values are:\n\n  * almost white\n  * sky and grass highlight - mid light\n  * ground plane - mid\n  * mountains and trees - mid dark\n  * evergreen foliage - dark\n\n#### Visualize the Painting As a Chess Board to Variegate Colors\n\nTo avoid replicating the monochromatic colors of nature, a great technique to keep in mind while painting is to imagine your painting is subdivided, like a chessboard, into eight squares in width and eight squares in height. In each square there should be a subtle color shift, and when possible a value shift.\n\nThe application of this concept will help you make skies become more exciting. While you are painting, if there is one square with a blue color only, you will feel compelled to add some hints of clouds. You will detect the moment your summer trees are becoming boring and will feel the need to add a variance of color. You will notice when your grass is too monotonous and add more green or yellow as needed. It will pressure you to echo the surrounding color in your snow shadows.\n\nAfter a while, this will become second nature. Because of this chessboard visualization tactic, you will sense something is missing when you leave out the color variegation. When the viewers scan your painting, they will appreciate the interesting shifts. Be careful not to over variegate or your painting will become busy.\n\n## Establishing Color Harmony\n\nMany books have also been written on this subject, so I will just put my two cents in for what I consider a simple solution for making colors harmonize in landscape paintings. Use an analogous color scheme. This means keep your main colors close together where they appear on the color clock, only using opposite colors for graying and cooling. The best policy is to make sure as many colors as possible in your artwork share the same common mother hue. This applies to everything where color is involved, even interior decorating in which the walls, rugs and furniture have similar colors. When doing autumn scenes, avoid the red hue and green hue as isolated colors. They don't share enough of the common yellow-orange denominator. I tend to use green just as a spice in autumn scenes in small amounts, leaving the yellow-orange, orange and red-orange as the predominant hues.\n\n#### Eliminating Colors\n\nIn this color scheme, I eliminated yellow because it rarely appears in landscapes. Yellow Ochre Pale and\/or Burnt Sienna can be added to green to make it more agreeable with the other pigments. All the colors will share yellow-orange. For over-the-counter pigments, a working palette for autumn foliage can be Yellow Ochre Pale, Cadmium Orange, Burnt Sienna, Permanent Rose and Viridian.\n\n#### Add Red to Greens to Unify\n\nSpice up your color mixtures with touches of red. With the exception of the mountain, most of the areas share a yellow-orange hue. There was a risk that the evergreen trees ended up being too green. To offset this, adding Burnt Sienna that contains the influence of the red-orange hue pulled them together with the yellow-orange trees. To keep them from looking isolated or out of place in autumn scenes, I tend to avoid showing any summer green colors that would not contain some red mixed in. They would at least be similar to a martini olive.\n\n#### Echo Surrounding Colors\n\nAnother way to establish color harmony is by repeating surrounding colors all around your painting. Snow, waterfalls and white walls will sing if you echo colors in a subtle way that appear elsewhere. This concept is known as reflected light.\n\nIn real life, when you look into cast shadows on snow, rocks, waterfalls and white water, they will take on a gray-blue appearance. You won't see the echoed colors. Nature has its own way of harmonizing color. With pigment, we don't have that luxury so we have to go the extra mile to end up with color unity. This means we will need to borrow colors from different areas of the painting, add them to other areas, and find pretexts to repeat these colors. In this painting, the cast shadow is picking the pinks from the flowers and the orange from the walls. The sky is the primary source of influential color. This is another example of why you can't paint just what you see in nature. Not only are we to echo colors in shadows, we must also weave surrounding colors into main areas. There are touches of green in the pink wall on the right. You can justify this green addition as mold on an old wall.\n\n#### Helpful Hints\n\n  * Avoid any primary hue by itself in a landscape painting. Ignoring the rare exceptions, they don't exist in nature.\n  * Greens tend to be quite garish. If you match the color of an olive, the amount of red present in the mixture will tone it down.\n  * Cool your greens in distant planes.\n  * Spice up your color mixtures with touches of red. Rain clouds look much better with touches of Indian Red in the blues. Adding Burnt Sienna to greens helps decrease saturation.\n  * Consider working from a black-and-white photo so you can invent your own colors, especially if it's a summer scene.\n  * If you have dry grass on the ground, you can echo that at the bottom of clouds by adding Yellow Ochre Pale.\n  * Rich color shows up the best in mid values. As the value gets closer to black, color fades. If you cannot make out the color of area by standing back ten feet, then you know that value is too dark. The closer you get to white, the colors become bleached out and chalky, so plan your paintings to show as much mid value as you can in broad daylight scenes.\n  * When reloading your brush with paint, make a habit of picking up a variation from the previous color you just applied.\n  * If you have problems varying color, try using chalk pastels until you get the hang of it.\n  * Double-load your brush with paint for automatic variances\n  * Greens take on a strong neon color in sunlight. Consider painting greens on overcast days.\n\n## Demonstration: Variegate Color in a Painting\n\nFollow the steps to variegate your colors in a painting and learn how to get monochromatic greens under control.\n\n#### Reference Photo\n\n#### MATERIALS\n\n**Surface**\n\nCanson Mi-Tientes paper\n\n**Pastels**\n\nPanPastels and pastel sticks in assorted colors\n\n**Other**\n\nfoam sponge blending tool, gum arabic eraser, pastel pencil, PanPastel applicator\n\n#### STEP 1: Sketch the Composition and Lay In the Background\n\nVery lightly sketch the composition with a pastel pencil\u2014just enough to see a hint of the drawing or it will show through the paint later.\n\nLay in the sky using a foam sponge tool and light blue PanPastel. Skip over some parts of the sky to allow the paper to show through in areas\u2014these will become the cloud forms.\n\nContinue working from the background forward. Indicate the hill with blue-violet.\n\n#### STEP 2: Lay In the Trees\n\nThe dark values of the trees must get cooler and lighter as they recede into the distance. Lay in the darkest greens first. Then build highlights on top of that. Try to avoid creating an equal balance of darks and highlights\u2014one should predominate. If some of the paper shows through, that's okay. Vary the greens to help break up the monochromatic color scheme.\n\nPaint shorter trees in front of the more distant trees to create depth. Use cool blues for areas of foliage in shade in the background. Warm up with violets in the middle ground. Each time you load the applicator, use a slight variation of the color you used previously. Double-loading it also helps. This will help you avoid making your painting too monochromatic.\n\n#### STEP 3: Build Up Layers and Texture\n\nNow that the base is down, switch to stick pastels to indicate a few individual leaves. Try to have them touch each other. Negative paint the dark indentations for depth. Add the sky holes, but be careful\u2014you don't want too many\u2014just enough so the trees look airy.\n\n#### STEP 4: Add the Tree Branches and Build Up Details\n\nPaint the tree branches. In nature, branches are quite dark. Keep the values close and try to hide them within the foliage so they won't stand out too starkly. Continue adding detail at the eye level and reduce the amount of detail in the top portion of the painting.\n\nNegative paint out a silhouette from the front tree to make it abstract. Use purple to carve out more indentations in the foliage and create depth. Don't go past one-third of the coverage of the total shape from the bottom up. Most of the time, artists place the sun at either 2 o'clock or 10 o'clock in order to have the light source come in at a ninty-degree angle. These areas should receive the most light.\n\n#### STEP 5: Lay In the Water and Grass\n\nYou can differentiate the horizontal plane from vertical plane by dramatically changing colors or values. Lay in the water in a curving \"S\" shape with gray-blue and blue-green hues. Lay in the grass with yellow-green. However, this will be too similar to the color of the trees on the left side of the painting, so it will have to be adjusted.\n\nLikewise, adjust the trees on the left to make them contrast more with the right-side trees and grass. Work some darker greens into the trees to take down the bright yellow glow.\n\n#### STEP 6: Define the Foreground and Add Details to Finish\n\nContinue building up the foreground layers and adding texture to the grass. Indicate just a few details like clumps in the grass and individual grass strands with Ochre hues using the stick pastels. Add the river bank, making it darker near the edges of the water to suggest erosion. This will also create a three-dimensional effect. Darken the corner to give a slope to the grass. Darken one side of the water and keep the other side lighter. Because of the overwhelming warm colors, add soothing grays at the bottom of the trees to represent dead branches and leaves. This will help subdue and unify the painting.\n\n_Summer Heat_\n\n_Pastel on Canson Mi-Tientes paper, 9\" \u00d7 12\" (23cm \u00d7 30cm)_\n\n# Chapter 4\n\n# Create Melodic Movement\n\nMisty Sunset\n\nOil on linen, 11\" \u00d7 14\" (28cm \u00d7 36cm)\n\nEach chapter so far has focused on the different virtues and defects of the macro world from an artistic perspective. In this chapter, we will address the concepts of visual lines and how important they are in relation to your paintings.\n\nA scientific study concluded that when subjects listened to music, their brains released endorphins. This is the reason they interpreted the music as pleasurable. This may very well be the case when viewers \"read\" paintings, so we artists must strive to produce melodic visual movement in our work. This is achieved by creating very interesting visual lines. Think of the lines in a painting as being sort of like the rhythm of a song.\n\nIn this chapter you will learn:\n\n  * How to handle problematic implied lines in creative ways.\n  * How to capitalize on desirable implied lines.\n  * How to move viewers through a painting in a slow and pleasing way.\n\n## Problematic Implied Lines\n\nIn Chapter 2, we explored the concept of our subconscious mind influencing us to repeat undesirable non-abstract shapes. The same applies to lines. When people look at paintings, they will unconsciously follow implied visual lines to help them process the information they're seeing. Because of this, you will want to create implied lines that are pleasing to viewers.\n\nEvery time you create a shape adjacent to another shape, it will have a contour. This contour becomes an implied line, hence, you have visual movement, which can be pleasant or unpleasant to the viewer. It stands to reason that if a shape is well designed, its contour line will also be pleasing. The key is to design implied visual lines that move the viewer's eye at the right pace in a graceful and melodic way.\n\nOnce you understand where nature is deficient, it will be easier for you to redesign deficient lines and become a good \"visual musician.\" Let's look at some examples.\n\n#### Implied Straight Lines\n\nThese are very abundant in nature. You will see them at shorelines and at the bottom of trees against grass, hill tops, distant trees, roads, tree trunks, horizon lines on seascapes, and on man made structures, of course. The implied straight lines move the viewer's eye too quickly. In general, it is best to avoid straight lines or adjust them to slow the pace.\n\n#### Implied Zigzag Lines\n\nThink of lines as musical notes on a scale. These would have pleasant variations. If the same note plays over and over again, it would be boring and monotonous. Evergreen trees tend to grow in such a pattern that they end up looking like a print out of an electrocardiogram. Zigzag lines are very unpleasant to viewers and should be kept to a minimum.\n\n#### Implied Repetitive Lines\n\nThese are normally found on contours of rolling hills, tree tops and clouds. When these lines form concave and convex lines with shallow indentations and protrusions that repeat across a contour, they are monotonous and should be redesigned. In the linear drawing, you can easily see that the wavy line is repetitive. This is because several trees are at the same height. It would be like hearing a flat song with no high and low pitches. The mountain also falls into a boring wavy line, so that would have to be cropped or substituted by a mountain that has more jagged edges. An untrained artist would just copy the layout as is.\n\n#### Implied Round, Concave or Convex Lines\n\nThis goes hand in hand with symmetrical shapes. Obviously if we have a shape that is too oval or round, the \"C\" contour of that shape would form a boring and swift linear movement.\n\n## Valuable Implied Lines\n\nWhenever possible, any problematic implied lines should be reworked into melodic lines, graceful lines or interrupted lines, and should be exploited to the utmost. They are vital compositional tools. These lines will result in pleasing eye movement.\n\n#### The Most valuable Compositional Lines\n\nThis image illustrates the three most attractive ways to move the viewer's eye through a painting. Think of an orchestra director when he is waving his baton. This will be moved in a graceful way. You can substitute the fast moving lines for these slower ones that are more pleasing to viewers. With this, you create your visual melody. A melodic line has a staircase effect to it, whereas a graceful line has a roller coaster effect with prominent protrusions and deep entrances. An interrupted line is a line that would otherwise be straight but is broken up into shorter segments. Its purpose is to slow down the visual pace. The gaps would be the speed bumps. (You could also call it a Morse-Code line or a connect-the-dots line.)\n\n#### Where to Place Lines\n\nSo where do we create all these compositional lines?\n\n##### Melodic Lines\n\n  * where water meets land, rocks, grass, clumps and floating tree trunks are handy tools\n  * where trees meet grass\n  * the bottom of cumulous clouds\n  * contours of rocks and rocky mountains\n  * contours of artistically designed evergreens\n  * to offset straight lines on buildings and tree trunks\n\n##### Graceful Lines\n\n  * contours of cumulous clouds\n  * contours of crashing waves and waterfalls\n  * deciduous trees (in a group or singular)\n  * visual paths, such as streams or rivers\n  * Interrupted Lines\n  * portions of roads peeking through the snow\n  * accents on bushes, grass, trees and under rocks\n  * cracks in stone walls\n  * to connect the dots for stones, bushes and wild flowers near each other\n  * rocks peeking through snow\n\n#### Melodic Lines\n\nYou can identify melodic lines by their \"staircase\" look. The reference photo shows an exquisite melodic line formed by the rocks against the water. Melodic lines are key to a successful landscape painting.\n\n#### Graceful Lines\n\nI would say there are deep enough dips in the contour of the autumn trees in this photo to classify this as a roller-coaster graceful line. Also the tops of the trees vary in height. When you see lines like these in nature, by all means\u2014exploit them.\n\n#### Melodic Line Shoreline\n\nThis is a good example of a designed melodic line. The eye enjoys \"reading\" the visual sentence until it reaches the crashing wave.\n\n#### Graceful Line Stream\n\nThe stream forms a pleasant graceful line that ushers the viewer to the sunlit area.\n\n#### Interrupted Line with Stones\n\nThe stones peeking through the snow form a Morse-Code pattern that slows down the visual speed.\n\n#### Seascapes\n\nSeascapes are very attractive because the contour of a wave can be designed into a graceful line. The rocks against the water form a melodic line.\n\nHere you can see the application of all the concepts you've just learned in one painting.\n\n## Lost-and-Found Lines\n\nOnce we have established which of the aforementioned lines is the most suitable in our composition, we will need to determine if the visual line should be well defined\u2014meaning hard edged, blurred, or a lost-and-found line, which is a combination of both.\n\n#### Diffused Contour Graceful Line\n\nThis is a graceful visual line whose entire contour is diffused.\n\n#### Lost-and-Found Graceful Line\n\nThis is a lost-and-found graceful line. This is the most exquisite and entertaining visual line. The diffused edge would read as foliage that is more distant. The hard edge would seem like the foliage is closer. The blurred-edged graceful line works well for waterfalls, foliage and clouds.\n\n#### Rain Clouds\n\nThe bottom of clouds that have shadows underneath make excellent melodic, lost-and-found implied lines. The fluffy part of the clouds forms a graceful line. The viewer's eye will travel along this line like reading a book, enjoying the process.\n\n#### Snow Scenes\n\nSnow scenes help offset the rigid lines of man made structures. I strategically placed the snow so that it would appear bumpy along the fence railings and roof lines. Be creative to slow the pace of the viewer's visual reading.\n\n#### Lost-and-Found edges\n\nIn this detail view of the above painting, note the lost-and-found edges on the contour of the trees against the sky. The hit-and-miss eye movement is well accepted by the viewer.\n\n#### Blur Portions of a Painting\n\nTo achieve blurred portions in watercolor, you can spot wet the paper, leaving some dry areas. To get blurred portions in other mediums, smudge randomly.\n\n## Solving Problematic Implied Lines\n\nYou will find many implied straight, zigzag, wavy and curved lines in nature. Here are some solutions:\n\n### Solving Implied Straight Lines\n\nImplied straight lines are most commonly found where water meets land, at the base of distant trees, distant hills, man made structures and roads, just to mention a few.\n\n#### Reference Photo\n\n#### Implied Straight Lines In Tree trunks\n\nThe bark peeling off the broken branches was all strategically made into melodic lines to avoid having the tree trunk show straight lines, as seen in the reference photo above.\n\n#### Implied Straight Lines at Shorelines\n\nWhere the river meets the land, we see a straight line. The visual movement is too fast. This also results in the river having a rectangle shape, which is not an abstract shape.\n\nBy adding a fallen tree trunk, some rocks and small coves, I was able to offset the straight line and slow down the visual thrust converting it to a melodic line. The tree in the foreground helped offset the rectangular shape of the water. On a side note, the mountain peak in the painting is now less triangular than in the reference photo. It is now an abstract shape.\n\n#### Implied Straight Horizon Lines\n\nSeascapes tend to have straight lines at the horizon. This can be counteracted by blurring that line, by adding fog, or by allowing waves and rocks to interrupt the line.\n\n#### Neutralize Straight Lines in Man Made Structures\n\nTo avoid rigid straight lines, subtle indentations were added to the edge of the stone wall that were not in the original scene. The tile roof looks damaged, but in paintings this adds character. Adding flowers to cover long straight lines is an excellent strategy. Many artists have made a living by applying this sole principle.\n\n### Solving Implied Zagazig Lines\n\nImplied zigzag lines are common when evergreen trees are grouped together.\n\n#### Pesty Zigzag Contours\n\nWhen the negative space between evergreens becomes repetitive and the widths of the evergreens are cloned, the result will be a zigzag eye movement. The solution to this is to open large gaps between some of the trees that are to be unequal and to vary the width and heights of these evergreens to the degree that the repetitive zigzag is gone. The contours of the mountains were designed into melodic lines.\n\n#### Advantages of Smudging\n\nSmudging to blend the distant forest into the background or sky will remove a zigzag contour line. Just leave a hint of some evergreens to let the viewers know what they are. Take into account that zigzag lines will be barely noticeable if their value is very close to the background, so they may not need to be smudged. The contour would be physically hard edged but not optically hard edged.\n\n### Solving Implied Wavy Lines\n\nImplied wavy lines are commonly found on tree tops and hills.\n\n#### Cropping\n\nObvious lines become strong attractions in paintings. Ask yourself if the line is leading the eye with a compositional purpose. If it isn't, take it out. Many times by cropping out or covering up a shape with an unnecessary line, you can avoid having the eye run like a subway back and forth. The long diagonal line on the background hill was not necessary so it was cropped.\n\n#### Create Deep Indentations\n\nIn the original scene, the tree top had very shallow negative shape indentations. By applying artistic license, I added some deep dips in some of the areas. Follow the contour of all the green deciduous trees. You will feel there is a roller coaster movement to the line. This now becomes a graceful line. The last tree does not need to be an obvious \"C\" line, due to the concave indentations.\n\n### Solving Implied Round and Curved Lines\n\nThese are slightly better than a straight line. Just like when a car approaches a curve, it needs to slow down but not enough to slow the pace to a comfortable visual movement. You can find curved lines in cloud formations, roads, rivers, streams, symmetrical trees and the contour of round rocks.\n\n#### Add Visual Speed Bumps\n\nThe \"C\" shaped line was solved by creating areas that protrude more, such as ice and rocks.\n\nThe \"C\" shape on the left side of the river is symmetrical. If left as is, it will rush the viewer.\n\n#### Interrupt the C Line\n\nAdd protruding bushes to convert a fast-moving \"C\" line into a graceful line.\n\n## Visual Paths\n\nNow we know that viewers are compelled to follow visual lines in paintings much like readers to street billboards. You also will want to have your viewers \"read\" the message in your paintings. The shapes are the words; the linear paths are the sentences. The goal is to set up visual paths to usher the viewer throughout your paintings, as well as to go as far into the background as you possibly can in a slow interesting way.\n\nIt is a common practice for most accomplished artists to resort to the foreground as being the entrance point, somewhat like the stairs that lead up into a house. The visual path should start there. Melodic and graceful lines will make visual paths very agreeable to the viewer. The most common visual paths in paintings are:\n\n  * cast shadows\n  * streams\n  * rivers\n  * shorelines\n  * roads\n  * bushes and wild flowers organized in a connect-the-dots sequence\n\n#### \"S\" Path Linear Movement\n\nIn this design, you can see a lazy \"S\" format to the linear path. Many professional artists use the \"S\" linear movement to lead the eye into the painting. You will see many examples of \"S\" visual paths in this book.\n\n#### Other Visual Paths\n\nThere are other ways to create linear paths that are not as obvious as roads or rivers. In this painting, I lined the sage brushes up in such a way that it would lead the eye. First you follow the bushes, then your eye follows the dirt area, then connects to the darker trees until your eye goes to the very back. Landscape paintings do not need focal points as long as you can move the eye throughout the painting well into the background.\n\nThe bales and the tall grass are organized in a way that they lead the eye to the background.\n\n#### Avoid the Train-Track Effect\n\nThe dirt road had two parallel lines. I offset one of them by overlapping it with the sage brushes. The grass against the dirt road forms a melodic line. The wild flowers are designed to grab the attention and subtly take the viewer to the distant cabin.\n\nThe logs are cleverly placed like toothpicks to help the viewer make the transition from the foreground to the mountain range. The protruding branches on the logs keep the eye from running over a straight line.\n\n#### Creating a Visual Lead-In\n\nOccasionally you will encounter reference photos in which the scene in its natural state does not provide a lead-in. Rather the eye will be rushed from side to side, and the viewer will feel compelled to exit the painting. This eye movement is inevitable when shorelines are placed in a certain way. In this painting, I had to create a melodic line with the shoreline to slow down the eye. I also applied artistic license and added waves to form the visual path from the foreground. The highlights on these waves form an interrupted line where the viewer connects the dots.\n\n#### Left-to-Right Visual Movement\n\nIn Western culture, we read from left to right. You will find that placing the visual movement from the left to right in most cases is preferable than the other way around. This painting has several melodic lines that the viewer will read in a pleasing way.\n\n#### Tip\n\nFlip your reference in a mirror before you draw it on the canvas.\n\nYou may get a better feel for it. Which version do you prefer from these two?\n\n#### Stop Visual Paths From Exiting At the Sides\n\nIf copied as is, the viewer will follow the contour of the cliff all the way to the right edge of the composition and go right out of the painting. It is better not to allow the viewer to exit on the side unless you provide a way back in near that exit.\n\n#### Solutions\n\nThis issue can be solved in two ways: Place fog to make the line and the area ambiguous, or put a \"stop sign\" before the edge. In this case, the protruding evergreen stops the line from inviting viewers to exit.\n\n### How To Indicate Rivers, Streams and Lakes\n\nIt is a common practice for artists to allow the bank of a river to exit at one of the sides as long as there is a reentry point an inch or so from that exit. The eye will make the connection at the short distance. This anchors the shape nicely and helps to avoid the feeling that the river is being fitted into the rectangle like socks in a drawer.\n\n#### Rivers\n\nWhen one part of the body of water originates from the side and the other from the bottom, it will give the impression it is a wider body of water such as a river. Make sure the two measurements from the corners are not the same.\n\n#### Streams\n\nWhen both sides of a body of water originate from the bottom, it will give the impression it is a narrow body of water, such as a stream.\n\n#### Lakes\n\nWhen both sides of the body of water come out from opposite sides, it will convey the impression that it is a lake or an ocean.\n\n#### Leading the Eye by Connecting the Dots\n\nIn a sense, this is an interrupted line. You can move a viewer visually by placing rocks, bushes, flowers or other things that would form a \"Hop Scotch\" pattern. These don't have to touch each other, but the gaps should be close enough to visually connect. The grass strands were placed strategically to invite the viewer in from the foreground and by connecting them, the eye goes to the cabins. There are narrow gaps that separate the grass but the eye still bridges them and moves forward.\n\n#### Leading the Viewer from the Top\n\nSo far I have only addressed visual paths that originate in foregrounds. You can also provoke eye movement coming from the top, much like the way we read newspapers. You can set it up where clouds, hills or the round tree foliage will give the viewer a sliding-board effect, so the eye slides into the painting. This can be done in conjunction with a visual path that would also originate from the foreground at the bottom.\n\nThe tree top guides the viewer in.\n\n#### Leading In From the Bottom\n\nThere is no question the steps are inviting. Note also that there are no distracting details in the immediate foreground.\n\n#### Bridge the Darks to Help Eye Flow\n\nVisually connect the dark elements. Either have them touch each other, or be close enough for the eye to make the leap without large gaps. Avoid the scattered billiard-ball effect. This way, the eye flows instead of jumping. If you cannot bridge dark spots, then slightly lighten the value. This would apply to accents in bushes, trees and rocks. Notice the pattern of darks in the negative painting and how close they are to one another.\n\n#### Visual Pointers\n\nThese are handy tools to direct the viewer to a certain area. These are normally tree branches, logs, leaves, long grass stands, etc. Think of visual pointers like a traffic policeman pointing towards the street so you can continue. In this painting, the tree has a couple of branches that direct the viewer past the gate. The semi-exposed concrete walkway is functioning as a visual path.\n\n## Establishing Rhythm\n\nOnce you design the major visual path, it is a good idea to have everything else follow that direction. Avoid lines that will contradict this eye flow. In a subtle way, keep all your lines moving towards the same direction.\n\n#### Follow Natural Lines\n\nFollow the sides of the rocks, their crevices and the flow of the water. You can feel there is an overall eye flow towards the waterfall where those lines converge.\n\n#### Poor\n\n#### Better\n\n#### Vehicles, People and Animals Should Not Face Edges\n\nIn the first picture, the viewer will unconsciously exit the painting. Turn vehicles, people and animals around to face inwardly. If people or animals are walking, make sure they are walking towards the center of your painting.\n\n## Demonstration: Create Melodic Movement in a Painting\n\nFollow the steps to invite the viewer into your painting from the foreground into the background. You will learn to work with a mixed palette of acrylics and oils.\n\n#### Reference Photo\n\n#### MATERIALS\n\nSurface\n\ncanvas glued to panel\n\n**Brushes**\n\nnos. 4, 6, 8 and 10 brights, thin riggers, thin watercolor brush\n\n**Acrylics**\n\nBurnt Sienna, Cadmium Orange, Cadmium Yellow, Permanent Rose, Ultramarine Blue, Violet\n\n**Oil Paints**\n\nBurnt Sienna, Cobalt Blue, Indian Red, Permanent Rose, Ultramarine Blue, Winsor Violet\n\nOther\n\nneutral violet pastel pencil, Liquin, palette knife, Liquitex super heavy gesso (for underpainting white)\n\n#### STEP1: Prepare the Surface, Sketch the Composition and Lay In the Sky\n\nTone the surface with Burnt Sienna acrylic paint. Sketch the composition with a neutral violet pastel pencil. This will blend into the paint later on. Lay in the background sky with a salmon-colored acrylic mixture with Cadmium Orange, Permanent Rose and white. This will imply a late sunset sky. Subdue the color intensity towards the peripheral area. Be more intense with the color where the sun will be placed.\n\n#### STEP 2: Finish Laying In the Sky\n\nScumble on some Winsor Violet at the top, away from where the sun will appear. (Placing cool colors next to warmer colors will make the overall scene appear even warmer.) Use Cadmium Yellow to create the sun, twisting your brush in circles like a drill. Scumble softly around the edge.\n\n#### STEP 3: Paint the Winter Trees\n\nDrybrush to indicate twigs. With a thin watercolor brush, paint the tree branches in Winsor Violet. Start lighter with the ones farther back and get darker as you come forward. Vary some of the lines. The tree trunks in the distance should have thinner lines and get thicker as you move forward.\n\nAvoid repeating gaps so the negative spaces aren't repetitive. Vary the slants. Make the trunks irregular by drybrushing. Keep them from looking too similar by putting tree knots in.\n\nWith a no. 4 bright, add in some orange right where the trees cross over the sun and scumble the paint on with a light feathery touch.\n\nPaint some snow stuck to the trees by randomly breaking the paint. Paint in between the branches making sure to keep the gaps different.\n\n#### STEP 4: Add Bushes and Snow\n\nPaint some bushes in the left area so that you have two different sides to the painting. Use drybrushing for this and get darker as you come forward.\n\nCreate a melodic line at the bottom of the bushes. Add grass at the bottom of the bushes by pulling your brush upward from the bottom. Add snow to the bushes and to the ground around the bushes.\n\n#### STEP 5: Paint the Water and River Bank\n\nPaint the water using cool purple tones. Drybrush the bushes in with Burnt Sienna, Indian Red and Ultramarine Blue. Create visual movement by painting snow along the bank, creating a melodic line between the snow and the water. Vary the blue and red tones on the snow, showing more red in the distance.\n\nPaint grasses in the foreground, using a portion of that to draw the viewer's eye in. (This way you aren't relying solely on the snow to do that.) Allow some of the orange underpaint to bleed through. Use a rigger brush to indicate a few individual grass strands with a quick flip of your wrist while holding the very tip of the brush. Work very fast so they look spontaneous.\n\n#### STEP 6: Finish with Details\n\nTime to switch to oils! Apply Liquin thinly over the whole painting. Paint in some ice, making it lighter than the water but darker than the snow bank. Add reflections from the bushes across the pond. Start at the ridge where the water meets the land and pull down in vertical strokes. Carve out some ice shapes to create the melodic line. Ice will not have any reflections.\n\nCreate small choppy strokes across the vertical reflections to create movement in the water. Keep those strokes as horizontal as possible. Add more snow to the frosted trees. Indicate tree branches with a palette knife. Add a few dark accents under the snow to lift it off the water using an interrupted line. Echo the sunlight onto the grass and snow. Keep it very subtle. Think in terms of romantic candle light\u2014less is more.\n\n_Seeking for Warmth_\n\n_Oil and acrylic on canvas glued to panel, 9\"\u00d7 12\" (23cm \u00d7 30cm)_\n\n# Chapter 5\n\n# Simplify\n\nCarmel Mission\n\nWatercolor on Fabriano cold-pressed watercolor paper, 12\" \u00d7 16\" (30cm \u00d7 41cm)\n\nEvery time a new student asks me how I know when a painting is finished, my answer is, \"It is never finished. You just stop working on it in time.\" A painting is not ready to be framed until you have taken out everything that a viewer who has not seen your reference photo will not miss. Remember, you are taking a large scene from the real world and scaling it down to mere inches. Instead of the eye moving between objects that are several yards apart, those details in a painting are much closer together. Unless the painting is quite large, too much detail can cause it to feel cluttered and unpleasing to the eye.\n\nThere will come a point in time that you mature past the concern of _how_ to depict things and will be more interested in _why_ a certain shape should be present. Does it serve a compositional purpose? If you can justify its presence from a design aspect, include it. If the answer is simply because it's in your reference, there may be no justification for it. For the sake of simplifying, you may want to exclude it.\n\nJust like with poetry, a simplified painting will stimulate the viewer to mentally wander into your artistic story, rather than having to visually process unnecessary information. The purpose of simplification is to reduce the viewer's need to mentally process too much visual information. It's a similar concept to editing a story, where unnecessary words are left out. In painting, the brushstrokes are your words, and a few masses and shapes are all you need. You can say more with less.\n\nIn this chapter you will learn:\n\n  * How to crop a scene in order to simplify its composition.\n  * How to reduce the amount of unnecessary detail in a painting.\n  * How to simplify natural and architectural elements found in reference.\n\n## Zoom In and Cut Out\n\nOne easy way to not try to say too much in one painting is to crop out what is not essential to tell the story. This allows the viewers to focus on only a few elements. Successful still life artists know this all too well. Too many objects will make the painting busy. Nothing changes in this regard to landscapes.\n\nThink of your rectangular canvas format like the square feet of your home. You want to make the best out of that limited space but not clutter things. I recommend you try to crop your photo several ways until you feel you have the right version. Most of the time, I find that zooming in ends up being the best policy as long as you don't suffocate the scene. Here you will need to rely on artistic asthetics and just follow your instincts on what to include or leave out.\n\n#### Competing Objects\n\nIn the top photo, there are two boats and several houses competing for attention. There is too much water and the stones with the bushes on the left will not add this to composition at all. After cropping and trying several alternatives, I ended up with the second picture that had enough of the information I needed to tell the story.\n\n## Simplifying Nature\n\nWe already know that the left side of the brain attempts to record and document literally, and this can cause artists to feel compelled to add unnecessary details to their work. The more detail you document, the less the viewer daydreams by adding his own ideas, because his brain will be too focused on interpreting the visual information. I believe a painting is successful when the viewer starts adding his own \"mental brushstrokes.\" When I create a lake scene and someone tells me that they can see themselves rowing and relaxing in a boat there, that's when I clap my hands and say, \"Eureka! I succeeded!\"\n\nOf all the paintings I have admired over the years, I have yet to see one that has been oversimplified. In nature, we will find an overwhelming abundance of details. There will be lots of individual stones by river banks, many tree branches on bare trees, countless sagebrushes squeezing themselves together in a field, and so on. The secret to making your artwork appealing is to reduce details. You can reduce the amount of detail to simplify a painting if you do _not_ :\n\n  * Indicate separate grass strands.\n  * Add too many branches to trees.\n  * Include unnecessary rocks and stones.\n  * Show too many white snow patches on mountains.\n  * Indicate too many cracks and indentations in cliffs or mountains.\n  * Depict too many separate leaves on trees.\n  * Show too many boughs on evergreen trees.\n  * Subdivide rock crevices too many times.\n  * Depict too many small clouds in a sky.\n  * Add too many wavelets to choppy water.\n\n#### Remove What Is Unnecessary\n\nThe cliff had too many crevices. Reducing them to the bare minimum helps calm the mental overload so viewers can instantly determine they are looking at a cliff. You will always find yourself battling the two different sides of your brain. Ultimately, if a photo doesn't need to be improved, then why paint a scene from it at all? You might as well just frame the photo and call it a day. Improving photos means removing unnecessary visual clutter to tell the same story.\n\n#### Simplify the Periphery\n\nCan this painting be more simplified? Yes! The cactus plant is distracting in the peripheral area and the stones are not adding to the scene. Out they go! Remember a painting is not done until you go back and remove what is not necessary with a giant mental broom.\n\n#### Limit Individual Stones\n\nJust a few stones are defined in the artistic interpretation of the photo, but your mind is putting many more in there like an optical illusion. Think of melting smaller things together. Also many of the subdivisions in the rocks in the foreground were merged into large forms.\n\n#### Reference Photo\n\n#### Visualizing Foliage\n\nAn effective way to visualize how to paint foliage is to depict it just like it appears on a non-high-definition television. The blurry television image simplifies trees, and leaves are fused into large clusters.\n\n#### Limit Individual Leaves\n\nHow many leaves can you count? This plein air painting was done on a 9\" \u00d7 12\" (23cm \u00d7 30cm) canvas. Because of the small size, I refrained from indicating individual leaves. I merged all the single leaves into large clusters. If the painting were larger, then it would look over simplified with no individual leaves showing, even when working at a larger scale, such as 18\" \u00d7 24\" (46cm \u00d7 61cm).\n\n#### Reduce Small Sky Holes in Foliage\n\nThis is one more example where you cannot apply how things appear in real life into your paintings. Trees in nature tend to have an overwhelming amount of small sky holes. You want to avoid this polka-dot effect, which will just tire the viewer.\n\n#### Create Larger Gaps\n\nViewers like to visually explore what is behind another plane by looking in between foliage. This tunnel effect enhances depth. The rest of the tree is quite solid with just a few sky gaps at the top third. Without these, it would appear to be pasted on.\n\n#### Reduce Sky Value to Blend With Foliage\n\nReduce the value of the sky in the gaps so they blend in better with the foliage, especially if the tree is dark. The value contrast will make them stand out too much otherwise.\n\n#### Merge Adjacent Trees and Bushes Together\n\nImagine your trees are made of plastic like the artificial plants you buy at a craft store. Pretend you heat the foliage with a blow torch. The moment they start to melt, you take away the heat. The way they end up looking melted together equates to how you would do foliage-related symbols with paint. Think of your foliage and grass in terms of metaphors.\n\n#### Sweep Away the Clutter\n\nWhen I did this plein air painting, I confess, I felt compelled to paint the fence into the scene simply because it was there. Once back in my studio, I applied the concept of sweeping away the clutter in order to simplify. I asked myself, \"What can I take out that would not be missed?\" I decided to remove the fence. If you had never seen the reference photo or the setting itself, you would not even know the fence was absent.\n\n#### Create Rest Areas\n\nIt's a good policy to have a patch that is void of detail right before the center of interest to bring relief. You can compare this to a carpet in a living room. The white snow void on information right before the house serves as the rest area in this painting.\n\n#### No Need to Paint Individual Grass Strands\n\nThink of your painting as the background for an animated movie. The viewers don't need details to put the story together. The mind will add grass strands. I drybrushed some texture in to create the illusion of clumps of grass.\n\n## Simplifying Architecture\n\nBecause buildings are man made structures that we can really associate with because of their symmetry, they become a strong attraction for an artist to depict at face value. The intellectual symmetrical brain will want to indicate all the details. The skill is to resist this and end up with just an impression of the scene, even a cartoonish look if possible.\n\n#### Do Not Emphasize Windows\n\nThis alley scene would be overwhelming to paint in detail. This was done in about three hours. The windows away from where the eye normally looks were down played so they would not be distracting. It's amazing how the mind adds to a simplified painting. The goal of this painting was to end up with only a simplified impression. As a result, you feel the place rather than seeing it.\n\n#### Helpful Hints\n\n  * If you have a small portion of sky you may not need to add clouds.\n  * The use of fog is an excellent agent for simplifying.\n  * When your paintings look like the background of an animation studio-produced movie, then you know you are on the right track.\n  * If you can count the brushstrokes in a shape you know it is not overworked.\n  * If you end up with a disastrously busy painting, try putting the entire scene into heavy fog by scumbling. You may end up loving it!\n  * Reduce the amount of white snow, white water on waterfalls, rapids and seascapes to a minimum.\n  * When facing a scene with clutter during plein air, pretend you are a well known movie director and you have a whole crew with cranes that can remove objects until you leave only the characters necessary for your story.\n\n#### Simplify Roofs and Reduce Stones and Bricks\n\nRefrain from indicating all the shingles an d tiles on roofs. Suggest just a few bricks and shingles placed well within the boundaries of the painting while respecting the peripheral area. Remember, let the viewer's imagination do the rest. Make them larger than scale so they can be easily distinguished from a distance. There is no need to do architectural renderings.\n\n#### Merge Leaves\n\nFor flowers and foliage, merge all the smaller flowers together in large clusters. The same applies to deciduous tree leaves. The presence of bushes and flowers also helps offset rigid straight lines in buildings. Notice the diffused edges of the flowers where they meet the walls.\n\n## Demonstration: Simplify Your Painting Composition\n\nUse acrylics for this painting in order to keep the hard edges of the mountain. As you work, use a fine-mist spray bottle to spray the pigments with water every fifteen minutes or so to keep them from drying out on you.\n\n#### Reference Photo\n\n#### MATERIALS\n\n**Surface**\n\nlinen glued to masonite board\n\n**Brushes**\n\nnos. 6, 8 and 10 brights (stiff from previous use with oils)\n\n**Open Acrylics**\n\nBurnt Sienna, Cobalt Blue, Dioxazine Purple, Permanent Deep Green, Transparent Red Oxide, Yellow Ochre\n\n**Other**\n\nfine-mist spray bottle, gel retarder, Liquitex super heavy gesso, neutral violet pastel pencil\n\n#### STEP 1: Sketch the Composition and Lay In the Sky and Mountain\n\nSketch the composition with a neutral violet pastel pencil. (This will go muddy and blend in with the paint later on.) Lay in the clouds with Yellow Ochre and a hint of Dioxazine Purple. Lay in the sky with Cobalt Blue and a bit of Yellow Ochre. Plan for the sky to be a lighter value than what the river will be, since water is always darker than sky. Position the sun on the left side so that the sky will be darker on one side than the other\u2014this creates a gradient plane. The two sides of the mountain look identical, so offset the symmetry by placing more clouds to one side. Paint the clouds with Liquitex super heavy gesso\u2014 it performs more like oil paint and will give you a good heavy texture, and increase the drying time.\n\nUse a blue-violet mixture for the mountain. (Keep in mind that acrylic paint dries a touch darker.) Variegate the hues slightly, adding more red in some areas and more blue in others. Do not simplify the ridges of the mountain or it will lose its character.\n\n#### STEP 2: Lay In the Hills and Begin Painting the Trees\n\nFor the distant hills, get darker and warmer as you begin to move closer to the foreground. Add more red into your blue-violet mixture. To keep the hill edge on the left from competing with the mountain edge, scumble and feather in the paint along the area to soften the edge where the hill meets the sky. Block in the evergreen trees with a muted green. Think of them as one unit when massing in. Do not repeat the gaps between the boughs, rather, simplify by reducing the number of boughs.\n\n#### STEP 3: Continue Painting the Trees and Lay In the Mid-Ground Rocks\n\nContinue painting the trees, varying the hues between the closest and receding trees, adding in Burnt Sienna to the closer ones. Keep the distant trees cooler. Ideally, no tree should be the same width or height, and the gaps between them should differ as well. Use a yellow-green mixture for the mid-ground cotton wood trees. Negative paint in the rocks with light gray-brown.\n\n#### STEP 4: Lay In the Water and Foreground Rocks\n\nLay in the water with a blue-green mixture. (Never use straight blue for water\u2014there is no way to harmonize it!) Make sure it's darker and more gray than the sky color. Paint around the rocks, trying to get lighter as the water recedes. This helps keep it from looking flat. Keep your brushstrokes straight and horizontal. Lay in the foreground rocks, focusing on the abstract shape of them rather than trying to copy them exactly. Create a melodic line at the bottom of the rocks where they meet the water. Eliminate the fallen trunks from the reference photo.\n\n#### STEP 5: Refine the Trees and Paint Reflections\n\nAdd highlights to the evergreens. Keep them darker than the mountain. Add some smaller trees in front and some taller trees in the back to avoid having them look like one big wall. Scumble the edges of the trees against the sky to break up the paint and create soft edges.\n\nAdd retarder to the water before you begin the reflections. They should be more subdued than what is on dry land. Keep all reflections about the same value. Negative paint around the rocks. Don't paint any reflections farther back, just in the foreground. Use vertical strokes for the reflections on the right and horizontal strokes for reflections on the left so they don't compete with each other.\n\n#### STEP 6: Add Details to Finish\n\nHighlight the mountain with white and a warm gray mixture. Think of the highlights as abstract shapes. Don't try to copy them directly from the photo. Use a mixture of white and a touch of yellow-orange for the snow caps. Make sure there is no confusion between what are clouds and what is snow. The cloud value should be darker. Lightly drybrush over the snow to break it up. Add blue shadows to the snow, but keep them slightly darker and more gray than the sky. Square off the rocks. Exaggerate the presence of brown in the trees to add interest.\n\n_The Teton_\n\n_Open acrylics on linen glued to masonite board, 8\" \u00d7 10\" (20cm \u00d7 25cm)_\n\n# Chapter 6\n\n# Avoiding Clones\n\nGrandma's Flower garden\n\nOil on canvas, 16\" \u00d7 20\" (41cm \u00d7 51cm)\n\nA painting can be technically perfect in terms of technique, but still turn out to look boring if the visual information you have on one side of the painting is quite similar to what is on the other side, or if one shape is similar to another. This creates what is known as _cloning,_ or a mirror-like effect. It is the artistic equivalent of telling the same story twice. The interest in your painting will dramatically increase if you ensure both sides are completely different.\n\nIn this chapter you will learn:\n\n  * How to identify the most commonly found implied clone shapes in nature.\n  * How to use artistic license to vary the size, shape and color of objects in a landscape to avoid cloning.\n  * How to plan your composition to avoid a mirror effect in your painting.\n\n## Identifying Clones\n\nI have done many field studies and I am still in awe of how so many nature scenes contain clones. Mother Nature once again throws curve balls at us artists. When I refer to cloned shapes, I mean that they are visually implied from an artistic point of view. Shapes can differ in height or width, yet still appear similar. It will not benefit the painting to have repeating forms demanding equal attention and competing with each other.\n\nDuring your artistic endeavors, you will find yourself recognizing and changing all forms that appear to be alike. When determining clones, take into account the negative space, not just the positive shape. Triangular shapes in the negative space between evergreens, mountain peaks and bare trees are common and can be repeated several times.\n\n#### Watch for Repeating Shapes\n\nThe trees in the first photo are cloned several times. Such a degree of repetition of forms is rare but it can happen. The three trees in the bottom image are somewhat different in size but close enough together in likeness to still be considered visually implied clones.\n\nArtistically speaking however, it is better for the shapes in a painting to be dramatically different from one another.\n\n#### Stones\n\nStones tend to appear like coins scattered on the ground.\n\n#### Mountain Peaks\n\nMountain peaks end up looking alike in a triangular fashion.\n\n#### Evergreens\n\nClones are easily found in evergreens. They tend to be about the same height and width as the adjacent ones.\n\n## Offsetting Clones\n\nOnce you know how to identify clones, there are several tricks you can employ to offset them and improve the harmony of your paintings.\n\n#### Depict Evergreens in a Clump\n\nThis avoids the singled-out aspect. The viewer will see this as a mass, which makes it easier to process the visual information.\n\n#### Change Colors\n\nConstant repetition of color is also cloning. The brown-orange tree is only stated once.\n\n#### Vary Height and Width of Objects\n\n  * Careful consideration was given to vary the size and width of each tree in this painting. There are variations with their colors as well. The two right trees are somewhat fused together to appear larger than the adjacent trees. The negative space between the evergreens is abstractly designed. None of the gaps are duplicated.\n\n#### Merge Rocks Into Larger Units\n\nSome rocks on the left are too close in size. This becomes a common problem when they appear in groups. By combing three smaller rocks into one, there is better diversity. While you are painting, think of the analogy of Goldilocks: Father, Mother and Baby Bear, with each representing a variation in size.\n\n#### Depicting Winter Trees\n\nWhen depicting trees in winter settings, offset any possible cloning by painting each tree so that it leans differently and all diameters are unequal.\n\n#### Reference Photo\n\nThe furthest mountain peaks are too similar. If copied at face value, they would be considered clones. What makes matters worse is that the negative white space between the peaks is too triangular.\n\n#### Manipulate Negative Space\n\nQuite a bit of artistic license was taken with the detail of this painting, which was based on the reference photo above. I modified the peaks by resizing them. The symmetrical triangular space in the blue sky is much less obvious. The last mountain peak is now blocked by an overpassing cloud to avoid creating a clone.\n\n#### Reference Photo\n\nThe erosion of water running over the wall of this mountain has formed some natural crevices. Painting these would section the areas into similar puzzle-piece sizes and make them appear too identical. They are so similar that they look like teeth.\n\n#### Avoid Crevices in Cliffs\n\nIn this close up section of a painting inspired by the photo above, just a few crevices are indicated. Each section is quite different from the next, and the divisions are simplified. All the puzzle pieces are different and abstract.\n\n## Avoid a mirror effect\n\nWhen you are out on the field or when selecting reference photos, draw an imaginary line down the middle and compare both sides to see if they are quite diverse in the information. The mountain range below looks asymmetrical, but the weight of the trees, the pond and the grass is about the same on both sides. If we put this photo in front of a mirror and reverse the image, it won't change much. It is doubtful this photo, without dramatically changing one of the sides, would make a successful painting. You will encounter many situations like this. Another key to being a successful artist is to know which elements will work in a painting and which ones won't. Some photos would make great posters, but good paintings will not necessarily result from them.\n\nTry to avoid having competing visual information on both sides of the image.\n\n#### Too Much Balance\n\nIf you looked at this Grand Canyon scene in real life, it would be breathtaking. If you put this in front of a mirror, both sides are too similar. As soon as you crop it, the visual information ends suddenly and does not gradually fade out in the peripheral vision. The duplicate sides will become very noticeable. Therefore we have to make the scene very entertaining to hold the viewer's attention.\n\n#### Use Several Reference Photos\n\nThis is from the same scene in the reference photo on the previous page. The group of rocks in the foreground was not in the original photo. Because two different views on each side was a priority, the vertical rocks were imported from a different photo. Think of your artwork like a movie script. Incorporate several photos to form a story board. You can literally move mountains with your artistic license. There are now two visually different sides to the painting.\n\n#### Offset Parallel Sides\n\nThe cactus plants in the foreground of this painting serve the purpose of offsetting parallel sides.\n\n#### Avoid Repeating Corners\n\nNormally when we paint blue skies or grass it is very easy to provide the viewer with the same visual information on both sides. This can lead to a boring outcome, and both corners will become rivals. Being aware of this will help you design your skies or foregrounds better. You can have a blue sky showing in one corner and a cloud on the other. The trees were purposely brought to the top to offset similar corners in the sky. The values of the water in the bottom corners are different.\n\n#### Helpful Hints\n\n  * Take a picture of your painting. Look at it as a thumbnail in a graphic editing program. You will spot discrepancies easier. Flip the image horizontally for a fresh view. Turn it upside down as well. You will notice things you may have missed in the original format.\n  * Because the symmetrical brain wants to participate in the activity, clones can creep into your painting when you least expect it. Be on guard!\n  * Turn your artwork upside down. You may be able to detect clones and symmetrical shapes easier because of the fresh view.\n\n#### Vary Corners With Clouds\n\nThis plein air painting shows a blue sky in the left corner and white clouds in the right corner. When I painted this outdoors, there was no blue sky. Skies will have blue areas, white clouds and clouds with shadows when they accumulate moisture for rain. Take advantage of these weather variances to offset equal corners on opposite sides. If you don't see them, then invent them or use an additional reference photo.\n\n#### Depicting Outdoor Stones, Bricks and Walls\n\nCareful consideration was given to just indicate a few individual bricks. The viewer will fill in the missing information.\n\n## Demonstration: Offset Clones in a Landscape Painting\n\nUse acrylic for this painting to easily overlayer the taller evergreen trees. As you work, use a fine-mist spray bottle to spray the pigments with water every fifteen minutes or so to keep them from drying out on you.\n\n#### Reference Photo\n\n#### MATERIALS\n\n**Surface**\n\ncanvas on masonite board\n\n**Brushes**\n\nnos. 6, 8 and 10 brights (stiff from previous use with oils)\n\n**Acrylics**\n\nBurnt Sienna, Cobalt Blue, Dioxazine Purple, Permanent Deep Green, Yellow Ochre\n\n**Other**\n\nfine-mist spray bottle, gel retarder, Liquitex super heavy gesso (for underpainting white), neutral violet pastel pencil\n\n#### STEP 1: Sketch the Composition and Lay In the Sky and Distant Hill\n\nSketch in the drawing with a neutral violet pastel pencil. (This will blend in with the paint later on). On the right side of the sky, lay in the clouds with Yellow Ochre and Liquitex super heavy gesso. It performs more like oil paint (allowing for texture) and it takes longer to dry. In this sense, white gesso is better than ordinary Titanium White. For the left side of the sky, use Cobalt Blue with a touch of Permanent Deep Green. Plan for the sky to be lighter in value than what the river will be. Bodies of water are usually darker than the sky. Use Cobalt Blue with a touch of purple and Burnt Sienna to indicate the very distant hill in a mid-value. Take into account that acrylics dry darker than when first applied. Soften the edges.\n\n#### STEP 2: Lay In the Hills and Begin Painting the Trees\n\nMix your colors until you achieve a blue violet in a mid-dark value. Block in the middle ground hill with that mixture. On top add the evergreen trees slightly varying the greens to about the color of an olive. Indicate some evergreen trees with Burnt Sienna. Add touches of light to the closer ones.\n\n#### STEP 3: Continue Painting the Trees and Lay In the Mid-Ground Rocks\n\nLay in the hill on the right side in the same manner as the last hill. Be careful to vary the gaps where the evergreen trees meet the sky to avoid cloning the trees. Indicate the rocky area with Cobalt Blue and Burnt Sienna. For the taller evergreens, make a mixture of a muted green (about the same color as an olive) with Permanent Deep Green, Burnt Sienna and purple. Make sure none of the evergreens repeat their width and their heights. Indicate the tree between the rocks using Burnt Sienna as the predominant color.\n\n#### STEP 4: Paint the Water and Foreground Rocks\n\nUse Cobalt Blue, Permanent Deep Green, purple and some Burnt Sienna (to gray the color a bit) to paint in the river. Lay in the water with a blue-green mixture. Do not use straight blue for water. It is difficult to harmonize the color. Keep your brushstrokes as horizontal as possible. Get lighter as the water recedes. Add the rocks with a mixture of Cobalt Blue, Burnt Sienna and Yellow Ochre. Make sure it gets pretty close to gray. The highlights on the rocks are done with the same mixture but with more Burnt Sienna and white. Apply what you have already learned and design those rocks into abstract shapes. Ignore the shapes in the photo.\n\n#### STEP 5: Refine the Trees and Paint Reflections\n\nAdd retarder over the river and immediately paint in the reflections with vertical strokes. Then break up the reflections close to where they end with horizontal strokes. Add just a few fallen tree trunks.\n\n#### STEP 6: Add Details to Finish\n\nDrybrush on top of the river with white and a touch of Yellow Ochre to indicate the white choppy water. Indicate some water ripples in the foreground only. Add the grass patch, but keep it simple. Be careful not to place the orange bush in the middle.\n\n_Yellowstone River, Yellowstone national Park_\n\n_Acrylic on canvas glued to masonite board, 9 \u00d7 12\" (23cm \u00d7 30cm)_\n\n# Chapter 7\n\n# Accentuate Depth\n\nWelcome In\n\nOil on canvas, 24\" \u00d7 30\" (61cm \u00d7 76cm)\n\nBy now you know that the three-dimensional field of depth is something that cannot be replicated on a two-dimensional surface. But we can convey the illusion of depth. Unfortunately, this aspect of painting is often ignored.\n\nThe ability to indicate depth was the skill that took longest for me to acquire. To make things appear as if they are receding requires skill and planning. For many years, I was more concerned with depicting shapes to be abstract rather than trying to make them appear three-dimensional. As a result, areas of my artwork ended up looking flat. The problem was the reference photos\u2014the field depth is totally lost the moment a photo of a scene is taken. This deficiency carried over into my paintings. I noticed my paintings dramatically improved when I began emphasizing and exaggerating the illusion of depth in my work.\n\nThe same applies when interpreting a scene done in plein air onto a flat canvas. Without proper application of techniques and deliberate intent to accentuate depth there may not be enough field depth simulation.\n\nIn this chapter you will learn how to use the following methods for accentuating depth in a painting:\n\n  * Overlapping\n  * Atmospheric Perspective\n  * Edge Manipulation\n  * Creating Multiple Planes\n  * Value Shifts\n  * Texture\n  * Foliage Indentation\n  * Gradient Planes\n  * Color Desaturation\n\n## Methods for Accentuating Depth\n\nAs artists we must go out of our way to create visual recession in the most convincing way possible by manipulating edges and forms. Use the following methods to convey a sense of depth in your landscape paintings.\n\n#### Overlapping\n\nBy placing one item in front of another, we send a message to the viewer that something is in front and something is behind. The fountain placed in front of the building helps convey a sense of depth. Take into account that the more we overlap something, we remove importance from the object when it is being partially blocked. Careful consideration is to be given how much you want something to overlap a center of interest, or you may minimize it.\n\n#### Atmospheric Perspective\n\nYou can see miles of depth in this painting. The closer cliffs take on a warm violet, shifting to blue-violet in the mid ground, and then blue in the furthest plane.\n\nUnless it is a foggy day, the obvious effect of atmospheric perspective is unnoticeable for planes that are just hundreds of feet away. In a normal day, you will start to see things getting bluer and lighter at about one mile away from you. You can really exploit this to create the illusion of depth.\n\n#### Fog\n\nNothing can beat this wonderful and handy tool to convey a sense of depth. It is great for separating planes. Otherwise they would all be the same value. In the forest area, it would be very difficult to convey the sense of recession without the fog. Solely overlapping the trees will not deliver a good enough sense of depth. Objects will always get lighter when they are yards apart and more simplified the deeper they recede into the fog. The fog also helps to keep the house from appearing as though it is sitting on top of the boat.\n\n#### Reference Photo\n\n#### Use Fog to Separate Buildings\n\nIf those fishing shacks were to be painted as they appear in the photo, the end result would be a sense of crowding them together. Logically we can measure the space in between each building, but visually we cannot. Because the photo flattened the scene, some buildings in this scene appear to be on top of each other. When there is nothing between the buildings, the sense of field depth is gone. This is why grass and fog were added between the houses.\n\n#### Exploit Thick Air for Moods\n\nWhen air molecules are thick because of high humidity, the atmosphere will absorb the warm rays of the late evening sunlight and give off a warm glowing light. This creates a mood which is very pleasant in paintings. Viewers tend to be drawn to paintings with moods.\n\n#### Ground Fog\n\nGround fog can give the viewer an out-of-the-ordinary view. Depicting ground fog in this painting is what got me Mexico's top award in watercolor media. This was done on a watercolor sheet called _Elephant Ear_ , which measured 60\" \u00d7 44\" (152cm \u00d7 112cm). I had to lie on the floor to do certain areas.\n\n#### Fog As a Cooling Agent\n\nA painting can be too cool or too warm. The trick is to find the correct balance between the two and to use colors of both temperatures to compensate each other. Autumn scenes can be disturbing because of all the warm colors that would look too garish. Fog can soothe this overwhelming color temperature. Also by not depicting sunlight, the oranges end up being toned down.\n\n#### Edge Manipulation\n\nContrasting blurry and sharp edges against each other is very effective for showing depth. Anything solid and static does not have diffused edges in the real world. Only things that contain water, such as foam or clouds will appear blurred. You will need to rely on blurring edges even though you cannot see them on solid objects. This becomes another tool to give the illusion that things are far away.\n\nThis house portrait shows overlapping from the lamp posts and the birch tree. The biggest asset for recession in this watercolor is the wet-on-wet technique in the background. When contrasted against the sharp edges of the house, it makes the foliage appear to recede several planes. Soft bleeding edges should always be present in watercolors. Watercolor allows for wonderful diffused edges, but lacks the ability to add thick impasto as texture.\n\n#### Diffused Edges\n\nBackgrounds will appear to be in a distant plane when the edges are diffused. In real life, a background is not soft. In this detail view, the house appears to come forward.\n\n#### Blurred Edges\n\nThe planes behind man made structures should be out of focus when it comes to foliage and hills. An exception to this would be rocky mountains. The angular structure which gives them character would become weakened.\n\n#### Create at Least Three Planes\n\nThe more planes a painting has, the more depth that is perceived. You can have sub planes within the three main planes (background, mid ground and foreground). Always create a minimum of three planes in your composition\u2014more if possible. In this painting, the idea was to make viewers feel like they could walk through the forest by creating layers of foliage as the forest gradually gets deeper. This painting gives a very convincing sense of depth in the background, which is nonexistent in the real life scene because the evergreens line up like birds on a wire and block anything behind them.\n\n#### Assign Values Per Plane\n\nThe principles of atmospheric perspective apply as long as all planes get the equal degree of light. All bets are off when a rain cloud casts a shadow over one plane and the sun is allowed to shed light on another plane. When this is the case, a background that is in shadow will not be lighter than a closer plane, such as the middle ground or foreground if the sun is peeking through the clouds only in those areas. When an overall plane is in a different value than another, the separation of these planes will be quite obvious as seen in this painting. Viewers will feel more invited when you darken a foreground plane and lighten the middle ground or background plane.\n\n#### Shift Values\n\nIn the first image, the closest plane of evergreens is lighter than the ones behind them. The value pattern was reversed in the second picture. The overall value of the planes can be interchanged and the sense of depth will still apply. If both planes of evergreens forests are in the same value, then our sense of field depth will be compromised and we would only rely on atmospheric perspective and size perspective to indicate depth.\n\n#### Texture\n\nHeavy impasto (thick paint) will convey that foreground objects are closer. You can reduce the thickness of paint for shapes in the mid ground. In the background avoid heavy paint\u2014use just enough to show the brushstrokes. Oil paint and acrylics have this advantage over other mediums.\n\n#### Building Texture\n\nThe surface was prepared with Liquitex super heavy gesso to build the texture before adding the colored pigment. The red-orange bush in the foreground was done with a drybrush technique and very thick paint. By applying a light touch, like tickling, the pigment peeled of the brush leaving the broken paint. Watercolor paper also works well for the drybrush technique. Hot-pressed (rough) paper leaves more gaps in between than cold-pressed (smooth) paper does.\n\n#### Foliage Indentations\n\nNegative painting creates visual orifices. Think of it as engraving an insignia in a ring. We can apply this same principle with foliage. Negative painting was used in this winter scene to bring out the positive shapes of the tree branches. This is a great way to create visual indentations for depth as well as establish the intent of design. This also forces you to work from your artistic brain, because as a child, you never did this so there is no preconceived memory of the process. No childhood habits will interfere. If there are no visual orifices in foliage, it will appear like a flat wall. There would be no place where a bird can protect itself from pouring rain and strong wind. The branches of the frosted trees were brought out by painting the dark spots into the lighter values. This reverse painting method brings out abstract negative shapes as well.\n\n#### Think Front-to-Back While painting\n\nIt is very common when foliage is about the length of a football field away from you that the bushes and trees seem to line up in a straight line like a wall. This will result in a visual pace that is too fast from side to side, and a rectangle will form from the horizontal grass planes. The sense of some trees being in front of other trees vanishes. Equate this to a chess game that has not begun. The trees and bushes in the picture line up like the chess pieces.\n\n#### Place Objects at 3\u20444 Position\n\nThink of a box. If we only show one side, it will look like a square, but as soon as we turn it we have a cube as long as both sides have different values. This concept applies to still lifes, portraits, wildlife and especially to buildings.\n\n#### Move Objects Like Chess Pieces\n\nWe all have the habit of writing from left to right in the Western world. We place words adjacent to each other. When we paint, we tend to repeat this habit with our landscape symbols like placing houses next to each other on a street. To break this habit, consciously position landscape objects unevenly in front of each other so there is recession from front to back. This is much more important than thinking side to side. Visualize a chess board and pretend you are moving trees, bushes, rocks, etc., like chess pieces coming forward. In the painting the large left tree was brought forward three squares. Some bushes were placed unevenly in front of the right tree, so the pawns were moved one and two squares.\n\nThe straight line where the foliage meets the grass in the photo, the rectangular portion of the grass, and the absence of field depth have all been corrected. Checkmate! I beat the photo!\n\n#### Recession Using Gradient Planes\n\nThis approach is used by animation illustrators and it is very effective. In a gradient plane, a value can become gradually darker or lighter in the distance or a color temperature can become warmer or cooler as it recedes. Gradient planes give a very good impression that horizontal planes are receding. Vertical planes seem to have more height and length when gradiated.\n\nThis foreground in the first picture is very flat. Since there is no river or stream to indicate a visual path, we can cast a shadow over the foreground to draw the viewer in. There is a convincing impression of depth in the second painting now. The value gradually gets lighter as it goes deeper in, hence the name, gradient plane.\n\n#### Avoid Flat Bodies of Water\n\nThis field study was done during an overcast day. I saw the same value of blue-gray in the entire body of water. Had I not lightened areas of that water, the painting would lack a convincing sense of depth. Lakes, seascapes and rivers give us great opportunities for gradient planes because they reflect the sky that can have so many variances of values.\n\n#### Gradient Planes Can be Reversed\n\nThis alternative view is showing a gradient plane, light to dark instead of dark to light like the picture above. The recession is still conveyed. It is just another version. This spot-lighting technique is an effective way to control where you want light. The rocks at the very bottom are darker than the ones further out into the distance. This also becomes a gradient plane. The grass in the middle ground gets darker towards the left edge as well. The ground becomes bluer and lighter near the far mountain range showing atmospheric perspective.\n\n#### Gradient Planes in Skies\n\nSkies can be boring and flat if the same value appears all the way across. In this painting, the right side is lighter indicating that the sun is just out of the picture. This is a great excuse to show a gradient plane in the sky for more interest.\n\nThe warm areas near the bottom of the mountains are reflected light off the lake, which would act like a mirror casting bounced sunlight near the bottom. This also is labeled a gradient plane. Some evergreens have a warm glow and are also gradient. This adds interest to that section. Again the transition from light to dark, warm to cool will achieve that.\n\n#### Gradient Planes on Vertical Walls\n\nThis scene has several subtle gradient planes. The wall with the arch is lighter and warmer at the bottom. The gray building is warmer near the bottom. The yellow arch is showing a lighter value right next to the wall. All this can be justified as reflective light bouncing off the adjacent planes. The cobble stone road is darker in the immediate foreground and gradually gets lighter as it recedes.\n\n#### Make Walls Recede\n\nReflective light will bounce off horizontal planes. In the stone building, the wall appears to recede much better than if it was a flat value all the way across. In real life, you probably would not see the wall progressively getting lighter. The roof starts with a cool blue and gradually fades into pink. This characterizes the house as being part of an animated movie. Under the eaves it is darker where the two sections of the roof form a \"V\". The bottom of the chimney is lighter than the top. Take into account that indicating gradient planes is an artificial technique, but very effective in paintings. Make sure the lightest value in the shadow side of a plane is darker than any area in the sunlit fa\u00e7ade. The 3\u20444 position of the building allows for these effects.\n\n#### Render Objects Into 3D Forms\n\nDepending on how the sun is positioned, many trees in photos do not show 3D volume, just height and width. If painted as they appear in real life or photos, they will have a flat two-dimensional look. These simple drawings show simplified versions of landscape shapes showing volume because of the shadow side. As you are painting, think of trees as spheres, tree trunks as cylinders, rocks and mountains as cubes, and evergreen trees as cones. Plan your light to come from the side so that the opposite side ends up with a darker side. Make sure that when you include animals, vehicles, people and buildings, you place them at a 3\u20444 position and have two different sides in two different values. All these factors accentuate to nullify the flatness.\n\n#### Desaturate Colors in the Distance in Grass Fields\n\nIn real life, the eye will see equal color intensity in a field of grass in the foreground compared to hundreds of yards away. Unless it is a muggy day, atmospheric perspective takes effect and becomes noticeable, not hundreds of yards away, but almost a mile away. We know the brain has its own mechanism to sense depth. Painted exactly as it appears, the grass will not recede enough in a painting. To achieve recession, reduce color intensity at the end of the field in case the colors of trees and grass are the same up front and in the distance. The color intensity in the bush was pumped up a bit to bring it closer compared to the one behind it. The furthest grass has been grayed down by adding Violet to the same mixture used in the foreground.\n\n#### Avoid Stacking light and Dark Values\n\nWhen areas of equal color and value are placed somewhere else and are disjointed, the top portion seems to hover above instead of receding.\n\nIn the first version of the painting, the snow patch in the distant mountain is the same value and color as the waterfall. It seems like two white poker chips on top of each other in the same stack separated by other colors.\n\nIn the corrected version, the snow was darkened. Now it seems that area recedes at least one mile. There is a better sense of field depth.\n\n#### Helpful Hints\n\n  * Liquitex super heavy gesso can be applied after your preliminary drawing where shapes of trees, rocks, fallen tree trunks, etc., are present before you apply the paint. This medium has quite a heavy body for texture.\n  * PanPastel, a relatively new medium that uses non compressed pastel powder, works very well in watercolors to indicate fog and add veils of atmosphere.\n  * Zinc White is a semi-transparent pigment that is very effective for depicting fog when scumbled over an area in oils or acrylics. Avoid placing a hard edge from one plane behind a hard edge from another plane. Where there is a plane shift, the closer plane should show a hard edge. Also avoid placing a soft edge behind another soft edge.\n  * Darken the bottom corner to make it more inviting to step in.\n  * Covert your artwork into a gray scale. You can spot flat looking areas more easily.\n\n## Demonstration: Accentuate Depth in A Background\n\nUse oils for this painting so the water foam can easily blend and create soft misty edges where the water meets the rocks.\n\n#### Reference Photo\n\n#### MATERIALS\n\n**Surface**\n\nstretched canvas or canvas board\n\n**Brushes**\n\nnos. 6, 8 and 10 brights\n\n**Oils**\n\nBurnt Sienna, Cobalt Blue, Indian Red, Underpainting White, Viridian, Winsor Violet, Yellow Ochre Pale\n\n**Other**\n\nneutral violet pastel pencil\n\n#### STEP 1: Sketch the Composition and Lay In the Water\n\nSketch in the drawing with a neutral violet pastel pencil. (This will blend with the paint later on.) Lay in the blue-green water using Cobalt Blue, Winsor Violet and Viridian. Show variances of each of these colors. Place the brush strokes in the same direction that the water would be running. Use thin paint so a second layer of paint can be added easily.\n\n#### STEP 2: Add the Rocks\n\nPremix Burnt Sienna, Cobalt Blue and a touch of Indian Red and white to a mid dark value. Don't over mix. Just allow the colors to mingle to kill the intensity. The colors should remain marbled on your palette. Paint in the rocks using abstract shapes. Add touches of Cobalt Blue with white to indicate the sky reflections on the wet rocks.\n\n#### STEP 3: Vary the Sides of the Waterfall\n\nContinue to indicate the rocks, but this time build, a larger rock and add Yellow Ochre Pale to it for variance so that left side has something different than the right side. Check that the water lines on both sides are quite different to avoid cloning. Add a few smaller rocks into the waterfall to give it a sense of belonging in the context of the scene.\n\n#### STEP 4: Create a Semi-Transparent Effect on the Water\n\nAdd more rocks into the waterfall, but this time make them semi-transparent to indicate that shallow water is running over them. Think of them as a bridal veil. Add the white water with a touch of Yellow Ochre Pale and white to the top third of the waterfall, only with thick paint. Keep it from mixing in with the darker blue. However, allow some the white to mix in with the blue foundation at the lower two thirds. You should be able to see two distinct values. Twirl your brush where the water meets the rocks until they form misty patterns.\n\n#### STEP 5: Add the Foliage\n\nThe front evergreens are done with a mixture of Viridian, Winsor Violet, Burnt Sienna and white. They should also be a mid-dark value. Add a gray mist behind the evergreen trees.\n\nHidden Falls, Teton national Park\n\nOil on canvas, 8\" \u00d7 10\" (20cm \u00d7 25cm)\n\n#### STEP 6: Create Rows of Trees to Finish\n\nFinally, add two more rows of evergreens behind the front row. Use the same mixture but add more Cobalt Blue, Burnt Sienna (to gray down the color) and white. Get progressively cooler and lighter as the forest recedes. Add mist behind the first row to enhance the sense of depth. Your painting should end up with three levels in the background. Add some bare tree trunks as seen in the finished version.\n\n## About the Author\n\nJohannes Vloothuis is a full-time professional artist and renowned art instructor with experience in all the main painting mediums. A frequent workshop instructor for WetCanvas, he has traveled all over North America doing plein air painting and giving painting workshops and demonstrations. Johannes has also taught classes online to more than 15,000 artists all over the world. He finds his true passion lies in sharing compositional secrets and seeing his students grow into better artists.\n\nNorth Light has labeled Johannes a Master Painter. He has won awards from the Mexican Society of Watercolor Artists, and his work has appeared in newspapers, magazines and museums worldwide.\n\nTo view more of Johannes' artwork and obtain more information about his classes, visit his website at improvemypaintings.com.\n**Landscape Painting Essentials with Johannes Vloothuis**. Copyright \u00a9 2015 by Johannes Vloothuis. All rights reserved. No part of this eBook may be reproduced in any form or by any electronic or mechanical means including information storage and retrieval systems without permission in writing from the publisher, except by a reviewer who may quote brief passages in a review. Published by North Light Books, an imprint of F+W, a Content + eCommerce Company, 10151 Carver Road, Suite 200, Blue Ash, OH 45242. (800) 289-0963.\n\nOther fine North Light products are available from your local bookstore, art supply store or online supplier. Visit our website at fwmedia.com.\n\neISBN: 9781440336287\n\nThis e-book edition: June 2015 (v.1.0).\n\n# Contents\n\n  1. Cover\n  2. Title Page\n  3. Special Offers\n  4. Table of Contents\n  5. Dedication\n  6. Introduction\n  7. Materials\n  8. Chapter 1: Paint How the Eye Sees\n    1. Visual Perception vs. Photographic Perception\n    2. Reference Photos: Friend or Foe?\n    3. The Peripheral Area\n    4. Simplifying Foregrounds\n    5. Blurred Edges\n    6. Demonstration: Paint a Landscape with a Simplified foreground\n  9. Chapter 2: Design With Abstract Shapes\n    1. Symmetrical Brain vs. Artistic Brain\n    2. Landscape Shapes\n    3. Techniques for Promoting the Artistic Brain\n    4. Negative Painting\n    5. Demonstration: Use Negative Painting to Create Abstract Shapes\n    6. Composition With Abstract Masses\n    7. Demonstration: Paint With Abstract Shapes\n  10. Chapter 3: Vary and Enrich Colors\n    1. Controlling Monochromatic Color Schemes\n    2. Demonstration: Color Matching\n    3. Color Temperature\n    4. Establishing Color Harmony\n    5. Demonstration: Variegate Color in a Painting\n  11. Chapter 4: Create Melodic Movement\n    1. Problematic Implied Lines\n    2. Valuable Implied Lines\n    3. Lost-and-Found Lines\n    4. Solving Problematic Implied Lines\n    5. Visual Paths\n    6. Establishing Rhythm\n    7. Demonstration: Create Melodic Movement in a Painting\n  12. Chapter 5: Simplify\n    1. Zoom In and Cut Out\n    2. Simplifying Nature\n    3. Simplifying Architecture\n    4. Demonstration: Simplify Your Painting Composition\n  13. Chapter 6: Avoiding Clones\n    1. Identifying Clones\n    2. Offsetting Clones\n    3. Avoid a mirror effect\n    4. Demonstration: Offset Clones in a Landscape Painting\n  14. Chapter 7: Accentuate Depth\n    1. Methods for Accentuating Depth\n    2. Demonstration: Accentuate Depth in A Background\n  15. About the Author\n  16. Copyright\n\n# Guide\n\n  1. Cover\n  2. Table of Contents\n  3. Start of Content\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\nUniversity of Manitoba Press\n\nWinnipeg, Manitoba\n\nCanada R3T 2M5\n\nuofmpress.ca\n\n\u00a9 Sarah Carter 2016\n\nPrinted in Canada\n\n20 19 18 17 16 1 2 3 4 5\n\nAll rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, or stored in a database and retrieval system in Canada, without the prior written permission of the University of Manitoba Press, or, in the case of photocopying or any other reprographic copying, a licence from Access Copyright (Canadian Copyright Licensing Agency). For an Access Copyright licence, visit www.accesscopyright.ca, or call 1-800-893-5777.\n\nCover design: Frank Reimer\n\nInterior design: Jess Koroscil\n\nCover image: Sarah Minnie (Waddy) Gardner on her horse\"Fly,\"Mount Sentinel Ranch, Alberta, 1915. Born Wexford, Ireland, 1879, died Calgary, 1959. Museum of the Highwood, MH995.002.008.\n\nCataloguing data available from Library and Archives Canada.\n\nISBN 978-0-88755-818-4 (pbk.)\n\nISBN 978-0-88755-532-9 (pdf )\n\nISBN 978-0-88755-530-5 (epub)\n\nThis book has been published with the help of a grant from the Federation for the Humanities and Social Sciences, through the Awards to Scholarly Publications Program, using funds provided by the Social Sciences and Humanities Research Council of Canada.\n\nThe University of Manitoba Press gratefully acknowledges the financial support for its publication program provided by the Government of Canada through the Canada Book Fund, the Canada Council for the Arts, the Manitoba Department of Culture, Heritage, Tourism, the Manitoba Arts Council, and the Manitoba Book Publishing Tax Credit.\nTO MY GRANDMOTHER JEAN MUNN (JENNIE MAY MARSHALL), 1899\u20131967, BORN ON HER PARENTS' HOMESTEAD, WELLWOOD, MANITOBA.\n\n_Photo: Family_ _Collection._\n\nDuring my stay in Canada I heard a good deal about farming for women, and how they ought to take up homesteads, therefore I was interested to come across the young daughters of a neighbouring farmer, who acted as hired men to their father. Mrs. Anderson [her employer] said they rode wonderfully, could handle a team better than most men, drive the \"binders,\" and do the whole work of a farm; but she considered that the life they led was unsuitable for a woman and was unfitting these girls for becoming wives and mothers in the future\u2014in fact, the feeling of the countryside was strongly against their father.\n\nElla C. Sykes, _A Home-Help in Canada_ , 1912\n\nPeople are beginning to waken up to the vast conception and imperialistic importance of tendering free homesteads as an inducement to women of strong moral force and high intellectual ability to come to our beautiful West and lend their aid in establishing a Canadian colony, a new and clean colony...\n\n\"Homesteads for Women,\" by \"Isobel,\" _Grain Growers' Guide_ , 25 October 1911\nCONTENTS\n\nLIST OF ILLUSTRATIONS\n\nLIST OF TABLES\n\nACKNOWLEDGEMENTS\n\nLIST OF ABBREVIATIONS\n\nNOTE ON TERMINOLOGY\n\nINTRODUCTION\n\nCHAPTER ONE\n\n**NARROWING OPPORTUNITIES FOR WOMEN:** FROM THE INDIGENOUS FARMERS OF THE GREAT PLAINS TO THE EXCLUSIONS OF THE HOMESTEAD REGIME\n\nCHAPTER TWO\n\n**\"LAND OWNERS AND ENTERPRISING SETTLERS IN THE COLONIES\":** BRITISH WOMEN FARMERS FOR CANADA\n\nCHAPTER THREE\n\n**WIDOWS AND OTHER IMMIGRANT WOMEN HOMESTEADERS:** STRUGGLES AND STRATEGIES\n\nCHAPTER FOUR\n\n**WOMEN WHO BOUGHT LAND:** THE \"BACHELOR GIRL\" SETTLER, \"JACK\" MAY, AND OTHER CELEBRITY FARMERS AND RANCHERS\n\nCHAPTER FIVE\n\n**ANSWERING THE CALL OF EMPIRE:** GEORGINA BINNIE-CLARK, FARMER, AUTHOR, LECTURER\n\nCHAPTER SIX\n\n**\"DAUGHTERS OF BRITISH BLOOD\" OR \"HORDES OF MEN OF ALIEN RACE\"?:** THE HOMESTEADS-FOR-BRITISH-WOMEN CAMPAIGN\n\nCHAPTER SEVEN\n\n**THE PERSISTENCE OF A \"CURIOUSLY STRONG PREJUDICE\":** FROM THE FIRST WORLD WAR TO THE GREAT DEPRESSION\n\nCONCLUSION\n\nNOTES\n\nBIBLIOGRAPHY\nLIST OF ILLUSTRATIONS\n\n_Figure 1._ Survey map of Township 12, Range 15, West of the Principal Meridian. Archives of Manitoba, N6411.\n\n_Figure 2._ \"Sioux Woman,\" the daughter-in-law of Hidatsa farmer Maxi'diwiac (Buffalo Bird Woman), demonstrates traditional farming methods, 1912. State Historical Society of North Dakota, item no. 0086-0281. Photo by Gilbert L. Wilson.\n\n_Figure 3._ An 1882 map for \"intending settlers,\" showing the dominion lands surveyed west of the border of Manitoba. Peel's Prairie Provinces, University of Alberta Libraries, Map 597.\n\n_Figure 4._ M\u00e9tis women and men at a sitting of the M\u00e9tis Scrip Commission at Devil's Lake, Saskatchewan, 1900. Saskatchewan Archives Board, S-B9750.\n\n_Figure 5._ Patent issued in 1883 to Manitoba homesteader Matilda McAskie. Library and Archives Canada, Western Land Grants, http:\/\/www.bac-lac.gc.ca\/eng\/discover\/land\/land-grants-western-canada-1870-1930\/pages\/item.aspx?IdNumber=461605&.\n\n_Figure 6._ \"The Primitive Farmer and Burden-Bearer, South Africa,\" from Otis T. Mason, _Women's Share in Primitive Culture_ (1899), 6.\n\n_Figures 7 and 8_. The Glynde School For Lady Gardeners in Sussex, England, established by Lady Frances Wolseley in 1902. Papers of the Viscountess Frances Wolseley, Hove Central Library, Hove, Sussex, Commonplace Book no. 196.\n\n_Figure 9._ Colonial Training Farm at Arlesey, England. _The Bystander_ , 16 September 1908, 610\u201311.\n\n_Figure 10._ \"Canada for Women\" promotion, Canadian Pacific Railway, 1910. _Daily Mail_ , 2 March 1910, 10.\n\n_Figure 11._ The Canadian Pacific Railway office, London, wants \"settlers, not suffragettes,\" 1913. Getty Images, no. 3424540.\n\n_Figure 12._ Englishwoman and Alberta rancher Agnes Bedingfeld. Glenbow Archives, NA-2467-12.\n\n_Figure 13._ Alberta homesteader Margaret de Tro earned extra income as a \"magnetic healer\" in Edmonton. _Edmonton Bulletin_ , 29 December 1905, 4.\n\n_Figure 14._ The auction sale of the estate of Madam M. de Tro of Hardisty, Alberta, in March 1916. _Edmonton Bulletin_ , 1 March 1916, 9.\n\n_Figure 15._ Rush for Free Homesteads at the Dominion Land Office, Moose Jaw, Saskatchewan, 1908. Peel's Prairie Provinces, University of Alberta Libraries, Postcard 18198.\n\n_Figure 16._ Homestead rush at Edmonton, Alberta, 1 September 1908. Peel's Prairie Provinces, University of Alberta Libraries, Postcard 6839.\n\n_Figure 17._ Women homesteaders near Square Deal, Alberta, c. 1912. Glenbow Archives, NA-206-27.\n\n_Figure 18._ Jane Gentles and sons, First World War. Saskatchewan Archives Board, homestead file 2092263.\n\n_Figure 19._ Eva Iddings of Indiana in front of her claim shack near Fort Benton, Montana. Barrows Collection, Overholser Historical Research Center, Fort Benton, Montana, 1910, BC11, 244.\n\n_Figure 20._ Ontario sisters Caroline (Carrie) Louise MacGregor and Mary Frances MacGregor homesteaded in Sheridan County, Montana, c. 1909. Courtesy Judy Archer (Carrie's granddaughter), Orillia, Ontario.\n\n_Figure 21._ Alice (Alix) Westhead, c. 1906. Glenbow Archives, NA-2925-2.\n\n_Figure 22._ Isobel \"Jack\" May, Sedgewick, Alberta. Currie Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ 31, 181 (1911).\n\n_Figure 23._ Louisa Wittrick farmed with \"Jack\" May, but her responsibilities focused on the domestic realm. Currie Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ 31, 181 (1911).\n\n_Figure 24._ May and Wittrick at Sedgewick. Currie Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ 31, 181 (1911).\n\n_Figure 25._ The \"bachelor girl settler.\" Currie Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ 31, 181 (1911).\n\n_Figure 26._ Qu'Appelle Industrial School students with older generation. Georgina Binnie-Clark, _Wheat and Woman,_ 70.\n\n_Figure 27._ Indigenous people at Victoria Day\/Empire Day at Fort Qu'Appelle, 1912. Georgina Binnie-Clark, _Wheat and Woman_ , 178.\n\n_Figure 28._ Portrait of Georgina Binnie-Clark. Courtesy Mr. Dennis Jenks.\n\n_Figure 29._ Doukhobor women pulling a plough in Saskatchewan, 1902. Glenbow Archives, NA-670-45.\n\n_Figure 30._ Press coverage from 1910 of Georgina Binnie-Clark's activities in England and Canada. _Gleichen Call_ (Alberta): \"Are Booming Canada,\" 9 June 1910, 7; \"Making Girl Farmers,\" 21 April 1910, 7.\n\n_Figure 31._ A pupil from Roedean School, Brighton, learning to farm at the Binnie-Clark farm, Fort Qu'Appelle, 1913. Georgina Binnie-Clark, _Wheat and Woman_ , 402.\n\n_Figure 32._ \"Land and The Woman,\" article by Georgina Binnie-Clark and photographs. _Canadian Courier_ 12, no. 12, 16 November 1912, 16.\n\n_Figure 33._ Homesteads-for-British-Women petition. Library and Archives Canada, Record Group 15, Department of the Interior, D-II-1, vol. 1105, file 2876596, pt. 2.\n\n_Figure 34._ Postcards of supporters of the homesteads-for-women campaign. Library and Archives Canada, Record Group 15, Department of the Interior, D-Ii-1, vol. 1105, file 2876596, pt. 2.\n\n_Figures 35 and 36._ \"Farmerettes\" of Ontario c. 1917\u201318. City of Toronto Archives, William James Family Fonds 1244, items 640 and 640A.\n\n_Figure 37._ Eaton's Department Store advertisement for \"Costumes for the Farmerette.\" _The Globe_ (Toronto), 25 May 1918.\n\n_Figure 38._ \"They Serve France.\" Canadian Victory Bonds poster. Library of Congress, 2003652830.\n\n_Figure 39._ \"Calgary's Land Army,\" _Grain Growers' Guide_ , 10 April 1918, 32.\n\n_Figure 40._ \"Canada West\" poster, 1923. Canadian Pacific Archives, Image no. BR. 194 \nLIST OF TABLES\n\n_Table 1._ The gender of Western Canadian homesteaders and their success rates at \"proving up,\" 1872\u20131882.\n\n_Table 2._ Numbers of male and female agriculturalists in the Censuses of Canada, with percentages of female agriculturalists.\nACKNOWLEDGEMENTS\n\nIf I were to identify when the initial seed of this project was planted it would be the first class I taught at the University of Calgary, a full-year night class in 1992\u201393 on Western Canada. We learn a lot from our students, and in that class one wrote an excellent essay on the homesteads-for-women campaign in Western Canada. It was new to me. Thanks to Richelle Brazunas, wherever you are! Having worked up to that time on how First Nations male farmers were stigmatized and excluded from the commercial grain economy I began to see other forms of exclusion through the distribution of land and roles in the settler colony of the West. And while some women worked to bring about a reconfiguration of this distribution, challenging and calling into question the reigning order of \"common sense\" about who could farm and own land, they (unfortunately) worked in the interests of a privileged few of British ancestry. Yet even if they had chosen another strategy, they would have found that this \"distribution of the sensible\" remained intransigent and impervious to calls for change.\n\nI have drawn on archives and libraries in Canada, the U.S, the U.K., and eventually as far away as Australia. I would like in particular to acknowledge the help of the archivists at the Saskatchewan Archives Board, the Archives of Manitoba, the Provincial Archives of Alberta, and the Glenbow Archives. Among the many archivists and librarians who have assisted me, I want to give special thanks to Sharon Maier, Regina Public Library; Susan Kooyman and Doug Cass at the Glenbow; Chris Kotecki and Eric Hallett at the Archives of Manitoba; Philip Hatfield and Carole Holden at the British Library; and Nadine Charabin at the Saskatchewan Archives, Saskatoon. Irene Kerr, Museum of the Highwood, searched their collection and provided the cover photograph for this book. Thanks also to Ken Robison and Henry L. Armstrong of the Overholser Historical Research Center in Fort Benton, Montana.\n\nThe Social Sciences and Humanities Research Council of Canada assisted me in this study, as did a Killam Research Fellowship. The research funds available to me as a University of Alberta Henry Marshall Tory Chair have been of critical importance to this project. My research in the U.K. was facilitated by several appointments for which I am very grateful: Eccles Visiting Professorship in North American Studies at the British Library; Visiting Fellow, Institute of Commonwealth Studies, University of London; and Visiting Scholar, Centre of Canadian Studies, University of Edinburgh. I visited the Australian National Archives while a Visiting Fellow at Australian National University's Research School of Social Sciences and its Australian Centre for Indigenous History. Thanks to Philip Davies, Eccles Centre at the British Library; Philip Murphy at the Institute for Commonwealth Studies; Annis May Timpson, Canadian Studies, University of Edinburgh; and Maria Nugent, Australian National University.\n\nCountless scholars over many years have inspired and encouraged me, and helped refine and clarify this project, as have conference sessions and invitations to speak or write. Special thanks to Ashleigh Androsoff, Jean Barman, Philip Buckner, Cathy Cavanaugh, Tonia Compton, Nancy Janovicek, Betsy Jameson, Fran Kaye, Nanci Langford, Briony McDonagh, Linda Mahood, Laurie Mercier, James Muhn, Maria Nugent, Adele Perry, Joan Sangster, Nikki Strong-Boag, Georgie Taylor, Nicola Verdun, and Angela Wanhalla. Thanks to my colleagues at the Universities of Alberta and Calgary.\n\nI am very grateful to my research assistants: Gretchen Albers, Alana Borque, Sydney Budgeon, Suzanne Daugela, Karine Duhamel, Corinne George, Patricia Gordon, Leslie Hall, Michel Hogue, Pernille Jakobsen, Amy McKinney, Erin Millions, Cheryl Purdey, Trevor Rockwell, and Claire Thomson. Special thanks to Catherine Ulmer for her help with the South African Scrip women homesteaders of Saskatchewan, and to Sara Tokay, who has been of great assistance with the many tasks of the home stretch.\n\nThe Alberta content of this book was enhanced by the University of Alberta's project Last Best West: The Alberta Land Settlement Infrastructure Project, funded by the Canada Foundation for Innovation, with Peter Baskerville as principal investigator and Sean Gouglas (and me) as co-investigators. The project digitized Alberta homestead files and made them available on the Web. Students and other employees hired for this project created an enormous databank from these files. They also alerted me to interesting homestead stories. Special thanks to Katie Pollock, Leigh Johnson, Silvia Russell, Richard Fletcher, and Melanie Niemi-Bohun as well as to Peter Baskerville and Sean Gouglas.\n\nIt was remarkable the number of people who stepped forward with research and stories, sometimes of family members. Judy Archer of Orillia, Ontario, kindly shared the story and photographs of her grandmother and great-aunt who left Ontario to homestead in Montana because they were denied that right in Canada. Thanks to Douglas Ramsay for his research on Agnes Balfour, and to Matthew Ostapchuk for information on Sarah Cleverly. Doris McKinnon provided me with Marie Rose Smith's homestead file. Thanks also to Joan Heggie, Teeside University, who, after hearing a talk I gave at the conference Women and Land in Hull in 2015, dug into the mystery of farmer \"Jack\" May and made some startling discoveries. I am grateful to Juliet Gayton (Exeter University), who unearthed and clarified information on Alberta rancher Alix Westhead, and also to Lionel de Rothschild, Exbury Estate, and Melanie Aspey, Exbury Archives.\n\nFor information on Georgina Binnie-Clark, I am grateful to her great-nephews Dennis Jenks and Richard Jenks. During a visit to Fort Qu'Appelle, Saskatchewan, I received a warm welcome and a great deal of information from the late Lynn Anderson, and from Derek Harrison, Doug and Marg Dawson, and Beverly Van der Breggan.\n\nEditor Gretchen Albers skillfully prepared the manuscript for submission. Thanks to everyone at the University of Manitoba Press, and in particular David Carr, Glenn Bergen, and Jill McConkey. Maureen Epp did an excellent job of copy-editing this manuscript.\n\nA few sections of this book have appeared as: (1) \"Britishness, 'Foreignness,' Women and Land in Western Canada, 1890s\u20131920s,\" _Humanities Research: The Journal of the Humanities Research Centre and the Centre for Cross-Cultural Research at the Australian National University_ 13, no. 1 (2006): 43\u201360, a special issue from the 2004 conference \"Britishness and Otherness: Locating Marginal White Identities in the Empire,\" Australian National University, Canberra; (2) my introduction to the 2007 reprint of Georgina Binnie-Clark, _Wheat and Woman_ (Toronto: University of Toronto Press, 2007); (3) \"'Hordes of Men of Alien Race' or 'Daughters of British Blood?' The Homesteads-for-Women Campaign in Western Canada,\" _Great Plains Quarterly_ 29, no. 4 (Fall 2009): 267\u201386; (4) \"'My Vocabulary Contains No Such Word as Defeat': Clara Lynch and Her Battle for Her Alberta Homestead, 1900\u20131909,\" _Alberta History_ 61, no. 3 (Summer 2013).\n\nFinally, thanks as always to Walter Hildebrandt for his encouragement and assistance, including accompanying me on excursions to prairie archives, museums, and small towns. I dedicate the book to my grandmother Jean Munn, whose Manitoba homestead roots are a point of origin for this study. My other grandmother, Nell Carter, born Nellie Weaver in Dartford, Kent (1882\u20131973), arrived in Moose Jaw, Saskatchewan, as a bride in 1915. I thought of her, too, as I wrote this book, with its focus on British women, and also about her sisters, who stayed in Kent. Clara, Emily, Florence, and Alice Weaver were all employed from a young age, mainly as teachers, and they did not marry. I am certain that they would have detested the label \"surplus\" women. \nLIST OF ABBREVIATIONS\n\nBWEA - British Women's Emigration Association\n\nCIL - Colonial Intelligence League for Educated Women\n\nCPR - Canadian Pacific Railway\n\nFANY - First Aid Nursing Yeomanry Corps\n\nIODE - Imperial Order Daughters of Empire\n\nOSC - Oversea Settlement Committee\n\nRCI - Royal Colonial Institute\n\nSAS - South African Scrip\n\nSOSBW - Society for the Oversea Settlement of British Women\n\nUFA - United Farmers of Alberta\n\nUJFS - Union Jack Farm Settlement\n\nVBA - Volunteer Bounty Act\n\nWLA - Women's Land Army\n\nWNLSC - Women's National Land Service Corps\n\nYWCA - Young Women's Christian Association\nNOTE ON TERMINOLOGY\n\nWHAT DID IT MEAN TO HOMESTEAD?\n\nWe think of the term today as synonymous with farming, or generally establishing a home in a rural area. But in Western Canada (and the U.S. West) the word \"homesteader\" had a much more specific meaning. It meant that you were located on a free grant of 160 acres on offer from the federal government. You paid ten dollars to legally locate there, and you then had to cultivate and live on the land before you legally owned the land. While by no means entirely \"free,\" given the costs involved in establishing a farm, it was much cheaper than purchasing land.\n\nTHE DOMINION LAND SURVEY\n\nAll of the land in the North-West Territories, with the exception of the \"postage stamp\" province of Manitoba, was under the control of the federal government after 1870. The survey that began in 1871 affirmed Canadian sovereignty over these lands and facilitated non-Indigenous settlement. The land was surveyed into townships of thirty-six square sections. Each section was one mile square and consisted of 640 acres. Sections were further subdivided into four quarter sections of 160 acres each. Township lines run east and west and were numbered north from the international boundary. The lines that run north and south are range lines. The First or Principal Meridian in Manitoba was located just west of Winnipeg, and additional meridians were added as the survey advanced west. For example, the Fourth Meridian forms the Saskatchewan-Alberta border and bisects Lloydminster.\n\nADMINISTRATION OF LAND\n\nIn 1871 the Dominion Lands Branch, a branch within the Department of the Interior, was created to administer the 1872 Dominion Lands Act. There were Dominion Land Offices in towns and cities of the West, employing agents, sub-agents, and homestead inspectors.\n\nSPECIAL SECTIONS\n\nThe odd-numbered sections in each township were railway land grants. The Canadian Pacific Railway was granted 25,000,000 acres. The Hudson's Bay Company was awarded one- and three-quarter sections in each township. Two sections in each township were set aside to support educational facilities and were called school sections. Railway, Hudson's Bay Company, and school lands were available for purchase, and the idea was that as the homesteaders improved their quarter sections they would seek to expand through purchase. The value of the land would increase as the homesteaders improved the land, and other buyers would also be enticed. These sections could also be available for leasing.\n\nENTRY ON A HOMESTEAD\n\nThe even-numbered sections in each township were available as homesteads under the Dominion Lands Act. The homesteader paid a ten-dollar filing fee and chose a quarter section (160 acres). A variety of terms were used for this process: the homesteader \"filed on,\" or \"claimed,\" or \"made entry\" on a homestead, generally in person at the local land office. Homesteaders often found the land unsuitable and then filled out a Declaration of Abandonment that specified why they were unable to farm or reside on that land, after which they were free to file on another quarter section.\n\nWHO COULD CLAIM A HOMESTEAD?\n\n\u2022 Under the Indian Act (1876) no one who was \"Indian\" could homestead.\n\n\u2022 Before 1874, any single woman or any male over the age of twenty-one could homestead. This was changed in 1874 to eighteen years of age.\n\n\u2022 In 1876, entry could be made by any person who was a sole head of a family or any male over the age of eighteen. Single women were no longer permitted to homestead. A woman could homestead only if she was a sole head of household with a minor child or children. This was generally interpreted to mean a widow.\n\nPROVING UP\n\nAfter filing on a quarter section, homestead duties had to be performed for a minimum of three years (and in many cases the process took longer). This process was known as \"proving up\" or \"perfecting\" your entry. Duties included residence and cultivation on the homestead to prove that he or she was a bona fide settler. In each year for three years the homesteader had to reside for at least six months on the homestead.\n\nAPPLICATION FOR PATENT\n\nAt the end of three years, if the homesteader fulfilled all of these duties, she or he gave six months' notice in writing of intention to apply for patent. The homesteader filled out an application for patent or clear title (i.e., outright ownership) that contained information on the applicant and family, including nationality and proof of naturalization and details on breaking\/cropping, livestock, and buildings. Two witnesses, usually neighbours, were required to attest to the truth of the application. Application was made before the local land agent or homestead inspector. If the application was approved, a patent would be issued to the homesteader, who was then the owner of the land.\n\nPRE-EMPTION\n\nFrom 1874 on, a homesteader could obtain a second quarter section of land adjacent to the homestead. At the time of filing on a homestead, the settler could also claim a pre-emption (for an additional ten-dollar filing fee). The homesteader had the right to purchase that land after receiving patent to the homestead and was given three years to make that purchase. Pre-emptions were cancelled in 1890 and restored in 1908, when cultivation requirements were added.\n\nPURCHASED HOMESTEADS\n\nBetween 1871 and 1918, a settler could purchase 160 acres of land within a nine-mile radius of his or her homestead at three dollars per acre.\n\n_Figure 1_. This township map documents the author's family history. Great-great-grandparents John and Mary Graham homesteaded in section 36, and just to the south in section 25, great-grandparents Alexander and Sarah (Graham) Marshall homesteaded. Her grandmother Jennie May Marshall was born here in 1899. Only one woman's name appears on the map, widow Elizabeth Cameron in section 21. Archives of Manitoba, N6411. Dominion Land Survey Township Plan, T12, R15, W, 1873. \nINTRODUCTION\n\nThe map of perfect geometrical squares from southwestern Manitoba that records the homesteaders of Township 12, Range 15, West of the Principal Meridian is like other maps from across prairie Canada\u2014except that this one documents my own family history. In the late 1870s my great-great-grandparents Mary (Kilgore) and John Graham homesteaded the southwest quarter of section 36. Their daughter Sarah Jane, my great-grandmother, married my great-grandfather Alexander Marshall, who homesteaded the adjoining section to the south, and my grandmother Jean was born there in 1899. Other Grahams married neighbouring homesteaders, and the related families of Grahams, Marshalls, Kilgores, Munroes, and McKinnons helped to form the Wellwood community of Scottish and Irish settlers, some of whom had arrived in Manitoba by way of sojourns in Ontario. Many are buried in the Graham-Munroe cemetery on my great-grandparents' land. In the cemetery you can learn the names of many of the early women settlers, as they are not on the map. Homesteading, the right to a grant of 160 acres, was overwhelmingly a male preserve. Married women were not eligible for the homestead grant and single women were excluded after 1876, leaving only women who qualified as \"sole\" heads of households, generally widows with children. There is one woman on the map of Township 12, Range 15: Elizabeth Cameron was a widow whose husband, Hugh, died before he \"proved up,\" or fulfilled the residency and cultivation requirements that came with a homestead grant, and so the patent to the land was issued to her. The death of a husband was one of the main ways a woman obtained land in her own name. It is readily apparent from gazing at any township map how land laws and policies were used to shape a society of male heads of household and dependent females, how the land was not neutral, how ideas about proper gender roles were embedded in the landscape. For most women the only way to get land was to get a man, or have a husband die, or be a widow with minor-aged children, which qualified women to enter or file on a homestead of their own.\n\nThis book is primarily about the failed effort to redraw maps of prairie Canada to include the names of women. British women spearheaded the charge, and at the height of the campaign in 1908\u201314 sought to obtain homestead rights for British and British-Canadian women only, excluding \"foreign\" women and replacing \"foreign\" men. They aspired to settle on what I am calling \"imperial plots\" that would have otherwise gone to \"ignorant, uncouth, lawless foreigners,\" or so they argued, so that refined and educated gentlewomen could contribute to the spadework of empire and plant British culture as well as crops. But this book is about more than the campaign to secure homestead rights for \"British-born\" women; it involves broader questions and debates that took place in both Canada and Britain about the capacity of women to farm, whether it was proper for them to do so, and whether they should participate in activities that threatened to masculinize them and to provide them with independence. It also draws in a much wider ensemble of women agriculturalists than just British women, beginning with the Indigenous farmers of the Great Plains. The book is about how women sought and fought to obtain land and cultivate the prairies, bringing to light many forgotten women farmers and ranchers.\n\nThe promoters, planners, and plotters of farming for British women on the Canadian prairies were middle-class or elite and educated women, located mainly in London, who were devoted to the British Empire. They were obsessed with finding solutions to the perceived problem of \"redundant,\" \"surplus,\" or \"superfluous\" women of the mother country. This book is also about less-privileged women, many British or British-Ontarian and almost all widows, who could spare little thought for the Empire but who came to prairie Canada to claim homesteads to support their families. Many succeeded, others were thwarted, but all faced an obstinate, sceptical, and powerful Canadian federal government bureaucracy. Women with capital who purchased land to farm or ranch on the prairies could escape the surveillance of the bureaucracy that policed the homesteaders, but they were scrutinized in the press and other publications that tended to cast them as abnormal and suspicious. While widespread opposition to the prospect of women farmers began to decline slightly in Britain\u2014where the idea of middle-class women farming small acreages and cultivating the least remunerative and most troublesome crops found a degree of acceptance\u2014powerful opponents in Canada and Canadian officials in England remained fiercely determined to shut almost all windows of opportunity throughout the decades of this study. To find out why this intransigence persisted, the colonial context of prairie Canada is critical.\n\nPrairie Canada was crafted as a colony of the British Empire, and hopes were high for its destiny as the brightest agricultural jewel in the imperial diadem. But the British were to transplant and cultivate not only the crops that would make the prairies the breadbasket of the Empire: here was a \"sparsely-peopled or savage-haunted\" place where they could plant, grow, and prune a \"dominating race.\" Scotswoman Jessie M. Saxby equated cultivation and farming with civilization, using garden analogies and eugenic allusions in her 1890 book, _West-Nor'-West_ , that urged the women and men of Britain to settle on the prairies:\n\nWe should look upon the British Isles as the cradle and nursery of the world\u2014a nursery garden where the best kinds of seedlings and saplings are trained into vigorous young life for the purpose of transplanting into wide gardens, lawns, and woodlands!\n\nWhat sort of a place would the nursery-garden become, what sort of plants would the promising shoots develop into, if incessant and careful transplanting were not carried out? What sort of credit would attain to the gardener who consigned to his customers only diseased, pining, puny, malformed plants?\n\nWe ought to send to our colonies\u2014to the whole uninhabited, or sparsely-peopled, or savage-haunted places of the earth\u2014\"well-assorted specimens\" from our home nursery-garden, and our transplanting of those goodly young shoots should be more systematic, more discerning, and more wholesale than it is at present.\n\n... When shall we fully accept, and show ourselves equal to, our unique destiny\u2014that of a dominating race which must absorb within itself all lower-races, and make itself the ruling power for good of a planet?\n\nDuring the time frame of this book (the 1870s to the 1930s) most of prairie Canada was gobbled up by white settlers, the squares on the map filled with their names. The Canadian West was a settler colony where First Nations were dispossessed and relegated to small reserves and prevented from obtaining other land on their former territory. As anthropologist Patrick Wolfe writes, settler colonies are driven by a \"logic of elimination.\" Indigenous people were not to play any role in the development of the new economy and society, except to serve as relics of a primitive past that were useful for comparative purposes when demonstrating \"strides in the march of progress.\" \"Your noble and idle savage who lives by hunting is dead or doomed,\" wrote an advocate of settling gentleman English farmers in Canada's West in 1885. \"He will not work himself, though he is not ashamed to beg... Another nobler race, quickened with some of the best blood in the 'old country'... should be ready to take its place among the masters of the richest parts of a young dominion.\" Agriculture on reserves was stymied and stifled, a process that was assisted by prevailing views of Indigenous men as inept farmers and shiftless workers. The township of my Manitoba family was on the Treaty One ancestral territory of the Cree and Anishinaabe (Ojibwa or Saulteaux), and there are seven reserves within the boundaries of that treaty occupied by those First Nations. There are also five small reserves of the Dakota, who were not signatory to any treaty.\n\nBritish settlers were favoured, and they were assigned the task of improving the land, which was considered to be lying \"tenantless and silent, only awaiting the Anglo-Saxon race to be transformed into a prosperous and thriving country.\" As an 1888 promotional publication from Manitoba described the prairie, \"Man alone is apparently the missing quantity, and his energy, industry and capital are the required elements in developing the young, but sturdy Dominion into the Greater Britain of the West\u2014the worthy scion of the grand old Motherland across the seas, whose pride is in the colonial gems which adorn the imperial diadem, of which Canada is one of the brightest and most valued jewels.\"\n\nThe use of the term \"man\" was not in this case intended to extend to and include \"woman.\" The job of empire building was man's work; the white, British, male settler or frontiersman was the heroic figure, taming the \"wild frontier into productivity and profitability.\" A 1910 poem valorizing these men of the far-flung colonies praised their work: \"For glory and Empire for home and for beauty; \/ Away on the fringe of Canadian prairies, \/ Far up on the heights of African aeries, \/ Cut off from his kin on Indian stations. \/ The sentinel frontiersman watches the Nations \/ In the bush of Australia way over the Seas, \/ On Islands from Fiji to far Hebrides.\"\n\nMany (ghastly) poems about the Canadian West, including \"The Prairie,\" by Jack Damusey, celebrated the manliness of empire building and the work of agriculture:\n\nI have place for men\n\nWith windy spaces for their square-walled homes;\n\nMy lonesomeness awaits the laugh of those who are young.\n\nYoung men I want:\n\nYoung men,\n\nStripped,\n\nPloughing,\n\nBuilding,\n\nScheming.\n\nIn sweaty jeans,\n\nYoung men with blood and muscles taut and backs of steel\n\nTo tame my winds of winter bleak,\n\nTo bear my summer's heat.\n\nMy breast is rich for them,\n\nBut let them be cruel,\n\nEager like wolves for grain,\n\nI have no valleys for the old;\n\nNo sacred woods for ancient gods,\n\nOnly the dry, windswept waste\n\nThat must be quelled.\n\nEstablishing farms was white man's work in the colonies. In _Sowing Empire: Landscape and Colonization,_ scholar Jill H. Casid writes that colonial farms and plantations \"justified and glorified patriarchally organized and controlled agricultural production and heterosexual reproduction as the necessary bases for family and for national and _imperial_ stability, peace and prosperity. At the heart of this mythic construction of empire is the farm\u2014a cultivated, constructed site of agriculture, of nature improved by the intervention of 'man' that functioned as both the material impress and reproducing sign of empire.\"\n\nIn the colony of prairie Canada, the British man would become more manly than his weaker and effete counterpart in the factories and offices of the mother country. Scottish settler Thomas Spence reported from Manitoba in 1879 that \"his muscles will be iron, his nerves steel. Vigor will characterize his every action; for climate gives quality to the blood, strength to the muscles, power to the brain.\" E.B. Osborn, literary editor of the London _Morning Post_ , wrote in 1900 that \"to live for a year or two in Western Canada is to learn the essential meaning of a man's manhood.\" As historian Philippa Levine has written, \"This vision of masculinity as that which could transform unproductive spaces profitably was simply not on offer to women or to the colonized.\"\n\nColonialism, founded on ideas about racial supremacy, reached its apogee at the same time as the consolidation of the liberal political order, supposedly devoted to ideals of freedom and self-government. Patterns of domination, hierarchy, and exclusion were at the core of liberal states, some of which had extensive and powerful empires. Patriarchy was also necessary to the functioning of the liberal order. Historian Adele Perry argues that \"imperialism and patriarchy were not complications of or exceptions to the liberal order; they were necessary to its very production.\" The \"liberal order project was predicated on the privatization of women and the relegation of non-Western peoples to various states of reduced humanity, savagery, unfreedom, or containment.\" The liberal order was premised on the exclusion of women: Liberal subjects were male and European, and they were the genuine political and economic subjects, while \"women and racialized people were not so, only potentially so, or at best provisionally and partially so.\" The liberal male subject was defined through wives' lack of economic autonomy. Wives were virtually excluded from the basic principle of the liberal contract, the right to own property, and while this was challenged and began to erode over the nineteenth century, this study demonstrates how white, mainly British or British-Ontarian settler men continued to secure exclusive rights to property well into the twentieth century through the exclusion of women and Indigenous people. They were assisted in this task by powerful and pervasive ideas of who constituted a capable farmer and landowner, and who was excluded from this category because they allegedly lacked the necessary strength, determination, knowledge, and skills.\n\nIf the British man became more masculine by crossing the ocean and settling on the prairies, the British woman was supposed to become even more feminine, her domestic role to be confirmed and preserved. While sailing to the colonies was an act of emancipation for men, firing them with new hopes and aspirations, landing them on their own plots where they could be autonomous and creative, women colonizers were vessels to transport and perpetuate British culture and identity. Women were not to quell the windswept waste. British settler women were to be protected, cared for and cosseted, defined and managed. The colonial tasks assigned to them were to make homes and babies, and it was made virtually impossible for them to do otherwise. This was to be the immutable foundation of the new society, the order of nature. Women were to be models of feminine deportment and conduct and of a cherished gender order that was undergoing turbulent challenge and change in Britain, but was to be transplanted to the colony unspoiled and unsullied. Their central duty and mission was to reproduce and to tame the wild colonial males. As summarized by a promoter: \"Colonization without women is futile. Only when women go out at the same time is there a chance of the men settling down soberly and steadily; and besides that, whereas a thousand Englishmen in a colony are a thousand men and no more, every Englishwoman that you take out at the same time carries with her, as it were, four potential English colonists as well.\"\n\nFeminist scholars have pointed out that \"settler colonialism rested on control of female reproduction, not only of indigenous inhabitants, but also of settler women.\" As historian of Australia Jane Carey has written, if \"settler colonialism was driven by the 'logic of elimination' in relation to Indigenous peoples, then the imperative of vigorous white propagation was its necessary corollary.\" In the Canadian West, the category of \"white\" was complicated by the presence of the \"foreign\" migrant, heightening anxieties about the degeneracy of the British fabric of the colony. It was British women who were to reproduce the most vigorously in the face of these racial anxieties.\n\nBritish women were not to toil in the fields, to become muscular and masculine, tanned and dark skinned. Impeccable behaviour and demeanour was expected of them, as they were to serve as sharp contrasts to Indigenous women and to peasant settler women from Eastern Europe. In these \"primitive\" societies, women were understood to be abused and brutalized, made to work outside, while the British allegedly protected and respected proper womanhood by relegating women to the home. The Doukhobors, settlers from Russia, were used to illustrate the stark contrast between the desired and the condemned activities for women. Doukhobor women had hitched themselves to the plough to break land in their settlements and had to \"sweat in the fields instead of horses.\" In Canada they needed to be reclaimed from the \"brute level to which they had been degraded, to the home, with its cooking, its spinning and its weaving.\" Levine writes that \"women thus became a fulcrum by which the British measured and judged those they colonized. Women became an index and a measure less of themselves than of men and of societies.\" In the colonies, British women were to be symbols of cleanliness and purity in contrast to women of other ethnicities, and they were to maintain and display genteel dress and deportment. Kitchen gardens and flower beds were acceptable, as they upheld and perpetuated genteel identities. Farm labour was not acceptable.\n\nBritish colonial women were, as scholar Anne McClintock writes, \"ambiguously placed\" within the process of imperial rule: \"Barred from the corridors of formal power, they experienced the privileges and social contradictions of imperialism very differently from colonial men... [they] made none of the direct economic or military decisions of empire and very few reaped its vast profits.\" They were bound in \"gendered patterns of disadvantage and frustration,\" McClintock writes, as it was \"white men who made and enforced laws and policies in their own interests.\" Colonial women held positions of power over colonized women and men and were thus not \"hapless onlookers of empire but were ambiguously complicit both as colonizers and colonized, privileged and restricted, acted upon and acting.\"\n\nIn prairie Canada, British women and Canadian-born women of British ancestry did not share in all of the privileges often associated with whiteness, such as the \"exercise of power and the expectation of advantages in acquiring property.\" Whiteness did not equate with power and privilege for other groups in the Canadian West, as certain types of immigrants from Europe were denounced as \"foreigners\" who were beneath the British. In the Canadian West, a sense of Britishness combined with whiteness to distinguish the elites who would rule from those who would be subject to rule. Frustrated that they were members of this elite yet did not make decisions, did not reap the profits, and did not enjoy all of the privileges and power of that elite, British settler women behind the homesteads-for-women campaign hoped to garner support by articulating an imperialist vision to demonstrate their fitness for the land denied to them yet available to \"foreign\" men. Situated on their homesteads instead of \"foreign\" men, British women would transport and transplant British civilization. This campaign also involved the denigration and denouncement of \"foreign\" women, in order to elevate their own status and bolster arguments for their entitlement. First Nations women were scarcely even in the picture, as they were relegated to reserves and subject to intense surveillance, laws, and policies.\n\nBut for British women to establish and operate their own homesteads and farms and work on the land was in direct contrast to their assigned role as models of domestic, feminine demeanour and deportment. Working out of doors was a remnant of an earlier, darker time. Only \"primitive\" settler women were obliged to labour in the fields and barnyard. There were grave fears that women were \"changing to masculinity\" as a result of doing work \"which men ought to do.\" According to one expert from 1910, this was a reversion to savagery, as \"women in the savage state were so like men in form that it was well-nigh impossible to tell them apart.\" As this book demonstrates, other British settler colonies shared the same aversion to any public display of women working in the fields. It might be acceptable in England, it was declared in a 1906 letter in an Australian newspaper on \"The Female Farmer,\" because there \"surplus\" women were \"driven into working to support themselves.\" Where white women were in the minority in a colony, however, they were to revert to their proper vocations as wives and mothers.\n\nIf a woman in the prairie West did succeed in obtaining land of her own to farm, she was likely to be seen as suspect, eccentric, and aberrant in her community, belonging in neither the masculine nor the feminine realms. An example was Lizzie Hillis, from Ireland, who homesteaded 320 acres north of Hanna, Alberta, having purchased South African scrip (to be discussed in Chapter 3). Hillis was remembered in her district as being able \"to keep up to any man and do any work he did, even hauling bundles on the threshing crew.\" One year while threshing it took the men \"several days before some of them realized she was a woman.\" She was known as \"Old Lizzie,\" and years of living alone allegedly made her strange, even crazy. She was \"famous for taking after people she didn't like with a pitchfork,\" and that included a priest. Hillis could \"hold her own with anybody and cuss like a trooper.\" While \"her batching\" was described as \"no worse than that of most of the men who were homesteaders,\" the message was clear that for a woman this was deviant and unacceptable. She made her own clothes out of flour sacks, and one outfit she wore had \"a clearly visible 'Alberta's Best' right across her seat.\" She returned to Ireland in the 1920s and died there. But the story of the Hillis farm did not end there. Her sister Mary came from Ireland to Lizzie's land in the mid-1930s and built a new house with an \"absolutely useless\" fireplace. According to the local history she was an \"old maid and partially paralyzed.\" Although a nephew lived with her for a time, she was all alone when she \"took sick and was found by the neighbors frozen to death under her kitchen table.\"\n\nAlthough settler women were to confine themselves to the domestic realm in theory, all women on homesteads\u2014whether widows, daughters, wives, sisters, or mothers; whether British, Doukhobor, or Ukrainian\u2014did a great deal of the physical labour required, particularly in the early years of homesteading and farming. English homesteader Edward West described the work of women in his book _Homesteading: Two Prairie Seasons_ :\n\nOne would meet them trudging alone over the prairie, hunting among the bluffs for stray cattle, or see them helping their husbands to dig out stones, or mounted on a plough or disc driving a team of bulls, or hear tales of how they had helped their husbands to dig wells or build the little shack. In some cases they would hold down the homestead with two or three young children while the husband was earning money (getting a \"grub stake,\" as it is called), or even go out themselves to do the same as cooks while their husbands performed the homestead duties.\n\nLocal histories often detail the work done by \"mother\" to secure the homestead. One son of homesteaders near the Montana-Saskatchewan border described how his mother, Mary Kluth, dug rocks and stooked and stacked grain on their land and for neighbours. She gave birth to a son in their homestead shack a day after baking fourteen loaves of bread, and five days later she was cooking for a threshing crew. In 1914 she made fourteen trips across the border to Malta, Montana, \"hauling grain one way and bringing back posts, wire, groceries, and the year's needs. Sometimes the weather wasn't too good but most of the time she slept under the wagon. Dad dug rock, tried to get more land broke and looked after us kids while Mother was on the road.\"\n\nA mother of six small children on a Saskatchewan homestead described the work she performed in 1905 while her husband was away with a threshing crew. This included building their first sod barn:\n\nThe job was hard and we did not have hardly anything to work with. We had gotten a fireguard broken and it was from this that we got the necessary sod. The two oldest children carried the sod between them on a board and I did the building. As this was an exceedingly slow way as the poor children could not carry enough to keep me busy, I made a harness for the cow and made her help us in the hauling the [ _sic_ ] sod. This was a little better but as the harness was not very substantial, it was breaking continually and made things very trying and because of this I had a job every evening of either repairing the old harness or making a new one. The utensils I had to make the sod level with consisted of an old butcher knife and sticks we found lying around. Finally it was completed and a roof was made from poplar poles which we managed to get out of the valley near by.\n\nAs women's rights activist Nellie McClung wryly observed in 1916: \"Women are doing homestead duties wherever homestead duties are being done... No person objects to the homesteader's wife having to get out wood, or break up scrub land, or drive oxen, so long as she is not doing these things for herself and has no legal claim on the result of her labour. Working for someone else is very sweet and womanly, and most commendable. What a neat blending there is of kindness and cruelty in the complacent utterances of the armchair philosophers who tell us that women have not the physical strength to do the hard tasks of life.\"\n\nYet the conviction that women should not work in the fields and farm their own land, nor be given any official encouragement or sanction to do so, prevailed among lawmakers and other decision makers, and was pressed into service well into the twentieth century. As historian Kathryn Gleadle has argued, the \"perpetuation of a dominant discourse concerning the feminized nature of women's public presence obscured cultural knowledge as to the vigorous activities which women often performed on the ground.\" It was also convenient for authorities to ignore, belittle, or minimize evidence of women's labour on farms.\n\nEnglishwoman, journalist, and Saskatchewan farmer Georgina Binnie-Clark challenged the view that British women were incapable of work on the land. In a 1913 presentation on \"Land and the Woman in Canada\" to the Royal Colonial Institute in London, she made the case that women should farm large acreages and grow grain, the most lucrative crop. Binnie-Clark argued that they were capable of all forms of farm labour, and that British women should be eligible to acquire homestead land so they could play a critical role in the \"spade-work of British expansion.\" She was harshly criticized in the discussion that followed by powerful men in the audience. J. Obed Smith, in charge of the London office of emigration from Europe to Canada and responsible for sending hundreds of thousands of men, women, and children to Canada, was utterly opposed to the idea of women farmers in \"this, that, or any other land.\" He said women were physically incapable of carrying on farming operations, and he \"dissociated himself entirely from the idea that a woman alone could pursue general farming in Canada.\" The next discussant agreed that \"it would be most disastrous not only for the woman, but for the reputation of Canada, for any woman to start grain farming in the West.\"\n\nInfluential men like J. Obed Smith and Frank Oliver, minister of the interior from 1905\u201311, were involved in controversial land speculation themselves, using their positions of influence and knowledge for their own benefit and, in the case of Oliver, to profit his allies and friends. Oliver was particularly adamant and unrepentant that the work of building empire and the profits to be secured were for men only, although this did not include Indigenous men. Oliver was also critical and sceptical of the capacity of \"foreign\" Europeans to assist in the development and settlement of the West.\n\nAll of these groups\u2014women, Indigenous people, Europeans of non-British descent\u2014were marginalized through a variety of political, material, and imaginative systems, or \"structures of constraint\" that perpetuated subordination and inferiority. The idea that women should not work outdoors was particularly imaginative as it defied what was happening throughout the prairies, where women's work was essential to the establishment of the agricultural economy of the West. But men such as Smith and Oliver had little interest in sanctioning any large-scale change that might undermine the benefits and profits accruing to them and their associates. They had a direct interest in asserting the representational system, however imaginary, that there was a \"true\" or \"normal\" gender order that relegated women to hearth and home and banished them from the fields.\n\nA primary reason that women in Canada were denied homesteads was because it would make them \"independent of marriage.\" Frank Oliver believed that \"women were already averse to marriage, and he considered that to admit them to the opportunities of the land grant would be to make them more independent of marriage than ever.\" In my book _The Importance of Being Monogamous_ , I detail Canada's determination to impose the monogamous, lifelong, intraracial, and heterosexual model of marriage on the diverse population of Western Canada as central to the nation-building project. The gendered ideals behind the homestead laws, which established the foundation of the economy and society of the prairies, ensured that women had little opportunity to stray from marriage. Nellie McClung summed up this mentality: \"The reason given for denying homesteads to women is that it will make them too independent of marriage and it is not independent women we want. It is population... It sounds as if the government was afraid that if women could do anything else, they would not get married.\"\n\nThe useful although imaginary idea that women should not work in the fields was clearly articulated by a Canadian general in 1921, when Canada sought to discourage British women, in particular the land army women of the First World War, from imagining they could come to Canada and work on the land or farm land of their own. Brigadier-General R. Manley Sims said that \"it must always be remembered that the Anglo-Saxon never willingly accepts the idea of women for outdoor labor. It is considered, and I think rightly, too heavy for them. It was a war emergency measure and we don't want it continued.\" This sentiment was echoed by a settler from England who wrote an account of his years in Western Canada and found that \"one of the finest of Canadian characteristics [was] the profound reverence with which their women are regarded. Quite rightly they believe that it is not a woman's duty to work the land.\"\n\nCora Hind, agricultural editor for the _Manitoba Free Press_ and a women's rights activist, was asked by an English journalist in the late 1920s if it was possible for a woman to farm in Canada. Hind replied that while it was possible, she did not advise it, and explained: \"You see, a woman can't go on the land as she would in England, for so many of the population of the prairies are low type Central Europeans, who, as a matter of course, make their womenfolk work outside. The result of this is that the Canadian farmer\u2014by that I mean a man of British stock\u2014says, 'I will have no \"white\" women working on my farm,' for he thinks if he does this he is sinking to the level of the 'bohunk.'\" Hind went on to point out that there were only two \"real openings for women in Western Canada. The first is domestic work, and the second is more domestic work\u2014marriage to a prairie farmer.\" There was little hope if even Cora Hind could not advise women to farm in Canada.\n\nThat British women colonizers sought land of their own in the colonies has been overlooked in sweeping studies of the \"great land rush\" or \"rise of the Anglo-world.\" Land seeking has been assumed to be and cast as a uniquely male and particularly British male obsession. Englishman Edward West described his \"hunt for homesteads\" on the prairies, writing that \"it was certainly interesting to see one square half-mile of land after another, with the prospect of owning one of them as a freehold, and one began to wonder if some of the immigration were not due to a sort of hereditary land-hunger, a sort of instinct, inherited from Saxon or other ancestors, to get hold of a bit of Mother Earth, there to have elbow-room and be able to develop ourselves and do our work, without cramping and artificial shackles.\" British women, too, exemplified this \"land hunger\" and tried \"to get hold of a bit of Mother Earth\" to participate in the \"great game\" and be true partners in empire. As many struggled to make a living to rise above poverty at a time when few vocations were available to them, they may have had even more need and desire for land than did the men, who had far more options.\n\nFrank G. Roe, homesteader, historian, and train engineer, described in his memoir how his mother, Mary Ann Roe, from Sheffield, England, proved up on her homestead in Alberta, earning her patent to her land at the age of sixty in 1902. Her husband and Frank's father died of pneumonia just over a year after arriving in Alberta, after he was \"lost on the prairie one night during a terrific rainstorm.\" Yet Mary Ann Roe persevered and flourished, according to her son, as she was a \"born pioneer\" who \"embraced the new life with joyous eagerness.\" In her estimation their tiny sod house, \"standing on its own acres and ours, was no step down in the world but a decided step up.\" Frank G. Roe described a \"passionate longing\" for land that was hardly reserved to men alone:\n\nIt will, one may hope, have been made plain that it was not from any poverty of ideas that such a woman found rest in her soul in the new sphere. Without some historical knowledge of the eviction of the disinherited English peasantry from these ancient \"common fields,\" which once, as their name indicates, were common to themselves conjointly with other classes, it is difficult to realize their passionate longing. The land was to them as the very marrow of their bones. Beyond measure, to such people the possession of acres of their own over which they could stride at will outweighed everything that could be thrown into the scales against it. This was their kingdom and even a sod house could become as a royal palace and she set about to make it one.\n\nSettler women were complicit in the enterprise of dispossessing Indigenous people. They too coveted Indigenous land and resources and were land takers. Migrant women, including those who were British, were homesteaders, speculators, squatters, and purchasers of land, including land fraudulently surrendered on First Nation reserves, and they profited and benefited from the core mission of the colonial project that rested on a foundation of dispossession. But as McClintock reminds us, colonial women were ambiguously complicit; they were both privileged and restricted. They had to struggle for a share in the bounty of Indigenous land, and they faced gendered roadblocks and barriers. As a columnist for the London paper the _Vote_ concluded with resignation in 1927, \"difficulties, almost insuperable, are put in the paths of women who wish, in our Dominions overseas, to be 'settlers' in the true meaning of the word.\" British women were largely unsuccessful in their quest for land of their own to farm in prairie Canada, unless they could afford to purchase it. But through understanding their efforts, their absence from the township maps, as well as the determination of colonial authorities to stymie and prevent them, we can better comprehend how \"the vast, fissured architecture of imperialism was gendered throughout.\"\n\nThe ideal of the independent colonial woman farmer was not confined to the British Empire. In German Southwest Africa there was hope that the single woman settler could farm independently, overcoming the prejudices that prevailed at home. Like Georgina Binnie-Clark, and at exactly the same time, travel writer Clara Brockmann promoted the idea of German women as farmers in African colonies. Brockmann was confident German women could do all the farming tasks a man could and also acquire the experience needed in \"the handling of their natives.\" And as we will see in the chapters that follow, women of many nationalities sought to establish themselves as farmers and landowners in British colonies. \"I had a farm in Africa, at the foot of the Ngong Hills\" is how Isak Dinesen (Karen Blixen), from Denmark, began her memoir _Out of Africa_ about her coffee plantation and six thousand acres of land in the British colony Kenya.\n\nWhile the British colonial context is critical, Canada's proximity to the United States is also essential to understanding the gendered history of the prairies, as the makers of Canada were determined that this British outpost would be forged in the image of the mother country and be distinct from the perceived disarray that prevailed to the south. Canadian laws drawn from the British legal heritage deliberately constituted a world in which white men were the genuine political and economic subjects and women only provisionally so. A British model of gender relations was idealized and emulated, while the perceived gender chaos of the United States was condemned and abhorred. The U.S. West was a much more welcoming environment to migrant women who were single, divorced, separated, or widowed. While still a minority, women homesteaders were significantly more numerous south of the forty-ninth parallel. As historian R. Douglas Hurt has summarized in his recent study _The Big Empty: The Great Plains in the Twentieth Century_ , \"homesteading offered an irresistible opportunity for thousands of women... who considered a quarter section (160 acres) of land nothing less than the promise of independence, freedom and security.\" They homesteaded for economic gain and to enhance family landholdings, and male homesteaders did the same. In states such as North Dakota, women constituted approximately 20 percent of homesteaders, and they proved up on their claims as often as\u2014and in some states with a higher degree of success than\u2014their male counterparts. Most were young and single, but there were also older women, many of whom had been widowed or were divorced. (In both the United States and Canada, married women were denied the right to homestead.) Like male homesteaders, they tended to settle among networks of family and friends, and also like male homesteaders, they generally had jobs that provided the capital necessary to establish a farm. Some, like male homesteaders, sold or rented their land after they proved up, while others stayed and kept their land in the family. The proportion of women homesteaders increased on the Great Plains of the United States in the twentieth century. Hurt concludes that \"homesteading strengthened the influence of women in their families, and it expanded their work roles in the home and community. Homesteading reinforced the ability of women to act independently as self-determining people who took responsibility for their own lives. By homesteading, single women gained access to property, managed their land, controlled resources, and decided how to spend their money.\"\n\nMigrant women to Western Canada were deliberately and systematically denied this access to property and the right to manage their own land and resources. The example of the United States as a situation to be avoided was paramount in the justifications Canadian officials provided for denying homestead rights to women. J. Obed Smith told Georgina Binnie-Clark after her 1913 talk at the Royal Colonial Institute in London that Canada had deliberately departed from the U.S. legislation that permitted single women to homestead, as in his view this had led to \"disastrous results.\" Looking back over the twentieth century, and basing his summary on many studies of women homesteaders in the United States, Hurt does not mention any \"disastrous results\" except that some women consolidated their homesteads with those of their husbands after marriage; that some, like men, failed to prove up; and that some used their land as an investment and moved on. Smith and other Canadian decision makers manufactured an imaginary but useful foil of a foreign land to the south where unscrupulous women were \"sham\" homesteaders, incompetent farmers, and devious manipulators of the laws.\n\nOver the course of researching and writing this book it became a project of unravelling the profound entanglement of colonial and metropolitan histories, and of discovering how the colonial culture of prairie Canada was constituted through a complex interplay of the local, the region across borders, the national, and the imperial. This book is an effort to write a history that looks beyond the nation in order to \"unsettle the naturalness of the nation-state as analytical framework.\" It is about the circulation of ideas and individuals within the British Empire and across the border shared with the United States. While the book stresses the importance of understanding the projects and the \"knowledge,\" assumptions, or understandings generated from metropoles, it is also about how imperial plots and plans were not monolithic but were contested, debated, and disputed in both the \"motherland\" and the colony.\n\nI begin with the ancient agriculture of the Great Plains of North America, where women were the farmers, owning their own land and raising produce for sale as well as for their families. The history of Indigenous agriculture is important in understanding that it was not natural or inevitable that women would be virtually excluded from the category \"farmer\" in the settlement era on the Canadian prairies. That the first farmers were Indigenous women is vital to comprehending why British women colonizers were to symbolize distance, departure, and progression from this earlier and ancient way of life. Chapter 1 then analyzes the gendered and racialized visions that were at the heart of the grid survey and homestead system that blanketed and suffocated Indigenous ways of living on the land. These visions had both American and British imperial antecedents, although there were significant variations in the opportunities for migrant women to own and farm land in British colonies and the U.S. West. There were no obvious and universally shared assumptions about which categories of settler men and women should be given land grants. In prairie Canada, First Nations people were relegated to small reserves where farming was encouraged among males but not females, and on a limited scale that would not require more land. Only a few widows managed to farm on reserves. Land grants to the M\u00e9tis, called scrip, were issued to men, women, and children, but the scrip system was designed to ensure that they were soon divested of their land. Once this stage was set, the Dominion Lands Act prevailed over the distribution of land on the prairies. Under this legislation, single women could obtain homesteads in prairie Canada, and this chapter traces the history of some of the women who claimed land in Manitoba. This right was abruptly removed in 1876 legislation, however, without discussion or debate, and while no official spelled out exactly why, this chapter speculates on the rationales for this deliberate eradication. From then on it was the white male colonizer only who was to make the wilderness productive and profitable. Single settler women were quickly dispatched and relegated to roles as domestic servants and as potential wives and mothers through this change in legislation. Although their labour on homesteads was expected and required, women were not to be the owners of land unless they were widows with children or could afford to purchase land. Just when the homestead right for most women was removed, one other short-lived opportunity was offered to them: the tree claim, which allowed women and men alike to acquire small plots of land to plant trees. The tree claim concept was soon abandoned, however, as it proved absurd in the prairie environment.\n\nThe focus of the second chapter is Britain, and particularly England, where in the nineteenth century the notion of women working in the fields and having land of their own to farm was vigorously debated and discussed. Prominent advocates of agriculture for \"gentlewomen\" arose by the late nineteenth century and succeeded to some extent in countering earlier views that women working outdoors was not feminine, civilized, or progressive. Farming on a small scale, in groups or settlements of women and concentrating on the \"lighter,\" more feminine branches of agriculture, was one of a number of useful vocations proposed as a solution to a perceived surplus of women. There ought to be an \"agricultural brigade of the monstrous regiment of women,\" as coined by one advocate. By about 1910 there was a \"widespread gardening and farming movement among women in England.\" The arguments and rationales that were advanced in Britain are important to understanding the debates in Canada, particularly during the years of the homesteads-for-women movement.\n\nOpposition to women farmers, gardeners, and horticulturalists remained intense, however, and there were hopes that the colonies could provide a more congenial environment where old prejudices and attitudes might vanish. Chapter 2 also considers the hopes and aspirations for British gentlewomen farmers in the colonies, particularly Canada, a cause that intersected and overlapped with that of sending \"surplus women\" to the colonies, as advanced by emigration societies and philanthropic individuals. Farming was one of a number of potential vocations for women in the colonies, and it was hoped that farming could attract migrants not drawn to domestic service, even when that was cloaked in more equal and respectable terms as \"home help.\" Many who advocated that British women emigrate to the colonies assumed that ultimately women of superior upbringing would not wish to soil their hands by working on farms, but would instead settle into their proper and expected functions as wives and mothers of a great imperial race on colonial soil. The colonies, including Canada, wanted domestic workers and were interested in few other categories of women. Colonial training schools for young women bloomed across Britain, and while some provided instruction in poultry or horticulture, all concentrated more on the domestic skills required in the colonies.\n\nIncreasingly, prairie Canada was seen as the most convivial destination for British women wanting to farm over more problematic colonies such as South Africa, where farm work was performed by \"Kaffirs\" while the white woman farmer would have to manage and direct their labour. The prairies were seen (incorrectly) as emptier\u2014a virtually Indigenousless land. The trend in favour of farming in prairie Canada is traced in the _Imperial Colonist_ , the journal published by the British Women's Emigration Association. Other organizations such as the Colonial Intelligence League, also with headquarters in London, sought to send women to Western Canada to farm. Fiction for girls set in the colonies presented robust and independent heroines who took on arduous outdoor work and often owned or managed land of their own. Advocates of the emigration of British women to prairie Canada included devoted imperialist Flora Shaw, of the _Times_ of London, whose proposals were augmented and advanced by Canadian journalist Mary Agnes Fitzgibbon, who advocated a training school for British women in the West that would prepare them to farm land of their own. In the very early years of the twentieth century, promotional publications of the Canadian Pacific Railway also cast women, particularly British women, as efficient owners and managers of farms on the prairies. There were also competing and compelling counter narratives presenting quite an opposite view of the woman settler in the colonies, some fictional and one based on the personal experience of a \"Lady Emigrant\" to Ontario.\n\nFollowing the 1876 legislation, there remained one category of women in Canada eligible to file for the homestead grant: those who were the \"sole\" head of their family. This was interpreted to mean a widow with at least one minor child entirely dependent upon her. A man over the age of eighteen and single was the \"sole\" head of his family even though he had no children, but the rules were read quite differently in the case of women. Chapter 3 details the experiences of some of these female household heads who homesteaded, many of whom were from Britain. The case of Virden, Manitoba, homesteader Susanna Willis, whose land was expropriated from her, demonstrates how very different rules could be applied to male and female homesteaders. Women who were unable to vote and had no political clout were easily expendable. The Willis case also demonstrates that when women homesteaders ended up with very valuable land, it was coveted by others.\n\nOver the years the categories of eligible women homesteaders were narrowed through rulings and decisions made by bureaucrats as they debated just what constituted a \"sole\" head of a family. The morality and virtue of the woman homesteader was policed through the legislation and the bureaucracy that interpreted and enforced it. The separated or divorced woman was subject to particularly intense scrutiny, as were those who adopted children because it was often assumed they had done so only to acquire land. Women were tenacious and inventive in their strategies to acquire and keep their homesteads. Through purchasing South African scrip, many women, regardless of marital status, were able to acquire 320 acres of homestead land in Western Canada, but they had to have significant capital to do so, and they were obliged to prove up on their land. A final strategy of women who wanted to acquire land was to cross the border and homestead in the United States, where single women could file on land and where there was greater leniency toward separated or divorced women.\n\nWomen were free to purchase land in Western Canada, regardless of their marital status, and if they did they could escape the surveillance of the Department of the Interior, although many were still subject to intense scrutiny and, in some cases, censure. Chapter 4 provides a range of examples of women who bought land as investors, speculators, farmers, or ranchers. Women bought land from the Canadian Pacific Railway, they obtained land through purchasing M\u00e9tis scrip, and they bought reserve land \"surrendered\" by First Nations. Jean Laidlaw, for example, originally from England, had a large ranch on Piikani (Peigan) reserve land that was placed on the market despite the protests of members of that First Nation. Some of these women farmers and ranchers attracted considerable attention from the press, becoming minor celebrities. Coverage varied in nature and purpose. Some was purely promotional, in an effort to generate sales of railway land. Feminist journalists were motivated to showcase women successfully establishing farms and ranches to counter prejudice and opposition. Almost all were careful to stress that the women farmers of the Canadian prairies retained their femininity. But some of the press coverage conveyed the message that this was rare, strange, and abnormal work for women. A particular focus in this chapter is the most famous woman farmer of the West, Isobel \"Jack\" May, who was well-known in England before she came to Canada. She was featured in articles throughout Canada, the United States, and the British Empire as the \"bachelor girl\" settler who dressed in \"male attire\" and had a female companion who took care of the domestic work on their Alberta farm. As a result May was subject to particularly close scrutiny. Some years later English author Patricia Carlisle (known also as Miss Peter Webber) briefly farmed in Alberta, wearing \"male attire\" and also with a female companion. The prairies, however, proved to be a hostile environment for women who did not conform to feminine ideals.\n\nThe other famous Englishwoman farmer of the prairies deserves her own chapter. In 1905 Georgina Binnie-Clark purchased a farm at Fort Qu'Appelle, Saskatchewan. She was a writer and had no experience with farming when she arrived on the prairies that summer to visit her homesteading brother. But from then on she became an ardent promoter of farming as a vocation for British women on the Canadian prairies. Binnie-Clark was also devoted to the British Empire and believed that there were many more women like her who could contribute to the \"spade work of British expansion.\" She not only farmed but published many newspaper articles, lectured in England between 1908 and 1914, and wrote two books about her experiences. For a time Binnie-Clark also trained young Englishwomen in agriculture at her Fort Qu'Appelle farm. Binnie-Clark had even grander schemes that never materialized, including cottage training farms that she hoped could be sponsored by the Canadian Pacific Railway. She was more radical than advocates in Britain, as she was not content with small holdings and \"lighter\" branches of agriculture, exhorting women instead that growing grain on large acreages was the most profitable return on their investment in land. She disdained housework, far preferred work on the land, and did not speak or write at any time that she or any other woman required a husband. She challenged the idea that women did not have the physical capacity to perform farm work, but unlike \"Jack\" May, Binnie-Clark was careful to appear in fashionable gowns when she spoke in public (although neighbours recalled her wearing \"britches and leggings\" on her farm.) She helped inspire the homesteads-for-British-women campaign that originated in 1908, was the first to advocate land grants for British women rather than \"foreign\" men, and was the central advocate of that cause in England.\n\nDrawn to the suffrage movement and confronting authorities of the Canadian federal government in various departments, however, Binnie-Clark alienated and aggravated less radical advocates of farming for British women, although she also had influential supporters. She became a lightning rod to those who were utterly opposed to women farmers, such as J. Obed Smith. While Binnie-Clark's 1913 presentation on \"Land and the Woman in Canada\" to the Royal Colonial Institute was perhaps the greatest achievement of her career and for the cause, it also generated harsh condemnation both in Canada and England. Her 1914 book _Wheat and Woman_ , published in England, should have helped to advance the cause of homesteads-for-British-women, but it appeared just before the start of the First World War and interest was diverted to much more pressing issues. Binnie-Clark helped to organize women workers on the land in England during the war, deserting her Saskatchewan farm, and she did not return until the mid-1920s. By that time she had dropped homesteads-for-women, although she continued to promote the settlement of British people in Canada, with an emphasis on families.\n\nWhile Binnie-Clark focussed on England in her lectures and publications, a homesteads-for-women campaign gained momentum on the prairies, and this is the subject of Chapter 6. The women's columns of the prairie farm journals became the focus of the campaign. Isabelle Beaton Graham of the _Grain Growers' Guide_ was the most determined and industrious in generating interest in and support for the cause _._ In 1910 an initial, Edmonton-based petition calling for homesteads for any unmarried woman in Canada over the age of thirty was organized by an American woman who had hoped to settle in Alberta and was surprised to find she could not homestead in Canada. This initiative did not go far but helped to inspire a much more concerted effort, led by women who took pride in their British ancestry and who eventually settled on the strategy of seeking homestead rights for themselves alone, excluding American and other women viewed as \"foreign.\" Like Binnie-Clark, they advanced an imperialist vision to justify their claims for land over the dubious claims of \"foreign\" men. As homesteaders they would help to squeeze out undesirable immigrants and cultivate British civilization along with their crops. Many other rationales were advanced: that women were interested in acquiring homesteads, that they had the strength and knowledge to farm, that they would not be lured to the evil cities but rather enjoy healthy lives in the outdoors, and that potential wives would be attracted to the West for the bachelors. Other rationales highlighted fundamental inequalities in Canada's land laws: families of boys could acquire large estates, while those with daughters were penalized. Women had helped establish homesteads all over the West as wives, yet the land was owned solely by the husband who, with the abolishment of dower rights, could sell without even asking his wife's permission. Single women could homestead in the U.S. West, and Canada was losing its \"daughters\" who headed south. But the rationale that took centre stage was that land should go to cultured and refined women \"of British birth,\" who were \"of strong moral force and high intellectual ability,\" rather than to uncouth \"foreigners.\" This was the core of a petition that was presented to the Canadian Parliament in 1913 with 11,000 signatures. But this tactic created fissures in the campaign, as some regarded it as a \"bald piece of discrimination.\" Opponents in government remained intransigent, even narrowing the eligible categories of women. The idea that women were not capable agriculturalists persisted. Some were convinced that British women were the least likely candidates for the tasks required of homesteaders on the prairies. The strategy of manipulating fears of racial and ethnic \"others\" in order to assist with the \"spade work of British expansion\" and to seek an alliance with and win the support of elite males failed. There were fundamental contradictions in the tactics around this petition, as they invoked prejudice and exclusion while calling for equality and justice.\n\nChapter 7 covers the era from the First World War to the late 1920s, demonstrating that if anything, opportunities for women farmers and homesteaders narrowed over time. The war set back the cause of educated British women farmers in Canada, and although it was revived and invigorated after the war, Canada's \"curiously strong prejudice\" persisted and became even more entrenched. Despite acute labour shortages, in prairie Canada there was no formal mobilization of women for farm work. This chapter analyzes why this was the case, in comparison to the land armies of the United States and Britain and the \"farmerettes\" of Ontario. Having told women they were not physically capable of farm work, it would have been difficult for authorities to suddenly reverse this stance maintained over decades and invite them into the fields. During the war and after, pressure to change the homestead legislation to include all\u2014not just British\u2014women continued, and there was hope that women's wartime service would help to bolster the claim. Advocates of emigration for British land army women hoped farm work and land on the prairies could be obtained in recognition of their wartime service. But there was deep and profound opposition at all levels of government in Canada to British land army and ex-service women as settlers unless as domestic workers. The women were viewed as potentially disruptive and troublesome elements whose wartime work experiences conflicted with the \"true\" and \"normal\" gendered identities perpetuated on the prairies. In the British settlement schemes of the 1920s there was an emphasis on families, or in the case of single landholders, on male agriculturalists and female domestics. Land and farming in the West remained overwhelmingly masculine, and the First World War helped to further this aim.\n\nThe goal of establishing British women homesteaders and farmers on the prairies withered and died in the 1930s. A brief conclusion makes this point by discussing the return of Georgina Binnie-Clark to her Saskatchewan farm and her short-lived and ill-conceived Union Jack Settlement, a plan to plant families rather than single women on imperial plots. There could not have been a worse time to initiate such a venture than the drought and Depression of the 1930s. In 1930, however, women (with the exception of First Nations women) were finally granted the right to homestead in Alberta under new provincial legislation, and hundreds took advantage of this offer. While a study of their experiences awaits their historian, they must have been disadvantaged by the Depression that gripped the prairies. Difficulties they faced would have been compounded by the fact that they had to choose homesteads in areas avoided by previous generations of settlers. The conclusion also discusses the persistent \"constraining myths\" that reinforce traditional gender relations and continue to marginalize women as farmers.\n\nImperial plots for British women were thus few by the 1930s, despite decades of effort to establish that they could be capable agriculturalists. They continually confronted the objection that farming would interfere with their ability to perform their most important work as wives and mothers. It was perhaps General Bramwell Booth of the Salvation Army who put this most succinctly in 1921, when he declared that \"Canada's two chief needs are a more thorough cultivation of the land and more God-fearing mothers in her homes... there is need all over Canada for more attention to the cultivation of children.\"\nCHAPTER ONE\n\nNARROWING OPPORTUNITIES FOR WOMEN\n\nFROM THE INDIGENOUS FARMERS OF THE GREAT PLAINS TO THE EXCLUSIONS OF THE HOMESTEAD REGIME\n\nOften in summer I rise at daybreak and steal out to the cornfields; and as I hoe the corn I sing to it, as we did when I was young. No one cares for our corn songs now.\" These were the words of Hidatsa farmer Buffalo Bird Woman (Maxi'diwiac) around 1912, when she was a resident of the Fort Berthold Indian Reservation in North Dakota. There she farmed a small plot of corn according to ancient methods. By that time there were very few Indigenous people who retained knowledge of their crop production methods, and fewer still who continued to practise them. In Indigenous America, women had been the farmers wherever there was agriculture, including on the Great Plains and in what is now Ontario. They were far more than \"gardeners\"\u2014the crops of women farmers of the Great Plains were the main economic drivers of their region's economy. These same crops continue to play a major role in the economies of Canada and the United States. The example of the ancient women farmers of the Great Plains demonstrates that it was not natural or inevitable that women were to be virtually excluded from that occupation in Western Canada as intensive settlement and the homestead regime took root. Nor was it inevitable that Indigenous people too were almost completely excluded from the new agricultural economy; both processes took work.\n\nThis chapter begins with Plains women agriculturalists and ends with the narrow and confined opportunities for immigrant women to obtain land and practise agriculture that were in place in Western Canada by the mid-1870s. It argues that gendered and racialized visions were at the heart of ideas, policies, and laws about property rights and land apportionment and improvement in Western Canada. Some were borrowed from the United States while others reflected the practices of the British imperial world. Yet women's access to land varied widely in these locations. Ideas, laws, and policies about which categories of women should have land and which could farm land were cultural constructs; they were not shared by all, as the example of homesteading single women in the U.S. West demonstrates. Canada made a very deliberate decision to depart from the U.S. model and ultimately excluded virtually all women but widows from the land grant of the homestead system.\n\nThe survey of the land into square homesteads covered and smothered Indigenous ways of living in the West, and it was intended to do so; those defined as \"Indian\" were denied the homestead land grant and instead relegated to reserves. The rights of immigrant women to homestead in Western Canada changed over the 1870s: single women could file on land until 1876, when the legislation was deliberately changed to exclude them. A significant number of women filed on land in Manitoba in the early 1870s and were more successful than their male counterparts at \"proving up\" and earning patents to their land. After 1876 there remained only one category of women who could homestead: widows with children. A short-lived opportunity to acquire a small grant of land was extended to all migrant women (regardless of marital status) in the late 1870s under the Forest Tree Culture legislation, but this window too was soon shut, as tree farming proved impractical on the prairies. In a few short years the Great Plains were transformed from a land where women had been the farmers to one where agriculture was overwhelmingly masculine, as was the ownership of land that was the foundation of this economy.\n\nFIRST FARMERS\n\nAgriculture long predated the arrival of Europeans on the northern Great Plains, and women were the farmers, raising corn, beans, squash, melons, pumpkins, and sunflowers. They excelled in the art of plant domestication, developing hardy, early maturing varieties of corn that could flourish even in the short growing season of the northern plains, and that could withstand hail and drought as well as early frost. Dried produce was made into a variety of products for families and communities, as well as for sale to neighbours and to European traders; the women were commercial farmers. For this time and place and available technology, this was large-scale agriculture and should not be dismissed or diminished as \"horticulture.\" It was also more than a trade or vocation; sacred songs and ceremonies were a central component that were critical to the work and success of the farmers and were handed down by women over generations. Indigenous women were deeply attached and strongly committed to caring for the land.\n\nEuropean observers wrestled with the sight of women farmers and traders; their comments generally contained a mixture of praise and disparagement. Describing the Arikara, one of the Upper Missouri village people, Scottish botanist John Bradbury wrote in 1810 that \"the women, as is the custom with Indians, do all the drudgery, and are excellent cultivators... I have not seen even in the United States, any crop of Indian corn in finer order, or better managed than the corn of their villages.\"\n\nThe most northerly of the upper Missouri River village agricultural people have long been assumed to be the Arikara, Mandan, and Hidatsa, but there is archaeological evidence that the village agricultural complex reached farther north into Manitoba. There was an agricultural settlement at Lockport, north of present-day Winnipeg on the banks of the Red River, between 800 and 1700 CE. Archaeology has revealed storage pits, bison scapula hoes, grinding stones for milling seeds, charred corn kernels, and ceramic vessels at this site. There are strong archaeological indications of other early agricultural settlements in Manitoba, although much evidence has been lost because of intensive cultivation of the land. An agricultural earth-lodge settlement of Cree in the Touchwood Hills of present-day Saskatchewan in the early nineteenth century grew \"considerable quantities of maize and potatoes.\"\n\nHidatsa farmer Maxi'diwiac was born about 1839 in an earth-lodge village along the Knife River in present-day North Dakota and moved to the new Like-a-Fishhook village established in 1845 by the remnants of the Mandan and Hidatsa. In the mid-1880s the people of that village, including Maxi'diwiac, were dispersed onto individual allotments on the Fort Berthold Indian Reservation. Maxi'diwiac passed along her knowledge of agriculture in meticulous detail to anthropologist Gilbert L. Wilson, who published _Agriculture of the Hidatsa Indians: An Indian Interpretation_ in 1917 (later published as _Buffalo Bird Woman's Garden_ ). Although Wilson's texts supposedly present the actual words of Maxi'diwiac, this is likely not entirely the case, but her knowledge is there, conveyed in words and sentences that were chosen and written down by Wilson. She did not speak English, so her son Edward Goodbird translated and interpreted her words. The text that resulted from this collaboration provides the most detailed account of Indigenous agriculture ever published, and as Jeffery R. Hanson writes in a new introduction to the text, \"One cannot read _Buffalo Bird Woman's Garden_ without marvelling at the array of technical skills which Hidatsa women developed and applied to everyday life: agriculture, architecture, construction, storage, crafts, and cooking constitute just a few of the dimensions of knowledge which Buffalo Bird Woman and other Hidatsa women contributed.\" Men played virtually no role in farming aside from assisting with the harvest and cultivating tobacco.\n\n_Figure 2._ In a field of corn and squash, \"Sioux Woman,\" the daughter-in-law of Hidatsa farmer Maxi'diwiac (Buffalo Bird Woman), demonstrates traditional farming methods of the Great Plains agriculturalists using a bison scapula hoe, 1912. State Historical Society of North Dakota, item no. 0086-0281. Photo by Gilbert L. Wilson.\n\nMaxi'diwiac explained that farmers preferred the bottomlands of the Missouri, where the soil was soft and easy to work, rather than the open prairies, where the soil was hard and dry. Before the introduction of iron implements, they could not have broken the prairie sod, as they used tools fashioned from the shoulder blades of bison. By Maxi'diwiac's time, iron hoes and axes were generally used rather than bison scapula hoes and wooden digging sticks, and her grandmother Turtle was one of the last women to use these traditional implements. Her hoe was precious; she kept it under her bed and \"when any of the children of the household tried to get it out to look at it, she would cry, 'Let that hoe alone; you will break it.'\"\n\nFarmers had individual plots, although there were also family plots worked with other women family members, particularly daughters. Maxi'diwiac's mother died when Maxi'diwiac was six, but she had three other women she called \"mother,\" sisters of her mother and wives of her father. She was also very close to her grandmother Turtle. These women worked their fields together. To prepare a new plot the land was first cleared, a task the men might assist with. The land was then burned, which \"left a good, loose soil.\" Every spring once the frost was out of the ground, the fields were dug up: \"Every foot must be turned up and loosened with the hoe\u2014a slow and toilsome operation.\"\n\nMost of Maxi'diwiac's narrative is devoted to the intricacies of corn cultivation. She provides a detailed account of the nine varieties of corn raised in her village, including their uses and characteristics. Corn planting started in May and could continue well into June, depending on the variety of seed. Hidatsa women were up before sunrise in planting season, preparing the hills they returned to each year. Of the varieties of corn that were grow, flint was the hardiest, as it could mature in just ten weeks and escape the early frosts of the northern plains.\n\nPlatforms or stages were built, where girls and women came to watch the crops, scare off predators, and sing. Maxi'diwiac explained, \"We cared for our corn in those days as we would care for a child; for we Indian people loved our gardens, just as a mother loves her children; and we thought that our growing corn liked to hear us sing, just as children like to hear their mother sing.\" Watching began in earnest in August as the corn ripened. The watchers' songs were usually love songs, as young men of the village would visit the platforms where the girls were stationed.\n\nThe corn was threshed in booths, under drying stages. The finest and longest ears of corn were braided, and from these the seed for the next spring was selected, using only the kernels in the centre of the cob for seed. Enough seed for two years was gathered from corn, squash, beans, sunflower, or tobacco, in case of a poor crop the next year. A family's corn supply usually lasted until August of the next year. Supplies were stored in deep cache pits, dug by the women and accessed through ladders. The caches held not only dried corn but dried meat and pemmican and dried wild produce, including berries and \"pommes blanches,\" or prairie turnips. Each family might have up to four cache pits. Fur trader, explorer, and writer Alexander Henry wrote in his journal in 1804 that \"so numerous about the village are these pits that it is really dangerous for a stranger to stir out after dark.\"\n\nWomen raised and dried produce for their families and also for sale. Their villages were visited by neighbouring Plains people, who traded their buffalo robes, skin, and meat for corn and other produce. Sometimes the village people travelled out to the plains to trade. Henry described Mandan women preparing for a trade fair: \"We observed the women all busy, taking their hidden treasures and making preparations for the approaching fair. I was surprised to see what quantities they had on hand: I am very confident they had enough to serve them at least twelve months without a supply of flesh or anything else.\" In 1804 Henry accompanied a party of Mandan and Hidatsa to meet the Cheyenne and Arapaho. Henry wrote that the women \"had their horses loaded with corn, beans, etc. themselves and children astraddle all over, like farmers going to the mill.\" They exchanged their produce for \"leather, robes, smocks\u2014as if at a country fair.\"\n\nThe agricultural people of the plains also established trade with Euro-American\/Canadian traders and explorers. Henry wrote that \"we purchased sweet corn, beans, meal and various other trifles. Having bought all we required, which was 3 horse loads, we were plagued by the women and girls who continued to bring bags and dishes full of different kinds of produce.\" American explorers Meriwether Lewis and William Clark in 1804 bought huge quantities of produce from the Mandan, noting on one occasion that \"a number of squaws and men dressed like squaws brought corn to trade for small articles with the men.\" Describing the trade in corn, geologist Ferdinand V. Hayden wrote that the women of one village sold from 500 to 800 bushels in a season to the American Fur Company and that the trade was \"carried on by the women, who bring the corn by panfuls and the squash in strings and receive in exchange knives, hoes, combs, beads, paint etc., also tobacco, ammunition, and other useful articles for their husbands. In this way each family is supplied with all the smaller articles needed for a comfortable existence; and though the women perform all the labor, they are compensated by having their full share of the profits.\"\n\nMany ceremonies and rituals, both public and private, were involved in achieving successful crops. The cultivated plots were sacred and thought to have souls that had to be cared for like children. The Goose society of the Mandan and Hidatsa, made up of women farmers, was devoted to the rites required to ensure good crops, including fertility and rainmaking rites. The largest and most important ceremony of the society was held when the first water birds arrived; it was believed that corn spirits went south each fall with the water birds, where they were cared for by Old-Woman-Who-Never-Dies. Respected members of the Goose society were believed to have corn spirits in their bodies. Other rituals performed by society members to protect crops included saying a prayer when each seed was planted and rubbing their bodies and clothing with sage each day when returning from the fields. Women farmers left offerings of meat, hide, or cloth. Sacred bundles hung on poles protected the crops. All of the crop was to be cherished and none of it wasted. In the Arikara legend of \"The Forgotten Ear,\" a woman heard a child calling when she was about to leave her field. \"She searched and found a small ear of corn she had overlooked, and when she gathered in that ear of corn the crying stopped.\"\n\nEuropean male observers wrestled with the fact that Plains women worked the land, owned their fields and their crops, and traded their surplus produce. They diminished women's work in various ways. It was often noted that because women were the agriculturalists, men were disdainful of working the land. Artist George Catlin wrote that among the Mandan, \"the old women [were] the owners of fields or patches of corn (for such are the proprietors and cultivators of all crops in Indian countries, the men never turning their hands to such degrading occupations).\" Another tendency of European observers was to criticize and disparage the skills and technology of women farmers. In his _Ethnography and Philology of the Hidatsa Indians_ (1877), Washington Matthews wrote that \"their system of tillage was rude. They knew nothing of the value of manuring the soil, changing the seed, or alternating the crops... they had no regular system of fallowing. They often planted a dozen grains of corn or more to the hill, and did not hoe very thoroughly.\" Matthews saw improvements in farming on the reservations, since ploughs were used, and also because \"the men apply themselves willingly to the labors of the field; and the number of working men is constantly increasing.\" This was not the opinion of Maxi'diwiac, who thought \"our old way of raising corn is better than the new way taught us by white men.\" Maxi'diwiac's people were instructed to plant corn on fields prepared by ploughs on the open prairie, but \"these fields on the prairie near the hills I do not think are so good as our old fields down in the timber lands along the Missouri. The prairie fields get dry easily and the soil is harder and more difficult to work.\"\n\nRudolph Friederich Kurz (1818\u201371), a Swiss painter and writer who visited the Upper Missouri village people between 1846 and 1852, carefully weighed the issue and was less condemnatory than others. He believed that \"agriculture is the basis upon which is builded [ _sic_ ] every firmly established state. In tilling his land the savage becomes attached to the soil and loyal to his native land. Upon husbandry depends settled habitations, spacious country residences; as the result of husbandry, business thrives, inventions are called into being, arts flourish, sciences are in demand, and laws are enacted for the better morality and better government that is essential to the prosperity of a state.\" Unlike other observers, Kurz did not dismiss Indigenous agriculture as \"gardening\" because it was done by women; he wrote that \"whether men or women worked the land when they first began to farm is a matter of no consequence. That the Indians did actually cultivate their land throughout the region lying between the Mississippi and the Atlantic Ocean is a fact to which travelers and adventurers who have visited this country since its discovery by Columbus collectively testify\u2014all of them, whether Spaniards, Frenchmen, or Britons.\" He also defended Indigenous women working the land against claims that this was cruel and brutal treatment: \"That Indian women work the land is not due to racial coarseness or brutality but to the fact that the men regard war as their chief aim in life... According to the contrary argument, European nations, where country women willingly work in the fields, must also be called cruel and brutal. It is far better for women to till the land, which is no disgrace, than to starve or beg alms.\" Kurz was certain, however, that once the land was densely colonized and settled, Indigenous women \"will have to adapt themselves to the same order of things,\" meaning that they would disappear from fieldwork. To Kurz, women working the land was not the normal or natural gender order.\n\nEven scholars who gained a deep appreciation for the knowledge and skills of Plains women farmers nonetheless labelled their work as \"gardening,\" as somehow less than \"agriculture,\" which was considered the work of modern man. George F. Will and George E. Hyde, who published _Corn among the Indians of the Upper Missouri_ in 1917, both praised and diminished the work of women farmers in this passage:\n\nMost of the early accounts give the impression that the women were drudges who were forced to perform most of the heavy labor, including that of the fields. To those who are acquainted with the Indians it will be easily understood that this conception of the position of Indian women needs to be considerably modified. While there is no question that the women's work was severe, yet there is abundant evidence that the women performed their tasks willingly and took great pride in doing their work well. To those who have seen the Indian woman patiently and solicitously working about her garden it must be evident that she loved her work there and enjoyed it. As a matter of fact in the Upper Missouri region the spring was longingly awaited as the time to commence work on the gardens which furnished much of the pleasure of the summer season; and the harvest time, though a season of rejoicing, yet was also a time of regret for the pleasant summer passed.\n\nThe Indian woman was a real gardener. Her methods were not those of the bonanza farmer of the present day, but resembled more closely that of the modern market gardener or greenhouse man. She attended to every little detail, working slowly and carefully and taking the utmost pains. She knew the habits of each of her plants and the habits of each separate variety of all the species cultivated, and she worked with careful regard for these differences.\n\nAside from being skilled in cultivating crops, the Indigenous people of North America, and particularly women, were experts in the science of plants and their environments, and they knew how to sustain and nurture the resources they drew upon for their own purposes and those of future generations. Over millennia they accumulated a vast, specialized, and complex knowledge about plants, their habitats, soil varieties, weather patterns, and seasonal changes. The Blackfoot, for example, drew on approximately 185 species of plants for food, ceremonies, housing, crafts, and medicines.\n\nGENDERED VISIONS: LAND SURVEYS AND GRANTS IN THE UNITED STATES\n\nThe land survey that Canada adopted from the United States and that carves up western North America has been described as \"one of the most astonishing man-made constructs on earth.\" The \"immaculate grid\" of perfect squares is particularly striking from the sky, forming a stunning patchwork quilt. It was not just lines that the surveyors set down on the land, it was a social ideology. As historian Ian McKay has written, \"Perhaps the _pi_ _\u00e8_ _ce de r_ _\u00e9_ _sistance_ of the Canadian liberal order was to carve upon the map, in lines that majestically remind us of Euclidean geometry and panoptical state power, the perfect geometry of the Province of Saskatchewan: perhaps even more impressive, however, than this quadrilateral demonstration of panopticism was the molecular checkerboard of quarter-sections and individual properties contained within the province's boundaries\u2014a social ideology set down on the land and hence made part of everyday western experience.\"\n\nThe grid, the policies and laws governing who could live on it and who could not, and the enormous bureaucracies needed to apply these rules and regulations moulded and sculpted the societies planted on it. The legacy of those rules remains, just as the grid remains. At the time of his retirement from government service in 1880, Canada's first surveyor general, Colonel John Stoughton Dennis, took pride in his role applying the perfect grid survey and formulating public lands policy in the Canadian West at a time when, in his view, \"the country was as a _white_ sheet.\" But the country was far from being a white sheet or blank slate. The West was home to ancient societies, and the grid obscured and ignored land use and tenure systems that were based on generations of accumulated knowledge of and sensitivity to the great variations in the landscape. The grid transformed Indigenous land into the \"public domain,\" meaning it was no longer owned by or available to the First Nations. Surveys created resentment, anger, and resistance. First Nations were excluded from living on the grid and confined to reserves. Immigrant women were discouraged from occupying land on the grid except within family units.\n\nThe grid framework was far from a uniquely _Canadian_ liberal order that was imposed on the land. The immaculate square survey is also the most obvious example of the long-standing and overwhelming influence of the United States on Canada. The graph paper extends seamlessly across the forty-ninth parallel\u2014a major step toward \"continental integration\" a century and more before the term was in vogue. As historian Chester Martin writes, the United States was a \"veritable quarry\" for Canadian policy. The perfect grid system was appealing to both nations because it expedited the mapping, absorption, and individual ownership of the terrain. It permitted the land to be sold, bought, and owned in the most uncomplicated and timely fashion. The grid set the stage for both Canadian and American federal governments to become real estate dealers on a massive scale.\n\nIt was American Founding Father Thomas Jefferson who decided after the American Revolution that the simplest, most advantageous method was to survey the land before occupation and divide it into simple squares, replacing the surveying technique known as \"metes and bounds,\" a haphazard system in which parcels of land were described by distinctive characteristics of the landscape and the property lines of previously surveyed lots. The master grid would be formed by \"principal meridians\" of longitude and \"base lines\" of latitude. There were to be thirty-six-square-mile \"townships\" divided into one-square-mile lots called \"sections,\" which were further divisible into half sections and quarter sections.\n\nThe grid system had many unique advantages. It facilitated the taking of the land from Indigenous inhabitants, creating instead an army of occupiers on small holdings. It assured clear boundaries and titles, avoiding turmoil and squabbles. Once a parcel of land was surveyed it could be singled out from any other square mile of territory from a land office hundreds of miles away. Every parcel of land had its unique identity. It was an ideal system for buying, trading, and speculating in land. There were disadvantages as well. The survey was laid down without any regard for terrain, climate, or soil. Many of the squares of land throughout North America would prove to be hopeless prospects as farms.\n\nThere was much more than commerce, convenience, and mathematics at the heart of the square survey. A desired cultural landscape was to be sculpted through land policies, and ideas of gender and race were at the heart of this ideal society. Jefferson believed that America's virtue rested on an agricultural foundation, and his vision was that these measured boxes would provide the framework around which a democracy would grow. At the centre of this agricultural economy would be the small family farm's independent yeoman\u2014an individual male who was \"virtuous, hard-working and faithful to the republic.\" Jefferson declared in 1787 that \"those who labour in the earth are the chosen people of God, if ever he had a chosen people, whose breasts he has made his particular deposit for substantial and genuine virtue.\" With farmers happily occupying their squares, it would be impossible for wealth and power to become concentrated in the hands of a few. Jefferson's vision was of a white, Anglo-Saxon republic of small-scale farmers, and he had concerns about other types of immigrants. Women were central to this vision as the reproducers of the ideal society of independent yeomen. Women were to be subservient to the yeoman farmer; they were to be on the land but under the control of men. As historian Peter Boag writes, \"The land itself then was to play a major role in the preservation of the 'natural' gender order.\"\n\nJefferson's system of survey for the land in the western territory was passed by Congress in 1785. The free homestead system came decades later, after acrimonious debate and in stages. The United States Homestead Act of 1862, setting out just who could live on the grid and with what settlement duties or payment, provided that \"persons over the age of 21 who were citizens or immigrants who had declared their intention to become citizens\" were eligible to file on up to 160 acres of surveyed land on the public domain. A homesteader had to cultivate the land, improve it by constructing a house or barn, and reside on the claim for five years. If these conditions were met (called \"proving up\"), the homesteader received full title, paying a fee of only ten dollars. Homesteaders could also gain quicker ownership of their land by exercising a \"commutation clause\" after six months of residence, which allowed them to purchase their homestead at the minimum cash price of $1.25 per acre.\n\nGender issues were at the heart of the debate over the wording of the U.S. legislation. Determining the eligible and desirable classes of persons for the land grant was not straightforward or obvious. Should only married men be eligible, ensuring that families would be established on the land? Should married men get more land than single men? Should grants of land go to young single men, capable of bearing arms, to build up an army of occupation? What categories of women should be eligible for the land grant? Congressmen changed their minds on the issue over the many years of debate. Proposals included excluding women entirely, permitting only widows with children, and permitting single women with children. There were weighty and lengthy deliberations on the eligibility of abandoned and divorced women. Widows were the most unproblematic category. As historian Tonia Compton argues, widows \"had already demonstrated their commitment to the gender order by having married.\" If they had children, widows were legally considered heads of households, and it was unanimously agreed that the land should go to heads of households. The eligibility of women who had children \"out of wedlock\" was discussed, and the conclusion was that granting them land was an \"utter impossibility,\" although the stand was later relaxed in practice.\n\nIt was assumed from the start (as later in Canada) that a married woman\u2014who was legally, civilly merged with her husband\u2014was under the husband's protection and control, and that for her the homestead privilege was out of the question. The result was that other categories of women, such as those who had never married, as well as widowed or divorced women, were granted this privilege in the U.S. federal legislation of 1862, despite the fact that most other rights of citizenship, such as voting, were denied them at this time.\n\nThe place of single women in the homestead scheme was the most perplexing and troubling question. In 1852 one congressman mocked the suggestion that homesteading would benefit \"maidens\" by asking if it was intended to \"propose a clause, providing for all the old maids in the country?\" Some argued women would never take advantage of the offer of land because they could not endure the hardships. Compton found that for congressmen it was difficult to accept the idea of single women living by themselves on homesteads. Other objections included that women could be defrauded by devious men who would use them to obtain land. And what would happen when a male and female homesteader married, each having claimed land while single? (This was to become a thorny and vexing issue.) Arguments for the rights of single women to acquire homesteads included \"They have as much right there as bachelors,\" and that \"if a female desires to possess a home, and is willing to conform to the requirements of the law, there is no reason why she should be an alien to the justice or the charity of her country. If she is unfettered by marriage ties she has the same natural right to be provided a home from the public domain that the unmarried man of the same age has.\" Supporters argued that the land grant could serve as a dowry for single women, helping to encourage marriage and ensuring the growth of the population of the West.\n\nThe right of single women in the United States to homestead under the 1862 Homestead Act was not the result of, and did not result in, a high estimation of women's ability to farm. Women in the American West had to \"negotiate a rocky terrain, littered with the racialized and gendered expectations which accompanied the American efforts to establish an empire in the West.\" Nor was there any great disruption to the dominant gender order as a result of women's enhanced property rights through the homestead privilege. Women's right to land was still tied to marital status. Women figured largely in debates about homestead bills not because they were ever intended to be the primary beneficiaries of free land measures, nor because Congress intentionally sought to hold out the promise of land ownership to women, but because homesteading was the foundation of the \"imperial enterprise\" in the West and women were central to this enterprise. White woman loomed large as \"wives, mothers, potential wives and former wives through the discussions about free land and western expansion.\" They were an essential component of the plan to populate the West with the \"right kind of Americans.\" They were to be the foundation of the families of the West and were sent to fulfill traditional gender roles, but at the same time they needed to be adventuresome, plucky, strong, and capable. The role of African American women in homesteading received no attention in debates over the free land grant.\n\nIt was not obvious, either, which categories of men should be granted the homestead privilege. Congress debated extensively about whether to include only married men\u2014heads of households\u2014and exclude single men. Race was also an issue. In 1854, for example, a congressman from Alabama proposed that \"any single free white male\" should be allowed to claim land. The 1862 legislation permitted freed slaves to homestead, and the act also extended land grants to naturalized citizens\u2014those who were not yet but would become citizens. Running through the debates about the various homestead measures was the idea that the process of transforming the land would create and shape American citizens out of foreign immigrants.\n\nThere were variations in the land laws of the states and territories, indicating that there was no obvious category of persons for land grants. In Oregon, for example, the Donation Land Claim Act of 1850 granted 320 acres to every unmarried white male citizen over the age of eighteen, and twice that amount (640 acres) to married couples, with the husband and wife each owning half of the grant in their own name. Also eligible for the Oregon land grant were \"half-blood\" Native Americans. In Texas, the federal Homestead Act did not apply because (as in British Columbia) Texas retained control of its public lands upon admission to the Union. Texas legislators limited the opportunities for single women to homestead, favouring single males and male heads of families. There were, however, approximately 1,500 women who filed homestead claims in Texas between 1845, when Texas was admitted to statehood, and 1898, when homestead land was no longer available.\n\nGENDER AND LAND GRANTS: THE BRITISH IMPERIAL CONTEXT\n\nThere was also a British imperial context to the system of survey and land settlement that was adopted in Western Canada. As historian John C. Weaver has explained, in the nineteenth century the globe was \"overlaid with rectangles, squares and triangles... maps defined the empire's nature\u2014transforming the exotic to the knowable, implementing science, dominance and separation.\" In each colony the appointment of a surveyor general was the first step in establishing a systematic approach to surveying acquisitions. In New Zealand, Australia, and South Africa, the landscape was ordered into individual holdings with reference to longitude and latitude, although rarely was the North American checkerboard adopted completely. New Zealand was the first location of a systematic topographic survey for the purposes of land settlement. As a surveyor in that colony explained: \"The main object of a colonial survey is to enable the settlement of the Crown lands to proceed on a system of survey and record, which, for the settler, will give him possession of a definite piece of land which cannot ever after be overridden by a rival claim.\" A system of registering land rights, linked to the scientific colonial survey, also characterized the white settler colonies of the British Empire. Known as the Torrens system, it was first devised for South Australia in the 1850s.\n\nThroughout the British settler colonies there were significant variations in the opportunities for British immigrant women to obtain land and potentially farm that land; moreover, the rules and regulations did not remain static but continually changed. Historian Kathryn Hunter found that in southeastern Australia the issue of land for single women troubled colonial authorities throughout the nineteenth century. In 1819 Eliza Walsh arrived in New South Wales with her married sister and brother-in-law, and, as she put it, \"made up my mind to settle a Farm in this country.\" She purchased a farm, and then sought more land, asking to have the same grant of land available to male \"Settlers according to means,\" which would permit her to cultivate and raise stock on a larger scale. Governor Lachlan Macquarie refused, stating it was \"contrary to late Regulations to give Grants to Ladies.\" Macquarie explained his reasoning to another official: \"I consider it very bad practice (except in some extraordinary and pressing cases of necessity) and very injurious to the Interests of the Colony to give grants of Land to single women. I have declined for some time past making such Grants on the ground that such persons are incapable of cultivating Land, and thereby not adding to the resources of the Colony.\"\n\nWalsh persisted, pointing out that \"it does not appear altogether a just measure to exclude ladies from making use of their money for the benefit of the Colony in consequence of their sex, nor can it be deemed a real objection that a Lady should not be able to conduct a Farm as well as a Gentleman.\" In the mid-1820s legislators decided that women (and men) possessing capital were eligible to receive grants of land. Walsh eventually received a grant of land but not until 1827.\n\nBy the 1860s attitudes about single settler women and land in southeast Australia had shifted, so that married white women were excluded but single women included. Land was then available to any man, widow, or single woman over the age of twenty-one for a price of one pound per acre, and land was surveyed in blocks from 40 to 320 acres. Historian Patricia Grimshaw demonstrated that in the Wimmera district under the terms of the 1869 Land Act, single women over eighteen and widows could select land, while married women could not. Single women were also granted Crown leases. Grimshaw found that single women selected land by or near other family members, helping to increase the size of family holdings. Hunter found land files from the state of Victoria demonstrating that a considerable number of single women selected land and farmed. The probate records also revealed the \"constant presence of women in farming in this wheat growing region.\" In Horsham, female farmers represented 21 percent of probated farmers between 1874 and 1900.\n\nBy the late nineteenth century there was concern in Australia that allowing single women to select land was discouraging marriage in the colony. In 1878 the suggestion was made to the Victorian Crown Lands Commission that married rather than single women be permitted to select land, in order to encourage marriage and to allow married couples to increase the viability of their farms. The matter was debated again in 1884, when amendments were made to the Land Bill and one Member of the House of Representatives \"pleaded the claim of married women, who are debarred from selecting.\" In his view married women deserved land more than single women for the following reasons, as described in the newspaper _Border Watch_ : \"The wives of selectors have been in the colony for years, they have proved themselves excellent colonists, and yet they have fewer rights than the single woman who landed from the old country yesterday... The fairer plan, Mr. Dow thinks, is to permit selection by the mother of families.\"\n\nOne category of married women could obtain land in Australia, although they did not exactly own their land. Through a system of \"marriage grants\" in South Australia, New South Wales, and Western Australia beginning in 1848, sections of Aboriginal reserve land were granted to Aboriginal women who married non-Aboriginal men. The woman could occupy the land for life and was entitled to enclose, clear, and cultivate the land, and upon her death the licence could be renewed in favour of her \"lawful offspring.\" This was not outright ownership; the state acted as trustee of all reserve land and the woman had permission to occupy the land. As Protector of Aborigines Matthew Moorhouse explained in 1848, the wife would not be disturbed on her land \"so long as she lives with her husband and they continue steady and industrious.\" The policy was intended to encourage legal, Christian monogamous marriage between Aboriginal women and non-Aboriginal men. The land was a form of dowry or enticement, but one that could not become the property of the husband. Such policy was also meant to encourage \"steady and industrious\" habits. There were changes in the marriage grant system over the years, but versions of it remained until 1911, when attitudes of officials toward these marriages had changed, complications emerged about who could be categorized as Aboriginal, and available land declined. Historians Mandy Paul and Robert Foster found that the records of these grants reveal the persistence of applicants in their struggle for land. Typical was Julia Simpson, who wrote the Protector in 1905: \"Will you kindly help me by getting me so many acres of land that I am entitled to... I think I would be able to get a living here by keeping fowls pigs & also a garden.\"\n\nNew Zealand had similar land enticements as incentives for interracial couples to legalize their marriages. Land grants were awarded to couples from the 1840s, but the system departed from that of the Australian colonies, as the title was in the name of the European husband, although he had no right to sell, mortgage, or lease the land.\n\nTHE SURVEY AND LAND GRANTS IN WESTERN CANADA\n\nThe grid (with the exception of river lots in some of the settlements that had predated the survey) was quietly and quickly adopted for Western Canada by 1869. This was a departure from the systems of survey used in the older provinces of Canada, where there were several lot and road patterns. That the uniform grid would be imposed on the West was decided with little consultation outside of a small circle, and no debate. The people residing in the West, overwhelmingly Indigenous people\u2014First Nations and M\u00e9tis\u2014were left completely out of the discussion. Imposing the grid on the West was the task of Surveyor General Colonel John S. Dennis. Dennis consulted with the U.S. Land Office as well as with officials of the Canadian Crown Land Department in coming up with exactly the same rectangular survey of townships and sections as had been adopted in the United States, with one main deviation: Dennis proposed larger townships consisting of sixty-four squares of 800 acres each. However, this idea was rejected in the interests of perfect, seamless conformity with the U.S. grid.\n\nWith the exception of the \"postage stamp\" province of Manitoba (one-eighteenth of its current size), the land in the Prairie provinces, then called the North-West Territories, and the District of Keewatin became the Dominion of Canada's vast inland empire with a \"stroke of the pen\" in 1870, and the land remained in federal control until 1930. The Manitoba Act of 1870 provided that \"all ungranted or waste lands\" were to be administered by the Government of Canada. Canada's secretary of state was responsible for administering this land until 1873, when this responsibility was handed over to the new Department of the Interior. The main discussion about the North-West that took place in May 1869 focused on few details of the survey, as there was a sense that great haste was required to immediately secure the territory for the new Dominion in the face of potential U.S. encroachment. The survey, the maps to document the survey, and a railroad would together declare the land as belonging to Canada, and these needed to be accomplished immediately. There was brief mention of \"free grants\" of land in the House of Commons in 1869, but no discussion or debate. The survey was needed, and immediately\u2014after that decisions could be made about who would live within the squares.\n\nIn the summer of 1869\u2014before the transfer of Rupert's Land (as the Hudson's Bay Company named the territory they claimed) to the Dominion of Canada, before any treaties with First Nations, and before the survey plan was formally approved by order-in-council\u2014Dennis was sent to the Red River settlement to begin the survey of the Principal Meridian. At this time Canada had no legal right to send surveyors west, and they had no authority to begin surveying. Dennis's son later wrote in his history of the surveys made under the Dominion lands system that \"in doing this, an approval of the scheme was anticipated which might not have been obtained, but no doubt it was realized that any scheme adopted would, in its main features, resemble the one proposed, and would authorize the survey of the country into rectangular townships.\" In the fall of 1869, the survey was the catalyst for the \"troubles\" with the M\u00e9tis at Red River, under the leadership of Louis Riel. The M\u00e9tis made up the largest population segment of the Red River settlement and had existing claims to property. Dennis's surveys therefore alarmed them. They resented the fact that they had not been consulted or informed, they feared their land rights would be disregarded, they feared a loss of livelihood, and they objected to the kind of survey that was reshaping the landscape and disregarding their river lots. The complex events that followed are beyond the focus of this book and have been the subject of many studies. The M\u00e9tis achieved some of their goals through their resistance, including recognition of their French language and Catholic rights, and \"provincehood\" for Manitoba, although these achievements were ephemeral or soon undermined. They also received a land grant of 1.4 million acres, to be distributed according to an ever-changing set of rules quite distinct from the free homestead system. Thus the land disposal system of Western Canada was immediately more complex than in the United States due to M\u00e9tis resistance to the survey and the second, complicated tier of land allotment policy devised for them.\n\nWhen the \"troubles\" ended the survey continued, with a few deviations for the river lots of the M\u00e9tis settlements along the Red and Assiniboine Rivers. The new lieutenant governor of Manitoba, Adams Archibald, appointed in 1870, helped to advance the process. He favoured adopting the U.S. survey with no deviations, arguing that this system was known \"all over the world to the Emigrant classes\" and that \"a lot of 160 acres is the acknowledged extent of an Emigrant's requirements for farm purposes.\" Archibald also looked to the United States in his recommendations regarding regulations governing the distribution of these lands. On 1 March 1871, an order-in-council endorsed the adoption of the American system of survey of townships of thirty-six sections, and the free homestead system, also as administered in the United States. In April 1871 the House of Commons debated some of the details of Canada's homestead legislation. An order-in-council approved on 19 April 1871 amended the policy in the light of some of these criticisms, bringing it even more into line with the U.S. legislation. Canada's 1872 Act Respecting the Public Lands of the Dominion was passed \"without opposition and almost without discussion.\" Ten years earlier the U.S. legislation was a stormy and protracted measure compared to the quiet and quick passage in Canada. A system of road allowances and adjustments for the earth's curvature were the main departures from the U.S. model. The proximity of the American West compelled Canada to adopt a similar approach, and quickly, in order to attract settlers to a setting that was already more daunting because of its colder climate and shorter growing season. It was also difficult to access, until the Canadian Pacific Railway was completed in 1885.\n\nINDIAN RESERVES\n\nAs the grid enveloped and altered the homeland of Indigenous people, small \"reserves\" of land were set aside for those who entered into the treaties that began in southern Manitoba with Treaties One and Two in 1871. According to these agreements, land was granted on the basis of 160 acres per family of five or less (in proportion to family size), although the Dakota received about half that amount of land, as they were regarded as \"not British Indians\" and were not permitted to enter into treaties. More land was granted in later treaties, but in comparison to the generous grant of 160 acres plus the opportunity to expand through second homesteads and pre-emption available to any male newcomer over the age of eighteen, the reserves were tiny. There were no mechanisms to expand reserve land; sons could not acquire neighbouring land as sons of settlers could under the homestead system. There were, however, detailed provisions under the Indian Act to alienate or \"surrender\" portions or all of reserves. Nor could any individual identified as an \"Indian\" obtain land off a reserve. In Treaty Three, the North-West Angle Treaty, reserves were not to \"exceed in all one square mile [640 acres] for each family of five, or in that proportion for larger or smaller families.\"\n\nWithin these reserves there was no individual ownership of land, although \"location tickets\" to small plots were issued to males who could pass these down to heirs. According to the federal Indian Act (1876), these location tickets could be issued to males or females, but in practice they were granted to males only. Women came into possession of location tickets generally only as widows; the widow would receive one-third interest and the rest would go to any children. In 1884 a new clause was added to the Indian Act stipulating that the widow would receive the location ticket \"provided she be a woman of good moral character and that she was living with her husband at the date of his death.\" The result was that widows were virtually the only women who farmed on reserves (just as they were the dominant category of women homesteaders), and they were fairly rare. Implements, oxen, and any other forms of assistance with agriculture promised under treaties were distributed to males, despite the fact that from ancient times women had been the agriculturalists on the Great Plains.\n\nExamples of widowed women reserve farmers include two on a Manitoba reserve in 1895 who had \"model homestead[s].\" One of them, the \"Widow Macleod,\" had \"a very fine new house, costing her some six hundred dollars.\" She was unusually wealthy. According to the agent, \"This was the last of a comfortable competency (eight thousand dollars) left by her father, the late Angus McBeth of the Hudson's Bay Company, a few years ago.\" Widow Macleod was one of the few reserve farmers who owned oxen, cattle, horses, chickens, wagons, mowers, and horse rakes, and raised grain and potatoes. Acreages under cultivation were tiny compared to the surrounding non-Indigenous farmers. A widow on the Alexander reserve in present-day Alberta was regarded as having a sizeable farm in 1896, with two acres of wheat, an acre each of oats and barley, and three-eighths of an acre of potatoes and vegetables. She also had \"a good house, two pretty fair stables, one steer, one heifer, ploughs, harrows, forks and axes.\" Widows could be moved off their location ticket land, however, at the discretion of officials of the Department of Indian Affairs and be replaced with a man perceived as capable of farming. This was the case with a widow on the Enoch reserve in Alberta who was removed and replaced in 1915 after her son died. She was compensated with $100 from band funds and signed a consent form with her mark.\n\n_Figure 3._ This 1882 map for \"intending settlers\" shows the dominion lands surveyed to the west of the border of Manitoba. The new and final route of the Canadian Pacific Railway to the south of the Qu'Appelle River and roughly parallel to it is illustrated. Indian reserves of the Treaty Four (1874) people appear on the map, not all in locations well-suited to agriculture. There was soon pressure to \"surrender\" Indian reserve land that was desirable for farming and close to the CPR. Peel's Prairie Provinces, University of Alberta Libraries, Map 597.\n\nVirtually excluded from the occupation of agriculture, women on reserves had few means of acquiring income. In southern Manitoba, where the \"pass system\" meant to keep people on their reserves was generally not enforced, reserve women of the early twentieth century sold their baskets, mats, moccasins, and beadwork off-reserve. They also gathered and sold Seneca root and berries. A few worked as domestics and seamstresses. Some worked in the fields of neighbouring farmers at harvest time. It was a common sight to see them in the harvest fields after the threshing crews were done, \"picking up what grain they could gather off the ground around the straw stacks. This grain was put in bags and then loaded on their buggies or wagons to be taken to the local elevators to be sold.\"\n\nOn the Kainai (Blood) reserve in southern Alberta, the largest in Canada, there was only one woman farmer in the 1920s and '30s. Marcia Belly Fat had first worked as a dressmaker in Lethbridge and in the early 1920s returned to the reserve and asked for land that she could cultivate. She was the only woman to drive a truck, and it was said she \"worked like a man.\"\n\nThe possession of land through the homestead system was made possible through the dispossession of the land and resources of First Nations, who were excluded and isolated on reserves. Their economic marginalization and deteriorating health were the results of Canada's nation-building program. Famine followed the disappearance of the buffalo. With poor housing and inadequate substandard rations, reserve people were susceptible to tuberculosis. The completion of the Canadian Pacific Railway in 1885 brought new waves of diseases; as historian James Daschuk writes, the railway was a \"fatal disease vector.\" Prairie reserve populations reached demographic lows by the early 1890s. As their lands were occupied and access to resources restricted, there were, as ethnobotanist Nancy Turner writes, \"direct impacts on virtually every aspect of their food systems, technologies, medicines, and Traditional Land and Resource Management Systems, including ceremonial practices and belief systems.\" Resources, species, and habitats were irrevocably changed.\n\nWhile officials disregarded and discredited Indigenous peoples' knowledge and systems of caring and managing their land and resources, there was some knowledge exchange, at least in the early settlement era. The daughter of homesteaders in the Cypress Hills of Saskatchewan remembered that the \"Indian women were a great help to my mother.\" They taught her how to keep a fire going, how to clear up diaper rash, how to \"wrap the babies Indian style when they were real tiny,\" and how to preserve berries for winter.\n\nReserve farmers faced many obstacles, including drought, frost, hail, and prairie fire; they also received little of the assistance promised in treaties in their transition to an agricultural economy. Yet by the late 1880s, agriculture was beginning to succeed on some prairie reserves, prompting their farmers to expand their acreages under cultivation and move in the direction of commercial farming. Yet just at that time reserve farmers were instructed to drastically limit their land under cultivation. The Department of Indian Affairs implemented a \"peasant\" farming policy on arable reserves in Western Canada that decreed reserve farmers cultivate only an acre or two, grow root crops, use rudimentary homemade implements, and have one cow (rather than cattle herds). The peasant scheme for reserves in Western Canada was devised to ensure that Indigenous farmers did not require any more land and that they not compete with non-Indigenous farmers. It was also intended to assist with the diminution of Indigenous land, which ultimately happened, particularly in the early years of the twentieth century. Agriculture never did become the foundation of an economy that could sustain people on reserves, despite all of the promises made in the treaties.\n\nM\u00c9TIS SCRIP\n\nAccording to Section 31 of the Manitoba Act of 1870, 1.4 million acres were granted to the M\u00e9tis of Manitoba. It was decided that those who were categorized as M\u00e9tis would not be granted reserves, nor would they be given parcels of land that had to be improved over a number of years before patent was granted, as with the homestead system. They were not assisted with agriculture as the treaty people were to a modest extent. Adams Archibald was an architect of the plan, and his goal was to ensure that the land did not long remain in the hands of the recipients. He recommended the land granted to \"half-breeds\" be surveyed in the same way as other land. He urged that Canada ignore the request of the French M\u00e9tis to have land laid off in one block, with no right to sell for at least a generation. Archibald was concerned that such land would be \"absolutely inalienable\" for a long period, which was \"feudal.\" He advocated that the M\u00e9tis be given outright title to land, an \"absolute deed,\" and he anticipated that they would \"as a class, be ready to convert their land into something they can use and will be sure to sell.\" It is clear Archibald hoped that the granting of outright title would mean that the land would quickly be sold and the M\u00e9tis dispersed. Archibald described the M\u00e9tis as \"hunters by profession, not farmers. Where the Buffalo go, they go. They could not bear the restraints which cultivation of a farm implies. They would rather forfeit their lots, than settle on them, if by settlement was meant, some degree of cultivation and improvement on the Lots.\"\n\nCertificates or notes, variously referred to as scrip, warrants, or bounties, were issued in Canada and the United States, and in colonies of the British Empire, as a means of payment for services and claims. In Western Canada there were land bounties for military and police service. Grants of land were awarded to early members of the North-West Mounted Police, to soldiers who participated in the Red River resistance in 1870, in the North-West Resistance of 1885, and in the South African War, although the terms of these varied. Most grants were devised and garnered support as a means of making the West white, military, and masculine, although we will see in a later chapter that purchasing South African scrip became one settler way for women to obtain homestead land in Western Canada.\n\nIn settler societies where lands and entitlements were awarded to Indigenous people as individuals rather than as collectives, the result was inevitably more lands transferred to the control of colonial powers or settlers. In Manitoba, adult M\u00e9tis were granted money scrip that could be exchanged for Dominion lands, while M\u00e9tis children were granted individual patents to 240 acres. Scrip commissions, inaugurated in 1885, extended the process to the M\u00e9tis of the North-West. They were offered money scrip (a coupon payable to the bearer and exchangeable at the Dominion Lands Office), or land scrip that required the grantee to be present at a land office to apply the scrip coupon to a legally defined parcel of land (240 acres), for which a patent would be issued. The scrip could be transferred or conveyed prior to the issue of the patent.\n\n_Figure 4._ M\u00e9tis women and men at a sitting of the M\u00e9tis Scrip Commission at Devil's Lake, Saskatchewan, 1900. Scrip was issued to M\u00e9tis women and girls as well as to M\u00e9tis men and boys, unlike the gendered restrictions of the homestead system. Saskatchewan Archives Board, S-B9750.\n\n\"Widespread corruption, if not outright fraud\" was the result of the individual and transferable rights awarded to the M\u00e9tis. William Street, a lawyer from Ontario who was a member of the 1885 scrip commission, described what happened to one M\u00e9tis woman at Qu'Appelle who reluctantly agreed to receive money scrip, despite the disapproval of her community about participating in the process:\n\nI prepared, and handed to her, scrip for $160.00, explaining its nature to her, and she went out of the door and was received by a crowd of curious friends, to whom she exhibited her scrip. They were not pleased with her for having allowed herself to be persuaded to come before us, and had almost succeeded in satisfying her and themselves that her scrip was valueless, when Charles Alloway, the agent of a banker in Winnipeg who, with other speculators, had come after us to purchase the scrip from the half-breeds, stepped up and offered her $80 in cash for it. This she gladly accepted, and the money was handed to her in clean, crisp $10 bills. The news quickly spread that we were really giving something which could be turned into cash, and from that hour we were besieged from morning til night by applicants.\n\nThe Qu'Appelle M\u00e9tis example demonstrates how a community could be quickly \"shunted to the fringes of the new society.\" From at least the 1860s there were many Qu'Appelle M\u00e9tis engaged in agriculture on an extensive and sophisticated scale, but almost all left their lands in the first few years after the advent of homestead settlement. Historian Lyle Dick has found evidence that they were divested of their lands by fraudulent means. Throughout the prairies there were frauds and abuses that deprived the M\u00e9tis of most of their land. Speculators used a number of tactics, including forgery and impersonation, to acquire land due to scrip holders. Imposters claimed to be the scrip holders at the land offices. As a columnist wrote in 1911: \"There are today in Winnipeg and elsewhere in the West, men who are in the millionaire and near-millionaire classes, who laid the foundation of their fortunes, and made the bulk of them, by their dealings in scrip.\" These included prominent men such as Donald Smith, Lord Strathcona. Charles Alloway, mentioned in the quotation above, had helped to establish the largest private bank in Canada, Winnipeg's Alloway and Champion Limited. The bank made huge profits by dealing in M\u00e9tis scrip, reselling lands to other speculators and to settlers. Charles Alloway, who was \"at home in the bush and fluent in Indian languages, facilitated most of this business.\"\n\nScrip was issued to women and girls as well as to men and boys, so there were many M\u00e9tis females as well as males who appear in the records of the Dominion lands. The files trace how scrip was acquired and reassigned. In 1905, for example, Isabella Favel made application for a quarter section of land in Saskatchewan, \"upon which I desire to locate half-breed land scrip to which I am entitled, and for this purpose I now deliver to Robert McIntosh of Saskatoon, sub-agent for the Regina district, scrip note number A7494.\" This land was then assigned to Winnipeg lawyer Benjamin Chaffey, who specialized in M\u00e9tis scrip, and the patent was issued in his name. Chaffey acquired thousands of acres of land in Western Canada. The local history of the Bailey district of Saskatchewan notes that the scrip of three M\u00e9tis women, Alice McKay, Agnes Archie, and Catherine Maurice, were all transferred to a Duncan McMartin through the work of the Regina law firm Balfour, Martin, Casey and Brown.\n\nWomen were among the purchasers of M\u00e9tis scrip, to be discussed in greater detail in Chapter 4. They included Sarah Green, the English wife of Scotsman John Sanderson, celebrated as Western Canada's homesteader number one, who filed on land near Portage la Prairie in 1871 and received his patent in 1881. Novelist and Manitoba settler Robert J.C. Stead wrote that \"although English, she [Sarah Green Sanderson] must have had some of the canny qualities of her husband, for she seized an opportunity to acquire a neighbouring quarter section by means of a half-breed scrip.\"\n\nHOMESTEAD RIGHTS\n\nThe definition of \"persons\" originally permitted to homestead under Canada's 1872 Dominion Lands Act closely adhered to the U.S. model. Homestead rights were not for First Nations\/Native Americans in either nation; they were to be confined to reserves in Canada (reservations in the United States). In Canada the 1876 Indian Act specifically excluded all those defined as \"Indian\" from the right to homestead. In the Prairie provinces a homestead was available from 1872 to \"any person who is the head of a family, or has attained the age of twenty-one years, who is subject to Her Majesty by birth or naturalization shall, after the 1st day of May 1871, be entitled to be entered for one quarter section [160 acres].\" The applicant had to pay a ten-dollar filing fee. Patents would not be granted before five years (later reduced to three), when the \"settler or his widow\" had to satisfy the land office that \"he or they have resided upon or cultivated the land for the five years.\" The homesteader had to prove up by having sufficient acres under cultivation, a habitable dwelling, and living for the required months per year on the land. To receive a patent (title in fee simple or outright ownership) a homesteader who was not a British subject had to be \"naturalized.\" (Naturalization was a process available to every person twenty-one or older who was \"not an idiot, lunatic or married woman\" who had lived in Canada for not less than three years. The applicant had to then swear an oath of allegiance and an oath that he or she intended to remain in Canada.)\n\nThis wording of Canada's original legislation, whether deliberately or not, permitted single women to file for homesteads. In contrast to the U.S. Congress debates about the suitability of women as homesteaders, there were no discussions about the issue in the Canadian House of Commons. If there were private debates, the records do not appear to have survived. An examination of earlier British North American colonial and later provincial legislation reveals that the place of women in free land grants was not obvious and straightforward, or natural. The instructions to Governor James Murray in 1763, for example, gave women\u2014except for Indigenous women (and men)\u2014remarkably equal consideration: \"one hundred acres of land [were to] be granted to every person being Master or Mistress of a Family, for himself or herself, and fifty acres for every white or black, Man, Woman, or Child, of which such Person's Family shall consist.\" Loyalist women acquired free land grants as married women and widows (although these grants were smaller than those received by men), and the daughters as well as the sons of Loyalists were entitled in equal measure to free land. These grants began as 100 acres for a head of household, plus 50 acres for each member of a Loyalist family. Prominent people, including women, got far more. Chief Justice Powell's family received over 12,800 acres; of this his wife and their seven children received 1,200 acres each. An 1848 free grant system for the Crown Lands in the Wellington and Huron districts, however, excluded women, permitting \"settlers being subjects of the Queen, males, and not under the age of eighteen years, [to] be assigned each a lot of fifty acres.\"\n\nThe most immediate Canadian precursor to the Dominion Lands Act was the Free Grants and Homestead Act of 1868, a statute of the Legislative Assembly of Ontario that was intended to encourage immigration and settlement. This legislation deliberately included both men and women, without regard to marital status. Following an 1869 amendment, allotments of up to 200 acres were available to any \"person... of the age of eighteen years or upwards.\" The wording of the legislation included both \"he\" and \"she.\" The person had to swear that he or she was eighteen or older, had not previously located any land under the act, and believed the land was suitable for settlement and cultivation. Patents to the land could not be issued for five years following \"settlement duties,\" which included at least fifteen acres cleared, at least two acres under cultivation each year, and a habitable house built.\n\nThe intensive labour that was required in Ontario to first clear the land and the hardships of the immigrant experience were described by English \"gentlewoman\" Susanna Moodie in _Roughing It in the Bush; Or Life in Canada_ (1852). Another memoir, the candid _Letters from Muskoka_ (1878), written by an anonymous Englishwoman and published in London, would not have inspired women to take advantage of the free land grants in that region of Ontario. The author was the widow of an army officer; they had been stationed in India, but since her husband's death she had been living in France. Her financial situation was dire, and the move to Ontario was part of a family strategy, as two sons and a married daughter also took up land. A son had gone out to Muskoka a year before. \"Emigrant Lady\" decided to join him there in 1871, taking with her an unmarried daughter. Her free land grant of 100 acres was beside her son's and son-in-law's grants. While the book contains humour and some happy moments, it is a grim portrait. The author describes life in the \"Bush\" as dreary, \"dull and primitive.\" There was no church, doctor, or town, nor proper roads to reach any of these. There were \"fearfully cold,\" \"dreadful winters of close imprisonment,\" followed by summers when they were besieged by mosquitoes. The neighbours were all \"steerage\" class people. It was possible to get a daughter of a settler to work as a servant, but such girls insisted on \"a footing of perfect equality with every member of the family, and have no inclination whatever to 'sit below the salt.'\" She described local Indigenous people as \"degenerate samples of 'Red Men!' The men appeared to me undersized and sinister-looking, the squaws filthy and almost repulsive.\" All of the settlers had to work desperately hard to clear land before they could cultivate anything. \"Emigrant Lady\" herself did not do this sort of labour but rather cooked, making do with few ingredients. There was almost no fresh meat, even wild game was scarce. But she wrote that \"an Indian officer in our regiment had declared she could make a good curry out of an old shoe,\" and she persevered. By the end of the second winter, she wrote, \"We remain striving, struggling and hoping against hope, that success may yet crown our endeavours.\"\n\nPart II of _Letters from Muskoka_ takes place two years later, but matters have improved little. \"Emigrant Lady\" feels deceived by the accounts of Muskoka that they had been given before they arrived; the \"capabilities of its soil for agricultural purposes have been greatly exaggerated.\" Years of extensive clearing would be required, and \"constant amelioration of the land by means of manure and other applications before it will be capable of bearing heavy grain crops; it is a poor and hungry soil, light and friable.\" The only reliable crops were oats and potatoes. Her eldest son's health and strength declined, as did her own. They all \"looked upon Bush life in the light of exile to a penal settlement without even the convict's chance of a ticket-of-leave.\" The conclusion to her account of four years on her free grant of land was bleak: \"I went into the Bush of Muskoka strong and healthy, full of life and energy, and fully as enthusiastic as the youngest of our party. I left it with hopes completely crushed, and with health so hopelessly shattered from hard work, unceasing anxiety and trouble of all kinds, that I am now a helpless invalid, entirely confined by the doctor's orders to my bed and sofa, with not the remotest chance of ever leaving them for a more active life during the remainder of my days on earth.\" Perhaps this description of the misery and destitution she endured inspired modifications to homestead legislation in Ontario.\n\nChanges to the Ontario legislation revoked the right of most women to obtain land grants or homesteads in that province, and privileged married men with children. In the 1890s (exact date not clear) the Regulations under the Free Grants and Homesteads Act were altered to narrow the categories of eligible women. Mirroring the changes that were made to the Dominion lands legislation for the prairies in 1876 (to be discussed later in this chapter) free grants of 100 acres were to be available to \"a single man over eighteen, or a married man without children under eighteen residing with him, or the female head of a family having children under eighteen residing with her.\" A free grant of 200 acres was available to \"the male head of a family having a child or children under eighteen residing with him... And such male head of a family is permitted to purchase another 100 acres at 50 cents per acre cash.\" A male head of family, then, was eligible for twice the amount of land as a female head of family, and he had the right to purchase more land at low cost. Some districts of Ontario departed from this model. In the Rainy River district the \"male head of a family or the sole female head of a family having a child or children under eighteen residing with him or her may locate for 160 acres, and may also purchase an additional 80 acres at $1 an acre.\" The term \"sole\" attached to the female head of family was also used on the prairies to limit the number of eligible women.\n\nBritish Columbia had separate and divergent land legislation that shifted and changed but eventually provided opportunities for immigrant women that were more generous than those on the prairies. While British Columbia was still a Crown colony, and under 1860 legislation, land could be acquired by \"British subjects and aliens who shall take the oath of allegiance to Her Majesty.\" There was no mention of gender. After 1870, British Columbia designed a land system that was distinct from the Canadian federal government-controlled Crown lands of the three provinces of Manitoba, Saskatchewan, and Alberta (except for a belt of land along the right of way of the Canadian Pacific Railway), which initially offered no opportunity for most immigrant women to acquire land. Under 1870 legislation for the \"pre-emption\" of Crown land, \"any male person being a British subject, of the age of eighteen years or over\" could acquire the right to any tract of unoccupied land. In a 1908 act, however, categories of British women subjects were also permitted to pre-empt Crown lands, including \"a widow,\" \"a femme sole who is over eighteen years of age and self-supporting,\" \"a woman deserted by her husband,\" and \"a woman whose husband has not contributed to her support for two years.\" British Columbia was thus to become a much more welcoming environment for the immigrant woman landowner and farmer than the Prairie provinces were. As in prairie Canada, First Nations in British Columbia were not permitted to pre-empt Crown lands. The 1908 legislation, for example, set out those persons who could obtain land, and continued with \"such right shall not extend: a) to any of the aborigines of this continent.\"\n\nIt is likely that in Western Canada, single women and women heads of households were deliberately included in the homestead privilege as it was originally devised, as in the United States. Since there is no evidence of any debate about the issue, however, it is difficult to know for sure. But the precedent of the Ontario legislation and the intense desire to compete with and match the U.S. offer to homesteaders would have compelled this deliberate inclusion. Under Canada's initial legislation, first passed in 1871, it was possible for women heads of families and women who had attained the age of twenty-one to select a homestead. The first published memorandum of 1871 on the Subject of the Public Lands in the Province of Manitoba had provided that \"any person who is the head of a family, or has attained the age of twenty-one years\" could secure a homestead. This same wording appeared in the 1872 legislation. Chester Martin wrote that the origins of Canada's homestead policy, \"direct or indirect, in the United States was conceded on every hand.\" Yet Canada rather quickly and deliberately took away the privilege of homesteading from single women in 1876, a significant departure from the U.S. legislation.\n\nIn both the American and Canadian West the goal of free land and the homesteading scheme was to quickly populate the land with a \"preponderance of fit and preferably youthful males.\" Land policies of both the United States and Canada were \"efforts to 'hire' settlers\" in order to combat the \"Indian's simultaneous claim on public lands and the cost imposed by this dispute over property right.\" In helping to establish U.S. and Canadian claims in their western territories, homesteading was a \"least-cost strategy,\" a \"substitute for direct military force [that] acts to mitigate the costs of violence.\" A preponderance of fit and preferably youthful males suited this purpose best, and the residence requirement was intended to make them stay put. Settlement had to be scattered to quickly lay claim to vast territories. A homesteader could not reside in a village and head out to the land from there. But restricting the plot size to 160 acres was intended to create relatively dense settlement. Yet in both nations the state had the discretion over where to locate settlers, as homesteading was restricted to surveyed land.\n\nBoth Canada and the United States sought to create not just economic development, but a desired social and cultural landscape through land policies. In both nations, administrators were determined to create small-scale holdings reminiscent of an idealized European (particularly British) landscape (despite mounting evidence of environmental limitations). As mentioned, both nations excluded Indigenous people from the homestead privilege, although in the United States, Indian homestead legislation of the 1880s provided some access to land on the public domain. In Western Canada, M\u00e9tis scrip provided access to individual plots of land. But in both nations the hope was that a white and patriarchal landscape would be created through the homestead system.\n\nIn both the United States and Canada, married women were not permitted to homestead. Under the doctrine of marital unity, a married woman had no legal existence. As explained by a commissioner of the U.S. General Land Office in 1864, a married woman's \"services and the proceeds of her labor being due and belonging to her husband... that if permitted to enter land because of having arrived at twenty-one years of age, the legal restrictions growing out of her matrimonial relations would at once be violated.\" A married woman could not apply as \"head of the family,\" because the husband was the \"head\" during the marriage. This general rule was seriously challenged in the United States in 1882 by Rachel McKee, who applied for a homestead in Colorado where her application was refused because she was married. Her attorney Daniel Witter made some compelling arguments, including that the homestead law allowed anyone over the age of twenty-one to make entry, as the act stated that \"every _person_ who is the head of a family or who has arrived at the age of twenty-one years... _shall be entitled to enter\"_ public land. Witter argued Mrs. McKee was a person as defined by John Locke, \"a thinking intelligent being that has reason and reflection.\" He also argued that Congress would have had to have explicitly excluded married women from making entry. Witter further argued that permitting married women to homestead would \"give new life to western emigration... and [would] send tens of thousands of families from poverty and dependence in the over populated east, to prosperity and independence in the new west.\" The appeal was lost, however, and the McKee decision settled the question of the eligibility of married women to make homestead entries in the United States.\n\nMANITOBA WOMEN HOMESTEADERS WHO FILED BEFORE 1876\n\nCanada's Dominion Lands Act of 1872 originally permitted certain categories of women to homestead\u2014single women and heads of families. And women took advantage of this offer. In the pages of the homestead land registers of the first homesteaders in Manitoba, the names of a few women begin to appear. The early 1870s saw a significant number of women applicants, some single, others widows, although the files do not always provide this information (See Table 1).\n\nThe first woman in Western Canada to apply for a homestead in her own name was Mary Walker, who made her entry on land in the House Creek district at the south end of Lake Manitoba in 1872 as homesteader number 214. She died in 1874 before proving up, and her land was patented to her son Peter in 1882, who amassed considerable land in the House Creek district but made his mother's quarter section his home until he sold the land in 1908.\n\nThe first woman on the Canadian prairies to receive a patent to her homestead was Isabella McKercher, who entered on a homestead in 1874 at Roseau Crossing, which soon became Dominion City, in south-central Manitoba. She was granted her title to the land in January 1878. She opted to purchase her land after fulfilling some of the homestead requirements, as her land suddenly became very valuable. McKercher came from Ontario with two brothers and her parents, Duncan and Mary, who were the \"first white settlers to arrive in Roseau Crossing.\" She filed on her land in September 1874 and by April 1877, when she swore an affidavit, she had lived on her homestead for fifteen months, and had a house measuring 16 x 12 feet, a stable and wood shed, and four acres under cultivation. In the spring of 1877 it was determined that the Pembina branch of the Canadian Pacific Railway would cross the Roseau River on McKercher's land, which was thus of \"exceptional value,\" in the words of Donald Codd of the Dominion Lands Branch in Winnipeg. McKercher decided to take the option to purchase her homestead, offered under a section of the Dominion Lands Act, and was likely able to sell the right-of-way at a sizeable profit. When in 1878 the last spike was driven on this branch line, a ceremony was held by the new trestle bridge, barely completed, over the Roseau River. While people took turns driving the spike, Isabella McKercher \"was too shy to get up in front of such a gathering, so she held back and watched the others tackle it.\" That same year she married Alexander Waddell, also a homesteader at Roseau Crossing.\n\nThe second woman to prove up was Susannah Jane Kennedy (homesteader number 591), who filed on her land in the Woodlands district in 1873 and received patent to her land five years later. Kennedy appears in the 1881 Manitoba census as born in Ireland, and age eighty. She was illiterate, signing her name on her homestead document with an X. Kennedy sold her original homestead and (incredibly) in 1892, at the age of ninety-four, applied for patent on another homestead, this time in the Souris district, where she was living with an adopted daughter and her husband.\n\nGlimpses of some of the earliest women homesteaders of the Canadian West can be gleaned from the homestead files, and local histories shed light on the identities and experiences of a few, particularly if the names of husbands or fathers or brothers are known. Many were single women to start with who later married. Elizabeth Moffatt, homesteader 615, married John Scott and her patent was thus issued to Elizabeth Scott.\n\nWhen a woman filed as a single woman, then married before applying for her patent, her husband often (but not always) had to swear an affidavit that his wife was the same person who had filed on land under another name. Malcolm Martin, for example, who married homesteader Kate Smith, had to swear that his wife was the Kate Smith who had entered on land under that name, and that Kate Smith and Kate Martin were one and the same. In 1883 William Ross had to swear that his wife was the same Margaret Campbell who had made homestead entry in 1874, and her brothers Robert and Donald were also asked to add their signatures to the document, verifying that Margaret Campbell and Margaret Ross were one and the same. The records do not always provide the marital status of women homesteaders, as in the case of Mary McLeod, whose land was in the Gladstone district of West Marquette. She filed on her land in 1874, began her residence in 1876, and applied for her patent in 1881, signing her name with an X, as did her witnesses Daniel Reece and John Ross. She was granted her patent to her land in 1882. Women homesteaders varied in age: Jane Leadbeater, who made her entry in 1874, was seventy-two years old when she received her patent in 1887.\n\nThese first homesteading women seem to have rarely travelled to Manitoba on their own; some were already residents and others arrived with family. Those whose background is known were not from overseas but from Ontario or Manitoba. Maria Barron filed on land in High Bluff in 1874 and began her residence and cultivation of the land in 1877. Her father was from Scotland and her mother from Ontario. Maria was born in Ontario and came to Manitoba with her parents and siblings in 1874 over the challenging Dawson Trail. Maria married Maxwell Wilton, and her patent was issued to Maria Wilton. The family acquired a lot of land in the High Bluff district.\n\nIt can be assumed that some of the women filed along with fathers, brothers, or sons, such as Catherine Doupe, whose entry is beside a Charles Doupe. Sisters filed together as was the case with Mary Matilda Corbett and Sarah Jane Corbett, who claimed homesteads in March 1873. Janet McKercher filed on land close to her parents and brother in 1874. She did not receive her patent until 1906, as her claim was controversial. Although her land had been cropped continuously since 1875, she did not live on her property, keeping house for her parents and then her brother. Two Lipsett women, Phoebe Louisa and Ann Jane, filed with two Lipsett men, Francis W. and James H., in July 1874. All cancelled out, but Caroline Matilda Lipsett, who had filed a few days earlier, eventually proved up in 1891. She was the mother of the other Lipsetts, and perhaps they combined their efforts on her land. Caroline was sixty-four in 1889 when she applied for her patent, declaring that she was a farmer by profession, that her family consisted of herself and eight children, and that when she first occupied her land in August 1875, all of the children were married but one. Her experience, like that of Isabella McKercher, indicates that women could acquire considerable wealth through the right to homestead. Early homesteaders had the right to pre-empt an adjoining quarter section, or to file on a second homestead. Caroline Lipsett became the owner of 320 acres of land in her section, as did other women such as Valletta Jane Nixon, who received her patent to 320 acres under her married last name, Edgar.\n\nIt is clear from the register of homesteads in Manitoba that times were difficult, by the number of cancellations as well as the number of years it took to prove up. Persistence was required. Louisa Irvine filed on land in Manitoba in 1874 but did not receive her patent until 1897, when title was issued to her under her married name, Louisa Munro. Weather, poor land, and grasshoppers accounted for delays and abandonments, but homesteaders also encountered bureaucratic problems. Louisa Irvine\/Munro first applied for the patent to her land in 1885, claiming that she had lived on her homestead from 1874 to 1877, had built a house, granary, and stable, and had six head of cattle and six sheep as well as one acre under cultivation. She was denied her patent in 1885 because at least fifteen acres under cultivation was required. The case was reconsidered in 1897, when it was noted that \"the land is unfit for grain growing\" and that regulations had since changed: \"more recently it has been customary to accept stock with a smaller amount of cultivation to satisfy the requirements of the Act, where it is clearly shown that the land is unfit for grain growing.\" It was decided that this was the case and Louisa Munro was finally granted her patent twenty-three years after she first filed on her homestead.\n\nFamily strategies included mothers homesteading beside sons. Widow Barbara Scott entered on land next to her son James Scott, who cultivated both his and his mother's land. All of his buildings were on his mother's homestead, however, and this proved a problem as he had not complied strictly with the wording of the legislation. In an 1884 memo, however, officials of the Department of the Interior decided that he had complied with the \"spirit\" of the law, and he was granted title to his land.\n\n_Figure 5._ Patent issued in 1883 to Manitoba homesteader Matilda McAskie, who filed on her homestead in 1874 as Matilda Graham. She was now the owner of the northwest quarter of section 36, township 12, range 10, west of the Principal Meridian. She also acquired an adjoining quarter section, becoming the owner of 320 acres of land. Library and Archives Canada, Western Land Grants, http:\/\/www.bac-lac.gc.ca\/eng\/discover\/land\/land-grants-western-canada-1870-1930\/pages\/item.aspx?IdNumber=461605&.\n\nIn 1874, the brother of widow Matilda Graham from Ontario filed on a homestead at High Bluff in Marquette West in the name of his sister. She married James McAskie in 1876 in Ontario, and together in 1878 they moved to Manitoba, settled on her claim, and lived there for one year. Her husband then took out a homestead as well, and they moved to his land in 1879, where they were living in 1881 when the land agent at Gladstone told them that \"it was not legal for her husband to hold a homestead [and] that one of them must be cancelled.\" A Matthew Harkness was interested in Graham\/McAskie's land and was trying to get her homestead cancelled, or \"jump her claim.\" In 1880 Harkness signed an affidavit (with an X) declaring that Graham\/McAskie had not resided on her claim for the last year. In 1881 Matilda McAskie opted to purchase her homestead at one dollar per acre, swearing that the land was \"entered by me as a homestead while a widow and a head of a family.\" She received patent to the northwest quarter section in 1882 and to the northeast in 1883.\n\nTragedies emerge from the files. Mary Mitchell filed on her homestead in 1873, later becoming Mrs. George Edie. She died in 1877, and her infant child was buried with her. When her husband applied for patent to her land ten years later, there were many hoops to jump through, including finding two people to swear that they had attended Mary Edie's funeral and had seen her buried. The homestead inspector wrote in 1887 that \"at the time of her death in 1877 settlers were few and much scattered, and these are the only two in the neighbourhood who were there at the time.\" Homesteader Hannah J. Whaley also died before she had the chance to prove up on her homestead that she filed on in 1873 in the Pine Creek district, and the patent to her land was issued to her husband Francis Blackmore in 1878.\n\nConditions were grim for Manitoba's first homesteaders. Plagues of grasshoppers (locusts) were an intermittent problem in Manitoba and the midwestern states to the south, and they returned with a vengeance in 1873\u201375, devouring all vegetation in their path. There was also a general economic depression to contend with that began in 1873, and in 1874 it was clear that the railway to and eventually through Manitoba would take many more years to build than anticipated. Settlers and Indigenous farmers lacked the equipment and the early maturing varieties of seed suitable to Western Canadian conditions. The number of immigrants plummeted: in 1875 there were 11,970, but in 1876 only between 3,000 and 4,000. Homesteads were deserted. Gerald Friesen writes in his history of the Canadian prairies: \"The rate of attrition\u2014the failure of the homesteader to 'prove up' and thus obtain a patent for his quarter-section\u2014was extraordinary. Chester Martin long ago calculated that four in ten prairie homestead applications were never fulfilled. Though admittedly rough, his statistics indicates a rate of failure of 20 per cent in Manitoba (1870\u20131905), 57 per cent in Saskatchewan (1911\u201331), and 45 per cent in Alberta (1905\u201330). This led him to note in his ironic fashion that 'in some respects \"free\" homesteads have been costly beyond computation.'\" The failure rate for the earliest homesteaders in Manitoba was likely much higher than the 20 percent Martin calculated.\n\nNotably, the early women homesteaders of Manitoba were generally more successful than their male counterparts at proving up. For example, of those who filed on land in 1874, 5 percent of the men proved up and 18 percent of the women; in 1875, it was 9 percent of the men and 57 percent of the women; and in 1876, 42 percent of the men and 75 percent of the women proved up. There were women homesteaders who proved up well before John Sanderson, \"Western Canada's first Homesteader,\" who filed on claim one in 1872 but did not receive his patent until 1881.\n\n_Table 1._ The gender of Western Canadian homesteaders and their success rates at \"proving up,\" 1872\u20131882. Note that statistics for applicants of unknown gender are not included in the table. Source: Library Archives Canada, Record Group 15 (Department of the Interior), Homestead Land Registers, vols. 1762\u20131766, reel T-2.\n\nCHANGES TO HOMESTEAD LEGISLATION: \"TO RENDER FEMALES... INELIGIBLE\"\n\nThe _Manitoba Free Press_ tried to report on the desperate conditions on the prairies while not completely scaring off prospective settlers. But on 7 July 1875 an editorial admitted that the people of Manitoba were in a state of destitution. The crops had failed in some districts for three and in others two successive years: \"The question that presents itself for consideration is this: Are the people of the Province, collectively speaking, in possession of the means to purchase their bread, in addition to other necessaries of existence? We answer, they are not.\" While many of the older settlers had livestock, \"the new settlers have but very little, and therefore have scarcely anything to fall back upon, in their day of need.\" Settlers needed relief, and they needed seed grain for the following spring. While settlers hoped to make a living off of the farm when crops failed, on the railway and city improvements, the market for jobs was saturated.\n\nThe \"homestead question\" dominated the editorials in the _Free Press_ in the spring and summer of 1875. Settlement of the province was in a precarious state. There was anger over speculators who, according to the _Free Press_ , had filed on homesteads but had no intentions of living on and cultivating their land. Distinctions were drawn between them and the \"actual\" or bona fide settlers, yet it was admitted that this was difficult to determine under the extraordinary circumstances of the grasshopper infestation. In April 1875 the federal government proposed that lands entered as homesteads and found without occupants in the summer of 1875 would have their entries cancelled, and the _Free Press_ had to admit this was not fair under the circumstances, as many \"actual\" settlers might not be found on their ravaged land that summer. \"Scarcely a day elapses that one or more cases of positive hardship, are not brought under our notice.\" The _Free Press_ in 1875 called not for cancellation but for a relaxation of the homestead requirements for a year, as was the case in the Dakota Territory and Minnesota, which were also experiencing the grasshopper devastation. There, settlers were allowed leaves of absence from their land. A problem with the wording of the homestead legislation had also led to some confusion. The original 1872 legislation read that to obtain a patent, proof was required of \"having resided upon _or_ cultivated the land for three years.\" According to a letter by a settler in the _Free Press,_ many homesteaders believed from this clause that they could cultivate their land without actually having to live there.\n\nOn 14 June 1875, an order-in-council was approved in response to a letter from Donald Codd, agent of Dominion lands in Manitoba, reporting on \"the depredations of grasshoppers in the Province, and the disastrous effects to the settlements in consequences thereof, unless some special consideration is extended to persons who have taken up homesteads by giving them leave of absence from their farms in order that they may earn subsistence for their families during the prevalence of the plague.\" Authority was given Codd to relax the rules and regulations so that those whose crops were destroyed and who were actually resident on their homesteads and prevented from putting in a crop because of the plague could, after furnishing unspecified evidence, receive written permission to be absent from their homesteads until 1 July 1876. This period of time could be counted as part of their three years' residence. (This was as recommended by the _Free Press_ and adopted from the U.S. model.) Such leave was only to apply, however, to a \"bona fide homestead settler.\"\n\nThe Honourable Luc Letellier de Saint-Just, minister of agriculture and immigration in the Alexander Mackenzie government, was sent in August 1875 to Manitoba to determine what measures should be taken to address the situation, including the destitution of the settlers. Letellier de Saint-Just recommended the expenditure of $60,000, authorized by order-in-council in August 1875, to purchase pork, flour, seed wheat, and barley. These were to be distributed as a loan or advance secured on the settlers' lands.\n\nIn his October 1875 report to Minister of the Interior David Laird, Surveyor Dennis wrote that he saw signs of hope for the future. The locusts had not left eggs in the soil, as in previous years. Dennis reported that the provision of seed grain and the permission to be absent for twelve months from homesteads had allayed discontent. He found that on the whole the Dominion Lands Act \"worked satisfactorily,\" but that \"there are certain important details connected with the operation of the homestead clauses in which it may be improved.\" From Dennis's wording it appears that Laird agreed with these changes, as he wrote that they had \"suggested themselves during your personal experience of the practical working of the law when in Manitoba and the North-West Territories last year.\" The very first of a list of eight recommended changes was \"to render females, not being heads of families, ineligible to enter for homesteads.\" Dennis provided no explanation for this change. There was no discussion or debate when the changes to the legislation came before the House of Commons. There was no debate about it in the press, and at the time, no protest from individuals or groups.\n\nIn May 1876, when the legislation was passed, the _Free Press_ explained that the changes had been made with a view to \"proper and efficient management\" of the land, at the suggestion of the minister or the land agent in the country, \"who watches closely the practical operation of existing land laws, and it thus enables him to make valuable recommendations from time to time.\" The second change mentioned in the same report (the first concerned military bounty warrants) was that \"women cannot obtain homestead grants unless they are _bona fide_ the independent head of a family.\" When the amendments based on Dennis's recommendations were passed, homesteads from then on were limited to \"any person, male or female, who is the sole head of a family, or any male who has attained the age of eighteen years.\"\n\nHistorians of the settlement era in Western Canada have not mentioned this as a development of any importance or interest, although to prohibit single immigrant women from homesteading was a major departure from the U.S. model that Canada wanted so desperately to match and even exceed. Why did this happen? As mentioned, women homesteaders during that small window of opportunity open until 1876 persisted and proved up on their land at a significantly higher rate than that of their male counterparts, but these statistics would not at that time have been available to policy makers (as it took many years for persistent homesteaders to prove up).\n\nThe most significant clue to the perception of the 1870s that Manitoba's single women homesteaders were not bona fide settlers comes from the 1879 observations of David Currie, who visited Manitoba as a special commissioner of the _Montreal Witness._ His letters were published the next year in pamphlet form as _The Letters of Rusticus: Investigations in Manitoba and the North-West for the Benefit of Intending Emigrants._ Currie was sceptical of the capacity and propriety of women farmers, reflecting views that will be further discussed in the next chapter. He believed they were incapable of homestead duties and that it was \"unnatural\" for women to cultivate land and live on their own. Currie noted the presence of single women homesteaders (and did not seem aware that as of 1876 they were no longer permitted to file on land), and he did not approve, writing that \"although the idea of single ladies faithfully performing homestead duties seems unnatural, yet a number of such have secured the land but that they have complied with the terms imposed by the Government is rather doubtful.\" Currie believed that by contrast, men were complying with the homestead laws: \"During my travels over this province I have met with a great many unmarried gentlemen who are fulfilling the letter if not the spirit of the law by 'baching' it on their homesteads; but I have not yet met with a single case where a maiden lady has been honestly endeavouring to comply with the law which gives her a title to her lands.\"\n\nCurrie admitted, however, that he had had little opportunity to observe single women homesteaders at their duties, as he found it difficult and improper for him to either search out or visit them, writing that \"indeed any attempt to do so would scarcely seem prudent in a country where the population is so very scattered.\" Yet he concluded that the \"only feasible way by which ladies might faithfully comply with the terms of the law giving them the right to 'homestead' land, is by forming a matrimonial alliance with some gentleman friend, in whose company homestead duties might be faithfully performed.\"\n\nCurrie was also concerned with the potential for fraud, that couples would delay marriage and would acquire more land than they were entitled to. He had heard of engaged couples where the man and woman each secured homestead rights in advance of their wedding, and \"by this means acquired double the amount of land that they could legally secure if they had postponed their homesteading until after they became man and wife.\" He continued that it was \"not desirable that persons after becoming 'one flesh' should each reside upon separate homesteads, consequently one of the claims must remain unoccupied.\" Currie assumed that this was why so many claims were unoccupied and found this \"reprehensible,\" writing that \"a large number [of homesteads] remain untenanted with only a few acres brought under cultivation, and perhaps the walls of a home erected, and not a few homesteads remain without any attempts to bring them under cultivation.\"\n\nIn the _Manitoba Free Press_ women homesteaders had not been singled out as part of the concern about bona fide settlers, but the serialized account of \"How Two Girls Tried Farming,\" published just at this time, might have encouraged readers to doubt the abilities of women farmers. The account, by Dorothea Alice Shepherd (pseudonym for Ella Farman Pratt), was originally published in the U.S. magazine _Atlantic Monthly_ and later as a book. It featured two friends, a \"housemaid\" and a teacher, who bought a small farm in Michigan after one of them inherited a thousand dollars. \"How Two Girls Tried Farming\" was a very popular story in the United States, as it was reprinted as a book several times; it was also controversial, raising issues of women's competency to farm on their own. It may have been serialized in the _Free Press_ to illustrate the mistakes, trials, and difficulties of women farmers (and they experienced many) and to show that farming was not a \"traditional\" enterprise for women. The two women of the story succeeded in some respects, although they had to abandon their \"small fruits\" plan in favour of corn, vegetables, and selling butter and eggs. It concluded with a reminder that for women, ploughing, shovelling snow, cleaning stables, and other chores were \"strange abnormal labours... But we do it, therefore others can.\"\n\nSurveyor Dennis made the recommendation to exclude single women from the homestead grant. Obsessed with the potential of the West, he was very concerned about the depressed conditions and possible collapse of the whole enterprise, and it may have been his personal view that women were not going to make the land productive. It is likely that Dennis shared his opinions with his friend and \"most trusted clerk\" at the Dominion Lands Branch, Donald Codd, who had been with Dennis on the original survey team sent to Red River. Codd had wide discretionary power in refusing claims, and the dramatic drop in the number of women homestead applicants in 1875 (when there were seven, compared to 109 in 1874), suggests that he may have been refusing or in some way discouraging women from filing on land in advance of the 1876 change in legislation. The decline in applications from women could not have had to do with grasshoppers; there were 1,920 male applicants in 1875, compared to only 416 the year before.\n\nThe necessity of wage labour for homesteaders to survive may have been an issue. Male homesteaders worked on railways, in lumber camps, and in the cities, and similar opportunities for women would have been limited. There was some talk of having homesteaders perform statutory labour. In an undated (early 1870s) set of recommendations about how land should be granted, James Cunningham, a member of Manitoba's first legislature of 1870, recommended that every settler be bound to work one day a week for five years on the railway at the rate of one dollar per day. Cunningham estimated this scheme would result in 1,100 men in each township working 250 days a year for five years. While ultimately this measure was not introduced, in any discussion of such a plan, women homesteaders would clearly have been seen as unsuitable candidates.\n\nSpeculation about other reasons for limiting women's right to homestead might include the paperwork that was required when single women homesteaders married before they proved up, as discussed above. The case of Matilda Graham\/McAskie also illustrates that complications emerged when a woman filed on a homestead as a single woman and then married a man who himself then filed on a homestead: one or the other was obliged to give up the claim, a problem that also emerged in the American West. There the legislation was changed several times to deal with the issue of \"entrywomen\" who married an \"entryman\" before proving up, and there were complex and contradictory legal decisions and interpretations on the matter. Bureaucrats at the Canadian Department of the Interior became increasingly obsessed with the opportunities for fraud in acquiring land, and women were seen as particularly suspect.\n\nCitizenship and naturalization may have also been an issue, one that was to complicate the lives of some female heads of households who filed on homesteads after 1876. Upon marriage a woman automatically was given her husband's citizenship; if a woman who had filed on a homestead married a neighbouring homesteader who was not yet a British subject, she lost her ability to apply for a patent until her husband changed his citizenship.\n\nThere may have been concerns about the dangers of settlement. The idea of immigrant women alone on isolated homesteads was perhaps unsettling to policy makers and legislators (although they did not waver in the United States, where there was more warfare and thousands more women homesteaders). Supporters of homesteads-for-women understood that the homestead right was rescinded because in the 1870s \"Indians were bold and bad\" and \"lawless\" and the railroad was not finished, and \"it was considered a big adventure for a hardy man to take up land in the genuinely wild and wooly West.\" (And they used this as a rationale for having the privilege restored, arguing that this threat from \"lawless\" Indians no longer existed.)\n\nMany people, women and men, were not prepared for the challenges of life on a prairie homestead. Englishwoman Mary (Mrs. Cecil) Hall described her first thoughts about the prairies in her 1882 book, _A Lady's Life on a Farm in Manitoba_ : \"O the prairie! I cannot describe to you our first impression. Its vastness, dreariness, and loneliness is appalling.\" That very year there was a \"shocking fatality\" in Manitoba that was news across the British Empire. At Meadow Lea, thirty miles west of Winnipeg, a fire broke out during the middle of a roaring blizzard, destroying the home of the Taylor family. The mother and three daughters were all found frozen to death on the prairie.\n\nThe idea that women would be poor custodians and cultivators was likely a rationale, as was the idea they would probably be mere investors or speculators in land. In a 1908 article explaining some of the differences between U.S. and Canadian homestead rules, Canada was complimented for its law that \"permits a young man to get an early start in life, while it discriminates against those women whose cultivation of the soil is apt to be perfunctory, and the homesteading a mere investment, and favours those cases where there is a real incentive to the making of a living out of the farm for the dependent children.\" (It was assumed a single male would eventually have children, while a \"spinster\" would not.)\n\nRobert Rogers, minister of the interior (1911\u201312) and a politician from Manitoba, stated that while homestead privileges had at one time been available to single women, they \"failed to claim them, or having done so, did not fulfil the necessary duties and thus forfeited their rights.\" This does not appear to have been the case, however; there were significant numbers of women who filed on homesteads during the small window of opportunity available, and they proved up with greater frequency than men. In 1913, a woman journalist with the _Saskatoon Star Phoenix_ said that Rogers's explanation sounded \"weak and spineless; not in keeping with that pioneer spirit which has made our women remarkable the world over.\"\n\nA few observers of Manitoba in the mid-1870s took note of the presence of women homesteading on their own. In 1874 the _Toronto Mail_ reported that \"under the Homestead Law, every individual over twenty-one years of age may take up a free grant of 160 acres of land, and happy are they who have large families of grown children. Our correspondent says he has known single families to have taken up five and even seven homesteads. Father, sons, daughters, maiden aunts and widows being entitled to enter each for 160 acres.\" This correspondent was not entirely critical of this, it seems, as he said that \"it would be of advantage to extend the right to all persons over eighteen years of age, as it would encourage early marriages, and consequent independence, and increase the number of actual farmers.\" His last comment, however, suggests that he did not include \"maiden aunts and widows\" in the category of \"actual farmers.\"\n\nWas the homestead privilege taken away from all but widows with minor children because farming and homesteading was not seen as suitably feminine for women colonists? This seems to have been in the mind of David Currie, who wrote that it was \"unnatural\" for women to perform homestead duties. A woman working in the field was not seen to conform to an idealized British femininity; they were to be delicate and fragile. Predominant representations of Indigenous women played a role by providing a contrast to ideals of a domestic and refined and British femininity. As stressed at the beginning of this chapter, women were the farmers on the Great Plains long before the arrival of Europeans. While Indigenous women working on farms and gardens might not have been very visible to newcomers of the 1870s because this work was being performed on Indian reserves, the representation of \"squaws\" as exploited and overworked drudges was widely promulgated. The corollary representation was that Indigenous men were reluctant and poor workers who relied on their women for all manual labour, while they relaxed and smoked. Travellers and other writers often commented on this. David Currie's 1879 description was typical: \"I observed two native gentlemen reclining on a small straw covered shed, smoking their pipes, seemingly at perfect peace with themselves and all mankind, whilst at the two nearest houses, and within less than one hundred yards of the two smokers, were two native ladies engaged in chopping the night's supply of stovewood from piles of poplar poles. The way that the ladies handled the axe showed plainly that they were no strangers to this occupation.\"\n\nA Toronto _Globe_ correspondent visiting the North-West in 1881 wrote that Indigenous \"men are nearly all, in the matter of physical strength, unable to endure manual labour. In the camp the women do all the hard work such as cutting wood etc.\" The men, by contrast, were \"indolent or incapable to do much.\" Indigenous men were frequently and widely condemned for the fact that women supplied wood for their families, while \"they themselves stay in the teepee, smoke, pound the tom tom with a club and see who can tell the biggest lie.\" The message was that manual labour was unsuitable for colonizing women, who must show superiority to these darker times and ways.\n\nIn common with the imperialist rhetoric of other colonial settings, it was white men who stood in contrast to Indigenous males. The white male colonizer would transform the wilderness into productive and profitable terrain. The ideal white male figure was physically capable, courageous, and industrious. The white woman colonizer was not to exemplify these traits. It was vital to demonstrate that the colonizers were superior, that they knew how to treat women in comparison to \"savage\" societies. Women were the farmers only in \"uncivilized\" societies, where they were cast as being forced unwillingly into such work by lazy men. In the 1899 book _Woman's Share in Primitive Culture_ by Otis T. Mason, a sketch of a sparsely clad woman, hoeing, with her unhappy child strapped to her back, was accompanied by the caption \"The Primitive Farmer and Burden-Bearer, South Africa.\"\n\nDid the arrival of women of varied ethnicities as immigrants play a role in excluding most women from the homestead grant? In this outpost of the British Empire, the colonizers needed to show superiority to the new arrivals of varying non-British origins. Immigrants from other places than the British Isles and Ontario began to arrive in the West in the mid-1870s, when Icelanders settled in the Interlake district of Manitoba and Mennonites from Russia on the plains south of Winnipeg. In these communities, as with the Doukhobors who arrived over two decades later, women worked in the fields and performed other critical manual labour. This was noted by the late 1870s. John Lowe, secretary of the Department of Agriculture and a Manitoba farmer (of an enormous farm of sixteen square miles), gave evidence before a federal committee on immigration to Canada that Mennonite women were seen \"ploughing in the fields.\" He also saw \"a woman thatching the roof of a building, the materials being handed up to her; and we next saw a girl plastering the outside of a house in apparently a very matter-of-fact way.\" He saw men, women, and children \"going out into the fields to work before the morning was grey. We also noticed these people working until it was dark in the evening.\" A member of the committee asked Lowe, \"Does this kind of work improve the condition of the women, or tend to their refinement?\" His reply was that \"this must be judged relatively. Their social ideas are certainly, in many respects, very different from ours, and I was told this hard work was considered to be of the highest good to the women. Any finery in dress is rigorously discouraged.\" It was to become a central rationale of officials, in response to requests for the right of British and Canadian-born women to homestead land, that to have them working in the fields would be \"disastrous... for the reputation of Canada.\" This was not the refined and genteel behaviour expected of them and required to set an example for Indigenous people and other immigrants.\n\n_Figure 6._ \"The Primitive Farmer and Burden-Bearer, South Africa,\" from Otis T. Mason, _Women's Share in Primitive Culture_ (1899), 6. According to British imperialist rhetoric, women were the farmers only in Indigenous societies, where they were cast as unwilling participants forced into the work by Indigenous men.\n\nGardening was acceptable; owning land and farming was not. As historian Dianne Lawrence has written, in the colonies gardens performed added functions. Through their gardens, genteel women colonizers \"contributed to the imperial cause by creating order out of chaos of the natural world.\" Their gardens were small-scale models of the wider imperial project. The flower beds and neat rows of vegetables proclaimed a superior civilization, triumphing over wilderness. Gardening or horticulture for women, rather than commercial farming on land they owned, was less threatening and challenging to the traditional gender order, as discussed in the next chapter. Women homesteaders such as Isabella McKercher could find themselves the owners of land that was very valuable as railroads were built and markets opened. Gender chaos could result if women had the opportunity for independence and incomes of their own. And profits, which were considerable when the economy boomed, would have to be shared. Women were begrudged small acreages while the predominantly male investors and speculators acquired massive landholdings in the West. For all of these reasons, the short-lived and impractical tree culture opportunity was seen as acceptable for women.\n\nA SHORT-LIVED OPPORTUNITY FOR WOMEN: FOREST TREE CULTURE\n\nAt the very same time as women, unless they were sole heads of families, were made ineligible to homestead, a new opportunity was offered them for land grants in the West\u2014tree farms, or forest tree culture. Minister of the Interior and Lieutenant Governor David Laird was particularly devoted to this initiative. In his report for 1875, Laird, from Prince Edward Island, wrote that during a trip from Fort Garry to Fort Qu'Appelle in the summer of 1874, \"nothing impressed itself upon my mind more than the treelessness of a vast portion of the country over which I passed. Day by day, as I crossed the wide extent of prairies utterly destitute of trees, the question presented itself: How is the settlement of these prairie provinces possible, if the settler is without wood for fencing, building and fuel?\" Laird had met with an experienced tree planter in Fargo, North Dakota, and learned how tree culture was to be encouraged there, and he was determined to provide the same opportunities north of the border.\n\nIn 1873 the U.S. Congress passed an act encouraging the cultivation of trees on the western prairies. This was available to anyone regardless of gender and marital status; the act stated that \"any person who shall plant, protect, and keep in a healthy growing condition for ten years forty acres of timber... shall be entitled to a patent for the whole of the said quarter-section.\" In the United States pressure had mounted from the 1860s to address the question of the cultivation of trees for the treeless prairies. As an editorial in an 1866 St. Cloud, Minnesota, newspaper showed, tree culture was considered work for women, who would be better off devoting themselves to the care of groves of trees than the \"patchwork quilts and other jim crackery upon which women waste their time and ruin their eyesight.\"\n\nIn his 1875 letter to Laird recommending that females who were not sole heads of families be ineligible to homestead, Surveyor Dennis urged similar legislation to promote forest tree culture in Manitoba and the North-West, which could transform small plots of \"apparently worthless\" prairie lands into valuable farms. These farms, according to Dennis, would improve the climate and provide fuel, building, and fencing material. Dennis reviewed the U.S. legislation and its early results at length, claiming that in Minnesota alone, \"the enormous area of 170,307 acres had been entered under the Acts encouraging tree planting.\" Dennis's glowing recommendations about tree planting indicate that he saw this as a more suitable task for women. Dennis wrote that \"this new industry, if prudently and patiently followed up, is even a surer source of wealth than wheat growing, and without the additional expense and anxiety connected with the latter.\" He quoted a U.S. expert who asserted that land properly cultivated and planted with trees could be sold for $100 per acre within twenty years.\n\nAs historian David M. Emmons has written, the Timber Culture Act of 1873 in the United States was prompted by a theory \"which gave expression to both the optimism and the desperation which accompanied the Americans in the settlement of their last frontier.\" Land previously seen as arid, sterile, and inhospitable had to be transformed into a green, bountiful, appealing prospect for agriculture and settlement. There were many theories about how rainfall could be increased, and the early 1870s saw influential champions of the idea that trees brought rain. The main authority was George Perkins Marsh, author of _Man and Nature_ (1864), who predicted that splendid forests could be grown on the plains, checking evaporation and ameliorating the harsh climate. Ferdinand Hayden, director of the U.S. Geological and Geographical Survey of the Territories, found rainfall increasing wherever there were settlers who planted trees, and he was confident that \"the Great American Desert had been converted; indeed as a continuous area it has already ceased to exist, even in imagination.\"\n\nCanada quickly followed with its own measures to bring rain and provide timber to the settlers, and new Forest Tree Culture provisions of Canada's Dominion Lands Act were added in the 1876. Enthusiasm for the measure was expressed in the _Manitoba Free Press_ , and an American expert was quoted who asserted that \"a grove of trees can be grown as surely as a crop of corn,\" that within five years ten acres of timber could supply fuel and fencing for a family, that \"apparently worthless prairie land\" could be sold within twenty years for $100 per acre if planted with timber, and that within ten years lands \"properly planted and cultivated with trees will... realize at the rate of ten to one as compared with the profits attending the raising of wheat.\"\n\nThe 1876 legislation provided women, regardless of marital status, as well as men, the opportunity to acquire land to plant trees: \"Any person, male or female, being a subject of Her Majesty by birth or naturalization, and having attained the age of eighteen years, shall be entered for one quarter section or less quantity of unappropriated Dominion lands as a claim forest tree planting.\" The use of both \"he and she\" throughout the complicated legislation setting forth the rules and regulations made it clear that this was quite deliberately inclusive. Was this to be a replacement for the right to homestead, offering all women an opportunity for a parcel of land in their own names?\n\nA tree claim was exceedingly complicated and demanding compared to homesteading. The applicant was to select up to 160 acres of land that was \"open prairie and without timber.\" One year after the date of entry on the land the claimant had to have cleared eight acres for tree planting, eight more the second year, and sixteen more within the third year. This acreage had to be planted with trees. After six years, and not before, the claimant could receive a patent if she or he had trees kept in good condition.\n\nSome of the significant differences from homesteading land may have convinced architects of the plan that tree culture was more suitable than homesteading for women. Claimants were not required to build a dwelling and reside on their land; tree farmers, unlike homesteaders, did not have to be isolated and alone living on the prairie. Presumably a tree claimant could live on a family homestead or in a town or city. It took twice as long, however, to be able to apply for patent to the land; homesteaders could apply after three years, while tree claimants had to wait for six years (and later eight). At any time during those six years, the tree grower was liable to forfeiture if he or she was not breaking land, planting, and tending the trees. For homesteaders the precise amount of land to be broken and cultivated each year was not specified until an amendment in 1884 that demanded ten acres a year, which was reduced to five in an 1886 amendment.\n\nTree claims did not catch hold of the imagination of prospective settlers, either women or men. Few seized the opportunity: in the first six months of 1877 in Manitoba, for example, there were 348 homestead entries and five forest tree culture entries. Problems with the initial legislation were addressed in the 1879 amendments to the Forest Tree Culture legislation. The number of acres that had to be broken each year was lowered from eight to five. Claimants were given two more years to plant and tend their trees; they could not apply for a patent until eight years, rather than six. After eight years the claimant had to prove that \"he or she has planted not less than two thousand seven hundred trees on each acre of the portion broken or ploughed and cultivated to crop.\"\n\nWriting in 1879 for the _Montreal Witness_ , David Currie stated that tree claims were being abused, that the scheme \"seems also to be only used as a means for securing unlawful possession of Government lands.\" He had \"not yet heard of one acre of these claims being planted with trees\" and knew of some who were cultivating grain on their tree claims.\n\nTimber culture was abandoned in the United States in 1891, when the act was repealed by Congress as part of a general reconsideration of land policy. It had been discovered that trees planted on the plains did not bring more rain. According to Emmons, \"nature did not prove quite as docile and malleable as the advocates of increased rainfall believed. Drought struck the plains in the mid-70s and again in the mid-80s. Trees planted in response to the Timber Culture Act withered and died.\" North of the border the same situation prevailed and the program was abandoned even earlier, in 1886. Tree claims proved utterly impractical. There was nowhere to acquire the thousands of seedlings and\/or cuttings the tree farmers were to plant. Winds could be severe, dry, and hot. Hail was also a frequent visitor. There was no income for the claimant for six to eight years. Donald Codd reported in 1878 that there were only thirty-five claims under the Forest Tree Culture provisions. Altogether there were only fifty-one tree claims entered in Manitoba. Most were south of Winnipeg along the banks of the Red River, where flooding was also an issue many years. Of these claims, only five patents were ever issued.\n\nInterviewed in 1913 about the homesteads-for-women petition, Isabelle Beaton Graham of the _Grain Growers' Guide_ spoke of the short-lived tree claim opportunity: \"They [women] were not allowed [homesteads] on the same terms as men, but could have tree claims and must have planted and have growing 500 trees before they could get a patent. Very few made good of course. The proposition was absurd because the trees were almost impossible to obtain, and even when induced to grow could yield no financial returns.\" Tree planting, another woman journalist wrote in 1913, was \"a healthful and interesting occupation... but when planted heaven sent no manna as fruit thereof. Even if the claimant succeeded in securing and getting into the ground the five hundred birch, elm soft maple etc. for which the Government clamoured she could not make a living out of them. She failed, and though it was from no fault of her own, the privilege was withdrawn.\"\n\nThe right of unmarried women to homestead was abolished in 1876, and the right, however impractical, to tree claim land was removed in 1886. But there did remain one category of eligibility for women\u2014the sole head of family. From 1876 the legislation read: \"Any person, male or female, who is the sole head of a family, or any male who has attained the age of eighteen years shall be entitled to be entered for one quarter-section.\" As understood by Canadian authorities, this meant that only widows with minor children dependent upon them were permitted to homestead.\n\nAs the homesteads-for-women campaign grew prior to the First World War, many commented that this was simply not fair. In a 1913 _Saskatoon Star Phoenix_ column entitled \"No Way for a Single Woman to Get a Farm, Unless She Captures a Man,\" Valance Patriarche wrote that \"a woman who wants a homestead must prove she has been clever and energetic enough to have previously captured a husband and either kept him or let him die. If she has him on hand he obtains the homestead; if she has let him slip away to a better land she is solaced by having the grant made out in her own name.\" That same year journalist Lillian Beynon Thomas also used humour to criticize the law that seemed far from fair to her, noting that \"there are no homesteads for women in Western Canada unless such women care to qualify by killing off any inconvenient husbands they happen to own.\"\n\nBritish women interested in farming and owning land in the colonies were urged to emigrate to a not entirely hospitable environment in prairie Canada, and the individuals and associations advocating this, the subject of the next chapter, appeared to know little of the challenges and obstacles that awaited. Canadian authorities wanted British women immigrants, preferably young, single, and robust, who could be wives and mothers. They were not at all interested in encouraging women to settle and farm on their own. They wanted to plant and nurture a traditional gender order, not cultivate new strains of independent women. Neither the unwelcoming conditions nor the discouragement of authorities, however, prevented the creation of a modest momentum for the cause of British \"gentle\" or educated women farmers for the prairies, which reached its zenith in the years just before the First World War. \nCHAPTER TWO\n\n\"LAND OWNERS AND ENTERPRISING SETTLERS IN THE COLONIES\"\n\nBRITISH WOMEN FARMERS FOR CANADA\n\nAt a meeting of the Colonial Section of the Royal Society of Arts in London in March 1913, English travel writer Ella C. Sykes spoke on \"Openings for Educated Women in Canada.\" She stressed the several occupations they might find in that colony, all of which were suitably feminine, and she included farming on a modest scale and \"taking up land on their own account.\" She noted, however, that \"so far the Canadian seems to object to women working on the land, the reason of this, perhaps, being that he finds them so valuable in the house.\" Yet Sykes called on educated women to take up the challenge of this \"imperial\" work: \"Canada has shown unmistakably that she wishes to have the British stamp, and that can never be if the women of our race refuse to do their part... The girl of the right type who cares for the Flag and what it stands for, can be in very deed a missionary of Empire in the Dominion.\"\n\nOne month later, and also in London, English author and Saskatchewan farmer Georgina Binnie-Clark spoke on \"Land and the Woman in Canada\" to the Royal Colonial Institute. Binnie-Clark was much more radical then Sykes, urging British women to grow grain on large acreages in prairie Canada. \"The commercial farmer,\" she stated, \"is not to farm for mere livelihood, she is to farm for independence.\" Like Sykes, Binnie-Clark saw this as an imperial enterprise. British women could play a critical role in the \"spade-work of British expansion in this, the supreme place of prosperity among British lands.\" \"It is time,\" Binnie-Clark stated, \"to shoulder one's spade and get off into the unknown country where a further stretch of the Empire is calling for the pioneer.\"\n\nThese two talks before prestigious patriarchal colonial institutes represent the apogee, the summit of enthusiasm and optimism for the prospect of British women farmers for Canada. Modest and slow momentum for this cause had been gathering for several decades in Britain, particularly England, and to a lesser extent in Canada. But opposition remained formidable and powerful, and any momentum gained was lost in the First World War. There was a moderate revival of the cause after the war, but the opposition was even more entrenched. This chapter traces the growth of support for the idea of sending British women to Canada to farm, an idea that generated mild support from some and zealous, energetic, and fervent support from a few. Starting in the late nineteenth century, British proponents of agriculture for women, emigration associations, colonial training schools, and imperially minded journalists and travel writers advocated farming and land-owning for \"gentlewomen\" in the colonies, particularly Canada. A number of factors and causes intersected and overlapped to create modest momentum for this initiative, including alarm about the \"surplus women\" of Britain, concern about the \"surplus men\" of the colonies, devotion to the Empire, the push to expand educational, professional, and vocational options for women, the opposition to women farmers or horticulturalists in the \"mother country,\" and the fact that there had to be more options than housework to tempt British women to cross the Atlantic. Fiction for girls and young women set in the colonies presented robust and independent heroines who owned or managed land of their own.\n\nProponents of sending British women to farm in Canada faced many opponents and obstacles. The colonies wanted women for domestic service, marriage, motherhood, and little else. Gentlewomen were reluctant, however, to cross the seas to scrub floors. There was an effort to camouflage domestic service in the colonies as something acceptable for refined women; they were to be \"home helps\" and treated as family members, not exploited servants. This subterfuge did not succeed in attracting the \"surplus women\" in significant numbers, and farming emerged as one option they might pursue in Canada. This would not only be a vocation, it would permit British women to truly be Empire builders. In _A Woman in Canada_ (1911), English garden author Marion Cran wrote that the \"wild beautiful West\" provided opportunities for lives of independence for women willing to give \"their best of mind and body for the race and for the Empire.\"\n\nSHIFTING ATTITUDES IN THE MOTHER COUNTRY\n\nOpinions about the respectability of women working in the fields in Britain shifted dramatically and rapidly throughout the nineteenth century, and varied according to factors such as class, age, marital status, and region. There was heated debate about the suitability of farm work for the educated \"gentlewoman,\" and by about 1900 there had emerged a degree of acceptance, although sceptics and opponents remained. Aspects of these debates and the more tolerant attitude that developed, particularly within England, are an important foundation and context for this study. Advocates of farming for women in the colonies drew on the arguments that were mustered for the same cause in Britain. Among these were that this would solve the \"surplus woman\" problem, and that farming would provide a healthy and useful vocation. Other rationales were that women's work on the land would remain feminine, because it would be limited to a few acres and to the \"lighter\" forms of agriculture. They would farm in settlements or clusters of women so that they would not have to hire and oversee labourers, or need expensive machinery. Yet while attitudes changed and a degree of acceptance developed in Britain, the same was not the case in Canada, where opponents resorted to age-old arguments that women working in the fields was an antiquated and despised abomination, a remnant of primitive times. Canada was not to be promoted or crafted as a colony where women did fieldwork. If they did in fact work in the fields (as did happen), this would be ignored and concealed and never officially endorsed or rewarded. Drawing on attitudes that prevailed by the mid-nineteenth century in the mother country, Canadian authorities saw women's confinement to the home and hearth as a key indicator of superiority over earlier, \"darker\" times, over other nations and colonies, and over the Indigenous peoples of the colonies. Fieldwork was believed to demoralize and uncivilize women; indoors became the only setting for proper femininity.\n\nPromoters of agriculture as a vocation for women were seldom interested in working-class women, as it was presumed they had a natural function or calling\u2014domestic service. They were concerned with educated women of some means, or \"gentlewomen.\" For some advocates, agriculture for women was part of a larger movement to secure women's political, civil, and educational rights, and farming was one profession that could provide economic independence and an alternative to marriage. Others had more conservative objectives. Viewing women as unsuitable for intellectual careers or for professions such as medicine and law, they saw farming as a viable occupation that demanded less mental aptitude and education. Women's fields and gardens would be safe and secure places where they would be kept isolated from the world; there they would be kept busy and not tempted to join in political agitation. Marriage remained the ultimate goal to these thinkers, and a knowledge of farming or gardening had the advantage of remaining useful even after marriage, whereas other professions would have to be abandoned. Yet it is difficult to neatly categorize proponents of agriculture for women into radical and conservative camps, as it was shrewd to pose as non-threatening to the male domain of agriculture and land ownership in the face of fierce and powerful opposition.\n\nWOMEN IN THE FIELDS: A REMNANT OF DARKER TIMES\n\nIn 1898 an article on \"Ladies as Farmers\" proclaimed that in Britain farming was \"quite the most fashionable occupation for women nowadays,\" and that \"a craze for agricultural pursuits [had] taken possession of ladies of fashion.\" English journalist Virginia M. Crawford was more measured but largely in agreement in her article of the same year, entitled \"Englishwomen and Agriculture,\" writing that \"the whole question of agricultural employment for women is, so to speak, in the air. It has emerged somewhat suddenly from the sea of future possibilities, and is fast developing into one of the social questions of the day.\" While \"in the air,\" the question of agriculture as a vocation for women faced formidable opposition from those who insisted it was unbecoming and inappropriate. Crawford argued that an \"active and ceaseless\" propaganda and public education campaign had to be waged to combat the idea that farm work was unladylike and to supplant it with that of the \"dignity and beauty of farm life.\"\n\nUntil the end of the eighteenth century, there was little disapproval of women carrying out farm tasks. But with complex factors such as urbanization, industrialization, and the expansion of the British Empire in the nineteenth century, the practice of women working in the fields came to be seen as backward, alien, a remnant of darker times. As an imperial power, Great Britain had to demonstrate that the women of its nation lived better lives than the Indigenous women of the colonies did. Historian Karen Sayer writes that \"as the urban became culturally superior to the rural, English culture was increasingly seen to be superior to that of native populations in the colonies.\" That the lives of British women were superior to the \"downtrodden\" dark and alien Indigenous women of the colonies and of \"foreign\" lands, who were allegedly treated little better than beasts of burden, was a common theme in Victorian imperial travel, missionary, and explorer narratives. As one English traveller to Bukhara (present-day Uzbekistan) observed in in 1835: \"The Kaffir women do all the out-door work, and follow the plough; and it is said that they are sometimes yoked in it along with an ox.\"\n\nWomen of the fields who were strong, robust, and energetic questioned and threatened Victorian ideals of passive, weak femininity. They were \"unnatural women, unable to fulfill the natural, feminine role of motherhood because of their labour and economic activity.\" Because they were vigorous, strong, and tanned from their work, women who did farm work crossed \"the boundaries of race. They therefore moved into the realm of alien, dark, sensual, sexual womanhood.\" According to a clergyman: \"Not only does it unsex a woman in dress, gait, manners, character, making her rough, coarse, clumsy, masculine, but it generates a further very pregnant social mischief, by unfitting her or indisposing her for a woman's proper duties at home.\"\n\nAgriculture changed dramatically in nineteenth-century Britain as the consolidation of larger-scale capitalist agriculture and mechanization brought an end to the small-scale farming of cottagers. The vast majority of agricultural workers, whether male or female, became landless labourers. Capitalist agriculture hastened the trend toward women's restriction to a limited range of tasks. Women were pushed into \"monotonous, low-status jobs, and [they were] deprived of the range of skills possessed by the farmer's or cottager's wife in the pre-industrial period.\" The wives of wealthier farmers \"began to lead a life more resembling that of the leisured wives of the bourgeoisie.\" Male married farmers took pride in having wives who did not have to do fieldwork, \"apparently adopting the middle-class ideology of domesticity.\" Farmers' organizations supported women's invisibility from outdoor farm work, arguing for a male breadwinning wage so that women would not have to go to the fields. Since many male farm labourers found themselves out of work due to the mechanization of agriculture, it was useful to insist women did not belong in the fields. Women were unwanted competition because they were paid about half the wage of their male counterparts on the farm. They could get much better wages in factories.\n\nBy the late nineteenth century, women who did continue to do farm work had become invisible. It was not respectable to be seen working in the fields; farming was by then \"ideologically viewed as 'man's work.'\" Outdoor activity was associated with men, while indoors was the respectable setting for women. Women might continue to engage in farm work, \"as long as these activities were kept out of sight.\" The woman who worked in the fields was \"a figure of the past, a ghost.\" These were the attitudes that advocates of farming for women in Britain had to contend with, and these were the attitudes that had a much longer shelf life in Canada, lasting well into the twentieth century.\n\nSMALL HOLDINGS, \"LIGHTER BRANCHES\" OF AGRICULTURE, AND \"FRIENDLY BANDS\" OF WOMEN\n\nAdvocates of farming for women in the nineteenth century had a variety of arguments that they drew on to challenge these attitudes. One was that women would remain distinctly feminine and would not compete with male farmers, as their work would be relegated to small holdings of a few acres, to the \"lighter\" forms of agriculture (dairying, poultry keeping, and horticulture), and that they would band together in farm settlements or colonies. Proponents \"had to tread a careful line between promoting an unusual career for middle-class women and maintaining a sense of social refinement and feminine respectability. After all, for decades, women had been told that work connected to the land was improper and unwomanly.\" The result was a division of agriculture into feminine and masculine spheres, with \"lighter\" agriculture enabling women to \"maintain their reputation and dignity,\" while not posing a direct challenge to male ownership of land and to the more profitable sphere of grain farming and large herds of livestock.\n\nA small-holdings movement of the nineteenth century in Britain, supported by politicians, social reformers, philanthropists, and agriculturalists, constitutes another point of origin for the growing pressure to admit women to the profession of farming. The ideal small holding was a \"market garden or family farm large enough to support the cultivator and his family, and small enough to be cultivated by the labor of the occupier and his family without substantial amounts of permanently hired labor.\" Discussions of the virtues of small holdings intersected with and involved the promotion of even smaller \"allotments\" of half an acre or less, for the production of vegetables and flowers, as particularly suited to women. The widely held assumption was that women did not have the physical capabilities and strength for larger acreages. Fruit, vegetables, flowers, and ornamental plants were the best crops for the woman small holder, and poultry, dairy cows, and bees were more suitable than livestock such as cattle. The 1903 book _The Lighter Branches of Agriculture_ , by Edith Bradley and Bertha La Mothe, is perhaps the fullest articulation of the realms of farm work seen as the province of women. \"Petite culture\" or the \"lighter branches\" meant \"all the work on the land which required skill rather than mere physical strength. It embraces work in the dairy, work in the garden and greenhouse; supervision of market gardens, culture of fruits, management of poultry and bees.\"\n\nSupporters of farming as a vocation for women rarely saw this as an individual endeavour. In her introduction to _The Lighter Branches of Agriculture_ , Lady Frances Evelyn (Daisy) Warwick, an influential advocate of agriculture for women, wrote that she looked forward to a time when \"a number of these settlements working on co-operative lines [would be] dotted all over England.\" Lady Frances Wolseley, who wrote extensively on horticulture for women and established a school for \"lady gardeners\" in Sussex, recommended that women garden in colonies, grouping themselves in \"friendly bands.\" Settlements or colonies of women would address the issue of isolation in the country; the gentlewoman needed companions of her own social standing or she might \"sink\" to the level of her neighbours.\n\nThere was heated debate, however, about the future of small allotment farming, which included more radical voices. Among the critics was Louisa Cresswell, the \"lady farmer\" of Sandringham Estate, a tenant of \"Bertie,\" the Prince of Wales. Cresswell was opposed to small holdings for anyone. After the death of her husband, she farmed 900 acres on the prince's estate for many years (until, she alleged, the prince's hunting parties destroyed her crops.) In her 1881 pamphlet, _How the Farming in Great Britain Can Be Made to Pay_ , Cresswell wrote that \"the proposal to establish an extensive system of small holdings or petite culture, as it is called, and which is argued by some to be a panacea for all ills, is likely to be a very hopeless undertaking.\" She championed larger farms: \"Upon arable lands, whether they be light, medium or clay, I do not think that 10,000 or 20,000 acres will be too much.\" \"I would also,\" she wrote, \"buy mighty machines and use them whenever practical... use self binders at harvest and every description of labour-saving machinery that the ingenuity of man can devise.\" Cresswell predicted (correctly) that there would be a revolution in agriculture with machinery. She was proud to say that her farm, where steam machinery was used extensively, had been \"pronounced by one of the keenest judges in England to 'have been left in the highest state of cultivation' and 'as clean as a garden.'\"\n\nIn her 1883 book, _My Home Farm_ , Katherine Burton, who was an experienced tenant farmer, advocated small but not tiny farms for women. She engaged in mixed farming, having dairy cows for milk, butter, and cheese, and raising pigs and sheep, poultry, and vegetables. She farmed for profit and not for family subsistence. Burton was critical of much of the advice given to women farmers: \"My own private belief is that the reason for the persistent recommendation of 'poultry farming' to 'ladies' is that gentlemen are aware that it is the most troublesome and least remunerative branch of the business\u2014at least if pursued separately.\" Prominent English farmer Katherine Courtauld also did not agree that women should pursue only the \"lighter branches\" of agriculture, instead advocating commercial large-scale farming. She farmed 2,000 acres, and in 1900 employed fifteen men and boys.\n\n\"THE AGRICULTURAL BRIGADE OF THE MONSTROUS REGIMENT OF WOMEN\"\n\nRationales for advancing the cause of women as farmers were varied and contradictory. Almost all, however, started with the assumption that there were \"surplus women\" in Britain who needed occupations or should be shipped off to the colonies (or both). The corollary was the \"surplus\" of men of the colonies (although this term was not used to describe them) who were in danger of degenerating. The problem of \"surplus,\" \"redundant,\" or \"excess\" women was first identified in the 1851 British census, which indicated there were 500,000 more women than men in the British Isles. The problematic \"surplus woman\" was middle class and educated; working-class women were not viewed as \"surplus,\" as they were believed to have occupations suitable to their station in domestic service or factories. Conventional occupations for the genteel single woman were as governess, companion, or seamstress, and these professions were underpaid and overcrowded. Who or what would shoulder the burden of supporting these women? And they were seen as burdens, as encumbrances, as pariahs. Women who did not conform to social expectations of marriage and motherhood had no obvious place in society. As will be discussed in greater detail later in this chapter, shipping \"excess\" women off to the colonies and dominions was widely seen as the best solution, proposed as early as 1862 by journalist W.R. Greg.\n\nLady Warwick was concerned with the educated \"daughters of professional men\" with large families but small incomes. Her object was to provide these daughters with a new field of work and means of livelihood through involvement in light agriculture. Women were advised to \"'go back to the land'; they can listen once more to the 'charm of birds,' and 'Nature, that sweet old nurse,' can teach them the wisdom and hope and love.\" Sending \"trained and cultured\" women into the country would \"have a salutary and energizing effect upon rural England. They can stimulate the local interest in village clubs, in cottage gardens, in the general principles of citizenship of a vast Empire, and in a hundred other ways can help to 'make the path a little brighter where they tread' by their sympathy and comradeship.\" If \"ladies\" could show they were healthy and happy working on the land, the more \"rustic damsels\" would be inspired to follow their lead.\n\nJournalist Virginia Crawford also saw agriculture as a solution to the problem of thousands of women from the country \"above the domestic servant class\" crowding into the cities, struggling to find work as teachers, governesses, bookkeepers, and secretaries. A few succeeded, but many failed, according to Crawford, losing their health and living a \"cramped and anxious existence in lonely lodgings or comfortless boarding houses and ... are thankful in old age to find a refuge in some governesses' institute or home for decayed gentlewomen.\"\n\nFarming as an occupation would be a blessing to the large number of \"idle women\" who would never become wives\u2014the \"surplus women.\" An 1879 article in _the Examiner_ , \"Gardening for Women,\" began: \"What is to be done with our surplus women?\" In her reply to an 1897 article entitled \"The Monstrous Regiment of Women,\" Edith Bradley, a social reformer who worked in partnership with Lady Warwick, wrote \"The Agricultural Brigade of the Monstrous Regiment of Women,\" proposing that women farmers could help to solve a myriad of problems facing England and the British Isles, including the \"surplus million.\"\n\nWomen of refinement and education were best equipped for the sort of outdoor work advocated by Frances Wolseley. She wrote that \"maidservants\" were \"totally unsuited\" to the profession of gardening, which required intelligent and educated ladies, \"daughters of professional men.\" The woman gardener who was untidy, had unkempt hair, disorderly clothing, and bad manners was not to be tolerated. \"Maidservants\" could work on farms if overseen by a farmer's wife who would \"look out for their moral welfare.\" The men employed in a private garden, according to Wolseley, would not tolerate a young woman of \"their own sphere,\" but would \"gladly allow a lady to direct their work.\" In her 1916 book, _Women and the Land_ , Wolseley gave further reasons why only refined and educated women were suited to the work, including that they were \"from their earliest days accustomed to riding and hunting; they play golf and out-of-door games, so that exercise in the open air comes to them quite naturally, and in fact many can barely exist without it.\" Women were required who could direct subordinate workers, and these \"should belong to the upper classes or upper middle classes.\" They had to be able to \"command and to exact respect.\"\n\nAside from addressing the \"surplus women\" issue, there were other rationales for involving women in agriculture. All sorts of anxieties that faced the nations and the Empire justified the cause. In \"The Agricultural Brigade of the Monstrous Regiment of Women,\" Edith Bradley wrote that women farmers could mitigate another of the most pressing national and social problems of the day, the \"wholesale desertion of the villages for the towns, or the emigration to foreign countries.\" The \"Agricultural Brigade of Women\" would \"stay the depopulation of our villages\" and \"keep some of the money in this country which is annually spent on foreign dairy, poultry and horticultural produce.\" Women of the agricultural brigade would be \"bringing back country life to England, and so assist in strengthening, not only the national, but the Imperial life of our Empire.\"\n\nRADICAL AND CONSERVATIVE ADVOCATES\n\nSupporters of agriculture and gardening for \"surplus women\" did not all share the same political views. Activists in the women's movement attempted to redefine the problem of \"surplus women,\" arguing that the issue was not the numerical excess but the lack of educational and occupational opportunities that could permit women independence outside of marriage. Useful work would be their salvation; the \"unproductive\" woman would become productive. Among the earliest of the nineteenth-century advocates of farming and land ownership for women were members of the middle-class feminist Langham Place Group, founded in the 1850s. They organized the Society for Promoting the Employment of Women and campaigned for married women's right to retain their property after marriage, for the right of women to take paid employment, and for wealthy women to own land and take up farming. Jessie Boucherett, the daughter of Lancashire landowners, was particularly devoted to this cause, but it was a small part of a broader campaign to expand women's involvement in skilled trades. She was determined to assist \"distressed gentlewomen.\" In her 1863 _Hints on Self-Help: Advice for Young Women_ , Boucherett proposed many professions, including home decoration, photography, nursing, bookkeeping, and shopkeeping. Farming was another idea proposed to enable women to support themselves. Social commentators such as Harriet Martineau wrote extensively about how attitudes needed to change toward women and work, that women as well as men should be educated for work, and that vast numbers of women were already working in industries. Martineau was the author of _My Farm of Two Acres_ , first published in 1865, which described her poultry, swine, and dairy enterprises and advocated women's economic independence through small-scale farming.\n\nThe significant number of women who operated farms on their own in Britain was cited by champions of women's rights, who raised questions about gender, land ownership, and the vote. Women farmers, who paid taxes and employed men who could vote while they could not, bolstered arguments for an extension of the franchise. Why, it was asked, should a woman farmer \"who in every way performs the duties of an employer... have no vote, whilst the keeper of a low beerhouse close by, who demoralizes laboring men, and is hardly able to write his name, exercises the right from which she is denied.\" An 1883 petition from 170 women farmers asked Prime Minister William Gladstone why \"the oft-time totally ignorant agricultural labourer\" should have the vote that was denied to them. Because they did not have the vote, \"widows and daughters of farmers are frequently rejected as tenants by large landowners for the sole reason that their sex disqualifies them from giving their landlord that Parliamentary vote which it has been his custom to expect from his tenants, and yet these same women have proved their undoubted business capacity by years of successful management during the illness or incapacity of their husband or father.\"\n\nIn 1884, Conservative Sir Robert Peel spoke of the injustice of women farmers being unable to vote while their male labourers could. He quoted an agricultural expert who stated: \"Fancy a woman farming 500 acres of land, and paying the usual contributions to the taxes of the country, having no voice in the representation of the country while her labourers have.\"\n\nSupporters of women's suffrage saw women gardeners and farmers as natural allies in the cause of the parliamentary franchise. Speaking in favour of women's suffrage at Birmingham in 1891, Millicent Fawcett declared there to be 38,000 female landowners in England and Wales, and of these 20,000 were actively engaged in farming. The census of 1891 \"showed that there were 21,692 female farmers and graziers in England and Wales, 564 female occupiers of market gardens or nurseries.\" Matilda Betham-Edwards, farmer and women's activist, and member of the Langham Place Group, was in favour of votes for women farmers. She wrote that in Suffolk in the early 1860s there were many \"lady farmers\" who were \"widows, sisters and daughters of deceased tenants to whom their lease had been renewed,\" with one widow leasing the largest farm in the parish.\n\nThe more radical advocates of gardening and farming for women advanced the rationale that this occupation could assist a woman in the event of marriage breakdown or the death of a husband or his failure to provide. As the author of a 1905 article observed, marriage \"did not necessarily mean for a woman provision for life.\" \"How many women,\" this author asked, \"one has known whose husbands have failed or been disappointed in life, to be thereafter chimney-corner encumbrances, leaving it to the wives to bring up, educate and launch the family?\"\n\nThere were also those with more conservative views, who did not wish to challenge or upset the gender order, who believed women's destiny was marriage and domesticity, but who nonetheless favoured some expansion of women's occupational opportunities to include certain forms of agriculture. Some advocated gardening or farming because they believed there were an \"immense number of women unfit for intellectual work.\" Farming and gardening was a \"reasonable\" vocation compared to \"unsuitable employments\" such as \"doctors, lawyers, members of Parliament, and heaven knows what else beside.\" The life of the gardener, small holder, or farmer was for \"our girls whose cleverness mainly lies in their hands... girls not brilliant at books.\" There would ever only be a \"small minority\" of women who \"would be able to embrace the learned professions, should those professions be universally thrown open to them.\"\n\nConservative advocates of farming for women were careful to stress that the \"lady gardener\" could retain her femininity. She could perform delicate work that did not require physical strength, such as \"budding dwarf fruit-trees... making cuttings, sowing and collecting seed, gathering and packing fruit, weeding, hoeing and the lighter parts of the tillage.\" Women gardeners were expected to have limited marketing ambitions and a low public profile; they would not supplant or compete with men gardeners, according to Frances Wolseley. Rather, they would \"supplement and increase the good work which men are doing for our land.\" They would assist by lending intelligence, refinement, and other womanly qualities. Another conservative impulse at work in counselling women to take up farming over other potential occupations, careers, or professions was that it would teach them skills that would remain useful after marriage. Women could garden both before and during marriage, which was still viewed by many commentators as the ultimate objective of a woman's life. As a writer for the _Leeds Mercury_ wrote in 1900:\n\nThere is one thing to be said of a training for women in gardening, especially which cannot be stated in reference to many another career for women, namely that, even if the student marries, the value of her training will not be lost, as is so often the case in other branches of industry. It is often said, with truth, that when a father goes to great expense in training his daughter for a profession or business, the outlay may be almost or entirely thrown away in the event of her marrying. But, unless a woman is to pass her life in the heart of a crowded town, training in horticulture will be valuable, and a source of delight to her, however much married she may be.\n\nPREPARING THE SOIL: EDUCATION\n\nAn obstacle identified by advocates of gardening, horticulture, and agriculture for women was the lack of available training and education. When Jane Chesney proposed a horticultural college for women in her 1879 article \"A New Vocation for Women,\" it was a \"bold suggestion.\" The lady gardener of her day, Chesney wrote, could learn only by reading, asking questions, and by \"sad and bitter experience,\" and as a remedy she advocated a course of training in horticultural principles and garden economies.\n\nGradual advances were made in admitting women to horticultural and agricultural education. The Horticultural College at Swanley, Kent, established in 1887, was originally intended for men only, but women were admitted beginning in 1891. By 1899 there were thirty-two women students taking the two-year course, and by 1903 it became a women-only institution, closing its doors to male students. Swanley reflected a shift in horticultural training from an apprentice-based system (that had excluded women) to one based on science and study.\n\nAt Swanley the students' time was divided between practical work and lectures. The students produced a regular supply of flowers, fruit, and vegetables for the London market. Professors from Oxford, Cambridge, and London lectured on natural sciences such as botany, geology, and entomology. Some women graduates from Swanley found positions as \"gardener's boys\" at the Botanic Gardens at Kew, and others at the Royal Botanical Gardens in Edinburgh and Dublin. Soon women trained at Swanley were teaching horticulture at places such as Lady Henry Somerset's Industrial Farm Colony (for \"female inebriates\") at Duxhurst.\n\n_Figures 7_ _and 8._ The Glynde School For Lady Gardeners in Sussex, England, established by Lady Frances Wolseley in 1902. The caption written by Wolseley for the top photo (Figure 7) is \"Students before they wore the kit invented by Miss [Elsa] More which was after adopted by other women who worked the land,\" c. 1902\u20138. In the bottom photo (Figure 8), from 1913\u201314 the students are wearing the \"kit\" designed for work on the land. Wolseley and her students encountered criticism such as only a \"complete failure as a woman could adopt such a career.\" Papers of the Viscountess Frances Wolseley, Hove Central Library, Hove, Sussex, Commonplace Book no. 196.\n\nIn 1898 the Lady Warwick Hostel in Reading was established, offering courses to women on horticulture, dairy work, market gardening, fruit culture, and beekeeping. The demand was high; there was a full complement of twenty-four students in the first year of operation and soon two more hostels were added. In 1903, Warwick moved her students to Studley Castle in Warwickshire, near her own stately home, Warwick Castle, and established the independent Lady Warwick College. This later become the Studley Horticultural and Agricultural College for Women and remained an all-women institution until it closed in 1969. By 1904, it was reported, there had been 250 graduates of Warwick's college since 1898, and of these twenty-four possessed small holdings of their own that they operated as dairy or poultry farms or market gardens. Other graduates were working at country houses, superintending dairies, gardens, and conservatories. In 1905 one journalist proclaimed that Warwick had \"convinced her bitterest opponents that in the lighter branches of agriculture\u2014such as dairy work, market gardening, poultry and beekeeping, and in the growing of fruit and flowers\u2014there is a means of livelihood for the gentlewoman in which she can live far more happily than in our grimy cities.\" Warwick also established in 1899 the Lady Warwick Agricultural Association, and in the same year launched the _Woman's Agricultural Times_ as its official organ.\n\nOther educational options included private gardening schools that began to spring up. By 1940 there were some nineteen such schools in England. Among them was Lady Frances Wolseley's school of gardening at Glynde, established in 1901. These schools were the preserve of women with income and the time needed to devote to two or three years of training. Private initiatives included the scheme of Victoria Woodhull on her estate at Bredon's Norton, Worcestershire, where by 1908 there were between twenty-five and thirty women studying agriculture through lectures, reading, and demonstrations. The school's purpose, according to Woodhull (the first woman to run for president of the United States) was not only to address the \"surplus women\" problem but to \"regenerate England,\" because the \"future of the race\" was in the land. All of these initiatives stand in sharp contrast to the situation in Canada, where well into the twentieth century there were very few opportunities for women to study agriculture or even horticulture.\n\n\"A DELUSION AND A SNARE\": OPPOSITION AND DEBATE\n\nThe idea that farming was a suitable profession for women and that agricultural education should be available to them was opposed by many. Advocates contended with ridicule and bemusement. The major objection was that farming was a \"man's domain\": women working in the fields defied a gender order, cast as timeless and traditional, in which they were relegated to hearth and home, and farm work defeminized women, making them unattractive to men. As one anonymous journalist objected in 1910, after noting that women were ploughing fields, this \"invaded what I regard as the last ditch of man's domain.\" He wrote that it was not \"good for women to lead laborious days behind the plough. Heavy manual labour produces a rough, unpleasant type of woman, and the only thing it qualifies her for is to plough that lonely furrow in life, which, however suitable to some politicians, is not the true destiny of women.\"\n\nCritics argued that industries such as cheese making, although once the domain of farm women, were not suitable for gentlewomen because they could be neither \"mistress nor maid,\" and there was nothing in between these two social positions. To be mistress required considerable means, since land, cows, and their own training in the skills required had all to be purchased. Nor could she be a maid; it was not possible for a \"young lady... go into a dairy-farm, in some cheese country, and give her services in return for her training and board.\" The dairymaid worked for years, \"lifting great weights, wielding heavy implements, straining every muscle in her body with reaching over the wide tubs, screwing up the ponderous presses, and turning and weighing the mighty cheeses which the ordinary run of ladies could no more carry to the scale than they could carry the farmhouse to the next parish... They would find hoeing turnips, or digging potatoes, light work in comparison.\"\n\nAn idea of the nature and intensity of opposition to women in the field is revealed in scrapbooks of clippings and correspondence kept by Frances Wolseley. For example, she received an anonymous postcard that read, \"I think if you taught those young ladies how to cook, they would be far more use in the world than [\u2014\u2014] up an old garden. P.S. Why don't you teach them housework to make them useful.\" There was heated debate in the letters to the editor section of _Country Life_ , also preserved in one of Wolseley's scrapbooks. As \"Cherry Tree\" wrote in response to an article about Wolseley's school: \"It makes one rather sad to think that an educated woman should be reduced to do the work suitable to a rough uneducated man, losing as she must all feminine grace and charm, and also the vantage ground her education ought to have given her over him. I can scarcely think that any except a girl without any intellectual faculties, and consequently one who could not rise to any position requiring mental gifts, would choose such a career. In other words, I cannot think that anyone not a complete failure as a woman could adopt such a career.\"\n\nOpponents insisted that training in agriculture was wasted on girls who were destined for marriage. In _The Revival of English Agriculture_ , P. Anderson Graham wrote: \"Educate women for what purpose you please, and map out the future for them as carefully as if it were to go in a Government survey, Love steps in at the end and upsets all the plans.\" He was willing to admit, however, that there was a \"residue\" of \"well born women... who in many cases pass unwedded lives,\" and he supposed that they might be able to pursue _la petite culture_ , although \"they certainly cannot do the hard work\u2014no woman can without sinking into the position of a drudge.\"\n\nSupporters countered with an array of arguments. One wrote in 1891 that \"there is something in the female mind that is peculiarly conformable to field culture and the care of stock. I need scarcely point out that ladies have always been the best gardeners, and the more field culture is made to correspond to garden culture the better will it be for all who have to do with the soil in this country.\" Phillip Astor wrote favourably of \"Lady Farmers\" in 1900 after a visit to the school at Swanley. The article began with a photograph of students ploughing. He argued that Swanley \"proves that women find the work of ploughing quite within their capacity, and do not suffer physically from the hard work. Of course, it is not intended that women should oust men from the work of the fields, but it is considered desirable that they should have a practical knowledge of it.\"\n\nAn 1898 article on \"Lady Gardeners\" by \"Darley Dale\" weighed the cons and pros. The profession was not for delicate women, and it would involve sacrifice from any woman. The lady gardener would have to rise early, work hard, stand a great deal, and be exposed to all weathers. She would not have \"very white, delicate hands; potting, planting, sowing, weeding, taking cuttings, all spoil hands.\" Nor would she be able to take care of her complexion, as \"she must be exposed to the east winds of spring, the hot sunshine of summer, the gales of autumn, and all the freaks of an English climate.\" But the lady gardener who made these \"sacrifices\" to \"feminine vanity\" would be \"a very bright, happy cheerful woman; the freedom of her life, and the exhilarating effect of being so much in the open air, probably contribute to this.\" The result, according to this author, would be \"a thoroughly womanly woman who has gained some masculine advantages without losing any of the tenderer qualities of womanhood.\"\n\nYet as the strong opposition illustrates, women seeking an occupation and an income, whether through agriculture or most other professions, were viewed with suspicion. They were \"icons of unsettling change.\" Their independent earnings and autonomy from families were altogether a departure from the white, Anglo-Celtic norm of feminine respectability, a dangerous challenge to the traditional gender order. Low-paid, exploited, wage-earning women were regarded as a moral problem, and reformers devised various techniques of regulating and controlling their activities. Equally unsettling and controversial were the \"New Women\" of the educated and middling classes. These \"New Women\" contested Victorian definitions of gender, some fighting for women's rights and seeking professional careers, and some even opting for a single lifestyle. They further fuelled fears that the gender order, the foundation of society, was cracking.\n\nThrough expectations of appropriate feminine dress and deportment, women's bodies were moulded to be more docile than men's, and their mobility was much more limited. There were (and remain) norms of feminine motility, a disciplinary regime of femininity that restricts women's posture and movements. Women were (and still are) trained to move with \"grace\" and not to reach and stretch and extend the body in sports and certain physical tasks. As Sandra Lee Bartky has argued, \"the imposition of normative femininity upon the female body required training,\" and \"the modes of training are cultural phenomena properly described as 'disciplinary practices.'\" In Victorian times, the clothing worn by middle-class and elite women restricted their movement and ability to do any manual labour. Long skirts, tightly laced corsets, bustles, hoops, weighty petticoats, and high-heeled shoes made it virtually impossible to bend, stoop, or adopt the many other postures agriculture and gardening required. In wearing this gear, women \"were suggesting that they had others employed to perform these functions.\" Thorstein Veblen wrote in his 1894 \"Economic Theory of Women's Dress\" that the corseted Victorian woman's inability to move was evidence of her role as a decorative ornament who did not have to perform any manual labour, signifying her husband's wealth and power.\n\nThose women who exercised and altered their bodies, becoming strong and athletic, were censured. In a 1900 article on \"The Redundancy of Spinster Gentlewomen,\" the author \"T.P.W.\" criticized women who were \"almost wholly given up to outdoor pastimes of a more or less robust and muscular character\":\n\nThe very exercise of muscular achievements suitable only for men has the effect of hardening and the roughening the feminine exterior; while it is too often associated with a strident voice, a self-assertive manner, a brusque and abrupt address to malekind, and a general lapse of attractiveness. All of which attributes tend to damp a man's matrimonial intents.\n\nWomen with the physical attributes to farm risked being seen as not-women, as desexualized and unattractive and \"unnatural.\" They were \"not seen as real farmers by men but as inferior others who try to be like men and cannot therefore be taken seriously.\" Single women farmers did the work on their own, it was assumed, only because they did not have husbands to do the work. Fathers, brothers, and labourers were seen as indispensable to the woman farmer, confirming that women could not farm without men. Single women farmers might perform the work themselves, but were still not able to farm like men. \"Physical strength, sturdiness, aggressiveness, competitiveness, speaking one's mind and dominance\" were masculine qualities, while women were to be \"slim, fragile, submissive, nurturing, quiet and withdrawn.\" A single woman farmer was not a potential wife, as she did not embody and perform feminine attributes. She was excluded from both the feminine and the masculine realms.\n\nThis was the fate of two sisters, Sarah Spencer and Mary Spencer, who farmed in Sussex. In an 1842 article on \"Female Farmers,\" the author adopted a kindly tone when describing the Spencers, explaining that they farmed because their marriage prospects were slim, that \"their persons, though not uncomely, were not so attractive as to flatter them that without fortunes, they could marry advantageously.\" While the author felt they were farming \"without ceasing to be _gentlewomen_ \" and that their farm was \"much to their credit and advantage,\" he also observed that they were not \"popular characters.\" He wrote: \"This was the hard fate of the Spencers, who, instead of gratitude, long experienced little else than discourtesies and opposition in the neighbourhood. The more active of them was called _Captain Sally_ ; and her sister, her _Man Mary_.\" Things had not changed dramatically by 1907 when Estelle Long, a \"girl farmer,\" was described as a reclusive character to be shunned. On her eighteen-acre farm in Surrey, she lived in a hut (a \"dreary\" and \"desolate\" spot) and did everything herself: \"reaps, hoes, sows, kills and dresses her poultry, takes her produce to market, grooms her pony, and cleans the harness and trap, and mows her hay.\" Long was a graduate of Lady Warwick's school of agriculture, and her father, J. Long, was a professor and authority on agriculture, but none of these credentials made her any less suspect. In her neighbourhood, it was said, \"the more superstitious of the villagers look upon her... as having 'turned witch' or something of that sort.\"\n\nThe few single women farmers of Western Canada were to be similarly stigmatized, and well into the twentieth century. Farmers such as Lizzie Hillis (mentioned in the introduction) and \"Jack\" May (to be discussed in Chapter 4) were criticized and marginalized. But in the 1890s there was optimism for the cause of the \"lady farmer.\" One advocate declared in 1891 that Queen Victoria herself could be claimed as \"the first lady farmer in this country,\" as she took great interest in her farms and was an \"illustrious example\" of the fact that \"in respect to stock-keeping, women have softer natures than men, and delight to pet and cherish dumb creatures of all kinds.\" Her \"chief source of pleasure\" allegedly, was her prize-winning cows. While at Balmoral she personally inspected her home farm every day, particularly the dairy, and she advised on butter and cheese making. The products of her farms were sold in London, and \"her thrifty Majesty earns many an honest penny in this way.\"\n\nProponents of farming for women had made important advances in challenging the conviction that women who worked outdoors were rough, coarse, indecent, and masculine, insisting instead that respectability and refinement would not be lost. Things had changed from the early 1800s, when a woman with \"pretensions to gentility... had to distance herself from farm production.\" By the early twentieth century, the topic of women in agriculture and horticulture was very popular and highly visible. In 1910, for example, a series of articles appeared in the London _Daily Mail_ with headlines such as \"The Successful Woman Farmer: How Two Women Run an Agricultural Farm in England,\" and \"The Woman Poultry Farmer: Experiences of a Two-Acre Farm.\" At that time Georgina Binnie-Clark wrote inspiring columns describing her experiences as a farmer in Saskatchewan (to be discussed in Chapter 5). Yet opposition remained intense, and grew in new directions as the competence of college-trained women farmers was questioned and denigrated. Some advocates for the \"gentlewoman\" farmer hoped that the colonies might provide a more welcoming and congenial environment, as Binnie-Clark appeared to illustrate.\n\n\"SURPLUS WOMEN\" FOR THE COLONIES AS \"HOME HELPS\"... AND FARMERS\n\nA host of keen imperialists devoted to \"civilizing\" the colonies through the importation of women of the British \"race\" were active by the late nineteenth century, and they were anxious that women of \"superior breeding\" and education be pressed into service. \"If the Mother Country sends us enough people we shall grow strong as British powers,\" wrote one staunch Australian imperialist, and \"if she does not we shall either evolve quietly into races determined by our alien immigration, or we shall be swamped and effaced by invaders.\" Women imperialists worked to dispel attitudes of indifference, suspicion, and fear toward the colonies among \"refined\" women and awaken their sense of patriotism toward the Empire. These transplanted women were to transport British culture and identity to the colonies, and nurture it there. Anxieties about being \"swamped and effaced by invaders\" were heightened in colonies such as Western Canada, where Americans and ethnically diverse Europeans began to arrive in significant numbers starting in the later nineteenth century.\n\nPromoters of emigration tried to persuade colonial employers of the virtues of educated \"home helps,\" a description that was intended to create a category well above the rank of domestic servants. Women who were home helps would fit comfortably into the family circle, eliminating the need for costly servants' quarters. They would \"tackle labour with their hands _and_ their brains.\" Explorer and writer Arthur Montefiore Brice explained in his 1901 article, \"Emigration for Gentlewomen,\" that in the colonies \"you have to pay atrociously high wages for a miserable servant, who has vulgar notions of what are her rights and her duties, who cares nothing for your comfort or your welfare, who will not do any work which is distasteful to her, and who leaves you at a moment's notice.\" A \"home help,\" however, a \"healthy amiable woman, educated somewhat, able to cook and clean, sew and mend,\" would be regarded as \"an equal, as a friend, as a member of the family\"; she would be treated as \"a near relative, even a sister of the mistress.\"\n\nA problem, however, was that domestic work did not appeal to the educated gentlewomen, despite assurances that being \"companion helps\" or \"home helps\" would entail no loss of social status. They were told that they would find adventure, happiness, and quite likely husbands, and would be doing a great service to the Empire. They were \"encouraged to see emigration to the colonies and employment in someone else's home as a logical path to financial stability, self-fulfillment, and sanctified heterosexual love.\" Here the problem of the \"surplus\" educated woman of the \"motherland\" intersected with and was seen as a solution to the \"servant problem,\" and to the bachelor (or surplus male) problem in the colonies. White women were needed to work on the farms and ranches of the colonies, rather than the \"half-caste or full-blooded native\" or whites of the serving class, who were also undesirable.\n\nIn the 1880s, a network of female imperialists began \"an aggressive long-lasting promotional campaign to entice single women above the working class to emigrate.\" Various associations were formed, becoming in 1901 the British Women's Emigration Association, established to encourage and assist women of \"good character\" to emigrate. Domestic service for educated women, thinly disguised as home help, historian Lisa Chilton writes, \"was primarily a means to an end\u2014the end being the proper feminization of the empire.\"\n\nNot all of those concerned with the \"surplus women\" problem saw emigration to the colonies, where they would perform domestic work and then marry, as the solution. Some feminists criticized emigration as a strategy to discourage activism for women's rights at home, and as a means of maintaining and transplanting to the colonies women's traditional roles as wives, mothers, and moral guardians. Feminists \"began to realize that the unclear distinction between emigrating to find work and emigrating to find husbands was embarrassing.\" The problem, as they saw it, was not \"surplus women,\" but restricted education and employment opportunities. To Jessie Boucherett the solution was not emigration but extending opportunities for occupations and education and reforming the institutions that treated women as unequal to men. Women needed to be trained for occupations and pursuits other than matrimony.\n\nAs early as in her 1863 book, _Hints on Self-Help,_ Boucherett identified a central conundrum: the colonies were not interested in genteel educated women. It was impossible to persuade potential employers in the colonies that the educated woman made a good domestic servant. Boucherett quoted a Canadian emigration agent as saying that \"there exists but a very limited demand in this province for the class of women in question.\" He warned that \"the introduction of such a class into Canada would be attended with consequences far from advantageous,\" and he requested the Government Emigration Board to \"discountenance the emigration to this country of any grade of women higher than the domestic servant.\" Boucherett wrote that the same answers came from Australia, and continued:\n\nNow, if this little history of the proposed emigration of educated women were not tragical, it would be comical. England so anxious to send them away, the colonies so afraid of having to receive them; England says, \"Why don't you go to the colonies? You are not wanted here, you are burdensome to us, and we will gladly pay your passage to get rid of you.\" The colonies hearing this indignantly exclaim, \"For mercy's sake, don't send us your useless creatures! We want men to fell our Woods, cultivate our land, tend our sheep and cattle, and women to cook our dinners, and wash our clothes, but as to educated women, we don't want them, and we won't have them; if they come they will be worse off than at home, for we have no workhouses to put them in.\n\nBoucherett proposed the radical idea (in part tongue-in-cheek) that every young man in England be compelled to emigrate when he reached twenty-one. The scarcity of male labour would mean that women would be employed in many occupations identified as male, enabling the superfluous women to be provided for and thus no longer superflous.\n\nHistorian Jane Hammerton argues that female emigration was initially a feminist project in the 1860s but then became an un-feminist project, as supporters of emigration were committed to a separate-spheres ideology. Others have since questioned this interpretation, arguing that female imperialist organizations had powerful links to a broader British women's movement. Lisa Chilton found that the dominant image these organizations created for public consumption celebrated feminine power, nurturing visions of a \"new class of women for the colonies.\" Promoters of emigration saw in the colonies possibilities unavailable in Britain, and had \"unbounded faith in the abilities of suitably educated women to be successful in whatever venture they might undertake.\" In the colonies, they \"would carve out meaningful roles and identities for themselves, and... reshape the mutable male environment of the colonial frontier.\" But as one devoted supporter of emigration of women to the colonies, Lady Knightley of Fawsley, wrote, the goal of marriage and motherhood in the colonies was paramount in the minds of the philanthropists who assisted women to emigrate: \"Helping women of every grade to stand for all woman is worth, in Empire building, in evangelizing work, in going where women are prayed for to make homes for good living men, where women can be mothers of quivers full, without fear of there ever being one too many, for there will be plenty of work for every hard-working boy of every class, and a Jack for every Jill.\"\n\nAware that domestic service, even when relabelled as the more exalted home help, held little appeal to educated women, some advocates of female emigration to the colonies cast about for other potential occupations, and farming was one that emerged from a \"range of possibilities.\" The promise of land and the vocation of agriculture, it was thought, could be held out as an inducement to emigrate for genteel educated women who would not stoop to domestic service. Proposals included \"Tea and Silk Farming in New Zealand\" as ideal enterprises for \"educated yet reduced gentlewomen.\" This sort of work would not \"rob them of one iota of dignity, or lower them a single inch in the social scale.\"\n\nWriter Jessie Weston, who was originally from New Zealand but who settled in London, wrote in 1891 in \"Hints for the Single Women of the United Kingdom\" that there had to be some inducement other than marriage and domestic service for women to leave England for the colonies. \"Marriage may not be the desire of many of the female sex in the mother country,\" Weston wrote, \"and still they might be induced to emigrate if sufficient inducement were found.\" They should become \"land owners and enterprising settlers in the Colonies.\" Weston was sceptical of farming opportunities for women \"in a severe climate like that of the Confederation [Canada],\" instead advocating agricultural pursuits for women in South Africa, New Zealand, Tasmania, and Australia. She wrote: \"All the means of earning a livelihood we have mentioned are of and from the soil, the possession of which in all times and countries is, and has been, the source of dignity and power to its owners. To be the proprietor of an orchard, a honey-farm, a chicken farm, a vegetable farm, would fill the lives of women, now wasting away for want of an object upon which to devote their energies, with an absorbing interest, would make them useful citizens, and add to their happiness. Independence and plenty to do are powerful factors in the total sum of human happiness.\"\n\nWeston recommended small-scale farming, \"which we presume would be the aim of sensible women, who are not likely to ruin themselves with great undertakings, like the male sex have so often done. As in farming, a piece of land from ten to forty acres is a source of greater profit and pleasure than a block of five hundred acres.\" Farming on a large scale, Weston observed, required \"capital, labour, and, more than common sense, knowledge, while the profits are relatively less.\" Women who farmed on a larger scale, she believed, were successful only if they carried on as widows \"what was left in good working order by their husbands.\" While capital was required for a small farm, Weston saw no reason why women without capital could not emigrate and soon save enough to purchase land.\n\nFor Weston, the goal of sending women agriculturalists to the colonies was to preserve rather than challenge the status quo. The \"surplus\" single women of the United Kingdom were, or sought to be, wage earners, and they thus \"help[ed] to block the labour market, thrusting out the heads of families, whether male or female.\" (In Weston's view, heads of families ought to be the wage earners.) She also believed that sending women to the colonies as a means of addressing \"the utter helplessness, the apathy of despair of the poor\" \"would be more to the credit of the female sex than all their exertions on the Suffrage question,\" and more useful as well: \"A practical exposition of the ability of the female sex to become land-owners and enterprising settlers in the Colonies will be of more material advantage to woman than all oratory and literary efforts to prove the equality of the sexes.\"\n\nThere were many others who chimed in, arguing that occupations other than marriage had to be offered to women sent to the colonies. The author of a 1902 article, \"The Need of Women Colonists in South Africa,\" wrote, \"It scarcely sounds decent to cart women out to the colonies for the simple purpose of matrimony, however laudable in itself and approved by ancient precedent. Some women, I am told are not 'nice' to marry, whilst, strange as it may appear to mere men, other women do not care about marriage.\" This author advocated training for potential women colonists in gardening, poultry raising, and beekeeping.\n\nCOLONIAL TRAINING SCHOOLS\n\nAdvocates of colonial farming for genteel women from the United Kingdom, concerned that the women would be unaccustomed to manual labour and to farm work, issued calls for training schools. There was a model to emulate: the Colonial College for sons of gentlemen, established in 1887 in Suffolk, where practical as well as scientific instruction was offered on a host of topics, including agriculture, surveying, and forestry. This institution addressed the problem of the \"greenhorn\" who arrived in a colony, only \"to undergo\u2014likely among rough and ignorant strangers\u2014things which his previous bringing-up has rendered distasteful to him... to work in the open fields from dark to dark, to eat the coarsest of prepared food, and to lodge in a wretched shanty.\"\n\nAround the turn of the century a large number of colonial training schools for females quickly materialized. In most the emphasis was decidedly upon domestic rather than farm work. The earliest to be established was the Leaton Colonial Training Home in Shropshire founded in 1890. The objective was \"to give practical training in domestic work to ladies wishing to proceed to the Colonies to join their relatives, or as Companion helps.\" Pupils were \"those of the middle and upper middle class, who have been well educated at school, but who have had little to no training in domestic duties, and who being obliged to work for their living, prefer to try their fortunes abroad rather than to seek employment in England where almost every branch of women's work is overcrowded.\" Miss A.L. Vernon, the \"lady superintendent\" of the school, wrote in a 1905 pamphlet on the Leaton Colonial Training Home published by the British Women's Emigration Association that the school was intended to be a\n\nmeans of fitting women who have no particular talents or gifts, for a useful, purposeful life, more easily to be found abroad than at home... Anyone who has come much in contact with that most hopeless individual, the middle-aged, unmarried woman with no profession and an income only sufficiently large (and often not even that) to keep herself alive, must desire to save girls of the coming generation from a similar fate. Women of first-class ability will probably always be able to find remunerative employment in England... but to the large class with no special qualifications and not great ability, life in the Colonies offers much brighter prospects.\n\nThe \"mother country,\" Vernon wrote, derived the advantage of the \"removal of superfluous women,\" while there was an \"even greater gain to the Colonies of receiving capable useful women, who are needed as servants, teachers, or nurses, and ultimately as wives.\" Vernon admitted that this last consideration was of the utmost importance to all who \"see in our Colonies only a Greater Britain which they wish to keep in the hands of English men and women, and to see peopled by the descendants of English parents.\" Aside from learning how to wash clothes, cook, and scrub floors, pupils learned poultry keeping. The school was located in an \"old-fashioned\" manor house that did not have \"modern conveniences,\" helping to make the pupils \"adaptable and resourceful, and able to do their work with the simplest appliances.\" The Leaton Colonial Training Home moved to Stoke Prior in 1907, by that time boasting that over 350 women had been trained, and \"nearly all have gone to and are living in the Colonies.\"\n\n_Figure 9._ Article on the Colonial Training Farm at Arlesey, England, \"to prepare girls who wish to emigrate for the exigencies of Colonial life.\" For two years students took lessons in plain cooking, breadmaking, laundry, pickling and preserving, gardening, dairying, poultry and pig farming, carpentry, chopping wood, and digging up rough ground. Arlesey focused on Canada as the destination for its graduates. _The Bystander_ , 16 September 1908, 610\u201311.\n\nIn 1902 Lady Warwick established a one-year course of colonial training at her school in Reading and then at Studley. This program placed more emphasis on domestic skills than on farming and\/or horticulture, with three months each devoted to \"cookery, housewifery, laundry and dressmaking, dairy and poultry-farming, flower, fruit and vegetable gardening.\" The students were also taught substitutes for ingredients or how to manufacture their own, such as making yeast from potatoes. \"Their training in fact, will consist very largely in doing without things,\" was one description of the colonial course.\n\nThe Swanley Horticultural College also established a Colonial Branch in 1902, anticipating an increase in the number of women emigrants to South Africa, offering a one-year course of \"practical training in Gardening, Dairying, Poultry, Cooking, Fruit Bottling and Jam Making, Laundry, Hygiene, Sanitation, South African Languages etc.\" Among the many competing institutions and programs, Swanley was distinct because of its curriculum that aimed at educating women to fill skilled occupations in teaching, gardening, and agriculture in the colonies, although domestic work was also included. The Swanley program also aspired to the goal of settlements or colonies of women engaged in the \"lighter branches\" of agriculture. By 1909, however, a change in the program's name to the Colonial and Home Domestic Training Branch acknowledged that there were few placements in the colonies of graduates in horticulture.\n\nIt seems that very little accreditation or inspection was required to open a training school for women headed to the colonies, and programs proliferated. In 1904 a school in Domestic Training for Gentlewomen: For Colonial and Home Life opened in \"a small private Ladies Club in Chelsea at very moderate fees.\" The pupils were taught plain cooking, house and parlour work, and domestic economy. The school advertised itself as the only residential training school in London devoted to the purpose of colonial training, meant specifically for the benefit of girls who could not afford a long and expensive education. That same year a new Training Home for Ladies opened in Devonshire, where the emphasis was on domestic economy, including cooking, jam making, dressmaking, laundry, plain gardening, simple carpentry, upholstery, butter making, and poultry raising.\n\nThe Arlesey House Colonial Training school at Hitchin opened in 1907. Here, as at Studley, the training focused on \"making do\" when \"far from civilization.\" The practical instruction included \"plain cooking, bread making, riding, driving, stable-management, [and] simple carpentry.\" There was, however, instruction in farming small holdings, and after taking the full two-year course the graduate was pronounced equipped to farm her own land if she so wished. A critic of the school commented on the \"vagueness\" of the training, as it was not clear for what colony or region of a colony the women were being trained: \"You might keep house for fifty years in most parts of New Zealand and never want to do most of the things taught at this school.\"\n\nTraining for Canada was increasingly the focus at Arlesey. Journalist Sarah A. Tooley visited Arlesey in 1910 and wrote an article in the _Globe_ (Toronto) on \"Training Girls for Life in the Colonies.\" A conference with the theme of Canada was hosted there that same year. The principal of the school, Miss J.S. Turner, explained that the theme was chosen because \"such a very large proportion of the girls who wrote to her about colonial training wanted to go to Canada.\" In the conclusion to her article Tooley wrote, \"The aim of the school is to fit women for colonial life, whether as cultivators of land on their own account, as gardeners, poultry-keepers, or as the wives and mothers of homesteaders.\" She also noted that Miss Turner had plans to establish branch schools in the various colonies, but this did not materialize in Canada.\n\nSeveral other colonial training schools were established by 1912. There were so many by this time that staffing them may have constituted one solution to the \"surplus women\" problem. Battersea Polytechnic offered a three-month program through its Training Department of Domestic Science: Preparation for Colonial Life, which included household management, cookery, laundry work, and needlework. At Lane House, Brandesburton, Hull, a Mrs. Harrison established \"a small private colonial Training School Highly recommended and conducted by Ladies. The house stands on its own grounds a few yards away from the farm, and the work is conducted as much as possible as it would be on a Colonial ranch.\" The training here covered housework, cooking, dairy and laundry, curing bacon and hams, fruit bottling, preserving, poultry raising, beekeeping, and gardening.\n\nIn 1914 an Overseas Training School for Women was established at Hoebridge Farm, Woking Surrey, by Rupert Guinness, of the wealthy brewing family. Guinness was a keen agriculturalist, as was his wife, Gwendolen Guinness, who was also involved in emigration societies such as the Colonial Intelligence League. Encouraged by the success of the Emigration Training Farm for young men from the public schools, the Guinnesses extended this work to women and girls. The school was for Englishwomen of the educated class desirous of making homes in the dominions, and its emphasis was on \"domestic science.\" A farmhouse was equipped under the direction of a Canadian woman, a graduate of the Macdonald Institute in Guelph. Housework would be undertaken \"according to Canadian practice,\" and students would learn to cook \"all dishes common in Canada.\" A short course of eight weeks for \"Home Makers Overseas\" was recommended to all women \"going to join husband, brother, or father, as well as for home helps or those to be engaged in the lighter forms of agricultural work such as dairying, poultry raising.\"\n\nGirls and women who attended the colonial training programs must have come to Western Canada, but there are few traces of their presence. Emma (Roberts) Ducie was born in Yorkshire in 1883 and came with her family to Saskatchewan in 1907. She had attended the Home and Colonial Training College supported by the Anglican Church before coming to Canada, and credited the training college \"and its far flung students with making her realize there was a world beyond Great Britain.\" This may have been an institution that trained teachers rather than providing the sort of domestic colonial training detailed above, which was designed for girls with little interest in intellectual pursuits. Ducie \"used her training to advantage\" while teaching school in Saskatchewan. She married a homesteader, and they farmed together for forty-two years and raised three children. Ducie organized the local Homemakers Club (later Women's Institutes) and planned reading courses for rural women on topics such as \"farming, gardening, international affairs and education.\"\n\nTHE IMPERIAL COLONIST AND WOMEN FARMERS FOR THE COLONIES\n\nA growing enthusiasm for sending British women as farmers to the colonies can be traced in the journal the _Imperial Colonist_. In the late nineteenth century the Women's Emigration Society, the United Englishwomen's Emigration Society (renamed in 1901 the British Women's Emigration Association, or BWEA), and the Society for the Overseas Settlement of British Women all worked to ensure that women of \"good character\" were sent to the colonies, arrived safely, and received adequate reception upon arrival. The BWEA published a monthly journal, the _Imperial Colonist_ , inaugurated in 1902 and edited by Lady Knightley of Fawsley, who was devoted to the cause of women's emigration to the colonies and who had a particular interest in agriculture. This organization advocated farming for single women in the colonies, among many other occupations, all rather uneasily alongside an even greater emphasis on domestic service or home help as a training ground for marriage. In the wake of the South African War, that colony was a major focus of the journal when it first appeared, and Fawsley was particularly devoted to South Africa. The _Imperial Colonist_ was filled with references to the need for women to transform \"the blood-stained veldt\" into \"a loyal and prosperous community living in peace and harmony beneath the British flag.\"\n\nBut from the first issue of the _Imperial Colonist_ , much attention was paid to Western Canada as a destination for girls and women who wanted a life out of doors, as home helps, as mothers' helps, or as sisters helping brothers. Slowly there also crept into the pages suggestions that women might farm land of their own in Western Canada. In any case, they would bring culture, music, and refined ways that would improve the lives of men in the outposts of empire. Founder and first president of the BWEA Ellen Joyce announced in the first issue: \"The women wanted in Western Canada are those healthy, countrybred women who love and understand animal life, and who prefer the freedom of the country to the conventionalities of the town. They must be women of some culture, but who have training in domestic arts by practicing them, and who will keep up the tone of the men with whom they mix by music and book lore when the day's work is done.\"\n\nDespite no expressions of interest in women farmers from any of the colonies, the idea of agriculture as a potential occupation for British women settlers gained momentum in the _Imperial Colonist_. Opportunities for women to study or attend conferences on agriculture before setting out for the colonies were advertised in the journal. In the third issue it announced that Lady Warwick intended to hold a conference of women engaged in the \"lighter branches\" of agriculture. Small holdings and horticulture were advocated in the journal: raising poultry, dairy, fruit, vegetables, or some combination of these (despite the fact that these sorts of enterprises were not characteristic of successful farms on the prairies). Colonies of small holders close to railways and towns or cities, rather than on the isolated prairies, were proposed. By the twelfth issue (1902), an article on \"Woman's Position in Canada\" noted that \"there is room in the country for single women with a little capital, who may invest in the establishment of poultry farms, either near one or other of the cities within reach of the railway.\" It was anticipated that the women would first work as home helps, however. In 1903 the journal annouced \"offers on the spot\" in Calgary \"for yeoman class women to go on ranches to join family life; work is hard but life is healthy.\" Marriage remained the true goal and gauge of success, however; the same issue noted that because so many of the home helps sent to farms had married, there would be many openings in the spring in the \"Far West\" of Canada.\n\nDetails about difficulties, challenges, and disadvantages that awaited women who wanted to farm land in Western Canada were not dealt with in the _Imperial Colonist_. The specifics of the \"free\" grant of homestead land (160 acres for a filing fee of ten dollars), a privilege available only to widows with children, were not described in any detail. Advertisements that ran in many issues for several years in the _Imperial Colonist_ proclaimed \"160 Acres in Western Canada Free. Healthy Climate. Good Crops. Free Schools. Light Taxes. Abundant Water,\" but made no mention that most women were not eligible for this land.\n\nNor was it ever mentioned that single women could have a free grant of homestead land if they moved to the American West. British women were directed only to the British colonies and encouraged to see themselves as vital to the great British imperial enterprise. The _Imperial Colonist_ discouraged emigration of single women to the United States with warnings that there would be no one to meet and house them, which would \"leave the Englishwoman stranded,\" and that she could then be lured by Mormons into a life of polygamy. Women were urged to go to Canada \"under our own flag,\" where they were needed to stem the tide of immigration from the United States into Canada.\n\nHopes that British women could farm in the colonies were not solely trained on Western Canada, and initially South Africa received a lot of attention. The _Imperial Colonist_ reported in January 1904 that the Agricultural Sub-Committee of the South African Colonization Society had devised a scheme for a dairy and poultry farm near Potchefstroom in South Africa. It was to be operated by two graduates from Swanley and ten others who would rent a farm, and there were hopes that this might form the nucleus for a prosperous settlement of women farmers. The scheme did not materialize. This was followed in March 1904 by the announcement of plans for a Women's Settlement in the Orange River Colony, where plots of irrigated land were to be offered to \"lady settlers.\" It was also hoped that women could play a part in the agricultural and horticultural development of the Transvaal, and there were calls in the _Imperial Colonist_ for women who had a little capital, some knowledge of climatic and other conditions, and \"the tact and power necessary for the management of native labour.\"\n\nThere were many reports in early issues of the _Imperial Colonist_ of Swanley graduates being sought in South Africa for positions as gardeners, and of the successes of a few who took up these positions. These reports generally stressed the success of women gardeners in managing \"Kaffirs.\" In February 1906, Mary Hewetson, a former Swanley student and head gardener at Pietermaritzburg, was managing about thirty acres of fruit, flowers, and vegetables, as well as a poultry yard, with the aid of \"six Kaffirs.\" A year later Hewetson had taken up a forty-acre plot of irrigated land of her own in Natal with a woman friend. This announcement, however, was soon followed by \"sad news of the death of Miss Hewetson,\" with no explanation of the cause. Hewetson was heralded in the September 1907 _Imperial Colonist_ as \"a Pioneer and a most able one in the work of establishing women in agricultural and horticultural pursuits in South Africa.\" A few months earlier, Mrs. Macdonald, the secretary of the Pietermaritzburg branch of the South African Colonization Committee, had been \"murdered by her Indian servant.\" Following these events there was less promotion in the _Imperial Colonist_ on opportunities for women farmers in South Africa. Poultry farms in Natal, it was reported, were precarious because of \"thieves and strange new diseases.\" Vegetable gardening there was \"chiefly in the hands of coolies who rent and cultivate most patches by rivers.\" This was seen to be difficult for the British woman gardener, as \"the hard-working, frugal Indian coolie has made market gardening his specialty and it needs skill, perseverance and some little capital in order to compete with him.\"\n\nArticles on South Africa in the _Imperial Colonist_ often focused on topics related to managing local servants. Stories about successful Swanley graduates stressed the proficiency of women gardeners in managing \"Kaffirs,\" while other articles discussed matters such as \"The Wrong Way to Manage Black Servants\" and \"The Peril of the Black.\" Even the somewhat successful Mary Heweston had found it a challenge to \"manage\" her servants; she reported in 1906 that \"I have a dozen or thirteen 'boys' of all kinds, some utterly raw, ignorant, unintelligible and stupid\u2014others, with fixed ideas of what they should or should not do\u2014a difficult team to drive, and often at night I wondered how I should get through the next day.\" A 1919 article on \"Empire Migration\" warned potential home helps headed to South Africa that the work \"may probably be to superintend the native servants, and she must be able to keep them in their right place and prevent any liberties, as familiarity might have terrible results.\" Yet the author did not want to frighten or discourage, adding: \"Not that there need be any fear for the safety of a sensible girl who follows advice, especially where there is a white man to act as protector.\"\n\nBeyond the _Imperial Colonist_ , concerns were being expressed about South Africa as a destination for British women who wanted to farm. In a 1909 presentation to the National Union of Women Workers of Great Britain and Ireland, Frances Taylor spoke on \"Conditions of Life for Women in South Africa,\" emphasizing that it was impossible for white female (or male) colonists to perform manual labour on farms or elsewhere. She explained that \"most of the hard work is done by natives, and therefore, unfortunately, manual labour on the part of the superior, or White Race, is looked down upon as derogatory and undignified... How quickly does the girl just arrived to undertake the ordinary duties of a domestic servant learn to say, 'Oh, that is Kaffir's work, I could not possibly do that.'\" South Africa did \"not want women doing manual labour out of doors, contending that it would bring them down to the level of 'Kaffirs.'\" Edith O'Connor, who farmed with her husband in the Transvaal, was more explicit in her explanation of the obstacles to British women farming independently in South Africa, stating that \"the attitude of the native toward women is the big and predominant difficulty. Even a small picaninny will be deeply hurt if hit by a woman, it being not the slap, but the sex of the slapper that insults him. Carry this attitude to the grown man, who, in addition to despising women, is uncontrolled in his sexual appetite, and the difficulty for a white woman can be imagined.\" O'Connor warned that a woman alone on a farm would have to sleep with a revolver handy and to have a guard dog. For many reasons, then, farming for women in South Africa was dismissed as an \"absurd expedient.\"\n\nAgricultural opportunities also existed for British women in New Zealand and Australia, according to the _Imperial Colonist_. Particularly favourable conditions were seen to prevail in New Zealand for small holdings. But increasingly, Western Canada was cast as the most congenial destination for women who wanted to farm. There were none of the problems with \"native servants\" that prevailed in South Africa; there was plenty of cleared prairie land available; and the climate was healthy and exhilarating. In a 1908 _Imperial Colonist_ , for example, a woman reported from \"Sunny Alberta,\" north of Edmonton, that she had bought land adjoining that of her daughter and son-in-law, where she had a poultry farm that made a profitable business through marketing chickens, geese, and turkeys. She wrote that \"it is really a very happy life, a quiet one certainly, but have plenty of books and papers, and we are all interested in our poultry, and animals, and gardening, and though it is a very quiet spot the country is most beautiful and life ideal. The climate is cold in winter, but air so clear and dry, one does not feel it as in England.\"\n\nIn 1910 agricultural opportunities for women in the Canadian West began to garner much more attention in the _Imperial Colonist._ It was announced that a colony of women poultry farmers was to be established by the Canadian Pacific Railway at Strathmore, Alberta; the colony would provide eggs and poultry to the transcontinental railway. (The initiative does not appear to have ever materialized.) And as will be discussed in Chapter 5, articles and lectures by Saskatchewan farmer Georgina Binnie-Clark helped to generate interest in farming for English women in the Canadian West.\n\nBut calls for British women to farm the prairies also generated criticism and warnings. In 1910 Eileen L. Burns wrote to the _Imperial Colonist_ to say that she could \"not possibly recommend farming for women in Western Canada.\" It was unsuitable and impossible. Few women, she wrote, had the physical strength and endurance required, and she continued: \"When farming is advocated as a career for women in this country, I most positively and definitely state that it is an absolutely visionary scheme, foredoomed to failure.\" Burns knew of only a few cases where women had succeeded, apart from widows who carried on with farms that were already \"going concerns.\" (She was the wife of cattle baron and meat packer Patrick Burns, one of the wealthiest men in Western Canada.)\n\nOverall, however, it must be admitted that there were many more articles in the _Imperial Colonist_ devoted to opportunities for home helps (as well as for nurses, stenographers, teachers, dressmakers, and tea-shop owners) in Western Canada than to the potential vocation of agriculture for single women. And a great deal of emphasis was placed on the immediate matrimonial destiny of the home helps. A 1902 article declared that so many of the home helps sent out to the \"Far West\" had married that there would be as many fresh openings in the spring. A primary concern of the journal was to draw attention to the \"White Women's Burden.\" The editorial note in a 1911 issue was typical: \"The Empires' call to the women of our race is clear, urgent and inspiring: never before so insistent as it is today. Our young men want mates of their blood in the great sunny uplands of the Empire... The Dominion needs wives, sisters, mothers, teachers, nurses, domestic helpers and home makers.\" Women farmers were not on the list.\n\nJOURNALISTS FLORA SHAW AND MARY AGNES FITZGIBBON, AND THE SCHOOL FOR \"LADY COLONISTS\" IN WESTERN CANADA\n\nFlora Shaw, the colonial editor of the _Times_ of London, saw it as the duty of British women to settle the Canadian prairies and wrote a series of columns on the subject in 1898. At that time she did not advocate that women farm land of their own, but she came later to endorse the idea. Others, particularly Canadian journalist Mary Agnes Fitzgibbon, built on Shaw's observations of the needs of the region to point out the potential for women farmers, and together they became linked with the scheme for a school for \"lady colonists\" on the prairies who would learn the skills required to farm land on their own.\n\nA devoted imperialist, Shaw aspired to advance the cause of the British Empire through her journalism. She was an intense student of what was happening in the colonies, she advocated imperial expansion and colonial economic development, and she sought to influence imperial politics and policy makers. Her work had attracted worldwide press attention and praise by 1898, when she was sent to investigate conditions in the Klondike, and she welcomed the opportunity because it also allowed her to visit and write about other parts of Canada. As part of a series called \"Letters From Canada,\" Shaw wrote several long articles on the prairies and the ranching, grain, and mixed-farming economies being established there. Her main concern was the preponderance of solitary men on their solitary homesteads, living in tiny, poorly built shacks. The new verb \"to batch,\" she noted, \"upon the prairies represents perhaps the _minimum_ of pleasure in existence with which man, civilized or uncivilized, has been known to content himself with.\" Shaw proposed that sisters be encouraged to join their brothers in the enterprise of farming the prairies. This was not a new idea for this journalist; in 1894 she had given a paper to the Royal Colonial Institute in London on the \"Australian Outlook,\" and had called on younger sisters to accompany brothers settling in the colonies.\n\nShaw did not in her published letters touch on the subject of women farming on their own on the prairies, and did not deal with the thorny issues of ownership of the farm and land that the sister and brother had jointly established, or what would happen to her if the brother married. Shaw's idea of the sister companion to the male homesteader in Western Canada gained supporters, however, who did address these issues. Arthur Montefiore Brice adopted many of Shaw's ideas and phrases but went much further, advocating an equal partnership. Brice wrote that on the Canadian prairies, \"brother and sister... should take up a farm together and work it on terms of equal partnership for... not less than four or five years.\" When one or both wanted to marry, \"it is only right and practical that then there should be a basis for the equitable division of, or allowance for, the results of their joint labours.\"\n\nBuilding on Shaw's proposals, and also publishing in the _Times_ of London some months after Shaw's articles about Canada appeared, Canadian journalist Mary Agnes Fitzgibbon (writing under her pen name, Lally Bernard) proposed a scheme for the establishment of a school in Western Canada for lady colonists who would then obtain land there on their own. This would not be for \"female emigration in the lower rank of life,\" but be \"in the interests of the numerous gentlewomen who are capitalists in a small way... Often such is the daughter of a small squire or a land-owner.\" A few months of practical work at such an institute, Fitzgibbon wrote, would fit a woman to take up land and \"invest her capital at a much higher rate of interest in Canada than she could ever hope to get at home.\" These colonists would be released from the \"worrying grind of genteel poverty.\" Fitzgibbon was eloquent in her call for women to take up this challenge rather than join the \"spinster army of Great Britain\":\n\nGranted the lady colonists will have much to learn and much to endure, still how many women have to go about the Continent with some browbeating dowager or spinster aunt, whose petty tyranny leaves her unhappy companion, a nervous wreck of womanhood, to take her place among the spinster army of Great Britain. They cling to their tradition of caste. Let them prove their claim to intrepid blood and face life in this newer Britain, fighting, it may be against the elements and certainly against difficulties and prejudices in their new surroundings. This was surely better than the striving to make a tiny income cover expenses which very probably increase as their already small interest diminishes.\n\nYet even Fitzgibbon saw these women primarily and ultimately as reproducers of the \"race\" rather than as farmers. She called on women to help give to the \"Anglo-Saxon world a new 'Viking' race\" to rule over \"the boundless waves of the prairie province, that vast rolling sea of earth ready for the seed man shall scatter and plough.\" The mothers of this Viking race, in Fitzgibbon's view, should be the \"daughters of British gentry... practical, intelligent and cultured\" and trained to \"face the vicissitudes of existence in the sparsely populated districts of the North-West.\" Daughters of British gentry could not simply go upon Canadian farms the way the sons could, they needed training and to be shown that \"interesting absorbing work can be found in activities connected with agriculture.\"\n\nFitzgibbon was herself struggling with \"genteel poverty\" at this time. Born Mary Agnes Bernard in Canada, in 1881 at age nineteen she travelled to England with her aunt, Lady Susan Agnes Macdonald, the second wife of Prime Minister John A. Macdonald, and made her debut in London that season. A year later she married an Irish lawyer of titled parentage, Clare Valentine Fitzgibbon. He was a grandson of the Earl of Clare, and the couple socialized among an elite London circle. Their daughter was born in 1885. But when her husband was confined to an asylum in 1896, Fitzgibbon had to find a way to support herself, her daughter, and her mother. She was a gentlewoman thrown on her own resources. She returned to Canada and lived in Toronto with her mother and stepfather, D'Alton McCarthy. McCarthy was killed in a carriage accident two years later. Fitzgibbon became a journalist, publishing mainly in the Toronto _Globe_. (After about 1900 she was known by the name \"Mrs. Clare Fitzgibbon,\" and she also published under the names \"Margo Meredith,\" \"Citoyenne,\" and \"Fitz-Clare\" as well as \"Lally Bernard.\") Her fourteen years in England had helped to make her a devoted \"Imperial Daughter\" who continued to return for visits, attending two coronations and \"helping to forge a strong link between Canada and the Mother Country.\"\n\nFitzgibbon's 1899 letter to the _Times_ on a school for lady colonists was soon followed by a _Times_ editorial endorsing the scheme, particularly the idea of a training school, but placing less emphasis on the women farming on their own. The editorial was clearly written by Flora Shaw, and she and Fitzgibbon were together associated with the scheme from then on. Shaw's \"Women and Colonial Settlement\" began by detailing the number of \"surplus\" of women that had risen alarmingly in the United Kingdom. Industrious, cheerful, and healthy women were needed in the colonies. The Canadian West was an \"admirable field\" for the initiation of an experiment of the kind proposed by Fitzgibbon, as the land was cheap, the soil good, markets were at hand, and \"nowhere more than the Canadian prairies are women needed for the purpose of investing the bare log houses known as 'shacks' with the comfort and dignity of homes.\" It was emphasized that there were no physical dangers to be faced on the prairies.\n\nThe _Times_ editorial endorsed the idea of a training home for women situated in Western Canada, operated at government expense in connection with a system of experimental farms. Women would be instructed in practical agriculture (dairying, gardening, poultry rearing, beekeeping) as well as in household arts, including cooking and laundry. The graduates \"might in some instances purchase and work land for themselves,\" but \"in the majority of cases it is supposed that they will in the first instance work in co-operation with their farmer brothers on a system of mutual profit.\" To keep the cost of this education within reason, Shaw called on the government to at least subsidize such an institution with the assistance of private subscriptions and endowments. She predicted that if such a scheme were successfully inaugurated, other colonies would soon copy the example, and Canada would \"render a service to the cause of Imperial consolidation.\"\n\nShaw explained why educated and refined women were needed for the colonies rather than working-class women: they were \"hardier, more active in out-of-doors habits, better bred and better fed than their contemporaries of the less-favoured labouring classes. They have the intelligence to initiate... and are driven by the wholesome spur of poverty either present or to come.\" She concluded with the hope that in one generation it would be commonly accepted that \"the young women no less than the young men of the United Kingdom should confidently seek a living wherever the British flag flies in a temperate climate.\"\n\nThe idea of a training school for lady colonists received widespread coverage in English and Canadian newspapers. Some were in favour. An editorial in the _Leeds Mercury_ of 12 April 1899 endorsed the scheme of training women in agriculture suitable to the region of prairie Canada. A school was essential for \"poor ladies, refined and well brought up, who may desire to exchange the pinched life and narrow means... for the greater independence, freedom and brighter outlook of which the colonial farm gives the assurance.\" The editors believed that the Canadian prairies would be the best colonial location for the scheme, as \"no better climate could be found, the soil is fruitful, and land so cheap that, we are told, one year's moderately successful crop will cover not only the cost of purchase, but the outlay on production.\"\n\nOthers, however, raised questions about the feasibility of the plan. Fitzgibbon elaborated and developed her scheme and addressed the concerns of critics. She stressed the efficiency of the North-West Mounted Police in ensuring a peaceful and law-abiding country. There was no influx of raucous gold seekers in the region. She faced the question of the cold winters with the reply about the \"dry cold\" that has since become standard when describing the Western Canadian climate. Fitzgibbon wrote that settlers on the prairies would rather face a temperature of fifty degrees below zero there than \"the cold which chilled them to the very marrow while dining in one of England's swagger country houses in November.\"\n\nIn October 1899, Fitzgibbon went to Western Canada for a six-week trip for the purpose of \"verifying exactly what life is like at the present there among the educated class of people.\" She also wanted to explore the feasibility of settling a number of women near Calgary, where they would raise poultry and market garden. Fitzgibbon continued to emphasize that the scheme was meant to promote women farmers, but she argued that they ought to devote their capital and energies to \"co-operative small farming, poultry-raising, fruit culture, dairying etc.\" It was nonetheless a radical plan, as she insisted there was scope for women \"as operators on their own account along co-operative lines.\" If they were \"girls,\" then they should go to the West as \"lady helpers\" rather than farmers. On this visit she declared Brandon, Manitoba, as a likely site for such a school, in conjunction with the experimental farm there. She also stated that she had submitted a plan to Minister of the Interior Clifford Sifton, \"from whom I received a decidedly ambiguous acknowledgement.\"\n\nFitzgibbon developed further rationales for choosing Canada over other colonies. In Canada, British women \"could go forth and fight their way in any line they may choose, just as their brothers are doing.\" No \"special machinery\" was required \"for the protection and placing of lonely women.\" Ignoring the Indigenous population, the writer explained that Canada was a \"white man's land from end to end\" and added, \"There are other Colonies where the 'native' question renders such a line or argument impossible.\"\n\n\"Influential women in the motherland,\" Fitzgibbon hoped, would lend their assistance to the scheme of a school for lady colonists, but this did not materialize. As one letter to the _Times_ replied in response to the initiative, there _was_ a training school for lady colonists, the Leaton Colonial Training Home, which not only trained suitable women but weeded out \"those who were unfit\" before they ever arrived in a colony. Nor did Fitzgibbon succeed in persuading the Canadian government to support the plan. Her own newspaper, the _Globe_ , thought private enterprise rather than government should take up the scheme. Despite the fact that no such training school was ever founded in Western Canada, Fitzgibbon's campaign helped to focus aspirations for British colonists and farmers in that region. Fitzgibbon had successfully argued that \"of all the colonies Canada has the greatest advantages to offer as a field for the enterprise of the future lady colonist.\" As Mrs. Archibald Colquhoun stated in her 1904 presentation to London's Royal Colonial Institute on \"Women and the Colonies,\" for middle-class women emigrants \"it was to Canada that they must look for their chief field of colonization,\" if they could be persuaded to have more courage and patriotism.\n\nIn her regular columns for the _Globe_ as Lally Bernard, Fitzgibbon stressed her \"deep interest in the question of agriculture and horticulture as a vocation for women.\" She wrote, \"I am often amused at the scorn with which the majority of people regard the idea of agriculture for women as being practicable and desirable. As a matter of fact, both in the U.S. and Canada farms of all kinds are most successfully run by women, and all branches of horticultural work are being run by women in every part of the world.\" She compared the opportunities for women to study agriculture in Canada unfavourably to those in Britain and other nations. In a 1901 column she had asked why the government did not open the horticultural department at the Agricultural College at Guelph to women students, given that the head of the department was \"most anxious\" for this to happen. She noted that \"already in Great Britain women are doing most successful work in horticulture... Lady orchardists and florists are to be found both in the United States and Great Britain and Belgium.\"\n\nFitzgibbon was disappointed, however, at the colonial training schools in England, where she found little emphasis on sending student colonists to Canada. The colonial training branch at Swanley, she observed in 1903, was directed toward opportunities in South Africa. She hoped that a patron could supply the school with a kitchen and entire \"Canadian outfit\" such as would be found in the West. By this point, Fitzgibbon had backed away from promoting colonial training in Canada, writing that it was beyond the means of most women who had to pay for their passage and find a job right away. She now highlighted the domestic skills women needed for Canada and downplayed their potential as farmers and landowners on their own. She often returned to the theme that lady colonists were what the West needed, but placed greater emphasis on their roles as wives, mothers, and home helps rather than as farmers.\n\nTHE COLONIAL INTELLIGENCE LEAGUE\n\nFounded in 1910, the Colonial Intelligence League for Educated Women (CIL) was the creation of Caroline (Mrs. Norman) Grosvenor, a novelist and artist, and member of an influential network of elite women interested in the settlement of British women in the colonies. Grosvenor had been an activist with the South African Colonization Society. For her it was an imperial mission and duty for women to emigrate. She believed, however, that girls and women could not be simply sent out as potential wives, and that farming could be the vocation that awaited some of them. Yet the CIL was somewhat cautious and muted in its support for women farmers in Canada, not wanting to appear radical and alienate potential donors and supporters, but instead reflecting the consensus that women were best suited to lighter agriculture on small holdings, clustered in settlements or colonies.\n\nGrosvenor was above all an ardent imperialist, and this was combined with an obsession about the fate of the \"surplus women\" of the genteel or educated classes. The plan was to send these \"superior\" women to the colonies, and the focus of the CIL was soon Canada. Here would be employed \"a vast amount of splendid material which is now being either wrongly used or entirely wasted\"; this would \"bring hope and a future to many thousands for whom life at present looks infinitely dark and difficult, and last and most important of all, it will help to keep the British Empire for the British race.\" Grosvenor was concerned that Englishwomen, \"charming, pretty, amiable as they might be[,] are hopelessly unfitted for the life of hard work\" that awaited them. In a 1909 column in the _Times_ of London, Grosvenor addressed the issue of training Englishwomen for conditions in the colonies. She argued first of all that unmarried daughters _must_ go to the colonies where \"the very best of our British race are sent to plough their lonely furrow.\" The women had to be trained, however; they could not simply be sent \"on the chance of their meeting suitable husbands,\" and Grosvenor recommended the Colonial Training College at Stoke Prior. She urged any woman under thirty who had \"the ancient inheritance of her race\u2014the spirit of adventure and the longing of a home of her own\" to set forth, but to first attend a training home. Small groups of women could establish market gardens, or poultry, dairy, or bee farms.\n\nThe three goals and objectives of the CIL, as set out in the first annual report of 1910, were to (1) maintain an \"Intelligence Office\" in England that estimated the demands for women's work in the colonies; (2) establish in each of the colonies expert agents who would investigate local opportunities and conditions; and (3) establish in each a \"Colony of Settlements for Women,\" where they could be trained for local conditions.\n\nThe focus of the CIL was the educated \"surplus woman.\" While other organizations were devoted to sending women to the colonies primarily for domestic service, the CIL would be solely aimed at the \"educated gentlewoman, accustomed to country life, with a knowledge of practical affairs, and [who], with a little capital might find an opportunity in some one of the many departments of intensive agriculture.\" Grosvenor's organization was also determined to gather \"intelligence\" about conditions in each of the colonies. The existing organizations, Grosvenor thought, provided the machinery for emigration, but there was a \"crying need for a proper intelligence department which shall estimate the demand of the Colonies and bring it into relation with the supply which we believe to exist.\" She wanted to be sure that women left for the colonies only when they were assured of suitable work. The plan was for the CIL to establish in each colony an agency to investigate local needs. And Grosvenor did investigate local needs herself (to some degree), travelling to Western Canada in 1911, 1912, and 1914, quickly focusing on British Columbia as the site for an \"agricultural training home\" for Englishwomen.\n\nLike many other and earlier advocates of agriculture for \"surplus women\" in the colonies, Grosvenor sought women who were not interested in intellectual pursuits but instead loved the outdoors. As a novelist, she provided descriptions more eloquent than those of many of her contemporaries and predecessors. Grosvenor \"spoke of the girls who have been brought up in the country, who amidst the moorlands of Scotland or Ireland, the dales of the North of England, the broad pastures of the Midlands, or the wind-swept downs of the South, have got into their blood the love of outdoor life, of outdoor things and animals.\" More than previous advocates of emigration, however, Grosvenor was focused on Canada, and she was more willing to articulate the difficulties to be faced. She outlined these in her most sustained statement on the issue in the _Times_ in 1913, under the title \"Women Farmers in Canada: A British Farm Settlement.\" The major problem was that there were no salaried positions for women in Canada on poultry or dairy farms because it was difficult to house them (\"hired\" men could sleep in rough conditions, but hired gentlewomen could not); because few farmers produced eggs, poultry, and dairy products for market; and because \"there exists in Canada a curiously strong prejudice against employing women in outside work.\"\n\nThe structure of the CIL departed to some extent from previous emigration societies, \"breaking away from past practices of amateurism and female voluntary work,\" but the upper-class background of its founders kept it a \"patrician organization.\" Its honorary president was Princess Christian of Schleswig-Holstein, and many elite women and men figured among the benefactors. Historian Andrew Yarmie has argued that the CIL was not as stridently imperialistic as its predecessors, placing less importance on imposing English ideas on the colonies and instead cautioning that the English woman must learn the \"ways and ideas\" of the colonies. While there was an emphasis on recruiting Englishwomen, the organization also had branch offices in Edinburgh and Glasgow. Some of the members were acquainted with Canada, such as Lady Sybil Grey, daughter of the Governor General of Canada Earl Grey. Lady Grey was an adventurous person (later a decorated nurse wounded in the First World War) who in 1909 visited the Yukon and staked a gold claim in the Klondike.\n\nEchoing the cause of Mary Fitzgibbon, Caroline Grosvenor believed that British women already trained in poultry farming or dairying in the \"Old Country\" required practical experience in Canada, in farm settlements, where they could learn about local conditions. She decided this following her 1911 visit to Western Canada. The belief that \"home help\" work was ill-suited to the educated woman was reinforced by the visit that same year of Ella Sykes, mentioned at the outset of this chapter. Sykes volunteered to visit Canada in 1911 on behalf of the CIL to investigate conditions for women in the West. Her book _A Home-Help in Canada_ was a result of this visit _._ She took five temporary \"home help\" positions in four provinces and was a guest on other farms. Her description of the life of a \"home help\" was negative, or at best ambivalent, and she did not recommend the work for the educated woman. Skykes was, however, like Grosvenor, convinced that British women needed to seek their fortunes in the colonies, that it was \"Imperial work to help girls of a high stamp to seek their fortunes beyond the seas\u2014women who will care for our glorious Flag and what it signifies.\"\n\nIt was after the 1911 visits to Canada of Sykes and Grosvenor that the CIL began planning a farm settlement in British Columbia, which began in 1913 with the purchase of fifteen acres. The Princess Patricia Ranch would train eight to ten women at a time, who would give their labour in return for board and lodging. The settlement would also demonstrate the capacity of British women as poultry keepers and vegetable growers and induce Canadian farmers to employ them. \"The Canadian needs 'ocular demonstration' to be convinced,\" Grosvenor wrote, \"but once convinced he will take up a new idea with lightning rapidity.\" The ranch was to be the first of others, as it was hoped that government aid would fund future such settlements. Grosvenor believed the scheme should appeal to both Canadian and British as \"sound Imperial statesmanship.\" As the first of many in Canada and other colonies, the Princess Patricia Ranch would be a \"stepping stone in a big movement, which will be of the greatest possible use in opening up enormous possibilities to women themselves, and to the country of their adoption.\" Ultimately these settlements would \"help to keep British possessions loyal to the flag.\"\n\nDespite its emphasis on \"colonial intelligence,\" the CIL appears to have gathered very little information on the conditions of farming, ranching, or gardening in Western Canada. In the organization's archival collection there is a substantial bound volume with the title \"Colonial Intelligence League Reference Book: Canada\" printed boldly on the front, along with \"N.B. The contents of this book are strictly private and confidential.\" Inside, however, there is surprisingly little \"intelligence.\" Most of the pages are blank. On farming there are a few entries, most of which are discouraging. From Calgary in 1912 it was reported that it was not possible for women to find positions there on poultry farms; they would need to work as hired helps, which meant \"grinding work.\" There was also no work in Calgary for women \"Jobbing Gardeners\" because of the \"long idle season. We are so high up that our gardens are always spoilt very early by a crushing frost. Last year it was in August, and after that there is nothing to do but gather up and burn the debris, cover all up with manure and wait until April.\" The real problem was, \"What would they do from October to April?\" From British Columbia it was reported that year that land was very expensive to purchase, that it took years to clear land and that it was arduous work: three to five years of \"waiting and struggling.\" Fruit trees did not produce for four or five years. Gardening in British Columbia was \"in the hands of the Chinese,\" and they undersold all others.\n\nThe CIL appears to have forged no links with the women who had been attempting to promote and facilitate farming for (British) women in prairie Canada through the homesteads-for-women campaign, to be discussed in Chapter 6. There is no record of any association with Binnie-Clark, for example, whose book _Wheat and Woman_ appeared in 1914. Binnie-Clark and others involved in Canada in the homesteads-for-women cause may have been viewed as too radical by membership of the CIL, anxious as the organizers were to raise funds for their \"experimental station\" in Canada. They likely could not afford to challenge the Canadian federal government in the way that Binnie-Clark and others had. Binnie-Clark spoke to suffrage organizations in England, and many of those involved in Western Canada were also committed to suffrage, dower, and other campaigns that posed fundamental challenges to property and land laws. Binnie-Clark's address to the Royal Colonial Institute in 1913, mentioned at the outset of this chapter and further discussed in Chapter 5, discredited her in the eyes of the Victoria _Daily Colonist_ as misleading to emigrants, particularly young women. For this reason it would not have been in the interest of Grosvenor and the CIL to make common cause with Binnie-Clark.\n\nThe CIL did, however, attract the notice and participation of Mary Agnes Fitzgibbon. The sole product of her campaign for colonial training for gentlewomen in Canada was the Queen Mary Coronation Hostel for Gentlewomen in Vancouver, British Columbia, founded in 1912 under the patronage of Queen Mary and with funding from Lord Strathcona. Fitzgibbon had moved to British Columbia in 1907, concentrating her energies there with the help of Lady Mary Minto (wife of the former Governor General). This initiative, along with the Princess Patricia Ranch, marked the growing tendency to see British Columbia rather than the prairies as the most suitable destination for the educated British woman emigrant. The hostel was operated in conjunction with the CIL. Unlike other hostels that received Canadian government funding and were intended for immigrant domestics, admission to the privately funded Queen Mary Hostel was restricted to \"gentlewoman.\" For a small fee, English gentlewomen were taught to become competent housewives. Gone was the emphasis on women owning and farming land of their own. They learned to split their own wood and to cook on a wood stove in a \"real Western shack\" situated on the grounds of the hostel, but that was the extent of their outdoor work. The majority of the women who stayed at the hostel found work in homes or clerical positions.\n\nYet the CIL's goal of training women to farm persisted (although it was not to last for long). In 1913 there were two women workers at the Princess Patricia Ranch at Vernon, British Columbia, along with a superintendent. Optimism was in the air, as British Columbia's Minister of Agriculture W. Scott was impressed with the potential for dairying, fruit growing, and poultry production. He recommended that the ranch become a government demonstration farm. Critics of the work of the CIL were also emerging. An editorial in a July 1913 _Daily Colonist_ of Victoria noted that an organization known as the Colonial Intelligence League had sent young English girls out to British Columbia to \"pick berries.\" The editorial continued: \"The _Colonist_ points out the absurdity of such girls working in the fields side by side with Indians, Chinese and Japanese. The League that is engaged in this particular form of pumping [ _sic_ ] the white man in to keep the yellow man out knows so little of British Columbia that it should be renamed the Lack of Intelligence League.\" According to the editorial, \"there is not an educated young woman in British Columbia who would think for a single moment of going out to the berry fields to work side by side with Indians, Chinamen and Japanese.\"\n\nMary Agnes Fitzgibbon was opposed to British women picking fruit, considering it a job for Chinese and Indian workers. Caroline Grosvenor did not believe it was suitable, either, but was willing to concede that it depended on the employer. Lady Sybil Grey was entirely opposed to British women fruit picking in British Columbia, \"where the work was usually done by Chinese or Indians, and by the less reputable workers of the district.\"\n\nThe _Daily Colonist_ was sceptical of the entire idea of women farmers in Canada. Also in 1913, they severely criticized Georgina Binnie-Clark's talk \"Land and the Woman in Canada,\" and her claims that British women could aspire to farm in Canada. The _Colonist_ claimed the CIL plans for a farm settlement of women would cause suffering and disappointment. That the organizers were \"unintentionally deceiving many of your girls is beyond all question.\" The Colonial \"Lack of Intelligence League\" was guilty of \"Mischievous Benevolence.\"\n\n\"GIVEN HEALTH AND INDUSTRY THERE IS A FORTUNE WAITING FOR THEM\": MARION CRAN AND A WOMAN IN CANADA\n\nEnglish writer Marion Cran's voice joined those calling for the \"educated gentlewoman\" to take up farming in Canada, although she was careful to point out the challenges and obstacles. Cran was a prolific author of gardening books, including _The Garden of Ignorance_ (1913), _The Garden of Experience_ (1921), and _The Joy of the Ground_ (1928), in which she wove the story of her garden on rented property in Surrey with stories of her three husbands, her children and parents, and her problems with finances. Cran used her gardening books to draw attention to inequalities in marriage and other restrictions women of her era encountered. Born in South Africa, she was a devoted imperialist, believing in the superiority of the British \"race.\" Cran was asked by the Canadian government to investigate conditions for British women immigrants in Canada, and her visit took place in 1908, with her findings published as _A Woman in Canada_.\n\nCran was enthusiastic about the potential of Canada, where she spent six and a half months, finding that \"the Englishwoman in Canada is everywhere welcomed and valued. In the North-West, where wives are scarce, a work of Empire awaits the woman of breed and endurance who will settle on the prairie homesteads and rear their children in the best traditions of Britain.\" Yet she went beyond the demand for women as wives and mothers, arguing that Canada needed \"educated, middle-class gentlewomen, and these are not the women to come out on the off-chance of getting married. They may be induced to come to the country if they can farm or work in some way to secure their absolute independence. They want, every nice woman wants, to be free to undertake marriage as a matter of choice, not of necessity.\" Once settled, these women might \"throw in their lot with the bachelor farmers of the prairie and British Columbia,\" but there had to be more than marriage in order to entice them to immigrate.\n\n_A Woman in Canada_ called on British women to consider farming in Canada. Cran's second chapter, \"A Woman Farmer and an Experimental Farm,\" is about meeting a woman who farmed 600 acres in Ontario, and this example was used by Cran to promote the opportunities on the land. Cran claimed she had never met a woman farmer before and was deeply impressed. The farmer, never named, was dignified and beautifully dressed. She was cultured, \"transplanted from the hectic life of Paris and London to this healthy, busy land.\" Cran quoted the farmer as declaring, \"almost passionately,\" that \"it is an indescribable joy, this turning of the wild into fertile plains,\u2014I can never have enough of it,\u2014I do not grudge one second of the work, hard and exacting as it is,\u2014I am repaid a thousandfold when my days and weeks of anxious care are borne into blossom like this.\"\n\nLeaving Ontario full of enthusiasm for farming, Cran headed west, where she was disappointed to find little evidence of women farmers. She had hoped to find \"bachelor women,\" women \"working the land 'on their own,' singly or in clusters,\" but did not find any and concluded that \"there are no women on the prairies except the wives and daughters of farmers, and they are scarce enough.\" She wondered why women \"should not come out and work it as well as men,\" and did not seem aware that homesteads were not available to most women, writing that as \"the labour of 'homesteading' would be very great for women, I can understand their shirking it.\" \"To 'make good' on a free farm,\" Cran wrote, \"a woman would need either much courage and capital, or considerable male labour, besides agricultural skill.\" She concluded that instead of taking up 160 acres, a woman should buy a small acreage within a few miles of the railway, and that \"given health and industry, there is a fortune waiting for them in that marvelous prairie loam, just as surely as for the men who go out to grow wheat and run stock-farms. Above all there is a splendid opening for our women gardeners.\"\n\nLike most of her counterparts in England, Cran advocated taking up small holdings, writing that men might prefer the \"big gamble of wheat growing,\" but the surer, steadier road to fortune was through vegetable, fruit, and flower growing, and she urged English women to consider farming cooperatively or in colonies: \"Here then, is the opportunity for Englishwomen. Let them come out in twos and threes, unless any single woman has sufficient capital, and (just as important) courage for a lonely life; let them settle within marketable driving distance of such cities as Saskatoon, Regina, Edmonton, Calgary, etc., and they will find awaiting them every facility for a life of independence and certain ultimate success in the grandest climate in the world. The brilliant bracing air, the bustle of industry and of hope which pervade the prairies are beyond my powers to describe.\"\n\nCran strongly discouraged women from homestead farming. She said it was not women's work, that the land would be so far from a railway that transportation problems would be endless and the loneliness \"unendurable.\" Wheat farming, according to Cran, was for men only. Wheat required large acreages; it was a venture that did not begin to pay until 160 acres were tilled, \"a feat which takes some doing in the bush-covered parts of the prairie with only a scrub-plough to help. The ploughing of a few acres, on the other hand, is not a very formidable undertaking, and returns in flowers and vegetables would be steady.\" Women could improve their smaller acreages at a slower, saner pace. Cran was particularly struck by the potential for women market gardeners at the Winnipeg Horticultural Exhibition, where she saw tomatoes, pumpkins, Swiss chard, cabbage, parsnip wine, cherry wine, raspberry vinegar, and sweet herbs such as thyme, sage, and marjoram. Poultry farming was another option for women in Cran's view, but she believed that British Columbia was a better environment for this industry and for fruit growing.\n\nCran concluded, however, that the majority of English \"bachelor women\" were not capable of facing the challenges and toils of life on the prairies. They were \"unfitted by our complete civilization.\" But she felt there were exceptional women, numbering \"in the thousands,\" who were \"fearless, enthusiastic, clean-bred.\" She wrote, \"There must be some who have the courage and health to leave the ready-made comforts of the old country, and come into this wild beautiful West, giving their best of mind and body for the race and for the Empire.\"\n\nFICTION SET IN THE COLONIES AND THE RECONFIGURING OF BRITISH NORMS OF FEMININITY\n\nAdventure fiction for girls set in the colonies bolstered the idea that it was possible to farm or pursue other occupations that might be seen as unfeminine, and thus unacceptable at home, while sharing in the task of building the Empire. In the late nineteenth century, British authors of adventure fiction for girls created independent, resourceful, and courageous heroines who rose to the challenges of the rugged environments they helped to colonize. These began to emerge decades after the appearance of equivalent books for boys by writers such as G.A. Henty and H. Rider Haggard. Author Bessie Marchant set her novels all over the British colonial world, creating robust heroines who took on arduous outdoor work (although most eventually married). Indigenous people are almost absent in her novels except as occasional \"expendable obstacles in the path of British rule\" and as extra players in the background. Marchant's books inspired her readers to question the idea that \"men must work and women must weep.\" Her readers were \"no longer content to be simply backers-up of male empire builders... [they] were seeking new worlds of their own to conquer.\"\n\nWomen's ownership or management of land and their responsibility for crops and livestock are prominent in several of Marchant's novels, as titles such as _Erica's Ranch_ suggest. In two of her novels written before the First Wold War, the protagonist is \"the sole possessor, in her own right and name\" of her \"own piece of the Empire.\" Often the father of the heroine is elderly and incapacitated, and she must run the farm or ranch. The heroines manage land, however, not to \"usurp the part of men, but [to] work toward self-sufficiency or the maintenance of family property in their absence.\" Many of Marchant's stories were set in Canada, including _Sisters of Silver Creek: A Story of Western Canada_. In this novel one of the sisters cultivates the land and attains self-sufficiency, becoming a manager of a jam business as well as a landholder. When she eventually marries, her command of her property and her work is curtailed, but Marchant had other heroines who remained autonomous and unmarried. In novels such as _The Loyalty of Hester Hope: A Story of British Columbia_ , the protagonist continues to enjoy hard work on her own land, irrespective of her marriage. Marchant's portrayal of strong and capable heroines presented hard work outdoors, independence, and self-sufficiency as all desirable qualities. Even the artwork on the covers conveyed the message that women could successfully farm and raise livestock.\n\nOther fiction writers of Empire helped women to imagine that they could have an imperial fresh start, take on new occupations, and lead invigorating lives in the colonies. In 1910 Mary Ward (who published under the name Mrs. Humphrey Ward) published her novel _Canadian Born_. The English heroine arrives in Canada as a widow and meets and marries a Canadian, after much consternation about whether she could bear to be transplanted to such an unfamiliar environment. But she and her husband buy a farm (with her money), and she hopes to not only set up a cottage hospital but also establish a \"training college for farm-students\u2014girls and boys.\"\n\nYet other writers conveyed more conservative messages about the potential for, or the wisdom of, British women farming and owning land in Canada. Scottish journalist and romantic fiction writer Annie S. Swan visited Western Canada several times and wrote a serialized novel, \"Prairie Fires,\" set in Alberta. One of the main characters is a British woman horse rancher, Lady Florence Belfield (Lady Flo), an accomplished rider who excells at \"men's talk,\u2014all about wheat, and stock and the breeding of horses.\" Hilary, the young, na\u00efve, and inexperienced English wife of Robin Merrick, an English homesteader, feels threatened by Lady Flo as her husband admires the horsewoman's knowledge and abilities. Hilary thinks Lady Flo is \"half a man,\" while her husband lectures her: \"It's a pity you can't take a leaf from her book, Hilary. Her's [ _sic_ ] is the only attitude possible for a woman in Canada if she's going to make a success of it.\" Hilary runs away to the United States but the couple reunites before long on the homestead. Hilary should never have been jealous of Lady Flo, it turns out, as her husband far prefers his wife, weak and fragile as she is. Lady Flo is far too masculine for any British settler to consider as a wife. Hilary becomes \"the mother of gallant sons and fair daughters... helping her husband to lift high the standard of life in the new country.\"\n\nCANADIAN INTEREST IN (BRITISH\/CANADIAN) WOMEN AS AGRICULTURALISTS\n\nThe topic of middle-class British women as potential farmers did not generate the same degree of interest in late nineteenth-century Canada as it did in Britain. There was no concern about a \"surplus women\" problem in Canada from which schemes to place women on the land in the colonies arose in Britain. Yet the work of journalist Mary Agnes Fitzgibbon indicates that there was interest in promoting the cause of British women farmers for the prairies.\n\nBenjamin F. Austin, principal of Alma Ladies' College in St. Thomas, Ontario, was one of the few vocal supporters of farming for women. In a chapter entitled \"Open Doors for the Women of To-Day\" in the 1890 book _Woman: Her Character, Culture and Calling_ , he argued that the cultivation of plants, fruits, and flowers was \"really adapted to woman's strength and tastes, opening a pleasant, profitable and health-giving occupation to her in the country.\" He believed that most of the labour required was not as hard as housework. Austin found the example of the United States most compelling, writing that there were \"sixty thousand female farmers, or agricultural laborers, in the United States,\" and that \"it is not thought improper for girls who work in the field to wear male attire. By doing so, they escape the cumbersome dress which would drag in the dirt and catch on weeds and briers.\" Austin asked, \"What would some of our small-waisted city belles, so tightly corseted, so unnaturally attired, so enfeebled by irrational modes of dress that a few minutes brisk walk, or the climbing of a flight of stairs throws them into palpitations, think of their sturdy sisters in the far West who plough, sow, pitch, cart and enjoy blessed exemptions from nervousness, heart disease and sick-headache?\" In Austin's view, light farm work was vastly preferable, better suited and \"far more wholesome in effect on health and happiness than the miserable slave life many women lead in factories, shops and stores where long hours, promiscuous associations and poor pay are the general rule.\"\n\nCanada's National Council of Women advocated agriculture as a suitable female vocation. Their 1900 publication _Women of Canada: Their Life and Work_ included a chapter by Adelaide Hoodless (founder of the Women's Institutes), in which she placed agriculture second on a list of \"women's industrial possibilities,\" after \"household arts.\" Through agriculture, Hoodless wrote, women could play a role in \"national development,\" as it is \"pre-eminently the great Canadian industry.\" The \"unlimited possibilities\" included dairying, raising poultry, bees, and fruit, and hot-house culture. She saw these as \"distinctly feminine agricultural pursuits,\" in contrast to grain farming and stock raising. Hoodless was an advocate of small holdings and colonies or settlements of women farmers: \"The tendency in Canada has been towards the cultivation of large tracts of land which has necessitated a greater expenditure in money and labor than would be possible for the average woman. These conditions, together with their attendant social isolation, have not proved sufficiently attractive to induce women to consider agriculture as a special vocation... Co-operative principles, with regard to farm labor, marketing etc., must prevail where women adopt agriculture as a means of livelihood.\"\n\nHoodless believed that agriculture for women would be a \"factor in promoting the health and morals of a nation.\" She was opposed to factory and office work for women, as she believed that women's primary role was as wives and mothers. Hoodless believed women should be educated in practical skills and roles that would strengthen the family. She was a strong advocate of agricultural education for women and of training in domestic or household science, then an emerging discipline that would be known eventually as \"home economics.\" Like some of the advocates of agriculture for women in Britain, she opposed female enfranchisement, arguing that women exercised their influence through their husbands and sons.\n\nIn _Women of Canada_ , the statistics compiled about women farmers were encouraging. According to the 1891 census there were \"11,590 women farmers in Canada. This is an increase of 4,794 in ten years, according to the census of 1881. These women own and work their own farms; 252 of them are in Manitoba, where in 1881 there were only 71.\"\n\nAt a 1909 Toronto meeting of the International Congress of Women, held under the auspices of the National Council of Women of Canada, a great deal of attention was paid to the topic of \"Women in Agriculture.\" Women with capital were called upon to purchase and farm land. They were exhorted not to sell inherited land but to \"keep your land; improve it; make it do your work and earn your money for you.\" They were urged to \"study, think, act intelligently; use judgement, study soil conditions and quality... Then set to work to master every detail of the business undertaken.\" The cooperative or colony farming option was gaining strength. Miss Yates of the Ontario Agricultural College at Guelph urged the \"bright-faced women across the ocean\" who were \"longing to put their powers to the test\" to consider farming on the cooperative plan in Canada. Yates stated that \"the very energies that are so valued upon the hockey and the gold fields at home are exactly what are wanted here in the game of life that is being played on these farm lands.\" She suggested that colonies of women could rent or purchase land and grow fruit and raise poultry.\n\nWell into the twentieth century, there were few opportunities for women in Canada to study agriculture or horticulture. The situation was dismal and in stark contrast to the various options in Britain. In Canada, instruction in dairying (at the Kingston Dairy School, the Agricultural College in Guelph, and the Government Dairy School in Winnipeg) was about all that was available to women except at the School of Horticulture at Wolfville, Nova Scotia, where in 1898 eighteen out of forty-nine students were women, and at the School of Agriculture at Truro, Nova Scotia, operated in connection with the Normal School, where all students took the same subjects, including biology, soils, dairying, gardening, and agricultural chemistry. In the agricultural colleges of Ontario, Manitoba, and Saskatchewan, \"farmers' daughters\" were steered toward courses in \"domestic sciences.\"\n\nSupport within Canada for sending educated gentlewomen from Britain to acquire land of their own on the prairies was occasionally expressed. In 1910 Marion Crerar of Hamilton, a regent of the Imperial Order of the Daughters of the Empire, wrote to the _Times_ of London to endorse the scheme of settling educated women on imperial plots, although she clearly thought these should be very small. Crerar was motivated by the desire to \"draw our beloved countries together\" and objected to the \"wretched specimens,\" the \"scourings from London streets\" who were being sent to Canada. She asked, \"Cannot England spare some of her well-bred and refined people to raise the tone of the whole country? Have you not an army of women of education who could be spared to build up this part of our Empire?\" Crerar pointed to the great need of such women on the prairies. Here was the chance for \"our 'Frontierswomen.'\" She endorsed the cooperative plan, suggesting four ladies select a town with a clergyman and buy a little piece of land and a house. One could teach music and lead the choir, another could teach sewing, and one might keep poultry. Together they would be the leaven for the district, they would \"be the props of the new and struggling parish, and the one gentle and refining influence on all the farming life around it.\" The added joy would be that all was done for \"King and country.\" They would not be carrying swords into distant lands like their male counterparts, but would be bringing their refining influence.\n\nTHE CANADIAN PACIFIC RAILWAY'S PROMOTION OF THE WEST FOR WOMEN\n\nIt was in the interests of the Canadian Pacific Railway (CPR) to appeal to potential purchasers of their land in the West, including women. A series of pamphlets from the early twentieth century, aimed specifically at women, featured stories of women who were capable workers and efficient owners and managers of farms. They were cast as having made substantial fortunes and as supporting large families. The CPR wanted to entice homesteaders who might then be motivated to expand their holdings by purchasing railway lands. In order to compete with the U.S. West, where single women could homestead, the CPR needed to show that there were opportunities for women as well as men in Western Canada. Through its office in London, the CPR bombarded Britain and northern Europe with pamphlets, posters, and maps of Western Canada. Their immigration offices were \"seductive parlours designed to trap passing pedestrians\" with posters of lush fields of grain and prosperous, happy settlers. Travellers carried the \"gospel of emigration\" into the British countryside so that according to one historian, \"no corner of Britain was left untouched; no station wall or hotel lobby was safe from one of the CPR's poster maps.\" Travelling promoters gave lectures with lantern slides, and exhibits of posters, photographs, and soil samples were displayed in town halls, at agricultural fairs, and at mechanics' institutes. The CPR also had a horse-drawn exhibition van decked out with prairie products that travelled to small towns. In 1893 the van attracted an incredible 1.75 million visitors in 593 places.\n\nIn 1903 the CPR published _Words from the Women of Western Canada_ , which featured many women farming on their own. In particular, the opportunities for widows to homestead were highlighted, and the pamphlet also advertised CPR railway lands that were for sale. The successes of women settlers from Britain were emphasized, although women of other ethnicities were mentioned. Women from the \"Old Country\" included \"A Wiltshire Woman,\" \"A Scotchwoman's Success,\" and \"A North of Ireland Woman's Words.\" There were no women from the United States in the 1903 pamphlet, but Mennonite, Doukhobor, and Romanian women were included, although briefly, and are clustered toward the end of the pamphlet.\n\n_Words from the Women of Western Canada_ cast women as capable owners and managers of farms who still retained their femininity and attended to domestic work as well. They reaped and ploughed, although generally only when the farm was short of male labour. Varied occupations were featured, including a bee farm and a dairy farm. Despite all of this, domestic skills were praised above all, and the pamphlet depicted any unattached women emigrants as destined for marriage. The concluding words were those of an \"old timer\" who had come to Manitoba in the 1870s. Her message was that \"as soon as these women immigrate they are snatched up by the hordes of well-to-do bachelors.\"\n\nWidows were not the only women featured in the 1903 pamphlet, but they predominated. While the reasons for the deaths of the husbands were not made explicit, readers may have wondered why so many husbands died, often soon after arriving in Canada, leaving their widows to struggle on their own. Despite the rags-to-riches stories of successful, prosperous widows, the ubiquitous death of the husbands may have limited the appeal of emigrating to Canada. In a 1906 pamphlet called _Women's Work in Western Canada: A Sequel to \"Words from the Women of Western Canada_ , _\"_ there was much less attention given to the untimely death of husbands. Perhaps this was because overall the pamphlet featured fewer examples of women homesteaders and placed more emphasis on the wisdom of purchasing CPR land. There was also less attention to women farming and\/or owning their land, while the family unit working together was stressed.\n\n_Figure 10._ Through its \"Canada for Women\" promotion, the Canadian Pacific Railway appealed to Englishwomen living \"wasted lives\" to emigrate. Allegedly quoting one such woman, the caption read, \"Ten thousand Englishwomen could be ranged in a line and shot. No one would be sorry. Everyone would be glad. _There isn't any place for them._ \" _Daily Mail_ , 2 March 1910, 10.\n\nThere were widows featured in the 1906 pamphlet, however, reflecting the fact that this was still the only way women could obtain homestead land. Maria Bird of Pipestone, Manitoba, formerly of Gloucestershire, ran a prosperous farm and also published stories of prairie life in journals such as _The Family Circle_. Her husband had died shortly after she arrived in the West, and she buried him \"on the lone plains which took the last dollar.\" But \"she bravely took up the work of the farm, seven children depending upon her; how she stuck to the plow; stood by the grain stack and put 'Stow-on-the-Wold' vim and vigor into the work.\" She had found fortune, and so had her children. \"How a Widow Won\" told the story of Agnes Balfour of Lumsden, Saskatchewan. She had arrived from Ontario as a widow with eight children. Her homestead was \"one of the prize places of the west,\" and her children had all prospered; three daughters settled in the Lumsden area, two sons farmed the old homestead, two other sons were in the mercantile business in that town, and one son was a \"leading lawyer\" in Regina.\n\nThe pamphlet also featured women settlers of means. Under the heading \"An Irish Lady's Winnings,\" Mrs. Westhead of Alix, Alberta, was presented as an example of an independent purchaser\/investor in land despite being married. She had bought land on a visit with her husband to Canada, and they then decided to emigrate. Mrs. Westhead was shown as the more active partner in superintending their prairie estate.\n\nThe final pamphlet in the CPR series, _Home Life of Women in Western Canada_ (1907), also focused on the work of farm wives in partnership with their husbands and on the prosperity of settler families from the \"Old Country.\" It featured very few widows farming on their own. A major message was the dire need of domestic workers. Perhaps as the issue of women and homestead rights began to heat up, with the Canadian government steadfastly opposed, the CPR did not wish to appear to be as welcoming to women as farmers as it had been in earlier pamphlets.\n\nThe CPR advertised the West as a destination for \"surplus\" women of Britain through newspapers such as the _Daily Mail_ where a 1910 advertisement, \"Canada for Women,\" showed three women in a wheat field. Right beneath were the words, allegedly from a woman in England who felt her own life to have been wasted: \"Ten thousand Englishwomen could be ranged in line and shot. No one would be sorry. Everyone would be glad. _There isn't any place for them._ \"\n\n_Figure 11._ In 1913, the windows of the Charing Cross office of the Canadian Pacific Railway were smashed by suffragettes as part of a campaign to punish businesses that did not lobby in support of votes for women. The windows were boarded up and the CPR posted the notice, \"We are looking for settlers, not suffragettes.\" Yet the company advertised in suffrage journals, clearly seeing potential settlers and even farmers in suffragettes. Getty Images, no. 3424540.\n\nIn 1913 the windows of the office of the CPR on Cockspur Street in Charing Cross, London were smashed by suffragettes as part of a campaign to punish businesses for not lobbying in support of votes for women. The CPR boarded up their windows and posted a notice: \"We are looking for settlers, not for suffragettes.\" The suffragette journal _Votes for Women_ pointed out that \"the Suffragettes _are_ settlers.\" But surprisingly, the CPR advertised extensively in the suffrage journals, including _the Suffragette_ and _Woman's Leader and the Common Cause._ A 1913 CPR advertisement \"Canada for Women\" in those journals showed a young woman with a pail confronting a cow with the caption \"Dairy Farming.\" That same year the CPR placed an advertisement in _the Suffragette_ : \"A Welcome to Women in British Columbia.\" The notice began, \"In these days of women's independence, when girls set out to earn their own living, it is perhaps not out of place to point out the opportunities for making a comfortable living out of Dairy Farming, Chicken Raising and Flower Gardening\u2014branches of agriculture in which women are particularly successful.\" Young women \"fond of outdoor life\" were urged to club together and run small farms in the Windermere district of British Columbia.\n\nBy 1913, as indicated by the talks by Skykes and Binnie-Clark described at the outset of this chapter, there was a great deal of optimism in the air both in Canada and the mother country about the potential for British women to farm land of their own on the prairies. But in all of the ink devoted to this cause\u2014the lectures, organizations, and intelligence-gathering trips\u2014there appears to have been precious little knowledge of or contact with the women who were attempting to homestead or otherwise farm the prairies. Legal obstacles and disadvantages were seldom referred to by the proponents of farms for British women. Ideas about small holdings and the \"lighter branches\" of agriculture and colonies of women farmers clubbing together could not simply be transplanted to prairie Canada because of environmental and climatic factors, because of the nature of the land survey system, and because markets were small and scattered. Authorities wanted women immigrants, other than those who arrived as members of families, to work as domestic servants and certainly not in the fields (at least not visibly). And while attitudes about educated gentlewomen as potential farmers might have been changing somewhat in Britain at this time, opposition persisted. When women worked on the land there during the First World War (to be discussed in Chapter 7), detractors were many.\n\nSimilar objections to women farmers prevailed in Western Canada, well into the twentieth century. On the prairies Indigenous women and some recent immigrant women were condemned as the \"beasts of burden\" or drudges of their communities. British women were not to stoop to this level; they were to be models of domesticity and gentility and not sweat in the fields. In spite of these admonitions, women\u2014British and of many other ethnicities\u2014laboured in the fields, and some established homesteads and farms of their own, as the next chapter describes.\nCHAPTER THREE\n\nWIDOWS AND OTHER IMMIGRANT WOMEN HOMESTEADERS\n\nSTRUGGLES AND STRATEGIES\n\nMrs. Bachelor [ _sic_ ], a lady farmer... has the finest and earliest fields of spring wheat that I have seen this year. This lady is a widow, but conducts one of the best managed farms I have seen in the West. The grain fields are clean. The plowing is well done, and all the buildings are comfortable and remarkably well kept.\n\nF.W. Hodson, editor of the _Farmers' Advocate_ , 1909 __\n\nF.W. Hodson was describing the fine grain fields of Eliza Ann Batchelor near North Battleford, Saskatchewan. Originally from England, Eliza Ann and her husband, Thomas, first emigrated to Japan, where he was a tobacconist. Their three children were born in Japan. In 1905 they left Japan to homestead in Saskatchewan, and Thomas (aged sixty-four) died a few months later after being thrown from his horse. The children were aged nine, six, and four. Eliza Ann, then forty-nine, completed the homestead duties, earned her patent to the land, and clearly became an accomplished farmer. From 1876 virtually the only way for a woman to obtain a homestead of her own on the prairies was to be or become a widow. As journalist Lillian Beynon Thomas (quoted in Chapter 1) wrote, \"There are no homesteads for women in Western Canada unless such women care to qualify by killing off any inconvenient husbands they happen to own.\"\n\nThis chapter is about women who homesteaded land in prairie Canada. While the chapter concentrates on British women, homesteaders of other ethnicities are included, as it is important to recognize that women from many nations were interested in \"free\" land in Canada. To understand the full range of obstacles they faced and the strategies they adopted, it is necessary to cast a wide net that includes migrant widowed women homesteaders of diverse ancestries along with women from Ontario, Quebec, and other provinces of Canada.\n\nThe \"imperial plots\" thread of this book is not always obvious in this chapter. Most of these women left few records beyond what is available in homestead files and local histories. The existing sources do not indicate whether they were influenced by or associated with the organizations in the mother country advocating farming for British women on the prairies, which focused on single, never-married \"surplus women,\" not widows with children. Organizations such as the Colonial Intelligence League were concerned with educated single \"gentlewomen,\" and the widowed homesteaders of prairie Canada were not necessarily from that class. There are no indications that any of these widows attended the colonial training schools intended to equip the woman settler with the skills she would need; they would not have had the time or income for such training. It is likely that the homesteading widows were motivated more by their personal and family economic situations and needs than by the desire to contribute to the \"spade-work of empire.\"\n\nChapter 1 ended with the homestead right being removed for most categories of women. As of 1876, a woman (other than an \"Indian\" under the Indian Act) was eligible to homestead only if she could establish that she was a \"sole\" head of a family. This was interpreted to mean widows with minor children. A considerable number of women, mainly widows, managed to homestead and prove up on their land in Western Canada, but they faced many roadblocks and obstacles. A complicated welter of Department of the Interior and Department of Justice \"rulings\" and \"opinions\"\u2014never debated in Parliament but decided by bureaucrats\u2014governed which women could homestead, and individual cases were carefully scrutinized by officials in Ottawa with the overall goal of severely restricting the numbers of eligible women. Widowed women homesteaders enjoyed privileges that were denied to First Nations people, yet they did not have the same virtually unfettered access to land extended to male migrants. They were under intense scrutiny by the formidable bureaucracy of the Department of the Interior, whose employees were concerned about the most personal details of their lives and were convinced that they would readily resort to devious methods to obtain land. Women fought this bureaucracy and made remarkable efforts to acquire and retain homestead land. Women who were not widows (married, single, divorced, or separated) could obtain 320 acres of homestead land if they could afford to purchase South African scrip, and many did, but they still had to perform all of the homestead duties and were subject to the surveillance of the bureaucracy. Women could also cross the border and settle in the American West, where single women could homestead and where the bureaucracy was much more lenient in permitting divorced, separated, or unmarried mothers to file on land.\n\nA WIDOWED LAND\n\nA ruling that was never clearly spelled out in the Dominion lands legislation, but was made policy, was that to be a sole head of a family a woman had to have a child or children under the age of eighteen. Nor did the Dominion lands legislation ever specify that an eligible woman must be a widow, but in publications of the Lands Branch it was made clear that this was the only category of woman eligible. For example, the 1903 Dominion Lands Branch pamphlet _Homestead Regulations of North-Western Canada_ stated that \"a woman who is a widow, having minor children dependent upon her, is entitled to a homestead entry.\" In a 1912 publication of the Grand Trunk Pacific Railway, readers were informed that these children had to be the widow's own: \"A widow having minor children of her own dependent upon her for support is permitted to make homestead entry as a sole head of a family.\"\n\nWidows with their children soon started to arrive in the West to claim homesteads. Like the early male homesteaders in the West, the majority were from the British Isles or Ontario, and were British-Ontarian. In the spring of 1878, Elizabeth McGavin (1838\u20131904) arrived with her ten children and filed on a homestead at Prairie Grove, Manitoba. She and her husband, James McGavin, were from Scotland and had first immigrated to Paisley, Bruce County, Ontario. It was there that James died in 1877 of food poisoning following a church picnic, leaving Elizabeth with three daughters and seven sons. Elizabeth had family members homesteading in Manitoba, and they headed there, mainly by lakes and rivers, until they landed at the old Lombard wharf in Winnipeg. The family was very poor and lived initially on deer, rabbits, prairie chickens, ducks, and fish. But the children received good educations, and three became physicians, including daughter Jessie Margaret McGavin, who in 1895 graduated in medicine from a Chicago university.\n\nWidow Ann McGregor, from Edinburgh, arrived in Manitoba in the mid-1870s with five sons while three daughters remained in Scotland. She filed on a homestead near Keyes, and three of her sons also homesteaded. From this cluster grew what was known as the McGregor settlement, later renamed Mekiwin, Cree for \"gift.\" Ann McGregor was a midwife in that district and ran the post office out of her home.\n\nHannah Stott came to Manitoba from England in 1883 with her children. Her husband had been lost at sea in 1877. Through homesteading and purchasing she acquired extensive tracts of land near Brandon, first 320 acres that she sold in 1890, and then another farm that she personally cultivated and improved until her death in 1907.\n\nOne of the early homesteaders in the Moose Jaw district of Saskatchewan was Grace Keay, a widow from Edinburgh who settled in the spring of 1885 with her two daughters (aged eleven and eight) and her son (fourteen). It was reported in 1896 that she \"works quite a farm,\" and by 1899 she and her son had together acquired 960 acres.\n\nHomesteading widows were often referred to as \"grandma\" in their districts. \"Grandma\" Eleanor Bell Cairns was forty-one when she and her five children from Morpeth, Northumberland, arrived in Manitoba in 1882, together with her father, John Bell, aged seventy-seven. Eleanor entered on a homestead, as did her father. To prove up they were supposed to have separate dwellings, but Eleanor wrote for and received permission to live in one home. The family had some very lean years but persisted, and Eleanor's home became an important community centre, where church services began in 1884. She had the first organ in the district, and dances and musical evenings were held at her home as well. She died at the age of eighty-seven in 1928.\n\nIsabella Beveridge, born on a ship on the Atlantic Ocean as her parents sailed from Scotland to Canada, married Thomas Burns in Ontario in 1865. They and their seven children moved to Washington State in 1889, where Thomas died. In 1893 Isabella Burns filed on a homestead in the ranch land of the Pincher Creek district of Alberta and successfully proved up.\n\n_Figure 12._ Englishwoman Agnes Bedingfeld was the widow of a lieutenant in the Madras Infantry. She homesteaded at Pekisko, Alberta, as did her son Frank, and together they established a prosperous ranch, which they sold in 1919 to Edward, Prince of Wales. Mrs. Bedingfeld was regarded as \"one of the most competent agriculturalists and livestock breeders in Alberta.\" Glenbow Archives, NA-2467-12.\n\nEnglishwoman Agnes Katherine Bedingfeld (born 1845) was the widow of a lieutenant in the Madras Infantry. The daughter of Robert Cobb, a Norfolk rector, she married Francis William Bedingfeld in 1862 when she was seventeen. He was from the landed gentry, his family occupying Ditchingham Hall, also in Norfolk. Their son Francis, known as Frank, was born in 1866 in Suffolk. After Lt. Bedingfeld died in 1869, leaving Agnes a widow at a young age, she and Frank came to Pekisko, Alberta, in 1883. The next year she filed on a homestead. In her application for patent (acquired in 1899), Agnes stated that she had lived in a tent on her land for a portion of 1883 and built her house in 1884. It was necessary for her to file as soon as she could, as Frank was seventeen when they came to Canada, and if she waited until he was eighteen she would not have been eligible. Mrs. Bedingfeld also worked as a housekeeper for Fred Stimson, of the Bar U Ranch. Frank also homesteaded, and his and his mother's log cabins were built together but on each side of the line dividing their quarter sections. Agnes took out a second homestead adjoining her first and received her patent to this land in 1906. The Bedingfelds eventually owned 1,400 acres and controlled another 4,000 acres through leases. They concentrated on raising Clydesdale horses but also had cattle. Agnes Bedingfeld was regarded as \"one of the most competent agriculturalists and livestock breeders in Alberta.\" She retired to Hertfordshire and she and Frank sold their ranch in 1919, when it was purchased by Edward, Prince of Wales, becoming the EP Ranch.\n\nChristina Anne (Bethune) Ritchie homesteaded in the Blackie region of Alberta, filing on her land in 1904. She was born in Nairn, Scotland, and in 1880 emigrated with her family to the Falkland Islands, where she married Scotsman John T.M. Ritchie. She and her husband, along with their three children, settled in Calgary in 1898. John Ritchie died in 1901, leaving Christina at age thirty-three with thirteen-year-old daughter Jennie, ten-year-old son John, and daughter Dora, sixteen months. Christina Ritchie first had to ask for an extension of six months after filing on her land, as she did not have the resources to settle on her homestead. In a statutory declaration of November 1901, she stated that she had \"been waiting for the means to be able to go to said land with my cattle, & as I am a widow with children dependent on me find far more difficulty in getting same than a man would do.\" According to the entry in the local history, Ritchie arrived at her new home in 1905 with \"15 cents in cash, a sack of flour, a pound of tea and 20 pounds of sugar; pretty meagre rations for a new beginning.\" She eventually had cattle and milk cows, but also worked off the farm. Cattle baron Patrick Burns had a beef camp close to her homestead, and Ritchie took in the laundry, baked, and mended for the cowboys. In 1907 newly arrived neighbours from England set up a training farm for students who were \"mostly the rich mens [ _sic_ ] sons and remittance men from England.\" There were over thirty students, and Ritchie cooked and kept house for them. The oldest daughter, Jennie, also worked off the farm doing general housework. Daughter Dora wrote in the local history book that her mother \"kept her homestead free of mortgage\u2014the only piece of land that I know of that didn't become mortgaged at one time or another. Many men lost their land owing to having to mortgage it.\" In 1908 Ritchie received her patent to her land; in her application she described herself as a \"rancher.\"\n\nSarah Jane Hill (n\u00e9e Castle), from Sheffield, England, was a widow and mother of eight who homesteaded at Melfort, Saskatchewan (Pleasantdale district), arriving in 1906 with five of her children. She was a nurse and midwife in her district working, with African-Canadian physician Dr. Alfred Schmitz Shadd. With the help of her sons, she cleared and broke bush land and hauled her grain by team and wagon. In the spring of 1920, Hill moved to a son's homestead, where \"they worked and cleared the land and farmed together.\" She was remembered as \"one of Pleasantdale's first and great pioneers. She loved the land, people and her family.\"\n\nWidow Mary Elizabeth Birss arrived in Canada in 1905 from Aberdeen, Scotland, filing on land in the Stonehenge district of southwest Saskatchewan in 1908. Her husband James had died of a stroke in 1894, leaving her to raise their eight children. Three of her sons settled on the prairies, and she later followed them. When she filed on her land she was fifty-two years old, and her youngest child was twelve. She proved up on both her homestead and a pre-emption and with four sons filing on land nearby, they established a considerable Birss empire. Mary Elizabeth died on her homestead in 1937, in the small two-storey home that was built in 1908 and occupied by the Birss family until 1967.\n\nIn 1906 widow Frances Powell and her family of four daughters and one son arrived in Lethbridge from Wales. She filed on a homestead in the Coyote Flats district of Alberta. Her brother homesteaded nearby but left for Australia soon after proving up. Frances persisted, however, and became \"well known throughout the district as 'Aunt Fanny.' She was a nurse and midwife and \"regardless of the weather or of how busy, she was always on hand to take charge if needed.\"\n\nEliza (Landymore) Garwood, born in Walsham-le-Willows, England, proved up on a homestead in the Inverlea district near Crossfield, Alberta, in 1907. A widow, she and her two children first settled in Calgary in 1902, then she filed on land near her homesteading brother. Garwood was a nurse in the Crossfield, Carstairs, and Madden districts. She remained on her homestead until her death in 1938.\n\nCatherine Corbet Sommerville, from Glasgow, Scotland, her daughter Margaret and sons John, Hugh, Robert, George, and James settled in the Ghost Pine district of Alberta in 1908. Catherine proved up on a homestead and a pre-emption, becoming the owner of 320 acres, and her sons filed on adjoining land, so the family acquired an extensive tract. According to the local history, the whole family \"took a prominent part in the social life of the Ghost Pine community for years.\" (In the summer of 2014, about 160 family members, all descendants of the Catherine Corbet Sommerville family, gathered at the Sommerville farm, which had been recognized with the Alberta Century Farm and Ranch Award.)\n\nIn 1912, following the death of her husband and a two-year-old daughter that same year, \"Grandma\" Barbara Bradshaw, a widow and mother of (originally) eight from Ayrshire, Scotland, travelled to Parkbeg, Saskatchewan, where a son was homesteading. A year earlier another son who had also homesteaded at Parkbeg had been killed in a railway accident. Bradshaw filed on the land of her deceased son and applied for her patent in 1917, swearing that she was \"the head of a family having at the time of my son's death 3 minor children to take care of, and at the present time I have one, namely Grace, who will be 15 years in October this year.\" In her district she was remembered for her love of Robbie Burns and for her \"famous Scotch scones.\"\n\nEntries in the local histories on homesteading widows are often brief. We learn little about \"Grandma Holman\" except that she was an early Manitoba homesteader and was married several times, as she was described as \"nee Harrison\u2014nee Hornsby, nee Ingleby.\" Ingleby was likely her maiden name, since she was allegedly \"a granddaughter of Lord and Lady Ingleby of England. She delivered the babies that were born to other homesteaders' wives.\" Cathy Jamieson was a Scottish widow who filed on 160 acres in 1896 and later bought another quarter section near Lacombe, Alberta. A lake on her land is named after her. (Given that the lake was also described as a slough, her land was not likely the best.) Jessie Kinnaird, from Alloa, Scotland, \"in an effort to keep her family together,\" followed her three sons to Saskatchewan. In 1912 she filed on a homestead northeast of Gull Lake, bringing her daughter Margaret with her. In the same district was widow Mary Attridge from Tyronne, Ireland, who had settled in Ontario where her husband died in 1905. She was a mother of ten, and her two youngest children were living with her when she filed on a homestead in 1910. Three older sons had homesteads nearby. A \"tiny lady, only five feet tall with red hair, [Attridge] was a hard worker. She milked cows, canned fruit... and acted as midwife for many miles around... She occupied her 'leisure time' braiding rugs, making quilts and reading tea cups.\"\n\nFlora S. Law, known as \"Granny Law\" (whose full name is not even provided in the local history biography), was a widow from Scotland with seven children. She homesteaded in 1906 in the Swift Current region of Saskatchewan near two of her sons who were already established there. Her home was a stopping place for the North-West Mounted Police and other travellers because it was on the road to Swift Current. Church services were also held at her house. She died in 1917, and her body was taken back to Scotland for burial. Isabel H. Brookes, from England, homesteaded near Moose Jaw starting in 1911, along with her son Harry, and received her patent in 1914. \"Grandma\" Catherine Gordon, from Scotland, first emigrated with her husband to New Brunswick, where he and six of their children died of tuberculosis. In 1906, at age sixty, she and two of her sons arrived in Saskatchewan, and she entered the next year on a homestead north of Shaunavon, proving up in 1914. Two of her grandchildren were dependent on her, as their parents had died of tuberculosis. Marguerite Douglas, a widow with one child, came from England to Saskatchewan in 1908. She worked as a housekeeper in Moose Jaw while she homesteaded, and by the time she received her patent in 1911 she was married to a neighbour. Martha Lucas, mother of three from Birmingham, filed on land near Lloydminster, Saskatchewan, in 1904 and proved up by 1907. Her husband, a draper, had died of pneumonia.\n\nSarah Cleveley of Bangor, Wales, was a widow with eight children when she sailed to Canada in 1912, with Edmonton as their destination. In 1914 she filed on land at Roselea, next to a quarter section homesteaded by a son. Sarah married neighbour George McCoy in 1918, but the next year she died in the flu epidemic.\n\nHomestead files leave traces of the widowed women who were not recalled in local histories. Olivia Thompson, from Dublin, Ireland, was seventy when in 1909 she filed on a homestead at Elm Springs, Saskatchewan. She did not strictly qualify, as the youngest of her four children was twenty-two. She had, however, squatted on the land for about seventeen years at the time of her homestead entry, made as soon as the land was surveyed. When she applied for her patent in 1912, she argued that she deserved title to her land as she had broken fifty acres, even though she lived on the adjoining quarter section with her son. She wrote on her statutory declaration of 1912 that \"I have lived with my son as I could not live alone & think after being the first white woman in the south country I should be entitled to me deed after living here over 21 years & having done all the improvements.\" There may have been debate in the land office about Thompson's entitlement, as she did not receive her patent until 1917, when she was seventy-nine years old.\n\nNUMBERS AND DIVERSITY OF WOMEN HOMESTEADERS\n\nWhile the widows depicted above were British women, the origins of women homesteaders were more diverse. This diversity is important to understanding the narrowness and elitism of the campaign that was launched for homesteads for women of \"British birth,\" to be discussed in Chapter 6. In southwestern Manitoba, however, most of the women homesteaders were British or British-Ontarian. Historian Kathryn McPherson found that between 1872 and 1900 at least 283 women possessed title to 418 quarter sections. Most of this land was purchased, but McPherson found ninety-two women homesteaders, and these were British citizens \"by birth\" (which would have included those born in Canada). Preliminary results of a database of Alberta homesteaders indicate that up until 1911 there were 1,587 women who had filed in their own names in what became that province. Information on place of birth is available for only 25 percent of these Alberta women homesteaders. Of this 25 percent, there were 126 from the U.S., 128 from Canada, and 75 from the British Isles. (The rest were from Scandinavia, Austria\/Hungary, Germany, and Russia). It is notable that women proved up with a greater success than did men. While patent success for male homesteaders was 69 percent, for women it was 85.4 percent.\n\nCensus data demonstrate increasing number of women farmers, but their numbers were tiny compared to their male counterparts. In Manitoba in 1881 there were 71 female farmers, and in the Territories, 9. The 71 in Manitoba represented 0.65 percent of the total number of farmers. By 1891 there were 252 women farmers in Manitoba, who were 1.2 percent of all farmers, and in the Territories 102, comprising 1.3 percent. By 1911 there were 3,575 female farmers, 1.4 percent of all farmers, while male farmers totalled 254,561. Also in 1911 there were 83 female ranchers or stock raisers (3,838 male), or 2.16 percent of the total. The 1911 census recorded 52 women gardeners (7.54 percent). In the census of 1921 there were 3,930 female farmers, comprising 1.57 percent. That year there were 65 women ranchers (6.28 percent). By 1931 there was a considerable increase in the numbers of female farmers, with 6,786 female farmers (2.57 percent) and 263,642 male farmers (see Table 2).\n\nMy study of the women homesteaders of the Wood Mountain district of Saskatchewan found 114 women who filed in their own names as solo homesteaders. Of these, 57 were widows and 45 of them successfully proved up, receiving patent to their land. There were 34 other solo women who filed on land in their own name, whose marital status is uncertain, and of these 21 proved up. There were 23 women\u2014married, single, widowed, and of unknown marital status\u2014who homesteaded and received patent to their land through South African scrip (to be discussed later in this chapter). There were other ways that women of Wood Mountain acquired land. For instance, if a wife on a homestead was deserted by her husband for a period of five years, and if this desertion was verified by the homestead inspector, his entry could be cancelled and she could make entry.\n\nMost of the widows and other women homesteaders of Wood Mountain filed in the years 1908\u201311, and most received their patents in 1914. There were three who long predated this land rush, who had been squatters before the land was surveyed. Of the widows who proved up, ten also successfully proved up on an adjoining quarter section acquired as a pre-emption. Of those whose place of birth is known, only eleven were from the British Isles. Twenty-six were from Canada, the majority from Ontario, and about half that number from Quebec. At a close second were twenty-three women from the United States, followed by England with nine, Romania and Austria six each, Hungary five, and France four. There were two from each of Norway, Sweden, and Germany, and one from each of Ireland and Scotland. Thirteen of these women homesteaders of Wood Mountain signed with X. Those who signed with an X were mainly from Hungary, Romania, and Austria, although one women of Canadian birth in the Wood Mountain district also signed with an X.\n\n_Table 2._ Numbers of male and female agriculturalists in the Censuses of Canada, with percentages of female agriculturalists. Source: Canada, Dominion Bureau of Statistics. For 1881, Table 14, 319\u201320; for 1885, Table 11, 48\u201350; for 1891, Table 12, 145\u2013146 and 181; for 1911, Table 5, 52\u20133, 96\u20137, 228\u20139; for 1921, Table 4, 242\u20133, 270\u20131, 292\u20133; for 1931, Table 11, 346\u20137, 358.\n\nSome homesteading widows in Western Canada had no knowledge of English. Marie Goueffic, from Brittany, France, immigrated to Saskatchewan in 1906 with her four sons, all under the age of twelve. Her husband had died of yellow fever in French Indo-China. They spoke no English. A sister, however, had come to Canada two years earlier and was living at Carlton, Saskatchewan. The Goueffics lived in a crude and cold shack with furniture consisting of a wagon box filled with straw, where they all slept. Marie Goueffic delivered their grain to the closest elevator at Duck Lake, a trip that took three days. The family eventually could afford a \"ready-made\" house from the Eaton's catalogue, and by the First World War they had the necessary machinery, and an automobile. One of the sons served overseas. A daughter-in-law wrote that Marie, who died in 1926, \"did not die of old age. She died from being worn out from all the hard work and hardship she had gone through.\"\n\nIn his study of the Peace River Country of Alberta prior to 1915, historian David Leonard found fifty-eight women who applied for homesteads, and fifty-four others who filed on land \"as a free grant or with some form of scrip.\" Widowed homesteader Katherine Sampson was originally from South Carolina, and she proved up on land in the Grande Prairie district in 1919, becoming the first African-American owner in the Peace River country.\n\nThere were also M\u00e9tis women homesteaders. Marie Rose Smith, originally from Manitoba, ranched at Pincher Creek, Alberta, until the death of her husband. Smith filed on a homestead in the Lethbridge district in 1915, earning her patent in 1923. Julie Rowand (n\u00e9e McGillis) received a patent to her Deville, Alberta, homestead in 1915 when she was sixty-six years old and a widow with no children living with her. She signed her name with an X. Rowland was one of the early settlers in the district and had been a squatter on her land before it was surveyed.\n\nStudies of homesteading on the prairies have demonstrated that the process required income, particularly in the start-up years. As the short profiles of the homesteading widows at the start of this chapter suggest, widowed homesteaders often earned outside income, sometimes significant, sometimes small. Several of those already mentioned were midwives and nurses. Agnes Balfour, who entered on her homestead near Lumsden, Saskatchewan, in 1883 \"quickly developed a reputation as a practical nurse and midwife. There was no doctor in the area until 1898, so Agnes tended the sick and delivered the babies for miles around. She was called out at any time of the day or night and never turned down a request for her assistance.\" Some women homesteaders laundered and baked for neighbouring bachelors, or worked as cooks and housekeepers. Alberta homesteader Florence Lavelle worked as a farm labourer for a neighbour.\n\nMargaret de Tro, homesteader near Hardisty, Alberta, and widow with three sons likely had the most unusual job. When she first began to advertise in Edmonton in 1905 she was \"Dr. de Tro: The Lady Healer\" but by 1907 had become \"Madame de Tro.\" She was a \"magnetic healer,\" and she established a \"Turkish Bath with Magnetic Massage\" business that she also called a \"sanatorium.\" According to her advertisement, she could treat \"any and all kind of diseases,\" and she defied \"any one to bring anything to my office that I cannot relieve and cure if my advice is strictly complied with.\" She also offered bathing facilities to the public, including Turkish and vapour baths. All Edmontonians could \"afford to be clean and fragrant\" if they bathed at her sanatorium, and she asked them to \"come and try one: makes old young and cures what ails you.\" As bathing days were Tuesdays, Thursdays, and Saturdays, it is difficult to determine how much time she spent on her land. She received her patent to her land in 1909 but died in 1913, aged fifty-eight, on her \"ranch.\" She had gone out shooting and did not return. Her friends found her unconscious, lying over her gun, and it was assumed she had been stricken with apoplexy. She was taken to hospital but never recovered. Sadly, the Lady Healer homesteader was unable to heal herself.\n\n_Figure 13._ Most homesteaders, whether male or female, had to earn money to help establish their farms and for basic survival in the start-up years. Alberta homesteader Margaret de Tro was a \"magnetic healer\" in Edmonton from 1906 to 1913 when she was not on her land near Hardisty. She earned her patent to her land in 1909 and died there in 1913. _Edmonton Bulletin_ , 29 December 1905, 4.\n\n_Figure 14._ The auction sale of the estate of Madam M. de Tro of Hardisty, Alberta, in March 1916 indicates that she had acquired about 562 acres of land. _Edmonton Bulletin_ , 1 March 1916, 9.\n\nHURDLES AND TRIBULATIONS\n\nThe experiences of Marion Ferguson Frazer (Pearce) demonstrate some of the obstructions and handicaps the woman homesteader faced. Frazer was from Largs in Ayreshire, Scotland, and she was a widow, nurse, and mother of two young sons in 1905 when she left for North America with her sons and brother, settling first in Virginia on a plantation. A year later the family moved north to Ontario, where Frazer worked as a nurse, and in 1909 she left her sons in the care of her brother to take a job nursing in Regina and explore the opportunities the West had to offer. A year later they joined her there, and in the spring of 1911 they loaded up a wagon and all set out for her homestead about 240 kilometres away at Wood Mountain. Frazer was forty-seven, her sons were eight and eleven, and her brother was sixty. They were joined by Willie, a cousin from Scotland. None of them had any farming experience, and they were heading toward one of the more desolate and dry regions of the West. Frazer's brother had been a \"drayman on a big steam ship,\" while Willie had been a cook on a sailing vessel.\n\nWithin a few months of her arrival, Frazer became Mrs. Pearce, marrying the man from whom she bought her team of oxen. He had filed on a homestead on the same section and the new Mrs. Pearce wrote to the Dominion Lands Office in December 1911 to ask if they could build one house and live together on her land. She added that \"we intend making this our home it is not a case of speculation.\" But these were the cases that land agents were wary of. Had they colluded to obtain two homesteads? Permission was denied. The newly married couple had to each have a residence on their separate homesteads to prove up.\n\nMarriage did not bring an easier life. Marion (Frazer) Pearce continued to nurse and attempted to farm on her very poor land. Her crops often failed. Her husband left her in 1917, abandoning his homestead without proving up, and she asked permission for her son to file on his land. The homestead inspector was sent to report on whether Mrs. Pearce was truly deserted, and he learned through \"careful enquiries\" that Mr. Pearce was \"afraid they [her sons] would shoot him\" and had left that part of the country. Eventually her son James was permitted to enter on the land deserted by his stepfather. As Marion Ferguson Pearce, she proved up on her land in 1919. But her homestead file documents the difficult circumstances of farming on what was at best range land, long after she got patent to her land. She was in debt for taxes and seed grain well into the 1920s. The whole region suffered from severe drought from 1918 to 1922; many provincial and federal officials argued that southern Saskatchewan should never have been homesteaded.\n\nDiscrimination against women homesteaders such as Marion Frazer (she reverted to that last name in 1924) continued. Once their children grew up, as children tend to do, women homesteaders were not eligible for land offers made to other settlers. In 1928 the outlook brightened for settlers of the Wood Mountain district, as an amendment was passed granting all those who had obtained their patent before 1925 the right to make a second homestead entry on the usual homesteading terms. This was in part a recognition of the very poor land and difficult circumstances everyone in that district experienced. But this opportunity was denied to Marion Frazer. Since her sons were no longer minors, she did not qualify for a second homestead. She was informed by the Acting Commissioner of Dominion Lands: \"You obtained homestead entry [in 1911] on the ground that you were a widow with two minor children, aged eight and eleven years, dependent upon you for support. Under the regulations the privilege of a first or second homestead is only extended to a woman who is a widow with minor children dependent upon her. It would appear that you have no minor children now dependent upon you for support and I regret to inform you that you are not entitled to another homestead.\"\n\nMary Ann McNab, from Scotland, who settled in 1882 in the Moose Mountain district of Saskatchewan, also struggled to obtain the right to a pre-emption of an additional 160 acres. Her husband Alexander had died a year after they arrived in Saskatchewan, leaving her with two of their children; seven of her other children had also died. McNab continued to live on and prove up on the homestead and was granted patent to that land in 1887, but she wanted to pre-empt another quarter section. In an October 1890 statutory declaration, Mary Ann McNab, then forty-six, wrote that she \"intended to take possession of this land last year, but I had both my arms broken and was not able to, I have paid a neighbour to draw the material for a house on the land, and I will take possession shortly. I am most desirous of keeping the land. I have had a very hard time providing for myself and two children.\"\n\nJohn Geddes, the Presbyterian minister at Carlyle, Saskatchewan, wrote to the secretary of the Department of the Interior in October 1890, explaining the circumstances of Mary Ann McNab and asking that she be granted the pre-emption. Geddes reminded the government that McNab had lost her husband and seven of her children; accordingly, he asked that the government \"consider the number of times she has stood on the brink of the grave.\" She was a \"woman of indomitable courage... obliged to do many things that fall, no doubt, within the province of a man.\" Geddes further described her as \"a talented woman, considering that she got only a common school education in Scotland.\" In particular, he admired her ability (which would have been rare among settlers) to speak the language of the neighbouring First Nation: \"She has learned the Assiniboine language, which I believe she can speak as fluently as English... I have heard her keep up a conversation with the Indians without a stutter.\" Geddes said that she had many skills, that she was \"quite a mechanic,\" and \"likewise a good needlewoman, a laundress, and a weaver; and when occasion is necessary, she can solder tin-plate.\" She knew \"the kinds of prairie weeds and flowers [that] are applied by the Indians in the healing art.\" (He recommended that she be hired to work among the people of the neighbouring reserve.) Yet according to Geddes, Mrs. McNab's ambition was \"to be tilling the ground.\" She was an excellent gardener, raising many varieties of vegetables; her work \"might compare favourably with the crops of any man that has made gardening a profession.\" The major goal of the letter was that Mrs. McNab be allowed to \"perform her duties on her second homestead.\" Geddes quoted from the Bible\u2014\"Plead for the widow\" (Isaiah 1:17)\u2014and asked that the government \"plead for her against those that would deprive her of one of the chances of making a living.\" Geddes asked, however, that his name be left out of any investigation that might be made as the \"parties against Mrs. McNab are in my congregation.\" Department of the Interior officials were sympathetic to the claim of Mrs. McNab, and in November 1890 she was given a further opportunity to comply with the conditions of the Dominion Lands Act. Mary Ann McNab received her patent to the pre-emption in 1897.\n\nThere were many ways in which the intricacies of the Dominion lands legislation made life difficult for the woman homesteader. She had to build a habitable dwelling and live on her homestead for six months of each year for three years. As was the case with Marion Frazer, if she married after she filed on her land but before she proved up, and if her husband was also a homesteader, they had to have separate residences, each on his or her own land during the six months of the year they were required to perform residency duties. If the woman homesteader had a son who filed on adjoining land, she could not live on his homestead (except during the six months she could be absent). Yet a son could live with her, never build his own shack, and still \"perfect\" his own entry. The legislation permitted a son who had parents in the vicinity to reside with his parents. The clause specified that the son homesteader could live with \"the father (or the mother, if the father is deceased).\" But a woman homesteader could not live on her son's homestead and still \"perfect\" her entry.\n\nThis rule was tested in 1898, when Saskatchewan homesteader Louisa Hill asked for permission to reside with her son on his adjoining quarter section and still prove up on her own homestead. Hill was informed that there was \"no provision in the law by which you can do residence duties while living with your son... there is no way of meeting your wishes.\" Correspondence on the matter continued for several years, with Hill claiming she had to live with her son because of ill health and because she lacked the means to live on her own. In September 1905 she was thrown from her rig and her arm was injured. That December she wrote to land officials that she was \"under the impression a mother could live with a son just as a son could live with a mother.\" But she was wrong. She had to live on her own homestead to perfect her entry. In 1906 it was decided that because she had been under an erroneous impression of the residence requirement, Louisa Hill would be permitted to purchase her land at one dollar per acre, and this payment must have been made because a patent was granted to her in 1907.\n\nThe issue of citizenship also complicated the life of the woman homesteader. To receive patent, a homesteader had to be a British subject or be naturalized, which meant an immigrant had to have resided in Canada not less than three years. At that point, \"He must take the oath of allegiance, and also an oath that he intends to remain in Canada.\" This process was available to \"every person who is of the full age of twenty-one years, and not an idiot, lunatic or married woman.\" Upon marriage a woman assumed the citizenship of her husband; if he became naturalized she was automatically naturalized. A woman homesteader, therefore, had to take great care if she married before she proved up. If, for example, she was a British subject either by marriage or birth but married a homesteader from the United States who was not yet naturalized, she would lose her right to her homestead because when she married she would become a U.S. citizen.\n\nThis became an issue in the American West among single women homesteaders, particularly those near the border of the United States and Canada. If a single woman homesteader born in the United States married a Canadian (or any other \"alien\") before she proved up on her land, she would lose her U.S. citizenship and her right to her homestead. The cause of these women was championed in 1917 by Jeanette Rankin, congresswoman from Montana. Campaigning for re-election, she learned that \"many of the girls along the border with Canada love Canadian boys and cannot marry them without losing their American citizenship and therefore also their Montana homesteads.\" Rankin found the situation \"ridiculous,\" saying that \"men are allowed to choose their own nations. Women should be accorded the same right.\" (The U.S. citizenship legislation was changed in 1925 to address this, and the process began in Canada with legislation of 1932.)\n\nDEBATING AND NARROWING THE CATEGORIES OF ELIGIBLE WOMEN: THE CASE OF SUSANNA WILLIS, VIRDEN HOMESTEADER\n\nAs the experiences of homesteaders such as Marion Frazer indicate, women contended with vicissitudes and difficulties over and above those that challenged their male counterparts. They held no political clout; they were without votes and without wealth. They could be shoved off their land if it was desired by a neighbour or a speculator. This was the case with homesteader Susanna Willis, whose entry was cancelled because she had valuable land. The stated rationale was that her children were too old; she was likely the first woman to have her homestead cancelled because of this reason. Willis was a widow, originally from Ireland, who had emigrated to Ontario in 1830, and at the time of her 1882 filing on a homestead in Manitoba was about sixty-three. Her land turned out to be very valuable, as it was just where the CPR decided to locate the town of Virden. Land for a townsite was highly sought after, and many speculators tried to anticipate where these sites might be located. Willis was suddenly rendered ineligible to homestead and was told that this was because she did not qualify as a head of family. She had built a house and had part of her land ploughed when she was informed of this, and also told that her land was required for the townsite. However, the main argument used to disqualify her was that while she was a widow and had two sons, she did not have a minor child or children, so she was no longer a head of family.\n\nWillis's case raised many questions at the time and for years later. The _Manitoba Free Press_ was sympathetic to her cause, reporting that \"a very dirty trick\" had been perpetrated on her and suggesting that the CPR wanted her off the land to be able to profit from the townsite:\n\nThe Government appears determined not to do justice to the widow, Mrs. Willis, whose homestead was taken from her last spring on a technicality because it was wanted for the town site of Virden. An Ottawa correspondent states that, failing to obtain any satisfaction from the Local Land Agency, Mrs. Willis appealed to the Government, and a few days ago when her solicitor laid her case before the department, he was told by a government official that the provision in the Land Act enabling widows to acquire homesteads, only applied to widows with very young children. A number of other equally brilliant excuses were given for depriving the woman of her homestead at the request of the [CPR] Syndicate.\n\nThere was fierce debate, however, about the right of the \"Widow Willis\" to her land. The _Winnipeg Daily Times_ supported the government's stand and insisted that \"although a widow, [she] is not a sole head of family in the sense of having a family dependent on her for support... on the contrary her sons are grown up and have second homesteads and pre-emptions for themselves.\" The _Times_ stressed that the _Free Press_ was trying to present this as the story of an \"Irish eviction\" and that other issues were involved, including that Mrs. Willis had not improved the land and was two months late in becoming a bona fide resident of her homestead (while the _Free Press_ claimed she was delayed by flooding). According to the _Times_ there was subterfuge involved, and Willis had filed on land as \"simply an attempt to obtain a second homestead for the son in the name of the mother.\"\n\nThe debate continued well into the next century, when it was proven that Thomas Mayne Daly, a Brandon lawyer (and elected mayor of Brandon in 1882) and later minister of the interior, had made huge profits from land sales in Western Canada, including from his \"ownership\" of land that became the town of Virden. A 1901 Northwest Town Sites Commission found that Daly had entered on the south half of the township in question, while Willis had the northeast quarter as her homestead. She made improvements and was living on her homestead, while Daly had made no improvements and had been in residence there only ten days. Willis's entry was cancelled for the official reason that her son was not a minor, and she received no compensation. Daly, however, made an enormous profit selling his \"rights\" to the south half for $6,400.\n\nInquiries revealed the documentary evidence. In May 1882 the CPR land agent at Winnipeg, J.H. McTavish, wrote to C. Drinkwater, secretary of the CPR in Montreal, to the effect that the Willis\/Daly section had been chosen for the station and town, and that \"Mrs. Willis has failed to comply with the homestead regulations, and I am taking steps to have her entry cancelled. Daly is prepared to abandon if we pay him $20 per acre or $6400.00 cash.\" Drinkwater replied yes, that they should \"deal with Daly and take the necessary steps against the widow Willis.\" Daly's claim was to be settled from the first sale of town lots in Virden. The matter was still being discussed in 1908, when the _Brandon Daily Sun_ asked, \"Would the CPR have made fish of Mr. Daly and fowl of the widow if Mr. Daly had not been backed by the Government at Ottawa? Was Mr. Daly as Minister of the Interior under any obligations thereafter to promote the interests of the CPR?\" No one, it seems, thought of asking Susanna Willis herself about the issue. She was still in Virden as late as 1901, when at age ninety-two she was living with her son Thomas (fifty-three), a farmer. At the time she was forced off her land in 1882, Thomas would have been nineteen, just out of \"minor\" status. Daly, by contrast, has been honoured for his \"distinguished legal and political career\" by the Historic Sites Advisory Board of Manitoba. There is a plaque outside his home, which is a museum in Brandon, and a pamphlet that recognizes his contribution to public affairs in Manitoba and Western Canada.\n\nWHO IS A \"SOLE\" HEAD OF A FAMILY?\n\nThe wording of the 1876 amendment to the Dominion Lands legislation left room for many questions, including whether in certain cases a \"spinster\" was a head of household and could homestead. In 1886 there was concern that an amendment to the law was necessary to make it clear that a spinster was not a head of household. The minister of justice concurred with the opinion of William Wilson, law clerk of the House of Commons, that \"under no circumstances can a spinster be considered eligible to make homestead entry.\" Wilson wrote, \"I fail to see how a spinster could be the head of a family in terms of the Dominion Lands Act. If she had servants or dependents they would, subject to the terms of their agreements, be free to go when they like and therefore could hardly be deemed to be a family... I therefore think that the practice which appears... to have obtained, of refusing them homestead entry is in accordance with the law, and that no amendment of the law in the direction indicated is necessary.\"\n\nYet there were rare instances when single women did manage to homestead. Isadore Harkness, a dressmaker at Prince Albert, Saskatchewan, filed on land as a single woman in 1882 and built a home there in February 1883. A document explaining her case over ten years later stated that the Agent of Dominion Lands at Prince Albert \"through inadvertence, and apparently under the impression that she was the sole head of a family, granted a homestead entry... to a spinster.\" Harkness lived on her land for several months each year (May to November) and in 1885 applied for her patent, having ten acres under cultivation. Her case was delayed, however, for over ten years after her initial application for patent, as the issue of her eligibility was debated at the highest levels of government and of the bureaucracy. In 1895, Minister of the Interior T.M. Daly (who had helped to divest Mrs. Willis of her land) was sympathetic. He thought there was evidence that Harkness was the sole support of her widowed mother and sisters. But Deputy Minister A.M. Burgess looked into the case and found that in fact the mother and a blind brother both had their own homesteads, and the mother was residing with her son. Although Burgess too was sympathetic, he concluded that \"we cannot say that she is the sole support or even chief support of the family.\" Minister Daly referred the matter to the Privy Council, recommending that letters patent be granted, that \"it would be a hardship now to deprive Miss Harkness of her homestead on the ground of her ineligibility to obtain a homestead entry, inasmuch as she secured her entry and complied with all the requirements of the law in good faith.\" Harkness finally was granted ownership of her land in May 1895.\n\nBut the majority of single women who inquired about their right to homestead were informed that they were not eligible. Ellen Margaret Cameron wrote to the Department of the Interior from Pittsburgh, Pennsylvania, in 1886, asking whether a head of family in the legislation could be interpreted to mean \"a young unmarried lady over 21 years of age who wished to have a homestead of her own independent of other members of the family (as is now quite customary in the United States).\" Her deceased mother, she noted, was a Canadian. Cameron was curtly informed in 1887 that \"a young unmarried woman does not come under the term 'sole head of a family' existing in the Dominion Lands Act.\"\n\nThe eligibility of women in other categories was debated by officials, including the case in 1893 of Margaret Spence, a M\u00e9tis woman and mother of \"illegitimate children.\" The evidence before the Departments of the Interior and Justice was that she was not legally married to Thomas Young, but had children with him, and had lived with him on land that \"Young squatted upon... and lived thereon until the year 1891, when he left the country.\" \"He had during all that time residing with him a Half-breed woman,\" was how an official of the Department of the Interior put it. In 1893 Margaret Spence wanted to be allowed to make homestead entry; she and her children were still living on the land, keeping up improvements, and paying taxes. The secretary of the Department of the Interior sought the opinion of the Department of Justice, noting that \"the practice of the Department of the Interior has been to interpret the expression 'sole head of family'... to be restricted to a widow with children some of whom at least are minor, and the Department has refused to recognise the mother of illegitimate children as entitled to make homestead entry.\" The two departments rummaged about for \"the proper definition of the term 'sole head of a family' but did not succeed in finding any record of such an opinion.\" The Minister of Justice decided that \"under the peculiar circumstances of this case... your Department may properly recognize Margaret Spence as a sole head of family, and permit her to make entry for the land in question.\" The minister would not, however, \"lay down any general rule on the subject.\" (There is no register of a land patent for Margaret Spence.) Documents pertaining to the scrip application of Margaret and Thomas's daughter Sarah suggest that her parents were in fact married, that her mother was Margaret Young and the widow of Thomas Young, who had died in Alaska in 1889.\n\nThe Margaret Spence case led to an intensive effort to create a \"general and final ruling\" on which women could homestead, and how terms such as \"sole\" and \"head\" were to be interpreted. In an 1894 memorandum, a Department of Justice clerk collected definitions of the meaning of the term \"head,\" including \"a person to whom others are subordinate\" and \"the most prominent or important member of any organized body.\" _Bovier's Law Dictionary_ defined \"Head of a Family\" as follows: \"Householder; one who provides for a family... There must be the relation of parent and child, or husband and wife.\" Because the term \"head of family\" could not be said to be a \"word of art\" (meaning a term that has a precise or specific meaning within a discipline or field), the clerk urged that \"the only safe general rules we can lay down must be founded upon a strict construction of the Statute, leaving doubtful cases to be decided according to their special circumstances.\" It was further noted that \"sole was not used in the U.S. legislation.\" In Canada the designation \"sole\" head of family was used to exclude a great variety of women, for example someone whose husband might still be alive, although ill or incapacitated. A woman who had adopted or was an older sister of siblings, or was caring for a sibling's children had to have the _sole_ legal right to custody or control of children in order to qualify.\n\nAn 1895 Department of Justice ruling set out the rights of women to make homestead entries. The most uncomplicated eligible category was that of widow, but the widow had to have a minor child or children\u2014if they were grown the applicant was not eligible. A person was considered a minor in the eyes of the law until age twenty-one. However, if the widow's only child (or only minor child) was a son who had reached the age of eighteen, the widow was no longer eligible, as the son could apply for his own homestead. If her child was a daughter the widow was eligible until the daughter was twenty-one.\n\nThe widowed applicant generally had to sign a statutory declaration that she indeed was a widow (although it is not clear just when this became a requirement), and provide the names and ages of her children. If it was later discovered that she was not a widow then she might be disqualified altogether, or she might be permitted to purchase her homestead, generally at a price between three dollars to one dollar per acre, or she could be sent to jail, as discussed in one case below.\n\nAccording to the 1895 ruling, a married woman deserted or separated with a minor child or children could \"sometimes\" be the sole head of a family, if the husband was presumed dead, for example, or \"where by a _binding agreement_ or by the Courts she has been given the custody or control of the children.\" In this and many other categories, when doubts arose, the cases were to be submitted to the Department of Justice. A married woman separated or deserted and having no children depending on her \"cannot be held to be the sole head of a family.\" Even with children, it was unlikely that a deserted woman would be permitted to homestead. A Mrs. Doig of Regina applied for permission to homestead nine years after her husband deserted her, went to the United States, acquired a divorce, and remarried. The reply to her request was that if she had minor children and had already performed settlement duties on a homestead acquired by her husband she was eligible to apply for title to that land, but if she was applying \"with a view to taking out land I should think that it ought not to be granted.\" Since Mrs. Doig had no children she was therefore not regarded as a sole head of a family, and her application was not granted. Even though her husband had deserted her and remarried, the decision still applied that \"a married woman who does not live with her husband, though not divorced under Canadian law, is not so entitled.\"\n\nDocuments had to be produced for the land office, and the files of some women homesteaders or would-be homesteaders include deeds of separation. In August 1913 Amanda Giller, widow and milliner of Grouard, Alberta, wrote directly to the secretary of the Department of the Interior, explaining that she was legally separated from her husband, Dr. Jean Louis Giller, that she was left with three children, and was \"absolutely obliged to see to their education, not knowing even where there [ _sic_ ] father is living.\" She wrote that she was twenty-nine years old and her husband seventy, and the children were two, three, and four. The local land agent had urged her to write directly to Ottawa for permission. She had a legal separation and produced the document, dated 9 June 1913. The document stated that they were from then on to live \"separate and apart,\" that \"Amanda Giller shall be as if she were feme sole, and shall henceforth be free from the control and authority of the said J.L. Giller.\" She was granted custody, but if she failed to provide for \"the necessaries of life, or to give them a proper education,\" she had to deliver the children to her husband. A further provision was that \"the said Amanda Giller shall conduct herself as a chaste and good woman and does not endanger at any time the moral welfare of the said children.\" It is not clear from the file whether she was permitted to enter on a homestead. No patent for land was ever issued to her. An Ottawa memo of 1914 in her file noted that her Agreement of Separation was not \"legally sealed,\" although in the margins an official wrote, \"She appears to be entitled under present practice.\" Perhaps during the many months when she heard nothing back from the Department of the Interior, she decided to pursue other survival strategies.\n\nA major concern about separated women was, as future prime minister R.L. Borden explained in the House of Commons in 1907, that to permit them to file for homesteads would encourage separation, because then both husband and wife could obtain homesteads. (This same reasoning was not applied to separated men.) Rulings with regard to deserted and separated wives were eventually relaxed, but in all cases women had to have minor children. Initially, women who could prove desertion for five years were permitted homestead entry, and in 1920 this was changed to two years, although the Department of the Interior would \"order an investigation by a Homestead Inspector regarding the BONA FIDES of the application,\" and when the report was received, there was no guarantee\u2014the case would be decided on its own merits. In 1914 separated women who could produce a proper agreement of separation could also be considered, and an investigation would be held. The homestead inspector's report had to \"clearly show that there is no danger of collusion\"\u2014of the husband and wife plotting to both acquire land. Throughout the correspondence of the government officials there was an evident lurking suspicion that deceptive and evasive tactics were being employed to acquire land.\n\nThe 1895 ruling on which women were eligible to make homestead entries also stated that a married woman \"validly divorced\" in Canada and having control or custody of minor children was entitled to be treated as a sole head of a family. A valid decree of divorce had to be submitted with an application. (There were very few such validly divorced women, as divorces were very rare at that time in Western Canada. There were no divorce courts in the Prairie provinces, and divorce was obtained by a special Act of Parliament, an expensive and public procedure. Alberta, for example, had one divorce case in 1906 and one in 1909, these being the only divorces to 1909 since Alberta became a province in 1905.) A foreign decree of divorce would have to be carefully scrutinized for its validity\u2014including American divorces, which were generally not recognized in Canada.\n\nThe 1895 ruling declared that \"spinsters without any one related or otherwise dependent upon them\" were not eligible to file for a homestead, nor were spinsters with servants or employees dependent upon them. Nor was a spinster with dependent brothers or sisters eligible, unless she had been given custody or control through a will or legal instrument or a competent court. There were exceptions, but these were carefully scrutinized. In 1904 Miss Matilda Bucknam requested permission to file on a homestead. Lawyer James MacLean of Yorkton wrote to J.G. Turriff, Commissioner of Dominion Lands in Ottawa, on her behalf and explained that \"Miss Bucknam is, and has been the support of her Mother, a widow and an invalid, and her brothers and sisters for many years. One boy, a minor of about 15 years now with her sick helpless mother is entirely dependent on Miss Bucknam for support... Miss Bucknam is desirous of having the privilege of taking up a Homestead in her own name. Her mother could not, owing to ill health, fulfil the homestead duties.\" The commissioner consented to this, and Bucknam filed on a quarter section near Edmonton, although she later had to abandon the claim, declaring in 1905 that \"I am unable to go to live upon it at the present time as the salary I am now earning is necessary to the support of myself and my mother who is a widow.\"\n\nAn unmarried woman with \"illegitimate\" children depending upon her \"may sometimes be eligible as it has been held that a mother has a natural right to the custody of her young children,\" but every such case was to be decided on its own merits. Generally the Department of Justice refused to recognize the mothers of illegitimate children as entitled to homestead entry, although a few cases were permitted. Initially grandmothers having custody of minor grandchildren were not considered eligible, but this ruling was reversed in 1896. However, in 1916 a widow named Mary Blackstock filed on a homestead, claiming she had a minor child dependent upon her for support, but when it was later shown that this was not her own but her daughter's child, cancellation proceedings were instituted on the ground of fraud.\n\nAn unmarried woman with adopted children was not eligible, unless, once again, this was \"by virtue of a will or other instrument, or the judgement or order or decree of a competent court.\" In 1888 Miss Bertha Livingston, who had some of her sister's children depending on her for support, was informed that she was not eligible. In the 1895 case of Eliza McFadden, who adopted the two children of Thomas Hare, it was not sufficient to produce a letter from Hare in which he agreed to relinquish and resign all his legal claims to these children as their parent. McFadden was found not eligible because she could not be considered the _sole_ head of a family, as \"a father cannot divest himself of his authority over or responsibility for his children by such an agreement.\"\n\nReplies to enquiries were terse. In 1904 Susan Walper of Yarrow, Alberta, wrote to the secretary of the Department of the Interior asking if she could enter on a homestead. She was thirty-two and single, and had a nephew in her care whose parents had died. She wrote that her \"sister's last wish was for me to provide for and bring up the child.\" She found it hard to make a living, and was ready to move onto the land and \"make it a future home for myself and my boy.\" The answer from P.G. Keyes was simply that \"you are not entitled to a homestead entry, as this privilege is restricted to women only who are widows with minor children dependent upon them.\" This was not what the legislation stated, but this was how it was consistently interpreted.\n\nProof of legal adoption was required. In 1911, when Miss Marion T. Thompson applied for entry on an Alberta homestead, she had to submit her \"Agreement as to Custody of a Child,\" dated 1908, at Newcastle upon Tyne. Through this agreement, widow Elizabeth Hopwood Thompson of Durham gave \"possession and custody of her son James\" to her sister Marion Thompson, who agreed to maintain, clothe, and educate him. At the time of the adoption agreement, Marion Thompson was a \"spinster\" living at the Pioneer Club, Grafton Street, London, which was a women's club devoted to the suffrage campaign and other feminist issues of the day. The club hosted lectures and discussions of a great variety of topics, and the potential for women to farm in the colonies may have been raised by speakers. James was seventeen years old when his adoptive mother filed on a homestead\u2014if she had waited one more year she would not have been eligible. Marion Thompson established a ranch at Swallowhurst, and she was often mentioned in the social columns of the Edmonton and area newspapers (although an adopted son was not mentioned). In a May 1912 issue of the _Edmonton Bulletin_ , it was noted that \"Miss Marion Thompson leaves next Monday with her maid for her ranch in Swallowhurst.\" She received her patent to the land in 1915.\n\nWhile older children could be of assistance to women homesteaders, the presence of young children must have impeded the progress of the farm. Imagine for a moment just how efficiently and quickly the prairies would have been settled if male homesteaders had been restricted to the category of widowers with young children they were solely responsible for. While children were not strictly required to reside on the land with the woman homesteader, the children might have to be produced for the homestead inspector, especially in the case of a widow coming from another country, as \"there would be some opening for misrepresentation if a widow... were granted entry merely upon her statement that she has a minor child or her own dependent on her for support, such child not being a resident of Canada.\"\n\nWives whose husbands were incapacitated by disease or injury could sometimes be granted the right to homestead, but these appear to have been exceedingly rare. Each case was individually examined, and in each case the applicants had to have minor children. In 1895 Mrs. Catherine Godkin wrote to the Department of the Interior for permission to homestead. She was the mother of four young children, and her husband had been confined in an insane asylum for seven years, with little hope for recovery. The decision was that Mrs. Godkin was not a sole head of her family within the meaning of the statute (presumably because her husband was still alive and thus she was not the _sole_ head). In the 1920s this was relaxed to some extent but not automatically; each case was still individually examined. The insane or incapacitated husband could not have previously filed on a homestead, and there had to be no chance of recovery. Decisions were not always as draconian as with the Godkin case. In 1887 a homestead entry near Yorkton was granted to Mrs. Jane Ferguson when evidence was filed that her husband John was \"hopelessly insane.\"\n\nTHE DEVIOUS WOMAN HOMESTEADER\n\nDespite having tried to clearly identify which women could qualify as a \"sole\" head of household, Dominion lands officials remained concerned about the potential for women to resort to devious means to obtain land. A new clause was added to the \"Eligibility for Homestead Entry\" section of the Dominion Lands Act in 1897: \"If in the case of any woman who, claiming to be the sole head of a family, makes application for a homestead entry, any doubt arises as to the right of such woman to be recognized as the sole head of a family, the Minister may decide from the special circumstances of the case whether such application shall be granted or refused.\"\n\nStories of these devious means were many, some true and others embellished. There were women who acquired or tried to acquire homestead land through falsely representing themselves as widows. Some were caught and prevented, while others managed to slip through the cracks of the bureaucracy, possibly because a local land agent and inspector relaxed the rigid rules. Hannah Surrey (n\u00e9e Osborne), from Essex, England, homesteaded in the Maple Creek district of the Cypress Hills. She settled in 1887 with three children. In the entry on Surrey in the local history, the author comments, \"Just what prompted a widow with 3 children to choose a four year old prairie town (so far from her native home) to rear her family is question not answered.\" But the same entry hints at an answer: \"She was accompanied by her brother-in-law John Harvey, who also had a young family.\" A Harvey family genealogist in recent years has (re)discovered that Hannah and John ran away together to Maple Creek. Hannah was the sister of John's wife (Charity Osborne Harvey). The scandal this must have generated would have motivated the couple to seek this distant location so remote from their home. In the 1906 census Hannah Surrey is listed as a \"widow\" and \"sister\" of the head of household, John Harvey, who is listed as \"married.\" They had become prosperous ranchers with 200 horses and 700 head of cattle. Hannah remained on the Maple Creek ranch until 1912, when she moved with daughter Jane to Victoria.\n\nElise Vane was a Manitoba homesteader, filing on her land in 1886. She arrived in Canada in 1882 from England (although she was originally from Germany) with her five children, along with Percy and Alice Criddle and their four children. Both Alice and Elise were Percy's wives and the mothers of his children. Elise Harrer, who changed her last name to Vane when they immigrated to Canada, was the first wife of Percy Criddle (although the term \"common law\" may be most apt for this marriage, as no marriage certificate has been found). She was German, and they had met in Heidelberg where they were both students. Later she moved to London, where Percy had a wine shop. Criddle then married Alice Nicol in 1874. They all shipped off together and settled north of Treesbank, where the family eventually acquired 6,000 acres.\n\nIn Elise Vane's quest for a homestead, both she and Percy Criddle declared that she was a widow. When she applied for her patent to her land in 1889 and was asked to clarify her status as a head of family, she wrote, \"I beg to tell you that I have been a widow since Sept. 1874 and that I am a head of a family having five living sons and one daughter. I thought I had already given this information.\" Further complications arose in obtaining her patent because she had been living with the Criddles and not on her homestead, except for three months of one year, and the land office initially insisted that she had to fully comply with the residency requirements. Vane objected, stating that she was a \"widow with scanty means\" and would lose her employment as housekeeper. She added that she considered her homestead her \"clear and undoubted right.\" But officials maintained that it seemed she had abandoned her homestead and changed her vocation. Then another complication arose. In January 1890, an anonymous letter arrived at the land office in Winnipeg, stating, \"If you take the trouble to look into the record of Mrs. (Miss) Vane... you will find that she is an unmarried woman living as a servant in the house of P. Criddle.\"\n\nThe homestead inspector was sent to investigate. From his interview with Vane, he reported that she was born in Germany of German parents and had married an Englishman in 1864; they lived in England and had five children. Vane stated that her husband had died in England in 1874, but that his death certificate and their marriage certificate were lost in Winnipeg in 1882. The inspector also spoke to Percy Criddle, whom he found to be a \"thoroughly reliable man.\" Criddle stated that Mrs. Vane had been their housekeeper since 1874 or 1875, that \"he has known her family for the past thirty years, and that he believes her to have been married and that she has always had a good character.\" Criddle was one of Vane's witnesses to her application for her patent, swearing that all her information was true. (In a letter to the Dominion Lands Commissioner in Winnipeg, Criddle wrote that he knew the real name of the author of the \"scurrilous\" letter, suggesting that the writer had reason to profit if Vane's application was rejected and that he wanted the letter so that he could have the handwriting analyzed.) The homestead inspector further reported that other male settlers in the neighbourhood stated that Vane was \"a respectable woman and that she is a bona fide settler.\"\n\nVane and Criddle persuaded officials that she was a sole head of a family, as letters patent were issued to her in March 1890. In the census for 1891, Elise Vane is identified as a widow, aged fifty; it appears she was living on her own land beside the Criddles, with sons Edwy, nineteen; Harry, eighteen; and Cecil, seventeen. In 1901 she is listed as a \"lodger\" in the Criddle home and a widow, but she identifies herself as a \"farmer.\"\n\nThe experiences of Elise Vane illustrate how women homesteaders were policed and monitored in a way that men were not. Inspectors were sent to see if male claimants were attending to their homestead duties of cultivation and residency but did not inquire into their marital status, their status as a sole head of family, or their morality. A man could have two wives and families and not have his affairs investigated and be declared \"thoroughly reliable.\" Widowed women homesteaders were often assumed to be the opposite\u2014trying to obtain land for devious purposes and through devious means.\n\n\"Collusion\" was the term often used to describe how a devious woman might conspire with a male partner or fianc\u00e9 to obtain two homesteads. At an Edmonton land rush on 31 August 1908, there was one woman among the several hundred men waiting to file on homesteads outside the land titles office. She was Margaret Conklin, who told the _Edmonton Bulletin_ she was a widow from Michigan. The paper reported that she did not have to stand in line all night, as a \"young man saw her intention and offered to hold her place. She had a good night's rest and resumed her stand this morning.\" She successfully filed on a quarter section. Journalist Gertrude Balmer Watt later wrote of her interview with Conklin as she stood in line. The widow said she was looking for a homestead for herself and her son, who was fifteen: \"She knew all about farming; could plough with the best of them; had studied gardening and chicken raising, and loved both occupations. She and her boy would work the farm themselves; she had her eye on a likely spot, which friends had looked over for her.\"\n\nJust days after the land rush it was reported that Conklin had married Fred Reed, also from Michigan, at Grace Methodist church in Edmonton. Reed had located a homestead on the adjoining quarter section and had been just ahead of her in the line. The _Bulletin_ commended this \"unique inauguration of a 320 acre farm and wished Mr. and Mrs. Reed their full share of health and happiness,\" but added that \"the subject of a very interesting inquiry would be whether the pair had the matter all arranged before coming to the city, or whether the gallant Reed sort of 'sprung it on her' as they stood in line.\" No such evidence was ever forthcoming. The couple, however, did not retain both homesteads. Fred proved up upon his and got a patent to his land, but Margaret abandoned her homestead in 1910, for reasons that the file does not reveal. Their story lived on and was retold as the \"romance at the land office... of the bachelor and young widow who filed on neighbouring quarter sections at the same time, compared notes on leaving the office, and in due course were married.\"\n\nMINISTER OF THE INTERIOR FRANK OLIVER AND FURTHER NARROWING OF OPPORTUNITIES\n\nUnder the administration of Frank Oliver, minister of the interior for the Wilfrid Laurier Liberals from 1905 to 1911, the applications of women for homesteads were subject to increasingly intense scrutiny, and many were rejected. Oliver was the member of Parliament for Edmonton and a newspaper publisher, politician, and land speculator who was implicated in many improper land transactions that enriched his friends and supporters, and lined his own pockets. In 1910 Oliver became particularly intransigent, perhaps in response to the growing campaign for homesteads-for-women. In January of that year Oliver \"dug his heels in\" and declared to employees of the department that the rules were to be rigidly interpreted and applied. In a memorandum to employees, Oliver warned them to guard against fraudulent applications by women. He told them that the homestead privilege was \"not to be granted to a widow who is the legal guardian of a minor child, nor to a widow who has an adopted minor child dependent on her for support except in cases where the adoption was made a sufficiently long time prior to the application for entry to satisfy the Department that such adoption was not made for the mere purpose of making her eligible for homestead entry.\" A few months later he told employees of the Department of the Interior: \"No woman should be granted permission to enter for a homestead unless she is clearly eligible to do so under the regulations, that is to say, a widow with minor children dependent upon her for support. This means that a woman who has been abandoned by her husband, or has in some other way become separated from him, is not to be granted homestead entry until her case has been passed upon by the Minister.\"\n\n_Figure 15._ A land rush was the prairie equivalent of a gold rush. As surveys were completed and new townships opened for entry, hundreds rushed to claim homesteads. Hopeful homesteaders might camp out for days outside the land office. While some land rushes were orderly, others were not, requiring police assistance. There were sometimes stampedes as people rushed to be at the front of the line once the office opened. Rush for Free Homesteads at the Dominion Land Office, Moose Jaw, Saskatchewan, 1908. Peel's Prairie Provinces, University of Alberta Libraries, Postcard 18198.\n\n_Figure 16._ At the Edmonton land rush on 1 September 1908, Margaret Conklin, a widow from Michigan, was the only woman among several hundred men lined up. She successfully filed on a homestead, and a day later, married Fred Reed, also from Michigan, who had been just ahead of her in the line. Had they \"colluded\" to obtain two homesteads, it was wondered? While she did not \"prove up,\" her husband did. Homestead rush at Edmonton, Alberta, 1 September 1908. Peel's Prairie Provinces, University of Alberta Libraries, Postcard 6839.\n\nOliver instructed his staff that cases of women applicants \"in which there is no merit are to be turned down promptly,\" and that any case with \"some merit\" was to be brought to his attention. It was in 1910 that a woman (Elizabeth Edmundson, further discussed below) claiming falsely to be a widow in order to file on a homestead was sent to jail when her husband was brought all the way from Buffalo, New York, to appear at her trial in Medicine Hat, Alberta. This courtroom drama was likely staged with the knowledge and approval of Minister Oliver. And in July 1910 Oliver personally ruled on the homestead application of Mrs. Louisa Pearkes, of Droitwich, England, who was reported to be on her way to join her two sons at Stauffer, Alberta. She had submitted an \"uncertified copy of a Deed of separation between herself and George Pearkes\" from 1907. Louisa Pearkes had one minor child, a daughter who was nineteen. Oliver denied permission: \"The separation is uncertified and too recent. In cases of separation any of less than five years will not be considered.\" If Oliver was concerned that the mother and sons were of dubious character because of her separation from her husband, he was to be proven wrong. Louisa Pearkes joined her sons with her daughter in Alberta in 1910 and found them living in impoverished circumstances. The sons had not wanted to \"add to their mother's problems,\" as she was separated from their father, and they were clearly receiving no assistance from him. Louisa Pearkes remained separated from her husband, later moving to British Columbia. Her homesteader son George was awarded the Victoria Cross for gallantry in the First World War, and he later became a major general in the Canadian Army, General Officer Commanding-in-Chief Pacific Command, a member of Parliament, the minister of National Defence, and Lieutenant Governor of British Columbia.\n\nIn June 1910 Oliver once again proved rigid and intransigent when he decided that Mrs. Oxilla Grant was not eligible for a homestead. Although her daughter was over the age of twenty-one, Grant had provided a statutory declaration and a medical certificate to the effect that her daughter \"Anna Grant, is an invalid and incapable of earning her living by her work.\" Oliver wrote tersely, \"Not eligible daughter is not a minor.\"\n\nTHE PROBLEM OF THE LIVING BUT ABSENT HUSBAND\n\nThere were cases when authorities decided that a woman homesteader was not entitled to have entered on a homestead after all because a husband was found to be alive, in the vicinity, or providing support. In some of these instances the woman homesteader was permitted to purchase her land. This was generally a humiliatingly public process, as the matter was referred to the Privy Council, an order-in-council had to be passed, and the result published in the _Canada Gazette_ four times. In January 1895, Maria Bell Heath from Ontario was permitted to enter on a homestead near Leduc, having claimed the right to make an entry as she had a deed of separation between herself and her husband. The deed of separation was dated 1880. The matter was referred, however, to the Department of Justice, and there it was decided that \"the said deed of separation does not make Mrs. Heath the sole head of a family within the meaning of the Dominion Lands Act to qualify her to obtain a homestead.\" Presumably because her husband was still alive, Mrs. Heath, whether separated or not, was not considered the sole head of her family. The matter was discussed at the level of the Privy Council, where evidence was presented that Mrs. Heath was \"to all intents and purposes a widow and has the care of a family, is desirous of obtaining the said land for the purpose of residing on and cultivating the same.\" While the council decided that she could not be allowed to homestead, even under the \"exceptional circumstances\" of the case, it was decided that she be allowed to purchase the land at one dollar per acre. This decision was approved in July 1895, but it still took years for the matter to be settled; she was not granted her patent until 1901.\n\nWomen homesteaders who were found to be separated from their husbands rather than widows, as they had claimed, were permitted to purchase their land. In 1907 Margaret Heffernan secured entry to an Alberta homestead, claiming to be a widow with minor children. However, a homestead inspector reported that Heffernan's husband was alive, that they had been separated for about twelve years, and that he still paid her twenty-five dollars per month. The clerk of the Privy Council reported in 1912 that \"as Mrs. Heffernan has been receiving support from her husband she is not properly entitled to a homestead entry in her own name.\" Yet she was permitted \"some consideration,\" as she had completed all of the homestead duties. It was decided that she would be allowed to purchase her land at one dollar per acre.\n\nA woman homesteader who falsely claimed to be a widow, however, could be sent to jail. This was the case with Elizabeth Edmundson, who filed on a homestead near Medicine Hat in 1910. She claimed not only that she was a widow, but that she had the care of a number of small children (also false). In the article on her trial for perjury in the _Medicine Hat Times_ , the reporter wrote that she claimed her husband had \"been under the sod since May 1, 1906... What must have been her joy then to see her deceased husband in the courtroom on Saturday afternoon. In fact she seemed so overwhelmed by emotion that she thought it better to make no defence at all to the charge of perjury.\" Husband William H. Edmundson was brought all the way from Buffalo, New York, to testify that Elizabeth had left him three years earlier with another man who had been boarding with them, taking their son with her. Mr. Edmundson followed his wife to Medicine Hat some time later, \"hearing that the son was being badly treated,\" and placed the son with his sister in Buffalo. Because the husband had been in Medicine Hat in 1907 to collect his son, the police knew that Mrs. Edmundson was not a widow as she claimed. While Elizabeth did not testify, there were hints in the questions of her lawyer that her husband had threatened her with a knife and was a drinker. In giving his decision the magistrate said that he was sorry that the accused had not been examined, as he believed that she had \"acted on the instigation of some man... who ought certainly to be brought to justice.\" While the punishment for perjury was two years in the penitentiary, magistrate O.W. Kealy stated that there were several circumstances that made this case \"peculiar.\" The first was that \"he was well aware of the fact that laxity as to the truth in obtaining homesteads was too prevalent altogether. Mrs. Edmundson happened to be the one caught.\" He was also \"sorry that she was a woman, because otherwise he would have imposed the full sentence. He said her offence had been deliberate and was without excuse. He hoped that it would be a warning to others who might be tempted to try similar methods.\" Elizabeth Edmundson was sentenced to nine months of imprisonment in the Calgary jail.\n\nDelia Bell presented herself as a widow when she first filed on a homestead at Grandview, Manitoba, in 1903. She wrote in June of that year to the land agent that \"I am a widow and have never had a homestead. I have 7 children.\" In the 1881 census, Delia was a Mrs. Wheeler, aged twenty-six, living with her farmer husband George Wheeler and four children in the Lisgar district of Manitoba. In the 1891 census, she was Mrs. Bell, living with her husband W.G. Bell (ten years younger than her), born in Scotland, who was a \"stable man\"; she had five children with the last names Wheeler and two younger children with the last name Bell. In the 1901 census, she was a \"widow\" operating a boarding house, with three of her children still with her; their last names were first recorded as \"Bell\" but then were crossed out and the last name \"Whaler\" recorded. In 1906 she was back with William Bell and no longer a widow; they were living on a farm in Grandview. In 1911 she was still living with William Bell and two children. These changing identifiers were to cause her problems as a homesteader.\n\nBell wanted to file on land abandoned by her son who had left for the United States. She was granted entry in 1903, but very soon there were reports from nearby settlers that she was not living on her land and making no improvements. The land agent at Dauphin supported Bell, writing in 1904 that he knew her well as she had \"lived in this town for some time where she kept boarders, she is a hard working and industrious woman, who advanced considerable money to her son T.H. Wheeler, who was the former holder of this land and is reported to have disposed of the cattle and equipment, purchased with her money, and left the country. I would ask the Commissioner to grant any protection possible in this case.\" Cancellation proceedings were abandoned, but there was persistent interest in the land from others who continued to insist that she did not live on or improve her homestead.\n\nIn May 1909, however, Delia Bell still did not have patent to her land when the Dauphin land agent reported that although she had made entry as a widow, \"I am given to understand that she is not a widow.\" Months later, in February 1910, the homestead inspector reported that \"Mrs. Bell claims that she and her husband were parted for seven years; she worked and was supporting her family and not getting any money from her husband so she considered herself a widow. Her husband came back in 1907.\" That fall her homestead entry was cancelled. This required an order-in-council (signed by Prime Minister Laurier) stating that Delia Bell had represented herself as a widow when she entered on her land and that \"it has since been shown that her husband is alive, and it has been decided to cancel her entry, as she was not eligible to take up a homestead in her own name.\" It was also found that she had made improvements on the land to the value of six hundred dollars. The order-in-council recommended that she be permitted to purchase her quarter section at the rate of three dollars per acre. Bell never did come up with the funds to complete this purchase, although she (illegally) sold it in 1920 to a cattle dealer, despite being warned in 1916 that the land was not hers to sell.\n\nWhile a woman separated from her husband might be granted the right to a homestead, the entry could be cancelled if he materialized. This was the case for Margaret Little, of Roblin, Manitoba (originally from Fergus, Ontario), who had been permitted, after \"careful consideration\" by the Commissioner of Dominion Lands, to enter on a homestead in 1909 after she signed a statutory declaration that she had been deserted and that she had been the sole support of minor children for ten years. A few months after she filed on her homestead, however, questions were raised about her eligibility. In February 1910 her husband, Lemuel Little, filed on a homestead not far from hers and stated to the clerk at the land office that he would live with his wife while he proved up. Immediately the couple was suspected of collusion to obtain two homesteads. The homestead inspector was dispatched to report \"very carefully\" upon whether Mr. Little had in fact abandoned his wife. The inspector reported that he was a \"constant visitor,\" that there was a bed for him in the house, that he was a horse dentist who was away frequently because of his occupation, and that the neighbours knew nothing of family trouble.\n\nMargaret Little fought back in many letters, arguing that there was no collusion to obtain two homesteads, as she had known nothing of her husband's plans until the homestead inspector told her. She signed another statutory declaration, dated 7 June 1910, that she was the sole support of herself and family, that she had not lived \"as wife\" with her husband for over eight years, and he had not supported them for over twelve. She admitted he occasionally called at her house to see their sons but that they never had \"any business with each other.\" She further swore that \"the neighbours are well aware we are not living together and never will.\" A few weeks later a neighbour who coveted her land wrote the land office in Dauphin that she was not entitled, as Mr. Little was at home and able to work.\n\nIn early December 1910, Margaret Little was informed that her entry was to be cancelled because \"the return of your husband removes the reason by which you were granted a homestead. You have no claim whatever to this land which is being re-opened for entry.\" She continued her letters, writing on 7 December 1910 that \"I am only a woman but please give me a hearing.\" She asked why the land office did not cancel her husband's homestead entry instead, arguing that he would sell his land as soon as he got the patent while she would pass her land to her family after her death. She also announced that she would stay on her land until these false accounts that her husband supported her could be proven. She asked how the government could take from \"me what they allowed me to have to help support my family when my husband would not.\" Then she came up with a brilliant strategy: when her land was thrown open for entry at the land office in Dauphin on 13 December 1910, Margaret Little and her son were at the head of the line, and she entered on the same land in the name of her son Roscoe. Although her son was still only seventeen, the rules permitted her to enter her son on a homestead and reserve the land for him until he would be old enough the following year. Roscoe did eventually receive patent to this land, although it took until 1919 due to various bureaucratic hurdles. Margaret continued to argue with Department of the Interior authorities that she deserved to enter on a homestead, but was told that she did not qualify and that only a widow with a minor child or children dependent upon her for support was eligible. Her husband, Lemuel, proved up on his homestead, and her son Roscoe proved up on the land that she had homesteaded. Of the three Littles, Margaret was the only one never permitted a homestead in her own name.\n\nMargaret Little's quest for a homestead was admired in the _Minnedosa Tribune_. Under the headline \"An Enterprising Lady,\" the article described how she successfully retained \"the homestead and also the improvements which she has put upon the place, and to which all will admit she is justly entitled.\" The tenor and sincerity of her letters suggest that she was indeed the sole support of her family and that her husband, though an occasional visitor to his children, had deserted them. One document in the land file corroborates Margaret Little's claims: her cousin William Hughes, a Manitoba homesteader, wrote to the Department of the Interior in 1903 asking if Little could make a homestead entry, writing that \"she has had to support herself and five of a family for the last three years. Her husband has left her and the family to support themselves.\" Hughes, who died in 1905, left his land to Margaret Little. It is curious, however, that one of the witnesses to his will was Margaret's husband, Lemuel Little.\n\nClara Lynch (from Iowa) waged an epic battle to secure her Alberta homestead and to prove that she was \"worse than widowed\" after her husband deserted her. She faced difficulties because of her status as a deserted wife, and because although she claimed to have a son dependent upon her, he was nowhere to be seen. Yet Lynch remained determined, resolute, and tenacious. She wrote to the highest Ottawa officials, consulted a lawyer, and trudged through deep snow to get the signatures of neighbours on a petition supporting her right to homestead. She confronted overwhelming legal and other obstacles, including a neighbour who coveted her land. Her perseverance eventually paid off, but not until 1909, four years after her death. Officials had insisted that she could not be considered a head of household, since \"her husband is alive, and is liable to come back any day.\" In one of many eloquent letters pleading her case, Lynch asked how an official of the Department of the Interior could dare \"to assert under the sacred Motto on Canada's shield 'God and my Right,' that I am not the head of a family; if he only knew the man that was my husband, but is such no longer, he would know, that I was _forced_ to be the head of the family whether I would or no. I can point you to at least a dozen creatures of the species, male bipeds, in my own immediate neighborhood, who have homestead entry, who are not, and in all human probability, never will be heads of families; I think his lexicon must be an obsolete one.\"\n\nStill fighting her battle, Lynch died on 5 May 1905 in Edmonton, at age thirty-nine, of \"abcess and tuberculosis.\" Yet the battle for her land was not over; it continued for four years after her death. After a mountain of correspondence, in which officials disagreed about and debated the case, Lynch's estate was finally granted patent to her land in April 1909, but her estate had to pay for it! She never was granted the right to homestead. A sad irony is that if Lynch had remained in the United States or returned there, she would have had no trouble securing a homestead. As a deserted woman, she would have been considered a head of household regardless of whether she had children or not.\n\nSOUTH AFRICAN SCRIP WOMEN HOMESTEADERS\n\nWhether single, married, divorced, or widowed, women could obtain homestead land in Western Canada if they could afford to purchase South African scrip (SAS). These women belong in the chapter on homesteaders because they did not purchase land, they purchased scrip that permitted them to homestead 320 acres. They did not own the land after purchasing scrip; they had to comply with all the rules and regulations involved in proving up and were under the watchful eye of the land agents and inspectors.\n\nIn July 1900, Harold Lothrop Borden, a lieutenant in the Royal Canadian Dragoons serving in the South African War (1899\u20131902), was killed at Witpoort, South Africa. He was just twenty-four, and a promising medical student in his third year at McGill. He was also the only son of Canada's minister of the militia Sir Frederick William Borden. Under the Volunteer Bounty Act (VBA) of 1908, volunteers domiciled in Canada who had served in the South African war, deceased or living (7,300 Canadians), were offered money scrip (sixty dollars) or land scrip that permitted the recipient to enter on 320 acres (two adjoining quarter sections) of homestead land in Western Canada. Recipients of land scrip had to fulfill all of the regular homestead duties of cultivation and residence over three years and could then receive patent to the land. The recipient or purchaser of scrip had to commence residence within twelve months of entry being made. Borden's father was his legal representative, and like many recipients of SAS he opted to sell the scrip, likely through an agent, rather than spending three years fulfilling homestead duties. The purchaser of Harold Borden's scrip, in 1911, was Anna Utech, a married woman with three children, and she successfully proved up on her homestead in Saskatchewan in 1914, earning her patent or outright ownership. Without the option of SAS, Anna Utech would never have qualified for homestead land in Western Canada because she was a married woman. Utech was among about 540 women of all marital and non-marital statuses who took advantage of the rare opportunity offered by SAS to homestead land in Saskatchewan, and some purchased more than one SAS, becoming the owners of not just 320 but 640 acres. These women, and the press attention some of them received, played a vital role in demonstrating that women were interested in obtaining homestead land and that they could successfully prove up on that land. They had to have some capital, as SAS sold for about $800, or more.\n\nThe VBA was passed after much discussion and debate in the House of Commons about the value of land grants to the military, but a majority of parliamentarians were eventually persuaded that the scheme could help to build a white, British, masculine West. The grant of land in return for military service was an ancient practice that was incorporated into Canada's Dominion Lands Act in several instances, including after the 1869\u201370 Red River Resistance and the 1885 North-West Rebellion. The idea was to encourage enlistment, reward service, and foster settlement of loyal, disciplined, men of British ancestry. SAS was intended to reward those who had served but also to attract the right kind of settler. As one member of Parliament stated, \"a young man who is sufficiently loyal to risk his life in South Africa is a pretty good kind of man to mix with certain elements that will go into that country.\" To ensure actual settlement and cultivation the homestead provisions of the Dominion Lands Act had to be complied with. Grantees had to live on the land for six months every year for three years, build a house and not a temporary shack, and cultivate the land. The idea of being able to appoint a substitute, if the grantee decided he did not want to homestead, was a point of considerable debate. The main concern was land speculation\u2014that SAS would be \"sold for a song to the scrip shark who has been the curse of the west.\" But substitutes were ultimately permitted and SAS could be sold to anyone, including women, regardless of marital status, in a twist that parliamentarians never anticipated.\n\nThe VBA included one category of women. The definition of volunteers was for the first time extended to female nurses who had served in South Africa, becoming the first exception to the general rule in Canada that women (except sole heads of households with dependent children) were ineligible for homestead entry. There were only twelve nurses from Canada in South Africa, however\u2014not enough to concern Canadian parliamentarians or to constitute a threat to the masculine West. One nurse who sold her scrip was Deborah Jane Hurcomb, who was with the Second Canadian contingent and who died in 1907. Her scrip was purchased by Mary Matalski of Verndale, Saskatchewan, a married mother of sixteen who successfully proved up in 1914.\n\n_Figure 17._ Homesteaders near Square Deal, Alberta, c. 1912. Both women acquired their homesteads through purchasing South African scrip. Johanna Solberg (right) was a stenographer in Bassano, Alberta, and Sebina Jacobsen a dressmaker, also in Bassano, when they filed on their homesteads of 320 acres each. Both were single. Purchasing South African scrip was virtually the only way a single woman could acquire homestead land in Western Canada. Glenbow Archives, NA-206-27.\n\nThere was also a high degree of interest in obtaining SAS among Canadian women teachers who volunteered in South Africa, but they were denied this reward. At least forty women teachers from Canada taught in the Boer concentration camps. An appeal was made in the House of Commons to have them included in the land grant. Teacher volunteer Winifred Johnston Plowden, whose letter of appeal was read in the House, argued, among other things, that for their loyalty to the British Empire and for all of the hardships they endured, teachers should have land rights over male volunteers who saw no action, or over foreign widows who could claim homesteads the teachers were denied. \"From my point of view many of the girls that went out suffered much more hardship than the last military contingent, who only landed at Cape Town and never went up country at all, and got a good grant for that.\" The teachers were as deserving of government recognition as \"some United States or Galician widows who may settle on western lands.\" \"I hope,\" Plowden wrote, \"that the government which has treated outsiders with the greatest generosity will see its way clear to a recognition of the first forty Canadian women who went half way round the world to impress upon a country shortly after its second birth into the British Empire, something of the acknowledged excellence of the Canadian public school system.\" The reward of SAS was not however extended to the teachers.\n\nYet teachers were among the women who purchased SAS and homesteaded land in Western Canada. The most celebrated of these was Mildred Williams, who made headlines across North America in May 1910 for her stamina and determination. She was from Lintonville, Minnesota, and had arrived in Canada eight months earlier. Williams was the sole supporter of her widowed mother, and perhaps she had hoped to qualify for a free homestead, but the rules did not permit her because she had no minor child or children dependent upon her for support. Single, in her early twenties, and working as a teacher in Saskatoon, Williams waited for twelve days and nights at the top of the stairs outside of the land office in Saskatoon in order to be able to file on a half section (320 acres) of land near Kindersley valued at eighteen to twenty dollars per acre. Williams purchased the SAS of Frederick Charles Snell, a storekeeper at Pilgrim's Rest, Transvaal, but previously of the Lord Strathcona Horse. He was a North-West Mounted Policeman who had risen in the ranks and served in the Yukon, where he got a grant of land for his service. He was just the sort the legislators hoped to entice to the West, but he decided to stay in South Africa, living out his days there. Instead, Mildred Williams got his 320 acres.\n\nWilliams carefully planned her vigil. She employed a woman to bring her meals and soft drinks, and another as a \"kind of scout and messenger.\" She sat in a reclining chair and made a kind of tent over this in the nights. She put up with a great deal of inconvenience during the twelve-day vigil. On her second day, she was challenged by a man who wanted the same property. He allegedly tried to push her off her chair at one point, but Williams's numerous supporters came to her aid, shoving him down the stairs, and he gave up. She successfully filed on the property, and when she emerged from the land office a large number of friends greeted her, cheering and applauding. Williams successfully proved up on this land and became the owner of 320 acres of valuable land. She may have later sold this land, for in 1917 the _Star Phoenix_ reported that she had resigned her position as teacher and gone to the Pacific coast.\n\nIn May 1910, columnists praised Williams's \"energy, determination and patience.\" Writing in the _Edmonton Bulletin_ (ironically, the paper owned by Minister of the Interior Frank Oliver, who opposed homestead rights for most women), Gertrude Seton Thompson predicted that \"in three years she will have property worth at the least $10,000.00, and this sum, properly invested, should give her an income of $1,000.00 per year\u2014Bravo!\"\n\nMildred Williams was far from alone. Of the 4,730 SAS entries in the Saskatchewan Archives Board (SAB) database, approximately 11 percent are women. Many of the files contain detailed and rich correspondence, documenting the challenges and difficulties the SAS women faced regardless of their marital status. Among the single women, some had the assistance of brothers or fathers, and the purchase of SAS involved family strategies to expand farms, while others appear to have been totally on their own. Marie Westphal, from Milwaukee, purchased SAS at Kindersley in 1910. She was single and had arrived in the Eatonia area of Saskatchewan to keep house for her homesteading brother Herman. She filed on land previously abandoned by another brother who was unable to take up residence. Marie was single when she proved up, but later married and settled in the district. Together the Westphals amassed considerable acreage in the Kindersley area, as their father also homesteaded nearby at age seventy-one.\n\nMarried women could add to family land holdings through purchasing SAS. In the Buffalo Lakes district of Peace River, Alberta, Emma Bradford of Manitoba was the largest single landholder, having proved up on a full section of land after purchasing two SASs. She was married, and along with her husband Andrew \"had the largest family holding with seven quarters compiled from three scrips and a homestead, all of which were proven up.\"\n\nLottie Kennedy of Winnipeg clearly had little idea of what she was signing up for when her fianc\u00e9 Edward Baird (a railway mail clerk also of Winnipeg) entered on a homestead in the Maple Creek district of Saskatchewan, and she entered on adjoining land in 1913 through SAS that had been purchased for her by her father as a wedding present. While Kennedy and Baird may have been planning to increase their land base through SAS, neither seemed to be aware that Kennedy would be required to perform actual residence on the land. The couple married and continued to live in Winnipeg. In 1915, Baird's uncle and a member of Parliament for Ontario, E. Guss Porter, wrote Minister of the Interior W.J. Roche to ask if breaking land on Mrs. Baird's homestead could \"count as a year's duty without actually going out there to live. They are living in Winnipeg now where he holds a position in the mail service and he does not like to give up his position and go out there to live on the land if it can be avoided.\" Porter was informed that nothing could be done, that Mrs. Baird had to perform her residence duties, and that \"it is only in the case of deceased, insane or physically incapacitated homesteaders that residence is dispensed with.\" The Bairds began residence duties in 1915, and Lottie Baird was granted her patent in 1918.\n\nOther single women SAS homesteaders were without a family network or strategy. Originally from Norway, Carrie Sveum was a cook for threshers at Olson, North Dakota, and then a cook at a hotel in Swift Current in 1910, when at age thirty-eight she purchased SAS, filing on land at Waldville, Saskatchewan, and successfully proving up in 1914. In 1914 she \"travelled to Norway and brought back a husband a Mr. Sagen. Together she and her new husband ran a successful restaurant and \"stopping place.\" When her husband died, she sold her land and moved back to Norway.\n\nThe single women who were SAS homesteaders ranged in age, but most were in their thirties or forties, and some were older. Sarah Birtles of Alexander, Manitoba, was sixty-two when in 1913 she applied for patent on her SAS at Colonsay, Saskatchewan. From Yorkshire, Birtles was a nurse who had immigrated with her family to Manitoba in the 1880s. She had some difficulty fulfilling her residency requirement but not because of her age\u2014rather, it was because when she was absent she was proving up on another SAS near Provost, Alberta, securing 640 acres for herself in two provinces. She was short in the residency requirement on her Saskatchewan claim by five days, so that the case was examined by a homestead inspector, who wrote, \"The applicant is a spinster 62 years of age having nearly completed her residence duties for this Scrip and at the same time having performed residence duties on another Scrip near Provost Alta. The difficulty appears to be loss of time consumed in moving from one place to the other.\" The shortages were overlooked, although officials were annoyed, because \"it is hardly the intention to allow the same person to locate more than once, although there is no legal objection of course to one person locating as many Volunteer Bounty Warrants as he can provided the ordinary duties can be completed.\" The same official wrote, \"I suppose we should be very careful about establishing a precedent in a case of this sort.\"\n\nThere were other older women who acquired land through SAS. Eliza Birmingham, from Meaford, Ontario, was sixty years old in 1910 (although she may have been trimming a few years) when she received patent to her homestead in the Battleford district of Saskatchewan. Her family then consisted of herself and two grandchildren. A year later she purchased the SAS of Alfred Arthur Lyndon of Toronto, and in 1914 (when she stated she was sixty-seven) successfully proved up on land in the vicinity of her first homestead.\n\nThere is no doubt that unlike Sarah Birtles, some single women found it challenging to prove up on one SAS. Like Lottie (Kennedy) Baird, Sophia Brauer, age thirty-four, seemed unaware when she purchased her scrip that she would be required to live on the land and perform homestead duties. Brauer was from the United States and was working as a dressmaker in Swift Current when she purchased SAS and filed on land at Lemsford in 1911. By early October of that year she was wondering if she could take a leave of absence until May, writing to the land office that \"I want to stay longer if the weather allows it. But I do not see how I could stay all winter as it is so far from town and such a new country with few conveniences, cold winters and blizzards. I am afraid of perishing out here.\" She offered to live in Swift Current for the winters. She was told that she had to meet the residency requirements and live for six months of each year on her land except in the case of \"serious accident, illness or calamity to the entrant, or to the wife or child of an entrant.\" Brauer did successfully meet her residency obligations and had sixty acres under cultivation in 1914 when she proved up.\n\nDespite the fact that some of the married women SAS homesteaders had husbands and older children to assist them in proving up, their lives were often more complicated than those of single women SAS homesteaders. Many married women could not (officially) live in their homes with their husbands for six months of each year for three years, because they had to live on their own land to perform their residence duties. Matters become even more complicated when young children were involved. Nellie Jane Sorsdahl filed on land at Macoun, Saskatchewan, in 1910 but did not prove up until 1917. By that time she was the mother of eleven children. She was threatened with cancellation proceedings on several occasions. In her correspondence with the Department of the Interior, Sorsdahl never mentioned the continual arrival of her children as the reason why she had difficulty meeting her residency requirements. In 1911, for example, she asked land officials if she could live with her husband on his SAS and perform her residence duties there, as her \"health has been failing.\" The reply was that \"it is regretted you cannot be permitted to live with your husband and thus satisfy the requirements of the Act as to residence... the regulations require that you shall live upon your own half section for at least six months in each of three years.\"\n\nJennie Cochrane, formerly Doyle, of San Francisco (but born in Canada), was the legal representative of her deceased son, George Doyle, a volunteer in the South African War who was granted SAS. Cochrane is the only woman so far located who took up land as a mother of a deceased volunteer. She was fifty years old in 1913 when granted patent to her land at Biggar, Saskatchewan, although the process was not without complications. Early in 1913 she wrote to the Department of the Interior from San Francisco (spelling mistakes in the original):\n\nI don more than was required of me in Building and also in Breaking paid for every thing out of the way taxes included I wish I never saw the old land at all, for I suffered hardship and privitations enough to kill a dog a yellow dog. of course you are aware that I came by that Government Grant through the Death of my only Son. who was out in South Africa. 23 Rigement Mounted Cavlery. Now I do hope thair will be no more draw backs with regard to getting my patent. I am pretty sick of this and some times I woner if the dear Honourable Government is not trying to grind our lives out. as you know I don everything to the best of my knolledge in getting things fixed properly before I left Biggar in a Leagel way and con do no more.\n\nJane Gentles was a teacher from England who was married with three sons in 1908 when she purchased SAS. She did not file on land until 1911, when she entered on 320 acres near Saskatoon that had been abandoned by one of her sons. In 1915 the government wanted to cancel her homestead entry, as she had not satisfied the inspector that the necessary homestead duties had been completed; she was ten weeks short of the time required. A neighbour had his eye on her land and had brought out the homestead inspector. But Gentles was teaching in Islington in London, England, at this time. All three of her sons served overseas in the First World War. Her husband stayed behind in Saskatchewan, taking care of her 320-acre homestead as well as one of their sons. Gentles was told by land officials, however, that she needed to be back in Saskatchewan completing her residency requirement. She wrote very vigorously in her own defence, asking that her war work count as residence duties on her land. Gentles was teaching at Drayton Park Boys School, taking the place of a male teacher who had enlisted, and she was in charge of fifty-one boys. \"And in that way,\" she declared, \"I am serving my country to the best of my ability.\" She added as a postscript: \"By Royal Proclamation in England any woman who undertakes work and by so doing liberates a man for the service of war is considered to be serving her country as truly as those serving in the trenches. I have given two sons out of three and the 3rd son is anxious to join the colours too but as he is all I have to help me he must stay behind unless it is absolutely necessary then he will join too.\" Gentles was sent a form to fill out, and in it she stated that \"my time [residency on land] is not quite completed but I have given myself and my sons to my country's cause and we are all serving her here at very great sacrifice and ask the department to allow war work time to count as residence duties.\"\" id=\"endref-rd son is anxious to join the colours too but as he is all I have to help me he must stay behind unless it is absolutely necessary then he will join too.\" Gentles was sent a form to fill out, and in it she stated that \"my time [residency on land] is not quite completed but I have given myself and my sons to my country's cause and we are all serving her here at very great sacrifice and ask the department to allow war work time to count as residence duties.\"\">rd son is anxious to join the colours too but as he is all I have to help me he must stay behind unless it is absolutely necessary then he will join too.\" Gentles was sent a form to fill out, and in it she stated that \"my time [residency on land] is not quite completed but I have given myself and my sons to my country's cause and we are all serving her here at very great sacrifice and ask the department to allow war work time to count as residence duties.\"\n\nJane Gentles's land was protected from cancellation until 1 May 1916, but at that time she had still not returned to complete her residence duties. She wrote once again to officials of the Department of the Interior to say that she was she was planning to return in time for seeding, but that \"the danger from torpedoes was very great at that time and my boys advised me to stay.\" Two of her sons were at Ypres; her oldest son should never have been accepted for duty as his sight was only 25 percent normal; and \"these are all the children I have and I have given them up to fight the Germans.\" She concluded, \"I think I was entitled to ask you to give me those few weeks time in face of the great sacrifices I had made.\" Gentles was fifty years old in 1919 when her patent to her land was finally approved.\n\nOf the hundreds of women in Western Canada who acquired homesteads through purchasing South African scrip, few made the headlines, but those who did, such as Saskatoon teacher Mildred Williams, became important to the homesteads-for-women campaign that was gathering momentum just at that time. The SAS women homesteaders demonstrated that women, whether single, married, divorced, or widowed, and regardless of whether they had children, were interested in obtaining homestead land and could successfully prove up on that land. The fact that women had to _purchase_ expensive scrip in order to homestead land also highlighted the discrimination at the foundation of the Dominion lands legislation. As columnist Gertrude Seton Thompson wrote in the _Edmonton Bulletin_ after describing the vigil of Mildred Williams: \"I hope the Dominion government will make a note of this, and give consideration to the question of women being allowed to homestead. That only by buying scrip can they homestead seems unfair. If allowed to take up land at all it should be on the same terms as men\u2014not under almost prohibitive conditions.\"\n\nHOMESTEADS FOR WOMEN IN THE U.S. WEST\n\nMigrant women could obtain homesteads by heading to the U.S. West, and many thousands of solo women did so. It is important to understand this context and opportunity in order to appreciate the dimensions of the homesteads-for-women debates, to be covered in Chapter 6. Both supporters and critics of the homesteads-for-women movement drew on the example of the \"entrywomen\" of the American West. It is also vital to understand the dramatic differences between the United States and Canada when it came to the gender of homesteading.\n\nThe U.S. rules permitted a much wider diversity of women to acquire homestead land, and overall there was a greater flexibility in how officials of land offices interpreted the regulations, and more acceptance of and assistance to women who would be stigmatized in Canada, such as unwed mothers and divorced women. Widows applying for homesteads did not need to have minor children dependent on them for support as they did in Canada. Single women with adopted children were eligible. Single, unwed mothers were permitted to make entry, even if they were not yet twenty-one years of age. Mormon women who were plural wives were permitted to enter on homesteads because their marriages were not recognized as legal. Deserted and divorced women could homestead without having to have minor children dependent on them. In the United States an abandoned wife or \"one whose husband is a confirmed drunkard\" was considered the head of a family. A married woman could make homestead entry if she had been \"actually deserted\" by her husband, or if her husband was in the penitentiary or \"incapacitated by disease or otherwise from earning a support for his family and the wife is really the head and main support of the family.\" Most of this was clearly itemized in U.S. legislation and available in the published guides to prospective homesteaders.\n\nBefore 1900 women homesteaders constituted less than 10 percent of all entries in the U.S. West, but their numbers grew dramatically thereafter. Numbers vary; one study of forty-three townships in North Dakota reveals that proportion of women homesteaders varied from 1 percent to 22 percent, with an average of 10 percent. In two counties in Colorado, women entrants were at 11 percent before 1900 while after that date, nearly 18 percent. In the peak years of the homestead rush in Cochise County, Arizona, from 1900 to 1918, 14 to 21 percent of the homesteaders were women. The majority of women homesteaders were single: in North Dakota, for example, 83 percent were single, 15 percent were widows, and 1 percent were divorced. Women homesteaders were as successful at proving up as their male counterparts. Felice Cohn, whose work as a federal assistant superintendent of public sales of Indian lands took her to the land offices of Montana, wrote in 1919 that \"the woman homesteader always lives up to the land regulations of the government. The homestead inspectors seldom have occasion to make an adverse report on a woman who is proving up on her land. Every regulation is always faithfully complied with.\"\n\nRecent studies that focus on counties in the U.S. West demonstrate that women homesteaders were everywhere. In the Yellowstone River Valley between 1909 and 1934, the federal government issued 4,066 land patents in Yellowstone County, and of these 18 percent, or 746, were issued to women who together claimed over 150,000 acres. In Valley County, Montana, which borders on Saskatchewan, there was a similar percentage of women homesteaders. There were over 900 women homesteaders who proved up on homesteads in Valley County. There were likely many more, as the names were taken from 104 plats of townships and ranges, and nearly half of these are missing. Women homesteaders comprised approximately 17 percent, or one-sixth, of the homesteaders in that county.\n\nLike male homesteaders, women often homesteaded in clusters\u2014sisters, cousins, and friends filed together and near each other. Three Chmelik sisters\u2014Anna, Mary, and Emily\u2014from Minnesota, took up adjoining homesteads in Chouteau County, Montana, in 1910. Anna was a teacher and Mary a seamstress. Their brother helped them build their cabins and break sod for their first crops. In 1912 Lena J. Michels and her two cousins, Mary Lambert and Frances Lambert, left South Dakota and filed on adjoining homesteads near Stanford, Montana, by the Genou post office. One settlement in the Hawarden district was called \"Ladyville\" because of its preponderance of women homesteaders. Daughters arrived with mothers, and all took out homesteads. Homesteaders sometimes built cabins close together but on their own claims, divided by the survey line. For example, Sophia Jefferson and Mildred Hunt filed on adjoining homesteads on the North Bench near Fort Benton in 1910, and their cabins were known in the area as \"twin shacks.\" Often filing on land was part of a family strategy. Daughters could help expand the family land base by taking out homesteads, filing alongside brothers, sisters, fathers, uncles, aunts, or other relatives. Ann Yoctorowic Obie filed on land near the homesteads of her father, sister, and three brothers near Joplin in Liberty County.\n\n_Figure 18._ Englishwoman, teacher, and mother Jane Gentles purchased South African scrip and filed on 320 acres of land near Saskatoon, Saskatchewan, in 1911. In 1915, when Gentles was in London teaching so that a male teacher could enlist, Canadian land officials wanted to cancel her entry. Gentles fought back, arguing that she was \"serving her country as truly as those serving in the trenches.\" She included this photograph of herself and two sons who were at the front. Officials relented and Gentles was granted a patent to her land in 1919. Saskatchewan Archives Board, homestead file 2092263.\n\n_Figure 19._ Eva Iddings of Indiana in front of her claim shack near Fort Benton, Montana. Eva filed on her homestead in 1910 and proved up in 1912. Three brothers and two aunts also filed on homesteads. Solo women homesteaders, rare in Western Canada, were abundant in the American West. Barrows Collection, Overholser Historical Research Center, Fort Benton, Montana, 1910, BC11, 244.\n\n_Figure 20._ Canadian women, ineligible to file on homesteads on the Canadian prairies, homesteaded in the American West. Sisters from Ontario Caroline (Carrie) Louise MacGregor and Mary Frances MacGregor homesteaded in Sheridan County, Montana. Carrie earned her patent to just over 156 acres in 1912, and Mary became the owner of 312 acres in 1914. According to an October 1909 description in the local paper, \"The Macgregor sisters have a large ranch about five miles down the valley from Redstone.... These girls have a fine dwelling and a good barn and granary, a great deal of the carpenter work being done by themselves. They have a fine bunch of horses, cows, pigs and chickens. They are both college graduates and musicians. It was a great pleasure to visit such well informed people so far out on the frontier.\" These photographs show the nature and range of their work on their land. Courtesy Judy Archer (Carrie's granddaughter), Orillia, Ontario.\n\nThe opportunity to cross the border and homestead in the United States was well known to women living in Canada, as discussion of the homesteads-for-women campaign will show. Caroline (Carrie) Louise MacGregor and her sister Mary Frances MacGregor, from Ontario, homesteaded in Sheridan County in Montana. Carrie earned her patent to 156 acres in 1912, and Mary earned her patent to 312 acres in 1914. They pooled resources and established a ranch together, which was described in the 1 October 1909 newspaper _The Searchlight_ (Culbertson, Montana): \"The Macgregor sisters have a large ranch about five miles down the valley from Redstone... These girls have a fine dwelling and a good barn and granary, a great deal of the carpenter work being done by themselves. They have a fine bunch of horses, cows, pigs and chickens. They are both college graduates and musicians. It was a great pleasure to visit such well informed people so far out on the frontier.\" Carrie was a graduate of the University of Toronto. She married Rev. William Archer in 1912 and moved to Quebec. Mary married a fellow homesteader Hans Madsen and was the mother of two young daughters when she died in the flu epidemic of 1919. According to her granddaughter Judy Archer, Carrie settled in Montana because the Canadian government would not grant homesteads to single women. Judy Archer writes that \"Carrie rode a horse bare back, with a long skirt on. She kept a pistol because the local Indians would ride past the knoll where the house was.\" As the photographs indicate, the sisters did the work required themselves, in long dresses.\n\nIn 1910 Alberta teacher Etta Smalley crossed the border to take up a homestead. Her movements back and forth across the forty-ninth parallel indicate how fluid the border then was. Smalley was originally from Ohio and settled in Alberta in 1904 with her family when her father filed on a homestead at Soda Lake. She completed her Alberta departmental exams in 1906 and attended the Provincial Normal School at Calgary. In 1910 she was teaching at the Bolan Marea School in the Soda Lake district of Alberta, where her students were Ukrainian and Romanian. Smalley boarded with the Woods family, where there were two daughters, and when Mr. Woods and one of the daughters filed on homesteads in Hill County, Montana, Etta decided she would join them. She claimed 320 acres, as she was able to take advantage of the Enlarged Homestead Act of 1909, and proved up while continuing to teach, at first in Alberta and then at Inverness, Montana. She earned her patent to her land in 1914 and that same year married a neighbouring homesteader, Will Bangs. They had four children. They lived at first on Will's homestead and persisted through drought, grasshoppers, and war, even as Inverness and nearby Joplin were \"all but abandoned.\" Will Bangs lost his homestead to the banks in 1926, but Etta retained hers. The family moved into her original homestead shack, and as described in her memoir, they bought a larger house in 1943 and had it moved to her land. The Bangs were still living on her homestead in 1954 when they retired and moved to Havre. Etta Bangs died in 1973 at the age of eighty-seven. In 1980 her homestead was turned over to her grandson Tom.\n\nBritish women also went to the U.S. West to obtain homesteads, ignoring calls to do their duty to the Empire and settle under the British flag. An example is Jessie de Prado MacMillan from Scotland who acquired 540 acres in New Mexico, and she was not alone; other Scottish women homesteaded nearby, one of whom served as her inspiration in leading her to homestead on Agua Chiquita Creek.\n\nWhile British women such as MacMillan opted to go to the American West, where homestead land could be obtained by a single female, a great number and variety of women overcame the considerable challenges and obstacles to obtaining homestead land in the Canadian West. Their numbers are difficult to ascertain because of the scattered and fragmentary records they left, but the evidence indicates that women were determined to acquire land and were willing to go to extraordinary lengths to do so. For its part, the Canadian government went to extraordinary lengths to ensure that women had very limited access to land, circumscribing the eligible categories of women and scrutinizing and rejecting their applications.\n\nThis scrutiny was intense. A weary and jaded Department of the Interior law clerk, T.G. Rothwell, expressed exasperation in 1914 correspondence that his job allowed no common sense leniency or discretion in interpreting the exact wording of the Dominion Lands Act. Rothwell was dealing with the case of Mary Briggs, a widow of Wood Mountain, and her right to a pre-emption or purchased homestead. She had obtained a homestead through the death of a son, and she was his legal representative. Hers was a complex and unique case in which officials were reluctant to depart one inch from the legislation because that might set a precedent, and Briggs was not strictly entitled to a homestead, although clearly a bona fide settler. Reviewing the case, Rothwell expressed his dismay with the intransigent bureaucrats who were so reluctant to call on the discretionary powers of the minister. He wrote that he himself had \"followed a practice that has been incorrectly followed ever since I have been an officer of this Department, over thirty years, a practice to which so many other members of its staff, some of them most capable and hard working officials, are glued\u2014soldered\u2014so closely, that it is not possible to detach them from it. That practice is to construe the provisions of the Dominion Lands Act literally\u2014to give the settler his pound of flesh only, and oftentimes not quite that.\" Bureaucrats did not care, Rothwell thought, about the central purpose of the act, which was to place agricultural settlers on the land and to afford the subject benefits and privileges. They feared \"leaving the well beaten track and establishing a precedent that may bring responsibility, as much as travellers in South Africa fear an approaching South African lion.\" In an earlier memo he had himself recommended that Mrs. Briggs be turned down in her request, but his assistant, a \"Miss Barber,\" had saved him from \"doing a great injustice to Mrs. Briggs.\" Rothwell felt it was ridiculous to be concerned about setting a precedent. He believed that another case such as hers would arise \"not in a hundred years, and so the granting of a purchased homestead or of a pre-emption to Mrs. Briggs will not form the dangerous precedent I have been warned it is certain to establish if this privilege is given to her.\"\n\nMigrant women faced vicissitudes, intense scrutiny, and hardships, but they did succeed in acquiring homestead land on the prairies. They enjoyed homestead privileges denied to Indigenous women and men, and participated in land acquisition that dispossessed Indigenous people. But none of these women homesteaders shared in the full range of privileges offered to male homesteaders. Reflecting the larger settlement patterns of the West, women homesteaders were diverse; from the earliest arrivals to the late nineteenth century they were British and British-Ontarian, and after 1900 they came from a variety of European nations and the United States. This diversity would be seized upon and criticized by advocates of homesteads for British-born women, who concluded that the strongest rationale for including British women in the homestead privilege was that it would help to exclude \"foreigners\" and assist in crafting a British West.\nCHAPTER FOUR\n\nWOMEN WHO BOUGHT LAND\n\nTHE \"BACHELOR GIRL\" SETTLER, \"JACK\" MAY, AND OTHER CELEBRITY FARMERS AND RANCHERS\n\nWhile migrant women who wished to homestead faced many restrictions, they were free to purchase land in Western Canada if they had the money. They could be single, married, separated, or divorced, young or old, with children or on their own, or in partnership with a female companion. Questions were not asked about their marital or parental status if they had the funds to buy land. As they were not homesteaders, they did not come under the intense oversight of the land office and the homestead inspectors who insisted they be widows with children. Yet women who bought land were still scrutinized, particularly in the press, because they were rare, and they were often cast as aberrant, abnormal, or eccentric, although some of the coverage was celebratory, hoping to widen and sanction such vocational opportunities. This chapter features Isobel \"Jack\" May, an English farmer who settled (briefly) in Alberta in 1911. She garnered particular attention throughout the British Empire and in the United States because she wore men's clothing and because she most clearly challenged the accepted norms of femininity and the spotlight on the white male pioneer figure. While May was English, this chapter does not focus exclusively on British women, since they were not alone in purchasing land. Purchasers of land, however, were less diverse than women homesteaders because they had to have capital.\n\nINDIAN RESERVE LAND AND M\u00c9TIS SCRIP\n\nLand that was for sale on the prairies included large areas that First Nations were induced to \"surrender,\" severely reducing the size of their reserves. In 1909, for example, a controversial sale of land on the Piikani (Peigan) reserve took place in southern Alberta. Although the majority of male band members (the eligible voters) had opposed the surrender of thirty-six sections, or 23,500 of their 116,000 acres of reserve land, the Department of Indian Affairs declared (fraudulently) that a fair vote was taken. This was part of a pattern of dispossession and diminishment of reserve land throughout prairie Canada. The Piikani applied for an injunction against the advertised sale of their land by public auction at Pincher Creek in November 1909, but this request was denied and the sale took place.\n\nTwo quarter sections were purchased by Jean Laidlaw of Ontario and her female partner. Laidlaw was originally from England and was working in Ontario as a kindergarten supervisor when she purchased this land. A 1920 article on Laidlaw is typical of the sort of scrutiny the reasonably rare woman rancher or farmer was placed under. In the Toronto _Globe and Mail_ under the headline \"Woman Rancher Tells of Life: Miss Jean Laidlaw Runs 320 Acres near Pincher Creek, Alberta: Shows Great Pluck,\" readers learned that together with a nephew, Laidlaw raised cattle, horses, pigs, and poultry on her land. She was described as \"nothing if not feminine. Petite, gentle-voiced, and with dimples that look as if the wearer must have been play-acting when the camera snapped her, arrayed in a pair of overalls, struggling with one or other of the 'chores' that punctuate farm life.\" Her crop had failed in 1919, but she still had \"hope and grit in her heart, ready to take her chances with next summer's weather.\" The article also noted that Laidlaw's land was on the Piikani reserve, and she had \"many amusing stories to tell of farm hands drawn from this tribe,\" including one \"who wound a pink ribbon around his Stetson, \"this gay garniture forming the frame of a picture of his girl, which adorned as a buckle might, the upturned brim of his headgear.\" The message was that both Laidlaw and her hired Indigenous helpers were odd and eccentric presences on an Alberta ranch.\n\nWomen purchased Indigenous reserve land after it was \"surrendered\" for sale for the purpose of speculation. In 1891 the Passpasschase reserve near Edmonton was sold at auction, and purchasers included Nancy Miquelon of Calgary and Belle Thomson of Quebec. In 1902, when the Enoch\/Stony Plain reserve was sold, Ellen Carruthers, the wife of the Indian agency clerk, acquired one quarter section. Some of the women purchasers may have been \"fronts\" for insiders who wanted to try to cover their tracks. For example, in 1903 Maria Allison of Ottawa bought land surrendered on the Michel reserve in Alberta, paying much less than its value. According to historian Peggy Martin-McGuire, Allison was \"guided in these purchases by Herbert N. Awrey, a clerk in the Department of Indian Affairs for whom she worked as a janitor. Her bids had been forwarded in a departmental envelope, and included clippings from typed copies of the surveyor's reports.\" At an auction of reserve land in the Battleford agency in 1905, M.J. Day, the wife of the Indian agent, bought two quarter sections. The auctioneer's wife also bought land. In 1907 Alice Tye, secretary to the Indian agent, bought land surrendered on the Cowessess reserve in Saskatchewan.\n\nMigrant women also acquired land on the prairies through purchasing M\u00e9tis scrip. As described in Chapter 2, the original M\u00e9tis recipient of land scrip was required to sign a form that identified the section of land on which he or she desired to locate their scrip. The land was then assigned to the purchaser of the scrip, and the patent issued in his or her name. Susan Jones Willoughby, the wife of prominent Moose Jaw barrister and senator W.B. Willoughby, K.C., acquired a lot of land in this way. She died in 1907, and when her husband died in 1932 it was noted that he \"was a heavy landholder in southern Saskatchewan.\" In 1900, for example, Mrs. Willoughby received patent to 320 acres through \"four assignments from Peter Dumont, Francois Gosselin, Emmanuel Gosselin and Norbert McGillis.\" There are many other examples, including Matilda Bucknam (mentioned in Chapter 3). She was permitted to \"scrip\" eighty acres of her quarter section and to purchase the rest. Her Edmonton lawyers wrote to Minister of the Interior Oliver, asking that if permission was granted for her to do this, \"we will be notified in order that we may hunt up the half-breed for whose scrip Miss Buckman has paid, in order to complete the transaction.\" Sarah J. Milligan acquired land in the Fort Qu'Appelle region by purchasing the scrip for 240 acres of Samuel George McNab of the Touchwood Hills.\n\nAlberta teacher Victoria Lepage used a variety of tactics including the purchase of M\u00e9tis scrip to acquire land near Lamoureux. In 1895 she bought a military bounty scrip and located a nephew on a half section of land, assigning him the homestead duties, although he soon abandoned the tasks. She planned to pay cash for eighty acres and \"apply a Half-breed land scrip upon 240 acres of the land in question.\" Lepage purchased the M\u00e9tis scrip, but for a variety of reasons she was not successful in this complicated venture, and her claim was cancelled. Among the causes was a neighbour (and likely a relative) Charles Lepage, who wanted her land for his son and who complained that no improvements had been made and believed that a single woman teacher was not a suitable owner of land. He wrote the land office that \"there are lots of hands who would be too glad to improve [this land] and put them in a shape [ _sic_ ] so that they would be a benefit to the country. The lady I refer to is a school teacher earning $600 a year, and a sure thing she does not need any land to speculate on.\" The Lepages were originally from Rimouski, Quebec. They came in a large family group to Lamoureux and amassed many sections of land in the district. Victoria Lepage, the youngest of thirteen children, was a celebrated pioneer teacher of Lamoureux but never able to acquire land of her own.\n\nBRITISH WOMEN PURCHASERS OF LAND\n\nWomen who could afford to purchase land could be single, married, separated, divorced, or widowed in contrast to homesteading women who had to be widows and mothers. There were no homestead inspectors reporting on whether they conformed to these categories. Local histories provide brief glimpses of some of the women who purchased land. In 1880, Fanny McClure became one of the earliest settlers in the Rapid City district of Manitoba. According to the local history, \"she was a wealthy English lady and bought the NW1\/4 34-13-19 sight unseen.\" Her brother, Colonel Thomas Martin, bought an adjoining quarter section. The brother and sister built two houses, and she lived in one with her son and his wife, but she disappeared from the district in the early 1890s. In 1898 Margaret Hunter and three sons, from Callander, Scotland, came to the Tremaine district of Manitoba, where she bought a farm.\n\n\"Madame\" Simpson (first name not recorded) settled in Grosse-Isle, Manitoba, in 1889 with four sons and one daughter. Originally from Ireland, this Quaker family had allegedly \"made farming experiments in many lands... the south of Ireland, Belgium and France were all tried and found wanting. On this continent they looked through California before winding up their grand tour in this district where they became large land owners.\" The Simpsons accumulated \"some 1600 acres of land.\"\n\nIn 1903 Isabella Wilson, from Wigan in Lancashire, England, arrived in Saskatchewan with two brothers. The two men filed on their free homesteads. As Isabella was not eligible to homestead, she bought a quarter section from a departing farmer and named her farm Broadlands. Neighbours helped her to build her log cabin, and it was to this home in 1905 that she welcomed the remainder of her family members from England, including her mother.\n\nMarried women purchased land, and in some cases they were the farmers rather than their husbands, who might still be present but not active on the land. It is a mistake to always assume that the husband was the farmer. The married woman farmer and purchaser of land could, however, encounter legal puzzles and impediments. This was case with Maggie Lindsay, who farmed with her husband near Yorkton. He had bought land from funds that Maggie received from her family in Scotland. When he was unable to meet his payments she offered to make them if he would assign the land to her, and he did. Maggie made all subsequent payments with money from her relatives. The husband owned the adjoining quarter section. Under executions against her husband, the sheriff seized a quantity of wheat grown on her land. The question before the court in 1907 in _Lindsay v. Morrow_ was, who owned the grain grown on her land? The creditors claimed that the crops were Mr. Lindsay's, as he did the work and that if otherwise, the onus was on her to establish that the husband was her servant and the farming business really hers. Maggie Lindsay as claimant called her husband as the only witness, and they both testified that \"the farming operations were carried on by Mrs. Lindsay with the help of two hired men; that she hired the men and that they took their orders from her... The husband worked on her land part of the time, but in return received help on his quarter from her hired men.\" Evidence also showed that she had her own implements, and that she purchased her own seed grain from the government. When the seed arrived she personally took delivery of it. It was found that the proceeds from her farm could not be held liable for her husband's debts.\n\nThere are several prominent examples of married British women who were the farmers in the family. Annie E. Williams, from Beaufort, Wales, was an enterprising and accomplished farmer north of Gleichen, Alberta. She and her husband, Frederick C. Williams, first came to Alberta in 1908. She purchased over 500 acres from the Canadian Pacific Railway, establishing Primrose Farm. She became well-known as a \"lady farmer.\" Annie Williams experimented with different kinds of wheat and flax seed. In 1912 she stopped by the office of the local newspaper, the _Gleichen Call_ , to report on the excellent results of the Alberta Government Laboratory test of the \"Stanley\" wheat grown on her farm. In 1913 she had a bumper crop of flax that yielded nearly thirty bushels to the acre, and she had other crops that yielded well, including her oats and spring wheat. Across Alberta she was featured in headlines such as \"Mrs. A.E. Williams Receives Big Price for Her Seed Flax,\" \"Mrs. Williams Grows Excellent Flax,\" and \"Lady Farmer Raises Record Crop.\" (The contribution, if any, of her husband to the farm work was never mentioned.) In 1916 Mrs. Williams purchased, for $12,500 in cash, two other farms that were \"some of the very best farm property in the Gleichen district.\" The Williamses stayed on the farm until 1923, but according to their son, crops were poor in the later years because of hail, frost, drought, grasshoppers, and caterpillars or cutworms.\n\nAlice (Alix) Westhead was another married Englishwoman who was the farmer and rancher in the family. The town of Alix, Alberta, is named for her, and she was featured in the 1906 Canadian Pacific Railway (CPR) pamphlet as a successful farmer, as mentioned in Chapter 2. Westhead was born Alice Charlotte Hall in 1863 in India and in 1881 at Rawalpindi, Pakistan she married her first husband, who died in 1887. As a widow in London in 1891 she married Charles George Westhead. They moved to Alberta in the mid-1890s and established their ranch together, but they drifted apart and she managed the enterprise. She purchased 1,440 acres from the Canadian Pacific Railway, and her husband purchased 480 acres (although it seems that he defaulted on his payments while she paid in full for her land).\n\n_Figure 21._ Alice (Alix) Westhead, c. 1906. She was born in Lahore, India, in 1863 and was living in Ireland with her second husband, C.G. Westhead, when they immigrated to Alberta in the mid-1890s. While they established the Quarter-Circle-One Ranch together near the town of Alix (named after Westhead), she was the owner and operator of the enterprise of over 2,000 acres. She returned to England around 1912 and the ranch was sold. Glenbow Archives, NA-2925-2.\n\nShe was well-known as a stock-raiser and agriculturalist in her district. Alix Westhead was honorary president of the Alix Agricultural Society in 1910, and the annual ploughing competition took place at her ranch. She was a friend of another famous Alix resident and fellow Englishwoman with family ties to India, Irene Parlby, who became well-known as an Alberta politician and cabinet minister in the United Farmers of Alberta government.\n\nIn 1911 an article titled \"A Woman Rancher in Alberta: A Visit to the Quarter-Circle-One Ranch,\" by Gertrude E. Seton Thompson, appeared in the _Canadian Home Journal_. Thompson wrote that Mrs. Westhead had arrived in 1895 \"from the Old Land with the idea of becoming a rancher, and had acquired over 2,000 acres.\" According to Thompson, Mrs. Westhead had \"expert knowledge on all matters relating to farming, and t[ook] a keen interest in the agricultural interests of the country.\" Her expertise in matters agricultural, readers learned, had begun on her husband's estate in Ireland, where she had started a creamery. The article made no mention of the presence of her husband.\n\nThe point of Thompson's article was that it was Mrs. Westhead who was the rancher. It was Mrs. Westhead who \"gives orders to her men and otherwise superintends the running of the ranch.\" She had sixty beautiful horses. The journalist traced a typical day on the ranch for Mrs. Westhead, which began with breakfast served and cleaned up by her domestic helper \"Scotch Jane.\" Then off to the garden to gather lettuce, peas, beans, and strawberries, followed by butter churning. After lunch and a siesta, Mrs. Westhead drove for tea to a neighbouring ranch. The article concluded, \"Mrs. Westhead's success as a rancher should prove encouraging to other women who, having some capital to invest and loving the outdoor life, feel a desire to launch into the wide sphere of farming or ranching.\" The same year as the article appeared, however, the ranch was sold, and Mrs. Westhead moved first to Edmonton and then to England. The last mention of her in Alberta was in a 1912 publication that stated she \"still owns and manages a ranch of some 3,500 acres.\" There was a hint in this publication that her land had become valuable as it was announced that the town of Alix was to have three transcontinental railways passing through it. After returning to England, Westhead lived in a farmhouse near Exbury and acted as a companion to Mrs. Marie-Louise de Rothschild, when she and her husband Lionel, who created his famous garden there, were in residence.\n\nJournalist Celesta Hamer Jackson (also known as Celesta Grivot de Grandcourt), who first arrived in Alberta on assignment with the London _Daily Mail_ in 1911, decided she would take up farming and ranching. She relocated her husband, George, and six children to the prairies, where she acquired 640 acres near Red Deer. The Hamer Jacksons had been experiencing some difficulties and challenges in England. In 1903 George, a London bookmaker, lost all of his money through his speculation on the stock exchange. He had started the business \"with a capital of 800 pound, lent to him by his wife.\" By 1910 George and Celesta were in business together as journalists under the name Hamer-Jackson and Co., when they were accused of copyright infringement for publishing some illustrations without permission. They proposed to make a payment to the plaintiff, who offered to stay the proceedings.\n\nNone of this was mentioned in Celesta Hamer Jackson's 1913 account of \"How I Made a New Home in Canada,\" published in the _Daily Mail_. There, she described how she had been attracted by \"the wonderful boundless prairies... its freedom from the trammels of civilization.\" Her husband was \"ready to give up everything\" (and perhaps he already had). She did not specify how they acquired their ranch of 640 acres, but in 1911 Celesta was one of three purchasers of 160 acres of CPR land that was assigned to her alone in June 1913. Hamer Jackson describes her family arriving with a party of others who were accustomed to \"all the comforts that European homes can possibly realise.\" They lived in tents for three months but then had barns and houses ready. They bought implements and horses, and thoroughbred cattle, pigs, and fowls. The men of the party soon constructed \"model\" piggeries and poultry houses. In her 1913 article she describes this as a \"profit-sharing farm\" where no one got a salary, but it seems they all worked for her as the owner-manager. She intended to build a model dairy and a cheese-making factory. Hamer Jackson confessed that \"not one of us had real working farm experience... But we all had pluck and perseverance. We all went with a resolve to succeed at all costs.\"\n\nIn newspapers as far away as Australia, Hamer Jackson was described as \"the most remarkable woman farmer in the Dominion of Canada.\" According to one account she had brought thirty people from England to help her, but she was \"her own managing director.\" She was described as a \"Canadian rancher\" who raised \"nothing but thoroughbred stock on her farm.\" This was achieved despite the fact that \"she had no previous knowledge of farming methods,\" had \"capital too trivial to mention,\" and was a \"slip of a woman.\" None of the press coverage mentioned her husband, other than to note that her family consisted of him and their children; all of the success was attributed to her. In 1914 the press declared that this \"Canadian rancher\" had \"struck the keynote of successful settlement in Western Canada.\" Hamer Jackson lectured in England on farming in Canada under the auspices of the CPR, and also published articles with the promotion of Canada to potential British settlers as her main theme.\n\nIt is not always possible to determine from the fragmentary evidence whether Englishwomen who farmed the prairies felt they were contributing to the \"spade work of Empire,\" but it seems likely in the case of Hamer Jackson. Her articles indicate she was an imperial enthusiast. She was concerned about the education of the \"foreigners\" in Western Canada, and about their proclivity to bring with them \"racial vices.\" Imperial views of the savage and civilized and the virtues of the British Empire were expressed in her 1931 book written for children, _Discoverers and Explorers of North America._ It is not clear how long Hamer Jackson farmed. She had moved by 1919 to Edmonton, where she was active in social circles, continued to publish articles, and was secretary of the Edmonton Women's Institute.\n\nAs the examples of Annie Williams, Alix Westhead, and Celesta Hamer Jackson demonstrate, women purchased CPR land intending to farm that land themselves. They also purchased CPR land as investors and as speculators. The CPR records for most of them include their marital status, describing them, for example, with terms like \"spinster,\" \"wife of...,\" or \"widow.\" There are seventy-nine records of land purchased by spinsters. Some were resident in the Canadian West. Maggie Dunn, spinster, was a resident of Ellisboro, Assiniboia, when she purchased her land in 1900, and when she paid in full in 1908, she was a Mrs. Merrifield, still of Ellisboro. Others were from distant U.S. locations, including Iowa, Illinois, the Dakotas, New York, and California. Frances Mabel Green, spinster, living in Los Angeles, California, paid for her 160 acres in full at the time of purchase. There were also buyers from England, including Alice Caton, spinster, who was among three purchasers from Blackpool. There are 1,849 records of married women purchasing CPR land, such as \"Margaret Ducklow, wife of James Ducklow, Osprey, Ont.\" who purchased CPR land in Manitoba in 1882. There are 320 records of widows purchasing CPR land.\n\nCELEBRATED WOMEN FARMERS AND RANCHERS\n\n_Mary Gilroy, \"Bachelor Girl\" Farmer of Regina \u2013_ While farmers and ranchers Annie Williams, Alix Westhead, and Celesta Hamer Jackson received considerable attention from journalists, there were others who were even more celebrated. Regina's Mary Gilroy was one. In her 1907 article \"Openings for Women in Canada,\" author Agnes C. Laut advocated \"fruit farming, chicken farming, ranching, even wheat growing\" for women and wrote that \"the number of women who have done this successfully is legion. I recall a girl who went to the Territories to teach painting. Now the West is not old enough for art. The paints were laid aside, and, as the head of her family of brothers and sisters, she bought land near Regina. On that land the banks advanced money for building and implements. Today the girl drives her own span, and is educating the other members of her family\u2014which she could never have accomplished from art.\" While the \"legion\" of women who successfully farmed is a challenge to locate, Laut's Regina farmer was Mary (Marie) Gilroy, \"one of the most famous woman settlers of the west.\" Yet when she died in Regina in 1949, there was little recollection of her achievements. It was noted in the _Leader-Post_ (Regina) that \"Miss Mary Victoria Gilroy,\" who died at age eighty-two, had arrived from Barrie, Ontario, in 1882, and that \"she was believed to have been one of the first women farmers in Saskatchewan.\" Little is known about Gilroy aside from the press coverage she received. She was born Mary Gilroy in 1867 in the Niagara district of Ontario. Her parents were from Ireland and her father was a farm labourer.\n\nGilroy was celebrated by the CPR in their 1903 publication _Words from the Women of Western Canada_ under the subtitle \"A Bachelor Girl Speaks.\" She was an important example in the pamphlet because as a single woman she could not acquire a homestead, but she could purchase land, preferably CPR land. According to the pamphlet, Gilroy was not a \"'toil-worn farm woman' [but] on the contrary, she appeared a well-to-do business woman, clad in a handsome seal jacket, a neat toque, completely up-to-date driving attire.\" She described herself as a \"genuine farmer... my art is merely a winter's amusement, for I was obliged to give it up as a means of livelihood some years ago.\" Her health was not good in her home province of Ontario, and she had consulted a physician who \"ordered me at once to the North-West, told me to burn my paint brushes and give myself a chance for life by imbibing the pure prairie air.\" He advised her to work on a farm, but instead Gilroy bought a half section of land. She told the author of the pamphlet that she ran the farm all alone, with one hired man and up to three others during seeding and harvest. Her brother, a student, lived with her, but she managed the work of the farm herself. Gilroy began as a grain farmer only but was considering mixed farming. She had at that time (1903) farmed for seven years, and she operated the plough and the binder and cleaned the stables. The pamphlet stressed her scientific knowledge of agriculture, including the chemical composition of the soil, but this was all acquired through experience. She described herself as\n\nan enthusiast on prairie farming: why not? From a semi-invalid, existing on a bare living brought in by my paintings, I've grown to be the healthiest of women! Well, no not exactly the \"wealthiest\" as well, but I've no reason to complain of my financial standing. I don't owe a dollar, I've a clear title to my 320 acres; 240 acres are broken and 210 acres ready for crop another season.... Life on a prairie farm is an ideal existence; that is if you don't get into a \"rut.\" I believe no life is so elevating as farm life; there's no \"drudgery\" about it unless you let it become drudgery. Yes it means close application: I am up at four every summer morning, but when my day's work is done, I have my books, music and my brush. I've made money from the start: any one can do the same, and if you run over the list of farmers in this district you won't find one failure\n\nIn 1906 Gilroy was visited by the Canadian Women's Press Club when representatives toured Manitoba, Saskatchewan, and Alberta. They were looking for \"evidence of the success of women in the West\" and found it \"beyond our ken\" that \"women entirely ignorant of farming or ranching could make a success in that line of life.\" Gilroy was cast as fiercely independent and as having great authority over the men she employed. Described once again as \"the bachelor girl farmer of Regina,\" Gilroy \"turned the first furrow of our disbelief and planted facts where fancies had grown rampant.\" She had known nothing of farming when she bought her land eleven years earlier for $2,000. She told the touring press women that \"if any men didn't do what I thought was right I discharged them and got others... Ask anybody for miles around if I can be imposed upon... I've a 'firing' reputation.\" The press women also reported, however, that Gilroy had sold her farm and stock for $13,750, a small fortune.\n\nGilroy was also featured in an article about women farmers in Western Canada in the _Minneapolis Journal_ of July 1906, called \"How Four Plucky Women Won Out in the Canadian Northwest.\" It began with \"'The bachelor girl farmer' is a personage of whom one hears fifteen minutes after arriving in Regina. 'She's a corkerjack, as you Americans say,' was how one enthusiastic man expressed it.\"\n\nSelling her farm in 1906 did not mean that Gilroy was excised from further promotion of women farmers. In the 1907 CPR pamphlet _Home Life of Women in Western Canada_ she appeared again, although it was noted that she had sold her \"country holding for the round sum of $15,000.00.\" The pamphlet described Gilroy as \"one of the big grain growers of the district\" and as \"one of the most written about business women in the West; her plucky venture, putting her last shilling in a prairie farm, her indomitable energy, spent in a hand-to-hand tussle with fortune.\" It was reported that she was touring Europe, \"taking pleasure from the result of her $2,000.00 investment on the prairie plains!\" Gilroy then faded into obscurity and has been forgotten. According to her obituary, she became an insurance \"saleswoman\" for Mutual Life Assurance Company of Canada. In 1911 she was a \"lodger\" in a rooming house on Retallack Street in Regina.\n\n_Lady Ernestine Hunt: Alberta Horse Rancher \u2013_ By 1906 \"the most adventurous Englishwoman of the day,\" Lady Ernestine Hunt, a daughter of the Marquis and Marchioness of Ailesbury, had a horse ranch near Calgary of (allegedly) between 30,000 and 40,000 acres. Her ranching activities were widely reported in Canada, the United States, and Britain in part because she was well-known for her exploits long before establishing her Canadian ranch. She was described as \"a modern feminine Don Quixote\" and as having \"crowded into her life more adventures than one usually comes across in the pages of a sensational novel.\" As Lady Ernestine Brudenell-Bruce, she established a reputation for \"handling a yacht... almost equal to the most experienced 'old salt.'\" As she told a reporter in 1906, \"As long as I can remember I have had a roving disposition, and have been fond of two things\u2014horses and the sea. By the time I was 24 I had been around the Horn, and I was a night staff nurse at Krugersdorp [South Africa] at the time of Jameson raid. A few months later I went to Australia in a sailing boat, returning in another sailer [ _sic_ ].\" In order to take command of her own yacht she required a yacht master's certificate, and she attended nautical school in Liverpool but was refused permission to write the final exam because she was a woman. While there she met Harry Brady Hunt from Ireland, and they eloped. He was a mate in the merchant service, and she sailed with him to Japan and many other locations. She also trained steeplechasers in Ireland.\n\nUnder headlines such as \"Titled Lady Has Ranch in the West\" and \"Canadian Woman Rancher: The Daughter of a Marquess Ships Horses to England,\" it was widely reported in 1906 that Lady Hunt was the \"only woman that has ever brought livestock across the ocean by herself,\" from her ranch near Calgary through the port of Montreal. She arrived at the port \"dressed in real cowboy fashion. She is a dark complexioned young woman about 28 years of age: wore a sombrero hat, black waist, khaki colored skirt reaching to the knees, leather leggings and shoes. Her hair was cut short.\" She shipped seventeen horses and personally supervised their conveyance, although they were yet to be broken and were still in a \"half wild state.\" She intended to ship them to her Irish estates at Ballylean, County Clare, and Kilcurly Adare, County Limerick. Several nights on board she had to give up her sleep to calm them. Hunt could \"handle them just about as she pleased, although the deck hands found it necessary to keep at a safe and respectful distance.\" Despite sleepless nights she was \"a picture of beauty and health.\"\n\nHunt was apparently dividing her time between Ireland and her ranch in Alberta in 1910 when she founded a colonial training school for girls at Cosham Park near Portsmouth. Situated on seven acres of meadow and orchard, the school was intended to train women to be independent once they arrived in the colonies. Hunt had found that \"girls who have left boarding school have a great deal to learn before they are fitted to seek a career of independence in the colonies of the empire.\" She appointed herself the principal of the school, and her aim was to give girls of eighteen or older training in subjects that would be useful to them in \"fending for themselves and their homes, whether in the colonies or in England.\" Graduates who did not wish to go to the colonies were qualified to become matrons, or housekeepers in large households. Horsemanship was the foremost subject. The students were taught to ride sidesaddle and astride, and single and pair driving. Other subjects included cooking, home nursing, first aid, darning, stable work, and gardening. There were to be no servants at the school, as the students were to do all the required work themselves. In summer the students were to sleep in tents.\n\nWhether the school was a success and just how long Hunt ranched in Western Canada are difficult questions to answer, since both ranch and school disappear from view. By 1908 she was busy in England with the First Aid Nursing Yeomanry Corps (FANY). A small organization made up of elite women who owned horses, FANY combined nursing skills with the sense of valour and patriotism of military service. In 1909 it was announced that Hunt was the first woman to receive a commission as lieutenant in the territorial division of the British Army. Reports at the time claimed that she still operated her horse ranch, that it was lucrative, and that \"she has a wonderful influence over the wildest horses, so much so that she astonished the cattlemen on her ranch, who declare that she is able to accomplish by mere gentle suasion what ranchmen can only attain by the hardest rough riding.\"\n\n_Grain on a \"Stupendous Scale\": Ruth Hillman and Fairview Heights Farm, Keeler, Saskatchewan \u2013_ Ruth N. Hillman, a farmer at Keeler, Saskatchewan, was featured in newspapers as far away as New Zealand and Australia. She purchased her land about 1906, and by 1911 she was operating a \"profitable farm of nearly 2,000 acres,\" despite having no previous farming experience. Hillman was born in St. Paul, Minnesota, and had been a \"stenographic reporter\" before she \"took what capital she had... and staked her savings in Canadian land.\" There were two years, however, between her purchase and her move, and during that time she allegedly studied and read all she could and made herself aware of the conditions of farming on the northern plains. She learned she needed to avoid \"any attempt to transplant the small farming methods of Minnesota to the broad acres of Saskatchewan.\" Hers was another version of \"rags to riches\": she declared that \"what she has done can be done by any girl working on a small salary. From small beginnings her land grew.\" The 1911 census shows that Hillman had a large workforce on her farm with a foreman and six labourers, plus her brother, aged fifteen. Her mother, too, was resident on the farm and listed as the head of household.\n\nAlso in 1911 it was reported that Ruth Hillman was in St. Paul to secure the cooperation of the Twin Cities \"jobbers and manufacturers... in the fight for free trade or reciprocal trade relations.\" She was quoted as saying, \"It would make your heart sick to see how some women and children almost starve themselves in their homestead shacks so that their husbands can raise the money to pay the exorbitant prices charged for American farm machinery.\" In this account Hillman was a \"writer of romances,\" as well as a manager of a farm \"aggregating 20,000 acres.\"\n\nDuring the First World War, Hillman was described as breeding Percheron horses and having a wheat crop of 40,000 bushels. In this report her femininity was stressed: she was a \"slim little person\" with \"dainty hands.\" Hillman allegedly declared that she did not do any of the \"actual manual labor\": \"You see I believe farming is just like any other big business and business systems should be introduced into it. I study for all I am worth, reading up what others have done, noting my mistakes and finding out why they are mistakes... then when my foreman comes for consultation I know what I want done.\" She had thoughts about farming as a profession for women: \"Women can be successful at it if they make up their minds to work, work, and then work. I can see where they would do splendidly near a big market, but as to away out on the prairie, they must be sure of their physical, moral and mental strength before they attempt it. It is a big test.\"\n\nHillman's enormous new house and barn were described in \"Who Said Women Can't Farm?,\" a lengthy feature article by Mary P. McCallum that appeared in a 1918 _Grain Growers' Guide_. At that time she had \"one of the finest herds of Percherons in Saskatchewan.\" Hillman was continuing to study agriculture and to experiment on her own with wheat varieties.\n\nThe author of this article concluded that Hillman was \"one of a long line of women who are forging for women new links in the chain of world industrialism and professionalism,\" and that the prairies could now boast many women farmers. Some were small-scale producers with little or no capital who faced \"unspeakable adversities,\" while others, like Hillman, were farming grain on a \"stupendous scale.\" Like Lady Hunt, Hillman also faded from the public eye. The local history reports only that she married Bob Lowe and left her farm, which she called Fairview Heights, during the Depression. At that time she likely got little or nothing for her farm, as it was in the centre of Saskatchewan's Dust Bowl.\n\n_Isobel \"Jack\" May and Her \"Ready-Made\" Farm at Sedgewick, Alberta \u2013_ The woman farmer of Western Canada to receive the most acclaim and notoriety was Isobel \"Jack\" May. Before she left for Alberta in 1911 she was known in England as \"Lady Jack,\" or the \"Lady Farmer.\" She had attracted attention from as far away as New Zealand for her work as a farm labourer and for her attire. Despite all of the press coverage she received, it is difficult to know for certain very much about her background or her own thoughts. There are no sources left by her, just vast press coverage, far from reliable. Most articles about her written after her arrival in Canada claimed that she was a daughter of Admiral Sir William Henry May, Commander of the Atlantic Fleet, and accustomed to mingling with elite society, including royalty, at dinners, balls, and receptions. It is unlikely, however, that she was his daughter, unless she was \"illegitimate.\" Press coverage contrasted her (alleged) former life as the daughter of an admiral with the solitude and demands of life on her Alberta farm. According to one description in a 1912 article entitled \"World's Happiest Girl Who Declares She Would Rather Plow Than Go to the Opera,\" she had been a \"frilly, frothy society belle, to whom the theatre, balls and card parties represented all that was worth living for.\"\n\nAccording to the press, Jack May, like Lady Hunt, served as a nurse in the South African War. Upon her return to England she enrolled at the Horticultural College at Swanley. After graduation she worked at two farms in Kent. There she attracted attention because of her work on the land and with animals, but also because of her clothing, which was described as \"male attire.\" One of the earliest descriptions of May is from her 1906 appearance as a witness in police court in Bromley, Kent, where her garb attracted much more attention than the details of the case at hand. It was reported that the witness was \"a young woman dressed in boys' clothing... Her name is Isabel May. Her hair is cut short and she wears leggings and a cap. The only exception to the male costume is a sort of smock reaching almost to the knees. Miss May, or, as she prefers to be called \"Jack\" is a most interesting young woman. Her ambition is to be a farmer and with this end in view has taken service with Mrs. Smith at St. Mary Cray. She is handsome and stalwart, and in the farming garb presents quite a picture of strength.\" The report further noted that May was \"certain that women can succeed on a farm if they try,\" and that no one \"doubts her ability as a mower, reaper, or plougher.\"\n\nAccording to other reports, May insisted that her garb was feminine and that she was \"hurt by the imputation that she wears male attire.\" She also contended that she \"does not work on the land but is engaged upon ordinary women's tasks, such as milking and butter making. In a later statement however, she said that at the farms in Kent she did every kind of farm work, including mowing, reaping and ploughing.\" In 1907 she left Kent and operated a flower and vegetable farm of several acres in Norfolk, and it was here that she began to wear trousers. Her goal, once she had enough experience, was to go to Canada and \"turn some capital that she has to account in farming on a large scale.\"\n\n_Figure 22._ Isobel \"Jack\" May, often referred to as the \"bachelor girl settler,\" was briefly a farmer at Sedgewick, Alberta in 1911\u201312. Her occupation and her \"male attire\" attracted press attention from around the globe. This photograph was used widely in the press to illustrate her farm work in Alberta, but it pre-dates her arrival in Canada. She was already a celebrity \"lady farmer\" before she left England with press attention from at least 1905. Currie Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ 31, 181 (1911).\n\n_Figure 23._ Louisa Wittrick farmed with \"Jack\" May, but her responsibilities focused on the domestic realm. Both women purchased \"ready-made\" Canadian Pacific Railway farms, and together they had 320 acres. Currie Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ 31, 181 (1911).\n\n_Figure 24._ May (seated) and Wittrick in front of their \"ready-made\" farm home at Sedgewick. Currie Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ 31, 181 (1911)\n\n_Figure 25._ A widely published photograph of the \"bachelor girl settler.\" Currie Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ 31, 181 (1911).\n\nMay's arrival in Saint John, New Brunswick, in April 1911 caused a sensation. When the CPR liner arrived with a group of fifty farmers from England headed for the CPR \"ready-made\" farms in the Canadian West, it was found that one was a female dressed as a male. This became big news, broadcast with headlines such as \"Miss Jack May in Male Attire: An Eccentric Young Woman Passenger on the Empress of Britain.\" According to one description, \"A female second cabin passenger who gave her name as 'Miss Jack May,' was detained by the Canadian immigration officials, she being attired in male costume. According to one report she 'shocked the... immigration agents, who had heard of no such thing in this part of the world, where there are no suffragettes or anything of that kind.'\" In the record of her arrival she is entered as a male, age 35, then this is crossed out and she is entered into the female column. May readily admitted that \"she was one of the opposite sex and said that she and her male companion had worked on a farm in England. She had her hair cropped short, wore leggings and tan boots and a short skirt that was not visible below a man's overcoat. Her age was about 30 and she was rather good looking.\"\n\nMay's \"male attire\" was regarded not only as odd or perverse but as suspicious, shady, even treacherous. She was \"masquerading\" as a man. In Canada and the United States, this was a crime. In 1914 at Fort William, Ontario, a woman was sentenced to six months in the penitentiary for \"masquerading as a man\" and working as a hotel porter. Her defence was she needed to \"keep from starving\" and that \"being in the guise of a girl she was under too great a handicap to make her way in the world.\" Four years later a woman was sentenced to two years in the Kingston women's prison because she had \"posed as a man, had her hair cut in military style, and went so far as donning a man's attire in order to do her bit in a log-driving bee.\" (This prison sentence, however, raised a \"storm of indignation.\") In the United States in 1911 a woman musician who dressed in trousers and waistcoats was given sixty days in jail in Portland, Oregon. In passing the sentence, the judge said that \"I hope that by the time your sentence has expired your friends will have provided you with clothing suitable to your sex.\" In 1913 a New York woman was arrested and jailed for \"masquerading\" as a man; she worked at a bookbindery and dressed as a man to earn better wages.\n\nThere was considerable debate about, and mixed reactions to, May's arrival in Canada in \"male attire.\" One rural Alberta newspaper, the _Gleichen Call_ , welcomed her: \"A woman with energy to study the science of farming and to work it as Miss May has done, would be a decided acquisition to any country, and the fact that she adapted her attire to her work shows her good sense. The sight of a woman in men's attire and doing man's work may be novel, but it does not make her any the less a lady.\" The _Daily Colonist_ of Victoria, British Columbia, was much more critical:\n\nMost women would rather not have read that this handsome and enterprising young lady considered it expedient to travel in men's costume. If at her work Miss May found it necessary to dress as a man she was certainly under no such compulsion while travelling. Few people find it necessary to wear the uniform of the workshop on the street. \"Jack\" May... may be a picturesque figure on a railway platform and make a good story for a reporter, but most women would prefer to see their daughters dressed less conspicuously. Conventions are not without meaning and no woman would lightly disregard them.\n\nMay stood out and was seen as odd, or worse, not only because of her attire but because of her occupation. She was reported to be \"the first woman to undertake farming on an extensive scale in the west.\" She had successfully applied for one of the CPR's ready-made farms at Sedgewick, Alberta, stating in her application that she had \"done every kind of farm work, from that of an ordinary farm hand to bailiff or manager.\" The ready-made farms were a scheme to help attract the \"sons of Britain,\" instead of peasants from Europe, to settle in Western Canada. Prospective farmers signed up for a plan that was intended to avoid many of the pitfalls of the free homestead system while making money for the CPR, as the farmers had to purchase their land. The settler had to pay a 10 percent down payment plus the cost of the improvements. In the contract the CPR agreed to provide each farmer with a four-room cottage, a barn with hayloft, and to have fifty acres on each farm broken, planted with crops, and fenced before the settlers left the old country. The farms were to be close to a railway, to market, churches, and schools\u2014unlike homesteads, which were often very isolated.\n\nMay was fortunate to be accepted into the scheme, as the conditions were that the applicants were to be married men actually engaged in agriculture. May qualified only for the latter. She purchased Farm No. 2 at the Sedgewick colony, consisting of 160 acres, at the price of sixteen dollars per acre. Her land was valued at $2,560 and the improvements at $2,227, for a total of $4,787.\n\nWhile May was reported to be with a \"male companion\" when she was detained by immigration officials at Saint John, when she arrived in Alberta her companion was identified as Miss Wittrick of Norfolk. From Wetaskiwin, Alberta, it was reported on 29 April that the two were on their way to Sedgewick: \"Miss May is a large property owner in the Old Country, and some six years ago adopted the male attire as a convenience in her duties of managing her large holdings. When they reach their new home Miss Wittrick will do the house-keeping and Miss May will do the farming. It is said that she is thoroughly proficient and can ride a horse or handle a plow like an expert. She also knows livestock and she has plenty of grit and ambition.\"\n\nIn the CPR records of the colony, Louisa May Wittrick had Farm No. 3 on the northwest quarter of the same section (NW 7-43-12-W4) as May's plot. Together they had 320 acres. May purchased her farm on 16 May 1911 and Wittrick, on 24 April 1911. Aside from Wittrick and May there was only one other woman among the Sedgewick ready-made farmers, Caroline Ann Potts (who received no press attention, and there is no record of the results of her farming adventure). In the extensive press coverage of Wittrick and May, Wittrick was always presented as looking after the domestic realm; she did not dress in male clothing. According to one description, the \"two young ladies are working in partnership. They find no difficulty in the arrangement, though the average farmer out there assures you that partnerships are unworkable in such a business. Each member is responsible for her own department but is always ready to help the other. Miss Wittrick looks after the dairy and the house... and she is a beautiful butter maker and an excellent cook, but she takes a hand in the field work whenever there's need of extra help.\" May did the ploughing, discing, harrowing, reaping, and binding, and she also marketed the grain.\n\nLouisa Wittrick wrote a letter to the _Canadian Gazette_ in January 1912, describing how the two were coping with their first winter on their farm and, despite noting that it had been as cold as 56 below (Fahrenheit), she was very positive: \"Somehow Jack and I have never found one day long enough. We are up at 6:30 and we are at it till past eight at night.\" It was very dry; the snow covered the ground but was not deep. Their cows and pigs were doing well; Jack had made a shed of saplings and straw. The CPR had dug a second well for them because their first was no good. They had spent a quiet but happy Christmas, enjoying the rest as they had to normally work every day of the week.\n\nThe Sedgewick colony farmers had faced some surprises upon their arrival They were angry to learn that the CPR was charging them three dollars an acre more than the price quoted them in England by the company agent. This resulted in a delay in the colonists' taking possession of their land. Edwin and Felicia Snowsell and their two children, from Gloucestershire, who arrived in 1911, were dismayed to find Sedgewick to be a tiny village with one street and \"all around bare prairie. Our spirits fell to zero.\" They also found that the well was not ready on the farm they had purchased. The CPR had done a poor job of ploughing the land. According to Frank Snowsell, the CPR contractors \"tried to squeeze the 50 acres out of areas without trees to avoid the added cost of clearing. Since many quarters had over 100 acres of poplar and willow brush with many sloughs, this required some tricky dodging around the wooded areas. Also, cultivating was practically non-existent.\" No one in the Snowsell family had any farming experience. Son Frank wrote years later, \"Dad had never done any farming, nor handled horses or any other animals until he came to Canada. Mother had never cooked a meal, washed clothes, nor done any of the usual prairie housewife's tasks until she arrived in Alberta.\" They had a poor first harvest due to rain that delayed the harvest, and then frost.\n\nCompared to the Snowsells, Jack May and Louisa Wittrick were well prepared and seemed to thrive, at least according to press reports. An April 1912 report observed that May and Wittrick were \"not among the old country people [of the CPR ready-made farms] who because their wheat was frozen left their valuable crop of potatoes to rot in the ground.\" Their successes were emphasized, and their contentment. They were in Sedgewick for only a few weeks when an article appeared in the _Canadian Courier_ called \"The Woman Who Never Looks Back.\" The author of the article, Norman S. Rankin, took his title from a poem by Mary I.S. Schaeffer, a choice that was not apt as the poem was about the farm wife who was \"comrade\" to her husband:\n\nWe speak of the man who has opened the door\n\nOf the great teeming West, that has brought to the fore\n\nThe wealth of the prairies\u2014so vast and so wide\n\nBut how many think of the one at his side\n\nThe one who has made him a home in the shack\n\nHis comrade\u2014the woman who never looks back.\n\nRankin's article exemplifies the intense scrutiny May received. He provided a detailed description of Jack May's appearance, noting that this was the first \"out-and-out professional woman-farmer\" he had ever heard of: \"Her face was pleasant, deeply bronzed, inclined to be square with a broad mouth and forehead over which a thick mass of auburn hair struggled from beneath her tweed cap. Brown eyes twinkled at you. Probably five foot three or four inches in height, she gave the impression of strength and endurance. Her costume\u2014about which so much publicity has ensued\u2014was certainly unique. A cloth jumper over a shirt waist, a cloth skirt, knee length, brown leather leggings and a three-quarter overcoat completed it. And as she strode across the platform with a grip in each hand and her cap set jauntily on the back of her head, one certainly would have thought 'A jolly good-looking fellow.' I did.\"\n\nRankin's article included two photographs: one with May on horseback with the caption \"Smart and well proportioned, she might have been taken for a college youth\"; and the other of her behind a horse and rake with two men with the caption \"She finds farming congenial and male costume much more fitted to the work she does than woman's.\" Rankin clearly struggled with May's attire, writing, \"She wears masculine garb because she wants to. One might wonder why she wants to, but it wouldn't do him any good, or bring him any nearer a solution. There's no argument open. She finds farming congenial, and male costume much more fitted to the work she does than woman's. And that's enough.\"\n\nMay was also featured as early as 1911 to help promote the ready-made farms and the CPR. In an article by Currie Love in a pamphlet about the \"phenomenal progress\" of Calgary and region, the Sedgewick women colonists were highlighted. Love was a Canadian journalist who spent some years as a special writer for the CPR, and she was quite likely working in that capacity when she wrote the article, as it promoted the ready-made farm scheme for British settlers. Love wrote that \"women will be interested to know that one of the most successful 'ready-made' farmers is Miss Jack May, daughter of Admiral May, of England, who with her friend Miss Louise Wittrick, has taken 320 acres.\" Although Love included much of the same detail as others had, she did not mention anything about May's male attire. Love was also interested in promoting the scheme for other women, writing that \"a woman needs to be pretty strong to do farm work in a new country but given sufficient capital and common sense any woman can succeed.\" She urged women to purchase the forty-acre ready-made farms. (The large acreages, grain crops, and equipment such as steam engines were for male farmers, according to Love.) On their smaller holdings, women could grow food for their cows, pigs, and hens. They could also grow various berries and vegetables. Money was required. Advocating poultry farming in particular, Love wrote that \"any young woman starting a poultry farm in Alberta should possess capital of from $2,500 to $3,000, ambition, a practical turn of mind, and a goodly amount of determination.\" She continued: \"In these twentieth century days when women are emulating men in almost every department of life, it is not surprising that they should follow masculine example and emigrate to a new country where opportunities are more plentiful than in the Old Land, and where the women who work for a living are neither regarded with suspicion nor ostracised from society.\"\n\nCurrie Love published much of the same material in a 1911 article entitled \"Farmer-Boy 'Jack'\" in the _Lady's Realm_ (London). A story of how \"two Englishwomen have solved the problem of work for women,\" the article began thus: \"Though not a suffragette, Miss Jack May, an Englishwoman who has come to Canada to farm her own lands, is an example of what the twentieth century woman can accomplish alone and unassisted.\" Love emphasized in this article how \"all their neighbours thoroughly respect them, and do all in their power to be of service to them.\" The farm hosted a steady stream of visitors, \"anxious to see the two women who have come thousands of miles from home to make a success of farming in Canada.\"\n\n\"The World's Happiest Girl\" was how May was described in an article featured in many newspapers in Canada, the United States, and New Zealand in late 1912 and early 1913. May stated (allegedly): \"I wouldn't go back to society again for worlds. I would rather plow than go to the opera. I would rather plant corn than attend a pink tea. I much prefer currying my horse to arraying myself in an evening gown. What's a butterfly life in damp and foggy England compared to real life in bright sunshine and bracing cold?\" She claimed to \"love the freedom of the life here and the highness of things here on the western prairies... In England one is bound by conventions, as one's fields are girt with hedges. Here I can do as I choose, I would not go back under any circumstances.\" When May \"dressed up\" she still refused to be corseted and constricted; rather, she wore \"a soft collar and tie, and a peasant smock of navy blue denim, which comes to her knees and is loosely belted around her waist.\"\n\nThe most detailed account of May and her farm is a 1914 article, \"Haymaking with Jack May: A Woman's Life on a Canadian Farm\" by Currie Love, published in _Quiver_ , a London illustrated magazine. Love reported that May did not even own a skirt: \"Can't be bothered with the things. Besides, women's fashions change every minute, and I can't afford to keep pace with them. My first reason for adopting men's clothes is that they are comfortable and sensible, and the only safe costume for farm work. Imagine me on a plough in a hobble skirt! Wouldn't I be a fine sight? You're liable to be thrown off a plough every twenty minutes or so, and a skirt would be absolutely dangerous under those circumstances. From wearing men's clothes to work, I gradually adopted them for everyday wear, and now I should be most uncomfortable in conventional feminine garb.\" According to Love, May was assisted not only by Louise Wittrick but by Miss Grace Hanson, also from England, aged eighteen. Hanson too opted for the comfort and safety of masculine dress: \"The very idea of corsets makes her shudder with disgust. 'Nasty stiff things,' she says: 'I wouldn't wear them for anything.'\" They had six cows, six horses, seventeen pigs, two dogs, and some hens. There were 150 acres sown of barley, wheat, and oats, and it was reported that May did all her own work with the grain\u2014ploughing, seeding, reaping, and binding. She also did her own carpentry work, building a barn and pigsty as well as shelves for the living room. The women had found their first Canadian winter \"delightful.\" The \"long days of bright sunshine and clear, bracing cold [were] so different from the damp fog of England.\" \"We had expected,\" [May] laughed, \"to find an Alberta winter a terrible experience, but we liked it even better than the summer.\" May declared she would not go back to England except to visit:\n\nTo see my people at home, but not to stay. I like the freedom of life here\u2014the bigness of things. No, I wouldn't go back to stay. I don't believe that Canada is a wonderland. I know you can't pick up gold off the streets, as some of the old-country people believe. I don't think the climate is the best in the world, or that anyone who comes here is bound to become wealthy in a year... But I do believe that Canada offers the greatest opportunity I know of to a man or woman with a little capital who is not afraid to work... If you want to work hard, have beautiful soil, own your farm and house, be your own landlord, and have a free, independent life, Canada is the place.\n\nSadly, Canada was not the place for Jack May. She lasted only a little over a year. Just why she left for good is not clear. When Currie Love's article in _Quiver_ was published in September 1914, May had already been gone for nearly two years. In December 1912 the _Sedgewick Sentinel_ reported that \"Miss Jack May left last week to spend the winter in England.\" She did not return. The 1 May 1913 issue of the _Sentinel_ noted that \"Miss Jack May, who went on a visit to the old country last fall, is not returning, she having taken a farm in the county of Shropshire, England.\" It was further noted in the same issue that \"Miss Hanson [the young assistant mentioned in the 1914 Love article] is entering into partnership with Miss Wittrick, in place of Miss Jack May.\" Finally, this same issue of the _Sentinel_ boasted that Sedgewick, particularly Jack May, was featured in a lengthy article in the _Calcutta Statesman_ of 2 February 1913.\n\nBut Jack May was gone for good. The local history of Sedgewick, published in 1982, provides clues. In her entry on \"Miss May Jack and Miss Louise Whittrick [ _sic_ ],\" Mary Weber wrote that \"Miss May left the farm for Australia in 1913 and Miss Whittrick took over the farm. At this time Mr. David Moore, the recently appointed supervisor of the CPR ready-made farms, bought the west half of section 17 in 1913\u201315. Mr. Moore and Miss Whittrick were married in Sedgewick in 1914, a most posh ceremony. Two sons were born to them on the farm but the eldest died as an infant. In 1922 Mr. and Mrs. Moore sold the farm, had a sale of their effects and, with their son Jack, about four years old, returned to Ireland.\"\n\nJack May disappears from view. Whether she in fact went to Australia or to a farm in Shropshire is unknown. Articles about her as a farmer in Canada, however, continued to be published, such as Love's 1914 piece in _Quiver_. A popular 1913 article about May was entitled \"Society Lady Who Prefers the Plow to the Pink Tea,\" although it was a re-hash of earlier articles. When speaking before the Royal Colonial Institute in London in 1913, Saskatchewan farmer Georgina Binnie-Clark referred to the injustices of Canada's land laws and the contribution women could make in the \"spade work of British expansion in this, the supreme place of prosperity among British lands.\" She used Jack May as her best example of this potential: \"And of the Sedgwick colony in 1911, the verdict from officials, dealers, tradesmen and neighbours concerning the work of Mrs. Jack May and her partner, Miss Louisa Wittrick, on their ready-made farm was, 'The women are the best men of the lot.'\" In 1914 an article published in the _Irish Homestead_ , and reprinted as \"Lady Farmers\" as far away as New Zealand, focused on May and Wittrick, and the author had allegedly recently visited them. As late as 1924, May was still being celebrated as one of the \"pioneer women of the West\" who, along with Miss Wittrick, was \"happy and flourishing\" on her farm at Sedgewick, that she had in fact long since left. She may have left for personal or economic\/agricultural reasons, or a combination of both.\n\nOne visitor to the May-Wittrick farm perhaps provides a clue. In his book _Canadian Trails: Hither and Thither in the Great Dominion_ , English writer Eldred G.F. Walker described his visit to Sedgewick in the summer of 1912, writing that he had resolved to \"go and see the lady settler, Miss Jack May.\" Walker was welcomed by May and her \"lady friend,\" and he found their home \"natty.\" He described May as liking her farm very much, as having the best dairy cows he had seen in that part of the country, and as having cut plenty of hay. But \"a tragedy had nearly occurred the day before, as during the storm the electric fluid had struck the windmill, and running down had found a metallic clothes-line, from which it had flashed into the hen-coop, killing twenty-two chickens and blinding the old hen.\" Altogether Walker seemed impressed with what they had done, writing that \"I had heard of the life of the Wild West, but it did not look as though life was so very wild when these two girls could have a home of their own all alone out on the open prairie.\"\n\nWalker also reported some discontent among the Sedgewick colony farmers. One complained that he could not get the CPR steam plough to do the promised breaking of the land. Many of the Sedgewick and other CPR colony farmers and homesteaders in Western Canada were soon or eventually discouraged, and sold up or abandoned their land. Their crop of 1911 was very poor, and they had to be provided with seed wheat for their crop of 1912. This seed was full of weeds. They found winters difficult with not enough fuel; their water would be frozen in the morning and their vegetables in the root cellar also froze. The houses that were built for the settlers had no insulation for the winter weather and were built of inferior materials. Elizabeth Snowsell taught school from 1913 to bring necessary income to the farm, as the grain crops could not be relied on. The Snowsells found it essential to hire casual labour, particularly at harvest time. After fourteen years, including several years of crop failures, the Snowsells abandoned their farm, leaving it in the hands of the CPR. Like that of May and Wittrick, the CPR record of Snowsell's contract reads \"Status of Purchase: Uncertain.\" Many other records read \"contract cancelled,\" or \"contract surrendered and cancelled.\" According to an account in the local history of Sedgewick, a great many of the colonists were from cities and had no experience in farming: \"Some of them didn't last out the year, and by the time ten years had rolled around, there were very few of those with no farming experience left here.\"\n\nCPR Sedgewick settler Jim Hallum, who arrived as a boy with his parents, wrote that the colonists were disappointed for many reasons, including the tiny houses, and the fifty acres on each farm that was supposed to be seeded to wheat upon their arrival, but was not. The wells were particularly disappointing, as they were so deep and equipped with steel rods that \"in order to pump water from a well like that, it really took some muscle and strength.\" But there were colonists who persisted under adverse circumstances. Bessie and David Black and their young son came from Essex to Sedgewick in 1912. David died that August,and another son was born two weeks after his death. Yet Bessie Black persisted, with the help of her parents who came out from England in 1913.\n\nThere was at least one other woman farmer in the district who appears to have persisted longer than Jack May, although she received very little press coverage by contrast; she must not have donned male attire. Miss Helena Hill of Seattle purchased CPR land near Sedgewick and in the spring of 1911 it was reported that she was sowing 100 acres to flax. Under the headline \"Another Woman Farmer,\" it was reported that Jack May \"is to have a rival in her fascinating occupation in Alberta.\" A Miss Hilliard, also of Seattle, would supervise the house, while Hill developed the farm, and it was further reported that she intended to go into farming on a large scale and bring 640 acres under cultivation. It seems Hill was much more successful than May at farming the prairies. The 7 November 1912 issue of the _Sedgewick Sentinel_ noted that \"Miss Hill shipped the first car of grain through the Farmers Elevator on Monday.\" (It was one month later that the same newspaper reported that \"Miss Jack May left last week to spend the winter in England\"\u2014and never returned.)\n\nDISRUPTING AND TRANSGRESSING: CROSS-DRESSING FARMERS\n\nJust how Jack May understood her own gender and sexual identity cannot be gleaned from the evidence available. Nor can it be known whether she and Wittrick were partners in more than just their farm. The name Jack, however, may have been adopted as a masculine nickname when she was developing a visible lesbian identity, as in the example of her contemporary Vera \"Jack\" Holme, actress, suffragette, and chauffeur (to the Pankhursts). According to historian Anna Kisby in an article on Holme, \"A recurrent theme among Jack's friends is their use of male pseudonyms. Making her identity as a lesbian apparent according to the conventions of the time, Jack's nickname and her masculine dress act as key signals of her sexual identity.\" As historian Peter Boag has shown in his book _Re-Dressing America's Frontier Past_ , \"cross-dressers\" included a wide spectrum of people. At one end were those for whom \"such an act was not crossing at all but was something that came naturally to them, as they really felt themselves to be other than the sex their bodies suggested them to be.\" At the other end were those \"who took on the garb of the opposite sex for purposes unrelated to either sexuality or gender identity.\" Boag also contends that when cross-dressers are remembered in Western history, a \"progress narrative\" is invoked that \"normalizes the cross-dresser by maintaining that 'she' changed her clothing for some purpose related to securing personal advancement in a world with a deck that was otherwise stacked against her. For example, she might have dressed in male attire to pass herself off as a man so that she could obtain better-paying employment.\" While Boag admits that there were \"logical and practical\" reasons why a woman might dress as a man in the nineteenth-century West\u2014for safety, for opportunities, or adventure\u2014digging deeper can reveal a \"bonanza\" of evidence that \"female-to-male cross dressers undertook a change of wardrobe to help them better express feelings of sexual and gender difference.\" In the case of Jack May, however, it is impossible to \"dig deeper\"; the sources are not there. Similarly, it cannot be determined from the press reports whether May had aspirations of political equality or economic independence for herself, her partner, and other women.\n\nDid May's male attire make her an oddity, an outcast in the Sedgewick colony and in Western Canada more broadly? Cross-dressers are disruptive figures \"invested with potent and subversive powers,\" as they throw into question the binary categories of \"male\" and \"female.\" As historian Ann McClintock writes, clothing became \"central to the policing of social boundaries.\" May's transgression of gender, the spectacle of boundaries crossed, clearly fascinated a reading public, but how did her neighbours feel? It is possible that Jack May did not receive a warm welcome from her neighbours in Sedgewick. In all the accounts of women performing farm work in the West, it is extremely rare to learn that they did so in men's clothing. One other example is Patricia Carlisle, an English writer (pen name David Lyle) who purchased the Sunnyslope Ranch of 800 acres near Priddis in 1924. There she was known as \"Miss Peter Webber,\" and the land was jointly worked with \"her companion Miss Goppel.\" They were known in the district as the \"farmerettes,\" as they were \"the first women locally to run a farm and operate machinery along with the men.\" It was explained in the local history that Carlisle did not use her real name in the district because \"she was the daughter of a well to do London, England, member of Parliament.\" These and other stories about her may or may not have been true. It was stressed that she had other abilities normally associated with men, that she was \"an expert driver\" and a \"good shot.\" She was \"extremely venturesome,\" had \"worked for the British Government in Turkey and India,\" and \"during the War she is supposed to have driven an ambulance in Serbia.\"\n\nCarlisle wore trousers and a cowboy hat. She did all the farm work, including driving a tractor, ploughing, and harvesting. She had a crop of 7,000 bushels in 1925. Yet the local history stressed the somewhat eccentric ways of the \"farmerettes.\" Carlisle and Goppel bought a tractor and grain separator in downtown Calgary and drove them all the way back to their ranch (thirty-seven kilometres), despite the fact that it was forbidden to drive the machines on the pavement in that city.\n\nLike Lady Hunt and the farmer to be discussed in Chapter 5, Georgina Binnie-Clark, Carlisle announced her intention to train English women to farm in Western Canada. (This was one way to solve the need for farm labourers\u2014by using unpaid help who were supposedly in training. As mentioned above, Jack May also had \"apprentices.\") Carlisle reported that after an interview with her was published in London, she received 500 letters from English women who wanted to emigrate to ranches in Canada immediately. Carlisle was quoted saying that \"farming is a profession as suitable for a woman as for a man for mechanical labour saving devices are every year entering more intimately into its operation. Actually it returns more for brains than for the muscle applied to it.\" In 1925 in London she (allegedly) interviewed 100 women as possible students, and it was announced that Carlisle would return from England to Alberta with a well-known London woman surgeon, three school teachers, and three business women. They were all to receive a \"thorough agricultural education and to engage in practical farm work.\" They would then set up farms of their own near Carlisle's. The plan was that each year several more women would join them.\n\nIn 1925 modest press attention was devoted to Carlisle under captions such as \"She Writes and Ranches,\" detailing her first successful crop and the plans for the future\u2014and then no more. The local history entry on the \"farmerettes\" indicates that this was a brief experiment. The entry on the couple ends with the marriage of Miss Goppel in the fall of 1924 to B.F. Rhodes of Cochrane, Alberta, and \"Miss Webber took off for England in November. Returning in 1925 she was on the Walker Ranch, Pine Creek, for awhile.\"\n\nThere are few other examples of women who farmed in \"male attire.\" Mrs. Chamberlain, a widow who established the Chamberlain Ranch at Wood Mountain, Saskatchewan, was one. Many stories were told about her, living without a husband in what was described as a wild and desolate region, where shots could be heard as \"rival bands fought on the ranges.\" This young widow with a daughter reportedly decided it was \"no place for an unprotected woman.\" The only thing she could think of was to \"give the appearance of there being a 'man in charge.' One morning she donned her husband's clothes\u2014and for ten years never wore her women's garments again.\" To the cowboys with whom she had little contact, she was known as the \"Yankee chap,\" and not one \"dreamed that the quiet, almost taciturn, slender little fellow who curtly repulsed all offers of help, was other than a man rancher who preferred to be left alone.\" As her herd grew the \"Yankee chap\" dealt with the traders and buyers, making shrewd bargains. It was not until the region was settled by families that she revealed the \"masquerade.\"\n\nA \"woman who made it alone\" in the Millicent district of Alberta, near Brooks, also \"put on men's clothing and did all the farm work\" after her husband left the farm. She was described in the local history as an odd, eccentric, cantankerous, and amusing diversion from the overwhelming norms of behaviour. Allegedly Jeanette Fleming had decided that her husband had to go back to the United States, as \"there can only be one boss on a place.\" She \"led an independent life,\" and \"her main ambition seemed to be to show the world that anything a man could do she could do better.\" She was recalled as a shrewd bargainer, and her sows raised more piglets per sow than those of her neighbours. She spent hours tutoring the children of the district in mathematics. But overall she was viewed as incompetent: \"Being a woman rancher and farmer, she had her own ways of doing things. At one time she kept 500 sheep and they were being killed by coyotes in the night. To combat this, she got 200 lanterns and hung them on the fence posts to keep the coyotes away.\" She flooded her and a neighbour's land when she attempted to irrigate her own fields. Insisting on never asking for help from her neighbours backfired on one occasion. Fleming was hammering shingles on her roof when her ladder blew down and she was stranded: \"She waved to cars that passed by and people waved back thinking that Jeanette was uncommonly friendly that day. Evening came and she was still up on the roof. Finally someone stopped to investigate and helped her down.\"\n\nPeter Boag concludes in his study of cross-dressing in the U.S. West that it was \"clearly a place and process where gender and sexuality were unstable, contentious and transgressive. It was a place where a wide variety of people who did not conform to gender and sexual expectations lived, loved and died.\" But was this the same north of the forty-ninth parallel? In 1917 at a Liberal convention in Winnipeg, a male farmer delegate objected to a resolution proposing homestead rights for women because \"if a woman settled alone in the midst of men who were homesteading rightly or wrongly her name would be tarnished.\" A single woman farmer would be morally suspect. One who dressed as a man would be even more suspect.\n\nThe 1923 novel _Cattle_ by Winnifred Eaton (Onoto Watanna) provides a hint of the way in which May and Carlisle might have been received by their neighbours. The central character, Angela Loring, is a cross-dressing farmer who broke her own land, put in her own crop, hayed, and fenced. An author and screenwriter born in Montreal of Chinese-British ancestry, Eaton lived on a ranch in the Alberta foothills for some years. Her novel _Cattle_ is a sharp critique of the treatment of and attitudes toward women in an Alberta ranching community Eaton called \"Yankee Valley.\" The woman farmer in _Cattle_ was known as \"Mr.\" Loring in her district: \"Her name, it appeared, was Angela Loring, but some wag had named her 'Mr.' Loring, because of her clipped hair and her working-man's attire, and this name stuck.\" Loring is regarded as a \"strange woman\" because of her occupation and dress and cropped hair, but also because she wants no contact with her neighbours:\n\nThe woman was a \"bug\" pronounced the farm people of Yankee Valley. At all events she was the kind of 'bug' they found it prudent to keep at a safe distance. She had met all overtures of friendship with hostility and contempt. She was on her own land. She desired no commerce with her neighbours. She needed no help. It was nobody's business but her own why she chose to dress and live in this way... Thus she became a sort of bugaboo in the popular imagination, but as time passed the country became used to the woman-hermit and gave her the desired wide berth.\n\nIn the novel the local doctor, a beloved figure in the community, takes a great interest in Loring, seeing feminine potential. He lectures her repeatedly about how her dress and occupation were unacceptable: \"Her cut hair he denounced unsparingly. No lass, he declared angrily, had a right to cut the hair from her head. Her man's clothes were unqualifiedly disgraceful. Her working the field was against Nature.\" Loring takes on a young woman assistant, Nettie Day, a single mother who was raped by Bull Langdon, the owner of the biggest ranch in the district. She too cuts her hair, adopts masculine garb, and works the land. Although there is more than a hint that Loring and Day are devoted to each other, by the end of the novel they have reverted to suitably feminine roles: Loring marries the doctor, and Day marries a neighbouring homesteader.\n\nThat it was not acceptable for women to dress in male attire, even while performing farm labour, was made clear to the British women who were part of the Princess Patricia Ranch experiment in British Columbia. When in 1913 they wore men's clothing while at work on the farm, they were instructed by their sponsors, the Colonial Intelligence League, to desist for fear that they were creating a poor impression in the community. A new rule was passed that residents \"must always wear skirts when working. The wearing of men's clothing is not permitted.\"\n\nIt will remain a mystery why Jack May left her Alberta farm so soon. She had more agricultural experience than the Snowsells, but faced the same challenges. She and Wittrick, like the Snowsells, had to be provided with seed wheat for the crop of 1912. Perhaps she found the press attention and constant visitors overwhelming, although in her own district\u2014at least if the _Sedgewick Sentinel_ is any indication\u2014little attention was paid to May. Did the community welcome or ostracize Jack May? Was she excluded from both the masculine and feminine realms of life in the community of Sedgewick? She may have thought she was travelling to a new setting where gender was more flexible, but she was surrounded in Sedgewick by other British settlers. As mentioned in Chapter 2, in England attitudes were being challenged and were slowly changing, but single women farmers were still viewed with suspicion, as \"unnatural\" women. They were \"not seen as real farmers by men but as inferior others who try to be like men and cannot therefore be taken seriously.\" Jack May was suspect if she demonstrated masculine qualities of \"physical strength, sturdiness, aggressiveness, competitiveness, speaking one's mind and dominance.\" She refused to appear \"slim, fragile, submissive, nurturing, quiet and withdrawn.\" A single woman farmer was not a potential wife, as she did not embody and perform feminine attributes. Louisa Wittrick was a potential wife and could find a place in Sedgewick society, while May could not as long as she farmed and worked in men's attire. Recall the \"girl farmer\" of Surrey, Estelle Long (introduced in Chapter 2), described as living all alone in a two-room hut with a ferocious mottled mongrel dog in a \"dreary and desolate\" spot with a \"double-barrelled gun by her bed and strong bolts and bars to the windows and strong locks to the door.\" In her neighbourhood she was regarded as \"having 'turned witch' or something of that sort.\"\n\nWHY THE ATTENTION?\n\nWomen farmers and ranchers of the Canadian West received a great deal of attention in the first decade or so of the twentieth century, through CPR promotional pamphlets and in the press. Often the coverage drew heavily on the information provided in the CPR publications, suggesting that the articles were engineered by that corporation. A 1907 article entitled \"Women as Farmers: Success of Some Who Have Taken Claims in the Northwest\" appears to have been based on a CPR pamphlet. The article featured Mary Gilroy and others, and was placed in newspapers as distant as New York, Michigan, and South Carolina, as well as in the Western Canadian press. \"How Four Plucky Women Won Out in the Canadian Northwest,\" which appeared in the _Minneapolis Journal_ in 1906, also drew a great deal on the CPR promotional publications.\n\nA 1910 article by Cynthia Westover Alden in the U.S. _Farmer's Review_ drew on some new examples under the headline \"Prosperous Women Farmers.\" Alden reported that she met half a dozen women farmers on her recent trip through Western Canada who were \"typical of what a woman can do.\" There was the \"clever widow\" of Saskatoon who was originally from Iowa, had invested in land, and made $50,000 in the last year. A woman known only as \"Mother\" in her district had a blind husband, and she had \"carved her fortune from the soil,\" creating a farm worth $20,000. A farmer still in her twenties \"intended to retire in the fall after her wheat was threshed and sold, having made a sufficient fortune to live on the rest of her days.\" Alden wrote that everywhere she went she \"talked with sun-browned and sturdy women who had as keen an eye for good soil and good crops as any man.\" She concluded that \"if a woman has enough capital to tide her through the first year, and wishes to be independent, she should go back to the land and use her brains and muscle as these Canadian women I met and as hundreds of them are doing every day.\"\n\nDespite the happy impression left by authors such as Alden that there were numerous \"prosperous\" women farmers in Western Canada, agriculture and farm ownership on the prairies was overwhelmingly a masculine domain and enterprise. These women illustrated what women could do, and created an impression of a welcoming, even liberating, environment, but they were fairly exceptional cases, and most of the women had been obliged to purchase their land rather than obtain it through homesteading. Why the concerted efforts to present this positive impression and to make relatively rare cases appear typical or representative? This was not unusual or unique to Western Canada; Australia too had celebrated women agriculturalists. Articles such as \"Lady Settlers in Australia\" featured Geelong sheep farmer Anne Drysdale, \"an elderly maiden lady from Scotland,\" who had rented a farm in Scotland before settling in Australia in 1840 for her health. The sheep farm was run in partnership with Englishwoman Caroline Newcomb, and together they lived in comfort and prosperity in a fine stone mansion overlooking Port Phillip Bay. Other examples of successful women agriculturalists in Australia included Eliza Forlonge (\"Mother of the Australian Wool Industry\"), Janet Templeton, Elizabeth Macarthur, and Mary Penfold, and unlike in Canada, many are still remembered and even celebrated today. (The Penfolds are still in the wine, port, and sherry business.) Some of these women were married, but with husbands absent from the colony. Women who owned or leased land and farmed independently however, were the smallest group of rural women, according to an economic history of women in Australia from 1788 to 1850, and very few were recorded as farmers or landholders in documents such as censuses of the period.\n\nThe CPR had an obvious interest in promoting the idea that Western Canada was a welcoming environment for women who wanted to farm, in order to compete with the United States, where single women could obtain homestead land, and to promote the sale of railway land. Some of the attention paid to women farmers came from journalists interested in encouraging women to pursue occupations that could provide them with independence outside of marriage. Most of the women farmers, however, were carefully depicted as maintaining femininity even while they undertook labour seen as masculine. The attention paid to Isobel \"Jack\" May, however, is of a different nature and scale. She traversed boundaries of proper femininity in her male attire, challenging and conflicting with norms of white British femininity. Her exploration of an alternative femininity, her behaviour, and her appearance served to confirm these norms, helping to define and articulate what was going to be considered acceptable and unacceptable in this society in the making. And there was to be little space and scope for the woman farmer.\n\nEven without male attire, the \"bachelor girl\" was suspect and unwanted. In 1912 the Alberta newspaper the _Redcliffe Review_ warned that the \"gay, careless life of the bachelor girl is apt to make her self centred and self absorbed. She grows selfish... and before she knows it life will not be full of bloom and fragrance. There will be barren spots. It will begin to take on the hue of the desert. And unless she heeds these signs of the times she will come to a rather desolate old age.\" While women who could afford to purchase land avoided the scrutiny of the homestead inspector concerned about their marital and parental status, they were still subject to intense pressure to conform to the norms of acceptable feminine behaviour and attire. \nCHAPTER FIVE\n\nANSWERING THE CALL OF EMPIRE\n\nGEORGINA BINNIE-CLARK, FARMER, AUTHOR, LECTURER\n\nIn August 1905, Georgina Binnie-Clark was a thirty-three-year-old writer with no farming experience when she impetuously bought an \"improved\" farm of 320 acres in Saskatchewan, despite having been in Canada for only a few weeks and despite the advice of family members who told her it was the \"maddest thing which you have ever done.\" Just a few years later she had become the most vocal advocate of \"Canadian Farms for English Spinsters\" and was well-known for this cause in Canada, Britain, and beyond. Through her writing and lectures, her farming and training of young Englishwomen agriculturalists, Binnie-Clark expressed her allegiance to the British Empire and asserted the superiority of the British, who she assumed should have a privileged status in the colonies. She was part of and a product of the female imperialist network who contributed to the journal the _Imperial Colonist_ and who believed that the British Empire was a force for great good in the world. Binnie-Clark also exemplified the new type of woman farmer that began to emerge in England at the turn of the century: not the daughter or widow of a farmer carrying on the family business, but \"the unmarried, middle-class educated townswoman, drawn to farming as a profession in which she could potentially secure health, happiness and an independent income.\" For Binnie-Clark this was to be accomplished in prairie Canada, and she made it her business to encourage others to follow her lead. While the celebrated farmers of the last chapter, many of them British, may have shared Binnie-Clark's enthusiasm for the cause of the British Empire, no records of them remain aside from the press coverage, and their degree of devotion is not clear. But for Binnie-Clark the cause of the Empire was paramount.\n\nBinnie-Clark was more radical than other \"genteel\" women pursuing a life on the land in that she was not content with the \"lighter,\" feminine branches of dairying, poultry raising, and horticulture; she was a wheat farmer who required a large acreage, and she advised others that this was the wisest and most profitable approach. She was determined not only to farm herself, but to publicize and promote opportunities for interesting and rewarding work for educated women in the colonies, particularly agriculture. Binnie-Clark detested housework and appeared to have no interest in marriage. She contended that women were capable of all categories of farm work. She pursued a demanding sphere of farming that was identified as male. Yet unlike farmer \"Jack\" May, Binnie-Clark performed her femininity in her lectures by wearing fashionable gowns, and in her writing she adopted a modest and self-deprecating tone. As she wrote in one of the final passages of her book _Wheat and Woman_ (1914),\n\nThe faithful chronicle of one's own difficulties may at first thought appear but a poor foundation for one's hope and firm belief that agriculture will prove to be the high-road and foundation of wealth and independence for Woman, but the strength of a chain is its weakest link... I had no training, inadequate capital, and my commercial instinct, though strong in theory, is weak in practice\u2014I fail to hold my own in buying or selling... but in spite of this I am still behind my conviction that three hundred and twenty acres of good land in Canada can be working to produce a net profit of \u00a3500 per annum to its owner, [and] my weak link is very much stronger.\n\nIMPERIAL DREAMS\n\nA devoted imperialist, Binnie-Clark counted herself among those who were \"fighting out the battle of our Empire with the pick and spade on unbroken soil.\" She was charmed by Quebec City, as it was \"stamped with associations which bear the glorious seal of dauntless, deathless, effectual moments in our imperial history, when we English knew how to fight for causes.\" She was devoted to the \"Mother Country\" and saw herself as helping to rear the \"daughter nation\" of Canada, \"our most important colony.\" Western Canada was \"unbroken soil,\" a mutable environment, a tabula rasa. In eloquent passages Binnie-Clark described the beauty of the prairie in all seasons\u2014its vastness and emptiness. This was a blank slate, a white sheet, where educated women from England \"would use their inherent personal advantages to carve out strong roles and identities for themselves in the mutable environment of the colonial frontier, to civilise and extend the boundaries of the British world.\"\n\nBinnie-Clark shared the view that the British Empire would uplift the \"darker\" races, but this was not her main concern or issue. She devoted only passing attention to Indigenous people in her writing and appeared to know little about them, even though her farm was located on Treaty Four land of the Cree, Assiniboine, and Saulteaux, who were relegated to reserves not far from her property. The non-treaty Dakota (Sioux) were also close neighbours. Her message was similar to that of Lally Bernard\/Mary Agnes Fitzgibbon: that Canada was a \"white man's land from end to end,\" and the solitary woman farmer had nothing to fear. Her first book, _A Summer on the Canadian Prairie_ (1910), conveyed a typical settler mentality that much was being done to \"graft civilization on the aborigines of our colonies with generosity and excellent intention,\" but that they refused to live in the good houses or till the good farms they were given. A photo in that book of \"An Indian's Home on the Prairie\" illustrated this point; they were content to live the way they always had, refusing to take advice and farm. An unstated message of the photo was that the land was now in much better hands, for settlers such as Binnie-Clark and other British and Ontarian colonists would cultivate, transform, and altogether improve the acres that until then were dormant. The Treaty Four First Nations had in fact been attempting to farm their reserves since 1874, but faced overwhelming obstacles, including government policies that limited their enterprise to farming tiny holdings using only rudimentary implements, drastically reducing their acres under cultivation and discouraging interest in agriculture. Just at the time Binnie-Clark arrived, Indigenous people were coping with a federal government determined to divest them of most of the best land on their reserves through dubious, and often illegal, land \"surrenders.\"\n\nIn _Wheat and Woman_ (1914), Binnie-Clark praised the work of missionaries, both Catholic and Anglican, for their \"brave, unselfish, dauntless\" work. She was particularly keen on the Roman Catholic industrial school for Indigenous children at Lebret in the Qu'Appelle Valley. She approved of the boys being taught useful trades, working in the farm and gardens of the school, so that they would be able to \"take possession of the opportunities civilization brought to the wonderful treasure-land of their fathers.\" All were acquiring \"good manners,\" and the priests and nuns had \"most truly bestowed on the children of the darker race the consolation of religion.\" Yet she admitted a tinge of regret that they had been robbed of their liberty. During a visit to the school \"one glorious summer afternoon,\" she was present when the children were let out to swim and saw how they clearly loved the freedom and release from the confinement of the school: \"Suddenly there was the impression of the opening of a great big door and a sense of wide liberty, followed by the crescendoing chorus of joy\u2014then the patter of many bare feet treading the path of pleasure.\" She wrote that when she left after a visit to the school and was back on the trail by the lake, enjoying the scents and scenes of an evening on the prairie, breathing the \"air of liberty,\" the \"fascination of life in the open tugs at the heart-strings [and] you know that the children of Hiawatha pay the price for those opportunities of civilization.\"\n\n_Figure 26._ From Georgina Binnie-Clark's _Wheat and Woman_ , this is a carefully staged photograph of students at the Qu'Appelle Industrial School, allegedly with their parents. It was intended to illustrate the dramatic contrast between the old and young generations. The caption is the original from her book and refers to Rev. Joseph Hugonnard, the principal of the school. Her farm was located not far from the school, on the Treaty Four land of the Cree, Saulteaux, and Assiniboine. A reserve of non-treaty Dakota was also located near Fort Qu'Appelle. Georgina Binnie-Clark, _Wheat and Woman,_ 70.\n\nYet a photograph included in _Wheat and Woman_ of four industrial school children with two elders was one of the propaganda images that the Department of Indian Affairs used to demonstrate the contrasts between the old and new generations, conveying the message that being robbed of their freedom was in the children's best interests. They too were the children of Mother Britannia, but they were in need of a stern but kindly guardian. The Indigenous people of Binnie-Clark's district, in her account, were tame, contained, and unable to travel freely as they had, but they were the beneficiaries of colonization. Although this photo emphasized several generations of women, there was almost no mention of Indigenous women in Binnie-Clark's books or articles, and her concerns for women's rights to homestead and farm did not extend to them. In _Wheat and Women_ she mentioned an Indigenous woman once. She was \"Soo\" (Sioux) and had walked from her \"village\" (presumably the Standing Buffalo reserve) to the Catholic mission at Lebret on Easter morning. Her name was \"Tosh,\" and she was deeply religious. Easter day was, according to Binnie-Clark, \"a beautiful oasis in her life.\"\n\nSome M\u00e9tis men of the Fort Qu'Appelle district were her only Indigenous acquaintances, according to her books, and she hired them to fence her land. (She praised their work, as they did the job thoroughly, and she could pay them by the mile, whereas she had to \"feed white men and pay them by day or week for the same job.\") Overall, however, Binnie-Clark's writing was not characterized by the same degree of pejorative, negative descriptions of Indigenous people that were to be found in the publications of many of her contemporaries, and she may have been trying to challenge misconceptions and assumptions. When her suspicion that two \"half breeds\" had stolen her bag of oats proved untrue, and they actually helped her find the oats and hoist them onto her buggy, she \"vowed to scorn suspicion and colour prejudice for evermore.\"\n\n_Figure 27._ The caption \"Victoria Day (Now Empire Day) at Fort Qu'Appelle, 1912,\" conveys the message that the Indigenous people of the West are loyal and grateful to the British Empire. A devoted imperialist, Binnie-Clark believed that the Empire would uplift what she called the \"darker\" races. Photographs of wheat fields, threshing, and other scenes of the prosperous future of the region constituted sharp contrasts to those of Indigenous people, representing the past. Georgina Binnie-Clark, _Wheat and Woman_ , 178.\n\nQUESTION MARKS: FAMILY HISTORY AND FICTION\n\nBinnie-Clark seemed an unlikely candidate for the calling and cause of agriculture for Englishwomen in Western Canada. She was born in 1872 in Sherborne, Dorset, the third child of Arthur Walter Binnie Clark, the son of a labourer. Clark was a valet to George Winfield Digby at Sherborne Castle when in 1866 he married Georgina's mother, Maria Setheby, the daughter of a gamekeeper. The Binnie-Clarks were proprietors of the Digby Arms Hotel in Sherborne. Georgina's father had prize-winning horses, and she once said to a journalist that her \"only previous farm experience had been as a girl on her father's farm in Dorsetshire, England where thorough-bred horses were bred and reared.\" In the 1891 census, \"Georgina B. Clark\" was a music student, aged nineteen. Other clues of her life before arriving in Saskatchewan are few, but they include a passage in _Wheat and Woman_ where she wrote that she had \"an intimate knowledge of the life of the educated working woman in Germany, Paris and in England,\" and that she had \"lived with and amongst women-workers.\" In one of her 1909 articles, Binnie-Clark wrote that before she farmed she \"lived for art alone, studied music on the Continent, and latterly became a writer. I visited Canada in 1905 for the purpose of securing 'copy'\u2014and stayed to farm.\" Georgina may have been the first (and possibly only) member of the family to hyphenate her last name. Her brother Louis, for example, signed his name \"Louis B. Clark.\"\n\nThere remain significant gaps in understanding important aspects of Binnie-Clark's life, such as where she was educated, how (or indeed whether) she established a reputation as a journalist, and exactly what she did and where she lived before her arrival in Canada in 1905. It is important to emphasize, as historian Susan Jackel points out in her 1979 introduction to a reprint of _Wheat and Woman_ , that it is not clear whether the information provided in Binnie-Clark's own books about herself, her family, and her farming is entirely reliable. But according to her first book, _A Summer on the Canadian Prairie_ , she ventured to the Canadian West to visit her brother (Louis, who is \"Lal\" in the book), who was a homesteader near Fort Qu'Appelle, Saskatchewan. Perhaps she was influenced by Flora Shaw's call for sisters to join homesteading brothers. But as stated above, she wrote that she was a writer in search of \"copy.\" She purchased a farm of 320 acres just a few months later near Fort Qu'Appelle, complete with a house, outbuildings, fencing, and crops. It is not completely clear what she paid for it, but in a 1908 article, \"A Woman's Way on the Prairie,\" Binnie-Clark described how she had to pay for her farm in five instalments each of \u00a3200 ($1,500.00). (In _A Summer on the Canadian Prairie_ she wrote that the farmer who sold her the farm demanded $5,000, with $1,000 down, another $1,000 when she sold the wheat of the 1905 crop, and the balance at 6 percent.) Also, according to _A Summer on the Canadian Prairie_ , she required from her father \"sufficient funds to cover the greater part of the first instalment,\" although she signed the papers without securing her father's permission, claiming she had sufficient income (presumably from her writing) to guarantee the payments. The book also indicates that she purchased the farm initially thinking it would be in partnership with her brother and possibly sister, as she uses the pronoun \"we.\" When there finally was communication from their father, he had included only \u00a3100 and stated that \"on no condition whatever were we to buy land.\" Georgina then, according to _A Summer on the Canadian Prairie,_ declared she would borrow from her father on the security of the income her work in England would bring her, and run the farm herself. In one of the final passages of the book her homesteading brother tells her, \"Ha, ha! A woman work a Canadian farm! Why you would be the laughing-stock of the country, if you could do it, which you can't.\" She set out to prove them wrong. She also had to prove that she could finance the farm through her writing.\n\n_Figure 28._ Georgina Binnie-Clark, writer, lecturer, and Saskatchewan farmer. She purchased 320 acres near Fort Qu'Appelle in 1905 and became devoted to the cause of English women farming wheat on the prairies. Courtesy Mr. Dennis Jenks.\n\nAs mentioned, Binnie-Clark's own accounts are not entirely reliable if searching for the facts. She changed the names of her family members, her neighbours, and hired men. \"Lal,\" for example, in _A Summer on the Canadian Prairie_ , was her brother Louis. His homestead records indicate that he was married and that his wife lived with him on his homestead from March 1906. Yet Lal is presented as a lazy bachelor who wants to abandon his homestead, and Georgina is the one to insist that he stay and prove up. (Louis filed on his homestead of 160 acres in 1904 and proved up in 1907, which meant that he must have been acceptably industrious, as many homesteaders took much longer.) Binnie-Clark's sister, called \"Hilaria,\" must have been Ethel, but if so, it is likely not the case that she hated the rural prairies and farming in the way Binnie-Clark described, as Ethel became a much more permanent resident of the farm than her sister, staying on after Georgina's death in 1947. But for her narrative, it is important to develop Hilaria's distaste for farm life on the prairies, which forms a contrast to Georgina's growing fascination with the West and wheat. And through Hilaria's efforts to find a job as a nurse and domestic servant, readers learn about the limited options for single women in Canada.\n\nTHE CANADIAN WEST IN 1905: PROFITS AND PREJUDICE\n\nArriving in Canada in 1905, Binnie-Clark absorbed the heady atmosphere of optimism about the future that prevailed at that time. The new provinces of Saskatchewan and Alberta were created that year. That season there was a \"bumper\" crop. An editorial in the _Progress_ (Qu'Appelle, Saskatchewan) of 20 July 1905 entitled \"A Halo O'er the Grain\" began, \"Still, the grain keeps growing. Night and day the farmer's profits are swelling, silently, surely. Everywhere is seen the bright and hopeful light of joyous anticipation of the largest crop in the history of the West.\" Binnie-Clark quite likely read this newspaper and was inspired by this editorial as she visited her brother nearby. It concluded by noting the \"stimulus in the air, a spirit of hope in every heart, that causes the prophetic imagination to look into the future when the vast prairie will be teeming with a population of untold millions, when the rich soil shall be made to yield a harvest sufficient to feed the world and when the riches wrested from Mother Nature shall be utilized in revitalizing the afflicted, civilizing the boor, and bettering mankind generally.\" Binnie-Clark became mesmerized and infatuated with wheat, a \"tall mass of living loveliness.\"\n\nThat same year\u20141905\u2014Frank Oliver was appointed Canada's minister of the interior, in charge of the administration of Dominion (homestead) land. As mentioned in Chapter 3, Oliver was a Liberal member of Parliament from Edmonton, he was devoted to the cause of the development of the West, and he was sceptical that women landowners and farmers had any role to play in that development. He was also made superintendent general of Indian Affairs and doggedly pursued the diminution of First Nations reserves, particularly when they occupied superior agricultural land that was close to a railway. Oliver believed that Indigenous people had no role to play in the development of the West either, and that they retarded and undermined the process and progress of settlement. Intense pressure was placed on the people who occupied reserves in the Fort Qu'Appelle area to surrender their land, particularly where it bordered the main line of the Canadian Pacific Railway (CPR). In many cases this pressure succeeded. In 1907, for example, after relentless pressure from Department of Indian Affairs officials, almost 54,000 acres of reserve land on the Crooked Lake Indian agency was alienated.\n\nIn 1905 Binnie-Clark would have quickly learned of another obsession of the time in Western Canada. The \"immigration peril\" was a concern shared by many of the British and Ontarian settlers, who were the first homesteaders in her district. Icelanders were tolerated, according to a 1905 editorial in the _Vidette_ of Indian Head, Saskatchewan, as they were \"superior and intelligent, and are closely allied with the Anglo-Saxon element of our own country.\" But people such as the Doukhobors from Russia and the Galicians (Ukrainians) were another matter. The editorial concluded, \"Canada wants no new race and language difficulties; she wants no elements that she cannot assimilate readily.\" A Presbyterian reverend was quoted in a column in the same paper a few months later, asking, \"How are we going to maintain in this new land, which we proudly call 'the Great Britain Beyond the Seas,' those principles and usages and ideals that have made Great Britain so strong and prosperous and influential? We have inherited the genius of the Anglo-Saxon race, a genius that is the product of the thought and toil of a thousand years.\"\n\nWanted were Ontarians (of British ancestry) and settlers from Britain, as another Presbyterian reverend, James Farquharson of Winnipeg, wrote in 1910: \"The multitudes moving from the Eastern provinces of Canada to the West come to us with ideals much like our own. They are of the same race, they glory in their allegiance to the same government, they acknowledge the same moral standards, they worship God in the same manner. There is rejoicing also in the arrivals from the British Isles, for they, like ourselves, are Celt or Saxon; their literature is ours... they and we are one in claiming as our own the past, the present and the future of the British Empire.\" By contrast the Ukrainians, according to Farquharson, had many \"defects of character,\" including their \"carousals, their drunkenness and brutal fights,\" as well as \"the readiness with which the lie comes to their lips.\"\n\nThe Doukhobors were singled out for particularly harsh condemnation because the women of these communities hitched themselves to ploughs in teams and performed other outdoor labour. Photographs of these women workers were widely published with the clear message that these women were little more than beasts of burden. A description by journalist Jean Blewett was typical, and began with the statement, \"The Doukhobor woman is no Venus... hard, incessant work does not tend toward beauty of face or form.\" Doing men's work out of doors made them masculine. Blewett continued: \"Taking her place at the plow while the first furrow is turned in the spring, planting, hoeing, making hay, harvesting the grain, threshing and grinding the same, doing the whole year round a man's work, had given her the figure of a man. She has muscles instead of curves; there is no roundness or softness visible. The sun has burned her face brown and her eyelashes white. Her hands and arms are the hands and arms of a working man.\" An 1899 article entitled \"Women Harnessed to Plows in Manitoba\" in the _Woman's Journal_ (Boston) admonished the Canadian government for not having taken steps to eradicate this practice, and predicted that \"sooner or later some official action will be demanded by the daughters of civilization in neighbouring communities regarding the subjection of their Russian sisters to slavery and drudgery in the harvest field.\" Binnie-Clark had to confront and contend with these attitudes, as she maintained that British women ought to take up land and perform farm labour. The example of the Doukhobors, however, became useful to supporters of homesteads-for-British-born-women, who argued that the West would then be rid of the \"foreigners\" who treated women in this manner.\n\n_Figure 29._ Doukhobor women pulling a plough in Saskatchewan, 1902. There was widespread condemnation of the \"slavery and drudgery\" Doukhobor women were \"subjected\" to, although this was not how these women saw their own contribution to the establishment of their farms. Women working in the fields was an aberration to be expunged in the course of establishing the West as a corner of the British Empire. Binnie-Clark had to contend with these views as she called on Englishwomen to farm the prairies. Glenbow Archives, NA-670-45.\n\nCHAMPION OF THE CAUSE IN ENGLAND\n\nAlthough Binnie-Clark spent stretches of time on her Saskatchewan farm, she also frequently returned to England. According to a 1912 newspaper interview, she spent every winter in England (aside from the winter of 1906\u20137 that she often lectured about.) Her sister Ethel was the more permanent resident of the farm, and brother Arthur Cameron Binnie Clark also helped out. (He died in Fort Qu'Appelle in 1921.) As Susan Jackel admitted, it is also not clear for how many years, and precisely when she was resident on her Saskatchewan farm.\n\nBinnie-Clark never entirely switched her allegiance or her abode to her Saskatchewan farm and to Canada. She had a flat in London's Chelsea district on Cheyne Walk, on the Embankment with a view of the Thames, from at least the First World War to the late 1930s, although there were times when the flat was rented out. Chelsea, and in particular Cheyne Walk, is a district that has long been associated with writers, artists, and activists, and Binnie-Clark was part of a literary and artistic circle that included a very good friend and neighbour of hers, Dame Ethel Walker, a leading British painter of her day. Walker also lived at the south end of Cheyne Walk on the Thames. Walker, best known for her portraits of women, is today recognized as one of a \"large number of significant twentieth-century European artists [who] focused on gay, lesbian and transgender themes.\" Another close neighbour on Cheyne Walk was prominent feminist Sylvia Pankhurst. Although in a \"posh\" area today, Binnie-Clark's accommodation was modest; she described hers as the \"vagabond end\" of Cheyne Walk.\n\nAccording to her own accounts and from evidence found in family papers, Binnie-Clark's financial situation was always precarious. She had to write, lecture, and take in students to sustain herself and her farm and to purchase the labour she required. She had to learn to milk, make bread, clean out the stables, pickle seed, stook, and to do numerous other chores that she could not afford to have done for her. Binnie-Clark described herself as \"desperately short of money\" in the winter of 1906\u20137, and in later correspondence wrote that she was \"always more or less hard up.\" It does not appear that her financial situation ever dramatically improved. (In 1936, for example, she wrote from England to a Fort Qu'Appelle acquaintance asking for the twelve dollars she had loaned her five years earlier.) She did not enjoy the power and privilege bestowed upon men, as she did not qualify for a homestead because of her gender. She was genteel but not well-to-do, and she had to support herself. She would not have been recognized as superior or elite in the Saskatchewan community she adopted; she was keenly aware of her status as an eccentric \"green\" Englishwoman. She cast herself, however, as well above the people of London's East End, whom she encountered (for the first time, it seems) in an immigrant shed in Quebec in their \"grotesque attire\" and \"squalid degradation.\" Yet she was critical of what she described as \"the creed of every Englishman to dislike or at best tolerate foreigners.\" She described the Hungarians who settled near her brother, for example, as generous and industrious; they commanded her \"unqualified admiration.\" She cast herself as much more tolerant than her brother, who, she wrote, \"imagines he detests them.\" Her admiration did not extend to \"Chinamen,\" as she called them, providing in _A Summer on the Canadian Prairie_ her version of the familiar \"no ticky no washy\" story.\n\nBinnie-Clark began to attract public attention during a visit to England in 1908 (leaving her farm in the charge of a couple from England), when she started to write articles for the _Canadian Gazette_ , published in London, which was a weekly journal aimed at a British readership but consisted of information concerning Canadian commerce, investments, emigration, and Canadians in the metropole. Initially, Binnie-Clark's cause was not the homestead grant for women, but to encourage others among \"the class of English gentlewomen from whom she sprang,\" as well as those of a \"lower social grade,\" to \"follow her pathway to the Canadian West,\" which would be of \"infinite benefit to themselves, to the country the relief of their superfluous presence, and to Canada which stands in need of their help in the upbuilding of a vigorous nationality.\" The message was that an Englishwoman who was \"frittering away her life in trivialities may find new life and a career of independence in prairie farming.\" According to a February 1908 editorial on \"The Woman Problem\" in the _Canadian Gazette_ , Binnie-Clark demonstrated \"the satisfaction a cultured Englishwoman may find in the life of a prairie homestead which she herself manages, rearing live stock, growing wheat, and thereby bringing to herself both money and a healthy, satisfying independence.\" In her columns she mentioned other opportunities for \"gentlewomen\" in Canada such as nursing, teaching, and housekeeping, but argued that \"land-work is far higher than housework, certainly more interesting, and there is no reason at all why women should not adopt it as a healthy, practicable and highly remunerative occupation.\"\n\nBinnie-Clark's first series of articles in the _Canadian Gazette_ , \"A Woman, Two Boys and \u00a3140,\" was in the form of letters to a prospective woman homesteader, a widow with two sons. She advised \"Mrs. Huntingdon\" to head to the prairies, despite the fact she had such limited capital, because she could claim her own homestead, and once her sons reached the age of eighteen they too could claim 160 acres each. Binnie-Clark provided details on a myriad of topics relating to emigrating and establishing a farm on the prairies. A subsequent series, \"A Woman's Way on the Prairie,\" was the story of her own farm, to be told in greater detail in _Wheat and Woman_ in 1914. As in her book, she did not try to conceal her mistakes, misfortunes, and calamities. Her point was that \"what I struggled through uncomfortably the woman of average intelligence and domestic habit can do at her ease.\" Nor did she disguise the horrors of the cold and \"sea of snow\" of her first winter, although she wrote that she \"never knew a dull or unhappy moment.\"\n\nThe story Binnie-Clark told in her articles, on the lecture circuit, and finally in _Wheat and Woman_ was that her first year's harvest realized \u00a3200, but that this was followed by a harvest of wheat that was infested with wild oats and a third harvest damaged by frost. She learned that she had to be very economical with her money, that the farm had to entirely supply the household, that effort had to be put into butter that could be sold, and that there was always a market for pigs. Her message was that it was still possible to make a living out of farming even if grain crops failed.\n\n\"A POWERFUL FACTOR IN THE STRENGTHENING OF THE EMPIRE\": ORIGIN OF THE HOMESTEADS-FOR-BRITISH-WOMEN CAMPAIGN\n\nBinnie-Clark's 1908 articles in the _Canadian Gazette_ led to many inquiries addressed to her concerning women's immigration and settlement in Western Canada. She reported that \"women of small capital earnestly seeking a means of self-support\" were \"constantly applying to me.\" One letter was from \"a little band of six who contemplate coming out with a capital of \u00a3500.\" Another was from \"a single woman with a capital of \u00a3100 only... [who] wrote to Mr. Obed Smith asking if I could obtain a Government grant of 160 acres, and was most surprised to find that the Canadian Government does not consider the claims of a mere spinster; as for getting land here [in England]\u2014well, the more progressive dailies have fought the battle for years of 'back to the land' in the interests of _the men_ only.\" Binnie-Clark's own rising debts and poor crops had demonstrated that women who had to purchase their land, rather than being able to take advantage of the homestead grant, were at a decided disadvantage from the start.\n\nIn a November 1908 article entitled \"A Woman's Plea from the West,\" Binnie-Clark first wrote of the inequities of Canada's Dominion lands legislation, that land was granted to a woman only if the sole head of a family, and not to single women. And it was here she first proposed her \"trial scheme\" for Englishwomen. She called on the Canadian government to grant \"say, twelve quarter-sections annually for three years to women selected and approved by the English agent and at the end of the time allow the result to determine further arrangement.\" She was brimming with enthusiasm and optimism for the idea, and offered to promote and organize the scheme in England, writing: \"The idea is original and full of interest to the world at large; it means advertisement and later it will mean an inestimable investment of English capital in Canadian land. Surely it is worth a little further consideration. As against all the male immigrants you have known to turn out failures, have you ever heard of an Englishwoman immigrant failure?\" An editorial in the _Canadian Gazette_ supported Binnie-Clark's pleas on behalf of homesteads for women, and called on the Canadian minister of the interior Frank Oliver and the other cabinet ministers to grant land annually for three years to carefully selected and approved Englishwomen. The editors wrote that \"the West stands greatly in need of women, and we believe it would be an act of wisdom to give the encouragement of free homesteads to women who have the capital, the independent spirit and proven capacity.\"\n\nIn November 1908 Binnie-Clark wrote from her farm (which she had named \"Binning\") to the Department of the Interior in Ottawa to ask that officials \"give personal consideration to the idea of 'Free Homesteads for Women,'\" articulating many of the rationales and arguments she had begun to present in her articles and that she would later develop. She stated her articles had generated a lot of correspondence from Englishwomen eager to follow her lead, and she reported that \"as a rule they have agricultural experience. I was a writer.\" These women had \"slender\" capital and for them the purchase of land was out of the question, but \"given a free homestead, two or three women farming together in a combined capital would be certain to do well.\" Here she first penned a sentiment she would use in the future, that \"if they [Englishwomen] do not get through as much work as a man in a day, they will get through considerably more in a season.\" Women, she argued, would not have the inclination or opportunity to \"roam around during the off season\"; they would instead pursue stock raising and dairy produce on their homesteads. \"The woman's homestead,\" she wrote, \"will be Home, the centre of life and interest. Schools, Churches, other agents in the process of civilized settlement of the country, can only gain in the woman settler.\" The \"class\" of women she had in mind were \"chiefly those who, in England, come under the category of working-gentlewomen, women of education\" who had capital and had attended an agricultural college or worked on a dairy farm. Binnie-Clark proposed that the government offer a limited number of homesteads to Englishwomen of capability and capital. She was certain that \"the experiment would succeed beyond imagination,\" and that in time it would become law. She was also certain that the offer would be received in the Old Country with the \"greatest enthusiasm on the part of all.\" She saw the only barrier to be \"the law\" and wrote that \"the laws of a Liberal government are always awaiting expansion, and the ear of the true law-giver is always alert for this whispering of Reason.\"\n\nSuperintendent of Immigration W.D. Scott replied swiftly, politely, but firmly and curtly that Binnie-Clark's letter was received and that \"I have noted your arguments in favour of giving homesteads to unmarried women, but unfortunately the law does not allow this and the Department does not make a law and has no power to alter it in this particular.\" Yet this reply did not deter Binnie-Clark, and on her way to England late in 1908 she visited Winnipeg, where she learned that the cause of homestead rights was being pursued by women there. She also stopped in Ottawa, where she had an appointment with Frank Oliver, although he did not keep that appointment. According to her account in _Wheat and_ Woman, she met with a deputy minister who simply said: \"She can't.\"\n\nThat year a similarly intransigent man was appointed to an influential position in London, and he would become Binnie-Clark's nemesis. In 1908 J. Obed Smith was appointed assistant superintendent of immigration at Canada's London office. He had served as commissioner of immigration in Winnipeg for the previous ten years. Smith was born in England, had homesteaded in Manitoba, and was a lawyer. From the London office, Smith was in charge of emigration to Canada from Europe, and he occupied this position until his retirement in 1924. He was a loyal Liberal. He promoted migration within the Empire, calling on \"the great colonizers of the British race to give up the comfort of an English home and put on the glorious armour of courage and of hope, in order to carry forward British civilization and push back the fringe of the wilderness a few feet each year.\" Yet, as will be discussed later in this chapter, he was utterly opposed to the idea of women farming on their own in Western Canada, whether they were from England or elsewhere. He remained adamant that women migrants could perform only the \"humbler duties of domestic work,\" and worked to ensure that domestic servants were secured for Canada.\n\nIt is interesting that like Frank Oliver, J. Obed Smith was implicated in land speculation. In 1907 there was a case heard at Winnipeg in which it was found that Smith was engaged in land deals, admitting that he had used knowledge of land values learned through his position to \"make a little money on the side,\" despite having taken an oath as a civil servant that he would not \"disclose without due authority any knowledge which came to him by reason of his office.\" Smith had been named in a lawsuit by parties to whom he had sold land. In 1907 the opposition in the House of Commons demanded to know \"whether an official receiving a salary of $3000.00 a year was to be permitted to engage in land speculation to the detriment of his attention to his public duties, using official information for the purpose.\" Smith's acts were, it was claimed, \"unconstitutional.\" The Liberal government, however, contended that this was not a violation of his office, that it was an isolated transaction, and that Smith was attentive to his duties. But perhaps this scandal was why Smith was sent overseas.\n\nBinnie-Clark kept up the pressure in her articles, beginning with \"Homesteads for Bachelor Women\" in February 1909, which started with the argument that the advent of single women homesteaders on the prairies would lead to the quick establishment of schools and churches and other markers of civilization. Through marriage they would bring an end to the preponderance of bachelor men, and rear the next generation: \"free homesteads to women will be a powerful factor in the strengthening of the Empire.\" Binnie-Clark asserted that \"there are many ladies in England who, from their knowledge of agriculture, would prove very successful farmers on the prairie, and to others the granting of free homesteads would open the way to relief from a life of genteel drudgery.\" Answering the question of whether she truly believed women were physically capable of working a homestead, Binnie-Clark wrote that the most progressive farm in her district was, to a large extent, run by a woman whose father was growing wealthy through her efforts. This woman \"breaks the land, discs and harrows, and thinks nothing of milking from five to ten cows daily, in addition to her other labours.\" (This may have been the family she referred to as the \"Mazeys\" in _Wheat and Woman._ ) She drew on this example in subsequent talks and articles, pointing out that this Canadian woman had no claim to the 160 acres \"which her Government grants to a male of any nation.\" Here is the beginning of the argument that was to take centre stage in the homesteads-for-women campaign in the West that Binnie-Clark helped to galvanize: that British and British-Canadian women were more deserving of homesteads than were \"foreign\" men.\n\nOther of her articles appeared in English journals such as the _Quiver_. In \"How Canada Welcomes the Emigrant Girl,\" Binnie-Clark wrote about staying at the YWCA in Winnipeg and visiting the \"Girls' Home of Welcome,\" and how she met other women immigrants from the \"Old Country.\" She encouraged one young woman from Ireland, who was working at the YWCA but had \"done all sorts and conditions of farm work,\" including ploughing, harrowing, and stoking, to consider farming on a cooperative plan with two or three other women. There were high wages paid for women's labour, and women who pooled their resources could afford to purchase land that was \"a safe and sure investment.\" Once the government realized this would help to benefit the country, \"it would extend to women the free grant of 160 acres of land, now limited to men and widows.\"\n\n_Figure 30._ Press coverage from 1910 of Georgina Binnie-Clark's activities in England and Canada to promote farming for Englishwomen on the Canadian prairies. Both are from the _Gleichen Call_ (Alberta): \"Are Booming Canada,\" 9 June 1910, 7; \"Making Girl Farmers,\" 21 April 1910, 7.\n\nBinnie-Clark's articles emphasized that women could perform tasks that were not normally included in the repertoire of feminine behaviour. In \"A Fight with Fire,\" published in the _Pall Mall Magazine_ in 1909, Binnie-Clark wrote of how she had fought a prairie fire, beating back flames threatening to destroy her home, barn, granaries, and seed, \"until my hands and eyes were as red-hot cinders caught in a whirlwind.\" The story of the fire was illustrated by a drawing of Binnie-Clark fighting the flames that had almost reached her buildings, and by photographs, including (oddly) one of the \"Soo [sic Sioux] village by the western lake of Fort Qu'Appelle,\" one of a tipi and cart and a man and women with the caption \"The way the Indians live,\" along with one of \"homestead quarters\" and \"the shooting-box of an English settler in the hills by Fort Qu'Appelle.\" Clearly the message was that perils and dangers such as prairie fires were worth battling in order to bring civilization to this corner of the British Empire.\n\nIn 1909 Binnie-Clark began to be featured in the Canadian press under headlines such as \"Western Suffragette: Miss Binnie-Clark Wants Free Homesteads for Women Who Can Farm,\" \"British Women on Canadian Homesteads,\" and \"Canadian Farms for English Spinsters.\" It was frequently noted that she always presented a very feminine appearance when she gave her public lectures and talked about an endeavour regarded as distinctly masculine. She was described as \"tall, slender and good looking, gracefully dressed in black and white... [she] scarcely looked as if she had combined the duties of farmer and housewife, had plowed her own land and tended without help of any kind 14 horses and cattle and any number of pigs through a whole winter.\"\n\nAt the National Union of Woman Workers in October 1909, Binnie-Clark's talk was on \"Conditions of Life for Women in Canada,\" and her main message was that \"the immigration of English women is a matter of vital importance to the Canadian race.\" She began by speaking about the opportunity for domestic service and argued that women \"of refinement\" should not fear accepting such positions, but she also spoke of the demand for teachers, stenographers, nurses, landscape gardeners, and vegetable and fruit gardeners. She spoke of the lives of married women and mothers on homesteads and farms and painted a positive picture of the conditions of social and economic life. But she paid the greatest attention to \"the finest investment in Canada... my own battleground, the land\" and to the cause of homesteads for women. Binnie-Clark read from a letter she had sent to Frank Oliver, in which she had written that \"the extension of the free land grant to women should have the same effect on new settlement that deep-ploughing has on the prosperity of the grain-grower: it should work towards Unity, the first condition of prosperity and content.\" The single women homesteader would be \"untrammeled by the special care of husband and children\" and would be able to devote energy to the establishment of schools and churches.\" She concluded her letter:\n\nEnglish women may not have so direct a claim on Canadian land as the women of Canada, but any country would be the richer for the coming of such Englishwomen as would be prompted to avail themselves of an offer of free land in Canada. Women of trained intelligence, nerve, energy, patience, good-will, foresight, perseverance, courage, power of endurance\u2014limited capital\u2014good comrades, not easily driven back from their purpose\u2014Englishwomen, not drawn from any particular class but forming a class of themselves summoned together from all classes by the bugle call of the decree, or desire to labour for a living\u2014or for life.\n\nShe ended her talk by mentioning that she had received many letters from women in support of her cause, indicating that women \"really want this free land grant,\" that \"it is in the nature of Englishwomen to love outdoor pursuits,\" and that many needed to support themselves.\n\nBinnie-Clark was developing a position that was radical in several ways. She advocated grain farming on large acreages as the most profitable, rejecting arguments for small holdings and the \"lighter branches\" of agriculture. She often criticized the home help concept and instead called for the \"advent of the hired woman on the land.\" She wrote that \"should I be offered the post of general help on a Canadian farm at a salary of twenty-five dollars a month, or land work at twenty dollars, I should not hesitate to decide on the outdoor occupation, in spite of the lesser remuneration.\"\n\nBinnie-Clark had many critics in both Canada and England, and one replied to her talk at Portsmouth in 1909. A Miss Beevor, who had visited Canada in the summer of 1909, believed that women should not be involved in the purchase of land, that it was risky and that it amounted to land speculation. She stated that \"it is only the exceptional woman who will succeed in this matter of land cultivation.\" Beevor pointed out that Binnie-Clark had purchased an improved farm and had not done the \"pioneer work\" herself. She hinted that the government of Canada was wise in not extending the homestead privilege to single women, as they could not obtain agricultural education there except in poultry farming and dairying. She also believed that Binnie-Clark had touched too lightly on the question of solitude, and that she had heard \"some sad stories about the break-down of women through excessive work and solitude.\" She concluded that the \"best advertisement for the scheme of getting free land granted to women would be for a few exceptional women to go out, buy land and farm it successfully. Meanwhile, I am afraid that one swallow does not make a summer and one Miss Binnie-Clark won't exactly carry this scheme.\" Beevor concluded by saying that she loved Canada, however, and that \"if I were younger I would be off tomorrow.\"\n\nBut Binnie-Clark's lectures and articles soon garnered considerable attention, interest, and approval. In a series of articles on \"How Can I Earn a Living\" in the _Woman Worker_ (London) in 1909 and 1910, Esther Longhurst wrote about openings for women in the colonies, including farming, and described the experiences and advice of Binnie-Clark under the title \"Farming and Freedom.\" Others could follow her lead if they were \"strong and sensible,\" liked \"an outdoor life and did not mind plenty of hard work.\"\n\nNew audiences were reached in 1909 and 1910 when Binnie-Clark published articles in the London _Daily Mail._ Her first, appearing in January 1909, was \"A Woman's Farm in Canada,\" in which she told the story of the purchase of her farm. This first column ended with a plea for homesteads for women that would help her countrywomen to \"adopt the same health-giving, somewhat exacting, but in many ways delightful means of self-support\" instead of \"the ghostly footfall of unemployment, which always lurks alongside the trail from which they view before them the beckoning hand that points with mocking gibe to the hour of superannuation.\" She expected the right would be granted by the Canadian government \"first experimentally, then conditionally, then _gratefully_.\" Other columns included \"Women Farmers,\" in which Binnie-Clark wrote that \"farm work for a woman is not looked upon as impossible in Canada.\" She described in greater detail than in previous articles her \"Canadian neighbor\" who farmed over a thousand acres and never hired labour except at threshing time, and had \"for many years entrusted his land work to his eldest daughter. She would plough, drive or harrow day in day out, frequently milking half a dozen cows before and after her field labour.\" Yet the eldest son had inherited the farm and the daughter, who was \"more competent to work a hundred and sixty acres of land than many homesteaders,\" had no right to the land grant.\n\nWith the 1910 publication of _A Summer on the Canadian Prairie_ , Binnie-Clark's profile was enhanced. The editors of the _Canadian Gazette_ were delighted: \"We have read more books on Canadian conditions than we care to recall; in none of them is the touch more sure, more sensitive to realities, and yet more sympathetic.\" An anonymous reviewer for the _United Empire: The Royal Colonial Institute Journal_ was not as glowing, comparing Binnie-Clark's book to Marion Cran's _A Woman in Canada_ and Mrs. Humphrey (Mary A.) Ward's _Canadian Born_ and finding it to be \"inferior to the other two in every respect but that of a convincing realism.\" Both Cran's and Ward's books, discussed in Chapter 2, conveyed more conservative messages about opportunities for women in Western Canada, with Ward emphasizing marriage as the ultimate destiny. The reviewer was disappointed that _A Summer on the Canadian Prairie_ ended abruptly \"when the heroine has just gathered in the first sheaves of her first Canadian harvest... and if the tale is as true as it sounds we should like to hear the sequel.\" Yet there were \"scattered among its pages words of wisdom and guidance for the intending settler.\"\n\nIn February 1910 Binnie-Clark was a guest at a London dinner of \"lady farmers and gardeners,\" organized by the Women's Agricultural and Horticultural International Union, and it was noted that she easily held the record for the largest farm. She was asked to reply to the toast of the colonial members of the union, and she spoke in glowing terms of the prospects offered to women by farming in Canada. As usual she appeared in very feminine attire and was described as a \"tall, dark-haired, slim young women, with pink malmasons [ _sic_ ] clustering in her black evening gown.\" In March she spoke at Caxton Hall, Westminster, London, a location that played a central role in the suffrage movement. Her talk \"attracted considerable attention.\" Here she elaborated on why she thought women should farm wheat, saying that \"it gives the quickest return.\" Growing fruit in British Columbia could mean no return for three or four years, while \"in the wheat belts, in Saskatchewan and Manitoba your returns are seen in the second year, and you also have immediate profits from poultry and dairy.\" She reiterated her belief that English women should farm cooperatively, and she stressed that she was \"not interested myself in any but educated women at the moment.\" Although she complimented the \"splendid\" work of the associations who sent out home helps, she reiterated, \"I would like to establish a channel between the educated women of England and Canada.\"\n\nSpeaking to a \"select audience at a woman's club in London,\" also in March 1910, Binnie-Clark \"disposed convincingly of the fallacious notion that women, to be successful farmers, must have men to do the rough work.\" Binding, for example, was \"jealously guarded by man,\" but \"this is part of the work excellently suited to women.\" As reported in the journal _Votes for Women_ , there was \"something wonderfully alluring in the picture conjured up\" by Binnie-Clark's talk of \"the large open spaces, the healthy out-of-door life.\" After quoting Mrs. Pethick Lawrence as stating that \"down through the vista of long eras we see the mothers of the human race not only the first builders of the home but... the first tillers of the soil,\" the author of the article concluded that it was \"only natural that women should turn to farming... and that they should be among the most enthusiastic exponents of the modern 'back to the land' movement.\"\n\nInfluential people were present at Binnie-Clark's lectures on many occasions. One of her papers was read at an \"at home\" at the Colonial Training School for Ladies in May 1910, and chaired by Lady Frances Balfour. Also in attendance were Marion Cran, along with G. Bethune-Gray, manager of the Irrigated Lands Department of the CPR, who \"told the audience about the land, and what could be done with it and on it by capable and young women.\"\n\nIn 1910 Binnie-Clark published a series of articles in the _Imperial Colonist_ entitled \"Are Educated Women Wanted in Canada?,\" in which she went into detail about opportunities such as nursing, dressmaking, and teaching, with little emphasis on her cause of farming for women and reforming the land laws of Canada. Perhaps she was asked to mute what had become her central message. After that she ceased to be a contributor to the _Imperial Colonist_ , and the journal gave no coverage to her lectures or publications. Her cause and her critique were likely becoming too radical for the women behind the British Women's Emigration Association.\n\nIn January 1910 Binnie-Clark attended a meeting in London concerning the CPR's \"ready-made\" farm scheme in Alberta. Held at the large Whitehall Room, the meeting was presided over by CPR president Sir Thomas Shaughnessy, who predicted that the plan would create the most densely populated and most highly productive large body of agricultural land in Canada, which would strengthen and foster imperial sentiment in Canada. Binnie-Clark asked Shaughnessy if the scheme would apply to women, and he replied to the effect that \"lady farmers\" were welcome, and that there were opportunities for women to raise poultry and eggs for the CPR hotels and dining cars. In subsequent lectures Binnie-Clark complimented the scheme. She hoped that some women would be among the applicants. Perhaps \"Jack\" May heard this plea. In October 1910 Binnie-Clark visited the colonists at Strathmore, Alberta, writing about her observations in the _Overseas Daily Mail_ of London. She found the colonists were \"proving themselves Britons of that type which cannot be beaten throughout the length and breadth of the universe,\" although, alas, drought had ruined the crops and the promised irrigation had arrived too late. She optimistically forecast, however, what would have happened if the land had been irrigated.\n\nBinnie-Clark's popularity reached new heights in 1910, with favourable coverage of her initiatives in Canadian, British, and colonial papers. Reports of her activities were often accompanied by a portrait. She was celebrated as a \"living, zealous, charming example of what an Englishwoman can do as a farmer.\"\n\nTRAINING PUPILS AT BINNING FARM, FORT QU'APPELLE\n\nWhile on the lecture circuit in England in 1910, Binnie-Clark announced a new initiative to be established on her land in Saskatchewan: a training farm for English girls. The intention was to \"build a 'bridge' from England to Canada for girls who may desire to become farmers.\" She hoped to raise \u00a320,000 collected from \"duchesses to factory girls,\" and the money would be invested in \"cottage training farms,\" with each being built on a section of land that would employ twelve tenants. The plan was that each of these cottage farms would make a net profit annually of \u00a31,000. As a start she was taking four English pupils back with her to Saskatchewan that spring, where she intended to teach them to farm, and each was paying her \u00a352. She hoped that her scheme would have the encouragement of Sir Thomas Shaughnessy, who had said that he would welcome women settlers, and that her pupils could supply the CPR with eggs and poultry. Binnie-Clark also hoped that bringing out pupils from England would be a way of \"clearly demonstrating the power of women to work the land, and whether my pupils personally need the Government grant or not, I expect them to fit themselves for the homestead test.\"\n\nBinnie-Clark's pupils, however, would serve another purpose: providing her with unpaid farm labour. (The Indian residential schools that she admired so much operated on much the same principal.) In her talks, Binnie-Clark advised the woman farmer to take pupils \"so as to be provided with free labour and a matron to look after the house\u2014to take, in fact, the part in domestic affairs a man farmer relegates to his wife.\" Student fees could also help to sustain the farm.\n\nThe grand scheme of raising money and establishing cottage training farms never materialized, but Binnie-Clark did train some pupils on her Saskatchewan farm. After her first season she reported success; the students had raised the cleanest crop of Number 1 Northern wheat in the neighbourhood. They had all learned to control a team of four horses pulling several implements, despite the fact that none of them had previous experience with horses. Her pupils had demonstrated \"an innate love of animals\" that assisted them in all of their farm work. While they were slower at ploughing than male labourers, they were much more thorough at working the land with disc harrows. All of the pupils had hauled water, milked, cleaned stables, shovelled manure, and performed other chores with \"good temper and excellent results.\" This demonstrated, according to Binnie-Clark, that the prejudice against women working out of doors and on the land was \"founded on an imperfect knowledge of the facts.\" She believed that while gardening was a strain on physical endurance, work with implements \"not only entails no physical fatigue but is positive physical refreshment.\" Challenging the division of farm work into men's and women's spheres, she continued: \"A conscientious intelligence is necessary in ploughing, but on the disc and harrow cart one sits at ease in the most exhilarating and nourishing air in the world. The work is entirely mechanical, and it is the only one place in the busy world, outside the rest-cure section of a nursing home, where one is free to indulge in day-dreams.\" The obstacles to women farming were a lack of capital and official encouragement, according to Binnie-Clark, not the physical incapacity of women to perform farm work.\n\nBinnie-Clark's students included some from the prestigious Roedean School near Brighton. One pupil was Kathleen Laughrin, who came out with six others in 1910, having seen an advertisement in the _Times._ An entry in the Fort Qu'Appelle local history written by Derek Harrison, Laughrin's son, provides insight into the sort of adventurous person who was willing to learn about farming in Saskatchewan with Binnie-Clark as instructor. Educated in France and an accomplished musician, Laughrin had travelled extensively. In Paris, she studied with the organist at Notre Dame Cathedral, and in 1903 she was in Russia, where she worked for a year as governess to Count Leo Tolstoy and family. Laughrin had worked as a journalist in London and lived in South America. In 1910, when she arrived in mid-May at Qu'Appelle station there was raging blizzard. This pupil's main memory of her experience with Binnie-Clark was that her bed at Binning was a block of ice; the bed could not be made as the bedding stuck to the frozen wall. In 1914 Laughrin married Roland Harrison, a neighbour of Binnie-Clark's.\n\n_Figure 31._ In 1910 Georgina Binnie-Clark established a training farm for English girls on her land at Fort Qu'Appelle that she called \"Binning.\" These included pupils from Roedean School, Brighton, as illustrated here. Pupils provided free labour and student fees could help sustain the farm. This student is \"stooking,\" or setting sheaves upright in stooks. Georgina Binnie-Clark, _Wheat and Woman_ , 402.\n\n_Figure 32._ \"Land and The Woman,\" by Georgina Binnie-Clark, begins, \"In Britain outdoor occupation for women is the word of the hour, but the obstacle placed in the way by the Canadian government in refusing women the right to take up homestead land, at present impedes the progress of women towards the place of independence, prosperity or wealth at which they would undoubtedly arrive in working their own land on the Canadian prairies.\" Yes, they could go to the U.S. West and obtain 160 acres for free, but \"the strength of the imperial and home tie is very strong, and British women, as a rule, refuse to take the severing step.\" Two of the photographs feature the English students she was training at \"Binning.\" Binnie-Clark appears in the bottom photograph with her horse \"Nancy.\" _Canadian Courier_ 12, no. 12, 16 November 1912, 16.\n\nE. Violet Bertram, who in 1913 published a series of articles in the _Canadian Gazette_ with the title \"Wanderings of a Single Woman,\" spent some time at an unnamed Fort Qu'Appelle \"ranch, demonstrating the feasibility of farming for women in Canada,\" that was clearly Binnie-Clark's, and had contradictory observations to report. On the one hand, she believed that the experience was of value, as the students had learned about the practical and hard conditions of life on the prairie, and the \"ranch owner is always ready to show, explain, expound: ploughing, disking, harrowing... harnessing, feeding and cleaning the horses.\" But on the other hand, their teacher was not always adept or competent. Clearly describing Binnie-Clark, Bertram wrote:\n\nWinter is vacation time here. Miss ___ was therefore immersed in her literary work, and was, in consequence, as absent-minded and unpractical as our old German professor, and this led to hilarious situations. \"Thinking of angels,\" she let the rope of our precious water bucket slip through her fingers to the bottom of the well, but with Bohemian resource and cleverness recovered it with the cunningly bent stove cleaner tied to a slim young tree! Interested in our conversation whilst driving the bobsleigh... home from Fort Qu'Appelle, the reins would slip through her fingers, and there we would sit helpless, till by fortuitous hills and cajoling cries of \"Whoa, Fanny,\" \"Gently, Emma!\" the two spirited mares could be persuaded to a standstill. Did we seek the dishcloth, it was found in some position of unmerited honour such as the mantelpiece, the back of the armchair, or handkerchiefwise on her writing bureau!\n\nBertram left in the spring and concluded that \"so large a ranch as this was an impossible undertaking for single women of small means.\" Yet her training at Binning may have been of some use. In 1915 Miss Violet Bertram, a \"co-operative small holder,\" was present at a conference on Women's Work in Agriculture and Horticulture held at the Royal Horticultural Hall, Westminster (along with Binnie-Clark). Bertram \"spoke at length on training applied in Canada, and gave instances of the work women are doing. She laid stress on the urgent necessity for a student to... study such important subjects as wages, the handling of people, auction rooms and buying and selling generally. She urged co-operation and advised women to work in couples, settle in groups and be ready to take advantage of any change that might come.\" In 1919 Bertram was running Vanguard Farm in Kent for severely disabled soldiers and sailors. It was a cooperative farm where men and their families settled on small plots. Bertram may have had learned some valuable lessons about farming from Binnie-Clark afterall.\n\nTHE FAMOUS FARMER, HER CRITICS, AND SUPPORTERS\n\nDespite her lectures and publications, Binnie-Clark made little headway converting influential men in England to her causes. In January 1912, Binnie-Clark was once again in England, where she attended a talk given by Arthur Hawkes, the special commissioner for immigration for the Dominion of Canada, at the Royal Colonial Institute (RCI), London. She and several other women in the audience, including journalists Currie Love and Mary Agnes Fitzgibbon, were disappointed that nothing was said about opportunities for women in Canada. Binnie-Clark introduced herself as a woman farmer, and she \"complained that women could not obtain free land, although any man from any nation could get 160 acres for nothing.\" She also said that so far only two women had been accepted into the ready-made farm scheme (presumably \"Jack\" May and Louisa Wittrick, as discussed in the last chapter), even though Sir Thomas Shaughnessy had promised they could enter on the same terms as men. Hawkes addressed much of his reply to Binnie-Clark's critique, providing what he believed would be the \"official view\" of her request. It was not fair, he said, for a man with a wife and children to be granted a homestead for each. One hundred and sixty acres was adequate for a head of a family. With tongue in cheek, and making a mockery of her cause, Hawkes said: \"I will be prepared to make this promise\u2014that I will presently recommend that homesteads shall be granted to single women all through Western Canada on their signing a hard-and-fast undertaking that they will not enter the state of matrimony in the next five years. However, whether the demand for homesteads for\u2014if you will pardon the word\u2014spinsters would be largely increased by facilities being granted I do not know.\"\n\nThis intransigence and mockery did not deter Binnie-Clark. Back in Western Canada that summer, she toured the prairies on a \"commission\" from the _Canadian Gazette_. Interviewed in Edmonton in August 1912, she was presented as an \"ardent suffragette,\" which was a cause she had not advanced publicly before, although she may well have long been a supporter. It was reported that she was opposed, however, to the militancy and \"frantic measures\" of the British suffragettes. Binnie-Clark was described as a \"charming woman, with very keen perception and the greatest amount of faith in her work as well as in the country she has chosen as her field. A woman of gentle, persuasive personality, convincing in the extreme, who fears not hard work, and who shows great perseverance.\"\n\nIn early 1913, Binnie-Clark gave a series of lectures in England. In March she spoke to the students at the Arlesey Colonial Training School, urging them to start farming in groups in Canada on smaller acreages near cities of the prairies or British Columbia. She assured them that what they were cultivating at Arlesey was exactly what they could grow in Canada. \"Beautiful limelight slides\" complemented her talk with images of the fruit and flowers of British Columbia as well as of her own farm in Saskatchewan. She also spoke to the Suffrage Club of London in April 1913, which indicates her growing involvement in this cause.\n\nBinnie-Clark's most sustained and fulsome lecture, and given to her most distinguished audience to that date, was her April 1913 paper entitled \"Land and the Woman in Canada,\" presented to the RCI in London. Although other women such as Flora Shaw had spoken before the RCI, they were not permitted to be members. In her paper, which was published in the RCI's journal, _United Empire_ , Binnie-Clark's main message was that women, with very little training, were able to plough, cultivate, seed, harrow, harvest, and market crops of wheat. She argued that the woman agriculturalist should aspire to commercial farming and an independent income. Binnie-Clark further asserted that women such as herself, educated and from England, should be eligible for the homestead grant. It was in this lecture that Binnie-Clark clearly articulated the argument that had been hinted at in some of her previous lectures and publications, that it was unjust to reward \"foreign\" men with land and deny this right to British women who were playing critical roles in the \"spade-work of British expansion in this, the supreme place of prosperity among British lands.\"\n\nThese were the themes at the core of her lecture, but Binnie-Clark ranged widely, beginning with the foundations of change in \"the once silent plains of the Prairie Provinces,\" with the settlement at Red River of the Earl of Selkirk and the first harvest of wheat, pointing out that women had played a role in this history and that \"history occasionally throws over the past a search-light which discovers the claim of the woman to her share in the land which, over a hundred and thirty years ago, woman helped to win by spirit and to hold by toil.\" Her message was radical in many ways, as she stressed that the woman contemplating agriculture in Canada should aspire to be a commercial farmer not just for her livelihood, but for her independence. She admitted, however, that smaller acreages could be successful depending on the climate, location, and the market. She described in detail how women could establish various kinds of farm operations in different regions of the West, including British Columbia (starting on five, fifty, or a hundred acres of land on a capital of \u00a3100, \u00a3500, or \u00a31,000), and how they could emerge after twenty years with \u00a35,000, which was her \"symbol of independence.\" She claimed that near Victoria was \"the most exquisite environment [and]... the most perfect conditions for any business that the heart of a woman can desire.\" Five acres could be acquired for a \u00a3100 down payment, and a young woman settler could grow \"bulbs by the seashore, fruit of varied and perfect kind, [and] vegetables for which there is always a demand.\"\n\nAdvice for the woman farmer with \u00a31,000 was to farm in the Qu'Appelle Valley like herself, and she made it clear that wheat would always be the main crop of prairie Canada. Binnie-Clark had many economic and demographic statistics and stressed how the dramatic increase in the populations of the prairie cities provided a ready market for the produce of grain, dairy, and market garden farmers. The details might have been somewhat tedious for her audience, as Binnie-Clark itemized how much land to seed to wheat, oats, and barley; how much capital to set aside for land, horses, cows, sows, and poultry; and how much should be spent on the shack, outbuildings, labour, and implements. She concluded that \"patience, endurance and energy\" was required of the woman farmer, and her audience might have agreed that these were also required to be alert for the entire lecture.\n\nBinnie-Clark complimented the efforts of \"Jack\" May and her partner, describing them as \"the best men of the lot\" of the Sedgewick farmers (not realizing that May had already left Alberta) and stating that they were \"helping to make Empire through the medium of the Canadian farm.\" She also declared, when describing how a Canadian government official had warned that the homestead grant would make women \"more independent of marriage than ever,\" that \"the woman of today will not have the commercial marriage, or marriage of convenience. She has arrived at the place where, if she cannot have marriage as an inspiration in her life, she refuses it as a mere resource; and to refuse dependence is half-way to independence.\" Canada, she concluded with indignation, \"has not yet outgrown the idea that women are needed for one purpose only.\"\n\nLively discussion and debate followed the 1913 lecture at the RCI. Sir Charles P. Lucas was in the chair. He was head of the Dominion Department of the Colonial Office and the author of books on the history of Canada and the British colonies. Other powerful men were in the audience, and they included both critics and admirers of Binnie-Clark. Richard Reid, government agent of Ontario, had no objection to extending homesteading to \"the fairer but not inferior sex,\" and he hoped other Englishwomen would follow Binnie-Clark's lead. Ellis T. Powell (prominent barrister, journalist, imperialist, and spiritualist, and friend of Sir Arthur Conan Doyle) was also in favour, and he too stressed that women who farmed could still be feminine. He was impressed with Binnie-Clark's sound economic knowledge, and he believed that she combined \"feminine charm and enterprising resolution which go to make the very best type of the Imperialist woman of the future.\" He was pleased, however, that ultimately the scheme would lead some of these women to marriage: \"If you have women who have pluck and capital to go out to Canada and commence colonising and working there on these lands and building up the Empire, do you not think that these women, either if they remain single and go towards a cheerful independence, or if they become mothers of Imperialists, are doing a work which is of immense moment... towards the ultimate strengthening and consolidation of the Empire which is the centre of all our affections?\" These capable women would be \"the germ of the very best and grandest Imperialism, which will secure the foundations of the Empire, not only for our generation but for all time to come.\" Other supporters included Stewart Gray, who was impressed with the farm work done by women in Scotland. Dr. T. Miller Maguire chimed in that in times of war in Germany and Bulgaria, women did a great deal of agricultural work, and he thought it would be much more preferable for the women in England to engage in pastoral pursuits than in factories \"working soul-destroying machinery.\"\n\nJ. Obed Smith, however, spoke at the greatest length and was utterly opposed to the idea of women farmers in \"this, that, or any other land.\" He said women were physically incapable of carrying on farming operations, and that he could count on two hands the number of women farming in Canada without the assistance of men. He \"dissociated himself entirely from the idea that woman alone could pursue general farming in Canada.\" Smith was prepared to admit that under special circumstances, women could succeed at poultry and dairy farms, but he insisted that they could not excel at grain farming. That they were not physically capable, he argued, was supported by the curricula of the agricultural colleges of Canada. He asked: \"How was it that these excellent institutions did not teach women ploughing, sowing, reaping and various other things that went to make up the life of the farmer? Instead of these they taught [women] sewing cookery, home management, keeping of account, dairying and laundry.\" He further argued that Canada had deliberately departed from the U.S. legislation that permitted single women to homestead, because it led to the \"pernicious practice of procuring two homesteads instead of one\" in the case of men and women homesteaders who then married. This legislation, in Smith's view, had led to \"disastrous results in the United States,\" and immigration officials did not desire the same results in Canada.\n\nThe next discussant, Jeffrey Bull of Toronto, spoke briefly and agreed with Smith, stating that \"it would be most disastrous not only for the woman, but for the reputation of Canada, for any woman to start grain farming in the West.\" \"Disastrous\" seems to have been the word of the day.\n\nThe sole woman discussant that evening was Miss J.S. Turner of the Arlesey House Colonial Training School, and she directly challenged J. Obed Smith, saying that the Canadian colleges only taught women to cook and sew \"because men did not like to do that sort of work themselves.\" She thought that \"any woman who had stamina and common sense had very much better go back to the land than sit about or run after mothers' meetings, or act as sort of junior curate, as so many of our daughters did now.\" Turner pointed out that Scottish women did half the labour on farms in Scotland, and that \"when she was a girl in Lincolnshire women worked on the land and were much better and healthier for it.\" She had trained many women who had gone to Canada, two to South Africa, and two to Australia, and those who went to Canada had done the best. Many had started out as domestic helps but were now \"following Miss Binnie-Clark's example.\"\n\nOne distinguished discussant commented that working in the fields was labour performed by Indigenous women of the colonies, and thus was not considered suitable work for British women. After listening to Binnie-Clark's talk, the former governor of the Bahamas Sir William Grey-Wilson said that in many areas of the world in which he had been posted it was the custom for the women to do all the agricultural work, adding that he was not prepared to admit it was the best of customs. Here was the objection at the heart of the matter: British women farming in the colonies would not be demonstrating a superior domesticity, but sinking to the level of Indigenous people.\n\nClearly Binnie-Clark still had some distance to go to persuade the influential men of the RCI, the Colonial Office, and Canada's immigration authorities overseas that the homestead grant should be available to unattached English women. The _Canadian Gazette_ , however, sprang to Binnie-Clark's defence in an editorial, declaring that her series of lectures was timely and useful and that the theme and text of her address to the RCI \"might well have the prophetic words of the great French agricultural statesman, Jules M\u00e9line, who says in his book 'The Return to the Land' (1906): 'When shall we make up our mind to provide real agricultural training for women, evoking in them appreciation of the life of the country, and making them realize the dignity and utility of farm work? Of all reforms undertaken in the interests of agriculture, there is none more important or more pressing than this.'\" The editors noted that this truth had not yet \"come home to any English statesman or agriculturalist.\"\n\nCritics in Canada were becoming more vocal. The Victoria _Daily Colonist_ led the charge in a May 1913 editorial under the headline \"Misleading Emigrants.\" The editorial writer took issue with many of Binnie-Clark's cost estimates for land, livestock, and equipment, and her projections of a comfortable living from five acres if young women of twenty-five followed her advice and settled on Vancouver Island or the mainland close to \"industrial populations.\" Particularly at issue was her estimate of land prices near cities such as Victoria. These were \"startling statements,\" according to the _Colonist_ , that were \"utterly out of keeping with the facts, and if accepted as true and acted upon by any young woman, would lead to such disastrous results that we can only characterize it as wicked in fact if not in intention.\" Binnie-Clark was doing \"incalculable harm\" with her \"astonishing statements.\" The editorial concluded by reminding readers of the acceptable vocations for women, and criticizing schemes to send young Englishwomen to Canada: \"There seems to be something very like a conspiracy to get a certain class of young Englishwomen to come to this country. While we are on this subject we may add that the only women of 25 who ought to think of coming here alone to make a living, are those qualified to become schoolteachers, competent stenographers, trained nurses... domestic servants who intend to be servants in fact as well as in name, and women of experience in gardening and farm work generally.\"\n\nWhen the text of Binnie-Clark's address to the RCI appeared in the _United Empire_ , other objections were raised. Canadian journalist Mrs. Donald Shaw, who was originally from England, wrote to that journal with great disapproval and revilement. Shaw was opposed to women's suffrage, and she wrote articles that lamented the changing world about her. One of her articles began with \"What is the world coming to? There seems to be a mad desire just now on the part of a large number of people to tear down and cast aside all the creeds, rules and laws that have in the past built up moral and stable nations.\" Women farmers, to Shaw, were part of this mad destructive desire. Shaw wrote, \"We don't want women farmers in Canada.\" She believed that \"not one woman in a thousand is physically fit\" for farm work, and \"certainly not one Englishwoman in a thousand.\" Even if they were capable, Shaw argued, the vocation would not produce a desirable type of woman. Echoing the _Daily Colonist_ , she wrote: \"Canada does not want women in the fields, but she badly wants women in their own sphere, that is as wives, mothers, cooks, servants, stenographers, teachers and nurses. Surely there is sufficient opening here for women without turning themselves into farm labourers. The idea seems more curious because in Canada women do not work in the fields (that is Canadian women), though they do an enormous amount of work in their houses, and Canadian men have a great aversion to seeing women engaged in outdoor occupations.\" Shaw recalled that her \"own countrywomen\" from Britain regarded doing housework as derogatory and asked, \"Is it less derogatory or more pleasurable to clear out cowhouses and feed pigs?\"\n\nShaw's letter was quoted at length in the _Daily Colonist,_ and the editor of the column \"In Women's Realm,\" Maria Lawson, disagreed with some of her opinions, particularly Shaw's refusal to believe that \"the average woman can farm.\" Lawson wrote that farming on the prairies or in Eastern Canada might be \"beyond the strength of most women, but there are many who contend that it is neither impossible nor unsuitable for women to cultivate large gardens or to engage in poultry keeping on small holdings. Englishwomen are engaged in such work in this Province both on the Island and the Mainland, but their success remains to be proven.\"\n\nIn 1913 another critic of Binnie-Clark, Elizabeth Keith Morris, published her book _An Englishwoman in the Canadian West_. Her references were oblique, but there was no doubt whom her remarks were aimed at. At the start of her chapter on \"Farming and Fruit Growing,\" Morris wrote:\n\nThrilling and picturesque stories of the lady farmer had assailed our ears, and through these we came to the conclusion that a woman had at last found an Utopian way of earning her own living... We heard of... wonderful machinery which turned work into play; and of the golden harvest which awaited those playful efforts at work; and then we came face to face with the facts, which differed in every respect from the fantastic, romantic tales which had been poured into our ears... for we discovered that only the strong, hardy, eminently practical and really hard-working woman could even hope to reap a good living from that wonderful black loam of the prairies... after many a heart-breaking experience and the absence of all luxuries and other comforts.\n\nMorris was opposed to Canada's granting the right to homestead to women; the \"hard and heavy\" work required was unsuitable for them.\n\nWHEAT AND WOMAN\n\nBinnie-Clark's book _Wheat and Woman_ (1914) drew together and added much rich detail to the lectures and articles that she had already published. It is a self-deprecating, often humorous account of her first three years of farming, detailing her ignorance of agriculture and the customs of Canada, her mistakes, misfortunes, financial woes, and her adventures\u2014which included being lost on the prairies in a summer deluge and being tossed head first into a snow bank when her beloved horse, Nancy, came to an unexpected and abrupt stop and then bolted, deserting Binnie-Clark. It includes an account of the long and viciously cold winter of 1906\u20137, perhaps the worst in prairie history. But _Wheat and Woman_ is also the story of the courtesy and kindness of Binnie-Clark's neighbours, her love for the prairies and for her animals, her fascination with wheat (a \"tall mass of living loveliness\"), and her own remarkable persistence and determination. It is a sobering tale of \"years of arduous toil and seasons of bitter disappointment,\" but ultimately the message was that women could succeed if they had capital, fortitude, tenacity, and good humour. It is also a sharp critique of Canadian land laws. The book challenged accepted norms of middle-class femininity; Binnie-Clark never mentioned marriage as the final destination for her or sister, and she did not take kindly to domestic duties such as having to prepare meals for her hired men. \"From the beginning,\" she wrote, \"I was perfectly happy working on the land, only I wished it was someone else's turn to get those tiresome three meals a day.\" And it was radical. The title _Wheat and Woman_ was a bold, concise, and deliberate choice; this was not about small holdings and fruit farming or bee keeping.\n\n_Wheat and Woman_ received positive reviews in England and Canada. In the _Times Literary Supplement_ , it was praised as a \"graphic and clear account of the difficulties encountered... winning her way to practical success through sheer pluck, persistence and... the indispensable equipment of a tough constitution capable of enduring an astonishing amount of hardship and fatigue.\" The review noted many details, including the \"bewildering succession\" of inept hired men who were \"with few exceptions unsatisfactory and addicted to leaving their employer in the lurch at the most inconvenient moments.\" Few of the reviewers appeared to agree with or to emphasize Binnie-Clark's central theme that the homestead laws discriminated against women. It was read as the story of one woman's amazing pluck and endurance, and as an eloquent description of life on the prairies. In the _Athenaeum_ , _Wheat and Woman_ was described as the story of a \"singularly brave, cheery and plucky woman of admirable self-control and steadfastness of purpose.\" The reviewer was pleased that there was only a \"hint of something like bitterness in her view of woman's position in the world.\"\n\nThe suffragist journal _Votes for Women_ praised the book and Binnie-Clark, and criticized the Canadian government: \"Of such stuff are the best pioneers. One would think that Canada or any colony would welcome such a settler with open arms as a valuable asset. Such a settler forms a centre, radiating wholesome energy, intelligence, sympathy, the best the old world has to offer. But the official mind, even in a new country, does not approve of the independent woman, however capable she may be. Man must be the landowner.\"\n\nOpinions varied. Writing in the _Globe_ , Mary MacLeod Moore concluded that _Wheat and Woman_ would discourage, rather than encourage, women to take up farming unless they were \"as exceptional a woman as Binnie-Clark herself.\" Moore wrote that \"otherwise disaster is fairly sure to overtake her efforts to farm alone, hampered as she is, in the first place, by the Homestead Law, and later by circumstances, climate, loneliness; the difficulties which surround the obtaining of reliable 'hired men' no matter at what price, and many others which develop as time goes on.\"\n\nBinnie-Clark may have inadvertently placed Canada in the public eye as a less-than-inviting destination for the British gentlewoman. In 1914 in the English newspaper the _Sunday Referee_ , a discussion took place about the position of women emigrants to Canada. There were two main objections raised about Canada as a destination. The first was that Canada refused the free grant of land to women available to men, and the second was that there was no dower law. The conclusion was that \"Australia, New Zealand and Rhodesia are at present far more suitable for women emigrants than Canada.\"\n\nIn his review in _Westminster Hall and Farthest West Review_ , Dan Munday also thought that _Wheat and Woman_ might discourage homesteaders from Britain, although he thought it was more honest than the \"land-of-promise\" literature used to lure them that led to so many abandoned homesteads. He wrote that because of the \"close regard for accuracy... the book can be of real value to one contemplating farming on the prairie.\" Munday noted that while a purpose of the book was to help secure homestead rights for women, this was not mentioned until the last chapter. In his conclusion he wrote that the author \"has no intention of settling permanently in Canada.\" That was, in fact, even more true when the First World War began in August 1914.\n\n_Wheat and Woman_ could not have appeared at a less opportune moment. Almost no one had time or energy for the homesteads-for-women cause in Britain or Canada, and that included Binnie-Clark, but her long-term promotion of women and farming had become timely and vital. Her agricultural skills were now of value at home. She was one of seven agriculturalists appointed by the Ministry of Labour to organize the work of women on the land and assigned the Yorkshire and Lincolnshire districts. One of the last events she attended as \"the pioneer woman farmer in Canada\" was a 1915 conference in Westminster that she chaired on Women's Work in Agriculture and Horticulture, mentioned above, which was also attended by her former student Violet Bertram. Binnie-Clark declared that \"no profession under the sun is so excellent for nervous diseases. In view of the changes which the war is bringing, the cry of 'back to the land' is one which vitally affects women and is of great importance to their economic status.\"\n\nFrom the First World War into the 1930s, Binnie-Clark also had a business at 14 Woodstock Street, a small street off Oxford Street, London's main shopping district, called \"The Fashion Journals Guild,\" where she sold patterns for dresses and hats. As a young boy of nine or ten in the 1930s, her great-nephew Dennis Jenks recalls visiting this small, cluttered office that she managed with the assistance of one employee. Just how she juggled her war work on the land, her business, and her farm in Saskatchewan is one of many puzzles about Georgina Binnie-Clark. Her sister Ethel ran the farm while she was gone; in her 1947 will, Georgina left land to Ethel \"as a mark of appreciation for the care she bestowed on the whole property during my absence by reason of my illness and the Great War.\" Georgina returned to her farm in 1926 and 1928, and again in the 1930s, in a final initiative of hers called the Union Jack Farm Settlement, to be dealt with briefly in the conclusion. She continued to promote the British Empire and the settlement of British people in Canada, but her emphasis on women famers was gone. Her writing career slowed and the direction of it changed during the war. She self-published a book for children called _Tippy: The Autobiography of a Pekingese Puppy_ , the proceeds of which were to \"buy comfort for the wounded soldiers & horses fighting in the Great War for Liberty.\"\n\nWhile the number of Binnie-Clark's critics mounted in Canada and overseas by 1914, she had helped to motivate a great number of women and their supporters to organize a homesteads-for-women campaign that followed the same trajectory\u2014gaining strength from 1910 to 1914 but losing momentum in the war years, although it did not disappear altogether. Campaigners in prairie Canada, however, faced formidable and intransigent opponents, and they weakened their own cause considerably by adopting a central strategy of denouncing \"foreigners\" as unsuitable homesteaders, and requesting the homestead privilege for \"British-born\" women only, alienating potential supporters. \nCHAPTER SIX\n\n\"DAUGHTERS OF BRITISH BLOOD\" OR \"HORDES OF MEN OF ALIEN RACE\"?\n\nTHE HOMESTEADS-FOR-BRITISH-WOMEN CAMPAIGN\n\nWhile Georgina Binnie-Clark focused her energies on publishing and lecturing in England about the opportunities for British women farmers in Western Canada and the injustices of Canada's Dominion Lands Act, a similar campaign was gaining steam on the prairies, which the woman wheat farmer of Fort Qu'Appelle helped to motivate and inspire. While supporters of homesteads for women devised many arguments for the entitlement of women to the land grant, they increasingly stressed the rights of British and Canadian-born women, in contrast to the dubious claims of \"foreigners,\" both male and female. The campaigners called for justice and equality, but only for a privileged few. A petition, submitted to the Canadian House of Commons in 1913, asked that the privilege of homesteading be granted to \"all women of British birth who have resided in Canada for six months.\" Faced with a climate that was inhospitable to women farmers, landowners, and voters, and ultimately facing a completely intransigent federal government, supporters articulated an imperialist vision to gain acceptance, to show that they could provide a solution to the problem of the \"foreign element\" and to demonstrate their fitness for the privileges of citizenship that were denied to them yet available to \"foreign\" men. Disparaging the suitability of settlers of \"foreign\" origin justified their own claims for inclusion. Promoters of homesteads for women manipulated ideas about racial and ethnic \"others\" in an effort to win elite support, while at the same time appealing to an egalitarian code of fundamental justice.\n\nAs Pamela Scully has observed about the rhetoric of race in the women's suffrage movement in South Africa, \"liberal campaigns for civic rights and equality can in fact depend upon invocations of its supposed antimonies\u2014prejudice and exclusion.\" Similarly, in the U.S. West, racist and nativist rationales surfaced in the rhetoric of some Anglo-American suffrage activists who were hostile toward the \"foreign\" men \"from the slums of the Old World [who] walk out of the steerage of the ships to become enfranchised citizens and ultimately to vote against giving the suffrage to American-born women.\" This elitist strategy failed, however, in the case of homesteads for women. The federal government remained intransigent as long as it was in control of Crown or public lands (to 1930), at which point there was little homestead land left. The imperial logic and elitist strategy alienated key constituencies, such as settlers from the United States, who were accustomed to single women having homestead rights and who expected the same privilege in Canada. No matter what the strategy, however, there was little hope for success in confronting deeply embedded views of women as unsuitable and incapable farmers and landowners.\n\nThose who organized for homesteads for women supported other causes that challenged the deliberate crafting of Western Canada as \"manly space,\" where the building block and organizing principle was the authority of the white, property-holding, male head of household. Control of land and therefore wealth was not to be shared with other groups, nor were there to be any hindrances for landowners who wanted to sell or buy. This shaping of \"manly space\" is illustrated not only in the homestead laws but in the abolition of women's dower rights in 1885 in Manitoba and 1886 in the North-West Territories, which meant that a husband could now sell the family home without his wife's consent or entirely cut her out of his will. Shaping \"manly space\" also involved a concerted campaign to impose the monogamous model of marriage on the diverse inhabitants of Western Canada. A national identity was to be forged that was distinct from that of the Indigenous people and was distinct, also, from that of the United States. It would be based on an idealized view of a traditional British gender order, of the obedient, submissive wife and the provider, head-of-family husband. All of this was fuelled by an image of the United States as a place of disrupted and dangerous alternatives to the \"natural\" gender order, and by a determination that pristine and pure Canada would be kept free of the immoral and corrupting influences from the south. Permitting women alternatives to marriage, such as acquiring homestead land for farming, was an indicator of a society run amok.\n\nGALVANIZING THE CAMPAIGN AND A FIRST PETITION\n\nThe homesteads-for-women campaign intersected and combined with the call for the reinstatement of dower rights on the prairies and for women's suffrage. Of these campaigns, homesteads for women was the greatest failure. Legislators never wavered on the issue\u2014women never received the right to homestead in Western Canada, except in Alberta after 1930. When the Prairie provinces assumed control of public lands from the federal government in 1930, the right to homestead was abrogated entirely in Manitoba and Saskatchewan, while in Alberta, where there was a little homestead land left, the provincial government drew up regulations that permitted every \"person\" to apply who was over seventeen, had resided in the province for three years, and was or declared the intention to become a British subject.\n\nAmong the early calls for homestead rights for women was one from a 1907 correspondent of the _Farmer's Advocate_ writing from Moose Jaw. Like Binnie-Clark, this supporter believed women homesteaders could be a means of strengthening the British fabric of the West. He proposed that all single women over twenty be given the right to enter on a homestead, and he was not at all perturbed that they might marry before they proved up, as \"this is exactly what is wanted in giving them homesteads, and I would go further and allow any such homesteader to at once receive patent to her 160 acres as soon as she is married.\" Echoing Flora Shaw's \"sister\" scheme, the writer proposed that if young men from Great Britain brought their sisters and each secured 160 acres, \"a new immigration movement would take place... We hear much of the 'all-red line of commerce.' This might well be called the 'all-white line of immigration.'\" \"The benefit,\" he wrote, \"to the whole Northwest, morally, socially, educationally, and spiritually, would be enormous.\"\n\nWhen Binnie-Clark visited Winnipeg in late 1908, she met with women who had \"already taken up the matter of Homesteads for Women with a deep sense of the injustice of a law which, whilst seeking to secure the prosperity of the country in enriching the stranger, ignores the claim of the sex which bore the brunt of the battle in those early and difficult days.\" She wrote her own letter to the Department of the Interior at that time (described in the previous chapter), proposing a settlement of English gentlewomen as an initial experiment, and she met with officials in Ottawa.\n\nIn 1910 the concept of homesteads for women was still seen as a \"novelty\" but was gaining traction. The _Toronto Telegram_ in January of that year declared support for the idea, noting that the present situation was \"both unfair and disadvantageous,\" and concluding that \"if women shrink from the hardships of pioneer life the fact has not been noticed in the history of the west. Then why should they be deprived of participation in its rewards?\" Other early voices included that of Louise Langton of Wetaskiwin, who wrote letters to the _Grain Growers' Guide_ on a wide range of issues, including suffrage, dower rights, and birth control. She asked, \"Must we go on giving birth to daughters whose fate will be the same as ours has been?\" Langton proposed that \"farm women of the west organize and help in this question of 'homesteads for women'... She made the argument that would eventually become the focus of the campaign, that they had more right to land than \"foreign\" men, that \"women of this great Dominion... [should] join forces, concentrate their powers... so that the same opportunities be given them that are given to the hordes of men with less ability than theirs, and who are pouring into this country every year.\" Langton's call to action was enthusiastically endorsed in the _Guide_ in April 1910. \"Onward\" wrote, \"Here's an emphatic vote in favour of Mrs. Langston's motion... [and] if we cannot organize... we can agitate, discuss, educate, and your page is just the place to begin.\"\n\nBut as Binnie-Clark found, there were formidable opponents. Frank Oliver articulated why he did not support homesteads for women in the House of Commons in April 1910, just a few weeks before Mildred Williams's twelve-day vigil (described in Chapter 3). Oliver was asked by member of Parliament W.J. Roche from Manitoba (later also minister of the interior) if his attention had ever been called to the idea of allowing women to homestead, and the letter of a reverend gentleman in Saskatchewan, published in a Winnipeg newspaper, was read into the record. Reverend W.W. Beveridge recommended allowing women over the age of eighteen to homestead as a means of addressing \"a great dearth of marriageable ladies\" in the province. He claimed to know of parents of daughters who refused to move west and asked \"why that man had not just as much right to homestead and get a quarter section for each of those girls as the man who happened to have four grown-up boys?\" Beveridge also knew of men with large families of strong, healthy girls in the Dakotas and Minnesota who would come to Canada if their girls could homestead, but because they could not, they were moving to Montana instead.\n\nOliver replied that the matter had been brought to his attention frequently, and his answer was that women homesteaders were \"not in the interest of the settlement of our country.\" He was aware of the different land law in the United States but was \"not aware that it is an advantageous law.\" Oliver explained that the purpose of giving free land to homesteaders was to make the land productive, and that \"in order that a homestead may be made fully productive, there should be not a single woman upon it, nor even a single man, but there should be both the man and woman in order that the homestead may be fully advantageous to the country. The idea of giving homesteads to single women would tend directly again that idea.\" He said that it was the job of the single man \"to get the woman, and for the woman who wants to settle on land in the Northwest to get the man, rather than that she shall have land of her own... Our experience is entirely against the idea of women homesteading.\" It was sufficient to permit land to widows with children old enough to help cultivate the land, according to Oliver.\n\nIn the _Manitoba Free Press_ , women's page editor Lillian Beynon Thomas (Lillian Laurie) mocked Oliver's reply and pointed out contradictions. Her column began, \"Were you ever at a meeting where the men, being in power, were discussing the advisability of giving women something they were asking for? If you have and the men referred to the women as the 'fair sex' then you know that they did not grant the request.\" Thomas wrote that \"nothing was said in the act about having children to cultivate the land and if women are not considered competent to bring the land to a condition of productiveness then the clause permitting women as sole heads of families to homestead is merely a humanitarian provision for the women, and the land has not been considered. To be consistent Mr. Oliver should have the law granting homesteads to women only if there were boys dependent on them for support and old enough to cultivate the land.\"\n\nOliver's response in the House of Commons helped galvanize the homesteads-for-women campaign in Western Canada. In late May 1910, a petition to Minister of the Interior Oliver, originating from Edmonton, was published in the _Bulletin_ , Oliver's own newspaper, under the headline \"Spinsters Want Homesteads.\" It asked that homestead lands be available to any unmarried woman in Canada over the age of thirty. The central argument advanced in the petition was that unmarried women settlers were as desirable as widows were. It was an injustice to favour widows only, as they often had an inheritance, while a \"noble class of women\" was just as deserving of land: women who found themselves \"at middle age thrown out upon their own resources, the majority of them having had to sacrifice opportunities of marriage and competence for the sake of remaining at home with one or more aged parents to provide and care for them in their old age.\" The minor children of widows permitted to homestead would become financial assets to their mother, whereas those women who cared for parents had no one to provide for them. Signatures were to be collected from \"the undersigned, unmarried women of Canada.\" A Miss Helen N. Weir of Edmonton was identified as the leader of the \"agitation.\"\n\nThe context for the petition was explained in a letter to the _Manitoba_ _Free Press_ , where the petition was also published in mid-June 1910. \"M.S.T.\" wrote that a number of women in the Edmonton district had asked her to organize a petition. She was from the United States and had moved to Alberta because of the advertisements she had read about \"free land.\" When she applied for a homestead, however, she was told she was ineligible. \"Well, I was surprised, just having refused to join another single woman, who with her father was filing on 160 acres of choice land in Arkansas.\" She believed there were hundreds of unmarried women who could homestead as successfully as men. She argued that unmarried women who had cared for aged parents \"should be rewarded, not looked down upon and called 'old maids' on the bargain counter.\" She understood that because of the \"scarcity of white women... good decent men are degenerating and marrying squaws,\" and further argued that women were far more capable of homesteading than the many \"foreigners who come to this country, men who have never pursued agriculture in their home country and know practically nothing about it.\" It was later reported in the _Free Press_ that the author of this petition had returned to the United States.\n\nMARSHALLING THE ARGUMENTS FOR WOMEN HOMESTEADERS\n\nIt is not clear how many signatures this first, Edmonton-based petition received, or whether it was ever submitted to Parliament. There was a fundamental strategic flaw, however, embedded in the petition, as it was organized by an American woman, and the petitioners were women and, of course, non-voters. Canadian legislators could easily dismiss it. Women reformers were divided about the value of petitions but there was agreement that \"petitions signed by women are usually treated as a joke by the electors,\" as prominent activist Nellie McClung told a suffrage rally in 1912. Although petitions were to become the main tactic of the homesteads-for-women campaign, strategies changed considerably after this initial petition that stressed that single women should have the same rights as widows.\n\nThe _Grain Growers' Guide_ became a focus for the campaign, and women's page editor Isabelle Beaton Graham (\"Isobel\" in her column \"Around the Fireside\") was the main voice of the campaign. Born in Ontario, Graham had attended the Alma Ladies College, where, as mentioned in Chapter 2, principal Benjamin F. Austin was an advocate of farming for women. She homesteaded in Manitoba with her husband, Francis Graham, also from Ontario. They had three daughters and one son, and Graham used the example of her own family to point out the inequities of the homestead system, as families with daughters did not have the same option to expand their holdings as families with sons. The Grahams moved to St. Boniface in 1906, where he was a founder of the Grain Growers Grain Company, and she wrote for the _Guide_ , founded in 1908. The _Guide_ had a cooperative reform agenda, and it supported women's suffrage from its first issue in 1908. Readers of the _Guide_ were asked to organize, agitate, and educate on the issues of homesteads for women and dower rights. Isabelle Beaton Graham was involved in the women's suffrage campaign in Manitoba, and was one of the participants in the Mock Parliament in Winnipeg in January 1914. Graham was the speaker of the house, while Nellie McClung was the premier and a delegation of men waited upon the government with a bill for \"Votes for Men.\"\n\nThe women's page editors of other major Western publications, including Mary S. Mantle, or Margaret Freeston, of the _Nor'West Farmer_ , and Lillian Laurie, or Lillian Beynon Thomas, of the _Manitoba Free Press_ , also supported homesteads for women. There were lively debates in many of these publications, including letters to \"Prim Rose\" of the Western edition of the Montreal-based _Family Herald._\n\nBinnie-Clark was not particularly active in the campaign in Western Canada (the focus of her lecturing and publishing was England), but she was used as evidence by organizers on the prairies of the interest in and ability of women to farm. Graham had some angles of her story incorrect, believing that Binnie-Clark had arrived in Canada hoping to homestead and had purchased land only after she \"was unable to persuade the Dominion government to grant her a free homestead.\" But Graham applauded her example, writing that she was \"a woman of pluck and determination. She came to Canada to farm, to experiment not only for her own benefit but also for the benefit of single women of her own social level left behind in England.\" Graham wrote that Binnie-Clark would \"make a great immigration agent to the old land among women like herself, women of culture and some means, when the Canadian government grants free homesteads to women.\"\n\nMany arguments were advanced in favour of homesteads for women. A central rationale was evidence that a large number of women wanted to homestead. Supporters pointed to the success of the widows, and to women's interest in obtaining homesteads through purchasing South African scrip (SAS); they had \"quietly and promptly availed themselves of the homestead privilege made possible by buying... scrip. This proves conclusively that it is only necessary to give women the opportunity and they are anxiously willing to be self-supporting, and no longer a drag upon the pension list of their masculine relatives.\" It was pointed out that it was not fair that only women with sufficient money could qualify for homestead land. It also seemed \"rather illogical that women can do duty on a scrip, for which they must pay, but cannot on a homestead.\" Women's ability to purchase and to prove up on homesteads through SAS also made a mockery of the assertion that only men had the strength and stamina to withstand the difficulties of homesteading.\n\nWomen wrote to farm journals and to officials of the Department of the Interior stating that they wanted to homestead. In 1910 an Englishwoman, resident in the West for three years who worked as hired help and living with her brother, wrote to the _Nor'West Farmer_ that she had read of Binnie-Clark's farming and \"would like to see the free land grant for women. I like to see women independent. I don't like the idea of an almshouse at the end of life.\" An \"English Violet\" from London wrote to \"Prim Rose\" of the _Family Herald_ in 1913 to say that she would take a homestead if offered to single women. She had worked for two years on a dairy farm on Vancouver Island, and for her farm life was ideal: \"The greatest fascination which farm life possesses is that it is so creative, so constructive and so vitally alive.\" \"Farmer's Daughter\" wrote that she had spent her life on farms in Ontario and the West and could see no reason why she should not be allowed to homestead, as she was \"very ambitious in every line of farm work, thoroughly enjoying it, as I find it ennobling to both mind and soul.\" \"Irish Jill of All Trades\" also wrote that she was a farmer's daughter, that she could \"drive horses, cut grain, disk, harrow, plough and even drive nails as well as most men. I don't see why women have not as much right to land as men. The average woman works as hard as a man and sometimes harder.\"\n\nIt was not just single and young women who sought homesteads. Married and older women expressed an interest in homesteading due to their family circumstances. A \"British born\" woman wrote to the _Nor'West Farmer_ in 1911 to say that she had lived in Canada for over forty years, that she had married a Canadian and had a family of girls, had worked very hard to raise and educate them, but \"now at fifty-eight, I find myself, through no fault of my own, without a home. My husband is old and broken in health, and he has exhausted his homestead rights. I also am not very strong but still could do homestead duties. No doubt there are hundreds in the same position that we are in.\" Another married woman, who had worked with her husband to prove up on a homestead, wrote to the _Guide_ in 1911 that she would soon have no home as her husband had mortgaged their farm and she had no say: \"It was my husband who had the rights to the homestead.\" If she had the right to take a homestead of her own, she would have a home.\n\nThe success of the widows who qualified to homestead was also evidence of women's capacity. As \"Lochinvar\" wrote to the _Guide_ in 1911, he \"could never see the right or reason of women being unable to make entry for land.\" His own mother, a widow, \"had two homesteads in the West, and I may say this just put her in first class circumstances.\"\n\nThe situation in the Canadian West was often compared to that of the U.S. West, where single women could homestead. A related argument for women's right to homestead was that Canada was losing girls and women to opportunities south of the border. Accounts by U.S. women homesteaders and farmers were published in the _Guide_ , such as \"Woman on Forty Acres,\" written by a woman farmer in Montana who grew wheat, oats, and sugar beets, raised poultry, and had a comfortable home of six rooms.\n\nAs a reader wrote to the _Nor'West Farmer_ , \"If American girls can do this, are we Canadian girls so far behind our American cousins that we can't?\" Editor Margaret Freeston replied that she knew two girls who went to the Dakotas because they could not secure homesteads in Canada and were \"now the proud possessors of deeds to the land. What a pity that 'good stuff' like these girls were made of should be lost to us!\" Will Channon, who wrote to Ottawa from Cordova, Manitoba, in support of homesteads for women in 1910, said this was necessary to \"stop many of them going over to the United States where they are privileged of homesteading.\" A.H. Cunningham from Ravine Bank, Saskatchewan, wrote to the _Guide_ that \"I have often thought it a shame that in the United States women could take land and here in Canada where there is so much more land they are not allowed the privilege. I have seen women in the States that did their duties far better than the average bachelor.\" \"Canada has never shown any kindness to her women that I ever could see,\" wrote a woman from Claresholm, Alberta, to the _Guide_ in 1912. \"Her girls are just as bright and intelligent as those in the United States. The latter were allowed to homestead while Canadian girls were pushed behind the door.\" She knew of women who had homesteaded in the States, sold out, and bought land in Canada, and she also knew Canadian women going to Montana to homestead and asked, \"Why could they not stay at home, as our land is just as good if not better?\" \"Long Bob,\" a widower, wrote to the _Family Herald_ in 1913 that the women homesteaders of \"Uncle Sam's domain... have invariably made a success of it. I cannot see why the women of Canada cannot do as well, or better, as invariably they are of a more rugged character than their southern sisters.\"\n\nNellie McClung was acquainted with women homesteaders in the United States, and she used their example to show that they were willing and capable, writing that four girls together were each homesteading a quarter of the same section after having worked in offices and stores, and saving a little money to make a start. They had cleared land of bush with only axes and hoes. McClung knew of one woman who went from Canada to Minnesota to homestead and was the owner of 160 acres. She was careful to stress that this woman had not lost her femininity or \"womanly charm,\" as she was to be married to a neighbouring homesteader. McClung wrote, \"I believe free grants would develop a splendid type of resourceful women for Canada. What a pity the government can't see it.\"\n\nMany supporters in the initial phase of the campaign were either from the United States or had lived and homesteaded there, or had been neighbours of women homesteaders. \"Another Farmer's Wife\" from Alberta wrote in 1912 to the _Family Herald_ to say that she had had many women homesteaders as neighbours in the United States and that they were \"college bred women who made a great difference to their districts to the bachelors especially.\" She argued that during the \"hard times... between 1893 and 1896,\" the men abandoned their homesteads but the women \"were not so ready to jump from the frying-pan into the fire. They hung on to the homesteads and today they are well-fixed and have their own fine homes. But the men\u2014not so with them; somebody else owns their homes today.\" She also believed that Alberta \"would be far more settled and a better country today, if women had their rights here as they should have.\" Many women, she believed, including her own daughters who had remained in the United States, would come to Alberta if they had homesteading rights. One woman homesteader in the United States took part in the debate. A \"Montana School-Ma'Am\" wrote to the _Family Herald_ to say that she was living on her 320-acre homestead and was \"as happy as a clam in the land of Uncle Sam.\"\n\nReaders of the women's columns in the farm journals and newspapers of the West were kept up-to-date on the success of women farmers in the United States and elsewhere. In early 1910, Margaret Freeston of the _Nor'West Farmer_ wrote about the great scope and variety of agricultural pursuits of women in California, including poultry, fruit, cattle, and horses, and described how they had formed a Women's Agricultural and Horticultural Union. She concluded, \"Thus it would seem a 'prosperous farmer' is not necessarily of the masculine gender.\" The _Nor'-West Farmer_ also published articles such as \"Women Prize Winners at Scottish Plowing Match.\" Developments elsewhere reported on in Western Canada included the organization in 1909 of a farm for \"spinsters\" in Boston, and in 1912 of a colony for women only in Australia, organized by the English Woman's Householders' League. In 1913 the _Family Herald and Weekly Star_ ran a story of five sisters who operated a farm of 200 acres in Buckinghamshire, England. There was also coverage of agricultural education elsewhere that was available to women. In a 1910 article, \"Girl Graduates in Agriculture,\" readers of the _Grain Growers' Guide_ learned about two sisters who graduated from the agricultural college at Cornell and operated the New York farm they inherited from their father. The author countered the argument that it was a waste to educate women as all would be lost if they married and left the farm, writing that \"the work of life goes on just the same after marriage.\"\n\nSupporters of homesteads for women argued that women had the physical strength and capability to homestead, which they were proving throughout the West by performing homestead duties on the farms of spouses, brothers, and fathers. In a letter to the Department of the Interior, a man from Saskatchewan wrote in 1913 that women worked very hard for years on homesteads, building sod barns and shacks, haying, ploughing, raising poultry and eggs, growing vegetables, planting flowers, \"& everything,\" and that men who had \"made good here do it by the help of the wife,\" as \"there is nothing too hard for them to work at it seems.\" Yet \"the wife for all her labour has not an inch of land her own.\" As \"X.Y.Z.\" wrote to the _Guide_ in 1913, \"A wife who can rise at four and five o'clock in the morning and wait on a lot of hired men, with the husband in bed, is quite capable of homesteading.\" In a 1912 letter, \"Bronco Buster\" wrote that she was alone on a Montana ranch with her father from the age of five, that she went on the round-up every year, that she could \"ride any kind of horse, throw a steer and tie him in four minutes, brand a colt and handle the rope in all its forms. I have two belts given me by Teddy Roosevelt and Governor [E.L.] Norris of Montana for expert horsemanship. I can do anything that can be done outside.\"\n\nThroughout the West on homesteads, farms, and ranches, women and girls worked in the fields and with livestock. This sight could surprise some observers. A government surveyor wrote in 1899 of his first encounter with women at work on a ranch in Alberta:\n\nThis is where I first saw young women on horseback, herding and rounding up cattle. These young women would ride at break neck speed, turning and twisting rapidly in all directions and as fearlessly as experienced cowboys. They mounted and dismounted as gracefully and easily as experienced men. I saw one young woman mount into her side saddle on a fair sized bronco from the level ground. I asked her to dismount and mount again, in order that I might see how it was done, and in an instant, she was off and on again from the same level as the horse.\n\nSupporters were also careful to emphasize that women could be feminine and still perform labour out of doors on their homesteads. \"Bronco Buster\" wrote that she was \"just as much of lady as I would have been had it been ten years in a convent\" rather than ten years on a ranch, and that \"a lady will be a lady no matter where she is or what she has to do.\" She could do \"fancy work,\" having learned it while taking care of 500 ewes, and she had cooked for a crew of seventeen men.\n\nHomesteading would keep women on the land and away from the evils of the city, offering them a healthy and invigorating environment. Graham argued that it was unfortunate that a daughter raised on a farm had to turn to teaching, dressmaking, or stenography when she had all the necessary skills to work on the land, that \"all her soul [would] call aloud for the prairie, for the grating of the plow, for the swish of the binder, and the hum of the threshing machine, never to mention old Brindle or Bess, or the little colt she had raised by hand... in the name of common sense and common humanity give them a chance to farm and live the life they love and are suited for.\" Arguments for the strength and stamina women would build on their homesteads dovetailed with beliefs in eugenics. Homesteads for women would develop a \"nobler race.\"\n\nAnother widely shared rationale was that homesteads for women would provide a source of wives for bachelors of the West. They would not have to marry women who were \"beneath\" them in refinement and education. The result would be \"contented, prosperous homes, instead of a region of vacant farms, with only the ruins of bachelors' shacks (monuments to a short-sighted policy), to break the monotony of the view.\"\n\nA central argument advanced by many supporters was that it was an injustice to award free land to families of boys, while those who had girls were penalized. A family with four boys could have five homesteads altogether while a family with all girls could only have one; the family of boys became wealthy while the family of girls became poorer, as pointed out in an editorial in the _Guide_ that concluded, \"Until the government of our land is entrusted with the power of ordaining the sex of children it does not seem fair that such discrimination should be made as is done in the case of our homestead laws.\"59 The homestead issue was linked to that of dower rights in many ways. As explained in a 1913 _Star Phoenix_ article, for a woman to obtain a homestead she had to marry a man and either keep him alive (and they both work to prove it up, although ultimately it would be his property when the patent was granted), or \"let him die\" (and as a widow, if she had young offspring, she could file on her own land). Valance Patriarche wrote that\n\nto an independent and wary spinster... the necessity of a husband brings not only a pause but a full stop. Unlike the Ontario benedict, the married man in the Prairie Provinces may sell, give away, or will away the home without so much as acquainting his wife with his intentions. Just as she has completed three years at hard labor on a farm and is wheezing out hymns of thanksgiving on the melodeon because they own their own land, he may saunter in and tell her he has given it all to the pretty summer visitor on Jones' farm, a proceeding quite within his legal rights. It is not to be wondered at that the hardy perennial spinster desires to bloom alone in prairie soil.\n\nIssues around homestead or farm inheritance were also part of the general critique of the injustices of land ownership and distribution on the prairies. In a 1910 column in the _Grain Growers' Guide_ , Graham wrote that \"in no country under the sun has woman been more directly responsible for increased land values than in Western Canada\" and yet sons, not daughters, inherited farms, based on the rationale that a son \"earns or helps to earn the land, therefore the land is sacredly reserved for him.\" The son might feed the cattle, while a daughter feeds the household; his work was valued, while hers was not. Graham called for daughters to inherit equal shares of farms and estates as a \"birthright.\" In many of Graham's pleas for \"equality,\" however, she also mentioned the entitlement of women, meaning British and\/or British-Ontarian women, over the rights of \"foreigners.\" In this column she continued: \"Parents who do not dower their daughters equally with their sons are worse than the Dominion government, that will not give homesteads to Canadian women, but prefers rather to dower the unspeakable foreigner.\"\n\nIn letters to the farm journals or to the Department of the Interior, the issues of dower and homestead rights were often intertwined. Mrs. Thomas McNeil wrote to the minister of the interior in 1913 to say that she had come from Ontario with her husband and eleven children, that they had entered on a homestead in 1909, but that\n\nafter he got his Patent for his Homestead sold it for $2800 and then hit away to Maple Creek with an excuse to buy Horses and to take a purchased Homestead, I have found out that he has drank the most of it by this time and has not took a purchased Homestead yet and about all the satisfaction I can get is that a man in the Saskatchewan can do as he likes with his own property but if he ever does take a purchased Homestead I would never go to live on it. I got hunger enough on this one. I would often have starved only for what my children had sent me.\n\nMrs. McNeil concluded her letter by saying that \"if it is ever in your Power to Help Women to get Homesteads I do hope that God Almighty will reward you for it all.\"\n\nA fundamental criticism of the homestead legislation was that women were just as deserving of the grant of land as men were. The land grant was cast as a birthright, inheritance, or reward that was owed to women as well as men. As one supporter of the campaign wrote in the _Guide_ : \"God put both Adam and Eve into the Garden of Eden. Evidently Eve had as much right there and on the land as her husband.\" As will be discussed later in detail, this rationale was usually bolstered by noting that land that (British or Canadian) women deserved was going to \"strangers\" or \"foreigners.\"\n\nWomen\u2014including married or deserted women\u2014had also earned this birthright, it was contended, as they were directly responsible for increased land values. Mrs. J.R. Long took this position in her letter to the _Nor'West Farmer_ :\n\nThere are millions of acres of land lying here waiting to be taken up\u2014any male subject over eighteen years can come and have a half section for the asking and the small entry fee, but a woman who is forced into the world to earn a living for herself and little family cannot have an acre unless her husband is deceased. Is a deserted wife with a family dependent upon her not more worthy of a homestead than perhaps her unworthy husband who may be in some other part of the country experiencing no difficulty in securing a homestead? And is a widow who either has no family or a family all married not worthy of some consideration?\n\nWriting the Department of the Interior from Stalwart, Saskatchewan, in 1913, Mrs. Fanny Elizabeth Shepherd asked this very question; she was not eligible for a homestead because her two sons were not minors. She kept house for one of her sons, but when he married she \"wanted a roof of my own over my head.\" She could not afford to purchase land. Shepherd stated she could complete the homestead duties satisfactorily, and she too argued she could \"do better than several half-witted fellows about here who have got [homesteads], or ignorant foreigners who cannot speak a word of English.\"\n\nWhile \"foreign\" men were singled out for criticism, some supporters of the campaign extended this to a larger group of males. W.F. Graham wrote from Pettapiece, Manitoba, that there were women in every Canadian city, including teachers, stenographers, and clerks, who were \"surely more valuable citizens than the drinking, carousing, cigarette smoking young fellows who loaf about bar rooms, and yet the latter have votes and homesteads and the former have neither.\"\n\nAlthough this facet of the argument was muted, perhaps in order to appear non-threatening, supporters of homesteads for women linked homestead and property rights to suffrage, arguing that with homestead rights, women would be landowners and would therefore have to become voters. In a letter to the _Free Press_ , \"Business Woman\" wrote, \"Why the Dominion government does not grant a homestead to each and all of our Canadian women who want one bad enough to do all the homestead duties the same as a man, instead of importing foreigners from all over Europe mostly factory and labouring hands, I cannot see, unless they are afraid that with women landowners we would the sooner get the vote.\" In the _Voice_ (Winnipeg), the newspaper of the western trade unions, it was noted that supporters of homesteads for women \"probably have in mind the anomalous position the woman will be in who homesteads, if the government will amend the law and grant her that right. She will be a freeholder of the fertile lands of the west... but will still be in the position of a minor or dependent, denied the right of the franchise. If women should have the right of homestead they should have the right to vote.\"\n\nThe issue of the franchise was also linked to that of the \"foreigner\" male, as \"Business Woman\" wrote above. The \"foreign\" man could not only obtain a homestead but could also vote. As \"School Teacher\" wrote to the _Manitoba Free Press_ in 1910, women's right to homesteads \"should go hand in hand with women suffrage. When foreigners receive 160 acres of Dominion land apiece with the franchise thrown in, surely a Canadian woman should receive much more. We have the right of common claim and assuredly deserve this act of common justice from our native land.\"\n\nThe rationale that began as muted but increasingly took centre stage was that homesteads for (some) women would address the \"foreign menace.\" \"A Saskatchewan Farmeress\" wrote in April 1910 to the _Guide_ that \"I know of no less than a score of good, honest, respectable girls of proper age, who would be a credit to any neighbourhood or province, and who will do more to improve not only the homesteads but the country, than all the Doukhobors in the province.\" The corollary of this was that the right sort of woman had to be encouraged to populate the West, and homesteading could entice that kind of woman while domestic service would not. \"Jemima\" argued in 1912 to the _Nor'West Farmer_ that the West needed to attract British and Canadian-born women who might establish dairy and poultry farms, or raise sheep and goats. She ventured to say that if domestic service had been the only thing offered to young men, then few would have settled in Western Canada.\n\nOPPONENTS\n\nOpponents of homesteads for women included powerful men such as Frank Oliver, who drew on a variety of counter-arguments, including that women would not be inclined to marry if they had the right to homestead on their own, and that married couples were required to establish homesteads and family farms on the prairies. Calgary Conservative politician, and later prime minister R.B. Bennett maintained that if separated women were allowed the right to homestead it would encourage couples to part ways. (Opponents did not seem to realize that the homestead laws caused people to postpone or even avoid marriage. As one observer noted, \"A certain widow and a certain man are living side by side, and, while they ought to marry, they cannot do so for a period of three years, until the widow has proved up on her homestead.\")\n\nFor opponents, the American West was not a source of inspiration. As discussed in the last chapter, J. Obed Smith told Binnie-Clark following her 1913 presentation to the Royal Colonial Institute that Canada did not want to pursue the same \"disastrous\" course as the United States had. He elaborated on this some months later in a \"despatch,\" explaining that in the United States, \"in nearly every case there was a distinct evasion of the spirit of the law... the American girls took up their homesteads, so did their fianc\u00e9s. Then they married and had two homesteads, contrary to the spirit of the law.\" In a 1904 article in the _Globe_ (Toronto), a special correspondent commented on differences between the Canadian and U.S. West, noting that the United States \"appears to be more liberal in its treatment of the fair sex.\" He had learned this at his hotel, where he could not get a cooked breakfast and discovered that the dining room waitress was \"out on her homestead.\" He reported that in the United States virtually no improvements were required before patent to a homestead was issued, and included a story of the mayhem that resulted from the lenient divorce laws of the United States and the laws that permitted women to homestead:\n\nThis holding of land by women is responsible for the story about the South Dakota married couple, a farmer and his wife, who held a quarter section, but wanted another one. They determined to take advantage of the lax divorce laws of the State, get divorced, after which, as a single woman, the lady could take up the adjoining quarter section after which they would be remarried. The idea worked out well at first. The divorce and the quarter section were both secured, and the farmer built a house half upon his own and half upon the lady's quarter section. But it was another case of the course of true love. Once divorced the lady fell in love with another man, married him and husband No. 2 secured the coveted quarter section. The story does not tell how the house was divided.\n\nIn his 1907 publication, _The Land Laws of Canada and the Land Experience of the United States_ , Ditlew M. Frederiksen was critical of the \"school marms\" who had been permitted to homestead in the U.S. West. Like Smith, Frederiksen found their claims a fraudulent abuse of the homestead laws. He quoted the findings of the 1905 U.S. report of the Public Lands Commission about entries made by \"female school teachers, who spend their vacations on their claims, commute the entries, and leave the country as soon as a better paying position can be found elsewhere.\" (Frederiksen found, however, that there was even more widespread abuse of the homestead laws by men in both the United States and Canada. Referring to Saskatchewan, he wrote that \"what greets the eye frequently is one shack after another without any signs of real fields, stables ... clothes hanging out to dry on the line, or other evidences of progress, family life and civilization.\")\n\n\"Rural legends\" of frozen young women homesteaders of the American West helped to point out their unsuitability and ineptitude. In 1906 it was rumoured that \"two girl homesteaders were frozen to death on their claims\" in northeast Montana, but it was also reported that \"no particulars are obtainable.\" In 1916 it was widely reported that two teacher homesteaders had been found frozen to death near Havre, in northern Montana close to the Canadian border. The tale had many touching details, including that they were sisters who penned notes saying goodbye to their mother. The story was found to be a hoax.\n\nJ. Obed Smith was convinced that women were incapable of the physical labour required on a farm, and other opponents agreed. \"Homo\" wrote to the _Family Herald and Weekly Star_ in 1910, \"Show me the woman who will handle horses, plough, pitch hay, stook grain etc. Oh, no. The very first thing she must do after securing her homestead is to hire, marry, or to otherwise obtain a man.\" He continued: \"Every woman in her heart knows full well that she is vastly inferior to man physically. If there are any who do not, they are to say the least, very foolish.\" (Such letters generally generated many more by women who were performing all of the tasks necessary on a homestead.) Opponents to homesteads for women also claimed that women could not hire and supervise men. The problem would then be idle and vacant land, and \"those who live in the west fully realize the great necessity of rapid development of the country.\"\n\nFor context, it is instructive to remember that there was a time in Western Canada when there was debate about whether it was proper for women to learn a host of skills or habits defined as masculine, such as smoking or driving machinery such as an automobile. In 1915 one critic of women's abilities wrote to the _Calgary Daily Herald_ that driving a car was \"the most severe test one can possibly have on the nerves.\" He doubted that women would be able to act decisively and without warning to avoid accidents, or that they were strong enough to steer and use the brakes. A Calgary alderman was in favour of a by-law prohibiting women from driving cars, saying, \"Women may be and doubtless are perfectly capable of driving an automobile but when they meet a sudden emergency in driving they are apt to lose their heads.\"\n\nIssues of femininity and propriety were raised by critics of women labouring outdoors. One woman wrote that any farmer husband would be \"ashamed to see [his] wife ploughing in the fields.\" Many commented that woman's place was as wife and mother, and that young women should be striving to marry the bachelors of the prairies who had homes established already. \"Homo\" wrote, \"I am of the opinion that if those few women of today, who are clamouring, shrieking, and wasting their time in a futile attempt to attain that which would be of little, if any, use to them, would devote their time to their children, and other duties for which they were created, they would be rendering a far greater service to their sex.\" Many insisted (despite the huge volume of letters to the contrary) that \"I have yet to meet any single woman who is anxious to go homesteading.\" \"Pencilitus\" continued: \"What young woman with any intelligence would want to cast her lot on the prairie without any protection and perhaps as far as twenty to forty miles from kith and kin.\" \"Pencilitus\" asked what would become of the country if \"women were given to grasping after the material things of this universe? What would become of our schools and colleges, our hospitals and kindergartens, and last, but not least, the home?\" Young women striving to get ahead of young men in material things would destroy the \"law of attraction.\"\n\n\"Silver Knight\" agreed that he knew of few Canadian girls who would \"forfeit their modesty and 'rough' it for three years at least, even for the sake of getting 160 acres of land for free.\" He added that Canadian mothers would not want to see their daughters live on a quarter section for three years. \"It oftentimes becomes a woman to relinquish her 'rights' and uphold her dignity,\" he wrote. \"Silver Knight\" had travelled extensively and knew of no other place where women were \"more respected, appreciated and rewarded than in western Canada.\" The \"sons of Canada\" treated the women of the region with \"chivalry, courtesy, respect.\" Women had to milk cows morning and night in Ontario, but \"it is a very unusual thing for a woman to be seen milking in Western Canada.\"\n\nReluctant supporters of land for women advocated that if women were to have homesteads, they should have much smaller acreages. \"Eureka\" wrote in 1912 from Saskatchewan to propose that 160-acre homesteads be broken up into twenty-acre plots for women to share. They could also share accommodation and save costs, and in this way \"make an independent living at poultry raising, dairying, gardening, or raising small fruits.\"\n\nEnglish travel writer Bessie Pullen-Burry gave some coverage to the homestead campaign in her 1912 book _From Halifax to Vancouver_ , but she was decidedly lukewarm toward the idea of encouraging women to emigrate for that purpose. In Winnipeg she met with journalist Ethel Osborne, who was a supporter of the cause, and Pullen-Burry provided a synopsis of the main arguments, but in her opinion, \"Canadian women in the West are the worst off of any of their sex among civilised peoples.\" She learned from a Scottish woman settler that \"to say that the conditions of life for educated gentlewomen in Canada were not a daily round of toil and monotony... would be to obscure and to pervert truth.\" Dangers lurked everywhere for the women settlers in solitary districts, and the Scottish woman believed it \"absolutely indispensable\" that women \"become practised shots.\" A young schoolteacher had allegedly recently been \"dragged to the woods by a ruffian.\" Pullen-Burry wrote that \"women living on these isolated farms, I assure you, go through periods of mental torture from sheer terror which men never realise until some horrid tragedy within a stone's throw of their own farms makes them uneasy as to the risks run by their womenfolk.\"\n\nElizabeth Keith Morris, author of _An Englishwoman in the Canadian West_ (1913), opposed homestead rights for women. She was a critic of the \"lady farmer,\" as she referred to Binnie-Clark (as mentioned in the previous chapter), and wrote that the Canadian government wisely limited the homestead right to men, realizing the difficulties and hardships women would confront. She agreed with the \"existing opinion amongst farmers in Canada\u2014that the hard and heavy work is unsuitable for women. We heard of odd cases where modern Amazons had many acres under cultivation, but these were exceptional and should not point the way to others.\" Only a very few would have the physical stamina: \"The gently-nurtured, sheltered and irresponsible type of English girl would be mad to dream of following such an occupation, for she is unsuited to any kind of life in the Dominion.\"\n\nThough their voices were few in the letters columns, \"foreigners\" objected to what was becoming a central element of the campaign, which was to question the entitlement of \"outsiders\" to land when British and British-Canadian women were denied homesteads. A \"foreigner\" wrote to the _Manitoba Free Press_ in 1910 to say that the majority of farmers on the prairies were \"foreigners of different nationalities,\" and that they were doing their share to improve the land and that surely they deserved homesteads. (He also believed it was not \"a woman's place\" to homestead, since women could \"get married and let the husband do the work\" while having plenty to do with home and offspring.)\n\nIt is interesting that in the debates that took place in the farm journals and newspapers of the West, none of the opponents argued that by farming, British or British-Ontarian women would sink to the level of \"foreign\" women or the Indigenous women of North America or other colonies. Yet this was implied through the widespread coverage of the Doukhobor women who hitched themselves to the plough. A 1911 article that was published in numerous newspapers of the West pronounced that Doukhobor women \"have been reclaimed from the plow. No longer do they sweat in the fields of Canada instead of horses... the new world's environments have drawn the women back from the brute level, to which they have been degraded, to the home, with its cooking, its spinning, and its weaving... The melting pot of the western world has recast even the Doukhobors.\"\n\nHOMESTEADS FOR SOME WOMEN BUT NOT OTHERS\n\nIncreasingly, the central rationale in the homesteads-for-women campaign was that land grants should be available to \"daughters of British blood\" rather than \"hordes of men of alien race.\" Similar arguments were being made by some supporters of women's suffrage. E.A. Partridge, founder of the _Grain Growers' Guide_ and a supporter of women's suffrage, argued in a 1909 editorial that it was an \"outrage to deny to the highest minded, most cultured native-born lady what is cheerfully granted to the lowest browed, most imbruted foreign hobo that chooses to visit our shores.\" At the _Guide_ , Isabelle Beaton Graham increasingly emphasized this argument for (some) women's homestead rights. In her 1909 column that helped launch the campaign, under the subheading \"Consider the Douks,\" she protested the gift of homestead land to the Doukhobors who \"so scandalize civilization.\" \"It is painful to realize that our own Canadian men,\" Graham wrote, \"our fathers and our brothers\u2014deliberately set us aside as undeserving of a share in our country... to bring in ignorant, uncouth, lawless foreigners to occupy lands that we desire, that we have labored for yet cannot have.\" In her next, most sustained column on the issue, \"Unearned Increments and Woman's Dower,\" Graham wrote that the federal government preferred to dower the \"unspeakable foreigner,\" while denying to women the proceeds of their own toil.\n\nThis argument found many supporters in the pages of the _Guide_ and other publications. \"Mother Scot,\" from Alberta, complained that their farm was surrounded by a \"colony of aliens whose habits and ways of looking at things make them hopeless as neighbors,\" and \"I often think how unfair it is to give these outlanders the privilege of homesteads and deny that privilege to their own race and blood, when it happens to be of the other sex. Is not the mother\u2014actual or prospective\u2014of sons and daughters of British blood at least as worthy of a share of God's free gift as the hordes of men of alien race who are given free homesteads without a condition?\" From Wapella, Saskatchewan, \"Lochinvar\" mocked the law that permitted any male to homestead while British and Canadian women were denied: \"He may be the greatest imbecile in the world, but, if he wears pants and keeps cool he can get the farm. He may come from the ill-fed, ill-bred and illiterate peoples of parts of Europe. He may come from the darkest jungles of darkest Africa. He may be the greatest villain the universe produced, he can get the land, but women, cultured, refined, able to make and keep home happy\u2014not on your life.\" This writer concluded that it was folly to provide land to \"semi-savages,\" who would take \"centuries to mould into a British subject, in preference to a British woman with British pluck, endurance and everything that makes for an enlightened Canadian citizenship.\"\n\nGraham and other supporters of homesteads for women manipulated fears of the \"foreign\" or \"alien\" element that prevailed among the British-Ontarian settlers. Intolerant attitudes toward immigrants seen as undesirable, including Mormons, Ukrainians, Jews, Doukhobors, and Asians, were stridently and widely broadcast in the late nineteenth and early twentieth century in Western Canada. Many of the most prominent newspapermen in the West, such as Frank Oliver and P.G. Laurie, editor of the _Saskatchewan Herald_ , Battleford, took the lead in propagating these views. How could \"the Greater Britain Beyond the Seas\" be forged from the peasantry of Europe? A further \"outrage\" was that these \"aliens\" could vote, \"men who have just emerged from serfdom... who are ignorant of they very alphabet of the public life of Canada.\"\n\nProponents of homesteads for women capitalized on fears of the \"foreigner\" to connect themselves to issues of national and imperial importance to which they could offer solutions. They were asking for equal treatment, but only for those British and Canadian-born women who qualified for inclusion. Like suffragists in the U.S. West and in other colonial settings, they \"manipulated ideas about racial and ethnic 'Others,' usually reinforcing contemporary racialist and racist attitudes, particularly those linking race, sex and 'civilization.'\" In Western Canada, however, supporters of homesteads for women could not claim superiority by virtue of their \"whiteness,\" since the \"foreign\" women they wanted to exclude from the privilege of homesteading were phenotypically similar. It was not particularly clear just who was \"white\" in Western Canada. As Catherine Hall has observed, the question of \"who was white\" was seldom straightforward in the colonies of the British Empire. Instead of whiteness, Britishness became the marker of privilege in Western Canada, and a British-Canadian elite dominated business, politics, the law, and education. Leaders of the homesteads-for-women campaign decided to align themselves and identify with this elite, arguing that British-Canadian women settlers would help maintain the hegemony of the group.\n\nThe manipulation of fears of racial and ethnic \"others\" among some supporters of homesteads for women reached a new level in 1911, when the likelihood loomed of a sizeable migration of African Americans from Oklahoma to Alberta and Saskatchewan. They had begun to appear in small numbers in 1905, increasing after 1907 when Oklahoma became a state and the first state legislature passed \"Jim Crow\" legislation, and again in 1910 when Oklahoma Democrats moved to disenfranchise African Americans. There was a strong reaction against this migration in Western Canada. Graham's columns in the _Guide_ were among the most racist, strident, and alarmist, containing utterly fabricated allegations. Her column \"The Negro\" of 3 May 1911 began,\n\nFireside would like well to know what the people, especially the country women of the west think about the negro invasion that is now pouring into the Canadian west and receiving free land grants from the Dominion government, and farming large settlements contiguous to and among the whites. There can scarcely be anyone who is not aware of the atrocities committed by members of these terrible communities, the only corresponding punishment for which is the lawless lynching, and even burning at the stake. Already it is reported that three white women in the Edmonton and Peace River districts have been victims of these outrages accomplished in peculiarly fiendish abandon. Where will the end be? ... How many of these industrious, courageous, unprotected, country women must be sacrificed to the horrors of negro attack before the slow and rusty machinery that drives the engine of state can be induced to erect a barricade against so dreadful an evil?\n\nAlthough it seems like an odd leap after pointing out the vulnerability of women alone on homesteads, the main point of Graham's column on \"The Negro\" was that women should be given the right to homestead. She concluded that \"it should be possible for Canadian women to secure from the government of their fathers, husbands, brothers and sons at least an equal share with the foreign negro, in the rich heritage of the Dominion's homestead lands.\" This was also Graham's first column to clearly articulate that homesteaders should not be \"foreign\" women who did not know the \"rigors of the country, and who are bound to fail through the discouragements of unexpected hardships. In their interest it is wise to hinder them at the start until fully assured that they understand the undertaking.\"\n\nIn the _Saskatoon_ _Star Phoenix_ , Valance Patriarche warned of the \"Foreign Menace\" that was a \"grave concern\" and a \"hazard that threatens the unity of Canada.\" She feared that the \"native population,\" by which she meant Canadian and British settlers, would soon be \"overwhelmed, lost amid the foreign invasion.\" Granting single women free homesteads would help to Canadianize this \"cosmopolitan element.\" She explained: \"Many wise thinkers are advocating a slower, finer growth for the West, and it is indisputable that the encouragement of Canadian and British women would be a step in the right direction. There is a crying need all through the West for teachers and church workers. On the other hand there is a longing in the heart of many a courageous moral and educated single woman for a home of her own, a chance to labor in the open air, as her own mistress, and to escape that most pitiable end\u2014a worked out woman dependent upon others for her help or support in her old age.\" Patriarche concluded that \"it is not surprising that the unmarried British woman of sound health considers that, providing she is capable of cultivating the land, she is as valuable an asset to her country as the male unmarried foreigner. Indeed, if she has thought at all she realizes she would be a help to the community where the foreigner is often a detriment.\"\n\nTHE SECOND PETITION: HOMESTEADS FOR \"ALL WOMEN OF BRITISH BIRTH\"\n\nA second homesteads-for-women petition, prepared by Isabelle Beaton Graham, was announced in the 24 May 1911 issue of the _Guide_. The arguments set forth in the petition were that widows had made successful and desirable settlers; that many others, including unmarried women and widows without young children, desired to homestead; that these women would foster education and health and encourage a \"better class of male settlers\"; that the homestead laws discriminated against families with daughters; that women contributed their share to the growth and prosperity of the nation and had helped to make Dominion lands valuable; and that the privilege of homesteading would afford women a healthy and economic method of securing an independent livelihood, easing congestion in towns and cities and drawing the population back to the land. The petition then asked that the Parliament of Canada grant the privilege of homesteading to \"all women of British birth who have resided in Canada for six months, and if residing with their father or mother or a near relative, are of the age of eighteen years, or if otherwise, are of the age of twenty-one years.\"\n\nThe wording of the petition was deliberately vague on the marital status of the would-be woman homesteader. It could be understood to include both single and married women. In answer to a reader who wrote that she would support the petition if it meant married women as well as single, Graham wrote that \"it is certainly intended that any woman, married or single, of British birth shall be eligible to homestead,\" but that it was \"not thought advisable to flaunt the married woman's claim before 'the powers that be.'\" She explained that married women were not specifically mentioned in the petition \"in the hope that thereby she might pass in unobserved, as it were, but she is certainly there, and who has a better right? It is the married woman, NOT the single man.\"\n\nThere was some debate and uncertainty about whose signatures should be obtained for the petition. In June 1911, Graham thought there should be separate petitions\u2014one for men and one for women\u2014\"so that it could easily be ascertained which are the voters and how many, and which are the non-voters.\" Only women over the age of twenty-one were to sign. But this strategy was shelved when it was later decided that only the signatures of voters (men) should be obtained. Graham explained that \"it will be taken for granted that all women desire the homestead privilege for their sisters even though they do not intend to take advantage of it themselves.\"\n\nMany letters requesting copies of the petition soon appeared in the _Guide._ Supporters sought signatures at summer agricultural fairs and events such as Dominion Day and Orangemen's picnics. Other tactics included postcards and letters sent directly to officials in Ottawa. In 1913 J.H. Perra of Winnipeg wrote to the minister of the interior that \"on the strength of the success that the women of the States have made in homesteading and that which the Canadian women are making on scrip which they have bought, can you not see your way to introduce a bill to give the women of Canada the right to homestead. We women of the west feel that our rightful inheritance is wrested away from us and given to strangers and all because we have committed the sin of belonging to the 'female species.'\"\n\n_Figure 33._ Homesteads-for-British-Women Petition that was presented to the Parliament of Canada in February 1913 with over 11,000 signatures. It was completely ignored. The petition, which asked that the privilege of homesteading be granted to \"all women of British birth,\" was criticized in the Winnipeg trade union newspaper the _Voice_ as a \"bald piece of discrimination.\" Library and Archives Canada, Record Group 15, Department of the Interior, D-II-1, vol. 1105, file 2876596, pt. 2.\n\n_Figure 34._ Supporters of the homesteads-for-women campaign were asked to send postcards directly to the Department of the Interior in Ottawa. These are two examples from Mrs. John Robbins of Morse, Saskatchewan, and Mrs. Frances Williams, Lac Ste. Anne, Alberta. Library and Archives Canada, Record Group 15, Department of the Interior, D-Ii-1, vol. 1105, file 2876596, pt. 2.\n\nThe Women's Labour League of Winnipeg endorsed the campaign in August 1911 after a \"lengthy discussion upon a point of technicality.\" They favoured this cause at the time over women's suffrage, as the League had not taken action on a request to circulate petitions for suffrage. The League used Labour Day in September 1911 to get signatures on the homestead petition at an event at River Park, where their display contrasted the ability of \"halfbreed\" and \"foreign\" men to get land with the lack of opportunities for British women. Their display created \"considerable interest,\" with cartoons that illustrated the following slogans: \"We help men to fight for liberty, need we pray for them to grant it to us?; Is the British woman less capable of ruling a homestead than the halfbreed?; Give the daughters increasing independence that they may be prepared to avoid the tragedy of a misspent life; When God gives me a sister shall I withhold the land from her feet? etc.\"\n\nBefore long, fissures appeared that weakened and undermined the campaign. Readers repeatedly asked Graham why American women were excluded under the wording of the petition. As E.L. Stow, born in the United States but resident in Saskatchewan, wrote, \"I do not see why I have not as much right to homestead as a woman of British birth. I am sure I know more about the work of a farm than a Britisher just out a year could do at first.\" She had \"run the binder, stooked, cut, raked, and stacked hay; plowed, disked and harrowed; in fact I think I have done everything necessary on a farm.\" \"Ex-American\" wrote, \"When I read your petition in Fireside all my fondest hopes were crushed for the petition reads that women of British and Canadian birth be allowed the privilege of homesteading and I first beheld the light of day under the Stars and Stripes.\" A Mrs. Paterson from Plateau, Saskatchewan, argued that women from the United States should be included, writing that \"a great number of the best and pluckiest settlers we have in Western Canada are American women.\"\n\nOn many occasions Graham was obliged to explain her reasoning for excluding all but women of British birth. She wrote on 16 August 1911 that she was \"not opposed to the American woman as a homesteader. She is akin to us in every attribute... with the exception of fealty to the British flag. But if we admit any nationality other than British, where shall we, or where can we, draw the line? Instantly the question will be raised, 'Is it in the interest of Canada to admit a heterogeneous mass of foreign femininity to the homestead privilege in Canada? Can we absorb them as fast as they will come? Even as it is the foreign men are a menace and hindrance.'\" Graham feared the petition would be unsuccessful if it asked for homestead rights for \"women who have no culture whatever, no education, and women who are unlikely to be anything but a drawback to the progress of Canadian institutions for years to come.\" No one could object, however, to \"an influx of law-abiding, industrious, refined and patriotic gentlewomen with some means into the bleak and bare stretches of the West.\" Graham also insisted that \"the American woman has least to complain of inasmuch as she has had the homestead privilege for years and years in her own country.\"\n\nThere was support for Graham's position that American and \"foreign\" women should be excluded. James Allan, of Cordova, Manitoba, declared he would not have signed the petition if it had not stated \"women of British birth.\" American women, he argued, could not \"just step across the line and expect to have the same rights as a Canadian born.\" Canadian women were entitled because \"they should have some birthright in their own country, and British next, because this is part of the British Empire and all the British born subjects should have equal rights.\" He wrote that he would \"oppose to the bitter end any act that would give to the Galician or German girl... the same rights as to our Canadian and British women.\"\n\nSpeaking up for the rights of \"foreign\" and immigrant women, \"Wilhelmina\" wrote from Alberta in 1913 to the _Family Herald and Weekly Star_ to say that \"Canada cannot afford to turn away women of foreign birth.\" She described her experiences as a homesteader in North Dakota, where she had filed her own claim in a community of other homesteaders. \"We built sod houses and sod barns and used flax straw and dry manure for fuel. All this we learned from foreigners, the stout Russians. I have learned many a good lesson from foreigners and hope that they will be carefully protected.\" She was in favour of homesteads for all males and all females over the age of eighteen, regardless of ethnicity. Some prominent people in the women's movement in Western Canada did not agree with the tactic of excluding \"foreign\" women. Francis Marion Beynon, who played a critical role in the suffrage campaign in Manitoba along with her sister Lillian Beynon Thomas, was a consistent defender of the rights of the \"foreigner,\" believing that all ethnic groups deserved equal treatment.\n\nSoon there were many voices objecting to the words \"of British birth\" in the petition. \"Is a woman of British birth any more entitled to homestead privileges than one of any other birth who comes here to live, and by so doing, helps build up the country, by helping her husband and neighbors transform a barren prairie to a garden spot of grain?\" asked H.G. Ahern, from Claresholm, Alberta. \"The women of British birth should not be so selfish and shortsighted as to try to put through a law of this kind... for if they succeed it will be a blot on the degree of their intelligence, and a factor of their lack of Christianity as practiced by them, which our historians will be sorry to relate.\" M.E. Graham, who acquired signatures at the Kitscoty Dominion Day celebration, reported that a great number of potential supporters of both sexes were not in favour of the clause \"of British birth.\" She added that she personally saw it as a mistake, as there were so many excellent women from the States, and she saw no reason why the homestead law for women should differ from that for men. In a letter sent directly to Ottawa, V.C. Bedier wrote from Chauvin, Alberta, to say that the measures Graham was trying to introduce through the petition ought to fail, \"because of it being so narrow let it be for all women... It certainly would be hard to find women less suitable to help build a country than some of these very ones she so very narrowly tries to favour.\"\n\nThe Winnipeg trade union newspaper the _Voice_ criticized the petition in an editorial in September 1911. (The _Voice_ 's editor was Arthur Puttee, whose wife, Gertrude, hosted meetings of the Women's Labor League that supported the petition.) The _Voice_ expressed some sympathy for the cause, as \"it strikes anyone as being a grave discrimination against the sex that the government should be offering to all and sundry men throughout the world the right to enter for free lands in Canada... and at the same time refuse that privilege to a Canadian woman who may see this means the road to economic freedom.\" The editorial disagreed with the petition, however, finding it was\n\nnot conceived on any broadminded lines, and does not provide any incitement for progressive women to enthuse. While the preamble of it may be satisfactory, it will be noticed by those who take the time to read it observingly... that it asks for the right to homestead for \"women of British birth\" only. How very restrictive this is can only be appreciated here in the west. For a dozen of years people have been pouring in from all the nations of the earth; invited, almost recruited by the government. Although they may have been naturalized in the interim their women folk are still to be debarred from homestead rights if the prayer of the petitioners is granted: indeed, the petition has been specially drawn to debar them. These are the women who would be most likely to want to homestead; and in the large proportion of cases they would be the women most suitable to undertake the hardships attendant theron. It is not often that a public petition includes such a bald piece of discrimination as this and we think the women would be well advised to alter the prayer of the petition or drop it.\n\nThe issue of continued support for the campaign was discussed at an October meeting of the Women's Labor League, which decided that while their organization could not discriminate against all nationalities having equal opportunities, the present petition had a chance to pass, being endorsed by prominent men, whereas one with a wider scope might not. The League was prepared to continue to support the petition, although there was regret that \"the measure shuts out several nationalities which might be beneficial to the country.\" They decided that the words \"British birth\" were\n\ninserted mainly to prevent the influx of those European women who are used as beasts of burden by men who cannot afford oxen, and while it has been reported that women may be seen in the prairie provinces hitched to the plow, the league would discountenance any scheme which tended to so degrade women, and it is thought that a bill which granted free homesteads to that class would introduce into this country too many who were willing to continue their old country habits and do the \"donkey work\" while the men smoked and drank the results of their toil, thus tending to lower the social and moral tone of the country.\n\nSupporters were optimistic in 1911 that a change in the federal government might usher in a new regime more sympathetic to their cause. Frank Oliver and the Liberals were defeated in the September election that year. The Conservative government of Robert Borden appointed Robert Rogers of Winnipeg as minister of the interior in 1911, and when he became minister of public works the next year, Dr. W.J. Roche, member of Parliament for Marquette, Manitoba, was appointed minister of the interior. In 1910 it was Roche who had introduced the issue of homesteads for women in the House of Commons, and he had seemed in favour, arguing that \"if this privilege were granted to the fair sex many would go into the west. As there was a surplus of men on the prairies such a movement would assist them in getting helpmates.\" Once in power, however, Roche's sympathy for the cause disappeared, but that was not immediately apparent. The petition remained the central strategy, and Graham remained steadfast in her insistence on the \"British birth\" clause as a route to the creation of a \"pure\" and \"moral\" colony. She wrote in October 1911: \"People are beginning to wake up to the vast conception and imperialistic importance of tendering free homesteads, as an inducement to women of strong moral force and high intellectual ability, to come to our beautiful West and lend their aid in establishing a Canadian colony, a new and clean colony that may, that will in no far-distant future, hold a shining lamp to shed a gleaming light of justice, of honor, of idealistic national purity, of all home comfort, of brotherly love, to all the wide world.\"\n\nIn the fall of 1911 a letter-writing contest on the topic of homesteads for women was featured in the _Guide._ The idea was to explain to the new minister of the interior Robert Rogers the need for and justice of the claim. Five prizes were to be awarded on the topic of \"Why women should be granted homestead privileges.\" The best letters were published in December 1911, and readers were asked to vote on which they felt deserved the prizes. The letters included eloquent pleas that echoed the rationales that have already been outlined here, although either the letter writers themselves or the editor did not include critiques of the \"foreigner\" being granted access to land. The writers contended that a land of contented, prosperous homes would replace the vacant farms and bachelor shacks; that women could enjoy a healthy open air life rather than factory work and unsanitary surroundings; that women could have property of their own in the event of financial calamity; that families with daughters would not be at a disadvantage; women would be induced to emigrate to the West; and that there would be wives for homesteaders.\n\nMrs. J.W. Moore in Ernfold, Saskatchewan, put the matter most succinctly in her essay, arguing that women had \"as much right to be independent as men,\" that they had done as much as men to advance the country, that they had endured as many hardships as men and had equally shared the homestead duties only to find that their husbands had mortgaged or sold their land, that girls needed to be encouraged to stay on the farms, and that if allowed to vote, women would use sound judgement.\n\nBy late 1911, Graham was replaced as the women's page editor of the _Guide_ , apparently in order to pursue the campaign full time, but it may also have been that her views were considered too controversial and extreme, after her racist condemnation of African-American settlers. She was replaced first, and briefly, by Mary Ford, and then by Francis Marion Beynon, who played a critical role in the suffrage campaign in Manitoba along with her sister Lillian Beynon Thomas and Nellie McClung. Beynon had been a consistent defender of the rights of the \"foreigner,\" believing that all ethnic groups deserved equal treatment. She once commented in response to a slur against people of colour, \"Because we of the Anglo-Saxon race have been able to bully less militant and aggressive peoples into handing over their territory to us is a poor basis for the assumption that we as a race are the anointed of God and the one and only righteous and virtuous people.\" Nellie McClung also endorsed ethnic diversity and promoted a vision of Canada as a place where \"every race, color or creed will be given exactly the same chance.\" In 1915 McClung spoke \"passionately in defence of the foreign women\" on the question of suffrage. At the same time her writing and speeches expressed deep pride in and admiration for the British Empire, and in 1917, she briefly redacted her defence of the rights of \"foreign\" women when she called for voting rights for Canadian and British-born women only as a war measure. McClung soon withdrew her support for this, however, and acknowledged her error when Beynon criticized her in the _Guide._ There were, however, other suffragists who used the same arguments advanced by Graham, asking how they could be disenfranchised when \"untutored\" \"foreigners\" could vote and determine their laws and future. They argued that the female franchise could offset the votes of illiterate immigrants, and that \"Canadian women had the well-being of the country more at heart than the average foreign immigrant.\"\n\nAfter Graham left the _Guide_ , the petition continued to circulate, although under Beynon's editorship there was much less emphasis and far fewer letters published on the issue. The petition was not submitted to Parliament until 1913, when it attracted little attention; the campaign was ultimately an utter failure. The elitist strategy of Graham and other proponents of homesteads for women that excluded rights for \"foreign\" women weakened rather than consolidated their base of support. Key potential constituencies were alienated, including settlers from the United States. But even without these fissures in the campaign, it seems unlikely that it would have succeeded. The reasons against granting homestead rights to women in Western Canada were clearly articulated in an editorial in the _Nor'West Farmer_ of 5 September 1912, explaining why the editors of that journal could not support the cause and wanted nothing to do with the issue of which women should be granted homestead rights. Homesteads for women were opposed \"on the simple ground that women are not naturally fitted to become independent, permanent, capable agriculturalists.\" To bestow 160 acres on every woman who should apply for it was \"an unwarranted dissipation of our public domain and a menace to our agriculture.\" As it was, there were enough \"agricultural scaliwags\" breaking the spirit of the homestead contract by making the smallest possible amounts of improvements. Capable, lifelong farmers were wanted. Some women might be able to farm on their own, but \"the average woman is lacking in the physical strength and natural independence and resource so necessary in a homesteading undertaking.\"\n\nAs historian Bradford Rennie has written, there was considerable support from male farmers in the West for the homesteads-for-women movement, but opinions were divided and there were limitations to this support. Rennie writes that men signed the petition, but \"many men opposed the campaign, including delegates to the 1912 Saskatchewan Grain Growers convention, and those in favour in Alberta were not sufficiently concerned to see a resolution on the subject brought before a UFA [United Farmers of Alberta] convention.\" According to Rennie, it was the homesteads-for-women campaign that helped to build a women's section of the UFA, mobilizing and training women to work for a cause, and encouraging them to join the agrarian movement. But as will be discussed in the next chapter, the demands of organized agrarian women for domestic servants were a priority and this was at odds with, or sat uncomfortably beside, the campaign for homestead rights.\n\nThe petition, bearing over 11,000 signatures as well as support from organizations such as the Winnipeg Board of Trade, the three provincial Grain Growers' Associations, the National Council of Women, and Women's Press Clubs across Canada was submitted to Parliament in February 1913. There was no debate on or interest in the issue. Minister of the Interior W.J. Roche simply said \"this matter is under consideration\" when asked if the petition had been received and what action the government proposed to take. The petition received nothing more than a polite written response from Roche to Isabelle Graham, who was informed that \"any matter pertaining to the welfare of the Canadian people will always receive my close and favorable consideration.\"\n\nLAST GASPS OF THE CAMPAIGN: THE \"NATURAL\" GENDER ORDER PRESERVED\n\nThat was not the end of interest in homesteads for women, but from here on the campaign lost steam. Disappointed in this as well as the dower campaign, organized women focused attention on the vote as a means of achieving their goals. In 1916 voting rights were granted to women, with the exception of Indigenous women, in the three Prairie provinces after years of intense campaigning. The petition remained a main strategy, and the one presented to the premier of Manitoba in 1915 had 39,584 signatures (indicating how comparatively few supporters there had been for homesteads for British women). The First World War also diverted attention away from issues such as homesteads for women. As mentioned in the previous chapter, Binnie-Clark's 1914 book, _Wheat and Woman_ , in which she stressed the obstacles faced by the woman farmer in Western Canada, could not have been published at a less ideal time. Even Binnie-Clark herself deserted the cause, returning to England for many years and devoting her attention to other, war-related issues.\n\nYet supporters had been won through the campaign. A 1915 editorial in the Toronto _Globe_ supported the homesteads-for-women cause (minus the preference for \"British-born\" women only). The homestead laws were a \"serious injustice\" that \"worked injuriously in many ways.\" The main argument advanced was that as the law stood, the male homesteader \"performs settlement duties as if in an obstacle race, without the intention of actual settlement, but with an outlook for speculative development. Were the discrimination against women removed there would be far less of this class of homesteading.\" The editorial concluded: \"The entrance of women into many occupations formerly reserved for men has not caused the social and economic derangements predicted, but has been almost invariably advantageous from the standpoint of progress and development. The change requested in the homesteading law rests on a basis of equity that is unassailable. Neither on grounds of justice nor expediency can it longer be refused.\"\n\nThat women did not have homestead rights in Western Canada to 1930 reflects the goals of the architects of the Canadian West, who imagined and fashioned the region as an extension of the British Empire, distinct from their neighbours to the south. Here the \"traditional\" and \"natural\" gender order was to be preserved. White women, preferably of British ancestry, were viewed as the key to order and civilization and to the agrarian ideal, but only if they were firmly tied to the home and domestic sphere. Importing young women as domestic servants rather than holding out the hope of land ownership and possible independence from marriage best served these goals. Promoters of agriculture as a suitable occupation for women in the pages of the _Imperial Colonist_ made little impact, nor did the example of the women homesteaders of the American West. Ownership of land (although not working on the land of their spouses, fathers, or brothers) disrupted cherished ideals of British femininity. As Kathryn M. Hunter has written about Australia, \"to accept the possibility of women involved in cultivation would have meant a subversion of heterosexuality, particularly when the women involved were single and childless. This would constitute a most inappropriate possession of land.\" These views were so deeply embedded that even the tactic of allying the cause with that of bolstering the British fabric of the West did not advance the right of women to their own homesteads. But there was more at work than a challenge to cherished ideals of femininity. Architects of the West knew that women were capable of the hard work and deprivation required of homesteaders, but it was useful to insist that they were not, just as the skills of Indigenous farmers were deprecated. Extending homesteading rights to women would mean having to share legal claims to the most valuable resource of the West\u2014land. Improvement of the land and profits from the land were to remain a white male preserve. Nellie McClung wrote in _Maclean's magazine_ in 1916, \"Women are doing homestead duties wherever homestead duties are being done.\"\n\nThe homesteads-for-women campaign failed for many reasons. It faced formidable opposition from those in authority who wished to keep land, property, and real estate a male preserve. McClung's article in _Maclean's,_ for example, was dismissed as \"unmitigated piffle\" and \"gross misrepresentation,\" and described as full of \"wild baseless assertions... and utter disregard for facts.\" She had gratuitously slandered the homesteaders of Western Canada through her suggestion that women had to perform tasks such as breaking scrub land. Intransigence prevailed at the top level of government. In Canada, women were to marry and to have no options outside of marriage. In 1910 Prime Minister Wilfrid Laurier replied to a single Canadian woman inquiring about a homestead that \"I would advise that you take a husband, to whom we will be happy to give the homestead.\"\n\nThe fissures created by the central strategy of the main organizers additionally undermined the cause. Women \"of British birth\" argued that they were superior to the \"heterogeneous mass of foreign femininity\" in their midst who should not be entitled to homestead land. They presented themselves as exemplars of a desirable, refined, and respectable British-Canadian femininity, who would introduce all of these qualities to homestead communities. Yet they were asking that they have the land that would permit them to farm and to work outdoors, the very activities for which \"foreign\" women were condemned. British-Canadian women were threatening to join them, not rise above them, becoming coarse, indecent, and a \"remnant of a darker time.\" The homesteads-for-women campaign gained steam just when it was being proudly proclaimed in the western press that \"the melting pot of the western world has recast even the Doukhobors.\" The melting pot was not, however, supposed to recast British-Canadian women as farmers, sweating in their fields and sinking to the \"brute level.\" \nCHAPTER SEVEN\n\nTHE PERSISTENCE OF A \"CURIOUSLY STRONG PREJUDICE\"\n\nFROM THE FIRST WORLD WAR TO THE GREAT DEPRESSION\n\nThe First World War brought an end to the organized homesteads-for-(some)-women campaign, although the cause did not die out entirely until 1930. The war also suspended the work of organizations like the Colonial Intelligence League (CIL), dedicated to training and placing British gentlewomen emigrants in Canada in vocations that included farming. Women were needed for farm work at home, and it was dangerous to emigrate by sea. Women in both Britain and Canada devoted themselves to war work, but while a women's land army was created in England and in the United States, and the Ontario government mobilized \"farmerettes,\" there was no such formal organization of women for farm labour on the prairies. Having informed women for years that they were not capable of working the land, it would have been difficult for authorities to suddenly reverse this stand. Yet women on the prairies did perform all varieties of farm work during the war, and it was hoped that the war had proven their capacity to farm. Some women's and men's farm organizations on the prairies continued to request homestead rights for women, adding that this would promote greater production. Even before the war was over there was optimism that British women farmers could find positions and land of their own in Canada, particularly those demobilized from the women's land army or the auxiliary services. This was not to be, however, as authorities remained as intransigent as before, and new rationales emerged to even further limit the homestead right to males, as any available homestead land was to be made available to returned soldiers. Domestic service, along with a few other suitably feminine vocations, remained the only openings for British women in Western Canada. The \"curiously strong prejudice\" against women farmers and farm labourers persisted and became even more entrenched by the 1930s.\n\nTHE FIRST WORLD WAR AND WOMEN'S FARM LABOUR IN BRITAIN AND THE UNITED STATES\n\nThe Colonial Training School at Stoke Prior (originally the Leaton Colonial Training Home founded in 1890) closed in 1915. The school had graduated over 700 students, and of these 200 had gone to the colonies, mostly Canada. But after August 1914 there were so few applicants that it was not possible to remain open. The women who had once trained to serve in the colonies were now needed for work on farms at home. But other institutions that trained women for agriculture and horticulture at home, rather than in the colonies, remained open and gained new relevance, vitality, and credibility. The Horticultural College for Women at Swanley introduced short courses in various aspects of agriculture as a war emergency. It was hoped that after the emergency and temporary work required of women on the land that there would be opportunities for a \"permanent open-air life\" in farms and gardens. Writing in the _Englishwoman_ , Alice Martineau stated, \"At last the opportunity has come to English women to show the stuff they are made of.\" And they did.\n\nDuring the First World War, Britain's food supply was threatened by submarine warfare and factors such as the harsh winter of 1915\u201316. The Women's Land Army (WLA) in Britain began to take shape in 1915 through the Board of Agriculture, the Board of Trade, and the War Agricultural Committees, although it did not formally begin to recruit until 1917. The purpose of the WLA was for women volunteers to work on the land, taking the place of men serving in the military. Before the formal creation of the WLA there were many smaller, local volunteer groups of women working on the land throughout Britain, such as the mobile hoeing force of girls from the University College of Wales, who attended to the turnip and other root crops. Women who played a prominent role in the creation of the mobile force of women farm workers that became the WLA included Louisa Jebb Wilkins, Meriel Talbot, and Lady Gertrude Denman. Before the war they had been involved in the promotion of agriculture for women, with causes such as small holdings for women and the settlement of British women in the colonies. There were also many women workers on the land during the war who were not members of the WLA. These were rural or village women already in the countryside well before the formation of the WLA; this was work they were accustomed to doing.\n\nDespite the increasing acceptability of agriculture as a suitable vocation for women from about 1900, there remained widespread scepticism and deep-seated prejudice against women engaging in farm labour that was perceived as male. There were many obstacles to overcome, including the attitude of male farmers that women could not take a man's place on the land, and some thought it preferable to recruit old-age pensioners. Demonstrations of women's work on the land, including ploughing, milking, tending cattle, and harnessing draught horses, were staged in 1916, and these were an \"outstanding success\" in altering the views of farmers and in recruiting women. But there were other challenges. Male farm workers were not happy to have their jobs done by unskilled volunteers, and there was also the fear that if women were employed on farms then the men would become liable for military service. Farm women were not happy to have to feed volunteer women. As the war situation and labour shortage became critical, however, farmers and farm workers reluctantly accustomed themselves to female farm labour. There was an alarming shortage of food by the fall of 1916, and with a crop failure in 1917, famine loomed.\n\nThe first appeal for recruits to the WLA was issued in March 1917, and 30,000 women applied. They were to sign up for one of three sections: agriculture, forage, or forestry. A recruit could sign on for six months or a year, had to be prepared to work wherever she was sent, and had to undergo rigorous training. Initially they were offered a small wage and no training, but this did not last long, as higher wages were needed to entice women to take on agricultural work, and training was necessary to convince farmers to hire them. The Selection Committee carefully selected the most suitable women \"of good temperament.\" It is estimated that by the end of 1917 there were 29,000 women employed on farms.\n\nThe WLA \"land girls\" were issued a free uniform. They wore overalls and breeches, but were cautioned to remain feminine. An image was carefully crafted of the land girl as \"hard-working, yet feminine, patriotic yet willing to return to the home once the war ended.\" The WLA _Handbook_ given to each recruit stated: \"You are doing a man's work and you are dressed rather like a man; but remember that just because you wear a smock and breeches you should take care to behave like an English girl... Noisy or ugly behavior brings discredit, not only upon yourself but upon the uniform, and the whole Women's Land Army.\"\n\nThere was criticism of the uniform, however. A \"woman farmer\" who wrote to the _Times_ of London in 1916 objected that \"harm is being done by the ridiculous and vulgar photographs which appear in the Press. I am perfectly ready to employ the right sort of woman. French women and North country girls have found it possible to work in a short petticoat, and they have not required the theatrical attractions of uniform and armlet to induce them to do their duty.\"\n\nTo keep an eye on morals and morale, eighty welfare officers were appointed in 1918 to visit the WLA workers, to make sure they were respecting their curfews and not visiting public houses or communicating with German prisoners of war. To keep their morale up and provide a sense of identity, the journal the _Landswoman_ , sponsored by the WLA and the Women's Institutes, started publication in 1918.\n\nIn the United States, the American Woman's Land Army (also known as the WLA) was organized in 1918, joining together a number of women's farm and garden committees. These women were also given a wage and basic training, and by the summer of 1918 about 15,000 women in twenty states were working on dairy, livestock, poultry, and grain farms. They too had a journal, the _Farmerette_ , that linked them and provided information on jobs, hours, wages, and training camps. Thirty-four women's colleges in the United States offered training for the American WLA recruits. The WLA of the United States also confronted prejudice from men who were unreceptive to female coworkers. The overwhelmingly white, Christian, and middle-class women of the WLA faced criticism that they would develop into a \"peasant type of woman.\" One land worker countered this with her conviction that \"women of intelligence will not degenerate mentally or physically through being farm laborers. Rather they will raise labor to their own level, will give it greater dignity.\"\n\nONTARIO'S \"FARMERETTES\"\n\nAlthough women performed agricultural labour during the First World War all over Canada, there was no comparable concerted program of mobilizing their work, except in Ontario. As part of the campaign for \"Greater Production,\" the Ontario government (Women's Farm Bureau, Trades and Labour Branch of the Department of Public Works) established the Farm Service Corps, calling on women to work on fruit, vegetable, mixed, and dairy farms, to cook for other rural workers, to work in the canneries preserving fruit and vegetables, and to take charge of milk routes. Single women were sought; those with children would be placed only in domestic work on farms. Free transportation was offered for farm workers, who were to make a \"solemn declaration\" that they would work for not less than three weeks. The Young Women's Christian Association helped with the work by running the camps that housed the workers. Wages varied, depending on the work. For example, on mixed and dairy farms the minimum wage was fifteen dollars per month.\n\nIn 1917 the Ontario Government Employment Bureau sent over 800 young women from Toronto to farms, and about 250 were sent from Hamilton and London. They \"assisted in all the various operations incidental to truck and fruit farming, some of them driving harrows and rollers, and some even operated 'dust' spraying outfits.\"\n\nMembers of the Farm Service Corps were dubbed the \"farmerettes.\" The term was explained as given \"half in playfulness, half in good-natured derision; there have been the suffragettes, and now you see the chauferette... no such word was known among the students of poultry farming, dairying and gardening ten years ago... 'Ette' is in the nature of a diminutive per ex. 'Mignonette,' or 'little darling.' You couldn't call the ladies who go out to help in the farm problem farmers, could you? But farmerette solves the difficulty.\" Their outfit was \"useful and ornamental.\" They wore \"sensible, durable\" costumes of khaki smocks and bloomers, cowboy hats, tan shoes, and puttees. Their femininity was still observable, however; they were equipped for hard work but were also \"an ornament in the landscape,\" with their \"bewitching curls that insisted on stealing out from under their cowboy hats.\"\n\n_Figures 35_ _and 36._ \"Farmerettes\" of Ontario c. 1917\u201318. During the First World War Ontario women were mobilized for work on the land to replace male farmers and labourers who were serving in the forces. Members of the Farm Service Corps were dubbed the \"farmerettes.\" There was no similar formal mobilization of women farm workers in Manitoba, Saskatchewan, and Alberta. City of Toronto Archives, William James Family Fonds 1244, items 640 and 640A.\n\nIn 1918 a three-week course for farmerettes was offered at the Ontario Agricultural College in Guelph \"to assist women to more intelligently cope with the work of a farm and to reduce in this way the amount of time which must necessarily be spent by a farmer in educating his assistant.\" That fall, however, there was another important breakthrough: for the first time \"farmer's daughters and farmerettes\" who possessed \"equal qualifications with the young men\" were to be admitted to the college's regular program. There were several young women in the freshman class that fall. The first two Canadian women to graduate with bachelor of science in agriculture degrees were Margaret Newton of Senneville, Quebec, and Pearl Clayton Stanford of Dartmouth, Nova Scotia.\n\nIn July 1918 there was great praise for the farmerettes from district agricultural representatives. That June, for example, ninety-five women at Drayton, Ontario, had pulled flax, \"applying themselves to the work with wonderful energy and determination.\" Doubts remained, however, about their capacity to perform certain tasks such as picking apples, as they \"can't handle the heavy ladders and baskets,\" but it was reasoned that as their wage per week was much lower than what was paid to men, less should be expected of them. Ontario Commissioner of Agriculture Dr. G.C. Creelman declared in 1918 that he was now convinced that \"women have a place in agriculture,\" although he admitted that he had been a sceptic when the plan was first proposed by Premier Sir William Hearst in 1917. Creelman had also been opposed to giving women a special course on agriculture at the Guelph Ontario Agricultural College.\n\nAlong with the high school boys of the Soldiers of the Soil, the farmerettes paraded in downtown Toronto in April 1918. It was the farmerettes who were seen as a \"new species.\" They were \"far more picturesque and useful than the peacetime suffragettes. The farmerettes are a new kind of girl, a pleasing combination of Little Bo-Peep and Little Boy Blue and Jack and Jill all in one.\" Their clothing, including bloomers, was described in detail, and the article concluded with approval: \"If this brand of rural maiden is to come into vogue, there will be no need of a 'back-to-the-land' campaign, the difficulty will be to stop the ebb tide.\"\n\n_Figure 37._ In May 1918 Canada's Eaton's Department Store offered \"Costumes for the Farmerette Who's Off to Do her Bit.\" \"Smocks, Breeches, Bloomers, and Middies in Styles Approved for Work in the Barn, field, Orchard and Vegetable Garden\" were available. _The Globe_ (Toronto), 25 May 1918, 24 (see also 7 May 1918, 16).\n\nNot all was rosy, and there were sceptics and critics. In the _Globe_ of 24 March 1916, a letter from a \"Patriot Farmer\" of Ontario was quoted with approval. The farmer did not believe women of Canada had the capacity for farm work, writing that \"women are working on the land in the old country, but people must remember Britain has a class of women who have been trained to work on the land since childhood. We have no such women in Canada, and I would like to see the women here who could do a long, hard day's work pitching hay or sheaves, or pitch manure or such heavy work as that.\" In his view only \"young able-bodied men\" were needed, who did not have to be assisted and instructed. A year later an Ontario farmer complained about the young women sent to help on his farm, the \"sweet things done up in khaki middy blouses and dark bloomers.\" He found their \"tender hands and soft muscles [were] completely unequal to anything like labor with either fork or hoe, and who would think of sending them afield with a spirited team of horses to tread all day the dusty clods or perhaps the miry ground?\" A \"young lady from the city\" sent to help them was scared of their pet cow and shouted at him to \"keep the brute away. She verily thought she was in danger of being impaled on the horns of the harmless cow.\" Farmers, he wrote, could not \"afford time to train and superintend the novices, and no half dozen of them could in any way take a skilled man's place.\"\n\nThere was criticism of the housing and treatment of the women land workers from their relatives. One mother of a farmerette complained that their camps were made up of tents discarded by the militia, that there was no protection for them from the \"elements or ruffians,\" and that her daughter's camp was in fact robbed. Following the robbery the girls went to the nearby hotel for breakfast but were turned away, as they \"were not gowned in proper style, and their farmerette costume might shock those who staying there.\" They were forced to go to work without breakfast. The mother further complained that they were treated as \"the lowest notch of humanity,\" and got a pittance in pay that scarcely covered their camp fees.\n\nWomen's work on the farms in Ontario was part of a wider campaign to have women free men for the trenches by doing their jobs at home. During the war, for example, about 35,000 women worked in munitions production in Canada. Yet it is striking that photographs of women at work in factories or farms were rarely featured in Canadian First World War propaganda, while these were popular images in British propaganda. When such images were used in Canada, they were accompanied by clear messages that the women had not strayed far from their roles as nurturing mothers; the \"unfeminine\" behaviour was excused due to the war. Their work was also cast as temporary, as a sacrifice for the emergency and for patriotism. Karen Ann Reyburn found that images of women in agricultural work \"contained some elements of domesticity or 'traditional' womanhood.\" Women were called upon to conserve rather than produce food, and to take charge of vegetable gardens and allotments.\n\n_Figure 38._ Reminiscent of the postcard of Doukhobor women pulling the plough, this poster conveyed the message that Canadian women were not to be asked to stoop to this behaviour, rather they could purchase and promote the purchase of victory bonds. In Western Canada women were asked to volunteer to help farmers' wives, rather than working in the fields or with livestock. Library of Congress, 2003652830.\n\nWOMEN AND FARM LABOUR IN PRAIRIE CANADA DURING THE FIRST WORLD WAR\n\nIn prairie Canada there was no mobilization of women agricultural workers. Paid farm labour remained essentially a male preserve. Labour shortages did become acute, but the farm workers pressed their advantage to demand higher wages. Farmers desired a \"cheap and docile\" labour force, and preferred to pay \"foreign\" workers or \"aliens\" from Europe a lower wage. The government assisted the farmers in finding new sources of labour, including soldiers in training, who were granted leaves to help with the harvest. \"City slackers,\" those who lounged about the billiard halls and theatres, were called upon to enlist so that the trained agriculturalists, the sons of farmers, could remain on the land. As in Ontario, teenage boys were recruited as \"Soldiers of the Soil\" and awarded a bronze badge. Others who contributed volunteer labour included professional and business men, civil servants, merchants, clerks, and artisans.\n\nThere were occasional calls for women to be mobilized for farm work on the prairies. The Saskatchewan Bureau of Labour asked local committees to obtain \"kinds of labour not heretofore fully or regularly employed in farming operations such as boys, girls, women, retired farmers, elevator and implement men etc.\" An editorial in the _Gleichen Call_ (Alberta) in January 1916, entitled \"Women Should Be Ready to Till the Soil,\" quoted a patriotic address by the English Earl of Selborne, President of the Board of Agriculture, appealing to \"women of every class... the squire's wife and the farmer's, and the parson's wife and the daughter of the labourer.\" Selborne had seen for the first time ever \"a woman ploughing.\" The editor of the _Call_ noted that the situation was not as grim in Canada, but that women could be seen ploughing in the West and even pulling the ploughs, \"although this was done among the foreigners.\" He called on Canada to \"make it fashionable for the ladies to work on the farm,\" reinforcing the idea that it was decidedly not fashionable, or acceptable, labour.\n\nWomen farm labourers were not desired for a variety of reasons, including that they might provide a rationale for conscripting farmers, farmers' sons, and farm workers. These categories were exempted from conscription until the spring of 1918, and in that year in Saskatchewan a report of the Special Committee on Farm Labour recommended that \"unlikely or reluctant sources of labour, including women and children,\" be pressed into service. But this did not happen. Farmers instead reduced labour-intensive farming practices and invested in machinery. In 1918 an \"anti-loafing\" law threatened every man between sixteen and sixty who was not gainfully employed with a jail sentence.\n\nThroughout the prairies women worked on farms, as they had always done, and they stepped in to do tasks normally done by missing husbands, brothers, fathers, and sons. Women from the cities and towns also pitched in. In 1917 women were reported to be \"doing their bit\" in the Alberta harvest fields. Alberta's Deputy Minister of Agriculture H.A. Craig reported that he had seen \"women wearing overalls, pitching hay, handling rakes and forks with a spirit and efficiency that makes the average harvest hand look like a slacker.\" The women helping with the 1917 harvest in Minnedosa, Manitoba, were similarly adept: \"One was driving a binder. She handled the long-lashed whip and lines of the four-horse team with the dexterity of a man, while the twine-bound sheaves dropped regularly off the carriage as she tripped the lever.\" When \"foreign\" farm workers brought in to work on a threshing outfit at Mather, Manitoba, left after one day on the job, women of the district stepped in, and \"on most outfits three or four women will be found driving teams.\"\n\nIn Manitoba in August 1917, Brandon's \"Telephone Girls\" went stooking. The \"hello\" girls of Manitoba Government Telephones had \"caught the fever and had formed a stooking gang,\" vowing to \"not return home until they have stooked one acre each.\" This was the first time in the Brandon district that \"men were supplemented by women workers.\" There were also thirteen young women among a gang of fifty stookers drawn from a laundry and creamery in Brandon at work that fall.\n\n_Figure 39._ Although never mobilized for work on the land during the First World War as they were in Britain, the United States, and Ontario, women on the prairies contributed to work on the land and to food production. Calgary teachers and office workers formed their own \"land army\" in 1917, working in the long summer evenings on three acres provided by the City of Calgary. Their official name was the \"Calgary Business Women's National Service Corps.\" Grain Growers' Guide, 10 April 1918, 32.\n\nCalgary organized a small \"land army\" of its own in 1917, called the Calgary Business Women's National Service Corps. They were \"patriotic business girls\" who worked in stores, offices, or schools by day, and \"instead of going to the golf links and tennis courts during the summer evenings, they were exercising with the hoe, and growing potatoes to increase production.\" They claimed to \"hate Wilhelm, and intend to do everything they can to defeat his object.\" The city loaned them three acres of raw prairie land and had it ploughed for them. The public was \"rather skeptical at first, but eventually they took it seriously, and folk would often drive out in their cars to 'see the girls working.'\" For 1918 the plan was to grow a wider range of vegetables on vacant lots in the city. They wore overalls, as skirts impeded their work, and \"at first many were reluctant to be seen on the streets in overalls, so they would hurry along on fine evenings wearing rain coats, but towards the end they got over this and did not mind being seen in man's attire.\" According to the _Grain Growers' Guide_ they all \"had lots of fun on the land, and thoroughly enjoyed the experience in spite of the fact that it was hard work.\"\n\nWomen's volunteer \"reserve corps\" were organized in other urban centres of the prairies during the First World War, but without any attention to farm work. The object was to \"be able to defend themselves in case of danger\" and to \"prepare so that in an emergency the women of the city could undertake the performance of all the duties of an army back of the firing line.\" There were first aid, telegraph, and telephone sections, and the women were trained in the use of rifles and riding. They also raised funds through events such as dances.\n\nWomen from other regions offered to help on prairie farms. In August 1917 there were 2,000 women from British Columbia available and willing to help with the prairie harvest. They had just finished the fruit harvest in that province, and the B.C. Consumers League which had organized them was prepared to take immediate steps to send them once given the green light from the National Service Commission. Perhaps permission was never received, as there is no record of an influx of women harvesters from British Columbia.\n\nThere were women from eastern Canada in the wartime harvest excursions who travelled west by train. Most were from Quebec and the Maritimes. This was not an entirely new departure, as women and children had come from the east to help with the harvest prior to the war. During the war, however, eastern women were recruited not to help in the fields but to assist the \"farmer's wife who finds herself at harvest time with a bunch of hungry men to cook for and no help available.\" The Canadian Northern Railway announced in August 1917 that for the first time women would be coming west in numbers that were large enough to warrant special cars, and that policemen would travel on every train to protect them. While the majority of the women were going to do household work in farm homes, particularly cooking, some had declared they were willing to work in the fields if needed.\n\nAs in the example of women harvest excursioners, women's war work remained restricted to the domestic realm, limiting their work in the fields, even in the last months of the war. Scepticism remained about the ability of women to farm. A 1916 article, \"Women and the Farm: A Mistake to Think That Women Are Capable of Hard Work,\" that appeared in the western press (reprinted from the Victoria _Daily Colonist_ ) presented the view that \"it is a mistake to think that women can bear as heavy burdens and lift as great weights as men can. The plow and the axe are not implements which women should be asked to use.\" Yet there was some room for compromise, as the (familiar) argument was made that young women were suited to the \"lighter branches\" of agriculture. The article concluded, however, that this activity was temporary, that while some women after the war might claim the right to high wages, \"the majority of women will be only too glad to return to their household duties.\"\n\nIn 1918 there were calls in Alberta for women volunteers, not to work in the fields but to take the place of men who would. As Edmonton journalist Miriam Green Ellis wrote in February of that year, urban women would be of little use on the farm, except to help the farm wife in the house and to liberate her to do work in the fields. Ellis was acquainted with a few women who farmed on their own, and one woman who knew far more about their prize shorthorn cattle than her husband, but these, in her view, were exceptions. Women could, however, work in offices, garages, freight sheds, hotels, restaurants, libraries, as janitors, chauffeurs, and mail carriers, freeing up ex-farmers who could return to the land. In March of that year a meeting was held in Edmonton of women volunteers who were ready to \"help out farm women at the cook stove\" and replace men in stores and offices.\n\nJournalists, editors, and women's organizations endorsed the idea that women were wanted on the prairies to help with domestic work. Zoa Haight, vice-president of the Women Grain Growers of Saskatchewan, met with the Saskatchewan minister of agriculture in 1918 to say that the question of domestic help for the farms should be put \"on a patriotic basis,\" meaning volunteer labour, as it was in the direct interest of greater production. The _Saskatoon Star Phoenix_ set out the classes of women who could pitch in: single women who could work in stores and offices; married women with older children or without children to work in farm homes; married women with domestics who could give them leave for three weeks or more to help in farm homes. Women were admonished for not seeing this work as an obligation. A Toronto _Globe_ editorial criticized Canadian women, commenting that \"very few have responded to the need of the country in the way in which thousands in France, Belgium and Great Britain have done. The need has not been so acute in the West until now, but by the time the crop is ready to harvest, there will be a need for women to help the farmer's wife, which, if it is not met, means a serious loss to the Allies.\"\n\nPrairie women, including First Nations women, were encouraged to undertake Red Cross work, to make bandages, and to knit. For some these tasks were added to work in the fields. At a January 1918 meeting of the Women Grain Growers of Saskatchewan, it was noted that it was difficult to find the time for the Red Cross Work. Zoa Haight, \"drove a binder for 10 days last fall, and kept up her Red Cross work at night.\"\n\nIn his 1916 book _Canada and the War: The Promise of the West,_ which looked forward into the postwar future of the West, J.H. Menzies saw the soldiers as fighting to preserve a gender order that was central to the British Empire. He noted that there would be many more single women after the war, but their place would be primarily in the home and associated domestic vocations. He wrote that men liked qualities and dispositions in women that were \"contrary to their own. They think best of the delicacy of form and amiable softness of the other sex, deeming the milder virtues\u2014gentleness, patience, compassion, tenderness, to sit with peculiar grace upon women, who are expected to excel too in piety, faith, hope and resignation.\" Delicate womanhood was a central component of the \"civilization\" that the soldiers were fighting to preserve. There were warnings of the masculinization of females in jobs that were normally male. Readers of the Alberta _Empress Express_ in 1918 were told that this was happening to women in munitions factories, that \"sociologists speak of this as the virility produced by heavy work\u2014forerunner of the Amazon women who are coming.\"\n\nThere were, however, signs of preparations for women to potentially work more visibly and in larger numbers on prairie farms. Beginning in 1916 some women attended the agricultural course at the Alberta Provincial School of Agriculture at Olds. According to the school, this was simply due to the fact that so many young men had been called to the colours, and \"under ordinary circumstances it is not necessary for young ladies to take the heavier class of work.\" In 1918 it was reported that \"one young lady, Miss Erma Poedler took the complete course.\" At the Manitoba Agricultural College in 1918, many of the students in the home economics class were also taking the regular course on operating gas engines and tractors. Yet the work of young women university students on farms on the prairies was rare enough to attract attention. The _Grain Growers' Guide_ noted that in 1917 Miss Annie Norrington, a science student at the University of Manitoba, had worked for the summer as a \"hired man\" on a farm in that province, and returned for the 1918 season. She ploughed, seeded, hayed, and mended fences.\n\nAt the _Grain Growers' Guide,_ women's page editor Mary P. McCallum wanted women to have a place in the production and not just conservation of food, and she urged they be employed to feed stock and care for poultry and vegetable gardens. She hoped the government would enlist the \"vast army of women workers in Canada today. We have one half of the population of Canada today absolutely overlooked and unorganized for war service on a national basis. Why can women not be given a definite and positive place in the production campaign?\" But there was debate in the _Guide_ about how women could contribute to the world's food supply and about the suitability of women for farm labour. Agreeing with Miriam Green Ellis, quoted above, in a February 1918 letter to the _Guide_ , Mrs. M.E. Graham of Alberta claimed that much of the work on a farm was \"beyond the strength of the average Canadian city girl.\" Graham contended it would take considerable training to equip the city woman to handle a four-horse team and plough. It required strength to stook and pitch hay or sheaves and load manure.\n\nMcCallum did not agree with Graham, and she wrote columns that challenged this view, including a feature article in March 1918 on Ruth Hillman of Keeler (discussed in Chapter 4) under the title \"Who Said Women Can't Farm: Miss R.M. Hillman... Disproves Any Such Fallacy.\" There was a lengthy article on \"Feminizing the Farm: How Ontario is Promoting Agriculture among Women\" by Laura E. Nixon, in a 1918 issue of the _Guide,_ that described the skill, energy, and enthusiasm of the farmerettes, who even included former \"society butterflies\" and who had learned to milk, feed livestock, care for poultry, run machinery, and take on numerous other tasks at the three-week course offered at the Ontario Agricultural College. An article by McCallum, in the fall of 1918, on \"Women and Their Gas Wagons\" was about how women on farms in the West were able to assist so much more once they learned to drive, making trips to town for marketing and repairs that would have previously been the job of the male farmer, who could instead stay at work on the land. Western women also had learned to drive tractors and enjoyed it, according to McCallum.\n\nHeadlines such as \"Woman Farmer, Husband in the Trenches, Meets Awful Accident While Preparing Land for Crop\" likely did not help the cause. The article described how in May 1917, Mrs. E.P. Arnott, of Elk Point, Alberta, lost an arm and an eye while running the disc behind a three-horse team. Thrown in a runaway when the team suddenly took fright, she was found by the hired man under the disc. Mrs. Arnott survived with the aid of the Canadian Patriotic Fund that paid for her doctor and nurse, and her neighbours rallied to put in the crop on the Arnott farm.\n\nIn the final months of the war there was a desperate call for the labour of \"every woman and every teenage girl\" to assist with the harvest of 1918. In the article \"War's Call to Farms: Men Must Fight and Women Must Reap\" that was printed in several western papers, it was noted that in Russia, Italy, France, Belgium, and Britain, women were engaged in all varieties of farm work and that \"what the women of Canada have done in this line is negligible yet, although there has been some brave pioneering in Eastern Ontario.\" Accompanied by photographs of women at work in England and Ontario, the article stated that Canada \"needed her daughters to rally now,\" before the grain rotted:\n\nThe time to act is now! It does not matter a scrap what is or ever will be: what her social status, her occupation, her share of this world's goods. There is a new democracy abroad\u2014a wonderful levelling of grades. Usefulness and service are the things that count. Every woman must search her soul and ask herself how she can best help in taking care of the harvest of 1918... In short every woman and every teenage girl can do something... It is one of the biggest things ever asked of a woman. It is for the sake of our allies. But most of all for our men\u2014\"over there.\"\n\nBut the West survived the war without ever forming a women's land army. Why were women of prairie Canada not mobilized for farm work in the same way as they were in Ontario? In fact there was almost an opposite reaction: women were deliberately steered away from field work and toward domestic work in farm homes. Reasons likely included organizational challenges, many of which were overcome in Ontario, but in the West the scale of the work was much more vast and the harvest season shorter. There were the prevailing attitudes discussed above, that women were physically incapable of farm work, but why were beliefs ignored, at least for the duration of the war, in the case of the farmerettes in Ontario? Did the absence of organized farm labour for women on the prairies also have something to do with the fact that for years before the war, federal government officials and politicians had declared, particularly in answer to calls for homestead rights, that women were not capable of the work required on farms? They could not suddenly seem to reverse this long-standing position.\n\nNEW RATIONALES AND RENEWED EFFORTS: HOMESTEADS FOR WOMEN AND BRITISH WOMEN SETTLERS\n\nWhile there was no longer a concerted campaign, pressure to permit women the homestead privilege continued during the war years, with the added rationale that women on their own homesteads would address the need for greater production. Another rationale was that if there was to be free land for returned soldiers, women too should be granted this right. Nellie McClung wrote her most sustained article on the topic in 1915, in \"Free Land for the Soldier,\" which had little to say about land for soldiers except for a brief introduction, and a conclusion that asked if nurses would be given land grants. Most of the article reviewed the rationales for the agitation that began years before the war. The emphasis on granting homesteads to women of \"British birth\" only had been dropped, although McClung anticipated that the land grant would attract \"a great many women from the old countries, fine, cultured, educated women, the type we need so badly to settle up our prairies.\" She mocked the responses of government officials: \"They cannot bear to contemplate [a] lovely woman engaged in the menial task of planting potatoes! They say it is not a woman's place. Of course women may plant potatoes for other people, and have been known to do quite as heavy work as that of proving up a homestead so long as she does not do it for herself, it is all right.\" McClung addressed the concern that there would not be enough land for everyone if returned soldiers were awarded by claiming that only 2.3 percent of land in Canada was under cultivation. Other wartime conditions provided McClung with additional arguments. She knew an English girl, a \"brave daughter of the Empire,\" who was maintaining her brother's Alberta homestead while he was at the front, minding his stock and travelling seventy-five miles to Edmonton to market pigs and fowl. \"Yet if this brave girl, this splendid citizen, wished to own an acre of land she must pay for it,\" McClung wrote. \"She may work like a man. She may endure all the hardships and discomfort and loneliness (against which there is no law). But there is no free land for such as she!\"\n\nIn 1915 the Toronto _Globe_ came out in support of an end to discrimination in the homestead law, arguing that extending the right to women would induce rural girls to stay away from cities. Supporters cited the war work of women on the land in Great Britain, where they were encouraged to cultivate the land, which led \"naturally to the wish to own land in their own right.\" Refusal to grant homestead rights was \"caused by the survival of the old spirit which refused to allow women to attend university and still in some places, closes the doors of certain professions against them.\" At a Liberal convention in Winnipeg in 1917, a resolution was adopted asking that women be allowed to homestead on the same terms as men. The overwhelming majority of the delegates supported the resolution, although opponents \"voiced the old arguments that women on account of their physical weakness could not possibly stand the rigorous homesteading life.\"\n\nIn 1918 the Local Councils of Women in Saskatchewan began to seriously agitate for homesteads on the same terms as men. According to the Regina _Leader_ , \"With the need of greater production being emphasized so strongly, there are many women endlessly thinking of what their duty is; and forever wishing they could become producers, by any other means than just becoming servants of some farmer's wife.\" That year the Alberta Women's Institutes convention called on Canada \"to make homesteads as easily available for women as for men.\" The rationales articulated in the resolution drew on wartime conditions, referring to a conference of representative women of Canada with the war committee of the Dominion cabinet that recommended \"wider participation of women in agricultural pursuits\" and short courses for women to fit them for agricultural labour. Nearly two dozen women at the Alberta convention spoke in favour of the resolution, describing the outdoor work they did on farms. Some had homesteads, and several spoke of how they operated farm machinery. Cecilia Dahl of Standard, Alberta, \"capped the climax when she stated she had run the mower with a baby in her lap.\" President Isabel Noble said that it had been demonstrated beyond doubt that \"homesteads were no trick for women to manage.\" It was also pointed out at the convention that in the summer of 1918 women expected to show that they were capable of working on a farm \"in a way they have never before attempted.\"\n\nLetters inquiring about women's homestead rights continued to arrive in Ottawa during the war years, and by 1918 there was a new element in the government's response. Estella B. Carter wrote from Maryland in June 1918 to ask if she and three other young women, three teachers and one with a business education, could obtain homesteads in \"a good wheat section of Canada.\" If they got located and liked it, they would be followed by a party of four others. They had taken a course in school gardening at the Normal School. She received the standard answer, and one new addition: \"While the Dominion Government offers to settlers in Western Canada free homesteads of 160 acres, a woman is not privileged to make homestead entry unless she is the sole head of a family having minor children dependent on her. Moreover, all the available free land within approximately fifteen miles of any existing railway line has been reserved for purposes of soldier settlement.\"\n\nThe war helped to further masculinize the prairie West in several ways. Beginning in 1917 it became easier for farm labourers to file on homesteads of their own through a War Measures Act that relaxed the residency requirements, allowing them to count farm employment (on the farms of others) \"as a like period of residence in connection with their respective entries.\" They had to submit sworn evidence of farm employment. The cultivation required to earn patent could be performed in two years instead of three. More than 89,000 homesteads were filed on during the war years. Plans for the settlement of returned soldiers in Western Canada began well before the war ended. A Soldier Settlement Act was first passed in 1917 and was confirmed in 1919. Under a March 1917 order-in-council, returned soldiers who had served overseas and who had been honourably discharged were given the prior right of one day to enter on a homestead in the event of land becoming available for settlement. A year later, to facilitate the acquisition of homestead land for returned soldiers, an order-in-council withdrew the privilege of pre-emption and purchased homesteads.\n\nBeginning in 1918, extensive sections of Dominion lands on the prairies were reserved for soldier settlers. There also began a concerted and successful attempt to acquire Indigenous reserve land from the occupants and make it available for returning non\u2013First Nations soldiers. As explained in the House of Commons by the minister of the interior, the idea was to assist and compensate \"those brave lads of ours who have gone from our country and who have been subjected to such terrible hardships. They have acquitted themselves in a manner that has won the admiration of the world. They have gone to the front and done their duty like men, and this offer is meant as some recognition on the part of a grateful country... If by offering this assistance we can place the soldiers upon the soil and increase our production we shall have accomplished what we have in view.\" The Empire Settlement Act of 1922 also favoured male agriculturalists; veterans and their families.\n\nThe issue of whether nurses who served overseas should be granted the right to homestead land under the Soldier Settlement Act was debated in the House of Commons in 1919. Isaac Pedlow, member of Parliament for South Renfrew said that \"settler\" in the act was defined as \"a person who at any time during the war 'has been therein engaged on active service in a military force.' Does not that definition include nursing sisters?\" Minister of the Interior Arthur Meighen replied that the act would not apply to nurses, that \"the policy of the board was definitely not to include women,\" and that \"the purpose of the Bill is settlement and the only women who come within its provisions are widows of fallen soldiers. They are included because it was felt, first, that they had a special claim, and secondly, because very frequently widows of soldiers have boys growing up who can render material assistance and make the proposition one of actual settlement. The ordinary nurse, I am afraid, could not come within that promising class, and I do not think that returned nurses should, in their own interests, be encouraged to make settlement on land their occupation in life.\" Pedlow stated that he had already had an application from a nurse who wanted a homestead and asked if the matter would be considered by the department, but the answer from Meighen was again no, that \"I do not propose to include women.\"\n\nHistorian Veronica Strong-Boag describes how the First World War nurse Mary Alice Blackwell Turner enlisted others who had served overseas in fighting to acquire the right to homestead, and Turner claimed a Peace River homestead. To clarify the issue, an amendment was made to the legislation in 1920 that formally excluded nursing sisters from the Soldier Settlement Act. This restriction varied throughout the British colonies. The First World War nurses could apply for land in their own right as veterans in Australia and New Zealand, for example. But in Canada, ex-soldiers received homestead land, loans, and in some cases training in farming, none of which was available to the nurses who had served overseas.\n\nThere was to be no postwar relaxation of the homestead laws; in fact, new rationales were added for excluding women. Nothing that women did during the war either overseas or at home persuaded federal government officials that women (other than widows with children) should be permitted to homestead. Nor did the fact that most non\u2013First Nations women in Canada (with the exception of Quebec) could vote. A resolution asking that homestead privileges be extended to women on the same basis as men was passed at the 1919 conventions of the United Farmers and Farm Women of Alberta. It read: \"Whereas women are taxed for the support of the Government the same as men, therefore we feel that any natural resources that the Government has to put at the disposal of its citizens should be free to all, irrespective of sex, and we most respectfully ask that Homesteading privileges be extended to women on an equality with men.\" The resolution was sent to the Department of the Interior, which replied that there was no reason why the policy that had been pursued in the past should be changed \"in view of the fact that homestead land is getting scarce, and all Dominion Lands within fifteen miles of a railroad are reserved for Soldier Settlement purposes.\" A departmental memorandum outlined further rationales for not acting upon any such resolution: \"Dealing with the question from the standpoint of the welfare of the women, it would not seem good policy to extend the privilege asked for as it would mean the homesteader would be practically isolated from easy access to the market or medical attention, and the position of the homesteader would be made harder in the Provinces of Manitoba and Saskatchewan where the winter climate is more severe than in the Province of Alberta.\"\n\n\"THEY ARE LONGING TO CROSS THE ATLANTIC\": BRITISH WOMEN FARMERS FOR CANADA\n\nInterest in placing British women on homesteads and farms in Western Canada did not entirely abate during the war, and there was optimistic anticipation for a new era after the war. In a series of articles on \"The Land of Hope\" by American-born English journalist Elizabeth Banks, published in the _Lady's Pictorial_ in 1917, the cause of British women farmers for Canada was presented once again. Banks believed that the agricultural training many were receiving during the war helped to suit them for the task. She wrote, \"To become a farmer, to stake out a claim, is not certainly a job for every woman. It needs strength, excellent health, great determination. But these are qualities in which many women of the Old Country are not lacking as witness the work they are now doing to release the men at the front.\" Banks called on Canada to give women the same privileges as men with regard to land.\n\nDuring the war, the perceived problem of \"surplus women\" emerged once again as a rationale for sending British women to the colonies. It was predicted that there would be an acute imbalance of men and women in the \"motherland,\" that marriage would be impossible for many women, and that they should, \"with the faith to venture and the courage to dare, move to those parts of the Empire where they are wanted.\" Journalist Amy B. Barnard wrote in 1916 that \"the Empire is making at this crisis a clear call to the strong, capable daughters of the Motherland to spread British civilization, language, just rule and righteous living in the overseas dominions.\" She singled out Saskatchewan and Alberta as most in need because \"we are in a minority\" there, and \"our wonderful Empire should be peopled by the British race.\" The war, according to Barnard, had strengthened the ties between the motherland and the overseas dominion. Barnard emphasized that teachers, nurses, stenographers, and bookkeepers were needed, but she stressed the need for \"home helps.\" In urging the prospective emigrant to think of the prairies, she comforted them that \"it is unnecessary for a woman to learn ploughing and rough farming, as some imagine.\" Yet farm skills were needed for work in the homes of others. Barnard urged that they take a course at the Hoebridge Overseas Training School at Woking, where a \"Canadian lady\" was introducing students to fruit and vegetable culture, and dairy and poultry work. With the article's emphasis throughout on women's mission to help build a \"sturdy race\" in the colonies, it was not surprising that it ended with the prediction that \"love and a happy marriage\" awaited many of the emigrants.\n\nThere is no doubt that wartime activities on the land made some women consider agriculture as a vocation, including the \"farmerettes\" of Ontario, some of whom wanted to continue to farm after the war and to have land of their own. In \"Farmerettes Want Farms\" (1918), Violet Dickens asked, \"Why should land fit for cultivation lie idle while there are women and girls willing to use it and increase production?\" Dickens favoured the idea of the government controlling \"idle\" land in Ontario (as in the West), and she advocated that the government assist women war workers to acquire small farms after the war.\n\nNurses who had served in the war declared a desire to go \"back to the land.\" In 1920 \"Polly Peele,\" writing for the Toronto _Globe_ , said that women as well as men sought peace and calm in the countryside for their \"overworked nerves and weary spirits,\" for which there was \"no balm like that of the blue sky overhead and the brown earth underfoot.\" She described the Ontario six-acre farm called \"Cornerways,\" occupied by two demobilized nurses who preferred the out-of-doors to their former profession. They had poultry and grew apple and cherry trees. Alice Watkins, a graduate of Royal Victoria Hospital in Montreal, had been stationed in Egypt and France. Her partner, Mary Spence, was from Scotland but had been nursing on the prairies before the war. Peele reported that another nurse from England had a position on a nearby farm, where she was doing \"the sort of service that, in ante-bellum days, would have been the work of a 'hired man.'\"\n\nThere had been optimism that the war would usher in a \"new day\" of opportunity for non-Indigenous women and the vocation of agriculture on the prairies. At the _Grain Growers' Guide_ , women's page editor Mary P. McCallum wrote in 1918 that the \"war is having the effect of bringing women in our own country to a realization that there is a place in agricultural operations for women. And women are needed in agriculture.\"\n\nReflecting this new optimism, Ellen M. Knox, principal of Havergal College, Toronto, included farming in her book _The Girl of the New Day_ , which detailed the opportunities that now beckoned. After the war women as well as men, Knox wrote, \"are longing for a road lying out of doors, a road lying in and 'about the feet of God.'\" She called on girls to take their place \"among the world's adventurers and explorers,\" becoming hewers and blazers of trails. There was a chapter on \"The Joy of Farming\" and one on \"The Call of the West.\" The war had demonstrated that women were capable farmers, although Knox emphasized the suitability of \"lighter branches.\" Knox wrote that it was \"somewhat late in the day\" to ask if small farming was \"physically within the reach of women\"... when \"during war time, countless women have tackled that hardest of all farming\u2014Western farming\u2014and 'kept the pot a-boiling' whilst their husbands were away.\"\n\nKnox urged young women to go to British Columbia, and she echoed the claims Binnie-Clark made in 1913 that a small farm on Vancouver Island could grow from modest beginnings into a \"large and profitable venture.\" She also endorsed the idea of a \"colony of capable women, enamoured of farming who are thrilled at new discoveries and new adventures.\" The best candidates, in her view, were \"out-of-door women\" \"of good stock, Canadian, Scotch and English ... exactly what will bring fresh vitality into places run down and discouraged by unscientific farming and intermarriage.\" (Intermarriage with \"foreigners\" or \"aliens\" was the implied meaning.) They should be \"cultured women\" who have been \"and always will be the true backbone of country as well as town life.\"\n\nBut even Knox herself did not anticipate an entirely \"new day.\" Despite the emphasis on vocations for women, including farming, throughout the book, and contradicting herself in many ways, Knox emphasized the need for suitable women as wives, particularly in her chapter \"The Call of the West.\" (Her final chapter, \"The Queen of Them All,\" was about the most honourable profession\u2014motherhood.) Women were not required on the prairies as cultivators, Knox argued, but as household helps and domestic servants. The \"chief mission of women in the West,\" Knox wrote, was \"the converting of shacks into homes.\" Women of \"gentle birth\" were needed to partner with the men who had \"'bached' in more or less discomfort or married half-breeds as a simple expedient for obtaining a housekeeper.\" She called on Canadian and English girls to head to the West as their duty: \"Surely women who have helped the men out so nobly in their fight against a foreign foe will play their part in the conquering of their own country. It is in these outposts that women are most needed. It is their privilege to lend a hand in the work at which men have far too long struggled single-handed, and it is their duty as well as privilege to help to lay the foundation of the social life of that glorious West that is the true Canada.\"\n\nOptimism for a \"new day\" for women was challenged and disputed, however. In \"Must We Rely on Girl Labor?,\" a _Globe_ columnist of May 1919 complimented women for \"stepping into the breach\" and tilling the fields, harvesting, picking fruit, handling stock, and other tasks. They were as hardworking and efficient as men, and their help was of \"vital importance.\" But \"women, to say nothing of growing girls, were not meant for farm labor in normal times any more than they were made for freight-handling or coalmining. It was an abnormality of circumstance that put them in agricultural life in actual outdoor work these past two years, and it is a false economic tenet that promises their continued employment.\" It was \"unworthy\" to suppose that required food \"is to be forthcoming from girl labor.\"\n\nLand Army workers in England wondered how they might be able to use their experience to make a living after the war, although there were warnings that openings would be limited, as men were returning to farm and garden work, and the \"lighter\" tasks would be suitable for the wounded ex-servicemen. Given that prospects for positions as farm or garden labourers were dismal, there was interest in how the former land girl could \"make good on [her] own land.\" Emigration to the colonies was one solution. Knox wrote, \"Women must emigrate. They see no prospect of betterment in England, and will not go back to the humdrum of pre-war days. They are longing to cross the Atlantic.\" While Knox thought that there were openings in domestic service for them, she believed it \"cheaper and wiser to provide outlets for them on farms.\"\n\nAnxious to get back into the business of sending \"gentlewomen\" as settlers to Western Canada, and convinced that a new era had dawned due to women's work on the land during the war, in 1918 Caroline Grosvenor, founder of the Colonial Intelligence League, wrote a \"private and confidential memorandum on emigration after the war.\" The CIL was in its last months of existence, as a process of amalgamation with the British Women's Emigration Association and the South African Colonisation Society was already begun. But Grosvenor, still wanting to address the need for openings for the \"educated\" woman, mounted arguments for the continuation of the CIL, working in cooperation with other emigration societies. She proposed that the CIL form a \"sort of women's overseas corps\" divided into two sections: domestic workers and land workers. She was concerned with the great number of women who were to be \"thrown out of work,\" including land workers, and she thought many would want to go to the overseas dominions. These women had learned to work hard and they would \"dislike going back to a rather objectless existence. There are already signs that a considerable number will want to go overseas.\" Grosvenor was convinced that the war had changed attitudes and opened new doors. Canada and Australia desperately needed workers on the land, and \"the number of men engaged in this work is alas! bound to be much smaller,\" while \"the old argument that women have neither the physique nor the experience of land work can be met by showing them what women land workers have done in this country during the last three or four years.\" She proposed that recruits be taken from upper-crust organizations such as the Women's National Land Service Corps and the Voluntary Aid Detachment Nurses, as these were women of \"the educated class.\"\n\nGrosvenor's private memo appears to have been sent to her colleagues in the other organizations, soon to be amalgamated into the Society for the Oversea Settlement of British Women (SOSBW). The CIL, determined to aid only the \"educated gentlewoman,\" was joining with associations that were concerned with working-class girls and women. Only one response to the private memorandum is included in the CIL papers, that of a polite Miss A.L. Vernon, who thought the corps idea to be excellent, but believed that all social classes had to be included in emigration schemes. Vernon wrote that there were many \"rough farms where the girl of the Land Army type would get on better than a WNLSC girl.\"\n\nWhen the war ended, there were more strident calls for the single women of England to emigrate as that \"cruel old phrase, 'superfluous woman'\" came back into use. Canada was seen as the most likely destination, but other colonies and dominions of the Empire were included _._ But little aside from domestic service awaited single women. Not much had changed as a result of women's participation in occupations previously the preserve of men in factories, farms, and forests. The dominions were clear that women were wanted as domestic servants, and as wives and mothers. In 1919 a Canadian official with External Affairs wrote that \"no encouragement should be given to skilled women workers to come to Canada.\" They were urged to emigrate primarily for the men of the dominions who \"want to marry but cannot find wives.\" The highest officials in immigration, both in Canada and England, continued to have a dim view of women farmers and no interest in encouraging them. Superintendent of Immigration W.D. Scott wrote to J. Obed Smith in February 1919: \"Personally I am of the opinion that patriotism had much to do with the energy displayed by women in agriculture and the cessation of the war will find very few who will continue.\" Scott believed that conditions were too difficult for women farmers in Canada and that few took up the career as a matter of choice.\n\nDemobilized or other British women contemplating Canada were warned: \"If you want to go to the colonies because you like the man's work you did during the War, and hope to get something of the same kind in the untrammeled new country more easily than you could in England, you are under an illusion. You are far more likely to be forced back into a traditionally feminine occupation in the colonies.\" Domestic work, nursing, and teaching were the only posts women could possibly obtain in the colonies. Even those with capital who wanted to eventually establish a business, including a fruit or poultry farm, in Canada were urged to go there first as a home help. Once again, as in the pre-war propaganda of emigration advocates, potential colonists were assured that they would find work among families \"of gentle breeding, of English or Scotch origin who would treat the girl from the Home Country as a younger sister.\"\n\nThe idea of emigration did appeal, however, to many women in Britain after the war, because of the contraction of employment opportunities there and the backlash they experienced if they wanted to continue in their new vocations. Approval of their work in wartime had been replaced by \"often vicious condemnation.\" They went from being \"saviours of the nation\" to \"ruthless self seekers, depriving men and their dependents of a livelihood.\" As historian Lucy Noakes has argued, the \"new\" women of the war, the ex-servicewomen and members of the Land Army, were \"troublesome and potentially disruptive.\" They had been tolerated as a \"rather regrettable necessity\" during the war, but were \"resented by the men they displaced, and criticized for both their allegedly masculine activities and appearance, and, conversely, for their supposed sexual promiscuity.\"\n\nThose who had served in the three auxiliary services\u2014the Queen Mary's Army Auxiliary Corps, the Women's Royal Navy Corps, and the Women's Auxiliary Air Force\u2014were seen as particularly problematic, \"bold,\" and masculine as a result of their military work. The land girls were reported to be \"inured to labour and have learned to love the soil, but now they want a change of scene, many hoping to find it in Canada.\" The British government was interested in sending these and other women to the colonies in order to help address the problem of unemployment due to demobilization after the war; they were not to be allowed to threaten the employment of ex-soldiers.\n\nA Free Passage Scheme was made available to ex-servicewomen (who had completed a minimum of six months service) as well as to men, to send \"trained defenders of the Empires' borders\" to the colonies, help strengthen bonds within the Empire, address the issue of \"falling numbers of white settlers,\" and help to balance the numbers of British men and women in the Empire. There was no mistaking the \"science\" of eugenics sentiments behind support for the emigration of women. An official involved with emigration to South Africa expressed concern about \"the danger to the Race both at home and in the Dominions if an active Post-War migration left large numbers of the best strains of Womanhood here unmated while it condemned the best strains of Manhood in the Dominions to Celibacy or to marriage with lower types.\"\n\nSingle women, orphans, and ex-servicewomen appeared to British government officials to be the likeliest candidates for emigration. An Overseas Settlement Committee (OSC) was formed in 1919, and it worked with the organizations that joined together to become the SOSBW. The British government members on the OSC (Lord Alfred Milner, Leo Amery) saw ex-servicemen as settlers and farmers in the colonies, while ex-servicewomen were understood to be future wives and mothers. Representatives from the pre-war emigration societies continued to contend, however, that more than marriage had to be offered to educated women. (The domestic class of emigrant women would be content with domestic work and marriage.) And they insisted that ex-servicewomen deserved recognition for their wartime service and should have opportunities for incomes of their own.\n\nBut little had changed; Canada was interested in women as home helps and in men as farmers. OSC delegates to the colonies found the same situation prevailed in all, that there was an urgent demand for domestic servants. Authorities in the colonies seemed to be unwilling to regard ex-servicewomen any differently from other female migrants. Yet the ex-servicewomen interested in emigrating were not willing to undertake domestic work at home. This was \"deeply unattractive\" employment for ex-servicewomen and other women, and the Free Passage Scheme failed to attract anything like the numbers initially predicted. In 1920 the home economics department of the Macdonald Institute of the Ontario Agricultural College in Guelph established a twelve-month program to provide British ex-servicewomen and ex\u2013Land Army women with training for Canada. The emphasis was mainly on housework and cooking, in order to \"re-domesticate\" them. (It is not clear how successful this was, but as few took up the offer for free passage, it seems likely that few enrolled in this program.)\n\nOSC commissioners Gladys S. Pott and F.M. Girdler were assigned to visit Canada in April 1919, meeting in Ottawa with ministers and deputy ministers of immigration, labour, and agriculture. They also visited some of the provinces, including Alberta, and consulted with various associations and institutions concerned with women's work. They found an \"urgent demand\" for cooks and domestic servants, nurses, teachers, and dressmakers. Federal authorities told them that ex-servicewomen were not able \"to avail themselves of the special facilities for Land Settlement allowed to demobilized soldiers.\" The report of the commissioners discouraged women from considering farming, pointing out the hardships of agriculture in Canada for women settlers, including the isolation \"which would not make such a life a pleasant one for women.\" Potts declared in 1920 that \"Canada is calling for strong, capable, well-educated women who are willing to take posts as home helps.\"\n\nIn response to a July 1919 enquiry to the federal Department of Agriculture from a woman in Liverpool as to whether there were \"prospects in Canada for young women who wish for open air work, whether on fruit or poultry farms, and who have during the war, been working on a farm,\" a letter was sent to each of the provincial agriculture departments. The replies from the West were the most discouraging. T.M. Molloy of the Saskatchewan Department of Agriculture seemed irritated; they had had\n\n\"inquiries of this nature from the Dominion Department of Immigration, the Repatriation Committee, the Dominion Council of the Y.W.C.A., the Y.W.C.A. of Great Britain, the Overseas Settlement Office in London.\" He added:\n\nI would state that there is practically no demand for women to do farm work in Saskatchewan, and as a matter of fact, we have discouraged the engagement of women for outside farm work preferring to place men in such situations as are available. There is, on the other hand, a very great demand for women for domestic or housework on our Saskatchewan farms, and if your Department knows of any way in which we can secure these women for farms you may direct at least five hundred to this province and we will guarantee situations for all of them. This is provided of course that they are competent and willing to accept domestic service in our farm homes.\n\nThe reply from Alberta was similarly negative: there was no work on the land for young English women, but \"there is now and doubtless will continue to be a demand for help for farm housework... If you feel that any of these women could be induced to undertake this line of work, we would be pleased to give every assistance possible.\"\n\nCompiling the results, federal Deputy Minister of Agriculture J.H. Grisdale concluded that \"there is very little demand for female labour on the farms in this country, except, of course, as help in farm homes.\" New Brunswick and Nova Scotia were the only provinces where there was a small but very seasonal demand. Grisdale found that \"the openings for this class of labour anywhere in this country are so limited that a woman would be ill-advised to emigrate to this country unless she had some other means of earning her livelihood should she fail to find employment at agricultural work.\"\n\nThere was some emigration of British ex-servicewomen after the war; one party of seventy-five arrived in Canada in November 1919, destined for the \"farming\" areas of Canada. \"All profess a willingness for household work,\" but \"the tarnished word 'domestic' is never breathed in the Canadian Emigration Office.\" All had \"worn uniform,\" and \"a hardier, healthier seventy-five lot of girls never left this land before,\" according to one report. In _The Girl of the New Day_ , Ellen Knox was enthusiastic about these \"seventy-five farm workers, women fully trained and hardened by war service, forerunners of the many to follow ... at this moment taking flight for their first essay in Western Farming. They cannot... settle down to the tedium of indoor or society life; they ask adventure, hard work and independence.\" More were anticipated. In June of 1919 the Salvation Army declared that it intended to bring \"many hundreds of farm girls to Canada\" who had served in the Land Army. That year headlines such as \"What Will Canada Do With These Girls?\" appeared, with reports noting the \"news from England that thousands of women contemplate emigration to Canada next spring, although they have no assured employment.\" Yet the seventy-five ex-servicewomen proved to not be \"forerunners of the many to follow,\" although there were a few others. In April 1920, eighty-three \"demobilized women\" who were \"deprived of employment in the old country\" arrived in Halifax. They had all agreed to \"abandon the work of war for the more peaceful pursuits of domestic service.\" But they did not arrive in the thousands as threatened.\n\nThere was an effort in 1919 to deliberately discourage women of the British Land Army from considering Canada as a postwar destination. J. Obed Smith, still the London-based Dominion immigration commissioner, had long been opposed to women farmers in Canada, but he now claimed that Canada's organized women were also opposed. He stated in October 1919 that while British land girls wanted to become \"Canadian farmerettes,\" \"the women of the Dominion will not let them in.\" Smith sent a cable claiming that \"opposition of women's associations in Canada to female farming is so determined that this class of immigration will not be allowed.\" This statement \"aroused considerable questioning\" in Canada. Mrs. L.A. Hamilton of the Committee on Agriculture for Women of the Canadian National Council of Women demanded to know the names of these associations. She said that to the contrary, her organization hoped that Land Army women might come to Canada, and would help them in every way if they did. Hamilton stated that \"their work in England kept us from many deprivations. Moreover, our Government asks for more production, and these are the women trained to put the request into effect.\" M. Catherine Straith of Toronto, and formerly principal of the Pennsylvania School of Horticulture for Women, wrote to the _Globe_ to say that she was not able to discover which women's associations had made these statements and asked, \"What justification can there be for discouraging the immigration of a desirable class of citizens who stand ready to solve one of our greatest problems?\" She noted the success of women farmers in the United States and Canada, and pointed out that schools of agriculture in Canada recently had admitted women. Straith concluded that \"personal prejudice should have no place in a policy for the general welfare of our country. A general survey of conditions should be taken before any pronouncement is made on a subject so vital to national progress as that of immigration of women farmers.\"\n\nYet there is no doubt that some women's organizations in Canada were calling for domestic workers; to provide single women with an opportunity to acquire homestead land would have worked directly against this supply of labourers. A Canadian Council of Immigration of Women for Household Service was formed in 1919 that was comprised of representatives from many organizations, including the Women's Christian Temperance Union, the Girl's Friendly Society, the Council of Women, and International Order Daughters of the Empire. This council worked to assure proper accommodation for British domestics, and members agreed to meet all boats and trains. As Mariana Valverde has written, this network of hostels and matrons was established ostensibly to protect and to assist the new arrivals, but it also functioned to \"ensure that once in Canada the prospective domestic servants did not escape their fate and seek other kinds of work or relationships with men.\"\n\nFarm women's organizations on the prairies also called for domestic help, and not for women farmers or farm labourers. In 1920 the Saskatchewan government inaugurated a plan to acquire domestic help from England. Miss Frances A. Biden was sent to Great Britain to \"select and arrange for the transportation of a number of British women and girls.\"\n\nThe CPR also recruited domestic workers in Western Canada. Organizations such as the Calgary Central Women's Colonization Board worked closely with the CPR to secure household workers. While workers from Britain were preferred, \"they would not refuse to handle women of other nationalities, particularly from northern European countries.\" Difficulties included, however, that British girls demanded more money than \"immigrant\" girls who could not speak English. They preferred to work in Eastern Canada where they got higher wages.\n\nWomen as farmers and farm labourers need not apply\u2014that was the prevailing message. Echoing J. Obed Smith's view, Premier of Quebec Sir Lomer Gouin told the Cross-Atlantic Service in May 1920 that Canada did not want British land girls as immigrants, that \"work on Canadian farms is too arduous for women. Moreover Canada is not employing women to usurp men's jobs. We need women in women's jobs, especially domestic servants and wives.\"\n\nDespite deliberate efforts at discouragement, interest remained in agricultural work in Canada for British women. The cover of Florence B. Low's _Openings for British Women in Canada_ (1920) featured a woman holding the reins of two horses harnessed for farm work, which illustrated her optimism for women's work as agriculturalists, and for the \"freedom, and independence and vitality\" of Canada in general, with its \"invigorating and exhilarating climate.\" The book was based on her trip to Canada in 1919\u201320. Low, too, emphasized that women were needed as domestic workers, teachers, and nurses, and to help solve \"the excess of men over women in Canada,\" but held out other enticing opportunities, including farming. She claimed that Canada would welcome educated women who would, \"as wives and mothers... play a great _role_ in the evolution of Canada's great destiny.\" Low devoted an entire chapter to \"Agriculture: A New Occupation for Women.\" She believed that the work women did on the land during the war had dispelled prejudice and objections. Low did, however, part ways with Binnie-Clark and the idea that women could farm grain on large acreages on the prairies, and she was silent on the subject of homestead rights for women. She wrote: \"Agricultural authorities and practical farmers are of opinion that large farming such as wheat farming and stock-raising as practiced in the Prairie Provinces, and in some parts of British Columbia, is quite unsuited to women. Farming that may involve the clearing of virgin forests, the ploughing up of virgin lands, the use of heavy machinery, and the handling of heavy loads, demands very great physical strength and endurance such as few women possess or should be called upon to exercise.\"\n\nBecause of the severity of the winters, feeding stock, Low found, was a \"man's job,\" and when hired men were required this posed \"obvious difficulties for women farmers.\" She advocated the less threatening small holdings and lighter forms of agriculture: \"'intensive farming' on a few acres\u2014fruit-farming, poultry-farming, bee-keeping, is suited to women, and although so few farmers have become farmers on their own account, experts are of opinion that there is no reason whatsoever why in this branch of agriculture women should not be just as successful as men.\" Low spoke to many experts who supported \"small farms\" for \"competent women,\" \"for there was nothing in such work that required the peculiarly masculine qualities.\" She also advocated women working in pairs or groups, arguing that \"two competent women together should be able to manage a 5\u201310 acre farm (and home) satisfactorily and profitably.\" She hoped that a \"wealthy imperialist\" would step up and fund a women's settlement in British Columbia. While she found interest in the scheme from government and academic authorities, she was cautioned that soldier settlement was the priority.\n\nThere was a mild and fleeting expression of interest in hiring former British Land Army members in British Columbia, although their potential as wives was once again highlighted. In 1920 British Columbia took the lead in advocating their emigration and work as labourers, mainly to harvest fruit. A 1920 headline announced that \"Women's Land Army to Invade Canada: English Farmerettes Expected to Solve Farm Labor Problem in British Columbia.\" The women were to take the place of \"Orientals,\" who \"can never be relied upon\" and who \"do not like to be bossed in the fields.\" The women would work for \"one quarter of what the men are asking in this part of the country for the same kind of work.\" Minister of Agriculture for British Columbia Edward D. Barrow favoured the scheme and announced that a representative group would visit to assess the conditions. Barrow approved because most were \"well-born and educated. During the war, for patriotic motives, they went into the fields. Now a majority of them are homeless. Their male relatives perished for humanity, and the women are left to make a living as best they can... They want to come somewhere where they will have a chance for the future. This country could absorb quite a large number of satisfactory farmerettes.\" He added, however, that \"taken from another standpoint they would make excellent wives for pioneer bachelors.\"\n\nHeadlines such as \"English Farm Girls for Canada: Thousands Will Seek Opportunities in the Western Provinces\" anticipated an influx of former Land Army soldiers, but this did not occur. Brigadier General R. Manley Sims, agent general of Ontario and a critic, did not mince his words. As quoted in the introduction, Sims stated in 1921 that while there might be a few openings for the \"demobbed land girls,\" \"it must be remembered that the Anglo-Saxon never willingly accepts the idea of women for out door labor. It is considered, and I think rightly, too rough and too heavy for them. It was a war emergency measure and we don't want it continued.\"\n\nAt the end of the war a plan to bring Britain's war widows to homesteads in Western Canada was proposed but did not materialize. In his 1920 book _Breaking Prairie Sod_ , Reverend (Captain) Wellington Bridgeman of Winnipeg, who lost both his sons in the war, was anxious to rid the West of \"aliens\" and replace them with British settlers, including \"fallen heroes' wives and children from England, Ireland and Scotland, and from the Island of Lewis... In this way we would be encouraging community life with our own flesh and blood, who have suffered far more than we, and at the same time would be building up a pure, clean, white British-Canadian commonwealth.\" Bridgeman assumed the widows would have sons, and that each of these would eventually have a farm and be \"a British-Canadian in a British country.\" In order to facilitate this, Bridgeman argued that \"we must let the enemy aliens go. They are still holding thousands of homesteads in all the provinces which our own should be occupying to-day.\"\n\nOptimism for a new land of opportunity for British women farmers and landowners on the prairies faded. A 1920 article on \"The Lure of the Land\" in the popular periodical _The Graphic_ (London) noted that \"work on the land has proved one of the most permanently popular of the war occupations undertaken by women,\" and that \"the farmer has overcome his prejudices so far as to admit that women had proved the equal, and in some classes of work, the superior of men on the farms.\" The author lamented, however, that while \"at home or in our Empire overseas... innumerable women are longing to make good in some form or another of farming activity ... the prospects for the educated land-worker in the Colonies are not at the moment very roseate.\" Columns in the _Imperial Colonist_ were increasingly pessimistic. It reported in 1921 that the \"land girls were beginning to wonder if there really is anywhere for women who want outdoor work.\" They were warned that in Canada, without capital they would have to \"combine housework with farm work and they will have to work for all they are worth.\" Letters and articles in the postwar _Imperial Colonist_ emphasized emigration for domestic service and little more. There was much less emphasis on opportunities for single women in the colonies and more on their roles within emigrating families, as wives of soldiers, for example.\n\nUnlike Caroline Grosvenor's now-defunct CIL, the SOSBW discouraged British women from thinking of agriculture as a vocation in Canada. Their 1923 \"Handbook for Women Who Are Thinking of Settling Overseas\" stated that \"there is no demand for women land workers in Canada. The work of the big wheat-growing farms in the prairie districts is not suitable to women, and the rigorous winter, during which little or no cultivation can be carried on in most parts of Canada, results in the engagement of as few permanent labourers as possible, and in all necessary agricultural processes being performed at a very high pressure during the summer months.\" Women would need to find alternative employment during the coldest months of the year and that difficulty was \"almost insuperable.\" This approach was echoed in Frances B. Low's _Women Out West: Life and Work in Canada_ (1924). Almost all mention of women as farmers was dropped, and there was greater emphasis on how the \"British housewife\" could succeed in Canada.\n\nThe annual reports of the SOSBW throughout the 1920s demonstrate that opportunities involving farm work for women were few. In 1925, five women were \"placed in agricultural posts in Canada,\" but all had to have capital. It was the same dismal story throughout the colonies. In 1926 the report on agriculture was brief: \"We do not show an encouraging record in regard to this profession. Only seven girls have been placed on farms during 1926 as compared with 22 the previous year.\" Of these, two young women had gone to New Zealand to raise poultry and fruit, and there was one placement each in Kenya and South Africa. There were no agricultural postings to Canada that year. Throughout the 1920s there were a few reports from women farmers in the colonies, but none from Canada. In 1928, for example, a British woman in Kenya had acquired 367 acres of forest land and she was trying to learn Swahili. As noted in the report for 1925: \"Although there are excellent schemes under which people can be absorbed into the Dominions, these are almost entirely restricted to single men for agriculture and to women with knowledge of domestic work.\"\n\nThe 1920s saw occasional resurrections of the idea that British women might one day farm the prairies. A series of articles by a \"Woman Farmer in Canada\" was published in the London _Daily Mail_ in the early 1920s. Though the farm was in Saskatchewan, the author was not Binnie-Clark (who did not return to her farm after the war until 1924). Articles with titles such as \"Saving the Crop\" and \"Getting in the Wheat\" chronicled this woman's efforts to cope with treacherous trails that still had huge snowbanks while preparing to sow her wheat in spring, and to save her crop from infestations of grasshoppers. She persevered through these difficulties, but the descriptions may have inspired few to follow her example.\n\nIn 1923 Sir Henry Thornton, president of the Canadian National Railway, offered scholarships to four young Englishwomen from the Federation of Young Farmers' Clubs of Great Britain, who were \"experts in farming,\" to tour Canada for four months and to study Canadian agriculture. Two of them attended courses at the Ontario Agricultural College, and two at the Manitoba Agricultural College. But they were not going to be able to stay, even though it was reported that they liked the West and \"very much regretted that they could not remain.\"\n\nIn 1925 Emily Pinder, a graduate of Leeds University experimental farm, studied Canadian agricultural methods in Winnipeg \"with a view to creating a movement to Western Canada of English farm girls.\" Pinder was certain that girls on farms in England were \"intensely interested in Canada. They are seeking an outlet for their energies and would migrate to the Dominion in large numbers if properly encouraged.\" She believed that many had sufficient funds to start farms of their own, and would \"prove a valuable asset to the development of the western country.\" No movement of English farm girls to Western Canada occurred.\n\nRachel Ard of the Kent Committee of the British Overseas Settlement Committee proposed a scheme in 1925 of \"training in agricultural schools for daughters of British settlers,\" but while the headlines describing her \"novel scheme\" hinted at more than housework for these girls, Ard emphasized the domestic training they required and argued that with this training they would \"make admirable wives for the Western farmer.\" She had spent that summer in the West and had lived in Saskatchewan from 1902 to 1909. Ard proposed that older daughters spend a winter in Canada studying domestic science to put them in the position to train their own mothers when they arrived the next spring. The older daughters so trained could then work as home helps for neighbours.\n\nThe cause of British women farmers was hopeless; domestic service beckoned and little else. In \"The Girl Emigrant: Her Chances in the Colonies,\" published in the _Manchester Guardian_ , author Muriel Harris declared that there was \"little to no room for the university woman in such countries as Canada and Australia. She has already been trained on lines which make her wholly unsuitable for colonial life. At the best her life would be one long, uncomfortable adaptation.\" Only young women were wanted, those willing to work as domestics and whose ideas and expectations had yet to be formed.\n\nIt was difficult for a woman to come to Canada under any other category than domestic servant, unless she was part of a family unit. A special category of \"Unaccompanied Women\" required an Emigration Permit. In Mabel Durham's _Canada's Welcome to Women_ (1929), women were cautioned that \"no woman, unaccompanied by husband, father or mother, may go to Canada with the intention of settling there without the sanction of the Superintendent of Emigration, who acts as the representative of the Canadian government in the British Isles.\" This policy had been adopted to ensure that \"none may go to that country seeking employment under any misconception as to the conditions there and the class of workers that is wanted. It will not allow any woman to go to Canada who might be in danger of becoming stranded there, or suffering disappointment.\" A woman on her own had to demonstrate that she had secured employment or had sufficient funds to provide for her needs while finding employment. British women receiving passage assistance (for domestic workers) had to submit to a medical examination before leaving home. In 1927 the British Women's Emigration League of Saskatchewan protested these requirements, arguing that they were humiliating.\n\nBritish Columbia became the focus of any lingering hopes for the \"educated\" British woman after the war, including agriculturalists and farm labourers. The Vancouver Queen Mary Coronation Hostel established by Mary Agnes Fitzgibbon (discussed in Chapter 2) closed in 1917 but reopened from 1922 to 1933, and it continued to concentrate on a narrowly defined category of \"gentlewomen by birth,\" despite being urged to take women who were not necessarily of this description but were educated. Most of those who emigrated and found work through this hostel in the decade it was open obtained positions as home helps, or in related work in poultry, dairy, sheep, or seed farms. But if the women worked out of doors they still had to combine that with housework. Lois Evans, who worked at a goat ranch on Vancouver Island, wrote: \"I am fond of all animals and have worked in England with cows, goats, pigs and poultry but I am keenest on goats. I have been with Miss Payne for 6 months... I did not realize until I arrived that I had all the indoor work including the cooking to do as well as the goats. I have had 5 years with goats and here I do the work that any lad of 14 could do.\"\n\nAlso in British Columbia, the Princess Patricia Ranch near Vernon, the project initiated by Caroline Grosvenor and the CIL, was rented during the war years and moribund by 1920. The Society for Overseas Settlement for British Women that inherited the experiment decided in 1920 to close the ranch, but the resources were transferred to a new location for training women in poultry and dairy farming at Merritt in the Nicola Valley. There were many, mostly financial reasons, for the demise of the Princess Patricia Ranch, but one was that orchard work was seen as less suitable for women than poultry and dairy work. There was the issue of labouring beside Chinese and Indian workers, and ploughing and spraying orchards was thought to be too demanding for women. Other factors, according to historian Andrew Yarmie, were \"problems of scale, poor soil conditions, and location and, at times, a weak market undermined the women's determined efforts to succeed.\"\n\nThroughout the West, there were some advances in the numbers of women farmers, as indicated in the 1931 census and discussed in Chapter 3 (see Table 2). By 1931 there were 6,786 women farmers on the prairies (as compared to 3,575 in 1921). There were 1,493 in Manitoba, 2,952 in Saskatchewan, and 2,341 in Alberta.\n\nIndividual success stories continued to be trumpeted. There was May Hazlett, an \"English girl\" who farmed in the Touchwood Hills of Saskatchewan. Her brother had been killed at Vimy Ridge and left his homestead to her. She was then working as a stenographer in Regina, and even though neighbours of her deceased brother urged her to sell, she decided to become a \"farmerette.\" It was reported in 1921 that she had over one hundred acres under cultivation and a fine herd of cattle. She was going to England to marry her fianc\u00e9 and return with him to her farm. Hazlett was an \"ardent advocate of homesteads for women.\"\n\nTwo Forward sisters (there were four altogether and it is not clear which were the farmers: Maud, Mable, Beatrice, and Clara) of Oak Lake, Manitoba, continued to be celebrated far into the 1920s. (They had appeared in the CPR pamphlets of the early years of the century.) The sisters were \"the most amazing examples of woman's heroic pioneer effort crowned with brilliant success.\" Their parents were from England and they migrated first to Quebec and then to Manitoba. After their father died in 1904, the daughters continued to operate the farm of 1,120 acres. According to a 1925 article in the _Imperial Colonist_ , two of the daughters, \"unaided, have wrought miracles in transforming the bald, uncultivated prairie into one of the fairest and most prolific farms of the countryside.\" They did all the work themselves: \"Since the father died a man's hand has never guided a plough or seized a fork on the place. Ploughing, seeding, haying, stooking, harvesting, feeding and the other 'chores' of farm life have been carried out solely by the two girls.\" In a 1922 article readers were reassured that the Forward sisters had \"all the feminine charm of womanhood. Their manlike occupation has not given them a masculine character or appearance as some of the older generations might imagine.\" In 1929 the \"Misses Forward\" were reported to be specializing in shorthorn cattle, sheep, swine, and poultry. Each year they had a herd of sixty or seventy cattle.\n\nMary Anderson, who came to Saskatchewan with her family in 1912, personally managed \"one of the most successful dairy herds in the province.\" She inherited the farm from her father in the early 1920s but had long had an interest in the business. The press coverage of her achievements indicates that successful women farmers were still tagged as rare and unusual. A 1923 article concluded, \"Though farming in western Canada must be considered in the main a man-sized job and general conditions are such as to discourage the entry of women into the pursuit on any large scale there are continually to be encountered cases of women making undoubted success against great odds all over the country.\"\n\nMiss Ellen Foss, of Stonewall, Manitoba, was a wheat farmer, and her 1925 crop of Number One Northern was the first carload sent to the Manitoba Wheat Board. She also had a herd of dairy cows. Foss believed \"women can succeed on the land as well as men. I myself do much of the practical farm work. I don overalls, drive a team, plough and help with the harvest. Others can do the same if they will.\"\n\nIsabelle Rogers Bryce, of Arcola, Saskatchewan, and originally from Scotland, won acclaim for her Clydesdale horses in local, national, and international shows. When her husband died in 1915 she took over the management of their Doune Lodge Farm. Her Clydesdale mare won the Reserve Grand Championship in Chicago in 1924. This was first time in the history of the show that the prize went to a woman. In 1928 she was the only woman exhibitor at the Chicago International Livestock Exposition.\n\nVarious English women were reported in the 1920s to be so enamoured following visits to the prairies that they decided to take up farming there. These included writer Patricia Carlisle, who purchased an Alberta ranch in 1925 (as discussed in Chapter 4). In 1921 English writer \"Mrs. Harold Bayley\" declared that she intended to settle on a farm of her own in Saskatchewan after a visit to a farm at Luseland that was owned and managed by a women. Edith Jones, of Leeds, Yorkshire, owned a farm near Plato, Saskatchewan, and had no previous experience with farming when she acquired it in 1924. After two years on her farm she could ride a horse for twenty miles and milk cows. Her crop of wheat was worth $12,000. She claimed her farm \"gave me a new lease of life, provided me with work I love, gave me splendid health and now furnishes me with the wherewithal for a long Christmas and New Year's holiday.\"\n\nLady Marjorie (Lowther) Rodney, with her husband Lord George Rodney, came to Alberta in 1919, and together they farmed and ranched 1,000 acres near Fort Saskatchewan. Lady Rodney took an active part in the enterprise, particularly the dairy and swine herds. Her pigs were famous and won many prizes. Before purchasing their own land, they had (allegedly) \"hired out\" as farm hands on a neighbouring ranch to become acquainted with conditions on the prairies. In the 1920s they trained other young British aristocrats (males) on their farm.\n\nSigns of change included the graduation in 1923 of Sheila Marryat with a bachelor of science in Agriculture from the University of Alberta. Marryat was the first woman with this degree at the University of Alberta. Born in London, Marryat moved with her parents to Alix, Alberta, in 1905, settling near her sister Irene Marryat Parlby (rancher, agrarian reformer, and Alberta legislator). Sheila and her sister were true \"daughters of the Empire.\" Their father, Colonel E.L. Marryat, had built and managed British railways in India; brothers of theirs were in Egypt, India, and Shanghai. In Alberta, Sheila Marryat and her partner, Jean Reed, raised poultry and eggs that were sold to the transcontinental dining cars. She then took a short course in agriculture at Guelph, followed by two years at the Provincial Agricultural School at Olds, Alberta, before enrolling in agriculture at the University of Alberta. Beneath her photograph in the 1923 yearbook Marryat was called \"One of the 'boys.'\" She said that she preferred the \"natural, simple beauty of the farm to the monotonous, superficial, superfluous, superimposed life of the city.\"\n\nIn Saskatchewan, Miss Ethel May Bradford made headlines in 1923 when she was hired to teach the newly established course in bee husbandry at the University of Saskatchewan. It was a great novelty that the course would be \"presided over by a lady.\" Bradford, who raised bees at Wawota, had attracted considerable attention as a lecturer on bee culture with the Saskatchewan Better Farming Train.\n\nYet there were also signs that little to nothing had changed over many decades. There was only one woman farmer, Miss Nora Fyffe of Qu'Appelle, Saskatchewan, among a party of sixty-eight Canadian farmers who visited England in 1928 under the auspices of the Canadian National Railways and White Star Line, to inspect facilities for handling and marketing Canadian farm produce. And there remained the ever-present emphasis on the need for women as wives and little else. An article that appeared in a 1928 issue of the _Aberdeen Press and Journal_ had the headline \"Jills for Jacks: Training Girls as Wives for Settlers.\" \"Jills for Jacks,\" it claimed, was the \"new slogan for Colonial immigration. Canada is crying for out for wifely comforts. From the homesteads and even from the prosperous mushroom cities comes the cry, 'We want wives.' The cry is being answered.\" A training institute to qualify young women for domestic duties on Canadian homesteads was to be established in Glasgow. The \"new slogan\" was far from new.\n\nLAST GASPS OF HOMESTEADS FOR WOMEN: NEW AND OLD RATIONALES FOR DENIAL\n\nHopes that homestead rights might be granted to women on the same basis as men continued until 1930. Journalist E.L. Chicanot thought that the renewed interest in the issue of equality with men in the right to file on homesteads was \"acutely stimulated by the movement from England of many girls who, having worked on the land or engaged in some other outdoor occupation during the war, were reluctant to resume their humdrum existences and sought a way to continue an out-of-door existence. They came to Canada because it offered them the opportunity denied at home. They are essentially Canadian women now.\" The journalist had to admit, however, that the right to homestead on the same basis as men had never been granted to women, and did not make it clear just what opportunities the English women immigrants had taken advantage of.\n\nIn the 1920s resolutions calling for homestead rights for women continued to be passed by various organizations and sent along to federal authorities. In 1921 the convention of the Federated Women's Institute, meeting at Edmonton, passed such a resolution. The following year a similar resolution was passed at the convention of the Saskatchewan Grain Growers. It was noted in the Didsbury, Alberta, newspaper in 1925 that a \"noticeable feature\" of the mail received at the local Dominion Lands Office was the \"number of women directing inquiries as to available homestead land.\"\n\nIn 1925 a Miss Nicholson, national secretary of the Imperial Order Daughters of Empire (IODE), wrote to the prime minister on the subject and the reply was: \"The question of granting homesteads to women on the same terms as men is not a new suggestion and the Dominion Lands Act enables the Department to grant a homestead entry to a woman who is the head of a family on the same terms as a homestead entry is granted to a man.\" (This was not correct; the woman had to have a minor child or children.) Nicholson was told that the \"free homestead policy was established to attract to Canada settlers who plan to engage in farming and it has never been the policy to grant homesteads to other than heads or potential heads of families.\" New reasons were added by government officials as available homestead land dwindled. By the mid-1920s the reply was no longer that any available homestead land was reserved for soldier settlers, but that extending homesteads to women was \"highly problematical owing to the majority of available Dominion lands now open for entry being more or less remote from settlement, and requiring, in part at least, to be cleared before the land can be broken.\" Queries from the United States continued. In 1924, for example, a \"girl orphan, Canadian by birth\" wrote from Niagara Falls, New York, to ask the Department of the Interior if she could take up a homestead and was told no.\n\nIn a 1928 memo contained in the Dominion Land Rulings, a Department of the Interior official summed up the \"practice of the Department\" on the issue of homesteads for women and added that while he did not know what prompted the government to refuse the right to homestead to single women, he could\n\nimagine one of the main reasons would be that a single woman is unfitted for a great many reasons for the lonely and isolated life led by the majority of homesteaders on prairie farms. Even if this concession were granted I think that very few women would be willing to face the loneliness and hard work entailed by taking up a free homestead. There is also the financial end of the matter, which I think would prove a considerable handicap as unlike men they would be unable to go out and work in the bush during the winter, or in the lumber mills, or work out during the threshing season, in order to earn additional money to develop their homesteads. The matter appears to be purely one of policy.\n\nThe same memo had another addition, possibly by the same author, that outlined why the policy should not be changed and noting (as had decades of previous administrators) that women were free to purchase land, and therefore nothing stood in their way of taking up farming as an occupation: \"While the past years have brought a tremendous change in the 'sphere' of women, I do not believe that the Department would be warranted in changing its present policy. Land of good quality can be purchased in the West for a moderate price, and land so obtainable is more advantageously situated, as a rule, with regard to churches, markets, etc. A woman who is fully qualified as a farmer need not be debarred from that occupation because she cannot get a homestead. The capital required for homesteading is not very much less than what would buy a farm.\"\n\nIn 1929 resolutions were passed at the United Farmers of Alberta convention and by the Canadian Council of Agriculture at Winnipeg, asking that homesteads be granted to women on the same terms as men. M.L. Burbank, of Carman, Manitoba, wrote to the _Western Producer_ in February 1929 that she held out little hope for the resolution, as she had recently written to the Department of the Interior and had received the standard reply that departure from the present practice was not deemed advisable. She wrote, \"As I see it, this reply simply means that, in the opinion of the government, land is much too valuable to be giving it away to women, and that securing homesteads for women in Canada looks rather hopeless as long as there are any homesteads worth having.\" \"It is truly amazing,\" she commented, \"that any one can claim that women are not quite as valuable 'heads of families' as men are, or that a new country does not need women quite as much as it does men.\" Burbank pointed out the fallacy in the argument that few women would be interested, writing that if that were correct, then little homestead land would be \"wasted,\" and that on the other hand, if \"free homesteads attracted any considerable number of women surely the country would not suffer from settlers of this type. In any event it would not seem that the privilege of homesteading, with its hard work and deprivations, is an unreasonable 'favor' to ask.\"\n\nNew rationales for excluding women were mingled with the old, including the persistent refrain that \"the Anglo-Saxon never willingly accepts the idea of women for out door labour.\" \"Foreign\" women immigrants might do so, but this marked them as boorish, coarse, and vulgar. And as quoted in the introduction, Cora Hind, the commercial, financial, and agricultural editor of the _Manitoba Free Press_ and women's rights activist, stated in the late 1920s that she did not recommend farming for women in Canada\u2014meaning white women of British ancestry\u2014explaining that: \"You see, a woman can't go on the land as she would in England, for so many of the population of the prairies are low type Central Europeans, who, as a matter of course, make their womenfolk work outside. The result of this is that the Canadian farmer\u2014by that I mean a man of British stock\u2014says, 'I will have no \"white\" women working on my farm,' for he thinks if he does this he is sinking to the level of the 'bohunk.'\" Women's choices according to Hind were two: domestic work, and \"more domestic work\u2014marriage to a prairie farmer.\"\n\nAs journalist E.L. Chicanot summarized the situation in the _Imperial Colonist_ in 1925: \"Broadly speaking, Canada does not encourage women to take up alone the pursuit of agriculture on her domain. There are, in any case, far too many men leading solitary lives and vainly hoping for helpmates. The magnitude on which general Canadian farming operations are carried on, with the arduous toil involved... largely precludes the engagement of women individually in these enterprises, no matter how much they love the work nor how much inclination leads them in that direction.\" Florence B. Low, too, had long since given up mentioning any opportunities for women to farm on their own. In \"The Empire's Call to Women\" (1928) Low continued to stress the need for migration and mentioned a few opportunities for wage work, but came right to the point: \"Unless British girls become the wives of British settlers in the Dominions, their population will be inspired by foreign ideals and a large part of the British Empire overseas will no longer be dominated by British character and British principles.\"\n\nA 1928 tour of twenty-five English schoolgirls to Canada was organized by the IODE, the SOSBW, and the Canadian and British governments. The tour was intended to strengthen Empire unity and encourage the migration of women, and the schoolgirls represented \"highly desirable 'British stock,' of the respectable classes.\" And they were to convey back to Britain an image of Canada as a thriving British-based society that was modern and technologically advanced. While Canada's agricultural wealth and other resources were displayed to the girls at many locations, there was no mention that they could take any part in developing these resources. The girls were \"displayed and naturalized as the most suitable 'stock' to populate Canada.\" The dream of sending British women to the prairie Canada as farmers was a London cause.\n\n_Figure 40._ This poster from 1923 illustrates the suitably domestic roles for women on the farms of prairie Canada. She is modern in many ways, as she is distant from the floor-length gowns, corsets, and long hair that restricted previous generations, but she was still to conform to the same expected gender roles of wife and mother. She was not the owner-operator of a farm. Canadian Pacific Archives, Image no. BR 194.\nCONCLUSION\n\nStarting in 1930, drought and dust settled over the Canadian prairies for nearly ten years. Very few \"imperial plots\" had been successfully carved out of the prairie soil by British women farmers. Overwhelming forces combined to ensure that women migrating to the prairies had to perform domestic work. This imperative seems to have grown even stronger over the decades. Women of British birth in Canada, and proponents of their emigration in the metropole, believed they had a strong claim, stronger than women of other ethnicities or countries of origin, to vocations and opportunities other than domestic work in this corner of what they saw as their Empire, including owning and working on the land.\n\nBut throughout the period of this study, Canada maintained its \"curiously strong\" prejudice against any such initiative. A 1930 Canadian Pacific Railway pamphlet _Household Work in Canada for Girls_ , published in London, is a stark indicator of how opportunities for the emigrant British woman had shrunk and shrivelled. It was quite distinct from the CPR pamphlets of the earliest years of the twentieth century that featured British women as farmers and landowners. In 1930 domestic service was the only vocation on offer, and this was made clear from the pamphlet's first sentences. \"Capable young women from Great Britain\" were wanted but were warned they \"must be ready to accept Canadian conditions and do domestic work.\" They had to \"pocket their pride\" and go \"smilingly into Canadian kitchens to cook and serve, and wash up the dishes, to scour pans and polish metal, to scrub and sweep, make beds, shake rugs, and lend generally with a genuine goodwill.\" A \"scheme\" had been started in Britain for training those who did not have household experience, with centres in Glasgow, Newcastle, Cardiff, and London.\n\nIt was nearly impossible for a girl or woman to emigrate for any other purpose than domestic work. To pursue the \"big future\" that awaited her and obtain the reduced rate of passage under the Empire Settlement Act, a girl could be nominated by friends or relatives, if they were prepared to employ her in domestic work. She could be nominated by a fianc\u00e9, if she came to Canada to marry him, but only if the man was \"actually doing farm work.\" A widow with her children could get the reduced rate if nominated by a farmer who would employ her, but if the children lived with her she would be paid a lower wage. The woman who paid full fare and emigrated to join friends or relatives in Canada had to be examined by a doctor of the Department of Health, who would sign her Identification Card. She also had to \"produce a letter, in the original envelope, from the friends, as proof that there is a home in Canada\" that had to be shown at the time of the medical examination.\n\nThis narrow range of opportunities was worlds away from the vision Georgina Binnie-Clark had of British women colonists raising grain on their valuable imperial plots that would help to make the prairies British by displacing Indigenous people and eradicating the need to bring in \"foreign\" settlers. Yet she and the other advocates of this vision had faced insurmountable obstacles. The homestead laws discriminated against single women. Powerful administrators of the laws in Canada over the decades were utterly opposed to the idea of women farmers. They drew on deeply entrenched and tenacious views of women as either physically incapable of the work required, or if they were able to do the work it would make them masculine. They did not want women to be independent of marriage. British migrant women were central to the plot of carving into the very landscape what was seen as the timeless, natural gender order of females for the hearth and men for the field. It was vital to recreate this order as the foundation of society in this outpost of the British Empire to demonstrate that it was modern, appealing to settlers of the right sort, and superior to the Indigenous societies of the previous centuries and the chaotic nation to the south. A key marker of civilization was this gender order, particularly important to uphold and buttress in a colony. A symbol of a darker and more primitive age was women at work in the fields; an activity that was allowable (and even necessary) out of public sight, but would never have official or visible sanction or encouragement. Women from Russia or Indigenous women might be more accustomed to this work, but they too had to conform to the gender order that was at the heart of the colonial order.\n\nBritish women in the metropole and in Canada who wanted to broaden opportunities in the colonies beyond the roles of wives, mothers, and domestic labourers stressed that they were enthusiastic, devoted imperialists, patriotic building blocks of a British West, superior to both Indigenous men and women and those of \"foreign\" lands, including Americans. They drew on a \"gendered ruralism\" to claim the right to participate in the \"Great Game.\" They would help to consolidate the Empire, plant British culture and civilization and crowd out the \"foreigner.\" But they would remain wholesome, nurturing, and feminine. For women to own and work on the land was potentially threatening and dangerous; advocates tried to raise the profile and acceptance of these endeavours by presenting this as an imperialist undertaking that would nurture and nourish a British race in this outpost of Empire. But authorities in Canada worked consistently over decades to ensure that very few women would be able to take up the challenge of owning and farming land.\n\nWhile this study is largely a history of dashed hopes and plans for imperial plots, it has uncovered a great many women, not just British women, who farmed or ranched on the prairies, some quite successfully. Many more would have liked to do so but were discouraged or prevented, through the land laws and through the intransigence of politicians and officials in various departments, including the Department of the Interior and Department of Immigration. Expressions of the deep and profound opposition at all levels of government in Canada to British women migrants as anything but domestic servants remained pronounced and strident in the 1920s. This was well after women (except those of First Nations) could vote in most of Canada (except in Quebec). The world had not been turned upside down, as some had predicted. Why the continued opposition? The woman farmer was still regarded as a disruptive and troublesome deviation from a \"true\" and \"normal\" feminine identity. Land and farming on the prairies remained overwhelmingly a masculine enterprise, and the war had helped to further this aim.\n\nThe same attitudes prevailed with respect to First Nations reserves far into the twentieth century. While women worked on the small farms and gardens of these communities, they were given no official encouragement or sanction or assistance. In the twentieth century the various Department of Indian Affairs initiatives on reserves, such as community farms, band farms, cooperative farms, and corporate farms, involved males only. Indigenous women were encouraged to participate in \"Indian Homemakers Clubs\" from the late 1930s, and these stressed suitably feminine activities such as sewing, canning, and handicrafts (although the clubs did become settings where women organized to address social, economic, and educational needs of their communities).\n\nGeorgina Binnie-Clark's final initiative at her Saskatchewan farm is a bellwether of the changing times. She had totally given up her campaign to attract British women as farmers to the prairies, but she continued to work for the cause of the British Empire with the establishment of the Union Jack Farm Settlement (UJFS) in 1930 for British immigrant families. She persisted with this until at least 1937. Unfortunately the inauguration of the project coincided with the start of the ten-year Depression that hit rural Saskatchewan more severely than all other regions of Canada. Evaporating with the crops and water of the West was any enthusiasm for British or any other settlers. The purpose of the UJFS was to assist British immigrant families to adapt to the conditions of the West by teaching them farming and assisting them to find work. Binnie-Clark believed that \"such families are the most eligible type for the 'army of occupation' we need for the guardianship of the King's Dominions Overseas.\" \"In the Union Jack Farm Settlement,\" Binnie-Clark wrote, \"we try to accomplish for human beings what the Experimental Farms, established throughout Canada by the Canadian government, have accomplished for the care and development of all that is most valuable in the life of seeds and plants and birds and stock.\"\n\nThere was little enthusiasm for Empire settlement schemes in Canada through much of the 1920s, and they were a hopeless, lost cause as the Depression deepened. Binnie-Clark's plan was also frustrated because the homestead privilege was no more in Saskatchewan; there were new \"purchase provisions\" for vacant land, but these were available only to those who had resided in the province for five years. Binnie-Clark also unsuccessfully sought royal sponsorship for the project, which she hoped to attract by setting aside, as a mark of allegiance, an acre in each farm to be known as the \"King's Acre,\" a promise she kept on her own land. A \"Birthday Book for the Farm Settlement of the Canadian Prairies,\" compiled by Binnie-Clark and published in 1935, was also a fund-raising strategy. It seems unlikely to have been successful in raising funds. The UJFS project received no significant financial backing and it limped along, remaining in operation until 1937.\n\nAlthough fondly remembered in the Fort Qu'Appelle community, Binnie-Clark was also seen as eccentric. And she was considered \"no farmer.\" Her sister Ethel did more to keep the farm going. How otherwise could Georgina have sustained her lecturing and writing career in England? In the local history of Fort Qu'Appelle, there is a special section on Binnie-Clark. She \"caused a sensation... because she was a woman farmer,\" and she \"lives on in local legend.\" One story told by a hired hand who worked for her in the early 1930s was that she had \"ended a discussion over who was going to clean a seeder\" by telling him, \"Paton, if I'd wanted to be dictated to by a man, I would've married one and let him keep me.\" She was remembered as kind and generous with children. But the overwhelming lasting impression was of \"benign eccentricity: of britches and leggings and a large floppy hat, worn seven days a week on the farm and off... of the cats that slept on the flour bag in the kitchen and the horses that were kept as pets long after they were of no use on the farm.\" When I visited Georgina's farm (still owned by great-nephews in England) on a warm August day one hundred years after she bought her land, it was fitting that there were horses grazing there, by the dilapidated shack that her sister Ethel had lived in up until her death in 1955. Georgina died in London in 1947, just short of her seventy-seventh birthday, and Ethel scattered her ashes over her Fort Qu'Appelle fields.\n\nIt is ironic that Binnie-Clark's goal of homesteads for women had a measure of success (in Alberta only) just at the time when she had deserted the cause. In 1930 Manitoba, Saskatchewan, and Alberta took control of their natural resources, including land, from the federal government. Alberta was the only province to enact homestead legislation similar to the former federal model, but it granted women the same rights as men. The Alberta Lands Act permitted homestead entry to \"persons of the full age of 17 years, British subjects or with the intention of becoming British subjects who had resided in the province for a period of at least three years.\" The homesteader had to have been resident in the province for at least three years. It was a way of trying to keep the West British through a method that Binnie-Clark would have approved. In Alberta there was immediate interest from women: in August 1931 there were a total of 863 homestead entries, and of these 327 were women. By early 1933, more than 2,000 women had answered the \"call of the land.\" They would have faced many challenges, including that the best land in the province had long been occupied, and that their homestead careers were beginning just as the Great Depression gripped the West. This movement of women onto the land in Alberta also gripped the public imagination, making headlines in newspapers as far away as the _New York Times_.\n\nWhile Binnie-Clark may have been \"no farmer,\" there were many women on the prairies who were, but they faced obstacles, including \"restraining myths\" that persist to this day. Females are seen as \"not farmers.\" They are still regarded as not the natural or likely inheritors of a farm. A 2015 article in the _Globe and Mail_ about the end of an era in the operation of a prairie family farm since 1925, written by daughter Carrie Tait, began, \"One day, when my sister and I were little, our dad walked into the kitchen and said something that has haunted us our whole lives. 'I am glad I had girls,' he said, 'so they don't have to grow up to be farmers.'\" Perhaps with the present perilous state of the family farm it is welcome that daughters are understood to have other choices and priorities, and do not have to face the pressure and expectation that they will carry on with the farm. But this also indicates the persistence of the belief that farms are masculine.\n\nIn a recent collection of memoirs from rural Canada, farmer Marianne Stamm wrote of how she falters when asked to identify her occupation despite having farmed in Switzerland, British Columbia, and Alberta since she was a \"six year old steering a tractor on a pioneer farm.\" Stamm continued, \"Some might say I wasn't really a farmer\u2014I was just a farmer's daughter. They don't understand.\" She was the mechanic and machinery operator in the family and chief tractor driver as a girl, and later with her husband established a successful grain farm. People then said she was \"a farmer's wife,\" Stamm wrote and continued, \"I was that\u2014I was married to a farmer. Being married to a farmer didn't automatically make me a farmer, though, anymore than being married to a teacher or doctor would make me one myself. Not just the farmer's wife. I was a farmer too.\" Women still battle to be able to identify themselves as farmers, to be seen as legitimate farmers, even if they have farmed all their lives. This battle is no longer required for other vocations that were exclusively masculine in the past such as being a doctor, lawyer, pharmacist, welder, or a host of others. Farming has uniquely retained its masculine association.\n\nA study of female farmers in Canada in the late twentieth century found that they continued to face constraints and issues of legitimacy that made many of them feel that they were not \"real\" farmers. They confronted \"restraining myths\" that limited what women could do or know, and these myths \"maintained and reinforced the traditional gender relations of farming by controlling the definition of who real farmers are.\" The three central restraining myths were (1) the \"myth of male technological know-how,\" the idea that men knew more about and were more adept with machinery and technology; (2) the \"myth of farming alone,\" which cast men as capable of farming on their own even if they hired labour, while if women hired labour they were not regarded as capable of farming \"alone\" and were thus not legitimate farmers; (3) the \"myth of physical strength\" that does not recognize that some women are as strong as some men, and that women have always done heavy work on farms.\n\nOpposition remained strong in England as well. An \"undercover academic\" who lived in a picturesque English village and published her findings in 2007 found that various categories of persons, including single women, were stigmatized and excluded. The childless single woman transgressed the norms of the rural idyll. She was seen as a moral threat to the family unit, particularly by other women. If women were not wives and mothers, \"thus transgressing traditional rural stereotypes about women's place, their experiences were constructed as inferior or even as threatening, because (married) motherhood was presumed to be the primary identity for adult women.\" Authors Frances Watkins and Ann Jacoby drew on sociologist Erving Goffman's concept of stigma as an \" _undesired_ differentness.\" Those who are stigmatized, according to Goffman, \"are seen by others as 'not quite human' and so the legitimate target for discrimination.\" The end result of stigmatization is social exclusion, with \"individuals being denied access to the benefits of belonging to the dominant group.\" It is interesting that Goffman was born in small-town Alberta (Mannville) and grew up in the town of Dauphin, Manitoba. His understandings of stigmatization must have drawn on his experiences in rural Western Canada.\n\nIn 1949 Elsie Hart of the United Farmers of Canada (Saskatchewan Section) and a farmer expressed anger at the absence of any progress. A \"brilliant\" young woman graduate of the University of Saskatchewan with a degree in agriculture, specializing in horticulture, had applied for a position with the Horticulture Division of the Experimental Farms Service of the Canadian government. She had been told that her application would not be considered because only males would be \"acceptable for the present and future vacancies.\" Hart wrote: \"Which means: It was very fine of you young woman to spend four years of your time to scientifically educate yourself in an important branch of agriculture but you must now get yourself some apple seeds and cherry seeds and grow nice apple trees and cherry trees or go to the U.S.A. or some other country where your knowledge and talent will be recognized and appreciated. Equality of opportunity regardless of sex!\u2014Bah.\"\n\nThat obstacles in Canada remained insurmountable is testament to the success of the project of crafting the prairies as a colony of the British Empire where a \"natural\" or \"normal\" gender order would be preserved, despite the challenges and criticisms, including by British-born women who wanted a corner of the colony to call their own. The presence of an array of other models of femininity, of Doukhobor women, for example, served to strengthen and justify resolve to eliminate women from work on the land. The profits to be gained from land and crops by men such as Frank Oliver and J. Obed Smith also strengthened resolve. It is interesting, however, to \"think back\" in time and realize that for farmers like Maxi'diwiac (Buffalo Bird Woman), eliminating women from work on the land would have been a perversion of an acceptable gender order. Asked if young men worked in the fields, Maxi'diwiac laughed heartily and replied, \"Certainly not.\" She owned and cultivated her own land, provided for her family, and she processed, marketed and sold her products. Women of the Plains villages were totally in charge of the agronomy that was the main economic activity of their region. The farming methods and crops that Maxi'diwiac and other Hidatsa and Mandan women developed over centuries endure to this day. Corn is today the number one cereal crop worldwide, and it plays a major role in the economies of Canada and the United States. It is the major agricultural crop of the United States, with over 84 million acres under cultivation on some 400,000 farms, and the third most valuable crop of Canada.\nNOTES\n\nINTRODUCTION\n\n1. Provincial Archives of Manitoba (PAM), homestead file 74916 W\u00bd 21-12-15-W1. Thanks to Eric Hallatt, archivist. Elizabeth Cameron, who signed her name with an X, was from Nova Scotia. She became the owner of this land in 1883.\n\n2. Clipping, Isabelle Beaton Graham, \"Homesteads for Women: A Western Woman's View of Man's Duty to Women,\" n.d., n.p. (1910), Library and Archives Canada (LAC), Record Group 15 (RG 15), Records of the Department of the Interior, vol. 1062, file 2029532.\n\n3. Verdon, \"Middle-Class Women's Work and the Professionalization of Farming.\"\n\n4. Saxby, _West-Nor'-West_ , 31\u201332.\n\n5. The literature on settler colonialism is vast and growing. See, for example, Veracini, \"'Settler Colonialism': Career of a Concept\"; and Jacobs, \"Parallel or Intersecting Tracks? The History of the U.S. West and Comparative Settler Colonialism.\"\n\n6. Wolfe, \"Settler Colonialism and the Elimination of the Native,\" 387.\n\n7. Anon., _The New West_ , preface, n.p.\n\n8. Jones, \"Gentlemen Farmers in Canada,\" _Leicester Chronicle and the Leicestershire Mercury_ , 25 April 1885, 1.\n\n9. Ibid.\n\n10. Carter, _Lost Harvests_.\n\n11. Anon., _The New West_ , preface, n.p.\n\n12. Ibid.\n\n13. Levine, \"Introduction: Why Gender and Empire?,\" 6; Tosh, _Manliness and Masculinities_ , 183\u201385.\n\n14. \"A Greeting 1910,\" _African Standard_ , 29 Jan. 1910, 8.\n\n15. Damusey, \"The Prairie,\" _Canadian Magazine_ 56, no. 6 (April 1921): 486.\n\n16. Wilson, \"Manly Art.\"\n\n17. Casid, _Sowing Empire_ , xxii.\n\n18. Spence, _The Prairie Lands of Canada_ , 6.\n\n19. Osborn, \"Our Western Chivalry,\" _Morning Post_ , 14 July 1900, 5. See also Henderson, \"'No Money, but Muscle and Pluck': Cultivating Trans-Imperial Manliness for the Fields of Empire, 1870\u20131901.\"\n\n20. Levine, \"Introduction: Why Gender and Empire?,\" 7.\n\n21. Losurdo, _Liberalism_ ; McKay, \"The Liberal Order Framework.\"\n\n22. Perry, \"Women, Racialized People, and the Making of the Liberal Order,\" 275.\n\n23. Ibid., 276.\n\n24. \"How to Use Our Newest Colony,\" an interview with Mr. Arnold White, _Pall Mall Gazette_ , 4 July 1885, 15.\n\n25. Jacobs, \"Parallel or Intersecting Tracks?,\" 158.\n\n26. Carey, \"'Wanted! A Real White Australia,'\" 136.\n\n27. Carter, \"Britishness, 'Foreignness,' Woman and Land.\"\n\n28. Carter, _Capturing Women_.\n\n29. \"The Doukhobors: Queer Russian Sect Which Has Become Canadianized,\" _Reflector_ , 8 Aug. 1911, 2.\n\n30. Levine, \"Introduction: Why Gender and Empire?,\" 7.\n\n31. Lawrence, _Genteel Women._\n\n32. McClintock, _Imperial Leather_ , 6.\n\n33. Ganley, \"What's All This Talk about Whiteness?,\" 13.\n\n34. Carter, \"Britishness, 'Foreignness,' Women and Land.\"\n\n35. \"Woman Changing to Masculinity?,\" _Saturday News_ , 17 Dec. 1910, 11.\n\n36. Ibid.\n\n37. \"Tiller,\" \"The Female Farmer,\" _Sunday Times_ , 27 May 1906, 3.\n\n38. Provincial Archives of Alberta (PAA), homestead file 1724101, reel 2843.\n\n39. James, _Hanna North_ , 606.\n\n40. Ibid., 607.\n\n41. West, _Homesteading_ , 201.\n\n42. Kluth, \"Mr. and Mrs. Reinhart Kluth,\" 75\u201377.\n\n43. Mrs. Ed Watson, \"Pioneering in Saskatchewan,\" Saskatchewan Archives Board (SAB), R-176, BP W44Z 1924.\n\n44. McClung, \"Speaking of Women,\" _Maclean's_ , 10 May 1916.\n\n45. Gleadle, _Borderline Citizens,_ 77.\n\n46. Binnie-Clark, \"Land and the Woman in Canada,\" 498.\n\n47. Ibid., 506.\n\n48. Ibid.\n\n49. Anon., _Our Western Lands._\n\n50. For example, one group of friends of Oliver received an irrigation grant in Alberta of over 380,000 acres in 1906 which they soon sold for an enormous profit. Gilpin, _Prairie Promises_ , 5\u20136; Schmidt, _Growing Up in the Oil Patch_ , 65.\n\n51. Young, _On Female Body Experience,_ 21.\n\n52. Binnie-Clark, _Wheat and Woman_ 1979, 308. Binnie-Clark is quoting the response that Cora Hind received from Frank Oliver when Hind met with Oliver about homesteads for women.\n\n53. Carter, _The Importance of Being Monogamous._\n\n54. McClung, \"Free Land for the Soldiers,\" _Edmonton Bulletin,_ 18 Sept. 1915, 3.\n\n55. Commander, \"Opportunities for Educated Englishwomen in Canada Are Not Recognized,\" _Carbon News_ , 13 April 1921, 7.\n\n56. Fripp, _The Outcasts of Canada,_ 174.\n\n57. Harrison, _Go West\u2014Go Wise!_ , 72.\n\n58. Ibid., 72\u201373.\n\n59. Weaver, _The Great Land Rush_ ; Belich, _Replenishing the Earth_.\n\n60. Roe, _\"Getting the Know-How_. _\"_\n\n61. Lacombe Rural History Club, _Wagon Trails to Hard Top_ , 164; PAA, homestead file 524559, reel 2055.\n\n62. _Wagon Trails to Hard Top_ , 164.\n\n63. Roe, _\"Getting the Know-How_ , _\"_ 16.\n\n64. Ibid., 16\u201317.\n\n65. _Vote_ , 27 Aug. 1927, 3.\n\n66. McClintock, _Imperial Leather_ , 6.\n\n67. Wildenthal, \"'She Is the Victor': Bourgeois Women, Nationalist Identities and the Ideal of the Independent Woman Farmer in German Southwest Africa,\" 80\u201385.\n\n68. Dinesen, _Out of Africa_ , 1.\n\n69. I explore dimensions of this in Carter, _The Importance of Being Monogamous_.\n\n70. Hurt, _The Big Empty_ , 5\u20136. See also Carter, ed., _Montana Women Homesteaders_.\n\n71. Hurt, _The Big Empty_ , 8.\n\n72. Binnie-Clark, \"Land and the Woman in Canada,\" 506. The commentary and discussion by J. Obed Smith and others in the audience was published together with Binnie-Clark's address.\n\n73. Ballantyne, \"Race and the Webs of Empire\"; Ballantyne, \"Colonial Knowledge.\"\n\n74. \"Where Women Are Farmers,\" _Globe_ , 19 July 1910, 5.\n\n75. \"Women for Canada,\" _Daily Mail_ , 4 April 1921, 6.\n\nCHAPTER ONE\n\n1. Quoted in Hanson, introduction to Wilson, _Buffalo Bird Woman's Garden_ , xxii. This book was originally published in 1917 by Wilson as _Agriculture of the Hidatsa Indians._\n\n2. See, for example, Trigger, _The Huron._\n\n3. See Kub, \"Buffalo Bird Woman's Farming Methods Still in Evidence Today,\" _Agfax_ , 7 Aug. 2013, available at http:\/\/agfax.com\/2013\/08\/07\/buffalo-bird-womans-farming-methods-still-in-evidence-today\/.\n\n4. The best book on Great Plains Indigenous agriculture is Wilson, _Buffalo Bird Woman's Garden._\n\n5. Bradbury, _Travels in the Interior of America_ , 175.\n\n6. Manitoba Culture, Heritage and Recreation, Historic Resources Branch, _The Prehistory of the Lockport Site_ , 11.\n\n7. Denig, _Five Indian Tribes of the Upper Missouri_ , 109\u201310.\n\n8. Hanson, introduction to Wilson, _Buffalo Bird Woman's Garden_ , xxi.\n\n9. Wilson, _Buffalo Bird Woman's Garden_ , 13.\n\n10. Ibid., 114.\n\n11. Ibid., 15.\n\n12. Quoted in Will and Hyde, _Corn among the Indians of the Upper Missouri_ , 78.\n\n13. Hurt, _American Agriculture_ , 61.\n\n14. Wilson, _Buffalo Bird Woman's Garden_ , 27.\n\n15. Quoted in Will and Hyde, _Corn among the Indians of the Upper Missouri_ , 54.\n\n16. Quoted in ibid., 136\u201337.\n\n17. Quoted in ibid., 190.\n\n18. Quoted in ibid., 192\u201323.\n\n19. Quoted in ibid., 193.\n\n20. Quoted in ibid., 196.\n\n21. Peters, _Women of the Earth Lodges_ , 114.\n\n22. Bowers, _Hidatsa Social and Ceremonial Organization_ , 203.\n\n23. Peters, _Women of the Earth Lodges_ , 120.\n\n24. Catlin, _Letters and Notes on the Manners, Customs and Conditions of the North American Indians,_ 189.\n\n25. Matthews, _Ethnography and Philology of the Hidatsa Indians_ , 11\u201312.\n\n26. Wilson, _Buffalo Bird Woman's Garden_ , 120.\n\n27. Smithsonian, _Journal of Rudolph Friederich Kurz_ , 289.\n\n28. Quoted in Peters, _Women of the Earth Lodges_ , 120\u201321. See also Fritze, \"Growing Identity, Growing a Home: Contrasting Functions of Two Nineteenth-Century Gardens.\"\n\n29. Turner, _Ancient Pathways, Ancestral Knowledge_ , 1.\n\n30. Lethbridge and District Horticultural Society et al., _Ethnobotany of the Plants in the Garden of Native Prairie Plants_ , 1; http:\/\/www.galtmuseum.com\/pdf\/NativePrairiePlantsGarden-Ethnobotany.pdf.\n\n31. Linklater, _Measuring America_ , 223.\n\n32. I have borrowed the term \"immaculate grid\" from Linklater, _Measuring America_ , where it is used as the title of Chapter 12.\n\n33. McKay, \"The Liberal Order Framework,\" 641.\n\n34. Frederick, \"John Stoughton Dennis,\" _Dictionary of Canadian Biography_ ; http:\/\/www.biographi.ca\/EN\/ShowBio.asp?BioId=39594&query=dennis.\n\n35. Martin, _\"Dominion Lands\" Policy_ , 356.\n\n36. Ibid., 70.\n\n37. Weaver, _The Great Land Rush_ , 232.\n\n38. Linklater, _Measuring America_ , 84, 166.\n\n39. Conlogue, \"Managing the Farm, Educating the Farmer,\" 4.\n\n40. Quoted in ibid., 3.\n\n41. Boag, \"Thinking Like Mount Rushmore,\" 44.\n\n42. Ibid., 46.\n\n43. Compton, \"Proper Woman\/Propertied Women,\" 81.\n\n44. Ibid., 83.\n\n45. Ibid., 86.\n\n46. Ibid., 89.\n\n47. Ibid., 88.\n\n48. Ibid., 3. See also Compton, \"Uncle Sam's Farm\"; http:\/\/digitalcommons.unl.edu\/historyrawleyconference\/15\/. See also LAC, Record Group 17 (RG 17) Records of the Department of Agriculture, vol. 26, f. 2351\u20132375, and RG 17, vol. 27, file 2382.\n\n49. Compton, \"Proper Woman\/Propertied Women,\" 79.\n\n50. Ibid., 80.\n\n51. Ibid., 86.\n\n52. Compton, \"Challenging Imperial Expectations: Black and White Female Homesteaders in Kansas.\"\n\n53. Ibid., 87.\n\n54. Ibid., 94.\n\n55. Chused, \"The Oregon Donation Act of 1850 and Nineteenth Century Federal Married Women's Property Law.\"\n\n56. Gould and Pando, _Claiming Their Land_ , iii, 15.\n\n57. Weaver, _The Great Land Rush_ , 237.\n\n58. Home, \"Scientific Survey and Land Settlement in British Colonialism,\" 2.\n\n59. Quoted in ibid., 7.\n\n60. Hunter, _Father's Right-Hand Man_ , 26\u201327.\n\n61. Quoted in ibid., 31.\n\n62. Ibid.\n\n63. Spender, ed., _Writing a New World_ , 12.\n\n64. Alford, _Production or Reproduction?_ , 75.\n\n65. Hunter, _Father's Right-Hand Man_ , 24.\n\n66. Ibid., 32.\n\n67. Ibid., 34.\n\n68. Ibid.\n\n69. Ibid., 32.\n\n70. Ibid., 31\u201332.\n\n71. _Border Watch_ , 2 Aug. 1884, 2.\n\n72. Wanhalla, _Matters of the Heart_ , 52\u201353.\n\n73. Paul and Foster, \"Married to the Land.\"\n\n74. Quoted in ibid., 54.\n\n75. Ibid., 68.\n\n76. Wanhalla, _Matters of the Heart_ , 52\u201356.\n\n77. See Harris and Warkentin, _Canada before Confederation_ , 123\u201325.\n\n78. Dennis was a military man who first saw active service during the 1866 Fenian invasion, which did little to enhance his reputation as he was later charged, although acquitted, of endangering his men and deserting them in the face of enemy fire. Dennis escaped the action disguised as a woman, while thirty-four of the men under his command did not. He returned to his surveying career after these embarrassments.\n\n79. Tyman, \"Patterns of Western Settlement.\"\n\n80. Canada, _House of Commons Debates_ , 2nd session, 1st Parliament, 32\u201333 Victoria, v. 2 (Ottawa: Information Canada, 1975), 492.\n\n81. Ibid., 498.\n\n82. Dennis, Jr., \"A Short History of the Surveys Made under the Dominion Lands System 1869\u20131889,\" Canada, _Sessional Papers_ 25, no. 9 (1892): 2.\n\n83. Order-in-council, 1869-0699, \"Survey of townships in the [Northwest Territories]-[Minister of Public] works submits system proposed by Lieut. Col. J.S. Dennis,\" in LAC, Record Group 2 (RG 2), Privy Council Office, Series A-1-a, vol. 270; http:\/\/www.collectionscanada.gc.ca\/databases\/orders\/001022-110.01-e.php?PHPSESSIC=vv9ugshn9vqt330oo509ncne978&q1=0699&q2=&13=1869&intererval=20.\n\n84. E.A. Meredith to A. Archibald, 4 Aug. 1870, in LAC, RG 15, vol. 229, file 1 (1871).\n\n85. This section is all from A. Archibald to the Secretary of State for the Provinces, 20 Dec. 1870, in LAC, RG 15, vol. 229, file 1 (1871).\n\n86. Order-in-council, 1871-0708, \"Public lands in the Province of Manitoba\u2014Memo, 1871\/03\/01, from Hon. A. Campbell on subject of [Recommending] rules for survey allotment of woods and [etc]\u2014And that all Crown lands be transferred to the control of the Secretary of State,\" in LAC, RG 2, Series A-1-a, vol. 285 and 5115; http:\/\/www.collectionscanada.gc.ca\/databases\/order\/001022-110.01-e.php?PHPSESSID=hfvknfu2n8abikmq264fioq9i7&q2=public+lands+&q3=1871&interval=20.\n\n87. Canada, _House of Commons Debates_ , 6 April 1871, 968.\n\n88. Order-in-council, 1871-0874, \"Lands in Manitoba\u2014Hon. A. Campbell submits revised regulations for dealing with\u2014And [recommends] same be approved,\" 20 April 1871, in LAC, RG 2, Series A-1-a, vol. 286; http:\/\/www.collectionscanada.gc.ca\/databases\/orders\/001022-119.01-e.php?&sisn_id_nbr=9032&page_sequence_nbr=1&interval=20&&PHPSESSID=0pv48r468mg1rmuvk2tv8l2f60.\n\n89. Martin, _\"Dominion Lands\" Policy_ , 140.\n\n90. Richtik, \"The Policy Framework for Settling the Canadian West,\" 617.\n\n91. Morris, _The Treaties of Canada_ , 282.\n\n92. Ibid., 315.\n\n93. Carter, \"Erasing and Replacing.\"\n\n94. Morris, _The Treaties of Canada_ , 322.\n\n95. Venne, ed., _Indian Acts and Amendments_ , 94.\n\n96. Canada, _Sessional Papers_ , Annual Report of the Department of Indian Affairs for the year ended 30 June 1895, 117.\n\n97. Canada, _Sessional Papers_ , Annual Report of the Department of Indian Affairs for the year ended 30 June 1896, 273.\n\n98. LAC, Record Group 10 (RG 10), Records of the Department of Indian Affairs, vol. 4082, file 486, 315.\n\n99. Canada, _Sessional Papers,_ Annual report of the Department of Indian Affairs for the year ended 31 March 1917, 27.\n\n100. Galloway, _I Lived in Paradise_ , 48.\n\n101. Goldfrank, _Changing Configuration in Social Organization of a Blackfoot Tribe During the Reserve Period_ , 68.\n\n102. Lux, \"We Demand 'Unconditional Surrender,'\" 667\u201369.\n\n103. Daschuk, _Clearing the Plains_ , 164.\n\n104. Ibid., 185.\n\n105. Turner, _Ancient Pathways, Ancestral Knowledge_ , 192.\n\n106. Burnett, _Taking Medicine_.\n\n107. _Cypress Hills Country_ , 297.\n\n108. Carter, _Lost Harvests_. See Chapter 6, \"Prelude to Surrender: Severalty and 'Peasant' Farming,\" 193\u2013236.\n\n109. The source of the section by and about Adams Archibald is LAC, RG 15, vol. 227, file, 1, A. Archibald to Secretary of State for the Provinces, 20 Dec. 1870.\n\n110. Ibid.\n\n111. Tough and Dimmer, \"'Great Frauds and Abuses.'\"\n\n112. Ibid., 206.\n\n113. Quoted in Augustus, \"'Half-Breed' Homestead,\" 57.\n\n114. Dick, _Farmers \"Making Good_ , _\"_ 27.\n\n115. Ibid., 25.\n\n116. Stead, \"The Story of Halfbreed Scrip,\" _Raymond Rustler_ , 20 January 1911, 11.\n\n117. Historical Buildings Committee, \"67 Main Street: Alloway & Champion Building,\" 28 Feb. 1986; http:\/\/www.winnipeg.ca\/ppd\/historic\/pdf-consv\/Main667-long.pdf.\n\n118. Ibid., 2.\n\n119. SAB, homestead file 123419A.\n\n120. LAC, Western Land Grants, search term \"Benjamin E. Chaffey\"; see, for example, http:\/\/www.collectionscanada.gc.ca\/databases\/western-land-grants\/001007-110.01-e.php?q1=&q2=&q3=&q4=&q5=chaffey&q6=&interval=20&sk=21&&PHPSESSID=r21gt83n4nfah59abrj8lhfr10.\n\n121. Eatonia History Book Committee, _A Past to Cherish_ , 33.\n\n122. Stead, \"Fifty Years in Western Canada: A Sketch of the Career of John Sanderson, the First Homesteader in Western Canada,\" _Better Farming_ , May 1923, 4\u20135.\n\n123. Carter, \"Erasing and Replacing.\"\n\n124. Venne, _Indian Acts and Amendments_ , 43. S.C. 1876 c. 18-70 reads: \"No Indian or non-treaty Indian, resident in the province of Manitoba, the North-West Territories or the territory of Keewatin, shall be held capable of having acquired or acquiring a homestead or pre-emption right to a quarter section, or any portion of land in any surveyed or unsurveyed lands in the said province of Manitoba, the North-West Territories, or the territory of Keewatin, or the right to share in the distribution of any lands allotted to the half-breeds.\"\n\n125. Lambrecht, _The Administration of Dominion Lands_ , 106.\n\n126. See the Dominion Lands Act 1872 on the Library Archives Canada website, at https:\/\/www.collectionscanada.gc.ca\/immigrants\/021017-119.01-e.php?&document_code=021017-26&page=1&referer=021017-2210.01-e.html&section_code=np-land&page_nbr=174&&&&&&&&&&&&PHPSESSID=if7k8pd6tjh43vjqd52vnjnne4.\n\n127. Canada, _Prosperity follows Settlement_ , 111.\n\n128. Quoted in Shannon, \"Brokers, Land Bankers, and 'Birds of Evil Omen,'\" 3.\n\n129. Ibid., 4\n\n130. Ibid., 5.\n\n131. Robertson, _The History of the County of Bruce_ , 530.\n\n132. _Journals of the House of Commons of the Dominion of Canada_ from 6 Nov. 1867 to 22 May 1869, vol. 1 (Ottawa: Hunter, Rose and Co., 1868): appendix 8, pp. 16\u201317.\n\n133. Moodie, _Roughing It in the Bush._\n\n134. \"Emigrant Lady,\" _Letters from Muskoka_.\n\n135. Ibid., 42.\n\n136. Ibid., 137.\n\n137. Ibid., 131.\n\n138. Ibid., 23.\n\n139. Ibid., 64.\n\n140. Ibid., 150.\n\n141. Ibid., 156.\n\n142. Ibid., 181.\n\n143. Ibid., 186.\n\n144. _Regulations under the Free Grants and Homesteads Act_ (Canada: s.n., 189?); http:\/\/eco.canadiana.ca\/view\/oocihm.93761\/2?r=0&s=1.\n\n145. Ibid., 1.\n\n146. Ibid., 5.\n\n147. \"Proclamation by His Excellency James Douglas,\" no. 15 (151) A.D. 1860, in _Appendix to the Revised Statutes of British Columbia, 1871_ (Victoria: Richard Wolfenden, 1871), 61\u201362. Thanks to Pernille Jakobsen, University of Calgary, for her research on BC legislation.\n\n148. \"An Ordinance to amend and consolidate the Laws affecting Crown Lands in British Columbia,\" no. 144, 1 June 1870, in _Appendix to the Revised Statutes of British Columbia, 1871_ , 492\u201394.\n\n149. \"An Act Respecting the Land of the Crown,\" 1908, c. 30, s. 1. _Revised Statutes of British Columbia_ 1911, 1518. Victoria: R. Wolfenden.\n\n150. Ibid., 1518\u201319.\n\n151. Martin, _\"Dominion Lands\" Policy_ , 393.\n\n152. Allen, \"Homesteading and Property Rights,\" 2.\n\n153. Quoted in Muhn, \"Women and the Homestead Act,\" 287.\n\n154. Ibid., 289.\n\n155. Ibid., 294.\n\n156. LAC, RG 15, Homestead Land Registers from 1872, reel T-2. Thanks to Leslie Hall for her research and analysis of the homestead land registers.\n\n157. Metcalfe, _The Tread of the Pioneers_ , entry on Peter Walker, 263\u201364.\n\n158. PAM, homestead file NE 20-2-3E, reel 2043.\n\n159. Waddell, _Dominion City,_ 18.\n\n160. Ibid., 30.\n\n161. LAC, RG 15, Homestead Land Registers from 1872, Reel T-2, 14.\n\n162. LAC, Census of 1881 for Manitoba, district 186 Marquette, Woodlands no. 24, 10.\n\n163. PAM, homestead file SW 24-20-6E, reel 2088.\n\n164. Ibid., homestead file SE 4-16-2-E1, reel 2025.\n\n165. Ibid., homestead file SW 9-14-11-W1, reel 2454.\n\n166. Ibid., homestead file NW 30-9-7 E1, reel 2098.\n\n167. Ibid., homestead file SE 32-12-5-W, reel 2258; Metcalfe, _The Tread of the Pioneers_ , 57, 270.\n\n168. PAM, homestead file SW 30-12-8-W, reel 2331.\n\n169. Ibid., homestead file SE 24-12-8-W1, reel 2207.\n\n170. LAC, RG 15, Homestead Land Register, Reel T-2, 80.\n\n171. Ibid., 65.\n\n172. PAM, homestead file NE 15-15-9W, reel 2372.\n\n173. Ibid., Secretary F.R.B. [?] to Secretary, Department of the Interior, 20 March 1897.\n\n174. PAM, homestead file NE 19-12-7-W1, reel 2295.\n\n175. Ibid., homestead file NW 36-12-10-W, reel 2415.\n\n176. Ibid., homestead file NE 33-10-6-E, reel 2088.\n\n177. LAC, RG 15, Homestead Land Register, Reel T-2, 33.\n\n178. Morton, _Manitoba_ , 174.\n\n179. Ibid., 177.\n\n180. Friesen, _The Canadian Prairies_ , 309.\n\n181. Stead, \"Fifty Years in Western Canada,\" 5.\n\n182. _Manitoba Free Press_ , 7 July 1875.\n\n183. Ibid., 26 April 1875, 2.\n\n184. Ibid., 18 June 1875, 2.\n\n185. Ibid., 1 June 1875, 2.\n\n186. Ibid., 9 June 1875, 2.\n\n187. Order-in-council, 1875-0670, \"Manitoba Grasshoppers\u2014Acting [Minister of] Interior 17 June\u2014[Recommends] authority to give leave of absence to occupants of Homestead\u2014During prevalence of the plague,\" in LAC, RG 2, Series A-1-a, vol. 335; http:\/\/www.collectionscanada.gc.ca\/databases\/orders\/001022-119.01-e.php?&sisn_id_nbr=6873&page_sequence_nbr=1&interval=20&&PHPSESSID=aqma40uu4ko0tlal1ocoe6v1h4.\n\n188. Order-in-council, 1875-0901, \"Relief of settlers in Manitoba rendered destitute by grasshopper ravages\u2014[Minister of Agriculture] 8 September, respecting expenditure of $60,000 authorized by [order in council] 27 August '75 and [employment] of Mr. J.Y. Shantz to purchase supplies,\" in LAC, RG 2, Series A-1-a, vol. 337; http:\/\/www.collectionscanada.gc.ca\/databases\/orders\/001022-119.01-e.php?&sisn_id_nbr=11998&page_sequence_nbr=1&interval=20&&PHPSESSID=aqma40uu4ko0tlal1ocoe6v1h4.\n\n189. Canada, _Sessional Papers_ , Annual Report of the Department of the Interior for the year ended 30 June 1875, no. 9, part III; no. 7, vol. 9, 1876.\n\n190. _Manitoba Free Press,_ 5 May 1876.\n\n191. Lambrecht, _The Administration of Dominion Lands_ , 106.\n\n192. Currie, _The Letters of Rusticus._\n\n193. Ibid., 38.\n\n194. Ibid.\n\n195. Ibid.\n\n196. Ibid.\n\n197. \"How Two Girls Tried Farming\" was serialized in the _Manitoba Free Press_ in the issues of 22, 23, 24, and 27 March 1875.\n\n198. Ibid., 27 March 1875.\n\n199. Sprague, \"Donald Codd,\" _Dictionary of Canadian Biography_ ; http:\/\/www.biographi.ca\/009004-119.01-ephp?BioId=40161.\n\n200. James Cunningham, n.d. (1870s), \"Sketch of scheme of construction of portion of Pacific Railway through the fertile regions and settlement of lands along the railway,\" in LAC, Alexander Mackenzie Papers, MG 26, Reel M-197, 694.\n\n201. See, for example, \"Government Aids Homesteaders,\" _Enterprise_ , 23 July 1914, 3.\n\n202. Patriarche, \"Husbandless Homesteads Are Wanted in the West,\" _Saskatoon Star Phoenix_ , 17 April 1913; and Thorne, \"Woman and the Land,\" _Globe_ , 21 May 1913.\n\n203. Hall, _A Lady's Life on a Farm in Manitoba_ , 24.\n\n204. \"Shocking Fatality in Manitoba,\" _New Zealand Herald_ 19, issue 6410 (3 June 1882): 7.\n\n205. Anon., \"A Study in Homestead Laws: Some Comparison of Canadian and American Practice,\" _Saturday News_ , 31 October 1908, 6.\n\n206. Patriarche, \"Husbandless Homesteads Are Wanted in the West,\" _Saskatoon Star Phoenix_ , 17 April 1913.\n\n207. Ibid.\n\n208. \"Manitoba,\" _Toronto Star_ , 21 Feb. 1874, 7.\n\n209. Currie, _The Letters of Rusticus_ , 18.\n\n210. \"Vox,\" \"The Indian Question,\" _Globe_ , 17 Aug. 1881, 7.\n\n211. _Prairie Illustrated_ 1, no. 15 (14 March 1891): 11.\n\n212. Levine, \"Introduction: Why Gender and Empire?,\" 7.\n\n213. Ibid.\n\n214. \"Where Women Are Farmers,\" _Globe_ , 19 July 1910, 5.\n\n215. Mason, _Woman's Share in Primitive Culture_ , 6.\n\n216. \"Minutes of Evidence Taken: Immigration to Canada: Mr. Lowe's Evidence,\" _Journals of the House of Commons of the Dominion of Canada_ (from the 7th February to the 10th May, 1878 being the 5th session of the 3rd Parliament of Canada, session 1878), A2-16.\n\n217. Ibid.\n\n218. J. Obed Smith, response to G. Binnie-Clark, in Binnie-Clark, \"Land and the Woman in Canada,\" 509.\n\n219. Lawrence, _Genteel Women_ , 180.\n\n220. Canada, _Sessional Papers_ , Annual report of the Department of the Interior for the year ended 30 June 1875, xvi.\n\n221. Ibid.\n\n222. Quoted in Emmons, \"American Myth, Desert to Eden,\" 6.\n\n223. _St. Cloud Democrat_ , 7 June 1866, 2.\n\n224. Canada, _Sessional Papers_ , Annual report of the Department of the Interior for the year ended 39 June 1875, 9.\n\n225. Emmons, \"American Myth, Desert to Eden,\" 6.\n\n226. Ibid., 8.\n\n227. Quoted in ibid., 11.\n\n228. _Manitoba Free Press_ , 25 March 1876, 4.\n\n229. Lambrecht, _The Administration of Dominion Lands_ , 131.\n\n230. _Manitoba Free Press_ , 30 June 1877, 5.\n\n231. Lambrecht, _The Administration of Dominion Lands_ , 132.\n\n232. Currie, _The Letters of Rusticus_ , 39.\n\n233. Emmons, \"American Myth, Desert to Eden,\" 14.\n\n234. Lambrecht, _The Administration of Dominion Lands_ , 34.\n\n235. Richtik, \"Manitoba Settlement 1870\u201386,\" 182.\n\n236. \"Homesteads for Women Asked for,\" N.d. n.p., in LAC, RG 15, D-II-1, vol. 1105, file 2876596.\n\n237. Patriarche, \"Husbandless Homesteads.\"\n\n238. Lambrecht, _The Administration of Dominion Lands_ , 106.\n\n239. Patriarche, \"Husbandless Homesteads.\"\n\n240. _Bow Island Review_ , 26 Dec. 1913, 7.\n\nCHAPTER TWO\n\n1. Sykes, \"Openings for Educated Women in Canada,\" 433, 435.\n\n2. Binnie-Clark, \"Land and the Woman in Canada,\" 500, 498, 497.\n\n3. Cran, _A Woman in Canada_ , 266.\n\n4. Verdon, _Rural Women Workers in Nineteenth-Century England_. Recent publications are confirming this regional variation; see Richardson, \"Women Farmers of Snowdonia\"; and Mark Riley, \"Bringing the 'Invisible Farmer' into Sharper Focus.\"\n\n5. Verdon, \"Middle-Class Women's Work and the Professionalization of Farming in England.\"\n\n6. \"Ladies as Farmers,\" _Daily News_ , 28 Dec. 1898, 3.\n\n7. Crawford, \"Englishwomen and Agriculture,\" 435.\n\n8. Ibid.\n\n9. Sayer, _Women of the Fields_ , 36.\n\n10. Ibid., 52\u201353.\n\n11. For Western Canada, for example, see Carter, _Capturing Women_.\n\n12. _Mirror_ 25, no. 714 (11 April 1835): 233.\n\n13. Sayer, _Women of the Fields_ , 41.\n\n14. Ibid., 178.\n\n15. Quoted in Bradley, _Men's Work, Women's Work_ , 89.\n\n16. Ibid., 84.\n\n17. Ibid., 82.\n\n18. Ibid., 87.\n\n19. Sayer, _Women of the Fields_ , 120.\n\n20. Bradley, _Men's Work, Women's Work_ , 87.\n\n21. Davidoff and Hall, _Family Fortunes_ , 275.\n\n22. Sayer, _Women of the Fields_ , 151.\n\n23. Verdon, \"Middle-Class Women's Work and the Professionalization of Farming in England,\" 402.\n\n24. Bone, \"Legislation to Revive Small Farming in England.\"\n\n25. Smith, _Land for the Small Man_ , 2. See also Allen, _Colonies at Home_.\n\n26. \"Gardening for Women,\" _Examiner_ , 30 Aug. 1879, 1119.\n\n27. Chesney, \"A New Vocation for Women,\" 341.\n\n28. Ibid.\n\n29. King, _Women Rule the Plot_ , 7\u201310.\n\n30. Warwick, introduction to Bradley and La Mothe, _The Lighter Branches of Agriculture_ , xv.\n\n31. Ibid., xx.\n\n32. Wolseley, _In a College Garden_ , 112.\n\n33. Cresswell [\"The Lady Farmer\"], _Eighteen Years on the Sandringham Estate_. Verdon, \"The Lady Farmer.\"\n\n34. Cresswell [\"Mrs. Gerard Cresswell\"], How the Farming in Great Britain Can Be Made to Pay, 25.\n\n35. Ibid., 24.\n\n36. Ibid.\n\n37. Burton, _My Home Farm_.\n\n38. Ibid., 3.\n\n39. Ibid., 105.\n\n40. King, _Women Rule the Plot_ , 108.\n\n41. Levitan, \"Redundancy, the 'Surplus Women' Problem, and the British Census.\" See also Kranidis, _The Victorian Spinster and Colonial Emigration_ ; Vicinus, _Independent Women_.\n\n42. Vicinus, _Independent Women_ , 3.\n\n43. Ibid., 5.\n\n44. \"The Field as a Profession for Women: Lady Warwick's Scheme,\" _Review of Reviews_ (June 1898): 578.\n\n45. Ibid.\n\n46. Crawford, \"Englishwomen and Agriculture,\" 428.\n\n47. \"Gardening for Women,\" _Examiner_ , 30 Aug. 1879, 1119.\n\n48. Ibid., 1118.\n\n49. Bradley, \"The Agricultural Brigade of the Monstrous Regiment of Women,\" _Fortnightly Review_ 63, no. 374 (February 1898): 334. This is in the form of a letter to the editor in response to Janet E. Hogarth, \"The Monstrous Regiment of Women,\" in _Fortnightly Review_ 62, no. 372 (December 1897): 926\u201336.\n\n50. Wolseley, _In a College Garden_ , 104.\n\n51. Ibid., 105.\n\n52. Wolseley, _Women and the Land_ , 206.\n\n53. Ibid., 208\u20139.\n\n54. Verdon, \"Middle-Class Women's Work and the Professionalization of Farming in England,\" 398.\n\n55. Bradley, \"The Agricultural Brigade of the Monstrous Regiment of Women,\" 334.\n\n56. Ibid., 337.\n\n57. Worsnop, \"A Reevaluation of 'The Problem of Surplus Women' in 19th-Century England,\" 23.\n\n58. Sayer, _Women of the Fields_ , 5, 133\u201334.\n\n59. Boucherett, _Hints on Self-Help_ , vi.\n\n60. Logan, _The Hour and the Woman_ , 36\u201377 (chapter 2).\n\n61. Bodichon, \"Reasons for the Enfranchisement of Women\" (1866), in Lacey, _Barbara Leigh Smith Bodichon and the Langham Place Group_ , 107.\n\n62. _Women's Suffrage Journal_ , (1 Sept. 1883): 164.\n\n63. Hansard Parliamentary Debates, House of Commons, 12 June 1884, 96.\n\n64. Darby, \"Current Agricultural Topics,\" _Jackson's Oxford Journal_ , 12 Dec., 1891.\n\n65. These statistics were quoted in _Otago Witness_ , 8 Feb. 1900, 55.\n\n66. Betham-Edwards, _Reminiscences_ , 60.\n\n67. I am using the terms \"radical\" and \"conservative\" as described by Worsnop in \"A Reevaluation of 'The Problem of Surplus Women' in 19th-Century England,\" 23.\n\n68. Anonymous, \"A Woof for Women,\" _Agricultural Economist_ , 1905, clipping in scrapbook 184, \"Common Place Book 1901\u20136,\" Papers of Viscountess Frances Wolseley, Hove Central Library.\n\n69. Freer, \"Horticulture as a Profession for the Educated,\" _Nineteenth Century: A Monthly Review_ (Nov. 1899): 775.\n\n70. \"Gardening for Women,\" _Examiner_ , 30 Aug. 1879, 1118.\n\n71. Anonymous, \"Horticulture as a Career for Women,\" _Times_ , 26 Dec., 1907.\n\n72. \"Gardening for Women,\" _Examiner_ , 30 Aug. 1879, 1119.\n\n73. Ibid., 1119.\n\n74. Wolseley, _Gardening for Women_ , xii.\n\n75. \"Ladies Gossip,\" _Otago Witness_ 2397, 8 Feb. 1900, 55; quoted from an article in _Leeds Mercury_.\n\n76. Chesney, \"A New Vocation for Women.\"\n\n77. Opitz, \"A Triumph of Brains over Brute.\"\n\n78. King, _Women Rule the Plot_ , 31.\n\n79. Ibid.\n\n80. Ibid.\n\n81. \"Lady Farmers: Work at Warwick College,\" _Tamworth Herald_ , 5 Nov. 1904, 8.\n\n82. \"Lady Farmers at Studley,\" _Western Times_ , 22 Aug. 1905, 7.\n\n83. Meredith, \"Horticultural Education in England, 1900\u20131940.\"\n\n84. Ibid., 70.\n\n85. Weston, \"Spinster Problem Solved,\" _Omaha Daily Bee_ , 15 March 1908, 5.\n\n86. \"Ladies at the Plough,\" _Essex County Chronicle_ , 28 Oct. 1910.\n\n87. \"From the Mountain\"; \"An Industrial Chance for Gentlewomen,\" _Once a Week_ 9, no. 219 (5 Sept. 1863): 291.\n\n88. Postcard, Commonplace Book 185, 1906\u20138, Papers of Viscountess Frances Wolseley, Hove Central Library.\n\n89. Ibid.\n\n90. Graham, _The Revival of English Agriculture_ , 177.\n\n91. Ibid., 177\u201378.\n\n92. Darby, \"Current Agricultural Topics,\" _Jackson's Oxford Journal_ , 12 Dec. 1891.\n\n93. Astor, \"Lady Farmers: Women as Agriculturalists,\" _Harmsworth Magazine_ 5 (Aug. 1900\u2013Jan. 1901): 221\u201327.\n\n94. Ibid., 224.\n\n95. Dale, \"Lady-Gardeners,\" _London Society_ , (Aug. 1898): 149\u201351.\n\n96. Strange, _Toronto's Girl Problem;_ Stansell _, City of Women_ ; Walkowitz, _City of Dreadful Delight_.\n\n97. Strange, _Toronto's Girl Problem_ , 5.\n\n98. Jusova, _The New Woman and the Empire_.\n\n99. Young, \"Throwing Like a Girl.\"\n\n100. Bartky, \" _Sympathy and Solidarity\" and Other Essays_ , 17.\n\n101. Green, _The Light of the Home_ , 130.\n\n102. Ibid.\n\n103. T.P.W., \"The Redundancy of Spinster Gentlewomen,\" _Scottish Review_ (July 1900): 95.\n\n104. Saugeres, \"She's Not Really a Woman, She's Half a Man,\" 642.\n\n105. Ibid., 646.\n\n106. Ibid., 648.\n\n107. Anonymous, \"Female Farmers,\" _Penny Magazine_ (16 July 1842): 11.\n\n108. \"A Girl Farmer,\" _Queenslander_ , 19 Oct. 1907, 4; \"A Professor's Daughter as a Farmer,\" _Western Gazette_ , 15 Nov. 1907, 11.\n\n109. Ibid.\n\n110. Darby, \"Current Agricultural Topics,\" _Jackson's Oxford Journal_ , 12 Dec. 1891.\n\n111. \"Queen Victoria's Cows,\" _Qu'Appelle Progress_ , 17 Nov. 1892, 3.\n\n112. Verdon, \"Middle-Class Women's Work and the Professionalization of Farming in England,\" 414.\n\n113. \"The Successful Woman Farmer,\" _Daily Mail_ , 1 April 1910; \"The Woman Poultry Farmer,\" _Daily Mail_ , 15 April, 1910.\n\n114. Verdon, \"Middle-Class Women's Work and the Professionalization of Farming in England,\"414.\n\n115. \"The Empty Lands,\" _United Empire_ 2 (1911): 778.\n\n116. Ibid.\n\n117. Chilton, _Agents of Empire_ , 79.\n\n118. Brice, \"Emigration for Gentlewomen,\" _Nineteenth Century: A Monthly Review_ (April 1901): 603.\n\n119. Ibid.\n\n120. Chilton, _Agents of Empire_ , 90.\n\n121. Barber, \"The Servant Problem in Manitoba.\"\n\n122. Brice, \"Emigration for Gentlewomen,\" _Nineteenth Century: A Monthly Review_ (April 1901): 603.\n\n123. Chilton, _Agents of Empire_ , 81.\n\n124. Ibid., 95.\n\n125. Levitan, \"Redundancy, the 'Surplus Women' Problem, and the British Census\" 367.\n\n126. Worsnop, \"A Reevaluation of 'The Problem of Surplus Women' in 19th-Century England,\" 23.\n\n127. Boucherett, \"How to Provide for Superfluous Women,\" 46.\n\n128. Ibid., 45.\n\n129. Ibid., 41\u201342.\n\n130. This historiography is reviewed in Chilton, _Agents of Empire_ , 93\u201394.\n\n131. Chilton, _Agents of Empire_ , 95.\n\n132. Quoted in Gordon, _Politics and Society_ , 35.\n\n133. Weston, \"Hints for the Single Women of the United Kingdom,\" _National Review_ 17, no. 98 (April 1891): 279.\n\n134. \"Tea and Silk Farming in New Zealand,\" _Chambers Journal of Popular Literature, Science and Arts_ , no. 917 (23 July 1881): 469.\n\n135. Weston, \"Hints for the Single Women of the United Kingdom,\" 280.\n\n136. Ibid., 283.\n\n137. Ibid., 284.\n\n138. \"Civis Britannicus,\" \"The Need of Women Colonists in South Africa,\" _Saturday Review of Politics, Literature, Science and Art_ , 20 Sept. 1902, 365.\n\n139. M. F-G. (Anonymous), \"Should Women Emigrate,\" _Monthly Review_ 27, no. 80 (May 1907): 99\u2013105.\n\n140. \"Colonial Training for Gentlemen's Sons,\" _Chambers Journal of Popular Literature, Science and Arts_ 2, no. 95 (Oct. 1995): 684.\n\n141. _Imperial Colonist_ 3, no. 25 (Jan. 1904): 11.\n\n142. Vernon, _Leaton Colonial Training Home_ , 4\u20135.\n\n143. Ibid., 12.\n\n144. Ibid., 5.\n\n145. Ibid., 8.\n\n146. _Imperial Colonist_ 6, no. 61 (Jan. 1907): 8.\n\n147. \"A Farming Hostel for Girls: An Appeal by Lady Warwick,\" _Review of Reviews_ 26, no. 152 (August 1902): 156.\n\n148. Ibid.\n\n149. Ibid.\n\n150. Ibid.\n\n151. Opitz, \"A Triumph of Brains over Brute,\" 51.\n\n152. Ibid., 52.\n\n153. Ibid., 53.\n\n154. _Imperial Colonist_ 3, no. 26 (Feb. 1904): 23\u201324.\n\n155. Ibid., 3, no. 27 (March 1904): 33.\n\n156. \"The Woman at Home,\" _The Review of Reviews_ 40, no. 239 (Nov. 1909): 47.\n\n157. Tooley, \"Training Girls for Life in the Colonies,\" _Globe_ , 9 July 1910, A4. See Doughty, \"Representing the Professional Woman.\"\n\n158. _Imperial Colonist_ 10, no. 121 (Jan. 1912): 17\u201318.\n\n159. Ibid., 12, no. 148 (May 1914): 79\u201380.\n\n160. Delahey, \"Emma Ducie Active at 100,\" _Western Producer_ , 12 May 1983, n.p., Glenbow Archives Clipping File, \"Agriculture-Women.\"\n\n161. Ibid.\n\n162. Oxendale, \"What Should They Know of England Who Only England Know?\" See Chapter 4.\n\n163. Gordon, _Politics and Society_ , 32.\n\n164. Blakeley, \"Women and Imperialism,\"136.\n\n165. _Imperial Colonist_ 1, no. 1 (Jan. 1902): 4.\n\n166. Ibid., 1, no. 12 (Dec. 1912): 114.\n\n167. Ibid., 2 no. 5 (June 1903): 69.\n\n168. Ibid., 2, no. 5 (May 1903): 59.\n\n169. Ibid., 112.\n\n170. Ibid., 2 no. 2 (Feb. 1903): 21\n\n171. Ibid., 3, no. 25 (Jan. 1904): 3.\n\n172. Ibid., 3, no. 27 (March 1904): 27.\n\n173. Ibid., 28.\n\n174. Ibid., 5, no. 50 (Feb. 1906): 39.\n\n175. Ibid., 5, no. 50 (Feb. 1906): 40.\n\n176. Ibid., 6, no. 65 (May 1907): 6.\n\n177. Ibid., 6, no. 69 (Sept. 1907): 3.\n\n178. Ibid., 6, no. 67 (July 1907): 2.\n\n179. Ibid., 8.\n\n180. Ibid., 10, no. 130 (Oct. 1912): 168.\n\n181. Ibid.\n\n182. Ibid., 10, no. 122 (Feb. 1912): 24.\n\n183. Quoted in Opitz, \"A Triumph of Brains over Brute,\" 52.\n\n184. \"Our Special Commissioner,\" \"Empire Migration: What are the Prospects for Educated Women,\" _Quiver_ , Jan. 1919, 611.\n\n185. Taylor, \"Conditions of Life for Women in South Africa,\" 122.\n\n186. Bush, _Edwardian Ladies and Imperial Power_ , 151.\n\n187. \"South African Women Farmers,\" _Vote,_ 19 July 1927, 237.\n\n188. \"The Review of Reviews,\" _Nineteenth Century_ 25, no. 148 (April 1902): 394.\n\n189. _Imperial Colonist_ 5, no. 6 (Dec. 1906): 177.\n\n190. Ibid., 6, no. 77 (May 1908): 8.\n\n191. Ibid., 8, no. 104 (Aug. 1910): 127\u201328.\n\n192. Ibid., 1, no. 12 (Dec. 1902): 112.\n\n193. Ibid., 9, no. 112 (April 1911): 282.\n\n194. Ibid., 9, no. 118 (Oct. 1911): 377.\n\n195. Helly, \"Flora Shaw and the Times.\"\n\n196. Anonymous (Flora Shaw), \"Letters from Canada VII, Prairie Settlement\u2014Part 1,\" Times, 22 Nov. 1898, 6.\n\n197. Helly, \"Flora Shaw and the Times,\" 122.\n\n198. Brice, \"Emigration for Gentlewomen,\" _Nineteenth Century: A Monthly Review_ (April 1901): 609.\n\n199. Bernard, \"A Training School for Lady Colonists in the Canadian North-West,\" Times, 5 April 1899, 5.\n\n200. Ibid.\n\n201. Barber, \"The Gentlewomen of Queen Mary's Coronation Hostel,\" 144.\n\n202. Lang, _Women Who Made the News_ , 49.\n\n203. Stoddard, \"Lally Bernard: An Imperial Daughter,\" _Canadian Magazine_ 46, no. 6 (1916): 513\u201315.\n\n204. Anonymous (Flora Shaw), \"Women and Colonial Settlement,\" _Times_ , 11 April 1899, 8.\n\n205. Quoted in _Leeds Mercury_ editorial, 12 April 1899.\n\n206. Ibid.\n\n207. See, for example, _Montreal Gazette_ , 22 April 1899, 11; _Leader_ , 22 June 1899; _Daily Mail and Empire_ (Toronto), 29 April 1899, 15 and 24.\n\n208. Fitzgibbon (Lally Bernard), \"Training Schools for Lady Colonists in the Canadian North-West,\" _Times_ , 23 May 1899, 10.\n\n209. _Weekend Herald_ (Calgary), 5 Oct. 1899, 4.\n\n210. \"M. F-G,\" \"Should Women Emigrate?,\" _Monthly Review_ 27, no. 80 (1907): 99\u2013105.\n\n211. Ibid., 103.\n\n212. _Times_ , 26 April 1899, 4.\n\n213. \"Women and the West,\" _Globe_ , 16 June 1899, 6.\n\n214. Fitzgibbon, _Times_ , 23 May 1889, 10.\n\n215. \"Women and the Colonies,\" _Times_ , 1 June 1904, 10.\n\n216. Bernard, \"Driftwood,\" _Globe_ , 5 Sept. 1903, 14.\n\n217. Ibid., \"Driftwood,\" _Globe_ , 1 June 190, 18.\n\n218. Ibid., \"Glimpses of the West,\" _Globe_ , 14 April 1900, 9.\n\n219. London School of Economics (LSE), Women's Library, Records of the Colonial Intelligence League (CIL); King, _Women Rule the Plot_ , 51\u201376; Oxendale, \"What Should They Know of England Who Only England Know?,\" 138\u2013155.\n\n220. Annual Reports CIL, no. 1 (1910), 10, Box 37, CIL Papers.\n\n221. \"Unmarried Daughters,\" _Times_ , 7 Dec. 1909, 10.\n\n222. Ibid.\n\n223. Annual Reports CIL, no. 1 (1910), 1, in LSE, Records of the CIL, Box 37.\n\n224. \"Women's Emigration,\" _Times_ , 16 April 1910.\n\n225. _Daily Colonist_ , 9 April 1911, 8; 14 June 1912, 5; 20 March 1913, 8; 20 June 1914, 2.\n\n226. Grosvenor, \"Women Farmers in Canada: British Farm Settlement,\" _Times_ , 27 Feb. 1913, 5.\n\n227. Ibid.\n\n228. Yarmie, \"I Had Always Wanted to Farm,\" 105.\n\n229. Ibid.\n\n230. \"Lady Sybil Grey Miner,\" _Globe_ , 18 Sept. 1909, 8.\n\n231. Yarmie, \"'I Had Always Wanted to Farm,'\" 106.\n\n232. Sykes, _A Home-Help in Canada_ , 304.\n\n233. \"Ranch for Women,\" _Ashburton Guardian_ vol. 33, no. 8799 (20 Feb. 1914): 6.\n\n234. Ibid.\n\n235. CIL Reference Book: Canada, in LSE, Records of the CIL.\n\n236. Barber, \"The Gentlewomen of Queen Mary's Coronation Hostel.\"\n\n237. Stoddard, \"Lally Bernard: An Imperial Daughter,\" _Canadian Magazine_ 46, no. 6 (91916): 514.\n\n238. Barber, \"The Gentlewomen of Queen Mary's Coronation Hostel,\" 150.\n\n239. The _Daily Colonist_ editorial is quoted in the _Globe_ , 19 July 1913, 6.\n\n240. Yarmie, \"'I Had Always Wanted to Farm,'\" 113.\n\n241. CIL Minute Book, meeting 16 Oct. 1913, 3, in LSE, Records of the CIL, Box 38.\n\n242. \"Mischievous Benevolence,\" editorial, _Daily Colonist,_ 11 July 1913, 4.\n\n243. Seaton, \"The Garden Autobiography,\" 110\u201311.\n\n244. Cran, _A Woman in Canada_. The book was published in England, Canada and the United States in 1911, and when it first appeared is not clear; it may have been as early as 1909.\n\n245. Cran, _A Woman in Canada_ , 14\u201315.\n\n246. Ibid., 22.\n\n247. Ibid., 39.\n\n248. Ibid., 38.\n\n249. Ibid., 153.\n\n250. Ibid.\n\n251. Ibid., 154.\n\n252. Ibid., 155.\n\n253. \"Women Farmers in Canada: A Great Future,\" _Warwick Examiner and Time_ s 21 June, 1909, 3.\n\n254. Cran, _A Woman in Canada_ , 162.\n\n255. Ibid., 266.\n\n256. Ibid.\n\n257. Smith, \"Adventurous Girls of the British Empire.\"\n\n258. Ibid., 12, 13.\n\n259. Ibid., 4.\n\n260. Ibid., 16.\n\n261. Ibid.\n\n262. Ward, _Canadian Born_. This book was published in the United States with the title _Lady Mereton, Colonist_.\n\n263. Harris, \"Hobart and 'Home' in Tasma and Mrs. Humphry Ward.\"\n\n264. Swan, \"Prairie Fires,\" _Quiver_ 48, no. 11 (Sept. 1913): 1044.\n\n265. Ibid., 1053.\n\n266. Ibid., 48, no. 12 (October 1913): 1130.\n\n267. Austin, _Woman_ , 35.\n\n268. Ibid.\n\n269. Ibid., 35\u201336.\n\n270. Hoodless, \"Trades and Industries: The Industrial Possibilities of Canada,\" in _Women of Canada: Their Life and Work_ , 92.\n\n271. Ibid., 95.\n\n272. Ibid.\n\n273. Crowley, \"Adelaide Sophia Hunger (Hoodless),\" _Dictionary of Canadian Biography_ , http:\/\/www.biographi.ca\/en\/bio\/hunter_adelaide_sophia_13E.html.\n\n274. _Women of Canada: Their Life and Work_ , 86.\n\n275. Strong, \"Horticulture as a Profession for Women,\" in _Report on the International Congress of Women_ , 319.\n\n276. Yates, \"Women in Agriculture,\" in _Report on the International Congress of Women_ , 308.\n\n277. _Women of Canada: Their Life and Work_ , 86\u201387.\n\n278. Ibid.\n\n279. Crerar, \"Educated Women for Canada,\" _Times_ , 30 May 1910, 6. On the International Order of the Daughters of the Empire, see Pickles, _Female Imperialism and National Identity_.\n\n280. Rees, _New and Naked Land_ , 8.\n\n281. Ibid.\n\n282. Ibid.\n\n283. Ibid., 10.\n\n284. Canadian Pacific Railway Company, _Words from the Women of Western Canada_.\n\n285. Ibid., 4.\n\n286. Ibid., 38.\n\n287. Canadian Pacific Railway Company, _Women's Work in Western Canada: A Sequel to \"Words from the Women of Western Canada.\"_\n\n288. Ibid., 26.\n\n289. Ibid., 38\u201339.\n\n290. Ibid., 45\u201346.\n\n291. Ibid., 13\u201314.\n\n292. Ibid., 13.\n\n293. \"Canada for Women,\" _Daily Mail_ 2 March, 1910: n.p.\n\n294. Chapman, \"The Argument of the Broken Pane: Suffragette Consumerism and Newspapers,\" _Media History_ 21:3 (2015): 247.\n\n295. Ibid.\n\n296. \"Canada for Women,\" _Woman's Leader and the Common Cause_ v. 210 (1913): 28.\n\n297. \"A Welcome to Women in British Columbia,\" _Suffragette_ , 7 March 1913, 339.\n\nCHAPTER THREE\n\n1. \"Western Farmers Exhibit Brightest Crop Prospects,\" _Edmonton Bulletin_ , 3 Aug. 1909, 1.\n\n2. Brada-Easthill-Roecliffe Historical Society, _Rural Roots_ , 82.\n\n3. 1906 Census of the Northwest Provinces, Library Archives Canada; http:\/\/data2.collectionscanada.ca\/e\/e049\/e001210880.jpg.\n\n4. _Bow Island Review,_ 26 Dec. 1913, 7.\n\n5. \"Free\" is often within quotation marks to indicate that while the Canadian government advertised the grant of 160 acres as free, this was far from the case, as the successful homestead involved considerable cost and labour. See the summary of debates about homestead costs in Russell, _How Agriculture Made Canada_ , 238\u201342.\n\n6. Canada, Dominion Lands Branch, _Homestead Regulations of North-Western Canada with an Abridgement of the Dominion Lands Act_ (Ottawa: Department of the Interior, 1903), 3.\n\n7. Grand Trunk Pacific Railway, General Passenger Department, _Land Seekers' Guide_ , 22.\n\n8. Dick, _Farmers \"Making Good_. _\"_\n\n9. This section is taken from Col. G.C. Porter, \"Homesteading Widow Raises 10 Children on Crusoe Cuisine,\" _Winnipeg Evening Tribune_ , 13 Feb. 1943, 22; and \"Jessie Margaret McGavin, Physician,\" Memorable Manitobans; http:\/\/www.mhs.mb.ca\/docs\/people\/mcgavin_jm.shtml.\n\n10. Richards, \"The Story of Beautiful Plains.\"\n\n11. Schofield, _The Story of Manitoba_ , 69\u201370.\n\n12. 1891 Census, Northwest Territories, Library and Archives Canada; http:\/\/data2.collectionscanada.gc.ca\/1891\/jpg\/30953_148228-00466.jpg. See also _Moose Jaw Herald,_ 11 Sept. 1896, 5; 1 Sept. 1899, 1.\n\n13. Oak Lake Historical Committee, _Ox Trails to Blacktop_ , 162\u201363.\n\n14. Alberta Historical Society, _Cypress Hills Country_ , 275\u201376.\n\n15. Biographical information is taken from the marriage notice of Agnes Katherine Cobb and Francis William Bedingfeld, in _Gentleman's Magazine and Historical Review_ , Nov. 1862, 627; information on Agnes Katherine Cobb, later Agnes Katherine Bedingfeld, and her son Francis is also from the U.K. census online from 1861, 1871, and 1881; see, for example, the 1881 census available at http:\/\/www.ukcensusonline.com\/search\/index.php?fn=agnes&sn=Bedingfeld&phonetic_mode=1&event=1881&token=5azQWxpqQ8pu77yZu0Y8-IdxpiGha8ER9SchU-hb_MM. Notice of the death of Lt. Francis W. Bedingfeld is from the _United Service Magazine_ 119 (1869): 453.\n\n16. PAA, homestead file 513196, reel 2053.\n\n17. Evans, _Prince Charming Goes West_ , 51.\n\n18. PAA homestead file 1208837, reel 2752.\n\n19. Lehr, \"The Making of the Prairie Landscape,\" 11\u201312; Evans, _The Bar U: Canadian Ranching History_ , 76, 78.\n\n20. \"The Prince of Wales as Rancher,\" _Red Deer News,_ 19 May, 1920, 9.\n\n21. History Book Society, _Fencelines and Furrows_ , 276\u201378.\n\n22. PAA, homestead file, file 819163, reel 2714.\n\n23. History Book Society, _Fencelines and Furrows_ , 277.\n\n24. Pleasantdale and District History Book Committee, _Memories of the Past_ , 496\u201397.\n\n25. Ibid., 497.\n\n26. SAB, homestead file 1591363: SE 28-9-3-W3; and 1774242: NE 21-9-3-W3. See also Mehain and Limerick Historical Society, _Prairie Trails and Pioneer Tales_ , 188\u201392.\n\n27. Coyote Flats Historical Society, _Coyote Flats Historical Review 1905\u20131965_ , 1:63.\n\n28. \"Another Oldtimer Passes from the District,\" _Crossfield Chronicle_ , 1 Sept. 1938; Anon., _Prairie Sod and Goldenrod: History of Crossfield and District_ , 96.\n\n29. Ghost Pine Community Group, _Memoirs of the Ghost Pine Homesteaders_ , 68.\n\n30. Ibid.\n\n31. \"Lyster\/Sommerville Clan Gather for A Reunion,\" _Three Hills Capital_ , 13 Aug. 2014.\n\n32. Parkbeg History Book Group, _Parkbeg Reflections_ , 234\u201335.\n\n33. Aberdeen Historical Society, _Aberdeen, 1907\u20131981_ , 117.\n\n34. Lacombe Rural History Club, _Wagon Trails to Hard Top_ , 568.\n\n35. Webb History Book Committee, _Prairie Memories_ , 595.\n\n36. Ibid., 652\u201353.\n\n37. Yellow Lake History Group, _Treasured Memories_ , 531.\n\n38. Parkbeg History Book Group, _Parkbeg Reflections_ , 236.\n\n39. Webb History Book Committee, _Prairie Memories_ , 1143\u201344.\n\n40. Notukeu History Book Club, _Next Year Country_ , 381.\n\n41. Kenyon, _Lone Rock to Marshall_ , 359.\n\n42. Rita Mary Cleveley, \"1796 through 1999... and All the Years Between,\" unpublished history of the Cleveley family. Thanks to Matthew Ostapchuk, MA, University of Alberta Department of History, for sharing his family history with me.\n\n43. SAB, homestead file 1863456: NE 20-5-1-W3.\n\n44. Ibid., statutory declaration by Mrs. O. Thompson, 14 Sept. 1912.\n\n45. McPherson, \"Was the 'Frontier' Good for Women?,\" 80.\n\n46. This data is from The Last Best West: The Alberta Land Settlement Infrastructure Project at the University of Alberta, with principal investigator Peter Baskerville and co-investigators Sarah Carter and Sean Gouglas. This preliminary data was provided by Peter Baskerville in an email of 14 April 2014.\n\n47. Blaine Lake and District Historical Book Committee, _Bridging the Years_ , 476.\n\n48. Ibid.\n\n49. Leonard, _The Last Great West_ , 565\u201366.\n\n50. Thanks to Doris J. MacKinnon, Red Deer, author of _The Identities of Marie Rose Delorme Smith: Portrait of a M\u00e9tis Woman, 1861\u20131960_ , for providing me with the homestead file of Marie Rose Smith.\n\n51. PAA, homestead file 1390105, reel 2077; LAC, RG 15, Metis Scrip Records, scrip application of Julia Rowland for her deceased son Angus Rowland, form D. no. 2770; Morrow, \"The Deville Story,\" 16.\n\n52. The debates about the cost of homesteading are summarized in Russell, _How Agriculture Made Canada_ , 238\u201342.\n\n53. Church-Staudt, \"Agnes (Martin) Balfour: Descendants Uphold Her Heritage,\" 21. Thanks to Douglas Ramsay for sharing information on Agnes Balfour and family.\n\n54. PAA, homestead file 3268427, reel 2462.\n\n55. Ibid., homestead file 1465905, reel 2789.\n\n56. _Edmonton Bulletin_ , 9 Jan. 1906, 3.\n\n57. Advertisement, _Edmonton Capital_ , 16 April 1910, 6.\n\n58. \"Death of Madame de Tro,\" _Edmonton Bulletin_ , 17 May 1913, 13.\n\n59. Wood Mountain Historical Society, _They Came to Wood Mountain_ , 194.\n\n60. LAC, Census of Canada 1911, Saskatchewan, district and subdistrict: Regina, item no. 7690602, 44.\n\n61. Wood Mountain Histortical Society, _They Came to Wood Mountain_ , 195.\n\n62. SAB, homestead file 2133402: SW 6-3-5-W3, Marion Pearce to Dominion Lands Office, 11 Dec. 1911.\n\n63. Ibid., F. Nelson to Pearce, 24 Jan. 1912.\n\n64. Ibid., homestead inspector's report, Sept. 1919.\n\n65. Potyondi, _In Palliser's Triangle_ , 96\u201399.\n\n66. SAB, homestead file 2133402, Acting Commissioner of Dominion Lands to Mrs. Frazer, 1928.\n\n67. See Hryrniuk and Korvemaker, _Legacy of Stone_ , 11\u201313.\n\n68. Ibid.\n\n69. John Geddes to the Secretary, Department of the Interior, 23 Oct. 1890, SAB homestead file 425772, SW2-9-5-W2.\n\n70. LAC, Western Land Grants, Mary Ann McNab, SW 2-9-5-W2.\n\n71. Lambrecht, _The Administration of Dominion Lands_ , 116.\n\n72. SAB, homestead file 500684: SE 14-14-10-W2.\n\n73. Canada, _Prosperity Follows Settlement_ , 111.\n\n74. \"Cupid Championed by Miss Rankin in Talk to Congress,\" _Washington Times_ , 8 Dec. 1917, 5.\n\n75. LAC, Census of Canada 1891 for the Province of Manitoba, Selkirk District, Virden Village.\n\n76. _Manitoba Free Press,_ 28 Dec. 1882.\n\n77. _Winnipeg Daily Times_ , 2 Oct. 1882.\n\n78. Ibid., 30 Sept. 1882, and _Manitoba Free Press_ , 28 Dec. 1882.\n\n79. See Kendle, \"Thomas Mayne Daly,\" _Dictionary of Canadian Biography_ ; http:\/\/www.biographi.ca\/en\/bio\/daly_thomas_mayne_1852_1911_14E.html.\n\n80. \"Money Flew Fast in the Good Old Tory Days,\" _Globe_ , 5 Jan. 1901, 5.\n\n81. These letters are quoted in \"Mr. Daly Had Strong Pull,\" _Brandon Daily Sun_ , 1 Oct. 1908, 1.\n\n82. \"Mr. Daly's Homestead,\" _Brandon Daily Sun_ , 16 Oct. 1908, 4.\n\n83. LAC, Census of Canada 1901, Province of Manitoba, District 6 Brandon, Village of Virden, p. 1.\n\n84. _Thomas Mayne Daly_ , Manitoba Culture, Heritage and Recreation.\n\n85. Letter, ____ Hall to E.L. Newcombe, 2 April 1896 in Circumstances under which married woman or widow may obtain a homestead entry, LAC, Record Group 13 (RG 13) Records of the Department of Justice, vol. 2247, file int. 25 74\/1896.\n\n86. Letter, William Wilson to A.M. Burgess, 28 April 1886, in LAC, RG 13, vol. 2247, file int. 25 74\/1896.\n\n87. SAB, homestead file 317719: NW 16-47-26-W2.\n\n88. Ibid., Clerk of the Privy Council to the Minister of the Interior, 18 Feb. 1895.\n\n89. Ellen Margaret Cameron to Department of the Interior, January 1887, in LAC, RG 15, D-II-1, vol. 477, file 130492.\n\n90. Secretary, Department of the Interior to E.M. Cameron, 19 Jan. 1887, in LAC, RG 15, D-II-1, vol. 477, file 130492.\n\n91. Letter, ____ Hall to E.L. Newcombe, 28 Sept. 1893. \"Homestead entry of Margaret Spence\u2014half-breed woman with illegitimate children,\" in LAC, RG 13, vol. 2271, file 150-1893.\n\n92. Letter, Deputy Minister of Justice to Secretary, Department of the Interior, 19 Oct. 1893, in LAC, RG 13, vol. 2271, file 150-1893.\n\n93. Scrip application. Young, Sarah. Address: Stonewall; born 8 Sept. 1885 at Rabbit Point: father: Thomas Young (Whiteman); mother Margaret Spence (Metis); scrip cert.: form E, no. 3492; claim no. 588. vol 1371, in LAC, RG 15, D-II-8-c.\n\n94. Memorandum, Department of Justice, 8 Nov. 1894, in LAC, RG 13, vol. 2247, file int. 25 74\/1896.\n\n95. LAC, RG 15, vol. 2108, ruling no. 167, 53\u201354.\n\n96. LAC, RG 15, Dominion Land Rulings, no. 1504, Memorandum, 27 Aug. 1914.\n\n97. See, for example, SAB, homestead file 2178290: NE 10-3-16 W3 (Mrs. Nettie Blackmer).\n\n98. LAC, RG 15, Dominion Lands Rulings, no. 496-1894, Deputy Minister of Justice to the Secretary, Department of the Interior, 8 Aug. 1894.\n\n99. PAA, homestead file, reel 2434, file 3006361.\n\n100. Canada, _Debates of the House of Commons_ , 3rd session, 10th Parliament, vol. 80 (Ottawa: S.E. Dawson, 1906\u20137), 4813\u201314.\n\n101. LAC, RG 15, Dominion Lands Rulings, no. 4171, vol. 1971, Department of the Interior circular letter, 21 July 1920.\n\n102. Thwaite, _Alberta: An Account of Its Wealth and Progress_ , 306\u20137.\n\n103. SAB, homestead file 861961: SW 28-25-24-W2.\n\n104. Ibid., James F. MacLean to J.G. Turriff, 30 Jan. 1904.\n\n105. LAC, RG 15, Dominion Land Rulings, no. 4369, Memorandum, 10 Feb. 1921.\n\n106. LAC, RG 15, vol. 2277, file 1895-242, Deputy Minister of Justice to the Secretary, Department of the Interior, 5 March 1895.\n\n107. PAA, homestead file 641486, reel 2074, images 1612\u20131614: SE 30-4-28-W4.\n\n108. Doughan, \"Pioneer Club,\" _Oxford Dictionary of National Biography_ ; http:\/\/www.oxforddnb.com\/templates\/theme.jsp?articleid=96079.\n\n109. _Edmonton Bulletin,_ 29 May 1912, 3.\n\n110. LAC, RG 15, Dominion Land Rulings, no. 2544, Memorandum, 27 Jan. 1917.\n\n111. LAC, RG 13, vol. 2377, file 105\/1895, E. Newcombe to L. Pereira, 31 May 1895.\n\n112. SAB, homestead file 467578: NE 26-26-5-W2.\n\n113. S.C. 1897 60\u201361 Victoria c. 29 s. 12; Lambrecht, _The Administration of Dominion Lands_ , 106.\n\n114. Pollock, _Our Pioneers_ , 92.\n\n115. See http:\/\/boards.ancestry.com\/thread.aspx?mv=flat&m=2835&p=surnames.harvey.\n\n116. LAC, Census of the Western Provinces, 1906; http:\/\/data2.collectionscanada.ca\/e\/e049\/e001207780.jpg.\n\n117. Pollock, _Our Pioneers_ , 92.\n\n118. Veldhuis, _For Elise: Unveiling the Forgotten Woman on the Criddle Homestead._\n\n119. PAM, 2255 #375, homestead file NW 28-8-26-W1, Elise Vane to Dominion Lands Agent, Brandon, 19 Aug. 1889.\n\n120. Ibid., Vane to A.H. Smith, Commissioner of Dominion Lands, Winnipeg, 30 Sept. 1889 and Vane to the Minister of the Interior 2 Oct. 1889.\n\n121. Ibid., Anonymous letter to the Commissioner of Dominion Lands, 31 Jan. 1890 from Aweme, Manitoba.\n\n122. Ibid., R.O. Cook to Commissioner of Dominion Lands, Winnipeg, 22 Feb. 1890.\n\n123. Ibid., Percy Criddle to Smith, 26 Feb. 1890.\n\n124. LAC, 1891 Census, district 7 Marquette, subdistrict South Cypress, Manitoba; http:\/\/data2.collectionscanada.gc.ca\/1891\/jpg\/30953_148095-00496.jpg.\n\n125. Ibid., for 1901; http:\/\/data2.collectionscanada.ca\/1901\/z\/z001\/jpg\/z000016439.jpg.\n\n126. \"Through Silent Night Watches,\" _Edmonton Bulletin_ , 1 Sept. 1908, 1.\n\n127. Watt, _Town and Trail_ , 67.\n\n128. \"Congratulations,\" _Edmonton Bulletin_ , 3 Sept. 1908, 8.\n\n129. PAA, homestead files, file 1681610, reel 2827; file 1238377, reel 2756.\n\n130. Fullerton, \"Our Homesteaders,\" _Canadian Magazine_ 16, no. 3 (January 1916): 253.\n\n131. Anon., \"Our Western Lands.\"\n\n132. LAC, RG 15, Dominion Lands Rulings, vol. 1957, p. 417, Memorandum Oliver to Greenway, 24 Jan. 1910.\n\n133. Ibid., 422, W.W. Cory to T. Greenway, 30 May 1910.\n\n134. Ibid., Memorandum, 23 May 1910.\n\n135. Ibid., Memorandum 16 July 1910, 479.\n\n136. Roy, \"A Berkhamstead Boy in the Foothills,\" 24.\n\n137. Ibid., 17, 29.\n\n138. LAC, RG 15, Dominion Lands Rulings, vol. 1957, 484, Memorandum, A.J. Fraser to F.F. Dixon, 16 June 1910.\n\n139. See, for example, the case of Margrit Hefferman, in PAA, homestead file 119536, reel 2750.\n\n140. LAC, RG2, orders-in-council, no. 2055, \"Sale lands Mrs. Marion [ _sic_ ] B. Heath of Leduc...\" 1895\/07\/02.\n\n141. Ibid.\n\n142. LAC, Maria Ann Bell-Heath land patent; http:\/\/www.bac-lac.gc.ca\/eng\/discover\/land\/land-grants-western-canada-1870-1930\/pages\/image.aspx?URLjpg=http%3a%2f%2fcentral.bac-lac.gc.ca%2f.item%2f%3fid%3de002979350%26op%3dimg%3dwesternlandgrants&Ecopy=e002979350.\n\n143. PAA, homestead file 1195365, reel 2750.\n\n144. \"Took Up Homesteading Illegally,\" _Minnedosa Tribune_ , 8 Sept. 1910, 2.\n\n145. This section is taken from \"Got Nine Months: Guilty of Perjury,\" _Medicine Hat Times_ , 25 August 1910, 7.\n\n146. PAM, homestead file SE 12-24-25-W.\n\n147. LAC, 1881 Census, Manitoba, Rockwood Division, Lisgar.\n\n148. LAC, 1891 Census, Manitoba, Marquette, Cypress South.\n\n149. LAC, 1901 Census, Manitoba, Marquette, Dauphin.\n\n150. LAC, 1906 Census, Manitoba, village of Grandview.\n\n151. LAC, RG2, order-in-council, number 1850, \"Dominion lands homestead sold Mrs. Delia Bell, homesteader at $3 p. acre,\" Minister of the Interior, 1910\/09\/15.\n\n152. PAM, homestead file SE 23-26-27-W of the Principal Meridian, Secretary of the Department of the Interior to Margaret Little, 26 Feb. 1909.\n\n153. Ibid., F. Herchmer to Secretary, Department of the Interior, 24 Feb. 1910.\n\n154. Ibid., Herchmer to F.E. McGregor, 18 April 1910, and McGregor to Herchmer, 7 May 1910.\n\n155. Ibid., Margaret Little to Secretary Department of the Interior, 9 May 1910.\n\n156. Ibid., statutory declaration of Margaret Little, 9 June 1910.\n\n157. Ibid., John A. Watson to Herchmer, August 1910.\n\n158. Ibid., Herchmer to M. Little, 2 Dec. 1910.\n\n159. Ibid., M. Little to Secretary, Department of the Interior, 7 Dec. 1910.\n\n160. Ibid., Herchmer to Secretary, Department of the Interior, 21 Jan. 1911.\n\n161. Ibid., letters patent to Ross Little.\n\n162. \"An Enterprising Lady,\" _Minnedosa Tribune_ , 19 Jan. 1911, 2.\n\n163. PAM, homestead file SE 23-26-27-W of the Principal Meridian, William Hughes to Commissioner of Dominion Lands, 12 Jan. 1903.\n\n164. Ibid., homestead file NW 10-26-28-W of the Principal Meridian, Last Will and Testament of William Hughes.\n\n165. Carter, \"My Vocabulary Contains No Such Word as Defeat.\"\n\n166. PAA, homestead file 570088, reel 2062, Clara A. Lynch to W.H. Cottingham, 2 June 1900. All of the rest of the correspondence in this section is from this file. Her land was Section 12, Township 40, Range 1, West of the 5th Meridian. For the history of Bentley, see Bentley and District Historical Society, _Bentley and District Early History._\n\n167. Turriff to Oliver, 3 April 1901.\n\n168. Lynch to Oliver, 15 May 1901.\n\n169. SAB, homestead file 2487207.\n\n170. SAB, Homestead Index and homestead files.\n\n171. Canada, _House of Commons Debates_ , 1907\u201308, 10 July 1908, 12607.\n\n172. Canada, _House of Commons Debates_ , 1907\u201308, vol. 88, 10 July 1908, 12617.\n\n173. SAB, homestead file 1780808.\n\n174. Canada, _House of Commons Debates_ , 1907\u201308, vol. 83, 25 Feb. 1908, 3782\u201383; Graham, _A Canadian Girl in South Africa: A Teacher's Experiences in the South African War, 1899_ _\u2013_ _1902_.\n\n175. _Manitoba Free Press_ , 17 May 1910; _Daily Phoenix_ , 16 May 1910; _Morning Leader_ , 17 May 1910.\n\n176. _Toledo Blade_ , 23 June 1910.\n\n177. SAB, homestead file 1915194.\n\n178. _Secret Service_ 611 (7 Oct. 1910): 29.\n\n179. _Saskatoon Star Phoenix_ , 20 Dec. 1917, 3.\n\n180. _Edmonton Bulletin_ , 21 May 1910.\n\n181. Ibid.\n\n182. SAB, homestead file 1513986.\n\n183. Eatonia History Book Committee, _A Past to Cherish_ , 463.\n\n184. Leonard, _The Last Great West_ , 563.\n\n185. SAB, homestead file 2125459.\n\n186. SAB, homestead file 1691732.\n\n187. Stone Diggers History Book Committee, _Prairie Wool_ , 181.\n\n188. SAB, homestead file 108200A.\n\n189. Birtles, \"A Pioneer Nurse,\" 2.\n\n190. SAB, homestead file 1773681.\n\n191. SAB, homestead file 1406319.\n\n192. SAB, homestead file 1884227.\n\n193. SAB, homestead file 2138434.\n\n194. SAB, homestead file 2138434.\n\n195. SAB, homestead file 1733160.\n\n196. SAB, homestead file 2092263.\n\n197. Ibid., Jane Gentles to Minister of the Interior, 1 April 1915.\n\n198. Ibid., statement of Jane Gentles, 21 July 1915.\n\n199. _Edmonton Bulletin_ , 21 May 1910.\n\n200. See, for, example Bauman, \"Single Women Homesteaders in Wyoming\"; Garceau, _The Important Things of Life_ ; Gould and Pando, _Claiming Their Land_ ; Lindgren, _Land in Her Own Name_ ; Patterson-Black, \"Women Homesteaders on the Great Plains Frontier.\"\n\n201. Muhn, \"Women and the Homestead Act,\" 286.\n\n202. James Muhn indicates that Mormon women involved in plural marriages were able to file on homesteads until 1878, when the General Land Office ruled that they would no longer be permitted to do so (\"Women and the Homestead Act,\" 290\u201391). Katherine Benton-Cohen, however, found that Mormon women \"finessed homesteading law to accommodate plural marriage or to help children born in Mormon colonies in Mexico to obtain land in the United States.\" Benton-Cohen, \"Common Purposes, Worlds Apart,\" 431.\n\n203. Memorandum, 8 Nov. 1894, LAC, RG 13, vol. 2247, file int. 25: 74\/1896.\n\n204. Anon., _Montana 1909_ , 48.\n\n205. Muhn, \"Women and the Homestead Act,\" 283. Many thanks to James Muhn, Land Law Historian for the U.S. Department of the Interior's Bureau of Land Management, for his assistance with my research and for sending me an offprint of this article.\n\n206. Smith, \"Single Women Homesteaders,\" 164.\n\n207. Benton-Cohen, \"Common Purposes, Worlds Apart,\" 435.\n\n208. Lindgren, _Land in Her Own Name_ , 20.\n\n209. Ibid., 224.\n\n210. _Hinsdale Tribune_ , 21 Dec. 1917.\n\n211. Walker-Kuntz, \"Land, Life and _Feme Sole_ ,\" 46.\n\n212. Egly Country Club, _Trails, Trials and Tributes_ , 40.\n\n213. Geraldine History Committee, _Spokes, Spurs and Cockleburs_ , 205.\n\n214. Liberty County Museum, _Our Heritage in Liberty_ , 184.\n\n215. U.S. Department of the Interior, Bureau of Land Mangment, General Land Office Records, Sheridan County, Montana; http:\/\/www.glorecords.blm.gov\/results\/default.aspx?searchcriteria=type=patent\/st=MT\/cty=091\/ln=macgregor\/sp=true\/sw=true\/sady=false.\n\n216. Many thanks to Judy Archer, Orillia, Ontario for the photographs and information on her grandmother and aunt.\n\n217. Etta Smalley Bangs, Reminiscence, Small Collections 116, Montana Historical Society Research Center. See also Carter, ed., _Montana Women Homesteaders._\n\n218. _Edmonton Bulletin_ , 27 July 1906, 5; 27 August 1906.\n\n219. Baergen, _Pioneering with a Piece of Chalk_ , 88.\n\n220. Cohen, \"Women's History Month: Out of Canada: Etta Smalley Homesteaded a New Life,\" _Missoulian_ , 23 July 2007; http:\/\/www.missoulian.com\/articles\/2007\/03\/16\/new\/local\/news04.txt.\n\n221. MacMahon, \"'Fine Hands for Sowing': The Homesteading Experiences of Remittance Woman Jessie de Prado MacMillan,\" 277\u201378.\n\n222. SAB, homestead file 3159536: SE 27-4-2-W3.\n\n223. Ibid., T. Rothwell, memorandum to the Minister of the Interior, 21 Feb. 1914.\n\nCHAPTER FOUR\n\n1. Martin-McGuire, \"First Nations Land Surrenders.\"\n\n2. Smith, _Liberalism, Surveillance, and Resistance_ , 210\u201311.\n\n3. Martin-McGuire, \"First Nations Land Surrenders,\" 410.\n\n4. LAC, Census of Canada 1911, item 4991575, subdistrict London, Ontario. Jean C. Laidlaw was forty-five years old, of Scottish ancestry, and born in England.\n\n5. \"Woman Rancher Tells of Life: Miss Jean Laidlaw Runs 360 Acres near Pincher Creek, Alberta: Shows Great Pluck,\" _Globe and Mail_ , 6 Feb. 1920, 10.\n\n6. Martin-McGuire, \"First Nations Land Surrenders,\" 329.\n\n7. Ibid., 343.\n\n8. Ibid., 348.\n\n9. Ibid., 354.\n\n10. Ibid., 372.\n\n11. \"Famed Prairie Barrister Dies,\" _Leader-Post_ , 2 Aug. 1932.\n\n12. SAB, homestead file 572137: W \u00bd 4 and all of 6-16-23-W2.\n\n13. SAB, homestead file 861961: SW 28-25-24-W2, letter from Short, Cross, Biggar and Ewing to Frank Oliver, 4 Oct. 1905. Her name is spelled both Buckman and Bucknam in the documents.\n\n14. SAB, homestead file 349942: SW 34-32-13-W2.\n\n15. PAA, homestead file, reel 2033, file 416715.\n\n16. Ibid., ____ to J.G. Turiff, 7 Dec., 1899.\n\n17. Fortier, _Lamoureux_ , 27\u201328.\n\n18. \"Un de nos pionni\u00e8res qui dispara\u00eet,\" _La Survivance_ , 4 March 1942, 5.\n\n19. McKenzie, _It's Time to Remember_ , 327\u201328.\n\n20. Ibid., 311\u201312.\n\n21. Rockwood-Woodlands Historical Society, _Rockwood Echoes_ , 78\u201379.\n\n22. Sonningdale Recreation Board, _Sonningdale Memories_ , 406\u20138.\n\n23. Lindsay v. Morrow, _Reports of Cases Heart in the Supreme Court of Saskatchewan,_ vol. 1 (Toronto: Canada Law Co. Ltd., 1909), 516\u201317.\n\n24. Gleichen United Church Women, _The Gleichen Call:_ _A History_ , 207.\n\n25. Glenbow Archives (GA) Canadian Pacific Railway Land Sales. Annie E. Williams purchased four tracts of land in 1908 See http:\/\/ww2.glenbow.org\/search\/archivesCPRResults.aspx.\n\n26. _Gleichen Call_ , 28 March 1912, 8.\n\n27. \"Mrs. Williams Grew Excellent Flax,\" _Gleichen Call_ , 1 Jan. 1913, 1; \"Mrs. A.E. Williams Receives Big Price for Her Seed Flax,\" _Gleichen Call_ , 5 June 1913, 5; \"Lady Farmer Raises Record Crop,\" _Wainwright Star_ , 13 Aug. 1913, 2.\n\n28. _Gleichen Call_ , 31 Aug. 1916, 1.\n\n29. Gleichen United Church Women, _The Gleichen Call: A History,_ 207.\n\n30. See \"Alix, Alberta,\" http:\/\/en.wikipedia.org\/wiki\/Alix,_Alberta.\n\n31. Thanks to Juliet Gayton, Winchester, England, for this genealogical research on Alice Westhead.\n\n32. GA, Canadian Pacific Railway Land Sales, Alice C. Westhead. See http:\/\/ww2.glenbow.org\/search\/archivesCPRResults.aspx.\n\n33. _Calgary Herald_ , 7 Sept. 1910.\n\n34. Cavanaugh, \"Irene Marryat Parlby.\"\n\n35. Thompson, \"A Woman Rancher in Alberta: A Visit to Quarter-Circle-One Ranch,\" _Canadian Home Journal_ , August 1911; https:\/\/archive.org\/stream\/canadawest0708westuoft\/canadawest0708westuoft_djvu.txt.\n\n36. _Edmonton Bulletin_ , 29 Sept. 1911, 3.\n\n37. Thwaite, _Alberta: An Account of its Wealth and Progress_ , 182.\n\n38. Alix Clive Historical Club, _Gleanings after Pioneers and Progress_ , 230\u201331.\n\n39. See \"An English Woman Farmer in Alberta,\" _Globe_ , 7 March 1914, 11; \"A Successful Lady Farmer,\" _Maitland Weekly Mercury,_ 20 Dec. 1913, 10.\n\n40. \"Law Report High Court of Justice, King's Bench,\" _Times_ 10 Jan. 1903, 12.\n\n41. \"Alleged Infringement of Copyright,\" _Times_ 7 Feb. 1910, 3.\n\n42. Hamer Jackson, \"How I Made a New Home in Canada,\" _Daily Mail_ , 17 Sept. 1913, 4 _._\n\n43. GA, Canadian Pacific Railway Land Sales, Mrs. Celesta Hamer Jackson. See http:\/\/ww2.glenbow.org\/search\/archivesCPRResults.aspx\n\n44. \"A Successful Lady Farmer,\" _Maitland Weekly Mercury_ , 20 Dec. 1913.\n\n45. \"An English Woman Farmer in Alberta,\" _Globe_ , 7 March 1914.\n\n46. On Hamer Jackson lecturing in England, see _Western Gazette_ , 16 Jan. 1914, 2; articles on education include C. Hamer Jackson, \"Prevention of Pauperism,\" _Daily Colonist_ , 31 May 1914, 4; and \"Education in New Country,\" _Edmonton Bulletin_ , 23 August 1923, 6.\n\n47. Ibid. (articles on education).\n\n48. GA, Canadian Pacific Railway Land Sales Database at http:\/\/ww2.glenbow.org\/search\/archivesCPRSearch.aspx.\n\n49. GA, Canadian Pacific Railway Land Sales Database, M 2272, vol. 122, contract number 13081.\n\n50. Ibid., vol. 2272, contract number 25990.\n\n51. Ibid., vol. 99, contract number 29695.\n\n52. Ibid., vol. 78, contract number 1515.\n\n53. Ibid., Canadian Pacific Railway Database.\n\n54. Laut, \"Openings for Women in Canada,\" _Pall Mall Magazine_ 40, no. 175 (Nov. 1907), 594\u201395.\n\n55. \"Women as Farmers in Western Canada,\" _Spokesman-Review_ , 14 July 1907, 27.\n\n56. \"Monday Interment for Pioneer Resident,\" _Leader-Post_ , 7 March 1949, 16. It is noted that her farm was near the RCMP barracks on Dewdney Avenue in present-day Regina. In the 1901 census Mary V. Gilroy is aged thirty-three, born in May 1867 in Ontario. Her occupation is \"Farmer,\" and she is the head of the household. The only other household member was John Archibald, aged twenty-one. Thanks to Sharon Maier, Regina Public Library Prairie History Room.\n\n57. LAC, 1871 Census; http:\/\/data2.collectionscanada.ca\/1871\/jpg\/4396332_00128.jpg.\n\n58. Canadian Pacific Railway Company, _Words from the Women of Western Canada_ , 31\u201333.\n\n59. Ibid., 32.\n\n60. \"Canadian Women's Press Club Tour: Girl Farmers and Ranchers in the West Have Made a Success of Their Work...\" _Quebec Saturday Budget_ , 7 July 1906, 1.\n\n61. \"M.H.A.,\" \"How Four Plucky Women Won Out in the Canadian Northwest,\" _Minneapolis Journal_ , 25 July 1906, part 6.\n\n62. Canadian Pacific Railway Company, _Home Life of Women in Western Canada_ , 21\u201322.\n\n63. _Leader-Post_ , 7 March 1949, 16.\n\n64. Census research by Sharon Maier, Regina Public Library, Prairie History Room.\n\n65. _Age_ , 3 Nov. 1906, 4.\n\n66. _St. John Sun,_ 6 Oct. 1906, 10; _Otago Witness_ , 30 Oct. 1907.\n\n67. \"The Woman Who Would Be a Sailor,\" _Bay of Plenty Times_ 24, no. 3676 (23 March 1898): 2.\n\n68. _Brantford Opinion_ , 7 Dec. 1906, 7.\n\n69. \"Titled Lady Has Ranch in the West,\" _St. John Sun_ , 6 Oct. 1906, 10; \"Canadian Woman Rancher,\" _Brantford Opinion_ , 7 Dec. 1906, 7.\n\n70. \"Titled Lady Has Ranch in the West,\" _St. John Sun_ , 6 Oct. 1906, 7.\n\n71. \"The Adventures of Lady Ernestine Hunt,\" _Eastern Daily Mail and Straits Morning Advertiser_ , 26 Nov. 1906, 5\n\n72. \"Titled Lady Has Ranch in the West,\" _St. John Sun_ , 6 Oct. 1906, 7.\n\n73. Ibid.\n\n74. _L'Abeille de la Nouvelle-Orl_ \u00e9 _ans_ , 15 May 1910, 6. See also \"Handy and Helpful Girls,\" _Brisbane Courier_ , 11 May 1910, 17.\n\n75. \"Nurses on Horseback: Picturesque Parade in the West End,\" _Wairarapa Daily Times_ , 17 July 1909, 6.\n\n76. Noakes, _Women in the British Army_ , 30\u201331.\n\n77. \"Lady Hunt is a Lieutenant,\" _Spokane Daily Chronicle_ , 28 April 1910.\n\n78. _Star_ , 19 June 1909, 3.\n\n79. \"A Woman Farmer's Success,\" _New Zealand Herald_ 48, no. 14667 (29 April 1911); _Brisbane Courier_ , 19 April 1911, 14.\n\n80. \"This Woman Owns Big Farm,\" _Edmonton Bulletin_ , 17 Jan. 1911, 4.\n\n81. LAC, Census of Canada 1911, item number 7745054; http:\/\/data2.collectionscanada.gc.ca\/1911\/jpg\/e002098158.jpg.\n\n82. \"This Woman Owns Big Farm,\" _Edmonton Bulletin_ , 17 Jan. 1911, 4.\n\n83. \"Woman Runs a Big Farm Successfully,\" _Claresholm Review-Advertiser_ , 28 April 1916, 3.\n\n84. McCallum, \"Who Said Women Can't Farm? Miss R.M. Hillman of Keeler, Saskatchewan, Disproves Any Such Fallacy,\" _Grain Growers' Guide_ , 27 March 1918, 8.\n\n85. Keeler History Book Committee, _Our Heritage: A History of the Keeler Community_ , 345.\n\n86. \"A Lady Farmer,\" _Clarence and Richmond Examiner_ , 5 May 1906, 7.\n\n87. \"A Lady Farm Laborer,\" _Wairarapa Daily Times_ , 25 May 1906, 6.\n\n88. Admiral William May had one daughter and three sons. The daughter's name was Kinbarra (also his wife's name). In 1881, William and Kinbarra are shown to be in Plymouth, a large naval base. Daughter Kinbarra Swene was born 1882, West Derby District; she died in Edinburgh in 1921 and the death certificate shows that she had suffered from ill health for some time. There are no other births during the period 1878\u201382 of a girl child called Isobel May born in any of the locations in which the May family was known to have been. Kinbarra Swene Marrow, the daughter born in 1882, is recorded in the England census for 1911 (which took place on 31st March) at the home of her parents in Kensington, London. She is of no occupation and aged 29 years. In none of the post-1911 press reports about \"Jack\" May is her first name, Isobel mentioned, but this is how her name is recorded in the land ledger of the Canadian Pacific Railway.\n\nMany thanks to Joan Heggie, Research Fellow, School of Social Sciences, Teesside University Middlesbrough, U.K. for her amazingly thorough research on \"Jack\" May and the Admiral May family.\n\n89. \"World's Happiest Girl,\" _Redcliff Review_ , 13 Dec. 1912, 4.\n\n90. \"A Woman Farmer,\" _Border Watch_ , 23 May 1906, 4.\n\n91. Ibid.\n\n92. Ibid.\n\n93. \"Mrs. 'Jack' May in Alberta,\" _Saturday News_ , 23 Sept. 1911, 8.\n\n94. Ibid.\n\n95. \"A Lady Farm Laborer,\" _Wairarapa Daily Times_ , 25 May 1906, 6.\n\n96. \"Miss Jack May in Male Attire,\" _Globe_ 15 April 1911, 4.\n\n97. \"Provincial Notes: Noted Lady Farmer Settles in Alberta,\" _Gleichen Call_ , 4 May 1911, 5.\n\n98. Thanks again to Joan Heggie, whose research indicates that May arrived on the _Empress of Ireland_. The entry in the passenger list on that ship includes Jack May, destined for Sedgewick, and her age of thirty-five, is first entered in the male column and then is crossed out and written across the female column.\n\n99. _Western Globe_ , 19 April 1911, 3.\n\n100. \"Girl Posed as a Man to Keep from Starving,\" _Globe and Mail_ , 1 Jan. 1914, 15.\n\n101. \"Young Girl Posed as Man,\" in _Globe and Mail_ , 8 June 1918, 13.\n\n102. _Spokane Daily Chronicle_ , 1 Dec. 1910, 8.\n\n103. _Gazette Times_ , 31 Aug. 1913.\n\n104. \"Provincial Notes: Noted Lady Farmer Settles in Alberta,\" _Gleichen Call_ , 4 May 1911, 5.\n\n105. _Daily Colonist_ , 14 Aug. 1911, 8.\n\n106. _Kindersley Clarion_ , 3 May 1911.\n\n107. \"Mrs. 'Jack' May in Alberta,\" _Saturday News_ , 23 Sept. 1911, 8.\n\n108. \"Canada's Golden West,\" _Hawera and Normanby Star_ 30 (1912): 2.\n\n109. _Wairarapa Daily Times_ , 5 June 1913, 4.\n\n110. GA, Canadian Pacific Railway Land Sales Catalogue; http:\/\/ww2.glenbow.org\/search\/archivesCPRResults.aspx.\n\n111. _Edmonton Bulletin_ , 29 April 1911, 5.\n\n112. \"Lady Farmers,\" _Kaipara and Waitemata Echo_ , 4 March 1914, 4.\n\n113. \"An English Girl's Experience of a Winter in Alberta,\" _Canadian Gazette_ , 25 March 1912, 973.\n\n114. Sedgewick Historical Society, _Sedgewick Sentinel: A History of Sedgewick_ , 24.\n\n115. Edwin Snowsell and Frank Snowsell, \"Starting Over on a 'Ready-Made' Farm, 1911\u201316,\" _Western People_ , 4 March 1982, 14\u201315.\n\n116. Ibid.\n\n117. _Daily Colonist_ , 14 April 1912, 8.\n\n118. Rankin, \"The Woman Who Never Looks Back,\" _Canadian Courier_ 10, no. 9 (29 July 1911): 16.\n\n119. Love, \"Where Opportunity Knocks,\" 6\u201312.\n\n120. _Morning Leader_ , 1 Oct. 1912, 12.\n\n121. Love, \"Where Opportunity Knocks,\" 7.\n\n122. Ibid., 10.\n\n123. Love, \"Farmer-Boy 'Jack,'\" _The Lady's Realm_ , Nov. 1911, 101\u20133.\n\n124. \"World's Happiest Girl,\" _Chicago Daily Tribune_ , 1 Oct. 1912; \"Girl Wears Trousers and Works Big Farm,\" _Carroll Herald_ , 8 Jan. 1913; \"World's Happiest Girl,\" _Redcliff Review_ , 12 Dec. 1912.\n\n125. _Tensas Gazette_ , 13 Dec. 1912.\n\n126. _Carroll Herald_ , 8 Jan. 1913.\n\n127. Love, \"Haymaking with Jack May: A Woman's Life on a Canadian Farm,\" _Quiver_ 49, no. 11 (Sept. 1914): 1075\u20131078.\n\n128. _Sedgewick Sentinel_ , 12 Dec. 1912, 4.\n\n129. Ibid., 1 May 1913, 5.\n\n130. Sedgewick Historical Society, _Sedgewick Sentinel: A History of Sedgewick_ , 379.\n\n131. \"Society Lady Who Prefers the Plow to the Pink Tea,\" _Edmonton Bulletin_ , 21 June 1913, 14.\n\n132. \"Women and Land in Canada: Their Disabilities and the Reason,\" _Globe_ , 18 April 1913, 6.\n\n133. Kennedy, \"Lady Farmers,\" _Kaipara and Waitemata Echo_ , 4 March 1914, 4.\n\n134. \"Jills without Jacks: Bachelor Girls at Spirit River: Pioneer Women of the West,\" _Nottingham Evening Post_ , 24 Jan. 1924, 4.\n\n135. Walker, _Canadian Trails_ , 85.\n\n136. Ibid., 84.\n\n137. Sedgewick Historical Society, _Sedgewick Sentinel: A History of Sedgewick_ , 15.\n\n138. Ibid., 17.\n\n139. Ibid., 16.\n\n140. Ibid., 197\u201398.\n\n141. \"Another Woman Farmer,\" _Claresholm Review_ , 8 June 1911, 7.\n\n142. _Sedgewick Sentinel_ , 7 Nov. 1912, 4.\n\n143. Ibid., 12 Dec. 1912, 4.\n\n144. Kisby, \"Vera 'Jack' Holme.\"\n\n145. Ibid., 122.\n\n146. Boag, _Re-Dressing America's Frontier Past_ , 18.\n\n147. Ibid., 19.\n\n148. Ibid., 40.\n\n149. McClintock, _Imperial Leather_ , 67.\n\n150. Ibid., 174.\n\n151. Millarville, Kew, Priddis and Bragg Creek Historical Society, _Our Foothills_ , 286\u201387.\n\n152. \"She Writes and Ranches,\" _Oyen News_ , 6 May 1925, 5.\n\n153. Ibid.\n\n154. \"Woman Author as Rancher: Calgary Experiment,\" _Devon and Exeter Daily Gazette_ , 28 May 1925, 2.\n\n155. Ibid. See also \"A Woman Pioneer,\" _Imperial Colonist_ 23, no. 5 (May 1925): 86\u201387.\n\n156. \"She Writes and Ranches,\" _Oyen News_ , 6 May 1925, 5.\n\n157. Millarville, Kew, Priddis and Bragg Creek Historical Society, _Our Foothills_ , 287.\n\n158. M.H.A., \"How Four Plucky Women Won Out in the Canadian Northwest,\" _Minneapolis Journal_ , 29 July 1906.\n\n159. Delday, _Brooks: Beautiful-Bountiful_ , 197.\n\n160. Ibid., 199.\n\n161. Boag, _Re-Dressing America's Frontier Past_ , 196.\n\n162. _Saskatoon Star Phoenix_ , 8 August 1917, 4.\n\n163. Watanna, _Cattle_ , 33.\n\n164. Ibid., 34.\n\n165. Ibid., 144.\n\n166. Yarmie, \"'I Had Always Wanted to Farm,'\" 112.\n\n167. Saugeres, \"She's Not Really a Woman, She's Half a Man,\" 642.\n\n168. Ibid., 646.\n\n169. Ibid., 648.\n\n170. \"A Girl Farmer,\" _Queenslander_ (Brisbane) 19 Oct. 1907, 4.\n\n171. See, for example, \"Women as Farmers,\" taken from the _New York Tribune_ , in the _Herald and News_ , 19 July 1907; \"Women Farmers of the Great North-West,\" _Detroit Free Press_ , 4 August 1907; \"Women as Farmers,\" _Sun_ , 6 July 1907; \"Women Homesteading,\" _Edmonton Bulletin_ , 7 August 1907.\n\n172. M.H.A., \"How Four Plucky Women Won Out in the Canadian Northwest,\" _Minneapolis Journal_ , 29 July 1906.\n\n173. Alden, \"Prosperous Women Farmers,\" _Farmer's Review_ , 19 Nov. 1910, 4.\n\n174. \"Lady Settlers in Australia,\" _Chambers Edinburgh Journal_ , 24 Nov. 1849, 334.\n\n175. On this partnership, see also Brown and Martin, \"Drysdale, Anne (1792\u20131853)\" in _Australian Dictionary of Biography_ , National Centre of Biography, Australian National University (first published in hardcopy by Melbourne University Publishing, 1966); http:\/\/adb.anu.edu.au\/biography\/drysdale-anne-2000. See also Roberts, _Miss D and Miss N An Extraordinary Partnership._\n\n176. See, for example, Kingston, _Elizabeth Macarthur_ ; Wymark, \"Pioneer Women,\" _Country Woman_ (May 1969): 10\u201311.\n\n177. See \"Penfolds\" http:\/\/en.wikipedia.org\/wiki\/Penfolds.\n\n178. Alford, _Production or Reproduction_ , 193.\n\n179. \"Canadian Women's Press Club Tour: Girl Farmers and Ranchers,\" _Quebec Saturday Budget_ , 7 July 1906.\n\n180. I use this argument in the case of Calgary's Irish settler Caroline \"Mother\" Fulham, who kept pigs and collected garbage, in Carter, \"Britishness, 'Foreignness,' Women and Land,\" 57.\n\n181. \"To the Bachelor Girl,\" _Redcliff Review,_ 19 April 1912, 6.\n\nCHAPTER FIVE\n\n1. Binnie-Clark, _Wheat and Woman_ , 303. Unless otherwise specified, all citations to _Wheat and Woman_ are to the 2007 edition.\n\n2. _Victoria Daily Colonist_ , 22 Oct. 1909, 12.\n\n3. Verdon, \"Middle-Class Women's Work and the Professionalization of Farming,\" 396.\n\n4. Binnie-Clark, _Wheat and Woman_ (rpr. 1979), 7.\n\n5. Ibid., 60.\n\n6. Binnie-Clark, _A Summer on the Canadian Prairie_ , 27.\n\n7. Ibid., 230, and _Wheat and Woman_ , 60.\n\n8. Chilton, _Agents of Empire_ , 53.\n\n9. Ibid., 245.\n\n10. The Indigenous people of the reserves surrounding Binnie-Clark's farm had made concerted efforts to farm from the time of the 1874 Treaty Four, and their efforts were met with a measure of success by the early 1880s. Government policies intervened to atrophy this development, however. In particular, the \"peasant\" farming policy, introduced in the late 1880s, demanded that reserve farmers limit their acreage and grow root, and not grain crops. Indigenous people were prohibited from using labour-saving machinery. A concerted government and settler-supported effort to reduce the size of the reserves gained momentum after the turn of the twentieth century, just at the time of the establishment of Binnie-Clark's farm, and this severely limited the amount of arable land on most Treaty Four reserves. See Carter, _Lost Harvests._\n\n11. Ibid.\n\n12. Binnie-Clark, _Wheat and Woman_ , 58.\n\n13. Ibid., 56.\n\n14. Ibid.\n\n15. Ibid., 57.\n\n16. Ibid., 224\u201325.\n\n17. Binnie-Clark, _A Summer on the Canadian Prairie_ , 218.\n\n18. Thanks to Richard Jenks and Dennis Jenks for sharing \"The Family History of Clark.\" Georgina's father was sometimes listed in the census returns as \"Binnie-Clark\" and sometimes as plain \"Clark.\" For example, in the 1901 census he was listed as \"Arthur W.B. Clark.\" There were seven children born to Arthur and Maria: Maria Elizabeth (b. 1868), Walter Douglas (b. 1869), Georgina (b. 1872), Louis (b. 1873), Arthur Cameron (b. 1874), Mabel (b. 1874), and Ethel (b. 1880). Georgina's brother Louis signed his name Louis B. Clark. See SAB, homestead file 1328338: SW 6-26-14-W2.\n\n19. \"British Women on Canadian Homesteads,\" _Taber Free Press_ , 22 April 1909, 1.\n\n20. Binnie-Clark, _Wheat and Woman,_ 304.\n\n21. Binnie-Clark, \"Homesteads for Bachelor Women,\" the _Canadian Gazette_ , 4 Feb. 1909, 447\u201348.\n\n22. SAB, homestead file 1328338: SW 6-26-14-W2.\n\n23. Binnie-Clark, _A Summer on the Canadian Prairie_ , 297.\n\n24. Ibid., 299.\n\n25. Ibid., 305.\n\n26. Ibid.\n\n27. SAB, homestead file 1328338: SW 6-26-14-W2.\n\n28. _Progress_ , 20 July 1905.\n\n29. Binnie-Clark, _Wheat and Woman_ , 236.\n\n30. Carter, _Lost Harvests_ , 185\u201386.\n\n31. Ibid., 186.\n\n32. _Vidette_ , 13 Dec. 1905. For the history of the settlement of this district by British-Ontarians, see Dick, _Farmers \"Making Good_. _\"_\n\n33. _Vidette_ , 13 Dec. 1905.\n\n34. Ibid., 14 Feb. 1906.\n\n35. Farquharson, \"The Problem of Immigration,\" 38.\n\n36. Ibid., 43.\n\n37. Jean Blewett, \"The Doukhobor Woman,\" published in _Collier's Weekly_ (n.d., n.p.) and in Carrel, _Canada's West and Farther West_ , 227.\n\n38. Ibid.\n\n39. \"Women Harnessed to Plows in Manitoba,\" _Women's Journal_ , 9 Sept. 1899, 282.\n\n40. \"Woman Farmer Visiting the City,\" _Edmonton Bulletin_ , 1 Aug. 1912, 3.\n\n41. Arthur Cameron Binnie Clark (1875\u20131921) and Ethel Binnie Clark (1886\u20131955) are both buried in the Lakeview Cemetery, Fort Qu'Appelle.\n\n42. Susan Jackel, introduction, _Wheat and Woman_ (rpr. 1979), xiii. In an undated seven-page typed manuscript in the Jenks Papers, Binnie-Clark wrote that she was at her farm in 1926 and 1928, and at that time \"I was just pulling out from the embarrassment that awaited me on my return to Canada after my absence during the war and following years.\" She also noted that \"Binning House had been destroyed by fire during the war and never replaced\" (2).\n\n43. Binnie-Clark may have had two different homes on Cheyne Walk. On 6 Nov. 1932 she wrote to Dorothy Cooper-Abbs, \"Our old house in Cheyne Walk was demolished.\" She had been renting the flat out for 100 pounds a year and this was an important source of income for her (Derek Harrison Papers). By February 1936, she was living at 125 Cheyne Walk and she lived there until her death in 1947. _Times_ , 11 Feb. 1936, 10.\n\n44. Dennis Jenks, conversation, 5 Oct. 2005, London, England. Binnie-Clark was known to family and friends as \"Avril.\"\n\n45. Devas, _Two Flamboyant Fathers_ , 213; Holme, _Chelsea._\n\n46. Youmans, \"Walker, Ethel (1861\u20131951),\" _GLBTQ Encyclopedia_ ; http:\/\/eds.a.ebscohost.com\/eds\/detail\/detail?vid=4&sid=5ebbdf3c-7c04-458c-8081-bc12d52e96a7%40sessionmgr4002&hid=4103&bdata=JnNpdGU9ZWRzLWxpdmUmc2NvcGU9c2l0ZQ%3d%3d#AN=40920590&db=qth.\n\n47. Binnie-Clark, _Tippy: The Autobiography of a Pekingese Puppy._ This was a book for children that was \"for six pennies or one shilling to buy comfort for the wounded soldiers and horses fighting in the Great War for Liberty.\" Much of the action takes place on Cheyne Walk.\n\n48. Binnie-Clark, _Wheat and Woman_ , 190; Jenks Papers, typed untitled document by Georgina Binnie-Clark, n.d. (c. 1932), beginning on p. 2.\n\n49. Georgina Binnie-Clark to Dorothy Harrison, 21 Feb. 1936, Derek Harrison Papers.\n\n50. Binnie-Clark, _A Summer on the Canadian Prairie_ , 30.\n\n51. Ibid., 124.\n\n52. Ibid., 240.\n\n53. \"The Woman Problem\" (editorial), _Canadian Gazette_ , 20 Feb. 1908, 501.\n\n54. Ibid.\n\n55. Binnie-Clark, \"Women's Chances in the West,\" _Canadian Gazette_ , 3 Oct. 1908, 28.\n\n56. Binnie-Clark, \"A Woman, Two Boys and \u00a3140,\" _Canadian Gazette_ , 27 Feb., 28 Feb., and 12 March 1908, 42.\n\n57. Binnie-Clark, \"A Woman's Way on the Prairie,\" _Canadian Gazette_ , 7 May 1908, 8.\n\n58. Binnie-Clark, \"A Woman's Plea from the West,\" _Canadian Gazette_ , 19 Nov. 1908, 179.\n\n59. Ibid.\n\n60. Ibid.\n\n61. Editorial, _Canadian_ Gazette, 19 Nov. 1908, 177.\n\n62. G. Binnie-Clark to the Department of the Interior, 17 Nov. 1908, in LAC, RG 15, D-II-1, vol. 1039, file 1713679.\n\n63. W.D. Scott to Binnie-Clark, 12 Nov. 1908, in in LAC, RG 15, D-II-1, vol. 1039, file 1713679. (Not clear why the response seems to be dated before Binnie-Clark's letter of 17 Nov.)\n\n64. Binnie-Clark, _Wheat and Woman_ , 307.\n\n65. John Obed Smith (1864\u20131937), \"Memorable Manitobans,\" Manitoba Historical Society, http:\/\/www.mhs.mb.ca\/docs\/people\/smith_jo.shtml.\n\n66. Smith, \"Migration within the Empire,\" _English Review_ (Feb. 1925): 248.\n\n67. Ibid., 247\u201348.\n\n68. \"J. Obed Smith's Land Speculation,\" _Globe,_ 7 March 1907, 1.\n\n69. Binnie-Clark, \"Homesteads for Bachelor Women,\" _Canadian Gazette_ , 4 Feb. 1909, 447.\n\n70. Binnie-Clark, \"Women Farmers\" (from the _Daily Mail_ ), _Wainwright Star_ , 24 March 1910, 2.\n\n71. Binnie-Clark, \"How Canada Welcomes the Emigrant Girl,\" _Quiver_ 44, no. 4 (March 1909): 399\u2013403.\n\n72. Binnie-Clark, \"A Fight with Fire: A Settler's Experience on the Canadian Prairie,\" _Pall Mall Magazine_ 44, no. 198 (Oct. 1909): 620.\n\n73. _Minnedosa Tribune_ , 28 Oct. 1909, 2; _Crossfield Chronicle_ , 30 Oct., 1909, 5; _Taber Free Press_ , 22 April 1909, 1; _Advertiser and Central Alberta News_ , 4 Feb. 1909, 2; _Victoria Daily Colonist_ , 22 Oct. 1909, 12.\n\n74. _L'Abeille de la Nouvelle-Orl_ \u00e9 _ans_ , 14 Dec. 1909, 6.\n\n75. Binnie-Clark, \"Conditions of Life for Women in Canada,\" 110.\n\n76. Ibid., 119.\n\n77. Ibid., 118.\n\n78. Ibid., 120.\n\n79. Longhurst, \"How Can I Earn a Living: Canada for the Woman Worker,\" _Woman Worker_ , 23 March 1910, 822.\n\n80. Binnie-Clark, \"A Woman's Farm in Canada,\" _Daily Mail_ , 23 Jan. 1909, 4.\n\n81. Binnie-Clark, \"Women Farmers,\" _Daily Mail_ , 25 Feb. 1910.\n\n82. Editorial, _Canadian Gazette,_ 24 March 1910, 687.\n\n83. \"Three Women in Canada,\" _United Empire_ 1 (1910): 413\u201315.\n\n84. _Western Times_ , 11 Feb. 1910, 7.\n\n85. \"Girl Farmers,\" _Colonist_ 42, issue 12759 (4 April 1910): 4.\n\n86. \"Women Farmers in Canada,\" _Globe_ , 5 March 1910, 6.\n\n87. _Votes for Women_ , 18 March 1910, 9.\n\n88. _Canadian Gazette_ , 5 May 1910, 132\u201333.\n\n89. Binnie-Clark, \"Are Educated Women Wanted in Canada?,\" part 1, _Imperial Colonist_ 8, no. 98 (Feb. 1910): 22\u201324; part 2, vol. 8, no. 99 (March 1910): 39\u201342.\n\n90. _Imperial Colonist_ , 13 Jan. 1910, 397\u201399.\n\n91. \"Women Farmers in Canada,\" _Globe_ , 5 March 1910, 6.\n\n92. Binnie-Clark, \"Ready-Made Homes: Why the Settlers Are Content\" ( _Overseas Daily Mail_ ), _Strathmore Standard_ , 22 Oct. 1910, 5.\n\n93. See, for example, Binnie-Clark, \"Women Farmers: Experiments in Canada,\" in _Tamworth Daily Observer_ , 9 March 1912, 3; and in _West Gippsland Gazette_ , 7 May 1912, 6.\n\n94. \"Are Booming Canada\u2014Englishwomen Are Training Girls to Come out Here,\" _Gleichen Call_ , 9 June 1910, 7.\n\n95. Ibid.\n\n96. _Canadian Gazette_ , 3 March 1910, 598.\n\n97. \"Women Farmers in Canada,\" _Globe_ , 5 March 1910, 6.\n\n98. \"Making Girl Farmers,\" _Gleichen Call_ , 21 April 1910, 7.\n\n99. _Glasgow Herald_ , 4 March 1910, 5.\n\n100. \"Woman Farmers,\" _Gleichen Call_ , 21 March 1912, 6.\n\n101. Thanks to Derek Harrison, Fort Qu'Appelle, for this information about his mother, Kathleen Laughrin Harrison.\n\n102. Fort Qu'Appelle and District History Book Committee, _Fort Qu'Appelle and Area: A History_ , 367\u201368.\n\n103. Bertram, \"Wanderings of a Single Woman: Fort Qu'Appelle,\" 2nd letter, _Canadian Gazette,_ 5 March 1913, 795.\n\n104. _Globe_ , 14 May 1915, 2.\n\n105. _Gentlewoman and Modern Life_ , 19 July 1919, 125.\n\n106. Hawkes, \"The Imperial Emigrant,\" _United Empire_ 3 (1912): 207\u201321.\n\n107. Ibid., 220.\n\n108. \"Woman Farmer Visiting the City,\" _Edmonton Bulletin_ , 1 August 1912, 3.\n\n109. \"Canada's New Phase,\" _Canadian Gazette_ , 15 April 1913, 39.\n\n110. Binnie-Clark, \"Land and the Woman in Canada,\" 498.\n\n111. Ibid., 501.\n\n112. \"Women and Land in Canada: Their Disabilities and the Reason,\" _Globe_ , 18 April 1913, 6.\n\n113. The discussion that followed Binnie-Clark's presentation to the Royal Colonial Institute was published along with her paper \"Land and the Woman in Canada,\" 505\u20138.\n\n114. Binnie-Clark, \"Land and the Woman in Canada,\" 506.\n\n115. Ibid.\n\n116. Ibid., 507.\n\n117. Ibid., 506\u20137.\n\n118. _Canadian Gazette_ , 12 April 1913, 38.\n\n119. _Daily Colonist_ , 8 May 1913, 4.\n\n120. Shaw's letter is quoted in _Daily Colonist_ , 19 Oct. 1913, 8.\n\n121. Mrs. Donald Shaw was so \"traditional\" that I have been unable to find out what her own first name was. See McKay, \"Debating Sexuality in Halifax, 1920: Mrs. Donald Shaw and Others,\" 336. See also Mrs. Donald Shaw, \"Where Canada Fails Us,\" _Canadian Magazine of Politics, Science, Art and Literature_ 43 (191): 464\u201365.\n\n122. Quoted in _Daily Colonist,_ 19 Oct. 1913, 8.\n\n123. Ibid.\n\n124. Morris, _An Englishwoman in the Canadian West_ , 174.\n\n125. Evans, _The Bar U_ , 134\u201341.\n\n126. Binnie-Clark, _Wheat and Woman,_ 236.\n\n127. Ibid., 119.\n\n128. Ibid., 151.\n\n129. \"Wheat and Woman,\" _Times Literary Supplement_ , 30 April 1914, 207.\n\n130. \"Women and Economics,\" _Athenaeum_ , no. 4527 (August 1914): 148\u201349.\n\n131. \"A Woman Farmer,\" _Votes for Women_ , 14 Aug. 1914, 693.\n\n132. Moore, review of _Wheat and Woman_ , _Globe_ , 14 Aug. 1914, 3.\n\n133. \"No Dower Rights Law and No Free Land Grant for Women,\" _Edmonton Bulletin_ , 5 March 1914, 2.\n\n134. Munday, \"A Woman Wheat Grower,\" _Westminster Hall Magazine and Farthest West Review_ 7, no. 4 (May 1915): 15\u201317.\n\n135. Jenks Papers, handwritten document, \"The Union Jack Farm Settlement,\" p. 113.\n\n136. _Globe_ , 30 April 1915, 5; and 14 May 1915, 2.\n\n137. Dennis Jenks to Sarah Carter, email correspondence, 14 Dec. 2005.\n\n138. Last Will and Testament of Georgina Binnie-Clark of 123 Cheyne Walk, Chelsea, London 4 April, 1947, Jenks Papers.\n\n139. In an undated seven-page typed manuscript in the Jenks Papers, Binnie-Clark wrote that she was at her farm in 1926 and 1928, and at that time \"I was just pulling out from the embarrassment that awaited me on my return to Canada after my absence during the war and following years.\" She also noted that \"Binning House had been destroyed by fire during the war and never replaced.\"\n\n140. Binnie-Clark, _Tippy: The Autobiography of a Pekingese Puppy_ , dedication page.\n\nCHAPTER SIX\n\n1. Jackel, introduction to _Wheat and Woman_ by Georgina Binnie-Clark (rpr. 1979), xx\u2013xxxii.\n\n2. LAC, RG 15, D-II-1, vol. 1105, file 2876595, pt. 1.\n\n3. Scully, \"White Maternity and Black Infancy,\" 70. See also Mehta, \"Liberal Strategies of Exclusion.\"\n\n4. Quoted in Grimshaw, \"Suffragists Representing Race and Gender in the American West,\" 88.\n\n5. On American immigration to Western Canada, see Troper, _Only Farmers Need Apply._\n\n6. Cavanaugh, \"No Place for a Woman.\"\n\n7. Cavanaugh, \"The Limitations of the Pioneering Partnership\"; Hawkins, \"Lillian Beynon Thomas, Woman's Suffrage and the Return of Dower to Manitoba\"; McCallum, \"Prairie Women and the Struggle for a Dower Law.\"\n\n8. Carter, _The Importance of Being Monogamous._\n\n9. Ibid., 56\u201357.\n\n10. \"Canada's Greatest Need,\" _Brandon Daily Sun_ , 13 Sept. 1907. The column quotes a Moose Jaw correspondent to the _Farmer's Advocate._\n\n11. Binnie-Clark, _Wheat and Woman_ , 307.\n\n12. \"What Others Say: Why Not Women Homesteaders?,\" _Edmonton Capital_ , 25 Jan. 1910, 2. This article is reprinted from the _Toronto Telegram._\n\n13. _Grain Growers' Guide_ , 9 March 1910.\n\n14. Ibid., 16 March 1910.\n\n15. Ibid.\n\n16. \"Let Us Organize,\" _Grain Growers' Guide_ , 27 April 1910.\n\n17. Canada, _House of Commons Debates_ , 30 April 1910, 8488\u20138490.\n\n18. Laurie, \"No Homesteads for Women,\" _Manitoba Free Pres_ , 9 May, 1910, 9.\n\n19. _Edmonton Bulletin_ , 21 May 1910.\n\n20. _Manitoba Free Press,_ 24 May 1910.\n\n21. Ibid., 18 June 1910.\n\n22. Quoted in Hawkins, \"Lillian Beynon Thomas, Woman's Suffrage and the Return of Dower to Manitoba,\" 76.\n\n23. _Toronto Sunday World_ , 22 Feb. 1915, 4.\n\n24. LAC, 1901 Census, item no. 253324, Brandon district, subdistrict Arthur.\n\n25. See \"Grain Growers' Guide,\" _Canadian Encyclopedia_ , http:\/\/www.thecanadianencyclopedia.com\/en\/article\/grain-growers-guide\/.\n\n26. McClung, _The Stream Runs Fast_ , 119\u201321.\n\n27. Ibid.\n\n28. _Grain Growers' Guide_ , 23 Feb. 1910, 29.\n\n29. Laurie, \"About Women and Men, Especially Women,\" _Manitoba Free Press,_ 9 May 1910.\n\n30. \"What about the Future?,\" _Nor'West Farmer_ 29, no. 17 (5 Sept. 1910): 72.\n\n31. \"Wishes to Homestead,\" _Family Herald_ , 30 May 1913, 6.\n\n32. \"Homesteads for Women,\" _Family Herald_ , 1 Oct. 1913, 6.\n\n33. \"Girls Want Homesteads,\" _Family Herald_ , 3 Dec. 1913, 8.\n\n34. \"Homesteads,\" _Nor'West Farmer,_ 21 Aug. 1911, 1027.\n\n35. \"Speaks from Experience,\" _Grain Growers' Guide_ , 13 Dec. 1911, 9.\n\n36. _Grain Growers' Guide_ , 20 Dec. 1911, 24.\n\n37. Ibid., 25 Oct. 1911, 24.\n\n38. _Nor'West Farmer_ , 21 Feb. 1910, 230.\n\n39. Ibid.\n\n40. Will Channon to Minister of the Interior, 4 January 1910, in LAC, RG 15, D-II-1, vol. 1062, file 2029532.\n\n41. _Grain Growers' Guide_ , 5 July 1911, 17.\n\n42. Ibid., 27 March 1912, 24.\n\n43. \"The Homesteading Woman a Success,\" _Family Herald_ , 24 Sept. 1913, 6.\n\n44. McClung, \"Free Land for the Soldiers,\" _Edmonton Bulletin_ , 18 Sept. 1915, 3.\n\n45. \"The Wife's Share,\" _Family Herald_ , 22 May 1912, 9.\n\n46. \"Montana School Ma'Am,\" _Family Herald_ , 7 May 1913, 6.\n\n47. _Nor'West Farmer_ 29, no. 2 (20 Jan. 1910): 93.\n\n48. \"Women Prize Winners at Scottish Plowing Match,\" _Nor'West Farmer_ , 20 March 1912, 385.\n\n49. \"Boston Women Want Farm for Spinsters,\" _Brandon Daily Sun_ , 8 April 1909, 1; \"Women Organize Farm Settlement: Great Colony to be Established in West Australia Exclusively for Females,\" _Family Herald and Weekly Star_ , 19 Jan. 1912, 25.\n\n50. \"Five Girls Run a 200 Acre Farm,\" _Family Herald_ , 5 March 1913, 6.\n\n51. G. Abrook to Department of the Interior, 24 March 1913, in LAC, RG 15, D-II-1, vol. 1105, file 2876596 pt. 1.\n\n52. _Grain Growers' Guide_ , 27 August 1913, 9.\n\n53. \"A Daughter of the Plains,\" _Family Herald_ , 14 Feb. 1912, 11.\n\n54. SAB, Department of the Interior, Surveyors Notes, C.F. Aylesworth to C. Douville, 28 June 1899, R-183, no. 9.\n\n55. \"A Daughter of the Plains,\" _Family Herald_ , 14 Feb. 1912, 11.\n\n56. _Family Herald and Weekly Star_ , 13 Dec. 1911, 10.\n\n57. _Manitoba Free Press_ , 1 June 1910.\n\n58. Ibid., 9.\n\n59. _Grain Growers' Guide_ , 8 June 1910, 24.\n\n60. Patriarche, \"Husbandless Homesteads Are Wanted in the West,\" _Saskatoon Star Phoenix_ , 17 April 1913.\n\n61. Graham, \"Unearned Increments and Woman's Dower,\" _Grain Growers' Guide_ , 6 July 1910, 23.\n\n62. Mrs. Thomas McNeil to Dr. Roche, Minister of the Interior, 6 March 1913, in LAC, RG 15, D-II-1, vol. 1105, file 2876596.\n\n63. _Grain Growers' Guide_ , 13 Dec. 1911, 9.\n\n64. J. M. Perra to Hon. J.M. Crothers or Dr. Roche, Department of the Interior, 29 April 1913, in LAC, RG 15, D-II-1, vol. 1105, file 2876596.\n\n65. Mrs. J.R. Long, _Nor'West Farmer,_ 5 May 1910.\n\n66. Fanny Elizabeth Shepherd to the Department of the Interior, 27 Feb. 1913, in LAC, RG 15, D-II-1, vol. 1105, file 2876596, pt. 2.\n\n67. \"Homesteads for Women,\" _Grain Growers' Guide_ , 19 April 1911, 14.\n\n68. _Manitoba Free Press_ , 2 June 1910.\n\n69. _Voice_ , 15 Sept. 1911, 6.\n\n70. _Manitoba Free Press,_ 1 June 1910.\n\n71. \"Here Is Progress,\" _Grain Growers' Guide_ , 6 April 1910.\n\n72. \"A Plea for the Daughters,\" _Nor'West Farmer_ , 5 Sept. 1912, 1170.\n\n73. Frederiksen, _The Land Laws of Canada and the Land Experience of the United States_ , 11.\n\n74. \"About Women Homesteading,\" _Minnedosa Tribune_ , 2 April 1914, 4.\n\n75. \"Where the Door Stands Open,\" _Globe_ , 22 June 1904, 8.\n\n76. Frederiksen, _The Land Laws of Canada and the Land Experience of the United States_ , 6.\n\n77. Ibid., 10.\n\n78. _Bismarck Daily Tribune,_ 24 Dec. 1906, 2.\n\n79. _Glasgow Democrat_ , 11 Feb., 1916.\n\n80. _Enterprise_ , 10 Feb. 1916, 4.\n\n81. \"Still Unconvinced,\" _Family Herald,_ 1 June 1910, 11.\n\n82. _Family Herald_ , 20 July 1910, 11.\n\n83. _Calgary Daily Herald_ , 24 April 1915, 6.\n\n84. Ibid., 21 April 1915, 1.\n\n85. _Family Herald_ , 11 May 1910, 11.\n\n86. Ibid., 1 June, 1911, 11.\n\n87. Ibid., 15 Nov. 1911, 11.\n\n88. _Manitoba Free Press_ , 16 May 1910.\n\n89. Ibid., 1 Feb. 1912, 9.\n\n90. Pullen-Burry, _From Halifax to Vancouver_ , 231.\n\n91. Ibid., 218.\n\n92. Ibid., 219.\n\n93. Morris, _An Englishwoman in the Canadian West_ , 175.\n\n94. Ibid.\n\n95. _Manitoba Free Press_ , 27 May 1910.\n\n96. The article \"The Doukhobors: Queer Russian Sect Which Has Become Canadianized,\" appeared in July and August 1911 in many western newspapers including the _Reflector_ (8 August 1911, 2), _Crossfield Chronicle_ , _Didsbury Pioneer, Claresholm Review, Gleichen Call,_ and in November in the _Bow Island Review_ (11 Nov. 1911, 6).\n\n97. Quoted in Kulba and Lamont, \"The Periodical Press and Western Woman's Suffrage Movements,\" 274.\n\n98. Graham, \"Homesteads for Women: A Western Woman's View of Man's Duty,\" clipping in LAC, RG 15, D-II-1, vol. 1062, file 2029532, n.d., n.p.\n\n99. _Grain Growers' Guide_ , 6 July 1910, 23.\n\n100. Ibid., 15 May 1912, 13.\n\n101. Ibid., 20 Dec. 1911 , 24.\n\n102. Palmer, _Patterns of Prejudice._\n\n103. Hildebrandt, \"The Aspirations of a Western Enthusiast.\"\n\n104. _Vidette_ , 14 Feb. 1906.\n\n105. Ibid.\n\n106. Mead, _How the Vote Was Won,_ 7.\n\n107. Hall, \"Of Gender and Empire,\" 49.\n\n108. Carter, \"Britishness, 'Foreignness,\" Women and Land in Western Canada.\" See also Pickles, _Female Imperialism and National Identity._\n\n109. Shepard, _Deemed Unsuitable._\n\n110. _Grain Growers' Guide_ , 3 May 1911, 4.\n\n111. Patriarche, \"Husbandless Homesteads Are Wanted in the West,\" _Saskatoon Star Phoenix_ , 17 April 1913.\n\n112. _Grain Growers' Guide_ , 24 May 1911, 25.\n\n113. Ibid., 14 June, 1911, 21.\n\n114. Ibid.\n\n115. Ibid., 24 May 1911, 25.\n\n116. Ibid., 16 August 1911, 20.\n\n117. Letter, J.H. Perra to J.M. Crother, 29 April 1913, in LAC, RG 15, D-II-1, vol. 1105, file 287659, pt. 2.\n\n118. \"Right of Women to Homestead,\" _Voice_ , 4 Aug. 1911, 1.\n\n119. \"Woman's Labor League,\" _Voice_ , 8 Sept. 1911, 3.\n\n120. _Grain Growers' Guide_ , 11 Oct. 1911, 18.\n\n121. Ibid., 21 June 1911, 21.\n\n122. \"Homesteads for American Women,\" _Grain Growers' Guide_ , 19 July 1911, 18.\n\n123. _Grain Growers' Guide_ , 16 August 1911, 20.\n\n124. Ibid., 19 July 1911, 18.\n\n125. Ibid., 16 August 1911, 20.\n\n126. Ibid.\n\n127. \"Should Be Restrictions,\" _Grain Growers' Guide_ , 20 Sept. 1911, 23.\n\n128. _Family Herald and Weekly Star_ , 1 Oct. 1913, 6.\n\n129. Cook, \"Francis Marion Beynon and the Crisis of Christian Reformism.\"\n\n130. _Grain Growers' Guide_ , 26 July 1911, 17.\n\n131. Ibid., 6 July 1911.\n\n132. Letter, V.C. Bedier to the Department of the Interior, 25 March 1913, in LAC, RG 15, D-II-1, vol. 1105, file 2876596.\n\n133. \"Homestead Rights for Women,\" _Voice_ , 15 Sept. 1911, 6.\n\n134. _Voice_ , 20 Oct. 1911, 3.\n\n135. \"Roche Wants Free Land for Women,\" _Minnedosa Tribune_ , 5 May 1910, 2.\n\n136. \"Homesteads for Women\" _Grain Growers' Guide_ , 25 Oct. 1911, 18.\n\n137. \"Homesteads for Women,\" _Grain Growers' Guide_ , 8 Nov. 1911, 4.\n\n138. Ibid., 13 Dec. 1911, 9\u201311.\n\n139. Cook, \"Francis Marion Beynon and the Crisis of Christian Reformism.\"\n\n140. Fiamengo, \"Rediscovering Our Foremothers Again,\" 155.\n\n141. Ibid.\n\n142. Quoted in Bacchi, _Liberation Deferred_ , 53\u201354.\n\n143. _Nor'West Farmer_ , 5 Sept. 1912, 1142.\n\n144. Rennie, _The Rise of Agrarian Democracy_ , 59.\n\n145. Jackel, introduction to _Wheat and Woman_ by Georgina Binnie-Clark (rpt. 1979), xxviii.\n\n146. Ibid.\n\n147. Hawkins, \"Lillian Beynon Thomas, Woman's Suffrage and the Return of Dower to Manitoba,\" 97.\n\n148. \"Discrimination in Homestead Law,\" _Globe_ , 17 July 1915, 6.\n\n149. Ibid.\n\n150. Hunter, \"The Big Picture Problem,\" 60.\n\n151. Carter, _Lost Harvests._\n\n152. McClung, \"Speaking of Women,\" _Maclean's_ , 10 May 1916.\n\n153. \"Speaking of Nellie McClung,\" editorial clipping, scrapbook 1916\u201317, Nellie McClung fonds, British Columbia Archives. The clipping is not dated and the newspaper is not identified.\n\n154. The letter from Sir Wilfrid Laurier is quoted in the column \"Society in the Capital,\" by Gertrude Seton Thompson, _Edmonton Bulletin_ , 29 April 1910, 3.\n\n155. \"The Doukhobors: Queer Russian Sect Which Has Become Canadianized\" (see n. 97 above).\n\nCHAPTER SEVEN\n\n1. Grosvenor, \"Women Farmers in Canada,\" _Times_ , 27 Feb. 1913, 5.\n\n2. _Imperial Colonist_ 13, no. 167 (Dec. 1915): 198\u201389.\n\n3. \"Women on the Land,\" _Review of Reviews_ 52, no. 308 (Aug. 1915): 146.\n\n4. Martineau's article from _Englishwoman_ was summarized in \"Women on the Land,\" ibid.\n\n5. White, \"Remembrance, Retrospection, and the Women's Land Army in World War I Britain,\" 165.\n\n6. Twinch, _Women on the Land_ , 1\u201318.\n\n7. Ibid., 20.\n\n8. See King, _Women Rule the Plot_ , Chapter 4, \"Highly Trained Women of Good Birth.\"\n\n9. Verdon, \"'The work is grand and the life is just what I have always longed for': British Women's Experiences of Working on the Land in the Great War,\" paper presented at \"Women, Land and the Making of the British Landscape,\" University of Hull, 30 June 2015.\n\n10. Rowbotham, _A Century of Women_ , 74.\n\n11. Twinch, _Women on the Land_ , 8\u20139.\n\n12. White, \"Remembrance, Retrospection, and the Women's Land Army in World War I Britain,\" 166.\n\n13. King, _Women Rule the Plot_ , 85.\n\n14. White, \"Remembrance, Retrospection, and the Women's Land Army in World War I Britain,\" 165.\n\n15. Quoted in King, _Women Rule the Plot_ , 93.\n\n16. \"Women on the Land,\" _Times_ , 13 March 1916, 9.\n\n17. Twinch, _Women on the Land_ , 33.\n\n18. Riley, _Inventing the American Woman_ , 220\u201321.\n\n19. Gowdy-Wygant, _Cultivating Victory_ , 56.\n\n20. Ibid.\n\n21. _Women's Work on the Land: How You May Assist in Food Production This Summer_.\n\n22. \"Girls Work on Fruit Farms Last Season,\" _Globe_ , 31 Oct. 1917, 17.\n\n23. _Globe_ , 11 July 1918, 2, letter from \"M.Y.\"\n\n24. \"Farmerettes Taking Course,\" _Globe_ , 13 May 1918, 8.\n\n25. Ibid.\n\n26. \"Guelph Agricultural College to Open 20th,\" _Globe_ , 12 Sept. 1918, 14.\n\n27. \"Girls Receive BSA Degree,\" _Grain Growers' Guide_ , 5 June 1918, 1253.\n\n28. _Globe_ , 18 July 1918, 8\n\n29. \"Girls Start at Flax Pulling,\" _Globe,_ 30 July 1918, 8.\n\n30. _Globe_ , 18 July 1918, 8.\n\n31. _Globe_ , 25 April 1918, 7.\n\n32. \"Organize Ontario's Farm Labour,\" _Globe_ , 24 March 1916, 4.\n\n33. \"Farming and Farm Help,\" _Globe_ , 7 March 1917, 15.\n\n34. _Globe_ , 30 Nov. 1918, 16.\n\n35. Reyburn, \"Blurring the Boundaries,\" 132.\n\n36. Ibid., 133\u201334.\n\n37. Ibid., 34.\n\n38. Danysk, _Hired Hands_ , 101\u20133.\n\n39. \"Labor Shortage in West,\" _Claresholm Review_ , 13 April 1917, 2.\n\n40. Ibid., 106.\n\n41. \"Women Should Be Ready to Till the Soil,\" editorial, _Gleichen Call_ , 13 Jan. 1916, 4.\n\n42. Danysk, _Hired Hands_ , 108.\n\n43. \"Anti-Loafing Law,\" _Edmonton Bulletin_ , 14 Sept. 1918, 1.\n\n44. \"Sufficient Harvest Help in Alberta,\" _Edmonton Bulletin_ , 25 Aug. 1917, 3.\n\n45. \"Women in the Fields,\" _Minnedosa Tribune_ , 30 Aug. 1917, 2.\n\n46. \"Farm Women to Help with Threshing,\" _Brandon Daily Sun_ , 5 Sept. 1917, 7.\n\n47. \"Telephone Girls Will Go Stooking,\" _Brandon Daily Sun_ , 27 Aug. 1917, 2.\n\n48. \"General Exodus of Brandonites to Help Garner Grain,\" _Brandon Daily Sun_ , 29 Aug. 1917, 1.\n\n49. Lindsay, \"Calgary's Land Army: Which Helps Win the War by Raising Food Ammunition,\" _Grain Growers' Guide_ , 10 April 1918, 32.\n\n50. \"Winnipeg Women Still Recruiting Their 'Army,'\" _Brandon Daily Sun_ , 17 Sept. 1915, 2; \"Women Volunteers Are Inspected,\" _Edmonton Bulletin_ , 29 Sept. 1915, 6.\n\n51. \"Enlist B.C. Women as Prairie Harvesters,\" _Daily Colonist_ , 22 August 1917, 8.\n\n52. \"About Eight Thousand Ontario Harvesters Now on Way to West,\" _Brandon Daily Sun_ , 14 Aug. 1908, 1. It was reported that there were 300 women and children among the 8,000.\n\n53. \"Women Harvest Hands,\" _Brandon Daily Sun_ , 22 August 1916, 4.\n\n54. \"Women Coming West for Harvest,\" _Brandon Daily Sun_ , 16 April 1917, 8.\n\n55. \"Women and the Farm,\" _Empress Express_ , 28 Sept. 1916, 7.\n\n56. Ellis, \"Women Volunteers are Needed,\" _Edmonton Bulletin_ , 2 Feb. 1918, 5.\n\n57. \"Women Volunteers to Replace Men in Stores and Offices Who Can Help Harvest Work on Farms,\" _Edmonton Bulletin_ , 20 March 1918, 1.\n\n58. \"Women for the Farms,\" editorial, _Globe_ , 25 June 1918, 6. This editorial quotes from an editorial in the _Saskatoon Star Phoenix._\n\n59. \"Women G.G. Doing Their Bit,\" _Grain Growers' Guide_ , 9 Jan. 1918, 12.\n\n60. Menzies, _Canada and the War_ , 55.\n\n61. Ibid., 40\u201343.\n\n62. \"The Really New Woman,\" _Empress Express_ , 17 Oct. 1918, 7.\n\n63. \"Farmerettes Take Ag. Course at Olds,\" _Coleman Bulletin_ , 11 Oct. 1918, 4.\n\n64. Ibid.\n\n65. \"Women Learning to Run Tractors,\" _Empress Express_ , 21 March 1918, 3.\n\n66. \"College Graduate Farmerette,\" _Grain Growers' Guide_ , 28 Aug. 1918, 1857.\n\n67. \"Women for Farm Labor,\" _Grain Growers' Guide_ , 20 Feb. 1918, 386.\n\n68. Ibid.\n\n69. McCallum, \"Who Said Women Can't Farm,\" _Grain Growers' Guide_ , 27 March 1918, 618.\n\n70. Nixon, \"Feminizing the Farm: How Ontario is Promoting Agriculture among Women,\" _Grain Growers' Guide_ , 4 Sept. 1918, 1876.\n\n71. McCallum, \"Women and Their Gas Wagons: Some Experiences of Women Who Drive Their Own Cars,\" _Grain Growers' Guide_ , 25 Sept. 1918, 9.\n\n72. \"Woman Farmer, Husband in the Trenches...\" _Edmonton Bulletin_ , 2 May 1917, 5; \"Aid Being Sent by Patriotic Fund to Elk Pt. Woman,\" _Edmonton Bulletin_ , 9 May 1917, 5.\n\n73. \"War's Call to Farms: Men Must Fight and Women Must Reap,\" _Bow Island Review_ , 2 August 1918, 3.\n\n74. McClung, \"Free Land for the Soldiers,\" _Edmonton Bulletin_ , 18 Sept. 1915, 3.\n\n75. \"Discrimination in Homestead Law,\" _Globe_ , 17 July 1915, 6.\n\n76. \"The Homestead Law,\" _Grand Forks Sun_ , 29 Oct. 1915, 5.\n\n77. \"Homesteads for Women,\" _Voice_ , 10 Aug. 1917, 5.\n\n78. _Morning Leader_ , 14 Jan. 1918, 5.\n\n79. \"Many Farm Women of Alberta Are Already Engaged in Outside Work Testimony at Convention,\" _Edmonton Bulletin_ , 9 March 1918, 3.\n\n80. \"Homesteads for Women in Great Favor,\" _Edmonton Bulletin_ , 11 March 1918, 4.\n\n81. LAC, Record Group 76 (RG 76) Records of the Department of Immigration, vol. 198, file 90212, pt. 5, Estella B. Carter to Deputy Minister, Department of the Interior, 1 June 1918.\n\n82. Ibid., W.D. Scott to Estella B. Carter, 8 June 1918.\n\n83. Danysk, _Hired Hands_ , 103.\n\n84. Ibid., 102.\n\n85. LAC, RG 76, vol. 198, file 80212, pt. 5 \"Notice to Homesteaders,\" from J. Bruce Walker, Commissioner of Immigration, 13 March 1917, 5.\n\n86. Ibid., W.D. Scott to M.V. MacInnes, 21 March 1918.\n\n87. Carter, \"An Infamous Proposal.\"\n\n88. Quoted in Lambrecht, _The Administration of Dominion Lands_ , 29\u201330.\n\n89. Pickles, _Female Imperialism and National Identity,_ 56.\n\n90. Canada, _Debates of the House of Commons_ , Session 1919, vol. 4, 23 June, 3864.\n\n91. Ibid.\n\n92. Strong-Boag, \"Making a Difference,\" 244.\n\n93. Roche, \"World War One British Empire Discharged Soldier Settlement in Comparative Focus,\" 9.\n\n94. Ibid.\n\n95. LAC, RG 15, D-II-1, vol. 1105, file 2876596, pt. 2, Homesteads for Women resolution passed by the Annual Conventions United Farmers of Alberta and United Farm Women of Alberta 1919.\n\n96. Ibid., Memorandum C. Harris to ___ Hume, 25 March 1919.\n\n97. Ibid.\n\n98. An article by Elizabeth Banks is quoted from in _Daily Colonist_ , 7 April 1917, 8.\n\n99. Barnard, \"Women's Emigration after the War,\" _Quiver_ 51, no. 6 (April 1916): 565.\n\n100. Ibid.\n\n101. Ibid., 566.\n\n102. Ibid., 567.\n\n103. Dickens, \"Farmerettes Want Farms,\" _Globe_ , 29 May 1918, 15.\n\n104. Peele, \"War Nurses Back to Land: Demobilized Women Prefer Out-of-Doors to Former Profession,\" _Globe_ , 5 June 1920, 10.\n\n105. McCallum, \"Girls Receive BSA Degree,\" _Grain Growers' Guide_ , 5 June 1918, 1253.\n\n106. Knox, _The Girl of the New Day_ , 200.\n\n107. Ibid., 70.\n\n108. Ibid., 57.\n\n109. Ibid., 52.\n\n110. Ibid., 67.\n\n111. Ibid., 201.\n\n112. Ibid., 211.\n\n113. \"Must We Rely on Girl Labor?,\" _Globe_ , 14 May 1919, 13.\n\n114. Our Special Commissioner, \"Can an Educated Woman Make Good on the Land?,\" _Quiver_ , May 1919, 534.\n\n115. Ibid.\n\n116. Knox, _The Girl of the New Day_ , 66.\n\n117. \"Private and Confidential Memorandum on Emigration after the War,\" 1918, in LSE, Records of the CIL, box 38, minute book, 233.\n\n118. A.L. Vernon to Caroline Grosvenor, 12 Nov., 1918, in LSE, Records of the CIL, box 38.\n\n119. Our Special Commissioner, \"Empire Migration,\" _Quiver_ , June 1919, 609.\n\n120. Noakes, \"From War Service to Domestic Service,\" 11.\n\n121. Quoted in ibid., 8.\n\n122. \"Empire Migration,\" _Quiver_ , June 1919, 609.\n\n123. Quoted in Yarmie, \"I Had Always Wanted to Farm,\" 113.\n\n124. \"Empire Migration,\" _Quiver_ , June 1919, 609\u201310.\n\n125. Ibid., 611.\n\n126. Quoted in Noakes, \"From War Service to Domestic Service,\" 6.\n\n127. Ibid., 5.\n\n128. \"British Women for Dominion,\" _Globe_ , 30 June 1919, 5.\n\n129. Quoted in Noakes, \"From War Service to Domestic Service,\" 10.\n\n130. Ibid., 15.\n\n131. Ibid., 24.\n\n132. _Imperial Colonist_ 18, no. 217 (April 1920): 58.\n\n133. \"Canadian Openings for Women,\" _Times_ , 12 Nov. 1919, 13.\n\n134. _Gleichen Call_ , 27 Oct. 1920, 3.\n\n135. LAC, RG 17, vol. 1351, file 268636, J.H. Grisdale to provincial departments of agriculture, 17 July 1919.\n\n136. Ibid., T.M. Molloy to J.H. Grisdale, 13 Aug. 1919.\n\n137. Ibid., Deputy Minister of Agriculture Alberta to J.H. Grisdale, 2 July 1919.\n\n138. Ibid., J.H. Grisdale to F.C. Blair, 26 Sept. 1919.\n\n139. \"British Women Sail for Canada,\" _Globe_ , 17 Oct. 1919, 1.\n\n140. \"Is First Party of Women Settlers,\" _Globe,_ 20 Nov. 1919, 1.\n\n141. Knox, _The Girl of the New Day_ , 200.\n\n142. \"British Women for Dominion,\" _Globe_ , 30 June 1919, 5.\n\n143. \"What Will Canada Do with These Girls?,\" _Wainwright Star_ , 27 Aug. 1919, 3.\n\n144. \"Demobilized Women to Settle in Canada,\" _Monitor News_ , 16 April 1920, 6.\n\n145. \"Women Objectors Not Known Here,\" _Globe_ , 28 Oct. 1919, 10.\n\n146. Ibid.\n\n147. \"Farm Women Are Wanted,\" _Globe_ , 3 Nov. 1919, 6.\n\n148. Roberts, \"A Work of Empire,\" 198\u201399.\n\n149. Valverde, _The Age of Light, Soap and Water_ , 127.\n\n150. SAB, Saskatchewan Grain Growers Association Minutes, 31 Jan. 1920, 72. S-B2, F. III-1.\n\n151. _Western Times_ , 8 Feb. 1921, 6.\n\n152. Memorandum for Mr. Van Scoy, 15 Nov. 1926, Glenbow Archives, Canadian Pacific Railway Fonds, M 2269, file 732.\n\n153. _Globe_ , 10 May 1920, 2.\n\n154. Low, _Openings for British Women in Canada_ , 13.\n\n155. Ibid., 10.\n\n156. Ibid., 11.\n\n157. Ibid., 53.\n\n158. Ibid., 54.\n\n159. Ibid.\n\n160. Ibid., 60.\n\n161. Vanderbilt Jr., \"Women's Land Army to Invade Canada,\" _New York Times_ , 1 Aug. 1920.\n\n162. Ibid.\n\n163. Ibid.\n\n164. \"English Farm Girls for Canada,\" _Daily Colonist_ , 9 Oct. 1920, 1, 6.\n\n165. Kingsmill Commander, \"Opportunities for Educated Women in Canada Are Not Recognized,\" _Carbon News_ , 13 April 1921, 7.\n\n166. Bridgeman, _Breaking Prairie Sod_ , 244.\n\n167. Ibid., 246.\n\n168. \"The Lure of the Land,\" _Graphic_ , 21 Feb. 1920, 275.\n\n169. _Imperial Colonist_ 18, no. 227 (July 1921): 94.\n\n170. \"Handbook for Women Who Are Thinking of Settling Overseas\" (London: Oversea Settlement Department, 1923), 15\u201316 in LSE, Women's Library, Papers of the Society for the Oversea Settlement of Women, IS0S\/12, box FL021.\n\n171. Low, _Women Out West: Life and Work in Canada_ , 13.\n\n172. _Annual Reports of the Society for the Oversea Settlement of British Women_ , no. 6 (1925): 9.\n\n173. Ibid., no. 7 (1926): 15.\n\n174. Ibid., no. 9 (1928): 57.\n\n175. Ibid., no. 6 (1925): 7.\n\n176. \"Saving the Crop,\" _Daily Mail_ , 23 Aug. 1921,4; \"A Prairie 'Social,'\" 27 Aug. 1921, 4; \"The Medicine Man,\" 22 Feb. 1923, 6; \"Getting in the Wheat,\" 10 May 1923, 8.\n\n177. \"English Girls Investigate Canadian Farm Methods,\" _Blairmore Enterprise_ , 7 June 1923, 2.\n\n178. \"English Girls Like West,\" _Irma Times_ , 14 Sept. 1923, 2.\n\n179. \"British Women Farmers,\" _Claresholm Review_ , 3 July 1925, 3.\n\n180. \"Greater Britain: Training Girls for Work in Canada,\" _Aberdeen Press and Journal_ , 3 Nov. 1926, 9; \"Canada... Novel Scheme,\" _Devon and Exeter Daily Gazette_ , 1 Nov. 1926, 7.\n\n181. Harris, \"The Girl Emigrant: Her Chances in the Colonies,\" _Manchester Guardian_ , 28 Oct. 1926, 6.\n\n182. Durham, _Canada's Welcome to Women_ , 5.\n\n183. \"Denials Are Issued about Allegations from Saskatchewan,\" _Globe_ , 1 Nov. 1927, 2.\n\n184. Barber, \"The Gentlewomen of Queen Mary's Coronation Hostel,\" 151.\n\n185. Quoted in ibid., 155.\n\n186. Yarmie, \"I Had Always Wanted to Farm,\" 110.\n\n187. Ibid., 109\u201311.\n\n188. \"A Woman Homesteader,\" _Didsbury Pioneer_ , 31 August 1921, 7; \"On Easy Street: Women 'Farmerettes' Make Money in Western Canada,\" _New Oxford Item_ , 8 June 1922, 6.\n\n189. Library Archives Canada, Census 1901, Brandon, Manitoba; http:\/\/data2.collectionscanada.ca\/1901\/z\/z001\/jpg\/z000014608.jpg.\n\n190. Chicanot, \"Some Canadian Women Pioneers,\" _Imperial Colonist_ , Oct. 1925, 198.\n\n191. \"On Easy Street: Women 'Farmerettes' Make Money in Western Canada,\" _New Oxford Item_ , 8 June 1922, 6.\n\n192. \"Successful Women Farmers in Canada,\" _Globe_ , 26 March 1929, 11.\n\n193. \"Makes Success of Dairying,\" _Irma Times_ , 7 March 1924, 2; \"Woman Farmer Makes Success of What Is Now Reckoned Man Size Job,\" _Edmonton Bulletin_ , 23 June 1923, 14.\n\n194. Ibid., _Edmonton Bulletin_ , 14.\n\n195. \"Women Farmers Raise Wheat in Canada,\" _Queensland Times_ , 13 April 1925, 10.\n\n196. Ibid.\n\n197. Champ, \"Heavy Horses at Saskatchewan's Fairs during the 1920s,\" prepared for the Western Development Museum, Winning the Prairie Gamble, 2005 Exhibit, 10 January 2002, 9.\n\n198. _Imperial Colonist_ 23, no. 2 (Feb. 1925): 23.\n\n199. \"English Writer Has Yearning for Farm in Western Canada,\" _Edmonton Bulletin_ , 6 Oct. 1921, 7.\n\n200. \"Woman Farmer's Success,\" _Mirror Mail_ , 19 Aug. 1926, 3.\n\n201. See PAA, oral interview with Hon. Diana Rodnay, 71.248, 11 July 1971; \"Titled Famers Till Canadian Prairies,\" _Wetaskiwin Times_ , 13 Oct. 1927, 2; Lady Rodney, \"Where Women Must Be Capable,\" _Wetaskiwin Times_ , 8 March 1928, 3.\n\n202. Chicanot, \"Canadian Women's New World,\" _Woman's Journal,_ 18 Oct. 1924, 12.\n\n203. Cavanaugh, \"Irene Marryat Parlby,\" 105.\n\n204. _Evergreen and Gold: The Annual Publication of the Students of the University of Alberta_ (1923), 75.\n\n205. \"Production of Honey in the Three Prairie Provinces Assuming Large Proportions,\" _Irma Times_ , 2 Feb. 1923.\n\n206. \"Canadian Farmers' Tour,\" _Times_ , 9 Jan. 1928, 13.\n\n207. \"Jills for Jacks: Training Girls as Wives for Settlers,\" _Aberdeen Press and Journal_ , 12 Nov. 1928, 7.\n\n208. Chicanot, \"Canadian Women's New World,\" _Woman's Journal_ , 18 Oct. 1924, 12.\n\n209. \"Fair Sex as Farmers,\" _Carbon News_ , 14 July 1921, 6; \"Full Discussion of Women's Right to File on Land,\" _Edmonton Bulletin_ , 23 June 1921, 2.\n\n210. \"Want Homesteads for Women,\" _Gleichen Call_ , 15 March 1922, 2.\n\n211. \"Women Want Homesteads,\" _Didsbury Pioneer_ , 10 Sept. 1925, 7.\n\n212. LAC, RG 15, Dominion Lands Rulings, 6602-6800, vol. 1984, p. 6750, Memorandum, 7 Feb. 1928.\n\n213. Ibid., vol. 1980, p. 5866, Deputy Minister to J. Pope, Under-Secretary of State for External Affairs, 5 Feb. 1925.\n\n214. LAC, RG 76, file 80212 pt. 6, vol. 198, B. Browne to Commissioner of Immigration, 22 March 1924.\n\n215. LAC, RG15, Dominion Lands Rulings, 6602-6800, vol. 1984, p. 6730, Memorandum, 7 Feb., 1928\n\n216. Ibid.\n\n217. LAC, RG 15, Dominion Lands Rulings, 7201-7400, vol. 1987, p. 7261, Memorandum, to Mr. Perrin, 17 April, 1929.\n\n218. _Western Producer_ , 14 Feb. 1929, 10.\n\n219. Kingsmill Commander, \"Opportunities for Educated Englishwomen in Canada Are Not Recognized,\" _Carbon News_ , 13 April 1921, 7.\n\n220. Quoted in Harrison, _Go West\u2014Go Wise!_ , 72.\n\n221. Ibid., 72\u201373.\n\n222. Chicanot, \"Some Canadian Women Pioneers,\" _Imperial Colonist_ 23, no. 9 (Sept. 1925): 177.\n\n223. Low, \"The Empire's Call to Women,\" _Britannia and Eve_ 1, no. 2 (5 Oct. 1928): 156.\n\n224. Pickles, _Female Imperialism and National Identity_ , 78.\n\n225. Ibid., 88.\n\nCONCLUSION\n\n1. Canadian Pacific Railway, _Household Work in Canada for Girls_ , 1.\n\n2. Ibid., 10.\n\n3. Oxendale, \"'What Should They Know of England Who Only England Know?,'\" 109. Oxendale created the term \"gendered ruralism.\" While she does not provide a concise definition she develops the concept as emerging from the recognition that the time of \"muscular\" imperialism was over, and there was new concern for racial purity, health and hygiene, and to nurturing these in the colonies. Oxendale writes that \"'Ruralism,' with its emphasis on traditional values, allowed for a robustness of character, indeed certain independence in a woman. In all, it provided a metaphor and a reality that allowed an active female role in shaping the meaning and the future of the empire\" (109).\n\n4. This is the topic of a forthcoming study by Sarah Carter, with Winona Wheeler, E. Leigh Syms, Robert Coutts, and Bret Nickels, \"Growing Pains: The Dynamics of Aboriginal Agriculture in Manitoba.\"\n\n5. Magee, \"'For Home and Country.'\"\n\n6. Binnie-Clark, foreword to _A Birthday Book for the Farm Settlement on the Canadian Prairie_ , 5. This \"birthday book\" was compiled by Binnie-Clark as a means of raising funds for the Union Jack Farm Settlement at Fort Qu'Appelle, Saskatchewan. She chose 365 messages from the Bible for each day of the year. Beside each day was a space for the book owner to pledge an amount to the Union Jack Farm Settlement.\n\n7. Schultz, \"Leaven for the Lump.\"\n\n8. Jenks Papers, John Barnett to G. Binnie-Clark, 8 Jan. 1931.\n\n9. Ibid., hand-written document, \"The Home Farm Settlement,\" 1933.\n\n10. Binnie-Clark, _A Birthday Book_.\n\n11. Fort Qu'Appelle and District History Book Committee, _Fort Qu'Appelle and Area: A History_ , 18.\n\n12. \"Alberta Homestead Regulations Contained in Act,\" _Wetaskiwin Times_ , 2 April 1931, 8.\n\n13. \"Alberta Homestead Entries in August,\" _Wetaskiwin Times_ , 17 Sept. 1931, 7.\n\n14. \"Women Homesteaders,\" _New York Times_ , 29 Jan. 1933.\n\n15. Ibid.\n\n16. Tait, \"Farming: All in the Family,\" _Globe and Mail_ , 4 July, 2015, Section F, 1.\n\n17. Stamm, \"I Am... a Farmer,\" 173.\n\n18. Ibid., 183.\n\n19. Leckie, \"Female Farmers in Canada and the Gender Relations of a Restructuring Agricultural System,\" 227.\n\n20. Watkins and Jacoby, \"Is the Rural Idyll Bad for Your Health?\"\n\n21. Ibid., 861.\n\n22. Ibid., 853.\n\n23. \"Bah! Indeed. Mrs. Elsie Hart in U.F.C. Information, August,\" _People's Weekly_ , 27 Aug., 1949, 4.\n\n24. Wilson, _Agriculture of the Hidatsa Indians_ , 115.\n\n25. See Kub, \"Buffalo Bird Woman's Farming Methods Still in Evidence Today,\" _Agfax_ 7 August, 2013, available at http:\/\/www.epa.gov\/agriculture\/ag101\/cropmajor.html.\nBIBLIOGRAPHY\n\nARCHIVAL SOURCES\n\nAnnual Reports of the Society for the Overseas Settlement of British Women\n\nBritish Columbia Archives\n\nNellie McClung Fonds\n\nGlenbow Archives (GA), Calgary, Alberta\n\nCanadian Pacific Railway Database\n\nCanadian Pacific Railway Fonds\n\nHarrison, Derek Papers, private collection, Fort Qu'Appelle, Saskatchewan\n\nHove Central Library, Hove, United Kingdom\n\nPapers of Viscountess Frances Wolseley\n\nJenks Family Papers, private collection.\n\nLibrary and Archives Canada (LAC)\n\nAlexander Mackenzie Papers\n\nCensus Records\n\nRecord Group 2 (RG 2), Privy Council\n\nOffice Orders-in-Council\n\nRecord Group 10 (RG 10), Records of\n\nthe Department of Indian Affairs\n\nRecord Group 13 (RG 13) Records of\n\nthe Department of Justice\n\nRecord Group 15 (RG 15), Records of\n\nthe Department of the Interior\n\nDominion Lands Rulings\n\nHomestead Land Registers\n\nWestern Land Grants\n\nRecord Group 17 (RG 17), Records of\n\nthe Department of Agriculture\n\nRecord Group 18 (RG 18), Records of\n\nthe NWMP\/RCMP\n\nRecord Group 76 (RG 76), Records\n\nof the Department\n\nof Immigration\n\nLondon School of Economics (LSE), The Women's Library\n\nRecords of the Colonial Intelligence League (CIL)\n\nMontana Historical Society Research Center,\n\nHelena, Montana\n\nEtta Smalley Bangs, Reminiscence\n\nProvincial Archives of Alberta (PAA),\n\nEdmonton, Alberta\n\nHomestead files\n\nProvincial Archives of Manitoba (PAM),\n\nWinnipeg, Manitoba\n\nHomestead files\n\nSaskatchewan Archives Board (SAB),\n\nSaskatoon, Saskatchewan\n\nHomestead files\n\nMrs. Ed Watson, \"Pioneering in Saskatchewan\n\nLena Kernen Bacon, \"Four Years in Saskatchewan from June 1904 to July 1908\"\n\nSaskatchewan Grain Growers Association Minutes\n\nNEWSPAPERS AND PERIODICALS\n\n_Aberdeen Press and Journal_ (Aberdeen, Scotland)\n\n_Advertiser_ (South Australia)\n\n_Advertiser and Central Alberta News_ (Lacombe, Alberta)\n\n_African Standard_ (Nairobi, Kenya)\n\n_Age_ (Melbourne, Australia)\n\n_Ashburton Guardian_ (Ashburton, New Zealand)\n\n_Athenaeum_ (London, United Kingdom)\n\n_Bay of Plenty Times_ (New Zealand)\n\n_Better Farming_ (Chicago, Illinois)\n\n_Bismarck Daily Tribune_ (Bismarck, North Dakota)\n\n_Blairmore Enterprise_ (Blairmore, Alberta)\n\n_Border Watch_ (Mount Gambier, South Australia)\n\n_Bow Island Review_ (Bow Island, Alberta)\n\n_Brandon Daily Sun_ (Brandon, Manitoba)\n\n_Brantford Opinion_ (Brantford, Ontario)\n\n_Brisbane Courier_ (Brisbane, Australia)\n\n_Britannia and Eve_ (London, United Kingdom)\n\n_Calgary Daily Herald_ (Calgary, Alberta)\n\n_Calgary Herald_ (Calgary, Alberta)\n\n_Canadian Courier_ (Toronto, Ontario)\n\n_Canadian Gazette_ (London, United Kingdom)\n\n_Canadian Home Journal_ (Toronto, Ontario)\n\n_Canadian Magazine_ (Toronto, Ontario)\n\n_Canadian Magazine of Politics, Science, Art and Literature_ (Toronto, Ontario)\n\n_Carbon News_ (Edmonton, Alberta)\n\n_Carroll Herald_ (Carroll City, Iowa)\n\n_Chambers Edinburgh Journal_ (Edinburgh, Scotland)\n\n_Chambers Journal of Popular Literature, Science and Art_ (Edinburgh, Scotland)\n\n_Chicago Daily Tribune_ (Chicago, Illinois)\n\n_Clarence and Richmond Examiner_ (Grafton, New South Wales)\n\n_Claresholm Adverstiser_ (1914\u201316) (Claresholm, Alberta)\n\n_Claresholm Review_ (1904\u201316)\n\n_Claresholm Review-Advertiser_ (1916\u201328)\n\n_Coleman Bulletin_ (Coleman, Alberta)\n\n_Collier's Weekly_ (New York, New York)\n\n_Colonist_ (Nelson, New Zealand)\n\n_Country Woman_ (Sidney, Australia)\n\n_Crossfield Chronicle_ (Crossfield, Alberta)\n\n_Daily Colonist_ (Victoria, British Columbia)\n\n_Daily Mail_ (London, United Kingdom)\n\n_Daily Mail and Empire_ (Toronto, Ontario)\n\n_Daily News_ (Perth, Australia)\n\n_Daily Phoenix_ (Saskatoon, Saskatchewan)\n\n_Daily Star_ (Fredericksburg, Virginia)\n\n_Daily Telegraph_ (Tasmania)\n\n_Detroit Free Press_ (Detroit, Michigan)\n\n_Devon and Exeter Daily Gazette_ (Exeter, United Kingdom)\n\n_Didsbury Pioneer_ (Didsbury, Alberta)\n\n_Eastern Daily Mail and Straits Morning Advertiser_ (Singapore)\n\n_Edmonton Bulletin_ (Edmonton, Alberta)\n\n_Edmonton Capital_ (Edmonton, Alberta)\n\n_Empire Review_ (London, United Kingdom)\n\n_Empress Express_ (Empress, Alberta)\n\n_English Review_ (London, United Kingdom)\n\n_Enterprise_ (Harlem, Montana)\n\n_Essex County Chronicle_ (Essex, United Kingdom)\n\n_Examiner_ (London, United Kingdom)\n\n_Family Herald_ (Montreal, Quebec)\n\n_Family Herald and Weekly Star_ (Montreal, Quebec)\n\n_Farmer's Review_ (Chicago, Illinois)\n\n_Fortnightly Review_ (London, United Kingdom)\n\n_Gazette Times_ (Pittsburgh, Pennsylvania)\n\n_Gentleman's Magazine and Historical Review_ (London, United Kingdom)\n\n_Gentlewoman and Modern Life_ (London, United Kingdom)\n\n_Glasgow Democrat_ (Glasgow, Montana)\n\n_Gleichen Call_ (Gleichen, Alberta)\n\n_Globe_ (Toronto, Ontario)\n\n_Globe and Mail_ (Toronto, Ontario)\n\n_Grain Growers' Guide_ (Winnipeg, Manitoba)\n\n_Grand Forks Sun_ (Grand Forks, North Dakota)\n\n_Graphic_ (London, United Kingdom)\n\n_Harmsworth Magazine_ (London, United Kingdom)\n\n_Hawera and Normanby Star_ (Hawera, New Zealand)\n\n_Herald_ (Glasgow, Scotland)\n\n_Herald and News_ (Newberry, South Carolina)\n\n_Hinsdale Tribune_ (Hinsdale, Illinois)\n\n_Imperial Colonist_ (London, United Kingdom)\n\n_Irma Times_ (Irma, Alberta)\n\n_Jackson's Oxford Journal_ (Oxford, United Kingdom)\n\n_Kaipara and Waitemata Echo_ (Helensville, New Zealand)\n\n_Kindersley Clarion_ (Kindersley, Saskatchewan)\n\n_L'Abeille de la Nouvelle-Orl_ \u00e9 _ans_ (New Orleans, Louisiana)\n\n_La Survivance_ (Edmonton, Alberta)\n\n_Lady's Realm_ (London, United Kingdom))\n\n_Leader_ (Regina, Saskatchewan)\n\n_Leader-Post_ (Regina, Saskatchewan)\n\n_Leeds Mercury_ (Leeds, United Kingdom)\n\n_Leicester Chronicle and the Leicestershire Mercury_ (Leicester, United Kingdom)\n\n_London Society_ (London, United Kingdom)\n\n_Maclean's_ (Toronto, Ontario)\n\n_Macmillan's Magazine_ (London, United Kingdom)\n\n_Maitland Weekly Mercury_ (Maitland, Australia)\n\n_Manchester Guardian_ (Manchester, United Kingdom)\n\n_Manitoba Daily Free Press_ (Winnipeg, Manitoba)\n\n_Manitoba Free Press_ (Winnipeg, Manitoba)\n\n_Medicine Hat Times_ (Medicine Hat, Alberta)\n\n_Minneapolis Journal_ (Minneapolis, Minnesota)\n\n_Minnedosa Tribune_ (Minnedosa, Manitoba)\n\n_Mirror_ (London, United Kingdom)\n\n_Mirror Mail_ (Mirror, Alberta)\n\n_Missoulian_ (Missoula, Montana)\n\n_Monitor News_ (Monitor, Alberta)\n\n_Monthly Review_ (London, United Kingdom)\n\n_Montreal Gazette_ (Montreal, Quebec)\n\n_Moose Jaw Herald_ (Moose Jaw, Saskatchewan)\n\n_Morning Leader_ (Regina, Saskatchewan)\n\n_Morning Post_ (London, United Kingdom)\n\n_National Review_ (London, United Kingdom)\n\n_New Oxford Item_ (New Oxford, Pennsylvania)\n\n_New York Times_ (New York, New York)\n\n_New Zealand Herald_ (Auckland, New Zealand)\n\n_Newcastle Courant_ (Newcastle-upon-Tyne, United Kingdom)\n\n_Nineteenth Century_ (London, United Kingdom)\n\n_Nineteenth Century and After: A Monthly Review_ (London, United Kingdom)\n\n_Nor'West Farmer_ (Winnipeg, Manitoba)\n\n_Nottingham Evening Post_ (Nottingham, United Kingdom)\n\n_Omaha Daily Bee_ (Omaha, Nebraska)\n\n_Once a Week_ (London, United Kingdom)\n\n_Otago Witness_ (Dunedin, New Zealand)\n\n_Overseas Daily Mail_ (London, United Kingdom)\n\n_Oyen News_ (Oyen, Alberta)\n\n_Pall Mall Gazette_ (London, United Kingdom)\n\n_Pall Mall Magazine_ (London, United Kingdom)\n\n_Penny Magazine_ (Gloucestershire, United Kingdom)\n\n_People's Weekly_ (Edmonton, Alberta)\n\n_Prairie Illustrated_ (Calgary, Alberta)\n\n_Qu'Appelle Progress_ (Qu'Appelle, Saskatchewan)\n\n_Quebec Saturday Budget_ (Quebec City, Quebec)\n\n_Queensland Times_ (Ipswich, Australia)\n\n_Queenslander_ (Brisbane, Australia)\n\n_Quiver_ (London, United Kingdom)\n\n_Raymond Rustler_ (Raymond, Alberta)\n\n_Red Deer News_ (Red Deer, Alberta)\n\n_Redcliff Review_ (Redcliff, Alberta)\n\n_Reflector_ (London, United Kingdom)\n\n_Reflector_ (Mirror, Alberta)\n\n_Review of Reviews_ (London, United Kingdom)\n\n_St. Cloud Democrat_ (Saint Cloud, Minnesota)\n\n_St. John Sun_ (Saint John, New Brunswick)\n\n_Saskatoon Star Phoenix_ (Saskatoon, Saskatchewan)\n\n_Saturday News_ (Edmonton, Alberta)\n\n_Saturday Review of Politics, Literature, Science and Art_ (London, United Kingdom)\n\n_Scottish Review_ (Paisley, Scotland, and London, United Kingdom)\n\n_Secret Service_ (New York, New York)\n\n_Sedgewick Sentinel_ (Sedgewick, Alberta)\n\n_Spokane Daily Chronicle_ (Spokane, Washington)\n\n_Spokesman-Review_ (Spokane, Washington)\n\n_Star_ (Christchurch, New Zealand)\n\n_Strathmore Standard_ (Strathmore, Alberta)\n\n_Suffragette_ (London, United Kingdom)\n\n_Sun_ (New York, New York)\n\n_Sunday Times_ (Sydney, Australia)\n\n_Sydney Mail_ (Sydney, Australia)\n\n_Taber Free Press_ (Taber, Alberta)\n\n_Tamworth Daily Observer_ (Tamworth, Australia)\n\n_Tamworth Herald_ (Tamworth, Australia)\n\n_Tensas Gazette_ (St. Joseph, Louisiana)\n\n_Three Hills Capital_ (Three Hills, Alberta)\n\n_Times_ (London, United Kingdom)\n\n_Times Literary Supplement_ (London, United Kingdom)\n\n_Toledo Blade_ (Toledo, Ohio)\n\n_Toronto Sunday World_ (Toronto, Ontario)\n\n_United Empire_ (London, United Kingdom)\n\n_United Service Magazine_ (London, United Kingdom)\n\n_Victoria Daily Colonist_ (Victoria, British Columbia)\n\n_Vidette_ (Indian Head, Saskatchewan)\n\n_Voice_ (Winnipeg, Manitoba)\n\n_Vote_ (London, United Kingdom)\n\n_Votes for Women_ (London, United Kingdom)\n\n_Wainwright Star_ (Wainwright, Alberta)\n\n_Wairarapa Daily Times_ (Greytown, New Zealand)\n\n_Warwick Examiner and Times_ (Warwick, Australia)\n\n_Washington Times_ (Washington, DC)\n\n_Weekend Herald_ (Calgary, Alberta)\n\n_West Gippsland Gazette_ (Warragul, Australia)\n\n_Western Gazette_ (Yeovil, United Kingdom)\n\n_Western Globe_ (Lacombe, Alberta)\n\n_Western People_ (Ballina, United Kingdom)\n\n_Western Producer_ (Camrose, Alberta)\n\n_Western Times_ (Devon, United Kingdom)\n\n_Westminster Hall Magazine and Farthest West Review_ (Vancouver, British Columbia)\n\n_Wetaskiwin Times_ (Wetaskiwin, Alberta)\n\n_Winnipeg Daily Times_ (Winnipeg, Manitoba)\n\n_Winnipeg Evening Tribune_ (Winnipeg, Manitoba)\n\n_Winnipeg Free Press_ (Winnipeg, Manitoba)\n\n_Women's Leader and the Common Cause_ (London, United Kingdom)\n\n_Women's Suffrage Journal_ (Manchester, United Kingdom)\n\nPUBLISHED PRIMARY SOURCES\n\nAnonymous. _Montana 1909_. Helena, MT: Independent Publishing, 1909.\n\n\u2014. _The New West: Extending from the Great Lakes across Plain and Mountain to the Golden Shores of the Pacific_. Winnipeg: Canadian Historical Publishing, 1888.\n\n\u2014. _Our Western Lands: Some Transactions of the Laurier Administration Exposed in the Sessions of 1906 and 1907_. Ottawa, c. 1908.\n\nAustin, Rev. Principal, ed. _Woman: Her Character, Culture and Calling_. Brantford, ON: The Book and Bible House, 1890.\n\nBernard, Lally [Mary Agnes Fitzgibbon]. _The Doukhobor Settlements: A Series of Letters._ Toronto: William Briggs, 1899.\n\nBetham-Edwards, Matilda. _Reminiscences_. London: G. Redway, 1898.\n\nBinnie-Clark, Georgina. _A Birthday Book for the Farm Settlement on the Canadian Prairie_. London: The Fashion Journals Guild, c. 1935.\n\n\u2014. \"Conditions of Life for Women in Canada.\" _Women Workers: The Papers Read at the Conference Held in Portsmouth, 1909_ , 110\u2013120 _._ London: The Office of the Union, 1909.\n\n\u2014. \"Land and the Woman in Canada.\" Paper read at a meeting of the Royal Colonial Institute on Tuesday, April 8, 1913. _United Empire_ 4 (New Series, 1913). London: Sir Isaac Pitman and Sons, 1914, 497\u2013508.\n\n\u2014. _A Summer on the Canadian Prairie_. London: Edward Arnold, 1910.\n\n\u2014. _Tippy: The Autobiography of a Pekingese Puppy._ London: The Fashion Journals Guild, n.d. (ca. 1916).\n\n\u2014. _Wheat and Woman_. Toronto: Bell and Cockburn, 1914. Reprinted with an introduction by Susan Jackel. Toronto: University of Toronto Press, 1979.\n\n\u2014. _Wheat and Woman._ Toronto: Bell and Cockburn, 1914. Reprinted with a new introduction by Sarah Carter. Toronto: University of Toronto Press, 2007.\n\nBoucherett, Jessie. _Hints on Self-Help: A Book for Young Women_. London: S.W. Partridge, 1863.\n\n\u2014. \"How to Provide for Superfluous Women.\" In _Woman's Work and Woman's Culture: A Series of Essays_ , ed. Josephine E. Butler, 27\u201348. London: Macmillan, 1869.\n\nBradbury, John. _Travels in the Interior of America in the Years 1809, 1810, and 1811_. 1819. Reprint. Lincoln: University of Nebraska Press, 1986.\n\nBradley, Edith, and Bertha La Mothe. _The Lighter Branches of Agriculture_. Vol. 6, The Woman's Library. London: Chapman and Hall, 1903.\n\nBridgeman, Rev. (Captain) Wellington. _Breaking Prairie Sod._ Toronto: The Musson Book Co., 1920.\n\nBurton, Mrs. J.H. [Katherine]. _My Home Farm_. London: Longmans, Green and Co., 1883.\n\nCanada. _Prosperity Follows Settlement: Settlers' Experience in Western Canada._ Ottawa: Department of the Interior, 1900.\n\nCanadian Pacific Railway. _Home Life of Women in Western Canada_. Montreal: Canadian Pacific Railway, 1907.\n\n\u2014. _Household Work in Canada for Girls_. London: Canadian Pacific Railway Department of Colonization, Women's Branch, 1930.\n\n\u2014. _What Women Say of the Canadian North-West_. Montreal: Canadian Pacific Railway, 1886.\n\n\u2014. _Women's Work in Western Canada: A Sequel to \"Words from the Women of Western Canada_. _\"_ Montreal: Canadian Pacific Railway, 1906.\n\n\u2014. _Words from the Women of Western Canada._ Montreal: Canadian Pacific Railway, 1903.\n\nCarrel, Frank. _Canada's West and Farther West: Latest Book on the Land of Golden Opportunities._ Toronto: Musson Book Co., 1911.\n\nCatlin, George. _Letters and Notes on the Manners, Customs and Condition of the North American Indians_. New York: Wiley and Putnam, 1844.\n\nCoulton, Sophia. _Our Farm of Four Acres and the Money We Made by It._ With an introduction by Peter B. Mead. 12th London ed. New York: C.M. Saxton, Barker & Co., 1860.\n\nCran, Mrs. George [Marion]. _A Woman in Canada._ London: W.J. Ham Smith, 1911.\n\nCrawford, Virginia M. \"Englishwomen and Agriculture.\" _Contemporary Review_ 74 (September, 1898): 426\u201335.\n\nCresswell, Louisa. [\"The Lady Farmer.\"] _Eighteen Years on the Sandringham Estate._ London: The Temple Co., 1887.\n\n\u2014. [\"Mrs. Gerard Cresswell.\"] _How the Farming in Great Britain Can Be Made to Pay_. London: Simpkin, Marshall and Co., 1881.\n\nCurrie, David. _The Letters of Rusticus: Investigations in Manitoba and the North-West for the Benefit of Intending Emigrants._ Montreal: John Dougall & Sons, 1880.\n\nDinesen, Isak (Karen Blixen). _Out of Africa._ London: Putnam, 1937.\n\nDurham, Mabel. _Canada's Welcome to Women_. London: Canadian Northern Railway, 1929.\n\n\"Emigrant Lady.\" _Letters from Muskoka_. London: R. Bentley, 1878.\n\nFarquharson, James. \"The Problem of Immigration: European and American.\" In _Canadian Problems_ , edited by W.R. McIntosh, n.p. Toronto: R. Douglas Fraser Presbyterian Publications, 1910.\n\nFitzgibbon, Mary Agnes. _Trip to Manitoba: Or, Roughing It on the Line_. London: R. Bentley, 1880.\n\nFrederiksen, Ditlew M. _The Land Laws of Canada and the Land Experience of the United States_. Canora, SK, 1907.\n\nFripp, Edward Fitz-Gerald. _The Outcasts of Canada: Why Settlements Fail. A True Record of \"Bull\" and Bale-Wire_. Edinburgh and London: William Blackwood and Sons, 1932.\n\nGraham, E. Maud. _A Canadian Girl in South Africa: A Teacher's Experiences in the South African War, 1899\u20131902._ Toronto: W. Briggs, 1905. Reprinted, edited, and with an introduction by Michael Dawson, Catherine Gidney, and Susanne M. Klausen. Edmonton: University of Alberta Press, 2015.\n\nGraham, P. Anderson. _The Revival of English Agriculture._ London: Jarrold and Sons, 1899.\n\nGrand Trunk Pacific Railway, General Passenger Department. _Land Seekers' Guide._ Winnipeg: General Passenger Department, Grand Trunk Pacific Railway, 1912.\n\nHall, Mrs. Cecil (Mary). _A Lady's Life on a Farm in Manitoba_. London: W.H. Allen, 1884.\n\nHarrison, Marjorie. _Go West\u2014Go Wise! A Canadian Revelation_. London: Edward Arnold, 1930.\n\nJack, Annie L. _The Canadian Garden: A Pocket Help for the Amateur_. Toronto: William Briggs, 1903.\n\nJackson, C. Hamer. _Discoverers and Explorers of North America._ Toronto: Nelson, 1931.\n\nKnox, Ellen M. _The Girl of the New Day._ Toronto: McClelland and Stewart, 1919.\n\nKurz, Rudolph Friedrich. _An Account of His Experiences Among Fur Traders and American Indians on the Mississippi and the Upper Missouri During the Years 1846 to 1852._ Smithsonian Institution Bureau of America Ethnology Bulletin 115. Washington, DC: Smithsonian Institution, 1937.\n\nLove, Currie. \"Where Opportunity Knocks.\" In _Merchants' and Manufacturers' Record: Calgary, Sunny Alberta and the Industrial Prodigy of the Great West_ , 6\u201314. Calgary: Jennings Publishing Co., 1911.\n\nLow, Florence B. _Openings for British Women in Canada._ London: William Stevens, c. 1920.\n\n\u2014. _Women Out West: Life and Work in Canada._ London: W.T. Cranfield, 1924.\n\nMcClung, Nellie. _The Stream Runs Fast: My Own Story_. Toronto: Thomas Allen, 1945.\n\nMarshall, A.C. \"Small Holdings for Women.\" In _Every Woman's Encyclopaedia._ Vol. 2, 1403\u20131406. London, 1910.\n\nMartin, Chester. _\"Dominion Lands\" Policy_. Canadian Frontiers of Settlement, edited by W.A. Mackintosh and W.L.G. Joerg, vol. 2. Toronto: The Macmillan Co. of Canada, 1938.\n\nMartineau, Harriet. _My Farm of Two Acres_. New York: Bunce and Huntington, 1865.\n\nMason, Otis Tufton. _Woman's Share in Primitive Culture_. London: Macmillan and Co., 1895.\n\nMatthews, Washington. _Ethnography and Philology of the Hidatsa Indians_. Washington, DC: Government Printing Office, 1877.\n\nMenzies, J.H. _Canada and the War: The Promise of the West._ Toronto: Copp Clark Co., 1916.\n\nMetcalfe, J.H. _The Tread of the Pioneers._ Toronto: Ryerson Press Printers, 1932.\n\nMoodie, Susanna. _Roughing It in the Bush; Or Life in Canada._ London: Richard Bentley, 1852.\n\nMorris, Alexander. _The Treaties of Canada with the Indians of Manitoba and the North-West Territories._ 1880. Reprint, Toronto: Coles, 1971.\n\nMorris, Elizabeth Keith. _An Englishwoman in the Canadian West._ London: Simpkin, Marshall, 1913.\n\nOsborn, E.B., \"Our Western Chivalry,\" _The Morning Post_ (London), 14 July, 1900: 5.\n\nPullen-Burry, B. _From Halifax to Vancouver._ London: Mills and Boon, 1912.\n\n_Report on the International Congress of Women_. International Congress of Women. Toronto: Geo. Parker and Sons, 1910.\n\nRobertson, Norman. _The History of the County of Bruce._ Toronto: William Briggs, 1906.\n\nSaxby, Jesse M. _West-Nor'-West_. London: James Nisbet and Co., 1890.\n\nSchofield, F.H. _The Story of Manitoba._ Vol. 3. Winnipeg: S.J. Clarke, 1913.\n\nSeton-Thompson, Grace G. _A Woman Tenderfoot_. Toronto: G.N. Morang, 1900.\n\nSpence, Thomas. _The Prairie Lands of Canada_. Montreal: Gazette Printing House, 1879.\n\nSykes, Ella C. _A Home-Help in Canada_. London: Smith Elder and Co., 1912.\n\n\u2014. \"Openings for Educated Women in Canada.\" _Journal of the Royal Society of Arts_ 61: 3146 (March 7, 1913), 430\u2013438.\n\nTaylor, Frances. \"Conditions of Life for Women in South Africa.\" _Women Workers: The Papers Read at the Conference Held in Portsmouth Arranged by the National Union of Women Workers of Great Britain and Ireland_ , 122\u2013128 _._ London: Office of the Union, 1909.\n\nThwaite, Leo _. Alberta: An Account of Its Wealth and Progress._ Porter's Progress of Nations Series. Chicago: Rand McNally, 1912.\n\nVernon, A.L. _Leaton Colonial Training Home_. Winchester: Warren and Son, 1905.\n\nWalker, Eldred G.F. _Canadian Trails: Hither and Thither in the Great Dominion_. Toronto: Musson Book Co., 1912.\n\nWard, Mary Augusta. _Canadian Born._ London: Smith, Elder, 1910.\n\nWatanna, Onoto. _Cattle._ London: Hutchinson and Co., 1923.\n\nWatt, Gertrude Balmer. _Town and Trail_. Edmonton: News Publishing Co., 1908.\n\nWest, Edward. _Homesteading: Two Prairie Seasons._ London: T. Fisher Unwin, 1918.\n\nWilkins, Louisa. _The Work of Educated Women in Horticulture and Agriculture_. London: J. Truscott, 1915.\n\nWill, George F., and George G. Hyde. _Corn among the Indians of the Upper Missouri_. 1917. Reprint, Lincoln: University of Nebraska Press, 1964.\n\nWilson, Gilbert L. _Agriculture of the Hidatsa Indians: An Indian Interpretation_. Studies in the Social Sciences 9. Minneapolis: University of Minnesota Press, 1917.\n\n\u2014. _Buffalo Bird Woman's Garden: Agriculture of the Hidatsa Indians._ With a new introduction by Jeffery R. Hanson. Saint Paul: Minnesota Historical Society Press, 1987.\n\nWolseley, Frances. _Gardening for Women_. London: Cassell and Co., 1908.\n\n\u2014. _In a College Garden_. New York: Charles Scribner's Sons, 1917.\n\n\u2014. _Women and the Land_. London: Chatto and Windus, 1916.\n\n_Women of Canada: Their Life and Work_. National Council of Women of Canada, 1900. Compiled for distribution at the Paris International Exhibition.\n\n_Women's Work on the Land: How You May Assist in Food Production This Summer._ Government of Ontario Trades and Labour Branch, Department of Public Works, n.d.\n\nSECONDARY SOURCES\n\nAberdeen Historical Society. _Aberdeen, 1907\u20131981_. Altona, MB: Friesen Printers, 1982.\n\nAlberta Historical Society. _Cypress Hills Country._ Altona, MB: D.W. Friesen and Sons, 1991.\n\nAlford, Katrina. _Production or Reproduction? An Economic History of Women in Australia, 1788\u20131850_. Melbourne: Oxford University Press, 1985.\n\nAlix-Clive Historical Club. _Gleanings after Pioneers and Progress._ Alix, AB: Alix-Clive Historical Club, 1981.\n\nAllen, Douglas W. \"Homesteading and Property Rights: Or, 'How the West Was Really Won.'\" _Journal of Law and Economics_ 34, no. 1 (April 1991): 1\u201323.\n\nAndrosoff, Ashleigh. \"A Larger Frame: 'Redressing' the Image of Doukhobor-Canadian Women in the Twentieth Century.\" _Journal of the Canadian Historical Association_ 18, no. 1 (2007): 81\u2013105.\n\nAnonymous. _Our Harvest of Memories: Foxdale, Sturgeon Valley, Silver Cliff, Three Creeks, Rayside, Rich Valley._ Altona, MB: Friesen Printers, 1983.\n\n_\u2014_ _. Prairie Sod and Goldenrod: History of Crossfield and District._ Altona, MB: Friesen Printers, 1977.\n\nArmitage, Sue. _Shaping the Public Good: Women Making History in the Pacific Northwest._ Corvallis, OR: Oregon State University Press, 2015.\n\nAugustus, Camilla. \"'Half-Breed' Homestead: The North West Metis Scrip Policy, 1885\u20131887.\" MA thesis, University of Calgary, 2004.\n\nBacchi, Carol Lee. _Liberation Deferred: The Ideas of the English Canadian Suffragists, 1877\u20131918_. Toronto: University of Toronto Press, 1983.\n\nBaergen, William. _Pioneering with a Piece of Chalk: The One-Room Country Schools of Alberta._ Stettler, AB: William Baergen, 2005.\n\nBallantyne, Tony. \"Colonial Knowledge.\" In _The British Empire: Themes and Perspectives_ , edited by Sarah Stockwell, 177\u201398. Oxford: Blackwell Publishing, 2008.\n\n\u2014. \"Race and the Webs of Empire: Aryanism from India to the Pacific.\" _Journal of Colonialism and Colonial History_ 2, no. 3 (2001). doi: 10.1353\/cch.2001.0045.\n\nBarber, Marilyn. \"The Gentlewomen of Queen Mary's Coronation Hostel.\" In _Not Just Pin Money: Selected Essays on the History of Women's Work in British Columbia_ , edited by Barbara K. Latham and Roberto J. Pazdro, 141\u201358. Victoria, BC: Camosun College, 1984.\n\n\u2014. \"The Servant Problem in Manitoba, 1896\u20131930.\" In _First Days, Fighting Days: Women in Manitoba History_ , edited by Mary Kinnear, 100\u201319. Regina: Canadian Plains Research Center, 1987.\n\nBartky, Sandra Lee. _\"Sympathy and Solidarity\" and Other Essays_. Oxford: Rowman and Littlefield, 2002.\n\nBauman, Paula. \"Single Women Homesteaders in Wyoming, 1880\u20131930.\" _Annals of Wyoming_ 58 (Spring 1986): 39\u201353.\n\nBelich, James. _Replenishing the Earth: The Settler Revolution and the Rise of the Anglo-World, 1783\u20131939._ Oxford: Oxford University Press, 2009.\n\nBennett, Jason B. \"Apple of the Empire: Landscape and Imperial Identity in Turn-of-the-Century British Columbia.\" _Journal of the Canadian Historical Association_ 9 (January 1998): 63\u201392.\n\nBentley and District Historical Society. _Bentley and District Early History_. Bentley and District Historical Society, 1982.\n\nBenton-Cohen, Katherine. \"Common Purposes, Worlds Apart: Mexican-American, Mormon, and Midwestern Women Homesteaders in Cochise County, Arizona.\" _Western Historical Quarterly_ 36, no. 4 (2005): 429\u201342.\n\nBirtles, William. \"A Pioneer Nurse.\" _Alberta History_ 43, no. 1 (Winter 1995): 2\u20136.\n\nBlaine Lake and District Historical Book Committee. _Bridging the Years: Era of Blaine Lake and District, 1790\u20131980_. Town of Blaine Lake and Rural Municipality of Blaine Lake, 1984. __\n\nBlakeley, Brian L. \"Women and Imperialism: The Colonial Office and Female Emigration to South Africa, 1901\u20131910.\" _Albion: A Quarterly Journal Concerned with British Studies_ 13, no. 2 (Summer 1981): 131\u201349.\n\nBoag, Peter. _Re-Dressing America's Frontier Past._ Berkeley: University of California Press, 2011.\n\n\u2014. \"Thinking Like Mount Rushmore: Sexuality and Gender in the Republican Landscape.\" In _Seeing Nature through Gender_ , edited by Virginia J. Scharff, 40\u201359. Lawrence: University Press of Kansas, 2003.\n\nBowers, Alfred W. _Hidatsa Social and Ceremonial Organization._ 1963. Reprint, Lincoln: University of Nebraska Press, 1992.\n\nBrada-Easthill-Roecliffe Historical Society. _Rural Roots_. Altona, MB: Friesen Printers, 1987.\n\nBradley, Harriet. _Men's Work, Women's Work: A Sociological History of the Sexual Division of Labour in Employment_. Minneapolis: University of Minnesota Press, 1989.\n\nBuddle, Melanie. _The Business of Women: Marriage, Family and Entrepeneurship in British Columbia, 1901\u201351_. Vancouver: University of British Columbia Press, 2010.\n\nBurnett, Kristin. _Taking Medicine: Women's Healing Work and Colonial Contact in Southern Albera 1880\u20131930._ Vancouver: University of British Columbia Press, 2011 _._\n\nBush, Julia. _Edwardian Ladies and Imperial Power._ London: Leicester University Press, 2000.\n\nCarey, Jane L. \"'Wanted! A Real White Australia': The Women's Movement, Whiteness and the Settler-Colonial Project.\" In _Studies in Settler Colonialism: Poltics, Identity, Culture_ , edited by F. Bateman and L. Pilkington, 122\u201339. London: Palgrave Macmillan, 2011.\n\nCarter, Sarah. \"Britishness, 'Foreignness,' Women and Land in Western Canada, 1890s\u20131920s.\" _Humanities Research_ 13, no. 1 (2006): 43\u201360.\n\n\u2014. _Capturing Women: The Manipulation of Cultural Imagery in Canada's Prairie West._ Montreal: McGill-Queen's University Press, 1997.\n\n\u2014. \"Erasing and Replacing: Property and Homestead Rights of First Nations Farmers of Manitoba and the Northwest, 1870s\u20131910s.\" In _Place and Replace: Essays on Western Canada_ , edited by Adele Perry, Esyllt W. Jones, and Leah Morton, 14\u201339. Winnipeg: University of Manitoba Press, 2013.\n\n\u2014. _The Importance of Being Monogamous: Marriage and Nation Building in Western Canada._ Edmonton: Athabasca University Press and University of Alberta Press, 2008.\n\n\u2014. \"'An Infamous Proposal': Prairie Indian Reserve Land and Soldier Settlement after World War I.\" _Manitoba History_ 37 (Spring\/Summer 1999): 9\u201321. http:\/\/www.mhs.mb.ca\/docs\/mb_history\/37\/infamousproposal.shtml.\n\n\u2014. _Lost Harvests: Prairie Indian Reserve Farmers and Government Policy._ Montreal: McGill-Queen's University Press, 1990.\n\n\u2014. \"'My Vocabulary Contains No Such Word as Defeat': Clara Lynch and Her Battle for Her Alberta Homestead, 1900\u20131909.\" _Alberta History_ 61, no. 3 (Summer 2013): 2\u201311.\n\nCarter, Sarah, ed. _Montana Women Homesteaders: A Field of One's Own_. Helena, MT: Farcountry Press, 2009.\n\nCasid, Jill H. _Sowing Empire: Landscape and Colonization._ Minneapolis: University of Minnesota Press, 2005.\n\nCavanaugh, Catherine A. \"Irene Marryat Parlby: An 'Imperial Daughter' in the Canadian West, 1896\u20131934.\" In _Telling Tales: Essays in Western Women's History_ , edited by Catherine A. Cavanaugh and Randi R. Warne, 100\u201322. Vancouver: University of British Columbia Press, 2000.\n\n\u2014. \"The Limitations of the Pioneering Partnership: The Alberta Campaign for Homestead Dower, 1909\u20131925.\" In _Making Western Canada: Essays on European Colonization and Settlement_ , edited by Catherine Cavanaugh and Jeremy Mouat, 186\u2013214. Toronto: Garamond Press, 1996.\n\n\u2014. \"'No Place for a Woman': Engendering Western Canadian Settlement.\" _Western Historical Quarterly_ 18 (Winter 1997): 493\u2013518.\n\nChapman, Jane. \"The Argument of the Broken Pane: Suffragette Consumerism and Newspapers.\" _Media History_ 21, no. 3 (2015): 238\u2013251.\n\nChilton, Lisa. _Agents of Empire: British Female Migration to Canada and Australia, 1860s\u20131930s_. Toronto: University of Toronto Press, 2007.\n\nChurch-Staudt, Barb. \"Agnes (Martin) Balfour: Descendants Uphold Her Heritage.\" In _Pioneers! O Pioneers!_ No. 4 _Regina Women of the Years_. Regina: Regina and District Old Timers' Association Inc., n.d.\n\nChused, Richard H. \"The Oregon Donation Act of 1850 and Nineteenth Century Federal Married Women's Property Law.\" _American Journal of Legal History_ 29, no. 1 (January 1985): 3\u201335.\n\nCohen, Marjorie Griffin. \"The Decline of Women in Canadian Dairying.\" _Histoire sociale-Social History_ 17, no. 43 (Nov. 1984): 307\u201334.\n\nCompton, Tonia M. \"Challenging Imperial Expectations: Black and White Female Homesteaders in Kansas.\" _Great Plains Quarterly_ 33, no. 1 (November 2013): 49\u201361.\n\n\u2014. \"Proper Woman\/Propertied Women: Federal Land Laws and Gender Order(s) in the Nineteenth-Century Imperial American West.\" PhD diss., University of Nebraska-Lincoln, 2009. http:\/\/digitalcommons.unl.edu\/historydiss\/19\/.\n\n\u2014. \"Uncle Sam's Farm: Congress and Free Land Policies in the Nineteenth Century.\" Paper presented at the 3rd annual James A. Rawley Conference in the Humanities, _Imagining Communities: People, Places, Meanings_ , Lincoln, NE, April 12, 2008. http:\/\/digitalcommons.unl.edu\/historyrawleyconference\/15\/.\n\nConlogue, William. \"Managing the Farm, Educating the Farmer: _O Pioneers!_ and the New Agriculture.\" _Great Plains Quarterly_ 21, no. 1 (Winter 2001): 3\u201315.\n\nConstantine, Stephen. \"Introduction: Empire Migration and Imperial Harmony.\" In _Emigrants and Empire: British Settlement in the Dominions between the Wars_ , edited by Stephen Constantine, 1\u201321. Manchester and New York: Manchester University Press, 1990.\n\nCook, Ramsay. \"Francis Marion Beynon and the Crisis of Christian Reformism.\" In _The West and the Nation: Essays in Honour of W.L. Morton_ , edited by Carl Berger and Ramsay Cook, 187\u2013208. Toronto: McClelland and Stewart, 1976.\n\nCoyote Flats Historical Society. _Coyote Flats Historical Review 1905\u20131965._\n\nCypress Hills (Alberta) Historical Soceity. _Cypress Hills Country: Our Roots_. Elkwater, AB: n.p., 1991.\n\nDagg, Anne Innis. _The Feminine Gaze: A Canadian Compendium of Non-Fiction Women Authors and Their Books, 1836\u20131945._ Waterloo: Wilfrid Laurier University Press, 2001.\n\nDanysk, Cecilia. _Hired Hands: Labour and the Development of Prairie Agriculture, 1880\u20131930_. Toronto: McClelland and Stewart, 1995.\n\nDaschuk, James. _Clearing the Plains: Disease, Politics of Starvation, and the Loss of Aboriginal Life._ Regina: University of Regina Press, 2013.\n\nDavidoff, Leonore, and Catherine Hall. _Family Fortunes: Men and Women of the English Middle Class, 1780\u20131850._ London and New York: Routledge, 2002. First published 1987 by Hutchinson Education.\n\nDelday, Eva. _Brooks: Beautiful-Bountiful_. Altona, MB: D.W. Friesen and Sons, 1975.\n\nDenig, Edwin Thompson. _Five Indian Tribes of the Upper Missouri: Sioux, Arickaras, Assiniboines, Crees, Crows_. Norman: University of Oklahoma Press, 1961.\n\nDevas, Nicolette. _Two Flamboyant Fathers_. London: Readers Union-Collins, 1968.\n\nDick, Lyle. _Farmers \"Making Good\": The Development of Abernethy District, Saskatchewan, 1880\u20131920._ Ottawa: National Historic Parks and Sites, 1989.\n\nDodd, Penny, and Marion Jankunis. \"Garden of Native Prairie Plants,\" Galt Museum, accessed December 8, 2015. http:\/\/www.galtmuseum.com\/pdf\/NativePrairiePlantsGarden-Ethnobotany.pdf.\n\nDoughty, Teri. \"Representing the Professional Woman: The Celebrity Interviewing of Sarah Tooley.\" In _Women in Journalism at the Fin de Si\u00e8cle: Making a Name for Herself_ , edited by F. Elizabeth Gray, 165\u201381. London: Palgrave Macmillan, 2012.\n\nEatonia History Book Committee. _A Past to Cherish._ Eatonia, SK: Eatonia History Book Committee, 1980.\n\nEgly Country Club. _Trails, Trials and Tributes_. Fort Benton, MT: 1974.\n\nEmmons, David M. \"American Myth, Desert to Eden: Theories of Increased Rainfall and the Timber Culture Act of 1873.\" _Forest History_ 15, no. 3 (Oct. 1971): 6\u201314.\n\nEvans, Simon. _The Bar U: Canadian Ranching History._ Calgary: University of Calgary Press, 2004.\n\n\u2014. _Prince Charming Goes West_ : _The Story of the E.P. Ranch_. Calgary: University of Calgary Press, 1993.\n\nFarm Women's Union of Alberta. _Pioneers Who Blazed the Trail: A History of High Prairie and District._ High Prairie, AB: South Peace News, 1968.\n\nFarrington, Jessie de Prado. \"Rocking Horse to Cow Pony.\" _New Mexico Historical Review_. Part 1: 30, no. 2 (April 1955): 115\u2013135. Part II: 30, no. 3 (July 1955), 221\u2013251. Part III: 30, no. 4 (October, 1955) 313\u2013339. Part IV: 31, no. 3 (January, 1956), 38\u201367.\n\nFenn, Elizabeth. _Encounters at the Heart of the World: A History of the Mandan People_. New York: Hill and Wang, 2014.\n\nFiamengo, Janice. \"Rediscovering Our Foremothers Again: Racial Ideas of Canada's Early Feminists, 1885\u20131945.\" In _Rethinking Canada: The Promise of Women's History_ , edited by Mona Gleason and Adele Perry, 144\u201363. 5th edition. Don Mills, ON: Oxford University Press, 2006.\n\nFort Qu'Appelle and District History Book Committee. _Fort Qu'Appelle and Area: A History._ Fort Qu'Appelle, SK: Fort Qu'Appelle and District History Book Committee, 1996. One copy in the Book and Record Depository of the University of Alberta.\n\nFortier, Hilaire J. _Lamoureux: Ses Debuts, Ses Pionniers._ Lamoureux, AB: Lamoureux Jubilee Committee, 1955.\n\nFriesen, Gerald. _The Canadian Prairies: A History_. Toronto: University of Toronto Press, 1984.\n\nFritze, Tamara. \"Growing Identity, Growing a Home: Contrasting Functions of Two Nineteenth-Century Gardens.\" _Studies in the History of Gardens and Designed Landscapes: An International Quarterly_ 22:4 (2002): 335\u2013344.\n\nGalloway, Margaret. _I Lived in Paradise_. Winnipeg: Bulman Brothers Ltd., 1942.\n\nGanley, Toby. \"What's All This Talk about Whiteness?\" _Dialogue_ 1, no. 2 (2003): 12\u201313.\n\nGarceau, Dee. _The Important Things of Life: Women, Work and Family in Sweetwater County, Wyoming, 1880\u20131929_. Lincoln: University of Nebraska Press, 1997.\n\nGeorge, Sam. _Botany, Sexuality and Women's Writing 1760\u20131830: From Modest Shoot to Forward Plant._ Manchester and New York: Manchester University Press, 2007.\n\nGeraldine History Committee. _Spokes, Spurs and Cockleburs_. Fort Benton, MT: River Press, 1976.\n\nGhost Pine Community Group. _Memoirs of the Ghost Pine Homesteaders._ Three Hills, AB: Ghost Pine Community Group, 1954.\n\nGilpin, John. _Prairie Promises: History of the Bow River Irrigation District._ Vauxhall, AB: Bow River Irrigation District, 1996.\n\nGleadle, Kathryn. _Borderline Citizens: Women, Gender and Political Culture in Britain, 1815\u20131867_. Oxford, UK: Oxford University Press, 2009.\n\nGleichen United Church Women. _The Gleichen Call: A History of Gleichen and Surrounding Areas, 1877\u20131968._ Calgary: North West Printing, 1968.\n\nGoldfrank, Esther S. _Changing Configurations in the Social Organization of a Blackfoot Tribe During the Reserve Period (the Blood of Alberta, Canada)_. Seattle and London: University of Washington Press, 1966.\n\nGordon, Peter, ed. _Politics and Society: The Journals of Lady Knightley of Fawsley_. London and New York: Routledge, 2005.\n\nGould, Florence C., and Patricia N. Pando. _Claiming Their Land: Women Homesteaders in Texas._ El Paso: Texas Western Press, 1991.\n\nGowdy-Wygant, Cecilia. _Cultivating Victory: The Women's Land Army and the Victory Garden Movement_. Pittsburgh: University of Pittsburgh Press, 2013.\n\nGreen, Harvey. _The Light of the Home: An Intimate View of Women in Victorian America_. New York: Pantheon Books, 1983.\n\nGrimshaw, Patricia. \"Suffragists Representing Race and Gender in the American West: The Case of Colorado.\" In _Dealing with Difference: Essays in Gender, Culture and History_ , edited by Patricia Grimshaw and Diane Kirkby, 79\u201381. Melbourne: History Department, University of Melbourne, 1997.\n\nHall, Catherine. \"Of Gender and Empire: Reflections on the Nineteenth Century.\" In _Gender and Empire_ , edited by Philippa Levine, 46\u201376. Oxford: Oxford University Press, 2004.\n\nHarper, Marjory, and Stephen Constantine. _Migration and Empire_. Oxford: Oxford University Press, 2010.\n\nHarris, Dianne. \"Cultivating Power: The Language of Feminism in Women's Garden Literature, 1870\u20131920.\" _Landscape Journal_ 13, no. 2 (Fall 1994): 113\u201323.\n\nHarris, Margaret. \"Hobart and 'Home' in Tasma and Mrs. Humphry Ward.\" _Australian Literary Studies in the 21st Century_ 28 (2001): 135\u201344.\n\nHarris, R. Cole, and John Warkentin. _Canada before Confederation: A Study in Historical Geography._ Ottawa: Carleton University Press, 1991.\n\nHawkins, R.E. \"Lillian Beynon Thomas, Woman's Suffrage and the Return of Dower to Manitoba.\" _Manitoba Law Journal_ 27, no. 1 (1999): 45\u2013113.\n\nHelly, Dorothy O. \"Flora Shaw and the _Times_ : Becoming a Journalist, Advocating Empire.\" In _Women in Journalism at the Fin de Si\u00e8cle: Making a Name for Herself_ , edited by F. Elizabeth Gray, 110\u201328. London: Palgrave Macmillan, 2012.\n\nHenderson, Jarett. \"'No Money, but Muscle and Pluck': Cultivating Trans-Imperial Manliness for the Fields of Empire, 1870\u20131901.\" In _Making it Like a Man: Canadian Masculinities in Practice_ , edited by Christine Ramsay, 17\u201337. Waterloo, ON: Wilfrid Laurier University Press, 2011.\n\nHenderson, Jennifer. _Settler Feminism and Race Making in Canada_. Toronto: University of Toronto Press, 2003.\n\nHigh River Pioneers and Old Timers Association. _Leaves from the Medicine Tree._ Lethbridge: _Lethbridge Herald_ , 1960.\n\nHildebrandt, Walter. \"The Aspirations of a Western Enthusiast: P.G. Laurie and the _Saskatchewan Herald._ \" MA thesis, University of Saskatchewan, 1978.\n\nHistory Book Society. _Fencelines and Furrows._ Calgary: Northwest Printing and Lithographing, 1969.\n\nHolme, Thea. _Chelsea._ London: Hamish Hamilton, 1972.\n\nHome, Robert. \"Scientific Survey and Land Settlement in British Colonialism with Particular Reference to Land Tenure in the Middle East 1920\u201350.\" _Planning Perspectives_ 21 (Jan. 2006): 1\u201322.\n\nHryniuk, Margaret, and Frank Korvemaker. _Legacy of Stone: Saskatchewan's Stone Buildings._ Regina: Coteau Books, 2008.\n\nHunter, Kate (Kathryn M. Hunter). \"The Big Picture Problem: Race and Gender in the Histories of Single Farming Women in Victoria, 1880\u20131930.\" In _Dealing with Difference: Essays in Gender, Culture and History._ Melbourne: University of Melbourne Press, 1997.\n\nHunter, Kathryn M. _Father's Right-Hand Man: Women on Australia's Family Farms in the Age of Federation, 1880s\u20131920s_. Melbourne: Australian Scholarly Publishing, 2004.\n\nHurt, R. Douglas. _American Agriculture: A Brief History._ Ames: Iowa State University Press, 1995.\n\n\u2014. _The Big Empty: The Great Plains in the Twentieth Century._ Tucson: University of Arizona Press, 2011.\n\nJacobs, Margaret. \"Parallel or Intersecting Tracks? The History of the US West and Comparative Settler Colonialism.\" _Settler Colonial Studies_ 4, no. 2 (2014): 155\u2013161.\n\nJames, Jean. _Hanna North: Our Roots._ Hanna, AB: Hanna North Book Club, 1978.\n\nJusova, Iveta. _The New Woman and the Empire_. Columbus: Ohio State University Press, 2005.\n\nKalmakoff, Elizabeth Ann. \"Woman Suffrage in Saskatchewan.\" MA thesis, University of Regina, 1993.\n\nKaye, Frances W. _Goodlands: A Meditation and History on the Great Plains_. Edmonton: Athabasca University Press, 2011.\n\nKeeler History Book Committee. _Our Heritage: A History of the Keeler Community_. Keeler, SK: Keeler History Book Committee, 1990.\n\nKenyon, Ron. _Lone Rock to Marshall._ Altona, MB: D.W. Friesen and Sons, 1976.\n\nKing, Peter. _Women Rule the Plot: The Story of the 100 Year Fight to Establish Women's Place in Farm and Garden_. London: Duckworth, 1999.\n\nKingston, Beverley. _Elizabeth Macarthur._ Elizabeth Bay, N.S.W.: Historic Houses Trust of New South Wales, 1984.\n\nKisby, Anna. \"Vera 'Jack' Holme: Cross-Dressing Actress, Suffragette and Chauffeur.\" _Women's History Review_ 23, no. 1 (2014): 120\u201336.\n\nKluth, Alton E. \"Mr. and Mrs. Reinhart Kluth.\" In _A Historical Tribute to the Pioneers South of the Whitemud_ , edited by Harrisland Sewing Club History Committee. Bracken, SK: Harrisland Sewing Club History Committee, 1975.\n\nKranidis, Rita S. _The Victorian Spinster and Colonial Emigration: Contested Subjects._ London: Macmillan Press, 1999.\n\nKulba, Tracy, and Victoria Lamont. \"The Periodical Press and Western Woman's Suffrage Movements in Canada and the United States: A Comparative Study.\" _Women's Studies International Forum_ 29, no. 3 (May\u2013June 2006): 265\u201378.\n\nLacey, Candida Ann, ed. _Barbara Leigh Smith Bodichon and the Langham Place Group_. New York and London: Routledge and Kegan Paul, 1987.\n\nLacombe Rural History Club. _Wagon Trails to Hard Top: History of Lacombe and Area._ Lacombe, AB: Lacombe Rural History Club, 1973.\n\nLambrecht, Kurt N. _The Administration of Dominion Lands, 1870\u20131930_. Regina: Canadian Plains Research Center, 1991.\n\nLang, Marjorie. _Women Who Made the News: Female Journalists in Canada 1880\u20131945._ Montreal: McGill-Queen's University Press, 1999.\n\nLangford, Nanci. \"First Generation and Lasting Impression: The Gendered Identities of Prairie Homestead Women.\" PhD diss., University of Alberta, 1994.\n\nLawrence, Dianne. _Genteel Women: Empire and Domestic Material Culture, 1840\u20131910._ Manchester: Manchester University Press, 2012.\n\nLeckie, Gloria J. \"Female Farmers in Canada and the Gender Relations of a Restructuring Agricultural System.\" _The Canadian Geographer_ 37, no. 3 (1993): 212\u201329.\n\nLehr, John C., John Everitt, and Simon Evans. \"The Making of the Prairie Landscape.\" _Prairie Forum_ 33, no. 1 (Spring 2008): 1\u201338.\n\nLeonard, David W. _The Last Great West: The Agricultural Settlement of the Peace River Country to 1914._ Calgary: Detselig Enterprises Ltd., 2005.\n\nLevine, Philippa. \"Introduction: Why Gender and Empire?\" In _Gender and Empire_ , edited by Philippa Levine. Oxford: Oxford University Press, 2004.\n\nLevitan, Kathrin. \"Redundancy, the 'Surplus Women' Problem, and the British Census, 1851\u20131861.\" _Women's History Review_ 17, no. 3 (July 2008): 359\u201376.\n\nLiberty County Museum. _Our Heritage in Liberty_. Chester, MT: Liberty County Times, 1976.\n\nLindgren, H. Elaine. _Land in Her Own Name: Women as Homesteaders in North Dakota_. Norman, OK, and London: University of Oklahoma Press, 1991.\n\nLinklater, Andro. _Measuring America: How an Untamed Wilderness Shaped the United States and Fulfilled the Promise of Democracy_. New York: Walker Publishing Company, 2002.\n\nLogan, Deborah Anna. _The Hour and the Woman: Harriet Martineau's \"Somewhat Remarkable\" Life_. DeKalb: Northern Illinois University Press, 2002.\n\nLosurdo, Domenico. _Liberalism: A Counter-History_. London: Verso, 2011.\n\nLutz, Otto. _A Mother Braving a Wilderness: Told by Her Son, Otto Lutz_ , edited by Thomas Gerwing. Muenster, SK: St. Peter's Colony Jubilee Steering Committee, 1977.\n\nLux, Maureen K. _Medicine that Walks: Disease, Medicine, and Canadian Plains Native People, 1880\u20131940_. Toronto: University of Toronto Press, 2011.\n\n\u2014. \"We Demand 'Unconditional Surrender': Making and Unmaking the Blackfoot Hospital, 1890s to 1950s.\" _Social History of Medicine_ 25, no. 3 (2012): 665\u2013684.\n\nMcCallum, Margaret. \"Prairie Women and the Struggle for a Dower Law, 1905\u20131920.\" _Prairie Forum_ 18, no. 1 (Spring 1993): 19\u201334.\n\nMcClintock, Anne. _Imperial Leather: Race, Gender and Sexuality in the Colonial Context._ New York: Routledge, 1995.\n\nMcKay, Ian. \"Debating Sexuality in Halifax, 1920: Mrs. Donald Shaw and Others.\" In _The Challenge of Modernity: A Readers on Post-Confederation Canada_ , ed. Ian McKay, 331\u2013345. Toronto: McGraw-Hill Ryerson, 1992.\n\n\u2014. \"The Liberal Order Framework: A Prospectus for a Reconnaissance of Canadian History.\" _Canadian Historical Review_ 81, no. 4 (Dec. 2000): 616\u201345.\n\nMcKenna, Katherine M.J. \"E. Cora's Hind's Feminist Thought: 'The Woman's Quiet Hour' in the _Western Home Monthly_ , 1905\u20131922.\" _Journal of the Canadian Historical Association_ 22, no. 1 (2011): 69\u201398.\n\nMcKenzie, Tully. _It's Time to Remember: A Hundred Years of Progress Tremaine-Hunterville Area._ Steinbach, MB: Carillon Press, 1975.\n\nMacKinnon, Doris J. _The Identities of Marie Rose Delorme Smith: Portrait of a M\u00e9tis Woman, 1861\u20131960._ Regina: Canadian Plains Research Center, 2013.\n\nMacMahon, Sandra Varney. \"Fine Hands for Sowing: The Homesteading Experiences of Remittance Woman Jessie de Prado MacMillan.\" _New Mexico Historical Review_ 74, no. 3 (July, 1999): 271\u2013294.\n\nMcPherson, Kathryn. \"Was the 'Frontier' Good for Women?: Historical Approaches to Women and Agricultural Settlement in the Prairie West, 1870\u20131925.\" _Atlantis: A Women's Studies Journal_ 25, no. 1, (Fall\/Winter 2000): 75\u201386.\n\nMagee, Kathryn. \"'For Home and Country': Education, Activism, and Agency in Alberta Native Homemakers' Clubs, 1942\u20131970.\" _Native Studies Review_ 18, no. 2 (2009): 27\u201349.\n\nManitoba Culture, Heritage and Recreation, Historic Resources Branch. _The Prehistory of the Lockport Site_. Winnipeg: Manitoba Culture, Heritage and Recreation, Historic Resources Branch, 1985.\n\n\u2014. _Thomas Mayne Daly_. Winnipeg: Manitoba Culture, Heritage and Recreation, Historic Resources Branch, 1985.\n\nMarsh, Jan. _Back to the Land: The Pastoral Impulse in England, 1880\u20131914_. London: Quartet Books: 1982.\n\nMartin-McGuire, Peggy. \"First Nations Land Surrenders on the Prairies.\" Ottawa: Indian Claims Commission, 1998.\n\nMead, Rebecca J. _How the Vote Was Won: Woman Suffrage in the Western United States, 1868\u20131914_. New York: New York University Press, 2004.\n\nMehain, Anne, and Limerick Historical Society. _Prairie Trails and Pioneer Tales._ Altona, MB: Friesen Printers, 1982.\n\nMehta, Uday S. \"Liberal Strategies of Exclusion.\" In _Tensions of Empire: Colonial Cultures in a Bourgeois World_ , edited by Frederick Cooper and Ann Laura Stoler, 59\u201387. Berkeley, Los Angeles, and London: University of California Press, 1997.\n\nMeredith, Anne. \"Horticultural Education in England, 1900\u20131940: Middle-Class Women and Private Gardening Schools.\" _Garden History_ 31, no. 1 (Spring 2003): 67\u201379.\n\nMillarville, Kew, Priddis and Bragg Creek Historical Society. _Our Foothills_. Altona, MB: D.W. Friesen and Sons, 1975.\n\nMorgensen, Scott Lauria. \"The Biopolitics of Settler Colonialism: Right Here, Right Now.\" _Settler Colonial Studies_ 1, no. 1 (2011): 52\u201376.\n\nMorrow, John. \"The Deville Story.\" _Alberta History_ 12, no. 4 (Autumn 1964): 15\u201318.\n\nMorton, W.L. _Manitoba: A History._ Toronto: University of Toronto Press, 1967.\n\nMuhn, James. \"Women and the Homestead Act: Land Department Administration of a Legal Imbroglio, 1863\u20131934.\" _Western Legal History_ 7, no. 2 (Summer\/Fall 1994): 283\u2013307.\n\nNoakes, Lucy. \"From War Service to Domestic Service: Ex-Servicewomen and the Free Passage Scheme 1919\u201322.\" _Twentieth Century British History_ 22, no. 1 (2010): 1\u201327.\n\n\u2014. _Women in the British Army: War and the Gentle Sex 1907\u201348._ London: Routledge, 2006.\n\nNotukeu History Book Club. _Next Year Country._ Notukeu, SK: Notukeu History Book Club, 1980.\n\nOak Lake Historical Committee. _Ox Trails to Blacktop_. Altona, MB: Friesen Printers, 1982.\n\nOpitz, Donald L. \"'Back to the Land': Lady Warwick and the Movement for Women's Collegiate Agricultural Education.\" _Agricultural History Review_ 62, no. 1 (June 2014): 119\u201345.\n\n\u2014. \"'A Triumph of Brains over Brute': Women and Science at the Horticultural College, Swanley, 1890\u20131910.\" _Isis_ 104, no. 1 (March 2013): 30\u201362.\n\nOxendale, Stephanie M. \"'What Should They Know Of England Who Only England Know?' Ideas of Englishness, Empire and Organized Women's Emigration, 1902\u20131927.\" PhD diss., State University of New York at Binghamton, 2000.\n\nPaice, Edward. _Lost Lion of Empire: The Life of Cape-to-Cairo Grogan_. London: HarperCollins, 2001.\n\nPalmer, Howard. _Patterns of Prejudice: A History of Nativism in Alberta_. Toronto: McClelland and Stewart, 1982.\n\nParkbeg History Book Group. _Parkbeg Reflections_. Regina: W.A. Print Works Ltd., 1982.\n\nPatterson-Black, Sheryl. \"Women Homesteaders on the Great Plains Frontier.\" _Frontiers_ 1 (Spring 1976): 67\u201388.\n\nPaul, Mandy, and Robert Foster. \"Married to the Land: Land Grants to Aboriginal Women in South Australia, 1848\u20131911.\" _Australian Historical Studies_ 34, no. 121 (April 2003): 48\u201368.\n\nPerry, Adele. \"Women, Racialized People, and the Making of the Liberal Order in Northern North America.\" In _Liberalism and Hegemony: Debating the Canadian Liberal Revolution_ , edited by Jean-Fran\u00e7ois Constant and Michel Ducharme, 274\u2013297. Toronto: University of Toronto Press, 2009.\n\nPeters, Virginia Bergman. _Women of the Earth Lodges: Tribal Life on the Plains._ Norman: University of Oklahoma Press, 1995.\n\nPickles, Katie. _Female Imperialism and National Identity: Imperial Order Daughter of the Empire._ Vancouver: UBC Press, 2002.\n\nPleasantdale and District History Book Committee. _Memories of the Past: History of Pleasantdale, Silver Park, Chagoness, and Kinistino Indian Band #91_. Pleasantdale, SK: Pleasantdale and District History Book Committee, 1981.\n\nPollock, Gwen. _Our Pioneers_. Maple Creek, SK: South Western Saskatchewan Old Timers' Association, 1978.\n\nPotyondi, Barry. _In Palliser's Triangle: Living in the Grasslands 1850\u20131930_. Saskatoon: Purich Publishing, 1995.\n\nPreston, Rebecca. \"'Hope you will be able to recognize us': The Representation of Women and Gardens in Early Twentieth-Century British Domestic 'Real Photo' Postcards.\" _Women's History Review_ 18, no. 5 (November 2009): 781\u2013800.\n\nRanci\u00e9re, Jacques. _The Politics of Aesthetics: The Distribution of the Sensible._ London: Continuum, 2006.\n\nRees, Ronald. _New and Naked Land: Making the Prairies Home_. Saskatoon: Western Producer Prairie Books, 1988.\n\nRennie, Bradford James. _The Rise of Agrarian Democracy: The United Farmers and Farm Women of Alberta._ Toronto: University of Toronto Press, 2000.\n\nReyburn, Karen Ann. \"Blurring the Boundaries: Images of Women in Canadian Propaganda of World War I.\" MA thesis, University of Guelph, 1998.\n\nRichards, Irene Lawrence. \"The Story of Beautiful Plains,\" _Manitoba Historical Society Transactions_ 3 (1951\u201352). http:\/\/www.mhs.mb.ca\/docs\/transactions\/3\/beautifulplains.shtml.\n\nRichardson, Frances. \"Women Farmers of Snowdonia, 1750\u20131900.\" _Rural History_ 25, no. 2 (October 2014): 161\u201381.\n\nRichtik, James M. \"Manitoba Settlement 1870\u201386.\" PhD diss., University of Minnesota, 1971.\n\n\u2014. \"The Policy Framework for Settling the Canadian West, 1870\u20131880.\" _Agricultural History_ 49, no. 4 (Oct. 1975): 613\u201328.\n\nRiley, Glenda. _Inventing the American Woman: An Inclusive History_. Vol. 2, Since 1877. 2nd ed. Wheeling, IL: Harlan Davidson Inc., 1995.\n\nRiley, Mark. \"Bringing the 'Invisible Farmer' into Sharper Focus: Gender Relations and Agricultural Practices in the Peak District.\" _Gender, Place and Culture: A Journal of Feminist Geography_ 16, no. 6 (2009): 665\u201382.\n\nRoberts, Barbara. \"'A Work of Empire': Canadian Reformers and British Female Immigration.\" In _A Not Unreasonable Claim: Women and Reform in Canada, 1880s\u20131920s_ , edited by Linda Kealey, 185\u2013201. Toronto: The Women's Press, 1979.\n\nRoberts, Bev. _Miss D and Miss N: An Extraordinary Partnership: The Diary of Anne Drysdale._ Victoria: Australian Scholarly Publishing, 2009.\n\nRoche, Michael. \"World War One British Empire Discharged Soldier Settlement in Comparative Focus.\" _History Compass_ 9, no. 1 (2011): 1\u201315.\n\nRockwood-Woodlands Historical Society. _Rockwood Echoes: Ninety Years of Progress 1870\u20131960_. Steinbach, MB: Derksen Printers, 1960.\n\nRoe, Frank Gilbert. _\"Getting the Know-How\": Homesteading and Railroading in Early Alberta._ Edmonton: NewWest Press, 1982.\n\nRowbotham, Sheila _. A Century of Women: The History of Women in Britain and the United States._ London: Viking, 1997.\n\nRoy, R.H. \"A Berkhamstead Boy in the Foothills.\" _Alberta Historical Review_ 20, no. 3 (Summer 1972): 17\u201329.\n\nRussell, Peter A. _How Agriculture Made Canada: Farming in the Nineteenth Century_. Montreal, QC: McGill-Queen's University Press, 2012.\n\nSaugeres, Lisa. \"'She's Not Really a Woman, She's Half a Man': Gendered Discourses of Embodiment in a French Farming Community.\" _Women's Studies International Forum_ 25, no. 6 (2002): 641\u201350.\n\nSayer, Karen. _Women of the Fields: Representations of Rural Women in the Nineteenth Century_. Manchester and New York: Manchester University Press, 1995.\n\nSayers, Sean. Review of _The Politics of Aesthetics: The Distribution of the Sensible_ , by Jacques Ranci\u00e9re. _Culture Machine_ 1 1 0 1, 2005.\n\nSchmidt, John. _Growing Up in the Oil Patch._ Toronto: Dundurn Press, 1985.\n\nSchultz, John A. \"'Leaven for the Lump': Canada and Empire Settlement.\" In _Emigrants and Empire: British Settlement in the Dominions between the Wars_ , edited by Stephen Constantine, 121\u201349. Manchester and New York: Manchester University Press, 1990.\n\nScully, Pamela. \"White Maternity and Black Infancy: The Rhetoric of Race in the South African Women's Suffrage Movement, 1895\u20131930.\" In _Women's Suffrage in the British Empire: Citizenship, Nation and Race_ , edited by Ian Christopher Fletcher, Laura E. Nym Mayhall, and Philippa Levine, 68\u201383. London and New York: Routledge, 2000.\n\nSeaton, Beverly. \"The Garden Autobiography.\" _Garden History_ 7, no. 1 (Spring 1979): 101\u201320.\n\nSedgewick Historical Society. _Sedgewick Sentinel: A History of Sedgewick and Surrounding District._ Sedgewick, AB: Sedgewick Historical Society, 1982.\n\nShannon, Bill. \"Brokers, Land Bankers, and 'Birds of Evil Omen': The Effect of Land Policies on Settlement in Upper Canada Collingwood Township 1834\u20131860.\" MA thesis, University of Ottawa, 1989.\n\nShepard, R. Bruce. _Deemed Unsuitable: Blacks from Oklahoma Move to the Canadian Prairies in Search of Equality in the Early 20th Century Only to Find Racism in Their New Home._ Toronto: Umbrella Press, 1997.\n\nShteir, Ann B. _Cultivating Women, Cultivating Science: Flora's Daughters and Botany in England, 1760\u20131860_. Baltimore and London: Johns Hopkins University Press, 1996.\n\nSmith, David. \"Instilling British Values in the Prairie Provinces.\" In _Immigration and Settlement, 1870\u20131939_ , edited by Gregory P. Marchildon, 441\u2013456 _._ Regina: Canadian Plains Research Center, 2009.\n\nSmith, Keith C. _Liberalism, Surveillance, and Resistance: Indigenous Communities in Western Canada, 1877\u20131927_. Edmonton: Athabasca University Press, 2009.\n\nSmith, Michelle. \"Adventurous Girls of the British Empire: The Pre-War Novels of Bessie Marchant.\" _The Lion and the Unicorn_ 33, no. 1 (January 2009): 1\u201325.\n\nSmith, Minnie. _Is It Just?_ 1911. Reprint with a critical introduction by Jenny Roth and Lori Chambers. Toronto: University of Toronto Press, 2011.\n\nSmith, Sherry. \"Single Women Homesteaders: The Perplexing Case of Elinore Pruitt Stewart.\" _Western Historical Quarterly_ 22 (May 1991): 163\u201383.\n\nSonningdale Recreation Board. _Sonningdale Memories, 1900\u20131980_. Sonningdale, SK: Sonningdale Recreation Board, 1982.\n\nSpender, Dale. _Writing a New World: Two Centuries of Australian Women Writers_. Sydney: Allen and Unwin Australia, 1998.\n\nStamm, Marianne. \"I Am... a Farmer.\" In _Country Roads: Memoirs from Rural Canada_ , edited by Pam Chamberlain. Halifax: Nimbus Publishing, 2010.\n\nStansell, Christine. _City of Women: Sex and Class in New York, 1789\u20131860._ Urbana: University of Illinois Press, 1987.\n\nStead, Robert J.C. \"Fifty Years in Western Canada: A Sketch of the Career of John Sanderson, the First Homesteader in Western Canada.\" _Better Farming_ , May 1923, 4\u20135.\n\nStone Diggers Historical Society. _Prairie Wool: A History of Climax and Surrounding School Districts_. Climax, SK: Stone Diggers Historical Society, 1980.\n\nStrange, Carolyn. _Toronto's Girl Problem: The Perils and Pleasures of the City, 1880\u20131930._ Toronto: University of Toronto Press, 1995.\n\nStrong-Boag, Veronica. \"Making a Difference: The History of Canada's Nurses.\" _Canadian Bulletin of Medical History_ 8 (1991): 231\u201348.\n\nTaylor, Jeffery M. _Fashioning Farmers: Ideology, Agricultural Knowledge, and the Manitoba Farm Movement, 1890\u20131925._ Regina: Canadian Plains Research Center, 1994.\n\nThompson, Jane Reid, \"'A Stronger and More Independent Self': Single, Middle-Class British Women Emigrants to the Canadian West, 1880\u20131930.\" PhD diss., University of Toronto, 2000.\n\nTosh, John. _Manliness and Masculinities in Nineteenth-Century Britain: Essays on Gender, Family and Empire._ London: Pearson, Longman, 2005.\n\nTough, Frank, and Kathleen Dimmer. \"'Great Frauds and Abuses': Institutional Innovation at the Colonial Frontier of Private Property: Case Studies of the Individualization of Maori, Indian and Metis Lands.\" In _Settler Economies in World History_ , edited by Christopher Lloyd, Jacob Metzer, and Richard Sutch, 205\u201349. Leiden; Boston: Brill, 2013.\n\nTrigger, Bruce G. _The Huron: Farmers of the North._ 2nd ed. Toronto: Holt, Rinehart and Winston, 1990.\n\nTroper, Harold Martin. _Only Farmers Need Apply: Official Canadian Government Encouragement of Immigration from the United States, 1896\u20131911_. Toronto: Griffin House, 1972.\n\nTurner, Nancy J. _Ancient Pathways, Ancestral Knowledge: Ethnobotany and Ecological Wisdom of Indigenous Peoples of Northwestern North America._ Vol. 1. Montreal: McGill-Queen's University Press, 2014.\n\nTwinch, Carol. _Women on the Land: Their Story during Two World Wars_. Cambridge: Lutterworth Press, 1990.\n\nTyman, John L. \"Patterns of Western Settlement.\" _Manitoba Historical Society Transactions_ 3, no. 28 (1971\u201372). http:\/\/www.mhs.mb.ca\/docs\/transactions\/3\/landsettlement.shtml.\n\nValverde, Mariana. _The Age of Light, Soap and Water: Moral Reform in English Canada, 1885\u20131925_. Toronto: University of Toronto Press, 2008.\n\nVeldhuis, Oriole A. Vane. _For Elise: Unveiling the Forgotten Woman on the Criddle Homestead._ Winnipeg: Oriole A. Vane Veldhuis, 2012.\n\nVenne, Sharon. _Indian Acts and Amendments 1868\u20131975: An Indexed Collection_. Saskatoon: University of Saskatchewan Native Law Centre, 1981.\n\nVeracini, Lorenzo. \"'Settler Colonialism': Career of a Concept.\" _The Journal of Imperial and Commonwealth History_ 41, no. 2 (2013): 567\u2013583.\n\nVerdon, Nicola. \"Middle-Class Women's Work and the Professionalization of Farming in England, 1890\u20131939.\" _Journal of British Studies_ 51, no. 2 (April 2012): 393\u2013415.\n\n\u2014 \"The 'Lady Farmer': Gender, Widowhood and Farming in Victorian England.\" In _The Farmer in England 1650\u20131980_ , edited by Richard W. Hoyle, 241\u2013262. London and New York: Routledge, 2013.\n\n\u2014. _Rural Women Workers in Nineteenth-Century England: Gender, Work and Wages._ Woodbridge: Suffolk Press, 2002.\n\nVicinus, Martha. _Independent Women: Work and Community for Single Women,_ _1850\u20131920_. Chicago: Virago Press, 1985.\n\nWaddell, James McKercher. _Dominion City: Facts, Fiction and Hyperbole._ Steinbach, MB: Derksen Printers, 1970.\n\nWalker-Kuntz, Sunday Anne. \"Land, Life and _Feme Sole_ : Women Homesteaders in the Yellowstone River Valley, 1909\u20131934.\" MA thesis, Montana State University, 2006.\n\nWalkowitz, Judith R. _City of Dreadful Delight: Narratives of Sexual Danger in Late Victorian London_. Chicago: University of Chicago Press, 1992.\n\nWanhalla, Angela. _Matters of the Heart: A History of Interracial Marriage in New Zealand._ Auckland: Auckland University Press, 2013.\n\nWatkins, Francine, and Ann Jacoby. \"Is the Rural Idyll Bad for Your Health? Stigma and Exclusion in the English Countryside.\" _Health and Place_ 13 (2007): 851\u201364.\n\nWeaver, John. _The Great Land Rush and the Making of the Modern World, 1650\u20131900._ Montreal: McGill-Queen's University Press, 2003.\n\nWebb History Book Committee. _Prairie Memories._ Steinbach, MB: Derksen Printers, 1982.\n\nWhite, Bonnie J. \"Remembrance, Retrospection, and the Women's Land Army in World War I Britain.\" _Journal of the Canadian Historical Association_ 22, no. 2 (2011): 162\u201394.\n\n\u2014. _The Women's Land Army in First World War Britain_. Houndmills, Basingstoke, Hampshire: Palgrave Macmillan, 2014.\n\nWilden, Anthony. _Man and Woman, War and Peace: The Strategist's Companion_. London and New York: Routledge and Kegan Paul, 1987.\n\nWildenthal, Lora. \"'She is the Victor': Bourgeois Women, Nationalist Identities and the Ideal of the Independent Woman Farmer in German Southwest Africa.\" _Social Analysis_ 33 (September 1993): 68\u201388.\n\nWilson, Catharine Anne. \"Manly Art: Plowing, Plowing Matches and Rural Masculinity in Ontario 1800\u20131930.\" _The Canadian Historical Review_ 95, no. 2 (June 2014): 157\u201386.\n\nWolfe, Patrick. \"Settler Colonialism and the Elimination of the Native.\" _Journal of Genocide Research_ 8, no. 4 (December 2006): 387\u2013409.\n\nWood Mountain Historical Society. _They Came to Wood Mountain._ Wood Mountain, SK: Wood Mountain Historical Society, n.d.\n\nWorsnop, Judith. \"A Reevaluation of 'The Problem of Surplus Women' in 19th-Century England: The Case of the 1851 Census.\" _Women's Studies International Forum_ 13, no. 1\/2 (1990): 21\u201331.\n\nYarmie, Andrew. \"'I Had Always Wanted to Farm': The Quest for Independence by English Female Emigrants at the Princess Patricia Ranch Vernon, British Columbia, 1912\u20131920.\" _British Journal of Canadian Studies_ 16, no. 1 (2003): 102\u201325.\n\nYellow Lake History Group. _Treasured Memories_. Steinbach, MB: Derksen Printers, 1982.\n\nYoumans, Joyce M. \"Walker, Ethel (1861\u20131951).\" _GLBTQ_ Encyclopedia. http:\/\/www.glbtqarchive.com\/arts\/walker_e_A.pdf.\n\nYoung, Iris. _On Female Body Experience: \"Throwing Like A Girl\" and Other Essays._ Oxford: Oxford University Press, 2005.\n\n\u2014. \"Throwing Like a Girl: A Phenomenology of Feminine Body Comportment, Motility, and Spatiality.\" In _The Thinking Muse: Feminism and Modern French Philosophy_ , edited by Iris Young and Jeffner Allen, 51\u201370. Bloomington: Indiana University Press, 1989.\n\nZiff, Bruce, and Sean Ward. \"Squatters' Rights and the Origin of Edmonton Settlement.\" In _Essays in the History of Canadian Law: Volume 10, A Tribute to Peter N. Oliver_ , edited by Jim Phillips, R. Roy McMurtry, and John T. Saywell, 446\u2013468. Toronto: Osgoode Society for Legal History, 2008.\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzqtjr b/data_all_eng_slimpj/shuffled/split2/finalzzqtjr
new file mode 100644
index 0000000000000000000000000000000000000000..13d1486c07d637d38ae0c74899eb60aad81883ae
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzqtjr
@@ -0,0 +1,5 @@
+{"text":"\n\n# Copyright\n\nCopyright \u00a9 2017 by Natalie Kossar\n\nIllustrations \u00a9 The McCall Pattern Company\n\nHachette Book Group supports the right to free expression and the value of copyright. The purpose of copyright is to encourage writers and artists to produce the creative works that enrich our culture.\n\nThe scanning, uploading, and distribution of this book without permission is a theft of the author's intellectual property. If you would like permission to use material from the book (other than for review purposes), please contact permissions@hbgusa.com. Thank you for your support of the author's rights.\n\nRunning Press\n\nHachette Book Group\n\n1290 Avenue of the Americas, New York, NY 10104\n\nwww.runningpress.com\n\n@Running_Press\n\nFirst Edition: October 2017\n\nPublished by Running Press, an imprint of Perseus Books, LLC, a subsidiary of Hachette Book Group, Inc.\n\nThe Hachette Speakers Bureau provides a wide range of authors for speaking events. To find out more, go to www.hachettespeakersbureau.com or call (866) 376-6591.\n\nThe publisher is not responsible for websites (or their content) that are not owned by the publisher.\n\nPrint book cover and interior design by Ashley Todd\n\nLibrary of Congress Control Number: 2017944791\n\nISBNs: 978-0-7624-6274-2 (print), 978-0-7624-6275-9 (ebook)\n\n1010\n\nE3-20170727-JV-PC\n\n# Contents\n\n  1. Cover\n  2. Title Page\n  3. Copyright\n  4. Dedication\n  5. Begin Reading\n  6. Acknowledgments\n\n# Navigation\n\n  1. Begin Reading\n  2. Table of Contents\n\nTO MOM & GRAM & GRAMMIE & GRUMS\n\n_And to the women before us who went unheard_\n\nI _absolutely cannot, under any circumstances, sew._ I just can't. When I was three years old my mom's sewing cabinet got knocked over and crashed onto me, sewing machine included. That was my first brush with sewing and I was not impressed. Subsequent attempts to engage with the threadly arts would prove equally disastrous. My mom and my grandma, bless them, went to great lengths to get me to enjoy something, anything, related to sewing. None of it took.\n\nMy mom brought me and my brother to fabric stores and encouraged us to pick out patterns and fabrics that we liked. It was fun for a while, but we got bored and would beg to leave. She pored over the catalogs and pattern drawers for what felt like hours. Eventually we learned that yarn skeins made good makeshift footballs, so we practiced our running patterns through the aisles, pretending to be Kordell Stewart and Jerome Bettis. He was Slash and I was The Bus.\n\nInspired by my yarn antics, my mom signed me up for a knitting club. It was held on Wednesday nights and led by the Chaplain's wife. The other girls were delighted to make complex winter hats and multicolored washcloths. I made one cat scarf* and called it quits.\n\nThe following summer, my grandma pulled me out of a literal woodpile to get my colors done. I reluctantly sat on the edge of her bed while she plopped fabric swatches onto my shoulders to see what season paired best with my complexion. She announced that I was \"a summer\" and politely suggested I wear something other than my dad's military undershirts. I asked if I could go back outside.\n\nSo. Despite a solid effort from Mom and Grums, I simply wasn't interested in sewing. I preferred to spend my time pretending to be a horse, or building forts out of scrap wood, or collecting live nightcrawlers from the backyard and feeding them to Barbles, my pet catfish. Girls who liked sewing were weak and boring. And I refused to be one of them.\n\nTwenty years later, I got an email from my mom asking me to help her find an old sewing pattern. Like a good millennial, I took to Google and ran a quick image search. Hundreds\u2014 _hundreds_ \u2014of vintage sewing patterns flooded my computer screen, and I was instantly transported to the plastic chairs of fabric stores and running the zig-zag plays of yarn football.\n\nSome of the images were from my mother's childhood (an era I've coined _polyesteryear_ ), some were from my grandma's youth, and many were from much earlier. Vintage patterns for men, women, and children dating back to the 1920's had been scanned and used as images in blogs or placed for sale\u2014all right there online. The drawings were certainly _of a time_ ; demonstrating outdated social ideals of gender or race or class structure. I was both delighted and horrified by what was considered acceptable even thirty years ago. The juxtaposition of the vintage images with modern dialogue generated a strong message of social growth and change. I captioned a few of the images and sent them to a handful of friends who agreed and encouraged me to keep going.\n\nPerhaps most importantly, the packets presented themselves in a new light. The women posed on the covers no longer seemed vapid, demure, or girly. I suddenly saw past the traditional notions of femininity\u2014notions I spent a lifetime rejecting\u2014and saw my foremothers as they truly were. These women were powerful. These women were complicated. These women had something to say.\n\nSo here I am, writing a book about sewing. Here I am researching a subject I once abhorred; burying myself in the patterns I couldn't escape as a kid. I am finally connecting to the world my mom and grandma share; the world they wanted to share with me since I was born. And I am glad to share in it. In my own woodpile, cat scarf, horsechild way.\n\nPlease enjoy.\n\n\u2014Natalie Kossar\n\n* _A cat-sized scarf, designed to be worn by cats._\n\nThanks first to one hundred Nicoles;\n\nTo Nicole Tourtelot, my amazing agent at DeFiore and Company, who is sharp and cool and always knows exactly what to say. She has permission to speak on my behalf even when I am very dead.\n\nI know what a literary agent is, Nicole.\n\nThanks to Nicole Chung, Nicole Cliffe, and Mallory Ortberg for being the first to agree to publish me on their brilliant website, www.the-toast.net, which is now defunct by total coincidence.\n\nThanks to my editor Jennifer Kasius from Running Press for taking a chance on me. And to my entire team at Running Press, for their enthusiasm and kindness. Thank you all for your patience with my technological incompetencies, which are many.\n\nThanks to Janet Wolfe, Stacey Long, and Meg McDonald at the McCalls Pattern Company, for agreeing to partner with me, for accommodating my research, and for making sure I wasn't locked in the closet during the fire drill.\n\nSeveral people leapt at the opportunity to help me during research; Tamara Nolte graciously hosted me in Brooklyn. Maia Wynn was my dog's handmaiden and is a top-notch cohabitator. Leonard Madrid and Stephanie Graner both gave me scanners to use, and I only broke one (sorry Stef). Jayme Swalby drove me to the airport and also hit me with her car.\n\nThanks to my attorneys, Josiah Jenkins and Michael Powalisz, who've had my back from the beginning, and let me abuse attorney-client privilege as an excuse to talk about relationships.\n\nThanks to the drunken misfit weirdos in the Chicago improv\/sketch community between 2006 and 2016. You developed, supported, and amplified a voice I knew existed but was afraid to use. You are my heart.\n\nM. Molly Backes (@mollybackes) not only forged a path, but installed lights and directions along the way. She was a tireless cheerleader and validator, and I would not have made it without her.\n\nSarah Armstrong (@oohsarahcuda) came out of nowhere and supported me in all of the right ways. If you're working on a project\u2014I'm telling you\u2014you want her on it.\n\nRobin Babb (@cixxxous) is an outstanding friend and editor (frienditor?). Thanks for the pink 100s.\n\nFinally, my unending thanks to Alex Garday, Nathan Jansen, Eric Lindberg, Eric Muller, Leslie Nesbit, Robert Perez, Nick Semar, and Sean Sullivan, who are my muses.\n\nAnd to Eileen Backes, Megan Backes, Katie Dufresne, Lisa Linke, and Jessie Stegner, who are my solid ground.\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \nContents\n\nCover\n\nHalf Title page\n\nTitle page\n\nCopyright page\n\nNotes on Contributors\n\nIntroduction\n\nNotes\n\nChapter 1: Imagining Cihuacoatl: Masculine Rituals, Nahua Goddesses and the Texts of the Tlacuilos\n\nSeparating gender from sexuality: the Nahua case\n\nThe Tlacuilo's text\n\nThe god(dess) Cihuacoatl\n\nThe god(dess) Coyolxauhqui\n\nThe fertility god(desse)s\n\nThe colonial death of the god(dess)\n\nRemembering Cihuacoatl\n\nNotes\n\nChapter 2: Power and Historical Figuring: Rachael Pringle Polgreen's Troubled Archive\n\nNotes\n\nChapter 3: Gender, Sexuality and the Formation of Racial Identities in the Eighteenth-Century Anglo-Caribbean World\n\nStructuring the colour lines in a British Caribbean slave society\n\nThe cultural application of meaning: maintaining a 'white' British identity\n\nThe practice of everyday life: race mixing on the periphery\n\nIndividual subjectivity: Jonathan Troup and the process of identification\n\nNotes\n\nChapter 4: Xing: The Discourse of Sex and Human Nature in Modern China\n\nKeywords, globalisation and translation\n\nXing as human nature\n\nFrom the obscene to the natural?\n\nTracing xing\n\nJapanese connections and return graphic loans\n\nConclusion\n\nGlossary\n\nNotes\n\nChapter 5: Epistemic Modernity and the Emergence of Homosexuality in China\n\nHistoriographical rationale\n\nMaking truth public\n\nCompeting authorities of truth\n\nIntellectual translation and disciplinary consolidation\n\nEast Asian scientia sexualis and the birth of a nationalistic style of argumentation\n\nNotes\n\nChapter 6: Overcoming 'Simply Being': Straight Sex, Masculinity and Physical Culture in Modern Egypt\n\nBetween pedagogic and performative modernity: the subject of Physical Culture\n\nBeyond pedagogic and the performative modernity: the limit of Physical Culture\n\nConclusion\n\nNotes\n\nChapter 7: Monitoring and Medicalising Male Sexuality in Semi-Colonial Egypt\n\nThe Egyptian context\n\nMonitoring male sexuality\n\nThe medicalisation of marriage\n\nGendering the law, sexualising its subjects\n\nConclusions: application and aftermath\n\nNotes\n\nChapter 8: The Volatility of Sex: Intersexuality, Gender and Clinical Practice in the 1950s\n\nDiagnosis\n\nTreatment\n\nManagement\n\nConclusion\n\nNotes\n\nChapter 9: 'A Certain Amount of Prudishness': Nudist Magazines and the Liberalisation of American Obscenity Law, 1947\u201358\n\n'Sunshine and Health'\n\nA prudish legal strategy\n\n'It is filthy, it is foul, it is obscene'\n\n'Gray can be a very drab and dirty color'\n\nNotes\n\nChapter 10: Cold War Conflicts and Cheap Cabaret: Sexual Politics at the 1975 United Nations International Women's Year Conference\n\nThe IWY scenario and anti-imperialist hauntology\n\nBetty Friedan and the cultivation of unity\n\nNancy C\u00e1rdenas and cheap cabaret\n\nDomitila Barrios de Chungara and the family drama\n\nApocrypha and excess in IWY accounts\n\nNotes\n\nChapter 11: Gender and Sexuality in Latina\/o Miami: Documenting Latina Transsexual Activists\n\nBorderlands between transgender and gay\n\nTAO and involvement of Latinas\n\nTranssexual Latina\n\nNotes\n\nIndex\nHistoricising Gender and Sexuality\nGender and History Special Issue Book Series\n\nGender and History, an international, interdisciplinary journal on the history of femininity, masculinity, and gender relations, publishes annual special issues which are now available in book form.\n\nBringing together path-breaking feminist scholarship with assessments of the field, each volume focuses on a specific subject, question or theme. These books are suitable for undergraduate and postgraduate courses in history, sociology, politics, cultural studies, and gender and women's studies.\n\nTitles in the series include:\n\nHistoricising Gender and Sexuality  \nEdited by Kevin P. Murphy and Jennifer M. Spear\n\nHomes and Homecomings: Gendered Histories of Domesticity and Return  \nEdited by K. H. Adler and Carrie Hamilton\n\nGender and Change: Agency, Chronology and Periodisation  \nEdited by Alexandra Shepard and Garthine Walker\n\nTranslating Feminisms in China  \nEdited by Dorothy Ko and Wang Zheng\n\nVisual Genders, Visual Histories: A special Issue of Gender & History  \nEdited by Patricia Hayes\n\nViolence, Vulnerability and Embodiment: Gender and History  \nEdited by Shani D'Cruze and Anupama Rao\n\nDialogues of Dispersal: Gender, Sexuality and African Diasporas  \nEdited by Sandra Gunning, Tera Hunter and Michele Mitchell\n\nMaterial Strategies: Dress and Gender in Historial Perspective  \nEdited by Barbara Burman and Carole Turbin\n\nGender, Citizenships and Subjectivities  \nEdited by Kathleen Canning and Sonya Rose\n\nGendering the Middle Ages: A Gender and History Special Issue  \nEdited by Pauline Stafford and Anneke B. Mulder-Bakker\n\nGender and History: Retrospect and Prospect  \nEdited by Leonore Davidoff, Keith McClelland and Eleni Varikas\n\nFeminisms and Internationalism  \nEdited by Mrinalini Sinha, Donna Guy and Angela Woollacott\n\nGender and the Body in the Ancient Mediterranean  \nEdited by Maria Wyke\n\nGendered Colonialisms in African History  \nEdited by Nancy Rose Hunt, Tessie P. Liu and Jean Quataert\n\nThis edition first published 2011  \nOriginally published as Volume 22, Issue 3 of Gender & History  \n\u00a9 Blackwell Publishing Ltd 2011\n\nBlackwell Publishing was acquired by John Wiley & Sons in February 2007. Blackwell's publishing program has been merged with Wiley's global Scientific, Technical, and Medical business to form Wiley-Blackwell.\n\nRegistered Office  \nJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom\n\nEditorial Offices  \n350 Main Street, Malden, MA 02148-5020, USA  \n9600 Garsington Road, Oxford, OX4 2DQ, UK  \nThe Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK\n\nFor details of our global editorial offices, for customer services, and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com\/wiley-blackwell.\n\nThe right of Kevin P. Murphy and Jennifer M. Spear to be identified as the authors of the editorial material in this work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988.\n\nAll rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.\n\nWiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.\n\nDesignations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.\n\nLibrary of Congress Cataloging-in-Publication Data\n\nHistoricising gender and sexuality \/ edited by Kevin P. Murphy, Jennifer M. Spear.  \np. cm. \u2013 (Gender and history special issue book series)  \n\"Originally published as Volume 22, Issue 3 of Gender & History.\"  \nIncludes bibliographical references and index.  \nISBN 978-1-4443-3944-4 (pbk.) \u2013 ISBN 978-1-4443-4392-2 (ePDF) \u2013 ISBN 978-1-4443-4395-3 (Wiley Online Library) \u2013 ISBN 978-1-4443-4393-9 (ePub) \u2013 ISBN 978-1-4443-4394-6 (Mobi)  \n1. Gender identity\u2013History. 2. Sex\u2013History. I. Murphy, Kevin P.,1963- II. Spear, Jennifer M.,  \n1967-HQ1075.H577 2011  \n306.701\u2013dc22\n\n2011014941\n\nThis book is published in the following electronic formats: ePDFs (9781444343922); Wiley Online Library (9781444343953); ePub (9781444343939); Mobi (9781444343946)\nNOTES ON CONTRIBUTORS\n\nKevin P. Murphy received his Ph.D. in history from New York University in 2001. He is associate professor of history at the University of Minnesota. His book, Political Manhood: Red Bloods, Mollycoddles, and the Politics of Progressive Era Reform, was published in 2008.\n\nJennifer M. Spear teaches early American history at Simon Fraser University. She is the author of Race, Sex, and Social Order in Early New Orleans (Johns Hopkins University Press, 2009) and several articles exploring race, gender, and sexuality in early North America, especially those regions colonised by France and Spain.\n\nPete Sigal is an associate professor of Latin American history at Duke University. He is the author of From Moon Goddesses to Virgins: The Colonization of Yucatecan Maya Sexual Desire (2000) and editor of Infamous Desire: Male Homosexuality in Colonial Latin America (2003). Most recently, as a participant in a forum on 'transnational sexualities', he published an article in the American Historical Review 114\/5 (2009), 'Latin America and the Challenge of Globalizing the History of Sexuality'. He is currently completing a study on the interaction of writing and sexual representation in sixteenth- and seventeenth-century Nahua societies (The Flower and the Scorpion: Sexuality in Early Nahua Culture and Society, Duke University Press, forthcoming).\n\nMarisa J. Fuentes completed her doctorate in the department of African American studies at Berkeley in 2007. She is an assistant professor at Rutgers University, in the departments of history and women's and gender studies. Her current book project explores the spatial, historical and symbolic confinement enslaved women experienced in eighteenth-century Bridgetown, Barbados.\n\nBrooke N. Newman has just completed research fellowships at the Rothermere American Institute at the University of Oxford and the Gilder Lehrman Center for Slavery, Abolition, and Resistance at Yale University. She is the co-editor of Native Diasporas: Settler Colonialism and Indigenous Identities in the Americas (forthcoming, University of Nebraska Press, 2011), and is currently at work on a book exploring mastery and the Anglo-West Indian connection during the age of slavery.\n\nLeon Antonio Rocha is D. Kim Foundation for the History of Science and Technology in East Asia postdoctoral fellow at the Needham Research Institute and the department of history and philosophy of science, University of Cambridge.\n\nHoward Chiang is a doctoral student in the department of history at Princeton University and a former visiting research student at the Institute of Modern History, Academia Sinica in Taipei, Taiwan, the Needham Research Institute in Cambridge and the Wellcome Trust Centre for the History of Medicine at University College London. His thesis, 'China Trans Formed', tells a critical history of sex change and sexology in modern China. He is currently completing an edited volume on 'Transgender China: Embodied Histories and the Trans Locations of Culture' and a co-edited volume on 'Queer Sinophone Cultures' (with Larissa Heinrich).\n\nWilson Chacko Jacob obtained his doctorate from the departments of history and Middle East and Islamic studies at New York University in 2005. He teaches in the history department at Concordia University in Montreal. His forthcoming book from Duke University Press is entitled Working Out Egypt.\n\nHanan Kholoussy is assistant professor of history and Middle East studies in the department of history at the American University in Cairo. She is the author of For Better, for Worse: The Marriage Crisis that Made Modern Egypt (2010) as well as a number of articles on gender, nationalism and law in modern Egypt.\n\nSandra Eder is a doctoral student in the history of medicine at Johns Hopkins University. Her thesis, 'The Birth of Gender: Intersexuality, Gender, and Clinical Practice in the 1950s', for which she received a Woodrow Wilson Women's Studies Fellowship, examines clinical practices around the conceptualisation of gender through the treatment of intersexual patients.\n\nBrian Hoffman completed his doctorate in history at the University of Illinois, Urbana\u2013Champaign. A version of this article won the 2007 Gender & History Graduate Student Essay Prize awarded at the Eighth Annual Graduate Symposium on Women's and Gender History held at the University of Illinois, Urbana\u2013Champaign. His thesis is titled 'Making Private Parts Public: American Nudism, 1929\u20131963'. He recently joined the department of anthropology, history and social medicine at the University of California at San Francisco as a post-doctoral fellow.\n\nJocelyn Olcott is an associate professor of history and women's studies at Duke University. She is the author of Revolutionary Women in Postrevolutionary Mexico (2005) and editor (with Gabriela Cano and Mary Kay Vaughan) of Sex in Revolution: Gender, Politics, and Power in Postrevolutionary Mexico (2006).\n\nSusana Pe\u00f1a is associate professor of ethnic studies at Bowling Green State University. Her publications include '\"Obvious Gays\" and the State Gaze: Cuban Gay Visibility and US Immigration Policy during the 1980 Mariel Boatlift' in Journal of the History of Sexuality (2007). She received a post-doctoral fellowship (AY 2004\u201305) from the Social Science Research Council's Sexuality Research Fellowship Program.\n\nIntroduction\n\nKevin P. Murphy and Jennifer M. Spear\n\nIn her influential 1984 essay, 'Thinking Sex: Notes Toward a Radical Theory of the Politics of Sexuality', Gayle Rubin asserted that 'although sex and gender are related, they are not the same thing, and they form the basis of two distinct arenas of social practice'. Building on this insight, and challenging the tendency of feminist theory to treat sexuality as derivative of gender, Rubin declared it 'essential to separate gender and sexuality analytically to reflect more accurately their separate social existence'.1\n\nOver the past two decades, historians writing across period and region have taken up Rubin's call to produce delineated analyses of 'sexuality' and 'gender'. Yet, these efforts have produced anything but a stable or coherent sense of how 'sexuality' and 'gender' have functioned throughout human history. Indeed, many scholars \u2013 especially those focusing on the pre-modern and non-western worlds \u2013 have productively questioned the conceptualisation of and distinction between these categories, some demonstrating that sexual desire and practices have intersected with gendered identities and norms in complicated, sometimes inextricable, ways.2 Likewise, scholarship on the history of homosexuality in the modern west has shown that identity categories such as 'homosexual' and 'lesbian' have been defined not only in relation to sexual object choice and sexual role, but also in relation to gender performance.3\n\nThe scholarship in this book takes up anew the question of the intersections between gender and sexuality. Many of the authors conclude that the constructions, practices and experiences of gender and sexuality are far more entangled and mutually constitutive than the formulation in 'Thinking Sex' intimates. Yet we would argue that it was precisely Rubin's call to refuse to subordinate sexuality under the rubric of gender that has enabled the explorations that these chapters engage in. Covering a wide range of contexts \u2013 from sixteenth-century New Spain to late twentieth-century Miami, Chinese sexology to American nudist magazines, free women of colour in the British Caribbean to Egyptian reformers \u2013 these chapters demonstrate the particularities not just of specific formulations of gender and sexuality in different historical contexts, but also of the very nature of the relationship between the categories themselves.\n\nThe volume begins with three chapters set in the colonial Americas that highlight the productivity of rethinking these issues in contexts that were profoundly shaped by cross-cultural encounters, which often highlighted the very contingency of conceptions of gender and sexuality and also led to their transformation.4 Pete Sigal's contribution is an examination of Cihuacoatl and other Nahua deities who combined masculine and feminine attributes, demonstrating the historical and cultural specificity of configurations of gender and sexuality. In pre-conquest Nahua culture, Cihuacoatl was simultaneously 'a feared deity, a defeated woman, and a cross-dressed man'. Spanish priests were confused by this 'jumble of attributes, skins that could be taken off or placed on at will', and sought to make sense of Cihuacoatl by reducing her to what they considered her essential self: 'only the feared goddess'. Unable to comprehend a deity who combined masculine and feminine attributes, who could both kill and heal, the priests' binary concepts of male and female, death and curing, overwhelmed the complex multiplicities of deities like Cihuacoatl, stripping them of contradictory attributes into simplistically coded figures comprehensible within a European Catholic worldview.\n\nPriests are not the only ones to have been challenged by Cihuacoatl's combination of masculine and feminine attributes. Scholars have struggled to make sense of her place in pre-conquest Nahua society (seen as organised around a strict gender division and hierarchy). It was not just the boundary between male and female that Cihuacoatl blurred; she also traversed the boundaries between the human and the divine, the secular and the religious, the chaste and the sexual. Yet the transgressions that Cihuacoatl and other Nahua deities were capable of, as well as those of the humans operating within a ritual sphere, were not acceptable practices of everyday life but were restricted to the divine and ritual realms. Rather than seeking Cihuacoatl's 'true sex', Sigal uses Cihuacoatl's 'jumble of attributes' to rethink Rubin's emphasis on the need to treat gender and sexuality as analytically distinct categories requiring their own tools of analysis. Sigal demonstrates that it is impossible to treat these as conceptually distinct categories for non-western peoples (and by extension pre-modern ones) without imposing western conceptions of sexuality and gender upon them.\n\nNahua 'categories of the intimate' (a rubric that Sigal contends better encapsulates their cultural conceptions than 'sexual') grouped together a wide range of activities \u2013 from vaginal and anal intercourse to burning maize \u2013 that we might not see as related and certainly not all as sexual or erotic. What linked these activities in the Nahua worldview was their relationship to fertility, a vital concern for these agriculturalists. Just as Rubin rejected the incorporation of 'sexuality' as a subset of 'gender', Sigal asks us to think carefully about presuming that fertility rituals and reproductive sex are necessarily a subset of 'sexual' categories. The Nahua, he argues, posited the reverse: they 'envisioned sexual relations as elements of a larger set of ritual practices designed to promote fertility: of gods, humans, animals and the earth'.\n\nIf fertility is the context for making sense of Nahua sexual practices, the next two chapters, by Marisa J. Fuentes and Brooke N. Newman, argue that sex in the Anglophone Caribbean in the eighteenth and nineteenth centuries cannot be understood apart from the racialised and gender power formations of colonial slave societies. Fuentes analyses the life and 'troubled archive' of Rachael Pringle Polgreen, 'a woman of colour, a former slave turned slave-owner' and owner of a brothel in the Barbadian capital of Bridgetown, while Newman centres on the articulation of a white Creole identity, its denigration by metropolitan observers, and the role of 'intimacy across the colour line' in both. For both Fuentes and Newman, Anglophone Caribbean slave societies cannot be explicated without attention to the ways in which both gender and sexuality were mobilised to define subjectivity, enable or constrain opportunity and legitimate colonial power regimes. For black women, whether enslaved, free or freed, their subjectivity as women was in great part defined by their sexual availability to white men whose masculinity was partially defined by their considerable sexual freedom and, in the sanctimonious opinion of metropolitan observers, their 'voracious appetite' for women of colour. These contributions demonstrate how colonial identities and the relations of power that defined colonial societies were constructed along the 'entangled axes of gender, sexuality and race'.\n\nGiven such power relations, enslaved and formerly enslaved women like Rachael Pringle Polgreen rarely make it into the archives and, when they do, it is most often as the object of the white male colonial gaze. In these respects, Polgreen was unusual. In addition to journalistic, editorial and fictional depictions of her life, she also left a will and newspaper advertisements, probably composed (if not actually penned) by herself, as well as documentation of her property ownership in an inventoried estate and tax records. As one of the few women of colour whose presence is discernable in the colonial archives, Polgreen has often stood in for the experience of enslaved and formerly enslaved women in Caribbean history. Yet it is precisely the same exceptionalism that renders her so visible to historians as a relatively wealthy, slave-owning, brothel-managing, former slave that leads Fuentes rightly to caution us against understanding her as representative of women of colour in slave societies, let alone those who spent their entire lives in slavery. Even so, as Fuentes's reading of Thomas Rowlandon's caricature of Polgreen reveals, Polgreen was, like all those women of colour, subjected to a colonial gaze that was simultaneously raced, gendered and sexualised.\n\nAs Newman demonstrates, it was not just enslaved and formerly enslaved women of African descent who were objects of this gaze. British observers of white Caribbean society were equally attentive to the racialised, gendered and sexualised differences they saw between themselves and their colonial counterparts. In particular, 'cross-racial unions, lineages and inheritance practices' as well as the admittedly rare inclusion of free people of African descent into the legal category of 'whiteness' were read by metropolitan observers as evidence of sexual excesses and 'physical and moral degeneration' from a metropolitan ideal of Britishness. In texts such as John Singleton's 1767 poem, A General Description of the West Indian Islands, white colonial men were depicted as 'overcome by dangerous passions' while their infidelities were blamed on their 'impetuous' and 'jealous' white wives. Newman profitably explores the contradictions between metropolitan and colonial gender norms through the private diary of Jonathan Troup, a Scottish physician who resided in Dominica between 1789 and 1791. Although Troup participated in the 'explicitly debauched, creolised version of British manhood' that included sexual access to women of colour, he ultimately committed himself 'to the stability and superiority of his own identity as a white metropolitan Briton'.\n\nAs these two contributions illustrate, at the heart of the particular racial and gendered relations that sustained Caribbean slave societies was white masculine access to the bodies of women of colour. The agency of those women has been a vexed question in the historiography of slave societies, one that both Fuentes and Newman tackle, although they reach different conclusions. For Newman, the possibility that some women of colour could wrest some advantages from such a disadvantaged position is embodied in the story of Susanna Augier, who successfully mobilised her relationships with white men \u2013 her father and two white consorts \u2013 to gain freedom, property and eventually legally inscribed whiteness for herself and her children. Newman carefully stresses how rare such incidents were, but these stories do reveal how such prospects were premised on the very social order that so disadvantaged women and subjected them to sexual exploitation in the first place. Fuentes is much more cautious in rendering actions like Augier's as expressions of agency and counsels us against seeing enslaved or free(d) women's agency in their sexual acquiescence to white men's sexual demands. Not only does such an interpretation downplay if not ignore the power dynamics that left enslaved black women wholly vulnerable in a racialised, patriarchal, slave society, it is also particularly difficult to reconcile the sense of heroic agency and resistance to slavery that has often been attributed to Polgreen with the narrative of her life since her wealth and security came from 'buying into a system of slavery', one that depended upon these 'hierarchies based on race and gender' and one that in Polgreen's case was based on the sexual exploitation of other black women.\n\nThese first chapters also highlight the interaction between systems of gender and sexuality that often took place in colonial or imperial contexts, as well as the reception and contestation of western concepts of gender and sexuality throughout the world. While Newman's Troup ultimately rejected a creolised British masculinity in favour of its metropolitan counterpart, Sigal's priests struggled, and eventually failed, to impose their European sexual mores onto a Nahua system that revolved around poles of moderation and excess rather than sin and salvation. Such metropolitan or western ideas were not always imposed from the outside, nor (as Sigal argues) were they always successful. The next chapter, by Leon Antonio Rocha, the first of two focused on modern China, examines the transnational flow of ideas about gender and sexuality in the twentieth century. Rocha reminds us that it is equally important to pay attention to the historical specificities and contestation of cultural exchange within modern regimes of globalisation. He asserts that we should never assume 'that people in the Third World merely copied, parroted, were \"interpellated\" by or inflicted with the discourse of the colonising Other'. Instead, he argues, 'globalisation [was] always already accompanied by localisation and indigenisation'.\n\nRocha's contribution provides just this kind of nuanced analysis of the globalisation of sexual knowledge through a tightly focused etymological analysis of xing, a character that meant 'human nature' in Classical Chinese but, in the first two decades of the twentieth century, came to denote both sex and human nature. This transformation was brought about by cosmopolitan Chinese intellectuals of the May Fourth New Culture period (c.1915\u201337), who consumed and translated the work of European, American and Japanese sexologists and sex education reformers, including the American birth control reformer Margaret Sanger and the German physician and homosexual rights advocate Magnus Hirschfeld. Rocha argues that radical Chinese intellectuals embraced the western notion of 'sex as fundamental property of humanity', a modern ideological development analysed by Foucault, as part of a broader project of Chinese nation-building in a period of massive upheaval. According to Rocha, '[s]ex became a panacea to China's weakness and degeneracy, and a revolution of the relationships between men and women, the reformulation of love and desire, the adoption of eugenics and birth control practices, were perceived as ways to enable the Chinese nation to \"catch up\" with the west and to become ready to participate in a global modernity'.\n\nHoward Chiang also analyses the profound transformative impact of western sexual science in modern China. His chapter examines the careers of two influential figures who shaped the field of Republican Chinese sexology, Zhang Jingsheng and Pan Guangdan, with the goal of illuminating 'the broader epistemic context in which the concept of homosexuality emerged as a meaningful point of referencing human difference and cultural identity in twentieth-century China'. Chiang argues that the engagement of Chinese intellectuals with western sexual scientific knowledge points to a broader transformation in the conceptualisation of 'personhood, subjectivity and identity'. Breaking with other historians, Chiang shows that homosexuality circulated in modern Chinese discourse not only as a signifier of social disorder, but as the marker of a new mode of subjectivity. He notes that although same-sex desire was discussed and regulated in imperial China, before the twentieth century 'the question of sexual identity did not even fall within the possible parameters of Chinese thinking'. Moreover, by closely examining the ways in which Zhang and Pan laid claim to sexuality as a legitimate field of empirical inquiry and debate, Chiang identifies the development of a modern epistemological regime, 'a public of truth, in which the authority of truth could be contested, translated across culture and reinforced through new organisational efforts'.\n\nLike Rocha, Chiang examines the ways in which this new form of sexual science became embedded within discourses of Chinese nationalism. By the mid-1930s, Chinese sexual experts, influenced by psychological models that pathologised same-sex desire, interpreted the prevalence of male homosexuality as evidence of national backwardness and therefore invoked the prevention of homosexuality as a pressing policy concern. Same-sex desire was now reconceived as antithetical to heterosexual relations, and some experts asserted that homosexuality could be cured through heterosexual marriage. Chiang calls attention to the gendered dimensions of these developments, demonstrating that women's maintenance of sexual hygiene played an important part in discouraging male homosexuality. He cites as an example Zhang's assertion that '[a]s long as women took good care of their vaginas and used them properly for sex... the \"perverted\", \"malodorous\", \"meaningless\" and \"inhumane\" behaviour of anal intercourse among men could be ultimately eliminated'.\n\nWhile Chiang's analysis focuses on the work of sexological experts, he also demonstrates that claims to expertise depended on a broader incitement to discourse, manifested in the collection of sexual narratives solicited from public audiences. Zhang, who issued a 'call for stories' that provided the material for his influential 1926 publication Sex Histories, also edited the popular magazine New Culture, which published the responses of Chinese urbanites to controversial articles on sexuality-related subjects and in which Zhang \u2013 who earned the moniker 'Dr Sex' \u2013 dispensed expertise to readers who shared their experiences and concerns. Wilson Chacko Jacob's contribution focuses on a similar history of the collaborative production of knowledge about sexuality and gender in modern Egypt. He offers a close reading of Physical Culture, a Cairo-based publication whose run extended from 1929 until the early 1950s. Jacob describes Physical Culture as 'an artefact of colonial modernity' that 'contributed to the vibrant public culture of the interwar period a forum in which the fantasy of the modern sovereign subject could be expressed in myriad ways that most frequently centred on a proper conception of sex and masculinity'. While readers' letters reflect a wide range of sexual concerns and practices, the primary educative function of the publication was to 'demonstrate the harms of sexual activity outside the legitimate bonds of marriage'. Expertise was marshalled to demonstrate the dangers of masturbation and venereal disease to the normative masculine body and a universalised model of heterosexuality, but Jacob shows that the production of 'an ostensibly seamless normative sphere of heterosocial and heterosexual life' developed gradually and unevenly through a process of 'creative adaptation'. Jacob suggests that this process ultimately involved rendering deviant and marginal figures like the khawal, cross-dressing male performers who had traditionally appeared at Egyptian wedding parties.\n\nThe contribution by Hanan Kholoussy examines a very different response to the same problem highlighted by Jacob. As Egypt moved towards independence from British colonialism, some Egyptian nationalists blamed their subjugation on 'the weak and sick bodies of Egyptian men'. While Jacob's protagonists, the publishers and readers of Physical Culture magazine, relied upon self-regulation and the 'culivati[on] of properly disciplined subjects', Kholoussy's reformers relied upon regulating male sexuality, so that husbands would not infect their wives and by extension their families. Both these solutions, however, were centred on constructing a normative, healthy and heterosexual male body.\n\nKholoussy's chapter, as well as the subsequent contribution by Sandra Eder, examine how gender and sexuality were inscribed on the body through constructions of what is healthy and normative, or diseased and in need of treatment. In their efforts to create a modern, post-colonial state, Egyptian reformers granted women the right to divorce husbands with venereal or other incurable diseases, thus medicalising marriage in the pursuit of 'creating a nationalist, nuclear, physically fit and \"modern\" family', While such a pro-family strategy was part and parcel of a global eugenics project at the turn of the twentieth century, Kholoussy argues that Egyptian uses of these strategies relied upon local inspiration for their legitimacy, especially since granting women a right to divorce was itself a challenge to Islamic patriarchy. Reformers pointed to a twelfth-century religious text which decreed that women could divorce husbands who suffered from maladies such as insanity, leprosy and 'disease of the sex organ', thus 'ingeniously borrow[ing] and combin[ing] principles from... Islamic law in an eclectic and unprecedented manner'.\n\nKholoussy also shows how the Egyptian semi-colonial state both echoed and was distinct from its British colonial predecessor, especially in its interest in regulating male as well as female sexuality. Between 1882 and 1922, in their efforts 'to protect the health of their military troops', British authorities focused their interventions on Egyptian prostitutes, subjecting them to registration requirements and weekly health inspections, while exempting their own soldiers from any regulations or inspections. Egyptian authorities, however, both before and after British occupation, demonstrated a willingness to expand the scope of their public health campaigns to monitor male and female heterosexuality. While the concern of the Ottoman Egyptian state was the production of 'industrious, physically fit bodies that would both increase agricultural production and strengthen military prowess', the semi-colonial state of the 1910s and 1920s focused its attention on the encouragement of healthy families, which in turn would produce healthy citizens.\n\nThe production of healthy citizens through medicalisation is also a central concern of Sandra Eder's contribution on the treatment of children with congenital adrenal hyperplasia (CAH) at the Harriet Lane Home for Invalid Children at Johns Hopkins University in Baltimore, Maryland in the mid-twentieth century. Caused by disorders in the adrenal glands, CAH often results in children experiencing premature signs of puberty: girls might have ambiguous, and boys 'precocious', genitalia. In diagnosing children with CAH, physicians and psychiatrists often emphasised sexual traits such as these as well as sexual behaviours. But the treatments they developed, while not ignoring the body, emphasised efforts to impose a gender identity that contained ambiguously sexed bodies and which were in great part about ensuring future heterosexual desires and practices. This was a disease whose identification depended upon the particularities of a sexed body, and whose treatment relied upon the cultivation of a normative gender role towards which the body's sex would be reshaped, all in the service of creating normatively gendered and sexualised citizens.\n\nThe diagnosis and treatment of CAH at Johns Hopkins is but one phase in the medicalisation of gender and sexuality in the modern west. Yet, as Eder's reading of these patient case records shows, it was one in which medical professionals were not always the most authoritative voices. As they struggled to assign a matching sex and gender to bodies that blurred the boundaries between male and female, man and woman, physicians could lose out to parents' insistence that their children's sex confirm the gender that they, the parents, had already determined and assigned. Her attention to the production of knowledge in the context of clinical practice \u2013 one that involved interactions among medical professionals, parents and children themselves \u2013 leads Eder to conclude that the contentious and protracted efforts to assign a 'true' or 'best' sex often resulted in the view that it was 'easier to fix ambiguous bodies than rigid gender roles' in the service of creating 'clearly gendered men and women', who were, in the eyes of their doctors, 'psychologically well-adjusted and functional' and who 'could \"live a normal life\"'.\n\nGender and sexuality are also revealed to be entangled and mutually constituted in the final section of this book, which comprises three chapters that focus on political and social activism in the twentieth century. Brian Hoffman's contribution examines the mid-century campaign by nudist movement leaders to challenge the 'modern obscenity regime' in the US. This campaign was spearheaded by the International Nudist Conference (INC), founded in 1933, which sought to position the nude body as healthy, natural and respectable, and asserted that the social experience of nakedness led to the promotion of more 'wholesome' relations between the sexes. INC's efforts to disseminate its beliefs through the publication of a monthly magazine, Sunshine and Health (S&H), which contained images of 'naked men, women and children of all body shapes and sizes', fell foul of federal obscenity law. In the series of legal challenges it mounted with the assistance of the American Civil Liberties Union in the 1940s and 1950s, INC chose not to attack obscenity law at its root, but rather to define its publication, and by extension the nudist movement, as distinct from and superior to commercialised representations of sexuality. To this end, Hoffman argues, INC promulgated a brand of sexual liberalism he defines as heteronormative. Although some consumers certainly found S&H to be an outlet for homoerotic fantasy, the magazine (with some exceptions) situated the respectable nude body within the context of the heterosexual reproductive family.\n\nHoffman's chapter demonstrates that the heteronormative ethos of the American nudist movement was produced through legal contestation between nudist movement activists, their legal representatives and the judiciary. This ethos was structured by categories of race and gender. For example, INC activists, the majority of whom were white, claimed that censorship of S&H amounted to anti-white discrimination, given that National Geographic and similar publications presented images of nude non-white bodies without legal censure. Hoffman shows that while nudist activists espoused racial liberalism, advocating 'integrated' nudist camps for example, some judges continued to insist on the legality of representing the 'primitive' non-white nude body as an appropriate anthropological subject. American judges also articulated distinctions among white gendered bodies, asserting that women's bodies that conformed to conventions of European female beauty might be read as respectable, whereas those that strayed from these conventions were to be considered obscene. Judges also made distinctions between the representation of men's and women's bodies, proving obstinately resistant to publishing images of male genitalia, for example. These gendered conventions regarding representations of the nude body have proven remarkably persistent (in material not marked as pornographic).\n\nThe historical production of heteronormativity also functions as an important theme in Jocelyn Olcott's contribution, which examines sexual politics at the 1975 United Nations International Women's Year (IWY) Conference in Mexico City, a 'watershed moment in transnational feminism'. Olcott's revelatory chapter focuses on the controversial discussions of sexual issues \u2013 namely prostitution, lesbianism and population control \u2013 at the conference and at the associated tribune attended by representatives of non-governmental organisations from throughout the world. Olcott argues that many Latin American participants \u2013 notably the Ecuadorean labour activist Domitila Barrios de Chungara \u2013 viewed the focus on sexual rights as a preoccupation of western feminists unconcerned with the materialist and anti-imperialist priorities of women from the global south. As Olcott notes, Barrios de Chungara and others who shared her views saw the concern with sexual rights as challenging traditional family structures and ideals, and responded with a 'definitive reassertion of gender complementarity and conventional heteronormative nuclear families'. The Mexican press also espoused this position; columnists asserted that North American radical lesbians and prostitutes' rights proponents pushed their agendas to the detriment of those advocating legitimate women's issues.\n\nYet, Olcott cautions the reader to reject a characterisation of these conflicts \u2013 espoused in many contemporary and retrospective accounts by participants and observers \u2013 as representing a clear-cut division between the sexual liberation agendas of western feminists who sought to challenge gender essentialism, and the economic and anti-colonialist imperatives of Marxist feminists who insisted on traditional norms of gender complementarity. To this end, she makes two important arguments. First, she shows that empowered North American feminists, notably Betty Friedan, the iconic leader of the National Organisation for Women, also proved resistant to the incursion of sexual causes at the IWY conference. As Olcott points out, Friedan, who saw herself as 'a broker and a model for feminists around the world', believed that these issues distracted from the important women's causes, such as equality in education and employment, that she prioritised. Indeed, Olcott's analytic focus on sexuality and sexual rights reveals that Friedan and Barrios de Chungara were in no way the antithetical figures that they have been imagined to be: 'Both expressed open homophobia and little patience with prostitutes' rights campaigns; both insisted that men and women collaborate rather than work against one another; and both blamed transnational corporations for women's continued oppression'.\n\nSecond, Olcott shows that, if Friedan and Barrios de Chungara 'stood in for the dominant official themes of equality and development' that animated the IWY conference, some non-western activists aggressively challenged such attempts to exclude sexuality and sexual rights from 'core' women's issues. She illuminates this second major argument by analysing the performance of Mexican theatre director Nancy C\u00e1rdenas, who led a participant-initiated forum on lesbianism, which featured 'Mexico's first lesbian manifesto, naming sexual recognition as a critical form of social liberation, tantamount to struggles against imperialism, apartheid and racism'. Olcott describes C\u00e1rdenas and other non-western lesbian feminists as embodying a form of 'cosmopolitan lesbianism' that countered nationalist maternalism and resisted 'assumptions of a zero-sum rivalry between sexual rights and human rights'. Olcott, in turn, cautions us not to map this oppositional structure onto our historical narratives of international feminist activism. Even if, as she suggests, 'a homophobic posture and antagonism toward sexual rights' continues in more recent iterations of anti-capitalist and anti-imperialist politics, she cautions us to pay attention to the political foundations of attempts to extract sexuality from women's rights and human rights causes, rather than to see this distinction as resulting from 'traditionalism, provincialism, or the conservative influence of the Catholic Church or the Communist Party \u2013 or even to a visceral or subconscious repugnance'.\n\nThe final contribution to this volume, Susana Pe\u00f1a's 'Gender and Sexuality in Latina\/o Miami: Documenting Latina Transsexual Activists', also emphasises the importance of historical specificity in analysing the relationship between gender and sexuality within activist movements. In this insightful and careful chapter, Pe\u00f1a grapples with a thorny question faced by historians more broadly: what are the implications of imposing contemporary analytical categories on historical actors in the past? This question has proven particularly challenging to historians studying the relationship between non-normative gender and sexuality, given the hegemony of western conceptions of homosexuality that fuse together in complicated ways a range of attributes and behaviours including gender performance, sexual object choice and sexual role. As Pete Sigal elucidates in the first chapter in this book, this problem is especially vexatious for scholars who do not focus on the modern western world, given vast differences in the organisation of gender and sexuality across time and place.\n\nPe\u00f1a confronts this question in a chapter that 'explores the borderlands between the concept of \"homosexual\" and \"transgender\" with a particular focus on Latina\/o communities in Miami, Florida' in the late twentieth century. Citing scholars Susan Stryker and David Valentine, Pe\u00f1a notes that 'transgender' is a relatively recent invention, gaining widespread usage only in the 1990s. While 'transgender' has often been invoked as a capacious and flexible category in the intervening years, its usage as a 'collective category of identity', according to Valentine, has been defined as 'explicitly and fundamentally different in origin and being from homosexual identification'. Responding to a critique of her previous work that focused on Cuban American gay male cultures in Miami after the Mariel Boatlift of 1980, Pe\u00f1a argues that to define the gender transgressive Cuban migrants as 'transgender' \u2013 a category that did not exist at the time \u2013 obscures the complexities of the interrelationship of gender and sexuality, even if some of the individuals involved have since come to define themselves as such. Indeed, Pe\u00f1a argues that many Marielitas (Cubans who arrived on the Mariel Boatlift) understood \u2013 and continue to understand \u2013 expressions of gender nonconformity as playing 'a central role in structuring homosexual\/queer self-identifications'.\n\nPe\u00f1a extends this analysis by examining the publications associated with the Transsexual Action Organisation (TAO), founded in Los Angeles in 1970 but based in Miami from 1972. TAO activists included a significant number of Latinas, whose experiences are recorded in a number of publications associated with the organisation. The active participation of Latinas in TAO occurred despite the racist narratives produced by its eccentric founder and leader, Angela Douglas, who, Pe\u00f1a argues, viewed 'Cubans and Latinas with both a desiring and despising gaze'. Pe\u00f1a's analysis yields a number of important insights with regard to the historical contingencies of sexuality and gender. First, she shows that, in one sense, TAO activists might be understood to be progenitors of the transgender movement, given that they made 'clear distinctions between gender identity and sexual orientation'. Although TAO leaders expressed solidarity with the gay and lesbian movements, they did not claim gender nonconforming individuals \u2013 including Marielitas \u2013 as transsexual. Pe\u00f1a also notes that TAO participants proved distinct from transgender activists in that they did not 'embrace a continuum of gender expressions'. Indeed, for most of its history, full membership was limited to pre- and post-operative transsexuals, and organisation leaders took care to distinguish between transsexuals and transvestites. Pe\u00f1a concludes by offering a useful caution to historians seeking to understand the relationship among gender expression, sexual orientation and sexual desire. Rather than mapping our categories onto historical actors, we should ask 'how they saw themselves, what communities they participated in, and what social meanings were available to them in their socio-historical context'.\n\nThe diverse scholarship in this book offers ample evidence that careful and contextualised analysis of the shifting relationship of gender and sexuality across space and time illuminates broader historical processes, from the workings of European colonialism to more recent regimes of globalisation. In recent years, scholars working in a range of disciplinary and interdisciplinary locations have demonstrated that the kind of analysis collected in these pages holds real implications for our own historical moment. For example, new work in the field of transgender studies has shown that subsuming categories of gender difference within an analysis of sexuality is problematic because it figures a western conception of homosexuality as normative. As Susan Stryker argues, this practice reinforces a politics of homonormativity, which she defines as 'a privileging of homosexual ways of differing from heterosocial norms, and an antipathy (or at least an unthinking blindness) toward other modes of queer difference'.5 Others have argued that the promotion of a politics of homonormativity based on a western model of homosexuality \u2014 described by Jasbir Puar as 'homonationalism'\u2014 often has the effect of othering non-western cultures as 'backwards' and 'homophobic', and therefore in need of reconstruction in the mode of the United States and its liberal western allies.6 This book helps to historicise these recent developments; the work collected here sheds new light on the ways in which gender and sexuality have functioned in relation to one another, as they have intersected with broader relations of power in a range of sites and contexts.\n\nNotes\n\n1. Gayle Rubin, 'Thinking Sex: Notes for a Radical Theory of the Politics of Sexuality', in Carole S. Vance (ed.), Pleasure and Danger: Exploring Female Sexuality (Boston: Routledge & Kegan Paul, 1984), pp. 267\u2013319, here p. 308.\n\n2. See e.g., Jennifer L. Morgan, Laboring Women: Reproduction and Gender in New World Slavery (Philadelphia: University of Pennsylvania Press, 2004); Tony Ballantyne and Antoinette Burton (eds), Bodies in Contact: Rethinking Colonial Encounters in World History (Durham, NC: Duke University Press, 2005); Annick Prieur, Mema's House, Mexico City: On Transvestites, Queens, and Machos (Chicago and London: University of Chicago Press, 1998); Tomas Almaguer, 'Chicano Men: A Cartography of Homosexual Identity and Behavior', differences 3 (1991), pp. 75\u2013100; Martin F. Manalansan IV, Global Divas: Filipino Gay Men in the Diaspora (Durham and London: Duke University Press, 2003).\n\n3. See e.g., George Chauncey, Gay New York: Gender, Urban Culture, and the Making of the Gay Male World, 1890\u20131940 (New York: Basic Books, 1994), esp. pp. 47\u201364; Nan Alamilla Boyd, Wide Open Town: A History of Queer San Francisco to 1965 (Berkeley: University of California Press, 2003), esp. pp. 25\u201362; Lisa Duggan, Sapphic Slashers: Sex, Violence, and American Modernity (Durham and London: Duke University Press, 2000), esp. pp. 9\u201331; Peter Boag, 'Go West, Young Man, Go East Young Woman: Searching for the Trans in Western Gender History', Western Historical Quarterly 36 (2005), pp. 477\u201397, here p. 487.\n\n4. Kathleen M. Brown, 'The Anglo-Algonquian Gender Frontier', in Nancy Shoemaker (ed.), Negotiators of Change: Historical Perspectives on Native American Women (New York: Routledge, 1995), pp. 157\u201375.\n\n5. Susan Stryker, '(De)subjugated Knowledges: An Introduction to Transgender Studies' in Susan Stryker and Stephen Whittle (eds), The Transgender Studies Reader (New York: Routledge, 2006), pp. 1\u201317, here p. 7. On homonormativity, see also Lisa Duggan, The Twilight of Equality: Neoliberalism, Cultural Politics, and the Attack on Democracy (Boston: Beacon Press, 2003), pp. 43\u201366; and Susan Stryker, 'Transgender History, Homonormativity, and Disciplinarity', Radical History Review 100 (2008), pp. 145\u201357.\n\n6. Jasbir Puar, Terrorist Assemblages: Homonationalism in Queer Times (Durham and London: Duke University Press, 2007). See also, 'What's Queer about Queer Studies Now', a special double issue of Social Text 84\u201385 (2005). Other scholars have noted that the privileging of the western category of homosexuality can have negative implications for public health, namely HIV\/AIDS prevention, and for the building of coalitional politics. See, e.g., Hector Carillo, The Night is Young: Sexuality in Mexico in the Time of AIDS (Chicago and London: University of Chicago Press, 2002) and Cathy J. Cohen, 'Punks, Buldaggers, and Welfare Queens: The Radical Potential of Queer Politics?', GLQ: A Journal of Lesbian and Gay Studies 3 (1997), pp. 437\u201365.\nChapter 1\n\nImagining Cihuacoatl: Masculine Rituals, Nahua Goddesses and the Texts of the Tlacuilos\n\nPete Sigal\n\nCihuacoatl: The savage serpent woman, ill-omened and dreadful, brought men misery. For it was said: 'She gives men the hoe and the tumpline. Thus she forces men [to work]'.\n\nThis description, written in Nahuatl in a late sixteenth-century text, the Florentine Codex, authored by a Franciscan friar and his indigenous aides, speaks of an important Nahua goddess, conceptualised in the pre-conquest Nahua universe alternately and concurrently as a feared deity, a defeated woman and a cross-dressed man.1 Here, in her post-conquest iteration, she becomes only the feared goddess, the one forcing men to work (elsewhere the same text describes sacrifices performed to satisfy her voracious appetite for human hearts). Indeed, pre-conquest images of Cihuacoatl suggest that Nahuas, the indigenous peoples of central Mexico, greatly feared her. Cihuacoatl, the dreaded serpent woman, presented Nahua men with a challenge: she forced them into a life of drudgery. She also could take their lives away; she could present them with certain death as she feasted upon their hearts, for 'she had a huge, open mouth and ferocious teeth. The hair on her head was long and bulky'. Thus she devoured men. But still 'she was clad in womanly garb \u2013 skirt, blouse and mantle \u2013 all white'.2\n\nIn Nahua gender ideology, Cihuacoatl's nature as a feared individual who could kill upon a whim and who forced individuals to work signified a powerful masculine individual. Yet her attire signified femininity. Cihuacoatl's aesthetics seem to us, as they seemed to the Catholic priests and friars who noted her appearance, confusing: a jumble of the masculine and the feminine \u2013 coming from a society that we believe rigorously separated masculine from feminine roles.3 We will see that the relationship between sixteenth-century Nahua notions of gender and sexuality allowed, and even required, Cihuacoatl and other Nahua goddesses to manifest themselves as bundles of attributes that in daily life could never connect to an individual woman, no matter how powerful that woman may be. These goddesses thus transgress our imagined boundaries, not just between gender and sexuality but also between human and divine.\n\nNeed we know if Cihuacoatl and the other fertility goddesses discussed in this chapter are goddesses rather than gods? Is it important to recall that the term teotl ('god') had no gender, or that Nahuatl does not contain gendered pronouns? This certainly begs an answer to a different question: how did the Nahuas understand gender and sexuality?4 I argue here that Nahuas related sexuality to fertility, a binary division between moderation and excess, and a concept of ritual that suspended daily rules on sexual activity. One wonders too if, while in everyday affairs a strict gender division was usually imposed, in ritual life this may not have been true. The gods and goddesses, who appear as a result of and within ritual, would never have to follow those rules, so the fertility goddesses did not follow the strict gender divisions often applied in daily life. Nahuas viewed Cihuacoatl as a warrior deity, but one who would be likely to play a major role in particular rituals and in childbirth; and they imagined another fertility goddess, Tlazolteotl (the teotl of tlazolli, 'trash'), as a highly sexual deity who also consistently engaged in battle with her enemies.5 This connection between gender and sexuality, in which the god(desse)s, beings that exceed our grammatical markers, do not adhere to quotidian principles, speaks to the problem of accepting Gayle Rubin's battle call for separating gender from sexuality as a given. Instead, in this chapter I argue for using Rubin's formulation as a starting point for reconsidering the ways in which we understand concepts of gender and sexuality as organising principles.\n\nThe imagining and reimagining of Cihuacoatl relates to religiosity, colonialism, gender and sexuality in the early colonial period in Mexico. Cihuacoatl complicates the modern notions in which we separate human from god, man from woman and religious from secular. In this chapter, I will discuss the importance of Cihuacoatl and other related god(desse)s to the maintenance of Nahua politics and culture both before and after the Spanish conquest. In order to understand the roles that these god(desse)s played in Nahua society, we need to develop theoretical and methodological tools that go beyond Rubin's call for a theory of sexuality.\n\nSeparating gender from sexuality: the Nahua case\n\nGender affects the operation of the sexual system, and the sexual system has had gender-specific manifestations. But although sex and gender are related, they are not the same thing, and they form the basis of two distinct arenas of social practice... It is essential to separate gender and sexuality analytically to more accurately reflect their separate social existence.6\n\nGayle Rubin\n\nThe call sent out for chapters for the current volume intrigued me as it harkened back to an article I had first read as an undergraduate, cited repeatedly as a graduate student, and that I now assign to my undergraduates. In 'Thinking Sex', Gayle Rubin provocatively argues that we must delineate gender from sexuality, and in particular that we must not assume that the theoretical tools feminism uses to analyse gender will be sufficient for the task of analysing sexuality. Such a critique at the time I read it seemed to me fair enough, and since Rubin's article came out twenty-seven years ago, many theorists, particularly those involved in queer theory, have answered her call.7\n\nStill, when I began my research into indigenous concepts of sexuality from the sixteenth to the eighteenth centuries, I became troubled by part of Rubin's assertion. While sex and gender are not identical, and the Nahuas would not have conflated the analytical terrain that these two concepts represent, the boundaries between the two, in this pre-modern, non-western culture, need significantly more analysis than Rubin's argument allows.8 How can the Nahua situation speak to Rubin's theorising of a separation between gender and sexuality? I suggest that Rubin's formulation can only be a provocative starting point, full of contradictions, when applied to the Nahuas. Cihuacoatl presents one example: was she a god or a goddess? Was she human or divine? Was she chaste or sexual? As we will see, neither Cihuacoatl nor any of the other Nahua god(desse)s can be defined easily based on these binary divisions.\n\nAs many scholars have shown, Nahua notions of gender at the time of the conquest incorporated both 'gender complementarity' and 'gender hierarchy'. In the complementary realm, we find symbolic equivalences (women who died in childbirth were equated the same high status as men who died in battle), quotidian senses of purpose (consent of both husband and wife generally was required to make all major household decisions) and material realities (networks of commoner families teamed together to make sure all could survive economically, with men generally engaging in farming activities and women generally controlling the markets to sell the produce from the land). Regarding gender hierarchy, we find that men controlled the bulk of the political system, the highest levels of religious office and the esteemed title of 'warrior'. The gender system of course changed after the Spanish conquest but, as many recent commentators have noted, these changes were not nearly as radical as earlier scholars had presumed.9\n\nNahuas connected these concepts of gender with related notions of sexuality, even if they did not term these things 'sexuality'. Nahua nobles and commoners before the Spanish conquest related their sexual lives with rituals of fertility and warfare. Still, Nahuas did not have a discreet category they called 'sex'. Instead, they constituted a variety of relations as 'categories of the intimate' in which the human couple engaged in bodily activities related to fertility. These activities included categories that we would invest with sexual meaning: vaginal and anal intercourse, manual and oral stimulation of male and female genitals, imaginary conditions designed to allude to these activities and stimulate a genital response, and the use of non-bodily objects in these actions.10 The Nahuas also had concepts of 'good' and 'bad' sex and rape and other forms of sexual violence. Yet these things that I have called 'categories of the intimate' also included activities that we would not consider sexual: the ritual killing of humans and animals, burning of maize, incense and other items, letting of blood and sweeping houses, streets and other areas. Nahua categories linked all of these activities together and suggested that they formed a part of the matrix of sacrifice. Much Nahua thought at the time of the Spanish conquest envisioned sexual relations as elements of a larger set of ritual practices designed to promote fertility: of gods, humans, animals and the earth.11 A cultural history of these rituals also shows that Nahuas closely linked the maintenance and expansion of the political system and the structures of governance with fertility rites.12\n\nTwo main principles organised Nahua thoughts about the sexual. First, sexual behaviour related directly to the fertility rituals, ceremonies large and small, in the many realms described above, promoting the notion that everything and everybody must exude fertility in order for the community to survive. Second, an individual's sexual possibilities divided between those acts determined moderate and those deemed excessive. Nahua thought considered moderation in sexual activity to be a virtue, excess a vice.13 Ceremonial performances from those of the household to the grand state rites, as well as ritual and quotidian discourse, marked both the encouragement of fertility and the distinction between moderation and excess.\n\nRepresentatives of the Catholic Church who encountered the Nahuas deemed their views of sexual behaviour problematic, and they debated how to change those views and behaviours. The result of that debate was the attempt to link sex with sin, often using particular indigenous concepts (dirt, dust, damage and excess being the most common) as signifiers of sinful behaviour. The means for such a linkage was the discourse of confession, whether through the actual confessional or through advancing such an analysis in the broader social field.14 The attempt at a sexual conquest through the confessional largely failed, instead eventually producing a hybrid sexual system that still survives today in many indigenous Mesoamerican societies.15\n\nThe Tlacuilo's text\n\nBefore the Spanish conquest, the Nahuas produced an extensive array of writings, though few have survived to this day. Here I focus on using pictorial manuscripts, produced both before and after the conquest, to analyse the relationship between gender, sexuality and the Nahua fertility god(desse)s. In conjunction with alphabetic texts, these pictorial manuscripts tell us stories about the ways in which our writer\/painters, called in Nahuatl tlacuilos, conceptualised particular approaches to sexual topics: those linked to religion, ritual and fertility. The authors of the pictorial manuscripts focused much of their attention on the gods and rituals that I relate to sexuality, but they paid less attention to the daily lives of the people.\n\nOur methods for reading such images cannot be facile, and we must engage in as much criticism of the images as we do of the alphabetic texts.16 Thus, we must note that the Nahuas before the conquest did not intend their texts to be read as transparent assertions of a witnessed reality. Nor did they produce texts that we can read as complete narratives. Nahua society had an oral culture, so the tlacuilos produced texts in interaction with other people, and they, along with various other textual experts, 'read' these documents out loud in public and private ceremonies by expanding on the images presented on the page. Thus, for us to read these images, we need some of the 'back story', provided by the contexts we find in archaeological and ethnohistorical studies.17\n\nFurther, we must know something about the tlacuilos, who played such an important role in pre-conquest Nahua society. Before the Spaniards arrived, Nahuas wrote texts in the form of various types of painted images, either on paper made from the bark of a tree or on stone edifices. The person who engaged in such writing was called a tlacuilo, a word that translates roughly as 'writer' or 'painter'. The Nahuas viewed this tlacuilo as a reflective artist, not as one who wrote down precisely what he saw. At the time of the Spanish conquest, the practices of the tlacuilos changed, as many became escribanos, who would write either Nahuatl or Spanish texts in the Roman alphabet. These scribes became intermediaries in the colonial project, and they overwhelmingly produced documents designed in some manner for the Spanish legal system. Moreover, the tlacuilos who continued to paint their images were influenced by European artistic conventions. Still, early tlacuilos were trained not only by friars but also by painters knowledgeable in pre-conquest aesthetics. And the evidence from idolatry investigations, criminal trials and Inquisition cases shows that these artists continued to get their works into the hands of a wide variety of indigenous people.18 Too much current historical writing either ignores the role of the scribe or considers his work to be a window onto Nahua reality. I argue that the window is the wrong metaphor; his writings instead signify a prism.\n\nThe images themselves require substantial interpretation based on a method for reading Nahua iconography, a method based on comparative studies within particular genres. So, for example, art historians have studied extensively the Borgia group, from which we receive all of the indisputably pre-conquest images I discuss here (from the Codex Borgia and the Codex Laud); we have found that the artists did not attempt to provide realistic portrayals of the human body \u2013 they tended to provide images in profile \u2013 and they had specific icons designed to signify such things as movement through space, the progress of time and, more to the point for our purposes, the position of fertility.19 The Borgia group also comes from outside the basin of Mexico (probably from near Tlaxcala or from Nahua-influenced areas of southern Mexico) and, as the foremost experts on these codices have noted, these texts represent the dominant religious views of the priestly class throughout the region.20\n\nThe post-conquest manuscripts that I will analyse became hybrid texts, at least in format, with influence from both European and Nahua styles. The first set of texts (the Codex Borbonicus and the Tonalamatl of Aubin), probably produced soon after the Spanish conquest in the basin of Mexico, appear to have little Spanish influence, though some aesthetic changes and\/or Spanish glosses appear.21 The second set of texts, the Magliabechiano group, betrays the influence of its Franciscan sponsors. Though produced largely in traditional Nahua style, the texts are primarily Spanish alphabetic documents, with images illustrating the narrative.22 The final text, the twelve-volume Florentine Codex written and illustrated by Franciscan friar Bernardino de Sahag\u00fan and his indigenous aides, is an extensive ethnographic study, based on interviews with old Nahua nobles from three different communities, produced in Hispanic style and with an agenda of promoting Christian thought, but with an interest in providing great detail \u2013 in the Nahuatl language, even if in the Roman alphabet \u2013 about Nahua religious practice.23\n\nThese texts together tell us a story: one in which war, fertility and sacrifice relate to emerging and always changing concepts of gender and sexuality. As we will see, these concepts not only exceeded the Spanish conceptualisation that equated sex with sin, but also exceed a theory of sexuality that maintains a division between sex and gender.\n\nThe god(dess) Cihuacoatl\n\nIn the Codex Borbonicus, authored in the basin of Mexico at around the time of the Spanish conquest, we witness Cihuacoatl in a description of the Toxcatl ceremony, a festival to celebrate the warriors of the city-state of Tenochtitlan, the capital of the ruling empire immediately before the Spanish conquest (see Figure 1). This early sixteenth-century pictorial codex, written in traditional Nahua style (though with some Spanish glosses), focuses on an individual called the cihuacoatl, the second-highest ranking person in a Nahua city-state.24 We see few figures in Nahua pictorial manuscripts that we know are cross-dressed individuals, but the cihuacoatl is one, and he runs the Toxcatl ceremony, a festival designed to promote masculine valour in warfare. His image in the centre of the ceremony shows him wearing a blouse and a skirt, both decorated in the manner of the god(dess), and carrying a well-decorated shield, a symbol of masculinity, and a weaving batten, a symbol of femininity. Why did this cross-dressing individual play such a powerful role in an important Nahua ceremony (and in wider Nahua politics)? Did Cihuacoatl, ostensibly a mother god(dess), come to symbolise warfare?\n\nFigure 1 Cihuacoatl.\n\nReprinted from Codex Borbonicus (facsimile) (Madrid, Vienna, Mexico City: Sociedad Estatal Quinto Centenario, Akademische Druck- und Verlagsanstalt, Fondo de Cultura Econ\u00f3mica, 1991), p. 34.\n\nDominican friar Diego Dur\u00e1n describes fearsome sacrifices dedicated to Cihuacoatl, and he says that the Nahuas killed more for her than for any other deity.25 Indeed, Cihuacoatl was a powerful warrior god(dess) often associated with the Mexica.26\n\nMuch of the Codex Borbonicus focuses on her as a central god(dess), largely because this codex is dedicated to warrior rituals. Yet the Borbonicus focuses not simply on the god(dess), but rather on her priest: a male priest dressed in her garb.27 In addition to his shield and his weaving batten, he, if we can call him that, wears a dress decorated with skulls at the bottom, and he has all of the standard markings of the god(dess). He also stands upon a platform decorated with a skull. This individual is the cihuacoatl of Tenochtitlan, a person, seemingly always male, the second-in-command of the community after the tlatoani. This powerful position for a cross-dressing individual belies the fact that Nahua society strongly ingrained a highly masculine image in young men in which they avoided all activity, including dress, associated with women's roles.28 Yet, Nahua leaders viewed the cihuacoatl as necessary for the effective functioning of society and, in the Toxcatl ceremony, for effective leadership in ritual warfare.\n\nImportantly, such cross-dressing in no way challenged the masculinity of the priest. He stands in the image across from and alongside well-decorated priests and warriors. In another image, he stands directly below Huitzilopochtli, the god of war.29 Just as the priest of Cihuacoatl wears the attire of the god(dess) (her figurative skin), the warriors wear the skins of animals and the priest of Huitzilopochtli wears the accoutrements of the god he signifies. In each case, the act of placing upon one's body the skin of another transforms the self. Huitzilopochtli's priest becomes the powerful warrior god \u2013 no longer simply human, he enters a space in which he remains the priest but also becomes the divine. The warriors become the powerful animals (coyotes, jaguars and so on) whose skins they wear. These animals allow them to go to war not only with the protection (armour) of the skin, but also with the martial skills of the animals, combined with the cunning of the human warrior: betwixt and between, through ritual (the Toxcatl ceremony), the self-identities of the warriors have become transformed.\n\nA similar process takes place in the case of the priest wearing Cihuacoatl's (female?) skin. He places upon his body the skirt and the blouse, and he holds the weaving batten because his self has been transformed into that of the god(dess)\/priest. No longer just human, he becomes a figure straddling the human and the divine, harnessing all the powers of the deity to attend to the success of the warriors in warfare. In doing so, this priest crosses boundaries not just between the human and the divine, as had Huitzilopochtli's priest, but also between male and female.\n\nIn these warrior rituals, why did the presence of Huitzilopochtli and other warrior gods not suffice? Why did our tlacuilo find it necessary to paint the image of Cihuacoatl? After all, Inga Clendinnen and Cecelia Klein, amongst others, have both carefully and correctly shown us that warfare was a male sphere, in many ways the ultimate portrayal of the masculine being in the Nahua universe.30\n\nThe answers to these questions, though, comes from Cihuacoatl's particular place in the Nahua pantheon, a place signified by her shield, and representing her as a warrior god(dess). While, as we will see, many of the fertility god(desse)s played a role in warfare, Cihuacoatl's role was unique. Cihuacoatl, while a central god(dess) to the apparatus of the Aztec empire, signified defeat. She was most strongly worshipped in the southern cities of Cuitlahuac and Xochimilco, and 'it is noteworthy that both cities were famed for their female sorcerers. Cuitlahuac is described repeatedly in the chronicles as the \"City of Sorcerers\"... while Xochimilco, which was regarded as a veritable hotbed of sorcery, is thought to house black art practitioners to this day'.31 Further, these southern cities were key to the survival of Tenochtitlan as leader of the empire, for, once conquered, they contributed substantial tribute.\n\nIt thus seems little coincidence that immediately after the Mexica conquest of Xochimilco in 1430, we find evidence that the cult of Cihuacoatl flourished in the capital city.32 Her presence signified both the power of the feminine in her cults in the southern cities, and her defeat, ritualistically, at the hands of Huitzilopochtli. This god(dess), always powerful and always dangerous, must also remain always defeated, or else the Aztec empire could end. Thus the performance of the cihuacoatl priest, always second-in-command, signified the continuing re-enactment of defeat.33\n\nReturning to the ceremonial performance of the cihuacoatl, though, we may ask why, if she, as Klein maintains, signified such defeat, she would perform an active role in the ritual. Why would she not simply sit at the feet of Huitzilopochtli or even of the warriors? We may answer partly, based on Klein's description, that Cihuacoatl's presence signified the position of a powerful god(dess) coming from a region in which female magic predominated, but we may go much further than this as we analyse the power of femininity and feminine sexuality in the Nahua god(desse)s of war.\n\nIn her image in the above text, we can see Cihuacoatl's ferocious look. She holds a batten as a weapon to signify her feminine role as a weaver (she also clearly wears a skirt). Her ferocious face, open mouth, long hair, well-decorated warrior garb and ornate shield frightened her enemies. The skull below her, upon which she stands, suggests that she makes her platform from the heads of enemy warriors.\n\nBut why would the Mexica use a female warrior in such imagery, when almost all of their warriors were men? One could not defeat the enemy with just the masculine, so the rituals needed to provide feminine power. In another ritual, titled Ochpaniztli ('The Sweeping'), in order for the ritual to succeed, a male priest needed to wear the skin of a woman slain as a fertility god(dess). In doing so, he harnessed the power of the fertility god(dess) and spread maize throughout the earth. As he accomplished this act, he was called by the name of the fertility god(dess).34 As the Nahuas viewed the feminine as absolutely necessary for fertility, they also saw femininity as vital for the promotion of warfare, in which they believed that they made the empire fertile. In the Ochpaniztli ritual, another priest, as he went into battle, wore the flayed thigh skin of the slain god(dess), only to bury that thigh skin in enemy territory, just as he would plant maize.35\n\nOne should also note that, as the Mexica defeated and\/or formed alliances with other city-states, they asserted feminine sexuality to do so. After the war was over, they would work to expand their influence over others by marrying high-level Mexica women to the rulers of the defeated city-state. While it would work the other way as well (leading maidens from the other city-state would marry the Mexica leader), the control over the outside, the other city-state, most often was ceded to the young Mexica women who married the leaders of those states.36 Thus state power was asserted through feminine sexuality, and Cihuacoatl signified that institution. Cihuacoatl promoted both the Nahua concept of the masculine, leading men into battle, and the feminine, promoting feminine sexuality and weaving, considered women's work.\n\nThis seems most appropriate to Cihuacoatl's position as the second-in-command of society. The most famous Cihuacoatl, Tlacaelel, was renowned for leading Mexica war parties. Cihuacoatl thus signified what the other god(desse)s did: a jumble of attributes, skins that could be taken off or placed on at will. She was the masculine warrior, the feminine weaver, the sorceress and the one given to the powerful Mexica leader as a sexual favour when he defeated the city from which Cihuacoatl emanated.\n\nOne can sense in this description the problem with Rubin's formulation: if we separate our theoretical tools for analysing sexuality from the feminist tools developed to analyse gender, do we lose the cross-pollination between what we would consider gender and what we would consider sexuality? Nahua ritual structures did not neatly separate the two, at least not in the case of Cihuacoatl. Still, as noted in the beginning, Nahua quotidian notions of gender and sexuality formed particular roles for women and men that did not apply to the deities. Would Rubin's formulation in 'Thinking Sex' allow for the parentheses in god(desse)s, or would it limit our grammatical abilities? I will argue below for a return both to Lacan and to 'The Traffic in Women'.\n\nThe god(dess) Coyolxauhqui\n\nOther Nahua god(desse)s signified the position of the defeated warrior. The mythology of the birth of the Mexica war god, Huitzilopochtli, involving him, his sister Coyolxauhqui and his mother Coatlicue, suggests a complex gendered and sexualised relationship linked closely with war and fertility. The mother, Coatlicue, became pregnant with Huitzilopochtli while she swept. She found a ball of feathers, which she placed in her bosom. That ball of feathers then disappeared, and Coatlicue was pregnant. Coyolxauhqui, Coatlicue's eldest daughter, led her brothers into battle, attempting to kill her mother before Huitzilopochtli was born. She did this because she believed that Huitzilopochtli would bring about destruction. Yet her stated reasons, according to the Florentine Codex, appear to critique Coatlicue's suspect sexuality. Thus she said, 'My elder brothers, she has affronted us; we must kill our mother, the angry one who is already with child. Who is the cause of that which is in her womb?'37 Coyolxauhqui then led her brothers to attack their mother, but Huitzilopochtli, still in his mother's womb, heard Coyolxauhqui's plans, and he burst out of her, already with weapons. He beheaded Coyolxauhqui and ripped her body into pieces. He then killed his brothers.38\n\nThe narrative asserts a battle on at least two levels related to the control over feminine sexuality and the female body. Coatlicue became sexually suspect, but Huitzilopochtli, through his expertise as a warrior, defended his mother's reputation. Coyolxauhqui's destroyed body then descended to the earth, propagating the fertile land of the basin of Mexico. The struggle between Huitzilopochtli and Coyolxauhqui also symbolically marked the movement of the Mexica from a subordinate group to a dominant one.39\n\nCoatlicue, the mother, remains an obscure figure in the Nahua pantheon. As Huitzilopochtli's lone parent, she suggests his 'illegitimacy' in the Nahua framework, a symbol for the illegitimacy of Mexica rule. In her own image, as we find in her statue (Figure 2), she has become a phallic figure: two serpents emerge from her severed head.40 Serpents also come out from her skirt (Coatlicue translates as 'serpent skirt'), signifying both her fertility and the association between her fertile nature and death \u2013 through the warfare of Huitzilopochtli.41 This fierce deity promoted the position of the phallic god(dess) in the Nahua pantheon.\n\nFigure 2 Statue of Coatlicue. Photograph by Pete Sigal (Museo de Antroplog\u00eda e Historia, Mexico City).\n\nHuitzilopochtli, as the key warrior god of the Mexica, defeated Coyolxauhqui in such a way as to establish male domination over the female body, just as the masculine Mexica established control over the feminine land.42 The main narrative promoted Huitzilopochtli as the leader of society, while Coyolxauhqui's shattered body, as memorialised on the main Mexica temple (Figure 3), became a key figure in the empire: both an element of resistance to male domination in Mexica society, and the disempowerment of the female body. The body's pieces signified both Coyolxauhqui's excessively sexual nature (through her nude body and exposed breasts) and her phallic empowerment (through her snakes \u2013 presented as phallic in Nahua iconography \u2013 and the presence of the loincloth, an ubiquitous sign of men).43\n\nFigure 3 Coyolxauhqui, from the Templo Mayor of Tenochtitlan. Photograph by Pete Sigal.\n\nYet, in the image, we witness her extraordinary phallic divestiture. As her body was destroyed, torn apart in every conceivable manner, she became divested of any power and thus became a symbol asserting the dominance of Huitzilopochtli. Thus, as Huitzilopochtli became a sign of Mexica dominance, Coyolxauhqui became a sign for any city-states that would attempt to challenge that dominance. In such a metaphorical story, those other city-states were feminised. All the serpents were killed along with Coyolxauhqui; she was beheaded and her body parts did not form a whole that could challenge Huitzilopochtli in any manner.\n\nHuitzilopochtli thus became in this story a warrior who would defend his mother \u2013 even if she had become sexually suspect \u2013 while asserting sexual control over his sister. The sexual control that Huitzilopochtli exerted over both his mother and sister may resemble to us a kind of patriarchal sexual control, and indeed much Nahua ritual points to male dominance. This may lead us to believe, however, that Nahua society had a similar system of sexual honour and virtue that many historians have argued comprised Spanish patriarchal discourse.44 But, as scholars studying Nahua gender have shown more fully, Nahua society at the time of the Spanish conquest was much more complex than this.45\n\nIn this narrative, we must recall the position of the land. The Mexica would not have been able to settle in Tenochtitlan, or to plant maize without the fertilising presence of the parts of Coyolxauhqui's body. In many senses, this recalls Rubin's point in 'The Traffic in Women', that women's bodies fertilise social relationships between men, who engage in gift exchange over the bodies of women.46 Thus, symbolically Coyolxauhqui's shattered body became the key to this exchange, just as women's bodies (as the women were married off to leaders of other city-states) would become similarly key to such an exchange in the social field.\n\nThe symbolic presence of Coyolxauhqui's phallus, through her loincloth, signifies not the imaginary presence of a penis, but rather a fear that Mexica leaders had regarding the potential of their subordinates to rise up. This feminine phallic power, also asserted through the presence of snakes, phallic figures connected with the earth, and thus also with femininity in the case of Coyolxauhqui, needed to be controlled in the Nahua universe. Such a phallic presence, though, points again to the symbolic import of feminine sexuality, an import that we cannot understand if we do not develop a theoretical framework that deals with the symbols and signifiers of sexuality, even when they become connected with the 'wrong' gender.47\n\nThe fertility god(desse)s\n\nNahua ritual texts at the time of the conquest closely connected war with fertility, and Cihuacoatl, like most other god(desse)s, signified both of these. Through her position alongside all of the male warriors, she presented the preferred warrior symbol. The men had to go forth into other territories, defeat their enemies and symbolically implant a new society. The only way to keep that new society moving forward was through sexual reproduction that made gods, humans, animals and the earth fertile. In order to accomplish this task, the warriors recognised that they needed both masculine and feminine principles; hence the position of Cihuacoatl as a warrior, particularly one continually re-enacting the defeat of those fighting against the Mexica.48 And the presence of the second skin of the priest, the clothing of the god(dess), would also mimic the warriors, who wore their own second skins, those of the animals.\n\nOther god(desse)s present us with further evidence of the power of fertility. In these god(desse)s, we see that for the Nahuas feminine sexuality connects with gender in particular ways that move us beyond Rubin's formulations. In the Tonalamatl of Aubin, we find an extraordinary and obscure image that signifies the roles of two fertility goddesses: Chalchiuhtlicue and Tlazolteotl (Figure 4).49 There we see Chalchiuhtlicue with Tlazolteotl's head emanating from between her legs like an outstretched penis. In Chalchiuhtlicue's more standard image, like that of the Codex Borbonicus (Figure 5), we see her unleashing the floods from beneath her throne, and we witness people caught in the torrents of water.50 Her nose ornament serves to present her as a fertility god(dess).51 And, importantly, one of the images across from her is Tlazolteotl's headdress. Here the people caught in the stream may be a man and a woman sacrificed to the god(dess), although they may also symbolise men and women born to the cleansing effects of Chalchiuhtlicue's water.52 As a midwife bathed a newborn, she called upon Chalchiuhtlicue. Either way, Chalchiuhtlicue's flood created and\/or destroyed both male and female.\n\nFigure 4 Chalchiuhtlicue.\n\nReprinted from Tonalamatl of Aubin (facsimile), Eduard Seler, ed. (Berlin, London: Hazell, Watson, Viney, 1900-01), p. 5.\n\nFigure 5 Chalchiuhtlicue.\n\nReprinted from Codex Borbonicus (facsimile) (Madrid, Vienna, Mexico City: Sociedad Estatal Quinto Centenario, Akademische Druck- und Verlagsanstalt, Fondo de Cultura Econ\u00f3mica, 1991), p. 3.\n\nChalchiuhtlicue controlled the water and bathed the newborn child, ridding her\/him of dirt. The important ceremony, bringing the child into the world, was partially controlled by this god(dess) and, by implication, by Tlazolteotl as well. The two were paired, as art historian Eloise Qui\u00f1ones-Keber maintains, because of the association between dirt and cleanliness. Tlaztoleotl's 'dual association with generation and filth is recognised; the latter is part of her name... Thus the pairing of Tlaztolteotl and Chalchiuhtlicue... may have been intended for contrasting purposes, one representing filth, the other the cleansing with water that followed birth'. 53 While Qui\u00f1ones-Keber places too much emphasis on these two as individual god(desse)s rather than complements, I agree on the necessity of both in Nahua thought for the maintenance of fertility.\n\nThe two god(desse)s in Figure 4 connect with each other in the cleansing process: one signifying water and the other trash. Chalchiuhtlicue, at least in the birthing process, would serve to clean the trash created by Tlazolteotl.54 Perhaps the tlacuilo who authored the Tonalamatl of Aubin saw Tlazolteotl as a masculine type of figure, relating to Chalchiuhtlicue's femininity. Yet, we may have problems supporting such a binary opposition. Chalchiuhtlicue's name derived from 'precious jade' (chalchihuitl) and 'skirt' (cueitl), while Tlazolteotl came from 'trash' (tlazolli). The skirt signified female identity but trash had no particular gender in Nahua thought. Further, as we will see, Tlazolteotl's gender is far from clear. And Chalchiuhtlicue, while consistently represented as feminine and having a female body, appears here to have had a penis; other images related her to warfare.55\n\nThe penile image, associating not the symbolism of the phallus (through the loincloth), but rather the physiological male member, seems entirely unique in the Nahua corpus. Perhaps the tlacuilo intended Tlazolteotl as penis to signify the fertility of both god(desse)s. In the images in the water in Figures 4 and 5, we witness the male and the female figures, both clothed (the male figure appears to wear only a loincloth).56 Chalchiuhtlicue symbolised both the destruction of the flood and the creation of birth. The use of Tlazolteotl could suggest two elements: first, the use of dirt and water in the washing away of the trash of the newborn child; second, the male and female principles involved in creation. But we cannot maintain Tlazolteotl as the masculine principle \u2013 and certainly not as the penis. Indeed, her headdress in Figure 5 probably signifies offerings to the god(dess) in order to protect children in the birthing process.\n\nA pre-conquest Nahua image common to several texts presented Tlazolteotl as an erotic god(dess) partnered with a similarly erotic (male) deity (Figure 6).57 Tlazolteotl gives birth to a glyph of a flower, symbolising her as the parent of sexual excess.58 Several other elements of this image are noteworthy. First, and most immediately apparent, Tlazolteotl is naked except for her headgear and her necklace. The nudity of women in pre-conquest manuscripts always appears to have signified sexual excess.59 Second, Tlazolteotl's headdress and earrings are made of a spindle and unspun cotton, signifying her as the god(dess) of spinning cotton.60 Third, her right foot sits on a flint knife, an implement used in blood sacrifice. The (male) deity below her also has a flower emanating from him (could the flower emanate from an umbilical cord?), and he has a cord ending in a skull coming out of his anus. The figures together signify the panoply of sexual excesses committed by the gods. These indeed were deities of sexual excess, and the Nahua pantheon required them to engage in activities that standard Nahua society would have viewed as excessive for men and women.\n\nFigure 6 Gods of Excess.\n\nReprinted from Codex Borgia (facsimile) (Graz, Austria: Akademische Druck- und Verlagsanstalt, 1976), p. 74.\n\nIn post-conquest times, Tlazolteotl not only continued but, more appropriately, she traversed the entire social field. Thus she became a signifier of sin, but she kept some of her role as a mother god(dess) who committed activities deemed excessive. She maintained her position as one who would pick up the trash, and she continued to provide more trash. She fomented an 'Eve-like' image, just as she also re-presented the holy mother, the Virgin Mary, in a somewhat different and more sexualised guise.\n\nIn a 1629 treatise, based on an idolatry investigation in a Nahua-speaking community in Guerrero, we find several incantations that invoked Tlazolteotl and closely related god(desse)s. In one, the Nahua informant discussed a cure that he called tetlazolaltiloni, 'bathing someone regarding tlazolli'.61 Of course the washing away of the trash would require water, so the shaman called upon a series of god(desse)s, including Chalchiuhtlicue. These god(desse)s signified fire, water and incense. Then he called upon the Tlazolteteoh, the god(desse)s of tlazolli.62 These together formed the cure for an illness caused by tlazolli and by what the Nahuas deemed 'excess'. And one should note here that Tlazolteotl was the guardian of the steam baths, places intended to cure individuals, but ones that Catholic priests argued fomented sexual sin by allowing for secret sexual liaisons.63 Nahuas regarded the steam bath, the temazcal, guarded by Tlazolteotl, as a place in which the fire, water and incense came together to help one engage in a cure.64 The being that created the disease was specifically coded as female, whereas the disease itself had no specific gendered markers, and the ill person could be either male or female. The curer, either male or female, led the diseased person to the steam bath, which cured him or her. Only through the careful invocation of both Chalchiuhtlicue and Tlazolteotl would the sick individual become cured. Thus, these god(desse)s, fundamental god(desse)s of fertility, could cure disease and save humanity. But they also could kill.\n\nIn the relationship established here between Tlazolteotl and Chalchiuhtlicue, we may see, as did the Catholic priests, a parallel with baptism.65 Yet, I would argue that we must instead interpret this cure in the context provided by the pre-conquest pairing of Chachiuhtlicue with Tlazolteotl. The two did not form moral opposites as in the case of baptism, where the holy water washes away the original sin. In the case of the ritual purification involved in the steam bath, the water did wash away the trash, but only as the trash god(dess) helped the water god(dess). The two together signified tlazolli; thus together they worked to move the diseased person ritualistically back into the realm of moderation. Chalchiuhtlicue required Tlazolteotl in order to help, in order to cure, the individual.\n\nTlazolteotl remained Chalchiuhtlicue's phallus even in the 1620s, but here she has become the phallus more in her traditional sense, as in the symbolic register in which Tlazolteotl combined male and female power within the same register. In other words, here the phallus becomes not a physiological manifestation of the male body, but rather a symbolic presentation of the power of gender and sexuality.\n\nThe colonial death of the god(dess)\n\nThe phallic imagery of the Chalchiuhtlicue\/Tlazolteotl relationship remains obscure until we analyse the place of the tongue in the images of the Nahua god(desse)s. In an image from the mid-sixteenth-century Codex Magliabechiano (Figure 7), a codex written in the Spanish language but preserving some traditional if decontextualised Nahua imagery, we see that Cihuacoatl survived the conquest intact and in some senses became scarier yet.66 But, as I have noted, the Codex Magliabechiano was primarily a Hispanic text, with the images performing an illustrative role. Still, according to Dominican friar Diego Dur\u00e1n, an astute observer of Nahua gods and rituals, Cihuacoatl's open mouth and tongue signified her lust for the hearts of men.67 At the same time, the tongue in much Nahua discourse signified a lascivious nature.68 We see again the relationship between warfare, sacrifice and feminine sexuality. Here the Spanish narrative says that Cihuacoatl celebrates the festival of the dead.69\n\nFigure 7 Cihuacoatl.\n\nReprinted from Codex Magliabechiano (facsimile). Published as The Book of the Life of the Ancient Mexicans, Zelia Nuttall, ed. (Berkeley: University of California Press, 1903), f. 45r.\n\nHow do we understand the ever-present tongues of the god(desse)s? We must turn to the rather ambiguous tzitzimime, death figures and underworld gods that art historian Cecelia Klein convincingly argues related closely to Cihuacoatl, their controlling god(dess), and whose flint-knife-like tongues appear prominently in their images.70 As we can see in Figure 8, from the Codex Magliabechiano, a snake appears to emanate from beneath the tzitzimitl. The cognate image from a related codex, the Codex Tudela, which was created from the same prototype as the Codex Magliabechiano, contains no snake; instead, blood comes from the tzitzimitl's open mouth, pouring down the front of the image, ending in an arrow-like point between the figure's legs.71 The blood signified the tzitzimitl's power, which stemmed from the figure's ability to get Nahuas to engage in sacrifice. The blood moving from the open mouth, between the legs, to the ground, replicates the positioning of the tongue, liver and snake on the body of the Magliabechiano tzitzimitl.\n\nFigure 8 Tzitzimitl.\n\nReprinted from Codex Magliabechiano (facsimile). Published as The Book of the Life of the Ancient Mexicans, Zelia Nuttall, ed. (Berkeley: University of California Press, 1903), f. 76r.\n\nThe Spanish text describing this figure in the Codex Magliabechiano says that the tzitzimitl is a 'dead man'.72 Yet we see that he wears a huipil, the top worn by Nahua women. His huipil covers his bony body, but the snake emanates prominently from beneath him to show his phallic power, just as he wears a necklace of hearts (with a liver at the centre) to show his ability to get people to engage in sacrifice for him.\n\nNahuas called these figures tzitzimime, underworld gods most often characterised as male. As we shall see, such a characterisation mistakes a colonialist re-inscription for pre-conquest reality. According to a wide variety of sources, Nahuas feared the tzitzimime in a similar manner as they feared the cihuateteo, women who became god(desse)s when they died in childbirth.73 The tzitzimime and the cihuateteo would come from the underworld and lurk in the forests, waiting to steal hearts. Only sufficient sacrifice could satisfy them.\n\nThese fearful (highly masculine?) figures thus signified the draw of the underworld, and they appropriately became recoded as demonic figures in the Nahua world.74 Or did they? Klein has shown that these figures in the pre-conquest imaginary appear female. In addition to the huipil, the tzitizmime wore skirts laced on the bottom with shells. The image from the Codex Tudela also has a red back panel laced with shells at the bottom \u2013 Nahua women wore both the skirt and the back panel. The lacing of the bottom with shells appears reminiscent of Cihuacoatl's costume. A few early colonial documents describe the tzitzimime as female. In fact, Klein shows that texts declaring the tzitzimime as male appear to actively and consciously seek to alter the identity of the tzitzimime to make them demonic. As the devil is male, likewise the tzitzimime became male.75\n\nIn Nahua cosmology, these tzitzimime did not signify as male, or as purely evil. They could help one with cures just as easily as they could kill an individual. But let us explore for a moment the reason that these figures became both male and demonic, at least in the Hispanic mind, during the early colonial period. First, as underworld gods who created mischief for people on earth, in the imaginations of Catholic priests it made great sense to categorise them as types of demons, ignoring the fact that Nahuas did not view them as universally evil. Second, as deities pictured with properties presumed phallic, the Spaniards could easily categorise them as male, ignoring sartorial codes that would problematise such a gender categorisation. These two rationales, though, suggest more of an unconscious process at work than the conscious re-categorisation process promoted in some of the secondary literature: in other words, it was not so much that the priests made an effort to re-categorise these individuals to fit into their agendas. Rather, they witnessed images that they automatically coded in their minds as demonic male figures, and they acted accordingly.\n\nCihuacoatl closely relates to the tzitzimime and the other death figures through her tongue. Figure 7 prominently displays Cihuacoatl's tongue, ready to penetrate the heart for which she waits. Further, as a warrior god(dess), she carried the name of 'woman serpent', a reference to one key phallic figure. We also see in her pre-conquest image the prominent role of her tongue, which in Figure 9, from the Mexica version of the calendar, is simply a flint knife, much like the tongue of the tzitzimitl in the Magliabechiano image. The flint knife, the phallic signifier of sacrifice, becomes equated with Cihuacoatl's tongue in the collective memory produced in this state-sponsored display.\n\nFigure 9 Cihuacoatl, from a Nahua calendar. Photograph by Pete Sigal.\n\nWe can also note the relationship of sexuality to the portrayal of the hair of Cihuacoatl and the tzitzimime. In another image, Cihuacoatl's hair is made up of centipedes, scorpions and other insects \u2013 all signifiers of sexual excess.76 Pre-conquest and colonial iconography consistently related such animals of the earth to excess.77 These relate to the common theme in Nahua sources: women portrayed as sexually excessive had tousled hair. The knives in the hair of the tzitzimime seem likely to portray a similar relation.\n\nThe sources prominently displayed the tongues of certain deities, and these tongues meant different things under different circumstances, but in each case the tongue signified a ritual element of excess unmistakably absent from accepted daily practices. Witness the tongues of the tzitzimime. These tongues present the excess related to feasting upon blood and heart. The tongue of Tlazolteotl signified her lascivious nature. In Figure 9, Cihuacoatl's flint-knife tongue signified her importance in sacrifice.\n\nThe tongue in each of these images presents us with a narrative related to power. The individual with the exposed tongue has power over others, and that tongue consistently signifies the excesses of ritual, prohibited in daily life. These phallic tongues, related closely with Cihuacoatl and other deities, suggest that god(desse)s have power over people.\n\nWhile Cihuacoatl was hardly a typical god(dess), she signified what all others did: a coming together of two principles, the feminine (fertility and feminine sexuality) and the masculine (warfare and masculine sexuality). It is this coming together of variously gendered phenomena that may force us to question whether these god(desse)s can be characterised as goddesses at all.\n\nIn pre-conquest times we find significant gender ambiguity in the positions of many supernatural figures. In the Codex Laud, the presence of the phallus asserted a dynamic power relationship between the phallicised deity and the humans portrayed in the act of childbirth. In two images from this codex, we find related death figures with both loincloths and skirts (see Figures 10 and 11).78\n\nFigure 10 Death figure.\n\nReprinted from Codex Laud (facsimile), Ferdinand Anders, ed. (Austria: Akademische Druck- und Verlagsanstalt; Mexico City: Fondo de Cultura Econ\u00f3mica, 1994), p. 27.\n\nFigure 11 Death figure.\n\nReprinted from Codex Laud (facsimile), Ferdinand Anders, ed. (Austria: Akademische Druck- und Verlagsanstalt; Mexico City: Fondo de Cultura Econ\u00f3mica, 1994), p. 30.\n\nIn Figure 10, we see that the death figure has his sacrificial knife pointed at the woman who appears to hand over her child. The obvious suggestion that this child will be sacrificed is less important to us than the phallic nature of the death figure. The symbolic role of sacrifice and the power of the sacrificial knife relate back to the loincloth \u2013 not necessarily seen as hiding a penis, but certainly as a symbolic registration of the phallic power of the death figure, here containing both male (loincloth) and female (skirt) attributes.\n\nIn another case, Figure 11, we see the same death figure, this time without a sacrificial knife, as the child has yet to be born. The death figure points to a naked pregnant woman. We also see a snake's tail pointing toward the woman, and a bird enters her mouth. Again, the death figure, with both skirt and loincloth, relates to the system of sacrifice (as well as the dangers of childbirth).\n\nThe images of the gods connect the loincloth closely with the power of the actor. Each deity maintains his or her power through the presence of some sign of the phallus. And in each case these phallic signifiers relate closely to sexual excess. I argue that the phallus placed on the body of the god(dess) asserts a type of (feminine) sexual power in the cosmological realm.\n\nWe witness these power dynamics further as we explore the relationship between the god(desse)s. As Chalchiuhtlicue had the identity of the 'precious jade skirt', and the skirt in Nahua discourse signified female, despite her penis in Figure 4, she appears to remain female.79 We must note that we have found few images of Nahua women with loincloths, so the portrayal of god(desse)s with loincloths, snakes and other phallic signifiers appears not to have extended to human women.80\n\nIndeed, the Nahuas viewed the bulk of the god(desse)s as combined warriors and fertility figures. The authors of these texts signify the roles of these god(desse)s through the representation of images of fertility (including presenting them as giving birth, but most often simply showing them with elements to spin or weave cotton, or with maize, as Nahuas linked both cotton and maize to fertility) and images of war (most often, as with the case of Cihuacoatl, with shields and bundles of arrows, but also including knives and other implements of sacrifice).\n\nNone of this will surprise those with knowledge of Nahua notions of childbirth. Nahuas provided a woman giving birth to a child the title of 'warrior'. In the Florentine Codex, a midwife exhorted the pregnant woman, about to give birth, to 'grasp well the little shield. My daughter, my youngest one: be an eagle woman. Face it. Imitate the eagle woman, Cihuacoatl'.81 The reference to 'eagle woman' (quauhcihuatl) referred to the eagle designation of an acclaimed warrior.82 The shield referred to Cihuacoatl's shield. Thus Cihuacoatl became the god(dess) who protected women during childbirth. Her warrior personality became the personality of the woman giving birth to the child.\n\nTlazolteotl also helped women through the process of childbirth, and her image suggests a similar combination of gendered attributes. But, unlike Cihuacoatl, who combined sartorial images of femininity with external accoutrements of masculinity, many other god(desse)s, including Tlazolteotl, 'played' with concepts of sexual excess and the human body while also asserting the coming together of genders. Thus we witness, in Figure 12 (from the Codex Laud), Tlazolteotl's exposed breasts signifying the sexed female body, while other elements signify a coming together of two genders and a phallic symbolism.83 We see that Tlazolteotl wears a skirt, a feminine cueitl, but even on the skirt we note a problematic notion: the bones signify her role in sacrifice, largely considered a masculine ritual sphere. Still, many sacrifices occur for the god(desse)s, so even though male priests and victims dominate most of the ceremonies from the vantage points of the viewers, the god(desse)s play a major role. Further, the cihuateteo commonly wore such skirts.84 More centrally, emanating from beneath Tlazolteotl's skirt, we find a loincloth, a seemingly exclusive signifier of the male body, intended to evoke the male member. As we rarely see penises in any Nahua texts, one might suggest that the author intends the loincloth to evoke the penis; to suggest its presence without directly showing it. The loincloth is thus a signifier without a signified.\n\nFigure 12 Tlazolteotl.\n\nReprinted from Codex Laud (facsimile), Ferdinand Anders, ed. (Austria: Akademische Druck- und Verla- gsanstalt; Mexico City: Fondo de Cultura Econ\u00f3mica, 1994), p. 29.\n\nThe signifier (loincloth) is a creative application of the signified (phallus) that does not exist in any place but the symbolic sphere. Thus, while a Nahua individual can imagine the possibility of a penis beneath Tlazolteotl's loincloth, just as that individual can imagine the possibility of a penis beneath the man's loincloth, in both cases the Nahua cultural and linguistic frames intend the loincloth not to assert such an imaginary, but rather to leave a symbolic imprint that relates to the power and prestige of the individual wearing the loincloth. The tlacuilo does not intend to make the Nahua commoner believe that Tlazolteotl's loincloth hides her penis. Rather, these authorial voices intend the loincloth to evoke a certain sense of awe at the power (encoded as phallic) of the individual thus portrayed.85\n\nBut Tlazolteotl cannot be coded as male. She gives birth to children, and she signifies a feminine sexuality that seems at one moment out of control and at another moment not only in control but also leading to the continuation of society. In another image from the Codex Laud (Figure 13), we see Tlazolteotl in much of her traditional costume and headdress.86 Here she holds cotton-spinning implements in one hand and sacrificial implements in the other. She wears a cueitl, but instead of the loincloth we saw above, she here has a serpent coming out from beneath her skirt. The serpent's head encloses the head of a man also seen on the other side of the image. The man wears the mask of Ehecatl, the god of wind. The man's head connects with a body that seems to disappear into a glyph that contains some serpent-like creatures. The man points a (beckoning? accusatory?) finger at Tlazolteotl. All the while, underneath the man, we see an unusual image of a naked woman in a squatting (childbirth?) position, with her pubic hair highlighted. This woman has many of the features of Tlazolteotl, but she lacks the facial paint and the identifying markers associated with spinning cotton. The woman connects with the highly feminine Tlazolteotl, who herself connects with the phallic figure, the god of wind. All together, they signify a coherent, if excessive, unity. Tlazolteotl becomes at once a phallic aggressor (using Ehecatl to have sex with the woman?) and a god(dess) engaged in feminine sexuality (being the woman, having sex with Ehecatl?).\n\nFigure 13 Tlazolteotl.\n\nReprinted from Codex Laud (facsimile), Ferdinand Anders, ed. (Austria: Akademische Druck- und Verlagsanstalt; Mexico City: Fondo de Cultura Econ\u00f3mica, 1994), p. 39.\n\nThus, for Tlazolteotl, her character as a god(dess) stems from her excessive activity, seemingly in both the masculine and feminine sexual spheres. Her phallus, whether as a snake or as a loincloth, never entirely obscures her skirt. Both are necessary for her to engage in her excessive behaviour.\n\nTlazolteotl's sexual excess, a central part of her character, points to her position as a gender-indeterminate deity. With her secondary sexual characteristics often shown, we must categorise her as a goddess. Yet here I have argued that the more important categorisation is the grammatically impossible position of the god(dess), one who signified the power of both genders, but primarily through symbolic structures and sexual excesses. If we are to 'separate gender and sexuality analytically to more accurately reflect their separate social existence', we fail to analyse Tlazolteotl, at least as she existed before the Spanish arrived. If instead, we use this theoretical intervention as a point of contention, we may be able to find a 'traffic in women' that is loaded with phallic significance \u2013 and colonial context.\n\nRemembering Cihuacoatl\n\nIn 1539 in the Nahua town of Culhuacan, the leader of the community led his people in the worship of a series of deities among the most prominent fertility gods, at a place called Xochitlan ('Flower Land'), probably referring to Tamoanchan, the home of the gods.87 Xochitlan related to a cave in Culhuacan in which they performed the ceremonies. The cave, signifying the womb of the earth god(dess), was the place where they worshipped Tezcatlipoca (a warrior god) and Cihuacoatl.88 There, several priests dressed in the (unspecified) clothes of the gods began to sacrifice their own blood. Then they performed a heart excision sacrifice of a youth, feeding his heart and his blood to Tezcatlipoca and Cihuacoatl.89\n\nAs little assimilation would have occurred by 1539, the promotion of such deities is unsurprising. Even in 1629, though, we find that Cihuacoatl survived in the memories and imaginations of some Nahuas. In an idolatry investigation, we find Nahuas worshipping this god(dess). There the god(dess) helped to capture deer and engage in curing rites.90\n\nHow is it possible that Nahua leaders promoted a religion devoted to Cihuacoatl and the others? How is it possible that commoners worshipped her and other fertility god(desse)s with such vigour? The seventeenth-century Nahua commoners produced a memory of fertility god(desse)s not because of the needs of an obscure pre-conquest system that we remember as the Aztec empire, but rather because of their contemporary needs and desires. They needed to make the earth fertile and to produce cures for disease. They desired gods that would aid them in sexual performance. Catholicism could not do this, so Nahua commoners used oral and written practice to keep re-producing their fertility god(desse)s. The commoners in particular imagined Cihuacoatl as a god(dess) linked closely with both warfare and fertility. And she promoted feminine sexuality.\n\nWe fail, though, to understand her position if we promote a strict division between gender and sexuality. Indeed, neither of these categories is adequate to describe and analyse the positions of the god(desse)s, their changes through colonialism and their ritual purposes. Rubin's call to separate gender and sexuality from each other becomes, in the story of the Nahuas, an incomplete project. While we must analyse sexuality as a unit distinct from gender, we cannot do so for non-western peoples unless we develop different theoretical and methodological frameworks for understanding the positions of Nahua deities and people.\n\nVictor Turner argues that the liminal space of ritual is likened to the womb, bisexuality and other elements.91 'Betwixt and between' and 'bisexual' sound like good ways to contextualise Nahua beliefs in Cihuacoatl, Tlazolteotl and the others. But Turner himself used this place to analyse not deities, but rather human participants in ritual performance. Moreover, the deities signify not liminality, but rather large containers, bundles of attributes that had the power to transform all. Through a close analysis of the ritual process, writ large and small, we can determine the ways in which the deities become entities that exceed gender and transform sexuality. Hence, as we re-enter the Nahua world in order to develop a better analysis of sexuality as it presents itself in non-western societies, we necessarily move beyond not only the all-encompassing category of gender, as Rubin advocates, but also the supposedly stable category of sexuality.\n\nNotes\n\n1. For the purposes of this chapter, I use the term 'Nahua' to refer to the bulk of the indigenous population of central Mexico, those who spoke the language of Nahuatl, at the time of the Spanish conquest. I will refer to the people from Tenochtitlan, the capital of the 'Aztec empire' in power when the Spaniards arrived, by the name that they used at the time, 'Mexica'.\n\n2. Diego Dur\u00e1n, Book of the Gods and Rites and the Ancient Calendar, ed. and tr. Fernando Horcasitas and Doris Heyden (Norman: University of Oklahoma Press, 1971), p. 210.\n\n3. Many have challenged this concept of a rigorous separation, but the mythology still prevails. For two very different types of challenges, see Inga Clendinnen, Aztecs: An Interpretation (Cambridge: Cambridge University Press, 1991); Susan Schroeder, Stephanie Wood and Robert Haskett (eds), Indian Women of Early Mexico (Norman: University of Oklahoma Press, 1997).\n\n4. While a complete answer to such a question would require a book (and the reader would remain unsatisfied even then), a few notes are warranted here.\n\n5. See Thelma D. Sullivan, 'Tlazolteotl-Ixcuina: The Great Spinner and Weaver', in Elizabeth Hill Boone (ed.), The Art and Iconography of Late Post-Classic Central Mexico (Washington, DC: Dumbarton Oaks, 1982).\n\n6. Gayle Rubin, 'Thinking Sex: Notes for a Radical Theory of the Politics of Sexuality', in Carol S. Vance (ed.), Pleasure and Danger (Boston: Routledge, 1984), here p. 308.\n\n7. See especially, Eve Kosovsky Sedgwick, Epistemology of the Closet (Berkeley and Los Angeles: University of California Press, 1990); Michael Warner, The Trouble with Normal: Sex, Politics, and the Ethics of Queer Life (New York: Free Press, 1999); Lee Edelman, No Future: Queer Theory and the Death Drive (Durham: Duke University Press, 2004).\n\n8. While the Nahuas did not have terms that easily translate as either 'gender' or 'sexuality', they did have concepts that related to these two. See Pete Sigal, 'Latin America and the Challenge of Globalizing the History of Sexuality', American Historical Review 114 (2009), pp. 1340\u201353.\n\n9. On the Nahuas before the conquest, see Cecelia Klein, 'The Shield Women: Resolution of An Aztec Gender Paradox', in Alana Cordy-Collins and Douglas Sharon (eds), Current Topics in Aztec Studies: Essays in Honor of Dr. H. B. Nicholson (San Diego, CA: San Diego Museum of Man, 1993); Cecelia Klein, 'Fighting with Femininity: Gender and War in Aztec Mexico', in Richard C. Trexler (ed.), Gender Rhetorics: Postures of Dominance and Submission in History (Binghamton: Medieval and Renaissance Texts and Studies, 1994); Sharisse D. McCafferty and Geoffrey G. McCafferty, 'The Conquered Women of Cacaxtla: Gender Identity or Gender Ideology', Ancient Mesoamerica 5 (1994), pp. 159\u201372; Susan Kellogg, 'The Woman's Room: Some Aspects of Gender Relations in Late Pre-Colonial Tenochtitlan', Ethnohistory 42 (1995), pp. 563\u201376. On post-conquest Nahuas, see esp. the articles in Schroeder, Wood and Haskett, Indian Women of Early Mexico. For a view that places a stronger emphasis on gender hierarchy, see Steve J. Stern, The Secret History of Gender: Women, Men, & Power in Late Colonial Mexico (Chapel Hill: University of North Carolina Press, 1995).\n\n10. See Noem\u00ed Quezada, Amor y magia amorosa entre los Aztecas: Supervivencia en el M\u00e9xico colonial (Mexico City: Universidad Nacional Aut\u00f3noma de M\u00e9xico, 1975).\n\n11. Several scholars have analysed the fertility rituals and the ways in which they allowed the Nahuas to connect different realms of existence. Particularly one can note the methods of these religious rituals in expressing a position for the performers that is in between the different realms described. See Alfredo L\u00f3pez Austin, Hombre-dios: Religi\u00f3n y pol\u00edtica en el mundo n\u00e1huatl (Mexico City: Universidad Nacional Aut\u00f3noma de M\u00e9xico, 1973); Y\u00f3lotl Gonz\u00e1lez Torres, El sacrificio humano entre los mexicas (Mexico City: Fondo de Cultura Econ\u00f3mica, 1985); Silvia Lim\u00f3n Olvera, Las cuevas y el mito de origen: Los casos inca y mexica (Mexico City: Consejo Nacional para la Cultura y las Artes, 1990); Serge Gruzinski, Man Gods of the Mexican Highlands: Indian Power and Colonial Society, 1520\u20131800 (Stanford: Stanford University Press, 1989); David Carrasco, City of Sacrifice: Violence From the Aztec Empire to the Modern Americas (Boston: Beacon Press, 2000); Clendinnen, Aztecs.\n\n12. David Carrasco makes this point in City of Sacrifice. While he provides far too much of a functionalist explanation for rituals of violence, his point linking governance with fertility rites seems particularly apt. See also Pete Sigal, The Flower and the Scorpion: Ritual and Sexuality in Early Nahua Culture (Durham: Duke University Press, forthcoming).\n\n13. Louise Burkhart, The Slippery Earth: Nahua-Christian Moral Dialogue in Sixteenth-Century Mexico (Tucson: University of Arizona Press, 1989).\n\n14. See Burkhart, Slippery Earth, pp. 98\u2013110, 181\u20133; Gruzinski, 'Individualization and Acculturation'.\n\n15. See Hugo G. Nutini and John M. Roberts, Bloodsucking Witchcraft: An Epistemological Study of Anthropomorphic Supernaturalism in Rural Tlaxcala (Tucson: University of Arizona Press, 1993); James M. Taggart, Nahuat Myth and Social Structure (Austin: University of Texas Press, 1983).\n\n16. For an example of such a historical reading in a western tradition, see Leo Bersani and Ulysse Dutoit, Caravaggio's Secrets (Cambridge: Massachusetts Institute of Technology Press, 1998).\n\n17. For two excellent examples of such contextual reading, see Gordon Brotherston, Painted Books from Mexico: Codices in UK Collections and the World They Represent (London: British Museum Press, 1995); Jeanette Favrot Peterson, The Paradise Garden Murals of Malinalco: Utopia and Empire in Sixteenth-Century Mexico (Austin: University of Texas Press, 1993).\n\n18. On the pre-conquest tlacuilo, see Eduard Seler, Collected Works in Mesoamerican Linguistics and Archaeology: English Translations of German Papers from Gesammelte Abhandlungen Zur Amerikanischen Sprach- Und Alterthumskunde, ed. Charles P. Bowditch, 5 vols (1939; Culver City: Labyrinthos, 1990); Karl Anton Nowotny, Tlacuilolli: Style and Contents of the Mexican Pictorial Manuscripts with a Catalog of the Borgia Group, ed. and tr. George A. Everett, Jr and Edward B. Sisson (Norman: University of Oklahoma Press, 2005); Donald Robertson, Mexican Manuscript Painting (Norman: University of Oklahoma Press, 1959); Brotherston, Painted Books from Mexico; Gordon Brotherston, Feather Crown: The Eighteen Feasts of the Mexica Year (London: British Museum Press, 2005); Elizabeth Hill Boone, Stories in Red and Black: Pictorial Histories of the Aztecs and Mixtecs (Austin: University of Texas Press, 2000); Patrick Johansson K., 'La imagen en los c\u00f3dices nahuas', Estudios de Cultura N\u00e1huatl 32 (2001), pp. 69\u2013124. On his post-conquest iteration, see Serge Gruzinski, La colonisation de l'imaginaire: Soci\u00e9t\u00e9s indig\u00e8nes et occidentalisation dans le Mexique espagnol, XVIe\u2013XVIIIe si\u00e8cle (Paris: Gallimard, 1988); James Lockhart, The Nahuas After the Conquest: A Social and Cultural History of the Indians of Central Mexico, Sixteenth Through Eighteenth Centuries (Stanford: Stanford University Press, 1992).\n\n19. For examples of interpretations from the Borgia group, along with the Mixtec codices, see Elizabeth Hill Boone (ed.), The Art and Iconography of Late Post-Classic Central Mexico: A Conference at Dumbarton Oaks, October 22nd and 23rd, 1977 (Washington, DC: Dumbarton Oaks, 1982).\n\n20. See particularly K. A. Nowotny's commentary, in Tlaculolli, on the Codex Borgia.\n\n21. Robertson, Mexican Manuscript Paintings; Brotherston, Feather Crown.\n\n22. Robertson, Mexican Manuscript Paintings.\n\n23. See Walden Browne, Sahag\u00fan and the Transition to Modernity (Norman: University of Oklahoma Press, 2000); Pete Sigal, 'Queer Nahuatl: Sahag\u00fan's Faggots and Sodomites, Lesbians and Hermaphrodites', Ethnohistory 54 (2007), pp. 9\u201334.\n\n24. On the importance of the tlatoani and the cihuacoatl, see Susan Gillespie, The Aztec Kings: The Construction of Rulership in Mexica History (Tucson: University of Arizona Press, 1992); Robert Haskett, Indigenous Rulers: An Ethnohistory of Town Government in Colonial Cuernavaca (Albuquerque: University of New Mexico Press, 1991).\n\n25. Dur\u00e1n, Book of the Gods, p. 217.\n\n26. Cecelia Klein, 'Rethinking Cihuacoatl: Aztec Imagery of the Conquered Woman', in J. Kathryn Josserand and Karen Dakin (eds), Smoke and Mist: Mesoamerican Studies in Memory of Thelma D. Sullivan (Oxford: British Archaeological Reports, 1988).\n\n27. Codex Borbonicus (facsimile) (Madrid, Vienna, Mexico City: Sociedad Estatal Quinto Centenario, Akademische Druck- und Verlagsanstalt, Fondo de Cultura Econ\u00f3mica, 1991), pp. 21, 24, 25, 34. The image is from p. 34.\n\n28. See Richard C. Trexler, Sex and Conquest: Gendered Violence, Political Order, and the European Conquest of the Americas (Ithaca: Cornell University Press, 1999); Clendinnen, Aztecs; McCafferty and McCafferty, 'The Conquered Women of Cacaxtla'; Rosemary Joyce, Gender and Power in Prehispanic Mesoamerica (Austin: University of Texas Press, 2000).\n\n29. Codex Borbonicus, p. 21.\n\n30. Clendinnen, Aztecs; Klein, 'Fighting with Femininity'.\n\n31. Klein, 'Rethinking Cihuacoatl', p. 239.\n\n32. Klein, 'Rethinking Cihuacoatl'.\n\n33. It is of course a phenomenon of interest in the game of statehood and alliances, as often Mexica princesses married powerful leaders of other states that had been conquered or to whom the Mexica were allied.\n\n34. See Bernardino de Sahag\u00fan, C\u00f3dice florentino (facsimile) (Florence and Mexico City: Biblioteca Medicea Laurenziana and Archivo General de la Naci\u00f3n, 1979), book 2, fol. 68r.\n\n35. Sahag\u00fan, C\u00f3dice florentino, book 2, fol. 69v.\n\n36. See Ross Hassig, Aztec Warfare: Imperial Expansion and Political Control (Norman: University of Oklahoma Press, 1988). See also Kay Read and Jane Rosenthal, 'The Chalcan Woman's Song: Sex as a Political Metaphor in Fifteenth-Century Mexico', Americas 62 (2006), pp. 313\u201348.\n\n37. See Sahag\u00fan, C\u00f3dice florentino, book 3, fol. 2r.\n\n38. See Sahag\u00fan, C\u00f3dice florentino, book 3, fols 2v\u20133v.\n\n39. Those who have looked at Coyolxauhqui as a feminist heroine have largely ignored the implicit and explicit critique of feminine sexuality in Coyolxauhqui's presence. While her dismembered body was remembered in the Nahua universe as feminine subordination, and thus may be resurrected in some way to assert feminist agency, one cannot ignore the sexually repressive nature of her role in this battle. See Gloria Anzald\u00faa, Borderlands\/La Frontera: The New Mestiza (San Francisco: Aunt Lute Books, 1987); Alicia Arriz\u00f3n, Queering Mestizaje: Transculturation and Performance (Ann Arbor: University of Michigan Press, 2006).\n\n40. Alfredo L\u00f3pez Austin, Tamoanchan, Tlalocan, tr. Bernard R. Ortiz de Montellano and Thelma Ortiz de Montellano (Niwot: University Press of Colorado, 1997), pp. 235\u20138; Michel Graulich, 'Les grandes statues azteques dites de Coatlicue et de Yollotlicue', in Raquel Thiercelin (ed.), Andes et M\u00e9so-Am\u00e9rique: Cultures et soci\u00e9t\u00e9s (Aix-en-Provence: Universit\u00e9 de Provence, 1991). See also Susan Milbrath, 'Decapitated Lunar Goddesses in Aztec Art, Myth, and Ritual', Ancient Mesoamerica 8 (1997), pp. 185\u2013206.\n\n41. See Cecelia Klein, 'A New Interpretation of the Aztec Statue Called Coatlicue, \"Snakes-Her-Skirt\"', Ethnohistory 55 (2008), pp. 229\u201350. Klein argues persuasively that the decapitated Coatlicue signifies not the woman punished in this battle, but rather the goddess who engages in self-sacrifice to serve humanity.\n\n42. The image comes from the Templo Mayor, an excavation of the main temple of Tenochtitlan.\n\n43. See Sigal, Flower and the Scorpion.\n\n44. On the Spanish, there is a vast literature. See particularly Ann Twinam, Public Lives, Private Secrets: Gender, Honor, Sexuality, and Illegitimacy in Colonial Spanish America (Stanford: Stanford University Press, 1999).\n\n45. See Schroeder, Wood and Haskett, Indian Women of Early Mexico; Susan Kellogg, Weaving the Past: A History of Latin America's Indigenous Women from the Prehispanic Period to the Present (New York: Oxford University Press, 2005).\n\n46. Gayle Rubin, 'The Traffic in Women: Notes on the Political Economy of Sex', in Rayna R. Reiter (ed.), Toward an Anthropology of Women (New York: Monthly Review Press, 1975), here pp. 173\u20137.\n\n47. See Jacques Lacan, 'The Signification of the Phallus', in \u00c9crits: The First Complete Edition in English, tr. Bruce Fink (1966; New York: Norton, 2002).\n\n48. See Klein, 'Rethinking Cihuacoatl'.\n\n49. Tonalamatl of Aubin (facsimile), <<http:\/\/www.famsi.org\/research\/loubat\/Tonalamatl\/thumbs0.html>> (accessed 21 May 2010), p. 5.\n\n50. Codex Borbonicus, p. 3.\n\n51. Codex Telleriano-Remensis (facsimile), in Eloise Qui\u00f1ones Keber (ed.), Codex Telleriano-Remensis: Ritual, Divination, and History in a Pictorial Aztec Manuscript (Austin: University of Texas Press, 1995), p. 170; Sullivan, 'Tlazolteotl-Ixcuina'.\n\n52. See Sahag\u00fan, C\u00f3dice florentino, book 1, fols 5r\u20136v.\n\n53. Codex Telleriano-Remensis, p. 171.\n\n54. Codex Telleriano-Remensis, pp. 170\u201371.\n\n55. See Codex Borgia (facsimile), ed. Gisele D\u00edaz and Alan Rodgers (New York: Dover, 1993), p. 65. See also the parallel image on p. 67, where a masculine god appears in the same position as Chalchiuhtlicue.\n\n56. Chalchiuhtlicue and Tlazolteotl together create a future. Through the figure of the phallic god(dess), we find that Nahua community will survive.\n\n57. Codex Borgia, plate 74.\n\n58. The flower signified the fertility of the world, and when connected with Tlazolteotl, related closely to sexual excess. On Tlazolteotl and all of the other goddesses in the Codex Borgia, see Mar\u00eda de los Angeles Ojeda D\u00edaz, Las Diosas en los C\u00f3dices del Grupo Borgia: Arquetipos de las mujeres del postcl\u00e1sico, <<http:\/\/www.arts-history.mx\/diosas>> (accessed 4 April 2009). On Tlazolteotl's relationship to the birthing process, see Ernesto De La Torre, 'El nacimiento en el mundo prehisp\u00e1nico', Estudios de Cultura N\u00e1huatl 34 (2003), pp. 369\u201390.\n\n59. See Cecelia Klein, 'Wild Woman in Colonial Mexico: An Encounter of European and Aztec Concepts of the Other', in Claire Farago (ed.), Reframing the Renaissance: Visual Culture in Europe and Latin America, 1450\u20131650 (New Haven: Yale University Press, 1995).\n\n60. See Sullivan, 'Tlazolteotl-Ixcuina'; Patrice Giasson, 'Tlazolteotl, diedad del abono, una propuesta', Estudios de Cultura N\u00e1huatl 32 (2001), pp. 135\u201357.\n\n61. Hernando Ruiz de Alarc\u00f3n, Treatise on the Heathen Superstitions That Today Live Among the Indians Native to this New Spain, 1629, ed. J. Richard Andrews and Ross Hassig (Norman: University of Oklahoma Press, 1984), p. 136.\n\n62. Ruiz de Alarc\u00f3n, Treatise on Heathen Superstitions, p. 136.\n\n63. See Pete Sigal, 'The Cuiloni, The Patlache, and the Abominable Sin: Homosexualities in Early Colonial Nahua Society', Hispanic American Historical Review 85 (2005), pp. 555\u201394.\n\n64. Codex Magliabechiano (facsimile) (Vienna: Akademische Druck- und Verlagsanstalt, 1970), p. 155.\n\n65. Ruiz de Alarc\u00f3n, in Treatise on Heathen Superstitions, pp. 137\u20138, states, 'Finally, it occurs to me that in this bath our Enemy has intended to imitate the Holy Sacrament of baptism since (as we Christians believe that by this means we attain the purity of the soul and the remedy against all the harms of faults and their results) this old and astute Enemy seeks that these unfortunate people, blind in their heathen errors, believe and persuade themselves that by these feigned baths they can attain the cleanliness of the body and free themselves of the diseases of temporal pains and harms. May God, through his mercy, disillusion them and bring them to a true knowledge, by inspiring in his ministers new fervors for the teaching of such a blind and barbarous people, in order that everything be converted into His great power and glory. Amen.' Here he repeats a common Catholic formula, often repeated in the Inquisition when Inquisitors pursue witches: the devil works to mimic Christian ritual in order fool people into believing that they are serving God. This is in fact what makes the devil so dangerous. For comments on this type of thought and the way it fits into conceptions of witchcraft, see Laura Lewis, Hall of Mirrors: Power, Witchcraft, and Caste in Colonial Mexico (Durham: Duke University Press, 2003).\n\n66. Codex Magliabechiano, p. 91.\n\n67. Dur\u00e1n, Book of the Gods and Rites and the Ancient Calendar, p. 210.\n\n68. See Klein, 'Fighting with Femininity'.\n\n69. Codex Magliabechiano, p. 90.\n\n70. See Cecelia Klein, 'The Devil and the Skirt: An Iconographic Inquiry into the Prehispanic Nature of the Tzitzimime', Ancient Mesoamerica 11 (2000), pp. 1\u201326.\n\n71. Codex Tudela (facsimile) (Madrid: Ediciones Cultura Hisp\u00e1nica, 1980), fol. 46r; Codex Magliabechiano, p. 153.\n\n72. Codex Magliabechiano, p. 152.\n\n73. See Klein, 'Devil and the Skirt'.\n\n74. See Lisa Sousa, 'The Devil and Deviance in Native Criminal Narratives from Early Mexico', Americas 59 (2002), pp. 161\u201379; Fernando Cervantes, The Devil in the New World: The Impact of Diabolism in New Spain (New Haven: Yale University Press, 1994).\n\n75. Klein, 'Devil and the Skirt'.\n\n76. See Klein, 'Devil and the Skirt', p. 14.\n\n77. Klein, 'Rethinking Cihuacoatl'.\n\n78. Codex Laud (facsimile) (Vienna: Akademische Druck- und Verlagsanstalt, 1966), pp. 27, 30.\n\n79. See F\u00e9lix B\u00e1ez-Jorge, La voces del agua: El simbolismo de las Sirenas y las mitolog\u00edas americanas (Xalapa: Universidad Veracruzana, 1992).\n\n80. In the standard image of a Nahua woman, she is represented by her skirt and often her huipil, but not by a loincloth, a prototypical male signifier.\n\n81. Sahag\u00fan, C\u00f3dice florentino, book 6, fol. 142r.\n\n82. See Hassig, Aztec Warfare.\n\n83. Codex Laud, p. 29.\n\n84. Indeed, Klein ('Devil and the Skirt', p. 10) notes, following Caso, that the skull and crossbones specifically signify the cihuateteo.\n\n85. This view of the phallus as a signifier without a signified, or as intended to play a role only in the symbolic sphere \u2013 to assert power rather than the penis in the social sphere, relates to Lacan's analysis of a very different society and time period. The phallus in the Nahua world was a key signifier, as we can witness in the variety of phallic images in the pre-conquest texts. While one cannot provide a Lacanian analysis of texts that do not fit into the society and timeframe of Lacan, I note the important parallels. For example, at one point Lacan argues, while critiquing another analyst's view of a particular woman, that nature and anatomy are irrelevant to analysis: 'Of course... [the phallus is] symbolic. It is in so far as the woman is in a symbolic order with an androcentric perspective that the penis takes on this value. Besides, it isn't the penis, but the phallus, that is to say something whose symbolic usage is possible because it can be seen'. Jacques Lacan, The Seminar of Jacques Lacan, book 2: The Ego in Freud's Theory and the Technique of Psychoanalysis, tr. Sylvana Tomaselli (1978; New York, Norton, 1991), p. 272. Thus the signifier does not necessarily link to a signified anatomy, though one may imagine such a bodily portrayal, but rather must link to the symbolic world through which the signifier derives meaning. The phallus, the place of desire in the androcentric perspective of the western world, becomes for the Nahuas not necessarily the signifier of desire, but instead the central place of fertility in the Nahua cosmological universe. Thus we will see the presence of the phallus as a sign that fertility goes well beyond the signified use of male (or female) anatomy.\n\n86. Codex Laud, p. 39.\n\n87. See L\u00f3pez Austin, Tamoanchan, Tlalocan.\n\n88. On the symbolism of the cave and the womb, see F\u00e9lix B\u00e1ez-Jorge, Eduardo Matos Moctezuma and Jacques Galinier, El lugar de la captura: Simbolismo de la vagina tel\u00farica en la cosmovisi\u00f3n mesoamericana (Miradores del Mar: Editora de Gobierno del Estado de Veracruz, 2008); Lim\u00f3n Olvera, Las cuevas y el mito de origen.\n\n89. Archivo General de la Naci\u00f3n, Mexico City, Inquisici\u00f3n 42, 18; Luis Gonz\u00e1lez Obreg\u00f3n, Procesos de Indios Id\u00f3latras y Hechiceros (Mexico City: Secretar\u00eda de Relaciones Exteriores, 1912), pp. 177\u201384.\n\n90. Ruiz de Alarc\u00f3n, Treatise on Heathen Superstitions, pp. 98, 205.\n\n91. Victor Turner, The Ritual Process: Structure and Anti-Structure (Chicago: Aldine, 1969), p. 95.\nChapter 2\n\nPower and Historical Figuring: Rachael Pringle Polgreen's Troubled Archive\n\nMarisa J. Fuentes\n\nScandal and excess inundate the archive... the libidinal investment in violence is everywhere apparent in the documents, statements and institutions that decide our knowledge of the past.1\n\nSaidiya Hartman\n\nHistory reveals itself only through the production of specific narratives. What matters most are the process and conditions of such narratives... Only through that overlap can we discover the differential exercise of power that makes some narratives possible and silences others.2\n\nMichel-Rolph Trouillot\n\nIt may be precisely due to Rachael Pringle Polgreen's 'exorbitant circumstances' during her life as a free(d) woman of colour in late eighteenth-century Bridgetown, Barbados, that her narrative has not changed since she appeared in the 1842 novel Creoleana.3 Apart from an important critique by Melanie Newton of the political and historical context of J. W. Orderson's Creoleana, the recounting of Polgreen's life story \u2013 her triumphs, extraordinary relationships and visual depictions \u2013 remains untouched since the nineteenth century. Thus, the archive and secondary historical accounts beg re-examination. She was a woman of colour, a former slave turned slave owner, and many stories circulate that she ran a well-known brothel without much legal controversy.4 The persistent historical representations of her life draw from an archive unusual for many free(d) and enslaved women of colour in eighteenth-century slave societies. Polgreen left a will and her estate was inventoried by white men upon her death \u2013 a process reserved primarily for the society's wealthier (white) citizens. Her relationships with elite white men and the Royal Navy are well documented in newspaper accounts and most significantly, in the nineteenth-century novel written by a resident of Bridgetown who may have been well acquainted with Polgreen. In the 1770s and 1780s, Polgreen appears in Bridgetown's tax records as a propertied resident and her advertisements in a local newspaper allude to the importance she placed on property. From a caricatured 1796 lithograph to the folkloric accounts of Prince William Henry's (later King William IV) rampage through her brothel, Polgreen's story has in many ways been rendered impermeable, difficult to revise and over-determined by the language and power of the archive.\n\nThe archive conceals, distorts and silences as much as it reveals about Rachael Polgreen. J. W. Orderson's 1842 novel, Creoleana, in which a 'complete' dramatised life story of Polgreen is narrated, provides a tantalising solution to gaps and uncertainties for historians who struggle with the fragmented and fraught records of female enslavement marked by the embedded silences, the commodified representations of bodies, and the epistemic violence of slavery's archive. However, for Polgreen, it is perhaps her hyper-visibility in images and stories that continues to obscure her everyday life, even when the archive appears to substantiate certain aspects of that life. I contend that such powerful narratives, visual reproductions and archival assumptions erase the crucial complexities of her personhood and obfuscate the violent and violating relationships she maintained with other women of colour in Bridgetown's slave society. The challenge then, is to track power in the production of her history while recognising that Polgreen's historical visibility is also an erasure of the lives of those she enslaved.\n\nIn the scholarship of slavery and slave society in Barbados, the lives of Polgreen and other free(d) women of colour are centred on narratives about business acumen and entrepreneurship. Several historians discuss the significant role prostitution played in the local and transnational market economy. Indeed, in many of the eighteenth-century Caribbean and metropolitan Atlantic port cities prostitution was rampant, serving a significant mobile military population as well as providing local 'entertainment'.5 'During the 1790s', Melanie Newton states, 'the symbol of non-white business success in Barbados was the female hotelier'.6 A number of free(d) women found slave owning and prostitution economically viable routes to self-sustenance as they and other free(d) people of colour in slave societies were systemically excluded from many other roles and opportunities.7 Though many references to free(d) women of colour mention their involvement in the sexual economy of port cities, we must also note that in Bridgetown there was a unique demographic of a majority white female population by the beginning of the eighteenth century. This white female (and mostly slave-owning) majority tended to own more women than men, and set the precedent for the selling and renting out of enslaved women for sexual purposes.8 Moreover, in a town setting with little arable land, white women profited from a surplus of domestic labourers by hiring them out to island visitors.9 It is thus within Bridgetown's bustling port environment of slaves, sailors, Royal Navy officers and other maritime traffic that Rachael Polgreen made her living.\n\nPolgreen necessarily appears in histories of gender and slavery in Barbados as she lived a remarkable life within a slave society. However, the other enslaved and freed women who lived in similar circumstances during her time are eclipsed and silenced by her seductive narrative. This article is a meditation on tracking how material and discursive power moves through the archive in the historical production of subaltern women.10 Moreover, revisiting the documentary traces of Polgreen's life and death illuminates several contradictions or historical paradoxes that make it problematic to characterise Polgreen or enslaved and free(d) women's sexual relations with white men as unmediated examples of black female agency. How does one write a narrative of enslaved 'prostitution'? What language should we use to describe this economy of forced sexual labour? How do we write against historical scholarship that too often relies upon the discourses of will, agency, choice and volunteerism, which reproduce a troubling archive that cements enslaved and free(d) women of colour in representations of 'their willingness to become mistresses of white men'?11 If 'freedom' meant free from bondage but not from social, economic and political degradation what does it mean to survive under such conditions?\n\nIn an analysis of the processes by which Polgreen is historically confined, I challenge previous assumptions about her lived experiences by attending to the ways in which enslaved and free(d) women enter history.12 The first part of this article sets the scene of Barbados and Bridgetown in the late eighteenth century in order to give context to the lives of these Afro-Barbadian women. Second, I re-examine the secondary literature and present new archival traces of Polgreen's material life to reveal an image incommensurate with a triumphant narrative. Engaging with secondary sources on Barbados illuminates the specific gendered and sexual representations of women in Caribbean slave societies, and demonstrates how these images are reproduced in the historiography. Presenting previously unexamined archival material from Barbadian deeds and British parliamentary debates on Caribbean slavery, this article demonstrates the ways in which Polgreen's 'agency' depended upon the sexual subjugation of other black women and supported a system of slavery established and perpetuated by the white colonial authority. At stake in this discussion of Rachael Polgreen's power (inhabited and represented) is the desire to make plain how the archive and historical production facilitate the survival of particular stories and the erasure of others.\n\n* * *\n\nBy the second half of the seventeenth century, Barbados was considered the 'crown jewel' of the British Caribbean colonies. As the first point of disembarkation for British slaving vessels and a significant port of call for the British military, the colony of Barbados was pivotal in the networks of trade and profit which propelled Britain to economic prosperity. According to Richard Dunn, Barbados dominated the sugar and shipping markets beyond any other British colony.13 In order to sustain sugar production, Barbados planters and merchants bought into and sustained the trade in African captives throughout the seventeenth and eighteenth centuries. By 1670, Barbados was firmly established as an economy dependent upon enslaved labour.14 Bridgetown, the capital port city in which Rachael Polgreen resided, received hundreds of ships a year laden with material products and captive Africans, who supplied the labour for sugar plantations as well as domestic labour in town. Although demographic sources are rare for the eighteenth century, Jerome Handler estimates that in 1786 there were approximately 62,115 slaves, 16,167 whites, and 838 free people of colour living in the colony.15 In the 1770s and 1780s, Bridgetown's free population of colour remained relatively small but experienced significant growth by the turn of the nineteenth century.16 This small group of 'free coloured' men and women survived through economic activities including store keeping, huckstering, shipbuilding, and in some cases prostitution. The military infrastructure built to support the Royal Navy in and around Bridgetown perpetuated the demand for an informal sexual economy beyond that which the white Barbadian slave-owners had already seized from enslaved women's bodies. As a former slave of a white owner who was possibly her own father, it is probable that Polgreen herself experienced or witnessed the sexual violations of black women that were an inherent part of their enslavement.17\n\nThe gender demographics of Barbados and Bridgetown were unique for a Caribbean colony. Though enslaved men tended to dominate in British plantation societies, there is evidence that Barbadian planters sought to balance the sex ratios amongst the labouring African population and, according to one historian, the island had actually attained a majority female enslaved population by the early eighteenth century.18 Moreover, and equally anomalous, white women constituted a slight majority among the white population during the same period (51 per cent according to the 1715 census) and remained so until the era of emancipation (1834\u201338).19 In Bridgetown, these female majorities influenced the character of urban slave society. For example, Hilary Beckles's scholarship challenges Caribbean historiography that focuses on the planter 'patriarch', showing that '58 per cent of slave owners in [Bridgetown] were female, mostly white... [and] women owned 54 per cent of the slaves in town'. Furthermore, he points out that 'white women also owned more female slaves than male slaves'.20 Thus, female slave-owners like Polgreen made up much of the landscape of urban life. However, Polgreen's business of brothel keeping reveals a divergence from white female slave-owners. Although many white women engaged in 'hiring-out' their female slaves for sexual purposes, there is no evidence suggesting that they engaged in running houses of prostitution in Bridgetown. While Polgreen's ability to accumulate wealth was comparable to her white counterparts, her avenues for profit restricted her to an arena that seems likely to have been shameful and disreputable to white women.\n\nDue to a shift in Caribbean historiography in the mid-1970s, the subject of gender and slavery has received a considerable amount of attention. The scholarship of Hilary Beckles and Barbara Bush opened a field into the study of enslaved and free(d) women of colour across the Caribbean. Out of this commendable effort emerged several studies in which enslaved and free(d) women were 'centred' in historical scholarship.21 For studies focused on Barbados specifically, Jerome Handler's two publications, The Unappropriated People: Freedmen in the Slave Society of Barbados (1974) and 'Joseph Rachell and Rachael Pringle-Polgreen: Petty Entrepreneurs' (1981), laid the blueprint for later discussions of Rachael Polgreen, free women of colour and prostitution.22 'The first of the Bridgetown taverns owned by a freedwoman', Handler asserts, 'appears to have begun operating in the early 1780s and said to have belonged to Rachael Pringle Polgreen'.23 Handler's discussion continues by recounting Polgreen's enslavement by William Lauder, her freedom and rise to 'business' woman \u2013 a story drawn directly from the nineteenth-century novel Creoleana:\n\nBorn around 1753, Rachael was the daughter and slave of William Lauder, a Scottish schoolmaster, and an African woman whom he purchased not long after emigrating to Barbados around 1750... [by] her 'juvenile days', Rachael was a \"remarkably well-made, good-looking girl, possessing altogether charms that [awakened] the libidinous desires of her [father] who made many [unsuccessful] attempts at her chastity.24\n\nIn describing her adult life, Handler uses Creoleana to explain that:\n\nRachael was bought from her father, and then manumitted, by a British naval officer whose mistress she had become; the house he provided for her in Bridgetown ultimately became her celebrated 'Royal Navy Hotel'. At her death in 1791, Rachael owned 'houses and lands' and nineteen slaves, six of whom were to be manumitted by the terms of her will.25\n\nUnderstandably, subsequent historical work has drawn extensively on Handler's authority on Polgreen and free(d) people of colour in Barbados.26 Indeed, several texts mention Polgreen's property accumulation, her relationships with white male elites, her shrewd business management and her demurring yet assertive challenge to the British prince.27 Barbados historian Pedro Welch examined Rachael Polgreen's emergence as a property owner, using the St Michael Levy Books from 1779, to describe the economic possibilities available to enslaved and freed women in town.28 For Welch, Polgreen exemplified resistance. Based on the logic of capitalism, he contends that hoteliers' property ownership 'managed [to] challenge the economic hegemony of whites'. Welch also argues 'that even where alternatives might have existed some slave and free coloured women either prostituted themselves or provided prostitution services for the financial and status gains which derived from such activities'.29\n\nWhile contemporary historians of Barbados have rightly characterised Polgreen as part of a 'coloured elite' who owned property \u2013 including slaves \u2013 and were able to maintain a standard of living comparable to their white counterparts, they do not deal critically with the ways in which 'discourses of seduction obfuscate the reality of violation'.30 By this, I mean to problematise how studies of slavery might too easily equate black female agency with sexuality. Discussions of black women, free or enslaved, using white men as an avenue to freedom often erase the reality of coercion, violence and the complicated positions black women were forced to inhabit in this system of domination. It would seem, based on the current scholarship, that women of colour wielded an inordinate amount of power in these sexual encounters. What is at stake in these interpretations is teasing out how discourses of 'resistance', 'sexual power' and 'will' shape our understanding of female slavery. How is will, as Hartman asks, 'an overextended approximation of the agency of the dispossessed subject\/object of property or perhaps simply unrecognizable in a context in which agency and intentionality are inseparable from the threat of punishment?' What kind of power is gained from the systematic sexual violation of other women? What does this reveal about slavery's system of domination, and Rachael Polgreen's role within it?\n\nMichel-Rolph Trouillot writes of historical power, arguing that history represents both the past (facts and archival materials) and the story told about the past (narrative).31 Polgreen's archival remains and the histories written about her clearly represent this interaction between the processes of historical production and demonstrate her limited power in self-representation (epitomised by her status as a woman of colour, her illiteracy, her former enslavement and engagement in the sex trade), as well as how authors of her subsequent narratives represented her agency through her material success. Throughout her life and afterlife, she served the agendas of divergent political discourses: she was used in the nineteenth century as a motif to remind white society that black women's sexuality must be contained; later, for the postcolonial Barbados elite, she exemplified loyalty to Britain, accommodation and peaceful negotiation.32\n\nWhat documents and processes, then, informed the making of archival records that fashion 'truths' about her experiences? What does it mean that discourses of commodity (that is, her material accumulations) constitute the most accepted sources of Polgreen's significance? In other words, Polgreen's inner self \u2013 her fears and confidences \u2013 remain difficult to retrieve using documents which were produced within a slave society limited by capitalist and elite perspectives.33 A critical re-engagement with the sources elucidates the complexities and contradictions she embodied.\n\nAlthough no existing birth record survives, historians contend that Rachael Polgreen was born Rachael Lauder sometime around 1753.34 Her burial was recorded on 23 July 1791 at the Parish Church of St Michael.35 At her death, her estate was worth 'Two Thousand nine hundred & thirty Six pounds nine Shillings four pence half penny', an amount comparable to a moderately wealthy white person living at the same time.36 According to her inventory, along with ample material wealth in the form of houses, furniture and household sundries, Polgreen owned thirty-eight enslaved people: fifteen men and boys, and twenty-three women and girls.37 In her will, Polgreen freed a Negro woman named Joanna, bequeathing to her an enslaved Negro woman named Amber. Joanna was also given her own son Richard, who was still enslaved. Polgreen also freed a 'mulatto' woman named Princess and four 'mulatto' children (not listed in familial relation to any 'parents'). Polgreen ordered that the rest of her estate \u2013 including William, Dickey, Rachael, Teresa, Dido Beckey, Pickett, Jack Thomas, Betsey, Cesar, a boy named Peter and nineteen other enslaved people \u2013 was to be divided among William Firebrace and his female relatives, William Stevens and Captain Thomas Pringle, all white people with whom she had social ties. The bequest (the enslaved as property) was to them and 'their heirs forever'.38\n\nThe above information survives precisely because of the value placed upon property. Thus, produced through her materiality, Polgreen's archival visibility relies upon the logic of white colonial patriarchal and capitalist functions, reproducing the terms of the system of enslavement. Her burial in the Anglican churchyard of Saint Michael's parish did not, as a triumphant narrative might argue, exemplify transcendence over racial and gendered systems of domination, but rather illustrates the power of her social connections, without which permission for a church burial would not have been granted. We may speculate on the limited degrees of her integration into the white Anglican religious community of Bridgetown, given her profession as a brothel owner. We can also surmise that Polgreen's participation in the sociality of slave ownership and the general acceptance of her economic position by the white community granted her unusual power.\n\nBeyond her will and estate inventory, a lithograph produced by the British artist Thomas Rowlandson and printed in 1796 is another remarkable surviving document (Figure 1).39 This image depicts a large and dark-skinned Rachael Polgreen seated in front of a house purported to be her 'hotel'. Her breasts are revealed through a low-cut dress as she sits open-legged and bejewelled. In the background of the lithograph are three other figures, a young woman and two white men. The young woman is pictured similarly dressed. Her bodice is cut lower, however, than that worn by the seated Polgreen. She stares, almost sullen-faced, at a large white man appearing to the rear of the picture in a tattered jacket and hat.40 Observing the young woman from the right side of the picture is a younger white man wearing a British military uniform. He is a partial figure, shown in profile only. A sign posted behind Polgreen reads: 'Pawpaw Sweetmeats & Pickles of all Sorts by Rachel PP'.41\n\nFigure 1 Illustration by Thomas Rowlandson, published by William Holland (London, 1796), from the collection of the Barbados Museum and Historical Society.\n\nIn 1958, an anonymous editorial preceded the first 'scholarly' article about Polgreen in the Journal of the Barbados Museum and Historical Society. The editorial read the image as a narrative about her life, contending that 'a gifted [caricaturist] such as Rowlandson would not... have placed as a background to the central figure of Polgreen in her later and prosperous years characters such as \"a tall girl in a white frock\", etc. and an officer looking through a window, which had no relation to her or to her career'.42 In the writer's view, the figures in the background represent a young Polgreen, averting the repulsive advances of her master\/father. The young military man represents her 'saviour', Captain Pringle, the man who is credited with granting her freedom. Corresponding with the most pervasive narrative about her life, Polgreen is said to have taken the name Pringle after Captain Pringle who allegedly purchased her from her father\/master William Lauder (d.1771). After settling Polgreen in a house in Bridgetown, Captain Pringle left the island to pursue his military career and in his absence, Rachael Pringle took the name of Polgreen.43\n\nThe editorial does not, however, read into the explicit sexual tone of the sign posted above Polgreen. 'Pawpaw Sweetmeats & Pickles of all Sorts' advertised more than the culinary items available for purchase. Free(d) and enslaved women in towns played a significant if not dominant role in the informal market economy, selling a variety of ground provisions to locals and incoming ships, and the sign above Polgreen clearly situates her within a well-established market system. She can easily assume the part of a market woman seated outside her 'shop'.44 However, the artist's phallic references on the sign also allude to the sexual services offered inside. The language of the consumption of 'Sweetmeats & Pickles' worked to both mask and advertise the sexually overt activities within the tavern. At the same time, the image reinforces the positionality of enslaved black women as sexually available, consenting, consumable and disposable. Many of Rowlandson's works depict London and maritime scenes, filled with sexual references.45 These include sailors and prostitutes in various sexual acts and stages of undress. It may not be surprising then, to find him dedicating an entire collection to what was then described as 'erotic' art.46 Rowlandson's caricature of Rachael Polgreen depicts an extravagant woman of colour in various stages of her life. In one frame, Polgreen is racialised, discursively and visually sexualised starting from her younger lighter self to an older, darker, larger self seated in the foreground. This visual production represents Polgreen's race, gender and sexuality and a complete narrative of her life story as the artist imagined her.\n\nThe material fragments of Polgreen's existence evident in her will, inventory and this visual depiction exemplify Trouillot's concept of archival power.47 Operating on two levels, archival power is present in influencing what is possible to know or not to know about her life. In the first instance, power is present in the making of the archival fragments during her particular historical moment. Her will, recorded by a white male contemporary, leaves evidence only of what was valued in Polgreen's time \u2013 the material worth of her assets in property. She left no diary or self-produced records.48 Second, illustrated by the lithographic representation, Polgreen's image and life history were imagined by a British man whose own socio-economic and racial reality limited and informed what he produced about a woman of African descent.\n\nIn 1842, nearly fifty-one years after Polgreen's death, Creoleana, or Social and Domestic Scenes and Incidents in Barbados in the Days of Yore by J. W. Orderson was published in London. Orderson was born in Barbados in 1767 and grew up in Bridgetown. His father, John Orderson, owned the Barbados Mercury (a local newspaper) and J. W. became its sole proprietor in 1795.49 Thus, he would have been a teenager when many of the events he included in Creoleana occurred, although he wrote about them when he was seventy-five years old. It was likely, as evidenced in numerous newspaper advertisements Polgreen made in his paper, that J. W. Orderson knew Polgreen.50\n\nIt is important to read Creoleana as a 'sentimental' novel of its time, for the historical context and the literary conventions within which the novel was written are as pertinent as Orderson's characterisation of Polgreen. The novel was, as Newton suggests, both 'a revision of slavery and a moral reformist tale to guide behaviour in postemancipation society'.51 Slavery and apprenticeship had officially been abolished in the British-colonised Caribbean by 1838, only four years prior to its publication. Orderson was clear about his nostalgia for a time in which the enslaved were 'happier' in their bondage than in freedom.52 Melanie Newton's critical reading of the novel enables an entr\u00e9e into the consequences of Polgreen's historical (re)production:\n\nIn the postslavery era, as had been the case during slavery, stereotyped and sexualized representations of women of colour, especially the 'mulatto' woman, often served as the means through which white reactionaries expressed both antiblack sentiment and fear of racial 'amalgamation'.53\n\nAcknowledging the pro-slavery project constituent to such representations raises questions about how to use a text like Creoleana as a primary source for Polgreen's historical 'reality'. This is not to dismiss completely the novel's potential to historically inform, but rather to offer insight into its distorting representations of Polgreen. At the moment when the British and North American anti-slavery movements were storming across the Atlantic and into the Caribbean, Orderson articulated his pro-slavery beliefs while condemning the 'perversion' of inter-racial sex.54 In a pamphlet published in 1816, Orderson responded to British parliamentary debates concerning the illicit international trade in Africans and gradual abolition of slavery in their colonies, but his remarks centre specifically on the growth of the free population of colour in Bridgetown. Using less symbolic language than that of the novel to describe his abhorrence of inter-racial sex and unions, Orderson explicitly expressed his opinions guided by his own 'moral' ideologies. Beyond even his disapprobation for the public display of inter-racial coupling between military men and women of colour, he remarks upon his belief in the moral decline of white society through 'licentious intercourse' with women of colour:\n\nI would, however, clearly be understood as deprecating in the highest degree every attempt to introduce such connections between [free women of colour] and the white inhabitants; for here, I own, the West India prejudice is sufficiently implanted in my mind to render such a connection, not only repugnant to my feelings, but contrary to my ideas of morals, religion and polity.55\n\nIt was precisely Orderson's disapproval of inter-racial sexual and social relations that led, ironically, to his contention that free(d) people of colour should be awarded rights in Barbados society. He argued that if they were given social and economic rights, removing the incentive for material rewards with white men, women of colour would return to seeking legitimate relationships among their own. More importantly, his discourses served to silence any coercion on the part of the white men he accused of moral decline. Orderson essentially silenced the women of colour sexually coerced by white men and erased even the possibility of their violations. At issue here then is illuminating Orderson's investment in pro-slavery and 'antiblack' discourses and their consequences that can be read in his representations of women of colour in his fiction. Furthermore, our own reproductions of Polgreen's historical experiences from his texts must be critically situated.\n\nThe novel Creoleana centres on the lives of two white characters, Jack Goldacre and Caroline Fairfield. A shadow character of Caroline's is a young 'mulatto' girl named Lucy, whose tragic death results from her 'voluntary' sexual encounter with an Irishman. Lucy's story remains encapsulated in an oft-reproduced trope of the virtuous white woman and the 'tragic mulatta' (read as illicit inter-racial sex, immorality and death). Though Rachael Polgreen is not a main character of the novel, Orderson includes a brief life-sketch of her bondage, abuse, humiliation, redemption and triumph. '\"Miss Rachael\" [was] the daughter and slave of the notorious William Lauder, a Scotch schoolmaster and an African woman he owned'.56 Orderson described how Polgreen was frequently abused by her owner\/father, a result of her physical 'charms that touched not the heart, but awakened the libidinous desires'.57 The author imagined Lauder's many 'unsuccessful attempts on her chastity' and recounted his resort to public punishment by the town 'jumper' for her disobedience.58\n\nIt is necessary here to interrogate the possibilities of what Lauder's sexually violent relationship to his 'daughter' exposes, as well the absence of previous scholarly attention to these incidents. What does the narrative of incest reveal about the author of Polgreen's 'history', the depths of her subjection and the erasure of her African mother? What of the liminal place in which her incestuous experiences remain, encapsulated within a novel (and perhaps Rowlandson's lithograph) but consequently outside of historical 'reality'? What also is at stake when the representations of such violent acts continue to elude the historian's critical gaze? Orderson regards the act of incest upon one's family member as the point at which the brutal nature of slavery is illuminated:\n\nLauder's conduct to his offspring, is a damning proof how debasing to the human mind is the power given us over our fellow creatures by holding them in bondage! The ties of consanguinity were all merged in the authority of the master, and he saw but the slave in his own daughter!59\n\nThe legal parameters of slavery and the violence which protected its existence severed the ties of 'family' for the enslaved.60 Elucidating a complicated formulation, literary scholar Hortense Spillers touches upon the nature of female enslavement, sexual violation and the disruption of the 'family' in slavery. The act of incest relies on a recognisable and legal biological bond that the laws and logic of slavery make impossible. The role and relationship of the 'father' to the 'daughter', in this instance Lauder to Polgreen, are confused and denied here. Essentially, incest performed or threatened in a system of slavery with 'its imposed abeyance of order and degree' cannot really exist. Or, as Spillers contends, this moment can speak for or illuminate the extant 'losses' of family and 'confusions' of the status of the enslaved person as both object and subject \u2013 person and property.61 Polgreen was at once non-human, daughter, woman, chattel and sexual object. Ultimately, it is only through the revelation of her abuses and the desecration of her body in a 'sentimental novel' that Polgreen's subjectivity is represented beyond her material accumulation in other archival fragments. Thus, the act of incest provokes recognition of Polgreen's humanity that is at the same instant destabilised by the laws of slavery.62\n\nImmediately following Orderson's discussion of incest, his sensational account of Polgreen's whipping implicitly sexualised her body, connecting it to her rescue by a white seaman:\n\nShe was already 'tucked up', in the indecorous manner of those days, and the brutal hand of the mercenary whipper, armed with the fatal 'cowskin', stretched forth to lay on the unpitying merciless lash, when a British tar! A gallant seaman rushed on the relentless executioner, seized the whip from his grasp, and rescuing his panting victim, carried her off in triumph amidst the cheers of a thronging multitude!63\n\nOrderson ends Polgreen's story with the visit of Britain's Prince William Henry to the island in 1789.64 As Barbadians celebrated the prince's presence by illuminating the town with lights, he used Polgreen's hotel as his on-land base from which to make his rounds dining with various planters and merchants. During his visit, the prince led a regiment on a drunken rampage through Polgreen's hotel, destroying nearly all of her property by 'breaking the furniture, &c., the very beds [were] cut up, and their contents emptied into the street, and the whole neighbourhood strewed with feathers'.65 As a final act, epitomising the pinnacle of patriarchal colonial power, 'he bid [Polgreen] 'good night', and to crown his sport, upset her and chair together, leaving her unwieldy body sprawling in the street, to the effable amusement of the laughing crowd'.66 Polgreen's narrative response, through Orderson's ventriloquism, leaves her in her place, 'calling out in her sweetest dulcet tones, \"Mas Prince! Mas Prince; you come ma-morning, to see wha' mischief you been do!\"'67 In closing, Orderson tells of Polgreen's industriousness, how she took immediate account of the damage to her property and sent a bill to the prince upon his departure of the island \u2013 'which was duly paid'.68 Not allowing the reader to remain long with her humiliation and abuse, Orderson's narrative forces Polgreen into an embodiment of triumph and guile. Through Creoleana, Orderson produced a distorted, disfigured and silenced Polgreen; creating an almost unchangeable snapshot of Polgreen's (imagined) intimacies by fixing her into a bounded frame of identity. For historians this novelistic representation has become the central understanding of her identity \u2013 its narrative power so pervasive as to inform most other historical representations of her life.69\n\nThe power of this novelistic representation has proven seductive, and several attempts have been made to historicise Polgreen's encounter with the prince. An editorial published in the Barbadian (1842) acknowledging the publication of Creoleana provided circumstantial evidence to support the novel's depiction of events. Yet, the editorial powerfully (re)fixed Polgreen's bodily image within the text of the newspaper and into the nineteenth century:70\n\nMany of the scenes [Orderson] has remarked we have a distant recollection of. We well remember the wild frolics and pranks of Prince William Henry [who] probably little thought that one of the Barbadians would, at this distant period of 55 years, amuse the world with his mischievous tricks at old Rachael Lauder's alias Rachael Pringle. We perfectly recollect this immense mass of flesh (she was nearly as big as a sugar hogshead) walking with the Prince, actually leaning on the Royal Arm, and accompanied by other Naval Officers, and a host of mulatto women.71\n\nHere Polgreen's archive is reproduced through an anonymous editorial. Referred to as 'an immense mass of flesh' Polgreen's post-mortem dehumanisation becomes her mytho-history and the despicable captivation she inspired in Barbadian lore implacably passes through time. Transparently despised in this moment of recollection, 'actually leaning on the Royal Arm', the author of this editorial degrades the memory of Polgreen. He shifts our understanding away from Orderson's victim-to-trickster representation to a Polgreen whose arrogance and audacity violated nineteenth-century mores.72 Aghast at the possibility that a woman of colour would take such liberties with royalty, the editorial discursively caricatures Polgreen and implicitly disempowers her role in relation to such a figure as a late king. Moreover, in this nineteenth-century moment, Polgreen's body is aged and reduced to mere flesh, 'as big as a sugar hogshead' refiguring the terms of her commodified captivity \u2013 literally and symbolically. Reduced to an object of commerce, the editorial deconstructs Orderson's representation of Polgreen as embattled yet empowered.\n\nPerhaps unsettling Orderson's novel as mere fiction, another important trace of Polgreen is revealed in an advertisement she had placed in the Barbados Gazette 31 January \u2013 4 February 1789:\n\nLost by subscriber, a small filigree waiter, scalloped round the edge, and bordered with a vignette, seven silver table spoons, seven tea-spoons; marked S.B. in a cipher, also two dessert spoons marked R.P. in a cipher. Whoever had found the same, and will deliver them to her or the printer of this paper, shall receive FOUR MOIDORES reward, or, in proportion part. Silver-Smiths and others are requested to stop the above articles if offered for sale.\n\nRACHAEL-PRINGLE POLGREEN73\n\nThis archival fragment coincides with Prince Henry's 1789 visit and according to Barbados historian Neville Connell, may represent the 'contents emptied into the street', during the prince's violent sweep through the hotel.74 Upon closer scrutiny, Polgreen's advertisement troubles a triumphant narrative of compensation from the prince. Merely being compensated for damage did not, it would seem, completely satisfy Polgreen's sentimental attachment to certain items. Furthermore, her call to the public for assistance in recovering these items illustrates that the significant impact of the damage, humiliation and theft lingered beyond the alleged payment.\n\n* * *\n\nTracing the manner in which Polgreen enters the historical record and accounting for the power with which her story is reproduced allows us to understand the productive nature of history \u2013 and illuminates what is silenced in the process. The following archival pieces were created in the midst of the trans-Atlantic abolition movement, while debates over ending the slave trade raged in the chambers of the British parliament. Historians have noted that 'abolitionist literature frequently contained gruesome depictions of drunkenness and acts of cruelty, especially rape and flogging, being committed against slaves, usually by white men'.75\n\nAlthough the following fragment cannot necessarily be characterised as abolitionist propaganda, it does reveal the dynamics of intra-racial and intra-gendered power.76 In an interview between a British military officer named Captain Cook and members of the Privy Council in 1791, a harrowing image of Polgreen appears. It reads:\n\n[Captain Cook, of the 89th Regiment of Foot, called in; and examined]\n\nWere you ever in the West Indies?\n\nYes.\n\nWhen, and in what islands?\n\nIn the years 1780 and 1781, in Barbados, St Lucia, St Christopher's &c.\n\nDid the Negro Slaves in general appear to you to be treated with mildness or severity?\n\nIn the towns I thought with very great severity.\n\nDo any particular instances occur to you of [slaves] being treated with severity?\n\nMany; one was an instance of a female Slave belonging to a woman named Rachael La[u]der, who I saw beat in a most unmerciful manner; She beat her about the head with the heel of her shoe, till it was almost all of a jelly; she then threw her down with great force on a child's seat of a necessary, and there attempted to stamp her head through the hole; she would have murdered her had she not been prevented by the interposition of two officers. [The girl's] crime was, not bringing money enough from aboard ship, where she was sent by her mistress for the purpose of prostitution.77\n\nThe system of slavery in which Polgreen operated provided her the power to enact violence upon the bodies of those she enslaved. Yet this incident described by a British officer reveals both Polgreen's power and the limits of her power. It is not known whether she was indicted upon the beating of this enslaved woman, but the toleration of 'prostitution' within the city and her position as a slave owner supports the assumption that she held a form of power over her slaves similar to white slave-owners. From the details Captain Cook provides about a 'child's seat of a necessary [toilet]', and the fact that two other military 'officers' \u2013 not the town's constable \u2013 intervened, it is possible that this violent scene occurred inside Polgreen's hotel. The officers, like Captain Cook (probably patrons of the brothel), were struck by the extreme violence perpetuated by Polgreen against this unnamed woman and were eager to recount this story.\n\nIn a gesture towards an alternative image of Polgreen's constructed history, we might also ask if this fragment draws us nearer to the otherwise invisible women she owned and the nature of their sexual labour tragically encapsulated by the 'libidinal investment in violence' characterising so much of slavery's archives.78 For the woman beaten by Rachael Polgreen, the labour demanded by her enslavement would have required her to find transportation (most likely by rowing boat) to the unknown lawless space of the ship in harbour, in order to secure a willing white patron who would pay for sexual acts.79 Not satisfying the patron could result in returning to her owner without the expected compensation. Moreover, due to her enslaved status, this beaten woman could never guarantee payment for her services in such a society. There were no laws to protect even Polgreen's expectation of profit.\n\nThe intensity of the beating also suggests a passion that went beyond the recovering of money, a willingness to murder a woman whose productive value she relied upon. Generally, violence against one's own property was not punishable by law, but Polgreen maintained her economic interests outside the law which did not support her status as 'citizen'. Due to her own liminality, Polgreen perpetuated her own discipline: she was her own overseer, labour negotiator and a slave master. At further inquiry, this incident also reveals the nature of Polgreen's agency: that which depended upon the subjugation of others. What does this scene expose about the very nature of this slavery? What does it mean that the beaten woman's labour required daily access to her sexualised body? What are the configurations of her labour \u2013 her enslavement? How can we make careful distinctions between the 'jobbing' slaves in town who scrambled for windows of autonomy in an urban landscape and women forced into selling their bodies only for the material gain of their owners? Through the enslaved women she owned, Polgreen amassed a small fortune. Her 'production of pleasure' for the sailors and military men she entertained, as well as the sexual labour she demanded from her slaves, hint at the many layers of her agency. The women she owned were forced into an 'economy of enjoyment' that they did not control. The performative nature of such an economy \u2013 'pleasurable' sexual service \u2013 must be carefully interrogated.\n\nIf we consider the brothel as a microcosm of racial and gendered social relations of eighteenth-century Barbados, we might understand it as a site where varying degrees of power are played out. Polgreen inhabited a liminal space within broader Bridgetown society. Though free, she was a woman of colour whose racial, gendered and sexual markers confined her to a particular economic function. She could have never inhabited the role of 'wife' as did white women of her time, and she sustained a vulnerability to white society's legal and social regulation and control of black bodies. Through her will, we understand she made connections with elite white males and their families. She also acquired the means to survive at a higher economic level than many of her free peers. This too depended upon her buying into a system of slavery from which she was not far removed. Within her brothel then, racial and gendered meaning (that is, hierarchies based on race and gender) sustained her liminal place within Bridgetown while further subjugating the women and men she owned.\n\nHenri Lefebvre argues that 'the city and the urban cannot be understood without institutions springing from relations of class and property'.80 Thus, the brothel cannot be imagined as a space where enslaved women were empowered by the mode of (sexual) production. Imagining the space in this way extricates both the site of the brothel and the women who laboured therein from the social and racial hierarchies that made the brothel possible in the first place. These relations between enslaved sexual labourers and their patrons depended upon hierarchical racial and gendered codes that placed enslaved women in subjugation and rendered them lascivious, sexually deviant and whorish. Moreover 'sexual intercourse, regardless of whether it is coerced or consensual, comes to describe the arrangements, however violent, between men and enslaved women'.81 And in the historical literature, sexual intercourse becomes the means by which enslaved women are ascribed power.82\n\nThe trans-Atlantic context of prostitution illuminates the expectation of the men who employed enslaved and free women in sexual services. By the late eighteenth century, prostitution was widespread in British port cities such as London and Liverpool.83 The sailors and military men sailing to the West Indies carried expectations of paid sexual services from experiences with prostitutes in such British cities. Most of the women who worked as prostitutes in London were lower-class white women. They too performed pleasure to the expectations of their patrons. Central to my argument is to elucidate the strikingly different nature of enslaved prostitution in the case of women, whose racial, gendered and non-class status kept them in a particularly subaltern position. These acts thus reproduced not an equal relation of power, but rather that of owner and owned; patriarch and submissive female. Put another way, the men who purchased sex from Polgreen's enslaved women purchased the illusion of consent \u2013 an imaginary erotic of mutuality that was performed in spite of their enslavement and powerlessness. In essence, enslaved women forced to prostitute for the pleasure of white males (re)produced degrading and violating racialised inequality. For the enslaved black women forced to labour in this particular manner, their 'personal desire or erotic interests' could not exist.84 Such labour forced enslaved women to serve the desires of the paying male without compensation and without a guaranteed avenue to 'freedom'. It is precisely due to the type of labour extracted from an enslaved female body that denies the possibility of pain or pleasure, rape and violence. I argue therefore that we cannot collapse this particular form of sexualised labour into definitions of 'prostitution'. Even as we search for 'in-between' categories inhabiting space between rape and consent, we are in effect re-inscribing the very terms which fundamentally fail to account for the sexual experiences of these enslaved women. Therefore, we must be critical when ascribing agency to enslaved women in these contexts.\n\nWe clearly see through this meditation how silences in the archive of women of colour in slave societies bury narratives of the most subaltern. Overshadowed by Polgreen's meta-narrative of material success, nearly all of the women owned by Polgreen disappear as quickly as they are mentioned in her will. However, this article presents new research from late eighteenth- century deeds that enable a fuller revision of Polgreen's narrative by shifting the focus to a woman she owned. As previously stated, in her will Polgreen requested that four women be freed upon her death. One of the women, Joanna (who was given her own son still enslaved, and also a woman named Amber) appears in succession several times in the register of deeds for this period. There are many aspects of Joanna's and Amber's lives we will never know. Indeed, Amber disappears completely from the historical record. These fleeting glimpses from an historical aperture that closes too fast make it nearly impossible to string together events in a neat narrative. Nevertheless, the information in these documents and the time frame of their production allude to Joanna Polgreen's destitute circumstances in 'freedom', her complicated labour negotiation and relationship with her former owner, the role of the military in the support and perpetuation of brothel culture, and the vulnerability of free people of colour to white legal and economic power.\n\nOn 20 July 1793, two years after Rachael Polgreen's death, Captain Henry Carter (mariner) and William Willoughby (gentleman) gave a deposition affirming that in 1779 or 1780,\n\nthey knew a certain Negro or Mulatto Slave named Joanna who had been the property of Rachael Pringle Polgreen & by her Sold or conveyed to one Joseph Haycock who was a Servant to General Ackland or Soldier in the Regiment... And that the Said Joseph Haycock did manumit and set free by Deed of Manumission the Said Joanna now known by the name of Joanna Polgreen.85\n\nThe purpose of this deposition by Carter and Willoughby was to act as witnesses to Joanna's freedom as, 'they have heard & been told by the Said Joanna Polgreen that it is alleged that her manumission was lost in the Hurrycane' of October 1780, and so 'at her particular request the Deponents came forward to prove and maintain the freedom of the Said Joanna Polgreen'.86\n\nAt first glance, this deposition appears to support the narrative of enslaved women and their 'room to manoeuvre' towards freedom in an urban slave society.87 Consistent with the literature on the military in Barbados and the sexual uses to which enslaved women were subjected, Maycock probably met Joanna in Polgreen's brothel and arranged for her purchase. Joanna's agency here might be easily linked with her ability to achieve her freedom through her sexual interactions with white men. However, another deed recorded earlier complicates what 'freedom' actually meant for many black women and reveals the cost of their survival in this slave society. On 3 December 1783, three years after her freedom was 'secured', Joanna set her mark of X to a deed asking Rachael Polgreen to legally and formally honour a contract of indenture while supplying Joanna with food, drink and clothing:\n\nI the underwritten do by these Presents Bind myself in the Capacity of an apprentice for and during the term of Twelve years from the date hereof unto Mrs. Rachael Pringle Polgreen... to be in her Service and Direction... And the Said Rachael Pringle Polgreen do by these presents for the respect She bears [Joanna] do hereby agree for her better maintenance to find her Victual, and Drink & [a] couple Suits of Decent apparel for her.88\n\nBased on this evidence, we must assume that if Maycock did in fact free Joanna he apparently did not provide for her maintenance. Joanna must not have been able to survive on her own. The dates of these documents and the time frame of their production allude to Joanna's destitute circumstances in 'freedom', forced to commit herself back into an unusually long (twelve-year) indenture binding her again to Polgreen.89 We can speculate that Joanna's use of this legal avenue stemmed from a mistrust of Polgreen's verbal promises. The language ('for the respect she bears for her') appealed to Polgreen's conscience to honour Joanna's request for material support. That it was necessary to ask for clothing and food forces us to consider whether Polgreen adequately provided for her slaves. It is curious too, that Joanna took Polgreen's last name, perhaps to establish her status as a free black woman. However, Joanna Polgreen's short-lived 'freedom' (1779\/1780 to 1783) and her 'voluntary' indenture challenges narratives of success and privileges afforded to free(d) women of colour in the urban context.\n\nIn his short biography of Rachael Polgreen, historian Jerome Handler described Joanna's relationship to Polgreen in the following terms: 'two other slaves [Richard and Amber] were bequeathed to a slave woman [Joannah] who won her freedom under the terms of Rachael's will'.90 But these additional sources show that Joanna's freedom was not so easily 'won' or retained. What then, did 'freedom' mean in such a society? Joanna sought to indenture herself in 1783 for the period of twelve years. Polgreen died before the end of Joanna's contract and in her will freed 'my Negro Woman Joanna' with no language clarifying the nature of Joanna's status. Was she to be freed from contract or from slavery? Perhaps, even more troubling, Joanna sought to substantiate her freedom based on circumstances outside of Polgreen's will \u2013 from her manumission by Joseph Maycock c.1780. Had she been freed in Polgreen's will there would have been no need for Joanna to elicit the testimony of two white men in an effort to prove her free status \u2013 this status of freedom, always ever under suspicion and under the threat of being stolen. If the executors of Rachael Polgreen's will had in fact performed her bequests, then Joanna would have been freed in 1791 thereby terminating the labour contract she had negotiated in 1783.91\n\nGiven Joanna's complicated legal entanglements, I ask us to re-examine what it means to valorise Polgreen's 'successes' in the face of the violence she may have endured herself in slavery and certainly the violence she may have perpetuated. Planters, merchants, white elites and the British colonial government created a system of economic development which set the terms of success in Barbados: slave ownership and material accumulation based on white supremacy and the bodily exploitation of 'other(ed) humans'. This system also depended upon the systematic sexual exploitation of enslaved women. The military complex, sustained by the Royal Navy, whose presence in the eighteenth-century West Indies protected British economic and political interests, was serviced by the informal sexual economy of enslaved prostitution.\n\nCentral to debates on 'enslaved agency' and resistance in contemporary scholarship on slavery are the ways in which agency has been gendered and sexualised concerning enslaved women and women of colour in slave societies and their sexual relations with white men.92 Moreover, even a feminist intervention on the definitions of agency might be revised if we focus specifically on Rachael Polgreen. Her status rested upon the axis of different types of power. First, the archive that produces her material life was created and sustained by white colonial power. This power is replicated in subsequent narratives of her lived 'experiences' in the secondary literature. In addition, the power attributed to Polgreen as slave holder and brothel keeper must be understood within the context of the processes (techniques, mechanisms and strategies) that enable a formerly enslaved woman to own other women of similar racialisation, and to coerce them into a sexual economy from which the benefits for them were not necessarily freedom and economic independence.93 It is not my intention to separate Polgreen from the system of racial and gendered domination within which she lived. Instead, I want to emphasise the particularities of that system that rendered her choices and the limits of her actions therein. A glance back at the system of slavery operating in eighteenth-century Bridgetown reveals the racial and gendered hierarchies in place (where white colonial power dominated and black women were placed at the bottom of the social hierarchy), and the implicit (white) societal desire for a sexual outlet for white men, both resident and transient. Polgreen's power and agency 'are not the residue of an undominated self that existed prior to the operations of power but are themselves the products of these operations'.94 In other words, Polgreen's economic and social power was produced by the system of slavery in place and was not harnessed by her in an effort to subvert that system.95\n\nThe scholarship of Rachael Polgreen centres on her success as a businesswoman. Certainly, she was an iconic figure whose life story has captivated historians' attention into the twenty-first century. Yet I would argue that understanding how she came by her 'success' is just as important as the unusual position she occupied in eighteenth-century Bridgetown \u2013 a quintessential slave society ruled by the commodification of black bodies. If the nature of her success depended on slave owning and the sexual labour she demanded from the women she enslaved, then those enslaved women's stories are also vital to understanding the nuances of gender and power in slave societies.\n\nIn this chapter, I argued that knowing more about Rachael Polgreen's relationships with women whose labour she owned changes the way we imagine Polgreen and also questions narratives of black women's 'success' within slave societies. But even more, I argue, unravelling Polgreen's seemingly unyielding story forces us to also reconsider how we produce histories of enslaved and free(d) women of colour in the Atlantic world using archives that significantly limit our efforts to access their lives. Their core experiences, shaped by sexual violence and impossible choices, are not necessarily fully elucidated by progressive notions of agency. Without discounting the imperative in historical scholarship since the 1960s to recover enslaved agency against attempts to render the enslaved as passive and utterly dominated, I ask us to consider now what other facets of enslaved lives can we discover beyond these heroic stories of resistance and survival. Agency cannot be examined outside the constraints of slavery's systematic mechanisms of domination. Joanna's desperate circumstances, read in tandem with Polgreen's 'success', make it difficult to write of Polgreen in isolation from her troubling power. Despite the effort to recover enslaved women from the 'archive's mortuary', those most disposable in their exchangeability and commodification \u2013 the thirty-seven other men, women and children owned by Polgreen at her death \u2013 remain confined by slavery's archive.\n\nNotes\n\nMany generous readers have provided valuable feedback on various iterations of this chapter. To name but a few I would like to thank the two anonymous reviewers and Kristen Block, Tina Campt, Saidiya Hartman, Jennifer Morgan, Gunther Peck, Patricia Penn Hilden, Kennetta Perry, Suzanna Reiss, Jennifer Spear, Ula Taylor and my colleagues at the Charles Warren Centre for Studies in American History at Harvard University. The CWC fellowship and support from the departments of women's and gender studies and history at Rutgers provided the resources to complete this chapter.\n\n1. Saidiya Hartman, 'Venus in Two Acts', Small Axe 26 (2008), pp. 1\u201314, here p. 5.\n\n2. Michel-Rolph Trouillot, Silencing the Past: Power and the Production of History (Boston: Beacon Press, 1995), p. 25.\n\n3. I take the term 'exorbitant circumstances' from Hartman, 'Venus in Two Acts', p. 2, where she describes how the invisibility of enslaved women in the archive is sometimes disrupted by 'an act of chance or disaster'. For the literary representation of Polgreen, see J. W. Orderson, Creoleana: Or, Social and Domestic Scenes and Incidents in Barbados in the Days of Yore and The Fair Barbadian and Faithful Black, ed. John Gilmore (1842; Oxford: Macmillan, 2002). See also Melanie J. Newton, The Children of Africa in the Colonies: Free People of Colour in Barbados in the Age of Emancipation (Baton Rouge: Louisiana State University Press, 2008), pp. 258\u201362. I employ the term free(d) here and throughout the chapter to refer to the status of people of colour like Polgreen who became free through manumission, in an effort to encompass the varied possibilities of 'status' in Bridgetown's slave society.\n\n4. See Orderson, Creoleana. See also Jerome S. Handler, The Unappropriated People: Freedmen in the Slave Society of Barbados (Baltimore: Johns Hopkins University Press, 1974); Roger Norman Buckley, The British Army in the West Indies: Society and the Military in the Revolutionary Age (Gainesville: University Press of Florida, 1998); Hilary Beckles, Centering Woman: Gender Discourses in Caribbean Slave Society (Kingston: Ian Randle, 1999); Pedro Welch and Richard Goodridge, 'Red' & Black Over White: Free Coloured Women in Pre-Emancipation Barbados (Bridgetown: Carib Research and Publications, 2000); Newton, Children of Africa in the Colonies; Pedro Welch, Slave Society in the City: Bridgetown, Barbados 1680\u20131834 (Kingston: Ian Randle, 2003).\n\n5. See Handler, Unappropriated People; Buckley, British Army in the West Indies; Beckles, Centering Woman; Welch and Goodridge, 'Red' & Black Over White; Newton, Children of Africa in the Colonies; Welch, Slave Society in the City.\n\n6. Newton, Children of Africa in the Colonies, p. 61.\n\n7. Free(d) and enslaved women's predominant participation as 'hucksters' in the produce and commodity informal markets in town exemplified the alternative to prostitution. See Newton, Children of Africa in the Colonies.\n\n8. See Hilary Beckles, 'White Women and Slavery in the Caribbean', History Workshop Journal 36 (1993), pp. 66\u201382.\n\n9. Beckles, Natural Rebels: A Social History of Enslaved Black Women in Barbados (New Brunswick: Rutgers University Press, 1989) pp. 143\u20134.\n\n10. Gayatri Spivak, 'Can the Subaltern Speak?', in Lawrence Grossberg and Carl Nelson (eds), Marxism and the Interpretation of Culture (Urbana: University of Illinois Press, 1988), pp. 271\u2013315.\n\n11. Buckley, British Army in the West Indies, p. 165.\n\n12. Hartman, 'Venus in Two Acts', p. 6.\n\n13. Handler, Unappropriated People, p. 8.\n\n14. See Beckles, Centering Woman; Richard Dunn, Sugar and Slaves: The Rise of the Planter Class in the British West Indies (Chapel Hill: University of North Carolina Press, 1972); Handler, Unappropriated People; Welch, Slave Society in the City.\n\n15. Handler, Unappropriated People, pp. 18\u201319.\n\n16. Handler, Unappropriated People, pp. 15\u201328; Newton, Children of Africa in the Colonies, pp. 27\u20138.\n\n17. For the original iteration of this narrative, see Orderson, Creoleana, p. 76.\n\n18. Beckles, Natural Rebels, p. 9. See also Jennifer Morgan, Labouring Women: Reproduction and Gender in New World Slavery (Philadelphia: University of Pennsylvania Press, 2004).\n\n19. Beckles, Natural Rebels, pp. 14\u201315.\n\n20. Beckles, 'White Women and Slavery in the Caribbean', pp. 69\u201370.\n\n21. See Hilary Beckles, Natural Rebels; Barbara Bush, Slave Women in Caribbean Slave Society 1650\u20131838 (Kingston: Heinemann, 1990). Deborah Gray White's text, Ar'n't I a Woman? Female Slaves in the Plantation South (New York: W. W. Norton, 1985), pioneered in the effort to document the experiences of enslaved women in the antebellum US and Jennifer Morgan made an important link between reproduction and slavery in Labouring Women.\n\n22. Handler, Unappropriated People; Jerome Handler, 'Joseph Rachell and Rachael Pringle-Polgreen: Petty Entrepreneurs', in David Sweet and Gary Nash (eds), Struggle and Survival in Colonial America (Berkeley: University of California Press, 1981), pp. 376\u201392.\n\n23. Handler, Unappropriated People, p. 134.\n\n24. Handler, 'Joseph Rachell and Rachael Pringle-Polgreen', p. 383.\n\n25. Handler, 'Joseph Rachell and Rachael Pringle-Polgreen', pp. 134\u20135.\n\n26. See e.g., Beckles, Centering Woman; Welch, Slave Society in the City; Newton, Children of Africa in the Colonies.\n\n27. See Orderson, Creoleana; Sir Algernon Aspinall, 'Rachel Pringle of Barbados', Journal of the Barbados Museum and Historical Society (JBMHS) 9\/3 (1942), pp. 112\u201319; Joel Augustus Rogers, Sex and Race: Negro-Caucasian Mixing in All Ages and All Lands (New York: J. A. Rodgers, 1944); Neville Connell, 'Prince William Henry's Visits to Barbados in 1786 & 1787', JBMHS 25 (1958), pp. 157\u201364; Handler, Unappropriated People; Karl S. Watson, 'The Civilised Island, Barbados a Social History, 1750\u20131816' (unpublished doctoral thesis, University of Florida, 1975); F. A. Hoyos, Barbados: A History from the Amerindians to Independence (London: Macmillan, 1978); Handler, 'Joseph Rachel and Rachael Pringle-Polgreen'; Hilary Beckles, Black Rebellion in Barbados: The Struggle Against Slavery, 1627\u20131838 (Bridgetown: Antilles Press,1984); Beckles, Natural Rebels; Warren Alleyne, Historic Bridgetown (St Michael: Barbados Government Information Service, 2003); Welch, Slave Society in the City. For contemporary visual depictions of Polgreen's sexuality, see the blog entry by Stuart Hahn, 'Rachel Pringle, The Notorious Barbados Madame', 2 February 2006, <<http:\/\/thebookmann.blogspot.com\/2006\/02\/rachel-pringle-notorious-barbadian.html>> on Richard Bolai's website 'Timeless-TheBookMan-Feinin, <<http:\/\/thebookmann.blogspot.com\/>> (accessed 19 February 2007). See also Cecily Jones, Engendering Whiteness: White Women and Colonialism in Barbados and North Carolina, 1627\u20131865 (Manchester: Manchester University Press, 2007); Newton, Children of Africa in the Colonies.\n\n28. Welch, Slave Society, p. 170.\n\n29. Welch, Slave Society, pp. 48, 89.\n\n30. See Saidiya Hartman, Scenes of Subjection: Terror and Self-Making in Nineteenth Century America (New York: Oxford University Press, 1997); Darlene Clark Hine, 'Rape and the Inner Lives of Black Women in the Middle West: Preliminary Thoughts on the Culture of Dissemblance', in Beverly Guy-Sheftall (ed.), Words of Fire: An Anthology of African American Feminist Thought (New York: New Press, 1995), pp. 380\u201388.\n\n31. Trouillot, Silencing the Past, p. 29.\n\n32. I thank anonymous reviewer two for bringing this important historiographical point to my attention.\n\n33. Hartman, Scenes of Subjection, p. 10.\n\n34. Handler, 'Joseph Rachell and Rachael Pringle-Polgreen', p. 383.\n\n35. Barbados Department of Archives (hereafter BDA), RL1\/5, Records of Baptisms and Burials, St Michael Parish Church, 23 July 1791, p. 538. William Lauder was her owner and her last name was presumably given by him.\n\n36. BDA, Estate Inventory of Rachael Pringle Polgreen, 13 August 1791. For a discussion of the monetary accumulation of free women of colour in Bridgetown, see Welch, Slave Society, pp. 166\u201381.\n\n37. This calculation is based solely on the Estate Inventory of Rachael Pringle Polgreen. Jerome Handler wrote in Unappropriated People that Polgreen owned nineteen slaves from his reading of Polgreen's will. In order to address this inconsistency, I used the inventory list as opposed to the more general language of Polgreen's will, wherein she refers to her unnamed enslaved people (those not explicitly freed) as 'All the Rest, Residue and Remainder of my Estate, real and personal, here or elsewhere'. BDA, RB6\/19, Will of Rachael Pringle Polgreen, 21 July 1791, pp. 435\u20136.\n\n38. BDA, RB6\/19, Will of Rachael Pringle Polgreen, pp. 435\u20136. In an attempt to track the manumissions of the women Polgreen requested be freed by her will, I traced manumission payments in the St Michael Parish Vestry Minutes from 1780 to 1788 and 1789 to 1805, BDA. Any slave holder wishing to manumit an enslaved person was to pay fifty pounds to the Church Vestry in the Parish which she\/he resided (this fee was raised to three hundred pounds in 1800 to discourage manumissions). I found no evidence that such manumission fees were paid for those Polgreen wished to free during the above-mentioned years. As J. W. Orderson explains, 'white men, who in general (it being often a stipulation with their favourite) purchase [enslaved women] of their owners, in many instances their own parent \u2013 and subsequently giving a certificate on the back of the deed of sale, annulling their right of property in the person of their favourite, in like manner give them a freedom not recognized by the laws'. New York Public Library (NYPL), J. W. Orderson, Cursory Remarks and Plain Facts Connected with the Question Produced by the Proposed Slave Registry Bill (London: Hatchard, Piccadilly, Hamilton, Paternoster Row and J. M. Richardson, 1816), p. 16.\n\n39. See Gilmore (ed.), 'Introduction' to Creoleana, p. viii; Handler, Unappropriated People, p. 135.\n\n40. Gilmore (ed.), 'Introduction' to Creoleana, pp. 1\u201318.\n\n41. Aspinall, 'Rachel Pringle of Barbados', p. 114.\n\n42. Editorial, 'Polgreen of Barbados', JBMHS 9\/3 (1942), p. 109.\n\n43. We know very little of how she acquired this name. In the historical works that write of Rachael Polgreen, none have ventured to find out Mr Polgreen's identity. For a summary sketch and unverifiable speculation of his life, see John Gilmore's notes to Creoleana, pp. 235\u20139. Additionally, a James Polgreen appears in the Bridgetown levy records in 1780 as the owner of several properties, but no clear linkage between he and Rachael Polgreen has been established. It is possible, however, that Rachael Polgreen forged a relationship with a Mr Polgreen similar to her 'relationship' with Captain Thomas Pringle.\n\n44. See Beckles, Natural Rebels, pp. 72\u201389; Newton, Children of Africa in the Colonies, pp. 34\u20135, 105\u20136. Similar to the experiences of free women of colour in the United States during slavery, free(d) Afro-Barbadian women faced stigmatism for their 'public' visibility. Due to racial and gendered stereotypes of their immorality stemming from their public roles as market women and tavern keepers, some Afro-Barbadian women sought to distance themselves from these images through philanthropic and religious work. I thank anonymous reviewer two for bringing this point to my attention.\n\n45. Thomas Rowlandson (1757\u20131827) was a half-French, half-British portrait, landscape and social-satirist painter of eighteenth- and nineteenth-century Britain. He was a contemporary of William Hogarth, whose work influenced many of Rowlandson's scenes of Georgian British life.\n\n46. Editorial, 'Polgreen of Barbados'.\n\n47. Trouillot, Silencing the Past, pp. 28\u20139.\n\n48. Polgreen signed her will with an 'X', indicating that she was probably illiterate.\n\n49. Gilmore, 'Introduction' to Creoleana, p. 3.\n\n50. Though Polgreen lacked literacy, she clearly understood the power of the written word. Over the course of three years, she placed at least three advertisements in the Barbados Gazette or the General Intellegencer. The first appeared in the 26\u201330 January 1788 edition advertising a lost gold ring. The next was for a raffle of 'paintings in oil' as well as her hosting a portrait taker named T. G. who offered accurate portraits to customers 'nothing required', 4\u20137 February 1788. Finally there was the advertisement of lost silverware, 31 January \u2013 4 February 1789, Bridgetown Public Library (BPL).\n\n51. Newton, Children of Africa in the Colonies, p. 259.\n\n52. See Orderson, Creoleana, pp. 91\u20132, describing the tale of a young African boy named Prince who in the service of a ship is given the chance to return to his kinsmen in 'Dahome'. Instead of accepting freedom, Prince returns to Barbados and enslavement proclaiming that, 'he liked the white people's ways, and their victuals and dress, and all that something in backara country, which he no have in he own'. See also Orderson, Cursory Remarks, pp. 9\u201310 wherein he contends that West Indian slavery exposed Africans to civilisation and skills with which they were better off than their counterparts who remained in Africa.\n\n53. Newton, Children of Africa in the Colonies, p. 259. See also pp. 259\u201362 wherein Newton critically engages the gendered and racial context and content of Orderson's Creoleana.\n\n54. See also Gilmore, 'Introduction' to Creoleana, p. 13.\n\n55. Orderson, Cursory Remarks, p. 22.\n\n56. Orderson, Cursory Remarks, p. 22.\n\n57. Orderson, Cursory Remarks, p. 22.\n\n58. Orderson, Creoleana, p. 76. The town 'jumper' referred specifically to a person who earned money by being hired to whip 'disobedient' slaves.\n\n59. Orderson, Creoleana, p. 76.\n\n60. Hortense Spillers, '\"The Permanent Obliquity of an In(Pha)llibly Straight\": In the Time of the Daughters and the Fathers', in Hortense Spillers, Black, White, and in Colour: Essays on American Literature and Culture (Chicago: University of Chicago Press, 2003), pp. 230\u201350, here p. 249.\n\n61. Spillers, 'Permanent Obliquity', p. 249.\n\n62. See also Doris Garraway's discussion of incest and miscegenation in the eighteenth-century French Caribbean in Doris Lorraine Garraway, The Libertine Colony: Creolization in the Early French Caribbean (Durham: Duke University Press, 2005) pp. 34, 278\u201381.\n\n63. Orderson, Creoleana, pp. 76\u20137.\n\n64. Orderson, Creoleana, pp. 76\u20138.\n\n65. Orderson, Creoleana, p. 78. See also Connell, 'Prince William Henry's Visits to Barbados'.\n\n66. Orderson, Creoleana, p. 79.\n\n67. Orderson, Creoleana, p. 79.\n\n68. Orderson, Creoleana, p. 79.\n\n69. See e.g., Handler, Unappropriated People; Welch, Slave Society.\n\n70. This editorial, found in the original 1842 issue of the Barbadian, was located with information gleaned from Connell, 'Prince William Henry's Visits to Barbados'.\n\n71. 'Editorial', 21 May 1842, Barbadian, BPL.\n\n72. Gilmore (ed.), 'Introduction', in Creoleana, p. 16.\n\n73. 'Advertisement by Rachael Pringle-Polgreen for a lost gold ring', in the Barbados Gazette, Or the General Intellegencer, Saturday 31 January \u2013 Wednesday 4 February 1789, BPL. This advertisement was also found with information from Connell's article.\n\n74. Orderson, Creoleana, p. 78; Connell, 'Prince William Henry's Visits to Barbados', p. 164.\n\n75. Newton, Children of Africa in the Colonies, p. 169.\n\n76. This testimony was gathered by the Privy Council of the British parliament on the slave trade and slavery in the colonies. House of Commons Sessional Papers of the Eighteenth Century, ed. Sheila Lambert, vol. 82 (Wilmington: Scholarly Resources, 1975).\n\n77. Sessional Papers of the Eighteenth Century, ed. Lambert, vol. 82, p. 203. Throughout Polgreen's archive, she is referred to as Rachael Pringle, Rachael Pringle Polgreen, Mrs Pringle Polgreen (in one newspaper advertisement referring to her hotel) and Rachael Lauder. The fact of her multiple namings in various sources reflects perfectly the archival power to which Polgreen had little access.\n\n78. Hartman, 'Venus in Two Acts', p. 5.\n\n79. See BDA, Estate Inventory of Rachael Pringle Polgreen, 1791. Upon her death she also owned three boats.\n\n80. Henri Lefebvre, The Production of Space (Oxford: Blackwell, 1991), p. 106. Emphasis in original.\n\n81. Hartman, Scenes of Subjection, p. 85.\n\n82. See e.g., Jerome Handler, Unappropriated People; Buckley, British Army in the West Indies; Douglass Hall, In Miserable Slavery: Thomas Thistlewood in Jamaica 1750\u201386 (Barbados: University of the West Indies Press, 1999); Trevor Burnard, Mastery, Tyranny and Desire: Thomas Thistlewood and his Slaves in the Anglo-Jamaican World (Chapel Hill: University of North Carolina Press, 2003).\n\n83. See Tony Henderson, Disorderly Women in Eighteenth-Century London: Prostitution and Control in the Metropolis, 1730\u20131830 (New York: Pearson, 1999).\n\n84. Julia O'Connell Davidson, 'The Rights and Wrongs of Prostitution', Hypatia 17\/2 (2002), pp. 84\u201398, here p. 86.\n\n85. BDA, RB3\/40, p. 442, Recopied Deed Record Books.\n\n86. BDA, RB3\/40, p. 442, Recopied Deed Record Books.\n\n87. See Welch, Slave Society in the City, p. 89.\n\n88. BDA, RB3\/40, p. 441, Recopied Deed Record Books.\n\n89. Typically indenture contracts for this time period were between four and seven years. I thank my colleague Gunther Peck for bringing to my attention the significance of the unusually long time frame of this indenture.\n\n90. Handler, 'Joseph Rachell and Rachael Pringle-Polgreen', p. 387. My emphasis.\n\n91. A final document further complicates Joanna(h)'s story. In a deed dated 1800 Joanna(h) frees her son Richard Braithwaite. This important document sheds light on Joanna(h)'s relationship to her son and the years she likely laboured in order to free him. See BDA, RB3\/40, p. 445.\n\n92. For important discussions of 'agency' in slavery scholarship, see Hartman, Scenes of Subjection; Walter Johnson, 'On Agency', Journal of Social History 37\/1 (2003), pp. 113\u201324; Diana Paton, No Bond but the Law: Punishment, Race and Gender in Jamaican State Formation, 1780\u20131870 (Durham: Duke University Press, 2004).\n\n93. Saba Mahmood, Politics of Piety: Islamic Revival and the Feminist Subject (Princeton: Princeton University Press, 2005), p. 17.\n\n94. Mahmood, Politics of Piety, p. 17.\n\n95. Mahmood, Politics of Piety, pp. 5\u20139.\nChapter 3\n\nGender, Sexuality and the Formation of Racial Identities in the Eighteenth-Century Anglo-Caribbean World\n\nBrooke N. Newman\n\nSince the mid-1990s, a growing interest in the centrality of sex\/gender and racial ideologies to British, and particularly English, settler colonialism in North America and the Caribbean has transformed the historiography of the Anglo-Atlantic world. By integrating the provisional hierarchies of gender, class and colour formed within localised but interconnected colonial cultures in the British Atlantic community, historians including Kathleen Brown, Kirsten Fischer, Jennifer Morgan, Trevor Burnard and Cecily Jones have identified strong links between gendered social identities and emerging systems of racial domination.1 Likewise, scholars adopting feminist, poststructuralist and deconstructive approaches in their research on Britain and the empire, most notably Ann Laura Stoler, Catherine Hall, Felicity Nussbaum and Kathleen Wilson, have revealed how the entangled axes of gender, sexuality and race became fused with and helped legitimate power regimes and identity processes throughout the British imperial world, as well as in Britain itself.2 Attending to the marking of difference across early America and the British empire has revitalised both of these fields, complicating our understanding of gender, race and national belonging during the long eighteenth century.\n\nMultitudes of heavily gendered and racialised identities (individual as well as national) arose from and were transformed by the aggregate social contexts and interactions of diverse peoples \u2013 diverse by language, religion, ethnicity, culture, appearance and country of origin \u2013 that characterised the British Atlantic empire.3 In the Caribbean island colonies, where minority populations of free West Indian slaveholders sought metropolitan recognition of their claim to British liberty, law and identity, citizenship became firmly linked to concepts of whiteness over the course of the eighteenth century.4 By the end of the Seven Years' War (1756\u201363), to self-identify as a 'British' West Indian, entitled to the same rights and privileges as a freeborn, essentially English subject at home, was necessarily to be 'white'. That Creole, or native-born, West Indian elites formulated a distinctly colonial version of white British identity does not mean, however, that this articulation went uncontested in the metropole.5 Rather, many contemporary observers believed that immersion in Caribbean slave society, with its predominantly African population, high mortality rates, endemic violence, deep-seated instability and sexual excesses, precluded British West Indian whites from identifying fully with either whiteness or Britishness.\n\nThis chapter explores how the daily interactions and intimate collisions of free Europeans and mostly enslaved Africans in the colonial Caribbean endangered evolving concepts of British national identity, as imagined and idealised in law and collective discourse, and as experienced and understood at the level of the individual. It takes the form of a series of theoretically informed accounts of personal experiences and views related to gender, racial mixture and the historical construction of whiteness in the Anglo-Caribbean world. Examining multiple overlapping levels of analysis, including social structure, culturally constituted meaning, everyday practices and subjectivity, the chapter illustrates the extent to which racialised anxiety about sex became wedded to concerns about colonial expressions of British identity from the mid-eighteenth century onwards.6 In this case, the lives and perspectives of marginalised individuals seeking closer ties with England, specifically free people of colour and middling Scots, provide crucial insight into the historical development of white British subjectivities in the Atlantic empire.\n\nSection one considers the relationship between freedmen and women and 'whiteness' as a legal identity marker in Jamaica, Britain's leading sugar colony, demonstrating the porous and shifting nature of eighteenth-century articulations of race and citizenship. The second section explores how intimacy across the colonial colour line affected white West Indians' status as Britons and shaped metropolitan understandings of human difference, mediated through discourses of poetry, travel and history produced between the 1760s and the 1790s. This critical transition period saw war, revolution, the rise of British anti-slavery and the hardening of racial boundaries, just as imperial administrators grappled with the legal, social and cultural complexities posed by large numbers of non-white, non-European populations to be absorbed into the expanding empire \u2013 not as slaves but as subjects.7 Section three draws on contemporary travel diaries, linking the everyday social practices of slavery in the colonial Caribbean to the gendered racial distinctions developing in British culture. The chapter concludes with an analysis of the psychology of Dr Jonathan Troup, a Scottish physician who practised in Dominica between 1789 and 1791, keeping a detailed account of his experiences there as a young doctor attached to a large medical practice, the clientele of which consisted of men, women and children across the spectrum of plantation social relations. The language of Troup's journal suggests how the colonial system of slavery interacted with metropolitan prescriptions to influence sexual behaviour and identity formation at the level of the individual.\n\nStructuring the colour lines in a British Caribbean slave society\n\nIn June 1763, Lovell Stanhope, agent for Jamaica, wrote a letter to John Pownall, the secretary of the Board of Trade, outlining reasons on the basis of which colonial authorities in Jamaica had justifiably passed major legislation two years earlier severely limiting the rights of free people of colour. Designed to protect white privilege, the 1761 'Act to prevent the inconveniences arising from exorbitant grants and devices to negroes' redefined who could pass officially as 'white' \u2013 only offspring, preferably legitimate, four degrees removed (rather than three) from an African ancestor \u2013 and prohibited all non-whites from inheriting or purchasing property in excess of \u00a31,200.8 In arguing the case of the parties interested in the statute, Stanhope commented at length on the growing disproportion of blacks to whites, focusing particularly on Jamaica's small number of white women, whose fatigue and disinterest due to the extreme heat of the climate 'has introduced, to a most scandalous degree, an unlawful commerce with Negro Slaves; which habit reconciles, and numbers sanctify'.9 As Stanhope saw it, white men's infatuation with women of colour was one thing; their devising of property to such 'Savages or their Bastard spurious progeny', necessarily distinguished in law from British subjects, was another thing entirely.10 The mere existence of political opposition to an act intended to check unauthorised 'fornication and concubinage', thus encouraging 'the legal propagation of Children by marriage' and the '[transmission] of property and power to a pure and legitimate race', served as clear evidence, he insisted, 'of the ascendency which the Mulattoes, especially the females, have already in that Country over dissolute Minds, and of the necessity which there is of restraining them'.11\n\nIf Lovell Stanhope meant to link the liberties associated with Britishness more firmly to the untainted white racial identity claimed by West Indian settlers, his letter pointed to something else entirely: the problematic nature of the British racial inheritance in the colonial Caribbean. The transference of this purportedly exclusive birthright to Susanna Augier, a wealthy free woman of colour, exemplifies the shifting meanings of whiteness and the uncertain place of white West Indians in the British empire during the second half of the eighteenth century. One of those allegedly manipulative mulatto seductresses, whom Stanhope and his ilk feared had entered the beds \u2013 and pocket books \u2013 of Jamaica's planter and merchant elite, Susanna Augier's story began in 1722, when her white father, the planter John Augier, freed her and her four other mulatto sisters, Mary, Jenny, Frances and Jane, in his will and granted them each a share of his estate.12 Like other persons of colour manumitted by will or deed, the Augiers received a limited sort of freedom; irrespective of sex, freed slaves could not vote, sit in the legislature, give evidence against whites or free-born persons of colour, serve on a jury, or participate fully in the economic life of the colony.13\n\nFaced with limited prospects and an ambivalent racial identity, it is unsurprising, then, that the Augier sisters chose to supplement their incomes by participating in Jamaica's informal concubinage system. As mistress first to Peter Caillard and later to Gibson Dalzell, both prosperous Kingston merchants, Susanna Augier attained the wealth and social connections necessary to become a respectable, accepted member of the white community. On 19 July 1738, in recognition of this transformation, the Jamaica legislature passed a private act entitling Augier and her two daughters, Mary and Frances, 'to the same Rights and Privileges with English Subjects born of White Parents'.14 This Act granted Susanna, Mary and Frances Augier, as well as 'their Issue hereafter born in this Island and begotten by white men', limited civil liberties and the legal right to pass as 'white'.15 Accordingly, the Augiers and their descendents would be tried for crimes, misdemeanours or offences, and allowed to give evidence at civil and criminal trials, 'as if they and every of them were free and natural born subjects of the crown of Great Britain and were descended of and from White Ancestors... any Law Custom or Usage to the Contrary notwithstanding'.16\n\nIt is important to emphasise that official grants of white status to private individuals were incredibly rare in Jamaica and accorded to only the lightest-skinned and most well-to-do mulattoes. Despite superficially inclusive language in the printed version of the law, few persons of African descent actually met the terms of a restrictive voting act passed in 1733, which permitted a select number of affluent Christian mulattoes above three degrees removed from their African ancestor(s) to assume formally a 'white' racial identity and enjoy its accompanying privileges.17 As Samuel and Edith Hurwitz's careful study of the manuscript legislation has uncovered, the Jamaica legislature passed a total of 128 private bills granting white privileges to free persons of colour during the eighteenth century, only four of which 'provided for the grant of all the rights of white men, including suffrage and office holding (subject, as in the case of whites, to property and religious qualifications)'.18 And it is clear that the majority of these remarkable cases involved the offspring born to the enslaved mulatto mistresses of white Creole men. Edward Long, the most important contemporary commentator on eighteenth-century Jamaica, noted that mulattoes receiving white privileges by private acts of assembly 'have chiefly been granted to such, who were inheritors of large estates in the island, bequeathed to them by their white ancestor'.19\n\nSusanna Augier and her descendents owed the official stripping-away of their mixed racial heritage to the generosity of three separate British West Indian white males: first, that of John Augier, who freed his daughter from slavery and left her property; and subsequently that of her lovers, Peter Caillard and Gibson Dalzell.20 In Caillard's will, dated 8 March 1727, he granted Augier a majority interest in both his real and personal property, worth an estimated \u00a326,150 8s. 1d. According to the calculations of James Lewis, clerk to the Jamaica Assembly, this significant entail included 'a valuable Penn in the parish of Saint Catherine, a profitable Mountain at May Water in the Parish of St. Andrew, [and] sundry houses in the Town[s] of Kingston and Saint Jago de la Vega', with the residuum to pass to Peter and Mary Augier. The Augier family apparently enlarged both their numbers and their fortunes further in 1755, when Dalzell devised a significant share of his personal estate, valued at \u00a36,854 1s. 3d., to Robert and Frances Dalzell, 'his reputed children by [a] Mulatto Woman named Susanna Augier'.21\n\nBy the mid-eighteenth century, such complicated cross-racial unions, lineages and inheritance practices had become relatively commonplace in Jamaica, a patriarchal slave society that afforded white men considerable sexual freedom and elevated the coloured female body as an object of desire. As the West Indian historian Bryan Edwards remarked in 1793, women of colour 'such as are young, and have tolerable persons, are universally maintained by White men of all ranks and conditions, as kept mistresses'. White Creoles frowned upon interracial marriage, however. 'No White man of decent appearance, unless urged by the temptation of a considerable fortune, would condescend to give his hand in marriage to a Mulatto! The very idea is shocking', Edwards proclaimed.22 Caribbean historians have long speculated that the prevalence of sexual relationships between white men and coloured women owed much to the coercion inherent in slavery, the absence of anti-miscegenation laws,23 the link between white women and the reproduction of freedom, and, most importantly, demographics.24 In Jamaica, where unmarried or widowed men made up the vast majority of the largely immigrant white community, pervasive interracial liaisons had a statistically significant effect on the complexion of the free population.25 Edwards estimated that in 1789 freedmen and women constituted 10,000, or 3.5 per cent, of Jamaica's 291,400 residents, the vast majority of whom were enslaved.26 Similarly, in the whole of the Leeward Islands in 1788, free persons of colour accounted for 1.6 per cent of the total population, or roughly 1,450 of the islands' 91,000 residents.27 In Barbados during the 1770s, by comparison, a reported 528 free coloureds made up 0.6 per cent of the island's nearly 88,000 inhabitants.28\n\nIn 1760, Tackey's revolt, a devastating slave insurrection that cost the lives of sixty whites and at least 400 slaves, prompted the passage of new legislation in Jamaica designed to firm up the colour line and bolster white hegemony.29 In the months following the rebellion, the Jamaica legislature redefined whiteness as a legal category; restrained the devises made to non-whites; ordered freedmen and women to register with their respective local parish; and, on paper at least, required persons of colour to wear a badge and carry a certificate of their freedom signed by the governor.30 Such measures worked to marginalise free persons of colour and keep them below or just above the poverty line, socially and economically subordinate to even the poorest whites.31 A handful of white Jamaicans complained about the statute limiting devises to persons of African descent, arguing that it undermined property rights \u2013 the cornerstone of British liberty \u2013 and placed an unnatural restraint on familial affection, 'by prohibiting all persons, under severe penalties, from giving any property beyond a certain value to their own offspring, even tho' they should be removed three Degrees from the Negro Ancestor, and consequently are seven eights white, and not distinguishable from white Persons'.32 Nonetheless, in a colony concerned with safeguarding white power on the one hand and maintaining credible claims to a British identity on the other, such arguments fell on deaf ears. As Lovell Stanhope, the voice of the majority of the Jamaica Assembly, retaliated:\n\nSo many large Estates have been of late devised to Negroes and Mulattoes, & the practice growing so common, it calls for the Aid of the Legislature to prevent the evil before it grows too enormous... Power ever follows property, and whenever they shall become possessed of the largest share of the Property, then it will be absurd and impossible to keep them out of Power; the Laws against them must be repealed... and the Island become a Colony of Negroes & Mulattoes.33\n\nAlthough changing legal constructions of race and citizenship enabled Jamaica's elites to reverse the hitherto provisional accommodations granted to free persons of colour in civic society, such institutional efforts principally demonstrated the vulnerability of whiteness in the colonial Caribbean. When considered alongside colour ascriptions used in official records post-1761, Susanna Augier's earlier elevation to the status of a 'white' subject of the British empire aptly demonstrates how the historical process of racial identification is, to borrow from Stuart Hall, 'lodged in contingency'.34 Legislative efforts to regulate and repress free persons of colour in Jamaica after Tackey's revolt testify to the insecurity of not only the lives but also the identities of British West Indian whites operating in remote colonial settings ruled by African chattel slavery.35 Moreover, these institutional changes are indicative of the growing importance of whiteness as a marker of British national identity in the context of a rapidly expanding overseas empire.\n\nThe cultural application of meaning: maintaining a 'white' British identity\n\nThe deep-seated, multifarious tensions that underlay plantation slave societies, shaping the intricacies of gender and racial identities in Jamaica and elsewhere in the Anglo Caribbean, found expression not only in the increasing structural advantages afforded to members of the white community, but also in cultural representations issued from the metropolis from mid-century onwards. Owing to an urban explosion fuelled by population growth and improved rates of capital available for the expansion of commerce and manufacturing in both England and Scotland, the later eighteenth century saw a profound transformation of British society, culture and economy.36 New consumption patterns and improved literacy rates paved the way for a more educated middle class with an insatiable taste for colonial commodities, especially tea and sugar, as well as visual images and secular forms of literature associated with Britain's overseas territories and trading partners.37 Emerging from within an imperial culture fully supported by colonial slavery, yet increasingly apprehensive about its implications for British national identity, texts by John Singleton, Edward Long and J. B. Moreton, among others, explored how the system of slavery intersected with Creole gender norms and sexual proclivities to influence the development of a West Indian racial order that had far-reaching implications.\n\nDeploying a highly gendered and eroticised discourse, British authors, many of whom had visited or formerly lived in the West Indies, introduced metropolitan readers to the local peculiarities of Caribbean slave societies, in which over a century's worth of amalgamation between Europeans and Africans had produced innumerable gradations of colour and hence complex categories of identity. Contemporary commentators agreed that West Indian colour lines, though some of the first to be drawn in the Atlantic empire, were regularly transgressed by white Creole males, 'too oft allur'd by Ethiopic charms', to use Singleton's phrasing.38 These interconnecting discourses surrounding sexuality, gender and racial mixture in Britain's island colonies are worthy of note precisely because they enhance our understanding of how representations are, like identities themselves, always in process, momentarily wedded to particular cultural, temporal and spatial contexts.39 Building on the increasingly racialised fears of unfamiliar, threatening or peripheral peoples that characterised seventeenth-century England, such texts also demonstrate how concepts of whiteness helped link Britons throughout the late eighteenth-century imperial world.40\n\nRepresentations of British West Indian societies simultaneously communicated ideas about the supremacy of whiteness and the strength of mind necessary to maintain its imagined purity. First printed in Barbados in 1767, John Singleton's quarto-volume blank-verse poem, A General Description of the West Indian Islands, celebrated the splendour and success of British colonisation in the Caribbean while decrying the illicit conduct of the resident white Creoles. In verse omitted from the abridged versions of the poem published in London in 1776 and 1777, Singleton portrayed white West Indians as crude miscreants whose reckless behaviour towards their black slaves and one another betrayed minds overcome by dangerous passions.41 'Awake at Nature's, Virtue's call, awake! Shun the false lure of Ethiopic charms', he urged white West Indian men.42 Yet in a tone indicating concern that his advice would fall unheeded, Singleton also posed the following: 'Or, can the frightful negro visage charm Thro' vague variety, or wanton lust, Whilst the blind fool an angel's bosom quits, To pillow in a fiend's unnat'ral arms, Where the fond master oft succeeds his slave?'43 For Singleton, the consummation of unauthorised interracial desire heightened the distinction between white and black, creating a circumstance of 'traded identity', as Roxann Wheeler has described in another context, in which master and slave, Briton and African, become 'exchangeable figures'.44 Such a frightening scenario was not rectified 'Tho' the lewd spark the tawny shou'd prefer To shining jet,' for 'Alas! that tawny draws Its copper hue from such an odious source'.45 Critically, Singleton held white Creole women \u2013 rather than the transgressors themselves \u2013 accountable for the most grievous sins of slave society. Observing that an unfaithful husband was, above all, 'sinful made by an impetuous wife', he advised Creole wives to refrain from fiery exhibitions of jealousy, lest marital strife should drive a loyal husband to seek 'looser joys abroad'.46\n\nJohn Singleton's depiction of white West Indian womanhood is similar to that of many other eighteenth-century British authors, the majority of whom found white Creole women sorely lacking in the virtues and refinements associated with the metropolitan feminine ideal.47 Writing in 1774, the former planter Edward Long argued that the pervasiveness of settled concubinage in Jamaica owed as much to the undesirability of white Creole women as to the masculine inclination 'to give loose to every kind of sensual delight'. Although, as Long explained, Jamaican whites were far from having 'converted into black-a-moors', as commonly supposed in England, white West Indian women's 'constant intercourse from their birth with Negroe domestics' made them entirely unfit marriage partners for sensible Britons.48 Writing nearly twenty years later, the historian J. B. Moreton, who spent five years as a bookkeeper in Jamaica, reinforced this derogatory image of the white Creole female as a type tainted by her close association with black domestics. Too many Creole women, he claimed, 'receive their education amongst negroe wenches, and imbibe great part of their dialect, principles, manners, and customs'. Moreton proposed that white Creole parents preserve their daughters' purity by sending them away to school, where they would be prevented from engaging in 'any intercourse, if possible, with any of the black or tawny race'.49 Only degradation would result for the white female confined to the society of the Creole household, where one commonly found, as Long maintained, 'a group of white legitimate, and Mulatto illegitimate, children all claimed by the same married father, and all bred up together under the same roof'.50\n\nThe writings of Singleton, Long and Moreton linked cultural and sexual miscegenation in the West Indies with the alleged degeneration of an uncorrupted British, and specifically an English, collective white identity. Appropriating the distinctive new racial vocabulary characteristic of late eighteenth-century philosophical and scientific discourse, they represented Caribbean racial mixture as posing a danger not only to the laws of matrimony and Christian civilisation, but also to the endurance of an undiluted whiteness that secured Britain's place at the pinnacle of the global racial hierarchy.51 Though defensive of Jamaica's white Creoles, Long lamented the frequency with which one found white men of every rank 'cohabiting with Negresses and Mulattas, free or slaves'. Nothing beneficial to society resulted from these 'goatish embraces', but rather 'a vast addition of spurious offsprings of different complexions', a 'tarnished train of beings', who 'for their own parts, despise the Blacks, and aspire to mend their complexion still more by intermixture with the Whites'. Worse still, he lamented, children only three degrees removed from their African ancestors 'are called English, and consider themselves as free from all taint of the Negroe race', even though incalculable generations would 'hardly be sufficient to discharge the stain'.52\n\nThough extreme, Moreton's barefaced diatribe against people of mixed heritage in 1793 is indicative of a growing apprehension in Britain that the sexual practices of West Indians had opened up a Pandora's box of racial identities on the frontiers of the Atlantic. Integrating the diverse colour gradations of Caribbean society under the umbrella term 'Mongrel', Moreton reasoned that while so-called 'Mongrels' might resemble illiterate white Creoles, only 'more negrofied', the process of racial amalgamation could never fully remove the stain of African ancestry. Hence 'Mongrels, though thirty generations distant from blacks['] blood, cannot be real whites'.53 Yet the vehemence of his attack on a particular woman of colour, whom he labelled 'a letcherous [sic] tawny whore', intent on seducing white men with her 'luring and lascivious invitations', suggests Moreton's locus in what Robert Young characterises as 'the ambivalent axis of desire and aversion: a structure of attraction, where people and cultures intermix and merge, transforming themselves as a result, and a structure of repulsion, where the different elements remain distinct and are set against each other dialogically'.54 In other words, the titillation underlying the discursive desire for the coloured female body met the dangerous transgression of fragile racial boundaries in its execution.55\n\nWhat these British authors seemed to abhor most, as each in turn contemplated the fragility of whiteness in the colonial Caribbean, was the idea that an empire undergirded by hardening racial distinctions might be imperilled by its own desires. Their nascent sense of racial superiority rested on notions of national difference, chiefly from the Spanish, whom Edward Long accused of producing a 'vicious, brutal, and degenerate breed of mongrels' as a result of Spanish male settlers' inability to control their passions in the Americas. If interracial sex was capable of bringing down the Spanish empire, then it would 'be much better for Britain, and Jamaica too, if the white men in that colony would abate of their infatuated attachments to black women, and... perform the duty incumbent on every good citizen, by raising in honourable wedlock a race of unadulterated beings'.56 Long's contention that the fulfilment of the white marital and procreative imperative in Jamaica would eradicate the proliferation of an Africanised mongrel breed of Britons reveals a great deal about the intersection of gender, race and sex in discursive formulations. At the level of meaning, metropolitan models of colour difference held enormous classificatory power both at home and in the wider imperial world, serving to define the social and sexual practices of colonial slavery as anomalous stains on an otherwise uncontaminated collective British self.57 Perhaps the most telling message of all in these late eighteenth-century popular texts is that centre and periphery are mutually constitutive and hence equally vulnerable to dislocations of identity.58\n\nThe practice of everyday life: race mixing on the periphery\n\nThe predominance of racial mixture in the British Caribbean colonies brought gender relations and sexual practices, as the origins of dangerous new categories of identity, to the forefront of Georgian cultural representations of white West Indians. Collectively, these discourses served to define interracial sex as a font of contagion responsible for polluting British national identity and destabilising its real and symbolic power on the world stage. Still, meaning is also organised within and emergent from social interaction, in the material practices through which gender, sexuality and race are constituted, enacted and continually renegotiated in specific temporal and spatial contexts. Racial identities are not simply constructed through gendered and eroticised discourse and prescription, but produced at yet another level\u2014that of everyday practices, through which individuals anchored to material reality attempt to identify with the key social impulses sustaining a diversity of cultural norms and activities.59 While daily processes are more difficult to trace than restrictions and representations, we might think of them, as Diane Richardson suggests, as 'performative practices' or routine behaviours capable of creating the illusion of permanence and stability.60\n\nPrivate travelogues by outside observers can help to illuminate the way overlapping categories of identity animated the practice and meanings of West Indian everyday life. In the cases of Antigua in the Leeward Islands and Dominica in the Windward Islands, portraits of plantation life written by two Scots, Janet Schaw and Jonathan Troup, both visitors to the sugar islands during the last quarter of the eighteenth century, reveal how gendered social practices developing around chattel slavery shaped whiteness as a lived category of human difference. Long after the 1707 Union, Schaw and Troup joined the thousands of Scots who set sail for the West Indies to engage in planting, trading, warfare, politics and medicine. Scottish involvement in transatlantic networks linking them to metropolitan and North American business partners and family members helped forge a unity among Britons in the Atlantic empire.61 Schaw's and Troup's interaction with white Creoles and enslaved and free persons of colour, and their growing sense of self-awareness and superiority to these colonial populations, highlight how the experience of unfamiliar cultural milieus in two different British Atlantic slave societies facilitated the identification of these Scottish observers with the metropolitan centre.62\n\nWhen Janet Schaw arrived in Antigua in December 1774, she paid close attention to the appearance and manners of the men and women she encountered, emphasising the most characteristic aspects of the island's central racial types: white Creole, black slave and mulatto. Reminiscent of many other eighteenth-century travel writers whose paths intersected momentarily with those of geographically and historically separate persons in what Mary Louise Pratt calls the 'contact zone', Schaw tended to highlight differences rather than points of commonality.63 She directed her most sustained attention to the bodies, traits and habits of the island's female inhabitants, drawing contrasts among the white, black and brown women in Antigua as well as between white women in the West Indies and those in Britain. Like her male contemporaries, Schaw approached the colonial encounter through a gendered lens.64 Drawing a sharp distinction between the appearance of white Creole women and those of African ancestry, for example, she described how 'the black women, wear little or no clothing, nothing on their bodies, and they are hardly prevailed upon to wear a petticoat'.65\n\nJanet Schaw remarked that white Creoles lived their lives strictly according to local gender conventions, one of which prevented white women from 'ever walk[ing] in this Country'. Another West Indian custom whereby white women ate little and drank nothing stronger than lime juice was observed to such an extreme that the Creole ladies would rather 'faint under it than transgress this ideal law'. Schaw determined that their strict adherence to a collective West Indian feminine ideal had reduced Antigua's local women to 'spiritless and indolent creatures'.66 These dull Creole women fell far short of the refined yet lively British female type idealised by late eighteenth-century metropolitan periodicals.67 Take the April 1771 issue of the Lady's Magazine, for instance, in which the editors lauded 'the fair sex' for exhibiting an admirable combination of qualities ranging from 'polite conversation, an agreeable vivacity' and 'a genteel and easy carriage' to 'delicacy of sentiment'.68 The social identity of white Creole womanhood thus posed a challenge to Schaw's understandings of proper British femininity, exaggerated by her singular exposure to metropolitan culture. Indeed, much of her discussion of white Creole women revolved around the contradiction between their embrace of localised gender norms and their dangerous attempts to emulate women in Britain by whitening their skin with harsh solvents.69\n\nJanet Schaw reported a similar feeling of disapproval with regard to white Creole men's voracious appetite for 'young black wenches', who, she alleged, consequently 'lay themselves out for white lovers, in which they are but too successful'. Her observations led her to determine that black women's desire to live as concubines to white men 'prevents them from marriage with their natural mates, and hence a spurious and degenerate breed [results], neither so fit for the field, nor indeed any work, as the true bred Negro'. Paralleling the observations of Edward Long, Schaw noted that while white Creole women strove desperately but failed to measure up to the metropolitan feminine ideal, the West Indian embodiment of British masculinity had everything to recommend it \u2013 save for white Creole men's indulgence for and immoderate attachment to black women. The towns of Antigua certainly displayed the results of 'their licentious and even unnatural amours', she emphasised, 'from the crouds of Mullatoes, which you meet in the streets, houses and indeed everywhere; a crime that seems to have gained sanction from custom, tho' attended with the greatest inconveniences not only to Individuals, but to the publick in general'.70\n\nThe private musings of such visitors to the Caribbean provide a window on more than just everyday life; they also tell us about the meanings metropolitan individuals may have attributed to the culturally specific behaviours, norms and attitudes found in early British slave societies. For Janet Schaw did not simply regard persons of African ancestry as 'others'. Her journal entries depict gendered West Indian social relations, particularly the sexual expression of white Creole manhood, as a threat to developing metropolitan classifications, capable of blurring boundaries between white and black, Briton and African, person and object. Most importantly, Schaw's diary suggests that she, like other contemporary commentators, found the social practices of West Indian slavery detrimental to the expansion and preservation of Britishness abroad.\n\nDr Jonathan Troup's detailed chronicle of his experiences in Dominica is even more revealing, as his gender enabled him to join the Creole men in mixing \u2013 socially and sexually \u2013 with the island's coloured women. Arriving in Dominica's capital city of Roseau in May 1789, Troup joined the practice of a fellow Scottish physician, Dr Fillan, and set about tending to the medical needs of the colony's free and enslaved populations.71 Offering an exclusive glimpse at one of Britain's younger Caribbean islands, his manuscript journal details the customary and blas\u00e9 race mixing that underlay plantation society in Dominica, an underdeveloped colony composed in 1787 of approximately 1,236 free Europeans and nearly 15,000 enslaved Africans.72 As a young unmarried white male, Troup participated quite readily in Dominica's masculine, heterosexual and sexually exploitative Creole culture. He frequented Roseau's popular mulatto balls, where there were often 'Parties of Girls young & old' at dances held on different nights of the week. At these interracial gatherings, visiting marines, merchants and sailors, as well as resident white Creole men, paid to interact with women of colour, who trolled, in effect, for white lovers and potential husbands in a safe intercultural zone with 'very few white women' present, according to Troup.73\n\nThrough his daily interactions with the doctors attached to his medical practice, Troup soon accustomed himself to the local Creole custom of keeping mulatto mistresses and sexually sharing black slave women. He described how Dr Fillan and his partner Dr Clark had '6 Children from Mullatoe Girls called always after the Man who takes them in keeping'. Not all men held ownership of their mixed-race offspring. Troup noted how one Creole, Mr Carson, 'has a child 5 months old to a handsome black girl of Dr Clarks a native of Antigua \u2013 it is a Mullatoe, a girl \u2013 he does not own it'.74 Some white West Indian males with little property regarded keeping a coloured mistress as a prohibitively costly proposition. 'I spoke w[ith] young Daniel', Troup noted, 'he finds it expensive to maintain Mullattoes & he is thinking of fixing himself in the matrimonial noose'.75 Despite the high costs purportedly attending the concubinage system, marriage was nonetheless poorly regarded in Dominica; when Creole men did marry, they often did so to improve their financial situation, continuing their sexual relations with coloured or black women on the side.76 Dr Fillan informed Troup at dinner one night that the gentlemen of Dominica rarely uttered the phrase 'his wife' in mixed company, for 'that is not but a vulgar expression & is never used by a man of breeding'. Troup's sketch and description of 'a veiled white woman carried on a Pole by two Negroes' is certainly suggestive of white Creole women's restrictive social lives and critical role as the reproducers of a 'legitimate' white identity in the tropics.77\n\nThe length of the racial continuum in Dominica amazed Jonathan Troup, although he considered himself an astute observer of human difference. 'But the complexions are very various here', he wrote; 'Jet black to European whiteness 8 or 9 different degrees very perceptible upon numerate examination \u2013 A mulattoe black & white interchanging alternately produces 6 different species these 6 uniting with W[hite] & Black 3 \u00d7 6, 18 different varieties'.78 When Troup, like the authors of popular British texts, contemplated the most undesirable consequences of racial mixture, he turned his attention to women of colour. The character summation he scribbled next to a watercolour sketch of a mulatto woman is a case in point: 'They are slaves too most of them \u2013 taken as housekeepers make shirts are very prolific at times when she is chaste if not many abortions are consequence \u2013 They are very cruel to the Blacks from whence they spring & a Black would do anything before they had her for her mistress'. Based no doubt on available published accounts as well as his own personal experiences, Troup stated that women of colour 'have quite immodest discourse all of them whores & they throw themselves into a number of tempting positions \u2013 sometimes almost quite naked... in a word nothing gives them shame'.79\n\nWhile Jonathan Troup may have had nothing positive to say about black or coloured women, less than a month after his arrival he reported that he had acquired a venereal disease from a 'Negroe wench of Dr C[lark]'. Venereal diseases were some of the most noticeable consequences of the widespread sharing of sexual partners in Roseau. Troup's particular case of 'virulent gonorrhea' put him in 'a great deal of pain' and made walking difficult for some time.80 Such agonising symptoms did not stop him from continuing to 'make love to a number of girls in my drunkenness', as he noted in his journal on 17 August 1789.81 Troup typically blamed drink for his behaviour, yet he also pointed to the realities of life for a white man residing in an uncultured slave society. He apparently agreed when a Mr Thorp remarked at dinner later, 'what can a young man do here to loose his time in evenings, he can't apply to books. Whores & money must be his Rescurer & cause of most of his misfortunes'.82 It is through Troup's own interracial liaisons, moreover, that he himself contributed to what some metropolitan observers might have regarded as the degeneration of whiteness: shortly before leaving the island for Britain, Troup learned that he had impregnated Nancy, a coloured woman.83 By describing how white men in Dominica regularly treated black and coloured women as their sexual property, Troup produced a vivid account of the ways in which Creole males negotiated their culturally determined gender role in a British West Indian colony. Additionally, Troup unintentionally provided documentation of the possibilities available to black, white and brown women, the ways they may have navigated an even more limited racialised gender role in a patriarchal slave society designed solely for the purposes of harnessing the physical, sexual and reproductive capabilities of the black body. Thus while Troup most likely did not intend for his personal experiences to reach a wider audience, his diary reveals the complications and intersections of gender norms, sexual practices and racial formations at the periphery of the British empire in the late eighteenth century.\n\nIndividual subjectivity: Jonathan Troup and the process of identification\n\nJonathan Troup's journal offers more than just a record of West Indian daily life and material practices; it also grants us access to the mind of an eighteenth-century British man torn between the societal expectations associated with his gender role in the metropolis, namely to marry, mix socially with refined ladies and uphold codes of polite sociability, and his philandering with black slaves and mulatto concubines in Dominica.84 His journal is suggestive of the extent to which the dynamic interplay among gender, sexuality and race occurs most radically at the level of individual subjectivity. On the one hand, Troup's account of race mixing in West Indian slave society gives strength to the representations produced by authors such as Edward Long and J. B. Moreton, and confirms the descriptions of other metropolitan travellers like Janet Schaw. His journal also takes us into new territory. Unlike other eighteenth-century male diarists like Thomas Thistlewood, who embraced Creole socio-sexual habits, Troup was reflective: he exhibited increasing levels of disgust with West Indian slave society.85 By virtue of his reflexivity, Troup's journal helps to demonstrate that the gendered sexual self is never a finished or fixed identity, but is continuously being recreated.86\n\nIt is Jonathan Troup's fixation with gaining the affections of an English woman named Mary Ford that grants us limited access to an individual psychology troubled by the prevalence of racial intermixture in the tropics. After meeting Mary Ford in Plymouth on his way to Dominica, Troup quickly placed her on a proverbial pedestal; he wrote love letters to Ford and waxed eloquently about her on numerous occasions. She represented everything he wanted in a marriage partner: sweetness, innocence, a mild and pliant mind, and skin unblemished by the rays of the sun. 'If I can get Mary & a moderate Livelyhood God bless us I'm content', he jotted.87 Mary Ford's imagined perfection stood in stark contrast to Troup's mental image of the white Creole women he encountered. Explaining why he had no desire to pursue a 'Miss Lee', for example, he described her as 'a pleasant enough girl but a large mouth rather clumsy habit & dark skin indeed the country will reduce her'.88 Troup evidently assumed that Miss Lee or any other white Creole woman for that matter would fall victim to the climate and imbibe the barbarous habits and sable countenance of the island's Africanised population.\n\nDominica's coloured and white Creole women became the objects of much criticism in Troup's journal. He complained of the indolence of the ubiquitous 'mulatto wenches' kept by the white overseers, yet noted 'how necessary it is to gain the favour of the women and how dangerous it is to incur their displeasure'.89 He described how Polly Armourer and Polly Clark, the mulatto daughters of Drs Clark and Armourer, treated their slaves appallingly and forced their own children to simulate the sex act. 'I have seen them when idle take their boys aged 2\u20133 years old and make a little black girl of the same years lie down and make them move as if they were in the act of copulation', Troup detailed.90 Just as women of colour had internalised the cruellest and most degrading aspects of slave society, so too had white Creole women degenerated in the tropics: 'The Creoles are impervious overruling women know nothing but Eat Drink Game Curse & beat the Negroes whereas the mild temper of Mary will sooth my pain in affliction & make the World's cares sit easy on my mind'.91 His unquestionably English Mary Ford, by contrast, embodied the metropolitan feminine ideal; her character and appearance suited the ambitions of an upwardly mobile Scot. Troup's burning desire to possess Ford pervaded his thoughts even while he wrote about acts of coercive interracial sex in his journal, as on the occasion when he described how 'Mrs Murray's Mullattoe Lydia come down to Mrs Laing's Kitchen, I suspect she has been try'd & to prevent any discovery make her Common \u2013 I dare say Mr Baird will have at her altho' he has his black Sabina \u2013 God grant I may have my mild Mary Ford \u2013 I'll wait for her two years & if I be then akin & her I shall have or want her'.92\n\nThe above passage hints that Jonathan Troup, though a full participant in Dominica's racially mixed slave society, was often, in his own mind at least, thousands of miles away \u2013 in metropolitan Britain. To put it another way, Troup may have acted like a white Creole male during his residence in the West Indies but he continued to think like a Scotsman eager to occupy a position of importance much closer to the centre of empire. The practice of his everyday life in Roseau, which included an exhibition of an explicitly debauched, creolised version of British manhood, accounts for only the most visible aspect of his individual subjectivity. Underneath Troup's surface behaviour was a psyche at once attracted to and repulsed by the gendered and racialised power relations evident in the British West Indies. As such, despite his personal enjoyment of white men's nearly limitless access to the bodies of coloured women in Dominica, Troup's journal indicates that he felt deeply discomforted by interracial sexuality and the brittle, artificial nature of racial\/national boundaries.\n\nOver time, Troup became convinced that West Indian social patterns and gender relations, predicated as they were on racial mixing, made it impossible for him to conform to metropolitan notions of polite manhood or to imbibe anything other than savagery, excess and vulgarity from Dominica's white, black and brown women.93 No small matter in an age when, as a number of scholars have demonstrated, developing articulations of gender, national and racial identities remained at risk in Britain, since the very links with the empire that facilitated the solidification of these categories also threatened their imminent disruption and potential collapse.94 Hence, Jonathan Troup's private journal is historically as well as theoretically important, in that it allows us to explore the extent to which the gendered racial self could be experienced and understood in the midst of such multiplicity, flux and metamorphosis.\n\nDetailed accounts written by contemporary visitors reveal how structural forces granting white Creole males institutional power and privilege intersected with cultural representations that eroticised the coloured female body and denigrated white Creole womanhood, guiding both gender relations and sexual practices in the Anglo Caribbean. At the same time, the violence of West Indian slavery, the distortion of metropolitan gender and sexual conventions and the embodied evidence of still permeable colour lines \u2013 in the form of a diverse array of racial identities in the tropics \u2013 led to a growing association of British West Indian whites with physical and moral degeneration rather than with Britishness. Far from cultivating the Anglicisation of the Atlantic world, white Creoles, both male and female, appeared to be growing more barbarous, tawny and Africanised by the day. With such inconsistencies between metropolitan and West Indian demographics, social structures, gender relations and sexual mores, it is no wonder Jonathan Troup's encounter with slave society in Dominica left him ambivalent and yet more resolved than ever with regard to the stability and superiority of his own identity as a white metropolitan Briton. By the final decade of the eighteenth century, the social, structural and intimate practices arising from African slavery in the Anglo-Caribbean world had given birth to not one but many contested and racialised understandings of Britishness.\n\nNotes\n\nI am grateful to Trevor Burnard, Dana Rabin, Gregory D. Smithers, Jennifer M. Spear and the anonymous readers at Gender & History for commenting on earlier drafts of this chapter.\n\n1. The seminal works on gender, sex and race in early British America, including the West Indies, are Kathleen M. Brown, Good Wives, Nasty Wenches, and Anxious Patriarchs: Gender, Race, and Power in Colonial Virginia (Chapel Hill: University of North Carolina Press, 1996); Kirsten Fischer, Suspect Relations: Sex, Race, and Resistance in Colonial North Carolina (Ithaca: Cornell University Press, 2002); Jennifer Morgan, Laboring Women: Reproduction and Gender in New World Slavery (Philadelphia: University of Pennsylvania Press, 2004); Trevor Burnard, Mastery, Tyranny, and Desire: Thomas Thistlewood and His Slaves in the Anglo-Jamaican World (Chapel Hill: University of North Carolina Press, 2004); Cecily Jones, Engendering Whiteness: White Women and Colonialism in Barbados and North Carolina, 1627\u20131865 (Manchester: Manchester University Press, 2007).\n\n2. This rich, influential body of new imperial scholarship includes Ann Laura Stoler, Carnal Knowledge and Imperial Power: Race and the Intimate in Colonial Rule (Berkeley: University of California Press, 2002); Catherine Hall, Civilising Subjects: Metropole and Colony in the English Imagination, 1830\u20131867 (Cambridge: Polity Press, 2003); Felicity Nussbaum, Torrid Zones: Maternity, Sexuality, and Empire in Eighteenth-Century England (Baltimore: Johns Hopkins University Press, 1995); Felicity Nussbaum, The Limits of the Human: Fictions of Anomaly, Race, and Gender in the Long Eighteenth Century (Cambridge: Cambridge University Press, 2003); Kathleen Wilson, The Island Race: Englishness, Empire, and Gender in the Eighteenth Century (New York: Routledge, 2003); Kathleen Wilson (ed.), A New Imperial History: Culture, Identity and Modernity in Britain and the Empire, 1660\u20131840 (Cambridge: Cambridge University Press, 2004); Anne McClintock, Imperial Leather: Race, Gender, and Sexuality in the Colonial Contest (New York: Routledge, 1995); Philippa Levine, Prostitution, Race and Politics: Policing Venereal Disease in the British Empire (New York: Routledge, 2003); Philippa Levine (ed.), Gender and Empire (Oxford: Oxford University Press, 2004).\n\n3. Colonial self-fashioning is discussed in John H. Elliott, 'Introduction', in Nicolas Canny and Anthony Pagden (eds), Colonial Identity in the Atlantic World, 1500\u20131800 (Princeton: Princeton University Press, 1989), pp. 3\u201313; Christer Petley, '\"Home\" and \"this Country\": Britishness and Creole Identity in the Letters of a Transatlantic Slaveholder', Atlantic Studies 6 (2009), pp. 43\u201361.\n\n4. On the increasing significance of whiteness to Creole identity, see David Lambert, White Creole Culture, Politics and Identity during the Age of Abolition (Cambridge: Cambridge University Press, 2005), pp. 1\u20139; Jones, Engendering Whiteness, esp. pp. 1\u201312; Deirdre Colman, 'Janet Schaw and the Complexions of Empire', Eighteenth-Century Studies 36 (2003), pp. 169\u201393.\n\n5. I use the term 'Creole' throughout to indicate native-born West Indians whose identities were formed through the complex process of cultural and linguistic hybridisation and expansion known as 'creolisation'. On creolisation, see Megan Vaughan, Creating the Creole Island: Slavery in Eighteenth-Century Mauritius (Durham: Duke University Press, 2005), pp. 1\u201332; David Buisseret and Steven G. Reinhardt (eds), Creolization in the Americas (College Station: Texas A&M University Press, 2000), pp. 3\u201318; Charles Stewart (ed.), Creolization: History, Ethnography, Theory (Walnut Creek: Left Coast Press, 2007); Ralph Bauer and Jos\u00e9 Antonio Mazzoti (eds), Creole Subjects in the Colonial Americas: Empires, Texts, Identities (Chapel Hill: University of North Carolina Press, 2009), pp. 1\u201351.\n\n6. My approach here is influenced by feminist and sociological attempts to understand how interrelated social, cultural and biological factors determine personal identity. See Judith Butler, Gender Trouble: Feminism and the Subversion of Identity (New York: Routledge, 1999), pp. 3\u201344; Judith Butler, Undoing Gender (New York: Routledge, 2004), pp. 1\u201356; Stevi Jackson, Heterosexuality in Question (London: Sage, 1999), pp. 1\u201328; Diane Richardson, 'Patterned Fluidities: (Re)Imagining the Relationship between Gender and Sexuality', Sociology 41 (2007), pp. 457\u201374; Stuart Hall, 'Old and New Identities, Old and New Ethnicities', in Les Back and John Solomos (eds), Theories of Race and Racism: A Reader (New York: Routledge, 2000), pp. 144\u201353; Stuart Hall and Paul Du Gay (eds), Questions of Cultural Identity (London: Sage, 1996), esp. pp. 1\u201317.\n\n7. Bruce P. Lenman, 'Colonial Wars and Imperial Instability, 1688\u20131793', in P. J. Marshall (ed.), The Oxford History of the British Empire, vol. 2: The Eighteenth Century (Oxford: Oxford University Press, 2001), pp. 163\u20137.\n\n8. 2 Geo. III. c. 7, 19 December 1761, Jamaica, An Abridgement of the Laws of Jamaica; being an Alphabetical Digest of all the Public Acts of Assembly now in Force (St Jago de la Vega, Jamaica, 1793), p. 105.\n\n9. The National Archives (TNA), Kew, CO 137\/33\/34, Lovell Stanhope, Agent for Jamaica, to the Board of Trade, 13 June 1763, Jamaica, Colonial Office Series, Original Correspondence, 1762\u20131765.\n\n10. TNA, CO 137\/33\/37.\n\n11. TNA, CO 137\/33\/39.\n\n12. I thank Trevor Burnard for sharing the earlier details of Susanna Augier's life with me. See Trevor Burnard, '\"A Very Nuisance to the Community\": The Ambivalent Place of Free People in Jamaican Free Society in the Eighteenth Century', unpublished paper, pp. 29\u201330.\n\n13. Bryan Edwards, The History, Civil and Commercial, of the British Colonies in the West Indies, 2 vols (London: printed for John Stockdale, 1793), vol. 2, pp. 18\u201320. On Jamaica's free coloureds, see Gad Heuman, Between Black and White: Race, Politics and the Free Coloureds in Jamaica, 1792\u20131865 (Westport and Oxford: Greenwood Press, 1981), esp. pp. 3\u201320; Gad Heuman, 'The Free Coloreds in Jamaican Slave Society', in Gad Heuman and James Walvin (eds), The Slavery Reader (London: Routledge, 2003), pp. 654\u201367.\n\n14. TNA, CO 139\/15\/20, An Act to intitle Susanna Augier a Mulatto woman of the Parish of Kingston and Mary Augier and Frances Augier two of the Children of the said Susanna Augier to the same Rights and Privileges with English Subjects born of White Parents, 19 July 1738, Jamaica Acts, March 1738 to October 1741.\n\n15. University of Aberdeen Special Collections and Archives (UASCA), MS 3175\/Z\/198\/1, Papers of Gibson Dalzell, Duff House\/Earls of Fife Papers, 1734\u20131759, Copy ratification of an Act of Governor, Council and Assembly of Jamaica allowing mulatto woman Susanna Augier and two of her children to have the same rights and privileges as English subjects born of white parents, 1741.\n\n16. TNA, CO 139\/15\/20.\n\n17. TNA, CO 139\/13\/139\u201342, An Act to Secure the Freedom of Elections... and to ascertain who shall be Deem'd Mulatto's for the future, 25 April 1733, Jamaica Acts, February 1731 to February 1733. The less detailed printed version is listed in Jamaica, An Abridgment of the Laws of Jamaica; being an Alphabetical Digest of All the Public Acts of Assembly now in Force (St Jago de la Vega, Jamaica, 1793), p. 273. For an interpretation of these private acts based solely on the published collections of Jamaican laws, see Winthrop D. Jordan, 'American Chiaroscuro: The Status and Definition of Mulattoes in the British Colonies', William and Mary Quarterly 19 (1962), pp. 183\u2013200, esp. pp. 198\u201399.\n\n18. Samuel J. Hurwitz and Edith F. Hurwitz, 'A Token of Freedom: Private Bill Legislation for Free Negroes in Eighteenth-Century Jamaica', William and Mary Quarterly 24 (1967), pp. 423\u201331, esp. pp. 424\u20135.\n\n19. Edward Long, The History of Jamaica, 3 vols (London, 1774), vol. 3, p. 320.\n\n20. Susanna Augier, Peter Caillard and Gibson Dalzell are discussed in Lucille Mathurin Mair, A Historical Study of Women in Jamaica: 1655\u20131844, ed. Hilary McD. Beckles and Verene A. Shepherd (Kingston: University of the West Indies Press, 2006), p. 91.\n\n21. TNA, CO 137\/33\/46\u201347, Vera Copia, James Lewis, Clerk to the Assembly, [1763].\n\n22. Edwards, History, Civil and Commercial, vol. 2, p. 22.\n\n23. It is doubtful whether officials ever enforced Antigua's anti-miscegenation law (1644). See TNA, CO 154\/1\/55\u201356, An Act against Carnall Coppulation between Christian & Heathen, Antigua, 20 November 1644, Laws of the Leeward Islands till 1672.\n\n24. On interracial sex in colonial Jamaica, see Trevor Burnard, 'The Sexual Life of an Eighteenth-Century Jamaican Overseer', in Merril D. Smith (ed.), Sex and Sexuality in Early America (New York: New York University Press, 1998), pp. 163\u201389; Trevor Burnard, '\"Do Thou in Gentle Phibba Smile\": Scenes from an Interracial Marriage, Jamaica, 1754\u20131786', in Darlene Clark Hine and David Barry Gaspar (eds), Beyond Bondage: Free Women of Color in the Americas (Urbana: University of Illinois Press, 2004), pp. 82\u2013105; Trevor Burnard, 'Inheritance and Independence: Women's Status in Early Colonial Jamaica', William and Mary Quarterly 48 (1991), pp. 93\u2013114; esp. pp. 110\u201311; Patricia Mohammed, '\"But Most of All Mi Love Me Browning\": The Emergence in Eighteenth- and Nineteenth-Century Jamaica of the Mulatto Woman as the Desired', Feminist Review 65 (2000), pp. 22\u201348; Henrice Altink, 'Deviant and Dangerous: Proslavery Representations of Jamaican Slave Women's Sexuality, ca. 1780\u20131834', Slavery and Abolition 26 (2005), pp. 271\u201388.\n\n25. Trevor Burnard, 'A Failed Settler Society: Marriage and Demographic Failure in Early Jamaica', Journal of Social History 28 (1994), pp. 63\u201382; Trevor Burnard, 'European Migration to Jamaica, 1655\u20131780', William and Mary Quarterly 53 (1996), pp. 769\u201396, here p. 772.\n\n26. Edwards, History, Civil and Commercial, vol. 1, p. 230.\n\n27. Elsa V. Goveia, Slave Society in the British Leeward Islands at the End of the Eighteenth Century (New Haven: Yale University Press, 1965), pp. 85, 96.\n\n28. Jerome Handler, The Unappropriated People: Freedmen in the Slave Society of Barbados (Baltimore: Johns Hopkins University Press, 1974), pp. 18\u201319.\n\n29. Tackey's revolt is detailed in TNA, CO 137\/32\/1\u201332, Jamaica, Original Correspondence, 1760\u20131762.\n\n30. TNA, CO 139\/21\/47, Jamaica Acts, 1760; Jamaica, An Abridgment of the Laws of Jamaica, pp. 104\u20135. See also Gad Heuman, 'White Over Brown Over Black: The Free Coloreds in Jamaican Society During Slavery and After Emancipation', Journal of Caribbean History 14 (1981), pp. 46\u201369.\n\n31. Heuman, Between Black and White, pp. 23\u201332; Douglas Hall, 'Jamaica', in David W. Cohen and Jack P. Greene (eds), Neither Slave Nor Free: The Freemen of African Descent in the Slave Societies of the New World (Baltimore: University of Maryland Press, 1972), pp. 192\u2013213.\n\n32. TNA, CO 137\/33\/40.\n\n33. TNA, CO 137\/33\/35.\n\n34. Stuart Hall, 'Who Needs Identity?', in Hall and Gay (eds), Questions of Cultural Identity, pp. 1\u201317, here p. 3.\n\n35. Trevor Burnard, 'Not a Place for Whites? Demographic Failure and Settlement in Comparative Context: Jamaica, 1655\u20131780', in Kathleen E. A. Monteith and Glen Richards (eds), Jamaica in Slavery and Freedom: History, Heritage and Culture (Mona: University of the West Indies Press, 2002), pp. 73\u201388, here p. 82.\n\n36. Richard Brown, Society and Economy in Modern Britain, 1700\u20131850 (London and New York: Routledge, 1991), pp. 232\u20135; Maxine Berg, 'Consumption in Eighteenth- and Early Nineteenth-Century Britain', in Roderick Floud and Paul Johnson (eds), The Cambridge Economic History of Modern Britain, vol. 1: Industrialisation, 1700\u20131860 (Cambridge: Cambridge University Press, 2004), pp. 357\u201387, esp. pp. 362\u20134; Christopher A. Whatley, Scottish Society, 1707\u20131830: Beyond Jacobitism, Towards Industrialisation (Manchester: Manchester University Press, 2000), pp. 96\u201399, 219\u201321; Richard B. Sheridan, Sugar and Slavery: An Economic History of the British West Indies (Barbados: Caribbean Universities Press, 1974), pp. 27\u201331.\n\n37. Margaret Hunt, 'Racism, Imperialism, and the Traveler's Gaze in Eighteenth-Century England', Journal of British Studies 32 (1993), pp. 333\u201357; Kathleen Wilson, 'The Good, the Bad, and the Impotent: Imperialism and the Politics of Identity in Georgian England', in Ann Bermingham and John Brewer (eds), The Consumption of Culture, 1600\u20131800 (New York: Routledge, 1997), pp. 237\u201362.\n\n38. John Singleton, A General Description of the West-Indian Islands, As far as Relates to the British, Dutch and Danish Governments, from Barbados to Saint Croix. Attempted in Blank Verse (Barbados: Esmand and Walker, for the author, 1767), p. 147, IV. 453.\n\n39. For representation as a cultural process, see Stuart Hall, 'The Work of Representation', in Stuart Hall (ed.), Representation: Cultural Representations and Signifying Practices (London: Sage, 1997), pp. 13\u201374.\n\n40. On racialised fears of the 'other' in seventeenth-century England, see Kim F. Hall, Things of Darkness: Economies of Race and Gender in Early Modern England (Ithaca: Cornell University Press, 1994); Margo Hendricks and Patricia A. Parker (eds), Women 'Race', and Writing in the Early Modern Period (New York: Routledge, 1994); Sujata Iyengar, Shades of Difference: Mythologies of Skin Color in Early Modern England (Philadelphia: University of Pennsylvania Press, 2005); Ania Loomba, Shakespeare, Race, and Colonialism (Oxford: Oxford University Press, 2002). For the development of eighteenth-century British racial categories, see Dror Wahrman, The Making of the Modern Self: Identity and Culture in Eighteenth-Century England (New Haven: Yale University Press, 2006); Roxann Wheeler, The Complexion of Race: Categories of Difference in Eighteenth-Century British Culture (Philadelphia: University of Pennsylvania Press, 2000); Beth Fowkes Tobin, Picturing Imperial Power: Colonial Subjects in Eighteenth-Century British Painting (Durham: Duke University Press, 1999), esp. pp. 139\u201373.\n\n41. John Gilmore discusses these omissions in his article, '\"Too oft allur'd by Ethiopic charms\"? Sex, Slaves and Society in John Singleton's A General Description of the West-Indian Islands (1767)', Ariel 38 (2007), pp. 75\u201395.\n\n42. Singleton, A General Description, p. 151, IV. 526\u20137.\n\n43. Singleton, A General Description, p. 152, IV. 547\u201351.\n\n44. Roxann Wheeler, 'Colonial Exchanges: Visualizing Racial Ideology and Labour in Britain and the West Indies', in Geoff Quilley and Kay Dian Kriz (eds), An Economy of Colour: Visual Culture and the Atlantic World, 1660\u20131830 (Manchester: Manchester University Press, 2003), pp. 36\u201359, here p. 37.\n\n45. Singleton, A General Description, p. 153, IV. 553\u20135.\n\n46. Singleton, A General Description, p. 147, IV. 454, 459.\n\n47. Changing ideals of femininity in Britain are analysed in Ingrid H. Tague, Women of Quality: Accepting and Contesting Ideals of Femininity in England, 1690\u20131760 (Rochester: Boydell Press, 2002), pp. 18\u201348; Robert W. Jones, Gender and the Formation of Taste in Eighteenth-Century Britain (Cambridge: Cambridge University Press, 1998), pp. 1\u201336.\n\n48. Long, History of Jamaica, vol. 2, pp. 274, 278\u20139.\n\n49. J. B. Moreton, West India Customs and Manners: Containing Strictures on the Soil, Cultivation, Produce, Trade, Officers, and Inhabitants; with the Method of Establishing and Conducting a Sugar Plantation (Printed for J. Parsons et al.: London, 1793), pp. 120\u201321.\n\n50. Long, History of Jamaica, vol. 2, p. 330.\n\n51. On the emergence of racial taxonomies in the British empire, see Robert Young, Colonial Desire: Hybridity in Theory, Culture, and Race (New York: Routledge, 1995), pp. 90\u2013117; Gregory D. Smithers, Science, Sexuality, and Race in the United States and Australia, 1780s\u20131890s (New York: Routledge, 2009), pp. 15\u201343.\n\n52. Long, History of Jamaica, vol. 2, pp. 328, 332, 261, respectively.\n\n53. Moreton, West India Customs and Manners, pp. 123\u20134.\n\n54. Moreton, West India Customs and Manners, p. 127; Young, Colonial Desire, p. 19.\n\n55. Young, Colonial Desire, p. 108.\n\n56. Long, History of Jamaica, vol. 2, p. 327.\n\n57. On the Spanish American 'whitening' process, see Ann Twinam, 'Racial Passing: Informal and Official \"Whiteness\" in Colonial Spanish America', in John Smolenski and Thomas J. Humphrey (eds), New World Orders: Violence, Sanction, and Authority in the Colonial Americas (Philadelphia: University of Pennsylvania Press, 2005), pp. 249\u201372; Ann Twinam, 'Purchasing Whiteness: Conversation on the Essence of Pardo-ness and Mulatto-ness at the End of Empire', in Andrew B. Fisher and Matthew D. O'Hara (eds), Imperial Subjects: Race and Identity in Colonial Spanish America (Durham: Duke University Press, 2009), pp. 141\u201366; Jennifer M. Spear, Race, Sex, and Social Order in Early New Orleans (Baltimore: Johns Hopkins University Press, 2009).\n\n58. The key discussion of centre and periphery as mutually constitutive is Ann Laura Stoler and Frederick Cooper, 'Between Metropole and Colony: Rethinking a Research Agenda', in Ann Laura Stoler and Frederick Cooper (eds), Tensions of Empire: Colonial Cultures in a Bourgeois World (Berkeley: University of California Press, 1997), pp. 1\u201356.\n\n59. Jackson, Heterosexuality in Question, p. 5.\n\n60. Richardson, 'Patterned Fluidities', p. 471.\n\n61. Douglas J. Hamilton, Scotland, the Caribbean and the Atlantic World 1750\u20131820 (Manchester: Manchester University Press, 2005), pp. 4\u20135; S. D. Smith, Slavery, Family, and Gentry Capitalism in the British Atlantic: The World of the Lascelles, 1648\u20131838 (Cambridge: Cambridge University Press, 2006), pp. 8\u20139.\n\n62. For empire as a means of Scottish identification with Britain, see Eric Richards, 'Scotland and the Uses of the Atlantic Empire', in Bernard Bailyn and Philip D. Morgan (eds), Strangers Within the Realm: Cultural Margins of the First British Empire (Chapel Hill: University of North Carolina Press, 1991), pp. 67\u2013114; Alan L. Karras, Sojourners in the Sun: Scottish Migrants in Jamaica and the Chesapeake, 1740\u20131800 (Ithaca: Cornell University Press, 1992), esp. pp. 1\u201345; Ned C. Landsman (ed.), Nation and Province in the First British Empire: Scotland and the Americas, 1600\u20131800 (London: Associated University Presses, 2001), pp. 15\u201335.\n\n63. Mary Louise Pratt, Imperial Eyes: Travel Writing and Transculturation (New York: Routledge, 1992), p. 7.\n\n64. For examples of the gendered gaze, see part 3 in Hendricks and Parker (eds), Women 'Race', and Writing, pp. 161\u2013240.\n\n65. Janet Schaw, Journal of a Lady of Quality; Being the Narrative of a Journey from Scotland to the West Indies, North Carolina, and Portugal, in the years 1774 to 1776, ed. Evangeline Walker Andrews and Charles Maclean Andrews (New Haven: Yale University Press, 1921), p. 87.\n\n66. Schaw, Journal of a Lady of Quality, pp. 78, 80.\n\n67. N. T. Phillipson, 'Politics, Politeness, and the Anglicisation of Early Eighteenth-Century Scottish Culture', in Roger A. Mason (ed.), Scotland and England 1286\u20131815 (Edinburgh: John Donald, 1987), pp. 226\u201346.\n\n68. The Lady's Magazine; Or Entertaining Companion for the Fair Sex, Appropriated solely to their use and Amusement. vol. 1 (London: printed for J. Wheeble, Pater-Noster Row, 1770\u201371), p. 411.\n\n69. Colman, 'Janet Schaw and the Complexions of Empire', pp. 176\u20139.\n\n70. Schaw, Journal of a Lady of Quality, p. 112.\n\n71. Troup's medical life in Dominica is detailed in Richard B. Sheridan, Doctors and Slaves: A Medical and Demographic History of Slavery in the British West Indies, 1660\u20131834 (Cambridge: Cambridge University Press, 1985), pp. 302\u20135.\n\n72. Sheridan, Doctors and Slaves, p. 302; Thomas Atwood, The History of the Island of Dominica (London, 1791), pp. 208\u20139.\n\n73. UASCA, MS 2070, Journal of Jonathan Troup, 1788\u20131790, fol. 12v.\n\n74. UASCA, MS 2070, fols 11, 13.\n\n75. UASCA, MS 2070, fol. 133v.\n\n76. Mair, Historical Study of Women in Jamaica, p. 97; Goveia, Slave Society in the British Leeward Islands, pp. 84, 215.\n\n77. UASCA, MS 2070, UA, fol. 29. The link between white womanhood and freedom is discussed in Hilary McD. Beckles, 'White Women and Slavery in the Caribbean', History Workshop 36 (1993), pp. 66\u201382.\n\n78. UASCA, MS 2070, fol. 77v.\n\n79. UASCA, MS 2070, fol. 107v.\n\n80. UASCA, MS 2070, fols 17, 19, 22.\n\n81. UASCA, MS 2070, fol. 45.\n\n82. UASCA, MS 2070, fol. 47.\n\n83. UASCA, MS 3027, Journal of Jonathan Troup, Physician, Dominica, West Indies, and Aberdeen, 1790\u201397, fol. 1.\n\n84. On polite manhood, see Philip Carter, Men and the Emergence of Polite Society, Britain 1660\u20131800 (Harlow: Longman, 2001), pp. 53\u201387; John Tosh, 'The Old Adam and the New Man: Emerging Themes in the History of English Masculinities', in Tim Hitchcock and Mich\u00e8le Cohen (eds), English Masculinities, 1660\u20131800 (Harlow: Longman, 1999), pp. 217\u201338; Mich\u00e8le Cohen, Fashioning Masculinity: National Identity and Language in the Eighteenth Century (New York: Routledge, 1996), pp. 42\u201353, 98\u2013110.\n\n85. Burnard, 'Sexual Life of a Jamaican Slave Overseer', p. 170.\n\n86. Jackson, Heterosexuality in Question, p. 24.\n\n87. UASCA, MS 2070, fol. 82.\n\n88. UASCA, MS 2070, fol. 173.\n\n89. UASCA, MS 2070, fol. 68.\n\n90. UASCA, MS 2070, fols 115\u2013115v.\n\n91. UASCA, MS 2070, fols 123\u20134.\n\n92. UASCA, MS 2070, fol. 157v.\n\n93. Carter, Men and the Emergence of Polite Society, pp. 66\u201370.\n\n94. See esp. Linda Colley, Britons: Forging the Nation, 1707\u20131837 (New Haven: Yale University Press, 1992); Kathleen Wilson, The Sense of the People: Politics, Culture and Imperialism in England, 1715\u20131785 (Cambridge: Cambridge University Press, 1995); Wilson, Island Race; Wheeler, Complexion of Race; Nussbaum, Limits of the Human; Wahrman, Making of the Modern Self.\nChapter 4\n\nXing: The Discourse of Sex and Human Nature in Modern China\n\nLeon Antonio Rocha\n\nWe begin with a straightforward question: 'What is the Chinese word for \"sex\"?' A Chinese speaker will reply, 'xing'! In Modern Chinese, xing is the character most frequently used to denote matters related to sex, gender and sexuality. Compounds associated with xing include xingjiao (sexual intercourse), xingbie (sexual difference), xingyu (sexual desire) and xing quxiang (sexual orientation). Professor Li Xiaojiang of the Centre of Gender Studies at Dalian University, one of the first institutions of its kind in China, claims:\n\nEverything seems crystal-clear: xing (sex) is purely bodily and hence primordial, whereas xingbie (gender), as its lexical structure indicates \u2013 xing \\+ bie, meaning 'difference' \u2013 refers to social identity produced, so to speak, by the bodily xing. Sex is the basis upon which rests gender... it is already physiological and nature-endowed.1\n\nLi goes on to comment on the sex\/gender distinction in the Chinese context. She points out the seeming 'crystal-clearness' of xing as a sex that is already endowed by nature. But she overlooks the historicity of the character, the convoluted career of xing. In Classical Chinese, the character meant 'human nature', and only in the early twentieth century came to signify both sex and human nature. How did this happen, and what was the significance of this? This chapter will begin with an etymological investigation, through which it will emerge that, in China in the late 1910s and early 1920s, sex became, to borrow Foucault's words, 'a kind of natural given which power tried to hold in check' and simultaneously 'an obscure domain which knowledge tried gradually to uncover'.2\n\nThe intellectuals of the May Fourth New Culture period (c.1915\u201337), who were responsible for translating and introducing sexological and sex education texts from Europe, America and Japan, reconceptualised sex as the index to human character, the originary, psychical truth. Xing became a new keyword, the point of anchorage for a sexual politics that regarded sex \u2013 and by extension human nature \u2013 as cruelly repressed by a 'hypocritical', 'feudalist', even 'cannibalistic' sexual morality of the 'Old China'. There was a concomitant intensification of attempts to produce 'real', 'truthful' knowledge on sexuality \u2013 a proliferation, an explosion of discourse. Sex became a panacea for China's weakness and degeneracy, and a revolution of the relationships between men and women, the reformulation of love and desire, and the adoption of eugenics and birth control practices, were perceived as ways to enable the Chinese nation to 'catch up' with the west and to become ready to participate in a global modernity. It is against this backdrop that we should think about sex and gender in this tumultuous period of Chinese history, as we seek to understand the motivations behind Chinese intellectuals' various inquiries into sex.\n\nKeywords, globalisation and translation\n\nMy approach here is modelled on Raymond Williams's classic Keywords (1976). Williams's project began life as an appendix to Culture and Society (1958) but evolved into a standalone publication which provided generations of scholars with short and concise discussions relating to a range of important terms which had delimited and circumscribed our thinking. Williams's intention is not to fix meanings; Keywords 'is not a dictionary or glossary of a particular academic subject', nor is it 'a series of footnotes to dictionary histories or definitions of a number of words'. Williams's book demonstrates that the semantics of a word changes in response to new socio-political situation and needs, and the way historical actors negotiated and struggled with their use of language to express new experiences. It is 'the record of an inquiry into a vocabulary: a shared body of words and meanings in our most general discussions, in English, or the practices and institutions which we group as culture and society'.3\n\nWilliams's inquiry is limited to European languages and predominantly British English, as pointed out by Tony Bennett and others in their 'sequel' to Keywords.4 It is necessary to point out that discussions of culture and society, including sex and gender, have flowed across national boundaries. My investigation of xing should absolutely not be regarded as a mere curiosity, appendage or even a supplement to more 'mainstream' work on the history of sexuality in Europe and America. It is not simply contributing to the world history of sexuality by adding the 'Chinese case' to the cauldron. Rather, following Ann Laura Stoler, I propose that it is impossible to appreciate the global nature of modernity, to comprehend the depth and power of empire and colonialism, to understand the spatialisation of scientific and medical knowledge, without a thorough consideration of the circulation of ideas and concepts between the 'west' (perceived as 'centre', 'primary', thus prioritised) and the 'east' (presumed 'peripheral', 'marginal', 'minority', 'secondary').5\n\nIn my thesis, I analyse the tremendous cacophony of scientific, medical, philosophical and literary discourses which Chinese intellectuals in the 1920s creatively appropriated in their political projects.6 Many of these cosmopolitan thinkers travelled abroad, studied in prestigious universities around the world, were fluent in a number of languages and brought back to China all sorts of new ideas which they thought would help their troubled, divided, 'backward' motherland. They invited European and American intellectuals to come to China to disseminate their ideas to the Chinese public, to engage in cultural exchange (involving celebrities such as John Dewey, Bertrand Russell, Hans Driesch, Margaret Sanger and Magnus Hirschfeld). What emerges is a complex picture of the globalisation of sexual knowledge, one that precedes the story told by Dennis Altman's Global Sex.7 Globalisation here should not be taken to entail homogenisation; the fact that ideas about sex had travelled from Europe, America and Japan to China by no means meant that everyone ended up believing the same things or acting in the same way.8 It resolutely does not bring us back to the old trap of 'authenticity' and 'imitation' that has often plagued conventional historiographies of colonialism \u2013 that people in the Third World merely copied, parroted, were 'interpellated' by or inflicted with the discourse of the colonising Other. Globalisation is always already accompanied by localisation and indigenisation; any historian should be obstinately committed to pointing out specificities, the situated character of knowledge, but at once concerned with a transnational stratosphere of discourse, the traffic and flow of ideas from one place to another. Xing here serves as an excellent example: although the conflation of sex with human nature into one word may be a response to the rhetoric of repression and emancipation found in western sexological texts, xing \u2013 qua both sex and human nature \u2013 is a particular Sino-Japanese linguistic innovation, a keyword manufactured and propagated by a network of translators, intellectuals and scientific practitioners in East Asia. To put this another way, a consequence of the global proliferation of a certain ideology of sexuality \u2013 sex as fundamental property of humanity \u2013 was that the conception of sexuality emerging in early twentieth-century China became quite similar to that found in the human sciences of Europe and America, which Michel Foucault analyses in the first volume of his History of Sexuality.9\n\nThrough the discussion of the history of xing, I would like to highlight the question of translation. It will be an extremely fruitful inquiry for historians of sexuality to take up Raymond Williams's Keywords project, and incorporate the problematic of translation and transmission, to study how different cultures tackled new terminologies such as 'sexuality' (and 'heterosexuality', 'homosexuality', 'sadomasochism', 'libido'), 'gender', 'science', 'race', 'class', 'revolution', 'movement' and so on.\n\nWe should ask: did intellectuals, academics and translators emphasise the alienness of these terms by inventing new characters or using unfamiliar compounds? Did they highlight their untranslatability or incommensurability, by using transliterations or leaving the word in its original form? Did they draw parallels with tradition and precedence, or deny the novelty of something, or domesticate a foreign term, by adopting a familiar character and subtly\/overtly stretching its semantics? Did they (de)emphasise the processes of negotiation? How did they standardise or claim ownership of new terminologies and neologisms through dictionaries, encyclopaedias and glossaries? How did they recruit other actors to speak using their new vocabularies, adhere to their terms of engagement? What would constitute a 'faithful' translation, and how were translations accepted or resisted? What resources (foreign philosophy, comparative linguistics, classical philology, Latin, Greek, Sanskrit, Classical Chinese) were mobilised? These are all crucial questions addressed in the Chinese context by Lydia Liu and Haun Saussy. For them, translation is one of the privileged sites in understanding colonialism and global modernity, communications, transmissions, interactions and exchange between the Chinese and the non-Chinese in history, and for me, a highly productive way to write multiple, comparative histories of sex and gender that are simultaneously sensitive to local conditions and yet never lose sight of the larger picture of transnational movements.10\n\nXing as human nature\n\nIn English-speaking academia, Frank Dik\u00f6tter, Judith Farquhar, Zhong Xueping and Deborah Sang have picked up on the strange life of xing; they all mention in passing that before the twentieth century xing did not mean sex. Zhong and Sang each dedicate a paragraph and two small footnotes, while Dik\u00f6tter, in his tremendously influential study of sex in modern China, skirts over this issue in a single sentence.11 There is no evidence cited or exploration accompanying these academics' assertions. Farquhar's treatment of xing is the more detailed amongst the four, yet she does not explain the mechanisms through which xing came to mean sex and human nature. Many Chinese-speaking scholars who write prolifically on the history of sexuality in China, and who are otherwise extremely sensitive to language, never seem to detect or deem it necessary to unpack the historicity of xing.12 This chapter should be read as an intervention in two important ways. First, the obvious: by drawing attention to the rich significances embedded in just one Chinese character, I attempt to prevent the story of the usage of xing from degenerating into a factoid, endlessly reiterated and assumed in the footnotes of academic monographs but never analysed.\n\nSecond, my historicisation of xing speaks to Tani Barlow's examination of the discourses of fun\u00fc and n\u00fcxing in her Question of Women in Chinese Feminism.13 Fun\u00fc and n\u00fcxing were two Chinese words, both used in the Chinese feminist movements in the twentieth century. Whereas fun\u00fc, an earlier term, situated women in the network of family and kinship relations \u2013 their responsibilities as childbearers and mothers of the nation \u2013 n\u00fcxing, literally 'woman' plus 'sex\/human nature' (n\u00fc plus xing) was a neologism for a biologically sexed woman. The neologism came into being also in China in the 1920s. The discourse of fun\u00fc in Chinese feminism pointed to the participation of women in public life and their rights in society, but tended to ignore, suppress, suspend or even sometimes erase the differences between men and women. The discourse of n\u00fcxing, on the other hand, sought to highlight women's repressed sexuality and sexual difference, and attempted to create a new and revolutionary subjectivity for women, different from that of men. N\u00fcxing therefore complicated the discourse of universal liberation and emancipatory politics promoted by the male May Fourth New Culture intellectuals, by introducing the question of sexual difference \u2013 since men and women were fundamentally different in sex and nature, therefore the pathways for men's liberation and women's liberation had to be different too. My present analysis of xing therefore aims to achieve something more primary than Tani Barlow's analysis. The construction of the discourse of n\u00fcxing relied fundamentally on xing being both sex and human nature in the first place. To put this another way, before it was possible to have a discourse of woman based on her sexual, biological, natural differences (that is, n\u00fcxing), sex had to first become human nature through the creation of the neologism xing.\n\nIf one opens the New China Character Dictionary (Xinhua zidian, 10th edn, 2004), the most popular reference work in China, one can see an elaborate entry on the character xing:\n\n(i) Natural instincts, inherent tendencies, the heavenly endowment in humans\n\n(ii) The nature of something (or of someone), its substance, its fundamental character\n\n(iii) Life \u2013 equivalent to the character sheng \u2013 living, or fate or destiny\n\n(iv) Disposition, temperament\n\nAnd further, (v) xing as sex, and compounds such as xingjiao (intercourse), xingbie (sexual difference), and (vi) xing in Modern Chinese as a suffix, roughly equivalent to '-ity' or '-ness' in English. For instance, 'possible' is keneng and 'possibility' is kenengxing, 'permanent' is yongjiu and 'permanence' becomes yongjiuxing.\n\nThe first four definitions are accompanied by sources in Classical Chinese. For the first usage of xing, 'natural instincts', the cited source is the Confucian text Mencius, in the chapter titled 'Gaozi' in which the eponymous philosopher engages in a protracted argument with Mencius on human nature. Gaozi states that the appetite for food and sex forms part of human nature, summed up in the famous phrase shi se xing ye. Here, sex is not represented by the character xing, but by se. Mencius rejoins that human nature (xing), which is heaven-endowed, consists of men's capabilities to act morally, rather than basic, animalistic needs for nourishment and procreation. Mencius's view on human nature as innately good became the orthodox definition of xing as laid down, for instance, in Explaining Simple and Analysing Compound Characters (Shuowen jiezi), a second-century dictionary. Deborah Sang astutely points out that xing in Classical Chinese had 'only a tangential, if not reverse, relation to sexuality'.14 Further instances of xing as human nature include: 'What Heaven has conferred is called \"Nature\"\/xing' from Doctrine of the Mean (Zhongyong); 'What cannot be learnt, and what requires no application to master, in human beings is called \"human nature\"\/xing' from the philosophical treatise Xunzi (third century BCE).15\n\nFor xing's second definition \u2013 the nature of something \u2013 the Xinhua once again cites Mencius, and further points out that xing was used to translate the Sanskrit words svabh va, prakrti and pradh na: 'the nature interpreted as embodied, causative, unchanging; independent or self-independent; fundamental nature manifestation or expression; the Buddha-nature immanent in all beings, the Buddha heart or mind'.16 Xing is contrasted to xiang, the superficial appearance of all things. The Chronicles of Zuo (Zuozhuan, fourth century BCE) contained the primary example of the usage of xing for 'life': 'The people enjoy their lives [xing], and there are no enemies or thieves' or 'New palaces are reared... the strength of people is taxed to an exhausting degree... the people feel that their lives [xing] are not worth preserving'. Finally, the 'Gaozi' chapter from Mencius supplies the source for xing as disposition and temperament: 'When Heaven is about to give someone a great responsibility, it first makes his mind endure suffering... Heaven stimulates his mind, stabilises his temper [xing] and develops his weak points'.17\n\nCrucially, the definitions of xing pertaining to sex, and the use of xing as a suffix, are both supplied without a single classical source. Lydia Liu and Federico Masini both assert that the use of xing as a suffix was introduced from the Japanese, though they do not comment on whether xing as sex came from the Japanese as well.18 Farquhar consulted Taiwan Academia Sinica's Encyclopaedic Dictionary of Chinese Language (1973) and found that xing as sex lacked a classical source.19 Another standard reference, the Lin Yutang's Chinese-English Dictionary of Modern Usage (1972), does not cite a classical source for the sex definition of xing, whilst Luo Zhufeng's Hanyu da cidian (2001) cites a 1989 article on sex education for the etymology. I consulted China Books' (Zhonghua shuju) Zhonghua dazidian (edited by Xu Yuangao, Lufei Kui and Ouyang Pucun), published between 1915 and 1923, and sex was nowhere to be found under the eight definitions of the character xing. The sex definition was altogether absent in the 1912 New Dictionary (Xin zidian).\n\nThe Zhonghua dazidian of Xu et al. was in turn based on the Kangxi zidian, commissioned by Qing Emperor Kangxi in 1710 and released in 1716. In the 1887 edition of Kangxi Dictionary, published by the Combined Literature Book House (Tongwen shuju), there is no mention of sex under the entry for xing. The 1916 Commercial Press's movable-type edition of Kangxi also lacked xing qua sex. In all the ancient Chinese dictionaries, such as the aforementioned Shuowen jiezi and Broadening the Refined (Guangya), there was no connection between xing and sex. If one takes for granted that dictionaries attempt to record usages of a certain word in common currency, then xing until the twentieth century continued to signify what Heaven had decreed; xing named an unsexed, ungendered concept of innate human nature or essence.\n\nMy thesis is that in the late 1910s and early 1920s, sex was implanted, slipped into, invested into xing \u2013 to the extent that the meaning of the character, as simultaneously sex and human nature (and thus sex as human nature) has by now become familiar, naturalised. A native Chinese speaker in the twenty-first century, upon hearing the utterance of xing or seeing it in print would think of sex, the crux of human nature, and would not usually be aware that this xing\/sex\/human-nature complex was a recent product: the process of linguistic engineering has been forgotten, de-emphasised. It is, however, paramount to clarify that the Chinese had had a host of words to denote matters related to sex before xing was endowed with a new sexual meaning, and a large number of these terms are still in regular use.\n\nFrom the obscene to the natural?\n\nYin was traditionally a character used to qualify sexual behaviours. Yin conjures a connotation of excess, an image of flooding or soaking, and is often combined with other characters to represent illicit sexual relations: yinf  (adulterer), yinf\u00f9 (adulteress or promiscuous woman), jianyin (adultery), shouyin ('illicit sex with hand', masturbation), zhengyin (incest). Yin points to the licentious, wanton, salacious, lascivious: yingui ('lewd demon', man obsessed with sex), yincong ('lewd pest'), yinnian (immoral thoughts), yinn\u00fce (obscene jokes), yinshu (pornographic book), yinxie (pornographic), yinshui ('waters of lust', genital fluids). Yin connotes excess as in: yinwei (despotic power), yinyi (debauchery, indulgence, greed), yinxing (torture). Committing acts of yin is deeply harmful to one's physical and spiritual wellbeing and disrupts the social order, so yin always already incorporates a moralistic warning, a normative prescription of what counts as legitimate sexual activity (reproductive, not overly frequent, with the correct partner). Late Qing revolutionary Tan Sitong (1865\u20131898) complained that yin became an overly broad term and expressed the urgent need to reform the Chinese mentality that all sex was necessarily yin and thus inherently dirty and evil. From Tan's Exposition of Benevolence (Renxue, 1897):\n\nSexual intercourse [nann\u00fc, literally 'man-woman'] is given the term 'lust' [yin]. This is how 'lust' is defined. Since the inception of mankind, the name yin has, through custom, continually been in use and has remained unchanged ever since. Hence we are used to regarding intercourse [yin] as evil. If since the inception of human beings, we had been accustomed to yin as, say, a rite practised in audiences at court, in imperial feasts, in imperial temples, in cities and towns, and before large crowds \u2013 like deep bowing with clasped hands and genuflection in China, or embracing and kissing in the west \u2013 and that, the custom had survived until the present, who would think that yin was evil?... Some may argue that the genitals [nann\u00fc zi ju, literally 'instruments of man\u2013woman relations'] born concealed, seldom seen by people, they therefore are different from the openly practised rites; yin is thus considered to be evil. By this line of reasoning, then rites and yin differ only in whether concealed or open, and not in whether they are good or evil. If, since the inception of human beings, their genitals had not been concealed, but appeared on the face, to be easily seen by raising one's eyes, yin would then be regarded as no more than a greeting. How could yin then be considered evil?20\n\nNote that Tan never used the term xing to denote sex anywhere. Instead, he was attempting to reclaim and rehabilitate yin. In 1898, sex had not yet acquired its 'scientific', supposedly 'natural' and 'neutral' name. Tan's passage here demonstrates the importance of language, getting the terms right, in an attempt to defamiliarise the character yin from its negative image.\n\nSe is another major character to describe sex. Whereas yin automatically suggests the obscene and abnormal sexual relations, se suggests lust, temptation and seduction, though there are overlaps between se and yin: seqing xiaoshuo (also a pornographic or erotic novel), segui (someone obsessed with sex), haose (someone who indulges in sex), se mimi (observing someone with a lustful look), jiese (abstinence), sexiang (sex appeal). Yu is desire; yinyu and seyu are carnal desires. Yuhuo is 'a flame of desire': a dangerous, all-consuming fire that can 'incinerate' someone's mind and body if not properly controlled. Rou is 'meat'\/'flesh', often placed in diametric opposition to the spiritual, ling. A crucial part of the rhetoric of radical May Fourth intellectuals is the reconciliation of the flesh and the spirit (lingrou yizhi). Love between a man and a woman should not simply remain on a spiritual level, and should not be about the sublimation of very real desires into something asexual, or 'Platonic'. They argue that this traditional ideal is contrary to xing, to human nature. The modern, perfect relationship must incorporate physical intimacy, sexual attraction and a deep level of emotional connection. Love and marriage are thus subsumed under xing, and are sexualised, eroticised.21\n\nThe Classical Chinese term for sex between a married couple was dunlun, from the Book of Rites (Liji). Sex was also 'business in the bedchamber': fangshi, xingfang, dongfang. The 'Art of the Bedchamber' is fangzhong shu. The characters ru and tong, quite simply 'enter' and 'go through', might also be used, as well as nann\u00fc, literally 'man and woman'. Sex was also described as the act of uniting, transferring, combining, bringing something together: thus jiaohe and jiaogou. More poetic expressions included: yunyu ('clouds and rain'), a reference to a fairy maiden in the Szechuan gorges who commanded clouds and rain; yuanyang xishui ('pair of mandarin ducks playing in water'); daofeng dianluan ('topple the male and female phoenixes'); tiandi ronghe, describing the coming together and harmonisation of Heaven (designated yang, male) and Earth (yin, female). Meanwhile, the older terms for different elements of the sexual script like oral sex were: pinxiao, 'savouring' or 'tasting with discrimination' a Chinese flute (fellatio), or pinyu, 'savouring jade' (cunnilingus). These came from the seventeenth-century novel Plum in the Golden Vase (Jin Ping Mei).22\n\nSame-sex relations were described in Classical Chinese as duanxiu, fentao\/yutao, longyang.23 Duanxiu, 'cutting the sleeve', was a reference to Han Emperor Ai (first century BCE) and his male concubine Dong Xian. When Dong Xian fell asleep on the emperor's sleeve, the emperor ordered his sleeve to be cut so he could leave the bed without waking his beloved. Fentao, 'sharing the peach', was recorded in Hanfeizi (third century BCE). Duke Ling of Wei had a beautiful boy called Mi Zixia, who once offered a peach, already bitten, to the duke. This would normally be a serious offence, but the duke showed his appreciation, suggesting the intimate bond between the two. Finally, longyang is a reference to the eponymous duke from the Warring States period. The duke went fishing with the Wei emperor, and when the emperor caught ten fish, the duke started weeping. The duke explained that the emperor, having caught larger fish, would then discard the smaller ones he previously captured. By analogy, once the emperor met other beauties, he would abandon the duke. The emperor was deeply touched and declared that, if anybody dared introduce more beauties to him, he would execute that person and eliminate his kin. Longyang or longyang pi (pi meaning 'obsession') thus became terms for same-sex relations between men. For female same-sex relations, two metaphors were used: mojing ('polishing\/rubbing the mirror') and duishi ('facing each other eating'). Duishi, implying mutual cunnilingus, referred to the sexual practices between women in the imperial harem. Mojing was an allusion to tribadism (mutual masturbation involving a woman rubbing her vulva against that of her partner). In Classified Collection of Anecdotes on the Qing Dynasty (Qingbai leichao, 1916), Xu Ke describes 'mirror-rubbing' as a common practice among the members of a man-loathing sisterhood in Shanghai in the late nineteenth century.24 One could contrast these with the terminologies for homosexuality and lesbianism in circulation in biology and sexology texts from the 1920s: tongxing lian\/ai\/lian'ai \u2013 composed of 'same' (tong), 'sex' (xing) and 'love' (lian\/ai\/lian'ai) \u2013 which evacuated the elaborate literary and historical references.25\n\nThis kaleidoscopic, perhaps bewildering, tour of older terms is by no means exhaustive, and cannot do justice to the massive vocabulary available in Chinese to talk about sexual behaviours, seriously or jokingly, approvingly or contemptuously, under different circumstances, at different audiences. In casual conversations today, sex may be simply shui ('sleep'), guanxi ('relationship'), zhao'ai ('make love'), shangchuang ('getting in bed'), gan ('do'\/'fuck') or even na'ge ('that thing'). Etymological research is difficult and time-consuming in Chinese and Japanese because of a shortage of reference works that provide genealogies on a character's historical usage; by contrast, in English, the Oxford English Dictionary supplies a brief, though not always comprehensive, chronology for most entries. Nor is there a work in Chinese comparable to Julie Coleman's masterly Love, Sex and Marriage: A Historical Thesaurus,26 which allows historians to trace the evolving usage of a term and to locate it within semantic fields. This is without diving into complications arising from regional variations. Cantonese speakers, for instance, have their own baffling set of insults, profanities and colloquial coinages to talk about sex, unintelligible to non-Cantonese speakers. Yet none of these 'non-serious' terms have the symbolic value invested in the 'respectable' xing \u2013 the standard word in circulation in scientific discussions ever since the 1920s.\n\nTo sum up this section, the purpose of discussing yin, 'cutting the sleeve' and so forth is to show how the older Chinese lexicon for sex might be classified: first, as terms which always already carried a negative, moralistic connotation, suggesting obscenity, excess, dirtiness; second, as euphemisms containing rich literary, mythical and historical allusions. The twentieth-century word xing and its associated compounds were, for the May Fourth New Culture generation, about 'neutrality'; they referred to biological facts of nature, they were 'modern'. To use xing for sex was to 'call a spade a spade': if sex was human nature, there ought not to be any shame in talking about it in a plain, straightforward, honest, unpretentious and immediate language, and there was no need to veil sex underneath thick layers of metaphors. But the point of xing-talk is that it is precisely not value-neutral at all. The 'sex\/human nature' complex embedded in xing mobilises a humanistic ideological weapon which Foucault calls the 'Repressive Hypothesis', that links together 'the revelation of truth, the overturning of global laws, the proclamation of a new day to come, and the promise of a certain felicity'.27 It is the conviction that the 'Old World' had painstakingly repressed and denied people's sexuality and their fundamental nature, and what was therefore most needed to transform society and nation was the fullest affirmation and liberation of human instincts. For the Chinese iconoclasts and modernisers, 'Confucian propriety' had produced nothing but prudishness, dishonesty and obfuscation surrounding sex which xing-talk would defy. A history of sexuality written in the vein of the Repressive Hypothesis would claim that there had never been a non-repressive discourse of sex and it would be up to the progressive scientific experts, the serious and rigorous investigators, to uncover\/recover the truths of our being and to inaugurate a language of xing. The lack of 'neutral' words for sex would then be construed as evidence supporting the claim. This mirrors the May Fourth conception that the history of China itself had been nothing but the history of repression, until the intellectuals took on the mission to emancipate (jiefang) the human spirit from the 'ironhouse'.28 I cannot possibly attempt something as ambitious as a complete analysis of the history of Chinese sexuality to address Foucault's 'first doubt': 'Is sexual repression truly an established historical fact?'29 What I can point out is that the repression\u2013liberation narrative, propounded in the 1920s and later deployed to legitimate the rule of the communist regime (the justification of radical social engineering and transcendence of the rule of law to 'liberate the masses'), has been directly attacked through many case studies.30 One should avoid inserting oneself into the 'critical discourse that addresses itself to repression' that may be 'in fact part of the same historical network as the thing it denounces (and doubtlessly misrepresents) by calling it \"repression'\".31 While it is doubtless difficult to resist the temptation to see the past as more 'repressed', 'conceited', 'close-minded' and 'hypocritical' than the present, one must stay sober in the discussion of the language of xing to avoid reproducing the teleology and rhetoric of progress embraced by our historical actors. For now, let us turn our attention to xing again, and track it down in Chinese texts in the early twentieth century.\n\nTracing xing\n\nAccording to Jai Ben-ray, Ye Dehui's (1864\u20131927) 'Preface to The Classic of the Plain Girl' (1907) contained possibly the earliest use of xing qua sex and human nature.32 The Classic of the Plain Girl (Su n\u00fc jing), a sex manual dated from the third to second century BCE, was reconstructed by Ye from the fragments recorded in one of the thirty volumes of Ishinp , the oldest surviving medical work from Japan. Ye Dehui, a local official, book collector and bibliographic scholar, regarded the resurrection of these 'Art of the Bedchamber' texts as 'part of a modernising project to bring sex into public discourse. China's ancient sexual love was firmly connected to the serious issue of ensuring the nation's social fitness through reproductive success'.33 In 1903, Ye published Plain Girl and other texts as The Double Plum Sun and Shadow Anthology (Shuang mei jing an congshu).\n\nPlain Girl was a dialogue between the eponymous maiden and the legendary yellow emperor, who sought wisdom on sexual practices. In this ancient text, sexual activity was described as a pleasurable practice which could contribute greatly to health and longevity, but excessive sex might lead to the depletion of the male essence (jing), grave illness and death. Ye Dehui, subsequently castigated as a pornographer spreading obscenity and superstition, had the same aims as May Fourth New Culture intellectuals, but ended up with a different project: instead of championing western sexology and denigrating older Chinese medical texts, Ye argued that China had always already had solutions to its own problems. He wrote:\n\nToday, western scholars in hygiene [weisheng] from afar, investigate and speculate on the subtle and hidden causes behind eating, drinking and sexual relations [yinshi nann\u00fc], and their works are translated as new books such as Genitalia [Shengzhi qi], New Theories on Sexual Intercourse [Nann\u00fc jiaohe xinlun], The Hygiene of Marriage [Hunyin weisheng xue]. The ignorant treated them as treasures, not knowing that the descendants of China's sacred emperors and ancient sages already discussed this learning four thousand years ago. For instance, The Record of Confucius Closing Off the House [Kongzi bifang ji] mentioned in the apocryphal texts [weishu], although it is not passed on through the generations, we know how ancient this study [of sex] is. Or the ancient methods of foetal education [taijiao] recorded in the Abundant Dew on the Spring and Autumn Annals [Chunqiu fanlu] and Records of Ritual Matters by Dai Senior [Da Dai liji], it is invariably about the rectification of character [xingqing] of the parents, multiplication of descendents and continuation of the progeny of the family [guangsi xu], to maximise the function of orderly cultivation [weiyu]. The spirit of the study of sex [xingxue], how could the pedantic Confucian scholars possibly be able to see its essence?34\n\nHere, the Chinese character xing appears twice. The first xing from xingqing means 'character' or 'temperament'. The second xing in xingxue directly refers to the study or scholarship of sex \u2013 xingxue became the standard translation of terms such as sexology, sexual sciences and sex research (sexologie\/Sexuologie, Sexualwissenschaft\/Sexualforschung). Ye's argument was that ancient China had an extremely sophisticated discourse on sex, and as such, the current translations of western texts that he encountered \u2013 Genitalia, New Theories on Sexual Intercourse and so on \u2013 were 'old news from afar'.35 This would be a source of national pride as China was superior to the west in the innovation of ideas. Another aim of Ye Dehui's rhetoric was to legitimise his own investigations \u2013 since sex was what people in the west were talking about, then of course the Chinese had to look into xing too.\n\nThe 1900s and 1910s were a transitional period. Intellectuals wrote about sex with a mixture of old categories \u2013 the aforementioned yin, se and yu \u2013 along with occasional uses of xing constructions. From a sample of articles on the women's movement written between 1842 to 1911, sex was described variously as rou ('flesh'), roujiao ('transactions of the flesh'), rouyu ('carnal desire'), fayu ('arousal'), nann\u00fc zhi yu ('desire between man and woman'), jiaohe (exchange, combine, come together).36 In 'The Relationship Between the Two Sexes' (Nann\u00fc liangxing de guanxi), published in the April 1907 issue of China's New Woman's World Magazine (Zhongguo xin n\u00fcjie zazhi), liangxing was used to describe the opposite sexes. Another early instance of xing in China could be found in the 1900 Chinese translation of a Japanese text, Fukuzawa Yukichi's On the Interactions Between Men and Women (Danjo k sai ron, 1886).37 There, the translator, following Fukuzawa, used the character xing to mean intercourse, an essential component of a relationship between a man and a woman.38 Yet, within the same article, sex was also called tijiao\/tipo zhi jiao ('bodily exchange'), showing that xing had not yet displaced the older categories, and some authors (for example Lufei Kui) continued to use exclusively se and yin in 1910.\n\nIn his influential article on polygamy in the August 1911 issue of Eastern Miscellany (Dongfang zazhi), Du Yaquan writes:\n\nThe key to the preservation of progeny (baozhong)... is to regulate sexual desire (xingyu)... if the system (jiguan) of sexual desire is overused, then other bodily systems will become atrophied (weisuo)... On the other hand, if sexual desire is well regulated, then other systems will prosper ( fada). To have a healthy body and a refined morality and passing these qualities to the offspring \u2013 this is the citizen's (guomin) duty to the future generation.39\n\nDu's article contains one of the earliest uses of the phrase xingyu for 'sexual desire'\/'libido', as opposed to the older yinyu. He writes about sex in the language of drives and instincts emerging from the European psychological sciences, which treat sex as one of the many vital and natural systems of the body. Xingyu is just as important as shiyu, the desire for food and drink. The careful balance of input and expenditure of energy in the bodily economy is key to the development of a healthy, moral human being, and the responsibility of a citizen (guomin, also a new 1920s term) in the Chinese nation is to prevent overspending in sex, achieved through the prohibition of polygamy and concubinage. For Du, sex is a perilous drive and its vigilant monitoring is of individual and collective interest, but to deploy the vocabulary of xing means that sex is no longer something dirty or taboo \u2013 the shift to xing-constructions is a symptom of the emerging discourse of sex qua natural property of all human beings in the early decades of republican China.\n\nIn another article in Eastern Miscellany, Gu Shaoyi explored the relationship between the olfactory sense and sexual desire. Gu similarly equated sexual desire to something that was fundamental to all humans, and adopted the phrase xingyu, which appeared thirty-three times in the text. Xing, as sex and human nature, appeared as a standalone character five times. The older terms seyu and qingyu still featured, but only employed eight and two times respectively, reflecting that Gu's intended audience, the emerging bourgeoisie in urban China, would be expected to understand the new usage of xing.40 By 1919 and 1920, some articles used only xing to refer to sex: for instance, two articles in Morning Light (Shuguang) by Wang Tongzhao and Wang Qirui, and Pan Gongzhan's 1920 review of Maurice Alpheus Bigelow's Sex Education: Knowledge of Sex in its Relation to Human Life (1915) in Education Magazine (Jiaoyu zazhi). If we survey the Comprehensive Catalogue of Republican Period Books, the major index of publications between the late Qing period and the communist takeover, the character xing (meaning sex) began to appear in book titles from 1920 onwards, and out of the 408 books on sex published, 263 were released in this decade.41\n\nThe alien nature of xing as a signifier of sex was often emphasised by the use of quotation marks. For instance, in Zhang Jingsheng's advertisement titled 'The Best Pastime for the Winter Vacation \u2013 An Announcement Made on Behalf of the \"Eugenics Society\"', which appeared in the literary supplement of Capital Daily (Jingbao fukan) in February 1926, quotation marks framed terms including sex (xing), sex histories (xing shi) and sexual knowledge (xing zhishi).42 Another case of the use of quotation marks or a different typeface to highlight the novelty of xing is Chen Dongyuan's influential History of Women's Lives in China (Zhongguo fun\u00fc shenghuo shi, 1926). When commenting on Margaret Sanger's visit to Peking University, Chen notes, '[Sanger] makes Chinese people become aware that matters related to \"xing\" are actually worth discussing using the Scientific Method!'43\n\nThe most suggestive clue to xing's linguistic career could be found through Zhang Dongmin, a writer and translator of popular science who published The Worship of Sex (Xing de congbai) in June 1927. In his book, which drew extensively from O. A. Wall's Sex and Sex Worship (1919), Zhang Dongmin argued that sex, in an unspecified primitive past, was something that was clean and decent, but became something evil and threatening under China's sexual morality. The underlying purpose of Zhang's book was to contrast sexual practices and attitudes in the past, perceived to be more relaxed and 'closer to nature', against the repression that Zhang saw in contemporary China. Of particular importance to us is the manner in which Zhang creatively appropriated the first two verses of the Three Character Classic (San zi jing, circa thirteenth century), which stated the central tenet of Confucianism as developed by Mencius: ren zi chu, xing ben shan; xing xiang jin, xi xiang yuan. The common translation for this would be, 'people at birth, are naturally good; their natures are similar, their habits make them different'. Here, 'naturally' and 'human nature' are represented by xing. Zhang Dongmin however interprets xing here as sex: 'The ancients had said, \"in the beginning, sex was decent\". This clearly stated that when human begins were in their primitive, beginning epochs, for them everything concerning sex was originally regarded as good and decent'.44 Zhou Zuoren, in his review of Zhang Dongmin's book, criticises this reading of xing as either a wilfully anachronistic interpretation or a mistake:\n\nLet us not for now go into a discussion on xing [as sex] as a new noun from Japan... [Zhang Dongmin] thinks that this xing [in the first verse of the Three Character Classic] is the xing in xingjiao [coitus], in fact this is clearly a mistake.45\n\nJapanese connections and return graphic loans\n\nLet us ignore Zhou Zuoren's advice, and now go into a discussion on xing as a new noun from Japan. We begin with the obligatory point of passage for all inquiries related to Japanese use of Chinese characters \u2013 kanji in Japanese \u2013 Morohashi Tetsuji's (1883\u20131982) Dai kanwa jiten, the definitive work of reference on Japanese and Chinese. In the 1984\u201386 edition, the entry on the kanji contains definitions such as temperament, nature, personality and sex; these correspond to the meanings of xing found in any contemporary Chinese dictionary. However, there are three possible pronunciations of the character in Japanese, as opposed to just one in Chinese. When used to refer to sex, the pronunciation is sei. The other two are shou and saga, used in compounds referring to character and nature. Deborah Sang, who cited the opinion of sexologist Zhang Minyun, stated that the 'importation of German sexology to Japan began in the late Meiji period (1868\u20131912) and reached its peak in the Taisho era (1912\u201326)'.46 This statement is broadly correct, as demonstrated by the work of Sabine Fr\u00fchst\u00fcck and Oda Makoto.47 Sang added that it was during the Meiji when 'Japanese intellectuals began to use sei [the character called xing in Chinese] to mean sex'. Unfortunately, neither Zhang nor Sang went any further beyond stating the sex-sei-xing connection.48\n\nA look at the most widely circulated dictionaries published in Japan in the late nineteenth and early twentieth centuries would give us some hints about the trajectory of sei. In the famous Sea of Words \u2013 Genkai (1891), edited by lexicographer Otsuki Fumihiko, there was no record of sei-sex, as with: Owada Tateki's Nihon da jiten (1897); Shozaburo Kanazawa's Forest of Words \u2013 Jirin (1907); Shigeno Yasutsugu's Sanseido kanwa dajiten (1910); Matsui Kanji and Uedo Kazutoshi's Fuzanbo dainihon kokugo jiten (1915). The 1920s however were a watershed, as sei-sex was institutionalised in Japanese reference works for the first time. In Ochiai Naobumi and Haga Yaichi's Fountain of Words \u2013 Gensen (1927), the fourth definition of the character reads, 'Sei. English: sex, the differences in the psychological and physical qualities of men and women'.49 The 1923 Shokai kanwa daijiten by Hattori Unokichi and Oyanagi Shigeta also included the sei-sex definition. The inclusion of the sex definition was by no means uniform across all dictionaries: the revised edition of the aforementioned Forest of Words (1925) and the expanded version of Sea of Words (Gensen, 1932\u201337) were two cases where a sei-sex entry could not be found. On the other hand, some English\u2013Japanese dictionaries recorded sei-sex well before the 1920s. For instance, Shibata Shoukichi and Koyasu Takashi's Eiwa jii (1873) defines sex and sexuality as sei, as with: the Japanese translation of Webster's Unabridged Dictionary (1888) by Tanahashi Ichiro and Frank Warrington Eastlake; Kanda Naibu's Mohan shin eiwa daijiten (1911) and Shuchin konsaisu eiwa jiten (1922). The pattern that emerges is that, until the twentieth century, the character called xing in Chinese was used in Japanese to also signify nature, life and so forth, and from the 1870s to 1880s, the kanji was used to signify sex and this new usage became more popular in the 1920s, displacing older words such as iro (the Japanese equivalent of the Chinese se). This corroborates Furukawa Makoto's finding that sei (as sex) became a fashionable word in the 1920s.50 From the chronology of the dictionaries investigated, combined with Zhou Zuoren's remark, we could venture the hypothesis that the Japanese used the kanji called xing in Chinese to translate 'sex' and 'sexuality' before the Chinese. To explain what is going on here, it is crucial to understand the structure of the Japanese language and its development.51\n\nThere are three systems of writings in Japanese: the syllabaries katakana and hiragana, and the ideogram system kanji ('Han characters'). The characters were appropriated by the Japanese around the fifth to sixth centuries from Buddhist scriptures and Chinese philosophical texts. By the seventh century, the Chinese characters mutated into two separate species in Japan: jun kanbun ('genuine writing') and hentai kanbun ('deformed writing'). Texts were written with various marks to inform the reader as to the particular arrangement of the kanji in each phrase so that a Japanese reading could be possible. The ability to do Japanese readings of Chinese characters was in turn the result of two methods of adaptation \u2013 the first was to use the Chinese characters semantically, and then give them Japanese sounds (kun reading). The second was to do the opposite: employ characters as phonemes and put together new words in Japanese with little regard for the original meaning of the Chinese symbols (on). The Japanese literati were very fond of bringing back neologisms in Chinese back to their home country, and invented idiosyncratic uses of ideograms which often bore no relationship to the characters' meanings in Chinese. Each Chinese character thus acquired a whole range of pronunciations, some of which were invented by the Japanese and some possibly Chinese pronunciations which fell out of use in China but survived in Japan.\n\nIn Japan, Chinese was the language of the elite. The literati would compose essays and poems in Chinese. Officials used it in government documents and the religious hierarchy to maintain manuscripts. By the ninth century, the clerics developed a separate system of diacritical marks placed alongside Chinese characters to clarify the way texts were supposed to be read. The marks were simplified forms or fragments of Chinese characters, and these were called kana. By the eleventh century, they were developed into two systems of writing Japanese sounds: katakana and hiragana. By the thirteenth century, hiragana became the syllabary used with kanji to form the backbone of the writing system. The katakana, meanwhile, acquired its principal use \u2013 the phonetic rendering of new foreign words, particularly heightened as a result of colonial encounters. As a result, modern Japanese writing is a melting pot of Chinese characters, hiragana and katakana: layer upon layer, permutations and combinations of sounds, images, semantics and annotations.\n\nWhat is supremely important to us is the process of neologistic construction in Japanese and Chinese. According to Lydia Liu, the influx of calques and other loanwords into Chinese in the late nineteenth to early twentieth century followed a typical pattern: 'the Japanese used kanji (Chinese characters) to translate European terms, and the neologisms were then imported back into the Chinese language'. These borrowings fall under three headings: (1) two character compounds made up of Chinese characters that are found only in pre-modern Japanese and do not appear in Classical Chinese; (2) Classical Chinese expressions used by the Japanese to translate western terms that were then imported back into Chinese with a radical change in meaning, such as geming [revolution; in Japanese kakumei], wenhua [culture; bunka], jingji [economy; keizai], kexue [science; kagaku]; (3) modern Japanese compounds that have no equivalent in Classical Chinese, such as zhongzu [race; in Japanese shuzoku], meishu [art; bijutsu], meixue [aesthetics; bigaku], guoji [international; kokusai]. The second of these types of borrowings is called return graphic loans. To clarify, the modern meaning of the Chinese compound wenhua, 'culture', is derived from the Japanese compound, written in exactly the same way but pronounced bunka, and it is through the process of borrowing from the Japanese that an equivalence was established between wenxue and 'culture'. In Classical Chinese, wenhua denoted 'the state of refinement or artistic cultivation as opposed to military prowess, carrying none of the ethnographical connotations of \"culture\" in today's usage'. Kexue, on the other hand, meant 'studies for the civil examinations' in Classical Chinese, but after the Japanese appropriation (kagaku), kexue became 'science' in twentieth-century China.52\n\nThe motivations for the Japanese in using Chinese characters are multiple. Yanabu Akira explains that, in large part, it is due to what he calls the cassette effect. A cassette here is a casket for jewels, letters or other precious items, itself made with a valuable material and richly ornamented. Chinese characters were held by the Japanese as valuable repositories and carriers of meaning. Moreover, these 'cassettes' drew a reader's attention to the newness and alien nature of the foreign, imported bits of knowledge. It was an act of linguistic engineering. Particularly for Meiji intellectuals who argued that the modernisation of the nation required the appropriation of modern thought, the acknowledgement of the power of language meant that such modern thought had to be expressed with new words, and the older terms had to be superseded. In China this was also the case, as Edward Gunn demonstrated in his work on the 'rewriting' of Chinese in the 1920s.53 For Yanabu, the cassette effect leads to the blind acceptance of loanwords and neologisms without interrogation of what they 'really' mean \u2013 the splendour, glamour, elegance of the cassettes dazzled and charmed readers into ignoring their contents. In that sense, a cassette becomes more akin to a Trojan horse, facilitating the 'smuggling' of ideas. As the new words become adopted and reiterated, readers 'feel' as though they know what they are talking about, or begin to be only capable of thinking about a certain problem through these terms, and are thus constrained by a linguistic straitjacket, become 'spoken' by a discourse.54 Yanabu's cassettes include 'society' (in Chinese shehui; in Japanese shokai), 'individual' (geren; kojin), 'love' (lian'ai; ren'ai), 'being' (cunzai; sonzai), 'nature' (ziran; shiran), 'liberty' (ziyou; jiyuu) and 'right' (quanli; kenri). One should note that all of Yanabu's cassettes also ended up as return graphic loans, reintroduced into China around the early twentieth century through Chinese translations of Japanese translations of European and American texts.55 These new words were mobilised by May Fourth New Culture intellectuals, circulated in what I call the 'marketplace of ideas' in 1920s China, institutionalised in dictionaries, glossaries and encyclopaedias, and entered public discourse.\n\nXing is precisely one of these 'return graphic loans'. Though it is difficult to pinpoint exactly who first used sei to mean sex (probably as a transliteration), Oda Makoto credits Mori Ogai (1862\u20131922) for popularising its use in Japan.56 Mori, a Japanese physician and novelist who studied public health in Germany, was one of the most important Meiji writers on sex and hygiene. Around 1902\u201303, Mori published a series of articles in Public Health (Koushuu iji) which discussed sex drive, menstruation, contraception, spermatorrhea and hygienics. Mori uses sei and its compounds throughout; his argument is that the sex drive is fundamentally a fact of human nature, and its suppression can lead to grave nervous illnesses. In 1909, Mori published Vita Sexualis (Wita sekusuarisu), a frank semi-autobiographical book in which the narrator describes his psychosexual development. Vita Sexualis was a clear expression of Mori's view that the desire for sex cannot be suppressed or silenced, and the open discussion of sex is necessary for the sake of self-improvement and one's mental health.57 The return of sei back to China was the result of translations of Japanese sexological texts and textbooks by Chinese and Japanese intellectuals, for instance the work of Fukuzawa Yukichi and gynaecologist Habuto Eiji's (d. 1929) New Sex Education.58 What these works achieved was to put sei\/xing and the double meaning of xing (sex\/human nature) into circulation.\n\nConclusion\n\nWhen sex, through xing, became the centre of human life, this necessitated rational, systematic inquiry into its 'true' nature. The aim of a science in sex was not simply descriptive \u2013 the classification of behaviours \u2013 but always prescriptive and normative. For British sexologist and social reformer Havelock Ellis, widely admired by republican Chinese intellectuals, the point of collecting and displaying all kinds of sexual fauna was to foster tolerance and acceptance. Since what was observed in the world 'out there' in nature was necessarily 'natural', homosexuality for instance ought to be accommodated as part of the diversity of all human beings, ultimately as unremarkable as differences in height or weight.59 There were equally men of science who believed that there was one 'true' human nature and one 'true' kind of sexuality, and all other behaviours would be pathological, opposed to 'Nature's Way', and thus had to be eliminated.\n\nThe various paradoxes arising from the mobilisation of 'nature' for political ends and to legitimise moral outlooks through 'biologisation' or 'naturalisation' have been analysed by many.60 On the one hand, nature is about spontaneity, something that one has always already 'known', or just there to be found and appropriately named because it is 'universal', deeply ingrained, an inherent tendency or immutable drive. Something appears to be 'natural' if one is compelled to do it or helpless against it; a person is absolved of moral responsibilities for acting in a certain way because there is never a conscious choice. On the other hand, the mass of sex manuals which provide detailed descriptions on how to behave 'naturally' or 'scientifically' can imply: what is 'natural' can after all be altered; or there is a possibility that human beings can act contrarily to nature; or that their drives may be corrupted, misaligned by 'culture' or 'society' and must be corrected, reformed, re-educated, rechanneled. The aim then is to redirect a person's energies to more useful ends, to restore the natural order of things, to eliminate any restraints which may hold back human beings from realising their true potential, from fulfilling their biological destiny, from playing their rightful roles. This position is absolutely crucial to the rhetoric of 1920s Chinese intellectuals and iconoclasts: the artificial pathological obstacle that had to be dismantled at all costs was 'Confucianism'. The symptoms of the 'Sick Man of Asia', twisted by 'Confucian ethics' included: treating sex as a taboo subject, not to be spoken about or only ever through euphemisms; wanton excesses in brothels and polygamous households; the mutilation of the female body through footbinding and chestbinding; the 'poor' quality of reproduction which led to a 'poor' quality of the population. A healthy, brand new sexual morality, erected on the modern edifice of western science, anchored in the direct, no-nonsense language of xing, would be the way to administer and manage people's lives, to rejuvenate a nation under siege. Effectively, xing became a new vessel, a placeholder given different shapes depending on the political project; it was up to intellectuals to fill the content of xing, writing sex\/human nature into being.\n\nThrough xing, some of the key developments in science and humanities in 1920s China make a good deal of sense. Why was there, for instance, an explosion of autobiographical writing, an effervescence of confessional novels written in the first person with frank, startling revelations of sexual lives? And why were there so many 'problem novels' (wenti xiaoshuo) which dealt with sex-related issues of the day such as premarital sex, pregnancy before marriage, same-sex desire? Why did intellectuals encourage the masses to keep diaries, to read up on questions like chastity and divorce, some even going as far as asking the general public to submit personal stories of sexual development and to compile case histories for all to scrutinise? Sex was 'implanted into bodies, slipped in beneath modes of conduct, made into a principle of classification and intelligibility, established as a raison d'\u00eatre and a natural order of disorder'.61 Sex became the locus of truth and a person's subjectivity, and so it would be an obligation upon all the Chinese people to speak out, to have one's voice registered in the world, to share one's painful sufferings: the public was invited not to feel ashamed or guilty, but to leave absolutely nothing unsaid \u2013 in short, it was an 'incitement to speak', an attempt to construct a 'machinery for producing true discourses about sex'.62 The foundation of human sciences in Chinese universities, the interest in anthropology, sociology and ethnography for the collection and comparison of everyone's daily lives and sexual customs, dovetails with the intellectuals' project of the 'Discovery of Man' (ren de faxian) and the liberation of his spirit. The 'facts of life' extracted from these inquiries were presumed to help the Chinese to work out rational strategies to transform the political economy of the body: they came up with something as grand as the compulsory sterilisation of the 'undesirables' or the control of reproduction of the 'invalids' in the Chinese population, or as seemingly trivial as washing one's genitals with soap and putting on clean underwear before going to bed. Contraceptive technologies, alongside the rules of dating and the virtues of French kissing, were vigorously debated in magazines such as Ladies' Journal (F\u00fcnu zazhi), New Women (Xin n\u00fcxing), New Family (Xin jiating), New Culture (Xin wenhua), Sex Magazine (Xing zazhi) and Sex Science (Xing kexue). Key foreign works on sex were translated: Key's Love and Marriage in 1923, Stopes's Married Love and Wise Parenthood in 1924, Carpenter's Love Coming-of-Age in 1922, parts of Ellis's Studies in the Psychology of Sex in 1927, and Freud around the mid-1920s. All of these phenomena were connected to the frantic drive to determine, to alter, to fix the content of xing, of sex and human nature.\n\nTo end, I would like to emphasise again the fruitfulness of studying cross-cultural exchange and the global circulation of the language and keywords of sex. Xing\/sei and sex\/human nature are not just a Sino\u2013Japanese phenomenon. We may equally want to ask how and when, for instance Russians, Turks, Filipinos, Indonesians came to adopt the term seks \u2013 a transliteration of sex \u2013 and expelled the older vocabulary? What sort of things did they do to\/with their words? In what ways were these stories connected to the global migration and mutation of sexual and biological knowledge \u2013 or biopower and governmentality \u2013 under the backdrop of imperialism and colonial modernity? Instead of focusing on how different parts of the sexual spectrum \u2013 heterosexuality, gay and lesbianism, transgender \u2013 manifest themselves in different parts of the world, as regional histories of sexuality have often tended to do, I propose that we may all start off with a much simpler question, 'What is the word for \"sex\" in this particular language, and why?'\n\nGlossary\n\n'1920 niandai de lian'ai yu xing xingdaode lunsu \u2013 cong Zhang Xichen canyu de sanchi lunzhan tanqi'\n\nNotes\n\nThe author is grateful to Susan Daruvala and John Forrester for their support, and to Eric Hayot and Haun Saussy for their time spent discussing the question of translation and linguistic innovation. Thanks also go to Sabine Fr\u00fchst\u00fcck, Peter Kornicki, Angus McLaren, Gregory Pflugfelder, Thekla Wiebusch, Theodore Jun Yoo and the participants of the Birkbeck Institute for Gender and Sexuality Seminar, University of London, for their advice, particularly on Japan. Finally, the author thanks the Wellcome Trust and the D. Kim Foundation for the History of Science and Technology in East Asia for their generous funding, and the original journal's anonymous reviewers for their invaluable comments.\n\nNote on romanisation and East Asian characters: The pinyin system of romanisation has been used throughout this chapter, except for: first, a few spellings best known outside China in another form, such as Chiang Kai-shek, Sun Yat-sen, Kuomintang, Peking University and Tsinghua University; second, names of Taiwanese persons which are often written with the Wade-Giles system. A glossary of Chinese and Japanese characters is supplied at the end of this chapter.\n\n1. Li Xiao-Jian, 'Xingbie or Gender', in Nadia Tazi (ed.), Keywords: Gender (New York: Other Press, 2004), pp. 87\u2013103, here p. 89. The correct romanisation of the author's name is Li Xiaojiang. However in Tazi's edited volume, Li's name is spelt idiosyncratically as Li Xiao-Jian.\n\n2. Michel Foucault, The History of Sexuality, vol. 1: Will to Knowledge, tr. Robert Hurley (1976; London: Penguin, 1978), p. 105.\n\n3. Raymond Williams, Keywords: A Vocabulary of Culture and Society (London: Croom Helm, 1976), p. 13.\n\n4. Tony Bennett, Lawrence Grossberg and Meaghan Morris (eds), New Keywords: A Revised Vocabulary of Culture and Society (Oxford: Blackwell, 2005).\n\n5. Ann Laura Stoler, Race and the Education of Desire: Foucault's History of Sexuality and the Colonial Order of Things (Durham: Duke University Press, 1995); Ann Laura Stoler, Carnal Knowledge and Imperial Power: Race and the Intimate in Colonial Rule (Berkeley: University of California Press, 2002).\n\n6. Leon Antonio Rocha, 'Sex, Eugenics, Aesthetics, Utopia in the Life and Work of Zhang Jingsheng (1888\u20131970)' (unpublished doctoral thesis, University of Cambridge, 2010).\n\n7. Dennis Altman, Global Sex (Berkeley: University of California Press, 2002).\n\n8. This is precisely Lisa Rofel's worry in her attack on Altman's 'emergence of a western-style politicised homosexuality in Asia', that is, the thesis that 'the ubiquity of western rhetoric means that many Asian gay men describe their realities and their own feelings through this rhetoric'. Rofel fears that this 'universalist' line of reasoning serves to negate differences and the erasure of Chinese voices of gay activism. See Lisa Rofel, Desiring China: Experiments in Neoliberalism, Sexuality and Public Culture (Durham: Duke University Press, 2007), pp. 88\u201391.\n\n9. A similar argument can be found in Howard H. Chiang, 'Rethinking \"Style\" for Historians and Philosophers of Science: Converging Lessons from Sexuality, Translation, and East Asian Studies', in Studies in History and Philosophy of Biological and Biomedical Sciences 40 (2009), pp. 109\u201318, esp. pp. 112\u201315.\n\n10. Lydia H. Liu, Translingual Practice: Literature, National Culture, and Translated Modernity \u2013 China, 1900\u20131937 (Stanford: Stanford University Press, 1995); Lydia H. Liu (ed.), Tokens of Exchange: The Problem of Translations in Global Circulations (Durham: Duke University Press, 1999); Haun Saussy, Great Walls of Discourse and Other Adventures in Cultural China (Cambridge: Harvard University Press, 2002).\n\n11. Frank Dik\u00f6tter, Sex, Culture and Modernity in China (London: Hurst, 1995), p. 68; Judith Farquhar, Appetites: Food and Sex in Post-Socialist China (Durham: Duke University Press, 2002), pp. 250\u201355; Zhong Xueping, Masculinity Besieged? Issues of Modernity and Male Subjectivity in Chinese Literature of the Late Twentieth Century (Durham: Duke University Press, 2000), p. 54; Deborah Tze-lan Sang, 'Translating Homosexuality: The Discourse of Tongxing'ai in Republican China (1912\u20131949)', in Liu (ed.), Tokens of Exchange, pp. 276\u2013304, here p. 299.\n\n12. Jiang Xiaoyuan, Yun yu: Xing zhangli xia de Zhongguo ren [Clouds and Rain: The Chinese People Under Sexual Tension] (Shanghai: Dongfang chuban zhongxin, 2005); Liu Dalin, Xing de lishi [The History of Sexuality] (Taipei: Commercial Press Taiwan, 2001); Ma Boying, Zhongguo yixue wenhuashi [A History of Medical Culture in China] (Shanghai: Shanghai renmin chubanshe, 1994); Ruan Fangfu, Sex in China: Studies in Sexology in Chinese Culture (New York: Plenum Press, 1991); Pan Suiming, Zhongguo xing xianzhuan [The Current State of Sex in China] (Beijing: Guangming ribao chubanshe, 1995); Li Yinhe, Fun\u00fc: Zui manchang de gemin [Women: The Longest Revolution] (Beijing: Zhongguo fun\u00fc chubanshe, 2007); Wang Yi-cha, Xing, wenming yu huangmiu [Sex, Civilisation and Absurdity] (Taipei: Ye'e chubanshe, 1994).\n\n13. See Tani E. Barlow, The Question of Women in Chinese Feminism (Durham: Duke University Press, 2003), esp. pp. 49\u201355; Tani E. Barlow, 'Theorising Woman: Funu, Guojia, Jiating', in Angela Zito and Tani E. Barlow (eds), Body, Subject, and Power in China (Chicago: University of Chicago Press, 1994), pp. 253\u201389.\n\n14. Deborah Tze-lan Sang, The Emerging Lesbian: Female Same-Sex Desire in Modern China (Chicago: University of Chicago Press, 2003), p. 103.\n\n15. The Doctrine of the Mean (Zhongyong) 1, in James Legge (tr. and ed.), The Chinese Classics, vol. 1 (London: Tr\u00fcbner & Co., 1861), p. 247; Xun Zi 23, 'Man's Nature is Evil' (Xing'e) 4, in John Knoblock (tr. and ed.), Xun Zi\u2014A Translation and Study of the Complete Works, vol. 3, (Stanford: Stanford University Press, 1990), p. 151.\n\n16. William Edward Soothill and Lewis Hodous, A Dictionary of Chinese Buddhist Terms, with Sanskrit and English Equivalents and a Sanskrit\u2013Pali Index (London: Kegan Paul, 1937), p. 258.\n\n17. The Chronicles of Zuo (Zuozhuan), 'Duke of Zhao Year XIX' (Zhao Gong shijiu nian) 1, in James Legge (tr. and ed.), The Chinese Classics, vol. 5 (London: Tr\u00fcbner & Co., 1872), p. 674; The Chronicles of Zuo (Zuozhuan), 'Duke of Zhao Year VIII' (Zhao Gong ba nian) 1, in Legge (tr. and ed.), The Chinese Classics, vol. 5, p. 620; Mencius (Mengzi), 'Gaozi II' 35, in James Legge (tr. and ed.), The Chinese Classics, with a Translation, Critical and Exegetical Notes, Prolegomena, and Copious Indexes, vol. 5 (London: Tr\u00fcbner & Co., 1861), p. 323.\n\n18. Liu, Translingual Practice, p. 348; Federico Masini, The Formation of Modern Chinese Lexicon and its Evolution Toward a National Language: The Period from 1840 to 1898, Journal of Chinese Linguistics monograph 6 (Berkeley: Project on Linguistic Analysis, 1992), p. 140 n. 30; Gao Mingkai and Liu Zhengtan, Xiandai hanyu wailai ci yanjiu [Studies of Loanwords in Modern Chinese] (Beijing: Wenzi gaige chubanshe, 1958).\n\n19. Farquhar, Appetites, p. 251.\n\n20. Tan Sitong, An Exposition of Benevolence: The Jen-hs\u00fceh of T'an Ssu-t'ung, tr. Chan Sin-wai (1897; Hong Kong: Hong Kong University Press, 1984), pp. 81\u20132. See also Luke S. K. Kwong, T'an Ssu-t'ung, 1865\u20131898: Life and Thought of a Reformer (Leiden: Brill, 1996), p. 158.\n\n21. See discussions in Lee Haiyan, Revolution of the Heart: A Genealogy of Love in China, 1900\u20131950 (Stanford: Stanford University Press, 2007), pp. 172\u20138; Hsu Hui-chi, '1920 niandai de lian'ai yu xing xingdaode lunsu \u2013 cong Zhang Xichen canyu de sanchi lunzhan tanqi' ['A Discussion of Love and the New Sexual Morality of the 1920s \u2013 via the three debates Zhang Xichen participated in'], in Jindai Zhongguo fun\u00fc shi yanjiu [Research on Women in Modern Chinese History] 16 (2008), pp. 29\u201392.\n\n22. Naifei Ding, Obscene Things: The Sexual Politics in Jin Ping Mei (Durham, NC: Duke University Press, 2002), p. 207.\n\n23. Wenqing Kang, Obsession: Male Same-Sex Relations in China, 1900\u20131950 (Hong Kong: Hong Kong University Press, 2009), pp. 19\u201340; Bret Hinsch, Passions of the Cut Sleeve: The Male Homosexual Tradition in China (Berkeley: University of California Press, 1990), pp. 34\u201354.\n\n24. Sang, Emerging Lesbian, pp. 17, 104, 119.\n\n25. Sang, Emerging Lesbian, pp. 102\u20136.\n\n26. Julie Coleman, Love, Sex and Marriage: A Historical Thesaurus (Amsterdam: Rodolpi, 1999).\n\n27. Foucault, History of Sexuality, vol. 1, p. 7.\n\n28. The 'ironhouse' metaphor comes from the Preface to Call to Arms (Nahan). Lu Xun, The Complete Stories of Lu Xun, Yang Xianyi and Gladys Yang (trs.) (Bloomington: Indiana University Press, 1981), p. ix. See also Leo Ou-fan Lee, Voices from the Iron House: A Study of Lu Xun (Bloomington: Indiana University Press, 1987).\n\n29. Foucault, History of Sexuality, vol. 1, p. 10; Hubert Dreyfus and Paul Rabinow, Michel Foucault: Beyond Structuralism and Hermeneutics (Chicago: University of Chicago Press, 1982), p. 126.\n\n30. I am referring to the growing\/glowing body of revisionist scholarship which challenges the historiography of repression. Zhang Yanwen, The Social Life of Opium in China (Cambridge: Cambridge University Press, 2005); Gail Hershatter, Dangerous Pleasures: Prostitution and Modernity in Twentieth-Century Shanghai (Berkeley: University of California Press, 1997); Matthew Sommer, Sex, Law, and Society in Late Imperial China (Stanford: Stanford University Press, 2000); Dorothy Ko, JaHyun Kim Haboush and Joan R. Piggott (eds), Women and Confucian Cultures in Pre-Modern China, Korea and Japan (Berkeley: University of California Press, 2003); Li Chenyang (ed.), The Sage and the Second Sex: Confucianism, Ethics, and Gender (Chicago: Open Court, 2000); Charlotte Furth, A Flourishing Yin: Gender in China's Medical History (Berkeley: University of California Press, 1999); Dorothy Ko, Cinderella's Sisters: A Revisionist History of Footbinding (Berkeley: University of California Press, 2005).\n\n31. Foucault, History of Sexuality, vol. 1, p. 10.\n\n32. Jai Ben-ray, 'Zhongguoren xing guan chutan' ['A Preliminary Investigation of the Chinese View on Sex'], in Si yu yan [Thought and Language] 33 (1995), pp. 27\u201375.\n\n33. Charlotte Furth, 'Rethinking van Gulik: Sexuality and Reproduction in Traditional Chinese Medicine', in Christina K. Gilmartin, Gail Hershatter, Lisa Rofel and Tyrene White (eds), Engendering China: Women, Culture, and the State (Cambridge: Harvard University Press, 1995), pp. 125\u201346, here p. 130.\n\n34. A very truncated and mistranslated version of this passage appeared in Furth, 'Rethinking van Gulik', p. 130.\n\n35. Nann\u00fc jiaohe xinlun [New Theories on Sexual Intercourse] is probably Sexual Science (1870) by phrenologist Orson Squire Fowler (1809\u20131887), translated by 'Youyazi'\/Yuashi into Chinese from a Japanese translation.\n\n36. Here I used the classic Li Yu-ning and Chang Y\u00fc-fa (eds), Jindai Zhongguo N\u00fcquan Yundong Shiliao 1842\u20131911 [Historical Materials on the Women's Movement in Modern China 1842\u20131911], 2 vols (Taipei: Juanji wenxue she, 1972).\n\n37. On Fukuzawa, see Carmen Blacker, Japanese Enlightenment: A Study of the Writings of Fukuzawa Yukichi (Cambridge: Cambridge University Press, 1964); Alan Macfarlane, The Making of the Modern World: Visions from the West and the East (London: Palgrave, 2002), pp. 139\u2013248.\n\n38. Fukuzawa Yukichi, Danjo k sai ron (translated into Chinese as Nann\u00fc jiaoji lun) [On the Interactions between Men and Women], in Liang Qichao (ed.), Qingyibao quanbian [Complete Edition of the Journal of Disinterested Criticism] vol. 5, juan 20 (1886 [1900]; Taipei: Wen Hai Press, 1987), pp. 20\u201327 [pp. 542\u20139].\n\n39. Du Yaquan, 'Lun xuqie' ['On Keeping Concubines'], in Dongfang zazhi [Eastern Miscellany] 8 (1911), pp. 16\u201320.\n\n40. Gu Shaoyi, 'Xiujue yu xingyu de guanxi' ['The Relationship between the Olfactory Sense and Sexual Desire'], Dongfang zazhi [Eastern Miscellany] 15 (1918), pp. 33\u20137.\n\n41. Beijing tushuguan [Beijing Library] (ed.), Minguo shiqi zong shumu [Comprehensive Catalogue of Republican Period Books], 20 vols (Beijing: Shumu wenxian, 1991\u201397), esp. 1995 volumes Ziran kexue: yiyao weisheng [Natural Sciences: Medicine and Hygiene] and Shehui kexue: zonglei bufan [Social Sciences: General Section].\n\n42. Zhang Jingsheng, Xingshi [Sex Histories] (1926; Taipei: Dala, 2005), pp. 24\u20137.\n\n43. Chen Dongyuan, Zhongguo fun\u00fc shenghuo shi [History of Women's Lives in China] (Shanghai: Commercial Press, 1926), p. 408.\n\n44. Zhang Dongmin, Xing de congbai [The Worship of Sex] (Shanghai: Beixin shuju, 1927), p. 5.\n\n45. Zhou Zuoren, 'Tan xing de congbai' ['On The Worship of Sex'], in Zhou Zuoren shuhua [Zhou Zuoren on Books], Zhou Zuoren quanji [The Complete Works of Zhou Zuoren], vol. 1 (1927; Taipei: Landeng wenhua chuban, 1993), pp. 103\u20135.\n\n46. Sang, Emerging Lesbian, p. 299.\n\n47. Sabine Fr\u00fchst\u00fcck, Colonising Sex: Sexology and Social Control in Modern Japan (Berkeley: University of California Press, 2003), pp. 83\u2013115; Oda Makoto, Ichigo no jiten: sei [Dictionary of One Word: Sex] (Tokyo: Sanseido, 1996), pp. 54\u201367.\n\n48. Sang, Emerging Lesbian, p. 299; Zhang Minyun, Xing kexue [Sexual Science] (Shanghai: Shanghai wenyi chubanshe, 1988), pp. 50\u201351.\n\n49. Ochiai Naobumi and Haga Yaichi, Fountain of Words: Comprehensive Japanese Dictionary (Gensen nihon dai jiten) (Tokyo: Nihon Tosho Senta, 1927), p. 2295.\n\n50. Furukawa Makoto, 'Ren'ai to seiyoku no daisan teikoku' ['The Third Empire of Love and Sex'], Gendai shiso [Modern Thought] 21 (1993), pp. 110\u201345; Saito Hikaru, 'Niju nendai Nihon yuseigaku no ikkyokumen' ['One Side of Japan's Eugenics during the 1920s'], in Gendai shiso [Modern Thought] 21 (1993), pp. 128\u201358.\n\n51. I rely on Scott L. Montgomery, Science in Translation: Movements of Knowledge through Centuries and Time (Chicago: University of Chicago Press, 2000), pp. 190\u201399.\n\n52. Liu, Translingual Practice, pp. 32\u20134. Liu points out that the etymological routes of these loans may be even more complicated, involving early\/mid-nineteenth-century Protestant missionaries and their Chinese assistants. These might have had limited impact in China at the start, but their Japanese adoption then catalysed its spread in China in the late nineteenth and early twentieth centuries. Liu calls this, 'round-trip dissemination of autochthonous neologisms'.\n\n53. Edward Gunn, Rewriting Chinese: Style and Innovation in Twentieth-Century Chinese Prose (Stanford: Stanford University Press, 1991).\n\n54. Yanabu Akira, Honyakugo seiritsu jijo [The History of Translating Words in Modern Japan] (Tokyo: Nihon Honyakuka Yosei Centre, 1982); Yanabu Akira, Modelnizierung der Sprache, tr. Florian Coulmas (Munich, Iudicium, 1991); Yanabu Akira, Kindai nihongo no shiso: honyaku buntai seiritsu jijo [Thoughts on Modern Japanese: Circumstances around the Establishment of Translation Styles] (Tokyo: Hosei Daigaku Shuppankyoku, 2004).\n\n55. Liu, Translingual Practice, pp. 302\u201342.\n\n56. Oda, Ichigo no jiten [Dictionary of One Word], pp. 39\u201340.\n\n57. Fr\u00fchst\u00fcck, Colonising Sex, p. 78.\n\n58. Wang Xuefeng, Jiaoyu zhuanxin zhi jin: ershi shiji shangbenye zhongguo de xing jiaoyu shixiang yu shijian [Mirror of the Education Paradigm Shift: Theories and Practices of Sex Education in China in Early Twentieth Century] (Beijing: Social Sciences Academic Press China, 2006), p. 81; Fr\u00fchst\u00fcck, Colonising Sex, p. 106.\n\n59. Paul Robinson, The Modernisation of Sex: Havelock Ellis, Alfred Kinsey, William Masters and Virginia Johnson (Ithaca: Cornell University Press, 1989), p. 24.\n\n60. Williams, Keywords, p. 219; Lorraine Daston and Fernando Vidal, 'Doing What Comes Naturally', in Lorraine Daston and Fernando Vidal (eds), The Moral Authority of Nature (Chicago: University of Chicago Press, 2004), pp. 1\u201320. See also Fa-ti Fan, 'Nature and Nation in Chinese Political Thought: The National Essence Circle in Early Twentieth Century China', in Daston and Vidal (eds), Moral Authority of Nature, pp. 409\u201337; Jeffrey Weeks, Sexuality and its Discontents: Meanings, Myths, and Modern Sexualities (London: Routledge, 1985), pp. 61\u201395; Leonore Tiefer, Sex Is Not a Natural Act and Other Essays (Boulder: Westview Press, 1995), pp. 31\u201340; Londa Schiebinger, Nature's Body: Gender in the Making of Modern Science (1993; New Brunswick: Rutgers University Press, 2004).\n\n61. Foucault, History of Sexuality, vol. 1, p. 44.\n\n62. Foucault, History of Sexuality, vol. 1, p. 69.\nChapter 5\n\nEpistemic Modernity and the Emergence of Homosexuality in China\n\nHoward Chiang\n\nIn 1950, the Time Bookstore in Shanghai published a book titled Sexual Science by Zhang Minyun.1 In nine chapters, the book summarises contemporary scientific research on animal and human sexuality, including perspectives from psychology, biomedicine, ethnology and sociology. Although the book provides no biographical information about the author, Zhang's familiarity with the history of sexual sciences outside China is demonstrated by his eloquent discussion of their developments in Japan, the part of Asia where the writings of European sexologists had made the deepest impression since the late nineteenth century.2 Zhang clarifies his authorial intention in the opening chapter: 'Especially in the east (such as in China and Japan), people have yet to fully appreciate sexual science. So the author has decided to compose this book: providing Chinese people with a reliable understanding of sexology is precisely the intent of the author'.3 According to Zhang, because the scientific study of sex was so underdeveloped in China, it was high time for the introduction of sexology to Chinese experts and laypersons.\n\nZhang's assertion, nonetheless, overlooked an entire generation of thinkers and cultural commentators who promoted sexological studies in the aftermath of the New Culture movement (1915\u201319). Among the famous May Fourth iconoclastic intellectuals, some not only translated texts and adopted methodological rigour from European sexology, but they also developed their own theories of human sexual behaviour and desire. They frequently engaged in heated debates over the meaning, principles and boundaries of a science of sexuality. Questions of competence, credentials, expertise and authority preoccupied those of the early twentieth-century urban intelligentsia who spoke seriously about sex in public. By the 1930s, disparate efforts and conversations converged in the founding of such periodicals as Sex Science. For the first time in China, sexuality was accorded a primacy of scientific 'truthfulness'.4\n\nThis chapter focuses on the intellectual journey of two pivotal figures in this rich tradition of Republican Chinese sexology: Zhang Jingsheng   and Pan Guangdan  . Historians have regarded Zhang's commentary on proper heterosexual conduct as a key feature of his sexological enterprise, especially as it was stamped by his controversial theory of the 'third kind of water'.5 Meanwhile, studies of Pan's contribution to Chinese sexology have typically focused on his annotated translation of Havelock Ellis's Psychology of Sex, which grew out of his lifelong interest in promoting eugenics in China.6 Less well studied, however, is their discussion of same-sex desire.7 From the early 1920s, Zhang and Pan also debated vociferously about each other's legitimacy as a scientist of sex. Frequently joined by an extended cast of sex educators, such debates reflected the complexity of their sexological manoeuvres. Moving away from the heteronormative and eugenic emphases of their work, I will draw from these examples a snapshot of the broader epistemic context in which the concept of homosexuality emerged as a meaningful point of referencing human difference and cultural identity in twentieth-century China.\n\nThe emphasis on homosexuality and the relevant stakes of scientific disciplinarity revises the limited scholarly literature on the history of Republican Chinese sexology. In his earlier study of the medico-scientific constructions of sex, Frank Dik\u00f6tter argues that early twentieth-century Chinese modernising elites did not fully grasp or reproduce European concepts of sexual 'perversions', including homosexuality.8 More recently, in response to Dik\u00f6tter, other scholars such as Tze-lan D. Sang and Wenqing Kang have exposed the ways in which selected May Fourth intellectuals \u2013 through various ideological debates \u2013 actually contributed to the increasing awareness of foreign categorisations of human sexuality in Chinese mass culture.9\n\nNonetheless, taken together these studies tend to depict Republican Chinese sexology as a unified field that treated homosexuality merely as a social, rather than a personal, problem.10 According to Kang, for example,\n\nWhereas in the West, sexological knowledge pathologized homosexuality as socially deviant, thus reducing it to an individual psychological problem, in China sexology as a form of modern knowledge was used more to diagnose social and national problems... As Chinese writers and thinkers introduced Western sexology to China, male same-sex relations were stigmatized more as a disruptive social deviance than a personal medical condition.11\n\nSang's analysis, too, seems to support the claim that no effect similar to the European 'individualisation' of homosexuality took place in Republican China. In the context of the May Fourth era, Sang observes, 'tongxing ai [same-sex love] is primarily signified as a modality of love or an intersubjective rapport rather than as a category of personhood, that is, an identity'.12\n\nIn this chapter, I suggest that this interpretation is an oversimplification. The view that homosexuality was only a social problem was not consistently shared by such pivotal sexologists as Zhang Jingsheng and Pan Guangdan. In the process of establishing sex as an appropriate object of scientific inquiry, they held different opinions on the etiology, prevention and significance of same-sex love. They even disagreed on the fundamental principles of sexological research. Given the multiple perspectives competing at the time, it is perhaps more compelling to suggest that homosexuality appeared to Chinese experts and popular audiences as much a personal problem as it was a social one \u2013 an explicit issue of personhood, subjectivity and identity. Open communications between 'sexperts', their readers and other 'sexperts' further enriched this incitement of a discourse that found truth in sex. Sexology in Republican China was indeed a new system of knowledge in which, literally, new subjects were made.\n\nUltimately, participants of this new discourse established for China what Michel Foucault has called scientia sexualis, which first distinguished itself in nineteenth-century Europe: a new regime of truth that relocated the discursive technology of the sexual self from the theological sphere of pastoral confession to the secular discourse of science and medicine.13 Contrary to previous studies, I argue that from the 1920s to the 1940s, the conceptual space for articulating a western-derived homosexual identity emerged in China precisely from the new regime of truth circumscribed by the arrival of European sexology. Moreover, whereas Dennis Altman, Lisa Rofel and Judith Farquhar have respectively claimed that 'gay identity' and scientia sexualis first appeared on the China scene only during the post-socialist era, my historicisation suggests that both have deeper roots that can be traced to an earlier epistemic turning point \u2013 in the Republican period.14\n\nPart of my disagreement with previous studies stems from the absence of a theoretical vocabulary that fully registers the complexity of sexological claims in this period. Chinese sexologists' conviction that western science held the key to effective modernisation suggests that claims about tradition and modernity were embedded within claims of sexual knowledge. Though distinct, these two layers of the production of sexual truth are somewhat confounded in the analyses of Dik\u00f6tter, Sang and Kang: for them, sexological research into homosexuality in the Republican period itself marked a condition of modernisation, rather than a condition that permits further referential points of argumentation about the authenticity, traditionality and modernity of Chinese culture. This conflation rests on the assumption that broader trajectories of historical change \u2013 such as modernisation and nationalisation \u2013 are more immediately relevant to the formation of a discourse of sexology in Republican China. But what if the stakes of the formation of such a discourse depended as much on these broader processes of historical change as on its internal disciplinary tensions and epistemic frictions? As generations of science studies scholars have shown, such dissonances are crucial to the consolidation of any kind of scientific valuation.15\n\nIn order to differentiate the two levels of truth production on which sexological claims operated, this chapter proposes and develops the analytic idea of 'epistemic modernity'. My application of 'epistemic modernity' in this chapter refers to an apparatus in the Foucauldian sense that characterises a historical moment during which a new science of sexuality gained epistemological grounding in Chinese culture. In the next section, I make even more explicit the historiographical rationale for implementing this theoretical neologism, including an operational definition appropriate for the purpose of this study. The main body of this chapter consists of three interrelated sections, each of which features an aspect of epistemic modernity. Together, they help reveal a macro, multidimensional picture of East Asian scientia sexualis: the creation of a public of truth, in which the authority of truth could be contested, translated across culture and reinforced through new organisational efforts, constitutes the social\u2013epistemic foundation for the establishment of sexology in Republican China. I conclude by coming back to the central issue of how homosexuality emerged as a meaningful category of experience in this context. Its comprehensibility, I argue, depends on a new nationalistic style of argumentation that arose from the interplay between the introduction of a foreign sexological concept and the displacement of an indigenous paradigm of same-sex desire.\n\nHistoriographical rationale\n\nThe rich history of male homoeroticism in traditional China has been a topic of in-depth scholarly discussion.16 This history, however, is not static but dynamic: over the years, the social significance of same-sex relations in pre-modern China evolved according to the relevant historical factors. As Matthew Sommer's work on Chinese legal history has shown, sodomy appeared in formal legislation in China only in the late imperial period. During the eighteenth-century Yongzheng reign (1723\u201335), male same-sex practice was for the first time directly 'assimilated' to heterosexual practice under the rubric of 'illicit sex'. This Qing innovation, according to Sommer, fundamentally reoriented the organising principle for the regulation of sexuality in China: a universal order of 'appropriate' gender roles and attributes was granted some foundational value over the previous status-oriented paradigm, in which different status groups were expected to hold unique standards of familial and sexual morality.17 But whether someone who engaged in same-sex behaviour was criminalised due to his disruption of a social order organised around status or gender performance, the world of imperial China never viewed the experience of homosexuality as a separate problem. The question was never homosexuality per se, but whether one's sexual behaviour would potentially reverse the dominant script of social order. If we want to isolate the problem of homosexuality in China, we must jump to the first half of the twentieth century to find it.\n\nThe relationship between forms of experience and systems of knowledge thus occupies a central role in this historical problem, if not only because what we have come to call 'sexuality' is a relatively recent product of a system of medico-scientific knowledge that has its own unique style of reasoning and argumentation.18 In the European context, Arnold Davidson has identified the emergence of sexuality from the new conceptual space conditioned by the nineteenth-century shift from an anatomical to a psychiatric style of medical reasoning. 'Before the second half of the nineteenth century', according to Davidson, 'anatomical sex exhausted one's sexual identity', because 'the anatomical style of reasoning took sex as its object of investigation and concerned itself with diseases of structural abnormality'. Hence, 'as little as 150 years ago, psychiatric theories of sexual identity disorders were not false, but rather were not even possible candidates of truth-or-falsehood. Only with the birth of a psychiatric style of reasoning were there categories of evidence, verification, explanation and so on, that allowed such theories to be true-or-false'.19 'Indeed', Davidson claims, 'sexuality itself is a product of the psychiatric style of reasoning'.20 The historical specificity and uniqueness of sexual concepts cannot be overstated, especially since our modern formulation of homosexuality, as the classicist David Halperin reminds us, does not anchor on a notion of object\u2013choice, orientation, or behaviour alone, but 'seems to depend on the unstable conjunction of all three'.21\n\nIf understanding the historical relationship between sexuality and knowledge claims in the western context involves such careful historicism, the situation in East Asia requires at least one additional layer of consideration. Since the mid-nineteenth century, the social situation of China was characterised by an increasingly conspicuous struggle to reconcile the existing canon of traditional Chinese medicine with foreign western biomedical knowledge. This preoccupation with bringing together two coexisting but often competing systems of medical epistemology was overwhelmingly articulated within a larger socio-political project conceived in terms of nationalism. Ideas and practices of nation-making would come to acquire the centre stage in Chinese political and cultural discourses, especially following the First Sino-Japanese War (1894\u201395).22\n\nTherefore, it is important to acknowledge that, unlike its western counterpart, the Chinese context of sexual knowledge does not represent a somewhat epistemologically sealed situation in which a previous anatomical style of reasoning actually existed, against which the nineteenth-century psychiatric style of reasoning could be so neatly juxtaposed. To ask the very least, why did modernising thinkers like Zhang Jingsheng, Pan Guangdan and others use western sexological ideas rather than traditional Chinese medical theory as a way to pathologise same-sex desire? What are the broader historical implications? The relationship between systems of knowledge and notions of modernity in East Asia requires problematisation as we historicise the concept of homosexuality itself. In order to carefully account for the historical condition under which homosexuality became a meaningful category in China, we need to complicate the epistemological and historiographical issues that we wish to address concerning the relation between sexuality and science in Chinese history.\n\nTo that end, I find what I call 'epistemic modernity', which builds on Prasenjit Duara's notion of 'the East Asian modern', particularly useful. When proposing the idea of 'the East Asian modern' in his groundbreaking study of Manchukuo, Duara aims to address two concomitant registers of historical production: how 'the past is repeatedly re-signified and mobilised to serve future projects' and the transnationality of 'the circulation of practices and signifiers evoking historical authenticity in the region'. The concept allows Duara to treat 'the modern' as a 'hegemonic' project, 'a set of temporal practices and discourses that is imposed or instituted by modernizers... rather than a preconstituted period or a given condition'.23 The emergence of homosexuality in early twentieth-century China reflects a parallel moment of contingent historicity.\n\nIn trying to highlight similar aspects of the transnational processes, flows and interactions of regimes of cultural temporality and specificity in East Asia, my notion of 'epistemic modernity' refers to the discursive apparatus that governs the implicit status of knowledge or truth claims about traditionality, authenticity and modernity: it essentially defines the index of imbrication in people's simultaneous preoccupation with the epistemology of scientific valuation and the determination of what counts as traditional, authentic or modern. The analytic rubric enables a perspective on the historical question of, to cite Tani Barlow from a different context, 'how our mutual present came to take its apparent shape' in 'a complex field of relationships or threads of material that connect multiply in space-time and can be surveyed from specific sites'.24 As such, epistemic modernity does not merely denote a system of knowledge; rather, it is a set of ongoing practices and discourses that mediates the relationship between systems of knowledge (for example, Chinese or western medicine) and modalities of power (for example, biopower) in yielding specific forms of experience (for example, sexuality) or shaping new categories of subjectivity (for example, homosexual identity).\n\nBy treating traditionality and authenticity as not ontologically given but constructed as such through the ongoing modernising technologies of nationalistic processes, I thus follow Duara's attempt to offer sharper insights concerning the regional mediation of globally circulating discourses, categories and practices in twentieth-century East Asia. The history of homosexuality in China, based on this model, is a history of how globally circulating categories, discourses and practices were mediated within that particular geobody we call 'China'. A major aim of this chapter is to show that, in the context of early twentieth-century China, homosexuality was precisely one of these categories; sexology exemplifies this kind of discourse; and the articulation of a western psychiatric style of reasoning about sexuality represents one of these practices. A relevant case in point is Ruth Rogaski's study of 'hygienic modernity', for one can understand the hygiene\u2013public health nexus as an exemplary model of how globally circulating discourses (of hygiene) and practices (as defined by public health campaigns) were mediated by the discursive apparatus of epistemic modernity in the historical transition from late imperial to national Republican China.25\n\nWhether our analytic prism is sexuality or hygiene, epistemic modernity presents an opportunity to take the growing global hegemony of western conceptions of health and diseases seriously without necessitating a full-blown self- or re-orientalisation, by which I mean an intentional project that continually defers an 'alternative modernity' and essentialises non-westernness (including Chineseness) by assuming the genealogical status of that derivative copy of an 'original' western modernity is somehow always already hermeneutically sealed from the historical apparatus of westernisation.26 Now that studies in the history of sexuality in non-western regions have begun to mature,27 historians should be even more cautious of any effort to view the broader historical processes of epistemic homogenisation as being less significant than forms of local (or 'oriental') resistance.28\n\nWhat I am concerned with, then, is not a social history of homosexuals in China 'from below', but an 'epistemological history' in the Foucauldian sense that 'is situated at the threshold of scientificity'. In other words, this is a study of 'how a concept [like homosexuality] \u2013 still overlaid with metaphors or imaginary contents \u2013 was purified, and accorded the status and function of a scientific concept. To discover how a region of experience [such as same-sex intimacy] that has already been mapped, already partially articulated, but is still overlaid with immediate practical uses or values related to those uses, was constituted as a scientific domain'.29 The rest of this chapter is devoted to examining closely the historical condition whereby the concept of same-sex desire came to fall within the realm of Chinese scientific thinking. Each of the following sections features an aspect of the cultural apparatus I call 'epistemic modernity': a public of truth, a contested terrain of authority and an intellectual landscape of disciplinarity. Each helps distinguish the two levels of truth production on which sexological claims operated: one concerning explicit claims about the object of scientific knowledge (for example, sexuality) and another concerning implicit claims about cultural indicators of traditionality, authenticity and modernity (for example, ways of narrating sexual truth). Operating together within the governing apparatus of epistemic modernity, they anchored the ways in which same-sex sexuality crossed the threshold of scientificity and reveal the very foundations upon which a scientia sexualis flourished in the cultural context of Republican China.\n\nMaking truth public\n\nNo other point of departure serves the purpose of our inquiry better than the sex education campaign that began to acquire some formality in the 1920s. In order to make sex a legitimate object of scientific inquiry and education, modernising elites of the time discussed human sexual behaviour and desire predominantly in the language of biology and psychology. In doing so, they taught people how to think about sexuality in scientific terms. They typically received advanced academic degrees at European, American or Japanese institutions. Upon returning from abroad, many of them participated in the sex education movement, which benefited from the broader cultural environment of the May Fourth intellectuals, by looking up to the British sexologist Havelock Ellis as a role model. They especially praised Ellis's seven-volume encyclopedic Studies in the Psychology of Sex as the epitome of scientific research on human sexuality. One of these modernising thinkers who emulated Ellis's work was China's own 'Dr Sex', Zhang Jingsheng (1888\u20131970).\n\nA university professor and a sex educator, Zhang Jingsheng treated his own sexological treatise, Sex Histories (Xingshi), as a Chinese adaptation of Ellis's Studies.30 After earning his doctorate in philosophy from the University of Lyon, Zhang returned to China in 1920 and initially taught at the Jingshan Middle School in Guangdong. For being educated abroad, Zhang was very much part of the work\u2013study movement promoted in the 1910s. Based on the close ties he had established in France with anarchists of the Guomingdang party such as Wang Jingwei and Cai Yuanpei, Zhang participated in the founding of the Sino-French Education Association, branches of which, by 1919, could be found in Shanghai, Guangzhou, Chengdu, Hunan, Shandong and Fujian.31\n\nZhang's participation in the association and the early work\u2013study movement significantly shaped his intellectual outlook. When he was forced to resign from his post at the Jingshan Middle School in 1921, Cai Yuanpei offered him a teaching position at Peking University, the epicentre of the May Fourth movement. Throughout the second half of the 1910s, the Sino-French Education Association actively promoted the view that overseas study in France offered a rare opportunity for Chinese people to learn European science and humanist thinking without relying entirely on Japan. Adopting this vision, Zhang saw in Cai's offer to teach at Peking (at the peak of the May Fourth era) a unique opportunity to enlighten the Chinese public. His first two books, A Way of Life Based on Beauty (1924) and Organizational Principles of a Society Based on Beauty (1925), expressed his conviction that the Chinese nation should be strengthened by learning from Europe, the United States and Japan, especially on the topics of economic structure and military organisation. Championing positive eugenics, Zhang even encouraged interracial marriage (and breeding) between Chinese people and those races that possessed strength where the Chinese race was weak, including the Europeans, Americans, Russians and even the Japanese.32\n\nFollowing these two well-received books, Zhang's publication of Sex Histories in 1926 earned him the popular title 'Dr Sex'. Sex Histories consists of seven life histories written in the form of first-person narrative by those who responded to Zhang's 'call for stories', which was originally published in the supplemental section of the newspaper Jingbao in early 1926. This 'call for stories' asked young people to contribute stories and any other relevant information about their sex lives.33 It also indicated that these stories would be 'psychoanalysed' and would help serve the purpose of 'hygienic' intervention.34 Zhang studied these life histories carefully and provided commentaries at the end of each story he included in Sex Histories. Therefore, Zhang's book adopted a case-study format similar to the way western sexologists typically organised and presented their research finding.\n\nIndeed, when Zhang published Sex Histories, he demanded that the book should be treated as 'a piece of science, because it documents facts'.35 For Zhang, there was nothing obscene or inappropriate about his compilation of people's sexual thought and behaviour. 'To keep a strict record of how things happened in the way they did is the type of mindset that any scientist should have', Zhang insisted.36 He ended the book with a reprint of the 'call for stories' entry, which also solicited collaborators for a project that he had envisaged on translating the Studies by Havelock Ellis.37 In sum, Zhang felt rather strongly that what he was doing in China resembled what the European sexologists were doing on the other side of the world.38\n\nZhang's appropriation of the methodological empiricism of western sexology \u2013 as exemplified by his case studies and effort to 'document facts' \u2013 illustrates a straightforward example of epistemic modernity: implicit in his self-proclaimed expertise on human sexuality lies a claim of another sort concerning referential points of tradition and modernity in Chinese culture. In Zhang's sexological project, knowledge about sexuality involves a modern phenomenon of narrating one's life history in a truthful manner. Whereas literature (fiction, poetry and so on) had been the traditional vehicle for the cultural expression of love and intimacy (including homoeroticism) in late imperial China, according to Zhang's sexology, this mode of representation was no longer appropriate in the twentieth century. His empirical methodology posited a new way of confessing one's erotic experience in the name of science, the domain of modernity in which the truthfulness of sexual desires was to be archived, investigated and explained.\n\nBy encouraging people to talk about their sexual experience, Zhang hoped to achieve more. As the 'call for stories' makes clear, narrators who were brave enough to speak up and report their sex life were rewarded with the unparalleled opinion of a 'sexpert' who, according to the entry, possessed the kind of enlightening scientific knowledge about sexuality from which laypersons could learn and benefit. So drawing on his academic training in philosophy and the empirical approach he had adopted from European sexologists, Zhang framed the modernism of his sexual science with another epistemological tool: theoretical innovation. He did this by developing a coherent set of guiding principles in human sexual conduct based on concepts from the western biosciences.\n\nHis theory of a 'third kind of water' is the most famous and controversial example. According to this theory, the female body produces three kinds of water inside the vagina: one by the labia, another by the clitoris and a third from the Bartholin glands. The release of all three kinds of water, especially the 'third kind', during sex would benefit the health and pleasure of both partners. Reflecting its eugenics underpinning, the theory claims that the release of this 'third kind of water' at the right moment, which normally means twenty to thirty minutes into sexual intercourse as both partners achieve simultaneous orgasm, is crucial to the conception of an intelligent, fit and healthy baby.39 At least one other self-proclaimed 'sexpert', Chai Fuyuan, author of ABC of Sexology (1928), supported Zhang's idea of female ejaculation.40\n\nInterestingly, besides portraying women as active agents in heterosexual intercourse (through such means as 'vaginal breathing'), Zhang also held them responsible for reducing male homosexual behaviour in China.41 In Sex Histories, for instance, Zhang reasoned that since the anus lacked 'momentum' and any kind of 'electrolytic qi', it could not compete with the vagina, which was filled with 'lively qi'. As long as women took good care of their vaginas and used them properly for sex, such as by following his theory of the 'third kind of water'; the 'perverted', 'malodorous', 'meaningless' and 'inhumane' behaviour of anal intercourse among men could be ultimately eliminated.42 This example powerfully illustrates the subtle ways in which male same-sex practice was coming to be discussed in the language of biological science: although not the direct cause of homosexuality per se, according to Zhang's theory the properties, quality and physiological mechanism of female reproductive anatomy were nonetheless understood as a key determinant of the prevalence of male homosexual conduct. Meanwhile, in prioritising western biology as a modernistic discourse for the cultural appreciation of female sexuality, his theoretical project implies the burden of Daoist alchemy as a symbol of tradition in conceptions of sexual health in Chinese culture.\n\nZhang ultimately sought to create a new public of truth about sex. The stories he included in Sex Histories was a major step in this endeavour. In his capacity as the editor of the popular magazine New Culture, he published translations of excerpts from Ellis's Studies in the Psychology of Sex. The periodical soon became a venue for other kindred spirits to present the science of sexology to a popular audience and to establish their own 'sexpertise'. But most importantly, New Culture was not an exclusive forum devoted to the voice of experts; it published readers' responses to not only its most controversial articles, but also any contemporary issues that seemed relevant to the scope of the magazine, including sexuality-related subjects.\n\nReaders, presumably many of whom resided in urban areas where Republican publications were most readily accessible, seized the opportunity to respond to Zhang's provocative writings. Some felt the need to confirm the scientific value of his work. One reader, for example, interpreted Sex Histories as an 'outstanding scientific piece of \"sex research\"'.43 Another even urged him to publish more sexological treatises like Sex Histories by asking 'why have you published only one volume of Sex Histories? Have you accomplished your goal with that single contribution?'44 Others similarly maintained that Sex Histories 'definitely cannot be viewed as a pornographic piece of work. Its content is all valid research material on sexual activities'.45\n\nAt the same time, the scientism of Dr Sex's advice did not seem problematic to all interested readers. From the outset, many took for granted that his words already constituted science. One woman wrote to Zhang:\n\nThere is one part of your advice that said 'the female partner should try to become excited, so that there will be a great amount of water released in the vagina. The male partner could then gradually insert his penis into her vagina... and rub it back and forth smoothly and easily'. This part, I think, is a little bit too idealistic. In fact, it cannot be accomplished: although I am a woman who has been married for over a year, if I follow your suggestion, I think it certainly will not work. This is because people who are impatient, men or women, would quickly lose sexual interest in the process. As for those who prefer to take it slow, they probably would start getting tired and annoyed of the process, and this might even have a negative effect on two persons' love for each other. What do you think?46\n\nThough disagreeing with Zhang's initial advice, the author still regarded him as the ultimate authority on matters related to sex. In fact, the letter squarely conveys her desire to contribute to Dr Sex's science by providing a personal perspective, which bears a similar empirical value to the case studies collected in Sex Histories. Another reader, Xu Jingzai, even offered Zhang his own insight concerning the proper way of 'sexual breathing'.47 Others similarly respected what Zhang had to offer, but either wanted to learn more about his theory of the 'third kind of water' from a male-centred perspective or expressed frustration with its impracticality based on their own experience in the bedroom.48\n\nSeveral readers directly responded to Dr Sex's brief discussion of homosexuality. Supporting Zhang's effort in promoting sex education on scientific grounds, a lady named Su Ya argued that the prevalence of undesirable sexual behaviours would decline once adequate sex education becomes common in China. Su wrote to Zhang, 'As long as sex education continues to be promoted and advanced, all the illegal sexual behaviours, such as rape, homosexuality, illegal sex, masturbation, etc., could be eliminated'.49 Miss Qin Xin, however, disagreed: 'Homosexuality is not a natural sexual lifestyle. It is a kind of perversion and derailment in human sexuality, so it should not have any proper place in sex education'.50 Another reader asked, 'It seems that homosexuality exists among both men and women, but could these people's \"sexual happiness\" be identical to the kind of enjoyment experienced in sexual activities with the opposite sex?' Zhang simply answered no: 'Other than being a personal hobby, homosexuality cannot be compared to the kind of happiness one achieves in heterosexual intercourse. Since on the physical level it cannot generate the kind of electric qi found in heterosexual mutual attraction, homosexuality also does not provide real satisfaction on the psychological level'.51 Zhang's response thus reminded his readers of the importance of knowing and practising the correct form of heterosexual intercourse, implying the paramount significance of following his theory of the 'third kind of water' that defined women's proper sexual performance, attitude and responsibility.\n\nTherefore, starting in the 1920s, under the influence of Dr Sex, some Chinese urbanites began to treat heterosexuality and homosexuality as scientific categories of discussion and sexology as a serious discourse of expertise knowledge. In 1927, one individual who worked for the Fine Arts Research Society (Meishu yanjiuhui) observed that 'due to the recent progress in academia, there is a new independent scientific field of study that surprises people. What kind of science is it? It's sexology'.52 In particular, Zhang Jingsheng's theory of the 'third kind of water' simultaneously biologised and psychologised sex. It biologised sex because it discussed people's erotic drives and motivations in the framework of the somatic functions of male and female reproductive anatomy. Zhang's theory psychologised sex by explaining people's sexual behaviour and activities in terms of what they thought and how they felt.\n\nThe methodological framework of these processes of knowledge production was consistent with the empirical approach of contemporary western sexology. Among the field's other founding fathers, Havelock Ellis, Sigmund Freud, Richard von Krafft-Ebing, Iwan Block, Max Marcuse and Magnus Hirschfeld all discussed, classified, understood, theorised and, in essence, made knowledge claims about human sexuality by collecting and studying individual life histories. This approach bears little resemblance to the statistical\u2013sociological method later adopted by Alfred Kinsey, the American sexologist who would assume an international reputation by the mid-century.53 As reflected in their correspondences, the Chinese Dr Sex and his readers faithfully believed that sexuality \u2013 hetero or homo \u2013 was something to be known scientifically, and that both the experts and non-experts mutually relied on one another for valuable information. In his attempt to enlighten the public with reliable and 'accurate' knowledge about proper heterosexual conduct, Zhang's sexological ethos gave true or false statements of homosexuality an unprecedented scope of conceptual comprehensibility in China.\n\nCompeting authorities of truth\n\nAs we have seen, the public dissemination of knowledge about sexuality was a hallmark of Zhang Jingsheng's 'utopian project', to borrow the phrase from Leon Rocha.54 In pushing for the public circulation of private sexual histories, Zhang's sexological enterprise simultaneously defined certain aspects of China's sexual culture as traditional or modern, whether in terms of modes of narration (literary vs scientific) or theoretical foundations (Daoist alchemy vs western biology). In this new public of truth, the nature of human desire and passion was openly debated by experts and their readers. But the cast in these debates included other public contenders as well. This section of the chapter extends the foregoing by highlighting another aspect of 'epistemic modernity' crucial to the epistemological grounding of scientia sexualis in Republican China: a public platform on which authorities of truth competed.\n\nWhereas a great majority of the urban mass idolised Zhang by calling him the 'Dr Sex', other mainstream scholars publicly gainsaid his teaching. These critics ridiculed Zhang's sexological work mainly for its lack of scientific integrity. The author of an article in Sex Magazine called Zhang's sexological theory 'fraudulent science' (weikexue) because Zhang 'does not even understand the most basic workings of human physiology'.55 Even though Zhou Jianren (1888\u20131984), the youngest brother of Lu Xun, had praised Zhang's first two books for their sound philosophical argument, he too attacked Zhang's theory of the 'third kind of water' immediately after the publication of Sex Histories. Author of numerous popular life-science books and an editor at the Shanghai Commercial Press, Zhou argued that Zhang's theory did not correctly account for the biological process of ovulation in the menstrual cycle. Zhou noted that if the female body produces an ovum only on a periodic basis, Zhang's advice for women to voluntarily release an egg and the 'third kind of water' in each sexual intercourse was evidently 'pseudo-scientific' at best. Another sex educator, Yang Guanxiong, even described Zhang as a public figure destructive to the entire sex education movement. For modernisers of the sex education movement like Zhou and Yang who were familiar with contemporary developments in the western natural sciences, the most problematic aspect of Zhang Jingsheng's sexology was its inaccurate grounding in human biology.56\n\nOf the many critics of Zhang, the most vociferous was probably Pan Guangdan (1899\u20131967), the famous Chinese eugenicist who also considered himself a loyal devotee of Havelock Ellis's work in sexology. Pan received his bachelor's and master's degrees in biological science, respectively, at Dartmouth College in 1924 and Columbia University in 1926. In light of his high academic performance, Pan was inducted into the Phi Beta Kappa honour society upon his graduation from Dartmouth.57 His educational experience in New York coincided with the peak of the American eugenics movement, the centre of which was located in the upper-class resort area of Cold Spring Harbor on Long Island. In 1904, the Station for Experimental Evolution was established there under the directorship of Charles Davenport with funds from the Carnegie Institution of Washington.58 In the summer of 1923 and between his undergraduate and graduate studies, Pan visited Davenport's Eugenics Record Office (founded in 1910) to learn more about human heredity research.\n\nAfter returning to China in 1926, Pan did not conduct experimental research in biology (given his interest in eugenics, experimentation with human breeding was of course not an option). Like most European and American eugenicists, he spent most of his time studying the ethno-social implications of sex instead by constructing extended family pedigrees and collecting other types of inheritance data.59 His Research on the Pedigrees of Chinese Actors (1941) is an exemplary outcome of his eugenics research.60 Like the Anglo-American eugenicists who he tried to emulate, Pan also prioritised the making of an 'eugenic-minded' public.61 He did this by delivering numerous lectures around the country and publishing extensively in both academic journals and the popular press to promote his positive vision of eugenics.62 The Chinese public in general viewed him as a trustworthy intellectual in light of his impressive academic credentials. Through Pan, 'eugenics' quickly became a household term in China in the late 1920s and 1930s.63\n\nHaving the same intellectual worries as Zhou Jianren, Pan regarded Zhang Jingsheng's writings on human sexuality as 'fake science'. Pan was particularly disdainful of anything Zhang had to say about the relationship between sex and eugenics, because he despised Zhang's lack of formal training in biological science. Even though Zhou, like Zhang, had a background in philosophy, his writings on evolutionary biology proved his erudition in the life sciences. On the contrary, in Pan's view, Zhang's ideas about human sexuality demonstrated an apparent failure in communicating principles of human biology. Responding to Zhang's theory of a 'third kind of water', Pan remarked in 1927:\n\n[Zhang] claims that he has discovered a 'third kind of water', but we do not know what it is. He has indicated that it simply refers to the secretion of the Bartholin glands. If that is the case, then it is really nothing new to any educated person with some familiarity with the physiology of sex... One of the functions of the Bartholin secretions is to decrease resistance during sexual intercourse. The amount of secretion increases as the female partner becomes more aroused, so the quantity of secretion depends entirely on the intensity of her sexual desire and arousal... Since this function is present in most females, one wonders on what statistical basis does [Zhang] claim that women in our nation usually do not release this third kind of water. When he claims that this kind of water is more typically released in the body of European urban women, one is equally suspicious about the kind of statistical evidence he relies on, if there is any at all. If he has none yet still speaks so confidently in these words, his intentions are dubious in making these unsupported claims.64\n\nPan subsequently attacked Zhang's understanding of eugenics by directly citing the statistical data collected in the works of Charles Davenport and Francis Galton. Pan even accused Zhang of having overlooked Galton's work completely: 'Since the Englishman Francis Galton published his Hereditary Genius in 1869, the book has become immensely useful; and the recent developments in intelligent testing have grown exponentially. Why doesn't [Zhang] consult these works a bit more? He probably is not even aware of the existence of these studies; one really cannot understand why someone would speak about eugenics so elaborately without some basic familiarity with these texts'.65\n\nIn his reply, Zhang showed no acquiescence. He pointed out that Pan's comments 'have in fact proven the scientific aspect of my theory. The third kind of water is, of course, something present in every woman... I am merely bringing people's attention to this kind of water and teaching them how to release it'.66 Zhang even described Pan's recourse to the work of Francis Galton as evidence of poor research and understanding of eugenics: 'In terms of heredity and eugenics, [Pan's] knowledge in these subjects is even more limited. He is familiar with Francis Galton's work, but Galton's theory does not seem well-grounded... Three years ago, I had already indicated in my book, A Way of Life Based on Beauty, that Galton's eugenic theory is not real science, but what we want is real science... Please allow me to invite [Pan] to study my work more carefully in addition to Galton's'.67 To Zhang, Pan was the one who lacked scientific and scholarly integrity.\n\nThis public correspondence between Pan and Zhang offers a window onto the ways in which, from the 1920s to the 1940s, experts defined and debated the boundaries of a scientific discourse of sexuality. An important aspect was the mutual contestation of the credibility and validity of expertise, as in any other scientific discipline. For Pan, formal training in the biological sciences represented a crucial feature of sexological credibility. Even if an expert lacked this credential, sexological competence could still be achieved by acquiring western scientific knowledge faithfully and refraining from making empirically unsubstantiated claims about sex. This is why he regarded Zhou Jianren as a better equipped sex educator and a more respectable scientist than Zhang Jingsheng. To Zhang, Pan had obviously misinterpreted what he was trying to do. In fact, Pan's oversight of Zhang's earlier scholarly output indicated a weakness of Pan's research and scholarship. In turn, Zhang even encouraged Pan to study his own writings more carefully in addition to the work of foreign scientists like Galton. Since he had already built a foundation of sexological expertise, Dr Sex believed that this foundation should be studied, or at least acknowledged, by incomers to the field of sex science such as Pan.\n\nThe debates between Zhang and his critics thus reveal the larger evolving context in which homosexuality became a matter of scientific discussion. This contested terrain of authority denotes a public platform on which self-proclaimed experts in sexology competed and challenged each other's scientific legitimacy. This 'legitimacy' comprised a host of criteria, including academic credentials (whether someone is trained in the humanities or sciences and in what discipline), methodological approach, accuracy in understanding and communicating the specific contents of western scientific knowledge, and evidence of candid research experience (including familiarity with previous scholarship), among others. In this regard, East Asian sexology, as a regionalised global discourse marked by the trends and currents of 'epistemic modernity', reflected the broader stakes of scientific disciplinarity looming over Chinese culture at the time. Similar to the famous 1923 'science versus metaphysics' controversy, debates over sexual knowledge contributed to the increasingly hegemonic intellectual agenda in which the interrogation of the very meaning of science became a preoccupation unique to the early Republican period. In a double move of sorts, the growing currency of debates on scientism \u2013 itself a new marker of modernity \u2013 contextualised the gradual process by which the category of homosexuality absorbed the dominant frame of thinking about same-sex desire in twentieth-century Chinese culture.68\n\nIntellectual translation and disciplinary consolidation\n\nIn addition to the invention of a new public of truth and a contested terrain of authority, the grounding of scientia sexualis in Republican China involved a third endeavour: the consolidation of its disciplinarity through the translation and reinforcement of specialised authority across culture. The novelty of Zhang Jingsheng's Sex Histories was highlighted in its incitement of a new Chinese discourse in which the truth of people's sexual experience was negotiated in public; but the book's cultural legacy and significance was even more pronounced in the way it reproduced the social dynamics between the observer (the sexologist) and the observed (sexual desire and behaviour) that characterised western sexual science. The criticisms levelled against him, by Pan Guangdan and others, broadened the purview of such power dynamics. They made public not only people's sex life, but also each other's (in)competence to speak about the scientific nature of sex. By the 1930s, through translating, reinforcing and re-contextualising the cultural authority of sexology, Chinese sex scientists accomplished more than disclosing sexual truths and the contested nature of their 'sexpertise' in public: they introduced, on the level of epistemology, a new style of reasoning about sexuality and, in the social domain, an unprecedented forum for intellectual debates that defined their project as culturally relevant, socially legitimate and disciplinarily independent.\n\nAt the point where Sex Histories had undergone numerous reprints and could be found in almost every corner of Shanghai and Beijing, it seemed urgent to sex educators that the study of sexuality required a more rigorous scientific grounding. This drew the line between Dr Sex, who was primarily concerned with popularising his 'theory of the third kind of water', and his critics, who increasingly viewed his work as narrow and unscientific. Again, this is exemplified by the difference between Zhang Jingsheng and Pan Guangdan in their approach to the empirical study of sex, including homosexuality.\n\nDespite their shared interest in emulating Havelock Ellis, Pan is considered by many as a more pivotal figure in pioneering the introduction of western sexology to China. For one, Zhang rarely offered insights concerning human sexuality other than heterosexual intercourse. In 1929, the author of an article, 'The Problem of Same-Sex Love', explained that he wrote the piece to illuminate 'the most unimaginable secret of sex \u2013 homosexuality', since even 'Professor Zhang's discussion of sex never falls outside the boundaries of male\u2013female sexual relations'.69 In contrast, Pan often discussed a wide range of 'deviant' sexual practices in writing and lectures. For critics of Dr Sex, investigation into diverse topics of human sexuality not limited to 'normal' heterosexual practice was a cornerstone of European sexology that Zhang Jingsheng had obviously missed.\n\nPan also translated more western sexological texts. While claiming that the facts and personal histories he solicited from readers formed the scientific basis of his sexological writing, Zhang translated a relatively modest quantity of foreign sexological works into Chinese. And even though Zhang frequently cited Ellis,70 Pan translated at least three monograph-length studies by Ellis, including the entire manuscript of Psychology of Sex: A Manual for Students.71 Pan was so intrigued by Ellis's discussion of sexual inversion that at the end of his annotated translation of Psychology of Sex, he even included an appendix on 'Examples of Homosexuality in Chinese Literature'.72 For the Ming\u2013Qing period, Pan listed twelve cases of male homosexuality and one case of female homosexuality.73 Other classics by prominent turn-of-the-century European sexologists such as Marie Stopes, August Forel and Solomon Herbert were also translated into Chinese, and they provoked similar public interest on the topic of same-sex affect.74 This was an endeavour beyond the intellectual concerns of Dr Sex.\n\nApart from topical diversity and the actual number of translated texts, Chinese sex scientists also valued the role of historical information in their appropriation of the cultural authority of sexology. If the hallmark of sexology for Dr Sex was merely the empirical understanding of sexual behaviour through compiling and collecting actual life histories, it also involved for Pan the rendition of historical data on sexual variations so as to illumine better their relevance in contemporary Chinese society. Elsewhere, throughout the 1920s and 1930s, other writers followed Pan in looking back on same-sex practice in ancient societies (most notably that of Greece) and discussing its implications for the modernisation and nationalisation of China.75 Though both valued empiricism, Zhang and Pan adopted contrasting approaches to emulating Havelock Ellis: whereas Zhang was more concerned with collecting and responding to the contemporary 'stories' or 'cases' that people had provided him about their sexual experience, Pan devoted more effort to translating Ellis's work, a project supplemented by his own historical, sociological and ethnological insights.\n\nBut besides Havelock Ellis, Pan also introduced Freud's ideas on human sexuality to the Chinese public. If American eugenicists like Davenport paid no attention to Freud,76 Pan certainly embraced Freudian psychoanalysis wholeheartedly and used it as a legitimate scientific theory to explain sexual desire. For example, in his psycho-biographical study of the late Ming poetess Feng Xiaoqing (1595\u20131612), Pan psychoanalysed Feng's writings and concluded that she had narcissistic tendencies.77 Other sinologists have viewed this effort as an early example of how psychoanalysis was transferred to China in the early twentieth century.78 According to Haiyan Lee, for instance, 'In [the hands of western-educated May Fourth intellectuals], psychoanalysis was divorced from its clinical setting and retooled as a critical hermeneutic strategy. It served the enlightenment agenda of displacing both the Confucian moral discourse of sex\/lust and the cultivational discourse of health\/generativity with a scientific discourse of sexuality'.79\n\nIndeed, Pan consistently used psychoanalysis in his writings as a modernising scientific tool for diagnosing the sexual problems of Chinese society. In his annotated translation of the chapter on 'Sexual Education' from Ellis's Sex in Relation to Society (the sixth volume of Studies in the Psychology of Sex), Pan, in a footnote, recapitulated a five-stage understanding of psychosexual maturation that he first articulated in his psycho-biographical study of Feng: '\"primary identification between mother and son\", \"maternal desire\", \"narcissism\", \"homosexuality\", and \"heterosexuality\"'.80 Two years later, in an article called 'Sexuality Today', Pan reiterated an identical pathway of psychosexual development: 'it is necessary for the development of sexual desire to go through several stages: (1) primary identification, (2) the objectification of the mother's body and the desire for her, (3) the realisation of self-awareness and narcissism, (4) homosexuality as a result of the expansion of narcissism, and (5) heterosexuality as the result of the maturation of sexual physiology and sexual psychology'.81 When his translation of Ellis's Psychology of Sex appeared in 1946, he would refer to this process of psychosexual development again in explaining the one case of female homosexuality he included in the appendix.82\n\nIn his 1910 revision of Three Essays on the Theory of Sexuality (1905), Freud added the following footnote on homosexuality:\n\nIn all the cases [of sexual inversion] we have examined we have established the fact that the future inverts, in the earliest years of their childhood, pass through a phase of very intense but short-lived fixation to a woman (usually their mother), and that, after leaving this behind, they identify themselves with a woman and take themselves as their sexual object. That is to say, they proceed from a narcissistic basis, and look for a young man who resembles themselves and whom they may love as their mother loved them.83\n\nTherefore, it appears that, from the 1920s to the late 1940s, Pan had completely endorsed Freud's explanation of homosexuality. Pan insisted throughout his publications that psychosexual maturation 'is like a stream of water, and two changes could occur in the middle of this process: arrested or reversed development'.84 Readers who found Pan's psychoanalytic explanations convincing would thus interpret same-sex desire in Freudian terms as an arrested or reversed phase of sexual maturation and as an inadequately developed psychological condition due to early childhood experience. As such, the absorption of the socio-cultural meaning of 'same-sex desire' by the scientific category of 'homosexuality' was in part enabled by the new conceptual framework of psychoanalysis.\n\nOther medical and scientific experts shared a similar view. In 1936, after returning from her psychiatric training at Johns Hopkins University, the practising gynaecologist Gui Zhiliang wrote in her widely read The Life of a Woman that 'homosexuality is a kind of intermediate or preparatory stage to heterosexuality; it is necessary for people to go through it'. According to Gui, those who are 'normally' developed would 'transit' (guodu) through homosexuality, but others would 'get blocked' (zuai) or 'bogged down' (tingzhi) in the process and express 'abnormal homosexuality' (buputong de tongxing'lianai). As Freud insisted as early as 1903, Gui did not think that homosexuality was necessarily 'treatable' or 'correctable'.85 Unlike Zhang Jingsheng's somatic-oriented interpretations of sexuality, the importation of Freudian psychoanalysis in the 1920s and 1930s offered a strictly psychogenic way of explaining same-sex desire. Serving as a new conceptualising and modernising tool, psychoanalysis operated as another cultural technology that made homosexuality an important candidate of scientific thinking, a subject whose truth-and-falsehood became debatable among doctors and scientists of sex.\n\nOne of the major debates on homosexuality in the 1920s and 1930s concerned the question of whether it could be treated or cured. Besides Gui, many other participants in the debate, who had either translated foreign (western or Japanese) sexological texts into Chinese or written about sex from a 'scientific' viewpoint themselves, did not consider homosexuality necessarily curable. In an article that appeared in the periodical Sex Science in 1936, for instance, the translator Chang Hong defined 'sexual perversion' as 'those expressions of sexual desire that neither accompanied male\u2013female love nor established procreation as its ultimate goal'.86 The author presented homosexuality as one among the many existing types of sexual perversion (others included bestiality, fetishism, sadism and masochism) and remarked that 'if a man expresses both feminine and homosexual tendencies, no natural treatment is effective. At the same time, there is no pharmaceutical cure for this kind of situation'.87 Despite this explicit acknowledgement that no effective treatment of homosexuality was available, the article still construed same-sex desire and behaviour as undesirable, especially by emphasising their categorical similarity to other kinds of sexual perversion like sadism, fetishism and bestiality.\n\nChang's translated piece offered just one among the many perspectives circulating in a thematic issue of Sex Science devoted to the topic of homosexuality. Another translated article with the title 'Can Real Homosexuality be Cured?' advocated a less stigmatising position. The author claimed that 'recent scholars have come to believe that the nature of homosexuality is inborn, congenital, and immutable. The only situation in which an individual's homosexual desire could be changed is if it is an \"acquired\" or \"fake\" homosexuality. I agree with this perspective'.88 Elsewhere in the same issue, treatment methods for homosexuality such as surgical castration or psychological hypnosis were often cast in a highly suspicious light.89\n\nBy and large, however, essays in this thematic issue of Sex Science emphasised the likelihood of homosexuality being acquired. While acknowledging that most experts had agreed on the inborn nature of homosexual tendencies, they nonetheless paid more attention to the prevalence of homosexual behaviour in unisex social settings, such as schools, dormitories, factories, military camps and prisons.90 Yang Kai, a doctor who earned his medical degree at the University of Hamburg in Germany, noted that the number of homosexuals 'among female students, employees, and workers is especially large in the present time'. At the same time as he recognised that the main cause of this 'perversion' is 'inherited', Yang still attributed the high frequency of homosexual practice to 'habits and the environment'.91 This was congruent with the impression one would get from reading the popular sexological handbook, ABC of Sexology, in which the author Chai Fuyuan noted that male same-sex love was more prevalent in schools, the military and temples, and that the incidence of female homosexuality was especially high in the workplace and factories.92 According to another lengthy (translated) article in this special issue of Sex Science, 'The Study and Prevention of Homosexuality',\n\nThe question of how homosexuality can be prevented is an empty question. Since homosexuality is widely recognized as a congenital situation, preventive methods are certainly very ineffective. But a hygienic social environment could suppress the occurrence of acquired, immature, or temporary homosexuality. Schools should be the primarily targets of hygienic intervention, because this could prevent the spreading of homosexuality on campuses.93\n\nBut this must be done with great caution, as the opening essay of the forum warned its reader: if the surveillance policies of school dormitories were too strict and rigid, students might become 'overly sensitive to sexual stimuli', and this would lead to a situation in which students were actually 'more likely to engage in masturbation and homosexuality'.94 Hence, most of the articles in this special issue of Sex Science recommended more opportunities of opposite-sex social interaction as a way to control or prevent homosexuality, implying that most same-sex erotic behaviours are perhaps more correctable than assumed.95\n\nCorrectable or untreatable, inborn or acquired, same-sex desire was now indisputably discussed via the western psychiatric style of reasoning. The acquisition and articulation of this novel style of reasoning gave same-sex desire a new epistemological grounding in twentieth-century China. In 1932, Gui Zhiliang, author of The Life of a Woman, stated in her book, Modern Psychopathology, that 'Some experts in psychopathology claim that homosexuality is the cause of paranoia... but although homosexuality could possibly induce paranoia, it does not have to be the sole cause of it'.96 Gui's allusion to the famous Freudian association of male homosexuality with paranoia reveals that the western psychiatric style of reasoning completely exhausted the linguistic meaning and comprehensibility of same-sex eroticism in the context of this knowledge claim by the early 1930s. When twentieth-century Chinese commentators used 'homosexuality' as a conceptual blueprint for understanding same-sex relations, they had completely displaced any of its non-pathological connotations in the pre-modern context. What they translated was not merely the vocabulary of homosexuality itself, but a whole new style of reasoning descended from western psychiatric thought about sexual perversion and psychopathology.\n\nIt should be noted that sex was not new to conceptions of health in traditional Chinese medicine. Concerns about the dangers of undisciplined sexual activities can be found in the very opening chapter of the Inner Canon's Basic Questions:\n\nThe people of archaic times who understood the Way modelled [their lives] on [the rhythms of] yin and yang, and accorded with the regularities imposed by disciplines [of self-cultivation]. Their eating and drinking were controlled, their activity and rest were regular, and they did not exhaust themselves capriciously... People of our times are not like that. Wine is their drink, caprice their norm. Drunken they enter the chamber of love, through lust using up their seminal essence (jing), through desire dispersing their inborn vitality (zhenqi)... Devoted to the pleasures of the heart and mind, they reject the bliss that accompanies cultivation of the vital forces.97\n\nUnlike the western psychiatric style of reasoning about sexual disorders, this passage makes it evident that traditional Chinese medical thinking conceptualised sexual desire and activity in quantitative terms, conveying a general rubric of 'sexual economy'.98 This economy of sex follows the idea of an orderly life, stressed by medical scholars since the first millennium, that requires strict moral self-regulation and a spiritual life lived in harmony with the environment. In this cosmically ordered world of imperial China, as Charlotte Furth reminds us, 'no kind of sex act or object of desire was singled out in medical literature as pathological'.99 To paraphrase Arnold Davidson, then, we can confidently say that as little as one hundred years ago, western psychiatric notions of sexual identity (for example, homosexuality) were not false in China, but rather were not even possible candidates of truth-or-falsehood. Only after the translation and introduction of a psychiatric style of reasoning by the modernising thinkers from the 1920s onwards were there ways of arguing, verifying, explaining, proving and so on that allowed such notions to be true-or-false.\n\nThe translation, mediation and introduction of this new psychiatric style of reasoning hinges on an intellectual landscape of sexological disciplinarity. Though priding itself on being a symbol of modernity, Zhang Jingsheng's Sex Histories soon triggered an opposite effect. His critics defined his sexological project as unscientific and attempted to move beyond its limitations. The scope of Pan's sexology, for example, included a broader range of topics not limited to 'normal' heterosexual intercourse, translated a significantly higher quantity of foreign sexological literature, sought and drew on historical data for valuable insights concerning contemporary sexual problems, introduced a purely psychological account of human sexuality in the language of Freudian psychoanalysis and thereby enabled debates on the etiology and prevention of 'deviant' sexual practices. The convergence of all these efforts formed the social\u2013epistemic foundations upon which sexology came to be established as an independent scientific discipline. This in turn provided sufficient grounds for bringing a foreign psychiatric style of reasoning into comprehensibility in Chinese culture. In depicting Zhang's sexological enterprise as hopelessly out of date, sex educators and scientists used it as a foil against which new measures of being 'scientific', 'modern' and by extension 'traditional' could be juxtaposed.\n\nNo other example illustrates the outcome of this epistemic modernity better than the existence of an academic periodical called Sex Science in 1930s China. At least a 'Chinese Academy of Health' was named as its official editorial governing board on the front page of each issue, and a 'Shanghai Sexological Society' was listed as the editorial collective of another periodical called Sex Magazine (Xing zazhi). Although there is no doubt that many modernising intellectuals at the time viewed human sexuality through the lens of social problems, the presence of these learned societies and disciplinary journals suggests that sexual problems were considered as topics worthy of serious investigation in their own right. In addition to providing a more focused venue for the translation of foreign sexological literature, Sex Science offered Chinese 'sexperts' an unique opportunity to publish original contributions and opinion pieces in direct dialogue with one another. Like its western counterparts such as the Journal of Sexual Science in Germany and Sexology in the United States, Sex Science functioned as a textual archive, reinforcing the specialised authority of sexology across culture. Its founding and circulation thus marked an important episode in the intellectual translation and disciplinary consolidation of scienta sexualis in Republican China.\n\nEast Asian scientia sexualis and the birth of a nationalistic style of argumentation\n\nIf Foucault was correct in asserting that western civilisation was 'the only civilization to practise a scientia sexualis', such practice had certainly spread to the East Asian world by the early twentieth century like never before.100 But this chapter has also attempted to show that the historical significance of this proliferation rested on a level deeper than the superficial transfer of ideas across cultural divides. The epistemological grounding of scientia sexualis in Republican China was governed by a discursive apparatus that I call 'epistemic modernity', in which explicit claims of sexual knowledge were imbricated with implicit claims about cultural indicators of traditionality, authenticity and modernity.101\n\nIn the context of Zhang Jingsheng's sexology, whether it is the dualism between literary representations of love versus scientific truthfulness of sex, or the juxtaposition between Daoist cultivational ideas in Chinese medicine versus the bio-psychological language of western biomedicine, epistemic modernity helps delineate the two registers of truth production on which sexological claims operated: one concerning explicit claims about the object of scientific knowledge (human sexuality), and the other concerning implicit claims about cultural markers of traditionality, authenticity and modernity (modes of narrating sex, theoretical frameworks of medicine, etc.). But Zhang's project quickly turned into the antithesis of science and modernity in the eyes of his contemporaries. Moving beyond the limitations of his work, they aimed to establish an independent discipline with greater resemblance to European sexology. By the mid-1930s, disparate efforts to make sexuality a legitimate subject of scientific discussion and mass education culminated in such projects of disciplinary consolidation as the founding of Sex Science. These unprecedented endeavours gave rise to a radical reorganisation of the meaning of same-sex desire in Chinese culture around a new psychiatric style of reasoning.\n\nIn the politically volatile context of Republican China, the introduction of western sexology often reframed same-sex desire as an indication of national backwardness. In his Sexual Science, after documenting the prevalence of homosexual practice in different western societies, Zhang Minyun concluded that 'the main social cause for the existence of homosexuality is upper-class sexual decadence and the sexual thirst among lower-class people'.102 This, according to Zhang, should help shed light on 'the relationship between homosexuality and nationality'.103 'For the purpose of social improvement', according to another concerned writer, 'the increasing prevention of homosexuality is now a pressing task'.104 Pan Guangdan expressed a similar nationalistic hostility towards the dan actors of traditional Peking opera: since they often participated in sexual relationships with their male literati patrons, Pan described them as 'abnormal' and detrimental to social morality. He explained that their lower social status prevented them from participating in the civil examination system, implying that a modernising nation in the twentieth century certainly had no place for them.105 The physician Wang Yang, known for his expertise in human sexuality and reproduction, went so far as to identify homosexuality as 'a kind of disease that eliminates a nation and its races'.106\n\nTherefore, if we take the insights of Lydia Liu and others seriously, the apparatus I call epistemic modernity that mediated the transmission of scientia sexualis into China ultimately characterises a productive historical moment.107 When Republican Chinese sexologists viewed the dan actors and other cultural expressions of homoeroticism as signs of national backwardness,108 they in essence domesticated the western psychiatric style of reasoning and turned it into a new nationalistic style of argumentation about same-sex desire.109 In addition to staging certain elements of the Peking opera field as being out of time and place, epistemic modernity occasioned an entrenched nationalistic platform, on which other aspects of this cultural entertainment also functioned as powerful symbols of quintessential Chinese tradition and authenticity. Rendered as a prototypical exemplar of the modern homosexual, the twentieth-century dan actor became a historic figure signifying a hybrid embodiment of the traditionality and what Duara aptly calls 'the regime of authenticity' of Chinese culture.110\n\nIt is therefore possible to contrast this new nationalistic style of argumentation with the culturalistic style of argumentation that underpinned the comprehensibility of same-sex desire in the late imperial period.111 For this purpose, we can turn to the late Ming essayist and social commentator, Zhang Dai, who reflects on his friend Qi Zhixiang's fondness for a young man, named Abao, in his Tao'an mengyi (dream reminiscence of Tao'an). Tao'an is Zhang's pen name, and this collection of miscellaneous notes serves as a good window onto literati lifestyle circa the Ming\u2013Qing transition, since Zhang is often considered as an exemplar of literati taste of the time. The title of this passage is 'The Obsession of Qi Zhixiang', and because it places seventeenth-century male same-sex love in the context of multiple desires, it is worth quoting in full:\n\nIf someone does not have an obsession (pi), they cannot make a good companion for they have no deep passions; if a person does not show some flaw, they also cannot make a good companion since they have no genuine spirit. My friend Qi Zhixiang has obsessions with calligraphy and painting, football, drums and cymbals, ghost plays, and opera. In 1642, when I arrived in the southern capital, Zhixiang brought Abao out to show me. I remarked, 'This is a divine and sweet voiced bird from [the paradise of] the western regions, how did he fall into your hands?' Abao's beauty was as fresh as a pure maiden's. He still had no care for decorum, was haughty, and kept others at a distance. The feeling was just like eating an olive, at first bitter and a little rough, but the charm is in the aftertaste. Like wine and tobacco, the first mouthful is a little repulsive, producing a state of tipsy lightness; yet once the initial disgust passes the flavour soon fills your mind. Zhixiang was a master of music and prosody, fastidious in his composition of melodies and lyrics, and personally instructing [his boy-actors] phrase by phrase. Those of Abao's ilk were able to realize what he had in mind. In the year of 1645, the southern capital fell, and Zhixiang fled from the city to his hometown. En route they ran across some bandits. Face to face with death, his own life would have been expendable, but not his treasure, Abao. In the year of 1646, he followed the imperial guards to camp at Taizhou. A lawless rabble plundered the camp, and Zhixiang lost all his valuables. Abao charmed his master by singing on the road. After they returned, within half a month, Qi again took a journey with Abao. Leaving his wife and children was for Zhixiang as easy as removing a shoe, but a young brat was as dear to him as his own life. This sums up his obsession.112\n\nThis passage also sums up what a man's interest in young males meant in the seventeenth century remarkably well: it was perceived as just one of the many different types of 'obsessions' that a male literatus could have \u2013 a symbol of his refinement. For Zhang, a man's taste in male lovers was as important as his 'obsessions' in other arenas of life, without which this person 'cannot make a good companion'. Despite all the hardship, the romantic ties between Qi and Abao still survived, and perhaps even surpassed Qi's relationship with his wife and children.113\n\nLet me now bypass roughly three centuries. For the most part, there was a distinct absence of discussion about same-sex sexuality in the numerous sex education pamphlets published throughout the late 1940s and 1950s.114 But in the few instances where homosexuality was actually mentioned, the way it was described and the specific context in which it was brought up would appear so strange and foreign to Ming\u2013Qing commentators on the subject. In a sex education booklet for adolescents published in 1955, the author wrote:\n\nCertainly, sometimes 'same-sex desire' is only psychological and not physical. For example, a girl might be very fond of another girl classmate, to the extent that she even falls in 'love' with her. Their relationship could be quite intimate, and they could possibly even have slept together on the same bed and felt each other, but there is actually nothing beyond that. For this type of same-sex love\/desire, it is easily curable. As long as they get married separately, whatever happened could be easily forgotten.115\n\nThe author, Lu Huaxin, went on to describe a symmetrical situation for those adolescent boys who have developed a similar kind of affection for same-sex classmates. But Lu insisted that 'as long as [these] teenager[s] get married, the pathological feelings will disappear'.116 Only for certain teenagers whose 'lifestyle has become decadent' and who 'really start pursuing abnormal sexual gratifications', Lu continued, 'their brain then really needs to be treated. Because their brain is unhealthy and filthy; they have been infected by the pornographic virus. If an individual of this type is identified, friends should encourage everyone to offer him help and assistance'.117\n\nBy the mid-twentieth century, same-sex desire had acquired a set of social meaning and cultural significance completely different from the way it was conceived before the onset of epistemic modernity. For one, the relationship between same-sex desire and heterosexual marriage is viewed as incommensurable or incompatible, even antithetical. One could not possibly be married to a member of the opposite sex while still passionately desiring someone of the same.118 In fact, according to Lu, heterosexual marriage is precisely the most useful 'cure' of same-sex desire. Same-sex desire now also means a pathological \u2013 and not just abnormal \u2013 tendency, based on which an autonomous relationship between two persons of the same sex is conceivable regardless of their social status. Lu located the seat of this deviant subjectivity inside the brain, via a vague notion of viral infection, which underscores the 'pathological' or 'unhealthy' nature of its psychological status. Again, as same-sex desire now represents something that is 'curable', heterosexual marriage could serve that function of cure most powerfully. No longer understood simply as one of the many 'tastes' or 'obsessions' a man of high status could have, erotic preference for someone of the same sex became something that could be eliminated with the help of friends, as opposed to something that could be appreciated by them.\n\nTo assess the epistemological transformation of same-sex desire in Chinese culture from an internal historical perspective, then, we can begin to reconstruct some of the polarised concepts that constitute two opposed styles of argumentation. We are presented, for instance, with the polarities between literati taste and sick perversion, refined obsession and pathological behaviour, cultural superiority and psychological abnormality, markers of elite status and signs of national backwardness. The first of each of these pairs of concepts partially makes up the culturalistic style of argumentation about same-sex desire, while the second of each of these pairs helps to constitute the nationalistic style of argumentation. These polarities therefore characterise two distinct conceptual modes of representation, two conceptual spaces, two different kinds of deep epistemological structure. It follows that the discursive apparatus of epistemic modernity has not merely mediated the introduction of the foreign sexological concept of homosexuality, but in doing so it has simultaneously catalyzed an internal shift in the conceptual paradigm of Chinese same-sex desire.\n\nAccording to Larissa Heinrich, in the nineteenth century China metamorphosed from being identified as 'the Cradle of Smallpox' to a pathological empire labelled as 'the Sick Man of Asia' with growing intensity.119 My analysis suggests that this transformation took another turn in the early Republican period. After the introduction of European scientia sexualis in the 1920s, the Chinese body could no longer be conceived in mere anatomical terms. It became rather appropriate, and perhaps even necessary, for us to conceptualise the Chinese body as explicitly sexual in nature. Chinese corporeality is now always linked to implicit claims of psychiatric reasoning and nationalistic significance. Put differently, a distinct problem in modern Chinese historiography has been the question of why, starting in the Republican period, Chinese modernisers began to view earlier expressions of same-sex eroticism (and gender transgression) as domestic indicators of cultural deficiency. And what I am suggesting is that, much as the gradual acceptance of an intrinsically pathological view of China helped the reception of western-style anatomy in nineteenth-century medicine, the epistemic alignment of pre-nationalistic homoeroticism with the foreign notion of homosexuality precisely undergirded the appropriation of a new science of western-style sexology in twentieth-century China.120\n\nWhat I call epistemic modernity, then, is more than just an example of 'translated modernity'; rather, it refers to a series of ongoing practices and discourses that could generate new ways of cultural comprehension and conceptual engagement, allowing for possible intersecting transformations in history and epistemology. If we ever wonder how to make sense of the prevalence of same-sex sexual practice in imperial China before the rise of an East Asian scientia sexualis, we only need to remind ourselves that, as little as a century ago, the question of sexual identity did not even fall within the possible parameters of Chinese thinking \u2013 for in China there is no such thing as homosexuality outside epistemic modernity.\n\nNotes\n\nThis chapter was the co-recipient of the 2010 Gregory Sprague Prize from the American Historical Association's Committee on Lesbian, Gay, Bisexual, and Transgender History. The author wishes to thank Benjamin Elman for his careful and insightful comments on an earlier version of this chapter, and Prasenjit Duara for his enthusiastic encouragement on the theoretical pursuit of this project at its inceptive stages. This chapter has especially benefited from the astute criticisms of Petrus Liu, Hongwei Bao and Wenqing Kang, and the meticulous reading of the original journal's two anonymous reviewers. The author alone is responsible for any remaining flaws. Research for this project was supported by pre-dissertation research grants from the East Asian Studies Program, the Department of History, and the Princeton Institute for International and Regional Studies at Princeton University. The author also wishes to thank participants at various conferences, seminars and workshops for their perceptive and pointed questions.\n\n1. Zhang Minyun, Xing kexue (Shanghai: Shidai shuju, 1950).\n\n2. See Gregory M. Pflugfelder, Cartographies of Desire: Male\u2013Male Sexuality in Japanese Discourse, 1600\u20131950 (Berkeley: University of California Press, 1999); Sabine Fr\u00fchst\u00fcck, Colonizing Sex: Sexology and Social Control in Modern Japan (Berkeley: University of California Press, 2003); Michiko Suzuki, Becoming Modern Women: Love and Female Identity in Prewar Japanese Literature and Culture (Stanford: Stanford University Press, 2009).\n\n3. All translations in this chapter are mine, unless indicated otherwise. Zhang, Xing kexue, p. 2.\n\n4. I have in mind, specifically, the notion of truthfulness used by Bernard Williams in Truth and Truthfulness: An Essay in Genealogy (Princeton: Princeton University Press, 2002). In this regard, I take my cue from Ian Hacking and use 'truth' in this chapter as a formal (as opposed to a strictly realist) concept. See Ian Hacking, Scientific Reason (Taipei: National Taiwan University Press, 2008), pp. 1\u201348.\n\n5. Charles Leary, 'Sexual Modernism in China: Zhang Jingsheng and 1920s Urban Culture' (unpublished doctoral thesis, Cornell University, 1994); Hiroko Sakamoto, 'The Cult of \"Love and Eugenics\" in May Fourth Movement Discourse', Positions: East Asia Cultures and Critique 12 (2004), pp. 329\u201376; Jing Tsu, Failure, Nationalism, and Literature: The Making of Modern Chinese Identity, 1895\u20131937 (Stanford: Stanford University Press, 2005), pp. 128\u201366; Haiyan Lee, 'Governmentality and the Aesthetic State: A Chinese Fantasia', Positions 14 (2006), pp. 99\u2013129; Wang Xuefeng, Jiaoyu zhuanxing zhi jing: Shiji shangban shi zhongguo de xingjiaoyu sixiang yu shijian (Beijing: Social Sciences Academic Press, 2006), pp. 249\u201365; Leon A. Rocha, 'Zhang Jingsheng (1888\u20131970): Love, Sex, Aesthetics, Eugenics, Utopia' (unpublished doctoral thesis, University of Cambridge, 2010). Leary's and Rocha's studies are the most detailed and comprehensive treatments of Zhang's life and work to date.\n\n6. Frank Dik\u00f6tter, The Discourse of Race in Modern China (Stanford: Stanford University Press, 1992); Gerald H. J. Lee, 'Pan Guangdan and the Concept of Minzu' (unpublished master's thesis, University of Cambridge, 1996); Yuehtsen Juliette Chung, Struggle for National Survival: Eugenics in Sino-Japanese Context, 1896\u20131945 (London: Routledge, 2002); Ruth Rogaski, Hygienic Modernity: Meanings of Health and Disease in Treaty-Port China (Berkeley: University of California Press, 2004), pp. 225\u201353; Tsu, Failure, Nationalism, and Literature, pp. 98\u2013166; Sakamoto, 'The Cult of \"Love and Eugenics\"'; Wang, Jiaoyu zhuanxing zhi jing, pp. 197\u2013232; Thomas S. Mullaney, 'Coming to Terms with the Nation: Ethnic Classification and Scientific Statecraft in Modern China, 1928\u20131954' (unpublished doctoral thesis, Columbia University, 2006); Haiyan Lee, Revolution of the Heart: A Genealogy of Love in China, 1900\u20131950 (Stanford: Stanford University Press, 2007), pp. 186\u2013217. The only published biographies of Pan to date are L\u00fc Wenhao, Pan Guangdan tuzhuan (Wuhan: Hubei renmin chubanshe, 2006); Wang Yanni, Guangdan zhihua (Wuhan: Changjiang wenyi chubanshe, 2006).\n\n7. For a brief analysis of Pan's sexological writings on homosexuality, see Tze-lan D. Sang, The Emerging Lesbian: Female Same-Sex Desire in Modern China (Chicago: University of Chicago Press, 2003), pp. 120\u201322. A more extended study can be found in Wenqing Kang, Obsession: Male Same-Sex Relations in China, 1900\u20131950 (Hong Kong: Hong Kong University Press, 2009), pp. 52\u20138.\n\n8. Frank Dik\u00f6tter, Sex, Culture, and Modernity in China: Medical Science and the Construction of Sexual Identities in the Early Republican Period (Honolulu: University of Hawaii Press, 1995), pp. 143\u20135.\n\n9. See Sang, Emerging Lesbian; Kang, Obsession.\n\n10. Dik\u00f6tter, Sex, Culture, and Modernity, pp. 140\u201341; Chou Wah-shan, Tongzhi: Politics of Same-Sex Eroticism in Chinese Societies (New York: Haworth, 2000), p. 50; Sang, Emerging Lesbian, pp. 7, 118; Kang, Obsession, pp. 42\u20133. For an account that stresses the role of western psychiatry and general political trends but does not touch on the significance of the translation of 'homosexuality', see Jin Wu, 'From \"Long Yang\" and \"Dui Shi\" to Tongzhi: Homosexuality in China', in Vittorio Lingiardi and Jack Drescher (eds), The Mental Health Professions and Homosexuality: International Perspectives (New York: Haworth, 2003), pp. 117\u201343.\n\n11. Kang, Obsession, pp. 42\u20133.\n\n12. Sang, Emerging Lesbian, p. 118.\n\n13. Michel Foucault, The History of Sexuality, vol. 1: An Introduction, tr. Robert Hurley (1976; New York: Vintage, 1990).\n\n14. Dennis Altman, Global Sex (Chicago: University of Chicago Press, 2001); Lisa Rofel, Desiring China: Experiments in Neoliberalism, Sexuality, and Public Culture (Durham: Duke University Press, 2007); Judith Farquhar, Appetites: Food and Sex in Post-Socialist China (Durham: Duke University Press, 2002). See also Loretta Wing Wah Ho, Gay and Lesbian Subculture in Urban China (London: Routledge, 2010); Travis Kong, Chinese Male Homosexualities: Memba, Tongzhi, and Golden Boy (London: Routledge, 2010); Joanne Mcmillan, Sex, Science and Morality in China (London: Routledge, 2006); James Farrer, Opening Up: Youth Sex Culture and Market Reform in Shanghai (Chicago: University of Chicago Press, 2002). On the argument for an emphasis shift in modern Chinese historiography to the Republican era, see Frank Dik\u00f6tter, The Age of Openness: China before Mao (Berkeley: University of California Press, 2008); and my argument about turning points in the history of sexuality in Howard Chiang, 'Liberating Sex, Knowing Desire: Scientia Sexualis and Epistemic Turning Points in the History of Sexuality', History of the Human Sciences 23 (2010), in press.\n\n15. For important examples in the history of the French life sciences, see Toby A. Appel, The Cuvier\u2013Geoffroy Debate: French Biology in the Decades before Darwin (New York: Oxford University Press, 1987); John Farley and Gerald L. Geison, 'Science, Politics and Spontaneous Generation in Nineteenth-Century France: The Pasteur\u2013Pouchet Debate', Bulletin of the History of Medicine 48 (1974), pp. 161\u201398.\n\n16. Robert H. van Gulik, Sexual Life in Ancient China (Leiden: Brill, 1974); Xiaomingxiong, Zhongguo tongxing'ai shilu (Hong Kong: Fenhong sanjiao chubanshe, 1984); Bret Hinsch, Passions of the Cut Sleeve: The Male Homosexual Tradition in China (Berkeley: University of California Press, 1990). For a lucid analysis that situates Xiaomingxiong's study in proper historical context, see Helen Leung, 'Archiving Queer Feelings in Hong Kong', Inter-Asia Cultural Studies 8 (2007), pp. 559\u201371.\n\n17. Matthew Sommer, Sex, Law, and Society in Late Imperial China (Stanford: Stanford University Press, 2000). For earlier works that look at the legal construction of sodomy in China, see Marinus J. Meijer, 'Homosexual Offences in Ch'ing Law', T'oung Pao 71 (1985), pp. 109\u201333, reprinted in Wayne R. Dynes and Stephen Donaldson (eds), Asian Homosexuality (New York and London: Garland, 1992); Vivian W. Ng, 'Ideology and Sexuality: Rape Laws in Qing China', Journal of Asian Studies 46 (1987), pp. 57\u201370; Vivian W. Ng, 'Homosexuality and State in Late Imperial China', in Martin B. Duberman, Martha Vicinus and George Chauncey (eds), Hidden from History: Reclaiming the Gay and Lesbian Past (New York: New American Library, 1989), pp. 76\u201389.\n\n18. I distinguish 'styles of argumentation' from 'styles of reasoning' more carefully in the conclusion. See also note 109.\n\n19. Arnold I. Davidson, The Emergence of Sexuality: Historical Epistemology and the Formation of Concepts (Cambridge: Harvard University Press, 2001), p. 36.\n\n20. Davidson, Emergence of Sexuality, p. 37.\n\n21. David M. Halperin, How to Do the History of Homosexuality (Chicago: University of Chicago Press, 2002), p. 131.\n\n22. See e.g., Prasenjit Duara, Rescuing History from the Nation: Questioning Narratives of Modern China (Chicago: University of Chicago Press, 1995); Rebecca Karl, Staging the World: Chinese Nationalism at the Turn of the Twentieth Century (Durham: Duke University Press, 2002); Karl Gerth, China Made: Consumer Culture and the Creation of the Nation (Cambridge: Harvard University Press, 2003); Tsu, Failure, Nationalism, and Literature.\n\n23. Prasenjit Duara, Sovereignty and Authenticity: Manchukuo and the East Asian Modern (Lanham: Rowman and Littlefield, 2003), pp. 3, 6 n. 6.\n\n24. Tani E. Barlow, 'Introduction: On \"Colonial Modernity\"', in Tani E. Barlow (ed.), Formations of Colonial Modernity in East Asia (Durham: Duke University Press, 1997), pp. 1\u201320, here p. 6.\n\n25. See Rogaski, Hygienic Modernity.\n\n26. For a recent reflection on the problem of Chinese self- or re-orientalisation, see Chu Yiu-Wai, 'The Importance of Being Chinese: Orientalism Reconfigured in the Age of Global Modernity', Boundary 2 35 (2008), pp. 183\u2013206. For an informative set of essays dealing with the problem of 'alternative modernity' in the context of modern Chinese history, see Madeleine Yue Dong and Joshua Goldstein (eds), Everyday Modernity in China (Seattle: University of Washington Press, 2006).\n\n27. In addition to the works cited above, other notable examples include Dorothy Ko, Cinderella's Sisters: A Revisionist History of Footbinding (Berkeley: University of California Press, 2005); Afsaneh Najmabadi, Women with Mustaches and Men without Beards: Gender and Sexual Anxieties of Iranian Modernity (Berkeley: University of California Press, 2005); Dror Ze'evi, Producing Desire: Changing Sexual Discourse in the Ottoman Middle East, 1500\u20131900 (Berkeley: University of California Press, 2006).\n\n28. See e.g., Dennis Altman, 'Rupture or Continuity? The Internationalization of Gay Identities', Social Text 14 (1996), pp. 77\u201394; Dennis Altman, 'Global Gaze\/Global Gays', GLQ: A Journal of Lesbian and Gay Studies 3 (1997), pp. 417\u201336; Peter Drucker, 'Introduction: Remapping Sexualities', in Peter Drucker (ed.), Different Rainbows (London: Gay Men's Press, 2000), pp. 9\u201342; Linda Garber, 'Where in the World Are the Lesbians?', Journal of the History of Sexuality 14 (2005), pp. 28\u201350; Afsaneh Najmabadi, 'Beyond the Americas: Are Gender and Sexuality Useful Categories of Analysis?', Journal of Women's History 18 (2006), pp. 11\u201321; Evelyn Blackwood, 'Transnational Discourses and Circuits of Queer Knowledge in Indonesia', GLQ 14 (2008), pp. 481\u2013507; Peter A. Jackson, 'Capitalism and Global Queering: National Markets, Parallels among Sexual Cultures, and Multiple Queer Modernities', GLQ 15 (2009), pp. 357\u201395; and my reappraisal of similar issues in Howard Chiang, 'Empire of Desires: History and Queer Theory in an Age of Global Affect', Critical Studies in History 1 (2008), pp. 50\u201371, reprinted in InterAlia: A Journal of Queer Studies 3 (2009).\n\n29. Michel Foucault, The Archeology of Knowledge and the Discourse on Language, tr. A. M. Sheridan Smith (1969; New York: Pantheon, 1972), p. 190.\n\n30. The edition that I rely on for this article is Zhang Jingsheng, Xingshi 1926 (Taipei: Dala, 2005).\n\n31. Paul Bailey, Reform the People: Changing Attitudes towards Popular Education in Early 20th Century China (Edinburgh: Edinburgh University Press, 1990), p. 236.\n\n32. Zhang Jingsheng, Meide renshengguan, in Jiang Zhongxiao (ed.), Zhang Jingsheng wenji, vol. 1 (Guangzhou: Guangzhou chubanshe, 1998), pp. 24\u2013138; Zhang Jingsheng, Meide shehui zuzhifa, in Jiang (ed.), Zhang Jingsheng wenji, vol. 1, pp. 139\u2013264. On Zhang's eugenic perspective, see Charles Leary, 'Intellectual Orthodoxy, the Economy of Knowledge, and the Debate over Zhang Jingsheng's Sex Histories', Republican China 18 (1994), pp. 99\u2013137; Leary, 'Sexual Modernism in China'; Sakamoto, 'The Cult of \"Love and Eugenics\"'; Lee, 'Governmentality and the Aesthetic State'; Tsu, Failure, Nationalism, and Literature, pp. 128\u201366; Wang, Jiaoyu zhuanxing zhi jing, pp. 249\u201365.\n\n33. Zhang Jingsheng, 'Yige hanjia de zuihao xiaoqian fa', reprinted in Zhang, Xingshi, pp. 24\u20137.\n\n34. Zhang, Xingshi, p. 26.\n\n35. Zhang, Xingshi, p. 31.\n\n36. Zhang, Xingshi, p. 31.\n\n37. Zhang, Xingshi, p. 27.\n\n38. See Hsiao-Yen Peng, 'Sex Histories: Zhang Jingsheng's Sexual Revolution', in Peng-hsiang Chen and Whitney Crothers Dilley (eds), Critical Studies: Feminism\/Femininity in Chinese Literature (Amsterdam: Rodopi, 2002), pp. 159\u201377.\n\n39. See Zhang Jingsheng, 'Disanzhong shui yu luanzhu ji shengji de dianhe yousheng de guanxi', New Culture (Xin wenhua; hereafter XWH) 1\/2 (February 1927), pp. 23\u201348. Zhang claims that there is even a 'fourth kind of water' produced inside the uterus\/womb. See Zhang, 'Disanzhong shui', p. 26; Zhang Jingsheng, 'Xingyu tongxin', XWH 1\/2 (February 1927), p. 111.\n\n40. Chai Fuyuan, Xingxue ABC (Shanghai: Shijie shuju, 1928), p. 42.\n\n41. On 'vaginal breathing', see e.g., Zhang Jingsheng, 'Xingbu huxi', XWH 1\/4 (May 1927), pp. 21\u201332; Zhang Jingsheng, 'Xingbu yu dantian huxi', XWH 1\/5 (July 1927), pp. 1\u201323.\n\n42. Zhang, Xingshi, pp. 110\u201311.\n\n43. Konggu, 'Tongxun', XWH 1\/1 (January 1927), p. 49.\n\n44. Zhengyi, 'Tongxun', XWH 1\/1 (January 1927), p. 47.\n\n45. Shifen, 'Tongxun', XWH 1\/1 (January 1927), p. 51.\n\n46. He Zhifen, 'Xingyu tongxin', XWH 1\/2 (February 1927), p. 100.\n\n47. Xu Jingzai, 'Xingyu tongxin', XWH 1\/3 (March 1927), pp. 59\u201363.\n\n48. On requests for a 'male-centered perspective', see Nan Xi, 'Xingyu tongxin', XWH 1\/3 (March 1927), pp. 66\u20137; Zhi Jun, 'Xingyu tongxin', XWH 1\/3 (March 1927), p. 73. For examples of frustration with the impracticality of Zhang's theory, see Chang Xuan, 'Xingyu tongxin', XWH 1\/3 (March 1927), pp. 69\u201370; Kuang Sheng, 'Xingyu tongxin', XWH 1\/3 (March 1927), p. 71.\n\n49. Su Ya, '\"Xing\" zhishi pupian le jiu meiyo \"qiangjian\"', XWH 1\/2 (February 1927), p. 104.\n\n50. Miss Qin Xin, 'Tongxing lian'ai taolun', XWH 1\/3 (March 1927), pp. 63\u20136, here p. 63.\n\n51. SSD, 'Xingyu tongxin', XWH 1\/3 (March 1927), pp. 71\u20133.\n\n52. Tang Hao, 'Lian'ai yu xing de jiqiao zhi meishuhua', Sex Magazine (Xing Zazhi; hereafter XZZ) 1\/2 (June 1927), pp. 1\u20136, here p. 1 (my emphasis).\n\n53. For a discussion of the epistemic tension between Kinsey's statistical notion of sexual normality and American psychiatrists' framework of psychopathology around the mid-twentieth century, see Howard Chiang, 'Effecting Science, Affecting Medicine: Homosexuality, the Kinsey Reports, and the Contested Boundaries of Psychopathology in the United States, 1948\u20131965', Journal of the History of the Behavioral Sciences 44 (2008), pp. 300\u201318.\n\n54. Leon Rocha, 'Zhang Jingsheng's Utopian Project' (paper presented at the 81st Annual Meeting of the American Association for the History of Medicine, Rochester, New York, 11\u201313 April 2008).\n\n55. Han, 'Wuhu! Zhang Jingsheng de luanzhu', XZZ 1\/1 (April 1927), pp. 1\u20133, here p. 2. Another writer for the periodical devoted twelve pages to a discussion of 'what the third kind of water exactly is' and concluded that 'Professor Zhang's understanding of the third kind of water as the secretion of the Bartholin glands is obviously incorrect'. See Qianqian, 'Disan zhongshui de yanjiu', XZZ 1\/2 (June 1927), pp. 1\u201312, here p. 10.\n\n56. See e.g., Zhang Jingsheng, 'Da Zhou Jianren xiansheng \"Guanyu Xingshi de jiju hua\"', Ordinary (Yiban) (November 1926), reprinted in Jiang (ed.), Zhang Jingsheng wenji, vol. 2, pp. 420\u201322; Zhou Jianren, 'Da Zhang Jingsheng xiansheng', Ordinary (November 1926), reprinted in Jiang (ed.), Zhang Jingsheng wenji, vol. 2, pp. 423\u20136; Yang Guanxiong, Xing jiaoyu fa (Shanghai: Liming shuju, 1930), pp. 150, 166. The only biography of Zhou to date is in Chinese: see Yang Dexian, Zhou Jianren pingzhuan (Chongqing: Chongqing chubanshe, 1991).\n\n57. L\u00fc, Pan Guangdan tuzhuan, p. 46.\n\n58. Daniel J. Kevles, In the Name of Eugenics: Genetics and the Uses of Human Heredity (New York: Alfred A. Knopf, 1985), p. 45.\n\n59. Kevles, In the Name of Eugenics, pp. 45\u20136.\n\n60. Pan Guangdan, Zhongguo lingren xieyuan zhi yanjiu (Shanghai: Commercial Press, 1941), reprinted in Pan Guangdan wenji, vol. 2 (Beijing: Peking University Press, 1994), pp. 73\u2013303. Pan has presented a similar view concerning Chinese musicians in an earlier article. See Pan Guangdan, 'Lujiang Huangshi de yinyuecai', Eugenics Monthly (Yousheng yuekan) 2\/2 (15 February 1932), reprinted in Pan Guangdan wenji, vol. 8, pp. 409\u201310. See also the impressive series of pedigrees that he constructed in 1937 and 1938: Pan Guangdan, Cunren xhuwu lishi renwu shixi biaogao, reprinted in Pan Guangdan wenji, vol. 4.\n\n61. Kevles, In the Name of Eugenics, p. 60.\n\n62. For Pan, individual and social health depended first and foremost upon heredity and not behaviour. He encouraged marriage and breeding among those deemed genetically superior, which would in turn strengthen the health of the nation. Both Frank Dik\u00f6tter's study on the Chinese conception of race and Ruth Rogaski's book on health and hygiene in Tianjin have situated the significance of Pan's eugenic visions within the larger social and cultural expressions of modernisation during the Republican period. See Dik\u00f6tter, Discourse of Race in Modern China; Rogaski, Hygienic Modernity, pp. 225\u201353. See also Chung, Struggle for National Survival.\n\n63. Frank Dik\u00f6tter, 'Eugenics in Republican China', Republican China 15 (1989), pp. 1\u201317.\n\n64. Pan Guangdan, 'Jinri zhi xingjiaoyu yu xingjiaoyuzhe', Shishi Xinbao Xuedeng (5 May, 14 June, 24 June 1927), reprinted in Pan Guangdan wenji, vol. 1, pp. 401\u201312, here pp. 402\u20133.\n\n65. Pan, 'Jinri zhi xingjiaoyu', p. 406.\n\n66. Zhang Jingsheng, 'Youchu yige guaitou', XWH 1\/4 (May 1927), pp. 126\u20138, here p. 126.\n\n67. Zhang, 'Youchu yige guaitou', p. 127.\n\n68. For other analyses of the debates between Zhang Jingsheng and people like Zhou and Pan on the proper meaning of 'sex science' and 'sex education', see Leary, 'Sexual Modernism in China', pp. 236\u201380; Chung, Struggle for National Survival; Wang, Jiaoyu zhuanxing zhi jing, pp. 267\u201374. On scientism in Republican China, see e.g., Wang Hui, 'Scientific Worldview, Culture Debates, and the Reclassification of Knowledge in Twentieth-Century China', Boundary 2 35 (2008), pp. 125\u201355.\n\n69. Yang Youtian, 'Tongxing'ai de wenti', Beixin 3\/2 (1929), pp. 403\u201339, here p. 403.\n\n70. One should also note that as the editor of New Culture, Zhang did publish several translated excerpts of Ellis's work (by himself or others) in the journal. One of these is an article on female homosexuality taken from Ellis's Sexual Inversion. See Xie Se (tr.), 'N\u00fc xuesheng de tongxing ai', XWH 1\/6 (1927), pp. 57\u201374. But in general, Zhang's effort in translating Ellis's work was neither as comprehensive nor as extensive as Pan's.\n\n71. Pan Guangdan (tr.), Xing xinli xue (Shanghai: Commercial Press, 1946), reprinted in Pan Guangdan wenji, vol. 12, pp. 197\u2013714.\n\n72. For an extensive study of this appendix, see Kang, Obsession, pp. 52\u20138.\n\n73. Pan, Xing xinli xue, p. 701.\n\n74. See e.g., Hu Buoken (tr.), Women de shenti (Shanghai: Kaiming shudian, 1933); Zhang Xishen (ed.), Xindaode taolunji (Shanghai: Liangxi tushuguan, 1925); Zhu Jianxia (tr.), Xing zhi shengli (Shanghai: Commercial Press, 1928), esp. pp. 108\u201313.\n\n75. My sources are replete with examples of this sort. See e.g., Cheng Hao, Jiezhi shengyu de wenti (Shanghai: Yadong tushuguan, 1925), pp. 148\u201353; Zhang Dongmin, Xing de chongbai (Shanghai: Beixin shuju, 1927), pp. 46\u20137; Bin (tr.), 'Tongxing'ai', Sex Science (Xing kexue; hereafter XKX) 1\/2 (January 1936), pp. 92\u20134; Zhou Guangqi, Xing yu fanzui (Shanghai: Zhenzhong shuju, 1936), p. 58.\n\n76. Kevles, In the Name of Eugenics, p. 53.\n\n77. Pan initially wrote a draft of this essay as a term paper for a history survey course taught by Liang Qichao at Qinghua University. See Nicole Huang, Women, War, Domesticity: Shanghai Literature and Popular Culture of the 1940s (Leiden: Brill, 2005), p. 181. He later revised it and published it as a book with additional material in 1929 after returning from the United States. Pan Guangdan, Feng Xiaoqin: Yijian yinglian zhi yanjiu, reprinted in Pan Guangdan wenji, vol. 1, pp. 1\u201366.\n\n78. Tsu, Failure, Nationalism, and Literature, pp. 98\u2013166; Lee, Revolution of the Heart, pp. 186\u2013217. On the importation of Freudian psychoanalysis in early twentieth-century China, see also Jingyuan Zhang, Psychoanalysis in China: Literary Transformations, 1919\u20131949 (Ithaca: Cornell University East Asia Program 1992); Dik\u00f6tter, Sex, Culture, and Modernity; Leo Ou-fan Lee, Shanghai Modern: The Flowering of a New Urban Culture in China, 1930\u20131945 (Cambridge: Harvard University Press, 1999); Shu-mei Shih, The Lure of the Modern: Writing Modernism in Semicolonial China, 1917\u20131937 (Berkeley: University of California Press, 2001).\n\n79. Lee, Revolution of the Heart, p. 189.\n\n80. Pan Guangdan (tr.), Xing de Jiaoyu (Shanghai: Qinnian xiehue shuju, 1934), reprinted in Pan Guangdan wenji, vol. 12, pp. 1\u201399, here p. 98.\n\n81. Pan Guangdan, 'Xingai zai jinri', Huanian 5\/45, 5\/49, 5\/50 (21 November, 19 December, 26 December 1936), reprinted in Pan Guangdan wenji, vol. 9, pp. 370\u201387, here pp. 375\u20136.\n\n82. Pan, Xing xinli xue, pp. 705\u20136.\n\n83. Sigmund Freud, Three Essays on the Theory of Sexuality, tr. and ed. James Strachey (1905; New York: Basic Books, 2000), pp. 10\u201311 n. 1.\n\n84. Pan Guangdan, 'Xingai zai jinri', p. 376.\n\n85. Gui Zhiliang, N\u00fcren zhi yisheng (Beijing: Zhengzhong shuju, 1936), pp. 63\u20136. But it seems that Gui did not entirely agree with Freud on the interpretations of other types of psychopathology. This is most evident in her textbook, Gui Zhiliang, Xiandai jingshen bingxue (Shanghai: Xinyue shudian, 1932). On Freud's view, see Henry Abelove, 'Freud, Male Homosexuality, and the Americans', in Henry Abelove, Michele Aina Barale and David M. Halperin (eds), The Lesbian and Gay Studies Reader (New York: Routledge, 1993), pp. 381\u201393; Davidson, Emergence of Sexuality, pp. 66\u201392.\n\n86. Chang Hong (tr.), 'Biantai xingyu yu qi liaofa', XKX 2\/1 (May 1936), pp. 3\u20137, here p. 4.\n\n87. Chang, 'Biantai xingyu', p. 6.\n\n88. Jian (tr.), 'Zhenzheng de tongxing'ai keyi zhiliao ma?', XKX 2\/4 (November 1936), pp. 4\u20138, here p. 6.\n\n89. Mo (tr.), 'Tongxing'ai de yanjiu he fangzhi', XKX 2\/4 (November 1936), pp. 15\u201326, esp. pp. 23\u20134.\n\n90. See Ping (tr.), 'Jiachong huo xide de tongxing'ai de tezhi', XKX 2\/4 (November 1936), pp. 9\u201311; Hong (tr.), 'N\u00fcxing de tongxing'ai he xing de biantai', XKX 2\/4 (November 1936), pp. 13\u201315. On sexuality in the prison environment, see also Xi Tuo (tr.), 'Meiguo qiufan de xing shenghuo', XKX 4\/1 (July 1937), pp. 51\u20137.\n\n91. Yang Kai, 'Xing de diandaozheng \u2013 tongxing'ai', XKX 2\/4 (November 1936), pp. 11\u201313, here p. 12.\n\n92. Chai, Xingxue ABC, p. 117.\n\n93. Mo, 'Tongxing'ai de yanjiu', p. 23.\n\n94. Kong Kongzhang (tr.), 'Xuesheng jian tongxing'ai yu fumu shizhang de jiaoyu', XKX 2\/4 (November 1936), pp. 2\u20134, here p. 3.\n\n95. There is evidence that the readers of these sexological writings very much shared this view. See e.g., Miss Qin Xin, 'Tongxing lian'ai taolun', pp. 64\u20136.\n\n96. Gui, Xiandai jingshen bingxue, p. 32.\n\n97. Translated and cited in Nathan Sivin, Traditional Medicine in Contemporary China (Ann Arbor: Center for Chinese Studies, University of Michigan, 1987), p. 98.\n\n98. This is the phrase that Ruth Rogaski uses to characterise discussions of sex in traditional Chinese medicine. See Rogaski, Hygienic Modernity, pp. 37\u201340.\n\n99. Charlotte Furth, 'Androgynous Males and Deficient Females: Biology and Gender Boundaries in Sixteenth- and Seventeenth-Century China', Late Imperial China 9\/2 (1988), pp. 1\u201331, here p. 6 (emphasis added). See also Paul Goldin, The Culture of Sex in Ancient China (Honolulu: University of Hawaii Press, 2002).\n\n100. Foucault, History of Sexuality, vol. 1, p. 58. For a fuller articulation of this problem, see also Howard Chiang, 'Double Alterity and the Global Historiography of Sexuality: China, Europe, and the Emergence of Sexuality as a Global Possibility', e-pisteme 2\/1 (2009), pp. 33\u201353, reprinted as 'The Historical Formation of Sexuality: Europe, China, and Epistemic Modernity Global', Critical Studies in History 2 (2009), pp. 2\u201318; Chiang, 'Liberating Sex, Knowing Desire'. For another in-depth study of Republican Chinese scientia sexualis, see Howard Chiang, 'The Conceptual Contours of Sex in the Chinese Life Sciences: Zhu Xi (1899\u20131962), Hermaphroditism, and the Biological Discourse of Ci and Xiong, 1920\u20131950', East Asian Science, Technology and Society: An International Journal 2 (2008), pp. 401\u201330.\n\n101. In some ways, Sean Lei has done something similar for statements about 'experience' in the history of Chinese medicine. See Sean Hsiang-lin Lei, 'How Did Chinese Medicine Become Experiential? The Political Epistemology of Jingyan', Positions 10 (2002), pp. 334\u201364.\n\n102. Zhang, Xing kexue, p. 78.\n\n103. Zhang, Xing kexue, p. 75.\n\n104. Yang, 'Tongxing ai de wenti', p. 436.\n\n105. Pan, Xing xinli xue, pp. 708\u20139. See also Pan, Zhongguo lingren xieyuan zhi yanjiu, pp. 255\u20138.\n\n106. Wang Yang, Fufu xing weisheng (Shanghai: Zhongyang shudian, 1935), pp. 49, 53.\n\n107. Lydia Liu, Translingual Practice: Literature, National Cutlure, and Translated Modernity \u2013 China, 1900\u20131937 (Stanford: Stanford University Press, 1995); Lydia Liu (ed.), Tokens of Exchange: The Problem of Translation in Global Circulations (Durham: Duke University Press, 1999).\n\n108. On the association of male homosexual practice with national backwardness in the Republican period, see also Kang, Obsession, pp. 115\u201344; Cuncun Wu and Mark Stevenson, 'Male Love Lost: The Fate of Male Same-Sex Prostitution in Beijing in the Late Nineteenth and Early Twentieth Centuries', in Fran Martin and Larissa Heinrich (eds), Embodied Modernities: Corporeality, Representation, and Chinese Cultures (Honolulu: University of Hawaii Press, 2006), pp. 42\u201359.\n\n109. On the epistemological applicability of 'style', see also Howard Chiang, 'Rethinking \"Style\" for Historians and Philosophers of Science: Converging Lessons from Sexuality, Translation, and East Asian Studies', Studies in History and Philosophy of Biological and Biomedical Sciences 40 (2009), pp. 109\u201318.\n\n110. Prasenjit Duara, 'The Regime of Authenticity: Timelessness, Gender, and National History in Modern China', History and Theory 37 (1998), pp. 287\u2013308. On the complicated historical layering of the dan figure, see John Zou, 'Cross-Dressed Nation: Mei Lanfang and the Clothing of Modern Chinese Men', in Martin and Heinrich (eds), Embodied Modernities, pp. 79\u201397; Joshua Goldstein, Drama Kings: Players and Publics in the Re-Creation of Peking Opera, 1870\u20131937 (Berkeley: University of California Press, 2007).\n\n111. For a classic discussion of the transformation from 'culturalism' to 'nationalism' in the Chinese political sphere, see Joseph R. Levenson, Confucian China and Its Modern Fate: A Trilogy (Berkeley: University of California Press, 1965).\n\n112. Zhang Dai, Tao'an mengyi (Shanghai: Shanghai shudian, 1982), pp. 35\u20136, as translated [with my own modifications] and cited in Cuncun Wu, Homoerotic Sensibilities in Late Imperial China (London and New York: RoutledgeCurzon, 2004), pp. 42\u20133.\n\n113. I am aware of Sophie Volpp's astute critique of historians' tendency to read literary accounts of male homoeroticism as evidence of its greater social tolerance in late Ming China. See Sophie Volpp, 'Classifying Lust: The Seventeenth-Century Vogue for Male Love', Harvard Journal of Asiatic Studies 61 (2001), pp. 77\u2013117; Sophie Volpp, 'The Discourse on Male Marriage: Li Yu's \"A Male Mencius's Mother\"', Positions 2 (1994), pp. 113\u201332; Sophie Volpp, 'The Literary Circulations of Actors in Seventeenth-Century China', Journal of Asian Studies 6 (2002), pp. 949\u201384. In many ways, Volpp supports Timothy Brook's argument that male homoeroticism was fashionable only among a small class of male literati elites. See Timothy Brook, The Confusions of Pleasure: Commerce and Culture in Ming China (Berkeley: University of California Press, 1998), pp. 229\u201333. In contrast, Giovanni Vitiello argues that 'male homoeroticism in late Ming culture can best be appraised when placed within the broader context of male homosociality. By relegating homoeroticism to elite or isolating it from other discourses on male relations and by stressing its ephemerality, we risk failing to appreciate its place and ramifications within the plot of late Ming culture and beyond'. Giovanni Vitiello, 'Exemplary Sodomites: Chivalry and Love in Late Ming Culture', Nan N\u00fc 2\/2 (2000), pp. 207\u201358, here p. 256. In other words, the emphasis need not be on the practice or description of homoeroticism per se, but the wider cultural context that was congenial for its literary or social expression. To me, whether same-sex behaviour was only practised among a small class of male elites or was much more culturally pervasive in late imperial China remains an interesting debate. I should emphasise, however, that my concern does not rest strictly on the level of social acceptance or tolerance of same-sex intimacy. In quoting the above passage by Zhang Dai, my more immediate task in this chapter has been to study the epistemological reconfiguration of same-sex desire in China. On a related note, historian Wenqing Kang has argued that preexisting Chinese ideas about male favorites and pi 'laid the ground for acceptance of the modern western definition of homo\/heterosexuality during [the Republican] period in China'. His first explanation is that 'both the Chinese concept pi (obsession) and western sexology tended to understand same-sex relations as pathological'. He then relies on Eve Sedgwick's model of the overlapping 'universalizing discourse of acts and minoritizing discourse of persons' to show that indigenous Chinese understandings shared a comparable internal contradiction in the conceptualisation of male same-sex desire. In his words, 'The concept pi which Ming literati used to characterize men who enjoyed sex with other men, on the one hand implied that men who had this kind of passion were a special type of people, and on the other hand, presumed that the obsession could happen to anyone'. My reading of Zhang Dai's passage on pi suggests that isolating both a pathological meaning and this internal conceptual contradiction of pi represents an anachronistic effort that reads homosexuality into earlier modes of thought. Zhang's remark precisely reveals the multiplicity of the meaning and cultural significance of pi that cannot be comprehended through a single definition of pathology or an independent lens of same-sex relations decontextualised from other types of refined human desire. Treating the discursive nature of discourse seriously necessitates paying closer attention to how old words take on a new meaning (and a new life) in a different historical context, rather than imposing later familiar notions on earlier concepts. Kang, Obsession, p. 21. For Sedgwick's original formulation, see Eve K. Sedgwick, Epistemology of the Closet (Berkeley: University of California Press, 1990). My disagreement with Kang in part can be viewed as the resurfacing of an earlier debate between Sedgwick and David Halperin, with whom my analysis sides, on the genealogy of homosexuality in western culture. For Halperin's response to Sedgwick, see Halperin, How to Do the History of Homosexuality.\n\n114. Harriet Evans, Women and Sexuality in China: Female Sexuality and Gender since 1949 (New York: Continuum, 1996), p. 206.\n\n115. Lu Huaxin, Shaonan shaon\u00fc xingzhishi (Hong Kong: Xuewen shudian, 1955), p. 53.\n\n116. Lu, Shaonan shaon\u00fc xingzhishi, p. 53.\n\n117. Lu, Shaonan shaon\u00fc xingzhishi, p. 54.\n\n118. I am being careful and specific when discussing 'marriage to a member of the opposite sex', because other scholars have unearthed the popularity of same-sex 'marriages' in eighteenth-century China, especially in the region of Fujian. See Michael Szonyi, 'The Cult of Hu Tianbao and the Eighteenth-Century Discourse of Homosexuality', Late Imperial China 19\/1 (1998), pp. 1\u201325.\n\n119. Larissa Heinrich, The Afterlife of Images: Translating the Pathological Body between China and the West (Durham: Duke University Press, 2008).\n\n120. In Obsession, Kang has refrained from advancing a claim about the occasioning of an epistemological break in the Republican era by showing that earlier concepts associated with male same-sex sexual practice (e.g., nanse or pi) jostled alongside and informed the new sexology discourse. But, again, I would argue that the congruency between earlier and later understandings of same-sex practice is itself a cultural phenomenon unique to the Republican period and not before (see note 113). Despite how Pan Guangdan's condemnation of the homosexuality of dan actors (and their patrons) was informed by the long-standing and still-continuing practices of male prostitution, his condemnation was made possible (and comprehensible) only by the arrival of a psychiatric style of reasoning that construed same-sex relations in stigmatising terms. Therefore, Chinese sexologists' establishment of an epistemic continuity between the foreign concept of homosexuality and earlier examples of homoeroticism does not undermine the kind of Foucauldian epistemological rupture this chapter substantiates, but actually exemplifies it.\nChapter 6\n\nOvercoming 'Simply Being': Straight Sex, Masculinity and Physical Culture in Modern Egypt\n\nWilson Chacko Jacob\n\nDear Cupid:\n\nI am a young man twenty-three years of age who is a foreigner in these lands. I began my working life at sixteen, that is, at puberty, and I used to think a lot about increasing my knowledge of the second sex at that time. Since then, sexual feelings have been raging through me. However, I was so shy my heart would start beating rapidly at the thought of speaking to a girl, even if it were just polite conversation. I slept in my own room and after my parents locked all the doors I'd spend the nights staying up. Some nights I'd stand at the window after midnight hoping to find women passing by alone or accompanied by a young man. If my wish were fulfilled, then I'd curse them both for their freedom and for enjoying [their] love safe from the eyes of censors. Then my blood would boil and I'd become like a madman. I sought freedom. Not much time had passed with me in this state before I was struck with fits of coughing, my body grew thin, and my eyes became hollow. I attracted pity from the family. I was always nervous about doctors prescribing too much medication with no benefit, so I travelled to Cairo with its renowned doctors and stayed for nearly six months.1\n\nThese are the first tortured lines penned by 'A.Y.D.' (alif ya dal) in a long letter dispatched from 'the extreme western border of Sudan', sent to the Egyptian magazine Physical Culture (al-Riyada al-badaniyya) and published in March 1936.2 The young man's epistle, titled 'A Voice from Unknown Africa', occupied more than three full pages of a letters section called 'What Would You Do in this Situation?'3 Physical Culture began publication in 1929, continuing until the early 1950s.4 A.Y.D.'s letter was one of hundreds from readers with similar concerns about love, sex and intimate relationships published in the magazine during the course of the highly unstable decade of the 1930s. Indeed, during different phases of its lifespan, the magazine featured multiple letters sections in the same issue; for example, appearing alongside 'What Would You Do in this Situation?' was a 'Health Advice' section fielding questions on exercise, masturbation and venereal diseases, where answers were proffered by none other than 'Hippocrates'.\n\nThis chapter considers Physical Culture as an artefact of colonial modernity, as a watermark of an ineffable style of performing gender and sexuality that has been in emergence all over the world since the second half of the nineteenth century.5 Accordingly, and ignoring its own protestations to the contrary, the magazine's national character is not explored here except to indicate the extent to which 'Egypt' appeared to contemporaries as a problematic limit to the materialisation of a universal subject of physical culture.6 In other words, that the actual cultivation of healthy and desirable bodies was constrained by Egypt's asymmetrical location in a global economic and political order constituted by colonialism was a well-established fact of social life by the end of the 1920s; consequently, the problem of the modern subject in Egypt was posed in terms that were not exclusively nationalist and examined in terms that were keenly attuned to the circulation of global cultural forms and discursive practices. Thus, precisely because many of the trappings of capitalist modernity and national sovereignty were absent from the Egyptian landscape, Physical Culture contributed to the vibrant public culture of the interwar period a forum in which the fantasy of the modern sovereign subject could be expressed in myriad ways that most frequently centred on a proper conception of sex and masculinity.7\n\nThree interrelated themes are examined here, all of which directly or indirectly address the problematic of deploying gender and sexuality as analytical categories across time and space, the special theme of this volume. I argue that Physical Culture constituted a virtual community of Arabic-speaking bourgeois subjects simultaneously inhabiting national, colonial and diasporic spaces; that sex was the grounding discourse tacking together these otherwise non-contiguous locations; and that gender formed the problem space of modernity as a civilisational norm. In a more speculative manner, this chapter also considers the point at which gender and sexuality as modern discourses confront their 'pre-modern' others, life forms that defy the terms of intelligibility of those discourses. To that end, I question this cultural medium shaped under the terms of colonial modernity about its silences: what was suppressed or subtracted in order thereby to produce an intelligible subject of the modern world, and do the exclusive terms of that discourse unwittingly repeat themselves in the historical narrative, which is itself a cultural form of a similar genealogy?\n\nBetween pedagogic and performative modernity: the subject of Physical Culture8\n\nTime for a new magazine\n\nIn late 1927, the lawyer Muhammad Fa'iq al-Jawhari and his brothers, Mukhtar and Ra'uf, opened the Physical Education Institute (ma'had al-tarbiyya al-badaniyya). In the same year, the Young Men's Muslim Association, with its own athletic facilities, was established not far from their location at 28 Sharia Fuad in Cairo.9 The following year, the brothers launched the monthly magazine Physical Culture. Its main focus was the care of the body \u2013 the literal translation of the Arabic expression al-riyada al-badaniyya. Under this rubric, the editor, Muhammad al-Jawhari, made it the magazine's mission to educate the Egyptian reading public about sex, love and physical beauty. Although the figure of the nation certainly made regular appearances as a legitimising trope, the magazine was part of a much broader modernist project and was intensely conscious of its role as a 'technology' in the process of self-fashioning.10\n\nThat consciousness was long in the making, the product of a complex apparatus of physical culture that had begun to take shape in the late nineteenth century and was by the mid-1920s a normal part of Egyptian social life serving as a marker of the emergent effendiyya class. The members of this class were professionals, government civil service employees, students, those occupied in the new business trades, and their spouses, sons and daughters.11 Physical culture was a story of the effendiyya's formation as a gendered site of bourgeois culture as much as it was a story of colonialism and nationalism.12 It took root in the 1880s and 1890s, as anti-colonial nationalists and reformers diagnosed the weak and sick bodies of Egyptian men as the cause of their subjugation by another power, and saw in physical culture a panacea for all the nation's ills.13 From the start, the engagement with practices and ideas associated with physical culture had a dynamic of its own apart from its ideological deployments, which ensured its proliferation and popularity.14 Indeed it was at its height after Egypt was granted nominal independence in 1922. While it would be easy to attribute this expansion of the field of physical culture to the rise of new social forms that were an outcome of the intersection of global capitalism and colonial modernity, an analysis of the magazine Physical Culture demonstrates the need for caution when explaining its determinations exclusively in terms of the social.\n\nWhile there are no circulation figures available, the provenance of the magazine's letters to the editor suggests an impressive distribution.15 The intended audience was quite clearly the effendiyya and its cognates in other global locations. It was read in every major city and several smaller towns throughout Egypt. Beyond Egypt, the letters to the editor suggest that it had readers in Sudan, Palestine, Jordan, Lebanon, Syria, Iraq and Bilad al-Arab (Arabian peninsula). The magazine may have circulated even among the Arabic-speaking diaspora in far-flung places like Brazil, Gambia, Sierra Leone and India.\n\nWithin Cairo (the most historically verifiable segment of the magazine's readership), the urban geography that was the proximate setting for the birth of Physical Culture had changed dramatically. The street on which the Jawharis established their institute in 1927 was a major artery in the heart of modern Cairo. By the First World War, the city had already experienced significant growth in terms of built space due to the expansion of habitable land through the construction of the first Aswan Dam in 1902 and an extensive tramway system by 1917. But it was after the war that Cairo truly became a major city in terms of population and geography. The demographic expansion of Cairo's population, matched by a startling expansion of its built space, created new administrative and policing concerns as well as new ways of imagining the city, which I explore extensively elsewhere.16 Significant additions to the urban landscape and urban culture included new kinds of spaces \u2013 the department store, the movie theatre, the theme park \u2013 and an expansion of the number of cafes and nightclubs. The tramway system enabled the geographic growth of Cairo and transformed physical movement within the city into an entirely new practice for all classes; by the end of the war, the system served 75 million passengers a year.17\n\nA self to call modern\n\nHow did the modern fantasy of a self-governing body within colonial space appear in a place like Egypt? From the evidence provided by Physical Culture, one could use labels like masculinist, patriarchal and heterosexist \u2013 not to mention classist and racist \u2013 but these should be avoided for now in order to bypass the conventional referent of such signifiers: the history of a Euro-American social order. This is easier said than done given the magazine's self-conscious mimicry of the terms, logics and vision deployed by metropolitan social-scientific discourses.\n\nThe last issue that I have of the magazine dates from October 1940, although in that issue the editor set forth his plan to launch an expanded version of the magazine in 1941. Arguably, the longevity of this 'sports' magazine \u2013 at a time when the lifespan of a new periodical often did not exceed a few months \u2013 was due precisely to its treatment of a controversial subject like sex. The magazine was organised into scientific sections presenting articles on health, sports and sex (abhath sihhiyya, abhath riyadiyya and abhath jinsiyya) and into fictional\/autobiographical sections presenting stories and letters from readers concerning love and marriage. Photographs of readers and of luminaries in the physical culture domain were often printed alongside articles and letters as illustrations of exercises, examples of achievement of goals and so forth.\n\nThe majority of the articles that pertain to sexuality, including the letters and stories, can be grouped along an axis that spans the distance between permissible desire and correctable deviance. In the letter with which we began this chapter, A.Y.D. continued by elaborating for the readers of Physical Culture the depths of his moral depravity and the resultant physical suffering he endured.18 Indeed the young man averred that he was only able to find his way back to the straight and narrow when he started reading Physical Culture. A concerned friend had mailed him some back issues of the magazine from 1933 and 1934, while he was hospitalised for a lengthy period after contracting a severe case of gonorrhea:\n\nI started to read through it and quickly fell in love with it. When I could finally leave the hospital, I was filled by this truthful idea [al-fikra al-sahiha] about life. I read a lot about harmful habits and the excesses of sexual relations; I found in front of me a guide to show me the way \u2013 through honest information about the second sex, which I had been yearning to learn. I left the hospital in better health, and I made the issues of Physical Culture my first priority. I used to read it every day, mastering the exercises. I got used to showering in cold water daily followed by a massage and sunbathing in the nude. My health improved and my weight increased from 122 pounds to 134 in less than two months. I also made friends who would play sports and take long walks with me.19\n\nAlthough the author of this letter appeared to have resolved his sexual crisis through the ingestion of new knowledge about sex and the practice of alternative physical activities, he remained in an ethical dilemma. Before becoming ill, he believed he had impregnated a woman he was in love with and with whom he was having a sexual relationship. After an initial period of confusion and as the news of her pregnancy began to spread, they agreed (according to the author it was a mutual decision) to maintain a distance. In fact, the author claimed his lover insisted that he move on and that he seek another companion. And being ever so compliant, this was how he found himself in the hospital with gonorrhoea. However, after leaving the hospital, he learned that his lover had delivered a black ('abd) baby who had 'a broad nose like the uncircumcised (qalalif) and eyes like the devil' \u2013 most definitely not his son:\n\nHere is where I ask you for the answer, Mr Cupid, or the honourable male readers \u2013 not females \u2013 to the [question]: Is it correct to subscribe to Schopenhauer's philosophy, mentioned in the November 1935 issue of your magazine, on women, their wiles, short-sightedness and ignorance \u2013 that all that was given to women in terms of talent are cunning and deception in order to be wooed and courted; she does not strive for the capacity to benefit humanity [al-insaniyya], rather to extract from a man an expression of interest in her so that she can reign over him. I ask you for a reply to this problem of mine. It will determine what I will do with this woman. Present [the problem] to them. Tell them that I haven't forgotten that my relationship with her was illicit, but they need to overlook whether it was licit [mashru'a] or illicit [ghayr mashru'a] and look at the issue from the perspective of a purely sexual relationship, which, if it takes hold of a young man leaves him no room to think about what is licit and illicit. So, does a woman deserve all of our respect and reverence and does she deserve that we submit our hearts to her in love and trust her with this love or with our offspring? Answer this question dear sir for it is the source of my problem, my confusion, and my misery.20\n\nNormally the responses of the readers and Cupid's own evaluation of the situation would appear in the following issue of the magazine. Unfortunately, I did not have access to a copy of Physical Culture from April 1936, so the reactions to A.Y.D.'s situation must remain a mystery for now.21 Nevertheless, it is safe to say that compared to others, the richness of this letter in terms of detail must have provoked a massive response from readers. There were nearly a thousand responses to another situation that was far less interesting, a case of marital infidelity in which the wife wanted to know from the public if she should stay with her cheating husband who her family was pressuring her to leave. The majority (790) enjoined 'Mrs S' to persevere and patiently reform her husband's ways by making herself more attractive to him! It is perhaps important to note that 185 respondents did encourage her to leave her husband.22 Readers' letters came from far and wide; one Abu al-Abbas Ahmad al-Attar from Bombay was awarded fifth prize for his opinion. First prize went to an unnamed male reader who confessed to having been in her husband's shoes; he advised her to remain the devoted wife and to try to obtain a transfer for her husband so they could move to another town.23\n\nIt was Cupid's role as the forum moderator to select the best solutions or analyses of the preceding month's problem and to award their authors prizes, ranging from one Egyptian pound for first place to various publications relevant to physical culture for second, third and so on. When this letters format was introduced in 1931, for the first few issues the magazine's editors ran the following explanatory note about the new forum which they labelled 'A Parliament for Readers': 'Do the people... around you understand you and do they provide you with compassion and support when you need it? If your answer was in the negative then you are in need of Cupid. He is ready to serve you in times of confusion, pain, and unhappiness'.24 Mrs S, like numerous others, certainly felt that her family did not understand her and turned to this virtual community of strangers for 'compassion and support'. According to the editors, Cupid answered most of the letters privately, and only the most 'complicated' problems were published. Indeed, the problems were sometimes too complicated for this 'parliament' to resolve.\n\nIn the same issue in which A.Y.D.'s letter was presented to the Physical Culture audience, the readers responded to a young woman's problem from a previous issue. Very briefly, this young woman had developed intense feelings for a classmate during their school years together. When the classmate went on to get married, she discovered that her feelings must be love since she had never been attracted to any of the boys she knew and since the thought of her friend betrothed to a man appeared to her as a loss that was utterly devastating. In this case, which Cupid billed a 'psychological problem deserving study and analysis', none of the responses were deemed to be a 'useful solution' and most were dismissive of her situation, although Cupid does add that several young women wrote in indicating how they could 'understand her psyche' and offered their consolation.25\n\nExperts: talking sex and gender\n\nA primary concern \u2013 it would not be an exaggeration to say an obsession \u2013 of the magazine evident in practically every issue was the problem of abnormality and the possibility of straight sex. In general, the domain of 'sexual deviancies' was delimited according to Physical Culture's mission to promote sex education (al-tarbiyya al-jinsiyya), hence the targets were most often masturbation and venereal diseases.26 Unsurprisingly, medical expertise \u2013 foreign and Egyptian \u2013 was regularly marshalled to demonstrate the harms of sexual activity outside the legitimate bonds of marriage. In the interwar period, scientific knowledge established itself as both the legitimate mode of inquiry into matters of concern for the nation and a means of legitimation: at times for nationalist politics but perhaps more importantly, in the long term, for the constitution of the social as the location of private problems ranging from agricultural techniques to reproduction.27 It is against this backdrop and through the frequent appearances of their articles and interviews in popular forums like Physical Culture that figures like Dr Fakhri Faraj and Dr Sabri Jirjis became familiar household names and images.28 The space that these figures occupied was at once a new public sphere of expanding media forms (print, radio and cinema) and a contested terrain of truth claims in which once hegemonic Islamic modalities of knowledge production were forced onto the defensive, muted or pressed into the service of modernist projects like Physical Culture.29\n\nIn a 1932 interview with Dr Faraj, he was presented to the readers as a pioneer in Egyptian medicine who had long called and worked for sex education.30 He launched his crusade in 1921 with a lecture at the Egyptian University, which apparently was not well received. For years after, the only venue that allowed him to lecture about sexual health issues was Ewart Hall of the American University in Cairo.31 However, he was not prevented from publishing extensively before he became a regular contributor to Physical Culture. He had written several volumes on female sexuality, reproduction, prostitution, venereal diseases, the woman question and sexual impotence.32\n\nWhen the interviewer asked whether his efforts had made a difference, he admitted that both at the government and popular levels only limited progress had been made. In a report on the spread of prostitution and ways to combat it, which he had submitted to King Fuad and to the first parliament in 1924, he recommended sex education programmes in government schools. His plan was partially implemented by the Ministry of Education: lessons on plant and animal reproduction were added to the primary school curriculum but the human reproduction component, which was meant for secondary schools and university, was not incorporated. Although he performed what he termed his 'civic duty' (wajibi al-ijtima'i) through his public lectures delivered at the American University, he acknowledged that the audience was not the mass of the population.\n\nFor the masses, especially the young, cases of sexually transmitted diseases were on the rise.33 According to Dr Faraj, this was commensurate with their total ignorance about sex: 'I am probably not exaggerating if I said that they don't know any of its details except for what is [necessary] to fulfil their sexual cravings. They are not different in this respect from their companions \u2013 wild animals'.34 Despite this state of sexual ignorance inhabited by the majority of Egypt's (peasant) population, Dr Faraj expressed his abiding confidence that 'the spirit of Egypt's intellectual renaissance' and 'the spirit of [its] leap forward' could not but address this problem too. He cited anecdotal evidence of doctors in the provinces imbued with this spirit, who were undertaking on their own initiative programs to educate the people about sex and sexually transmitted diseases.\n\nAlthough the politics of sex education was not addressed directly in this interview, it did rear its head when Dr Faraj mentioned in passing opposition from 'the guardians of public morals'. According to the editor, the magazine was constantly subjected to erroneous charges of encouraging immorality.35 Muhammad al-Jawhari introduced his editorial comments a few months after the interview with Dr Faraj by reflecting on the historical case of the European Wars of Religion as an example of fighting for a cause \u2013 of the principled assault. He contrasted this to the attacks on the magazine, which he deemed hypocritical because of their intentional misrepresentation of its educational mission to enlighten people about the dangers of abusing their bodies sexually. It is when one wonders who was doing the attacking \u2013 since they go unnamed \u2013 that the example drawn from European history becomes intelligible. Unlike the Wars of Religion, wherein questions of belief were ostensibly at the heart of conflict, the editor of Physical Culture was suggesting that his magazine was being attacked in the name of religion by people who should and did know better. In other (unuttered) words, Islam was being twisted to meet ends that were not necessarily Islamic.36\n\nEven the American University was not impervious to the reach of the 'guardians of public morals'. Dr Faraj was taken to court for a lecture he delivered there (presumably) in 1931 about the need to revise personal status codes to reflect the advances of modern civilisation. Although I was unable to discover the specific charges, it is likely from the context that he was accused of offending the 'revealed religions'. After the court acquitted him, the lecture was serialised in Physical Culture, with a preface emphasising the good doctor's courage in carrying out his civic duty.37 The radical aspect of Dr Faraj's lecture seemed to lie in his criticism of the 'Eastern Christian authorities' for their antiquated approach to divorce and inheritance rights. Although only the Catholic Church was named in his critique, his call for a unified civil code on personal status issues implicated Copts and Muslims as well.38 This was a position that was sure to stir up controversy as the religious establishments were struggling merely to hold ground lost over the preceding decades to an interventionist state, but it did not necessarily correspond to a belief in gender equality.39 His major concern, as an expert on venereal disease, was the consequence to society of women who became prostitutes or bad mothers simply because of insufficient legal safeguards that did not prevent their impoverishment in cases of death or divorce.40\n\nOn the issue of equality between men and women, he expressed indignation at those who would even pose such a question and accused them of living in a 'fantasy world'. Ostensibly, the little political responsibility women already had was a burden too heavy for them. Echoing the late nineteenth-century discourse on motherhood, Dr Faraj pointed to Egyptian men marrying foreign women as a sign of the failure of Egyptian women in their nationalist duty to raise sons with good nationalist values.41 In any case, according to Faraj, nature and biology had already invalidated the very possibility of equality. For motherhood was a natural right given only to women, through which they had power over others: children, husband, family. Men could never possess this right, thus denying them that route to power.\n\nThe other regular contributor to the magazine's pedagogic mission, Dr Sabri Jirjis, offered his expert knowledge on abnormal and deviant sexuality. He was first introduced to the readers of the magazine in August 1931 as a new 'volunteer' member of the 'Physical Culture family'. Dr Jirjis practised at the VD clinic in Bani Suwayf, south of Cairo. The editor described him as a 'young sportsman' (shab sbur). A letter from the good doctor followed the introduction. He praised the magazine for its dual mission of bringing physical culture and sex education to the youth of Egypt. About physical culture, he wrote:\n\nIts share in the prosperity of European states is well known, and its influence in moulding the character of [their] youth is evidently clear. We perceive it every day when we read the news of pilots, swimmers, and athletes. It has, thanks to God and serious effort, begun to penetrate the hearts of boys and girls in this country.42\n\nDr Jirjis, it turned out, was extremely well read in contemporary European theories on sexuality and sexual disorders. Indeed, one of the reasons behind his desire to join Physical Culture's 'virtual family' was his search for a venue to present his Arabic translation of the oft-cited 1905 study by the Swiss sexologist August Forel, The Sexual Question (al-Mas'ala al-Jinsiyya).43\n\nJirjis noted the resistance to sex education in Egypt and commended Physical Culture for staying the course:\n\nSex education, despite the newness of research on it in Europe, has taken major strides in the last few years such that today it has become a science with its [own] rules and principles. However, in Egypt, tradition \u2013 or say a false shame \u2013 has prevented us from producing a reformer, an intellectual, or a parent who would discuss with his children sexual matters scientifically and truthfully.44\n\nThe effect of this pedagogic neglect was utter 'moral chaos'; that is:\n\nUntil you [al-Riyada al-Badaniyya] advanced onto the field \u2013 [where] previous weak attempts were crushed and died in their cradles without anyone noticing \u2013 and continued fighting and struggling in an environment [wasat] not acclimated to revolting against tradition [al-thawra 'ala al-taqalid], until you emerged victorious through the force of the truth, the conviction of the believer, and the steadfastness of the confident. Meanwhile, the columns on sex education in your magazine became the principle [source] that a young man can read and benefit from rather than just be entertained. That, I swear, is a major victory in a short time.45\n\nAside from the blatant self-serving flattery, Jirjis's letter points to the emerging relationship between medical science and social reform. His contributions over the years would illustrate the quest for a scientific cure for the persistent sense of uncertainty about the future of the national community. With the progress of time, ambiguities surrounding Egypt's political and cultural identity only seemed to proliferate; hence securing a proper order in the domain of gender and sexuality became all the more important. Through the course of the 1930s and especially in the 1940s, better theories and better science were seen as the key to resolving protracted social and political crises.46\n\nJirjis supplemented his medical knowledge with a critical social-scientific lens for better viewing the relationship between sex-gender and social progress. The intellectual tools available to Dr Jirjis were revealed in a very interesting article titled 'On Politics and Political Economy'.47 He began by explicating the difference between the two:\n\nPower and wealth were always the two objects targeted by politics. However, political-economy [al-iqtisad al-siyasi] is a science that studies the different conditions of [groups of] people, and all of its theories are based in history, statistics, and observations. Its aim is to determine laws for organizing production and distribution of products, for the division of labour, and for the social regulation of peoples in terms of public health, population (over or under), and rates of birth and death (increase or decline).48\n\nHe proceeded to identify a significant absence in political economy, which he labelled 'natural history' \u2013 by this he meant the history of the body and psychology as they related to sex and reproduction. It was this lacuna that undermined the ability of political economy to produce solutions for the imminent population crisis. His next move was to trace the roots of eugenics to Malthus and theories of rational selection, agreeing with the current view that people like the Chinese posed a threat to humanity's future if they continued to breed like rabbits. It was on a Social Darwinist basis that Dr Jirjis advanced his support for sex education and women's rights.49\n\nHe rejected what he termed the traditional tendency to explain any strange or extraordinary social developments with an injunction to 'examine women' (ibhath 'an al-mar'a). Women were not left out of the equation altogether, but the starting point, according to Dr Jirjis, should be to 'examine the sexual impulse' (ibhath 'an al-dafi' al-tanasuli). Such an investigation was warranted, he maintained, since desire and emotion (ahwa' wa 'awatif) were more common determinants of human action than reason and logic, with the sexual impulse being the most powerful. The 'role of women' was essential here in connecting sex to the social and political. Only through the liberation of women (tahrir al-mar'a) would society advance. Reversing Faraj's argument, Jirjis maintained that by making women equal partners with men in social life through encouraging their participation in work and granting women the right to vote and be elected, the sexual relationship would necessarily be transformed as women's object status was eliminated. Moreover, as the sex act became elevated from the depths of selfish lust and was redirected at smart reproduction, it would be aligned more with the social good.50\n\nDr Jirjis's writing on sexuality and deviance exemplified the work of Physical Culture towards the normalisation of heterosexuality as a key to Egyptian modernity. Essential to this goal was the scientific constitution of society as an object that could be acted upon; conversely, the localisation of social problems in the individual human body, in this case in the male sex, made possible the administrations of Physical Culture.51 As noted, the male subject of Egyptian modernity had been problematised since the late nineteenth century as lacking the proper qualities of masculinity. After a lull in the discourse around the revolutionary years following 1919, Egyptian masculinity returned in the pages of magazines like Physical Culture facing a new endangered future, sapped by excessive masturbation and the contraction of venereal diseases.\n\nThe magazine mainly concentrated its critique on forms of deviance (al-shudhudh) resulting from what it considered a lack of masculine self-control or willpower; that is, the individual exerting excessive sexual energy, either upon himself or with a partner of the opposite sex (making prostitution a favourite object of criticism). More monstrous forms of deviance were left lurking in the shadows. For example, the figure of the cross-dressing male performer, the khawal, who still seemed to have made appearances even at elite wedding parties as late as the 1930s, was never treated explicitly by this discourse.52 One possible explanation for this absence is that the scientific tools available to Egyptian social commentators were not calibrated to deal with this form of home-grown difference. Thus it appeared only as a passing unnamed reference.53\n\nDr Jirjis, however, did write about homosexuality as a form of sexual deviance. His article 'Homosexuality' (rendered as 'ishq al-jins) from March 1933 was part of a series he did on 'Psychosexual Illnesses' in which he presented translated excerpts of Dr Forel's The Sexual Question.54 In fact, he seemed to have coined the expression 'ishq al-jins to capture the scientific significance of 'homosexuality' as an illness deserving public sympathy and serious medical attention and care.55 He also addressed the desire for same-sex marriage in his article on 'Prostitution and Civil Marriage'.56 His objective here was to advocate for the legal recognition of a system of heterosexual marriage based on love between two 'companions' (rafiqan). In the case of those 'afflicted with same-sex desire', for whom there was no marriage provision at all within law, he ventriloquised Forel's argument, that as long as there was no injury to a third party and as long as neither of the partners was 'normal', then the law should simply overlook them; in other words, let them live out their (literally sick) fantasies as long as they did not spread their disease.57\n\nIn short, sex education and a rational regime of caring for the self were prescribed as the way to achieve proper gender relations and a healthy sexuality. Even homosexuality, a deviation from the person's nature, could be averted through this programme.58 The magazine was, however, ambivalent in its advocacy for the prohibition of prostitution, mainly because it recognised that demand created supply in this instance. This also explains why the problem of prostitution was often routed through the discourse on marriage and sexuality. In 'Prostitution from a Medical Perspective', an unnamed expert on venereal diseases disagreed with those calling for a ban on official prostitution arguing on the one hand that there was no correlation between rising numbers of STDs and prostitution, and on the other that a sudden prohibition would cause more harm than good.59 Another article blamed misogyny inherent in the laws for the failure to curb prostitution; it attacked as 'social cowardice' the implementation of laws that only punished one partner and highlighted the complicity of male lawmakers with male clients of prostitutes.60 Ultimately the magazine's position was one of self-help; the resolution to these social problems lay in the process of cultivating properly disciplined subjects.\n\nWhat may appear as striking about these engagements with contemporary European theories on sexuality was a blatant disconnection from Egyptian social and sexual realities. The absent presence of the multitude of labouring bodies \u2013 women, khawal, peasant \u2013 in this 'modern' discourse is only one, perhaps 'extreme', indicator of how the emergence of the effendi as a representative masculine subject depended on the suppression or erasure of other disruptive figures. However striking it may be, this pattern of exclusion\/inclusion was not specifically Egyptian and neither was the lack of fit or distorting distance between categories of knowledge, their subjects and objects. This was the work of colonial power in the constitution of the modern subject the world over. The difference of metropole and colony was surely a matter of political-economic asymmetry, but that alterity had to be figured somehow in the prevailing liberal discourse to effect its own historical legibility as unique to one civilisation while simultaneously keeping open the possibility of universal emancipation into, and identity with, the modern.\n\nBeyond pedagogic and the performative modernity: the limit of Physical Culture\n\nOn the one hand, Physical Culture's assemblage of texts \u2013 of letters, articles, stories and photos (not discussed here) \u2013 points to a pedagogical project that sought to normalise a global bourgeois conception of heterosexuality and its attendant gendered subject for a national project; on the other hand, read critically, it may illustrate a 'creative adaptation' of that discourse to the local conditions of colonial modernity.61 The hybrid nature of Physical Culture, however, as a material object between the pedagogic and the performative becomes intelligible only when desire, the colonial and the modern are situated as a part of and apart from the Egyptian social reality of the interwar period. In other words, this object \u2013 as magazine with pages, text and images and as a particular discourse of sexuality and self \u2013 existed in tension with both the 'local' and the 'foreign', stood for and against normative sexuality, circulated in spaces that were colonial, national and diasporic at once, and produced a virtual (and, somewhat anachronistically, transnational) field of desiring subjects and discursive engagements with unpredictable outcomes. Accordingly, the discourse of gender and sexuality that took shape in and around the pages of Physical Culture was not willed into existence solely through the interests of the editors and authors of the magazine. Furthermore, the full significance of that discourse would be missed if viewed exclusively as the product of economic and political change, wherein the latter is conceived as a reality prior to discourse. Neither can its emergence be explained through ahistorical psychological states of 'anxiety' or 'crisis'. It was through continuous repetition in forums like Physical Culture and movement through various social and spatial networks that the terms of a new corporeality, gender and sexuality overlapped, producing by the 1930s an ostensibly seamless normative sphere of heterosocial and heterosexual life.62\n\nDespite the complex history enabled by this polyvocal source, the possibilities for imagining Egypt's past as plural and its history as open-ended only emerge when its privileged subject \u2013 effendi, nationalist, masculine, modern and so on \u2013 no longer appears as a historically foregone conclusion.63 For example, the historical translation of desire into respectable heterosociality and sexuality, which came to define effendi-national culture of the interwar period, might be made legible historically without eliding the fact that it was only one possible representation of sexual desire, one possible worlding of love \u2013 albeit the ultimately dominant one. Indeed it was in the very slippage between moral and immoral (acts, images and thoughts) that Physical Culture managed to stake its claim on Egypt's modernity. Scantily clad foreign cover girls and bare-chested local muscle men were juxtaposed with narratives and epistolary tales of libidinal excess, all of which were used in a pedagogic mission \u2013 perhaps sincere, perhaps not \u2013 to produce the necessary bodies for a sovereign Egypt of the future. Yet, the charges of immorality levelled at the magazine for its sexual rhetoric also hint at the 'unanticipated' use of the magazine as a masturbatory aid.\n\nPhysical Culture might still reveal more than the existence of this somewhat obvious space between modernist intentions and acts, pedagogy and performance. Another question to this source could have been about the fantasy it organised around a silence \u2013 a silence that was perhaps ironically the outcome of a boisterous colonial programme to police homosexuality. Was the discourse of physical culture serving as a 'masquerade that has screened away something more'?64 The supplement here might be represented in shorthand as the impossible subjects of colonial modernity, the suppressed history of which was, and is, contingent on reading this moment exclusively as a struggle between the norm and its deviation.\n\nThe realm of bourgeois masculinist fantasy represented by Physical Culture conforms to and confounds Judith Butler's rearticulation of the relationship between gender and the norm in terms of the emancipatory 'work of fantasy' which attempts 'to rework the norms by which bodies are experienced'.65 The performativity of gender reads quite differently and is at cross-purposes in a colonial context.66 The discourse of physical culture in Egyptian colonial modernity was a bodily investment in advancing a broader claim to humanity that was paradoxically both more inclusive and more exclusive than in the preceding era. The new national public sphere of citizen-subjects was indeed informed by a universality that at least promised another world from the previous 'religio-political' order with its paternalistic and patriarchal hierarchies. However, the burden of producing the human central to realising this modern order was compounded and consistently deferred by the colonial.67\n\nWithin this constellation of figures \u2013 coloniser, colonised, citizen, universal human \u2013 the particular histories of Egyptians that neither fit within this 'system' nor within the construction of the prior order of despots and aliens was subject to erasure. An example of the historical repetition of modernity's silences is my own marginalising to a footnote of the fragmentary sighting of the khawal (alluded to above). Indeed, in this case, the khawal did not even bear its proper name but was rather subsumed under the category of 'awalim: female entertainers who sang, danced and played instruments at weddings and other ritual occasions.\n\nThe occasion for this appearance was a monthly advice column, 'The Tales of Venus', in the August 1932 issue of Physical Culture. The special topic for this month was 'The Wedding Night' (laylat al-dukhla). 'Venus', using a highly satirical and bourgeois moralistic tone, set out to expose the vanity and excessive folly of all classes \u2013 but specifically of women \u2013 when it came to marriage celebrations. The potential for disorderly conduct of various kinds was persistently underscored. After narrating a series of untoward happenings at weddings that Venus had attended over her lifetime, ranging from the competition among women to be the best-looking to fights breaking out over trivial matters, she arrived at the most scandalous and most prevalent wedding phenomenon: the 'awalim, in her own ironic words, 'the most important group upon which a wedding celebration depends'.68 Venus cautioned against inviting this lowliest of life forms into respectable homes because of the 'awalim's foul language and their even fouler deeds, the most brazen of which could be the seduction of the groom. Venus went on:\n\nBut the strangest of all was when I attended a wedding where I happened to be seated near the 'awalim. My gaze landed on one of them with her ambiguous [munakkara] shape and unpleasant face. She ended up talking to me without pause about one thing or another until she asked me about the gown I was wearing and just as I was about to answer her, with all politeness of course, one of my acquaintances whispered in my ear advising me to distance myself from this woman because she was... watch out... a man! I was stunned by her words and left him angrily. I went to the hostess and told her that it was absolutely improper of her to allow a man entry into a gathering of women. I was beyond shock when I saw that she was bemused by what I had said and then replied that there was no need for all this anger since the 'aalima or the 'aalim that I was talking about although biologically differed completely from the biology of our sex, he was closer to [being] a woman than he was to a man.69\n\nIn spite of Venus's apparent shock and indignation, it is telling that no memory of men dressed as women in performance could be recalled bearing its proper name, that her language could not accommodate this difference. Was this because khawal as signifier had already undergone its second semantic transformation: first, from slave and servant as it appeared in the medieval lexicon Lisan al-'Arab to male performer in drag by the nineteenth century; then to faggot, as the term is derogatorily deployed in Egypt today?70 Perhaps. But how may we historicise and critically grasp this specific failure of language beyond its own dominant signifying practices?\n\nOne might begin by regarding the rigid divisions between gender and sex established above as heteronormative and by contrasting it with the more fluid understanding allowed by a 'religious' figure like Rifa 'a Rafi' Tahtawi in the nineteenth century. The latter described the androgyny of boys that made them attractive to men during the pre-pubescent stage (mabda' shabubiyya) without any apparent sense of disapproval. Indeed, at least three major new works using a variety of sources demonstrate that pre-colonial Islamic societies were practically if not juridically more tolerant of deviances such as pederasty and gender crossings.71 Given Dr Jirjis's approach to homosexuality as an illness in the same way it was treated in Europe, it seems that the object field for gender normativity had begun to crystallise in interwar Egypt as medical practitioners and others earnestly advocated a relatively protestant approach to sex and marriage. Indeed between the rare discursive deployment of homosexuality and the frequent performative reiterations of heteronormative masculinity and femininity, the spectral presence of the cross-dressing khawal as late as the 1930s sheds light, however faint, on another terrain of gender, sexuality and sociality that was in the process of rapidly receding.\n\nIn the exchange above between Venus and the host of the wedding, we might, if we strained, hear a whisper of the unspeakable of colonial modernity: otherwise gendered lives that were seemingly intelligible but were in the process of being moved from the domain of the real to the unreal, indexing perhaps the loss of their purchase on communal norms that had ensured their persistence in the past. Additionally, rather than producing the conditions for a resignification with the aim of expanding the purview of the human, the colonial genealogy of gender as a norm conditioned and reproduced by the apparatuses of modern regulatory power has consistently narrowed the confines of the subject and foreclosed possibilities for subjective proliferation.\n\nPut this way, the disappearance and return of the khawal in twentieth-century Egypt pushes to the forefront the imperial context in which norms of gender and sexuality were constituted in both metropoles and colonies, First and Third Worlds and presently in the global north and south. One should be attentive to the historical specificities of the moments mapped by these loose spatial designations, but conceiving the relational dynamic of gendered subject formations across these spaces can productively complicate performative theories and extend the range of history. It does so by inquiring into the asymmetries of power that effect the material conditions for the iterability and potential resignification of norms governing the subject. The affect of colonial modernity in Egypt \u2013 overcoming simply being \u2013 was implicit in the vanishing sociality of the cross-dressing khawal, but the category was not extinguished altogether. Indeed, following Butler, there occurred a resignification that momentarily allowed the posing of a question that cannot be answered: who are you? Although it is only in the interstices of questions and answers that were intelligible, in penumbral corners, for fleeting moments, and between the lines of a quintessentially modern text that one might virtually dwell with the silent other, that possibility, however much a chimera, might bespeak other beings and other dwellings in time.\n\nConclusion\n\nPhysical Culture was essentially a 'sports' magazine and significantly a site of fantasy. Its broad condition of possibility in either incarnation was colonial modernity, the material and discursive frame with no originary location and within which the world was made singular and plural at once. It marked a specific moment in the historical trajectories of culture as a form of nationalist pedagogy and as site of global performances, wherein a particular national horizon was constituted and exceeded. Thus, the subject of Egyptian colonial modernity as inscribed in the pages of Physical Culture was contingent on multiple and polyvalent sources for its formation.72 However, the stakes of producing such a subject \u2013 sovereignty and freedom \u2013 required submission to the modern terms of gender and sexuality which, even though coming from everywhere, appeared originally western, rendering their translation and authorisation within the Egyptian context a fraught process by the interwar period.73\n\nIn this chapter, rather than erasing the tension between originals and copies of modernity, which the benefit of hindsight and sophisticated historical methods have exposed as narrative fictions, I have tried to redeploy it as a technique for reading the ambivalences of the physical culture discourse in Egypt. That is, rather than resolve the problem of authenticity, which became a crucial issue in cultural debates from the second half of the 1920s, I have tried to read along the grain of those linguistic performances, regarding what they did in what they said or could not say. Hence, on the one hand, by the interwar period, the legitimacy of physical culture understood as sports and fitness was no longer in question; on the other hand, the concerns of the magazine Physical Culture demonstrate that expanding its bailiwick to include sex education was a problematic move. The reproduction of beautiful bodies was easily assimilated to a nationalist horizon, whereas the problem of sex, even when elaborated in terms of public health and the collective good, stirred up opposition. Perhaps even more telling, however, was the less active form of resistance to Physical Culture's normalising project that was silently present as an absence, in unnameable forms of deviance. It would be tempting to explain the latter problem as being a result of poor translations. That however presupposes an original which, under the terms of colonial modernity, was an impossibility, since gender and sexuality were shaped globally through repeated encounters within the imperial social formation. In fact, the coeval proliferation of sexuality around the globe was contingent on a process of diagnosing and documenting pathologies and perversions which, as the example of Dr Jirjis demonstrates, was familiar terrain for Physical Culture.74\n\nThus, colonial modernity as an explanatory instrument reaches a similar impasse to that reached by Physical Culture in the 1930s in the face of the unintelligible subject. Although thinking through the joining of the colonial and the modern are historically and theoretically generative, especially in the study of gender and sexuality, colonial modernity is intrinsically incapable of envisioning its outside. While re-conceptualisations of the colonial encounter in terms of interaction, mutual constitution, creative adaptation and so on have been crucial for debunking Eurocentric historical models of cultural creativity and diffusion, the modern subject stubbornly retains its libratory inscription that belies particular liberal notions of sovereignty and freedom. Accordingly, the subject presupposed or mapped in studies of colonial modernity tends to resemble the desirable subject figured in Physical Culture to the extent that they inhabit similar positions in relation to the future. That future of human being is exclusively narrativised as a movement from bondage to freedom driven by a dynamic of domination and resistance, or subjugation and resignification in a poststructuralist register.75 Other forms of political and ethical life remain invisible or impossible to theorise. That the modern subject would run up against limits is by itself a banal point. However, for the historiography of gender and sexuality, considering the limit and its implications is crucial for giving an account of life forms such as the khawal, that are marked by a temporality and conception of the self which seem to exceed the bounds of intelligibility in colonial modernity. Thus, approaching the past as plural and envisioning a broader horizon for the human in the present would require critically attending to colonial modernity as a history of overcoming simply being.\n\nNotes\n\nThis chapter has benefited greatly from the sharp readings of too many people to name individually, but I must thank Walter Armbrust for his especially incisive and detailed comments. I also want to express my gratitude to the 'Formation of National Culture in Egypt' conference, and specifically to Walter Armbrust, Ron Nettler and Lucie Ryzova for inviting me to Oxford University and granting me the all-too-rare opportunity to exchange ideas with specialists in the field. Presentations of previous versions at Cornell and McGill have also provided valuable feedback that has helped with the revisions for this chapter.\n\n1. All translations are my own unless otherwise noted.\n\n2. Henceforth, when it appears in the body of the text, the name of the magazine will be rendered only in its translated form. In notes, it will appear as RB. Titles of articles and other sources that were in Arabic in the original appear only in translation, unless they are deemed major texts, in which case the Arabic and its translation are both provided.\n\n3. RB, March 1936, pp. 333\u20136.\n\n4. I am uncertain as to when exactly its run came to an end, but it seems not to have survived long past the Second World War. Walter Armbrust has located issues of the magazine from 1951.\n\n5. Colonial modernity is used here in a specific manner to indicate a mutually constitutive space\/time, not an alternative modernity that is colonial. For an elaboration of this point, see Tani E. Barlow, 'Introduction: On \"Colonial Modernity\"', in Tani E. Barlow (ed.), Formations of Colonial Modernity in East Asia (Durham: Duke University Press, 1997), pp. 1\u201320.\n\n6. Due to space constraints, rather than elaborate 'the subject' (of discourse) here, it is hoped the intended meaning will become clear through usage in context. For a fuller discussion of the modern subject as a discursive formation and of its Egyptian historical context, see Wilson Chacko Jacob, Working Out Egypt (Durham: Duke University Press, forthcoming 2011).\n\n7. Fantasy, as it is used here, does not index a realm absolutely separate from reality; rather, following Judith Butler's elaboration of subject formation in language, it is conceived as a performative space in which the real and the unreal are mutually constitutive and distinguished through a relation to norms, which cohere and are potentially destabilised through their repetition. In this formulation of fantasy, the subject does not exist prior to its expression in language but only in and through its enactment. See e.g., Judith Butler, Bodies That Matter: On the Discursive Limits of 'Sex' (New York: Routledge, 1993).\n\n8. 'Performative' is used here in the sense of a formation (social and linguistic) whose determinations and outcomes are not fixed even as its pronouncement simultaneously produces a reality in fact. 'Pedagogic' is used in the sense of instruction but with an allusion to regulatory discourses in general. Performative modernity, unlike pedagogic modernity, cannot be located in originary moments, places, or persons and remains open to resignification through repeated acts.\n\n9. This was the address of the institute in 1938; I was not able to establish whether it was always in the same location. Interestingly, the YMMA continues to exist and operate in the same location while the ma'had has disappeared entirely, even from memory.\n\n10. There are obvious echoes here of the process of subject constitution that Foucault critically elaborates on in Michel Foucault, The History of Sexuality, vol. 1: An Introduction, tr. Robert Hurley (New York: Vintage, 1990), see esp. 'The Deployment of Sexuality', pp. 124\u20136.\n\n11. Effendiyya may be read loosely to signify 'middle class' or 'bourgeois' in the cultural sense, and an effendi is a male member of the class. There is no female equivalent. To some extent, an effendi in the interwar period was any male (and theoretically, female) who could effect the proper style and possessed the right repertoire.\n\n12. In Working Out Egypt, using the rubric of 'effendi masculinity' I map the formation of Egypt's desired subject in performances of physical culture that range from early textual elaborations of its nationalist benefits to its manifestations in activities such as competitive sports and the Scouts.\n\n13. Egypt, which had been a province of the Ottoman empire since 1517, was occupied by the British in 1882, ostensibly with the intention to leave once European financial interests had been secured (they ended up staying for seventy years).\n\n14. Early translations index physical culture's mode of circulation across the imperial social formation and show that its ideas, practices and objects were all of interest to the effendiyya. So, one may find expositions on the best use of weights for exercise alongside the biography of English strongman performer Eugen Sandow alongside Frenchman Edmond Demolins's widely disseminated assessment of British public school education (which included a rigorous programme of physical training) as the secret to their imperial success. See Jacob, Working Out Egypt, chapter 3.\n\n15. This information was culled from the 'letters to the editor' and the magazine's own statements about its distribution. By 1937, RB had formal arrangements with agents in Luxor, Khartoum, Port Sudan, Mecca, Jaffa, Akka, Gaza, Damascus, Aleppo, Tripoli, Basra and Baghdad.\n\n16. Wilson Chacko Jacob, 'Eventful Transformations: Al-Futuwwa between History and the Everyday', Comparative Studies in Society and History 49 (2007), pp. 689\u2013712.\n\n17. Andr\u00e9 Raymond, Cairo, tr. Willard Wood (Cambridge: Harvard University Press, 2000), p. 324.\n\n18. The author of the letter explicitly requested that Cupid, the mediator of this epistolary forum, only solicit advice on his problem from male readers of Physical Culture.\n\n19. RB, March 1936, pp. 335\u20136.\n\n20. RB, March 1936, p. 336.\n\n21. Although unsatisfactory, one could speculate based on the reactions to analogous situations about the solutions readers may have offered A.Y.D. Answers would for the most part have been very pragmatic, in which A.Y.D. would have been told to move on, to forget the traitorous woman, to have his parents find him a proper partner, and to remain vigilant on his new path to good health and virtuous living.\n\n22. These numbers indicate letters received; only a handful of letters were ever published. Even if the figures were highly inflated by the magazine's editors, the claims of the existence of an interested public with differing opinions about intimate issues in a stranger's life is not only intrinsically interesting but also points to an important aspect of the discursive constitution of 'the public'.\n\n23. RB, May 1932, pp. 120\u201324.\n\n24. RB, May 1931, p. 108.\n\n25. RB, March 1936, p. 333.\n\n26. This very same source has been read through its visual images of women as peddling soft-core porn in the guise of exercise and health. See Lucy Ryzova, '\"I Am a Whore But I Will Be a Good Mother\": On the Production and Consumption of the Female Body in Modern Egypt', Arab Studies Journal (2004\/2005), pp. 80\u2013122. While this may well have been true, and might indeed partially account for the longevity of the magazine, the textual evidence suggests a very different reality closer to its stated goals of promoting smart, modern and healthy sexuality. That said, if the male images were read along the same erotic lines, then there was a definite subversion of these stated goals and the ideology of heteronormativity. Nevertheless, these transgressive 'readings' would reinforce the point that norms of gender and sexuality needed to be reconstituted as a condition of possibility for a 'modern' Egyptian subject.\n\n27. Omnia El Shakry, The Great Social Laboratory: Subjects of Knowledge in Colonial and Postcolonial Egypt (Stanford, CA: Stanford University Press, 2007). The publicity of private issues was not in itself new. Matters of sex and reproduction had been of central concern to Islamic society for over a millennium, as attested to in laws and customs surrounding gender roles, marriage and inheritance. What was new was the partial displacement of the regulation of sex and gender onto a reconstituted social body (in and for which laws were discerned by modern science) while paradoxically predicating the private individual as the condition of possibility for the social.\n\n28. Other contributing medical experts included Dr Husayn 'Izzat, Dr Muhammad Kamil al-Khuli, Dr Muhammad Abd al-Hamid Bey, Dr Husayn al-Harawi and Dr Muhammad Shahin Pasha.\n\n29. On the development of a mass culture during this period through popular magazines and cinema, see Walter Armbrust, Mass Culture and Modernism in Egypt (Cambridge: Cambridge University Press, 1996).\n\n30. 'Sex Education: An Hour with Dr Fakhri Faraj, The Famous Doctor of Venereal Diseases', RB, May 1932, pp. 6\u201312.\n\n31. Bruce Dunne discusses the role of the AUC and Faraj's lecture series in the dissemination of knowledge about sexual health as part of colonial and national efforts to 'civilize' Egyptians in chapter six of his thesis 'Sexuality and the \"Civilizing Process\" in Modern Egypt' (unpublished doctoral thesis, Georgetown University, 1996).\n\n32. Fakhri Faraj, al-Mar'a wa falsafat al-tanasuliyyat (Cairo: al-Matba'a al-'Asriyya, 1924); Fakhri Faraj, Taqrir 'an intishar al-bagha' wa al-amrad al-tanasuliyya bi al-qutr al-misri wa ba'd al-turuq al-mumkin itba'uha li- muharabatihima (Cairo: al-Matba'a al-'Asriyya, 1924). I could not locate the following works by Fakhri Faraj: al-Tanasul fi al-hayawan wa al-insan wa al-nabat; Hal tatasawi al-mar'a bi al-rajul fi al-huquq wa al-wajibat?; al-Amrad al-tanasuliyya wa 'ilajuha; al-Du'f al-tanasuli fi al-dhukur wa al-anath wa 'ilajuhu.\n\n33. Given the absence of much statistical data related to sexually transmitted diseases from this period, it is very difficult to corroborate this claim. Making it his life's work suggests at least that it was a major concern for Dr Faraj and not solely a rhetorical device.\n\n34. RB, May 1932, p. 9.\n\n35. Muhammad Fa'iq al-Jawhari, 'The Honourable Attack', RB, October 1932, pp. 4\u20135. Interestingly, criticism also seems to have been launched against the magazine from a third position that found the magazine's message of chastity puritanical and outdated. For a defence of their philosophy on sex education, see 'Girls and Diminished Morals', RB, February 1935, pp. 113\u201314. Essentially, the magazine maintained that knowledge about sex would encourage self-control, which was what distinguished humans from animals. An important component of their philosophy was the belief that there was a causative element to sex-knowledge and the outcome was ultimately empowerment.\n\n36. This reading is supported by the magazine's inclusion of religious experts alongside the medical experts to opine on issues related to sexuality and the right to research and discuss them publicly. Another likely proposition is that the editor was manipulating religion just as interestedly as his opponents in order to enhance magazine sales that depended on 'sexual' content.\n\n37. Fakhri Faraj, '[Part I] Why Women Have Revolted?' RB, December 1932, pp. 33\u20138; '[Part III] Motherhood and a Social and Intellectual Life', RB, February 1933, pp. 43\u20138; '[Part IV] The Duties and Rights of Women', March 1933, pp. 65\u201371. I was not able to obtain the January 1933 issue of RB and thus could not consult Part II of Dr Faraj's lecture.\n\n38. RB, March 1933, pp. 65\u201371.\n\n39. The gradual transformation of the law in the nineteenth century, from a hybrid of Islamic and western forms to one based predominantly on the Napoleonic Code, relegated 'religious' law to the domain of personal status issues. For the possible repercussions of voicing too loudly a call for equal inheritance rights, see Margot Badran, Feminists, Islam, and Nation: Gender and the Making of Modern Egypt (Princeton: Princeton University Press, 1995), p. 134.\n\n40. For another angle on this problem, see Mukhtar al-Jawhari, 'Prostitution and the Problem of Orphans: How We Can Overcome [the Problems] through Proper Sex Education', RB, November 1932, pp. 6\u20139.\n\n41. Hanan Kholoussy, 'Stolen Husbands and Foreign Wives: Mixed Marriage, Identity Formation, and Gender in Colonial Egypt, 1909\u20131923', Hawwa 1 (2003), pp. 206\u201340.\n\n42. RB, August 1931, p. 122.\n\n43. Forel's text was originally composed in German; Jirjis based his Arabic translation on an English edition by C. F. Marshall (which edition however is not clear). August Forel, The Sexual Question: A Scientific, Psychological, Hygienic and Sociological Study, tr. C. F. Marshall (1905; New York: Medical Art Agency, 1911). It may be noted that 1905 was also the year in which Sigmund Freud's first rendition of The Theory of Sexuality appeared.\n\n44. RB, August 1931, p. 123.\n\n45. RB, August 1931, p. 123.\n\n46. On the science of population, see Omnia El Shakry, 'Barren Land and Fecund Bodies: The Emergence of Population Discourse in Interwar Egypt', International Journal of Middle East Studies 37 (2005), pp. 351\u201372. For a broad survey of the place of social science and its practitioners in discursively producing and practically managing Egypt, see Timothy Mitchell, Rule of Experts: Egypt, Techno-Politics, Modernity (Berkeley: University of California Press, 2002). See also El Shakry, The Great Social Laboratory.\n\n47. Dr Sabri Jirjis, 'On Politics and Political Economy', RB, March 1934, pp. 15\u201321.\n\n48. Jirjis, 'On Politics and Political Economy', p. 15.\n\n49. The major figure propounding Social Darwinism during this period was Salama Musa, whose work Jirjis must have read. See Joseph Massad, Desiring Arabs (Chicago: University of Chicago Press, 2007), pp. 128\u201341.\n\n50. Massad, Desiring Arabs, pp. 20\u201321.\n\n51. The use of the body as a social and political metaphor was of course already quite old by then. Its modern use to describe national communities in Egypt can be traced to at least as far back as Rifa'a Rafi' Tahtawi's al-Murshid al-Amin lil-banat wa al-banin [The Trusted Guide for Boys and Girls] (1872; Cairo: Supreme Council for Culture, 2002). One of the most explicit and extended treatments of the 'organic body' (jism 'udwi) as both a metaphor for and constitutive of modern society was Ahmad Amin's al-Akhlaq [Morality] (Cairo: Lajnat al-Ta'lif wa al-Tarjama wa al-Nashr, 1920).\n\n52. This point is elaborated below. See Venus, 'The Wedding Night', RB, August 1932, pp. 81\u20134. Evidence of the khawal as a historically important figure on the Egyptian sexual landscape at the end of the nineteenth century appears in the memoirs of Ibrahim Fawzi. See Wilson Chacko Jacob, 'History and the Masculine Subject of Colonialism: The Egyptian Loss of the Sudan', in Lahoucine Ouzgane and Robert Morrell (eds), African Masculinities: Men in Africa from the Late Nineteenth Century to the Present (New York: Palgrave, 2005), pp. 153\u201369.\n\n53. For a survey of expanding state powers and the policing of sexuality from the nineteenth century to the early twentieth century, see Dunne, 'Sexuality and the \"Civilizing Process\"'. For a treatment of how the disavowal of sexual difference constituted an Arabic canon, see Massad, Desiring Arabs.\n\n54. RB, March 1933, pp. 30\u201337.\n\n55. On the complexity of sexual terminology in pre-modern and modern Arabic, see Everett Rowson, 'The Categorization of Gender and Sexual Irregularity in Medieval Arabic Vice Lists', in Julia Epstein and Kristina Straub (eds), Body Guards: The Cultural Politics of Gender Ambiguity (New York: Routledge, 1991), pp. 50\u201379; Fr\u00e9d\u00e9ric Lagrange, 'Male Homosexuality in Modern Arabic Literature', in Mai Ghoussoub and Emma Sinclair-Webb (eds), Imagined Masculinities: Male Identity and Culture in the Modern Middle East (London: Saqi Books, 2000), pp. 169\u201398.\n\n56. RB, November 1933, pp. 14\u201322.\n\n57. It is hard to tell whether Jirjis believed this or was 'simply' acting as a translator. These are Forel's words from The Sexual Question, p. 378.\n\n58. 'Sexual Deviance', RB, October 1934, pp. 19\u201321.\n\n59. RB, March 1935, pp. 18\u201321.\n\n60. RB, November 1936, pp. 1008\u201309.\n\n61. Dilip P. Gaonkar, 'On Alternative Modernities', in Dilip P. Gaonkar (ed.), Alternative Modernities (Durham: Duke University Press, 2001), pp. 1\u201323.\n\n62. The emergence of a discourse on monogamous marriage and the proper household has been traced to the 1870s, which tentatively can serve as the birth date for the ideology of bourgeois heteronormativity that silently subtended the physical culture discourse of the 1930s. See Kenneth M. Cuno, 'Ambiguous Modernization: The Transition to Monogamy in the Khedivial House of Egypt', and Mary Ann Fay, 'From Warrior-Grandees to Domesticated Bourgeoisie: The Transformation of the Elite Egyptian Household into a Western-style Nuclear Family', both in Beshara Doumani (ed.), Family History in the Middle East: Household, Property, and Gender (Albany: State University of New York Press, 2003), pp. 247\u201370, 77\u201397 respectively. See also Lisa Pollard, Nurturing the Nation: The Family Politics of Modernizing, Colonizing and Liberating Egypt, 1805\u20131923 (Berkeley and London: University of California Press, 2005), p. 44.\n\n63. Of course, in a sense, it was never the case anyway. The desire for a resolution to the instability surrounding the future of the effendi marked and formed the condition of possibility for new cultural productions such as Physical Culture. But locating the ambivalence in its discourse of gender and sexuality \u2013 that on the one hand acknowledged the deviance of Egyptians and on the other refused its colonial implications \u2013 is a critical move in their resignification.\n\n64. This is from Afsaneh Najmabadi's formulation of how the standard narration of Iranian modernity as the simultaneous and conflicted struggle to secure cultural authenticity and progress figures gender exclusively within this tension \u2013 usually marked geographically between east and west \u2013 and consequently writes out the particularities of gender's ambiguity in Iran's 'pre-modern' history. In other words, histories of gender in Iranian modernity that leave untroubled the assumption of heterosexuality as a natural occurrence reproduces the 'historical erasure' of figures like the mukhannas\/amradnuma and the amrad. Afsaneh Najmabadi, Women with Mustaches and Men without Beards: Gender and Sexual Anxieties of Iranian Modernity (Berkeley: University of California Press, 2005), p. 141.\n\n65. Judith Butler, Undoing Gender (New York: Routledge, 2004), p. 28.\n\n66. For a critique of Butler's theorisation of performativity from a slightly different perspective, see Saba Mahmood, Politics of Piety: The Islamic Revival and the Feminist Subject (Princeton: Princeton University Press, 2005).\n\n67. For a brilliant new study that interrogates the colonial production of the human in modern law as a moment of rupture in Egyptian history, see Samera Esmeir, 'The Work of Law in the Age of Empire: Production of Humanity in Colonial Egypt' (unpublished doctoral thesis, New York University, 2005).\n\n68. RB, August 1932, p. 82.\n\n69. RB, August 1932, p. 84.\n\n70. Lagrange, 'Male Homosexuality in Modern Arabic Literature', p. 197 n. 58.\n\n71. Tahtawi, al-Murshid al-amin, p. 39. See also Najmabadi, Women with Mustaches and Men without Beards; Khaled el-Rouayheb, Before Homosexuality in the Arab-Islamic World, 1500\u20131800 (Chicago: University of Chicago Press, 2005); Dror Ze'evi, Producing Desire: Changing Sexual Discourse in the Ottoman Middle East, 1500\u20131900 (Berkeley: University of California Press, 2006).\n\n72. From a different context, Lisa Duggan has made a similar argument in terms of the subject of lesbianism. Lisa Duggan, 'The Trials of Alice Mitchell: Sensationalism, Sexology, and the Lesbian Subject in Turn-of-the-Century America', Signs 18 (1993), pp. 791\u2013814.\n\n73. Khaled Fahmy has insisted on the different dynamics involved in borrowing ideas and practices from Europe during the first half of the nineteenth century, when it was a less loaded question (personal communication with author). Samia Mehrez has noted the difficulties in the present of translating gender into Arabic by contrasting the ease with which jins (genus, ethnicity, and later sex and nationality) was directly borrowed from ancient Greek during the establishment of the Islamic empire. Samia Mehrez, 'Translating Gender', Keynote Address at 'Gendered Bodies, Transnational Politics: Modernities Reconsidered' Conference, American University in Cairo, 12\u201314 December 2003; an expanded version was published in the Journal of Middle East Women's Studies 3\/1 (2007), pp. 106\u201327.\n\n74. Attempts to intervene positively in that discourse were subject to increasing repression from the late nineteenth century, accelerating in the 1930s. Indeed one of the first major book burnings organised by the Nazis targeted the collection of the Institute for Sexual Science, which had been established in Berlin in 1919 by Magnus Hirschfeld. Further highlighting the global dimension of the sexuality discourse during the interwar period, one of the anonymous reviewers of another version of this article noted that Hirschfeld visited Egypt during the winter of 1931\u201332 and delivered lectures at the AUC. I am grateful to the reviewer for drawing my attention to this fact.\n\n75. Mahmood, Politics of Piety.\nChapter 7\n\nMonitoring and Medicalising Male Sexuality in Semi-Colonial Egypt\n\nHanan Kholoussy\n\nThis chapter examines the ways in which Egyptian legislators and reformers drafted and debated new regimes of monitoring male sexuality in nineteenth-century and early twentieth-century Egypt. An exploration of the state's legislation on marriage, prostitution and venereal disease reveals that the state assumed an unprecedented role in monitoring and medicalising the sexuality of Egyptian men. Its goal was to create 'healthy', disciplined men who would create fit and modern families that would serve as the foundation for a postcolonial nation free of socio-medical ills. In their attempts to medicalise male sexuality and regulate female prostitution, legislative reformers were delineating and gendering the normative heterosexuality of the healthy male colonial subject for the emerging nation.\n\nRecent scholarship has brought much-needed attention to the medicalisation of reproduction, prostitution and venereal disease in colonial and contemporary Egypt, but it has overwhelmingly focused on the health of females since they were the ones who bore and raised the future citizens of the nation.1 In contrast, this chapter analyses legislation that concentrated on the sexual practices of male colonial subjects to demonstrate how a new heterosexually normative male body became inextricably linked to the success of the emerging Egyptian nation. It highlights how Egyptian notions of sexual diseases were gendered and explains why certain diseases were an issue of concern only if men had contracted them. Specifically, it briefly reviews the Ottoman and colonial legislation related to female prostitution before it analyses Article 9 of Egyptian Personal Status Law 25 of 1920 \u2013 the last successful attempt of the interwar state to regulate male sexuality \u2013 which granted a wife the right to divorce her husband if he contracted a chronic ailment such as venereal disease. This chapter argues that the Egyptian monitoring and medicalisation of male sexuality was part and parcel of the larger worldwide eugenics movement in the early twentieth century that resulted in the medicalisation of sex, marriage and reproduction in many other parts of the world like colonial India, Bolshevik Russia, Nazi Germany and the American south. Not only did Egyptians participate in the international movement by cautiously deploying its various models in eugenics; perhaps more significantly, they departed from the global movement by localising various eugenic examples and drawing inspiration from medieval Islamic religious texts rather than western scientific treatises to fit their own unique socio-political and medico-legal context.\n\nThe Egyptian context\n\nAlthough Britain occupied Egypt in 1882 and established a new colonial regime, Egypt nominally remained a province of the Ottoman empire as it had been since 1517. As a result, Egyptians continued to maintain and oversee many of their indigenous institutions such as the Islamic courts whose jurisdiction had been limited mostly to issues of religious endowments and personal status (marriage, divorce, child custody and inheritance) over the course of the nineteenth century.2 At the onset of the First World War in 1914, the British placed Egypt under a temporary protectorate, ending all remaining official ties with the Ottoman empire. When they failed to remove this protectorate status and grant Egypt political independence after the war, Egyptian nationalists initiated an intense struggle for independence beginning with the 1919 revolution. Three years of Anglo-Egyptian negotiations culminated in 1922 when the British abolished their protectorate over Egypt, conferred nominal independence and instituted a parliamentary monarchy. Under this new agreement, Egyptians assumed responsibility for their internal affairs, while the British retained a political and military presence to safeguard their interests and maintain influence over Egyptian affairs. All traces of British control ended when Gamal 'Abd al-Nasser led a coup d'\u00e9tat in 1952 and established a completely independent Egypt by 1954.3\n\nBecause of Egypt's awkward position of quasi-independence and semi-colonial British rule, its experiences with gender, sexuality and eugenics differed from those of other European colonies and western nations.4 Unlike in colonial India, for example, British officials did not reform the Islamic legal system in Egypt, despite their frequent criticisms of it.5 The Egyptian administration reformed this legal system of its own accord and drafted, debated and passed Islamic personal status legislation without any direct colonial interference.6 Gendered historiography of colonialism tends to concentrate on colonisers' assumptions and perceptions of marriage, gender and sexuality more than those of the colonised.7 While British colonial authorities legislated and supervised Egyptian female prostitution, the Egyptian state had been monitoring and medicalising the sexual and marital practices of its subjects decades before the British arrived. As a result, internal dialogues among Egyptians were not steeped in colonialists' debates on racial difference. The Egyptian discourse on marriage, sexuality and prostitution was part and parcel of the larger international movement of eugenics that engaged with various western discussions on diseased, colonised and minorities' bodies, but it also had its own indigenous roots long before the western eugenics movement began in the late nineteenth century.\n\nMonitoring male sexuality\n\nHalf a century before the term 'eugenics' was coined in Britain in 1883, Ottoman Egypt witnessed a broad array of public health campaigns.8 Muhammad 'Ali's state (r.1803\u201348) conducted many of these campaigns primarily to provide his building and military projects with the industrious, physically fit bodies that would both increase agricultural production and strengthen military prowess.9 Motivated mostly by his desire to develop the health and discipline of his burgeoning modern army, 'Ali banned prostitution in Cairo and all military camps, and banished prostitutes to Upper Egypt in 1834. While prostitution had been legal in the Ottoman province of Egypt, prostitutes had been taxed, monitored and registered by the state since the beginning of Ottoman rule in the sixteenth century.10\n\nThroughout the nineteenth century, syphilis was a 'frequent disease in every part of Egypt' amongst all social classes and by the 1830s it had become a significant problem in the army.11 Between 1847 and 1848, for example, more than 33 per cent of the patients at Cairo's main military hospital were treated for venereal diseases.12 Because treatment of venereal disease required infected soldiers to be removed from duty in order to undergo treatment, the military's physical and disciplinary problems were blamed on its soldiers' excessive sexual encounters with women. Their interactions with prostitutes were not viewed as the only sources of contagion, however. Even their conjugal relations with their wives came under state supervision. Military wives were no longer permitted to accompany their husbands on duty. Like prostitutes, they were forbidden from entering military barracks and, like soldiers, they became subjected to weekly medical examinations. By the mid-nineteenth century, soldiers were not even allowed to marry without securing official permission.13 While the history of Egyptian prostitution and sexuality often focuses on the policing of women, a look at Muhammad 'Ali's army reveals that state regulation of female sexuality was very much about attempting to control male sexuality. The protection of men's health, not the improvement of women's welfare or the safeguarding of public morality, was the state's underlying objective because it was men who provided the physical labour and military strength for the state's nation-building projects and its viceroy's expansionist imperial ambitions.\n\nWhen the British occupied Egypt in 1882, they legalised prostitution for the same reason that Muhammad 'Ali had restricted it half a century earlier: to protect the health of their military troops stationed in Egypt. By 1884, Egyptian female prostitutes (but not foreign female prostitutes, who held exclusive extraterritorial capitulatory privileges that exempted them from local laws) were forced to undergo weekly inspections.14 By 1885, these women were required to register with the government and carry health certificates verifying their medical clearance. British colonial authorities established a formalised system of control in 1905, and the Egyptian Ministry of Interior codified these regulations legalising prostitution and monitoring prostitutes. The Egyptian administration left these laws in place even after Egypt gained nominal independence in 1922 and throughout the widespread anti-prostitution campaigns in the interwar period. They did not outlaw prostitution until 1951. The regulations collectively limited prostitution to registered venues in certain neighbourhoods and mandated prostitutes, who had to be adult (post-puberty) women who obtained working permits, to undergo weekly examinations for venereal disease.15 Their (male) clients, whether British or Egyptian, were never subject to examination.\n\nAlthough Muhammad 'Ali's state and the colonial state were motivated by similar interests to protect male sexuality in their regulation of female prostitution, the former also monitored male sexuality while the latter did not. The British were only concerned with Egyptian sexuality when it could contaminate the purity of their own subjects, whether male or female.16 Hence, their main preoccupation was with the Egyptian female prostitutes who could infect their white men. Yet the Egyptian administration did not continue Muhammad 'Ali's surveillance of Egyptian male sexuality in the colonial period, perhaps because it felt pressured to follow its coloniser's example. While a few sporadic attempts were made to limit or eradicate prostitution in the 1890s and early 1900s, none sought to regulate male sexuality. After the editor-in-chief of Egypt's popular daily al-Ahram published a translation of a Greek study on the danger of venereal disease in Egypt in 1907, for example, a number of brothels were closed by the following year. According to the Egyptian Director of Public Security, the rate of infection of venereal disease rose so dramatically after the closure of these brothels in one Egyptian red light district that its subjects demanded the government reopen its regulated brothels.17\n\nSocial reformers also called for the abolition of prostitution long before their successors launched a vociferous campaign in the 1920s and 1930s. In 1893, for example, the prominent nationalist thinker 'Abdallah al-Nadim launched a vituperative press attack against prostitution, which he blamed exclusively on the British occupation in the pages of his newspaper, al-Ustadh. It was, however, Shaykh Muhammad 'Abdu, the prominent Islamic reformer and revered Grand Mufti of Egypt from 1899 to 1905, who exclusively blamed Egyptian male bachelors and not the British or even female prostitutes for the spread of venereal disease in British-occupied Egypt. In 1902, he wrote:\n\nThe so-called educated [bachelors]... have not benefited from [western] education except to learn how to speak a European language so that they can copulate with western prostitutes... instead of [marrying] honourable native women. If it were not for those educated, the market for prostitution would not have flourished in Egypt. If it were not for those educated, syphilis would not have appeared in the nation.18\n\nAccording to 'Abdu, educated bachelors used their western education to frequent the western prostitutes living and working in Egypt rather than marry moral Egyptian women. Egypt was a major terminus for European prostitutes, willing or forced, under British rule, but the expansion of the Mediterranean steamship service and the opening of the Suez Canal in 1869 drew a steady flow of European prostitutes to Egypt long before the inception of official colonial occupation.19 'Abdu's anti-colonial bent was more subtle, but nonetheless apparent in his ridicule of the utility of western education and his neglect to mention the Egyptian prostitutes who outnumbered the western prostitutes.\n\n'Abdu's contempt for western-educated bachelors was more explicit. He held them responsible for introducing prostitution and venereal disease to the struggling nation. He did not merely reproach these decadent men for prostitution and disease. He also held their immoral upbringing, western education and illicit activities responsible for their lack of manhood, as well as the British occupation: 'If you engage in premarital sex rather than marriage... you must struggle to improve yourself... if moral upbringing and education existed among us, we would have had [real] men... there would be [national] wealth and there would be independence'.20 As in anti-prostitution struggles in the United States and Europe, abolition advocates like 'Abdu believed marriage was an institution that would discipline men into productive citizens who would contain their sexual desires within marriage and rid the nation of venereal disease.21 Early twentieth-century Egyptian prostitution abolitionists argued that marriage would be 'morally and materially uplifting' because it would deter the social perversions of prostitution and illicit sexual relations, 'effectively normalising middle-class sexuality'.22 For these social reformers, men's natural, even uncontrollable, sexual appetite itself did not compromise an Egyptian subject's moral manliness if it was contained within marriage.23 In contrast, emerging hegemonic notions of masculinity in nineteenth-century European discourses repeatedly emphasised control of the passions, restraint of the appetites and moderation in marital sex, where puritans argued sex was solely for procreation.24 Early twentieth-century Egyptian discourses on prostitution, on the other hand, were merely calling for the containment of sex to marriage, where non-reproductive sexuality was condoned and celebrated in Islam.25 What Egyptian reformers shared with their European counterparts, however, was a belief that the government was responsible for outlawing prostitution, regulating sexuality and legislating marriage. As Michel Foucault observes, 'the marriage relation was the most intense focus of constraints' for most nineteenth-century European governments.26\n\nThe influx of prostitutes and boom in brothels and red light districts to serve the some 84,000 British, Australian and New Zealand troops stationed in Egypt during the First World War further spurred public concern over the spread of venereal disease. As more than 10,000 of these troops in Cairo were treated for venereal disease during the first five months of 1916, Egyptians worried that the rate of infection would increase among them. They anxiously followed the British debates over whether combating venereal disease demanded medical prophylaxis or moral restraint, as colonial military officials intensified their commitment of state medicine to social hygiene for the sake of national health and racial progress. Egyptian nationalists selectively appropriated, adapted and deployed British discourses of venereal peril, social purity and hygiene to fit their own constructions of the Egyptian nation and proper male sexuality. Venereal disease and prostitution were not only viewed as wartime problems of the military, but as affecting everyone all the time. As a result, Egyptian reformers applauded British authorities' efforts to reduce venereal disease and purify social space.27 Soon after, they too demanded that their own administration institute policing measures for the sake of its own (future) citizens as they struggled for national independence.\n\nThe medicalisation of marriage\n\nThroughout the 1920s and 1930s, social reformers in Egypt waged battles to ban female prostitution and medicalise marriage, in large part to prevent the venereal diseases that Egyptian men were purportedly contracting from prostitutes.28 Legislators and prostitution abolitionists shared a common fear that Egyptian bachelors who contracted venereal diseases from prostitutes would later infect their future wives and offspring, the next generation of Egyptian national subjects. They viewed colonial bachelors as a conduit through which moral and medical disease would spread through the body of the burgeoning nation.29\n\nThe anti-prostitution movement of the interwar period ultimately failed: prostitution remained legal until 1951 after state-licensed brothels had been closed in 1949. Despite the main objective of the interwar abolitionist campaigns, prostitution was not outlawed to protect the health of its subjects, male or female, on the eve of the 1952 revolution that removed all vestiges of British colonial power. The Egyptian state ultimately banned prostitution partly to present itself as the guardian of Egyptian and Islamic morality in the face of a surging conservative nationalist fervour following Egypt's defeat by Israel in the first Arab\u2013Israeli War and the Muslim Brotherhood's alleged assassination of Egypt's Prime Minister Mahmud Fahmi al-Nuqrashi in 1948. The government's decision to outlaw prostitution, which was closely associated with colonial subjugation because of the British military's use of brothels and the privileged status enjoyed by European prostitutes over their Egyptian counterparts, was also in response to its subjects' intense anti-British demonstrations in the late 1940s.30\n\nWhile the anti-prostitution campaigns of the interwar period failed to outlaw female prostitution, a significant state intervention in monitoring and medicalising male sexuality was made in 1920 before the widespread campaigns to outlaw female prostitution and medicalise marriage. Article 9 of Law 25 of 1920 granted a wife the right to divorce her husband if he contracted a chronic ailment such as venereal disease. This legal article was motivated by a rapidly growing Egyptian discourse on eugenics-inspired reform. It was not inspired by a women's rights discourse that sought increased female access to divorce as legal scholars have traditionally contended, especially as the 1920 law was passed three years before the Egyptian Feminist Union was founded in 1923, and its campaign to reform personal status law was not launched until the late 1920s.31\n\nWomen's studies scholars of modern Egypt generally view the 1920 personal status legislation, discussed in detail below, as institutionalising a patriarchal order that is responsible for the present subjugation of Egyptian women.32 When one interrogates how and why the 1920 law (as well as its 1929 amendment) was proposed, how the larger public reacted to it and where they fit into articulations of Egyptian nationalism, however, it becomes clear that state legislators did not necessarily intend to improve the lot of women or intentionally seek to oppress women. Rather, the Egyptian government sought to pass marital laws in order to take a more active role in creating a nationalist, nuclear, physically fit and 'modern' family.33 To rephrase Etienne Balibar's term, the intention of Egyptian legislators was the 'nationalisation of marriage', that is, the creation of married subjects who would form adult, permanent, preferably monogamous families that, in turn, would serve as the foundation for a modern nation free of social and medical ills.34 State officials made attempts to abolish or limit Islamic marriage and divorce laws that it deemed unfit for a modern healthy nation.\n\nIn a patriarchal society where many did not favour female-initiated divorce, Egyptian legislators deemed Article 9 of Law 25 of 1920 appropriate because its intention was to preserve the physical welfare of the family and by extension the nation. Egyptian discussions about the need for strong healthy bodies for the nation multiplied during the two decades preceding the introduction of the 1920 law as the Egyptian struggle for independence gained momentum. Egyptian nationalists, reformers and doctors started demanding that the government establish new means of monitoring the sexual and marital habits of the population to ensure that only adult Egyptians would marry and reproduce. Legislation designed to curtail the marriage of minors in 1914 and 1923, for example, was motivated by medical discourses that argued early marriage of girls led to premature and fatal pregnancies and nationalist discourses that claimed only physically mature and educated women were capable of producing and raising future citizens for the nation.35 These calls, however, were not limited to proposing minimum age limits to marriage.\n\nDuring the 1914 debates over the marriage of minors, for example, Ilyas al-Ghadban wrote to the editors of the popular daily al-Ahram to condemn families that married off their 'disease-ridden' sons and daughters, proposing that the government adopt a law that would require brides and grooms to submit a medical certificate testifying that they were not afflicted with disease for the sake of their offspring.36 Because a healthy family was seen as the cornerstone of the burgeoning nation, many implored the state to assume a central role in ensuring that only physically fit Egyptians had the right to marry and reproduce. Despite proposals in 1928 and 1941 to mandate medical examinations of couples before marriage to ensure their sexual and reproductive health and to protect the future generations of a nation that was ostensibly plagued with disease, the bill was never passed.37 The semi-colonial state, however, did manage to medicalise male sexuality through its 1920 personal status legislation.\n\nAs part of its ongoing effort to 'modernise' the emerging Egyptian nation, the Ministry of Justice codified nationwide a revised set of Islamic personal status laws in 1920, further amended in 1929, which largely continue to govern Egyptian marriage, divorce and the family to this day.38 Law 25 of 1920 institutionalised three official grounds on which women could sue for judicial divorce. Egyptian legislators departed from the Hanafi legal school \u2013 one of the four major Sunni schools of law, that formed the official law of the Ottoman empire and its Egyptian province for the preceding four centuries \u2013 and drew on the more liberal Maliki and Shafi'i schools to provide women with these additional grounds.39 The first two introduced specific circumstances under which a woman could seek judicial divorce if her husband failed to support her financially. These two articles, which have been discussed extensively by scholars, did not introduce innovative concepts to Egyptian Islamic law.40 The financial responsibilities of Muslim husbands toward their wives had been clearly elaborated in the 1875 Egyptian Hanafi Personal Status Code.41\n\nHowever, the third basis \u2013 disease \u2013 introduced a novel justification to Hanafi law, which did not view this as a valid justification for female-initiated judicial divorce. The only health-related condition under which Hanafi law permitted female-initiated judicial divorce was if a husband were sexually impotent, because a wife's sexual satisfaction and reproductive capability were paramount objectives of Islamic marriage.42 Article 9 of Law 25 of 1920 stated:\n\nThe wife is entitled to ask for a judicial divorce from her husband if she finds [in him] chronic defects, for which a cure is impossible or only curable after a long period of time and she cannot live with him without harm, such as insanity, leprosy and skin diseases. [This is the case] whether he had such a defect before the contract [of marriage] and she did not know about it or [whether it] occurred after the contract and she refuses [to live with him]. But if she married him knowing about the defect or if the defect occurred after the contract and she accepted it explicitly or implicitly, then judicial divorce is not permitted.43\n\nMarriage and divorce together functioned as a powerful social site where Egyptian legislators created new categories of disease and defect that \u2013 as scholars in disability studies have demonstrated \u2013 are social constructs that are intentionally ambiguously defined and used.44 It was thus that a new normative male body, defined as healthy and free from disease, became inextricably linked to the success of the emerging Egyptian nation. The broader socio-legal and medical debates regarding the health of Egyptian subjects to marry, reproduce and raise future citizens for the nation influenced the perceptions of the 1920 personal status committee to the point that its members introduced a completely new concept to Egyptian divorce legislation. They explicitly linked the emerging developments and understandings of medicine, health and eugenics to introduce a novel interpretation and formulation of female-initiated judicial divorce to traditional Egyptian Hanafi conceptions of Islamic law.\n\nDuring this same time period, various sexual hygiene reformists were calling for laws in a number of countries to limit or prohibit marriage by persons infected with venereal disease.45 The various western eugenics movements, which were followed closely in the Egyptian press, may have influenced the legislators of the 1920 law.46 The legislative committee included a mix of Islamic scholars and secular politicians: the Rector of al-Azhar University, the Shaykh of the Maliki legal school, the head of the Supreme Islamic Court, the Mufti of Egypt, the Minister of Justice, the President of the Cabinet of Ministers and the King of Egypt.47 The legislators did not, however, find inspiration for this new law in the west, but rather in medieval Islamic law. The committee could not devise laws prohibiting the marriage of infected men and women that had no basis in Islam, thus explaining why bills in 1928 and 1941 proposing that couples undergo medical examinations before marriage were never passed.\n\nConsidering how careful Islamic jurists and even secular politicians were to find a religious basis for their legislation, where did they find religious justification for the new pretext of a husband's disease as a valid reason for female-initiated divorce? Article 9 was taken almost verbatim from a twelfth-century Maliki legal manual. Like Hanafi law, Maliki law was one of the four Islamic schools of legal thought, but it was not the official law of the Ottoman empire and did not serve as the manual for Egyptian judges and lawyers as did the Egyptian Hanafi Personal Status Code, which the Ministry of Justice published in 1875.48 While the majority of Muslims in Upper Egypt personally adhered to the teachings of the Maliki legal school, an 1880 law had instructed Islamic judges to implement the Hanafi school of law, despite the personal affiliation of the litigants.49\n\nIn the twelfth century, long before modern movements of eugenics and nationalism materialised, the renowned Maliki jurist, philosopher and physician Ibn Rushd (d.1198), better known in the west as Averroes, decreed almost identical terms of a husband's disease for female-initiated divorce in his manual of Maliki law, which were spelled out practically verbatim in Article 9 of the 1920 law.50 Although twentieth-century Islamic conceptions of the body and its defects differed drastically from their medieval counterparts,51 Ibn Rushd's examples of defects (insanity, leprosy and skin disease) were identical to those listed in the 1920 law except for an additional example that Ibn Rushd provided, which the 1920 law did not: 'disease of the sex organ'.52 While venereal disease was not specified in Article 9, syphilis was often mistaken for leprosy in Egypt (and elsewhere) until only recently because the two contagious diseases, which were very widespread in Ottoman and semi-colonial Egypt, shared similar symptoms that typically manifested as 'skin diseases' and were not easily curable.53 The 1920 Egyptian personal status committee's examples of syphilis and skin diseases and overall vaguely worded stipulations of chronic defects in general enabled and facilitated wives to cite their husbands' venereal diseases as a cause for judicial divorce.54\n\nWhat was also so innovative about the committee's introduction of this Maliki clause in 1920 was that it was the first time the state deviated from Hanafi doctrine to ingeniously borrow and combine principles from the other schools of Islamic law in an eclectic and unprecedented manner.55 The committee that devised and passed the first major marital legislation largely followed, albeit after a gap of two decades, the judicial advice of Islamic reformers Muhammad 'Abdu and Qasim Amin56 to embrace this process of selectively employing other legal views and minority opinions such as adopting Maliki views of judicial divorce.57 It is likely that 'Abdu's views, as well as the nineteenth- and early twentieth-century socio-legal regulations of male sexuality and prostitution to eliminate sexually transmitted disease, encouraged the committee to adopt a law that would enable wives to divorce their husbands infected with venereal disease. In semi-colonial Egypt, the state perceived an infected husband who could contaminate his wife and their children, the future citizens of the nation, as a threat to his wife, their future family and by extension the emerging nation. Syphilis was particularly worrisome because of its inheritable nature, which was commonly believed to be the leading cause of Egypt's high infant mortality rate and the reason behind epilepsy, hysteria and insanity in offspring.58\n\nGendering the law, sexualising its subjects\n\nBritish and other western eugenics discourses often targeted and monitored only women to protect the health of men. By the mid-1870s, British administrators throughout the globe had established the Contagious Diseases (CD) ordinances and regulations that held female prostitutes solely responsible for venereal disease. While this system differed from colony to colony, female sex workers in nearly every British colony were forced to register officially as prostitutes with the colonial authorities and undergo weekly examinations designed to detect venereal disease.59 In Egypt, however, British administrators only required indigenous female prostitutes to register, undergo weekly medical examinations and carry medical certificates attesting to their health status. British and other European female prostitutes in Egypt were never required to undergo examinations. Their supervision of prostitution took on racist dimensions when they subjected only Egyptian prostitutes to their regulations and examinations. European women were granted immunity by the legal capitulations that the Ottoman regime established with various European powers to encourage and protect western interests from the sixteenth century onwards. While the Ottoman empire collapsed by 1918, the capitulations were not eliminated in Egypt until 1937.60 While protecting British male sexuality was of the utmost concern to the colonial authorities, they never mandated their subjects to any formal sexual regulation. The Egyptian administration, on the other hand, had made it part of state policy to monitor and regulate male sexuality, at least military male sexuality, from the early nineteenth century. Egyptian military men were subjected to regular medical examinations and they were not permitted to have their sexual partners \u2013 be they wives, girlfriends or prostitutes \u2013 accompany them on duty. Their female partners, whatever their status, were also subject to medical testing. Like the British, Egyptian state officials' concern was the physical protection of their men who provided labour for the state through military and other state-building projects. Unlike the British, though, they did not target females alone for the sake of men.\n\nEgyptian Muslim men, however, were the only targets of Article 9 of Law 25 of 1920. Why does this article speak only to the health status of men as husbands, and not to women? At first glance, the answer seems quite simple. Muslim men did not need a reason to divorce their wives. Islamic law granted only men the unilateral and unlicensed right to divorce their wives whenever, wherever and for whatever reason they wished.61 The 1875 Egyptian Hanafi Personal Status Code clearly stated that 'The husband and not the wife has the right to break, by repudiation, the tie of a validly contracted marriage'.62 In Islamic law, a woman did not have the right to divorce. Rather, a divorce had to be given to her either by her husband or by a judge because Islamic law viewed her as a passive participant in the dissolution of marriage. Prior to the introduction of Law 25 of 1920, an Egyptian Muslim woman had three possible, but often unachievable, avenues to divorce: first, she could ask her husband to stipulate her right to divorce in their marriage contract; second, she could ask the court to grant her a judicial divorce; or third, she could ask her husband to divorce her by mutual agreement.63 Before the 1920 law, then, an Egyptian woman married to a mentally or terminally ill man could not usually be granted a divorce on the basis of his condition alone.\n\nArticle 9 of the 1920 law did not target women's health specifically. But it highlights the way Egyptian notions of disease were gendered. Certain diseases were considered male diseases, or at least were only an issue of concern if men had contracted them. Despite its ambiguous wording, it becomes clear that venereal disease was the primary concern of Article 9 when the law is situated in the larger socio-political and medico-legal milieu of Ottoman and semi-colonial Egypt. Sexually active Egyptian women were not the concern here, because it was presumed that women who engaged in pre-marital sex or sex work and contracted venereal diseases would never be marriageable in a society that valued female virginity. These women would not and should not marry and reproduce. The health of a woman in this specific law was not a concern because of the already existing policing of her body and social world. Just as the state was supposedly expanding women's access to divorce, women were not the objects of the legislation and their best interests were not the intent of the legislation. Although the law may have sought to protect a wife from contracting her husband's disease, the aim appears to have been more about protecting her children, the future generation who would lead Egypt to full independence. The role that reformers and legislators wanted the Egyptian state to assume in monitoring and medicalising marriage and male sexuality confirms that the formation of the modern family was largely the result of medico-legal state intervention, that sought to consolidate and control the nuclear family as an apparatus to create 'the healthy, clean, fit body' in 'a purified, cleansed, aerated domestic space'.64\n\nConclusions: application and aftermath\n\nThe fact that the anti-prostitution movement, which was largely motivated by fears of the spread of venereal disease, gained major momentum during the two decades following Law 25 of 1920 suggests that the law did little to alleviate concerns over venereal disease in semi-colonial Egypt, regardless of whether or not its incidence was as high as British colonial officials and Egyptian prostitution abolitionists claimed. Complete statistics \u2013 impossible to obtain when men (as well as unlicensed prostitutes, foreign prostitutes and single sexually active women) were no longer forced to undergo any sort of medical examinations \u2013 were unavailable.\n\nFurthermore, Article 9 did not translate easily into practice. It appears that few women attempted to sue for judicial divorce from their husbands on the basis of venereal disease or any other type of defect in interwar Egypt.65 The paucity of such suits invites two plausible interpretations: either the incidence of disease (venereal and other) among Egyptian men was not nearly as high as the Egyptian state and press portrayed; or most wives knew that it would be very difficult to prove the chronic contagious condition of their husbands' illness. For the most part, those divorces that were granted on the basis of Article 9 were only given to wives whose husbands met all the conditions laid out therein. If the disease was curable, if the judge determined that the husband's illness did not cause his wife intolerable injury, if evidence suggested the wife knew about the ailment beforehand or had agreed to live with her husband regardless, or if the judge had reason to believe that her suit arose from an ulterior motive, then the judge did not grant the wife a divorce.66\n\nContrary to the opinion of Egyptian nationalists and contemporary legal scholars, Egyptian personal status legislation in 1920 (and its 1929 amendment) often made divorce more difficult, not easier, by codifying official grounds for divorce.67 Article 9 granting a wife a divorce based on her husband's disease is no exception. There is no doubt that this clause was vaguely worded \u2013 much more so than the other sections of Law 25 of 1920 \u2013 and used uncertain terms like 'chronic defect' or 'insanity'. While the legislators' ambiguity might lead us to believe that they were leaving the door open for judges to interpret the law loosely and consider modern diseases like syphilis, the opposite actually occurred. By providing only three examples of chronic disease, legislators ended up limiting the judges \u2013 government employees who were appointed, promoted, transferred, retired and paid a fixed salary by the Egyptian administration \u2013 who did not want to depart from hegemonic interpretations. Until the 1970s, for example, judges mostly granted divorces to wives whose husbands were proven to have had only leprosy or insanity \u2013 the only examples of illness specified in Article 9 \u2013 and no other disease that would make their wives' lives unbearable or infect their health.68\n\nNevertheless, the fact that the state even managed to list male disease as a pretext for female-initiated divorce in a society where most did not favour female-initiated divorce is noteworthy. A simple reading might lead us to believe that the emerging nation-state was attempting to expand women's access to divorce. A more nuanced reading of the law in its larger socio-political and medico-legal context, however, invites another explanation. Egyptian legislators deemed female-initiated divorce appropriate in this instance if its intention was to preserve the physical welfare of the family \u2013 the basic building block of the nation \u2013 and by extension the fitness of the nation. When Law 25 of 1920 is read in succession to earlier regulations regarding prostitution, male sexuality, venereal disease and marriage enacted in nineteenth-century Egypt, its continuities with the pre-colonial Egyptian state's attempts to monitor and medicalise Egyptian male sexuality become evident. The regulations and debates of the British colonial regime, as well as the international eugenics movements, all of which were closely followed by Egyptian reformers and legislators, also impacted their views on normative healthy male sexuality. However they refused to appropriate blindly western conceptions of healthy bodies and sexual and marital practices. Rather, they found inspiration in their own pre-colonial state practices and in medieval Islamic texts. As a result, other attempts to medicalise marriage that had no basis in Islam, like requiring couples to undergo medical examinations before marriage, failed to pass in semi-colonial Egypt. The only successful attempt of the interwar semi-independent Egyptian state to reconcile its nationalist vision of healthy modern men, marriages and families for the future nation with Islamic law was Article 9 of Personal Status Law 25 of 1920.\n\nNotes\n\nI would like to thank the two anonymous reviewers for their invaluable suggestions, which greatly improved this chapter. Special thanks are also owed to Omnia El Shakry, Richard Gauvain, Farida Makar, Caitlin McNary, Amy Motlagh and Sherene Seikaly for their critical insights. I alone, of course, am responsible for any oversights or errors.\n\n1. See e.g., Kamran Asdar Ali, Planning the Family in Egypt: New Bodies, New Selves (Austin: University of Texas Press, 2002); Laura Bier, 'From Mothers of the Nation to Daughters of the State: Gender and the Politics of Inclusion in Egypt, 1922\u20131967' (unpublished doctoral thesis, New York University, 2006); Laura Bier, 'Prostitution and the Marriage Crisis: Bachelors and Competing Masculinities in 1930s Egypt' (paper presented at the annual meeting for the Middle Eastern Studies Association, San Francisco, CA, 20 November 2001); Bruce W. Dunne, 'Sexuality and the \"Civilizing Process\" in Egypt' (unpublished doctoral thesis, Georgetown University, 1996); Omnia El Shakry, 'Barren Land and Fecund Bodies: the Emergence of Population Discourse in Interwar Egypt', International Journal of Middle East Studies 37 (2005), pp. 351\u201372; Omnia El Shakry, The Great Social Laboratory: Subjects of Knowledge in Colonial and Postcolonial Egypt (Stanford: Stanford University Press, 2007); Omnia El Shakry, 'Schooled Mothers and Structured Play: Child Rearing in Turn-of-the-Century Egypt', in Lila Abu-Lughod (ed.), Remaking Women: Feminism and Modernity in the Middle East (Princeton: Princeton University Press, 1998), pp. 126\u201370. See also Liat Kozma, 'Women on the Margins and Legal Reform in Late Nineteenth-Century Egypt, 1850\u20131882' (unpublished doctoral thesis, New York University, 2006); Mario M. Ruiz, 'Intimate Disputes, Illicit Violence: Gender, Law, and the State in Colonial Egypt, 1849\u20131923' (unpublished doctoral thesis, University of Michigan, 2004); and Amira El-Azhary Sonbol, The Creation of a Medical Profession in Egypt, 1800\u20131922 (Syracuse: Syracuse University Press, 1991).\n\n2. Nathan Brown, 'Shari'a and State in the Modern Middle East', International Journal of Middle East Studies 29 (1997), pp. 359\u201376, here p. 360; Khaled Fahmy and Rudolph Peters, 'The Legal History of Ottoman Egypt', Islamic Law and Society 6 (1999), pp. 131\u20134.\n\n3. For general works on this period in Egyptian history, see Afaf Lutfi al-Sayyid Marsot, A Short History of Modern Egypt (Cambridge: Cambridge University Press, 1985); Gabriel Baer (ed.), Studies in the Social History of Modern Egypt (Chicago: University of Chicago Press, 1969); Israel Gershoni and James P. Jankowski, Egypt, Islam, and the Arabs: The Search for Egyptian Nationhood, 1900\u20131930 (New York: Oxford University Press, 1986); P. M. Holt (ed.), Political and Social Change in Modern Egypt: 1850\u20131950 (London: Oxford University Press, 1968).\n\n4. Because Egypt was never officially a colony of Great Britain, because Egypt was considered somewhat sovereign from 1922 onwards and because Egyptians exercised great control over their internal affairs, especially over laws relating to marriage, gender and sexuality on which this chapter focuses, during much of the Ottoman and British presence in Egypt, I refer to Egypt during this period as 'semi-colonial' rather than 'colonial'. I would like to thank Khaled Fahmy and Zachary Lockman who encouraged me to question and rethink Egypt's muddled status during the early twentieth century.\n\n5. Nathan Brown, The Rule of Law in the Arab World: Courts in Egypt and the Gulf (Cambridge: Cambridge University Press, 1997), pp. 38\u20139.\n\n6. It should be noted, however, that the reforms of the multiple Egyptian legal systems, introduction of western laws and privatisation of religion constituted part of a larger westernising reform movement that was partly responding to colonialism, even if it was undertaken by Egyptians. Laws pertaining to women, the family and sexuality, however, were to remain Islamic in semi-colonial and postcolonial Egypt. See Talal Asad, Formations of the Secular: Christianity, Islam, Modernity (Stanford: Stanford University Press, 2003), pp. 205\u201356.\n\n7. See e.g., Dipesh Chakrabarty, 'The Difference-Deferral of a Colonial Modernity', in David Arnold and David Hardiman (eds), Subaltern Studies VIII (Delhi: Oxford University Press, 1994), pp. 50\u201388; Partha Chatterjee, The Nation and Its Fragments: Colonial and Postcolonial Histories (Princeton: Princeton University Press, 1993); Partha Chatterjee, Nationalist Thought and the Colonial World: A Derivative Discourse? (London: Zed Books, 1986); Philippa Levine, Prostitution, Race, and Politics: Policing Venereal Disease in the British Empire (New York: Routledge, 2003); Mrinalini Sinha, Colonial Masculinity: The 'Manly Englishman' and the 'Effeminate Bengali' in the Late Nineteenth Century (Manchester: Manchester University Press, 1995); Ann Laura Stoler, Carnal Knowledge and Imperial Power: Race and the Intimate in Colonial Rule (Berkeley: University of California Press, 2002); Ann Laura Stoler, Race and the Education of Desire (Durham: Duke University Press, 1995).\n\n8. Marouf A. Hasian, Jr, The Rhetoric of Eugenics in Anglo-American Thought (Athens: University of Georgia Press, 1996), p. 1.\n\n9. Ali, Planning the Family in Egypt, p. 25; Laura Bier, 'From Birth Control to Family Planning: Population, Gender and the Politics of Reproduction in Egypt' (paper presented at the University of North Carolina at Chapel Hill, 11 April 2003), p. 4 n. 2. For a detailed study of the disciplinary methods of the Ottoman viceroy's regime, see Khaled Fahmy, All the Pasha's Men: Mehmed Ali, His Army and the Making of Modern Egypt (Cambridge: Cambridge University Press, 1997).\n\n10. Khaled Fahmy, 'Prostitution in Egypt in the Nineteenth Century', in Eugene Rogan (ed.), Outside In:On the Margins of the Modern Middle East (London: I. B. Tauris, 2002), pp. 77\u2013103, here p. 78.\n\n11. Dunne, 'Sexuality and the \"Civilizing Process\" in Egypt', p. 82.\n\n12. LaVerne Kuhnke, Lives at Risk: Public Health in Nineteenth-Century Egypt (Berkeley: University of California Press, 1990), p. 137.\n\n13. Dunne, 'Sexuality and the \"Civilizing Process\" in Egypt', pp. 81, 83.\n\n14. Margot Badran, Feminists, Islam, and Nation: Gender and the Making of Modern Egypt (Princeton: Princeton University Press, 1995), p. 195.\n\n15. Badran, Feminists, Islam, and Nation, p. 196; Fahmy, 'Prostitution in Egypt in the Nineteenth Century', p. 87; Judith E. Tucker, Women in Nineteenth-Century Egypt (Cambridge: Cambridge University Press, 1985), pp. 151\u20135.\n\n16. On British fears about sexual interactions between Egyptian men and British women, see Hanan Kholoussy, 'Stolen Husbands, Foreign Wives: Mixed Marriage, Identity Formation, and Gender in Colonial Egypt, 1909\u20131923', Hawwa: Journal of Women in the Middle East and the Islamic World 1 (2003), pp. 206\u201340.\n\n17. Emad Hilal, al-Baghaya fi Misr: Dirasa Tarikhiyya Ijtima'iyya, 1834\u20131949 (Cairo: al-'Arabi, 2001), pp. 202\u20133.\n\n18. Muhammad 'Abdu, 'al-Zawaj wa-Shubban Misr wa-Shawabbuha', al-Manar 5, no. 9 (5 August 1902), p. 340. Unless otherwise noted, all translations from Arabic into English are my own.\n\n19. Badran, Feminists, Islam, and Nation, pp. 192\u20134.\n\n20. Badran, Feminists, Islam, and Nation, p. 343.\n\n21. See Levine, Prostitution, Race, and Politics; Sharon R. Ullman, Sex Seen: The Emergence of Modern Sexuality in America (Berkeley: University of California Press, 1997), p. 86. Unlike in other nationalist rhetoric, an Egyptian fear of the possible homosexual tendencies of bachelors was rarely raised in the nationalist press. The silence, however, does not mean such a fear did not exist, but perhaps that it was too dangerous even to mention in a bourgeois public forum because of the overwhelming unacceptability of a supposedly deviant, unnatural practice that was religiously forbidden in the normative context of early twentieth-century Egypt. While heterosexual sex beyond the confines of marriage was also deemed religiously and socially unacceptable, it was at least considered a natural legitimate male desire as opposed to homosexual desire, which was deemed unnatural. On historic representations of Egyptian and Arab homosexuality, see Joseph A. Massad, Desiring Arabs (Chicago: University of Chicago Press, 2007).\n\n22. El Shakry, The Great Social Laboratory, p. 190.\n\n23. The observance of the uncontrollable licentiousness of colonised men has been examined in studies of masculinities in other colonial societies, which demonstrate how colonial discourses constructed the sexually controlled manliness of the coloniser in stark opposition to the excessive licentiousness of the 'effeminate' or 'savage' colonised male. See e.g., Gail Bederman, Manliness and Civilization: A Cultural History of Gender and Race in the United States, 1880\u20131917 (Chicago: University of Chicago Press, 1995); Mrinalini Sinha, Colonial Masculinity.\n\n24. Michel Foucault, The History of Sexuality, vol. 1: An Introduction, tr. Robert Hurley (New York: Pantheon Books, 1978); George L. Mosse, Nationalism and Sexuality: Respectability and Abnormal Sexuality in Modern Europe (New York: Howard Fertig, 1985), pp. 23\u201347; Ann Laura Stoler, Race and the Education of Desire: Foucault's History of Sexuality and the Colonial Order of Things (Durham: Duke University Press, 1995); John Tosh, Manliness and Masculinities in Nineteenth-Century Britain: Essays on Gender, Family, and Empire (Harlow: Pearson, 2005), pp. 61\u201382.\n\n25. On the celebration of sexuality in Islam, see Basim Musallam, Sex and Society in Islam: Birth Control before the Nineteenth Century (Cambridge: Cambridge University Press, 1983).\n\n26. Foucault, History of Sexuality, vol. 1, p. 37.\n\n27. Dunne, 'Sexuality and the \"Civilizing Process\" in Egypt', pp. 172\u20133, 181, 194, 262.\n\n28. Bier, 'Prostitution and the Marriage Crisis', p. 2. See also Badran, Feminists, Islam, and Nation, pp. 192\u2013206; Dunne, 'Sexuality and the \"Civilizing Process\" in Egypt', pp. 253\u2013313; Yunan Labib Rizk, 'A Diwan of Contemporary Life (393): Backroads', al-Ahram Weekly, 7\u201313 June 2001; Omnia El Shakry, 'Science: Medicalization, and the Female Body', in Suad Joseph and Afsaneh Najmabadi (eds), Encyclopedia of Women and Islamic Cultures, vol. 3: Family, Body, Sexuality and Health (Leiden: Brill, 2005), pp. 353\u20139, here p. 354. See also El Shakry, The Great Social Laboratory, p. 173.\n\n29. Bier, 'Prostitution and the Marriage Crisis', p. 2.\n\n30. Scott Long, 'Appendix', in Human Rights Watch order, In a Time of Torture: The Assault on Justice in Egypt's Crackdown on Homosexual Conduct (New York: Human Rights Watch, 2004) available at <<http:\/\/www.hrw.org\/en\/node\/12167\/section\/10>> (accessed 22 June 2010). See also Badran, Feminists, Islam, and Nation, pp. 195\u2013206.\n\n31. James N. D. Anderson, Islamic Law in the Modern World (New York: New York University Press, 1959), p. 26; John L. Esposito, Women in Muslim Family Law (1982; 2nd edn, Syracuse: Syracuse University Press, 2001), p. 50.\n\n32. Badran, Feminists, Islam, and Nation, p. 135; Selma Botman, Engendering Citizenship in Egypt (New York: Columbia University Press, 1999), p. 23; Mervat Hatem, 'The Enduring Alliance of Nationalism and Patriarchy in Muslim Personal Status Laws: The Case of Modern Egypt', Feminist Issues 6 (1986), pp. 19\u201343, here p. 26; Amira El Azhary Sonbol, 'Introduction', in Amira El Azhary Sonbol (ed.), Women, the Family, and Divorce Laws in Islamic History (Syracuse: Syracuse University Press, 1996), pp. 1\u201320, here p. 11.\n\n33. Hanan Kholoussy, 'The Nationalization of Marriage in Monarchical Egypt', in Arthur Goldschmidt, Jr, Amy J. Johnson and Barak Salmoni (eds), Re-Envisioning Egypt, 1919\u20131952 (Cairo: American University in Cairo Press, 2005), pp. 317\u201350, here p. 319.\n\n34. Etienne Balibar, 'The Nation Form: History and Ideology', in Etienne Balibar and Immanuel Wallerstein (eds), Race, Nation, Class: Ambiguous Identities (London: Verso, 1991), pp. 86\u2013106, here pp. 101, 102.\n\n35. Kholoussy, 'Nationalization of Marriage in Monarchical Egypt', pp. 320\u201324.\n\n36. Ilyas al-Ghadban, 'Zawaj al-Mu'allin wa-Hal Min al-Amkan Mana'hu', al-Ahram 39, no. 10972 (31 March 1914), p. 2.\n\n37. El Shakry, The Great Social Laboratory, p. 173.\n\n38. These personal status laws remained virtually unchanged throughout the remainder of the twentieth century until Law 1 of 2000, which slightly amended Law 25 of 1929. See Kenneth M. Cuno, 'Divorce and the Fate of the Family in Modern Egypt', in Kathryn M. Yount and Hoda Rashad (eds), Family in the Middle East: Ideational Change in Egypt, Iran, and Tunisia (New York: Routledge, 2008), pp. 196\u2013216.\n\n39. James N. D. Anderson, 'Recent Developments in Shari'a Law V', Muslim World 41 (1951), pp. 278\u201388; Beth Baron, 'The Making and Breaking of Marital Bonds in Modern Egypt', in Nikkie R. Keddie and Beth Baron (eds), Women in Middle Eastern History: Shifting Boundaries in Sex and Gender (New Haven: Yale University Press, 1991), pp. 275\u201391, here p. 285; Esposito, Women in Muslim Family Law, p. 51.\n\n40. See Kholoussy, 'Nationalization of Marriage in Monarchical Egypt', pp. 324\u201332 for an extensive analysis of the 1920 and 1929 personal status laws.\n\n41. Sections 150\u2013205 in Muhammad Pasha Qadri, Code of Mohammedan Personal Law According to the Hanafite School, tr. Wasey Sterry and N. Abcarius (London: Spottiswoode, 1914), pp. 41\u201351.\n\n42. Sections 298\u2013302 in Qadri, Code of Mohammedan Personal Law, pp. 75\u20136.\n\n43. 'Qanun Nimrat 25 li-Sennat 1920', in Majmu'at al-Qawanin wa-l-Marasim al-Mutalaqa bi-l-Shu'un al-'Amma lil-Thalathat al-Ashur al-Awla min Sennat 1920 (Cairo: Matb'a al-Amiriyya, 1921), pp. 37\u20138.\n\n44. See e.g., Simi Linton, Claiming Disability: Knowledge and Identity (New York: New York University Press, 1998), pp. vii\u2013viii; Susan Wendell, The Rejected Body: Feminist Philosophical Reflections on Disability (New York: Routledge, 1996), p. 45.\n\n45. It is worth noting that although eugenicists agreed that the sexual hygiene laws helped their cause, they did not view them as strictly eugenic because venereal diseases were not hereditary. See Edward J. Larson, Sex, Race, and Science: Eugenics in the Deep South (Baltimore: Johns Hopkins University Press, 1995), p. 22.\n\n46. El Shakry, The Great Social Laboratory, p. 149.\n\n47. See 'Qanun Nimrat 25 li-Sennat 1920', p. 36.\n\n48. See Muhammad Pasha Qadri, Kitab al-Ahkam al-Shar'iyya fi al-Ahwal al-Shakhsiyya 'ala Madhhab al-Imam Abi Hanifa al-Nu'man (Cairo: Ministry of Justice, 1875).\n\n49. Ron Shaham, Family and the Courts in Modern Egypt: A Study Based on Decisions by the Shari'a Courts, 1900\u20131955 (Leiden: Brill, 1997), pp. 12\u201313.\n\n50. Ibn Rushd, The Distinguished Jurist's Primer: A Translation of Bidayat al-Mujtahid, vol. 2, tr. Imran Ahsan Khan Nyazee (Reading: Garnet, 1996), p. 59.\n\n51. Sara Scalenghe, 'Being Different: Intersexuality, Blindness, Deafness, and Madness in Ottoman Syria' (unpublished doctoral thesis, Georgetown University, 2006), p. 13.\n\n52. Ibn Rushd, The Distinguished Jurist's Primer, p. 59.\n\n53. Kuhnke, Lives at Risk, p. 30.\n\n54. Shaham, Family and the Courts in Modern Egypt, pp. 119, 125 n. 25; Ron Shaham, 'Revealing the Secrets of the Body: Medical Tests as Legal Evidence in Personal Status Disputes in Modern Egypt', Medicine and Law 22 (2003), pp. 131\u201354, here p. 136.\n\n55. Anderson, 'Recent Developments in Shari'a Law V', pp. 278\u201388; Baron, 'The Making and Breaking of Marital Bonds in Modern Egypt', p. 285; Esposito, Women in Muslim Family Law, pp. 29, 51; Shaham, Family and the Courts in Modern Egypt, p. 14. This patchwork process has since become a permanent feature of Islamic legislation in Egypt. See Oussama Arabi, Studies in Modern Islamic Law and Jurisprudence (The Hague: Kluwer Law International, 2001), p. 15.\n\n56. Qasim Amin is often inaptly considered 'the father of Arab feminism' because of his 1899 treatise, The Liberation of Women, that called for women's reform, which was believed to be written in part by his teacher Muhammad 'Abdu. See Soha Abdel Kader, Egyptian Women in a Changing Society, 1899\u20131987 (London: Lynne Rienner, 1987), p. 8; Juan Ricardo Cole, 'Feminism, Class, and Islam in Turn-of-the-Century Egypt', International Journal of Middle Eastern Studies 13 (1981), pp. 387\u2013407, here p. 401; Yvonne Y. Haddad, 'Islam, Women and Revolution in Twentieth-Century Arab Thought', Muslim World 74 (1984), pp. 137\u201360, here p. 160; Robert Tignor, Modernization and the British Rule in Egypt, 1882\u20131914 (Princeton: Princeton University Press, 1966), p. 341. The following scholars have criticised the overemphasis on Amin because he was neither a feminist who called for full equality between the sexes, nor the only Egyptian intellectual of his generation calling for the advancement of women: Lila Abu-Lughod, 'The Marriage of Feminism and Islamism in Egypt: Selective Repudiation as a Dynamic of Postcolonial Cultural Politics', in Lila Abu-Lughod (ed.), Remaking Women: Feminism and Modernity in the Middle East (Princeton: Princeton University Press, 1998), pp. 255\u201369; Leila Ahmed, Women and Gender in Islam: Historical Roots of a Modern in Debate (New Haven: Yale University Press, 1992), pp. 162\u20133; Badran, Feminists, Islam, and Nation, pp. 18\u201319; Beth Baron, The Women's Awakening in Egypt: Culture, Society, and the Press (New Haven: Yale University Press, 1994), pp. 4\u20136; Timothy Mitchell, Colonising Egypt (Berkeley: University of California Press, 1991), pp. 111\u201313.\n\n57. For Muhammad 'Abdu's support for female-initiated divorce, see Muhammad 'Imara, al-Islam wa-l-Mar'a fi Rayy al-Imam Muhammad 'Abdu (Cairo: Dar al-Hilal, 1979), pp. 25\u201331, 78\u201395; Ahmad Muhammad Shakir, Nizam al-Talaq fi al-Islam (1936; 2nd edn, Cairo: Dar al-Tab'a al-Qawmiyya, 1389 H. [1969\u20131970 AD]), pp. 9\u201311. For Amin's views, see Qasim Amin, The Liberation of Women and the New Woman: Two Documents in the History of Egyptian Feminism, tr. Samiha Sidhom Peterson (Cairo: American University in Cairo Press, 2000), pp. 99\u2013100. See also Kholoussy, 'The Nationalization of Marriage in Monarchical Egypt', pp. 325\u20136.\n\n58. Dunne, 'Sexuality and the \"Civilizing Process\" in Egypt', pp. 278\u20139, 292. For similar concerns in early twentieth-century Iran, see Cyrus Schayegh, '\"A Sound Mind Lives in a Healthy Body\": Texts and Contexts in the Iranian Modernists' Scientific Discourse of Health, 1910s\u201340s', International Journal of Middle East Studies 37 (2005), pp. 167\u201388, here p. 173.\n\n59. See Levine, Prostitution, Race, and Politics.\n\n60. Badran, Feminists, Islam, and Nation, pp. 193, 194\u20135, 199\u2013204.\n\n61. Musallam, Sex and Society in Islam, p. 11.\n\n62. Section 217 in Qadri, Code of Mohammedan Personal Law, p. 56.\n\n63. For an expanded discussion of Egyptian women's greater access to divorce prior to Law 25 of 1920 (and men's greater facility in divorce prior to Law 25's amendment of 1929), see Hanan Kholoussy, For Better, For Worse: The Marriage Crisis that Made Modern Egypt (Stanford: Stanford University Press, 2010), pp. 49\u201376.\n\n64. Michel Foucault, 'The Politics of Health in the Eighteenth Century', in Power\/Knowledge: Selected Interviews and Other Writings, 1972\u20131977 (Brighton: Harvester, 1980), pp. 173\u20136.\n\n65. Kholoussy, For Better, For Worse, pp. 49\u201376; Shaham, Family and the Courts in Modern Egypt, p. 119; Shaham, 'Revealing the Secrets of the Body', p. 135.\n\n66. Shaham, Family and the Courts in Modern Egypt, p. 125.\n\n67. Kholoussy, 'The Nationalization of Marriage in Monarchical Egypt', pp. 324\u201332.\n\n68. Shaham, Family and the Courts in Modern Egypt, p. 125 n. 45.\nChapter 8\n\nThe Volatility of Sex: Intersexuality, Gender and Clinical Practice in the 1950s\n\nSandra Eder\n\nDated January 1951, the admittance record listed the referring physician's observations: 'Could not tell if boy or girl, urinates often, drinks much, vomits occasionally'.1 The patient's parents had made the long journey from their home in the American northeast to Baltimore, Maryland to have Andy, their ailing newborn, treated at the Clinic for Pediatric Endocrinology (CPE) at Johns Hopkins's Harriet Lane Home for Invalid Children (HLH). The child left the clinic in June with the life-threatening symptoms under control, thanks to the steroid cortisone \u2013 and re-assigned as a girl. In the hospital record, the name Andy was crossed out and replaced by 'Ann'. Between 1951 and 1959, Ann's parents would bring her back to the clinic at least six more times for treatment and study.\n\nAndy\/Ann's diagnosis was congenital adrenal hyperplasia, CAH for short. In CAH, the adrenal glands fail to produce sufficient corticosteroids, producing instead considerable amounts of androgens, leading to disruption of salt metabolism, developmental problems in both sexes and ambiguous genitals in girls. The latter symptom put chromosomal female CAH patients in the category of female pseudo-hermaphrodites or, as we would say today, a person with intersex condition or disorder of sexual development (DSD).2 In chromosomal boys, the excess androgen production also leads to sexual symptoms such as sexual precocity manifested by premature growth of the penis and pubic hair.\n\nAndy\/Ann was brought to Hopkins at a crucial moment in the medical conception of sex. The head of the Clinic for Pediatric Endocrinology, Dr Lawson Wilkins, had just developed a new treatment for CAH using the steroid hormone cortisone. In 1951, he hired a young psychologist, John Money, to psychologically evaluate the treatment and to resolve the question of sex in patients who had contradictory biological and psychological sexual characteristics. Money proposed that the sex in which a child with an intersex condition was raised, rather than any single biological determiners of sex, determined whether it saw itself as man or woman. He called this one's 'gender role'.3 Gender role was learned, he argued, in a critical early phase and eventually became firmly 'imprinted' into the child's mind.4 Money, together with psychiatrists Joan and John Hampson, proposed a set of treatment guidelines for intersex patients, which recommended early and consistent assignment of one of two sexes, male or female, and which stressed that it was essential for the optimal gender development to fit a child's genitals as early as possible to the assigned sex. These recommendations would dominate the treatment of children with intersex for the next forty years, until intersex activists challenged them in the early 1990s.5\n\nHermaphroditism, Alice Dreger has argued, became increasingly medicalised in the late nineteenth century as scientific interest in ambiguous sex led to a surge in published case studies. At the same time, medical experts insisted that in most cases a person's 'true sex' could be determined via his or her gonads.6 Three trends emerge from recent scholarship. First, the gonadal gold standard of sexual differentiation was clinically impractical, because few technologies existed to determine the nature of the gonad in the living body. The 'truth' was often only revealed by autopsy.7 Even as medical and surgical techniques improved, a proliferation of biological sex variables such as hormones and chromosomes complicated the quest for a person's 'true sex', as they were often contradictory to a person's appearance or identity.8 Diagnostic and therapeutic approaches differed widely across and within disciplines. The decades before 1955 were a period of idiosyncrasy in which sex was often assigned on a case-by-case basis, until the coining of the term 'gender' at Hopkins created 'a mechanism of control and consolidation' in the treatment of intersexuals.9\n\nSecond, at the centre of concern stood the presumed threat of sex transgression and homosexuality. Physicians, it is argued, insisted on the binary of sex and tried to ensure heterosexuality in their patients. Genitals had to match sexual desire, and sexual desire had to be directed at the 'opposite sex'.10 Surgery to establish hermaphrodites within the heterosexual matrix had already become an acceptable procedure at the beginning of the twentieth century.11 The Hopkins protocols, as the publications that resulted from Money's study became known, created a sense of emergency that encouraged physicians to assign sex quickly and to alter the body surgically in order to achieve psychological healthiness in children with intersexual conditions.12 The ethics of these medical interventions have been criticised extensively, as adult patients started challenging the irreversible surgery and culture of secrecy and shame that had permeated their treatment.13 Money's thesis that gender was learned was quickly replaced by more biological determinant theories.14 Nevertheless, the practice of early surgical intervention continues to this day.\n\nThe third trend integrates medicine as a practice into scholarly analysis, and is illustrated by two recent contributions. Geertje Mak has suggested a 'praxiographic' approach to medicine, a move from epistemological criticism to an analysis of clinical practice, in order to investigate how sex is enacted within the clinical encounter. Sex is not situated in 'the antagonistic opposition between a medical gold standard of \"true\" sex and a personal \"true\" sex', but within a complex relationship between the two.15 Similarly, Katrina Karkazis in her ethnography of the medical management of intersexuality in the United States shows how clinicians became the 'specialised interpreters of the body' and transformed a problem of social gender into a biological anomaly.16 Acknowledging clinicians' strong motivation to help parents and children, she shows how the medical incentive to treat is situated within the binary framework of sex and of heterosexuality, which shapes conceptions of normality.17\n\nBuilding on Mak and Karkazi's focus on medical practice, I base my analysis of the introduction and incorporation of gender role into medical practice on twenty-five detailed records of CAH patients treated at the HLH. These previously unavailable sources provide a rare insight into the clinical practice of Wilkins and his team.18 Ranging in length from eight to 300 pages and in scope from a one-time visit to relationships lasting many decades, these records are a highly formalised yet strikingly intimate literary form, including patient histories, graphs, blood counts, chemistry lab and x-ray reports, pictures of the child, letters from parents and social workers. They provide a rare glimpse into how this clinic ran on a day-to-day basis, illustrating the physicians' specific medical logic that structured the clinical encounter between doctors, parents and patients. The pervasive logic of patient records clearly privileges the physicians' voice, and to a certain extent the narrative of the parents.19 A careful reading of the clinical records, however, shows how clinical practice structured enactments of sex and gender, of health and disease.\n\nI suggest that reframing the emergence of gender as an element in the development of a specific medical treatment for an endocrinological condition \u2013 rather than as the primary aim of a set of doctors \u2013 excavates the complex and contingent historical factors that led to the formulation of gender role in the Hopkins context. To be sure, surgical and medical procedures that shape the intersex body to conveniently fit the male\/female binary are profoundly normalising. They are, however, also situated within the medical attempt to cure what physicians perceived as a specific 'disease' with multiple symptoms.20 In this chapter, I focus on a specific endocrinological disorder, CAH, rather than on the category of 'intersex'. I show how sex and gender are folded into the diagnosis, treatment and maintenance of what Wilkins and his team defined as an adrenal dysfunction that caused many symptoms beside ambiguous genitals in girls. For them, CAH affected both chromosomally male and female children and demanded long-term medical management, as cortisone, though an effective treatment, was not a cure but part of life-long treatment of a chronic condition.\n\nAs George Canguilhem observed, medical treatment is always, in a sense, about normalising the body. 21 Vital norms, according to Canguilhem, stem from the normativity of life, the capacity of an organism to adapt to its environment. In this context, 'health' is a dynamic category denoting the ability to function in the world. Social norms, on the other hand, represent a particular order of society, and it is the incorporation of the social into the vital that I address here. Normalisation, as described by Foucault, becomes a process in which vital and social norms are conflated and integrated in a historically contingent manner into a notion of 'health'.22 In other words, both treating adrenal hyperplasia with cortisone to lower a patient's 17-Ketosteroid level, which Canguilhem would label a vital normative procedure, and surgical and psychological procedures to make the same patient appear and act more feminine, so as to satisfy social norms, become medical attempts to 'heal'.\n\nDiagnosis\n\nFounded in 1935, the paediatric endocrinology clinic of the Harriet Lane Home for Invalid Children at the Johns Hopkins Hospital was the first clinic of its kind in the US.23 Its founder Lawson Wilkins served as director of the clinic until his retirement in 1960. Paediatric endocrinology as a newly emerging specialisation was concerned with questions of development and growth, paediatric diabetes, sex differentiation, metabolism and various hormonal and glandular conditions in children and young adults.24 The care for children with hormonal disorders was still only a small subset of paediatric concerns and the setting of the clinic first enabled physicians to study a larger group of patients with rare (but scientifically interesting) diseases. In 1940, Wilkins published a case report on a three-and-a-half-year-old boy with symptoms of advanced growth, precocious development of male sex organs, darkening of skin and gums, salt craving and halted mental development.25 After only a few days in the hospital, the child died suddenly and the autopsy revealed hyperplasia of the adrenal cortex. Also, his androgen titers were those of an adult male, leading the authors to conclude, 'our case is the first of which at autopsy a diffuse bilateral hyperplasia of the adrenals has been found in the male causing a condition analogous to pseudohermaphroditism in the female'.26 This conclusion laid the foundation for Wilkins's systematic study of CAH.27 It also provided a definition of CAH that is mostly overlooked in the scholarship on intersexuality; an adrenal hyperplasia that occurred in both boys and girls, the females showing 'pseudo-hermaphroditism' and the males early development of secondary sex characteristics. The latter Wilkins termed 'macrogenitosomnia praecox'.28\n\nAndy\/Ann came to the clinic just as the steroid cortisone had been implemented as a successful treatment and diagnostic tool. Andy's case was typical in many respects. Born in November 1950, Andy 'seemed strong and vigorous at birth... but there was occasional vomiting during the first 8 days'.29 Further, 'abnormal external genitalia were noted at birth. There has been considerable difference of opinion with regard to the sex, but the general consensus seems to have been that the infant was male'. After Andy's discharge from the local hospital, the child started to rapidly lose weight and become dehydrated, so the treating physician recommended that the parents seek expert advice from Wilkins at Hopkins. At Andy's admittance, Dr John Crigler diagnosed the child as 'a well developed and moderately well nourished female pseudohermaphrodite with congenital adrenal hyperplasia'. He also noted that Andy was a salt-loser, a symptom that alarmed the physicians because, in severe cases, children would die from adrenal shock or waste away from salt loss.\n\nWilkins and his colleagues diagnosed CAH by three markers: external genitals, metabolism and development. Genitals that looked ambiguous or precocious, growth of pubic hair in early infancy, feeding problems that could not be explained otherwise and precocious growth indicated the possibility of adrenal hyperplasia. The practitioners also paid attention to skin pigmentation, voice and body hair growth. Besides anatomical examination, the level of 17-Ketosteroids (17-KS) in the urine was a critical diagnostic tool. These substances, which form when the body breaks down androgens, were a measure of the level of androgens in the patient. Elevated 17-KS levels were the defining characteristic of CAH. If the elevated level was decreased by cortisone, the diagnosis of CAH was confirmed. Cortisone was thus both a diagnostic test and a treatment for CAH.\n\nWhile the life-threatening metabolic effects of CAH demanded immediate medical attention, children's ambiguous genitalia triggered another form of urgent intervention. Wilkins and his colleagues insisted on diagnosing the sex of their patients, a concern they shared with parents in cases such as Andy's where 'at the time of birth it was impossible to decide if the baby was boy or girl'.30 However, despite the uncertainty of sex, Andy's parents had given him a male name, tentatively leaning towards boy; perhaps because they had already lost their first child, a boy, to 'severe dehydration + vomiting' \u2013 suggesting that this child, too, had suffered from the severe, salt-losing form of CAH.31 Diagnosing a child's sex enabled Wilkins and his colleagues to design a specific treatment plan conditioned by gendered medical and social expectations.\n\nCases of doubtful sex were common in children with CAH, even if in most cases an answer was found quickly and sometimes this initial confusion is only present in a few lines in the record. Given that Wilkins and his colleagues believed that the child could only be either male or female, determining somebody's sex was a contentious task. Only in a few cases, such as Andy\/Ann, was it thought that one 'could not tell if boy or girl'. Rather, parents and local physicians often 'knew' the child's sex and only at admission to the clinic would Wilkins cast doubt on the original sex assignment. Diagnosis of the child's sex involved the doctors, the parents and the family. Through the early twentieth century, patients had played a yet more active role, because they had come in as adults, often to have a genital problem fixed before marriage and because of failure of the onset of menses or puberty.32 Physicians could only recommend but not force adult patients to change to their gonadal sex in case of erroneous sex assignment at birth.33 The new patient group \u2013 babies and small children \u2013 were brought in by their parents, sometimes on account of symptoms other than ambiguous genitalia, and had no say in terms of sex assignment.34\n\nClinical practices reveal the tentativeness of medical theories on sexual differentiation when confronted with a living patient. Determination of the 'true sex' of a patient also rested on the physician's techniques in the physical examination of the patient.35 Even in the mid-twentieth century, the diagnosis of the 'true sex' often still depended on the physicians' experience and the medical and surgical techniques and technologies available. A child's appearance could be deceiving and some of the diagnostic procedures were inadequate. In the patient records, the physicians still used palpating techniques, such as feeling for testes or ovaries, penetrating the urethra and anus with fingers and instruments to feel for a vagina or a womb. Feeling the inside of the body was, however, often misleading and the techniques to make the inside of the body visible through x-rays and insertion of liquids into body orifices sometimes were inconclusive. A laparotomy \u2013 surgically opening the abdomen and examining the body cavity for the presence of sexual organs \u2013 was the only way to know a child's sex for certain. Because the androgen exposure affected mainly the external genitals and the appearance of a CAH girl's body, the presence of uterus, ovaries and fallopian tubes indicated female sex for the physicians. From 1952 onwards, the newly introduced Barr-Body test for sex chromosomes would become another diagnostic tool for sex. It, however, did not solve the puzzle of sex as the practitioners had hoped.36 Rather, sex chromosomes were added to the proliferation of sex, speaking a particular truth of the body.\n\nThe diagnosis of sex in CAH children was structured by the available medical technologies, the skill and experience of the physicians, the presenting symptoms of the endocrinological condition, the families' wishes and the already assigned sex of the child. Richard, for example, was born January 1949 and first came to Hopkins in summer of 1954.37 He had been diagnosed at the local hospital as a precocious boy with metabolic problems due to adrenal hyperplasia, with a history of convulsions. Richard's parents took him to Johns Hopkins's cardiac clinic to find out the cause of his convulsions and for evaluation of his cortisone therapy. When they arrived at the hospital, they did not doubt the sex of their son. In the general examination, a physician confirmed the child's sex as he examined and measured the penis and stated that the 'right testicle was palpable and of the size of a small olive. Left testes [sic] could not be felt'. Richard was diagnosed with the 'salt-losing type of adrenal hyperplasia'. He was discharged to the 'family physician's care'. Dr Judson Van Wyk, the treating physician in Wilkins's absence, was mainly concerned to control the accelerated growth caused by the boy's excess androgen level and thought that 'with adequate suppression he could probably attain a socially acceptable stature'. It was recommended that Richard should come back in the autumn or spring for further evaluation by Wilkins himself and for dosage adjustment.\n\nIn 1955, Richard returned and this time the testis, which had been felt at the boy's last visit, was nowhere to be found. Wilkins wondered whether Richard might be a female pseudohermaphrodite with congenital adrenal hyperplasia. The previous year's testis might have been an 'inguinal lymph node' and 'in addition this boy's phallus does not seem to be as hypertrophied as most males with macrogenitosomia praecox due to adrenal hyperplasia'. Wilkins thought it wise 'to exclude' this possibility 'by means of a study of the sex chromatin pattern in skin biopsy and by urethroscopic examination to determine whether there might be a communicating vagina'. A Barr test for Richard revealed an 'apparently male pattern'.38 Dr Scott did a urethroscopic examination and found no evidence of a vaginal pouch. Despite the chromosomal proof of sex, Wilkins remained doubtful and at the next admission in the summer of 1956, Wilkins ordered an exploratory laparotomy and another chromosomal sex test \u2013 with surprising results. This time, the pattern was female and a Dr Rosenthal wrote that Richard 'had buccal mucosa smear this AM which revealed female sex chromosome pattern, so on [2 days later] at 10 AM will have laparotomy to remove female gonads'. It had taken two years for Wilkins and his colleagues to pinpoint Richard's sex and in the end genetic sex and the presence of a small uterus and ovaries \u2013 which now suddenly could be felt via rectal exam \u2013 indicated female.\n\nTrusting his experience with physical examination of CAH patients over gonadal and chromosomal evidence, Wilkins had remained sceptical about Richard's sex. Although genetically female, Richard had been raised as a boy, and on finding gonadal and chromosomal proof of his female sex, Wilkins and his team stuck to their diagnosis of Richard as male. No discussion is found in the record of the implications of ignoring the genetic sex of the child. The operating surgeon, Dr Howard Jones, simply stated, 'A routine total abdominal hysterectomy was then performed with excision of both tubes and ovaries. The vaginal vault was closed... in the usual manner'. 39 The post-operative diagnosis read: 'congenital adrenal hyperplasia in a genetic female with psychological sex of male'. For the physicians, psychological sex, or gender, and the fact that Richard had already lived as a boy for the last seven years supported the decision to keep him in the male sex. Once the decision was made, biological traces of femininity were surgically removed.\n\nParents sometimes challenged physicians' authority on matters of sex and gender. Charles was born in the autumn of 1955 and 'said to be a normal male infant at birth'.40 From the beginning, he was a poor feeder, vomiting frequently and his parents had 'noted \"for a long time\" that his penis was larger than that of his brother at similar age'. When Charles started growing pubic hair at the age of two, his parents took him to the local physician, where a Barr test revealed a female pattern. When he was admitted to the HLH in 1958, the emotional turmoil this announcement had caused still resonated in the patient history the attending physician was taking: 'The parents were told the findings, the diagnosis of congenital adrenal hyperplasia was made, and it was recommended that the patient undergo plastic repair and be raised as a female. Some family member objected to this approach and the pt [patient] was referred here for further evaluation and Rx [prescription]'. At the clinic, Charles was diagnosed with 'congenital adrenal hyperplasia, female pseudohermaphrodite, salt losing type'. The gynaecological examination revealed female reproductive organs and another Barr test confirmed the female pattern. To solve the issue, the mother met with Money, who was 'of the opinion that this entire family is strongly oriented in the direction of masculine gender for this patient'. Charles was only two-and-a-half years old, and with the advent of cortisone treatment the recommendation would have been to re-assign Charles as a girl.41 However, 'the parents seem to feel rather strongly about raising this child as a boy [their underlining]'. A few days later, Jones removed fallopian tubes, ovaries and the uterus. Charles's genitalia were consistently referred to in terms of penis, phallus and scrotum from the first day, though the anaesthesia record reads 'Diagnosis and operation: Female pseudohermaphroditism due to congenital adrenal hyperplasia'. At the top of the page, where the patient's sex was noted, F for Female was circled, crossed out and M for male was circled.\n\nAs the case records show, knowing a patient's sex for certain was a contentious task, which depended on the available medical technology and techniques as much as on the physician's experience of the specific condition and the manifold ways 'sex' presented itself to the observer. Even in the face of gonadal and chromosomal 'evidence' of a child's sex, Wilkins, who by the mid-1950s had observed eighty cases of CAH \u2013 sixty female and twenty male patients \u2013 relied on his experience.42 However, even if sex had finally been pinned down according to a chosen category \u2013 increasingly a genetic one \u2013 it often did not make sense to the parents and the physicians in the face of contradictory somatic and social variables.\n\nTreatment\n\nWilkins and his team addressed treatment in two stages: immediate interventions and long-term management of a chronic adrenal disorder. When Andy\/Ann came to the clinic, once the diagnosis of congenital adrenal hyperplasia was confirmed, the treating physicians had a twofold concern. The first was to control the salt loss: 'Obviously control of her electrolyte abnormality was the most important and primary object'.43 The physicians immediately placed Andy\/Ann on a special diet with extra salt. The next step was finding the right dosage of cortisone and to make sure the treatment would be continued after the child left the hospital. By 1955, Wilkins had established a therapeutic cortisone protocol, which had to be adjusted individually to each patient and \u2013 like insulin treatment \u2013 had to be monitored and evaluated.44 Children therefore faced long stays in the clinic during which Wilkins and his colleagues tried to find the right level of cortisone that successfully suppressed the 17-KS level. Once the right dosage was found, it was evaluated at least once a year. While Wilkins's first concern was the balancing of the metabolic disturbances caused by the adrenal hyperplasia, he also wondered how to balance his patients' contradictory sex variables.\n\nWilkins's studies of how to efficiently and adequately treat with cortisone was, from 1951 onwards, accompanied by Money's and the Hampsons' psychological evaluation of 105 intersex patients treated in the clinic, the biggest single group being CAH patients.45 Money and the Hampsons used the proliferation of sex to their advantage. Comparing five biological categories \u2013 gonadal, hormonal and chromosomal sex, external genital morphology and internal accessory reproductive structures \u2013 and sex of rearing with a person's gender role, they concluded that in case of contradictions of sex variables, a child's gender role was most likely to be congruent with the sex it had been raised in. Money specifically argued against the old gold standard of sex assignment, gonadal sex, and against the newly emerging biological determinant, sex chromosomes. During the study, a group of patients previously thought to be females with delayed development was identified to be chromosomally male. Money and the Hampsons stressed that these patients who had been uniformly reared as girls 'in all respects... fulfilled the cultural and psychological expectations of femininity so completely that it was, in each instance, impossible to envisage the person as a boy or man'.46 The newly achieved accessibility of chromosomal sex strengthened their argument that chromosomes did not determine gender role.\n\nThe first two publications were both focused on patients with hyperadrenocorticism and the specific therapeutic and psychological problems of CAH patients: 'hermaphroditism in the females, and virilising precocity in both males and females'.47 Untreated adult female CAH patients, they argued, had adapted to the sex they had been raised in: if raised female they identified as women, despite 'virilised' bodies; if raised male, they identified as men, despite female sex chromosomes and gonads. Money also discussed at length another psychological problem specific to CAH: children with CAH were precocious and looked much older than they actually were, raising expectations they could not meet \u2013 a problem which was addressed at every visit of the patients.48\n\nAt the time of Money's study, most CAH children who came into the hospital already had a sex picked by their parents and\/or local physicians. Wilkins and his team wondered whether to change an existing sex assignment now that cortisone would arrest the 'virilising' effects of the androgens. This ad hoc approach eventually turned into rigid treatment guidelines to assign sex early \u2013 ideally, before the age of two and a half years \u2013 and to rid the body of all visible contradiction, so that gender role could be acquired without disturbances.49 Implementation of the protocols was facilitated by their integration into the literature; they also filled a clinical vacuum providing a systematic multi-stage treatment plan that privileged sex of rearing over biological markers.50 Next most important were the child's genitals and whether they could be adapted to the chosen sex so that the child could grow into its gender role without facing any somatic contradictions.\n\nAs Bernice Hausman has shown, Money's and the Hampsons' work represents a gradual shift away from a person's 'true sex' towards the idea of the 'best sex', in the context of genital morphology and psychological make-up.51 Money's concept of gender role, I argue, made this move possible because as a category it was more fixed than the unstable bodies the practitioners were dealing with. Though I agree with Hausman that this move was enabled by newly developed medical technologies, the study's results emerged out of the specific context of the introduction of cortisone therapy for CAH. Cortisone worked beyond the usual surgical intervention targeting the underlying condition. Checking the androgens in CAH girls '(re-)feminised' their overall appearance and promoted breast growth and menstruation. It also arrested and reversed the problematic premature growth and disturbances in salt metabolism in both CAH girls and boys. Money's and the Hampsons' results balanced the dreaded plasticity of the hermaphroditic body through the introduction of a more rigid category: gender role.\n\nCAH, as defined by Wilkins, is determined biologically as much as it is culturally. Definitions of 'disease' are always the effect of pathology as well as of the social meaning they acquire in their historical context. Concepts of the body, medical technologies, clinical traditions, material conditions in the laboratory and clinic, and cultural notions of masculinity and femininity form a framework within which CAH became a seemingly purely natural disease entity. The pathological definition of CAH was hyperplasia of the adrenal cortex, and Wilkins treated the multiple effects of the adrenal pathology as a comprehensive cluster of symptoms. Since he defined CAH as a specific endocrinological disorder, 'ambiguous sex or genitals' could be treated as simply one effect of CAH and gender role became part of the treatment regime.\n\nWilkins and his team attempted to control and if possible reverse the presenting symptoms of CAH such as virilisation and precocity, especially precocious growth in children of both sexes which made them appear much older than they actually were and eventually led to a premature arrestment of bone growth. To be sure, in this context excessive 'virilisation' was never a good thing, but for Wilkins the degree of intervention depended on the prescribed sex. In female CAH patients raised as girls, the prescribed goal of the physicians was to completely check all effects of excessive androgen through cortisone therapy and surgery. In CAH girls raised as boys, cortisone therapy was often reduced or supplemented with testosterone to get adequate virilisation, though carefully balanced so that growth would not be arrested prematurely. In CAH boys, who looked sexually mature beyond their age, cortisone therapy was aimed to arrest precocious virilisation and sexual development. Both genital symptoms caused a great amount of anxiety in physicians and parents who inquired and worried about erections and masturbation.\n\nIn boys, Wilkins and parents hoped that cortisone would arrest their 'precocious' sexual behaviour. Robert for example \u2013 a very precocious six-year-old with CAH \u2013 was referred to Wilkins in 1949.52 His mother, during his stay at Hopkins, came to see the medical social worker 'in great distress'. Robert 'had been having erections both during day and night'; these erections were reported to be 'painful' and kept him 'from sleeping'; they were 'also very noticeable'. The boy also masturbated frequently and his mother hoped that some 'hormonal' treatment would put an end to his behaviour. Wilkins also arranged a psychological evaluation for the child. Throughout the records, children's sexuality caused a high level of anxiety in parents, especially as they feared psychological problems.\n\nIn girls, special attention was paid to the enlarged clitoris, and surgical reduction or amputation was the usual intervention. Surgeons at Hopkins performed clitorectomies on CAH children who were raised as girls, a procedure that was neither discussed nor questioned in the patient records.53 In the sixteen cases in my sample where 'enlarged clitoris' was listed as one of the complaints, surgeons performed a clitorectomy at the earliest possible time after admission on all but one patient. Hopkins seemed to have had an already existing tradition of clitorectomies that persisted through the introduction of cortisone and Money's gender concept.54\n\nAs with boys, a major concern for physicians and parents was frequent erections of large clitorises and masturbation. Physicians regularly inquired after such behaviour and often parents addressed it themselves. This resonates with a longer medical tradition to cure masturbation (and insanity) through clitoral surgery.55 At the Hopkins clinic, this tradition was combined with the social concern that psychological difficulties might arise from growing up as a girl with an enlarged clitoris or phallus; it would raise doubts concerning her sex and trouble her gender role. Psychological adjustment justified depriving 'a patient of what some authorities have declared the most significant erotic zone in the female'.56 Again, the body was thought to be more flexible than a child's gender role. Clearly, an enlarged clitoris initially was more upsetting to parents and physicians than to the children themselves.57\n\nManagement\n\nCortisone was not a cure, but part of a life-long management strategy for a chronic condition. In his study of another chronic disease, diabetes, the historian and paediatrician Chris Feudtner has shown that insulin transformed this disease from acute to chronic with ironic results. While insulin was a virtual lifesaver, to live day by day with a chronic condition transformed all aspects of a person's life.58 The patient's life was constantly observed through the prism of his or her condition, and effective treatment translated into the living of a 'normal' life.59 However, 'disease' as defined by medicine, and 'illness' as experienced by patients and their family often come to carry radical different meanings.60 CAH treatment meant life-long management of the cortisone dosage and its effects as well as surgical adjustment of the child's body and psychological evaluation of its development. Considerable work was invested into effecting a 'normal' gender identity that fit the contemporary (heterosexual) standard of male and female.61\n\nChildren came in yearly, for evaluations and re-adjustments of cortisone dosage. During these sessions, behaviour and adaptation of gender role was evaluated and measured as well. Over the course of four years, Ann (n\u00e9e Andy) was admitted three more times for study and adjustment of the cortisone dosage as well as for surgery.62 Her stays always followed the same procedure applied to all patients in my sample: a patient history, usually taken from the parents; physical examination, with special attention to genitals and growth; an ad hoc assessment of behavioural adjustment; impression of feminine or masculine appearance and of gender role; blood and urine tests; x-rays to assess osseous development; and sometimes psychological evaluation including IQ tests. In the records, we find multiple assessments of Ann's developmental stage, accounts of her growth, mental abilities and general 'social adjustment' side by side with measurements of her gender role. 'She has a rare clitoral erection' and 'a 24h attack of vomiting'; 'she is still considered smarter than her other playmates. She has ridden a tricycle for 11\/2 year. She has been looking forward to hospitalisation and to seeing Dr Wilkins'. She is 'a happy, active, likeable child. Her shortness and round face give her an appearance very similar to her father'. 'She is more quick witted than the usual and her social adjustment is superior'. Gender assessment here is folded neatly into general assessment of development, sexuality and psychological adjustment.\n\nAnn's record ends in 1959, eight years after her first admittance. Other patients came to the clinic for twenty years and longer. The social aspects of medical intervention become increasingly visible in the practice around the life-long management of the condition. The communication between physicians and parents and later between physicians and patients reveals the integration of medical and social concerns. Physicians asked about the child's behaviour in kindergarten, in school and in college, they inquired about grades, dating and summer camp. The level of social integration was discussed even more when children grew into adults; the doctors checked endlessly whether the patients behaved according to their assigned sex and also whether they looked sufficiently male or female. Gender was always foregrounded, especially in those cases where contradictions between sex of rearing and one or more biological variable sex existed.\n\nRichard, who despite his chromosomal female sex remained a boy, returned to the clinic four more times until 1964 and his body and behaviour were observed for signs of maleness and femaleness.63 The treating physician described him as a 'large, somewhat clumsy male child appearing well' whose 'well proportioned hips have contours somewhat female in type with no deformity'. Dutifully reporting his progress in letters to the physicians, his mother wrote in 1960, 'He is all boy now, well adjusted with his playmates and will be in the 6th grade when he passes this June'. The treating physician commented, 'this patient is actually a female who has been ovariectomised' and wondered how best to balance the continuation of the cortisone treatment (to avoid precocious growth) and giving him testosterone for masculinisation. Four years later, the mother again confirmed her assessment of Richard's gender, by writing to the physicians, 'with exception of his height, he is an average boy of 15 years'. What is striking here is the mantra of gender, the reiteration of gender and sex that became a self-fulfilling prophecy.64 Correct gender role was folded into the management of CAH as one aspect of successful treatment. For Wilkins and his team, gender role was on a long list of physical and psychological markers to be checked in the process of normalisation.\n\nThe main proclaimed treatment\/management goal of the physician was to make the patients into what they perceived as psychologically well-adjusted and functional, clearly gendered men and women that could 'live a normal life'. For the physicians this meant to fit in socially, to be accepted as boy or girl, as man or woman, to succeed in chosen education or profession, to be happy and cooperative, to date and to get married. Deviation in gender role was marked down in the records in the same manner as elevated 17-KS levels. Gender role was measured by assessment of the child's behaviour during examination and by psychological interviews and tests. In the case of Carol, a patient who was first seen by Wilkins in 1941, long before cortisone treatment, Wilkins had been resigned to the increasing virilisation of CAH girls; he had told her mother that she would never marry.65 Indeed, before cortisone, Wilkins had thought girls with CAH doomed to progressive virilisation and even suggested that in some cases they would be better off being raised as boys.66 Carol's behaviour over the years was noted and closely followed during each admission as Wilkins and his colleagues assessed her appearance and her performance. In 1944, they wrote, 'She is a very bright, active, precocious child. Appears quite intelligent. Her appearance and actions seems to be quite feminine'. The following year Wilkins thought she had a 'very feminine appearance'. In 1946, he was worried that the 'child continues to grow and virilise at a rapid rate' but in his 'opinion the patient is not abnormal in her sexual interests and curiosity'. The question of sexual normality had come up because of 'the neighbourhood problem' \u2013 Carol's condition had put her at the centre of 'much sexual attention' by little boys. 'One of the neighbours has called on the mother to get more detailed information about [Carol]'s condition,' Wilkins wrote and advised the parents to move.\n\nWilkins assessed Carol's gender on every visit, noting in 1948 that she was a 'tomboy' and that 'she still will p[l]ay as easily with boys' toys as with girls, which causes her mother some concern'. 'The child in general,' he wrote, 'is hyperactive, rough in her play and has a rather deep voice'. Again, somatic effects of CAH (deep voice) were paired with assessments of behaviour and demeanour. After Carol was put on cortisone in 1950, the gender measurements became more consistent. Her 17-KS values were falling and Wilkins remarked 'there were no changes on physical examination'. However, 'her mother thought she was much less boisterous and more feminine in her actions but this could be reasonably ascribed to her long hospitalisation and its attendant benefits in the way of good discipline and mental hygiene'. The perceived behaviour change was of only short time, her mother thought that after her first bout of treatment 'she was more feminine in behaviour for a while but later became boyish again'.\n\nGendered behaviour was rarely detailed or evaluated; a child just behaved like a boy or a girl. It was measured by cultural tropes of gender and heterosexuality. Carol now had 'a boyfriend', Wilkins noted in 1954, 'who took her to a ball last night'. Two years later, she came to the examination 'wearing high heels and acting quite grown up' \u2013 all markers of a 'normal' female gender role in the 1950s. Cortisone and gender role made the goal of a 'normal life' possible, which was structured by physicians', parents' and often patients' belief in the existence of only two sexes, male and female.\n\nThe management of the multiple aspects of CAH was intertwined with all aspects of the patients' lives. Physicians and parents alike were concerned about the psychological adjustment of CAH children. While this was connected to the perceived 'problematic' sexual status of the children, it was also an effect of problems caused by patients living with a chronic condition. Again, this treatment goal was concerned with but not limited to sex. It also included social problems arising from CAH children looking 'different' not just sexually. Children with CAH looked much older than their chronological age, thus raising a set of social and intellectual expectations they could not fulfil. For CAH patients themselves and their parents, being healthy often meant not having any of the signs of visible difference, including height, auxiliary hair, acne, male baldness and masculine features in girls, weight \u2013 cortisone often led to obesity \u2013 and skin pigmentation. In complicated ways, some of these signs were connected to sex. But being healthy was always also about being able to function in the world.\n\nConclusion\n\nUsing patient records from the clinic of paediatric endocrinology where Money and the Hampsons coined the term 'gender role' and Wilkins introduced cortisone as a treatment for CAH girls, I have described the process of normalisation around the diagnosis, treatment and management of what physicians defined as a specific endocrinological pathology. My sources suggest that diagnosing and assigning sex at the clinic in the 1950s was sometimes a long and contentious enterprise as Wilkins and his team struggled to pinpoint sex. Furthermore, in one of two cases of CAH girls being raised as boys, it was the parents who insisted that their child was a boy and kept her, with the psychological sanctus of John Money, in the male sex.67 Treatment and management of CAH at the clinic was an enduring process that included quick medical interventions in the case of severe salt-wasting CAH and a life-long management of what was perceived as a chronic adrenal disorder. Physical development and hormonal levels, psychological adjustment and healthiness, and sexual appearance and gender role were checked and controlled in yearly evaluations. This way, finding and adjusting to the optimal gender role was folded into the management of CAH as one aspect of successful treatment. It was on a long list of physical and psychological markers to be checked in the process of normalisation.\n\nClearly, CAH's sexual symptoms, such as 'virilised' genitals in girls and precocious genitals in boys, caused anxieties in parents and physicians. Medical\/surgical intervention provided a solution to a social problem of ambiguous or precocious sex. It seemed easier to fix ambiguous bodies than rigid gender roles, which would become imprinted during the child's early years. Nevertheless, Wilkins and his team defined CAH as a complex endocrinological disorder caused by adrenal hyperplasia affecting the whole development of children of both sexes. They considered its sexual symptoms in conjunction with other the somatic effects of the adrenal hyperplasia. Physicians' and parents' main treatment goal became for their children to lead a 'normal' life \u2013 that is a life unhindered by what was defined as a chronic endocrinological condition. This goal was structured by the highly normative sexual roles of the 1950s as much as by the actual underlying adrenal pathology. Normalisation was a process in which treating somatic effects and assuring psychological healthiness were deeply enmeshed in the conviction that a normal life was only possible as a clearly gendered and sexed person.\n\nNotes\n\nI wish to thank Hester Betlem, Angela Craeger, Mary Fissel, Dan Todes, two anonymous reviewers, and especially Nathaniel Comfort, whose suggestions have greatly improved this text. Many thanks go to Judith Walkowitz and Mary Ryan, along with the other participants of the Gender Workshop of the Johns Hopkins History Department, who commented on an earlier version of this chapter.\n\n1. Case 8, Ann\/Andy. All details and quotes are taken from the Harriet Lane Home medical records. The identities of all patients are protected. I assigned each case a random number (1\u201325) and name. The key is available for other researchers at the Alan Mason Chesney Medical Archives at Hopkins according to the regulation of the Johns Hopkins Privacy Review Board.\n\n2. For a discussion of DSD as a new term, see Elizabeth Reis, Bodies in Doubt: An American History of Intersex (Baltimore: Johns Hopkins University Press, 2009), pp. 153\u201362.\n\n3. John Money, Joan G. Hampson and John L. Hampson, 'An Examination of Some Basic Sexual Concepts: The Evidence of Human Hermaphroditism', Bulletin of the Johns Hopkins Hospital 97 (1955), pp. 301\u201319, here p. 302.\n\n4. John Money, Joan G. Hampson and John L. Hampson, 'Imprinting and the Establishment of Gender Role', Archives of Neurology & Psychiatry 77 (1957), pp. 333\u20136.\n\n5. Most notably the Intersex Society of North America (ISNA) founded by Cheryl Chase, <<http:\/\/www.isna.org\/>> (accessed 28 June 2010). See also Alice D. Dreger and April M. Herndon, 'Progress and Politics in the Intersex Rights Movement: Feminist Theory in Action', GLQ: A Journal of Lesbian and Gay Studies 15 (2009), pp. 199\u2013224; Sarah M. Creighton, Julie A. Greenberg, Katrina Roen and Del La Grace Volcano, 'Intersex Practice, Theory, and Activism: A Roundtable Discussion', GLQ 15 (2009), pp. 249\u201360.\n\n6. Alice Domurat Dreger, Hermaphrodites and the Medical Invention of Sex (Cambridge: Harvard University Press, 1998), p. 29.\n\n7. Dreger, Hermaphrodites and the Medical Invention of Sex, p. 150.\n\n8. Bernice L. Hausman, Changing Sex: Transexualism, Technology, and the Idea of Gender (Durham: Duke University Press, 1995), p. 77. See also Stephanie Hope Kenen, 'Scientific Studies of Human Sexual Difference in Interwar America' (unpublished doctoral thesis, University of California, 1998), pp. 34\u2013209.\n\n9. See Alison Redick, 'American History XY: The Medical Treatment of Intersex, 1916\u20131955' (unpublished doctoral thesis, New York University, 2004), p. 9.\n\n10. Reis, Bodies in Doubt, p. 55.\n\n11. See Christina Matta, 'Ambiguous Bodies and Deviant Sexualities: Hermaphrodites, Homosexuality, and Surgery in the United States, 1850\u20131904', Perspectives in Biology and Medicine 48 (2005), pp. 74\u201383. On the role of surgery, see also Reis, Bodies in Doubt, pp. 82\u2013114.\n\n12. On intersex as social emergency, see Redick, 'American History XY', p. 8.\n\n13. Katrina Karkazis, Fixing Sex: Intersex, Medical Authority and Lived Experience (Durham and London: Duke University Press, 2008). See also Suzanne J. Kessler, Lessons from the Intersexed (New Brunswick: Rutgers University Press, 1998); Alice Domurat Dreger, Intersex in the Age of Ethics (Hagerstown: University Publishing Group, 1999); Sharon E. Preves, Intersex and Identity: The Contested Self (New Brunswick and London: Rutgers University Press, 2003).\n\n14. On the scientific construction of sexuality, see Rebecca M. Young, 'Sexing the Brain: Measurement and Meaning in Biological Research on Human Sexuality' (unpublished doctoral thesis, Columbia University, 2000). On biological determinism of gender, see also Marianne van den Wijngaard, Reinventing the Sexes: Feminism and Biomedical Construction of Femininity and Masculinity, 1959\u20131985 (Amsterdam: Uitgeverij Eburon, 1991).\n\n15. Geertje Mak, 'Doubting Sex from Within: A Praxiographic Approach to a Late-Nineteenth-Century Case of Hermaphroditism', Gender & History 18 (2006), pp. 332\u201356, here p. 351.\n\n16. Karkazis, Fixing Sex, p. 98.\n\n17. Karkazis, Fixing Sex, p. 115.\n\n18. My sample was taken from eighty-six patients listed on the Edward Park index cards at the Chesney Medical Archives; of these I could locate twenty-five patients born between 1933 and 1955; eight had their first admission at the clinic before 1950.\n\n19. On the specific nature of paediatric records, see Jonathan Gillis, 'Taking a Medical History in Childhood Illness: Representations of Parents in Pediatric Texts since 1850', Bulletin of the History of Medicine 79 (2005), pp. 393\u2013429, here p. 417. On using patient records, see e.g., Guenter B. Risse and John Harley Warner, 'Reconstructing Clinical Activities: Patient Records in Medical History', Social History of Medicine 5\/2 (1992), pp. 183\u2013205. On the role of patient records in constructing the patient, see Marc Berg and Paul Harterink, 'Embodying the Patient: Records and Bodies in Early 20th-Century US Medical Practice', Body & Society 10\/2\u20133 (2004), pp. 13\u201341.\n\n20. On disease as a social entity, see e.g., Charles E. Rosenberg, 'What Is Disease? In Memory of Owsei Temkin', Bulletin of the History of Medicine 77 (2003), pp. 491\u2013505; Charles E. Rosenberg, 'The Tyranny of Diagnosis: Specific Entities and Individual Experience', Milibank Quarterly 80\/2 (2002), pp. 237\u201360.\n\n21. See Georges Canguilhem, On the Normal and the Pathological, Studies in the History of Modern Science, vol. 3 (Dordrecht and Boston: D. Reidel, 1978).\n\n22. See Michel Foucault, Discipline and Punish: The Birth of the Prison, tr. Alan Sheridan (1975; New York: Pantheon, 1977).\n\n23. On the Harriet Lane Home, see Edwards A. Park, The Harriet Lane Home: A Model and a Gem (Baltimore: Department of Pediatrics, School of Medicine, Johns Hopkins University, 2006).\n\n24. On Paediatric Endocrinology, see Delbert A. Fisher, 'A Short History of Pediatric Endocrinology in North America', Pediatric Research 55 (2004), pp. 716\u201326. Lawson Wilkins wrote the first textbook of paediatric endocrinology. Lawson Wilkins, The Diagnosis and Treatment of Endocrine Disorders in Childhood and Adolescence (Springfield: Thomas, 1950). Dr Nathan Talbot, who established a paediatric endocrine clinic at the Massachusetts General Hospital in 1942, wrote the second textbook in 1952, N. B. Talbot, E. H. Sobel, J. W. McArthur and J. D. Crawford, Functional Endocrinology from Birth through Adolescence (Cambridge: Harvard University Press, 1952).\n\n25. L. Wilkins, W. Fleischmann and J. E. Howard, 'Macrogenitosomia Precox Associated with Hyperplasia of the Androgenic Tissue of the Adrenal and Death from Corticoadrenal Insufficiency', Endocrinology 26 (1940), pp. 385\u201395.\n\n26. Wilkins, Fleischmann and Howard, 'Macrogenitosomia Precox', p. 394.\n\n27. Nathan Talbot at Massachusetts General also researched CAH. See Nathan B. Talbot, Allan M. Butler and R. A. Berman, 'Adrenal Cortical Hyperplasia with Virilism: Diagnosis, Course and Treatment', Journal of Clinical Investigation 21 (1942), pp. 559\u201370, here p. 559.\n\n28. Wilkins, Diagnosis and Treatment of Endocrine Disorders, p. 224.\n\n29. Case 8, Andy\/Ann.\n\n30. Case 8, Andy\/Ann. On the physicians' and parents' role in sex determination, see Karkazis, Fixing Sex, pp. 179\u2013215.\n\n31. Case 8, Andy\/Ann.\n\n32. See e.g., the case histories in Dreger, Hermaphrodites and the Medical Invention of Sex. See also Hugh Young cases in Kenen, 'Scientific Studies of Human Sexual Difference in Interwar America'.\n\n33. Mak, 'Doubting Sex from Within', pp. 350\u201351.\n\n34. For changes in childbirth practices, see Charlotte G. Borst, Catching Babies: The Professionalization of Childbirth, 1870\u20131920 (Cambridge: Harvard University Press, 1995). On the effects of these early interventions, see Karkazis, Fixing Sex, pp. 89\u2013178.\n\n35. Mak, 'Doubting Sex from Within', p. 340.\n\n36. For the introduction of the Barr test into clinical practice, see Fiona Alice Miller, '\"Your True and Proper Gender\": The Barr Body as a Good Enough Science of Sex', Studies in History and Philosophy of Biological and Biomedical Sciences 37 (2006), pp. 449\u201383.\n\n37. Case 21, Richard.\n\n38. The 1948 Barr skin biopsy test for chromosomal sex was quickly introduced into clinical practice. See K. L. Moore, M. A. Graham and M. L. Barr, 'The Detection of Chromosomal Sex in Hermaphrodites from a Skin Biopsy', Surgery, Gynecology & Obstetrics 96.6 (1953), pp. 641\u20138.\n\n39. Case 21, Richard.\n\n40. Case 22, Charles.\n\n41. Post-cortisone, XX CAH children were usually raised as girls. See Karkazis, Fixing Sex, p. 57.\n\n42. For patients' statistics, see Lawson Wilkins, Diagnosis and Treatment of Endocrine Disorders, pp. 9\u201310.\n\n43. Case 8, Ann\/Andy.\n\n44. Lawson Wilkins, 'The Diagnosis of the Adrenogenital Syndrome and Its Treatment with Cortisone', Journal of Pediatrics 41 (1952), pp. 860\u201374. For the first patient treated and published on, see L. Wilkins, R. A. Lewis, R. Klein and E. Rosemberg, 'The Suppression of Androgen Secretion by Cortisone in a Case of Congenital Adrenal Hyperplasia', Bulletin of the Johns Hopkins Hospital 86 (1950), pp. 249\u201352.\n\n45. Money had already formulated his ideas in his dissertation on hermaphroditism. See John Money, 'Hermaphroditism: an Inquiry into the Nature of a Human Paradox' (unpublished doctoral thesis, Harvard University, 1952. The results of the study were first published during 1955 and 1956. Joan G. Hampson, 'Hermaphroditic Genital Appearance, Rearing and Eroticism in Hyperadrenocorticism', Bulletin of the Johns Hopkins Hospital 96 (1955), pp. 265\u201373; John Money, 'Hermaphroditism, Gender and Precocity in Hyperadrenocorticism: Psychological Findings', Bulletin of the Johns Hopkins Hospital 96 (1955), pp. 253\u201364; Money, Hampson and Hampson, 'An Examination of Some Basic Sexual Concepts'; John Money, Joan G. Hampson and John L. Hampson, 'Hermaphroditism: Recommendations Concerning Assignment of Sex, Change of Sex and Psychological Management', Bulletin of the Johns Hopkins Hospital 97 (1955), pp. 284\u2013300; John Money, Joan G. Hampson and John L. Hampson, 'The Syndrome of Gonadal Agenesis (Ovarian Agenesis) and Male Chromosomal Pattern in Girls and Women: Psychologic Studies', Bulletin of the Johns Hopkins Hospital 97 (1955), pp. 207\u201326; John Money, Joan G. Hampson and John L. Hampson, 'Sexual Incongruities and Psychopathology: The Evidence of Human Hermaphroditism', Bulletin of the Johns Hopkins Hospital 98 (1956), pp. 43\u201357.\n\n46. Money, Hampson and Hampson, 'Syndrome of Gonadal Agenesis', p. 218.\n\n47. Money, 'Hermaphroditism, Gender and Precocity in Hyperadrenocorticism', p. 253. See also Hampson, 'Hermaphroditic Genital Appearance'.\n\n48. Money, 'Hermaphroditism, Gender and Precocity in Hyperadrenocorticism', esp. pp. 256\u201364.\n\n49. See Karkazis, Fixing Sex, pp. 47\u201363.\n\n50. Karkazis, Fixing Sex, pp. 60\u201362. The two publications are Wilkins, Diagnosis and Treatment of Endocrine Disorders; Howard Wilbur Jones and William Wallace Scott, Hermaphroditism, Genital Anomalies and Related Endocrine Disorders (Baltimore: Williams & Wilkins, 1958).\n\n51. Hausman, Changing Sex, p. 79. Also referred to as the 'optimum gender of rearing' model. See Dreger and Herndon, 'Progress and Politics in the Intersex Rights Movement', p. 202.\n\n52. Case 5, Robert.\n\n53. These operations were mainly performed by Howard Jones and John Blizzard. See Jones and Scott, Hermaphroditism, Genital Anomalies and Related Endocrine Disorders. On history of clitoral anatomy, see Thomas Walter Laqueur, Making Sex: Body and Gender from the Greeks to Freud (Cambridge: Harvard University Press, 1990); Lisa Jean Moore and Adele E. Clarke, 'Clitoral Conventions and Transgressions: Graphic Representations in Anatomy Texts, c.1900\u20131991', Feminist Studies 21 (1995), pp. 255\u2013301; Darlaine Claire Gardetto, 'Engendered Sensations: Social Construction of the Clitoris and Female Orgasm, 1650\u20131975'(unpublished doctoral thesis, University of California, Davis, 1992).\n\n54. For earlier practices see Hugh Young, Genital Abnormalities: Hermaphroditism & Related Adrenal Diseases (Baltimore: Williams & Wilkins, 1937). For a more cautious approach, see Talbot, Sobel, McArthur and Crawford, Functional Endocrinology from Birth through Adolescence, p. 234. For a discussion of clitorectomy, see Karkazis, Fixing Sex, pp. 148\u20139.\n\n55. On clitorectomy, see Elizabeth Sheehan, 'Victorian Clitoridectomy: Isaac Baker Brown and His Harmless Operative Procedure', Gender Issues 5 (1985), pp. 39\u201353. On the emergence of gynaecology, see Ornella Moscucci, The Science of Woman: Gynaecology and Gender in England, 1800\u20131929 (Cambridge and New York: Cambridge University Press, 1990).\n\n56. Hampson, 'Hermaphroditic Genital Appearance', p. 270.\n\n57. Karkazis, Fixing Sex, pp. 158\u20139.\n\n58. John Christopher Feudtner, Bittersweet: Diabetes, Insulin, and the Transformation of Illness, Studies in Social Medicine (Chapel Hill: University of North Carolina Press, 2003).\n\n59. For comparison of diabetes and DSD, see e.g., Ellen K. Feder, 'Imperatives of Normality. From \"Intersex\" to \"Disorders of Sex Development\"', GLQ 15 (2009), pp. 225\u201347, here p. 239.\n\n60. See e.g., Arthur Kleinman, The Illness Narratives: Suffering, Healing, and the Human Condition (New York: Basic Books, 1988).\n\n61. Feder, 'Imperatives of Normality', p. 237.\n\n62. Case 8, Ann\/Andy.\n\n63. Case 21, Richard.\n\n64. On the role of the parent, see Karkazis, Fixing Sex, pp. 179\u2013215.\n\n65. Case 4, Carol.\n\n66. Wilkins, Diagnosis and Treatment of Endocrine Disorders, esp. pp. 223\u20134.\n\n67. Case 22, Charles.\nChapter 9\n\n'A Certain Amount of Prudishness': Nudist Magazines and the Liberalisation of American Obscenity Law, 1947\u201358\n\nBrian Hoffman\n\nIn March 1947, the United States Post Office seized Sunshine and Health (S&H) from the mail in Chicago, New York, Philadelphia and several cities in Ohio. The coordinated action by local post offices across the country signalled an unprecedented effort to remove the flagship nudist magazine from the mail. While officials had long tolerated nudist representations that resembled the young attractive Vargas Girls of Esquire or the nude female centrefolds in Playboy, they objected to the recent effort by the magazine to show the genitalia of naked men, women and children as well as a range of body types not normally revealed in commercial publications. Officials asserted that permitting the magazine unrestricted access to American homes would be tantamount to accepting the 'rights of all kinds of pornography' to use the 'mails to destroy public morals'.1 Facing 'complete financial ruin', but unwilling to censor its images, the editors of S&H declared the looming court battle a 'challenge to every nudist, to every reader of this page, to every lover of freedom'.2 The legal debates that erupted around nudist magazines in 1947 and culminated in the US Supreme Court's decision in 1958 to stop the Post Office's censorship of S&H redefined what constituted obscenity in the United States.\n\nA legal history of nudism provides valuable insight into the long-running debate over what could be seen, displayed and consumed in the United States. In the twentieth century, a modern obscenity regime emerged that rejected the moral absolutism of the nineteenth century, but policed the moral boundaries of what John D'Emilio and Estelle Freedman termed 'sexual liberalism'.3 The growing social, cultural and legal tolerance of heterosexual pleasure in American society, historians have argued, depended on the exclusion of threatening, violent or deviant forms of sex. Once-reviled material such as birth-control pamphlets, literature dealing with sexual themes and titillating men's magazines gained reprieve in the early 1930s with court rulings that protected material with literary or scholarly merit.4 Yet depictions of homosexuality, films dealing with interracial sex and burlesque shows that catered to male audiences endured greater scrutiny and suppression as the courts continued to use repressive nineteenth-century laws or subjective community standards to exclude materials that challenged heteronormativity.5 An analysis of the legal battles over the decency of nudist magazines shows that this modern obscenity regime quickly broke down as judges and juries found it increasingly difficult to disentangle so-called deviant material from examples of morally acceptable heterosexual display and behaviour. The variety of content included in S&H allowed for multiple readings and appealed to a variety of sexual identities. The magazine showed uncensored genitalia, non-white bodies and an assortment of body types that communicated the therapeutic and recreational orientation of nudism while also appealing to men and women of all sexualities. The nudist movement's struggle to negotiate the respectable and illicit in its flagship magazine created a 'grey area' in American obscenity law that precipitated the explosion of 'all kinds of pornography' in the last decades of the twentieth century.\n\nThe nudist movement considered the defeat of longstanding American obscenity laws essential to ensuring the physical and moral health of its members as well as the future stability of the movement. Nudism promoted therapeutic principles that directly challenged American assumptions that linked the body with shame and immorality. Nudists believed that knowledge of and familiarity with the body were essential to both physical and mental health. Recreational social nudity improved bone growth and prevented sickness by maximising the production of Vitamin D. It also served a hygienic purpose by removing clothing that blocked the excretory functions of the skin, collected sweat and restricted free-flowing movement by clinging to the body. In addition, going naked in front of the opposite sex satisfied the 'natural' curiosity to see and know about the body, promoted a 'wholesome' way of thinking and ultimately strengthened the relations between men and women.6 Efforts to censor and conceal the body from public view, according to nudists, resulted in illicit behaviours and thoughts that prevented men and women from receiving the therapeutic benefits that came from exposing the body to the fresh air and sun.\n\nThe nudist movement's effort to redefine nakedness as healthy and wholesome also exposed the racial assumptions that shaped the boundaries of sexual expression in mid-century America. Nudist leaders mobilised a discourse of racial liberalism to promote sexual liberalisation. In their legal battles with the Post Office, nudist advocates argued that American obscenity law discriminated against white nudist representations when censors permitted the display of non-white naked bodies in magazines like the National Geographic or in anthropological documentary films. The racial liberalism used by nudist leaders in the courtroom, however, failed to resonate with many members who felt threatened by the 'sexually promiscuous' African American woman and the violent male African American 'sexual predator'.7 The racial arguments made by nudist leaders proved to be ineffective in a society, and a movement, still divided along lines of race.\n\nThe anti-communist politics of the Cold War made the defence of S&H attractive to the American Civil Liberties Union (ACLU) because the nudist movement advocated natural healing rather than radical politics. The institution of the Federal Loyalty Program on 21 March 1947 along with the sensational trials of suspected Soviet spies and political radicals made the ACLU vulnerable to anti-communist attacks from organisations such as the American Legion. To avoid controversy and political persecution, moderate ACLU leaders like Roger Baldwin and Morris Ernst shifted the organisation's focus away from the defence of political radicals to an agenda centred on civil rights, the separation of church and state and the issue of censorship.8 Yet the vocal resistance to public forms of sexuality in mid-century America also made the defence of S&H a risky proposition. Several leaders within the organisation feared that an extreme position in favour of sexual expression would produce adverse reactions from hostile local community groups. As a result, the ACLU followed the path of respectability that many other organisations and individuals deployed to publicly address issues of sexuality in post-war America.9 Although legal absolutists and nudists demanded that all forms of sexual display be protected under the first amendment, the moderate leadership of the ACLU used the therapeutic principles that defined American nudism to avoid the issue of communism and to distance S&H from commercial sexual display. The attempts by the ACLU to distinguish between good and bad representations of sex ultimately exposed the inability of the courts to maintain the contradictions of twentieth-century sexual liberalism.\n\n'Sunshine and Health'\n\nOrganised nudism burst onto the American scene in the early 1930s through a series of illustrated books that detailed the authors' experiences visiting German nudist parks. Nudism first emerged in Europe at the beginning of the twentieth century as part of the German life reform movement (Lebensreform Bewegung) that advocated a return to the 'genuine forces of life through vegetarianism, anti-alcoholism, nature healing, land reform and the advocacy of garden cities'.10 After Germany's defeat in the First World War, nudism became increasingly popular as a way to strengthen the race and regenerate the nation.11 The growing popularity of the German nudist movement likely caught the attention of American publishing companies in desperate need of profitable books during the Great Depression. Alfred A. Knopf, a press known for printing leading European and American literary trends, and Garden City Publishing Company, a division of Doubleday Books, published a series of books introducing the practice of nudism as well as the movement's therapeutic principles and moral philosophy. Avoiding censorship with distant pictures displaying small naked figures, Maurice Parmelee's Nudism in Modern Life (1931), Frances and Mason Merrill's Among the Nudists (1931) and Nudism Comes to America (1932) and Jan Gay's On Going Naked (1932) sold several editions and generated a great deal of interest in nudism in the United States.12 Individuals, couples and groups began to organise meetings in urban gymnasiums and on isolated country farms across the nation.\n\nThe many books published on nudism in the early 1930s generated enthusiasm among immigrants who had participated in German nudism, health enthusiasts and sex reformers, but they provided very little information about how and where nudism might be practised in the United States. The need to communicate to groups and individuals scattered across large geographical spaces led the Reverend Ilsley Boone, a Baptist minister trained in theology at Brown University, to establish a monthly magazine dedicated to nudism. Boone began participating in nudism in 1929 as a member of Kurt Barthal's American League for Physical Culture, one of the earliest nudist organisations in the United States, and quickly became an avid proponent of organised social nudity. In 1933, Boone, who served as the editor of Missions, the National Organ of the Baptist Church, began publishing The Nudist to carry out the goals and principles of his International Nudist Conference (INC).13 Boone established the INC to place the 'experience of each group at the disposal of all', to campaign for the 'formation of an informed and understanding public opinion', and to aid in legal and legislative problems facing nudist groups.14 The monthly magazine, distributed through the mail and sold on newsstands around the country, published numerous articles, editorials and commentaries that introduced the philosophy and ideals of nudism to readers and provided information about an emerging network of nudist clubs. A 'letters to the editor' section also fostered a sense of community through the regular presentation of readers' thoughts and opinions from around the country. Through the INC and The Nudist, Boone transformed nudism into a distinctly American phenomenon defined by health, sexual expression and recreation.\n\nAlthough The Nudist provided crucial information for individuals interested in nudism, sales of the flagship nudist magazine far exceeded the total membership of the movement. Featuring numerous pictures on large glossy pages, the inaugural May 1933 issue sold 10,000 copies and the following month the magazine increased its readership five-fold to 50,000. Over the next few years, sales of the 25 cent magazine ranged between 40,000 and 100,000 a month. Of these, 6,000 to 8,000 went directly to mail subscribers, while newsstands distributed the other 30,000 to 60,000 issues.15 The large number of copies sold on newsstands especially signalled the availability of the magazine to a wider audience interested in sexual display. At the fifth annual meeting of the INC held in 1936, several leaders bemoaned the fact that many 'burlesque theatre managers, night club troupes, disorderly road houses and exposition side shows' used the terms 'nudist' and 'nudism' to 'further their own business enterprise in the field of commercialized pornography'. The findings committee then recommended that the organisation and its flagship magazine change its name to avoid associations with 'morbid and burlesque types of nakedness'.16 To promote the movement's emphasis on health and recreation, nudists adopted the new moniker American Sunbathing Association (ASA) to represent the national organisation and renamed The Nudist as Sunshine and Health (S&H). The renaming of the organisation and its magazine revealed that many readers saw S&H as another form of pornography.\n\nThe editor's effort to define the images in S&H as healthy and respectable appealed to readers who feared the social consequences of purchasing explicit pornography. Boone asserted that the numerous photographs dotting almost every page of S&H \u2013 whether as full-page inserts, as illustrations for specific articles, or in two-page monthly collages that brought together dozens of snapshots \u2013 exhibited the physical benefits that came from going naked and promoted the recreational activities of nudist camps. The images showed naked men, women and children \u2013 of all body shapes and sizes \u2013 playing volleyball, swimming, participating in group calisthenics, practising archery, taking a short hike or just sunbathing. Although Boone conceded that there was 'sex content to the illustrations... which appear in nudist magazines and books', he maintained that this content did not constitute obscenity. Only material that conveyed 'sexual impurity', such as publications designed to 'incite lust, suggest impure and libidinous thoughts, be offensive to chastity, pander to the prurient taste', should be considered obscene. The 'sex frankness' of the magazine, according to Boone, 'removes them [issues of S&H] at once from every vestige of suspicion that they are designed for any ulterior, base or unworthy purpose'.17\n\nThe immediate need to reach readers, however, forced Boone and the American nudist movement to compromise its commitment to sexual expression. In 1933, hoping to avoid costly delays and legal troubles, Boone submitted the first four issues of his magazine to the New York Society for the Suppression of Vice (NYSSV). Beginning in 1873, federal legislation gave Anthony Comstock, the head of the NYSSV, the power to remove from the mail any 'obscene book, pamphlet, picture, print, or other publication of a vulgar and indecent character'.18 Under the so-called Comstock Law, postal officials seized birth-control information, literature dealing with sexually explicit themes such as adultery and homosexuality, and images of the naked body. Throughout the first decades of the twentieth century, however, sex radicals, birth-control advocates and free speech proponents attacked the agency for denying adults access to legitimate materials because they might influence young or vulnerable readers. John Sumner, who assumed leadership of the NYSSV after Anthony Comstock's death in 1915, attempted to restore the authority of the infamous vice institution by recasting the agency as less prudish and puritanical. Rather than condemn S&H outright, he found the magazine to be 'non-violative [sic] of the statute [Comstock Law]' as long as it did not display 'genitalia and pubic hair'.19 Boone preferred to show the entire body but he lacked the financial resources and public support necessary to contest Sumner's criteria. For the next decade, he reluctantly removed the genitalia of men and women from the pages of S&H.\n\nThe censorship of genitalia severely restricted the types of pictures that could be used in S&H. The editors preferred to avoid airbrushing or scratching out the pubic area of men and women. This not only looked grotesque (see Figure 1), but, in direct opposition to nudist principles, communicated shame and scorn for the natural body. Instead, they relied heavily on posed images that hid the pubic area but still appeared natural. In requesting pictures from readers, the magazine's editors discouraged snapshots that seem to 'call undue attention' to the pubic area such as 'full front views'.20 Instead, they asked photographers to send in pictures using 'front quarter views and semi-side views' in order to 'produce a 100 percent nudist picture to which no adverse criticism can be brought'.21 The magazine also relied on action pictures that were 'usually distant enough to enable Mrs Grundy to look at them without passing out'.22 Using images that censored genitals and displayed awkwardly posed bodies, Boone gained access to the United States postal system and established S&H as the voice of the American nudist movement.\n\nFigure 1 The Nudist, and later Sunshine and Health, airbrushed the genitalia of men and women from many of its pictures to ensure the magazine would be sold on newsstands and delivered through the United States postal system. The February 1934 cover of The Nudist reprinted with the permission of Courtney Bischoff.\n\nA policy of self-censorship persisted until the Second World War threatened to end organised nudism in the United States. The war disrupted the growth of the movement when it forced individual camp owners as well as national leaders into combat, or to relocate for wartime employment.23 In addition, the 'necessary rationing of tires and gas' limited travel and vacationing opportunities across the country and reduced 'regular attendance to a minimum' at many camps.24 The growth of S&H leading up to the war offered a way for the struggling movement to support itself financially despite rationing and war mobilisation efforts. The 'educational and scientific' appearance and content of nudist magazines complemented Second World War military policies that attempted to satiate soldiers' sexual appetites with respectable female companions, rather than prostitutes who, in the First World War, were blamed for spreading venereal disease and undermining troop morale.25 The numerous articles dedicated to explaining nudism as a health movement and even the many pictures featuring awkwardly posed bodies or censored genitalia defined S&H as a harmless, perhaps even as a respectable, way for troops to see naked male and female bodies. In the September 1944 issue, the editors of S&H reported that 'several commanding officers' endorsed the publication's 'shipment to their commands abroad' and 'certified that nudist publications were in\n\nthe interests of the morale of the forces'.26 To support its struggling clubs and maintain its organisation during the Second World War, nudist leaders began to accentuate the erotic appeal of S&H by transforming the flagship nudist magazine to appeal to men of all sexualities.\n\nTo attract the American soldier, the images, content and style of S&H changed dramatically. Prior to the war, covers emphasised nature, communicated recreational activity through distinctly un-erotic movements and featured family groups that included men, women and children of all body types. During and after the Second World War, the editors began experimenting with 'full color, duotones, combination of line cut and half tone, crayon reproduction, water colors and oil paintings' on covers that almost exclusively featured voluptuous topless women in suggestive poses.27 The March 1947 issue, for example, featured a crayon sketch of a full breasted smiling woman with windblown hair from the chest up.28 The editors also began highlighting its 'Letters from Men Far Afield' section with the silhouette of a naked woman leaning against a globe and standing in front of a large image of the letter V (see Figure 2).29 The silhouette made little effort to mute the eroticism of the female body. It took the shape of a reclining woman with hair back, nipples erect, arms open and awaiting the embrace of a lover. The increasingly erotic images in S&H helped to allay public anxieties caused by the massive mobilisation of troops into sex-segregated environments where men might experiment with homosexuality.30 Displaying more graphic images than most pin-ups but under the guise of a health movement, S&H entertained troops while still maintaining the appearance of respectability.\n\nFigure 2 During the Second World War, the editors of Sunshine and Health changed the magazine's appearance to appeal to the sexual desires of heterosexual American soldiers. Page 3 of the May 1944 issue of Sunshine and Health reprinted with the permission of Courtney Bischoff.\n\nThe sexual objectification of women on the covers of S&H protected readers in search of male nudity and homoeroticism. Although very little homoerotic content appeared in the magazine during the 1930s, the growth of homosexual communities during the war resulted in images, articles and advertisements that appealed directly and indirectly to a gay audience.31 Allen Ellenzweig noted that physique magazines that had for a 'half century been variously marketed to health cultists and 'art appreciators... began more strongly than ever in the 1950s to target a specifically homosexual audience'.32 Unlike male physique magazines though, the depiction of nudist activities in S&H required the presence of both male and female bodies and shielded readers from accusations of homosexuality. In between images of attractive women sunbathing, children splashing in pools or mixed sexed groups playing volleyball, gay readers found large attractive images of naked young, athletic and muscled men flexing for the camera (see Figure 3). Readers might also find short homoerotic stories hidden amid the many articles detailing the physical and mental benefits of nudism. In one short expos\u00e9 titled, 'A Nude Night in Normandy', the magazine featured the romantic story of two male soldiers determined to sleep naked in a bunker being heavily bombed by Nazi forces. Alone and setting camp for the night, the two men planned to 'take off all our clothes, sleep in the nude above ground, and be really comfortable for a change'.33 With strong homoerotic tones, the article then described how the two soldiers 'crawled luxuriously down between the blankets, snuggled up against each other, and prepared for a really heavenly night'.34 The article alluded almost explicitly to a sexual encounter between the two men only to have bombs interrupt the scene.\n\nFigure 3 Other images in Sunshine and Health strongly resembled those in male physique magazines and probably appealed to homosexual readers. Inside cover of the March 1948 issue of Sunshine and Health reprinted with the permission of Courtney Bischoff.\n\nS&H also provided a space for homosexual readers to contact and communicate with one another. In the back of each issue appeared numerous classified advertisements offering private and confidential developing of uncensored 'art photos'. Martin Meeker found that gay men who feared arrest under the Comstock Law often exchanged nude images using terms like 'physique photos' or 'athletic model photos'.35 One advertisement for a 'graduate masseur' named Leo Lehman suggested that S&H ads also used coded language like 'body building' and 'Swedish Massage' to signal either a desire for photos, sexual contact or both. The advertisement, which began appearing in the July 1942 issue of S&H and ran continuously for the next five years, also listed an address that located him near a part of Los Angeles known by police as a 'gay pick-up ground'.36 Hidden behind covers of naked women, but placed next to images of nude men, articles like a 'Nude Night in Normandy' along with subtle classified advertisements revealed how S&H increasingly catered to a homosexual readership.\n\nThe growing eroticisation of male and female bodies during the war also caught the attention of individuals who desired images of pre-pubescent and pubescent youth. For nudists, the joy children exuded while going naked testified to the natural pleasures of nudity freed from the unnecessary modern social conventions that linked the body with shame. In addition, as will be discussed later in more detail, prior to the 1970s naked images of minors, especially those that appeared to represent youth and innocence, frequently evaded censorship laws.37 Free to display the naked child, the prominent exhibition of youth in S&H attracted members who occasionally acted on their desires for children's bodies. In Rock Island, Illinois, Stanley MacWilliams, a single fifty-two-year-old arms plant worker, resigned as the president of the Sunshine Club and confessed to local authorities after a seven-year-old girl's parents accused him of taking 'indecent liberties with children'.38 In Yelm, Washington, nudist leaders quickly took defensive measures to protect the movement when the police charged a member of the Cobblestone Suntanners with 'Carnal knowledge and having a 14-year old girl pose in the nude for him'.39 The display of children's bodies in S&H and the regular attendance of children at nudist parks led to instances of cross-generational sex. Although the magazine risked linking nudism to paedophilia, S&H continued to display images of naked children as a way of representing the body as healthy and free of shame.\n\nThe effort to recruit African Americans into the movement during the Second World War also threatened to erode the movement's respectability. The war against fascism as well as the migration of thousands of African Americans to urban centres where they worked in war industries influenced nudist leaders to challenge the racial divisions that structured American society and the nudist movement. Alois Knapp, long-time owner of Zoro Nature Park in Roselawn, Indiana and 1943 President of the ASA, called for nudists to have the 'courage' to accept people of all races into the movement since the 'blood of many of them [soldiers] mingles into one pool, oozing out of the body of the white man, Negro, Indian, yellow man, brown man'.40 He asserted that nudists could not 'seriously criticise the anti-social philosophy of our enemies until we ourselves get the all human viewpoint'.41 The following year, the editors of S&H published a series of articles by an African American veteran named E. J. Samuels who had recently joined a nudist park with his wife in San Diego. Samuels called on readers to accept African Americans at nudist parks, asserting: 'now that you have removed your clothing it will be just as easy to remove racial prejudices'.42 In 1951, Ebony magazine profiled the efforts of Mr and Mrs Samuels to integrate American nudism as an eccentric example of racial progress.43\n\nDespite the rhetoric of racial liberalism espoused by nudist leaders and presented in S&H, many nudists considered the participation of African Americans at nudist clubs a sexual threat that might also undermine the movement's respectability. The visible and physical transgression of African American bodies into intimate white spaces, such as the restrooms of wartime factories, public beaches or swimming pools, sparked the staunchest resistance to desegregation in northern and southern white communities.44 Many nudists were also 'fearful' that the interaction of naked white and non-white bodies would pose a physical threat to members and 'considered any discussion of this question as untimely'.45 One reader claimed that only a person with a 'sinister object in mind' would want to bring other races into nudist camps.46 Urging fellow members to 'keep the nudist camps free from scandals', he suggested that 'separate camps for Negro and separate camps for white [sic] can hurt no one'.47 The effort of nudist leaders to encourage the participation of African Americans, despite the objections of their own membership, revealed a strong commitment to question American attitudes towards race and sex.\n\nBoone hoped to maintain the recreational character of American nudism alongside the erotic content in S&H by making his daughter, Margaret A. B. Pulis, head editor. Also elected president of the ASA in 1948, Pulis, a mother, grandmother and an active member of her local Parent Teacher Association, countered the growing perception of nudism as a source of pornography and as a place to make sexual contacts with other men or even children. Pulis encouraged female nudists to participate in their local communities and to volunteer in organisations like 'state Mental Hygiene Associations, the Boy Scouts, the Parent Teacher Association, the YMCA and YWCA'. Here, members might contribute to 'building a broader and wider understanding of nudism in the minds of the general public' while also demonstrating that 'nudists are nice people, willing workers, valued members of the community'.48 As editor of S&H, Pulis included columns that took up the topics of pregnancy, childbirth, parenting, cooking, shopping and exercise. Articles sought to make the homemaker's daily routine a little easier or more enjoyable. Pulis's own column, 'Eat Healthy and Like It', listed recipes that 'reduce the homemaker's work' and save the family money.49 'Marge's Mail Mart' offered women advice on shopping and provided the option of purchasing domestic products such as flexiclogs, potholders, knife holders, bathroom tissue holders, matching his and her watches and a marriage medal, through the magazine.50 Although the voluptuous women that almost exclusively graced the covers of S&H continued to appeal to male readers, many of the magazine's pages also read like a woman's magazine.\n\nThe popularity of S&H among men and women of all sexualities during the war period emboldened nudists to further challenge the boundaries of acceptable representation. Readers had long voiced their disgust for the 'mutilated pictures' that regularly appeared in S&H.51 Numerous letters to the editor called for the publication to stop the practice, leaders within the movement felt it disgraced the natural body,52 and nudist photographers decried the omissions as unartistic.53 By the end of the war, the establishment of a regular readership interested in practising nudism as well as in consuming heterosexual and homoerotic visual display gave the editors of S&H the public support and financial security necessary to stop censoring images in the flagship nudist magazine. In the magazine's first ten years, 1933 to 1943, very few images of genitalia appeared in the nudist publication. In the next seven years, almost 370 images that included genitalia graced the pages of the magazine.54 Initially, the publishers sneaked a glimpse of pubic hair into the magazine amid the many pictures that avoided or airbrushed the region. It then began using uncensored images of men and women taken from a distance, gradually including pictures of women standing and facing the camera completely uncensored, and, by the end of the war, violating the taboo against showing close-up images of the male penis. The uncensored display of male and female genitalia reflected the movement's long-time goal to shamelessly exhibit the naked body while also satisfying many of its readers' desire for more explicit erotica.\n\nA prudish legal strategy\n\nThe transformation of S&H's content and appearance during and after the war caught the attention of the United States Post Office. In 1947, letter carriers began seizing the magazine at various points of delivery around the nation. Boone immediately demanded a hearing to determine the mailability of S&H and the Post Office appointed a trial examiner to evaluate the decency of the flagship nudist magazine. At these hearings, postal officials argued that the promotion of nudist principles in S&H concealed its commercial appeal to both heterosexual and homosexual readers. Calvin Hassell, who represented the Post Office, observed that with the 'exception of an occasional volleyball game and people gathered around a swimming pool' the images showed 'little activity \u2013 just naked people sitting or standing around'. He concluded that 'without the nude pictures the publication would have little if any sales appeal'. Hassell also targeted the subtle ways that homosexual men communicated with each other through the magazine's many classified advertisements. He believed the magazine acted as a 'clearinghouse for obscene matter' because it provided readers 'information directly and indirectly' about obtaining 'obscene, lewd, lascivious and indecent matter' in 'blind advertisements', 'pen pal advertisements' and 'photo lab advertisements'. Hassell singled out the 'wording of the photo developing advertisements' because he suspected that homosexuals used coded language to make sexual contacts. He believed advertisements for 'nude art photos' offering 'confidential' service and promising readers that no pictures 'would be altered or refused' revealed the 'intentions of the advertisers' to exchange photos more graphic than those displayed in the magazine. The Post Office disregarded the mission of S&H and argued that the magazine constituted pornography.\n\nThe ACLU saw S&H as the official publication of a social movement and considered the Post Office's seizure of the magazine an attack on freedom of speech and the press. Roger Baldwin, one of the central figures involved in the founding of the ACLU and a moderate voice within the organisation, saw the defence of nudist magazines as a way to avoid associations with communism during the Cold War. Not wanting to link the ACLU to radical ideologies, Baldwin explained that he did not 'sponsor or endorse the beliefs of nudists'. Rather, he 'supported their [nudists'] right to pursue their health ideas'.55 He then devised a legal strategy that built on the nudist movement's contention that 'commonplace nudity, far from stimulating immorality... serves to diminish prurience' and approached the seizure of S&H as a 'freedom of press issue... far different from that raised by a nude calendar or an entertainment magazine'.56 Baldwin believed that 'a certain amount of prudishness' would remove the magazine from the 'terms of the statutes and the court decisions and thus free it in the mails'.57 To highlight the absence of commercial sexual display and the movement's commitment to health and sexual frankness, Baldwin solicited the opinion of several hundred expert witnesses including doctors, academics, publishers and businessmen. He asked if they thought the images in S&H 'incite the average person to lustfulness or thought of sexual impurity', and requested that the witnesses compare these representations to the 'lurid photographs in tabloid newspapers, and suggestive advertisements and illustrations widely seen today'.58 Trying to distinguish nudist magazines from pornography, Baldwin presented S&H as tame compared to the racy images of tabloid newspapers.\n\nLegal absolutists within the ACLU along with nudist leaders took issue with Baldwin's strategy to distance nudism from sexually explicit material. The Reverend Ilsley Boone wanted a 'definite gauge of obscenity as clear and distinct as a yard stick' that would end the 'constant and unbearable litigation'.59 He believed that tolerating the censorship of certain indecent materials would leave nudists vulnerable to future censorship. Elmer Rice, a playwright and free speech activist in the ACLU, objected to Baldwin's strategy on different grounds. He feared that it set up standards of 'propriety and impropriety' when the ACLU should be striving to defeat all standards of obscenity. He asserted that it was 'completely out of line with ACLU policy' to tolerate the censorship of lustfulness. He did not like the 'prudishness' of this strategy and urged him to approach the issue of free speech and press with the 'same objectivity that we do all others'.60\n\nBoone employed a more confrontational approach that furthered the movement's commitment to sexual frankness and challenged the racial assumptions behind censorship. Although most Americans violently opposed the intimate interaction of black and white bodies and many nudists voiced fears about admitting African Americans into nudist clubs, Boone used images of the indigenous non-white body to argue that the censorship policies of the Post Office discriminated against white nudist representations. When it seized the March 1947 issue of S&H, the Post Office announced a policy that 'the breasts of white women but not the breasts of coloured women' should be censored from the mail.61 The assumed illicit sexuality of non-white bodies had long given licence to discussions and depictions of sex. According to Catherine Lutz and Jane Collins, colonial racial assumptions combined with the National Geographic Magazine's scientific and literary prestige to make it one of the 'few mass culture venues where Americans could see women's breasts'.62 In protest, Boone juxtaposed the images of a white topless woman next to a similarly naked African American woman and asserted that the National Geographic Magazine had 'published thousands of breasts of coloured women without the slightest objection on the part of the post office' (see Figure 4).63 Boone explained in the African American newspaper the New York Amsterdam News that he published the two photographs to 'force a showdown from the department' that would ultimately free his magazine from the obscenity statutes.64 Boone's dramatic display of white and non-white bodies clashed with Roger Baldwin's effort to distinguish nudist images from commercial sexual display.\n\nFigure 4 In a dramatic full page layout, the Reverend Ilsley Boone protested against the Post Office's policy that 'the breasts of white women but not the breasts of colored women' should be censored from the mails. Pages 14 and 15 of the July 1947 issue of Sunshine and Health reprinted with the permission of Courtney Bischoff.\n\n'It is filthy, it is foul, it is obscene'\n\nThe ACLU's strategy to distance S&H from pornography initially proved successful in the courts. Since 1947, the Post Office seized issues of S&H at random points of delivery and relied on local hearings administered by its own trial examiners to avoid formal legal proceedings with Boone. In several high-profile post-war congressional hearings, Postmaster General Arthur Summerfield claimed that numerous children received 'pornographic filth in the family mailbox', and in 1953 the local post office in Mays Landing, New Jersey, where Boone published and distributed S&H, stopped the mailing of the magazine at the point of origin.65 This action allowed Boone to seek an injunction against the Post Office in the DC Circuit Court. At trial, Boone and the ACLU argued that the pictures in S&H showed 'people practicing nudism in a normal and healthy environment and in the happy enjoyment of thoroughly innocent activities' and were the 'antithesis of anything suggestive or pornographic'.66 On 23 June 1953, the majority of judges ruled that the magazines 'were not likely to promote lustful feelings or excite sexual passions' and granted a permanent injunction blocking the Post Office from seizing S&H from the mail.67 The Post Office feared that this decision threatened to limit the powers that Congress granted it to censor materials under the 1873 Comstock Act and immediately appealed the decision asserting that the lower court 'incorrectly substituted its own opinion for the determination of the postmaster general'.68 Boone and the ACLU argued before the DC Circuit Court of Appeals that the Post Office's seizure of S&H constituted a 'prior restraint upon the freedom of the press' and, as a result, violated the First and Fourth Amendments of the Constitution. On 16 December 1954, the majority of judges affirmed the lower court's injunction because the actions of the Post Office posed 'grave constitutional questions'.69 The New York Times announced the significance of the decision when it declared in a headline: 'Post Office Power as Censor Curbed'.70\n\nThe Post Office reacted to the DC Circuit Court of Appeals decision by immediately defying it. On 23 December 1954, two days before Christmas and only a week after the DC Circuit Court of Appeals' decision, the postmaster in Mays Landing seized 400 copies of the 1955 February issue of S&H. Boone and the ACLU, confident that the courts would once again rule in their favour and bolster the legal status of S&H, filed a civil suit against the Post Office in the DC Circuit Court. Judge Kirkland, who presided over the trial, saw the seizure of S&H as an issue of obscenity rather than a challenge to the First or Fourth Amendments. Kirkland intended to establish 'what is art on the one hand, pornography on the other; what is decent on the one hand as what is indecent on the other'.71 Kirkland's detailed written opinion provided the legal precedent that the US Supreme Court would ultimately use to reshape modern American obscenity law.\n\nKirkland rejected Boone's argument that the nudist movement's commitment to sexual frankness legitimated the display of the naked body in S&H. He particularly objected to images that attempted to represent the 'normal, natural person and reveals her as she was in fact'. One 'unusual picture' taken 'within 12 feet of the camera' displayed two women in their 'late twenties or early thirties', one of whom stood 5 foot 7 and weighed 'in the neighbourhood of 250 pounds', and who Kirkland described as 'exceedingly obese' with 'elephantine breasts that hang from her shoulder to her waist' and thighs which were also 'very obese' (see Figure 5). The effort to frankly show a range of body types in S&H challenged the increasingly dominant preference for the slender female body in the early twentieth century. The transition from the moral maternalism of the Victorian period to a modern conception of womanhood that emphasised sensuality and consumerism resulted, as historian Peter Stearns has argued, in a 'misogynist' emphasis on the thin female form achieved through rigorous dieting regimens designed to constrain the indulgences of the new woman.72 Judge Kirkland, as a result, considered nudist representations that did not conform to the idealised white slim female body to be indecent.\n\nFigure 5 The effort to show frankly a range of body types in Sunshine and Health challenged the increasingly dominant preference for the slender female body. Page 29 of the February 1955 issue of Sunshine and Health reprinted with the permission of Courtney Bischoff.\n\nThe February 1955 cover, conversely, did not warrant censorship despite displaying a woman wearing heels with wind blowing in her hair, smiling widely with her chest pushed outwards, and positioned against a rocky grey background that made her soft pale skin stand out (see Figure 6). Although the ACLU attempted to distinguish S&H from similar examples of commercial sexual display, Kirkland saw no reason to object to the photograph because it did not show the 'pubic area and there is no show of the genitalia by the angle at which the picture is shot'. He acknowledged that the photographer used 'shadowing on her chest' to create the effect of a 'bosom larger by far than normal' and saw that it was 'shot at such an angle as to elongate and make quite massive the breast as distinguished from the very small nipple', but he reasoned that the 'plunging neckline has been accepted in the mores of the people' and that the 'revealing of the breast would not in itself be obscene'.73 According to historian Joan Jacobs Brumberg, the breasts represented a 'particular preoccupation of Americans in the years after World War II'. Movie stars known for their bust line, like Jayne Mansfield, Jane Russell and Marilyn Monroe, dominated the 1950s box office.74 Similar naked female images in S&H that pleased the male heterosexual gaze posed little threat to public decency.\n\nFigure 6 Images of young svelte naked women did not draw the objections of Judge Kirkland. Cover of the February 1955 issue of Sunshine and Health reprinted with the permission of Courtney Bischoff.\n\nJudge Kirkland also did not object to the exposure of the nude non-white body. At trial, Boone again objected to obscenity laws that permitted the display of non-white naked bodies in publications like National Geographic and wondered if the judicial system had 'grown up enough' not to 'draw a distinction because the picture happens to be of a white person rather than a Negro'.75 In response, the Post Office asserted that 'we are a clothed people' and that the practices of indigenous people in 'Africa or some other foreign country in some other time is not the standard by which we should judge these pictures'.76 Judge Kirkland agreed with the Post Office and rejected nudist attempts to make comparisons to a documentary film titled La Tuka. Nudist attorneys argued that it should not make 'any difference' that the film showed life in an African tribe rather than everyday Americans, only to have Judge Kirkland retort that 'people... living on the tropical belts would not be relevant'.77 In his final written decision, Judge Kirkland made the racial politics of obscenity clear when he found nothing indecent about a 'suggestive picture' of what appeared to be a 'woman of Mexican birth, a very dark complexioned woman'.78 Entrenched racial stereotypes of non-white bodies as primitive, accessible and hyper-sexual permitted the exhibition of the naked racial other. Since naked indigenous bodies probably aroused audiences just as much as those in S&H, the racial arguments made by nudist advocates did little to mute the magazine's eroticism.\n\nKirkland, however, ruled unequivocally that any photographs that showed the penis 'obviously have no place even in illustrating the principles of nudism'.79 Judge Kirkland probably considered the images of naked men to be directed towards gay male readers since many so-called beefcake photos in the post-war period masked their homoerotic content by embracing a rhetoric of health or bodybuilding that resembled the nudist movement's promotion of health and fitness.80 In addition, Thomas Waugh has argued that since the nineteenth century the public has associated the 'homosexual artist' and homoeroticism with the 'representation of the male nude'.81 Recognising this historic relationship, Kirkland described the 'corona' of the penis in one photo as 'clearly discernable' to the point that one can see that the 'man is circumcised' and, despite the very small size of the man in the photo, he strongly condemned the image, decrying: 'it is filthy, it is foul, it is obscene, and the Court will hold such as a matter of fact'82 (see Figure 7). Although small, captured from a distance, or not the main focus of the camera, the penis stood out as an exceptionally offensive image since it attracted homosexual desire.\n\nFigure 7 In contrast, photographs showing full frontal male nudity drew the objections of the court despite the subject's distance from the photographer. Page 9 of the February 1955 issue of Sunshine and Health reprinted with the permission of Courtney Bischoff.\n\nJudge Kirkland, the Reverend Ilsley Boone and the ACLU did reach a consensus regarding the decency of naked children's bodies. Kirkland ruled that 'photographed children of the front view which reveals the diminutive and underdeveloped genitalia' should not be considered obscene 'by virtue of their age of innocence'.83 He supported this decision by stating that 'such a view' represented the 'common acceptance of the American people'.84 Evaluating an image of a young naked girl sitting on a swing with her 'labia majora' clearly discernible, Judge Kirkland asserted that one would have to be 'prudish to hold that was an obscene picture'85 (see Figure 8). Judge Kirkland's permissive policy towards the display of children reflected an emerging effort by child psychologists to encourage a non-repressive attitude towards the child's body. Many post-war parenting guides relied on Freudian psychoanalysis to recommend a permissive response to childhood sexuality. In the 'Facts of Life' section of his bestselling The Common Sense Book of Baby and Child Care (1957), Dr Benjamin Spock addressed the topic of nudity in the home by recognising that the 'excessive modesty' of the Victorian period had given way to 'today's casual attitude that is a lot healthier'.86 The effort to avoid psychological maladjustment through a permissive attitude towards childhood sexuality influenced Judge Kirkland to allow the display of naked children.87\n\nFigure 8 Many judges did not object to photographs of children that displayed genitalia. Page 7 of the February 1955 issue of Sunshine and Health reprinted with the permission of Courtney Bischoff.\n\nAlthough Judge Kirkland did not object to the display of attractive women, non-white bodies or children's genitalia, he ultimately dismissed the ACLU's strategy to distance S&H from commercial sexual display when he ruled that the inclusion of full-frontal male and female nudity constituted the main criteria for judging obscenity. He did not oppose artistic, medical or scientific journals, books, magazines and literature that showed the 'human form merely in the nude and beyond that not revealing the pubic area or the male or female genitalia'. The fact that the nudists offered S&H 'freely for sale to the general public who are not members of the nudist organisation' while also exhibiting photographs 'clearly revealing genitals, breasts and other portions of the body normally covered in public' revealed the profit motive of the magazine and, according to Judge Kirkland, made it obscene and non-mailable.88\n\nRoth v. United States\n\nThe ACLU and Boone hoped to reverse the Kirkland decision when the US Supreme Court, after almost three decades of silence, took up the issue of obscenity in a case involving a notorious smut dealer named Samuel Roth. Since the Supreme Court ruled in Ulysses (1933) that literature dealing with sexual themes and that exhibited scholarly merit should not be considered obscene, courtrooms around the country struggled to reach a consensus on the issue of obscenity. Chief Justice Warren observed that judges determined obscenity based 'largely upon the effect that the materials have upon those who receive them', and as a result the 'line dividing the salacious or pornographic from literature or science is not straight and unwavering' and 'may have a different impact, varying according to the part of the community it reached'.89 The lack of a clear national obscenity standard compelled the justices of the US Supreme Court to hear Roth v. United States in 1957.\n\nDespite Roth's established pornography business, the ACLU followed the strategy it used to defend S&H and shied away from taking an absolutist position against Post Office censorship. The Post Office considered Samuel Roth 'one of the biggest dealers in obscenity in the nation',90 and in 1956 federal prosecutors arrested him for advertising and selling a publication called American Aphrodite which contained literary erotica and nude photography. The ACLU, as it had done in its defence of S&H, made arguments implying that certain forms of sexual expression warranted censorship. In its amicus brief, ACLU attorneys contended that the US Supreme Court should not uphold Roth's arrest since the prosecutors had not introduced any evidence that his publications 'will probably and immediately cause anti-social conduct'.91 This argument assumed that the introduction of evidence showing the danger of pornography justified postal censorship.\n\nIn a six to three decision, the US Supreme Court upheld Roth's conviction and instituted a legal test of obscenity that distinguished acceptable representations of sex from commercial sexual display. Writing for the majority, Justice William Brennan stated that the First Amendment did not protect obscenity. He ruled that the decency or indecency of materials should be determined according 'to the average person, applying contemporary community standards, the dominant theme of the material taken as a whole, appeals to prurient interests'. Stating that 'sex and obscenity are not synonymous', Justice Brennan echoed the moderate legal strategies used by the ACLU in Roth and in its defence of S&H. Limiting censorship to commercial representations of sex, Brennan explained that the 'portrayal of sex in art, literature and scientific works is not sufficient reason to deny material the constitutional protection of freedom of speech and press'.92 Other justices, however, thought any restrictions placed on the First Amendment, especially a test that relied on community standards, still defined obscenity too broadly. In his dissent, Justice William O. Douglas asserted that the First Amendment should 'allow protests even against the moral code that the standard of the day sets for the community'.93 The US Supreme Court upheld Roth's conviction because the materials he distributed through the mail appealed directly to so-called 'prurient interests' rather than to an academic or scholarly audience. In its Roth decision, the justices of the US Supreme Court intended to limit the types of materials considered obscene without granting full First Amendment protection.\n\nDespite the intentions of the justices, the federal courts used Roth to further restrict sexual expression. Boone and the ACLU argued that Judge Kirkland violated the First Amendment when he declared many of the pictures in S&H to be obscene and non-mailable. The DC Circuit Court of Appeals, however, asserted that the pictures 'speak for themselves' and found Kirkland's 'extensive, particularised descriptions of the offending and offensive material' to be 'amply sustained'. They ruled that S&H 'deals with \"sex in a manner appealing to prurient interest\" and hence is obscene, as Roth tells us'.94 The DC Circuit Court of Appeals affirmed the Kirkland decision because it equated S&H with the types of materials that Samuel Roth sent through the mails. The decision by the DC Circuit Court of Appeals confirmed the fears of First Amendment advocates like Justice Douglas and the Reverend Ilsley Boone.\n\nFor the US Supreme Court, however, the variety of content and images in S&H did not constitute obscenity under the test it established in Roth. Filing a writ of certiorari with the US Supreme Court to review the recent decision issued by the DC Circuit Court of Appeals, the ACLU continued to argue that the display of naked men, women and children in S&H did not constitute commercial sexual display. Just as he had done in the Kirkland decision, Boone supplied the US Supreme Court with copies of the 1955 February issue of S&H and on 13 January 1958, in a unanimous decision, the US Supreme Court granted a writ of certiorari and reversed the ruling of the DC Circuit Court of Appeals. Citing only Roth v. United States in its opinion, the justices ordered the lower court to take into account the therapeutic and recreational character of nudism when deciding on the decency of the pictures the movement displayed in its magazine.95 In his concurring opinion in Roth, Chief Justice Warren reasoned that 'it is not the book that is on trial; it is the person' and asserted that the 'conduct of the defendant is the central issue'.96 As a known publisher of pornography, the materials Samuel Roth sent through the mail constituted obscenity. S&H, on the other hand, displayed similar images while also promoting the therapeutic benefits of going naked. According to the justices, this placed the publication outside the test it established in Roth. The US Supreme Court's approval of S&H redefined the boundaries of acceptable sexual display.\n\n'Gray can be a very drab and dirty color'\n\nGovernment censors and political leaders took notice when the US Supreme Court ruled that the Post Office did not have the power to deny nudist magazines mailing privileges. In 1961, the House Committee on Post Office and Civil Service held several hearings to re-evaluate the issue of 'Obscene Matter Sent Through the Mail'.97 In her opening statement, Representative Kathryn Granahan, a Democrat from Pennsylvania and chair of the committee, expressed concern about the new threat posed by 'gray area products' like nudist magazines.98 In her interpretation, the recent US Supreme Court decisions on obscenity benefited publications that 'pussyfoot around the edges but shrewdly stay just clear of subjecting themselves to prosecution'.99 Granahan considered magazines like S&H to be 'more poisonous in their appeal to young boys and girls' since they 'tend to overcome home and church and civic guidance'. She declared that 'Gray can be a very drab and dirty color'.100\n\nMany long-time nudist leaders joined Granahan in expressing concern about the movement's legal victories. Although the nudist movement took advantage of the recent US Supreme Court decision to display the naked body without the shame communicated by censorship, many leaders feared that the original ideals and principles of nudism would be lost to an unregulated market of magazines that linked nudity and nudism to the commercialisation of sex. In the years after the movement's legal victories, the understated sensuality that had long played a role in defining nudism exploded in the United States. New magazines, all claiming to represent nudist ideals and principles, flooded newsstands. Magazine publishers, some with only slim ties to the movement, used the familial character and health-oriented principles of nudism to include erotic images and content. Testifying before the committee, the Reverend Henry Huntington, the first president of the National Nudist Council, regretted that S&H's 'pictures, especially on the cover' promoted the 'suggestion of the girly-girly magazine'. Huntington declared that the pictures made him 'quite furious inside because really the movement is the essence of good health'.101 Other nudist leaders also continued to cling to the image of respectability that had helped the movement defeat the censorship of its magazines. In response to the renewed opposition of the Granahan Committee, for example, Ilsley Boone, his son Berton Boone and his daughter Margaret A. B. Pulis all testified to the respectable character of American nudism. Referring several times to Boone as 'Dad', Pulis answered questions about the images in S&H by invoking her status as a daughter, mother, grandmother and member of the PTA.102 The three long-time nudist leaders wanted to maintain the family-oriented image of the movement.\n\nIronically, the continuing effort to position S&H within the heteronormative boundaries of sexual liberalism precipitated the flagship nudist magazine's bankruptcy in 1963. The growing acceptance of the naked body at newsstands meant that the movement's continuing promotion of health, nature and family no longer seemed necessary or relevant to most readers. Committed to advancing the therapeutic ideals and familial orientation of nudism, the flagship nudist publication that began in 1933 and fought to defeat censorship laws across the country could no longer compete in a marketplace that offered even more explicit material uninterrupted by nudist principles and philosophy. The nudist movement's legal victories and the bankruptcy of its flagship publication signalled the fall of modern sexual liberalism and the explosion in eroticism that became a central feature of late twentieth-century American society.\n\nNotes\n\nI would like to thank Mark Leff, Elizabeth Pleck, Leslie J. Reagan, Elizabeth Watkins and the anonymous readers for their advice and comments on various drafts of this chapter, and the editors of Gender & History for their assistance. I am also especially grateful to Helen Fisher for giving me full access to the unique materials at the American Nudist Research Library (ANRL) in Kissimmee, Florida, and Courtney Bischoff for granting me permission to use Sunshine & Health.\n\n1. William O'Brien, 'Official Transcript of Proceedings before the Post Office Department', National Archives and Records Administration, College Park, Maryland (hereafter NARA\u2013CP), RG 21, US District Court for DC, Civil Action #74\u201355, Sunshine Book Company v. Summerfield, Box 1578, tabbed, 16W3\/17\/32\/02, p. 93.\n\n2. 'Publisher's Desk \u2013 In Temporary Mourning', Sunshine and Health, May 1947, p. 1.\n\n3. Rochelle Gurstein, The Repeal of Reticence: A History of America's Cultural and Legal Struggles Over Free Speech, Obscenity, Sexual Liberation, and Modern Art (New York: Hill and Wang, 1996); Marjorie Heins, Not in Front of the Children: 'Indecency', Censorship and the Innocence of Youth (New York: Hill and Wang, 2001); Alison M. Parker, Purifying America: Women, Cultural Reform, and Pro-Censorship Activism, 1873\u20131933 (Urbana: University of Illinois Press, 1997); John D'Emilio and Estelle B. Freedman, Intimate Matters: A History of Sexuality in America (Chicago: University of Chicago Press, 1997), pp. 222\u201374.\n\n4. Leigh Ann Wheeler, Against Obscenity: Reform and the Politics of Womanhood in America, 1873\u20131935 (Baltimore: Johns Hopkins University Press, 2004); Helen Lefkowitz Horowitz, Rereading Sex: Battles over Sexual Knowledge and Suppression in Nineteenth Century America (New York: Alfred A. Knopf, 2002); Molly McGarry, 'Spectral Sexualities: Nineteenth Century Spiritualism, Moral Panics, and the Making of U.S. Obscenity Law', Journal of Women's History 12 (2000), pp. 8\u201329; Nicola Beisel, Imperiled Innocents: Anthony Comstock and Family Reproduction in Victorian America (New Jersey: Princeton University Press, 1997); Linda Gordon, Woman's Body, Woman's Right: A Social History of Birth Control in America (New York: Grossman, 1976).\n\n5. Marc Stein, 'Boutilier and the U.S. Supreme Court's Sexual Revolution', Law and History Review 23 (2005), pp. 491\u2013536; Andrea Friedman, Prurient Interests: Gender, Democracy, and Obscenity in New York City, 1909\u20131945 (New York: Columbia University Press, 2000); Leslie J. Reagan, When Abortion Was a Crime: Women, Medicine, and Law in the United States, 1867\u20131973 (Berkeley: University of California Press, 1997); George Chauncey, Gay New York: Gender, Urban Culture, and the Making of the Gay Male World, 1890\u20131940 (New York: Basic, 1994); Whitney Strub, 'Black and White and Banned All Over: Race, Censorship and Obscenity in Post War Memphis', Journal of Social History 40 (2007), pp. 685\u2013715; Leigh Gilmore, 'Obscenity, Modernity, Identity: Legalizing The Well of Loneliness and Nightwood', Journal of the History of Sexuality 4 (1994), pp. 603\u201324.\n\n6. 'Principles and Standards', The Nudist, May 1933, p. 3.\n\n7. Miriam G Reumann, American Sexual Character: Sex, Gender, and National Identity in the Kinsey Reports (Berkeley: University of California Press, 2005), p. 115; Mary L. Dudziak, 'Josephine Baker, Racial Protest, and the Cold War', Journal of American History 82 (1994), pp. 543\u201370; Regina Kunzel, 'White Neurosis, Black Pathology: Constructing Out-of-Wedlock Pregnancy in Wartime and Post War United States', in Joanne J. Meyerowitz (ed.), Not June Cleaver: Women and Gender in Postwar America, 1945\u20131960 (Philadelphia: Temple University Press, 1994), pp. 304\u201333.\n\n8. The American Civil Liberties Union formed in response to the Red Scare of 1919 in order to oppose anti-union government policies and to defend the civil liberties of political radicals. Samuel Walker, In Defense of American Liberties: A History of the ACLU (Carbondale: Southern Illinois University Press, 1999), pp. 11\u201345; Judy Kutulas, The American Civil Liberties Union and the Making of Modern Liberalism, 1930\u20131960 (Chapel Hill: University of North Carolina Press, 2006), pp. 1\u201315.\n\n9. Joanne J. Meyerowitz, How Sex Changed: A History of Transsexuality in the United States (Cambridge: Harvard University Press, 2002); Martin Meeker, Contacts Desired: Gay and Lesbian Communications and Community, 1940s\u20131970s (Chicago: University of Chicago Press, 2006).\n\n10. George Mosse, Nationalism and Sexuality: Respectability and Abnormal Sexuality in Modern Europe (New York: H. Fertig, 1985), p. 50.\n\n11. John Williams, Turning to Nature in Germany: Hiking, Nudism, and Conservation, 1900\u20131940 (Stanford: Stanford University Press, 2007); Josie McLellan, 'State Socialist Bodies: East German Nudism from Ban to Boom', Journal of Modern History 79 (2007), pp. 48\u201379; Chad Ross, Naked Germany: Health, Race and the Nation (Oxford: Berg, 2005); Karl Eric Toepfer, Empire of Ecstasy: Nudity and Movement in German Body Culture, 1910\u20131935 (Berkeley: University of California Press, 1997); Brandon Taylor and Wilfred van der Will (eds), The Nazification of Art: Art, Design, Music, Architecture and Film in the Third Reich (Winchester: Winchester School of Art Press, 1990).\n\n12. Maurice Parmelee, Nudism in Modern Life (New York: Alfred A. Knopf, 1931); Frances and Mason Merrill, Among the Nudists (New York: Alfred A. Knopf, 1931); Francis and Mason Merrill, Nudism Comes to America (New York: Garden City, 1932); Jan Gay, On Going Naked (New York: Garden City, 1932).\n\n13. Hugh C. Lester, Godiva Rides Again: A History of the Nudist Movement (New York: Vantage Press, 1968), p. 61.\n\n14. 'INC', The Nudist, May 1933, p. 2.\n\n15. Calvin W. Hassell, 'In the Matter of the Mailability of the May and July 1948 Issues of Sunshine and Health Under the Provisions of 18 US Code 334', American Civil Liberty Union Archives 1950\u20131990, History and Philosophy Library, University of Illinois Urbana\u2013Champaign, 7 (hereafter ACLU\/UIUC), Box 759, Folder 2, Sunshine and Health 1947\u201350, p. 7.\n\n16. 'Fifth Annual Meeting of the International Nudist Conference (Newly Named the American Sunbathing Association)', The Nudist, November 1936, p. 7.\n\n17. Ilsley Boone, 'On the Obscenity of Nudist Pictures', Sunshine and Health, October 1942, p. 28.\n\n18. Quoted in Lefkowitz Horowitz, Rereading Sex, p. 358.\n\n19. Ilsley Boone, 'Defense Statement at U.S. Post Office Department Hearing', 28 July 1947, ACLU\/UIUC, Box 759, Folder 3, Sunshine and Health Cont., pp. 3\u20134.\n\n20. 'Photography Guide for S&H', Sunshine and Health, October 1944, p. 30.\n\n21. 'Photography Guide for S&H'.\n\n22. Herbert Webb, 'A Nudist Photographer Talks', Sunshine and Health, January 1942, p. 13.\n\n23. 'The Five Year Plan and the Annual Meeting', Sunshine and Health, August 1942, p. 22.\n\n24. 'The Five Year Plan Moves On', Sunshine and Health, March 1943, p. 6.\n\n25. Marilyn Hegarty, Victory Girls, Khaki-Wackies, and Patriotutes: The Regulation of Female Sexuality during World War II (New York: New York University Press, 2007), p. 85; Allan M. Brandt, No Magic Bullet: A Social History of Venereal Disease in the United States since 1880 (New York: Oxford University Press, 1987), pp. 31\u20137; Mark Thomas Connelly, The Response to Prostitution in the Progressive Era (Chapel Hill: North Carolina University Press, 1980); Ruth Rosen, The Lost Sisterhood: Prostitution in America, 1900\u20131918 (Baltimore: Johns Hopkins University Press, 1982).\n\n26. 'Editorial Comment', Sunshine and Health, September 1944, p. 9.\n\n27. 'Publisher's Desk', Sunshine and Health, January 1947, p. 1.\n\n28. Sunshine and Health, March 1947, cover.\n\n29. 'Letters From Men far Afield', Sunshine and Health, May 1944, p. 3; 'Letters From Men far Afield', Sunshine and Health, June 1944, p. 3.\n\n30. Despina Kakoudake, 'Pinup: The American Secret Weapon in World War II', in Linda Williams (ed.), Porn Studies (Durham: Duke University Press, 2004), pp. 335\u201369.\n\n31. John D'Emilio, Sexual Politics, Sexual Communities: The Making of a Homosexual Minority in the United States, 1940\u20131970 (Chicago: University of Chicago Press, 1998); Leisa Meyer, Creating G.I. Jane: Sexuality and Power in the Women's Army Corps During World War II (New York: Columbia University Press, 1996).\n\n32. Allen Ellenzweig, The Homoerotic Photograph: Male Images from Durieu\/Delacroix to Mapplethorpe (New York: Columbia University Press, 1992); Tracey Morgan, 'Pages of Whiteness: Race, Physique Magazines and the Emergence of Public Gay Culture', in Brett Beemyn and Mickey Eliason (eds), Queer Studies: A Lesbian, Gay, Bissexual and Transgender Anthology (New York: New York University Press, 1996), pp. 280\u201397.\n\n33. 'A Nude Night in Normandy', Sunshine and Health, March 1945, p. 6.\n\n34. 'A Nude Night in Normandy'.\n\n35. Meeker, Contacts Desired, p. 26.\n\n36. Whitney Strub, 'The Clearly Obscene and the Queerly Obscene: Heteronormativity and Obscenity in Cold War Los Angeles', American Quarterly 60 (2008), pp. 386\u20139.\n\n37. James Elias, Veronica Diehl Elias, Vern L. Bullough, Gwen Brewer, Jeffrey J. Douglas and Will Jarvis (eds), Porn 101: Eroticism, Pornography, and the First Amendment (Amherst, NY: Prometheus, 1999), p. 501.\n\n38. 'Girls' Charges Jail President of Nudist Club', Chicago Daily Tribune, 4 July 1943, p. A10; 'Nudists Facing Rough and Chill Reception', Chicago Daily Tribune, 28 July 1943, p. 15.\n\n39. Letter from Fred Burnett to Norval Packwood, 5 January 1957, American Nudist Research Library, Kissimmee, Florida.\n\n40. Alois Knapp, 'President's Message', Sunshine and Health, June 1943, p. 25.\n\n41. Knapp, 'President's Message', p. 25.\n\n42. E. J. Samuel, 'On Negro Nudism', Sunshine and Health, August 1945, p. 21.\n\n43. Herbert Nipson, 'Nudism and Negroes', Ebony, March 1951, pp. 93\u2013111.\n\n44. Jeff Wiltse, Contested Waters: A Social History of Swimming Pools in America (Chapel Hill: University of North Carolina Press, 2007), pp. 121\u201380; Strub, 'Black and White and Banned All Over'; Eileen Boris, '\"You Wouldn't Want One of 'Em Dancing with Your Wife\": Racialized Bodies on the Job in World War II', American Quarterly 50 (1998), pp. 77\u2013108.\n\n45. 'Is There a Color Line in Nudism', Sunshine and Health, June 1943, p. 9; 'Readers' Forum, For Racial Segregation', Sunshine and Health, January 1946, p. 3; Steve Brenton, 'A Plan for Colored Nudists', Sunshine and Health, June 1945, p. 7.\n\n46. 'Is There a Color Line in Nudism'.\n\n47. 'Is There a Color Line in Nudism'.\n\n48. Margaret A. B. Pulis, 'President's Message', Sunshine and Health, December 1948, p. 25.\n\n49. Margaret A. B. Pulis, 'Eat Healthy and Like It', Sunshine and Health, April 1948, p. 21.\n\n50. 'Marge's Mail Mart', Sunshine and Health, September 1956, p. 22.\n\n51. 'A Nudist Photographer Talks'.\n\n52. 'On the Obscenity of Nudist Pictures'.\n\n53. 'Photography Guide for S&H'.\n\n54. I arrived at this number by systematically counting the images in Sunshine and Health from 1933 to 1963.\n\n55. Roger Baldwin, 'Affidavit: In the Matter of Sunshine and Health, May 1948 Issue', June 1948, ACLU\/UIUC, Box 759, Folder 3, Sunshine and Health Cont., Annex A.\n\n56. Baldwin, 'Affidavit'.\n\n57. 'Letter to Mr Elmer Rice from Roger Baldwin', 7 January 1948, ACLU\/UIUC, Box 759, Folder 2, Sunshine and Health, 1947\u201350.\n\n58. Baldwin, 'Affidavit'.\n\n59. 'Letter to Roger Baldwin from Ilsley Boone', 14 October 1947, ACLU\/UIUC, Box 759, Folder 2, Sunshine and Health, 1947\u201350.\n\n60. 'Letter to Roger Baldwin from Elmer Rice', 2 January 1948, ACLU\/UIUC, Box 759, Folder 2, Sunshine and Health, 1947\u201350.\n\n61. 'Letter to Roger Baldwin from Elmer Rice'.\n\n62. Catherine A. Lutz and Jane L. Collins, Reading National Geographic (Chicago: University of Chicago Press, 1993), pp. 172\u20138.\n\n63. Sunshine and Health, February 1955, p. 14.\n\n64. 'Nude Bodies Pose Problem', New York Amsterdam News, 28 June 1947, p. 1.\n\n65. Quoted in Andrea Friedman, 'Sadists and Sissies: Anti-Pornography Campaigns in Cold War America', Gender & History 15 (2003), p. 216.\n\n66. Summerfield v. Sunshine Book Company, No. 12,026, DC Cir., 221 F. 2d 42 (1954), p. 4.\n\n67. Summerfield v. Sunshine Book Company, p. 5.\n\n68. Summerfield v. Sunshine Book Company, p. 44.\n\n69. Summerfield v. Sunshine Book Company, p. 48.\n\n70. Luther Huston, 'Post Office Power as Censor Curbed', New York Times, 17 December 1954, p. 22.\n\n71. Sunshine Book Company v. Summerfield, 128 F. Supp. 564 (1955).\n\n72. Peter Stearns, Fat History: Bodies and Beauty in the Modern West (New York: New York University Press, 1997), pp. 71\u201388.\n\n73. Sunshine Book Company v. Summerfield (1955), p. 570.\n\n74. Joan Jacobs Brumberg, The Body Project: An Intimate History of American Girls (New York: Vintage, 1997), pp. 108\u20139; Marilyn Yalom, A History of the Breast (New York: Alfred A. Knopf, 1997), pp. 191\u2013202.\n\n75. John Rogge, 'Official Transcript of Proceedings before the Post Office Department', NARA\u2013CP, RG 21, US District Court for DC, Civil Action #74\u201355, Sunshine Book Company v. Summerfield, Box 1578, tabbed, 16W3\/17\/32\/02, pp. 58\u201359.\n\n76. O'Brien, 'Official Transcript of Proceedings before the Post Office Department', pp. 46\u20137.\n\n77. Sunshine Book Company v. Summerfield, 'Proceedings', NARA\u2013CP, RG 21, US District Court for DC, Civil Action #74\u201355, Sunshine Book Company v. Summerfield, Box 1578, tabbed, 16W3\/17\/32\/02, pp. 29\u201330.\n\n78. Sunshine Book Company v. Summerfield (1955), p. 573.\n\n79. Sunshine Book Company v. Summerfield (1955), p. 571.\n\n80. Maria Wyke, 'Herculean Muscle! The Classicizing Rhetoric of Body-Building', Arion 4 (1997), pp. 59\u201360.\n\n81. Thomas Waugh, Hard To Imagine: Gay Male Eroticism in Photography and Film from their Beginnings to Stonewall (New York: Columbia University Press, 1996), p. 9.\n\n82. Sunshine Book Company v. Summerfield (1955), p. 571.\n\n83. Sunshine Book Company v. Summerfield (1955), p. 570.\n\n84. Sunshine Book Company v. Summerfield (1955), p. 570.\n\n85. Sunshine Book Company v. Summerfield (1955), p. 571.\n\n86. Benjamin Spock, The Common Sense Book of Baby and Child Care (New York: Duell, Sloan and Pearce, 1957), p. 379.\n\n87. Henry Jenkins, 'The Sensuous Child: Benjamin Spock and the Sexual Revolution', in Henry Jenkins, The Children's Culture Reader (New York: New York University Press, 1998), pp. 209\u201330.\n\n88. Sunshine Book Company v. Summerfield (1955), p. 573.\n\n89. 'Supreme Court of the United States, No 582 and 61 Mr. Chief Justice Warren, concurring in the Result', Earl Warren Papers, Library of Congress, Washington DC, Box 437, Folder 1, p. 2.\n\n90. 'Dealer in Obscenity Gets a 5-Year Term', New York Times, 8 February 1956, p. 26.\n\n91. Walker, In Defense of American Liberties, p. 234.\n\n92. Roth v. United States, 354 US 476 (1957).\n\n93. 'Supreme Court of the United States, Nos 582 and 61, Mr. William O. Douglas, dissenting in the Result', William O Douglas Papers, Library of Congress, Washington DC, Box 1183, Folder 4, p. 6.\n\n94. Sunshine Book Company v. Summerfield, 101 US App DC 358 (1957).\n\n95. On the same basis, the Supreme Court also ruled in favour of nudist magazines in Mounce v. United States, 355 US 180 (1957), a companion case that involved the seizure of imported magazines.\n\n96. 'Mr Chief Justice Warren, concurring in the Result', p. 2.\n\n97. House Committee on Post Office and Civil Service, Obscene Matter Sent Through the Mail: Hearings Before the Subcommittee on Postal Operations, 87th Congress, 1st Sess., 1961.\n\n98. House Committee on Post Office and Civil Service, p. 2.\n\n99. House Committee on Post Office and Civil Service, p. 2.\n\n100. House Committee on Post Office and Civil Service, p. 2.\n\n101. House Committee on Post Office and Civil Service, p. 106.\n\n102. House Committee on Post Office and Civil Service, pp. 311\u201313.\nChapter 10\n\nCold War Conflicts and Cheap Cabaret: Sexual Politics at the 1975 United Nations International Women's Year Conference\n\nJocelyn Olcott\n\nDomitila Barrios de Chungara, a Bolivian tin miner's wife and leader of the Housewives' Committee of the Siglo XX miners' union, recalled her enthusiastic anticipation of the non-governmental organisation (NGO) tribune of the United Nations' 1975 International Women's Year (IWY) conference in Mexico City. Having missed the tribune's first few days, she and an Ecuadorian compa\u00f1era crowded into a packed conference hall, anxious to make up for lost time. She hoped to 'hear things that would make me get ahead in life, in the struggle, in my work'.1 She harboured a sense of her responsibility to represent the voz popular of Bolivian workers and expected to confer with 'people like me... people with similar problems, you know, poor people'.2 Instead, however, she experienced a profound sense of alienation at the IWY tribune, an alienation that she linked most explicitly to participants' discussions of sexuality \u2013 in particular of lesbian sexuality, prostitutes' rights and reproductive control. Such responses generate discomfort among feminists and progressive historians, who often ascribe an organic radical egalitarianism to subaltern actors such as Barrios de Chungara and have minimised or elided this aspect of her testimony.3\n\nIn her co-authored memoir, Barrios de Chungara recalls that just as she and her new Ecuadorian friend squeezed into the crowded room, 'at that moment a gringa went over to the microphone with her blond hair and with some things around her neck and with her hands in her pockets, and she said to the assembly: \"I've asked for the microphone so that I can tell you about my experience. Men should give us prostitutes a thousand and one medals because we, the prostitutes, have the courage to go to bed with many men\"'.4 They fled the room amid applause and shouts. 'Well', she recalled:\n\nmy friend and I left because there were hundreds of prostitutes in there talking about their problems. And we went into another room. There were the lesbians. And there, also, their discussion was about how 'they feel happy and proud to love another woman... that they should fight for their rights'. Like that. Those weren't my interests. And for me it was incomprehensible that so much money should be spent to discuss those things in the Tribunal.\n\nHaving come prepared to represent the political and economic challenges she witnessed in Bolivia, these concerns seemed superfluous. 'I felt a bit lost', she explained to her interviewer.\n\nWe need to read Barrios de Chungara's account, however, not as a transparent recounting of events but rather as a quintessential example of testimonio \u2013 the witness-bearing representations that gained traction amid Latin American counterinsurgency campaigns of the 1970s and 1980s and that by the 1990s precipitated anxious debates about subaltern truth-telling.5 Comparison of her description with the documentary record of these events at the tribune, elaborated below, reveals that she has jumbled events here and carefully marked sexual rights as a western issue, stressing the prostitute's blond hair.6 Barrios de Chungara's testimonio offers a representation of her own political performance at the IWY tribune, but she was hardly alone in misreading the politics of sexuality. As the conference neared its conclusion, for example, the Ecuadorian activist Marisa de los Andes \u2013 quite possibly the same Ecuadorian who accompanied Barrios de Chungara for her disorienting arrival at the tribune \u2013 confronted the US liberal feminist Betty Friedan, decrying that Friedan 'only cared about prostitution and lesbianism', failing to address the issues of imperialism, exploitation, transnational corporations and US policies towards Chile and Cuba.7 This would be the same Betty Friedan who notoriously dubbed lesbians a 'lavender menace' and completely disavowed prostitutes' rights, who at the IWY tribune had been far more vocal in her criticism of transnational corporations than in her support for lesbian liberation.8 Surely something had been lost in translation.\n\nThis antagonism persists in contemporary political activism. 'In development circles', the anthropologist Ara Wilson notes, 'the issue of sexuality often gets pitted against economic issues, in a pie model of struggle that presents gains for sexual rights as losses for more substantial economic concerns. After Beijing, for example, US NGO workers told me that the advance of lesbian and sexual rights at the UN conference came at the expense of economic justice'.9 Although Wilson concentrates her attentions on the post-Cold War period, her call for a historicist approach certainly pertains to the 1975 conference. Indeed, the far more extensive scholarship about post-Cold War international conferences and NGOs offers ready comparisons to demonstrate the historical contingency of these debates as well as the continuities across the chronological rubicon of the falling Berlin Wall. While terms such as globalisation and imperialism conveyed quite different meanings in 1975, the objections at the IWY tribune presaged an enduring divide. 'What seems to be informing their critiques', Wilson observes, 'is the sense that sexual rights are part of the very problem they are battling: that is, globalization, Westernization, or imperialism... What is clear is that sexual rights are associated with the forces of global capitalism'.10\n\nThat the Marxist left offered some of the most virulent attacks has become a point of chagrin as rights around sexual identity have become a staple of progressive politics. At the IWY, many Marxists \u2013 including Barrios de Chungara \u2013 conflated lesbians and prostitutes and allowed issues of sexuality, sexual agency and reproductive freedom to signify the self-indulgence and dissolution of western feminism, depicting a zero-sum game in which gains for sexual rights detracted from other agendas.11 The intransigence of this zero-sum model creates an urgency to understand why it emerged and how it is reproduced.\n\nThe performance theorist Diana Taylor would describe Barrios de Chungara's testimonio as the archival version of the more ephemeral and embodied events that she dubs 'repertoire', which transmits knowledge through the performance of meanings and identities.12 The significance of performances such as those at the IWY tribune hinges upon their attendant scenarios, the 'meaning-making paradigms that structure social environments, behaviours and potential outcomes'.13 Building on the more familiar historical concept of context, the scenario \u2013 the costumes and sets and locales that surround the acting \u2013 informs expectations by gesturing to well-known plots and story lines. 'The scenario makes visible, yet again, what is already there: the ghosts, the images, the stereotypes', Taylor explains. 'The scenario structures our understanding. It also haunts our present, a form of hauntology that resuscitates and reactivates old dramas. We've seen it all before. The framework allows for occlusions; by positioning our perspective, it promotes certain world views while helping to disappear others'.14 While performances naturalise identities and actions, their meanings changed or became unintelligible within a scenario such as the NGO tribune that had its own scripts and assumptions and that included performances imported from still other scenarios. Deracinated from the scenarios that generated them, inserted into a newly fabricated scenario and communicating with multiple audiences at once, the performances at the IWY tribune produced a confusion of meanings. As Barrios de Chungara noted, 'We spoke very different languages, no?'15 William Sewell reminds us, however, that it is precisely amid this Geertzian 'confusion of tongues' that 'social encounters contest cultural meanings or render them uncertain'.16\n\nThe IWY events offered an unusual opportunity for performances \u2013 both ontological and representational \u2013 not only of political identities but also of womanhood itself.17 This chapter, which draws on research from a book on the IWY conference, explores how participants' postures regarding sexuality signified politically as struggles over sexual rights and recognition became proxy wars in larger battles over incipient neoliberalism and its attendant emphasis on individualism and commodification. Critics of sexual rights frequently linked \u2013 as Barrios de Chungara did \u2013 issues of lesbianism, prostitution and birth control. Perhaps because of its novelty in public discussions, lesbianism drew the most notice and will receive the most attention here. Examining three prominent performances at the NGO tribune \u2013 those of Friedan, Barrios de Chungara and the Mexican lesbian activist Nancy C\u00e1rdenas \u2013 reveals the stakes of these performances and how their historically contingent readings and misreadings fuelled tensions over sexuality and sexual rights.\n\nThe IWY scenario and anti-imperialist hauntology\n\nIn mid-June 1975, thousands of people converged on Mexico City as the IWY conference opened with considerable fanfare, drawing some 1,200 delegates to the intergovernmental conference and an estimated 6,000 more to the NGO tribune. While observers may disagree about whether the IWY conference ended up as the 'greatest consciousness-raising event in history' \u2013 as its organisers billed it \u2013 most concur that it marked a watershed moment in transnational feminism.18 Although hardly the first instance of international women's organising, it witnessed a significant expansion, achieving a more global reach in terms both of regions represented and of social sectors involved.19 As the first major international women's organising effort since the near-universal granting of women's political rights, the IWY events not only drew a motley bunch but also included many women who had received political educations either formally or through their labour unions and community organisations. They arrived in Mexico City ready to do battle over a broad range of issues that informed women's lives, expanding the agenda considerably from customary emphases on pacifism, child welfare and labour reform. The organisers had structured the conference around the themes of equality, development and peace \u2013 with the expectation that these themes loosely represented the concerns of the industrialised nations, the growing Third Worldist movement and the Soviet Bloc \u2013 but peace seemed to drop out of most planning discussions, leaving the focus on balancing equality and development.\n\nOnce underway, the events quickly became stages for political performances directed not only at an international audience but also at audiences in participants' home countries and communities, resulting in a cacophony of mingling performances rooted in different contexts and intended not only for fellow tribune participants but, perhaps more importantly, for an array of allies and rivals not present. Performances ranged from the sartorial \u2013 with some attendees wearing national or ethnic attire and others donning European-style suits \u2013 to the ideological \u2013 pitting Soviet Bloc countries against NATO supporters, anti-colonial revolutionaries against pro-investment liberals and Zionists against Palestinian nationalists. Bodies served as sites to express politics, nationalism, ideology and ethnic identity, and observers offered constant commentary on women as embodied political subjects, including not only remarks upon women's dress, adornment and hair styles but also discussions about the comparative beauty of first ladies Leah Rabin and Jihan al Sadat or US feminists Gloria Steinem and Kate Millett.\n\nThe intergovernmental conference offered an unprecedented opportunity to put women at the centre of international policymaking, while the less decorous and more free-wheeling NGO forum became what the New York Times described as 'the scene of much shouting, scheming, plotting and general hell-raising'.20 The events featured an international all-star cast of prominent intellectuals, activists and political leaders, and every major metropolitan newspaper ran regular articles about the conference and its attendant parties, press conferences and diplomatic manoeuvres. This extensive media coverage generated both excitement and apprehension among participants, who expressed particular concern about how the 'mass communications media' represented the IWY events and women in general. Mexican organisers touted the conference press office to increase visibility and facilitate reporting, and tribune organisers put particular energy into producing a daily newspaper, Xilonen, to inform participants and shape the historical record.21 As participants debated topics ranging from abortion to Zionism, media coverage extended the reach of these performances, heightening anxieties around the still-taboo subject of women's sexuality.\n\nPerhaps unsurprisingly, the more staid intergovernmental conference barely touched on issues of sexuality, deliberating only the issue of prostitution and its coercion. When the Thai delegate proposed legalising voluntary prostitution, the Cuban delegation immediately responded with a call for the complete eradication of the sex trade.22 French Minister for Women Fran\u00e7oise Giroud glibly told reporters that prostitution was 'not a problem of women at all, but of men' and that she would 'gladly help any women who didn't like the life, but some seemed to enjoy it' and it might be 'looked on as an advantage that women had this power to make money'. Marie-Pierre Herzog, the director of UNESCO's Human Rights Coordination Unit, called for investigations into cases where women and girls were imprisoned and tortured in brothels. 'We are not speaking here of so-called free prostitution', she assured the New York Times.23\n\nQuestions of sexuality arose more frequently at the NGO tribune. As only the third UN conference with a parallel NGO tribune, the IWY conference witnessed a turning point in NGOs' role in international activism, organising and governance, creating opportunities for historically marginalised groups, including those agitating for sexual rights, to gain access to financial and logistical assistance but also privatising \u2013 and to some extent commodifying \u2013 democratic processes.24 The more established NGOs such as International Planned Parenthood Federation (IPPF) and the Young Women's Christian Association (YWCA) enjoyed official consultative status with the UN and disdained the upstart organisations that overwhelmed the tribune, but these smaller, more nimble organisations had strategic advantages and greater popular support. 'The conference served to open the UN to many more NGOs', recalls one UN activist. 'While earlier it was the bigger, more established NGOs that attended the international conferences, at Mexico City, many smaller, South-based non-traditional NGOs found a meaningful space for themselves that went beyond tokenism'.25 The consultative NGOs, with a highly developed sense of UN protocol, had defined the tribune's formal agenda, centring it on themes such as education and training opportunities, nutrition and health care, and promoting artisanal production. It was the smaller non-consultative NGOs \u2013 with a more radical, participatory sense of democratic process and an impulse to shake up 'the establishment' \u2013 that pushed issues of sexuality through informal gatherings and participant-initiated sessions.\n\nBarrios de Chungara's lament apparently refers to two events that followed a standing-room-only session on 'attitude formation and socialization processes' that occurred the morning of her arrival, where 'participants crowded to the microphones' to express their views about everything from impotence to lesbianism. The Bangladeshi panellist Rounaq Jahan lamented that women remained too 'submissive in bed', while Laurie Bebbington of the Australian Student Union insisted, 'amid whistles and jeering', that liberation was not only economic but also sexual and inverted the notion of lesbianism as deviance, arguing instead that obligatory heterosexuality perverted the process of socialisation and that homophobia resulted from cultural imperialism.26\n\nThe following day, Mexican theatre director Nancy C\u00e1rdenas acceded to the exhortations of some 'visiting lesbians' to lead an open, participant-initiated forum on lesbianism, which filled the auditorium and initially barred reporters and photographers. C\u00e1rdenas recalled her dismay at hearing about her comrades' behaviour during the previous day's sexuality forum. 'They told me that the Communists, my own compa\u00f1eras from earlier in the party, abandoned the conference hall when an Australian girl said \"I'm a lesbian feminist\"', she recalled later in an interview. 'They said, \"Throw out the sickos, we're out of here\" and abandoned the hall. That seemed to me to give an incomplete image of Mexico, because I was also a leftist militant, was a lesbian, and I had another position and raised my finger'.27 The forum featured Mexico's first lesbian manifesto, naming sexual recognition as a critical form of social liberation, tantamount to struggles against imperialism, apartheid and racism.28\n\nBebbington and others participated in the forum, but C\u00e1rdenas drew reporters' attention as the most recognisable participant. According to security reports, neighbourhood women picketed her presentation with signs reading 'Out with that Antisocial and Disoriented C\u00e1rdenas', 'Out with the Lesbians and Homosexuals' and, most alarmingly, 'Death to Nancy C\u00e1rdenas'.29 (Reading even these performances poses difficulties; a US-based feminist newsletter reported that C\u00e1rdenas introduced herself to the picketer calling for her demise, and the protester explained that the chief of the Cuauht\u00e9moc delegation police department had paid her to demonstrate.)30 C\u00e1rdenas remembered reporters descending upon her as she left the room. 'Suddenly, I had forty or fifty reporters around me', she recalled, 'like Sophia Loren in Via Appia! I couldn't think. The assault was aggressive: are you a lesbian? Who else is? Why did you agree to come? What does this mean? It was one question after another. I couldn't even answer. The only thing I managed to tell them was: so long as the laws of my country do not offer guarantees for homosexuals, neither I nor anyone can answer your questions'.31\n\nAs C\u00e1rdenas fended off reporters and protesters, Margo St James and Flo Kennedy, the high-profile leaders of the San Francisco-based prostitutes' rights group COYOTE (Call Off Your Old Tired Ethics) similarly provoked both fascination and denunciations. In an interview, St James explained, 'sex is a biological necessity, as much in men as in women, [but] a hypocritical society has hidden this. We perform an essential service, and we ask that we be recognized, since it is as natural as eating, sleeping and defecating'.32 Indicating that they did not want the government to serve as their pimp (pachuco), they demanded social security, retirement benefits and taxes for themselves and their clients. 'We are supported by the feminist solidarity of all the groups that struggle for women's emancipation', insisted Kennedy. 'We are all one woman, and we do not cease being women because we are prostitutes'. When security guards instructed St James and Kennedy to leave the conference hall and cease distributing their pamphlet, the COYOTE leaders \u2013 quite possibly with an ironic wink at public expectations \u2013 responded that they would return the following day, this time with the lesbians who had spoken up earlier in the day.33\n\nJust as the C\u00e1rdenas and COYOTE episodes challenge the assumption that sexual rights stood apart from solidarity movements, the climate of the mid-1970s also belies the presumed opposition between sexual freedom and human rights. Much like political dissidents, gay men (and to a lesser extent lesbians) faced violence and police repression in Mexico City and Rio de Janeiro as well as New York City and San Francisco. Advocates of sexual rights frequently also participated in struggles against racism, imperialism and human-rights abuses.34 A year earlier, COYOTE had boycotted a Chilean ship docking in San Francisco, indicating that it had been used by the Pinochet regime the year before as a 'floating prison'.35 NOW roundly condemned the 'sexual torture' of Chilean women political prisoners, and the US feminist press included particularly lurid accounts of women political prisoners being raped and tortured, occasionally even sending activists to report from Santiago.36 Meanwhile, a Mexican magazine article about the widely syndicated Argentine cartoon Mafalda described how the title character openly mocked women who expressed horror at the growth of mariconer\u00eda (faggotry).37\n\nFurthermore, notwithstanding de los Andes's and Barrio de Chungara's objections, questions of women's sexuality received relatively little attention at the IWY events. As one Mexican activist recalled, after the lesbianism forum, 'the Tribune and the conference did not talk further about lesbianism or take any actions to support the issue which most still viewed as outrageous'.38 The tribune programme included only one formal session and three informal participant-initiated sessions on sexuality.39 The exhibition hall, which displayed materials from dozens of participating organisations, reportedly included no materials depicting women's sexuality. What is surprising in de los Andes's and Barrios de Chungara's descriptions, then, is the centrality they give to issues of sexuality in a setting where these issues barely arose and were quickly swept aside.\n\nBefore the opening session, journalists anticipated conflicts between 'Third World women', who tended to focus on structural problems of economic inequality, and 'western feminists', who concentrated their energies on sex-specific issues such as reproductive freedom, wage equity and women's educational and professional opportunities. The New York Times noted, 'Observers agree that the major goal set out by the organizers \u2013 improving the status of women \u2013 is not going to be an easy one in light of the political arguments that are expected to erupt between delegates of the industrialized countries and the third world'.40 More pointedly, Pacifica Radio titled its interview with Friedan, 'Betty Friedan versus the Third World'.41 In Mexico City, Friedan emerged in media representations as a metonym for Cold War liberalism, personifying expectations of the 'reactivated drama' of a Third World\u2013First World showdown.\n\nBetty Friedan and the cultivation of unity\n\nWell before the IWY events were under way, Friedan found herself fighting a battle on many fronts. The threat of anti-feminist backlash loomed, and even NOW \u2013 to say nothing of the more radical feminist organisations \u2013 had taken the feminist movement in directions she disparaged, particularly around questions of sexuality.42 Campaigns for lesbian recognition and prostitutes' rights as well as regular seminars on sexuality and sexual fulfilment had reinvigorated the flagging feminist movement. The New York City NOW chapter, with which Friedan maintained ties, reported throughout 1974 and 1975 that events on sexuality drew larger attendance \u2013 generating more revenue and new members \u2013 than any other NOW activity.43 NYC\u2013NOW's ad hoc committee on sexuality aimed to 'encourage every woman to define, explore and enjoy her own sexuality' to 'end discrimination based on sexual preference'.44 To activists animated by labour, civil-rights and decolonisation movements \u2013 who imagined a collective or even global scale of transformation and a constant struggle against the liberal impulse to individualise both problems and solutions \u2013 such campaigns seemed like only so much vulva-gazing. To Friedan, this development extended the intrusion of 'sex\/class warfare' \u2013 demands for recognition by lesbians, sex workers and women of colour \u2013 that distracted feminists with issues better left to civil-rights and civil-liberties organisations.45\n\nHaving spearheaded a campaign to gain UN consultative status for NOW, Friedan saw the IWY tribune as an opportunity for NOW to play an expanded role and for Friedan to regain her footing on the more comfortable terrain of demands for equality in education and employment.46 Friedan clearly perceived herself as a conference puppeteer. Describing herself to New York Times Magazine editor Gerald Walker as the 'symbol' of the women's movement, she predicted that activists and officials alike would look to her for leadership. 'I am obviously going to be in the thick of it', she explained, 'out front in the non-governmental Tribune and privy to the behind-the-scene maneuvering of the official conference, where the new women-politics cuts across the usual lines'.47 Friedan, then, gauged her performance to establish her role as a broker and a model for feminists around the world steering women's activism back towards what she perceived as core women's issues.\n\nFriedan's dominant role, however, raised the ire of many participants who saw the NGOs' growing role not as democratisation but rather as the consolidation of a power bloc against incursions by the hoi polloi. 'I think we are going to see the fruition of their efforts to pre-empt, co-opt, obfuscate and distort the feminist vision at that Mexico City UN Conference in July', Los Angeles-based feminist Carol Downer wrote to Robin Morgan.\n\nI expect to see Friedan, the World YWCA, the Population Crisis Committee (a similar organization to [Gloria] Steinem's) running the show. Planned Parenthood has footed most of the bill, of course. We will find ourselves in the interesting position of being on the outside of the outside (the Tribune is the parallel non-governmental conference). Of the several thousand American women who are attending, I doubt that most of them will perceive the contradictions... We will be staying with a small, beleaguered band of feminists in Mexico City who are disgusted with the whole thing.48\n\nEvoking Friedan as a caricature \u2013 and lumping her in with her rivals \u2013 allowed Downer to insert herself into the drama alongside the 'beleaguered band of feminists' who apparently shared a particularly developed political consciousness.\n\nLatin American participants and reporters cultivated a somewhat different caricature once the tribune was under way, accusing her of fomenting a counterproductive battle between the sexes. Diplomats and the professionalised activists of the consultative NGOs had referenced concerns that Friedan was seen as a 'radical'.49 Notably, the tribune newspaper Xilonen labelled NOW as a radical organisation in the Spanish \u2013 but not the English \u2013 version of an article describing the tribune.50 When the Mexican Attorney General, Pedro Ojeda Paullada, was elected to preside over the intergovernmental conference, Friedan dismissed the choice as 'outrageous' and chalked it up to holding the conference in the 'land of machismo'.51 The Mexican press \u2013 referring to Friedan with a dizzying array of Semitic names and dubbing her Betty 'La Terrible' \u2013 responded with a spate of interviews with Latin American women, who insisted that the dispositive factor was not sex but rather effective advocacy for women's rights. Mexico City politician Marta Andrade del Rosal dismissed Friedan's 'rabid feminism', and the federal deputy Aurora Navia Mill\u00e1n pointed out that Ojeda Paullada (unlike his US counterpart) had ushered through a constitutional amendment putting Mexican women 'at the vanguard in terms of jurisprudence'.52 The Venezuelan delegate Martha Regalado averred, 'I think that Friedman [sic] errs in saying that it is an insult that a man presides over the meeting, since that is how they discriminate against our problems'.53\n\nHalfway through the conference, Friedan endeavoured to represent the tribune, assuming the role of global feminist leader and leveraging her notoriety to meet with UN leaders. The Argentine Edith Reinaldo protested, 'Mrs. Friedan does not represent the Tribune. [She] arrived here with an aura of fame from her book, The Feminine Mystique, which she has exploited'. Barrios de Chungara objected that 'only the bourgeoisie' enjoyed the right of representation at the UN and that Friedan made 'mostly feminist points, and we [the Latin American caucus] didn't agree with them because they didn't touch on some problems that are basic for Latin American women'.54\n\nFriedan and other NOW leaders had steeled themselves for such criticism, perceiving it within the scenario of anti-patriarchal struggle. 'Already, it is clear', she wrote to Walker:\n\nthat the Communist, Arabs and the Vatican are joining in a line that 'women's liberation', 'equality' and the like are Western imperialist inventions, irrelevant to the interests of the majority of women of the world, especially the Third World women who 'need to have 12 children', as the line goes, 'are happily integrated into feudal economies, extended families, and tribal cultures whose ingrained values of male supremacy must be respected, etc'. The proponents of this line want to turn the whole International Women's Year into a promotion of a 'new economic order', or 'down with western imperialism'. They do not want any discussion of women's concrete situation at all, especially in their own countries in fact, from tales around the UN, the last months, one sometimes gets the idea that the main 'enemy' from which they want to protect their women is the likes of me: the feminists.\n\nKaren DeCrow, the president of NOW's National Board, had similarly warned in preparation for IWY that there would be 'not too many feminists' there. 'It is essential that the feminists of the world get together to discuss (not foreign affairs) but ways in which we can cooperate to assure legal rights for women, the right to choose abortion, child care, equal opportunities in education and training, getting feminists into politics and government, and so forth'.55 To DeCrow and Friedan, any agenda outside what they considered proper 'women's issues' threatened to 'politicise' the tribune and distract it from its true objectives. Elaine Livingstone reassured Friedan and other NOW leaders that the UN's draft World Plan of Action 'contains many of our objectives: equality of economic and educational opportunities, equal sharing between men and women of household and child rearing duties, day care centres, etc'.56\n\nFriedan's anxiety could only have mounted as anti-imperialist politics at the IWY threatened to eclipse these issues. Waves of decolonisation had made the normative liberal subject a minority at the UN, calling into question the most fundamental practices and protocols that formerly distinguished politics from citizenship. Mexican President Luis Echeverr\u00eda openly aspired to succeed Kurt Waldheim as UN secretary-general and touted his leadership advocating the New International Economic Order (NIEO), calling for national sovereignty over natural resources.57 At a Caracas planning meeting, Mexican diplomats campaigned to make the IWY conference into a forum for NIEO reforms, provoking objections from the US State Department.58 As the IWY events progressed and debates over the NIEO and Zionism indeed overshadowed issues of women's literacy and public health, Friedan grew increasingly frustrated. She told reporters that only the tribune addressed women's concerns and that the intergovernmental conference 'made political football out of women's problems'.59 Dissatisfied with what she saw as the chaotic tumble of the NGO tribune and concerned that the CIA fomented division, Friedan launched her own lunchtime caucus, 'to get something out of this conference we can present each other and our governments with. Let's forget the dirty linen of each government delegation, and get on with what concerns us'.60 Who counted among 'us', however, remained unclear. 'Despite every effort to keep the women divided', she later recounted, 'including violent disruptions played up by the media \u2013 we women united in Mexico City \u2013 women from the Third World, Latin-Americans, Africans in turbans, Indians in saris, antifascists from Greece, feminists from Japan, Australia, Mexico and women who didn't want to be called feminists from Nigeria and Ecuador, as well as Americans, black, brown and white \u2013 to insist that women's equality couldn't wait on a \"New Economic Order\"'.61\n\nIf for Friedan the tribune scenario reactivated dramas of CIA conspiracy and sexual liberation that she had hoped to leave behind in New York, Friedan herself \u2013 or the caricature of Friedan \u2013 also played an important role in the hauntologies of other participants. Whether for feminists like Downer or labour militants like Barrios de Chungara, the conjured image of Friedan allowed them to position themselves relationally as the beleaguered feminist disdaining the establishment or as the committed labour militant dismissing feminism as a bourgeois distraction from class struggle.\n\nNancy C\u00e1rdenas and cheap cabaret\n\nIf Friedan fought against sexual liberationists and anti-imperialists on her left to insist on feminist unity, Nancy C\u00e1rdenas's political performance required her to balance carefully between exploiting the support and solidarity of 'visiting lesbians' and insisting that Mexican lesbians were not simply dupes of cultural imperialism.62 US activist Charlotte Bunch, who did not attend the tribune for fear of 'dominating it as gringas', recalled, 'I followed the reports from Mexico feeling proud that the word lesbian had made it onto the floor and sad that it was dismissed by many as outrageous and western'.63 The Mexican feminist movement, as Marta Lamas describes it, remained a small, middle-class movement of women with high levels of education and politics that trended to the left.64 Most distanced themselves from the IWY events, viewing them as government-orchestrated publicity stunts without much to offer a movement rooted in the dissident student movements of 1968 and deeply suspicious of all things official. Despite scepticism, the IWY events arguably offered a useful moment of feminist consolidation and created an opening for frank discussions of women's sexuality. Albeit cynically, Echeverr\u00eda had used the occasion to pass an equal-rights amendment to the constitution and provided substantially more resources than, for example, the United States, to support IWY programs and commissions; more than 2,000 Mexican women registered to attend the tribune, and others showed up to participate; and 1976 witnessed the unification of two leading feminist organisations and the launching of two major feminist magazines, Revuelta and Fem.\n\nNotably, Mexican lesbian feminists do point to the IWY as a pivotal moment, and many trace a new candour about women's sexuality precisely to the session that most alienated Barrios de Chungara \u2013 the session in which C\u00e1rdenas and others presented the lesbian manifesto.65 Although activist Claudia Hinojosa laments Mexican lesbians' reluctance to enter the fray at the IWY tribune, she credits the episode with shoving Mexican lesbian organisations out of the closet and into the street. 'It's true that nobody anticipated that this conference would be converted into the forum for the first public discussion of lesbianism in Mexico', she recalls. 'I remember that I observed all those incidents, surprised and confused, from the darkest corners of the closet'.66 The first year of Fem included a special issue on women's sexuality, and in 1977 and 1978 respectively, the open lesbian organisations Lesbos and OIKABETH came onto the scene. In the summer of 1975, however, C\u00e1rdenas could not have foreseen the coming changes. She struggled to maintain alliances not only amid hostility from feminist organisations but also with gay men's organisations.67 Only a week before the IWY events, she had vocally protested against the arrest of roughly 300 gay men during a police raid of a local bar.\n\nPerhaps because of her theatrical training, C\u00e1rdenas clearly understood the performative aspects of these encounters, stressing the importance of reiterating and witnessing performed sexuality, writing sexuality into the mainstream political scripts, and reaching a broader audience by forming coalitions linking sexual rights with other demands. During the open forum on lesbianism, several organisers attempted to bar the press from the meeting, arguing that it was not a media event and that they should make room for the women left standing outside, unable to squeeze into the packed meeting hall. C\u00e1rdenas disagreed. 'Compa\u00f1eras', she argued, 'it is necessary for the press to be here, since in a country as machista as Mexico, we must openly discuss these themes and make them known'.68 C\u00e1rdenas understood the importance not only of performing a particular brand of deliberative activist feminism at the IWY tribune but also of having an audience for that performance; it required recognition in order to generate significant social change.\n\nDespite C\u00e1rdenas's efforts, the Mexican press generally either ignored or disdained sexual-rights campaigns in general and lesbian activism in particular. As El Universal columnist Roberto Blanco Moheno quipped, 'They should have made a rule for the meeting with the aim of not allowing to slip in so many marimachos [dykes] who indeed look like men, which is horribly disagreeable. All my homage, my respect, my love for the woman \u2013 the woman who knows the dignity of woman. To the marimachos...'.69 The ruling party newspaper El Nacional downplayed the episodes, covering the lesbianism forum under an obfuscating headline about rural poverty, and the government's monthly IWY magazine published no articles on sexuality and included no coverage of the tribune sessions on sexuality.70 El Universal, meanwhile, demonstrated a certain ethnographic fascination: in addition to interviews and photographs of the flashy COYOTE leaders, its coverage included articles explaining the 'causes' of lesbianism, anecdotes and interviews about lesbians' life experiences and photographs of unnamed audience members and speakers at the lesbianism forum, as if to exhibit the curiosity of actual lesbians. The El Universal article in the forum also featured a photograph of Marisa de los Andes, along with a caption lamenting that the tribune 'didn't deal with the problems that really affected the feminine sex'.71\n\nWhat must have most dismayed C\u00e1rdenas, however, was the particularly vitriolic response from the Mexico City daily Exc\u00e9lsior, which went beyond disdain, resorting to pathologising and vilifying prostitutes and lesbians together. The newspaper had valiantly defended the 1968 student protesters in the face of official repression, and its editor, Julio Scherer Garc\u00eda, was widely considered among Mexico's most ethical newsmen and was a close friend of the prominent gay-liberation supporter, Carlos Monsiv\u00e1is. The day after the lesbianism forum, Exc\u00e9lsior columnist Guillermo Jordan, chiding that the only liberation on the horizon was liberation from IWY itself, openly mocked Bebbington for defending lesbianism and for pleading that 'society cease to consider people with this deformation as \"forbidden and invisible\". At this moment, nobody could ignore them, since many wore shirts with the visible slogans \"Radicalesbians\", \"Equality for Homosexuals\" and the like'.72 Another columnist grumbled, 'The lamentable thing about the Conference is that many groups of women abandoned their issues to allow themselves to be manipulated by political interests of the left or right... Certain North Americans have broken the record, such as the \"radicalesbians\" as well as those who promote the oldest profession in the world'.73\n\nCosmopolitan lesbianism emerged as the opposite number to nationalist maternalism, a public celebration of Mexican motherhood as a national treasure not to be adulterated by foreign materials. Nationalist discourses served the objectives not only of Echeverr\u00eda's personal ambitions but also of the broader Third Worldist NIEO agenda. Within this context, any insistence on the emancipatory potential of western-identified cosmopolitanism posed a threat to a global political project of anti-imperialism that had only recently gained control of the General Assembly. A particularly hostile columnist, Pedro Gringoire, argued, 'some extremists have assumed the exorbitant pretension of converting woman into a marimacho, totally repudiating maternity and home'.74 Bemoaning feminists' efforts to replace men with artificial insemination and public childcare, Gringoire called for a return to celebrations of motherhood. 'We cannot help but view with sorrow', he continued,\n\nhow certain feministoid groups \u2013 we call them that because the authentic feminism has very positive values \u2013 has put, even more than the Conference, the Tribune at risk of being converted, morally speaking, into a cheap cabaret or an indecorous carnival. Groups that, in the name of the 'emancipation of women', have come to give exhibitions of cynicism and shamelessness, as if emancipation had only one aim: to give free rein to all the passions, including the most aberrant and depraved.\n\nAppalled that organisers had dedicated an entire workshop to lesbianism, Gringoire went on to challenge the 'repugnant form' in which lesbians demanded rights and suggested that they seek medical or psychiatric treatment for their 'pathetic and pathological deviation'. In a perverse attempt at humour, he suggested that they had wandered into the wrong room at the Centro M\u00e9dico, where the tribune took place.\n\nThese discussions raised the thorny question of agency \u2013 of being versus becoming \u2013 within women's sexual subjectivity. Gringoire attributed lesbianism to 'glandular deficiency or a hormonal imbalance' or, more often, 'an important gap in their upbringing [educaci\u00f3n]', while the Brazilian sociologist Jo\u00e3o Guilherme Corr\u00eaa de Souza repudiated lesbianism as a failure of upbringing rather than a 'biological aberration'.75 Participants in the lesbianism forum, however, encouraged women to choose lesbianism as an empowering option. Pointing to the ways that heterosexuality reinforced a patriarchal status quo, International Lesbian Caucus spokespeople Fowler and Lease asserted, 'For these reasons, lesbianism is more than a bedroom issue. It is a highly political position that many women choose to take'.76 Charlotte Bunch, writing retrospectively about an experience in July 1971, said she 'had become a lesbian six months earlier in the context of the women's movement in Washington, DC'.77\n\nThe rhetorical intensity of observers like Gringoire, then, reflects not an unfamiliarity with women's sexual rights but rather mounting anxiety over their increasing prominence within Mexican women's activism, sparking fears precisely that the 'context of the women's movement' would induce Mexican women to 'become lesbians'. The prevailing narrative of the lesbianism forum reinforces this expectation. Norma Mogrovejo asserts that the 'presence of foreign lesbians during the [IWY conference] brought lesbian issues to the fore'.78 Activist Yan Mar\u00eda Yaoy\u00f3lotl Castro attributes developments later in the 1970s to the 'pressure' applied by European and North American feminists at the IWY events.79 Hinojosa explains that C\u00e1rdenas 'recalled being nearly \"pulled from the closet\" by circumstances [at the IWY tribune] \"which simply surpassed me\". So it was for many lesbians at the time of the Mexico conference'.80\n\nHinojosa's statement leans on a bit of hyperbole, however. By 1975, C\u00e1rdenas \u2013 rather than being 'pulled from the closet' \u2013 was arguably Mexico's most prominent lesbian. Having attended UNAM and the Yale School of Drama, she travelled and studied in Europe and then, upon her return to Mexico City, became actively involved in the political upheaval, even getting arrested during the 1968 student protests. After helping to establish the Frente de Liberaci\u00f3n Homosexual in 1971, C\u00e1rdenas publicly proclaimed herself a lesbian in a nationally televised 1973 interview on the popular talk show 24 Horas. C\u00e1rdenas's biography seemed to lend credibility to Gringoire's argument that foreign influences \u2013 in her case, a restless cosmopolitanism \u2013 fuelled the 'becoming' of Mexican lesbianism. C\u00e1rdenas recalled in an interview, 'We got all the foreign lesbians together and I invited them to a meeting in my house to introduce Mexican lesbians to them... When they told me that they too had been unable to overcome [the men-versus-women] problem, a feeling of relief swept over me. It was not my personal clumsiness'.81\n\nThis support from 'foreign lesbians' signified, depending on the scenario, transnational solidarity or cultural imperialism. C\u00e1rdenas clearly intended her performance to highlight the former, linking her campaign to progressive internationalism. Nevertheless, after her presentation to the lesbianism forum, a coalition of Latin American leftist feminist groups staged a press conference inviting participants and reporters to a counter-conference protesting that the themes of lesbianism and prostitution had distracted attention from 'others of importance and transcendence'.82 According to security reports, nearly 1,000 people attended this three-hour event focusing on abuses by the Pinochet regime and ending with a chorus of the 'Internationale'.83 The implication that lesbian rights could only come at the expense of ignoring Chilean atrocities bolstered assumptions of a zero-sum rivalry between sexual rights and human rights.\n\nDomitila Barrios de Chungara and the family drama\n\nLike C\u00e1rdenas, Barrios de Chungara also struggled in a political scenario informed by nationalist maternalism, but she lived and worked in a milieu where gender complementarity \u2013 and the gender discipline it entails \u2013 had profoundly material consequences. Housing in the tin mining communities, for example, depended upon a male continuing to work for the mining company. 'Our position is not like the feminists' position', she explained in her testimonio. 'We think our liberation consists primarily in our country being freed forever from the yoke of imperialism... For us, the important thing is the participation of the compa\u00f1ero and the compa\u00f1era together. Only that way will we be able to see better days, become better people and see more happiness for everyone'.84 Even as she describes her husband drinking and beating her, belittling her and impeding her activism, she never deviates from her insistence that they must struggle shoulder-to-shoulder; the archived performance of her testimonio showcases women's union militancy on a par with (or even exceeding) men's. Distancing herself from both feminism and sexual liberation shored up her bona fides as a trustworthy Marxist unionist.\n\nSexuality remains conspicuously absent from Barrios de Chungara's testimonio. Despite having seven children by the end of her narrative, she never recounts a moment of intimacy or even tenderness with her husband. She insists on the union movement's asexuality, denying that her compa\u00f1eras were union officials' mistresses. She references sexuality most explicitly as a tool of abuse, as when a colonel's son indicated that her activism evidenced her husband's failure to satisfy her or when the local subprefect broadcast over the radio that all women participating in demonstrations must be prostitutes.85 As participants jockeyed for space and media attention at the IWY tribune, Barrios de Chungara saw discussions of sexuality not only as a filibuster against any meaningful discussion of the life-or-death struggles she faced in Bolivia, but also as an assault on gender complementarity that, for most poor women, played a critical role in their survival strategies. 'In one way or another', she recalled, 'they tried to distract the Tribunal with problems that weren't basic. So we had to let the people know what was fundamental for us in all of that'.86\n\nThe contemporary emphasis on family planning in both feminist activism and development policy only heightened this anxiety. Population control formed a central tenet of development programmes, but widespread evidence of forced sterilisations of poor women and women of colour made the policies look more like genocide than development.87 While middle-class feminists saw family planning and reproductive freedom as indispensable to women's efforts to control their own lives and opportunities, poorer women saw these measures as state- and elite-led efforts to police their bodies and a dehumanising campaign to cast the poor as unworthy to consume resources. Barrios de Chungara took issue with 'the women who defended prostitution, birth control and all those things', arguing that the Bolivian government resorted to 'indiscriminate birth control' to avoid addressing issues of resource distribution and starvation wages.88 Abortion became a particular lightning rod for conflict, especially with delegates from the Vatican, and served as a measure for women's emancipation, especially among educated urban women, in many parts of the world.89 Indeed, at the precise time that roughly 1,000 communists had collected near the city's historic centre at the Teatro Hidalgo, another 700 communists and socialists met five miles to the east in Chapultepec Park to demand legal state-funded abortion.90\n\nPopulation control campaigns, combined with the outspokenness of lesbians and prostitutes, opened a challenge \u2013 implicit but clearly perceived \u2013 to conventional heteronormative family structures. The prominent Mexican sociologist Rodolfo Stavenhagen published a lengthy editorial just prior to the IWY inauguration calling for a wholesale restructuring of family life, preferably following a collectivised model such as the Israeli kibbutz or the Chinese commune.91 In a tribune session on family organisation, the Dutch sociologist Ruut Veenhoven also advocated dramatically reconceptualised family formations. 'There are many groups upon which an individual might depend and live', he explained. 'And the individual will have to have the ability and the capacity to choose and to depend upon more extensive nuclei than the traditional family, since we cannot say that that structure is the best'.92\n\nMany participants responded to even these tentative challenges to traditional family structures with a definitive reassertion of gender complementarity and conventional heteronormative nuclear families. In an open letter circulated among tribune participants, a group of Mexican activists insisted, 'The objective and purpose of this International Meeting of Women should be to sustain the following principles: a) The human couple [pareja] is the unity; b) This couple forms the vital cell; c) From this cell derives the family; d) From the family derives the state and all forms of social organization'.93 Conference secretary-general Helvi Sipil\u00e4 'denied that it is necessary to change the modern family to end women's domestic slavery'.94 Prime Minister Sirimavo Bandaranaike of Sri Lanka insisted in her plenary statement, 'We must not think of the man and the woman separately but rather of the couple'.95 Mexican First Lady Mar\u00eda Esther Zuno de Echeverr\u00eda similarly asserted, 'Man and woman cannot be considered in isolation nor as signifying antagonism. They should fulfil themselves through integration and reciprocity... Man and woman are not rivals; man and woman do not substitute for one another; man and woman signify unsurpassed complements; man and woman are the very essence of equality, development and peace'.96\n\nZuno de Echeverr\u00eda invoked a long-standing Latin American feminist tradition of stressing gender complementarity to highlight women's social, cultural and economic worth. Many Latin American activists saw liberal individualism and equality campaigns as blunting their most effective weapon: a politics structured around highly essentialised and biologised gender differences. The long-time Uruguayan activist Dr Sof\u00eda de Demicheli warned women to proceed cautiously with their own liberation. 'The woman who wants to compare herself to man in everything either speaks from rote or doesn't know what she says', she chided. 'The result is so absurd that the man that she wants seems in all ways like a woman. Women in pants, men in skirts. Unisex. Hijo de mi vida, those are aberrations'.97 These 'aberrations' \u2013 not only the 'gender trouble' but also the efforts to remake family structures \u2013 threatened to undermine both support networks and the long-held feminist strategy of claiming gender complementarity as a means to gain recognition for the vast amounts of uncommodified labour performed overwhelmingly by women.\n\nTaking place during the UN's Second Decade for Development, the IWY events cultivated a productivist ethos that stressed incorporation of women into labour markets and erased women's massive contributions to food production and other subsistence labour.98 Amid prevailing Marxist paradigms and developmentalist emphases on 'productive' labour, women like Barrios de Chungara struggled for recognition of their own labours. In a subsequently written didactic pamphlet, Barrios de Chungara would later describe going on strike and withholding her household labour to convince her husband to support her activism.99 She recounts how Siglo XX women kept track of their hours spent performing domestic labour and then presented their compa\u00f1eros with a bill, highlighting the value of their reproductive labour. In both this pamphlet and her testimonio, Barrios de Chungara simultaneously stresses both her organisation's ongoing struggle to recognise women's political and domestic labours and its rejection of feminism. Describing the challenges they faced in forming the housewives' committee, she recalled the Siglo XX men whistling and shouting at them, 'Go home! Cook, clean, do chores!' and women tut-tutting that the committee members neglected their domestic obligations.100\n\nIf 'housewives' committee' sounded to US feminists like a prim ladies' auxiliary or the Junior League, they were sorely mistaken.101 The group's first action had been a hunger strike, launched to demand the release of their compa\u00f1eros from prison, and it maintained a record of radical actions throughout the 1970s.102 Indeed, Barrios de Chungara recounts two harrowing periods of imprisonment for her militancy.103 The committee always functioned, however, as an adjunct to the tin miners' union, and its members conceptualised their demands and their actions as part of a programme in concert (if also sometimes in tension) with the union. They agitated within a scenario where the 'reactivated drama' recalled a struggle against transnational corporations backed by an authoritarian government. In her pamphlet, Barrios de Chungara described feminism as an ideology of moneyed women whose idea of liberation was to be able to 'party like men', and she described machismo as an invention of capitalists to divide men and women. 'For this reason, the capitalists also created feminism', she explained, 'so that men and women would fight each other'. As if to leave nothing to the imagination, this argument was accompanied by a cartoon of a 'feminist' dressed in leggings and a midriff-bearing bustier and smoking a cigarette, and another of a lanky, spread-eagled Uncle Sam holding men and women apart from one another.104 The separatist arguments of the International Lesbian Caucus or the Radicalesbians would have conjured the hauntology of this feminist imaginary \u2013 of a world not so materially structured around gender complementarity.\n\nApocrypha and excess in IWY accounts\n\nRetrospective accounts of the IWY events focused on an apocryphal confrontation between Friedan and Barrios de Chungara, which stands as a synecdoche for the anticipated standoff between western liberal feminism and non-western (non-white) revolutionary nationalism.105 In most accounts, Barrios de Chungara stands as the authentic voice of the subaltern, and her bravery in speaking truth to power at the UN tribune marks the turning point in transnational feminism when 'Women of diverse cultures and ethnicities and social and economic strata became aware of the urgency and immediacy of one another's concerns'.106 According to the extensive coverage in the Mexican press, however, this altercation never occurred. In the tribune's closing days, Barrios de Chungara confronted not Friedan but rather the Mexican feminist Esperanza Brito de Mart\u00ed, the president of the Movimiento Nacional de Mujeres and arguably Friedan's Mexican counterpart.107 According to one newspaper account, while Brito attempted to deliver her address, 'a tubby, dark, toothless woman in humble clothing emerged from the audience and advanced confidently toward the microphone'.108 Cutting off Brito's calls for feminist unity, Barrios de Chungara exclaimed, 'How can we women be equals when we, the wives of labourers, are thrown in jail for organizing to protest their imprisonment? We cannot speak of equality between games of canasta. Women cannot be equals any more than poor and rich countries can be equals'.\n\nThe ex post facto ascendance of the imagined Friedan\u2013Barrios de Chungara encounter appears ironic when viewed in light of their views on sexuality and sexual rights. Both expressed open homophobia and little patience with prostitutes' rights campaigns; both insisted that men and women collaborate rather than work against one another; and both blamed transnational corporations for women's continued oppression. Certainly, if Friedan and Barrios de Chungara stood in for the dominant official themes of equality and development, then C\u00e1rdenas remained outside this imaginary. Even as they each struggled to ventriloquise an 'authentic' women's voice, neither saw C\u00e1rdenas within the bounds of what they might represent. In the invented scenario of the IWY tribune, however, their interventions reactivated the dramas of imperialism and exploitation, casting Barrios de Chungara in the role of the authentic subaltern and Friedan as the defender of lesbians and prostitutes.\n\nBrito's and Friedan's calls for unity and their search for an authentic feminist subject \u2013 the subject concerned with the imagined 'women's issues' \u2013 only begged the question, however.109 Each of these performances tried to shape the scenario, conjuring particular histories and languages that would locate themselves within an imagined trajectory of social and political transformation. As the feminist theorist Elizabeth Grosz has observed, 'Questions about culture and representation, concepts of subjectivity, sexuality, and identity, as well as concepts of political struggle and transformation all make assumptions about the relevance of history, the place of the present and the forward-moving impetus directing us to the future'.110 These assumptions manifest at the IWY as enactments and projections of imagined political scripts. The tenor of these different performances took on increased importance amid persistent concerns at the IWY events about what constituted legitimate women's issues \u2013 and what distinguished them from the more interested domain of politics \u2013 and produced particularly acute anxiety and uncertainty when they touched on questions of sexuality.\n\nThe performances at the NGO tribune were shaped as much by scenarios in participants' home communities as by the atmosphere in Mexico City. Whereas for many US activists their insistence on sexual rights marked them as pushing feminism in radical new directions, for Latin American leftists, establishing their political credentials required an emphasis on combating racism, imperialism and economic injustice. For many US feminists, the gender complementarity of Barrios de Chungara would have conjured the essentialising 'cultural feminism' they struggled to keep at bay, and her homophobia would have seemed an attack on the hard-fought gains of the early 1970s. In the US scenario, her political performance followed the script not of a radical or revolutionary but rather of a liberal or even a conservative. In the Mexican scenario, it became increasingly untenable to contain the contradictions between sexual rights and gender complementarity. As Marta Lamas notes, the feminists' rejection of official politics restricted their bargaining power, and 'the weakness of the movement also stems from the fact that although many people and political organizations incorporate the feminist thesis, they do not accept that it is identified with lesbianism and abortion'.111 By the end of the decade, the Mexican national women's movement that had consolidated in 1975 would splinter over the issue of lesbian rights as the communists, who had played a critical role in mobilising women, broke with the women's liberation movement.\n\nNotably, apart from the literature on Mexican lesbianism, Nancy C\u00e1rdenas drops out of retrospective accounts. Her politics exceeds the available paradigms, which centre principally on the 'global south' struggling against the neo-imperialist north, followed by a rapprochement between these two camps at the 1995 Beijing conference. C\u00e1rdenas's dissident cosmopolitanism has no role in this script. But if a homophobic posture and antagonism towards sexual rights continues to constitute a critical performative aspect of anti-capitalist or anti-imperialist politics, it remains necessary to historicise the political foundations for this hostility rather than chalking it up to traditionalism, provincialism, or the conservative influence of the Catholic Church or the Communist Party \u2013 or even to a visceral or subconscious repugnance. Instead, we should remain attuned to the contingencies as well as the structures of political performance \u2013 to the ways in which the multiple audiences for these performances appropriated and transformed their meanings. Even as various actors engaged in a complicated politics of gesture and self-representation that resisted facile categorisations, participants, activists and scholars have tried to reinsert them into more legible scenarios.\n\nNotes\n\n1. Domitila Barrios de Chungara and Moema Viezzer, Let Me Speak! Testimony of Domitila, a Woman of the Bolivian Mines, tr. Victoria Ortiz (New York: Monthly Review Press, 1978), pp. 198\u2013201.\n\n2. Barrios de Chungara and Viezzer, Let Me Speak!, p. 197.\n\n3. Francesca Miller, Latin American Women and the Search for Social Justice (Hanover and London: University Press of New England, 1991), pp. 199\u2013201; Bina Agarwal, 'From Mexico 1975 to Beijing 1995', Indian Journal of Gender Studies 3 (1996), pp. 87\u201392.\n\n4. Barrios de Chungara and Viezzer, Let Me Speak!, p. 198.\n\n5. On testimonio and its reconsideration, see especially John Beverley, 'The Real Thing (Our Rigoberta)', Modern Language Quarterly 57 (1996), pp. 129\u201339; Diane Nelson, 'Indian Giver or Nobel Savage: Duping, Assumptions of Identity, and Other Double Entendres in Rigoberta Mench\u00fa Turn's Stoll\/En Past', American Ethnologist 28 (2001), pp. 303\u201331.\n\n6. In the original Spanish version of the testimonio, Barrios describes the speaker as 'una gringa con su cabellera bien rubia'. Moema Viezzer, 'Si me permiten hablar...': Testimonio de Domitila, una mujer de las minas de Bolivia (Mexico City: Siglo Veintiuno, 1979), p. 220. The 'prostitution workshop' was led by the decidedly not-blonde COYOTE organisers Margo St James and Flo Kennedy.\n\n7. El Nacional, 1 July 1975, p. 8. The Mexico City newspapers mention Marisa de los Andes speaking up at the session on 23 June 1975.\n\n8. Betty Friedan, 'Up from the Kitchen Floor', New York Times Magazine, 4 March 1973, pp. 8\u20139, 28\u201335, 37; El Nacional, 21 June 1975, p. 1.\n\n9. Ara Wilson, 'The Transnational Geography of Sexual Rights', in Mark Philip Bradley and Patrice Petro (eds), Truth Claims: Representation and Human Rights (New Brunswick: Rutgers University Press, 2002), pp. 251\u201365, here pp. 257\u20138.\n\n10. Wilson, 'Transnational Geography of Human Rights', p. 258. See also Ara Wilson, 'NGOs as Erotic Sites', in Amy Lind and Suzanne Bergeron (eds), Queering Development (forthcoming).\n\n11. Walter Benjamin famously discusses the prostitute and the lesbian as divergent icons of modernity in The Arcades Project, tr. Howard Eiland and Kevin McLaughlin (Cambridge: Belknap Press, 1999). See Susan Buck-Morss, 'The Fl\u00e2neur, The Sandwichman, and the Whore: The Politics of Loitering' and Esther Leslie, 'Ruin and Rubble in the Arcades', in Beatrice Hanssen (ed.), Walter Benjamin and the Arcades Project (London and New York: Continuum, 2006), pp. 33\u201365, 87\u2013112, respectively.\n\n12. Diana Taylor, The Archive and the Repertoire: Performing Cultural Memory in the Americas (Durham: Duke University Press, 2003). The NGO forum presents particular methodological challenges since it issued no official statements and allowed no one to represent the sentiment of the tribune. Thus the documentary record privileges the professionalised activists who organised the tribune, ran its daily newspaper and produced the final reports on the proceedings.\n\n13. Taylor, The Archive and the Repertoire, p. 28.\n\n14. Taylor, The Archive and the Repertoire, p. 28.\n\n15. Barrios de Chungara and Viezzer, Let Me Speak!, p. 199.\n\n16. William H. Sewell, Jr, Logics of History: Social Theory and Social Transformation (Chicago: University of Chicago Press, 2005), p. 196.\n\n17. Taylor, The Archive and the Repertoire, pp. 53\u201378; Judith Butler, 'Performative Acts and Gender Constitution: An Essay in Phenomenology and Feminist Theory', Theatre Journal 40 (1988), pp. 519\u201331; Rosalind C. Morris, 'All Made Up: Performance Theory and the New Anthropology of Sex and Gender', Annual Review of Anthropology 24 (1995), pp. 567\u201392.\n\n18. The scholarship indicating the IWY conference marked a turning point in transnational feminism is too extensive to cite here. It ranges, however, from literary critic Jean Franco, Plotting Women: Gender and Representation in Mexico (New York: Columbia University Press, 1989), pp. 184\u20135 to the sociologist Myra Marx Ferree, 'Globalization and Feminism: Opportunities and Obstacles for Activism in the Global Arena', in Myra Marx Ferree and Aili Mari Tripp (eds), Global Feminism: Transnational Women's Activism, Organizing, and Human Rights (New York: New York University Press, 2006), pp. 3\u201323, here p. 11. Journalists and organisers alike referred to the IWY events as a global consciousness-raising session. Margaret Bruce, the head of the UN's Commission on the Status of Women, told a meeting of the AAUW at the UN that 'IWY, it is hoped, will result in a worldwide consciousness raising'. National Archives and Records Administration, College Park, Maryland (hereafter NARA\u2013CP), RG 220, Records of the US Center for International Women's Year, Subject Files, 1973\u20131975, A\u2013AS; Box 1, Folder 'AAUW'. See also 'International Women's Year World Conference Opening in Mexico', New York Times, 19 June 1975, p. 41; 'Women in the News', Nation, 19 July 1975, p. 36.\n\n19. Bonnie Smith has pointed out that this proliferation of forms of women's activism requires us to consider feminisms in the plural. Bonnie Smith, Global Feminisms since 1945: A Survey of Issues and Controversies (New York: Routledge, 2000).\n\n20. New York Times, 29 June 1975, p. 2.\n\n21. Organisers expressed concerns about countering 'aggressive activity by women lib groups in North America, many of which have their own well-established media outlets', Sophia Smith Collection, Smith College, Northampton, MA (hereafter SSC), International Women's Tribune Centre Records (IWTC), undated internal memo, 'Aide Memoire for Discussions in New York: Mexico City Newspaper Project, Some Considerations for IPPF', Box 3.\n\n22. Archivo General de la Naci\u00f3n (AGN), Mexico City, Direcci\u00f3n Federal de Seguridad (DFS), 27 June 1975, Exp. 9\u2013342\u201375, Leg. 9, Hoja 13\u201318.\n\n23. Xilonen, 25 June 1975, p. 3.\n\n24. Akira Iriye sees the 1970s as a turning point in the expansion of numbers and influence of international NGOs. Akira Iriye, Global Community: The Role of International Organizations in the Making of the Contemporary World (Berkeley: University of California Press, 2002). For a discussion of the growing role of NGOs in international governance, see Elisabeth J. Friedman, Kathryn Hochstetler and Ann Marie Clark, Sovereignty, Democracy, and Global Civil Society: State-Society Relations at UN World Conferences (Albany: State University of New York Press, 2005). For a reconsideration of NGOs' role, see Sonia E. Alvarez, 'Beyond NGO-ization? Reflections from Latin America', Development 52 (2009), pp. 175\u201384.\n\n25. Devaki Jain, Women, Development, and the UN: A Sixty-Year Quest for Equality and Justice (Bloomington and Indianapolis: Indiana University Press, 2005), p. 68.\n\n26. El Nacional, 24 June 1975, p. 7; El Universal, 24 June 1975, p. 1.\n\n27. Norma Mogrovejo, Un amor que se atrevi\u00f3 a decir su nombre: La lucha de las lesbianas y su relaci\u00f3n con los movimientos homosexual y feminista en Am\u00e9rica Latina (Mexico City: Centro de Documentaci\u00f3n y Archivo Hist\u00f3rico L\u00e9sbico (CDAHL), 2000), p. 67.\n\n28. Claudia Hinojosa attributes the unsigned Declaraci\u00f3n de las lesbianas de M\u00e9xico to C\u00e1rdenas. Claudia Hinojosa, 'Gritos y susurros: Una historia sobre la presencia p\u00fablica de las feministas lesbianas', Desacatos 6 (2001), p. 179.\n\n29. AGN, DFS, 26 June 1975, Exp. 9\u2013342\u201375, exp. 7, p. 156.\n\n30. Sister: A West Coast Feminist Newsletter, vol. 6, no. 2, p. 3; El Universal, 25 June 1975, p. 21.\n\n31. Hinojosa, 'Gritos y susurros', p. 180.\n\n32. El Universal, 24 June 1975, p. 19.\n\n33. AGN, DFS, Exp. 9\u2013342\u201375, exp. 7, p. 10; El Nacional, 25 June 1975, p. 8.\n\n34. James N. Green, '(Homo)sexuality, Human Rights, and Revolution in Latin America', in Jeffrey N. Wasserstrom, Greg Grandin, Lynn Hunt and Marilyn B. Young, Human Rights and Revolutions, (2000; 2nd edn, Lanham: Rowman & Littlefield, 2007), pp. 139\u201354.\n\n35. Washington Post, 21 June 1974, p. A3.\n\n36. Tamiment Library\/Robert F. Wagner Labor Archives, New York University Libraries, NYC\u2013NOW Papers (hereafter NYC\u2013NOW Papers), President's Report, 19 December 1974 meeting, Box 8, Folder 4. See also, 'Chile: Before and After the Coup', Sister: A West Coast Feminist Newspaper, vol. 4, no. 10, p. 10; 'Torture of Women in Chile', What She Wants September 1974, p. 3; Peace and Freedom (WILPF newsletter), vol. 34, no. 2 (February 1974), p. 1.\n\n37. Mar\u00eda del Carmen Conroy, 'Identif\u00edcate: \u00bfMafalda o Susanita?' Rumbo (Mexico City), March\u2013April 1975, p. 23.\n\n38. Charlotte Bunch and Claudia Hinojosa, Lesbians Travel the Roads of Global Feminism (New Brunswick: Rutgers University, Center for Women's Global Leadership, 2000), p. 6.\n\n39. The programme included 34 official sessions, and the final report on the tribune stated that 192 informal sessions took place \u2013 a number that included only meetings that secured a room through the tribune organisers. SSC, IWTC, 'Report, International Women's Year Tribune \u2013 1975', November 1975, Box 3.\n\n40. New York Times, 19 June 1975, p. 41. US State Department officials anticipated a similar conflict. Secretary of State to All Diplomatic Posts, 22 May 1975, <<http:\/\/history.state.gov\/historicaldocuments\/frus1969-76ve14p1\/d178>> (accessed 15 May 2010).\n\n41. Pacifica Radio Archives, Betty Friedan vs. the Third World (North Hollywood: Pacifica Radio Archives, 1975), sound recording.\n\n42. On Friedan's work with NOW around IWY, see NYC\u2013NOW Papers, 'Minutes of the NOW\u2013NY Chapter General Meeting of February 20, 1975', Box 2, Folder 15; NYC\u2013NOW Papers, Karen DeCrow's report to the national board, 29 March 1975 Box 25, Folder 2; Arthur and Elizabeth Schlesinger Library on the History of Women, Radcliffe Institute for Advance Study, Betty Friedan Papers (hereafter, Friedan Papers), Elaine Livingstone to Arlie Scott, Betty Friedan, Karen DeCrow and Jackie Ceballos, 22 March 1975, Box 107, file 1247.\n\n43. By February 1975, the sexuality committee reported that it regularly turned away about fifty people per week from their Saturday evening rap sessions (informal discussion groups), and that five or six new members signed up every week. NYC\u2013NOW Papers, Minutes of the NOW\u2013NY Chapter General Meeting of 20 February 1975, Box 2, Folder 15. The Boston Area Socialist Feminist Organization also established a Gay Liberation Work Group, although apparently with a considerably less enthusiastic response. Tamiment Library, Leslie Cagan Papers, January 1975 newsletter, Box 1, Folder 13.6.\n\n44. NYC\u2013NOW Papers, Box 6, Folder 4.\n\n45. Friedan, 'Up from the Kitchen Floor', p. 33.\n\n46. Friedan Papers, Livingstone to Scott et al., 22 March 1975, Box 107, File 1247.\n\n47. Friedan Papers, Friedan to Walker, 19 May 1975, Box 107, File 1248.\n\n48. Duke University Rare Book, Manuscript and Special Collections Library, Durham, NC, Robin Morgan Papers, Carol Downer to Robin Morgan, 3 June 1975, Box C5.\n\n49. US Ambassador to Secretary of State, 4 April 1975, <<http:\/\/history.state.gov\/historicaldocuments\/frus1969-76ve14p1\/d177>> (accessed 15 May 2010); Fran Hosken to Mildred Persinger, 10 March 1975, IWTC, Box 2.\n\n50. 'Tribuna: La voz del Movimiento Feminista', Xilonen, 19 June 1975, p. 1 (compare with 'Tribune \u2013 Where All Are Experts' on same page). Funded by the Ford Foundation and run by the Philadelphia-based editor Marjorie Paxson, Xilonen usually offered sympathetic depictions of US feminists.\n\n51. Washington Post, 22 June 1975, p. A12.\n\n52. El Nacional, 22 June 1975, pp. 6, 9. In late December 1974, Echeverr\u00eda had pushed through an amendment to Article 4 of the Mexican constitution, declaring men and women equals before the law \u2013 a development that highlighted the Equal Rights Amendment's continued floundering.\n\n53. El Universal, 22 June 1975, p. 9. The El Universal article insisted that in a 'survey' (of unspecified size and method) of Latin American women, 99 per cent responded similarly.\n\n54. Barrios de Chungara and Viezzer, Let Me Speak!, pp. 201\u20132.\n\n55. NYC\u2013NOW Papers, Report to the National Board, 29 March 1975, Box 25, Folder 2.\n\n56. Friedan Papers, Livingstone to Scott et al., 22 March 1975, Box 107, File 1247.\n\n57. The UN General Assembly affirmed the NIEO in December 1974 in the Charter on the Economic Rights and Duties of States, which Mexican diplomats dubbed the 'Carta Echeverr\u00eda'.\n\n58. Summary of Caracas meeting available in: UN Economic Commission for Latin America, Annual Report, vol. 1, supplement 9, E\/CEPAL\/989\/Rev.1, p. 152. State Department correspondence: Ruth Bacon's report to Henry Kissinger regarding the IWY tribune, 24 July 1975; telegram from Curtis H. Taylor (head of US mission to UN) to Secretary of State, 9 May 1975; all in NARA\u2013CP, RG 220, Records Relating to the UN IWY World Conference, Mexico City, June\u2013July 1974, Subject File A\u2013G, Box 22.\n\n59. El Nacional, 28 June 1975, p. 7.\n\n60. Washington Post, 25 June 1975, p. A27; New York Times, 29 June 1975, p. 2.\n\n61. Betty Friedan, 'Scary Doings in Mexico City', in 'It Changed My Life': Writings on the Women's Movement (Cambridge: Harvard University Press, 1998), p. 440.\n\n62. Contemporary lesbian groups conspicuously gesture towards national icons such as Sor Juana In\u00e9s de la Cruz and Frida Kahlo to establish themselves as legitimately autochthonous. Anahi Russo Garrido, 'Field Note: \"And We Were Mexicans\": Notes on the Use of National Symbols by Lesbian Groups in Mexico', Women's Studies Quarterly 35 (2007), pp. 226\u20139.\n\n63. Bunch and Hinojosa, Lesbians Travel, p. 7.\n\n64. Marta Lamas, 'Fragmentos de una autocr\u00edtica', in Griselda Guti\u00e9rrez Casta\u00f1eda (ed.), Feminismo en M\u00e9xico: Revisi\u00f3n hist\u00f3rico-cr\u00edtica del siglo que termina (Mexico: Universidad Nacional Aut\u00f3noma de M\u00e9xico, Programa Universitario de Estudios de G\u00e9nero, 2002), pp. 71\u20139, here p. 72.\n\n65. Many websites mention this moment as pivotal; most of them cite Hinojosa, 'Gritos y susurros'. See also Mogrovejo, Un amor que se atrevi\u00f3 a decir su nombre, pp. 65\u20139. Elsewhere, I have pointed to this moment as the 'event' of the Mexican lesbian, in Alain Badiou's sense of the constitution of a coherent, identifiable political subject. 'Pulled From the Closet? International Women's Year and the Event of the Mexican Lesbian', paper presented to the Princeton Program in Latin American Studies, 23 September 2009.\n\n66. Hinojosa, 'Gritos y susurros', p. 179.\n\n67. Yan Mar\u00eda Yaoy\u00f3lotl Castro, 'El movimiento l\u00e9sbico feminista en M\u00e9xico: Su independencia respecto a los movimientos feminista heterosexual y gay y su mision hist\u00f3rica', paper presented to the VI Encuentro de Lesbianas Feministas de Latinoam\u00e9rica y El Caribe, Mexico City, 2004, pp. 14\u201315.\n\n68. El Universal, 25 June 1975, p. 8. When contemporary activists point to this moment's importance in lesbian history, they highlight the importance of having the word 'lesbian' appear in the mainstream Mexico City press. See e.g., Ochy Curiel, 'El Lesbianismo Feminista: Una propuesta pol\u00edtica transformadora', La Agencia Latinoamericana de Informaci\u00f3n \u2013 ALAI, <<http:\/\/alainet.org\/active\/show_text.php3?key= 17389>> (accessed 9 May 2010); Hinojosa, 'Gritos y susurros', pp. 177\u201386.\n\n69. El Universal, 23 June 1975, p. 4.\n\n70. El Nacional, 25 June 1975, p. 8. M\u00e9xico 75: A\u00f1o Internacional de la Mujer ran from January to December 1975.\n\n71. El Universal, 24 June 1975, p. 1.\n\n72. Exc\u00e9lsior, 25 June 1975, p. 7\u2013A.\n\n73. Exc\u00e9lsior, 3 July 1975, p. 7\u2013A.\n\n74. Exc\u00e9lsior, 1 July 1975, p. 6\u2013A. Pedro Gringoire was the pen name of evangelical Methodist and public intellectual Gonzalo B\u00e1ez-Camargo (1899\u20131983), who borrowed the name from Victor Hugo's Notre Dame de Paris.\n\n75. Exc\u00e9lsior, 1 July 1975, p. 6\u2013A; El Universal, 25 June 1975, p. 8; El Nacional, 25 June 1975, p. 8.\n\n76. Xilonen, 27 June 1975, p. 4.\n\n77. Bunch and Hinojosa, Lesbians Travel, p. 7.\n\n78. Norma Mogrovejo, 'Sexual Preference, the Ugly Duckling of Feminist Demands: The Lesbian Movement in Mexico', in Evelyn Blackwood and Saskia Wieringa (eds), Female Desires: Same-Sex Relations and Transgender Practices across Cultures (New York: Columbia University Press, 1999), pp. 308\u201336, here pp. 319\u201320.\n\n79. Castro, 'El movimiento l\u00e9sbico feminista en M\u00e9xico', p. 15.\n\n80. Bunch and Hinojosa, Lesbians Travel, p. 6.\n\n81. Cited in Mogrovejo, 'Sexual Preference, the Ugly Duckling of Feminist Demands', p. 320.\n\n82. AGN, DFS, 26 June 1975, Exp. 9\u2013342\u201375, exp. 7, p. 156.\n\n83. AGN, IPS, Caja 1163\u2013A, vol. 1, Hoja 579\u201386.\n\n84. Barrios de Chungara and Viezzer, Let Me Speak!, p. 41.\n\n85. Barrios de Chungara and Viezzer, Let Me Speak!, pp. 143, 73, respectively.\n\n86. Barrios de Chungara and Viezzer, Let Me Speak!, p. 200.\n\n87. Matthew Connelly, Fatal Misconception: The Struggle to Control World Population (Cambridge: Harvard University Press, 2008); Laura Briggs, Reproducing Empire: Race, Sex, Science, and U.S. Imperialism in Puerto Rico (Berkeley: University of California Press, 2002).\n\n88. Barrios de Chungara and Viezzer, Let Me Speak!, pp. 199\u2013200.\n\n89. Xilonen, 27 June 1975, p. 3; El Universal, 21 June 1975, pp. 5, 11; El Universal, 22 June 1975, p. 7; El Universal, 2 July 1975, p. 5; Exc\u00e9lsior, 19 June 1975, p. 7\u2013A.\n\n90. AGN, IPS, Caja 1163\u2013A, vol. 1, Hojas 587\u201390.\n\n91. Exc\u00e9lsior, 17 June 1975, p. 7.\n\n92. Exc\u00e9lsior, 28 June 1975, p. 19\u2013A.\n\n93. Carta abierta a las participantes de la Conferencia Mundial del A\u00f1o Internacional de la Mujer, con sede en M\u00e9xico (1975).\n\n94. El Universal, 16 June 1975, p. 1.\n\n95. El Universal, 21 June 1975, p. 1.\n\n96. Exc\u00e9lsior, 16 June 1975, p. 1.\n\n97. El Nacional, 26 June 1975, p. 5.\n\n98. Jocelyn Olcott, 'The Battle within the Home: Development Strategies and the Commodification of Caring Labors at the 1975 International Women's Year Conference', in Leon Fink (ed.), Workers, the Nation-State and Beyond: Essays in Labor History Across the Americas (New York: Oxford University Press, forthcoming).\n\n99. Domitila Barrios de Chungara, La mujer y la organizaci\u00f3n (La Paz: UNITAS, CIDOP, CIPCA, 1980), pp. 17\u201323.\n\n100. Moema Viezzer, 'El \"Comit\u00e9 de Amas de Casa del Siglo XX\": Una experiencia pol\u00edtica boliviana', Nueva Antropolog\u00eda 2\/8 (1977), pp. 33\u20134.\n\n101. Debates among US feminists over whether housewives could develop feminist consciousness became particularly pronounced amid the wages-for-housework debates. See e.g., Carol Lopate, 'Letter to the Movement: Women and Pay for Housework', Liberation, May\/June 1974, pp. 8\u201311; Carol Lopate, 'Unpaid Labor: The Wages for Housework Perspective', Hera: A Philadelphia Feminist Publication 1 (1975), p. 16.\n\n102. By 1971, Barrios de Chungara herself was prominent enough to feature in the internationally circulated documentary 'El Coraje del pueblo' (1971) by the Bolivian filmmaker Jorge Sanjin\u00e9s.\n\n103. Barrios de Chungara and Viezzer, Let Me Speak!, pp. 120\u201332, 42\u201355, respectively.\n\n104. Barrios de Chungara, La mujer y la organizaci\u00f3n, pp. 7, 24.\n\n105. Miller, Latin American Women, p. 200; G\u00f6ran Therborn, Between Sex and Power: Family in the World, 1900\u20132000 (London and New York: Routledge, 2004), p. 103.\n\n106. Miller, Latin American Women, p. 201.\n\n107. Barrios de Chungara describes this confrontation in Barrios de Chungara and Viezzer, Let Me Speak!, pp. 202\u20133. On the MNM, see Ana Lau Jaiven, La nueva ola del feminismo en M\u00e9xico: Conciencia y acci\u00f3n de la lucha de mujeres (Mexico City: Editorial Planta, 1987), p. 18.\n\n108. El Universal, 1 July 1975, p. 1; El Nacional, 1 July 1975, p. 1.\n\n109. Gayatri Spivak points to the elaborate 'theatre' feigning women's unity at the 1995 UN Beijing women's conference to eclipse growing inequalities. \"'Woman\" as Theatre: United Nations Conference on Women, Beijing 1995', Radical Philosophy, May\/June 1996, <www.radicalphilosophy.com\/default.asp?channel_id=2187&editorial_id=10716> (accessed 15 October 2008).\n\n110. Elizabeth A. Grosz, Time Travels: Feminism, Nature, Power (Durham: Duke University Press, 2005), p. 1.\n\n111. Grosz, Time Travels, pp. 76\u20137.\nChapter 11\n\nGender and Sexuality in Latina\/o Miami: Documenting Latina Transsexual Activists\n\nSusana Pe\u00f1a\n\nTransgender studies is emerging as a distinct field of study that, according to Susan Stryker, 'claims as its purview transsexuality and cross-dressing, some aspects of intersexuality and homosexuality, cross-cultural and historical investigations of human gender diversity, myriad specific subcultural expressions of \"gender atypicality\", theories of sexed embodiment and subjective gender identity development, law and public policy related to the regulation of gender expression and many similar issues'.1 In the 1990s, the term 'transgender' gained more widespread usage, and Stryker remarks upon the 'startling rapidity with which the term itself took root'.2 Since then, transgender has been used to refer to numerous practices, identities and political agendas in a range of geographical settings and historical periods. Although Stryker presents a widely inclusive definition of transgender studies as a field of study, David Valentine argues that as a 'collective category of identity... transgender identification is understood... to be explicitly and fundamentally different in origin and being from homosexual identification'.3 It is precisely this border between homosexual and transgender identity that this chapter seeks to explore.\n\nMy interest in transgender issues emerges out of my previous research on Cuban American gay male cultures in Miami, Florida. In this research, I argue that male homosexuality in Cuba was historically associated with 'gender transgressions'.4 This association between gender expression, sexual practice and identity was, of course, not distinct to Cuba. In his summary of the extensive literature on male homosexuality in Latin America, Tom\u00e1s Almaguer argues that whereas sexual object choice is the primary determinant of one's sexual identity in the United States (a man who chooses to have sex with another man is 'gay' or homosexual while a man who desires to have sex with a woman is 'straight'), in Latin America sexual aim (the desire to penetrate or be penetrated) forms the primary determinant of identity. According to this system, the penetrated partner \u2013 referred to by terms such as pasivo, maric\u00f3n, mariposa, or loca \u2013 is much more stigmatised than the active\/penetrating man.5\n\nThe point I highlight in my work is that these sexual roles (active\/passive) are assumed to correspond to outward gendered manifestations that are socially visible. The revolutionary Cuban state in the 1960s and 1970s specifically targeted visible male homosexuality, a construct whose 'characteristics' included a wide range of gender transgressive practices, including, but not limited to, long hair, tight pants, colourful shirts, 'effeminate' mannerisms, 'inappropriate clothing' and 'extravagant hairstyles'.6 Therefore, although the system Almaguer describes highlights sexual role, it is gender identity that most often speaks to that sexual role and its corresponding sexual identity. In other words, in most Latin American social contexts, men exhibiting characteristics socially associated with women or socially defined as 'effeminate' are assumed to be members of socially marked category of maricones and assumed to be passive. On the other hand, men who appear masculine are less likely to be accused of being a maric\u00f3n, more often assumed to be an activo, and less likely to be stigmatised as a homosexual \u2013 even if they have sex with men. The importance of gender appearance lies not so much in its correspondence with sexual role. Rather, gender markers become significant insofar as how they mark or mask sexual difference to others.\n\nThese visible markers were not just a way of facilitating enforcement of homosexual repression. Rather, visibility and gender transgressions themselves formed a central part of the problem identified by the revolution. Even in the severest period of enforcement, Marvin Leiner reminds us, private homosexual expression was never the main target. Rather, 'during this period of the camps and public arrests, the major concern, as it had always been, was with the public display of homosexuality'.7 The gravest crime was not same-sex sexual acts per se but rather transgressing gender norms in ways associated with male homosexuality, or in other words, being visibly or 'obviously' gay. It should therefore not be surprising that after the severest period of Cuban persecution, a concentration of gender transgressive homosexual men left Cuba in the 1980 Mariel Boatlift.8\n\nAs I put this research on Cuban American gay male culture in dialogue with the field of transgender studies, a troubling question emerges with respect to the interplay of what is categorised as gay male\/homosexual expression as opposed to transgender expression. Many of the signs that marked a man as homosexual within a Cuban and Cuban American social context \u2013 wearing women's attire, having long hair and walking with a stride deemed effeminate, for example \u2013 are characteristics that might be associated with transgender communities today. Put another way, these characteristics may be seen as signs of non-normative gender identity unrelated to sexual orientation. As I think of the case of Cuban American gay male culture in relationship with transgender studies, I am intrigued by a set of questions: if outward manifestations that we would now call 'transgender' were understood in other historical and cultural contexts as 'homosexual', how do we label such manifestations today? By labelling them as homosexual, are we simply reinscribing the marginalisation of transgender individuals? On the other hand, by labelling them as transgender, are we anachronistically imposing a contemporary category and thereby performing another kind of intellectual violence?\n\nIn a survey article on Latino\/a transpopulations, Marcia Ochoa directly critiques my work for misusing the term gay men to refer to gender transgressive populations:\n\n[Pe\u00f1a] collapses transgender (MTF) Marielitas [Cuban Americans who arrived on the Mariel Boatlift] into the category of 'gay men'... preferring to focus on performativity and public visibility rather than on transgender experience... [Pe\u00f1a] includes mentions of 'drag queens' and locas but although transgender Marielitas have been documented elsewhere, Pe\u00f1a's analytic lens, like those of many researchers, keeps MTF Marielitas within the category 'gay'. I argue this practice makes trans experience invisible.9\n\nAlthough I do not want to make trans experience invisible, Ochoa is right to note my hesitation in calling gender transgressive Marielitas transgender or transg\u00e9nero because I find no evidence that 'transgender' as an identity category or community group had any relevance to Cubans and Cuban Americans in Miami in 1980. Rather, my research indicates that gender expressions we identify today as transgender played a central role in structuring homosexual\/queer self-identifications. In other words, many homosexual men understood gender transgression as a socially recognisable way to mark himself or herself as homosexual. While it is clear that some gender transgressive Marielitas now define themselves as transgender and\/or transsexual \u2013 best known is probably the case of Adela Vasquez documented in the graphic novel Sexile \u2013 many others continue to understand their gender expression as specifically related to male homosexuality.10 If we say, using contemporary categories, that the gender transgressive practices of Cuban immigrants in 1980 are transgender, does it follow that the individuals exhibiting them were or are not homosexual men?11 I do not mean to suggest that there were not Cubans who understood their gender nonconformity as unrelated to sexual desire and orientation. However, I am suggesting that one would not be able to distinguish these individuals from those who understood themselves as part of a homosexual culture simply based on their outward gender manifestations.\n\nToday, transgender seems increasingly relevant to Latina\/o communities, and scholars and activists are increasingly using the terms 'trans' and 'transgender' to discuss Latin American and US Latino\/a communities.12 It is important to note that the terms trans, trans-, transgender and\/or transg\u00e9nero are used slightly differently in these texts. For example, Lawrence La Fountain-Stokes defines transloca performers as those who explore 'homosexuality, transvestism, and spatial displacement' even as he acknowledges the slang definition of loca as an 'effeminate homosexual'.13 This usage resonates with my discussion of contemporary Cuban American gay male practices in that it examines gender transgression as a cultural element of expression among some male homosexual Latinos and\/or Latin Americans. Therefore even though 'trans-' is increasingly relevant to Latino\/a and Latin American populations, I believe we should be cautious about what precisely such usage implies about the relationship among transgender, homosexual and\/or queer. In his ethnographic exploration of the category of transgender, for example, Valentine juxtaposes the meanings of transgender among primarily white activists (who see gender identity as distinct from homosexuality) and primarily poor and working-class people of colour (whose identifications suggest that they understand gender expression as related to sexual identity). To some of the activists, these working-class people of colour are 'laboring under \"false consciousness\" because they are unable to distinguish their \"gendered\" and \"sexual\" identities'.14 Valentine begins Imagining Transgender with a quote from Fiona, an African American male-bodied person who identifies as a woman and as gay ('indexing her attraction to other male-bodied people'). According to Valentine, transgender social service providers and activists he worked with believed:\n\nFiona's view of gendered and sexual identity was not merely an alternative categorisation but a false one. In their view, Fiona was using an outmoded view of gendered and sexual identity that conflates or confuses her transgender identity with homosexual desire. This is a result, they argue, of class, racial, or cultural inequalities which have left Fiona and her peers outside the conversations and historical developments which make this distinction possible.15\n\nThis assertion involves a:\n\nmodernist telos wherein the recognition of gendered and sexual identification as separate... is more accurate, more true, more valid. Thus, the Meat Market fem queens like Rita become almost figures of premodernity, people who have not been 'educated', who adhere to the 'mistaken' belief that homosexual identification involves cross-gender identification.16\n\nValentine found that among working-class people of colour, it was quite common to understand gender and sexual identity to be related to one another, and that although they were hailed under the umbrella term 'transgender', they rarely used the term to define themselves.\n\nThis chapter explores the borderlands between the concept of 'homosexual' and 'transgender' with a particular focus on Latina\/o communities in Miami, Florida. My previous work on Cuban Americans lead me to identify Miami, the US city with the largest concentration of Cuban Americans, as a research site. Latina\/o Miami, is not, however, all Cuban. Therefore, this project expands on my previous questions and engages with the complexities of a multi-ethnic Latina\/o urban setting, where different national origin groups coexist. I have searched for Miami Latina political groups, organisations and representations explicitly labelled as 'transgender' or 'transsexual' by participants. I focus on the earliest case I have found, namely the activism of transsexual Latinas in early 1970s Miami, for transsexual activism is one important antecedent to contemporary transgender activism. Specifically, I analyse the rarely discussed Latina activists who participated in the Transsexual Action Organisation (TAO) \u2013 an early transsexual rights organisation. I am particularly interested in the complicated and contradictory identity practices of Latina TAO members, the ways they discussed the connections and distinctions between transsexual communities and other groups categorised by gender and sexuality such as feminists and gay male communities and the ways TAO invoked elements of Cuban culture (such as Santeria religious practices) to articulate a transsexual identity in Miami. In addition, I discuss TAO director Angela Douglas's conflicted relationship with Cuban Americans and other Latino\/as in Miami.\n\nBorderlands between transgender and gay\n\nAccording to Stryker, the current definition of transgender emerged in 1992 through Leslie Feinberg's Transgender Liberation and Sandy Stone's 'posttranssexual manifesto'. Feinberg called for a 'political alliance between all individuals who were marginalised or oppressed due to their difference from social norms of gendered embodiment and who should, therefore, band together in a struggle for social, political and economic justice'.17 An important antecedent to the Transgender Rights movement, transsexual and transvestite activists in the 1970s articulated a distinct agenda and actively distinguished themselves from gay\/lesbian and women's political movements. For example, Stonewall veterans Sylvia Rivera and Marsha Johnson formed Street Transvestite Action Revolutionaries (STAR) in 1970 after being marginalised by the gay political organisations.18\n\nThat same year, Angela Douglas founded the Transsexual Action Organisation (TAO) in Los Angeles.19 The organisation and its publications moved to Miami Beach, Florida in 1972. Joanne Meyerowitz describes TAO as one of only two transsexual organisations in the 1970s with a national presence, and Stryker adds that TAO was 'the first truly international grassroots transgender community organisation, with a worldwide mailing list and loosely affiliated chapters in various cities'.20 This chapter draws on the organisation's publications, Moonshadow and Mirage Magazine (1972\u201375) as well as Douglas's self-published autobiographical texts, Triple Jeopardy: The Autobiography of Angela Lynn Douglas (1983) and Hollywood's Obsession (1992).21 Latinas such as Colette Tisha Goudie, Tara Carn and Kimberly Elliot constituted an integral part of the public face of this pioneering transsexual organisation, often serving in leadership positions, appearing in pictorials in the organisation's publications and representing TAO in interviews with mainstream media outlets.\n\nThat transsexual Latinas were so prominent throughout this organisation and that documentation of their participation has survived is a great contribution to GLBT historical records that, by and large, tend to under-represent people of colour.22 This data set also poses serious limitations, the most challenging of which is the centrality of Angela Douglas's narratives and the absence of competing narratives. Douglas's accounts are highly eccentric, weaving together her sexual and gender journey with accounts of UFO sightings and the relationship between the struggles of transsexuals and extra-terrestrial beings. Her second autobiography is devoted to proving that representations of transsexuals in the media were mostly plagiarised variations of her story, hence the title, 'Hollywood's Obsession'. According to Stryker, Douglas 'suffered several psychotic breaks as a young adult' and was 'more of a gadfly and provocateur than a movement builder'.23 Meyerowitz describes Douglas as a 'disruptive figure' with a 'disruptive personality' whose '\"second wave\" radicalism put off many transsexuals whose politics differed from hers... Douglas lambasted the people who disagreed with her and made increasingly strange accusations that put off virtually everyone else'.24 I strive to highlight Douglas's work as a radical activist who was able to inject transsexual issues into local and national political debates, and I want to avoid reinforcing stereotypes of transsexuals (as crazy, unstable and dangerous) without omitting significant strands from her story.\n\nThe racial\/ethnic perspective provided by Douglas's account is another limitation of the data. My analysis of TAO's publications (in which several transsexual Latinas were regular contributors) is substantially complemented by Douglas's autobiographies. I use the lengthier accounts by the Anglo leader of this group in order to access a more textured description of Latina transgender activists and the social context in which TAO existed. This choice is not troubling because Douglas is Anglo per se, but rather because she has a very complicated relationship with race\/ethnicity and Cuban Americans in particular.\n\nA few details from Angela Douglas's biography will flesh out this point. From her earliest recollections, Douglas presents herself as someone with liberal attitudes about race who challenged the racist conceptions of family members, and she certainly had connections with Latinas and Latinos throughout her life.25 She also often interprets Latinos and blacks through a racist lens. When Douglas was fourteen, the Czinky family (Douglas's biological family) moved to the South Florida neighbourhood of Hialeah. In 2010, Hialeah, la ciudad que progresa, is over 90 per cent Hispanic. In the late 1950s, the neighbourhood's Hispanic population was much smaller but still significant. At Hialeah High School, Doug Czinky (Angela Douglas's name before transition) met his first love, Norma Arcadia Rodr\u00edguez, 'a Cuban-born beauty from Puerto Padre'. The Rodr\u00edguezes \u2013 including father Goduel, mother Onelia and brother Jackson \u2013 became Douglas's 'surrogate family'.26\n\nThe Czinky family opposed his marriage to a Cuban woman. As she narrates this story, Douglas reveals her evaluation of Cubans in general. She remembers responding that Rodr\u00edguez 'may be Cuban but has genius IQ'.27 Therefore, in Douglas's own tale of anti-racism she actually confirms her racist assumption that an intelligent Cuban is an anomaly. Czinky's descriptions of Norma focus upon her sexuality, calling her a 'sex goddess' and a 'Cuban bombshell' and describing letters Norma wrote as 'torrid, sexy, hard-core, [she] would have made a fortune writing porno novels'.28 Doug and Norma eventually married and had a rocky relationship that ended when Norma left him, pregnant with his child, to be with her lesbian lover, Joan Black. In Douglas's autobiographical texts, Norma is a recurrent theme.\n\nThe sexualised language used to describe Norma evidences one of the first revelations of the racialised way in which Douglas sees Cubans, Latinos and other racialised groups. Douglas underwent an extreme racist period during 1978\u201379 when she actively participated in US Nazi politics. During this period, Douglas's politics shifted to the far right and her racism was highly explicit and confrontational. She suggests that this activism might have been caused by mind control by her enemies. Rather than dwell on this period, I prefer to provide an example from outside the Nazi period of the discourse that characterises the majority of the autobiography. For instance, while critiquing the treatment of transsexuals in prison, Douglas makes the point that for transsexuals jail is much like the outside world because in jail, 'the most ignorant black, Latin, or anyone is still above us and can control our lives to a great extent, with the full weight of a sexist, callous Society and legal system on their side'.29 In general, Douglas uses racist language freely when harassed and provoked by blacks and Latinos. Douglas seems to view Cubans and Latinas with both a desiring and despising gaze.\n\nTAO and involvement of Latinas\n\nAngela Douglas describes 1972 as the 'Year of the Transsexual in Miami Beach: hundreds were there, from all over the nation, and many Puerto Ricans and Cubans'. In the drag bars and discos in South Miami Beach, 'the cha-chas became as thick as tourists; the Latin transsexuals were referred to as \"cha-chas\"'.30 It was in this Latina\/o and transsexual environment that Douglas reformed TAO. Therefore, it is not surprising that Latinas were a core part of the TAO leadership. Three out of six of the women tapped to participate in TAO Miami were Latina.\n\nI should clarify that I am identifying someone as Latina only if the text provides specific information indicating her ethnicity\/nationality \u2013 not by surname alone.31 The use of Spanish surnames, an already imprecise way of identifying Latinos, becomes further complicated among transsexual individuals who usually adopt a new name during gender transitioning. This renaming and re-identifying sometimes also involves shifting or blurring racial\/ethnic signifiers: most of the transsexual women I can unequivocally identify as Latina do not go by a Spanish surname. On the other hand, one woman I have not been able to identify in racial\/ethnic terms, Barbara Rosello, does have a Spanish surname well known in South Florida and the Caribbean. It is important to note that phenotypical features related to race could set limits on the amount of ethnic blurring a transsexual woman could achieve. For example, a lighter-skinned Latina who adapted an English surname could hope to be interpreted as Anglo\/white. A darker-skinned Latina adopting the same name might be interpreted as African American, an arguably more stigmatised group in South Florida.\n\nBelow I provide biographical sketches of three of the original Latina members of TAO Miami: Colette Tisha Goudie, Tara Carn and Kimberly Elliot. I model my biographical sketches on the presentations self provided on the pages of TAO magazine. Since all of the women were TAO officers and some were editors and contributors to the publications, I hope that the sketches reveal some of the ways in which they preferred to present themselves or self-identify. Although some of the details presented in these stories might run contrary to contemporary transgender preferences for self-identification, I include them in order to indicate the sets of concerns and characteristics Latina transgendered women in the 1970s chose to highlight in one venue.\n\nColette Tisha Goudie\n\nThe most prominent of the transsexual Latinas, Colette Tisha Goudie was the third president of TAO. She took over after the brief tenure of Barbara Rosello, who resigned due to family pressures and nerves. Goudie also served as TAO's vice-president and defense director (1973). Goudie, who had been living as a woman since 1969, was one of the more popular models in the magazines and her pictures were featured on several covers and many pictorials. Douglas describes Goudie as a 'very feminine, beautiful transsexual from Miami' whom she met during the 1972 protests of the presidential national conventions in Miami Beach. In her first published statement as president, Goudie says she had been an active TAO member since 1973 and that she was 'elated to be the third president' of the organisation. As president, she pledged to:\n\ncall demonstrations whenever necessary to protest our oppression and I hope you will support them as much as possible. We will also make ourselves more available to the media to explain about transexualism and transexual liberation, as education for the public is most important. When I served as Defense Director for TAO we held several actions, all of them fairly effective, and in a way, educational as well. TAO needs more members and officers who want to do more than see their names in print or their faces on television screens... I will do all I can to build TAO and help achieve liberation for all transexuals, transvestites, whether they are rich or poor, white or black, Cuban, Puerto Rican or whatever.32\n\nIn TAO publications, Goudie is not identified as Latina or Cuban American at first, but this aspect of her ethnic identity is eventually unveiled. The first time she appears in the magazines, Goudie is described as a twenty-six-year-old, pre-op transsexual 'student of the occult' who is 'originally from France'. In 1974, she is identified as having 'French Cuban extraction' and having 'lived in Florida for many years'.33 In the February 1975 issue that featured her on the cover, Goudie reiterates that she was born in France but adds that she 'was raised in Cuba as my mother is Spanish and then in Miami'.34 Goudie's mother's very Cuban nickname ('China') as well as her familiarity with Afro-Cuban religious practices suggests a strong Cuban American background. Although she describes studying the occult in general (including voodoo and satanism), she wrote about Afro-Cuban Santeria. Moonshadow's August 1975 issue featured Goudie on the cover and included an article on Chango-Santa Barbara, one of the 'transsexual and intersexual deities... found in Afro-Latin beliefs'. Written by Douglas and Goudie with help from someone identified only as 'Maria', the article explains that Chango 'is viewed as a transvestite by some cults, legend saying he assumed feminine dress to escape his enemies and liked it so well he continued'. The Catholic saint with whom Chango was syncretised, Santa Barbara, was a king who 'assumed feminine disguise, continuing to live as a woman off and on during the rest of his life'. Santa Barbara\/Chango is worshipped 'by many Latin Americans, particularly [by] Cubans'. The story discussed other Santeria deities including Yemaya that 'some say... is the protector of male and female homosexuals'.35\n\nAfter Douglas left Miami, she travelled throughout the country spending substantial amounts of time in California and Hawaii. Douglas's and Goudie's paths crossed repeatedly. Douglas admits she was 'madly in love with [Goudie although] she hardly returned the same amount of affection'.36 In the early 1980s, Douglas says she visited Goudie in her home in South Miami. Douglas had dinner with Goudie and her mother, China, and describes them as 'aloof'.37 Goudie had 'claimed' she had sex reassignment surgery, gone to college and visited Paris and Rome.38 Douglas describes being suspicious of all these claims; subsequently, they had their final break-up around this time when Goudie announced that she was a born-again Christian, did not want to see Douglas anymore, planned to tape their calls and refused to return copies of the magazine. After this, Douglas reportedly went to the local police to complain that Goudie was taping her calls and to the FBI to report her suspicion that 'Tisha and her mother were Castro agents, which I concluded for a number of reasons'.39\n\nTara Carn\n\nAccording to Douglas, Goudie's arch-rival was Tara Carn, a Puerto Rican-born, New York-raised transsexual woman who was also one of the original members of TAO Miami. In her autobiography, Douglas describes 'Tara Lopez Carn' as 'a gorgeous, very wild blonde Puerto Rican'. As in other descriptions of Latinas (both transsexual and not), Douglas's language reeks of stereotypes of the hot, highly sexual and passionate Latin spitfire. Douglas tells us that Goudie and Carn were 'both very beautiful and wild and hated each other with a hot passion. Getting them to work together was nearly impossible'.40\n\nCarn describes Miami as boring at times but acknowledges that she always came back to the city. When asked to appear in her first pictorial in Mirage, Carn reports that her boyfriend was 'terrified' because he did not want anyone to know that his girlfriend was a transsexual, but she 'felt differently'. She is quoted as saying: 'I'm proud of what I am, and I want to help anyway I can'.41 Although above she refers to a boyfriend, she is also quoted as saying that she is a 'lesbian at heart' because she likes 'other transsexuals and girls'.42\n\nDouglas describes Carn as one of the most militant of TAO members. At the beginning of the organisation she was a pre-op transsexual who had lived several years as a woman and had 'little trouble being accepted as a woman, although some people can't accept the fact that she is a transsexual'. She was a popular target of Miami Beach police officers who followed her around and harassed her by telling the men she picked up that she was 'a fag in a dress'. Douglas states that they 'loved to embarrass Tara, who was extremely womanly'.43 Carn developed an ingenious strategy to get back at the police:\n\nTo retaliate, the beautiful Tara sometimes went to a crowded beach, started dancing topless to music from a radio and after a crowd of applauding people surrounded her, would take off her bikini panties, display her male genitals and cause a near riot. Police would arrive and she'd shake her genitals at them, screaming 'you say I'm a man'... She was taken to jail, fined, and sometimes went back and repeated the performance.44\n\nLater in the 1970s, Carn underwent sex reassignment surgery. Both Douglas and Carn left Miami separately around 1976, and Douglas reports that she disbanded TAO at this time. Tara is only briefly mentioned again in Douglas's autobiography when their paths crossed in Hawaii. Douglas reports that Carn had gone to Honolulu based on her suggestion. When Douglas runs into Carn with Cynthia Platt (another former TAO member), she says they were 'dripping with expensive clothes and money' and 'were cold, unfriendly, and made it clear that they wanted nothing to do with me'. A few months after this encounter where Douglas felt snubbed, she read Carn had been arrested on a prostitution charge and escaped. 'I guess she is still running'.45\n\nKimberly Elliot\n\nKimberly Barreiro (who changed her name to Kimberly Elliot when she married Steve Elliot) was also one of the original Miami TAO members.46 Cuban-born Elliot served as TAO's Miami Beach director, a member of TAO's central committee and associate director of Mirage. Douglas described the young Elliot (only twenty-one in 1974) as 'tiny, bubbly'.47\n\nElliot was one of the first in the group to undergo surgery, and Douglas said that she transitioned fully in less than a year.48 In a 1974 pictorial, Elliot is quoted as saying she is 'elated with the results' of the surgery. 'I don't regret it all. But the pain was incredible. I don't know if I could go through it again'.49 Elliot was found dead in 1980 at Miami Beach's Midtown Plaza due to a drug overdose Douglas saw as suspicious. She was buried in North Miami Beach, and Douglas reports that 'many old TAO people attended her funeral'.50\n\nTranssexual Latina\n\nIn addition to documenting the lives of individual Latina transsexual activists, I also want to explore the ways in which race and ethnicity emerged in TAO and its publications. An imagined Latina\/o audience is signalled in a range of ways in the organisation's pages. Both Moonshadow and Mirage regularly included information about conditions faced by transsexuals in Latin America, and these reports occasionally came from TAO members who travelled to those countries.51 For example, Jennifer Raquel Otero, identified as the 'third place winner in the Miss Universe contest held in Caracas', reported that police harassment was 'intense' and 'hormone and silicone treatments are also illegal' in Venezuela.52 In addition, TAO publications included regular updates on prominent Latina transvestites Silvia Rivera and Holly Woodlawn, although their Latina descent is never mentioned.53 TAO publications also include other culturally significant references, like the previously mentioned full-page discussion of Chango and Santeria.\n\nSpanish language was used in a variety of ways in the publication \u2013 ranging from the use of short phrases to full stories being printed entirely in Spanish. One issue of Moonshadow features a line drawing of a woman with flowing wavy hair wearing a fashionable leisure suit looking over her shoulder at a map of Florida's east coast. A cartoon bubble indicates that she is remarking '\u00bfQu\u00e9 pasa?' The familiar salutary address (similar to 'What's up?') is so widely familiar to English monolingual speakers that its inclusion, in and of itself, does not suggest a Spanish-speaking audience. However, the fact that the phrase is properly punctuated and accented (with an inverted question mark and an acute accent) suggests that a Spanish speaker edited the text, taking care to make the Spanish 'correct', possibly with bilingual readers in mind.54\n\nAnother Moonshadow issue includes extensive use of the Spanish. The third page begins with the description of the magazine and TAO in Spanish \u2013 'Moonshadow es la publicaci\u00f3n oficial de la Transexual Action Organization, un efuerzo de liberaci\u00f3n transexualista fundado por Angela K. Douglas' \u2013 followed by the English language translation. Similarly, international news from Puerto Rico, Sweden and Canada was printed first in Spanish and followed by its English translation.55 On the outside cover of another issue, only two words appear: the title, 'Moonshadow' and 'gratis' indicating in Spanish that the publication is free. Inside we find a picture of Goudie identified as 'TAO President' and information about TAO, magazine distribution and TAO membership in several languages with Spanish appearing first.56\n\nTAO publications also critiqued Latino homophobia and transphobia. These critiques can be interpreted several ways. On the one hand, they might speak particularly strongly to Latina\/o readers who had themselves fallen victim to oppression from their compatriots, therefore drawing those readers in. Also, they acknowledge the cultural presence of Latinos as part of Miami's landscape. On the other hand, they can be understood to portray all Latino cultures in a derogatory way. These multiple effects are all demonstrated in one short piece, entitled 'Mariposa Mierda', that critiques a local Cuban American musical recording called 'Mariposa': 'Some Cuban morons have released a record called \"Mariposa\" (butterfly) which ridicules effeminate gays and TVs. Mariposa is an insult, like \"maric\u00f3n\" or \"pato\", i.e., faggot or queer. It's a best-seller in Miami'. The critique of Cuban homophobia quickly devolves into an anti-Cuban 'go-back-where-they-came-from' diatribe that resonates with much of Douglas's autobiography: 'Too bad they can't go back to Cuba, where they won't find many mariposas; we'll be glad to steal a boat for them. By the way, didn't they come to find liberty and justice? Apparently they don't know what it is'. The short piece ends somewhat incongruously with a shout out to the Santeria deities: 'Viva Inle and Yemaya'.57 This particular article seems addressed to someone unfamiliar with Cuban cultural references from someone who is familiar with them \u2013 therefore the need to explain a term like mariposa \u2013 a term that would be widely familiar to Cubans and other Spanish speakers in Miami. It also demonstrates knowledge about Cuban American culture and even ends with using Cuban cultural references to Santeria to critique Cuban homophobia. On the other hand, the centre of the argument involves sending ignorant Cubans 'back where they belong'.\n\nAlthough many Latinas were TAO members and\/or magazine contributors, it is unclear how much editorial control they exercised. Given that Douglas's lengthy autobiography is not countered by any similar type of document from Goudie, Carn or other TAO Latinas, it is difficult to answer this question. Clearly, in a visual sense, images of Latinas filled the pages of Moonshadow and Mirage. Whether actual photographs or line drawings adapted from photographs, the faces and bodies of transgendered Latinas like Goudie and Carn became the image of TAO.\n\nLikewise, when TAO spoke to the mainstream media, Latinas were almost always present. One of the significant accomplishments of TAO is that they were able to get mainstream media outlets to feature stories about transsexuals. While the stories are mixed and sometimes include denigrating language (like referring to transsexuals as 'boy girls'), they also included information about the day-to-day challenges faced by transsexuals.58 For example, in 1974 TAO appeared on the 'Marsh and Adams Show' on WKID television in Fort Lauderdale. Tisha Goudie was one of three TAO members featured. The show discussed some of the challenges faced by transsexuals: housing discrimination, police harassment, difficulties receiving proper medical attention and difficulties with getting identification.59 During June 1974, the Miami News published a series on transsexual issues. Two of the four featured transsexuals were Latina: Tara Carn and Colombian American Crystal Gresham. Previewing the interview before the story was published, Mirage reported that Carn and another transsexual, Sharon Martin, gave the journalist John Maguire and photographer Bill Rankin 'a long look at the wonders wrought by silicone and hormones'. Predictably, the Miami News story voyeuristically reported that they had 'breasts that rival a Playmate's' and that their faces 'epitomize[d] one ideal of classy looks'. The writer seemed most taken with Gresham (formerly Crystal Lein) who served as TAO's Miami Beach director. Gresham is described as a 'perfect lady' and 'personifying elegance in name, voice and gesture'. During the interview, 'she wore a lace dress with white earrings... Her appearance and demeanor were impressive'. According to the article, Gresham 'live[d] fully as a female except when teaching ballroom dance to elderly women in Miami Beach'.60\n\nOne of my original questions was how TAO defined their relationship with other political movements and social identities. Membership policies begin to answer this question. When founding the organisation on the west coast, Douglas conceived it as catering to both transvestites and transsexuals. However, she shortly reconsidered this position, so transvestites were not invited to be part of TAO Miami. In a published interview, Douglas asks then-TAO president Goudie how she feels about transvestites:\n\nI have nothing against them. Some transsexuals say they are transvestites because it's easier for the world to comprehend. But it's not the same. A transvestite is a man who dresses up like a woman for a little while and then becomes a man again. A transsexual, like you and me and so many others, live as we are all of the time. It is so different... I don't think it's good for both TVs and TSs to belong to the same groups, as the values are so different, the laws and problems are so different. In some ways the problems overlap, but not completely.61\n\nFor most of TAO's history, full membership was restricted to pre- and post-operative transsexuals, not a larger 'queer' community, and several issues suggest that 'proof' (such as medical documents or a note from a doctor) were required to receive a membership card. This relationship to medical technologies is one issue that distinguished transsexuals from transvestites. Although TAO critiqued the mainstream media's focus on 'medical aspects' of transsexualism at the expense of more severe problems, the magazine included regular information about the costs and accessibility of medical procedures. Do-it\u2013yourself medical technologies, while probably not uncommon among TAO members, were not discussed or promoted in TAO publications. As Meyerowitz points out, the 1970s marked the growth of the 'privatization of medical treatment' of transsexuals that exponentially increased access.62 Dr John Brown was a controversial figure (Meyerowitz said he 'won a well-earned reputation as a back-alley butcher') who provided cheaper and quicker surgeries for transsexuals who wanted it.63 Although when Douglas met Dr Brown in 1974 she did not yet decide to have surgery, she claims, 'he wanted to help aid me and came up with several thousand dollars cash to help publish Mirage Magazine. In exchange, I promoted him considerably'.64 Dr Brown's patronage, as well as the eagerness of transsexuals who had previously been denied access to surgical interventions and medical recognition, probably fuelled the inclusion of information about medical technologies.\n\nAlthough transvestites were not full members of TAO Miami, TAO added 'units' or associate memberships for non-transsexual members, including the lesbian and transvestite units, and in 1975 full membership was granted to intersexuals.65 As only one of many examples, one issue clarifies the relationship between TAO and other social movements related to gender and sexuality:\n\nTAO also strongly relates to the problems and efforts of transvestites, gay men and women and feminists. However, we consider transexualist values of paramount importance and are not subject to the values of other sociosexual liberationist movements, such as the feminist and gay liberation movements. We prefer to meet members in person.\n\nIn another article, Douglas describes 'transexual and transvestite liberation' as 'seeking full independence from the feminist and gay liberation movements'.66 As in the national political landscape, eruptions emerged between women's liberation activists and transsexuals because of the exclusion of male-to-female transsexuals from 'women's' spaces. When this issue came up in the pages of TAO's publications, group members mostly did not identify specific local instances of discrimination but rather referred to national and international issues, yet tensions with the gay\/lesbian movement did seem to respond to local issues. TAO broke off relationships with Gay Action Alliance (GAA-Miami) after the gay\/lesbian group refused to include transsexuals in a lawsuit countering police brutality in Miami Beach.67 This was particularly upsetting to TAO since, from their point of view, they had been the ones to take actions on the street level to challenge the police.68 As Douglas clarifies, the point of their actions was that transsexuals were targeted more than gay men and other groups. In an interview, Goudie explains that only transsexuals can 'really understand each other and help each other. We have our experiences and goals and non-transexuals have theirs... We do not really belong in the gay or women's movements, although I don't really care if people think I'm gay or not'.69 In response to a National Gay Task Force media issue, Joann Ocasio is quoted as saying: 'I am not a homosexual and do not want homosexuals representing me'.70 The article elaborates that this is the position held by most TAO members.\n\nI would say these positions represent the majority (although not all) of the positions expressed in TAO publications. A few issues complicate the assertion of an explicitly separatist agenda. A review of the articles, advertisements and Douglas's autobiographies suggests a very concentrated social space in which most transsexuals lived, worked and\/or socialised. This area of South Miami Beach, about nine square blocks around Twenty-first Street beach, was at the time also Miami's primary gay male neighbourhood. In her autobiography, Holly Woodlawn, the Puerto Rican-born actress best known for her role in Andy Warhol's Trash, describes her first encounter with Twenty-first Street beach in the early 1960s:\n\nI had stumbled upon the only gay beach in all of Florida... Loud Cuban salsa music blared from a nearby radio as all these men yukked it up, having the time of their lives. I had never before seen a real-life, honest-to-God homosexual \u2013 ever! Here were actual 'queers', 'fairies', 'pansies', 'Nancies' and 'fags'. And with that kind of terminology floating around my head, how could I have helped but assume that all homosexuals were nellie little darlings with poofy hair coiffed to perfection, their shoulders caressed by feather boas, wearing a rock on every finger and talking with a dead-giveaway lisp!? Boy, was I ever in for a surprise.\n\nThere they were, a smorgasbord of every type imaginable: exotic, outrageous, fabulous, decadent! Big, little, hunky, chunky.71\n\nTherefore, approximately a decade before TAO emerged in Miami Beach, Woodlawn describes a vibrant and diverse homosexual community at the beach. The presence of 'loud Cuban salsa music' and the description of 'exotic' men, suggests the presence of Latino homosexual men amid the scene. In the early 1970s (and well into the 1980s), this area was still a well-known gay male gathering place. The political tensions that emerged between transsexual activists and gay groups were probably a product of sharing this confined social\/urban space. In other words, the need to articulate a separate identity and political agenda emerged from the proximity and shared social space of these social groups (transsexuals, gay men and transvestites) rather than their social distance. Also, while Goudie sees herself as quite distinct from a transvestite, she and other TAO members knew that this distinction was meaningless in the eyes of the police. This blurring is evidenced by the regular reporting of violence and harassment of transvestites and cross-dressers as well as transsexuals in the pages of TAO publications.72 Miami Beach laws outlawing cross-dressing (which were found unconstitutional in 1972 but reportedly still enforced) were used to harass both transvestites and transsexuals. Even given this shared harassment, TAO clearly articulated the specificity of their experiences as transsexuals \u2013 taking pains to explain the ways in which transsexuals had needs and identities different from transvestites, gay men and feminists.\n\nEarlier, I asked how Cuban immigrants, especially those who migrated to the US in 1980, fit into these gender\/sexual schemas. After 1980, Miami underwent a demographic transformation with the mass immigration of Cuban and Haitian immigrants. Many Cuban gender transgressive (male-to-female) immigrants entered the United States as part of the 1980 Mariel Boatlift.73 This particular subgroup is probably the one most likely to be claimed as 'transgender', as Ochoa's pointed critique indicates. How did transsexual activists view these gender transgressive Mariel immigrants? Were they seen as part of the transsexual group? Soon-to-be-transsexuals? Homosexuals? Or something else? The accounts by TAO activists reveal that, prior to 1980, there existed a group of Latinas, including Cuban Americans, who saw themselves as transsexuals and understood themselves as different from gay men and transvestites.\n\nIn her autobiography, Douglas provides some sense of how newly arrived gender transgressive Cubans were seen. She describes the changes in South Miami Beach (what is now known as South Beach) when she returned to the city in 1981 and 1982, shortly after the Mariel migration:\n\nthe Beach was dying. Cuban refugees by the thousands had moved in and had turned ratty South Miami Beach into a Cuban slum... Italian and Jewish stores and restaurants had been taken over by Cubans, one by one. Lovely Lincoln Road had been transformed into a pathetic cheap-goods shopping mall run by Cubans. The Beach had deteriorated so badly I was horrified.74\n\nDouglas interprets the dramatic increase in the Cuban population as a negative turn for this Miami neighbourhood. During this time, Douglas lived in South Miami Beach's Drake Hotel. The Drake, like other South Beach hotel\/apartment buildings, had become home to gender transgressive migrants, many of whom arrived during the Mariel Boatlift, because they provided small, relatively inexpensive, rental units. Douglas felt tormented by the 'young gays and Cuban drag queens' with whom she lived at the Drake.75 A few pages later, Douglas repeats that 'a group of very idiotic, offensive young gays lived there, all prostitutes, and a bunch of Cuban drag queens lived there, too'.76 These quick references suggest that Douglas did not identify the newly arrived Cuban gender transgressive migrants as transsexuals, nor did she see them as part of a group to which she belonged. This outsider status is related to a combination of gender expression, sexual orientation, race\/ethnicity and immigrant status. Based on the framing of the Drake population as 'young gays' and 'Cuban drag queens', it also seems that Douglas did not see the gender transgressive Marielitos as part of the community of homosexual men who lived in Miami Beach prior to 1980. Other sources have commented on how gender transgressive Marielitos challenged the attitudes and lifestyles of gay men who already lived in Miami in part because of their class-based and ethnically distinct expressions.77\n\nTransgender studies demands that contemporary scholars analyse and not assume the relationships between communities and individuals marginalised due to gender and sexual non-conformity. Transgender studies provides two interrelated insights. First, sexual orientation and gender identity are not necessarily related, and we should not assume that a transgressive gender identity corresponds with sexual preference. Second (and perhaps conversely), it is important for scholars to think about relationships between gender transgressive groups that may not see themselves as members of the same identity groups or communities. In other words, transgender studies posits the relationships among a wide continuum of gender transgressive practices. People embodying some characteristics on this continuum might not see themselves as related to others along the continuum. Examining the possible (but not assumed) relationship between gender and sexual orientation and analysing the ways in which different manifestations of gender transgression function socially in relation to one another can only make our scholarship more precise.\n\nApplying these insights, however, is not the same as saying that individuals at different historical moments and in different cultural contexts were transgender. This statement would imply that individuals identified with a particular social identity that emerges from a different social context. My research highlights why we should not assume that 'transgender' identities and alliances existed in historical moments before the term was mobilised. For example, TAO publications reflect that organisation leaders saw a clear distinction between sexual orientation and gender identity. This is most clearly revealed by the tensions that emerged between more gender normative gay men in the area and the organisation. In this way, TAO members reflect a notion of transgender similar to the more socioeconomically privileged transgender activists Valentine discusses. On the other hand, TAO did not really embrace a continuum of transgender expressions either. They made clear distinctions between their members, defined as transsexuals, and other forms of gender transgressors including cross-dressers and transvestites. Also, it is unclear how the mass migration of gender transgressive Cubans was interpreted by the former TAO membership. Douglas's impressions survive, and they mark these recent immigrants as not one 'of us'.\n\nWhile there is still a lot of work left to be done to further explore this issue, it is important to remember that in places like Cuba (and in some US centres of Latino\/a concentration), gender expression was (and is?) seen as related to sexual orientation and sexual desires. As this chapter demonstrates, gendered homosexual identities coexisted with transsexual identities that participants understood as independent from their sexual orientation. While I think it is wrong to label TAO activists as 'homosexuals', I am still not convinced that all the gender transgressive Mariel immigrants were 'transgender'. To place individuals in these categories we need to know something about how they saw themselves, what communities they participated in and what social meanings were available to them in their socio-historical context. These are not always things we can access through the historical record, but I hope this study contributes to the project.\n\nNotes\n\nI am grateful to Susan Stryker for pointing me towards Angela Douglas and the Transsexual Action Organization's documents at the Gay, Lesbian, Bisexual and Transgender Historical Society in San Francisco (GLBTHS). Without her original suggestion of these sources, this project would have never emerged. I met Susan as a result of my participation in the Social Science Research Council's Sexuality Research Fellowship Program, and I remain indebted to that program and its support from the Ford Foundation. Discussions and debates with Joelle Ruby Ryan, transgender studies scholar\/activist and my former advisee, helped me clarify my arguments. I want to thank the staffs at the University of Michigan's Labadie Collection and GLBTHS, especially Willie Walker of the latter who provided great assistance during my first visit to an archive. I am grateful to everyone who provided feedback on earlier versions of this chapter including Nancy San Martin, the co-editors of this book, Kevin P. Murphy and Jennifer M. Spear, two anonymous reviewers and those who attended my presentation at Oberlin College's '\"My Name is My Own\": Queering the Intersections of Race, Class, Gender and Sexuality' series. I want to especially acknowledge the thoughtful, engaged and thorough feedback provided by participants in the Newberry Library Seminar in Borderlands and Latino Studies.\n\n1. Susan Stryker, '(De)Subjugated Knowledges: An Introduction to Transgender Studies', in Susan Stryker and Stephen Whittle (eds), The Transgender Studies Reader (New York: Routledge, 2006), pp. 1\u201318, here p. 3.\n\n2. Stryker, '(De)Subjugated Knowledges', p. 2.\n\n3. David Valentine, Imagining Transgender: An Ethnography of a Category (Durham: Duke University Press, 2007), p. 4.\n\n4. Susana Pe\u00f1a, '\"Obvious Gays\" and the State Gaze: Gay Visibility and Immigration Policy During the 1980 Mariel Boatlift', Journal of the History of Sexuality 16 (2007), pp. 482\u2013514; Susana Pe\u00f1a, 'Visibility and Silence: Mariel and Cuban American Gay Male Experience and Representation', in Eithne Luibh\u00e9id and Lionel Cant\u00fa (eds), Queer Migrations: Sexuality, U.S. Citizenship, and Border Crossings (Minneapolis: University of Minnesota Press, 2005), pp. 125\u201345.\n\n5. Tom\u00e1s Almaguer, 'Chicano Men: A Cartography of Homosexual Identity and Behavior', Differences 3\/2 (1991), pp. 75\u201398.\n\n6. Pe\u00f1a, '\"Obvious Gays\" and the State Gaze'; Pe\u00f1a, 'Visibility and Silence', p. 487. For examples of visible markers associated with homosexuality used by the state, see Marvin Leiner, Sexual Politics in Cuba: Machismo, Homosexuality, and AIDS (Boulder: Westview Press, 1994), pp. 31\u20132; Luis Salas, Social Control and Deviance in Cuba (New York: Praeger, 1979), p. 155.\n\n7. Leiner, Sexual Politics in Cuba, p. 31.\n\n8. See Pe\u00f1a, '\"Obvious Gays\" and the State Gaze'; Pe\u00f1a, 'Visibility and Silence'.\n\n9. Marcia Ochoa, 'Latino\/a Transpopulations', in Marysol Asencio (ed.), Latina\/o Sexualities: Probing Powers, Passions, Practices, and Policies (New Brunswick: Rutgers University Press, 2010), here p. 234.\n\n10. Jaime Cortez, Sexilio\/Sexile, ed. Pato Hebert, tr. Omar Ba\u00f1os in consultation with Adela Vasquez (Los Angeles: Institute for Gay Men's Health, 2004).\n\n11. Discussion of sexual orientation within transgender studies literature usually identifies homosexual orientation in relation to the gender one presents in and identifies with, and not with gender of origin. Due to medicalisation of transsexuality in the United States, only transsexuals who claimed a future heterosexual orientation would be approved for sex reassignment surgery (SRS). In other words, a male-to-female candidate for SRS would be granted permission to transition surgically only if she sexually desired men and only men. Transgender rights activists are extremely critical of the medical policing of transgender populations. When Minter refers to 'transsexual people who are lesbian, gay, or bisexual', he is referring to 'male-to-female transsexuals who are sexually attracted to women or female-to-male transsexuals who are sexually attracted to men'. Sharon Price Minter, 'Do Transsexuals Dream of Gay Rights?: Getting Real About Transgender Inclusion', in Paisley Currah, Richard M. Juang and Sharon Price Minter (eds), Transgender Rights (Minneapolis: University of Minnesota Press, 2006), p. 151.\n\n12. See Ochoa, 'Latino\/a Transpopulations'; Minter, 'Do Transsexuals Dream of Gay Rights?', p. 151. See also Mauro Cabral and Paula Viturro, '(Trans)Sexual Citizenship in Contemporary Argentina', in Currah, Juang and Price Minter (eds), Transgender Rights, pp. 262\u201373; Tim Retzloff, 'Eliding Trans Latino\/a Queer Experience in U.S. LGBT History: Jos\u00e9 Sarria and Sylvia Rivera Reexamined', Centro Journal 19\/1 (2007), pp. 140\u201361; Jessi Gan, '\"Still at the Back of the Bus\": Sylvia Rivera's Struggle', Centro Journal 19\/1 (2007), pp. 124\u201339; Salvador Vidal-Ortiz, 'The Figure of the Transwoman of Color through the Lens Of \"Doing Gender\"', Gender & Society 23 (2009), pp. 99\u2013103.\n\n13. Lawrence La Fountain-Stokes, 'Entre Boleros, Travestismos y Migraciones Translocales: Manuel Ramos Otero, Jorge Merced y El Bolero Fue Mi Ruina Del Teatro Pregones Del Bronx', Revista Iberoamericana 71 (2005), pp. 887\u2013907; Lawrence La Fountain-Stokes, 'Trans\/Bolero\/Drag\/Migration: Music, Cultural Translation, and Diasporic Puerto Rican Theatricalities', WSQ: Women's Studies Quarterly 36\/3\u20134 (2008), pp. 190\u2013209, here p. 194.\n\n14. Valentine, Imagining Transgender, p. 245.\n\n15. Valentine, Imagining Transgender, pp. 4\u20135.\n\n16. Valentine, Imagining Transgender, p. 245.\n\n17. Stryker, '(De)Subjugated Knowledges', p. 4.\n\n18. Susan Stryker, Transgender History (Berkeley: Seal Studies, 2008), p. 86.\n\n19. Douglas went by the names Angela Keyes Douglas and Angela Lynn Douglas. Angela Douglas, Hollywood's Obsession (self-published, 1992), p. 5, Gay, Lesbian, Bisexual, and Transgender Historical Society, San Francisco (hereafter GLBTHS). In addition she went by the name Anita for a while because she feared being associated with the 'Communist' Angela Davis. Moonshadow (August 1975), GLBTHS. All issues of Moonshadow and Mirage from GLBTHS were compiled in a document titled 'Transsexual Action Organization Publications 1972\u20131975' that was 'created and published by Angela Douglas'. After cross-checking this compilation with individual issues archived at University of Michigan's Labadie Collection, it is clear that the collection at GLBTHS is selectively edited and compiled by Douglas. Apparently, Douglas blocked out pictures of herself she found unflattering, intentionally or unintentionally blocked out both lines and chunks of text and reordered pages so that pages from one issue appear to be in a previous issue.\n\n20. Joanne Meyerowitz, How Sex Changed: A History of Transsexuality in the United States (Cambridge: Harvard University Press, 2002), p. 237; Stryker, Transgender History, p. 88.\n\n21. Douglas, Hollywood's Obsession; Angela Lynn Douglas, Triple Jeopardy: The Autobiography of Angela Lynn Douglas (self-published, 1983), GLBTHS.\n\n22. Meyerowitz notes that when Douglas moved TAO to Miami in 1972, the new branch included 'several Latina (Cuban and Puerto Rican) members', but that is the extent of her discussion. Meyerowitz, How Sex Changed, p. 239.\n\n23. Stryker, Transgender History, pp. 88\u20139.\n\n24. Meyerowitz, How Sex Changed, p. 240.\n\n25. Douglas, Triple Jeopardy, p. 5.\n\n26. Douglas, Triple Jeopardy, p. 6.\n\n27. Douglas, Triple Jeopardy, p. 7.\n\n28. Douglas, Triple Jeopardy, pp. 10, 14, 7 respectively.\n\n29. Douglas, Triple Jeopardy, p. 32.\n\n30. Douglas, Triple Jeopardy, p. 38.\n\n31. All the women discussed here are first generation immigrants.\n\n32. Colette Goudie, 'Statement by President Goudie', Moonshadow (September\/October 1974), p. 2, Labadie Collection, University of Michigan Library, Ann Arbor (hereafter UMLC).\n\n33. Mirage 1\/1 (1974), GLBTHS.\n\n34. Mirage 1\/4 (February 1975), GLBTHS.\n\n35. Moonshadow (August 1975), GLBTHS. This article is identified as part 1 of a series on 'Transexual and Intersexual Gods'. I have been unable to find any additional installments of this series. STAR founder Silvia Rivera also identified Santa Barbara as a kindred deity. She 'set up an altar with incense and candles where residents of the STAR House would pray to the saints, particularly to Saint Barbara (reputed to be the saint of queer Latinos)'. Gan, 'Still at the Back of the Bus', p. 134. Salvador Vidal-Ortiz discusses the role of Chango amongst Santeria practitioners who were sexual minorities, emphasising the hypermasculine nature of the god of thunder. He remarks that 'Chang\u00f3's Catholic deity form is Saint Barbara, who in some radical Catholic circles is not well respected because of the idea that Saint Barbara \u2013 not Chang\u00f3 \u2013 used to be a man'. Salvador Vidal-Ortiz, '\"Sexuality\" and \"Gender\" in Santeria: Towards a Queer of Color Critique in the Study of Religion' (unpublished doctoral thesis, City University of New York, 2005), p. 137.\n\n36. Douglas, Triple Jeopardy, p. 47. Also, Douglas describes Goudie's visit to Berkeley. Douglas believes Goudie was jealous because Douglas had undergone surgery, but Goudie had not. Douglas describes sending Goudie back to Miami on an aeroplane, p. 53.\n\n37. This is the second reference to Goudie's mother, China. This reference is notable since no other transsexual's parents are referenced in the autobiography, apart from Douglas's with whom she had a troubled and inconsistent relationship.\n\n38. Douglas, Triple Jeopardy, p. 67.\n\n39. Douglas, Triple Jeopardy, p. 68.\n\n40. Douglas, Triple Jeopardy, p. 39. In all issues of Mirage and Moonshadow, Tara is identified as 'Tara Carn'. However, in Triple Jeopardy, Douglas refers to her as Tara Lopez Carn. I have chosen to use the name used by the publications that involved the editorial input of Carn and other Latinas.\n\n41. Mirage 1\/1 (1974), GLBTHS.\n\n42. Mirage 1\/2 (1974), GLBTHS. Please note this issue does not correspond to the same issue found at UMLC.\n\n43. Douglas, Triple Jeopardy, pp. 44\u20135.\n\n44. Douglas, Triple Jeopardy, pp. 44\u20135. One of these incidents was also reported in Mirage 1\/2 (1974), GLBTHS and UMLC.\n\n45. Mirage 1\/2 (1974), p. 61, GLBTHS.\n\n46. Moonshadow reports that Elliot was one of the first TAO members legally to marry. In this issue, she expresses that she is seeking a divorce from her husband. See Moonshadow (August 1975), GLBTHS. However, I found no confirmation that she actually divorced.\n\n47. Douglas, Triple Jeopardy, p. 39.\n\n48. Douglas, Triple Jeopardy, p. 39.\n\n49. Mirage (Autumn 1974), pp. 24\u20135, GLBTHS.\n\n50. Douglas, Triple Jeopardy, p. 66. Reportedly Kimberly Elliot and her husband are mentioned in Art Kelps's Millbrook: A Narrative of the Early Years of American Psychedelianism (1994; rev. Austin: Original Kleptonian Neo-American Church, 2004), under the pseudonyms Kim and Steve Newell.\n\n51. Occasionally there was also information about gays and lesbians. For example, see story about lesbian visibility in Puerto Rico in Mirage Magazine (Autumn 1974), p. 6.\n\n52. Mirage (February 1975), p. 4, GLBTHS. Rodrigo Navarrete reports that the Miss Venezuela Gay pageant has been held in Venezuela since at least the 1970s. Winners went on to represent Venezuela in international competitions such as Miss Gay Universe. It is likely that the competition referred to in Mirage is Miss Venezuela Gay. Rodrigo Navarrete, 'En una noche tan linda como \u00e9sta: Misses y Misters en la econom\u00eda pol\u00edtica y simb\u00f3lica de la Venezuela actual', in Carlos Colina (ed.), Sabanagay: Disidencia y diversidad sexual en la ciudad (Caracas: Editorial Alfa, 2009), pp. 183\u2013206, here p. 201. Other TAO publications include brief references to Peru, Chile, Cuba, South American nations and Puerto Rico.\n\n53. Mentions of Silvia Rivera and STAR include: Moonshadow (August 1973), GLBTHS; Moonshadow (September 1973), UMLC; Mirage (February 1975), GLBTHS. Holly Woodlawn is mentioned in Mirage (March\/April 1974), GLBTHS.\n\n54. Moonshadow (January\/February 1974), GLBTHS and UMLC.\n\n55. Moonshadow (September 1973), UMLC.\n\n56. Moonshadow (November 1975), GLBTHS.\n\n57. Moonshadow (January\/February 1974), p. 17, GLBTHS and UMLC. Puerto Rico's Comunidad de Orgullo Gay also protested against a 'homophobic song called \"Las Mariposas\"' in 1975. Frances Negr\u00f3n-Muntaner, 'Echoing Stonewall and Other Dilemmas: The Organizational Beginnings of a Gay and Lesbian Agenda in Puerto Rico, 1972\u20131977 (Part II)', Centro Journal 4\/2 (1992), pp. 106\u20137.\n\n58. Article series by John Maguire appeared in the Miami News between 16 and 19 June 1974 and was reprinted in Mirage 1\/2, pp. 22\u20133.\n\n59. Mirage (Autumn 1974), GLBTHS. There is also a reference to a videocassette, Transexualism and TAO, featuring Colette Tisha Goudie and Joann Ocasio in Moonshadow (November 1975).\n\n60. The Miami News articles were reprinted in Mirage (February 1975), GLBTHS.\n\n61. Mirage (February 1975).\n\n62. As cited by Meyerowitz, How Sex Changed, p. 239.\n\n63. Meyerowitz, How Sex Changed, p. 271.\n\n64. Douglas, Triple Jeopardy, p. 46. Dr Brown did operate on Douglas in the late 1970s.\n\n65. Moonshadow (October 1973), UMLC; Moonshadow (July\/August 1974), UMLC; Moonshadow (August 1975), GLBTHS.\n\n66. Angela K. Douglas, 'Transexual and Transvestite Liberation', Mirage 1\/2 (1974), pp. 15\u201316, GLBTHS and UMLC.\n\n67. In her autobiographies, Douglas repeatedly uses strongly derogatory language to refer to gay men and lesbians. For instance, when she confronts Norma's lover, Joan, she refers to her as a 'facsimile of a man'. Douglas, Triple Jeopardy, pp. 16\u201317. Homosexual men are referred to as 'perverts', 'degenerates' and 'faggots' throughout the text.\n\n68. TAO members employed or threatened street protests on several issues. For example, when Miami Beach police threatened to rewrite an anti-cross-dressing ordinance that had been found unconstitutional by the lower courts, Kilo (also identified as Kilopelo and Ramon Lenoa), and 'other local transsexuals and TVs vowed street demonstrations'. 'Transreceiver', Mirage 1\/2 (1974), GLBTHS (does not correspond to same issue in UMLC). Kilo is described as a twenty-two-year-old pre-op TS who was a 'popular performer' who had appeared at the Stonewall club in a production of 'Wild Side Story'. Kilo died in a house fire in 1974\/1975, and specific information about her ethnicity is not provided. 'Transreceiver', Mirage 4 (1975), GLBTHS.\n\n69. Angela K. Douglas, 'Interview with Colette Goudie', Mirage 1\/4 (1975), pp. 9\u201312, GLBTHS.\n\n70. 'Other News', Moonshadow (August 1975), p. 6, GLBTHS.\n\n71. Holly Woodlawn with Jeff Copeland, A Low Life in High Heels: The Holly Woodlawn Story (New York: St Martin's Press, 1991), pp. 37\u20138. For more on Woodlawn, see 'From Puerto Rico with Trash' in Frances Negr\u00f3n-Muntaner, Boricua Pop: Puerto Ricans and the Latinization of American Culture (New York: New York University Press, 2004), pp. 87\u2013114.\n\n72. For example, Moonshadow reported that on 20 July 1973, Goudie and Carn were arrested on Twenty-first Street beach for disorderly conduct. Unlike most instances of police interaction reported on in TAO publications, Goudie and Carn 'reported they were treated well by the police'. Moonshadow (August 1973), GLBTHS.\n\n73. Pe\u00f1a, '\"Obvious Gays\" and the State Gaze'; Pe\u00f1a, 'Visibility and Silence'.\n\n74. Douglas, Triple Jeopardy, p. 67.\n\n75. Douglas, Triple Jeopardy, p. 68.\n\n76. Douglas, Triple Jeopardy, p. 70.\n\n77. Elinor Burkett, 'The Price', Miami Herald, 1 April 1990, pp. 9\u201317.\nIndex\n\nabortion\n\ngenitalia\n\nambiguous\n\nAmerican Civil Liberties Union (ACLU) defence of Sunshine and Health magazine\n\nRoth v. United States\n\nanal intercourse\n\nAntigua\n\nAugier, Susanna\n\nBarbados\n\nBarrios de Chungara, Domitila\n\nbirth control\n\nBoone, Ilsley\n\nCAH see congenital adrenal hyperplasia (CAH)\n\nC\u00e1rdenas, Nancy\n\nCaribbean slave societies\n\nabolitionist literature\n\nAntigua\n\nBarbados\n\nBritish national identity\n\nCreole identity\n\nCreoleana\n\nDominica\n\n'enslaved agency'\n\nfreed women of colour\n\ninter\u2013racial sex\n\nJamaica\n\nprostitution\n\nwhite status\/whiteness\n\nwhite West Indian women\n\nCarn, Tara\n\nCatholic Church\n\nand Nahua culture\n\ncensorship: nudist magazines\n\nchildbirth\n\nchildren\n\ninter\u2013racial\n\nsee also congenital adrenal hyperplasia\n\nChina\n\nfeminism\n\nMay Fourth New Culture period\n\n'Sick Man of Asia'\n\nChinese sexology\n\nclassical texts\n\n'epistemic modernity'\n\neugenics\n\nhomosexuality\n\nbiological and psychological argumentation\n\ncontrol and prevention\n\nhistorical and cultural context\n\ninfluence of Freud\n\npathological status\n\nsocial and nationalistic argumentation\n\ntreatment and cures\n\nlesbianism\n\nPan Guangdan\n\nscientific study of sex\n\nse\n\nsex education\n\nSex Science\n\nsexual difference\n\ntraditional Chinese medicine\n\ntranslation of foreign terms\n\ntranslation of foreign texts\n\nxing\n\nas human nature\n\nneologistic construction in Japanese and Chinese\n\nyin\n\nyu\n\nZhang Jingsheng\n\nCihuacoatl\n\ndepiction in the Codex Borbonicus\n\ndepiction in the Codex Magliabechiano\n\nhair\n\npriests\n\nritual defeat\n\nsacrifices to\n\nshield\n\ntongue\n\nworship of\n\nsee also Nahua culture\n\nclitoral surgery\n\ncolonialism\n\nanti\u2013imperialism and the UN International Women's Year Conference\n\nEgypt\n\nglobalisation and\n\nNahua culture and Spanish conquest\n\nsee also Caribbean slave societies\n\ncongenital adrenal hyperplasia (CAH)\n\ndiagnosis\n\ngender role\n\nmanagement\n\ntreatment\n\nclitoral surgery\n\ncortisone\n\ncortisone\n\nCreole identity\n\nCreoleana\n\ncross\u2013dressing\n\nEgypt: the khawal\n\nNahua culture\n\nCuban American community\n\ngay male culture\n\nhomophobia\n\nreligious practices (Santeria)\n\nDavenport, Charles\n\ndivorce: Egyptian women's rights\n\nDominica\n\nDouglas, Angela\n\nEgypt\n\ncolonialism\n\ncross\u2013dressing: the khawal\n\neugenics\n\nmedicalisation of male sexuality\n\nmedicalisation of marriage\n\nnormative model of heterosexuality\n\nprostitution\n\npublic health campaigns\n\nsexually transmitted diseases\n\nwomen's rights\n\nsee also Islam; Physical Culture magazine\n\nElliot, Kimberley\n\nEllis, Havelock\n\neugenics\n\nChina\n\nEgypt\n\nfamily planning see birth control feminism\n\nChina\n\nIWY Conference 1975 see UN International Women's Year Conference\n\nlesbian feminists\n\nUN International Women's Year Conference\n\nMarxist feminists\n\nwestern sexual liberation agenda\n\nfertility goddesses\n\nfertility rites\n\nFoucault, Michel\n\nFreud, Sigmund\n\nFriedan, Betty\n\nGalton, Francis\n\ngender\n\nseparation from sexuality\n\nnon\u2013western peoples and\n\ntransgender and homosexual identity\n\ngender role\n\nfemininity and masculinity in:\n\nEgypt\n\nNahua culture\n\nCaribbean slave societies\n\nthe United States\n\nGermany: nudist movement\n\nglobalisation\n\nGoudie, Colette Tisha\n\nhermaphroditism (pseudo\u2013)\n\nheteronormativity\n\nAmerican nudist movement\n\nEgypt\n\nhistorical perspective\n\nsexual politics and the UN International Women's Year Conference\n\nhomonormativity\n\nhomophobia\n\nhomosexuality\n\nChina\n\nbiological and psychological argumentation\n\ncontrol and prevention\n\nhistorical and cultural context\n\ninfluence of Freud\n\npathological status\n\nsocial and nationalistic argumentation\n\ntreatments and cures\n\nCuban American gay male culture\n\nmagazine audiences\n\ntransgender identity and\n\nsee also lesbians\/lesbianism\n\nincest\n\nindigenous societies: Nahua see Nahua culture\n\nInternational Nudist Conference (INC)\n\nInternational Women's Year Conference see UN International Women's Year Conference\n\nintersex conditions: medical treatment\n\nsee also congenital adrenal hyperplasia (CAH)\n\nIslam\n\nlaw and legal system\n\nmarriage and divorce\n\npersonal status legislation\n\nmedieval religious texts\n\nsexual morality\n\nJamaica\n\nJapanese language\n\nKinsey, Alfred\n\nLatina\/o transgender communities\n\nand homosexual identity\n\nCarn, Tara\n\nGoudie, Colette Tisha\n\nhomophobia and transphobia\n\npolice harassment\n\nSpanish language\n\nTranssexual Action Organisation (TAO)\n\nlaws and legal systems\n\nIslamic\n\nCaribbean slave societies\n\nmarriage\n\nprohibited sex acts\n\nprostitution\n\nsee also Islam: law and legal system; nudism and the law; obscenity\n\nlesbians\/lesbianism activism\n\nUN International Woman's Year Conference\n\nRelationship with Transsexual Action Organisation\n\nChina\n\nidentity\n\nterminology\n\nsee also homosexuality\n\nmagazines and periodicals\n\nmale physique magazines\n\nMirage (US)\n\nMoonshadow (US)\n\nNational Geographic\n\n(The) Nudist (US)\n\nPhysical Culture (Egypt) see Physical Culture magazine\n\nSex Science (China)\n\nSunshine and Health (US) see Sunshine and Health magazine\n\nMarielitas\n\nMarxist feminists\n\nmedicalisation of sex: Egypt\n\nmale sexuality\n\nmarriage\n\nMexico\n\nIWY Conference 1975 see UN International Women's Year Conference\n\nNahua culture see Nahua culture\n\nNahua culture\n\nabsence of gendered pronouns in Nahuatl\n\nCatholic Church and\n\ncihuateteo\n\ncross\u2013dressing and\n\ndeities\n\nChalchiuhtlicue\n\nCihuacoatl see Cihuacoatl\n\nCoatlicue\n\nCoyolxauhqui\n\ndeath figures and underworld gods: the tzitimime\n\nfertility goddesses\n\nHuitzilopochtli\n\nphallic figures\n\nsacrifices to\n\nTezcatlipoca\n\nTlazolteotl\n\ntongues\n\nworship of\n\ngender complementarity and hierarchy\n\npriests\n\nsexual honour and virtue\n\nsexuality and fertility\n\nsorcery\n\ntlacuilos : iconography\n\nwarriors\n\nNational Geographic magazine\n\nnudist movement\n\nhistorical context\n\nobscenity laws and\n\ndefence of Sunshine and Health magazine\n\nRoth v. United States\n\nracial liberalism\n\nSunshine and Health (US) see Sunshine and Health magazine therapeutic principles\n\nobscenity\n\nChinese sexology\n\nsee also nudism and the law\n\nOrderson, J. W.: Creoleana\n\npaedophilia\n\nPan Guangdan\n\nphallic figures\n\nPhysical Culture magazine\n\nintended audience\n\nreaders' letters\n\nsex education\n\nPolgreen, Joanna\n\nPolgreen, Rachael Pringle\n\narchive and secondary historical accounts\n\nCreoleana\n\nbirth and death\n\ndepiction\n\nencounter with Prince William Henry\n\nmanumission of Joanna Polgreen\n\nname\n\npower and agency\n\nsubjugation of other women\n\nwealth and estate\n\npopulation control\n\npornography\n\nnudist magazines and\n\nsee also Roth v. United States\n\nprostitution\n\nCaribbean slave societies\n\nEgypt\n\nMiami\n\nprostitutes' rights\n\nUN International Women's Year Conference\n\npsychiatry\n\npsychoanalysis\n\nracialised power relations\n\nLatina\/o transgender communities\n\nnudist movement and racial liberalism\n\nsee also Caribbean slave societies\n\nRoth v. United States\n\nRubin, Gayle\n\nSanteria\n\nSchaw, Janet\n\nsex education\n\nChina\n\nEgypt\n\nsex differentiation\n\nsee also gender role\n\nsex\/gender distinction\n\nsex reassignment surgery\n\nsexual liberation\n\nsexual politics\n\nsexuality\n\nseparation from gender\n\nnon\u2013western peoples and\n\ntransgender and homosexual identity\n\nsee also heteronormativity; homosexuality; lesbian\/lesbianism\n\nsexually transmitted diseases\n\nCaribbean slave societies\n\nEgypt\n\nSpock, Benjamin\n\nSunshine and Health magazine\n\narticles on health and homemaking\n\ncensorship of genitalia\n\ndefence by American Civil Liberties Union (ACLU)\n\nefforts to show a range of body types\n\nhomosexual readers\n\nlegal victories and eventual decline\n\npictures of children\n\nSecond World War\n\nsexual objectification of women\n\ntlacuilos\n\ntransgender identity\n\nAfro\u2013Cuban deities\n\nhomosexuality and\n\npolice harassment of transsexuals\n\nsex reassignment surgery\n\ntransphobia\n\nTranssexual Action Organisation (TAO)\n\nCarn, Tara\n\nDouglas, Angela\n\nElliot, Kimberly\n\nGoudie, Colette Tisha\n\nMirage magazine\n\nMoonshadow magazine\n\nrelationship with other political and social identities\n\ntransvestites\n\nTroup, Jonathan\n\nUN International Women's Year Conference\n\nanti\u2013imperialism\n\nconflicting agendas\n\npresumed opposition between sexual freedom and human rights\n\nfamily planning and population control campaigns\n\ngender complementarity\n\nmedia coverage\n\nparticipants\n\nBarrios de Chungara, Domitila\n\nC\u00e1rdenas, Nancy\n\nFriedan, Betty\n\nNGOs\n\nprostitution and\n\nrecognition of women's domestic labour\n\nvenereal diseases see sexually transmitted diseases\n\nWilkins, Lawson\n\nWilliams, Raymond: Keywords\n\nxing\n\nas human nature\n\nneologistic construction in Japanese and Chinese\n\nZhang Dai\n\nZhang Dongmin\n\nZhang Jingsheng\n\nZhang Minyun\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\n_White Bluffs, Hanford Reach National Monument_\n\n_Placid Swan Lake in the Okanogan Highlands_\n\n_Looking toward the Pend Oreille River valley from Sherlock Peak ridge_\n\n_Big Rock is prominent in the Dishman Hills Conservation Area._\n\n_Tall pines and firs silhouetted in evening light on the Shedroof Divide_\n\n_Fawn hunkered in meadows on Clackamas Mountain_\n\n_Palouse River careening through a basalt canyon_\n\n_Blue Mountain's forest fires scorched the edges of Middle Point Ridge._\n\n_Sunset at the Crowell Ridge trailhead below Sullivan Mountain Lookout_\n\n_There's gold in them thar hills (in October) in the Kettles._\n\nDAY HIKING\n\n# Eastern\n\nWashington\n\nKettles\u2013Selkirks\/Columbia Plateau\/Blue Mountains\n\nby Rich Landers   \n& Craig Romano\n\n  | **THE MOUNTAINEERS BOOKS**  \n _is the nonprofit publishing arm of The Mountaineers, an organization founded in 1906 and dedicated to the exploration,_ _preservation, and enjoyment of outdoor and wilderness areas._  \n---|---\n\n1001 SW Klickitat Way, Suite 201, Seattle, WA 98134\n\n\u00a9 2013 by Rich Landers and Craig Romano\n\nAll rights reserved\n\nFirst edition: first printing 2013, second printing 2014\n\nNo part of this book may be reproduced in any form, or by any electronic, mechanical, or other means, without permission in writing from the publisher.\n\nDistributed in the United Kingdom by Cordee, www.cordee.co.uk\n\nManufactured in the United States of America\n\nCopy Editor: Julie Van Pelt  \nBook Design: The Mountaineers Books  \nCover design and layout: Jennifer Shontz, www.redshoedesign.com  \nCartographer: Pease Press Cartography  \nAll photographs by authors unless otherwise noted.\n\nCover photograph: _Gypsy Peak, Eastern Washington's highest summit, as seen from the Salmo Divide Trail_ (Photo by Craig Romano)\n\nFrontispiece: _Copper Butte carpeted with wildflowers_ (Photo by Craig Romano)\n\n_Library of Congress Cataloging-in-Publication Data_  \nLanders, Rich, 1953\u2013\n\nDay hiking Eastern Washington : Kettles\u2013Selkirks, Columbia Plateau, Blue Mountains \/ by Rich Landers and Craig Romano.\n\np. cm.\n\nIncludes index.\n\nISBN 978-1-59485-494-1 (pbk)\u2014ISBN 978-1-59485-495-8 (ebook) 1. Hiking\u2014Washington (State), Eastern\u2014Guidebooks. 2. Washington (State), Eastern\u2014Guidebooks. I. Romano, Craig. II. Title.\n\nGV199.42.W2L36 2013\n\n796.51097971\u2014dc23\n\n2012042303\n\nMaps shown in this book were produced using National Geographic's TOPO! software. For more information, go to www.nationalgeographic.com\/topo.\n\nISBN (paperback): 978-1-59485-494-1  \nISBN (ebook): 978-1-59485-495-8\n\n## Table of Contents\n\n_Legend_\n\n_Overall Map_\n\n_Hikes at a Glance_\n\n_Acknowledgments_\n\n_Preface_\n\n_Introduction_\n\nColumbia Highlands: Okanogan Highlands\n\n1. Similkameen Trail\n\n2. Whistler Canyon and Frog Pond\n\n3. Mount Bonaparte via Antoine Trail\n\n4. Mount Bonaparte via South Side Trail\n\n5. Strawberry Mountain\n\n6. Big Tree Botanical Area\n\n7. Beth and Beaver Lakes\n\n8. Virginia Lilly Trail\n\n9. Pipsissewa Trail\n\n10. Clackamas Mountain\n\n11. Maple Mountain\n\n12. Fir Mountain\n\n13. Swan Lake and Swan Butte\n\n14. Golden Tiger Pathway\n\n15. Curlew Lake Nature Trail\n\nKettle River Range\n\n16. Gibraltar Trail\n\n17. Thirteenmile Canyon\n\n18. Thirteenmile Mountain\n\n19. Edds and Bald Mountains\n\n20. Snow Peak Cabin\n\n21. Sherman Peak\n\n22. Barnaby Buttes\n\n23. White Mountain\n\n24. Columbia Mountain\n\n25. Jungle Hill\n\n26. Wapaloosie Mountain\n\n27. Copper Butte via Marcus Trail\n\n28. Copper Butte via Old Stage Trail\n\n29. Midnight Mountain\n\n30. Mount Leona\n\n31. Ryan Cabin\u2013Stickpin Loop\n\n32. Sentinel Butte\n\n33. Taylor Ridge\n\n34. US Mountain\n\n35. King Mountain\n\n36. Sherman Creek and Log Flume Heritage Site\n\n37. Emerald Lake and Hoodoo Canyon\n\n38. Old Kettle Falls Trail\n\nSelkirk Mountains\n\n39. Frater Lake\n\n40. Big Meadow Lake\n\n41. Rogers Mountain and Gillette Ridge\n\n42. Sherlock Peak\n\n43. Abercrombie Mountain\n\n44. Mill Butte\n\n45. McDowell Lake\n\n46. Sullivan Mill Pond\n\n47. Elk Creek Falls\n\n48. Red Bluff\n\n49. Sullivan Lake Shoreline\n\n50. Hall Mountain\n\n51. Crowell Ridge\n\n52. Gypsy Peak\n\n53. Salmo River\n\n54. Shedroof Mountain (Shedroof Divide)\n\n55. Thunder Creek and Mountain (Shedroof Divide)\n\n56. Mankato Mountain (Shedroof Divide)\n\n57. Grassy Top Mountain\n\n58. Roosevelt Grove of Ancient Cedars\n\n59. Little Grass Mountain\n\n60. Kalispell Rock\n\n61. Hungry Mountain\n\n62. Bead Lake\n\n63. Pend Oreille County Park\n\n64. Mount Spokane Summit\n\n65. Day Mountain\n\n66. Burping Brook Basin\n\n67. Quartz Mountain\n\nAround Spokane\n\n68. Antoine Peak\n\n69. Liberty Lake\n\n70. Saltese Uplands\n\n71. Iller Creek and Rocks of Sharon\n\n72. Eagle Peak\n\n73. Beacon Hill\n\n74. Downtown Spokane Bridges\n\n75. South Hill Bluff\n\n76. Fish Lake Trail\n\n77. James T. Slavin Conservation Area\n\n78. Palisades Park\n\n79. T. J. Meenach Bridge\u2013Fort George Wright (Spokane River)\n\n80. Fort George Wright\u2013Bowl and Pitcher (Spokane River)\n\n81. Bowl and Pitcher (Spokane River)\n\n82. Deep Creek Canyon\n\n83. Indian Painted Rocks\u2013Saint George's School (Little Spokane River)\n\n84. Little Spokane River Overlook\n\n85. McLellan Conservation Area\n\nColumbia Plateau\n\n86. Turnbull National Wildlife Refuge Auto Tour Trails\n\n87. Pine Lakes\n\n88. Frenchman Coulee\n\n89. Quincy Lakes\n\n90. Beezley Hills\n\n91. Steamboat Rock\n\n92. Northrup Canyon\n\n93. Fort Spokane\n\n94. Crab Creek (Columbia National Wildlife Refuge)\n\n95. Frog Lake\n\n96. Hanford Reach North\n\n97. Hanford Reach South\n\n98. Badger Mountain\n\n99. Chamna Natural Preserve\n\n100. Amon Basin\n\n101. Bateman Island\n\n102. Burbank Slough Wildlife Trail\n\n103. Juniper Dunes Wilderness\n\n104. Z Lake\n\n105. Twin Lakes\n\n106. Lakeview Ranch\n\n107. Crab Creek\n\n108. Hog Canyon\n\n109. Fishtrap Lake\n\n110. Escure Ranch\u2013Towell Falls\n\nPalouse Hills\n\n111. Kamiak Butte\n\n112. Palouse Falls\n\nBlue Mountains\n\n113. Lewis and Clark Trail State Park\n\n114. Mill Creek\n\n115. Deadman Peak\n\n116. Middle Point Ridge\n\n117. Sawtooth Ridge\n\n118. Twin Buttes\n\n119. Grizzly Bear Ridge\n\n120. Oregon and West Buttes\n\n121. Panjab Loop\n\n122. Tucannon River\n\n123. Diamond Peak and Sheephead Corral\n\n124. North Fork Asotin Creek\n\n125. Puffer Butte\n\n_Conservation and Trail Organizations_\n\n_Index_\n\nBUT WAIT! THERE'S MORE!\n\nStill need more hikes? See the appendix in the back of this book for information about access to 25 more hikes including:\n\nIn the Okanogan Highlands:\n\n\u2022 McLoughlin Canyon\n\n\u2022 Island Park\n\n\u2022 Fourth of July Ridge\n\n\u2022 Ten Mile Trail\n\n\u2022 Long Lake\n\nIn the Kettle River Range:\n\n\u2022 Profanity Trail\n\nIn the Selkirk Mountains:\n\n\u2022 Pierre Lake Trail\n\n\u2022 Newport Wolf Trails\n\n\u2022 Halliday Trail\n\n\u2022 Silver Creek Trails\n\nIn the Columbia Plateau:\n\n\u2022 Umatilla Rock\n\n\u2022 Blythe and Chukar Lake\n\n\u2022 Saddle Mountain\n\nAround Spokane:\n\n\u2022 McKenzie Conservation Area\n\n\u2022 Glenrose Conservation Area\n\n\u2022 Dwight Merkel Trail\n\n\u2022 Spokane River Centennial Trail\n\n\u2022 West Branch Little Spokane River Wildlife Area\n\n\u2022 Medical and West Medical Lakes\n\n\u2022 Columbia Plateau Trail\n\n\u2022 Sacajawea State Park\n\n\u2022 Badger Mountain (Waterville Plateau)\n\n\u2022 Odessa Craters\n\nIn the Palouse:\n\n\u2022 Lyons Ferry\n\n\u2022 Bill Chipman Palouse Trail\n\n## Hikes at a Glance\n\n## Acknowledgments\n\nWorking on _Day Hiking Eastern Washington_ was fun, exciting, and a lot of hard work. I couldn't have finished this project without the help and support of the following people. A big thanks to my co-author Rich Landers for bringing me onboard. It has been an honor working with you. A big thanks too to all the great people at Mountaineers Books; especially publisher Helen Cherullo, editor in chief Kate Rogers, and project manager Mary Metz for allowing us to hike all over Eastern Washington!\n\nI want to especially acknowledge once again, my editor, Julie Van Pelt. I have worked with her on all my Day Hiking books and I feel that we have hiked the state together. Your professionalism and attention to detail has greatly contributed to making this book a finer volume.\n\nWhile I spent a lot of time in my tent and the back of my pickup researching this book, it was nice to know that in Republic, I had a \"second home.\" A big thanks to Kathy Ciais of the Northern Inn for setting me up with a comfortable base camp in town!\n\nI want to thank the folks that accompanied me on the trail while researching this book: Alicia Glass, Ellen Picken, Joe Theisen, and especially Aaron Theisen. Aaron, you have been a vast source of knowledge on Eastern Washington and your love of the Kettles rivals mine! I look forward to working with you on an upcoming book!\n\nI want to thank God for once again watching over me while on the trail. And lastly, but most importantly, I want to thank my loving wife, Heather, for supporting me while I worked on yet another guidebook. Thanks for hiking with me too, to some of the special places in this book. The Kettles are our mountains!\n\n\u2014 ** _Craig Romano_**\n\nIn the Spokane area, special thanks for help from the Spokane Mountaineers, Inland Northwest Hikers, and fire lookout historian Ray Kresek.\n\n\u2014 ** _Rich Landers_**\n\n## Preface\n\nDay hiking is the root of all outdoor exploration. Before humans backpacked, rode bikes, toured on skis, launched ships, and took off in airplanes, they day hiked. Craig Romano and I explored all those modes of travel before joining to research and write this guidebook involving our most basic travel instinct. When we first met over coffee to chart a collaboration, we discovered we had similar passions for muscle-powered exploration. We're veterans of backpacking adventures in the Northwest, North America, and beyond. Both of us have ridden our bicycles across the United States, climbed the region's tallest mountains, and paddled extensively. We've done as much dirtbagging and sleeping on the ground as some critters that live in the forest.\n\nMost important, both of us settled in the Northwest with an obsession for exploring outback trails\u2014and taking notes along the way. Writing is our profession. Our craft is the vehicle for sharing the sweat equity we've invested in researching worthwhile routes and encouraging conservation of the land and water around them. We consider those our major qualifications, aside from being on our wives' top ten list for handsome men. Promoting day hiking is our way of exposing Eastern Washington's outdoor treasures to the widest base of people, young and old, whether they're trail veterans or taking their first steps out of town. We have enjoyed working together to share this with you.\n\n\u2014 **_Rich Landers_**\n\nIt was Rich Landers' _100 Hikes in the Inland Northwest_ that first lured me east of the Cascades in search of trails in 1989 (a mere four months after settling in Washington)\u2014and I've been an Eastern Washington disciple ever since! The Salmo-Priest Wilderness, Hanford Reach, Kettle River Range, and Blue Mountains rank right up there in my all-time hiking greats list with Mount Rainier, the Olympic Peninsula, and the Columbia River Gorge.\n\nNortheastern Washington in particular is a very special place to me. Curlew Lake State Park in Ferry County was the first place I went camping with a young woman I had met at the University of Washington (sorry Cougs). The Kettles became our mountains and that woman became my wife ten years later at Curlew Lake State Park.\n\nThe Pacific Northwest is blessed with an abundance of natural areas rife with excellent hiking trails\u2014the regions of Eastern Washington among them. But Eastern Washington often delivers more of a wilderness experience than the national parks and wilderness areas of the Cascades. In Eastern Washington, grizzlies, wolves, caribou, wolverines, and lynx still roam the backcountry. Just knowing these majestic megafauna are out there with me is one of the best attributes of hiking this area.\n\nRich and I are excited to share these trails with you. I am honored to be working with the person who first introduced me to the region. Now, with Rich's help, I'm paying it forward.\n\n\u2014 **_Craig Romano_**\n\n_Wetlands have been restored at the James T. Slavin Conservation Area near Spokane._\n\n## Introduction\n\nDay hiking has an attractive cost-benefit ratio compared with other means of venturing outdoors. It requires a minimal investment in equipment for traveling the widest variety of routes. Since day hikers often need little time for packing and planning, they have more time and incentive to discover new places. Carrying less weight, you can cover more ground and tackle more elevation than you could carrying a heavy backpack\u2014with a lower toll on your knees and other body parts. Day hikers are more likely than bikers, paddlers, and backpackers to \"stop and smell the roses\" or snap photos, identify a new bird species through binoculars, investigate a track or scat, take a side trail, or pause to harvest a quart of huckleberries.\n\nBottom line: Day hiking is so cheap and uncomplicated, even doubters are left with few excuses to stay inside. A gray sky and drizzle don't have to be deterrents, since a day hiker can enjoy the vibrant colors of a wet landscape with the promise of heading back to the comfort of a car camp, restaurant, or home. For many people\u2014perhaps all of us at one time or another\u2014this is the way to go.\n\nDay hiking is genuinely good low-impact exercise for the body and soul. It's equally rewarding solo or with a group; a chance to lighten up for a few hours or reflect on what's truly important. As America grows more urban and attached to electronics, day hiking is an attractive antidote to the temptation of being sedentary. Families in particular can take advantage of day hiking within limited budgets and busy schedules while still confronting the \"nature deficit syndrome\" afflicting our nation's youth.\n\nThis book is written to help you discover good walking routes that are virtually under your nose as well as those in choice places you may not have considered. For example, the route connecting eighteen bridges over the Spokane River in downtown Spokane (Hike 74) is so inspirational and handy for Spokane residents, coauthor Rich Landers and his wife annually invite friends to join them on this hike to celebrate their wedding anniversary. Badger Mountain, Chamna Natural Preserve, Amon Basin, and Bateman Island (Hikes 98\u2013101) are located within the Tri-Cities\u2014a place many hikers wouldn't immediately consider for day hiking.\n\nOn the other hand, serious backcountry isn't far away from anyone on the east side of the state. Day hikers with a yen to get away from it all will find fascinating oneday routes in the 7140-acre Juniper Dunes Wilderness just outside of Pasco (Hike 103). Or head to the remote, extreme northeast corner of the state into the 41,335-acre Salmo-Priest Wilderness. One highly rated route leads to a challenging scramble to the top of Gypsy Peak (Hike 52), the highest point in Eastern Washington.\n\nThis book also zeroes in on the best day hikes into more than 200,000 acres of roadless areas proposed for wilderness designation in the Okanogan-Wenatchee and Colville National Forests. Check out the Twin Sisters, Profanity, Snow-Bald, and Thirteenmile Canyon roadless areas of the Kettle River Range (Hikes 17\u201335) and see why proponents consider them wilderness-worthy. We have hiked these regions for years and still discovered new, exciting routes while researching this book. Eastern Washington is big on remote places.\n\nThe hikes in this guidebook are those you can do in a day. The hikes can be shortened or extended, and many can be converted into overnighters and explored as introductions to longer trips. Be our guests! Let these featured trips be your springboard to the best day hikes in the wide-ranging landscape of Eastern Washington, from the sagebrush-steppe flats and canyons of the Columbia Plateau to lush forests and fire lookout sites of past and present. You'll find something for every season of the year. Some of the hikes are in or near towns such as the Tri-Cities, Walla Walla, Lewiston-Clarkston, Republic, and Colville. One group of treks (Hikes 68\u201385) highlights the natural areas being protected in and near Spokane\u2014Washington's second-largest city.\n\nChoose from hikes that are perfect for children, ideal for old friends, welcoming to dogs, or notably splendid with birds or wildflowers. Explore trails of historical relevance or those of special interest to waterfall connoisseurs. Many hikes are likely places for observing wildlife. In time, these experiences will connect you with trails that lead to where you've never been before\u2014to the top of a mountain or another sort of high point in your life. Ultimately, we hope you find a connection with the land surrounding these routes too.\n\n### USING THIS BOOK\n\nThe Day Hiking guidebooks were developed to be easy to use while still providing enough detail to help you explore a region. They include all the information you need to find and enjoy the hikes but leave enough room for you to make your own discoveries. We have hiked every mile of trail described in _Day Hiking Eastern Washington_ so you can follow the directions and advice with confidence. However, conditions can change. More on that later in this introduction.\n\n### What the Ratings Mean\n\nEach hike starts with two subjective ratings: a rating of 1 to 5 stars for overall appeal, and a numerical score of 1 to 5 for a route's difficulty. This is purely subjective and based on our impressions of each route, though the assessments do follow a formula of sorts.\n\nThe overall **rating** is based on scenic beauty, natural wonder, and other unique qualities, such as solitude potential and wildlife-viewing opportunities.\n\n***** | Unmatched hiking adventure, great scenic beauty, and wonderful trail experience\n\n---|---\n\n**** | Excellent experience, sure to please all\n\n*** | A great hike, with one or more fabulous features to enjoy\n\n** | May lack the \"killer view\" but offers lots of little moments to enjoy\n\n* | Worth doing as a refreshing walk, especially if you're in the neighborhood\n\nThe **difficulty** score is based on trail length, overall elevation gain, steepness, and trail conditions. Generally, trails that are rated more difficult (4 or 5) are longer and steeper than average. But it's not a simple equation. A short, steep trail over talus slopes may be rated 5 while a long, smooth trail with little elevation gain may be rated 2.\n\n**5** Extremely difficult: Excessive elevation gain and\/or more than 5 miles one-way\n\n**4** Difficult: Some steep sections, possibly rough or poorly maintained trail\n\n**3** Moderate: A good workout but no real problems\n\n**2** Moderately easy: Relatively flat or short route with good trail\n\n**1** Easy: A relaxing stroll in the woods\n\nTo help explain the difficulty scores, you'll also find **round-trip mileage** (unless otherwise noted as one-way), total **elevation gain** , and **high point**. While we have measured the hikes using GPS and have consulted maps, a trip's distance can vary depending on how you customize the route. The elevation gain measures the _cumulative_ gain and loss you'll encounter on a trip, accounting for all significant changes in elevation along the way. As for the trip's high point, it's worth noting that not all high points are at the end of the trail\u2014a route may run over a high ridge before dropping to a lake basin, for instance.\n\nThe recommended **season** is a tool to help you choose a hike. Many trails can be enjoyed from the time they lose their winter snowpack right up until they're buried in fresh snow the following fall. But snowpacks vary from year to year, so a trail that's open in May one year may be snow-covered until July the next. The hiking season for each trail is an estimate. Contact land managers for current conditions.\n\nThe **maps** noted for each hike are usually 7.5-minute USGS topographical maps. However, we also list maps available from local groups, agencies, or national forests. USGS topo maps\u2014highly recommended for hikes in remote areas\u2014are available online and from some retail stores. The **contact** listed for each hike should have information about localized maps. Each hike lists the area's governing agency, along with website and\/or phone number, so you can get current access and trail conditions. **Notes** for each trip detail things like permits required, road conditions, possible hazards, and seasonal closures. Trailhead **GPS coordinates** are provided to help get you to the trail\u2014and back to the car should you wander off-trail.\n\nFinally, **icons** at the start of each hike give a quick overview of what each trail has to offer:\n\n  | Kid-friendly\n\n---|---\n\n  | Dog-friendly\n\n  | Exceptional wildflowers in season\n\n  | Exceptional waterfalls\n\n  | Exceptional old growth\n\n  | Fishing options\n\n  | Bird-watching\n\n  | Historical relevance\n\n  | Endangered trail (threatened with loss or closure)\n\n  | Saved trail (rescued from permanent loss)\n\nThe route descriptions tell you what might be found on the hike, including geographic features, scenic potential, flora and fauna, and more. Thorough driving directions from the nearest large town or geographic feature will get you to the trailhead. Options for extending your trip round out many hikes.\n\n### PERMITS, REGULATIONS, AND FEES\n\nHikers have a responsibility to know and abide by regulations governing the areas they explore. As our public lands have become increasingly popular, and as both state and federal funding have declined, regulations and permits have become components in managing our natural heritage. The US Forest Service, National Park Service, Washington State Parks, and other land managers have set sometimes complex regulations governing the use of these lands.\n\n_Beargrass blooms along Eagle Crest Trail in the Mount Spokane Nordic skiing area._\n\n**Federal lands:** National forests in Eastern Washington may or may not charge parking fees at trailheads. Most Umatilla and Okanogan-Wenatchee National Forest parking areas require that vehicles display a Northwest Forest Pass or federal equivalent (like the America the Beautiful Pass described below). The Colville National Forest does not require the Northwest Forest Pass, except at one site. The Northwest Forest Pass sells for $5 a day or $30 for an annual pass that's good throughout Washington and Oregon.\n\nHikers who frequent national parks and forests should consider buying the annual America the Beautiful Pass (<http:\/\/store.usgs.gov\/pass>) for $80. This pass grants the driver and three other adults in a vehicle access to all federal recreation sites that charge a day-use fee (children under sixteen are admitted free). These include national parks, national forests, national wildlife refuges, and Bureau of Land Management areas throughout the country. For example, without the American the Beautiful pass (or a federal Duck Stamp), visitors have to pay a $3 day-use vehicle entry fee to Turnbull National Wildlife Refuge (Hikes 86 and 87).\n\n**State lands:** Washington State Parks and other state lands adopted the Discover Pass (www.discoverpass.wa.gov) for vehicle access in 2011. This is a political solution to keep the underfunded state parks system alive. Until lawmakers find another solution, a Discover Pass costs $10 per vehicle per day or $30 for up to two vehicles annually. Purchase the pass online or at many retail outlets or, better yet, from a state park office to avoid a $5 handling fee.\n\n**Local areas:** Local parks, such as Liberty Lake County Park (Hike 69), may charge an entrance fee at certain times of year.\n\nAll required fees and permits (subject to change) are listed for each hike.\n\nWHOSE LAND IS THIS?\n\nAlmost all of the hikes in this book are on public land. That is, they belong to you and the rest of the citizenry. What's confusing, however, is who exactly is in charge of this public trust. More than half a dozen different governing agencies manage lands described in this guide.\n\nMost of the hikes are on land administered by the **US Forest Service**. A division of the Department of Agriculture, the Forest Service strives to \"sustain the health, diversity, and productivity of the nation's forests and grasslands to meet the needs of present and future generations.\" The agency purports to do this under the notion of \"multiple-use.\" However, supplying timber products, providing grazing allotments, managing wildlife habitat, and developing motorized and nonmotorized recreation options have a tendency to conflict with each other. Some of these uses may not exactly sustain the health of the forest either. Several areas within the forests featured in this book have been afforded stringent protections as federal wilderness (see \"Untrammeled Eastern Washington\" sidebar in the Blue Mountains section), barring development, roads, and motorized recreation.\n\nThe **US Bureau of Land Management** manages 245 million acres across the country, more than any other agency. Uses on these lands include development for energy, grazing, recreation, wildlife, and conservation. BLM areas featured in this book are off-limits to motorized recreation but open to limited livestock grazing.\n\nThe **National Wildlife Refuge System** is a network of lands and waters for the conservation, management, and, where appropriate, restoration of the fish, wildlife, and plant resources and their habitats. Recreation also is encouraged on most refuges, as well as limited hunting and fishing in some areas.\n\n**State and county park lands** are managed primarily for recreation and preservation.\n\n**State Department of Natural Resources lands** are managed primarily for timber harvest, with pockets of natural-area preserves.\n\n**State wildlife areas** , overseen by the Department of Fish and Wildlife, are managed primarily for protecting habitat while providing access to wildlife-related recreation, including hunting and fishing.\n\nBe aware of the agency that manages the land you'll be hiking on, for each agency has its own rules and fees. And remember, we have a say in how public lands are managed. Agencies have planning periods during which public participation can have a big impact.\n\n\u2014 _C. R._\n\n### WEATHER\n\nEastern Washington ranges from low elevations along the Snake and Columbia Rivers, through the open scablands, to high elevations in the Selkirk Mountains. You could experience the gamut, from T-shirt weather to a snow blizzard in a day's drive. The Juniper Dunes area near Pasco receives about 8 inches of rainfall a year, while the wet cedar forests in the Salmo-Priest Wilderness average around 50 inches of annual precipitation.\n\n_Summer storms build over Abercrombie and Hooknose Mountains._\n\nLate February into June are premier times to find the Columbia Plateau snow-free, welcoming spring migrant birds, and blooming with wildflowers. The heat that bears down on the Channeled Scablands of the plateau starting in late June through August spurs on the wildflower bloom and huckleberry crop in the mountains. Trails in the higher elevations of the Columbia and Okanogan Highlands, the Selkirks, and the Blue Mountains aren't snow-free until June or early July. September and October are the months when all of Eastern Washington is accessible and weather conditions are generally most inviting across the board.\n\nGeneralities aside, short-term forecasts are key to planning the safest and most enjoyable trip. A high-pressure system could offer a week of premier weather in May, while a low-pressure system could present a week of wetness in June. We have experienced snow in the high country in August two days after the temperatures soared into the 90s.\n\nPlan your hike according to your weather preference. But no matter where you hike in the region, the following should be standard procedure:\n\n\u2022 Check the National Weather Service forecast for the region before you go, and plan accordingly.\n\n\u2022 Pack raingear. Even in arid areas, being caught in a sudden rain and windstorm without adequate clothing can lead to hypothermia (loss of body temperature), which is deadly if not immediately treated. Most hiking fatalities related to hypothermia (exposure) occur during the milder months when hikers get caught in a sudden change of temperature accompanied by winds. Always carry extra clothing layers, including rain and wind protection.\n\nBEFORE LIGHTNING STRIKES\n\nThunderstorms are common throughout Eastern Washington, especially during the summer. The lightning produced by these powerful storms poses a threat worth taking seriously. If you hear thunder, you're within striking distance.\n\nWaste no time getting off summits or exposed ridges and away from water. Take shelter, but not under big trees or rock ledges. The taller an object is relative to its immediate surroundings, the more likely it is to be struck by lightning. Any tree can be a conductor, although hunkering in a grove of small trees or under a blowdown is a bit safer than being around an area's taller trees.\n\nAfternoon is prime time for thunderstorms during summer, especially in higher elevations. Savvy hikers and climbers time ascents to the high country for early morning so they can retreat before noon from open alpine areas where lightning is more likely to pound. The safest place to be in a lightning storm is sitting in your vehicle.\n\nIf you're caught in an electrical storm, seek the lowest point in the area; crouch down, making minimal contact with the ground; and wait for the boomer to pass. Remove metal-framed packs and ditch the trekking poles! Wrap yourself in raingear or a tarp for protection from the wind and rain. No, a foam sleeping pad will not insulate you from lightning that strikes the ground.\n\n\u2014 _R. L._\n\nEpisodes of rain and snow also create conditions and hazards to consider. River and creek crossings can be extremely dangerous after periods of heavy rain or snowmelt. Always use caution and sound judgment when fording.\n\nSnowfields left over from the previous winter's snowpack can be hazardous, especially for hikers who head into steep high-country slopes early in the hiking season. Depending on the severity of the past winter, and the weather conditions of the spring and early summer, some trails may not melt out until well into summer. In addition to treacherous footing and difficulties in routefinding, lingering snowfields can be prone to avalanches or slides. Use caution crossing them. You may need to review techniques for self-arrest.\n\nStrong winds can be a concern anywhere in the region. Avoid hiking during high winds, which carry with them the hazards of falling trees and branches.\n\n### ROAD AND TRAIL CONDITIONS\n\nTrails generally vary little year to year, but change can occur. A heavy storm can cause a river to jump its channel, washing out sections of a trail or access road in moments. Windstorms can blow down trees across trails by the hundreds, making paths unhikable. And snow can bury trails well into the summer. Avalanches, landslides, and forest fires can damage or obliterate trails. Lack of funding is also responsible for trail neglect and degradation.\n\nOn the other hand, some trails are created, improved or rerouted over the course of time. Groups such as the Washington Trails Association, Kettle Range Conservation Group, the Spokane Mountaineers, and friends groups for state parks and federal refuges have been sources of countless hours of volunteer labor, helping local, state, and federal crews build and maintain trails in this book. These groups and more are listed at the end of the book to help you connect with them\u2014and perhaps add some muscle power or other expertise to the cause.\n\n_Cedars border the gently graded trail into the Salmo River Basin._\n\nManagement decisions can have greater impacts than floods and fires. For example, as national forests have cut back on timber production for reasons ranging from watershed damage to political and market forces, many forest roads have been closed and some have been decommissioned (see Hike 59, Little Grass Mountain). This can be good\u2014as in providing more solitude for a person willing to walk away from motor vehicles. In many cases, closed forest roads can become excellent hiking routes. In other cases, a closed road can be an inconvenience, adding distance to the approach. In the worst cases, abandoned roads wash out or grow over, cutting off access entirely.\n\nSome trails are being neglected or abandoned because of budget shortfalls. In other cases, the usage of a trail might change from hiking to allowing motorized vehicles such as dirt bikes and ATVs. Only a few trails in this book are open to motorized vehicles, sometimes for short periods, such as at Towell Falls at Escure Ranch (Hike 110) or the Clackamas Mountain area (Hikes 10 and 11), where motorbikes are allowed but rarely encountered. The value of the routes override the possible disruption. Where motorized vehicles are prohibited, hikers still might share the route with mountain bikers and\/or equestrians. Occasional conflicts are possible, but it's more productive for hikers to think of these other trail users as allies in the cause for more and better trails.\n\nThis guide includes several trails that are in danger of becoming unhikable because of threats from motorized use, access, or other issues. These Endangered Trails are marked with a special icon in this book. On the other side of the coin, we've had some great trail successes in recent years, thanks in large part to a massive volunteer movement spearheaded by statewide and local organizations. These Saved Trails are marked too, to help show that individual efforts do make a difference. As you enjoy these Saved Trails, stop to consider the contributions made by fellow hikers. And consider getting involved.\n\nEach hike in this book lists the land manager's contact information so you can find out about current road and trail conditions prior to your trip.\n\n### WILDERNESS ETHICS\n\nEnsuring the long-term survival of our trails and the wildlands they cross requires a group effort. To avoid fouling our own nest, hikers have nourished a \"wilderness ethic\" to leave the land as good as or better than we found it.\n\nInstead of merely complying with no-litter rules, bring a bag and carve out time to pick up after others. Avoid creating unauthorized trails. Rest on rock and camp on bare ground when possible to avoid tramping down and killing vegetation in fragile dryland or alpine areas. Don't pollute streams or lakes with soaps or chemicals. In the words of others who've boiled the ethic down: Take only pictures, leave only footprints.\n\nWilderness ethics, most of which apply to visiting all public open-space lands, rise from attitude and awareness rather than rules and regulations. The following are the accepted principles of the Leave No Trace concept:\n\n**Plan ahead and prepare:** Know the regulations of the area you plan to visit. Call ahead for current conditions. Check the weather forecast. Bring proper gear. Plan for emergencies. Consider the abilities of your group. Assure that the group understands wilderness ethics. Protect food from bears and other critters to avoid turning them into nuisance\u2014or dangerous\u2014beggars.\n\n**Travel and camp on durable surfaces:** Stay on the trail. Avoid tramping parallel trails to talk with a companion or avoid mud. Don't cut switchbacks. Picnic and camp on hard, dry surfaces such as rock, sand, gravel, or pine-needle duff rather than on vegetation or meadows. Take special care to avoid tramping or camping within 100 feet of backcountry stream or lake shorelines.\n\n**Dispose of waste properly:** Pack out everything you pack in. Human food and trash is unhealthy for animals and leads to harmful habituation by animals to human presence and food. Bury human waste at least 100 feet from water sources, trails, or campsites. Use toilet paper sparingly and pack it out. A plastic bag confines odors effectively and double bagging it prevents any accidental contamination.\n\n**Leave what you find:** Wildflowers, fossils, and other natural objects of beauty or interest should be left for others to discover and enjoy.\n\n**Minimize campfire impacts:** Where fires are permitted, use existing fire rings if possible. Never cut live trees or branches for firewood. Most fires are not necessary, but if you must build one, be sure it's dead out when you leave. A small, thoughtfully built fire can be completely extinguished and the ashes removed or buried to leave no trace.\n\n**Respect wildlife:** Never feed wild animals or leave food available to them. This is for your own good and the protection of those who follow, regardless of the size of the critter. Observe from a distance, for your safety as well as to prevent the animal from unnecessary exertion or danger. Keep pets under control so they don't disturb wildlife.\n\n**Be considerate of other visitors:** Read on to find out how.\n\n### TRAIL ETIQUETTE\n\nWhile wilderness ethics hone our respect for the land, trail etiquette steers us into balance with others we might see along the way. Common sense and courtesy will smooth out the possible bumps in any encounter. Beyond that, here are a few guidelines:\n\n\u2022 **Right-of-way:** When meeting other hikers, the uphill group has the right-of-way. There are two general reasons for this. First, on steep ascents, hikers may be watching the trail and might not notice the approach of descending hikers until they're face-to-face. More importantly, it's easier for descending hikers to break their stride and step off the trail than it is for those who have gotten into a good, climbing rhythm. But by all means, if you're the uphill trekker and you wish to grant passage to oncoming hikers, go right ahead with this act of trail kindness.\n\n\u2022 **Moving off-trail:** When meeting other user groups (like bicyclists and horseback riders), the hiker should yield. This is because hikers are more mobile and flexible than other users.\n\n\u2022 **Encountering horses:** When meeting horseback riders, the hiker should step off the downhill side of the trail unless the terrain makes this difficult or dangerous. All hikers in a group should move to the same side of the trail. Remain visible and talk in a normal voice to the riders. This calms the horses. If hiking with a dog, keep your buddy very close and under control.\n\n\u2022 **Hiking with dogs:** Hikers should have their dog on a leash or under very strict voice command at all times while on the trail. Some areas require dogs to be on-leash, such as state and local parks, national wildlife refuges, and Spokane County Conservation Areas. One of the most contentious issues in hiking circles is whether dogs should be allowed on trails. Some people are uncomfortable with loose dogs that rush toward them\u2014and they may have had a bad experience to justify that. Respect their right to a dog-free space. On the other hand, a well-behaved leashed dog can help warm up these hikers to canine companions.\n\n_Rich Landers' English setter detects a dusky grouse on Crowell Ridge in the Salmo-Priest Wilderness._\n\n\u2022 **Never roll rocks off trails or cliffs:** You risk injuring someone or something below.\n\n### WATER\n\nAs a general rule, treat all backcountry water sources to avoid Giardia, waterborne parasites, and other aquatic nasties. Assume that all water is contaminated. Treating water can be as simple as boiling it, using an ultraviolet light purifier, chemically purifying it with iodine tablets, or pumping it through a water filter and purifier. Note: Pump units labeled as filters generally remove everything but viruses, which are too small to be filtered out. Pumps labeled as purifiers use a chemical element\u2014usually iodine\u2014to render viruses inactive after filtering out all the other bugs.\n\n### FISHING\n\nSome hikers consider a fishing rod essential gear in their daypacks. A fishing icon at the start of a hike in this book indicates the trip will bring you into the realm of angling opportunity. However, fishing is a highly regulated sport, with seasons, gear restrictions, and catch limits that can vary by fish species as well as by stream or lake. Anglers age fifteen and older must have a Washington State fishing license. Regulations and requirements are spelled out in the Sport Fishing Rules pamphlet available at the Washington Department of Fish and Wildlife website (www.wdfw.wa.gov).\n\n### HIKING AMONG HUNTERS\n\nMany public lands are opened to hunting. The season dates vary, but generally big-game hunting begins in early August and ends in December. While hiking in areas frequented by hunters, it's best to make yourself visible by donning an orange cap and vest. If hiking with a dog, your buddy should wear an orange vest, too. The majority of hunters are responsible, decent folks (and conservationists who provide significant support for public lands), and you should have little concern when encountering them in the backcountry. Still, if being around outdoors-people schlepping rifles is unnerving to you, stick to hiking where hunting is prohibited, such as in national and state parks and county conservation areas.\n\nSAFETY AMONG PREDATORS: TOP FIVE TIPS\n\nSeveral notable \"hunters\" roam Eastern Washington, including bears, cougars, and wolves. Like their human counterparts, they rarely pose a threat to hikers. Keep it that way by following the top five tips experts suggest:\n\n**1. Bear spray** can be an effective deterrent in many tense wildlife encounters.\n\n**2. Store food and garbage** in vehicles or other places where wildlife won't be attracted to it.\n\n**3. Don't run** when confronted by bears, cougars, or wolves. This can trigger the predator's instinct to chase prey.\n\n**4. Keep dogs leashed** and under control.\n\n**5. Closely spaced groups** of four or more hikers are an effective deterrent in confrontations with bears, cougars, and wolves. A lone person far ahead or behind a group is at higher risk.\n\n\u2014 _R. L._\n\n### WILDLIFE\n\n### The Bear Essentials\n\nEastern Washington's forested areas harbor a healthy population of black bears, especially the Columbia Highlands and Selkirk Mountains in the northeast and the Blue Mountains in the south. The Selkirks have the bonus of being home to some grizzly bears.\n\nMost hikers consider themselves lucky to catch a glimpse of a bear's bottom as it reacts normally to human scent\u2014by running away. But occasionally a bruin may want to get a look at you. In very rare cases, a bear may act aggressively. To avoid an un-bearable encounter, heed the following advice compiled from bear experts:\n\n\u2022 **Respect a bear's need for space.** If you see a bear in the distance, make a wide detour around it. If that's not possible, leave the area.\n\n\u2022 **Avoid direct eye contact** if you encounter a bear at close range, and, most important, **do not run.**\n\n\u2022 **Talk in a low, calm manner** to the bear to help identify yourself as a human.\n\n\u2022 **Wave your arms slowly** above your head to make yourself look taller.\n\n\u2022 **Slowly move upwind** of the bear if you can do so without crowding the bear. The bear's strongest sense is its sense of smell, and if it can sniff you and identify you as human, it may retreat.\n\n\u2022 **Know how to interpret bear actions.** A nervous bear will often rumble in its chest, clack its teeth, and \"pop\" its jaw. It may paw the ground and swing its head violently side to side. If the bear does this, watch it closely (without staring directly at it). Continue to speak low and calmly.\n\n\u2022 **If you cannot safely move away from the bear, and the animal does not flee,** try to scare it away by clapping your hands or yelling.\n\n\u2022 **A bear may bluff-charge** \u2014run at you but stop well before reaching you\u2014to try and intimidate you. Resist the urge to run, as that would turn the bluff into a real charge and you will not be able to outrun the bear.\n\n\u2022 **In the case of a bear attack** , a human without the benefit of bear spray should react differently depending on whether the bear is being predatory or defensive. **In the case of a predatory confrontation** (more typical of the rare black bear that's stalking you), fight back aggressively. **In the case of a defensive confrontation** (more typical of grizzly encounters, especially sows with cubs or food caches), drop to the ground and play dead if contact is about to be made. Lie on your stomach, clasp hands behind your neck, and use your elbows and toes to avoid being rolled over. If the bear succeeds in rolling you over, keep rolling until you're on your stomach. Remain still and try not to struggle or scream. A defensive bear will stop attacking once it feels it has stopped the threat. Do not move until you're sure the bear has left the area.\n\nTHE BENEFITS OF BEAR SPRAY\n\nBear spray is highly recommended for people who hike in bear country, especially grizzly bear country. It's far more effective than a firearm, according to surveys conducted in Alaska. It's easier to hit the target, and both the humans and the bear have a good chance of coming out of an encounter alive. Win-win. Wildlife biologists also say it can be effective in the rare encounter with gray wolves, which are expanding in Washington.\n\nBuy cans labeled \"bear spray,\" not \"pepper spray.\" There can be a difference in the active ingredients as well as in the nozzle. Buy cans 12 ounces or larger that indicate they will spray for at least 9 seconds. Bear spray should be used in bursts. A bear that's deterred by the first burst could advance again, and you want to have more spray left in the can.\n\nCarry bear spray in a holster readily accessible on a pack strap or belt.\n\nIf bear spray must be deployed, use two hands and shoot a burst on the ground directly in front of the bear to form a cloud-like barrier that may deter the bear from advancing. Montana bear-spray experts who studied how people perform using bear spray found the force of the propellant usually pivoted the can in a user's hand so the spray was going into the air above the target. While they were shooting into the sky, disabling birds and butterflies, a bear would advance directly under the cloud, unaffected. The spray should be aimed down in front of the bear. When the spray hits the ground, it billows up and creates a barrier most bears will not want to penetrate. Stand your ground and continue shooting bursts of spray just ahead of the bear or into its face as needed.\n\nOnline information sources include the Washington Department of Fish and Wildlife (<http:\/\/wdfw.wa.gov\/living>) and the Center for Wildlife Information (www.centerforwildlifeinformation.org).\n\n\u2014 _R. L._\n\n### WHERE COUGARS ROAM\n\nCougars, also called mountain lions, are among the most secretive of the apex predators lurking in the wilds of Eastern Washington. They're linked to virtually anywhere deer are found in good numbers. Even though it's extremely rare even for avid outdoor folks to see a cougar, they're around. Therefore, it's wise to know a bit about _Felix concolor_.\n\nCougars are curious critters (after all, they're cats). They will follow hikers simply to see what kind of beasts we are, but they rarely (almost never) attack adult humans. Heed the following recommendations of the Washington Department of Fish and Wildlife:\n\n**While recreating in cougar habitat:**\n\n\u2022 Keep small children close to the group, preferably in plain sight just ahead of you.\n\n\u2022 Don't approach dead animals, especially deer or elk; they could have been cougar prey left for a later meal.\n\n_The Roosevelt Grove of Ancient Cedars protects 2000-year-old specimens._\n\n**If you encounter a cougar:**\n\n\u2022 **Stop, stand tall, and don't run.** A cougar's instinct is to chase. Pick up small children.\n\n\u2022 **Don't approach the animal** , especially if it's near a kill or with kittens.\n\n\u2022 **Try to appear larger than the cougar.** Don't crouch down or try to hide.\n\n\u2022 **Never take your eyes off the animal or turn your back.**\n\n\u2022 **If the animal displays aggressive behavior, shout, wave your arms, and throw rocks.** The idea is to convince the cougar that you are not prey, but a potential danger.\n\n### THE WOLF IS BACK\n\nAfter humans used guns, traps, and poison to extirpate the gray wolf from Washington and the rest of the West by the 1940s, endangered species legislation, followed by reintroductions in Yellowstone Park and Idaho wilderness areas in the mid-1990s, paved the way for a wolf comeback.\n\nWolves have not been released in Washington, but they are naturally moving in and staking out territories. Washington's first recovery-era breeding pack was documented in the Okanogan-Chelan County region in 2008. In 2012, wildlife biologists confirmed nine breeding packs and suspected other packs had been formed.\n\nWolf-country hikes in this book include those in the Columbia and Okanogan Highlands, the Selkirk Mountains\u2014which has the highest known concentrations\u2014and the Blue Mountains. Hikers who frequent these areas have a decent chance of hearing wolves howl. That said, resist the temptation to approach wolves, their kills, or dens.\n\nShould you have a close encounter with wolves while hiking, Washington Fish and Wildlife experts recommend the following:\n\n\u2022 **Stand tall** and make yourself look larger.\n\n\u2022 **Act aggressively** , making noise, throwing objects, waving clothing.\n\n\u2022 **Slowly back away.**\n\n\u2022 **Maintain eye contact** \u2014this is different than the recommendation for confrontations with bears.\n\n\u2022 **Don't run** or turn your back to a wolf.\n\n\u2022 **Keep dogs on-leash and under control.** This is critical in wolf country. Wolves view dogs as competitors or territorial intruders and have attacked and killed them, especially in remote areas.\n\n### GIVE MOOSE THEIR SPACE\n\nWashington's entire population of about a thousand moose lives in Eastern Washington, mostly in the northeast quarter. They can be found on many of the trails in this book, including those near Spokane. Despite their docile demeanor, moose can be aggressive, especially:\n\n\u2022 In late spring and early summer, when a cow feels her very young calf is in danger\n\n\u2022 In fall, when a breeding bull is competitive and agitated\n\n\u2022 In winter, when moose are hungry and tired from walking in deep snow\n\n\u2022 Anytime dogs chase or bark at them\n\n\u2022 Anytime people approach them too closely\n\nIf you encounter a moose, don't approach it. A moose that sees you and walks slowly toward you is not trying to be your friend. It's probably warning you to keep away (or looking for a handout if someone has been foolish enough to give it food). A moose can easily weigh more than 600 pounds and it's as unpredictable as a bison. Give it lots of space. Back off; change direction; look for the nearest tree, fence, building, or other obstruction to hide behind if the moose is becoming aggressive. Enjoy the animal from a distance.\n\n_Hiking to the summit of Mount Kit Carson in Mount Spokane State Park_\n\nIf you're charged by a moose, don't fall to the ground and play dead\u2014you'll get pummeled by hooves. If a moose knocks you down, it may continue running, or it could start stomping and kicking. Curl up in a ball, protect your head with your arms and hands, and hold still. Don't move or try to get up until the moose moves a safe distance away, or it may renew its attack.\n\n### PLANTS AND CRITTERS WITH A BITE\n\nPoison oak and poison ivy are found along hiking routes in Eastern Washington, as are ticks (especially in early season) and rattlesnakes (in certain areas during warm months). Don't be alarmed\u2014just be aware.\n\n**Rattlesnakes:** Rattlesnakes generally keep to themselves. If you get too close, they'll usually let you know by rattling their tails. Fair enough! Simply move away slowly and go widely around the snake. Problem solved.\n\nRattlesnake bites are very rare. The two most common scenarios in which a hiker might get bit are:\n\n\u2022 Climbing through rock outcroppings and accidentally stepping or reaching a hand to a ledge where a snake is resting.\n\n\u2022 Messing with a snake intentionally. Never try to catch, provoke, or pursue a rattlesnake.\n\nShould you be bitten by a rattlesnake, regardless of its size, remain calm. Wash the bite. Immobilize the limb. Apply a wet wrap. Seek medical attention immediately.\n\n**Ticks:** Ticks want blood. These hard-shelled arachnids wait in grass and on shrubs or leaves for the chance to cling onto any warm-blooded critter, including you. If they go unnoticed, they'll eventually attach and engorge themselves as they feed on the blood of their host. The main concern in Eastern Washington is their role as a vector for disease, such as relapsing fever and Rocky Mountain spotted fever.\n\n_Female Rocky Mountain wood tick_ (Photo by James Gathany, Center for Disease Control)\n\nTicks are found throughout Eastern Washington. They become active as early as late February in the grass and sage of Columbia Basin's Channeled Scablands. From April well into June, they're notably active up into the low forest areas.\n\nDuring tick season, take precautions to keep ticks from gaining contact with your skin. Wear long sleeves, tuck pant legs into socks, and check yourself and your companions regularly (and your dog too). If you wear convertible hiking pants, check the flap of material that covers the zipper of the removable pant legs. Ticks will crawl up and snuggle under that flap.\n\nBefore going hiking, consider using permethrin to treat the lower leg and waist of your pants and the collar and sleeve cuffs of your shirt. Treated hats are helpful too. DEET repellent is effective.\n\nIf one of the little buggers has fastened himself to you, gently squeeze its head right next to the skin with your fingers or tweezers. Pull slowly and steadily and the tick will come free, mouth parts and all. Wash and disinfect the bite area. Monitor the bite. If a rash develops, see a doctor.\n\n**Poison oak and poison ivy:** Poison ivy, and poison oak to a lesser extent, is found in the lower elevations of Eastern Washington. The adage we all heard as kids still works: Leaves of three, let them be.\n\nBoth can grow as a vine, shrub, or brush, although poison ivy in this region tends to grow mostly along the ground. The leaves and twigs of these plants contain urushiol, a surface oil that causes an allergic reaction in most people who contact it with their skin. Symptoms range from mild itching to blistering, and the reaction can last up to two weeks, inflicting discomfort. Wearing long pants and long-sleeve shirts can help you avoid contact, but it's important to be able to identify the plants. Leaves of three is your first clue, but even the leafless, hairy stems contain the irritant oils.\n\n_Summer wildflowers on the Snow Peak Trail_\n\nIf your skin contacts poison ivy or poison oak, immediately wash the area with a high volume of water. Go into a stream or lake if possible so you can dilute the oil and get it off rather than just spread it around on your skin. By 30 minutes after contact, most of the oil has been absorbed into your skin and can't be washed off. Urushiol can also remain active on clothing and your dog. Both should be thoroughly washed if they come in contact with these plants.\n\n### DAY HIKING GEAR\n\nWhile gear is beyond the scope of this book (which is about where to hike, not how to hike) it's worth noting a few points. No hiker should venture up a trail without being properly equipped. Starting with the feet, a good pair of boots\u2014and good socks\u2014can make all the difference between a wonderful hike and a blistering affair. Keep your feet happy and you'll be happy.\n\nFor clothing, wear whatever is most comfortable unless it's cotton. Cotton is a wonderful fabric, but not the best for hiking. When it gets wet, it stays wet and lacks insulation value. In fact, wet cotton sucks away body heat, leaving you susceptible to hypothermia. Think synthetics and layering.\n\nWhile your gear list will vary from another hiker's, a few items should be universal in every daypack. Every hiker who ventures deep into the woods should be prepared to spend the night out, with emergency food and shelter. Mountain storms or whiteouts can whip up in a hurry, catching fair-weather hikers by surprise. And there's always the chance of an illness or injury that could prevent you from getting back to the trailhead immediately. Be prepared with the Ten Essentials.\n\n### The Ten Essentials\n\n**1. Navigation (map and compass):** Carry a topographic map of the area you plan to be in and knowledge of how to read it. Take a compass, too, and know how to use it.\n\n**2. Sun protection (sunglasses and sunscreen):** Even on gray days, carry sunscreen and sunglasses. The burning rays of the sun penetrate the clouds. At higher elevations your exposure to UV rays is much more intense than at sea level. Burning is significantly enhanced by the reflectiveness of snow and water.\n\n**3. Insulation (extra clothing):** It may be 70 degrees at the trailhead, but at the summit it can be 45 and windy. Even a summer thunderstorm can cool the air temperature by 40 degrees in minutes. Snow is possible any time at high elevations. Carry raingear, wind protection, and extra layers.\n\n**4. Illumination (flashlight\/headlamp):** If caught after dark, you'll need a headlamp or flashlight to follow the trail. If forced to spend the night, you'll need it to set up emergency camp and gather wood. Carry extra batteries too.\n\n**5. First-aid supplies:** At a minimum, your kit should include bandages, moleskin, gauze, scissors, tape, tweezers, pain relievers, antiseptics, and perhaps a small first-aid manual. Consider first-aid training.\n\n**6. Fire (firestarter and matches):** If you're forced to spend the night, an emergency campfire will provide warmth and light. Be sure you keep matches dry. Resealable plastic bags do the trick, but a hard plastic container is better. Firestarter can be purchased commercially. One homemade version is cotton balls swabbed in petroleum jelly and stored in a container. Tip: The Vaseline-coated cotton ball will glow with a better, longer-lasting fire-starting flame if you pull tufts of greased fibers out in every direction before lighting. A candle can come in handy too.\n\n**7. Repair kit and tools (including a knife):** A knife is helpful; a compact multitool is better, adding lightweight pliers and scissors to your options. A basic repair kit should include nylon cord, a small roll of duct tape, and a small tube of superglue. A few safety pins can work wonders too.\n\n**8. Nutrition (extra food):** Always pack more food than what you need for your hike. Energy bars are easy options for a pick-me-up or emergency rations.\n\n**9. Hydration (extra water):** Carry two full water bottles, unless you're hiking entirely along a water source. You'll need to carry iodine tablets or a purifying device on longer or remote hikes.\n\n**10. Emergency shelter:** This can be as simple as a large garbage bag, or something more useful and efficient such as a reflective space blanket. A poncho can double as an emergency tarp.\n\n### BEFORE YOU GO\n\nAlways tell somebody reliable\u2014best to write it down\u2014where you're going, what you're doing, and when you plan to be home. Also include which land manager, agency, or emergency operator to contact should you not return in a reasonable time.\n\n### TRAILHEAD CONCERNS\n\nSadly, crime occasionally occurs at trailheads. The most common issue is vehicle break-ins. Never leave anything valuable in a vehicle left at a trailhead. Avoid leaving anything, such as bags or even empty coolers, in sight that might tempt a vandal to break a window or punch a lock just to see if there's something valuable inside.\n\nViolence at trailheads in Eastern Washington is exceedingly rare, but not out of the question. Be aware of your surroundings. If something doesn't feel right, it probably isn't. If someone looks suspicious, take action by leaving the place or situation immediately. Record descriptions and license plate numbers and report them to authorities if necessary, but avoid confronting questionable situations in remote areas.\n\n### ENJOY THE TRAILS\n\nMost importantly, be safe and enjoy the thrill of discovery and exercise on the trails in this book. They exist for our enjoyment and for the enjoyment of future generations of hikers.\n\nIf you enjoy these trails, consider stepping up to be one of their advocates. Your involvement can be as simple as picking up trash, signing up for a volunteer work party, joining a trail advocacy group, educating fellow citizens, or writing a letter to Congress or your state representatives. Introduce children to our trails. We need to continue a legacy of good trail stewards. All of these seemingly small acts can make a big difference. At the end of this book is a list of organizations working on behalf of trails and wildlands in Eastern Washington. Many of them organize great group hikes into the areas covered by this book and beyond. Check them out.\n\nHappy hiking!\n\nA NOTE ABOUT SAFETY\n\nSafety is an important concern in all outdoor activities. No guidebook can alert you to every hazard or anticipate the limitations of every reader. Therefore, the descriptions of roads, trails, routes, and natural features in this book are not representations that a particular place or excursion will be safe for your party. When you follow any of the routes described in this book, you assume responsibility for your own safety. Under normal conditions, such excursions require the usual attention to traffic, road and trail conditions, weather, terrain, the capabilities of your party, and other factors. Because many of the lands in this book are subject to development and\/or change of ownership, conditions may have changed since this book was written that make your use of some of these routes unwise. Always check for current conditions, obey posted private property signs, and avoid confrontations with property owners or managers. Keeping informed on current conditions and exercising common sense are the keys to a safe, enjoyable outing.\n\n\u2014 _The Mountaineers Books_\n\n## columbia highlands: okanogan highlands\n\n_Curlew Lake State Park_\n\nReaching from the Okanogan River to Idaho, from the Canadian border to the Columbia Plateau, the Columbia Highlands are a sprawling region in the northeast corner of Washington. Part of the geological province known as the Okanogan Highlands, the Columbia Highlands consist primarily of two mountain ranges lining the Columbia River as it enters Washington from British  \nColumbia.\n\nWest of the Columbia, the Kettle River Range runs north\u2013south for approximately 75 miles. East of the Columbia, the Selkirk Mountains also run north\u2013south, but unlike the Kettles, which consist of a single high crest with radiating ridges, the Selkirks are composed of parallel subranges. Both the Kettle and Selkirk Ranges are part of the Rocky Mountains. They form a transitional zone, rich in biological diversity, between interior ranges and the coastal Cascades.\n\nWhile the Okanogan Highlands generally refers to the geological province ranging from the Okanogan River to the Idaho border and north into British Columbia, in this book it describes the region between the Okanogan and Sanpoil Rivers. A sparsely populated region of isolated mountains, deep valleys, and open rolling hills, the Okanogan Highlands contain great mineral wealth and is dotted with mines (old and still active) and ghost towns. This region contains some of the least-known trails in the state, rewarding intrepid hikers who discover them with solitude, scenic splendors, and a few surprises.\n\n  Similkameen Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/1 | 7.2 miles | 245 feet\/1060 feet | Year-round\n\n**Map:** USGS Oroville; **Contact:** BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane; **Notes:** Wheelchair-accessible. Open to mountain bikes, horses; **GPS:** N 48 56.302 W 119 26.647\n\n  _**Walk down a sage- and pine-scented canyon cut by the Similkameen River, along an old rail line that once transported ore from the mines of Hedley, British Columbia, to the now ghost town of Nighthawk. Pass frothy rapids and sunny ledges where lizards and snakes bask in the warm Okanogan sun. Reflect on the past with the help of interpretive displays\u2014and admire the power and beauty of the river from a gorge-spanning bridge.**_\n\n### GETTING THERE\n\nFrom Tonasket, follow US Highway 97 north for 16.8 miles to Oroville, turning left onto 12th Avenue (near Frontier Foods grocery store). Proceed one block west and turn right onto Ironwood Street. Proceed one block north (passing Old Oroville Depot Museum and Visitors Center) and turn left onto Kernan Road. Continue 0.3 mile, passing soccer fields, to the trailhead (elev. 935 ft) located on your right.\n\n### ON THE TRAIL\n\nOpened in 2009 and slated to be part of the Pacific Northwest Trail (see \"North by Northwest\" sidebar), the Similkameen Trail is shaping up to be a recreational gem in the growing trail system near Oroville. Thanks to government agencies, local businesses, and dedicated volunteers, including local students, this trail is well maintained and lined with benches and interpretive signs. This route overflows with historical interest, and the bird-watching and spring flower gazing are pretty good too.\n\nFrom the trailhead walk a couple of hundred feet north to the old rail line. The Great Northern began construction on this line in 1909 and it remained in use until 1972. Now heading west, pass some apple warehouses and a couple of pines and cottonwoods. There isn't too much shade on this trail, so hike early or late in the day.\n\nAt about 0.3 mile, the Similkameen River comes into view. Starting in British Columbia's Manning Provincial Park, the river is named for a band of Okanogan First Peoples and means \"treacherous waters.\" It flows more than 120 miles into the Okanogan River at Oroville.\n\nAfter crossing a dirt road, the trail climbs a little, leaving its original right-of-way to bypass a vineyard. At 1.4 miles, come to the Taber trailhead (elev. 1025 ft) on Loomis\u2013Oroville Road\u2014an alternative start. Continue west, and then switchback east and wind down to the Girder Bridge (elev. 980 ft), which replaced the original trestle in 1952. The 375-foot span hovers 86 feet above the churning river in a tight chasm.\n\nContinue west, leaving crushed gravel tread for double-track, and start traversing open range (close gate after you). Pass through a cut where quails and the occasional rattler may be startled (or may startle you) and continue upstream, passing rapids and good views of Kruger Mountain across the river.\n\n_The Girder Bridge spanning the Similkameen River_\n\nNORTH BY NORTHWEST: THE PACIFIC NORTHWEST TRAIL\n\nDuring the backpacking boom of the 1970s, transplanted New Englander Ron Strickland was struck with a novel idea. How about adding another classic long-distance hiking trail to our country's trail inventory? One that would accompany and rival the likes of the Appalachian, Pacific Crest, and Colorado Divide Trails. Such began his quest to build the Pacific Northwest Trail (PNT), a 1200 mile path from Cape Alava on the Olympic Peninsula to Montana's Glacier National Park.\n\nSoon forming the Pacific Northwest Trail Association, Strickland and a good number of tireless volunteers set out to promote, construct, and maintain the new trail. Utilizing existing trails along with new tread, the PNT traverses a good chunk of northeastern Washington. And while parts of the trail still exist only on paper (following roadway where no tread yet exists), much of the Pacific Northwest Trail is currently hikable; and more than a handful of backpackers have already through-hiked it. The trail has been receiving more attention as the result of President Obama signing a bill in 2009 designating the Pacific Northwest Trail as our newest national scenic trail\u2014a status the PCT and the AT hold.\n\nMany hikes in this book follow portions of the Pacific Northwest Trail. They are a diverse lot and offer some of the best hiking in Eastern Washington. Among them: Similkameen Trail (Hike 1), Whistler Canyon (Hike 2), Antoine Trail (Hike 3), South Side Trail (Hike 4), Clackamas Mountain (Hike 10), Thirteenmile Canyon (Hike 17), Thirteenmile Mountain (Hike 18), Edds and Bald Mountains (Hike 19), Sherman Peak (Hike 21), Columbia Mountain (Hike 24), Copper Butte (Hikes 27 and 28), Ryan Cabin Loop (Hike 31), Sentinel Butte (Hike 32), Abercrombie Mountain (Hike 43), Crowell Ridge (Hike 51), Gypsy Peak (Hike 52), and Shedroof Divide (Hike 54).\n\nVisit the Pacific Northwest Trail Association online (www.pnt.org) for more information.\n\n\u2014 _C. R_.\n\nOld mines litter the surrounding hillsides. Pines and firs shroud the north-facing slopes to your left, contrasting with the sagebrush-steppe ridges to your right. At 2.8 miles, cross a side creek in a lush draw. Good bird observing here. At 3.2 miles, pass through a cut with glacial till left behind from the Ice Age.\n\nAt 3.6 miles, come to a gate (elev. 1060 ft) and the end (for now) of the line. Look northwest to the 1907-built Enloe Dam, with the river thundering over it. Once the dam is relicensed and the area surrounding it improved, trail advocates hope to open the second phase of this great trail, to Nighthawk and including a tunnel.\n\n  Whistler Canyon and Frog Pond\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 5.1 miles | 1250 feet\/1950 feet | Mar\u2013Dec\n\n**Maps:** USGS Oroville, USGS Mount Hull; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to horses. Keep dogs under strict control so as to not disturb bighorn sheep; **GPS:** N 48 54.300 W 119 25.335\n\n  **_Whistlers? yes\u2014and ground squirrels too! But the biggest animal attraction is California bighorn sheep. The largest band in the state roams Whistler Canyon, and it's not unusual to see more than fifty at a time. Wildflowers and views of the Okanogan Valley also abound along this recently opened section of the Pacific Northwest Trail. And miles of connector trails entice you to explore farther._**\n\n### GETTING THERE\n\nFrom Tonasket, follow US Highway 97 north for 14.5 miles to the trailhead turnoff, signed and upgraded in 2012. The trailhead turnoff is about 0.3 mile north of the gravel pit at milepost 329. (From Oroville, the turnoff is 2.4 miles south of city center.) Continue 0.2 mile to trailhead (elev. 1000 ft) located in a field below some impressive ledges.\n\n_The trail to Whistler Canyon climbs out of the Okanogan River valley._\n\n### ON THE TRAIL\n\nColonies of ground squirrels greet you at the trailhead. And colonies of marmots\u2014aka whistlers\u2014greet you as the trail angles beneath rocky ledges. Thank the Back Country Horsemen, Pacific Northwest Trail Association, and other volunteers for the recently constructed, well-built trail. A private-property owner had closed the previous access point, putting this mostly public-lands trail off-limits. But that's all in the past\u2014so keep hiking.\n\nAfter winding along ledges and through a small pine grove, reach a junction (elev. 1200 ft) at 0.3 mile with the Frog Pond Trail. This is a mandatory side trip. Follow this rose-lined trail left, beneath a canopy of ponderosas and up through a rocky cleft. At 1 mile from the trailhead, reach a junction (elev. 1500 ft) with the 0.3-mile loop circling Frog Pond. More of a mosquito incubator (and therefore a frog feeder), the pond isn't much to look at. The real treat is the ledgy lookout on the west side of the loop: peer out at Oroville, Osoyoos Lake, and into British Columbia; and straight down at the oxbowing confluence of the Similkameen and Okanogan Rivers. Consider a trip at sunset.\n\nRetrace your steps to the junction and continue left, shortly intersecting an old road. Turn left and after a few steps follow a bypass around private property, returning to the old road at 0.5 mile from the trailhead. Now within BLM land, follow the road into Whistler Canyon. Whistler Creek tumbles below. Watch above for the bighorns and if you spot them (better chances early and late in the day), tread quietly in their presence. Look for deer, turkeys, cedar waxwings, and whistlers\u2014and rubber boas, a docile constrictor fairly common to these parts.\n\nAt 0.9 mile from the trailhead, pass a campsite (elev. 1600 ft) in a grove of pines and cottonwoods. Then leave the creek and angle left, traversing ledges with excellent viewing out over the Okanogan Valley, before switchbacking right and returning above the creek. Look for a semihidden waterfall below. The trail eventually enters a forest of pine and fir, reaching a gate (elev. 1950 ft) and national forest boundary at 1.7 miles from the trailhead. Just beyond, the trail\u2014now an old woods road\u2014crosses the creek. This is a good spot to turn around, savoring good valley views and perhaps catching sight of that band of bighorns.\n\n### EXTENDING YOUR TRIP\n\nThe Whistler Canyon Trail continues in thick forest along Whistler Creek for 0.6 mile, before leaving the canyon, reaching FR 3525 more than 10 miles later near Summit Lake at 4200 feet. The trail is primarily used by equestrians and Pacific Northwest Trail through-hikers. Several side trails diverge, but routefinding can be tricky. Skip the steep McDonald Trail, which climbs in forest to a draw beneath McDonald Mountain before climbing a ridge to meet FR 5255. But consider the 2.5-mile Black Diamond Lake loop, which takes off left 0.6 mile from the suggested turnaround. The upper part of the loop\u2014after crossing and climbing out of the canyon\u2014traverses open slopes with nice views west to the Loomis State Forest high country and snowy North Cascades.\n\n  Mount Bonaparte via Antoine Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/5 | 15.2 miles | 3360 feet\/7257 feet | mid-June\u2013Nov\n\n**Maps:** USGS Mount Bonaparte, USGS Havillah; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to horses, mountain bikes; **GPS:** N 48 48.115 W 119 11.882\n\n  _**It's a long way to the top of Eastern Washington's third-highest summit via the Antoine Trail. Why go this way when there's a much shorter route? For one thing, you'll follow a quiet trail carpeted in soft larch and fir needles instead of a rutted, dusty ATV track. And you'll see an old trapper's cabin, a couple of cool dark ravines fed by crashing creeks, groves of big firs, and miles of excellent furry-and-feathered-critter habitat. It's a good workout rewarded with extensive views from Bonaparte, or a pleasant walk in the woods if you just want to sample this quiet path in the Okanogan Highlands.**_\n\n### GETTING THERE\n\nFrom the junction of State Route 20 and US Highway 97 in Tonasket, head north on US 97 for 0.4 mile, turning right onto Whitcomb Avenue (signed \"Havillah 17\" and \"Sitzmark Ski Area\"). Immediately bear right onto Jonathan Avenue, which soon becomes Havillah Road (County Road 9467). Follow this good road for 15.4 miles, turning right (before reaching the hamlet of Havillah) onto Mill Creek Road (Forest Road 3230 and signed \"Highlands Sno-Park\"). At 1.3 miles, pass the Sno-Park and continue on FR 3230 for another 0.4 mile, coming to gated FR Spur 150 on your left. Park here; this is the trailhead (elev. 3900 ft).\n\n### ON THE TRAIL\n\nThe most direct way to Mount Bonaparte, Mount Bonaparte Trail No. 306, can no longer be recommended. Back in the early 1990s, the Forest Service converted this once-pleasant path into an ATV track for transporting supplies to the fire lookout. What followed was unregulated motorized use that pulverized this path to dust. What a shame. In 2007, the Forest Service closed the trail to public motorized use, but a lack of rehabilitation and the occasional illegal motorized user still render it unacceptable. Except as a winter route, skip it and opt for the three other longer but appealing trails traversing this 9500-acre wilderness study area.\n\nThe way via Antoine Creek starts by following gated FR Spur 150. A logging operation several years past obstructed the lower part of the Antoine Trail, so it's wiser to walk the pleasant road instead of the original tread. Traversing an area selectively cut and grazed by cattle, the way winds around a small knob. The rolling terrain and territorial views warrant a return visit with skis in winter. At 2.6 miles, turn left and leave the road at an old logging landing (elev. 4400 ft).\n\nFollow an old jeep track, first through an old cut, then through old-growth western larch that are stunning come October. Admire new tread compliments of volunteers who welcomed the Antoine Trail as part of the newly designated Pacific Northwest Trail. At 3.3 miles, reach the dilapidated Napol Cabin, an old trapper's domicile. The Roggow Cabin on the Fourth of July Ridge Trail on Bonaparte's southwest slopes is in much better condition and is occasionally used by outdoors folks.\n\nJust beyond the cabin, at 3.5 miles, reach a junction (elev. 4850 ft) with the Napol Cabin Trail. This trail connects with the Fourth of July Ridge Trail in about 2.5 miles near the Roggow Cabin. It is used primarily by equestrians. For Bonaparte, continue left into a thick lodgepole pine forest, soon coming to a bridged crossing of a tributary of Antoine Creek. Now on bona fide trail, reach another tributary crossing (last reliable water) at 4 miles.\n\nThe way transitions into a Douglas-fir forest interspersed with big larches as you traverse a slope on good trail. At 5.1 miles, bear right at an unmarked junction (elev. 5400 ft) and begin steadily climbing to attain the ridge crest. Now through a forest of lodgepole pine, snag teaser views through the trees.\n\nContinue upward, and eventually the alpine-suited whitebark pines indicate you're getting close. At 7.1 miles, reach the Bonaparte Trail (elev. 6890 ft) just shy of the summit. Turn right and follow this dusty track (or pick up pieces of the old trail) for 0.5 mile to the broad 7257-foot summit. This stand-alone peak commands far-reaching views, but you'll need to climb the \"new\" fire lookout, built in 1961, to get them. Admire the Kettle Crest (east), Moses Mountain and the Columbia Plateau (south), the Okanogan Valley and North Cascades (west), and British Columbia's Baldy and Big White Mountains (north). When you're finished, marvel over the \"old\" fire lookout, built in 1914 from hand-hewn logs. It's on the National Register of Historic Places and one of our oldest lookouts still standing.\n\n_The 1914 lookout cabin still graces Bonaparte's summit._\n\n  Mount Bonaparte via South Side Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 10.8 miles | 2730 feet\/7257 feet | June\u2013Nov\n\n**Map:** USGS Mount Bonaparte; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to mountain bikes, horses. Watch for ticks; **GPS:** N 48 47.913 W 119 04.175\n\n  _**Horizon-spanning 360-degree views await you from Eastern Washington's third-highest summit. A granite dome rising well above the surrounding ridges, 7257-foot Mount Bonaparte stands all alone. It's graced by two fire lookouts\u2014one built in 1914, a testament to the early days of the Forest Service, and one built in 1961, still staffed in the summer. This is not the shortest way to the Bonaparte's summit, but it's one of the nicer routes, complete with views, flowers, old forest, and solitude.**_\n\n### GETTING THERE\n\nFrom Tonasket follow State Route 20 east for 20 miles, turning left onto Bonaparte Lake Road (County Road 4953, signed \"Bonaparte Recreation Area\"). (From Republic, follow SR 20 west for 20 miles, turning right onto CR 4953.) Proceed on Bonaparte Lake Road (which eventually becomes Forest Road 32), bearing left at 8.5 miles onto FR 33. Continue 5.3 miles to a four-way junction (FR 34 and Lost Lake access). Proceed straight on FR 33 for another 0.4 mile, turning left onto FR Spur 100. (Alternatively, approach via Hike 3 directions, continuing 0.6 mile to Havillah instead of turning onto Mill Creek Road. Then turn right onto Lost Lake Road\/CR 4850, which becomes FR 33, driving 10.3 miles to FR Spur 100.) Follow FR Spur 100 for 4.7 miles (passing the upper trailhead for the Pipsissewa Trail at 4.3 miles) to the trailhead (elev. 4600 ft). Parking is tight; there is better parking at the Pipsissewa trailhead (Hike 9).\n\n### ON THE TRAIL\n\nThe shortest way to Mount Bonaparte, Mount Bonaparte Trail No. 306, is an unappealing mess from years of motorized use, even though the Forest Service closed it to public motorized access in 2007. Fortunately, other trail options exist within this 9500-acre wilderness study area. Unfortunately, accessing Bonaparte's summit from the south side still requires some hiking on the dusty north trail. But the views are well worth it.\n\nThe trip up Bonaparte from the south side was once much longer, having started from Bonaparte Lake. But FR Spur 100 severed the trail, knocking considerable distance and elevation off the hike. The lower trail still exists and has since been renamed the Pipsissewa Trail (Hike 9). With this in mind, ignore the trailhead sign that says the lookout is 8 miles away: The Forest Service moved this sign from the lower trailhead and never adjusted the mileage.\n\nThe way starts in a selectively cut forest, providing lots of warming sun. The grass-lined trail (be tick aware) steadily ascends. Mount Bonaparte is a _monadnock_ , an Abenaki word that means \"mountain standing alone\" (and the name of southern New Hampshire's historically prominent and well-loved Mount Monadnock). Geologists have since used the term in place of another, _inselberg_ , meaning \"isolated mountain\"\u2014which Mount Bonaparte is indeed!\n\nAt 0.6 mile, come to a spring (elev. 5000 ft) and an eroded section of trail. Tread improves as the way traverses first parkland forest, then dark forest of spruce and fir, then lodgepole pines punctuated with granite ledges and boulders. Steadily climbing, the way switches east to round a small ridge before resuming a westward direction. At 2.2 miles, cross Myers Creek (elev. 5750 ft) flowing through patches of huckleberry.\n\nReach a junction with the Fourth of July Ridge Trail (elev. 5825 ft) at 2.6 miles. Continue right, over big granite ledges. Slightly drop into a small gulch and reach the Mount Bonaparte Trail (elev. 5750 ft) at 3.4 miles. Now turn left on radically different tread\u2014wide and trenched and covered in dust. Just beyond the junction, a spur leads right 0.1 mile to a spring, the last reliable water.\n\n_The \"new\" fire lookout is still seasonally staffed._\n\nSlogging upward, the path cuts through dense stands of lodgepole pine. Some sections of the old trail along the way offer some relief from the dust. At 4.9 miles, come to a junction with the Antoine Trail (elev. 6890 ft). Continue left 0.5 mile through groves of whitebark pine (and look for Clark's nutcrackers fond of pine nuts), before approaching Bonaparte's broad granite summit from the east.\n\nAdmire the historic 1914 fire lookout and then head up the \"new\" lookout to take in the views. They're exceptional and reach as far as Mount Rainier on a clear day: Bonaparte Meadows and the monadnocks Mount Annie and Moses Mountain are closer to the south. Loomis country is to the west, with Chopaka Mountain's 6000-foot prominence above the Similkameen Valley. Lake Osoyoos and British Columbia's 7558-foot Mount Baldy are to the north. And to the east trace the entire Kettle Crest into Canada's Granby country.\n\n  Strawberry Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/2 | 3.4 miles | 890 feet\/4742 feet | May\u2013Nov\n\n**Map:** USGS Mount Bonaparte; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to mountain bikers; **GPS:** N 48 51.135 W 119 02.959\n\n  _**This is a sweet hike to the top of Strawberry Mountain, where you'll find Lost Lake twinkling below and bulky Mount Bonaparte rising above. Through pine and larch groves, wind up gentle slopes to this old fire lookout site. It's easy enough for young children and neophyte hikers and satisfying enough for hikers who want to stretch their legs more by combining it with the nearby Big Tree Trail (Hike 6).**_\n\n_Stands of western larch add a golden hue to Strawberry Mountain in the autumn._\n\n### GETTING THERE\n\nFrom Tonasket, follow State Route 20 east for 20 miles, turning left onto Bonaparte Lake Road (County Road 4953, signed \"Bonaparte Recreation Area\"). (From Republic, follow SR 20 west for 20 miles, turning right onto CR 4953.) Proceed on Bonaparte Lake Road (which eventually becomes FR 32), bearing left at 8.5 miles onto FR 33. Continue 5.3 miles to a four-way junction. Turn left onto FR Spur 50 and drive 0.4 mile, turning right into the Lost Lake Campground. Park at the historic Civilian Conservation Corps guard station (elev. 3850 ft). Privy available.\n\n### ON THE TRAIL\n\nAfter admiring the simple elegance of the old guard house, walk 0.1 mile south on FR Spur 50, along lovely Lost Lake, to the Strawberry Mountain trailhead. Begin gently climbing through open forest that was selectively cut. Deer are profuse. Pass an electric line and at 0.3 mile cross a logging road.\n\nContinue through larch, Doug-fir, and aspen groves. In autumn the forest is streaked yellow, while the trail is carpeted with soft golden needles. Gently ascending the broad forested peak, cross another road (elev. 4150 ft) at 0.6 mile; then return to open forest.\n\nAfter skirting an old selective cut, the way levels off before making a steep final pitch. Cross yet another road (this one old and making for some good wandering) and soon afterward emerge on the broad grassy summit (elev. 4742 ft).\n\nAll that remains of the fire lookout that stood here from 1934 to 1963 are four concrete foundation blocks, but you won't need a tower to enjoy the views. Lost Lake ripples directly below, with Mount Bonaparte's broad forested ridges providing an emerald backdrop. To the north, British Columbia's Mount Baldy hovers above golden hills. South you can catch a glimpse of Mount Annie and rows of rolling ridges.\n\nOn an evening hike in the summer, you might hear the eerie call of the loon echoing below. And yes, there are strawberries here, but just the small wild type ( _Fragaria virginiana_ ), favored more by woodland critters and birds than hungry hikers.\n\n  Big Tree Botanical Area\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 2.8 miles | 100 feet\/3850 feet | Apr\u2013Nov\n\n**Map:** USGS Mount Bonaparte; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Partly wheelchair-accessible; **GPS:** N 48 51.135 W 119 02.959\n\n  _**Hike to a pair of towering larches more than 900 years old. Saunter beneath ancient ponderosa pines. While the botanical preserve is more readily accessed from Forest Road 33, take the longer route from Lost Lake via the Big Tree Trail and enjoy one of the region's more peaceful walks. Well-graded and nearly level, it's ideal for all ages and perfect for an evening stroll if you're camped at Lost Lake.**_\n\n### GETTING THERE\n\nFrom Tonasket, follow State Route 20 east for 20 miles, turning left onto Bonaparte Lake Road (County Road 4953, signed \"Bonaparte Recreation Area\"). (From Republic, follow SR 20 west for 20 miles, turning right onto CR 4953.) Proceed on Bonaparte Lake Road (which eventually becomes FR 32), bearing left at 8.5 miles onto FR 33. Continue 5.3 miles to a four-way junction. Turn left onto FR Spur 50 and drive 0.4 mile, turning right into the Lost Lake Campground. Park at the historic Civilian Conservation Corps guard station (elev. 3850 ft). Privy available.\n\n### ON THE TRAIL\n\nBegin directly across the campground road from the Lost Lake Guard Station. Called both the Big Tree Trail and the Lost Lake Trail, the trail connects these two popular and lovely attractions. Start with a short descent and soon afterward cross FR Spur 50.\n\n_The Big Tree Trail weaves through towering larches, pines, and firs._\n\nContinue under a cool canopy supported by giant pillars of western larch. Pass (or sit and contemplate) the first of several inviting benches along the trail. At about 0.25 mile, a spur trail leads right, to a church camp. Continue left through a swinging gate, entering open range. Then continue through open larch and fir forest carpeted with pipsissewa.\n\nAfter crossing a forest road at 0.5 mile, the trail meanders through some impressive boulders and granite slabs. At 1 mile, reach FR 33 and the main trailhead (start here if you're short on time), complete with privy (elev. 3800 ft). Continue on a wheelchair-accessible trail, soon coming to a junction. The way loops from here. Continue right, dropping into a draw (elev. 3775 ft) and then out of it, reaching a junction at 1.3 miles. Absolutely head right on the 0.1-mile spur, dropping to a pair of giant ancient western larches more than 900 years old. Retrace your steps back to the loop and continue right. At 1.7 miles, close the loop. You know the way back to the trailhead from here.\n\n  Beth and Beaver Lakes\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/2 | 3.8 miles | 190 feet\/2850 feet | Apr\u2013Nov\n\n**Map:** USGS Bodie; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to mountain bikes; **GPS:** N 48 51.893 W 118 59.896\n\n_Evening reflections on Beaver Lake_\n\n  _**Hike through a cool narrow canyon along two slender lakes teeming with fish and anglers intent on luring them. Beth and Beaver Lakes are two of the popular high-country gems of the Tonasket Ranger District's Five Lakes Area. Each season offers its own delights, with fall being exceptionally nice, when western larches cast golden reflections across placid waters.**_\n\n### GETTING THERE\n\nFrom Tonasket follow State Route 20 east for 20 miles, turning left onto Bonaparte Lake Road (County Road 4953, signed \"Bonaparte Recreation Area\"). Proceed on Bonaparte Lake Road (which eventually becomes FR 32) for 11.7 miles to Beaver Lake Campground (alternate trailhead), at the junction with CR 9480. Turn left and drive 1.8 miles, passing Beth Lake Campground (another alternate trailhead), to the trailhead (elev. 2800 ft). (From Republic, follow SR 20 west for 16.5 miles, turning right onto Toroda Creek Road\/CR 9495. Continue 13.5 miles, turn left onto CR 9480, and follow it 5.9 miles to the trailhead.)\n\n### ON THE TRAIL\n\nThis is a nice little trail along two little, quiet lakes connecting two little, quiet campgrounds. While you can easily access this trail from the campgrounds, day-use parking is limited. It's best to begin at the northern trailhead if you're just out for the day.\n\nStart by crossing North Fork Beaver Creek on a small bridge and enter a forest of big larches and firs. The trail bends south to hug the western shore of Beth Lake. The road hugs the eastern shore of both lakes, but traffic is light, so frog and bird song, along with happy campers, are the sounds you'll likely hear. Travel through forest, occasionally crossing small scree slopes, nearly always within sight of water. Keep an eye out for handsome wood ducks.\n\nAt about 0.4 mile, the way climbs about 50 feet over a ledge and then drops back down to round the wider eastern half of the lake. Cross an earthen dam and reach Beth Lake Campground at 0.8 mile. Turn right on the campground road, and pick up the trail near campsite number 7.\n\nSkirt a wetland cove and arrive at Beaver Lake. Climb about 50 feet over a ledge, where the lake bends, and then drop closer to the water, resuming your shoreline strolling. The lake is murky, but it reflects the surrounding mature trees nicely. Scan for roosting eagles, and watch the lake surface for dippers.\n\nPass by an odd structure before crossing a small scree slope. Then climb 40 feet around a small rib near Beaver Lake's outlet. The trail winds down off it and crosses a little creek before terminating near campsite number 5 (elev. 2700 ft). Consider spending the night at one of the campgrounds and taking a moonlit stroll along this pleasant trail.\n\n  Virginia Lilly Trail\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 3.5 miles | 900 feet\/4270 feet | Apr\u2013Nov\n\n**Map:** USGS Bodie; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Range area; **GPS:** N 48 49.392 W 118 55.772\n\n  _**Named not for a southern flower but for an Okanogan Highlands resident who cherished the region's threatened old growth and ecologically diverse landscapes, this delightful loop through parkland forest, wildflower meadows, and sun-kissed ridges is dedicated in her memory. Solitude is almost guaranteed here, on one of the least-hiked trails in the Mount Bonaparte area.**_\n\n### GETTING THERE\n\nFrom Tonasket, follow State Route 20 east for 20 miles, turning left onto Bonaparte Lake Road (County Road 4953, signed \"Bonaparte Recreation Area\"). (From Republic, follow SR 20 west for 20, miles turning right onto CR 4953.) Proceed on Bonaparte Lake Road (which eventually becomes FR 32) for 7.1 miles, turning right onto FR 3240 (1.3 miles beyond Bonaparte Lake Campground). At 1 mile, bear left and continue on FR 3240 for another 5.7 miles to the trailhead on your left (elev. 4050 ft).\n\n### ON THE TRAIL\n\nAfter languishing for a few years, the Virginia Lilly Trail is finally getting a little upkeep. The new trailhead avoids driving a rough road, though you can still walk up the road to access the trail. And the Forest Service, in cooperation with several groups and individuals, put together a booklet to go along with the hike (more literary than field guide; download it from www.fs.fed.us\/outdoors\/naturewatch\/resources\/virginialilly-old-growth-trail.pdf). But don't believe the Forest Service's description of this trail as 2 miles long. It's nearly twice that length.\n\nHike counterclockwise to end going downhill. Head southwest across a selectively cut area, soon coming to a junction on an open hillside in about 0.25 mile. Now on the main loop, continue straight, across grassy slopes and through groves of big ponderosa pines. Watch for cows as you plod through this open range country.\n\n_Virginia Lilly Trail offers good views of the golden hills of the Okanogan Highlands._\n\nThe way turns north, makes a short climb, and then drops into a grove of firs. Make a short steep climb up an open knoll (elev. 4075 ft) with excellent views east to Bodie and Clackamas Mountains. Reenter forest and steeply descend 300 feet into a damp draw. With numerous cattle paths diverging from and intersecting the trail, it's easy to go astray here. Note trail markers.\n\nNow climbing again, the way cuts through meadows accented with stately pines and splotched gold in spring by arrowleaf balsamroot. Deer are profuse, and your approach will send them scampering. At 1.6 miles, top a grassy rocky knoll (elev. 4025 ft) with good views of the Toroda Creek valley east, Mount Bonaparte west, and the old mining town of Chesaw and new mining area of Buckhorn Mountain north.\n\nThe trail then loops back south, dropping back into forest to a cool draw (elev. 3800 ft), before once again climbing. At 2.5 miles, reach a cow-trampled, larch-encircled, cattail-sporting wetland. Then continue climbing to a 4100-foot bump. Turn right, following cairns through a lovely aspen grove before making a steep ascent up an open grassy knoll (elev. 4270 ft). Kick back and walk along the open hillock, coming to a post at 3.2 miles. To complete the loop, either continue straight across meadows, reaching the spur back to the lower trailhead, or turn right to reach the upper trailhead and walk a short distance on the spur road back to your car.\n\n  Pipsissewa Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 4.2 miles | 860 feet\/4420 feet | May\u2013Nov\n\n**Map:** USGS Mount Bonaparte; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to mountain bikes; **GPS:** N 48 47.570 W 119 03.786\n\n  _**From the inviting shoreline of Bonaparte Lake to sunny ledges high above it, the delightful Pipsissewa Trail takes in stately pines, showy rock gardens, and breathtaking views of the Bonaparte Meadows. And pipsissewa? Also known as prince's pine, this small member of the heath family brightens the dry, cool woodlands in the summer with its pink and white flowers.**_\n\n### GETTING THERE\n\nFrom Tonasket, follow State Route 20 east for 20 miles, turning left onto Bonaparte Lake Road (County Road 4953, signed \"Bonaparte Recreation Area\"). (From Republic, follow SR 20 west for 20 miles, turning right onto CR 4953.) Proceed on Bonaparte Lake Road for 5.8 miles, turning left into the Bonaparte Lake Campground. Continue 0.1 mile, passing the boat launch, to a small parking area near campsite number 27 and the hike's start (elev. 3560 ft). Privy available.\n\n### ON THE TRAIL\n\nFrom the campground loop, locate a sign indicating the trailhead is 500 feet away. Walk north on a quiet dirt road that leads to seasonal cabins. Soon after crossing the lake's outlet stream, come to the trail as it veers left into the forest. Bypass a row of cabins and moderately ascend above Bonaparte Lake.\n\nUnder a cool canopy of large ponderosa pines and western larches, the good trail continues to gain elevation along a couple of sweeping switchbacks. Cross several grassy openings, which in spring and summer display pretty floral arrangements. In fall, western larches and aspens add soothing touches of gold.\n\nThroughout most of the summer, the small delicate flowers of pipsissewa (incorrectly spelled on the trail signs) add touches of pink and white to the dry forest floor. This relative of the wintergreen family thrives across the northern states and southern Canada. Numerous First Peoples used it for medicinal purposes.\n\nContinue gaining elevation, traversing a few seeps and maneuvering around a couple of granite slabs. At 2.1 miles, the trail comes to its end at FR 33-100 (elev. 4420 ft). Yes, you could have driven here\u2014but why? You've instead earned the fantastic views from the sunny ledges here at trail's end: Bonaparte Lake twinkling below, piney hills and Bodie Mountain to the east, and the lush Bonaparte Meadows west to Mount Annie. On the return, consider sampling the waters of Bonaparte Lake by submersion!\n\n_Pipsissewa Trail ends at an excellent viewpoint of Bonaparte Lake._\n\n### EXTENDING YOUR TRIP\n\nThe Pipsissewa Trail was part of the South Side Trail (Hike 4) until FR Spur 100 severed it. Challenge yourself with a 15-plus mile hike by subduing Mount Bonaparte from Bonaparte Lake. Consider spending a night in the family-friendly lakeside campground afterward.\n\n  Clackamas Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 9.4 miles | 2400 feet\/5450 feet | May\u2013Nov\n\n**Map:** USGS Wauconda Summit; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to horses. Range area; **GPS:** N 48 40.827 W 118 54.284\n\n  _**One of the finest ridgeline, wildflower, and larch hikes in the Okanogan Highlands\u2014and a loop too. Enjoy far-reaching views from this little-known peak. Centerpiece of a wilderness study area, Clackamas Mountain is excellent habitat for rare and threatened fauna and flora, including lynx and the Okanogan fameflower. This hike ascends via two long ridges, circling the Sweat Creek basin without making you expend too much sweat.**_\n\n### GETTING THERE\n\nFrom Tonasket, follow State Route 20 east for 31 miles. (From Republic, travel 8.5 miles west on SR 20.) Turn left into the Sweat Creek Picnic Area and trailhead (elev. 3550 ft). Privy available.\n\n### ON THE TRAIL\n\nStarting from a former car campground, now a picnic area, hike north along Sweat Creek into a cool forest, coming to a junction at a stile at 0.1 mile. You'll be returning on the left-hand trail, so head right on the Sweat Creek Basin Trail, briefly following a power-line swath and fence line before turning northward. Start climbing an at-times open, at-times steep ridge that's cloaked in wildflowers in spring. Balsamroot, lupine, cinquefoil, daisy, arnica, desert parsley, larkspur, shooting star\u2014the list goes on!\n\nWhen your nose isn't to the ground, look up and out to Fir Mountain to the south. At about 1.8 miles, ascend a knoll and descend slightly as you walk along a ridgeline through parkland forest of old larches and Douglasfir. At about 2.5 miles, a short spur leads left to an outcropping (elev. 4850 ft) with views over the Sweat Creek basin.\n\n_A hiker heading through flowered parkland meadows on Clackamas Mountain_\n\nPass an old mileage post. This trail was one of many that once traversed the surrounding ridges and peaks straddling the Okanogan-Ferry County border. Most of them have faded into memory, but this trail is now part of the Pacific Northwest Trail.\n\nAt 3.5 miles, come to Hunter Spring and Camp (elev. 5000 ft) and the unmarked junction with the Maple Mountain Trail (Hike 11) just beyond it. Continue north through larches, cresting a rocky knoll (elev. 5200 ft) before descending slightly and passing a small wetland and open ledges with good views south and glimpses north.\n\nAfter a short steep drop into a 4800-foot saddle, start climbing again, to a junction (elev. 4850 ft) at 4.5 miles. The Pass Spring Trail heads left into the basin, following Sweat Creek for about 3 miles back to the trailhead. Keep hiking right, coming to another junction (elev. 5200 ft) at 4.8 miles. The trail right is the old West Fork Cougar Creek Trail, now part of the Pacific Northwest Trail. Continue left instead on the Clackamas Mountain Trail, reaching the forested 5450-foot summit at 5.3 miles.\n\nPass above a small frog pond, and after a few ups and downs start descending through open forest and on ledges. At 6.7 miles, emerge onto an open ridgeline (elev. 5250 ft) with excellent views south to Fir and Annie, west to Bonaparte, and east to the Kettle Crest. Savor the wildflowers too, perhaps spotting the indigenous Okanogan fameflower among the sedums. Be careful not to go astray on one of the many cattle paths here. Look across the Sweat Creek drainage to the ridge you hiked up\u2014Clackamas Mountain's southern ridges form a huge horseshoe.\n\nAt about 7.5 miles, the way crests a 4900-foot knoll, enters forest, and steeply drops. The tread is now sketchy in places, crying out for a maintenance party to pay a visit. The trail bends eastward, passing a spring (elev. 4200 ft) as it descends into the Sweat Creek basin. Pass big ponderosa pines, and at 8.9 miles come to the Pass Spring Trail at Sweat Creek among a confusion of windfall. Cross the creek (may be tricky early in the season) and soon afterward cross it again. Don't put dry socks on just yet, because you need to cross the creek one more time before coming back to the junction at the stile and closing your loop at 9.3 miles. Your vehicle awaits 0.1 mile to the right.\n\n  Maple Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 5.2 miles | 1750 feet\/5299 feet | May\u2013Nov\n\n**Maps:** USGS Storm King Mountain, USGS Wauconda Summit; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to horses; **GPS:** N 48 41.888 W 118 49.948\n\n  _**The maples won't impress you on Maple Mountain, but the larches and Douglas-firs will. They're old, large, and profuse and represent some of the finest Inland Northwest ancient forests in the state. The views across the golden hills of the Okanogan Highlands aren't too bad either. Like its neighbors on Clackamas Mountain, this lonely but much admired trail has been saved from obscurity thanks to the Ferry County chapter of the Back Country Horsemen.**_\n\n### GETTING THERE\n\nFrom Republic, travel 2.5 miles west on State Route 20, turning right onto Trout Creek Road (County Road 257). (From Tonasket, follow SR 20 east for 37 miles, turning left onto Trout Creek Road\/CR 257.) Drive north 0.7 mile, bearing left onto Sheridan Road (CR 253). Continue 4.1 miles (road becomes rough at about 2 miles; later becomes FR 2086) to the trailhead (located about 0.1 mile north of national forest boundary), on your left (elev. 3900 ft). Limited parking.\n\n### ON THE TRAIL\n\nThe trail starts in a forest of big firs and larches, slowly descending to a narrow valley cut by Granite Creek (elev. 3725 ft). At 0.5 mile, cross the creek on a fairly new and rather sturdy boardwalk (thanks volunteers!); then begin a steep climb.\n\nNo silly switchbacks here\u2014it's get down to business and scale that summit. Ascend grassy slopes shaded by a canopy of massive western larches (consider this hike in October). Pocket meadows with views east to Storm King Mountain (a name shared by countless summits from the Olympics to the Appalachians) give reason to pause and catch your breath.\n\nAt about 1.4 miles, cross a fence line (elev. 4500 ft), leaving Ferry County and Colville National Forest for Okanogan County and the Okanogan-Wenatchee National Forest. After traversing glades of mature fir, the grade eases a little, now following along a ridgeline. Forest cover thins and views expand, especially east to Storm King and the Kettles, while stately Douglas-firs and western larches in this parkland forest hold up the sky.\n\n_Hikers pause to admire a towering western larch._\n\nAt 2.2 miles, the trail cuts across a steep open slope (elev. 4900 ft) beneath the 5299-foot summit of Maple Mountain. Take in good views down Maple Creek and out to Fir Mountain. In summer, this south-facing slope sports showy blossoms. Look for bitterroot, biscuitroot (a parsley), and the rare and endemic Okanogan fameflower (in the miner's lettuce family).\n\nThe trail continues across the open slope for about another 0.25 mile before descending. Continue, or consider summiting Maple Mountain, an easy 0.4-mile off-trail hike from this point. Just turn north and pick a route across the grassy ledges, climbing about 350 feet for good views and even better flower gazing.\n\n### EXTENDING YOUR TRIP\n\nAdventurous hikers can continue on the Maple Mountain Trail all the way to Clackamas Mountain. From the flowered slopes, reach Maple Spring in about 0.4 mile, where the trail is easy to lose among cow paths. Angle above the spring and across a meadow to pick up tread again, and round a ridge (elev. 5000 ft) before dropping to a 4650-foot saddle. Then it's about 2.1 miles through larches and over and around open knolls to the Sweat Creek Basin Trail (elev. 5100 ft). Arrange a car shuttle and exit via one of the three trails down Clackamas to the Sweat Creek trailhead.\n\n  Fir Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/4 | 5.2 miles | 2200 feet\/5687 feet | June\u2013Nov\n\n**Map:** USGS Wauconda Summit; **Contact:** Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen; **Notes:** Open to horses. Range area. Watch for ticks; **GPS:** N 48 40.567 W 118 53.911\n\n  _**It's a stiff climb to this lonely peak in the heart of the Okanogan Highlands. Long gone is the fire lookout, but views from the rocky open summit remain in all directions. This short trail, though close to Republic, hasn't netted many visitors. Expect solitude, except for the deer\u2014they're prolific here. In summer, woodland wildflowers are abundant, and in autumn, larches brush the slopes gold.**_\n\n### GETTING THERE\n\nFrom Republic, travel west on State Route 20 for 8.5 miles, turning left onto Forest Road 31 (directly across from Sweat Creek Picnic Area). (From Tonasket, head east on SR 20 for 31.5 miles, turning right onto FR 31.) Continue 0.5 mile to the trailhead (elev. 3500 ft) located on your right.\n\n_Clackamas Mountain, Maple Mountain, and Storm King Mountain viewed from Fir's open summit_\n\n### ON THE TRAIL\n\nStart by passing through a gate (and be sure to close it after you). Fir Mountain, like most of the Okanogan and Columbia Highlands, is open range country. After a short initial climb, the way gradually ascends through open forest that has been selectively logged. Plenty of big pines, firs, and larches remain. High grasses line the tread, so be tick wary early in the season. Abundant snags make this a good trip for spotting woodpeckers.\n\nAt 1.2 miles, cross a creekbed (elev. 4175 ft) that is usually dry by late summer. Next come some brushy sections, and the grade gets serious. Climb steadily and steeply to reach an open grassy area at about 2 miles. Teaser views east hint at what lies ahead. The trail works its way up, over, and around Fir's granite and gneiss ledges. Admire some unusual rock formations and use caution along the ledges, especially if they're wet, icy, or snowy.\n\nAfter traversing some open ledges and negotiating a small cleft that warrants a handhold or two, emerge just below the broad open summit. Head right, through a clump of evergreens hiding a privy long out of operation. Then pop back out onto open rock and make the final short ascent to Fir's 5687-foot summit at 2.6 miles.\n\nSome debris remains of the fire lookout last used in the 1950s. Mount Bonaparte dominates the view north, while British Columbia's Baldy and Midway Mountains can be spotted beyond. Just across SR 20, admire Clackamas, Maple, and Storm King Mountains, which share Fir's geological features. The jagged North Cascades line the western horizon, foregrounded by the rounded and gentler Mount Annie and Moses Mountain. South is Swan Butte, east the Kettle Crest. Lookout worthy to say the least.\n\n  Swan Lake and Swan Butte\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 3.1 miles | 360 feet\/3960 feet | mid-Apr\u2013Nov\n\n**Map:** USGS Swan Lake; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Dogs permitted on-leash except on beach; **GPS:** N 48 30.932 W 118 50.138\n\n  _**Hike around a lovely lake encircled by cool forest high above the sweltering Sanpoil River valley, with a jaunt to Swan Butte. A popular swimming hole, Swan Lake is also popular with breeding loons. Wander along the tranquil shoreline in early evening or morning to hear this threatened bird's primeval calls.**_\n\n### GETTING THERE\n\nFrom Republic, follow State Route 21 south for 6.7 miles, turning right onto Scatter Creek Road (Forest Road 53). Follow it for 7.3 miles to Swan Lake Campground and another 0.3 mile to the day-use area and trailhead (elev. 3720 ft). Privy and camping available.\n\n_Loon cries can often be heard from Swan Lake's placid waters._\n\n### ON THE TRAIL\n\nFrom the day-use area, head down a stairway to the lakeshore (elev. 3660 ft) to pick up the trail, and start hiking right. Pass a swimming area and a rustic but charming kitchen shelter constructed by the Depression-era Civilian Conservation Corps. Then continue on the trail, rounding a boggy area.\n\nFree of gas-powered boats, the lake is serene, as is the surrounding forest. But the air is filled with the chatter of ground and Douglas squirrels and a cacophony of birdsong from nuthatches, chickadees, and warblers. The buzz of mosquitoes is also frequent in early season.\n\nTrace Swan's shoreline up and over ledges, through pine and fir groves, beneath big cottonwoods and larches, and across huckleberry patches. In late spring, arnica, lupine, penstemon, and wild strawberries brighten the way.\n\nAt about 0.6 mile, come to an area prone to early season flooding. Shortly afterward, come to some shoreline ledges perfect for lunching, sunning, and napping. Then round a cove, scamper across a floating bridge, and pass by another marshy area. Look for moose and beaver.\n\nAt 1.3 miles, after rounding a ledge providing excellent lake views, reach a junction. The trail right leads to Swan Butte in 0.5 mile\u2014take the flower-lined trail to the 3960-foot butte, with its tattered flag and decent views of the Kettle Crest.\n\nRetrace your steps to the junction and resume looping around the lake. The way passes by yet another quiet cove before utilizing an old road lined with cedars. At 2.7 miles (including the 1-mile butte round-trip), come to FR 53. Turn left. Pass the boat launch and find the trail once more as it travels 0.4 mile through the campground, back to the spur leading to the day-use area.\n\n### EXTENDING YOUR TRIP\n\nSpend the night at the inviting Swan Lake Campground and check out the nearby short trails along Fish and Long Lakes.\n\n  Golden Tiger Pathway\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 4.6 miles | 80 feet\/2435 feet | Mar\u2013Dec\n\n**Map:** USGS Republic; **Contact:** Ferry County Trails Association, <http:\/\/fctrails.com>; **Notes:** Wheelchair-accessible. Dogs permitted on-leash. ATVs, motorcycles permitted parallel to paved trail; **GPS:** N 48 38.744 W 118 43.281\n\n  _**Located on the eastern edge of the little gold-mining city of Republic, this short paved path is one of the most scenic rail trails in the state. Traversing sunny slopes, stately pine groves, and deep notches blasted into stubborn ledges, the Golden Tiger Pathway chugs along on a route once used for transporting ore to Canadian smelters. The path makes for a nice run or a leisurely hike with pauses at scenic overlooks of the pastoral Sanpoil River valley and the imposing Kettle River Range.**_\n\n### GETTING THERE\n\nFrom the junction of State Routes 20 and 21-south in Republic, head east on SR 20 for 0.6 mile (just past the high school) to the western trailhead (elev. 2425 ft) located on your right. Access for wheelchair users is on the left, 0.2 mile west of the main parking area. (From Kettle Falls, the eastern trailhead is 0.2 mile west of the SR 20\/21-north junction, on SR 20 at milepost 305.)\n\n### ON THE TRAIL\n\nThis trail was named for Republic High School's mascot, and plenty of golden tigers and alumni use this trail that connects the high school to the Ferry County Fairgrounds. The trail uses just a couple of the 28 miles of a former Great Northern Railroad trunk line (built in 1902) that extended from Republic to Danville on the Canadian border. A coalition of trail users and citizens are working hard to keep the section beyond the Golden Tiger nonmotorized (see \"On Track with the Ferry County Rail Trail\" sidebar). The Golden Tiger is unique in that it has a nonpaved motorized section running beside it. Motorized use is light and should not dissuade you from enjoying this wonderful trail.\n\nCarefully cross the highway and come to a junction. The trail left leads to the wheelchair-accessible parking lot. Turn right and enjoy the old rail grade as it runs along sun-soaked south-facing slopes, home to ground squirrels, yellow-bellied marmots, lizards, and the occasional snake.\n\nPass groves of big ponderosas, through cuts below cliffs, and above creek-cradling ravines. Stop to read interpretive signs (the work of Eagle Scout Austin Thompson in 2008) and gaze out from numerous overlooks at the Sanpoil Valley below, and Gibraltar Mountain hovering above it (from this angle, resembling the big European rock of the same name). Enjoy, too, views of the rooftop of Ferry County\u2014the Kettle River Range\u2014off in the east.\n\nON TRACK WITH THE FERRY COUNTY RAIL TRAIL\n\nIn the golden hills and emerald mountains of Ferry County, a broad coalition of folks called the Ferry County Rail Trail Partners (FCRTP) are moving full-steam ahead trying to create the state's next great rail trail. Realizing the potential this trail has for four-season muscle-powered recreation (and other benefits, including as a safe nonmotorized route for schoolchildren and an economic driver spurring tourism) the partners have their hands full trying to convince critics of the plan and interests that would rather see the corridor opened to motorized recreation.\n\nThe partners see the former 28-mile rail line that once serviced timber and mining lands as ideal for hikers, cyclists, and cross-country skiers, taking them along a corridor from the historic gold-mining city of Republic to Danville on the Canadian border. They're also hoping to tie in to British Columbia's Kettle Valley Rail Trail, making the Ferry County Rail Trail the first international rail trail in the western United States.\n\nWith stunning views of the Kettle River and the lofty and wild Kettle River Range, the new trail has great potential to lure visitors and promote an economy based on sustainable ecotourism. A major highlight along the trail, Curlew Lake (Hike 15), is home to one of Washington's loveliest state parks, with lakeshore camping and wonderful swimming, fishing, and paddling opportunities. At the north end of the 7-mile-long lake is a historic trestle, destined to be a popular feature along the trail.\n\nFor more information, visit the FCRTP online (www.ferrycountyrailtrail.com).\n\n\u2014 _C. R_.\n\n_The Golden Tiger pathway makes a good running route as well as a fine hiking path._\n\nAt 1.3 miles, reach what we like to call Privy Depot, which aside from its obvious function as a pit stop also offers an excellent valley and mountains view. At 2.2 miles, the paved path bends right to leave the railroad grade, descending a little to reach the eastern trailhead (elev. 2355 ft) near the fairgrounds. It's worth it to walk the last 0.1 mile or so, as it skirts wildlife-rich wetlands fed by the Sanpoil River.\n\n### EXTENDING YOUR TRIP\n\nWhile most of the Ferry County Rail Trail is currently better suited for mountain biking and cross-country skiing than hiking, the section on the north end of Curlew Lake sports a classic trestle spanning a cove on the lake. Access the trail from Kiwanis Road off of SR 21.\n\n  Curlew Lake Nature Trail\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 1.6 miles | 160 feet\/2500 feet | Mar\u2013Nov\n\n**Maps:** USGS Republic, state park map online (not accurate); **Contact:** Curlew Lake State Park, (509) 775-3592, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Dogs permitted on-leash; **GPS:** N 48 43.069 W 118 39.847\n\n  _**Enjoy a leisurely hike over grassy bluffs and along a pine-scented shoreline in one of Washington's prettiest and remotest state parks. Cherished for its boating, fishing, and family-friendly camping, Curlew Lake State Park also has a couple of miles of wonderful trails. Walk beneath stately pines. Scout a quiet cove. And enjoy a sweeping view of the narrow lake cradled by golden hills.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 2.9 miles to a junction with SR 21 (just past the county fairgrounds). (From Kettle Falls, follow SR 20 west for 40 miles to the junction.) Follow SR 21 north for 6 miles, turning left onto the state park road. Pass the ranger residence and bear left to reach a day-use parking area near a beach in 0.8 mile. The trailhead (elev. 2340 ft) is located just south of the restrooms in the campground loop.\n\n### ON THE TRAIL\n\nPick up the trail in the small campground. Within a few steps, the way splits. The trail left was once the main route\u2014now offering a shortcut. Veer right on newer tread cushioned with soft needles from the impressive ponderosa pines overhead.\n\nThe trail hugs the shore of the long, slender lake, coming to a nice point at 0.2 mile, complete with a bench for contemplation. When boats aren't present, this is a truly peaceful spot\u2014and a great vantage for bird-watching. Eagles, geese, osprey, and ducks can often be observed, and dragonflies usually flit about. Then hike alongside a quiet cove frequented by docile deer. The rocky-sandy soil of the hillside is moraine left from the great glaciers of the Ice Age.\n\nAt 0.4 mile, come to a junction. The trail left heads back to the trailhead. Continue right, soon coming to an observation deck. Come in the evening and sit still for the bird-watching. The largest North American shorebird, long-billed curlews favor dry grasslands like the ones found in this valley, but they're not common here despite the place name (try the Columbia Basin instead).\n\nContinue past the observation deck and follow a service road a short distance before picking up trail once more. At 0.6 mile, come to another junction (elev. 2400 ft). The loop continues left, but first go right for 0.2 mile\u2014an absolute-must side trip to a viewpoint (elev. 2500 ft) at the edge of an airstrip. Don't venture onto the runway, but do enjoy the sweeping view of Curlew Lake from this vantage.\n\n_Towering ponderosa pines grace Curlew's shoreline._\n\nRetrace your steps to the junction and continue straight, soon coming out to the park entrance road. Cross it and find the trail just to the right of the ranger residence. After 0.1 mile, you'll reach the main campground loop. Head left on the campground road to the boat launch. Pick up the trail for a final time and continue 0.3 mile along the lake-shore beneath a canopy of pines, returning to the beach and your vehicle.\n\n### EXTENDING YOUR TRIP\n\nVenture by car to the north end of Curlew Lake for a short hike along the old railbed to an intact, historic, and highly scenic trestle. Park where the Ferry County Rail Trail crosses Kiwanis Road (1.7 miles from the junction with SR 21), and walk a short distance west.\n\n## kettle river range\n\n_Barnaby Buttes and White Mountain from alpine meadows on Bald Mountain_\n\nCorralled by the Kettle River in the north and northeast, the Columbia River in the east and south, and the Sanpoil River in the west, the Kettle River Range forms an imposing wall across the western Columbia Highlands, with several peaks exceeding 7000 feet. It's an impressive range, yet these peaks\u2014among the oldest in Washington\u2014are gentle giants. Their smooth contours and rounded ridges make them more like the Smoky Mountains of North Carolina than the North Cascades. The surrounding countryside resembles Montana, with its big-sky valleys, parkland pine forests, and golden grassy hillsides. Deer are profuse and other wildlife abundant too. The Kettles contain some of the largest roadless tracts of national forest lands in Eastern Washington. To the Colville First Peoples, these mountains were sacred\u2014a sanctuary for young warriors to engage in vision quests. With miles of excellent trails traversing them, including a 43-mile route across the range's rooftop crest, the Kettles offer some of the finest hiking in the state.\n\n  Gibraltar Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 3.2 miles | 550 feet\/4200 feet | May\u2013Nov\n\n**Map:** USGS Bear Mountain; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Trail is under construction. Call ahead for updates, closures. Completed trail will be 12+-mile loop connecting to Ferry County Fairgrounds; **GPS:** N 48 35.856 W 118 41.478\n\n  _**Locally known as Old Gib, 3782-foot Gibraltar Mountain rises 1200 feet above the quaint mining town of Republic. Long admired from the valley, now thanks to a consortium of recreationists this beloved local landmark is sprouting a network of scenic trails. The first few miles are in place, and you can amble along a rolling ridge bursting with wildflowers and sweeping views, from Republic nestled below to the nearby lofty Kettle Crest.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 7.3 miles, turning right onto Hall Creek Road (Forest Road 99) (4.3 miles beyond the junction with SR 21). (From Kettle Falls, head west on SR 20 for 36 miles, turning left onto FR 99.) Continue 0.3 mile and turn right onto FR 2053. Follow this good dirt road 5 miles to the trailhead (elev. 3675 ft) located on your left. Privy available.\n\n### ON THE TRAIL\n\nNot since the 1930s, when the Civilian Conservations Corps was in full swing, has there been any major trail building in the hills above Republic. But all that changed in 2010 when recreation and conservation groups, in cooperation with the Forest Service, broke ground on a new trail network. Hard-working volunteers from Conservation Northwest, the Ferry County Trails Association, the Kettle Range Conservation Group, the Spokane Mountaineers, and the Washington Trails Association, along with trail crews from the Forest Service and the Curlew Job Corps (for disadvantaged youth), have constructed the first few miles of trail in what will eventually become a 12-mile loop with a connecting 6-mile spur to the Ferry County Fairgrounds.\n\nClose to town and open to hikers, equestrians, and mountain bikers, and with an elevation low enough to allow for early and late-season rambling, the Gibraltar Trail is sure to become a popular destination for locals and visitors alike. As of summer 2014, about half the trail has been constructed, including a short but highly scenic section to a 4200-foot knoll.\n\n_While the Kettles are shrouded in clouds, balsamroot embraces spring sunshine._\n\nIn the summer of 2013 the trail had not been built to the trailhead parking area. To reach the section of trail currently built, walk a short distance left on FR 2053 and then turn right onto a secondary dirt road. Yes, you could drive this road, but it makes for nice walking and gives you a little more exercise.\n\nFollow this road 0.7 mile to an old gravel quarry (elev. 3825 ft). Look just to the west and notice new tread. Heading north, the way immediately leaves the forest for flowered slopes. Wind up balds and ridges bursting with blossoms, and enjoy emerging views along with the floral show. Locate Brown Mountain's open pyramidal summit to the south. Just in front of it, notice the open slopes of the Camel Back. The trail is slated to wrap around that enticing ridge!\n\nContinue on newly constructed tread, gently climbing and wrapping around a 4200-foot knoll at 1.4 miles. Views are excellent\u2014especially southwest down the Sanpoil River valley and southeast over the Thirteen-mile Canyon region. The Kettle Crest rises prominently to the east, but that view gets better, so keep hiking along the ridge, with flowers like shooting stars, balsamroot, and phlox at your feet, to name just a few.\n\nAt 1.6 miles, leave the trail left in a small saddle (elev. 4175 ft). Continue just a short distance to a 4200-foot open knoll for a sweeping view that encompasses Mount Bonaparte and the Okanogan Highlands and the Kettle Crest from Mount Leona to White Mountain. Republic sits snuggly below, between hills that once yielded gold and that turn gold each fall thanks to larches. The peak just to your north is Old Gib, where a spur trail will eventually lead and then continue on to the fairgrounds. Anticipate more great hiking in the near future.\n\n### EXTENDING YOUR TRIP\n\nBeyond the saddle, follow the trail downhill into groves of larch and impressive ponderosa pines, passing a few small ponds along the way. Then follow new tread utilizing old woods roads that will eventually return to the trailhead at about 4.3 miles. The southern loop will traverse more open ridges, with a spur to 4784-foot Quartz Mountain, before dropping into a drainage, wrapping around the Camel Back, and crossing Camel Creek to meet up with the present tread. It will be glorious! As of 2013 over a mile of this route has been built.\n\n  Thirteenmile Canyon\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 9 miles | 1700 feet\/3750 feet | Apr\u2013Nov\n\n**Maps:** USGS Thirteenmile Creek, USGS Bear Mountain; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Watch for rattlesnakes, ticks; **GPS:** N 48 28.904 W 118 43.643\n\n  _**Venture through some of the most lonely, rugged, and spectacular backcountry in all of northeastern Washington. Traverse a deep and narrow canyon flanked by towering granite walls, before emerging onto its lofty rim graced with groves of stately old-growth ponderosa pine and sprawling meadows awash with wildflowers. Bears, deer, and cougars prowl this wild corridor, while eagles and hawks ride thermals above looking for bounty.**_\n\n### GETTING THERE\n\nFrom Republic, follow State Route 21 south for 12.3 miles to the trailhead (elev. 2050 ft), located just within the Colville Indian Reservation at milepost 148. (From Wilbur, follow SR 21 north for 56 miles to the trailhead.) Privy and primitive camping available.\n\n### ON THE TRAIL\n\nThe Thirteenmile Trail leads 18 miles from the cottonwood-lined Sanpoil River to Hall Creek Road near the pine and larch\u2013shrouded Kettle Crest. An old sheep and cattle drive, this trail travels through the 4700-acre Cougar Mountain and 12,700-acre Thirteenmile Roadless Areas. Both parcels are rich in wildlife and old growth and have long been sought by area conservation groups for inclusion in the national wilderness preservation system.\n\nThese lands are also historically significant and were once part of the Colville Confederated Tribes' reservation. But by the late 1800s, settlement in this region had accelerated, as miners, ranchers, and squatters trespassed onto these Native lands. Bowing to pressure, Congress withdrew the northern half of the Colville Reservation in 1892, reducing the reservation by 1.5 million acres. The influx of homesteaders brought an increase in ranching, logging, sheep grazing, and mining. Remnants and relics of these early pursuits can be seen along this trail.\n\n_Some of the biggest and oldest ponderosa pines in the state grow in the Thirteenmile Canyon._\n\nThe way immediately enters the impressive canyon of Thirteenmile Creek. Extreme heat is common in the summer, but big pines provide some shade relief. Spring is lovely, with agreeable temperatures and carpets of wildflowers that brighten the canyon floor. Look for larkspur, calypso orchid, and arnica. And keep an eye out for rattlesnakes\u2014the canyon harbors a healthy population.\n\nAt about 1 mile, cross a scree slope and begin working your way up out of the canyon. The tread can be rocky at times. When not watching your footing, stare up at the impressive sheer canyon walls surrounding you. At about 1.8 miles, reach an overlook (elev. 3000 ft) of the canyon and the terrain you just traversed. Then enjoy easy going along the rim through pine groves and thickets of Douglas maple that add golden streaks to the forest come autumn.\n\nAt about 2.2 miles, reach a draw that usually harbors a flowing creek. Just shy of 3 miles, come to another creek-flowing draw (elev. 2900 ft). Continue through open forest and grassy areas (watch for ticks), coming to a small wetland and the remains of an old herder camp at about 3.4 miles. A quarter mile beyond, reach an old road (elev. 3050 ft). Carry on if curiosity and wanderlust persist.\n\nAt 4.5 miles, crest a small ridge (elev. 3750 ft) that grants views of the surrounding wild and lonely hills and meadowy Thirteen-mile Mountain to the east. This is a good spot to call it a day. From here the trail switchbacks downward, reaching the Cougar trailhead (elev. 3550 ft) on FR 2054 in about 0.8 mile.\n\n### EXTENDING YOUR TRIP\n\nContinue beyond the Cougar trailhead for 3.2 miles to Thirteenmile Mountain (Hike 18), traversing impressive old-growth groves of ponderosa pines and some of the wildest and prettiest country in northeastern Washington. Or, arrange a car shuttle for a one-way trip from the Bear Pot or Cougar trailheads down to the Sanpoil River trailhead.\n\n  Thirteenmile Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 9.2 miles | 1800 feet\/4885 feet | May\u2013Nov\n\n**Maps:** USGS Bear Mountain, USGS Edds Mountain; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Watch for ticks. FR 2053 is rough in spots, requires high-clearance; **GPS:** N 48 30.998 W 118 36.069\n\n  _**From Thirteenmile Mountain you can see for miles and miles and miles. Follow an old sheep drive to a historic lookout site that overlooks a magnificent canyon, golden hillsides, and parkland pine forests of the nearly 13,000-acre Thirteenmile Roadless Area. Moose, cougars, wolverines, and the occasional grizzly traipse here, through one of the wildest corners remaining in northeastern Washington.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 7.3 miles, turning right onto Hall Creek Road (Forest Road 99) (4.3 miles beyond the junction with SR 21). (From Kettle Falls, head west on SR 20 for 36 miles, turning left onto FR 99.) Follow this at-first good gravel road 5.2 miles to where FR 600 bears left. (Note: County Road 233 through Refrigerator Canyon is washed out, hence this longer approach.) Continue right, now on Nine Mile Road (FR 2053), and come to a junction in 2.7 miles. Bear left onto FR 2054, passing the Nine Mile Falls trailhead (an excellent 0.3-mile trail to the falls), and after 0.6 mile bear left onto FR 2055. Follow it for 3.4 miles to a primitive campground and the trailhead at road's end (elev. 4200 ft).\n\n_An endless landscape of rolling hills and grassy slopes can be viewed from the old lookout site._\n\n### ON THE TRAIL\n\nThe hike begins on the Bear Pot Trail near a seasonal wetland. Follow the good trail through boggy forest and at 0.5 mile reach an old trapper's cabin. Then continue through a stand of lodgepole pine, and after a brief climb reach a junction (elev. 4400 ft) with the Thirteenmile Trail at 0.8 mile.\n\nAn old sheep drive, the Thirteenmile Trail travels nearly 18 miles from the Sanpoil River to Hall Creek Road near the Kettle Crest. Except for a handful of intrepid Pacific Northwest Trail through-hikers and a few deer hunters in the fall, expect to be alone. Chances are better of meeting up with four-legged trail users\u2014deer, moose, bear, coyotes, and cougars. Moose tracks and droppings attest to the frequency of at least these visitors.\n\nTurn right, heading west through parkland ponderosa pine forest, with its carpet of golden grasses (watch for ticks in spring) and clusters of shrubby Douglas maples (admire colors in fall) that provide excellent forage for woodland critters. After ascending a small knoll (elev. 4575 ft) and passing an old mine bore, the way drops into a small lush ravine. At 1.9 miles, cross Thirteenmile Creek (elev. 4150 ft), a mere trickle at this point; then begin climbing 125 feet or so out of the canyon.\n\nNow traversing south-facing slopes, wander by some pines impressive in age and stature. Pass meadows and an old burn rife with big snags that harbor all types of insects, birds, and small mammals. At 3.4 miles, skirt a large grassy wetland lined with aspen (elev. 4175 ft). Then begin climbing again, weaving through more ancient groves of giant ponderosas. The way rounds some knolls and makes a few dips, crossing meadows and forest of spruce and larch. The habitat diversity is rich.\n\nAt 4.1 miles, reach an old jeep track (elev. 4500 ft) once used to access the fire tower on Thirteenmile Mountain. Known as FR Spur 300, it can still be driven by high-clearance vehicles and offers a much shorter (and less interesting) approach to this hike. Walk left along the track a short way, and then turn left back onto the trail.\n\nClimb across open grassy slopes, skirting just below the summit of Thirteenmile Mountain. At about 4.4 miles (elev. 4650 ft), where the trail begins to curve west, leave the tread and head directly north for 0.2 mile off-trail, up to the 4885-foot summit. All that remains of the fire lookout are concrete blocks, some well-weathered timbers\u2014and spellbinding views in every direction: North along the Kettle Crest to British Columbia's Midway Mountains. West to Mount Bonaparte and the rolling Okanogan Highlands. South, trace Thirteenmile Creek through its magnificent canyon. And east, admire the well-rounded lofty summits of Granite, Fire, and Seventeenmile Mountains. Resembling Appalachian peaks with their well-worn fa\u00e7ades, these mountains are among the oldest in Washington.\n\n### EXTENDING YOUR TRIP\n\nFor a truly lonesome journey, follow the Thirteenmile Trail east from the Bear Pot Trail junction. The way climbs to a 5150-foot gap between Fire and Seventeenmile Mountains (both nice off-trail scrambles) before descending 800 feet through ancient ponderosas to reach FR 600 at 4.9 miles.\n\n  Edds and Bald Mountains\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/4 | 10.6 miles | 2450 feet\/6300 feet | June\u2013Nov\n\n**Map:** USGS Edds Mountain; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Watch for ticks. FR 99 is rough in spots, requires high-clearance; **GPS:** N 48 33.999 W 118 33.642\n\n  _**Hike one of the Kettle River Range's loneliest trails to one of its most beautiful alpine meadows set beneath one of its most distinguished summits. It's a stiff climb with many rewards: solitude, stunning scenery, and the opportunity to scramble a couple of soaring summits. The wildflower displays along this trail rank among the finest in Eastern Washington, and the habitat traversed is some of the best in the state for elusive megafauna.**_\n\n_A \"holy\" snag among the sprawling meadows of Bald Mountain._\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 7.3 miles, turning right onto Hall Creek Road (Forest Road 99) (4.3 miles beyond the junction with SR 21). (From Kettle Falls, head west on SR 20 for 36 miles, turning left onto FR 99.) Follow this at-first good gravel road 4.4 miles and turn left onto FR Spur 300. Continue 1.5 miles to the trailhead (elev. 4350 ft). Privy and primitive campsites available.\n\n### ON THE TRAIL\n\nThe way starts by following an old logging road. The grade is gentle and the walking pleasurable, but the roadway is covered in tall grasses, so be tick aware early in the season. At 1.9 miles, come to the old trailhead (elev. 4880 ft). Turn left and follow cairns to begin climbing\u2014steeply at times\u2014up a ridge and through the 1988 White Mountain burn zone (hot and dry; carry lots of water). Clumps of willows and hardy evergreens that survived the fire dot the hillside, and wildflowers paint the open hillsides.\n\nSavor the sweet smell of juniper and sage and admire lichen-blotched granite ledges along the way. Survey the countryside too. The views west and south are expansive. Look south at Granite, Fire, and Seventeen-mile Mountains\u2014they look like they belong in the Appalachians. The last Ice Age did a nice job wearing down these peaks, among the oldest in Washington.\n\nClimbing higher, the way steepens and the tread gets sketchy across grassy slopes. Watch for cairns. The trail skirts below Edds's 6550-foot summit, topping out at about 6300 feet at 3.6 miles. It's an easy scramble to the mountain's high point if you're so inclined. Otherwise, continue on what soon becomes one of the prettiest sections of trail in the entire Kettle River Range.\n\nAcross sprawling meadows bursting with blossoms, slowly descend to a saddle. Only the views can rival the wildflowers: Look south to the Barnaby Buttes, Grizzly Mountain, and White Mountain along the Kettle Crest. Locate the Hall Ponds, a research area with rare flora, straddling the high divide between Hall and Ninemile Creeks. And stare east at pyramidal Bald Mountain, the rockiest and craggiest of all the Kettles. When viewed from the north Bald looks forbidding, but from the south the summit appears more subdued, wrapped in inviting alpine meadows.\n\nAfter passing through a patch of pines that escaped the big fire of 1988, reach the saddle (elev. 6050 ft) between Edds and Bald Mountains at 4.1 miles. Then gently ascend and traverse sublime meadows, high across Bald's southern slopes, to crest a ridge (elev. 6300 ft) at 5.3 miles. This is a good turnaround point. From here the trail drops 300 feet in 0.5 mile, reaching the Kettle Crest Trail at a spring.\n\nIn the past few years, there have been a few confirmed grizzly sightings in this lonely and wild country. Whether this monarch of the mountains will survive in Washington is a matter of public policy. Groups like Conservation Northwest advocate and educate about the importance of retaining and recovering grizzly populations in the Northwest.\n\n### EXTENDING YOUR TRIP\n\nBald Mountain's 6940-foot summit makes a nice scramble. Head up open slopes to the summit block, and then carefully pick your way up through jumbled talus to the pointy peak for one of the best 360-degree views in the Kettles.\n\n  Snow Peak Cabin\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 6.4 miles | 1275 feet\/6350 feet | June\u2013Nov\n\n**Map:** USGS Sherman Peak; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Watch for ticks. Reserve the cabin at www.recreation.gov; **GPS:** N 48 35.058 W 118 31.916\n\n  _**Hike across an eerily beautiful landscape of silver snags left behind from the 1988 White Mountain Burn. It's been over a quarter century since much of Snow Peak went up in flames, but a new and regenerating forest is busy reclaiming the mountain. Enjoy prolific wildflowers and sweeping views en route to a charming mountain cabin set high along the Kettle Crest.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 7.3 miles, turning right onto Hall Creek Road (Forest Road 99) (4.3 miles beyond the junction with SR 21). (From Kettle Falls, head west on SR 20 for 36 miles, turning left onto FR 99.) Follow this at-first good gravel road for 3.3 miles, turning left just beyond a cattle guard onto FR Spur 100. Reach the trailhead (elev. 5250 ft) in 4.7 miles.\n\n_The Snow Peak Cabin sits on a high gap beneath the summit of Snow Peak._\n\n### ON THE TRAIL\n\nImmediately starting in the old burn zone, the trail wastes no time climbing. A few surviving big firs provide some shade among the many snags. The understory is grassy here (planted after the fire to prevent erosion), so watch for ticks early in the season. The open forest and plentiful forage favors deer. You should see plenty. Lots of flowers too\u2014asters and lupine paint the hillsides purple.\n\nContinue ascending. At times the trail is lined with walls of willows and 15- to 20-foot pines\u2014nature in action regenerating the mountain. At 2.3 miles, crest a 6325-foot knoll. Then descend slightly, coming to a junction with the Kettle Crest Trail (elev. 6300 ft) at 2.5 miles. Turn right and traverse the high open slopes of Snow Peak. At 7103 feet, Snow is the second highest of the Kettle peaks and, as its name suggests, often harbors snow into the summer months. A popular backcountry skiing destination, the cabin you are heading to is well used and appreciated by winter recreationists.\n\nAfter a little more climbing, reach a spring (elev. 6350 ft); then begin descending across open slopes. Lupine, paintbrush, fireweed, and pearly everlastings contrast with the silver snags and blackened logs left behind by the fire. Views are excellent to pointy Bald Mountain (south) and across the Okanogan Highlands to Mount Bonaparte, Clackamas Mountain, and Bodie Mountain.\n\nAt 3.1 miles, come to a junction near a spring. Take the trail right for a short distance to the Snow Peak Cabin (elev. 6200 ft). Resembling a pioneer cabin (with solar panels!), it has space for six people (dogs allowed). It was built by the Snow Peak Shelter Alliance (consisting of various recreation groups) and the Colville National Forest, and it opened to the public in 1996. If it's unoccupied, check it out. Otherwise, please respect the privacy of any groups staying at the facility. Stargazing is amazing from the cabin site\u2014and morning coffee on the porch looking out at Snow Peak is divine.\n\n### EXTENDING YOUR TRIP\n\nThe Kettle Crest Trail south to the Edds Mountain Trail offers lonely rambling and nice views east. And the 7103-foot summit of Snow Peak makes for a good cross-country ramble. Although steep, it's fairly straightforward, across alpine meadows. The views are amazing, from British Columbia's Rossland Range to Lake Roosevelt.\n\n  Sherman Peak\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 6 miles | 1200 feet\/6400 feet | mid-June\u2013  \nNov\n\n**Maps:** USGS Sherman Peak, USGS Copper Butte; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses; **GPS:** N 48 36.514 W 118 28.605\n\n  _**Enjoy striking views of the forces of nature. This full circle around 6998-foot Sherman Peak passes through two radically different landscapes: a lush, green old-growth forest and one that was scorched by wildfire, leaving surreal silver snags behind. But nature has come full circle too, as the fire-consumed forest is nicely regenerating. And with these diverse forest communities, wildlife is prolific. Don't forget the binoculars.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 16.8 miles to Sherman Pass. (From Kettle Falls, follow SR 20 west for 26 miles to Sherman Pass.) Turn left (north) and follow the access road 0.1 mile to the trailhead (elev. 5500 ft). Privy available.\n\n### ON THE TRAIL\n\nEasy access, being a loop, and having plenty of views make this hike one of the more popular in the Kettles. From the trailhead, head left (south) on the Kettle Crest Trail, quickly coming to a junction with the Sherman Pass Trail (which travels 4 miles to the Jungle Hill Trail) and the Sherman Pass Tie Trail (which heads 0.7 mile to the Sherman Overlook Campground). For Sherman Peak, continue right, dropping steeply into a cool, wet, tight ravine (elev. 5360 ft). Climb out of it and come to SR 20 at 0.4 mile. The trail resumes on the other side of the highway; be careful crossing the road.\n\nIn cool larch and lodgepole pine forest, gently climb, winding around granite ledges and passing window views east. At 1 mile, come to a junction (elev. 5800 ft) by a creek and winter emergency cache. You'll be returning from the right on the Sherman Peak Loop Trail, so continue left on the Kettle Crest Trail. At 1.4 miles, after skirting beneath a large talus slope, reach the edge of the 1988 White Mountain burn zone (elev. 5900 ft). This lightning-caused fire burned more than 20,000 acres, but more than twenty-five years later, new green growth has crowded out the silver snags and blackened logs.\n\nBegin a long sweeping traverse of Sherman's eastern ridge. Rows of 10+-foot-tall pines and fragrant lupines line the way. Pause to take in excellent views north of Columbia, Wapaloosie, King, and Mack Mountains. At 2.4 miles, crest the ridge in a small saddle (elev. 6300 ft). Then traverse Sherman's southern slopes, with views of Snow Peak, the Barnaby Buttes, and White Mountain.\n\nAster and lupine paint Sherman a purple mountain majesty. Woodpeckers and nuthatches flit upon the snags. The mountain is vibrant and alive. The trail climbs higher but doesn't go to the top of Sherman. It's an easy scramble to the 6998-foot pyramidal summit if you feel like peak bagging.\n\nAt 3.2 miles, just beyond a faint trail leading down to a campsite, come to a junction (elev. 6400 ft). The Kettle Crest Trail continues south to the Snow Peak Cabin (Hike 20). Head right instead, onto the Sherman Peak Loop Trail, crossing gorgeous meadows and savoring sweeping views west across snaking Highway 20 to the Okanogan Highlands and North Cascades.\n\nThe way then descends at a good clip to reenter forest before wrapping around the north side of Sherman Peak. At 4.1 miles, take a break at a ledge that grants a superb view of Columbia Peak and Sherman Pass. Then leave the burn zone at 4.4 miles, entering cool stands of pine and larch. Skirt beneath a scree slope and by little Sherman Pond, one of the few ponds located within this mountain range. Cross its outlet and shortly afterward, at 5 miles, reach a familiar junction and turn left to close the loop in 1 mile.\n\n_Silver snags punctuate grassy slopes on Sherman Peak._\n\n  Barnaby Buttes\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 7.4 miles | 1975 feet\/6534 feet | June\u2013early  \nNov\n\n**Map:** USGS Sherman Pass; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 738-7700, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Last 1.5 miles of FR 2014-500 are rough, requires high-clearance; **GPS:** N 48 32.274 W 118 26.741\n\n  _**Follow an old fire road, first through thick timber, then through silver forest to an old fire lookout site propped above meadows flush with flowers and fauna. Only four pillars and a concrete staircase remain of the Barnaby Buttes lookout tower. But the views from this lonely post across this wild corner of the Kettles are still grand. This is moose, bear, coyote, and cougar habitat, so you might luck into seeing them on this seldom-hiked route.**_\n\n### GETTING THERE\n\nFrom Kettle Falls, drive west on State Route 20\/US Highway 395 for 3.6 miles to where the routes split. Continue west on SR 20 (Sherman Pass National Scenic Byway) for 10.3 miles, turning left onto South Fork Sherman Creek Road (FR 2020). Follow this good gravel road for 6.5 miles to a junction. (From Republic, follow SR 20 east for 20.5 miles, turning right onto FR 2020\u20143.6 miles east of Sherman Pass. Continue south for 5.9 miles to the junction with FR 2014.) Bear left onto Barnaby Creek Road (FR 2014), and after 0.3 mile turn right onto FR 2014-500. Follow this road for 2.4 miles (bear left at 0.9 mile) to the trailhead (elev. 4600 ft).\n\n### ON THE TRAIL\n\nBeginning on an old, well-graded fire road, immediately start climbing through a thick stand of pine and larch. Skirt a creek (the only water along the way) and an old cut, and continue beneath a cool forest canopy. The way may be littered with moose and deer droppings and plenty of tracks from the predators that pursue them, particularly cougars and coyotes.\n\nAt 2.1 miles, after making a couple of sweeping switchbacks, enter the 1988 White Mountain burn zone. The forest is recovering well, but plenty of snags and blackened logs still provide excellent habitat for insects and birds. White Mountain, where the fire began, can be seen to the south. Its northern slopes of granitic talus fields put the \"white\" into the mountain.\n\nAt 2.6 miles, come to a junction with the Kettle Crest Trail, atop the crest itself (elev. 6060 ft). Left leads to White Mountain (Hike 23). Right meanders toward the Barnaby Buttes\u2014your objective. Cutting a path through 5- to 8-foot-tall lodgepole pines, the trail soon leaves the old fire road to march up a knob cloaked in golden grasses. Enjoy excellent views down into the wild Hall and Thirteenmile Creek drainages.\n\nSlightly descend into a pocket of greenery spared from the conflagration of 1988, and once again follow the old woods road. At 3.4 miles (elev. 6300 ft), come to a signed junction with the spur leading to the old lookout site. The spur exists only in memory. Numerous blowdowns obfuscate the way, which completely disappears in the grassy slopes below the summit. Don't let that hinder your exploration. Just make your way north across the open slope, aiming for a small knob graced with aspen and juniper. After about 0.3 mile, reach the 6534-foot summit with its staircase to heaven.\n\nViews are grand across Barnaby's lofty lawns to Huckleberry Mountain and Calispell Peak to the east; White Mountain and Grizzly Mountain to the south; Thirteenmile, Fire, Granite, and Moses Mountains to the west; and Edds and Bald Mountains to the north. A sliver of Lake Roosevelt can often be seen shimmering in the late-afternoon sun. Consider staying on the summit late into the day, for it abounds with wildlife.\n\n_White Mountain from Kettle Crest Trail on the way to Barnaby Buttes_\n\n### EXTENDING YOUR TRIP\n\nHike to White Mountain (Hike 23) from the Barnaby Buttes and Kettle Crest Trail junction. It's about 1.5 miles to the summit spur trail and another 0.3 mile to the top.\n\n  White Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 6.8 miles | 1725 feet\/6923 feet | mid-June\u2013  \nNov\n\n**Map:** USGS Sherman Pass; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 738-7700, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Respect this sacred site of the Colville Confederated Tribes. Do not disturb artifacts or rock pits; **GPS:** N 48 30.092 W 118 25.312\n\n  _**A broad, lofty summit along the Kettle Crest, White Mountain provides stunning views down to Lake Roosevelt and across the vast ridges and valleys of northeastern Washington. Sacred site to Native peoples for vision questing, and home to moose, wolverine, and the occasional grizzly, White will instill a sense of reverence for nature in all who hike its wildflower-carpeted slopes.**_\n\n### GETTING THERE\n\nFrom Kettle Falls, drive west on State Route 20\/US Highway 395 for 3.6 miles to where the routes split. Continue west on SR 20 (Sherman Pass National Scenic Byway) for 10.3 miles, turning left onto South Fork Sherman Creek Road (FR 2020). Follow this good gravel road for 6.5 miles to a junction, and bear left onto Barnaby Creek Road (FR 2014). (From Republic, follow SR 20 east for 20.5 miles, turning right onto FR 2020\u2014the junction is 3.6 miles east of Sherman Pass. Continue south for 5.9 miles to the junction with FR 2014.) Continue on FR 2014 for 4.1 miles, turning right onto FR Spur 250. Follow this rough road 4.4 miles to the trailhead (elev. 5225 ft).\n\n### ON THE TRAIL\n\nThe epicenter of a 1988 wildfire that scorched more than 20,000 acres along the Kettle Crest, White Mountain's natural communities were radically altered\u2014but not destroyed. Nature is resilient and always in flux. It didn't take long for feisty pine saplings to burst from the blackened soil. Grasses and a profusion of wildflowers now carpet the once scorched forest floor. And the now-more-diverse floral cover favors a wider variety of wild critters. Moose, deer, bear, coyote, and cougar are abundant, woodpeckers and raptors profuse.\n\n_Sunny flowered slopes on White Mountain_\n\nWhile patches of mature fir and larch survived the fire, shade is at a premium. Start early, don't forget the sunscreen, and carry plenty of water. Start in the burn zone and weave through a few lone larches and thickets of willows. After about 0.4 mile, start to climb. After about another 0.4 mile, skirt a talus slope of the shiny white granite that gives the mountain its name.\n\nAt 1.2 miles, begin to switchback near a spring and stock trough (elev. 5600 ft). Steadily ascend nicely graded switchbacks through patches of mature forest. At 1.8 miles, emerge in sprawling meadows bursting with summer wildflowers. Views are excellent south into the Colville Indian Reservation, of Grizzly Peak and the Hall Creek drainage.\n\nAt 3 miles, crest the mountain's southwestern shoulder (elev. 6770 ft). Enter forest and slightly descend, coming to a small meadow at about 3.1 miles. The unmaintained trail to the summit heads to the right (look for a weathered sign on a snag) and may be hard to follow in spots, but the route is pretty straightforward. After about 0.3 mile, reach White's 6923-foot summit and its extensive views: from the Columbia Plateau south to all along the Kettle Crest north, and from the Selkirks east to the North Cascades west. Just below the old lookout site are talus slopes dotted with rock pits built by young tribal members for vision quests. Close your eyes. Listen to the winds. Feel the sun's rays. A powerful place indeed.\n\n### EXTENDING YOUR TRIP\n\nThe Kettle Crest Trail begins here and travels more than 43 miles along some of the highest summits in Eastern Washington, making it a fine backpacking route. And Barnaby Buttes (Hike 22) is just a few miles north along the trail.\n\n  Columbia Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 8 miles | 1360 feet\/6782 feet | June\u2013Nov\n\n**Maps:** USGS Sherman Peak, USGS Copper Butte; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Range area; **GPS:** N 48 36.519 W 118 28.609\n\n_You'll find excellent views of Wapaloosie and King Mountains from Columbia's summit loop trail._\n\n  _**Roam high-country meadows carpeted with dazzling wildflowers. Enjoy sweeping views south to the lofty, lumpy Kettle Crest and east to the unbroken swaths of forest cloaking the Sherman Creek valley, King Mountain, and the Twin Sisters. Flush clutches of grouse and greet herds of deer while ambling to a historic fire lookout cabin that has graced this summit since 1914. These are some of the charms awaiting you on this easily accessible hike.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 16.8 miles to Sherman Pass. (From Kettle Falls, follow SR 20 west for 26 miles to Sherman Pass.) Turn left (north) and follow the access road 0.1 mile to the trailhead (elev. 5500 ft). Privy available.\n\n### ON THE TRAIL\n\nSherman Pass offers the easiest access to the 43+-mile Kettle Crest Trail. A national recreation trail, lucky Trail No. 13 (the trail's official number) winds along the soaring spine of the Kettle River Range. Heart of the Columbia Highlands and transition zone between the coastal Cascades and interior Rockies, the Kettles are rich in biological diversity and act as an ecological bridge between those two other ranges.\n\nFollow the Kettle Crest Trail north through cool groves of pine and fir and carpets of lupine, arnica, and other showy flowers. At 0.2 mile, cross a power-line swath and then enter the 29,000-acre Profanity Roadless Area, the largest unprotected roadless tract remaining in Eastern Washington (see \"Untrammeled Eastern Washington\" sidebar in the Blue Mountains section). This and other nearby roadless areas were left out of the 1984 Washington Wilderness Act, and conservationists\u2014most notably the Kettle Range Conservation Group\u2014continue to advocate that these areas receive federal wilderness protection.\n\nWILDERNESS, JOBS, AND A WAY OF LIFE IN THE BALANCE\n\nNortheast Washington's Columbia Highlands is the Evergreen State's final frontier. It's a land of wide-open spaces still harboring some of the West's wildest and most threatened species\u2014grizzly, caribou, wolverine, and lynx. It's sparsely populated by folks who still make a living working off the land.\n\nWhile large portions of the Columbia Highlands consist of public lands, just less than 3 percent of it is protected as wilderness. Conservationists would like to see more wilderness established to protect habitat for endangered and threatened species; preserve the area's old-growth forests; and provide unparalleled opportunities for hiking, horseback riding, skiing, hunting, and other sustainable forms of recreation. And while mining, ranching, and forestry still make up a large percentage of the economy here, economic forces are threatening to change that, affecting the livelihoods of thousands of residents in this remote corner of the state. Sounds like all of the makings for a jobs versus wilderness scenario, doesn't it?\n\nNot this time around. Conservation groups have been seeking cooperative and collaborative solutions rather than combative ones. An effort called the Columbia Highlands Initiative has been seeking to restore forests, promote working ranches, and join with the New Forestry Coalition (formerly the Northeast Washington Forestry Coalition), a diverse group of forest products manufacturers, conservation leaders, government officials, business owners, educators, loggers, hikers, and citizens at large. The goal is to help ensure that the Colville National Forest is managed in a balance that preserves wilderness, guarantees outdoor recreation opportunities, and sustains jobs in the region.\n\nThe initiative calls for creating up to 350,000 acres of new wilderness from existing roadless areas as well as providing for enough timber from managed areas to sustain local forestry jobs. The initiative and even the Forestry Coalition have detractors. But US Department of Agriculture officials have pegged the effort as a model for finding common ground on land-use issues.\n\nFor more information, visit the Northeast Washington Forestry Coalition online (www.newforestrycoalition.org).\n\n\u2014 C. R.\n\nA pure delight to hike, the trail climbs gently, weaving around granite ledges. Soon you'll meander through sage-scented pocket meadows flanked by patches of aspen that glow golden in autumn. At 1.6 miles, come to a small ledge granting good views west. Then enter mature forest, including groves of Engelmann spruce.\n\nPass a spur that leads left to a cattle trough. Cattle paths throughout the Kettles have caused more than a few hikers to go astray. At 2.4 miles, reach a junction (elev. 6130 ft). Turn right, immediately coming to a fence-enclosed spring. Then steadily gain elevation, passing big mossy-trunked Douglas-firs. At 3 miles, come to another junction (elev. 6425 ft).\n\nIf your sole objective is to Columbia's summit, head left. But you'll miss a scenic loop around the mountain, so reconsider and head right instead; first across sun-kissed meadows bursting with wildflowers, then through cool larch and fir forests teeming with huckleberries. After dropping about 75 feet, gain it back and then some, working your way over north-facing ledges with breathtaking views of Wapaloosie, King, and Mack Mountains. In October stare out across waves of gold, compliments of the Kettle's profusion of larches.\n\nAt 4.1 miles, just after cresting a small gap, reach yet another junction (elev. 6500 ft). The loop trail continues right 0.3 mile, bringing you back to familiar territory. But first, turn left and steadily climb 0.3 mile through rows of lodgepoles to reach the 6782-foot summit of Columbia Mountain. Immediately be wooed by a fire lookout cabin, built in 1914. Gracing this peak since the Woodrow Wilson administration, this structure is on the National Historic Register and was lovingly restored by the Forest Service through their Passport in Time program, which connects volunteers with professionals for archeological and historical preservation projects. The lookout cabin on Mount Bonaparte (Hikes 3 and 4), also built in 1914 (and still standing), is nearly identical.\n\nBe sure to wander around the broad summit for excellent views south of Sherman and Snow Peaks, pointy Bald Mountain and Granite, Fire, and Seventeenmile Mountains. Moses Mountain can be seen to the southwest, and Mount Bonaparte dominates the northwest horizon.\n\n### EXTENDING YOUR TRIP\n\nFrom the Columbia Mountain trail junction, the Kettle Crest Trail continues north through big firs and western larches that set the range aglow in yellow come October. At 1.2 miles from the junction is a piped spring and good camp.\n\n  Jungle Hill\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/4 | 8 miles | 2250 feet\/6550 feet | late May\u2013Nov\n\n**Map:** USGS Copper Butte; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses; **GPS:** N 48 38.085 W 118 27.062\n\n  _**Few people venture onto this obscure peak in the Kettle River Range. That's because Jungle Hill's 6544-foot summit is forested and no trail leads to it. The little-used Jungle Hill Trail, however, will lead you close, delivering you high on the lonesome Kettle Crest, where an abundance of deer track and paw prints prove that this wilderness path is far from lightly traveled.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 21 miles, turning left onto Albian Hill Road (FR 2030) (4.2 miles beyond Sherman Pass). (From Kettle Falls, head west on SR 20 for 22 miles, turning right onto FR 2030.) Follow FR 2030 for 0.5 mile, turning left onto a spur. Continue 0.25 mile to the trailhead (elev. 4350 ft) at a small campground. Privy available.\n\n### ON THE TRAIL\n\nThe trail starts with a short descent to Sherman Creek (elev. 4300 ft), reaching a junction at 0.1 mile with the Sherman Pass Trail. Continue straight on the Jungle Hill Trail, crossing the creek and beginning to climb. The trail parallels Sherman Creek for a short distance and eventually pulls away from it, although you'll hear its tumbling waters for most of the hike.\n\nWinding through giant larches and clusters of aspens, this path is quite colorful come late September. But owing to its southern exposure, the Jungle Hill Trail is a good choice for spring hiking too, often snow-free by late spring. Along a sun-kissed ridge, the way steadily gains elevation, steeply at times and occasionally via short switchbacks.\n\nAt about 1.5 miles, come to a ledge (elev. 5100 ft) with views of nearby Columbia Mountain and the basin cradling the head-waters of Sherman Creek. About 0.5 mile farther, Jungle Hill comes into view. The trail continues upward, now traversing lodge-pole pine forest punctuated with pocket meadows. At about 2.5 miles, reach alpine meadows that bake in the afternoon sun.\n\n_The views east are extensive from Jungle Hill._\n\nCool forest soon offers relief, and an easier grade some respite. Walking along the meadow edge fragranced with sage is pure delight, with more excellent views eastward over the Sherman Creek valley and out to Huckleberry Mountain and Calispell Peak; westward through a gap in the Kettle Crest out to Moses Mountain and the North Cascades; and south along the crest itself. At 4 miles, near a campsite and spring, reach the Kettle Crest Trail (elev. 6550 ft). Call it a hike, or consider rambling farther.\n\n### EXTENDING YOUR TRIP\n\nWapaloosie Mountain (Hike 26) is an easy 1.2 miles north along the Kettle Crest Trail, primarily through open meadow. Or, if you're up for a big adventure, make a loop by following the Kettle Crest Trail south for 7 miles to Sherman Pass, and then take the Sherman Creek Trail 4 miles back to the trailhead.\n\n  Wapaloosie Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/3 | 6 miles | 2000 feet\/7018 feet | late May\u2013  \nNov\n\n**Map:** USGS Copper Butte; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses; **GPS:** N 48 39.828 W 118 26.402\n\n  _**One of the highest summits on the Kettle Crest, 7018-foot Wapaloosie Mountain offers extensive views and some of the finest alpine meadows in the Columbia Highlands. The trail traverses slopes of sagebrush interspersed with pine and fir groves. And thanks to a southeastern exposure, the trail usually melts out by midspring, when arrowleaf balsamroot speckles the mountainside bright yellow. Later, lupines add shades of violet to the soft greens of the summit's sedges and grasses before western larches give a golden performance and finally winter's white blanket descends.**_\n\n_A pair of hikers admire the extensive view south across the Kettle Crest._\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 21 miles, turning left onto Albian Hill Road (FR 2030) (4.2 miles beyond Sherman Pass). (From Kettle Falls, head west on SR 20 for 22 miles, turning right onto FR 2030.) Follow FR 2030 for 3.3 miles to the trailhead (elev. 5025 ft) at a small campground. Privy available.\n\n### ON THE TRAIL\n\nMaintained by the Ferry County Back Country Horsemen, this popular trail is in excellent shape. Beginning in a thick forest of lodgepole pine, follow the trail as it crosses a tributary of the North Fork Sherman Creek\u2014the only reliable water on this hike. Then get down to business climbing and after about 1.2 miles, break out from under the forest canopy to begin traversing Wapaloosie's sprawling meadows.\n\nThe climb eventually eases as the trail takes to a series of long, sweeping switchbacks. The eastern side of the Kettle Crest sees less range activity than the western slopes, allowing native fescue to proliferate. By late spring, wildflowers brush pastels and bright colors across the meadows, and sun-baked sage permeates the air.\n\nViews grow with elevation gained. Look northwest to British Columbia's Rossland Range and the Abercrombie-Hooknose Highlands. The Twin Sisters, Mack Mountain, and King Mountain are emerald sentinels guarding the eastern flank of the Kettle Crest. Flickering birds, scurrying ground squirrels, and flitting butterflies will keep your eyes focused nearby too.\n\nAt 2.7 miles, amid glorious alpine meadows, reach the Kettle Crest Trail (elev. 6850 ft). From this junction it's a short and easy off-trail ramble to Wapaloosie's 7018-foot summit. Head northeast through meadows and open forest of Engelmann spruce and whitebark pine for about 0.25 mile. A large cairn marks the broad summit's high point.\n\n### EXTENDING YOUR TRIP\n\nContinue south along the Kettle Crest Trail for about 1.2 miles to the Jungle Hill Trail for (Hike 25)\u2014more delightful meadows and views. You can make a 12-mile loop by returning via the Jungle Hill Trail and walking 3 miles on FR 2030 back to the trailhead.\n\n  Copper Butte via Marcus Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/4 | 9.6 miles | 2340 feet\/7140 feet | June\u2013Nov\n\n**Map:** USGS Copper Butte; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikes, horses. Range area; **GPS:** N 48 41.884 W 118 30.715\n\n  _**At 7140 feet, Copper Butte is the highest summit in the Kettle River Range and the sixth-highest mountain in Eastern Washington. Of the several ways to reach this lofty peak, none is more beautiful than the Marcus Trail. On this lightly traveled trail, you'll pass through old-growth, fire-succession, and subalpine forests; and traverse prolific alpine meadows. The views from this old lookout site, down the Kettle spine and out to the Selkirks and a myriad of Canadian peaks, are just as dazzling.**_\n\n_The trail traverses sprawling meadows with far reaching views west._\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 2.8 miles to the junction with SR 21 (just past the county fairgrounds). (From Kettle Falls, follow SR 20 west for 40 miles to the junction.) Head north on SR 21 for 0.8 mile, turning right at the Ferry County PUD onto Old Kettle Falls Road (County Road 280). After 2.4 miles, turn left onto CR 287 (access for Kinross Mine). Continue 0.8 mile, bearing right onto Hatchery Road (CR 284). Then continue east (past mining operations) 0.6 mile and bear right onto FR 2152. Proceed (staying right at 0.7 mile) for 3.3 miles, bearing left onto FR 2040. Follow FR 2040 for 5.2 miles to a junction with FR Spur 250 (signed Marcus Trail No. 8). Turn right and come to the trailhead (elev. 4800 ft) in a small clearing at 1.5 miles.\n\n### ON THE TRAIL\n\nIf you want to reach the king of the Kettles by the fastest route possible, don't hike this trail. Head on over to the Old Stage Trail (Hike 28) instead. But if you want to wander through the most supreme wildflower meadows in these parts, this is your trail! The route once extended to the small town of Marcus on the confluence of the Kettle and Columbia Rivers. It's much shorter now, but just as wild as it was in the late 1800s.\n\nFrom an old logging yard, the trail starts by following an old road through tall timber. Despite selective logging over the years, you'll pass lots of big old ponderosa pines, western larches, and Douglas-firs. Soon afterward, enter a large area that succumbed to fire in the early 1990s. At 0.6 mile, cross a creek (elev. 5025 ft) that has been heavily trampled by cattle. This is active range area, so beware of confusing cow paths. At 0.9 mile, be sure to stay left as one of those cow paths veers right.\n\nAs you climb the at-times dusty path, the surrounding countryside slowly begins to reveal itself as views emerge. Head back into mature forest and then back into the burn zone. After passing a spring (elev. 5550 ft) at 1.5 miles, the climb eases. Then round a ridge, staying uphill of more confusing cow paths. Forest soon yields to meadows.\n\nAt 2.2 miles, reach Copper Butte Spring (elev. 5925 foot), a popular watering hole for the resident bovines. Paths diverge everywhere. The trail you want heads left uphill and away from the spring. It soon reenters forest for a short ways. Come to Copper Butte Spring 2 (elev. 6075 ft), and then break back out into meadows.\n\nFor over a mile, traverse the sun-kissed southwestern slopes of Copper Butte, delighting in westward views and outstanding floral shows that include bistorts, lupines, yarrows, roses, golden peas, asters, buttercups, buckwheat, harebells, locoweed, bluebells, paintbrush, and more.\n\nAt 3 miles, pass another spring. The grade eases as you reenter forest and come to an intersection with the Kettle Crest Trail in a saddle (elev. 6400 ft) at 3.4 miles. Turn left and head north 1.4 easy miles through cool lodgepole pine forest, pocket meadows, and corridors of wildflowers to the broad 7140-foot summit of Copper Butte. Once home to a fire lookout, all that remains is a rusty bed frame. Wander around the butte for horizon-spanning views to the Cascades west, Idaho's Selkirks east, Mount Spokane south, and British Columbia's Rossland Range north.\n\n  Copper Butte via Old Stage Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 6 miles | 1615 feet\/7140 feet | mid-June\u2013Nov\n\n**Map:** USGS Copper Butte; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses; **GPS:** N48 42.595 W 118 26.579\n\n  _**Follow an old wagon road to a gap high on the Kettle Crest. Then climb steeply through silver forests adorned with showy wildflowers to the highest point in the Kettle River Range. From this lofty perch, a mile above the surrounding golden valleys, survey the wild and expansive Columbia Highlands. The views are breathtaking from this former fire lookout site, from Idaho to the North Cascades and all along the imposing wall of the Kettle Crest, from the Colville nation to the nation of Canada.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 21 miles, turning left onto FR 2030 (Albian Hill Road) (4.2 miles beyond Sherman Pass). (From Kettle Falls, head west on SR 20 for 22 miles, turning right onto FR 2030.) Follow FR 2030 for 7.1 miles, turning left onto the spur to the Old Stage Trail. Reach the trailhead (elev. 5525 ft) in 0.2 mile. Privy available.\n\n### ON THE TRAIL\n\nOf the several routes to Copper Butte, this is the shortest to this highest point in the Kettles. And thanks to a starting elevation of more than 5500 feet, it's short on elevation gain too. The hike starts on the Old Stage Trail, a restored section of a wagon road constructed in 1892. An early attempt by legislators to construct a northern east\u2013west route across the state, the Old Stage route was short lived, replaced in 1898 by one over Sherman Pass.\n\nBeginning by a creek (the only water on this hike) in cool forest, the way gradually climbs on a gentle grade. After rounding a ridge, the trail breaks out into a recovering burn zone. More than 10,000 acres on Copper Butte and adjacent Midnight Mountain went up in flames following a 1995 lightning strike. The forest is recovering, but with much of the canopy gone this can be a hot hike in July and August.\n\n_Copper Butte offers good views of the lofty lumpy Kettle Crest._\n\nAfter 1.6 miles of enjoyable strolling, reach a junction with the Kettle Crest Trail at a high windblown saddle (elev. 6050 ft). A nice albeit waterless campsite invites hikers interested in experiencing sunrises and sunsets from the lofty crest. For Copper Butte, turn left (south) and very soon afterward, turn left again. The Old Stage route continues straight to Lambert Creek (Hike 29), but you're now following the 43+-mile Kettle Crest Trail. Up the steep northern slopes of Copper Butte, steadily climb through snags and rejuvenating greenery. Blueberry bushes provide forage for grouse and create a crimson carpet come October. Views can be had west and north, but they pale in comparison to what awaits.\n\nA couple of switchbacks ease the climb, and then it's one final push to the top. At 3 miles, crest the broad butte. A big cairn marks the mountain's 7140-foot high point. The site of a fire lookout from 1921 until the 1950s, all that remains is a rusted bed frame and some scattered debris. But the views haven't changed: Look south along the rounded Kettle Crest to bulky peaks cloaked in golden lawns and emerald canopies. Peer northward and trace the lumpy spine of the crest into British Columbia. Gaze west over sprawling rangelands in spacious valleys carved by retreating glaciers from another era. Then cast your eyes east to a sea of peaks rising progressively higher on the horizon. Not a bad visual payoff for such a nontaxing hike!\n\n  Midnight Mountain\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 10.6 miles | 2250 feet\/6150 feet | June\u2013Nov\n\n**Maps:** USGS Cooke Mountain, USGS Copper Butte; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.usda.gov\/main\/colville; **Notes:** Open to mountain bikers, popular with equestrians. Range area; **GPS:** N 48 43.711 W 118 31.297\n\n  _**This trip takes you through recovering fire-scorched hillsides, fragrant alpine meadows, and parkland forests of towering western larch. Follow a historic wagon road up to a lofty pass in the shadow of Copper Butte, highest summit in the Kettles. Then traverse sage-scented flowering meadows high upon Midnight Mountain before slowly descending along a ridge through forest and field. Come in summer for the blossoms, fall for the colors, anytime for sweeping sublime views of the Okanogan Highlands.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 2.8 miles to the junction with SR 21 (just past the county fairgrounds). (From Kettle Falls, follow SR 20 west for 40 miles to the junction.) Head north on SR 21 for 9 miles, turning right onto Lambert Creek Road (CR 546). At 6 miles, bear right onto FR 2156 and continue for another 1.2 miles to the trailhead at Lambert Creek Campground (elev. 3900 ft). Privy available.\n\n### ON THE TRAIL\n\nThe trail begins next to a beautiful wooden sign depicting the route, compliments of the Ferry County chapter of the Back Country Horsemen. Rock-hop across Lambert Creek and reach a junction in 0.3 mile. You'll be returning left, so continue right on the Old Stage Trail. Constructed in 1892, just three years after statehood, this old wagon road was an early attempt by legislators to construct a northern east\u2013west route across the state. It was short lived, replaced in 1898 by a route over Sherman Pass that proved more favorable for hauling freight.\n\n_Copper Butte from Midnight Mountain_\n\nIn the 1990s much of the surrounding forest burned. Lack of shade warrants postponing this hike on the hottest of summer days, but spring and fall are lovely and surprisingly colorful. New greenery continues to colonize the scorched slopes. Flowers are dazzling in spring, and autumn colors are brilliant thanks to the blueberry bushes, cascaras, and currants. Look for woodpeckers among the snags and spruce grouse feasting on the buds of new plants.\n\nThe grade is gentle, with wide sweeping switchbacks. At 1.8 miles, bear left at a junction. The trail right connects to an old forest road. At 2.7 miles, come to a spring (elev. 4700 ft), which like most in the Kettles should be treated because of contamination by cattle.\n\nAfter passing a grove of large fire-spared larches, the trail rounds a ridge to grant viewing of Midnight Mountain and then advances through a thicket of lodgepole pine. At 4.5 miles, cross a small creek. At 5 miles, skirt a small wetland. Alpine breezes high on the slopes of Copper Butte often leave more than a few downed snags across the trail here for you to hone your hurdling skills.\n\nAt 5.8 miles, intersect the Kettle Crest Trail (elev. 6000 ft) at a high pass just north of the blocky butte. Continue left a few steps to a high and dry campsite and another junction. The old wagon road continues east to Albian Hill Road (see Hike 28). Your route carries on north along the crest, ascending a little more to top out at about 6150 feet. Enjoy a good view south to Copper Butte with its dog-hair stands of silver snags and west across the Curlew Valley to Bodie Mountain and the Bonaparte Highlands. Views are even better from the 6660-foot summit of Midnight Mountain, which can easily be attained by leaving the trail and angling northeast across sage-dotted meadows.\n\nOtherwise, keep hiking north and reach a junction with the Midnight Ridge Trail at 6.1 miles. Bear left onto the heavily cow-and horse-hoofed trail and begin descending across meadows and through patches of aspen. At 6.7 miles, pass a spring (elev. 5800 ft). Continue losing elevation, traversing young pine forest, before coming to groves of impressive old Doug-firs, ponderosa pines, and western larches. The larches in particular are quite grand.\n\nWinding farther down Midnight Ridge, the trail drops more rapidly. At 10.3 miles, come to a familiar junction with the Old Stage Trail. Turn right and reach the trailhead in 0.3 mile.\n\n### EXTENDING YOUR TRIP\n\nConsider side trips along the Kettle Crest, south to Copper Butte or north to meadows high on Lambert Mountain.\n\n  Mount Leona\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 6 miles | 1500 feet\/6474 feet | June\u2013late  \nOct\n\n**Map:** USGS Mount Leona; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses. Range area. Last few miles of road are rough, requires high-clearance; **GPS:** N 48 45.922 W 118 29.278\n\n  _**An easy climb to a prominent Kettle Crest summit, Mount Leona offers far-reaching views across the Okanogan Highlands and into the Boundary Country of British Columbia. A lonely peak except for the cows, chances are good of seeing wilder ungulates\u2014and perhaps a carnivore as well. Wildfires have scorched the mountain in the last two decades, but each year the peak gets a little greener and arrangements of sun-loving wildflowers soften the fires' impact.**_\n\n_Profanity Peak from Mount Leona's summit_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 2.8 miles to the junction with SR 21 (just past the county fairgrounds). (From Kettle Falls, follow SR 20 west for 40 miles to the junction.) Head north on SR 21 for 12.4 miles, turning right onto Saint Peters Creek Road (County Road 584) at Malo Store (milepost 175). At 1.1 miles, the pavement ends. At 1.7 miles, bear right. At 5.7 miles, bear left onto FR 2157 and follow it for 3.9 miles to the trailhead (elev. 5000 ft) in a large clearing on the left.\n\n### ON THE TRAIL\n\nFrom the trailhead clearing, look up at Leona, straight ahead and straight up. But your route is much gentler. First follow a cow-pied cow path to an old road. This is open range, and the views west across the golden Curlew Creek valley look like they're right out of Montana.\n\nLeona's open southern slopes rise above as you skirt east around the mountain. Raptors catch thermals while busy nuthatches work the trees lining the way. Stay on the main path, avoiding cattle trails and spurs to nowhere. At 0.8 mile, the trail swings left, steepens, and then soon eases. Come to a spring and stock trough (elev. 5375 ft) at 1.2 miles. Water sources beyond are less reliable. At 1.7 miles, at the edge of a burn zone, reach a saddle on the Kettle Crest (elev. 5600 ft) and a junction with the Kettle Crest Trail and Leona Loop Trail.\n\nViews from this gap east are excellent to Clackamas Mountain, Bodie Mountain, and Mount Bonaparte. Winds whistle through the snags, and lupines paint the forest floor purple. To summit Mount Leona, take the trail to your left. It receives minimum maintenance, so expect to be hopping over some windfall as you work your way\u2014steeply at times\u2014up Leona's south shoulder.\n\nAt 2.1 miles, bear left at a sign (elev. 5975 ft), crawling over a big blowdown. The tread gets a little tricky to follow\u2014angle to the northwest. At 2.3 miles, reach an unmarked junction (elev. 6100 ft) at the edge of a small meadow. The trail right is a continuation of the Leona Loop Trail, leading back to the Kettle Crest Trail. Unless you're a pine marten, you'll want to avoid this trail, as it is covered with blowdown and is a nightmare to travel.\n\nHead left up an old jeep track. Numerous cow paths make it easy to get lost. Stay along the ridge and head up, eventually emerging in a trampled meadow. Pick your way up through sage and juniper, looking for cairns and a resumption of trail. The route once again becomes clear as you travel up the increasingly open ridge crest. At 3 miles, reach the 6474-foot rocky summit, with its sedums and gilia and a communications tower.\n\nLook northwest to British Columbia's Mount Baldy; northeast to Profanity Peak and Taylor Ridge; east to the Twin Sisters Roadless Area and the Selkirks beyond; west across the Okanogan Highlands to the North Cascades; and south along the Kettle Crest to Lambert Mountain, Midnight Mountain, and Copper Butte, granddaddy of the crest.\n\n### EXTENDING YOUR TRIP\n\nFollow a jeep track off the summit northwest to Leona's western summit. Or, from the junction with the Kettle Crest Trail, travel south along the crest to Lambert's sprawling meadows.\n\n  Ryan Cabin\u2013Stickpin Loop\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 6.4 miles | 1365 feet\/5600 feet | mid-June\u2013  \nNov\n\n**Map:** USGS Mount Leona; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses. Range area. Last 4 miles of approach road can be rough; **GPS:** N 48 45.671 W 118 26.093\n\n  _**This easy loop hike in the northern Kettles follows two lightly traveled trails and a section of the Kettle Crest Trail that sees nary a soul. Human souls that is. Moose, deer, and other large mammals are another story. Stroll through sunny wildflower patches and cool streamside forest. Take in a few nice views along the way too as you try to locate Ryan's dilapidated cabin.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 21 miles, turning left onto Albian Hill Road (FR 2030) (4.2 miles beyond Sherman Pass). (From Kettle Falls, head west on SR 20 for 22 miles, turning right onto FR 2030.) Follow FR 2030 for 11.8 miles (the last 4 miles can be rough) to a junction with FR Spur 900 (signed Stickpin Trail No. 71, Ryan Cabin Trail No. 30 Trailhead). Turn left and proceed on rough road, bearing left at 0.2 mile, left again immediately afterward, and right in another 0.1 mile. Reach the Stickpin trailhead in 0.3 mile and Ryan Cabin trailhead (elev. 4450 ft) 0.1 mile beyond on the right. Park here.\n\n### ON THE TRAIL\n\nOn good tread, start climbing through a windblown forest of lodgepole pine. Visible north through gaps in the forest is Profanity Peak with its inviting meadows. But the bushwhacking involved in getting to that trail-less summit may provoke its namesake from your lips. Stay on the blueberry- and pipsissewa-lined trail instead and enjoy the hike.\n\nAt 1.2 miles, after entering mature forest, reach a small spring (elev. 4825 ft). See if you can locate the Ryan Cabin nearby, an old trapper's cabin rapidly being recalled by nature. Beyond the cabin site, switchback up a sunny slope speckled with granite ledges and glacial erratics, reaching the Kettle Crest Trail (elev. 5150 ft) at 1.7 miles.\n\nHead south on the Kettle Crest Trail, dropping into a cool notch (elev. 5025 ft) before beginning a steep climb through cool forest. At 2.8 miles, reach a 5500-foot gap between Mount Leona and Ryan Hill and a junction with the Leona Loop Trail. Unmaintained, only a fisher or pine marten will appreciate this littered-with-blowdown trail. Best to continue on the Kettle Crest Trail, traversing the east slopes of Mount Leona. Soon enter a 1990s burn zone that is rapidly reforesting. The way can be brushy at times but also abundant with wildflowers.\n\nCross two small creeks (elev. 5435 ft) that occasionally run dry late in the season, and then round a ridge with an excellent view of Profanity Peak. Continue across a meadow, passing a cow-trampled spring and some good views east along the way. At 4.2 miles, come to a junction (elev. 5600 ft) with the Stickpin Trail.\n\nTurn left and begin descending, soon coming to a big wildflower-filled meadow. Across an herbaceous hillside, continue losing elevation, eventually reentering forest. At 4.8 miles, reach a bridge across the South Fork Boulder Creek, a mere trickle here. The trail then follows the creek into a lush valley, one of the few creek-hugging trails in the Kettles.\n\nTraverse cool spruce and cedar groves, muddy seeps, and thimbleberry patches\u2014this is one of the wetter areas in the Kettles. A few boardwalks help keep your boots dry. At 6.3 miles, reach the Stickpin trailhead (elev. 4425 ft). Turn left and walk the road 0.1 mile back to your vehicle to complete the loop.\n\n_Stickpin Trail traverses boggy forest._\n\n### EXTENDING YOUR TRIP\n\nYou can easily hike to Mount Leona's summit from this loop. Before turning off on the Stickpin Trail, head south on the Kettle Crest Trail for a little over 0.1 mile to the trail to Leona, taking off right (see Hike 30).\n\n  Sentinel Butte\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/2 | 7 miles | 1025 feet\/5625 feet | May\u2013Nov\n\n**Map:** USGS Mount Leona; **Contact:** Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses. Popular cross-country ski route, winter Sno-Park Pass required; **GPS:** N 48 51.823 W 118 23.721\n\n  _**A popular winter skiing destination, this forested loop at the northern terminus of the 43+-mile Kettle Crest Trail is pretty quiet the rest of the year. It's an excellent area for seeing moose and other large mammals, but the best features are the trees\u2014particularly the larches. Majestic western larches line the way and by October streak the slopes gold and brighten the trail with a carpet of flaxen needles.**_\n\n### GETTING THERE\n\nFrom Republic, drive 2.8 miles east on State Route 20, turning left onto SR 21. Continue for 18.4 miles to Curlew and turn right onto Boulder Creek Road (County Road 602). Proceed 11.2 miles to the trailhead at Deer Creek Summit (elev. 4600 ft). Privy available. (From the junction of US Highway 395 with SR 20 west of Kettle Falls, follow US 395 north for 16 miles and turn left onto CR 602, continuing 11.8 miles to trailhead.)\n\n### ON THE TRAIL\n\nStart by taking the Kettle Crest Trail\u2014you'll be returning on the road just to the west of it. Beginning its 43-mile journey southward across the spine of the Kettle River Range, the excellent trail moderately ascends, traversing groves of larch, fir, and pine. Occasional openings offer good viewing west across the Kettle River valley to the Bonaparte Highlands and north to Mount Baldy in British Columbia.\n\nRounding Sentinel Butte, the trail takes a break from climbing at about 1.5 miles. After dipping about 50 feet, it resumes the ascent. Make a couple of switchbacks, skirt a couple of knolls. The walking is peaceful and delightful through grassy openings and by granite outcroppings.\n\nAfter reaching a high point of 5625 feet, the trail descends. At 3.5 miles, before Long Alec Creek, come to a junction with an old road (elev. 5400 ft). The way left ascends and travels along Taylor Ridge. Head right, following grassy tread for about 0.4 mile to another old road. Turn right again and follow this old ski path, which eventually becomes FR 455 (and an excellent ski run in winter), for 3.1 miles back to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nVenture out on the Taylor Ridge Trail (Hike 33), or saunter on more ski trails that take off north from the campground at Deer Creek Summit.\n\n_Moose are frequent travelers along the Kettle Crest Trail._\n\n  Taylor Ridge\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 5.8 miles | 1200 feet\/6190 feet | mid-June\u2013  \nNov\n\n**Maps:** USGS Mount Leona, USGS Bulldog Mountain; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses. Range area; **GPS:** N 48 47.557 W 118 20.362\n\n  _**A lonely hike in the northern reaches of the Kettles, Taylor Ridge lacks a \"wow\" factor but is packed with little surprises. There are good views to colorfully named and little-known peaks\u2014like Profanity Peak, Alligator Ridge, Togo Mountain, and Stickpin Hill. There are a few historical relics from the Colville National Forest's early days and the Civilian Conservation Corps. And there's always a good chance of hiking into a bear, deer, or moose. In autumn, larches streak the ridge gold.**_\n\n### GETTING THERE\n\nFrom the junction of US Highway 395 with State Route 20 west of Kettle Falls, follow US 395 north for 16 miles and turn left onto Boulder Creek Road (County Road 602). Drive west 8.8 miles, turning left onto FR 6113 (signed Bulldog Cabin). (From Republic, drive 2.8 miles east on SR 20, turning left onto SR 21. Continue 18.4 miles to Curlew and turn right onto Boulder Creek Road\/CR 602. Proceed 13.9 miles, 2.8 miles beyond Deer Creek Summit, turning right onto FR 6113.) Follow this good gravel road for 8.9 miles to a cattle guard near a road spur and trailhead for Taylor Ridge east. Continue south 0.4 mile to the trailhead for Taylor Ridge west (elev. 5050 ft) and limited parking on the left-side road shoulder.\n\n_Good views south to King Mountain, US Mountain, and the Kettle Crest from Taylor Ridge_\n\n### ON THE TRAIL\n\nThe trail over Taylor Ridge is in decent shape. Word is slowly getting out among mountain bikers about this trail's riding appeal. And a fair number of hunters visit each fall, enough so that the path usually gets brushed out each season. But for the most part, this is one of the lonelier trails in the Kettles.\n\nStarting nearly a mile high, gradually climb along the edge of an old clear-cut, passing by some big western larches. The forest is fairly open and, like much of Kettle country, is open to cattle grazing. Watch your step! At 1.1 miles, come to an old road (elev. 5400 ft). Walk left for a few steps and then resume your way back on the trail.\n\nAt about 1.4 miles, reach an opening with nice viewing south along the Kettle Crest. Continue steadily climbing through open forest, rounding one of the many knobs and summits along Taylor Ridge. After a slight descent and a few minor ups and down, continue upward toward the ridge's high point. Skirt meadows graced with juniper and wildflowers, and then briefly climb steeply to just below the ridge's high point, 2.8 miles from the trailhead and just before the trail transforms into an old jeep track. Look for a faint path heading left. Follow it a mere 0.1 mile over ledges to reach Taylor Ridge's 6190-foot high point.\n\nMost of the summit is treed, but there are good views south to King, Mack, Twin Sisters, and US Mountains as well as along the Kettle Crest from Snow Peak to Profanity Peak. Snoop around and you'll find an old cabin foundation and other remnants of a long-gone fire lookout. This country is pretty wild now, but for much of the past century it saw its share of miners, trappers, and loggers.\n\n### EXTENDING YOUR TRIP\n\nContinue west 3 miles or so along Taylor Ridge on old road to reach the Kettle Crest Trail. If you can arrange transportation for a pickup at Deer Creek Summit, it makes for a good one-way adventure. Or follow the eastern section of the ridge trail for a couple of miles, but be aware that it has become abandoned and obstructed by logging near Bulldog Mountain.\n\n  US Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/3 | 5.8 miles | 1450 feet\/6232 feet | mid-June\u2013Nov\n\n**Map:** USGS Copper Butte; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses, motorized use. Range area; **GPS:** N 48 42.846 W 118 26.634\n\n  _**An obscure but prominent peak just east of the Kettle Crest, US Mountain sees more bovine than boot prints. Follow an old jeep track through forests of pine and larch to high-country meadows with good views of the lofty Kettles and the thickly wooded Twin Sisters. Once worked by miners and now grazed by cattle, US is a great peak for wandering back into the past. It's also an excellent hike for solitude.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 21 miles, turning left onto Albian Hill Road (FR 2030) (4.2 miles beyond Sherman Pass). (From Kettle Falls, head west on SR 20 for 22 miles, turning right onto FR 2030.) Follow FR 2030 for 7.5 miles to an obscure road on right signed \"600\" (0.4 mile north of the Old Stage trailhead). This is the trailhead (elev. 5350 ft). Park in a small clearing just up the road or in a small pullout along Albian Hill Road. Do not block FR Spur 600.\n\n_Meadows below the summit of US Mountain offer good views south into the Twin Sisters Roadless Area._\n\n### ON THE TRAIL\n\nWhile this trail is open to four-wheel-drive recreationists (and snowmobiles when snow-covered), outside of deer season and winter, the chances of encountering motorists, or anyone for that matter, is slim. Most of the way is on an old road, and if it wasn't for the occasional 4\u00d74-er, alders would have overtaken it long ago.\n\nHead up the double-track, bearing right at a junction in 0.1 mile. From here the way climbs steeply. Don't let the grade and the tunnel of alders discourage you\u2014this is the only lousy section, and it's short. The way soon levels out, with some minor ups and downs through stands of lodgepole pine and western larch.\n\nAt 1.3 miles the grade steepens, leaving thick woods for pocket meadows. Soon afterward, skirt a big meadow that invites ambling across it for good views of the Twin Sisters, and King and Mack Mountains. At 1.9 miles, crest a 6125-foot knoll. Then start descending, skirting ledges along the ridgeline. Look for openings in the forest to your left. Views are excellent here of Copper Butte, Midnight Mountain, and the impacts of a 1994 forest fire.\n\nAt 2.2 miles, come to a faint trail junction. The trail right drops to a fence-enclosed spring and then continues down the east side of US Mountain, ending at FR Spur 500 off Boulder Creek Road (FR 6110). It is lightly traveled and maintained. Continue left on the road track instead, reaching a saddle (elev. 5940 ft), and then resume climbing.\n\nAt 2.5 miles (elev. 6025 ft) the track once again descends (rapidly and dead-ending shortly afterward). Don't continue after descending about 50 feet\u2014instead look for a small track right leading to an old mining area. Now off-trail, angle to the right of the old mine and through open forest and meadow to reach US Mountain's 6232-foot summit after 0.4 mile.\n\nViews are extremely limited from the summit, but meadows just below the high point on the south side grant wonderful viewing of the 13,000-acre Twin Sisters Roadless Area and high Kettle Crest summits from Copper Butte to Snow Peak.\n\n  King Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 7.4 miles | 1520 feet\/6660 feet | mid-June\u2013Nov\n\n**Map:** USGS Copper Butte; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses, motorized use; **GPS:** N 48 40.885 W 118 26.577\n\n  _**The highest peak in the Kettle River Range not situated along the Kettle Crest, King Mountain provides royal views of the lofty crest and of scores of equally impressive and intriguing surrounding summits. Follow a rarely traveled old jeep track along a thickly timbered ridgeline to a rocky pinnacle rarely set foot upon by human feet, and gaze upon some of the loneliest and wildest country in the region.**_\n\n_Lifting clouds reveal a rugged and wild landscape surrounding King Mountain._\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 21 miles, turning left onto Albian Hill Road (FR 2030) (4.2 miles beyond Sherman Pass). (From Kettle Falls, head west on SR 20 for 22 miles, turning right onto FR 2030.) Follow FR 2030 for 4.8 miles to the trailhead (elev. 5500 ft), located at junction with the Twin Sisters Motorized Trail. Do not block this trail when parking.\n\n### ON THE TRAIL\n\nYour route begins immediately to the right (south) of the 4\u00d74 Twin Sisters Trail (Spur 200). The way to King Mountain is also open to motorized use, but don't let that discourage you. Outside of deer season, this route sees very little use, motorized or non. You're far more likely to encounter a four-legged trail user.\n\nThe way starts out in a thick forest of lodgepole pine. Dependent on frequent fires for seed germination and to suppress competing species, lodgepole pine is ubiquitous in the Kettles, often growing in thick dog-haired stands. First Peoples of the Rocky Mountains and Great Plains favored this tree's straight and slender trunks for teepee construction, hence its name.\n\nClimb steadily and steeply at times. A few short switchbacks break up the grunt. Keep your mind off the climb by looking for spruce grouse and listening for nuthatches. At about 0.8 mile, come to the first of several small openings in the forest. Take in views of the southern Kettle Crest, and in early summer admire a carpet of wildflowers.\n\nAt about 1.1 miles, the trail crests a ridge (elev. 6250 ft), bringing respite from the climbing. Wander a short distance off-trail to the south for some nice views. Then continue along the trail through thick stands of pine and fir. At 2.1 miles, round a lesser summit (elev. 6500 ft) and begin a slow descent. After passing a waterless campsite in a broad saddle (elev. 6335 ft), resume climbing, reaching King's western summit (elev. 6640 ft) at 3 miles. Mostly treed, the summit may perhaps disappoint you. However, look southeast across the small summit meadow and notice a rocky and intriguing nearby peak. That's King's slightly higher eastern summit, and that's where the extensive views are\u2014keep hiking!\n\nAfter passing over a small knob, rapidly drop to a saddle (elev. 6525 ft), coming to a junction soon afterward at 3.5 miles. The main trail continues right, skirting the rocky pinnacle on its eastward march toward Mack Mountain. Veer left on a rougher track, soon coming to an excellent viewpoint north. Directly across the North Fork Deadman Creek valley locate the Twin Sisters\u2014centerpiece of the 13,300-acre roadless area you have been trudging across. Identify Profanity Peak to the north, with its sun-kissed meadows, and emerald Taylor Ridge to its east. Scattered about are other little-known peaks sporting colorful names\u2014Alligator Ridge, Jackknife Mountain, US Mountain, and Bulldog Mountain.\n\nNotice a trail taking off from the viewpoint. Take it and carefully pick your way up an outcropping of crumbling rock to King's 6660-foot eastern summit. Here is your true visual reward for all your effort: the Kettle Crest from White Mountain to Copper Butte, and obscure summits with intriguing names like Graves Mountain, Scalawag Ridge, and Bangs Mountain, to name a few.\n\nWith the old rotten rock below your feet and the rounded well-worn summits surrounding you, it's easy to see that these mountains are the oldest in the state, at over 60 million years old and rich in biological diversity.\n\n  Sherman Creek and Log Flume Heritage Site\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 1.6 miles | 60 feet\/2230 feet | May-Dec\n\n**Map:** USGS South Huckleberry Mountain; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Wheelchair-accessible. Dogs permitted on-leash; **GPS:** N 48 34.922 W 118 13.618\n\n  _**A delightful path along a tumbling waterway, the paved Sherman Creek Trail is perfect for children and hikers of all ages who may want to stretch their legs while out on a trip along the Sherman Pass National Scenic Byway. One of the few nonmountainous hikes in the region, this trail is exceptionally attractive in spring when woodland flowers add cheer to the terrain, and snowmelt from the Kettles adds a roar to the river.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 32.3 miles, turning right into the Log Flume Heritage Site. (From Kettle Falls, head west on SR 20 for 10.7 miles, turning left into the Log Flume Heritage Site.) The trailhead is at the southwest end of the parking area (elev. 2170 ft). Privy available.\n\n### ON THE TRAIL\n\nSherman Creek starts in the high meadows of Jungle Hill and Columbia Peak, its South Fork in the high basins beneath Snow Peak, Bald Mountain, and the Barnaby Buttes, and together they drain a large area of the southern Kettles. Paralleling SR 20 for a good portion of its way to the Columbia River, Sherman Creek cuts through larch groves and cottonwood flats, cascades over ledges and careens through chasms. It's a sight to see, but not when you're buzzing by at 50 miles per hour. This trail enables you to enjoy it safely, at your own pace.\n\n_A silhouette from the past works the old sluiceway._\n\nFrom the parking lot, the trail heads through open forest to immediately reach the river bank. Head west and upstream through meadow and open forest, savoring the sweet serenity of Sherman Creek. Nootka roses perfume the air, while aspen and cottonwood leaves rustling in the warm breezes add a nice background score. The creek itself plays a fine melody, its mood varying with the season and snowmelt.\n\nAt about 0.6 mile, cross the river on a nice bridge and continue walking upstream through a meadow of lupine shaded by big cottonwoods. The trail ends in the Canyon Creek Campground along the banks of Canyon Creek, which drains the northern slopes of South Huckleberry Mountain. Contemplate spending the night here as you saunter back to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nTake the time to walk the 0.4-mile loop through the Log Flume Heritage Site. Learn about early logging operations that included sluicing logs down a large flume, remnants of which still exist and can be seen along the trail.\n\n  Emerald Lake and Hoodoo Canyon\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/2 | 6.2 miles | 825 feet\/3500 feet | Apr\u2013Nov\n\n**Map:** USGS Jackknife; **Contact:** Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 775-3305, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes. Access road gated in winter to protect wildlife. Watch for ticks; **GPS:** N 48 37.429 W 118 14.384\n\n  _**A surprisingly lush canyon at the eastern edge of the Kettle River Range, Hoodoo houses wildlife-rich lakestucked below shiny granite ledges. The trail through this slot in the mountains is a pure delight: gorgeous groves of towering pines and cedars year-round. In springtime, a riot of wildflowers brighten the canyon floor. And in autumn, aspen, Douglas maple, birch, and serviceberry streak Hoodoo red and gold.**_\n\n### GETTING THERE\n\nFrom Republic, head east on State Route 20 for 34 miles, turning left onto Trout Lake Road (FR 020), 1.7 miles beyond the Log Flume Heritage Site. (From Kettle Falls, head west on SR 20 for 9 miles, turning right onto FR 020.) Follow FR 020 for 5.1 miles to its end at the Trout Lake Campground and Hoodoo Canyon trailhead (elev. 3050 ft). Privy available.\n\n### ON THE TRAIL\n\nEmerald Lake sits about halfway in Hoodoo Canyon and can be accessed from either north or south. The northern approach from Deadman Creek is lightly used but involves more elevation gain and is steeper. The approach here from Trout Lake sees more use but is easier to get to and easier to hike. You can't go wrong either way, and strong hikers can easily hike the entire trail round-trip.\n\nFrom the south end of the little car campground on the south shore of Trout Lake, find the start of the Hoodoo Canyon Trail and immediately come to the lake's outlet. Cross it on a log bridge and then begin climbing. The way switchbacks from the cool canyon floor, cutting through Oregon grape, snowberry, current, thimbleberry, and dogwood. After about 0.4 mile, the climb eases and you are now high above Trout Lake.\n\n_A hiker surveys Hoodoo Canyon from high on the trail. (Photo by Aaron Theisen)_\n\nHeading north now, along the canyon's sun-catching slopes, hike through very different vegetation than below. Beneath giant ponderosa pines lined with tall grasses (watch for ticks in the spring\u2014they're profuse), traverse the canyon's eastern wall. If it's early in the season, admire the floral show\u2014arnica, paintbrush, lupine, larkspur, balsamroot, buttercup, and more.\n\nAfter reaching 3500 feet elevation, the way descends slightly. At 2.6 miles, shortly after crossing a small creek (dry later in the season), come to the junction with the Emerald Lake Trail (elev. 3450 ft). Turn left and head 0.6 mile, dropping a little more than 300 feet to reach the shores of the appropriately named lake at the bottom of the canyon (elev. 3125).\n\nThe water levels fluctuate throughout the year, either exposing big rocks or flooding shoreline birches and cottonwoods. Moose frequent the lake, as do various species of waterfowl. So sit quietly for awhile and observe some nature in action.\n\n### EXTENDING YOUR TRIP\n\nFrom the Emerald Lake Trail junction, continue north on the Hoodoo Canyon Trail for 0.4 mile, climbing to a cliff overlooking the canyon (elev. 3700 ft). From there the trail leaves the canyon and rapidly descends through a lush forest of cedar and spruce to Deadman Creek (elev. 2825 ft). Cross the creek on a good bridge, and reach the northern trailhead (elev. 2900 ft) off of Deadman Creek Road (FR 9565) at 4.7 miles from the southern trailhead. If it's early in the season, mosquitoes are an annoyance.\n\n  Old Kettle Falls Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*\/1 | 2.6 miles | none\/1300 feet | May\u2013Dec\n\n_The trail crosses a channel before heading into a tunnel of aspen._\n\n**Map:** USGS Kettle Falls; **Contact:** Lake Roosevelt National Recreation Area, (509) 633-9441, www.nps.gov\/laro; **Notes:** Wheelchair-accessible. Dogs permitted on-leash; **GPS:** N48 35.953 W118 07.194\n\n  _**The falls are no more. Gone too is the original townsite of Kettle Falls. The impounded waters of the Grand Coulee Dam claimed them both in 1939. The town relocated to higher ground to the east. The falls receded into memory. One of the greatest fisheries on the Columbia River was claimed by the need for hydroelectric power. Walk the Old Kettle Falls Trail through abandoned homesteads and hallowed fishing grounds and let voices from the past cast insight, inquiry, and perhaps a little lament too.**_\n\n### GETTING THERE\n\nFrom Colville, follow State Route 20\/US Highway 395 west for 10 miles to the junction with SR 25 in Kettle Falls. Continue west on SR 20\/US 395 for another 2.2 miles and turn left (south) onto Boise Road (just before the bridge over the Columbia River). Continue 1.6 miles, bearing right where Boise Road bears left to become the Old Kettle Falls Road. In 0.2 mile, come to the ranger station and the Kettle Falls Campground entrance. Park here. The trailhead (elev. 1300 ft) is just a few yards away on the south side of the campground entrance road. Privy available.\n\nMAPMAKER, MAPMAKER, MAKE ME A MAP\n\nWhile most Americans are familiar with Lewis and Clark and their 1804\u20131806 journey, few are familiar with David Thompson, who explored the vast Oregon Country around the same time, rivaling the Corps of Discovery in his mappings, findings, and influence on the American and European settlement of North America.\n\nIn 1784, the British-born Thompson came to British Canada (Churchill, in what is now Manitoba) at the age of fourteen. He apprenticed with the Hudson's Bay Company as a fur trader but quickly learned that his talents lay in surveying and mapmaking. In 1797, at age twenty-seven, he defected to Hudson's Bay Company's bitter rivals, the Northwest Company of Montreal, for whom he extensively mapped what is now northern Minnesota, eastern Ontario, and southern Manitoba.\n\nIn 1806, because of concerns of the Lewis and Clark Expedition and American claims to markets and settlements in the Northwest, Thompson set off for the Rocky Mountains to find a route to the Pacific Ocean. In 1807, he began exploring and mapping the headwaters of the Columbia River and the river's vast basin and tributaries. In 1811, the same year the Pacific Fur Company established Fort Astoria, the first American settlement in the Northwest at the mouth of the Columbia, the intrepid Thompson became the first recorded person to travel the entire length of the river. His 1814 map of the Columbia Basin was considered so accurate that the Canadian government continued to use it for nearly one hundred years.\n\nIn all, Thompson mapped a land mass of more than 1.5 million square miles. An accomplished and dedicated mapmaker, he was also a dedicated husband to his wife, Charlotte, for fifty-eight years. Thompson died in 1857 at the age of eighty-six. His legacy and accomplishments continue to intrigue historians and explorers\u2014and many hikers and paddlers too.\n\nAward-winning Spokane-based writer Jack Nisbit's _In The Mapmaker's Eye: David Thompson on the Columbia Plateau_ (WSU Press, 2005) and _Sources of the River: Tracking David Thompson across North America_ (Sasquatch Books, 2007) are excellent reads if you're interested in learning more about this fascinating individual.\n\n\u2014 _C. R_.\n\n### ON THE TRAIL\n\nThis nearly perfectly flat trail is well used by locals walking their dogs and by campers on evening strolls. It may lack stunning scenery, but it's full of historical relics. The forest is pleasant too, and the surrounding wetlands great for bird-watching.\n\nHead south on the wide trail, and after 0.1 mile cross the boat-launch access road. Continue straight and soon come to a bridge spanning a draw lined with aspen. The water level fluctuates with the dam's drawdowns. The trail utilizes an old road briefly and then turns left, passing an old foundation and reaching the group-camp access road at 0.5 mile.\n\nCross the road and come to a much nicer stretch of trail. Pass by old homesteads and through pastures, orchards, and thickets of young pines and old locust trees. At 0.8 mile, cross another draw that may or may not be flowing with water. Continue along a piney \"ridge\" and then alongside a grassy marshy area that usually teems with wildlife.\n\nAt 1.1 miles, come to a junction. The trail left crosses a bridge over a cottonwood-lined draw, reaching a picnic area in 0.1 mile. Continue right instead, over sandy tread to a piney bluff. The trail ends at 1.3 miles, but when the water level is low you can walk out on the flats of the Columbia River. Just downstream is the Colville River. The town of Kettle Falls was relocated just upriver on this waterway, where the town of Meyers Falls once sat. The new transplants insisted on renaming Meyers Falls, Kettle Falls. They got their way.\n\n### EXTENDING YOUR TRIP\n\nTo see the site of the actual falls, visit the Saint Paul Mission located just north of the junction of Boise Road and SR 20\/US 395. Check out the restored 1847 mission chapel built by Jesuit missionaries and Native Peoples. Then walk the 0.4-mile loop at the confluence of the Kettle and Columbia Rivers, where the famed explorer David Thompson, of the Northwest Company of Montreal, first passed by in 1811. His French Canadian fur traders named the falls Les Chaudieres\u2014the Kettles\u2014for the huge, kettle-shaped holes in the ledge below the falls. Occupied by Native Peoples for more than 9000 years, this spot was once the second-largest fishery on the Columbia River.\n\n## selkirk mountains\n\n_The trail to the top of Hall Mountain near Sullivan Lake offers vast views of the Selkirk Mountains_.\n\nEastern Washington and northern Idaho share the sprawling group of peaks known as the Selkirk Mountains. The southern end of the range is near Spokane (either at the granite climbing rocks on the north bank of the Spokane River or farther south at Mica Peak and the Rocks of Sharon, depending on which geologist you ask). From Spokane, the range stretches north into British Columbia, with notable landmarks such as Mount Spokane, Sullivan Lake, the Salmo-Priest Wilderness, and Gypsy Peak (elev. 7309 ft), the highest point in Eastern Washington.\n\nThe Salmo-Priest Wilderness is one of only three wilderness areas in Eastern Washington, so rugged that even the forest industry had little trouble bequeathing its 41,335 acres to preservation in 1984. The Pend Oreille County portion of the Selkirks is unique in Washington because of the critters that roam there. Forest roads are gated in certain high areas to curb motor-vehicle traffic and protect habitat for marquee species, including grizzly bears, gray wolves, bighorn sheep, and woodland caribou; the latter is one of the most critically endangered mammals in the United States.\n\n  Frater Lake\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 1.8 miles | 125 feet\/3318 feet | May\u2013Nov\n\n**Maps:** USGS Ione, Colville National Forest Frater Lake Sno-Park trail map; **Contact:** Colville National Forest, Three Rivers Ranger District, Colville, (509) 684-3711, www.fs.fed.us\/r6\/colville; **Notes:** Partly open to mountain bikes, motorized use; **GPS:** N 48 39.275 W 117 29.096\n\n_Trails circumnavigate Frater Lake._\n\n  **_The kilometers on posted trail markers are a tip that this 10-mile system of forested loop trails was designed for cross-country skiing, a sport that clings to its metric European origin. While a part of this trail is open to motorcycles, the route featured here quickly whisks you into a peaceful forest to circumnavigate Frater Lake, one of seven lakes in a 6-mile stretch of theLittle Pend Oreille River valley. The lake is stocked with trout, dappled with lily pads, and home to a lodge of beavers, visiting waterfowl\u2014and occasional hikers._**\n\n### GETTING THERE\n\nFrom State Route 20\/31 about 47 miles north of Newport, turn west on SR 20 at Tiger. Drive 6.3 miles to the trailhead parking area (elev. 3270 ft) on the north side of the road at milepost 384. (From Colville, drive east on 3rd Avenue\/SR 20 for 29 miles to the trailhead). Privy available.\n\n### ON THE TRAIL\n\nThe Tiger Loop Trail No. 150 begins between the kiosk and the restroom. It's a multiuse trail for nearly 0.2 mile to Coot Junction. Bear right on the nonmotorized trail along the lake. Pass between the log warming hut and outhouse, through the gate, and continue on the Tiger Loop.\n\nSeveral bridges lead over a small creek. The strange boards on the railings are barriers to keep Nordic skiers from toppling over the bridges while making turns. Notice the carpet of kinnikinnick, a native ground cover that develops red berries (not poisonous, but not palatable either). The hoary elfin butterfly lays its eggs on its foliage.\n\nAt Scudder Junction, bear right. The trail leads to a fence with a view into the Teepee Seed Orchard, established in 1989. The Forest Service says that by 2020 this 24-acre tree farm will be producing enough Engelmann spruce and western white pine seeds to meet the reforestation needs of the eastern half of the 1.1-million-acre Colville National Forest.\n\nFrom the fence, the trail doubles back into the forest as a pleasant single-track trail. Soon you'll come to a junction with the option of turning left for a loop that adds 0.6 mile. Or bear right and follow the main trail back to the lake and trailhead.\n\n### EXTENDING YOUR TRIP\n\nAt Coot Junction, turn left and follow the 4.8-mile Coyote Rock Trail, which gains more elevation, offers some views, and adds more than 2 miles to your hike. Frater Lake parking area also is the base for Trail No. 155, a 2.5-mile network of loops starting just across SR 20 and extending southwest to Lake Leo.\n\n  Big Meadow Lake\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/2 | 2.8 miles | 320 feet\/3460 feet | May\u2013Nov\n\n**Maps:** USGS Aladdin Mtn, Colville National Forest map; **Contact:** Colville National Forest, Three Rivers Ranger District, Colville, (509) 684-3711, www.fs.fed.us\/r6\/colville; **Notes:** Partly wheelchair-accessible. Dogs permitted on-leash; **GPS:** N 48 43.768 W 117 33.866\n\n  **_Kids love this area, with its easy trails, fishing lake, and homestead cabin. The centerpiece is a wildlife-viewing platform overlooking Meadow Creek and the lake. The roofless tower is built from a fire lookout that once perched on North Baldy Mountain._**\n\n### GETTING THERE\n\nFrom Colville, head east on 3rd Avenue\/State Route 20 toward Ione. Drive 1.1 miles to the top of the hill across from the airport and turn left on Aladdin Road, which eventually becomes Northport Road (CR 9435). Drive 19 miles and turn right on Big Meadow Creek Road (CR 2695). Drive 7.5 miles and turn right into the Big Meadow Lake Recreation Area (elev. 3300 ft). (From the Pend Oreille River valley at Ione, you can reach the lake by driving 7 miles west on gravel roads.) Privy available.\n\n_The Meadow Creek Trail features a replica homestead._\n\n### ON THE TRAIL\n\nStart at the trailhead across from the parking area and vault toilet. Follow the paved path to the wildlife-viewing tower. Continue north on the wheelchair-accessible loop path for 0.2 mile and turn left through the gate onto Meadow Creek Trail No. 125.\n\nHike 0.3 mile and turn right on the 0.3-mile spur to the replica of a homestead cabin. Retrace your steps to the Meadow Creek Trail and turn right to continue the loop. After hiking a total of 1.6 miles, you'll reach the west end of the loop and cross Meadow Creek. Enjoy the changes in forest type as you hike back toward the lake. The trail drops past campsites to the campground access road. Turn left on the road and hike north along the lake, over the outlet, and past the shore-fishing area to the parking area.\n\n### EXTENDING YOUR TRIP\n\nAdd 1.5 miles by hiking around Big Meadow Lake if high water has not inundated the route. Connect to Lakeshore Trail No. 126 from the trailhead at the south-side campground. The trail merges with a road for a short way at the east end of the lake and then splits off left and follows the north shore back to the recreation area entrance road.\n\nHIGH TIMES OVER FOR FIRE LOOKOUTS\n\nFire lookouts had their heyday in the first half of the twentieth century, especially during a Depression-era building boom. The Civilian Conservation Corps was dispatched to help erect cabins and towers for fire detection on accessible peaks with the best views of the landscape below. But after more than sixty years of service, most of the wooden sentinels and those who staffed them have met a foe more permanent than any wildfire: technology. Aircraft, computers, and imaging have taken over the lofty task.\n\nLookouts were torn down almost as quickly as they were built in a demolition campaign that surged across the country in the 1960s and 1970s. Of the 678 fire lookout sites in Washington, fewer than 90 still have standing structures. About 20 are staffed five days or more a season by various agencies or tribes. About 50 are maintained for emergency use.\n\nTo save some of the historic structures, the Forest Service and other agencies were convinced to rent some of the cabins and towers to campers. The Quartz Mountain Lookout in Mount Spokane State Park (Hike 67) is an excellent room with a view, available by reservation. The lookout was formerly on top of Mount Spokane. Instead of being destroyed, it was disassembled so State Parks staff and volunteers could relocate and rebuild it.\n\nAbout two dozen of the hikes in this book lead to the eye-pleasing, lofty locations of fire lookout sites, former and active. Incidentally, the Idaho Panhandle was once the mecca of fire lookouts, with nearly 300 towers in roughly 150 miles from Priest Lake to the Saint Joe River country. Only about two dozen are still in use, nearly half of them as recreational rentals.\n\n\u2014 _R. L_\n\n  Rogers Mountain and Gillette Ridge\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 5 miles | 1200 feet\/5770 feet | June\u2013Oct\n\n**Maps:** USGS Aladdin, USGS Gillette Mountain, Colville National Forest map; **Contact:** Colville National Forest, Three Rivers Ranger District, Colville, (509) 684-3711, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, motorized use; **GPS:** N 48 44.601 W 117 43.245\n\n  **_Rise above years of logging to a former lookout site atop Rogers Mountain, overlooking the working forest. Extend your trip to bag another peak of the same name while hiking through larch, cedar, Douglas-fir, delightful lodgepole pine and subalpine fir, rocky outcrops, and subalpine meadows._**\n\n### GETTING THERE\n\nFrom US Highway 395 in Colville, drive east on 3rd Avenue toward Ione and State Route 20 for 1 mile and turn left (north) across from the airport onto Aladdin Road. Go north 15 miles and turn left on unmarked Forest Road 500. Cross the cattle guard and head up 3.3 miles. Bear right at the junction with FR 620 (which leads to an optional trailhead). Continue on FR 500 for 1.6 miles and turn left and uphill at a junction with an unmapped spur road. Go another 1.2 miles to the trailhead (elev. 4670 ft) off a short spur road to the left.\n\n_Cruising the trail between Rogers Mountain (background) to Mount Rogers_\n\n### ON THE TRAIL\n\nGillette Ridge Trail No. 131 extends 9.7 miles from this trailhead to the Onion Creek trailhead (where the access road is no longer maintained) offering several options.\n\nThe trail heads up and switches back through a stand of larches (golden around the third week of October) and climbs out of a 2011 timber sale. Soon a switchback points you north, to look at Canadian peaks in the distance. Then the route bends decidedly southwest, transitioning as it climbs into a forest of scattered lodgepole pine and low-growing huckleberry.\n\nAt 2 miles, cross the old lookout access road, which leads to the top, but the trail is a nicer route, leading 0.5 mile up to the broad summit of Rogers Mountain. Four cement anchors are all that remain of a lookout tower built in 1933. The tower blew down in 1959 and was never replaced. (Even the name of this 5770-foot mountain has been removed from the latest Colville National Forest map.) Enjoy the views and return to your car.\n\n### EXTENDING YOUR TRIP\n\nFor a highly recommended 12-mile round-trip, continue south and down off Rogers Mountain and follow the trail to Mount Rogers. The trail descends 2 miles to a saddle and a lush cedar forest before beginning a gradual 1.8-mile climb to the 5557-foot summit. (At 5.2 miles you'll pass the junction with the 0.6-mile trail to FR 620. Signs may still indicate Mount Rogers Loop Trail No. 130, but the lower segment of that loop appears to have been obliterated by logging.)\n\n  Sherlock Peak\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 8.2 miles | 2000 feet\/6365 feet | June\u2013Oct\n\n**Maps:** USGS Leadpoint, USGS Deep Lake, Colville National Forest map; **Contact:** Colville National Forest, Three Rivers Ranger District, Colville, (509) 684-3711, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses. High-clearance recommended; **GPS:** N 48 53.048 W 117 31.926\n\n **_Even peak baggers with aging knees will enjoy this trail's generally easy grade to a knockout viewpoint above the Pend Oreille River valley._**\n\n### GETTING THERE\n\nFrom US Highway 395 in Colville, drive east on 3rd Avenue toward Ione and State Route 20 for 1 mile and turn left (north) across from the airport onto Aladdin Road. Go nearly 25 miles (the route becomes Aladdin-Northport Road\/County Road 9435) to a Y and bear right onto Deep Lake\u2013Boundary Road (CR 9445). (This area also is accessible via forest roads over Smackout Pass from Ione.) Continue 7.2 miles, passing Deep Lake, and turn right (east) at Leadpoint onto Silver Creek Road (CR 4720). Drive 0.5 mile and bear left at a Y, continuing on CR 4720. Go 1.3 miles and bear right at the next Y onto Forest Road 070 toward Silver Creek trailheads. Drive 0.4 mile and bear right onto FR 075. Drive 4.5 slow miles to the trailhead at road's end (elev. 4540 ft).\n\n_Sherlock Peak looms behind the snags._\n\n### ON THE TRAIL\n\nSherlock Peak Trail No. 139 heads up for the first 1.3 miles on a road that's fairly nondescript through the timber. A switchback leads to a single-track trail and the views start to open up.\n\nAt 2.3 miles the trail breaks into a glorious west-facing hillside of wildflowers above the headwaters of Republican Creek. As the route tops a ridge, check out the trail to the right that climbs briefly to a fine open vantage and campsite with views north to your destination at Sherlock Peak.\n\nThen drop back down and follow the ridge and intermittent trail through the scattered subalpine fir, beargrass, and lupine. Go on the west side of the first knob and where the going gets steep, angle around the east side of the peak, skirt a bog, and begin angling up to a swale of green pine grass that leads to Sherlock's summit at 4.1 miles.\n\nThe view from the top is stunning: snowy peaks in Canada, Abercrombie Mountain, the Pend Oreille River valley, Crowell Ridge in the Salmo-Priest Wilderness, Idaho's Selkirk Crest in the distance to the east, the clear-cut swath of the international boundary, and when clear, the North Cascades to the west.\n\n### EXTENDING YOUR TRIP\n\nFrom the campsite vista, explore the open untrailed ridge that extends south and southwest from Sherlock.\n\n  Abercrombie Mountain\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/3 | 7.3 miles | 2350 feet\/7308 feet | June\u2013Oct\n\n**Maps:** USGS Abercrombie, Colville National Forest map; **Contact:** Colville National Forest, Three Rivers Ranger District, Colville, (509) 684-3711, www.fs.fed.us\/r6\/colville; **Notes:** Open to horses. Proposed wilderness; **GPS:** N 48 55.799 W 117 29.085\n\n **_Abercrombie Mountain is the centerpiece of a lofty roadless area proposed for wilderness protection. It's the second-highest mountain in Eastern Washington (next to Gypsy Peak), joining its neighbors Sherlock Peak and Hooknose Mountain in a trio of prominent high points between the Columbia River to the west and the Pend Oreille River to the east. The open rocky summit offers great views in every direction._**\n\n_Rocky rubble covers Abercrombie Mountain's summit; Hooknose Mountain is in the distance._\n\n### GETTING THERE\n\nFrom US Highway 395 in Colville, drive east on 3rd Avenue toward Ione and State Route 20. Near the edge of town, turn left (north) across from the airport onto Aladdin Road. Go nearly 25 miles (the route becomes Aladdin\u2013Northport Road\/County Road 9435) to a Y and bear right onto Deep Lake\u2013Boundary Road (CR 9445). (This area also is accessible via forest roads over Smackout Pass from Ione.) Continue 7.3 miles, passing Deep Lake, and turn right (east) at Leadpoint onto Silver Creek Road (CR 4720). Drive 0.5 mile and bear left at a Y, continuing on CR 4720 about 1 mile. Cross a cattle guard onto national forest land. Drive 0.4 mile and turn left onto CR 7078. (Continuing straight onto FR 070 leads 1.3 miles to a campground and longer alternate route at Silver Creek Trailhead.) Drive 4.5 miles on CR 7078, turning right onto FR 300, a less-developed route, and drive about 3.3 miles to the trailhead at road's end (elev. 4990 ft).\n\n### ON THE TRAIL\n\nAbercrombie Mountain Trail No. 117 angles uphill through cool forest and soon begins switchbacking to gain more than 900 feet of elevation in the 1.5 miles to the junction with Silver Creek Trail No. 119. Turn left, contouring before starting another series of nine well-graded switchbacks that lead to the open south ridge guarded by old silvery snags.\n\nHead up the wide ridge. Soon start watching carefully for the junction with Flume Creek Trail No. 502, which contours off to the right at 3.5 miles. At this junction, turn left as Trail No. 117 leads uphill through snags and tenacious wildflowers on a route that's marked occasionally by cairns maintained by hikers. Finally, the route becomes a promenade over a rockway, past flat-stone hideouts to Abercrombie's broad 7308-foot summit, site of a dismantled fire lookout.\n\n### EXTENDING YOUR TRIP\n\nFor a rugged but excellent off-trail route to nearby Hooknose Mountain, go just south of the Abercrombie summit and follow Trail No. 502 down the mountain's northeast ridge for about 0.6 mile. Where the trail angles off the ridge to begin its descent into Flume Creek, bear left and stay on the ridge (a user trail is apparent in some places). From here it's 1.5 rough miles cross-country, skirting some of the rocky knobs and through trees, to the summit of Hooknose (elev. 7210 ft) and a precipitous 1100-foot drop-off overlooking tiny Hooknose Lake. You can supersize the Abercrombie Mountain mileage by starting from the Silver Creek Campground trailhead, for a round-trip of 16.4 miles.\n\n  Mill Butte\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 4.2 miles | 680 feet\/2615 feet | May\u2013Nov\n\n**Maps:** USGS Cliff Ridge, refuge map; **Contact:** Little Pend Oreille National Wildlife Refuge, (509) 684-8384, www.fws.gov\/littlependoreille; **Notes:** Dogs permitted on-leash. Hunting allowed in most of refuge; **GPS:** N 48 27.687 W 117 43.846\n\n_Glaciers transported huge boulders and left them on Mill Butte._\n\n **_Little Pend Oreille National Wildlife Refuge is a 41,568-acre jewel in northeastern Stevens County, with its namesake stream, lakes, and a wide range of wildlife. Hiking to Mill Butte offers lessons in modern habitat management by fire as well as prominent features left by glacial ice. The trail is the 2010 product of an active refuge friends group and the Washington Trails Association._**\n\n### GETTING THERE\n\nFrom Colville's Main Street (US Highway 395), turn east on 3rd Avenue (State Route 20) and drive nearly 6 miles. Just past White Mud Lake, turn right onto Artman\u2013Gibson Road. Drive 1.5 miles to a four-way intersection and turn left onto Kitt\u2013Narcisse Road. Drive 2.1 miles to a fork and bear right onto Bear Creek Road. Drive 2.5 miles and continue straight at an intersection another 0.6 mile to the parking area and kiosks at the refuge headquarters (elev. 2040 ft). Privy available at nearby Cottonwood Campground.\n\n### ON THE TRAIL\n\nCheck out the educational information at the parking area, then proceed to the trailheads across Bear Creek Road from the headquarters. Head out the parking area's lower entrance to the lower trailhead and hike the loop counterclockwise.\n\nThe trail leads up a ridge and into a thinned forest of ponderosa pine and western larch that's been treated with controlled burns to leave it open with good views. Wild-flowers can be prolific at times, although Saint John's wort\u2014a tall, yellow-blooming noxious weed\u2014dominates some areas. Even when the hillsides dry out in midsummer, pockets of pine grass remain brilliant green. At 1.7 miles, the trail climbs to cross a small ridge and passes two large, out-of-place rocks. These glacial erratics were carried by glaciers some 10,000 years ago and deposited a considerable distance from their place of origin.\n\nAt 2.3 miles, continue up the short spur trail to Mill Butte for an open panorama of the vast forest landscape. Then head down and continue the loop. Notice the shrub clumps that start appearing. This is bitterbrush, introduced decades ago as winter food for the white-tailed deer the refuge was geared toward harboring. However, while mule deer eat bitterbrush (mule deer are rare on the refuge), the whitetails ignore this species of bitterbrush, refuge managers say.\n\nThe trail drops through carpets of kinnikinnick to an old roadbed that begins paralleling a spring-fed ravine on the left. The trail roughly follows the lush creek back to the upper trailhead across from the Little Pend Oreille refuge headquarters.\n\n### EXTENDING YOUR TRIP\n\nSee McDowell Lake (Hike 45).\n\n  McDowell Lake\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/1 | 1.3 miles | 95 feet\/2365 feet | May\u2013Nov\n\n**Maps:** USGS Cliff Ridge, refuge map; **Contact:** Little Pend Oreille National Wild-life Refuge, (509) 684-8384, www.fws.gov\/littlependoreille; **Notes:** Partly wheelchair-accessible. Dogs permitted on-leash. Trout fishing allowed in main lake under special rules; **GPS:** N 48 28.513 W 117 41.142\n\n  **_This trail is prized as an environmental education destination. In the course of a mile, you'll see five distinct ecological habitats, from riparian to semiarid. Thanks to the Friends of the LPO Refuge, a boardwalk leads over a cattail marsh and a group observation blind puts you in touch with the wide range of birds and other wildlife._**\n\n### GETTING THERE\n\nFrom Colville's Main Street (US Highway 395), turn east on 3rd Avenue (State Route 20) and drive 6 miles. Just past White Mud Lake, turn right onto Artman\u2013Gibson Road. Drive 1.7 miles to a four-way intersection and turn left onto Kitt\u2013Narcisse Road. Drive 2.2 miles to a fork and turn left on Narcisse Creek Road (straight takes you to refuge headquarters). Drive 1 mile to a Y and bear right. Bear right again toward McDowell Lake on the auto tour route. Go 1.7 miles to the trailhead on the right (elev. 2310 ft), just after the bridge over the Little Pend Oreille River. Privy available.\n\n### ON THE TRAIL\n\nIn early spring, be prepared to wade a few inches of water on the first part of the trail. Otherwise the first 0.6 mile is a breeze and universally accessible. Borrow a brochure from the trailhead and enjoy the interpretive stops along the way, including a chance to see rare marsh lupine, which blooms in late June or July.\n\nFollow the boardwalk and then the dike road to a picnic area on the north end of McDowell Lake. An observation blind faces north over the marsh. Look for sign of moose, beavers, deer, great blue herons, ducks, dragonflies, and rising trout along the dike.\n\nAt the end of the dike road, the trail narrows into a single track and heads north.\n\n_The off-trail route along McDowell Lake goes by wildflowers and mineral licks._\n\nSULLIVAN LAKE BASE CAMP\n\nBase camps are remarkably enjoyable and efficient launch pads for day hiking. Get to where the action is, make a car camp with the comforts afforded by a cooler, camp stove, and lawn chairs, and then head out and gobble up some trail miles.\n\nOf the many, many good base-camp options in Eastern Washington, Sullivan Lake stands out in the wild northeast corner of Pend Oreille County. For starters, the Nature Trail, Shoreline Trail, and Hall Mountain Trail are easily accessible from Colville National Forest developed campgrounds at both ends of the lake. The Forest Service ranger station is nearby for information during the week. A sandy swimming beach is prized by families.\n\nA dozen of the Selkirk Mountain hikes in this book are either a short bike ride or easy drive from the lake, including trails into the Salmo-Priest Wilderness. Numerous other attractions are within easy striking distance, such as huckleberry picking, paddling the Z Canyon stretch of the Pend Oreille River starting from Metaline or taking a field trip to Gardner Cave at Crawford State Park off the Boundary Dam Road.\n\nSullivan Lake, which is remarkably clean and warm during summer, will be waiting to rinse off the trail dust in a posthike dip. Only a tiny section of the northeast corner is developed with a few cabins, helping this base-camp gem stay off the grid of power-boating maniacs. _Shhh_. Share this only with your most worthy friends.\n\n\u2014 _R. L_.\n\nInvasive species such as Saint John's wort and knapweed are taking over in a few areas, but in August, after many of the native wildflowers have gone to seed, these weeds are blooming and bustling with the activity of bees and butterflies.\n\nThe trail climbs higher to a bench for an overview of the marsh before winding back down to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nWhere the dike road narrows to a single track, veer off the main loop and follow the user trail southeast on the bluffs above McDowell Lake. Follow a spine-like ridge (trail is faint) past the Rookery Road Auto Tour overlook almost to the water. Turn right and loop back on the faint shoreline game trail. As you approach the dike at the end of McDowell Lake, notice where deer regularly come to lick minerals from the soil. Near the last lick, climb the slope and turn left to rejoin the main loop.\n\n  Sullivan Mill Pond\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 2 miles | 280 feet\/2575 feet | May\u2013Nov\n\n**Maps:** USGS Metaline Falls, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446\u20137500, www.fs.fed.us\/r6\/colville; **Notes:** Partly wheelchair-accessible. Dogs permitted on-leash. Trails subject to change after planned stream restoration; **GPS:** N 48 51.528 W 117 17.992\n\n  **_Big changes were underway for the Mill Pond Historic Site as this guidebook went to press. The pond\u2014created in 1910 to store water for a mind-boggling 3-mile-long wood flume to supply hydropower to a Metaline Falls cement plant\u2014was scheduled to be drained. Planning was underway to restore Sullivan Creek's winding path through the resulting meadow. But the trail, blacksmith cabin, and displays detailing the history of a unique hydroelectric system will remain. The best of the site is available only to hikers._**\n\n_Sullivan Creek enters the Mill Pond site._\n\n### GETTING THERE\n\nFrom Metaline Falls, drive north for 2 miles on State Route 31 and turn right onto Sullivan Lake Road (County Road 9345). Go 3.2 miles and turn right into the trailhead parking at Mill Pond Historic Site (elev. 2600 ft). Privy available.\n\n### ON THE TRAIL\n\nFrom the parking area, head down to the right to begin the Mill Pond Flume Trail No. 520 interpretive walk. Signs detail the history of the area's first major development, starting in 1910 with a major wilderness work camp that used steam-powered machinery to build and service a covered wood aqueduct so large its roof became a boardwalk to Metaline Falls.\n\nThe trail leads across the dam site. At a junction, go right to reach the blacksmith shop and cabin displays. Read about the maintenance nightmares that ultimately doomed the flume project in 1956.\n\nThe trail then bends back and joins with Mill Pond Loop Trail No. 550, heading east through the trees above the Mill Pond site to Sullivan Creek, where most hikers will turn back for a 2-mile round-trip.\n\n### EXTENDING YOUR TRIP\n\nIn low water, Sullivan Creek can be forded. Cross the creek to the campground area and turn left on the trail that crosses Elk Creek and contours around the north side of the Mill Pond site back to the trailhead (see Hike 47).\n\n  Elk Creek Falls\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/2 | 2.1 miles | 550 feet\/3035 feet | May\u2013Nov\n\n**Maps:** USGS Metaline Falls, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Dogs permitted on-leash. Use caution crossing highway; **GPS:** N 48 51.555 W 117 18.036\n\n  **_Forest Service biologists consider this foot-only trail a showcase of wildlife habitats especially appealing to bird-watchers. In 2 miles, explore mixed deciduous and conifer forest, open shrublands, a riparian area, and a cool, cascading waterfall. The shrub field is the product of a 1980s controlled burn to revitalize habitat for elk._**\n\n### GETTING THERE\n\nFrom Metaline Falls, drive north for 2 miles on State Route 31 and turn right onto Sullivan Lake Road (County Road 9345). Go 3.2 miles and turn right into the trailhead parking at Mill Pond Historic Site (elev. 2600 ft). Privy available.\n\n_Elk Creek Falls tumbles through cedars._\n\n### ON THE TRAIL\n\nFrom the parking area, Elk Creek Trail No. 560 heads uphill and crosses Sullivan Lake Road. The nicely routed single track is easy to follow as it winds through forest and open areas. It gains altitude for the first 0.6 mile before contouring into open areas and an overlook of the Mill Pond Historic Site below.\n\nYou'll encounter Douglas-fir and aspen as well as serviceberry, chokecherry, ninebark, ocean spray, snowberry, and flowers such as Indian paintbrush, lupine, larkspur, and queen's cup bead lily. A trail highlight\u2014also the high point\u2014is at Elk Creek Falls, which cascades refreshingly through cedars and below a footbridge at the halfway point of this hike.\n\nBegin a winding descent, staying close to the creek and crossing another footbridge at 1.5 miles. Drop and cross Sullivan Lake Road. At a trail junction, you could turn left for a short walk to the Mill Pond Campground. But to finish the loop, turn right and hike west 0.3 mile to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nSee Sullivan Mill Pond (Hike 46).\n\n  Red Bluff\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 9 miles | 2200 feet\/3920 feet | May\u2013Nov\n\n**Maps:** USGS Boundary Dam, USGS Metaline Falls, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes. Grizzly and wolf habitat; **GPS:** N 48 51.252 W 117 17.247\n\n  **_Take a pleasant walk through the woods\u2014well-maintained and thoughtfully graded despite the total elevation gain\u2014just outside the border of the Salmo-Priest Wilderness. The Red Bluff name derives from the reddish iron oxide in the Gypsy quartzite formations above. The trail is suitable for turning around at any point for a shorter hike, but ultimately it leads to the North Fork Sullivan Creek, a wild spot where we spotted a gray wolf while scouting this trek._**\n\n_Giant cedars line the banks of North Fork Sullivan Creek._\n\n### GETTING THERE\n\nFrom Metaline Falls, drive north for 2 miles on State Route 31 and turn right onto Sullivan Lake Road (County Road 9345). Drive 4 miles and turn left into the small trailhead parking area (elev. 2720 ft). (From Sullivan Lake Ranger Station, drive 1.8 miles northwest to the trailhead.)\n\n### ON THE TRAIL\n\nRed Bluff Trail No. 553 leads uphill on a knee-friendly grade past thimbleberry, queen's cup bead lily, wild strawberry and raspberry, lupine, and kinnikinnick as you weave through mountain maple, birch, and aspen mixed into the forest. Pearly everlasting graces trailside areas in summer through fall. And there's an assortment of mosses and fungi, along with long patches of twin-flower, near the high point of the hike.\n\nAt 0.9 mile, ford Elk Creek, which is a dry hop on stepping stones for most of the season, but during spring look for a downed log bridge or plan on wading.\n\nAt 3 miles, the route tops out (elev. 3920 ft) and switchbacks down into darker forest of cedars and trees that choke out sunlight and limit forest-floor vegetation growth. Soon, after the last of several pleasant cruising stretches, the trail begins a long gradual descent to the North Fork Sullivan Creek, where a few giant cedars shade a pleasant break spot before you begin the hike back.\n\n### EXTENDING YOUR TRIP\n\nFord the creek and explore Halliday Trail No. 522 or North Fork Sullivan Creek Trail No. 507, which climbs all the way to Crowell Ridge. Or, cool off in a bathtub-size hole in the creek downstream from the trail crossing, but watch out for the devil's club along the shore.\n\n  Sullivan Lake Shoreline\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 9.2 miles | 650 feet\/2835 feet | Apr\u2013Nov\n\n_Viewpoint off Sullivan Lake Shoreline Trail_\n\n**Maps:** USGS Metaline Falls, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Dogs permitted on-leash. Trail hikes equally well from north or south end of lake; **GPS:** N 48 50.420 W 117 16.712\n\n **_Countless calories from s'mores have been burned off on this route linking the campgrounds at the north and south ends of Sullivan Lake. An interpretive nature trail adds a shorter option and educational value, while the east shoreline trail can be a half-day experience. The trek offers a surprising smorgasbord of terrain, great views of Pend Oreille County's largest lake, plus swimming and even a peek into a bat cave. And don't worry about the occasional low-flying aircraft: Sullivan Lake is unique in the region for its north shoreline airstrip and campsites for pilots._**\n\n### GETTING THERE\n\nFrom Metaline Falls, drive north for 2 miles on State Route 31 and turn right onto Sullivan Lake Road (County Road 9345). Drive 4.7 miles and turn left onto Forest Road 22. Drive 0.4 mile and turn right into the East Sullivan Lake Campground. Drive 0.2 mile to the trailhead and free parking area for hikers on the left (elev. 2690 ft). Privy available. (See Hike 50 for directions to the south trailhead.)\n\n### ON THE TRAIL\n\nFrom the north end of Lakeshore Trail No. 504, hike up a short distance and turn left on Nature Trail No. 509. Interpretive brochures are available at a kiosk (or from the ranger station on Sullivan Lake Road). Learn about springs, see remnant signs of a 1926 forest fire, marvel at a 250-year-old western larch, and check out the \"witches' broom\" that's putting a spell on trees.\n\nFinish the 0.6-mile loop (leave your brochure at the kiosk if you no longer need it) and continue hiking on the Lakeshore Trail. _Lakeshore_ will seem a misnomer at first, as the trail gains elevation. Pass a trail that drops down to the right to a parking area for a remarkably small group of private cabins considering this is a 1550-acre lake.\n\nThe uphill effort soon proves worthwhile with a great down-lake view. Descend to cross a small creek and head up a mossy slope. At about 2 miles, the trail cuts across the first of five rock slides along the shoreline. Pass a small picnic area with access to the water and room for a small tent.\n\nThe trail has fewer ups and downs in the last mile as it heads into a birch forest and thimbleberries. Around the last bay, look for a path that heads up a short way to an old mining adit. Forest Service biologists have put a bat-friendly gate on the entrance to keep people out while allowing Townsend's big-eared bats to continue using the cave.\n\nJust before reaching the south trailhead at the Noisy Creek Campground boat launch, the Lakeshore Trail passes a popular swimming area, usually equipped with a rope swing for launching out over the lake. Be wary of the condition of the rope\u2014and the tree. Several former ropeswing trees have naturally toppled into the lake.\n\n### EXTENDING YOUR TRIP\n\nLock a bike near the trailhead at one end of the lake before hiking the Lakeshore Trail from the other end. Then pedal the paved, lightly traveled Sullivan Lake Road back to your starting point for a round-trip of 10 miles.\n\n  Sullivan Lake Shoreline\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/4 | 14 miles | 4130 feet\/6323 feet | July\u2013Oct\n\n**Maps:** USGS Metaline Falls, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses. Fording Noisy Creek can be difficult in high runoff; **GPS:** N 48 47.272 W 117 16.886\n\n **_Hall Mountain casts its shadow on Sullivan Lake each morning, beckoning a few of the hearty visitors from the lakeside campgrounds. Being the former site of a fire lookout guarantees a view from the summit in all directions. The scene includes wilderness and proposed wilderness critical to megafauna, including bighorn sheep, grizzly bears, and rare woodland caribou._**\n\n### GETTING THERE\n\nFrom its junction with State Route 20 north of Cusick, drive SR 31 north toward Ione for 3.1 miles and turn right on Sullivan Lake Road (County Road 9345). Cross the Pend Oreille River and angle left, staying on Sullivan Lake Road (don't take a sharp left onto the river road). Drive 7.5 miles and turn into the Noisy Creek Campground Recreation Area at the south end of Sullivan Lake. Go a short way and turn right toward the Hall Mountain Trail. Follow the sign and another right turn into the trailhead and free parking area for hikers (elev. 2610 ft). Privy available.\n\n_Lupine along the last mile to Hall Mountain summit_\n\n### ON THE TRAIL\n\nThis hike heads immediately uphill through thimbleberries on Noisy Creek Trail No. 588 with eight nicely graded switchbacks in the first 0.8 mile. At 1.7 miles, ford Noisy Creek\u2014easy rock-hopping most of the time but high and tricky in early season. Check out the remains of an old miner's cabin along the creek just below the ford.\n\nThe thimbleberries start giving way to devil's club as the trail follows Noisy Creek, climbing along with the sound of rushing water\u2014yes, the creek's name is appropriate. You'll be treated to the din of countless little waterfalls roaring through the woods until the route finally bends northward at 3.8 miles to gain a ridge and higher, dryer ground. If you need more water, get it at Noisy Creek.\n\nAt 5.2 miles you'll hit the junction with Trails 533 and 540. Turn left (west) and continue on Hall Mountain Trail No. 540 for the last 1.8 miles to the summit. The route soon begins a broad sweep around the mountain through open slopes of grasses, lupine, other wildflowers, and even sage. Great views will start grabbing your attention even before the trail skirts past aspen stands to a lofty overlook of Sullivan Lake.\n\nPass silvery snags in the last few switchbacks through rock outcroppings to the broad summit, where concrete foundations are all that remain of the fire lookout built in 1930 and destroyed in the 1950s. Look north to see the still-used Sullivan Mountain Lookout and Crowell Ridge. Look northeast to Pass Creek Pass and the Shedroof Divide. Look east to Grassy Top and the Idaho Selkirk Mountains. Look south to Molybdenite Mountain and the roaming area for one of the first wolf packs to repopulate Washington. Look west to the Pend Oreille Divide, Abercrombie Mountain, and the prominent silhouette of Hooknose.\n\n### EXTENDING YOUR TRIP\n\nFrom the junction of Trails 588 and 540, head east on a third trail, Grassy Top Trail No. 533, which rolls delightfully over timbered high-ridge terrain for 5 miles to Trail No. 503 near Pass Creek Pass (Hike 57). Tip: For a 5-mile round-trip to Hall Mountain, with 75 percent less elevation gain, access the north side of the mountain via Johns Creek Road (FR 500), open only July 1\u2013August 14.\n\n  Crowell Ridge\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 8.4 miles | 2700 feet\/6880 feet | July\u2013Oct\n\n**Maps:** USGS Gypsy Peak, Colville National Forest map; **Contact:** Colville National For est, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** High-clearance recommended. Wilderness trail, mechanized equipment prohibited, grizzly habitat; **GPS:** N 48 52.696 W 117 14.691\n\n **_Crowell Ridge is often admired from valley roads but rarely traversed by humans. Some vehicles can't even negotiate the rough access roads. Even fewer people head northeast on this spine of scattered trees and open rocky stretches that lead toward the highest peak in Eastern Washington. That's part of this trip's wonder and why this is one of the most lonesome and rewarding natural high routes in the Salmo-Priest Wilderness. Crowell Ridge is the parallel counterpart to Shedroof Divide to the east._**\n\n### GETTING THERE\n\nFrom Metaline Falls, drive north for 2 miles on State Route 31 and turn right on Sullivan Lake Road (County Road 9345). Drive 4.3 miles and turn left on Highline Road (FR 2212). Drive about 3 miles and turn left on Forest Road 245 toward the Sullivan Mountain Lookout (high-clearance vehicle recommended). The trailhead is on the north side of the road near the switchback below the lookout (elev. 6220 ft).\n\n### ON THE TRAIL\n\nCrowell Ridge Trail No. 515 weaves through open timber before breaking into the openness of shrubs, rocks, and snags. On a good day, it's breathtaking, but bring appropriate clothing for a turn in the weather.\n\nAfter 1 mile, the trail climbs for the next mile to 6740 feet and then heads down, but it skirts the rocky pinnacles of the ridgeline peaks. Continue on the ridge past an unmaintained trail on the right that heads down toward Smart Creek.\n\nIn a saddle at 3.9 miles, North Fork Sullivan Creek Trail No. 507 splits left and quickly plunges into the creek and roadless area below. Trail No. 515 bears right and contours around the east side of a knob. But for this hike, leave both trails and hike northward instead, straight up the ridge in front of you, for 0.3 mile to the site of a fire lookout abandoned around 1950 (elev. 6880 ft). This is a premium spot to size up the Salmo-Priest surroundings, including the Shedroof Divide to the east.\n\n_Crowell Ridge hikers see Idaho's Selkirk Mountains in distance._\n\n### EXTENDING YOUR TRIP\n\nTwo other high spots beckon. Trail No. 515 leads toward 7309-foot Gypsy Peak, the highest point in Eastern Washington (map and compass or GPS essential; recommended for very fit hikers only). After 2 miles\u2014at a saddle where the trail begins a notable descent toward Bear Pasture and FR 200\u2014leave the trail and head north. See Hike 52 for the directions from here. Another option is back at the trailhead: hike 0.5 mile up the gated road to the Sullivan Mountain Lookout (elev. 6483 ft) and take in great views to Abercrombie and Hooknose Mountains to the southwest.\n\n  Gypsy Peak\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/5 | 6.5 miles | 2000 feet\/7000 feet | July-  \nmid\u2013Oct\n\n**Maps:** USGS Gypsy Peak, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** FR 200 is rough in places, closed Aug 15\u2013Nov 30. Wilderness trail, mechanized equipment prohibited. Cross-country scrambling involved. Grizzly habitat; **GPS:** N 48 55.040 W 117 08.370\n\n **_Hikers have short window of opportunity to enjoy this relatively convenient access to the highest peak in Eastern Washington before the seasonal road closure to protect the occasional grizzly bear heading to the high berry fields. The first half of the hike climbs on an excellent subalpine route to the expanses of Crowell Ridge, one of two prominent spines in the Salmo-Priest Wilderness. From there, the trip requires open-ridge map navigation and cross-country travel over talus, leading to the best viewpoint of Gypsy Peak as it looms over Watch Lake. Most hikers can't resist a scramble to the summit._**\n\n### GETTING THERE\n\nFrom its junction with State Route 20 north of Cusick, drive SR 31 north toward Ione for 3.1 miles and turn right on Sullivan Lake Road (County Road 9345). Cross the bridge over the Pend Oreille River and angle left, staying on Sullivan Lake Road (don't take a sharp left on the river road). Drive 7.5 another 4.5 miles along Sullivan Lake. Turn miles to Noisy Creek Campground and then right on Forest Road 22. Drive 6 miles and bear left at the junction onto FR 2220 toward Salmo Mountain. Drive 1.5 miles and bear left on FR 2212. Drive 4.6 miles and continue straight on FR 200. Drive 6.5 miles (rough in places) to the trailhead at the road's end (elev. 5560 ft).\n\n_Gypsy Peak looms over Watch Lake._\n\n### ON THE TRAIL\n\nCrowell Ridge Trail No. 515 heads uphill on an old road that soon narrows to a single track through an already subalpine environment of scattered firs, beargrass, and huckleberries. Reach the wilderness boundary after about 15 minutes of walking with pleasant views of the open ridges that wait for you above.\n\nCross a tiny creek that drains one of several alpine wetlands you'll look down upon later. Head up a few switchbacks and then traverse an open slope with great views east to the Idaho Selkirk Mountains. Climb three switchbacks to the crest of Crowell Ridge at 1.6 miles, where the trail bends left and heads southwest on the ridge. Gypsy Peak seekers must turn right and begin cross-country hiking. Gypsy is hidden behind a distant ridge to the north.\n\nStart by scrambling almost directly up (north), over, and down the ridge (a faint user trail shows occasionally). Immediately the route begins climbing the next ridge. Enjoy the rolling benches that stair-step up the ridge to a steep rock outcropping. Contour to the left (west) side of the ridge, angling toward the saddle ahead.\n\nFrom the next saddle, hike up to where the ridge gets steep again and angle left (west), just below the talus. Then begin angling up the slope to the ridge that overlooks Watch Lake. Very little elevation gain is needed on this last traverse to reach a campsite at the low notch overlooking Watch Lake and the spectacle of Gypsy Peak. However, it's more scenic to gain the ridge at around 7000 feet for the best views, before dropping down to the campsite. This campsite is a good rest stop for deciding whether to turn around\u2014or to press on.\n\n### EXTENDING YOUR TRIP\n\nTo fulfill your Gypsy fortunes, from the campsite contour over onto the untrailed but easy-to-see south ridge that leads up open rocky slopes to the summit of Gypsy Peak. This highly recommended side trip adds 1.5 miles and 700 feet of elevation gain round-trip. For even more, scramble down the ridge northwest from the summit for views down to the Gypsy Lakes.\n\n  Salmo River\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 6 miles | 2110 feet\/5920 feet | late  \nJuly\u2013Nov\n\n**Maps:** USGS Salmo Mountain, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Open to horses. Wilderness trail, mechanized equipment prohibited. Grizzly habitat; **GPS:** N 48 57.328 W 117 04.888\n\n **_While this book generally features the high points of the Salmo-Priest Wilderness, this hike explores the depth of the area to its namesake stream. A nicely engineered trail will help you forget the serious elevation loss and gain as you explore a wilderness north slope shaded by cedars andhemlocks and graced with lacy ferns, fungi, and wildflowers. The soothing river is a magnet for overnight campers seeking a quick wilderness experience._**\n\n_An abandoned cabin along Salmo River_\n\n### GETTING THERE\n\nFrom its junction with State Route 20 north of Cusick, drive SR 31 north toward Ione for 3.1 miles and turn right on Sullivan Lake Road (County Road 9345). Cross the bridge over the Pend Oreille River and angle left, staying on Sullivan Lake Road (don't take a sharp left on the river road). Drive 7.5 miles to Noisy Creek Campground and then another 4.5 miles along Sullivan Lake. Turn right on Forest Road 22. Drive 6 miles and bear left at the junction onto FR 2220. Drive 12.8 miles to the trailhead near the road's end (elev. 5920 ft). Privy available. ( **Tip:** In this last 12.8 miles, you'll pass several campsites, a good group site at Gypsy Meadows, trail-heads for several other Salmo-Priest hikes, and the road to Salmo Mountain Lookout.)\n\n### ON THE TRAIL\n\nThe first half of this hike is all downhill, but on gently graded Salmo Basin Trail No. 506 leading into old-growth forest. You'll cross a small creek a few times and pass various wildflowers in the summer season.\n\nAfter 3 miles, reach the Salmo River (elev. 4100 ft). Turn back if the river is high in early season. By midsummer the river is usually easy to ford; by late summer, you can usually hop across on configured stones. Campsites stretch along the river on a bench above the north shore.\n\n### EXTENDING YOUR TRIP\n\nOnce across the river, head downstream (left) through the campsites. Near the last heavily used campsite, hike off-trail up a short slope and continue downstream on another bench. Soon you'll cross a small stream channel. Then go across the flat about 400 yards and look for a Depression-era cabin (GPS: N 48 58.979 W 117 04.492) built by fur trappers Maynard Cook and Bill Ritter. For an on-trail extension from the Salmo River crossing, continue upstream on Trail No. 506 for 2.3 miles to a junction and spur leading to the meager remains of the Salmo Cabin, built in the 1930s as a Forest Service backcountry station and used until 1951. To take in a nearby fire lookout, on the return drive down from the trailhead on FR 2220, turn right on FR 270 and drive 2.1 miles to the Salmo Mountain Lookout.\n\n  Shedroof Mountain (Shedroof Divide)\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/4 | 8.8 miles | 1920 feet\/6764 feet | July\u2013Oct\n\n**Maps:** USGS Salmo Mountain, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Open to horses. Wilderness trail, mechanized equipment prohibited. Grizzly habitat; **GPS:** N 48 57.333 W 117 04.857\n\n  _**Get the best Shedroof Divide views for the least output of energy. Starting from a high-elevation trailhead, the route winds through timber and open slopes to the summit of Shedroof Mountain for views into the Rockies of Canada and down on Upper Priest Lake in Idaho.**_\n\n### GETTING THERE\n\nFrom its junction with State Route 20 north of Cusick, drive SR 31 north toward Ione for 3.1 miles and turn right on Sullivan Lake Road (County Road 9345). Cross the bridge over the Pend Oreille River and angle left, staying on Sullivan Lake Road (don't take a sharp left on the river road). Drive 7.5 miles to Noisy Creek Campground and then another 4.5 miles along Sullivan Lake. Turn right on Forest Road 22. Drive 6 miles and bear left at the junction onto FR 2220. Drive 12.8 miles to the trailhead at the end of the road (elev. 5940 ft). Privy available. (Note: In this last 12.8 miles, you'll pass several campsites, a good group site at Gypsy Meadows, trail-heads for several other Salmo-Priest hikes, and the road to Salmo Mountain Lookout.)\n\n_Priest Lake and the Idaho Selkirks can be seen from Shedroof Mountain._\n\n### ON THE TRAIL\n\nSalmo Divide Trail No. 535 begins as an old road for 1 mile to the wilderness boundary. The single-track trail then snakes through the woods along a ridge to an opening at 2 miles, with full views of Crowell Ridge, southern Shedroof Divide, and back over your shoulder to the gleaming Salmo Mountain Lookout.\n\nAt 3 miles, reach a small campsite and the junction with the Shedroof Divide Trail No. 512. Head right (south) toward Shedroof Mountain. In the next 0.5 mile, climb nine switchbacks and up a short, steep last gasp to a ridge. An unmaintained trail takes off to the left through false azalea and blowdowns and leads directly to the top of Shedroof Mountain in 0.4 mile. To take the longer, maintained route, continue on the main trail.\n\nHike nearly 0.5 mile and look for a trail branching off to the left just before the main trail crests a small ridge. The unsigned spur trail gains 320 feet and leads 0.4 mile to the summit (elev. 6764 ft).\n\nFootings for the old fire lookout are still intact\u2014the lookout started as a tent in 1915, became a cabin in 1918, sported a cupola in 1926, and graduated to a 30-foot pole-tower cabin in 1938, before its ultimate destruction in the 1950s. Marvelous views remain: Snowy Top Mountain and far into Canada to the north; the Idaho Selkirks to the east; Upper Priest and Priest Lakes to the southeast. You can see the Shedroof Divide Trail skirting a slope to the north, and even farther north the clear-cut swath that indicates the US-Canada boundary.\n\n### EXTENDING YOUR TRIP\n\nHike north or south on the Shedroof Divide Trail as far as your endurance, water, and daylight allow. It's more than 6 miles north (elev. +1280\/-800 ft) to the spur trail up to the Little Snowy Top Mountain Lookout. See also Hikes 53 and 55. And on the return drive from the trailhead down FR 2220, turn right on FR 270 and drive 2.1 miles to the Salmo Mountain Lookout.\n\n  Thunder Creek and Mountain (Shedroof Divide)\n\nRATING\/DIFFICULTY | ROUND\u2013TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/5 | 14.4 miles | 2485 feet\/6560 feet | mid\u2013July  \nmid-Oct\n\n**Maps:** USGS Salmo Mtn, USGS Helmer Mtn; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Open to horses. Wilderness trail, mechanized equipment prohibited. Grizzly habitat; **GPS:** N 48 54.033 W 117 04.896\n\n  _**Hike to a lonely lookout site along the Shedroof Divide within the grizzly bear and woodland caribou\u2013harboring Salmo-Priest Wilderness. Wander through groves of giant cedars and catch good views of the surrounding wild country. Savor succulent huckleberries in fall and cherish solitude no matter the season.**_\n\n### GETTING THERE\n\nFrom Metaline Falls, drive 2 miles north on State Route 31, turning right onto Sullivan Lake Road (County Road 9345). Proceed 4.7 miles, turning left onto FR 22 just before Sullivan Lake. Continue 6 miles to a junction just after the Sullivan Creek bridge crossing. Bear left onto FR 2220 and proceed 6 miles to the Thunder Creek trailhead (elev. 4300 ft) located across from the Gypsy Meadows camping area.\n\n_Old cedars line the way._\n\n### ON THE TRAIL\n\nStarting on a decommissioned logging road, head west through old growth and cross a small creek. Soon begin traversing an old clear-cut on a well-graded route through rapidly regenerating forest. When not hiking through an alder tunnel, you can catch some sunlight along the way and views of Prouty and Gypsy Peaks across the valley. Cottonwoods and larches make this Salmo-Priest portal a golden entryway come October.\n\nAt 2.3 miles, the road walking ends (elev. 4740 ft) and a well-built single-track leads into old growth. Bridges over the numerous creeks and cribbage and puncheon through the boggy areas help keep you dry and mud free.\n\nAt 3.1 miles (elev. 4900 ft), in a small saddle, enter the Salmo-Priest Wilderness. Then begin to descend through thick forest that bears scars from past fires. The large square holes on some of the cedars and big snags are old traps for pine martens, a member of the weasel family that's an agile tree climber.\n\nAt 3.6 miles, cross a side creek (elev. 4675 ft) in a dark cedar grove and resume climbing. Come upon Thunder Creek in a spectacular grove of ancient forest at 4.1 miles. Now following alongside the creek, traverse some of the grandest old growth in Eastern Washington. Precipitation and moisture retention in this valley give it a west-of-the-Cascade-Crest appearance, but the larches make it solidly east side.\n\nAt 5.5 miles, reach Shedroof Divide Trail No. 512 in a narrow saddle (elev. 5525 ft). Gently climb through open forest with views out to Idaho peaks. After a saddle at about 6.2 miles, the way climbs more steadily and the forest grows thicker. Skirt beneath some cliffs and pass through patches of mature timber, eventually reaching an unmarked junction (look for nails in a tree) at 6.5 miles (elev. 6075 ft).\n\nHead left for 0.7 mile on the unmaintained and slightly brushy path to the 6560-foot summit of Thunder Mountain. The fire lookout is long gone and trees obscure the views, but decent gazing can be had northeast and southwest along the Shedroof Divide. Blueberries grow on the summit in profusion and you can share them with the abundant grouse.\n\n### EXTENDING YOUR TRIP\n\nFrom the Thunder Creek Trail junction on the Shedroof Divide, head west along the divide for about 1.7 miles to the saddle between Helmer Mountain's two summits. The 6734-foot high point is an easy off-trail romp to the right. Or for a nice loop from Thunder Mountain, head east on the Shed-roof Divide Trail. After soon passing a good spring, follow, dip and climb along the high divide, passing good viewpoints out to the Priest and Sullivan River valleys. At 5.2 miles, head left on the Shedroof Cut-Off Trail (Sullivan Creek is unbridged). At 7.2 miles, reach FR 2220. Turn left and walk the road 0.6 mile to close the loop. It's only slightly longer than returning the way you came but involves more elevation gain.\n\n  Mankato Mountain (Shedroof Divide)\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/3 | 7 miles | 2220 feet\/6590 feet | July\u2013Oct\n\n**Maps:** USGS Pass Creek Pass, USGS Salmo Mountain, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Open to horses. Wilderness trail, mechanized equipment prohibited. Grizzly habitat; **GPS:** N 48 47.860 W 117 07.667\n\n  _**_This easy-access trip samples the best of the Salmo-Priest's Shedroof Divide Trail: ridge walking around peaks, expansive views, moose and black-bear sightings, and thermal-riding hawks and ravens. This route tops out on the summit of Mankato Mountain, where a lifetime of future hikes can be seen and planned in every direction._**_\n\n### GETTING THERE\n\nFrom Metaline Falls, drive north 2 miles on State Route 31 and turn right on Sullivan Lake Road (County Road 9345). Drive 4.7 miles and turn left on Forest Road 22. Drive 6 miles and bear right at the junction on FR 22. Drive 7.9 miles to Pass Creek Pass, where several cars can be thoughtfully parked. The trailhead (elev. 5410 ft) is on the east side of the pass, up the road a short way from parking for another two vehicles. (This area is also accessible from the east side of the pass via Priest Lake, Idaho.)\n\n### ON THE TRAIL\n\nStart hiking up Shedroof Divide Trail No. 512, which is notched into steep hillside through a landscape familiar with lightning-caused forest fires. Fireweed is prolific. Just when you want a change from looking east to the crest of Idaho's Selkirk Mountains, the trail winds past Round Top Mountain for views toward the west.\n\nThe Shedroof Divide is a regular hangout for a few moose. Bears are not uncommon, especially when huckleberries are ripe in August and September.\n\nSoon the trail weaves along the center of a ridge, with views both east and west, before it skirts left on the west side of the divide, again through an old burn. Mankato Mountain's grassy slopes are dead ahead, upstaging the more timbered slopes of Helmer Mountain farther along to the left.\n\nAt 3.2 miles, you'll be at the base of Mankato where the trail bends around to the east side of the divide. Leave the trail and hike up the semi-open south slope. Gain 345 feet in 0.3 mile through scattered blow-downs, huckleberry, beargrass, fescue, and lupine. The open 6590-foot summit offers a delicious panorama. On a nice day, gaze at Gypsy Peak and Bear Pasture to the northwest; Salmo Mountain Lookout and Snowy Top and the Canadian Selkirks to the north; miles of Idaho Selkirks like the edge of a battered saw blade to the east; and Grassy Top and Molybdenite to the south.\n\n_Bull moose along Shedroof Divide Trail_\n\n### EXTENDING YOUR TRIP\n\nFollow the mostly open ridge cross-country from Mankato's summit northwest to the top of an unnamed but attractive peak (elev. 6680 ft).\n\n  Grassy Top Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 7.8 miles | 1470 feet\/6253 feet | July\u2013Nov\n\n**Maps:** USGS Pass Creek, Colville National Forest map; **Contact:** Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville; **Notes:** Open to mountain bikes, horses. Grizzly habitat. Proposed wilderness; **GPS:** N 48 47.897 W 117 08.048\n\n  _**Grassy Top is a timbered mountain that doesn't have the airy feeling of open peaks, but this beautifully maintained trail has a wild flavor because of views to the east and west of roadless forest proposed for wilderness protection. The route is especially colorful in late autumn, when huckleberry bushes are crimson and western larches are golden yellow.**_\n\n### GETTING THERE\n\nFrom Metaline Falls, drive 2 miles north on State Route 31 and turn right on Sullivan Lake Road (County Road 9345). Drive 4.7 miles and turn left on Forest Road 22. Drive 6 miles and bear right at the junction on FR 22. Drive 7.8 miles to the trailhead (elev. 5355 ft) on the right. But park a short way farther at Pass Creek Pass, where thoughtful drivers can park several cars. (This area is also accessible from the east side of the pass via Priest Lake, Idaho.)\n\n_Grassy Top larch turn gold in October._\n\n### ON THE TRAIL\n\nGrassy Top Trail No. 503 drops from the road and soon begins gaining a ridge in four long, gentle switchbacks above the Pass Creek drainage. Once on the ridge, cruise a fine trail that weaves to the east and west sides of knobby peaks.\n\nAt 2.7 miles, continue straight past the junction with Trail No. 533 (which heads toward Hall Mountain). Soon Trail No. 503\n\nsidehills across a grassy slope above the Middle Fork Harvey Creek drainage. This stretch is particularly impressive from mid-October to November, when fall colors are glowing.\n\nSoon the trail leads into the woods on a timbered ridge, with sheltered views to the east. The trail splits at a grassy opening: Left goes unceremoniously to the summit of Grassy Top, with views to the east. The right fork is worth exploring to see the views it offers to the south.\n\n### EXTENDING YOUR TRIP\n\nTrail No. 503 leads 3 miles to Harvey Creek Road, the quickest route to Grassy Top for people camping at Sullivan Lake, but not as rewarding. For an excellent 8-mile ridge walk, drop a car at the end of FR 500 (open July 1\u2013August 14) on your way to Pass Creek Pass and hike out on Trail No. 533: 5.1 miles toward Hall Mountain, turn right on Trail No. 540, and hike 0.5 mile to your shuttle car; or add 3 miles round-trip by continuing straight on Trail No. 533 and taking the spur to Hall Mountain (elev. 6323 ft).\n\n  Roosevelt Grove of Ancient Cedars\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 2.5 miles | 300 feet\/3600 feet | May\u2013Nov\n\n**Maps:** USGS Helmer Mtn, Kaniksu National Forest map; **Contact:** Kaniksu National Forest, Priest Lake Ranger District, (208) 4432512, www.fs.usda.gov\/ipnf; **Notes:** Dogs permitted on-leash. Supervise children closely on overlook trail; **GPS:** N 48 45.990 W 117 03.743\n\n  **_Around 1919, foresters in the business of cutting down trees recognized the aesthetic value of this stand of old-growth cedars and appealed for its protection. A 1926 forest fire destroyed about 75 percent of the grove, but 22 acres attest to its original majesty. The trees are 800 years old on average, and a few may be more than 2000 years old. The white-water rush of Granite Falls adds to the ambiance. Incidentally, Stagger Inn was the name given to the camp at this site for workers fighting that 1926 fire, describing the condition of the exhausted crews._**\n\n### GETTING THERE\n\nFrom Metaline Falls, drive north 2 miles on State Route 31. Turn right on Sullivan Lake Road (County Road 9345). At Sullivan Lake, turn east on Forest Road 22 toward Priest Lake, Idaho. Drive 21 miles (over Pass Creek Pass), and turn south at Granite Pass toward Nordman, Idaho. Go 1.7 miles on FR 302 and turn into Stagger Inn Campground and trailhead (elev. 3300 ft). (From Priest River, Idaho\u2014the best access in early season, when Pass Creek Pass can be snowbound\u2014drive north 36 miles on SR 57 to Nordman. Continue on SR 57 another 2 miles and bear left on FR 302 for 11 miles to the campground and trailhead.) Privy available.\n\n_Cascades below Granite Falls near Roosevelt Grove of Ancient Cedars_\n\n### ON THE TRAIL\n\nFrom the trailhead kiosk, start with a short side trip to the left. Follow your ears to the rush of water tumbling through the rocks below the 70-foot slide of Granite Falls. Then return to the trailhead and head up the Overlook Trail, which quickly leads to a view of the lower falls from a platform that hangs over the rock cliff. The trail then gets more rocky and rugged up to a natural overlook of Granite Creek plunging into pools.\n\nSoon the Overlook Trail joins with the main trail, a smooth, wide path born from an old logging road. Turn left and hike 0.5 mile to the upper cedar grove, which covers about 20 acres between the trail and the creek. A few paths wander through the peacefulness of the giant trees, and so should you before hiking the main trail back 1 mile to the trail-head. Follow your ears to the 20-foot drop of La Sota Falls.\n\n### EXTENDING YOUR TRIP\n\nThe Granite Falls Trail continues past the upper cedar grove for miles.\n\n  Little Grass Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/5 | 10.5 miles | 2520 feet\/5695 feet | July\u2013Oct\n\n**Maps:** USGS Helmer Mtn, Kaniksu National Forest map; **Contact:** Kaniksu National Forest, Priest Lake Ranger District, (208) 4432512, www.fs.usda.gov\/ipnf; **Notes:** Open to horses. Grizzly habitat. Last 0.8 mile of trail may not be maintained; **GPS:** N 48 45.784 W 117 03.661\n\n  _**A former fire lookout site, Little Grass Mountain offers vast views of the northeastern Washington and Idaho Panhandle forests, a sweeping stretch of the Idaho Selkirk Crest, and Priest Lake. On the way, get a healthy dose of mileage and elevation gain, cross a few creeks, and feast on the sight of an enchanting cedar grove and the flavor of late-season huckle-berries. There's little competition for any of it.**_\n\n### GETTING THERE\n\nFrom Metaline Falls, drive 2 miles north on State Route 31. Turn right on Sullivan Lake Road (County Road 9345). At Sullivan Lake, turn east on Forest Road 22 toward Priest Lake, Idaho. Drive 21 miles (over Pass Creek Pass), and turn south at Granite Pass toward Nordman, Idaho. Go 1.7 miles on FR 302. The trailhead (elev. 3310 ft) is 100 yards north of Stagger Inn Campground. (From Priest River, Idaho\u2014the best access in early season, when Pass Creek Pass can be snowbound\u2014drive north 36 miles on SR 57 to Nordman. Continue on SR 57 for 2 miles and bear left on FR 302 for 11 miles to the campground.) Privy available.\n\n_Lush ferns feather Little Grass Mountain trail._\n\n### ON THE TRAIL\n\nTrail No. 266 heads steeply up into the trees and some switchbacks before continuing up in a long traverse. After 2 miles, it eases onto a bench with a creek, where water spreads to nourish fern meadows and a long grove of ancient cedars that extends up and across the Washington\u2013Idaho state line at 2.5 miles. Huckleberries that don't ripen until late in the season begin showing up among the beargrass. Usually there's no shortage of evidence that elk are in the area.\n\nDrop down a slope and then start up again to the left as you pass the junction with Trail No. 256. Continue straight across a slope of springs and lush vegetation (including stinging nettles) that often obscures the trail. Soon you'll be in a narrow ravine that leads up to Boulder Meadows.\n\nThe trail bends northwest and soon ends at decommissioned FR 1014. If you reach the road, you've gone about 100 yards past the unmaintained 0.8-mile spur that heads southwest and then west up a ridge to the summit of Little Grass Mountain. If you lose the trail, use your map and compass to help you navigate up the ridge. The south side of the ridge is more open. Soon you'll break out into open grassy slopes for an easy walk up through wildflowers to the concrete footings of a lookout tower built in 1934 and destroyed in 1960.\n\n### EXTENDING YOUR TRIP\n\nCheck out the Huff Lake Interpretive Site 0.2 mile south on FR 302. It's a peatland study of at least five rare plant species: bristle-stalked sedge, creeping snowberry, northern starflower, bog willow, and bog cranberry.\n\n  Kalispell Rock\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 5.6 miles | 1490 feet\/5200 feet | June-Oct\n\n**Maps:** USGS Monumental Mtn, Colville and Kaniksu National Forest maps; **Contact:** Kaniksu National Forest, Priest Lake Ranger District, (208) 443-2512, www.fs.usda.gov\/ipnf; **Notes:** Open to mountain bikes, horses. Trails east of Pend Oreille Divide are maintained by the Idaho Panhandle national forests; **GPS:** N 48 38.021 W 117 06.101\n\n  **_This once-popular hiking area lost its charm in the early 1980s when clear-cutting was rampant. But the wildlife-rich forest is reviving and the attraction is back. Kalispell Rock sports the remains of a Forest Service cabin in the shadow of massive mushrooms of granite overlooking the Priest River drainage. Deer and moose frequent this route, as do, possibly, elk and bear._**\n\n### GETTING THERE\n\nFrom State Route 20 north of Newport, turn east into Usk. Follow Kings Lake Road over the Pend Oreille River and turn left on Leclerc Road (also known as Newport\u2013Ione Road). Drive 16 miles and bear right on Leclerc Creek Road. Drive 0.9 mile and bear right on East Branch Road (becomes Forest Road 1934). Drive 14.1 miles (the road becomes FR 308 at a pass) and bear right at a Y. Go 0.1 mile, still on FR 308, to the guardrail blocking a spur road on the right. This is the trailhead (elev. 3910 ft).\n\n### ON THE TRAIL\n\nGo past the gate, over the earthen berm that blocks motor vehicles, and head up Kalispell Rock Trail No. 370, a former logging road. At 0.5 mile, bear left at the junction with another old road and continue up. (Take care to note the road junctions heading up the ridge; they can be easy to miss on the way down.)\n\nAt 1.5 miles, just after the road slips over to the north side of the ridge, turn left on a lesser road that climbs sharply to the spine of the ridge. This is the sweet section of the old-road portion of the route. At 2.3 miles, the route drops to a grassy opening and a trail junction. Trail No. 103 continues ahead (south), but Trail No. 370 makes a turn to the right and up on single-track. Ah, now the hike is getting good.\n\n_The old lookout tender's cabin is decomposing below Kalispell Rock._\n\nBut pay attention. After hiking and climbing 0.2 mile, the trail levels and descends slightly. Just before reaching a more open area (where the trail eventually fades away), look for the main trail doubling back sharply to the right. This easy final 0.3 mile to the old lookout cabin site is the sweetest part of the hike.\n\nThe tallest granite slabs at the lookout site are dangerous to climb. But just below the cabin site to the east is a rock slab that makes a great lunch spot. The cabin was built in 1927 as a refuge for the lookout staffer, who would climb a ladder to the alidade (firefinder) shelter on top of Kalispell Rock.\n\nThe shelter was removed and the cabin left to decay after 1935. On the fourth log up the north inside-wall of the old cabin, for as long as it lasts, is the inscription \"Pete van Gelder\" followed by a string of dates, '48\u2013'81. Van Gelder was a legendary member of the Spokane Mountaineers. The dates indicate his visits, leading volunteer groups, often with lookout historian Ray Kresek, to maintain this trail and others.\n\n### EXTENDING YOUR TRIP\n\nTrail No. 103 to the south eventually becomes a single-track that follows the divide toward Hungry Mountain and North Baldy Mountain (Hike 61). Or spend some time at tiny Petit Lake, east from the trailhead on FR 311, with its low-key campsite and good trout fishing, especially in late summer and early fall. Bring a small boat to enjoy it fully.\n\n  Hungry Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 8.4 miles | 2180 feet\/5955 feet | June\u2013Oct\n\n**Maps:** USGS North Baldy, Colville and Kaniksu National Forest maps; **Contact:** Kaniksu National Forest, Priest Lake Ranger District, (208) 443-2512, www.fs.usda.gov\/ipnf; **Notes:** Park before trailhead to avoid rough road. High-clearance recommended regardless. Trail open to mountain bikes, horses. Trails east of Pend Oreille Divide are maintained by Idaho Panhandle national forests; **GPS:** N 48 32.784 W 117 09.482\n\n  **_If you love ridge rambling, don't overlook this lightly used north\u2013south trail. It caters to serious leg stretching on top of a timbered divide between the Pend Oreille River drainage to the west and the Priest Lake and River drainage to the east. We saw elk, moose, and deer on a single trip. We also saw scats or tracks from predators taking an interest in those animals, including black bears and a mountain lion._**\n\n### GETTING THERE\n\nFrom State Route 20 north of Newport, bear right and head east through Usk on Kings Lake Road. Cross the bridge over the Pend Oreille River and turn left on Leclerc Road (also known as Newport\u2013Ione Road). Drive 13 miles and just after crossing Mill Creek, turn right on Mill Creek Road (Forest Road 1200). Drive 10 sometimes dusty miles to Pyramid Pass junction. Turn left onto FR 306 toward North Baldy Mountain. Drive 4 miles and park at turnouts on the right (elev. 5725 ft); the road heads left and traverses the west-facing slope of North Baldy, becoming extremely rough.\n\n### ON THE TRAIL\n\nHike 0.5 mile up the rough road and look for Trail No. 103 taking off down to the left. This is the trip high point (elev. 5955 ft). The trail heads downhill for more than a mile through timber and beargrass before coming to a gated logging road. Turn right on the road and walk about 20 yards. Then turn left off the road and hike north on Trail No. 103.\n\n_Looking south to North Baldy from Hungry Mountain_\n\nThe route from here has gentle ups and downs through beargrass and huckleberries. It passes a startling outcropping of granite boulders in a small meadow and then heads up and cruises along a ridge. To the east, the timber is mostly intact to protect the Priest Lake watershed. To the west, second growth is healing the landscape nuked by ill-conceived clear-cutting. Let's hope we learned our lesson.\n\nAt 4 miles, reach a junction. Turn right, leaving Trail No. 103, and head up Stateline Trail No. 162, cross a small meadow where the trail briefly fades, and bear left up the fall line, reaching the top of Hungry Mountain (elev. 5541 ft) 0.2 mile from the trail junction. From the granite slabs on the timbered summit, look south to the trailhead at North Baldy Mountain.\n\n### EXTENDING YOUR TRIP\n\nStateline Trail No. 162, which descends significantly from Hungry Mountain, is worth exploring. You can also continue north on Trail No. 103 to Kalispell Rock (Hike 60) and back for a rewarding 16-mile round-trip. For a shorter side trip, from the Hungry Mountain trailhead hike 0.3 mile up the rough access road to the top of North Baldy Mountain (elev. 6173 ft).\n\n  Bead Lake\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 11.2 miles | 2100 feet\/3100 feet | Mar\u2013Nov\n\n**Maps:** USGS Bead Lake, Colville National Forest map; **Contact:** Colville National Forest, Newport Ranger District, (509) 447-7300, www.fs.fed.us\/r6\/colville; **Notes:** NW Forest Pass required Apr 15\u2013Oct 1, only at boat-launch trailhead. Open to mountain bikes, horses; **GPS:** N 48 17.195 W 117 06.556\n\n  **_At 720 acres, Bead Lake is the second largest lake in Pend Oreille County (behind Sullivan), yet it has a deep, clear high-mountain feel. Explore its east shore's rocky points, wildflowers, cedar groves, campsites, and notable giant white pine. This trip is a gem, whether the water beckons for a summer dip or awes you with its glimmering ice cap in early spring._**\n\n_Early spring hiking at Bead Lake_\n\n### GETTING THERE\n\nFrom Newport, follow US Highway 2 across the Pend Oreille River into Idaho and take the first left onto Leclerc Road. Continue north 2.7 miles and turn right on Bead Lake Road. Drive 6.1 miles and choose from two options: To reach the boat-launch trailhead, turn right on paved Bead Lake Drive (Loop Road) and drive 0.2 mile. To reach the no-fee upper trailhead, turn right just before Bead Lake Drive on gravel Bead Lake Ridge Road (FR 3215), and drive 0.5 mile to a small parking area for several cars (elev. 3015 ft). Privy available in season (near the boat launch).\n\n### ON THE TRAIL\n\nBead Lake Trail No. 127 switchbacks down toward the lake from the upper trailhead. At 0.2 mile and the junction with the trail from the boat-launch trailhead, continue ahead, with the lake on your left. At 0.7 mile, pass the spur down to the Mineral Bay boat-in campsite. At 1.2 miles, the trail passes through a cedar grove and the hike-in Enchantment Camp at the end of the anchor-shaped lake's southeast arm.\n\nHike overland through a saddle in a peninsula, and drop to a gully with a path that leads to the water and another boat-in campsite. At 3.5 miles, after the trail passes through a cedar grove flat\u2014just before reaching a series of footbridges\u2014look up-slope to the right for a giant white pine more than 15 feet in circumference.\n\nAt about 4.6 miles, the trail passes Lodge Creek Camp. Head left, leaving the main trail and cross the footbridge over Lodge Creek. This Spur Trail No. 127.1 travels above the shoreline, affording good views of the lake, before it dead-ends in 1.1 miles.\n\n### EXTENDING YOUR TRIP\n\nFrom the Lodge Creek footbridge, Trail No. 127 heads up the east side of the creek, first gently through cedars, then crossing the creek and gaining 600 feet to end at FR 3215 in 1.5 miles.\n\n  Pend Oreille County Park\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 4.1 miles | 750 feet\/2780 feet | Mar\u2013Nov\n\n**Maps:** USGS Elk, Pend Oreille County Park trails map; **Contact:** Pend Oreille County Works Department, (509) 447-4513, www.pendoreilleco.org\/county\/parks.asp; **Notes:** Facilities open Memorial Day\u2013Labor Day. Trail open to mountain bikes, horses. Dogs permitted on-leash. Watch for ticks; **GPS:** N 48 04.825 W 117 19.558\n\n_Arrowleaf balsamroot in Pend Oreille County Park_\n\n  _**The Back Country Horsemen of Washington, schools, and service groups rescued this fine 440-acre park from neglect. Although the picnic area and rustic campground are open only during summer, the 7-mile trail system is open year-round. Explore wildflower areas, old-growth pines, cedars, and high overlooks above the valley.**_\n\n### GETTING THERE\n\nNorth of Spokane, from the intersection of Deer Park\u2013Milan Road (at Riverside Schools), drive 8.2 miles north on US Highway 2 and turn west at milepost 318 into the entrance of Pend Oreille County Park. Leave your car in the lot next to the highway before going through the gate, which is locked to keep out motor vehicles except in summer. Walk past the gate on the paved road 100 yards to the unmarked trailhead on the left (elev. 2340 ft). Privy available.\n\n### ON THE TRAIL\n\nLeave the paved entrance road (a portion of the old Newport Highway) on Orion's Path, which soon becomes single-track. At a meadow, the route continues ahead on a double-track that leads to the paved entrance road 0.7 mile later. Turn left on the old highway for a short way and then turn right on the double-track trail, which soon funnels into the sweet, single-track Big Sky Loop.\n\nMOUNT SPOKANE TRAILHEADS\n\nMount Spokane State Park offers a wealth of day-hiking options, most accessible from the main Mount Spokane Park Drive, open year-round, and Summit Road, open during summer.\n\nFrom the park entrance at milepost 15.4 of Mount Spokane Park Drive (State Route 206), set your vehicle trip odometer and find the following trailheads (Discover Pass required):\n\n**At 0.2 mile:** The park's first public parking spot accesses Trail No. 110, the main trail linking to upper-mountain destinations.\n\n**At 1.7 miles:** The hairpin-turn parking lot offers trailhead access to the Mount Kit Carson Lower Loop Road, Burping Brook picnic area, and Trail Nos. 100, 110, and 140 and others that link to three of the park's most popular summits.\n\n**At 3 miles:** A four-way junction offers several options.\n\n\u2022 Go straight to reach the downhill ski area.\n\n\u2022 Turn right to reach the Selkirk Lodge and cross-country ski trails, including the trailhead for Quartz Mountain.\n\n\u2022 Park at this junction to access Trail Nos. 100 and 130 for longer hikes to Day Mountain, Mount Kit Carson, the Mount Spokane summit, or other destinations in the core trails area.\n\n\u2022 Turn left to drive up Summit Road to more trailheads.\n\n**At 1 mile up Summit Road:** Turn right for Bald Knob picnic area parking to access Trail No. 130 to the CCC Cabin and Day Mountain.\n\n**At 1.6 miles up Summit Road:** A small parking area offers access to shorter routes to the CCC Cabin and Trail No. 140 to the top of Mount Spokane.\n\n**At 3 miles up Summit Road:** The road ends at the top of the mountain near the lovely stone Vista House. Here you will find restrooms near the top of the chairlift and the summit trailhead for Trail No. 140. It's all downhill from here.\n\n\u2014 _R. L_\n\nThe trail climbs in short bursts for 1.5 miles almost to the park's high point on a brushy ridge overlooking the valley. Then it drops quickly. At 2.5 miles from the start, continue past a post marking Junction 8 (a shortcut back, called Arrowleaf Ridge Trail) as the Big Sky Loop contours over to a bench before dropping again. Check out the short Penstemon Point Loop at the Junction 7 marker.\n\nAt Junction 6, bear left on the double-track for a short way, and then turn right onto the single-track at Junction 5. At Junction 4, continue straight as the Big Sky Loop bends into a lusher area with cedars.\n\nSoon the trail bears left and heads down to the campground. Turn left on the campground road, and then turn left on the old highway and follow the pavement back to your car.\n\n### EXTENDING YOUR TRIP\n\nExplore up to 3 more miles of fire roads, connectors, and spur trails in the park.\n\n  Mount Spokane Summit\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 2.4 miles | 700 feet\/5880 feet | Year\u2013round\n\n**Maps:** USGS Mt Spokane, state park map from Friends of Mount Spokane State Park, www.mountspokane.org; **Contact:** Mount Spokane State Park, (509) 238-4258, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Park open 6:30AM\u2013dusk. Trail open to mountain bikes, horses. Dogs permitted on-leash. Privy at summit; **GPS:** N 47 55.070 W 117 07.367\n\n  **_Mount Spokane is the high point in the Spokane region, and the summit is a highlight destination, where hikers, bikers, and drivers converge to be on top of it all. This hike in Washington's standout year-round state park provides plenty of options for savoring the forest, wildflowers, and critters before emerging at the top, where chairlifts deposit skiers during winter. The Vista House near the summit is a tribute to the craftsmanship of 1930s Civilian Conservation Corps stone masons._**\n\n### GETTING THERE\n\nFrom US Highway 2 north of Spokane (or take the Argonne Road exit from I-90 and go north on Argonne and Bruce Roads), head east on Mount Spokane Park Drive (State Route 206) to the park entrance at milepost 15.4. Continue 3 miles on Mount Spokane Park Drive and turn left onto Summit Road. Drive 1.6 miles (passing the campground) to the parking area (elev. 5190 ft) before a hairpin turn.\n\n_The stone Vista House on Mount Spokane_\n\n### ON THE TRAIL\n\nWalk up the paved road a short way to the hairpin turn. The gated Mount Kit Carson Loop Road on the left is an option for your return route.\n\nHead up the double-track just to the right of the Mount Kit Carson Loop Road. Go a short way to a communications tower structure and walk straight through it, continuing up through the ferns to connect with Trail No. 140. Turn right and head uphill about 1 mile on switchbacks to the summit of Mount Spokane.\n\nTurn left at the road, walk through a parking area, past a vault toilet and Chair-lift 1, to the Vista House. This stone structure, built on a granite outcropping by the Civilian Conservation Corps in 1934, is open for shelter and picnicking. The views are excellent toward Spirit Lake to the east, as well as a portion of Twin Lakes and south to Newman Lake.\n\nReturn the way you came, or add a slight variation by bypassing the spur you came up from the trailhead and continuing on Trail No. 140 and a spur out to the Mount Kit Carson Loop Road. Turn left on the road to walk back out to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nIf you make the alternate return, turn right on the loop road and then left to visit the CCC Cabin at Beauty Mountain (elev. 5180 ft). For a bottom-to-top summit hike, leave your vehicle at the first trailhead 0.2 mile from the park entrance, and hike Trail No. 110, crossing Lower Kit Carson Loop Road and continuing up to Upper Kit Carson Loop Road and a junction with several trails. Cross the road and head up Trail No. 140 to the summit. This route to the top is about 11 miles round-trip and gains 3100 feet. For a 5.4-mile round-trip to the summit, start on Trail No. 130 at the junction with Summit Road, 3 miles from the park entrance.\n\n  Day Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/2 | 6 miles | 880 feet\/5170 feet | June\u2013Oct\n\n**Maps:** USGS Mt Kit Carson, USGS Mt Spokane, state park map from Friends of Mount Spokane State Park, www.mountspokane.org; **Contact:** Mount Spokane State Park, (509) 238-4258, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Park open 6:30AM\u2013dusk. Trail open to mountain bikes, horses. Dogs permitted on-leash; **GPS:** N47 54.774 W117 06.774\n\n_Spokane Valley looms below Day Mountain._\n\n  **_While most of the trails in Mount Spokane State Park seem to go up and down, this choice route follows a ridge, minimizing elevation gain but still getting to the top of a mountain! Can't beat that. Open slopes, pleasant timbered stretches, hillside springs, and wildflowers greet you, as well as some nifty stonework steps, handiwork of the 1930s Civilian Conservation Corps. Day Mountain, 800 feet lower than Mount Spokane, offers a pleasant view of the Spokane Valley below._**\n\n### GETTING THERE\n\nFrom US Highway 2 north of Spokane (or take the Argonne Road exit from I-90 and go north on Argonne and Bruce Roads), head east on Mount Spokane Park Drive (State Route 206) to the park entrance at milepost 15.4. Continue 3 miles on Mount Spokane Park Drive and turn left on Summit Road. Drive 1 mile, turn right at the trailhead (elev. 5120 ft), and park at the Bald Knob picnic site. Privy available.\n\n### ON THE TRAIL\n\nWalk back out the parking lot entrance and cross Summit Road to Trail No. 130, a nice single-track that starts in an old burn area with open views of the Spokane Valley. Soon the openings trend to grassy meadows and then turn to a forest of older, more scattered trees.\n\nAt 1 mile, reach a junction. The right fork heads up a couple of hundred yards to the rock steps and pathway leading to the CCC Cabin on Beauty Mountain (elev. 5180 ft). Some two hundred members of the Civilian Conservation Corps built these area roads and other facilities during the Great Depression. They used stone to build the Vista House on the Mount Spokane summit in 1933 (Hike 64). The CCC Cabin was rebuilt on its original site in 1998.\n\nFor Day Mountain, bear left at the fork and drop immediately to Mount Kit Carson Loop Road, where you have two options: Turn left and hike down the road, which switches down to Saddle Junction at 1.7 miles from the trailhead. Or, turn right, hike about 20 yards, and look for a trail that drops steeply to \"cut the switchback\" to the road below. Trail Nos. 110, 130, 140, and 160 meet at Saddle Junction, where there's a privy and signs.\n\nContinue left and up past the outhouse toward Mount Kit Carson. Go about 20 yards and bear right on the newer trail built in 2010. After making a switchback and angling upslope, come to a junction with the old trail. Turn right, staying on Trail No. 160. Go about 20 yards and turn right on single-track Trail No. 130 toward Day Mountain.\n\nAt 2.4 miles, reach another junction with Trail No. 160. Continue straight. Hike through a fairly thick stand of lodgepole pine before breaking into a more parklike grassy forest of older Douglas-firs. Head uphill.\n\nAs the trail rounds the top of Day Mountain, you're still in the trees. Continue downhill on the other side until the trail leads to an open ridge. At 3 miles, the trail fades into a rocky outcropping\u2014a good place for a break with good views below of Peone Prairie and the Spokane Valley.\n\n### EXTENDING YOUR TRIP\n\nLook carefully and you'll find Trail No. 130 continuing northward; follow it for a while if you wish. On your return to the trailhead turn right off of Trail No. 130 onto Trail No. 160 and make a short climb to the summit of Mount Kit Carson. Enjoy another view, and another summit, before continuing on Trail No. 160 northeast back to Saddle Junction and then back to the trailhead.\n\n  Burping Brook Basin\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 6.2 miles | 1660 feet\/5020 feet | June\u2013Oct\n\n**Maps:** USGS Mt Kit Carson, state park map from Friends of Mount Spokane State Park, www.mountspokane.org; **Contact:** Mount Spokane State Park, (509) 238-4258, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Park open 6:30AM\u2013dusk. Trail open to mountain bikes, horses. Dogs permitted on-leash; **GPS:** N 47 54.271 W 117 07.489\n\n  **_This route is the core of the Mount Spokane State Park single-track trail system. It appeals to people who relish variety in a good forest walk, with liberal doses of ups, downs, terrain changes, running water, and extension options. Explore the three forks in the Burping Brook headwaters on trails beautifully thought out and routed by volunteers through firs, cedars, and hemlocks, with sites for picnicking._**\n\n### GETTING THERE\n\nFrom US Highway 2 north of Spokane (or take the Argonne Road exit from I-90 and go north on Argonne and Bruce Roads), head east on Mount Spokane Park Drive (State Route 206) to the park entrance at milepost 15.4. Continue 1.7 miles on Mount Spokane Park Drive to a parking area before a hairpin turn (elev. 3860 ft).\n\n### ON THE TRAIL\n\nFrom the parking area, use caution as you walk uphill and cross the road. The route begins at the hairpin turn, through the gate on Mount Kit Carson Loop Road. Hike the road 50 paces and bear right on Trail No. 103. Go another 50 yards, bear left onto Trail No. 100, and cross the creek. Hike 0.35 mile and bear right to leave Trail No. 100 and continue uphill on Trail No. 110. Contour and switchback nearly 2 miles to reunite with Mount Kit Carson Road at Saddle Junction.\n\nTurn left (west) onto Trail No. 140, being careful not to branch out on Trail Nos. 130 to Day Mountain or 160 to Mount Kit Carson (unless you want to take side trips). Trail No. 140 contours along the flank of Kit Carson and then drops down: Look for a left turn onto the newer single-track. (Continue on the decommissioned double-track for a short way if you want a meadow view.)\n\nTrail No. 140 switches back southward to Mount Kit Carson Loop Road at Smith Gap. Hike the road a short way, and then turn left onto Trail No. 100. Contour above the road for 1.1 miles, take the Trail No. 104 connector trail down a few switchbacks to the Burping Brook picnic site, and then hike 0.3 mile up Mount Kit Carson Loop Road to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nFrom Saddle Junction, out-and-back trails lead to good views at Mount Kit Carson, Day Mountain, or Mount Spokane's summit. At the least, make a side trip to Kit Carson's rock outcropping overlooking Spokane Valley.\n\n_Enjoying sunset on Mount Kit Carson_\n\n  Quartz Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 5.5 miles | 860 feet\/5160 feet | June\u2013Oct\n\n**Maps:** USGS Mt Kit Spokane, state park map from Friends of Mount Spokane State Park, www.mountspokane.org; **Contact:** Mount Spokane State Park, (509) 238-4258, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Park open 6:30AM\u2013dusk. Trail open to mountain bikes, horses. Dogs permitted on-leash. Reserve Quartz Mountain Lookout at (888) 226-7688, www.parks.wa.gov; **GPS:** N47 54.188 W117 05.992\n\n  **_A fire lookout that once stood on Mount Spokane was retired and reassembled in 2005 for recreation on Quartz Mountain. You can rent the lookout or simply visit for one of the best views of Mount Spokane and northern Idaho below. The hike takes advantage of the state park's 25-mile core Nordic ski trail system, which is rich with wildlife, wildflowers, and huckleberries._**\n\n### GETTING THERE\n\nFrom US Highway 2 north of Spokane (or take the Argonne Road exit from I-90 and go north on Argonne and Bruce Roads), head east on Mount Spokane Park Drive (State Route 206) to the park entrance at milepost 15.4. Continue 3 miles on Mount Spokane Park Drive. Drive to a four-way junction. Turn right and drive 0.1 mile through the large parking lot. At a junction, make a right-hand hairpin turn and park by Selkirk Lodge, the base area for the cross-country trail system, and the trailhead (elev. 4630 ft). Privy available.\n\n### ON THE TRAIL\n\nFind the large trail system signboard and map above the lodge. From this trailhead, five double-track trails lead to Junction 1. For simplicity, go left on the Mountain View Trail and follow it 0.3 mile to Junction 1, a large grassy meadow. From here, stay left and walk up a road for a short way, bearing left on the first trail, called Sam's Swoop (Sam is a perennial volunteer, worthy of a trail name). Note the diversity of plants: huckle-berry, beargrass, wild strawberry, ferns, and much more.\n\nAt 1 mile, reach Junction 2, another meadow, where seven trails meet with a road (Lodgepole Trail) running through the middle. Bearing left on the road is the fastest way to Quartz Mountain, but it's more interesting to hike the Eagle Crest Trail, just to the right of the road.\n\nAt 1.6 miles, the Eagle Crest Trail peaks at a meadow and viewpoint worth a stop. Then the trail heads down. At about 2 miles, the trail ends at the Nova Hut warming shelter and privy. Turn left at the junction. Go about 30 yards and turn right on the road that services the Quartz Mountain Lookout. Continue straight past a junction with a double-track trail that heads left. In another 60 yards, at a junction of two trails, bear left on the single-track. The gravel below your feet indicates why it's called Quartz Mountain.\n\nAt 2.5 miles, the single-track trail meets the lookout access road. Turn immediately left and continue uphill. The trail eventually ends at 2.9 miles at the Quartz Mountain Lookout, where there's a picnic table and privy.\n\n_The Quartz Mountain Lookout is a rental room with a view._\n\nIf the lookout is not occupied by renters, climb up for a view: Mount Spokane, with its ski lifts and transmission towers, looms large to the north. Mount Kit Carson is the knob to the left of the big mountain. The Idaho Selkirks look jagged in the distance to the northeast. From the south-facing catwalk, you can see three lakes below (left to right): Twin Lakes and Hauser Lake in Idaho, then Newman Lake in Washington.\n\nFollow the road to loop off the summit back to Junction 3. Explore some of the other cross-country trails to loop your way back to your car. Signs and maps at the major junctions help keep you oriented. Lodgepole Trail is the shortest way back to Junction 2. Or try Blue Jay back to Junction 1 and the Valley View Trail from Junction 1 to the trailhead to enjoy open views to the south.\n\n### EXTENDING YOUR TRIP\n\nIf you're good with map and compass, explore the Ragged Ridge Natural Area Preserve. A trail can be followed off and on to the scenic rocky ridge. You can also explore other ski trails on the way back to the trailhead.\n\n## around spokane\n\n_McLellan Conservation Area overlooks Lake Spokane, an impoundment on the Spokane River._\n\nThe local visitors center describes Spokane as _Near nature, near perfect_. At least half of that slogan is indisputable. Wildness is just out the door in every quadrant of the city and all around the county, protected in havens such as Riverside and Mount Spokane State Parks, the Little Spokane River Natural Area, and more than two dozen Spokane County Conservation Futures areas. Turnbull National Wildlife Refuge and its abundance of wildlife on display is just another feather in the areas near-nature cap. Best of all, public routes ranging from pine-needle-padded footpaths to the paved Fish Lake Trail and Spokane River Centennial Trail beckon visitors to all the best spots.\n\n Antoine Peak\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 6.8 miles | 1230 feet\/3375 feet | May\u2013Nov\n\n**Maps:** USGS Greenacres, Antoine Peak Conservation Area map; **Contact:** Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks; **Notes:** Open to mountain bikes, horses. Dogs permitted on-leash; **GPS:** N 47 43.257 W 117 11.817\n\n  _**Minutes from I-90, Antoine Peak is a 1066-acre sanctuary for wildlife watching secured by the Spokane County Conservation Futures program. We have seen turkey vultures, hawks, and ravens soaring over the peak, all at one time; a days-old whitetail fawn 50 yards from the summit towers; and tracks of wild turkey, quail, deer, moose, elk, and bear. Did we mention this is just minutes from the Spokane Valley Mall?**_\n\n### GETTING THERE\n\nFrom I-90 in Spokane Valley, take exit 291B and drive 2.2 miles north on Sullivan Road. Turn left on Wellesley Avenue, go to a four-way stop, and turn right on Progress Street. At the next stop sign, turn right on Forker Road. Go uphill 0.4 mile and turn right on Jacobs Road. Drive 0.7 mile and turn left on Robbins Road. Drive 0.4 mile to the west-side trailhead (elev. 2500 ft) at the top of the hill.\n\n_Antoine Peak trails are ideal for groups_.\n\nSPOKANE COUNTY INVESTS IN CONSERVATION FUTURES\n\nThe Spokane County Conservation Futures program has opened the doors to hiking several of the choice routes featured in this book. Private land destined for subdivision and development was preserved as open space for wildlife to roam and muscle-powered visitors to enjoy.\n\nThe program, administered by Spokane County Parks and Recreation, preserves open spaces with a voter-approved property tax of up to 6.25 cents per $1000 of assessed value. The funds are earmarked for acquiring property and development rights to benefit wildlife, conserve natural resources, increase passive recreation, provide educational opportunities, and improve the quality of life for area residents. From its inception in 1994 through 2012, the program purchased about 6300 acres in about thirty acquisitions. Hikers, equestrians, and outdoor groups often chip in to build or maintain trails in the areas.\n\nThe conservation areas are public, but they are nestled amid private property that must be respected by visitors. Park carefully to the side of the road when parking lots are not available, and don't block gates or stray onto private property.\n\nNatural areas purchased or expanded by Conservation Futures funding include Antoine Peak (Hike 68), Liberty Lake County Park (Hike 69), Saltese Uplands (Hike 70), Iller Creek (Hike 71), Dishman Hills Natural Area (Hike 72), South Hill Bluff (Hike 75), Slavin Conservation Area (Hike 77), and Palisades Park (Hike 78). Keep these prime areas in mind for your next hike\u2014and the next time the program comes up for a vote.\n\nMore conservation areas worthy of visits are listed on the Spokane County Parks and Recreation website (www.spokanecounty.org\/parks).\n\n_\u2014R. L._\n\n### ON THE TRAIL\n\nGo through the gate and head 0.8 mile up the summit access road (closed to unauthorized vehicles) to a fork. Bear left (you'll return to this junction near the end of the loop). At 1.3 miles, bear right at a fork (you'll be returning to this road soon too), continuing up another 0.5 mile to the summit.\n\nWalk past the first radio tower (if you listen, you might hear FM radio tunes), catch the great views looking north to Mount Spokane and south to Liberty Lake. Then head to the second tower. A road heading down to the right is a shortcut to the loop road.\n\nTo continue the circumnavigation of the peak, retrace your steps down the way you came and take a sharp right (passing another shortcut on the right, down an old skid road that starts near the first tower's southwest guyline anchor). The trail soon begins climbing around the west side of the peak, and then it angles down and bends around the cooler, lusher, more heavily timbered north side.\n\nAt 3.9 miles, the loop road meets a junction on the east side of the peak. An eroded skid trail comes down steeply from above, and a road heads down to the left toward a broad ridge called Antoine Park, then to a pond and the east trailhead. Bear right at this junction to continue the loop, reaching another junction in about a half mile with the road shortcut from the summit. About 100 yards farther along the loop, reach yet another junction and take a sharp right.\n\nFrom here, at 4.6 miles, the loop road has its ups and downs, but it primarily contours around the mountain for another 1.4 miles to a familiar junction. Turn left and hike the last 0.8 mile to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nFrom the east side of Antoine Peak, take the old road that leads to the east trailhead and reach Leland Pond in 2.2 miles (look for turtles). It's anothermile to the east trailhead off Lincoln Road (accessed by leaving I-90 at exit 293, driving north on Barker Road, turning right on Trent Avenue, driving 1 mile east to turn left on Campbell Road, driving north 1.6 miles to turn left at Lincoln Road, and finally driving 0.6 mile to the parking area on the left; privy available).\n\n Liberty Lake\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON  \n---|---|---|---\n\n****\/3 | 9 miles | 1550 feet\/3280 feet | May\u2013Oct\n\n**Maps:** USGS Liberty Lake, USGS Mica Peak; **Contact:** Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks; **Notes:** $2 entrance fee Memorial Day\u2013Labor Day. Open to horses. Dogs permitted on-leash; **GPS:** N 47 37.866 W 117 03.517\n\n  _**A Spokane County park and a 455-acre county conservation area join at a clear-water lake to create one of the region's most diverse and refreshing hiking areas. The developedarea ranges from a sandy swimming beach to a campground and picnic area. Then the wildness begins on trail that leads past beaver dams, into an ancient cedar grove, past a cascading waterfall, and up to scenic views down onto Liberty Lake.**_\n\n### GETTING THERE\n\nFrom I-90 east of Spokane, take Liberty Lake exit 296. Turn south on Liberty Lake Road. Drive 1 mile and turn left on Sprague Avenue, which becomes Neyland Road in another mile. Continue another 0.8 mile, bear right at the Y, and then turn right on Lakeside Road. Drive 0.7 mile and turn right on Zephyr Road to reach the Liberty Lake County Park entrance parking area (elev. 2090 ft). Privy available. An alternate connector trail is planned from the equestrian trailhead parking area on the road above the main entrance.\n\n### ON THE TRAIL\n\nFrom the pay station, follow the route past the day-use restrooms and picnic shelter for 0.5 mile to the restrooms area at the far end of the campground. Look for the main trailhead kiosk and gate (near campsite 21), and head up along Liberty Creek. At 0.8 mile pass a junction with the old trail coming in from the right. A new route was built in 2011 so hikers could avoid the lower portion of the creek, home to busy beavers.\n\nAt 1.1 miles, reach a junction that starts the loop (you'll be returning from the right). Continue straight and cross the little footbridge over Split Creek (the trail fork leads to the horse ford).\n\nClimb steadily, now along Liberty Creek, and at 2.5 miles reach an open grove of large cedars, one of the first acquisitions of Spokane County Conservation Futures (see the sidebar in this section). This is a popular destination for picnicking under towering giants.\n\nTo continue the loop, bear right on the footbridge across the creek and begin the twelve switchbacks up Sam Hill. A viewpoint looking northwest to Liberty Lake is on the twelfth one. Antoine Peak is straight down the valley in the distance, and Mount Spokane is the highest point to the right.\n\n_Hikers continue above the Liberty Creek Falls._\n\nAt 3.5 miles, come to the cool respite at the base of cascades known as Liberty Falls. The vast majority of hikers turn around here for a 7-mile round trip. But for the full loop, switchback up from the falls. Hike through a more open forest and cross the creek on a bridge at about 4 miles.\n\nA short way farther, continue straight at a trail crossing and go uphill to the high point of this hike near an old outhouse. Turn right here and head down to the Camp Hughes Cabin (elev. 3250 ft), a shelter built in the mid-1970s.\n\nBack on the main loop, head downhill on the Edith Hansen Riding Trail, occasionally used by horse riders. At 6.3 miles, stay right at a fork (the trail left is worth exploring all the way to Mica Peak). At 7.1 miles, come to a junction just past the horse trail sign and a big wooden wall structure. Turn right on the single-track to avoid the boggy area of Liberty Creek flooded by beaver activity. Soon you'll cross a footbridge over Liberty Creek and then come to the main trail you hiked up earlier. Turn left and return to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nHikers with good endurance and map-reading skills can hike all the way to Mica Peak. Take a trail south off the Edith Hansen Riding Trail. Follow the route uphill to a saddle south of Boundary Mountain and along the west side of Stump Ridge to a main ridge at about 4700 feet. Soon the route up the ridge follows jeep roads. Stay on the ridge, heading up the steepest routes to a better road that leads to the FAA radar dome at 5205 feet.\n\n  Saltese Uplands\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 7.3 miles | 1185 feet\/2640 feet | Mar\u2013Dec\n\n**Maps:** USGS Greenacres, USGS Liberty Lake, Spokane County Conservation Futures map; **Contact:** Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks; **Notes:** Open to mountain bikes, horses. Dogs permitted on-leash; **GPS:** N 47 38.625 W 117 07.872\n\n  _**Spokane County delivered a one-two punch for conservation and recreation in 2010\u201311, first by securing 510 acres of wetlands on Saltese Flats, then by acquiring the adjacent 552-acre Saltese Uplands Conservation Area overlooking the flats. From top to bottom, the uplands are a gem for walkers and wildlife watchers, with more than 9 miles of trails and roads for nonmotorized recreation. Mountain biking and horse riding are allowed, but the sight lines are good in this mostly open terrain, making it easy for everyone to share the trail.**_\n\n### GETTING THERE\n\nFrom I-90 east of Spokane, take Barker Road exit 293 and drive 0.5 mile south on Barker Road. Turn left on Sprague Avenue and Drive 0.9 mile. Turn right on Henry Road and go 0.8 mile to the trailhead parking area on the left (elev. 2070 ft). Privy available.\n\n### ON THE TRAIL\n\nFollow the trail south paralleling Henry Road and turn left at a junction, onto an old road. Go up a short way to a junction with two single-track trails. If you like, make an out-and-back side trip by going left on the Mulligan Trail for 0.5 mile to where the trail dead-ends in a basin at a big pear tree\u2014attractive to deer in the early fall.\n\nBack at the junction, cross the old fire road and take the other single-track, the Palisades Trail, which quickly starts gaining elevation in big switchbacks. Enjoy the curvy trail, which keeps serving up a different view ahead.\n\nPass a spring. When the single-track joins a road, look for the single-track splitting off to the left and heading uphill to a fence near the water tank for the private Legacy Ridge Estates development on the other side of the ridge. Take a break here to drink in views over Saltese Flats. Follow the fence westward a couple hundred yards to look down the Spokane Valley: Antoine Peak (Hike 68) lies to the north, Palisades Park (Hike 78) is in the distance to the west, Iller Creek Conservation Area and Dishman Hills near Tower Mountain (Hikes 71 and 72) are closer to the west.\n\nThe open slopes of the Saltese Uplands generate updrafts that attract numerous raptors, which feast on the bounty of rodents and ground squirrels that find easy burrowing in the fine Palouse topsoil. The trails were lumpy with critter burrows\u2014and coyote scat\u2014just weeks after they were originally carved out of the hillside with pulaskis in 2011.\n\n_Mark Pinch designed and labored on Saltese Uplands trails._\n\nNow follow the fence line to the east and pick up the trail again. Shortly you'll go over the crest for a great view of Liberty Lake, and then the single-track winds down off the ridge. Cross the rough power-line road and wind down to a junction at another double-track. (The right-hand road is a shortcut back to the trailhead, but you'll get to hike it later in this trip.) Go left to continue the longer loop, and follow the old farm road down to another fence.\n\nPass the junction with a single-track trail (you'll return to this spot in 2.3 miles) and continue straight on the double-track over the open hillside. Bear right on the next single-track and go down. Turn right at a junction with the trail that parallels the road and hike 0.5 mile north to another junction. Straight ahead is a the easiest walk back to the trailhead. But to get the most out of this hike, turn right and head 0.6 mile up the single-track Pincher Creek Trail to a familiar junction. Bear left and follow the double-track back to Henry Road, turning right on the single-track that leads to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nTrails and old ranch roads crisscross and connect, for even more exploring of the Saltese Uplands.\n\n  Iller Creek and Rocks of Sharon\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/3 | 5.5 miles | 1250 feet\/3580 feet | Apr\u2013Dec\n\n**Maps:** USGS Spokane SE, Spokane County Conservation Futures map; **Contact:** Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks; **Notes:** Open to mountain bikes. Dogs permitted on-leash; **GPS:** N 47 36.089 W 117 16.903\n\n  _**You'll find yourself between a Big Rock and a hard place to leave as you explore some of the wild and lofty 950+ acres in Spokane Valley preserved for nature lovers and critters, including moose. Spokane County secured the Iller Creek Unit of the Dishman Hills Conservation Area, and Dishman Hills Conservancy preserved the adjacent Rocks of Sharon. This hike has it all, from a dank creek bottom to scenic granite-quartzite rock outcroppings and a glorious view of the Palouse region.**_\n\n### GETTING THERE\n\nFrom I-90 in Spokane Valley, take Argonne Road exit 287 and head south. At the intersection with Sprague Avenue, continue straight onto Dishman\u2013Mica Road. Go 2.4 miles and turn right at the traffic light onto Schafer Road. Drive 0.8 mile and turn right on 44th Avenue. Go one block and take the first left on Woodruff Road. Go 0.3 mile, turn right on Holman Road, and follow it about 0.7 mile to the trailhead (elev. 2400 ft). Don't block the private road. Privy available.\n\n### ON THE TRAIL\n\nHead through the gate and immediately turn left. The trail soon begins switchbacking up a brushy open slope. At 0.8 mile, the trail gains the ridge, with views to the east (left) of Mica Peak (elev. 5205 ft) and its summit FAA radar dome. Follow the ridge, soon heading into scattered ponderosa pines and eventually Douglas-firs. At 1.5 miles the trail forks. Continue left.\n\n_Big Rock stands out among the Rocks of Sharon._\n\nSoon the ridge trail flattens into a parklike setting with views to both sides. Walk through balsamroot, lupine, ocean spray, serviceberry, and other classic native plants of this region. Ease down into a saddle and then begin climbing again. At 1.9 miles, come to another junction. Stay left for now, but take note for the return trip.\n\nAt nearly 2.4 miles, turn right at a T junction on an east\u2013west ridge and head up. The trail forks into parallel trails that rejoin at the first big outcropping of the Rocks of Sharon (elev. 3530 ft). Protruding from an east ridge off Tower Mountain, the Rocks of Sharon perhaps got their name in the early 1900s, when weekend visitors would detrain from the old Spokane-to-Pullman electric line at the long-gone Sharon store and hike up to picnic in the rocks.\n\nScramble around for views of the Palouse farmlands to the south, with Steptoe Butte (elev. 3612 ft) jutting up like a distant spike in the middle of nowhere. Just below you is Big Rock, a granite-quartzite monolith and playground for rock climbers. Down from the rocks is Stevens Creek Road, another access to this area off the Palouse Highway.\n\nBegin your return by heading back the way you came for nearly 0.5 mile and take the sharp left on the single-track trail you noted on the way up. The trail leads down into a lusher forest, including hemlock, grand fir, and Pacific yew. Cross the creek and continue down.\n\nAt the junction with an old eroded trail that drops to the right along the main creek, bear left on a niftier hiking route into an area damp with little creeks. Numerous dips in the trail attract mountain bikers.\n\nSoon you'll merge with the creekside trail and continue down. A short way before reaching the trailhead, you'll come to a creek ford that's easy most of the year, but during runoff it can be over your boots.\n\n### EXTENDING YOUR TRIP\n\nFrom the Rocks of Sharon, the trail continues west. A left fork drops down, angles to the base of Big Rock, and loops back up from a junction with the access trail coming from Stevens Creek Road. A right fork eventually drops steeply to Iller Creek. The main trail heads up to communication towers on East Tower Mountain (Krell Hill). Tower Mountain ridges are good for cruising north and south, but they are private land and access is not assured.\n\n  Eagle Peak\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 4 miles | 690 feet\/2425 feet | Mar\u2013Dec\n\n**Maps:** USGS Spokane NE, Dishman Hills Conservancy map, www.dhnaa.org; **Contact:** Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks; **Notes:** Dogs permitted on-leash; **GPS:** N 47 39.249 W 117 17.366\n\n  _**Citizens rallied in the 1960s to preserve 530 acres of choice Spokane Valley real estate for wildlife and walkers instead of trophy homes and pavement. The Dishman Hills Natural Area is a staple for school field trips and nature observations, starting from the green lawn at Camp Caro and ranging into an urban wilderness. You can devote days to exploring here, from damp nooks to basalt crannies. This hike hits many highlights, including ponds, a high-peak overlook, springs, and all the wildlife opportunities in between.**_\n\n_Bitterroots bloom early spring in Dishman Hills; watch your step!_\n\n### GETTING THERE\n\nFrom Spokane on eastbound I-90, take Sprague Avenue exit 285 and continue straight on Appleway Boulevard. Go past Vista Road 0.3 mile and turn right on Sargent Road, and then immediately right again into the Camp Caro\u2013Dishman Hills parking area (625 South Sargent Road). The trailhead (elev. 1960 ft) is at the south end. Privy available at Camp Caro in summer.\n\n### ON THE TRAIL\n\nYou can become disoriented in this area's evolving maze of trails. Trail signs were planned as this book went to press; some trails were to be obliterated. Note: Any trail heading north will eventually lead back to Camp Caro or at least to Appleway Boulevard. Let this route description guide your first trek to Eagle Peak, then unleash yourself in this rich wild area.\n\nFollow the path from the south end of the gravel parking area to a paved parking area and go through (yes, through) the Camp Caro lodge. Continue straight, leaving the paved path and going onto the dirt trail past the kiosk.\n\nHike up some steps and continue toward Goldback Spring, staying on the main trail with the rimrock on your left. At a fork near a park bench, bear left and continue toward Goldback Spring. (The right fork leads into Enchanted Ravine.) At the next junction, bear left again toward Goldback Spring.\n\nThe trail crosses a footbridge over the spring and lush vegetation. Turn right and climb the steps on the trail heading to East\/West Ponds and Eagle Peak. At the next intersection with a trail that heads back to Camp Caro, bear left and continue hiking uphill.\n\nBear left at another junction just a short way up the trail. (Take note: you'll return to this junction later.) Just a short way farther, turn right at another junction with the less obvious Eagle Peak Loop Trail and begin climbing. Bear right at the next two intersections, continuing the uphill trend.\n\nThe trail finally tops a ridge of basalt outcroppings at yet another junction. Before continuing the loop to the left, follow the spur trail straight ahead that leads to the top of Eagle Peak (elev. 2425 ft), the highest point in the Dishman Hills Natural Area, with a great view of the Spokane Valley, Mount Spokane to the north, Antoine Peak closer to the northeast, and Mica Peak to the east. The higher areas south of Eagle Peak are private property, where you can see signs of the 2008 wildfire that burned several acres and homes.\n\nRetrace your steps back to the last junction, turn right and head through the basalt formations. Turn right at the next trail junction as you drop from the rocky ridge and begin heading north. Soon you'll come to a fork. Go left to explore Lost Ponds if you wish, but to continue the loop trail, bear right and stay on the Ridge Top Trail.\n\nSoon begin a long descent to a junction you passed earlier. Bear left toward Camp Caro. Go a short way to another familiar junction and bear left again toward East\/West Ponds. Also go left at the next two junctions. (Trails heading right, including to Enchanted Ravine, are quick exits to Camp Caro.)\n\nPass a viewpoint with a bench on the right, and then wind up onto a flat of basalt. Continue on the trail straight and down a slab of rock at this junction toward East\/West Ponds. Pass a spur trail heading left and soon drop down another tier to a junction at stair steps. Turn left here to visit East\/West Ponds, which are just up the trail to the left at the next junction.\n\nAfter checking out the ponds (chorus frogs sing here in April or May, ducklings swim in July, and moose pay occasional visits), retrace your route to the junction above the steps and head down the wood-beam staircase\u2014one of many Eagle Scout projects in the natural area.\n\nBear right at the next two junctions down through the series of steps and water bars, go through the chain link fence, and turn left on the paved path along the green lawn at Camp Caro.\n\n### EXTENDING YOUR TRIP\n\nAt some point, you must hike the Enchanted Ravine and explore the rocky spine of Deep Ravine on the east side of the natural area.\n\n  Beacon Hill\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/3 | 4.2 miles | 780 feet\/2600 feet | Mar\u2013Dec\n\n**Maps:** USGS Spokane NE, Beacon Hill Recreation Area map; **Contact:** Spokane City Parks and Recreation Department, (509) 625-6200, www.spokaneparks.org, and Fat Tire Trail Riders Club, www.fttrc.org; **Notes:** Open to mountain bikes. Dogs permitted on-leash; **GPS:** N 47 41.203 W 117 20.808\n\n  _**Beacon Hill's summit is swarmed by communications towers and transmission lines, and the slopes around it tend to be dominated by mountain bikers. But hikers find plenty of room and a surprising amount of beauty in more than 900 acres of city, county, and private land just north of the Spokane River near Upriver Dam. Ponderosa pines dominate slopes distinguished by granite outcroppings near this southern extent of the Selkirk Mountains. The area is a riot of wildflowers from late April into June.**_\n\n### GETTING THERE\n\nFrom I-90 in Spokane, take exit 283B. Go straight along the highway and turn north on Freya Street, which eventually becomes Greene Street. At 2.3 miles, the road bends left and then right (up a hill) and becomes Market Street. Turn right at the stoplight and head east on Euclid Avenue. Go 0.8 mile (Euclid becomes Frederick Avenue) and turn left on Havana Street. Drive two blocks to the dirt parking area (elev. 1990 ft) for Minnehaha Park.\n\n### ON THE TRAIL\n\nThe west side of Beacon Hill has fewer trails than other areas here, but the trails and old jeep roads still can be confusing. Signage has been proposed. If you get off track on your way to Beacon Hill summit, just head up.\n\nStart at the gate on the paved trail along the grassy developed park. At the ball field, just past rock pillars, bear right off the paved trail onto a wide dirt path that heads up. Soon skirt the Esmeralda Golf Course parking lot and stay left, paralleling it (in this case, _don't_ take the double-track routes that head up). Go through some concrete barriers, then up. When you come to a jeep road that continues up, turn left on the single-track Trail No. 20, which continues north, paralleling the golf course.\n\n_Beacon Hill is a quick hiking getaway in Spokane._\n\nThis single-track generally bears left at most intersections, climbing gently as it contours northward. As you make a sweeping bend to the east, continue straight up on the single-track at a five-prong junction of trails and jeep roads. After a dogleg south and then north, come to a bench before the power lines. The single-track continues straight across two jeep roads in fairly quick succession.\n\nFrom here, the single-track is easy to follow as it snakes up the steeper hillside eastward to a rim of rocks south of Beacon Hill summit, which is dominated by communication towers. Enjoy expansive views (albeit through power lines and other man-made obstacles). Few places in Spokane's urban area have such a sweeping view of the Spokane Valley east and west.\n\n### EXTENDING YOUR TRIP\n\nExplore to your heart's content. Private landowners ask the public to stay out of some parcels in the low areas directly south of Beacon Hill. But some of the most captivating nooks in the area are in the rock outcroppings found on myriad paths generally heading southeast toward John Shields Park (locally known as Minnehaha Rocks), a training area for rock climbers. The Shields Park parking area on Upriver Drive also offers good hiker access to Beacon Hill trails.\n\n  Downtown Spokane Bridges\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 7.7 miles | 430 feet\/1880 feet | Year-round\n\n**Maps:** USGS Spokane NW, Spokane city map; **Contact:** Spokane Regional Convention and Visitors Bureau, (509) 624-1341, www.visitspokane.com; **Notes:** Partly wheelchair-accessible. Dogs permitted on-leash. Watch for city traffic; **GPS:** N 47 39.348 W 117 27.236\n\n_Don Kardong Bridge over Spokane River_\n\n  _**Marmots, deer, waterfowl, and fish are more common on this urban route than on many remote wilderness trails. The route takes you over 18 of downtown Spokane's 22 river bridges, joining with the Spokane River Centennial Trail and making a grand tour of Riverfront Park en route. Spokane Falls is a highlight, the Spokane River your constant companion. And as near to nature as you are on this hike, you're also never far from a place to eat, drink, or shop.**_\n\n### GETTING THERE\n\nFrom Monroe Street in downtown Spokane, drive 1.3 miles west on Riverside Avenue. Just before crossing the Hangman Creek Bridge, turn right on Clark Avenue to reach the trail-head parking area (elev. 1750 ft).\n\n### ON THE TRAIL\n\nFollow the paved path and cross the Sandifur Bridge over the Spokane River. The path winds up to Ohio Avenue. Follow the sidewalk upstream, overlooking the river gorge. Pass a scenic rest spot at the Hamblen Conservation Area overlook.\n\nCross the Maple Street Bridge overpass and continue straight on Ohio through the Kendall Yards development. An extension of the Spokane River Centennial Trail is planned here, leading all the way under the Monroe Street Bridge. Until that's complete, work your way upstream and carefully cross Monroe Street to the small bridge-side memorial park. Turn south to cross the Monroe Street Bridge, enjoying a view of Spokane Falls. At the south end of the bridge, follow the sidewalk left and continue upstream along Spokane Falls Boulevard. Cross Post Street and turn left on the sidewalk, heading north along the Bloomsday runner sculptures.\n\nThe sidewalk leads north across the Post Street Bridge up to Broadway. Turn right for a block and head straight ahead and down the paved path that leads back to the river. Cross North Fork North Bridge (bridge no. 4) and then immediately turn right to cross the North Fork South Bridge, where spring-runoff walkers can get wet with spray from water roaring over the \"fang\" of basalt in the falls just upstream.\n\nHike past the \"Washington Water Power Upper Falls Power Plant\" and immediately turn right along the access road. Cross a South Fork bridge (no. 6) and turn left, switchbacking up the path built during Expo '74 that loops up and crosses the little river fork four more times, bringing the bridge count to 10. At the top, bend left along the big pool toward the Rotary Fountain.\n\nJust before the Carrousel, turn left (north) to cross the Howard Street Bridge South. At the end, bear left on the path that soon continues northward (toward the Spokane Arena), crossing the Howard Street Bridge and the Howard Street Bridge North in quick succession. Then turn right (upstream) on the path along the river. Go through the underpass and take the upstream stairs to cross the Washington Street Bridge (no. 14). On the other side, exit on the stairs to the left and then immediately turn right to follow the path up (restrooms to the left). Then bend right, along the Pavilion, for a short way. Turn left on the path down through the grass. Cross the Clock Tower Footbridge and turn left.\n\nHike upstream past the Red Wagon and the INB Performing Arts Center and turn left to cross the King Cole Footbridge (no. 16). Bear right and wind down, heading northward to cross the wooden bridge leading to a group of hotels. Immediately turn right and follow the walkway upstream on the north riverbank. Bear right onto the pedestrian trail that leads under the Division Street Bridge. Continue on a boardwalk. Then follow the paved path upstream through open expanses of the Gonzaga University campus.\n\nWhere the paved path comes to the Don Kardong Bridge, scramble up the short gravel path and turn right on the Centennial Trail to cross the bridge. Congratulations, this is bridge no. 18. Now you're headed back downstream.\n\nFollow the trail, staying right at junctions to stay along the river's south shore. Soon you'll be back at the INB Performing Arts Center. Continue straight downstream and eventually cross Post Street at the Blooms-day runner sculptures. Continue west and carefully follow the two pedestrian crossings to the west side of Monroe Street.\n\nTurn left (south) across Main Avenue and follow the sidewalk around to the right in front of the Spokane Club. Follow Riverside Avenue all the way back through Brown's Addition to the trailhead, with only one more traffic crossing at the Maple Street Bridge onramp.\n\n### EXTENDING YOUR TRIP\n\nWhen you first reach the Don Kardong Bridge (no. 18), head east (upstream) and hike the Centennial Trail to Mission Street, where you could bag another bridge. Serious bridge baggers can hit 21 spans by making sidewalk detours to cross the Maple and Division Street Bridges.\n\n  South Hill Bluff\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/1 | 3 miles | 350 feet\/2340 | Feb\u2013Dec\n\n**Maps:** USGS Spokane NW, USGS Spokane SW, and Spokane city map; **Contact:** Spokane Regional Convention and Visitors Bureau, (509) 624-1341, www.visitspokane.com; **Notes:** Open to mountain bikes. Dogs permitted on-leash; **GPS:** N 47 37.714 W 117 25.780\n\n  _**More than 23 miles of trails grace the steep swath of undeveloped Spokane City Parks land between High Drive and the Hangman Creek\/US Highway 195 corridor below. The trails initially were built on the sly by volunteer biker-hikers who had a vision long before the city thought sustainable trails could be carved into the steep, sandy slopes. This is the place to be for a stunning sunset, and the bluff is especially brilliant with blooming arrowleaf balsamroot and serviceberry in april and May.**_\n\n### GETTING THERE\n\nFrom Monroe Street, drive west on 29th Avenue three blocks to the end of the road. Turn right at High Drive and then immediately left into a South Hill Bluff trailhead parking area (elev. 2290 ft). More parking is available near Bernard Street, close to the turnaround for this hike.\n\n### ON THE TRAIL\n\nThis is the easiest of the _many_ hiking options on the South Hill Bluff. Walk this route with a map in hand, and soon you'll start to put together the many trail combinations that make for invigorating hikes between the rim and the valley. You can't get lost. Paved roads are above, Hangman Creek below.\n\nFrom the 29th and High Drive trailhead, follow the concrete sidewalk down and then left, and start walking on a trail. It angles down for a short way but then generally traverses the slope, roughly paralleling below High Drive with gentle ups and downs. You'll pass a few trails heading back up to High Drive and several trails forking down to the lower slopes and Hangman Creek. Stay on this upper-tier trail.\n\n_South Hill Bluff Trail above Hangman Creek_\n\nAfter 1.4 miles, the trail angles up to High Drive near the intersection with Manito Boulevard. This is the turnaround point. Drop back down and hike the same trail back. Or drop down to a lower-level trail that contours back. Several trails eventually will lead you up to High Drive again and the trailhead.\n\n### EXTENDING YOUR TRIP\n\nExplore any of the trails branching down off the top-tier trail. Or, from the 29th and High Drive trailhead, drop down the concrete path and continue straight on the trail that heads north along High Drive. This trail offers a pleasant walk to Polly Judd Park trailhead at the west end of 14th Avenue.\n\n  Fish Lake Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 15 miles | 375 feet\/2155 feet | Mar\u2013Nov\n\n**Maps:** USGS Spokane NW, Spokane SW, Fish Lake Trail brochure; **Contact:** Spokane City Parks and Recreation Department, (509) 625-6200, www.spokaneparks.org; **Notes:** Wheelchair-accessible. Dogs permitted on-leash. Hikers stay right, share route with cyclists and skaters; **GPS:** N 47 38.829 W 117 27.172\n\n_Fish Lake Trail users make use of abandoned railroad bridges._\n\n  _**The Fish Lake Trail has been a public route since 1991, when Spokane assumed ownership of the abandoned Union Pacific Railway that runs 10.2 miles from Spokane to Cheney. Sections near Cheney and Marshall were paved around 1995, but the trail's popularity soared when this section leading out of Spokane was developed and paved in 2009\u201310. Walkers and bicyclists of all types enjoy out-and-back treks of any length on this gentle ribbon of flatness through the ponderosa pines.**_\n\n### GETTING THERE\n\nFrom Maple or Ash Street near downtown Spokane, drive west on 2nd Avenue, which bends left after a few blocks and becomes Sunset Boulevard. Stay right on Sunset Boulevard (do _not_ drop down below the underpass). Drive to the stoplight and turn left at Government Way. Then take the first left, on Milton Street. (Alternate access comes from US Highway 195 via 16th Avenue to Lindeke Street and Government Way.) Drive into the trailhead parking area (elev. 1900 ft). Privy available.\n\n### ON THE TRAIL\n\nFish Lake Trail immediately leads to restructured railroad bridges that cross I-90. The paved trail eases through a neighborhood of scattered homes and across another bridge over 16th Avenue at 0.5 mile. By the time you cross the Thorpe Road overpass at 1 mile, you're pretty much into the woods.\n\nThe trail parallels US 195 for about 2 miles, buffered by ponderosa pines and basalt walls. Buttercups bloom here in March or April. Cross Marshall Road at 2.1 miles as the trail bends away from US 195 and takes you farther away from it all.\n\nBetween Marshall Road and the small town of Marshall, hikers aching for more ups and downs can sneak off the flat, paved Fish Lake Trail and walk the rocky fire-break road separating the west side of the trail from the active railway above.\n\nAt 6.8 miles, go under the Cheney\u2013Spokane Road overpass. Exit the tunnel-like structure and hike a short way farther to the Scribner Road trailhead. The slight grade on this trail is imperceptible, but relish the fact that you've hiked uphill all the way from Spokane, and the return trip is all downhill.\n\n### EXTENDING YOUR TRIP\n\nSomeday the trail may go all the way to Cheney without a gap. Until funding is available, the 2.5 miles from Scribner Road to Fish Lake are undeveloped and blocked. The 3-mile section from Fish Lake to Cheney is developed and paved. At Cheney, the Fish Lake Trail transforms into the unpaved Columbia Plateau Trail, managed by Washington State Parks. For a hike with less bicycle traffic, drive to the southeast end of Cheney's main drag (State Route 904) and park at the Cheney\u2013Plaza Road trailhead. The developed portion of the Columbia Plateau Trail heads westward for 23 miles, including part of Turnbull National Wildlife Refuge.\n\n  James T. Slavin Conservation Area\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 5.5 miles | 370 feet\/2415 feet | Feb\u2013Dec\n\n**Maps:** USGS Spokane SW, Spokane County Conservation Futures map; **Contact:** Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks; **Notes:** Open to horses. Dogs permitted on-leash. Watch for ticks; **GPS:** N 47 32.223 W 117 24.733\n\n_Restored wetlands at James T. Slavin Conservation Area_\n\n  _**Wetlands and water-fowl abound in this 628-acre preserve secured by Spokane County Conservation Futures in the Rosa Butte area south of Spokane. Restoration projects put water back where it belongs: in a 5-acre lake and nearly 200 acres of seasonal ponds and wetlands. The result is a natural scabland of pines, aspens, rocky bluffs, wildflowers, and wetness that attracts everything from songbirds to elk\u2014plus hikers and equestrians who enjoy the trails.**_\n\n### GETTING THERE\n\nFrom I-90 in Spokane, take exit 279. Drive south on US Highway 195 about 8.4 miles and turn west at milepost 87.5 onto Washington Road. Drive 0.5 mile and turn right on Keeney Road, and then immediately turn left into the James T. Slavin Conservation Area parking lot and trailhead (elev. 2170 ft). Privy available.\n\n### ON THE TRAIL\n\nFrom the trailhead, walk into the open meadow about 20 yards and go left at the first junction on a single-track trail that heads southwest toward aspens. At 0.5 mile, by a contorted pine, the trail meets an old farm access road (Diamond Lane). Turn left, hike the road about 60 yards and turn right on a single-track trail just before reaching a fence.\n\nThe trail winds up and at 0.7 mile makes a short climb to an open, rocky bluff. The trail traces the rim briefly before angling over a flat and into the forest. Signs memorialize the pets the Slavin family buried in the area in the 1900s.\n\nAt a fork, bear left and continue south along the wetlands on a double-track trail. Go a short way to a junction with a single-track trail that heads right. This is a good option in early spring or fall, but portions can be marshy in spring or shrouded with tall grass in summer. Stay left for the more dependable 0.5-mile route to the dike at the upper end of the main lake. Turn around here for a round-trip of nearly 4 miles.\n\nBut if conditions allow, continue across the earthen dike and bear right into the woods. The trail here dips and can be knee-deep in water during spring.\n\nTurn right at a junction to head north on high ground on the west side of the main lake. (Shorebirds join waterfowl here, as water recedes and exposes mud along the lake's edge.) Bear right at the next two junctions, keeping the water almost always in sight to your right as you wind through the pine woodlands to the end of the main lake and your turnaround point at 2.9 miles. Although the trail continues down into deep grass and loops into a meadow and back to the trailhead, it's a better hike to retrace your steps.\n\nReturn to the dike, cross it, and take the familiar high (dry) or low (may be wet or grassy) route. To make a loop, stay straight at the junction with the trail that leads to the unofficial pet cemetery. The way wraps below a bluff and into the woods. Then it turns sharply left and crosses a meadow (can be wet in spring). Bear right onto Diamond Lane. Shortly after, bear left onto a single-track through a timbered flat and continue straight past spur trails. The trail winds through hawthorns, aspens, and prolific spring wildflowers.\n\nSoon the trail breaks into the open meadow. Halfway across the open area, turn right and walk 0.2 mile east to the trailhead. A small post office once sat near the high point of the meadow, about 100 yards from the trailhead.\n\n  Palisades Park\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 4.2 miles | 520 feet\/2200 feet | Mar\u2013Dec\n\n**Maps:** USGS Spokane SW, and Palisades Park map, www.palisadesnw.com; **Contact:** Spokane City Parks and Recreation Department, (509) 625-6200, www.spokaneparks.org; **Notes:** Partly wheelchair-accessible. Open to mountain bikes, horses. Dogs permitted on-leash; **GPS:** N 47 39.281 W 117 29.175\n\n  _**Palisades Park offers one of the best cityscape views of Spokane while also letting you slip away into native wild-lands. And don't miss the outstanding example of 1930s Civilian Conservation Corps rock masonry that many visitors overlook. This city park is a walker's gift, rescued from trash dumpers and partiers by citizen volunteers working with the city to block out motorized vehicles.**_\n\n### GETTING THERE\n\nFrom southwest Spokane at the intersection of Government Way and Sunset Boulevard, drive 0.8 mile north on Government Way. Turn left (west) on Greenwood Road. Drive 1 mile on Greenwood, bearing right at the fork with Indian Canyon Road, and turn left on the gravel road to the parking spots (elev. 2175 ft).\n\n### ON THE TRAIL\n\nWalk across Greenwood Road to the trail-head sign on Rimrock Drive. This area is brilliant with blooming balsamroot in April. Portions of trails can be wet or muddy in spring. Begin hiking to the left of the signs on Trail No. 101. Go nearly 0.3 mile and turn left at a junction with a spur trail coming from Rimrock Drive. The route forks at about 0.8 mile. Go left on Trail No. 122. (Trail No. 101 to the right is a shortcut).\n\nTrail No. 122 follows a fence line and crosses a seasonal wet spot. At a T with the Fairchild Air Force Base water pipeline road, turn right. At the junction with Rimrock Drive (overlooking Fort Wright and Spokane Falls Community College), turn right again and soak in views from Spokane all the way to Mount Spokane in the distance.\n\nRimrock Drive traverses a splendid bit of CCC stone work, forming a bridge over a small seasonal creek. Cross the bridge and walk out on the point to look back and appreciate it.\n\nContinue on Rimrock Drive about 60 yards to the end of the roadside boulders and drop left sharply into a slot onto Trail No. 101. As the trail begins bending left, take the single-track to the right. At the next junction with double-track Trail No. 123\/101, turn right and follow No. 101 as it goes up, then down into an open ponderosa pine forest, generally paralleling the railroad south to Greenwood Road.\n\nCross the paved road and walk through the gates to continue straight on a fire road (Trail No. 102). Where the fire road begins going up to the right, bear left and down onto the single-track connector trail, which soon switchbacks left and down to ford a creek on slippery stones. Climb up. Turn right at a trail junction and head upstream, staying above the creek on Trail No. 121 through a pleasant open-timber area.\n\nThe trail merges into the Trail No. 102 fire road near a waterfall viewpoint. The falls is a trickle in summer, but flows can be good in spring. Ice climbers practice here in winter. A steep, dangerous trail goes to the base of the falls.\n\nTo continue the loop, follow the fire road as it bends right over the top of the falls and head back downstream (north). When you reach an open flat on your left\u2014once used as a winter camp by the Spokane Indian Tribe\u2014look for a sometimes faint trail heading left through the meadow. Hike through the open area, under the power lines and into the trees, where the trail becomes more obvious.\n\nBear left at the junction with Trail No. 105 and continue toward the bluff on Trail No. 106, which climbs briefly through thick shrubs to the Greenwood parking area.\n\n### EXTENDING YOUR TRIP\n\nTrail No. 120 offers interesting single-track alternatives for getting off the fire road near the waterfall.\n\n_Civilian Conservation Corps built this rock bridge in Palisades Park._\n\nT. J. Meenach Bridge\u2013Fort George Wright (Spokane River)\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 4.3 miles | 500 feet\/1860 feet | Feb\u2013Dec\n\n**Maps:** USGS Spokane NW, state park map; **Contact:** Riverside State Park, (509) 465-5064, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Partly wheelchair-accessible. Open to mountain bikes. Dogs permitted on-leash; **GPS:** N 47 40.730 W 117 27.196\n\n  _**This unsung city walk starts on a sidewalk, enters quiet woods, and offers a chance to splash in the Spokane River before climbing to overlooks of the river valley. The loop route joins the paved Centennial Tail and passes a military cemetery that dates back to the 1800s. A neat side trip leads to a rare glimpse of where the Spokane Aquifer\u2014source of the city's drinking water\u2014springs out of a hillside.**_\n\n### GETTING THERE\n\nFrom I-90 in Spokane, take exit 280 and drive about 1.3 miles north on Maple Street, crossing the Spokane River on the Maple Street Bridge. Turn left (west) on Maxwell Avenue and drive 1.1 miles (the road becomes Pettet Drive). Near the bottom of the grade, turn left into the parking area (elev. 1710 ft) before reaching the T. J. Meenach Bridge.\n\n### ON THE TRAIL\n\nFrom the parking area, use the crosswalk and follow the sidewalk up and along the upstream side of the T. J. Meenach Bridge for 0.2 mile to the south side of the river. The trail starts here (elev. 1740 ft) as part of the paved Spokane River Centennial Trail, bending left and heading downstream. After passing under the bridge, bear right off the Centennial Trail and onto single-track Trail No. 100.\n\n_Spring runoff floods a Spokane River beach below Fort George Wright Cemetery._\n\nSuddenly you're in the woods, away from traffic. At 0.4 mile, a trail angles off the main trail to descend closer to the shoreline. Follow it if you wish. It loops back to the main trail after a few hundred yards.\n\nAt 0.9 mile, the main trail continues past the rock foundation of a long-gone house. At 1.2 miles, angle left above the first of several utility buildings for a power substation. At 1.4 miles the trail sweeps down past the last of the buildings, out of the woods, and joins the gravel road that serves the utility site. Bear left and follow the road about a 100 yards, bearing right on a double-track trail.\n\nSeveral spur trails head to the right, to the shoreline. While the river can be fast and dangerous in high spring runoff and early summer flows, a large eddy quiets down by midsummer, making a good place to picnic or let dogs frolic.\n\nSoon you'll come to a trail heading steeply left to the Centennial Trail and the service road to the Fort George Wright Cemetery trailhead. Continue straight, climbing a single-track to a trail junction on the bluff above the river at 2 miles (elev. 1745 ft). This scenic viewpoint is a good turnaround point for a shorter hike.\n\nTo make a loop, turn left and follow the single-track to the paved Centennial Trail. Follow the Centennial Trail past the Fort George Wright Cemetery and trailhead for 2.3 miles to your car.\n\n### EXTENDING YOUR TRIP\n\nFrom the turnaround, the trail continues on Trail No. 100 in Riverside State Park (Hike 80). From the south end of T. J. Meenach Bridge, a route starts below the fenced river-gauge facility and continues upstream to Riverside Memorial Park (it involves some private land). And from the parking lot on Pettet Drive, a trail runs upstream for miles, paved at first and leading in 0.1 mile to a rare opening to the Spokane Aquifer, which spills clear, cold spring water into the Spokane River.\n\n  Fort George Wright\u2013Bowl and Pitcher (Spokane River)\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 6.8 miles | 680 feet\/1850 feet | Mar\u2013Dec\n\n**Maps:** USGS Spokane NW, state park map; **Contact:** Riverside State Park, (509) 465-5064, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Open 6:30AM\u2013dusk. Partly wheelchair-accessible. Open to mountain bikes, horses. Dogs permitted on-leash; **GPS:** N 47 40.864 W 117 28.756\n\n  _**Starting at the old Fort george Wright Cemetery, opened in 1899 and overlooking the Spokane River, hikers get a brief taste of the paved Spokane River Centennial Trail before breaking off on a dirt trail that's a constant companion to the Spokane River as it winds its way to the roar of the Bowl and Pitcher rapids.**_\n\n### GETTING THERE\n\nFrom just west of Spokane Falls Community College, at the intersection of Government Way with Fort George Wright Drive, head 0.6 mile north on Government Way. Turn right on Houston Road into the Centennial Trail parking area at Fort George Wright Cemetery (elev. 1850 ft). Privy available.\n\n_Groomed grounds at Fort George Wright Cemetery; Mount Spokane in background_\n\n### ON THE TRAIL\n\nFrom the parking lot, bow briefly to about 650 graves of soldiers and some family members with birth dates as early as 1832.\n\nHead left (west) on the paved Centennial Trail, down a gully and up. Where the paved trail bends left, bear right past a bench and along a fence overlooking the Spokane River onto a single-track trail (Trail No. 100, likely unsigned). Pass a trail that drops to the river and a nice swimming beach in low-water conditions (part of Hike 79).\n\nStay on the main trail as it heads downstream and slices across a steep slope. Watch out for poison ivy. At 0.9 mile, the trail forks. Left goes up to more trails and a loftier view; take the right fork and drop to old ponderosa pines along the rocky shoreline just above the river. Head up an incline. You'll pass several road or trail junctions in quick succession. The rule: Stay right, keeping to the trail on the rim above the river.\n\nAt 1.5 miles, pass the Spokane sewage treatment plant across the river. It's surprisingly uneventful. At 1.9 miles, pass the junction with Trail No. 101. At 2.5 miles, pass another junction, following the rule of staying to the right, along the river. At this point, Trail No. 100 is also part of the 25-Mile Loop Trail around the core of Riverside State Park. (Another day, maybe?) Historically, the Spokane Indian Tribe stored roots in cool talus areas at the base of basalt rock formations in this area.\n\nAt 2.8 miles, a short spur goes to the right to a good overlook of the river\u2014a sweet spot to be snacking if river rafters are heading into the rapids downstream at the Bowl and Pitcher, named for the shapes of the huge basalt formations.\n\nAt about 3 miles, the trail forks, but both trails reunite shortly. (The left fork along the scree slope is easiest.) A short way farther, the trail drops to a junction. Turn right and down the steps, so you can cross the footbridge over the Spokane River and enjoy the rapids below. The Bowl and Pitcher Recreation Area here has water, toilets, and a picnic area, should you have such needs before you turn around and retrace your route.\n\n### EXTENDING YOUR TRIP\n\nEnjoy trails downstream from the Bowl and Pitcher (Hike 81) or farther upstream from the Fort Wright Cemetery trailhead (Hike 79). Some walkers enjoy the paved Centennial Trail in either direction from the trailhead.\n\n  Bowl and Pitcher (Spokane River)\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 5.1 miles | 180 feet\/1760 feet | Mar\u2013Dec\n\n**Maps:** USGS Airway Heights, USGS Spokane NW, state park map; **Contact:** Riverside State Park, (509) 465-5064, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Open 6:30 AM\u2013dusk. Partly wheelchair-accessible. Open to mountain bikes, horses. Dogs permitted on-leash. Shots might be heard from nearby shooting range; **GPS:** N 47 41.775 W 117 29.746\n\n  _**This hike has something for everyone\u2014and it's along the Spokane city limits in a choice niche of Riverside State Park. From a developed picnic area and campground, the trail crosses a footbridge over Spokane River rapids at the iconic Bowl and Pitcher basalt formations. The route hugs the river to one of the area's most notable white-water landmarks and secluded shoreline break spots. Then it climbs to overlooks and an old cliff-hanging railroad grade unknown to most park visitors.**_\n\n### GETTING THERE\n\nFrom west Spokane, follow Fort George Wright Drive or Pettet Drive to the T. J. Meenach Bridge over the Spokane River and head downstream on Downriver Drive. Bear left onto Aubrey White Parkway into Riverside State Park. Drive 2 miles and turn left into the Bowl and Pitcher Recreation Area. (From northwest Spokane, drive west on Francis Avenue to Assembly Street, where Francis becomes Nine Mile Road (State Route 291). Continue 0.8 mile on Nine Mile Road and turn left on Rifle Club Road. Drive 0.5 mile and turn left on Aubrey White Parkway. Drive 1.3 miles and turn right into the Bowl and Pitcher Recreation Area.) Drive to the day-use parking area just past the entry station. The trailhead (elev. 1760 ft) is near a kiosk across the parking lot below the restrooms (which are closed in winter).\n\n### ON THE TRAIL\n\nFollow a wheelchair-accessible path across the suspension bridge over the Spokane River. Enjoy the rapids and the Bowl and Pitcher's namesake basalt formations.\n\nOn the west side of the river, head up the steps and bear right on Trail No. 25 above the picnic shelter. At 0.3 mile, turn right at the junction with Trail Nos. 210 and 211 to continue on Trail No. 25. Bear right at any spur-trail junctions to stay along the river.\n\n_Rafters head toward Spokane River footbridge at Bowl and Pitcher basalt formations._\n\nAt 1.2 miles, pass mile marker 20 (and a spur to a low-water riverside beach). There's a good view downstream to the Devils Toenail Rapid. Its namesake basalt rock spikes out of the middle of the river, creating a white-knuckle rafting attraction. Bear right at the next two forks to a nifty overlook at Devils Toenail. From the overlook, the trail drops on a rocky stretch along the river. At high spring flows, this section can be inundated, forcing hikers up (left) to the paved Spokane River Centennial Trail.\n\nAt 1.75 miles, the trail angles up from the river and skirts the edge of the Centennial Trail before splitting right as a single-track down to a flat. At 2.5 miles, the trail forks just after coming close to the river again. A side trip right and down leads to Little Vietnam, with lush vegetation and several places to enjoy the river shoreline in low flows.\n\nTo complete the loop and get the \"high view\" of the river, bear left at this junction and again at the next one (don't go right on a trail that angles up to Gate 36). Shortly after, turn right on another trail that leads gently up to the pavement, and turn right for 50 yards on the Centennial Trail. Then turn sharply left on Trail No. 211, heading southwest along a flat for a few hundred yards to a sharp right turn on Trail No. 200. Turn left on Trail No. 201 and head up the spine of the ridge to another stair-step plateau\u2014a sweet spot between the river flats and the vertical basalt rimrock.\n\nStay right at the first unmarked fork. Hike a short way to another fork and go left on Trail No. 25\/210 (right leads to a neat spur, at Trail No. 25 mile-marker 3, built by mountain bikers). As the way bends left and begins heading downhill, Trail Nos. 210 and 25 split. Continue straight on Trail No. 210, cross the Centennial Trail, and come to a familiar junction with Trail Nos. 211 and 25. Turn right to return to your car.\n\n### EXTENDING YOUR TRIP\n\nFrom the junction of Trail Nos. 210 and 25 near the end of the loop, turn right and head uphill on Trail No. 25 to an abandoned railway that hangs almost imperceptibly on a ledge around the rimrock. Explore it in either direction.\n\n  Deep Creek Canyon\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/4 | 4.6 miles | 900 feet\/2200 feet | Apr\u2013Dec\n\n**Maps:** USGS Nine Mile Falls, state park map; **Contact:** Riverside State Park, (509) 465-5064, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Open 6:30AM\u2013dusk. Partly wheelchair-accessible. Open to mountain bikes, horses. Dogs permitted on-leash; **GPS:** N 47 46.319 W 117 33.128\n\n  _**Deep Creek Canyon is its own little world within sprawling Riverside State Park. An intermittent stream dropping decisively to join the Spokane River is confined by basalt cliffs towering as high as 300 feet above and narrowing as close as 60 feet across. Lush greenery is unceremoniously interrupted by bulging basalt outcroppings and swaths of scree resembling explosion rubble. Blue-green swallows swoop through the canyon and ospreys nest nearby. The highlight might be climbing from the bowels of Deep Creek Canyon to Pine Bluff and savoring where you've been from a bird's-eye view.**_\n\n### GETTING THERE\n\nFrom the intersection of Francis Avenue and Assembly Street in northwest Spokane, head west toward Nine Mile Falls on Francis Avenue, which becomes Nine Mile Road (State Route 291). Drive 6.1 miles and turn left at Nine Mile Dam onto Charles Road. Drive 0.1 mile, crossing the Spokane River, and turn left on Carlson Road. Drive 0.4 mile and turn right into the Spokane River Centennial Trail trailhead parking area (elev. 1590 ft). Privy available.\n\n_Basalt towers stand guard over Deep Creek._\n\n### ON THE TRAIL\n\nHike back down the road a short way and descend through the gate on the Centennial Trail. Follow the paved route above the Nine Mile Reservoir portion of the Spokane River. Taking note of trail options on the right to explore later, cross the bridge, pass the picnic site at Deep Creek, and continue on the Centennial Trail up the hill. At 1.1 miles, turn right and hike the road that leads 0.4 mile to the Deep Creek Overlook. Enjoy the views of unique basalt formations and down into Deep Creek Canyon.\n\nContinue up the road another 0.3 mile and drop sharply to the right on Trail No. 25, which plunges to the canyon bottom. This trail is part of a 25-mile loop through Riverside State Park, and you'll encounter it several times on this hike.\n\nTurn right and follow the creekbed a short distance before the trail heads up the other side. Gain a bluff to the junction with Trail No. 411 (a side trip right leads into a moonscape of basalt outcroppings and scree). Continue on Trail No. 25 uphill to a junction and turn left on the connector trail that leads up toward Pine Bluff.\n\nAt the top of the switchbacks, turn right on Trail No. 410. Go a few hundred yards up to an opening and take the trail to the right to an overlook of the Spokane River and Nine Mile Dam. The trail works up a secondary bluff to the higher Pine Bluff and another good overlook. Ospreys nest on the power-line poles below. Bring binoculars in summer for the rare opportunity to look _down_ into a nest and possibly see osprey chicks.\n\nPast the power lines, reach a junction that reunites you with Trail No. 25. Turn right on the double-track trail. It heads up and then loops down through the ponderosa pines along the power lines, winding to a T junction with a service road.\n\nTurn right, go 30 yards, and turn right again to continue on Trail No. 25. Go another 30 yards and turn right yet again, to continue on Trail No. 25. Eventually the trail drops to a junction with Trail No. 401. Bear left and continue down to another junction, where you turn right on Trail No. 402.\n\nAs you descend and pass another junction with Trail No. 25, Trail 402 narrows to a single-track for its last leg\u2014with a view over Nine Mile Reservoir\u2014to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nRestart the loop along the Centennial Trail to Deep Creek Bridge and enjoy a well-deserved picnic. Then explore trails up from the picnic area into interesting rock formations.\n\nIndian Painted Rocks\u2013Saint George's School (Little Spokane River)\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 4.7 miles | 600 feet\/1790 feet | Mar\u2013Nov\n\n**Maps:** USGS Dartford, state park map; **Contact:** Riverside State Park, (509) 465-5064, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Open 6:30AM\u2013dusk. No dogs or bikes allowed in natural area. Buggy in summer; **GPS:** N 47 46.826 W 117 29.745\n\n  _**The 1993-acre Little Spokane River Natural Area, protecting more than 7 miles of the serpentine river's corridor on the north edge of Spokane, is one of the region's richest wildlife habitats. It's distinguished for attracting a spring-summer diversity of bird species unmatched in the region. This route explores the best hiking along the river stretch between Indian Painted Rocks and the Saint George's School area.**_\n\n### GETTING THERE\n\nFrom Maple Street in north Spokane, head 1 mile west on Francis Avenue (State Route 291). Turn right (north) on Indian Trail Road and drive 4.7 miles to a junction with Rutter Parkway. Continue straight onto the parkway, dropping down to the Little Spokane River. Shortly after crossing a bridge, turn left into the Indian Painted Rocks parking area (also popular with river paddlers) and trailhead (elev. 1420 ft). Privy available.\n\n### ON THE TRAIL\n\nFrom the Indian Painted Rocks trailhead, walk south on Rutter Parkway (stay to the edge of the road and be careful of traffic), cross to the south side of the Little Spokane River, and look for the trailhead to the left. The trail leads upstream and across a huge meadow that gets tall with grass during summer.\n\nAt 0.7 mile, the trail begins ascending a single-track into a forest of granite outcroppings and gullies, passing a cattail-lined wetland. After hiking up and out of an enchanting ravine at 1.3 miles, bear left at a fork. Hike 0.3 mile to an overlook of Saint George's School. Then backtrack a short way and look for the easy-to-miss trail heading left (south) up to a gated double-track trail.\n\nAt the gate, turn right on the double-track and hike a short way to a junction with another double-track. Right heads back to the trailhead. To make a loop, turn left on the double-track and hike through a section of thinned forest to another gate. Turn right at the gate onto a single-track that leads back to the granite-lined \"enchanted ravine.\"\n\nTurn left at the ravine and follow the main trail 1.3 miles back to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nFrom the gate above Saint George's School, go left through the gate instead of right. The mostly double-track trail leads 2.5 miles upstream to a trailhead near the Spokane Fish Hatchery, with a spur option to a view of Mount Spokane. This route includes an abrupt 500-foot ascent followed by easy walking below Five Mile Prairie to a prettier but similarly abrupt 540-foot descent to the hatchery trailhead off Waikiki Road. The hatchery, fed by a pure spring right out of the Spokane Aquifer, is worth a visit.\n\n_Wild turkey gobbler on Little Spokane River Trail_\n\n  Little Spokane River Overlook\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 6.5 miles | 1150 feet\/2470 feet | Apr\u2013Nov\n\n**Maps:** USGS Dartford, USGS Nine Mile Falls, state park map; **Contact:** Riverside State Park, (509) 465-5064, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Open 6:30AM\u2013dusk. No dogs or bikes allowed in natural area. Watch for rattlesnakes; **GPS:** N 47 46.973 W 117 29.788\n\n  _**The Little Spokane River Natural Area, managed by Riverside State Park, got an upland boost with the addition of the Van Horn, Edburg, Bass woodlands secured through Spokane County Conservation Futures. While most visitors hike or paddle in the river valley, this 701-acre property takes you from the depths of the river canyon to a high overlook, offering a top-to-bottom perspective of the habitats that attract waterfowl and eagles, muskrats and beavers, raccoons and coyotes, rattlesnakes and mountain lions, deer and moose.**_\n\n### GETTING THERE\n\nFrom Maple Street in north Spokane, head 1 mile west on Francis Avenue (State Route 291). Turn right (north) on Indian Trail Road. Drive 4.7 miles to a junction with Rutter Parkway. Continue straight onto the parkway, dropping down to the Little Spokane River. Shortly after crossing a bridge, turn left into the parking area (popular with river paddlers) and trailhead (elev. 1420 ft). Privy available.\n\n### ON THE TRAIL\n\nFrom the Indian Painted Rocks trailhead, the kid-friendly version of this hike simply follows the trail along the Little Spokane River as far out and back as the kids want to go. For the longer loop, head the other way, north past the toilets, away from the river. After a short way, the trail bends back to a gate off Rutter Parkway. Turn left here onto the double-track trail. (This is an alternate access point, with limited parking.)\n\nThe route goes up a draw, previously logged but regaining its natural, wild stature. Nearing the head of the timbered draw, turn left on a single track that will switchback up the other side and rejoin the double track on the ridge. This can be a midday hot stretch, but by evening it's shady. At 2.5 miles, the trail gains the ridge, a mostly untouched area of timber, native plants, and basalt outcroppings. Views to the right include the Spokane River and down into Lake Spokane (Long Lake).\n\nContinue up to a bench, where the trail bends left and off the ridge. At this point, a single-track spur trail heads to the right a couple hundred yards to big granite boulders for an excellent vista at 2.7 miles. This knob is locally known as Knothead. Look south to the Deep Creek basalt outcroppings (Hike 82) and the Nine Mile area of Riverside State Park, location of the Spokane River Centennial Trail terminus. Look southwest to the Spokane airport area and down to SR 291 and the boat launch at the confluence of the Spokane and Little Spokane Rivers (a short off-trail walk southeast to another knob offers a view down toward the Little Spokane River to where you began).\n\n_Near Knothead, overlooking Spokane River_\n\nBacktrack to the junction at the bench and turn right. Hike through parklike openings on the south-facing slope. After a few minutes, turn left on a nifty single-track re-route that eventually returns to the double track. Just before a gate at River Park Lane, the trail turns left toward SR 291. Drop a couple hundred yards, cross the paved road, and descend toward the Little Spokane River.\n\nWatch for a marker where the trail makes a 90-degree right turn. The trail winds around a bluff with a good view up the Little Spokane River valley before making another drop down to River Park Lane and a trailhead off of SR 291 at nearly 5 miles. Make a hard left turn off the pavement onto the trail that parallels the river 1.6 miles back to your start at Indian Painted Rocks.\n\n### EXTENDING YOUR TRIP\n\nSee Indian Painted Rocks (Hike 83).\n\n  McLellan Conservation Area\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 3.8 miles | 380 feet\/1760 feet | Mar\u2013Dec\n\n**Maps:** USGS Tumtum, USGS Four Mound Prairie, McLellan Conservation Area map; **Contact:** Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks; **Notes:** Open to mountain bikes, horses. Dogs permitted on-leash. Shots might be heard from distant shooting range; **GPS:** N 47 52.489 W 117 41.463\n\n  _**Just west of Riverside State Park, the McLellan Conservation Area\u2014secured by Spokane County Conservation Futures\u2014preserves 410 acres on a scenic bend of Lake Spokane (the confusing name for the Spokane River reservoir behind Long Lake Dam). The area includes 1.5 miles of shoreline and adjoins a 640-acre parcel managed by the Department of Natural Resources. The thinned ponderosa and Douglas-fir forest and shoreline habitats are important year-round for wildlife large and small. April through May is prime time to enjoy the riot of wildflowers. At the time of this writing, no formal trail was maintained. But the route is easy to find.**_\n\n### GETTING THERE\n\nFrom the intersection of Francis Avenue and Assembly Street in northwest Spokane, drive 6.1 miles west toward Nine Mile Falls on Francis Avenue, which becomes Nine Mile Road (State Route 291). At Nine Mile Dam, turn left on Charles Road. Cross the Spokane River, continue 5 miles (passing Sontag County Park), and turn right onto South Bank Road. Go 5.8 miles, turn right onto McLellan Lane, and drive 0.8 mile to the trailhead at road's end (elev. 1760 ft).\n\n_McLellan hikers rise above Lake Spokane anglers._\n\n### ON THE TRAIL\n\nAt the gate, follow the fence to the left (west), after which there's a more discernible trail. Leave this trail where it bends right and continue straight along the bluff to a natural overlook by an old-growth tree above Lake Spokane (previously called Long Lake). Turn right from the overlook and hike cross-country, keeping the bluff and the reservoir on your left and letting them be your guide.\n\nContour to the right along a deep ravine until it's shallow enough to let you drop down to an old road. Follow the road left and down to a parklike spot at the water's edge. Then either backtrack up the road or walk a short way upstream and climb a steep ridge back up. Either way, continue following the bluff. After a long flat area, the route stair-steps down to a lower bluff. (Look for a pet memorial.) Drop down to the lower bluff when convenient and look for an old cabin site at 2 miles.\n\nThen follow the faint road southeastward from the cabin. The old track is often littered with downfall and droppings from wild turkeys. Bear right at a junction with another faint road (it heads left toward the reservoir and fades away). Soon you'll enter a more open area of timber thinned for fire control. Some private buildings stand along the shore to the left.\n\nContinue up on the road and bear right. The road eventually leads to a gate. From here, the road swings to the right and then back up to the fence and the trailhead. Or, leave the road and head cross-country, keeping the fence on your left.\n\n## columbia plateau\n\n_Big Sky Country\u2014the Beezley Hills_\n\nThe Columbia Plateau (also referred to as the Columbia Basin) is a sprawling area south and east of the Columbia River consisting of ancient basalt flows scoured and shaped by Ice Age floods into channeled scablands. Within the rain shadow of the Cascade Mountains, the Columbia Plateau sees the lowest amount of rainfall in the state. But massive irrigation projects have transformed large parts of it into croplands and vineyards. Sparsely populated in its northern reaches, its southern reaches consist of one of the fastest growing metropolitan areas in the country. A land of sagebrush-steppe, canyons, coulees, sand dunes, and mesas, the plateau possesses incredible geological and biological diversity. Public lands scattered across it provide excellent hiking opportunities for discovering a land that lacks big mountains\u2014but is big on wide-open spaces and scenic delights.\n\n  Turnbull National Wildlife Refuge Auto Tour Trails\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/1 | 3 miles | 110 feet\/2290 feet | Mar-Dec\n\n**Maps:** USGS Cheney, refuge brochure; **Contact:** Turnbull National Wildlife Refuge, (509) 235-4723, www.fws.gov\/turnbull; **Notes:** Federal pass or $3 vehicle fee Mar 1\u2013Oct 31. Open daylight hours. Partly wheelchair-accessible. Dogs permitted on-leash. Stay on designated roads and trails; **GPS:** N 47 26.321 W 117 32.052\n\n  _**This easy-going hike combines two trails that are part of an auto tour in the Turn-bull National Wildlife Refuge. The Kepple Peninsula Trail leads to a wildlife observation blind as it loops from open area, into pine forest, and along the shore of Kepple Lake. Then hike (or drive) 0.4 mile to the 30-Acre Lake Trail for an out-and-back walk featuring aspens and cattails.**_\n\n### GETTING THERE\n\nFrom the intersection of 1st and K Streets at the south end of Cheney's business district, turn east onto Cheney-Plaza Road toward Williams Lake. Drive 4.2 miles south and turn left on Smith Road toward Turnbull Refuge headquarters. Stop at the self-pay station on the right and check the maps. Continue 1.8 miles (past a parking area, kiosks, and restrooms), and turn left on the Pine Creek Auto Tour route. Drive past the Blackhorse Lake trailhead at 0.7 mile on the tour route, then pass the south trailhead for 30-Acre Lake at 1.1 miles, then pass the Kepple Lake Overlook trailhead at 2.3 miles. Finally, after 2.6 miles, pull into the Kepple Peninsula Interpretive Trail parking area (elev. 2280 ft). Privy available.\n\n### ON THE TRAIL\n\nStart on the paved wheelchair-accessible trail with interpretive signs for an easy walk to a wildlife-viewing blind at the far end of the peninsula that juts into Kepple Lake. Continue the loop clockwise by following the single-track dirt trail along the wetlands from the waterfowl exhibit back to the trailhead.\n\nThen walk (or drive) another 0.4 mile on the tour route to the 30-Acre Lake north trailhead. Hike through the gate onto the double-track trail that heads through open forest and past aspens and scablands.\n\nSoon you'll see a fenced enclosure on the right that's part of a study to see how well aspens regenerate when they're protected from elk foraging. The plots indicate that elk have had a devastating impact on the aspens, which are important to a variety of wildlife. The research was part of the scientific justification for allowing controlled hunting seasons on portions of the refuge (not around the auto tour route or public-use trails).\n\n_Kepple Lake is one of Turnbull's easy strolls._\n\nMIMA MOUNDS: A MYSTERY\n\nOn hikes such as the Pine Lakes Loop (Hike 87) in Turnbull National Wildlife Refuge and Fishtrap Lake (Hike 109), hikers will notice mima (MY-ma) mounds and wonder: What created these clumps of rock and grass that can be 4\u20136 feet tall and 30 feet wide, together looking like a junkyard of giant baseball pitcher's mounds? Scientists wonder too.\n\nResearchers who looked into the matter by digging through mima mounds debunked the myth that they're Native American burial sites. But they turned up no conclusive answers, just dozens of hypotheses: freeze-and-thaw cycles, erosion, wind working with vegetation, earthquakes, flood cycles, volcanic eruptions\u2014giant prehistoric prairie dogs? Your guess is as good as theirs.\n\nAlthough Eastern Washington offers many examples of these geological attractions, a 445-acre Mima Mounds Natural Area Preserve in Western Washington south of Olympia is dedicated to revealing them to the public. The state-protected area has a good walking path.\n\nFor information, visit Washington Trails Association, www.wta.org\/go-hiking\/hikes\/mima-mounds.\n\n\u2014 _R. L._\n\nTules gobble up most of 30-Acre Lake, with little water showing much of the year. Reach the south trailhead after 0.75 mile and retrace your steps. Consider leaving a bike at the south trailhead during your drive in and pedaling the tour route back to the Kepple Peninsula trailhead.\n\n### EXTENDING YOUR TRIP\n\nHike the other three short trails along the auto tour route mentioned in the Getting There directions. On the drive out, stop at 4.4 miles around the tour loop to bag the Blackhorse Lake Boardwalk.\n\n  Pine Lakes\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 6 miles | 400 feet\/2375 feet | Mar\u2013Dec\n\n**Maps:** USGS Cheney, refuge brochure; **Contact:** Turnbull National Wildlife Refuge, (509) 235-4723, www.fws.gov\/turnbull; **Notes:** Federal pass or $3 vehicle fee Mar 1\u2013Oct 31. Open daylight hours. Partly wheelchair-accessible. Dogs permitted on-leash. Stay on designated roads and trails; **GPS:** N47 24.891 W117 32.283\n\n  **_The diked lakes and marshes on Pine Creek are a magnet for waterfowl and other wildlife, including some standouts, such as trumpeter swans. You'll get a flavor for the refuge's habitat diversity by following the featured loop as it ranges from the creek basin to the open grasslands and potholes that border farmed fields._**\n\n### GETTING THERE\n\nFrom the intersection of 1st and K Streets at the south end of Cheney's business district, turn east onto Cheney-Plaza Road toward Williams Lake. Drive 4.2 miles south and turn left on Smith Road toward Turnbull Refuge headquarters. Stop at the self-pay station on the right and check the maps. Continue 1.5 miles to the trailhead parking area and kiosk (elev. 2260 ft). Privy available.\n\n### ON THE TRAIL\n\nFrom the parking area, cross the road to the Pine Lakes Loop trailhead and check out Winslow Pool observation area before proceeding down on the paved path. Hike past Winslow Pool, a favorite area for red-wing blackbirds and a variety of waterfowl, including migrating tundra and nesting trumpeter swans. At the first junction, bear right and continue down along the next pool. During spring and early summer, the paved trail is often littered with the droppings of geese and coyotes. The trail soon bends left and crosses the earthen dike at the end of Middle Pond.\n\n_Trumpeter swans return to Turnbull as soon as winter ice recedes._\n\nAt a Y junction, bear right onto the gravel path (left leads to an observation blind and the way you'll return to the trailhead at the end of this hike). Go a short way to a junction and turn right at 0.75 mile. Go a short way farther to another junction, and turn right onto a gravel roadway that is your path heading south into a more open area along the Pine Lakes. Scoured by Ice Age floods, the landscape features \"scabs\" of basalt rock exposed above rich soil and wetlands.\n\nAt the next junction, make a mental note that you'll return here, from the left. Continue straight, and at 1.6 miles come to the dike at the end of Pine Lakes. Turn left and head up onto the Stubblefield Trail. Hike briefly to the next junction and turn left through the former fence gate and into a pine forest thinned for fire control in the years just after 2000.\n\nSoon the trail breaks into open range land. The route can have numerous wet spots during spring, as the scablands basalt foundation prevents water from soaking into the ground. At the next junction, bear left away from the fence. Stubblefield Lake, on your right, dries up significantly by late summer.\n\nThe trail stays in the open, but tracks of critters such as elk and deer suggest that you may have observers just inside the forests on each side. Soon the route arches gradually over the trek's high point (elev. 2375 ft) before bending down to a familiar junction. Turn right on the Pine Lakes Trail and return to the trailhead, looping by the observation blind to return via the east side of Middle Pond.\n\n### EXTENDING YOUR TRIP\n\nFive short trails can be accessed along the refuge's 5.4-mile Pine Creek Auto Tour (see Hike 86, Turnball National Wildlife Refuge).\n\n  Frenchman Coulee\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 4 miles | 100 feet\/875 feet | Mar\u2013Dec\n\n**Map:** USGS Babcock Ridge; **Contact:** Washington Department of Fish and Wild-life, Columbia Basin Wildlife Area, Moses Lake, 509-765-6641, <http:\/\/wdfw.wa.gov\/lands\/wildlife_areas>; **Notes:** Discover Pass required; **GPS:** N 4701.381 W 119 59.516\n\n  **_Follow an old jeep track on an easy journey through a harsh landscape of sage, sand, and basalt. Frenchman Coulee is small but impressive, with its imposing canyon walls, sculptured rock formations, and plummeting waterfall. Marvel at the old highway blasted into steep canyon walls and spanning deep clefts. Summer can be blistering hot and winter blustery and bone-chilling. But fall is delightful, with agreeable temperatures, and spring simply divine, when the canyon floor comes alive in a dazzling display of blossoms._**\n\n### GETTING THERE\n\nFrom Moses Lake, follow I-90 west to exit 143, turning right (north) onto Silica Road. (From Ellensburg, follow I-90 east to exit 143, turning left onto Silica Road.) Proceed 0.8 mile and turn left onto Vantage Road (old Highway 10). Follow this road west for 3.6 miles down into Frenchman Coulee, passing popular pull-outs for climbers and coming to the trailhead on your right (elev. 875 ft).\n\n### ON THE TRAIL\n\nStarting on a shelf at the edge of the Columbia River, head east on an old jeep track. Closed to motorized travel, it's obvious from the tire tracks that scofflaws can't read or don't care about this regulation meant to protect this fragile environment. Managed by the Washington Department of Fish and Wildlife, Frenchman Coulee is part of the multiunit 192,000-acre Columbia Basin Wildlife Area, consisting of outstanding sagebrush-steppe ecosystems, including the nearby Ancient and Dusty Lakes. A popular hunting area, be sure to don orange when hiking here in the fall.\n\n_Seasonal waterfall at the head of Frenchman Coulee_\n\nAt just shy of 0.2 mile, come to a Y junction (elev. 845 ft). The way left travels north along Babcock Bench, offering some good views of the Columbia River (here dammed as Wanapum Lake) and Whiskey Dick Mountain (long-winded here, with its turbines) rising behind it. Bear right instead to journey up the coulee.\n\nThe track parallels the old highway, coming pretty close to it at about 0.4 mile before the road pulls away to start climbing out of the coulee. The old jeep track stays pretty level while canyon walls flanking the north and south rise precipitously. At 0.8 mile, come to another jeep-track junction (elev. 825 ft). The track left leads back to meet the one you started on 0.4 mile north of where you left it. Consider returning that way for some variation. Meanwhile, head right to continue your journey into the heart of the coulee.\n\nAt 0.9 mile, skirt the base of some steep, stark basalt cliffs littered with rusting car parts and other debris. Look up at the old highway blasted into ledges and spanning deep chasms. Try to envision cars puttering up this highway back in the 1930s and 1940s under a scorching hot sun, pulling over in distress with steam spouting from radiator caps.\n\nThe tread now gets a little sandier and softer, hence the slower walking. Skirt big talus slopes that harbor reptiles and small mammals. Now well below the highway and away from popular climbing spots, engine and human sounds are replaced by wind and birdsong and the falling water from the nearing cascade.\n\nPass beneath high-tension power lines and begin angling north toward a creek cascading from the coulee rim. At 2 miles, reach the base (elev. 875 ft) of the cascade near a big talus slope. The flow is regulated by runoff and by irrigation needs from above, which means it sometimes dries up. Willows and sage along the outflow indicate that water does flow this way on occasion.\n\n_KLAHOWYA TILLICUM_ : CHINOOK JARGON\n\nMany place names in Eastern Washington, like much of the Pacific Northwest, come from the Chinook Jargon. Not an actual language, Chinook is a collection of several hundred words drawn from various Native American languages (primarily Coast Salish) as well as English and French. It was used as a trade language among Native peoples, Europeans, and American settlers and explorers in the Pacific Northwest throughout the nineteenth century. A unique part of our Pacific Northwest cultural heritage, Chinook names are sprinkled throughout our landscape. Below are some Chinook words you may encounter when hiking in Eastern Washington:\n\n_chuck_ . . . . . . . . . . . . . . . . . . . . . . water, river, stream\n\n_cultus_ . . . . . . . . . . . . . . . . . . . . . . bad, worthless\n\n_elip_ . . . . . . . . . . . . . . . . . . . . . . . . first, in front of\n\n_hyas_ . . . . . . . . . . . . . . . . . . . . . . . big, powerful, mighty\n\n_ipsoot_ . . . . . . . . . . . . . . . . . . . . . . hidden\n\n_kimtah_ . . . . . . . . . . . . . . . . . . . . . behind, after\n\n_klahowya_ . . . . . . . . . . . . . . . . . . . hello, greetings, how are you?\n\n_klip_ . . . . . . . . . . . . . . . . . . . . . . . . deep, sunken\n\n_lemolo_ . . . . . . . . . . . . . . . . . . . . . wild, crazy\n\n_lolo_ . . . . . . . . . . . . . . . . . . . . . . . . carry, lift\n\n_memaloose_ . . . . . . . . . . . . . . . . . dead\n\n_mesachie_ . . . . . . . . . . . . . . . . . . . bad, evil, dangerous\n\n_moolock_ . . . . . . . . . . . . . . . . . . . . elk\n\n_muckamuck_ . . . . . . . . . . . . . . . . food\n\n_ollalie_ . . . . . . . . . . . . . . . . . . . . . . berries\n\n_pil_ . . . . . . . . . . . . . . . . . . . . . . . . . red\n\n_saghalie_ . . . . . . . . . . . . . . . . . . . . above, high, on top, sacred\n\n_sitkum_ . . . . . . . . . . . . . . . . . . . . . half of something, part of something\n\n_skookum_ . . . . . . . . . . . . . . . . . . . big, strong, mighty\n\n_tenas_ . . . . . . . . . . . . . . . . . . . . . . small, weak, children\n\n_tillicum_ . . . . . . . . . . . . . . . . . . . . friend, people\n\n_tupso_ . . . . . . . . . . . . . . . . . . . . . . pasture, grass\n\n_tyee_ . . . . . . . . . . . . . . . . . . . . . . . chief, leader\n\n\u2014 _C. R._\n\nAdmire the falls and the ravens and raptors that ride the thermals above it. Marvel, too, at the depth and scope of the coulee from here, deep inside it. Scout around, noting the scattered debris warranting a much needed cleanup of the canyon. During springtime delight in the dazzling floral carpet.\n\n### EXTENDING YOUR TRIP\n\nIt is possible to continue beyond the waterfall, picking up a good jeep track once more and following it for about 0.4 mile up and out of the coulee. It emerges 2 miles east from the trailhead. Return the same way or walk the road back for a loop. Consider hiking the track along Babcock Bench to a nice knoll about 1.3 miles from the trailhead, with good views of the Columbia River.\n\n  Quincy Lakes\n\n**Ancient Lakes**\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 4.4 miles | 280 feet\/1000 feet | Feb\u2013Nov\n\n**Dusty Lake**\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 6 miles | 350 feet\/1000 feet | Feb\u2013Nov\n\n**Map:** USGS Babcock Ridge; **Contact:** Washington Department of Fish and Wild-life, Columbia Basin Wildlife Area, Moses Lake, 509-765-6641, <http:\/\/wdfw.wa.gov\/lands\/wildlife_areas>; **Notes:** Discover Pass required; **GPS:** N 4709.610 W 119 58.845\n\n  **_Hike to a series of pothole lakes lying within deep basalt canyons carved by ancient glacial floodwaters. Follow old jeep tracks beneath stark cliffs and across sage-scented flats and along grassy slopes. One of the most popular hiking destinations in the Channeled Scablands and Columbia Basin, the Quincy Lakes are especially delightful in spring, with its ample sunshine and profuse wildflowers._**\n\n### GETTING THERE\n\nFrom Moses Lake, follow I-90 west to exit 151. (From Ellensburg, follow I-90 east to exit 149). Then head north on State Route 281 for 5 miles, turning left onto White Trail Road (Rd 5 NW). Continue 7.8 miles, turning left onto Rd 9 NW. (From Wenatchee, follow SR 28 east for 26 miles to White Trail Road, 0.7 mile beyond the rest area. Then proceed south 1 mile, turning right onto Rd 9 NW.) After 2.2 miles, the pavement ends and the road becomes Ancient Lakes Road. Continue 3.7 miles to the road's end and trailhead (elev. 1000 ft). Privy available.\n\n### ON THE TRAIL\n\nStart on an old jeep track long closed to vehicles and head south through open country along the Babcock Bench, which rises several hundred feet above the Columbia River. The wide track is perfect for those skittish about hiking in snake country. Winter is best for totally avoiding these necessary components of this ecosystem as well as for escaping the stifling heat of summer.\n\nMeander beneath a mesa, across sage flats, and along wetlands of cattails and willows. The wetlands as well as the lakes were an unintended consequence of irrigation projects begun in the 1940s in the Columbia Basin. Seepage from canals created these oases, which have since become wildlife havens.\n\nAt 0.4 mile, pass a not-so-obvious trail leading left for the Ancient Lakes. The main (preferred) way (elev. 940 ft) to the lakes is reached at 0.6 mile. Turn left here, following a secondary jeep track into the well-vegetated Potholes Coulee. The way descends about 40 feet and then regains it, climbing a small knoll that overlooks the first of the three Ancient Lakes.\n\nThen follow a boot-beaten path down off the knoll to a small grassy rise (elev. 830 ft) between the lakes. The path ends at 2.2 miles at the base (elev. 860 ft) of the coulee wall, where there are some good views overlooking two of the lakes and a waterfall crashing from above the coulee rim. Roam at will, letting western meadowlarks serenade you.\n\nFor Dusty Lake, which attracts fewer visitors because of its longer approach and harsher setting, bypass the Ancient Lakes turnoff and continue straight. Ignoring side tracks, round a ridge (elev. 990 ft) that separates the coulees housing Dusty and the Ancient Lakes, and take in good views west of Whiskey Dick's wind farm and the Colockum country. Then descend and cross beneath some high-tension power lines (ubiquitous in the Columbia Basin). And at 1.5 miles, near a power-line tower, come to a junction (elev. 900 ft).\n\nBear left, following a good track into Potholes Coulee, slowly climbing its broad sage-filled bottom (elev. 950 ft) before descending to Dusty Lake (elev. 850 ft) at 3 miles. The lake is set beneath talus slopes and stark canyon walls. Listen to water crashing from the rim, to wind whistling across the coulee bottom, to the birds and insects of the sagebrush-steppe. Good campsites (often occupied on weekend nights) invite you to hang around and listen to coyotes' and owls' calls all night.\n\n_Dusty Lake lies beneath stark basalt walls._\n\n### EXTENDING YOUR TRIP\n\nA short but highly scenic trail starts from the coulee rim and drops into the canyon, passing several small ponds on its way to the east shore of Dusty Lake. Trail access is from the U road that traverses the Quincy Lakes Unit of the Columbia Basin Wildlife Area. Due to repeated vandalism, the road may be closed, but it's open to foot traffic.\n\n  Beezley Hills\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 2.2 miles | 250 feet\/2800 feet | Mar\u2013Nov\n\n**Maps:** USGS Monument Hills, USGS Ephrata SW; **Contact:** Washington Nature Conservancy, (206) 343-4345, www.nature.org\/washington; **GPS:** N 47 19.109 W 119 47.982\n\n  **_The Beezley Hills stretch from the Columbia River to Ephrata and consist of some of the finest and wildest sagebrush-steppe habitat remaining in the state. Named after an early rancher, the hills are dotted with springs that provide exceptional breeding and foraging grounds for a wide array of species, including pygmy rabbits, badgers, sage grouse, and prairie falcons. The Nature Conservancy began establishing a preserve here in the late 1990s, and it now totals more than 30,000 acres. The preserve also harbors rare plants, including sulphur lupine, which sports white blossoms. The pink-blossomed hedgehog cactus grows in profusion. Listen for bluebird song in the windswept, sage-scented slopes. Watch the sun rise above the channeled Columbia Plateau, or watch it set behind a frosty wall of Cascade peaks._**\n\n### GETTING THERE\n\nFrom Moses Lake, follow I-90 west to exit 151. (From Ellensburg, follow I-90 east to exit 149.) Then head north on State Route 281 for 10 miles to its junction with SR 28 in Quincy. Turn right (east) on SR 28 (F Street SE), continuing 0.8 mile. Just before reaching West Canal, turn left onto Columbia Way (which becomes P Street) and continue north. At 3.1 miles, the pavement ends and the road becomes Monument Hill Road. Follow this good gravel road for 4.1 miles to the trailhead (elev. 2800 ft), located near a spur road to communication towers. Park on the road shoulder.\n\n### ON THE TRAIL\n\nPass through a stile and follow an old jeep track through wide-open country. A fainter set of tracks diverge left\u2014it meets back up with the main track after 0.25 mile. Soak up the sun and breezes and admire the farmed plains to the south, Moses Lake to the east, and lofty Mission Ridge to the west. In spring the way is muddy, with fresh imprints from passing critters. By later in the summer the ground is hard and cracked.\n\n_This Nature Conservancy Preserve is renowned for its hedgehog cacti._\n\nThe way bends southeast and slowly descends. Early in the season the hills can appear drab. But come here in April and May and be treated to a dazzling floral display. Balsamroot, buckwheat, bitterroot, blue-bells, lupine, phlox, desert parsley, larkspur, prairie starflower, and others brighten the landscape. Start looking for hedgehog cacti as you approach a flat after a short little drop. They appear as spiny little barrels perched among lichen-covered rocks.\n\nAt about 1.1 miles, the old jeep track reaches a small knoll (elev. 2550 ft) and then peters out. Return the way you came.\n\n### EXTENDING YOUR TRIP\n\nIt's possible to continue exploring by following game trails, but be sure to walk softly on the land, and don't leave the preserve and stray onto abutting private property. In nearby Ephrata you can hike through the eastern extent of the Beezley Hills on a series of service roads and trails. Access is from Cyrus Road (reached from 1st Avenue near the canal). Trails are numerous and unmarked, but city officials hope to eventually develop the area into a major park. Also consider exploring the Moses Coulee section of the Nature Conservancy Preserve. Dutch Henry Falls near Jameson Lake (accessed from Jameson Lake Road off of US Highway 2) offers some nice roaming on quiet trails through spectacular canyon country.\n\n  Steamboat Rock\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 3.2 miles | 760 feet\/2300 feet | year-round\n\n**Maps:** USGS Steamboat Rock SW, USGS Steamboat Rock SE, state park map online (not accurate); **Contact:** Steamboat Rock State Park, (509) 663-1304, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Dogs permitted on-leash. Watch for rattlesnakes; **GPS:** N 47 51.837 W 119 07.305\n\n  **_Stand upon this massive basaltic butte within the Grand Coulee and try to visualize the floods of biblical proportions that carved out the Channeled Scablands of the Columbia Plateau. Marvel at the man-made lake now flooding the surrounding canyon, and cherish the extraordinarybeauty of this harsh but ecologically vibrant landscape. Roam Steamboat Rock's rim, watching for deer, jackrabbits, wrens, and swallows. And come in spring when the rock is awash in a riot of blossoms._**\n\n### GETTING THERE\n\nFrom Spokane, follow US Highway 2 west to Wilbur and turn right (north) onto State Route 21. After 0.25 mile, bear left onto SR 174 and follow it for 19 miles to its junction with SR 155 in Grand Coulee. Turn left and follow SR 155 south for 10.1 miles, turning right onto the Steamboat Rock State Park entrance road. (From Wenatchee, follow SR 2 east to 2 miles beyond Coulee City, bearing left onto SR 155. Continue 15.6 miles north on SR 155, turning left onto the park entrance road.) Proceed 2 miles to park entrance gate. Continue another mile, passing campgrounds, to the day-use area and trailhead (elev. 1580 ft). Privy available.\n\n_Dramatic views of Banks Lake from Steamboat Rock_\n\n### ON THE TRAIL\n\nStarting in open sagebrush-steppe that comes alive in April, particularly with lupine and balsamroot blossoms, hike toward the basaltic behemoth. The trail heads for a gap between the two \"summits\" of the mesa-like rock. Pass a draw harboring a few pines and trudge across some sandy tread before marching beneath the base of the hulking rock.\n\nAt 0.3 mile, come to a junction (elev. 1750 ft) at a couple of picnic tables set among five lonely ponderosa pines. The trail left leads to the Dune Loop Campground. The trail and service road straight lead to the Sage Loop Campground. You want to head right\u2014straight up a steep scree slope to a small cleft in the wall of the rock. Watch your footing; you'll need the use of your hands in a few places. Admire Steamboat Rock's stark face as you clamber up this passage to its heights. Notice all the lichens growing on the basalt and adding blotches of green and orange to the gray.\n\nThe grade eases after 0.1 mile. Grasses and flowers and big glacial erratics line the way. At 0.6 mile on a shelf, high on the rock, reach a junction (elev. 2100 ft). Maps show either two loops or one giant loop circling the top of the rock. Don't believe them\u2014it's more like one obscure loop and one out-and-back. But you really can't get lost on this 600-plus-acre rock, since steep drop-offs keep you from wandering too far!\n\nThe best explorations lie to the right along a well-defined path, so follow it. After a short, steep climb, crest the grassy plateau (elev. 2270 ft). Now walk along the rim (use caution), watching swallows skim the sky. Admire Northrup Canyon directly east and Banks Lake, which nearly surrounds you. Nature made the coulee thanks to great Ice Age floods (see \"In the Wake of Ice Age Floods\" sidebar). But man made the nearly 30-mile-long lake, part of the massive Columbia Basin Project. Water from the Columbia River is pumped into the Grand Coulee and stored for irrigation for nearly 700,000 acres across the Columbia Plateau. It is the largest water-reclamation project in the country and it has brought great changes, both positive and negative, to the basin. Steamboat Rock, once an island in the Columbia River (when it flowed through the Grand Coulee), is once again surrounded (almost) by water.\n\nIN THE WAKE OF ICE AGE FLOODS\n\nWhile not obvious at first glance, Eastern Washington is a geological wonder as awesome as the Grand Canyon, considering how the landscape was formed. The rimrock lakes, potholes, coulees, canyons, and dry waterfalls aren't the product of wind and raindrops over millennia. Rather, they were created by Ice Age floods that scoured the region 15,000\u201318,000 years ago. The floods rank as one of the earth's most significant geological events in the past two million years.\n\nThe Channeled Scablands, which begin just south of Spokane and spread over more than 3000 square miles, were created by torrents of biblical proportions. Waters burst from ice dams near Clark Fork, Idaho, and emptied Glacial Lake Missoula several times over a couple thousand years with unimaginable force. Scientists say the floodwaters raced over Steamboat Rock at 65 miles per hour\u2014nearly ten times faster than any flood modern humans might see. The volume of water in one of these floods was roughly equivalent to ten times the combined flow of all the rivers of the world.\n\nEvidence of the sudden, violent flooding is apparent throughout Eastern Washington, including lake-size potholes created by the mortar-and-pestle grinding of rocks in whirlpools; steep basalt cliffs bordering wide, flat channels; megaripples and thousands of foreign granite boulders that floods carried from hundreds of miles away and deposited in unlikely places, such as a current wheat field.\n\nCongress has created an Ice Age Floods National Geologic Trail that someday may be enhanced by visitors centers, highway signage, printed materials, and maps to guide tourists from one point of interest to another. Check out the enlightening guidebook, _Washington's Channeled Scablands Guide_ , by John Soennichsen (Mountaineers Books, 2012), and the Cheney-Spokane Chapter of the Ice Age Floods Institute, with its active programs and field trips (www.iceagefloodsewa.org).\n\nMeanwhile, about two dozen of the hikes in this book put walkers on the path of the Ice Age floods, no life jacket required.\n\n\u2014 _R. L._\n\nAt 1.4 miles, reach one of the rock's high points (elev. 2300 ft) and admire sweeping views north to the Columbia River cut (but the river isn't visible), Moses Mountain, and the Kettle River Range. West lie the North Cascades' serrated silhouette.\n\nAt 1.6 miles, good tread ends at the north tip of the plateau (elev. 2260 ft). Retrace your steps or consider the loop option described below.\n\n### EXTENDING YOUR TRIP\n\nA faint path leads south from where the good tread ends on the rock's northern tip. Follow it along a shelf across ledge and by erratics, coming to a junction in 0.5 mile. The way left leads back to the main trail in 0.25 mile. The way right travels for about 0.8 mile to return to the junction with the trail coming up from below. About 0.1 mile before that junction is a well-defined trail that climbs right 0.2 mile to a huge erratic and great viewpoint south down the Grand Coulee. You can continue 0.6 mile beyond to the southern tip of the rock on very faint (if any) tread, where a colony of marmots may greet you.\n\n  Northrup Canyon\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 6.2 miles | 685 feet\/2260 feet | Year-round\n\n**Maps:** USGS Steamboat Rock SE, USGS Electric City, state park map online (not accurate); **Contact:** Steamboat Rock State Park, (509) 663-1304, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Partly wheelchair-accessible. Dogs permitted on-leash. Watch for rattlesnakes. Old Wagon Road Trail closed Nov 15\u2013Mar 15 to protect wintering eagles; **GPS:** N 47 51.960 W 119 04.950\n\n  **_An old homestead, fish-hopping lake, pine and aspen groves, and a few other surprises make this dramatic subcanyon of the Grand Coulee a delight to hike. But not in summer, when temperatures soar and rattlesnakes abound. Come in spring for the blossoms, fall for golden aspens, or winter for a profusion of bald eagles._**\n\n### GETTING THERE\n\nFrom Spokane, follow US Highway 2 west to Wilbur, turning right (north) onto State Route 21. After 0.25 mile, bear left onto SR 174 and drive 19 miles to its junction with SR 155 in Grand Coulee. Turn left and follow SR 155 south for 6.8 miles, turning left onto Northrup Canyon Road. (From Wenatchee, follow SR 2 east to 2 miles beyond Coulee City, bearing left onto SR 155. Continue 18.9 miles north on SR 155, turning right onto Northrup Canyon Road.) Proceed 0.6 mile to the trailhead (elev. 1800 ft). Privy available.\n\n### ON THE TRAIL\n\nAdded to Steamboat Rock State Park in the 1970s, Northrup Canyon contains a small lake, a reliably flowing stream, and one of the few forested areas within the Columbia Plateau. Perhaps the canyon's most notable feature is that it's one of the most important roosts in Eastern Washington for wintering bald eagles. From late fall to early spring, up to two hundred of them spend the night in the canyon's tall pines and firs after fishing in the nearby Columbia River and Banks Lake.\n\nBefore heading up the gated road, check out the kiosk with information on the Northrup family who homesteaded in the canyon. Then start hiking. Just after the gate, a short path diverges left to a spot used for winter eagle observation. Shortly after that, the Old Wagon Road Trail leaves right and makes an excellent side trip. Consider coming back again if you don't have time or energy for it on this trip.\n\nContinue on the old road left, through open sage with good views up the canyon. The way then bends right and descends 50 feet, passing an old dump site from the Coulee Dam construction days. Soon pass beneath a cool canopy of ponderosa pine and Douglas-fir. Stands of aspen light up with the canyon with brilliant yellows come October.\n\nFollow the road along the base of the north canyon walls, undulating between forest groves and sagebrush-steppe. After a short climb, skirt a grassy wetland, and then climb again to cross Northrup Creek on a plank bridge. Continue upcanyon, across fertile flats, reaching the old Northrup homestead (elev. 1870 ft) at 1.8 miles. Snoop around the former park residence and older homestead buildings before heading to Northrup Lake.\n\nLocate the lake trail taking off left from the old chicken coop. Now traversing much rougher terrain, wind up a thinly forested tight draw, going up and over and around ledges and boulders. Sections are like a labyrinth that should intrigue young explorers.\n\nAt 2.1 miles, crest a small rise (elev. 2100 ft) before descending to a wetland (elev. 2025 ft) ringed with cattails. Pass more wetland pools, and after traversing a grassy flat begin a rather steep climb up ledges that showcase pretty blossoms in spring. At 2.8 miles, crest a pine-shrouded ridge (elev. 2260 ft) within the canyon walls. Then descend, passing through grassy flats before coming to Northrup Lake (elev. 2160 ft) at 3.1 miles.\n\n_Ruins of the original Northrup homestead_\n\nSet in a basaltic bowl lined with scree, reeds, dogwoods, and pines, the lake is scenic and serene. Grab some lunch and watch fish jump while listening to blackbird song.\n\n### EXTENDING YOUR TRIP\n\nFrom the lake, a rough path continues above it if you're inclined to go farther. From the homestead, a primitive path continues along Northrup Creek, but it can be tricky to find and follow. Instead, hike the Old Wagon Road Trail (note seasonal closures), which served as a freight line for wagons between Almira and Bridgeport in the 1880s. The way traverses the south canyon wall, across scree slopes and ledges, and must have been quite a task to complete. At 0.9 mile, it leaves the canyon for a sage-covered draw, reaching the canyon rim and a junction (elev. 2275 ft) at 1.1 miles, where the old wagon route continues left, leaving state park property. Follow the lightly used path straight for 0.4 mile to a 2325-foot overlook and breathtaking view on the canyon rim (use caution). In spring, the canyon rim bursts with bitterroot and other blossoms.\n\n  Fort Spokane\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/1 | 2.5 miles | 260 feet\/1660 feet | Mar\u2013Dec\n\n**Map:** USGS Fort Spokane; **Contact:** Lake Roosevelt National Recreation Area, (509) 633-9441, www.nps.gov\/laro; **Notes:** Visitors center usually open mid-June\u2013Labor Day. Partly wheelchair-accessible. Dogs permitted on-leash; **GPS:** N 47 54.184 W 118 18.529\n\n  _**Wander through the grounds of one of the last frontier forts built in the West. Pause at interpretive plaques, peek into restored buildings, and peer out over a bunchgrass bench above the Columbia River. Then climb to a bluff above the fort to survey the surroundings. Aside from excellent views of the 1880 fort grounds, admire the landscape here at the confluence of the Columbia and Spokane Rivers, where sagebrush-steppe transitions into ponderosa pine forest.**_\n\n### GETTING THERE\n\nFrom Spokane, follow US Highway 2 west for 35 miles to Davenport. (From Wenatchee, follow US 2 east for 125 miles to Davenport.) Then head north on State Route 25 for 22.4 miles, turning left into Fort Spokane. Continue 0.3 mile to the parking lot and trailhead (elev. 1400 ft). Privy available.\n\n### ON THE TRAIL\n\nPart history walk and part nature walk, this hike incorporates two of the three trails traversing the grounds of Fort Spokane. Located within the Lake Roosevelt National Recreation Area, a 129-mile long corridor along the Columbia River from the Grand Coulee Dam to Onion Creek just south of Northport on the Canadian border, the fort is one of several historic sites within this national park unit. Established in 1946 after the flooding of the river by the Grand Coulee Dam, Lake Roosevelt is a very different environment than the free-flowing river that was here in 1880 when the US Army began construction of Fort Spokane.\n\nStrategically built at the confluence of the Spokane and Columbia Rivers, the infantry and cavalry stationed here were in charge of keeping the peace between the seminomadic Spokane and Colville Tribes, who had been relegated to reservations, and land-seeking settlers encroaching upon Native lands. But the Fort saw no skirmishes. In 1898 most of the fort's troops deployed for combat in the Spanish-American War, and the fort was soon decommissioned and transferred to the Bureau of Indian Affairs. After serving as a boarding school, tuberculosis sanatorium, and hospital, the fort was closed in 1929. Grab the excellent free booklet at the trailhead to get the most out of your trip around the fort.\n\nThe recommended route begins on the wide, well-groomed, and perfectly flat Sentinel Trail and follows the interpretive posts (there are plenty of options for shortening or lengthening this hike). At 0.1 mile, reach the guardhouse (a visitors center in the summer). Turn left and walk the periphery of the fort grounds. The Park Service has replanted the grounds with native plants and grasses. Admire flowers in late spring and early summer and enjoy the sweet melodies of various breeding birds.\n\n_A lone pine stands watch over Fort Spokane._\n\nAt 0.3 mile, near the Bachelor Officers Quarters, the Beach Trail descends 100 feet off the bluff, coming to a beach on the river at 0.4 mile. The Sentinel Trail continues straight, passing the officers' row and parade grounds. At 0.75 mile, cross the park road and continue walking through the fort grounds to the quartermaster stables and the powder magazine.\n\nAt 1.1 miles, in a ponderosa pine grove that once fed the fort sawmill, come to the junction with the Bluff Trail. Turn left on it and enjoy hiking through one of the few forests in Lincoln County. Savor the cooler air trapped within the pine groves. After skirting a scree slope. come to the old reservoir and pump house at 1.3 miles.\n\nThe trail resumes beyond the pump house, climbing steeply (but paved and utilizing some staircases) up a scree slope before resuming natural tread upon cresting the bluff. The way then turns eastward through pines and flower gardens, reaching a wonderful viewpoint at 1.6 miles at its terminus (elev. 1660 ft). Try to imagine what the fort looked like in its heyday in the 1890s, when forty-five buildings once stood on the grounds.\n\nRetrace your steps back to the beginning of the Bluff Trail and finish the Sentinel Trail loop by walking past the stables and orchard, returning to your vehicle at 2.5 miles.\n\n### EXTENDING YOUR TRIP\n\nAdd another 0.8 mile by heading down the Beach Trail and back. Enjoy big pines and look for roosting eagles and osprey.\n\n  Crab Creek(Columbia National Wildlife Refuge)\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 2.6 miles | 40 feet\/870 feet | Year-round\n\n**Maps:** USGS Corfu, USGS Soda Lake; **Contact:** Columbia National Wildlife Refuge, (509) 546-8300, www.fws.gov\/columbia; **Notes:** Dogs permitted on-leash; **GPS:** N 47 46 57.009 W 119 15.286\n\n  _**One of three interconnecting nature trails within the 30,000-acre Columbia National Wild-life Refuge, the Crab Creek Trail offers an awful lot of biological bang for its short distance. Paralleling Crab Creek through a lush riparian environment within a sagebrush-steppe coulee, enjoy the contrasts\u2014and birds. This is one of the best bird-watching hikes on the Columbia Plateau\u2014and one of the easiest to hike, with its near-level course.**_\n\n### GETTING THERE\n\nFrom Spokane, take I-90 west to exit 179 in Moses Lake. Head south on State Route 17 for 2 miles, turning right onto Road M SE. Follow it for 6.4 miles, turning right onto SR 262. Continue west for 2.4 miles, turning left (directly across from a large boat launch and just before reaching the O'Sullivan Dam), into the Columbia National Wildlife Refuge. (From Ellensburg, take I-90 east to exit 137. Then follow SR 26 for 25 miles east, turning left onto SR 262. Proceed 17.7 miles to the refuge road.) Follow this gravel road south, passing a spur to Soda Lake Campground, and come to a junction at 2.2 miles. Turn right and bear left in 0.2 mile, reaching the trailhead (elev. 860 ft) on your left in another 0.4 mile (2.8 miles from SR 262), just before a junction with Morgan Lake Road.\n\n_Crab Creek provides excellent habitat for birds and amphibians._\n\n### ON THE TRAIL\n\nThe Columbia National Wildlife Refuge is a land of imposing basaltic coulees within the heart of the Columbia Plateau. Despite receiving less than 8 inches of rain a year, the refuge is littered with lakes and marshes thanks to seepage from surrounding reclamation and irrigation projects. Its canyons, lakes, wetlands, and sagebrush-steppe environment provide important habitat for a wide array of species. Located along the Pacific Flyway, the refuge is a stop-over and wintering ground for many migratory birds, including thousands of lesser sandhill cranes. Visit in fall and spring for the best bird-watching. Most of the refuge is within the Drumheller Channels, a national natural landmark within the Channeled Scablands, which were formed by ancient cataclysmic floods. Both nature and humans have left a large imprint here, benefiting scores of avian residents.\n\nHead south on the wide and well-groomed trail, soon coming to a kiosk. Then cross Crab Creek (elev. 850 ft) on a bridge and scan the shorelines cloaked in reeds and cattails for songbirds and waterfowl. Crab Creek used to be an ephemeral stream, but thanks to constant seepage, it runs yearlong. Take time to read the interpretive signs along the way.\n\nAt 0.4 mile, the trail splits. Go left\u2014you'll be returning right. Follow the rose-lined path along the creek. Depending on time of year, a small waterfall may be flowing into the creek from the canyon wall to the east. At 0.6 mile, come to another junction. Right leads back to the trailhead\u2014head left first, through thick riparian vegetation lining the bottom of the coulee. Mosquitoes can be fierce here in spring and early summer. While you're swatting at them, remember that they feed all of those birds and amphibians in the refuge.\n\nAt 0.9 mile, the trail climbs some steps to travel along a sage-shrouded bench (elev. 870 ft) above the creek bottom. Enjoy good views of the coulee and Marsh Lake to the south. At 1.3 miles, reach the trailhead (elev. 860 ft) for the Frog and Marsh Lake Trails (Hike 95). Continue farther or return to your trailhead and save these great trails for another visit.\n\n  Frog Lake\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 3 miles | 235 feet\/1055 feet | Year-round\n\n**Maps:** USGS Corfu, USGS Soda Lake; **Contact:** Columbia National Wildlife Refuge, (509) 546-8300, www.fws.gov\/columbia; **Notes:** Dogs permitted on-leash; **GPS:** N 46 56.207 W 119 14.667\n\n  _**The lake isn't much\u2014in fact it may not be at all\u2014but the views from the basalt butte beyond it are really good! One of three interconnecting nature trails within the 30,000-acre Columbia National Wildlife Refuge, this one offers the most variety as it rambles through riparian habitat and sagebrush-steppe and roams across rim-rock cliff tops.**_\n\n### GETTING THERE\n\nFrom Spokane, take I-90 west to exit 179 in Moses Lake. Head south on State Route 17 for 2 miles, turning right onto Road M SE. Follow it for 6.4 miles, turning right onto SR 262. Continue west for 2.4 miles, turning left (directly across from large boat launch and just before reaching the O'Sullivan Dam), into the Columbia National Wildlife Refuge. (From Ellensburg, take I-90 east to exit 137. Then follow SR 26 for 25 miles east, turning left onto SR 262. Proceed 17.7 miles to the refuge road.) Follow this gravel road south, passing a spur to Soda Lake Campground, and come to a junction at 2.2 miles. Turn right and bear left in 0.2 mile. Pass the Crab Creek trailhead in another 0.4 mile, and come to a junction with Morgan Lake Road shortly afterward. Turn left and reach the trailhead (elev. 860 ft) in another mile (3.9 miles from SR 262).\n\n_Co-author Craig Romano checks out the basalt butte above Frog Lake._\n\n### ON THE TRAIL\n\nFrom the trailhead kiosk two trails diverge. The trail left heads north along Crab Creek (Hike 94). The trail straight drops off the small bench you're on, leading to the Frog Lake and Marsh Loop Trails. Go straight and walk across an earthen dam (elev. 840 ft), one of several responsible for the nearby large wetland ponds teeming with birdlife. The refuge is a bird lover's delight. Between its diverse habitats and being located along the Pacific Flyway, more than 225 species of birds have been recorded on the refuge, including burrowing owls, prairie falcons, and ferruginous hawks. But the refuge's most famous avian resident is its migratory lesser sandhill cranes. Arriving in March and flying in large flocks resembling phalanxes of pterodactyls (and sounding like them), they are spectacular to watch.\n\nAfter a little more than 0.1 mile, come to a junction. The Marsh Loop Trail (an excellent add-on to this hike) heads right. Hop along left on the Frog Lake Trail. After a short walk along a pond dike, the trail heads into the sagebrush-steppe and begins to climb. Be sure to read the interpretive displays along the way. Notice all the canine scat in the tread. Coyotes are abundant here. Other mammals too\u2014look for yellow-bellied marmots and, if you're lucky, Washington ground squirrels, a threatened species.\n\nCross a bridge over a draw and continue climbing, enjoying nice views of the Crab Creek drainage. At 0.7 mile, reach Frog Lake (elev. 920 ft) in a small basin, which will more than likely be dry. Not exactly an amphibian's delight. Follow the trail up a small cleft in the basalt wall behind the lake. The way then bends right, following along basalt cliffs before climbing once again to reach a junction at 1.2 miles.\n\nHere a trail loops 0.6 mile around the 1055-foot mesa. Go either way. The views are wonderful in every direction. Look out over the Drumheller Channels surrounding you. A significant part of the Channeled Scablands, these basalt buttes and canyons were scoured by ancient giant floods. In the 1940s significant change occurred again as the US Bureau of Reclamation's Columbia Basin Project inadvertently created hundreds of lakes and wetlands within the channels, through seepage.\n\nAs you walk along the mesa rim counting lakes below, watch for raptors, swallows, and other birds that make their homes in the cliffs. Close the loop and return to your vehicle once you're content with your nature observations.\n\n### EXTENDING YOUR TRIP\n\nBy all means hike the Marsh Loop Trail while you're here. The trail\u2014actually a wide service road\u2014loops 1.8 miles (with a shortcut option) around large wetland ponds that harbor hundreds of waterfowl and other birds. There are nice interpretive displays along the way too.\n\n  Hanford Reach North\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/3 | 7 miles | 500 feet\/725 feet | Year-round\n\n**Map:** USGS Locke Island; **Contact:** Hanford Reach National Monument, Mid-Columbia River National Wildlife Recreation Complex, (509) 546-8300, www.fws.gov\/hanfordreach; **Note:** Watch for rattlesnakes; **GPS:** N 46 40.630 W 119 26.673\n\n  _**Towering white bluffs, massive sand dunes, pelican colonies, brilliant wild-flowers, and the last free-flowing nontidal section of the Columbia River all help make the Hanford Reach one of the most dramatic natural areas in the state. Follow a rudimentary trail across bluff tops and to shifting dunes. Survey a wild riverbank and a restricted area across the Columbia, where the atomic age was born.**_\n\n### GETTING THERE\n\nFrom Spokane, follow I-90 west to Ritzville. Continue 30 miles south on US Highway 395 to its junction with State Route 26. Follow SR 26 west for 21 miles to its junction with SR 24 in Othello. Continue west on SR 24 for 16 miles, turning left onto an unmarked gravel road just before milepost 63. (From Ellensburg, follow I-90 east to exit 137, heading south on SR 26 for one mile. Bear right onto SR 243 and after 14 miles turn left onto the 24SW Road. Follow it for 13.7 miles to SR 24, first passing through Mattawa. Turn left and continue 10 miles east to the turnoff right, just past milepost 63.) Pass through a solar-powered gate (closed at night), following a good gravel road 3.9 miles south to a four-way junction. Turn right and continue 1.3 miles to the trailhead (elev. 400 ft) located on the right (before the boat launch at the old ferry crossing), near a locust grove.\n\n### ON THE TRAIL\n\nSince the Hanford Reach became a national monument in 2000 (see \"From Manhattan Project to National Monument\" sidebar), more and more hikers are discovering that what they thought would be a desolate part of the state is actually thriving with fauna and flora. Thanks to being withdrawn from the public for decades and remaining in a relatively natural state, the Hanford Reach represents one of the last large undeveloped and uncultivated parts of the Columbia Plateau. One of the driest parts of the state (annual rainfall averages 7 inches), the Hanford Reach is a harsh but fragile environment. Tread softly. And be sure you're well prepared with ample water and sun protection.\n\nFROM MANHATTAN PROJECT TO NATIONAL MONUMENT\n\nIn 1943, in the midst of World War II, the US government launched the Manhattan Project, which would forever change the course of history with the birth of the atomic bomb\u2014and forever change the landscape of the lower Columbia River basin. To facilitate the processing of plutonium, a large remote area was needed, with an ample nearby power source. The federal government chose the Hanford Site, an area of more than 428,000 acres mostly in Benton County. Two communities\u2014Hanford and White Bluffs\u2014were condemned, and the little town of Richland was transformed into a government city of 25,000.\n\nOperations at Hanford were expanded during the Cold War to ultimately include nine nuclear reactors and five plutonium-processing complexes responsible for supplying the US nuclear weapons arsenal. As the Cold War dissipated, Hanford's weapons-production reactors were decommissioned, leaving behind significant amounts of radioactive waste and contaminated groundwater. Today the site is one of the nation's largest Superfund cleanup areas. The site still hosts one nuclear power plant as well as numerous scientific research and development labs.\n\nIronically, this massive government project with its large buffer zones ended up preserving large tracts of natural habitat\u2014some of the last significant undeveloped sections of the Columbia Plateau's sagebrush-steppe ecosystem. In 2000, President Clinton invoked the Antiquities Act of 1906 (which President Teddy Roosevelt used to protect the Grand Canyon and other major natural sites) and proclaimed 195,000 acres of the buffer zone around the Hanford Site as a national monument.\n\nAs well as containing rare plants, endemic species, elk herds, and more than 250 species of birds, the monument also contains a 51-mile free-flowing stretch of the Columbia River. The monument is managed by the US Fish and Wildlife Service, and 57,000 acres of it are open to the public. In 2011, Congressman Doc Hastings began procedures to open to the public the section of the monument housing Rattlesnake Mountain. While this could potentially create new hiking opportunities, it may also open the mountain to ORV use, threatening the integrity of this important and shrinking ecosystem.\n\n\u2014 _C. R._\n\nThe unsigned and unofficial trail starts by a post near a grove of locust trees. At first grassy, then more defined, the path heads up an open slope that dazzles with flowers in spring. The impressive White Bluffs immediately come into view. So does the Columbia River. Watch for white pelicans below and swallows along the bluffs. At about 0.5 mile, stay on a path right, staying clear of the steep and prone-to-erosion bluff face. The path can be sketchy, vanishing at times in dunes. Just work your way up and down along the bluff tops, staying away from cliff edges.\n\n_A hiker enjoys a Sahara-like hike across the sand dunes of the Hanford Reach._\n\nEnjoy excellent views of Locke Island below, Rattlesnake Mountain west, and Saddle Mountain north. At about 2 miles, reach impressive dunes that may make you feel like you're in the Sahara. Walk across the dunes, continuing north. While always shifting, some of the higher dunes form pyramidal \"summits,\" topping out at elevations of more than 725 feet.\n\nFrom these vantages more than 300 feet above the river, you have commanding views of the shoreline below the bluffs. Scan it and the wetland pockets between the dunes for deer, coyotes, jackrabbits, and mice\u2014there are three species of the latter: deer, western harvest, and the northern grasshopper mouse.\n\nAt 3.5 miles, the dunes end. While you can continue hiking another mile farther north, paths are practically nonexistent and brush can be thick. Best to return to the trailhead instead, slowly sauntering back across this dramatic landscape.\n\n  Hanford Reach South\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 5.4 miles | 700 feet\/880 feet | Year-round\n\n**Maps:** USGS Locke Island, USGS Hanford; **Contact:** Hanford Reach National Monument, Mid-Columbia River National Wildlife Recreation Complex, (509) 546-8300, www.fws.gov\/hanfordreach; **Notes:** Watch for rattlesnakes; **GPS:** N 46 37.9710 W 119 23.729\n\n  **_Follow an abandoned highway down to the last free-flowing section of the Columbia River. Listen to birdsong and to cottonwood leaves bristling in warm afternoon breezes\u2014and to the heavy machinery across the river that's cleaning up the contaminated remains of the world's first plutonium production reactor. Then explore the canyons and fluted ridges of the White Bluffs, a dramatic badlands of sandstone that gives off a muted glow in the hot sun and in spring comes to life in a dazzling carpet of wildflowers._**\n\n### GETTING THERE\n\nFrom Spokane, follow I-90 west to Ritzville. Continue 30 miles south on US Highway 395 to its junction with State Route 26. Follow SR 26 west for 21 miles to its junction with SR 24 in Othello. Continue west on SR 24 for 16 miles, turning left onto an unmarked gravel road just before milepost 63. (From Ellensburg, follow I-90 east to exit 137, heading south on SR 26 for one mile. Bear right onto SR 243 and after 14 miles turn left onto the 24SW Road. Follow it for 13.7 miles to SR 24, first passing through Mattawa. Turn left and continue 10 miles east to the turnoff right, just past milepost 63.) Pass through a solar-powered gate (closed at night), following a good gravel road 3.9 miles south to a four-way junction. Continue straight for another 4 miles to road's end and trailhead (elev. 880 ft) at an overlook.\n\n### ON THE TRAIL\n\nPass a gate and follow an old paved road south. The road was closed when the US government, during World War II, chose the surrounding area to host a massive plutonium-processing complex and several nuclear reactors. The towns of Hanford and White Bluffs were condemned and evacuated. All that remains of them are a schoolhouse and several roads and side-walks. As you saunter down this road, try to imagine what life was like for those two rural communities on the Reach in 1942\u2014and how quickly life changed when the Manhattan Project went into effect in 1943 (see \"From Manhattan Project to National Monument\" sidebar).\n\nIn 2000, land use on the Reach changed again when President Clinton declared 195,000 acres of the buffer zone around the Hanford site a national monument, permanently protecting the last free-flowing nontidal stretch of the Columbia and some of the last large undisturbed tracts of sagebrush-steppe in the state. The Reach is a harsh but delicate environment; walk softly and be sufficiently prepared for extreme weather. Fall and spring can be delightful times to explore the area.\n\nFollow the old road downward, taking in excellent views of the White Bluffs and subsidiary bluffs and dunes. Look for white pelicans on the river's islands. Look out across the flats housing the Hanford complex and west to Rattlesnake Mountain (also within the monument and currently closed to public entry) and north to Saddle Mountain (within the monument and open to the public). On clear days you can see Mount Rainier hovering in the distance. Heat can be intense here\u2014so too the winds. Notice the old guard railings being swallowed by sand.\n\nAt 1 mile, just beyond a gully to the left and guardrail to the right, and just before the road drops through a cut to the river, locate a faint trail (elev. 590 ft) heading left across a grassy flat. Take it, traversing a level bench. Round a gully and at 1.5 miles pass a spur trail leading to the right, to the road. Continue straight on a now-obvious trail along a ridgeline of sorts. To the right, enjoy sweeping views across the Columbia River; to the left, an isolated valley comes into view, backed by bigger and higher bluffs.\n\nCrest a 625-foot high point and then drop a little before steeply climbing, reaching a 750-foot high point on the ridge with commanding views at 2.1 miles. Continue south another 0.3 mile, dropping into a small gap (elev. 650 ft) and reaching a junction. You can continue hiking along the ridge straight if you'd like. The suggested route is to head right 0.4 mile, descending off the bluff and returning to the road (elev. 400 ft).\n\nWhen you reach the road, the way left shortly comes to a gate and is an alternative starting point near some transmission lines. Turn right instead to head back to your starting point. Here, at near river level, watch for cormorants fishing and terns diving for fish. Watch for raptors too.\n\n_The White Bluffs make for a striking backdrop against the Columbia River._\n\nEnjoy a nice walk along the base of the bluffs. Notice the locust groves, remnants of the area's agricultural past before being transformed into an atomic energy center. Eventually you'll leave the riverbank and begin climbing again. At 4.4 miles, pass a familiar trail junction. From here it's 1 more mile and 300 feet of climbing back to your vehicle.\n\n### EXTENDING YOUR TRIP\n\nYou may want to wander (no formal trails) other parts of the national monument. Saddle Mountain and Wahluke Lake offer some decent exploring options.\n\n  Badger Mountain\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*****\/2 | 4.4 miles | 675 feet\/1550 feet | Year-round\n\n**Maps:** USGS Badger Mountain, Friends of Badger Mountain map online; **Contact:** Friends of Badger Mountain, www.friendsofbadger.org; **Notes:** Open to mountain bikes, horses. Dogs permitted on-leash; **GPS:** N 46 14.534 W 119 20.565\n\n  **_Marvel at horizonspanning views, from the sun-baked Hanford Reach to snowy Cascades volcanoes, all from a windswept and wildflower-carpeted mountain at the edge of the Tri-Cities. One of the region's newest parks and trail systems, Badger Mountain is already a classic Washington hiking destination. Three trails ascend this landmark above the Columbia River, allowing for a satisfying loop or a stunning ridgeline traverse._**\n\n### GETTING THERE\n\nFrom Pasco, follow I-182 west to I-82, proceeding east on I-82 to exit 104. (From Yakima, follow I-82 east to exit 104.) Turn left onto Dallas Road and drive 1.8 miles, turning right onto a dirt road. Be sure to follow the middle road of the three that diverge from this spot. Reach the Westgate trailhead (elev. 875 ft) in 0.1 mile. Privy available.\n\n### ON THE TRAIL\n\nThere are three ways to the summit. The Canyon Trail, which starts from a Richland city park on the mountain's northeastern slopes, is the most popular. The Skyline Trail from the east is another way up\u2014and combined with the Sagebrush Trail makes a nice loop with the Canyon Trail. These ways are wonderful and well-hiked and are accessed right from the city of Richland. The approach described here is the preferred route for first-time Badger Mountain hikers and its access is much easier to find for outof-towners.\n\nFollow the wide and well-built Skyline Trail through sagebrush-steppe bordered by orchards. Badger Mountain stands as an oasis of natural habitat in an area rapidly being paved over and converted to agricultural uses. Alarmed citizens feared the loss of this locally prominent peak to development and in 2003 formed the Friends of Badger Mountain, which helped spearhead the creation of the 650-acre Badger Mountain Centennial Preserve. Conservationists and public officials continue to work on expanding the preserve as well as protecting adjacent peaks and ridges through the Ridges to River Open Space Network. There is great potential for an expanded trail system through their efforts.\n\nOn a good grade, wind up the mountain's western shoulder, crossing a service road after about 0.5 mile. Volunteers from the Friends of Badger Mountain, Washington Trails Association, and REI are responsible for constructing this multiuse, nonmotorized trail as well as the hiker-only Canyon Trail. At 0.8 mile, reach a marker denoting the maximum elevation of Lake Lewis (elev. 1250 ft) formed during the Missoula Floods 16,000 years ago (see \"In the Wake of Ice Age Floods\" sidebar).\n\n_The Tri-Cities sprawl out below Badger Mountain._\n\nWhile Badger appears barren from a distance, a walk on this mountain in spring reveals a different story. Wildflowers are profuse: lupine, vetch, balsamroot, phlox, larkspur, fleabane, bluebell, prairie star, hawksbeard, lomatium, and many more. And if you can lift your eyes from the ground, cast a glance or two outward to breathtaking views of the Columbia River just below, all the way to Mounts Rainier, Adams, and Hood in the distance. The Horse Heaven Hills lie to the west, the Blue Mountains east, and Candy, Red, and Rattlesnake Mountains north.\n\nContinue across an open slope of swaying grasses and sweet-scented sage. At 1.4 miles, once again cross a service road (elev. 1500 ft). Now traverse along the south face of the mountain, staying below a handful of communications towers and the peak's 1579-foot summit. At 2.1 miles, reach a junction (elev. 1530 ft) with the Canyon Trail. Turn left, continuing for 0.1 mile to a service road just below the summit tower (elev. 1550 ft). This is a good place to turn around (as the trail descends beyond), after absorbing a wonderful view of the Tri-Cities spread out below.\n\n### EXTENDING YOUR TRIP\n\nFrom Richland's Trailhead Park (elev. 700 ft) at the mountain's eastern base, make a nice 3.3-mile loop by following the recently refurbished Canyon Trail west to the Skyline Trail, then to the Sagebrush Trail, and then back to Trailhead Park. Strong hikers can do all of the Badger Mountain trails in a day for a up-and-over-the-mountain-twice 7.7-mile lollipop loop.\n\n  Chamna Natural Preserve\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 3.6 miles | none\/360 feet | Year-round\n\n**Maps:** USGS Richland, USGS Badger Mountain, Tapteal Greenway Association map online; **Contact:** Tapteal Greenway Association, (509) 637-3621, www.tapteal.org\/pages\/chamna.html; **Notes:** Dogs permitted on-leash. Watch for rattlesnakes; **GPS:** N 46 15.447 W 119 17.211\n\n  **_Wander on miles of trail through a rich riparian zone and wildlife haven right in the middle of the Tri-Cities. The Chamna Natural Preserve protects 276 acres at the confluence of the Yakima and Columbia Rivers. The preserve used to be overwhelmed by illegal dumping and dirt biking, but a coalition of concerned citizens started cleaning up the place in the late 1990s, transforming it into an inviting greenbelt where birds are prolific_.**\n\n### GETTING THERE\n\nFrom Pasco, follow I-182 west to exit 5B. (From Yakima, follow I-82 east to I-182 east and exit 5B.) Exit onto George Washington Way, merging into the left lane and proceeding to the first set of traffic lights. Turn left onto Adams Street, and then immediately turn left onto Aaron Drive. Continue 0.6 mile on Aaron Drive, turning left onto Jadwin Avenue. Proceed 0.2 mile, crossing the interstate and coming to a junction with Carrier Road. Turn right and continue 0.5 mile (follow signs for Chamna Natural Preserve) to the trailhead (elev. 360 ft). Privy available.\n\n### ON THE TRAIL\n\nOne of several preserves and parks spearheaded by the Tapteal Greenway Association, Chamna is an important link in an emerging 30-mile greenbelt along the Yakima River from Bateman Island, at the confluence of the river with the Columbia, to the Kiona Bend in Benton City. Tapteal is the original name of the Yakima River.\n\nThe Tapteal Greenway Association is busy working with government officials and private citizens to create this greenbelt, not only for environmental protection, but also to provide recreational opportunities. The master plan includes a long-distance interconnected trail system. But no need to wait, for there are currently miles of trails in place. The Chamna Natural Preserve alone boasts more than 11 miles of nonmotorized trails.\n\nThe trail system is well marked. Hike as long and as much as you'd like, from a quick lunch-break stroll to an all-day, leave-no-tread-untouched expedition! The hike recommended here travels the periphery of the preserve and can be shortened (or lengthened) at will along the way.\n\nStarting on the River Trail, head east. The Yakima River soon comes into view. The plain you're hiking across was known to the Cham-na-pam peoples as Chem-na. It was the site of a Catholic mission before it was farmed by early settler families. More recently, volunteers have removed more than sixteen tons of trash and Chamna is once again becoming a vibrant ecosystem.\n\n_A young hiker looks for wildlife along the River Trail in Chamna Natural Preserve._\n\nSoon come to the first of many junctions, this one with the Jack Rabbit Trail. Stay right here and at the next several trail and service-road junctions, remaining on the River Trail. Pass benches for resting and watching kingfishers and waterfowl. Come upon old foundations and irrigation ditches. Silver maples introduced from the eastern United States and Russian olives from Asia line the way. While both are nonnative, certain native wildlife species have adapted to and benefited from these trees.\n\nAt about 1.3 miles, the River Trail ends at an old service road. Turn right and access the 0.8-mile Peninsula Loop Trail, continuing east along the river and then looping back west to the service road. Look for beavers, otters, deer, and coyotes. Did you see any ospreys? Now walk the old service road north to either the Sage Trail or the more direct Chamna Trail (passing the Midpoint Trailhead, an alternative starting point near the water-treatment plant) back to the trailhead, for a grand loop of about 3.6 miles.\n\n### EXTENDING YOUR TRIP\n\nSample the other trails on the preserve as well as the other nearby Tapteal Greenway parks and preserves. The Duportail Trail leads 2.3 miles north from Chamna to Richland's 236-acre W. E. Johnson Park, with its several miles of trails.\n\n  Amon Basin\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n*\/1 | 2.3 miles | 50 feet\/525 feet | Year-round\n\n**Map:** USGS Badger Mountain; **Contact:** Tapteal Greenway Association, (509) 627-3621, www.tapteal.org; **Notes:** Dogs permitted on-leash; **GPS:** N 46 12.981 W 119 15.155\n\n  **_One of the last large undeveloped parcels remaining within the Tri-Cities, Amon Basin consists of old-growth sage and riparian sagebrush-steppe\u2014crucial habitat for badgers, river otters, and black-tailed jackrabbits. The Tapteal Greenway Association has been developing trails within the basin and advocating for its protection. Hike this threatened areaand decide if you'd like to see it paved over or forever protected as a natural area_.**\n\n### GETTING THERE\n\nFrom Pasco, follow I-182 west to exit 5A onto State Route 240. Continue east on SR 240 for 1.5 miles to the Columbia Park Trail exit. Turn right (west) onto Columbia Park Trail and continue 0.6 mile, turning left onto Leslie Road. Follow it 1.9 miles south, turning left onto Broadmoor Street (0.7 mile beyond the Gage Boulevard intersection). (From Yakima, follow I-82 east to exit 109. Turn right onto Badger Road and proceed 0.2 mile, turning left onto Leslie Road. Continue 1.5 miles, passing the southern trailhead at 0.6 mile, and turn right onto Broadmoor Street.) Follow Broadmoor Street for 0.6 mile to Claybell Park and the trailhead (elev. 475 ft). Privy available.\n\n### ON THE TRAIL\n\nFrom the east end of the parking lot, follow the blocked roadway south, quickly coming to a junction. You'll be heading right on the wide trail into the 100-acre Amon Basin Nature Preserve. Much of the land to the southeast of where you are standing was approved in 2013 to begin sprouting more than four hundred houses, seriously compromising the ecological integrity of the existing preserve and forever diminishing the prospects of what the Tapteal Greenway Association (TGA) envisions as a Central Natural Park for the Tri-Cities. The TGA has been working with the Washington Department of Fish and Wildlife, the Trust for Public Lands, and other agencies and citizens trying to secure $2 million to purchase the 119-acre parcel slated for development. TGA continues to fight to protect this area despite the major recent setbacks.\n\nWalk the wide trail west along the demarcation of natural sagebrush-steppe (or new house lots) and the manicured lawns of Claybell Park. Several parallel and diverging trails lead from this path into the sage and you may want to explore them, although they may be confusing to follow. At 0.2 mile, turn left on a wide path along the sewer line, paralleling the West Fork Amon Creek. The Amon Creek corridor is the last natural connection within the Tri-Cities between the Columbia River and the basalt ridges to the west. Like nearby Little Badger Mountain hovering over this basin, development pressure is great here, threatening to turn this entire locale into housing and pavement. Not good for the resident jackrabbits, badgers, and more than 150 species of birds.\n\n_Amon Basin consists of rich riparian habitat threatened by development._\n\nAt 0.4 mile, intersect a wide east\u2013west trail. Continue south along the sewer line through rows of recently planted native species, compliments of the TGA. At 0.5 mile, come to a pump house and more trail options. The wide sewer-line path veers right, crossing the creek to terminate on Leslie Road near the south trailhead. It can be followed for an alternative loop. The path left heads across sage into the heart of what will either be a grand park or a grand development. Continue south along the irrigation retention pool, coming to an easy-to-miss junction at 0.6 mile.\n\nYou'll be returning on the trail right, so keep hiking straight uphill to a junction (elev. 525 ft) with an old road at 0.7 mile. Turn right and on a near level track enjoy excellent views of the Amon Creek drainage below and Little Badger Mountain to the west. At 1 mile, just before a bench, come to a junction with a trail leading down to the creekside trail you'll be returning on. Continue straight on the old road, coming to the BPA service road at 1.1 miles.\n\nTurn right and within a few hundred feet come to a trail junction. The road continues straight a few hundred more feet, crossing Amon Creek and reaching the south trailhead located off of Leslie Road (an alternative starting point). Head right on the trail along a lovely wetland bursting with blackbird song. The way weaves around and over bluffs along the wetland's east shore, providing excellent bird-watching.\n\nAt 1.3 miles, come to the first of two viewing platforms. The second one is 0.1 mile farther, just before a junction with the way leading right back to the old road. Stay left and continue on a grassy bluff, eventually dropping down to creek level. Notice all of the beaver sign. At 1.6 miles, return to a familiar junction just south of the retention pool. Turn left and retrace your steps 0.7 mile to Claybell Park.\n\n### EXTENDING YOUR TRIP\n\nExplore some of the radiating trails if the preserve has been successfully expanded.\n\n  Bateman Island\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 2.4 miles | 20 feet\/370 feet | Year-round\n\n**Map:** USGS Kennewick; **Contact:** Richland Parks and Recreation, (509) 942-7529, <http:\/\/richlandparksandrec.com>; **Notes:** Dogs permitted on-leash; **GPS:** N 46 14.288 W 119 13.536\n\n_Bateman Island is connected to the mainland by a tree-lined causeway._\n\n  _**Hike across a small causeway to a 160-acre island in the Columbia River. The Yakima River flows into the Columbia here, creating a delta rich with wildlife\u2014and surrounded by one of the fastest-growing metropolitan areas in the country. Enjoy good views to the west of the sage-covered hills and mountains flanking the Tri-Cities and to the east the stately homes lining the Columbia. Embrace the wind, the sun, and the West's grandest river from this easy and interesting hike in the heart of the Tri-Cities.**_\n\n### GETTING THERE\n\nFrom Pasco, follow US Highway 395 south across the Columbia River into Kennewick, bearing right onto State Route 240. Continue 4 miles west to the Columbia Center Boulevard exit and turn right. (From Yakima, follow I-82 east to I-182 east and take exit 5A. Continue 2.7 miles east on SR 240 to the Columbia Center Boulevard exit and turn left.) Proceed 0.3 mile (0.4 mile if coming from Yakima) to the Columbia Park Trail and turn left, driving 0.1 mile to Wye Park and the trailhead (elev. 370 ft). Privy available.\n\nSCOUTING TRAILS IN THE TRI-CITIES\n\nNearly the entire length of the Columbia River within Kennewick, Pasco, and Richland is graced with paved trails, making the Tri-Cities a wonderful place to bring your bike or walking and running shoes. The bulk of this trail system consists of the Sacagawea Heritage Trail, a 23-mile lollipop loop that travels through all three cities and across two of its vehicle bridges. It's named for the young Lemhi Shoshone woman who, with her infant son, accompanied Lewis and Clark as a scout and interpreter. Sacagawea visited the area on October 16 and 17, 1805, on the expedition's way to the Pacific. They made camp at the confluence of the Snake and Columbia Rivers at what is now Sacajawea State Park.\n\nThe heritage trail begins at the state park and travels north along the Columbia through Pasco, before crossing the river on the I-182 bridge. Here you can veer north along the Columbia on the 7-mile Richland Riverfront Trail. The Sacagawea Heritage Trail continues south through nature preserves on the Yakima River delta and then on through Kennewick's sprawling Columbia Park, before crossing the Columbia on the cable bridge and returning to Pasco. There are lots of wonderful interpretive sites, displays, and sculptures along the way.\n\nAt the 284-acre Sacajawea State Park, you can visit the Sacajawea Interpretive Center as well as one of the seven interpretive displays that make up the Confluence Project, which was commissioned for the bicentennial of the Lewis and Clark Expedition. Designed by famed Chinese American artist Maya Lin, these outdoor displays located at seven major confluences draw on history, Native American lore and culture, and from the diary entries of both Lewis and Clark.\n\nNote that the state park and the trail have two different spellings of the scout's name. This reflects a pronunciation controversy. While the state park contains the traditional spelling, pronounced sack-uh-juh-WEE-uh, the heritage trail represents the traditional pronunciation, tsa-caw-gaw-WEE-aw, derived from the Hidatsa words for bird ( _cag\u00e1\u00e0ga_ ) and woman ( _m\u00ed\u00e0_ ) for which Sacagawea was named.\n\nFor more information about the trail, visit the Tri-Cities Visitor and Convention Bureau \"Friends of Our Trail\" page (www.visittri-cities.com\/visitors\/heritage-&-eco-tourism\/friends-of-our-trail).\n\n\u2014 _C. R._\n\n### ON THE TRAIL\n\nBefore dropping 20 feet down the riverbank to Bateman Island, read the informative sign at the Wye Park parking lot. There's a lot of history and birdlife waiting for you on that small island. Cross the paved 23-mile Sacagawea Heritage Trail (see \"Scouting Trails in the Tri-Cities\" sidebar) and pass a gate at the entrance to the causeway. Bateman Island was farmed from the 1870s to the 1950s, and you'll see plenty of evidence of this\u2014old roads, foundations, nonnative trees. A fire swept the island in 2001, and you'll see evidence of that too.\n\nSoon after reaching the island, a side trail bears right. Many of these trails are brushy and unmaintained. It's best to stay on the old farm roads that make up this loop. At 0.3 mile, bear left at a junction (you'll be returning on the old road to your right). Continue left on the south side of the island, through high reeds and grasses and groves of locust trees. Pass thickets of dogwoods and Russian olives too. Stop occasionally to hear birdsong against the background noises of the surrounding urban area.\n\nIgnore side trails and stay on the wide old road. At 0.8 mile, pass an old foundation and a handful of catalpa trees, native to the American South and often referred to as cigar trees after their long, bean like seedpods. At 1 mile, come to a junction near a nice beach. Stay straight and venture 0.2 mile to the northern tip of the island, taking in good views of the I-182 bridge and Badger, Candy, and Rattlesnake Mountains. Lewis and Clark visited the island in October 1805, the farthest up the Columbia River they explored after paddling down the Snake River.\n\nReturn to the junction and follow the road-trail east across open fields. It soon bends south, passing through burned and recovering forest. Bear right at a junction at 1.6 miles, rounding a wetland flush with avian activity. At 1.9 miles, bear right again, returning to the main trail in another 0.2 mile. Turn left and cross the sumac-lined causeway once more, returning to your vehicle in 0.3 mile.\n\n### EXTENDING YOUR TRIP\n\nStretch your legs further by walking along the Sacagawea Heritage Trail. Nearby Columbia Park is a well-shaded, well-liked, and lovely park for hiking, running, cycling, and lethargically whiling away the day.\n\n  Burbank Slough Wildlife Trail\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/1 | 2.8 miles | 25 feet\/355 feet | Year-round\n\n**Maps:** USGS Humorist, refuge brochure **Contact:** McNary National Wildlife Refuge, (509) 546-8300, www.fws.gov\/mcnary; **Notes:** Partly wheelchair-accessible. Dogs permitted on-leash. Watch for rattlesnakes; **GPS:** N 46 12.070 W 118 59.588\n\n  _**More than 250 bird species frequent the McNary National Wildlife Refuge. The Burbank Slough Wildlife Trail is a good place to start looking for them. From the refuge's new environmental education and administrative center, head out on this easy and inviting shoreline trail. Be sure to visit the native plant garden; children will enjoy the on-site teepee.**_\n\n### GETTING THERE\n\nFrom the junction of US Highway 395 and I-182\/US 12 (exit 14) in Pasco, follow US 12 4.4 miles east to a junction with SR 124 (shortly after the Snake River Bridge). Continue 1.2 miles east on US 12, turning left onto East Humorist Road. After 0.1 mile, turn left (north) onto Lake Road and proceed 0.3 mile to the trailhead at McNary National Wildlife Refuge headquarters and education center (elev. 350 ft). Privy available.\n\n### ON THE TRAIL\n\nBe sure to grab a pamphlet at the parking lot kiosk before you start exploring. You may want to snoop around the environmental education center too, before taking to the trail. Opened in 2009, this facility has been a real boon to area schoolchildren, helping them bond with the outdoors. The nicely displayed and labeled native plant garden is a great way to become familiar with the flora of the lower Columbia Basin. Kids will enjoy the animal tracks in the pathway.\n\n_The Burbank Slough is an old river oxbow that teems with birdlife._\n\nThen head out 0.2 mile on a paved path to the bird blind on Burbank Slough (elev. 340 ft). How many red-winged and yellow-headed blackbirds do you see in the reeds and tules? Any teals, shovlers, canvasbacks, or scaups on the water? How many mallards? More than half of the mallards that use the Pacific Flyway winter in and near the refuge. The refuge was established in 1956 to replace habitat lost downstream to the McNary Dam. It consists of more than 15,000 acres within several units, including the one here that protects the long Burbank Slough.\n\nContinue on a grassy jeep track, heading west along the slough and at the edge of a cornfield. Human activity has greatly altered this landscape, changing drainage patterns and introducing exotic species, such as the prolific Russian olive. But that riparian shrub has actually benefited some native species, such as magpies that build their nests in them.\n\nAt 0.6 mile, a spur heads out to the water's edge. Just beyond is a junction with a small loop trail near some big Chinese elm trees. You'll return left\u2014so head right on sandy tread, soon coming to a small bridge. At 0.9 mile, near a nest platform, come to a junction with the loop. But first head right, along the northern shore of the slough. Look for burrowing owls\u2014they nest here\u2014and prickly pear cactus, which provides fruit favored by many refuge birds and animals.\n\nAt 1.3 miles, the trail ends at a gate near Lake Road (elev. 355 ft). Enjoy a good view of the eastern end of the slough and out to the towered Jump-off Joe, a peak across the Columbia River. Traffic and no shoulder make it inadvisable to walk the road back to the refuge center. Besides, you have the loop still left to hike, so double back 0.3 mile to the previous junction and continue straight.\n\nHike past sand dunes and patches of sweet-scented sage bushes, their trunks blotched with red lichen. And angle around wetland pools shaded by cottonwoods. Look for harriers above and amphibians and reptiles below. At 2.1 miles, return to the main trail. From here it's 0.7 mile back to the trailhead. If it isn't too hazy out, you should be able to see the Blue Mountains in the distance to the east. If it's early morning or evening, you should be able to see plenty of birds on the way back to your vehicle.\n\n### EXTENDING YOUR TRIP\n\nHike the 4-mile horse trail along the Walla Walla River in the Wallula Unit of the refuge. Access it from Madam Dorian Park, located about 10 miles south on US 12.\n\n  Juniper Dunes Wilderness\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/2 | 2 miles | 200 feet\/1000 feet | Mar\u2013May\n\n**Map:** USGS Levey NE; **Contact:** BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane\/index.php; **Notes:** Access is via private land. Southern approach not recommended due to poor roads, changing landownership stipulations. Northern approach recommended, only permissible Mar 1\u2013May 31. No overnight parking. Respect private property. Wilderness trail, mechanized equipment prohibited. Pack sufficient water. Watch for rattlesnakes; **GPS:** N 46 25.721 W 118 49.518\n\n  **_Enclosed by fences and containing no mountains, nolakes, no rivers, and practically no trails, Juniper Dunes is an anomaly among our state's wilderness areas. Surrounded by agricultural lands and adjacent dune areas ravaged by off-road vehicles, the 7140-acre Juniper Dunes Wilderness protects the state's largest remaining natural groves of junipers and some of its biggest dunes. And while this landscape may appear harsh, it's actually a pretty sensitive environment\u2014one harboring a plethora of fauna and flora._**\n\n### GETTING THERE\n\nFrom Spokane, follow I-90 west to exit 220 in Ritzville, continuing 14 miles south on US Highway 395. Take the Lind exit and follow SR 21 24 miles south to Kahlotus. Turn left onto SR 260, and after 0.2 mile turn right onto SR 263. Follow it for 0.7 mile, bearing right onto the Pasco\u2013Kahlotus Road. Continue 16.5 miles south on this good road, turning right at the Star School District House onto Snake River Road. (From Pasco, follow US 12 east, exiting onto the Pasco\u2013Kahlotus Road. Follow it 24 miles north, turning left at the Star School District House onto Snake River Road.) Follow Snake River Road 3.4 miles west, turning left onto graveled Blackman Ridge Road. Continue 2.4 miles, turning left onto graveled Joy Road and driving 2 miles to the road's end and trailhead (elev. 800 ft).\n\n### ON THE TRAIL\n\nThis hike begins on private land owned by the Juniper Dunes Ranch. Access is only from March 1 until May 31 and only during daylight hours. Please respect all posted rules and close all gates. The owners can deny access at any time, so it's important to be a good guest on their land. The access window is short, but it's during the spring months when temperatures aren't too extreme and the dunes are awash in wildflowers.\n\nFrom the trailhead you can see the dunes rising in the immediate distance. Walk through a gate, crossing a small corner of the ranch, and within 0.2 mile come to another gate. Pass through it and enter the 7140-acre wilderness area, the only one within Washington administered by the Bureau of Land Management and the only one completely enclosed by fences. The fences ensure that off-road-vehicle riders on adjacent BLM-administered dune lands don't encroach upon this protected environment. The wilderness still sports scars from ORVs that traversed it before it became protected in 1984.\n\n_The Juniper Dunes Wilderness contains one of the largest dune complexes in the state._\n\nTrails of sorts traverse the dunes, but generally the exploring is cross-country across what can be a forbidding land when temperatures soar. Pack plenty of water and sunscreen and note markers so as not to get lost. If you do get disoriented, you'll eventually come to a fence line, which you can follow back to the trailhead. It's not a bad idea to have a GPS unit on hand.\n\nThe dunes are fascinating to explore. Winds sculpt beautiful patterns in them. Check out parabolic mounds and sandy bowls. Lizards and small mammals such as pocket gophers and kangaroo rats leave their signatures in the sand. Bigger mammals too\u2014like badgers, coyotes, bobcats, and deer. Look for flowering plants in spring: sandwort, milk vetch, prickly pear cactus, penstemon, balsamroot buckwheat, larkspur, and many others. And the dunes support rabbitbrush, wheatgrass, ricegrass, and of course the area's namesake western junipers.\n\nFrom the wilderness boundary, follow a path of sorts 0.3 mile up a sprawling dune (elev. 1000 ft) that rises well over 150 feet above the adjacent farmland. Views are good of the Sahara-like terrain as well as of the Saddle Mountains to the north and the Blue Mountains to the southeast.\n\nDrop down, passing by grassy pockets and continuing west to some nice juniper groves at about 1 mile. These trees are adapted to dry habitat, so this area's 8 inches of annual rainfall suits them just fine. This is a good turnaround point, giving you a nice taste of this wilderness. However, the biggest junipers are located farther to your south, if you feel inclined to locate them.\n\n  Z Lake\n\nRATING\/DIFFICULTY | ONE-WAY | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n**\/3 | 3.5 miles | 275 feet\/2310 feet | Mar\u2013Dec\n\n**Maps:** USGS Rocklyn SW, BLM Spokane District Telford Recreation Area map; **Contact:** Washington Department of Fish and Wildlife, Swanson Lake Wildlife Area, (509) 636-2344, www.wdfw.wa.gov\/lands\/wildlife_areas; **Notes:** Discover Pass required. Open to mountain bikes, horses. Range area. Watch for rattlesnakes, ticks; **GPS:** N 47 36.774 W 118 24.029\n\n  _**This long, skinny rimrock lake with a crook and narrows in the middle was out-of-sight and off-limits on private land for decades. It doesn't even have an official name. Locally known as Z Lake, the area has gradually gained attention since being acquired by the Washington Department of Fish and Wildlife and added to the 21,000-acre Swanson Lakes Wildlife Area. The area merges with the Bureau of Land Management Telford Recreation Area. One study pegged Z Lake as the most productive habitat for aquatic invertebrates in the region, luring walk-in anglers to cast for the few but plump trout. The management priority is protecting wildlife habitat, but cattle are still allowed to graze here\u2014and they make most of the trails. Explore this area wearing sturdy boots.**_\n\n### GETTING THERE\n\nFrom Davenport, drive 13.5 miles west on US Highway 2. Just west of the highway rest area, turn south on Telford Road. Drive 7.5 miles to the trailhead parking area (elev. 2300 ft) at Whittaker Lake Road.\n\n### ON THE TRAIL\n\nThis hike can be done as an out-and-back from either the north or south trailhead. It's described here as a one-way hike from the north trailhead, easily accomplished by leaving a vehicle or bicycle on Telford Road, just 1.5 miles along the road from your starting trailhead.\n\nGo through the gate and head west on Whittaker Lake Road (closed to unauthorized motor vehicles). At 0.5 mile, continue straight where the gravel portion of the road bends north. Soon, a bit of the long north\u2013south ribbon of a lake will come into view below the basalt cliffs in the distance. This is a good point to pause with binoculars. Mule deer, coyotes, and other critters often can be seen taking cover when there's movement on the horizon\u2014including you.\n\nContinue down to a fence corner and go through the gate. There's no defined trail at this point. Continue straight west, weaving through the mounds on game trails. Rugged boots are recommended for hiking because of the basalt scree that must be negotiated through the flats.\n\n_A dogleg gives narrow Z Lake its name._\n\nHike to the water and then turn south. It's easy to find your own path along the east shore above the lake. Pass the old windmill tower and the solar panels that power the lake aerator, which helps provide oxygen for trout during the winter freeze-up.\n\nA little farther south, an aluminum rowboat has traditionally been left for anglers to use. Check it out if it's still there. Use it if you like, but bring it back off the water and turn it upside down with the oars inside\u2014just as you should have found it.\n\nSoon you'll come to the zigzag feature that gives the lake its name. Turn west and hike up into the rocky outcropping where the lake makes two right-angle turns. This is a great spot for a break and watching up and down the lake: look up for kestrels, marsh hawks, and opsreys; and look down to the water for waterfowl, turtles, and fish.\n\nContinue south along the shoreline. The walking gets easier. At the south end of the lake (can be wet in spring), eventually bend right to hit a ranch road. The way goes right briefly and dead-ends at the lake.\n\nTo finish the hike, continue south on the road. At an old corral area near some tall trees, follow the road as it bends left past a spring and eastward to the south trailhead and limited parking at Telford Road.\n\n### EXTENDING YOUR TRIP\n\nCross-country hikers can circumnavigate the lake. The west side has higher bluffs for loftier views.\n\n  Twin Lakes\n\nRATING\/DIFFICULTY | LOOP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 10 miles | 830 feet\/2250 feet | Mar\u2013Dec\n\n**Maps:** USGS Rocklyn SW, USGS Swanson Lakes, BLM Spokane District Twin Lakes Recreation Area map; **Contact:** BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane; **Notes:** Open to mountain bikes, horses. Range area. Watch for rattlesnakes, ticks; **GPS:** N 47 31.795 W 118 30.352\n\n  **_Get your fix of wide-open spaces in this hike that links Channeled Scablands water features in Lake Creek Canyon with the surrounding sage and grazing lands. Starting from a fishing lake and small campground, follow old jeep tracks through a portion of 14,000 acres of range and wet-lands managed by the Bureau of Land Management for recreation and wildlife. Cattle are allowed to graze here among the deer and other wildlife. Spring is prime time for hiking, as the sagebrush-steppe blooms and migrant waterfowl pass through._**\n\n### GETTING THERE\n\nFrom its junction with US Highway 2 in Davenport, head south on State Route 28. Drive 12.7 miles to Harrington and turn right (west) onto Coffeepot Road. Drive 13.5 miles and turn right (north) onto Highline Road. Drive 1.3 miles and turn right (east) onto the BLM Twin Lakes access road. Drive 2 miles down to the lakeside campground and go past the boat ramp. The trailhead (elev. 1915 ft) is in the second big parking area near the outlet creek on the left. Privy available.\n\n### ON THE TRAIL\n\nThe trail starts at a footbridge across the creek between Upper and Lower Twin Lakes. Cross the bridge and bear right on the south side of Upper Twin. Go through a gate. Gain a little elevation and look down on the lake where anglers come to catch bass, crappie, perch, and trout. Soon the trail bends south away from the lake and heads right and around a grove of aspens. Pass a spring\u2014source of the wet spot producing the aspens.\n\nThe trail works up a small draw onto a broad sagebrush plateau. The area has numerous wildflowers in the spring, but it can be desertlike in the summer. Hot-weather hikers should take a cue from the wildlife and be hiking at sunrise.\n\nAt 1.2 miles, pass through another gate. (For a shorter loop hike, take the road [or trail] on the left that is a few hundred yards farther on.) In late May or early June, you might see bitterroots blooming directly in the trail. At 2.9 miles, the trail skirts the right side of a wetland and trees. Look for wild iris and wild onion blooming in spring. At 3.1 miles, continue straight on the main track at a faint junction. At 3.3 miles, the track turns right around some rock-filled fence-corner anchors. Suddenly the scenery becomes more interesting as the topography breaks up with basalt cliffs along the drainage between Wall Lake and Upper Twin Lake. A few pine trees crop into the picture as the trail drops into the canyon.\n\nAt 3.8 miles, go through a gate and continue down through a wildlife-rich area and then up to a ford over Lake Creek at 4.6 miles. In all but the highest spring water, there are usually enough rocks here to hop across without getting boots too wet.\n\nWhen you reach a fence, go up through the sagebrush to the left and parallel the fence a short way to the walk-through gate. (The road gate usually is locked.) Pass through several more gates on the way toward the deserted buildings of the old Rock Ranch. At the corrals of a formerly bustling cattle operation at 5.5 miles, turn left through another gate toward the house.\n\n_A campground at Upper Twin Lake_\n\nTo continue the loop, head left (west) from the house, up the access road (open to vehicles) and past the metal buildings. At 6.1 miles, go through gate no. 8. Continue to a kiosk at the junction with Reiber Road and go through another gate to get back on a nonmotorized track. Continue west through reclaimed farmland for 1 mile before going through a gate and coming to more interesting native rangeland. At 7.7 miles, bear right at a fork. Pass a seasonal lake in a pasture at 8.2 miles.\n\nAt 8.4 miles, pass through the tenth gate of the trek. At 9.2 miles, the trail intersects the Twin Lakes access road. You can turn left and head directly down to the lake and trailhead, or end the hike on a sweeter trail by turning right on the access road, going 100 yards, and turning left off the road onto a trail. It drops into the Twin Lakes canyon before hooking back to join the access road again at nearly 10 miles. Turn right and follow the access road down to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nFrom the corral and buildings at Rock Ranch, a track heads 1 mile east to Wall Lake, a nice side trip.\n\n  Lakeview Ranch\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n****\/3 | 13 miles | 600 feet\/1800 feet | Year-round\n\n**Maps:** USGS Pacific Lake, USGS Sullivan Lake, BLM map online, www.blm.gov\/or\/resources\/recreation\/site_info.php?siteid=275; **Contact:** BLM Spokane District, (509) 536-1200; www.blm.gov\/or\/districts\/spokane; **Notes:** Open to horses. Partly open to mountain bikes, motorized use. Watch for rattlesnakes. Pack sufficient water; **GPS:** N 47 24.830 W 118 44.474\n\n  **_You'll get more than just a lake view hiking this 12,000+-acre former ranch. Canyons, craters, grasslands, and bluffs await\u2014and lots of wildlife too. Hike one of the longest trails on the Columbia Plateauand with each step through this varied terrain, scenic surprises greet you. The several lakes in the area, including 1.5-mile-long Pacific Lake, have mostly gone dry because of controversial deep-well irrigation that has lowered the vast Odessa Aquifer. Still, the lakes and their basalt cliff surroundings are fascinating flashbacks to a prehistoric time._**\n\n### GETTING THERE\n\nFrom Spokane, follow I-90 west to exit 245 at Sprague. Head for about 13 miles north on State Route 23, turning left onto Mohler Road. After about 10 miles, reach SR 28. Turn left and drive 16 miles to Odessa. (From Ellensburg, follow I-90 east to exit 206. Then drive 18 miles north on SR 21 to Odessa.) Head 2.8 miles north on SR 21, turning left onto graveled Lakeview Ranch Road. Go 3.3 miles and just before a right-angle turn, note an alternate access for a quick walk down to Bobs Lakes. Then continue 1.9 miles on Lakeview Ranch Road to Lakeview Ranch and the trailhead (elev. 1600 ft) on the left behind the barns.\n\n### ON THE TRAIL\n\nAcquired for the public by the Bureau of Land Management in the 1990s, this former working ranch offers miles of roads and trails to explore. The hike described here utilizes part of the 12.9-mile Odessa\u2013Lake Creek (OLC) Trail to travel into the Lake Creek Coulee. That trail begins just north of the ranch buildings\u2014but its first few miles are open to motorized use, posing little interest to hikers.\n\nStart your hike instead by following the old jeep track west from the trailhead. You can make a short side trip north to Lakeview Ranch Crater. This crater, like the nearby and more defined Odessa Craters, was created not by meteor activity but by scouring from Ice Age floods. The Odessa Crater in Texas, however, was formed by a meteor hit.\n\n_A hiker climbs out of a large canyon on the Odessa-Lake Creek Trail_.\n\nTraversing open grasslands teeming with birds and wildflowers (in spring), pass Walter Lake on your left\u2014which may be a dry lake bed. After about 1 mile of level terrain, the path swings into some low rolling hills and comes to a good-sized lake on your right. Pass several more smaller lakes that vary in size depending on the season and amount of recent rainfall. Good opportunities for bird-watching here. The surrounding sage-dotted hills also harbor numerous bird species and mammals\u2014look for jackrabbits.\n\nBLM RANGE LANDS INVITE HIKERS\n\nA new era started in 1987 with 156 acres purchased at the Lakeview Ranch near Pacific Lake north of Odessa. The US Bureau of Land Management\u2014once the runt of land-management agencies in Eastern Washington\u2014began a campaign to build its stature one parcel at a time.\n\nTwo decades later, after a series of land trades, acquisitions, and consolidations, the agency has become a regional giant for wildlife habitat restoration and public access to sagebrush-steppe wild lands. The BLM has increased its Washington landholdings from about 308,000 acres in 1985 to about 446,000 acres. More importantly, instead of being small parcels, scattered and sometimes inaccessible, the acreage is largely consolidated into large tracts in Eastern Washington, especially in Lincoln County. All of it is open to hikers.\n\nBy seeking willing sellers and acquiring an 8000-acre ranch here and a 10,000-acre ranch there, the BLM built a handsome spread where fish and wildlife can be housed and managed on equal or higher terms with livestock. In many cases, the agency has offered lease-back arrangements so ranchers selling land can continue ranging livestock, although the amount of grazing is reduced by up to 60 percent. Hunters, hikers, equestrians, and mountain bikers can enter through gates and travel freely all day through the scablands without stepping off public land.\n\nStandout examples include more than 20,000 acres in the Odessa area near Lakeview Ranch (Hike 106), about 17,000 acres in the Coffeepot\u2013Twin Lakes areas west of Harrington (Hike 105), and about 8000 acres along Hog Canyon and Fishtrap Lakes off I-90 (Hikes 108 and 109). The 14,000-acre Escure Ranch straddling the Adams-Whitman county line south of Lamont, a former sheep and cattle operation, is a public plum that includes 8 miles of Rock Creek, along with Wall Lake (Hike 110).\n\nFor more information, contact the US Bureau of Land Management, Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane.\n\nAt 2.1 miles, reach a junction with the OLC Trail (elev. 1700 ft). It's a jeep track here and open to motorized travel. Don't let that discourage you though\u2014use is fairly light. Turn left and hike the track, coming to a junction at 2.6 miles. The way left is the OLC route. It drops 100 feet to Waukesha Spring along a fence line (private property beyond, so don't think of walking on the paths heading east); then it climbs back up. Skip it, saving 0.6 mile and a small climb. Instead, continue straight on a shortcut that meets back up with the OLC Trail in 0.4 mile.\n\nThen continue right, coming to the end of motorized use at an old rusty combine part at 3.5 miles. The views here are pretty decent east across the small coulee housing Lake Creek and out to distant wheat fields. Now follow the trail along a fence line, climbing higher on a slope of golden grasses. At 4.5 miles, reach a hillcrest (elev. 1800 ft) and begin descending into the coulee. Aside from not losing the sketchy tread (pay attention for trail markers), take care not to twist an ankle in the numerous burrows in the trail. Enjoy good views of imposing basalt cliffs and the wide canyon floor housing Bobs Lakes, a series of shallow bodies of water (or salt flats).\n\nAfter descending a steep draw, reach a gate at 5.8 miles at a bench above the coulee floor. The way turns right along the bench, eventually dropping to the grassy coulee bottom and reaching a bridge over Lake Creek (elev. 1425 ft) at 6.5 miles. For most day hikers, this is a good spot to turn around. But first feel free to explore the canyon.\n\n### EXTENDING YOUR TRIP\n\nMake a loop by walking north along the Bobs Lakes to an old jeep track, reaching the Lakeview Ranch Road in about 2.5 miles. It's then a 2 mile walk north on that road back to your vehicle. Better yet, leave a car at the Odessa trailhead for the OLC Trail (0.3 mile west of Birch Street) and make a one-way journey. From the bridge, the way climbs out of the coulee, passing a spring and good views of the Odessa Towers rock formations. An up-and-down course across grassy hills and sagebrush-steppe leads toward Crab Creek Coulee before following a utility road a short way, then trail again, to reach the trailhead in 6.2 miles\u201412.7 miles from the ranch trailhead. Also, go to the campground area just a few hundred yards northeast of the Lakeview Ranch buildings and hike the north rim of dry but scenic Pacific Lake.\n\n  Crab Creek\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/3 | 6 miles | 320 feet\/1830 feet | Feb\u2013Dec\n\n**Maps:** USGS Harrington SE, BLM Spokane District Rocky Ford map; **Contact:** BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane; **Notes:** Open to horses. Watch for rattlesnakes, ticks. Safest for dogs in late fall or winter. Range area; **GPS:** N 47 18.092 W 118 15.298\n\n  **_Water in a desertlike environment creates a wildlife magnet as Crab Creek flows through this stretch of public land in Lincoln County. Transitions are dramatic, from winter brown to the lush spring greenery that virtually hides the creek in some areas. While the route can be hiked almost year-round, it's especially pleasing as the area blooms with life from March through early May and again in late fall, when ticks and rattlesnakes have retreated._**\n\n### GETTING THERE\n\nFrom I-90 east of Ritzville, take Tokio exit 231 and head north. The road becomes Danekas Road. Follow it about 1.4 miles and turn right on Hills Road (also known as the Harrington\u2013Tokio Road). Drive north over the railway, go 6 miles. Just after crossing a bridge over Crab Creek, pass a parking area and kiosk on the right (upstream side of the road) and turn left. (From Harrington, head south on State Route 23. At the edge of town, turn right toward Ritzville on the Harrington\u2013Tokio Road. Drive 12 miles to the Crab Creek access on the right.) Drive to the end of the large undeveloped BLM camping area and the trailhead (elev. 1825 ft). Privy available.\n\n### ON THE TRAIL\n\nThe trailhead is near a corralled spring. Go through the gate and follow the stock trail downstream. This trail can fade or braid in places, but the route generally heads downstream on the first bench level above the creek. It's much easier to follow from fall through early spring than it is from late spring through summer, when the creekside grass and vegetation leafs out thick.\n\n_A mallard hen distracts hikers from her nearby brood._\n\nBasalt outcroppings rise on the right, forming condo sites for swallows and other nesting birds. The trail soon heads to the edge of the creek, and then it skirts to the right of the first large thicket of wild roses and hawthorns by angling away from the creek and hugging the basalt outcropping.\n\nSoon the creek returns to greet the trail. If the grass isn't too high, you'll see waterfowl. Many ducks hatch here in May and early June. If you see an adult duck splashing downstream in a broken-wing act, just keep hiking. The parent is luring you from the clutch of ducklings hidden in the grass. It will return to its brood after you pass.\n\nThe trail fades in and out in a series of game and stock trails. At 1 mile, pass through a creekside opening in a fence. Although this is classic mule deer country, we have seen whitetails up a draw across the creek at 2.5 miles.\n\nAt 2.7 miles, as the trail fades, the terrain offers an easy angle to the top of a basalt ledge, where you can continue hiking downstream for a change of scenery just above the creek. At 2.9 miles, the creek begins a big sweeping left turn. Angle uphill, keeping the creek in view, for an easy, gradual cross-country climb to the top of the bluffs overlooking the creek.\n\nThe bluff top is a good place for further exploration, or simply pull up a rock and enjoy a snack and the vista of the creek below. Return from here for a round-trip trek of 6 miles.\n\n### EXTENDING YOUR TRIP\n\nFrom the parking area, cross the highway to another trailhead and hike a similar trail along Crab Creek upstream for about 1 mile.\n\n  Hog Canyon\n\nRATING\/DIFFICULTY | ROUND-TRIP | ELEV GAIN\/HIGH POINT | SEASON\n\n---|---|---|---\n\n***\/4 | 5.4 miles | 670 feet\/2200 feet | Mar\u2013Dec\n\n**Maps:** USGS Fishtrap, BLM Spokane District Fishtrap map; **Contact:** BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane; **Notes:** Open to mountain bikes, horses. Range area. Watch for ticks; **GPS:** N 47 21.672 W 117 49.721\n\n  **_Every season has its moment on this showcase in the Channeled Scablands scoured by the great Ice Age floods. March to early May is prime time to catch the blooming arrowleaf balsamroot and other wildflowers in the open ponderosa pine forest and to see the waterfall at the north end of Hog Canyon. Hog Lake is one of just four in the region designated for winter fishing (December 1\u2013March 31), which overlaps with the end and the beginning of hiking season. Aspens brighten the route in October. Deer, coyotes, and other wildlife are active early on summer mornings, which also is the best time to hike the open portions of this route when daytime temperatures soar._**\n\n### GETTING THERE\n\nFrom I-90 about 25 miles west of Spokane, take Fishtrap exit 254 and head south on Sprague Highway. Drive nearly 2.5 miles and turn left on Fishtrap Road. Drive 0.6 mile to a multi-trailhead parking area on the right (elev. 2170 ft).\n\n### ON THE TRAIL\n\nFrom the parking area, walk the paved road 0.1 mile toward Fishtrap Lake Resort. Turn left on the first dirt road. Take the first or second gate on the right through the barbed-wire fence (the gate paths merge in about 100 ft) to begin hiking the single-track trail toward Hog Lake.\n\nThe trail drops into a grassy draw and then climbs the slope on the opposite side and through a fence gate. Take note of the single-track's direction here to avoid confusion on the way back. Soon the trail heads down to the right and quickly changes character as it drops into the ponderosa pines. This area is open to periodic livestock grazing and cattle trails could cause occasional confusion. When in doubt, look for the vertical trail posts the BLM uses to mark the route.\n\nThe trail bends left, levels onto a bench, and contours along Hog Canyon, which is not too deep at this point. Cattails vegetate the canyon bottom, and the wildlife tracks and beauty of the scabland terrain make it easy to overlook the cow pies. The trail then steps down to another broader, more meadowlike bench. At 1.5 miles, pass a little aspen grove that's luscious green in spring and summer, stunning yellow in October, and almost as eye-catching as naked white-barked skeletons for the next five months.\n\n_A scablands waterfall is a highlight of the Hog Lake hike_\n\nThe trail continues a short way on a double-track. Then bear right on the singletrack as it enters the Hog Lake access site. Walk to the boat launch and bear left onto the angler trail along the lake's northwest shore. After a few hundred yards, the user trail angles up toward the rim. It fades as it crosses a short patch of scree near the top but becomes evident again as it follows the edge of the bluff, with great views looking down on the lake and across Hog Canyon. Where the user trail finally peters out above the wide bend in the lake, head left 30 yards or so to the main double-track trail and continue up-lake, although the water will not be in view.\n\nHike a few hundred yards. Just as the double-track enters scattered timber, about 60 yards before it switchbacks up toward the rim on the left, take the cow trail that gently drops to the right. Contour past the first little draw and around a little knob where the trail becomes a more obvious single-track again and climbs a short slope to a ridge. From here, drop down the ridge toward the lake to an excellent viewpoint overlooking Hog Canyon Falls. Best viewing is in late winter or spring, when the runoff is surging. The falls, virtually dry in summer and autumn, is on private land.\n\n### EXTENDING YOUR TRIP\n\nFrom the trailhead gate, walk north on the access road to the old buildings of Folsom Farm.\n\n  Fishtrap Lake\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n***\/2 | **6.4 miles** | 350 feet\/ **2180 feet** | Mar\u2013Dec\n\n**Maps:** USGS Fishtrap, BLM Spokane District Fishtrap map; **Contact:** BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane; **Notes:** Open to mountain bikes, horses. Range area. Watch for ticks; **GPS:** N 47 21.635, W 117 49.844\n\n  _**A trail along old ranch roads runs the length of Fishtrap Lake, a remnant of the Ice Age floods and centerpiece of the Bureau of Land Management's 7000-acre Fishtrap Recreation Area. The sageland scenery is spectacular during spring wildflower blooming and colorful during fall foliage. The lake is stocked with rainbow trout and is especially popular with anglers late April\u2013May. Most anglers concentrate at the north end out of Fishtrap Lake Resort, where patrons from Spokane once came by train to dine and dance. But this hike strides away from the lakeshore, hooking back at the south end of the lake to Farmers Landing, an ideal tranquil lakeshore site for a picnic and water-fowl watching.**_\n\n_Fishtrap Lake from Farmers Landing_\n\n### GETTING THERE\n\nFrom I-90 about 25 miles west of Spokane, take Fishtrap exit 254 and head south on Sprague Highway. Drive nearly 2.5 miles and turn left on Fishtrap Road. Drive 0.6 mile to a multi-trailhead parking area on the right (elev. 2170 ft).\n\n### ON THE TRAIL\n\nFrom the trailhead parking lot, go through the gate and follow the double-track trail that heads south toward a lakeside residence surrounded by trees. When the road reaches a fence around the private property, just walk along the right side of the enclosure and pick up the trail again as it exits the enclosure on the south side.\n\nThe route parallels the shoreline of Fishtrap Lake, but you won't see the water until you gain a little elevation in an open area after hiking 1.5 miles. At 2 miles, the trail forks. (Right goes 1.2 miles to the BLM Ranch House trailhead and the area manager's residence.) Take the left fork, go through a gate, and continue toward Farmers Landing. (If you hiked cross-country to the east, you'd come to the narrows of Fishtrap Lake.)\n\nGo through some timber and past a seasonal wetland on the right. At 2.9 miles, come to a junction in a grove of older pines. (The double-track to the right heads 1.4 miles to the Farmers Landing trailhead.) Head left and hike 0.3 mile to the lakeshore at Farmers Landing. This open spot overlooking the south end of the lake is ideal for picnics. You'll likely be alone, except on the fourth weekend in April when the fishing season opens.\n\n### EXTENDING YOUR TRIP\n\nHorse riders have pioneered some singletrack trails that run north from the BLM Ranch House trail. If you're up for some exploring, give one of them a try, or just head north cross-country from the Ranch House trail. Use a compass to make sure you keep heading north as you skirt scabland ponds and meadows, and you'll eventually hit Fishtrap Road near the trailhead. Other options: Shuttle a bicycle or vehicle to the Ranch House trailhead for a one-way hike of 2.2 miles, or to the Farmers Landing trailhead for a one-way hike of 4.4 miles.\n\n  Escure Ranch\u2013Towell Falls\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/2** | **6.4 miles** | **530 feet\/1565 feet** | **Feb\u2013Dec**\n\n**Maps:** USGS Honn Lakes, USGS Revere, BLM Spokane District Escure Ranch map; **Contact:** BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane; **Notes:** Open to mountain bikes, horses, hunting. Partly open to motorized use. Range area. Watch for rattlesnakes, ticks; **GPS:** N 47 00.856 W 117 56.613\n\n  _**From a ranch house and corrals, wear out your boot soles in more than 14,000 acres of the Bureau of Land Management's Rock Creek Management area, most of which was formerly a working cattle operation called Escure Ranch. This is largely open grazing land, scabbed with basalt outcroppings and mesas\u2014and a river running through it. The ranch can be remarkably receptive or harsh, depending on the day or month. The terrain was scoured by Ice Age floods, leaving scattered lakes\u2014Wall, Turtle, Perch\u2014where raging floods gouged divots between basalt cliffs. Trails, if you need them, are old ranch roads, which are sometimes but not always open to motorized use.**_\n\n### GETTING THERE\n\nFrom I-90 at Sprague, take exit 245 and head south (through town) on State Route 23 toward Saint John and Steptoe. Drive 12 miles from I-90 and, at a sharp left bend in the highway, turn right onto Davis Road. Drive 6.8 miles and turn left on Jordan\u2013Knott Road. Head south 2.2 miles, crossing the bridge over Rock Creek, and turn right into the Rock Creek Management Area. Drive another 2.4 miles on a sometimes rough road to the trailhead (elev. 1460 ft). Privy available.\n\n### ON THE TRAIL\n\nThe trail to Towell Falls starts through the gate near the kiosk and heads south on an old ranch road. This road is open to motorized use roughly from April, when the ground dries, to early June, when it's closed to prevent fires. Wildflowers peak in April and early May. Common wildlife sightings include coyotes, mule deer, and hawks. Rock Creek holds rainbow and brown trout, and some of the ranch lakes hold bass and panfish. Special Washington fishing regulations apply. Keep dogs on-leash to protect them during snake season.\n\n_Rock Creek's Towell Falls at Escure Ranch_\n\nThe route parallels Rock Creek before the stream bends west and away from the road. After hiking 2.8 miles, ascend to a basalt bluff overlooking the creek and affording the first glimpse of Towell Falls in the distance. The route then drops to a small seasonal parking area.\n\nA marker leads you on a faint trail straight toward the larger lower falls. Take the faint path down toward the creek and bend to the right along a small basalt cliff, heading upstream. Skirt right onto an old road cut around a small grove of aspens, and then drop off the bluff onto the scabrock bench that leads to the creek. You can walk to the edge of the upper falls.\n\n### EXTENDING YOUR TRIP\n\nExplore another mile downstream to the south end of the BLM property. For a real workout, add the 8-mile round-trip to Wall Lake. From the Ranch House trailhead, cross the bridge over Rock Creek, follow the road through the old ranch house gates, and continue west up the hill. Follow the vertical trail signs across the upper flats. Pass through four more gates en route to Wall Lake. If you can navigate well with map and compass or GPS, a nifty 11-mile loop can be made by hiking from Wall Lake cross-country (rugged) to Perch Lake and then following an old ranch road southeast, parallel to Rock Creek, a short way back to the trailhead.\n\n## palouse hills\n\n_Palouse River upper falls_\n\nThe Palouse is a fertile farming area that resembles an ocean of waves whipped up in a major storm. The Ice Age floods that scoured the Channeled Scablands deposited rich ripples of silt over about 3000 square miles of Eastern Washington land just north of the Snake River. Those rolling hills have been developed into rich fields of wheat, lentils, and canola, along with thousands of acres seeded to grass under the federal Conservation Reserve Program.\n\nThe Palouse is the darling of landscape photographers trying to capture subtle light, shadows, and textures. Fingers of forest and streams string through the rough seas of farm fields. Images change character hourly with the movement of the sun and seasonally with the different shades of crop ripeness and harvest. Steptoe Butte and Kamiak Butte are prime unfarmed natural-area destinations for overlooking the spectacle from remnant preserves of native grasses and wildflowers.\n\nWhat's the wildest area in the Palouse? The Palouse River and 186-foot-high Palouse Falls are top candidates, but the distinction should likely go to the Washington State University campus in Pullman, home of the Cougars.\n\n  Kamiak Butte\n\n**RATING\/DIFFICULTY** | **LOOP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n***\/2 | 2.9 miles | 800 feet\/3641 feet | Mar\u2013Oct\n\n**Maps:** USGS Albion, Kamiak Butte County Park brochure online; **Contact:** Whitman County Parks and Recreation Department, Colfax, (509) 397-6238, www.whitmacounty.org; **Notes:** Park and picnic area open 7AM\u2013dusk, spring\u2013fall. Campers must stay inside closed gate at night. Park subject to closure if fire danger is extreme. Picnic shelters can be rented. Dogs permitted on-leash; **GPS:** N 46 52.214 W 117 09.187\n\n  _**Kamiak Butte is a natural-area island that rises abruptly from a sea of wavelike Palouse hills. Textures of fertile grain fields below create a stunning landscape. Shadows on the rolling hills change by the hour, sometimes as dramatically as the green-to-gold of the growing season. Because of the sweeping monocultures below, the native flora of the timbered mountain (a more precise term than \"butte\") is especially attractive to wildlife. About 130 bird species have been documented living or pit-stopping in the 298-acre county park, along with several endangered plant species and all sorts of other critters, including white-tailed deer and the occasional moose. This hike leads to the 3641-foot summit of Kamiak Butte, the second-highest point in Whitman County. Bring a wildflower field guide.**_\n\n### GETTING THERE\n\nFrom downtown Colfax, turn east on Canyon Street and continue as it becomes State Route 272 (Palouse Highway) for 5.3 miles. Turn right on Clear Creek Road. Go 8.1 miles and make a sharp right onto Fugate Road (County Road 5100), continuing 0.5 mile. (From Pullman, take State Route 27 north 11.6 miles. Turn left on Clear Creek Road and drive 0.4 mile. Turn left on Fugate Road and drive 0.6 mile.) Turn south into Kamiak Butte County Park and drive to the trailhead (elev. 2900 ft) at the day-use area. Privy available.\n\n_Palouse farm fields look like ocean waves below Kamiak Butte._\n\n### ON THE TRAIL\n\nA map sign marks the Pine Ridge trailhead from the day-use area. The trail heads up a wide path, making several long switchbacks to the top of the ridge. Here you can begin to understand why this island of habitat is designated a national natural landmark for its natural and geologic significance. The cooler, denser north side of the ridge (including some cedars) you just ascended gives way to a dryer remnant grassland prairie habitat facing south, including arrowleaf balsamroot and other plants associated with lower sagelands. Wildflowers bloom here as early as February, peaking in May and June.\n\nKamiak Butte, a name honoring Chief Kamiakin of the Yakama Tribe, can be seen in the distance from this ridge. Steptoe Butte is the prominent peak 15 miles to the northwest. The Blue Mountains can be seen far to the south on a clear day.\n\nExplore the trail that heads left (east) on the ridge spine for a short walk to the park boundary, and then return to the junction, where a few braided trails head southwest. Take the most traveled trail upward and stay near the spine of the ridge. After a long, gradual climb, contour on the south side of a knob and begin dropping to a saddle and junction. Continue left on the short spur to the rocky and sparsely timbered Kamiak Butte summit at 3641 feet. The ridge trail splits around both sides of the summit but merges into one trail. Stretch your legs for another 0.25 mile west to the fence that blocks access to private land and communications towers at the end of the butte.\n\nDouble back to the summit and back to the saddle junction. Bear left and downhill to leave Pine Ridge and continue the loop. The downhill return on the north side of the ridge leads pleasantly through a lusher, wetter habitat. Halfway down, a denser stand of smaller trees indicates where a short-lived ski run was cut in the 1950s. From here to the trailhead, two spur trails drop downhill to the campground.\n\n### EXTENDING YOUR TRIP\n\nSeveral trails wander around the campground, offering more views. Expect to see deer at the forest edges moving in and out of the grain fields early and late in the day.\n\n  Palouse Falls\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n****\/2 | 1.3 miles | 150 feet\/925 feet | Year-round\n\n**Maps:** USGS Palouse Falls, state park map online; **Contact:** Palouse Falls State Park, (509) 646-9218, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Dogs permitted on-leash. Watch for rattlesnakes; **GPS:** N 46 39.835 W 118 13.637\n\n  _**Plummeting nearly 186 feet within a stark canyon of basalt, Palouse Falls is one of the most striking waterfalls in the Pacific North-west. Here the Palouse River thunders through a deep channel that was scoured across the Palouse Hills during the great Ice Age floods. While you can easily view this spectacle of nature from the parking lot, a couple of enticing trails lead along the canyon rim high above the plunging waters\u2014and deep into the canyon to a series of rapids upriver from the awesome falls.**_\n\n### GETTING THERE\n\nFrom Spokane, follow I-90 west to exit 221 in Ritzville. Then drive 41.5 miles south on SR 261, turning left onto Palouse Falls Road. Reach the trailhead (elev. 900 ft) in Palouse Falls State Park after 2.4 miles. (From Pasco, take US Highway 395 north to Connell. Then follow SR 260 east for 25 miles, turning right onto SR 261. Reach the state park turnoff after 8.6 miles.)\n\n### ON THE TRAIL\n\nUpon exiting your vehicle, you'll immediately be greeted by the roar of the Palouse River dropping 186 feet into a plunge pool beneath steep-shelved cliff walls. The First Peoples of the Palouse called these falls _Aputaput_ , meaning \"falling water.\" They tell of how the falls was created by four giant brothers pursuing a mythological creature called the Big Beaver. The river once flowed smoothly into the Snake River, the story goes, until the Big Beaver was pursued and speared five times. Wounded, he gouged out canyon walls and forced the river to change course to plummet over a cliff. Big Beaver's claw marks can still be seen in the canyon walls\u2014the basalt columns. And the river indeed changed course. It once flowed through the Washtucna Coulee until the Ice Age floods forced its relocation to where you are now standing.\n\nFeel free to first walk the paved path to falls vistas and interpretive signs. Then start this hike, which begins on a service road at the north end of the parking area. Saunter past willows and through sage and flowers\u2014lots of them. Depending on the season, look for camas, lupine, desert parsley, arrowleaf balsamroot, bluebells, yellow bells, and more.\n\nAt 0.1 mile, a well-defined path branches right along the canyon rim above the falls. You'll be returning left, so take the path right and proceed with caution, staying a safe distance away from the canyon's edge. Avoid the social paths that head into the canyon, as they can be extremely dangerous. Look for snakes and yellow-bellied marmots along the way\u2014and of course stop to marvel at the river below.\n\nAt 0.25 mile, reach a spot above the thundering falls. Peer down at Castle Rock with its turrets and parapets. Then continue along the rim, enjoying vertigo-inducing views into the chasm below. A series of rapids in a bend in the river beneath an impressive face of columnar basalt soon comes into view. That's your destination.\n\nAt 0.5 mile, come to the end of a service road (elev. 925 ft). The trail continues right through a small gap, steeply dropping (use caution) to a set of railroad tracks. The line is still in use, so stay clear. Walk to the right, along the tracks, for 0.1 mile and then pick up trail again. Descend across a basalt talus slope, reaching the canyon floor in another 0.1 mile. Then on easy trail continue through pockets of head-high sage, reaching the river's edge at the rapids (elev. 775 ft). This is a nice spot to sit and ponder. Or feel free to scout around the canyon floor, but stay snake awake! When ready to return, retrace your steps to the service road and follow it 0.3 mile back to the trailhead.\n\n_While not as breathtaking as Palouse Falls, the upper falls sit in a wild and gorgeous canyon._\n\n### EXTENDING YOUR TRIP\n\nFrom the trailhead, take a short trail south to the Fryxell Overlook. From there a trail heads a short distance south along the railroad tracks before descending to a bench in the canyon. Adventurous and sure-footed souls may want to check it out.\n\n## blue mountains\n\n_Sulphur buckwheat brightens the rugged terrain near Deadman Peak in the Blue Mountains._\n\nPlateaus flanked by narrow ridges and slopes that drop steeply into deep canyons characterize the Washington portion of the Blue Mountains. Stray from the river drainages or high plateaus and the terrain falls into the general category of vertical. The range stretches about 190 miles from central Oregon into southeastern Washington, where the Blues are the headwaters for Snake and Columbia River tributaries sought by steelhead returning from the ocean to spawn.\n\nWhile just a fraction of the 1.4 million-acre Umatilla National Forest, the Pomeroy and Walla Walla Ranger Districts maintain hundreds of miles of trails in the Eastern Washington portion of the Blues. The marquee destination for hikers and horse packers is the 177,465-acre Wenaha-Tucannon Wilderness, named for the area's two major river drainages. The Washington Department of Fish and Wildlife also manages 70,000 acres of public land primarily for fish and wildlife habitat in the Blue Mountains Wildlife Area Complex. The busiest period in the Blues is October through early November, when most campsites and turnouts are filled with hunters pursuing Rocky Mountain elk.\n\n  Lewis and Clark Trail State Park\n\n**RATING\/DIFFICULTY** | **LOOP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n***\/1** | **0.8 mile** | **none\/1400 feet** | **Year-round**\n\n**Maps:** USGS Huntsville, state park map online; **Contact:** Lewis and Clark Trail State Park, (509) 337-6457, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Dogs permitted on-leash; **GPS:** N 46 17.376 W 118 04.281\n\n  _**Saunter through a lush forest that embraces the trout-filled Touchet River. Surrounded by sun-baked hills of golden grasses, this small forested tract retains moisture, making it a cool green haven on a hot summer's day. Old-growth ponderosa pines and cottonwoods help shade the way. Some of them graced this grove when Lewis and Clark passed through on May 2, 1806, on their return from the Pacific.**_\n\n### GETTING THERE\n\nFrom Pasco, head east on US Highway 12, turning left onto State Route 124 just after crossing the Snake River Bridge. Follow SR 124 for 45 miles to Waitsburg, picking up US 12 once again and continuing east 4.3 miles to the Lewis and Clark Trail State Park. (From Dayton, travel west on US 12 for 5.3 miles.) Turn left (north) into the park, proceeding to the campground restroom building and trailhead (elev. 1400 ft).\n\n### ON THE TRAIL\n\nBehind the restrooms, with silhouettes of the intrepid duo Lewis and Clark pointing the way, find the trailhead for the Fur, Fins, and Feathers Nature Trail. Grab an interpretive brochure (or ask the ranger for one), and then set out west (right) on this delightful little loop. You'll immediately notice how thick the vegetation is. Nettles grow head high\u2014stay on the trail or be zapped. The trail circles the campground, often resonating with the sounds of happy families. During quieter times, birdsong fills the air.\n\nAfter crossing a service road and the campground loop road, begin circling back under an impressive canopy of cottonwoods. The trail brushes alongside the Touchet River, providing good views out to the open countryside beyond. It was this promising countryside that attracted early settlers to the region, particularly French Canadians who came with the early fur brigades. Touchet is derived from the French word _toucheur_ , which means \"cattle driver.\"\n\nBut long before the fur trappers and Lewis and Clark, this region bustled with the activity of First Peoples. They traversed the area via the Nimipooiskit Trail, which extended from the Rocky Mountains to the Pacific Ocean. Remnants of this trail still exist in the valley.\n\nNotice the heavy sediment along the riverbank, evidence of past flooding and the reason why this area is so lush with vegetation and hosts a healthy assortment of birds. Look up at overhanging limbs for osprey. Look in the grasses for scurrying quails. And look out in the open fields for magpies. The delightful trail soon skirts the group camp before turning away from the river to head back west. Cross the campground loop road once more and return to your start.\n\n_A giant cottonwood along the Touchet River_\n\n### EXTENDING YOUR TRIP\n\nThe park continues on the south side of US 12, where there's a short but nice nature trail and interpretive displays on Lewis and Clark. Learn, too, about the Bateman family who homesteaded this tract in 1864 and sold it to the state during the Great Depression. During this austere time, park officials and townsfolk constructed the restroom building from 10,000 stones acquired from the Touchet River. During summer months, park personnel provide historical interpretation and guided walks.\n\n  Mill Creek\n\n**RATING\/DIFFICULTY** | **LOOP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/1** | **5.2 miles** | **155 feet\/1270 feet** | **Year-round**\n\n**Maps:** USGS Walla Walla, Army Corps trail map available online; **Contact:** US Army Corps of Engineers, Walla Walla District, (509) 527-7160, www.nww.usace.army.mil; **Notes:** Bennington Lake open 5:00AM\u201310:00PM. Partly open to mountain bikes, horses. Partly wheelchair-accessible. Dogs permitted on-leash; **GPS:** N 46 04.575 118 16.371\n\n  _**Thanks to damaging floods during the late eighteenth and early nineteenth centuries, Walla Walla residents now have in their backyard a 612-acre public tract of rolling hills, forested creeks, and trails. More than 20 miles worth, actually, embracing Mill Creek and circling Bennington Lake\u2014all part of a flood-control project that overflows with great hiking opportunities.**_\n\n### GETTING THERE\n\nFrom Walla Walla, head east on US Highway 12, exiting onto Airport Way. Head south on Airport Way, reaching intersection with Isaacs Avenue in 0.2 mile. Proceed straight onto Tausick Way, pass Walla Walla Community College, and cross Mill Creek and turn left on Reservoir Road after 0.4 mile. Continue 0.5 mile to parking and the trailhead (elev. 1160 ft) at the Mill Creek Office. Privy available.\n\n_Concrete blocks across the spillway make for a fun (or nerve-wracking) crossing._\n\n### ON THE TRAIL\n\nMore than 20 miles of multiuse, nonmotorized trails, and service roads traverse Mill Creek, the largest tract of public land in the Walla Walla Valley. The suggested hike here incorporates two of the three loop trails within the complex, offering a nice half-day hike. Feel free to shorten, lengthen, or create your own loops and combinations.\n\nFrom the trailhead, head east on the King-fisher Loop, following a service road along the creek, tiered and between levees (you're on one) as part of the flood-control project. Originating high in the Blue Mountains, the creek's waters are clean and sparkling. The way is practically level and lined with cottonwoods and other greenery. At 0.8 mile, come to a bridge and a junction. If you're just out for a short hike, cross the bridge and head left downstream (right leads to Rooks Park, another alternative trailhead). The paved Mill Creek Recreation Trail comes to another bridge that takes you back to the trailhead for a 1.7-mile loop.\n\nThe suggested hike continues straight 0.1 mile to a diversion dam and a service road (part of the Whitetail Trail loop). Head right on the service road over a grassy hillside that parallels a diversion spillway and reach a junction (elev. 1270 ft) with the Meadowlark Loop trail at 1.3 miles. Turn left and walk across the spillway, getting your feet wet or, if you're determined not to, hopping across a series of concrete blocks. Ignore side trails and stay on the Meadowlark Loop alongside and encircling Bennington Lake. While motor-free, the lake isn't quiet, echoing with the sounds of happy paddlers and swim-mers\u2014much to the chagrin of fishermen and women in pursuit of rainbows.\n\nPass through pockets of deciduous trees\u2014pretty in fall and shade-granting in summer. The way is near level. Cross the Mill Creek Dam (elev. 1225 ft) and pass through the busy parking lots and picnic areas along the lake's southwest shore. Catch some nice views of the Blues across the lake. Then resume quieter ambling through fields, returning to the spillway junction at 3.9 miles. Return to Mill Creek and take the Kingfisher Loop back to your vehicle for a hike of 5.2 miles.\n\n### EXTENDING YOUR TRIP\n\nFor near-shoreline access to Bennington Lake, from the Mill Creek trailhead drive 1 mile east on Reservoir Road to parking and trailheads at Bennington Lake.\n\n  Deadman Peak\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/3** | **6 miles** | **1780 feet\/5960 feet** | **late June\u2013Oct**\n\n**Maps:** USGS Deadman Peak, Umatilla National Forest map; **Contact:** Umatilla National Forest, Walla Walla Ranger District, (509) 522-6290, www.fs.fed.us\/r6\/uma\/walla2; **Notes:** Open to mountain bikes, horses. Rough access road. Access restricted south of trail into Mill Creek watershed; **GPS:** N 46 03.765 W 117 54.891\n\n  _**Except for a few dozen hunters who get special permits to probe this area in late October, the Intake\u2013Deadman Peak Trail is rarely tramped by hikers. It has no trailhead sign and is not clearly listed among hiking options on the Forest Service website. The route forms the boundary around a portion of the pristine Mill Creek Watershed, which is monitored occasionally by patrols to keep people away from the drinking-water source for Walla Walla. Vehicle access includes a few miles on the rough but scenic mile-high kendall Skyline Road, completed in 1928. A short side trip leads to the Table Rock Lookout. Like forbidden fruit, you can look at Deadman Peak from the lookout and hike within a couple hundred feet of its summit on the trail, but the top is just inside the watershed boundary and off-limits.**_\n\n### GETTING THERE\n\nFrom US Highway 12 in Dayton, turn south toward Bluewood Ski Area on 4th Street, which eventually becomes Kendall Skyline Road (Forest Road 64). Drive 23.2 miles to a junction with FR 46 and continue straight. Go 0.3 mile farther and turn left, continuing on FR 64 toward the Table Rock Lookout. Drive 2 miles on this rough, talcum-powder-dusty road segment and look for an unauthorized road heading up the open slope to the right just past Blakely Spring. This is a possible parking spot. Continue as FR 64 bends south for 0.2 mile and look to the uphill side for the first of many steel posts with 12-inch-wide signs designating the Mill Creek Watershed Boundary. This first sign is the trailhead, with room for one vehicle to park clear of the road if two wheels are up on the slope (elev. 5820 ft).\n\n### ON THE TRAIL\n\nThe Forest Service clearly makes no effort to make the beginning of the route apparent. But another watershed boundary sign up the slope helps get hikers on course. Intake Trail No. 3211 soon becomes a single-track route, with boundary signs on your left every few tenths of a mile or so.\n\n_Deadman Peak is seen in the distance beyond Table Rock Lookout._\n\nThe trail undulates on a north slope lush with shrubs, including huckleberry and false hellebore. Columbines might catch your eye in August. Soon the landscape opens to sweeping views of the Columbia and Walla Walla County farmlands below. As the trail drops into a notch, Deadman Peak is in full view, about 0.8 mile ahead, distinguished by a bald basalt outcropping lapping over from the summit.\n\nThe trail contours around the north side of Deadman Peak, tantalizingly close to the summit. But anywhere there's a short scramble route to the peak, there's likely to be a watershed boundary sign reminding you that it's off-limits. The trail continues around to an open point on the west side of the peak and a ridge that would lead gently to the summit, if only it weren't forbidden.\n\nThen the trail begins a long steady descent. It's a total of 2 miles to the open point of the ridge where the trail drops left and contours southward. Turn back here for a 4-mile round trip. However, the next mile is interesting for wildlife enthusiasts. The trail passes Switchback Spring at the headwaters of Green Fork Creek, where elk thoroughfares often can be seen. A bit farther, the trail breaks out onto an open ridge, where you can see back to the Table Rock Lookout without violating watershed restrictions.\n\nAt 3 miles you can see where the restricted Deadman Creek Trail starts up and over the lip and drops down into the restricted watershed. Turn back here for a 6-mile round trip.\n\n### EXTENDING YOUR TRIP\n\nDrive south on FR 64 about 3 miles and hike or drive up the 0.2-mile spur (high-clearance required for driving) to the Table Rock Lookout (elev. 6250 ft) for the best view of Deadman Peak and the entire surrounding area. Privy available.\n\n  Middle Point Ridge\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/3** | **5.5 miles** | **1730 feet\/5130 feet** | **June\u2013Nov**\n\n**Maps:** USGS Eckler Mountain, USGS Godman Spring, Umatilla National Forest map; **Contact:** Umatilla National Forest, Walla Walla Ranger District, (509) 522-6290, www.fs.fed.us\/r6\/uma\/walla2; **Notes:** NW Forest Pass or federal equivalent required. Occasional motorcycle use; **GPS:** N 46 08.154 W 117 48.520\n\n  _**A paved road from Dayton leads to a route through forest that was burned\u2014some old monarchs were spared\u2014by the 110,000-acre Columbia Complex forest fires of 2006. Up from the North Fork Touchet River, the trail offers good views and an even better workout as it climbs to pleasant strolling on Middle Point Ridge. The entire hike is just a smidge off-piste from the Bluewood Ski Area.**_\n\n### GETTING THERE\n\nFrom US Highway 12 in Dayton, turn south toward Bluewood Ski Area on 4th Street, which eventually becomes Kendall Skyline Road (Forest Road 64). Drive a total of 16.5 miles to the trailhead on the left (elev. 3390 ft). Privy available.\n\n### ON THE TRAIL\n\nMiddle Point Trail No. 3116 drops from the paved parking area, crosses a footbridge over the North Fork Touchet River, and heads down along the stream. Soon it begins a nicely graded climb to the first switchback. Then the grade steps up a notch, angling toward the ridge and switchbacking into rock bands.\n\n_Some hearty trees survived forest fire on Middle Point Ridge._\n\nAt the ridge, you'll begin getting a close look at the aftermath of the 2006 fires. The trail becomes a pleasant walk on the ridge up to an open high point with distant views, a good turnaround point.\n\n### EXTENDING YOUR TRIP\n\nContinue south on the trail 1.5 miles on a nice ridge route to the more timbered Middle Mountain (elev. 5724 ft). From there, you're more likely to encounter motorized vehicles as the trail heads toward Kendall Skyline Road.\n\n  Sawtooth Ridge\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/3** | **5.8 miles** | **850 feet\/5930 feet** | **June\u2013Nov**\n\n**Maps:** USGS Godman Spring, Umatilla National Forest map; **Contact:** Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.fed.us\/r6\/uma\/pomeroy; **Notes:** NW Forest Pass or federal equivalent required. Open to horses. Wilderness trail, mechanized equipment prohibited; **GPS:** N 46 03.701 W 117 50.642\n\n  _**This hike samples the scenic high portion of a trail that eventually drops 14 miles to the Wenaha River in the heart of the Wenaha-Tucannon Wilderness. Views constantly change. The Forest Service tends the trail well, yet use is light except for the occasional horse group.**_\n\n_Early morning is prime time to hike Sawtooth Ridge._\n\n### GETTING THERE\n\nFrom US Highway 12 in Dayton, turn south toward Bluewood Ski Area on 4th Street, which eventually becomes Kendall Skyline Road (Forest Road 64). Drive a total of 23.2 miles to a junction and turn left on FR 46 toward Godman Guard Station. Drive 3.7 miles and turn right into a large horse-staging area. Privy available. If your vehicle can climb the rocky little incline, continue 0.2 mile to the trailhead (elev. 5620 ft) and more parking at the end of Burnt Flat Road (FR 240).\n\n### ON THE TRAIL\n\nFrom the Sawtooth Trail No. 3256 trailhead, go down into an open forest. At 1.5 miles, break into openings with big views out to adjacent canyon rims. The route assumes a ridge that alternates from desertlike landscape to lush woods. Sulfur buckwheat blooms from a rocky crust-like soil in a vibrant show, even in the heat of August.\n\nAt about 3 miles, take the right fork at a cairned junction. (Left goes to a horse-camping area on Burnt Flat.) Soon break out onto an open ridge. On a clear day the view to the south includes the Wallowa Mountains of northeastern Oregon.\n\nThen the trail drops steeply into a notch. You may want to turn back here, but it's worthwhile to continue along the next finger ridge. Leave the trail when it begins dropping significantly again into the trees and wander for the views on both sides of the open ridge before hooking up with the trail again back to the trailhead.\n\n### EXTENDING YOUR TRIP\n\nTake the left (southeast) fork at the cairned junction and explore the Burnt Flat area for interesting campsites and springs that attract wildlife. The trail isn't always maintained.\n\n  Twin Buttes\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/3** | **3.8 miles** | **700 feet\/5674 feet** | **June\u2013Oct**\n\n**Maps:** USGS Godman Spring, USGS Oregon Butte, USFS Wenaha-Tucannon Wilderness map; **Contact:** Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.fed.us\/r6\/uma\/pomeroy; **Notes:** NW Forest Pass or federal equivalent required. Open to horses. Wilderness trail, mechanized equipment prohibited. Rough road; **GPS:** N 46 01.696, W 117 46.676\n\n  _**This trip is one of the most painless ways to experience the Wenaha-Tucannon Wilderness, considering the access road offers the deepest penetration into the otherwise roadless area. You'll be surrounded by wilderness as you leave the trailhead. The trail to Twin Buttes leads to views overlooking a wilderness known for its carved canyons rather than its peaks. Expect hunting camps at the trailhead when big-game seasons open in October.**_\n\n### GETTING THERE\n\nFrom US Highway 12 about 4 miles west of Pomeroy (or 8 miles east of the junction with State Route 127), turn south near milepost 399 on Tatman Mountain Road. Follow the signs for Camp Wooten, joining the Tucannon River Road after 9 miles. (From points farther west, get on the Tucannon River Road at Dayton.) Turn south on Tucannon River Road. Pass Camp Wooten, drive about 2 miles, and turn right onto Forest Road 4620. Drive 4 miles and turn left on Kendall Skyline Road (FR 46). Go south on FR 46 for nearly 17 miles, passing the Godman Guard Station, and turn left onto rougher FR 300. Drive about 5 miles and bear left at a Y (may not be marked) to the trailhead and camping area at Twin Buttes Spring (elev. 5350 ft). Privy available.\n\n### ON THE TRAIL\n\nHike 0.3 mile on an old roadbed to a junction with the trail to Grizzly Bear Ridge (Hike 119) and turn left onto East Butte Creek Trail No. 3112. The trail sidehills to the spine of the ridge before following a few waves of terrain to an opening. No distant views here, but the next opening offers fine views into the wilderness. Keep going.\n\n_Steep terrain sprawls below Twin Buttes._\n\nAfter another short climb, the trail angles up along the north butte at 1.5 miles from the trail junction. You'll want to head up off-trail to the right and soak in the view from the top. But first, continue another few hundred yards to the precipitous view down into the canyon bowels from the first switchback as the trail begins its drop toward Butte Creek.\n\nGo back a couple hundred yards and scramble a short way up to the butte. Don't miss it. The knob was so important to one family we encountered during research for this book that they scattered a parent's ashes on the summit.\n\n### EXTENDING YOUR TRIP\n\nThe trail down to Butte Creek makes for an 8-mile round-trip. Very fit hikers can hike 12 miles one-way all the way to a shuttle vehicle at the Godman trailhead on FR 46 about 5 miles north from the junction with FR 300.\n\n  Grizzly Bear Ridge\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/3** | **8.2 miles** | **1350 feet\/5400 feet** | **June\u2013Nov**\n\n**Maps:** USGS Godman Spring, USGS Oregon Butte, USGS Elbow Creek, USFS Wenaha-Tucannon Wilderness map; **Contact:** Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.fed.us\/r6\/uma\/pomeroy; **Notes:** NW Forest Pass or federal equivalent required. Open to horses. Wilderness trail, mechanized equipment prohibited; **GPS:** N 46 01.696, W 117 46.676\n\n  _**Although signs of elk are common, no grizzlies are found in the Wenaha-Tucannon Wilderness. If somebody gave Grizzly Bear Ridge its nameto help maintain the area's solitude, it worked. Trail No. 3103, open only to hikers and horses, is one of the gentlest and most interesting routes from the high country down into the heart of the 177,465-acre wilderness. This trip takes on just the upper portion of this 8-mile trail before it plunges to the Wenaha River.**_\n\n### GETTING THERE\n\nFrom US Highway 12 about 4 miles west of Pomeroy (or 8 miles east of the junction with State Route 127), turn south near milepost 399 on Tatman Mountain Road. Follow the signs for Camp Wooten, joining the Tucannon River Road after 9 miles. (From points farther west, get on the Tucannon River Road at Dayton.) Turn south on Tucannon River Road. Pass Camp Wooten, drive about 2 miles, and turn right onto Forest Road 4620. Drive 4 miles and turn left on Kendall Skyline Road (FR 46). Go south on FR 46 for nearly 17 miles, passing the Godman Guard Station, and turn left onto rougher FR 300. Drive about 5 miles and bear left at a Y (may not be marked) to the trailhead and camping area at Twin Buttes Spring (elev. 5350 ft). Privy available.\n\n### ON THE TRAIL\n\nHike 0.3 mile on an old pre-wilderness roadbed to the junction with East Butte Creek Trail No. 3112 (Hike 118) and continue straight on Trail No. 3103 toward Grizzly Bear Ridge. Enjoy alternating through forest and big meadows sparse with grass as you gradually head down the ridge toward the heart of the Wenaha River canyon.\n\nAt 1.7 mile, cross a small drainage and a trickle of water called Coyote Spring before heading into an opening that becomes desertlike by late summer. The trail can fade here, but it's easy to find on the fall line of the ridge. Watch along the trail for shredded saplings, likely the late-summer and early fall work of bull elk as they polish their antlers and mark territory for the September mating season.\n\nAt the top of a startling 0.4-mile-long uphill grade in this generally downhill route, there's a grassy knob to explore off-trail to the left. It's prominent on maps at an elevation of 5162 feet.\n\nThen continue down the trail along a semi-open slope and look for signs indicating the Washington-Oregon border. Some people will call this good\u2014a nice place to picnic and turn back for a round-trip of 7 miles. But it's worthwhile to continue down the trail, watching the forest type change. More ponderosa pines are coming up, and there's a grove of western larch in the basin to the west. Soon the trail heads slightly uphill to daylight and open views on a knob before descending again. You've hiked 4.1 miles, just over halfway to the Wenaha River. This is a good spot to rest, take in the view over Rock Creek, and turn back.\n\n_Grizzly Bear Ridge crosses the Washington\u2013Oregon border._\n\n### EXTENDING YOUR TRIP\n\nStrong hikers can continue on trail another 4 miles to the Wenaha River for a total elevation drop of 2800 feet. Along the way you'll pass through rare old-growth ponderosa parklands. The trail drops more steeply in the last 3 miles down to the river. Backpackers can enjoy a two- or three-day 18-mile loop by heading upstream along the Wenaha and then climbing the steep Slick Ear Trail No. 3104 to a trailhead just 2 miles from the Twin Buttes Spring trailhead.\n\n  Oregon and West Buttes\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n******\/2** | **6.1 miles** | **800 feet\/6387 feet** | **June\u2013Nov**\n\n**Map:** USFS Wenaha-Tucannon Wilderness map; **Contact:** Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.usda.gov\/umatilla; **Notes:** NW Forest Pass or federal equivalent required. Open to horses. Wilderness trail, mechanized equipment prohibited; **GPS:** N 46 07.104 W 117 42.914\n\n  _**An easy and highly scenic loop to the highest summit in Washington's Blues, this hike is suitable for folks of all ages and abilities. Stand upon open summits, taking in sweeping views of rugged high tableland ridges and deep forested canyons cut by pristine waterways. Visit a historic fire lookout, flower-speckled ridges, and cool evergreen groves. And in this corner of the state where human visitation is light, chances are always good for viewing wild critters.**_\n\n### GETTING THERE\n\nFrom Pomeroy, head 4.5 miles west on US Highway 12 and turn left (near milepost 399) onto Tatman Mountain Road, proceeding 9 miles to Tucannon River Road (follow signs for Camp Wooten: The main paved road becomes Linville Gulch Road after about 1.2 miles and at about 6.5 miles you bear right onto Blind Grade Road). Now turn left and continue 11 miles south on Tucannon River Road (which becomes Forest Road 47; the pavement ends at 9 miles), turning right onto Patrick Grade Road (FR 4620). Proceed 4.1 miles to a junction with Kendall Skyline Road (CR 1424). (From Dayton, head east on Patit Road for 14 miles, turning left onto Hartsock Grade and driving 3 miles to the Tucannon River Road. Turn right and continue 13 miles, turning right onto Patrick Grade Road\/FR 4620. Proceed 4.1 miles to the junction with CR 1424. Or reach this point from Dayton via shorter routes involving longer gravel sections.) Continue south on CR 1424 (which becomes FR 46 for 11.6 miles), bearing left onto FR 4608 at Godman Guard Station. Follow FR 4608 for 5.8 miles to the road's end at Teepee Campground and the trailhead (elev. 5500 ft). Privy available.\n\n### ON THE TRAIL\n\nGetting to the trailhead is the tough part. Now from a high starting point, enjoy a nice hike into a small section of the sprawling 177,465-acre Wenaha-Tucannon Wilderness spanning the Blues in both Washington and Oregon. Starting from the Teepee Campground, which is generally pretty quiet except for deer and elk season, enjoy good views south into the Butte Creek drainage. Locate the Mount Misery Trail and start hiking. This trail travels 13 miles across the rooftop of the Blues, allowing for more day-hiking options (see Hikes 121 and 123) as well as for some fine backpacking.\n\nOn good trail enter a mature forest of western larch. Thanks to these trees, the Blues turn gold come October. Reach a saddle after about 0.5 mile and then climb more steeply to an unsigned junction (elev. 6100 ft) at about 1.1 miles. The trail was recently rerouted left around West Butte. Head right on the old trail (returning later on the newer trail) to check out West Butte. After hopping over some downed trees the way is pretty easygoing. Soon enjoy good views to the south and southwest.\n\nAt 1.7 miles the trail skirts just below the summit of 6292-foot West Butte. From this summit, fourth-highest in the Washington Blues, take in excellent views of nearby Oregon Butte and the impressive Wallowa Mountains in Oregon. Locate the misspelled benchmark pointing to \"Oreon Butte.\" It's another classic, like the \"Ceder Butt\" benchmark in the Snoqualmie Pass area.\n\n_Oregon Butte's sun-kissed open grassy slopes_\n\nThe trail continues east, switchbacking down to reach a junction with the Mount Misery Trail (elev. 6000 ft) at about 2.1 miles. Left returns to the trailhead\u2014but, Oregon Butte awaits first. Head right and drop to a saddle (elev. 5940 ft) shaded with larches. Then start climbing again, passing reliable Oregon Butte Spring (elev. 6000 ft) and camps (just beyond) at 2.4 miles. Continue climbing via a few switchbacks to a junction (elev. 6160 ft) at 2.6 miles. Bear right, passing nice camps, and attain the northern shoulder of Oregon Butte. Traverse a grassy ridgeline and admire expanding views and windblown firs and whitebark pines.\n\nUNTRAMMELED EASTERN WASHINGTON\n\nLarge portions of the mountains and forests of northeastern and southeastern Washington lie within national forest land, but that doesn't necessarily mean they're protected. National forests are managed for \"multiple use.\" While some uses (like hiking) are fairly compatible with land preservation, other uses (such as mining, logging, and off-road-vehicle use) usually aren't.\n\nRecognizing that parts of our natural heritage should be altered as little as possible, Congress overwhelmingly passed the Wilderness Act in 1964 with bipartisan support (the House approved passage 373\u20131). One of the strongest and most important pieces of environmental legislation in our nation's history, the Wilderness Act afforded some of our most precious wild landscapes a reprieve from exploitation, development, roads, and harmful activities, such as motorized recreation. Even bicycles are banned from federal wilderness areas. Wilderness is \"an area where the earth and community of life are untrammeled by man,\" states the act. \"Where man himself is a visitor who does not remain.\"\n\nWhile federal lands in northeastern and southeastern Washington had no shortage of areas qualified for inclusion in the wilderness system back in 1964, none were included. In 1978, with the passage of the Endangered American Wilderness Act, Eastern Washington received its first wilderness area (sharing it with Oregon): the 177,465 Wenaha-Tucannon Wilderness in the Blue Mountains. In 1984, a sweeping statewide wilderness bill was signed into law by President Reagan, creating the 7140-acre Juniper Dunes Wilderness on BLM lands and the 41,335-acre Salmo-Priest Wilderness in the Colville and Kaniksu National Forests.\n\nWhile Washington ranks fourth among the states for total wilderness acres, nearly all of it is in the western half of the state. Only 3 percent of the Colville National Forest is protected as wilderness. Many conservationists feel that it's not enough. Large tracts of Eastern Washington national forest lands are under pressure to be developed or opened to more motorized recreation, especially the latter. While some of our public lands base should be designated for those uses, most of our last remaining roadless tracts of pristine wild country should be considered for their wilderness potential. The issue isn't about \"locking up lands\" for solitude. Water quality and wildlife security, for example, are major benefits of wilderness.\n\nAreas in this book that some conservation groups have recommended for wilderness include Mount Bonaparte (Hikes 3 and 4); Thirteenmile (Hikes 17 and 18); Profanity, Twin Sisters, and Bald-Snow in the Kettles (Hikes 19-36); Abercrombie-Hooknose (Hikes 42 and 43); Grassy Top (Hikes 50 and 57); Upper Tucannon and Mill Creek in the Blues (Hike 122).\n\n\u2014 _C. R._\n\nAt 3.1 miles, pass a hitching post and continue south 0.1 mile to the 6387-foot summit of Oregon Butte, graced with a lone fir and a 1931-built fire lookout that is still periodically staffed. The views from this point, highest summit in Washington's Blues, are wonderful. Stare south down the Crooked Creek drainage, over the mesas and tableland ridges that make up the Blue Mountains, and out to the lofty and rugged Wallowas. Look west across windswept ridges and east to Mount Misery and Diamond Peak, two more summits worth exploring.\n\nOnce you've had enough time wallowing in the blues, return. Hike 0.6 mile back to the Mount Misery Trail and head west, reaching a familiar junction with the old trail at 1.1 miles. This time, however, bear right on the newer trail, traversing cool forest on West Butte's north side. At 1.8 miles, continue right at the west junction (elev. 6100 ft) of the West Butte Trail and descend, coming to the trailhead at 2.9 miles, for a total round-trip of 6.1 miles.\n\n### EXTENDING YOUR TRIP\n\nJust west of the Oregon Butte summit spur-trail junction is the Smooth Ridge Trail junction. Follow this trail for about 1.9 miles to 5461-foot Danger Point for a unique perspective of the surrounding deeply cut canyons. Strong hikers can also travel 3.3 miles on the Mount Misery Trail along high and lonely ridges to Indian Corral (elev. 5700 ft), with its excellent campsites and reliable spring.\n\n  Panjab Loop\n\n**RATING\/DIFFICULTY** | **LOOP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n******\/4** | **13.3 miles** | **3030 feet\/5720 feet** | **June\u2013Nov**\n\n**Maps:** USGS Panjab Creek, USFS Wenaha-Tucannon Wilderness map; **Contact:** Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.fed.us\/r6\/uma\/pomeroy; **Notes:** NW Forest Pass or federal equivalent required. Open to horses. Wilderness trail, mechanized equipment prohibited; **GPS:** N 46 12.332 W 117 42.435\n\n  _**This challenging hike is a showcase of the Wenaha-Tucannon Wilderness. From easy-to-reach trailheads, you'll experience the sun-baked slopes, deep canyons, high plateaus, recovering burns and cool creeks of a very wild place.**_\n\n### GETTING THERE\n\nFrom US Highway 12 between Dayton and Pomeroy, turn south toward Camp Wooten on Tucannon River Road (which becomes Forest Road 47). Drive 32 miles to Rattlesnake Trailhead on the left (elev. 3015 ft). Privy available. The trailhead is across from the entrance to the Washington Fish and Wildlife Department's Panjab South Campground (Discover Pass required) and just before the Umatilla National Forest's Panjab Campground (Northwest Forest Pass required). If you have another vehicle or bike, shuttle it up the road 2.3 miles to Panjab Trailhead, a popular staging area for equestrians.\n\n### ON THE TRAIL\n\nRattlesnake Trail No. 3129 starts with a ford of Panjab Creek after a rambling start into the Panjab Campground. Bring sandals for the ford, which is behind campsite 1, or go farther up Panjab Creek and look for a fallen log to cross.\n\nThe trail immediately climbs from the creek (and the nearby Tucannon River) and begins switchbacking through the fireweed, brush, and snags that recall the area's 2005 forest fires. An early start helps you cope with sun that beats down on this climb during summer mornings.\n\nClimbing efforts are rewarded around 2.5 miles as the ridge trail gains the plateau. Rims that once loomed above in the distance are now your equals across the canyons. The plateau ranges from lush fireweed and plants revegetating the burns to wide-open meadows\u2014briefly green in the early season but soon turning desertlike in the coarse, dry soil.\n\n_The Blue Mountains offer expansive meadows._\n\nAt 3 miles, a sign marks Alnus Spring, which wets the greenery in the forest below the trail. The trail fades in some of these open stretches but is easy to pick up again. Soon you'll be cruising along forest edges in mostly open country. At 6 miles, watch for a four-way junction (shown as three-way on some maps) that's usually marked by a sign propped up with rocks in a starkly open slope near Indian Corral.\n\nFrom this point, Rattlesnake Trail ends and continues ahead as Trail No. 6144 to Oregon Butte (Hike 120). Going left heads onto Trail No. 6144 eastward to Diamond Peak (Hike 123). (Nearby Dunlap Spring is developed for stock.) To continue on the loop trip, head down to the right (west) on a spur toward Panjab Creek. Drop into the woods and then descend a short steep shot to a junction as you enter the creek drainage. Turn left and head down unsigned Panjab Trail No. 3127.\n\nSuddenly you're in another world of greenery and water, crossing several creeks. In fact, the trail and an upper fork of Panjab Creek are one in the same for a short stretch. Enjoy the trail as it descends steadily along with the creek. At a junction with Turkey Creek Trail No. 3136, continue straight for the last mile to Panjab Trailhead for a hike of 11 miles.\n\nIf you didn't leave a bike or shuttle vehicle at this developed horse-staging area, you have an additional 2.3 miles of road walking downstream to Rattlesnake Trailhead.\n\n### EXTENDING YOUR TRIP\n\nExplore Turkey Creek Trail No. 3136, which heads up along creeks 5 miles from Panjab Trailhead to Teepee Campground. Also in the area, just 1.5 miles south on FR 4713 from Panjab Trailhead, is Meadow Creek Trail No. 3123.\n\n  Tucannon River\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/2** | **8 miles** | **500 feet\/4050 feet** | **May\u2013Nov**\n\n**Map:** USFS Wenaha-Tucannon Wilderness map; **Contact:** Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891; www.fs.usda.gov\/umatilla; **Note:** NW Forest Pass or federal equivalent required. Open to horses; **GPS:** N 46 11.315 W 117 37.519\n\n  _**Enjoy this cool and shaded trail in a land of sun and hot temperatures. Hike up a deep canyon alongside the rippling Tucannon River through lush groves of old-growth fir, spruce, pine, and larch. A great hike in early season when the high country is still covered with snow, the Tucannon River Trail with its easy grade and inviting campsites also makes for a nice beginner's backpacking destination.**_\n\n### GETTING THERE\n\nFrom Dayton, head east on Patit Road for 14 miles, turning left onto Hartsuck Grade and following it 4 miles to Tucannon River Road. (From Pomeroy, head 4.5 miles west on US Highway 12 turning left near milepost 399 onto Tatman Mountain Road and proceeding 9 miles to Tucannon River Road.) Continue 13.2 miles south on Tucannon River Road (which becomes Forest Road 47) to a Y-intersection. Bear left onto FR 4712 and follow this rough-at-times road 4.7 miles to its end and the trailhead (elev. 3550 ft). Privy available.\n\n### ON THE TRAIL\n\nStart by crossing Sheep Creek on a sturdy bridge. The way follows a recently decommissioned road for about a 0.25 mile before transitioning to older roadbed. Traversing a bench above the Tucannon River, the trail skirts the Wenaha-Tucannon Wilderness before briefly passing through a small section of it. The 177,465-acre wilderness was created in 1978 to protect the habitat of one of the largest herds of Rocky Mountain elk. They were introduced into the region in 1913. Hunters covet them, and during elk season this trail and many others in the region see quite a bit of human activity. Otherwise, it's pretty quiet in the backcountry of the Blues.\n\n_Majestic ponderosa pines\u2014standing and fallen along the Tucannon River_\n\nWhile most of this trail is outside the wilderness, the 12,600-acre Upper Tucannon River Roadless Area it traverses is as wild and pristine as any part of the adjacent wilderness area. The way passes through some recent burns, but plenty of towering trees survived the fires. The forest here is lush and cool, and where sunlight penetrates the canopy wildflowers grow in profusion. Pass through dark groves of spruce and open groves of pine. The river is always nearby, filling the forest with water songs.\n\nAt about 1.5 miles, come to Ruchert Camp (elev. 3675 ft). Just beyond, the river passes through a tighter stretch, where accompanying breezes funnel through and help keep the valley cool. Pass more riverside campsites and impressive groves of old trees.\n\nAt about 4 miles, just past where Bear Creek tumbles down the slopes to your south into the river, reach a junction with the Bear Creek Trail (elev. 4050 ft). To the left it climbs steeply out of the valley, and to the right it fords the Tucannon River (difficult in early season) before also climbing steeply out of the valley\u2014making this a good spot to turn around.\n\n### EXTENDING YOUR TRIP\n\nFollow the Bear Creek Trail in either direction for some lung-busting climbing with good views as your reward. The trail left melts out early, climbing more than 1500 feet in 2.5 miles up open slopes bursting with flowers (and ticks in early summer), reaching Hunter Spring and a trailhead accessed from FR 40. The trail right steeply climbs 1800 feet, accessing a ridge that it then follows 4.2 miles to the Mount Misery Trail near Diamond Peak (Hike 123). Solitude is guaranteed.\n\n  Diamond Peak and Sheephead Corral\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n******\/3** | **5.8 miles** | 1300 feet\/6379 feet | **mid-June\u2013  \nNov**\n\n**Map:** USFS Wenaha-Tucannon Wilderness map; **Contact:** Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.usda.gov\/umatilla; **Notes:** Open to horses. Wilderness trail, mechanized equipment prohibited. Last 2.7 miles of FR 4030 are rough, high-clearance recommended; **GPS:** N 46 07.096 W 117 31.806\n\n  _**Follow the Mount Misery Trail\u2014a rather pleasant path actually\u2014along the rooftop of Washington's Blues to stunning viewpoints and wild, rarely hiked country. Traverse meadows flush with wildflowers and mile-high ridges cloaked in larch, pine, and fir. Hike to Diamond Peak, second-highest summit in southeastern Washington, savoring breathtaking views of the deep canyons and cloud-piercing peaks south in Idaho and Oregon.**_\n\n### GETTING THERE\n\nFrom Dayton, head 37 miles east on US Highway 12 to Pomeroy. (From Clarkston, travel 29 miles west on US 12 to Pomeroy.) Continue through town 0.5 mile past the historic courthouse, turning right onto 15th Street (signed for Umatilla National Forest and City Park), which eventually becomes Peola Road (and Mountain Road after that). At 15 miles, the pavement ends at the national forest and the road becomes Forest Road 40. After 7.8 miles, bear right at the junction with FR 42, continuing on FR 40. After 7.7 more miles, turn right onto FR 4030. Follow it for 4.5 miles (the last 2.7 miles may be rough for low-clearance vehicles) to the trailhead (elev. 5850 ft).\n\n### ON THE TRAIL\n\nStart by leaving misery behind\u2014that's Mount Misery, which looms over the trail-head to the east. For the stockmen who drove their cattle and sheep to the lofty hinterlands of southeastern Washington back in the early twentieth century, more than a few miserable moments often waited. To commemorate their efforts, or perhaps commiserate over them, they left the name \"Misery\" upon a spring and a prominent 6366-foot peak, third-highest summit (and an easy scramble from the trailhead) in Washington's Blues.\n\nFollowing the Mount Misery Trail west, immediately enter the 177,465-acre Wenaha-Tucannon Wilderness, created in 1978 as part of the Endangered American Wilderness Act and spanning the Blues in both Washington and Oregon. Climbing at first on road and then bona fide trail, traverse slopes graced in blueberries and larches, which in fall add vibrant colors to this muted landscape. Pass through a gap that provides a preview of the sweeping views lying ahead, ranging from Hells Canyon to the high Wallowa Mountains of northeastern Oregon.\n\nAt 0.7 mile, emerge onto the first of several open, grassy, and flower-sporting \"balds.\" Stay left at an unmarked junction (elev. 6275 ft) at 0.8 mile, unless you want to follow the Bear Creek Trail down into the Tucannon River valley (Hike 122). Follow the unmarked side trail that veers left for 0.4 mile to 6379-foot Diamond Peak, highest summit in Garfield County. Lying just outside of the wilderness boundary (hence the communications tower), this peak sports breathtaking views south, especially during sunrise and sunset. Scan the canyon country sprawled below, including the magnificent Grande Ronde Valley. Notice any mountain mahogany on the peak? Washington's Blues are the northern limit for this tree\u2014a species ubiquitous in the Great Basin.\n\n_Looking south across stark canyon country from Diamond Peak_\n\nThe trip to Diamond Peak is short, so you may want to hike a little more. Return to the Mount Misery Trail and continue west, dropping into a forested saddle (elev. 6175 ft) where the Melton Creek Trail begins its long journey south to the Wenaha River valley. Your trail climbs steeply (albeit not for long), cresting a bald knob (elev. 6350 ft) with excellent views back to Diamond Peak.\n\nCarry on, undulating between sage-scented meadows and fir and larch groves. There are plenty of good views along the way of waves upon waves of blue ridges lapping at the horizon. Check for animal tracks in the granite-pumice-till that blankets the ridges. See any cougar tracks? The big cats are abundant here. At 2.5 miles (from the trailhead), after a descent, come to the Sheephead Corral and spring (elev. 5975 ft)\u2014a good place to rest, have lunch, camp, and call it a hike.\n\n### EXTENDING YOUR TRIP\n\nIf you want to push on a little farther, continue on the Mount Misery Trail another 0.5 mile climbing to a locally known knob called Sheephead (elev. 6125 feet) where there are excellent views out to Oregon Butte. The trail continues all the way to the Teepee Car Camp making it (with its numerous springs and camps) a great backpacking choice.\n\n  North Fork Asotin Creek\n\n**RATING\/DIFFICULTY** | **ROUND-TRIP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/2** | **20 miles** | **1750 feet\/3080 feet** | **Mar\u2013Dec**\n\n**Maps:** USGS Potter Hill, USGS Pinkham Butte, USGS Harlow Ridge, Umatilla National Forest map; **Contact:** Washington Department of Fish and Wildlife, Asotin Wildlife Area, Clarkston, (509) 758-3151, http:\/\/wdfw.wa.gov\/lands\/wildlife_areas\/asotin, and Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.fed.us\/r6\/uma\/pomeroy; **Notes:** Discover Pass required. Open to mountain bikes, horses. Motorcycles permitted after July 1. Watch for rattlesnakes, ticks; **GPS:** N 46 15.693 W 117 17.922\n\n  _**Late-winter and spring hikers in particular will appreciate the Asotin Wildlife Area's sanctuary from motorized traffic, which is prohibited part of the year to protect wintering Blue Mountains deer, elk, and big-horn sheep in the valley near the Snake River. The trail along North Fork Asotin Creek leads high into the Umatilla National Forest, creating options to please hikers of all levels. The creek has special status in wildlife circles: It's a spawning area for steelhead that swim hundreds of miles upstream from the ocean, a calving area for elk, a mountain quail recovery area, and a magnet for wintering swarms of ladybird beetles, better known as ladybugs.**_\n\n### GETTING THERE\n\nFrom Clarkston, follow Riverside Drive (State Route 129) south to Asotin. Just before crossing the bridge at Asotin, turn right on Bauermeister Drive (which becomes Asotin Creek Road). Drive 2.9 miles and turn right on County Road 1100. Go 11.2 miles and bear right at the fork onto South Fork Asotin Creek\u2013Lick Creek Road (CR 181). Go 0.5 mile to an Asotin Wildlife Area gate, which is locked December 1\u2013April 1. Drive or walk another 0.3 mile to the trailhead (elev. 1990 ft) on the left at the confluence of Lick Creek and North Fork Asotin Creek.\n\n### ON THE TRAIL\n\nImmediately you must hop rocks across Lick Creek before starting on the trail that skirts a crop field planted for wildlife forage and heads up North Fork Asotin Creek. Soon the rush of water will be a nearly constant companion. Hike this trail as long as you please before turning around, to get your desired mileage.\n\n_Spring break along North Fork Asotin Creek_\n\nSpring hikers are likely to see signs of big game as well as wild turkeys. Grouse lurk in the thick streamside vegetation. Keep an ear open toward the steep open slope of basalt outcroppings for the chuckle of chukar partridges and the cascading call of canyon wrens. With so much prey concentrated here, it's no wonder that signs of black bears and cougars also can be found.\n\nHike nearly 4 miles on a pleasant cruising-speed trail that is wide enough for the ATVs the Asotin Wildlife Area managers use for maintaining the route. After crossing the cattle guard into national forest land, the trail eventually narrows into a single-track.\n\nUnderstory vegetation includes elder-berry, sumac, and Oregon grape. Potential hazards include the occasional rattlesnake, thorny blackberry vines, and scattered patches of poison ivy.\n\nAs the canyon begins to narrow, huge ponderosa pines shade the way. After 8 miles, a series of springs emerge from mossy basalt cliffs before you reach a small grassy meadow near the confluence of the Middle Branch of North Fork Asotin Creek. Check out this area, but tread lightly and don't linger. Thousands of ladybird beetles hibernate here in the matted grass and bark of dying trees.\n\nThis is a good turnaround point for a round trip of nearly 20 miles.\n\n### EXTENDING YOUR TRIP\n\nThe trail continues up the North Fork for about 1.5 miles. Then it switchbacks up a steep ridge to Pinkham Butte, where the views can be stunning. After the Lick Creek Road opens and snow melts, you can leave a car at the west trailhead on Lick Creek Road (11.5 miles west from the lower trailhead, near the junction of FR 41 and FR 4026) for an excellent 14-mile one-way trek in either direction. **Notes:** Trail No. 3125 upstream from the Middle Fork was scheduled for rerouting, possibly in 2013.\n\n  Puffer Butte\n\n**RATING\/DIFFICULTY** | **LOOP** | **ELEV GAIN\/HIGH POINT** | **SEASON**\n\n---|---|---|---\n\n*****\/2** | **2.5 miles** | **600 feet\/4500 feet** | **Apr\u2013Nov**\n\n**Maps:** USGS Fields Spring, state park map online; **Contact:** Fields Spring State Park, (509) 256-3332, www.parks.wa.gov\/parks; **Notes:** Discover Pass required. Dogs permitted on-leash; **GPS:** N 46 04.805 W 117 10.142\n\n  _**Wildlife abounds in this lightly visited region of high plateaus, deep canyons, and pine-forested hills. Washington's rugged and isolated southeastern corner consists of some of the most dramatic landscapes in the state. This short hike up Puffer Butte within Fields Spring State Park rewards you with stunning views that span east across the Snake River to Idaho and south to the lofty jagged Wallowa Mountains of Oregon. And while the views are grand, so are the wildflowers.**_\n\n### GETTING THERE\n\nFrom Clarkston, drive 30.5 miles south on State Route 129 to Fields Spring State Park (the entrance is 4 miles past the tiny community of Anatone). Turn left into the park and come to a four-way junction in 0.4 mile. Continue straight for 0.1 mile to the large parking lot before the campground entrance. Locate the trailhead (elev. 4000 ft) on the south side of the lot.\n\n### ON THE TRAIL\n\nPuffer Butte sits at the eastern edge of the Blue Mountains, teetering high above the sweltering Grande Ronde Valley. With its lofty elevation above 4000 feet, the butte is cloaked with cool pine, larch, and Douglas-fir forest. The butte's namesake was a family\u2014the Puffers\u2014who frequently drove their cattle to the top of this butte when they observed Nez Perce peoples travel through the canyon below. The Nez Perce were forcibly removed from southeast Washington\u2014once part of their traditional lands\u2014in the 1870s.\n\nThe trail begins in mature conifer forest with a lush understory of maple. At 0.2 mile, just after crossing a closed-to-vehicles woods road (excellent for skiing in winter), reach a junction. Continue right\u2014you'll be returning on the trail to your left. Soon afterward, reach another junction. Bear left\u2014the trail right leads to the Wohelo Lodge, one of two environmental learning centers within the 792-acre state park.\n\n_Grand views of the Grande Ronde Valley from Puffer Butte_\n\nAs you ascend gentle slopes, keep your senses tuned to the surroundings for wildlife. Elk and deer are profuse here, as are grouse and wild turkeys. There's little doubt that you'll be flushing these game birds out of the brush. At 0.8 mile, once again cross one of the park's service roads; then soon afterward, cross another one.\n\nNow easily hiking along the broad butte, reach a junction at 1 mile with a short spur that bears right to Puffer's wooded, viewless 4500-foot summit. Visit if you like\u2014then continue straight, reaching another junction at 1.2 miles at the edge of a sprawling meadow. Just to the right at timber's edge is the park's winter warming hut. If you haven't figured it out yet, Fields Spring State Park is a popular and excellent snowshoe and ski-touring center in the winter.\n\nYour loop hike heads left across wide-open meadows of swaying grasses and dazzling wildflowers, including penstemon, daisies, desert parsley, scarlet gilia, sego lilies, and arrowleaf balsamroot. And outdoing the floral arrangement is the view\u2014it's breathtaking! Stare south across the Grande Ronde Valley to the sky-piercing Wallowa Mountains; and east to the Craig Mountains of Idaho hovering above the massive Snake River Canyon.\n\nThe way then bends north, descending from the grassy slopes into pine forest. Continue losing elevation and after crossing a park road reach a junction at 1.9 miles. The trail right leads to primitive camping and more woods road\u2014stay left, soon reaching the Puffer Butte Environmental Learning Center Lodge (elev. 4000 ft).\n\nLocate the Spotted Bear Trail on the west side of the lodge and follow this short path 0.3 mile through pine forest, across a park road, and back to the main trail at a familiar junction (elev. 4100 ft). Turn right and return to the trailhead in 0.2 mile.\n\n### EXTENDING YOUR TRIP\n\nEasily extend your hike by roaming the park's miles of old woods roads. Visit Fields Spring near the Wohelo Lodge and consider spending a peaceful night camping in the park under a cool canopy of pine and fir.\n\n## Conservation and Trail Organizations\n\n### GENERAL\n\n### Blue Mountain Land Trust\n\n(509) 525-3136\n\n<http:\/\/bmlt.org>\n\n### Chelan-Douglas Land Trust\n\n(509) 667-9708\n\nwww.cdlandtrust.org\n\n### Conservation Northwest\n\n(360) 671-9950\n\nwww.conservationnw.org\n\n### Ferry County Rail Trail Partners\n\nwww.ferrycountyrailtrail.com\n\n### Ferry County Trails Association\n\n<http:\/\/fctrails.com>\n\n### Friends of Badger Mountain\n\nwww.friendsofbadger.org\n\n### Friends of Little Pend Oreille National Wildlife Refuge\n\n<http:\/\/refugefriends.com>\n\n### Intermountain Alpine Club\n\nwww.imacnw.org\n\n### Kettle Range Conservation Group\n\nwww.kettlerange.org\n\n### Pacific Northwest Trail Association\n\n(877) 854-7665\n\nwww.pnt.org\n\n### Tapteal Greenway Association\n\n(509) 627-3621\n\nwww.tapteal.org\n\n### Washington Nature Conservancy\n\n(206) 343-4345\n\nwww.nature.org\/washington\n\n### Washington Trails Association\n\n(206) 625-1367\n\nwww.wta.org\n\n### SPOKANE REGION\n\n### The Backpacking Club\n\n(509) 467-8099\n\nwww.backpackingclub.macwebsitebuilder.com\n\n### Dishman Hills Conservancy\n\nwww.dhnaa.org\n\n### Friends of Mount Spokane State Park\n\nwww.mountspokane.org\n\n### Friends of the Spokane River Centennial Trail\n\n(509) 624-7188\n\nwww.spokanecentennialtrail.org\n\n### Friends of Turnbull National Wildlife Refuge\n\nwww.fotnwr.org\n\n### Hobnailers\n\nwww.inlandnorthwesttrails.org\/events\/Hobnailers.asp\n\n### Inland Northwest Hikers\n\nwww.meetup.com\/Inland-Northwest-Hikers\n\n### Inland Northwest Land Trust\n\n(509) 328-2939\n\nwww.inlandnwlandtrust.org\n\n### Inland Northwest Trails Coalition\n\nwww.inlandnorthwesttrails.org\n\n### The Lands Council\n\n(509) 838-4912\n\nwww.landscouncil.org\n\n### Palisades\n\nwww.palisadesnw.com\n\n### Riverside State Park Foundation\n\n<http:\/\/riversidestatepark.org>\n\n### Spokane Mountaineers\n\n(509) 838-4974\n\nwww.spokanemountaineers.org\n\n## INDEX\n\nThe index that appeared in the print version of this title was intentionally removed from the eBook.Please use the search function on your eReading device to search for terms of interest. For your reference, the terms that appear in the print index are listed below.\n\nAbercrombie Mountain\n\nAmon Basin\n\nAncient Lakes\n\nAntoine Peak\n\nAntoine Trail\n\nAsotin Creek Wildlife Area\n\nAsotin Creek\n\nBabcock Bench\n\nBack Country Horsemen\n\nBadger Mountain\n\nBald Mountain\n\nBarnaby Buttes\n\nBateman Island\n\nBeacon Hill\n\nBead Lake\n\nBear Creek Trail\n\nBear Pot Trail\n\nbear spray\n\nbears\n\nBeaver Lake\n\nBeezley Hills\n\nBennington Lake\n\nBeth Lake\n\nBig Meadow Lake\n\nBig Rock\n\nBig Tree Botanical Area\n\nBighorn sheep\n\nBlack Diamond Lake\n\nBlue Mountains\n\nBluewood Ski Area\n\nBluff Trail\n\nBobs Lakes\n\nBonaparte Lake\n\nBowl and Pitcher\n\nBurbank Slough Wildlife Trail\n\nBureau of Land Management (BLM)\n\nBurping Brook Basin\n\nCamel Back\n\nCanyon Trail\n\ncaribou\n\nChamna Natural Preserve\n\nChanneled Scablands\n\nChinook Jargon\n\nCivilian Conservation Corps\n\nClackamas Mountain\n\nClaybell Park\n\nColumbia Basin Wildlife Area\n\nColumbia Highlands\n\nColumbia Mountain\n\nColumbia National Wildlife Refuge\n\nColumbia Park\n\nColumbia Plateau Trail\n\nColville Confederated Tribes\n\nConservation Northwest\n\nconservation organizations\n\nCopper Butte\n\nCougar Mountain Roadless Area\n\ncougars\n\nCrab Creek (Columbia NWR)\n\nCrab Creek (Rocky Ford)\n\nCrawford State Park\n\nCrowell Ridge\n\nCurlew Job Corps\n\nCurlew Lake State Park Nature Trail\n\nDay Mountain\n\nDeadman Creek\n\nDeadman Peak\n\nDeep Creek Canyon\n\nDiamond Peak\n\nDishman Hills\n\nDishman Hills Conservancy\n\ndogs\n\nDrumheller Channels\n\nDuportail Trail\n\nDusty Lake\n\nEagle Peak\n\nEdds Mountain\n\nElk Creek Falls\n\nEmerald Lake\n\nEscure Ranch\n\nFerry County Rail Trail\n\nFields Spring State Park\n\nFir Mountain\n\nfire lookouts\n\nFish Lake (Ferry County)\n\nFish Lake Trail\n\nfishing\n\nFishtrap Lake\n\nFort George Wright Cemetery\n\nFort Spokane\n\nFourth of July Ridge\n\nFrater Lake\n\nFrenchman Coulee\n\nFrog Lake (Columbia NWR)\n\nFrog Pond (Whistler Canyon)\n\nFryxell Overlook\n\nFur, Fins, and Feathers Nature Trail\n\ngear\n\nGibraltar Mountain\n\nGibraltar Trail\n\nGillette Ridge\n\nGolden Tiger Pathway\n\nGrassy Top Mountain\n\nGreat Northern Railroad\n\nGrizzly Bear Ridge\n\nGypsy Lakes\n\nGypsy Peak\n\nHall Mountain\n\nHalliday Trail\n\nHanford Reach National Monument\n\nhedgehog cactus\n\nHelmer Mountain\n\nhiking clubs\n\nHog Canyon Lake\n\nHoodoo Canyon\n\nHooknose Mountain\n\nhorses\n\nHungry Mountain\n\nHunter Spring\n\nhunting\n\nIce Age Floods\n\nIller Creek Conservation Area\n\nIndian Corral\n\nIndian Painted Rocks\n\nInland Northwest Hikers\n\nJack Rabbit Trail\n\nJungle Hill\n\nJuniper Dunes Wilderness\n\nKalispell Rock\n\nKamiak Butte\n\nKepple Lake\n\nKettle Crest Trail\n\nKettle Range Conservation Group\n\nKettle River Range\n\nKettle Valley Rail Trail\n\nKing Mountain\n\nKingfisher Loop\n\nLake Leo\n\nLake Lewis\n\nLake Roosevelt National Recreation Area\n\nLake Spokane (Long Lake)\n\nLakeview Ranch\n\nLeona Loop Trail\n\nLewis and Clark\n\nLewis and Clark State Park\n\nLiberty Lake Park\n\nlightning\n\nLittle Grass Mountain\n\nLittle Pend Oreille National Wildlife Refuge\n\nLittle Spokane River\n\nLog Flume Heritage Site\n\nLong Lake (Lake Spokane)\n\nLong Lake (Ferry County)\n\nLost Lake Campground\n\nMadam Dorian Park\n\nManhattan Project\n\nMankato Mountain\n\nMaple Mountain\n\nMarcus Trail\n\nMarsh Loop Trail\n\nMcDowell Lake\n\nMcLellan Conservation Area\n\nMcNary National Wildlife Refuge\n\nMeenach Bridge\n\nMica Peak\n\nMiddle Point Ridge\n\nMidnight Mountain\n\nMidnight Ridge Trail\n\nMill Butte\n\nMill Creek\n\nMill Creek Recreation Trail\n\nmima mounds\n\nMolybdenite Mountain\n\nmonadnock\n\nmoose\n\nMoses Coulee\n\nMount Bonaparte\n\nMount Kit Carson\n\nMount Leona\n\nMount Misery\n\nMount Misery Trail\n\nMount Rogers\n\nMount Spokane State Park\n\nmountain mahogany\n\nNapol Cabin\n\nNew Forestry Coalition\n\nNez Perce\n\nNine Mile Falls\n\nNisbit, Jack\n\nNorth Baldy Mountain\n\nNorthrup Canyon\n\nNorthrup Lake\n\nOdessa Craters\n\nOdessa Lake Creek Trail\n\nOdessa Towers\n\nOkanogan fameflower\n\nOkanogan Highlands\n\nOld Kettle Falls Trail\n\nOld Stage Trail\n\nOld Wagon Road Trail\n\nOregon Butte\n\nPacific Lake\n\nPacific Northwest Trail\n\nPalisades Park\n\nPalouse Falls\n\nPalouse Hills\n\nPalouse River\n\nPass Spring Trail\n\nPend Oreille County Park\n\nPend Oreille River\n\nPeninsula Loop Trail\n\npermits\n\nPine Lakes\n\nPipsissewa Trail\n\npoison ivy\n\npoison oak\n\nPriest Lake\n\nProfanity Roadless Area\n\nPuffer Butte\n\nQuartz Mountain\n\nQuincy Lakes\n\nrail trails\n\nRattlesnake Mountain\n\nrattlesnakes\n\nRed Bluff\n\nRiverfront Park\n\nRiverside State Park\n\nRocks of Sharon\n\nRogers Mountain\n\nRoggow Cabin\n\nRoosevelt Grove of Ancient Cedars\n\nRound Top Mountain\n\nRyan Cabin Trail\n\nSacagawea Heritage Trail\n\nSacajawea\n\nSacajawea State Park\n\nSaddle Mountain\n\nSagebrush Trail\n\nSaint Paul Mission\n\nSalmo River\n\nSalmo-Priest Wilderness\n\nSaltese Uplands\n\nsandhill crane\n\nSawtooth Ridge\n\nSelkirk Mountains\n\nSentinel Butte\n\nSentinel Trail\n\nShedroof Divide\n\nShedroof Mountain\n\nShedroof Cut-off Trail\n\nSheephead Corral\n\nSherlock Peak\n\nSherman Creek\n\nSherman Pass Trail\n\nSherman Peak\n\nSherman Pond\n\nSimilkameen Trail\n\nSkyline Trail\n\nSlavin, James T., Conservation Area\n\nSnow Peak\n\nSnow Peak Cabin\n\nSnowy Top Mountain\n\nSouth Hill Bluff\n\nSouth Side Trail\n\nSpokane\n\nSpokane Aquifer\n\nSpokane bridges\n\nSpokane County Conservation Futures\n\nSpokane Indian Tribe\n\nSpokane Mountaineers\n\nSpokane River\n\nSpokane River Centennial Trail\n\nSpotted Bear Trail\n\nSt. George's School\n\nSteamboat Rock\n\nSteamboat Rock State Park\n\nSteptoe Butte\n\nStickpin Trail\n\nStrawberry Mountain\n\nSullivan Lake\n\nSullivan Mill Pond\n\nSwan Butte\n\nSwan Lake\n\nSwanson Lakes Wildlife Area\n\nSweat Creek Basin Trail\n\nTable Rock Lookout\n\nTapteal Greenway Association\n\nTaylor Ridge\n\nTelford Recreation Area\n\nten essentials\n\nThe Nature Conservancy\n\nThirteen Mile Roadless Area\n\nThirteenmile Canyon\n\nThirteenmile Mountain\n\nThirty-Acre Lake\n\nThompson, David\n\nThunder Creek\n\nThunder Mountain\n\nticks\n\nTowell Falls\n\ntrail etiquette\n\nTrailhead Park\n\nTri-Cities\n\nTrout Lake campground\n\nTucannon River\n\nTurnbull National Wildlife Refuge\n\nTwin Buttes\n\nTwin Lakes\n\nTwin Sisters Roadless Area\n\nUpper Tucannon River Roadless Area\n\nUS Mountain\n\nVirginia Lilly Trail\n\nWahluke Lake\n\nWall Lake (Escure Ranch)\n\nWall Lake (Twin Lakes)\n\nWapaloosie Mountain\n\nWashington Trails Association\n\nWatch Lake\n\nwater\n\nweather\n\nWenaha River\n\nWenaha-Tucannon Wilderness\n\nWest Butte\n\nWest Fork Cougar Creek Trail\n\nWhistler Canyon\n\nWhite Bluffs\n\nWhite Mountain\n\nWhite Mountain Burn\n\nWhitetail Trail\n\nWilderness Act\n\nwilderness ethics\n\nwildlife\n\nwolverine\n\nwolves\n\nZ Lake \n\n## Bonus Hikes\n\nEastern Washington is so flush with good trails, we couldn't resist including thirty additional hikes worth exploring!\n\n### COLUMBIA HIGHLANDS: OKANOGAN HIGHLANDS\n\n**1. McLoughlin Canyon:** Short, 1.5-mile trail along part of the historical fur-trading route and Cariboo Trail to British Columbia goldfields; and the site of an 1858 ambush and massacre. Access is from McLoughlin Canyon Road, milepost 311 4 miles south of Tonasket. Information: BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane\/index.php.\n\n**2. Island Park:** Community-built trail system along Okanogan River in the city of Okanogan. Currently 1.4 miles of trail are in place, with more planned. Access is just south of the Okanogan City Maintenance Department (1601 1st Avenue South).\n\n**3. Fourth of July Ridge:** Long and lonely 7-mile trail along the high southwest ridge of Mount Bonaparte. Connects to Southside Trail and Napol Cabin Trail, leading to Antoine Trail, allowing for loop around Mount Bonaparte. Access is from FR 3230. Information: Okanogan-Wenatchee National Forest, Tonasket Ranger District, (509) 486-2186, www.fs.fed.us\/r6\/okawen.\n\n**4. Tenmile Trail:** Lightly hiked 2.5-mile trail from Sanpoil River valley up steep slopes above Tenmile Creek, through scree slopes and pine groves. Good spring flower hike. Access is from Tenmile Campground on SR 21 south of Republic. Information: Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.fed.us\/r6\/colville.\n\n**5. Long Lake:** Along with nearby Fish Lake, hike 1.5 level miles along two small lakes popular with fishermen and -women. Some scree and some brush. Access is off of FR 53 near Swan Lake south of Republic. Information: Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.fed.us\/r6\/colville.\n\n### KETTLE RIVER RANGE\n\n**6. Profanity Trail:** Hard to find and hard to follow 1.5-mile trail through alpine meadows to Kettle River Range. Access is from FR 2160 off of Aeneas Road north of Republic on SR 21. Information: Colville National Forest, Republic Ranger District, (509) 775-7400, www.fs.fed.us\/r6\/colville.\n\n### SELKIRK MOUNTAINS\n\n**7. Pierre Lake Trail:** Family-friendly 0.8-mile trail along a small lake in the \"wedge,\" the highlands between the Kettle and Columbia rivers. Access is from the USFS Pierre Lake Campground off of Stevens County Road 4015 northeast of Orient. Information: Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 738-7700, www.fs.fed.us\/r6\/colville.\n\n**8. Newport Wolf Trails:** A series of loops form nearly 5 miles of forested trails at the edge of Newport. Named in memory of former Newport Miner publisher Fred Wolf, the trails are easy and suited for families. The 0.75 mile Trail No. 305 connects through forest to 1.5-mile Trail No. 304. The trails are graced by wildflowers in May and lead to viewpoints of the Pend Oreille River and Ashenfelter Bay. The 2.5 miles of upper trails are geared more to Nordic skiing and mountain biking. Access to the lower trails is from SR 20 on the north edge of Newport: turn north on Warren Avenue and drive 1 mile to the lower trailhead. Access to the upper trails is from SR 20: turn west onto Larch Street, go one block, turn north on Laurelhurst Drive, and then go 0.5 mile to the parking area. Information: Colville National Forest, Newport Ranger District, (509) 447-7300, www.fs.fed.us\/r6\/colville.\n\n**9. Halliday Trail:** Easily accessible from SR 31 just south of the US\u2013Canada border, Halliday Trail No. 522 runs 4.2 miles through a remarkably diverse forest and along the Halliday Fen, a tranquil wetland protected as a research natural area. This trail links to Red Bluff Trail No. 553 and North Fork Sullivan Creek Trail No. 507, which leads into the Salmo-Priest Wilderness all the way up to Crowell Ridge Trail No. 5115. Access is from Metaline Falls: Follow SR 31 north 6.5 miles. Turn right at the Halliday trailhead sign and then immediately left on the spur to the trailhead. Information: Colville National Forest, Sullivan Lake Ranger District, (509) 446-7500, www.fs.fed.us\/r6\/colville.\n\n**10. Silver Creek Trails:** The Silver Creek Campground just southwest of Abercrombie Mountain is a base for two good hikes. South Fork Silver Creek Trail No. 123 crosses creeks and gains 2200 feet in 7 miles. North Fork Silver Creek Trail No. 119 leads nearly 6 miles to a junction with Abercrombie Mountain Trail No. 117--a good hike in itself--or continue another 5.9 miles to the top of Abercrombie for a marathon round-trip of nearly 24 miles. See Hike 43 for access northeast of Colville. Information: Colville National Forest, Three Rivers Ranger District, Kettle Falls, (509) 738-7700, www.fs.fed.us\/r6\/colville.\n\n### AROUND SPOKANE\n\n**11. McKenzie Conservation Area:** Nearly 5 miles of volunteer-built trails on 421 acres on forested slopes along Newman Lake near the Idaho border. Access is from I-90 at Liberty Lake: Go north 2.4 miles on Harvard Road. Turn east on Trent Avenue (SR 290), go 2.2 miles to a four-way intersection, and turn left (north) on Starr Road. Drive 3 miles and turn right at the Y onto Hauser Lake Road. Drive less than a half mile and turn left on Muzzy Road. Drive 4.5 miles (Muzzy Road becomes West Newman Lake Road) to the trailhead down to the left. Information: Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks.\n\n**12. Glenrose Conservation Area (proposed):** About 4 miles of routes lead through timber and grassy meadows to two good viewpoints overlooking the Spokane Valley. Access is from the Palouse Highway in south Spokane: Go east on 57th Avenue, which becomes Glenrose Road as it bends left (north). Follow Glenrose and turn east on 34th Avenue. Turn right on Eastern Road. Just past Dyer Rod, turn north on Thierman Road and drive to the trailhead at the end of the pavement. Park off the road; don't block roads or the gate. Information: Spokane County Parks and Recreation, (509) 477-4730, www.spokanecounty.org\/parks.\n\n**13. Dwight Merkel Trail:** Beautifully graded connector in a network of volunteer-built trails, leading from recreational sports fields in northwest Spokane to trails in Riverside State Park. Enjoy the bustle of youthful activity on the baseball and soccer fields along the 3.1-mile perimeter trail around the Dwight Merkel Sports Complex and Joe Albi Stadium, some of it paved. Trails take off into woods west from the Merkel Complex. Access is from Assembly Street in northwest Spokane. Information: Spokane City Parks and Recreation, (509) 625-6200, www.spokaneparks.org\/parks.\n\n**14. Spokane River Centennial Trail:** The Spokane area's most popular paved trail, running 37 miles from Nine Mile Falls east to the Idaho state line (and farther into Idaho). It links Riverside State Park, downtown, and neighborhoods for hiking, biking, commuting, running, skating, and bicycling. The path generally contours the Spokane River, with 30 miles of trail completely separated from roads and traffic. Access is from Riverside State Park at Nine Mile Falls, from the state line exit off I-90, or from numerous points in between. Information: Friends of the Centennial Trail, (509) 624-7188, www.spokanecentennialtrail.org.\n\n**15. West Branch Little Spokane River Wildlife Area:** Numerous unmarked and unmapped old logging roads and trails lace this 2772-acre diamond in the rough in Pend Oreille County, including wildlife-rich wetlands and uplands from Horseshoe Lake south to Fan Lake. Access is from US 2: Head west on Eloika Lake Road to the locked gate off the corner of Horseshoe Lake Road and Holly Road. Information: Washington Department of Fish and Wildlife, Spokane office, (509) 892-1001, <http:\/\/wdfw.wa.gov\/lands\/wildlife_areas>.\n\n**16. Medical and West Medical Lakes:** Two good fishing lakes on the outskirts of their namesake city. From the popular Waterfront Park, the paved Lake Trail circumnavigates Medical Lake in 3 miles. The wooded west side stays away from homes. Paths to the southeast corner of the lake lead to popular cliff-jumping areas. West Medical Lake, just a short way west of Medical Lake, has a nice 1.7-mile single-track along the lake's west shore. The informal trail starts through a hole in the chain link fence near the boat ramp at the far end of the public access parking lot. Access is from the Medical Lake exit (exit 272) off of I-90: Follow SR 902 west about 5 miles to the city of Medical Lake. Turn left (south) on Lefevre Street through downtown to the entrance of Waterfront Park. Information: City of Medical Lake, (509) 565-5000, www.medical-lake.org\/citserv\/parks.asp.\n\n### COLUMBIA PLATEAU\n\n**17. Columbia Plateau Trail:** This rail trail managed as a state park runs 130 miles from Cheney to Pasco, following a portion of the abandoned Spokane, Portland and Seattle Railroad. The choice route for walking or mountain biking runs from Cheney through the west side of Turnbull National Wildlife Refuge and southwest for a total of 15 miles. (Another 15 miles runs from Ice Harbor Dam to Snake River Junction.) The 3-mile paved portion of the Fish Lake Trail also leaves from the Cheney trailhead. Access is from Cheney, just off Cheney\u2013Spangle Road (the route to Turnbull National Wildlife Refuge). Information: Washington State Parks, Columbia Plateau Trail, (360) 902-8844, www.parks.wa.gov\/parks.\n\n**18. Umatilla Rock:** Explore several miles of dirt roads and trails at the base of Dry Falls in Monument Coulee, in 4000-acre Sun Lakes State Park. Access is off of SR 17 just south of Coulee City. Information: Washington State Parks, (509) 632-5583, www.parks.wa.gov\/parks.\n\n**19. Blythe and Chukar Lakes:** Round-trip of 3 miles to two large lakes in the Drumheller Channels south of the Potholes Reservoir. Access is off of SR 262 (across from Mar Don Resort), 3.6 miles west of the refuge road leading to the Crab Creek trails. Information: Columbia National Wildlife Refuge, (509) 546-8300, www.fws.gov\/columbia.\n\n**20. Saddle Mountain:** From the mountaintop trailhead, roam for miles on primitive paths across 2000-plus-foot Saddle Mountain, admiring flowers and views of the Hanford Reach and Columbia Basin. Access is off of SR 24 west of the road to White Bluffs trails. Information: Hanford Reach National Monument, (509) 546-8300, www.fws.gov\/hanfordreach.\n\n### AROUND TRI-CITIES\n\n**21. Sacajawea State Park:** Several miles of quiet trails in a pretty 284-acre state park at the confluence of the Snake and Columbia rivers. Lewis and Clark interpretive displays, big trees, and lots of wildlife. Access is off of US 12 just east of Pasco. Information: Washington State Parks, (509) 545-2361, www.parks.wa.gov\/parks.\n\n### BUREAU OF LAND MANAGEMENT AREAS\n\n**22. Badger Mountain (Waterville Plateau):** Several miles of trails in the Duffy Creek and Douglas Creek recreation sites on Badger Mountain south of Waterville. Access is off of US 2 via either Titchenal Canyon Road or Road H. Good map online. Information: BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane.\n\n**23. Odessa Craters:** Two short trails to two unique craters formed by the Great Missoula Floods. Access is on SR 21 just north of the Lakeview Ranch. Information: BLM Spokane District, (509) 536-1200, www.blm.gov\/or\/districts\/spokane.\n\n### PALOUSE AND SNAKE RIVERS\n\n**24. Lyons Ferry:** Hike an easy mile to Chief Old Bones's grave on a scenic bluff at the confluence of the Snake and Palouse rivers in this nice park administered by the Port of Columbia. Access is on SR 261 a few miles south of Palouse Falls. Information: Port of Columbia, (509) 382-2577; <http:\/\/portofcolumbia.org>.\n\n**25. Bill Chipman Palouse Trail:** An 8-mile paved rail trail, roughly paralleling SR 270 between Pullman and Moscow, Idaho, including thirteen bridges over Paradise Creek. Access is from the Quality Inn in Pullman and at Perimeter Drive in Moscow. Information: Pullman Civic Trust, www.pullmancivictrust.org.\n\n**26. Klemgard County Park:** Family-friendly 0.9-mile loop in a 59-acre green oasis surrounded by the rolling Palouse wheat fields. The park's playground and picnic shelters are a popular gathering spot in a forested canyon along Union Flat Creek. The trail leads high above the park through woods and along a creek. Access is from Colfax: Drive south on US 195 for 6 miles (to milepost 30.7), and turn west on Hamilton Hill Road toward Klemgard Park. Drive 2.5 miles to the bottom of Canyon Flat and turn right on Union Flat Road. Go 1 mile to the park. Information: Whitman County Parks and Recreation, Colfax, (509) 397-6238, www.whitmancounty.org.\n\n**27. Snake River Trail:** Hiking-biking trail along the shore of the Snake River, running 3.5 miles from Almota Creek near the well-developed Boyer Park Marina and Campground to the base of Lower Granite Dam. Access is from Colfax: Follow Almota Road 15 miles to the Snake River. Turn left and follow Granite Road 3 miles to Boyer Park. Information: Boyer Park and Marina, (509) 397-3208, www.bpark.biz.\n\n### BLUE MOUNTAINS\n\n**28. Asotin Creek Wildlife Area:** Although it has few maintained trails, this 34,000-acre wildlife area offers many miles of vehicle-restricted roads and ridges for hiking in the foothills of the Blue Mountains. Access is from the town of Asotin. Get maps and explore. Information: Washington Department of Fish and Wildlife, Spokane office, (509) 892-1001, www.wdfw.wa.gov\/lands\/wildlife_areas.\n\n**29. Slick Ear Trail:** Plunge to the Wenaha River in the Wenaha-Tucannon Wilderness after a gentle mile on a ridge. Slick Ear Trail No. 3104 descends on many switchbacks for 0.5 mile, with great views. The rest of the hike to the river is more gentle along Slick Ear Creek, but the round-trip is 10.4 miles and you'll gain 2500 feet of elevation on the way out. Access is from south of Dayton: Drive FR 46 toward Godman Spring, linking with FRs 300 and 301 to reach the trailhead. Information: Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.fed.us\/r6\/uma\/pomeroy.\n\n**30. Wenaha River Trail:** Although it's in Oregon just south of the Washington border, Wenaha River Trail No. 3137 is popular with Eastern Washington hikers, especially in early spring. It's one of the region's first long wilderness hikes to be free of snow, although spring runoff can make it impossible to safely cross Crooked Creek, the first drainage inside the Wenaha-Tucannon Wilderness boundary. The entire trail runs 31 miles. Temperatures soar on the trail during hot weather. Access is at the trailhead just outside Troy, Oregon. Information: Umatilla National Forest, Pomeroy Ranger District, (509) 843-1891, www.fs.fed.us\/r6\/uma\/pomeroy.\n\n## About the Authors\n\n**_Rich Landers (left) and Craig Romano_ (Photo by Aaron Theisen)**\n\n**Rich Landers,** a native Montanan, has been the Outdoors editor for the _Spokesman-Review_ in Spokane since 1977, covering hiking, conservation, hunting, fishing, climbing, bicycling, public lands, and other outdoor pursuits. He is a contributing writer for _Field and Stream_ magazine and author of _100 Hikes in the Inland Northwest_ and _Paddling Washington_.\n\n**Craig Romano** grew up in rural New Hampshire, where he fell in love with the natural world. He has traveled from Alaska to Argentina, Sicily to South Korea, seeking wild and spectacular landscapes. He ranks Washington State among the most beautiful places on the planet, and he has hiked it from Cape Flattery to Puffer Butte. He is a columnist for _Northwest Runner_ and _Outdoors NW_ and author of nine books, among them _Day Hiking Olympic Peninsula, Day Hiking North Cascades, Day Hiking Columbia River Gorge, Backpacking Washington_ , and _Columbia Highlands: Exploring Washington's Last Frontier_ , which was recognized in 2010 as a Washington Reads book for its contribution to the state's cultural heritage. When not hiking and writing, he can be found napping with his wife, Heather, and cats, Giuseppe and Scruffy Gray, at his home in Skagit County. Visit him at <http:\/\/CraigRomano.com> and on Facebook at \"Craig Romano Guidebook Author.\"\n\nTHE MOUNTAINEERS, founded in 1906, is a nonprofit outdoor activity and conservation organization whose mission is \"to explore, study, preserve, and enjoy the natural beauty of the outdoors. . . .\" Based in Seattle, Washington, it is now one of the largest such organizations in the United States, with seven branches throughout Washington State.\n\nThe Mountaineers sponsors both classes and year-round outdoor activities in the Pacific Northwest, which include hiking, mountain climbing, ski-touring, snowshoeing, bicycling, camping, canoeing and kayaking, nature study, sailing, and adventure travel. The Mountaineers' conservation division supports environmental causes through educational activities, sponsoring legislation, and presenting informational programs.\n\nAll activities are led by skilled, experienced volunteers, who are dedicated to promoting safe and responsible enjoyment and preservation of the outdoors.\n\nIf you would like to participate in these organized outdoor activities or programs, consider a membership in The Mountaineers. For information and an application, write or call The Mountaineers Program Center, 7700 Sand Point Way NE, Seattle, WA 98115-3996; phone 206-521-6001; visit www.mountaineers.org; or email info@mountaineers.org.\n\nThe Mountaineers Books, an active, nonprofit publishing program of The Mountaineers, produces guidebooks, instructional texts, historical works, natural history guides, and works on environmental conservation. All books produced by The Mountaineers Books fulfill the mission of The Mountaineers. Visit www.mountaineersbooks.org to find details about all our titles and the latest author events, as well as videos, web clips, links, and more!\n\n  | The Mountaineers Books\n\n1001 SW Klickitat Way, Suite 201\n\nSeattle, WA 98134\n\n800-553-4453\n\nmbooks@mountaineersbooks.org\n\n---|---\n\n  The Mountaineers Books is proud to be a corporate sponsor of The Leave No Trace Center for Outdoor Ethics, whose mission is to promote and inspire responsible outdoor recreation through education, research, and partnerships. The Leave No Trace program is focused specifically on human-powered (non-motorized) recreation.\n\nLeave No Trace strives to educate visitors about the nature of their recreational impacts and offers techniques to prevent and minimize such impacts. Leave No Trace is best understood as an educational and ethical program, not as a set of rules and regulations.\n\nFor more information, visit www.lnt.org, or call 800-332-4100.\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\n**Contents**\n\nGin Martini Calls\n\nHow to Value a Species and Why We Should Care\n\nCreating a Synopsis\n\nWoolly Mammoth\n\nRalph emails: Anyway \u2013 starting is necessary...\n\nForeword\n\nHumphead Wrasse\n\nSingapore Freshwater Crab\n\nGrunting Spiked Turt\n\nAmur Leopard\n\nInvasion of the Gonzovationists\n\nGroglick\n\nRed Wowlet\n\nJamaican Iguana\n\nSumatran Rhinoceros\n\nMountain Gorilla\n\nHawksbill Turtle\n\nBornean Orangutan\n\nSumatran Orangutan\n\nChinese Pangolin\n\nSunda Pangolin\n\nPygmy Tarsier\n\nManed Three-toed Sloth\n\nThe Visitation\n\nHector's Dolphin\n\nHippopotamus\n\nIrrawaddy Dolphin\n\nAfrican Elephant\n\nAsian Elephant\n\nBonobo\n\nSaiga Antelope\n\nNorthern Hairy-nosed Wombat\n\nAngelshark\n\nPygmy Three-toed Sloth\n\nTarzan's Chameleon\n\nBlack-footed Ferret\n\nPrzewalski's Horse\n\nStriped Spirit Wint\n\nCuban Crocodile\n\nKanab Ambersnail\n\nPool-strutting Monkeychick\n\nPhilippine Crocodile\n\nSeychelles Sheath-tailed Bat\n\nDigg Soiler\n\nDratsab\n\nWhite Rhinoceros\n\nAtlantic Bluefin Tuna\n\nSouthern Bluefin Tuna\n\nPacific Bluefin Tuna\n\nGolden-rumped Sengi\n\nLord Howe Island Stick Insect\n\nLuristan Newt\n\nRat-arsed Skunk\n\nAye-aye\n\nBaad Guttering\n\nGnat Flutterby\n\nLittle Mother Moth\n\nRed Wolf\n\nTiger\n\nGrevy's Zebra\n\nGiant Panda\n\nBorneo Pygmy Elephant\n\nSnow Leopard\n\nChimpanzee\n\nTerry Cotter \u2013 the Island's Potter\n\nFin Whale\n\nGal\u00e1pagos Sea Lion\n\nBlack Rhinoceros\n\nBlue Whale\n\nGolden Bamboo Lemur\n\nLong-nosed Gwylim\n\nBlack Spider Monkey\n\nSuicide Palm\n\nAddax or White Antelope\n\nAfrican Wild Dog\n\nAmazonian Manatee\n\nAmerican Manatee or West Indian Manatee\n\nAfrican Manatee\n\nGrey Nurse Shark\n\nGarden Bumblebee\n\nPolar Bear\n\nArticulated Bumlice\n\nGreek Red Damsel\n\nLion\n\nHula Painted Frog\n\nIndri\n\nDelhi Sands Flower-loving Fly\n\nWestern Long-beaked Echidna\n\nEastern Long-beaked Echidna\n\nSir David's Long-beaked Echidna\n\nVisiting the Steadman Uncontinuum\n\nMongolian Beaver\n\nVolcano Rabbit\n\nAfrican Wild Ass\n\nDylis Voryd\n\nPeacock Parachute Spider\n\nSaint Lucia Racer\n\nIndian Python\n\nHorrid Ground-weaver Spider\n\nWhy-me?\n\nSkimleach\n\nFrigate Island Giant Tenebrionid Beetle\n\nChinese Giant Salamander\n\nVaquita\n\nLeatherback Sea Turtle\n\nRed Squirrel\n\nSaola\n\nMonarch Butterfly\n\nLargetooth Sawfish\n\nWalrus\n\nWhite-headed Langur\n\nMasai Giraffe\n\nReticulated Giraffe\n\nSouthern Giraffe\n\nNorthern Giraffe\n\nBactrian Camel\n\nLemur Leaf Frog\n\nDugong\n\nWestern European Hedgehog\n\nWe're two gonzovationists\n\nThat's conservation with a twist\n\nAnd laughter has to be the key\n\nWhen we smile we are engaged\n\nBut the stories on each page\n\nTell the damage wreaked by humanity\n\nThe pictures give great cheer\n\nBut the words are full of fear\n\nAs critters fall throughout the day\n\nProgress owns an iron fist\n\nA swift flick of its wrist\n\nDestroys whatever's in its way\n\nBe a gonzovationist\n\nSupport the critters in our midst\n\nThere is a need to gonzovert the crowd\n\nTo help the vast array\n\nOf wildlife every day\n\nTo roam freely would make us truly proud\n\n_By Levy\/Steadman_\n\n_Ralph_ : What are we going to do next?\n\n_Ceri_ : I reckon we concentrate on all the endangered creatures in the world other than birds. I am busy compiling a list of the critically endangered species in the world and there are over 4,500 of them.\n\n_Ralph_ : You know how to discourage me, with your wretched lists and numbers of critical critters in the thousands.\n\n_Ceri_ : Critical Critters! I like it. Don't worry, Ralph, we won't do them all. There are three or four we can leave out.\n\n_Ralph_ : Oh dear... Better get some more ink in. Right then, you're the Navigator, better get the _Steadmanitania_ where it needs to go.\n\n_Ceri_ : Aye aye, Cap'n. Good to be back on board with you. We have many stories to relay in our roles as gonzovationists.\n\n_Ralph_ : That is the purpose of our mission. You write it all down and I'll draw it.\n\n_Ceri_ : And one last thing to remember... No beaks this time round.\n\n**Gin Martini Calls**\n\nOur books always start with a phone call from Se\u00f1or Gin Martini, our publisher at Bloomsbury. 'So what's the plan for the third book of the trilogy? What bird angle have you got covered now?' I reply, 'We've done birds, extinct ones and endangered ones. What could we do next with them other than all the ones that are having a cheerful and fine time? We're not very good at doing plain old happy. Not really our thing. We need to sink our teeth into a subject, stick up for something we can fight for and believe in. And Ralph needs to stop putting beaks on everything. Beak addiction is a terrible thing. He needs to start drawing other appendages and animal attributes, like paws and claws, trunks and proboscides. (I looked it up and that is genuinely the plural of proboscis. I had expected it to be proboscii or some such thing, but what do I know?) We need different creatures, critically endangered creatures, we should be sticking up for lions and tigers and bears with the odd troubled newt thrown in for good measure. We could call the book _Critical Critters_.'\n\n' _Critical Critters_ is good for a working title,' says Gin, 'We just need a synopsis and I'll get it cleared with the board. Can you sort that out?' I huff in indignation. 'A synopsis? From us? We don't do that sort of thing. We didn't do one for the first two books and I can't see the need for it now. It would ruin the surprise too. If you need a synopsis then you should write it. You know what you're looking for.' 'Speak to Ralph, maybe you can come up with something between you.'\n\nWith my haughtiness in full cry and my hackles raised I tell Ralph about the need for a synopsis and he says rather philosophically, 'You're so sniffy! If Jim wants a synopsis then we should give him a synopsis. What kind of critter do you think it would look like? I'll draw a Synopsis.' We giggle like a couple of geese cackling into our tea. And with that I know we are back. Critters here we come. It's your turn to feel Ralph's brush tickling your areas into life on that good old A1 paper, while I describe your measurements. Critterific.\n\nRalph has put me in the right frame of mind with his simple idea of drawing a synopsis and this, in turn, has focused my attention on the matter at hand \u2013 and I realise it's time to do some research. Just how precarious a state do the world's animals find themselves in? We know how bad it is for birds, but is it the same for all the other living things out there and where is the best place to begin our journey?\n\nWhat we want to achieve is to show the incredible diversity of species that are threatened and to show that across the board we have critically endangered critters, from fungi, reptiles, plants and marine life to birds and mammals. We have covered the birds in our last two books, _Extinct Boids_ and _Nextinction_ , so you won't see one in here. Well, in principle you won't but I should never say never, especially where Ralph is concerned. I am trying to wean him off birds but I feel he will sneak the odd beaky one in here and there.\n\n_Ralph_ : Look at what I just discovered in the studio. An ark! I can't remember what it was for but it was many moons ago.\n\n_Ceri_ : Is there nothing you haven't tried? Perhaps we can dust it down and get it back out on the water. Could we pimp it up a bit for the 21st century? Hot-rod it and modernise it a little? Soup it up and crash through the waves?\n\n_Ralph_ : No. We're sticking with the _Steadmanitania_ , no ark. You just want me to draw you again like I did for the original _Steadmanitania_ and get yourself in another picture.\n\n_Ceri_ : It was a great likeness that you captured for that image. You portrayed my best side and best features. I liked it a lot. It was and remains, the finest portrait of me that I have ever seen. It has that certain ' _je ne sais quoi_ ' about it. So you receive my eternal gratitude for not showing me up in your inks. You could have been withering if the mood had taken you. I liked being a Ralph 'stickman'.\n\n_Ralph_ : That's me, Ralph Stickman.\n\n_Ceri_ : That'll stick, Stickman. But thinking about it maybe the _Steadmanitania_ could be an Ark Gallery. We find the critters, I research them, you draw them, and we don't need to collect any critters at all. Sorted. Better dust down the _Steadmanitania_ , Cap'n.\n\nOriginal black and white version of the _Steadmanitania_ image with Ralph and Ceri onboard.\n**How to Value a Species and Why We Should Care**\n\nThere is a thought that not all species are valued in the same way. It is considered that some Non-governmental Organisations (NGOs) may prioritise their agendas and work to conserve certain species and decide which ones may prove to have some intrinsic human value. Is the last of the Willow Blister fungi, found in only one Welsh location, worth saving as much as a Black Rhino? It may be that there is a conservation pecking order. But isn't all life to be appreciated? Do we, as humans, not take ugly people into hospital to be cured? Yes, we do. There is no beauty gauge as to which particular person we decide to help, so shouldn't we treat all species the same way? Undoubtedly there is a discussion to be had.\n\nIn 2012, the ZSL (Zoological Society of London) and the IUCN (International Union for the Conservation of Nature) released _Priceless or Worthless_ , a review of the 100 most threatened species that may be allowed to die out because there are no human advantages to keeping them alive and kicking. This does suggest that it's a case of species discrimination. I think we should protect the 'uglies' as much as any other creature. After all, everything has a mother and she would love her offspring \u2013 well, apart from the munching matriarchs that may occasionally eat their nearest and dearest. But that's another matter.\n\nI have just read the _Living Planet_ report, which has been produced by the ZSL and the WWF (World Wide Fund for Nature). It is unpleasant reading as everything points to the fact that our wild creatures are facing the greatest period of mass extinction since the dinosaurs were wiped out 65 million years ago. That ancient extinction can't be blamed on humans, but this present-day wipeout of species is pretty much all our fault and the worst of it is that we know how to stop this species decline but for one reason or another we choose not to. It's all about our production and consumption. The way we farm, the way we eat, the way we share, the way we build, the way we energise and the way we live. We need to re-evaluate our relationship with the natural world and the environment we share with so many other species. It's not too late but it is pretty damn close. After all, the world around us provides us with the tools to live, whether that be energy or resources, simple air and water, or the rewards of joy or contentment. Nature can be our inspirational muse, from whom we benefit physically, mentally and spiritually and we should look to support our greatest ally in our adventure of existing on this earth.\n\nThe _Living Planet_ report starkly presents the reality that our populations of birds, fish, mammals, reptiles and amphibians declined by 58 per cent between 1970 and 2012. This trend means that by 2020 we may well have lost two-thirds of our wildlife unless we alter our usage of this planet.\n\nWe live in the Holocene Epoch, which is the current period of geologic time. This began approximately 12,000 years ago and replaced the Pleistocene Ice Age. Temperatures rose, glaciers retreated and forest replaced tundra. Creatures that had adapted to the extreme cold such as mammoths became extinct. Humans had to resort to hunting smaller creatures, supplementing their diet with plant materials. And as our dietary requirements changed so did our use of the planet. Agriculture took root and we began adapting the earth to our needs and wants. With the advent of the Holocene Epoch came a more stable climate, and most notably it is the time within which human civilisation has developed exponentially: populations have boomed, urbanisations have sprung up and consequently we have grown into the species we are today. This has been the age of man. But once more change is upon us and we are potentially moving from one epoch into another quicker than has happened before \u2013 it is our influence and actions upon this planet that has accelerated this change.\n\nNew epochs are brought into existence when the world and its conditions change dramatically, and scientists seem to be in agreement that because of our treatment and alteration of this Earth, we have already created the next age. Welcome to the Anthropocene Epoch, in which the calm waters of the Holocene will give way to more turbulent seas.\n\nSo what are the terms and conditions that qualify for us to be living in a brand new epoch? The key factor is the significant effect of human activities upon the world's geology and ecosystems. Over geologic time the start of a new epoch has often been marked by climate change, dramatic changes in the life forms on Earth, or by the occurrence of mass extinctions. Looking around me, it is beginning to look a lot like a new epoch is indeed upon us.\n\nWhen did this happen? When did the Anthropocene Epoch begin? It has been mooted that it may have commenced with the Industrial Revolution, but now the consensus within the scientific community is that it should be considered to have started around 1950, soon after nuclear bombs were tested and then dropped as an act of war. This seems like a forceful marking point and moment in time to acknowledge change. Add to that the damage done by the recent inventions of plastic and concrete and it would appear that we have altered the planet in an enormous way. This is the age of pollution, radiation, habitat loss, extinction, bad economics and selfishness. Add other words as you see fit and realise that this period of time we exist in is like no other age. It is now so different to what we considered the Holocene Epoch that the change in epoch feels inevitable.\n\nBut there is also the thought that this mountain of disastrous damage done to the planet could be a jumping-off point for a new way of life and we could become a somewhat different entity. Perhaps science fiction will prove to be correct and we will evolve into a more advanced species, learning from the mess we have created. Perhaps we will move forward, riding the digital and technological highway to transcend the follies of humankind and travel the universe armed with the knowledge of how not to do things and find somewhere new to colonise \u2013 and ultimately, perhaps intelligently, terraform our way across the galaxies. It seems impossible now \u2013 but so did Leicester City winning the English Premier League in 2016. (For non-football fans, Leicester City is an English football team who had never won a major title in their history and against all odds won the greatest English football prize, the Premier League, beating illustrious teams such as Chelsea and Manchester City to the title.) Plus an aficionado would tell you that it is highly improbable to happen again for a long time. You can think of your own against-all-odds analogy and insert as you wish to replace the Leicester City story. The most pressing issue is that humans need to find a positive way out of this mess. We can't be so stupid as to destroy everything we have in this world, can we? Let's hope not. Time to boost up those dilithium crystals and head for warp factor eight. We may need to get out of here fast \u2013 although it would be best to fix the damage done before heading off in search of new horizons.\n\nWe await the decision by science to accept the Anthropocene Epoch into the geological time scale and then we will all be New Agers, living in our brand new self-created epoch. Bring it on and let's see if we can find a way to turn over a new leaf and mark this new dawn with a positive twist. Saving the critters within this book would be a pretty good start.\n\nEvery time I watch animals in the wild or nature programmes on TV, I am struck at the levels of intelligence shown by so many creatures, an intelligence beyond instinct or survival, and I wonder if many species are much smarter than we give them credit for. Perhaps we refuse to accept their intelligence because we would then feel guilt for everything we have done to them. Do we call so many animals dumb or stupid because we can't bear to accept the intelligence before us? What constitutes intelligence anyway? It surely must equate to the particular creature's environment and place within it. All sorts of creatures utilise objects and use implements as tools to help them in their lives. Is this not intelligence? We know that crows can remember people, chimpanzees can recognise other chimpanzees and dolphins communicate with each other, yet we refuse to accept that this exchange between dolphins is a language. I remember when I was a kid I decided I wanted to learn Welsh and bought myself a _Teach Yourself Welsh_ book. I loved it and I learnt a little. _Cymru am byth_ (Wales for ever) has always stood me in good stead, but why can't I get a _Teach Yourself Dolphin_ book? Shouldn't we be learning the languages of the animals? I believe they are there. OK, there are scientific arguments against the acceptance of language and most of it is to do with syntactic structures first described by Noam Chomsky in the 1950s. It is apparently all to do with the rules that govern the order of words. But don't we, as humans, decide on these rules and their parameters? What if there are other rules created by other species? Is everything judged by our experience of living? Seemingly, yes. We are regularly told that there is a huge difference between language and communication and that the two are not one and the same thing. Perhaps our attempts at animal language recognition are not advanced enough to admit that we are not alone with our ability and instinct for language. Perhaps we have just been turning the wrong keys. But everything that we know about other creatures suggests that there is more intelligence within them than we are aware of and as we are changing the epoch maybe our thinking about other animals needs to change too. When do we start to admit intelligence exists within other species? When we decide to accept it, I guess. Then, just maybe, we will begin to treat them better. Life should be a way to treat an animal. God bless Kurt Vonnegut.\n\n**NOTE** : Ceri Levy is not a scientist, never has been a scientist, and probably never will be a scientist. He has recently completed a course in Crittology at Grossenheimer's University, of which Dr Ralph Steadman is currently the principal, and was deemed fit enough to become a Professor of Loudmouth Chicanery. He is actively looking for further education within the world of Crittology conservation.\n\n**Creating a Synopsis**\n\n_Ralph_ : What do you know of a Synopsis? What do you know of its appearance?\n\n_Ceri_ : A snuffling Synopsis with a protruding proboscis? A rare treat. They have become critically endangered, perhaps even extinct, in the wild.\n\n_Ralph_ : That's not good. I will draw one back into existence.\n\n_Ceri_ : I think the Synopsis is a forest dweller. Perhaps he rummages around searching for food amongst the leaves on the ground? Or maybe he's a creature that climbs?\n\n_Ralph_ : There are a lot of things I could do with a snuffling Synopsis. Although he could be snivelling more than snuffling. I prefer snivelling. Always moaning.\n\n_Ceri_ : ( _in a nasally voice, imitating a Synopsis_ ) Why me? Everyone wants my viewpoint of an idea and then blames me if it's not good enough. I hate being a Synopsis.\n\n_Ralph_ : That's the sort of thing. We just have to make a start.\n\n_Ceri_ : The first splat and the first words. It's being brave enough to begin and let it evolve.\n\n_Ralph_ : That's what you got to do to be a gonzovationist. Be brave to start something like a Synopsis. Never be afraid, for fear is the enemy of the pen. Then we better sort out the Furry Prologue.\n\n_Ceri_ : And never forget the Hairless Epilogue or that dangerous swine the Addendum and his sidekick the Erratum. Grammatical creatures abound. Grammati-critters, if you will.\n\n_Ralph_ : The Unnumbered Index. Nothing worse. Looking something up in an index, discovering it exists but no idea where. Just an annoying list.\n\n_Ceri_ : Sounds familiar. Maybe I should number my lists for you.\n\n_Ralph_ : Yours will always be annoying. It's what you do. Annoy.\n\n**Later that afternoon**\n\n_Ralph holds up a sheet of paper upon which is a tantalisingly odd creature_.\n\n_Ralph_ : So here is the Synopsis. You're being very quiet.\n\n_Ceri_ : I'm a serious gonzovationist and I'm studying the Synopsis and evaluating him. I think he is pointing the way forwards for us! Ever upwards.\n\nThe Synopsis is searching for a general overview by climbing this tree. Once he sees where he is and what is happening, he is very good at encapsulating the scene and describing it succinctly and economically. He is the master of explaining any given situation.\n\nRalph has been exploring his copy of _Popular Encyclopaedia, or Conversations Lexicon_ , published in 1882 by Blackie & Sons. It is full of steel engravings by Thomas Archer \u2013 they have an other-worldly quality about them and are as detailed as anatomical drawings. These pictures have captivated Ralph, and there is a flavour of these images within the Synopsis.\n\n_Ralph_ : I love this book. It's a funny way to go but it's not a bad way to go. It's idiosyncratic.\n\n_Ceri_ : Idiot-syncratic, perhaps?\n\n_Ralph_ : If you want to make fun of me and treat me like a fool, then yes. Things were so much better without cameras and people had to draw to record things. Fox Talbot who invented the camera has a lot to answer for. Asshole!\n\n_Ceri_ : You don't mean that. After all you have taken some wonderful photos thanks to his invention.\n\n_Ralph_ : At the moment I do mean it. But I will forgive him later. This book could be a trial for me.\n\n_Ceri_ : We won't put you on trial for the first drawings. I think you're onto something. Let's just settle into it and see where we end up.\n\n_Ceri's Diary_: Today is the day that the Synopsis goes before the Bloomsbury board to get the yay or nay on its future existence along with all the other critical critters we intend to bring into being. I hate waiting for news and I spend half the time unable to concentrate on other things. I decide to phone Gin Martini and put myself out of my self-induced misery. 'What news?' 'I was just emailing you. Good news! The Synopsis was a success and everyone is very happy to go for the third book in the trilogy. Actually, we should think of a name for the three books, an umbrella title for them like Batman's Dark Knight trilogy. What do you and Ralph have as your trilogy moniker? Let me know what you and Ralph come up with. Toodle pip!'\n\n_Ceri_ : Good news! Everyone is happy for us to get going on _Critical Critters_. It's official. This being the third book in our very own animal lexicon after _Extinct Boids_ and _Nextinction_ , Jim reckons we should come up with a title for the trilogy. Robertson Davies wrote the Deptford Trilogy, in films there's the Godfather trilogy and the original Star Wars trilogy and musically there was Bowie's Berlin trilogy. Good things come in threes and therefore we should name our trio. Then we could create a beautiful box set.\n\n_Ralph_ : Buy the threee, with an extra third e, and get a trolley free!\n\n_Ceri_ : Why a trolley?\n\n_Ralph_ : Because that box set will be damn heavy considering the size of our books. It's far too heavy to carry normally. You would be off your trolley not to use a trolley!\n\n_Ceri_ : The Trolley Trilogy?\n\n_Ralph_ : It would be a thrill to get a set in a trolley.\n\n_Ceri_ : The Thrillogy Trollogy?\n\n_Ralph_ : That would work. Buy three, get one less (of your choice).\n\n_Ceri_ : Not sure that works but I like it. When we started our book escapades did you think we would be writing a third book?\n\n_Ralph_ : No I didn't and it defies all of Grossenheimer's Laws of Adiabatic Masses. Quite a feat and will surprise the world of academia.\n\n_Ceri_ : Maybe we should call it the Grossenheimer Trilogy in the academic world and the Thrillogy Trollogy in the real world. Let's just call it the Thrillogy Trilogy.\n\n_Ralph emails_ :\n\nAgreed. Gonna have a look through the drawers for inspiration and see if there is anything useful in them, animal-wise.\n\n_Ceri's Diary_ : The first thing Ralph finds in his drawers is this picture entitled Wildlife Pie. I start thinking about it and realise we don't 'alf eat a lot of this world. Many creatures are happy with a few target food sources, whereas we will try and eat most things and only stop if we find it could be harmful to us. I remember travelling in Cambodia, where I was amazed at the array of food that was on offer, whether it was snakes, spiders or bugs. I asked our guide if there was anything off the menu and he calmly stated 'Mosquitoes', because it was impossible to catch enough of them to make a worthwhile plate of food. That sums up humanity and its bottomless stomach.\n\nI bet if a restaurant were opened called Critical Critters, where all the food came from endangered animals, it would be a resounding success. That's how ridiculous the world has become. Imagine walking into a bank and presenting this idea as a serious business plan. It would probably be taken more seriously than an idea for a clothes shop or a bookshop and would most likely get funding. Profit over ethics works for so many of the modern-day moneymen. Until we change this mind-set, the world of critters will always come a poor second to economics and 'progress'. Tragic.\n\n**Woolly Mammoth**\n\n_Mammuthus primigenius_\n\nDuring the Pleistocene Epoch a dozen mammoth species roamed the world, but the Woolly Mammoth is the one we all know and imagine when we think of a mammoth. It is believed it became extinct due to a mix of climate change and hunting. It certainly figured on the dinner menu for early humans and was also hunted for its pelt, which was ideal for warmth and clothing. About 10,000 years ago, at the end of the last Ice Age, the mammoths finally became extinct across the planet apart from a small population on Wrangel Island, situated off the coast of Siberia, which kept the name of the Woolly Mammoth alive until 1700 BC. No one is quite certain why this last group became extinct and for years inbreeding was blamed for their extinction, but recent DNA testing suggests this is not the case and it is more likely that climate change was the reason for their disappearance. There is not yet any evidence to suggest predation by humans was a factor in the loss of these mammoths, although the arrival of humans on the island does tie in with the last days of the mammoth. This is quite probably a coincidence and the search continues to ascertain why the last Woolly Mammoths became extinct.\n\nAnd now our present-day search begins, the aim being to identify the most troubled critters out there. It's time to stoke up the _Steadmanitania_ , and get back to the high seas and start seeking out our subjects and their particular stories.\n\n**Animal Art Safari**\n\nThere are a multitude of drawings in different drawers of Ralph's studio that have never seen the light of day and today is no exception. Ralph has been on his animal art safari hunting high and low through the studio digging out picture after picture of relevance and irrelevance to our project. At first I thought it was just birds that had regularly appeared in past pictures but now I find that much of the animal kingdom has had some contact with Ralph's pen and often he has no idea why he did some of these pictures and most have never been seen before. I think some would handsomely complement the work he will create for this book and they deserve to be seen. Just look at this creature, a baby mammoth. I would call this a transitional painting, as the mammoth's feet look distinctly bird-like and I'm certain that they're not the right feet. It just shows that it's hard to give up the beak and talon.\n\nIt is symbolic that Ralph has turned up this picture, as it sums up everything we are striving to avoid with our creatures today. We don't want extinctions and the mammoth is nearly as well known as a symbol of extinction as the Dodo. Ralph doesn't know if he painted this recently or some years ago, let alone why he did it, but this is irrelevant as it is perfect for use in the here and now of our book \u2013 and what better creature is there than the mammoth to start our roll call of endangerment?\n\n_Ralph_ : I have no idea why I did this. Or when I did it. Why do I do these things?\n\n_Ceri_ : I don't know, but I think this is a wonderful portent of what we are embarking upon.\n\n_Ralph_ : A wonderful portent? Don't be seen with a poor tent, how's that wonderful? Get a more expensive one, people judge you by the quality of your tent.\n**_Ralph emails:_ Anyway \u2013 starting is necessary...**\n\n_Ceri's Diary_ : But where do we start? I'm not quite sure how we are going to tackle the whole world of critters. Ralph is concerned that people will want true representations of animals, whereas I'm sure they will want Ralph's imagination to be in play. This is not going to be a guidebook. I have nearly completed a list to work from but inspiration is needed. Where will we find it? As usual, the answer is not too far away, in fact it is a Skype call away and this changes everything. We will find a way to create as we have never done before. This is time for...\n\n**The Path of Evolution**\n\n_Ralph_ : The strangest thing happened last night. Throughout my drawing day I clean my brushes and pens in a container of water that stands by the side of my drawing board. I knocked it over and I spilt the day's dirty inky water onto a piece of paper, which was lying on the floor for no good reason. It created a giant blotty splurge on the sheet and my first reaction was 'Blast it! What a mess I've made.' And then I watched the blot of inky water tendrils spread, weaving a pattern as they slowly swam across the paper and I was intrigued at the shapes they were forming as they went. I knew that this was a chance encounter with a mistake, one that promised something other than a dirty great mess. I thought to myself, 'I'm not going to clean this up, I'm going to let this dry out and see what happens' and blow me I came across to the studio this morning and I love what I see sitting on the floor. The paper is covered with forms and contours and I want to draw onto and into them, right now.\n\nRalph then holds up a sheet of inky light-blue stained paper.\n\n_Ceri_ : It looks aquatic, doesn't it? I love the shapes that have formed. I start squinting and I begin to see things in the mess.\n\n_Ralph_ : Yes, it looks very fishy to me. Maybe we're meant to use this sheet for a critter.\n\n_Ceri_ : Wow, that's an interesting thought. So you would work into the splatted chaos and draw lines through it, using it like a background or a texture or an indicator of what lurks within. If it's a sea creature then perhaps it could be a Humphead Wrasse? That's in big trouble. What do you think?\n\n_Ralph_ : Send me a picture and I will have a look. But we may just have something to work on here. Mind you, it could just turn out to be rubbish. I will try to please you but you're a hard taskmaster and I only want you to be happy with my work so that you don't get nasty to me and abuse me.\n\n_Ceri_ : I think you exaggerate somewhat, my dear Cap'n.\n\n_Ralph_ : I've told you a zillion times that I don't.\n\nThe disruption is apparent in the title. How critters ... can be critical? Actually this is a much more existential question than you might think. Life on Earth has evolved to such a level of complexity (and magnificence) that its very diversity is a critical condition for its permanence. You may say that life supports life itself. At the same time the concept of nature is still quite often misunderstood. For example, what is a forest? The green mass somehow hides the truth \u2013 the truth that is about the thousands of species of plants, animals, fungi and bacteria and the billions of living organisms that together interact and make up a 'living forest'. These are the critters the book talks about.\n\nI love the unconventional approach of this book, the way it highlights the extinction crisis and how 'critters' are disappearing fast. We are losing species at a rate up to 1,000 times faster than natural rates. In the last 40 years, less than a generation, we have lost 60% of the vertebrate populations. Disturbing and astonishing.\n\nAnd by the way this is not just about critters. If you imagine life on earth as a wall, the species are the bricks. If we are taking away one brick after another the wall of life will collapse. This is not just about the critters, it has a lot to do with us. We, our wellbeing, our economy, our social stability and even our happiness depend on healthy and rich nature. The air we breathe, the water we drink and use to produce crops and goods, the food and fibres that come directly from ecosystems, climate stability, rainfall patterns, pollination and so much more. Not to mention inspiration and amazement.\n\nThe undeniable truth is that we do not recognise the value of the 'wild' and we continue to take nature's services for granted. We do great damage to the planet, failing to learn how to grow our economy without harming the environment. In the past 60 years we have seen an exponential acceleration of the unsustainable and wasteful use of natural resources. Whether you consider energy, water, timber, fish or fertilisers, all follow the same steep acceleration curve. If we continue to produce, consume and power our lives the way we do right now, forests, oceans and weather systems could be overwhelmed and seriously damaged.\n\nBut the inspiring news is that even though the planet is continuing to deteriorate, we are at the same time witnessing an unprecedented level of evidence, awareness and most importantly response. Climate instability, extreme weather events and water scarcity feature at the top of the World Economic Forum's list of risks for businesses. Governments for the first time have come together on a global agreement on climate and the Sustainable Development Goals bring the world's nations around an integrated agenda for society, economy and the environment. We are beginning to break the siloes.\n\nWe also know what to do. We have most of the solutions, from affordable renewable energy technology to ways to produce green commodities. We have entered a transition towards a more sustainable future. We must focus on scale and acceleration. Everyone can play a role in this. The way we choose our energy source, the food we eat, the way we invest our savings. All this can make a huge difference.\n\nThe main contribution of this book perhaps, is to draw our attention to the importance of the critters. Although climate change is becoming increasingly relevant and is now a cause of serious concern for many of us, too many people still fail to recognise the loss of nature and the sharp decline of wildlife. Climate change and the loss of nature are the two sides of today's ecological crisis. It is critical to address both \u2013 and urgently. This is the most existential challenge our civilisation has ever confronted: to define a new sustainable relationship with the planet where we learn to live and develop within the boundaries of its finite systems and resources. We can do it. Everyone is in it. There is no time to waste.\n\n**Humphead Wrasse**\n\n_Cheilinus undulatus_\n\nThe wrasse is found swimming through the Indo-Pacific coral reefs, searching for its staple diet of molluscs, crustaceans and starfish and would be quite happy to continue to do so with nary an agitated glance left or right. But sadly, it's a tasty critter for humans to devour and overfishing is the primary reason why the population is becoming depleted. For the moment it is considered as Endangered, but from experience we know it is not such a large step for it to become Critically Endangered. It is a giant of the reef with males growing up to two metres in length, while the female clocks in at up to one metre. If left to their own devices wrasse can live for over 30 years, and they aren't mature enough to breed until they are eight years old.\n\nHumphead Wrasse are involved in a complex relationship with their surroundings and play an important part in ensuring the continued existence of the fragile reef. They hoover up quantities of Crown-of-Thorns Starfish, which eat growing corals, thus keeping the damage to the reefs to a minimum and helping keep the reefs healthy. If the Humphead Wrasse disappears, that is one less predator in the food chain. It will upset the equilibrium of the delicate underwater environment even further and could lead to yet more damage to the reef. Everything has its place in the ecosystem, but intensive fishing is endangering the wrasse. It is extremely popular as a luxury food in the live fish trade across Southeast Asia and is one of the most expensive live reef fish, coming in at $250\u2013300\/kg in China. What is the live fish trade? That's where you enter a restaurant and are shown to a fish tank and choose which one you want removed and cooked for your dinner. It's akin to eating in an aquarium.\n\nI have discovered a very interesting fact about the wrasse. Some of them are born female but undergo a sex change at around nine years of age, and then continue to live their lives as males up until their death. Nature is truly extraordinary.\n\nIn Malaysia, the WWF has been working on a reintroduction programme through a buyback scheme with local fishermen. Wrasse that were caught and were destined to be sold into the live fish trade have thus been reintroduced to the reef. Since 2010 over 860 wrasse have been released and swum back into their natural world. Much better than being in a restaurant's fish tank.\n\nThe sound of Skype calls me to my screen. I answer it and there swimming before my eyes is a Humphead Wrasse. It makes sounds, 'Blup,blup,blup.' A Humphead Wrasse is conversing with me.\n\nYesterday I saw an abstract painting caused by spilt dirty water on a sheet of drawing paper, which Ralph left to dry overnight. I thought the patterns and shapes that were formed by chance were quite beautiful. What was an aquatic-looking splattered watery sheet last night is now transformed and here we are today with our very first authentic and endangered real-life critter, the Humphead Wrasse. The lines that Ralph has drawn through the accidental painting are remarkable and quite take my breath away. He has captured from within the filthy water, the essence of the wrasse and has portrayed him in his inimitable style. Once Ralph bestows his Ralphness upon the fish I want to know more about it and what can be done to save it. Perhaps that is why an artist can get a message across in a different way to a photographer or scientist. It's that coded communiqu\u00e9 within a picture's painted DNA that hits the spot. My words can only back up the meaning that Ralph paints and his work makes me want to be a participant in conservation and not an observer. Hats off to you, Ralph, my fishy friend.\n\nIt is the first critter to appear. The experiment has truly worked and I feel that this could be the best way to approach the subject. Maybe Ralph should splatter more pages and we can find more animals within the accidents that happen. I am just about to suggest this to Ralph when he pops up from inside the wrasse's aquarium and interrupts my racing thoughts. 'Blup!'\n\n_Ceri_ : This is incredible. I adore him. It works so well, Ralph. Maybe you should do some more accidental painting...\n\n_Ralph_ : I've already got several more sheets on the studio floor drying. Maybe we should experiment with this as an idea. What do you think? Do you really think this one is any good? I quite like him as he's got a certain look in his eye.\n\n_Ceri_ : Doctor Watson was always one step behind. I think it's a perfect idea to do more. I love this picture. Something magical happened with that filthy wrasse.\n\n_Ralph_ : I think so. And dare I say it, it makes the thought of doing all these damn critters almost \u2013 and I say almost, bearable.\n\n_Ceri_ : It's all in the technique from what I can see, and no doubt you will develop it further.\n\n_Ralph_ : Ha! Glad you like him. I'll continue with the filth. Is that Jackie walking behind you? Jackie! What do you think of this fishy picture?\n\n_Jackie (my wife)_ : I love it. The fish is amazing. I think it's quite organic. It's like where we all came from when we crawled out of the mud.\n\n_Ceri_ : You should be writing this book.\n\n_Ralph_ : That's a good point, Jackie, write that down, Levy. That's a good point indeed that we all came out of the dirty water and the slime.\n**Singapore Freshwater Crab**\n\n_Johora singaporensis_\n\nThe 3cm pebble-sized Critically Endangered Singapore Freshwater Crab is endemic to Singapore and recently made it into the world's top 100 threatened species. This crab is an omnivorous scavenger, usually surviving on plant-based detritus, but when necessary it will eat smaller animals and can be cannibalistic, sometimes eating young crabs. It is known to exist in a handful of freshwater hill streams in Singapore and is only found in three locations, Bukit Batok, Bukit Gombak and Bukit Timah Nature Reserve. It plays an important part in the ecosystem as it recycles nutrients within the waters and its disappearance would imbalance the situation even further.\n\nHabitat loss due to land conversion for uses such as urbanisation has reduced the number of crabs and their locations to a fraction of the creature's historical range. Also the quality of stream water has deteriorated thanks to a mixture of causes. High acidification of some waters because of acid rain has impacted heavily on the crabs and adversely affected the populations in Bukit Timah. Other pollutants, including chemicals used for dengue fever control have also created problems, leading to a fall in water quality.\n\nMonitoring of the species is under way and a captive breeding programme has begun at Wildlife Reserves Singapore, which manages the country's zoological institutions. The aim is to understand more about the biology of the crab and eventually to reintroduce them into the wild to help form a sustainable population. The hope is to stabilise the crab population and ultimately to return numbers to a higher level than before and to establish a wider distribution for the species. It is also important for the future of the crab to promote it as a conservation icon, making Singaporeans proud of this crustacean and for it to become a symbol for conservation and to promote environmental awareness. Sounds like the Singapore Freshwater Crab is destined to become a superstar.\n\n_Ceri_ : You're really getting into these dirty water sheets. So you're throwing water and coloured inks onto paper every evening when you leave the studio and then leaving it to dry overnight?\n\n_Ralph_ : It depends on the depth of water used. I have a sheet which has been drying for three days on the floor in the studio because it was so wet and is taking an age to dry out. Let me see if I can pick it up and show it to you. It will still run a bit but that will add to the creation of the piece.\n\nHe goes off into the studio and returns with the drying piece. He lifts it up and water and colour move slowly across the paper. It is a filthy lemony yellow colour.\n\n_Ralph_ : Have you got any idea what this could turn in to?\n\n_Ceri_ : Yes. It looks like a great plant I saw today. A Cayman Islands Ghost Orchid. The exact colour of it. It's a critically endangered plant.\n\n_Ralph_ : You thought you saw one. Who's going to believe you saw a ghost? And we're doing critters, not plants, aren't we? I think it's a bit more crabby than planty.\n\n_Ceri_ : If you want to go crabby I guess there's always the Singapore Freshwater Crab, that's Critically Endangered. But I do think we should go across the board and include the odd tree or bug that is endangered. I think 'critters' is short for Critically Endangered, not just a term for creatures. Therefore we can include anything and everything if we see fit to do so. We could even do habitats that are endangered, Amazon forest, marshlands, coral reefs...\n\n_Ralph_ : No, no, no! Not Coral Reefs. Never liked a single one of her movies.\n\n_Ceri_ : I'm busy finalising the list of critters for you to consider painting. Will get it over to you tonight. OK?\n\n_Ralph_ : I'm worried how long this book will take. I'm getting old, you know.\n\n_Ceri_ : Ah yes, but you're young of mind.\n\n_Ralph_ : That means bugger all when you're staggering about on your pins!\n\n_Ceri_ : This project won't take as long as you think, Ralph. I would like us to finish this book before you get a birthday letter from the Queen.\n\n_Ralph_ : I'm glad you're finding amusement in my pain, anguish and dotage. Oh dear. I need sustenance. I better hobble over for dinner.\n\n_Ceri's Diary_ : Firstly, I must point out that Ralph's drawing of the crab is not exactly telling the truth, as being affected by oil slicks is not one of the reasons for its demise. So please cut him some slack and let's put this down to artistic licence, which I'm sure will be used from time to time.\n**Grunting Spiked Turt**\n\n_Circuitus magnus_\n\nThe Turt is a chameleon-like critter that has an affinity for artists and writers. It is said that if one is found it will bring good luck to all creative work. Once it has nested then the chosen location remains home for life. So it looks like Ralph has a new studio companion. It is also a fact that turts cannot get lost. Their sense of direction is second to none and they will always find their way home. In this world, direction is everything.\n\n_Ceri's Diary_ : I'm really feeling we have made a good start here. We are just embarking on the project and now that we are chatting most days about the book it feels like the journey has really begun and this new Ralphschach technique is proving to be a success. I finally sent the list of potential critter candidates to Ralph last night and am waiting to hear from him and to discuss how much I have upset him by drawing up such a long list of contenders for a place in the book. I am always nervous about sending him a list, as he gets extraordinarily irate with me for doing so. But he needs a list to either work from or choose to ignore. Once he gets huffy about a list, things usually start happening \u2013 and I just feel that last night was the right time to send him said list.\n\n_Ralph emails_ :\n\nCERI!!\n\nI have been looking at your List and they all look so difficult to draw \u2013 not to mention that I would be poaching on other people's fine photography to get a look at 'em! I might have to go out to Borneo and all them other places and draw them on site.\n\nBewildered and apprehensive\n\nRuff\n\n_Ceri's Diary_ : I knew Ralph would mention the list and I suppose it could be worse but I really don't want him to be agitated by it \u2013 but then I notice there is an attachment and I look at it and it is a Grunting Spiked Turt. I presume this is a rebellion against the list. Well, that didn't take long, did it? As usual I am faced with the normal dilemmas and have to concede that a book of creatures would have no place in the world without the input from within the crittarium of Ralph's head. A Grunting Spiked Turt is as relevant in this book as any other animal. I like the way he is cocking a back leg at the viewer and I wonder if that is not intended for my dreaded list and me. I'm probably reading too much into it. I'll find out when I speak to Ralph.\n\n_Ralph_ : Did you get the Turt? I found him nesting in the studio last night.\n\n_Ceri_ : I sure did. You know he is not on the list, don't you?\n\n_Ralph_ : Yes, in fact as soon as I saw him I realised you had somehow left him off the list and thought I should draw him because of your oversight. That's what teamwork is about. Covering all eventualities and your backside.\n\n_Ceri_ : How kind, well noticed that he wasn't on the list. How remiss of me. Do you know much about him? Is he cocking his leg at my list of critters to do and me?\n\n_Ralph_ : Read what you will into it. I only work from what I see. You have to do all the academic and clever stuff. It's over to you, your Clevership.\n**Amur Leopard**\n\n_Panthera pardus orientalis_\n\nThis is one of the big hitters in the world of the Critically Endangered. Everyone loves the big cats, don't they? But love alone is not enough to save this animal from finding itself in big trouble. The Amur Leopard, which numbers no more than 70 in the wild, is found in the Russian Far East and northern China, where there is one last population left.\n\nThe Amur Leopard is threatened by several factors including habitat loss and the poaching of the leopard and its prey, which includes Roe Deer and Sika Deer. Poachers have always desired the leopard's fur, although I can't believe in this day and age that anyone could look themselves in the mirror and say, 'Today I really must get a nice Amur Leopard-skin pill-box hat.' (Thanks to Bob Dylan for the influence on that line.)\n\nIn 2012, the Russian government created the Land of the Leopard National Park. This extends over nearly 2,630 square kilometres (1,015 square miles) and contains all of the leopard's breeding grounds and roughly 60 per cent of its habitat. The good news is that this park, along with intensive conservation work, is starting to pay off. In 2007, leopard numbers were believed to be down to no more than 30 individuals, but efforts to save the leopard have begun to pay off and the population has approximately doubled in the last 10 years, with reports of 57 leopards in the National Park and 8\u201312 big cats recorded in nearby parts of China. This may be due to a combination of things. Conservation has played a major part and also the monitoring of the leopard has become better as technology has advanced and survey techniques have improved. Whatever the reasons, the one thing that is certain is that the population is slowly growing.\n\nNow is the time to make sure that the conservation initiatives carry on being implemented and are continually enhanced and updated to further the progress made and to ensure a brighter future for the leopard. After all, it was not that long ago that conservationists were fearful for the survival of the Amur Tiger and now its numbers are firmly on the rise \u2013 showing that conservation does work. There are about 250 Amur Leopards within various breeding programmes in Russia, America, Japan and Europe and these will be the source of animals to be reintroduced into the wild, creating a secondary population in an area the leopards used to inhabit up until the 1970s. This is an insurance policy in case the wild population does die out. Release dates for some of these creatures could be as early as 2019.\n\n**The Ralphschach Technique**\n\n_Ceri's Diary_ : Ralph is finding his way into the drawings and his water throwing reminds me of action paintings from the 50s and 60s. A splurge of painty water is thrown across a pristine sheet of paper and whilst holding the page our captain steers the water to lick the sheet in whatever direction he chooses and it leaves its impression crawling and spreading in many paths. Then this gestural abstraction is left to dry and is converted into figurative art and finally becomes a creature. This is an interesting new concept in Ralph's art although it is a straightforward step from his blots and splats. As Ralph holds up a new disfigured sheet we look at it carefully and start to see shapes and then emergent forms of animals appear to us. Like magic, once stared at, a splurge or smear of dried coloured water turns into a head, a paw, a tail, a fin, a tendril and a creature begins to appear. Some more readily than others as some need to be wheedled out from the lyrical dribbling. Like the Rorschach technique...\n\n_Ceri_ : This is the Ralphschach Technique! That's what's going on here.\n\n_Ralph_ : The Ralphschach Technique, indeed. Actually, I quite like that.\n\n_Ceri_ : So tell me, what do you see Mr Steadman? Do you see creatures within the waters?\n\n_Ralph_ : I'm not sure what I see but something is in there.\n\n_Ceri_ : These are your inkblot tests. We can assess our psychological identities and the condition of all our emotional issues just by staring at the patterns and referencing what we see. We will project our own personalities into the shapes and thereby give away our innermost trials and tribulations, our visions identifying our true makeup. This could be a fascinating exercise, making this book relevant to the twenty-first century, as all the talk of mindfulness is perfect for what we are uncovering. We will read the blots and study our responses.\n\n_Ralph_ : Or we could just see if we can see some damn critter for me to draw!\n\nHermann Rorschach was a Swiss psychologist who developed the Rorschach technique in the early part of the twentieth century. Ten cards with inkblot patterns upon them are shown to a subject. The results are analysed in order to determine the subject's psychological state of mind, personality and character as well as their emotional behaviour and whether there are any underlying mental disorders.\n\n_Ceri's Diary:_ My email pings and it is one of those had-to-be-there moments as the image loads onto my desktop and I see our first big cat. A haughty, somewhat bored-looking creature, who appears to be expecting something to happen but at the same time may not deign to move a single paw if he decides he can't be bothered. A diffidence bordering on arrogance pervades the picture, but let's not forget that he can get to wherever he needs to go to much quicker than we could ever dream of. So he can just wait and wait.\n**Invasion of the Gonzovationists**\n\n_Ralph_ : I've got some photos here and I don't know where they were taken. Might be the Turbine Hall at Tate Modern. Very nice place with wonderful architecture full of bent girders and...\n\n_Ceri_ : Sounds like a Scandinavian environmentalist. Bent Girders.\n\n_Ralph_ : I heard he was a crittologist.\n\n_Ceri_ : That well-known Norwegian expert on all things crittercal.\n\n_Ralph_ : That's him. I knew there was something about these photos that would be of use. I think there are foxes about as I keep hearing scratching sounds at the back door to the studio. But I'm not letting them in. All they do is eat my pictures. I also need to get my pool fixed. The filters aren't working properly. Very annoying. Oh dear.\n\nThe phone rings in Ralph's studio and Ralph answers it and hits the speakerphone button and a voice intrudes upon our conversation. 'Hello, your blottiness. Please excuse my interruption but I am a huge fan of yours and believe that you and your strange sidekick navigator are moving in the right direction to aid and abet the critters of the world. I believe you have recently discovered the work of my mentor Dr Bent Girders, I am phoning on his behalf and my behalf. We work together and I think we could be of mutual benefit to each other. My name is Professor Lars Overhang. Could you possibly let me in so I can talk directly to you both? For it is I that is scratching at your door.'\n\n_Ralph lets him in and is so struck by his appearance that he begins to draw him while Overhang talks. I sit back and listen as Ralph paints and Lars tells us his story. You couldn't make such a thing up._\n\n'I am the director of the Water pH Excess Balance Institute and my whole life has been devoted to water, its quality and what is contained within its wateriness. This has led me to look at the origins of life and the belief that every living thing came from water and dirty water at that. This fascination with the origins of life has taken me up the scientific garden path and I started to look to the beginning of everything in the universe and the Big Bang Theory, which goes something like this: some 13.7 million years ago there was a big bang when all the matter in the universe was contained and condensed within one miniscule point and because of a huge, hot explosion this tiny point exploded outwards creating the universe around us. I started thinking about this one particular point and concluded that it was more than a single pointy point. I believe it was actually an inky blot and the explosion forced this blot to spread like blots do and everything we are surrounded by was inked into existence. This I termed My Big Blot Theory. Is it conceivable that before anything there was just a single blot in the universe and from this explosion of ink the universe was drawn into shape? Is it conceivable that this created the universe we live within and therefore the inky dirty water was responsible for the final march of creatures from the murky liquids? Of course it's conceivable! But the big question is, who created the blot?'\n\n_Ralph and I look aghast but intrigued at each other on our Skype windows._\n\n'I own every book you have ever done and have followed you on Twitter and Facebook for years. You recently tweeted pictures of the Humphead Wrasse and the Singapore Freshwater Crab and before you could say boo to a goose I saw a connection between my theories and your paintings and I believed more than ever that the universe is a blot creation. I am certain it all started with a blot and this belief I call Blottationism, therefore I am a Blottationist and because you, more than any other person on this planet, have spent a lifetime exploring the motion and nature of blots I have decided to rename My Big Blot Theory as the Theory of Ralphativity.'\n\n_I splutter over my tea at this. I wish I had thought of that. Bugger. He's a clever Professor, this one._\n\n'I can't tell you how flattered I am to be being painted by you, dear Ralph, but I wonder if I could trouble you to design a coat of arms for a new venture that several of us like-minded people have created. As well as being Blottationists we are also Muckists and have recently established the Muckist United College of Crittercal Kare (MUCCK) on Toadstool Island. We have collected examples of every critical critter in the world and it is our ambition to halt their impending nextinctions. We believe life is derived from muck and dirty water and this combination has an essential part to play in their salvation. Our motto is \" _If it's muck then spread it_.\" Come and see the work we are doing, you'll be impressed. Our Critical Critters Curator will be in touch as he is the only one who knows the route through the Toadstool Archipelago to the College. I'm useless at directions. I only found your place by following a trail of red ink through the Kent countryside. Can I cadge a lift to the island if you decide to go once you have spoken to the Curator? Would make life hunky dory for me. I saw your pool wasn't working and on my way out I'll fix your filters, test the pH balance of your water by drinking it and purify it by sending in a Skimleach to cleanse the pool. Your water will be silkier than ass's milk by the time I finish with it. Tutty-bye for now, dear Ralph and Cerithio.'\n\n_And with that the Professor is out the door and jumps into the pool._\n\n_Ceri_ : Did that really happen?\n\n_Ralph_ : Probably not. I don't know where to draw the line sometimes. I just let things happen. And now I've got to do a coat of arms. So much to do and then we have to do all the critters. It's all too much, really.\n\n_Ceri_ : You'll be fine and it's another journey into the unknown.\n\n_Ralph_ : Why can't we journey into the known? It would be much safer.\n\n_Ceri_ : But way more boring. This will keep us on our toes, like ballet dancers.\n\n_Ralph_ : Sounds painful. Have you seen the balls of my feet? Not sure ballet is my forte.\n\n45 minutes later and Ralph is presenting me with a coat of arms on Skype.\n\n_Ceri_ : You've spelt crittercal wrong.\n\n_Ralph_ : It's a wrong word and I thought it was a bit obvious.\n\n_Ceri_ : You mean you forgot to spell it incorrectly.\n\n_Ralph_ : Something like that. Anyway, it's not crittercal... well it is but it isn't. You know what I mean.\n\n_Ceri_ : Quite often I don't.\n\nI get an incoming email stating that the Critical Critters Curator is ready to talk to us. I read it aloud.\n\n_The Critical Critters Curator emails_ :\n\nDear Cherry and Rafe,\n\nThe Professor has been in touch and I understand that you have a desire to learn more about Critical Critters. I can help you on your quest. For I am The Curator of them all. Skype me or tweet me. I'm also a Blottationist, a believer.\n\nCritically yours, CCC (Critical Critters Curator)\n\ncriticallycriticalcurator@bodminmoorguesthouse.com\n\nRalph says that normally we would ignore this kind of madman, but considering everything that has happened so far we can't resist this latest intervention on our working routine and like a couple of incontinent kittens we just can't hold back the suspense. I invite him to a group chat. The crazed Curator appears.\n\n_CCC_ : Good afternoon Ruff and Sherry. So, you wish to record the stories of the Critical Critters. I can help you with your task. As you now know your easiest option is to journey back to the Toadstool Archipelago and I will direct you to your end goal, the lands where the Criticals congregate and live on a part of Toadstool Island you have never seen... The Mid Lands! (Dramatic _dah dah daaah_ music emphasises the name.) The price of entry to this place is a lift to the island for the Professor and myself, as I am totally brassic at the moment. Oh and I need a portrait to be painted of me by the Great Blotty One, Ralph.\n\n_Ralph_ : I don't do portraits to order.\n\n_CCC_ : It's not an order, it's a request.\n\n_Ralph_ : But if I don't do your portrait then we get no help. So technically it is an order. It's just a little more polite than most people who hold me to ransom. Harrumphh.\n\n_Ceri_ : Ralph, this is a wonderful opportunity to avoid a tiring search around the globe, visiting each individual critter's domain. We can travel to one place and learn from the entire group about their problems, which we know will be the usual array of man-made issues. It has to be worth a blot or two.\n\n_Ralph_ : Alright, alright. I'll do it.\n\n_Ceri_ : Just as a matter of interest, Mr Curator, why do you wear an eye patch?\n\n_CCC_ : I was trying to rescue a unicorn from an angry group of mermaids in Godalming. You know how these rescue missions go.\n\n_Ceri_ : Actually I don't but that must have been awful to lose your sight speared by a unicorn. Unbearable pain.\n\n_CCC_ : No, no, no, the eye's fine! I just hate looking at things with stereoscopic vision after that. Much easier in monovision. I get scared looking at things with my two eyes. Too real. I suggest we start our journey first thing tomorrow, as there is no time to lose. Did you find a Grunting Spiked Turt recently? I asked him to come to your studio and to bond with you. I presume he has arrived.\n\n_Ralph_ : Yes he's here. He's busy licking my tomato plants.\n\n_CCC_ : Turt spittle is wonderful for toms. Wait till you see the size of them next season. If you could bring the Turt along that would be marvellous, as we'll need to use his directional skills for navigational purposes. Here's to our excursion. Pip pip, see you in the morning on board the _Steadmanitania_. (The Curator leaves the conversation.)\n\n_Ceri_ : I never got to ask him about his horns.\n\n_Ralph_ : Would probably be another cock and bull story. Literally! See what you've got us into now Ceri? It's another fine mess.\n\n_Ceri_ : Well, we'll just keep him below decks and out of the way through the voyage. He does seem a little unhinged.\n\n_Ralph_ : But I guess this isn't a trip for the sane and somehow I liked his honesty. Will let you know how he turns out as a picture.\n\n**The next day**\n\n_Ralph emails_ :\n\nMaking a mark is how it starts! And size is important!! Good chat yesternightlateafternoon!! As for the Curator he looks a bit frenetic and irresponsible!>>>>>> Portrait done.\n\n_Ceri replies_ :\n\nYou've captured the very effervescence of the Curator. I guess we're all ready to go on another madcap adventure. Get ready to blow your penny whistle, Cap'n, and let's get the _Steadmanitania_ moving.\n\nThanks to the Critical Critters Curator we are once more headed towards the Toadstool Archipelago, and this time our search is for the land of critters. Professor Overhang remains in his cabin working on philosophical paradigms, which takes up all of his waking moments. Meanwhile the Curator is useless at guiding us in to Toadstool Island, as he hates water, which gives him the heebie-jeebies and he can't bear to look at it and therefore he remains in his quarters and sleeps around the clock, waking briefly to eat his gruel three times a day. But before we left he gave me some advice on how to navigate through the archipelago to reach the correct destination. (We first discovered Toadstool Island by chance and to find it again would be impossible as I'm not really a navigator, but don't tell the Captain.)\n\nThis archipelago has its own set of geographical rules, which we must adhere to if we are to succeed in achieving our destination. Last time we were here I bought a Toadstoolian compass from the Needless Smut, who said it could come in handy at some point, although he had no idea how to use it. But old Smutty is such a charmer I bought it anyway as a keepsake. It is a strange device as it seems to be incomplete and has four small raised platforms in the middle of its dial. We showed this to the Curator before we set sail and he told us that it was a Turtophonic Directional Navigator and would make our journey much easier \u2013 and that was why we had to bring the Grunting Spiked Turt with us. Around the rim are several letters, including H, TA, MTI, DSI, SOT and ML. The Curator explains these initials stand for Home, Toadstool Archipelago, Mainland Toadstool Island, Dark Side of the Island, Sea of Treacle and Mid Lands. Upon his instruction I turn the dial to TA and then place the Turt on the dial, one foot on each platform. The compass needle wildly oscillates as the Turt becomes one with the equipment. 'When he cocks a leg it will point in the direction we must take.' On cue the Turt raises a limb pointing eastwards and we sail accordingly. 'The next setting to make is for the Sea of Treacle, and then finally the Mid Lands. For now I shall take to my bed, as I detest the sea and all it contains. Call me when we are in sight of our destination.'\n\n**Groglick**\n\n_Bibere multum_\n\nThe Groglick whiles away his days staring out to treacle wishing someone would turn up with some grog to guzzle. He spends his time making up grog rhymes in his eternal wait for his beloved drink. 'Grog, four parts water to one part rum, drink it down yum yum yum, that's the way to fill my tum, grog is needed, come, come, come.'\n\nAs we prepare to alight from the _Steadmanitania_ we see the Groglick waiting for us at the Mid Lands passport control. He is the overseer of this disembarkation point, although he doesn't have much work to do as hardly anyone comes here. Without a Grunting Spiked Turt to show the way, the chances are that no seaman will find his way here by happenstance.\n\nDuring the voyage, the Critical Critters Curator advised us to make up several gallons of grog to present to the Groglick in payment for smoothing our entry onto the island. He has also advised us that we have to partake in a nip or two of it before we dock. This is because the Groglick will lick our lips in order to check that we drink the same grog as found in the bottles we will present to him and that we are not fobbing him off with a rougher version of his favourite tipple. This is customary round these parts and sounds suitably unpleasant.\n\nWe disembark and the Groglick bounces over to see us, leaps into the air and on his way down licks our Captain's face and lips. 'Mmm, good grog.' Then he does the same to the Curator, the Professor and myself. It can only be likened to being licked by a wet, dead and rotting scaly fish. The Groglick breaks open the first bottle of our grog, tastes it approvingly and then proceeds to down three-quarters of it in one. As we march off, he screams, 'Passports!' Shocked by his authoritarian tone, we hand over our passports, which he opens, licking a page in each one and leaving a slimy residue dribbling from them, snaps them shut and hands back our sticky passports complete with our brand new entry visas. Not quite like Heathrow or JFK. This is our welcome to the land of the critters. He swigs some more grog, hiccups, belches and says, 'Welcome to the Mid Lands. Have a nice day.' We have certainly arrived. We walk away and head for the interior plains to watch the wowlets, when we hear a voice rising through the air from behind us, 'I'm the island's Groglick, no amount can make me sick, let me drink it quick quick quick, I'm the island's Groglick.'\n\n**Into the Toadstool Archipelago**\n\nWe continue upon our journey and when I recognise the beginnings of the Toadstool Archipelago I turn the dial to SOT and the Turt shows us the way. Then without warning we grind to a sticky halt in the Sea of Treacle. I make the last turn of the compass to head for our final destination. The Turt dances madly and Cap'n Ralph steers us this way and that, zigzagging through the viscous sea. I spy land ahoy. The Curator advised that to locate the disembarkation point we should look out for either flocks of wowlets or a Groglick looking wistfully out to sea, which is what I now find slap bang in the middle of my telescope. I cry out for the Professor and the Curator to shiver their timbers and to join Cap'n Ralph and myself on deck and then I spy wowlets, a herd of Red Wowlets racing across the plains. Wow! Wowlets! The Curator appears wearing two eye patches so he doesn't have to look at the sea and my Captain peers through my scope at my discovery, 'You know what this means, don't you?' 'Cap'n, I think it means we're here. The Mid Lands.'\n\nNow that we are in sight of our destination the Curator sits us down and gives us a bit of background information on the Mid Lands. 'Situated between the land of the Extinct and the dark side of the island, which contains the Nextinct, are the Mid Lands where all the Critical Critters hang out. This is where the Extinct Critters used to live, but they have moved to the Island of Simply Gone a few kilometres northsouth of Toadstool Island. Why did the extinct critters move out of the Mid Lands? Because the rate of entry of species from today's Critical Critters was far too high and caused too many incidents between the Extinct Critters and the Critical Critters. Arguments proliferated (but not among the birds, as they often fly away from an argument and are generally better behaved than a lot of the critters \u2013 birds and boids don't pick so many fights and are nowhere near as grumpy). So a meeting was held and it was decided that there was only room for one set of grumpy critters on the island and those that proved themselves to be the grumpiest would be shipped out to Simply Gone. This led to the Great Thirty Days of Grumpiness, which was won paws and fins down by the Extinct Critters, who became unusually happy as they trundled off to their very own island. Since that day the Mid Lands have belonged to the Criticals and extremely happy they are there too. It's almost a wrench when one of them is brought back from the brink of extinction and they are deemed no longer Critical. Of course everyone is happy they have been saved but then they have to go back to the Human World and deal with THAT painful coexistence again. That's not easy after an amount of time on Toadstool Island.' The Curator pauses, stretches and states, 'I'm starting to feel like myself again. Thank you for bringing me back. Just holler if you need anything, but now it's time for you to meet the Groglick. After you, Cap'n Ralph.'\n\nRalph takes one small step...\n**Red Wowlet**\n\n_Obstupefactus bestia_\n\nLooking like the love child of a giraffe and a Brachiosaurus (which of course would be impossible on so many levels), the Red Wowlet roams the landscape in a continual state of amazement. Everything it comes into contact with surprises the wowlet and excites it and is met with a long hooting 'wow' sound. It doesn't matter whether it's a flower, a tree, a toilet roll or an artist with board and easel; it's all one big _wow wow wow_ for the wowlet. If only we could always live in such wonder at the world around us. Oh, to be a creature of astonishment!\n\nIt's a creature of perpetual motion, never stopping for too long in one place. Wowlets have hoe-like feet, which dig into the ground and flick earth upwards as they run up and down the landscape. They are natural farmers, turning over and breaking up soil wherever they go, and are known locally as the tilling machines.\n\n**Wowlet Trivia**\n\nOne rumour that continually persists is that wowlets sang the backing vocals on Kate Bush's Wow in 1978.\n\n_Ceri's Diary_ : There are many petitions to sign online, to help endangered animals and pledge virtual support. This surely can't do harm, but I always worry that people who sign things online feel they have made a real difference. I think a digital commitment is not a real-life commitment at all, it is a mopping of one's own brow and I feel the only way to truly help is to do something tangible. Become an activist for real. Donate money, participate in real-world practical conservation and find out how to help those animals in need. Participation by the public needs guidance from conservationists and people need to feel engaged and involved with projects. With the right advice we can genuinely help wildlife.\n\nIn this digital age we can be a part of work in far-flung places like never before and I believe conservation could benefit as technology advances. VR (virtual reality) or live video feeds would allow us the opportunity to experience travelling with rangers as they carry out their rounds or go looking for illegal activities. What if poachers are found, or worse, a poached rhino is found? We would surely feel connected in a way that only the present moment can ever supply us with. But I guess we have to be careful that it doesn't end up as a voyeuristic exercise with no input from us. Perhaps a charge for a live channel would help, raising money for the particular project one is viewing. Or we could crowd-fund conservation projects, people could be party to the project if they had paid the relevant amount to qualify for a live feed. It would be live-streaming conservation TV. Remote monitoring of animals and live webcams are used abundantly these days, but this could take things one stage further. This would be revolutionary and could bring much-sought-after funds to wildlife. The world is shrinking and I believe that conservationists realise that, but the terms of engagement still have to be realised and negotiated between the public and those who are professionally engaged in conservation. I do believe that people who care will make a difference, but they need to be utilised correctly.\n**Jamaican Iguana**\n\n_Cyclura collei_\n\nOnce considered to be a common reptile on Jamaica, the iguana went into a major decline during the nineteenth century, most likely due to the introduction of the Indian Mongoose. This, coupled with habitat loss and an increase in the human population, led to the belief that the iguana had left this planet forever and from the 1940s it was considered extinct. But then, in the 1970s, there was a reported sighting of an iguana and in 1990 a small population was discovered in the Hellshire Hills in southern Jamaica. Since then the IUCN SSC (Species Survival Commission) Iguana Specialist Group has worked with local conservation partners to protect and increase the numbers of the wild population of the iguana. This effort has led to an estimated 200 or so individuals out in the wild today.\n\nThe Jamaican Iguana is still considered to be Critically Endangered and some of the reasons for this have not changed since the nineteenth century. Invasive alien species, such as the already mentioned mongoose and cats, dogs and pigs, have all played their part in the decimation of the iguana population. But the main threat is the decimation of the Hellshire Hills because of illegal tree cutting. Once this was a local enterprise providing charcoal for the community, but it has now developed into an export business. Charcoal burning destroys habitat in a way that does not allow the forest to regenerate and return to good order. There is also the fear that large-scale mining for limestone could hinder the conservation efforts for the iguana. The creation of an infrastructure to serve the mines would further ruin the environment and would allow people to work deeper in the forest, thus destroying more of it.\n\nThe Hellshire Hills are owned by the Jamaican government and are legally protected, but this is not properly enforced, hence the destruction of so much of the habitat. The Jamaican Iguana Research and Conservation Group, which was established upon the rediscovery of the iguana in 1990, seeks to protect, preserve and understand the species. It is now known as the Jamaican Iguana Recovery Group. A headstarting programme was established with Hope Zoo, which means that young wild iguanas are taken from their nests and are raised in captivity until they are large enough to avoid predation by mongooses and are returned to the hills. So far, approximately 175 iguanas have been successfully returned to the wild and the project has expanded to international zoos. There is also a plan to create other populations on the outlying Goat Islands, as long as they can be cleared of predators. Government support and financial aid for this is currently pending. Let's hope this succeeds and a self-sustaining population of iguanas once again roams in abundance through the hills and islands of Jamaica.\n\n**Ralph's Dirty Water Period**\n\nThe earth's creatures stepped out from the waters at the beginning of our time on this planet and we must have been pretty filthy then \u2013 and these critters that are appearing through the murk of Ralph's splattered patterns, or perhaps splatterns, are no different. They fight their way through the murk of the inkiness to greet us and announce their arrival.\n\nPicasso had many phases in his art including his blue, rose and Cubist periods and the more I think about it the more I realise that Ralph is going through his dirty water period. What he has hit upon is unique, innovative and exciting and as the pages start to dry and the images appear, I am certain we are on the right track to do the critters proud. He has found an extraordinary way of turning science into art like no other.\n**Sumatran Rhinoceros**\n\n_Dicerorhinus sumatrensis_\n\nWhat a painting this is. Deep within the splots and splats of this elemental page lurks a Sumatran rhino. Its eyes capture me and shout out 'I'm here.' And possibly it is more here than where it should be, which is in Sumatra.\n\nThis once wide-roaming rhino is only found in Sumatra and Borneo and is now down to two subspecies, the Western and Eastern Sumatran Rhinoceroses. A third subspecies, the Northern Sumatran Rhinoceros, is believed to have become extinct. Vying with the Javan Rhinoceros for the title of the most threatened rhino in the world, the Sumatran Rhino, the smallest of the living rhinoceroses, probably just edges it by a horn. Or by two horns \u2013 because it is the only Asian rhino to have two of them. That's double bubble for the poachers in one fell swoop and unfortunately this is big business. Despite the calls from the Chinese medicine community to stop using rhino parts, the horn and other body parts, are still sought after for various concoctions and the Vietnamese now see rhino as a cure for cancer. The other issue is habitat loss. For example, Bukit Barisan Selatan National Park hosts one of the largest populations of rhinos on its land but much of this and especially the forest cover is being lost to the influx of illegal settlers who are converting land to grow crops of coffee and rice.\n\nWork is needed to ensure a future for the 100 or so Sumatran Rhinos that are left and to increase that number so that the rhinos may meander once more across the region. More rangers, better monitoring and stricter regulations can provide much-needed protection for the existing rhinos and because the rhino population is divided into small groups it is considered important to consolidate them within no more than three sites. This will allow rhinos to interact with and meet other rhinos and breed \u2013 a rhino dating agency, if you will. The captive breeding programme will prove important too and bring more animals into the communities. International help and finance is working, but now the Indonesian government needs to support the conservation work and bring this rhino back from the brink.\n\n_Ralph_ : So many of these animals scare me rigid. I wake every day terrified of what animals may be sitting on my drawing board in the studio. After all, so many of them are scary. Do we really need to save all of the especially frightening ones?\n\n_Ceri_ : The world is made up of all sorts of artists and animals. Don't they all have a right to survive? And I'll have a word and ask them to be less intimidating around you. Can't say fairer than that.\n\n_Ralph_ : OK, as long as they listen to you.\n**Mountain Gorilla**\n\n_Gorilla beringei beringei_\n\nMay I introduce man to gorilla, for the two of you are extremely close relatives and as such shouldn't we humans be looking after our family much better than we have? The Eastern Gorilla was considered to be a subspecies of the Western Gorilla but all that changed in 2001 when it was deemed to be a separate species with two subspecies of its own: the Grauer's Gorilla and the Mountain Gorilla, which Ralph has depicted here. In 2016, the Eastern Gorilla was designated as Critically Endangered, with numbers of Grauer's gorillas at an estimated 3,800, down from roughly 20,000 in the 1980s. The Mountain Gorilla, with a population of about 880, has been listed as Critically Endangered since 1996.\n\nThe Mountain Gorilla was first discovered in 1902 and inhabits two locations of montane and bamboo forest within the Virunga National Park, in the Virunga range of extinct volcanic mountains on the borders of the Democratic Republic of Congo, Rwanda and Uganda. It is also found in the Bwindi Impenetrable National Park in Uganda. The Mountain Gorilla can live for between 30 and 35 years in the wild and lives in sociable family groups led by one dominant silverback gorilla. (At about 12 or 13 years old, males reach maturity and develop silver fur on their backs, hence the term silverback.) This leader is more concerned about defending his group than his territory. These gorillas maintain a true sense of family, which we would do well to remember.\n\nOver the century or so since it was first discovered, the gorilla has been threatened by habitat loss and poaching, and it has also been caught in the crosshairs of civil war and unrest with several fatalities reported. It had been hunted not just for its meat but also as a trophy and the infants were often sold as pets. This has more or less stopped now. Meanwhile, much of its habitat has been lost to land cultivation by impoverished locals and in 2004 illegal settlers cleared great swathes of the forest to create agricultural and pastoral land. As more people move into the area and tourists come to see the gorillas, they have become exposed to a series of human diseases and ailments. The flip side of this is that the money gorilla tourism brings in does contribute significantly to the conservation work.\n\nThere is a small silver (back) lining, as conservation efforts have meant that the population numbers of mountain gorillas have picked up, increasing from 620 individuals in 1989 to just under 900 today. Many initiatives are in place including reforestation, anti-poaching patrols and teaching locals about environmental issues, educating them about the gorilla and showing them how ecotourism can benefit them and bring money into their communities. It is a case of nurturing people and coming up with sustainable alternatives to activities such as illegal charcoal production, which destroys the gorilla's habitat. The people have a major part to play in the continuing gorilla story and can keep their close relative going through the hard times. That's what family does.\n\n_Ceri's Diary_ : A portrait of a Mountain Gorilla thumps into my inbox. This is a close-up of an unhappy and deeply gloomy Mountain Gorilla. This is almost immediately followed by another picture showing the gorilla heading our way. The elements are really working in Ralph's favour as this grumpy gorilla marches out of the dirty water and into view. These images are not perfect representations of the creatures they depict but they contain the essence of these animals, a spontaneous glimpse of all that is a Mountain Gorilla and it connects with me in a primal way. This is earthy and I can almost smell the gorilla, which is unfortunate, as the artist has portrayed the ape breaking wind. I apologise for Ralph's toilet humour but I can imagine that a gorilla passing wind could be extremely noxious. I will look it up online... Excuse me for a minute... (Time passes.) Right, I have discovered some videos of said action and it is very similar to the human equivalent. I have also made the revelatory discovery that a Gorilla Fart is a name for a pretty potent cocktail. Who would have thought that? In case you want to make one up, here is the recipe:\n\nTake a shot glass. Pour 2\/3 of a shot of whisky; add 1\/3 of a shot of overproof rum and two dashes of Tabasco. Down in one and remove yourself from friends.\n\nSome recipes call for cr\u00e8me de bananes (banana liqueur) to be added instead of Tabasco and to divide the drink into equal 1\/3 measures. I guess it just depends on your mood, and whichever drink you choose I guess your mood will alter sufficiently to consider it a success or a failure depending on your own expectations. Maybe that's what happened to this mountain gorilla. Too many shots down at The Gorilla's Arms methinks. Right, back to the picture and the subsequent scientific stuff.\n\nOne can feel the misery of the gorilla as he strides towards the viewer. I know in one glance that he isn't content with what life has concocted for him. His future is in doubt and he knows it. But what can he do? What can any of us do? That is the answer we need to discover and we can only do that by asking the question first. Why is this creature in trouble?\n**Hawksbill Turtle**\n\n_Eretmochelys imbricata_\n\nThe Hawksbill Turtle is one of seven turtles that swim the seas of the world and pretty much all of them are Endangered. Hawksbills are amongst the worst off within the turtle family and are sadly classified as Critically Endangered. Sea turtles are part of a group of reptiles that have swum the oceans for, give or take a year or two, 100 million years. But there is a fear that this long-time existence is under threat because of human actions over the last 100 years. How can this have happened?\n\nThe Hawksbill Turtle is found across the globe in tropical and some subtropical waters. It nests in over 70 countries around the world and is believed to inhabit the waters of over 108 countries. It is a well-seasoned traveller and spends a lot of its time within coral reefs feeding on jellyfish, sea anemones and sponges, which it digs out of crevices using its pointed beak, hence its name hawksbill. The turtle's presence helps maintain the coral reef's health.\n\nIt is protected by the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES) but this has not been enough to stop the continuing trade in turtle shells and other turtle-based products. We are all familiar with tortoiseshell being used in various items, especially in jewellery, but what I never realised was that most tortoiseshell comes from the carapace of Hawksbills. Tortoiseshell has been popular since ancient times and has been utilised in the manufacture of combs, frames, furniture inlays and guitar picks. CITES outlawed the trade in tortoiseshell in 1973 and it was replaced by imitation materials, but the trade in genuine tortoiseshell goes on and this is still the primary threat for the species. Raising awareness locally about the turtle, its environmental significance and its plight is an important part of changing its future. It is also necessary to provide ideas for alternative work, to persuade local people that other economic options are available as opposed to relying on turtle products for income. Ecotourism may well be one of the ways forward, as ecotourists who want to see turtles in the wild will bring money in to communities that live near them. Habitat protection is also essential, for both nesting and breeding areas and there are many sites where local rangers regularly patrol and protect them \u2013 but nevertheless more protection for the turtles wouldn't go amiss.\n\nThe other issue is that turtles all too often feature as bycatch in the fishing industry. The WWF is running a competition called Smart Gear, which encourages entrants to design equipment that minimises the fishing bycatch issue. This isn't just a problem faced by sea turtles, it is estimated that billions of marine creatures are caught and unnecessarily killed each year. So far there has been great success with Smart Gear and a couple of winners have included designs that have lessened the bycatch of turtles on tuna longlines and one that enables them to avoid gillnets. This sort of thinking will go a long way to ensure a future exists for the Hawksbills. Initiatives like this are just what the twenty-first century needs, fresh ideas and different thinking. Then wildlife may just stand a chance of seeing the twenty-second century.\n\nFor too long turtle products have been seen as luxury items in shops, but wouldn't it be the height of luxury to watch these gentle giants go about their everyday activities, swimming freely and unhindered in our seas? That is what we have to strive for.\n\n_Ceri's Diary_ : I have just discovered a fascinating new magazine entitled **_enDanger_** , which goes deeper into the issues that threaten our endangered critters than any other. It was established by Bent Girders and I'm suitably impressed. It marries artistic endeavours with conservation and focuses on ideas from those who are not necessarily from a scientific background. Girders has always maintained that creative talents have a major part to play in getting the conservation messages of concern out to a different, wider audience than those who are already knowledgeable about the state of our wildlife. The plight of so many critters needs to be spread further than ever before and trying to gain the attention of the general public is not easily achieved through dry scientific texts and papers. We need alternative engagement.\n\nI'm looking forward to reading this and sense that we are discovering new allies for our journey.\n**Bornean Orangutan**\n\n_Pongo pygmaeus_\n\n**Sumatran Orangutan**\n\n_Pongo abelii_\n\nThe orangutan is the only great ape that exists in Asia. It was once widespread across the continent but today its range has shrunk to the threatened rainforests of Sumatra and Borneo. The Bornean Orangutan is Endangered and the Sumatran Orangutan is considered as Critically Endangered. In the last 100 years numbers of orangutans have plummeted from a total of probably more than 300,000 individuals to populations of 45,000\u201369,000 Bornean Orangutans and around 14,000 Sumatran Orangutans.\n\nIn Malaysian, orangutan means 'man of the forest', although nowadays I have seen it described as person of the forest. Orangutans potentially have a long life cycle, as they can live up to 50 years. Females don't start to reproduce until between 10 and 12 years old and give birth at most every 3\u20135 years \u2013 sometimes there can be a 10-year gap between babies. Such a low birth rate makes it hard for the species to recover from sharp population declines.\n\nHabitat loss is the greatest problem for orangutan populations, as much of their tropical rainforest homelands are being cleared to make way for oil palm plantations. Unfortunately palm oil production is on the rise and the markets for it are expanding all the time. Illegal mining and logging, forest fires (often caused because fire is used to clear land for the plantations), hunting and the pet trade are members of the supporting cast of threats, which are seeing off the orangutan. Orangutans are often considered pests that destroy crops when they are seeking food. Consequently, a mother may be killed, leaving an orphaned infant, which will either enter the pet trade \u2013 where they are much sought after by collectors \u2013 or with luck end up in a rehabilitation centre.\n\nThe Orangutan Foundation has existed since 1990. Faced with the ongoing destruction of the forest, it has rescued and reintroduced many orangutans into protected areas. This remaining wild forest needs protection before time runs out for the species and there is a real danger that the orangutan could become the first great ape to become extinct. We can't let this happen on our watch.\n\nThere is protection for an amount of the habitat but this needs to be increased and more forest patrols and guard posts are needed to deter and halt illegal activities. The race is on to protect the 50 per cent of orangutans that live outside of protected areas and which find themselves living in the path of industry, machines and chainsaws. Many conservationists are searching for ways to resolve the orangutan problem and are implementing action that is working. Local awareness and education programmes will build a more harmonious relationship between humans and orangutans and create a deeper knowledge of the importance of the rainforest ecosystem. I look at Ralph's picture and after my research I now realise how much time it took for that baby to be born and how precious that single life is. It isn't going to get a brother or sister in a hurry and consequently needs as much help and protection as it can get. We have to find a way to stop the madness that engulfs so many species.\n\n**Update**\n\nThe dreadful thing about this book is that every time I check through my facts and figures something changes and I have to correct the book. Since writing the entry on the orangutans, the Bornean Orangutan has been upgraded to Critically Endangered on the IUCN Red List. So sad.\n\n_Ceri's Diary_ : I thought I would share a piece of Bent's writing from **_EnDanger_**. It gives an insight into what makes him tick and I hope our paths cross sooner rather than later.\n\n_As a crittologist, I am forever searching for new ways of explaining the situation that our world faces and in particular the dangers that are crushing the life out of our nature and wildlife. I was born in a small town in Norway and was surrounded by interesting animals and also interesting traditions. We ate puffin, seal and whale. This was not unusual but I found it difficult to eat creatures that I had marvelled at in their natural environment. I became a vegetarian and environmentalist, but I certainly did not hold a grudge against my fellow northern countrymen. As my beard began to grow so did my ambitions. I wanted to help those animals that suffered and which had no champions to root for them and their lives. I moved from the north and headed south to work in zoos and conservation organisations and discovered that no one had ever created a space purely for the endangered critters of this world. I had come across Toadstool Island and had found an area of land, the Mid Lands, to be a perfect resting ground for endangered species and where with the appropriate people I might be able to concentrate on plans to halt their demise and the imminent collapse of the world's ecosystems. And so the Muckist College of Crittercal Kare came into being and I run this forward-thinking venture alongside my fellow Muckists including Professor Lars Overhang and the Critical Critters Curator._\n**Chinese Pangolin**\n\n_Manis pentadactyla_\n\n**Sunda Pangolin**\n\n_Manis javanica_\n\nThere are eight species of pangolins, four living in Africa and four in Asia and all are protected both nationally and internationally. The Chinese and the Sunda Pangolins are considered to be Critically Endangered, while the Indian and Philippine Pangolins are classified as Endangered. The Black-bellied, White-bellied, Temminck's Ground and Giant Ground Pangolins are all Vulnerable with a threat of moving to a more endangered category sooner rather than later, as all populations of pangolins are decreasing.\n\nSo what are the threats to this prehistoric-looking but somehow endearing mammal? Habitat loss has put huge pressure on the pangolin populations and they are hunted for their meat and scales, particularly in Africa, China and Vietnam. Their flesh is considered a mealtime delicacy, but it is their scales and their usage within folk and traditional medicine that is proving the greater evil. For centuries African healers have used pangolins in their traditional medicines for a number of problems including arthritis (as in Asia), spiritual protection and financial rituals. In China, pangolin scales, fetuses and blood have been a part of Chinese medicine for thousands of years and an increasing Chinese population coupled with greater wealth is now creating a higher demand than ever before. China allows selected hospitals to use the scales in medicine as a sign of respect for tradition \u2013 but as far as I can see you sometimes have to let traditions disappear and be consigned to the pile marked 'Thoroughly Outdated'. China's pangolin population has been decimated by 94 per cent and pangolins are being imported from Indonesia, Malaysia and Africa to satisfy the Chinese lust for pangolin parts. Consequently, organised crime is at the centre of pangolin trafficking, which since the turn of the millennium has allegedly taken over one million creatures from the wild. It is a lucrative business and the pangolin is the most trafficked mammal on the planet.\n\nRecently two Chinese nationals were apprehended by Nigerian customs officers and were found to be attempting to smuggle eight bags of pangolins as well as 678 pieces of elephant tusks aboard a flight. The weight was 381 kilograms. You're not getting that through as hand luggage. Meanwhile in the same week a story of more thwarted smuggling came out of Kenya when the Kenya Wildlife Service seized 500 kilograms of pangolin scales for the second time in a matter of months at Nairobi airport. The scales were destined for Laos. It shows how brazen people are when it comes to trafficking and the risks they are prepared to take.\n\nIt has been mooted that a controlled legal trade in pangolins might be the way forward, but where there's money, there's cheats. I am certain criminals would still continue plying their business irrespective of new laws. Without education there will always be a hunger for forbidden food and a desire for rare medicine \u2013 an awareness programme would be helpful. Pangolin conservation is a moderately new concept, as historically the creature has received little conservation support or attention from an international audience. But times are changing as more people learn about the plight of the pangolin and with support this little armoured tank of a mammal can survive the battle \u2013 as long as it has support from the troops.\n\n_Ralph_ : People will think these pictures are created by accident. Which is true up to a point.\n\n_Ceri_ : But it's a matter of knowing what to do with that accident. It becomes a wilful and deliberate accident. Then you walk through the wreckage and put it together in your own way.\n\n_Ralph_ : I will find a good angle on the Pangolin.\n\n_Ceri_ : The pangle angle.\n\n_Ceri's Diary_ : This tail end appears in my inbox first. I wonder what it belongs to and then it all becomes clear as the rest of the creature follows behind, although surely that should be the other way around. But no matter, this is Ralphicity in action. It is a Pangolin. The colours and spray of inks make this little critter appear to be on fire and he leaps off the page, which of course can be dangerous as he is a tough little animal and needs to be handled with care. Sadly he is being handled extremely roughly in the big wide world out there.\n**Pygmy Tarsier**\n\n_Tarsius pumilus_\n\nThe status of this odd-looking primate is Data Deficient. What does that mean? It means that this creature is known from only three specimens found in southern and central Sulawesi, Indonesia and therefore no judgement has yet been made on its actual status. It just shows that there are still so many mysteries and secrets withheld from us. We most certainly don't know everything. If it were still extant, it would probably live in montane forests, which are becoming increasingly threatened by human encroachment into these areas.\n\nAll I can say is that I hope that the Pygmy Tarsier lives in abundance as I think he looks like a very fine animal to grace this world. It is tailor-made for Ralph's pen to draw him. In fact, maybe Ralph and I should head up an expedition to Sulawesi and see if we can find out the truth about the Pygmy Tarsier. Are you up for it, Ralph? Whatever the outcome, I think he looks just fine nestled within this collection. Boggle-eyed and bonkers. Perfect.\n\n_Ralph emails_ :\n\n'Family : Anglo-Saxon Wars \u2013 Descended from Norwegian Royal Family \u2013 Crown Prince Bentley Girders \u2013 addicted to lavish Hunting Orgies from the sixteenth century \u2013 Contests for numbers killed \u2013 needlessly \u2013 particularly those critters with FUR and slimy Critters for their leather Salamander-like Textures! Polar Bears \u2013 Arctic Wolves and Volcanic Rabbits \u2013 FUN KILL Weekends for invited Guests from other Aristocritties believed to go back as far as ARISTITTLETATTLE and SOCRAHIGHTEAS.\n**Maned Three-toed Sloth**\n\n_Bradypus torquatus_\n\nThe Maned Three-toed Sloth is endemic to the Atlantic coastal forests of eastern Brazil. Recent research work and surveys have enabled this sloth to be downlisted from Endangered to Vulnerable but there is still the belief that population numbers are falling. This sloth is not out of the woods yet (pardon the clich\u00e9) and the species needs careful monitoring to check for any change in status, especially as much of its habitat is in decline and the population is severely fragmented. There may well be a very real threat to the species from poaching, especially within areas where the sloth populations are small and are being picked off by local hunters for food.\n\nDeforestation has slowed down in this part of Brazil but habitat loss still continues, albeit at a slower pace. Another problem is the release of confiscated sloths without knowledge of their origins, as these can damage the genetic integrity of the populations they are released into. More knowledge about the species is needed to ascertain the conservation needs for the sloth and then a plan can be put into action to help this weird-looking critter and ensure a safer future for it.\n\n_Ralph emails_ :\n\nMy Dear BENT Admirer,\n\nHow would you like to actually see my new Poortrait of BENT GIRDERS our Critterologist done in \u2013 Green SLIME!!!??? As yet \u2013 he has NO BEARD!!! \u2013 or he just shaved it off \u2013 to meet the Press!! Perhaps that is a decision YOU will have to make \u2013 but he does have a \u2013 MONOCULAR Implant on his right Temple \u2013 a Family Trait \u2013 Is his Doctorate an Honorary one??? But first a slooow slooowth.\n\n_Ceri replies_ :\n\nI think this sloth is fantastic. Oddly scary-looking too. Cannot wait to see Bent. I have been a fan of his for a long time.\n**The Visitation**\n\n_Ceri's Diary_ : These pictures Ralph has been creating are his impressions of the animals, not perfect replicas of them but emotional responses to them, someone who admires them is the Father of Crittology, renowned art critteric and crittologist, Dr Bent Girders.\n\nHe has become a bit of a hero in our world, especially now that we know of the work that he has been carrying out on Toadstool Island at the Muckist College and, consequently, Ralph invited him to the studio to paint his portrait. Ralph rarely bestows such an honour upon anybody but he was adamant that he wanted to meet Bent and to discuss whether he felt his art was moving in the right direction and whether it was worth doing a book about critters considering that everything seems so hopeless. The answer from Bent was a resounding yes.\n\nBelow is Bent's article about his visit to meet Ralph, which was recently published in his magazine, **_enDanger_**.\n\n**Ralph Steadman's Dirty Water Period**\n\n**_By Dr Bent Girders_**\n\n_Having been summoned to the artist Ralph Steadman's abode to be painted by him, I was nervous at the possible outcome of his sometimes vicious line and was curious to discover his views on critters and the desperate plight they find themselves in through no fault of their own. I had heard that he thought some were too ugly to live and that others were pointless or dangerous or just 'damned unnecessary'. I hoped that this would turn out not to be the case and that I would find an ally for the creatures that I have devoted every waking moment towards. I would not be disappointed. I found Mr Steadman to be charming, a raking wit and an innovator even at the tender age of 80, a birthday he had celebrated only days before our encounter._\n\n_On entry into the studio I see art everywhere. Ralph tells me to be careful, as there are large sheets of paper splattered with inky dirty water lying on the floor. 'These are the latest blotted works and I am waiting for them to dry. Once dry and after discussions with Ceri Levy they will be turned into the next endangered critters. It's akin to reading tea leaves like a fortune teller, but with ink instead.' Pointing to the ink-soaked sheets, he states, 'That sheet over there, looks like a slippery varmint to me and this one looks menacing and that one doesn't look like anything... yet. They all become something though.' I start squinting, trying to visualise what these dripping pages may become and I ask how this unusual process began._\n\n_'This all started one day when I accidentally spilt inky, filthy water from my work desk onto a sheet of paper and became entranced by the shapes that fanned out across the page and I realised this could be a technique I could utilise in my work. Now, at the end of every day I throw inky water onto a sheet of paper on the floor. Immediately the water spreads in different directions and shapes emerge and I let these form and dry overnight. It's_\n\n_an evolutionary process much like our own evolution. Everything comes from dirty water and so do these. There is an element of chance as to what they will become but it is seeing what to do with that chance which is most important. From filthy water come beautiful and interesting creatures that I hope people will engage with. The filth is the key.'_\n\n_We tiptoe across the studio and find ourselves facing a pile of completed paintings. As we flick through them I see blotted page after blotted page, all converted from the initial stains and inkblots into critter portraits of great ingenuity and beauty. There is a freedom of thought and line in these images and I believe this is true alchemy in action, a conversion from one style and medium into another. Abstraction to figuration all because of the artist using his mind's eye and departing on his alchemical journey. 'These are my impressions of the critters, my response to them as I study them and get a feel for them. I'm not trying to draw perfect replicas of them. There are plenty of artists who do that and much better than I can. I just paint them in my way and I hope that is enough for people to respond to them even though some of them are so damn ugly.'_\n\n_Ralph sits me down for the portrait session and then asks, 'What is your inside leg measurement? It is essential for me to know to draw you properly.' I reply honestly, '39 on the left side and 36 on the right.' 'That would explain your lilting wobble. Perfect! On with the drawing.' And he draws and draws and draws. Then he tells me, 'Right, time to draw you! Sorry, I forgot about you, had to finish off the Angel Shark.' He picks up an altogether different sheet of filthy paper, looks at it and shows me a splatter of black and slime-green. 'This filth is definitely you.' Silence reigns and this time I believe he is drawing me._\n\n_During this period of quietude I have time to reflect on his work and I cannot crittercise it. I find that I am responding to these paintings in a primal way, in a way that I have never connected with 'animal art' before. These are gestural works that are born out of the same artist's pot used by abstract expressionists such as de Kooning, Franz Kline, Pollock and the Tachistes, including Marc Tobey, Georges Mathieu and Sam Francis. But there is something different about Mr Steadman's work. Once blotted and dried, he draws out from the splatters, recognisable creatures, revealing critters from a world of lyrical figurative abstraction. Perhaps he has invented a new art form, perhaps he has not, but what is certain is that there is more empathic feeling for critters in this body of work than I have seen in an age. And the eyes! The eyes of his critters draw me in, they capture me and a visceral connection is made. I am lost to their owners. This is animal magic at work, conjured up by a sorcerer of art. I look back across the room at the drying paper and marvel at the inventiveness \u2013 from the painter's very own wastewater, if you'll pardon the expression, comes life. The critter world should be thankful to have such a champion of filth in their corner and I predict that this collection of critical critters will prove to be the filthiest book ever made._\n\n(Reproduced by kind permission of Bent's publishing company, Bent Out Of Shape And Then Back Again \u2013 also known as the catchy BOOSATBA.)\n\n**Hector's Dolphin**\n\n_Cephalorhynchus hectori_\n\nAt the moment I'm not so sure that this Endangered Hector's Dolphin is quite as good-humoured as Ralph has depicted it, given the state of its population, although it apparently does have a proclivity for playing with seaweed (one of my favourite pastimes), blowing bubbles and other fun activities. It is endemic to New Zealand and is found exclusively swimming in the shallow coastal waters along the country's shores. It is the smallest as well as the rarest of all marine dolphins. Its North Island subpopulation, which has recently been recognised as a subspecies, the Maui's Dolphin, has an estimated population of just 55. Because of this low count it was immediately deemed to be Critically Endangered. The total population of Hector's Dolphins is estimated at approximately 7,270 individuals.\n\nThe main threat to the species is bycatch, as the dolphins get tangled in gillnets and can become seriously injured and more likely killed. Gillnetting has been banned in part of the dolphin's range, but surely until it is banned across its full range there will be further casualties? Other factors that threaten the dolphins include polluted habitat, coastal developments and being hit by boats. But if the gillnet problem can be sorted out once and for all then population numbers could begin to rise and then we can encourage Hector's Dolphin to become a playful old Hector once again.\n\n_Ralph_ : Right, I have to get on. Water is a-dryin'. Very soon I'm going to do a Good Oboe. Very musical. A Bonobo. Get it?\n\n_Ceri_ : Actually I do. It makes perfect sense. I think we have some strange mind synchronicity after all this time and all these birds and creatures.\n\n_Ralph_ : Well I have to start somewhere and make a James Joyce...\n\n_Ceri_ : Choice. Rhyming slang. Rosamund Pike it.\n\n_Ralph_ : What are you talking about? Nonsense as usual.\n\n_Ceri_ : Must do a Panda soon.\n\n_Ralph_ : Amanda the Panda and her friend Miranda. Out on the veranda speaking with perceptive and insightful candour.\n**Hippopotamus**\n\n_Hippopotamus amphibius_\n\nSo, the Hippopotamus is a creature that is only considered as Vulnerable. But hey, you got to draw what you can see in the Ralphschach inks and I think you'll agree that this big fella is well worth seeing now that Ralph has completed him. And Vulnerable is Vulnerable. That still means it is facing issues and the hippo is not just breezing through life with nary a care in the world. Today's Vulnerable species is potentially tomorrow's Endangered species.\n\nThere are two species of hippos in Africa, one is the one we will discuss here and then there is the Pygmy Hippopotamus, which is much smaller and lives in the forests of West Africa and is considered to be Endangered.\n\nThe Hippopotamus grows up to 4 metres long and 1.5 metres tall, weighs up to 3.5 tonnes and can live up to 50 years. It is a Goliath of the animal kingdom and this herbivore inhabits the rivers and swamps of East Africa. Its main predators are lions, crocodiles and humans, but each one of these faces a possible beat down if the hippo is in the right mood. Ralph's hippo is not actually belching, as this wide yawn is in fact a coded threat \u2013 it is showing off its teeth, which can bite a crocodile in half. So steer clear if you see one of these heading your way and you think it looks sleepy. Hippos have been wrongly misrepresented as sluggish, docile creatures when the truth is they are one of the most aggressive and dangerous animals in the world. A hippo can easily outrun a human, reaching speeds of approximately 25 kilometres per hour over short distances and it is estimated that 3,000 people a year are killed by not very happy hippos.\n\nThe main threats away from natural predators are poaching and habitat loss. The Hippopotamus is hunted for its meat and ivory, found in the canine teeth and a dramatic increase in desire for hippo ivory was noticed when the elephant ivory ban was decreed in 1989. This has not abated and is a continuing story. Habitat loss is increasing as water gets diverted for agricultural purposes and large-scale developments are built in and around wetland areas, which in turn has led to a rise in human and hippo fatalities suffered in hippo\u2013human conflicts.\n\nIt is vital to protect the hippo from further decline, as their place in the wetland ecosystems of Africa is crucial. In 1996 the hippo population was widespread and considered secure. Since then, we are seeing a species go into a downward spiral in too short a space of time. At the moment options are still being considered to plan a way forward for the hippo. But it does need help now so it's no wonder this critter gets riled up and angry and lets out a roar instead of a belch. Wouldn't you if you were thus threatened?\n\n_Ceri's Diary_ : It's another night of studying the blots with Dr Steadman. He holds up the page and immediately I see it. It's obvious.\n\n_Ceri_ : It's a hippo.\n\n_Ralph_ : Correction, It's a belching hippo.\n\n_Ceri_ : How remiss of me to miss that obvious action. The hippo verily burpeth.\n\nOriginal blot page \u2013 a Hippoblotamus.\n**Irrawaddy Dolphin**\n\n_Orcaella brevirostris_\n\nRalph has painted these dolphins with what looks like a huge smile upon their faces but that is genuinely how they appear. They are sometimes referred to as 'the smiling face of the Mekong' but if it were possible that smile would be wiped off their faces, as the future is looking pretty insecure.\n\nDon't ask me why our fine artist has decided to call these dolphins Irish, as there is nothing further from the truth. You will not find these swimming off the coast of Donegal. You may find Orcas and other cetaceans but you won't see one of these babies there. No way man, you're going to have to travel much further to get a sighting of these unique dolphins. So pack your bags and head on down to south and southeastern Asia where they live in small populations in both salt and fresh water. They inhabit the coastal waters and two brackish water bodies or lakes in India (Chilka) and Thailand (Songkhla) as well as three rivers: the Ayeyarwady in Myanmar, the Mahakam in Indonesian Borneo and the Mekong, where it inhabits a stretch of river between Cambodia and Laos. This particular population is considered Critically Endangered, with between 75 and 90 individuals left in the water. The species as a whole is considered as Vulnerable, although the population trend for the Irrawaddy Dolphins is decreasing and there is a fear that they could destined for upgrading to a higher level.\n\nGillnet fishing is the main threat to the dolphins, as they are often bycatch and get entangled within the nets and can die. The dolphin is loved and revered in many parts of Asia but there are still people who will occasionally capture them to sell for display in aquariums. There is also a fear that the building of dams in the Mekong catchment will harm their habitat and the explosions needed to build them could damage the sensitive hearing of the river swimmers.\n\nWithout doubt, the most important thing to realise is that there is an urgent need to regulate the use of gillnets and to stop completely the use of illegal fishing gear \u2013 and then possibly we may be able to make this particular dolphin smile not just on the outside but on the inside too.\n\n_Ralph_ : Some of these animals on your sniffy list are bloody useless. I wish they weren't here then I wouldn't have to draw them. Maybe we should have a useless critter section. Fetch me my swatter there's a rare wasp on the window!\n\n_Ceri_ : I think with a little gentle persuasion you will change your tune. Everything has a value.\n\n_Ralph_ : A Gentle Persuasion. I wonder what that would look like.\n**African Elephant**\n\n_Loxodonta africana_\n\n**Asian Elephant**\n\n_Elephas maximus_\n\nElephants are the largest land mammals on earth and are found in Africa and Asia. The Savannah and Forest Elephants from Africa are considered as Vulnerable, whilst the Endangered Indian, Sumatran and Sri Lankan Elephants are found in Asia. The African Elephant differs from its smaller relative the Asian Elephant in several ways. The size difference is great, its ears are much larger and both males and females grow tusks, whereas only some Asian males grow them. Incidentally, elephants are left- or right-tusked, much as we are left or right handed. I wonder if I dare call them ambi-tusk-rous?\n\nThe main threats in both parts of the world are human conflict, habitat loss, and poaching for meat and ivory. The African Elephants have larger tusks than their Asian counterparts, though ironically most of the African ivory is headed for Asia. In particular it finds its way to China, where it is thought of as an equal to gold or diamonds \u2013 plus it is a cultural symbol, which has been used and treasured for thousands of years.\n\nApproximately 30,000 elephants are murdered each year for the ivory trade, and across the world this is an issue people are trying to address. For example, the antiques trade is looking at banning all sales of it, including vintage examples of ivory used in carvings or ornaments, billiard balls or piano keys. Times change and the desire to turn an elephant into a finial for a tea caddy should be over. The main problem is that where there's ivory, there's money, greed and sadly death \u2013 and the elephant has suffered greatly for economic wealth. The 1980s were particularly appalling for the African Elephant, with an estimated 100,000 animals slaughtered annually. There are thought to be around 470,000 left in the wild, whereas in the last century the number of elephants in the world was anywhere between three and five million. That is a staggering loss of elephants and poaching has been making a real comeback as the demand for ivory increases once more.\n\nIn the UK, it has been estimated that 40 per cent of all customs seizures are ivory pieces. In 2015 over 100 kilograms of ivory was halted at Heathrow airport alone. There are calls for a complete ban on the trade of ivory worldwide and here in the UK the Conservative government (let's face it, not particularly environmentally or wildlife-friendly) has dragged its heels on carrying through its manifesto commitment to halt the ivory trade between 2010 and 2015. The non-closure of this market allows illegal ivory to be passed off as legal and until this is stopped, smuggling and poaching will continue as there is still an easily accessible market trading in this dirty business. We need to get our house in order before we righteously start pulling other countries up on their habits. We are lagging behind the rest of the world in addressing this issue.\n\nElephants journey in herds and need large amounts of food and water every day as well as huge amounts of land to roam in. This often means they come into conflict with humans over resources, especially as more and more elephant habitat and traditional migratory routes are being lost as people expand their settlements and plantations into once wild areas. These in turn require an infrastructure of roads, pipelines and canals to service them, which further damage the habitat. To avoid more conflict, conservationists are working with local communities to protect crops from elephants and to make sure there are areas for elephants to roam freely without excessively compromising their lifestyle. It is not easy for humans and elephants to live alongside each other in harmonious accord. As for combatting hunting, new and established protected areas are under increasing surveillance by anti-poaching patrols to counter the ivory traders.\n\nThe Asian Elephant now only inhabits 15 per cent of its former range. At the beginning of the twentieth century over 100,000 Asian Elephants existed in the wild, but now that number has fallen by at least 50 per cent and is still decreasing. The threats are the same as in Africa but there is also the added threat of being taken for the tourist trade, particularly in Thailand. Here they perform all sorts of tricks \u2013 I saw a video of an elephant painting a picture of itself by holding a brush with its trunk. How amazing that an elephant can be taught such a thing and how appalling that an animal that is so obviously intelligent should be made to do such a thing for the pleasure of holidaymakers. God knows what the treatment meted out to it is like during the learning process.\n\nIt may be time to ask for help from Lord Ganesha, the elephant-headed Hindu deity, also known as the Remover of Obstacles. Interestingly, he can place obstacles in the way of those that need to be halted. Surely now is a perfect time for a supreme intervention from him.\n\n**Bonobo**\n\n_Pan paniscus_\n\nThe Bonobo is one of the species that make up the genus _Pan_ , the other being the Chimpanzee and these two apes are our closest relatives on Earth, as they share 98.7 per cent of their DNA with us. The Bonobo only became a full species in 1933 as up until then it had been misidentified as a Chimpanzee. To separate them it was first termed as a Pygmy Chimpanzee until it got its modern name of Bonobo in 1954. Bonobos live in a female-led society and lead a far more harmonious and peaceful existence than the male-led chimpanzees. Perhaps humans could learn something from this.\n\nThe Bonobo is found in the Congo Basin rainforest in the Democratic Republic of the Congo (DRC). Its population size is unknown due to a lack of surveys across its range but it is considered as Endangered. The threats to this ape are manifold. There is civil war in the country, which has affected the Bonobo population and has damaged much of the habitat. There are concerns that as war dissipates, commercial agriculture will move in and take over vast areas of land. The most troubling thought is that 99.2 per cent of the Bonobo's range is suitable for oil palm plantations, which could savagely destroy much of the ape's habitat. Other habitat loss has been caused by slash-and-burn agriculture, logging, human encroachment and migration. Where Bonobos live near human communities there is a worry that human diseases and infections could affect them. They are susceptible to respiratory viruses and it is feared that the Ebola virus could decimate the population. Agriculture needs to be controlled without continually removing Bonobo habitat and farmers and industries have to learn to coexist with conservation. To halt the relentless demand for bushmeat locals need to be educated and if ever an awareness-building programme was needed then it is surely here.\n\nThe greatest immediate threat is poaching. Despite the Bonobo being a protected species, with hunting illegal and in some areas taboo, poaching is at an all-time high. The commercial bushmeat trade is slaughtering apes in the wild at an alarming rate and they are also being captured for the pet trade and used in traditional medicine. Because of these threats and a low reproductive rate, it will be hard for Bonobos to replace what they are losing in population numbers and a decline is predicted to continue for the next 50 years or so.\n\nThere has been a concerted effort to strengthen guard numbers in national parks as they are under-protected and suffer greatly from illegal poaching. A governmental operation in Salonga National Park, called Operation Bonobo, is confiscating military weapons from hunters, increasing patrols and seizing back control of the land from poachers. The DRC government also plans to set up a special unit to deal with similar poaching in all national parks.\n\nLastly, research and surveys are necessary to determine the status of the Bonobo and how to make life better for our close relation. Every time I look at a picture of a Bonobo, I find myself ashamed at how we treat it. All I see is us looking back at me.\n\n_Ralph emails_ :\n\nBonobo the hobo plays on his oboe as he sits in his rowboat. He got stuck in the mud and needed a towboat and then he ended up playing a bum note.\n\nOn another note the Saiga Antelope is \u2013 believe me \u2013 a brilliant MESS!!! Tomorrow!!!!>>>>>>>>\n\nOriginal blot page.\n**Saiga Antelope**\n\n_Saiga tatarica_\n\nI feel an affinity with the Critically Endangered Saiga Antelope, as I saw one when I was travelling across Kazakhstan in search of Sociable Lapwings. An antelope ran across the landscape not far from our car and our driver said that it was the first one he had seen in two years and that it was in grave danger of becoming an extinct species. It is strange that once viewed with one's own eyes a wild creature can form a bond with the spectator. We need to get people out into the wild more and create these connections. Human interaction with nature can only be beneficial for animals, as we care more about them once we have shared a moment together.\n\nThe Saiga Antelope roams the dry steppe grasslands and semi-arid deserts of Central Asia and bears a remarkable resemblance to Jar Jar Binks, which I won't hold against it. The odd-looking drooping nose is its most prominent feature and it is vitally important \u2013 for in winter it heats up cold air as the antelope inhales and in dry and dusty summers it acts as a filter system, allowing the animal to breathe in clean air.\n\nSaiga Antelope numbers have fallen dramatically since the 1990s when there was an estimated population of over a million. Now, approximately 50,000 remain and there has been a population decline of over 80 per cent in the last ten years. The primary threat to the antelope is hunting, which has increased since the break-up of the Soviet Union with little or no control over shooting. It is hunted for meat locally, although the real money is in the prized Saiga horns, which adorn the males of the species. These are as revered in Chinese medicine as rhino horn and are used for colds, detoxification and the treatment of lung disease. This hunting of the males has led to an imbalance in the sex ratio and consequently there has been a ruinous drop in birth rates. Habitat loss and destruction are other factors in the creature's demise as lands that were once used for agriculture are left abandoned and the cattle that grazed here have left the area. They performed an important role and without them to maintain the integrity of the grassy species, other plants have invaded the area, which the Saiga Antelopes cannot eat. It's a dangerous thing when the ecosystem loses an ally. Harsher winters have also proved to be a killer of the species and climate change is a genuine concern.\n\nSome areas of the antelope's range are protected but vast swathes of land are unprotected, although there are calls within the Russian Federation government to extend the protected areas. Law enforcement must combat illegal poaching, raising public awareness of Saiga conservation is imperative and a ban on antelope meat and the horn trade seems essential. A captive breeding programme may play an important part in the future of the species and enable it to recover some of its heavy losses. Until then the Saiga Antelope faces an uncertain future.\n\n_Ralph_ : If there's not enough room on the cover for both our names we could have the author and artist combined. We could be: RALERI LEADMANEVY.\n\n_Ceri_ : He sounds important and wise and a renowned expert in his field.\n\n_Ralph_ : Or he's very stupid. And perhaps he should have stayed in his field and dug a very big hole for himself.\n\nWho would have thought this would become a Saiga Antelope?\n**Northern Hairy-nosed Wombat**\n\n_Lasiorhinus krefftii_\n\nWelcome to the book, dear wombat, for you are the rarest of Australian marsupials and you are classified as Critically Endangered. Once found across Queensland and New South Wales, only one small population of this wombat species remains, in Epping Forest (not the one in Essex, England) National Park in central Queensland. The numbers fell dramatically in the 1980s to around 35 individuals, but conservation efforts have managed to provoke a rise in numbers to around 200 wombats in the wild now.\n\nThe main threats to the Northern Hairy-nosed Wombat have been habitat loss and competition with introduced grazing species as well as predation by another introduced animal, the Dingo. Also, the fact that there is only one small population leaves the wombats open to extinction if one catastrophic natural event such as fire, drought, flooding or disease occurs.\n\nProtective and Dingo-proof fences surround the wild population and wardens oversee the safety of the wombats and make sure there is enough food and water for them. They also protect them from natural disasters and are continually working on improving their habitat. Research has gone into a captive breeding programme as well as looking into translocation of the marsupials, as it would be better for the wombat if there were more than just one population in one location in the wild. As always, the protection of a species takes time and money and a slow rise in numbers is just the beginning for the hairy-nosed wombat \u2013 but with the support that it is getting there must be a chance that the future is not as bleak as it once was.\n\n_Ralph_ : Who are you calling a hairy-nosed wombat?\n\n_Ceri_ : I'm not calling you a hairy-nosed wombat. I didn't make it up and it's not a term of abuse. The Northern Hairy-nosed Wombat is one of the most threatened animals in the world.\n\n_Ralph_ : I know how you can be with your word trickery and fooling me into believing your animalistic lies with your callous observations. Next you'll tell me there is a Southern Hairy-nosed Wombat too and that all points of the compass go in the direction of a wombat.\n\n_Ceri_ : Actually, there is a Southern Hairy-nosed Wombat but that's where they stop other than the Bare-nosed Wombat. Although, just so you know, there is a creature called a Numbat, or Banded Anteater, which is Endangered and also lives in Australia...\n\n_Ralph_ : Stop with your bats! You're driving me batty. Just pick one bat.\n\n_Ceri_ : Let's tell the tale of the Northern Hairy-nosed Wombat.\n**Angelshark**\n\n_Squatina squatina_\n\nIn the nineteenth and early twentieth century, the Angelshark was common from Scandinavia to Africa and all points in between, happily discovered on the southern and eastern coasts of England as well as in the Atlantic and the Mediterranean. But what a difference a hundred years or so can make, and in 2006 the Angelshark's status was upped to Critically Endangered due to overfishing and bycatch. In fact, what a difference six years can make, as in 2000 the status of the Angelshark was considered as Vulnerable. It has been estimated that it has lost 80 per cent of its population over three generations. The rate of decline is staggering for this species.\n\nI think it can be safely said that the twentieth century proved to be one of the worst centuries that wildlife and the environment has had since the dinosaurs woke to find themselves needing thermals \u2013 and it's a fair bet that the twenty-first will prove to be even more calamitous. It is believed that the range of the Angelshark has shrunk to an area around the Canary Islands and it is not to be found anywhere else in its former domains other than by pure coincidence. Because the Angelshark lives on the bottom of the sea it is more prone to bycatch in fishing by trawlers. Work is being carried out to raise awareness of the plight of the Angelshark and protection of habitat and prevention of disturbance by fishing, sport fishing and tourist activities in its habitat is essential.\n\nIn 2016, a Conservation Action Plan was developed by the Angel Shark Project, which will steer the next ten years of conservation work to ensure the future of the Angelshark and its relatives, collectively (if slightly confusingly) known as the angel sharks. The Angel Shark Project is a collaboration between three European partners: the University of Las Palmas de Gran Canaria, the Zoological Society of London and the Zoological Research Museum Alexander K\u00f6nig. Their vision is to safeguard the Angelshark's last stronghold in the Canaries, stabilise the population and eventually increase their numbers. By doing this there is a chance that the species may begin to reappear across its former range. The future is uncertain but the Angelshark is not alone, thanks to the Angel Shark Project.\n\n_Ceri's Diary_ :\n\nRalph seems to have hair on the brain at the moment after the hairy-nosed wombats, as he has just sent me this Hula Cute Hairy Ray. I don't know why he has made him hairy but if that is the artist's wont then so be it and he is pretty cute too. Returning to other fishy matters at hand, it's now the turn of the Angelshark to be placed under scrutiny by the artist.\n\n**Pygmy Three-toed Sloth**\n\n_Bradypus pygmaeus_\n\nThe island of Escudo de Veraguas, located off the Panamanian coast, is the sole habitat for the Pygmy Three-toed Sloth and there are fewer than 100 individuals living here. Hence its status currently stands as Critically Endangered. This tree-dweller only leaves the trees and descends to the ground when it needs to go to the toilet. It can only crawl when on the ground although it is apparently a very good swimmer. Their suspected singular food source is the leaves of the Red Mangrove trees within which they live. This is also the reason why the sloth is in so much trouble. Local fishermen are chopping down the mangrove trees illegally for firewood and timber and this is leaving less food and habitat for the sloth. The animal has begun to be occasionally discovered in the interior of the island within dense tropical rainforest, probably because it has had to go in search of what it needs to survive. There is a plan to further protect the habitat for the sloth but unfortunately there are also ideas being bandied about for the development of a tourist infrastructure on the island, which could include a casino, a marina, a banking centre and an eco-lodge. But nothing is certain, and the only definite fact is that this small, slow sloth needs help and needs it quick.\n\n_Ralph emails_ :\n\nShould you chance to make contact today \u2013 I may show you Tarzan's Comedian \u2013 plus various dirty splats that may well entice ideas of a critical variety. Tried to ring you but it said you were fierce busy!!!! Black-footed Ferrets are not emerging too well \u2013 but I will persist \u2013 Meanwhile \u2013 LONG before I knew you I did this Critter \u2013 and I may even have shown it to you \u2013 but maybe not \u2013 but needs savin'!!!\n\n_Ceri's Diary_ : Habitat loss is a key part of many species' decline and often one can forget that the disappearance of these areas is as important if not more important than the creatures they contain and that they are endangered too. As I am discovering throughout my research every living thing needs a place to call home and home should be a safe haven. The rainforests of the world are a prime example of how much damage is being done to the planet. Most of us know that trees and plants remove harmful carbon dioxide from the air, absorbing it for photosynthesis, an energy-creating process, which transforms the CO2 into oxygen, which is then released back into the air and yields carbon, which enables the tree or plant to grow. The disappearance of so much rainforest is damaging the way the world breathes. We have all experienced a bad chest and know how hard it is to get on with everyday life when we are short of breath. It is debilitating to our lives and that is what is happening to the world. The world has the largest chest infection and simple antibiotics won't cure it \u2013 it may be turning into pneumonia. We need to find a remedy \u2013 and stopping chopping and illegal logging is imperative.\n**Tarzan's Chameleon**\n\n_Calumma tarzan_\n\nSo why is this Tarzan's chameleon? Did Tarzan discover it? Would that mean Tarzan exists? No, it is so named because it was discovered in Madagascar, as recently as 2009, just outside the village of Tarzanville, in Tarzan's Forest. (Why Tarzanville? Why Tarzan's Forest? Let's leave it for the moment, shall we? And just as a matter of information, Tarzanville is currently known as Ambodimeloka.) As soon as it was found it was immediately categorised as Critically Endangered, because unfortunately the chameleon's habitat has become terribly fragmented due to deforestation of the area because of slash-and-burn agriculture. Illegal logging is also being carried out in parts of the forest and this has also been having a negative effect. More information about the chameleon's lifestyle is important and further survey work may be able to ascertain the full range and habits of the creature. Then the best way forward to ensure a future for this rather endearing lizard can be determined.\n\nDid you notice how I avoided all vine and swinging gags? I must be getting older to have such self-control. Well done me. Tarzan goes into a pub...\n\nRalph: ( _voice from offstage_ ) STOP IT! STOP IT NOW!!!\n\n_Ralph_ : Stupid list. You're being ridiculous again! Stop it. I'm not falling for this again! Just because they've recently brought out a new Tarzan film. What is this, the follow-up? Tarzan's Chameleon? Well, where's Jane's?\n\n_Ceri_ : Trust me, I'm a crittologist.\n\n_Ralph_ : Twittologist, more likely. And Bent's the real crittologist anyway.\n\n_Ceri_ : You're so hurtful, no one realises how much you torment me.\n\n_Ralph_ : You're just too sensitive! More importantly, how am I going to remember the difference between Cuban and Philippine crocodiles? They're next on your fearful list after ferrets and horses.\n\n_Ceri_ : Easy. Cuban crocs are spotty and Philippine crocs are stripy.\n\n_Ralph_ : OK. Spotty goes first. Will get to it in my own good time.\n**Black- footed Ferret**\n\n_Mustela nigripes_\n\nOver the last 30 years the Black-footed Ferret has been making something of a recovery across North America, which considering it was believed to have become extinct in the wild in 1987 is without doubt a wonderful thing. Thanks to conservation efforts nearly 300 ferrets once more roam the States seeking out their favourite food, prairie dogs (White-tailed Prairie Dogs in some places, Black-tailed elsewhere). In fact, the two animals are connected in such a way that the fate of the ferret is inextricably tied to the fate of the prairie dogs. Why? Because the ferrets rely on the prairie dogs' wellbeing not only for food but also because they use their burrows as accommodation for shelter and raising their young, or kits as they are known.\n\nBut this masked marauder remains one of the continent's most endangered creatures and not until numbers have risen to 3,000 will the ferret be considered out of danger. Habitat loss due to conversion of prairie to croplands has taken its toll on the ferret and the dog. Farmers and ranchers have killed many prairie dogs because their burrows adversely affected crop fields and this has impacted on the ferret community. Disease has also had a lasting effect on numbers of ferrets and dogs, particularly sylvatic plague, but recovery is under way. The WWF is working alongside zoos, conservation organisations, state and federal agencies, landowners and Native American tribes to reintroduce ferrets back into the wild and look after and increase the numbers of existing populations. With so much goodwill and support there has to be a chance of survival for this ferrety fellow.\n\n_Ralph emails_ :\n\nI am worried about what to do about all the FILTH!!! CRITTERS are comin' out me marf!!!! My waters are getting too dirty! WHAT A MESS!!!! Was this the blot you got and liked a lot!!!??? Look what happened to it!!! An 'orse to follah bloomin' soon.\n\n_Ceri replies_ :\n\nYes! I love him! Wonderful. You're as cunning as a ferret.\n\n_Ceri's Diary:_ This collection of Black-footed Ferrets peering out of the blots has just arrived in my mailbox and makes me smile even though they look quite glum. There is a perfect insanity to them as Ralph has worked the lines deftly through the splattered page and creates a ferrety family unit for us to digest (not literally) and discuss.\n**Przewalski's Horse**\n\n_Equus przewalskii_\n\nPrzewalski's Horse is almost unbelievably the last true wild species of horse left in the world. All other supposed 'wild horses' are in fact descended from escapees from domesticated herds. The P-Horse, as it is known as in rarefied scientific circles, has never been domesticated. How's that for a wild thing? How to pronounce it? Easy, it's a Polish name and is apparently pronounced _shuh-val-skee_ with a silent Pr. Simple enough? The weird thing is that it was a Russian naturalist and explorer, Colonel Nikolai Przhevalsky, who discovered the horse and described it in 1881. His name was of Polish origin and hence the Polish spelling became the horse's name, although in the fifteenth century Johann Schiltberger had first documented the horse in his journals as he was travelling across Mongolia as a prisoner of a Mongol Khan.\n\nThe downfall of this horse began when a German merchant, Carl Hagenbeck, who specialised in selling wild animals to zoos as well as P.T. Barnum, captured pretty much all the wild populations of the horse. Habitat loss and over-hunting was already impacting on the herds but Hagenbeck drove the nail into the coffin firmly and surely. By 1945, just 31 P-Horses remained in two zoos in Munich and Prague. This was the darkest of times for the P-Horse.\n\nToday more than 1,500 individual P-Horses exist and every one of them is descended from nine of the 31 that were left in 1945. Thanks to a reintroduction programme this horse is now found on the steppes of central Asia and up to 300 horses gambol around in Mongolia. China's own captive breeding programme has also successfully reintroduced a herd of horses into the wild once more. There are further small bands of horses in Russia and Hungary that are doing well and Przewalski's Horse is now considered as only Endangered, which is an incredible turnaround considering it had been deemed as extinct in the wild up until 2008.\n\n_Ralph emails_ :\n\nHorses galore! What the Devil was the name of that slimy red SNAIL!!???\n\n_Ceri replies_ :\n\nThe Kanab Ambersnail I think you mean.\n\n_Ralph replies_ :\n\nNever mind that \u2013 I have got a book of Horse Diseases and Health Problems \u2013 and CROC 1 is done \u2013 CROC 2 is still drying!!!! Plus I trod in some KANAB this morning!!! I aim for SIX NEW critters by FRIDAY!!!! Many dirty water critterdom things await!!\n\nATTENTION!!!\n\nThere is a Horse Landscape in this month's Sotheby's Catalogue up for Auction \u2013 Estimate \u00a34,000,000 to \u00a36,000,000. Shall I get it for the Upstairs Guest Lavatory?????? I would scan it but my scanner needs reinstalling.\n\nSCANman aka RALPH PUDDwiddle\n**Striped Spirit Wint**\n\n_Spiritus protector_\n\nObviously concerned about spots and stripes, Ralph has conjured up a Striped Spirit Wint to watch over the spotty crocodile. It is one of the great air gods of the Nextinct animals and to see one hovering above a creature is a sure sign that the wint is doing everything in its power to restore that animal to its past glory. Wints are part of the fabric of time itself and can often be seen rolling in the folds of the past, present and future of existence. Unfortunately this can make them incredibly dizzy and can leave them in a stuporific state for millennia. This one that Ralph has found has just awoken and is realising that an awful lot has been happening whilst it has been in its catatonic state. There is much work for it to do and its job starts here. It concentrates and focuses its mind on the job in hand by sucking on a spoonful of Marmite, which for those of you that don't know is an English spread made from yeast extract and I love it nearly as much as the wint. Once fully revved up on Marmite, the wint will look for fellow wints and together they will start the process of restoring a natural order to our dysfunctional planet. I hope this works.\n\n**Cuban Crocodile**\n\n_Crocodylus rhombifer_\n\nNever mind the Cuban missile crisis way back when, there's a Cuban Crocodile crisis going on now. There are only 4,000 or so left in the wild and they are only found in the Zapata Swamp and in the Lanier Swamp on the Isle of Youth. It has become Critically Endangered through illegal hunting for meat, habitat loss and decline in habitat quality as well as hybridisation resultant from breeding with the abundant American Crocodile. This problem of the gene pool becoming sullied through interbreeding has yet to be resolved and it is believed that hybrids have become part of the two remaining wild populations of Cuban Crocodiles. Hunting them for food has been on the rise since the 1990s as demand has grown locally and in restaurants serving the tourist trade. Protection is needed to halt the hunting and captive breeding programmes and reintroductions into the wild are under way.\n\nTalking of reintroductions, in 2015 the Skansen aquarium and zoo in Stockholm sent ten baby Cuban Crocodiles to Cuba to be introduced into the wild. But these were no ordinary crocs, they were the offspring of a pair of crocodiles given in the 1970s by Fidel Castro to Russian cosmonaut Vladimir Shatalov as a token of solidarity between the two communist countries. Shatalov kept the crocodiles in his Moscow flat until they outgrew the apartment and he offered them to the Moscow Zoo. Unfortunately they had nowhere suitable for them and eventually a home was found in Sweden. Since 1984, this pair, now named Castro and Hillary (Clinton), have produced more than 100 crocodiles, which have been exported around the world and they were approached by Cuban authorities to see if there was a possibility of taking some back to their roots. The Swedes readily accepted the invitation and so ten little crocs began their journey home. Who would have thought, so many years after the journey made by Castro and Hillary to Sweden, that this would prove to be a successful captive breeding programme, benefiting the Cuban Crocodile population and strengthening its gene pool? This is crocodile solidarity of the highest order.\n\n_Ralph_ : Was going to do one more and then you get in touch! You're so irritating.\n\n_Ceri_ : You're so sniffy.\n\n_Ralph_ : And you're so insisty! Insist on this, insist on that...\n\n_Ceri_ : Well, I insist you listen to me because I want to say that I think you've had a brilliant week. You've drawn and drawn and come up with some incredible critters. Do you ever get bored of drawing?\n\n_Ralph_ : Not when it's going well and I love it when the blots surprise me. I look down and see where I was going to put an eye is actually the nose. When the pictures keep changing it makes it interesting for me. Your teacup is disgusting. The inside of it looks vile and stained!\n\n_Ceri_ : It's clean. There's no staining.\n\n_Ralph_ : Well, Skype makes tea look awful then. ( _Quietly_ ) But I think you have a filthy cup. Filthy water for filthy tea! ( _Louder_ ) Right, I'll have a little throw before I go, now that I am in the flow... and clean your cup. Night night.\n**Kanab Ambersnail**\n\n_Oxyloma kanabense_\n\nSmaller than a thumbnail, the Critically Endangered Kanab Ambersnail is endemic to the United States and is now only known from two sites: Three Lakes Canyon outside Kanab in Utah and Vasey's Paradise, a spring-fed tributary of the Colorado River inside the Grand Canyon National Park. The Three Lakes site is under threat as the owner is considering commercial development. The best hope for the snail is the protected national park site, although the threats here include water releases from the Glen Canyon Dam, which can flood or wash downstream the snail, its food source and its habitat.\n\nCaptive breeding has led to releases of snails into the wild and these have been placed high enough within the landscape to avoid being affected by the normal dam activity. These reintroductions have met with mixed results and snail counts have not been as high as expected. But there has been some good news in the fact that recent studies of ambersnails have discovered that the Vasey's Paradise snails and 11 different populations of snails from southern Utah and northern Arizona are, in fact, the same species. This could lead to the Kanab Ambersnail being downgraded or even delisted once this is certain. It could also mean its taxonomic identity may be changed and they may or may not be Kanab Ambersnails at all. But things always take a little longer when you're dealing with snails. After all, what's the hurry, it may or may not even be threatened by extinction. Time will tell... slowly.\n\n_Ralph_ : Snails don't go on dates and that's why this one is so sad.\n\n_Ceri_ : That's because they're hermaphrodites. They've got it all going on in-house. Don't need a date. They are, wait for it, hermaphrodates. Boom boom!\n\n_Ralph_ : Hmmm. ALL Snails without fails are Hermaphrodites. They ALL lay eggs and can ALL futilize!! Mums are Dads and Dads are Cads!!!\n\n_Ceri's Diary_ : The Kanab Ambersnail believes that it is slowly but inexorably approaching the line of no return of its critical endangerment and Ralph has captured more than a whiff of resignation about it as it trudges towards some strange building in the distance. Is it the Snail's Elysium? Is that where this gastropod is heading? Or is there a different outcome to this story? Read on. For what was once believed does not always remain so.\n**Pool- strutting Monkeychick**\n\n_Morum terribilis_\n\nMonkeys often get a bad press for misbehaving but it's not their fault. Well, let me introduce you to a particular monkey, which should know better and is quite simply one of the worst-behaved animals on Toadstool Island, especially near swimming pools, which are its natural habitat. Most bad things that happen in the vicinity of a Pool-strutting Monkeychick are most definitely its fault. When Professor Overhang had to purify Ralph's pool, the first time we all met, he found that the problems were caused by a monkeychick, which was secretly living in the pump house. It transpires that when Ralph wasn't looking it was messing with the water temperature and doing those things that we are taught never to do in pools... a lot! He was reprimanded and we took him back to Toadstool Island on the _Steadmanitania_.\n\nAt holiday resorts, Monkeychicks parade up and down the poolside area craving attention and when they get it they do what is known as the Monkeychick Flick, whereby they flick indelible ink, secreted from their body pores, all over the onlookers. Shrieking with monkey cries of laughter the Monkeychick will then race away, taunting all and sundry with abuse. This is hugely offensive Monkeychick filth but luckily most people don't speak monkeychick, so don't understand the stream of obscenities.\n\nThe sound of scolding is heard across the island. 'Bad Monkeychick' is an oft-used phrase and there seems no respite from their fiendishly naughty ways. It has been said that the only way to make a Monkeychick behave is a custard pie in the face. Then it will begin to listen, as it hates custard, which provokes a stasis within the creature and it will not move until the custard has been removed. Flans at the ready, aim, fire!\n\n_Ralph_ : I think a custard pie or a custard flan to an opponent's face could settle all wars. Why can't we have custard pie fights instead of battles? Plus who doesn't think it's funny?\n\n_Ceri_ : We could use it to settle any dispute. Neighbourly disputes, parliamentary elections, drawn football matches, parking tickets, the list is endless.\n\n_Ralph_ : Now that's a list I like.\n\n_Ralph emails_ :\n\nDEAR CRITTWEN\n\nI have consulted with Professor Whitby PIDDLESHOT \u2013 the Toadologist \u2013 as there was a gorgeous toad spread-eagled on the bottom of the pool this morning. At first I thought it was dead \u2013 but when I picked it up it began to struggle \u2013 so \u2013 I laid it carefully on Poolside and we had a chat and his throat began to pulse \u2013 so I was very relieved. What a lovely Critter he is and I called him Terry! When he finally got bored with my chat he turned his butt toward me and wet-footed it behind a Plant Pot. When I looked again \u2013 he had gone in a wisp of slime!!! I reckon a monkeychick threw him in there. That's what they do!!! Swine!!! Custard Pie them all!!! Andy (son-in-law) was there and took pics of him with his iPhone \u2013 which he will send me later today! \u2013 that is \u2013 IF YOU ARE REMOTELY INTERESTED!!! Terry was just oozing with Tonal Toadality.\n\nLots of Croaks\n\nCrimley STIGGint\n\n_Ceri replies_ :\n\nOf course I'm interested. Who wouldn't love a toad? It was raining cats and toads earlier toaday. I'm swamped in toads and they're trying to get in the house. I kid you not. We are toadally in sync. Maybe we could introduce our toads to each other and start a toad dynasty together. Terry meet Talullah.\n\n_Ralph emails_ :\n\nHere's the little guy I saved this morning!! This is TERRY!!!\n\n**Philippine Crocodile**\n\n_Crocodylus mindorensis_\n\nThe Critically Endangered Philippine crocodile is endemic to the Philippines and is found mainly in freshwater areas such as lakes, ponds, tributaries of large rivers and freshwater marshes. Traditionally it has been hunted for its skin and was often killed on sight in encounters with humans, purely out of fear. Now it is a protected species and killing a crocodile comes at the price of a large fine. Habitat loss, as humans expand and convert land for agricultural purposes, is causing major problems for the species.\n\nIn 1992 it was estimated that 1,000 crocodiles existed in the wild but now it is reckoned that perhaps only 200 remain. Captive breeding programmes and release into the wild are seen as the possible way forward to stop this croc from disappearing forever.\n\nI really wanted to write dis-snap-pearing but I restrained myself.\n\n_Ralph emails_ :\n\nDear Mr Lovey\n\nPonce de Lyon gave me your email. He said you were an expert on Odourless Flatulence and this is the reason so many creatures are blamed and critically endangered \u2013 even though it was a Humanus Corpus not unlike you \u2013 and not me! \u2013 who are to blame. Is the NAME of the SHAME a book worth reading!???\n\nJust wondered \u2013 but Red Wolves are criticall-endangled but will it soovive!????\n\nPratchley Phewpoo\n\n_Ceri's Diary_ : OK, time to spot the deliberate mistake with this crocodile picture. Got it? No? Are you as bed a spellur as Ralf is? Phillipine and not Philippine is a terrible mistake to make by a man of his years. I think I will buy him a dictionary for his next birthday, as his internal spellchecker doesn't seem to bee wurkin!\n**Seychelles Sheath-tailed Bat**\n\n_Coleura seychellensis_\n\nDeep within the Indian Ocean lie the Seychelles islands. Here, undisturbed for millions of years, the flora and fauna existed happily alongside each other and continued their lives uninterrupted by humans, until 250 years ago that is, when the first settlers came ashore and life began to dramatically change. Since then people have altered the habitat of the islands and cleared much of the land and life is not as it once was. Introduced species have left their imprint on the lives of many of the original native species that were first found here all those years ago. There have already been extinctions and populations of many species have dramatically fallen to hazardous levels. Problems will always arise for species when they have small populations in restricted ranges, or even worse in a single location, as a single event can decimate or destroy such a population. Time is running out for certain critters on these still exquisite islands. The endemic Critically Endangered Seychelles Sheath-tailed Bat is feeling the heat more than many as the swing of the extinction pendulum counts down the time remaining for the winged mammal.\n\nThis insectivorous bat is found on the islands of Mah\u00e9, the beautifully named Silhouette and Praslin, where it may have already become extinct. This once abundant bat is decreasing in numbers rapidly and the population is estimated at fewer than 250 individuals in the wild and perhaps even as few as 100, with no single population having more than 50 bats within it.\n\nThe main cause of decline for the bat has been the clearance of woodland to make way for coconut plantations, which has created a lack of invertebrates for the bats to dine upon. This happened during the late 1800s and early 1900s, but the creature has never recovered and since then numbers have continually tumbled. Other probable threats include predation by introduced cats and barn owls as well as roost cave entrances becoming blocked off by introduced Kudzu vine.\n\nA conservation plan is needed immediately if the bat is to stand the slimmest of chances of survival. For a start the introduced species need to be controlled, then roost entrances need to be cleared and protected and habitat restoration is essential. Time is a precious commodity and very little remains for this poor little critter. We surely can't just leave the Sheath-tailed Bats hanging.\n\n_Ralph emails_ :\n\nIt's hard when your computer doesn't like you. And mine doesn't. All because it heard that I put an ice pick through an iPhone. Technology makes machines talk to each other, as we know. They communicate and gossip about us and have long memories. I am trying out an obsolete keyboard in the hope that my computer says, 'Ah! That's better! It's like meeting an old friend.'\n\nI thought about old friends \u2013 and many of them are old. Never mind! I am too. None of my friends, old or new, are in any position to grant me a knighthood \u2013 not that I expected one, mind!! There are some people who just don't deserve one \u2013 and I believe that I am one of them.\n\n_Ceri replies_ :\n\nWell I suggested you for a dayhood if that's any consolation.\n\n_Ralph replies_ :\n\nNow you're just being absurd.\n**Digg Soiler**\n\nDigg Soiler was born in the soil, literally. His mother, instead of a water birth, decided an earth birth was what was required for little Digg and from that moment forth his connection with the ground beneath his feet has been solid. He lives to grow things, whether that be trees, crops or flowers. He collects all the animal waste that he can and puts it to good use for his many projects, including a reforestation programme on the borders between the dark side of the island and the Mid Lands. He is the saviour of habitats and is loved by the critters as he ensures every one of them has the perfect living quarters to ensure a healthy existence. Many people in this world could do with taking a course on environmental care under his tutelage at the Muckist United College of Crittercal Kare, where he is the Chief Insmuckter in residence. His courses teach the benefit of utilising the muck around us and spreading it far and wide to enrich our land. Consequently he is also the College's Animal Site Waste Clearer \u2013 and a fine job he does too.\n\nThe motto on the college coat of arms is ' _If it's Muck, then spread it!_ ' This refers to a key moment in the birth of the Muckists as an environmental movement. This was the moment Bent Girders and Professor Overhang first became aware of Digg at a seminar to promote awareness about the probable nextinction of many of the world's creatures. In one particular talk about reforestation and reforming habitats, the lecturer said it was important to spread the word amongst locals to engender support from them. Digg stood up and shouted, 'Never mind spreading the word, spread the muck! Life comes from muck!' He then picked up great handfuls of animal waste from a huge bag he had brought with him and showered all and sundry with it. At first the crowd was disgusted and then they understood. A chant went up, 'Spread the muck! Spread the muck! We are the Muckists!' Digg was raised upon their shoulders and sprayed his muck far and wide. Bent and Lars knew this man had something special about him and that he could inspire people to do wondrous things for the world, so they invited Digg to Toadstool Island, where building work had begun on their as yet unnamed college and the MUCCK was born along with its new found motto.\n\nApplication forms can be found on the college's website. Payment, if accepted, is by waste only. Go on, do a good thing, spread the muck.\n\n_Ralph_ : I get sciatica because I paint like a snooker player. I should do it more like an artist.\n\n_Ceri_ : I guess I don't help with all my demands for critters. I must give you a case of Skypatica.\n\n_Ralph_ : I might even laugh a little if it didn't hurt so much.\n**Dratsab**\n\n_Mirum dentium_\n\nHere the artist has painted that classic subject in art, a portrait of mother and child. Ralph has captured a tender moment between the pair as the adoring mummy Dratsab tends to her young child, who is dressed in a onesie. We see the mother having her snout licked by the infant Dratsab as she dotes adoringly over her little beastie. But woe betide anyone who interferes with a moment like this or threatens the family unit. Those razor-sharp teeth, which seem somehow gentle in this tender snapshot, are more often than not snapping at the heels of whatever creature has intruded into the Dratsab's space. Its jaw moves faster than a pneumatic drill, more rapid than the finest sewing machine and can tear through brickwork in the blinking of a baby Dratsab's eye. This is true power and, when measured against the heavy biters of the animal kingdom, the Dratsab wins jaws down. Animal bites can be measured in pounds per square inch (psi), which is the force the jaw snaps down with when biting. The Saltwater Crocodile and the Nile Crocodile vie for top spot with a bite force that has been measured between 3,800 and 5,000 psi and it is believed that a very large Saltwater Croc would be the winner at a tidy 7,000 psi. In comparison the lion measures a measly 600 psi and the hippo a more respectable 1,821 psi. The Dratsab comes in at an enormous 7,600 psi and has been itching to take on both crocs and become the undisputed world chomp.\n\nThe Dratsab has been on Toadstool Island since time immemorial and in that period has won the annual Great Toadstool Bite Off competition every year apart from one \u2013 and that was because of a cavity in a tooth, which made it impossible to bite. Finding a dentist to attend to a Dratsab dental disaster is never easy and finally the task was taken up by Digg Soiler, as he has the aptitude for rooting around, digging about, clearing out muck and filling in holes. Since that tense encounter, the Dratsab faithfully helps out Digg whenever he needs help and watches over him protectively.\n\nThe Dratsab was once feared, as no creature was safe from its teeth and it was known as the Land Piranha of the prairies on Toadstool Island because of its love of biting. It was threatened with banishment and was banned from biting critters, birds and boids \u2013 now the Dratsab has turned over a new leaf and has become a worthy member of the community and the only living things it chooses to attack are invaders threatening the island. The Dratsab has stuck to the truce with other islanders and has proved itself invaluable in biting down crop harvests in record time, which is an enormous boon to Digg Soiler and enhances the island's wellbeing \u2013 and consequently it has become a much-respected figure in society.\n\n_Ralph_ : We're not doing mosquitoes because they're bastards.\n\n_Ceri_ : All creatures have a place. So mind your language. Use some backslang if you're going to talk that way. You're an absolute Dratsab. And I'm...\n\n_Ralph_ :... an utter Dratsab. I feel a drawing coming on.\n**White Rhinoceros**\n\n_Ceratotherium simum_\n\nHere's a creature we all know. It's one of the big players in the animal kingdom and high in the popularity stakes. It is the White Rhinoceros. Known because it's white, right? Wrong. It apparently takes its name from the Dutch word for wide, in reference to the rhino's mouth. In Dutch wide is wijd and somewhere at some time an English speaker heard tale of the wijd rhinoceros and it became the White Rhinoceros we know it as today. It is also known as the square-lipped rhinoceros, but whatever we call it you can't deny it's got a big mouth. It is also in big trouble. They live in Namibia, Zimbabwe, Kenya and South Africa with two subspecies: the Southern White Rhinoceros, which is considered as Near Threatened and the Northern White Rhinoceros, which is Critically Endangered and has become extinct in the wild. There are just three remaining individuals, which live in captivity in Kenya.\n\nPoaching for its horn for the Asian market, as with the Black Rhino, has seen the rapid descent of the species into a dark void. There is talk of a last-ditch attempt at IVF treatment to save the Northern White Rhino, but this is a long shot. Is it not putting off the terrible inevitable truth? But it has to be worth one last attempt to rescue this magnificent creature from extinction.\n\nThe story is rosier for the Southern White Rhino. It was considered to be extinct in the nineteenth century until a group of 100 rhinos was discovered in South Africa. After many years of good conservation work, its population stands at more than 20,000 individuals and it is the only member of the rhino family that is not endangered. These rhinos live in fully protected areas and private reserves \u2013 although where there are rhinos there are poachers and hundreds of White Rhinos are still killed every year. Security for the rhinos needs to be improved and the horn trade needs to be halted. Only then will the rhino be able to continue on its merry way.\n\nIn the meantime enjoy Ralph's existential rhino poem. Just don't tell him a white rhino isn't white.\n\n_Ceri's Diary_ : There is a real punk ethic at work here. The dirtying of the paper, the deconstruction of the animal, the reconstruction of its constituent parts and the anarchic defiance of the animal appearing before me makes my heart rise and I search for the story of each one of these creatures. I want my writing to do justice to every line, splatter and filthy blot of Ralph's animal kingdom. I can never get over how self-effacing he is as he completes these drawings, always putting them under scrutiny and wondering if he is on the right track. Meanwhile I am leaping with joy at every new beast that is placed before me and lapping up each species as it appears. He draws these animals in a very different way, dare I say it, to any other artist that has ever attempted to describe them. Ralph is unique in every way. Right, eulogy over. Time to move on to the next drawing.\n\n_Ralph emails_ :\n\nIf I were YOU, I would not cross\n\nEven a small rhinoceros\n\nA crossed rhinoceros will charge\n\n(Even a little one is LARGE)\n\nAnd those he catches do not live\n\nTo murmur, 'Sorry! DO forgive.'\n\nEdward Lucie-Smith wrote this in the 70s!!!! I did an illustration for it... but this isn't it!!! This is another early rhino though!!!\n\nRUFF\n\n**Atlantic Bluefin Tuna**\n\n_Thunnus thynnus_\n\n**Southern Bluefin Tuna**\n\n_Thunnus maccoyii_\n\n**Pacific Bluefin Tuna**\n\n_Thunnus orientalis_\n\nThere are three species of bluefin tuna, Atlantic, Pacific and Southern. The first two are listed as Endangered and the Southern Bluefin Tuna is considered to be Critically Endangered. Three species, one story and it's probably the same outcome for all of them unless things change. Overfishing has been the problem for all these fish and may well account for other members of the tuna family in time. So how did we get here?\n\nWhat we forget about tuna is that they are top predators of the seas and consequently help to maintain a balance within the ocean environment. Tuna are fast hunters with keen eyesight, who look for schools of fish such as herring and mackerel. They are powerful animals. They can dive to more than 1,200 metres and can live up to 40 years of age, although it is probably wishful thinking that they could be left in peace for that long any more.\n\nMany of us have come to rely on picking up a few tins of tuna from the supermarket or the local corner shop and we make a nice, quick bowl of pasta with it, thinking to ourselves that we have just eaten healthily and wisely. But the issue of tuna is a real symbol of everything that is wrong with the way that we take from the seas, how we police them and how we abuse them.\n\nIt is important to check the information on tins when buying tuna. A lot of tuna are caught in terrible ways that affect other creatures such as turtles, dolphins, sharks, albatross and other seabirds. Longline fishing, gillnets and drift nets are hideous inventions that cause great problems. Even though longline fishing can be adapted to create safer fishing it often isn't. Cans proudly announce their credentials when possible and one should look for words like caught by handline, pole and line, or troll fishing. But does this mean that if nothing is mentioned on the can the tuna has been caught by other, damaging methods? If so, would this not ask a question or two of the stockist and how they can justify putting it on the shelves for us to buy in the first place? I would suggest that an unmarked can of tuna with no information on the catching technique is a dereliction of duty and a shameful comment on how we live today. Maybe it is time for supermarkets to remove it from the shelves (which seem to be stacked higher than ever before) and for tuna fishing to be halted worldwide until there is an abundance of tuna again. OK, I know that is never going to happen, but we can dream can't we?\n\nIn particular, the scarcity of bluefin tuna has given rise to an unprecedented demand for the fish. Approximately 80 per cent of the bluefin tuna that is caught ends up as sushi and sashimi in Japanese restaurants, where it is considered the finest of all tunas and a delicacy second to none, revered for its flavour, especially the fatty underbelly, which is called _otoro_. In fact, it is so prized that prices for it have risen astronomically and at the first tuna sales at the beginning of every year the cost has been disgustingly high. In 2016 a 200kg fish cost a whopping 14 million yen, which is $118,000 or \u00a380,000 at the rate of exchange at the time. It is as if the very fact that the bluefin tuna may soon be extinct enhances the flavour as well as the price. This is surely wrong on every level, and it is now known that the last 100 years of overfishing and overeating has depleted the population of Pacific Bluefin Tuna by 96 per cent.\n\nThe craving for fish has created another problem in that there is now more illegal fishing than ever before. It is believed that the mafia have moved into the market, which has become as lucrative as other illicit activities. Forget sex trafficking, heroin or coke, fish is where it's at now. It has been estimated that illegal, unregulated and unreported fishing is worth up to $23bn. Hence the seas are under siege and the policing of such vast waters is proving difficult in the face of this new offensive. More needs to be done to combat this organised crime \u2013 perhaps we need more planes in the skies looking for suspect boats and satellite technology which could monitor the position of boats. It is finding a way to see the whole picture, not only of what is going on boat-wise on the surface of the seas but also what is happening under the surface. If we have a clue where boats are then we may get a picture of what's being smuggled and when and where. But it is a huge ask to patrol the seas well enough to halt this new onslaught of organised fish crime and it will take a concerted effort to make this a viable proposition. Perhaps we need a new approach to the protection of our seas.\n\nSince I wrote this the first Tokyo fish auction of 2017 saw a 212kg Bluefin Tuna sell for a staggering 74.2 million yen, which is $636,000 or \u00a3517,000.\n\n**Golden- rumped Sengi**\n\n_Rhynchocyon chrysopygus_\n\nOut of the midst of puddled ink steps the sengi or elephant-shrew and why does it have this name? It's obvious isn't it? It's a relation of the shrew and it looks like an elephant complete with its own resplendent trunk. That was simple enough, wasn't it? Well, think again, as science is weirder than fiction. After various studies it has been decreed that the sengi, of which there are probably 19 species living in Africa, are not related to shrews at all but are in fact a distant relative of the \u2013 drum roll, please \u2013 yes, you guessed it, the elephant! Ta-daa! Well who would have thought it? Isn't nature a mysterious beast?\n\nThe majority of the sengi species are considered of Least Concern, but two giant sengis (giant is a loose term when dealing with elephant-shrews) are at risk. The Grey-faced Sengi is deemed to be Vulnerable and the Golden-rumped Sengi is considered Endangered. Most shrews are faced with habitat loss and habitat fragmentation and the Kenyan Golden-rumped Sengi is no different. It lives in the small forests of the coastal area of Malindi. Approximately 13,000 live in the Arabuko-Sokoke forest region and an extremely small population of 20 or so lives in the Gede forest. Logging and agricultural encroachment threatens the Arabuko-Sokoke population and, for the moment, a monitoring programme is the only conservation measure being taken. But it does look as though habitat protection is the most realistic next step \u2013 and it is needed sooner rather than later for all sengi.\n\n_Ceri's Diary_ : After discovering the issues that numerous fish are facing I realise that thinking outside of the box is crucial for the protection of many endangered species. One group of people who are doing this are the Black Fish, founded by Wietse van der Werf, a Dutch activist. They are certain that more needs to be done to support the authorities and provide them with more information of what is happening out on the waters. The Black Fish run 28 projects in 12 European countries and the evidence of illegal activity that they gather is handed over to state authorities. This kind of citizen detective work is a good way forwards, although when observing, recording information and then handing the notes over to the correct bodies it is vital to do so without becoming involved and without taking matters a step too far. There is a fine line to be drawn and it is a hard line to tread well. I know from experience of watching illegal bird hunting in Malta how the line can suddenly disappear with one word or action out of place. The first thing that hit me when I watched a Bee-eater being shot out of the sky was pure anger and hatred for the hunter. I wanted to forget my role as a recorder of fact and wanted the emotion to take me over and go after the killer. But that does no good. All that happens is a messy confrontation, which inevitably leads to the perpetrator becoming the victim. So a cold heart with a warm thought needs to be in place. Seeing illegal activity being carried out on wildlife is distressing, but in the moment the emotion has to be removed. Every fact and action noticed and noted is a nail in the guilty party's future. Law enforcement officers can only work up to a point as not enough of them are out there. They need suppor, and, if handled correctly, everyday people can only be a boon to these services.\n**Lord Howe Island Stick Insect**\n\n_Dryococelus australis_\n\nThe Lord Howe Island Stick Insect was believed to have become extinct sometime around 1920 and this was due to the introduction of Black Rats to the island in 1918. In the 1960s there were various reports of sightings of large stick insects on Balls Pyramid, a rat-free rocky outcrop 23 kilometres from Lord Howe Island. Time passed and eventually a scientific research team managed to visit the rock in 2001 and ascertain that the Lord Howe Island Stick Insect really was alive. In 2003, another team was able to take two breeding pairs from their home and transport them back to mainland Australia. Melbourne Zoo conducts the largest captive breeding programme for the stick insect, which will help the species, as the population out on Balls Pyramid is believed to number only between 20 and 30. Hence it is considered as Critically Endangered, which is a tad better than being thought of as extinct, as it was before 2001.\n\nMelbourne Zoo is conducting research into the insect's lifestyle, behaviour, biology and diet to learn more about the creature. The ultimate goal is to reintroduce the stick insect to Lord Howe Island, but before that can happen the rats must be eradicated from the island. Then, and only then, does this particular critter have a chance of returning home.\n\n_Ralph_ : I just read what you sent me about the tuna and illegal fishing along with unregulated and unreported fishing being worth up to $23bn.\n\n_Ceri_ : It's quite an incredible figure isn't it?\n\n_Ralph_ : I know a fishmonger who doesn't earn that much in a year! And he sells salmon too.\n\n_Ceri_ : Wild?\n\n_Ralph_ : He's pretty angry a lot of the time.\n\n_Ceri_ : Did you ever fish?\n\n_Ralph_ : I did fish a lot with Hunter in the rivers of the Rocky Mountains. I particularly remember Roaring Fork River just outside Aspen. That was in a time before you and before you said I should stop fishing and hunting animals.\n\n_Ceri_ : I never imagined you as a fisherman.\n\n_Ralph_ : What does that say about your imagination? I fished with my father at Llanfair Talhaiarn, south of Abergele in North Wales.\n\n_Ceri_ : You've done it all your life.\n\n_Ralph_ : Yes, viciously.\n\n_Ceri_ : Fishously.\n\n_Ralph_ : Officiously. As they say, you live in Hope and die in Caergwrle.\n\n_Ceri's Diary_ : Caergwrle is not a mathematical equation, for my non-Welsh-speaking friends. This is an old saying from the two old villages of Hope and Caergwrle on the borders of Wales and England. We all want to live in Hope, right?\n**Luristan Newt**\n\n_Neurergus kaiseri_\n\nThis beautiful and striking-looking amphibian is a case of look but don't touch. As with many species of newts the Luristan newt gives off toxic skin secretions and the pattern and colours of its skin are a warning sign of this and not an invite to 'pick me up because I'm beautiful'. It is endemic to four streams in the southern Zagros Mountains of Iran, where it lives during the breeding season. Here it hides under rocks and stones in the arid shrubland surrounding these waters. Habitat loss due to locals collecting firewood, as well as drought and the possible effects of damming of the streams are compounded by the fact that the newt is a desired creature for which there is an increasing demand in the international pet trade. It is estimated that there are only 1,000 of this Critically Endangered critter left in the wild and this figure appears to be decreasing. It is a protected species but more needs to be done to prevent export of the newt for the pet trade. A captive breeding programme may be the only way forward to bolster the numbers of this beaut newt.\n\n_Ceri's Diary_ : There are wonderful sketchbooks turning up in the studio with some beautiful critters in them. Ralph as usual can't remember when he did them. His line is so strong but yet delicately powerful. I adore this hippo.\n\n_Ralph_ : My grandson Ollie and I now call this the Ollie and Stan Newt!\n\n_Ceri_ : That's funny. Did you know that the Laurel and Hardy catchphrase we use so often, 'That's another fine mess you've gotten me into' is incorrect? It is ' _Here's_ another _nice_ mess you've gotten me into.'\n\n_Ralph_ : And here's a quote from my father that I won't get wrong. He used to say this at Waterworth's the greengrocer's. 'Two-penneth of fruit please and not too many watermelons.'\n**Rat- arsed Skunk**\n\n_Arsius stinkittimus_\n\nThe Rat-arsed Skunk is the stinkiest, smelliest, pongiest, most reeking and malodorous critter upon Toadstool Island. But everybody loves the skunk as it uses its putrid spray, which is accompanied by a warm pungent acrid wind, to keep out those unwanted invaders that would invade and infest the island if they could. The chief objects of the venting are rats. This is why it is called rat-arsed, not because of a drinking problem but because its role is to keep rats away. Skunks can normally spray their oily liquid up to a distance of three metres but our fellow can spray its torrential vile rain as far as three hundred metres. Something about the aroma of his stench affects a rat's olfactory system, disorientates them, attacks their brains and makes them scamper as far away as possible. Hence no rat has ever stayed upon the island and this foulest of fellows is to thank for that.\n\nWhen not out patrolling the island, the skunk can be found having a Pernod and black down at The Old Elephant's Trunk with various well-wishers who always insist on buying the skunk its favourite tipple. But the limit is two per day as Pernod seems to engorge the scent factory within and can set off a malodorous reaction, which can close the pub for weeks on end. This drink limit is the island's attempt to stamp out any chance of stink-driving.\n\n_Ralph emails_ :\n\nYou sure know how to charm a crazed critter!!!!!!\n\n**Aye- aye**\n\n_Daubentonia madagascariensis_\n\nCoded message or not, there is a perfectly reasonable explanation why the Aye-aye has a middle finger that is so much longer, thinner and gnarlier than any of his others. It's a percussive forager. Simple. End of story. A percussive forager, what's that? OK, let me explain. Percussive foraging happens thus. The Aye-aye taps out a little rhythm on a wooden surface to determine where there are cavities inside and then, listening with its large disc-like ears and probably using echolocation, it decides exactly where the grubs are for grub time. It uses its incisors to make a small hole in the surface and then it inserts its especially extended digit into said hole and hey presto it pulls its dinner out of the opening, thus giving the invertebrates inside it the actual finger. And this actual finger is articulated by sitting on a ball and socket joint, allowing the finger to move and swivel the full 360 degrees. So watch out, the Aye-aye can get hold of you wherever you are.\n\nThe Aye-aye is a lemur which hails from Madagascar. It is now considered as Endangered and the population is sadly on the decline due to habitat loss and hunting. It is a nocturnal creature and noted from various different habitats including rainforest, mangrove swamps and dry scrub areas. It is nothing if not adaptable. It has had to be, as more and more forest is being destroyed. It is also hunted for meat and because farmers fear it will damage their crops, although there is no evidence to support this. I am afraid superstition plays a weighty part in this odd lemur's life as it is also killed because it is considered to be evil: dead Aye-ayes are often hung upside down outside a village to ward off evil spirits. I guess this persecution is because the Aye-aye is not the most handsome of creatures and even demonic-looking but I really like him \u2013 after all, beauty is in the eye of the beholder. In the face of these problems it is high time for a conservation action plan to be mapped out and surveys across its range are essential to understand the lifestyle of the creature. There are several ongoing captive breeding programmes but these have not proved successful with second-generation creatures and the work continues. Solutions need to be found \u2013 otherwise we may have to say bye-bye to the Aye-aye.\n\n_Ralph_ : This next critter is carrying an important message for you.\n\n_Ceri_ : What do you mean?\n\n_Ralph_ : Have a look.\n\n_Ceri_ : Aye-aye, Cap'n!\n\n_Ceri's_ Diary: Aye-aye, it's the Aye-aye. And as I look at this scary, crazed animal I can almost hear it screaming my name. He is terrifyingly funny and I try to decipher the message. Is it that it is Endangered? That it needs help? Or is this strange fellow giving me the finger? A coded message from my beloved Cap'n Ralph, perchance? Hmmm, I will have to ask him.\n**Baad Guttering**\n\nBaad Guttering is the PR guru and chief administrator at the Muckist College. He tirelessly promotes the scientific work that is being carried out at the college and works on advertising the various courses that people can apply to attend. These include 'How to raise awareness and engage local people with a species', 'We don't need to destroy this habitat, there's another way', 'Boo to hunters', 'Come on, that's not a fair way to fish', 'Let's all take an eco-holiday' and 'How to stop megalomaniac politicians and corporations destroying the environment in the name of progress'.\n\nBaad explains the situation regarding the conservation courses to Ralph and myself. 'These courses are often booked a year in advance but I am trying to double the amount of courses available by hiring extra lecturers. This is the problem with conservation in general. So many people would like to engage with conservation action but there are not enough places on courses such as ours to learn about how to become a conservationist. This is compounded by the fact that once people are qualified the big wide world does not offer enough jobs to employ people within conservation. This is why there are so many volunteers on nature reserves and projects, because there is no money available to employ people. Conservation could become a vocational career for so many more people than are actually employed at the moment. Kids are interested in wildlife but as they go through the education process they have to veer away from the world of wildlife and head in other directions, only a small minority can find employment within conservation. It should be teeming with people in their 20s, 30s and 40s but it isn't and volunteers are usually those wonderful people who have retired from their life's work and can afford to be unpaid and help out with critters. It's wonderful that they do this, but why can't we get more money directed into the conservation sector? I am certain it's because big companies don't see it as a profitable option and that is the disgrace of the modern world. \"If there's no mark-up in saving the world then what's the point?\" That is the general corporate viewpoint of the situation. If we could persuade governments and corporations to take our natural world seriously we could probably get things fixed up in a jiffy. The people are out there, the money to fix things is most certainly out there, but the engagement with them isn't. We need to change our mentality and we need to change it sooner rather than later. Those with wealth need to understand that the wealth of our planet is becoming ecologically raped and all the money in the world will not mend it when everything has gone.'\n\nAll monies raised through the college are ploughed straight back into their research and conservation work including captive breeding programmes, critter population surveys, governmental negotiators and the policing of truly wild areas.\n\n**Gnat Flutterby**\n\n_Amor iniectio_\n\n**Little Mother Moth**\n\n_Paucis mater_\n\nBaad hands us a PR pack entitled _The Love Bug_. He explains what the title means. 'This is our flagship captive breeding programme. As we all know gnats can bite people and suck blood out but the Gnat Flutterby, under the auspices and training of the Little Mother Moth, actually injects its targets with a virus, which we call the love bug. The Little Mother Moth cares for the gnat and loves the gnat in a way that no gnat has ever been loved before and this engenders warmth and love within the gnat and triggers a chemical reaction creating viral venom filled with all-encompassing love. Once a person is bitten it renders them full of love and warmth for the natural world and the creatures within it. The infected become incapable of harming wildlife or habitat and become fully rational and methodical in finding alternative solutions to environmental issues \u2013 the virus stops the desire to damage our planet any further. At the moment we are also discovering that the longer the gnat is loved and nurtured by the Little Mother Moth, the more durable and longer-lasting the gnat's virus becomes. There is no downside to this release of environmental love either. Tests have proved conclusively that humans will become a better species as soon as they have had their inoculation against the powers of progress and the economically driven decimation of this earth. Love truly conquers all. Gnat's the way to do it.\n\n_Ceri's Diary_ : Baad takes us to the college's captive breeding centre where he wants to show us a particular species they are working on which could have a far-reaching impact on the world and its attitude towards the state of our environment. This is the top-secret Gnat Flutterby programme.\n**Red Wolf**\n\n_Canis rufus_\n\nThe Red Wolf's range has shrunk and shrunk over time and it was finally termed as Extinct in the Wild in 1980. But in 1987 the United States Fish and Wildlife Service (USFWS) released a population from captivity into northeastern North Carolina. There are 50 or so in the wild today but alarm bells are ringing significantly for the future of these wolves. The problem has been hybridisation with Coyotes. When the wolves were first placed in North Carolina there seemed to be an absence of Coyotes, which made the placement all the more ideal. But during the 1990s Coyotes became well settled in the area and Red Wolves and Coyotes can mate and next thing you know there is a hybrid scenario going on. It is believed that the Red Wolf could make a decent recovery but for the issue of hybridisation. There are about 175 wolves in captivity in the United States and Canada so the Red Wolf will continue existing, but trouble is afoot.\n\nThe USFWS is deciding whether to continue this programme or to cancel it because of the issue of hybridisation. This has caused a stir in America with half a million people signing a petition to save the project. Will this do any good and will it be enough to sway the authorities to change their actions? Do we, the people, truly have any say in these things? I am not so sure that we do.\n\nFor all the people who want to keep the wolves going there are also a number who want to see them gone, not trusting in the company of wolves. Farmers and landowners often shoot Coyotes, as they want to keep them off their land and this often occurs at night when Red Wolves can be mistaken for Coyotes and are shot instead.\n\nFaced with all this information the USFWS will make a decision and whichever way it goes, it will upset some people and make others happy. For me, I think a wolf is a magnificent creature and my Native American Indian zodiac sign is that of the wolf, so I have a peculiar affinity with this beast, I would hope that the crossroads it is now standing at doesn't turn into a dead end.\n\n_Ralph_ : Robert FitzRoy was the captain of Darwin's _Beagle_ and on that voyage he termed the phrase 'weather forecasting', which has been with us ever since. He was an extremely religious man and disagreed with Darwin about evolution and argued that dinosaurs became extinct because the doors on Noah's Ark were too small to allow entry to them.\n\n_Ceri_ : And that's why you can't always believe the weather forecast.\n**Tiger**\n\n_Panthera tigris_\n\nTigers are indigenous to Asia and there are six subspecies still in existence. Three subspecies, the Bali Tiger, the Javan Tiger and the Caspian Tiger, have already been lost to extinction during the harshness we know as the wasteland of the twentieth century. In April 2016 it was announced that after years of constant decline for the Tiger population, the future was looking brighter as numbers had increased from approximately 3,200 wild Tigers in 2010 to an estimated 3,890 today. Hard work and cooperation between NGOs, philanthropists, governments, local authorities and communities have paved the way for this success, but more is needed if the Tiger is to be removed from the danger list altogether. The WWF is still keen to point out that the target is to double the original number by 2022.\n\nTigers, whose range stretches across 13 Asian countries, have lost much of their habitat for numerous reasons. Change of land use for agricultural purposes, the felling of forests and human encroachment all play a significant role. Consequently, Tigers exist in smaller and smaller fragmented areas than ever before, making them more susceptible to poaching, especially as they increasingly share the same space as humans. The Tigers may have to resort to taking domestic livestock as food and local people who have to utilise the forests for food and wood are open to attacks by Tigers. This leads to a continual conflict between man and big cat, which sadly can result in the Tigers being killed or taken and sold on the black market.\n\nIn fact, after a short trawl through the Internet it becomes apparent that there is a thriving market for Tigers with dead ones fetching $5,000, a live one available for $50,000 and a cub for a paltry $3,200. A little bit of interior decoration? A pelt could set you back $35,000. Might as well buy a dead one and do-it-yourself. If all you need is Tiger penis then that will stand you in at $1,300. Why would you want one? So you can soak it in wine and then drink it, as it has become an aphrodisiac, that's why.\n\nTiger bones are ground up and used in Chinese medicine to treat rheumatism (not just in China but also in Vietnam and Thailand) and the thirst for these treatments continues unabated. Perhaps education is never going to work and therefore the hard yards have to be put in to stop the business of wildlife products. But where there's money there's illegal activity. Always. And there is undoubtedly a market for these things in the US and across Europe. We cannot live in self-denial and point the finger of blame towards distant parts of the world. We are all culpable. But the Asian market, especially in China, drives the trade, as their medicine dictates that wild animal parts have healing qualities. If you have a fever then just take a spoonful of bear bile. Cancer? Turtle meat should do you. Cobra should put lead in your pencil and crocodile meat will not only sort out any lung problems but will restore the memory. Thank God for wildlife. It really benefits us to have so many creatures around.\n\n_Ralph emails_ :\n\nTIGER PAGE! Scaring me silly!!! In the GLOOM!!!!\n\n_Ceri replies_ :\n\nLove the tigers... They look like quite a bunch! Wouldn't trust them with my Cornetto!\n\n_Ceri's Diary_ : 'All tigers deserve a page' is the decree upon this page. I utterly adore this group, especially as Ralph has encapsulated tigers in all their glory. My favourite is the ghostly cross-eyed one right in the middle of the page, which I have only just noticed. My eyes keep wandering across the different faces and little trails of drawn lines amongst the splatter and I think about tigers for a minute and realise what a strange relationship we have with so many creatures in this world. Many people say how much they love tigers and look at how many kids have cute cuddly tiger toys that they adore \u2013 but do any of us want to find ourselves close to one in the wild other than from a very safe and protected distance? I doubt it. But there is such a majestic beauty about such a dangerous animal that we find ourselves wanting to increase the number of them that exist out there because the world would be a different place without them. This is the dichotomy of the modern world. How do we restore the correct balance to a world that has become so unbalanced?\n**Grevy's Zebra**\n\n_Equus grevyi_\n\nIt is estimated that there are roughly 2,000\u20132,500 Grevy's Zebra remaining in the wild in Ethiopia and Kenya and, though unsubstantiated, a population may be found in southern Sudan. Its range used to be much larger across East Africa but populations have declined by approximately 55 per cent between 1988 and 2007 and the Grevy's Zebra is therefore considered as Endangered. It is herbivorous and lives in arid and semi-arid grasslands and likes to have permanent water nearby, although they can survive for up to five days without it, but it's not ideal. Lack of water sources is one major reason for the decline in numbers, as well as habitat loss, hunting, disease and competition for food and water with people, cattle and other livestock. There's just not enough for everyone. In Kenya, the survival of zebra juveniles is a major problem due to the demands upon the natural resources and overgrazing. Another problem used to be hunting for skins, which was a major issue in the 1970s. In fact, I can remember someone at school showing me a zebra skin complete with head in their house and I couldn't fathom out why someone would want such a thing. It seemed macabre. But it was the 1970s and _Love thy Neighbour_ was considered a decent sitcom. (For those too young or from abroad, this was an English comedy based on racism and abuse and was prime-time viewing for many. I guess it wouldn't get made today, so some things have definitely got better.) But hunting for the beautiful zebra skins apparently still happens in Ethiopia.\n\nThe Grevy's Zebra is a protected species in Ethiopia and there has been a hunting ban since 1977 in Kenya, where it is also waiting to be conferred with the status of a protected animal. More needs to be done to protect the zebra's range, as only 0.5 per cent of it is protected at the moment, but where protection has taken place and the competition with livestock has been reduced, zebra populations have increased. More has to be understood about the movements of the animal and conservation plans must be drawn up, whilst local communities need to become involved in the conservation actions. Then, this stripy beauty, can once more roam across Africa in greater numbers.\n\n_Ceri_ : Some of your pictures are, how shall I put it... quite anatomical.\n\n_Ralph_ : The trouble with ink is it runs. And this ink made a dash for it and that's why the zebra's manhood is so prominent.\n\n_Ceri's Diary_ : What is surprising is how many farms there are dedicated to farming many of these endangered animals. In Asia there are turtle farms, crocodile farms, tiger farms and snake farms. You name it, there is a farm supplying the animals that are wanted. This is a multi-billion-dollar industry. Look at all the effort that goes into it. Can you imagine if all the people who run these businesses for economic gain made a volte-face and became conservationists, working diligently to restore the world's wildlife to abundant levels in the wild? We wouldn't have an endangered or nextinct creature in the world other than those due for a natural extinction. This would be a beautiful place. But we are greedy, selfish, money-grabbing swine on the whole and we always want to make things better for ourselves. Not the world around us.\n\nI'm so full of rage that I think I had better stop writing for a while.\n\nTime passes...\n**Giant Panda**\n\n_Ailuropoda melanoleuca_\n\nIn 1981, the WWF became the first international organisation to work in China and the panda has needed that amount of time to move from beleaguered conservation-reliant icon to conservation success story. Time, work, money and passion have made this happen. A census in 2014 found there were 1,864 Giant Pandas in the wild (excluding cubs) and it is estimated that panda numbers have risen by 17 per cent in the last decade.\n\nThe panda's range has shrunk considerably due to fragmentation and loss of habitat on account of human encroachment and today it is found in the Chinese provinces of Sichuan, Shaanxi and Gansu. It is restricted to mountain ranges, as much of the lower forested habitat the panda used to live in has been destroyed. More than 30 per cent of China's forests were lost between 1950 and 2004 and this period saw a spiralling fall in panda numbers.\n\nPandas eat bamboo (a very low-protein food source) and they must eat up to 12.5kg of it a day to obtain their daily requirements. This diet means they poo more than 100 times a day. Sheesh... Remind me never to get into bamboo! The need for bamboo was a primary cause for the panda's problems. When bamboo flowers or dies off, the panda used to be able to move up or down the slopes to eat different species of bamboo at varying elevations. Human encroachment into lower areas cleared the habitat and destroyed copious amounts of bamboo species, which consigned the panda to a life at a higher elevation with less variety in bamboo. There is a fear that even with the recovery of some habitat and the rise in the panda's fortunes climate change may well decimate future stocks of bamboo, which could send panda numbers tumbling again.\n\nPoaching is non-existent now, although the occasional bear may be caught in traps set for other animals. There are now 67 panda reserves, which protect 67 per cent of the panda population. This equates to 1.4 million hectares of prime panda habitat. The recovery of much habitat has been due to some wonderful initiatives that have benefited man and bear alike. The Natural Forest Conservation Programme, established in 1997, banned logging within panda habitat and slowed deforestation and erosion, which was causing flooding. The Grain-to-Green Programme, which incentivised farmers by offering grants to plant trees on bare slopes to halt further erosion and to convert cultivated land back into forest, is also succeeding. Between them, these projects are creating or restoring three million hectares of forest cover each year. Good for everyone. This is the age of eco-compensation.\n\nThe future will not be without challenge, but the way conservation has dealt with pandas is really an example for the rest of the world to notice, admire and then support the next needy critter.\n\n**++ NEWS FLASH: PANDA NO LONGER ENDANGERED ++ NEWS FLASH:**\n\nBut hold on just one bamboo-pickin' minute. Today, the IUCN has announced that the panda has moved one step away from the abyss of extinction and it has been downgraded to Vulnerable. This shows that with a lot of help, care and attention, animals can come back from the edge and continue life as a more stable species. Remember 4 September 2016. This is positive and we must harness that positivity and renew our fight against everything that threatens our wildlife. It can be done. When the WWF was founded in 1961 by Sir Peter Scott, he chose to paint it for the logo and that logo has remained with us ever since. Generationally, the panda has grown up with us and today has become a symbol of hope. Happy days.\n\n_Ceri's Diary_ : The Giant Panda is a creature we all know and are familiar with from an early age. There is nothing like it and pandas look so appealing with that striking black and white fur. It is the symbol of the WWF and many of us wore their panda badge as a kid. Hence it was a shoe-in for the book as it is probably the symbol for endangered creatures as much as the Dodo is the symbol for extinction. Hence Ralph is drawing this Endangered critter.\n**Borneo Pygmy Elephant**\n\n_Elephas maximus borneensis_\n\nWhen I think of a pygmy elephant I imagine it as a lovely, tiny, cute little elephant that comes up to my waist, but the truth is that this bundle of elephant charm still stands between 2.5 and 3 metres high. Not as small as I thought but definitely a perfect package of all the elephantine things that I like. Floppy ears, sweet face, long tail. Ralph has captured the joy of this elephant's life as it hops through the watery page splatters.\n\nAbout 1,500 Pygmy Elephants are to be found in Borneo and it has become Endangered because of the loss and fragmentation of much of its forest habitat due to human encroachment. Oil palm plantations, conversion of land for agriculture and logging are also taking their toll on the pygmy elephants and increasing numbers of people living in the same location creates more human and elephant conflict. Snares are often laid to catch small creatures but it is believed that they have injured 20 per cent of all elephants.\n\nBecause so little is known about the pygmy elephants' lifestyle the WWF is carrying out scientific research \u2013 including satellite tracking, which was begun in 2005 \u2013 to understand better their movement and use of the forest. The more that is known about the elephants the greater the chance of helping them survive and thrive. What is known so far is that the elephant forests need to be managed and logging needs to be controlled and sustainable, so that the elephants can continue breeding in the forests. Also, the WWF is working with plantation owners on creating wildlife corridors, which would reconnect the separated forests. A forest superhighway, if you will, to handle animal traffic and which elephants and other creatures can use. You don't want to get stuck in the slow lane in one of those.\n\n_Ralph emails_ :\n\nMaybe you don't give a hoot for Borneo Pygmy Elephants \u2013 well I dun one o' them \u2013 he is just a lot of fun and makes me smile! I know you were feeling down so this pygmy elephant is a little pygmy-up for you. ROLFZ\n\n_Ceri replies_ :\n\nHe is so cheerful and his eye radiates happiness. What a beauty.\n\n_Ceri's Diary_ : How fitting that this morning's arrival is an elephant, as today a Kenyan court found Feisal Mohamed Ali guilty of ivory trafficking. The man they call 'the Godfather of Ivory' has been sentenced to 20 years in prison.\n\nIn April 2016, the Kenyan president, Uhuru Kenyatta, set fire to ivory worth more than $100 million and weighing over 100 tonnes. This was a symbolic gesture to state that Kenya was hands-on in the fight with the ivory poachers and sent out a message to the world that more still needs to be done. This amount represents 5 per cent of the total stock of ivory and some people were worried that it would just be seen by the poachers as a signal that they needed to replenish the diminished supplies. But we have to take on these disgusting people and make a stand. The Ali case became a cause cel\u00e8bre. What would the outcome be? After all, African courts have often been accused of letting those responsible for wildlife crime walk free from court. Would things change with the trial of Ali?\n\nThe story began in June 2014 when two tonnes of ivory was seized at Fuji Motors car yard in Mombasa. This had a market value of $440,000. A warrant for boss man Ali's arrest was issued but somehow he wasn't taken into custody. Then, in October, Interpol announced that he was one of the world's most wanted environmental criminals and was on the run. He was eventually found in Tanzania and was arrested on Christmas Eve 2014. Merry bloody Christmas to you.\n\nWhen Ali eventually came to court in 2016, many within the conservation world sat with bated breath. This wasn't a low-level poacher or criminal, this was a major player in the ivory trade. A person of significant ivory interest. Would he get justice for his crimes? When the sentence was announced it was met with joy. 20 years and a $200,000 fine seemed like the law was working, although his co-defendants were all acquitted due to a lack of evidence. It may not bring back the murdered elephants but it is a decision that sticks up for the tusky guys.\n\nThis follows hot on the heels of the news that China's 'Ivory Queen' has been arrested in Tanzania. Just as a point of order, why are we so committed to giving names and titles to criminals? 'Godfather of Ivory' and 'Ivory Queen' gives these horrid humans a sense of grandeur. Yang Feng Glan, a 66-year-old Chinese businesswoman, was arrested in June 2016 for allegedly smuggling tusks from more than 350 elephants. Along with two Tanzanian businessmen, she is accused of buying and selling 706 pieces of ivory, worth more than \u00a31.6 million, between 2000 and 2014. Fragile little old lady or barbaric, murderous smuggling mastermind? The courts will decide.\n**Snow Leopard**\n\n_Panthera uncia_\n\nYou have to be pretty powerful to deal with the arduous climbing needed to traverse the steep and decidedly rocky mountain regions of Central Asia and the Snow Leopard is perfectly built to deal with this terrain. Once prey was plentiful across the 12 countries it inhabits and it was the king of all that it surveyed. It had no predator to threaten it until you-know-who appeared on the scene... humans. Since then the Snow Leopard population has fallen into decline and it is now another Endangered animal. In 2003 it was estimated that between 4,080 and 6,590 leopards were left in the wild and the population was decreasing. Hunting, habitat, loss of prey and conflict with local people are the threats that have arisen since people came to live in the leopard's manor. Wild, natural prey such as the Argali sheep are hunted by human and leopard alike, creating competition for the same food source. This competition leads a hungry leopard to take livestock and because of this they are often persecuted.\n\nPoaching is also a problem as there is a growing demand in China for fur, bones and animal parts and, incredibly, some zoos and circuses want and receive live animals. Stricter measures through tougher laws and stronger enforcement are believed to be the answer to halt the progress of the hunters. The range of the Snow Leopards is a difficult one to manage as it extends across many volatile countries and borders and military activities regularly occur, affecting much wildlife and habitat. These conflicts cause displacement of people, who sometimes resort to trading in wildlife as a means to an end. Patrols are needed to clamp down on poaching and better livestock and grazing management is needed to promote a more harmonious relationship with wildlife such as the leopard. An awareness programme would not go amiss for local communities to seek out alternative ways for humans and leopards to coexist happily together and to find financial incentives for them to conserve and look after the Snow Leopard, including ecotourism and handicrafts.\n\nJust remember there's no leopard like the Snow Leopard and we want the Snow Leopard not NO leopard to be living within its environment.\n\n_Ralph emails_ :\n\nOle Blue Eyes is back.\n\n_Ceri replies_ :\n\nOne of the founding members of the Cat Pack.\n**Chimpanzee**\n\n_Pan troglodytes_\n\nChimps have been a part of our culture forever. They have appeared in books and films, have become movie and TV stars, and some, like Congo in the 1950s, have become artists. They have even flown into space, including Ham the astro-chimp \u2013 and still we can't look after them properly. Think of all the famous ones you know, such as Cheetah who kept Tarzan company, the PG Tips performing monkeys who sold us tea bags on British TV during the 60s and 70s, or Lancelot Link, an American spy-chimp who worked for A.P.E. Is it because they remind us of how we used to be that we find them so endearing? Do we love the way they can mimic us and look like little humans? Well, the thing is that chimps (along with bonobos) are our closest relatives and they share 98 per cent of our genes. They really are mini versions of us.\n\nChimpanzees have a range larger than any other great ape, stretching over 2.6 million square kilometres across the forests of Africa. There are four subspecies: Western Chimpanzee, Nigeria\u2013Cameroon Chimpanzee, Central Chimpanzee and Eastern Chimpanzee. Population numbers have been in major decline for the last 20\u201330 years and numbers are expected to continue to fall for the next 30\u201340 years. Threats to these African great apes include habitat loss, disease and poaching. The Chimpanzees are threatened by bushmeat hunters and are either shot or snared. Often when adults are killed, their infants are taken as pets or sold even though it is outlawed to hunt or trade Chimpanzees. As humans expand into the primates' habitat, more land is converted for agricultural use and Chimps that take from crops may be killed in retribution. Slash-and-burn agriculture destroys great swathes of habitat and logging, mining and drilling for oil are pushing the forests ever further back. Added to this is the effect of industrial agriculture, in particular the new oil palm plantations, which are moving into Africa as Asia reaches its capacity for this crop. All of these hazards are compounded by the need for a better infrastructure of roads, which will decimate the habitat even further.\n\nLastly, chimpanzees are susceptible to the same diseases and infections that we are affected by. Therefore tourism, as much as it brings money into the communities, can present a problem as infectious diseases such as respiratory problems can be transmitted to the apes. At the moment the Ebola virus is top on the list for damage being done and has caused many Chimpanzee deaths.\n\nThe management of land cleared for plantations and other extraction processes such as mining and logging needs to become more effective. Chimpanzees are a protected species, but unless a stricter enforcement of wildlife laws is carried out then more primates will be lost to this world. Even in protected areas the Chimpanzees are not necessarily safe as there is acute under-staffing in many of the national parks and it is necessary to increase the policing within them.\n\nI want this primate to be my mate but the only way to assure this is to prove just how much we care for him.\n\n_Ralph emails_ :\n\nHe is done and looks pretty good \u2013 enigmatic, arthritic and the Little Guy has got a hair lip! And remember! If anything comes up \u2013 CHANGE YOUR DIET!!! Also what goes without saying \u2013 is invariably overstated!!! HA! HA! HOOO!!!\n\nMust do TREES! TOO! ALSO! SKUPPERED DUNT drying on the floor. Took a quick snap.\n\n**Terry Cotter \u2013 the Island's Potter**\n\nEvery island has its own ceramicist and Toadstool Island is no different. Terry Cotter was associated with the Cornish potters in St Ives but was deemed a ridiculous failure within the studio pottery world as his pots' main attribute was that they leaked and not just a little bit. You would never put a Terry Cotter pot filled with flowers and water on a piano as in the morning the water damage would be insurmountable due to the leak from said pot. Dame Lucie Rie gave him a bit of advice, 'Dearest Terry, you are a sweet boy but pottery to you is akin to what darts are to Margot Fonteyn. It's just not your game. Give it up and give it up now.'\n\nHe ignored this kindly advice and became a laughing stock. The last straw was when he handmade a ceramic bath for pottery collectors Sir Ledley Rosefinch and his wife, Rose. On taking her first bath Lady Rosefinch relaxed and leant backwards, expecting to wallow in comfort, but the bathtub made a deep resonating cracking sound and rent asunder, splitting the tub down the middle. The weight of water broke through the now exposed floor and disintegrated the ceiling below and her ladyship went straight through the hole and ended up, wet, wriggling and naked on a gaming table as Sir Ledley entertained some of his friends from the Shoot it or Else conservation club over a game of strip Rummy Cube. (The rules are somewhat murky.)\n\nReaching for his gun, Sir Ledley headed off into the night as Terry only lived ten minutes away. Luckily, Terry had decided to have a drink at the Potters Bar and was supping his favourite real ale, On the Pot, when he heard that Sir Ledley was seeking him out. He realised his days were numbered and he rushed down to the harbour and sought passage on the _No Idea_ , which had no particular destination. It was the perfect fit for Terry and he happily became the ship's potter, making leaky pots for all. The captain decided that Terry's pots were perfect for dried flowers and suddenly leaks were a forgotten thing.\n\nAfter many years they found themselves in the Toadstool Archipelago and weighed anchor at Toadstool Island and Terry went for a walk to be inspired by nature. 'Be back soon, Terry. We may have a tight schedule.' Terry became side-tracked by the sight of a herd of wowlets and wandered across the islands with his potter's wheel on his back and his kiln on wheels trailing behind him. It was arduous stuff but after two years and unaware of the time he got back to where he had disembarked and found there was no _No Idea_ waiting for him. How peculiar, he thought. So he stayed right there for six months until he decided it might be best to give up on the waiting lark and so he built a little shack and set up shop. It was a roaring success, and the extinct and nextinct birds and critical critters immediately admired and took a shine to his work. The miserable extinct critters didn't give two hoots. Or was that the Mauritius Owl? It all becomes a bit of a blur, really, but he has been awarded the prize of Potter of the Year every year since his arrival. Not surprising really as his only competition is the Dratsab and he makes Terry Cotter look like Hans Coper. I wonder what Dame Lucie would have made of it all.\n\n**Fin Whale**\n\n_Balaenoptera physalus_\n\nThe Fin Whale swims pretty much across the world's oceans and is considered by many, although not all, to consist of two subspecies, the Northern Hemisphere and Southern Hemisphere Fin Whales. The only creature larger than a Fin Whale is the Blue Whale and I am certain we will be talking about him later in the book. In the meantime this whale can grow up to 27 metres long and is able to swim at speeds of 37 kilometres per hour. Over short distances it can sprint at 47km\/hour, which means that Usain Bolt, whose fastest speed was registered at 44.64km\/hour, would be nudged into second place. This rapidity through the water has given the Fin Whale the nickname of the 'greyhound of the sea'. It was this speed that meant it was not hunted for years as no whaling boat could keep up with it, but times changed and soon it was as susceptible to hunting as any other whale.\n\nThe population is believed to have decreased by 70 per cent over the last three generations (1929\u20132007), but this is largely explained by the depletion of the Southern Hemisphere population, as numbers of Northern Hemisphere Fin Whales have quite possibly increased \u2013 though the population of Fin Whales in the North Atlantic is now classified as Endangered.\n\nLike many other large whales the Fin Whale is threatened by habitat loss, pollution, climate change and of course commercial whaling. Only a handful of countries still hunt for whales and these include Norway, Japan and Iceland.\n\nThe Japanese run a scientific whaling programme, which for all intents and purposes is a cover-up for their commercial whaling operation. It has come in for condemnation as very little research has been produced and the majority of the meat ends up being eaten.\n\nThe majority of whale meat generated in Iceland is exported to the ever-hungry Japanese market, as there is not much of an appetite for whale meat amongst the Icelanders. In fact, polls would suggest that only 3 per cent of the Icelandic population eats whale meat regularly and in 2016 a petition asking the Icelandic government to ban whaling was signed by over 100,000 locals and visitors. Whale watching as opposed to whale eating is becoming a growing attraction for more than 350,000 tourists, a little more than the entire population of Iceland itself, and this generates an annual income of \u00a310 million. One can only assume that the export trade in whale meat is a monetary issue but keeping these creatures in the water can raise great funds too. Time to change, dear Iceland.\n\nThe International Whaling Commission is the organisation responsible for whaling and for overseeing the state of the cetaceans within the oceans. But, for the moment, it seems at a loss as to how to move forward and stop the whale hunts that are damaging so many species. Perhaps more petitions and participation in awareness programmes from everyday people is the way forward. One thing is certain, the taste for whale meat is decreasing \u2013 and surely now is the time for all whaling to cease. Then we can have fin whales, fat whales any size of whale safely swimming the seas of our world.\n\n_Ralph emails_ :\n\nI was going to do a fat whale but instead I done a fin one. Older whales found too! This was a book that never happened.\n\n_Ceri replies_ :\n\nThey are exquisite. All the whales being glimpsed through the surface of the water are extraordinary and the young whale with its mother is a tender portrait. How do you get the eyes to do what they do? Life pours out of your creatures.\n\n**Gal\u00e1pagos Sea Lion**\n\n_Zalophus wollebaeki_\n\nFound in the Gal\u00e1pagos archipelago, this sea lion was once considered a subspecies of the California Sea Lion, but recent studies have unequivocally proved it to be its own species. In 1978 it was considered that the total population of Gal\u00e1pagos Sea Lions was about 26,400, but this had decreased to somewhere between 9,200 and 10,600 in 2001. This is a decline in numbers of 60\u201365 per cent, and on the strength of that, the species is now classified as Endangered.\n\nEl Ni\u00f1o events can have disastrous effects on the sea lion populations as they affect marine productivity and can destroy marine life. The Gal\u00e1pagos Sea Lion, which is dependent on this food, suffers drastically. It is estimated that in particularly strong events, reproduction can cease and 100 per cent of pups, 50 per cent of yearlings and vast numbers of adults may die. In the future it is uncertain whether El Ni\u00f1o will increase or decrease with climate warming. What is certain is that these events will continue and will continue to threaten the wildlife. Infectious diseases are also a concern as they can spread quickly through a population. The main concerns regarding illnesses are introduced species, such as dogs, which carry diseases that can easily be transmitted to sea lions. When times are hard and little food is available, young pups are at risk of becoming dinner for male sea lions. Infanticide is never the best way to keep population numbers up. Gal\u00e1pagos Sea Lions can also become victims of bycatch in fisheries, whilst plastic waste and other pollutants can entangle and endanger them as well as expose them to germs and bacteria. The dumping of sewage into the seas exacerbates these issues and the waters need to be cleaned of this filth. A conservation plan has to be worked out to help the sea lion population survive the continual threat to its existence. This is the perfect moment for us to perform our tricks for the Gal\u00e1pagos Sea Lion and help it out of its current predicament.\n\n_Ceri's Diary_ : It is easy to take creatures for granted and not think about the state of their populations. As a kid I remember sea lions appearing on telly performing tricks and they were resounding favourites in circuses and marine parks, as they were considered as amusing and talented animals. But we began to learn that perhaps this was not the best way to treat animals. Is there a decent reason why these attractions should still attract? I'm not sure there's much of a case to be made for them and personally I would prefer to see the animals in the wild.\n**Black Rhinoceros**\n\n_Diceros bicornis_\n\nJust over 96 per cent of the existing population of Black Rhinos occurs in four countries: Namibia, South Africa, Zimbabwe and Kenya. Recently, conservation has been good for Black Rhinos, but it remains to be seen whether numbers can rise to previous levels. It is worth remembering that one subspecies, the West African Black Rhinoceros, has already become extinct \u2013 which shows just how precarious a rhino's lot can be. The other three, the Eastern, Southwestern and South Central rhinos, need constant assistance to maintain their existence but they are doing better now than for a long time.\n\nOnce the most populous rhino of them all, its population may at one stage have stood as high as 850,000 individuals, but human encroachment, conversion of habitat for agricultural purposes and constant hunting saw numbers dwindle to 100,000 by 1960. Incessant poaching of the dual-horned Black Rhino accounted for 98 per cent of this population but numbers have started to increase and now there are nearly 5,000 Black Rhinos roaming across Africa.\n\nRhino horn has long been considered as a status symbol and an adornment of wealth and desired in many countries for ornamental use. In particular, there was a demand for carved dagger handles in Yemen, but this market has now largely been shut down. Unfortunately, there is still an international trade in rhino horn, especially in Asian countries where it is used in Chinese medicine to treat all manner of ailments including fevers, rheumatism, gout, headaches and snakebites. It is also believed to stop possession by bad spirits, but I would suggest the truly evil spirits are the ones spiriting the horns away from the beast to the marketplace.\n\nOne of the newest horn hotspots of the world is Vietnam. It transpires that some years ago it was reported that a politician had been cured of cancer by taking powdered rhino horn and this caused a stampede for the substance. The politician has never been identified nor his story verified, but tragically the demand continues. This rise in demand in Vietnam is alarming and an awareness campaign is necessary to teach people about rhinos and the need for their conservation. Perhaps education could change attitudes and reduce this burgeoning market.\n\nConservation in Africa suffers because there is much civil unrest and ongoing military action in various parts of the continent. This damages wildlife habitat and the creatures themselves as they get caught up in the consequences of war. While wars rage there is very little thought for conservation interests from governmental bodies and the political will to help wildlife is pretty much non-existent. Also, it is a certain fact that military personnel exchange rhino horn for guns and ammunition. Sadly, everyone knows the value of this precious commodity.\n\nInternational law enforcement needs to improve in order to halt the continual flow of rhino horn across the world and reduce the amount of horn that finds its way into the dark markets that sell it. Meanwhile, back in Africa, even though Black Rhino numbers are on the rise, protection and monitoring of the species must continually improve and policing needs to get stronger and tougher to deal with the latest upsurge in poaching. It is a relentless battle but one that can be won. Support for the beast is ever growing and the IUCN SSC Rhino African Specialist Group coordinates rhino conservation across Africa. Long may their work continue, to ensure a brighter future for the African rhinos.\n\nCeri's Diary:\n\n**Rhino Fact**\n\nI have never understood the ornamental desire for rhino horn, as contrary to popular belief it is a different material to elephant tusks. It is not ivory. But it is used to make decorative items similar to ivory. The rhino's horn is actually made of keratin and is similar in structure to horses' hooves and turtle beaks. So why is there no market for hooves or beaks \u2013 or indeed human toenails, which are made of the same stuff? By the way, I am not advocating creating a market, just curious as to why rhino horn is so in demand as a material for objects away from the medicinal market. Maybe it is nice to carve but there has to be a tie-up with the exotic nature of the animal and because it is a creature of a distant land. It is quite baffling.\n**Blue Whale**\n\n_Balaenoptera musculus_\n\nYou couldn't swing a cat for Blue Whales in our oceans up until the twentieth century and then it all changed. Whaling became bigger and better at what it does and the seas rapidly became emptier worlds.\n\nThe Blue Whale, which is found in most oceans, can weigh up to 22 tonnes and is the largest animal on Earth. The global population is estimated at between 10,000 and 25,000 individuals. Considering that records show that approximately 341,830 Blue Whales of the Antarctic population have been recorded caught in the twentieth century, the scale of the loss of Blue Whales must be enormous. It is estimated that we are left with 3\u201311 per cent of what the population was in 1911. Hence it is Endangered. The Blue Whale belatedly became a protected species in 1966 and since then numbers have slowly risen. But is not easy to come back from the apocalypse.\n\nWe often think of the seas as silent worlds, but nothing could be further from the truth. To give you an idea of how loud it is underwater, the Blue Whale's call has been registered at 188 decibels, which is louder than a jet engine, which is recorded at approximately 140 decibels. The oceans are noisy places. A whale's sounds can be heard for hundreds of miles and this 'whale song' is how they communicate with each other over great distances. In general, whales use sound to navigate their courses and use sonar to locate prey. Once they have found their food, they make loud sounds to confuse their prey and then attack them in the resulting mayhem. For whales and dolphins their ability to listen is like our ability to see. They are living in a blind world if they cannot hear properly and one wonders how they are affected by the sounds of our invasive world. Sea traffic, underwater exploration, military activities, sonar and other noise pollutants must interfere with their lives. Recent surveys would indicate that this is the case and the ocean worlds are dramatically affected by our audio interference. It is now believed that so much noise can physically harm whales and damage their hearing and their navigation. This can lead to whales becoming disorientated and beached on the shoreline, which more often than not, without outside help, leads to death.\n\nIf my neighbour were playing music too loud so that I couldn't live my life then I would be well within my rights to complain and eventually get a noise abatement authority involved to take the matter further if the interference with my world persisted. Unfortunately there are no marine noise regulations or accepted international standards regarding noise at sea and this would be an important issue to deal with. A quieter sea makes a safer sea for all within it.\n\nIn July 2016 a Californian Court of Appeal ruled that the US Navy was in violation of the US Marine Mammals Protection Act by using low-frequency sonar during training. The US Navy is using this method across much of the world's oceans to detect quiet submarines. What this ruling means in the greater scheme of things is yet to be understood but it does show that some authorities are recognising that there is an issue that needs to be addressed.\n\n_Ceri's Diary_ : I'm not sure you will ever find a Blue Whale acting in the way that Ralph has depicted this cheery whale but they do occasionally breach, although it is rare. (I am certain Ralph meant to write breaching not beaching but just got carried away in the moment). Breaching means the whale leaps out of the water into the air. Normally, smaller cetaceans such as dolphins, porpoises and lesser whales do this, but no doubt Blue Whales can do it too and Ralph has caught one of these unusual moments on paper. Who are we not to believe him?\n**Golden Bamboo Lemur**\n\n_Hapalemur aureus_\n\nIn 1983, the Golden Bamboo Lemur was discovered in the rainforests of southeastern Madagascar. Since then its state of endangerment has seesawed one way or another. From 1990 to 1996 it was firstly considered as Endangered and then became Critically Endangered until it was downgraded to Endangered again in 2008. Unfortunately it has since been upgraded to Critically Endangered once more, as the total number of mature individuals in the wild is now less than 250.\n\nThe Golden Bamboo Lemur lives among forests and marshes that contain bamboo and reeds. Their diet consists mainly of giant bamboo shoots, which surprisingly contain high levels of cyanide, but their digestive systems are able to process this without harm to the lemur. Quite how this is possible is not clear, although pandas can also digest the cyanide found within giant bamboo shoots. But humans can't do this, so don't go trying to follow the diet of lemurs and pandas. We need to process and cook bamboo properly before it is harmless to us.\n\nSlash-and-burn agriculture has destroyed much of the lemur's habitat and also the taking of bamboo to build houses and for other local uses has devastated the lemur's surroundings and food supply. Poaching is also known to exist and there is a thought that lemurs are being taken for the pet trade.\n\nLaw enforcement needs to be more watchful over this protected species, as even in the national parks illegal activities are carried out and threaten the future of the Golden Bamboo Lemur. More surveys are needed to truly understand the range of the creature and its lifestyle and there is talk of a captive breeding programme, as time could soon be up for this cyanide-digesting critter.\n\n_Ceri's Diary_ : There is a ghostly impression left by many of the critters captured in Ralph's pictures. They are halfway between this world and the next, as they phase in and out of the splats, much like their existence in the wild, rocking in and out of focus as their hopes for survival diminish or increase\n**Long- nosed Gwylim**\n\n_Nares poetica_\n\nOne of the greatest achievements so far for the Muckists has been the success of their campaign to save the Long-Nosed Gwylim from the brink of extinction and return a small band of them to the Dylan Thomas mountain range in the western region of the Mid Lands in an area known as Poetry's Corner. There the Gwylims recite poetry all day long in honour of their own salvation. In these lands, poems are not dead and the words of Dylan Thomas, Walt Whitman, T. S. Eliot, e e cummings, Charles Bukowski, Allen Ginsberg and Saul Williams boom out around the lands thanks to the vocal mastery of the Gwylims.\n\nThe Gwylims are responsible for keeping poetry's rhyme and meter alive across the archipelago and the Chief Gwylim teaches a course in sound patterns at the MUCCK. Its ambition is to make sure that poetry is not lost to the world and it teaches as many critters as possible the virtues of the spoken word, grunt, caterwaul, squeak or peep. Have you ever heard an Aye-aye perform slam poetry? It's a marvel to behold \u2013 and it learned this skill at the feet, or should I say snout, of the Chief Gwylim.\n\nAt the moment the Gwylims are busily working on the first ever critter poetry festival, called Get Rhyming, and have invited all creatures and other inhabitants of Toadstool Island to write their own poems about extinction and nextinction.\n\n_AN INVITE TO WRITE_\n\n_We invite you all to write_\n\n_A poem about our plight_\n\n_And we'll show them to the people of this earth_\n\n_An angry verse or two_\n\n_Could break the ice for you_\n\n_And persuade these very people of our worth_\n\n_These are desperate times_\n\n_And we suggest that rhymes_\n\n_Can seriously place a marker in the sand_\n\n_And the more that people hear it_\n\n_Then the more they will believe it_\n\n_And we will enlarge our conservation band_\n\n_All entries must be received before the 12th of Never and should be sent to:_\n\n_The Chief Gwylim at MUCCK,_\n\n_The Mid Lands, Toadstool Island, Toadstool Archipelago._\n\n**Black Spider Monkey**\n\n_Ateles paniscus_\n\nThe Black Spider Monkey, sometimes known as the Red-faced Black Spider Monkey, lives in the Amazon forests of Brazil, French Guiana, Guyana and Suriname. The population has declined by approximately 30 per cent over the last 45 years, making it a Vulnerable species. But the writing is on the wall for this monkey.\n\nTheir position in the ecosystem is important as they swallow fruits and seeds, which they then defecate out of their systems, thus making them key dispersers of the seeds of roughly 140 different species throughout their range. They're like a travelling garden centre, planting as they go.\n\nThe Black Spider Monkey is threatened by habitat loss due to logging and it needs a constant variety of fruiting trees to keep its diet varied. The fact that the female monkey only gives birth to one offspring every three or four years doesn't help with the population numbers either. Even though it lives in many protected areas, hunting is a constant threat across its range as the monkey is a large species and provides a lot of meat.\n\nMore protection is needed to save the habitat, otherwise the monkey population is going to fall into steeper decline \u2013 that would be shameful. If we don't take care of this critter now, we could end up more red-faced than the monkey.\n\n**Suicide Palm**\n\n_Tahina spectabilis_\n\nXavier Metz is the manager of a cashew plantation, which is located on a peninsula in northwest Madagascar near a village called Antanamarina. One day in 2006 he was out walking with his family when he noticed a large palm tree he didn't recognise. He placed photos of it online and within 24 hours the Royal Botanic Gardens at Kew had seen the pictures and had become involved, setting out to unravel the story of the mysterious palm. It was found to be a new species and with only 30 mature trees in existence in the vicinity of where the first one was discovered, it was deemed to be Critically Endangered.\n\nWith such a small distribution, fire is considered to be the main risk as well as the grazing of livestock, which may damage the habitat and threaten the regeneration of the Suicide Palm. There is also a threat from the illegal collection of seeds for horticultural purposes.\n\nWhy is it called the Suicide Palm? Because this palm is hapaxanthic, which means that it flowers just once in its life and then dies. In effect, the effort of flowering and releasing its seeds is just too much for the palm to continue living.\n\n**Update**\n\nRecently, the scientists from Kew went over to see how the palm was doing and were delighted to find that numbers were on the increase and even that a new seedling site had developed 1.5 kilometres away from the original discovery. In fact, there are now 740 individual plants in the area. Having now returned from Madagascar, the team from Kew are determining the best conservation plan to preserve the species. The trip has painted a much brighter future for the species than expected and, even with the palm's suicidal tendencies, there is hope that this palm's future has been read and things are looking more secure than previously anticipated.\n\n_Ceri_ : What I really love is the way you take these creatures to their absolute abstracted form.\n\n_Ralph_ : No, it's absolute abstracted blots. Technically you abstract the blots, subtract them, detract them and abstract them again. That is the mathematical artistic equation.\n\n_Ceri_ : I have no idea what you just said. But then you're the artist. And I see you have made an artistic decision to paint the Suicide Palm alongside the Black Spider Monkey. How very obtuse of you. They're not even from the same continent.\n\n_Ralph_ : It could be on holiday or just visiting.\n**Addax or White Antelope**\n\n_Addax nasomaculatus_\n\nThe Addax is also known as the White Antelope or the Screwhorn Antelope. It was once found across all types of Saharan terrain but the nomadic Addax population now stands at less than 100 individuals and the majority of these are found in the Termit Massif and Tin Toumma desert region of Niger. In 2012 the Niger government declared this whole area to be a national nature reserve and at nearly 100,000 square kilometres it is the largest single protected area in Africa bar none.\n\nThe threats to the Addax have been various and include disturbance from oil exploration, drought and pastoralism (which is a way of life dependent on the raising of livestock) and it has been spreading into the desert regions and threatening the Addax. But the singular most deadly threat has been the merciless hunting of the Addax throughout the twentieth century and into the twenty-first, for its meat and its hide.\n\nIt is to be hoped that because large swathes of land have become protected the fortunes for this animal could change. There are plenty of White Antelopes in captive breeding and about 5,000 that are held privately in the USA and the Middle East. Some antelopes have been released into enclosures in Tunisia and Morocco and there are plans for further reintroductions in the near future. For those few animals left in the wild it's important to provide incentives for local people to protect them and other wildlife too, otherwise that small number of Addax out there is going to recede and disappear like a mirage into the distance of the setting desert sun.\n\n_Ralph emails_ :\n\nYou should read this from infamous Doodaaist, Gavin Twinge. He's on our wavelength.\n\n_You are a beast. I am a beast. We are all beasts. Animals are beasts. All beasts have spirit. No beast has a soul. Only Man has a soul, because he said so. The only difference between Man, and the other beasts, we tell ourselves, is that human beasts are blessed with the power of reason, the power to THINK._\n\n_First we reasoned, and thought, as we emerged and rose out of, and then above, the scum of primeval slime, that we would use the scum, and even the slime, as a weapon of distinction. As we stood up and looked about us like hunted prey, we reasoned that the scum would draw the line, between us, and the others, who lived beneath the scum and the slime._\n\n_We reasoned that we are the chosen ones, as we emerged to civilise, emerged to change the world, as though it needed changing, emerged to rationalise, institutionalise, sterilise, and most importantly, emerged to colonise._\n\n_We wanted the best of both worlds. Our beastly instincts were still intact, so we evicted the others to suit ourselves. At that moment HOMO HABILIS was born, and we explored the new world. We became proud and evolved into HOMO ERECTUS. Then we domesticated our natural processes, and called ourselves HOMO SAPIENS. We were no longer, culturally, a part of the kingdom of beasts. The beasts, the others, were a part of our kingdom, and were there merely for our convenience, a lower order, with no feelings and no rights._\n\n_We invented a God, many gods, and many devils, a heaven and a hell on earth._\n\n_Our driving force is guilt._\n\n_Our conscience is self-interest in the guise of compassion. Our only certainty, and our unique discovery, is that we must all die._\n\n_So we invent futures for ourselves, to soften the brutal knowledge. But we remain beasts because we fight, and kill, for territory, yet we are still beneath the animals, because we do not always kill merely to survive. We invented a moral code, in a vain attempt to disguise our naked appetites, and our aggressions. We have not succeeded, but we are perhaps blessed with one other facet of reason, the reason to hope that things may get better, and that a future is a reasonable expectation..._\n\n_My mind is made up. We are the brutes who render the animals incapable of being themselves. We repress them in the name of the God we invoke, to bless us, and slaughter them, in the name of our own stupidity. We are the disgrace of the Animal Kingdom._\n\n_Gavin Twinge._\n**African Wild Dog**\n\n_Lycaon pictus_\n\nThe Endangered African Wild Dog is estimated to have a population of 6,600 mature individuals spread across 39 individual subpopulations. It has been wiped out from most of its former range across much of Africa and can now be found mainly in southern Africa and the southern part of East Africa.\n\nMore and more people have settled in and around reserve areas that were once Wild Dog territories and thus their habitat has become more and more fragmented. Packs of Wild Dogs need a lot of space and they like to work the edges of their territory as they hunt: this means they can venture outside their reserves into areas where now there are many more human settlements than ever before. This leads to increasing numbers of Wild Dog and human conflicts and encounters with human activities, resulting in death or the transmission of infectious diseases from domestic animals. Fencing can do a job but there is still the chance of Wild Dogs getting through them and it is not the ultimate answer to the problem. The subpopulations of Wild Dogs are small groups often numbering between 50 and 100 individuals and this leaves them open to extinction whether by human hand or Lion mouth due to their low population densities.\n\nMuch must to be done to improve the African Wild Dog's chances of survival. One of the most important quandaries to solve is how to find a way to develop the relationship between Wild Dog and human and effectively reduce the conflict between the two. Surveys have to be carried out across the Wild Dog's range to determine its distribution and status and land needs to be managed to ascertain how to expand the decreasing population.\n\n_Ralph emails_ :\n\nHERE be African Wild dogs!!!\n\n**Amazonian Manatee**\n\n_Trichechus inunguis_\n\n**American Manatee or West Indian Manatee**\n\n_Trichechus manatus_\n\n**African Manatee**\n\n_Trichechus senegalensis_\n\nHerbivorous manatees are strange beasts and looking at them from different angles I am reminded of different creatures, as if they have been made up from several other species such as seal, whale or hippo. They have an allure about them and a questioning look upon their faces. Many sailors believed that these animals with their long tails could be mermaids.\n\nThe three species of manatee are all categorised as Vulnerable. The Amazonian and African Manatees are thus considered because they are expected to lose 30 per cent of their population within the next three generations, and the American\/West Indian Manatee because numbers are below 10,000 individuals and expected to decrease by at least 10 per cent over the next three generations. The writing is on the wall, but it is to be hoped that enough can be done to stop these animals being upgraded to Endangered or Critically Endangered.\n\nThe main threats to manatees are hunting, loss of habitat and encounters with humans and the man-made world. Because the manatee is a slow mover through water, ship strikes frequently occur and these leave manatees badly maimed or even dead. Another major concern is the animal becoming entangled in fishing nets, which again can lead to death.\n\nIn Africa the manatee is still being hunted for its meat even though it is now illegal to do this. In the Ivory Coast, Togo and Nigeria, manatee skin and bones are used in rituals and the preparation of traditional medicines. South America faces similar problems with illegal hunting for meat, which is mainly carried out with harpoons. The American\n\nManatee also has issues with hunting in various parts of its range and is prone to suffering from the effects of human activities, such as pollution, fishing and boat accidents. There has been habitat loss as people have spread along the Florida coast over the last 50 years, which has removed enormous chunks of coastal wetland habitat.\n\nManatees have built up a huge following of fans and an ecotourism industry has built up around them. At some of their wintering sites they are visited by thousands of people who come to see the manatees and to swim with them. It has been discovered that manatees have started changing their behavioural patterns after these close encounters of the human kind. This is probably not a good thing and shows that ecotourism has a responsibility to understand when it is moving too far into an animal's world. I have been on whale-watching boats and find it wrong when the person in charge of the boat decides to move ever closer to a wild animal. As far as I'm concerned it is all about keeping the right distance between the wild creatures and us.\n\nAll manatees are protected species but in some parts of the world this means nothing. Education programmes and working with local people to help them understand the creatures and their importance in the world is imperative. In addition, the extremely poor need to be provided with alternative food sources so that they no longer need to rely on manatee meat. Without local community support, the manatees may not survive. Research needs to continue to learn about the three species of manatee, to improve their fortunes and to discover the best way to keep these strange, alluring creatures as the sirens of the seas.\n\n**Grey Nurse Shark**\n\n_Carcharias taurus_\n\nLet's be honest, sharks get a really bad press and we consider them as a permanent threat to our aquatic behaviour, whether that be diving or swimming in the sea. But the truth is most sharks would prefer to leave us alone and the Grey Nurse Shark is no different. It is quite an easy-going creature, which swims low over the sea floor and prefers to munch on smaller sharks, fish, crustaceans, rays and squid as opposed to a morsel of human flesh.\n\nThe Grey Nurse Shark is found across most subtropical and warmer oceans, except for the Eastern Pacific waters. In Australia it comprises two populations, the west coast population, which is deemed Vulnerable and the east coast population, which is considered Critically Endangered.\n\nThe shark is prized as food on the Japanese market and has also been fished extensively over the years for oil and for its fins, which are used for soup. One of the main threats to the Grey Nurse Shark is getting caught accidentally by line fishing and becoming bycatch because of bottom-set gillnets and trawl nets. It also becomes enmeshed within beach nets set up to protect swimmers from sharks. Smaller meshes on nets may be a way forward to help this protected species and it is hoped that continuing action to preserve the shark will meet with positive results. It's time to nurse the Grey Nurse Shark back to health.\n\n**Osprey Mountain**\n\nWhen the universal Big Blot occurred, the first-born was Osprey Mountain. She became the first witness to the birth of all other life and watched as evolution developed through its many guises. Throughout time the mountain has nurtured all beings and provided them with love and protection, especially during the precarious infancy of existence and she became known as the Mothering Mountain. Today she still casts calmness over all who find themselves within her sheltering peak and her rockiness radiates warmth, giving a comforting welcome for travellers to her stony heart. She is also the mother of the Ooshut Doorbang, the great god and protector of the nextinct and she is determined that between them they will prolong life's adventure on this earth and will not allow human beings to decimate the future for all.\n\nOsprey Mountain is a sacred place for bird, boid or critter and it is every creature's duty to make a pilgrimage here. Ancient island folklore states that all beings must make their way at least once to this spiritual space; for here they will find succour and love exuding from the mountain. This fills the visitors with a renewed strength, belief and vigour for survival in their fight against mankind's damaging progress and destructive ways. It is also a fact that every creature that has journeyed up the narrow pathway, reached the peak itself and sat within the osprey's beak has never become extinct. This has been a physical problem for some of the larger creatures, but the Needless Smut, the beloved mayor of Toadstool Island, has commissioned the building of a normal lift and a water tank lift up the side of the mountain. These are both made from natural resources, which hydraulically raise large land and sea dwellers to the summit, giving them the accessibility needed for their potential redemption. Good old Smutty, does it again.\n\nEvery year, all the creatures gather and take part in the Procession of the Beasts, which travels around the island and ends up at Osprey Mountain, where each species sings an ode to life. This is a cathartic and uplifting event for all that take part and provides a sense of unity for the inhabitants of Toadstool Island.\n\nRalph took this photo when we first came across the mountain and I think he caught its best side. The mountain told us she was happy for us to publish the picture, and who are we to disagree?\n**Garden Bumblebee**\n\n_Bombus hortorum_\n\nI had no idea how many different types of bumblebees there are in the world and I was staggered to find that there are 275 different species that exist out there.\n\nIn the UK we are home to 25 species of bumblebees and have lost two other species since the start of the twentieth century, the Cullem's Bumblebee and the Short-haired Bumblebee. These losses serve as a stark reminder to us all about the vulnerability of the other species. The main problem that affects all our bumblebees is the loss of wild flowers across the nation. How has this happened? Well, more and more land has been converted for greater food production and coupled with a change in agricultural practices this has resulted in our landscape being altered beyond recognition. It is estimated that we have lost 97 per cent of our species-rich grasslands since the 1930s. Simply put, the once abundant wild flowers are just not out there as they once were. Abundance is not an oft-used word in terms of wildlife in the UK any more unless it is coupled with the word loss because we don't have a country teeming with wildlife these days. Our treatment of our wild spaces has ensured a countryside that has become bereft of flora and fauna and we are losing our local wildlife sites at an alarming rate and the look and feel of our scenery is changing and disappearing from sight. Do we really need to lose so much of our nature?\n\nIronically, bumblebees are extremely useful to agriculture as they are excellent pollinators and can help many commercial crops such as apples, peas and tomatoes. They also play a major part in our biodiversity as many wild plants depend on them for pollination. Without the presence of bumblebees our natural world could become a whole lot more difficult to maintain.\n\nBees and other pollinators are responsible for fertilising three-quarters of this planet's crops, and with some crops, come certain problems that need to be addressed. Neonicotinoid pesticides have been proven to be harmful to pollinators and since 2013 they have been banned by the EU, although there will be a review of this ban in 2017. The United States is still studying evidence and considering whether to impose a similar ban on the use of neonicotinoids. New research by the University of Stirling in Scotland has revealed that bees' learning abilities and their memory are reduced by exposure to these pesticides. Bees collect pollen by brushing it from flowers, but some crop flowers, such as tomatoes and potatoes, need to be shaken firmly to release the pollen. Bees exposed to neonicotinoids are unable to learn this ability and this limits the amount of pollen they collect and creates less successful colonies of pollinators.\n\nOrganisations like the Bumblebee Conservation Trust work to raise awareness of the problems faced by bumblebees and also work with sympathetic farmers on how to farm in a more bee-friendly manner. There are things we can all do to help bumblebees and the most obvious is to choose the sorts of plants and flowers they like best, if we have gardens. Between us we can change the way our landscape looks and make the UK more of a haven for our bumblebees. Right, off to the garden centre, there's some planting to do this weekend and then we can arrest the plight of the Garden Bumblebee and its relatives.\n\n_Ralph emails_ :\n\nHere BEE HERE!>>>>caught in the evening loight! Even the flowers are glum about the bee situation.\n\n**Polar Bear**\n\n_Ursus maritimus_\n\nThere are 19 subpopulations of Polar Bears living across the Arctic, some of which, depending on their location, can spend all year living and hunting seals on the sea ice. But many others have to leave the ice when it melts during the summer and head ashore. Winters are spent on the ice, eating and building up fat reserves to see them through the summer months when they have to retreat onto the mainland where there is much less food. They have to wait for the sea ice to refreeze before they can return to eating. But there is a problem and that is global warming. The ice now melts earlier and refreezes later than it used to, leaving the bears on land for much longer than before. This means that bears may not have fed sufficiently to store enough fat to get through the season. It is estimated that bears are staying ashore one day longer each year, which is not a sustainable situation. There is also a thought that warmer weather could bring unfamiliar diseases and parasites to the Arctic and we have no idea whether these might pose a threat to the bears.\n\nOther threats include increasing oil exploration and development, which can result in oil spills and pollutants that harm the bears, or which could cover their prey in oil resulting in bears ingesting hazardous substances. Hunting used to be an issue, but since 1973 there has been a worldwide ban, which has seen numbers of bears rise to an estimated 20,000\u201325,000. Norway and Russia don't allow subsistence hunting but Canada, the US and Greenland do. This provides meat and clothing for local communities and brings in income from the sale of hides or other objects made from the bear \u2013 with a strict quota on the number of animals killed. Sport hunting is also indulged and brings in a substantial amount of money, but any animal killed counts towards the quota, which cannot be exceeded. The annual harvest is 700\u2013800 animals and this is believed to be sustainable. There is very little illegal killing except in Russia where it is estimated that annually as many as 100\u2013200 bears are killed. There are also deaths due to conflict with humans. The Polar Bear is increasing in tourist value and this will bring in much-needed revenue to remote settlements. Perhaps one day we won't need to shoot bears at all.\n\nThe Polar Bear is a giant of the animal kingdom (it can stand on its hind legs to a height of 3 metres) and is considered as Vulnerable, but things look bleaker for the Polar Bear than for some Critically Endangered creatures because we can foresee the possible future for this animal if the world continues warming up as it is. Is this why we are so fascinated by Polar Bears? Is it the creature that makes us truly aware of what's going on in the environment? If it goes extinct will we accept that we have truly got a problem on our hands?\n\nA Circumpolar Action Plan was signed in 2015 by the five countries that are home to Polar Bears and seeks to continue to preserve and protect the populations of bears found in the Arctic. It remains to be seen just how helpful our climate is with this plan. Nothing is certain, but we may well have the answers to this particular creature's fortunes sooner rather than later \u2013 and with that we may know where we, the human race, ultimately stand. Too dramatic? I don't think so.\n\n_Ceri_ : What do you call a Polar Bear with haemorrhoids?\n\n_Ralph_ : I don't know.\n\n_Ceri_ : A Polaroid.\n\n_Ralph_ : That's quite snappy of you.\n**Articulated Bumlice**\n\n_Posterior prurientes_\n\nThe Curator has decided to take us out to a part of the island we may never have discovered in our solo wanderings. 'I will take you to see a colony of Greek Red Damsels that we have been working with. The species is in a parlous state and we are not sure if we can prevent its extinction, but we are giving it a damn good go. Just watch out for a nasty little critter that also lives here, the Articulated Boom-lee-chay. It's a creature that luckily only inhabits this small portion of the island, but it can cause extreme problems.' I interrupt and ask, 'How do you spell Boom-lee-chay?' The Curator replies, 'B-u-m-l-i-c-e.' 'What? That's not how it sounds. That spells Bumlice.' 'It is what it is. You're in a foreign land, my friend, a foreign land,' says the Curator. 'The Articulated Boom-lee-chay is leech-like and is an invasive little beast and worth avoiding as it can articulate in any direction and get into any nook or cranny. So please tuck socks into boots and shirts into trousers. You don't want an encounter with one of these.'\n\nAs all travellers to exotic places know, alien environments can present unexpected and unwanted bodily visitors such as mosquitoes, venomous spiders, leeches or airborne viruses and Toadstool Island proves to be no exception. The Cap'n and I nervously shuffle behind the Curator, when\n\nall of a sudden he shrieks, 'Help me! One's got in my trousers! I don't know how that's possible.' I notice a small hole in the seat of his pants and something wriggling inside. The Curator drops his trousers and we see the Bumlice in all its hideousness. 'There's only one solution,' the Curator cries. 'Get my quorn sausages from my rucksack and lure him away from me. Boom-lee-chays can't resist them. Please hurry.' Ralph pipes up, 'Hold on, I'm just drawing this scenario for posteriority. It's important to document moments such as these.'\n\nI find the quorn sausages and gently wave them in front of the horrific-looking critter. The Bumlice looks up and tries to snatch the sausages with its snapping mouth and drools with delight. I can see it ready to leap towards me and in the nick of time I throw the quorn sausages far away from us. The Articulated Bumlice tears after the airborne quorn and as they land he munches on them instead of the Curator's backside. Who would have thought quorn could be so popular or so useful. I then patch up the Curator's trousers with my essential roll of gaffer tape \u2013 second only to toilet paper as king of the rolls \u2013 and, with everything back to normal, we head off in pursuit of the colony of Greek Red Damsels.\n\n**Greek Red Damsel**\n\n_Pyrrhosoma elisabethae_\n\nThe Greek Red Damsel is closely related to the European Large Red Damselfly and is endemic to the southern Balkans. Here it is known from only ten locations in Greece and southern Albania and has already become extinct in some of these places. It is considered Critically Endangered as it is expected to lose up to 50 per cent of its population within the next 10 years. Little to nothing is really known about its needs or habitat but it is believed that it lives where streams, brooks and even rivers have a plentiful supply of vegetation.\n\nThis kind of habitat is poorly managed in Greece and Albania and it is feared that increasingly dry summers due to climate change will lead to dry brooks and streams, thus affecting the damsel populations. Pollution of water is also an issue, as is the over-management and clearance of vegetation within the waters. It is imperative to visit the known locations to establish whether the species still exists \u2013 only then can a conservation plan be considered.\n\nOnce again, I realise that such diversity of wildlife is facing critical times. I have always loved seeing the way damselflies and dragonflies scoot around, a whizzing elongated blur of colour and motion. I often just sit by a riverbank and watch them go about their business. I would hate to lose that vision.\n\n_Ralph emails_ :\n\nDear Twaddle Face, here is a fine beautiful mess!!!\n\nRingRALPH\n\n_Ceri replies_ :\n\nWho you calling Twaddle Face?\n\n_Ralph replies_ :\n\nTWADDLE FACE!? Not you!!!!>>>>>> \u2013 My grandson Toby's Friendly DOGPANTS here>>>>\n\nPay attention! \u2013 and if you can't do that \u2013 PAY ME!!!!\n\n_Ceri replies_ :\n\nHow did you see a dog in those scrumpled trousers? Incredible.\n\n_Ralph replies_ :\n\nToby sculpted the pants by tearing them off in a sculptor way. They are naturally sculpted by him and then subtly drawn by me. It must be in the jeans!!!\n\n**Lion**\n\n_Panthera leo_\n\nThe Lion once roamed far and wide from Northern Africa to Southwest Asia and was seen from Europe in the west to India in the east. But it has disappeared from much of these lands and the population is continually decreasing. There is only one species of lion and there are African Lions and Asiatic Lions. The African Lion is Vulnerable but the West African subpopulation is considered as Critically Endangered. The Asiatic Lion is categorised as Endangered with a single population of 500 animals holding on in the Indian state of Gujarat. Since 1993, the African Lion population has fallen by an estimated 43 per cent, with numbers now possibly as low as 20,000 in the wild. Compared to the number of Lions in the 1940s, which was believed to be about 450,000, the Lion finds itself in a precarious pickle. There have been certain successful subpopulations, with increases of up to 12 per cent in Botswana, Namibia, South Africa, Zimbabwe and India and this has kept the Lion as a Vulnerable species, but across the rest of its range it would be considered as Endangered. Statistics don't always tell the full story.\n\nThere are several reasons for the Lion's decline including habitat loss, prey base depletion and the killing of Lions in defence of livestock and human life. This conflict between man and beast is believed to be the main threat to Lions outside their protected areas and more needs to be done to protect livestock and to find a way to compensate owners for animal losses. There is also an illegal trade in Lion bone and body parts for traditional medicine, with an increasing demand from China, Laos and Vietnam, although there is no historical use of Lion parts in Asian medicines.\n\nTrophy hunting, handled correctly, is believed to benefit conservation by providing much-needed finance for Lions and local communities. But there are some serious concerns that this hunting can be mismanaged with more Lions being taken than the set accepted limit. Some will call me a lily-livered tree-hugging leftie but why do we have to kill creatures at all, least of all in the name of sport? Couldn't those that can afford to shoot a Lion just put the money into conservation and be happy with shooting a photograph? I guess not. Trophy hunting needs a prize and the appropriation of one Lion's life is considered an acceptable price to pay to help other Lions. In 2015, an American dentist on a hunting trip in Zimbabwe provoked a global outcry when he legally shot a Lion called Cecil, with his bow and arrow. For a brief moment the world was horrified that such a thing could have happened. It seemed that this might be an important moment in the dialogue about how we treat our wildlife, but soon we forgot and trophy hunting continued once more. Modern society's attention span is so short and thanks to rolling news feeds and continually updating social media, what was important yesterday is no longer of interest or value today.\n\nIt is our attitude to wildlife that needs to change as there are healthier ways to engage with big cats instead of killing them and putting their heads on a wall. Wildlife tourism brings a lot of money to the conservation table and we must ensure that more Lions end up being born free, living free and dying free without fear of persecution from humanity.\n\n_Ceri's Diary_ : I remember seeing _Born Free_ as a kid and was moved by my first cinematic experience of witnessing an emotional connection between people and animals. It was all about an orphaned Lion cub called Elsa, which was raised by Joy and George Adamson and then released into the Kenyan landscape. I recall watching this story unfold and wanting to go and work with animals in Africa and to help them get through tough times. The film inspired me and I am certain that I joined the WWF that very week. I wanted to stand up for wildlife as I began to understand that humans and animals had a precarious relationship.\n\nThe actors who played Joy and George Adamson were the husband and wife team of Bill Travers and Virginia McKenna and after making the film they became immersed in animal welfare and conservation. In 1984, they set up the Born Free Foundation, which to this day seeks to protect threatened animals and to halt animal suffering.\n\n**Hula Painted Frog**\n\n_Latonia nigriventer_\n\nThis little feller is endemic to the Hula marshes in Israel and actually doesn't have too much to be pleased about because he is considered to be Critically Endangered. This frog was believed to have become extinct in the 1950s when the Hula marshes were drained in an attempt to dispel malaria and to change the habitat for agricultural purposes. After drainage, only 5 per cent of the original marshland remained and this was turned into the Hula Nature Reserve in 1964. In 1996, the species was finally declared as Extinct in the Wild and that was that. It was officially no more, although scientists in Israel kept it in their files as Critically Endangered in the vain hope that just maybe everyone was wrong. Then, amazingly, the frog was rediscovered in 2011 on the reserve. How many are out there no one knows but it just goes to show that a little blind faith can be a marvellous thing. Keep looking and you never know what you may find.\n\n**Update**\n\nAnd as if by magic the Hula Painted Frog is not so rare after all. It transpires that just a couple of months ago, researchers found more than 150, yes that's one hundred and fifty, of these frogs hanging out in the reserve. Apparently, they had been looking in the wrong place all the time as it turns out the frogs love being in the water and not the land and only come out at night. Mystery solved. Now what it will become classified as is anyone's guess. Maybe it will be taken off the Red List completely. What a wonderful story that would be and it would explain just why Ralph's frog looks so happy. He's had the last laugh on all of us. What a stupendous comeback.\n\n_Ralph emails_ :\n\nI have just done the HULA Painted FROG \u2013 and I remember where I saw the Frog. I was looking down onto the HULA Valley from the GOLAN Heights many years ago.\n\n_Ceri replies_ :\n\nI think this is a case of a Hula Overpainted Frog as I don't think they are this brilliant orange. But who am I to complain if it gets people to look at the creature and worry about it?\n\n_Ralph replies_ :\n\nIndeed. You're just sooo PICKY!!!!\n**Indri**\n\n_Indri indri_\n\nThe Indri is the largest lemur on the island of Madagascar and lives within areas of the rainforests from Anjanaharibe-Sud and Antohaka Lava, near Andapa in the north, down to the region of Anosibe An-ala in the south. Deforestation has threatened much of its habitat, plus there is hunting pressure for its skin and meat. This has led to a predicted population reduction of up to 80 per cent over the next 36 years, hence it is now listed as Critically Endangered. Hunting is a recent phenomenon. It was often felt that the Indri was protected by traditional taboos, which are known locally as _fadys_ , but these have been broken for several reasons including the immigration of different ethnicities as well as locals finding a way round the forbidden killing of the Indri as the meat is highly valued. The present-day levels of hunting are unsustainable and need to be halted. An educational programme has been suggested but so far has not been realised. Time is of the essence, otherwise there will soon be no Indree in a tri to si.\n\n_Indri indri_ is a Latin name I can remember. Short, simple, to the point and memorable. I wonder why these Latin names are as they are. And why is this creature named twice? There must be a scientific explanation and I need to know why. Give me a moment... I am leafing through my animal tomes. I shall have my answer. And indeed, now I have discovered why this happens. The reason for this is simple. _Indri indri_ is a tautonym.\n\n**Word of the Day**\n\n**Tautonym** \u2013 A taxonomic name where the genus and species name are the same \u2013 e.g. _Gorilla gorilla_ , _Rattus rattus_ and _Indri indri_. By being named thus it means that the species is the type of the genus. Mystery solved, although I need to think about it and digest this fact. I have also discovered that tautonyms are fine for animals but forbidden for plants. Science, it gets me every time.\n\nBinomial nomenclature is the system used to name species. This name consists of two parts, the first being the genus identifier and the second identifying the species within that genus. This name is known as the taxonomic name, or scientific name, or binomial name, or Latin name. In the case of _Indri indri_ , the genus is _Indri_ and the species within is the same, meaning that this creature is worthy of the football chant, 'There's only one _Indri indri_ , one _Indri indri_...' I'm sure the Indri would be happy with this, as his own plaintive and distinctive cry, which fills his Madagascan rainforest home, would not be out of place on football ground terraces when your side has just gone one down in the final minute of an important game.\n\n_Ralph emails_ :\n\nINDRI is here now and is the cutest critter I ever drawed! It looks so \u2013 unreal! Why is it here!? The leaf is a mess \u2013 I must add more interesting muck and bother to make it happen \u2013 perhaps teeth and a handbag!!!?? and did you see that programme on MINK, LYNX & other PELTS killed for Luxury Ladies \u2013 even the way they are kept in restricted cages \u2013 DISGUSTUDIOUS!!!\n\nCERRIBUL!!!!\n\n_Ceri's Diary_ : Ralph is right, this little fella is cute and yet still has a Ralph-induced crazed and boggle-eyed thousand-yard stare shining through. As he munches his way through the greenery of his lunchtime foliage, I feel the urge to scoop him right off the page and place him right beside me and get to know him more. But I fear this Indri would run riot through the house and would be more than anyone could cope with. This Indri is in a tree for a very good reason. It's where he belongs and where we have to try and keep him.\n**Delhi Sands Flower-loving Fly**\n\n_Rhaphiomidas terminatus abdominalis_\n\nIt may sound like a creation from the psychedelic era of the 1960s or a Las Vegas hotel but this is a real creature and it is in serious bother. It is endemic to a small area of dunes in southern California, which once measured more than 40 square kilometres but is now reduced to a handful of hectares. The rest of the land has been built upon and forms the foundation of several towns.\n\nIn 1993 the fly was added to the American Endangered Species List, but this has been a prickly issue ever since. Firstly, it is the only fly ever to have been put on the list and secondly many have cited the fly as a dirty disease-carrying critter that shouldn't be saved and should be allowed to die off. Whether this is because there are plans afoot to build on the last remaining land is a moot point as research suggests that the fly isn't as filthy as people suggest. Is it a case of development over habitat and species? Where have we heard this before? Just about everywhere.\n\nProtecting the fly and its last remaining wild habitat protects other species of the dunes such as Western Meadowlark, Burrowing Owl and the Los Angeles Pocket Mouse, but even with a protected species in the area development still continues. Only 2\u20133 per cent of the original habitat remains thanks to ongoing urban development, agricultural land conversion and mining. The dwindling natural space is enclosing the fly and its fellow compadres and soon we will find the vanishing point and all will be gone except for kids, cars, barbecues and houses. I'm not sure this is a fight the fly can win and flight looks impossible. Searches are being carried out with the aim of relocating the flies to another suitable habitat \u2013 but would it be totally ridiculous to suggest it might be easier to build elsewhere instead? Just a thought and I'm sure my suggestion would not be appreciated by the developers; after all we're talking about some good old-fashioned prime real estate and the time is ripe to build, build, build. The mantra of the modern world. And guess what, you get a free fly swatter with every purchase.\n\n_Ralph_ : Why am I doing flies? Horrible things. Dirty, dirty, dirty. Isn't it good they're disappearing?\n\n_Ceri_ : Everything has its place and wait until you see this one. And what a name.\n\n_Ralph_ : Well, I'm just standing up for my rights as an artist who thinks flies are awful things. But it is an interesting looking critter. I'll give you that.\n**Western Long-beaked Echidna**\n\n_Zaglossus bruijnii_\n\n**Eastern Long-beaked Echidna**\n\n_Zaglossus bartoni_\n\n**Sir David's Long-beaked Echidna**\n\n_Zaglossus attenboroughi_\n\nThe Platypus and the echidnas are the only egg-laying mammals in the world. But the egg-laying is starting to become a concern for the long-beaked echidnas, of which there are three types in existence, all residing in New Guinea. The first, Sir David's, has not been seen since 1961 and is deemed to be Critically Endangered, if indeed it survives at all. The Western Long-beaked Echidna is also classified as Critically Endangered and has not been officially recorded since the 1980s. The Eastern Long-beaked Echidna is the best contender for survival, as it is merely considered as Vulnerable. It has been hunted to extinction in local areas but is still abundant in hard-to-reach and inaccessible areas. But as always man marches forward to tame the untamed.\n\nAmong the threats for all of these creatures are loss of habitat, land conversion and of course hunting by humans. Normally echidnas are troublesome to locate as they are nocturnal and do not hang out in large groups. Hunters get round this by using trained dogs to sniff out their daytime hideaways. The urgency for hunting regulations cannot be stressed enough and more studies and research are needed to determine the true numbers of each species in existence \u2013 and then a conservation plan needs to be put into action.\n\nCeri's Diary: Tomorrow Jackie and I will visit the Steadmans to check on the art and look through the critters to see which pictures I may never have seen before and to check if any critters have been lost on the journey from painting area to the sanctuary of the archived drawer. The last two books have seen some birds fly mysteriously from the roost of Ralph's studio never to return. For example, there were a couple of Pale Blue Piddles that were drawn for _Extinct Boids_ that vanished down a black hole and were never seen again. Sadie (Ralph's daughter and keeper of the Steadman Art Collection) and I searched high and low but all to no avail and we had to consign those damn piddles to the definitely extinct pile. Luckily we had a small photo of them so at least the world could see what had been lost forever. Extinction is a painful reality and we are still mourning their loss. We still harbour the hope that one day we will discover them in some far reach of the studio where they thrive in isolation from us. We know this is a vain hope to hold on to but we must continue to dream and believe there is a possible positive outcome, otherwise we may as well give up, and that is something we will always refuse to do. We have to keep the fight going, even in the face of the greatest adversity.\n\nThis time I am certain we will be OK, as Sadie has been photographing critters as we go and then filing them accordingly. So all should be fine \u2013 but there is also the slight worry that this is Ralph's domain where time and space twist into corridors of artistic vortexes and imagined realities. This is the Ralph space-time continuum, also known scientifically as the Steadman Uncontinuum. It occurs somewhere between Ralph's hands and the area where the pictures are to be photographed. This is the Steadman no man's land, the handover space for the finished art, the most dangerous of all spaces in the studio as it contains the spatial drawer of disappearance. Sadie and I fear this whole area, as it is godforsaken and lawless. But this time we are confident that we have handled everything just as we should. We will see tomorrow.\n**Visiting the Steadman Uncontinuum**\n\nWe have arrived at the studio and are going through the pictures. Great bumpy coatings of paint dress many of the creatures and they feel sculptural and alive as they explode from the paper. I have my checklists and my only regret is that we didn't record every single blotted page before they were drawn upon. However, the problem is that often Ralph may see the idea for the dirty page in a flash before we have had the chance to discuss the possibilities for a critter, so he draws until he has finished what he needs to do. I don't mind this, as to hold up the muse and wait for my input would be a dangerous proposition \u2013 and an upset muse is not a thing to trifle with. We have to let them do as they see fit, as they can disappear quicker than any Pale Blue Piddle if treated incorrectly.\n\nEverything seems to be correct and in order and we breathe a sigh of relief but then something nags away at me. There was another creature that I vaguely remember. Or was there? I dismiss it and we flick through the zoo of pictures in front of us. It is like finally meeting pen pals after a long and distant relationship. I chuckle at the ballet of dolphins and the cheek of the apes, the majesty of the African wildlife and the madness of the Aye-aye. Old friends well met.\n\nAnd then it hits me. The Skuppered Dunt! That's what's missing. A disappeared dunt. I haven't seen it.\n\n'Sadie,' I shout through to the studio, 'Have you ever seen a Skuppered Dunt in your travels?' 'A what?' she shouts back. Oh no, I think, once seen a dunt is always known. 'A Skuppered Dunt,' I reply. There is a pause of silence and then a low rumbling _no_ comes back at me. Sadie appears at my side in a flash. 'I have never heard of such a thing. Are you sure there is such a thing?' 'Oh yes.\n\nLet me search his computer.' I input Skuppered Dunt and the photo of it drying on the floor appears, including versions of variants with computer coloured backgrounds. Sadie has never seen it before. 'Oh God, not again,' we both cry.\n\nWe begin to search through various folders and drawers as Ralph reappears and asks what we are doing. We tell him and he replies, 'I hid him because he's shy. He will be somewhere.' Ah, that old chestnut. Everything is somewhere but not necessarily in any dimension that the likes of us mere mortals can access. This is the Steadman Uncontinuum in all its twisted reality. We search and we search as the light begins to dim and we realise we will have to admit defeat once more. Then Sadie gets the idea that her father may have painted over it and created another critter or that it may be on the back of one of the ones we have looked at, but neither possibility bears any fruit. At least we have a record of its existence and what a suitably harsh being it is. We accept that the Skuppered Dunt has scarpered.\n\nOther than that one incident everything goes swimmingly and I suggest to Ralph that it would be good to watch a dirty water piece begin its creation and he agrees with me, picks up a sheet of paper and places it on the floor. I take pictures as Ralph begins his process and spills filthy water over the paper. It spreads everywhere and sits in inky puddles, which Ralph then tilts gently in different directions. It is so much fun watching the artist wallow in his filth and then, as quickly as it had begun, the pouring is over and he suggests we leave it for a while.\n\nNow we are looking through drawers of never used and often never seen pictures that Ralph has done over the years. I am certain we can use some of them in the book. His whale drawings in particular are beautiful. 'I can't draw like that anymore,' says Ralph wistfully, as we look through these beauties. 'Well, you couldn't draw like you are drawing now back then.' I reply.\n\nIt's a couple of hours since Ralph splurged the paper and we are looking at how it is shaping up. Pools of ink stand still and then Ralph decides to add a little colour and drops green and red ink into the lakes of inky muck. The ink hits in a vibrant splash and then dilutes with the water and these coloured tendrils creep through the water, spreading ever further. There is an ape-like look about it but then I start seeing other creatures too and every time I turn away the picture changes. We will just have to wait a couple of days to see how it dries out and then make a decision.\n\nIn the meantime it is time to get back up the motorway and just before we depart Ralph shows us his tomato plants, which are in rude health. As a parting gift he gives us three of them to take back with us. Have tomato plants will travel. And off we go to face the wonders and true filth, not like Ralph's artistic filth, of the Dartford Crossing. The horror, the horror.\n\n**Mongolian Beaver**\n\n_Castor fiber birulai_\n\nEurasian Beavers were once plentiful across Europe and Asia but hunting and a loss of wetland habitat depleted the species' numbers and lessened its range. Firm conservation action was needed and a mixture of hunting restrictions, habitat protection and reintroductions and translocations did the trick. The Eurasian Beaver is now considered a species of Least Concern.\n\nHowever, the population of one subspecies, the Mongolian Beaver, has been in great trouble over the years. Hunting for beaver skins, meat and castoreum has created huge problems and this still goes on in some places although it is not as widespread as it once was. Castoreum? What's that? It's what beavers secrete from their castor sacs, located between the pelvis and the tail, when they are marking their territory. It is also used in the making of some perfumes and as a food additive, as an enhancer for vanilla, raspberry and strawberry flavourings. It is used less than ever before, which can only be a good thing for beavers.\n\nIn 1964 it was estimated that there were only between 100 and 150 individual Mongolian Beavers left in the wild and in 1991 this number had increased to 300. Estimates today suggest that there are approximately 500 beavers living in the Ulungur watershed in China and Mongolia. These increases are due to conservation action having been taken, most notably numerous translocations and introductions over the last 50 years and the establishment in 1965 of the Bulgan Gol Nature Reserve in Mongolia.\n\nHuman settlements and therefore human activities are on the increase and threatening the beaver habitat and the beaver population. In Mongolia, hunting of the beaver continues and this threat is compounded by the clearance of willow from large areas of beaver habitat along the Bulgan River, which it relies on for food and shelter. This has a knock-on effect of isolating populations, which causes inbreeding. Water pollution is also an issue and a hydroelectric dam, which has been built on the Chinese part of the Bulgan River, has stopped the migration of beavers within the area. In China, logging for firewood has destroyed much of the forest on which the beaver depends and the grazing of livestock has severely depleted much vegetation, which is also needed for the beaver's existence.\n\nInterestingly the Mongolian Beaver doesn't build dams as it lives in deep waters, but in 1982, during a drought, the beavers built dams in the shallow waters to raise the water levels. Just shows how adaptable and intelligent animals can be.\n\nIt is important to manage the wetlands and restore the habitat if the beaver is to survive the influx of people to its surroundings. It has also been suggested that the creation of a new Beaver Nature Reserve may be the way forward but this would need the cooperation of the Mongolian and the Chinese authorities. Dam it all, how hard can it be?\n\n_Ceri_ : Your new hat looks better.\n\n_Ralph_ : It's starting to fit more. And my head's getting bigger and starting to fill it. It's all these compliments you keep giving me.\n\n**Volcano Rabbit**\n\n_Romerolagus diazi_\n\nI guess when your name includes the word volcano then there is every chance that you have a bit of a problem with your lifestyle. Live by the volcano, die by the volcano. But volcanic eruptions are the least of the Volcano Rabbit's problems as habitat destruction, human encroachment, farming, livestock grazing, the building of roads and forest fires have all damaged its future. In some areas the rabbit is hunted and it is believed that increasing temperatures and climate change adversely affect this rabbit. The population has fragmented and lives in clusters across four volcanoes in the Transverse Neovolcanic Belt in Mexico. All of these factors have ensured that the Volcano Rabbit is deemed as Endangered.\n\nIt is a protected species but in actuality the laws governing its welfare are poorly enforced and many people simply do not realise that this rabbit is Endangered. An education programme is crucial to teach the local people about this threatened animal and provoke empathy for the rabbit within the community. There is a captive breeding programme, which has had mixed results and a land management programme coupled with strict law enforcement on illegal activities is vital for the future safety of the Volcano Rabbit. When all of these protective measures have been put into place then the only thing left for the rabbit to do is keep an eye on those pesky volcanoes.\n\n_Ceri's Diary_ : I am looking at the most beautiful volcano erupting out of the splatter on this page and I see that it is entitled Volcano Rabbit Erupting Mexico. But I don't see the rabbit and I wonder if Ralph has forgotten to put him in the picture. And then I see him! Perching on the side of the mountain is an immediately endearing Volcano Rabbit. Sorry Ralph! I missed the subtlety of the moment. It's a case of the big picture overshadowing the little feller. Quite apt, really.\n**African Wild Ass**\n\n_Equus africanus_\n\nWhen you see a donkey, just remember that the 'Kiss Me Quick' everyday domestic donkey is descended from the African Wild Ass and this, the progenitor, is now in deep trouble. No more than 200 individuals exist in the wild and these are found in Eritrea and Somalia. There may be a few dotted around in other countries but it is less than certain. There are two subspecies, the Nubian and the Somali Wild Ass and there is a fear that the total number of asses out there may number under 50, so it is described as Critically Endangered.\n\nIn the arid and semi-arid bushland and grassland, the ass is now competing with domestic livestock for food and water: a change of habitat for agricultural purposes has made it harder for the ass to access water sources. Another potential concern is hybridisation with domestic donkeys and of course there is the issue of hunting. In Ethiopia and Somalia, the ass is hunted for its meat and is used in traditional medicine, which dictates the use of body parts and the cooking of soups from bones to treat a variety of ailments ranging from rheumatism to tuberculosis \u2013 this is the biggest threat to its future.\n\nThere is ongoing work to educate and involve locals with conservation efforts on behalf of the wild ass and it is hoped that through knowledge of the plight of the ass a more harmonious relationship between man and beast will develop. Research needs to ascertain the true distribution of the ass and then determine the conservation route forward for this familiar animal, and then perhaps we can consign Wild Ass Cup-a-Soup to history.\n\n_Ralph emails_ :\n\nCHERI!\n\nWe forgot to mention DYLIS VORYD from Rhyl! She is a Feminist CRITTERESSOLOGIST \u2013 who believes that all of the female Critters are being systematically cancelled out \u2013 and are the Girl Elephants in the room in Balletic TUTUs! Ask Dylis VORYD about creepy skimleaches and stuff... PHUGH!!!! What do YOU know of her other than her Rhyl Origins and blue Spiddurs!!!! Her portrait will follow this Wildest of Asses!!!\n\nLOVE TOMATOES!!!!\n\nRALPH YOGATO\n\n_Ceri replies_ :\n\nI have heard tale of this legendary woman. I'm glad she is getting the coverage she deserves.\n**Dylis Voryd**\n\nOn Toadstool Island the natural order of hunting and eating prey has gone out of the window. Because all the animals are in a precarious state of nextinction, Dylis Voryd, the critteressologist, who was brought to the island by Bent Girders, handles the feeding of critters and their mealtimes. She runs a strict regime and insists the critters stick to her ways and don't return to instinctive patterns. OK, the smaller guys have to watch out and make sure they don't annoy the top predators but Dylis has set the rules and a harmonious world order exists and equilibrium is maintained. If a Lion wants to attack an Addax, that's not permitted here. It may be the way of the world outside the Toadstool Archipelago but not on the island. Respect is everything and the Lion has to wait for general mealtimes when Dylis Voryd will feed every critter. Harmony reigns supreme thanks to the Law of Dylis. One simple, golden rule. Don't eat other critters.\n\nDylis is strict but fair and many times she has pulled a smaller creature from the jaws of a bigger one and a serious scolding ensues. This always leads to embarrassment for the caught-out critter and a sheepish (although there are no sheep here) shrug usually occurs before the law-breaking beast saunters off with a slap on the behind and a 'Woe betide you if you do that again...' call from Ms. Voryd. Then she usually chuckles, picks up the nearly meal that is the smaller critter and comforts it through its anxiety. Dylis once threatened a whole herd of elephants with extinction if they didn't 'settle down and stop causing such a rumpus' as they were continually arguing with many of the other critters. They believed she would and could do such a thing and they quickly became as meek as mice, which is funny, as they have never really liked mice as a species. Dylis may come across as a stern person but her heart is in the right place, well, it's on the right because she is a mirror child, but you get the picture. There is nothing she won't do to save these animals from extinction and she has to run a tight unit otherwise with all the conflicting critter egos, the Mid Lands would become the Bad Lands and no one wants that. Keep on trucking, Miss Voryd.\n\nMiss Voryd often takes a critter under her wing and looks after it personally, and her latest venture is the Peacock Parachute Spider. She works hard to learn the language of animals and at the moment is studying spider talk. This will enable her to open a dialogue with the spider to learn about its lifestyle and the issues and problems it faces. So far she has had one answer that she understands. When asked what was the biggest threat to its existence, the spider replied, 'Humans.' Miss Voryd will also provide therapy throughout the spider's recovery.\n\n**Peacock Parachute Spider**\n\n_Poecilotheria metallica_\n\nThe Peacock Parachute Spider is only known from one location within the Andhra Pradesh Forest in India and is considered as Critically Endangered. The species was rediscovered in 2001 having last been seen in 1899. Since then a handful of spiders have been caught by wildlife pet traders and have then appeared for sale. There is very little information available on the spider and surveys and research are desperately needed to determine the size of the population, its location and its lifestyle. The spider is threatened by habitat fragmentation and the destruction of suitable territory, due to logging, collection of firewood and human encroachment into the forest. It is believed that if action is not taken soon then the spider will parachute out of existence.\n\nPerhaps Miss Voryd will come up with a suitable plan after further discussions with the critter.\n\n**Saint Lucia Racer**\n\n_Liophis ornatus_\n\nOnce common across the Caribbean island of Saint Lucia, the indigenous and non-venomous racer snake was deemed to be extinct in 1936. Its decline had been brought about because of predation by the mongooses that had been introduced to the island in the nineteenth century and the racer raced no more, or so it was thought.\n\nThen in 1973 a single racer snake was discovered on the rocky offshore islet of Maria Major and a few sightings of the snake followed afterwards, but it was finally concluded that the snake had become extinct. Then, in 1983, the Saint Lucia government created the Maria Islands Nature Reserve,. In 2011 a group of conservationists made a concerted effort to discover whether the racer snake was or was not extant and a search of the outlying reserve led them to discover 11 individuals, which were microchipped and then released. Further research has led to the belief that the population is some 18 strong and some would say that the total might be nearer to 100 individuals. Work continues to ascertain the actuality of the situation. But the one thing that is certain is that this snake is one of the rarest snakes in the world, if not the rarest of all. Plans are under way to protect it and increase its numbers to create a more secure population of the Saint Lucia Racer and for it never to be thought of as extinct again.\n\n**Page of**   **Number 1**\n\n_Ralph_ : Don't make me do snakes and spiders. I hate them. Horrible beastly things. They make me go funny. Don't think I can do them. Don't think it's possible.\n\n_Ceri_ : Calm down, just breathe... and relax.\n\n_Ralph_ : Not sure I can. Oh dear...\n\n_Ralph emails_ :\n\nFound some spiders I have done previously and I have sent you another page that makes me go ugh.\n\n**Indian Python**\n\n_Python molurus_\n\nThe Indian Python is divided into two subspecies, the western type found in the South Asian subcontinent and the eastern type found across China and Southeast Asia. They prefer wooded territories and are an important predator for removing pests such as rabbits, mice and rats. Interestingly, where humans have wiped out pythons, then diseases have been brought into their communities by these former python targets. For centuries people have killed pythons out of fear and have hunted it for food, for its skin, from which to make fashion accessories and for its blood, which is believed to have medicinal properties. Fresh blood drained from a live snake at a dining table is reckoned to put lead in the pencil. It is also desired as a pet although the trade in pythons is now illegal.\n\nMuch of the snake's habitat is being lost to logging, firewood collection and an expanding human population. For the moment the species is termed as Near Threatened, although there is a 'watch this space' right by its name and regular check-ups on its health are essential. It's never too early to protect a critter.\n\n**Horrid Ground-weaver Spider**\n\n_Nothophantes horridus_\n\nPlymouth in the southwest of England is the next port of call for us and who would have thought that this is where a unique species, not found anywhere else in the world, would be discovered? This is the home of the Horrid Ground-weaver Spider. Trust me, this is not a fictional creature born out of the mayhemical machinations of Ralph's mind, this is a truly legitimate creature. I kid you not.\n\nThis spider was first discovered in 1989 and was known from only three sites in Plymouth. One of these sites was lost to development and another site, Radford Quarry, has been under similar threat. But thanks to a concerted effort by the conservation charity Buglife, the Devon Wildlife Trust, the RSPB and local communities, Plymouth City Council turned down the planning application in favour of the wildlife that roamed the quarry, including Plymouth's finest Critically Endangered spider. The spider is also found at another quarry at Billacombe and, in March 2016, thanks to a Buglife crowd-funding appeal, enough money was raised to finance further surveys across the area and another spider population was discovered at an industrial site in the Cattedown area of Plymouth.\n\nThe surveys are continuing and Buglife are working with site owners to keep the Horrid Ground-weaver Spiders safe and perhaps more populations will be found. This is one creature that may not have such a horrid future in front of it.\n\n**Why- me?**\n\n_Sempiterno quaestio_\n\n'Why me?' is the cry most often heard from creatures when they first arrive and this is also the name of the island's psychotherapist. The Why-me? consults with critters unable to mentally cope with their impending extinction and translocation to Toadstool Island. A good listener and understands all animal language even the lispy S's of the python's snake tongue, even if at times it does talk out of its snake bottom.\n\n**Skimleach**\n\n_Male lacte_\n\nThe Skimleach drinks semi-skimmed milk, which then combines with its stomach acids, creating a perfect skin cleanser. It regurgitates the altered milk, spraying those customers who seek the benefits of a Skimleach skin purify. It is also used for cleansing swimming pools.\n\n**Page of**   **Number 2**\n\n_Ralph emails_ :\n\nThis page is quite one of the worst to come out from my nib and ink. Horrid, horrid, horrid. Going to lie down. Do not call me.\n\n_Ceri's Diary_ : I guess you were wondering what happened to the ink-splattered page that I took photos of when Jackie and I visited Ralph recently. Well, after a few days it successfully dried out and Ralph has now done this to it. It's fascinating to see how he uses the runs of ink to create the shapes of animals. It may be a page of ugh to Ralph but it makes me go wow like a wowlet.\n\n**Frigate Island Giant Tenebrionid Beetle**\n\n_Polposipus herculeanus_\n\nThe Frigate Island Giant Tenebrionid Beetle is found in coastal woodland habitat on the Seychelles island of Fr\u00e9gate, to give it the proper spelling, although we often call it Frigate Island. The beetle lives in trees by day and forages on the forest floor by night. It was once found on Round Island, Mauritius, but introduced rabbits and goats led to the destruction of the beetle's habitat and ultimately caused the bug's extinction.\n\nOn Fr\u00e9gate Island, there was a fear in the 90s that an invasion of Brown Rats would wipe out great numbers of the beetles, but an eradication programme was successful and the beetle population was saved. It was the fear of the effect of rats that led to the beetle becoming Critically Endangered but now it has been downgraded to Vulnerable. Then, around 2000, a fungal disease affected many trees associated with the beetle but careful management and a forest restoration programme kept the beetle numbers up and their habitat was restored to health. Climate change could alter conditions for the beetle, but for the moment it is believed to be safer than it has been for years. It's a bug's life.\n\n**And that concludes the Pages of**\n\n**Page of**   **Number 3**\n\n_Ralph_ : I hated doing those snakes. They're one of life's mistakes.\n\n_Ceri_ : Imagine if there were no snakes. What would the world be like?\n\n_Ralph_ : Snakeless and then I wouldn't worry about them.\n\n_Ceri's Diary_ : Here's a sad fellow. I presume he's feeling sorry for his relative who's in trouble all those miles away.\n\n**Chinese Giant Salamander**\n\n_Andrias davidianus_\n\nWelcome to this weird brute, which happens to be the largest amphibian in the world, which can measure up to 1.8 metres in length. That's 5 feet 11 inches for all you non-metric people out there. Its now fragmented range is spread across southwestern, southern and central China and it resides in forested hill streams. Once it was a fairly common creature but times have changed and this strange animal is now Critically Endangered, with a population that has plummeted by 80 per cent since 1960. The building of dams and pollution from mining have led to habitat change, which has impacted heavily on the salamander, but probably the greatest cause of the decline is the consumption of salamander, which is considered a gourmet meal. Why do we have to eat everything? In fact, the desire for the salamander is so high that it is being farmed in China in great numbers. In 2011, research carried out by the Chinese Giant Salamander Conservation Programme discovered that in Shaanxi Province alone, it was estimated that there were 2.6 million salamanders on a huge host of farms and the numbers involved show the major economic importance to those that breed and harvest them. You might think this could help conservation, but it is more likely that infectious diseases will spread via farm wastewater or from farmed animals to wild populations of salamanders, especially if they are moved from place to place.\n\nThe Chinese Giant Salamander is an important species within Chinese conservation and much is being done to save it before it's too late. It is believed that regular monitoring will help to understand its distribution and the impact of the various threats it faces. There is also the thought that a captive breeding programme may prove worthwhile, but much also needs to be done to protect its dwindling natural habitat. An awareness programme for all those who come into contact with the salamander as well as the general public will hopefully change opinions on the salamander and stop it being part of people's dinner. Once it is off the shopping list then the salamander can move forwards again.\n\n_Ralph_ : Don't ask me to do ants of any kind.\n\n_Ceri_ : I think you're OK on that score. But why don't you want to do ants?\n\n_Ralph_ : I sat on an ant's nest in Abergelly as a child. Never been able to look an ant in the eye since.\n\n_Ceri_ : They bit you?\n\n_Ralph_ : All over my abergellies.\n**Vaquita**\n\n_Phocoena sinus_\n\nLiving in the northern part of Mexico's Gulf of California, the Vaquita is the smallest and the rarest member of the cetacean family. It is estimated that no more than 60 individuals still swim in these waters and it is hence considered Critically Endangered. Such a tiny population, living in such a small area, leaves the Vaquita open to being affected by climate change, habitat loss or degradation but the primary threat comes from fishing. They can be killed by fishing equipment or become caught in illegal gillnets being used to catch the Vaquita's co-resident of these waters, a fish called the Totoaba. In 2015, the Mexican government pledged support for the Vaquita by stopping gillnet fishing and promising to fund and support local fishermen and their communities.\n\nThis was considered a breakthrough in the Vaquita's survival hopes, but the Totoaba is a desired commodity and commands huge prices, in particular for the swim bladders, which are considered a delicacy in... can you guess where? Yes, that's right, in China. The Totoaba is now deemed Critically Endangered and is also a protected species. Illegal fishing will wipe out both the Totoaba and the Vaquita and that looks likely to happen in a short space of time.\n\nIn 2014 it was believed that 97 Vaquitas were to be found in the Gulf of California but since then numbers have fallen drastically, by 40 per cent, with a high proportion dying because of illegal fishing activities. It doesn't take Einstein to do the maths on this one to realise that there is an imminent and potentially insurmountable problem ahead if swift action is not taken immediately.\n\nSadly, Totoaba fishing is on the increase and the Mexican government needs to find a way to halt it forthwith. Perhaps the only way to save these species is by banning fishing completely within this area and then a recovery plan can be put in place for both species. It shows how one species can be inadvertently affected by the fortunes of another and their futures can become inextricably linked forever.\n\nIn July 2016, the USA and Mexico announced that they would work together to protect and save the Vaquita. An international committee has been formed, entrusted with the development and implementation of safe fishing equipment. This is essential work, and more will be done to halt the illegal fishing and trade of Totoaba. China needs to become a part of the dialogue and address the issue of the demand for Totoaba within its country, for without this market the Totoaba and Vaquita would have a pretty pleasant time of it. It's time to end the poaching and the desire for swim bladders and let these creatures swim.\n\n_Ralph emails_ :\n\nHad to give a talk for half an hour this morning to the NORTH LOOSE Preservation Society! WE missed you! Where is Ceri? They chimed \u2013 Where is HE!!? Showed them my Dirty Water Experiments and I told them that it was YOUR Dirty Water from the Ruts and Crannies of your Gutters. I said you were Master of Critters in Rutland \u2013 so unable to hear me rabbiting on... a couple of the audience had 12 Bore Shotguns with them because I said that I would show a couple of rare Critters and they decided they would have a pot shot at them!! They blew a hole in the ceiling of the Schoolroom!! Lousy shots they were!!!\n\nAnyway, tried to Skype but silence. You said you would be on line \u2013 You Lying Swine!? Have we done a critical LYING SWINE!??????\n**Leatherback Sea Turtle**\n\n_Dermochelys coriacea_\n\nThe Leatherback Sea Turtle is the world's largest sea turtle and is the most well-travelled as it migrates across the Atlantic and Pacific Oceans covering thousands of kilometres and surviving on a diet of jellyfish and other soft-bodied snacks. Unfortunately debris and plastic bags, mistaken for jellyfish, can be ingested by the turtles and block their digestive tracts, which can lead to death. These encounters happen too often and show the dangers of simple everyday objects finding their way into the environment. Many of these bags are not biodegradable, which seems like lunacy considering that we now know the dangers that plastics can cause within the natural world.\n\nEvery year it is estimated that hundreds of thousands of sea turtles are caught in shrimp trawler nets and gillnets or on longline hooks. Being caught in a net usually leads to death by drowning, as turtles need to come to the surface to breathe at regular intervals. Habitat loss due to human encroachment onto nesting beaches is a major concern, as is the loss of many specific feeding grounds such as coral reefs and sea grass beds. The problems don't stop there, as hunting and egg collecting for subsistence and commercial gain are rife throughout the Indian Ocean, Central America and Southeast Asia, where, incredibly, egg collecting remains a legal activity and has led to extinction in Malaysia and enormous population declines across the region.\n\nThe IUCN lists the Leatherback Sea Turtle as Vulnerable although several of the subpopulations are considered as Critically Endangered. Various measures are needed to arrest the decline in sea turtle numbers and to make sure that not all subpopulations of them become Critically Endangered. Working with fishermen to stamp out gillnets and bycatch from longline fishing is an imperative to allow the turtles to freely swim their enormous distances. Patrols of nesting areas are needed to protect turtles and their eggs, local communities need educating about the possible extinction of the turtles and perhaps ecotourism can bring in monies lost from the sale of eggs. There is much to do, but the turtle can be saved.\n\n_Ralph emails_ :\n\nDEAR IREC\n\npsssst1233456789070564859=O\/O\n\nAnyway..... think about it!!!\n\nPhlar NAMdeats\n**Red Squirrel**\n\n_Sciurus vulgaris_\n\nThe Red Squirrel is found across Europe and its conservation status overall is that of Least Concern, but the story in northern Italy and the British Isles is very different. This is the tale of two squirrels and what happens when their worlds collide.\n\nThere used to be plenty of Red Squirrels in Britain and perhaps they would have been regularly seen sat atop a bird feeder as Ralph has depicted this one. But now they have all but disappeared from our daily landscape and the last remaining 140,000 UK Red Squirrels are found largely in Scotland (120,000) and within small pockets of England, Wales and Northern Ireland.\n\nIn the late nineteenth century, Grey Squirrels were brought over to Europe from North America as a wildlife accoutrement to our landscape. Fast-forward to the present day and 2.5 million Grey Squirrels roam the land and are painted as the angry invader that has beaten up and conquered our indigenous squirrel. There is no violent relationship between the two \u2013 the Greys do rely on the same food sources as the Reds but they can coexist quite happily. It is possible that because the vast number of Greys can eat more efficiently and have a wider diet than the Reds, it is leaving a shortage of foods for the Red Squirrels. The Greys also have a different digestive physiology, meaning they can digest seeds with high tannin content, such as acorns, which the Reds are unable to digest. This allows the Greys to find more food, which keeps them going through the tougher winter months.\n\nThe Red Squirrel is also threatened by habitat loss and fragmentation, especially of its woodland habitat. This makes for smaller populations and leaves them susceptible to competition from the Greys and open to disease, such as the squirrel poxvirus, which is usually fatal. It has been suggested that this disease is carried by the Grey Squirrels, as many have the antibodies to the illness within them and are unaffected by it, but this remains unproven. There has only ever been one case of a Grey Squirrel becoming infected, while Red Squirrels die within a week of contracting the illness. More research is being carried out to determine the origins of the virus and whether it is transmitted between Grey and Red Squirrels.\n\nFor the moment the most important thing is to preserve the existing populations of Red Squirrels and to reintroduce the species into parts of its former range where the habitat can be maintained well enough to support new populations of our native squirrel.\n\n_Ralph emails_ :\n\nI'm no Darwin but that evolution stuff is not right. I am certain we are descended from squirrels but all that's happened is that over time we've lost our bushy tails. That's nuts! Talking of which, where did I bury that last lot of nuts? I'm feeling a tad peckish.\n\nP.S. Have you seen the Crockery Dile? It's a teapot with teeth.\n\n_Ceri replies_ :\n\nDon't you mean a teethpot?\n**Saola**\n\n_Pseudoryx nghetinhensis_\n\nThe Saola was discovered in 1992 by the Ministry of Forestry of Vietnam and the WWF and was the first previously unknown large mammal to be discovered in over 50 years. Endemic to the evergreen forests of the Annamite Mountains in Laos and Vietnam, the Saola is an extraordinarily rare creature. Due to the lack of information it is impossible to declare a definite size of population but the theory is that there is a maximum of a few hundred in existence and the number could possibly be as low as 25. Whatever the true size of the population out there, this is an elusive beast.\n\nThe main threats to its existence are habitat loss and hunting. The forests are being destroyed as humans move further into the area, changing the land for agricultural use and plantations and carrying out illegal logging, thus fragmenting the Saola's habitat. The recently built Ho Chi Minh Road, which now runs through the mountains, has fragmented the land still further. Hunting for meat exacerbates these problems and, although it is not usually a primary target for hunters, it is caught in snares set for other animals such as wild boar or deer. The continual influx of people to this region has meant there are more hunters who are willing to supply animals to the illegal wildlife trade and there is a belief that Chinese traditional medicine and food suppliers in Laos and Vietnam drive this market. Unfortunately, the Saola gets caught in the crossfire of the illegalities, suffers and dies because of it.\n\nThe WWF helps educate local communities and works with them to create community-led forest management. Locals are trained and employed as WWF forest guards and work hard to remove thousands upon thousands of traps and search for and stop illegal activity, but this is a huge undertaking. Between 2012 and 2013, WWF forest guards and the Forest Protection Department cleared 13,394 snares and shut down 336 illegal hunting camps. All this work is helping enormously, but will it be enough? Can the forests be completely cleared of the hunters and their guns and snares, which are making the Saola one of the clearest candidates for an imminent extinction in the world today?\n\n_Ceri's Diary_ : Not sure what this Saola is trying to get in its mouth but it looks like a smiling butterfly antelope, if there were such a thing, which there isn't. At least, there wasn't and then Ralph drew it, which means that now there is. I present Saola with Smiling Butterfly Antelope.\n**Monarch Butterfly**\n\n_Danaus plexippus_\n\nButterflies look so gentle and delicate, I watch them and wonder how they get through the day without damage. Well they are actually much hardier than you think and the Monarch Butterfly has to be the kingpin of all butterflies as it migrates from Canada to Mexico every year, which is a distance that can reach up to 4,500 kilometres. These are durable critters. Not all Monarchs migrate as some stay exactly where they are; for example, the Florida population is a mix of migratory and resident Monarchs.\n\nThe butterfly's journey is an extraordinary feat as Monarchs normally live for five weeks or so but the migration south can be an eight-week flight. Through some inbuilt setting they stay the course and arrive in warmer climes. The journey back is a different story as it can take three to four generations of butterflies to make the journey northwards to the United States and Canada. It shows just what an epic feat it was for the initial journey south to Mexico. It has become a Near Threatened species due to illegal logging and extreme weather, in particular heavy winds, which have felled many trees in the Monarch's winter hibernation habitat of the mountain forests in central Mexico. Agriculture and conversion of habitat also play their part, as does climate change, which could significantly affect the Monarch's migration. In the potential future, wetter and colder Mexican winters would decimate the numbers of butterflies able to migrate to the States and Canada and hotter summers could move habitats further north. A 2013 report issued by the WWF showed that the number of butterflies wintering in Mexico was at its lowest level for 20 years. In the States, the main threat is the use of herbicides, which is destroying much milkweed, the primary food source for the butterflies.\n\nThe Mexican government has created the Monarch Butterfly Biosphere Reserve to protect the butterfly's habitat from the threat of illegal logging and, with the support of the WWF, this area has expanded to ensure a safer future for the butterfly. The Monarch Butterfly Conservation Fund was also created by the WWF to encourage and offer economic incentives to local communities to work on behalf of the habitat and to reduce illegal logging. They have also established mushroom and tree nurseries, with the mushrooms providing protein as well as a source of income. The tree nurseries provide 1.5 million trees for reforestation every year, providing a wealth of work for local people.\n\nEvery year more than 150,000 butterfly tourists visit the Mexican hibernation colonies and this provides a source of income for the communities, who are also being helped by local authorities and the WWF to establish a better infrastructure to cope with the influx of people. They are being taught to be tourist guides and are learning how to help visitors make the most of their time with the butterflies and, of course, this engenders economic remuneration. Locals also patrol the forest, keeping their eyes peeled for illegal logging and forest fires and have become the guardians of the area taking great pride in their work and their region. With commitment like this there is every chance that the butterfly will remain the monarch of migration.\n\n_Ceri_ : I think we should do a butterfly in the book. A Monarch Butterfly. Then we can show that even butterflies have problems. People don't think of creatures like that having existence issues.\n\n_Ralph_ : Everything has an existence issue in this day and age. Everything.\n\n_Ceri_ : You're right. Creatures, habitat, people, jobs and lifestyles. Everything is endangered. Look at politicians. Not sure they will exist for much longer. Perhaps that wouldn't be a bad thing. We need an evolution from that tired old format of politician and party. After all, even you are bored with drawing them, as they just aren't the same any more.\n\n_Ralph_ : That's true and that's why I now draw butterflies. I think I will do him as a Rorschach butterfly.\n\n_Ceri_ : You mean a Ralphschach butterfly.\n\n_Ralph_ : Apparently I do. He might be nice like that. I'll do him tomorrow.\n\n_The next day_\n\n_Ralph_ : Damn and blast it!\n\n_Ceri_ : What's wrong?\n\n_Ralph_ : I've been thinking about that butterfly all day and finally I get round to doing him and then you ring, which made me spill this bottle of red ink all over my hand. Look!\n\n_The mark of the red hand waves at me from Ralph's studio._\n\n_Ceri_ : It looks like you bleed ink. It's rather splendid.\n\n**Largetooth Sawfish**\n\n_Pristis pristis_\n\nThis sawfish has four subpopulations in the Eastern and Indo-West Pacific and the Eastern and Western Atlantic oceans. Details of the population sizes are undetermined but sightings and recordings of this sawfish, also known as the Common Sawfish, have become increasingly rare: with that increased rarity comes an increased demand for parts of the sawfish. Those that are illegally traded are the skin, meat, organs, fins and, of course, the rostrum, the large elongated snout, which is lined with saw-like teeth, hence the name sawfish. But you knew that. These rostra are sadly wanted as ornamental objects and fetch a pretty penny too, making it a lucrative business for fishermen. The fins are used in shark fin soup (surely a trade descriptions issue) and Chinese traditional medicine calls for the use of body parts including the liver and gall bladder. The skin is used to make high-quality leather and the meat is usually consumed locally. Unfortunately, the sawfish is popular for too many detrimental reasons.\n\nBecause of their snaggle-toothed rostra, sawfish are prone to being caught in fishing nets and even though it is now a protected species, it is still being caught not only illegally but also accidentally, which is threatening its existence. Habitat loss is also damaging the populations and it is imperative that stringent law enforcement is carried out across the sawfish range. Many people need to be taught about the sawfish and its plight, while something has to be done about gillnets and trawling to stop their devastating effect on the sawfish population. A conservation plan is needed for the species, but it is going to be hard to implement one when the range of the sawfish is so vast and the species is hosted by so many nations. But we have to find a way to stop the sawfish becoming no more than a curious object and a historical relic on a dusty shelf.\n\n_Ceri_ : You'll need a holiday after you've done all these critters.\n\n_Ralph_ : I don't like going on holidays. I like to stay at home and sit quietly on a Lutyens bench and smoke Will's Woodbines furiously and crittically. I also ponder who we borrowed Lent from?\n\n_Ralph emails_ :\n\nHere is the one you have craved since records began!! Common Sawfish \u2013 drawn with ink and he still looks silly \u2013 and it is only in line with a daft expression!\n\nRUDE RALF \u2013 friend of dead common things!!! PS. His name is TOMMY!\n**Walrus**\n\n_Odobenus rosmarus_\n\nThe Walrus is divided into two subspecies, the Atlantic and the Pacific Walruses. For the moment, the Atlantic Walrus is considered as Near Threatened and the Pacific Walrus as Data Deficient, therefore the Walrus as a species is classified as Vulnerable. The Atlantic Walrus is found mainly between Canada and Greenland and the Pacific Walrus inhabits the northern waters off Russia and Alaska down to the Chukchi Sea. It is estimated that the Atlantic Walrus numbers approximately 25,000 and the Pacific Walrus up to 200,000 individuals, but this is not a confirmed figure. Interestingly, the US Geological Survey has just released data on Walruses, which have been gathered over 160 years of Walrus records and collated into one giant Walrus database. This includes information taken from nineteenth century diaries, maps created by explorers, aerial surveys and expedition accounts. It is hoped that this information will inform the decision makers and help them decide how best to protect the Walrus and to fully determine its status as a species and decide whether it should be considered as Endangered.\n\nFor many years the Walrus was harvested for meat, bones, ivory and skin by the native people of the Arctic, but commercial hunting was the beast that severely damaged the Walrus population. In the 1970s commercial hunting became illegal and since then the Walrus has been protected throughout much of its range. The exception was Russia, but hunting stopped there in 1991 when their Walrus industry collapsed. Subsistence harvesting still occurs for local communities in Alaska, Canada, Greenland and Russia, often with quotas put in place, but for the moment this harvesting is believed to be within sustainable limits.\n\nWhen out of the water, Walruses congregate in groups known as haul-outs. These can number thousands of animals, which is a social and defensive strategy as it protects them from attacks by its only natural predators, Polar Bears and Killer Whales. Outside of the winter breeding season, the sexes do not mix in these gatherings and the males will camp out away from the females and their calves. Haul-outs do leave them susceptible to oil spills and boat collisions but the Walrus database has recorded all known haul-out sites. This will help those that work in and navigate through these waters to avoid the Walrus populations and therefore protect the species even further.\n\nEvery spring the male walruses congregate on southerly islands and coastal areas while the females head to the northern ice floes to give birth and raise their young. Climate change is melting the sea ice at an alarming rate and no one is quite sure how the females will adapt to the increasing loss of icy habitat. It has been noted that females have begun to form their own haul-outs as the sea ice has been disappearing, which is something groups of females have never done before. Perhaps this is how they will cope with further habitat change. Whatever happens, there is concern over the future of the Walrus and how it will adapt to the changes brought about by climate change.\n\n_Ralph emails_ :\n\nThis morning I was ordered to go down to Maidstone to buy new Pants, shoes and sherts not covered in Ink Splats from your wretched Critter Crappers! This has been a messy book!!\n\n_Ceri replies_ :\n\nA Crittologist's lot is not an easy one.\n\n_Ralph replies_ :\n\nFunny you should say that. Here is a picture I have just done of a Crittologist's lot!\n\n**White- headed Langur**\n\n_Trachypithecus poliocephalus_\n\nThe White-headed Langur consists of two subspecies, one found on Cat Ba Island in the World Heritage site of Halong Bay in northern Vietnam and the other in southern China, in the province of Guangxi. It is not certain whether this Chinese population is a subspecies or perhaps its own species and the debate continues. Whatever the outcome may be, the langur's prospects are looking precarious because of hunting and habitat loss, which has seen a decrease in population size of 80 per cent over the last three generations. Hence it is considered as Critically Endangered.\n\nIn China, agricultural change and the clearing of land by fire have led to fires spreading into langur territory and firewood collection has created further habitat loss. These threats, coupled with poaching, have had a terrible effect on the langurs and have created a decreasing population, which now numbers between 600 and 800 individuals. A nature reserve has been created for one of the largest populations of about 250 langurs at Chongzuo Eco Park but more has to be done to ascertain the chances of survival for the species and what aid can be given to it to ensure the future for the White-headed Langur in China.\n\nThe Vietnamese langurs number 64 in total over seven fragmented subpopulations. Hunting for meat and use in traditional medicines have all but wiped out this subspecies and, just to help it on its way, a rising human population has adversely affected the habitat. Cat Ba Island has become a tourist centre and a National Park but it is not well managed and the tourist trail and its resultant activities damage and disturb the langur habitat even further. Because the population is so small there is a danger of potentially harmful inbreeding and of course a natural or man-made disaster could destroy the species in an instant. Since 2000, the Cat Ba Langur Conservation Project has sought to protect the White-headed Langur and its habitat on the island. A sanctuary has been created where about one-third of the langurs live and are protected and local people have been mobilised to protect a further third of langurs that live outside the sanctuary. This is an attempt to halt poaching and human encroachment for ever more and once again shows the importance of engaging local communities to become part of the conservation story.\n\n_Ralph emails_ :\n\nPlease don't think I am whining like some Lesser Spotter Finger Dinger \u2013 but I have been plagued for the last 12 hours by a Godawful pain in my right hand wrist and joint jangler fingers \u2013 suggesting that flicking and splatting is becoming critical cringe-makingly awful \u2013 so it is a good job we are off to US tomorrer mornin' for me exhibition \u2013 back next Monday \u2013 so I hope I don't have to shake hands with important Wallies \u2013 who always want to shake your hand!! MINE! \u2013 NOT yours!!!!\n\nSorry to make you laugh again \u2013 its just a bad habit>>>>>>> Picture of the Pain attached!!!\n\nDIGITFIDGET\n\n_Ceri replies_ :\n\nI hope you enjoy your show in the US of A. I hope your hand gets a break, not literally, as you have worked so hard on these critters and I hope your flicking hand gets better. You're a bloody marvel, boy bach! Speak when you get back.\n\n_Ralph replies_ :\n\nI will bring you back an EXCYCLE or a PEEdada!! If I can fit it in my JCB!!!\n\nGOOD TO TALC \u2013 did you get powder all over you also!!!?\n\n_Ceri replies_ :\n\nI'm covered in talc! I wish you wouldn't use so much. Safe journeying, dear Ralphito....\n**Masai Giraffe**\n\n_Giraffa tippelskirchi_\n\n**Reticulated Giraffe**\n\n_Giraffa reticulata_\n\n**Southern Giraffe**\n\n_Giraffa giraffa_\n\n**Northern Giraffe**\n\n_Giraffa camelopardalis_\n\nAs we head towards the end of the book, I think to myself that writing about the giraffe will be easy as it is listed by the IUCN as of Least Concern. I think this will be a nice simple piece to write and that numbers of giraffe have been decreasing but on the whole it is surviving. Sure, it's one to keep an eye on like so many other creatures but it's doing OK. But then whammo blammo!\n\nEverything changes and I am reminded that scientists and conservationists are continually working, studying and researching to understand our planet and its inhabitants better and science changes and keeps moving on.\n\nIt has always been assumed that there was one species of giraffe with up to eleven subspecies being recognised, although nine subspecies is the accepted norm. But the genetic differences between each subspecies have never been fully understood or fully examined. Until now, that is. When I woke up this morning the world had changed while I slept: yesterday's single species of giraffe has become four species of giraffe.\n\nThe giraffe world has been changed thanks to research conducted by the Giraffe Conservation Foundation in collaboration with the Senckenberg Museum in Frankfurt, Germany and partners \u2013 and this research will inform and affect the future of giraffe conservation. The giraffe yesterday is not the same scientific being today. There's been a total change in the giraffe team and here's the line-up. We have Masai Giraffe, Reticulated Giraffe, Southern Giraffe, with two subspecies of Angolan and South African Giraffes and, finally, Northern Giraffe, which has three subspecies, consisting of Kordofan, Nubian and West African Giraffes.\n\nFigures show there are fewer than 4,750 Northern Giraffe individuals and under 8,700 Reticulated Giraffes in the wild. This would surely mean that they should be moved into a higher category of threat. This will mean a rethink for the classification of the giraffes and their conservation status in the IUCN Red List. Coupled with the fact that giraffe populations have tumbled by 40 per cent in the last 30 years, from more than 150,000 individuals to under 100,000 today, we may see some of the giraffes moved from Least Concern to a more worrying status. What is extraordinary is that gaping holes have been uncovered in the story of the creature and it shows how under-studied this African giant has been, compared to other large creatures like rhinos, lions and elephants. It's time for the giraffe to take centre stage, as scientifically it has been an often-overlooked creature. Although how you overlook a critter that stands between 4 and 6 metres tall is beyond me.\n\nThreats to the giraffe include competition with livestock for food and water resources, regional instability, habitat destruction and poaching, as the giraffe is hunted for its meat. There is also a belief in certain parts of Africa that giraffe bone marrow and brains can cure HIV and AIDS. Despite being so iconic, still very little is known about the giraffe and the way it lives. But the recent research has shown the way forward for the animal and now the four species can be singly assessed and a conservation plan for each one can be mapped out. The future can be bright for this elegant beast.\n\n_Ralph emails_ :\n\nBOO!!! We made it back \u2013 show went well and I have now been given the status of Saint Ralph>>>>>>@@@@@@ King Ralph was too lowly!\n\n_Ceri replies_ :\n\nDon't scare me like that! Glad you're a Saint as you have the right attributes... Nice eyes, good legs etc.\n**Bactrian Camel**\n\n_Camelus ferus_\n\nFor a long time the wild Bactrian Camel was believed to have been descended from the domesticated Bactrian Camel ( _Camelus bactrianus_ ), but recent DNA tests show that there are major genetic differences between the two camels and it is now believed that there was a divergence long before domestication began. Consequently the wild Bactrian Camel is considered as a separate species altogether, although this means that it finds itself a Critically Endangered critter.\n\nIt is found in four subpopulations and locations in Mongolia and China and may be extinct in one of these, the Chinese Taklamakan Desert. Numbers of camels in the wild are believed to be decreasing, with roughly 600 individuals in China and about 350 in Mongolia. It roams the Gobi and Gashun Gobi deserts of northwest China and southwest Mongolia and is well equipped to deal with the harshness of these desert regions, being able to hold out against drought and food shortages. It is also able to drink salt water if needs be.\n\nThreats come from wolves and humans who hunt it for subsistence and sport. Strangely, the camel seems impervious to radiation, as for 45 years what is now the Arjin Shan Lop Nur Nature Sanctuary was China's nuclear test site and the camel has lived through that without any signs of adverse effects. These tests have thankfully stopped although toxic illegal mining is now being carried out in the area and it is estimated that 20 camels are killed each year by miners and hunters for food. Around 25\u201330 camels are also being killed annually in Mongolia as they cross to China on the southernmost border of the protected Great Gobi Reserve A. Again this hunting is for subsistence.\n\nHybridisation with domestic Bactrian Camels is also a problem in keeping the genetic strain pure and domestic livestock are damaging much of the Mongolian habitat. There are a number of threats for the camel to deal with and urgent conservation action is necessary. A second nature reserve in China is essential whilst the Wild Camel Protection Foundation has initiated a captive breeding programme in Mongolia and is determined to educate local people in both China and Mongolia about the importance of protecting this wildest of camels. It is a difficult time for the Bactrian Camel but there are hopes that the present-day actions will give the creature a fighting chance of survival.\n\n_Ceri_ : Why have you done so many animal drawings? What were they all for?\n\n_Ralph_ : How should I know?\n\n**Lemur Leaf Frog**\n\n_Hylomantis lemur_\n\nThe Lemur Leaf Frog is found in Colombia, Costa Rica and Panama and, due to an enormous population decline of probably more than 80 per cent, it is deemed to be Critically Endangered. This nocturnal tree frog's population has always been nominal in Colombia but it was once common across Costa Rica, where it has all but disappeared across the country and is now only found there in three locations. It is still considered common in central and eastern Panama, although numbers have been decimated in western Panama.\n\nHabitat loss has played its role in the demise of the Lemur Leaf Frog but the main culprit is believed to be the disease chytridiomycosis. This is caused by a fungus, which infects the frog's skin, affecting its breathing and natural defences.\n\nResearch is ongoing to ascertain the definite cause of the decline of the species and its potential remedies. In the meantime several institutions, including Atlanta Botanical Garden, Manchester Museum and Bristol Zoo, have all been running captive breeding programmes, which will build up numbers of the frog to a healthy level and will ultimately help support the population in the wild.\n\n_Ralph emails_ :\n\nI have didded a lemur frog defferunt to uvver frogs!!! I'll show ya if ya wont!!?? I tryde ta swipe yer \u2013 but yoo wuz kippin shchtum.........!\n\nPS Writing a song!!! Will Skipe ya shawtly! ANd weee can av a tawk abaht itt! The song is about a LINNET \u2013 so dont BIN IT!!! OK. We can speak later... We can SING laterdotdotdot! Bit washed out \u2013 can't walk and my wrists still have rep-stress-wrist-whip!!!!! Learning to sign with my feet now!!!!\n\n_Ceri replies_ :\n\nCan't wait to hear the song and it sounds like you are going to have to give it a rest with your ink flicking for a while.\n\n_Ralph replies (a bit later)_ :\n\nHere are the lyrics so you can sing along wiv mee.\n\nThe GONZOVATIONIST BIRDSONG\n\nby Ralph STEADman egged on by that CERI LEVY\n\nI try each day\n\nTo imitate\n\nThe dulcet tones\n\nof a LINNET\n\nThat hangs around\n\nTo play with my pet Crane\n\nThey're Worlds apart\n\nBut they insist\n\nThat we're the best\n\nWe're the GONZOVATIONISTS!\n\n\u2013 And anyway\n\nWe live down Lancet Lane\n\nListen to the Birdies sing?!\n\n(Whistle! Whistle! \u2013 Whistle! Whistle!!)\n\nIsn't that a hopeful sign of Spring!!!?\n\nA Fool's Eternity...\n\nHow long can that be??\n\nHow long can a Fool\n\nBelieve the Lie!???\n\nWell, it don't make sense\n\nTo gather Moss\n\nAnd think your Life's\n\nA bloody loss\n\nAnd give up living life\n\nWithout a try\n\nSo... be obstinate\n\nAnd GONZOVATE\n\nAnd change the minds\n\nOf those who hate\n\nGONZOVATIONISTS\n\nWe estimate \u2013\n\nAre Folks\n\nLike YOU and I-I-I-I-i-I-I-I-I>>>>>>>>>\n**Dugong**\n\n_Dugong dugon_\n\n_Da-du-gong-gong-gong, da-du-gong-gong_. It fits the Crystals song perfectly and I can't stop singing it. Right, shape up and let's have a look at this creature in a little more depth. Previously I stated that sailors used to mistake manatees for mermaids. But it is also said about the Dugong, which is obvious really as the Dugong and the three manatees together make up the order Sirenia. When I imagine a mermaid it usually looks like a Dugong more than a manatee. What about you?\n\nDugongs live in the coastal waters of at least 37 countries in the South China and East China Seas and the Indo-Pacific. They occur from East Africa to the Philippines and good numbers are found in Bahrain, Qatar and the United Arab Emirates. Tens of thousands live in the northern coastal waters of Australia and Papua New Guinea.\n\nThese herbivorous mammals eat sea-grass and, like manatees, are often called 'sea-cows', maybe because their underwater grazing is similar to 'land-cows'. Interestingly, the Dugongs in Moreton Bay, Australia are omnivorous as they will eat invertebrates when the sea-grass is depleted. Among the threats to the Dugong are entanglement in fishing nets, boating accidents, habitat destruction and loss of sea-grass. Hunting is illegal in most countries, although certain indigenous people, on cultural and historical grounds, carry out legal subsistence hunting. This happens in Australia, Papua New Guinea, Vanuatu and New Caledonia. For the moment the Dugong is considered as Vulnerable but a steep decline in numbers has been predicted. There are protected areas for the Dugong but law enforcement is not as strict as it should be and conservation action is urgently required to protect the Dugong from becoming the Du-gone.\n\n**The Mystery of the Missing Dugong**\n\n_Ceri's Diary_ : Ralph has finished his drawings and today is the dreaded Day of Reckoning. I am at the studio and Sadie and I are checking that we have no missing critters as Marina from Bloomsbury is collecting them later today to be photographed for the book. We know that the Skuppered Dunt is M.I.A. and hope nothing else has joined it in the dreaded drawer of disappearance. Ticking everything off I see a creature I have never seen before. A dog-gone Dugong. There's always a surprise whenever I set foot in the studio and this is a good one. But how come I have never seen it before?\n\n_Ralph_ : You didn't think I was going to give you everything, did you?\n\n_Ceri_ : Funnily enough I did!\n_Ralph emails_:\n\nJolly well Done ole sport! FINISHANDERO! Unless we do the critically overpopulated Traffic Jam Butty or the OVEREGGED LEGover!! Tried to leave coherent message \u2013 have a last picture of a lovely hedgehog you may not be aware of>>>>>> So anyway, I think we done good work for all the Critters!!\n\n_Ceri replies_ :\n\nYou sure did do a good thing! It's been a wonderful journey as always. Thank you Cap'n. And thanks for all the animals.\n\n**Western European Hedgehog**\n\n_Erinaceus europaeus_\n\nIn the UK, the British Hedgehog Preservation Society, the People's Trust for Endangered Species and the British Trust for Ornithology, have carried out research which indicates that rural numbers of UK hedgehogs have fallen by at least 50 per cent, while urban numbers have decreased by up to 30 per cent since the turn of the century. In the 1950s, it was estimated there were over 30 million hedgehogs in the UK but by 1995 the number had crashed to 1.5 million. Latest projections indicate this number has reduced further to fewer than a million hedgehogs. Could this lead to a local extinction? I don't know and research continues to discover the answer. Across the rest of its European range the hedgehog seems to be doing fine and the species is classified as of Least Concern.\n\nSo why is there such a rapid disappearance in the UK? The research points at the growth of agriculture, busier roads and more of them, loss of habitat, climate change and their natural predators, Badgers. Rurally, many hedgerows and other suitable habitats have disappeared and the use of herbicides, pesticides and agricultural intensification has made the world a less inviting place for the Hedgehog. In urban areas, the loss of gardens, the continual conversion of space to housing, the endless building of walls and the lack of thought for the lifestyle of the Hedgehog have left it with precarious footholds in towns and cities.\n\nThe Hedgehog has been a favourite amongst our storytellers over the years and has been utilised by the Brothers Grimm, Aesop, Shakespeare and Lewis Carroll. For example, there is Beatrix Potter's creation, Mrs Tiggywinkle, while in Alice in Wonderland, the Queen of Hearts plays croquet with flamingo mallets and Hedgehogs for balls. It is one of those creatures many of us have grown up with. They have accompanied us across the road of childhood without getting squashed and have a special place in many of our hearts.\n\nThe starting point on our journey through Critical Critters was the Woolly Mammoth and it is fitting that our end species in our adventure is the Hedgehog. Why? Well, here's one of those facts that takes a moment to get one's head around. The Hedgehog has been on this planet for more than 15 million years and pre-dates the Woolly Mammoth. It is a survivor. But it is significant that such an elderly states-creature of this world is facing a struggle to survive in several parts of the globe. It has become a very thin line between living and extinction.\n\nHistory rests heavily on our shoulders and we must not buckle under the weight. Every creature has its day but we cannot allow animals like the Hedgehog to disappear and no longer delight our future generations. We need our animal kingdom, we need our wildlife and we need to grow into a new age of caring and protectionism for the creatures of this world. The future of the critters is down to us and it is our responsibility to ensure that every living thing keeps its place on this planet. There is room for all of us on this spinning globe but we have to manage the space better than we have done in the last hundred years or so. If this moment of time were to be the beginning of the Anthropocene Epoch, then wouldn't it be good to mark it with a new attitude towards the natural environment? For now we only have this world as our home and it is in urgent need of repair, as is our relationship with the critters we share it with. It is the time for action.\n\n**++ STOP PRESS ++ STOP PRESS ++ STOP PRESS ++ STOP PRESS ++**\n\nChina has announced that it will ban the ivory trade by the end of 2017. This could be a game changer and it allows us to believe that we can change the world around us and save the critters. There's just a few more things to do...\n\n_Ralph_ : It's time to pack up and head home.\n\n_Ceri_ : Aye-aye, Cap'n. I will set a course for Blighty.\n\n_Ralph_ : You can drop me at the end of the road, got to pick up a copy of the Kent Messenger and see what's been happening while I've been away. I have to say that all this running around has left me parched.\n\n_Ceri_ : I'll put the kettle on for the journey home. Only got the merest splash of giraffe milk left though, so will have to go easy on it but at least you'll be able to wet your whistle.\n\nCeri's Diary:\n\nWith the mention of whistle, Ralph gives two sharp blasts on his penny whistle to signal that it is time to leave the Mid Lands and Toadstool Island. With the kettle boiling and the sun setting over the Sea of Treacle, I place the Turt on the Turtophonic Directional Navigator, set the dial to H, for home and we begin to move slowly forwards. This slow boat home will give us both time to reflect on what we have seen and what we have learnt. We look behind us and see Bent Girders and his team waving goodbye to us, while the Groglick leaps up and down trying to lick them. This has been our most extraordinary adventure yet and I believe that we can all make a difference in the world. It's time to make changes for our critters.\n\n  |  |   |  |   |  |   |  |    \n---|---|---|---|---|---|---|---|---  \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****  \n  |  |   |  |   |  |    \n****|  | ****|  | ****|  | ****|  | ****\n\nJackie Ankelen\n\nAnna Steadman\n\nSadie Williams\n\nSadie Steadman (it's all her fault)\n\nHolly Craven\n\nDaniela Galvez Fountain\n\nTriana Galvez Fountain\n\nOllie Williams\n\nToby Williams\n\nBloomsbury People \u2013 Jim Martin\n\nAlice Ward\n\nMarina Asenjo\n\nHugh Brazier\n\nJulie Dando, Fluke Art\n\nMarco Lambertini\n\nJo Cook \u2013 Amur Leopard & Tiger Alliance\n\nDuncan Macdonald\n\nJimi Goodwin\n\nNat Sobel and Adia Wright at Sobel Weber Associates, Inc.\n\nJeff Barrett and the Caught By The River crew \u2013 Robin Turner, Andrew Walsh, Danny Mitchell and Carl Gosling\n\nLady Catherine Saint Germans and the Port Eliot Festival\n\nCeri's Bird Effect Diaries can be found at www.caughtbytheriver.net\/category\/the-bird-effect\n\nRalph and his work can be found at www.ralphsteadman.com\n\nKurt Vonnegut quotes \u00a9 Kurt Vonnegut LLC. www.vonnegut.com\n\nEdward Lucie-Smith poem \u00a9 Edward Lucie-Smith\n\nNosetweak photograph by Sadie Williams and other photos by Ceri Levy\n\n**Music to write books by:**\n\nTinashe \u2013 _Nightride_\n\nAgnes Obel \u2013 _Aventine_ , _Philharmonics_ , _Citizen of Glass_\n\nLambchop \u2013 _Flotus_\n\nJessie Ware \u2013 _Tough Love_ , _Devotion_\n\nAlicia Keys \u2013 _Home_\n\nA Winged Victory for the Sullen \u2013 _A Winged Victory for the Sullen_\n\nHomeboy Sandman \u2013 _Kindness for Weakness_\n\nNoname \u2013 _Telefone_\n\nWhitney \u2013 _Light Upon the Lake_\n\nDonald Fagen \u2013 _Nightfly_\n\n**Recommended websites:**\n\nAmur Leopard \u2013 www.altaconservation.org\/amur-leopard\/amur-leopard-factfile\/\n\nWWF (World Wide Fund for Nature) www.worldwildlife.org\n\nwwf.panda.org\n\nIUCN (International Union for Conservation of Nature) www.iucnredlist.org\n\nZSL (Zoological Society of London) www.zsl.org\n\nThe Nature Conservancy www.nature.org\n\nWildlife Conservation Society www.wcs.org\n\nWildAid www.wildaid.org\n\nWildlife Conservation Network www.wildnet.org\n\nDurrell Wildlife Conservation Trust www.durrell.org\n\nMarine Conservation Society www.mcsuk.org\n\nThe Black Fish www.theblackfish.org\n\nEnvironmental Investigation Agency www.eia-international.org\n\nFauna & Flora International www.fauna-flora.org\n\nConservation International www.conservation.org\n\nUnited for Wildlife www.unitedforwildlife.org\n\nAmur Leopard & Tiger Alliance www.altaconservation.org\n\nIguana Specialist Group www.iucn-isg.org\n\nSave the Rhino www.savetherhino.org\n\nGorillas - The Gorilla Organization www.gorillas.org\n\nInternational Gorilla Conservation Programme www.igcp.org\n\nTurtle Conservancy www.turtleconservancy.org\n\nOrangutan Foundation www.orangutan.org.uk\n\nIUCN SSC Pangolin Specialist Group www.pangolinsg.org\n\nWhales and Dolphins www.whales.org\n\nHector's Dolphin www.whaledolphintrust.org.nz\/projects\/hectors-dolphins\/\n\nAfrican Conservation Foundation www.africanconservation.org\n\nInternational Fund for Animal Welfare www.ifaw.org\/\n\nSave the Elephants www.savetheelephants.org\n\nBonobo Conservation Initiative www.bonobo.org\n\nSaiga Conservation Alliance www.saiga-conservation.org\n\nThe Wombat Foundation www.wombatfoundation.com.au\n\nAngel Shark Project www.angelsharkproject.com\n\nRed Wolf Coalition www.redwolves.com\n\nBorn Free Foundation www.bornfree.org.uk\n\nSave The Tiger Fund + Panthera www.panthera.org\/initiative\/save-tiger-fund\n\nSnow Leopard Trust www.snowleopard.org\n\nGalapagos Conservation Trust www.galapagosconservation.org.uk\n\nLemur Conservation Network www.lemurconservationnetwork.org\n\nRoyal Botanic Gardens, Kew www.kew.org\n\nShark Trust www.sharktrust.org\n\nBumblebee Conservation Trust www.bumblebeeconservation.org\n\nAustralian Wildlife Conservancy www.australianwildlife.org\n\nBuglife www.buglife.org.uk\n\nAmphibian Survival Alliance www.amphibians.org\n\nButterfly Conservation www.butterfly-conservation.org\nBloomsbury Natural History\n\nAn imprint of Bloomsbury Publishing Plc\n\n50 Bedford Square | 1385 Broadway  \n---|---  \nLondon | New York  \nWC1B 3DP | NY 10018  \nUK | USA\n\nwww.bloomsbury.com\n\nThis electronic edition published in 2017 by Bloomsbury Publishing Plc\n\nBLOOMSBURY and the Diana logo are trademarks of Bloomsbury Publishing Plc\n\nFirst published 2017\n\nCopyright \u00a9 illustrations by Ralph Steadman, 2017\n\nCopyright \u00a9 text by Ceri Levy, 2017\n\nRalph Steadman and Ceri Levy have asserted their right under the Copyright, Designs and Patents Act, 1988, to be identified as Authors of this work.\n\nAll rights reserved  \nYou may not copy, distribute, transmit, reproduce or otherwise make available this publication (or any part of it) in any form, or by any means (including without limitation electronic, digital, optical, mechanical, photocopying, printing, recording or otherwise), without the prior written permission of the publisher. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages.\n\nNo responsibility for loss caused to any individual or organization acting on or refraining from action as a result of the material in this publication can be accepted by Bloomsbury or the author.\n\nBritish Library Cataloguing-in-Publication Data\n\nA catalogue record for this book is available from the British Library.\n\nLibrary of Congress Cataloguing-in-Publication data has been applied for.\n\nISBN: 978-1-4729-3671-4 (HB)  \nISBN: 978-1-4729-3673-8 (eBook)  \nISBN: 978-1-4729-3672-1 (ePDF)\n\nDesigned in UK by Julie Dando, Fluke Art\n\nTo find out more about our authors and their books please visit www.bloomsbury.com where you will find extracts, author interviews and details of forthcoming events, and to be the first to hear about latest releases and special offers, sign up for our newsletters.\n\n#\n\n  1. Cover\n  2. Title Page\n  3. Contents\n  4. Gin Martini Calls\n  5. How to Value a Species and Why We Should Care\n  6. Creating a Synopsis\n  7. Woolly Mammoth\n  8. Ralph emails: Anyway - starting is necessary...\n  9. Foreword\n  10. Humphead Wrasse\n  11. Singapore Freshwater Crab\n  12. Grunting Spiked Turt\n  13. Amur Leopard\n  14. Invasion of the Gonzovationists\n  15. Groglick\n  16. Red Wowlet\n  17. Jamaican Iguana\n  18. Sumatran Rhinoceros\n  19. Mountain Gorilla\n  20. Hawksbill Turtle\n  21. Bornean Orangutan\n  22. Sumatran Orangutan\n  23. Chinese Pangolin\n  24. Sunda Pangolin\n  25. Pygmy Tarsier\n  26. Maned Three-toed Sloth\n  27. The Visitation\n  28. Hector's Dolphin\n  29. Hippopotamus\n  30. Irrawaddy Dolphin\n  31. African Elephant\n  32. Asian Elephant\n  33. Bonobo\n  34. Saiga Antelope\n  35. Northern Hairy-nosed Wombat\n  36. Angelshark\n  37. Pygmy Three-toed Sloth\n  38. Tarzan's Chameleon\n  39. Black-footed Ferret\n  40. Przewalski's Horse\n  41. Striped Spirit Wint\n  42. Cuban Crocodile\n  43. Kanab Ambersnail\n  44. Pool-strutting Monkeychick\n  45. Philippine Crocodile\n  46. Seychelles Sheath-tailed Bat\n  47. Digg Soiler\n  48. Dratsab\n  49. White Rhinoceros\n  50. Atlantic Bluefin Tuna\n  51. Southern Bluefin Tuna\n  52. Pacific Bluefin Tuna\n  53. Golden-rumped Sengi\n  54. Lord Howe Island Stick Insect\n  55. Luristan Newt\n  56. Rat-arsed Skunk\n  57. Aye-aye\n  58. Baad Guttering\n  59. Gnat Flutterby\n  60. Little Mother Moth\n  61. Red Wolf\n  62. Tiger\n  63. Grevy's Zebra\n  64. Giant Panda\n  65. Borneo Pygmy Elephant\n  66. Snow Leopard\n  67. Chimpanzee\n  68. Terry Cotter - the Island's Potter\n  69. Fin Whale\n  70. Galapagos Sea Lion\n  71. Black Rhinoceros\n  72. Blue Whale\n  73. Golden Bamboo Lemur\n  74. Long-nosed Gwylim\n  75. Black Spider Monkey\n  76. Suicide Palm\n  77. Addax or White Antelope\n  78. African Wild Dog\n  79. Amazonian Manatee\n  80. American Manatee or West Indian Manatee\n  81. African Manatee\n  82. Grey Nurse Shark\n  83. Garden Bumblebee\n  84. Polar Bear\n  85. Articulated Bumlice\n  86. Greek Red Damsel\n  87. Lion\n  88. Hula Painted Frog\n  89. Indri\n  90. Delhi Sands Flower-loving Fly\n  91. Western Long-beaked Echidna\n  92. Eastern Long-beaked Echidna\n  93. Sir David's Long-beaked Echidna\n  94. Visiting the Steadman Uncontinuum\n  95. Mongolian Beaver\n  96. Volcano Rabbit\n  97. African Wild Ass\n  98. Dylis Voryd\n  99. Peacock Parachute Spider\n  100. Saint Lucia Racer\n  101. Indian Python\n  102. Horrid Ground-weaver Spider\n  103. Why-me?\n  104. Skimleach\n  105. Frigate Island Giant Tenebrionid Beetle\n  106. Chinese Giant Salamander\n  107. Vaquita\n  108. Leatherback Sea Turtle\n  109. Red Squirrel\n  110. Saola\n  111. Monarch Butterfly\n  112. Largetooth Sawfish\n  113. Walrus\n  114. White-headed Langur\n  115. Masai Giraffe\n  116. Reticulated Giraffe\n  117. Southern Giraffe\n  118. Northern Giraffe\n  119. Bactrian Camel\n  120. Lemur Leaf Frog\n  121. Dugong\n  122. Western European Hedgehog\n  123. Acknowledgements\n  124. eCopyright\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \n250 Recipes in **15** , **20** , **30** Minutes\n\n# **weightwatchers**\n\n_Cook it Fast_\n\nST. MARTIN'S GRIFFIN   NEW YORK\n\nFour-Vegetable Stir-Fry with Tofu, here\n\nThe author and publisher have provided this e-book to you for your personal use only. You may not make this e-book publicly available in any way. **Copyright infringement is against the law. If you believe the copy of this e-book you are reading infringes on the author's copyright, please notify the publisher at:http:\/\/us.macmillanusa.com\/piracy.**\n\n# About Weight Watchers   \nInternational, Inc.\n\nWeight Watchers International, Inc. is the world's leading provider of weight-management services, operating globally through a network of company-owned and franchise operations. Weight Watchers holds over 40,000 meetings each week where members receive group support and learn about healthful eating patterns, behavior modification, and physical activity. **WeightWatchers.com** provides innovative subscription weight-management products over the Internet and is the leading Internet-based provider of these products in the world. In addition, Weight Watchers offers a wide range of products, publications (including **_Weight Watchers Magazine,_** which is available on newsstands and in Weight Watchers meeting rooms), and programs for those interested in weight loss and weight control. For the Weight Watchers meeting nearest you, call **1-800-651-6000.** For information about bringing Weight Watchers to your workplace, call **1-800-8AT-WORK.**\n\n**Weight Watchers Publishing Group**\n\n_VP, Editorial Director_\n\nTheresa DiMasi\n\n_Creative Director_\n\nEd Melnitsky\n\n_Photo Director_\n\nDeborah Hardt\n\n_Managing Editor_\n\nDiane Pavia\n\n_Assistant Editor_\n\nKaterina Gkionis\n\n_Food Editor_\n\nEileen Runyan\n\n_Editor_\n\nJackie Mills, R.D.N.\n\n_Nutrition Consultant_\n\nU. Beate Krinke\n\n_Photographers_\n\nRita Maas\n\nAlan Richardson\n\n_Food Stylists_\n\nAnne Disrude\n\nMichael Pederson\n\n_Prop Stylists_\n\nCathy Cook\n\nBette Blau\n\nChicken and Napa Cabbage Salad, here\n\n# Contents\n\n_A Quick Note_\n\n_Weight Watchers and the Simply Filling Technique_\n\n44 Recipes That Work with the Simply Filling Technique\n\n_About Our Recipes_\n\n[15 Minute Meals  \n ](part01.xhtml)\n\n15 Minute Breakfasts\n\n15 Minute Lunches\n\n_Buy Some Time_\n\n15 Minute Dinners\n\n15 Minute Snacks and Sweets\n\n_Organize Your Kitchen for Speed_\n\n[20 Minute Meals  \n ](part02.xhtml)\n\n20 Minute Breakfasts\n\n20 Minute Lunches\n\n_9 Rules for Shortcut Cooking_\n\n20 Minute Dinners\n\n_Got 5 Minutes?_\n\n_10 Essential Kitchen Time-Savers_\n\n20 Minute Snacks and Sweets\n\n[30 Minute Meals  \n ](part03.xhtml)\n\n30 Minute Breakfasts\n\n30 Minute Lunches\n\n_Express Shopping_\n\n30 Minute Dinners\n\n_You_ Can _Make It Quick_\n\n_7 Superfast Sides_\n\n30 Minute Snacks and Sweets\n\n[Bonus\u2013On the Weekend  \n ](part04.xhtml)\n\nSpend Some Time\n\n_Time Well Spent_\n\nSlow Cookers Save Time\n\nSomething Sweet\n\n_Life's Too Short to Make_\n\n_Recipes by ** _PointsPlus_** \u00ae value_\n\n_Index_\n\n# A Quick Note\n\nAdmit it. There's something thrilling about serving up a delicious, home-cooked meal in 15, 20, or 30 minutes flat. Lucky then that, in this book, you'll find dozens of dishes and lots of clever tricks and shortcuts that will help you do just that.\n\nBecause we want you to cook. It's healthier, it's usually less expensive, and you'll feel a sense of accomplishment and delight in knowing you created something delectable in a snap. There's nothing more enjoyable than gathering your family and friends around a table and serving a fresh-from-the-oven roast, a nourishing soup, or a scrumptious pie. Why deny yourself these pleasures?\n\nThe difficulty is we lead busy lives, so it's easier to order in or go out to restaurants rather than make ourselves something wonderful and comforting to eat. Those options are okay once in a while; we're not saying you have to cook every single meal. But we do think that when you see how easy it is to do you'll find it a viable and healthier alternative to dining out.\n\nTo make cooking fast and fuss-free, we've carefully written each recipe so it's easy to follow, with few ingredients and short, precise steps\u2014no previous cooking knowledge needed. Turn the page and you'll discover meals that will satisfy a variety of tastes from many cultures and countries. We've included Weight Watchers member favorites, recipes we know are crowd-pleasers, and meals we've made time and time again for our own families and friends. In short, we've assembled our greatest hits and hope these recipes will become your greatest hits, too.\n\nFor the weekends when you opt for leisure over pace, we've included a chapter devoted to dishes that take a little longer to prepare\u2014restorative, comforting, toothsome concoctions\u2014but are still uncomplicated, including slow-cooker meals that let you relax while dinner cooks itself. Many of these dishes serve six or eight, so you can use them when you entertain or have enough leftovers for an effortless meal later in the week.\n\nIn addition to great recipes, you'll find tips for decluttering and organizing your kitchen, menu planning, and buying the best time-saving tools. We talk about shopping for quality ingredients because starting with fresh, seasonal produce means you get maximum flavor minus the fuss. We tell you which kitchen tasks are worth the time (like maintaining your quick-meal pantry) and which are not (who has time to make homemade pasta?). We also give you our take on which convenience products to invest in and absolutely essential canned goods to keep on hand.\n\nWeight Watchers wants to make it easy for you to enjoy delicious, satisfying meals that don't sacrifice flavor\u2014or use too many **_PointsPlus_** \u00ae values. With this indispensible cookbook, you'll gain confidence in the kitchen, and the pleasure of knowing your family will be eating nourishing, healthy food. Meanwhile, you still get \"me\" time at the end of the day and extra hours to spend with the people you love. So go ahead\u2014throw away those takeout menus and start cooking fresh food, fast!\n\n\u2014Theresa DiMasi\n\nEditor in Chief \/ VP, Content\n\nGrilled Salmon with Quick Tomato Tapenade, here\n\nSliced Steak with Crispy Polenta, here\n\n# Weight Watchers and   \nthe Simply Filling Technique\n\nWeight Watchers is with you\u2014and for you\u2014all the way to your weight goal. Our meetings provide support, motivation, and accountability. Our digital tools for subscribers include access to a robust suite of apps for iOS and Android devices, and provide access to our considerable database of foods and their **_PointsPlus_** values; a barcode scanner app; great community features; thousands of recipes; interactive cheat sheets; videos; articles and more. All these products are designed to help you toward your goal.\n\nWe created the Simply Filling technique for those times when you don't want to track your **_PointsPlus_** values against your budget. To follow it, just eat from the list of satisfying Weight Watchers Power Foods\u00ae (they're the foods that help fill you up faster and stay full longer, plus they deliver more nutrients for the **_PointsPlus_** value). Bonus: You don't need to track any of them! Or, enjoy the fact that we've taken the work out of it for you and pick from the list of recipes below that follow Simply Filling:\n\n44 Recipes That Work with the Simply Filling Technique\n\n15 MINUTE MEALS\n\n**_15 Minute Breakfasts_**\n\nProven\u00e7al Omelette\n\n**_15 Minute Lunches_**\n\nHam and Swiss Panini\n\nTropical Turkey Salad\n\nFruity Chicken Salad\n\n**_15 Minute Dinners_**\n\nHerb-Crusted Filets Mignons\n\nAfrican-Spiced Turkey and Squash Stew\n\nGrilled Ginger Chicken with Peach Salsa\n\nHalibut with Salsa Verde\n\nThai Shrimp and Melon Salad\n\n**_15 Minute Snacks and Sweets_**\n\nChili-Spiced Popcorn\n\n20 MINUTE MEALS\n\n**_20 Minute Breakfasts_**\n\nCorn and Green Chile Frittata\n\nBell Pepper and Sun-Dried Tomato Omelette\n\nHash Brown and Egg Skillet Breakfast\n\nBreakfast Bruschetta\n\n**_20 Minute Lunches_**\n\nGingery Turkey-Couscous Salad\n\nTuna and White Bean Salad\n\n**_20 Minute Dinners_**\n\nCod with Tomato-Oregano Sauce\n\nBlackened Scallops with Lemon-Caper Mayonnaise\n\n**_20 Minute Snacks and Sweets_**\n\nBlack Bean-Tomatillo Dip\n\n30 MINUTE MEALS\n\n**_30 Minute Breakfasts_**\n\nSpanish Frittata\n\nSpice-Roasted Pears with Yogurt\n\n**_30 Minute Lunches_**\n\nBeef and Black Bean Burgers\n\nAsian-Style Pork, Mushroom, and Noodle Soup\n\nEdamame Salad with Basil Vinaigrette\n\nTabbouleh with Shrimp\n\nHearty Lentil Salad with Radicchio\n\n**_30 Minute Dinners_**\n\nSliced Steak with Crispy Polenta\n\nFlank Steak with Tomato-Fennel Salad\n\nHearty Steak and Vegetables\n\nSpaghetti with Quick Bolognese Sauce\n\nStir-Fried Beef with Asparagus\n\nRoast Pork Tenderloin with Black Bean Salsa\n\nSaucy Pan-Roasted Pork Chops with Ziti\n\nMinted Lamb Chops with Lemony Bulgur\n\nGrilled Lamb Chops and Asparagus with Lemon-Garlic Mayonnaise\n\nQuick Chicken Satay with Asparagus\n\nTeriyaki-Glazed Tofu and Vegetable Kebabs\n\nChunky Vegetable Paella\n\n**_30 Minute Snacks and Sweets_**\n\nBlueberries with Whipped Ricotta and Balsamic Syrup\n\nBONUS\u2014ON THE WEEKEND\n\n**_Spend Some Time_**\n\nCuban-Style Shredded Beef and Rice\n\nStuffed Butterflied Leg of Lamb\n\nSpaghetti with Fresh Tomato Sauce and Meatballs\n\n**_Slow Cookers Save Time_**\n\nLamb and Vegetable Stew\n\nChicken and Vegetable Curry\n\nSpaghetti with Fresh Tomato Sauce and Meatballs, here\n\nShrimp Salad with Fennel, Red Onion, and Orange, here\n\n# About Our Recipes\n\nWhile losing weight isn't only about what you eat, Weight Watchers realizes the critical role it plays in your success and overall good health. That's why our philosophy is to offer simple, straightforward recipes that are nutritious as well as delicious. We make every attempt to use wholesome ingredients and to ensure that our recipes fall within the recommendations of the U.S. Dietary Guidelines for Americans for a diet that promotes health and reduces the risk for disease. If you have special dietary needs, consult with your health-care professional for advice on a diet that is best for you, then adapt these recipes to meet your specific nutritional needs.\n\nTo achieve these good-health goals and get the maximum satisfaction from the foods you eat, we suggest you keep the following information in mind while preparing our recipes.\n\nGet Started, Keep Going, and Enjoy Good Nutrition\n\n\u2022 Recipes in this book have been developed for Weight Watchers members who are just getting started and for members who are further along toward their goals, including those who are using our **_PointsPlus_** plan, as well as anyone else interested in smart weight loss.\n\n\u2022 **_PointsPlus_** values are given for each recipe. They're assigned based on the amount of protein, carbohydrates, fat, and fiber contained in a single serving of a recipe.\n\n\u2022 Recipes include approximate nutritional information: they are analyzed for Calories (Cal), Total Fat, Saturated Fat (Sat Fat), Trans Fat, Cholesterol (Chol), Sodium (Sod), Total Carbohydrate (Carb), Dietary Fiber (Fib), Protein (Prot), and Calcium (Calc). The value provided for Total Carb includes sugars, starches, and fiber. The nutritional values are calculated by registered dietitians, using nutrition analysis software.\n\n\u2022 Substitutions made to the ingredients will alter the per-serving nutritional information and may affect the **_PointsPlus_** value.\n\n\u2022 Our recipes meet Weight Watchers Good Health Guidelines for eating lean proteins and fiber-rich whole grains and for having at least five servings of vegetables and fruits and two servings of low-fat or fat-free dairy products a day, while limiting your intake of saturated fat, sugar, and sodium.\n\n\u2022 Health agencies recommend limiting sodium intake. To stay in line with this recommendation, we keep sodium levels in our recipes reasonably low; to boost flavor, we often include fresh herbs or a squeeze of citrus instead of salt. If you don't have to restrict your sodium, feel free to add a touch more salt as desired.\n\n\u2022 Cook's Note suggestions have a **_PointsPlus_** value of **_0_** unless otherwise stated.\n\n\u2022 Recipes that work with the Simply Filling technique are listed here. Find more details about the Simply Filling technique at your meeting.\n\n\u2022 For information about the science behind lasting weight loss and more, please visit **WeightWatchers.com\/science.**\n\n**_PointsPlus_** value not what you expected?\n\n\u2022 You might expect some of the **_PointsPlus_** values in this book to be lower when some of the foods they're made from, such as fruits and vegetables, have no **_PointsPlus_** values. Most fruits and veggies have no **_PointsPlus_** values when served as a snack or part of a meal, like a cup of berries with a sandwich. But if these foods are part of a recipe, their fiber and nutrient content are incorporated into the recipe calculations. These nutrients can affect the **_PointsPlus_ **value.\n\n\u2022 Alcohol is included in our **_PointsPlus_** calculations. Because alcohol information is generally not included on nutrition labels, it's not an option to include when using the hand calculator or the online calculator. But since we include alcohol information that we get from our nutritionists, you might notice discrepancies between the **_PointsPlus_** values you see in our recipes, and the values you get using the calculator. The **_PointsPlus_** values listed for our recipes are the most accurate values.\n\nShopping for Ingredients\n\nAs you learn to eat healthier and add more Power Foods to your meals, consider the following to help you choose foods wisely:\n\n**Lean Meats and Poultry.** Purchase lean meats and poultry, and trim them of all visible fat before cooking. When poultry is cooked with the skin on, we recommend removing the skin before eating. Nutritional information for recipes that include meat, poultry, and fish is based on cooked, skinless, boneless portions (unless otherwise stated), with the fat trimmed.\n\n**Seafood.** Whenever possible, our recipes call for seafood that is sustainable and deemed the most healthful for human consumption so that your choice of seafood is not only good for the oceans but also good for you. For more information about the best seafood choices and to download a pocket guide, go to **environmentaldefensefund.org** or **montereybayaquarium.org.** For information about mercury and seafood go to **weightwatchers.com.**\n\n**Produce.** For best flavor, maximum nutrient content, and the lowest prices, buy fresh local produce, such as vegetables, leafy greens, and fruits, in season. Rinse them thoroughly before using, and keep a supply of cut-up vegetables and fruits in your refrigerator for convenient healthy snacks.\n\n**Whole Grains.** Explore your market for whole-grain products such as whole wheat and whole-grain breads and pastas, brown rice, bulgur, barley, cornmeal, whole wheat couscous, oats, and quinoa to enjoy with your meals.\n\nPreparation and Measuring\n\n**Read the Recipe.** Take a couple of minutes to read through the ingredients and directions before you start to prepare a recipe. This will prevent you from discovering midway through that you don't have an important ingredient or that a recipe requires several hours of marinating. And it's also a good idea to assemble all ingredients and utensils within easy reach before you begin a recipe.\n\n**Weighing and Measuring.** The success of any recipe depends on accurate weighing and measuring. The effectiveness of the Weight Watchers Program and the accuracy of the nutritional analysis depend on correct measuring as well. Use the following techniques:\n\n\u2022 Weigh foods such as meat, poultry, and fish on a food scale.\n\n\u2022 To measure liquids, use a standard glass or plastic measuring cup placed on a level surface. For amounts less than \u00bc cup, use standard measuring spoons.\n\n\u2022 To measure dry ingredients, use metal or plastic measuring cups that come in \u00bc-, \u2153-, \u00bd-, and 1-cup sizes. Fill the appropriate cup, and level it with the flat edge of a knife or spatula. For amounts less than \u00bc cup, use standard measuring spoons.\n\n# **15**  \nMinute meals\n\n15 Minute Breakfasts\n\nSpinach-Feta Scramble\n\nAsparagus and Chive Omelette\n\nProven\u00e7al Omelette\n\nVeggie Breakfast Burrito\n\nSouthwestern-Style Huevos Rancheros\n\nBacon, Cheddar, and Egg-Topped English Muffins\n\nWaffles with Blueberries and Maple Cream\n\nCinnamon French Toast\n\nBreakfast Berry Parfaits\n\nMorning Chai\n\nPeanut Butter Blast\n\nSoy-Blueberry Breakfast Shake\n\n15 Minute Lunches\n\nHam and Swiss Panini\n\nChicken and Roasted Pepper Sandwiches\n\nGrilled Chicken and Jack Cheese Sandwiches\n\nTurkey Wraps with Lemon-Yogurt Sauce\n\nAsian-Style Duck Roll-Ups\n\nSalmon Salad Sandwich\n\nQuick Turkey Tostadas\n\nCilantro-Lime Shrimp Salad Pitas\n\nCalifornia Health Sandwiches\n\nBest BLTs\n\nAvocado, Spinach, and Feta Wrap\n\nHam and Navy Bean Confetti Soup\n\nWinter Squash Soup with Lime Cream\n\nSouthern Vegetable Gumbo\n\nRoast Beef Salad with Creamy Horseradish Dressing\n\nMexicali Chicken Salad\n\nGreek-Style Chicken Salad\n\nTropical Turkey Salad\n\nFruity Chicken Salad\n\nChicken Salad with Fennel, Arugula, and Blue Cheese\n\nChinese Chicken Slaw\n\nKey West-Style Shrimp Salad\n\n15 Minute Dinners\n\nMaple and Chili-Broiled T-Bone Steaks\n\nFilets Mignons with Cauliflower Puree\n\nHerb-Crusted Filets Mignons\n\nCaesar-Style Steak Salad\n\nGrilled Citrus Pork with Cucumber-Orange Salad\n\nLamb and Onion Kebabs with Mint\n\nSuperfast Barbecued Chicken\n\nEasy Chicken Cutlets Parmesan\n\nTurkey Cutlets with Mushroom-Wine Sauce\n\nGrilled Chicken Salad with Raspberries and Goat Cheese\n\nAfrican-Spiced Turkey and Squash Stew\n\nGrilled Ginger Chicken with Peach Salsa\n\nGrilled Salmon with Quick Tomato Tapenade\n\nSalmon au Poivre with Watercress\n\nTuna Steaks with Avocado-Orange Relish\n\nHalibut with Salsa Verde\n\nRoast Halibut with Chunky Roasted Pepper Sauce\n\nThai Shrimp and Melon Salad\n\nSesame Scallops\n\nSesame Noodles with Green Vegetables\n\n15 Minute Snacks and Sweets\n\nCottage Cheese and Sun-Dried Tomato Dip\n\nDried Cranberry-Popcorn Mix\n\nChili-Spiced Popcorn\n\nOpen-Faced Roast Beef Sandwich Bites\n\nTurkey and Roasted Pepper Lettuce Wraps\n\nVanilla Yogurt Sundae\n\nMixed Melon with Honeyed Ricotta\n\nHoneydew-Strawberry Soup\n\nPineapple Crush Smoothies\n\nStrawberry Colada Cooler\n\n# breakfasts\n\n# Spinach-Feta Scramble\n\nSERVES 1\n\n**1 large egg**\n\n**3 large egg whites**\n\n**1 cup lightly packed baby spinach**\n\n**2 tablespoons crumbled reduced-fat feta cheese**\n\n**\u00bc teaspoon black pepper**\n\n**1 teaspoon canola or olive oil**\n\n1. Whisk together egg and egg whites in medium bowl. Stir in spinach, feta, and pepper.\n\n2. Heat oil in medium nonstick skillet over medium heat. Pour in egg mixture and cook, stirring, until eggs are set and cheese is slightly melted, about 3 minutes.\n\n**PER SERVING** (1 plate): 197 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 218 mg Chol, 432 mg Sod, 4 g Total Carb, 1 g Fib, 20 g Prot, 66 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Asparagus and Chive Omelette\n\nSERVES 1\n\n**\u00bd cup fat-free egg substitute**\n\n**\u215b teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n**1 teaspoon canola oil**\n\n**2 tablespoons shredded low-fat Swiss cheese**\n\n**\u00bc cup frozen chopped asparagus, thawed**\n\n**\u00bc cup frozen peas, thawed**\n\n**\u00bc cup chopped red bell pepper**\n\n**2 tablespoons chopped fresh chives or scallions**\n\n1. Whisk together egg substitute, salt, and black pepper in medium bowl.\n\n2. Heat oil in medium nonstick skillet over medium heat. Add egg mixture and cook, stirring gently, until underside is set, about 1 minute.\n\n3. Sprinkle Swiss, asparagus, peas, and bell pepper over half of omelette. Fold unfilled half of omelette over to enclose filling. Cook until cheese is melted, about 2 minutes.\n\n4. Slide omelette onto plate and sprinkle with chives.\n\n**PER SERVING** (1 omelette): 181 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 5 mg Chol, 615 mg Sod, 13 g Total Carb, 4 g Fib, 20 g Prot, 206 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\n# Proven\u00e7al Omelette\n\nSERVES 2\n\n**2 large eggs**\n\n**2 large egg whites**\n\n**1 tablespoon fat-free half-and-half**\n\n**\u00bc teaspoon salt**\n\n**\u00bd teaspoon herbes de Provence**\n\n**1 teaspoon olive oil**\n\n**\u00bd cup grape tomatoes, halved**\n\n**\u00bc cup shredded fat-free Cheddar cheese**\n\n**Chopped fresh parsley**\n\n**2 slices reduced-calorie whole wheat bread, toasted**\n\n1. Whisk together eggs, egg whites, half-and-half, salt, and herbes de Provence in medium bowl.\n\n2. Heat oil in medium nonstick skillet over medium heat. Add egg mixture and cook, stirring gently with heatproof rubber spatula, until underside is set, about 2 minutes.\n\n3. Sprinkle tomatoes and Cheddar evenly over half of omelette. Fold unfilled half of omelette over filling and continue to cook until eggs are set, about 1 minute longer.\n\n4. Slide omelette onto plate and cut in half; sprinkle with parsley. Serve with toast.\n\n**PER SERVING** (\u00bd omelette and 1 slice toast): 213 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 215 mg Chol, 745 mg Sod, 18 g Total Carb, 4 g Fib, 17 g Prot, 188 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nTo dress up the plates and make a delicious partner for the omelette, serve fresh berries in small clear dishes alongside.\n\nProven\u00e7al Omelette\n\n# Veggie Breakfast Burrito\n\nSERVES 1\n\n**\u00bd cup fat-free egg substitute**\n\n**\u215b teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n**1 teaspoon canola oil**\n\n**1 (7-inch) whole wheat tortilla, warmed**\n\n**3 tablespoons shredded fat-free Cheddar cheese**\n\n**\u00bd small tomato, chopped**\n\n**\u00bc cup diced green bell pepper**\n\n**2 scallions, thinly sliced**\n\n1. Whisk together egg substitute, salt, and black pepper in small bowl.\n\n2. Heat oil in medium nonstick skillet over medium heat. Add eggs to skillet and cook, stirring, until just set, about 2 minutes.\n\n3. Place tortilla on plate and top with egg mixture. Top with Cheddar, tomato, bell pepper, and scallions. Roll up tortilla to enclose filling.\n\n**PER SERVING** (1 burrito): 233 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 4 mg Chol, 923 mg Sod, 29 g Total Carb, 4 g Fib, 23 g Prot, 263 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Southwestern-Style Huevos Rancheros\n\nSERVES 1\n\n**\u00bc teaspoon canola oil**\n\n**2 scallions, thinly sliced**\n\n**1 large egg**\n\n**3 large egg whites**\n\n**\u00bc teaspoon chili powder**\n\n**\u00bc cup shredded fat-free Cheddar cheese**\n\n**1 (6-inch) corn tortilla, warmed**\n\n**3 tablespoons fat-free salsa**\n\n1. Coat small nonstick skillet with oil and set over medium heat. Add scallions and cook, stirring frequently, just until softened, about 2 minutes.\n\n2. Whisk together egg, egg whites, and chili powder in medium bowl. Pour mixture into skillet and add Cheddar. Cook, stirring, until eggs are set and cheese is melted, about 2 minutes.\n\n3. Spoon eggs onto tortilla and top with salsa.\n\n**PER SERVING** (1 filled tortilla): 272 Cal, 7 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 218 mg Chol, 835 mg Sod, 23 g Total Carb, 2 g Fib, 29 g Prot, 376 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nBacon, Cheddar, and Egg-Topped English Muffins\n\n# Bacon, Cheddar, and Egg-Topped English Muffins\n\nSERVES 2\n\n**2 large eggs**\n\n**1 teaspoon canola oil**\n\n**2 (1-ounce) slices Canadian bacon**\n\n**1 whole wheat English muffin, split and toasted**\n\n**2 (\u00be-ounce) slices fat-free Cheddar cheese**\n\n**Snipped fresh chives**\n\n**Black pepper**\n\n1. Fill medium skillet with 1\u00bd inches of water and bring to boil. Reduce heat so water is barely simmering.\n\n2. Break each egg into small cup. Slip eggs, one at time, into water. Cook until yolks just begin to set, about 2 minutes. Using slotted spoon, transfer eggs to paper towels to drain.\n\n3. Pour out water and wipe out skillet. Add oil to skillet and set over medium-high heat. Add Canadian bacon and cook until heated through, about 1\u00bd minutes on each side.\n\n4. Place muffin half on each of 2 plates and top each with slice of Cheddar. Top each with 1 slice of bacon and 1 egg. Sprinkle with chives and pepper.\n\n**PER SERVING** (1 topped muffin half): 243 Cal, 10 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 230 mg Chol, 877 mg Sod, 17 g Total Carb, 2 g Fib, 20 g Prot, 265 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nTop each muffin half with a tomato slice or a few slices of roasted red bell pepper (not oil-packed) before adding the Cheddar, bacon, and egg.\n\n# Waffles with Blueberries and Maple Cream\n\nSERVES 4\n\n**2 cups fat-free ricotta cheese**\n\n**\u00bc cup maple syrup**\n\n**\u00bd teaspoon cinnamon**\n\n**\u215b teaspoon ground nutmeg**\n\n**4 frozen (4-inch) low-fat whole wheat waffles, toasted**\n\n**1 pint blueberries**\n\n**\u00bc cup pecans, chopped**\n\n1. Stir together ricotta, maple syrup, cinnamon, and nutmeg in small bowl.\n\n2. Place waffles on plates and top evenly with ricotta mixture. Sprinkle evenly with blueberries and pecans.\n\n**PER SERVING** (1 waffle, \u00bd cup blueberries, and 1 tablespoon pecans): 322 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 12 mg Chol, 322 mg Sod, 48 g Total Carb, 4 g Fib, 20 g Prot, 278 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nThis sweet-spiced ricotta topping is a snap to make and adds a homemade touch to frozen waffles. Substitute any fresh fruit in season for the blueberries and any nuts that you have on hand for the pecans.\n\n# Cinnamon French Toast\n\nSERVES 4\n\n**2 cups fat-free egg substitute**\n\n**\u00bc cup fat-free milk**\n\n**1 teaspoon cinnamon**\n\n**\u00bd teaspoon vanilla extract**\n\n**8 slices whole wheat bread**\n\n**\u00bd teaspoon canola oil**\n\n**\u00bd cup reduced-calorie pancake syrup, warmed**\n\n1. Whisk together egg substitute, milk, cinnamon, and vanilla in large shallow bowl or pie plate. Dip bread into egg mixture, one slice at a time, until evenly soaked.\n\n2. Coat large nonstick skillet with oil and set over medium heat. Add soaked bread to skillet, in batches, and cook until browned, about 2 minutes on each side.\n\n3. Transfer French toast to plates and serve with warm syrup.\n\n**PER SERVING** (2 slices toast and 2 tablespoons syrup): 263 Cal, 2 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 575 mg Sod, 42 g Total Carb, 5 g Fib, 20 g Prot, 287 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\n# Breakfast Berry Parfaits\n\nSERVES 2\n\n**8 strawberries, hulled and sliced**\n\n**1 cup vanilla low-fat yogurt**\n\n**2 tablespoons granola**\n\n**1 banana, peeled and sliced**\n\n**\u00bd cup blueberries**\n\nDivide strawberries evenly among 2 parfait glasses; top each with \u00bc cup of yogurt. Top evenly with granola, then with remaining yogurt, banana slices, and blueberries.\n\n**PER SERVING** (1 parfait): 213 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 6 mg Chol, 91 mg Sod, 42 g Total Carb, 4 g Fib, 8 g Prot, 226 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nDo it Faster\n\nNo time to eat breakfast? Layer a parfait in a small plastic container and take it to work to eat at your desk.\n\n# Morning Chai\n\nSERVES 4\n\n**4 cups cold water**\n\n**5 regular or decaffeinated black tea bags**\n\n**1 (3-inch) cinnamon stick, broken in half**\n\n**8 whole cardamom pods, crushed**\n\n**12 whole black peppercorns**\n\n**1\u00bd cups vanilla soy milk**\n\nCombine all ingredients except milk in large saucepan and bring to boil. Reduce heat and simmer 5 minutes. Stir in soy milk and cook, stirring, just until heated through, about 1 minute. Pour through sieve into cups or mugs.\n\n**PER SERVING** (1 cup): 63 Cal, 2 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 60 mg Sod, 10 g Total Carb, 1 g Fib, 3 g Prot, 118 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nIf soy milk is not your favorite, chai, a traditional spiced tea drink from southern India, is a delicious way to incorporate soy into your diet. If you prefer it cold, you can let the chai cool slightly, and then serve over ice.\n\n# Peanut Butter Blast\n\nSERVES 1\n\n**1 small banana**\n\n**\u00bd cup vanilla fat-free yogurt**\n\n**\u00bd cup fat-free milk**\n\n**1 tablespoon creamy peanut butter**\n\n**\u00bc teaspoon vanilla extract**\n\n**Pinch cinnamon**\n\nCombine all ingredients except cinnamon in blender and process until smooth. Pour into tall glass and sprinkle with cinnamon.\n\n**PER SERVING** (about 1 cup): 328 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 5 mg Chol, 190 mg Sod, 53 g Total Carb, 6 g Fib, 14 g Prot, 356 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\n# Soy-Blueberry Breakfast Shake\n\nSERVES 1\n\n**1 cup calcium-fortified plain fat-free soy milk**\n\n**1 cup frozen unsweetened blueberries**\n\n**\u00bd banana**\n\n**2 teaspoons honey**\n\n**1 teaspoon vanilla extract**\n\nCombine all ingredients in blender and process until smooth. Pour into tall glass.\n\n**PER SERVING** (2 cups): 296 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 62 mg Sod, 67 g Total Carb, 7 g Fib, 7 g Prot, 413 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\n# lunches\n\n# Ham and Swiss Panini\n\nSERVES 2\n\n**4 slices reduced-calorie whole wheat bread**\n\n**6 (1-ounce) slices lean reduced-sodium ham**\n\n**2 slices fat-free Swiss cheese**\n\n1. Spray ridged grill pan with nonstick spray and set over medium-high heat or heat panini sandwich maker according to manufacturers' instructions.\n\n2. Top 2 bread slices evenly with ham and Swiss cheese. Top with remaining bread slices. Spray sandwiches lightly with olive oil nonstick spray.\n\n3. Place sandwiches in pan and cover with heavy skillet or place in sandwich maker. Grill until bread is well marked and cheese is melted, about 5 minutes. (Turn sandwiches halfway through cooking time if using grill pan.) Cut in half and serve.\n\n**PER SERVING** (1 sandwich): 203 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 35 mg Chol, 949 mg Sod, 21 g Total Carb, 5 g Fib, 22 g Prot, 223 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nServe these quick and easy sandwiches with Creamy Tomato Soup, here.\n\n# Chicken and Roasted Pepper Sandwiches\n\nSERVES 4\n\n**\u00bc cup light cream cheese (Neufch\u00e2tel), softened**\n\n**2 teaspoons grated lemon zest**\n\n**\u00bd teaspoon Italian seasoning or dried oregano**\n\n**\u00bc teaspoon black pepper**\n\n**8 thin slices whole wheat bread**\n\n**1\u00bd cups shredded skinless deli roast chicken breast**\n\n**\u00bd cup roasted red pepper, thinly sliced (not packed in oil)**\n\n**8 large fresh basil leaves**\n\n1. Stir together cream cheese, lemon zest, Italian seasoning, and black pepper in small bowl. Spread cheese mixture evenly over one side of 4 slices of bread.\n\n2. Top evenly with chicken, roasted red pepper, and basil. Cover with remaining slices of bread. Cut each sandwich in half.\n\n**PER SERVING** (1 sandwich): 246 Cal, 7 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 54 mg Chol, 317 mg Sod, 21 g Total Carb, 4 g Fib, 23 g Prot, 75 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# buy some time\n\nSometimes, paying a little extra for convenience is really worth it. Here are our top picks for saving you 5, 10, or even 15 minutes in the kitchen without sacrificing flavor.\n\n**Save 5 Minutes**\n\n**EGG WHITES.** Buy cartons of refrigerated egg whites from the dairy section of your supermarket. Instead of having to separate eggs for whipping or for omelettes, simply measure out 2 tablespoons for each large white called for.\n\n**PEELED GARLIC.** Use a lot of garlic? Then consider investing in a bag or container of peeled cloves. Look for ivory (not yellowed) cloves with a mild aroma, and they should keep for 1 to 2 weeks in your fridge.\n\n**PITTED OLIVES.** Save yourself the hassle of pitting them yourself by buying good-quality pitted olives. Most olive bars stock a selection of pitted varieties, including Kalamata, Picholine, and other varieties of green olives.\n\n**PRESHREDDED CHEESE.** Quality shredded cheeses are now available in regular, low-fat, and fat-free varieties. Just make sure you use them within a week or so as they tend to lose their freshness faster than chunk cheeses do.\n\n**PREWASHED LETTUCE.** This is the gold standard for quick salads, and new mixes make it a more interesting option than ever. Also look for spinach, arugula, and baby kale for your salads.\n\n**SLICED MUSHROOMS.** Packages of trimmed, cleaned, presliced mushrooms are usually available in a number of varieties: classic button, cremini, shiitake, and mixed exotic.\n\n**Save 10 Minutes**\n\n**FROZEN VEGGIES.** Fresh is often best, but when it comes to making soups and stews frozen veggies are a convenient alternative. Staples like frozen diced onions, bell pepper strips, chopped spinach or collards, and diced potatoes can be a big time-saver.\n\n**MICROWAVE-IN-THE-BAG VEGETABLES.** Nothing beats the convenience of the new crop of vegetables that steam themselves in your microwave in mere minutes. They're already washed, trimmed, and ready to go. Season them to your liking after cooking.\n\n**PEELED SHRIMP.** Sure, they cost a little more, but you'll save a lot of time not having to peel and devein them. You can find peeled shrimp\u2014both fresh and frozen\u2014at most grocery stores.\n\n**PRECUT KALE.** Save time spent rinsing and trimming kale and seek out bags of washed, cut kale in the produce section next to bagged lettuces.\n\n**PRECUT PINEAPPLE.** Look for cored, peeled fresh pineapple in the produce department and say good-bye to wrestling with a spiny whole fruit.\n\n**Save 15 Minutes or More**\n\n**COOKED PEELED BEETS.** The new wave of refrigerated cooked, peeled beets give you great beet flavor and texture along with super convenience. They're perfect for salads, soups, and sides.\n\n**CUT-UP BUTTERNUT SQUASH.** Look for peeled, seeded, and cut butternut squash in the produce section of most supermarkets, and skip laboring over this tough customer.\n\n**FROZEN WHOLE GRAINS.** Brown rice, quinoa, wheat berries, and more are now available in the freezer section of most supermarkets. They're ready after just a few minutes of reheating.\n\n**ROTISSERIE CHICKEN.** Just remove the skin and you'll have healthful servings of roasted chicken for salads, sandwiches, soups, and more.\n\n# Grilled Chicken and Jack Cheese Sandwiches\n\nSERVES 2\n\n**4 slices reduced-calorie whole wheat bread**\n\n**2 teaspoons Dijon mustard**\n\n**6 ounces thinly sliced reduced-sodium deli chicken breast**\n\n**1 small tomato, sliced**\n\n**2 (\u00be-ounce) slices reduced-fat pepper Jack cheese**\n\n1. Spread 2 slices of bread with mustard. Layer evenly with chicken, tomato, and pepper Jack.\n\n2. Top with remaining 2 slices of bread. Spray top slices of bread with olive oil nonstick spray.\n\n3. Heat large nonstick skillet over medium heat. Place sandwiches in skillet, sprayed side down, and cook until lightly browned, about 3 minutes. Spray tops of sandwiches with nonstick spray. Turn and cook until bread is browned and cheese begins to melt, about 3 minutes longer.\n\n**PER SERVING** (1 sandwich): 342 Cal, 11 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 87 mg Chol, 648 mg Sod, 21 g Total Carb, 4 g Fib, 38 g Prot, 220 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\n# Turkey Wraps with Lemon-Yogurt Sauce\n\nSERVES 2\n\n**\u00bd cup plain reduced-fat yogurt**\n\n**2 teaspoons fresh lemon juice**\n\n**\u00bd teaspoon ground cumin**\n\n**\u215b teaspoon cayenne pepper**\n\n**2 (7-inch) whole wheat tortillas**\n\n**\u00bc pound sliced reduced-sodium deli turkey breast**\n\n**2 green leaf lettuce leaves**\n\n**1 tomato, cut into thin wedges**\n\n**\u00bc small red onion, thinly sliced**\n\n1. Stir together yogurt, lemon juice, cumin, and cayenne in small bowl.\n\n2. Top tortillas evenly with turkey, lettuce, tomato, and onion. Drizzle \u00bc cup yogurt sauce over filling. Roll up wraps tightly and drizzle with remaining yogurt sauce.\n\n**PER SERVING** (1 wrap and 2 tablespoons sauce): 224 Cal, 5 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 52 mg Chol, 280 mg Sod, 22 g Total Carb, 4 g Fib, 24 g Prot, 148 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nTurkey Wraps with Lemon-Yogurt Sauce\n\n# Asian-Style Duck Roll-Ups\n\nSERVES 4\n\n**2 cups shredded cooked skinless duck breast or chicken breast**\n\n**\u00bc cup hoisin sauce**\n\n**2 scallions, thinly sliced**\n\n**4 (7-inch) whole wheat tortillas, warmed**\n\n**\u00bd small red bell pepper, thinly sliced**\n\n**8 arugula leaves, trimmed**\n\n1. Stir together duck, hoisin sauce, and scallions in medium bowl.\n\n2. Top tortillas evenly with duck mixture, then with bell pepper and arugula. Roll up tortillas and cut in half.\n\n**PER SERVING** (1 roll-up): 203 Cal, 2 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 59 mg Chol, 554 mg Sod, 22 g Total Carb, 3 g Fib, 24 g Prot, 34 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nPackaged cooked duck breast is found in specialty food stores. If it comes with the skin on, be sure to remove it before shredding the duck.\n\n# Salmon Salad Sandwich\n\nSERVES 2\n\n**1 (7\u00bd-ounce) can salmon, drained and flaked**\n\n**3 tablespoons plain fat-free yogurt**\n\n**\u00bd cup peeled, seeded, and chopped cucumber**\n\n**2 scallions, thinly sliced**\n\n**2 tablespoons chopped fresh dill**\n\n**1 tablespoon capers, drained**\n\n**Grated zest and juice of \u00bd lemon**\n\n**\u00bd (10-ounce) whole wheat baguette**\n\n1. Stir together salmon, yogurt, cucumber, scallions, dill, capers, and lemon zest and juice in medium bowl.\n\n2. Split baguette in half lengthwise and remove soft bready center. Spoon salmon mixture into bottom half of baguette and cover with top of baguette. Cut sandwich in half.\n\n**PER SERVING** (\u00bd sandwich): 321 Cal, 7 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 73 mg Chol, 839 mg Sod, 34 g Total Carb, 6 g Fib, 32 g Prot, 389 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nQuick Turkey Tostadas\n\n# Quick Turkey Tostadas\n\nSERVES 2\n\n**1 teaspoon canola oil**\n\n**2 (6-inch) corn tortillas**\n\n**2 cups thinly sliced romaine lettuce**\n\n**4 (1-ounce) slices low-sodium skinless deli turkey breast or chicken breast, cut into strips**\n\n**2 plum tomatoes, chopped**\n\n**\u00bd avocado, halved, pitted, peeled, and sliced**\n\n**\u00bc cup fat-free ranch dressing**\n\n**\u00bc cup fat-free salsa**\n\n1. Heat oil in small skillet over medium-high heat. Add tortillas to skillet, one at a time, and cook until lightly browned and crisp, about 2 minutes on each side.\n\n2. Place 1 tortilla on each of 2 plates and layer evenly with lettuce, turkey, tomatoes, and avocado.\n\n3. Drizzle dressing evenly over tostadas and serve with salsa.\n\n**PER SERVING** (1 tostada): 271 Cal, 10 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 51 mg Chol, 477 mg Sod, 27 g Total Carb, 6 g Fib, 21 g Prot, 77 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\n# Cilantro-Lime Shrimp Salad Pitas\n\nSERVES 4\n\n**\u00bc cup light mayonnaise**\n\n**\u00bc cup fresh lime juice**\n\n**\u00bc cup chopped fresh cilantro**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd pound frozen cooked medium shrimp, thawed and chopped**\n\n**1 small green bell pepper, chopped**\n\n**1 small red onion, chopped**\n\n**4 (6\u00bd-inch) whole wheat pitas**\n\n**4 green leaf lettuce leaves**\n\n1. Stir together mayonnaise, lime juice, cilantro, and black pepper in large bowl. Add shrimp, bell pepper, and onion to mayonnaise mixture and toss to coat.\n\n2. Cut off top third of each pita and discard. Line each pita with lettuce leaf and fill evenly with shrimp salad.\n\n**PER SERVING** (1 stuffed pita): 230 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 124 mg Chol, 903 mg Sod, 29 g Total Carb, 4 g Fib, 18 g Prot, 74 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# California Health Sandwiches\n\nSERVES 2\n\n**1 cup thinly sliced romaine lettuce**\n\n**\u00bd cup shredded carrot**\n\n**2 tablespoons fat-free Italian dressing**\n\n**2 tablespoons hummus**\n\n**4 slices whole-grain bread, toasted**\n\n**1 tomato, thinly sliced**\n\n**\u00bd small avocado, thinly sliced**\n\n**\u00bc teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n1. Toss together lettuce, carrot, and dressing in small bowl.\n\n2. Spread hummus evenly on 2 slices of bread. Layer evenly with tomato, avocado, and lettuce mixture. Sprinkle with salt and pepper. Top with remaining 2 slices of bread. Cut each sandwich in half.\n\n**PER SERVING** : (1 sandwich): 258 Cal, 9 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 813 mg Sod, 35 g Total Carb, 9 g Fib, 10 g Prot, 101 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Best BLTs\n\nSERVES 2\n\n**4 teaspoons fat-free mayonnaise**\n\n**2 teaspoons basil pesto**\n\n**4 slices whole wheat bread**\n\n**\u00bd cup lightly packed baby arugula**\n\n**\u00bc avocado, halved, pitted, peeled, and thinly sliced**\n\n**1 tomato, sliced**\n\n**6 slices turkey bacon, crisp-cooked**\n\n1. Stir together mayonnaise and pesto in small bowl.\n\n2. Spread mayonnaise mixture evenly on 2 slices of bread. Layer bread evenly with arugula, avocado, tomato, and bacon. Cover sandwiches with remaining slices of bread.\n\n**PER SERVING** (1 sandwich): 280 Cal, 10 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 33 mg Chol, 799 mg Sod, 31 g Total Carb, 5 g Fib, 16 g Prot, 105 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nCook turkey bacon up to several hours ahead and drain on paper towels. When ready to use, microwave on High just until heated through, about 30 seconds.\n\nBest BLTs\n\n# Avocado, Spinach, and Feta Wrap\n\nSERVES 2\n\n**\u00bd avocado, halved, pitted, and peeled**\n\n**\u00bc teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 (10-inch) spinach tortilla wrap**\n\n**1 cup lightly packed baby spinach**\n\n**1 small zucchini, shredded**\n\n**\u00bc cup crumbled fat-free feta cheese**\n\n**1 tablespoon balsamic vinegar**\n\n**1 teaspoon olive oil**\n\nMash together avocado, salt, and pepper in small bowl. Spread mixture evenly on tortilla. Top with spinach, zucchini, and feta; drizzle with vinegar and oil. Roll up tortilla to enclose filling. Cut wrap in half.\n\n**PER SERVING** (\u00bd wrap): 250 Cal, 15 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 13 mg Chol, 577 mg Sod, 26 g Total Carb, 6 g Fib, 7 g Prot, 166 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\n# Ham and Navy Bean Confetti Soup\n\nSERVES 4\n\n**3 cups fat-free reduced-sodium chicken broth**\n\n**6 ounces cooked lower-sodium lean ham, diced**\n\n**1 (15\u00bd-ounce) can no-salt-added navy beans, rinsed and drained**\n\n**1 carrot, shredded**\n\n**1 celery stalk, thinly sliced**\n\n**\u00bd cup diced red bell pepper**\n\n**\u00bd cup frozen chopped onion**\n\n**2 tablespoons chopped fresh parsley**\n\nCombine all ingredients except parsley in medium saucepan; cover and bring to boil. Reduce heat and simmer, covered, until vegetables are tender, about 5 minutes. Stir in parsley just before serving.\n\n**PER SERVING** (1\u2153 cups): 200 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 23 mg Chol, 849 mg Sod, 25 g Total Carb, 9 g Fib, 18 g Prot, 87 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nEnjoy a simple cheese sandwich with this soup to make it a filling meal. Two slices of reduced-calorie whole wheat bread filled with 1 ounce of fat-free Cheddar cheese, tomato slices, and shredded lettuce per serving will increase the **_PointsPlus_** value by **_4._**\n\nWinter Squash Soup with Lime Cream\n\n# Winter Squash Soup with Lime Cream\n\nSERVES 4\n\n**2 (12-ounce) boxes frozen squash puree, thawed**\n\n**2 (14\u00bd-ounce) cans reduced-sodium vegetable or chicken broth**\n\n**1 teaspoon ground cumin**\n\n**\u00bd teaspoon salt**\n\n**3 tablespoons fat-free sour cream**\n\n**Grated zest of 1 lime**\n\n**2 teaspoons fresh lime juice**\n\n**2 teaspoons water**\n\n1. Combine squash, broth, cumin, and salt in medium saucepan; bring to boil over high heat. Reduce heat and simmer 3 minutes.\n\n2. Meanwhile, stir together sour cream, lime zest and juice, and water in small bowl.\n\n3. Divide soup evenly among 4 bowls and drizzle with lime cream.\n\n**PER SERVING** (1\u00bc cups soup and 1 tablespoon lime cream): 91 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 1 mg Chol, 789 mg Sod, 19 g Total Carb, 5 g Fib, 5 g Prot, 77 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nFor a satisfying lunch, serve this quick soup with Hearty Lentil Salad with Radicchio, here.\n\n# Southern Vegetable Gumbo\n\nSERVES 4\n\n**1\u00bd tablespoons unsalted butter**\n\n**2 tablespoons all-purpose flour**\n\n**3 cups reduced-sodium vegetable broth**\n\n**\u00bd pound frozen okra**\n\n**1 cup frozen corn kernels**\n\n**1 cup frozen pearl onions**\n\n**1 (14\u00bd-ounce) can sliced potatoes, drained and rinsed**\n\n**1 (14\u00bd-ounce) can diced tomatoes, drained**\n\n**2 bay leaves**\n\n**Hot pepper sauce**\n\n1. Melt butter in large saucepan over medium-high heat. Stir in flour and cook, stirring constantly, until mixture becomes golden, 1\u20132 minutes. Slowly stir in broth, stirring until mixture is smooth.\n\n2. Add okra, corn, onions, potatoes, tomatoes, and bay leaves. Increase heat to high and cook, stirring occasionally, until gumbo is bubbling and vegetables are heated through, about 8 minutes. Discard bay leaves and serve with pepper sauce on side.\n\n**PER SERVING** (1\u00be cups): 179 Cal, 5 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 11 mg Chol, 574 mg Sod, 33 g Total Carb, 5 g Fib, 4 g Prot, 85 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Roast Beef Salad with Creamy Horseradish Dressing\n\nSERVES 4\n\n**3 tablespoons fat-free mayonnaise**\n\n**3 tablespoons plain fat-free Greek yogurt**\n\n**2 teaspoons bottled horseradish**\n\n**\u00bc teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd pound thinly sliced lean deli roast beef, cut into strips**\n\n**1 small head romaine lettuce, thinly sliced (about 6 cups)**\n\n**1 cup cherry tomatoes, halved**\n\n1. To make dressing, whisk together mayonnaise, yogurt, horseradish, salt, and pepper in serving bowl.\n\n2. Add roast beef, lettuce, and tomatoes to dressing; toss to coat.\n\n**PER SERVING** (about 2 cups): 174 Cal, 9 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 44 mg Chol, 300 mg Sod, 7 g Total Carb, 2 g Fib, 16 g Prot, 58 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\n# Mexicali Chicken Salad\n\nSERVES 4\n\n**\u00be cup fat-free salsa**\n\n**\u00bc cup fat-free ranch dressing**\n\n**1 head romaine lettuce, chopped**\n\n**1 large tomato, diced**\n\n**1 small jicama, peeled and shredded**\n\n**1 cup shredded reduced-fat Monterey Jack or pepper Jack cheese**\n\n**1 cup canned black beans, rinsed and drained**\n\n**\u00bc cup diced sweet onion**\n\n**2 cups diced cooked skinless chicken breast**\n\n**12 baked tortilla chips, broken up**\n\n1. To make dressing, stir together salsa and ranch dressing in large serving bowl. Add lettuce, tomato, jicama, Jack cheese, beans, and onion to bowl and toss to coat.\n\n2. Divide salad evenly among 4 plates. Top salads evenly with chicken and sprinkle with tortilla chips.\n\n**PER SERVING** (3 cups salad, \u00bd cup chicken, and 3 tortilla chips): 384 Cal, 10 g Total Fat, 5 g Sat Fat, 0 g Trans Fat, 80 mg Chol, 980 mg Sod, 38 g Total Carb, 12 g Fib, 37 g Prot, 297 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nMild-tasting sweet onions are fantastic for serving in dishes such as this where the onion is eaten raw. Try Walla Walla, Oso Sweet, or Vidalia onions in your favorite salad recipes.\n\n# Greek-Style Chicken Salad\n\nSERVES 4\n\n**\u00be cup plain fat-free yogurt**\n\n**3 tablespoons chopped fresh mint**\n\n**3 tablespoons chopped fresh dill**\n\n**Grated zest and juice of 1 lemon**\n\n**1 garlic clove, minced**\n\n**2 teaspoons olive oil**\n\n**2 cups diced roasted chicken breast**\n\n**3 cups torn romaine lettuce leaves**\n\n**2 large tomatoes, cut into wedges**\n\n**1 cucumber, peeled, seeded, and diced**\n\n**\u00bd cup chopped red onion**\n\n**8 pitted Kalamata olives, coarsely chopped**\n\n**\u00bd cup crumbled fat-free feta cheese**\n\n1. To make dressing, whisk together yogurt, mint, dill, lemon zest and juice, garlic, and oil in small bowl.\n\n2. Toss together chicken, lettuce, tomatoes, cucumber, and onion in serving bowl. Drizzle dressing over salad and toss to coat. Sprinkle with olives and feta.\n\n**PER SERVING** (generous 1\u00bd cups): 230 Cal, 7 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 59 mg Chol, 514 mg Sod, 14 g Total Carb, 3 g Fib, 28 g Prot, 199 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nYou'll want to make this salad a staple for summer meals. You can vary the salad depending on what's fresh at the farmers' market. Use cherry tomatoes instead of regular tomatoes, zucchini or yellow squash instead of cucumber, and basil and parsley instead of the mint and dill.\n\n# Tropical Turkey Salad\n\nSERVES 4\n\n**3 tablespoons fresh lemon juice**\n\n**2 teaspoons olive oil**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 cups diced cooked skinless turkey breast**\n\n**1 large Granny Smith apple, cored and sliced**\n\n**1 mango, peeled, pitted, and diced**\n\n**1 papaya, peeled, halved, seeded, and diced**\n\n**\u00bd cup chopped red onion**\n\n**1 jalape\u00f1o pepper, seeded and minced**\n\n**Red leaf lettuce leaves**\n\n1. To make dressing, whisk together lemon juice, oil, salt, and black pepper in serving bowl.\n\n2. Add turkey, apple, mango, papaya, onion, and jalape\u00f1o to dressing and toss to coat. Line 4 bowls with red leaf lettuce. Top evenly with turkey salad.\n\n**PER SERVING** (1\u00bd cups): 283 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 60 mg Chol, 482 mg Sod, 30 g Total Carb, 11 g Fib, 27 g Prot, 58 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nServe the salad with plain fat-free Greek yogurt topped with fresh berries for dessert (\u00bd cup of plain fat-free Greek yogurt per serving will increase the **_PointsPlus_** value by **_1_** ).\n\nTropical Turkey Salad\n\n# Fruity Chicken Salad\n\nSERVES 4\n\n**\u2154 cup fat-free mayonnaise**\n\n**\u00bc cup chopped fresh cilantro**\n\n**1 tablespoon apple-cider vinegar**\n\n**2 cups cubed cooked skinless chicken breast**\n\n**1\u00bd cups fresh pineapple chunks**\n\n**1 papaya, peeled, seeded, and cut into \u00be-inch chunks**\n\n**1 small orange, peeled and coarsely chopped**\n\n**\u00bd small red onion, thinly sliced**\n\n1. To make dressing, stir together mayonnaise, cilantro, and vinegar in serving bowl.\n\n2. Add chicken, pineapple, papaya, orange, and onion to dressing and toss to coat.\n\n**PER SERVING** (about 1\u00bd cups): 198 Cal, 2 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 62 mg Chol, 474 mg Sod, 24 g Total Carb, 4 g Fib, 22 g Prot, 51 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nTo make this dish more filling, add a chopped apple to the salad and serve each portion on a generous mound of baby arugula.\n\n# Chicken Salad with Fennel, Arugula, and Blue Cheese\n\nSERVES 2\n\n**1 (5-ounce) bag baby arugula**\n\n**4 tablespoons fat-free vinaigrette**\n\n**1\u00bd cups diced cooked skinless chicken breast**\n\n**1 small fennel bulb, thinly sliced**\n\n**1 cup cherry tomatoes, halved**\n\n**\u00bd small red onion, thinly sliced**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bc cup crumbled blue cheese**\n\n**2 teaspoons pine nuts**\n\n1. Toss together arugula and 2 tablespoons of vinaigrette in large bowl. Divide arugula evenly between 2 plates.\n\n2. Combine chicken, fennel, tomatoes, onion, remaining 2 tablespoons vinaigrette, and pepper in same bowl and toss to coat.\n\n3. Spoon chicken mixture evenly on top of arugula and sprinkle with blue cheese and pine nuts.\n\n**PER SERVING** (1 salad): 288 Cal, 10 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 85 mg Chol, 652 mg Sod, 16 g Total Carb, 3 g Fib, 33 g Prot, 211 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nFor more fresh anise flavor, reserve the feathery green tops from the fennel bulb, chop about a tablespoon, and sprinkle over the salads just before serving.\n\n# Chinese Chicken Slaw\n\nSERVES 4\n\n**1 (1-pound) bag coleslaw mix**\n\n**3 scallions, sliced**\n\n**1 (8-ounce) can sliced water chestnuts, drained**\n\n**1 cup shredded cooked skinless chicken breast**\n\n**1 cup frozen shelled edamame, thawed**\n\n**\u00bc cup chopped fresh cilantro**\n\n**\u2153 cup seasoned rice-wine vinegar**\n\n**2 tablespoons reduced-sodium soy sauce**\n\n**1 teaspoon Asian (dark) sesame oil**\n\n**1 garlic clove, minced**\n\n**1 teaspoon grated peeled fresh ginger**\n\n1. Toss together coleslaw mix, scallions, water chestnuts, chicken, edamame, and cilantro in large bowl.\n\n2. Whisk together vinegar, soy sauce, oil, garlic, and ginger in small bowl. Pour over coleslaw mixture and toss to combine.\n\n**PER SERVING** (2 cups): 190 Cal, 5 g Fat, 1 g Sat Fat, 0 g Trans Fat, 22 mg Chol, 772 mg Sod, 22 g Total Carb, 7 g Fib, 14 g Prot, 92 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\n# Key West-Style Shrimp Salad\n\nSERVES 4\n\n**\u2153 cup fat-free mayonnaise**\n\n**\u2153 cup sour cream**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 pound cooked, peeled, and deveined medium shrimp**\n\n**2 cups fresh pineapple chunks**\n\n**2 cups strawberries, hulled and thickly sliced**\n\n**\u00bc cup thinly sliced fresh mint**\n\n**2 scallions, thinly sliced**\n\n**1 jalape\u00f1o pepper, seeded and minced**\n\n**4 cups mixed baby salad greens**\n\n1. To make dressing, whisk together mayonnaise, sour cream, salt, and black pepper in serving bowl.\n\n2. Toss together shrimp, pineapple, strawberries, mint, scallions, and jalape\u00f1o pepper in large bowl.\n\n3. Divide salad greens evenly among 4 plates. Top evenly with shrimp mixture. Serve dressing alongside.\n\n**PER SERVING** (2\u00bd cups salad and 2\u00bd tablespoons dressing): 205 Cal, 2 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 223 mg Chol, 728 mg Sod, 22 g Total Carb, 5 g Fib, 26 g Prot, 105 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# dinners\n\n# Maple and Chili-Broiled T-Bone Steaks\n\nSERVES 6\n\n**1 canned chipotle en adobo, minced**\n\n**2 tablespoons maple syrup**\n\n**2 garlic cloves, minced**\n\n**Grated zest of \u00bd orange**\n\n**1 teaspoon salt**\n\n**1 teaspoon chili powder**\n\n**1 teaspoon ground cumin**\n\n**1 teaspoon onion powder**\n\n**2 (1\u00bd- to 1\u00be-pound) T-bone steaks, \u00bd inch thick, trimmed**\n\n1. Spray broiler rack with nonstick spray and preheat broiler.\n\n2. Stir together chipotle, maple syrup, garlic, orange zest, salt, chili powder, cumin, and onion powder in small bowl. Rub chipotle mixture on both sides of steaks.\n\n3. Place steaks on broiler rack and broil 4 inches from heat until an instant-read thermometer inserted into side of steak registers 145\u00b0F for medium, about 5 minutes on each side. Transfer steaks to cutting board and let stand 5 minutes. Cut each steak into 3 portions.\n\n**PER SERVING** (1 piece steak): 244 Cal, 9 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 59 mg Chol, 520 mg Sod, 7 g Total Carb, 0 g Fib, 32 g Prot, 14 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nServe the steaks with a side dish of grilled red and yellow bell peppers and spring onions. Use your stovetop grill and grill the vegetables while the steak broils.\n\nMaple and Chili-Broiled T-Bone Steaks\n\n# Filets Mignons with Cauliflower Puree\n\nSERVES 4\n\n**2 (10-ounce) packages frozen cauliflower florets, thawed**\n\n**\u00bd cup reduced-sodium chicken broth**\n\n**1 teaspoon unsalted butter**\n\n**\u00bd teaspoon salt**\n\n**4 (5-ounce) filets mignons, trimmed**\n\n**1 tablespoon chopped fresh parsley**\n\n**1 tablespoon chopped fresh rosemary**\n\n**1 tablespoon chopped fresh sage**\n\n1. Combine cauliflower and broth in food processor and pulse until smooth. Transfer mixture to medium saucepan and cook over medium heat until heated through, about 5 minutes. Add few tablespoons of water if puree seems dry, then stir in butter and \u00bc teaspoon of salt.\n\n2. Meanwhile, spray large skillet with nonstick spray and set over medium-high heat. Sprinkle filets mignons with remaining \u00bc teaspoon salt. Add steaks to skillet and cook until an instant-read thermometer inserted into side of steak registers 145\u00b0F for medium, about 4 minutes on each side. Sprinkle steaks with parsley, rosemary, and sage. Serve with cauliflower puree.\n\n**PER SERVING** (1 steak and \u2154 cup puree): 226 Cal, 10 g Total Fat, 4 g Sat Fat, 2 g Trans Fat, 74 mg Chol, 457 mg Sod, 7 g Total Carb, 3 g Fib, 27 g Prot, 44 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nDo it Faster\n\nFor a fast and flavorful side dish, chop extra amounts of the herbs and toss them with steamed green beans. Season with salt and pepper to taste.\n\n# Herb-Crusted Filets Mignons\n\nSERVES 2\n\n**\u00bd teaspoon dried basil**\n\n**\u00bc teaspoon dried rosemary**\n\n**\u00bc teaspoon crushed fennel seeds**\n\n**\u00bc teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 (\u00bc-pound) filets mignons, trimmed**\n\n**Lemon wedges**\n\n1. Spray broiler rack with nonstick spray and preheat broiler.\n\n2. Stir together basil, rosemary, fennel seeds, salt, and pepper in small bowl. Rub mixture on both sides of filets mignons. Place steaks on broiler rack and broil 5 inches from heat until an instant-read thermometer inserted into side of steak registers 145\u00b0F for medium, about 3 minutes on each side. Let steaks stand 5 minutes. Serve with lemon wedges.\n\n**PER SERVING** (1 steak): 147 Cal, 7 g Total Fat, 3 g Sat Fat, 1 g Trans Fat, 57 mg Chol, 334 mg Sod, 1 g Total Carb, 0 g Fib, 19 g Prot, 18 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nFor an easy dinner, serve this flavorful steak with steamed broccoli and mashed potatoes (\u00bd pound of red-skinned potatoes, cooked and mashed with salt and pepper to taste will increase the per-serving **_PointsPlus_** value by **_2_** ).\n\n# Caesar-Style Steak Salad\n\nSERVES 2\n\n**6 ounces lean boneless sirloin steak, trimmed**\n\n**\u00bc teaspoon black pepper**\n\n**\u215b teaspoon salt**\n\n**8 cups chopped romaine lettuce (about 1 medium head)**\n\n**\u00bc red onion, thinly sliced**\n\n**\u00bc cup fat-free Caesar dressing**\n\n**\u00bc cup grated Parmesan cheese**\n\n1. Heat ridged grill pan or cast-iron skillet over high heat. Sprinkle steak with pepper and salt. Place steak in pan and cook until an instant-read thermometer inserted into side of steak registers 145\u00b0F for medium, about 4 minutes on each side. Transfer to cutting board and let stand 5 minutes.\n\n2. Toss together lettuce, onion, dressing, and Parmesan in large bowl. Divide salad evenly between 2 plates. Cut steak into 10 slices and divide evenly between salads.\n\n**PER SERVING** (3 cups salad and 5 slices steak): 213 Cal, 6 g Total Fat, 3 g Sat Fat, 1 g Trans Fat, 57 mg Chol, 866 mg Sod, 11 g Total Carb, 4 g Fib, 27 g Prot, 246 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Grilled Citrus Pork with Cucumber-Orange Salad\n\nSERVES 4\n\n**\u00bd cup fresh orange juice**\n\n**2 tablespoons fresh lime juice**\n\n**2 garlic cloves, minced**\n\n**1 tablespoon canola oil**\n\n**\u00be teaspoon salt**\n\n**4 (\u00bc-pound) lean boneless center-cut pork loin chops, trimmed**\n\n**1 cucumber, peeled and diced**\n\n**1 orange, peeled and diced**\n\n**1 red bell pepper, diced**\n\n**\u00bc cup sliced black olives**\n\n1. Whisk together orange juice, lime juice, garlic, oil, and salt in large bowl. Pour half of mixture into medium bowl and add pork chops. Turn to coat.\n\n2. Spray ridged grill pan with nonstick spray and set over medium-high heat. Remove pork from marinade, discard marinade. Place pork on grill pan. Grill, turning once, until an instant-read thermometer inserted into side of chop registers 145\u00b0F, about 4 minutes.\n\n3. Meanwhile, add cucumber, orange, bell pepper, and olives to orange juice mixture in large bowl and toss to coat. Serve salad with pork.\n\n**SERVING** (1 chop and \u2154 cup salad): 266 Cal, 13 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 72 mg Chol, 385 mg Sod, 10 g Total Carb, 2 g Fib, 26 g Prot, 39 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\n# Lamb and Onion Kebabs with Mint\n\nSERVES 4\n\n**1 pound lean lamb loin, trimmed and cut into \u00be-inch cubes**\n\n**1\u00bd cups frozen pearl onions, thawed**\n\n**2 garlic cloves, minced**\n\n**1 tablespoon olive oil**\n\n**1 tablespoon fresh lemon juice**\n\n**\u00bd teaspoon salt**\n\n**2 teaspoons grated lemon zest**\n\n**3 tablespoons chopped fresh mint**\n\n1. Spray grill rack with nonstick spray; preheat grill to high or prepare hot fire.\n\n2. Toss together lamb, onions, garlic, oil, lemon juice, and salt in large bowl. Thread lamb and pearl onions alternately on 8 metal skewers. Place on grill rack and cook, turning frequently, until lamb is browned and cooked through, 4\u20135 minutes.\n\n3. Sprinkle lemon zest and mint over kebabs just before serving.\n\n**PER SERVING** (2 skewers): 219 Cal, 11 g Fat, 3 g Sat Fat, 1 g Trans Fat, 75 mg Chol, 356 mg Sod, 5 g Total Carb, 1 g Fib, 24 g Prot, 24 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Superfast Barbecued Chicken\n\nSERVES 4\n\n**3 tablespoons ketchup**\n\n**1 tablespoon hoisin sauce**\n\n**1 tablespoon apple-cider vinegar**\n\n**2 teaspoons molasses**\n\n**2 teaspoons reduced-sodium soy sauce**\n\n**4 (\u00bc-pound) skinless boneless chicken breasts**\n\n**\u00bc teaspoon black pepper**\n\n1. Stir together ketchup, hoisin sauce, vinegar, molasses, and soy sauce in small bowl.\n\n2. Spray ridged grill pan with nonstick spray and set over medium heat. Sprinkle chicken with pepper and place in grill pan. Grill, turning often, until chicken is cooked through, about 8 minutes, brushing with ketchup mixture during last 3 minutes of cooking time.\n\n**PER SERVING** (1 chicken breast): 228 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 97 mg Chol, 745 mg Sod, 7 g Total Carb, 0 g Fib, 36 g Prot, 28 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Easy Chicken Cutlets Parmesan\n\nSERVES 2\n\n**4 (3-ounce) thin-sliced skinless boneless chicken breasts**\n\n**\u00bd cup fat-free marinara sauce**\n\n**\u00be cup shredded fat-free mozzarella cheese**\n\n**2 tablespoons grated Parmesan cheese**\n\n**2 tablespoons chopped fresh basil**\n\n1. Spray large skillet with nonstick spray and set over medium heat. Add chicken and cook until browned and cooked through, about 2 minutes on each side.\n\n2. Place chicken in small baking dish in one layer and top evenly with marinara sauce; sprinkle with mozzarella and Parmesan. Microwave on High until cheese is melted, about 2 minutes. Sprinkle with basil.\n\n**PER SERVING** (2 pieces chicken): 343 Cal, 8 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 118 mg Chol, 926 mg Sod, 11 g Total Carb, 1 g Fib, 54 g Prot, 493 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\n# Turkey Cutlets with Mushroom-Wine Sauce\n\nSERVES 4\n\n**4 (\u00bc-pound) turkey breast cutlets**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd teaspoon salt**\n\n**1 tablespoon unsalted butter**\n\n**2\u00bd cups (6 ounces) thinly sliced fresh cremini mushrooms**\n\n**2 garlic cloves, minced**\n\n**\u00be cup dry red wine**\n\n**\u00bd teaspoon dried thyme**\n\n**2 tablespoons chopped fresh parsley**\n\n1. Spray large skillet with nonstick spray and set over medium-high heat. Sprinkle turkey with pepper and \u00bc teaspoon of salt; cook until browned and cooked through, about 2 minutes on each side. Transfer to plate and keep warm.\n\n2. Place butter in skillet and swirl so butter melts and coats skillet. Add mushrooms, garlic, and remaining \u00bc teaspoon salt; cook, stirring frequently, until mushrooms brown, about 3 minutes. Add wine and thyme; simmer until most of liquid has evaporated, about 4 minutes. Spoon mushrooms over turkey and sprinkle with parsley.\n\n**PER SERVING** (1 turkey cutlet and \u00bc cup mushroom sauce): 174 Cal, 4 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 84 mg Chol, 351 mg Sod, 4 g Total Carb, 0 g Fib, 28 g Prot, 34 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nIf your supermarket has variety packs of mushrooms, use one for this recipe. A blend of different types of mushrooms will intensify the flavor and give sauce dish visual appeal.\n\nGrilled Chicken Salad with Raspberries and Goat Cheese\n\n# Grilled Chicken Salad with Raspberries and Goat Cheese\n\nSERVES 4\n\n**4 (\u00bc-pound) thin-sliced skinless boneless chicken breasts**\n\n**\u00be teaspoon salt**\n\n**1 (7-ounce) bag mixed baby salad greens**\n\n**2 tablespoons raspberry or red-wine vinegar**\n\n**2 teaspoons olive oil**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd cup crumbled soft (mild) goat cheese**\n\n**2 (6-ounce) containers raspberries**\n\n**3 scallions, thinly sliced**\n\n1. Spray ridged grill pan with nonstick spray and set over medium-high heat. Sprinkle chicken with \u00bd teaspoon of salt. Place chicken in pan and grill until cooked through, about 3 minutes on each side.\n\n2. Meanwhile, combine salad greens, vinegar, oil, remaining \u00bc teaspoon salt, and pepper in large bowl; toss to coat.\n\n3. Add goat cheese, raspberries, and scallions to salad and gently toss to combine. Divide salad evenly among 4 plates. Halve chicken breasts and place 2 pieces on top of each salad.\n\n**PER SERVING** (1 piece chicken and 2 cups salad): 252 Cal, 10 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 76 mg Chol, 586 mg Sod, 10 g Total Carb, 5 g Fib, 30 g Prot, 85 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# African-Spiced Turkey and Squash Stew\n\nSERVES 4\n\n**1 tablespoon canola oil**\n\n**1 pound turkey breast cutlets, cut into 1-inch pieces**\n\n**\u00be cup frozen chopped onion, thawed**\n\n**3 garlic cloves, minced**\n\n**1 teaspoon ground cumin**\n\n**\u00bd teaspoon ground coriander**\n\n**\u00bd teaspoon cinnamon**\n\n**1 (14\u00bd-ounce) can reduced-sodium chicken broth**\n\n**1 (12-ounce) box frozen squash puree, thawed**\n\n**1 cup frozen corn kernels**\n\n**\u00bd teaspoon salt**\n\n**Chopped fresh cilantro**\n\n1. Heat oil in large skillet over medium-high heat. Add turkey and cook, stirring occasionally, until lightly browned, about 5 minutes. Add onion, garlic, cumin, coriander, and cinnamon. Cook, stirring, until fragrant, about 1 minute.\n\n2. Add broth, squash, corn, and salt; bring to boil. Cook, stirring occasionally, until corn is tender, about 2 minutes. Ladle stew into 4 bowls; sprinkle with cilantro.\n\n**PER SERVING** (1\u00bc cups): 260 Cal, 8 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 68 mg Chol, 601 mg Sod, 20 g Total Carb, 4 g Fib, 29 g Prot, 62 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nWhole wheat couscous makes a fast-cooking accompaniment to this stew (\u00bd cup cooked whole wheat couscous per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Grilled Ginger Chicken with Peach Salsa\n\nSERVES 4\n\n**2 teaspoons minced peeled fresh ginger**\n\n**1 garlic clove, minced**\n\n**2 teaspoons canola oil**\n\n**\u00bd teaspoon salt**\n\n**4 (\u00bc-pound) thin-sliced skinless boneless chicken breasts**\n\n**3 peaches, pitted and diced**\n\n**1 tomato, diced**\n\n**\u00bd small red onion, chopped**\n\n**1 jalape\u00f1o pepper, seeded and minced**\n\n**\u00bc cup chopped fresh cilantro**\n\n**2 teaspoons fresh lime juice**\n\n1. Combine ginger, garlic, oil, and \u00bc teaspoon of salt in small bowl; rub mixture over chicken.\n\n2. Spray ridged grill pan with nonstick spray and set over medium-high heat. Place chicken in pan and grill until cooked through, about 3 minutes on each side.\n\n3. Meanwhile, to make salsa, toss together peaches, tomato, onion, jalape\u00f1o, cilantro, lime juice, and remaining \u00bc teaspoon salt in serving bowl. Serve chicken with salsa.\n\n**PER SERVING** (1 piece chicken and 1 cup salsa): 218 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 68 mg Chol, 360 mg Sod, 14 g Total Carb, 2 g Fib, 26 g Prot, 27 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nWhile you grill the chicken, grill a vegetable side dish, too. Cut 2 zucchini lengthwise into quarters; spray lightly with nonstick spray. Grill, turning occasionally, until crisp-tender, 6\u20138 minutes. Season to taste with salt and pepper.\n\nGrilled Salmon with Quick Tomato Tapenade\n\n# Grilled Salmon with Quick Tomato Tapenade\n\nSERVES 4\n\n**4 (\u00bc-pound) skinless salmon fillets**\n\n**\u00bc teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n**\u00bc cup pitted Kalamata olives**\n\n**\u00bc cup coarsely chopped rehydrated sun-dried tomatoes (not packed in oil)**\n\n**3 tablespoons coarsely chopped fresh basil or parsley**\n\n**2 tablespoons pine nuts**\n\n1. Spray ridged grill pan with nonstick spray and set over medium-high heat. Sprinkle salmon with salt and pepper. Place salmon in pan and cook until just opaque in center, about 4 minutes on each side.\n\n2. Meanwhile, to make tapenade, combine olives, tomatoes, basil, and pine nuts in mini food processor and process until finely chopped. Top salmon evenly with tapenade.\n\n**PER SERVING** (1 salmon fillet and 2\u00bd tablespoons tapenade): 201 Cal, 9 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 65 mg Chol, 437 mg Sod, 3 g Total Carb, 1 g Fib, 26 g Prot, 28 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nServe the salmon with fresh watercress sprigs.\n\n# Salmon au Poivre with Watercress\n\nSERVES 4\n\n**4 (6-ounce) skinless salmon fillets**\n\n**1 tablespoon mixed peppercorns, cracked**\n\n**\u00be teaspoon salt**\n\n**3 bunches watercress, trimmed**\n\n**\u00bc red onion, thinly sliced**\n\n**1\u00bd tablespoons fresh lemon juice**\n\n1. Sprinkle salmon evenly with peppercorns and \u00bd teaspoon of salt.\n\n2. Spray large skillet with nonstick spray and set over medium heat. Add salmon and cook until lightly browned and just opaque in center, about 4 minutes on each side.\n\n3. Meanwhile, toss together watercress, onion, lemon juice, and remaining \u00bc teaspoon salt in large bowl. Divide watercress salad evenly among 4 plates and top each serving with piece of salmon.\n\n**PER SERVING** (1 salmon fillet and 1\u00bd cups salad): 266 Cal, 11 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 94 mg Chol, 584 mg Sod, 3 g Total Carb, 1 g Fib, 37 g Prot, 101 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nBefore cooking, it's best to run your fingers lightly over surface of salmon fillets to check for any small bones that may be embedded in flesh. If you find any, use clean tweezers or needle-nose pliers to pull them out.\n\n# Tuna Steaks with Avocado-Orange Relish\n\nSERVES 4\n\n**2 teaspoons canola oil**\n\n**2 teaspoons reduced-sodium soy sauce**\n\n**4 (5-ounce) tuna steaks**\n\n**1 tablespoon red-wine vinegar**\n\n**2 teaspoons flaxseed oil**\n\n**1\u00bd teaspoons minced peeled fresh ginger**\n\n**\u00bc teaspoon salt**\n\n**\u00bd avocado, halved, pitted, peeled, and diced**\n\n**1 (11-ounce) can unsweetened mandarin orange sections, drained**\n\n**\u00bc small red onion, chopped**\n\n1. Spray broiler rack with nonstick spray and preheat broiler.\n\n2. Whisk together canola oil and soy sauce in small bowl. Brush mixture on both sides of tuna. Place steaks on broiler rack and broil 5 inches from heat, about 3 minutes on each side for medium or until desired doneness.\n\n3. Meanwhile, to make relish, whisk together vinegar, flaxseed oil, ginger, and salt in medium bowl. Add avocado, orange sections, and onion; toss to coat. Serve tuna with relish.\n\n**PER SERVING** (1 tuna steak and \u00bd cup relish): 259 Cal, 9 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 66 mg Chol, 303 mg Sod, 8 g Total Carb, 2 g Fib, 35 g Prot, 32 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nFlaxseed oil is great source of vitamin E and heart-healthy omega-3 fatty acids. You can use canola oil instead of the flaxseed oil in this recipe if flaxseed oil is not available.\n\n# Halibut with Salsa Verde\n\nSERVES 4\n\n**4 (6-ounce) skinless halibut fillets**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 teaspoons canola oil**\n\n**1 cup fat-free salsa verde**\n\n**Cilantro sprigs**\n\n**Lime wedges**\n\n1. Sprinkle halibut with salt and pepper.\n\n2. Heat oil in large skillet over medium-high heat. Add halibut and cook until just opaque in center, about 3 minutes on each side.\n\n3. Place 1 fillet on each of 4 plates and top evenly with salsa verde. Garnish with cilantro sprigs and lime wedges.\n\n**PER SERVING** (1 fillet and \u00bc cup salsa): 198 Cal, 5 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 90 mg Chol, 634 mg Sod, 5 g Total Carb, 1 g Fib, 33 g Prot, 36 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nAccompany the halibut with steamed baby carrots and brown rice with a sprinkle of chopped fresh cilantro stirred in (\u00bd cup cooked brown rice per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Roast Halibut with Chunky Roasted Pepper Sauce\n\nSERVES 4\n\n**4 (6-ounce) halibut steaks, about \u00be inch thick**\n\n**2 teaspoons olive oil**\n\n**\u00bc teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 (12-ounce) jar roasted red pepper, drained and chopped (not packed in oil)**\n\n**16 pitted black and\/or green olives, coarsely chopped**\n\n**\u00bc cup chopped fresh basil**\n\n**1 tablespoon sherry vinegar or red-wine vinegar**\n\n**1 tablespoon drained capers, coarsely chopped**\n\n**1 garlic clove, minced**\n\n1. Preheat oven to 425\u00b0F and spray shallow roasting pan with nonstick spray.\n\n2. Place halibut in roasting pan; brush with oil and sprinkle with salt and black pepper. Roast fish until just opaque in center, about 10 minutes.\n\n3. Meanwhile, to make sauce, toss together roasted red pepper, olives, basil, vinegar, capers, and garlic in medium bowl. Serve halibut with sauce.\n\n**PER SERVING** (1 halibut steak and about \u2153 cup sauce): 215 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 90 mg Chol, 662 mg Sod, 6 g Total Carb, 1 g Fib, 33 g Prot, 48 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Thai Shrimp and Melon Salad\n\nSERVES 4\n\n**Grated zest of 1 lime**\n\n**3 tablespoons fresh lime juice**\n\n**2 tablespoons reduced-sodium teriyaki sauce**\n\n**1 serrano or jalape\u00f1o pepper, seeded and minced**\n\n**1\u00bc pounds medium cooked, peeled, and deveined shrimp**\n\n**3 Kirby cucumbers, diced**\n\n**1 red bell pepper, diced**\n\n**2 carrots, shredded**\n\n**\u00be cup chopped fresh cilantro**\n\n**\u00bc cup thinly sliced fresh mint**\n\n**1 shallot, very thinly sliced**\n\n**\u00bd honeydew melon, seeded, peeled, and cut into thin wedges**\n\n1. Whisk together lime zest and juice, teriyaki sauce, and serrano pepper in large bowl. Add shrimp, cucumbers, bell pepper, carrots, cilantro, mint, and shallot; toss to coat.\n\n2. Arrange honeydew evenly on 4 plates; top evenly with shrimp salad.\n\n**PER SERVING** (1\u00bc cups shrimp salad and about 3 melon wedges): 202 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 160 mg Chol, 484 mg Sod, 30 g Total Carb, 6 g Fib, 20 g Prot, 116 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nIn the summer, you can make this salad with whatever melon is available. Try watermelon, cantaloupe, casaba, Galia, or Persian.\n\nThai Shrimp and Melon Salad\n\n# Sesame Scallops\n\nSERVES 4\n\n**1 cup quick-cooking brown rice**\n\n**3 tablespoons sesame seeds**\n\n**\u00bc teaspoon cracked black pepper**\n\n**1\u00bc pounds sea scallops**\n\n**2 teaspoons olive oil**\n\n**2 tablespoons reduced-sodium soy sauce**\n\n**2 teaspoons unseasoned rice vinegar**\n\n**2 tablespoons finely chopped fresh chives**\n\n1. Prepare rice according to package directions, omitting salt if desired.\n\n2. Meanwhile, combine sesame seeds and pepper on sheet of wax paper. Dip flat sides of each scallop in sesame mixture.\n\n3. Heat oil in large skillet over medium-high heat. Add scallops and cook until browned and just opaque throughout, about 2 minutes on each side.\n\n4. Whisk together soy sauce, vinegar, and chives in small bowl. Serve scallops over rice and drizzle with soy sauce mixture.\n\n**PER SERVING** (6 scallops, \u00bd cup rice, and scant 1 tablespoon sauce): 239 Cal, 8 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 38 mg Chol, 899 mg Sod, 20 g Total Carb, 4 g Fib, 20 g Prot, 98 mg Calc.\n\n**_PointsPlus_** value **_6._**\n\n# Sesame Noodles with Green Vegetables\n\nSERVES 4\n\n**6 ounces whole wheat capellini**\n\n**Florets from 2 broccoli crowns**\n\n**\u00bd pound frozen sugar snap peas**\n\n**\u00bd pound frozen shelled edamame**\n\n**3 scallions, trimmed and sliced**\n\n**2 tablespoons reduced-sodium soy sauce**\n\n**1 tablespoon Asian (dark) sesame oil**\n\n**\u00bd garlic clove, minced**\n\n1. Cook capellini according to package directions, omitting salt if desired. Four minutes before pasta is done, add broccoli, snap peas, and edamame and cook until pasta and vegetables are tender. Drain, reserving \u00bd cup of cooking water.\n\n2. Transfer capellini mixture to large bowl; add reserved cooking water, scallions, soy sauce, oil, and garlic and toss to coat.\n\n**PER SERVING** (1\u00be cups): 311 Cal, 7 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 356 mg Sod, 47 g Total Carb, 12 g Fib, 16 g Prot, 123 mg Calc.\n\n**_PointsPlus_** value **_7._**\n\nDo it Faster\n\nThin or small pasta such as capellini, macaroni, mini penne, rotini, and orzo are the quickest cooking. Keep a variety of these on your pantry shelf for fast weeknight meals.\n\n# snacks and sweets\n\n# Cottage Cheese and Sun-Dried Tomato Dip\n\nSERVES 4\n\n**1 (16-ounce) container fat-free cottage cheese**\n\n**\u00bc cup fat-free mayonnaise**\n\n**\u00bc cup moist sun-dried tomatoes (not packed in oil), chopped**\n\n**2 scallions, chopped**\n\n**1 tablespoon grated Parmesan cheese**\n\n**2 teaspoons fresh lemon juice**\n\n**Pinch cayenne pepper**\n\n**2 tablespoons chopped fresh basil or parsley**\n\nCombine all ingredients except basil in food processor and process until smooth. Transfer cheese mixture to serving bowl and stir in basil.\n\n**PER SERVING** (generous \u00bd cup): 102 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 7 mg Chol, 618 mg Sod, 10 g Total Carb, 1 g Fib, 13 g Prot, 102 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nServe this dip with baked fat-free bagel chips (1 ounce of fat-free bagel chips per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Dried Cranberry-Popcorn Mix\n\nSERVES 8\n\n**1 tablespoon olive oil**\n\n**2 teaspoons curry powder**\n\n**6 cups plain air-popped popcorn**\n\n**\u00bd cup dried cranberries**\n\n**\u2153 cup dry-roasted peanuts**\n\n1. Stir together oil and curry powder in microwavable cup. Microwave on High until fragrant, about 1 minute.\n\n2. Toss together popcorn, cranberries, and peanuts in large bowl. Drizzle curry oil over popcorn mixture and toss to coat.\n\n**PER SERVING** (\u00be cup): 94 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 51 mg Sod, 11 g Total Carb, 2 g Fib, 2 g Prot, 10 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\nChili-Spiced Popcorn and Smoky Pumpkin Seeds, here\n\n# Chili-Spiced Popcorn\n\nSERVES 6\n\n**6 cups plain air-popped popcorn**\n\n**1 tablespoon chili powder**\n\n**\u00bd teaspoon paprika**\n\n**\u00bd teaspoon onion powder**\n\n**\u00bd teaspoon ground cumin**\n\nPlace popcorn in large bowl and spray with nonstick spray; toss to coat. Sprinkle remaining ingredients over popcorn and toss to coat evenly.\n\n**PER SERVING** (1 cup): 36 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 14 mg Sod, 7 g Total Carb, 2 g Fib, 1 g Prot, 9 mg Calc.\n\n**_PointsPlus_** value: **_1._**\n\n# organize your kitchen for speed\n\nIf you're not organized, you'll spend too much time in the kitchen looking for ingredients, equipment, and tools. The first step to being a shortcut cook is to set up your kitchen for streamlined cooking. Here's how:\n\n**DOWNSIZE AND DECLUTTER.** Give away unused kitchen items and unnecessary multiples of tools. You'll probably never use a bagel slicer or a garlic peeler. You need several wooden spoons and spatulas, but only one vegetable peeler, box grater, or salad spinner. For items you rarely use, like a bread machine, waffle baker, muffin pan, or holiday cookie cutters, remove them from the kitchen and store in the attic, garage, or a closet.\n\n**CREATE A FUNCTIONAL WORK ZONE.** Place wooden and slotted spoons, ladles, spatulas, and tongs in a decorative container near the stove. Place the 6 spices you use most often in a drawer away from the heat of the stove, but close by. Keep a set of stackable dry measuring cups, a liquid measuring cup, and a set of measuring spoons near where you do food prep. Store knives in a knife block or on a wall-mounted magnetized knife rack near a large cutting board.\n\n**DIVIDE AND CONQUER STORAGE AREAS.** Instead of having kitchen drawers become a jumble of tools, buy shallow containers of different lengths or drawer dividers. Separate tools by size for easy visibility and access. Buy bins or baskets for deep cupboard shelves. You can pull out the bin to find what you're looking for, rather than looking through a whole shelf of bottles or cans. To save space, buy sorter racks to allow you to store cutting boards, baking sheets, and pot lids vertically.\n\n**KEEP THE REFRIGERATOR WELL ORGANIZED.** Discard foods with expired sell-by dates and odd condiments that you'll never use to free up space. Set up zones on each shelf for the way you and your family cook and eat. Leftovers can go on one shelf, foods you've pre-prepped for future meals on another, and foods that are up for grabs for snacks on another. Keep fruits and vegetables in crisper drawers to keep them fresher longer and all in one place.\n\n**USE COUNTER SPACE WISELY.** Keep items you use daily on the counter. The microwave, toaster, and coffee pot are in constant use and should be left out all the time. Less frequently used appliances like a stand mixer, blender, or juicer can take their place on a lower shelf in a distant cabinet to free up work space.\n\n**MAXIMIZE SHELF SPACE.** Buy risers so you can store plates on the shelf and saucers or bowls on the riser above them. Use them in the pantry to double storage space for cans and boxes. Install hooks for hanging cups and mugs to clear out space on the shelf below.\n\n**STORE ITEMS IN CLEAR CONTAINERS.** Keep pantry staples such as flour, sugar, rice, and pasta in see-through plastic or glass containers so you can instantly see how much you have on hand. These look pretty in your cupboard, too, and will keep you motivated to stay organized.\n\n# Open-Faced Roast Beef Sandwich Bites\n\nSERVES 4\n\n**3 tablespoons bottled horseradish, drained**\n\n**3 tablespoons fat-free mayonnaise**\n\n**20 slices cocktail (party-style) rye bread, toasted**\n\n**5 (1-ounce) slices lean roast beef, each cut into 4 pieces**\n\n**10 cherry tomatoes, halved**\n\n1. Stir together horseradish and mayonnaise in small bowl. Spread horseradish mayonnaise evenly over slices of toast.\n\n2. Place 1 piece of roast beef on each slice of toast. Thread party toothpick through each tomato half and insert toothpick into each sandwich.\n\n**PER SERVING** (5 sandwiches): 153 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 19 mg Chol, 725 mg Sod, 22 g Total Carb, 3 g Fib, 11 g Prot, 38 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\n# Turkey and Roasted Pepper Lettuce Wraps\n\nSERVES 8\n\n**8 green leaf lettuce leaves**\n\n**8 (1-ounce) slices deli roast turkey breast**\n\n**8 (\u00be-ounce) slices Swiss cheese**\n\n**2 tablespoons coarse-grain Dijon mustard**\n\n**1 (12-ounce) jar roasted red pepper (not packed in oil), drained and cut into strips**\n\n1. Lay out lettuce leaves on work surface. Layer 1 slice of turkey and 1 slice of Swiss on each lettuce leaf. Spread evenly with mustard and top evenly with roasted red pepper.\n\n2. Fold in two opposite sides of filled lettuce leaf, then roll up to enclose filling. Secure with toothpick. Repeat to make total of 8 rolls.\n\n**PER SERVING** (1 roll): 137 Cal, 6 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 44 mg Chol, 270 mg Sod, 4 g Total Carb, 1 g Fib, 15 g Prot, 187 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\n# Vanilla Yogurt Sundae\n\nSERVES 1\n\n**1 (\u00bd-cup) scoop frozen vanilla fat-free yogurt**\n\n**1 tablespoon toasted wheat germ**\n\n**1 tablespoon chopped walnuts**\n\n**2 tablespoons thawed frozen fat-free whipped topping**\n\n**1 fresh sweet cherry or maraschino cherry**\n\nPlace yogurt in dessert dish. Top with wheat germ, walnuts, whipped topping, and cherry.\n\n**PER SERVING** (1 sundae): 181 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 2 mg Chol, 65 mg Sod, 26 g Total Carb, 2 g Fib, 8 g Prot, 179 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Mixed Melon with Honeyed Ricotta\n\nSERVES 4\n\n**2 cups fat-free ricotta cheese**\n\n**1 tablespoon plus 1 teaspoon honey**\n\n**2 teaspoons vanilla extract**\n\n**\u00bc teaspoon ground nutmeg**\n\n**4 cups cubed cantaloupe**\n\n**4 cups cubed honeydew**\n\n**4 cups cubed watermelon**\n\n**\u00bc cup toasted wheat germ**\n\n1. Stir together ricotta, honey, vanilla, and nutmeg in medium bowl. Toss together cantaloupe, honeydew, and watermelon in large bowl; divide evenly among 4 dessert dishes.\n\n2. Spoon ricotta mixture evenly over fruit and sprinkle evenly with wheat germ.\n\n**PER SERVING** (3 cups melon cubes, \u00bd cup ricotta mixture, and 1 tablespoon wheat germ): 211 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 8 mg Chol, 101 mg Sod, 38 g Total Carb, 3 g Fib, 14 g Prot, 159 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Honeydew-Strawberry Soup\n\nSERVES 4\n\n**8 cups cubed chilled honeydew**\n\n**1 teaspoon grated lime zest**\n\n**2 tablespoons fresh lime juice**\n\n**2 teaspoons sugar**\n\n**1 cup sliced strawberries**\n\n**2 tablespoons sliced fresh mint**\n\n1. Puree honeydew in blender or food processor. Pour puree into large bowl and stir in lime zest and juice and sugar.\n\n2. Ladle soup evenly into each of 4 chilled bowls. Top evenly with strawberries and sprinkle with mint.\n\n**PER SERVING** (1 cup): 92 Cal, 0 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 11 mg Sod, 30 g Total Carb, 2 g Fib, 1 g Prot, 27 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\nCook's Note\n\nUse leftover mint from this recipe to add refreshing flavor to green salads, stir-fries, or iced tea.\n\n# Pineapple Crush Smoothies\n\nSERVES 3\n\n**1 ripe banana, peeled and cut into chunks**\n\n**1 (8-ounce) can crushed pineapple in juice**\n\n**\u00bd cup plain low-fat yogurt**\n\n**\u00bd cup fresh orange juice**\n\n**1 tablespoon honey**\n\n**5 ice cubes**\n\nCombine all ingredients in blender and process until smooth. Pour into 3 tall glasses.\n\n**PER SERVING** (1 cup): 148 Cal, 1 g Fat, 0 g Sat Fat, 0 g Trans Fat, 3 mg Chol, 30 mg Sod, 35 g Total Carb, 2 g Fib, 3 g Prot, 90 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nDo it Faster\n\nIf you have any leftover smoothie, pour it into a popsicle mold or a small paper cup and freeze for a healthful treat another day.\n\n# Strawberry Colada Cooler\n\nSERVES 1\n\n**\u00bd cup halved strawberries**\n\n**\u00bd cup fresh pineapple chunks**\n\n**\u00bd cup fat-free milk**\n\n**\u00bd cup vanilla low-fat yogurt**\n\n**\u00bc cup light (reduced-fat) coconut milk**\n\n**2 ice cubes**\n\nCombine all ingredients in blender and process until smooth. Pour into tall glass.\n\n**PER SERVING** (1 smoothie): 235 Cal, 4 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 5 mg Chol, 145 mg Sod, 44 g Total Carb, 3 g Fib, 9 g Prot, 332 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nDo it Faster\n\nTo quickly remove the hulls of strawberries, use the pointed end of a vegetable peeler, or cut them away with a small paring knife.\n\n# **20**  \nMinute meals\n\n20 Minute Breakfasts\n\nCorn and Green Chile Frittata\n\nFrittata Italiana\n\nBell Pepper and Sun-Dried Tomato Omelette\n\nPea, Mushroom, and Cherry Tomato Frittata\n\nHash Brown and Egg Skillet Breakfast\n\nCottage Cheese Pancakes\n\nBreakfast Bruschetta\n\n20 Minute Lunches\n\nQuick Quesadillas\n\nPan Bagnat\n\nChicken and Tzatziki-Stuffed Pitas\n\nPitas Stuffed with Tofu-Egg Salad\n\nClam and Corn Chowder\n\nChickpea Soup\n\nBlack Bean Soup with Rice\n\nHam and Macaroni Salad-Stuffed Bell Peppers\n\nChicken and Napa Cabbage Salad\n\nGingery Turkey-Couscous Salad\n\nSmoked Turkey, Carrot, and Raisin Salad\n\nLight and Luscious Cobb Salad\n\nSalmon with Corn, Black Bean, and Tomato Salad\n\nTuna-Potato Salad\n\nTuna and White Bean Salad\n\nShrimp Salad with Fennel, Red Onion, and Orange\n\nCurried Tuna Salad\n\nWhite Bean Salad with Feta-Pita Crisps\n\nCrab Salad-Stuffed Tomatoes\n\nMaui Tortilla Pizzas\n\n20 Minute Dinners\n\nSteak Fajitas\n\nThai-Style Beef Salad\n\nOrange Beef with Broccoli\n\nGinger Steak and Broccoli Stir-Fry\n\nSummer Squash Stuffed with Beef and Olives\n\nPork with Sweet Coconut-Peanut Sauce\n\nPork Chops with Ginger and Snow Peas\n\nChicken Piccata\n\nChicken in Coconut-Curry Sauce\n\nChicken Tikka with Cucumber Raita\n\nBraised Bok Choy and Chicken with Soba Noodles\n\nTurkey Cutlets Milanese\n\nTurkey Cutlets with Orange Sauce\n\nMediterranean Turkey Burgers\n\nCod with Tomato-Oregano Sauce\n\nSweet-and-Spicy Salmon with Broccoli Slaw\n\nArctic Char with Cranberry Couscous\n\nCalifornia Fish Tacos\n\nShrimp and Spaghetti Arrabbiata\n\nShrimp with Cherry Tomatoes and Feta\n\nVegetable Fried Rice\n\nBlackened Scallops with Lemon-Caper Mayonnaise\n\nLinguine with White Bean Puttanesca\n\nFettuccine with Goat Cheese, Arugula, and Tomatoes\n\n20 Minute Snacks and Sweets\n\nBlack Bean-Tomatillo Dip\n\nSun-Dried Tomato Hummus\n\nChunky Guacamole\n\nRed Pepper and Sun-Dried Tomato Dip\n\nSpicy Cereal and Pretzel Snack Mix\n\nCrispy Green Plantains\n\nMicrowave Apple-Pear Crisp\n\nBrown Sugar Plums\n\nBananas Foster\n\n# breakfasts\n\n# Corn and Green Chile Frittata\n\nSERVES 4\n\n**6 large eggs**\n\n**1 cup frozen corn kernels, thawed**\n\n**1 (4\u00bd-ounce) can chopped mild green chiles, drained**\n\n**\u00bc cup fat-free milk**\n\n**2 teaspoons chopped fresh thyme or \u00bd teaspoon dried**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**3 dashes hot pepper sauce**\n\n**\u00bd teaspoon canola oil**\n\n**12 yellow or red cherry tomatoes, halved**\n\n1. Whisk together eggs, corn, chiles, milk, thyme, salt, pepper, and pepper sauce in large bowl.\n\n2. Coat medium nonstick skillet with oil and set over medium heat. Add egg mixture and sprinkle with tomatoes. Cover and cook until eggs are set, about 10 minutes. Cut frittata into 4 wedges. Serve hot, warm, or at room temperature.\n\n**PER SERVING** (1 wedge): 168 Cal, 8 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 318 mg Chol, 493 mg Sod, 12 g Total Carb, 2 g Fib, 12 g Prot, 74 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nHalf of a toasted whole wheat English muffin makes a crispy partner for the frittata (\u00bd of a whole wheat English muffin per serving will increase the **_PointsPlus_** value by **_2_** ).\n\nCorn and Green Chile Frittata\n\n# Frittata Italiana\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**2\u00bd cups fat-free egg substitute**\n\n**\u215b teaspoon black pepper**\n\n**1 large tomato, chopped**\n\n**4 scallions, sliced**\n\n**2 cups shredded fat-free mozzarella cheese**\n\n**2 tablespoons grated Parmesan cheese**\n\n**\u00bc cup chopped fresh basil**\n\n1. Heat oil in large nonstick skillet over medium heat. Add egg substitute and pepper. Cook until eggs are almost set, about 3 minutes, lifting edges frequently with heatproof rubber spatula to allow uncooked egg to flow underneath.\n\n2. Sprinkle eggs with tomato, scallions, and mozzarella. Cover skillet. Reduce heat to low and cook until cheese is melted and eggs are set, about 3 minutes longer.\n\n3. Sprinkle frittata with Parmesan and basil. Cut into 4 wedges. Serve hot, warm, or at room temperature.\n\n**PER SERVING** (1 wedge): 216 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 11 mg Chol, 963 mg Sod, 13 g Total Carb, 2 g Fib, 31 g Prot, 749 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nDo it Faster\n\nDesperate for a superfast dinner idea? Quick egg dishes such as this frittata make fast, filling evening meals, too.\n\n# Bell Pepper and Sun-Dried Tomato Omelette\n\nSERVES 2\n\n**6 sun-dried tomato halves (not packed in oil)**\n\n**3 large egg whites**\n\n**2 large eggs**\n\n**\u00bc teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n**2 teaspoons olive oil**\n\n**\u00bc cup thinly sliced red onion**\n\n**\u00bc cup diced bell pepper**\n\n**1 garlic clove, minced**\n\n1. Place sun-dried tomatoes in bowl and add boiling water to cover by 1 inch. Let stand 5 minutes; drain and cut into thin slices.\n\n2. Meanwhile, whisk together egg whites, eggs, salt, and black pepper in separate bowl.\n\n3. Heat 1 teaspoon of oil in 10-inch nonstick skillet over medium heat. Add sun-dried tomatoes, onion, bell pepper, and garlic; cook, stirring occasionally, until vegetables soften, 4\u20135 minutes. Transfer vegetables to bowl and set aside.\n\n4. Wipe out skillet and return it to medium heat. Add remaining 1 teaspoon oil. Pour in egg mixture and cook, stirring gently, until underside is set, about 1 minute. Spread bell pepper mixture evenly over half of omelette; with spatula, fold other half over filling. Continue to cook until filling is heated through and eggs are set, 1\u20132 minutes longer. Cut omelette in half and slide each half onto plate.\n\n**PER SERVING** (\u00bd omelette): 181 Cal, 10 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 212 mg Chol, 653 mg Sod, 9 g Total Carb, 2 g Fib, 14 g Prot, 50 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nTry a plain toasted bagel flat with the omelette (1 plain toasted bagel flat per serving will increase the **_PointsPlus_** value by **_3_** ).\n\nPea, Mushroom, and Cherry Tomato Frittata\n\n# Pea, Mushroom, and Cherry Tomato Frittata\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**4 shiitake mushrooms, stems removed and caps sliced**\n\n**1 onion, chopped**\n\n**3 garlic cloves, minced**\n\n**1 teaspoon dried basil**\n\n**1 cup cherry tomatoes, halved**\n\n**1 cup frozen green peas**\n\n**4 large eggs, lightly beaten**\n\n**2 large egg whites, lightly beaten**\n\n**3 tablespoons grated Parmesan cheese**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n1. Preheat broiler.\n\n2. Heat oil in 10-inch cast-iron or other ovenproof skillet over medium-high heat. Add mushrooms, onion, garlic, and basil; cook, stirring occasionally, until onion begins to brown, about 5 minutes. Add cherry tomatoes and peas; cook until tomatoes begin to wilt, 2 minutes.\n\n3. Meanwhile, whisk together eggs, egg whites, Parmesan, salt, and pepper in bowl. Pour over mushroom mixture. Reduce heat to medium and cook until eggs begin to set, 3 minutes. Place frittata under broiler and broil 5 inches from heat until eggs are set, about 2 minutes. Cut into 4 wedges.\n\n**PER SERVING** (1 wedge): 186 Cal, 9 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 216 mg Chol, 496 mg Sod, 14 g Total Carb, 3 g Fib, 13 g Prot, 116 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nIf your skillet does not have a metal handle, wrap it with a couple of layers of foil to protect it from the heat of the broiler.\n\n# Hash Brown and Egg Skillet Breakfast\n\nSERVES 4\n\n**2 teaspoons canola oil**\n\n**3 russet potatoes, scrubbed, shredded, and squeezed dry**\n\n**\u00bd onion, chopped**\n\n**1 garlic clove, minced**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**Pinch ground sage**\n\n**4 large eggs**\n\n**4 scallions, sliced**\n\n1. Heat oil in large nonstick skillet over medium heat. Add potatoes, onion, garlic, salt, pepper, and sage; cook, stirring, until softened, about 5 minutes.\n\n2. Using spatula, press down on potato mixture to make an even layer. Continue to cook, without stirring, until potatoes are lightly browned, about 5 minutes longer.\n\n3. Place large plate on top of potato cake and carefully turn skillet over. Slide potato cake back into skillet. Using spoon, make 4 indentations in potato cake that are large enough to hold an egg.\n\n4. Break 1 egg into each indentation. Sprinkle eggs and potatoes with scallions. Cover skillet and cook until eggs are set, about 3 minutes. Cut into quarters.\n\n**PER SERVING** (\u00bc of potato and egg mixture): 223 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 212 mg Chol, 369 mg Sod, 30 g Total Carb, 4 g Fib, 9 g Prot, 73 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nServe this breakfast with a fresh colorful fruit salad made with cubed cantaloupe, sliced strawberries, and peeled and sliced kiwifruit.\n\n# Cottage Cheese Pancakes\n\nSERVES 6\n\n**1 cup low-fat cottage cheese**\n\n**1 cup vanilla low-fat yogurt**\n\n**3 large eggs**\n\n**1 teaspoon vanilla extract**\n\n**1 cup all-purpose flour**\n\n**\u2153 cup whole wheat flour**\n\n**1 tablespoon sugar**\n\n**\u00bc teaspoon salt**\n\n1. Whisk cottage cheese, yogurt, eggs, and vanilla together in large bowl. Stir in all-purpose flour, whole wheat flour, sugar, and salt.\n\n2. Spray large skillet or griddle with nonstick spray and heat over medium heat. Pour batter by \u00bc-cup measures onto griddle. Cook until small bubbles just begin to appear on top of pancakes and they are golden brown underneath, about 2 minutes. Flip and cook until second side has browned, about 2 minutes longer.\n\n**PER SERVING** (2 pancakes): 207 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 110 mg Chol, 309 mg Sod, 30 g Total Carb, 1 g Fib, 13 g Prot, 111 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nIf you have leftover pancakes, place them on a wire rack and let cool completely. Stack the pancakes with a sheet of wax paper between each one and place in a heavy zip-close plastic bag. Freeze for up to 3 months. To reheat, wrap two pancakes in a paper towel and microwave on High for 20\u201330 seconds.\n\n# Breakfast Bruschetta\n\nSERVES 2\n\n**1 teaspoon olive oil**\n\n**1 green bell pepper, chopped**\n\n**\u00bd onion, chopped**\n\n**1 carrot, shredded**\n\n**1 garlic clove, minced**\n\n**1\u00bc cups fat-free egg substitute**\n\n**\u00bc teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n**2 slices reduced-calorie whole-grain bread, toasted**\n\n1. Heat oil in medium nonstick skillet over medium heat. Add bell pepper, onion, carrot, and garlic; cook, stirring frequently, until vegetables are softened, about 5 minutes.\n\n2. Stir in egg substitute, salt, and black pepper. Cook, stirring, just until egg is set. Spoon half of egg on top of each slice of toast.\n\n**PER SERVING** (1 bruschetta): 186 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 716 mg Sod, 21 g Total Carb, 5 g Fib, 19 g Prot, 300 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nAdd fresh cantaloupe slices to make this a colorful and filling meal.\nBreakfast Bruschetta\n\n# lunches\n\n# Quick Quesadillas\n\nSERVES 4\n\n**4 (8-inch) whole wheat tortillas**\n\n**4 thin slices prosciutto**\n\n**4 thin slices pepper Jack cheese**\n\n**4 scallions, thinly sliced**\n\n**\u00bc cup chopped fresh cilantro**\n\n**\u00bc cup fat-free salsa**\n\n1. Spray large skillet with nonstick spray and place over medium-high heat.\n\n2. Place tortilla on counter and cover with one fourth of prosciutto and pepper Jack. Sprinkle bottom half with one-fourth of scallions and cilantro. Fold tortilla in half, covering fillings. Repeat with remaining tortillas, prosciutto, pepper Jack, scallions, and cilantro.\n\n3. Place 2 quesadillas in pan and cook, turning once, until tortillas are browned and cheese has melted, about 3 minutes. Repeat with remaining quesadillas. Cut each quesadilla into 3 wedges and serve with salsa on side.\n\n**PER SERVING** (1 quesadilla and 1 tablespoon salsa): 165 Cal, 7 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 25 mg Chol, 592 mg Sod, 22 g Total Carb, 3 g Fib, 11 g Prot, 130 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nDo it Faster\n\nQuesadillas are a superquick lunch or light dinner option for weeknights\u2014and both kids and adults love them!\n\n# Pan Bagnat\n\nSERVES 4\n\n**3 tablespoons red-wine vinegar**\n\n**3 tablespoons chopped fresh parsley**\n\n**2 tablespoons reduced-sodium chicken broth**\n\n**1 tablespoon olive oil**\n\n**1 garlic clove, minced**\n\n**\u00bc teaspoon black pepper**\n\n**1 (8-ounce) loaf Italian bread**\n\n**2 (5-ounce) cans chunk light tuna packed in water, drained and flaked**\n\n**1 small red onion, thinly sliced**\n\n**2 ripe tomatoes, thinly sliced**\n\n**4 radishes, thinly sliced**\n\n**\u00bc cup pitted Ni\u00e7oise olives**\n\n1. To make dressing, whisk together vinegar, parsley, broth, oil, garlic, and pepper in small bowl.\n\n2. Using serrated knife, split bread loaf in half lengthwise, making bottom of loaf slightly thicker than top. Use your fingers to pull out and discard some of soft interior of bread. Brush inside of loaf with half of dressing.\n\n3. Cover bottom section of bread with tuna, onion, tomatoes, radishes, and olives and drizzle with remaining dressing. Cover with bread top and cut into 4 sandwiches.\n\n**PER SERVING** (1 sandwich): 254 Cal, 7 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 19 mg Chol, 559 mg Sod, 27 g Total Carb, 3 g Fib, 21 g Prot, 67 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nThese sandwiches can be eaten immediately or wrapped tightly and chilled for up to 6 hours, so they're perfect for packing for lunch or taking on a picnic.\n\nChicken and Tzatziki-Stuffed Pitas\n\n# Chicken and Tzatziki-Stuffed Pitas\n\nSERVES 2\n\n**\u00be cup plain fat-free yogurt**\n\n**\u2153 cup shredded cucumber**\n\n**1 small garlic clove, minced**\n\n**\u215b teaspoon black pepper**\n\n**2 (7-inch) whole wheat pitas, halved**\n\n**1\u00bd cups shredded cooked chicken breast**\n\n**1 large tomato, cut into 8 slices**\n\n**4 small romaine lettuce leaves**\n\n**\u00bc cup crumbled fat-free feta cheese**\n\n1. Stir together yogurt, cucumber, garlic, and pepper in small bowl.\n\n2. Cut each pita in half. Spread half of yogurt mixture inside pitas. Layer chicken, tomato, lettuce, and feta evenly inside pitas. Top with remaining yogurt mixture\n\n**PER SERVING** (1 sandwich): 464 Cal, 6 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 88 mg Chol, 783 mg Sod, 54 g Total Carb, 8 g Fib, 48 g Prot, 280 mg Calc.\n\n**_PointsPlus_** value: **_11._**\n\nDo it Faster\n\nTo make this recipe fuss free, use purchased rotisserie chicken.\n\n# 9 rules for shortcut cooking\n\nWhen time is short on busy weeknights, you can still prepare a fresh homemade meal for your family if you follow these rules:\n\n**PLAN YOUR MEALS FOR THE WEEK.** Jot down a bare-bones menu for every night you'll make dinner for the week. With a plan as simple as \"steak fajitas and rice,\" \"spaghetti with meat sauce and salad,\" and \"saut\u00e9ed chicken, couscous, and green beans\" you can organize recipes and create a shopping list in just a few minutes.\n\n**KEEP MENUS TO TWO OR THREE SIMPLE ITEMS.** Don't try to do too much or get too fancy. Your family will enjoy a quickly prepared homemade meal that's as simple as baked pork chops, mashed potatoes, and salad (from pre-washed greens, of course). Keep seasonings as simple as salt and pepper with a dash of grated lemon zest, minced garlic, or a sprinkle of fresh or dried herbs.\n\n**KEEP A WELL-STOCKED FREEZER.** Always keep a stash of quick-cooking staples such as boneless skinless chicken breasts, ground beef, and fish fillets on hand for pulling a fast meal together from ingredients you have on hand. Use the defrost setting on the microwave to thaw foods quickly before cooking.\n\n**ASSEMBLE INGREDIENTS AND EQUIPMENT BEFORE COOKING.** Before you begin to cook, gather the ingredients you need, the measuring cups and spoons, and pots and pans you'll need to prepare the meal. Use pots and pans that look good enough to go straight from oven to table. Once everything is out on the counter or stovetop, you can focus on getting the meal prepared without the distraction of searching for needed items.\n\n**START LONG-COOKING FOODS FIRST.** For instance, get pasta water on to boil or rice on to cook before you begin what you'll serve with it. Then, start on a pasta sauce or chicken stir-fry.\n\n**CLEAN UP AS YOU GO.** Keep a trash bowl nearby. If you're preparing a meal that requires peeling and chopping fruits or vegetables, take a tip from chefs and keep a small bowl near the cutting board for peelings, trimmings, and cores. You'll save trips to the trash can and then you can discard all the debris at once.\n\n**MULTITASK.** If you're waiting on a sauce to simmer or a chop to broil, make a green salad to serve with the meal, cut up some fruit to enjoy for dessert, put dirty dishes in the dishwasher, wipe down kitchen counters, put away any appliances you've used.\n\n**ENLIST HELP.** Get your spouse and children to help with the meal. When it's crunch time, the smallest task can be helpful. Setting the table, getting out bread or rolls, tossing a salad, or putting away ingredients can shave minutes off your kitchen time.\n\n**MAKE WEEKEND COOKING COUNT.** Make food in big batches on the weekend to refrigerate or freeze for effortless meals later on. Chilis, soups, and stews freeze perfectly and will be a delicious welcome on nights when you don't have time to cook. Roast a chicken, turkey breast, beef or pork roast, or leg of lamb on the weekend and use the leftovers for another meal or two later in the week.\n\n# Pitas Stuffed with Tofu-Egg Salad\n\nSERVES 4\n\n**1 (14-ounce) container reduced-fat firm tofu, drained**\n\n**2 large hard-cooked eggs**\n\n**1 celery stalk, chopped**\n\n**1 carrot, shredded**\n\n**2 tablespoons minced red onion**\n\n**\u00bc cup fat-free mayonnaise**\n\n**1 tablespoon white-wine vinegar**\n\n**2 teaspoons Dijon mustard**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon hot pepper sauce**\n\n**4 (6-inch) whole wheat pita breads, halved**\n\n**2 cups salad greens**\n\n1. Crumble tofu onto clean kitchen towel. Roll up towel and twist to remove as much liquid as possible. Mash eggs with fork in large bowl. Add tofu, celery, carrot, onion, mayonnaise, vinegar, mustard, salt, and pepper sauce and mix well.\n\n2. Fill each pita half with \u2153 cup of salad and \u00bc cup greens.\n\n**PER SERVING** (2 filled pita halves): 297 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 108 mg Chol, 830 mg Sod, 41 g Total Carb, 9 g Fib, 17 g Prot, 100 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nYou can make the salad up to 2 days ahead and store, refrigerated, for a quick lunch.\n\n# Clam and Corn Chowder\n\nSERVES 4\n\n**2 (6\u00bd-ounce) cans chopped clams**\n\n**1\u00bd cups frozen corn kernels**\n\n**\u00bc teaspoon hot pepper sauce**\n\n**\u00bc teaspoon dried thyme**\n\n**1 (14\u00bd-ounce) can reduced-sodium chicken broth**\n\n**1 (14\u00bd-ounce) can sliced potatoes, rinsed and drained**\n\n**\u00bd cup frozen chopped onion, thawed**\n\n**\u00bd cup fat-free half-and-half**\n\n**3 tablespoons chopped fresh parsley**\n\n1. Heat clams and their juice, corn, pepper sauce, and thyme in large saucepan over high heat.\n\n2. Meanwhile, puree broth, potatoes, and onion in blender. Add to pot with clams and corn; bring to boil. Reduce heat and simmer, stirring occasionally, about 3 minutes. Stir in half-and-half and heat through. Remove from heat and stir in parsley.\n\n**PER SERVING** (1\u00bd cups): 190 Cal, 2 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 29 mg Chol, 501 mg Sod, 29 g Total Carb, 4 g Fib, 16 g Prot, 90 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nRye bread makes a flavorful accompaniment to the creamy chowder (1 rye flat roll per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Chickpea Soup\n\nSERVES 4\n\n**5 cups reduced-sodium chicken broth**\n\n**2 (15\u00bd-ounce) cans chickpeas, rinsed and drained**\n\n**2 teaspoons olive oil**\n\n**2 carrots, thinly sliced**\n\n**1 red bell pepper, chopped**\n\n**1 onion, chopped**\n\n**3 garlic cloves, minced**\n\n**2 teaspoons fresh rosemary**\n\n**\u00bc teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 tablespoons chopped fresh parsley**\n\n1. Puree broth with chickpeas, in batches, in blender.\n\n2. Heat oil in large saucepan over medium heat. Add carrots, bell pepper, onion, and garlic; cook, stirring, until carrots are crisp-tender, about 5 minutes.\n\n3. Stir in chickpea mixture, rosemary, salt, and black pepper. Stir in a little water if soup is too thick. Cook over medium heat until heated through, about 4 minutes. Serve sprinkled with parsley.\n\n**PER SERVING** (about 1\u00bd cups): 315 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 879 mg Sod, 49 g Total Carb, 11 g Fib, 18 g Prot, 124 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nServe this Mediterranean-inspired soup with rosemary pita bread. Lightly spray a whole wheat pita bread with olive oil nonstick spray and sprinkle with fresh minced rosemary. Broil, turning once, until heated through, 2 minutes (one 1-ounce) whole wheat pita bread per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# Black Bean Soup with Rice\n\nSERVES 4\n\n**2 teaspoons canola oil**\n\n**1 onion, chopped**\n\n**1 celery stalk, chopped**\n\n**1 green bell pepper, chopped**\n\n**2 garlic cloves, finely chopped**\n\n**2 teaspoons chili powder**\n\n**1\u00bd teaspoons ground cumin**\n\n**2 (15\u00bd-ounce) cans black beans, rinsed and drained**\n\n**1 (14\u00bd-ounce) can reduced-sodium chicken broth or vegetable broth**\n\n**1 tomato, chopped**\n\n**\u00bc cup chopped fresh cilantro**\n\n**2 cups hot cooked brown rice**\n\n1. Heat oil over medium heat in large saucepan. Add onion, celery, bell pepper, and garlic and cook, stirring occasionally, until softened, about 4 minutes. Add chili powder and cumin and cook 1 minute longer.\n\n2. Add beans to saucepan and mash coarsely with potato masher or large fork. Add broth and tomato; increase heat to high and bring soup to boil. Stir in cilantro. Ladle evenly into 4 serving bowls and top with \u00bd cup rice.\n\n**PER SERVING** (1\u00bd cups soup and \u00bd cup rice): 296 Cal, 5 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 568 mg Sod, 50 g Total Carb, 12 g Fib, 13 g Prot, 84 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nTo preserve fresh cilantro and other herbs, chop them, place in ice cube trays, cover with water, and freeze. Store the frozen cubes in a zip-close bag and pop them into recipes at the end of cooking. The small amount of water in the ice cube won't make a difference in your dish.\n\n# Ham and Macaroni Salad-Stuffed Bell Peppers\n\nSERVES 4\n\n**1 cup whole wheat macaroni**\n\n**\u2153 cup fat-free mayonnaise**\n\n**2 tablespoons apple-cider vinegar**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd pound lean turkey ham, diced**\n\n**1 (5-ounce) jar roasted red pepper, drained and chopped (not packed in oil)**\n\n**4 scallions, thinly sliced**\n\n**2 tablespoons sweet pickle relish**\n\n**4 red bell peppers, halved lengthwise through stems and seeded**\n\n1. Cook macaroni according to package directions, omitting salt. Drain and rinse under cold running water; drain again.\n\n2. Transfer macaroni to large bowl. Add mayonnaise, vinegar, and black pepper; toss to coat. Add turkey ham, roasted red peppers, scallions, and relish; toss to combine.\n\n3. Spoon salad evenly into bell pepper halves.\n\n**PER SERVING** (2 stuffed pepper halves): 256 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 43 mg Chol, 927 mg Sod, 40 g Total Carb, 6 g Fib, 16 g Prot, 42 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nWhen you cook the macaroni for this salad, make extra and use it instead of rigatoni to prepare Vegetable Minestrone with Pasta, here, on the weekend.\n\n# Chicken and Napa Cabbage Salad\n\nSERVES 4\n\n**2 tablespoons fresh lime juice**\n\n**2 teaspoons Asian (dark) sesame oil**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**5 cups thinly sliced Napa cabbage**\n\n**2 cups shredded, cooked skinless chicken breast**\n\n**1 cup matchstick-cut carrots**\n\n**1 green bell pepper, thinly sliced**\n\n**2 scallions, thinly sliced on diagonal**\n\n1. Whisk together lime juice, sesame oil, salt, and black pepper in large serving bowl.\n\n2. Add cabbage, chicken, carrots, bell pepper, and scallions and toss to coat.\n\n**PER SERVING** (about 2 cups): 173 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 57 mg Chol, 653 mg Sod, 8 g Total Carb, 3 g Fib, 23 g Prot, 121 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nDo it Faster\n\nWondering what all those blades that came with your food processor actually do? One of them will probably cut matchstick carrots for this recipe in seconds.\n\nChicken and Napa Cabbage Salad\n\n# Gingery Turkey-Couscous Salad\n\nSERVES 2\n\n**\u00bd cup whole wheat couscous**\n\n**5 teaspoons unseasoned rice vinegar**\n\n**5 teaspoons reduced-sodium soy sauce**\n\n**1 garlic clove, minced**\n\n**2 teaspoons minced peeled fresh ginger**\n\n**1\u00bd cups shredded, cooked, skinless turkey breast**\n\n**1\u00bd cups small broccoli florets**\n\n**1 large red bell pepper, cut into \u00bd-inch pieces**\n\n**3 scallions, thinly sliced**\n\n**\u00bc cup chopped fresh cilantro**\n\n1. Prepare couscous according to package directions, omitting fat and salt if desired. Transfer to shallow bowl to cool.\n\n2. Meanwhile, whisk together vinegar, soy sauce, garlic, and ginger in serving bowl. Add couscous, turkey, broccoli, bell pepper, scallions, and cilantro and toss to coat.\n\n**PER SERVING** (2 cups): 357 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 86 mg Chol, 279 mg Sod, 34 g Total Carb, 8 g Fib, 39 g Prot, 93 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\n# Smoked Turkey, Carrot, and Raisin Salad\n\nSERVES 4\n\n**\u2153 cup light mayonnaise**\n\n**1 teaspoon grated lemon zest**\n\n**1 tablespoon fresh lemon juice**\n\n**\u00bd teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n**1 (6-ounce) piece cooked smoked turkey breast, diced**\n\n**6 carrots, shredded (about 3 cups)**\n\n**\u2153 cup dark raisins**\n\n**8 cups lightly packed baby romaine**\n\n**\u00bc cup coarsely chopped unsalted peanuts**\n\n1. To make dressing, whisk together mayonnaise, lemon zest and juice, salt, and pepper in large bowl.\n\n2. Add turkey, carrots, and raisins to dressing; toss to coat.\n\n3. Divide romaine evenly among 4 plates. Top with turkey mixture and sprinkle evenly with peanuts.\n\n**PER SERVING** (about 3 cups): 199 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 28 mg Chol, 696 mg Sod, 22 g Total Carb, 4 g Fib, 10 g Prot, 75 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nTo add more color and crunch, add 1 diced red or green apple to the salad.\n\nLight and Luscious Cobb Salad\n\n# Light and Luscious Cobb Salad\n\nSERVES 4\n\n**3 tablespoons sherry vinegar**\n\n**2 teaspoons olive oil**\n\n**\u00bc teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**6 cups lightly packed torn romaine lettuce**\n\n**2 cups diced cooked turkey breast**\n\n**2 large tomatoes, diced**\n\n**\u00bd avocado, halved, pitted, peeled, and diced**\n\n**2 large hard-cooked egg whites, chopped**\n\n**6 slices turkey bacon, crisp-cooked and coarsely crumbled**\n\n**\u00bc cup crumbled blue cheese**\n\n1. To make dressing, whisk together vinegar, oil, salt, and pepper in small bowl.\n\n2. Spread lettuce on platter. Arrange turkey, tomatoes, and avocado in rows on top of lettuce. Sprinkle with egg whites, bacon, and blue cheese. Serve dressing on side.\n\n**PER SERVING** (about 1\u00bd cups): 292 Cal, 14 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 85 mg Chol, 939 mg Sod, 8 g Total Carb, 4 g Fib, 32 g Prot, 94 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nTo save the other half of the avocado, drizzle it with lemon juice, wrap in plastic wrap, and refrigerate for up to 3 days. If the exposed flesh does darken, just cut away a thin layer to reveal the bright green avocado below.\n\n# Salmon with Corn, Black Bean, and Tomato Salad\n\nSERVES 6\n\n**2 tablespoons fresh lime juice**\n\n**1 teaspoon olive oil**\n\n**1 teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 (15\u00bd-ounce) can black beans, rinsed and drained**\n\n**2 cups drained canned corn kernels**\n\n**1 large tomato, diced**\n\n**\u00bd small red onion, finely chopped**\n\n**\u00bd cup coarsely chopped fresh cilantro**\n\n**1 jalape\u00f1o pepper, seeded and minced**\n\n**6 large Boston lettuce leaves**\n\n**6 (3-ounce) prepared poached salmon fillets**\n\n1. To make dressing, whisk together lime juice, oil, salt, and black pepper in large bowl.\n\n2. Add beans, corn, tomato, onion, cilantro, and jalape\u00f1o pepper to dressing; toss to coat.\n\n3. Divide lettuce among 6 plates; top with salmon. Spoon bean salad alongside fish.\n\n**PER SERVING** (1 salmon fillet and about 1\u00bc cups salad): 311 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 83 mg Chol, 635 mg Sod, 26 g Total Carb, 7 g Fib, 33 g Prot, 61 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nTo poach salmon, bring 2 cups of reduced-sodium chicken broth to a simmer in a large skillet. Add 6 (4-ounce) skinless salmon fillets to the broth. Cover and simmer until the salmon is just opaque, 4 to 5 minutes. Serve the salmon warm, at room temperature, or chilled.\n\n# Tuna-Potato Salad\n\nSERVES 4\n\n**\u00bc cup fat-free mayonnaise**\n\n**\u00bc teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 (5-ounce) cans chunk light tuna packed in water, drained and flaked**\n\n**1 pound packaged cooked diced potatoes**\n\n**2 large shallots, finely chopped**\n\n**4 cups mixed baby salad greens**\n\n**Lemon wedges**\n\n1. To make dressing, whisk together mayonnaise, salt, and pepper in large bowl.\n\n2. Add tuna, potatoes, and shallots to dressing and stir to combine well.\n\n3. Divide salad greens evenly among 4 plates. Top evenly with tuna-potato mixture. Serve with lemon wedges.\n\n**PER SERVING** (1\u00bc cups): 208 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 21 mg Chol, 706 mg Sod, 29 g Total Carb, 4 g Fib, 20 g Prot, 49 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nTo add more delicious veggies to the salad, surround each one with cucumber and plum tomato slices.\n\n# Tuna and White Bean Salad\n\nSERVES 4\n\n**\u00bd cup reduced-sodium chicken broth**\n\n**2 teaspoons olive oil**\n\n**Grated zest and juice of 1 lemon**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**6 cups torn fris\u00e9e lettuce**\n\n**2 different colored bell peppers, chopped**\n\n**1 large tomato, chopped**\n\n**3 scallions, thinly sliced**\n\n**2 (5-ounce) cans chunk light tuna packed in water, drained and flaked**\n\n**1 (15\u00bd-ounce) can cannellini (white kidney) beans, rinsed and drained**\n\n1. To make dressing, whisk together broth, oil, lemon zest and juice, salt, and black pepper in serving bowl.\n\n2. Add fris\u00e9e, bell peppers, tomato, scallions, tuna, and beans to dressing and toss to coat.\n\n**PER SERVING** (generous 2 cups): 235 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 19 mg Chol, 749 mg Sod, 27 g Total Carb, 8 g Fib, 25 g Prot, 82 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nFor a satisfying finish to lunch, enjoy a piece of fresh fruit and a cup of herbal tea for dessert.\n\nTuna and White Bean Salad\n\nShrimp Salad with Fennel, Red Onion, and Orange\n\n# Shrimp Salad with Fennel, Red Onion, and Orange\n\nSERVES 4\n\n**1 tablespoon fresh lemon juice**\n\n**2 teaspoons olive oil**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1\u00bc pounds cooked, peeled, and deveined medium shrimp**\n\n**2 large navel oranges, peeled and cut into \u00be-inch pieces**\n\n**1 fennel bulb, trimmed and very thinly sliced**\n\n**\u00bd small red onion, thinly sliced**\n\n**12 pitted Kalamata olives**\n\n1. To make dressing, whisk together lemon juice, oil, salt, and pepper in serving bowl.\n\n2. Add shrimp, oranges, fennel, onion, and olives and toss to coat.\n\n**PER SERVING** (about 2 cups): 241 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 276 mg Chol, 759 mg Sod, 17 g Total Carb, 5 g Fib, 31 g Prot, 136 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nDon't be tempted to make this salad ahead. The acid from the lemon juice will cause the shrimp to become rubbery and tough.\n\n# Curried Tuna Salad\n\nSERVES 2\n\n**1 (5-ounce) can chunk light tuna packed in water, drained and flaked**\n\n**1 celery stalk, chopped**\n\n**2 tablespoons chopped fresh cilantro**\n\n**1 shallot, chopped**\n\n**2 tablespoons golden raisins, chopped**\n\n**2 tablespoons fat-free mayonnaise**\n\n**1 teaspoon curry powder**\n\n**4 red leaf lettuce leaves**\n\n**2 hard-cooked large eggs, peeled and sliced**\n\n1. Toss together tuna, celery, cilantro, shallot, raisins, mayonnaise, and curry powder in small bowl.\n\n2. Divide lettuce evenly between 2 plates. Mound tuna salad evenly on lettuce and surround with eggs.\n\n**PER SERVING** (2 lettuce leaves, \u00bd cup tuna salad, and 1 egg): 212 Cal, 7 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 207 mg Chol, 428 mg Sod, 14 g Total Carb, 2 g Fib, 24 g Prot, 67 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nTo quickly add more flavor to this tuna salad, stir in a teaspoon of grated lime zest.\n\n# White Bean Salad with Feta-Pita Crisps\n\nSERVES 4\n\n**4 (7-inch) whole wheat pitas**\n\n**1 cup crumbled reduced-fat feta cheese**\n\n**1 (15\u00bd-ounce) can Great Northern or other white beans, rinsed and drained**\n\n**1 red or green bell pepper, chopped**\n\n**\u00bd small red onion, chopped**\n\n**\u00bc cup chopped fresh parsley**\n\n**2 teaspoons olive oil**\n\n**Grated zest and juice of 1 lemon**\n\n**\u00bc teaspoon black pepper**\n\n1. Preheat broiler. Line baking sheet with foil.\n\n2. Lay pitas on baking sheet and sprinkle evenly with feta. Broil 5 inches from heat until cheese is melted and pitas are crisp, about 3 minutes. Cut each pita into 6 wedges.\n\n3. Meanwhile, toss together beans, bell pepper, onion, parsley, oil, lemon zest and juice, and black pepper in large bowl. Serve salad with pita wedges.\n\n**PER SERVING** (1 cup salad and 6 pita wedges): 371 Cal, 7 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 10 mg Chol, 945 mg Sod, 62 g Total Carb, 11 g Fib, 19 g Prot, 208 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nTo remove about 40 percent of the sodium in canned beans, always rinse and drain them before using in a recipe.\n\n# Crab Salad-Stuffed Tomatoes\n\nSERVES 2\n\n**\u2153 cup orzo**\n\n**2 large tomatoes**\n\n**1 cup crabmeat, picked over for pieces of shell**\n\n**\u2153 cup chopped black or green olives**\n\n**2 tablespoons crumbled reduced-fat feta cheese**\n\n**2 tablespoons chopped fresh dill**\n\n**2 teaspoons balsamic vinegar**\n\n**\u215b teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n1. Cook orzo according to package directions, omitting salt if desired. Drain and rinse under cold water; drain again.\n\n2. Meanwhile, cut thin slice off tops of tomatoes; reserve tops. Using spoon, carefully scoop out seeds and pulp; reserve for another use.\n\n3. Gently toss together crabmeat, olives, feta, dill, vinegar, salt, and pepper in medium bowl. Spoon crabmeat mixture evenly into tomato shells and cover with reserved tomato tops.\n\n**PER SERVING** (1 stuffed tomato): 279 Cal, 10 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 67 mg Chol, 795 mg Sod, 30 g Total Carb, 2 g Fib, 19 g Prot, 130 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nScoop the seeds and pulp from the tomatoes into a storage container. Cover and freeze up to 4 months and toss them into a soup or stew.\n\nCrab Salad-Stuffed Tomatoes\n\n# Maui Tortilla Pizzas\n\nSERVES 4\n\n**4 (7-inch) whole wheat tortillas**\n\n**\u00bc pound piece lean deli ham, diced**\n\n**4 (1-ounce) slices reduced-fat Swiss cheese**\n\n**\u00bd red bell pepper, chopped**\n\n**1 (8-ounce) can well-drained unsweetened pineapple chunks, chopped**\n\n**3 tablespoons chopped macadamia nuts or almonds**\n\n1. Preheat oven to 400\u00b0F. Line baking sheet with foil.\n\n2. Lay tortillas on baking sheet. Layer evenly with ham, Swiss, and bell pepper. Bake until cheese is melted and bubbling, about 10 minutes. Sprinkle evenly with pineapple and macadamia nuts.\n\n**PER SERVING** (1 pizza): 226 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 25 mg Chol, 493 mg Sod, 23 g Total Carb, 4 g Fib, 17 g Prot, 294 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nBecause of their high fat content, nuts can become rancid quickly if stored at room temperature. To keep them fresh longer, place nuts in an airtight container and store in the freezer.\n\n# dinners\n\n# Steak Fajitas\n\nSERVES 4\n\n**1 (1\u00bc-pound) lean flank steak, trimmed**\n\n**\u00bd teaspoon salt**\n\n**2 teaspoons canola oil**\n\n**1 green bell pepper, thinly sliced**\n\n**1 red bell pepper, thinly sliced**\n\n**1 onion, thinly sliced**\n\n**2 garlic cloves, minced**\n\n**\u00bc teaspoon black pepper**\n\n**4 (7-inch) whole wheat tortillas, warmed**\n\n**2 tablespoons taco sauce**\n\n1. Spray ridged grill pan with nonstick spray and set over medium-high heat. Sprinkle steak with \u00bc teaspoon of salt. Place steak in grill pan and cook until an instant-read thermometer inserted into side of steak registers 145\u00b0F for medium, about 5 minutes on each side.\n\n2. Meanwhile, heat oil in large nonstick skillet over medium heat. Add bell peppers, onion, and garlic; sprinkle with remaining \u00bc teaspoon salt and black pepper. Cook, stirring, until softened, about 8 minutes.\n\n3. Transfer steak to cutting board and let stand 5 minutes. Cut steak across grain into 20 slices.\n\n4. Lay tortillas on work surface and top evenly with steak and bell pepper mixture; drizzle with taco sauce. Fold tortillas in half.\n\n**PER SERVING** (1 fajita): 375 Cal, 15 g Total Fat, 5 g Sat Fat, 2 g Trans Fat, 68 mg Chol, 542 mg Sod, 30 g Total Carb, 4 g Fib, 31 g Prot, 121 mg Calc.\n\n**_PointsPlus_** value: **_10._**\n\nCook's Note\n\nTo get an accurate measure of the temperature of a steak or other thin cut of meat or poultry, insert the thermometer sideways into the food. Make sure beef, pork, and lamb reach at least 145\u00b0F, ground meats reach 160\u00b0F, and all poultry, including ground poultry, reaches 165\u00b0F.\n\n# Thai-Style Beef Salad\n\nSERVES 4\n\n**3 teaspoons canola oil**\n\n**2 (\u00bc-pound) filet mignon steaks, trimmed**\n\n**\u00bc cup fresh lime juice**\n\n**2 teaspoons Asian fish sauce**\n\n**2 teaspoons packed light brown sugar**\n\n**\u00bc teaspoon red pepper flakes**\n\n**3 cups mixed baby greens**\n\n**1 cup fresh mint leaves**\n\n**1 cup fresh cilantro leaves**\n\n**1 cup thinly sliced cucumber**\n\n**\u00bd red onion, thinly sliced**\n\n1. Heat 2 teaspoons of oil in medium skillet over medium-high heat. Add beef and cook, turning once, until instant-read thermometer inserted into side of each steak registers 145\u00b0F for medium, 8\u201310 minutes. Transfer meat to cutting board and let stand 5 minutes.\n\n2. Meanwhile, whisk together lime juice, fish sauce, sugar, red pepper flakes, and remaining 1 teaspoon oil in large bowl.\n\n3. Just before serving, add greens, mint, cilantro, cucumber, and onion to bowl with dressing. Cut the steaks into \u00bc-inch-thick slices, then slice in half again lengthwise. Toss warm beef with salad.\n\n**PER SERVING** (2 cups): 157 Cal, 8 g Fat, 2 g Sat Fat, 0 g Trans Fat, 25 mg Chol, 271 mg Sod, 8 g Total Carb, 2 g Fib, 15 g Prot, 54 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\n# Orange Beef with Broccoli\n\nSERVES 4\n\n**1 pound lean sirloin steak, trimmed and cut into thin strips**\n\n**2 tablespoons reduced-sodium soy sauce**\n\n**2 garlic cloves, minced**\n\n**2 teaspoons minced peeled fresh ginger**\n\n**\u215b teaspoon red pepper flakes**\n\n**2 teaspoons canola oil**\n\n**5 cups small broccoli florets**\n\n**1 onion, thinly sliced**\n\n**1 tablespoon grated orange zest**\n\n**\u00bc cup fresh orange juice**\n\n**1 teaspoon cornstarch**\n\n1. Combine steak, soy sauce, garlic, ginger, and red pepper flakes in large shallow dish; toss to coat.\n\n2. Heat large deep skillet or wok over high heat until drop of water sizzles in pan. Add oil and swirl to coat skillet. Add beef and stir-fry until lightly browned, about 3 minutes. Using slotted spoon, transfer beef to plate. Add broccoli and onion to skillet and stir-fry until broccoli is bright green, about 3 minutes.\n\n3. Stir together orange zest and juice and cornstarch in small cup until smooth; add to skillet. Stir-fry until sauce thickens and bubbles, about 1 minute. Stir in beef and stir-fry until heated through, about 2 minutes longer.\n\n**PER SERVING** (1\u00be cups): 244 Cal, 7 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 73 mg Chol, 334 mg Sod, 13 g Total Carb, 3 g Fib, 33 g Prot, 60 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nTo quickly add more flavor to this stir-fry, stir in a handful of chopped fresh basil or cilantro just before serving.\n\n# got 5 minutes?\n\nHave a few moments to spare? Add a fast flourish to your meals with one of these speedy suggestions.\n\n\u2022 Grate a little **orange zest** or **tangerine zest** over your morning oatmeal, pancakes, or French toast for a hit of bright flavor.\n\n\u2022 Instead of eating your morning yogurt with a spoon, throw it in the blender with a few ice cubes and half a cup of chopped fruit for a **satisfying smoothie** you can enjoy with a straw.\n\n\u2022 Stir a little **grated fresh ginger** into unsweetened applesauce or fruit preserves for a hint of exotic flavor.\n\n\u2022 Slice or dice **fresh apples or pears** and add them to a sandwich or salad for natural sweetness and crunch.\n\n\u2022 Toss a handful of **fresh** **whole basil, mint, or parsley leaves** into a green salad to add a punch of fresh flavor.\n\n\u2022 Thin **fat-free Greek yogurt** with a little water and drizzle it over bowls of soup or chili for a touch of richness and color contrast.\n\n\u2022 Add a hint of deep, smoky flavor to baked or pan-seared meat, fish, or poultry with a sprinkle of **smoked paprika or smoked sea salt**.\n\n\u2022 Chop parsley, garlic, and lemon zest together for a **quick gremolata** to use as a garnish for stews or roast meats.\n\n\u2022 Finely chop a **hard-cooked egg white** and use it as a protein-rich topping for side dishes, salads, or soups.\n\n\u2022 Sprinkle an **exotic spice blend** like za'atar, Berber seasoning, or Cajun spice on steamed vegetables or cooked whole grains to wake up their flavor.\n\n\u2022 Use a vegetable peeler to make **long strips of raw carrot, zucchini, or yellow squash** to add color and texture to your next salad.\n\n\u2022 Perk up bottled salad dressing with some **chopped fresh herbs and minced shallot\u2014** it will taste almost as good as homemade.\n\n\u2022 Add half a **diced onion and a bay leaf** to the water when you cook whole grains to give them pilaf-like flavor.\n\n\u2022 Add a few **sliced strawberries and mint leaves** to glasses of seltzer for a refreshing accompaniment to meals or snacks.\n\n\u2022 Split open a **pomegranate** and use the seeds as a crunchy, flavorful garnish for salads or desserts.\n\n\u2022 Shave or grate a little antioxidant-rich **dark chocolate** over desserts, fruits, or yogurt and you'll have a healthful fix for a chocolate craving.\n\n# Ginger Steak and Broccoli Stir-Fry\n\nSERVES 2\n\n**2 teaspoons Asian (dark) sesame oil**\n\n**10 ounces lean sirloin steak, trimmed and cut into thin strips**\n\n**1 tablespoon minced peeled fresh ginger**\n\n**2 garlic cloves, minced**\n\n**2 cups small broccoli florets**\n\n**4 scallions, cut into 1-inch lengths**\n\n**1 tablespoon reduced-sodium soy sauce**\n\n**\u00bd teaspoon hot chili paste (optional)**\n\n1. Heat large deep skillet or wok over high heat until drop of water sizzles in pan. Add oil and swirl to coat skillet. Add steak and stir-fry until lightly browned, about 2 minutes. Transfer to plate.\n\n2. Add ginger and garlic to skillet and stir-fry until fragrant, about 30 seconds. Add broccoli and scallions and stir-fry until just softened, about 2 minutes longer.\n\n3. Return steak to skillet along with soy sauce and chili paste, if using. Stir-fry until beef is just cooked through, about 2 minutes longer.\n\n**PER SERVING** (1\u00bd cups): 262 Cal, 11 g Total Fat, 3 g Sat Fat, 1 g Trans Fat, 80 mg Chol, 400 mg Sod, 10 g Total Carb, 5 g Fib, 32 g Prot, 113 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nTo easily cut the steak into thin strips, put it in the freezer for about 30 minutes before slicing.\n\n# Summer Squash Stuffed with Beef and Olives\n\nSERVES 4\n\n**2 large (\u00bd pound) yellow summer squash**\n\n**\u00bd teaspoon salt**\n\n**1\u00bd teaspoons canola oil**\n\n**\u00be pound lean ground beef (7% fat or less)**\n\n**\u00bd cup frozen chopped onion**\n\n**3 garlic cloves, chopped**\n\n**\u00bd teaspoon Italian seasoning**\n\n**\u00bc cup chopped black olives**\n\n**\u00bc cup fat-free sour cream**\n\n**3 tablespoons plain dried bread crumbs**\n\n1. Cut each squash in half lengthwise. Using small spoon, scoop out and discard most of flesh, leaving \u00bc-inch border all around. Place squash halves on microwavable plate, sprinkle insides of squash with salt, and cover loosely with wax paper. Microwave on High until squash is very tender but still holds its shape, 2\u20133 minutes; set aside.\n\n2. Meanwhile, preheat broiler and line baking sheet with foil.\n\n3. Heat oil in large skillet over high heat. Add beef, onion, garlic, and Italian seasoning and cook, breaking meat up, until meat is no longer pink and vegetables are tender, about 4 minutes. Stir in olives, sour cream, and 2 tablespoons of bread crumbs and remove from heat.\n\n4. Mound beef mixture into squash halves and sprinkle tops with remaining 1 tablespoon bread crumbs. Broil 5 inches from heat until tops are browned, about 2 minutes.\n\n**PER SERVING** (1 stuffed squash half): 201 Cal, 8 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 49 mg Chol, 465 mg Sod, 13 g Total Carb, 2 g Fib, 19 g Prot, 75 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nDo it Faster\n\nItalian seasoning is a time-saving herb blend to keep on hand. It contains oregano, thyme, and basil\u2014all the herbs you would usually add to an Italian dish, but in one container.\n\n# Pork with Sweet Coconut-Peanut Sauce\n\nSERVES 4\n\n**\u2153 cup light (reduced-fat) coconut milk**\n\n**\u2153 cup reduced-sodium chicken broth**\n\n**2 tablespoons peanut butter**\n\n**1 tablespoon packed light brown sugar**\n\n**2 teaspoons grated peeled fresh ginger**\n\n**4 (\u00bc-pound) lean boneless pork loin chops, trimmed**\n\n**\u00bc teaspoon cayenne pepper**\n\n**\u00bc teaspoon salt**\n\n**1 tablespoon peanut or canola oil**\n\n**3 scallions, thinly sliced**\n\n1. Combine coconut milk, broth, peanut butter, sugar, and ginger in small bowl and stir until smooth. Set aside.\n\n2. Sprinkle pork with cayenne and salt. Heat oil in large nonstick skillet over medium heat. Add pork and cook, turning once, until an instant-read thermometer inserted into side of each chop registers 145\u00b0F, 6\u20138 minutes. Transfer pork to plate and cover loosely with foil to keep warm.\n\n3. Add coconut milk mixture to same skillet; set over medium heat and cook, stirring, until sauce is slightly thickened, about 2 minutes. Pour over chops and sprinkle with scallions.\n\n**PER SERVING** (1 chop and 2 tablespoons sauce): 290 Cal, 17 g Total Fat, 5 g Sat Fat, 0 g Trans Fat, 70 mg Chol, 288 mg Sod, 7 g Total Carb, 1 g Fib, 27 g Prot, 22 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nCayenne pepper adds spice to this dish, but if you're making it for young ones, you can omit it. This dish is also delicious made with skinless boneless chicken breasts instead of the pork chops.\n\nPork Chops with Ginger and Snow Peas\n\n# Pork Chops with Ginger and Snow Peas\n\nSERVES 4\n\n**4 (5-ounce) lean bone-in pork loin chops, trimmed**\n\n**\u00bc teaspoon salt**\n\n**2 teaspoons canola oil**\n\n**\u00bd cup reduced-sodium chicken broth**\n\n**2 tablespoons hoisin sauce**\n\n**2 tablespoons matchstick-thin strips peeled fresh ginger**\n\n**2 garlic cloves, sliced**\n\n**2 teaspoons reduced-sodium soy sauce**\n\n**1 teaspoon Asian (dark) sesame oil**\n\n**1\u00bd cups frozen snow peas, thawed**\n\n**1 teaspoon toasted sesame seeds**\n\n1. Sprinkle pork with salt. Heat canola oil in large nonstick skillet over medium heat. Add pork and cook, turning once, until an instant-read thermometer inserted into side of each chop registers 145\u00b0F, 6\u20138 minutes. Transfer pork to plate and cover loosely with foil to keep warm.\n\n2. Add broth, hoisin sauce, ginger, garlic, soy sauce, and sesame oil to same skillet. Cook, scraping up any browned bits from bottom of pan with wooden spoon, until mixture is slightly thickened, 2\u20133 minutes. Stir in snow peas and cook until heated through, 1 minute.\n\n3. Sprinkle snow peas with sesame seeds and serve with chops.\n\n**PER SERVING** (1 chop and \u2153 cup snow peas): 260 Cal, 13 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 70 mg Chol, 483 mg Sod, 9 g Total Carb, 2 g Fib, 27 g Prot, 36 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nDo it Faster\n\nTo quickly make matchstick-thin strips of peeled ginger, thinly slice a piece of ginger, keeping the slices in a neat stack. Then, cut the slices into thin strips.\n\n# Chicken Piccata\n\nSERVES 4\n\n**2 tablespoons all-purpose flour**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**4 (\u00bc-pound) thin-sliced skinless boneless chicken breasts**\n\n**2 tablespoons unsalted butter**\n\n**\u00bd cup reduced-sodium chicken broth**\n\n**\u00bc cup fresh lemon juice**\n\n**1 tablespoon drained capers**\n\n**2 tablespoons chopped fresh parsley**\n\n1. Combine flour, \u00bd teaspoon of salt, and \u215b teaspoon of pepper in large bowl. Working one at a time, dip both sides of chicken into flour mixture and shake off excess. Place on large plate.\n\n2. Melt 1 tablespoon of butter in large skillet over medium-high heat. Add chicken and cook until lightly browned and cooked through, 3\u20134 minutes on each side; transfer chicken to plate and cover to keep warm.\n\n3. Add broth, lemon juice, and capers into skillet and bring to boil. Reduce heat and simmer until slightly reduced, about 2 minutes. Remove from heat, then swirl in parsley and remaining 1 tablespoon butter, \u00bc teaspoon salt, and \u215b teaspoon pepper. Pour sauce over chicken.\n\n**PER SERVING** (1 piece chicken and 2 tablespoons sauce): 211 Cal, 9 g Total Fat, 5 g Sat Fat, 0 g Trans Fat, 84 mg Chol, 635 mg Sod, 4 g Total Carb, 0 g Fib, 26 g Prot, 22 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nServe this classic quick dish with whole wheat angel hair pasta (\u00bd cup cooked whole wheat angel hair pasta per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# Chicken in Coconut-Curry Sauce\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 onion, diced**\n\n**2 teaspoons curry powder**\n\n**1 cup light (reduced-fat) coconut milk**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**2 tablespoons tomato paste**\n\n**1 pound skinless boneless chicken breast, cut into 1-inch cubes**\n\n**\u00bc teaspoon salt**\n\n**1 (5-ounce) bag baby spinach**\n\n**1 cup frozen peas**\n\n1. Heat oil in large nonstick skillet over medium heat. Add onion and cook, stirring occasionally, until softened, about 4 minutes. Stir in curry powder. Add coconut milk, tomatoes, and tomato paste and bring to boil.\n\n2. Add chicken and salt to skillet and cook until chicken is no longer pink in center, about 4 minutes. Add spinach and peas and cook until spinach is wilted and peas are tender, about 2 minutes.\n\n**PER SERVING** (1\u00bd cups): 272 Cal, 9 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 63 mg Chol, 440 mg Sod, 21 g Total Carb, 7 g Fib, 28 g Prot, 75 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nBrown basmati rice is the perfect accompaniment to this quick curry dish. It takes about 50 minutes to cook, so make a batch on the weekend to serve with meals throughout the week (\u00bd cup cooked brown basmati rice will increase the **_PointsPlus_** value by **_3_** ).\n\n# Chicken Tikka with Cucumber Raita\n\nSERVES 4\n\n**1 cup plain fat-free yogurt**\n\n**Juice of \u00bd lemon**\n\n**2 garlic cloves, peeled**\n\n**1 tablespoon peeled minced fresh ginger**\n\n**\u00be teaspoon salt**\n\n**\u00bd teaspoon garam masala**\n\n**\u00bd teaspoon ground coriander**\n\n**\u00bd teaspoon ground turmeric**\n\n**Pinch cayenne pepper**\n\n**1\u00bc pounds skinless boneless chicken breasts, cut into 1-inch pieces**\n\n**1 cucumber, finely diced**\n\n**\u00bc cup chopped fresh mint**\n\n**Pappadam or other flatbread, toasted (optional)**\n\n1. Preheat broiler. Line baking sheet with foil and spray foil with nonstick spray.\n\n2. Stir together \u2153 cup of yogurt, lemon juice, garlic, ginger, \u00bd teaspoon of salt, garam masala, coriander, turmeric, and cayenne in large bowl; add chicken and toss to coat.\n\n3. Thread chicken on 8 (12-inch) metal skewers. Place skewers on baking sheet. Broil 5 inches from heat until chicken is browned and cooked through, about 4 minutes on each side.\n\n4. Meanwhile, to make raita, stir together remaining \u2154 cup yogurt, cucumber, mint, and remaining \u00bc teaspoon salt in serving bowl. Serve raita with chicken and pappadam, if using.\n\n**PER SERVING** (2 skewers and \u2153 cup raita without pappadam): 181 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 79 mg Chol, 461 mg Sod, 6 g Total Carb, 1 g Fib, 31 g Prot, 90 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nServe the chicken skewers arranged on a bed of brown rice (\u00bd cup cooked brown rice per serving will increase the **_PointsPlus_** value by **_3_** ).\n\nChicken Tikka with Cucumber Raita\n\n# Braised Bok Choy and Chicken with Soba Noodles\n\nSERVES 4\n\n**1 (8-ounce) package soba noodles**\n\n**1 pound skinless boneless chicken breast, thinly sliced**\n\n**\u00bc teaspoon salt**\n\n**4 scallions, sliced**\n\n**1 tablespoon grated peeled fresh ginger**\n\n**2 garlic cloves, minced**\n\n**2 tablespoons hoisin sauce**\n\n**8 heads baby bok choy, quartered**\n\n**2 teaspoons Asian (dark) sesame oil**\n\n1. Cook noodles according to package directions; drain, reserving \u00bd cup of cooking liquid.\n\n2. Meanwhile, spray large skillet with nonstick spray and set over medium heat. Sprinkle chicken with salt; add to skillet and cook, stirring frequently, until lightly browned, about 3 minutes. Add scallions, ginger, and garlic and cook, stirring occasionally, 1 minute. Stir in hoisin sauce. Add bok choy and \u00bd cup of pasta cooking liquid. Cover skillet and cook until bok choy is tender, 4 minutes.\n\n3. Add noodles and oil to skillet and toss until combined.\n\n**PER SERVING** (2 cups): 243 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 63 mg Chol, 422 mg Sod, 20 g Total Carb, 4 g Fib, 29 g Prot, 183 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nDo it Faster\n\nSoba noodles are thin buckwheat noodles that are a smart addition to your weeknight cooking rotation. They cook in about 5 minutes and are perfect for serving with stir-fries when you don't have cooked rice on hand.\n\n# Turkey Cutlets Milanese\n\nSERVES 4\n\n**8 cups baby romaine**\n\n**1 cup cherry tomatoes, halved**\n\n**3 tablespoons fat-free balsamic dressing**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon black pepper**\n\n**1 large egg white**\n\n**1 tablespoon fresh lemon juice**\n\n**\u00bc cup yellow cornmeal**\n\n**2 tablespoons grated Parmesan cheese**\n\n**4 (\u00bc-pound) turkey breast cutlets**\n\n**4 teaspoons olive oil**\n\n1. Toss together romaine, tomatoes, dressing, \u00bc teaspoon of salt, and \u00bc teaspoon of pepper in large bowl; set aside.\n\n2. Whisk together egg white and lemon juice in large shallow bowl. Mix together cornmeal, Parmesan, remaining \u00bc teaspoon salt, and \u00bc teaspoon pepper on sheet of wax paper.\n\n3. Dip each cutlet into egg white mixture, then coat with cornmeal mixture, pressing lightly so it adheres.\n\n4. Heat oil in large nonstick skillet over medium heat. Add cutlets and cook until browned and cooked through, about 3 minutes on each side.\n\n5. Transfer cutlets to 4 plates; top evenly with salad.\n\n**PER SERVING** (1 turkey cutlet and about 1\u00bd cups salad): 251 Cal, 7 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 77 mg Chol, 570 mg Sod, 15 g Total Carb, 3 g Fib, 31 g Prot, 116 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Turkey Cutlets with Orange Sauce\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**4 (\u00bc-pound) turkey breast cutlets**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 shallot, minced**\n\n**2 teaspoons grated orange zest**\n\n**\u2153 cup fresh orange juice**\n\n**\u2153 cup reduced-sodium chicken broth**\n\n**1 tablespoon cornstarch**\n\n**2 tablespoons chopped fresh chives**\n\n1. Heat oil in large skillet over medium-high heat. Sprinkle turkey with salt and pepper. Add cutlets to skillet and cook until lightly browned and cooked through, about 3 minutes on each side. Transfer to plate and cover to keep warm.\n\n2. Reduce heat to medium and add shallot to skillet. Cook, stirring, until softened, about 2 minutes.\n\n3. Whisk together orange zest and juice, broth, and cornstarch in cup until smooth. Add cornstarch mixture to skillet and cook, stirring, until sauce thickens and bubbles, about 1 minute.\n\n4. Transfer turkey to 4 plates; drizzle evenly with sauce. Sprinkle with chives.\n\n**PER SERVING** (1 turkey cutlet and 2\u00bd tablespoons sauce): 166 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 75 mg Chol, 347 mg Sod, 5 g Total Carb, 0 g Fib, 28 g Prot, 20 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nIf you don't have chives on hand, add some thinly sliced scallion tops to add color and flavor to this dish.\n\n# Mediterranean Turkey Burgers\n\nSERVES 4\n\n**1 pound ground skinless turkey breast**\n\n**\u00be teaspoon dried oregano**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd cup finely crumbled feta cheese**\n\n**2 teaspoons olive oil**\n\n**2 large whole wheat pitas, halved**\n\n**1 (5-ounce) jar roasted red peppers, drained (not packed in oil)**\n\n**2 cups mixed baby salad greens**\n\n1. Mix together turkey, oregano, and black pepper in large bowl. With damp hands, shape mixture into 8 thin patties.\n\n2. Place 2 tablespoons of feta in middle of each of 4 patties. Top with remaining patties and pinch edges to enclose cheese and to seal patties.\n\n3. Heat oil in large skillet over medium heat. Add burgers and cook until an instant-read thermometer inserted into side of burger (without touching cheese) registers 165\u00b0F, 5 minutes on each side.\n\n4. Place each burger in pita half. Top evenly with roasted red pepper and salad greens.\n\n**PER SERVING** (1 stuffed pita): 317 Cal, 8 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 91 mg Chol, 717 mg Sod, 25 g Total Carb, 3 g Fib, 34 g Prot, 139 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nThe feta cheese should be in small crumbles for stuffing inside the burgers. This is easiest to do when the cheese is cold, so take it from the refrigerator and immediately break it into fine crumbles.\n\n# Cod with Tomato-Oregano Sauce\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**2 scallions, chopped**\n\n**1 garlic clove, minced**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**\u00bc teaspoon dried oregano**\n\n**1 (1\u00bd-pound) cod fillet, about 1 inch thick, cut into 4 pieces**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n1. Stir together oil, scallions, and garlic in large shallow glass bowl or casserole dish. Cover with wax paper and microwave on High until fragrant, about 1 minute. Stir in tomatoes and oregano. Cover and microwave on High 3 minutes.\n\n2. Spray shallow microwavable dish with nonstick spray. Place cod in dish in one layer. Sprinkle fish with salt and pepper. Cover dish with wax paper and microwave on High until fish is just opaque in center, about 6 minutes. Spoon tomato sauce over fish.\n\n**PER SERVING** (1 fillet cod and \u2153 cup sauce): 194 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 65 mg Chol, 614 mg Sod, 6 g Total Carb, 1 g Fib, 28 g Prot, 43 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nServe the fish with a side of steamed green beans and some whole wheat orzo to soak up the flavorful tomato sauce (\u00bd cup cooked whole wheat orzo per serving will increase the **_PointsPlus_** value by **_2_** ).\n\nCod with Tomato-Oregano Sauce\n\n# Sweet-and-Spicy Salmon with Broccoli Slaw\n\nSERVES 4\n\n**2 tablespoons packed light brown sugar**\n\n**1 teaspoon five-spice powder**\n\n**\u00bc teaspoon salt**\n\n**4 (\u00bc-pound) pieces skinless salmon fillet**\n\n**2 tablespoons reduced-sodium soy sauce**\n\n**2 tablespoons rice vinegar**\n\n**2 teaspoons Asian (dark) sesame oil**\n\n**1 (12-ounce) package broccoli slaw**\n\n**\u00bc cup chopped fresh cilantro**\n\n**3 scallions, thinly sliced**\n\n1. Preheat broiler. Spray broiler pan with nonstick spray and place about 6 inches from heat until pan is hot.\n\n2. Meanwhile, stir together brown sugar, five-spice powder, and salt in small bowl. Sprinkle mixture over tops of salmon fillets.\n\n3. Carefully place salmon fillets on hot broiler pan and broil until salmon is just opaque in center, about 7 minutes.\n\n4. Meanwhile, whisk together soy sauce, vinegar, and oil in large bowl. Add broccoli slaw, cilantro, and scallions and toss to combine. Serve salmon with slaw.\n\n**PER SERVING** (1 salmon fillet and 1 cup slaw): 224 Cal, 7 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 65 mg Chol, 561 mg Sod, 13 g Total Carb, 4 g Fib, 27 g Prot, 77 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nA package of broccoli slaw or regular cabbage slaw is a great item to keep on hand for weeknight meals. You can, of course, use it to make slaw, but you can also quickly saut\u00e9 it for a side dish, add some to a stir-fry, or use it as a crunchy sandwich topping.\n\n# Arctic Char with Cranberry Couscous\n\nSERVES 4\n\n**1\u00bc cups water**\n\n**1 cup whole wheat couscous**\n\n**\u2153 cup dried cranberries or cherries**\n\n**1 teaspoon olive oil**\n\n**1 teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 scallions, chopped**\n\n**\u2153 cup chopped fresh parsley**\n\n**4 (\u00bc-pound) arctic char fillets**\n\n1. Bring water to boil in medium saucepan. Stir in couscous, cranberries, oil, \u00bd teaspoon of salt, and pepper. Remove saucepan from heat. Cover and let stand 5 minutes, then fluff couscous mixture with fork. Spoon couscous mixture into serving bowl and stir in scallions and parsley.\n\n2. Meanwhile, sprinkle arctic char with remaining \u00bd teaspoon salt. Spray large skillet with nonstick spray and set over medium-high heat. Add fish and cook until just opaque in center, about 3 minutes on each side. Serve with couscous.\n\n**PER SERVING** (1 piece arctic char and scant 1 cup couscous): 317 Cal, 10 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 65 mg Chol, 657 mg Sod, 31 g Total Carb, 5 g Fib, 28 g Prot, 83 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nMost Arctic char sold in the United States is farmed sustainably, so it is a good choice to make at the seafood counter. If it is unavailable, you can substitute salmon in this recipe.\n\nCalifornia Fish Tacos\n\n# California Fish Tacos\n\nSERVES 4\n\n**2 (6-ounce) skinless halibut fillets**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon ground cumin**\n\n**8 small taco shells**\n\n**1 cup tender watercress sprigs**\n\n**1 avocado, halved, pitted, peeled, and diced**\n\n**\u00bc cup chopped fresh cilantro**\n\n**\u00bd cup fat-free salsa**\n\n**Lime wedges**\n\n1. Spray broiler rack with nonstick spray and preheat broiler.\n\n2. Sprinkle halibut with salt and cumin. Place fillets on broiler rack and broil 5 inches from heat until fish is just opaque throughout, about 3 minutes on each side. Transfer fish to plate and use fork to flake fish.\n\n3. Divide fish evenly among taco shells. Top evenly with watercress, avocado, and cilantro. Serve with salsa and lime wedges.\n\n**PER SERVING** (2 tacos and 2 tablespoons salsa): 295 Cal, 12 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 60 mg Chol, 685 mg Sod, 23 g Total Carb, 5 g Fib, 25 g Prot, 66 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nHalibut has a firm texture that you can break into large flakes that are perfect for tacos. Other good options are cod, tilapia, or catfish.\n\n# Shrimp and Spaghetti Arrabbiata\n\nSERVES 4\n\n**8 ounces whole wheat spaghetti**\n\n**4 teaspoons olive oil**\n\n**1 pound large peeled and deveined shrimp**\n\n**\u00be teaspoon salt**\n\n**3 garlic cloves, minced**\n\n**1 (15-ounce) can crushed tomatoes**\n\n**3 tablespoons tomato paste**\n\n**\u00bd teaspoon dried oregano**\n\n**\u00bc teaspoon red pepper flakes**\n\n**6 large basil leaves, thinly sliced**\n\n1. Cook spaghetti according to package directions, omitting salt if desired; drain and keep warm.\n\n2. Meanwhile, heat 2 teaspoons of oil in large nonstick skillet over medium heat. Sprinkle shrimp with \u00bd teaspoon of salt. Add half of shrimp to skillet and cook until just opaque in center, about 2 minutes on each side. Transfer to plate. Repeat with remaining shrimp.\n\n3. Add remaining 2 teaspoons oil to skillet. Add garlic and cook, stirring, until fragrant, about 30 seconds. Stir in tomatoes, tomato paste, oregano, and red pepper flakes; cook until slightly thickened, about 5 minutes. Add shrimp, basil, and remaining \u00bc teaspoon salt; cook, stirring occasionally, just until shrimp are heated through, about 1 minute.\n\n4. Divide pasta evenly among 4 plates and top evenly with shrimp and sauce.\n\n**PER SERVING** (1 cup pasta and about \u00bd cup shrimp with sauce): 367 Cal, 7 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 168 mg Chol, 782 mg Sod, 52 g Total Carb, 10 g Fib, 29 g Prot, 102 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nAn Italian-inspired salad is the perfect accompaniment to this traditional dish. Toss together romaine lettuce, halved cherry tomatoes, thinly sliced pepperoncini, sliced red onion, and your favorite fat-free Italian dressing.\n\nShrimp and Spaghetti Arrabbiata\n\n# Shrimp with Cherry Tomatoes and Feta\n\nSERVES 4\n\n**\u2154 cup whole wheat couscous**\n\n**2 teaspoons olive oil**\n\n**\u00be pound medium shrimp, peeled and deveined**\n\n**\u00bc teaspoon salt**\n\n**1 pint cherry tomatoes, halved**\n\n**2 garlic cloves, finely chopped**\n\n**1 teaspoon dried oregano**\n\n**\u00bc cup reduced-sodium chicken broth**\n\n**\u00bc cup chopped fresh dill**\n\n**3 tablespoons crumbled feta cheese**\n\n1. Prepare couscous according to package directions, omitting salt if desired.\n\n2. Meanwhile, heat oil in large skillet over medium-high heat. Add shrimp and salt and cook, stirring, until shrimp begin to turn pink, 1\u20132 minutes.\n\n3. Add tomatoes, garlic, and oregano and cook until tomatoes soften, about 1 minute. Add broth and cook until most of liquid has evaporated, 1\u20132 minutes. Stir in dill and feta and cook 1 minute longer. Serve over couscous.\n\n**PER SERVING** (1 cup shrimp mixture and \u00bd cup couscous): 263 Cal, 5 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 132 mg Chol, 415 mg Sod, 35 g Total Carb, 6 g Fib, 21 g Prot, 87 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nDo it Faster\n\nIt saves time to buy shrimp already peeled and deveined, but to do it yourself as efficiently as possible, peel the shrimp, then use kitchen scissors to slit the flesh on the back of each shrimp. Hold each shrimp under cold running water to rinse away the vein.\n\n# Vegetable Fried Rice\n\nSERVES 6\n\n**1 teaspoon canola oil**\n\n**4 scallions, trimmed and sliced**\n\n**2 garlic cloves, finely chopped**\n\n**1 tablespoon grated peeled fresh ginger**\n\n**\u00bc pound snow peas, sliced lengthwise**\n\n**1 red bell pepper, chopped**\n\n**2 cups cooked white rice**\n\n**2 cups cooked brown rice**\n\n**1 (10-ounce) package frozen mixed vegetables, thawed**\n\n**8 ounces firm tofu, diced**\n\n**2 large eggs, beaten**\n\n**3 tablespoons reduced-sodium soy sauce**\n\n**2 teaspoons Asian (dark) sesame oil**\n\n1. Heat canola oil in large skillet over medium-high heat. Add scallions, garlic, and ginger and cook, stirring, until fragrant, about 30 seconds. Add snow peas and bell pepper and cook until bell pepper softens, about 1 minute. Add white and brown rice, mixed vegetables, and tofu and cook, stirring, until heated through, about 5 minutes.\n\n2. Push rice mixture to edge of skillet, making hollow in center. Pour in eggs and cook, stirring, until eggs are cooked. Stir eggs into rice, drizzle with soy sauce and sesame oil, and toss to combine.\n\n**PER SERVING** (1\u00bc cups): 293 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 71 mg Chol, 358 mg Sod, 42 g Total Carb, 5 g Fib, 14 g Prot, 307 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nIf picky eaters at your house are not sold on the idea of healthy brown rice, this recipe is a good start. With a blend of white and brown rice, this flavor-packed dish might win them over.\n\nBlackened Scallops with Lemon-Caper Mayonnaise\n\n# Blackened Scallops with Lemon-Caper Mayonnaise\n\nSERVES 4\n\n**3 tablespoons fat-free mayonnaise**\n\n**2 teaspoons drained capers, chopped**\n\n**\u00bd teaspoon grated lemon zest**\n\n**1 teaspoon fresh lemon juice**\n\n**1 teaspoon paprika**\n\n**\u00be teaspoon dried oregano**\n\n**\u00bd teaspoon ground coriander**\n\n**\u00bd teaspoon salt**\n\n**12 large sea scallops (about \u00be pound)**\n\n**2 teaspoons olive oil**\n\n1. Combine mayonnaise, capers, zest, and lemon juice in small bowl; cover and refrigerate.\n\n2. Combine paprika, oregano, coriander, and salt on sheet of wax paper. Dip one side of each scallop into spice mixture and set them on plate, spice side up.\n\n3. Heat oil in large skillet over medium-high heat until very hot. Add scallops, spice side down, and cook until scallops are browned and opaque in center, 2\u20133 minutes on each side.\n\n4. Stick small wooden skewer into side of each scallop so that it looks like a lollipop; serve with sauce on side.\n\n**PER SERVING** (3 scallops and scant tablespoon sauce): 80 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 24 mg Chol, 536 mg Sod, 2 g Total Carb, 1 g Fib, 10 g Prot, 57 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nMake these scallops the centerpiece of a \"small plates\" dinner by serving them with Black Bean-Tomatillo Dip with fresh vegetables, here, and plates of roasted red bell peppers (not oil-packed) sprinkled with crumbled fat-free feta cheese (1 ounce of fat-free feta per serving will increase the **_PointsPlus_** value by **_1_** ).\n\n# 10 essential kitchen time-savers\n\nIf you're determined to make healthy, home-cooked meals for your family in minimal time, these tools can make cooking a pleasure.\n\n**FOOD PROCESSOR.** Of course you can use this essential kitchen appliance for making pureed soups, hummus, pesto, and bread crumbs. But, with the basic blade attachments, you can slice, shred, or chop large amounts of vegetables or cheese in seconds.\n\n**HANDHELD ELECTRIC MIXER.** For making small-batch cake and cookie batters and whipping up the fluffiest mashed potatoes ever, a lightweight, easy-to-clean mixer is a must-have. Some models also have attachments for making smoothies and kneading bread dough.\n\n**IMMERSION BLENDER.** With this handy appliance, you can blend soups and puree sauces right in the pot, saving the time it takes to transfer foods to a blender or food processor. Choose a model that does double-duty with an ice crushing attachment.\n\n**SLOW COOKER.** Yes, a slow cooker can help you make fast meals! With a few minutes prep in the morning, you can come home to a ready-made dinner. All you have to do is set the table. See the section \"Slow Cookers Save Time\" here for 19 delicious slow-cooker dishes.\n\n**RICE COOKER.** A rice cooker doesn't cook rice any faster, but this ingenious appliance saves you the time and stress of constantly checking rice to see if it's done while keeping watch over other parts of the meal. With a rice cooker, you add rice and water, turn it on, and then focus on preparing the rest of your dinner.\n\n**KITCHEN SHEARS.** Once you keep a pair of these handy scissors in a kitchen drawer, you'll put them to use every day. They make fast work of peeling and deveining shrimp, trimming fat from steaks and chops, snipping herbs, cutting up dried fruit, and cutting up whole tomatoes right in the can.\n\n**STOVETOP GRILL PAN.** When you're craving the smoky flavor of a grilled dinner, but don't want to spend the time it takes to fire up the grill\u2014not to mention clean up\u2014a stovetop grill pan is the answer. These pans are perfect to grill favorites like steaks, burgers, skinless boneless chicken breasts and thighs, pork chops, shrimp, and salmon fillets.\n\n**HANDHELD GRATER.** Our favorite is the super-sharp Microplane grater, which creates thin shards of citrus zest, hard cheese, nutmeg, chocolate, or coconut in seconds. For cleanup, just toss it in the dishwasher.\n\n**SILICONE BRISTLE BRUSH.** Cooking healthy meals means making a little fat go a long way. With one of these dishwasher-safe brushes, you can coat a baking pan or skillet with a tiny amount of oil in just seconds. Unlike other brushes, these are heat resistant and dishwasher safe\u2014no more laborious hand washing to remove stubborn oils from the bristles!\n\n**PARCHMENT PAPER.** If you hate the time and hard work of scrubbing baking pans, parchment paper will free you from this tedious task. Not only is it good for cake and cookie pans, but use it to line the pan when you bake lasagna, meatballs, or chicken, or when you roast vegetables. Cleanup takes seconds instead of minutes.\n\n# Linguine with White Bean Puttanesca\n\nSERVES 4\n\n**6 ounces whole wheat linguine**\n\n**1 tablespoon olive oil**\n\n**1 onion, chopped**\n\n**3 garlic cloves, minced**\n\n**1 teaspoon dried oregano**\n\n**\u00bc teaspoon red pepper flakes**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**12 pimiento-stuffed olives, sliced**\n\n**1 tablespoon drained capers, chopped**\n\n**1 (15\u00bd-ounce) can small white beans, rinsed and drained**\n\n**\u00bc teaspoon salt**\n\n**2 tablespoons chopped fresh parsley**\n\n1. Cook linguine according to package directions, omitting salt if desired; drain and place in large serving bowl.\n\n2. Meanwhile, heat oil in large skillet over medium-high heat. Add onion, garlic, oregano, and crushed red pepper flakes; cook, stirring occasionally, until onion softens, 2\u20133 minutes. Stir in tomatoes, olives, and capers; simmer, stirring occasionally, until sauce thickens, 6\u20137 minutes. Add beans and salt; cook until heated through, about 1 minute.\n\n3. Pour beans and sauce over linguine, sprinkle with parsley.\n\n**PER SERVING** (1\u00bd cups): 324 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 897 mg Sod, 57 g Total Carb, 10 g Fib, 15 g Prot, 139 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\n# Fettuccine with Goat Cheese, Arugula, and Tomatoes\n\nSERVES 4\n\n**1 (9-ounce) package fresh fettuccine**\n\n**1 (4-ounce) log goat cheese, crumbled**\n\n**1 (5-ounce) bag baby arugula**\n\n**1\u00bd cups cherry or grape tomatoes, quartered**\n\n**\u00bd teaspoon black pepper**\n\n1. Cook fettuccine according to package directions; drain, reserving 1 cup of cooking water.\n\n2. Return pasta to pot with \u00bd cup of cooking water and place over low heat. Add goat cheese, arugula, tomatoes, and pepper; toss until cheese melts and arugula just begins to wilt, about 1 minute. Add more cooking water if pasta is too dry.\n\n**PER SERVING** (1\u00bc cups): 270 Cal, 9 g Total Fat, 5 g Sat Fat, 0 g Trans Fat, 49 mg Chol, 323 mg Sod, 36 g Total Carb, 3 g Fib, 12 g Prot, 119 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nFor a milder dish, you can make this recipe using baby spinach instead of the peppery arugula.\nFettuccine with Goat Cheese, Arugula, and Tomatoes\n\n# snacks and sweets\n\n# Black Bean-Tomatillo Dip\n\nSERVES 6\n\n**2 (15\u00bd-ounce) cans black beans, rinsed and drained**\n\n**1 (12-ounce) can tomatillos, drained and coarsely chopped**\n\n**1 (4\u00bd-ounce) can chopped green chiles, drained**\n\n**3 scallions, chopped**\n\n**\u00bd cup chopped fresh cilantro**\n\n**2\u20134 tablespoons water**\n\n**3 tablespoons fresh lime juice**\n\n**2 teaspoons chili powder**\n\n**2 teaspoons ground cumin**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon black pepper**\n\n1. Combine beans and tomatillos in food processor and pulse until chunky puree forms.\n\n2. Transfer bean mixture to large bowl and add remaining ingredients; stir until well combined.\n\n**PER SERVING** (\u2153 cup): 102 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 390 g Sod, 17 g Total Carb, 7 g Fib, 6 g Prot, 38 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nFor a satisfying vegetarian lunch, start with this dip paired with any fresh vegetables you have on hand. Then enjoy a bowl of Winter Squash Soup with Lime Cream, here.\n\n# Sun-Dried Tomato Hummus\n\nSERVES 4\n\n**6 sun-dried tomatoes (not packed in oil)**\n\n**1 (15\u00bd-ounce) can chickpeas, rinsed and drained**\n\n**2 tablespoons tahini**\n\n**1 tablespoon fresh lemon juice**\n\n**1 garlic clove, chopped**\n\n**\u00bc teaspoon salt**\n\n**Pinch cayenne pepper**\n\n1. Put tomatoes in small bowl and add boiling water to cover. Let stand 10 minutes; remove tomatoes and reserve liquid.\n\n2. Combine tomatoes and remaining ingredients in food processor and pulse until smooth, adding some of reserved liquid if hummus seems too thick.\n\n**PER SERVING** (\u00bc cup): 56 Cal, 5 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 14 mg Chol, 176 mg Sod, 2 g Total Carb, 0 g Fib, 2 g Prot, 19 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nHummus is a handy condiment to have on hand. Serve it with celery and carrot sticks for a snack, spread it on bread and top with tomato slices for a lunchtime sandwich, or serve it alongside grilled chicken or salmon for dinner.\n\nFrom top, clockwise: Chunky Guacamole, Black Bean-Tomatillo Dip, here, and Crispy Green Plantains, here\n\n# Chunky Guacamole\n\nSERVES 6\n\n**2 Hass avocados, halved, pitted, and peeled**\n\n**1 small tomato, seeded and chopped**\n\n**\u00bc cup chopped fresh cilantro**\n\n**\u00bc cup finely chopped onion**\n\n**1\u00bd tablespoons fresh lime or lemon juice**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**4 drops hot pepper sauce**\n\nCoarsely mash avocados in medium bowl. Add remaining ingredients and stir until combined. Serve at once or press piece of plastic wrap directly onto surface to prevent guacamole from browning. Refrigerate up to 3 hours.\n\n**PER SERVING** (2 tablespoons): 82 Cal, 7 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 204 mg Sod, 5 g Total Carb, 3 g Fib, 1 g Prot, 10 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nServe this classic Tex-Mex dish with fresh cut-up vegetables for a snack or with grilled shrimp for an easy, yet flavorful main dish.\n\n# Red Pepper and Sun-Dried Tomato Dip\n\nSERVES 12\n\n**1 (8-ounce) package light cream cheese (Neufch\u00e2tel)**\n\n**\u00bd cup jarred roasted red pepper (not packed in oil), drained**\n\n**6 moist sun-dried tomatoes (not packed in oil), sliced**\n\n**1 small garlic clove, crushed with a press**\n\n**1 teaspoon Italian seasoning or dried oregano**\n\n**\u00bc teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\nCombine all ingredients in food processor and puree.\n\n**PER SERVING** (about 2 tablespoons): 111 Cal, 4 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 14 mg Chol, 141 mg Sod, 1 g Total Carb, 0 g Fib, 2 g Prot, 16 mg Calc.\n\n**_PointsPlus_** value: **_1._**\n\nCook's Note\n\nServe the dip with any fresh vegetables that you have on hand. Try small white mushrooms or cherry tomatoes, cucumber spears, broccoli florets, or celery sticks.\n\n# Spicy Cereal and Pretzel Snack Mix\n\nSERVES 10\n\n**2 tablespoons unsalted butter, melted**\n\n**1 tablespoon curry powder**\n\n**1 tablespoon reduced-sodium soy sauce**\n\n**1\u00bd teaspoons sugar**\n\n**1\u00bd teaspoons paprika**\n\n**1 teaspoon ground cumin**\n\n**\u00bc teaspoon salt**\n\n**\u215b\u2013\u00bc teaspoon cayenne pepper**\n\n**2\u00bd cups crispy rice cereal squares**\n\n**2\u00bd cups crispy corn cereal squares**\n\n**\u00bd cup tiny pretzel twists**\n\n**3 tablespoons lightly salted peanuts**\n\n1. Stir together butter, curry powder, soy sauce, sugar, paprika, cumin, salt, and cayenne in small bowl.\n\n2. Toss together rice cereal, corn cereal, and pretzel twists in large bowl. Add butter mixture to cereal mixture and toss until evenly coated. Stir in peanuts. Store in an airtight container at room temperature up to 2 weeks.\n\n**PER SERVING** (about \u00bd cup): 100 Cal, 4 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 6 mg Chol, 273 mg Sod, 15 g Total Carb, 1 g Fib, 2 g Prot, 53 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\n# Crispy Green Plantains\n\nSERVES 4\n\n**4 teaspoons olive oil**\n\n**2 green plantains, peeled and cut on diagonal into \u00bd-inch slices (about 20 pieces)**\n\n**1 teaspoon salt**\n\n1. Heat oil in large nonstick skillet over medium heat. Cook plantains, in batches, until tender and golden brown, about 5 minutes on each side. Transfer plantain slices to double thickness of paper towels to drain. With bottom of heavy plate or saucepan, gently press down on slices, one at time, to flatten to \u00bc-inch thickness.\n\n2. Spray same skillet with olive oil nonstick spray and set over medium heat. Add plantain slices, in batches, and cook until nicely browned, about 1 minute on each side. Sprinkle with salt while hot.\n\n**PER SERVING** (about 5 pieces): 185 Cal, 3 g Total Fat, 0 Sat Fat, 0 g Trans Fat, 0 Chol, 153 mg Sod, 44 g Total Carb, 3 g Fiber, 1 g Prot, 4 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nHere's how to peel a plantain: cut off both ends, then cut it crosswise in half. Using small knife, slit the skin along its ridges, cutting down to the flesh, then peel off the skin.\n\n# Microwave Apple-Pear Crisp\n\nSERVES 6\n\n**2 Golden Delicious apples, peeled, cored, and thinly sliced**\n\n**2 Bartlett pears, peeled, cored, and thinly sliced**\n\n**\u00bc cup dried cherries or cranberries**\n\n**4 tablespoons packed light brown sugar**\n\n**\u00be teaspoon cinnamon**\n\n**1 cup low-fat granola**\n\n**2 tablespoons unsalted butter, melted**\n\n1. Spray microwavable 8-inch square dish with nonstick spray.\n\n2. Stir together apples, pears, dried cherries, 3 tablespoons of brown sugar, and \u00bd teaspoon of cinnamon in large bowl. Spread evenly in baking dish.\n\n3. Toss together granola, butter, and remaining 1 tablespoon brown sugar and \u00bc teaspoon cinnamon in small bowl. Sprinkle granola mixture evenly over fruit mixture. Microwave on High until apples and pears are tender, about 8 minutes. Serve warm or at room temperature.\n\n**PER SERVING** (1\/6 of crisp): 202 Cal, 5 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 10 mg Chol, 72 mg Sod, 41 g Total Carb, 4 g Fib, 2 g Prot, 27 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Brown Sugar Plums\n\nSERVES 4\n\n**\u00bc cup plus 1 tablespoon sliced almonds**\n\n**3 tablespoons packed brown sugar**\n\n**2 teaspoons unsalted butter, melted**\n\n**6 ripe red or purple plums, halved and pitted**\n\n**\u00bd cup plain fat-free Greek yogurt**\n\n**1 tablespoon honey**\n\n1. Preheat oven to 425\u00b0F. Spray large baking sheet with nonstick spray.\n\n2. Combine \u00bc cup of almonds and brown sugar in food processor and pulse until almonds are finely ground. Add butter and process just until combined.\n\n3. Arrange plums, cut side up, on baking sheet. Fill cavity of each plum half with level \u00bd teaspoon of almond mixture; reserve remaining mixture. Roast until almond mixture is browned and plums are softened, about 15 minutes.\n\n4. Meanwhile, stir together yogurt and honey in small bowl.\n\n5. Stir together remaining ground almond mixture with remaining 1 tablespoon almonds in small bowl. Place 3 plum halves on each of 4 plates. Spoon generous 2 tablespoons of yogurt mixture on each plate and sprinkle evenly with remaining almond mixture.\n\n**PER SERVING** (3 plum halves and 1 tablespoon almond mixture): 176 Cal, 6 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 6 mg Chol, 28 mg Sod, 29 g Total Carb, 2 g Fib, 4 g Prot, 94 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nBrown sugar is made by combining white granulated sugar with molasses. Light brown and dark brown sugar can be used interchangeably in most recipes, though dark brown sugar has a slightly more robust flavor.\n\n# Bananas Foster\n\nSERVES 6\n\n**1\u00bd tablespoons unsalted butter**\n\n**\u00bc cup packed dark brown sugar**\n\n**2 teaspoons lemon juice**\n\n**1 teaspoon vanilla extract**\n\n**\u00bc teaspoon cinnamon**\n\n**2 firm-ripe bananas, cut on an angle into \u00bc-inch-thick slices**\n\n**2 tablespoons orange liqueur**\n\n**2 cups fat-free vanilla frozen yogurt**\n\n1. Heat medium nonstick skillet over medium-low heat. Add butter, sugar, lemon juice, vanilla, and cinnamon; cook, stirring, until butter melts and sugar dissolves, about 1 minute. Add bananas and cook, stirring occasionally, until bananas soften, 3\u20134 minutes.\n\n2. Pour in orange liqueur. Touch lit match to surface of skillet to ignite; cook, shaking pan, until flame goes out, about 30 seconds. Remove skillet from heat.\n\n3. Place \u2153 cup scoop of frozen yogurt into each of 6 bowls. Top with warm banana mixture and serve at once.\n\n**PER SERVING** (\u2153 cup bananas and \u2153 cup frozen yogurt): 188 Cal, 3 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 9 mg Chol, 50 mg Sod, 37 g Total Carb, 1 g Fib, 3 g Prot, 127 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nUse long match or long-handled sparker to safely ignite the liqueur. If you'd prefer not to use alcohol, substitute 2 tablespoons orange juice and skip this step.\n\n# **30**  \nMinute meals\n\n30 Minute Breakfasts\n\nSpanish Frittata\n\nFlorentine Frittata\n\nMini Mexican Frittatas\n\nRanch-Style Eggs over Polenta\n\nBrown Rice and Honey Pancakes\n\nWild Blueberry and Cornmeal Pancakes\n\nPeach Muesli with Almonds\n\nCreamy Couscous Breakfast Pudding\n\nSpice-Roasted Pears with Yogurt\n\n30 Minute Lunches\n\nPhilly Cheese Steak Sandwiches\n\nOpen-Faced Garlicky Steak Sandwiches\n\nCuban Beef Lettuce Wraps\n\nBeef and Black Bean Burgers\n\nHoney-Mustard Turkey Sandwiches\n\nDilled Salmon Sandwiches with Caper Sauce\n\nTuna Steak Sandwiches with Roasted Pepper Relish\n\nCrunchy Fish Sliders\n\nQuesadillas with Guacamole and Pepper Jack\n\nAsian-Style Pork, Mushroom, and Noodle Soup\n\nManhattan Clam Chowder\n\nSmoky Vegetarian Chili\n\nHearty Corn Chowder\n\nPotato-Watercress Soup\n\nCreamy Tomato Soup\n\nCremini Mushroom, Tomato, and Rice Soup\n\nEdamame Salad with Basil Vinaigrette\n\nPasta Salad with Apple and Chicken\n\nTabbouleh with Shrimp\n\nHearty Lentil Salad with Radicchio\n\nGreek Pita Pizzas with Spinach and Feta\n\n30 Minute Dinners\n\nFilets Mignons with Tomato-Bean Salsa\n\nSliced Steak with Crispy Polenta\n\nGrilled Flank Steak with Tomato-Fennel Salad\n\nCurried Beef Kebabs with Basmati Rice\n\nHearty Steak and Vegetables\n\nSpaghetti with Quick Bolognese Sauce\n\nStir-Fried Beef with Asparagus\n\nRoast Pork Tenderloin with Black Bean Salsa\n\nCajun-Spiced Roast Pork Tenderloin\n\nSaucy Pan-Roasted Pork Chops with Ziti\n\nPork and Mushroom Stir-Fry\n\nHam with Apples and Mustard\n\nMinted Lamb Chops with Lemony Bulgur\n\nGrilled Lamb Chops and Asparagus with Lemon-Garlic Mayonnaise\n\nMoroccan-Style Chicken\n\nChicken and Vegetables with Fettucine\n\nLemony Chicken Kebabs with Couscous\n\nTeriyaki Chicken and Snow Pea Stir-Fry\n\nQuick Chicken Satay with Asparagus\n\nChicken Picadillo\n\nWarm Lentil Salad with Baked Salmon\n\nRoasted Salmon with Caramelized Onions and Carrots\n\nTilapia with Tomato and Feta\n\nSalmon Patties with Chunky Tomato Relish\n\nCreole-Style Cod Fillets\n\nTeriyaki-Glazed Tofu and Vegetable Kebabs\n\nChunky Vegetable Paella\n\nLinguine with Fontina and Artichokes\n\nFour-Vegetable Stir-Fry with Tofu\n\n30 Minute Snacks and Sweets\n\nEdamame Dip\n\nSmoky Pumpkin Seeds\n\nPizza Margherita\n\nMushroom, Scallion, and Cheddar Quesadillas\n\nRicotta, Bacon, and Spinach Pizza\n\nBaked Cheesy Nachos\n\nBlueberries with Whipped Ricotta and Balsamic Syrup\n\nOven-Roasted Peaches with Raspberries and Sorbet\n\nFrozen Vanilla Yogurt with Sugared Shredded Wheat\n\nBlack and White Muffin Bites\n\n# breakfasts\n\n# Spanish Frittata\n\nSERVES 4\n\n**\u00bd teaspoon canola oil**\n\n**1 small red bell pepper, diced**\n\n**\u00bd cup diced onion**\n\n**1 (14\u00bd-ounce) can sliced potatoes, rinsed and drained**\n\n**6 large eggs**\n\n**6 large egg whites**\n\n**\u00bc teaspoon black pepper**\n\n**Paprika**\n\n**2 tablespoons chopped fresh parsley**\n\n1. Preheat broiler.\n\n2. Coat 10-inch ovenproof nonstick skillet with oil and place over medium heat. Add bell pepper and onion and cook until softened, about 8 minutes. Add potatoes, breaking up larger slices with side of wooden spoon.\n\n3. Whisk together eggs, egg whites, and pepper in medium bowl. Pour over vegetables in pan and stir gently. Cook, lifting edges frequently with spatula to let any uncooked egg flow underneath, until eggs are almost set, about 5 minutes.\n\n4. Place skillet under broiler 5 inches from heat and broil until eggs are set and top is lightly browned, 4 minutes. Invert frittata onto plate, sprinkle with paprika and parsley, and cut into 4 wedges.\n\n**PER SERVING** (1 wedge): 203 Cal, 8 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 318 mg Chol, 651 mg Sod, 15 g Total Carb, 3 g Fib, 17 g Prot, 56 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nServe the frittata with reduced-calorie whole wheat toast (1 slice of reduced-calorie whole wheat toast per serving will increase the **_PointsPlus_** value by **_1_** ).\n\n# Florentine Frittata\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 small onion, chopped**\n\n**1 (10-ounce) package frozen chopped spinach, thawed and squeezed dry**\n\n**3 large eggs**\n\n**5 large egg whites**\n\n**\u00bc cup crumbled reduced-fat feta cheese**\n\n**\u00bc teaspoon salt**\n\n**\u00bd cup shredded part-skim mozzarella cheese**\n\n**1 cup grape tomatoes, halved**\n\n1. Heat 1 teaspoon of oil in 10-inch ovenproof nonstick skillet over medium heat. Add onion and cook, stirring frequently, until softened, about 5 minutes.\n\n2. Preheat broiler. Scrape onion into large bowl and add spinach, eggs, egg whites, feta, salt, and \u00bc cup of mozzarella. Mix with fork until well blended.\n\n3. Heat remaining 1 teaspoon oil in same skillet over medium heat. Pour egg mixture into skillet and scatter tomatoes on top. Cover skillet and cook until eggs are just set around edges, 5 minutes.\n\n4. Place skillet under broiler 5 inches from heat and broil until frittata is lightly browned and just set in center, about 4 minutes. Sprinkle with remaining \u00bc cup mozzarella; broil until cheese melts, about 1 minute longer. Cut into 4 wedges.\n\n**PER SERVING** (1 wedge): 191 Cal, 10 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 170 mg Chol, 494 mg Sod, 9 g Total Carb, 3 g Fib, 17 g Prot, 240 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nDo it Faster\n\nTo quickly thaw frozen spinach, remove it from the package, place in a microwavable bowl, cover with wax paper, and microwave on the defrost setting for 2 to 3 minutes, breaking spinach up halfway through defrosting.\n\n# Mini Mexican Frittatas\n\nSERVES 6\n\n**4 large eggs**\n\n**\u00bc cup low-fat (1%) milk**\n\n**\u00bc cup mild salsa**\n\n**\u00bc cup shredded reduced-fat Cheddar cheese**\n\n**\u00bc teaspoon ground cumin**\n\n**\u00bc teaspoon salt**\n\n1. Preheat oven to 350\u00b0F. Spray 6-cup muffin pan with nonstick spray.\n\n2. Whisk together eggs, milk, salsa, Cheddar cheese, cumin, and salt in medium bowl. Ladle mixture evenly into muffin cups.\n\n3. Bake until egg mixture puffs up and edges are golden brown, about 20 minutes. Remove pan from oven, run knife around edge of each cup, and lift frittatas out.\n\n**PER SERVING** (1 frittata): 71 Cal, 5 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 145 mg Chol, 218 mg Sod, 2 g Total Carb, 0 g Fib, 6 g Prot, 63 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nFreshen up the flavor of purchased salsa by stirring in chopped fresh cilantro and a squeeze of lime before using it in recipes.\n\n# Ranch-Style Eggs over Polenta\n\nSERVES 4\n\n**1 (16-ounce) tube fat-free polenta, cut into 12 slices**\n\n**1 (15\u00bd-ounce) can pinto beans, rinsed and drained**\n\n**1 cup fat-free chunky salsa**\n\n**\u00bd teaspoon ground cumin**\n\n**\u00bd teaspoon canola oil**\n\n**4 large eggs**\n\n**\u00bd cup shredded reduced-fat Cheddar cheese**\n\n**2 tablespoons chopped fresh cilantro**\n\n1. Preheat oven to 425\u00b0F. Spray baking sheet with nonstick spray.\n\n2. Arrange polenta slices in single layer on baking sheet. Spray polenta lightly with nonstick spray. Bake until hot, about 15 minutes.\n\n3. Meanwhile, combine beans, salsa, and cumin in small saucepan; bring to boil. Reduce heat and simmer, covered, about 10 minutes.\n\n4. Coat large nonstick skillet with oil. Crack eggs into skillet; set over medium heat and cook until yolks just begin to set, 2\u20133 minutes. Remove skillet from heat and sprinkle eggs with Cheddar cheese and cilantro. Cover skillet and let stand until cheese melts, about 2 minutes.\n\n5. To serve, place 3 polenta slices on each of 4 plates. Spoon beans over polenta and top with an egg.\n\n**PER SERVING** (3 slices polenta, \u00bd cup beans, and 1 egg): 301 Cal, 9 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 215 mg Chol, 945 mg Sod, 37 g Total Carb, 6 g Fib, 19 g Prot, 177 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nDo it Faster\n\nPrepared polenta is a must-have staple for quick meals. It's delicious for breakfast with eggs or drizzled with a touch of syrup or honey, at lunch it's a great way to serve topped with saut\u00e9ed veggies, or enjoy it for dinner with a quick Bolognese sauce.\n\nBrown Rice and Honey Pancakes\n\n# Brown Rice and Honey Pancakes\n\nSERVES 2\n\n**\u00bd cup cooked brown rice**\n\n**1 cup fat-free milk**\n\n**2 tablespoons honey**\n\n**\u2153 cup all-purpose flour**\n\n**3 tablespoons wheat germ**\n\n**1 teaspoon baking powder**\n\n**\u00bc teaspoon salt**\n\n**\u00bc cup fat-free egg substitute**\n\n**\u00bd teaspoon canola oil**\n\n**1 cup unsweetened applesauce**\n\n**2 tablespoons ground flaxseed**\n\n1. Combine rice, milk, and honey in small saucepan and bring to boil over medium-high heat. Reduce heat and simmer 5 minutes. Transfer mixture to shallow bowl and let cool about 10 minutes.\n\n2. Meanwhile, whisk together flour, wheat germ, baking powder, and salt in medium bowl. Stir in lukewarm rice mixture and egg substitute.\n\n3. Coat nonstick griddle or large nonstick skillet with oil and set over medium heat. Drop batter by \u00bc cupfuls onto griddle and cook pancakes until bubbles appear and edges look dry, about 3 minutes. Turn and cook until deep golden brown, about 2 minutes longer.\n\n4. Transfer pancakes to 2 plates and top evenly with applesauce and flaxseed.\n\n**PER SERVING** (3 pancakes and \u00bd cup applesauce): 379 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 2 mg Chol, 792 mg Sod, 73 g Total Carb, 7 g Fib, 15 g Prot, 373 mg Calc.\n\n**_PointsPlus_** value: **_10._**\n\nCook's Note\n\nTop the pancakes with sliced banana or a handful of fresh berries.\n\n# Wild Blueberry and Cornmeal Pancakes\n\nSERVES 4\n\n**1 cup reduced-fat all-purpose baking mix**\n\n**1 cup yellow cornmeal**\n\n**1\u00bc cups low-fat (1%) milk**\n\n**1 large egg, beaten**\n\n**3 tablespoons sugar**\n\n**1\u00bc cups fresh or frozen wild blueberries**\n\n**\u00bd teaspoon canola oil**\n\n1. Stir together baking mix, cornmeal, milk, egg, and sugar in large bowl just until moistened. Gently stir in blueberries.\n\n2. Coat nonstick griddle or large nonstick skillet with oil and set over medium heat. Drop batter by heaping \u00bc cupfuls onto griddle and cook pancakes until bubbles appear and edges look dry, about 3 minutes. Turn and cook until browned, about 2 minutes longer.\n\n**PER SERVING** (3 pancakes): 341 Cal, 5 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 56 mg Chol, 388 mg Sod, 64 g Total Carb, 4 g Fib, 10 g Prot, 136 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nWild blueberries are often available in the freezer section of large supermarkets. They are appreciated for their intense sweet-tart flavor. You can substitute regular blueberries if you wish.\n\n# Peach Muesli with Almonds\n\nSERVES 6\n\n**2 cups rolled (old-fashioned) oats**\n\n**1 cup fat-free milk**\n\n**\u00be cup chopped dried peaches**\n\n**\u00bc cup golden raisins**\n\n**\u00bc cup apple juice**\n\n**1 cup plain fat-free yogurt**\n\n**2 tablespoons honey**\n\n**\u00bc cup sliced almonds**\n\n1. Stir together oats, milk, peaches, raisins, and apple juice in medium bowl; let stand 25 minutes, stirring occasionally.\n\n2. Meanwhile, stir together yogurt and honey in small bowl.\n\n3. Divide oat mixture evenly among 6 bowls. Top evenly with yogurt mixture and almonds.\n\n**PER SERVING** (\u00bd cup): 255 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 2 mg Chol, 53 mg Sod, 48 g Total Carb, 5 g Fib, 10 g Prot, 165 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nMake the muesli a more filling breakfast by topping it with a small sliced banana or if you like a little crunch, a chopped fresh apple.\n\n# Creamy Couscous Breakfast Pudding\n\nSERVES 6\n\n**1\u00bd cups water**\n\n**1 cup whole wheat couscous**\n\n**Pinch salt**\n\n**3 cups fat-free milk**\n\n**2 tablespoons packed brown sugar**\n\n**\u00bd teaspoon grated orange zest**\n\n**\u00bc cup fat-free egg substitute**\n\n**\u00bc cup toasted wheat germ**\n\n**\u00be teaspoon vanilla extract**\n\n1. Bring water to boil in large heavy saucepan over high heat. Stir in couscous and salt. Reduce heat and simmer until water is absorbed, about 2 minutes. Remove saucepan from heat and fluff couscous with fork. Cover and let stand about 5 minutes.\n\n2. Whisk milk, brown sugar, and orange zest into couscous. Bring to boil over medium-high heat, whisking frequently to break up any lumps. Reduce heat to medium-low and cook, stirring frequently, until mixture is slightly thickened, about 5 minutes. Remove saucepan from heat.\n\n3. Whisk together \u00bd cup of couscous mixture and egg substitute in small bowl. Return mixture to saucepan and cook over low heat, stirring, until pudding is thick and creamy, about 5 minutes longer. Stir in wheat germ and vanilla.\n\n**PER SERVING** (generous \u00be cup): 152 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 2 mg Chol, 123 mg Sod, 28 g Total Carb, 3 g Fib, 9 g Prot, 190 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nTop the pudding with fresh raspberries and sliced almonds (1 tablespoon sliced almonds per serving will increase the **_PointsPlus_** value by **_1_** ).\n\nCreamy Couscous Breakfast Pudding\n\n# Spice-Roasted Pears with Yogurt\n\nSERVES 4\n\n**4 ripe Bartlett or Comice pears, peeled, halved lengthwise, and cored**\n\n**1 tablespoon fresh lemon juice**\n\n**\u00be teaspoon cinnamon**\n\n**\u215b teaspoon ground allspice**\n\n**\u00bc cup plain fat-free yogurt**\n\n1. Preheat oven to 450\u00b0F. Spray baking sheet with nonstick spray.\n\n2. Combine pears, lemon juice, cinnamon, and allspice in medium bowl; toss well.\n\n3. Using sharp knife, cut each pear half lengthwise almost through to base into \u00bc-inch-thick slices, keeping base intact. Carefully transfer sliced pear halves cut side down to baking sheet with spatula. Gently press down on each half to fan slices open slightly. Bake until pears are tender, about 20 minutes.\n\n4. Using spatula, transfer 2 pear halves to each of 4 dessert plates. Top each serving with 1 tablespoon yogurt.\n\n**PER SERVING** (1 pear and 1 tablespoon yogurt): 107 Cal, 0 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 14 mg Sod, 27 g Total Carb, 6 g Fib, 2 g Prot, 51 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\nCook's Note\n\nEnjoy the pears with a toasted light multigrain English muffin (1 light multigrain English muffin per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# lunches\n\n# Philly Cheese Steak Sandwiches\n\nSERVES 4\n\n**1 teaspoon canola oil**\n\n**2 large onions, thinly sliced**\n\n**2 Italian frying peppers, sliced**\n\n**2 garlic cloves, finely chopped**\n\n**\u00bc teaspoon salt**\n\n**\u00be pound lean boneless sirloin steak, trimmed and thinly sliced**\n\n**4 (\u00be-ounce) slices reduced-fat provolone cheese**\n\n**1 dill pickle, sliced**\n\n**4 small (2-ounce) crusty whole wheat rolls, split lengthwise**\n\n1. Heat oil in large skillet over medium-high heat. Add onions, peppers, and garlic and sprinkle with \u215b teaspoon of salt. Cook, stirring occasionally, until onions are browned, about 10 minutes. Transfer to small bowl and set aside.\n\n2. Wipe out skillet and spray with nonstick spray. Place over medium-high heat. Sprinkle steak with remaining \u215b teaspoon salt and place half of steak in skillet. Cook until browned on both sides, about 2 minutes; transfer to plate. Repeat with remaining steak.\n\n3. Place 1 slice of provolone and few pickle slices on each roll. Divide beef and onion mixture among rolls.\n\n**PER SERVING** (1 sandwich): 352 Cal, 12 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 59 mg Chol, 755 mg Sod, 37 g Total Carb, 6 g Fib, 29 g Prot, 348 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nDo it Faster\n\nTo remove the papery peel from a clove of garlic, put the garlic on a cutting board, place the flat side of the blade of a chef's knife on the clove, and carefully press down on the knife.\n\nOpen-Faced Garlicky Steak Sandwiches\n\n# Open-Faced Garlicky Steak Sandwiches\n\nSERVES 4\n\n**1 (1-pound) lean boneless sirloin steak, trimmed**\n\n**2 teaspoons dried oregano**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon black pepper**\n\n**2 cups water**\n\n**6 garlic cloves, unpeeled**\n\n**1 pint cherry or grape tomatoes, halved**\n\n**\u00bd large English (seedless) cucumber, peeled and diced**\n\n**\u00bd red onion, thinly sliced**\n\n**\u00bc cup chopped fresh cilantro**\n\n**1 jalape\u00f1o pepper, seeded and minced**\n\n**3 tablespoons apple-cider vinegar**\n\n**1 tablespoon olive oil**\n\n**4 (\u00bd-inch) slices whole-grain country-style bread, toasted**\n\n1. Spray broiler rack with nonstick spray and preheat broiler.\n\n2. Sprinkle steak with oregano, salt, and pepper. Broil steak 5 inches from heat until an instant-read thermometer inserted into side of steak registers 145\u00b0F, about 5 minutes on each side. Transfer to cutting board and let stand 5 minutes. Cut steak across grain into thin slices.\n\n3. Meanwhile, combine water and garlic in small saucepan and bring to boil over high heat. Reduce heat and simmer until garlic is very tender, about 10 minutes; drain and rinse under cold running water. Peel garlic; place in small bowl and mash with fork.\n\n4. To make salsa, stir together tomatoes, cucumber, onion, cilantro, jalape\u00f1o, vinegar, and oil in medium bowl.\n\n5. Spread mashed garlic evenly over bread. Top bread evenly with steak and salsa.\n\n**PER SERVING** (1 sandwich): 303 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 73 mg Chol, 474 mg Sod, 20 g Total Carb, 4 g Fib, 35 g Prot, 72 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\n# Cuban Beef Lettuce Wraps\n\nSERVES 4\n\n**1 large onion, chopped**\n\n**4 garlic cloves, minced**\n\n**1 pound ground lean beef (7% fat or less)**\n\n**\u00bc teaspoon salt**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**\u00bd (4-ounce) can tomato paste**\n\n**\u2153 cup sliced pitted green olives**\n\n**\u2153 cup raisins**\n\n**2 teaspoons dried oregano**\n\n**2 teaspoons ground cumin**\n\n**8 large Boston or butter lettuce leaves**\n\n1. Spray large skillet with nonstick spray and set over medium-high heat. Add onion and garlic and cook, stirring occasionally, until softened, about 4 minutes.\n\n2. Add beef and salt; cook, breaking meat up with wooden spoon, until browned, about 3 minutes. Stir in tomatoes, tomato paste, olives, raisins, oregano, and cumin. Simmer over medium-low heat, stirring occasionally, until mixture is thickened, about 8 minutes.\n\n3. To serve, spoon into lettuce leaves.\n\n**PER SERVING** (1\u00bc cups picadillo and 2 lettuce leaves): 264 Cal, 7 g Total Fat, 2 g Sat Fat, 1 g Trans Fat, 62 mg Chol, 650 mg Sod, 24 g Total Carb, 3 g Fib, 27 g Prot, 103 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nDo it Faster\n\nTo core a head of Boston or iceberg lettuce in a few seconds, rap the core of the lettuce on the counter to loosen it from the leaves and pull it out in one neat piece.\n\n# Beef and Black Bean Burgers\n\nSERVES 6\n\n**1 (14\u00bd-ounce) can black beans, rinsed and drained**\n\n**\u00be pound ground lean beef (5% fat or less)**\n\n**\u00bc cup fat-free mild salsa**\n\n**\u00bc cup chopped fresh parsley**\n\n**\u00bc teaspoon salt**\n\n**6 reduced-calorie whole wheat hamburger buns**\n\n1. Preheat broiler. Spray broiler pan with nonstick spray.\n\n2. Place beans in large bowl and mash coarsely with potato masher or large fork (some beans should remain whole for texture). Add beef, salsa, parsley, and salt and mix with spoon or your hands until blended.\n\n3. Shape into 6 patties and place patties on broiler pan. Broil, turning once, until cooked through and browned, about 10 minutes. Serve in buns.\n\n**PER SERVING** (1 sandwich): 239 Cal, 6 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 38 mg Chol, 497 mg Sod, 29 g Total Carb, 6 g Fib, 19 g Prot, 66 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nQuick-cooking baby potatoes are a perfect accompaniment to these hearty burgers (3 ounces baked baby potatoes per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# express shopping\n\nGrocery shopping is one of the most time-consuming household tasks, yet it has to be done at least once a week. Be sure to take the few extra minutes to read labels and choose sustainably raised meats, poultry, seafood, and eggs. Visit local farmers' markets or shop at supermarkets that support local farmers for your produce. And use these tips to streamline the time you spend in the aisles.\n\n**ALWAYS SHOP WITH A LIST.** Create a list based on what you'll be cooking for the entire week, including any special events like a family potluck or cupcakes you need to bake to donate to the school fundraiser. Organize the list by food category and the layout of the supermarket aisles. This way, you'll get everything you need in one aisle of the store before moving on to the next. Use an online grocery list template, a grocery list app, or your own paper list.\n\n**SHOP ONLY ONCE A WEEK.** Making fewer trips to the store is one of the best timesaving tricks there is. That's why it's so important to make a comprehensive weekly shopping list so you're not stopping by the store after work wasting half an hour to buy the one thing you forgot. This saves money, too, because you're sure to pick up more than one thing once you're inside the store.\n\n**GO AT OFF-PEAK TIMES.** If your schedule allows, try hitting the store early in the morning or mid-afternoon before the after-work rush. Nights are less crowded, but the shelves may not be as well-stocked as they are during the day. Avoid weekends whenever possible.\n\n**SHOP ALONE.** You'll get through the aisles faster without the distraction of children asking for sugar-sweetened cereal or a spouse leading you to the sausage sampling station set up at the meat counter.\n\n**STAY FOCUSED.** Skip going down aisles with food that is not on your list, say \"no thank you\" to anyone offering food samples, and if you run into anyone you know, say a quick hello and be on your way.\n\n**BE A LOYAL CUSTOMER.** Decide which one or two supermarkets are your favorites and always do your shopping there. You'll become familiar with where items are located in the aisles, cutting down on backtracking for forgotten items. You'll also get to know the staff of the store and learn to identify which cashiers will get you through the checkout lane the quickest.\n\n**QUESTION COUPONING.** Keep track of how much money you save using coupons versus how much time you spend searching for them online or in magazines and newspapers, keeping them organized, and the extra time it takes in the checkout lane. Unless you're a coupon pro, it's probably not worth your time. A quicker way to save money is to scope out weekly specials at the supermarket and stock up when pantry staples are on sale.\n\n**BE A CLEVER CLICKER.** Many supermarkets offer timesaving online shopping and grocery delivery for a nominal fee. Check the cost at your market and decide if the time saved is worth the money. If you feel you need to choose fresh produce, meats, and seafood in person, you'll still save time if you get pantry staples delivered and shop for fresh food yourself.\n\n# Honey-Mustard Turkey Sandwiches\n\nSERVES 4\n\n**\u00bc cup Dijon mustard**\n\n**2 tablespoons honey**\n\n**1\u00bd teaspoons reduced-sodium soy sauce**\n\n**\u00be cup plain dried bread crumbs**\n\n**4 (\u00bc-pound) turkey breast cutlets**\n\n**4 whole wheat ciabatta rolls, split and toasted**\n\n**4 leaf lettuce leaves**\n\n**2 plum tomatoes, sliced**\n\n1. Preheat oven to 400\u00b0F. Spray baking sheet with nonstick spray.\n\n2. Whisk together mustard, honey, and soy sauce in small bowl. Place bread crumbs on plate. Dip turkey into mustard mixture, then into bread crumbs. Place on baking sheet. Spray turkey lightly with nonstick spray and bake, turning once, until cooked through, about 20 minutes.\n\n3. Serve turkey in rolls topped with lettuce leaves and tomato slices.\n\n**PER SERVING** (1 sandwich): 388 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 76 mg Chol, 818 mg Sod, 48 g Total Carb, 5 g Fib, 34 g Prot, 105 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nDo it Faster\n\nTo make cleanup easy, lightly spray the measuring spoon with nonstick spray before measuring the honey.\n\n# Dilled Salmon Sandwiches with Caper Sauce\n\nSERVES 4\n\n**1 (14\u00bd-ounce) can red sockeye salmon, drained, skin and bones discarded**\n\n**\u00bd cup plain dried bread crumbs**\n\n**\u00bd cup chopped red onion**\n\n**\u00bc cup plus 3 tablespoons fat-free mayonnaise**\n\n**1 large egg, lightly beaten**\n\n**2 tablespoons chopped fresh dill**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd teaspoon canola oil**\n\n**\u00bd cup roasted red bell peppers (not packed in oil)**\n\n**\u215b teaspoon hot pepper sauce**\n\n**2 tablespoons drained capers**\n\n**4 whole wheat sandwich rolls, split and toasted**\n\n**\u00bd English (seedless) cucumber, peeled and sliced**\n\n1. To make salmon patties, combine salmon, bread crumbs, onion, \u00bc cup mayonnaise, egg, dill, and black pepper in medium bowl. Stir, breaking up any large chunks of salmon, until just combined. Form mixture into 4 patties.\n\n2. Coat large nonstick skillet with oil placed over medium heat. Add patties and cook until browned and heated through, about 5 minutes on each side.\n\n3. Meanwhile, to make sauce, combine remaining 3 tablespoons mayonnaise, bell peppers, and hot pepper sauce in blender; puree. Add capers and pulse until just combined.\n\n4. Spread cut sides of rolls with sauce; fill with salmon patties and cucumber slices.\n\n**PER SERVING** (1 sandwich): 305 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 113 mg Chol, 984 mg Sod, 32 g Total Carb, 5 g Fib, 27 g Prot, 300 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nDo it Faster\n\nIf peeling cucumbers and other vegetables is taking longer than it should, it could be that you need to replace the blade on your vegetable peeler or buy a new one.\n\n# Tuna Steak Sandwiches with Roasted Pepper Relish\n\nSERVES 4\n\n**4 (6-ounce) tuna steaks**\n\n**\u00bd teaspoon paprika**\n\n**\u00bd teaspoon ground cumin**\n\n**\u00bc teaspoon black pepper**\n\n**2 teaspoons canola oil**\n\n**\u00bc teaspoon salt**\n\n**1 cup thinly sliced roasted red bell peppers (not packed in oil)**\n\n**2 tablespoons chopped fresh basil**\n\n**2 teaspoons grated lemon zest**\n\n**2 teaspoons fresh lemon juice**\n\n**4 (\u00bd-inch) slices crusty whole wheat bread, toasted**\n\n1. Sprinkle tuna with paprika, cumin, and \u215b teaspoon black pepper; cover and refrigerate 10 minutes.\n\n2. Heat oil in large skillet over high heat. Sprinkle tuna with \u215b teaspoon salt. Add tuna to skillet and cook until seared and cooked to desired doneness, about 2 minutes on each side for medium.\n\n3. Meanwhile, stir together bell peppers, basil, lemon zest, lemon juice, remaining \u215b teaspoon salt, and remaining \u215b teaspoon black pepper in small bowl.\n\n4. Place bread on 4 plates; top with tuna steaks. Top sandwiches evenly with bell pepper mixture.\n\n**PER SERVING** (1 open-faced sandwich): 365 Cal, 12 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 59 mg Chol, 515 mg Sod, 21 g Total Carb, 4 g Fib, 42 g Prot, 70 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nDo it Faster\n\nSet aside a new toothbrush to use in the kitchen specifically for quickly removing all the citrus zest and fresh ginger from your grater. This quick extra step prevents waste and speeds cleanup.\n\n# Crunchy Fish Sliders\n\nSERVES 4\n\n**\u00be pound cod fillet**\n\n**\u00bc cup all-purpose flour**\n\n**\u00bd cup buttermilk**\n\n**\u00be cup whole wheat cracker crumbs**\n\n**1 tablespoon finely chopped fresh parsley**\n\n**\u00bc teaspoon salt**\n\n**\u00bc teaspoon garlic powder**\n\n**2 teaspoons olive oil**\n\n**4 mini whole wheat buns**\n\n1. Cut fish into 4 equal squares. Place flour in shallow bowl and buttermilk in another bowl. Stir together crumbs, parsley, salt, and garlic powder in third bowl. Coat each piece of fish first with flour, then with buttermilk, and finally with crumb mixture.\n\n2. Heat oil in medium nonstick skillet over medium heat. Add fish and cook, turning once, until browned and just opaque in center, about 8 minutes total. Place each piece in bun.\n\n**PER SERVING** (1 sandwich): 277 Cal, 8 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 34 mg Chol, 477 mg Sod, 34 g Total Carb, 4 g Fib, 19 g Prot, 85 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nFill the sandwiches with **_0 PointsPlus_** value toppings of your choice. Try lettuce leaves, tomato slices, red onion rings, or dill pickles.\n\n# Quesadillas with Guacamole and Pepper Jack\n\nSERVES 4\n\n**1 cup canned fat-free refried beans**\n\n**8 (6-inch) whole wheat tortillas**\n\n**\u00bd cup shredded reduced-fat pepper Jack cheese**\n\n**1 small tomato, chopped**\n\n**\u00bc small red onion, chopped**\n\n**2 tablespoons chopped fresh cilantro**\n\n**1 cup purchased guacamole**\n\n**1 cup fat-free refrigerated salsa**\n\n1. Spread beans evenly over 4 tortillas. Sprinkle evenly with pepper Jack, tomato, onion, and cilantro. Cover with remaining 4 tortillas, pressing down lightly.\n\n2. Spray medium skillet with nonstick spray and set over medium heat. Cook quesadillas, one at a time, until crisp and heated through, about 2 minutes on each side. Cut each quesadilla into 4 wedges and arrange on platter. Serve with guacamole and salsa.\n\n**PER SERVING** (1 quesadilla, \u00bc cup guacamole, and \u00bc cup salsa): 253 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 6 mg Chol, 982 mg Sod, 36 g Total Carb, 9 g Fib, 12 g Prot, 147 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nTo make a filling lunch, serve the quesadillas with a crunchy slaw. Toss together 1 cup each shredded jicama and green cabbage, 2 large shredded carrots, and a handful of chopped fresh cilantro with fresh lime juice and salt and pepper to taste.\n\n# Asian-Style Pork, Mushroom, and Noodle Soup\n\nSERVES 4\n\n**4 ounces whole wheat capellini or spaghetti**\n\n**4 cups reduced-sodium chicken broth**\n\n**2 cups water**\n\n**3 cups thinly sliced Napa cabbage**\n\n**8 shiitake mushrooms, stems removed and caps sliced**\n\n**4 scallions, sliced on diagonal**\n\n**1 large tomato, seeded and diced**\n\n**1 cup frozen baby peas**\n\n**1 tablespoon minced peeled fresh ginger**\n\n**1 tablespoon reduced-sodium soy sauce**\n\n**6 ounces cooked lean boneless center-cut pork loin chops, trimmed and cut into thin strips**\n\n**3 drops hot pepper sauce**\n\n1. Cook pasta according to package directions, omitting salt if desired; drain.\n\n2. Meanwhile, bring broth and water to boil in large pot. Add cabbage, mushrooms, scallions, tomato, peas, ginger, and soy sauce; reduce heat and simmer until cabbage is tender, about 5 minutes.\n\n3. Add pasta, pork, and hot pepper sauce to soup; simmer until pork is heated through, about 2 minutes.\n\n**PER SERVING** (about 2\u00bd cups): 270 Cal, 5 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 35 mg Chol, 866 mg Sod, 35 g Total Carb, 6 g Fib, 24 g Prot, 106 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nFor an easy, elegant dessert, serve thinly sliced fresh mango sprinkled with grated lime zest.\n\nAsian-Style Pork, Mushroom, and Noodle Soup\n\n# Manhattan Clam Chowder\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 onion, finely chopped**\n\n**1 carrot, finely chopped**\n\n**1 celery stalk, finely chopped**\n\n**1\u00bd cups water**\n\n**1 (14\u00bd-ounce) can petite diced tomatoes**\n\n**1 (8-ounce) bottle clam juice**\n\n**1 large all-purpose potato, peeled and chopped**\n\n**\u00bd teaspoon dried thyme**\n\n**\u00bc teaspoon black pepper**\n\n**2 (6\u00bd-ounce) cans chopped clams, undrained**\n\n1. Heat oil in large saucepan over medium heat. Add onion, carrot, and celery; cook, stirring, until softened, about 3 minutes.\n\n2. Add water, tomatoes, clam juice, potato, thyme, and pepper; bring to boil over medium-high heat. Reduce heat and simmer, partially covered, until vegetables are tender, about 12 minutes.\n\n3. Add clams and simmer just until heated through, about 2 minutes.\n\n**PER SERVING** (about 1\u00be cups): 174 Cal, 3 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 25 mg Chol, 358 mg Sod, 25 g Total Carb, 4 g Fib, 12 g Prot, 99 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nThis soup calls for a crusty roll to serve alongside (a 1\u00bd-ounce light roll per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# Smoky Vegetarian Chili\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 onion, chopped**\n\n**1 red bell pepper, chopped**\n\n**3 garlic cloves, minced**\n\n**1 tablespoon chili powder**\n\n**1 teaspoon ground cumin**\n\n**1 teaspoon dried oregano**\n\n**1 (28-ounce) can diced tomatoes**\n\n**1 (15\u00bd-ounce) can pinto beans, rinsed and drained**\n\n**1 (15\u00bd-ounce) can red kidney beans, rinsed and drained**\n\n**\u215b teaspoon salt**\n\n**3 drops liquid smoke**\n\n**4 scallions, sliced**\n\n**\u00bd cup shredded reduced-fat Cheddar cheese**\n\n**\u00bd cup fat-free sour cream**\n\n1. Heat oil in large saucepan over medium-high heat. Add onion, bell pepper, garlic, chili powder, cumin, and oregano; cook until vegetables are softened, about 5 minutes.\n\n2. Stir in tomatoes, pinto beans, kidney beans, salt, and liquid smoke; bring to boil. Reduce heat and simmer until chili thickens slightly, about 15 minutes.\n\n3. Divide chili evenly among 4 bowls and top evenly with scallions, Cheddar, and sour cream.\n\n**PER SERVING** (1 cup chili, about 2 tablespoons scallions, 2 tablespoons cheese, and 2 tablespoons sour cream): 337 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 6 mg Chol, 854 mg Sod, 57 g Total Carb, 16 g Fib, 20 g Prot, 298 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nDo it Faster\n\nUse your kitchen shears to make quick work of slicing scallions or chives.\n\n# Hearty Corn Chowder\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 red or green bell pepper, diced**\n\n**1 onion, chopped**\n\n**3 cups frozen corn kernels**\n\n**\u00be pound red potatoes, scrubbed and diced**\n\n**1 cup reduced-sodium chicken broth**\n\n**\u00bc teaspoon black pepper**\n\n**3 cups fat-free milk**\n\n**4 slices turkey bacon, crisp-cooked and coarsely crumbled**\n\n1. Heat oil in large saucepan over medium heat. Add bell pepper and onion; cook, stirring, until softened, about 5 minutes. Add corn, potatoes, broth, and black pepper; bring to boil over medium-high heat. Reduce heat and simmer, covered, until potatoes are tender, about 10 minutes.\n\n2. Puree \u00bd cup of vegetable mixture with 1 cup of milk in blender until almost smooth. Stir puree along with remaining 2 cups milk back into soup. Cook over medium heat, stirring occasionally, until heated through, about 5 minutes. Serve sprinkled with bacon.\n\n**PER SERVING** (about 2 cups): 319 Cal, 7 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 17 mg Chol, 552 mg Sod, 52 g Total Carb, 6 g Fib, 16 g Prot, 266 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nPureeing some of the soup takes a bit of extra time and effort, but it's worth it for the creaminess and body it adds to this satisfying chowder.\n\n# Potato-Watercress Soup\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 onion, chopped**\n\n**4 Yukon Gold potatoes, peeled and coarsely chopped**\n\n**1 bunch watercress, tender sprigs only**\n\n**4 cups reduced-sodium chicken broth**\n\n**1 cup fat-free half-and-half**\n\n**\u215b teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n1. Heat oil in large saucepan over medium heat. Add onion and cook, stirring, until softened, about 3 minutes. Add potatoes, watercress, and broth; bring to boil over medium-high heat. Reduce heat and simmer, covered, until potatoes are tender, about 12 minutes. Let cool 5 minutes.\n\n2. Puree potato mixture, in batches, in blender. Return soup to saucepan and stir in half-and-half, salt, and pepper. Cook over medium heat until heated through, about 2 minutes; do not boil.\n\n**PER SERVING** (about 1\u00bc cups): 230 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 3 mg Chol, 738 mg Sod, 43 g Total Carb, 4 g Fib, 8 g Prot, 123 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nServe this comforting soup with a salad made with fresh baby spinach, sliced mushrooms, thinly sliced red onion, white wine vinegar, and salt and pepper to taste.\n\nCreamy Tomato Soup and Ham and Swiss Panini, here\n\n# Creamy Tomato Soup\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 onion, chopped**\n\n**2 garlic cloves, minced**\n\n**4 large tomatoes, coarsely chopped**\n\n**1 cup reduced-sodium chicken broth**\n\n**4 teaspoons chopped fresh thyme or 1 teaspoon dried**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**3 cups fat-free milk**\n\n**\u00bc cup tomato paste**\n\n1. Heat oil in large saucepan over medium heat. Add onion and garlic; cook, stirring, until softened, about 5 minutes.\n\n2. Stir in tomatoes, broth, thyme, salt, and pepper. Cover and simmer until vegetables are tender, about 5 minutes longer. Let cool 5 minutes.\n\n3. Puree tomato mixture, in batches, in blender. Return mixture to saucepan.\n\n4. Whisk together milk and tomato paste in small bowl; whisk mixture into soup. Cook, stirring occasionally, just until heated through, about 5 minutes; do not boil.\n\n**PER SERVING** (1\u00bc cups): 198 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 4 mg Chol, 574 mg Sod, 29 g Total Carb, 4 g Fib, 11 g Prot, 263 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nFor an update on a classic menu, serve the soup with Ham and Swiss Panini, here, and crisp celery stalks.\n\n# Cremini Mushroom, Tomato, and Rice Soup\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**2 leeks cleaned and chopped, white and light green parts only**\n\n**1 pound cremini mushrooms, sliced**\n\n**2\u00bd cups reduced-sodium chicken broth**\n\n**1 (14\u00bd-ounce) can fire-roasted diced tomatoes**\n\n**\u00bc teaspoon salt**\n\n**\u215b teaspoon black pepper**\n\n**\u00bd cup quick-cooking brown rice**\n\n1. Heat oil in large saucepan over medium-high heat. Add leeks and cook, stirring, until softened, about 5 minutes. Add mushrooms and cook, stirring, until tender, about 5 minutes.\n\n2. Add broth, tomatoes, salt, and pepper; simmer 5 minutes. Stir in rice and cook until tender, about 10 minutes longer.\n\n**PER SERVING** (1\u00bd cups): 145 Cal, 3 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 657 mg Sod, 24 g Total Carb, 4 g Fib, 8 g Prot, 78 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nCheese toast is an easy partner for this comforting soup. To make it, top 1 slice of reduced-calorie whole wheat bread with 1 slice of fat-free Swiss cheese and broil until the cheese melts (1 cheese toast per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# Edamame Salad with Basil Vinaigrette\n\nSERVES 4\n\n**1 cup frozen shelled edamame**\n\n**3 tablespoons red-wine vinegar**\n\n**1 tablespoon olive oil**\n\n**1 garlic clove, minced**\n\n**\u00bc teaspoon salt**\n\n**1 (15\u00bd-ounce) can cannellini (white kidney)beans, rinsed and drained**\n\n**1 large tomato, diced**\n\n**1 celery stalk, sliced**\n\n**\u00bd red onion, diced**\n\n**\u00bd cup chopped fresh basil**\n\n1. Bring small pot of water to boil. Add edamame and cook 5 minutes; drain, rinse under cold water, and pat dry.\n\n2. Combine vinegar, oil, garlic, and salt in large bowl. Add edamame, cannellini beans, tomato, celery, onion, and basil; mix well. Let stand at room temperature about 15 minutes before serving.\n\n**PER SERVING** (generous 1 cup): 206 Cal, 6 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 395 mg Sod, 27 g Total Carb, 8 g Fib, 12 g Prot, 143 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nServe this salad with mixed fresh fruit for dessert. Try sliced kiwifruit and nectarines sprinkled with blueberries for a fresh, colorful finish.\n\n# Pasta Salad with Apple and Chicken\n\nSERVES 4\n\n**6 ounces whole wheat penne**\n\n**\u2153 cup fresh orange juice**\n\n**3 tablespoons balsamic vinegar**\n\n**1 tablespoon Dijon mustard**\n\n**1 tablespoon pure maple syrup**\n\n**1 cup diced cooked skinless chicken breast**\n\n**1 (5-ounce) bag baby arugula**\n\n**1 small Granny Smith apple, cored and diced**\n\n**1 large shallot, finely chopped**\n\n**\u00bc cup pecans, coarsely chopped**\n\n1. Cook penne according to package directions, omitting salt if desired. Drain and rinse under cold running water; drain again.\n\n2. To make dressing, whisk together orange juice, vinegar, mustard, and maple syrup in large bowl. Add pasta, chicken, arugula, apple, shallot, and pecans to dressing; toss to coat.\n\n**PER SERVING** (about 2 cups): 315 Cal, 8 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 29 mg Chol, 284 mg Sod, 46 g Total Carb, 5 g Fib, 19 g Prot, 100 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nIf you like the robust flavor of whole-grain mustard, it's a delicious option for using in this recipe.\n\nPasta Salad with Apple and Chicken\n\n# Tabbouleh with Shrimp\n\nSERVES 4\n\n**1\u00bc cups water**\n\n**1 cup bulgur**\n\n**1 pound cooked, peeled, and deveined medium shrimp**\n\n**1 small cucumber, peeled, seeded, and chopped**\n\n**2 tomatoes, cut into \u00bd-inch pieces**\n\n**2 scallions, chopped**\n\n**\u00bd cup chopped fresh parsley**\n\n**\u00bc cup chopped fresh mint**\n\n**3 tablespoons fresh lemon juice**\n\n**2 teaspoons olive oil**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n1. Pour water over bulgur in medium bowl. Cover and let stand until water is absorbed, about 25 minutes. Fluff bulgur with fork; transfer to serving bowl.\n\n2. Add remaining ingredients to bulgur; toss to combine.\n\n**PER SERVING** (about 2 cups): 246 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 161 mg Chol, 501 mg Sod, 32 g Total Carb, 8 g Fib, 23 g Prot, 80 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nServe the salad with pita bread, the traditional Mediterranean accompaniment (a 100% whole wheat pita bread per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Hearty Lentil Salad with Radicchio\n\nSERVES 4\n\n**1\u00bd cups brown lentils, picked over and rinsed**\n\n**1 bay leaf**\n\n**6 cups water**\n\n**1 large head radicchio, quartered, cored, and very thinly sliced**\n\n**1 cup cherry tomatoes, halved**\n\n**4 scallions, chopped**\n\n**1 carrot, shredded**\n\n**\u00bd cup chopped fresh basil**\n\n**2\u00bd tablespoons red-wine vinegar**\n\n**1 tablespoon olive oil**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n1. Combine lentils, bay leaf, and water in medium saucepan and bring to boil over medium-high heat. Reduce heat and simmer, covered, until lentils are tender but still hold their shape, about 20 minutes; drain. Discard bay leaf and rinse lentils under cold running water; drain again.\n\n2. Meanwhile, combine remaining ingredients in large serving bowl. Add lentils and toss again.\n\n**PER SERVING** (1\u2154 cups): 292 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 482 mg Sod, 46 g Total Carb, 14 g Fib, 19 g Prot, 86 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\n# Greek Pita Pizzas with Spinach and Feta\n\nSERVES 4\n\n**1 teaspoon olive oil**\n\n**1 onion, chopped**\n\n**3 garlic cloves, minced**\n\n**\u00bc teaspoon dried oregano**\n\n**1 (10-ounce) package frozen chopped spinach, thawed and squeezed dry**\n\n**\u2153 cup crumbled reduced-fat feta cheese**\n\n**4 (6-inch) whole wheat pita breads**\n\n**1 cup grape tomatoes, halved**\n\n**\u00be cup shredded part-skim mozzarella cheese**\n\n1. Preheat oven to 425\u00b0F.\n\n2. Heat oil in large nonstick skillet over medium heat. Add onion and cook, stirring frequently, until softened, about 4 minutes. Stir in garlic and oregano; cook, stirring, about 1 minute. Stir in spinach and cook until hot, about 2 minutes. Remove skillet from heat and stir in feta.\n\n3. Arrange pitas on baking sheet. Top with spinach mixture, spreading it to edges. Arrange tomatoes on top. Bake until pitas are crisp, 8\u201310 minutes.\n\n4. Sprinkle pizzas with mozzarella; bake until melted, about 3 minutes.\n\n**PER SERVING** (1 pizza): 281 Cal, 8 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 15 mg Chol, 596 mg Sod, 40 g Total Carb, 7 g Fib, 15 g Prot, 296 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nDo it Faster\n\nTo quickly squeeze the water out of thawed spinach, separate it into small handfuls and squeeze it as tightly as you can over the sink. If it still seems wet, blot the spinach with paper towels to remove more moisture.\n\n# dinners\n\n# Filets Mignons with Tomato-Bean Salsa\n\nSERVES 4\n\n**4 (\u00bc-pound) lean filets mignons, trimmed**\n\n**\u00bd teaspoon ground cumin**\n\n**\u00bc teaspoon black pepper**\n\n**1 (15\u00bd-ounce) can small white beans, rinsed and drained**\n\n**2 tomatoes, seeded and chopped**\n\n**1 Kirby cucumber, peeled and chopped**\n\n**\u00bc cup finely chopped red onion**\n\n**\u00bc cup diced avocado**\n\n**2 tablespoons chopped fresh basil**\n\n**1 tablespoon red-wine vinegar**\n\n**\u00bd teaspoon salt**\n\n**1\u00bd teaspoons olive oil**\n\n1. Sprinkle filets mignons with cumin and pepper; cover and refrigerate 10 minutes.\n\n2. Meanwhile, to make salsa, toss together beans, tomatoes, cucumber, onion, avocado, basil, vinegar, and \u00bc teaspoon of salt in serving bowl.\n\n3. Heat oil in large skillet over medium-high heat. Sprinkle steaks with remaining \u00bc teaspoon salt. Add steaks to skillet and cook until an instant-read thermometer inserted into side of steak registers 145\u00b0F for medium, about 2 minutes on each side. Serve with salsa.\n\n**PER SERVING** (1 steak and about 1 cup salsa): 323 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 46 mg Chol, 567 mg Sod, 24 g Total Carb, 7 g Fib, 33 g Prot, 90 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nSliced Steak with Crispy Polenta\n\n# Sliced Steak with Crispy Polenta\n\nSERVES 4\n\n**1 (1-pound) lean flank steak, trimmed**\n\n**\u00bd teaspoon ancho or regular chili powder**\n\n**\u00bd teaspoon salt**\n\n**1 (16-ounce) tube fat-free polenta, cut into 12 slices**\n\n**1\u00bd cups fresh or thawed frozen corn kernels**\n\n**1 red bell pepper, chopped**\n\n**\u00bd red onion, chopped**\n\n**1 jalape\u00f1o pepper, seeded and minced**\n\n**2 tablespoons chopped fresh cilantro**\n\n1. Spray ridged grill pan with nonstick spray and set over medium-high heat. Sprinkle steak with chili powder and salt. Place steak in pan and cook until an instant-read thermometer inserted into side of steak registers 145\u00b0F for medium, about 5 minutes on each side. Transfer steak to cutting board and let stand 5 minutes. Cut on diagonal into 16 slices.\n\n2. Meanwhile, spray broiler rack with nonstick spray and preheat broiler. Arrange slices of polenta on rack and broil 5 inches from heat until crispy and heated through, about 2 minutes on each side.\n\n3. Spray medium skillet with nonstick spray and set over medium heat. Add corn, bell pepper, onion, and jalape\u00f1o pepper; cook, stirring, until softened, about 5 minutes. Remove skillet from heat and stir in cilantro.\n\n4. Place 3 slices of polenta on each of 4 plates and top each serving with 4 slices of steak. Divide corn mixture evenly among plates.\n\n**PER SERVING** (4 slices steak, 3 slices polenta, and \u00be cup corn mixture): 312 Cal, 5 g Total Fat, 2 g Sat Fat, 1 g Trans Fat, 83 mg Chol, 345 mg Sod, 29 g Total Carb, 3 g Fib, 37 g Prot, 16 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nDo it Faster\n\nTo neatly and quickly remove the kernels from an ear of corn, place a bowl in the sink, stand the corn on end inside the bowl, and cut off the kernels with a knife. Any fly-away kernels will end up in the sink.\n\n# you _can_ make it quick\n\nFast, convenient, and economical, canned foods can be a real time-saver and a smart way to supplement fresh and frozen ingredients in your meals. Better yet, they will last for years, so you'll practically never have to worry about them going bad. Here are our top picks for canned staples that combine quality with good nutrition.\n\n**BEANS.** No pantry should be without an assortment of ready-to-eat beans. Beans are a classic example of foods that do beautifully in cans, and no-salt-added varieties are a terrific option for lowering the sodium in home-cooked meals.\n\n**BROTHS.** Canned or packaged broths can flavor everything from soups to stews to pilafs. Look for broths labeled low-sodium or no-salt-added to avoid excess sodium.\n\n**COCONUT PRODUCTS.** Many coconut products are sold in convenient and economical cans or shelf-stable cartons. Keep lite (reduced-fat) coconut milk and coconut water as pantry staples. A splash of coconut milk adds tropical flavor to a smoothie and coconut water makes a refreshing drink for only **_1 PointsPlus_** value per cup.\n\n**FRUITS.** Avoid fruits canned in sugary syrups, but keep water-packed or juice-packed favorites such as pineapple, pears, peaches, and mandarin oranges on hand. They're a great addition to sweet and savory recipes, or you can enjoy them on their own for snacks and desserts.\n\n**SEAFOOD.** Canned salmon, tuna, and sardines are great to have on hand for quick salads and sandwiches. Make sure the fish is packed in water (not oil) to avoid excess fat, and look for no-salt-added options when possible. Canned clams are excellent for adding to pasta dishes or as a pizza topping.\n\n**SOUPS.** Keep a few cans of low-fat, low-sodium soup around for days when you have no time to cook. Cans and cartons of vegetable-based soups such as tomato, butternut squash, or red bell pepper can also be handy for composing soups on the fly: add some diced leftover chicken or tofu and leftover rice or pasta and you'll have a superquick, filling meal.\n\n**TOMATOES.** Canned tomatoes are tops when it comes to getting big, bold, consistent tomato flavor year-round. Canned tomato sauce is also a healthy time-saver\u2014just be sure to read the label and make sure the product does not contain added sugar.\n\n**VEGETABLES.** Veggies from a can can be a smart alternative to fresh. Canned corn kernels, cream-style corn, sauerkraut, lima beans, beets, artichoke hearts, and hearts of palm are delicious, convenient options for recipes.\n\n**A note about BPA**\n\nThe chemical Bisphenol A (BPA) is sometimes used as an interior coating on cans to keep food from coming in contact with metal. There is evidence that the chemical may leach into food. Although the FDA has concluded that amounts are too minimal to pose a health risk, if you're concerned you can look for cans or cartons labeled as BPA-free, or rinse and drain canned foods like beans and corn to minimize exposure.\n\n# Grilled Flank Steak with Tomato-Fennel Salad\n\nSERVES 4\n\n**4 plum tomatoes, each cut into 6 wedges**\n\n**2 tablespoons chopped fresh flat-leaf parsley**\n\n**2 teaspoons grated lemon zest**\n\n**1 tablespoon lemon juice**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 (1-pound) flank steak, trimmed**\n\n**1 fennel bulb, cut lengthwise into \u00bd-inch-thick slices**\n\n1. Spray grill rack with nonstick spray; preheat grill to medium-high or prepare medium-high fire.\n\n2. Combine tomatoes, parsley, lemon zest and juice, \u00bc teaspoon of salt, and \u215b teaspoon of pepper in medium bowl. Set aside.\n\n3. Sprinkle steak with remaining \u00bd teaspoon salt and remaining \u215b teaspoon pepper. Lightly spray fennel with nonstick spray. Place steak and fennel on grill rack. Grill, turning fennel occasionally, and turning steak once, until fennel is tender and instant-read thermometer inserted into center of steak registers 145\u00b0F, about 10 minutes. Remove core from fennel; coarsely chop fennel. Stir fennel into tomato mixture. Cut steak into 12 slices and serve with salad.\n\n**PER SERVING** : (3 slices steak with 1 cup salad): 191 Cal, 7 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 42 mg Chol, 519 mg Sod, 7 g Total Carb, 2 g Sugar, 3 g Fib, 25 g Prot, 55 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nTo make this meal more filling and nutritious, serve the steak and salad over a bed of curly endive or mixed baby greens along with corn-on-the-cob (\u00bd of a small ear of corn will increase the **_PointsPlus_** value by **_1_** ).\n\n# Curried Beef Kebabs with Basmati Rice\n\nSERVES 4\n\n**1 cup basmati rice**\n\n**1\u00bc pound lean boneless sirloin steak, trimmed and cut into 1-inch chunks**\n\n**1 red onion, quartered and separated into slices**\n\n**1 yellow squash, thickly sliced**\n\n**4 baby pattypan squash, halved**\n\n**2 teaspoons canola oil**\n\n**2\u00bd teaspoons curry powder**\n\n**\u215b teaspoon salt**\n\n**\u00bc cup whole fresh cilantro leaves**\n\n1. Prepare rice according to package directions, omitting salt if desired.\n\n2. Spray broiler rack with nonstick spray and preheat broiler.\n\n3. Combine beef, onion, squashes, oil, curry powder, and salt in large bowl; toss to coat.\n\n4. Thread beef, onion, and squashes alternately on 8 (12-inch) metal skewers. Place skewers on broiler rack and broil 5 inches from heat, turning occasionally, until an instant-read thermometer inserted into chunk of beef registers 145\u00b0F for medium, about 10 minutes. Serve with rice and sprinkle with cilantro.\n\n**PER SERVING** (2 skewers and \u00be cup rice): 435 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 92 mg Chol, 675 mg Sod, 46 g Total Carb, 2 g Fib, 42 g Prot, 39 mg Calc.\n\n**_PointsPlus_** value: **_11._**\n\nDo it Faster\n\nNo time to thread skewers? Simply place the steak and vegetables directly on the broiler pan and broil as directed.\n\nCurried Beef Kebabs with Basmati Rice\n\n# Hearty Steak and Vegetables\n\nSERVES 4\n\n**1\u00bd cups quick-cooking brown rice**\n\n**1 pound lean beef top round steak, trimmed and thinly sliced**\n\n**\u00be teaspoon chili powder**\n\n**\u00bc teaspoon salt**\n\n**2 teaspoons olive oil**\n\n**2 zucchini, halved lengthwise and sliced**\n\n**2 red bell peppers, sliced**\n\n**1 onion, sliced**\n\n**\u00bd teaspoon ground cumin**\n\n1. Cook rice according to package directions, omitting salt if desired.\n\n2. Meanwhile, toss together steak, chili powder, and \u215b teaspoon of salt in large bowl.\n\n3. Heat oil in large skillet over high heat. Add steak and cook, stirring frequently, until lightly browned, about 5 minutes. Transfer to plate.\n\n4. Reduce heat to medium-high. Add zucchini, bell peppers, onion, cumin, and remaining \u215b teaspoon salt to skillet; cook, stirring frequently, until vegetables are softened, about 5 minutes.\n\n5. Return steak to skillet and cook just until heated through, about 2 minutes. Serve over rice.\n\n**PER SERVING** (2 cups steak and vegetables and \u00be cup rice): 385 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 84 mg Chol, 647 mg Sod, 38 g Total Carb, 7 g Fib, 39 g Prot, 45 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nTo enjoy even more veggies with this healthy dinner, make a salad of plum tomato wedges and sliced cucumbers tossed with a pinch of cumin, fresh lime juice, and salt and pepper to taste.\n\n# Spaghetti with Quick Bolognese Sauce\n\nSERVES 4\n\n**8 ounces whole wheat spaghetti**\n\n**1 pound lean ground beef (5% fat or less)**\n\n**1 onion, chopped**\n\n**1 green bell pepper, chopped**\n\n**2 garlic cloves, minced**\n\n**1 (28-ounce) can diced tomatoes**\n\n**2 teaspoons dried basil**\n\n**\u00bc teaspoon salt**\n\n**Pinch red pepper flakes**\n\n1. Cook spaghetti according to package directions, omitting salt if desired.\n\n2. Meanwhile, cook beef in large skillet over medium-high heat, breaking it apart with wooden spoon, until lightly browned, about 4 minutes. Stir in onion, bell pepper, and garlic; cook, stirring occasionally, until vegetables are softened, about 5 minutes. Stir in tomatoes, basil, salt, and red pepper flakes; bring mixture to boil. Reduce heat and simmer, stirring occasionally, until slightly thickened, about 10 minutes. Toss pasta with sauce.\n\n**PER SERVING** (1\u00bd cups spaghetti and sauce): 413 Cal, 8 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 64 mg Chol, 693 mg Sod, 56 g Total Carb, 8 g Fib, 33 g Prot, 114 mg Calc.\n\n**_PointsPlus_** value: **_11._**\n\nCook's Note\n\nTo make a **_0 PointsPlus_** value tossed salad to serve with the pasta, toss together chopped romaine, halved cherry tomatoes, sliced cucumber, thinly sliced red onion, red-wine vinegar, and salt and pepper to taste.\n\nStir-Fried Beef with Asparagus\n\n# Stir-Fried Beef with Asparagus\n\nSERVES 4\n\n**1 cup quick-cooking brown rice**\n\n**2 teaspoons canola oil**\n\n**1 pound lean beef top round steak, trimmed and cut into thin strips**\n\n**4 garlic cloves, thinly sliced**\n\n**1 tablespoon minced peeled fresh ginger**\n\n**1 pound asparagus spears, trimmed and cut into 2-inch pieces**\n\n**1 red bell pepper, thinly sliced**\n\n**4 scallions, thinly sliced**\n\n**1 (5-ounce) can sliced water chestnuts, drained**\n\n**\u00be cup reduced-sodium chicken broth**\n\n**1 tablespoon reduced-sodium soy sauce**\n\n1. Cook rice according to package directions, omitting salt if desired.\n\n2. Meanwhile, heat large skillet or wok over high heat until drop of water sizzles in pan. Add oil and swirl to coat skillet. Add beef and stir-fry until browned and cooked through, about 4 minutes. Using slotted spoon, transfer beef to plate.\n\n3. Add garlic and ginger to skillet and stir-fry until fragrant, about 30 seconds. Add asparagus and bell pepper and stir-fry until crisp-tender, about 2 minutes longer. Return beef to skillet and add remaining ingredients. Stir-fry until liquid is almost evaporated, about 3 minutes longer. Serve with rice.\n\n**PER SERVING** (1\u2153 cups stir-fry and \u00bd cup rice): 354 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 84 mg Chol, 810 mg Sod, 30 g Total Carb, 6 g Fib, 39 g Prot, 53 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nTo serve the stir-fry with an Asian salad, toss together thinly sliced Napa cabbage, shredded carrots, thinly sliced scallions, and reduced-sodium soy sauce to taste. For a touch of spice, add a tiny bit of chili-garlic paste.\n\n# Roast Pork Tenderloin with Black Bean Salsa\n\nSERVES 2\n\n**\u00bd teaspoon ground cumin**\n\n**\u00bd teaspoon ancho or regular chili powder**\n\n**\u00bc teaspoon salt**\n\n**1 (\u00be-pound) lean pork tenderloin, trimmed**\n\n**1 cup black beans, rinsed and drained**\n\n**\u00bd cup thawed frozen corn kernels**\n\n**3 scallions, thinly sliced**\n\n**1 plum tomato, chopped**\n\n**\u00bd jalape\u00f1o pepper, seeded and minced**\n\n**2 tablespoons chopped fresh cilantro**\n\n**1\u00bd tablespoons fresh lime juice**\n\n1. Preheat oven to 425\u00b0F.\n\n2. Mix together cumin, chili powder, and salt in cup; sprinkle all over pork.\n\n3. Spray large ovenproof skillet with nonstick spray and set over medium-high heat. Add pork and cook until browned on all sides, about 5 minutes.\n\n4. Transfer skillet to oven and roast until an instant-read thermometer inserted into center of pork registers 145\u00b0F, about 10 minutes. Transfer to cutting board and let stand 5 minutes. Cut tenderloin into 12 slices.\n\n5. Meanwhile, to make salsa, toss together remaining ingredients in serving bowl. Serve with pork.\n\n**PER SERVING** (6 slices pork and 1 cup salsa): 385 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 106 mg Chol, 386 mg Sod, 32 g Total Carb, 10 g Fib, 47 g Prot, 60 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nSteamed kale or mustard greens make an easy side dish for the pork tenderloin.\n\n# Cajun-Spiced Roast Pork Tenderloin\n\nSERVES 4\n\n**1 tablespoon paprika**\n\n**\u00bd teaspoon ground cumin**\n\n**\u00bd teaspoon sugar**\n\n**\u00bd teaspoon salt**\n\n**\u215b teaspoon cayenne pepper**\n\n**1 (1-pound) lean pork tenderloin, trimmed**\n\n1. Preheat oven to 400\u00b0F.\n\n2. On sheet of wax paper, combine paprika, cumin, sugar, salt, and cayenne. Roll pork in mixture until evenly coated.\n\n3. Spray large ovenproof skillet with nonstick spray and set over medium-high heat. Add pork and cook until lightly browned on all sides, about 5 minutes.\n\n4. Transfer skillet to oven and roast until an instant-read thermometer inserted into center of tenderloin registers 145\u00b0F, about 12 minutes.\n\n5. Transfer pork to cutting board and let stand 5 minutes. Cut into 16 slices.\n\n**PER SERVING** (4 slices pork): 139 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 63 mg Chol, 337 mg Sod, 2 g Total Carb, 0 g Fib, 23 g Prot, 10 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\nCook's Note\n\nTo accompany the pork tenderloin, make microwave-baked sweet potatoes. Prick 4 (5-ounce) sweet potatoes in several places with a small knife, wrap in paper towels, and microwave on High until tender, 8 to 10 minutes, turning once (a 5-ounce baked sweet potato per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Saucy Pan-Roasted Pork Chops with Ziti\n\nSERVES 4\n\n**4 ounces whole wheat ziti or penne**\n\n**2 garlic cloves, minced**\n\n**1 (14\u00bd-ounce) can tomato puree**\n\n**\u00be teaspoon Italian seasoning**\n\n**Pinch red pepper flakes**\n\n**4 (\u00bc-pound) lean bone-in pork loin chops, trimmed**\n\n**\u00bc teaspoon black pepper**\n\n**\u215b teaspoon salt**\n\n**\u00bc cup shredded fat-free mozzarella cheese**\n\n**2 tablespoons chopped fresh basil**\n\n1. Cook ziti according to package directions, omitting salt if desired.\n\n2. Meanwhile, spray medium saucepan with olive oil nonstick spray and set over medium heat. Add garlic and cook, stirring, until fragrant, about 20 seconds. Add tomato puree, Italian seasoning, and red pepper flakes and bring to boil; reduce heat and simmer, stirring occasionally, 10 minutes.\n\n3. Spray large skillet with nonstick spray and set over high heat. Sprinkle pork with black pepper and salt. Add chops to skillet and cook until lightly browned, about 2 minutes on each side. Reduce heat to medium-low and sprinkle chops evenly with mozzarella. Cover skillet and cook until cheese is melted and an instant-read thermometer inserted into side of chop registers 145\u00b0F, about 4 minutes.\n\n4. Divide ziti evenly among 4 plates and top with tomato sauce and pork chop. Sprinkle with basil.\n\n**PER SERVING** (1 cup linguine, 1 pork chop, and scant \u00bd cup sauce): 357 Cal, 11 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 75 mg Chol, 717 mg Sod, 33 g Total Carb, 4 g Fib, 34 g Prot, 108 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nFor a quick green vegetable side dish, make steamed spinach tossed with lemon juice and salt and pepper to taste.\n\nSaucy Pan-Roasted Pork Chops with Ziti\n\n# Pork and Mushroom Stir-Fry\n\nSERVES 6\n\n**1 tablespoon peanut or canola oil**\n\n**1 pound lean boneless pork loin, trimmed and cut into 1** **\u00d7 \u00bc-inch strips**\n\n**1 red bell pepper, thinly sliced**\n\n**\u00bc pound snow peas, trimmed**\n\n**4 scallions, cut into 1-inch pieces**\n\n**1 tablespoon grated peeled fresh ginger**\n\n**1 tablespoon minced garlic**\n\n**1 (15-ounce) can straw mushrooms, drained**\n\n**1 cup drained canned baby corn**\n\n**\u00bc cup reduced-sodium vegetable broth**\n\n**3 tablespoons reduced-sodium teriyaki sauce**\n\n**1 teaspoon cornstarch**\n\n**3 cups hot cooked brown rice**\n\n1. Heat large skillet or wok over medium-high heat until drop of water sizzles in pan. Add 1\u00bd teaspoons of oil and swirl to coat skillet. Add pork, in batches, and stir-fry until browned and cooked through, about 4 minutes. Transfer to plate.\n\n2. Add remaining 1\u00bd teaspoons oil to skillet. Add bell pepper, snow peas, scallions, ginger, and garlic; stir-fry 2 minutes. Add mushrooms and corn and stir-fry until heated through, about 1 minute longer. Return pork to skillet.\n\n3. Stir together broth, teriyaki sauce, and cornstarch in cup until smooth, then add to skillet. Stir-fry until sauce thickens and bubbles, about 2 minutes. Serve with rice.\n\n**PER SERVING** (1\u00bd cups pork mixture and \u00bd cup rice): 347 Cal, 10 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 48 mg Chol, 972 mg Sod, 41 g Total Carb, 8 g Fib, 24 g Prot, 51 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nCooked brown rice will keep in the refrigerator for up to 5 days, so cook a batch on the weekend to enjoy with meals all week long.\n\n# Ham with Apples and Mustard\n\nSERVES 4\n\n**4 (3-ounce) slices reduced-sodium lean deli ham, trimmed**\n\n**1 small onion, chopped**\n\n**3 red apples, cored and cut into \u00bd-inch wedges**\n\n**1\u00bd cups apple cider**\n\n**2 teaspoons Dijon mustard**\n\n**1 tablespoon cornstarch**\n\n**2 tablespoons cold water**\n\n1. Spray large skillet with nonstick spray and set over medium heat. Add ham and cook until lightly browned, about 2 minutes on each side. Transfer to plate.\n\n2. Add onion to skillet and cook, stirring frequently, until softened, about 5 minutes. Add apples, cider, and mustard; cook, stirring frequently, until apples are tender, about 5 minutes longer.\n\n3. Stir together cornstarch and water in cup until smooth, then add to skillet. Cook, stirring constantly, until sauce thickens and bubbles, about 2 minutes. Return ham to skillet and cook until heated through, about 1 minute longer.\n\n**PER SERVING** (1 slice ham and about \u00bd cup apple mixture): 254 Cal, 5 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 45 mg Chol, 890 mg Sod, 34 g Total Carb, 4 g Fib, 19 g Prot, 28 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nIf you prefer, you can use a \u00be-pound ham steak for this recipe and cut it into 4 pieces before cooking.\n\n# Minted Lamb Chops with Lemony Bulgur\n\nSERVES 4\n\n**1 cup bulgur**\n\n**4 tablespoons chopped fresh mint**\n\n**2 garlic cloves, minced**\n\n**2 teaspoons olive oil**\n\n**\u00bd teaspoon salt**\n\n**4 (\u00bc-pound) lean boneless lamb loin chops, trimmed**\n\n**1 large tomato, coarsely chopped**\n\n**Grated zest and juice of 1 lemon**\n\n**2 tablespoons chopped fresh chives**\n\n1. Prepare bulgur according to package directions, omitting salt if desired.\n\n2. Meanwhile, spray broiler rack with nonstick spray and preheat broiler.\n\n3. Stir together 2 tablespoons of mint, garlic, oil, and salt in large shallow bowl. Add lamb and turn to coat evenly. Place lamb on broiler rack. Broil 5 inches from heat until an instant-read thermometer inserted into side of chop registers 145\u00b0F for medium, about 5 minutes on each side.\n\n4. Stir tomato, lemon zest and juice, remaining 2 tablespoons mint, and chives into bulgur. Serve with lamb.\n\n**PER SERVING** (1 lamb chop and \u00be cup bulgur): 319 Cal, 10 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 74 mg Chol, 367 mg Sod, 30 g Total Carb, 7 g Fib, 29 g Prot, 37 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nTo broil a vegetable side dish while you broil the chops, arrange 2 thinly sliced red or yellow bell peppers on the broiler rack alongside the chops. Lightly spray with olive oil nonstick spray. Broil, turning occasionally, until crisp-tender, 6 to 8 minutes. Season to taste with salt and pepper.\n\n# Grilled Lamb Chops and Asparagus with Lemon-Garlic Mayonnaise\n\nSERVES 4\n\n**\u00bc cup fat-free mayonnaise**\n\n**1 small garlic clove, minced**\n\n**1 teaspoon grated lemon zest**\n\n**1 teaspoon fresh lemon juice**\n\n**\u00bd teaspoon olive oil**\n\n**4 (5-ounce) lean lamb loin chops, about 1 inch thick, trimmed**\n\n**1 pound thick asparagus spears, trimmed**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon black pepper**\n\n1. Spray grill rack with nonstick spray. Preheat grill to medium-high or prepare medium-high fire.\n\n2. Stir together mayonnaise, garlic, lemon zest, lemon juice, and oil in small bowl; cover and refrigerate until ready to serve.\n\n3. Sprinkle lamb and asparagus with salt and pepper. Spray asparagus with olive oil nonstick spray. Place lamb and asparagus on grill rack. Grill lamb until an instant-read thermometer inserted into center of chop registers 145\u00b0F for medium, about 4 minutes on each side, and until asparagus is browned in spots and crisp-tender, about 5 minutes. Serve lamb and asparagus with garlic sauce.\n\n**PER SERVING** (1 lamb chop, 5 asparagus spears, and 1 tablespoon mayonnaise): 260 Cal, 11 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 94 mg Chol, 505 mg Sod, 8 g Total Carb, 3 g Fib, 31 g Prot, 44 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nServe the chops with a side of whole wheat orzo tossed with grated lemon zest and chopped fresh mint (\u00bd cup of cooked whole wheat orzo per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# Moroccan-Style Chicken\n\nSERVES 4\n\n**4 (5-ounce) skinless boneless chicken breasts, cut into 1-inch pieces**\n\n**2 teaspoons canola oil**\n\n**1 teaspoon ground cumin**\n\n**1 teaspoon salt**\n\n**1 (3-inch) cinnamon stick**\n\n**4 carrots, sliced**\n\n**1 red onion, chopped**\n\n**2 garlic cloves, minced**\n\n**2 yellow squash, diced**\n\n**1 (14\u00bd-ounce) can petite diced tomatoes, drained**\n\n**1 cup reduced-sodium vegetable broth**\n\n**1 cup canned chickpeas, rinsed and drained**\n\n**\u00bc cup dark raisins**\n\n1. Stir together chicken, 1 teaspoon of oil, cumin, salt, and cinnamon stick in medium bowl.\n\n2. Stir together carrots, onion, garlic, and remaining 1 teaspoon oil in microwavable 3-quart casserole with lid. Cover and microwave on High until onion is softened, about 4 minutes.\n\n3. Add squash, tomatoes, broth, and chicken to casserole. Cover and microwave on High until chicken is almost cooked through, about 3 minutes, stirring once halfway through cooking.\n\n4. Stir in chickpeas and raisins. Cover and microwave until chicken is cooked through, about 2 minutes longer. Discard cinnamon stick.\n\n**PER SERVING** (1 chicken breast and about 1 cup vegetables): 365 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 86 mg Chol, 985 mg Sod, 36 g Total Carb, 7 g Fib, 38 g Prot, 124 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nCouscous is the traditional accompaniment to this Moroccan meal (\u00bd cup cooked whole wheat couscous per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Chicken and Vegetables with Fettuccine\n\nSERVES 6\n\n**12 ounces whole wheat fettuccine**\n\n**\u00bd pound asparagus, trimmed and cut into 2-inch pieces**\n\n**1 pound skinless boneless chicken thighs, cut into 1-inch pieces**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**4 teaspoons olive oil**\n\n**1 fennel bulb, sliced**\n\n**1 small red bell pepper, sliced**\n\n**1 small yellow bell pepper, sliced**\n\n**1 red onion, sliced**\n\n**\u00bc pound cremini mushrooms, sliced**\n\n**2 garlic cloves, minced**\n\n**\u00bd cup reduced-sodium chicken broth**\n\n**\u00bd cup fresh basil leaves, thinly sliced**\n\n1. Cook fettuccine according to package directions omitting salt if desired. Four minutes before pasta is done, add asparagus and cook until pasta and asparagus are tender. Drain and keep warm.\n\n2. Meanwhile, sprinkle chicken with \u00bc teaspoon of salt and \u215b teaspoon of black pepper. Heat 2 teaspoons of oil in large skillet over medium-high heat. Add chicken and cook, turning occasionally, until browned and cooked through, about 5 minutes. Transfer chicken to plate and cover to keep warm.\n\n3. Add remaining 2 teaspoons oil to same skillet. Add fennel, bell peppers, onion, mushrooms, remaining \u00bc teaspoon salt, and remaining \u215b teaspoon black pepper and cook, stirring occasionally, until vegetables are lightly browned and crisp-tender, about 5 minutes. Add garlic to skillet and cook, stirring constantly, until fragrant, 30 seconds. Return chicken to skillet; add fettuccini mixture and broth, and cook, stirring constantly until heated through, 2 minutes. Stir in basil.\n\n**PER SERVING** (2 cups): 368 Cal, 10 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 50 mg Chol, 312 mg Sod, 49 g Total Carb, 10 g Fib, 25 g Prot, 71 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\n# Lemony Chicken Kebabs with Couscous\n\nSERVES 4\n\n**1 pound skinless boneless chicken breasts, cut into 1-inch pieces**\n\n**2 teaspoons grated lemon zest**\n\n**1 tablespoon fresh lemon juice**\n\n**2 teaspoons olive oil**\n\n**2 garlic cloves, minced**\n\n**1 teaspoon ground cumin**\n\n**\u00be teaspoon salt**\n\n**\u215b teaspoon cayenne pepper**\n\n**1 red onion, quartered and separated into layers**\n\n**1 cup whole wheat couscous**\n\n**3 tablespoons chopped fresh cilantro**\n\n**2 teaspoons sesame seeds, toasted**\n\n1. Combine chicken, lemon zest and juice, oil, garlic, cumin, salt, and cayenne in large bowl; toss to coat.\n\n2. Spray ridged grill pan with nonstick spray and set over medium-high heat. Alternately thread chicken and onion onto 8 metal skewers. Place skewers in pan and cook, turning occasionally, until chicken is cooked through, about 12 minutes.\n\n3. Meanwhile, prepare couscous according to package directions, omitting salt if desired. Add cilantro and sesame seeds to couscous and stir to combine. Serve with chicken.\n\n**PER SERVING** (2 skewers and \u00be cup couscous): 289 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 68 mg Chol, 835 mg Sod, 26 g Total Carb, 5 g Fib, 30 g Prot, 48 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nDo it Faster\n\nTo quickly toast sesame seeds, put them in a small dry skillet and set over medium heat. Toast seeds, stirring frequently, until fragrant and lightly browned, about 2 minutes. Transfer to a plate to cool.\n\n# Teriyaki Chicken and Snow Pea Stir-Fry\n\nSERVES 4\n\n**2 teaspoons Asian (dark) sesame oil**\n\n**1 pound skinless boneless chicken breasts, cut into thin strips**\n\n**2 garlic cloves, minced**\n\n**1 (\u00bd-inch) piece fresh ginger, peeled and minced**\n\n**1 red bell pepper, thinly sliced**\n\n**4 scallions, thinly sliced**\n\n**1 (5-ounce) can sliced water chestnuts, drained**\n\n**6 ounces snow peas, trimmed**\n\n**\u00bc cup reduced-sodium chicken broth**\n\n**\u00bc cup teriyaki sauce**\n\n**Pinch red pepper flakes**\n\n**2 cups hot cooked brown rice**\n\n1. Heat large skillet or wok over medium-high heat until drop of water sizzles in pan. Add oil and swirl to coat skillet.\n\n2. Add chicken to skillet and stir-fry until browned and cooked through, about 5 minutes. Using slotted spoon, transfer chicken to plate.\n\n3. Add garlic and ginger to skillet and stir-fry until fragrant, about 30 seconds. Add bell pepper, scallions, and water chestnuts; stir-fry 2 minutes. Add snow peas and stir-fry until bright green. Add broth, teriyaki sauce, and red pepper flakes; stir-fry until sauce is slightly reduced, about 1 minute longer.\n\n4. Return chicken to skillet and stir-fry until heated through, about 1 minute. Serve with rice.\n\n**PER SERVING** (1\u00bd cups chicken mixture and \u00bd cup rice): 325 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 70 mg Chol, 805 mg Sod, 33 g Total Carb, 4 g Fib, 32 g Prot, 65 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nStir-fries are one of the quickest meals you can make, but once you start cooking, there's little time to do anything but stir! Prep all your ingredients and arrange them near the stove before you begin for stress-free stir-frying.\n\nQuick Chicken Satay with Asparagus\n\n# Quick Chicken Satay with Asparagus\n\nSERVES 2\n\n**2 (5-ounce) skinless boneless chicken breasts, each cut into 6 long strips**\n\n**5 teaspoons reduced-sodium teriyaki sauce**\n\n**16 asparagus spears, trimmed**\n\n**2 teaspoons reduced-sodium soy sauce**\n\n**2 teaspoons canola oil**\n\n**Lemon wedges**\n\n1. Preheat oven to 375\u00b0F. Line baking sheet with foil and spray with nonstick spray.\n\n2. Toss together chicken and teriyaki sauce in medium bowl.\n\n3. Thread 2 pieces of chicken on each of 6 (12-inch) metal skewers and arrange on baking sheet. Place asparagus next to chicken in one layer. Brush asparagus with soy sauce and oil. Roast until chicken is cooked through and asparagus is tender, about 15 minutes. Serve with lemon wedges.\n\n**PER SERVING** (3 skewers and 8 asparagus spears): 256 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 86 mg Chol, 700 mg Sod, 7 g Total Carb, 3 g Fib, 35 g Prot, 49 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nIf using wooden skewers, soak them in water for 30 minutes to prevent them from burning.\n\n# Chicken Picadillo\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 onion, chopped**\n\n**2 garlic cloves, minced**\n\n**1 pound ground skinless chicken breast**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**\u00bc cup dark raisins**\n\n**\u00bc cup pimiento-stuffed olives, coarsely chopped**\n\n**1 teaspoon ground cumin**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bc cup slivered almonds**\n\n1. Heat oil in large skillet over medium heat. Add onion and garlic and cook, stirring, until softened, about 5 minutes.\n\n2. Add chicken to skillet. Cook, breaking up chicken with wooden spoon, until browned, about 8 minutes.\n\n3. Stir in tomatoes, raisins, olives, cumin, salt, and pepper, and bring to boil over medium-high heat. Reduce heat and simmer until slightly thickened, about 5 minutes. Stir in almonds.\n\n**PER SERVING** (generous 1 cup): 278 Cal, 12 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 68 mg Chol, 652 mg Sod, 17 g Total Carb, 3 g Fib, 28 g Prot, 84 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nYou can make the picadillo using ground skinless turkey breast instead of chicken breast if you wish.\n\n# Warm Lentil Salad with Baked Salmon\n\nSERVES 4\n\n**4 cups water**\n\n**1 cup green (French) lentils, picked over and rinsed**\n\n**1 (1-pound) piece center-cut salmon fillet, skinned**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd cup roasted red bell pepper, chopped (not packed in oil)**\n\n**\u00bc cup reduced-sodium chicken broth**\n\n**2 teaspoons olive oil**\n\n**1\u00bc teaspoons white-wine vinegar**\n\n**\u00bd teaspoon salt**\n\n**2 cups torn fris\u00e9e lettuce**\n\n**\u00bd small red onion, finely chopped**\n\n1. Bring water to boil in medium saucepan. Add lentils and cook until just tender, about 15 minutes; drain.\n\n2. Meanwhile, preheat oven to 300\u00b0F. Line baking sheet with foil.\n\n3. Put salmon, skinned side down, on prepared baking sheet. Sprinkle with salt and black pepper. Bake until just opaque in center, about 15 minutes.\n\n4. Meanwhile, puree bell pepper, broth, oil, vinegar, and salt in blender. Transfer mixture to large bowl. Add lentils, lettuce, and onion and toss to combine.\n\n5. Cut salmon into 4 portions and put 1 piece of salmon on each of 4 plates. Spoon lentil salad alongside.\n\n**PER SERVING** (1 piece salmon and 1\u00bc cups salad): 347 Cal, 9 g Total Fat, 2 g Sat Fat, 0 Trans Fat, 75 mg Chol, 709 mg Sod, 24 g Total Carb, 9 g Fib, 37 g Prot, 65 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nDo it Faster\n\nTo quickly and neatly pick over lentils or beans, pour them into one side of a jelly-roll or other large rimmed pan. Slide the lentils to the other side of the pan using your hand and looking for stones or other debris as you go. Always rinse them before cooking.\n\n# Roasted Salmon with Caramelized Onions and Carrots\n\nSERVES 4\n\n**1 teaspoon olive oil**\n\n**2 red onions, thinly sliced**\n\n**\u00bc teaspoon dried thyme**\n\n**1 carrot, cut into thin 2-inch-long strips**\n\n**2 garlic cloves, minced**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 teaspoon white-wine vinegar**\n\n**4 (6-ounce) skinless salmon fillets**\n\n**4 teaspoons Dijon mustard**\n\n1. Arrange oven rack in middle of oven; preheat oven to 450\u00b0F. Spray baking sheet with nonstick spray.\n\n2. Heat oil in medium nonstick skillet over medium heat. Add onions and thyme; cook, stirring occasionally, until onions start to brown, about 12 minutes. Add carrot, garlic, \u00bc teaspoon of salt, and \u215b teaspoon of pepper; continue cooking until onions are golden, 3\u20134 minutes longer. Stir in vinegar and cook 1 minute; remove from heat and keep warm.\n\n3. Meanwhile, sprinkle salmon with remaining \u00bd teaspoon salt and \u215b teaspoon pepper and place on baking sheet. Brush top of each fillet with 1 teaspoon of mustard. Roast until fish is opaque in center, 8\u201310 minutes.\n\n4. Top each fillet with \u00bc cup of onion mixture.\n\n**PER SERVING** (1 fillet and \u00bc cup onion mixture): 299 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 112 mg Chol, 683 mg Sod, 10 g Total Carb, 2 g Fib, 37 g Prot, 50 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nSalmon fillets often have small bones\u2014known as pinbones\u2014in their flesh. Before cooking, run your fingertips along the flesh to feel for them. If you find any, use needle-nose pliers or tweezers to pull them out.\n\n# Tilapia with Tomato and Feta\n\nSERVES 4\n\n**1 (15-ounce) can crushed tomatoes**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon dried oregano**\n\n**\u00bc teaspoon black pepper**\n\n**2 (\u00bd-pound) tilapia fillets, cut crosswise in half**\n\n**\u00bc cup crumbled reduced-fat feta cheese**\n\n**1 cup whole wheat couscous**\n\n1. Preheat oven to 350\u00b0F. Spray 7 \u00d7 11-inch baking dish with nonstick spray.\n\n2. Stir together tomatoes, \u00bc teaspoon of salt, oregano, and \u215b teaspoon of pepper in small bowl.\n\n3. Spread half of tomato mixture in prepared baking dish. Arrange tilapia on top of sauce in one layer. Sprinkle fish with remaining \u00bc teaspoon salt and \u215b teaspoon pepper. Spoon remaining tomato sauce evenly over fish and sprinkle with feta. Cover dish tightly with foil. Bake until fish is just opaque in center, about 20 minutes.\n\n4. Meanwhile, prepare couscous according to package directions, omitting fat and salt if desired. Serve with fish.\n\n**PER SERVING** (\u00bd tilapia fillet, about 3 tablespoons sauce, and about \u2154 cup couscous): 305 Cal, 4 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 55 mg Chol, 894 mg Sod, 35 g Total Carb, 6 g Fib, 32 g Prot, 82 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nQuickly dress up the couscous by stirring 2 thinly sliced scallions and a minced garlic clove into the cooking water when you add the couscous.\n\n# Salmon Patties with Chunky Tomato Relish\n\nSERVES 4\n\n**2 large tomatoes, seeded and diced**\n\n**\u00bc cup chopped fresh basil**\n\n**2 shallots, finely chopped plus 1 shallot, halved**\n\n**2 teaspoons fresh lemon juice**\n\n**2 teaspoons olive oil**\n\n**\u00be teaspoon salt**\n\n**\u00bd teaspoon black pepper**\n\n**1 pound salmon fillet, skinned and cut into small pieces**\n\n**2 tablespoons chopped fresh parsley**\n\n**1 teaspoon grated lemon zest**\n\n1. To make relish, toss together tomatoes, basil, chopped shallots, lemon juice, oil, \u00bc teaspoon of salt, and \u00bc teaspoon of pepper in serving bowl.\n\n2. To make salmon patties, combine salmon, parsley, halved shallot, lemon zest, and remaining \u00bd teaspoon salt and \u00bc teaspoon pepper in food processor; pulse until finely chopped. With damp hands, form salmon mixture into 4 (\u00bd-inch-thick) patties.\n\n3. Spray large skillet with olive oil nonstick spray and set over medium heat. Add patties and cook until browned and cooked through, about 5 minutes on each side. Serve with relish.\n\n**PER SERVING** (1 patty and \u00bd cup relish): 214 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 75 mg Chol, 518 mg Sod, 7 g Total Carb, 2 g Fib, 26 g Prot, 38 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nThe tomato relish is delicious with grilled chicken or shrimp, too.\n\nSalmon Patties with Chunky Tomato Relish\n\n# 7 superfast sides\n\n**All recipes serve 4.**\n\n**Kale and Apple Salad**\n\nWhisk together **1 tablespoon olive oil, 1 tablespoon apple-cider vinegar, 2 teaspoons honey,** **\u00bc** **teaspoon salt,** and **\u00bc** **teaspoon black pepper** in large bowl. Toss in **\u00bd** **pound kale, stems removed and leaves thinly sliced, 1 Gala apple, cut into thin strips,** and **2 tablespoons grated Parmesan cheese**. **_PointsPlus_** value: **_3._**\n\n**Lemony Spinach and Avocado Salad**\n\nWhisk together **1 teaspoon grated lemon zest, 2 tablespoons fresh** lemon juice, 1 tablespoon olive oil, **\u00bd** **teaspoon Dijon mustard,** **\u00bc** **teaspoon salt,** and **\u215b** **teaspoon black pepper** in large bowl. Toss in **4 cups baby spinach,** **\u00bd** **avocado, pitted, peeled, and chopped,** and **\u00bc** **cup thinly sliced red onion**. **_PointsPlus_** value: **_2._**\n\n**Minted Green Beans with Pine Nuts**\n\nCook **1 pound trimmed green beans** in boiling water until crisp-tender; drain. Transfer to serving bowl; toss in **2 tablespoons chopped fresh mint, 2 tablespoons toasted pine nuts, 2 teaspoons olive oil, grated zest and juice of 1 lemon,** **\u00bc** **teaspoon salt,** and **\u215b teaspoon black pepper.** **_PointsPlus_** value: **_2._**\n\n**Buttered Broccoli with Cilantro and Lime**\n\nPlace **4 cups broccoli florets** in microwave-safe dish; cover with wax paper and microwave on High until crisp-tender, about 3 minutes. Drain and transfer to serving bowl. Toss in **2 teaspoons unsalted butter, 1 tablespoon chopped fresh cilantro, grated zest and juice of 1 lime,** and **\u00bc** **teaspoon salt**. **_PointsPlus_** value: **_1._**\n\n**Rosemary-Parmesan Oven Fries**\n\nCut **1 pound baking potatoes** into \u00bd-inch sticks; place in baking pan. **Add 2 teaspoons olive oil,** **\u00bc** **teaspoon salt,** and **\u215b teaspoon black pepper** and toss to coat. Bake at 425\u00b0F, turning once, until potatoes are tender, 30 minutes. Transfer to platter; sprinkle with **2 tablespoons grated Parmesan cheese, 1 garlic clove, minced,** and **1 teaspoon minced fresh rosemary** and toss to coat. **_PointsPlus_** value: **_3._**\n\n**Polenta with Goat Cheese and Chives**\n\nBring **2 cups reduced-sodium chicken broth** to boil in medium saucepan. Slowly pour in **\u00bd cup instant polenta** in thin, steady stream, whisking constantly. Cook, whisking constantly, until thick and creamy, 5 minutes. Remove from heat and stir in **2 ounces crumbled goat cheese, 1 tablespoon minced fresh chives, \u00bc** **teaspoon salt,** and **\u215b teaspoon black pepper.** **_PointsPlus_** value: **_3._**\n\n**Herbed Parmesan-Garlic Pasta**\n\nCook **6 ounces whole wheat linguine** according to package directions. Heat **2 teaspoons olive oil** in large nonstick skillet. Add **2 cloves minced garlic** and cook, stirring constantly, just until garlic begins to brown. Add pasta and toss to coat. Remove from heat and stir in **3 tablespoons minced fresh parsley, basil, or dill, or a combination,** **\u00bc** **cup grated Parmesan,** **\u00bc** **teaspoon salt,** and **\u215b teaspoon black pepper**. **_PointsPlus_** value: **_5._**\n\n# Creole-Style Cod Fillets\n\nSERVES 4\n\n**2 cups spicy vegetable juice or tomato juice**\n\n**2 green bell peppers, thinly sliced**\n\n**1 onion, thinly sliced**\n\n**2 celery stalks, thinly sliced**\n\n**4 (6-ounce) cod fillets**\n\n**2 tablespoons chopped fresh parsley**\n\n**2 cups hot cooked brown rice**\n\n1. Combine vegetable juice, bell peppers, onion, and celery in large skillet; bring to boil over medium-high heat. Reduce heat and simmer until vegetables are just softened, about 4 minutes.\n\n2. Nestle cod into vegetables. Cover and cook until fish is just opaque throughout, about 8 minutes. Sprinkle with parsley and serve with rice.\n\n**PER SERVING** (1 cod fillet, 1 cup vegetables with sauce, and \u00bd cup rice): 313 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 90 mg Chol, 761 mg Sod, 34 g Total Carb, 6 g Fib, 36 g Prot, 70 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nIf you have leftover vegetable juice from this recipe, consider it for an afternoon pick-me-up. The spicy flavor will wake you up without caffeine\u2014and for only **_1 PointsPlus_** value in a 1-cup serving.\n\nTeriyaki-Glazed Tofu and Vegetable Kebabs\n\n# Teriyaki-Glazed Tofu and Vegetable Kebabs\n\nSERVES 4\n\n**\u2154 cup whole wheat couscous**\n\n**1 (14-ounce) container firm tofu, drained and cut into 1-inch cubes**\n\n**\u00bd fresh pineapple, peeled, cored, and cut into 1-inch chunks**\n\n**2 different colored bell peppers, cut into 1-inch pieces**\n\n**1 small red onion, quartered and layers separated**\n\n**16 small white mushrooms**\n\n**3 tablespoons reduced-sodium teriyaki sauce**\n\n**3 tablespoons chopped fresh cilantro**\n\n1. Prepare couscous according to package directions, omitting fat and salt if desired.\n\n2. Meanwhile, spray ridged grill pan with nonstick spray and set over medium-high heat. Alternately thread tofu, pineapple, bell peppers, onion, and mushrooms onto 8 metal skewers; brush with teriyaki sauce.\n\n3. Place skewers in pan and cook, turning frequently, until tofu is browned and vegetables are softened, about 10 minutes. Serve sprinkled with cilantro.\n\n**PER SERVING** (2 skewers and \u00bd cup couscous): 203 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 707 mg Sod, 31 g Total Carb, 6 g Fib, 14 g Prot, 232 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nDo it Faster\n\nSave time by buying recipe-ready pineapple for this dish. Most large supermarkets sell fresh peeled and cored pineapples in tall plastic containers in the produce section.\n\n# Chunky Vegetable Paella\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**4 celery stalks, thickly sliced**\n\n**1 onion, chopped**\n\n**1 large red bell pepper, cut into \u00be-inch pieces**\n\n**1 large zucchini, quartered lengthwise and cut into \u00be-inch pieces**\n\n**2 garlic cloves, minced**\n\n**\u00bd teaspoon salt**\n\n**\u00be cup quick-cooking brown rice**\n\n**2\u00bc cups water**\n\n**1 (15-ounce) can cannellini (white kidney) beans, rinsed and drained**\n\n**1 (14\u00bd-ounce) can fire-roasted diced tomatoes, drained**\n\n1. Heat 1 teaspoon oil in large nonstick skillet over medium heat. Add celery, onion, bell pepper, zucchini, garlic, and salt and cook, stirring, until softened, about 5 minutes. Transfer vegetables to bowl.\n\n2. Wipe out skillet; add remaining 1 teaspoon oil to skillet and set over medium heat. Add rice and cook, stirring, until lightly toasted, about 2 minutes. Stir in water; reduce heat and simmer, covered, until rice is tender and liquid is absorbed, about 10 minutes.\n\n3. Return vegetables to skillet and add beans and tomatoes. Cook, stirring occasionally, until heated through, about 5 minutes.\n\n**PER SERVING** (about 2 cups): 249 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 715 mg Sod, 46 g Total Carb, 11 g Fib, 11 g Prot, 147 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nTo add more healthful veggies to this dinner, serve the paella with a salad of baby spinach tossed with thinly sliced fresh fennel bulb, grated lemon zest, fresh lemon juice, and salt and pepper to taste.\n\n# Linguine with Fontina and Artichokes\n\nSERVES 4\n\n**6 ounces whole wheat linguine**\n\n**4 plum tomatoes, chopped**\n\n**2 garlic cloves, minced**\n\n**1 (9-ounce) package frozen quartered artichoke hearts, thawed**\n\n**\u215b teaspoon black pepper**\n\n**4 ounces fontina cheese, diced**\n\n**\u00bd cup thinly sliced fresh basil**\n\n1. Cook linguine according to package directions, omitting salt if desired. Drain linguine, reserving \u00bd cup of cooking water.\n\n2. Add tomatoes and garlic to pasta pot. Cook over medium heat, stirring, until tomatoes begin to soften, about 2 minutes.\n\n3. Return pasta to pot along with artichokes and pepper. Cook, stirring, until heated through, about 4 minutes. (If pasta seems dry, stir in some of reserved cooking water.)\n\n4. Transfer pasta mixture to serving bowl; add fontina and basil and toss to coat.\n\n**PER SERVING** (1\u00bd cups): 310 Cal, 10 g Total Fat, 6 g Sat Fat, 0 g Trans Fat, 33 mg Chol, 452 mg Sod, 44 g Total Carb, 8 g Fib, 17 g Prot, 221 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nTo safely reserve the cooking water from pasta, use a ladle to spoon out a little of the water into a bowl just before you drain the pasta. The ladle will keep your hands away from the boiling water and you can use it to drizzle as much cooking water as you need into your pasta dish.\n\n# Four-Vegetable Stir-Fry with Tofu\n\nSERVES 4\n\n**1 cup quick-cooking brown rice**\n\n**2 teaspoons canola oil**\n\n**2 garlic cloves, minced**\n\n**2 teaspoons minced peeled fresh ginger**\n\n**12 shiitake mushrooms, stems removed and caps thickly sliced**\n\n**3 cups broccoli florets**\n\n**2 carrots, thinly sliced**\n\n**1 yellow bell pepper, thinly sliced**\n\n**1 (14-ounce) container firm tofu, drained and cubed**\n\n**2 tablespoons reduced-sodium soy sauce**\n\n**1 teaspoon dark (Asian) sesame oil**\n\n1. Cook rice according to package directions, omitting salt if desired.\n\n2. Meanwhile, heat large skillet or wok or over high heat until drop of water sizzles in pan. Add canola oil and swirl to coat skillet. Add garlic and ginger and stir-fry until fragrant, about 30 seconds.\n\n3. Add mushrooms, broccoli, carrots, and bell pepper; stir-fry until tender, about 6 minutes. Add tofu, soy sauce, and sesame oil; stir-fry until heated through, about 1 minute longer. Serve with rice.\n\n**PER SERVING** (1\u00be cups stir-fry and \u00bd cup rice): 267 Cal, 9 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 754 mg Sod, 38 g Total Carb, 8 g Fib, 14 g Prot, 251 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nSave the stems of the broccoli when you prepare the broccoli florets. Shred them to make a slaw for serving with sandwiches later in the week.\nFour-Vegetable Stir-Fry with Tofu\n\n# snacks and sweets\n\n# Edamame Dip\n\nSERVES 4\n\n**1 cup frozen shelled edamame**\n\n**4 ounces silken tofu**\n\n**1 scallion, sliced**\n\n**1 garlic clove, chopped**\n\n**1 tablespoon fresh lemon juice**\n\n**1\u00bd teaspoons olive oil**\n\n**\u00bd teaspoon ground cumin**\n\n**\u00bc teaspoon honey**\n\n**\u00bc teaspoon salt**\n\n**12 whole wheat crackers**\n\n**12 carrot or other vegetables sticks**\n\n1. Cook edamame according to package directions. Drain and rinse under cold running water; drain again.\n\n2. Place edamame, tofu, scallion, garlic, lemon juice, oil, cumin, honey, and salt in food processor; process until smooth, 1\u20132 minutes. Serve with crackers and vegetable sticks.\n\n**PER SERVING** (about \u00bc cup dip, 3 crackers, and 3 carrot sticks): 169 Cal, 7 g Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 264 mg Sod, 18 g Total Carb, 5 g Fib, 9 g Prot, 78 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nEdamame, or green soybeans, are a great source of protein and fiber and they cook in about 5 minutes, making them perfect for quick meals and snacks. Try them in soups, stir-fries, and salads to appreciate their nutty taste, firm texture, and spring-green color.\n\n# Smoky Pumpkin Seeds\n\nSERVES 16\n\n**2 cups shelled pumpkin seeds (about 10 ounces)**\n\n**2 teaspoons Worcestershire sauce**\n\n**1 teaspoon liquid smoke**\n\n**1 teaspoon ground cumin**\n\n**1 teaspoon chili powder**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon garlic powder**\n\n**\u215b teaspoon cayenne pepper**\n\n1. Preheat oven to 325\u00b0F. Line large baking sheet with parchment paper.\n\n2. Toss together pumpkin seeds, Worcestershire sauce, and liquid smoke in large bowl.\n\n3. Combine remaining ingredients in small bowl. Sprinkle spice mixture over pumpkin seeds and stir vigorously with wooden spoon until evenly coated.\n\n4. Spread pumpkin seeds on prepared baking sheet. Bake, stirring twice, until dried and lightly browned, about 15 minutes. Let cool on baking sheet on rack.\n\n**PER SERVING** (2 tablespoons): 152 Cal, 12 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 160 mg Sod, 8 g Total Carb, 2 g Fib, 10 g Prot, 16 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nYou can store this healthy snack in a zip-close plastic bag or airtight container at room temperature for up to 1 month.\n\nPizza Margherita\n\n# Pizza Margherita\n\nSERVES 6\n\n**1 (10-ounce) prebaked thin whole wheat pizza crust**\n\n**3 plum tomatoes, thinly sliced**\n\n**2 garlic cloves, minced**\n\n**2 cups shredded fat-free mozzarella cheese**\n\n**\u00bc cup thinly sliced fresh basil**\n\n**1 teaspoon dried oregano**\n\n**2 teaspoons olive oil**\n\n1. Preheat oven to 450\u00b0F. Spray baking sheet with nonstick spray.\n\n2. Place crust on baking sheet. Arrange tomatoes on crust and sprinkle with garlic. Top evenly with mozzarella, basil, and oregano; drizzle with oil. Bake until cheese is melted, about 8 minutes. Cut into 6 wedges.\n\n**PER SERVING** (1\/6 of pizza): 198 Cal, 4 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 4 mg Chol, 544 mg Sod, 25 g Total Carb, 4 g Fib, 17 g Prot, 609 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nTurn this quick pizza into dinner by tossing a big green salad to serve alongside while the pizza bakes. For dessert, enjoy a scoop of vanilla fat-free frozen yogurt topped with a teaspoon of raspberry fruit spread (\u00bd cup fat-free frozen yogurt and 1 teaspoon fruit spread will increase the **_PointsPlus_** value by **_3_** ).\n\n# Mushroom, Scallion, and Cheddar Quesadillas\n\nSERVES 8\n\n**8 ounces sliced white mushrooms**\n\n**8 (7-inch) fat-free whole wheat flour tortillas**\n\n**\u00be cup shredded reduced-fat Cheddar cheese**\n\n**2 scallions, thinly sliced**\n\n**2 tablespoons sliced pickled jalape\u00f1o peppers, drained and finely chopped**\n\n1. Spray large skillet with nonstick spray and set over medium heat. Add mushrooms and cook, stirring occasionally, until liquid is evaporated, about 6 minutes. Using slotted spoon, transfer mushrooms to plate and let cool slightly.\n\n2. Lay out 4 tortillas on work surface. Layer each with one-fourth of mushrooms, Cheddar, scallions, and jalape\u00f1os. Top with remaining 4 tortillas, pressing down lightly.\n\n3. Wipe skillet clean. Spray with nonstick spray and set over medium heat. Add 1 quesadilla and cook until crisp and cheese begins to melt, about 1\u00bd minutes on each side. Transfer to cutting board and cover loosely with foil to keep warm. Repeat with remaining 3 quesadillas. Cut each quesadilla into 4 wedges, making total of 16 wedges.\n\n**PER SERVING** (2 wedges): 128 Cal, 1 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 2 mg Chol, 468 mg Sod, 23 g Total Carb, 4 g Fib, 8 g Prot, 124 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\nMushroom, Scallion, and Cheddar Quesadillas\n\n# Ricotta, Bacon, and Spinach Pizza\n\nSERVES 6\n\n**2 slices bacon, chopped**\n\n**2 garlic cloves, thinly sliced**\n\n**1 (5-ounce) package baby spinach**\n\n**\u00bc teaspoon red pepper flakes**\n\n**1 (10-ounce) prebaked whole wheat thin pizza crust**\n\n**\u2154 cup fat-free ricotta cheese**\n\n**\u00bd cup reduced-fat shredded mozzarella cheese**\n\n1. Preheat oven to 450\u00b0F. Spray large baking sheet with nonstick spray.\n\n2. Cook bacon in large skillet over medium-high heat, stirring occasionally, until crisp, about 5 minutes. Transfer bacon to plate lined with paper towels. Drain off and discard all but 1 teaspoon drippings.\n\n3. Add garlic to skillet; cook over medium heat, stirring constantly, until golden, about 1 minute. Add spinach to skillet a few handfuls at a time, stirring constantly and adding more spinach as it will fit. Continue cooking until spinach is wilted, about 2 minutes more. Stir in reserved bacon and red pepper flakes.\n\n4. Place crust on baking sheet. Spread ricotta evenly over crust. Top evenly with spinach mixture. Sprinkle with mozzarella. Bake until mozzarella cheese is bubbling, about 8 minutes. Cut into 6 wedges.\n\n**PER SERVING** (1 wedge): 218 Cal, 6 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 13 mg Chol, 438 mg Sod, 27 g Total Carb, 5 g Fib, 11 g Prot, 203 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Baked Cheesy Nachos\n\nSERVES 4\n\n**36 baked low-fat tortilla chips**\n\n**1 (15\u00bd-ounce) can pinto beans, rinsed and drained**\n\n**2 tomatoes, chopped**\n\n**\u00bd small red onion, chopped**\n\n**1 jalape\u00f1o pepper, seeded and minced**\n\n**1 tablespoon fresh lime juice**\n\n**\u00bd cup fat-free sour cream**\n\n**1 cup shredded fat-free Monterey Jack or Cheddar cheese**\n\n**3 tablespoons chopped fresh cilantro**\n\n1. Preheat oven to 400\u00b0F. Spray 9 \u00d7 13-inch baking dish with nonstick spray.\n\n2. Arrange 24 tortilla chips in single layer in baking dish. Top evenly with beans, tomatoes, onion, jalape\u00f1o pepper, lime juice, and sour cream.\n\n3. Crush remaining 12 tortilla chips and sprinkle over sour cream. Top evenly with Monterey Jack. Bake until heated through and cheese is melted and bubbling, about 20 minutes. Sprinkle with cilantro.\n\n**PER SERVING** (\u00bc of dish): 266 Cal, 2 Fat, 0 g Sat Fat, 0 g Trans Fat, 6 mg Chol, 514 mg Sod, 36 g Total Carb, 6 g Fib, 15 g Prot, 500 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nBlueberries with Whipped Ricotta and Balsamic Syrup\n\n# Blueberries with Whipped Ricotta and Balsamic Syrup\n\nSERVES 4\n\n**\u00bd cup balsamic vinegar**\n\n**1 cup fat-free ricotta cheese**\n\n**2 teaspoons grated orange zest**\n\n**2 pints blueberries**\n\n**Orange zest strips**\n\n1. Bring vinegar to boil in medium saucepan over medium-high heat; boil until reduced by half, about 4 minutes. Remove saucepan from heat and let cool about 10 minutes.\n\n2. Meanwhile, puree ricotta in food processor. Transfer cheese to small bowl and stir in orange zest.\n\n3. Divide blueberries evenly among 4 dessert dishes; top evenly with ricotta mixture. Drizzle evenly with vinegar and sprinkle with orange zest strips.\n\n**PER SERVING** (1 cup blueberries and \u00bc cup ricotta): 137 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 10 mg Chol, 76 mg Sod, 26 g Total Carb, 6 g Fib, 6 g Prot, 133 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\n# Oven-Roasted Peaches with Raspberries and Sorbet\n\nSERVES 4\n\n**4 ripe peaches halved and pitted**\n\n**1\u00bd tablespoons sugar**\n\n**1 pint sorbet, such as lemon or raspberry, slightly softened**\n\n**1 (6-ounce) container raspberries**\n\n1. Preheat oven to 425\u00b0F.\n\n2. Arrange peaches on baking sheet, cut side up, and sprinkle evenly with sugar. Roast fruit until softened, about 20 minutes. Set aside until just warm.\n\n3. Place 2 peach halves on each of 4 plates. Place \u00bc-cup scoop of sorbet in each peach half. Scatter raspberries around peaches.\n\n**PER SERVING** (1 dessert): 229 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 10 mg Sod, 59 g Total Carb, 6 g Fib, 2 g Prot, 24 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nDo it Faster\n\nSorbet is a quick cook's secret ingredient for dressing up dessert. Serve it alongside pound cake, angel food cake, or any fresh fruit to instantly elevate the ordinary into something special\u2014and \u00bd cup sorbet has just **_2 PointsPlus_** value.\n\nOven-Roasted Peaches with Raspberries and Sorbet\n\n# Frozen Vanilla Yogurt with Sugared Shredded Wheat\n\nSERVES 4\n\n**2 original-size shredded wheat cereal**\n\n**1 tablespoon unsalted butter, melted**\n\n**1 tablespoon sugar**\n\n**1 pint frozen vanilla low-fat yogurt**\n\n**2 cups mixed berries**\n\n1. Preheat oven to 400\u00b0F.\n\n2. Break each piece of shredded wheat crosswise into quarters and place in medium bowl. Drizzle with butter and toss to coat. Sprinkle with sugar and toss to coat.\n\n3. Arrange shredded wheat in one layer on baking sheet. Bake until deep golden brown, about 15 minutes. Let cool about 5 minutes on baking sheet.\n\n4. Place \u00bd-cup scoop of yogurt in each of 4 dessert dishes. Divide berries evenly among dishes. Coarsely crumble shredded wheat on top of yogurt.\n\n**PER SERVING** (1 dish): 242 Cal, 5 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 15 mg Chol, 78 mg Sod, 44 g Total Carb, 3 g Fib, 7 g Prot, 209 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Black and White Muffin Bites\n\nSERVES 18\n\n**1 cup all-purpose flour**\n\n**\u00bd cup sugar**\n\n**\u2153 cup unsweetened cocoa**\n\n**1 teaspoon baking soda**\n\n**\u00bc teaspoon salt**\n\n**\u00bd cup fat-free milk**\n\n**3 tablespoons canola oil**\n\n**1 large egg**\n\n**1 large egg white**\n\n**1 teaspoon vanilla extract**\n\n**\u00be cup white chocolate chips**\n\n1. Preheat oven to 350\u00b0F. Line 36 mini muffin cups with paper liners.\n\n2. Whisk together flour, sugar, cocoa, baking soda, and salt in large bowl. Whisk together milk, oil, egg, egg white, and vanilla in small bowl. Add milk mixture and \u00bd cup of chocolate chips to flour mixture, stirring just until moistened. Spoon batter evenly into prepared muffin cups, filling each about halfway.\n\n3. Sprinkle remaining \u00bc cup chocolate chips evenly over tops of muffins. Bake until muffins spring back when lightly pressed, about 10 minutes. Let muffins cool in pans on wire racks 10 minutes. Remove muffins from pans and let cool completely on racks.\n\n**PER SERVING** (2 mini muffins): 116 Cal, 6 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 14 mg Chol, 118 mg Sod, 16 g Total Carb, 0 g Fib, 2 g Prot, 28 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\n# **bonus**  \non the weekend\n\nSpend Some Time\n\nBeef-Vegetable Soup\n\nCuban-Style Shredded Beef and Rice\n\nBeef-Barley Stew with Roasted Vegetables\n\nCitrus-Marinated Roast Pork\n\nPork and Bean Adobo Chili\n\nApricot-Mustard Glazed Pork Roast\n\nBaked Stuffed Potatoes with Ham and Cheese\n\nRoasted Leg of Lamb\n\nStuffed Butterflied Leg of Lamb\n\nCacciatore-Style Chicken and Vegetables\n\nEasy Chicken Florentine with Spaghetti\n\nBest-Ever Country Captain\n\nChicken with Mushrooms and White Wine\n\nChicken and Vegetable Ragu with Herbed Dumplings\n\nChicken and Rice with Artichoke Hearts\n\nSpaghetti with Fresh Tomato Sauce and Meatballs\n\nRosemary Chicken Thighs with Roast Potatoes\n\nLentil and Sausage Soup\n\nProven\u00e7al-Style Vegetable-Chickpea Stew\n\nBaked Ziti with Summer Squash\n\nSlow Cookers Save Time\n\nBountiful Beef Stew\n\nBeef and Bean Soft Tacos\n\nBeef Stew Proven\u00e7al\n\nBeef, Beet, and Cabbage Soup\n\nLow-and-Slow Sloppy Joes\n\nLamb and Vegetable Stew\n\nPork Marrakesh\n\nChicken and Vegetable Curry\n\nBraised Chicken in Riesling\n\nEasy Chicken Gumbo\n\nChicken and Vegetable Tagine\n\nGarlicky Braised Turkey Breast\n\nChuck Wagon-Style Turkey Chili\n\nFirecracker Turkey Chili\n\nCaribbean Seafood Stew\n\nVegetarian Burritos with Salsa Verde\n\nShrimp Chowder with Dill\n\nVegetable Minestrone with Pasta\n\nOnion Soup with Herbed Cheese Toasts\n\nSomething Sweet\n\nCarrot-Apple Cupcakes with Cream Cheese Frosting\n\nSpice-Glazed Cherry Bundt Cake\n\nPumpkin Pie Muffins\n\nApricot and Toasted Almond Galette\n\nPeach-Blueberry Crostatas\n\nBanana-Walnut Bread\n\nBrown Rice-Banana Pudding\n\nLemon Souffl\u00e9s\n\nPumpkin-Cranberry Bread Puddings\n\nOrange Flan with Macerated Oranges\n\nTriple Berry Summer Pudding\n\nFrozen Strawberry-Maple Yogurt\n\nRaspberry-Orange Sorbet\n\nWarm Spice-Baked Apples\n\nWhite Wine-Poached Pears\n\nChunky Pink Apple-Raspberry Sauce\n\nRoasted Pears with Balsamic Glaze\n\nMixed Berry Shortcakes\n\nWhole Grain and Fruit Oatmeal Cookies\n\nChocolate-Cherry Brownies\n\n# spend some time\n\n# Beef-Vegetable Soup\n\nSERVES 6\n\n**1 tablespoon olive oil**\n\n**\u00be pound lean top round steak, trimmed and cut into \u00bd-inch pieces**\n\n**4 carrots, thinly sliced**\n\n**4 celery stalks, sliced**\n\n**3 parsnips, peeled and diced**\n\n**1 large onion, chopped**\n\n**5 cups reduced-sodium beef broth**\n\n**1 (14\u00bd-ounce) can petite diced tomatoes**\n\n**\u00bd teaspoon dried thyme**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 cups lightly packed baby spinach**\n\n**1\u00bd cups hot cooked brown rice**\n\n1. Heat oil in Dutch oven over medium heat. Add beef, in batches, and cook, stirring, until browned, about 4 minutes. Using slotted spoon, transfer beef to plate.\n\n2. Add carrots, celery, parsnips, and onion to Dutch oven; cook, stirring, until slightly softened, about 5 minutes. Add beef and any accumulated juices, broth, tomatoes, thyme, salt, and pepper; bring to boil. Reduce heat and simmer until beef is tender, about 20 minutes longer. Stir in baby spinach and rice.\n\n**PER SERVING** (about 1\u2153 cups): 255 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 31 mg Chol, 658 mg Sod, 38 g Total Carb, 7 g Fib, 20 g Prot, 95 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nFinish with a fresh dessert of plain fat-free Greek yogurt topped with sliced strawberries (\u00bd cup of plain fat-free Greek yogurt per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# Cuban-Style Shredded Beef and Rice\n\nSERVES 4\n\n**1 (1-pound) lean flank steak, trimmed**\n\n**1 (14\u00bd-ounce) can reduced-sodium beef broth**\n\n**3 garlic cloves, peeled plus 2 garlic cloves, minced**\n\n**1 teaspoon olive oil**\n\n**1 onion, chopped**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**1 jalape\u00f1o pepper, seeded and minced**\n\n**1 teaspoon dried oregano**\n\n**1 teaspoon ground cumin**\n\n**\u00bc cup chopped fresh cilantro**\n\n**4 cups hot cooked brown rice**\n\n**Lime wedges**\n\n1. Combine steak, broth, and peeled garlic in medium skillet and bring to boil over high heat. Reduce heat and simmer, covered, until steak is very tender, about 1 hour.\n\n2. Remove skillet from heat and let stand 15 minutes. Reserve \u00bd cup of broth; save remaining broth for another use. Discard garlic. Transfer steak to cutting board; with two forks, shred beef.\n\n3. Wipe out skillet. Add oil and set over medium-high heat. Add onion and minced garlic and cook, stirring occasionally, until onion is slightly softened, about 4 minutes. Stir in tomatoes, jalape\u00f1o, oregano, and cumin; cook, stirring, 5 minutes longer. Stir in shredded beef and reserved \u00bd cup broth. Continue to cook until most of liquid is evaporated, about 3 minutes.\n\n4. Remove skillet from heat and stir in cilantro. Serve with rice and lime wedges.\n\n**PER SERVING** (\u00be cup beef mixture and 1 cup rice): 466 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 82 mg Chol, 824 mg Sod, 55 g Total Carb, 9 g Fib, 42 g Prot, 85 mg Calc.\n\n**_PointsPlus_** value: **_11._**\n\nCook's Note\n\nFinish this hearty dinner with a quick fruit dessert made with sliced papaya, mango, and orange segments tossed with grated orange zest.\n\nBeef-Barley Stew with Roasted Vegetables\n\n# Beef-Barley Stew with Roasted Vegetables\n\nSERVES 8\n\n**1 celery root, peeled and cut into \u00be-inch chunks**\n\n**4 carrots, cut into \u00be-inch chunks**\n\n**2 parsnips, peeled and cut into \u00be-inch chunks**\n\n**2 onions, chopped**\n\n**1 tablespoon chopped fresh thyme or 1\u00bd teaspoons dried**\n\n**1\u00bd pounds lean boneless beef chuck, trimmed and cut into 1-inch chunks**\n\n**6 cups reduced-sodium beef broth**\n\n**3 garlic cloves, chopped**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 (8-ounce) package sliced cremini mushrooms**\n\n**1 cup pearl barley, rinsed**\n\n1. Preheat oven to 450\u00b0F and spray large shallow roasting pan with nonstick spray.\n\n2. Put celery root, carrots, parsnips, onions, and thyme in pan and spray with nonstick spray; toss to coat. Roast, stirring occasionally, until vegetables are browned and crisp-tender, about 30 minutes.\n\n3. Meanwhile, spray Dutch oven with nonstick spray and place over medium-high heat. Cook beef, in batches, until browned on all sides, about 4 minutes. Transfer beef to plate as it is browned.\n\n4. Return beef to pot. Add 5\u00bd cups of broth, garlic, salt, and pepper; bring to boil. Reduce heat and simmer, covered, for 45 minutes.\n\n5. Stir in mushrooms and barley and bring to boil. Reduce heat and simmer, covered, stirring occasionally, 15 minutes. Stir in roasted vegetables and bring to boil. Reduce heat and simmer, covered, until beef is fork-tender and barley is tender, about 15 minutes, adding remaining \u00bd cup broth if stew seems too thick.\n\n**PER SERVING** (generous 1 cup): 318 Cal, 11 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 44 mg Chol, 366 mg Sod, 35 g Total Carb, 7 g Fib, 22 g Prot, 61 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nServe the stew with steamed Swiss chard and a reduced-calorie whole wheat roll (1 reduced-calorie whole wheat roll per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# Citrus-Marinated Roast Pork\n\nSERVES 8\n\n**\u2153 cup fresh lime juice**\n\n**\u00bc cup finely chopped onion**\n\n**6 garlic cloves, minced**\n\n**1 tablespoon olive oil**\n\n**1 teaspoon dried oregano**\n\n**1 teaspoon ground cumin**\n\n**\u00bc teaspoon red pepper flakes**\n\n**1 (2-pound) lean boneless center-cut pork loin roast, trimmed**\n\n**1 teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**12 carrots, cut into 2-inch chunks**\n\n1. Combine lime juice, onion, garlic, oil, oregano, cumin, and red pepper flakes in large zip-close plastic bag. Add pork to bag. Squeeze out air and seal bag; turn to coat pork. Refrigerate, turning bag occasionally, for about 3 hours.\n\n2. Preheat oven to 425\u00b0F. Place rack in large roasting pan and spray rack with nonstick spray.\n\n3. Remove pork from plastic bag and place on rack. Discard marinade. Sprinkle pork with salt and black pepper. Spray carrots with olive oil nonstick spray and scatter around pork. Roast until an instant-read thermometer inserted into center of pork registers 145\u00b0F and carrots are tender, about 35 minutes.\n\n4. Transfer pork to cutting board and let stand 10 minutes. Cut pork into 16 slices and serve with carrots.\n\n**PER SERVING** (2 slices pork and about \u2154 cup carrots): 252 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 72 mg Chol, 404 mg Sod, 0 g Total Carb, 3 g Fib, 26 g Prot, 47 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nServe the pork with a flavorful brown rice side dish. Toss cooked brown rice with thinly sliced scallions, chopped fresh cilantro, and lime zest and juice to taste (\u00bd cup cooked brown rice per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Pork and Bean Adobo Chili\n\nSERVES 5\n\n**1 tablespoon olive oil**\n\n**1 pound boneless pork loin, trimmed and cut into \u00bd-inch pieces**\n\n**1 onion, chopped**\n\n**1 green bell pepper, chopped**\n\n**1 red bell pepper, chopped**\n\n**3 garlic cloves, minced**\n\n**1 (14\u00bd-ounce) can fire-roasted diced tomatoes**\n\n**2 teaspoons chopped canned chipotle en adobo**\n\n**2 teaspoons chili powder**\n\n**2 teaspoons ground cumin**\n\n**\u00be teaspoon salt**\n\n**1 (15\u00bd-ounce) can red kidney beans, rinsed and drained**\n\n1. Heat 1\u00bd teaspoons of oil in large saucepan over medium-high heat. Add pork and cook, stirring occasionally, until browned, about 4 minutes. Transfer to plate.\n\n2. Add remaining 1\u00bd teaspoons oil to saucepan. Add onion, bell peppers, and garlic; cook, stirring occasionally, until softened, about 5 minutes. Stir in tomatoes, chipotle, chili powder, cumin, and salt; bring to boil. Add beans and pork to saucepan. Reduce heat and simmer, covered, until pork is tender, about 10 minutes.\n\n**PER SERVING** (about 1\u00bc cups): 292 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 58 mg Chol, 666 mg Sod, 23 g Total Carb, 6 g Fib, 27 g Prot, 74 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nServe a refreshing citrus-dressed salad with this hearty chili. Toss together baby greens, halved grape tomatoes, lime zest and juice, and salt and pepper to taste.\n\n# Apricot-Mustard Glazed Pork Roast\n\nSERVES 4\n\n**3 garlic cloves, minced**\n\n**1 tablespoon chopped fresh rosemary or 1 teaspoon dried**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 (1\u00bc-pound) lean boneless center-cut pork loin roast, trimmed**\n\n**2 tablespoons apricot jam**\n\n**2 tablespoons Dijon mustard**\n\n1. Preheat oven to 400\u00b0F. Spray roasting pan with nonstick spray.\n\n2. Stir together garlic, rosemary, salt, and pepper in small bowl. Rub mixture over pork. Place pork in roasting pan and roast 30 minutes.\n\n3. Stir together jam and mustard in small bowl and brush all over pork. Continue to roast pork until an instant-read thermometer inserted into center registers 145\u00b0F, about 5 minutes longer. Transfer to cutting board and let stand 10 minutes. Cut roast into 12 slices.\n\n**PER SERVING** (3 slices pork): 237 Cal, 10 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 79 mg Chol, 696 mg Sod, 8 g Total Carb, 0 g Fib, 28 g Prot, 46 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nToss 1 pound of halved baby or fingerling potatoes with minced fresh rosemary, salt, and pepper and lightly spray with nonstick spray. Arrange in the roasting pan with the pork and roast until tender; the per-serving **_PointsPlus_** value will increase by **_2_**.\n\nApricot-Mustard Glazed Pork Roast\n\n# Baked Stuffed Potatoes with Ham and Cheese\n\nSERVES 4\n\n**4 (8-ounce) baking potatoes**\n\n**\u2153 cup fat-free sour cream**\n\n**\u215b teaspoon black pepper**\n\n**1 cup diced lean deli ham**\n\n**1 cup shredded fat-free Cheddar cheese**\n\n**Chopped fresh chives**\n\n1. Preheat oven to 400\u00b0F. Line baking sheet with foil.\n\n2. Using fork, prick potatoes in several places. Place on baking sheet and bake until fork-tender, about 50 minutes.\n\n3. Wearing oven mitts, cut off and discard thin lengthwise slice from each potato. Scoop out potato pulp, leaving \u00bc-inch wall. Transfer pulp to medium bowl and mash with sour cream, and pepper. Spoon filling evenly back into potato shells. Top potatoes evenly with ham and Cheddar.\n\n4. Meanwhile, preheat broiler. Return potatoes to baking sheet and broil 5 inches from heat until cheese is melted, about 3 minutes. Sprinkle with chives.\n\n**PER SERVING** (1 filled potato): 292 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 26 mg Chol, 732 mg Sod, 47 g Total Carb, 4 g Fib, 21 g Prot, 297 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nServe the potatoes with a healthy green vegetable such as steamed broccoli, zucchini, or green beans.\n\n# Roasted Leg of Lamb\n\nSERVES 8\n\n**3 garlic cloves, minced**\n\n**1 tablespoon paprika**\n\n**2 teaspoons poultry seasoning**\n\n**1\u00bd teaspoons salt**\n\n**\u00bd teaspoon black pepper**\n\n**1 (2\u00bc-pound) lean boneless leg of lamb, trimmed**\n\n**4 onions, sliced**\n\n**\u00be cup dry white wine or dry vermouth**\n\n1. Preheat oven to 400\u00b0F. Spray roasting pan with nonstick spray.\n\n2. Stir together garlic, paprika, poultry seasoning, salt, and pepper in small bowl. Add enough water to form thick paste and rub all over lamb.\n\n3. Place lamb in roasting pan and top with onions. Pour wine into pan. Roast until an instant-read thermometer inserted into center of lamb registers 145\u00b0F for medium, about 1 hour.\n\n4. Transfer lamb to cutting board and let stand 10 minutes. Cut into 24 slices and serve with onions.\n\n**PER SERVING** (3 slices lamb and about \u00bd cup onions): 228 Cal, 9 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 88 mg Chol, 514 mg Sod, 7 g Total Carb, 1 g Fib, 28 g Prot, 31 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nAn instant-read thermometer is a must-have tool for cooking meats and poultry to a safe temperature as well as ensuring that you don't overcook beef, pork, or lamb roasts. It's an inexpensive investment that will make you a better\u2014and safer\u2014cook.\n\nStuffed Butterflied Leg of Lamb\n\n# Stuffed Butterflied Leg of Lamb\n\nSERVES 8\n\n**1 tablespoon olive oil**\n\n**3 garlic cloves, minced**\n\n**1 tablespoon chopped fresh rosemary**\n\n**1\u00bd teaspoons salt**\n\n**\u00be teaspoon black pepper**\n\n**1 (2\u00bd-pound) butterflied lean leg of lamb, trimmed**\n\n**1 cup whole wheat couscous**\n\n**\u00bd cup finely chopped fresh parsley**\n\n**\u00bd cup finely chopped red bell pepper**\n\n1. Stir together oil, garlic, rosemary, 1\u00bc teaspoons of salt, and \u00bd teaspoon of pepper in small bowl; rub all over lamb. Place lamb on plate; cover and refrigerate at least 2 hours or up to 8 hours.\n\n2. Meanwhile, prepare couscous according to package directions, omitting fat and salt if desired. Stir in parsley, bell pepper, and remaining \u00bc teaspoon salt and \u00bc teaspoon black pepper.\n\n3. Preheat oven to 400\u00b0F.\n\n4. Place lamb, boned side up, on work surface. Spread couscous mixture evenly over lamb. Starting from long side, roll up lamb to enclose filling. Tie lamb securely at 2-inch intervals with kitchen string.\n\n5. Place rack in roasting pan and spray rack with nonstick spray. Place lamb on rack and roast until an instant-read thermometer inserted into thickest part of lamb registers 145\u00b0F for medium, about 1 hour.\n\n6. Transfer lamb to cutting board and let stand 10 minutes. Remove string and cut lamb into 16 slices.\n\n**PER SERVING** (2 slices stuffed lamb): 272 Cal, 11 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 98 mg Chol, 650 mg Sod, 10 g Total Carb, 2 g Fib, 32 g Prot, 25 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nHere's how to roast asparagus to serve along with the lamb: When the lamb is almost done, place 2 pounds fresh asparagus spears in a shallow baking pan. Lightly spray with olive oil nonstick spray, sprinkle with salt and pepper and toss to coat. Roast at 400\u00b0F, tossing once, until the asparagus is crisp-tender, about 15 minutes.\n\n# Cacciatore-Style Chicken and Vegetables\n\nSERVES 6\n\n**3 pounds bone-in chicken breasts and thighs, skin removed**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 tablespoon olive oil**\n\n**2 red bell peppers, thinly sliced**\n\n**1 (8-ounce) package sliced cremini mushrooms**\n\n**1 celery stalk, thinly sliced**\n\n**1 carrot, thinly sliced**\n\n**1 red onion, sliced**\n\n**3 garlic cloves, minced**\n\n**2 teaspoons chopped fresh rosemary**\n\n**2 cups fat-free marinara sauce**\n\n1. Sprinkle chicken with salt and black pepper.\n\n2. Heat 2 teaspoons of oil in large skillet over medium-high heat. Add chicken and cook until browned, about 4 minutes on each side. Transfer chicken to plate and set aside.\n\n3. Add remaining 1 teaspoon oil to skillet. Add bell peppers, mushrooms, celery, carrot, onion, garlic, and rosemary; cook, stirring, until vegetables are slightly softened, about 3 minutes.\n\n4. Return chicken to skillet. Add marinara sauce and bring to simmer. Reduce heat and simmer, covered, until chicken is cooked through and vegetables are tender, about 20 minutes.\n\n**PER SERVING** (1 piece chicken and \u00be cup vegetables with sauce): 296 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 95 mg Chol, 635 mg Sod, 12 g Total Carb, 3 g Fib, 36 g Prot, 69 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nServe the saucy cacciatore with a slice of crusty bread (a 1-ounce slice of Italian bread will increase the **_PointsPlus_** value by **_2_** ).\n\nCacciatore-Style Chicken and Vegetables\n\n# Easy Chicken Florentine with Spaghetti\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**1 small onion, chopped**\n\n**2 (10-ounce) packages frozen leaf spinach, thawed**\n\n**\u00bc teaspoon black pepper**\n\n**4 (5-ounce) skinless boneless chicken breasts**\n\n**1 cup shredded fat-free mozzarella cheese**\n\n**2 tablespoons grated Parmesan cheese**\n\n**4 ounces whole wheat spaghetti**\n\n**\u00bd cup fat-free marinara sauce, heated**\n\n**2 slices bacon, crisp-cooked and crumbled**\n\n1. Preheat oven to 350\u00b0F and spray 8-inch square baking dish with nonstick spray.\n\n2. Heat 1 teaspoon of oil in large skillet over medium-high heat. Add onion and cook, stirring frequently, until softened, about 5 minutes. Add spinach and pepper to skillet. Cook until most of liquid has evaporated, about 5 minutes longer. Spoon spinach mixture evenly into prepared baking dish.\n\n3. Wipe out skillet. Add remaining 1 teaspoon oil to skillet and set over high heat. Place chicken in skillet and cook just until browned, about 2 minutes on each side.\n\n4. Arrange chicken over spinach mixture in one layer; sprinkle evenly with mozzarella and Parmesan. Bake until cheeses are melted and chicken is cooked through, about 20 minutes.\n\n5. Meanwhile, cook spaghetti according to package directions, omitting salt if desired; drain. Toss together spaghetti and marinara sauce. Sprinkle chicken with bacon and serve with spaghetti.\n\n**PER SERVING** (\u00bc of casserole and \u00bd cup pasta): 432 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 97 mg Chol, 870 mg Sod, 35 g Total Carb, 7 g Fib, 51 g Prot, 473 mg Calc.\n\n**_PointsPlus_** value: **_11._**\n\nCook's Note\n\nSkinless boneless chicken breasts are a universal favorite for easy-to-make dinners. If you use them often, save time and money by buying in bulk when they're on sale. Then, portion them into zip-close bags in the quantity you prepare for most recipes (usually 4), and freeze up to 6 months.\n\n# Best-Ever Country Captain\n\nSERVES 4\n\n**2 teaspoons canola oil**\n\n**1\u00bc pounds skinless boneless chicken breasts, cut into 1-inch pieces**\n\n**1 large onion, chopped**\n\n**1 Granny Smith apple, peeled, cored, and diced**\n\n**1 green bell pepper, chopped**\n\n**1 tablespoon minced garlic**\n\n**1 tablespoon minced peeled fresh ginger**\n\n**1 tablespoon Madras curry powder**\n\n**\u00bc teaspoon cinnamon**\n\n**\u00bc teaspoon salt**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**1 cup reduced-sodium chicken broth**\n\n**\u00bc cup dark raisins**\n\n**1 tablespoon sliced or slivered almonds, toasted**\n\n1. Heat 1 teaspoon of oil in Dutch oven or large saucepan over medium-high heat. Add chicken and cook, turning occasionally, until browned, about 6 minutes. Transfer to plate.\n\n2. Add remaining 1 teaspoon oil to Dutch oven and reduce heat to medium. Add onion, apple, bell pepper, garlic, and ginger; cook, stirring, until vegetables are softened, about 5 minutes. Stir in curry powder, cinnamon, and salt; cook, stirring, 1 minute longer.\n\n3. Return chicken to Dutch oven along with tomatoes, broth, and raisins; bring to boil. Reduce heat and simmer, covered, until chicken is cooked through, about 15 minutes. Serve sprinkled with almonds.\n\n**PER SERVING** (about 1\u00bd cups): 309 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 86 mg Chol, 516 mg Sod, 24 g Total Carb, 4 g Fib, 35 g Prot, 90 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nDo it Faster\n\nToasting almonds enhances their flavor and crisps their texture. To toast sliced or slivered almonds in a hurry, place them in a small heavy skillet over medium heat. Toast, shaking the pan frequently, until the nuts are lightly browned, about 5 minutes. Transfer to a plate to cool.\n\nChicken with Mushrooms and White Wine\n\n# Chicken with Mushrooms and White Wine\n\nSERVES 4\n\n**4 (5-ounce) skinless boneless chicken breasts**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 teaspoons olive oil**\n\n**\u00bc pound mixed mushrooms, halved**\n\n**1 onion, chopped**\n\n**1 carrot, chopped**\n\n**1 celery stalk, chopped**\n\n**3 garlic cloves, minced**\n\n**1 teaspoon herbes de Provence**\n\n**1 tablespoon all-purpose flour**\n\n**1 cup reduced-sodium chicken broth**\n\n**\u00be cup dry white wine**\n\n**8 ounces whole wheat fettuccine**\n\n**Chopped fresh parsley**\n\n1. Sprinkle chicken with salt and pepper. Heat 1 teaspoon of oil in large skillet over medium-high heat. Add chicken and cook, turning occasionally, until browned, about 4 minutes. Transfer chicken to plate.\n\n2. Add remaining 1 teaspoon oil and mushrooms to skillet. Cook, stirring frequently, until mushrooms are browned, about 5 minutes. Stir in onion, carrot, celery, garlic, and herbes de Provence. Cook just until onion is softened, about 3 minutes, then sprinkle with flour. Cook, stirring constantly, 1 minute longer. Stir in broth and wine and bring to boil.\n\n3. Return chicken and any accumulated juices to skillet. Reduce heat and simmer, covered, until sauce is thickened and chicken is cooked through, about 10 minutes.\n\n4. Meanwhile, cook fettuccine according to package directions, omitting salt if desired; drain.\n\n5. Divide fettuccine among 4 plates; top with chicken and sauce. Sprinkle with parsley.\n\n**PER SERVING** (1 chicken breast, \u2154 cup sauce and vegetables, and 1 cup pasta): 466 Cal, 7 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 84 mg Chol, 528 mg Sod, 51 g Total Carb, 8 g Fib, 42 g Prot, 67 mg Calc.\n\n**_PointsPlus_** value: **_12._**\n\nCook's Note\n\nHerbes de Provence is a blend of dried rosemary, marjoram, thyme, and savory that adds the unique flavor of Southern France to a dish. If you don't have it, you can substitute dried thyme in this dish and it will still be delicious.\n\n# Chicken and Vegetable Ragu with Herbed Dumplings\n\nSERVES 4\n\n**1 pound skinless boneless chicken breasts, cut into 1-inch pieces**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 onion, chopped**\n\n**1 tablespoon plus \u00bd cup all-purpose flour**\n\n**2 cups reduced-sodium chicken broth**\n\n**2 (5-ounce) red potatoes, scrubbed and diced**\n\n**\u00bc cup whole wheat flour**\n\n**1\u00bd teaspoons baking powder**\n\n**\u00bd cup fat-free milk**\n\n**2 teaspoons unsalted butter, melted**\n\n**2 tablespoons chopped fresh parsley**\n\n**2 tablespoons chopped fresh chives**\n\n**1\u00bd cups frozen mixed peas and carrots, thawed**\n\n**1 teaspoon dried thyme**\n\n1. Spray Dutch oven with nonstick spray and set over medium-high heat. Add chicken and sprinkle with \u00bc teaspoon of salt, and pepper. Cook, stirring occasionally, until chicken is lightly browned, about 6 minutes. Add onion and cook until softened, about 4 minutes longer.\n\n2. Stir in 1 tablespoon of flour and cook, stirring constantly, 1 minute. Stir in broth and potatoes and bring to boil. Reduce heat and simmer, covered, until potatoes are tender, about 15 minutes.\n\n3. Meanwhile, to make dumpling dough, whisk together remaining \u00bd cup all-purpose flour, whole wheat flour, baking powder, and remaining \u00bd teaspoon salt in medium bowl. Add milk, butter, parsley, and chives; stir just until soft dough forms. Set dumpling dough aside.\n\n4. Stir peas and carrots and thyme into Dutch oven and simmer 2 minutes. Drop 8 rounded tablespoonfuls of dumpling dough onto surface of simmering stew. Cover and simmer 8 minutes. Uncover and simmer until dumplings are doubled in size and cooked through, about 3 minutes longer.\n\n**PER SERVING** (1 cup stew and 2 dumplings): 390 Cal, 7 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 74 mg Chol, 920 mg Sod, 47 g Total Carb, 6 g Fib, 35 g Prot, 211 mg Calc.\n\n**_PointsPlus_** value: **_10._**\n\n# Chicken and Rice with Artichoke Hearts\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**4 (5-ounce) skinless bone-in chicken thighs**\n\n**\u00bd teaspoon dried oregano**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**2 red bell peppers, chopped**\n\n**1 onion, chopped**\n\n**3 garlic cloves, minced**\n\n**1 cup brown rice**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**1 cup water**\n\n**1 cup frozen artichoke hearts, thawed and coarsely chopped**\n\n**1 tablespoon capers, drained**\n\n1. Heat 1 teaspoon of oil in large nonstick skillet over medium heat. Sprinkle chicken with oregano, \u00bc teaspoon of salt, and black pepper. Add chicken to skillet and cook until browned, about 3 minutes on each side. Transfer to plate.\n\n2. Add remaining 1 teaspoon oil to skillet. Add bell peppers, onion, and garlic; cook, stirring frequently, until vegetables begin to soften, about 4 minutes. Add rice and cook, stirring, 1 minute longer. Return chicken to skillet. Add tomatoes, water, and remaining \u00bc teaspoon salt; bring to boil. Reduce heat and simmer, covered, until rice is tender, liquid is absorbed, and chicken is cooked through, about 40 minutes longer.\n\n3. Uncover pan and scatter artichokes and capers over rice. Cook, covered, just until artichokes are heated through, about 3 minutes.\n\n**PER SERVING** (1 chicken thigh and 1\u2153 cups rice mixture): 422 Cal, 10 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 57 mg Chol, 602 mg Sod, 56 g Total Carb, 6 g Fib, 27 g Prot, 106 mg Calc.\n\n**_PointsPlus_** value: **_11._**\n\nCook's Note\n\nA peppery watercress salad is the perfect partner for this one-pan meal. Toss together watercress sprigs, plum tomato wedges, balsamic vinegar, and salt and pepper to taste.\n\n# Spaghetti with Fresh Tomato Sauce and Meatballs\n\nSERVES 4\n\n**8 ounces whole wheat spaghetti**\n\n**1 pound ground skinless turkey breast**\n\n**1 large egg white**\n\n**1 tablespoon cornmeal**\n\n**1 teaspoon dried oregano**\n\n**\u00bd teaspoon salt**\n\n**3 teaspoons olive oil**\n\n**2 garlic cloves**\n\n**8 plum tomatoes, chopped**\n\n**1 teaspoon dried basil**\n\n**Pinch red pepper flakes**\n\n1. Cook spaghetti according to package directions, omitting salt if desired. Drain and keep warm.\n\n2. Meanwhile, mix together turkey, egg white, cornmeal, oregano, and \u00bc teaspoon of salt in large bowl. With damp hands, shape mixture into 24 meatballs.\n\n3. Heat 2 teaspoons of oil in large nonstick skillet over medium heat. Cook meatballs, in batches, turning often, until browned, about 4 minutes. Transfer to plate.\n\n4. To make sauce, wipe out skillet and set over medium heat. Add remaining 1 teaspoon oil and garlic. Cook, stirring, until garlic is fragrant, about 30 seconds. Add tomatoes, basil, remaining \u00bc teaspoon salt, and red pepper flakes; cook, stirring frequently, until tomatoes are softened, about 5 minutes. Return meatballs to skillet and simmer, covered, until cooked through, about 5 minutes longer.\n\n5. Divide pasta evenly among 4 large bowls and top evenly with meatballs and sauce.\n\n**PER SERVING** (1 cup spaghetti, 6 meatballs, and 1 cup sauce): 392 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 75 mg Chol, 574 mg Sod, 51 g Total Carb, 6 g Fib, 37 g Prot, 60 mg Calc.\n\n**_PointsPlus_** value: **_10._**\n\nCook's Note\n\nYou can serve the pasta sprinkled with freshly grated Parmesan cheese (1 tablespoon grated Parmesan cheese per serving will increase the **_PointsPlus_** value by **_1_** ). If served with Parmesan, this recipe does not work with Simple Start or with the Simply Filling technique.\n\nSpaghetti with Fresh Tomato Sauce and Meatballs\n\n# time well spent\n\nUse these kitchen tricks when you have some extra time on the weekends. They take a little effort, but will pay off with big rewards when you're in a weeknight time crunch.\n\n**FREEZE YOUR FAVORITE BREAKFAST.** Premade muffins, pancakes, and waffles make breakfast a breeze with just a zap in the microwave.\n\n**PREP AND FREEZE FRUITS FOR SMOOTHIES.** If fruits like mangos, peaches, and berries are prepped and frozen ahead of time, it makes your morning smoothie fuss-free. You're more likely to make nutritious fruit a part of your day if it's easy to do.\n\n**DOUBLE UP.** Always make two batches of soups, chilis, casseroles, or other dishes that freeze well for instant meals later on. No more starting dinner from scratch on a rushed weeknight. It feels good to come home to something made earlier.\n\n**OR, COOK ONCE FOR THE WEEK.** Invest some time on the weekend to prepare foods for the entire week. Make a casserole or a stew to reheat for an effortless dinner. Whip up a pesto sauce, marinara sauce, or salad dressing that you can use in several dishes throughout the week. If your weekday schedule is jam-packed, this may be the perfect solution to make sure you have healthy meals.\n\n**PREP AHEAD.** Chop onions and other vegetables for the week and store them in sealed containers in the refrigerator. Wash three days' worth of lettuce and greens, dry them, and store refrigerated in plastic bags. If you come home feeling too tired to cook, remind yourself that most of the work is already done.\n\n**COOK EXTRA WHOLE GRAINS.** With cooked barley, farro, or wheat berries on hand, it's easy to add them to pancake batter, soups, or meat loaves to boost flavor and fiber. And, they all make delicious side dishes on their own when seasoned with salt, pepper, and a fresh grating of lemon zest. Store them in clear containers in the refrigerator so you can see exactly what you have on hand at a glance.\n\n**MAKE A MENU AND SHOPPING LIST.** Mapping out a weekly menu and shopping list will save trips to the supermarket, save time spent shopping, and take away the stress of what to cook for dinner every night.\n\n**MAINTAIN A QUICK-MEAL PANTRY.** When you shop each week, check for long-lasting pantry staples that are on sale and stock up. Keep your shelves replenished with canned beans, tomatoes, tomato sauce, and broths; dried pasta; and grains such as rice, quinoa, and bulgur. Always have oils and vinegars, soy sauce, and bouillon cubes on hand. Buy red onions, celery, carrots, garlic, and a few fresh herbs such as basil and flat-leaf parsley each week. With these mealtime building blocks, you can make a healthy dinner in minutes.\n\n**MASTER A FEW NO-BRAINER DISHES.** When you've got to make dinner fast, but don't have the time or energy for anything that requires a recipe, learn to make quesadillas, frittatas, grilled sandwiches, and pasta with sauce. With a well-stocked pantry, you can alter the ingredients in these dishes based on what you have on hand\u2014no recipe required!\n\n**LABEL LEFTOVERS.** Store leftovers in plastic or glass containers and label them with what is inside (if you don't have clear containers) and the date. You'll save time looking through containers to find what you're looking for.\n\n# Rosemary Chicken Thighs with Roast Potatoes\n\nSERVES 4\n\n**4 (\u00bc-pound) skinless boneless chicken thighs**\n\n**2 teaspoons olive oil**\n\n**2 garlic cloves, minced**\n\n**1 teaspoon grated lemon zest**\n\n**1 tablespoon fresh lemon juice**\n\n**1\u00bd teaspoons dried rosemary**\n\n**1 teaspoon dried thyme**\n\n**\u00be teaspoon salt**\n\n**6 small new potatoes, scrubbed and quartered**\n\n1. Combine chicken, 1 teaspoon of oil, garlic, lemon zest and juice, rosemary, thyme, and \u00bd teaspoon of salt in large zip-close plastic bag. Squeeze out air and seal bag; turn to coat chicken. Refrigerate, turning bag occasionally, at least 30 minutes or up to overnight.\n\n2. Toss together potatoes and remaining 1 teaspoon oil and \u00bc teaspoon salt in medium bowl. Spray rimmed baking sheet with nonstick spray and spread potatoes on baking sheet. Place potatoes in oven and turn oven on to 425\u00b0F. When temperature reaches 425\u00b0F, remove potatoes from oven. Toss potatoes, then push them to one side of pan.\n\n3. Remove chicken from marinade and place on baking sheet alongside potatoes. Discard marinade. Roast until chicken is cooked through and potatoes are tender and browned, about 20 minutes.\n\n**PER SERVING** (1 piece chicken and \u00bd cup potatoes): 273 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 71 mg Chol, 512 mg Sod, 16 g Total Carb, 2 g Fib, 25 g Prot, 57 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nThis herbal lemon marinade is also great to use for pork chops or pork tenderloin.\n\n# Lentil and Sausage Soup\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**2 carrots, thinly sliced**\n\n**1 onion, diced**\n\n**2 garlic cloves, minced**\n\n**\u00bc pound turkey kielbasa, thinly sliced**\n\n**1\u00bc cups brown lentils, picked over and rinsed**\n\n**5 cups water**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n1. Heat oil in large saucepan over medium heat. Add carrots, onion, and garlic; cook, stirring frequently, until softened, about 5 minutes.\n\n2. Add kielbasa, lentils, and water; bring to boil. Reduce heat and simmer until lentils are tender, about 30 minutes.\n\n3. Stir in tomatoes, salt, and pepper. Simmer until heated through, about 5 minutes longer.\n\n**PER SERVING** (1\u00be cups): 296 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 15 mg Chol, 760 mg Sod, 44 g Total Carb, 12 g Fib, 21 g Prot, 95 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nTurkey kielbasa is a great ingredient for the shortcut cook to keep on hand. As you'll see in this recipe, just a small amount is so flavorful that you don't need to add other herbs or spices to a dish to make it satisfying and delicious.\n\nLentil and Sausage Soup\n\nProven\u00e7al-Style Vegetable-Chickpea Stew\n\n# Proven\u00e7al-Style Vegetable-Chickpea Stew\n\nSERVES 4\n\n**1 eggplant (1 pound), cut into \u00be-inch cubes**\n\n**2 teaspoons olive oil**\n\n**1 (28-ounce) can fire-roasted diced tomatoes, drained**\n\n**3 tablespoons tomato paste**\n\n**2 red bell peppers, cut into \u00be-inch pieces**\n\n**1 large zucchini, cut into \u00be-inch pieces**\n\n**1 large onion, coarsely chopped**\n\n**2 large garlic cloves, minced**\n\n**1 teaspoon dried thyme**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bc cup chopped fresh parsley**\n\n**2\u00bd cups rinsed and drained canned chickpeas**\n\n**\u00bc cup grated Parmesan cheese**\n\n1. Stir together eggplant and oil in large microwavable bowl. Cover bowl with wax paper. Microwave on High until eggplant is softened, about 4 minutes.\n\n2. Add all remaining ingredients except chickpeas and Parmesan to eggplant and stir to combine. Cover bowl with wax paper. Microwave on High until vegetables are softened, about 15 minutes, stirring every 5 minutes. Stir in chickpeas and let stand about 5 minutes. Serve warm or at room temperature sprinkled with Parmesan.\n\n**PER SERVING** (about 1\u00bd cups): 119 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 405 mg Sod, 18 g Total Carb, 6 g Fib, 4 g Prot, 55 mg Calc.\n\n**_PointsPlus_** value: **_3._**\n\nCook's Note\n\nIntensely flavored ingredients like fire-roasted tomatoes add fantastic taste to a dish with little effort. These tomatoes are cooked over an open flame, which concentrates their flavor and adds a touch of smokiness.\n\n# Baked Ziti with Summer Squash\n\nSERVES 5\n\n**2 cups (about 6 ounces) whole wheat ziti or penne**\n\n**2 teaspoons olive oil**\n\n**1 yellow summer squash, thinly sliced**\n\n**1 small zucchini, thinly sliced**\n\n**2 garlic cloves, minced**\n\n**2 cups fat-free marinara sauce**\n\n**2 cups fat-free ricotta cheese**\n\n**1 cup shredded fat-free mozzarella cheese**\n\n1. Cook ziti according to package directions, omitting salt if desired; drain.\n\n2. Preheat oven to 375\u00b0F. Spray 8-inch square baking dish with nonstick spray.\n\n3. Heat oil in large nonstick skillet over medium heat. Add squash, zucchini, and garlic; cook, stirring, until softened, about 6 minutes. Stir in cooked ziti and marinara sauce.\n\n4. Transfer mixture to prepared baking dish and top evenly with ricotta and mozzarella. Bake until heated through and bubbling, about 20 minutes.\n\n**PER SERVING** (generous 1\u00bd cups): 370 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 13 mg Chol, 956 mg Sod, 55 g Total Carb, 5 g Fib, 26 g Prot, 409 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nTo add even more flavor to this dish with just a couple minutes effort, stir a handful of chopped fresh basil into the pasta before baking.\n\n# slow cookers save time\n\n# Bountiful Beef Stew\n\nSERVES 4\n\n**1 tablespoon olive oil**\n\n**1 pound lean boneless beef bottom round, trimmed and cut into 1-inch chunks**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**3 onions, thinly sliced**\n\n**1\u00bc pounds baby red potatoes, halved**\n\n**1\u00bd cups baby carrots**\n\n**1 (14\u00bd-ounce) can reduced-sodium beef broth**\n\n**2 teaspoons finely chopped fresh tarragon**\n\n**\u2153 cup water**\n\n**2 tablespoons all-purpose flour**\n\n1. Heat oil in large skillet over medium-high heat. Add beef and sprinkle with salt and pepper. Cook, turning frequently, until browned, about 4 minutes. Transfer beef to 5- or 6-quart slow cooker.\n\n2. Add onions to skillet; cook, stirring occasionally, until softened and browned, about 8 minutes. Transfer onions to slow cooker and stir in potatoes, carrots, broth, and tarragon. Push potatoes down into liquid. Cover and cook until beef and vegetables are fork-tender, 4\u20136 hours on high or 8\u201310 hours on low.\n\n3. About 20 minutes before cooking time is up, whisk together water and flour in small bowl until smooth. Whisk in \u00bc cup of stew liquid until blended; stir flour mixture into stew. Cover and cook on high until mixture simmers and thickens, about 15 minutes longer.\n\n**PER SERVING** (1\u00be cups): 403 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 84 mg Chol, 454 mg Sod, 41 g Total Carb, 6 g Fib, 40 g Prot, 74 mg Calc.\n\n**_PointsPlus_** value: **_10._**\n\nBeef and Bean Soft Tacos\n\n# Beef and Bean Soft Tacos\n\nSERVES 6\n\n**1\u00bd cups reduced-sodium beef broth**\n\n**1 teaspoon chili powder**\n\n**1 (1-pound) lean flank steak, trimmed**\n\n**\u00be cup chunky tomato salsa plus additional for serving (optional)**\n\n**\u00bd cup rinsed and drained canned black beans**\n\n**\u00bc cup chopped fresh cilantro**\n\n**2 tablespoons canned chopped mild green chiles, drained**\n\n**12 (6-inch) flour tortillas, warmed**\n\n**\u00bc cup fat-free sour cream**\n\n1. Whisk together broth and chili powder in 5- or 6-quart slow cooker. Add steak. Cover and cook until steak is fork-tender, 4\u20135 hours on high or 8\u201310 hours on low.\n\n2. Transfer steak to cutting board; discard all but \u00bc cup of cooking liquid. Using two forks, finely shred beef. Return beef to slow cooker and stir in reserved cooking liquid, \u00be cup of salsa, beans, cilantro, and chiles. Cook on high until heated through, about 5 minutes.\n\n3. Top each tortilla evenly with beef mixture and sour cream. Fold tortillas in half and serve with additional salsa on side, if using.\n\n**PER SERVING** (2 tacos without salsa): 274 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 56 mg Chol, 373 mg Sod, 30 g Total Carb, 4 g Fib, 28 g Prot, 78 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nDo it Faster\n\nThis dish requires just a few minutes prep before going into the slow cooker, making it perfect for rushed mornings when you want to get something cooking for dinner before you leave for work.\n\n# Beef Stew Proven\u00e7al\n\nSERVES 6\n\n**1 pound lean boneless beef bottom round, trimmed and cut into 1-inch chunks**\n\n**4 leeks, cleaned and sliced, white and light green parts only**\n\n**1 fennel bulb, diced (fronds reserved)**\n\n**6 garlic cloves, minced**\n\n**1 (28-ounce) can diced tomatoes**\n\n**1 cup dry red wine**\n\n**2 teaspoons herbes de Provence or Italian seasoning**\n\n**\u00be teaspoon salt**\n\n**2 teaspoons olive oil**\n\n**1\u00bd pounds white mushrooms, halved**\n\n**\u00bd cup pitted black olives**\n\n**Grated zest of \u00bd orange**\n\n1. Stir together beef, leeks, diced fennel bulb, garlic, tomatoes, wine, herbes de Provence, and salt in 5- or 6-quart slow cooker. Cover and cook until beef is fork-tender, 4\u20135 hours on high or 8\u201310 hours on low.\n\n2. About 20 minutes before cooking time is up, heat oil in large skillet over medium-high heat. Add mushrooms and cook, stirring, until browned and liquid is evaporated, about 5 minutes.\n\n3. Stir mushrooms and olives into slow cooker. Cover and cook on high until mushrooms are very tender, about 10 minutes longer.\n\n4. Meanwhile, chop enough of reserved fennel fronds to equal 3 tablespoons. Combine fennel fronds and orange zest in small bowl.\n\n5. Ladle stew evenly into 6 serving bowls; sprinkle evenly with fennel frond mixture.\n\n**PER SERVING** (1\u00bd cups): 262 Cal, 7 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 56 mg Chol, 642 mg Sod, 23 g Total Carb, 5 g Fib, 29 g Prot, 127 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\n# Beef, Beet, and Cabbage Soup\n\nSERVES 8\n\n**2 teaspoons olive oil**\n\n**1 pound lean boneless beef bottom round, trimmed and cut into \u00be-inch pieces**\n\n**2 onions, thinly sliced**\n\n**8 cups reduced-sodium beef broth**\n\n**4 beets, trimmed, peeled, and diced**\n\n**3 carrots, sliced**\n\n**1 cup thinly sliced green cabbage**\n\n**1 (14\u00bd-ounce) can petite diced tomatoes**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 bay leaf**\n\n1. Heat oil in large skillet over medium-high heat Add beef, in batches, and cook, stirring, until browned, about 8 minutes. Transfer beef to 5- or 6-quart slow cooker.\n\n2. Add onions to skillet and cook, stirring, until softened, about 5 minutes. Add onions to slow cooker. Add broth, beets, carrots, cabbage, tomatoes, salt, pepper, and bay leaf to slow cooker; stir to combine. Cover and cook until beef and vegetables are fork-tender, 4\u20136 hours on high or 8\u201310 hours on low.\n\n3. Remove and discard bay leaf. Ladle soup evenly into 8 bowls.\n\n**PER SERVING** (about 1\u2153 cups): 197 Cal, 9 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 29 mg Chol, 474 mg Sod, 14 g Total Carb, 3 g Fib, 16 g Prot, 53 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nTo complete the meal, serve the soup with a 1\u00bd-ounce light roll, and finish with fresh strawberries for dessert (a 1\u00bd-ounce light roll per serving will increase the **_PointsPlus_** value by **_2_** ).\n\n# Low-and-Slow Sloppy Joes\n\nSERVES 6\n\n**1 pound ground lean beef (7% fat or less)**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**1 small onion, chopped**\n\n**1 celery stalk, chopped**\n\n**3 tablespoons packed dark brown sugar**\n\n**2 teaspoons Worcestershire sauce**\n\n**1\u00bd teaspoons ground cumin**\n\n**1 teaspoon chili powder**\n\n**\u00bd teaspoon salt**\n\n**6 whole wheat sandwich rolls, split**\n\n1. Spray large skillet with nonstick spray and set over medium-high heat. Add beef and cook, breaking it apart with wooden spoon, until browned, about 5 minutes.\n\n2. Transfer beef to 5- or 6-quart slow cooker. Stir in tomatoes, onion, celery, brown sugar, Worcestershire sauce, cumin, chili powder, and salt. Cover and cook until sauce is slightly thickened, 3\u20134 hours on high or 6\u20138 hours on low.\n\n3. Spoon \u00bd cup of beef mixture into each roll.\n\n**PER SERVING** (1 sandwich): 239 Cal, 6 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 43 mg Chol, 526 mg Sod, 26 g Total Carb, 4 g Fib, 20 g Prot, 83 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nTop the sandwiches with thinly sliced cabbage, and serve kosher dill pickles on the side.\n\n# Lamb and Vegetable Stew\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**3 red onions, thinly sliced**\n\n**1 (24-ounce) package frozen stew vegetables, thawed**\n\n**1 pound lean boneless leg of lamb, trimmed and cut into 1-inch chunks**\n\n**2 cups reduced-sodium vegetable broth**\n\n**\u00be teaspoon dried thyme**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n1. Heat oil in large nonstick skillet over medium heat. Add onions and cook, stirring, until softened, about 8 minutes.\n\n2. Transfer onions to 5- or 6-quart slow cooker and stir in stew vegetables, lamb, broth, thyme, salt, and pepper. Cover and cook until lamb and vegetables are fork-tender, 4\u20136 hours on high or 8\u201310 hours on low.\n\n**PER SERVING** (2 cups): 340 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 78 mg Chol, 534 mg Sod, 32 g Total Carb, 6 g Fib, 30 g Prot, 82 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nServe this saucy stew over creamy polenta (\u00bd cup of cooked polenta per serving will increase the **_PointsPlus_** value by **_3_** ).\n\n# Pork Marrakesh\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**4 (\u00bc-pound) boneless pork rib or loin chops, trimmed**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**3 small red onions, thinly sliced**\n\n**12 dried apricot halves, sliced**\n\n**\u00be cup unsweetened apple juice**\n\n**2 teaspoons minced peeled fresh ginger**\n\n**\u00bd teaspoon dried thyme**\n\n**1 (3-inch) cinnamon stick**\n\n**\u00bc cup chopped fresh cilantro**\n\n1. Heat 1 teaspoon of oil in large skillet over medium-high heat. Sprinkle pork chops with \u00bc teaspoon of salt and pepper. Add chops to skillet and cook until browned, about 2 minutes on each side. Transfer to plate.\n\n2. Reduce heat to medium and add remaining 1 teaspoon oil. Add onions and remaining \u00bd teaspoon salt and cook, stirring, until onions are golden, about 10 minutes.\n\n3. Place half of apricots and half of onions in bottom of 5- or 6-quart slow cooker. Top with pork chops and remaining onions and apricots. Add apple juice, ginger, thyme, and cinnamon stick. Cover and cook until pork is fork-tender, 3\u20134 hours on high or 6\u20138 hours on low. Remove cinnamon stick and serve pork sprinkled with cilantro.\n\n**PER SERVING** (1 pork chop and \u00bd cup onion mixture): 281 Cal, 11 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 73 mg Chol, 492 mg Sod, 18 g Total Carb, 2 g Fib, 27 g Prot, 32 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\nServe the chops with whole wheat couscous (\u00bd cup cooked whole wheat couscous per serving will increase the **_PointsPlus_** value by **_3_** ).\n\nPork Marrakesh\n\n# Chicken and Vegetable Curry\n\nSERVES 4\n\n**2 teaspoons olive oil**\n\n**2 large onions, thinly sliced**\n\n**1 teaspoon garam masala or curry powder**\n\n**1\u00bd cups reduced-sodium chicken broth**\n\n**1 pound skinless boneless chicken breasts, cut into 1-inch pieces**\n\n**3 small sweet potatoes, peeled, halved lengthwise, and cut into \u00bd-inch slices**\n\n**\u00bc teaspoon salt**\n\n**\u00bc\u2013\u00bd teaspoon cayenne pepper**\n\n**1 cup brown rice, preferably basmati**\n\n**1 (16-ounce) bag frozen broccoli, cauliflower, and carrots, thawed**\n\n1. Heat oil in large nonstick skillet over medium heat. Add onions and cook, stirring, until softened, about 6 minutes. Remove skillet from heat and stir in garam masala.\n\n2. Transfer onions to 5- or 6-quart slow cooker. Add broth, chicken, sweet potatoes, salt, and cayenne to slow cooker; stir to combine. Cover and cook until chicken and potatoes are fork-tender, 4\u20136 hours on high or 8\u201310 hours on low.\n\n3. Meanwhile, cook rice according to package directions, omitting salt if desired.\n\n4. About 20 minutes before cooking time is up, add thawed vegetables to slow cooker. Cover and cook on high until vegetables are crisp-tender, about 20 minutes longer.\n\n5. Divide rice among 4 bowls and top evenly with curry.\n\n**PER SERVING** (1\u00be cups curry and \u00bd cup rice): 353 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 55 mg Chol, 690 mg Sod, 47 g Total Carb, 9 g Fib, 27 g Prot, 80 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nFinish this Indian-inspired meal with fresh slices of mango tossed with fresh lime juice and grated lime zest.\n\n# Braised Chicken in Riesling\n\nSERVES 6\n\n**6 skinless chicken thighs, trimmed**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 tablespoon olive oil**\n\n**1\u00bd cups finely shredded green cabbage**\n\n**1 onion, thinly sliced**\n\n**1 cup baby carrots**\n\n**3 garlic cloves, peeled**\n\n**\u00be cup Riesling or other white wine**\n\n**\u00be cup reduced-sodium chicken broth**\n\n**2 tablespoons tomato paste**\n\n**\u2153 cup water**\n\n**2 tablespoons all-purpose flour**\n\n1. Sprinkle chicken with salt and pepper.\n\n2. Heat oil in large skillet over medium-high heat. Add chicken and cook, turning, until browned, about 8 minutes. Transfer chicken to 5- or 6-quart slow cooker.\n\n3. Add cabbage and onion to skillet. Reduce heat to medium and cook, stirring, until onion is softened, about 5 minutes. Transfer to slow cooker and top with carrots and garlic.\n\n4. Whisk together wine, broth, and tomato paste in bowl, then pour over chicken. Cover and cook until chicken and carrots are fork-tender, 4\u20136 hours on high or 8\u201310 hours on low. Using slotted spoon, transfer chicken to deep platter. Keep warm.\n\n5. Whisk together water and flour in small bowl until smooth. Whisk in about \u00bc cup of hot stew liquid until blended, then stir flour mixture into slow cooker. Cover and cook on high until mixture simmers and thickens, about 15 minutes. Spoon sauce over chicken.\n\n**PER SERVING** (1 chicken thigh and \u00bd cup vegetables with sauce): 177 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 43 mg Chol, 367 mg Sod, 9 g Total Carb, 2 g Fib, 16 g Prot, 44 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nIf you prefer not to use wine for this recipe, you can substitute an equal amount of reduced-sodium chicken broth.\n\nEasy Chicken Gumbo\n\n# Easy Chicken Gumbo\n\nSERVES 4\n\n**1 tablespoon olive oil**\n\n**2 onions, thinly sliced**\n\n**4 skinless boneless chicken thighs, trimmed and cut into \u00bd-inch slices**\n\n**3 cups thawed frozen or fresh okra**\n\n**1 (14\u00bd-ounce) can petite diced tomatoes**\n\n**5 celery stalks with leaves, sliced**\n\n**3 garlic cloves, peeled**\n\n**1\u00bd cups reduced-sodium chicken broth**\n\n**1 teaspoon dried thyme**\n\n**\u00bc\u2013\u00bd teaspoon cayenne pepper**\n\n**2 teaspoons gumbo fil\u00e9 powder**\n\n**2 cups hot cooked brown or white rice**\n\n1. Heat oil in large skillet over medium-high heat. Add onions and cook, stirring, until softened, about 6 minutes.\n\n2. Transfer onions to 5- or 6-quart slow cooker and stir in chicken, okra, tomatoes, celery, and garlic.\n\n3. Whisk together broth, thyme, and cayenne in large glass measure and add to slow cooker. Cover and cook until chicken is fork-tender, 4\u20136 hours on high or 8\u201310 hours on low. Discard garlic. Turn off slow cooker and stir in fil\u00e9 powder. Cover and let stand 10 minutes.\n\n4. Divide rice evenly among 4 bowls and top evenly with gumbo.\n\n**PER SERVING** (1\u00bd cups): 343 Cal, 10 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 43 mg Chol, 749 mg Sod, 43 g Total Carb, 7 g Fib, 23 g Prot, 243 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\nCook's Note\n\nFil\u00e9 powder, used to thicken gumbo and other Creole dishes in New Orleans, is made from ground dried leaves of the sassafras tree. It is always stirred into dish after it is removed from the heat, otherwise it becomes stringy.\n\n# Chicken and Vegetable Tagine\n\nSERVES 6\n\n**3 zucchini, halved lengthwise and cut into \u00bd-inch slices**\n\n**1 (15\u00bd-ounce) can chickpeas, rinsed and drained**\n\n**1 (14\u00bd-ounce) can diced tomatoes**\n\n**1 cup reduced-sodium chicken broth**\n\n**2 garlic cloves, minced**\n\n**1 (3-inch) cinnamon stick**\n\n**2 teaspoons ground ginger**\n\n**\u00be teaspoon salt**\n\n**\u00bc teaspoon cayenne pepper**\n\n**6 skinless bone-in chicken thighs, trimmed**\n\n**1 (12-ounce) package whole wheat couscous**\n\n1. Combine zucchini, chickpeas, tomatoes, broth, garlic, cinnamon stick, ginger, salt, and cayenne in 5- or 6-quart slow cooker. Add chicken and press it down into liquid. Cover and cook until chicken is fork-tender, 4\u20136 hours on high or 8\u201310 hours on low.\n\n2. About 8 minutes before serving, cook couscous according to package directions, omitting fat and salt if desired.\n\n3. Divide couscous evenly among 6 plates and top evenly with chicken. Discard cinnamon stick. Using slotted spoon, spoon vegetable mixture evenly over chicken. Discard liquid.\n\n**PER SERVING** (\u00be cup couscous, 1 chicken thigh, and generous \u00be cup vegetables): 431 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 43 mg Chol, 309 mg Sod, 64 g Total Carb, 12 g Fib, 29 g Prot, 119 mg Calc.\n\n**_PointsPlus_** value: **_11._**\n\n# Garlicky Braised Turkey Breast\n\nSERVES 12\n\n**2 tablespoons unsalted butter, softened**\n\n**3 garlic cloves, minced**\n\n**2 teaspoons poultry seasoning**\n\n**1 teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**1 (6-pound) whole bone-in turkey breast**\n\n**2 onions, sliced**\n\n**\u00bc cup reduced-sodium chicken broth**\n\n**2 tablespoons cornstarch**\n\n1. Mash together butter, garlic, poultry seasoning, salt, and pepper in small bowl. With your fingertips, gently loosen skin from breast meat. Rub butter mixture all over meat under skin.\n\n2. Stir together onions, broth, and cornstarch in 5- or 6-quart slow cooker. Place turkey on top of onion mixture. Cover and cook until turkey is fork-tender, 4\u20135 hours on high or 8\u201310 hours on low.\n\n3. Transfer turkey to platter and carve breast into 36 slices. Serve with broth and onions. Remove turkey skin before eating.\n\n**PER SERVING** (3 slices turkey and \u00bc cup broth with onions): 215 Cal, 3 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 123 mg Chol, 281 mg Sod, 2 g Total Carb, 3 g Fib, 43 g Prot, 23 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nDo it Faster\n\nIf you want to save time on cooking during the week, this is a perfect recipe to make on the weekend. You can reheat the leftovers, or make salads and sandwiches using the leftover turkey.\n\n# Chuck Wagon-Style Turkey Chili\n\nSERVES 4\n\n**1 pound ground skinless turkey breast**\n\n**1 large onion, chopped**\n\n**1 large red bell pepper, diced**\n\n**1 large green bell pepper, diced**\n\n**2 carrots, diced**\n\n**3 garlic cloves, finely chopped**\n\n**1 (15\u00bd-ounce) can pinto beans, undrained**\n\n**\u00be cup hickory-flavored barbecue sauce**\n\n**\u2153 cup tomato paste**\n\n**\u2153 cup water**\n\n**2\u20133 tablespoons chili powder**\n\n**\u00bd teaspoon ground cumin**\n\n**\u00bd teaspoon dried oregano**\n\n**3 scallions, thinly sliced**\n\n1. Spray large skillet with nonstick spray and set over medium-high heat. Add turkey and cook, breaking it up with wooden spoon, until no longer pink, about 5 minutes.\n\n2. Transfer turkey and any juices to 5- or 6-quart slow cooker. Add all remaining ingredients except scallions and stir well. Cover and cook until vegetables are softened, 4\u20135 hours on high or 8\u201310 hours on low, stirring in little additional water if chili seems dry.\n\n3. Spoon chili evenly into 4 bowls and sprinkle with scallions.\n\n**PER SERVING** (1\u2154 cups): 386 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 75 mg Chol, 897 mg Sod, 57 g Total Carb, 13 g Fib, 37 g Prot, 132 mg Calc.\n\n**_PointsPlus_** value: **_9._**\n\n# Firecracker Turkey Chili\n\nSERVES 6\n\n**1 tablespoon olive oil**\n\n**1 pound hot Italian-style turkey sausage links, cut into \u00be-inch slices**\n\n**2 onions, coarsely chopped**\n\n**2 tablespoons chili powder**\n\n**1 tablespoon ground coriander**\n\n**3 (14\u00bd-ounce) cans diced tomatoes with green chiles**\n\n**2 (15\u00bd-ounce) cans red kidney beans, rinsed and drained**\n\n**Chopped fresh cilantro**\n\n1. Heat oil in large skillet over medium-high heat. Add sausage and cook, stirring, until browned, about 5 minutes. Transfer sausage to 5- or 6-quart slow cooker.\n\n2. Add onions to skillet and cook, stirring, until they begin to soften, about 5 minutes. Remove skillet from heat and stir in chili powder and coriander.\n\n3. Transfer onion mixture to slow cooker and stir in tomatoes and beans. Cover and cook 4\u20136 hours on high or 8\u201310 hours on low.\n\n4. Ladle chili evenly into 6 bowls and sprinkle with cilantro.\n\n**PER SERVING** (scant 2 cups): 198 Cal, 9 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 34 mg Chol, 844 mg Sod, 17 g Total Carb, 4 g Fib, 13 g Prot, 63 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nCook's Note\n\nThis chili is great for no-fuss entertaining or for when you want to have leftovers for effortless meals later in the week.\n\n# Caribbean Seafood Stew\n\nSERVES 6\n\n**1 onion, chopped**\n\n**3 large Yukon Gold potatoes, peeled and cut into 1-inch chunks**\n\n**3 garlic cloves, minced**\n\n**3 (14\u00bd-ounce) cans diced tomatoes with green chiles**\n\n**1 red bell pepper, coarsely chopped**\n\n**1 (8-ounce) bottle clam juice**\n\n**\u00bc teaspoon salt**\n\n**\u00bc\u2013\u00bd teaspoon cayenne pepper**\n\n**1 pound halibut or cod fillets, cut into 1-inch pieces**\n\n**\u00bd pound medium shrimp, peeled and deveined, tails left on, if desired**\n\n**2 dozen littleneck clams, scrubbed**\n\n**\u00bc cup shredded sweetened coconut, toasted**\n\n**Grated zest of 1 lime**\n\n1. Combine onion, potatoes, garlic, tomatoes, bell pepper, and clam juice in 5- or 6-quart slow cooker. Stir in salt and cayenne. Cover and cook until potatoes are fork-tender, 4\u20135 hours on high or 8\u201310 hours on low.\n\n2. Add halibut and shrimp to slow cooker. Cover and cook 10 minutes. Add clams. Cover and cook until halibut and shrimp are just opaque throughout and clams open. Discard any clams that do not open.\n\n3. Turn off slow cooker and let stew stand 5 minutes before serving. Ladle stew evenly into 6 soup bowls and sprinkle with coconut and lime zest.\n\n**PER SERVING** (about 2 cups): 313 Cal, 3 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 89 mg Chol, 636 mg Sod, 45 g Total Carb, 6 g Fib, 28 g Prot, 125 mg Calc.\n\n**_PointsPlus_** value: **_8._**\n\nCook's Note\n\nAny firm white fish fillets will work well in this stew. Tilapia and catfish are widely available and inexpensive options.\n\nCaribbean Seafood Stew\n\n# Vegetarian Burritos with Salsa Verde\n\nSERVES 8\n\n**1 (14\u00bd-ounce) can fire-roasted diced tomatoes**\n\n**2 (15\u00bd-ounce) cans black beans, rinsed and drained**\n\n**1 (8\u00be-ounce) can corn kernels, drained**\n\n**3 tablespoons taco seasoning or Mexican seasoning**\n\n**2 cups lightly packed sliced Swiss chard**\n\n**8 (7-inch) whole wheat tortillas, warmed**\n\n**1 cup reduced-fat pepper Jack cheese**\n\n**\u00bd cup fat-free sour cream**\n\n**\u00bd cup salsa verde**\n\n1. Drain tomatoes and reserve all but \u00bd cup of liquid. Put tomatoes and reserved liquid in 5- or 6-quart slow cooker. Add beans, corn, and taco seasoning. Cover and cook until flavors are blended, 3\u20134 hours on high or 6\u20138 hours on low.\n\n2. About 20 minutes before cooking time is up, stir in Swiss chard. Coarsely mash bean mixture with potato masher or wooden spoon.\n\n3. Spoon \u00bd cup of bean mixture onto each tortilla. Top evenly with pepper Jack, sour cream, and salsa verde. Roll up tortillas to enclose filling.\n\n**PER SERVING** (1 burrito): 271 Cal, 5 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 11 mg Chol, 948 mg Sod, 45 g Total Carb, 12 g Fib, 14 g Prot, 210 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Shrimp Chowder with Dill\n\nSERVES 6\n\n**1 pound medium shrimp, peeled and deveined, shells reserved**\n\n**2 teaspoons canola oil**\n\n**1 large onion, chopped**\n\n**1 tablespoon all-purpose flour**\n\n**1 (14\u00bd-ounce) can no-salt-added diced tomatoes**\n\n**4 small Yukon Gold potatoes, peeled and diced**\n\n**2 celery stalks with leaves, chopped**\n\n**4 cups reduced-sodium chicken broth**\n\n**4 cups water**\n\n**\u00bc teaspoon black pepper**\n\n**\u00bd cup fat-free half-and-half**\n\n**3 slices turkey bacon, crisp-cooked and crumbled**\n\n**2 tablespoons chopped fresh dill**\n\n1. Put shrimp shells on square of cheesecloth. Gather ends of cloth and tie them together with length of kitchen twine. Refrigerate shrimp and set shells aside.\n\n2. Heat oil in large nonstick skillet over medium heat. Add onion and cook, stirring occasionally, until softened, about 6 minutes. Sprinkle flour over onion and cook, stirring constantly, 2 minutes longer.\n\n3. Transfer onion to 5- or 6-quart slow cooker. Add package of shrimp shells, tomatoes, potatoes, celery, broth, water, and pepper. Cover and cook until vegetables are fork-tender, 4\u20135 hours on high or 8\u201310 hours on low.\n\n4. About 20 minutes before cooking time is up, remove and discard shrimp shell package and stir in shrimp. Cover and cook on high until shrimp are just opaque in center, about 15 minutes. Stir in half-and-half and cook 5 minutes longer.\n\n5. Ladle chowder evenly into 6 bowls; sprinkle evenly with turkey bacon and dill.\n\n**PER SERVING** (about 2 cups): 217 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 85 mg Chol, 928 mg Sod, 27 g Total Carb, 3 g Fib, 16 g Prot, 106 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nVegetable Minestrone with Pasta\n\n# Vegetable Minestrone with Pasta\n\nSERVES 6\n\n**1 (15\u00bd-ounce) can chickpeas, rinsed and drained**\n\n**1 (14\u00bd-ounce) can petite diced tomatoes**\n\n**2 carrots, diced**\n\n**2 onions, diced**\n\n**2 small zucchini, halved lengthwise and sliced**\n\n**1 small yellow squash, halved lengthwise and sliced**\n\n**2 celery stalks with leaves, sliced**\n\n**\u00bd pound green beans, trimmed and cut into 1-inch pieces**\n\n**2 garlic cloves, minced**\n\n**\u00bd teaspoon salt**\n\n**\u00bc teaspoon black pepper**\n\n**7 cups water**\n\n**1\u00bd cups whole wheat rigatoni or other short pasta**\n\n**\u00bc cup chopped fresh basil or parsley**\n\n1. Combine all ingredients except rigatoni and basil in 5- or 6-quart slow cooker. Cover and cook until vegetables are fork-tender, 4\u20135 hours on high or 8\u201310 hours on low.\n\n2. About 30 minutes before cooking time is up, cook rigatoni according to package directions, omitting salt if desired. Stir pasta and basil into soup.\n\n**PER SERVING** (about 2 cups): 247 Cal, 2 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 408 mg Sod, 50 g Total Carb, 9 g Fib, 12 g Prot, 111 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nCarry out the Italian theme with a fresh green salad to serve with the soup. Toss together romaine lettuce, halved cherry tomatoes, thinly sliced zucchini, red-wine vinegar, and dried oregano, salt, and pepper to taste. Top each salad with 1 tablespoon shredded fat-free mozzarella cheese.\n\n# Onion Soup with Herbed Cheese Toasts\n\nSERVES 6\n\n**1 tablespoon olive oil**\n\n**6 large onions (about 3 pounds), sliced**\n\n**\u00bd teaspoon salt**\n\n**1 tablespoon all-purpose flour**\n\n**8 cups reduced-sodium beef broth**\n\n**\u00bd teaspoon black pepper**\n\n**\u00bd cup light cream cheese (Neufch\u00e2tel)**\n\n**6 (\u00bd-inch) slices French or Italian whole wheat bread, toasted**\n\n**1 teaspoon chopped fresh thyme**\n\n1. Heat oil in large Dutch oven over medium heat. Add onions and salt and cook, stirring occasionally, until deep golden brown and very soft, about 35 minutes. Sprinkle flour over onions and cook, stirring constantly, until flour is lightly browned, about 2 minutes longer.\n\n2. Combine onions, broth, and \u00bc teaspoon of pepper in 5- or 6-quart slow cooker. Cover and cook until flavors are blended, 4\u20135 hours on high or 8\u201310 hours on low.\n\n3. Spread cream cheese evenly over slices of toast. Sprinkle evenly with thyme and remaining \u00bc teaspoon pepper.\n\n4. Ladle soup evenly into 6 bowls and float slice of toast in each bowl.\n\n**PER SERVING** (1\u2154 cups soup and 1 cheese toast): 258 Cal, 10 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 15 mg Chol, 652 mg Sod, 31 g Total Carb, 5 g Fib, 14 g Prot, 94 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\n# something sweet\n\n# Carrot-Apple Cupcakes with Cream Cheese Frosting\n\nSERVES 12\n\n**1\u00bc cups all-purpose flour**\n\n**\u2154 cup granulated sugar**\n\n**2 carrots, shredded**\n\n**1 apple, peeled, cored, and shredded**\n\n**\u2153 cup golden raisins**\n\n**\u00bc cup sweetened flaked coconut**\n\n**1 teaspoon grated orange zest**\n\n**1 teaspoon cinnamon**\n\n**1 teaspoon baking soda**\n\n**\u00bc teaspoon salt**\n\n**2 large eggs, lightly beaten**\n\n**\u00bc cup canola oil**\n\n**6 ounces fat-free cream cheese, at room temperature**\n\n**\u00bc cup confectioners' sugar, sifted**\n\n**1 tablespoon milk**\n\n**1 teaspoon vanilla extract**\n\n1. Preheat oven to 350\u00b0F. Spray 12-cup muffin pan with nonstick spray.\n\n2. Stir together flour, granulated sugar, carrots, apple, raisins, coconut, orange zest, cinnamon, baking soda, and salt in large bowl. Beat eggs and oil together in another bowl. Stir egg mixture into flour mixture just until combined. Spoon batter evenly into muffin cups and bake until toothpick inserted into center of each cupcake comes out clean, 20\u201325 minutes. Cool in pan on rack 5 minutes; remove cupcakes from pan and cool completely on rack.\n\n3. To make frosting, combine cream cheese, confectioners' sugar, milk, and vanilla in bowl of electric mixer and beat just until creamy. Spread frosting over cooled cupcakes.\n\n**PER SERVING** (1 frosted cupcake): 202 Cal, 6 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 38 mg Chol, 262 mg Sod, 32 g Total Carb, 1 g Fib, 5 g Prot, 81 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nSpice-Glazed Cherry Bundt Cake\n\n# Spice-Glazed Cherry Bundt Cake\n\nSERVES 20\n\n**3 cups all-purpose flour**\n\n**1\u00be cups granulated sugar**\n\n**4 teaspoons baking powder**\n\n**\u00bd teaspoon ground nutmeg**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon cinnamon**\n\n**1 cup plus 4\u00bd teaspoons fat-free milk**\n\n**1 cup dried cherries**\n\n**6 tablespoons canola oil**\n\n**4 large egg whites, lightly beaten**\n\n**1 tablespoon grated orange zest**\n\n**\u00bd teaspoon almond extract**\n\n**1 cup confectioners' sugar**\n\n1. Arrange oven rack in middle of oven; preheat oven to 350\u00b0F. Spray 10-inch Bundt pan with nonstick spray.\n\n2. Whisk together flour, granulated sugar, baking powder, nutmeg, salt, and \u00bc teaspoon of cinnamon in large bowl. Stir together 1 cup of milk, cherries, oil, egg whites, zest, and almond extract in separate bowl. Add milk mixture to flour mixture and stir until well combined. Pour batter into prepared pan.\n\n3. Bake until toothpick inserted into center of cake comes out clean, 40\u201345 minutes. Cool in pan on rack 15 minutes. Remove cake from pan and let cool completely on rack.\n\n4. To make glaze, stir together confectioners' sugar and remaining \u00bc teaspoon cinnamon in bowl. Slowly stir in remaining 4\u00bd teaspoons milk until thick glaze forms. Drizzle glaze over top of cooled cake. Let cake stand until glaze sets, about 20 minutes; cut into 20 slices.\n\n**PER SERVING** (1 slice): 226 Cal, 4 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 174 mg Sod, 44 g Total Carb, 1 g Fib, 3 g Prot, 80 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nBundt pans make it easy to make an attractive dessert because of the pretty pattern they create in a cake. However, the crevices in the pan that make the decorative look sometimes result in the cake sticking to the pan. Be sure to thoroughly spray a Bundt pan with nonstick spray, taking care to coat the entire pan.\n\n# life's too short to make...\n\nThough you may think homemade is always best, many foods are not worth your precious time to prepare. These store-bought versions will save you hours of time and taste just as good.\n\n**BEEF, CHICKEN, AND VEGETABLE BROTHS.** Good-quality prepared broths are available everywhere and easy to keep on your pantry shelf in cans or resealable cartons. Besides, so many recipes use broths, you could never make enough!\n\n**DRIED BEANS.** Cooking your own beans is a big time commitment and since canned varieties are delicious, inexpensive, and recipe-ready, why bother?\n\n**GRAHAM CRACKERS.** This crunchy, low-fat, lightly sweetened snack is tough to replicate. Leave it to the manufacturers.\n\n**GREEK YOGURT.** Even the fat-free version of this strained yogurt tastes rich and thick. It's a healthy staple for adding tangy flavor to meals and snacks, but leave the straining to someone else.\n\n**HOMEMADE PASTA.** Unless you're an Italian \"nonna\" with time on your hands, fresh or dried pasta from the supermarket is almost as good.\n\n**ICE CREAM AND FROZEN YOGURT.** These might be nostalgic and fun to make for a summer get-together (see Raspberry-Orange Sorbet, here and Frozen Strawberry-Maple Yogurt, here), but the rest of the year, pick them up on your cruise through the frozen foods aisle.\n\n**KETCHUP, MUSTARD, AND MAYONNAISE.** Foodies may extol the delights of homemade recipes, but leave it to food company chefs to create new-fangled versions of your favorite sandwich spreads.\n\n**MARSHMALLOWS.** No need to spend hours whipping up this delicate confection; your supermarket baking aisle will accommodate all your needs.\n\n**PEELED AND DEVEINED SHRIMP.** Buy shrimp that's ready to use in your favorite pasta or soup recipe and save yourself the time and tedium of peeling and deveining. It's definitely worth the extra price per pound for someone else to do this kitchen chore.\n\n**PHYLLO DOUGH.** Making this flaky pastry from translucent sheets of dough will take many more hours than it's worth. Instead, use good-quality frozen phyllo for all your recipes.\n\n**PRESERVES, JELLY, AND MARMALADE.** Even if you grew up canning your own with grandma, with your busy life, you don't have time. Stock up on jars of fruity, low-sugar options.\n\n**PUMPKIN PUREE.** There's no discernible difference in flavor or quality of canned pumpkin puree and the homemade version. Save yourself hours of prep and use convenient, silky-textured cooked canned pumpkin.\n\n**ROASTED RED PEPPERS.** No time to roast your own? Not to worry! The jarred varieties are just as good as homemade and they add fabulous flavor to salads, soups, pasta dishes, meat loaf, and stews. Just make sure to buy varieties that are not packed in oil.\n\n**SUSHI.** Don't try this messy, time-consuming dish at home. Get your sushi fix at a restaurant or a fish counter.\n\n**WHOLE-GRAIN BREAD.** Kneading your own loaves may make you feel self-sufficient, but bread making can take up an entire afternoon. Local bakery and supermarket versions are almost as delicious and much more convenient.\n\n# Pumpkin Pie Muffins\n\nSERVES 12\n\n**1 cup all-purpose flour**\n\n**\u00be cup whole wheat pastry flour**\n\n**1\u00bc cups Sucanat or granulated sugar**\n\n**1\u00bc teaspoons baking soda**\n\n**1 teaspoon cinnamon**\n\n**\u00bd teaspoon salt**\n\n**\u00bd teaspoon ground nutmeg**\n\n**\u00bd teaspoon ground cloves**\n\n**\u00bd cup raisins**\n\n**2 large eggs, lightly beaten**\n\n**1 cup canned pumpkin puree**\n\n**\u2153 cup canola oil**\n\n**\u2153 cup water**\n\n**2 tablespoons raw pumpkin seeds**\n\n1. Preheat oven to 350\u00b0F. Spray 12-cup muffin pan with nonstick spray.\n\n2. Whisk together all-purpose flour, pastry flour, Sucanat, baking soda, cinnamon, salt, nutmeg, and cloves in large bowl; stir in raisins. Beat eggs, pumpkin puree, oil, and water together in another bowl. Add pumpkin mixture to flour mixture and stir just until blended.\n\n3. Spoon batter into muffin cups, filling each about two-thirds full. Sprinkle with pumpkin seeds. Bake until toothpick inserted into muffin comes out clean, about 20 minutes. Cool in pan on rack for 10 minutes; remove muffins from pan and serve warm or cool completely on rack.\n\n**PER SERVING** (1 muffin): 235 Cal, 8 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 35 mg Chol, 241 mg Sod, 40 g Total Carb, 2 g Fib, 4 g Prot, 20 mg Calc.\n\n**_PointsPlus_** value: **_7._**\n\nCook's Note\n\n_Sucanat_ is short for \"sugar cane natural.\" It's made from evaporated sugar cane juice, giving it a light brown color and a natural molasses flavor.\n\nApricot and Toasted Almond Galette\n\n# Apricot and Toasted Almond Galette\n\nSERVES 8\n\n**1\u2153 cups all-purpose flour**\n\n**\u00bd cup, plus 2 tablespoons sugar**\n\n**1 tablespoon baking powder**\n\n**Pinch salt**\n\n**\u2153 cup part-skim ricotta cheese**\n\n**2 tablespoons cold unsalted butter, cut into pieces**\n\n**2 large egg whites**\n\n**2 teaspoons water**\n\n**2 pounds ripe apricots, halved, pitted, and cut into \u00bd-inch wedges**\n\n**2 tablespoons slivered almonds**\n\n1. To make dough, combine flour, \u00bd cup of sugar, baking powder, and salt in food processor and pulse to mix. Add ricotta, butter, 1 egg white, and water to food processor; pulse just until dough begins to come together. Shape dough into disk and wrap in plastic wrap; refrigerate at least 1 hour or up to overnight.\n\n2. Preheat oven to 350\u00b0F. Lightly spray large baking sheet with nonstick spray.\n\n3. Roll out dough between 2 sheets of wax paper to form 10-inch round. Place dough on prepared baking sheet. Fold edge of dough over to form \u00bd-inch rim. Bake for 10 minutes, then let cool on rack, about 5 minutes.\n\n4. Lightly beat remaining egg white and brush it over crust. Arrange apricots on crust in concentric circles and sprinkle with remaining 2 tablespoons sugar and almonds. Bake until crust is golden and apricots are softened, about 10 minutes. Let cool slightly on rack.\n\n5. Cut into 8 wedges. Serve warm or at room temperature.\n\n**PER SERVING** (1 wedge): 241 Cal, 5 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 11 mg Chol, 246 mg Sod, 45 g Total Carb, 2 g Fib, 5 g Prot, 145 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Peach-Blueberry Crostatas\n\nSERVES 8\n\n**\u00bd cup whole wheat pastry flour**\n\n**\u00bd cup all-purpose flour**\n\n**\u00bd teaspoon salt**\n\n**2 tablespoons cold unsalted butter, cut into pieces**\n\n**2 tablespoons canola oil**\n\n**2\u20134 tablespoons ice water**\n\n**2 ripe peaches, peeled, halved, pitted, and cut into \u00bd-inch wedges**\n\n**1 cup fresh blueberries**\n\n**3 tablespoons granulated sugar**\n\n**\u00bd teaspoon fresh lemon juice**\n\n**1 tablespoon fat-free milk**\n\n**2 teaspoons turbinado or granulated sugar**\n\n1. Whisk together whole wheat flour, all-purpose flour, and salt in medium bowl. Using pastry blender or two knives used scissor-fashion, cut in butter and oil until mixture resembles coarse crumbs. Gradually add water to flour mixture, tossing lightly until pastry is just moist enough to hold together. Shape dough into 4 equal-size disks. Wrap each disk in plastic wrap and refrigerate until chilled, at least 30 minutes or up to overnight.\n\n2. Preheat oven to 425\u00b0F. Line large baking sheet with foil; spray with nonstick spray.\n\n3. Toss together peaches, blueberries, granulated sugar, and lemon juice in medium bowl.\n\n4. Using floured rolling pin, roll out each disk of dough on sheet of floured wax paper to form 6-inch round. Flip dough onto baking sheet and peel away wax paper. (If dough tears, patch it together with your fingers.) Mound one-quarter of fruit filling on each round, leaving 1-inch border. Fold rim of dough over filling, pleating it as you go around. Brush crusts with milk and sprinkle evenly with turbinado sugar. Bake until peaches are tender and crust is browned, about 25 minutes. Let cool slightly on rack.\n\n5. Cut each crostata in half and serve warm or at room temperature.\n\n**PER SERVING** (\u00bd crostata): 158 Cal, 7 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 8 mg Chol, 150 mg Sod, 27 g Total Carb, 2 g Fib, 2 g Prot, 12 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nPeach-Blueberry Crostatas\n\n# Banana-Walnut Bread\n\nSERVES 18\n\n**\u00be cup sugar**\n\n**5 tablespoons unsalted butter, softened**\n\n**2 large eggs**\n\n**3 ripe bananas, mashed**\n\n**\u00bd cup fat-free milk**\n\n**1\u00bd teaspoons vanilla extract**\n\n**1\u00be cups all-purpose flour**\n\n**1 tablespoon baking powder**\n\n**\u00be teaspoon salt**\n\n**\u00bd cup walnuts, coarsely chopped**\n\n1. Arrange oven rack in middle of oven; preheat oven to 350\u00b0F. Spray 5 \u00d7 9-inch loaf pan with nonstick spray.\n\n2. Combine sugar and butter in medium bowl; beat with an electric mixer on medium speed until light and fluffy, about 3 minutes. Beat in eggs, beating well after each addition. Beat in bananas, milk, and vanilla. In separate bowl, whisk together flour, baking powder, and salt. Add flour mixture to banana mixture and mix on low speed until just combined. Stir in walnuts.\n\n3. Pour batter into pan and bake until toothpick inserted into center of loaf comes out clean, 50\u201355 minutes. Cool in pan 10 minutes. Remove bread from pan and cool completely on rack. Cut into 18 slices.\n\n**PER SERVING** (1 slice): 153 Cal, 6 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 29 mg Chol, 190 mg Sod, 23 g Total Carb, 1 g Fib, 3 g Prot, 63 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nBanana bread is always a welcome gift and it freezes beautifully. When you have extra bananas on hand, make a loaf and freeze it for up to 3 months to have on hand when you need to give a special handmade gift, but have no time.\n\n# Brown Rice-Banana Pudding\n\nSERVES 2\n\n**1 cup cooked brown rice**\n\n**1 cup fat-free milk**\n\n**Pinch salt**\n\n**1 ripe banana, mashed**\n\n**1 teaspoon vanilla extract**\n\n**\u00bd teaspoon cinnamon**\n\n1. Combine rice, milk, and salt in medium saucepan and bring to boil over medium-high heat. Reduce heat and simmer, stirring occasionally, until slightly thickened, about 15 minutes. Transfer rice mixture to medium bowl and let cool.\n\n2. Stir in banana, vanilla, and cinnamon. Spoon pudding evenly into 2 dessert dishes.\n\n**PER SERVING** (\u2154 cup pudding): 212 Cal, 2 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 2 mg Chol, 138 mg Sod, 44 g Total Carb, 4 g Fib, 8 g Prot, 164 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nLemon Souffl\u00e9s\n\n# Lemon Souffl\u00e9s\n\nSERVES 4\n\n**2 teaspoons plus \u2153 cup granulated sugar**\n\n**\u2153 cup fat-free milk**\n\n**2 large eggs, separated**\n\n**1\u00bd tablespoons all-purpose flour**\n\n**3 tablespoons fresh lemon juice**\n\n**2 teaspoons grated lemon zest**\n\n**1 large egg white**\n\n**\u215b teaspoon salt**\n\n**2 teaspoons confectioners' sugar**\n\n1. Preheat oven to 400\u00b0F. Spray 4 (6-ounce) ramekins or custard cups with nonstick spray and coat them with 2 teaspoons granulated sugar.\n\n2. Combine milk, egg yolks, flour, lemon juice, and remaining \u2153 cup granulated sugar in small saucepan over medium-low heat. Cook, whisking constantly, until mixture becomes thick and creamy, 6\u20137 minutes; do not allow mixture to boil or yolks will scramble. Immediately transfer to bowl and stir in zest; let cool to room temperature.\n\n3. Beat 3 egg whites with salt in bowl with an electric mixer on medium speed for 20 seconds. Increase speed to high and beat just until soft peaks form, 1\u20132 minutes. Stir one-fourth of egg whites into cooled yolk mixture to lighten. Gently fold in remaining whites in two additions until just mixed.\n\n4. Spoon mixture into ramekins; use paper towel to wipe off edge of each. Place on small baking sheet and bake until souffl\u00e9s have risen above rims of ramekins and edges are set (the centers will still be slightly loose), about 12 minutes. Sprinkle top of each with confectioners' sugar and serve at once.\n\n**PER SERVING** (1 souffl\u00e9): 140 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 106 mg Chol, 127 mg Sod, 24 g Total Carb, 0 g Fib, 5 g Prot, 42 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nWhile it's true that souffl\u00e9s need to be eaten immediately out of the oven, you can make the batter partially ahead. Prepare the recipe through step 2, cover the cooled mixture with plastic wrap, and refrigerate for up to 24 hours. Return the mixture to room temperature before folding in the egg whites. Bake as directed.\n\n# Pumpkin-Cranberry Bread Puddings\n\nSERVES 12\n\n**3 cups fat-free half-and-half**\n\n**1 cup fat-free egg substitute**\n\n**\u00bd cup packed dark brown sugar**\n\n**\u00bc teaspoon ground allspice**\n\n**1 teaspoon cinnamon**\n\n**\u00bc teaspoon ground nutmeg**\n\n**\u00bc teaspoon salt**\n\n**1 cup canned pumpkin puree**\n\n**2 teaspoons vanilla extract**\n\n**1 (1-pound) loaf day-old whole wheat bread, cut into 1\u00bd-inch pieces**\n\n**\u00bd cup dried cranberries**\n\n**\u00bd cup chopped pecans**\n\n1. Bring half-and-half to boil in medium saucepan over medium-high heat; remove saucepan from heat.\n\n2. Whisk together egg substitute, brown sugar, allspice, cinnamon, nutmeg, and salt in medium bowl. Slowly add \u00bd cup of hot half-and-half to brown sugar mixture, whisking constantly.\n\n3. Add egg substitute mixture to saucepan and set over medium-low heat. Cook, whisking constantly, until custard thickens and coats back of spoon, about 5 minutes. Immediately pour custard through sieve set over medium bowl. Whisk in pumpkin and vanilla. Add bread and cranberries to bowl, gently stirring until moistened. Let stand about 20 minutes.\n\n4. Meanwhile, preheat oven to 325\u00b0F. Spray 12 (6-ounce) ramekins or 10-cup baking dish or casserole with nonstick spray.\n\n5. Pour pudding mixture into prepared ramekins and sprinkle evenly with pecans. Place ramekins in roasting pan. Add enough boiling water to roasting pan to come halfway up sides of ramekins. Cover tightly with foil. Bake individual puddings 20 minutes and large pudding 1 hour. Uncover and bake until knife inserted into center comes out clean, 5\u201315 minutes longer. Serve warm or at room temperature.\n\n**PER SERVING** (1 pudding): 239 Cal, 5 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 3 mg Chol, 438 mg Sod, 41 g Total Carb, 2 g Fib, 8 g Prot, 143 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nPumpkin-Cranberry Bread Puddings\n\nOrange Flan with Macerated Oranges\n\n# Orange Flan with Macerated Oranges\n\nSERVES 12\n\n**1 cup plus 1 tablespoon sugar**\n\n**\u00bd cup water**\n\n**6 large eggs, lightly beaten**\n\n**1\u00bc cups fresh orange juice**\n\n**1 cup low-fat (1%) milk**\n\n**\u00be cup fat-free sweetened condensed milk**\n\n**2 teaspoons grated orange zest**\n\n**3 navel oranges**\n\n**2 tablespoons fresh lemon juice**\n\n1. Preheat oven to 350\u00b0F.\n\n2. Combine 1 cup of sugar and water in heavy-bottomed medium saucepan over medium-high heat; bring to boil and cook, shaking pan occasionally, until sugar turns into golden caramel, about 12 minutes. Immediately pour caramel into 9-inch deep-dish glass pie plate. Carefully tilt pan to coat bottom evenly with caramel; set aside until hardened, about 10 minutes.\n\n3. Whisk together eggs, orange juice, low-fat milk, sweetened condensed milk, and zest in bowl. Pour mixture into pie plate.\n\n4. Place pie plate in large roasting pan. Pour enough hot water into roasting pan to come halfway up side of pie plate. Bake until custard is set and jiggles just in center when shaken, 45\u201350 minutes. Remove pie plate from roasting pan and cool completely on rack. Cover with plastic wrap and refrigerate at least 3 hours or up to 2 days.\n\n5. Meanwhile, with sharp knife, peel oranges, removing all white pith. Working over bowl, cut between membranes to release segments. Stir in remaining 1 tablespoon sugar and lemon juice; cover and refrigerate.\n\n6. To serve, run tip of knife around edge of flan. Place large plate upside down over top of pie plate and quickly invert; lift off pie plate. Cut flan into 12 wedges; spoon caramel sauce that collects on plate over wedges and garnish with orange segments.\n\n**PER SERVING** (1 wedge and 2 tablespoons orange segments): 202 Cal, 3 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 107 mg Chol, 60 mg Sod, 39 g Total Carb, 1 g Fib, 6 g Prot, 113 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\n# Triple Berry Summer Pudding\n\nSERVES 6\n\n**2 pints blueberries**\n\n**\u2153 cup sugar**\n\n**2 tablespoons water**\n\n**Grated zest and juice of \u00bd lemon**\n\n**1 (6-ounce) container raspberries**\n\n**1 (6-ounce) container blackberries, halved if large**\n\n**10 slices firm-textured white bread, crusts removed**\n\n**1 cup thawed frozen fat-free whipped topping (optional)**\n\n1. Combine blueberries, sugar, water, and lemon zest and juice in large saucepan and set over medium heat. Cook, stirring, until berries begin to release their liquid, about 3 minutes. Bring to boil over medium-high heat. Cook, stirring occasionally, until slightly thickened, about 5 minutes. Remove saucepan from heat and stir in raspberries and blackberries.\n\n2. Line 2-quart bowl with 2 sheets of overlapping plastic wrap, allowing excess to extend over rim of bowl by 4 inches. Line bottom and side of bowl with bread, cutting to fit as needed. Spoon berry mixture into bowl. Cover with layer of bread. Fold plastic wrap over top of pudding. Place plate, slightly smaller than bowl, on top of pudding and weigh it down with two heavy cans of food. Refrigerate at least 8 hours or up to 2 days.\n\n3. Fold back plastic wrap and invert pudding onto serving plate. Lift off bowl and remove plastic wrap. Cut pudding into 6 wedges. Serve with whipped topping, if using.\n\n**PER SERVING** (1 wedge without whipped topping): 205 Cal, 2 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 229 mg Sod, 46 g Total Carb, 4 g Fib, 4 g Prot, 65 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\nCook's Note\n\nServe each portion of the pudding with a sprinkle of fresh berries and a sprig of mint if desired.\n\n# Frozen Strawberry-Maple Yogurt\n\nSERVES 8\n\n**1 (1-pound) container strawberries, hulled and chopped**\n\n**1 cup sugar**\n\n**2 tablespoons fresh lemon juice**\n\n**1 cup maple or vanilla low-fat yogurt**\n\n**1 cup fat-free half-and-half**\n\n**\u00bd teaspoon maple extract**\n\n1. Stir together strawberries, sugar, and lemon juice in medium bowl; let stand 30 minutes.\n\n2. Whisk together yogurt, half-and-half, and maple extract in large bowl. Stir in strawberry mixture. Cover and refrigerate until chilled, at least 2 hours or up to overnight.\n\n3. Pour strawberry mixture into an ice-cream maker and freeze according to manufacturer's instructions.\n\n4. Transfer yogurt to freezer container and freeze until firm, at least 2 hours or up to 6 hours.\n\n**PER SERVING** (\u00bd cup): 159 Cal, 1 g Total Fat, 1 g Sat Fat, 0 g Trans Fat, 3 mg Chol, 100 mg Sod, 37 g Total Carb, 1 g Fib, 3 g Prot, 91 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\n# Raspberry-Orange Sorbet\n\nSERVES 8\n\n**2 cups water**\n\n**\u00bd cup sugar**\n\n**2 (3-inch) strips orange zest, removed with vegetable peeler**\n\n**3 tablespoons fresh orange juice**\n\n**3\u00bd cups fresh or thawed frozen unsweetened raspberries**\n\n1. To make sugar syrup, combine water, sugar, and orange zest in medium saucepan and set over high heat. Bring to boil, stirring until sugar is dissolved. Reduce heat and simmer 5 minutes. Remove saucepan from heat and let cool about 5 minutes. Discard orange zest; stir in orange juice.\n\n2. Puree 1 cup of sugar syrup with raspberries in food processor or blender. Stir raspberry mixture into sugar syrup in saucepan. Pour raspberry mixture through sieve set over medium bowl, pressing on solids to extract as much liquid as possible. Discard solids. Cover berry mixture and refrigerate until chilled, at least 2 hours or up to overnight.\n\n3. Transfer raspberry mixture to an ice-cream maker and freeze according to manufacturer's instructions.\n\n4. Transfer sorbet to freezer container and freeze until firm, at least 2 hours or up to 6 hours.\n\n**PER SERVING** (about \u00bd cup): 90 Cal, 0 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 44 mg Sod, 22 g Total Carb, 1 g Fib, 43 g Prot, 17 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Warm Spice-Baked Apples\n\nSERVES 4\n\n**4 baking apples, cored and halved**\n\n**2 tablespoons packed brown sugar**\n\n**1 teaspoon pumpkin pie spice**\n\n**3 tablespoons water**\n\n**\u00bc cup chopped walnuts or pecans, toasted**\n\n1. Preheat oven to 400\u00b0F.\n\n2. Place apples, cut side up, in 9 \u00d7 13-inch baking dish. Sprinkle evenly with brown sugar and pumpkin pie spice.\n\n3. Sprinkle water in bottom of baking dish. Cover baking dish with foil. Bake apples until tender when pierced with tip of knife, about 25 minutes. Sprinkle apples evenly with walnuts.\n\n**PER SERVING** (2 apple halves): 144 Cal, 4 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 3 mg Sod, 30 g Total Carb, 5 g Fib, 2 g Prot, 38 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nIf you don't have an apple corer, cut each apple in half, then use a melon baller or a small paring knife to remove the core.\n\n# White Wine-Poached Pears\n\nSERVES 8\n\n**4 cups water**\n\n**1 cup dry white wine**\n\n**1 cup sugar**\n\n**Zest of 1 lemon, removed with vegetable peeler**\n\n**1 tablespoon fresh lemon juice**\n\n**4 large firm-ripe Bartlett or Bosc pears, peeled, halved, and cored**\n\n1. Combine all ingredients except pears in large saucepan and bring to boil over high heat; boil 10 minutes. Remove saucepan from heat.\n\n2. Add pears to saucepan. Reduce heat and gently simmer, covered, until pears are tender when pierced with fork, about 15 minutes. Using slotted spoon, carefully transfer pears to large shallow bowl.\n\n3. Bring poaching liquid to boil over high heat; boil until reduced to about 2 cups, about 15 minutes. Pour poaching liquid over pears and refrigerate until cool before serving.\n\n**PER SERVING** (\u00bd pear and \u00bc cup syrup): 172 Cal, 0 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 8 mg Sod, 44 g Total Carb, 4 g Fib, 0 g Prot, 17 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nDo it Faster\n\nPeeling and coring pears is quick and simple to do. Use a vegetable peeler to cut away the skins, then cut the pears in half lengthwise. To scoop out the core, use a teaspoon or a melon baller.\n\nWhite Wine-Poached Pears\n\n# Chunky Pink Apple-Raspberry Sauce\n\nSERVES 4\n\n**2 pounds red apples, cored and coarsely chopped**\n\n**\u00bc cup water**\n\n**2 tablespoons packed light brown sugar**\n\n**\u00bc teaspoon grated lemon zest**\n\n**1 tablespoon fresh lemon juice**\n\n**1 (6-ounce) container raspberries**\n\n1. Combine all ingredients except raspberries in large heavy saucepan and bring to boil over high heat. Reduce heat to medium and cook, stirring occasionally, until apples are softened, about 20 minutes.\n\n2. Remove pan from heat and let stand, covered, until apples are completely tender, about 10 minutes longer. Mash apples, then gently stir in raspberries. Divide apple-raspberry sauce among 4 dessert dishes.\n\n**PER SERVING** (\u00be cup): 157 Cal, 1 g Total Fat, 0 g Sat Fat, 0 g Trans Fat, 0 mg Chol, 6 mg Sod, 41 g Total Carb, 8 g Fib, 1 g Prot, 30 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\n# Roasted Pears with Balsamic Glaze\n\nSERVES 4\n\n**2 teaspoons unsalted butter, melted**\n\n**2 teaspoons fresh lemon juice**\n\n**4 ripe pears, halved and cored**\n\n**\u00bc cup packed brown sugar**\n\n**1 tablespoon balsamic vinegar**\n\n**4 (\u00bd-ounce) slices soft (mild) goat cheese**\n\n1. Preheat oven to 425\u00b0F.\n\n2. Stir together butter and lemon juice in small bowl.\n\n3. Place pears, cut side up, on large baking sheet. Brush cut side of pear halves with butter mixture. Roast until softened when pierced with fork, about 30 minutes.\n\n4. Meanwhile, combine brown sugar and vinegar in small saucepan and cook over low heat, whisking until dissolved. Increase heat to high and boil until thickened, about 30 seconds. Transfer to cup.\n\n5. Arrange 2 pear halves on each of 4 plates and place slice of goat cheese next to each pear. Using teaspoon, drizzle balsamic glaze over pears. Serve warm.\n\n**PER SERVING** (2 pear halves and 1 slice goat cheese): 202 Cal, 5 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 12 mg Chol, 61 mg Sod, 39 g Total Carb, 5 g Fib, 3 g Prot, 48 mg Calc.\n\n**_PointsPlus_** value: **_5._**\n\nMixed Berry Shortcakes\n\n# Mixed Berry Shortcakes\n\nSERVES 8\n\n**1 (16-ounce) bag frozen unsweetened mixed berries, thawed**\n\n**2 teaspoons fresh lemon juice**\n\n**\u00bd cup sugar**\n\n**1\u00be cups all-purpose flour**\n\n**2 teaspoons baking powder**\n\n**\u00bd teaspoon ground ginger**\n\n**\u00bc teaspoon salt**\n\n**4 tablespoons cold unsalted butter, diced**\n\n**\u2154 cup fat-free milk**\n\n**\u00be cup thawed frozen fat-free whipped topping**\n\n1. Preheat oven to 425\u00b0F. Spray baking sheet with nonstick spray.\n\n2. Combine berries, lemon juice, and \u00bc cup of sugar in medium bowl.\n\n3. Combine remaining \u00bc cup sugar, flour, baking powder, ginger, and salt in large bowl. Using pastry blender or two knives, cut butter into flour mixture until mixture resembles coarse crumbs. Using rubber spatula, stir in milk until mixture is just moistened. With your hands, gather dough into ball and knead once or twice until it just holds together.\n\n4. Turn dough out onto lightly floured surface. Press dough out until it is about \u00bd inch thick. Cut 8 shortcakes with 2\u00bd-inch biscuit cutter; press dough scraps together to cut more biscuits if necessary. Transfer shortcakes to baking sheet and bake until they are golden brown, 12\u201315 minutes. Remove from oven and cool on rack at least 5 minutes. (Biscuits can be cooled completely and stored in an airtight container up to 24 hours.)\n\n5. To serve, cut shortcakes in half horizontally and fill each with \u00bc cup of berries and 1\u00bd tablespoons of whipped topping.\n\n**PER SERVING** (1 filled shortcake): 241 Cal, 6 g Total Fat, 4 g Sat Fat, 0 g Trans Fat, 16 mg Chol, 209 mg Sod, 43 g Total Carb, 2 g Fib, 4 g Prot, 107 mg Calc.\n\n**_PointsPlus_** value: **_6._**\n\n# Whole Grain and Fruit Oatmeal Cookies\n\nMAKES 36\n\n**1\u00bd cups rolled (old-fashioned) oats**\n\n**\u00bd cup whole wheat flour**\n\n**\u00bd cup toasted wheat germ**\n\n**\u00bd cup low-fat granola**\n\n**\u00bc cup golden raisins**\n\n**\u00bc cup mini semisweet chocolate chips**\n\n**2 tablespoons unsalted sunflower seeds**\n\n**2 tablespoons finely chopped dried apricots**\n\n**1 teaspoon baking powder**\n\n**\u00bd teaspoon salt**\n\n**\u00bd cup (1 stick) unsalted butter, softened**\n\n**\u00bd cup packed brown sugar**\n\n**\u00bc cup water**\n\n**1 large egg**\n\n**1 teaspoon vanilla extract**\n\n1. Preheat oven to 375\u00b0F. Spray 2 large baking sheets with nonstick spray.\n\n2. Toss together oats, whole wheat flour, wheat germ, granola, raisins, chocolate chips, sunflower seeds, apricots, baking powder, and salt in large bowl.\n\n3. Using electric mixer on medium speed, beat butter and brown sugar until light and fluffy. Beat in water, egg, and vanilla just until smooth. Using rubber spatula, stir in flour mixture until combined.\n\n4. Drop dough by level measuring tablespoons, about 1 inch apart, onto baking sheets and flatten until 1\u00bd inches in diameter. Bake until cookies are golden brown and edges are deep brown, 10\u201312 minutes.\n\n5. Let cookies cool slightly on baking sheet on wire rack. Using metal spatula, transfer cookies to rack to cool completely. Repeat with remaining dough.\n\n**PER SERVING** (1 cookie): 79 Cal, 4 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 13 mg Chol, 54 mg Sod, 10 g Total Carb, 1 g Fib, 2 g Prot, 17 mg Calc.\n\n**_PointsPlus_** value: **_2._**\n\nCook's Note\n\nThese forgiving cookies will save you a trip to the grocery store, since you can use almost any dried fruits or nuts to make them. Substitute chopped almonds or walnuts for the sunflower seeds and dried cranberries or raisins for the apricots.\n\n# Chocolate-Cherry Brownies\n\nSERVES 16\n\n**\u00be cup all-purpose flour**\n\n**\u00bd cup unsweetened cocoa powder**\n\n**1 teaspoon baking powder**\n\n**\u00bc teaspoon baking soda**\n\n**\u215b teaspoon salt**\n\n**2 large eggs, lightly beaten**\n\n**1 cup granulated sugar**\n\n**2 teaspoons vanilla extract**\n\n**5 tablespoons unsalted butter**\n\n**1 ounce semisweet chocolate, chopped**\n\n**\u2154 cup dried cherries**\n\n**1 tablespoon confectioners' sugar (optional)**\n\n1. Preheat oven to 350\u00b0F. Spray 8-inch square baking pan with nonstick spray.\n\n2. Whisk together flour, cocoa powder, baking powder, baking soda, and salt in large bowl. Combine eggs, granulated sugar, and vanilla in separate bowl.\n\n3. Combine butter and chocolate in top of double boiler or a bowl set over saucepan of simmering water and stir until melted, about 3 minutes. Let cool about 1 minute; stir into egg mixture. Stir chocolate mixture into flour mixture, stirring until just combined. Fold in cherries. Pour batter into pan and even top.\n\n4. Bake brownies until toothpick inserted into center comes out with few moist crumbs clinging to it, about 20 minutes. Cool in pan on rack about 15 minutes. Remove brownies from pan, cut into 16 squares, and sprinkle with confectioners' sugar, if using.\n\n**PER SERVING** (1 brownie): 145 Cal, 5 g Total Fat, 3 g Sat Fat, 0 g Trans Fat, 36 mg Chol, 77 mg Sod, 24 g Total Carb, 2 g Fib, 2 g Prot, 30 mg Calc.\n\n**_PointsPlus_** value: **_4._**\n\nCook's Note\n\nFor the moistest brownies, take care not to overbake them. The toothpick should not come out with batter clinging to it, but don't bake the brownies so long that the toothpick comes out clean.\n\n# Recipes by **_PointsPlus_** value\n\n**_1 PointsPlus_** value\n\nChili-Spiced Popcorn\n\nRed Pepper and Sun-Dried Tomato Dip\n\n**_2 PointsPlus_** value\n\nBlack Bean-Tomatillo Dip\n\nBlackened Scallops with Lemon-Caper Mayonnaise\n\nChunky Guacamole\n\nCottage Cheese and Sun-Dried Tomato Dip\n\nMini Mexican Frittatas\n\nMorning Chai\n\nSun-Dried Tomato Hummus\n\nWhole Grain and Fruit Oatmeal Cookies\n\nWinter Squash Soup with Lime Cream\n\n**_3 PointsPlus_** value\n\nBlack and White Muffin Bites\n\nBlueberries with Whipped Ricotta and Balsamic Syrup\n\nCajun-Spiced Roast Pork Tenderloin\n\nDried Cranberry-Popcorn Mix\n\nHoneydew-Strawberry Soup\n\nMushroom, Scallion, and Cheddar Quesadillas\n\nProven\u00e7al-Style Vegetable-Chickpea Stew\n\nSpice-Roasted Pears with Yogurt\n\nSpicy Cereal and Pretzel Snack Mix\n\nTurkey and Roasted Pepper Lettuce Wraps\n\n**_4 PointsPlus_** value\n\nAsparagus and Chive Omelette\n\nBanana-Walnut Bread\n\nBreakfast Bruschetta\n\nChicken and Napa Cabbage Salad\n\nChicken Tikka with Cucumber Raita\n\nChinese Chicken Slaw\n\nChocolate-Cherry Brownies\n\nChunky Pink Apple-Raspberry Sauce\n\nCorn and Green Chile Frittata\n\nCreamy Couscous Breakfast Pudding\n\nCremini Mushroom, Tomato, and Rice Soup\n\nEdamame Dip\n\nFrozen Strawberry-Maple Yogurt\n\nHam and Navy Bean Confetti Soup\n\nHerb-Crusted Filets Mignons\n\nLemon Souffl\u00e9s\n\nManhattan Clam Chowder\n\nOpen-Faced Roast Beef Sandwich Bites\n\nPineapple Crush Smoothies\n\nRoast Beef Salad with Creamy Horseradish Dressing\n\nThai-Style Beef Salad\n\nTurkey Cutlets with Mushroom-Wine Sauce\n\nTurkey Cutlets with Orange Sauce\n\nWarm Spice-Baked Apples\n\n**_5 PointsPlus_** value\n\nAsian-Style Duck Roll-Ups\n\nBaked Cheesy Nachos\n\nBananas Foster\n\nBeef, Beet, and Cabbage Soup\n\nBell Pepper and Sun-Dried Tomato Omelette\n\nBraised Chicken in Riesling\n\nBrown Sugar Plums\n\nCaesar-Style Steak Salad\n\nCarrot-Apple Cupcakes with Cream Cheese Frosting\n\nChicken Piccata\n\nCitrus-Marinated Roast Pork\n\nClam and Corn Chowder\n\nCod with Tomato-Oregano Sauce\n\nCottage Cheese Pancakes\n\nCreamy Tomato Soup\n\nCrispy Green Plantains\n\nCurried Tuna Salad\n\nEdamame Salad with Basil Vinaigrette\n\nFirecracker Turkey Chili\n\nFlorentine Frittata\n\nFrittata Italiana\n\nFruity Chicken Salad\n\nGarlicky Braised Turkey Breast\n\nGrilled Flank Steak with Tomato-Fennel Salad\n\nGrilled Ginger Chicken with Peach Salsa\n\nGrilled Salmon with Quick Tomato Tapenade\n\nHalibut with Salsa Verde\n\nHam and Swiss Panini\n\nKey West-Style Shrimp Salad\n\nLamb and Onion Kebabs with Mint\n\nMixed Melon with Honeyed Ricotta\n\nOrange Flan with Macerated Oranges\n\nPea, Mushroom, and Cherry Tomato Frittata\n\nPeach-Blueberry Crostatas\n\nPizza Margherita\n\nQuick Quesadillas\n\nRicotta, Bacon, and Spinach Pizza\n\nRoast Halibut with Chunky Roasted Pepper Sauce\n\nRoasted Pears with Balsamic Glaze\n\nSalmon Patties with Chunky Tomato Relish\n\nShrimp Chowder with Dill\n\nSmoked Turkey, Carrot, and Raisin Salad\n\nSmoky Pumpkin Seeds\n\nSouthern Vegetable Gumbo\n\nSpanish Frittata\n\nSpinach-Feta Scramble\n\nSummer Squash Stuffed with Beef and Olives\n\nSuperfast Barbecued Chicken\n\nSweet-and-Spicy Salmon with Broccoli Slaw\n\nTeriyaki-Glazed Tofu and Vegetable Kebabs\n\nThai Shrimp and Melon Salad\n\nTuna-Potato Salad\n\nVanilla Yogurt Sundae\n\nWhite Wine-Poached Pears\n\n**_6 PointsPlus_** value\n\nApricot and Toasted Almond Galette\n\nApricot-Mustard Glazed Pork Roast\n\nBacon, Cheddar, and Egg-Topped English Muffins\n\nBeef and Black Bean Burgers\n\nBraised Bok Choy and Chicken with Soba Noodles\n\nBreakfast Berry Parfaits\n\nBrown Rice-Banana Pudding\n\nCalifornia Health Sandwiches\n\nChicken and Roasted Pepper Sandwiches\n\nChunky Vegetable Paella\n\nCilantro-Lime Shrimp Salad Pitas\n\nFilet Mignons with Cauliflower Puree\n\nFrozen Vanilla Yogurt with Sugared Shredded Wheat\n\nGinger Steak and Broccoli Stir-Fry\n\nGreek-Style Chicken Salad\n\nGrilled Chicken Salad with Raspberries and Goat Cheese\n\nGrilled Lamb Chops and Asparagus with Lemon-Garlic Mayonnaise\n\nHam and Macaroni Salad-Stuffed Bell Peppers\n\nHam with Apples and Mustard\n\nHash Brown and Egg Skillet Breakfast\n\nLow-and-Slow Sloppy Joes\n\nMaple and Chili-Broiled T-Bone Steaks\n\nMaui Tortilla Pizzas\n\nMicrowave Apple-Pear Crisp\n\nMixed Berry Shortcakes\n\nOrange Beef with Broccoli\n\nOven-Roasted Peaches with Raspberries and Sorbet\n\nPan Bagnat\n\nPotato-Watercress Soup\n\nProven\u00e7al Omelette\n\nPumpkin-Cranberry Bread Puddings\n\nQuesadillas with Guacamole and Pepper Jack\n\nQuick Chicken Satay with Asparagus\n\nRaspberry-Orange Sorbet\n\nRoasted Leg of Lamb\n\nSalmon au Poivre with Watercress\n\nSesame Scallops\n\nShrimp Salad with Fennel, Red Onion, and Orange\n\nSpice-Glazed Cherry Bundt Cake\n\nStrawberry Colada Cooler\n\nTabbouleh with Shrimp\n\nTriple Berry Summer Pudding\n\nTropical Turkey Salad\n\nTuna and White Bean Salad\n\nTuna Steaks with Avocado-Orange Relish\n\nTurkey Cutlets Milanese\n\nTurkey Wraps with Lemon-Yogurt Sauce\n\nVegetable Minestrone with Pasta\n\nVegetarian Burritos with Salsa Verde\n\nVeggie Breakfast Burrito\n\n**_7 PointsPlus_** value\n\nAfrican-Spiced Turkey and Squash Stew\n\nAsian-Style Pork, Mushroom, and Noodle Soup\n\nAvocado, Spinach, and Feta Wrap\n\nBaked Stuffed Potatoes with Ham and Cheese\n\nBeef and Bean Soft Tacos\n\nBeef Stew Proven\u00e7al\n\nBeef-Vegetable Soup\n\nBest BLTs\n\nBlack Bean Soup with Rice\n\nCacciatore-Style Chicken and Vegetables\n\nCalifornia Fish Tacos\n\nChicken in Coconut Curry Sauce\n\nChicken Picadillo\n\nChicken Salad with Fennel, Arugula, and Blue Cheese\n\nCinnamon French Toast\n\nCrab Salad-Stuffed Tomatoes\n\nCreole-Style Cod Fillets\n\nCrunchy Fish Sliders\n\nCuban Beef Lettuce Wraps\n\nFettuccine with Goat Cheese, Arugula, and Tomatoes\n\nFour-Vegetable Stir-Fry with Tofu\n\nGreek Pita Pizzas with Spinach and Feta\n\nGrilled Citrus Pork with Cucumber-Orange Salad\n\nHearty Lentil Salad with Radicchio\n\nLemony Chicken Kebabs with Couscous\n\nLentil and Sausage Soup\n\nLight and Luscious Cobb Salad\n\nOnion Soup with Herbed Cheese Toasts\n\nOpen-Faced Garlicky Steak Sandwiches\n\nPeach Muesli with Almonds\n\nPork and Bean Adobo Chili\n\nPork Chops with Ginger and Snow Peas\n\nPork Marrakesh\n\nPumpkin Pie Muffins\n\nQuick Turkey Tostadas\n\nRoasted Salmon with Caramelized Onions and Carrots\n\nRosemary Chicken Thighs with Roast Potatoes\n\nSesame Noodles with Green Vegetables\n\nShrimp with Cherry Tomatoes and Feta\n\nSouthwestern-Style Huevos Rancheros\n\nStuffed Butterflied Leg of Lamb\n\nTilapia with Tomato and Feta\n\nVegetable Fried Rice\n\n**_8 PointsPlus_** value\n\nArctic Char with Cranberry Couscous\n\nBeef-Barley Stew with Roasted Vegetables\n\nBest-Ever Country Captain\n\nCaribbean Seafood Stew\n\nChicken and Vegetable Curry\n\nChickpea Soup\n\nDilled Salmon Sandwiches with Caper Sauce\n\nEasy Chicken Cutlets Parmesan\n\nFilets Mignons with Tomato-Bean Salsa\n\nGrilled Chicken and Jack Cheese Sandwiches\n\nHearty Corn Chowder\n\nLinguine with Fontina and Artichokes\n\nLinguine with White Bean Puttanesca\n\nMediterranean Turkey Burgers\n\nMinted Lamb Chops with Lemony Bulgur\n\nPasta Salad with Apple and Chicken\n\nPitas Stuffed with Tofu-Egg Salad\n\nPork with Sweet Coconut-Peanut Sauce\n\nRanch-Style Eggs over Polenta\n\nSalmon Salad Sandwich\n\nSalmon with Corn, Black Bean, and Tomato Salad\n\nSliced Steak with Crispy Polenta\n\nSmoky Vegetarian Chili\n\nSoy-Blueberry Breakfast Shake\n\nStir-Fried Beef with Asparagus\n\nTeriyaki Chicken and Snow Pea Stir-Fry\n\nWaffles with Blueberries and Maple Cream\n\nWarm Lentil Salad with Baked Salmon\n\n**_9 PointsPlus_** value\n\nBaked Ziti with Summer Squash\n\nChicken and Vegetables with Fettuccine\n\nChuck Wagon-Style Turkey Chili\n\nEasy Chicken Gumbo\n\nGingery Turkey-Couscous Salad\n\nHearty Steak and Vegetables\n\nHoney-Mustard Turkey Sandwiches\n\nLamb and Vegetable Stew\n\nMexicali Chicken Salad\n\nMoroccan-Style Chicken\n\nPeanut Butter Blast\n\nPhilly Cheese Steak Sandwiches\n\nPork and Mushroom Stir-Fry\n\nRoast Pork Tenderloin with Black Bean Salsa\n\nSaucy Pan-Roasted Pork Chops with Ziti\n\nShrimp and Spaghetti Arrabbiata\n\nTuna Steak Sandwiches with Roasted Pepper Relish\n\nWhite Bean Salad with Feta-Pita Crisps\n\nWild Blueberry and Cornmeal Pancakes\n\n**_10 PointsPlus_** value\n\nBountiful Beef Stew\n\nBrown Rice and Honey Pancakes\n\nChicken and Vegetable Ragu with Herbed Dumplings\n\nSpaghetti with Fresh Tomato Sauce and Meatballs\n\nSteak Fajitas\n\n**_11 PointsPlus_** value\n\nChicken and Rice with Artichoke Hearts\n\nChicken and Tzatziki-Stuffed Pitas\n\nChicken and Vegetable Tagine\n\nCuban-Style Shredded Beef and Rice\n\nCurried Beef Kebabs with Basmati Rice\n\nEasy Chicken Florentine with Spaghetti\n\nSpaghetti with Quick Bolognese Sauce\n\n**_12 PointsPlus_** value\n\nChicken with Mushrooms and White Wine\n\n# Index\n\nThe index that appeared in the print version of this title does not match the pages in your eBook. Please use the search function on your eReading device to search for terms of interest.\n\nFor your reference, the terms that appear in the print index are listed below.\n\n**15-Minute Meals**\n\n_See also_ _specific meal categories_\n\nbreakfast\n\ndinner\n\nlunch\n\nfor Simply Filling technique\n\nsnacks and sweets\n\n**20-Minute Meals**\n\n_See also_ _specific meal categories_\n\nbreakfast\n\ndinner\n\nlunch\n\nfor Simply Filling technique\n\nsnacks and sweets\n\n**30-Minute Meals**\n\n_See also_ _specific meal categories_\n\nbreakfast\n\ndinner\n\nlunch\n\nfor Simply Filling technique\n\nsnacks and sweets\n\nA\n\nAfrican-Spiced Turkey and Squash Stew\n\nalcohol, **_PointsPlus_** calculations and\n\napple(s)\n\nCupcakes with Carrot and\n\nHam with Mustard and\n\nPasta Salad with Chicken and\n\nand Pear Crisp\n\nSalad with Kale and\n\non sandwiches\n\nSauce, Raspberry and Pink\n\nWarm Spice-Baked\n\nApricot and Toasted Almond Galette\n\nApricot-Mustard Glazed Pork Roast\n\nArctic Char with Cranberry Couscous\n\nAsian-Style Duck Roll-Ups\n\nAsian-Style Pork, Mushroom, and Noodle Soup\n\nasparagus\n\nBeef Stir-Fried with\n\nChicken Satay with\n\nLamb Chops with\n\nroasted\n\nAsparagus and Chive Omelette\n\navocado\n\nGuacamole, Chunky\n\nand orange relish\n\nSalad with Lemony Spinach and\n\nstorage of\n\nAvocado, Spinach, and Feta Wrap\n\nB\n\nBacon, Cheddar, and Egg-Topped English Muffins\n\nBaked Cheesy Nachos\n\nBaked Stuffed Potatoes with Ham and Cheese\n\nBaked Ziti with Summer Squash\n\nBananas Foster\n\nBanana-Walnut Bread\n\nbeans\n\ncanned\n\nChili, Adobo, with Pork and\n\nrinsing\/sorting of\n\nsodium in\n\nTacos, Soft, with Beef and\n\nbeef\n\nBurgers, with Black Bean\n\ncooking temperature for\n\nCuban-Style Shredded\n\nFilet Mignon, with Cauliflower Puree\n\nFilets Mignons, Herb-Crusted\n\nFilets Mignons, with Tomato-Bean Salsa\n\nGrilled Flank Steak with Tomato-Fennel Salad\n\nKebabs, Curried, with Basmati Rice\n\nLettuce Wraps, Cuban\n\nOrange\n\nSalad, Roast Beef with Creamy Horseradish Dressing\n\nSalad, Thai-Style\n\nSandwich, Philly Cheese Steak\n\nSandwich, Roast\n\nSloppy Joes, Low-and-Slow\n\nSoup, with Beet and Cabbage\n\nSoup, with Vegetable\n\nSteak Fajitas\n\nSteak, Hearty, with Vegetables\n\nSteak, Maple and Chili-Broiled T-Bone\n\nSteak, Pepper\n\nSteak, Sliced, with Crispy Polenta\n\nStew, Bountiful\n\nStew Proven\u00e7al\n\nStew, with Barley and Roasted Vegetables\n\nStir-Fry, with Asparagus\n\nStir-Fry, with Ginger Steak and Broccol\n\nSummer Squash Stuffed with Olives and\n\nTacos\n\nBeef and Bean Soft Tacos\n\nBeef and Black Bean Burgers\n\nBeef-Barley Stew with Roasted Vegetables\n\nBeef, Beet, and Cabbage Soup\n\nBeef Stew Proven\u00e7al\n\nBeef-Vegetable Soup\n\nbell pepper(s)\n\nHam and Macaroni Salad-Stuffed\n\nBell Pepper and Sun-Dried Tomato Omelette\n\nBest BLTs\n\nBest-Ever Country Captain\n\nBlack and White Muffin Bites\n\nBlack Bean Soup with Rice\n\nBlack Bean-Tomatillo Dip\n\nBlackened Scallops with Lemon-Caper Mayonnaise\n\nBlueberries with Whipped Ricotta and Balsamic Syrup\n\nblueberry(ies)\n\nCornmeal Pancakes and Wild\n\nCrostatas of Peach and\n\nShake, with Soy\n\nWaffles and Maple Cream\n\nwith Whipped Ricotta and Balsamic Syrup\n\nbonus meals, weekend. _See also_ _specific categories_\n\nslow-cooker\n\nspend-some-time\n\nsweet\n\nBountiful Beef Stew\n\nBPA (Bisphenol A)\n\nBraised Bok Choy and Chicken with Soba Noodles\n\nBraised Chicken in Riesling\n\nbread\n\nBanana-Walnut\n\nPuddings, Pumpkin-Cranberry\n\nBreakfast Berry Parfaits\n\nBreakfast Bruschetta\n\nbreakfasts, 15-minute\n\nAsparagus and Chive Omelette\n\nBacon, Cheddar, and Egg-Topped English Muffins\n\nBreakfast Berry Parfaits\n\nCinnamon French Toast\n\nMorning Chai\n\nPeanut Butter Blast\n\nProven\u00e7al Omelette\n\nSouthwestern-Style Huevos Rancheros\n\nSoy-Blueberry Breakfast Shake\n\nSpinach-Feta Scramble\n\nVeggie Breakfast Burrito\n\nWaffles with Blueberries and Maple Cream\n\nbreakfasts, 20-minute\n\nBell Pepper and Sun-Dried Tomato Omelette\n\nBreakfast Bruschetta\n\nCorn and Green Chile Frittata\n\nCottage Cheese Pancakes\n\nFrittata Italiana\n\nHash Brown and Egg Skillet Breakfast\n\nPea, Mushroom, and Cherry Tomato Frittata\n\nbreakfasts, 30-minute\n\nBrown Rice and Honey Pancakes\n\nCreamy Couscous Breakfast Pudding\n\nFlorentine Frittata\n\nMini Mexican Frittatas\n\nPeach Muesli with Almonds\n\nRanch-Style Eggs over Polenta\n\nSpanish Frittata\n\nSpice-Roasted Pears with Yogurt\n\nWild Blueberry and Cornmeal Pancakes\n\nbreakfasts, Simply Filling\n\nbroccoli\n\nButtered, with Cilantro and Lime\n\nOrange Beef with\n\nSlaw, with Sweet-and-Spicy Salmon\n\nStir-Fry, Ginger Steak and\n\nbroth, store-bought\n\nBrown Rice and Honey Pancakes\n\nBrown Rice-Banana Pudding\n\nBrown Sugar Plums\n\nBulgur, Lemony\n\nBurritos with Salsa Verde, Vegetarian\n\nButtered Broccoli with Cilantro and Lime\n\nC\n\nCacciatore-Style Chicken and Vegetables\n\nCaesar-Style Steak Salad\n\nCajun-Spiced Roast Pork Tenderloin\n\ncakes\n\nBundt, Spice-Glazed Cherry\n\nCarrot-Apple Cup-\n\nMixed Berry Short-\n\nCalifornia Fish Tacos\n\nCalifornia Health Sandwiches\n\ncanned foods\n\nCaribbean Seafood Stew\n\ncarrot(s)\n\nSalad with Turkey, Raisin, and\n\nSalmon Roasted with Caramelized Onions and\n\nCarrot-Apple Cupcakes with Cream Cheese Frosting\n\nCauliflower Puree\n\ncheddar cheese\n\nBacon and Egg-Topped English Muffins with\n\nBaked Stuffed Potatoes with Ham and\n\nNachos Baked with\n\nQuesadillas with Mushroom, Scallion, and\n\ncheese. _See also_ _specific types_\n\npre-shredded\n\nToasts\n\nchicken\n\nBarbecued\n\nBraised, in Riesling\n\nCacciatore-Style, with Vegetables\n\nwith Coconut-Curry Sauce\n\ncooking temperature for\n\nCountry Captain, Best Ever\n\nCurry\n\nCutlets, Easy, with Parmesan\n\nFettuccine, with Vegetables\n\nFlorentine, with Spaghetti\n\nGrilled, with Ginger and Peach Salsa\n\nGumbo, Easy\n\nKebabs with Couscous and Lemony\n\nMoroccan-Style\n\nwith Mushrooms and White Wine\n\nwith Napa Cabbage Salad\n\nPasta Salad with Apple and\n\nPicadillo\n\nPiccata\n\nPitas stuffed with Tzatziki and\n\nRagu, with Vegetables and Herbed Dumplings\n\nand Rice with Artichoke Hearts\n\nrotisserie\n\nSalad, Fruity\n\nSalad, Greek-style\n\nSalad, Mexicali\n\nSalad, with Fennel, Arugula, and Blue Cheese\n\nSalad, with Raspberries and Goat Cheese\n\nSatay, with Asparagus\n\nSlaw, Chinese\n\nSoba Noodles with Braised Bok Choy and\n\nStir-Fry with Snow Peas and Teriyaki\n\nTagine\n\nThighs, Rosemary, with Roast Potatoes\n\nTikka, with Cucumber Raita\n\nChicken and Napa Cabbage Salad\n\nChicken and Rice with Artichoke Hearts\n\nChicken and Roasted Pepper Sandwiches\n\nChicken and Tzatziki-Stuffed Pitas\n\nChicken and Vegetable Curry\n\nChicken and Vegetable Ragu with Herbed Dumplings\n\nChicken and Vegetables with Fettuccine\n\nChicken and Vegetable Tagine\n\nChicken in Coconut-Curry Sauce\n\nChicken Picadillo\n\nChicken Piccata\n\nChicken Salad with Fennel, Arugula, and Blue Cheese\n\nChicken Tikka with Cucumber Raita\n\nChicken with Mushrooms and White Wine\n\nchickpea\n\nSoup\n\nStew, Proven\u00e7al-Style with Vegetables\n\nchili. _See also_ soup(s); stew(s)\n\nPork and Bean Adobo\n\nTurkey, Chuck Wagon-Style\n\nTurkey, Firecracker\n\nVegetarian, Smoky\n\nchili spice\n\nT-Bone Steaks Broiled with Maple and\n\nChili-Spiced Popcorn\n\nChinese Chicken Slaw\n\nChocolate-Cherry Brownies\n\nchowder\n\nCorn and Clam\n\nCorn, Hearty\n\nManhattan Clam\n\nShrimp, with Dill\n\nChuck Wagon-Style Turkey Chili\n\nChunky Guacamole\n\nChunky Pink Apple-Raspberry Sauce\n\nChunky Vegetable Paella\n\nCilantro-Lime Shrimp Salad Pitas\n\nCinnamon French Toast\n\nCitrus-Marinated Roast Pork\n\nClam and Corn Chowder\n\nClam Chowder, Manhattan\n\nclams, canned\n\ncoconut\n\ncanned\n\n-Curry Sauce\n\n-Peanut Sauce\n\ncod\n\nCreole-Style Fillets\n\nSliders, Crunchy\n\nwith Tomato-Oregano Sauce\n\ncorn\n\nBlack Bean and Tomato Salad with\n\nChowder, Hearty\n\nChowder, with Clam\n\nFrittata, with Green Chile\n\nkernel removal\n\nPancakes, with Wild Blueberry\n\nPopped, with Chili-Spice\n\nPopped, with Dried Cranberry\n\nCottage Cheese and Sun-Dried Tomato Dip\n\nCottage Cheese Pancakes\n\ncouscous\n\nCranberry\n\nGingery Turkey-\n\nwith Lemony Chicken Kebabs\n\nPudding, Creamy Breakfast\n\nCrab Salad-Stuffed Tomatoes\n\ncream\n\nCheese Frosting\n\nLime\n\nMaple\n\nCreamy Couscous Breakfast Pudding\n\nCreamy Tomato Soup\n\nCremini Mushroom, Tomato, and Rice Soup\n\nCreole-Style Cod Fillets\n\nCrispy Green Plantains\n\nCrunchy Fish Sliders\n\nCuban Beef Lettuce Wraps\n\nCuban-Style Shredded Beef and Rice\n\ncucumber\n\n-Orange Salad\n\nRaita, with Chicken Tikka\n\nCurried Beef Kebabs with Basmati Rice\n\nCurried Tuna Salad\n\nD\n\nDilled Salmon Sandwiches with Caper Sauce\n\ndinners, 15-minute\n\nAfrican-Spiced Turkey and Squash Stew\n\nCaesar-Style Steak Salad\n\nEasy Chicken Cutlets Parmesan\n\nFilet Mignon with Cauliflower Puree\n\nGrilled Chicken Salad with Raspberries and Goat Cheese\n\nGrilled Citrus Pork with Cucumber-Orange Salad\n\nGrilled Ginger Chicken with Peach Salsa\n\nGrilled Salmon with Quick Tomato Tapenade\n\nHalibut with Salsa Verde\n\nHerb-Crusted Filets Mignons\n\nLamb and Onion Kebabs with Mint\n\nMaple and Chili-Broiled T-Bone Steaks\n\nRoast Halibut with Chunky Roasted Pepper Sauce\n\nSalmon au Poivre with Watercress\n\nSesame Noodles with Green Vegetables\n\nSesame Scallops\n\nSuperfast Barbecued Chicken\n\nThai Shrimp and Melon Salad\n\nTuna Steaks with Avocado-Orange Relish\n\nTurkey Cutlets with Mushroom-Wine Sauce\n\ndinners, 20-minute\n\nArctic Char with Cranberry Couscous\n\nBlackened Scallops with Lemon-Caper Mayonnaise\n\nBraised Bok Choy and Chicken with Soba Noodles\n\nCalifornia Fish Tacos\n\nChicken in Coconut-Curry Sauce\n\nChicken Piccata\n\nChicken Tikka with Cucumber Raita\n\nCod with Tomato-Oregano Sauce\n\nFettuccine with Goat Cheese, Arugula, and Tomatoes\n\nGinger Steak and Broccoli Stir-Fry\n\nLinguine with White Bean Puttanesca\n\nMediterranean Turkey Burgers\n\nOrange Beef with Broccoli\n\nPork Chops with Ginger and Snow Peas\n\nPork with Sweet Coconut-Peanut Sauce\n\nShrimp and Spaghetti Arrabbiata\n\nShrimp with Cherry Tomatoes and Feta\n\nSteak Fajitas\n\nSummer Squash Stuffed with Beef and Olives\n\nSweet-and-Spicy Salmon with Broccoli Slaw\n\nThai-Style Beef Salad\n\nTurkey Cutlets Milanese\n\nTurkey Cutlets with Orange Sauce\n\nVegetable Fried Rice\n\ndinners, 30-minute\n\nCajun-Spiced Roast Pork Tenderloin\n\nChicken and Vegetables with Fettuccine\n\nChicken Picadillo\n\nChunky Vegetable Paella\n\nCreole-Style Cod Fillets\n\nCurried Beef Kebabs with Basmati Rice\n\nFilets Mignons with Tomato-Bean Salsa\n\nFour-Vegetable Stir-Fry with Tofu\n\nGrilled Flank Steak with Tomato-Fennel Salad\n\nGrilled Lamb Chops and Asparagus with Lemon-Garlic Mayonnaise\n\nHam with Apples and Mustard\n\nHearty Steak and Vegetables\n\nLemony Chicken Kebabs with Couscous\n\nLinguine with Fontina and Artichokes\n\nMinted Lamb Chops with Lemony Bulgur\n\nMoroccan-Style Chicken\n\nPork and Mushroom Stir-Fry\n\nQuick Chicken Satay with Asparagus\n\nRoasted Salmon with Caramelized Onions and Carrots\n\nRoast Pork Tenderloin with Black Bean Salsa\n\nSalmon Patties with Chunky Tomato Relish\n\nSaucy Pan-Roasted Pork Chops with Ziti\n\nSliced Steak with Crispy Polenta\n\nSpaghetti with Quick Bolognese Sauce\n\nStir-Fried Beef with Asparagus\n\nTeriyaki Chicken and Snow Pea Stir-Fry\n\nTeriyaki-Glazed Tofu and Vegetable Kebabs\n\nTilapia with Tomato and Feta\n\nWarm Lentil Salad with Baked Salmon\n\ndinners, bonus. _See_ slow-cooker meals; spend-some-time dishes\n\ndinners, Simply Filling\n\ndip(s)\n\nBlack Bean-Tomatillo\n\nChunky Guacamole\n\nEdamame\n\nSun-Dried Tomato\n\nSun-Dried Tomato and Red Pepper\n\nSun-Dried Tomato Hummus\n\ndressing. _See also_ dip(s); sauce(s)\n\nCreamy Horseradish\n\nLemon-Caper Mayonnaise\n\nLemon-Garlic Mayonnaise\n\nDried Cranberry-Popcorn Mix\n\nDumplings, Herbed\n\nE\n\nEasy Chicken Cutlets Parmesan\n\nEasy Chicken Florentine with Spaghetti\n\nEasy Chicken Gumbo\n\nEdamame Dip\n\nEdamame Salad with Basil Vinaigrette\n\negg(s)\n\non Bacon, Cheddar, and English Muffins\n\nBreakfast Bruschetta with\n\nfrittatas\n\nHash Brown Skillet Breakfast with\n\nOmelette, Asparagus and Chive\n\nOmelette, Proven\u00e7al\n\nRanch-Style, over Polenta\n\nSalad, Tofu and\n\nScramble, with Spinach-Feta\n\nSouthwestern-Style Huevos Rancheros\n\nwhites\n\nF\n\nfajitas\n\nfeta\n\nGreek Pita Pizzas with Spinach and\n\nShrimp with Cherry Tomatoes and\n\n-Spinach Scramble\n\nTilapia with Tomato and\n\nWhite Bean Salad with Pita Crisps of\n\nWrap with Avocado and Spinach\n\nFettuccine with Goat Cheese, Arugula, and Tomatoes\n\nfil\u00e9 powder\n\nFilet Mignon with Cauliflower Puree\n\nFilets Mignons with Tomato-Bean Salsa\n\nFirecracker Turkey Chili\n\nfish. _See_ seafood\n\nFlorentine Frittata\n\nfontina cheese\n\nfood processors\n\nFour-Vegetable Stir-Fry with Tofu\n\nfrittata(s)\n\nCorn and Green Chile\n\nFlorentine\n\nItaliana\n\nMini Mexican\n\nPea, Mushroom, and Cherry Tomato\n\nSpanish\n\nFrittata Italiana\n\nFrozen Strawberry-Maple Yogurt\n\nFrozen Vanilla Yogurt with Sugared Shredded Wheat\n\nfruit\n\nBreakfast Berry Parfaits\n\ncanned\n\npineapple\n\nFruity Chicken Salad\n\nG\n\nGarlicky Braised Turkey Breast\n\ngarlic, peeled\n\nGinger Steak and Broccoli Stir-Fry\n\nGingery Turkey-Couscous Salad\n\ngoat cheese\n\nFettuccine with Arugula, Tomatoes and\n\nGrilled Chicken Salad with Raspberries and\n\nPolenta with Chives and\n\ngrains, whole\n\ncooking tips for\n\nGreek Pita Pizzas with Spinach and Feta\n\nGreek-Style Chicken Salad\n\nGrilled Chicken and Jack Cheese Sandwiches\n\nGrilled Chicken Salad with Raspberries and Goat Cheese\n\nGrilled Citrus Pork with Cucumber-Orange Salad\n\nGrilled Flank Steak with Tomato-Fennel Salad\n\nGrilled Ginger Chicken with Peach Salsa\n\nGrilled Lamb Chops and Asparagus with Lemon-Garlic Mayonnaise\n\nGrilled Salmon with Quick Tomato Tapenade\n\nGuacamole\n\nChunky\n\ngumbo\n\nChicken, Easy\n\nVegetable, Southern\n\nH\n\nHalibut with Salsa Verde\n\nHam and Macaroni Salad-Stuffed Bell Peppers\n\nHam and Navy Bean Confetti Soup\n\nHam and Swiss Panini\n\nHam with Apples and Mustard\n\nHash Brown and Egg Skillet breakfast\n\nHearty Corn Chowder\n\nHearty Lentil Salad with Radicchio\n\nHearty Steak and Vegetables\n\nHerb-Crusted Filets Mignons\n\nHerbed Parmesan-Garlic Pasta\n\nherbs\n\npreservation of\n\nHoneydew-Strawberry Soup\n\nHoney-Mustard Turkey Sandwiches\n\nK\n\nkale\n\nKale and Apple Salad\n\nkebabs\n\nBeef, Curried, with Basmati Rice\n\nChicken, Lemony, with Couscous\n\nLamb and Onion with Mint\n\nTofu, Teriyaki-Glazed, and Vegetable\n\nKey West-Style Shrimp Salad\n\nL\n\nlamb\n\nChops, Grilled, with Asparagus and Lemon-Garlic Mayonnaise\n\nChops, Minted, with Lemony Bulgur\n\ncooking temperature for\n\nLeg of\n\nLamb and Onion Kebabs with Mint\n\nLamb and Vegetable Stew\n\nlemon\n\nBulgur\n\nChicken Kebabs with Couscous and\n\nmarinade with herbs\n\nMayonnaise with Capers and\n\nMayonnaise with Garlic and\n\nand Yogurt Sauce\n\nLemon Souffl\u00e9s\n\nLemony Chicken Kebabs with Couscous\n\nLemony Spinach and Avocado Salad\n\nLentil and Sausage Soup\n\nlettuce\n\nprewashed\n\nWraps, Cuban Beef\n\nWraps, Turkey and Roasted Pepper\n\nLight and Luscious Cobb Salad\n\nlime\n\nButtered Broccoli with Cilantro and\n\nand Cilantro Shrimp Salad Pitas\n\nCream, with Winter Squash Soup\n\nzest\n\nLinguine with Fontina and Artichokes\n\nLinguine with White Bean Puttanesca\n\nLow-and-Slow Sloppy Joes\n\nlunches, 15-minute\n\nAsian-Style Duck Roll-Ups\n\nAvocado, Spinach, and Feta Wrap\n\nBest BLTs\n\nCalifornia Health Sandwiches\n\nChicken and Roasted Pepper Sandwiches\n\nChicken Salad with Fennel, Arugula, and Blue Cheese\n\nChinese Chicken Slaw\n\nCilantro-Lime Shrimp Salad Pitas\n\nFruity Chicken Salad\n\nGreek-Style Chicken Salad\n\nGrilled Chicken and Jack Cheese Sandwiches\n\nHam and Navy Bean Confetti Soup\n\nHam and Swiss Panini\n\nKey West-Style Shrimp Salad\n\nMexicali Chicken Salad\n\nQuick Turkey Tostadas\n\nRoast Beef Salad with Creamy Horseradish Dressing\n\nSalmon Salad Sandwich\n\nSouthern Vegetable Gumbo\n\nTropical Turkey Salad\n\nTurkey Wraps with Lemon-Yogurt Sauce\n\nWinter Squash Soup with Lime Cream\n\nlunches, 20-minute\n\nBlack Bean Soup with Rice\n\nChicken and Napa Cabbage Salad\n\nChicken and Tzatziki-Stuffed Pitas\n\nChickpea Soup\n\nClam and Corn Chowder\n\nCrab Salad-Stuffed Tomatoes\n\nCurried Tuna Salad\n\nGingery Turkey-Couscous Salad\n\nHam and Macaroni Salad-Stuffed Bell Peppers\n\nLight and Luscious Cobb Salad\n\nMaui Tortilla Pizzas\n\nPan Bagnat\n\nPitas Stuffed with Tofu-Egg Salad\n\nQuick Quesadillas\n\nSalmon with Corn, Black Bean, and Tomato Salad\n\nShrimp Salad with Fennel, Red Onion, and Orange\n\nSmoked Turkey, Carrot, and Raisin Salad\n\nTuna and White Bean Salad\n\nTuna-Potato Salad\n\nWhite Bean Salad with Feta-Pita Crisps\n\nlunches, 30-minute\n\nAsian-Style Pork, Mushroom, and Noodle Soup\n\nBeef and Black Bean Burgers\n\nCreamy Tomato Soup\n\nCremini Mushroom, Tomato, and Rice Soup\n\nCrunchy Fish Sliders\n\nCuban Beef Lettuce Wraps\n\nDilled Salmon Sandwiches with Caper Sauce\n\nEdamame Salad with Basil Vinaigrette\n\nGreek Pita Pizzas with Spinach and Feta\n\nHearty Corn Chowder\n\nHearty Lentil Salad with Radicchio\n\nHoney-Mustard Turkey Sandwiches\n\nManhattan Clam Chowder\n\nOpen-Faced Garlicky Steak Sandwiches\n\nPasta Salad with Apple and Chicken\n\nPhilly Cheese Steak Sandwiches\n\nPotato-Watercress Soup\n\nQuesadillas with Guacamole and Pepper Jack\n\nSmoky Vegetarian Chili\n\nTabbouleh with Shrimp\n\nTuna Steak Sandwiches with Roasted Pepper Relish\n\nlunches, Simply Filling\n\nM\n\nManhattan Clam Chowder\n\nMaple and Chili-Broiled T-Bone Steaks\n\nmarinade\/glaze\n\nApricot-Mustard\n\nBalsamic\n\nCitrus\n\nlemon-herb\n\nMaple-Chili\n\nSpice\n\nTeriyaki\n\nMaui Tortilla Pizzas\n\nmayonnaise\n\nLemon-Caper\n\nLemon-Garlic\n\nmeatballs\n\nmeats. _See also_ _specific types_\n\nlean cuts of\n\nMediterranean Turkey Burgers\n\nmelon\n\nwith Honeyed Ricotta\n\nwith Thai Shrimp\n\nMexicali Chicken Salad\n\nMicrowave Apple-Pear Crisp\n\nMini Mexican Frittatas\n\nMinted Green Beans with Pine Nuts\n\nMinted Lamb Chops with Lemony Bulgur\n\nMixed Berry Shortcakes\n\nMixed Melon with Honeyed Ricotta\n\nMorning Chai\n\nMoroccan-Style Chicken\n\nmushroom(s)\n\nChicken with White Wine and\n\nFrittata with Peas, Cherry Tomato, and\n\nQuesadillas\n\nsliced\n\nSoup with Asian-Style Pork, Noodle, and\n\nSoup with Rice, Tomato, and Cremini\n\nStir-Fry with Pork and\n\nand Wine Sauce\n\nMushroom, Scallion, and Cheddar Quesadillas\n\nO\n\nolives, pitted\n\nOnion Soup with Herbed Cheese Toasts\n\nOpen-Faced Garlicky Steak Sandwiches\n\nOpen-Faced Roast Beef Sandwich Bites\n\norange(s)\n\nand Avocado Relish, with Tuna Steaks\n\nBeef\n\ncanned\n\nFlan\n\nSalad with Cucumber and\n\nSalad with Shrimp, Fennel, Red Onion, and\n\nSauce over Turkey Cutlets\n\nSorbet of Raspberry and\n\nzest\n\nOrange Beef with Broccoli\n\nOrange Flan with Macerated Oranges\n\norganizational tips. _See also_ timesaving tips\n\nOven-Roasted Peaches with Raspberries and Sorbet\n\nP\n\nPan Bagnat\n\npancakes\n\nBrown Rice and Honey\n\nCottage Cheese\n\nWild Blueberry and Cornmeal\n\nparchment paper\n\nparmesan cheese\n\npasta\n\nBaked Ziti with Summer Squash\n\nChicken with Mushrooms, White Wine and\n\ncooking speed of\n\nEasy Chicken Florentine with Spaghetti\n\nFettuccine with Chicken and Vegetables\n\nFettuccine with Goat Cheese, Arugula, and Tomatoes\n\nHerbed Parmesan-Garlic\n\nLinguine with Fontina and Artichokes\n\nLinguine with White Bean Puttanesca\n\nSalad\n\nShrimp and Spaghetti Arrabbiata\n\nSpaghetti with Fresh Tomato Sauce and Meatballs\n\nSpaghetti with Quick Bolognese Sauce\n\nVegetable Minestrone with\n\nZiti with Saucy Pan-Roasted Pork Chops\n\nPasta Salad with Apple and Chicken\n\npeach(es)\n\ncanned\n\nOven-Roasted, with Raspberries and Sorbet\n\nSalsa\n\nPeach-Blueberry Crostatas\n\nPeach Muesli with Almonds\n\nPea, Mushroom, and Cherry Tomato Frittata\n\nPeanut Butter Blast\n\npear(s)\n\nand Apple Crisp, Microwave\n\ncanned\n\nRoasted, with Balsamic Glaze\n\non sandwiches\n\nWhite Wine-Poached\n\nYogurt and Spice-Roasted\n\npepper jack cheese\n\nPhilly Cheese Steak Sandwiches\n\npineapple\n\ncanned\n\nprecut\n\nPineapple Crush Smoothies\n\nPitas Stuffed with Tofu-Egg Salad\n\npizza\n\nGreek Pita, Spinach and Feta\n\nMargherita\n\nMaui Tortilla\n\nRicotta, Bacon, and Spinach\n\nPlantains, Crispy Green\n\n**_PointsPlus_** system\n\nrecipes arranged by\n\npolenta\n\nEggs, Ranch-Style, over\n\nSteak, Sliced, with Crispy\n\nPolenta with Goat Cheese and Chives\n\npopcorn\n\nChili-Spiced\n\nDried-Cranberry\n\npork\n\nBaked, Stuffed Potatoes with Cheese and\n\nChili\n\nChops, Saucy Pan-Roasted, with Ziti\n\nChops, with Ginger and Snow Peas\n\ncooking temperature for\n\nGrilled Citrus\n\nHam with Apples and Mustard\n\nMarrakesh\n\nPanini, Ham and Swiss\n\nPizza, Maui Tortilla\n\nQuesadillas, Quick, with\n\nRoast, Apricot-Mustard Glazed\n\nRoast, with Citrus-Marinade\n\nSalad-Stuffed Bell Peppers\n\nsandwiches\n\nSoup, Asian-Style with Mushroom and Noodle\n\nSoup, Ham and Navy Bean Confetti\n\nSoup, with Lentil and Kielbasa\n\nStir-Fry\n\nTenderloin Roast, Cajun-Spiced\n\nTenderloin Roast, with Black Bean Salsa\n\nPork and Bean Adobo Chili\n\nPork and Mushroom Stir-Fry\n\nPork Chops with Ginger and Snow Peas\n\nPork Marrakesh\n\nPork with Sweet Coconut-Peanut Sauce\n\npotato(es)\n\nBaked and Stuffed with Ham and Cheese\n\nOven Fries, Rosemary-Parmesan\n\nRoasted, with Rosemary Chicken Thighs\n\nSalad, with Tuna and\n\nsweet\n\nPotato-Watercress Soup\n\npoultry. _See also_ chicken; turkey\n\ncooking temperature for\n\npreparation. _See also_ timesaving tips\n\nshopping in\n\ntimesaving tips for\n\nutensils\/equipment for\n\nweighing and measuring tips for\n\nProven\u00e7al Omelette\n\nProven\u00e7al-Style Vegetable-Chickpea Stew\n\npudding\n\nBread, Pumpkin-Cranberry\n\nBrown Rice-Banana\n\nCreamy Couscous Breakfast\n\nTriple Berry Summer\n\nPumpkin-Cranberry Bread Puddings\n\nPumpkin Pie Muffins\n\nPumpkin Seeds, Smoky\n\nQ\n\nquesadillas\n\nMushroom, Scallion, and Cheddar\n\nQuick\n\nQuesadillas with Guacamole and Pepper Jack\n\nQuick Chicken Satay with Asparagus\n\nQuick Quesadillas\n\nQuick Turkey Tostadas\n\nR\n\nRanch-Style Eggs over Polenta\n\nraspberries\n\nGrilled Chicken Salad with Goat Cheese and\n\nOven-Roasted Peaches with Sorbet and\n\nSauce, Pink Apple and\n\nRaspberry-Orange Sorbet\n\nRed Pepper and Sun-Dried Tomato Dip\n\nrelish\n\nAvocado-Orange\n\nChunky Tomato\n\nRoasted Pepper\n\nrice\n\nBasmati, with Curried Beef Kebabs\n\nand Beef, Cuban-Style\n\nChicken and\n\nPancakes with Honey and Brown\n\nPudding, Banana and Brown\n\nSoup, with Black Bean\n\nSoup, with Cremini Mushroom, Tomato\n\nVegetable Fried\n\nrice cookers\n\nRicotta, Bacon, and Spinach Pizza\n\nricotta cheese\n\nHoneyed\n\non Pizza with Bacon and Spinach\n\nWhipped, with Blueberries and Balsamic Syrup\n\nRoast Beef Salad with Creamy Horseradish Dressing\n\nRoasted Leg of Lamb\n\nRoasted Pears with Balsamic Glaze\n\nroasted pepper\n\nLettuce Wraps with Turkey and\n\nSandwiches with Chicken and\n\nsauce\n\nTuna Steak Sandwiches with Relish of\n\nRoasted Salmon with Caramelized Onions and Carrots\n\nRoast Halibut with Chunky Roasted Pepper Sauce\n\nRoast Pork Tenderloin with Black Bean Salsa\n\nRosemary Chicken Thighs with Roast Potatoes\n\nRosemary-Parmesan Oven Fries\n\nS\n\nsalad(s)\n\nBeef, Thai-Style\n\nChicken and Napa Cabbage\n\nChicken, Fruity\n\nChicken, Greek-style\n\nChicken, Mexicali\n\nChicken, with Fennel, Arugula, and Blue Cheese\n\nChicken, with Raspberries and Goat Cheese\n\nCobb, Light and Luscious\n\nCorn, Black Bean, and Tomato\n\nCrab, in Stuffed Tomato\n\nCucumber-Orange\n\nEdamame, with Basil Vinaigrette\n\nLentil, Hearty, with Radicchio\n\nLentil, Warm, with Baked Salmon\n\nPotato-Tuna\n\nRoast Beef, with Creamy Horseradish Dressing\n\nSalmon\n\nShrimp, Key West-Style\n\nShrimp, Thai-Style, with Melon\n\nShrimp, with Fennel, Red Onion, and Orange\n\nSteak, Caesar-Style\n\nTabbouleh, with Shrimp\n\nTuna and White Bean\n\nTuna, Curried\n\nTuna-Potato\n\nTurkey, Carrot and Raisin\n\nTurkey-Couscous, Gingery\n\nTurkey, Tropical\n\nWhite Bean, with Feta Pita Crisps\n\nsalmon\n\nBaked, with Warm Lentil Salad\n\ncanned\n\nwith Corn, Black Bean, and Tomato Salad\n\nGrilled, with Quick Tomato Tapenade\n\npoached\n\nRoasted, with Caramelized Onions and Carrots\n\nSweet-and-Spicy, with Broccoli Slaw\n\nSalmon au Poivre with Watercress\n\nSalmon Patties with Chunky Tomato Relish\n\nSalmon Salad Sandwich\n\nSalmon with Corn, Black Bean, and Tomato Salad\n\nsalsa\n\nBlack Bean\n\nPeach\n\nTomato-Bean\n\nVerde, with Halibut\n\nVerde, with Vegetarian Burritos\n\nsandwich(es). _See also_ wrap(s)\n\nBLT, Best\n\nBurger, Beef and Black Bean\n\nCalifornia Health\n\nChicken and Roasted Pepper\n\nChicken and Tzatziki-Stuffed Pita\n\nChicken, Grilled with Jack Cheese\n\nHam and Swiss Panini\n\nPan Bagnat\n\nRoast Beef, Open-Faced\n\nSalmon, Dilled, with Caper Sauce\n\nSalmon Salad\n\nShrimp Salad, with Cilantro-Lime\n\nSloppy Joes, Low-and-Slow\n\nSteak, Garlicky, Open-Faced\n\nSteak, Pepper\n\nSteak, Philly Cheese\n\nTofu-Egg Salad\n\nTuna Steak with Roasted Pepper Relish\n\nTurkey Burger, Mediterranean\n\nTurkey, with Honey-Mustard\n\nsardines, canned\n\nsauce(s)\n\nArrabbiata\n\nBarbecue\n\nBolognese, Quick\n\nCoconut-Curry\n\nCucumber Raita\n\nFresh Tomato\n\nHoney-Mustard\n\nLemon-Yogurt\n\nMushroom-Wine\n\nPink Apple-Raspberry\n\nRoasted Pepper\n\nTomato-Oregano\n\nTomato Tapenade\n\nTzatziki\n\nSaucy Pan-Roasted Pork Chops with Ziti\n\nscallops\n\nBlackened, with Lemon-Caper Mayonnaise\n\nSesame\n\nseafood. _See also_ _specific types_\n\ncanned\n\nhealthy types of\n\nSliders, Crunchy\n\nStew, Caribbean\n\nTacos\n\nSesame Noodles with Green Vegetables\n\nSesame Scallops\n\nshopping tips\n\nshrimp\n\nChowder\n\npeeled\n\nSalad, Cilantro-Lime\n\nSalad, Key West-Style\n\nSalad with Fennel, Red Onion, and Orange\n\nTabbouleh with\n\nThai, ix\n\nShrimp and Spaghetti Arrabbiata\n\nShrimp Chowder with Dill\n\nShrimp with Cherry Tomatoes and Feta\n\nside dishes, quick\n\nButtered Broccoli with Cilantro and Lime\n\nHerbed Parmesan-Garlic Pasta\n\nKale and Apple Salad\n\nLemony Spinach and Avocado Salad\n\nMinted Green Beans with Pine Nuts\n\nPolenta with Goat Cheese and Chives\n\nRosemary-Parmesan Oven Fries\n\nSimply Filling dishes\n\nslaw\n\nBroccoli\n\nChicken, Chinese\n\nSliced Steak with Crispy Polenta\n\nslow-cooker meals. _See also_ spend-some-time dishes\n\nBeef and Bean Soft Tacos\n\nBeef, Beet, and Cabbage Soup\n\nBeef Stew Proven\u00e7al\n\nBountiful Beef Stew\n\nBraised Chicken in Riesling\n\nCaribbean Seafood Stew\n\nChicken and Vegetable Curry\n\nChicken and Vegetable Tagine\n\nChuck Wagon-Style Turkey Chili\n\nEasy Chicken Gumbo\n\nFirecracker Turkey Chili\n\nGarlicky Braised Turkey Breast\n\nLamb and Vegetable Stew\n\nLow-and-Slow Sloppy Joes\n\nOnion Soup with Herbed Cheese Toasts\n\nPork Marrakesh\n\nShrimp Chowder with Dill\n\nVegetable Minestrone with Pasta\n\nVegetarian Burritos with Salsa Verde\n\nSmoked Turkey, Carrot, and Raisin Salad\n\nSmoky Pumpkin Seeds\n\nSmoky Vegetarian Chili\n\nsmoothies\/shakes\n\nPeanut Butter Blast\n\nPineapple Crush\n\nSoy-Blueberry Breakfast Shake\n\nStrawberry Colada\n\nsnacks, 15-minute\n\nChili-Spiced Popcorn\n\nCottage Cheese and Sun-Dried Tomato Dip\n\nDried Cranberry-Popcorn Mix\n\nHoneydew-Strawberry Soup\n\nMixed Melon with Honeyed Ricotta\n\nOpen-Faced Roast Beef Sandwich Bites\n\nPineapple Crush Smoothies\n\nStrawberry Colada Cooler\n\nTurkey and Roasted Pepper Lettuce Wraps\n\nVanilla Yogurt Sundae\n\nsnacks, 20-minute\n\nBananas Foster\n\nBlack Bean-Tomatillo Dip\n\nBrown Sugar Plums\n\nChunky Guacamole\n\nCrispy Green Plantains\n\nMicrowave Apple-Pear Crisp\n\nRed Pepper and Sun-Dried Tomato Dip\n\nSpicy Cereal and Pretzel Snack Mix\n\nSun-Dried Tomato Hummus\n\nsnacks, 30-minute\n\nBaked Cheesy Nachos\n\nBlack and White Muffin Bites\n\nBlueberries with Whipped Ricotta and Balsamic Syrup\n\nEdamame Dip\n\nFrozen Vanilla Yogurt with Sugared Shredded Wheat\n\nMushroom, Scallion, and Cheddar Quesadillas\n\nOven-Roasted Peaches with Raspberries and Sorbet\n\nPizza Margherita\n\nRicotta, Bacon, and Spinach Pizza\n\nSmoky Pumpkin Seeds\n\nsnacks, Simply Filling\n\nsodium intake\n\nsorbet\n\nRaspberry-Orange\n\nsoup(s). _See also_ chili; stew(s)\n\nBeef, Beet, and Cabbage\n\nBeef-Vegetable\n\nBlack Bean, with Rice\n\nbutternut squash\n\nChickpea\n\nChili, Smoky Vegetarian\n\nChowder, Clam and Corn\n\nChowder, Hearty Corn\n\nChowder, Manhattan\n\nChowder, Shrimp, with Dill\n\nCremini Mushroom, Tomato, and Rice\n\nGumbo, Southern Vegetable\n\nHam and Navy Bean Confetti\n\nHoneydew-Strawberry\n\nLentil and Sausage\n\nNoodle, with Asian-Style Pork and Mushroom\n\nOnion, with Herbed Cheese Toasts\n\nPotato-Watercress\n\nstore-bought\n\nTomato, Creamy\n\nVegetable Minestrone, with Pasta\n\nWinter Squash, with Lime Cream\n\nSouthern Vegetable Gumbo\n\nSouthwestern-Style Huevos Rancheros\n\nSoy-Blueberry Breakfast Shake\n\nSpaghetti with Fresh Tomato Sauce and Meatballs\n\nSpaghetti with Quick Bolognese Sauce\n\nSpanish Frittata\n\nspend-some-time dishes. _See also_ slow-cooker meals\n\nApricot-Mustard Glazed Pork Roast\n\nBaked Stuffed Potatoes with Ham and Cheese\n\nBaked Ziti with Summer Squash\n\nBeef-Barley Stew with Roasted Vegetables\n\nBeef-Vegetable Soup\n\nBest-Ever Country Captain\n\nCacciatore-Style Chicken and Vegetables\n\nChicken and Rice with Artichoke Hearts\n\nChicken and Vegetable Ragu with Herbed Dumplings\n\nChicken with Mushrooms and White Wine\n\nCitrus-Marinated Roast Pork\n\nCuban-Style Shredded Beef and Rice\n\nEasy Chicken Florentine with Spaghetti\n\nLentil and Sausage Soup\n\nPork and Bean Adobo Chili\n\nProven\u00e7al-Style Vegetable-Chickpea Stew\n\nRoasted Leg of Lamb\n\nRosemary Chicken Thighs with Roast Potatoes\n\nSpaghetti with Fresh Tomato Sauce and Meatballs\n\nStuffed Butterflied Leg of Lamb\n\nSpice-Glazed Cherry Bundt Cake\n\nSpice-Roasted Pears with Yogurt\n\nSpicy Cereal and Pretzel Snack Mix\n\nspinach\n\nGreek Pita Pizzas with Feta and\n\nSalad with Avocado and Lemony\n\nthawing tips for\n\nWrap with Avocado and Feta\n\nSpinach-Feta Scramble\n\nSteak Fajitas\n\nstew(s). _See also_ soup(s)\n\nBeef-Barley, with Roasted Vegetables\n\nBeef, Bountiful\n\nBeef Proven\u00e7al\n\nLamb and Vegetable\n\nSeafood, Caribbean\n\nVegetable-Chickpea, Proven\u00e7al-Style\n\nStir-Fried Beef with Asparagus\n\nstir-fry(ies)\n\nChicken Teriyaki and Snow Pea\n\nPork and Mushroom\n\nSteak, with Ginger and Broccoli\n\nTofu and Four-Vegetable\n\nStrawberry Colada Cooler\n\nStrawberry-Honeydew Soup\n\nStuffed Butterflied Leg of Lamb\n\nSucanat\n\nSummer Squash Stuffed with Beef and Olives\n\nSummer Squash with Baked Ziti\n\nSun-Dried Tomato Hummus\n\nSuperfast Barbecued Chicken\n\nSweet-and-Spicy Salmon with Broccoli Slaw\n\nsweets\/desserts-minute\n\nDried Cranberry-Popcorn Mix\n\nHoneydew-Strawberry Soup\n\nMixed Melon with Honeyed Ricotta\n\nPineapple Crush Smoothies\n\nStrawberry Colada Cooler\n\nVanilla Yogurt Sundae\n\nsweets\/desserts-minute\n\nBananas Foster\n\nBrown Sugar Plums\n\nMicrowave Apple-Pear Crisp\n\nsweets\/desserts-minute\n\nBlack and White Muffin Bites\n\nBlueberries with Whipped Ricotta and Balsamic Syrup\n\nFrozen Vanilla Yogurt with Sugared Shredded Wheat\n\nOven-Roasted Peaches with Raspberries and Sorbet\n\nsweets\/desserts, bonus\n\nApricot and Toasted Almond Galette\n\nBanana-Walnut Bread\n\nBrown Rice-Banana Pudding\n\nCarrot-Apple Cupcakes with Cream Cheese Frosting\n\nChocolate-Cherry Brownies\n\nChunky Pink Apple-Raspberry Sauce\n\nFrozen Strawberry-Maple Yogurt\n\nLemon Souffl\u00e9s\n\nMixed Berry Shortcakes\n\nOrange Flan with Macerated Oranges\n\nPeach-Blueberry Crostatas\n\nPumpkin-Cranberry Bread Puddings\n\nPumpkin Pie Muffins\n\nRaspberry-Orange Sorbet\n\nRoasted Pears with Balsamic Glaze\n\nSpice-Glazed Cherry Bundt Cake\n\nTriple Berry Summer Pudding\n\nWarm Spice-Baked Apples\n\nWhite Wine-Poached Pears\n\nWhole Grain and Fruit Oatmeal Cookies\n\nsweets\/desserts, Simply Filling\n\nSwiss cheese\n\nSyrup, Balsamic\n\nT\n\nTabbouleh with Shrimp\n\ntacos\n\nBeef and Bean, Soft\n\nCalifornia Fish\n\ntemperature, food\n\nTeriyaki Chicken and Snow Pea Stir-Fry\n\nTeriyaki-Glazed Tofu and Vegetable Kebabs\n\nThai Shrimp and Melon Salad\n\nThai-Style Beef Salad\n\nTilapia with Tomato and Feta\n\ntimesaving tips\n\ncanned foods and\n\nfor food add-ins\n\nfor food preparation\n\norganization-based\n\nfor shopping\n\nfor side dishes\n\nutensils and\n\ntofu\n\nFour-Vegetable Stir-Fry with\n\nKebabs, with Vegetables and Teriyaki-Glazed\n\nPitas Stuffed with Egg Salad and\n\ntomato(es)\n\ncanned\n\nChicken Picadillo with\n\nCrab Salad-Stuffed\n\nDip, Red Pepper and Sun-Dried\n\nFettuccine with Goat Cheese, Arugula, and\n\nFrittata with Peas, Mushroom, and Cherry\n\nOmelette with Bell Pepper and Sun-Dried\n\nRelish, with Salmon Patties\n\nSalad with Corn, Black Bean, and\n\nSalsa, with Bean\n\nSauce, Fresh\n\nSauce, with Oregano\n\nShrimp with Feta and Cherry\n\nSoup, Creamy\n\nsoup, store-bought\n\nSoup with Cremini Mushroom, Rice, and\n\nStuffed with Crab Salad\n\nSun-Dried, in Hummus\n\nTapenade, with Salmon\n\nTilapia with Feta and\n\nTriple Berry Summer Pudding\n\nTropical Turkey Salad\n\ntuna\n\ncanned\n\non Pan Bagnat\n\nSalad, Curried\n\nSalad, with Potato\n\nSalad, with White Bean\n\nSteak Sandwiches, with Roasted Pepper Relish\n\nSteaks, with Avocado-Orange Relish\n\nturkey\n\nBreast, Garlicky Braised\n\nBurgers, Mediterranean\n\nCarrot and Raisin Salad with Smoked\n\nChili, Chuck Wagon-Style\n\nChili, Firecracker\n\ncooking temperature for\n\nCouscous Salad with Gingery-\n\nCutlets\n\nmeatballs\n\nSalad, Tropical\n\nSandwiches, Honey-Mustard\n\nSquash Stew with African-Spiced\n\nWraps\n\nTurkey and Roasted Pepper Lettuce Wraps\n\nTurkey Cutlets Milanese\n\nTurkey Cutlets with Mushroom-Wine Sauce\n\nTurkey Cutlets with Orange Sauce\n\nTurkey Wraps with Lemon-Yogurt Sauce\n\nU\n\nU.S. Dietary Guidelines for Americans\n\nV\n\nVanilla Yogurt Sundae\n\nvegetable(s)\n\nBurritos\n\ncanned\n\nChicken, Cacciatore-Style, with\n\nChili, Smoky\n\nCurry with Chicken and\n\nFettuccine with Chicken and\n\nfrozen\n\nGumbo\n\nKebabs, with Teriyaki-Glazed Tofu\n\nmicrowaved\n\nMinestrone\n\nPaella, Chunky\n\nRagu with Chicken and Herbed Dumplings\n\nRoasted, with Beef-Barley Stew\n\nSesame Noodles with Green\n\nSteak and\n\nStew, Proven\u00e7al-Style, with Chickpea and\n\nStew, with Lamb\n\nStir-Fry with Tofu and Four\n\nTagine with Chicken and\n\nVegetable Fried Rice\n\nVegetable Minestrone with Pasta\n\nVegetarian Burritos with Salsa Verde\n\nVeggie Breakfast Burrito\n\nW\n\nWaffles with Blueberries and Maple Cream\n\nWarm Lentil Salad with Baked Salmon\n\nWarm Spice-Baked Apples\n\nweighing\/measuring tips. _See also_ timesaving tips\n\nWeight Watchers\n\ndigital apps for\n\nGood Health Guidelines by\n\n**_PointsPlus_** values in\n\nSimply Filling technique in\n\nweb site for\n\nWhite Bean and Tuna Salad\n\nWhite Bean Puttanesca Linguine\n\nWhite Bean Salad with Feta-Pita Crisps\n\nWhite Wine-Poached Pears\n\nWhole Grain and Fruit Oatmeal Cookies\n\nwhole grains. _See_ grains, whole\n\nWild Blueberry and Cornmeal Pancakes\n\nWinter Squash Soup with Lime Cream\n\nwrap(s). _See also_ sandwich(es)\n\nAvocado, Spinach, and Feta\n\nBeef, Cuban-Style, Lettuce\n\nDuck Roll-Up, Asian-Style\n\nTurkey and Roasted Pepper Lettuce\n\nTurkey Tostada, Quick\n\nTurkey, with Lemon-Yogurt Sauce\n\nY\n\nyogurt\n\nFrozen, Strawberry-Maple\n\nFrozen, with Sugared Shredded Wheat\n\nSauce of Lemon and\n\nSpice-Roasted Pears with\n\nSundae\n\nVanilla\nNote: Many recipes in this book were previously released in the _Momentum Cookbook_ and _Pantry to Plate,_ both Weight Watchers meeting room cookbooks.\n\nWEIGHT WATCHERS COOK IT FAST. Copyright \u00a9 2014 by Weight Watchers International, Inc. All rights reserved. Printed in the United States of America. For information, address St. Martin's Press, 175 Fifth Avenue, New York, N.Y. 10010.\n\nPasta Salad with Apple and Chicken and Grilled Flank Steak with Tomato-Fennel Salad\n\nwww.stmartins.com\n\nEditorial and art produced by W\/W Twentyfirst Corp., 675 Avenue of the Americas, New York, NY 10010.\n\nWEIGHT WATCHERS is a trademark of Weight Watchers International, Inc. Printed in the USA\n\nThe Library of Congress Cataloging-in-Publication Data is available upon request.\n\nISBN 978-1-250-05295-7 (trade paperback)  \nISBN 978-1-4668-5481-9 (e-book)\n\neBooks may be purchased for business or promotional use. For information on bulk purchases, please contact Macmillan Corporate and Premium Sales Department by writing to MacmillanSpecialMarkets@macmillan.com.\n\nFirst Edition: August 2014\n\n10 9 8 7 6 5 4 3 2 1\n\n# Contents\n\n  1. Cover\n  2. Title Page\n  3. Copyright Notice\n  4. About Weight Watchers International, Inc.\n  5. Contents\n  6. A Quick Note\n  7. Weight Watchers and the Simply Filling Technique\n    1. 44 Recipes That Work with the Simply Filling Technique\n  8. About Our Recipes\n  9. 15 Minute Meals\n    1. 15 Minute Breakfasts\n    2. 15 Minute Lunches\n    3. Buy Some Time\n    4. 15 Minute Dinners\n    5. 15 Minute Snacks and Sweets\n    6. Organize Your Kitchen for Speed\n  10. 20 Minute Meals\n    1. 20 Minute Breakfasts\n    2. 20 Minute Lunches\n    3. 9 Rules for Shortcut Cooking\n    4. 20 Minute Dinners\n    5. Got 5 Minutes?\n    6. 10 Essential Kitchen Time-Savers\n    7. 20 Minute Snacks and Sweets\n  11. 30 Minute Meals\n    1. 30 Minute Breakfasts\n    2. 30 Minute Lunches\n    3. Express Shopping\n    4. 30 Minute Dinners\n    5. You Can Make It Quick\n    6. 7 Superfast Sides\n    7. 30 Minute Snacks and Sweets\n  12. Bonus-On the Weekend\n    1. Spend Some Time\n    2. Time Well Spent\n    3. Slow Cookers Save Time\n    4. Something Sweet\n    5. Life's Too Short to Make...\n  13. Recipes by PointsPlus value\n  14. Index\n  15. Copyright\n\n## Guide\n\n  1. Cover\n  2. Copyright\n  3. Contents\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzsjrd b/data_all_eng_slimpj/shuffled/split2/finalzzsjrd
new file mode 100644
index 0000000000000000000000000000000000000000..bc33dd31841ba271f5cab56ecb442bf6d4ed51ec
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzsjrd
@@ -0,0 +1,5 @@
+{"text":"#\n\n#\n\nhaute enfance\n\nCollection dirig\u00e9e\n\npar Colline Faure-Poir\u00e9e\n\n#\n\nMichel Chaillou\n\nL'hypoth\u00e8se de l'ombre\n\n# Table des mati\u00e8res\n\nCouverture\n\nCollection\n\nTitre\n\nD\u00e9dicace\n\nExergue\n\nChapitre 1\n\nChapitre 2\n\nChapitre 3\n\nChapitre 4\n\nChapitre 5\n\nChapitre 6\n\nChapitre 7\n\nChapitre 8\n\nChapitre 9\n\nChapitre 10\n\nChapitre 11\n\nChapitre 12\n\nChapitre 13\n\nChapitre 14\n\nChapitre 15\n\nChapitre 16\n\nChapitre 17\n\nChapitre 18\n\nChapitre 19\n\nChapitre 20\n\nChapitre 21\n\nChapitre 22\n\nChapitre 23\n\nChapitre 24\n\nChapitre 25\n\nChapitre 26\n\nChapitre 27\n\nChapitre 28\n\nChapitre 29\n\nChapitre 30\n\nChapitre 31\n\nCopyright\n\nPr\u00e9sentation\n\nDu m\u00eame auteur\n\nAchev\u00e9 de num\u00e9riser\n\n#\n\n_Pour Annette et Jean-Claude_\n\n#\n\nJe suis un homme qui pense \u00e0 autre chose.\n\nVICTOR HUGO\n\n#\n\nIl sentit que cela venait d'une mani\u00e8re ou d'une autre mais que cela venait. Il \u00e9tait assis. Combien de fois ne s'\u00e9tait-il pas assis devant cette fen\u00eatre ? Le jour avait perdu une partie de sa clart\u00e9 et lui \u00e9tait d\u00e9sormais trop las pour r\u00e9agir, aller voir de pr\u00e8s si la v\u00e9g\u00e9tation l'apostrophait aussi durement qu'aux premi\u00e8res heures. N'\u00e9tait-il pas un corps \u00e9tranger ? Quelqu'un d'ailleurs ? Pourquoi cette haute demeure l'accepterait-elle illico sans autres pourparlers pr\u00e9alables avec ses ombres ? On ne s'introduit pas comme cela chez quelqu'un, surtout en son absence. Le pr\u00e9ambule du hall ne suffit pas et ce geste qu'il voulut pourtant familier pour repousser au moins un volet. Cela chancelait. Indubitablement cela chancelait. La table au pied de l'escalier magistral avait perdu toute son estime. Il n'aimait plus y appuyer les coudes. Et puis le jardin, quelle pourriture ! On lui avait pourtant dit... Mais \u00e9tait-il encore apte \u00e0 entendre ce qu'on dit ? Certes cela passera, l'orage passe bien et les \u00e9clairs. N\u00e9anmoins, il peinait \u00e0 conserver son calme, des restes de tumulte l'habitaient. D'accord, il n'aurait pas d\u00fb agir de cette fa\u00e7on, mais la fa\u00e7on comment la reprendre, l'effacer m\u00eame, alors qu'elle a eu lieu, que tout s'est produit ? Existe-t-il une gomme du d\u00e9lictueux, qui vous rend \u00e0 nouveau page blanche, malgr\u00e9 le noir des marges ?\n\nIl se leva. Trop peu de mots. Il disposait de trop peu de mots. Et ceux qu'il poss\u00e9dait avaient perdu toute leur raison. Il sortit, besoin de respirer l'air plus libre du dehors, osa s'aventurer subrepticement jusqu'au portail d'entr\u00e9e. Apr\u00e8s s'engageaient la route, la lande et tout ce satan\u00e9 pays qui remontait comme on remonte son col par crainte du froid. Il frissonna. Avait-il gard\u00e9 ses yeux d'enfant ? Cette moisissure des alentours et la mythologie qu'elle engendre, la mousse d\u00e9j\u00e0 verte de peur d'avoir \u00e0 \u00e9touffer des pas. \u00c0 moins de t\u00e9l\u00e9phoner ? Mais le t\u00e9l\u00e9phone risquait de sonner dans le vide. Outre que sa propre voix s'\u00e9tranglerait \u00e0 entendre celle esp\u00e9r\u00e9e au bout du fil. Et si tout cela n'\u00e9tait que du simple vague \u00e0 l'\u00e2me ?\n\nLes arbres n'\u00e9taient manifestement plus ses potes et la piscine vid\u00e9e de son eau derri\u00e8re sa grille, qu'un f\u00e9roce trou ciment\u00e9, une caverne \u00e0 l'air libre qui attendait son ogre. Et l'ogre ? son fant\u00f4me en nage qu'on recherchait sans nul doute sur toutes les routes de France. Du moins se l'imaginait-il ! Mais c'est vrai qu'il se sentait en sueur comme apr\u00e8s un cross un peu soutenu. Curieuse course, se rem\u00e9morait-il : un train, un car, une flop\u00e9e de lieux \u00e0 peine nommables o\u00f9 pourtant l'on descend, d'autres d'o\u00f9 vite l'on s'enl\u00e8ve, un carrefour anonyme, l'amorce d'une venelle, un village, parfois une c\u00f4te assez rude, des portions de pav\u00e9s o\u00f9 le pas sonne clair. Mais o\u00f9 se situait donc ce mur gris qui n'en finissait plus avant le portail massif d\u00e9fendu de cha\u00eenes o\u00f9 un chien aboya sur son passage ? C'\u00e9tait hier ou avant, il cherchait alors les d\u00e9serts, les endroits d\u00e9shabit\u00e9s ou bien les meutes de passagers en transit devant les gares, tous ces gens SNCF encrass\u00e9s par l'id\u00e9e du voyage qui n'ont m\u00eame plus le temps de pr\u00eater attention au v\u00f4tre. Ce qu'il souhaitait, se fondre : n'\u00eatre plus qu'un dos qui s'\u00e9loigne sur un quai.\n\nIl retourna vers la cuisine, ficha une bougie dans une carafe. Il aurait pr\u00e9f\u00e9r\u00e9 allumer pleins phares la salle \u00e0 manger, le salon, les chambres, que tous les recoins de la haute demeure brillent en m\u00eame temps, qu'il ne reste plus comme obscurit\u00e9 que la sienne \u00e0 laquelle il fallait d\u00e9sormais qu'il s'accoutume en plus de celle quotidienne du soir. H\u00e9las, pas de meilleure torche pour signaler sa pr\u00e9sence.\n\nS'il pouvait seulement se faire une omelette, surtout occuper ses mains et puis d\u00e9boucher une bouteille. La villa \u00ab modern style \u00bb disposait dans ses tr\u00e9fonds d'une richissime cave \u00e0 vous d\u00e9salt\u00e9rer jusqu'\u00e0 la fin des temps. Oui, mais le vin l'affaiblirait. Il existerait au bout de plusieurs verres diminu\u00e9 du tiers, ou du quart, peut-\u00eatre m\u00eame de la moiti\u00e9 ? Or, il lui fallait rester vigilant. Il \u00e9couta. Une part de lui \u00e9coutait. Car pour l'autre part, il n'osait y songer, la surveiller. Son programme \u00e9tait simple : s'\u00e9tourdir de petits gestes, s'absorber par exemple dans le fait de battre des \u0153ufs, mais il n'en figurait plus au frigidaire depuis belle lurette, ou alors ouvrir une bo\u00eete de conserve, fricoter quelque chose \u00e0 griller avec la po\u00eale. Surtout \u00e9viter la m\u00e9moire, cette folle qui distribue des r\u00f4les. Or, justement comme il en avait trop tenu un !\n\n\u00ab Plus jamais \u00e7a ! \u00bb prof\u00e9ra-t-il soudain bouche mauvaise devant la glace. Un noble miroir \u00e0 la belle eau tranquille dans le salon encadr\u00e9 de dorures, juste au-dessus du riche canap\u00e9, \u00e0 deux pas du piano, meuble laqu\u00e9 dont h\u00e9las il n'aurait su jouer. Il promena machinalement ses doigts sur les touches. Peut-\u00eatre que le mieux, tant que le jour tanguait aux fen\u00eatres, e\u00fbt \u00e9t\u00e9 de rester vivre au-dehors, de ne rentrer qu'\u00e0 la nuit pour manger ou dormir (se couvrir d'un toit renfor\u00e7ait trop ses obsessions), ou alors pour se d\u00e9gourdir l'\u00e2me d'aller \u00e0 pied au centre du patelin, l\u00e0 o\u00f9 hier le sauvage taxi le d\u00e9posa, mais si, rappelez-vous, pr\u00e8s de la chapelle, cette pauvrette, et le tas de ruines antiques qui l'avoisine, de nobles pierres vaguement celtiques ou romaines dont le temps se d\u00e9lesta et qui s'accumulent depuis des si\u00e8cles entre les platanes d'une place. Et lui-m\u00eame n'\u00e9tait-il pas en ruine ? Ne fallait-il pas qu'il se reconstruise ? Y mettre une \u00e9nergie comparable \u00e0 celle de cet inlassable oc\u00e9an plut\u00f4t hagard, juge-t-il, sur ce coin de c\u00f4te, tant perp\u00e9tuellement il vocif\u00e8re, vous n'entendez pas ? Impossible de ne pas l'entendre, il \u00e9cume de rage contre les rochers, ces abrupts d\u00e9mons qui barrent l'entr\u00e9e du port.\n\nOui, \u00e0 la r\u00e9flexion, il pourrait peut-\u00eatre profitant du cr\u00e9puscule, ce compagnon noir, se m\u00ealer aux groupes de touristes, se glisser ni vu ni connu dans quelque boutique, acheter du pain, de la viande, des fruits par exemple. Que risquait-il ? Il n'a quand m\u00eame pas sa photo dans les journaux. Oui, il pourrait se rendre en ville, \u00e0 Saint-Pierre par exemple, le bourg o\u00f9 s'amus\u00e8rent tant ses jeunes ann\u00e9es. Une corv\u00e9e d'une heure, davantage sans doute avec sa jambe ? Mais il y aurait des choses allum\u00e9es, des passants d\u00e9celables, un h\u00f4tel, le caf\u00e9 d'en face, la sympathie.\n\nIl tira les rideaux, la nuit approchait trop. La nuit approche plus vite \u00e0 la campagne. Une terrasse courait autour de la maison avant la pelouse et ce fou de fourr\u00e9 inextricable. Plusieurs all\u00e9es y divaguaient. Qui pourrait se douter qu'il niche dans ce repli obscur ? Le taxi l'avait l\u00e2ch\u00e9 en plein centre au milieu d'un tas de maisons. Il entendait encore la voiture d\u00e9raper en repartant. Et comme lui aussi il d\u00e9rapa... Un jour d\u00e9j\u00e0, et des heures qui se cognent aux heures.\n\nIl r\u00e9fl\u00e9chissait. Oui, comment son chauffeur e\u00fbt-il pu retrouver la villa qu'il occupe ? L'homme plut\u00f4t rude avait eu beau le fixer souvent au r\u00e9troviseur ! En quoi sa personne assez d\u00e9licate d'allure m\u00e9ritait-elle un tel examen ? Il lui laissa d'ailleurs un bon pourboire pour endormir sa m\u00e9fiance. Car par ici elle vous suit partout \u00e0 la fa\u00e7on d'une chienne errante, se rappela-t-il. Une m\u00e9fiance devant tout \u00e9tranger entretenue par ce pays de cl\u00f4tures et de haies. Que n'enfermeraient-elles pas ?\n\nIl passa un pull. Si on y r\u00e9fl\u00e9chissait tout cela n'avait en r\u00e9alit\u00e9 ni queue ni t\u00eate. Il \u00e9pelait toujours convenablement son nom, le visage dans la glace \u00e9tait toujours le sien, plus du tout celui dans la tourbe laiss\u00e9 l\u00e0-bas. Il soupira, plus qu'un soupir, une plainte de l'\u00e2me.\n\nL'id\u00e9e lui vint de monter observer les alentours par l'une des quatre fen\u00eatres des combles. Mais qu'y avait-il donc d'observable ? La rue un peu simplette tournait toujours \u00e0 gauche, du c\u00f4t\u00e9 de la conserverie. En face, dans une villa biscornue, g\u00eetait un couple de vieillards \u00e0 la vue basse occup\u00e9s par leur jardinet, et plus haut c'\u00e9tait bitume et solitude, de rares derni\u00e8res maisons et aussit\u00f4t la route nue oublieuse du flux et du reflux fon\u00e7ant \u00e0 toute vitesse vers l'int\u00e9rieur des terres.\n\nCette campagne l'\u00e9touffait. Pourtant ne serait-ce pas elle la gu\u00e9risseuse, capable d'introduire du calme dans ses veines ? La mare au fond du parc scintillait et cette vol\u00e9e de peupliers paraissait \u00e9trangement y accourir comme pour s'y baigner. Qu'ils en profitent les bougres, la glace viendra bient\u00f4t et sa cousine moins coupante, la neige. \u00c0 elles deux, elles effaceront, sculpteront son remords, lui donneront un autre profil. Il pressentait en cette heure grise les flocons encore retenus dans les r\u00e9silles de l'air pr\u00eats \u00e0 tomber, s'\u00e9parpiller, recouvrir, dissimuler. Manteau sur le corps de la terre prompt \u00e0 effacer les rides, traits de douleur.\n\nRien dans le pass\u00e9 ne se produisit, tout cela n'est qu'un leurre, une formidable appr\u00e9hension de l'esprit qui se retourne sur lui-m\u00eame et qui veut garder pr\u00e9sente dans l'id\u00e9e l'ombre de ce qu'il laissa, abandonna. \u00c0 l'entr\u00e9e de l'hiver, des subtils frimas, la page de la vie s'offrira \u00e0 nouveau vierge. Il pourra repartir, changer d'alphabet comme on change d'habits, trouver une autre destination \u00e0 ses phrases, fournir \u00e0 son destin un emploi plus heureux. Qui soup\u00e7onnera jamais ? Certes la villa alors d\u00e9sert\u00e9e parlera de lui, mais seulement une ou deux semaines, le temps pour elle de se r\u00e9habituer au silence, de fortifier sa solitude, de retrouver \u00e0 nouveau son quant-\u00e0-soi. Il l'avait tellement mise dans tous ses \u00e9tats \u00e0 bouger ainsi d'une pi\u00e8ce \u00e0 l'autre, \u00e0 croire, s'imaginer que le moindre r\u00e9duit parlait de sa personne d\u00e8s qu'il en sortait. Il a toujours eu l'amiti\u00e9 des choses. Depuis sa naissance, il les sent presque comme ses complices. D'ailleurs comment cette aust\u00e8re b\u00e2tisse de deux \u00e9tages avec ses combles vendus aux oiseaux e\u00fbt-elle pu t\u00e9moigner ? La poussi\u00e8re brouill\u00e9e sans cesse par ses all\u00e9es et venues ne pourrait livrer \u00e0 son heure aucune pointure acceptable. Il d\u00e9sirait tellement se fondre, appartenir au ramage du monde.\n\nIl fouilla dans un tiroir \u00e0 la recherche d'une pr\u00e9sence, qu'il ne reste plus seul dans son infortune actuelle. Un simple mot lui aurait suffi, un bout de phrase griffonn\u00e9 \u00e0 la h\u00e2te, du n'importe quoi sur le n'importe quoi des heures, qu'il entende enfin une voix m\u00eame sur du papier pli\u00e9 en quatre. Or il savait cet ami aujourd'hui \u00e0 l'\u00e9tranger volontiers graphomane \u00e0 ses moments perdus. Et des moments de cette esp\u00e8ce, l'homme, un ancien danseur, en dispersait une multitude depuis que retir\u00e9 \u00e0 jamais des corps de ballet il avait choisi de ne plus accompagner aussi vivement son ombre. N'\u00e9tait-ce pas cet ami qui lui avait avou\u00e9 un jour tenir une mani\u00e8re de journal, de comptabilit\u00e9 de ses propres instants ? \u00c0 moins que ce ne soit son \u00e9pouse, la discr\u00e8te Solange, qui se laisse toujours pr\u00e9c\u00e9der par les pas d'autrui, qui n'ose devant vous franchir un seuil ou \u00e9puiser une all\u00e9e, qui avait fini par lui rapporter la chose, lui expliquant avec malice que \u00ab c'\u00e9tait mine de rien pour son toujours jeune mari une autre fa\u00e7on de danser que de voltiger ainsi \u00e0 la pointe de son crayon ! \u00bb.\n\nIl sourit. N'occupait-il pas, les sachant pour quelques mois au Nouveau Monde, leur maison ? Peu de chances qu'ils aient la vue assez per\u00e7ante pour l'apercevoir depuis la Virginie. Mais aussi pourquoi lors de son dernier s\u00e9jour dans cette villa en leur compagnie, pourquoi lui avoir montr\u00e9 \u00e0 lui, il est vrai presque de leur famille, o\u00f9 ils cachaient leur clef, dans le creux d'une souche d'arbre qui apparemment ne songe plus \u00e0 pousser, \u00e0 agrandir sa silhouette. N'\u00e9tait-ce pas leur fa\u00e7on \u00e0 eux de lui sugg\u00e9rer d'en profiter durant leur absence outre-Atlantique ? \u00ab Si tu as besoin de changer d'air \u00bb, avaient-ils d'ailleurs cru bon d'ajouter avec leur inimitable ton mi-figue, mi-raisin. \u00ab Pourquoi pas \u00bb, avait-il alors r\u00e9pliqu\u00e9 ! Il ne croyait pas si bien dire.\n\nAussi, quand la n\u00e9cessit\u00e9 de dispara\u00eetre s'imposa \u00e0 lui, il y songea tout de suite. Et puis avec cet oc\u00e9an mouvement\u00e9 qui ne cesse de r\u00e9pandre ses h\u00e2bleries le long de cette c\u00f4te dite sauvage, les gens du cru ont bien d'autres chats \u00e0 fouetter. Qui aura d'ailleurs jamais l'id\u00e9e de venir l'interpeller l\u00e0, au milieu de tous ces meubles \u00e9trangers dont il apprenait peu \u00e0 peu les usages ?\n\nIl vida le tiroir sur le lit. L'ombre \u00e0 la fen\u00eatre s'aggravait. Bient\u00f4t la nuit et son pelage \u00e0 faire peur. Il n'\u00e9parpilla que des colifichets, pauvres d\u00e9tails d'une vie absente, factures, lettres assommantes de sentiments divers. Hier avec le taxi, il aurait pu quand m\u00eame se montrer plus causant, se livrer par exemple \u00e0 un simple commerce des l\u00e8vres, parler de tout et de rien, de rien surtout, des nuances du temps qui change, de ce sacr\u00e9 automne. Non qu'il regrett\u00e2t de s'\u00eatre mur\u00e9 dans un trop long silence, mais les mots ne lui venaient pas, influence des bois taciturnes qu'il traversait, des coups de volant trop brusques du chauffeur, puis ensuite de l'inertie de la route suivie, droite, droite, sans l'aventure de nombreux virages.\n\nDe toute fa\u00e7on, interrog\u00e9, ce type que pourrait-il dire le concernant ? Oui un maintien un peu \u00e9mu, des traits sur le visage pr\u00eats \u00e0 s'enfuir. Non il ne pourra pas dire cela. On voit bien aux yeux gris du bonhomme que ce n'est pas son vocabulaire. Mais pourquoi alors le fixer tant au r\u00e9troviseur ? Il ne s'est jamais r\u00e9pandu dans les m\u00e9dias, a toujours voulu cacher sa pr\u00e9sence au monde. Taille moyenne, oui le type peut r\u00e9pondre taille moyenne, cheveux boucl\u00e9s ch\u00e2tains, un brun blond v\u00eatu \u00e0 l'artiste, costume violet de haut en bas, chaussures de ville. Ah, il boite ! claudique plut\u00f4t corrigea-t-il, suite \u00e0 une chute, et pas pour longtemps.\n\nIl se rass\u00e9r\u00e9na. Non il n'avait pas laiss\u00e9 grand-chose de lui dans cette voiture ! Peut-\u00eatre \u00e0 l'arriv\u00e9e quand il \u00e9prouva le besoin de serrer la main osseuse du type. Besoin qu'il ne s'expliquait toujours pas, lui qui n'appartenait plus d\u00e9sormais \u00e0 l'humanit\u00e9 vraisemblable. Apr\u00e8s, il ne lui restait plus qu'\u00e0 se perdre dans une rue, une autre, gagner le rond d'une place avant de secr\u00e8tement obliquer, d\u00e9passer la poissonneuse conserverie, enfin atteindre les derni\u00e8res b\u00e2tisses de ce village marin, juste avant le trouble des champs.\n\nMais \u00e0 quoi bon remuer tous ces faits et gestes, c'\u00e9tait hier, et sa crainte que ladite clef ne soit plus dans la souche. Par bonheur, elle s'y trouvait cette innocente et apr\u00e8s ce ne fut plus qu'un jeu, forcer la r\u00e9sistance de la porte de la cuisine qui s'en plaignit un peu, humer l'air du dedans, courir jusqu'aux lits du premier \u00e9tage pour se r\u00e9jouir de la pr\u00e9sence des draps, s'assurer du bon fonctionnement des rideaux m\u00e9talliques afin qu'ils livrent passage \u00e0 cette pauvre clart\u00e9 de son intrusion. Plein de journaux datant au moins d'un demi-si\u00e8cle \u00e9paississaient comme en ao\u00fbt dernier la table encaustiqu\u00e9e du salon assortis de multiples magazines style revues de dentiste.\n\nIl avait \u00e9cout\u00e9. Rien, que les bruits habituels d'une maison laiss\u00e9e \u00e0 elle-m\u00eame, soupir des boiseries, plancher qui craque. Dans la niche du chien, il n'y avait plus que le souvenir du labrador et son odeur yeux suppliants et langue pendante.\n\nUn d\u00e9fi de ses amis que de cacher leur clef dans un arbre avec l'espoir sans doute qu'elle finisse, \u00e0 dormir ainsi dans la mousse, par devenir v\u00e9g\u00e9tale et ouvre aussi bien le dedans que le dehors. Une id\u00e9e folle \u00e0 eux. Mais ils n'en manquaient pas d'id\u00e9es de cette sorte, que ce d\u00e9mon de Jean-Marc si virtuose utilisait souvent dans ses ronds de jambe dans l'entier de sa chor\u00e9graphie lunaire. Que n'e\u00fbt-il pas dans\u00e9 ? Son chemin d'incertitudes actuelles par exemple. En un \u00e9clair, il crut apercevoir cet ami parapher \u00e0 sa place de quelques gestes irr\u00e9els son d\u00e9sarroi jusqu'\u00e0 la chemin\u00e9e.\n\nIl se rappelait l'\u00e9t\u00e9 dernier, quand ce couple l'avait h\u00e9berg\u00e9 une bonne huitaine, lui et ses probl\u00e8mes (il en tra\u00eene de pleines valises), eux lui \u00e9voquant \u00e0 la moindre occasion leur prochain s\u00e9jour aux \u00ab States \u00bb comme ils consentaient un rien snobs \u00e0 pr\u00e9ciser du bout des l\u00e8vres, glorifiant sans qu'on les en prie l'exotique demeure qui, selon eux, d\u00e9j\u00e0 les esp\u00e9rait mise \u00e0 leur disposition \u00e0 Charlottesville par l'universit\u00e9 de Virginie qui ne fait pas les choses \u00e0 moiti\u00e9, et o\u00f9 lui enseignerait la danse et elle la litt\u00e9rature durant un bon semestre. Oui, avant leur retour in\u00e9luctable dans notre Ancien Monde, dans leur villa coutumi\u00e8re, cette b\u00e2tisse m\u00eame que lui, l'intrus, supposait effarouch\u00e9e par sa propre pr\u00e9sence. Oui, il a toujours accord\u00e9 du sentiment aux choses. Comment les portes ne se plaindraient-elles pas d'\u00eatre toujours repouss\u00e9es ? Et les fen\u00eatres si criantes de v\u00e9rit\u00e9 quand on les ouvre ? s'interroge-t-il souvent \u00e0 sa fa\u00e7on biblique. La v\u00e9rit\u00e9 ? Cette pauvresse qui d'apr\u00e8s lui demeure toujours en for\u00eat et s'oppose \u00e0 ce qu'on la sorte du noir des bois. Ce n'est pas une fille des clairi\u00e8res, ass\u00e8ne-t-il, que la v\u00e9rit\u00e9 ! En v\u00e9rit\u00e9, le mot lui ab\u00eemait la bouche.\n\nIl se demanda bizarrement si parmi les arbres du jardin croissaient aussi des trembles, ces peupliers si \u00e9motifs qui fr\u00e9missent au moindre coup d'air. Et comme lui en \u00e9tait devenu un ! Il veut dire une mani\u00e8re d'\u00eatre, de se tenir bouscul\u00e9 par on ne sait quoi parmi les vivants, brouillage confus dont son image dans la glace a parfois honte. Encore heureux que ce miroir accepte aujourd'hui de le r\u00e9fl\u00e9chir, ose-t-il encore penser. Pas d'\u0153ufs dans le frigidaire, ni rien de consommable, il lui fallait de toute \u00e9vidence faire son march\u00e9. Du saucisson peut-\u00eatre pour se mettre la vie en bouche, des radis ? Il r\u00e9p\u00e9tait comme un somnambule la liste n\u00e9cessaire \u00e0 glisser dans le sac qui bient\u00f4t allongerait son bras, du poisson, oui, du poisson, un vivace tout juste mordu par la mar\u00e9e du jour !\n\nAllait-il pleuvoir ? L'averse le laverait-elle de tout soup\u00e7on ? Il emprunta un des parapluies du vestibule. Devant la conserverie, une dame avanc\u00e9e en \u00e2ge parlait chien \u00e0 son chien. Il passa vite. Sur le port, la mer qui se d\u00e9montait secouait comme une d\u00e9mente les bateaux \u00e0 l'ancre. Acqu\u00e9rir des pommes de terre ne fut qu'un jeu. Pour les concombres et les radis, l'\u00e9pici\u00e8re s'\u00e9ternisait en propos larges qui englobaient le monde entier, l'actualit\u00e9, la politique, les guerres lointaines, la violence actuelle, que plus personne ne respectait personne, Dieu sait quoi encore ? Il n'en voyait pas le bout et acquies\u00e7ait par de vagues monosyllabes au risque de passer pour un monsieur pas tr\u00e8s causant. Qu'acheta-t-il ensuite \u00e0 cette triomphante comm\u00e8re qui s'ennuyait ferme parmi ses l\u00e9gumes ? Elle s'\u00e9tait mise \u00e0 \u00e9num\u00e9rer une tripot\u00e9e de faits-divers, le prenait m\u00eame \u00e0 t\u00e9moin. Il craignit qu'emport\u00e9e par sa faconde elle n'en vienne \u00e0 \u00e9voquer le sien. Aussi la quitta-t-il assez brusquement, elle et ses tomates d'un rouge sang. Que fit-il alors dans cette abrupte localit\u00e9 adoss\u00e9e \u00e0 sa butte de terre soulev\u00e9e ? \u00c0 un moment, on perd un peu sa silhouette dans le lacis des rues assez marchandes o\u00f9 n'importe qui devient vite quelqu'un d'autre. Il semble avoir taquin\u00e9 une brasserie. \u00c0 moins que le client qui boit au comptoir vo\u00fbt\u00e9 sur son demi de bi\u00e8re d\u00e9j\u00e0 ne f\u00fbt plus lui ? La nuit s'approchait pour soulager les humains de leurs ombres. Combien de temps pourrait-il demeurer dans cet endroit ? L'\u00e9t\u00e9 dernier, il avait pris bien soin, m\u00fb par on ne sait quelle prescience des \u00e9v\u00e9nements \u00e0 venir, de se mettre en \u00e9vidence. Que les rues aujourd'hui ne s'\u00e9tonnent plus de sa pr\u00e9sence et ne le traitent pas comme un \u00e9tranger. Devant la mairie, il s'accorda un instant de r\u00e9flexion.\n\n#\n\nIl sentait que cela lui revenait : des images, des phrases, une r\u00e9plique, le simulacre d'une sc\u00e8ne ancienne avec la neige au-dehors qui glisse dans la nuit sa copie blanche. L'affaire lui occupait trop l'esprit. Un simple d\u00e9tail suffisait, \u00e0 l'\u00e9tage par exemple le papier peint d\u00e9chir\u00e9 par endroits dans une chambre au d\u00e9bouch\u00e9 de l'escalier et qui lui rappelait... Comment mieux dire ? l'armoire aussi, ouverte sur un d\u00e9ballage de linge intime et qui forc\u00e9ment lui faisait penser... Les serviettes surtout d'analogue couleur et ces deux idiotes de chaises aupr\u00e8s du lit qui semblaient assister les derniers soupirs de quelqu'un. Aussi d\u00e9cida-t-il de coucher en face, dans la pi\u00e8ce de droite, pour que ses id\u00e9es, elles aussi, le redeviennent, il voulait dire droites, dans ce simple r\u00e9duit bon enfant \u00e0 toucher la salle de bains o\u00f9 se lavent tous les malheurs du monde. Il prit d'ailleurs une douche pour laver le sien, avec l'espoir qu'entrer ainsi en \u00e9bullition avec lui-m\u00eame le sortirait au moins pour la nuit de son marasme.\n\nUn coucher de soleil assez sanglant contaminait en effet les vitres. Il redescendit au rez-de-chauss\u00e9e. Sur la table embarrass\u00e9e du hall, un des multiples magazines \u00ab people \u00bb \u00e9voquait un mariage princier et sur une dizaine d'autres des cr\u00e9atures d\u00e9nud\u00e9es s'\u00e9tiraient en maillot de plage. Il songea \u00e0 son infortune des jours derniers, en \u00e9grena m\u00e9lancolique un peu le sable. Apr\u00e8s tout, l'essentiel \u00e9tait de se faire oublier, qu'on perde \u00e0 jamais ses traces, \u00ab il suffit d'\u00e9viter le mouill\u00e9 \u00bb osa-t-il se marmonner, car dans le \u00ab sec \u00bb tous les pieds se confondent, se m\u00ealent. Il se souriait \u00e0 vide devant la glace.\n\nLa t\u00e9l\u00e9vision hors d'usage n'offrait qu'un \u00e9cran mort, mais la radio d'un mod\u00e8le peu courant fonctionnait bien. Il baissa le son pour les informations. \u00c0 quoi bon savoir ce qu'il savait ? Encore heureux qu'aucun journaliste ne s'avis\u00e2t de donner des nouvelles de cette chose qui le contraignait d\u00e9sormais \u00e0 vivre retir\u00e9 sur un point quelconque du territoire dans l'ombre d'une villa d\u00e9sert\u00e9e. Il entendait l'oc\u00e9an vague apr\u00e8s vague battre sa coulpe au bout de l'avenue. Se sentait-il coupable lui aussi avec tous ces gens qu'il naufragea ?\n\nLe premier soir, il se fit des \u0153ufs au plat, il retrouvait l'app\u00e9tit, bon signe. Comment supporter la solitude ? Il ne savait comment s'y prendre avec cette dame. Il para\u00eet qu'\u00e0 vivre seul on \u00ab s'habite \u00bb mieux, qu'alors nos pens\u00e9es faute d'interlocuteur se parlent davantage. Et il se parlait du haut en bas de l'escalier, un d\u00e9val\u00e9 de marches peu loquaces en marbre. Il enflait la voix par moments pour entendre si l'\u00e9cho renvoyait autre chose que lui- m\u00eame. N'importe quoi d'ailleurs, son double pr\u00e9nom : Charles-Andr\u00e9, pas son nom qui l'aurait trop d\u00e9nud\u00e9. Il subissait d\u00e9j\u00e0 assez l'interrogatoire des meubles, des hauts miroirs. Quoi ? C'\u00e9tait lui, ce p\u00e2le personnage aux cheveux boucl\u00e9s disant encore sa jeunesse ? Dans la cuisine, il s'\u00e9prouvait plut\u00f4t gai, mais le salon assez t\u00e9n\u00e9breux le r\u00e9exp\u00e9diait derechef \u00e0 son affliction. Comment s'en d\u00e9barrasser ? L'eau au robinet allait-elle comme avant se satisfaire seulement de r\u00e9jouir ses mains et le savon polisson lui \u00e9chapper sans arri\u00e8re-pens\u00e9e pour glisser malicieusement dans l'\u00e9vier ? Il s'y essaya \u00e0 plusieurs reprises. Fonctionner ainsi par petits gestes, pour oublier le grand qui l'avait jet\u00e9 aux enfers. \u00c0 ce prix, il retrouverait \u00e0 coup s\u00fbr sa tranquillit\u00e9.\n\nLe pays o\u00f9 il se cachait, un m\u00e9lange de Bretagne et de quelque chose d'inexprim\u00e9 qu'inlassable l'oc\u00e9an pourtant r\u00e9citait, le baignait d'une sorte de qui\u00e9tude. Il ne s'\u00e9tait rien pass\u00e9, les mots lui manquaient pour dire qu'il ne s'\u00e9tait rien pass\u00e9. Mais alors pourquoi s'enfuir ? D\u00e9sirer \u00e0 tout prix se coiffer d'une autre identit\u00e9 ? Maquiller ses papiers ? Cette vieille photo de lui rep\u00each\u00e9e Dieu seul sait o\u00f9 ? Son nez, oui son nez, sa bouche, oui sa bouche, mais l'expression g\u00e9n\u00e9rale du visage qu'un nuage visiblement obscurcissait ? Un nuage qui avait \u00e9t\u00e9 en son temps travers\u00e9 par un \u00e9clair dont la foudre l'\u00e9tonnait encore.\n\nIl sortit sur le perron pour accueillir la nuit ! Demain, il emprunterait l'un des costumes de Jean-Marc, rep\u00e9r\u00e9 dans la penderie. De dos et pour un \u0153il qui ne s'attarde pas, on pourrait en effet presque le prendre pour son ami danseur, taille, corpulence identiques, bien que sa chor\u00e9graphie ne soit certes pas la m\u00eame, l\u00e0 o\u00f9 l'autre touche \u00e0 peine terre, lui se r\u00e9v\u00e8le plus amant de la pesanteur, avec sa d\u00e9marche un peu gauche.\n\nIl s'\u00e9tait dit, dans les chambres retir\u00e9es de son \u00eatre il s'\u00e9tait dit, vouloir rester ici une bonne huitaine, le temps que les braises de son affaire ne rougeoient plus, qu'il n'en reste somme toute que les cendres, sans rien qui puisse en r\u00e9activer l'ardeur. Le mot \u00ab affaire \u00bb d'ailleurs convenait-il \u00e0 cette vague dispute, des phrases plus des phrases, la flamme d'un juron, \u00e0 cette aventure de porte \u00e0 l'\u00e9tage qu'on n'ose d'abord repousser pour que la lumi\u00e8re au moins du lugubre couloir \u00e9claircisse l'objet d'une crainte qu'on esp\u00e8re infond\u00e9e. Il en avait tellement connu dans ses jeunes ann\u00e9es des heures de cette sorte, heureusement vite d\u00e9gringol\u00e9es de l'horloge, de ces moments en suspens o\u00f9 l'on se demande si sur le cadran o\u00f9 soudain tout s'attarde, se d\u00e9r\u00e8gle, la petite aiguille ne joue pas trop les grandes.\n\nCharles-Andr\u00e9, qui apr\u00e8s le d\u00e9c\u00e8s pr\u00e9matur\u00e9 de sa jeune m\u00e8re avait trouv\u00e9 refuge aupr\u00e8s de sa tante d\u00e9sormais charg\u00e9e de son \u00e9ducation, revoyait ses dix douze ans aux c\u00f4t\u00e9s de cette femme si folle de J\u00e9sus (son randonneur pr\u00e9f\u00e9r\u00e9, pr\u00e9tendait-elle avec humour), lequel en effet guidait le moindre de ses pas. Une cr\u00e9ature des \u00e9glises avec une voix de sacristie, \u00e0 peine audible, une pi\u00e9t\u00e9 qui sentait encore l'encens de l'office d'o\u00f9 elle paraissait perp\u00e9tuellement sortir. \u00c9tait-ce \u00e0 cause de cette presque Marie-Madeleine qu'il avait agi ainsi ?\n\nLe hameau \u00e0 l'entr\u00e9e de la presqu'\u00eele, une vingtaine de chaumi\u00e8res trapues qui s'\u00e9tiraient entre deux rues, deux saign\u00e9es \u00e0 ciel ouvert, suscitait l'admiration des rares touristes qui osaient s'y aventurer, \u00e9merveill\u00e9s de tant de pittoresque et qu'on puisse vivre si paisible devant une telle \u00e9paisseur de vagues et un horizon qui se d\u00e9montait d'un rien. Au bar de la Jet\u00e9e, ils en venaient presque \u00e0 redouter l'\u00e9cume de leurs bi\u00e8res. Du moins, c'\u00e9tait d\u00e9j\u00e0 l'opinion saugrenue de Charles-Andr\u00e9. F\u00fbt-ce \u00e0 cette sombre humeur sal\u00e9e qu'il emprunta son geste inattendu ? Qui aurait pu croire \u00e0 le voir si discret de maintien qu'il puisse s'animer de cette fa\u00e7on ? Que sa prime enfance e\u00fbt \u00e9t\u00e9 tr\u00e8s t\u00f4t confront\u00e9e \u00e0 une si folle fr\u00e9n\u00e9sie marine ne suffisait quand m\u00eame pas \u00e0 justifier... Oui, on lui reprochait d\u00e9j\u00e0 son langage trop \u00e9lectrique, mais de l\u00e0 \u00e0 imaginer un tel court-circuit et l'obscurit\u00e9 qui en r\u00e9sulta... Oui, tout gamin ses mots interloquaient, sa m\u00e8re cherchant d'o\u00f9 ils pouvaient provenir, de quelle terre aux ar\u00eates plus tranch\u00e9es ? \u00ab Mais qui t'a appris \u00e7a ? \u00bb, elle s'apeurait, certainement pas elle, pauvre robe noire perdue dans le souci emm\u00eal\u00e9 de ses jours. Ils habitaient alors face au large, rien d'\u00e9troit chez eux, \u00e0 cause des fen\u00eatres, trois impassibles ouvertes dans le granit qu'aucune temp\u00eate ne paraissait effrayer. Et puis il y avait la lande, cette d\u00e9mone d'herbe rase aupr\u00e8s de qui il courait jusqu'\u00e0 l'\u00e9cole, l\u00e0-bas, une baraque h\u00e9rit\u00e9e de la derni\u00e8re guerre \u00e0 l'autre bout de la presqu'\u00eele. \u00ab Votre fils a beaucoup de vocabulaire \u00bb, s'\u00e9tonnait l'instituteur qui le classa tr\u00e8s vite premier en r\u00e9daction.\n\n\u00ab J'apprends tout des mouettes, r\u00e9torquait-il parfois \u00e0 sa m\u00e8re en guise d'explication, tu as entendu comme elles causent bien ? \u00bb Il prenait \u00e0 t\u00e9moin leur jacassement criard et leur vol ailes d\u00e9ploy\u00e9es dans le p\u00e2le soleil, en nourrissait d'ailleurs certaines en douce. Qu'il pleuve, pour lui c'\u00e9tait sa tristesse d'enfant qui inondait les vitres, qu'il se produise une \u00e9claircie et il s'en \u00e9clairait jusqu'au soir, malgr\u00e9 le ciel redevenu sombre et la nuit qui s'approchait dans l'haleine des loups. \u00ab Quel loup ? r\u00e9clamait alors sa m\u00e8re, arr\u00eate de faire le b\u00eate ! \u00bb\n\nIl sourit \u00e0 cette \u00e9vocation, se tailla une tartine dans un quignon de pain rassis, l'assortit d'un bout de saucisson. Cette nuit, il dormirait \u00e0 l'\u00e9tage, rideaux m\u00e9talliques non baiss\u00e9s pour de son lit apercevoir la cime agit\u00e9e des trembles, ses fr\u00e8res en v\u00e9g\u00e9tation qu'un simple coup de vent d\u00e9concerte. Et comme une assez forte brise s'\u00e9tait lev\u00e9e, il les apercevait en pleines palabres. \u00c0 l'image de lui-m\u00eame qui peinait \u00e0 retrouver l'enti\u00e8re possession de son esprit. Le moindre bruit l'alarmait, que le plancher craque et il en sursautait, qu'une porte d'elle-m\u00eame s'entreb\u00e2ille, et il lui supposait aussit\u00f4t des myst\u00e8res, le sien ne restait-il pas \u00e0 d\u00e9chiffrer ?\n\nLundi se passa ainsi, partag\u00e9 entre ses soliloques et des livres tir\u00e9s des \u00e9tag\u00e8res de la biblioth\u00e8que d\u00e9fra\u00eechie qui couvrait plusieurs murs. Ses amis affectionnaient manifestement la vulgate \u00e0 l'eau de rose, les m\u00e9los sur papier bible ou a contrario le roman panique. Mais la sienne lui suffisait amplement pour demeurer longtemps entre leurs pages. Impossible de s'installer dans la qui\u00e9tude d'une lecture suivie, le jour se d\u00e9chirait trop \u00e0 la fen\u00eatre et c'\u00e9tait encore lui qui tenait le couteau. Bizarrement, dans le salon, il surprit au-dessus du piano tout un concile de livres religieux vou\u00e9s \u00e0 la vie du Christ et peupl\u00e9s d'images du d\u00e9sert rocailleux de la Jud\u00e9e et d'autres terres \u00e9vang\u00e9liques qu'il se promit une autre fois de mieux parcourir.\n\n\u00ab Quand je serai plus en jambes \u00bb, se dit-il. Au fait, il ne boitait plus, son genou droit avait retrouv\u00e9 toute son \u00e9lasticit\u00e9 d'antan, un vrai miracle.\n\n#\n\nIl s'\u00e9tait interdit certaines pi\u00e8ces. \u00c0 quoi bon pousser des portes, ouvrir de nouvelles fen\u00eatres, le premier \u00e9tage lui suffisait et la tonitruante salle de bains. Fut-ce la matin\u00e9e o\u00f9 il rep\u00e9ra un indice dans un quotidien local ? Il se revoyait devant le caf\u00e9-tabac-maison de la presse et cette phrase apparemment anodine sous une photo en bas de page. Il avait achet\u00e9 le journal pour mieux le scruter ligne \u00e0 ligne \u00e0 la villa, voir si ce n'\u00e9tait pas plut\u00f4t son esprit malade qui ajoutait du sens \u00e0 la l\u00e9gende de ce clich\u00e9 d'une vieille demeure \u00e9mergeant \u00e9tonn\u00e9e du si\u00e8cle, en haut d'une c\u00f4te qu'il s'imaginait reconna\u00eetre :\n\n\u00ab Si toutes les pentes gravissent la mienne \u00bb, se morig\u00e9na-t-il. Mais quand m\u00eame le long mur gris assez ruin\u00e9 et la grille, et ce qu'on soup\u00e7onnait d'inhabituel derri\u00e8re. Qui sait, peut-\u00eatre sur la gauche en entrant une grange peupl\u00e9e d'outils \u00e0 faire fructifier la terre, l'amorce d'une all\u00e9e autour de l'\u00e9difice en brique rouge, et le parc immense et jaune \u00e0 cause de cette fin octobre pourrie de feuilles mortes. D'un peu, il e\u00fbt presque entendu les voix si ch\u00e8res, revu cette maudite serre, cause de tous ses maux actuels.\n\nIl plia le journal. Ne s'occuper que des titres, ne plus entrer dans les d\u00e9tails. Une femme lui souriait assise \u00e0 la terrasse d'une brasserie proche. Le devait-il \u00e0 son air un peu interloqu\u00e9 ? Il froissa son journal, l'enfouit furtivement dans son sac. \u00c9tait-il le jouet d'une ressemblance ? Rien ne ressemble plus \u00e0 une vieille maison qu'une vieille maison se rassura-t-il. Cette grille on peut l'ouvrir ailleurs et ce pressentiment de parc qui lui para\u00eet familier, sans nul doute un jeu d'ombres de n'importe o\u00f9 qu'attrapa le photographe.\n\nIl se rass\u00e9r\u00e9na. Pourquoi cette b\u00e2tisse qu'il fuyait tant l'aurait-elle aussi vite rattrap\u00e9 ? Cette feuille de chou ne donne que des nouvelles du coin, des p\u00eacheurs perdus en mer, pas de ceux \u00e0 son image perdus en terre.\n\nIl s'approuva muettement devant une vitrine, content de la formule qui h\u00e9las n'\u00e9tait que trop vraie ! Qui pourrait avoir jamais l'id\u00e9e de venir le rechercher dans ce patelin informe, \u00e0 peine plus haut que ses vagues ? Ici, il n'y a que l'oc\u00e9an qui interpelle, vous met \u00e9ventuellement la main au collet. N'\u00e9tait-il pas redevenu citoyen de son enfance ? ll aurait presque pu ressusciter ses \u00e9clats de rire d'\u00e9colier entre ces villages qui refusent de civiliser la lande. Toujours sa petite herbe (tondue par l'effroi d'un si grand voisinage \u00e9cumeux autour de la presqu'\u00eele) qui s'infiltre partout pour s'opposer \u00e0 l'extension des hameaux. Retourna-t-il dans le pays de ses primes ann\u00e9es pour s'inventer un nouveau pass\u00e9, repartir du bon pied sous un autre nom, mais lequel ? Il se vivait comme rescap\u00e9 d'un naufrage avec des traits, un visage d\u00e9form\u00e9 par les profondeurs. Plus Charles-Andr\u00e9 mais d\u00e9j\u00e0 Andr\u00e9-Charles, et pourquoi pas Luc ou Matthieu ? N'\u00e9taient-ce pas les pr\u00e9noms d'ap\u00f4tre dont la s\u0153ur de sa m\u00e8re, une biblique en mal d'enfant, parfois affublait ses dix douze ans ? Si seulement il avait pu se r\u00e9fugier aupr\u00e8s d'elle, profiter de ses conseils. Mais le temps l'avait aval\u00e9e une nuit dont aujourd'hui encore il se r\u00e9veillait \u00e0 peine. Il regrettait sa voix si pleine de jardins, le myst\u00e8re de ses exclamations. Elle vivait une vie \u00e9tonn\u00e9e. Pas d'autre homme aupr\u00e8s d'elle que J\u00e9sus avec qui elle marmonnait le dimanche dans les \u00e9glises. Une grande fille, des yeux bleu clair toujours en mouvement, guettant le facteur, alors que personne ne lui \u00e9crivait, sauf...\n\nIl soupira. Ses journ\u00e9es, il allait les construire de cette fa\u00e7on : lever tardif, petit d\u00e9jeuner au bar de la Jet\u00e9e, coup d'\u0153il \u00e0 la presse, commissions \u00e0 Saint-Pierre, quelques kilom\u00e8tres pour se d\u00e9gourdir les jambes, d\u00e9jeuner \u00e0 la villa, amorce de sieste, puis promenade \u00e0 travers la lande livr\u00e9e alors \u00e0 ses conflits int\u00e9rieurs, enfin retour, souper, et dodo. Dans huit jours, il ne sera plus l\u00e0 o\u00f9 on le prend pour un vague parent de ses amis partis provisoirement aux \u00c9tats-Unis. L'argent ne lui manquait pas, et il pourra toujours en retirer \u00e0 la banque une fois tout tumulte apais\u00e9. L'avenir qu'il d\u00e9chiffrait dans son miroir lui paraissait soudain plus supportable. Pourquoi alors songer \u00e0 ce samedi d'il y a \u00e0 peine un peu plus d'un mois, sur cette place d'un autre \u00e2ge ? \u00e0 ce pauvre matin du march\u00e9 aux puces de Nantes \u00e9clair\u00e9 par les restes brouill\u00e9s d'un \u00e9t\u00e9 qui en cette fin septembre ne brillait que pour la forme avec un soleil d'occasion pr\u00eat lui aussi pour la brocante ? Il se tenait l\u00e0, dans ce vieux troquet au nom illisible, retenu par l'ardeur d'un jus de fruits, alors que la plupart autour de lui, malgr\u00e9 l'heure matutinale, en \u00e9taient d\u00e9j\u00e0 au muscadet, causaient cet idiome de fonds de verres, de raclures, de rin\u00e7ures diverses si familier \u00e0 ses oreilles, quand soudain...\n\n\u00c0 quoi bon aller plus loin, vouloir se rem\u00e9morer cette sc\u00e8ne entre deux vins o\u00f9 tout s'engagea ? N'avait-il pas \u00e9t\u00e9 abus\u00e9 par une vague ressemblance ? Le voisinage des antiquailles expliquait-il les ressorts fatigu\u00e9s de cet incident, bon pour la ferraille ? La rouille de tous ces objets d\u00e9pareill\u00e9s mis en vente sur cette place l'avait-elle gagn\u00e9 ? Bien s\u00fbr qu'il s'\u00e9tait alors m\u00e9pris, tromp\u00e9 par une illusoire analogie de traits, de mani\u00e8res, car comment la personne \u00e0 laquelle il pensait alors aurait-elle pu revenir de sa mort et s'accouder \u00e0 ses c\u00f4t\u00e9s \u00e0 sa table ?\n\n\u00ab Comment pouvez-vous ? \u00bb s'\u00e9tait-il offusqu\u00e9. La femme, plut\u00f4t incertaine d'allure, s'\u00e9tait relev\u00e9e perdue en mille excuses.\n\nIl rentrait chez lui avec ces images d\u00e9risoires en t\u00eate. Apr\u00e8s tout il pouvait dire \u00ab chez lui \u00bb, car c'\u00e9tait provisoirement sa maison, sa niche, cette villa Rose qu'il occupait depuis \u00e0 peine deux jours avec d\u00e9j\u00e0 tous ces instants froiss\u00e9s dans les fauteuils, les chaises, ce lit qu'il submergeait de ses songes. \u00c0 la cuisine, c'\u00e9tait bien pour un vivant qu'il mijotait des plats. En lui, le sang circulait librement, il n'en avait pas sur les mains. Pourquoi s'\u00e9tait-il donc mis en t\u00eate ?... Bien s\u00fbr, \u00e0 Nantes il y aura bient\u00f4t une semaine, les circonstances qui rappelaient celles d'autrefois : cette neige pr\u00e9coce (\u00f4 combien inhabituelle en cette mi-automne), l'heure matinale, le d\u00e9sert blanc de l'instant, le parc autour pressant de ses ombres qui se l\u00e8vent t\u00f4t, la vaste demeure familiale alors inhabit\u00e9e, qui aurait pu r\u00e9sister \u00e0 une telle analogie ? Et ce foutu \u00e9tang qui se montre toujours pr\u00eat \u00e0 refl\u00e9ter, \u00e0 t\u00e9moigner.\n\nIl chassa d'un coup de pied un malheureux caillou, respira un bon coup ! Il remontait l'avenue en pleine possession de lui-m\u00eame et d'un pas alerte, l'oc\u00e9an d'ailleurs plus chien fid\u00e8le s'\u00e9tait calm\u00e9 avec ses vagues aujourd'hui toutes maintenues en laisse. \u00c0 une porte, un vieillard se montra qui lui fit un signe auquel poliment il r\u00e9pondit. En somme, en dehors de ce paquet d'anxi\u00e9t\u00e9s qu'il aurait bien aim\u00e9 renvoyer par la poste, si une telle poste e\u00fbt pu exister pour des choses de cette nature, il disposait d'un alibi confortable si par hasard on parvenait \u00e0 lui mettre la main dessus, aussi pourquoi tant s'angoisser ?\n\nIl repassait devant la conserverie, les rues qui changent vite de nom ont beau courir \u00e0 leur perte, lui ne courait pas \u00e0 la sienne. \u00c0 la porte de la villa Rose, il sonna, pour bien montrer \u00e0 cette b\u00e2tisse imperturbable qu'il n'\u00e9tait qu'un visiteur, qu'il ne comptait pas se couvrir de son toit plus d'une huitaine, que bient\u00f4t la clef allait retrouver sa cache originelle dans le tronc moussu. Le mettre ainsi dans le secret n'\u00e9tait-ce pas, de la part de ses amis, une fa\u00e7on bien \u00e0 eux de l'inciter \u00e0 en profiter ? Curieuse id\u00e9e d'ailleurs que de tenter ainsi le hasard, ce grand voleur !\n\nIl s'assit sur l'unique banc du jardin. Il \u00e9prouvait le besoin de respirer, de remettre un peu d'ordre dans ses id\u00e9es. Il r\u00eavassait, et quand il r\u00eavasse ses yeux vont plus loin que ce qu'ils regardent. Ainsi de ces gens d'autrefois qu'il croit parfois identifier dans le pr\u00e9sent le plus proche... Par exemple, la femme de la brocante de Nantes en septembre dans cet aberrant estaminet qui paraissait avoir adopt\u00e9 la tournure, l'\u00e9clat de sa d\u00e9funte tante ou ce type massif, entrevu un autre samedi de march\u00e9 aux puces, debout contre le comptoir qui lui rappelait il ne savait plus quel ogre de son enfance rue Marzelle ou ailleurs ? Ses mains fortes surtout qui papillonnaient autour de son visage, et cette voix rauque de fond de chopine, de rin\u00e7ure de verre, qu'il s'imaginait avoir d\u00e9j\u00e0 vu vid\u00e9e.\n\nIl ne sait pas pourquoi tant d'images disparates hantent son \u00eatre depuis toujours. C'est comme une mar\u00e9e charg\u00e9e d'algues \u00e0 certaines heures o\u00f9 il s'emp\u00eatre. Du pass\u00e9 qui remonte tout cru \u00e0 la faveur d'une phrase, d'un geste, d'une attitude. Vivrait-il encombr\u00e9 de fant\u00f4mes ? C'est tout juste si, \u00e0 table, il ne se retiendrait pas parfois d'ajouter des assiettes. On vit m\u00eal\u00e9 aux morts, pense-t-il. D'ailleurs cette histoire qu'il s'efforce d'oublier a-t-elle vraiment eu lieu comme il se l'imagine ? Certes, la haute demeure existe \u00e0 Nantes profan\u00e9e par son geste et il n'inventa pas la profusion v\u00e9g\u00e9tale autour et l'\u00e9tang o\u00f9 il jeta... \u00ab Moi qu'alors j'ai jet\u00e9 \u00bb, se r\u00e9p\u00e9tait-il. Cela expliquait-il son air depuis si noy\u00e9, ses pens\u00e9es si vaseuses ?\n\nLa villa de ses amis n'avait pas boug\u00e9 d'un pouce durant son absence. Il referma doucement la porte, crainte de la r\u00e9veiller de son long sommeil. Par la fen\u00eatre, les trembles du jardin, agit\u00e9s de leur folie coutumi\u00e8re, lui faisaient de grands signes. \u00c9tait-ce pour le faire souvenir ? Mais comment ces peupliers fous auraient-ils pu savoir ? Qu'une bande de leurs cong\u00e9n\u00e8res en furent t\u00e9moins n'impliquait pas forc\u00e9ment qu'eux aussi soient d\u00e9j\u00e0 au courant. Non, c'\u00e9tait leur gestuelle habituelle, le vent sans doute, une quelconque \u00e9motion de l'air !\n\nIl e\u00fbt \u00e9t\u00e9 bien incapable pr\u00e9sentement de s'exposer \u00e0 lui-m\u00eame les circonstances du drame, si drame il y eut ! Les faits \u00e9taient encore trop frais dans son esprit. Il ne disposait pas du recul n\u00e9cessaire. Il lui fallait attendre qu'ils vieillissent, ces faits, que ses mots encore \u00e9tonn\u00e9s d'un tel \u00e9v\u00e9nement d\u00e9raisonnent moins, qu'il retrouve enfin son parler tranquille de professeur de lettres et un certain d\u00e9tachement.\n\nIl \u00e9coutait. \u00c9coutait-il sa propre \u00e9coute ? Il allait et venait, passait d'une pi\u00e8ce \u00e0 l'autre, embarrass\u00e9 par sa personne, ne sachant \u00e0 quoi l'employer. La villa autour de lui \u00e9grenait son propre silence. Il finit par s'asseoir dans l'un des profonds fauteuils. Qu'il tende le cou et l'horloge murale aurait pu lui dire l'heure. Mais la sienne trop pleine de moments perdus quelle aiguille sur un cadran e\u00fbt pu l'indiquer ? Il se montrait plus riche en minutes et en secondes que la moindre pendule ! Aussi qu'on soit t\u00f4t le matin ou tard dans l'apr\u00e8s-midi importait peu, lui ne disposait plus que du m\u00eame \u00e9tat cr\u00e9pusculaire.\n\nS\u00fbr, il repartira dimanche, dans une semaine exactement. Il venait de s'y d\u00e9cider en allant vers la cuisine, la pi\u00e8ce la plus rassurante. Sans doute \u00e0 cause de sa table de bois blanc un peu simplette o\u00f9 l'on pose les coudes, de la vaisselle sale de la veille empil\u00e9e dans l'\u00e9vier. Certes, il y avait eu le coup de t\u00e9l\u00e9phone de tout \u00e0 l'heure. Qui pouvait bien appeler ? Il se d\u00e9menait dans la chambre du haut, le temps qu'il descende, la sonnerie s'arr\u00eata, restaient son interrogation planante au-dessus de la table \u00e9paisse surcharg\u00e9e de revues du hall et la p\u00e2leur de son image dans le miroir du salon. D'un peu, il aurait cru entendre sur la terrasse... Mais il n'y avait personne.\n\nIl avait beau essayer d'oublier, lui remontait \u00e0 l'esprit une nouvelle fois ce qui l'avait conduit ici. D'autres \u00e0 sa place n'auraient certes pas fait le m\u00eame choix. S'en \u00e9tait-il sorti d'ailleurs ? Quelle part de lui-m\u00eame l\u00e0-bas \u00e0 Nantes rue Marzelle grin\u00e7ait encore avec les portes, se froissait dans le lit d\u00e9fait ? Et cette voix avin\u00e9e qui hantait ses oreilles ? L'alcool et les verres qui se choquent n'expliquent pas tout. Dans la vaste demeure ancestrale qu'il visitait \u00e0 nouveau \u00e0 moiti\u00e9 endormi, sa grand-m\u00e8re d\u00e9licieusement vivante \u00e9tait descendue de son portrait. Sans doute r\u00eavait-il ? Car comment justifier qu'elle, d\u00e9c\u00e9d\u00e9e depuis des lustres et qu'il ne connut qu'en peinture, ait fait le voyage avec lui jusqu'\u00e0 la villa Rose, et se tienne l\u00e0, au-dehors mains fr\u00e9missantes, interpellant un vague butor qui s'adresse \u00e0 elle depuis les ombres en trop du jardin ?\n\n#\n\nPlus tard, il avisera. S'il avait choisi de se r\u00e9fugier dans la presqu'\u00eele de son enfance, n'\u00e9tait-ce pas pour se laver dans ses deux mers, noyer \u00e0 jamais dans les transports de l'\u00e9cume ce qu'il ne r\u00e9ussissait pas encore \u00e0 chasser de son \u00eatre ? Confier \u00e0 telle plage, ceci, \u00e0 telle autre, cela, ce terrible \u00ab cela \u00bb et ne plus y remettre les pieds, que les rochers tourment\u00e9s seuls en conservent le tourment, plus lisible \u00e0 mar\u00e9e basse. Lui vivra d\u00e9sormais \u00e0 mar\u00e9e haute. Le hasard avait bien fait qu'un couple de ses amis poss\u00e8de dans cette m\u00eame presqu'\u00eele une solitude. En avoir la clef, c'\u00e9tait en effet d\u00e9tenir celle du large qu'ouvraient les deux \u00e9tages de ses larges fen\u00eatres, acqu\u00e9rir un horizon. Et il en manquait tellement apr\u00e8s toutes ces petitesses ! N'\u00e9tait-il pas condamn\u00e9 depuis ces \u00e9v\u00e9nements \u00e0 l'\u00e9cho plus qu'aux voix qui le firent na\u00eetre ? Il avait eu beau refermer la b\u00e2tisse du drame, tirer des rideaux qu'il e\u00fbt souhait\u00e9 certes plus \u00e9pais, afin qu'aucun regard indiscret ne puisse jamais les percer, il n'en demeurait pas moins agit\u00e9 d'une folle inqui\u00e9tude. Que ce sombre d\u00e9sordre, cet odieux quiproquo de choses et de gens que de savants miroirs eurent presque honte de r\u00e9fl\u00e9chir reste cach\u00e9 aux yeux du monde. Qu'il en oublie presque l'existence.\n\nOui, vraiment, plus tard, beaucoup plus tard, il avisera, se murmurait-il. Et ce n'est pas cette bande de trembles assez voyous qui avaient eu l'audace, \u00e0 l'image des actuels peupliers de la villa Rose, de pousser leurs ramures \u00e0 toucher les baies vitr\u00e9es du premier \u00e9tage de l'aust\u00e8re demeure de la rue Marzelle, comme pour d\u00e9signer \u00e0 d'\u00e9ventuels enqu\u00eateurs le lieu m\u00eame du d\u00e9lit, qui pourraient t\u00e9moigner contre lui. Songe-t-on \u00e0 interroger les arbres ? \u00c0 entrer en pourparlers avec l'insidieuse r\u00e9sine ? se marmonnait-il avec insistance, une fa\u00e7on bien \u00e0 lui de tourner en d\u00e9rision ce qui l'oppresse le plus. Et il s'oppressait sans raison s'empressa-t-il aussit\u00f4t de penser, car en effet ce n'est pas le mur en ruine de la propri\u00e9t\u00e9 o\u00f9 tout apparemment d\u00e9buta par des r\u00e9flexions a priori insignifiantes, ni le b\u00e2timent des communs aux volets rabattus qui pourraient colporter quoi que ce soit, encore moins le si peu loquace \u00e9tang (bien qu'avec ce dernier si preste \u00e0 r\u00e9fl\u00e9chir n'importe quelle anomalie de ses bords...) ou le serviteur noir en veste rouge de la serre, un mannequin en bois ne parle pas !\n\nNon, \u00e0 y bien r\u00e9fl\u00e9chir, il faudra du temps avant qu'on s'\u00e9tonne dans le voisinage d'une grille perp\u00e9tuellement close, d'une absence d'all\u00e9es et venues autour de cette folie en brique. Il sera lui, alors, Dieu sait o\u00f9 ?\n\nIl respira plus fortement. Sans doute l'atmosph\u00e8re de cette pr\u00e9sente villa de ses amis \u00ab am\u00e9ricains \u00bb qu'il occupait ill\u00e9galement ? Apr\u00e8s en avoir quitt\u00e9 une si ch\u00e8re \u00e0 son c\u0153ur \u00e0 des centaines de kilom\u00e8tres, se retrouver par n\u00e9cessit\u00e9 dans le silence d'une autre demeure chargeait trop ses \u00e9paules.\n\nIl sortit sur la terrasse. On est lundi ou dimanche ? se demanda-t-il. Il ne savait plus \u00e0 quel jour attribuer cette m\u00eame clart\u00e9 p\u00e2le. Si seulement Jean-Marc et Solange avaient pu se tenir \u00e0 ses c\u00f4t\u00e9s, au lieu de baguenauder comme ils le font en Virginie, ils l'auraient aid\u00e9 \u00e0 combler ce vrai trou d'air qu'\u00e9tait devenue sa vie. Que penseraient- ils de son intrusion ? Mais aussi confier la clef \u00e0 un arbre moussu n'\u00e9tait-ce pas de leur part d\u00e9j\u00e0 inviter l'inconnu ? Et inconnu, il l'\u00e9tait d\u00e9sormais, y compris pour lui-m\u00eame !\n\nUne mani\u00e8re comme une autre de lui dire de profiter de leur absence ? \u00ab Si tu as besoin d'oxyg\u00e8ne \u00bb, avait m\u00eame cru bon semble-t-il d'ajouter Jean-Marc, une phrase de cette nature apr\u00e8s l'un de ses entrechats coutumiers. Car par moments, il ne peut s'emp\u00eacher de joindre le geste \u00e0 la parole, de prolonger par une volte ou deux ce qu'il vient d'\u00e9noncer. En Am\u00e9rique, se tient-il aussi en \u00e9quilibre aigu sur le bord du trottoir \u00e0 la grande stup\u00e9faction des passants ?\n\nCharles-Andr\u00e9 e\u00fbt bien aim\u00e9 se m\u00ealer \u00e0 ces citoyens des States, s'\u00e9tonner avec eux de ce \u00ab frenchie \u00bb capable \u00e0 ce point de barboter dans l'air. Il ignore la pesanteur, leur aurait-il alors expliqu\u00e9 dans son mauvais anglais. Tous ses pas sont r\u00e9gl\u00e9s par une musique que lui seul entend !\n\nIl choisit de descendre au village. Hier, au bruyant bar de la Jet\u00e9e, des p\u00eacheurs du coin discutaient \u00e0 plusieurs des agitations de la mer qu'ils jugeaient trop surmen\u00e9e pour la saison. \u00ab Apr\u00e8s tout on n'est qu'en novembre \u00bb, gueulait l'un, repris en ch\u0153ur par \u00ab Qu'est-ce que \u00e7a va \u00eatre en hiver, d'ici que les Japonais nous exp\u00e9dient... Comment tu dis ? \u00bb.\n\nLeur \u00ab tsunami \u00bb, avait eu envie de leur souffler Charles-Andr\u00e9 attabl\u00e9 devant sa bi\u00e8re ! Au pays, on le prenait pour l'un des parents des propri\u00e9taires de la villa, un cousin, avait-il laiss\u00e9 entendre. Personne autour de lui n'\u00e9tait assez \u00e2g\u00e9 pour reconna\u00eetre le gamin qui courait tant la lande. D'ailleurs de ces ann\u00e9es soixante-dix, il ne restait rien sur son visage d\u00e9sormais un peu plus affirmatif, un regard qui flotte peut-\u00eatre, et encore ! Toujours autant de cheveux boucl\u00e9s mais le nez s'\u00e9tait \u00e9paissi qu'autrefois sa tante jugeait mutin. Le chalet de son enfance avec sa d\u00e9funte m\u00e8re et o\u00f9 ensuite encore tout m\u00f4me veill\u00e9 par sa tante il passait ses vacances \u00e9tait toujours debout \u00e0 quelques kilom\u00e8tres. Comment s'appelait le voisin d\u00e9j\u00e0 ? Messager, c'est \u00e7a l'abb\u00e9 Messager, un pr\u00eatre \u00e0 la retraite, plus soucieux de fleurs que de pr\u00eaches. Un mur de parpaings au fond de son jardin lui cachait la vue du large. Mais le large il devait l'avoir en lui, le disaient assez ses yeux clairs quand il les relevait de son br\u00e9viaire.\n\nQue penserait-il de cette affaire ? Sa Bible trouverait-elle la solution ? \u00c0 quelle page conviendrait-il que lui, Charles-Andr\u00e9, l'ouvre pour se rass\u00e9r\u00e9ner entre ses saintes marges ? L'obligeant eccl\u00e9siastique si attentif \u00e0 ses jeunes interrogations n'\u00e9tait plus l\u00e0 pour lui r\u00e9pondre. D'ailleurs, il ne savait plus ses pri\u00e8res d'enfant de ch\u0153ur. Aucune ne remontait depuis les tr\u00e9fonds de son \u00eatre pour gagner ses l\u00e8vres. \u00c9tait-il coupable ou pas ? Seul le J\u00e9sus de sa tante et de l'abb\u00e9 e\u00fbt pu le lui dire. \u00c0 la villa Rose, il avait rep\u00e9r\u00e9 dans le coin du piano, coinc\u00e9 entre deux missels \u00e0 tranche dor\u00e9e, un vieux bouquin tout jauni illustr\u00e9 de photos assez vieillottes retra\u00e7ant les premiers pas du Christ en Galil\u00e9e, en Jud\u00e9e, qu'il feuilleta faute de mieux toute une matin\u00e9e. Mais l'image assez pel\u00e9e du mont Hermon qui atteindrait les trois mille m\u00e8tres ou celle du lac de Tib\u00e9riade ne le gu\u00e9rissaient gu\u00e8re de ses anxi\u00e9t\u00e9s. Il e\u00fbt fallu \u00e0 ses c\u00f4t\u00e9s une mer plus calme, moins pa\u00efenne, or ce diable d'oc\u00e9an, c\u00f4t\u00e9 sauvage de la presqu'\u00eele, rugissait comme le tonnerre. Quel soutien pouvait-il esp\u00e9rer de tant de vagues, ces d\u00e9mones qui ne songent qu'\u00e0 submerger, noyer ? J\u00e9sus n'\u00e9tait pas l\u00e0 pour tancer un tel d\u00e9ferlement, apaiser l'\u00e9cume comme il le fit para\u00eet-il un jour devant ses premiers disciples, de simples p\u00eacheurs. M\u00eame que ce charmant fils de Dieu, non content d'avoir annul\u00e9 cette temp\u00eate, aurait une autre fois r\u00e9veill\u00e9 une morte. Faudrait-il qu'\u00e0 son exemple Charles-Andr\u00e9 prononce \u00e0 son tour ces quelques mots dans leur langue de l\u00e0-bas : \u00ab Talitha Koumi \u00bb, un truc comme \u00e7a, qu'il venait de lire, \u00ab l\u00e8ve-toi \u00bb, pour qu'en effet toute cette terrible histoire qui le met tant \u00e0 bas se rel\u00e8ve, que ses id\u00e9es redeviennent droites, avec juste ce qu'il faut d'ombre, pas plus, pas moins. Contre toute raison, il s'y essaya \u00e0 la porte de la cuisine, \u00e0 grommeler ce \u00ab Talitha Koumi \u00bb, en r\u00e9alit\u00e9 Dieu seul sait quoi ! Une chaise en craqua, la porte g\u00e9mit, quant au robinet au-dessus du sombre \u00e9vier il avait \u00e9t\u00e9 mal referm\u00e9. Et pourquoi la radio n'\u00e9tait-elle pas \u00e9teinte ?\n\nIl d\u00e9cida de se rendre \u00e0 l'\u00e9glise du village, une chapelle pittoresque que v\u00e9n\u00e8rent les touristes, coinc\u00e9e entre deux rochers. Non qu'il esp\u00e9r\u00e2t quoi que ce f\u00fbt de ces saints vermoulus, statufi\u00e9s aux flancs de la pauvre nef, mais seulement pour s'y asseoir, obliger un instant son \u00e2me \u00e0 ne plus faire la gueuse, qu'elle et lui retrouvent un semblant de qui\u00e9tude et ne courent plus la pr\u00e9tentaine d'hypoth\u00e8ses plus folles les unes que les autres. Non, il ne se passa rien, c'est l'ombre, la criminelle avec ses habits de fausset\u00e9. Elle qui m\u00e9lange tout. D'abord, \u00e9tait-il vraiment l\u00e0 ? Comment sait-on qu'on est l\u00e0 ? On peut avoir la t\u00eate ailleurs. Ensuite qui pourrait l'accuser ? La grille qui r\u00e9sista \u00e0 sa pouss\u00e9e ? Elle r\u00e9siste toujours. Et quand il appela, qui vint ouvrir ? Mais justement appela-t-il ? Certes de toute fa\u00e7on pas l'un des douze ap\u00f4tres \u00e0 la parole irr\u00e9prochable, mais encore moins la personne \u00e0 laquelle il pense et qui n'est plus quelqu'un. Sauf s'il se leurre et retrace plut\u00f4t une pr\u00e9c\u00e9dente visite ? Car \u00e0 la derni\u00e8re qui l'entra\u00eena d'un trait jusqu'ici, il n'entrait pas, il sortait, si on peut appeler \u00ab sortir \u00bb cette furie t\u00e2tonnante !\n\nIl conviendrait, se chapitra-t-il, d'\u00e9plucher un peu mieux ses jours, veiller \u00e0 une comptabilit\u00e9 plus pr\u00e9cise de ses heures, tenir peut-\u00eatre jusqu'\u00e0 un journal de ses dix doigts, savoir exactement \u00e0 chaque instant ce que font ses mains par exemple ; ses pieds encore, il ne l'ignore pas par le chemin parcouru, mais ses mains...\n\n\u00ab Comme tu parles ! \u00bb lui aurait \u00e0 tout coup reproch\u00e9 sa tante, une \u00e9plor\u00e9e qui joignait souvent les siennes, tout en effet \u00e9tait pr\u00e9texte \u00e0 pri\u00e8res \u00e0 cette folle du Christ qui lui servit de m\u00e8re, mais la Bretagne n'est pas la Samarie o\u00f9 l'on peut croiser J\u00e9sus et lui offrir en bonne Samaritaine un verre d'eau pour \u00e9tancher sa soif.\n\nIl referma son livre de pi\u00e9t\u00e9. La Bible a peut-\u00eatre envisag\u00e9 une situation comparable \u00e0 la sienne ? Ne conviendrait-il pas qu'il s'en informe davantage pour se tirer d'affaire ? fasse un moment son abb\u00e9 Messager, br\u00e9viaire ou missel \u00e0 la main parmi les fleurs du jardin ?\n\nIl r\u00eavassa un peu autour du piano, effleura par pure manie surtout les touches noires du clavier. Comment s'appelait d\u00e9j\u00e0 le labrador de ses amis dont il flairait la niche \u00e0 quelques pas, dans le vestibule ? Il d\u00e9cida d'aller prendre l'air au village, d'entendre parler les gens, de se m\u00ealer \u00e0 l'humanit\u00e9 \u00e0 une table de caf\u00e9, que sais-je encore ? Le fait est qu'on le retrouve ce mardi midi un peu \u00e9tonn\u00e9 aux alentours de la poste.\n\n#\n\nEt les jours pass\u00e8rent. Un moment, il pensa laisser avant de repartir un petit mot \u00e0 ses amis, bien en \u00e9vidence sur le rev\u00eatement de marbre de la commode du salon, pour qu'\u00e0 leur retour d'Am\u00e9rique ils sachent au moins que, mis par eux dans la confidence de leur clef tapie dans le tronc moussu, il s'\u00e9tait permis en leur absence de profiter fortuitement de leur hospitalit\u00e9, mais, qu'ils se rassurent, il n'avait touch\u00e9 \u00e0 rien de fondamental de cette noble villa, \u00e0 peine d\u00e9rang\u00e9 quelques grains de poussi\u00e8re qu'il n'avait pas omis avant son d\u00e9part d'expulser dans un grand m\u00e9nage associant balais et plumeaux.\n\nPuis, il changea d'avis, car n'\u00e9tait-ce pas mettre la police sur sa piste, si police il y avait ? N'aspirait-il pas plut\u00f4t pour l'instant \u00e0 effacer toute trace de son passage sur cette terre ? \u00ab Je parle comme la Bible \u00bb, constatait-il amus\u00e9.\n\nEn cet endroit de la presqu'\u00eele, la c\u00f4te moins affirmative se dissout plut\u00f4t en sables divers. Il n'y a que quelques rochers au loin pour combler les anfractuosit\u00e9s du large. Il s'y prom\u00e8ne souvent jusqu'\u00e0 un bois de pins familier \u00e0 ses jeunes ann\u00e9es quand, en compagnie de sa tante (l'\u00e9namour\u00e9e du Christ qui l'avait recueilli apr\u00e8s le brusque d\u00e9c\u00e8s de sa m\u00e8re survenu un apr\u00e8s-midi que grandissaient les ombres), il jouait avec sa prime enfance.\n\n\u00ab Charles \u00bb, appelait sa tante inqui\u00e8te de ne plus l'apercevoir entre les arbres. \u00ab Charles-Andr\u00e9 \u00bb, mourait-elle encore de dire tournant sur elle-m\u00eame, regardant de tous c\u00f4t\u00e9s.\n\n\u00ab Reviens ! \u00bb criait-elle, le suppliant de prendre un peu mieux en compte son anxi\u00e9t\u00e9 originelle et d'\u00e0 nouveau se montrer \u00e0 l'or\u00e9e du bois. D\u00e9j\u00e0 ce d\u00e9sir en lui, t\u00e9t\u00e9 avec le lait de sa maternelle, de s'enfouir, se cacher et pas seulement du soleil, de se dissimuler aux yeux de tous, d'entendre la r\u00e9alit\u00e9 lui courir aux trousses, le bon sens qui le somme en pure perte de r\u00e9appara\u00eetre au grand jour, de l'adjurer de ne pas trop s'\u00e9carter de la compagnie de ses semblables. Le sont-ils ? r\u00e9pondrait-il d\u00e9sormais. N'appartient-il pas \u00e0 une autre esp\u00e8ce n\u00e9e plus \u00e0 l'ombre ? Car pourquoi si petit cette m\u00e9lancolie ? Ce chagrin sans cause qui lui tirait les traits, cette p\u00e2leur, ces joues qui n'aspiraient qu'\u00e0 se creuser ? Alors, on le jugeait dissimul\u00e9, pas franc du collier. \u00c0 l'\u00e9cole, \u00e0 la r\u00e9cr\u00e9ation, il bouge peu, nich\u00e9 dans son coin, d\u00e9plorait d\u00e9j\u00e0 l'instituteur, se demandant ce que ce pourtant assez bon \u00e9l\u00e8ve avait bien pu commettre de si r\u00e9pr\u00e9hensible dans son dos de magister pour se terrer ainsi comme un puni, un d\u00e9j\u00e0-coupable dans le coin le plus obscur du pr\u00e9au ?\n\nAdulte, n'a-t-il pas toujours la m\u00eame attitude ? \u00c0 la radio pourtant, au bulletin d'informations, rien ne transpirait de son drame. Comment faire aujourd'hui pour ressusciter ses ann\u00e9es ing\u00e9nues et ressortir du bois aussi innocent qu'\u00e0 cette \u00e9poque, apr\u00e8s avoir abandonn\u00e9 dans la profondeur des halliers ce qui s'\u00e9tait r\u00e9ellement pass\u00e9 ?\n\n\u00ab R\u00e9ellement \u00bb, se r\u00e9p\u00e9tait-il, et l'adverbe lui parut subitement manquer de conviction. Sa tante ? Que penserait-elle de sa situation pr\u00e9sente ? Jugerait-elle \u00e0 son tour son ombrageux neveu trop sous le pr\u00e9au ? Son instituteur \u00e0 elle, c'\u00e9tait le bon abb\u00e9, son voisin, avec qui elle \u00e9changeait des propos \u00e9vang\u00e9liques depuis leurs respectifs potagers. Une fois elle avait rougi d'apprendre son pr\u00e9nom, un que Charles-Andr\u00e9 depuis oublia mais qui n'allait pas, lui semblait-il, \u00e0 la corpulente silhouette de l'eccl\u00e9siastique qui avait d\u00fb se goinfrer de trop d'hosties, du moins c'\u00e9tait son opinion actuelle, un peu sacril\u00e8ge.\n\nIl songeait \u00e0 leur charmant duo, d'un jardinet \u00e0 l'autre s\u00e9par\u00e9s par un grillage que leurs paroles traversaient et le ciel parfois tonnant au-dessus d'eux, l'averse soudaine qui les force \u00e0 s'interrompre et \u00e0 rentrer chacun dans son confessionnal, leur chalet voulait-il dire. Si seulement il avait pu les r\u00e9unir ici autour d'un verre, la cuisine ne manque pas de vin de messe ! Peut-\u00eatre eussent-ils \u00e9t\u00e9 plus \u00e0 m\u00eame que lui de d\u00e9brouiller la situation inextricable o\u00f9 il se trouvait, de d\u00e9terminer par exemple si le fait de refermer une porte sur un couloir ambigu, d'avoir au cours d'une soir\u00e9e soi-disant familiale m\u00eal\u00e9 trop son vin \u00e0 d'autres vins m\u00eal\u00e9s, de s'\u00eatre laiss\u00e9 ainsi emporter en des contradictions diverses jusqu'\u00e0 l'injure, bref, tout ce feu de paroles qu'il se reprochait d'avoir attis\u00e9, ce furieux des faits et gestes qu'il ne cessait de s'\u00e9num\u00e9rer dans l'arri\u00e8re-cour de sa t\u00eate faisaient de lui... Il n'osait exprimer le mot que n'illustrait que trop son visage coupable dans le haut miroir du salon.\n\nLa villa de ses amis d'outre-Atlantique s'\u00e9l\u00e8ve on le sait \u00e0 deux pas d'une conserverie et \u00e0 trois d'une route assez passante, face \u00e0 une maison coquette peupl\u00e9e de cris d'enfants. Il avait d\u00e9j\u00e0, pour dissiper toute id\u00e9e de malentendu, fait un brin de causette avec ses propri\u00e9taires, une femme rousse plut\u00f4t dans l'\u00e2ge, et son mari, ancien matelot qui allait encore en mer, mais qui n'avait jamais \u00e9t\u00e9 en Am\u00e9rique comme vos cousins. \u00ab C'est \u00e0 cause qu'il est danseur qu'ils ont \u00e9t\u00e9 invit\u00e9s ? \u00bb s'informa- t-il d'une voix un peu emp\u00each\u00e9e. Charles-Andr\u00e9 opina. \u00ab Et vous-m\u00eame, demanda la dame, vous faites quoi ? \u2014 Professeur, r\u00e9pondit-il, mais en arr\u00eat maladie. Pour cela qu'ils m'ont pr\u00eat\u00e9 leur maison, pour que mes poumons profitent du bon air. \u00bb\n\n\u00ab Ah ! en Bretagne, on n'en manque pas. Vous rendez-vous compte ! \u00bb glosa l'encourageant voisin mains dans les poches de son pantalon de velours bleu, avec une \u00e9vidente satisfaction. \u00ab Ici, on a deux mers \u00e0 notre service, de l'\u00e9cume, en veux-tu, en voil\u00e0. \u2014 Mais trop de lapins dans la lande \u00bb, minauda son \u00e9pouse, qui vilipendait l'activit\u00e9 de ces longues oreilles qui ne d\u00e9testaient pas leurs carottes.\n\nEt tout cela, dans la crainte de la pluie, un matin orageux sur le bord du trottoir. Charles-Andr\u00e9 leur avait m\u00eame confi\u00e9 qu'il ne lui restait plus qu'une semaine de cong\u00e9, ce qui avait conclu bizarrement l'entretien.\n\nDe cette p\u00e9riode, que retenir ? Il va et vient, ressort, entre \u00e0 nouveau, ne tient pas en place. Mais sa place justement, o\u00f9 la situer d\u00e9sormais ? Le jour s'enfonce d\u00e9j\u00e0 presque en hiver. Il fait gris, froid. De noires pens\u00e9es l'ent\u00e9n\u00e8brent, o\u00f9 donc se trouve la lumi\u00e8re, la solution ? Installer des chaises vides autour de la table de la salle \u00e0 manger lui rendrait-il la pr\u00e9sence des convives et la narration du fatal d\u00eener, l'\u00e9change chaleureux malgr\u00e9 tout des paroles et des plats ? Il se revoyait proposant son aide m\u00e9lancolique \u00e0 la cuisini\u00e8re, Mme Joliette la lui refusant gaiement, d'une voix aujourd'hui rentr\u00e9e dans sa gorge.\n\nFaute de mieux, il s'aventura dans la lande, essayant d'emprunter un peu d'\u00e9nergie \u00e0 la fr\u00e9n\u00e9sie des vagues qui \u00e9claboussaient la presqu'\u00eele, d\u00e9signant de la main comme un enfant les lointains confondants du grand large. Vivre ainsi bras tendu dans l'enthousiasme de l'\u00e9cume, se promettait-il am\u00e8rement. Que le reflux me devienne moins important que le flux. \u00ab Au diable la m\u00e9moire ! \u00bb gueula-t-il.\n\nDes id\u00e9es extravagantes de cette sorte lui traversaient ainsi l'esprit. Il marchait. Les villages, hameaux qui personnifient la presqu'\u00eele, donnant une couleur humaine \u00e0 son herbe sauvage, n'avaient pas boug\u00e9 d'un pouce depuis ses dix douze ans, toujours le m\u00eame granit, fortifi\u00e9 par le m\u00eame silence avec parfois une ombre qui s'escamote \u00e0 une porte basse et le vent, l'\u00e9ternel messager qui rend fous les jardinets, les maigres arbustes qu'il ne cesse de tourmenter, de plaquer contre la pierraille des murs.\n\nIl longea un moment la voie ferr\u00e9e. Le train, il viendra bient\u00f4t le prendre arm\u00e9 de son unique baluchon \u00e0 la gare mouvement\u00e9e, devant la place et l'\u00e9cole \u00e9l\u00e9mentaire qu'il hanta durant tant d'ann\u00e9es. Que ne pouvait-il se d\u00e9lester de son fardeau, l'\u00e9crire \u00e0 la craie sur l'un des tableaux noirs afin que le chiffon du ma\u00eetre aussit\u00f4t l'efface. H\u00e9las, il n'\u00e9tait plus le petit gar\u00e7on du fond de la classe, celui qui h\u00e9sitait toujours \u00e0 intervenir, ses quarante-trois ans \u00e9taient justement trop intervenus, il ne pouvait plus s'asseoir sur l'un de ses bancs innocents. Plus personne pour lui faire la le\u00e7on, le tirer de son embarras actuel, \u00e9tait-il... ? N'\u00e9tait-il pas... ?\n\nEmbarras lui parut soudain un mot trop l\u00e9ger pour qualifier, d\u00e9finir ce qu'il avait r\u00e9cemment \u00e9prouv\u00e9. \u00ab La criminalit\u00e9 obscure des galetas. \u00bb Pourquoi cette phrase sur ses l\u00e8vres ? Rien \u00e0 sa connaissance ne la justifiait.\n\nRestait-il d'ailleurs trop l'homme d'hier, r\u00e9ussira-t-il gr\u00e2ce \u00e0 la paix de ce pays o\u00f9 seuls les nuages se font la guerre \u00e0 devenir celui d'aujourd'hui, un simple quidam en veine touristique qui s'assoit sans r\u00e9serve \u00e0 la table d'un caf\u00e9, qui ramasse les minutes comme autant de fleurs \u00e0 signaler sa pr\u00e9sence, celui qui tresse l'heure comme un bouquet dont il respire fort le parfum ?\n\nS\u00fbr, ce soir, il soupera \u00e0 Saint-Pierre, dans le sympathique troquet sur le port o\u00f9 la patronne, une corpulente aux bons endroits, lui fait, croit-il, les yeux doux. Son apparente distinction sans doute. Qui pourrait en effet jamais soup\u00e7onner en l'apercevant qu'il garde en lui une telle r\u00e9serve d'ombres ? Une seule l'avait devin\u00e9, Diane, sa derni\u00e8re compagne. Il n'avait eu jusqu'\u00e0 pr\u00e9sent que de vagues amours, mais celle-l\u00e0, qu'un autre lui avait h\u00e9las chip\u00e9e, ne pouvait plus sous son nouveau nom de jeune mari\u00e9e, Marchand, l'appeler au t\u00e9l\u00e9phone. D'ailleurs comment aurait-elle su qu'il se lamentait dans ce coin ? Il n'avait plus son oreille, lui exposer les faits n'\u00e9tait plus chose possible, y e\u00fbt-elle d'ailleurs port\u00e9 un quelconque cr\u00e9dit ? Non, il \u00e9tait vraiment condamn\u00e9 \u00e0 se les ressasser, \u00e0 en faire sa Bible, son cat\u00e9chisme, sa marotte, ses dix commandements, car qui en ce bas monde aurait pu supporter sans fr\u00e9mir l'\u00e9nonc\u00e9 possible de tels aveux ? Mais ne se trompait-il pas en s'imaginant si coupable ? Un passant qui s'enfonce dans la nuit d'une venelle est-il responsable de son \u00e9ventuel d\u00e9dale ?\n\nQuoi qu'il en soit, parvenu au faramineux troquet, il s'assit \u00e0 la m\u00eame table, et \u00e0 l'avenante patronne commanda une bi\u00e8re.\n\n#\n\nD'abord il y eut, mais ensuite ? La porte de la cuisine fermait mal, un coup d'air et le vent, ce voyou, s'invitait autour de la table pour embrouiller les couverts. L'eau dans la carafe en dansait m\u00eame un peu. Des constatations journali\u00e8res qui aga\u00e7aient Charles-Andr\u00e9. La maison de ses amis craquait de toutes ses jointures. En supporterait-il longtemps l'atmosph\u00e8re ? Il avait beau la peupler de ses pens\u00e9es, laissant une id\u00e9e l\u00e0, une autre ici se froissant avec le lit d\u00e9fait de sa derni\u00e8re nuit, il s'impatientait. \u00c0 l'escalier, il e\u00fbt bien ajout\u00e9 des marches pour monter ailleurs, mais o\u00f9 ? Tra\u00eenera-t-il d\u00e9sormais comme un boulet le souvenir de cette mis\u00e9rable affaire ? Et puis, il y avait eu ce nouveau coup de t\u00e9l\u00e9phone. Non, il s'\u00e9tait bien gard\u00e9 de d\u00e9crocher. Ce pouvait \u00eatre l'une de ces publicit\u00e9s qui vous harc\u00e8lent \u00e0 longueur de journ\u00e9e ou quelqu'un du coin qui sachant la villa \u00e0 nouveau habit\u00e9e souhaitait prendre des nouvelles de ses amis. \u00c0 moins que l'un des invit\u00e9s de cette m\u00e9morable soir\u00e9e qui le lancinait tant n'ait retrouv\u00e9 sa trace ? Mais il ne voyait pas comment. Il ne s'en \u00e9tait ouvert \u00e0 personne et le chemin suivi pour venir dans la presqu'\u00eele s'entretenir avec son enfance restait si int\u00e9rieur. En tous les cas, le serviteur noir de la serre, t\u00e9moin muet du drame, n'aurait pu appeler. Un mannequin en bois peint ne t\u00e9l\u00e9phone pas.\n\nSi seulement Charles-Andr\u00e9 avait su danser comme Jean-Marc, expulser en quelques gestes l\u00e9gers le plus lourd de ses soucis, s'inventer une chor\u00e9graphie du sauve-qui-peut pour sortir de son effroi ! Il se r\u00e9p\u00e9tait pour la milli\u00e8me fois l'\u00e9trange sc\u00e8ne, la porte \u00e0 peine entreb\u00e2ill\u00e9e o\u00f9 il glisse un \u0153il, pas les deux, dans le lit, la m\u00eame forme confuse, la neige au-dehors qui en rappelle une autre, le couloir, la vaste respiration de la maison d\u00e9serte, lui t\u00e2tonnant dans l'escalier complice, la m\u00eame clef, cette fois plus rouill\u00e9e dans la main, pour ouvrir, vite refermer la grille du myst\u00e8re. Il part, il fuit plut\u00f4t. Existe-t-il une criminalit\u00e9 de la nuit ? La main du sombre a-t-elle encore frapp\u00e9 ? Pr\u00e9monitoire, la panne d'\u00e9lectricit\u00e9, la veille au soir, plongeant leur tabl\u00e9e tumultueuse dans le noir : Laurence \u00e9tait-ce encore Laurence ? Maryvonne, Maryvonne ? On ne savait plus qui \u00e9tait qui ? Et quoi ? Pas \u00e9tonnant que ce matin t\u00f4t dans la clart\u00e9 du soleil levant qui d\u00e9j\u00e0 enqu\u00eate, il ne sache plus lui-m\u00eame ce qu'il est et pourquoi ?...\n\nIl soupira. \u00c0 bas les id\u00e9es fatales ! Aujourd'hui, il se proposait le bar de la Jet\u00e9e. Quelle heure d\u00e9j\u00e0 ? L'\u00e9tablissement aux vitres rendues brumeuses par les mar\u00e9es domine le port, d'o\u00f9 son nom... Le matin de nombreux p\u00eacheurs rentr\u00e9s d'une nuit au large s'affalent sur ses bancs parmi un mobilier disparate comme sauv\u00e9 d'un naufrage. Charles-Andr\u00e9 e\u00fbt souhait\u00e9 parfois en apprendre plus sur cette population noueuse de tables et de chaises, de tabourets plus musculeux. Mais le patron n'est gu\u00e8re causant. Il vous \u00e9coute, vous entend plut\u00f4t, plisse le visage en signe d'approbation et s'accoude \u00e0 sa caisse. Parfois une vague plus dominatrice que ses cong\u00e9n\u00e8res para\u00eet vouloir inonder le pas de la porte. Car le caf\u00e9 ouvre sur le quai, un pav\u00e9 glissant qui d'un rien vous entra\u00eenerait dans les profondeurs, surtout si la bi\u00e8re vous a trop charg\u00e9 de son \u00e9cume.\n\nCharles-Andr\u00e9 aime s'y asseoir, et sa r\u00e9flexion prend poupe et proue des bateaux \u00e0 l'ancre, s'\u00e9tire plus loin que la jet\u00e9e. Gagner le large lui aussi, mais pas seulement pour une nuit ! Heureusement qu'actuellement il ne manque pas d'argent. Doit-il \u00e0 l'issue de ce voyage aux sources retourner chez lui, retrouver son identit\u00e9 : plus Charles qu'Andr\u00e9 (Charles, le pr\u00e9nom sage de son p\u00e8re pourtant si tumultueux, Andr\u00e9, celui un tantinet dissident de son oncle maternel, le fr\u00e8re tant aim\u00e9 de sa m\u00e8re), se comporter comme si de rien n'\u00e9tait, monter descendre ses \u00e9tages avec all\u00e9gresse, r\u00e9pondre avec politesse \u00e0 ses coll\u00e8gues au lyc\u00e9e o\u00f9 il est cens\u00e9 enseigner les lettres, ou fuir dans le d\u00e9sespoir de ce que la police ne manquera pas un jour ou l'autre de d\u00e9couvrir. Dans quelques jours la Toussaint o\u00f9 l'on f\u00eate les morts, et lui, il en avait pas mal \u00e0 f\u00eater !\n\nHier, il s'\u00e9tait promen\u00e9 \u00e0 la recherche de ses premi\u00e8res ann\u00e9es c\u00f4t\u00e9 baie, l\u00e0 o\u00f9 l'oc\u00e9an si mouvement\u00e9 se transmue en une onde paisible qui vient vous l\u00e9cher les pieds. Il e\u00fbt presque ressuscit\u00e9 la voix planante de sa tante l'appelant aux quatre vents de la plage. \u00c0 Saint-Pierre, il ne s'\u00e9tait pas attard\u00e9 devant sa villa d'\u00e9t\u00e9 qui l'abrita tant durant son enfance, ni devant celle contigu\u00eb de l'abb\u00e9 Messager. Aucun des deux n'\u00e9tait plus l\u00e0 pour l'entendre en confession. D'ailleurs, qu'aurait-il pu leur avouer de si tangible ? Une porte referm\u00e9e en toute h\u00e2te signe-t-elle une culpabilit\u00e9 ? Les fleurs de leurs jardinets, au moins les petites-filles ou les arri\u00e8re-petites de celles qu'ils \u00e9duquaient avec tant de soins (l'abb\u00e9 avec une onction tout eccl\u00e9siastique), poussaient en d\u00e9sordre m\u00eal\u00e9es \u00e0 une herbe sans nom, \u00ab l'herbe du Malin \u00bb, pronon\u00e7a-t-il aussit\u00f4t avant de toucher du doigt le bois du portillon d'entr\u00e9e pour conjurer cette mauvaise parole. Aucune fum\u00e9e ne s'\u00e9levait en point d'interrogation au-dessus des deux toits. Leurs nouveaux propri\u00e9taires s\u00e9journeraient-ils eux aussi aux States ? Et allait-il en voir sortir un de leurs amis plut\u00f4t sans g\u00eane qui \u00e0 son exemple se serait permis d'y habiter en leur absence ? L'id\u00e9e lui vint de Jean-Marc entra\u00eenant la Virginie et Solange, son \u00e9pouse \u00e0 malices, dans une danse d\u00e9r\u00e9gl\u00e9e. Cette image l'apaisa.\n\n\u00c0 la radio rien ne filtrait de son histoire, sauf qu'une fois il avait eu un haut-le-c\u0153ur d'entendre la description d'un fait-divers qui s'approchait un peu du sien. Non, il pouvait reprendre une marche plus assur\u00e9e, calmer son reflet f\u00e9brile dans les miroirs, r\u00e9pondre pos\u00e9ment \u00e0 son nom. Et d'ailleurs pourquoi vouloir cacher les noms, la presqu'\u00eele (cette main de son enfance pos\u00e9e doigts \u00e9cart\u00e9s sur les flots), on l'a devin\u00e9 de toute \u00e9ternit\u00e9, c'est forc\u00e9ment celle de Quiberon. De toute fa\u00e7on, n'importe quel sursaut de terre que brusque l'oc\u00e9an ferait l'affaire ! Et lui-m\u00eame, osa-t-il se dire, n'en \u00e9tait-il pas devenu une, une presque presqu'\u00eele, avec ses quarante-trois ans de distractions, songeries, billeves\u00e9es en tout genre qui le d\u00e9tachent un peu trop du bon sens pour l'entra\u00eener vers le large ? Mais de quel large s'agit-il ? Lui aussi a son c\u00f4t\u00e9 apais\u00e9, son c\u00f4t\u00e9 baie, disons Charles plus qu'Andr\u00e9, et un autre c\u00f4t\u00e9 sans nom, plus \u00e9cumeux dont chacune de ses nuits bat le rappel !\n\nFut-ce ce m\u00eame jour qu'il crut entrevoir Ang\u00e8le \u00e0 sa fen\u00eatre derri\u00e8re l'\u00e9glise de Saint-Pierre scrutant la rue en pente ? Ang\u00e8le, une copine d'autrefois, son a\u00een\u00e9e de cinq six ans, devait aujourd'hui flirter avec la cinquantaine. Le temps qu'il s'en assure, elle avait quitt\u00e9 son balcon. Allait-il sonner ? Il passa outre. Pourtant, ce n'est pas elle qui aurait pu lui reprocher de vouloir m\u00ealer ses pas d'homme fait \u00e0 ceux de ses primes ann\u00e9es.\n\n\u00c9tait-ce \u00e0 cause du brusque soleil, il se sentait cet apr\u00e8s-midi-l\u00e0 malgr\u00e9 tout moins naufrag\u00e9. D'accord, le naufrage avait bien eu lieu, mais il s'en \u00e9tait tir\u00e9, avait regagn\u00e9 le rivage. Qui pourrait se douter qu'il y ait tremp\u00e9 ? Rien dans son apparence, dans l'ensemble de ses expressions n'indiquait qu'il ait pu avoir \u00e0 un moment quelconque la t\u00eate sous l'eau.\n\nCette fa\u00e7on imag\u00e9e de parler qu'on lui reproche tant depuis sa naissance ne peut plus lui co\u00fbter la chambre noire, cette pi\u00e8ce secr\u00e8te des hauts de la vieille maison d'hiver rue Marzelle \u00e0 Nantes o\u00f9 tout gamin on mena\u00e7ait de l'enfermer, sans jamais l'y mettre d'ailleurs, pour tous ses \u00e9carts, qu'ils soient de langage ou d'autre chose. Une pi\u00e8ce dont le plancher peu s\u00fbr craque \u00e0 la moindre mauvaise pens\u00e9e, para\u00eet-il, entre des murs ciment\u00e9s de remords, lui d\u00e9crivait sa tante en mal d'\u00c9vangile. Dieu sait ce qu'elle et sa sainte Bible lui inventaient aux oreilles quand il se conduisait mal. \u00ab Car l'ombre a son cat\u00e9chisme \u00e9crit par le Malin \u00bb, lui murmurait-elle apeur\u00e9e. Elle l'avait recueilli au d\u00e9c\u00e8s de sa m\u00e8re et ils vivaient ensemble de fa\u00e7on un peu d\u00e9sordonn\u00e9e l'\u00e9t\u00e9 dans ce coquet chalet de Saint-Pierre o\u00f9 encore b\u00e9b\u00e9 il fit ses premiers pas, une b\u00e2tisse impassible contigu\u00eb \u00e0 celle de l'abb\u00e9 Messager, et l'hiver aux confins de Nantes rue Marzelle dans cette haute maison de brique trop grande pour eux o\u00f9 justement...\n\nNe serait-ce pas cette chambr\u00e9e obscure qui, profitant de la mort de sa tante, aurait depuis rayonn\u00e9, peupl\u00e9, contamin\u00e9 tous les recoins de la demeure familiale du grenier jusqu'\u00e0 la cave et qui aurait expliqu\u00e9...\n\nD'apr\u00e8s sa d\u00e9vote tutrice volontiers proph\u00e9tique, on n'en sortait pas comme on y \u00e9tait entr\u00e9. Il n'avait jamais pu la situer exactement. Comment aurait-il pu, songe- t-il aujourd'hui, si elle n'existait que nich\u00e9e dans les imaginations de sa tante ? Il y avait bien \u00e0 toucher le grenier, un r\u00e9duit assez sombre o\u00f9 s'empilaient de vieilles frusques, un ramassis d'antiques valises toutes coutur\u00e9es par les voyages, mais \u00e0 l'\u00e9vidence, ce n'\u00e9tait pas celle-l\u00e0 ! Car la s\u0153ur quelque peu illumin\u00e9e de sa m\u00e8re ne faisait qu'en rire quand il lui \u00e9voquait l'objet de ses recherches. Elle \u00e9chafaudait alors pour lui toutes sortes d'escaliers t\u00e9n\u00e9breux, un lacis de couloirs, des portes o\u00f9 ne frappe jamais le soleil. \u00ab Car l'enfer nous c\u00f4toie \u00bb, tonnait-elle. Et devant son air effar\u00e9 s'empressait de corriger : \u00ab Mais non grand nigaud, je plaisante. \u00bb\n\nPlaisantait-elle ? Parmi l'\u00e9ventail de ses gestes enfantins, en avait-il, \u00e0 l'entendre, fourbi \u00e0 son insu d\u00e9j\u00e0 quelques-uns de nature plus douteuse qui auraient m\u00e9rit\u00e9 qu'on lui mette entre les mains au moins une fois et sans qu'il s'en aper\u00e7oive la clef de suie de ce diabolique incroyable galetas ? Serait-ce cette clef qui lui permit r\u00e9cemment...\n\nUne simple hypoth\u00e8se, condescendait-elle parfois \u00e0 avouer quand elle le voyait s'agiter trop ! Mais enferme-t-on un enfant dans une hypoth\u00e8se ? N'avait-elle pas tort d'infliger \u00e0 son neveu qu'elle avait pour charge de mener dans le droit chemin cette id\u00e9e qu'il retrouvait ensuite dans ses cauchemars que dans les replis de toute ombre se faufile un d\u00e9dale, que nos mauvaises actions en sont les concierges ? La preuve ! Quarante ans plus tard, il s'\u00e9tait m\u00eame, d\u00e8s son entr\u00e9e dans la villa de ses amis, abaiss\u00e9 \u00e0 en rechercher l'\u00e9quivalent, un endroit confin\u00e9, se souvenait-il, o\u00f9 la nuit, cette louve, guette la fin du jour et le retour quotidien de ses filles d'ombre qu'elle rappelle au soir dans sa tani\u00e8re.\n\nDes b\u00eatises quoi, des r\u00eaveries que sa tante allait p\u00eacher dans ses lectures aupr\u00e8s du lac de Tib\u00e9riade, \u00e0 l'\u00e9poque de son flirt avec les ap\u00f4tres, avec son J\u00e9sus comme elle r\u00e9p\u00e9tait avec amour. Aucun homme n'avait su \u00e0 ses yeux l'incarner, aussi \u00e9tait-elle rest\u00e9e farouchement c\u00e9libataire. Dans le voisinage, on la jugeait un peu toqu\u00e9e, mais si charmante. \u00ab Un peu d'obscurit\u00e9, et tu ma\u00e7onnes autour \u00bb, lui jetait-elle parfois en guise d'explication quand ses dix douze ans insistaient trop pour enfin savoir le vrai du faux ou le faux du vrai !\n\n#\n\nCe fut Ang\u00e8le qui la premi\u00e8re l'identifia. Il s'attardait \u00e0 Quiberon, sur la jet\u00e9e de Port Maria, l\u00e0 o\u00f9 on s'embarque pour Belle-\u00cele, attentif \u00e0 tous ces gens qui ont le d\u00e9sir d'entreprendre, d'aller voir de pr\u00e8s les curiosit\u00e9s de l'horizon. Elle avoua avoir h\u00e9sit\u00e9, mais des restes d'enfance sur le visage glabre de cet homme grand et mince au regard soutenu la firent se d\u00e9cider \u00e0 l'interpeller. Ils s'embrass\u00e8rent. Et apr\u00e8s quelques premi\u00e8res paroles forc\u00e9ment convenues engag\u00e8rent une conversation plus intime \u00e0 la terrasse d'une brasserie fertile en all\u00e9es et venues. Il confirma \u00eatre sur le point de repartir, n'\u00eatre l\u00e0 que pour quelques jours. Oui, il habite toujours Nantes, lui cita une rue illusoire du c\u00f4t\u00e9 de Sainte-Croix, si elle conna\u00eet un peu la ville, et avoir \u00e9t\u00e9 invit\u00e9 par de chers amis actuellement aux \u00c9tats-Unis \u00e0 profiter durant leur absence de leur splendide villa \u00e0 Portivy, mais, avoua-t-il assez comique, cela fait beaucoup de pi\u00e8ces \u00e0 occuper pour un homme seul. Aussi en change-t-il chaque soir pour \u00e9viter toute jalousie entre les chambres et que l'une ou l'autre ne prenne pas pour du d\u00e9dain s'il ne s'est pas encore aventur\u00e9 \u00e0 y coucher.\n\nElle rit : \u00ab Tu n'as pas chang\u00e9. Toujours le m\u00eame petit gar\u00e7on au v\u00e9lo bleu qui d\u00e9raillait autant que son d\u00e9railleur. \u00bb\n\nIl rit aussi. Elle se tenait assise \u00e0 ses c\u00f4t\u00e9s, croisant et d\u00e9croisant les jambes, un peu \u00e9mue de leurs retrouvailles. Sous ses abondants cheveux fris\u00e9s sortis r\u00e9cemment tout blonds des mains du coiffeur, des expressions de la fillette de nagu\u00e8re couraient sur son visage encore assez beau, autour d'une bouche qu'il n'e\u00fbt pas d\u00e9test\u00e9 nagu\u00e8re cueillir de deux ou trois baisers. Il retrouvait le fond bleu de ses yeux bleus, et cette parole enjou\u00e9e qui autrefois lui mettait le c\u0153ur en f\u00eate. Ils d\u00e9cid\u00e8rent de ne pas se quitter tout de suite, de d\u00e9jeuner par exemple ensemble. Oui elle vivait d\u00e9sormais \u00e0 longueur d'ann\u00e9e dans la presqu'\u00eele. \u00ab Les hivers y passent plus vite \u00bb expliquait-elle, et puis elle s'y sent davantage en s\u00e9curit\u00e9. Depuis la mort de son mari, oui un capitaine au long cours comme son propre p\u00e8re, elle flotte un peu, ne sait plus trop quoi faire d'elle-m\u00eame. \u00c0 Saint-Pierre, elle a ses relations, se sent moins seule.\n\nBref, ils caus\u00e8rent, cherch\u00e8rent du m\u00eame pas un restaurant agr\u00e9able avec vue sur la mer qui ce jour-l\u00e0 manifestait une certaine mauvaise humeur avec toutes ces vagues qui s'\u00e9croulaient de col\u00e8re sur la plage.\n\nBref, c'\u00e9tait l'interpr\u00e9tation de Charles-Andr\u00e9. Elle en souriait, accepta de sa part un doigt de vin, plus quelques exclamations encore plus imag\u00e9es qui les men\u00e8rent sans plus de fa\u00e7ons au dessert. L'ennui le gagnait. Il s'endormait presque tout en parlant yeux mi-clos qu'il ouvrit soudain tout grands quand elle lui rappela d'une voix gourmande, les l\u00e8vres enivr\u00e9es par sa glace \u00e0 la vanille, la maison au fond du parc touffu o\u00f9 toute leur bande assoiff\u00e9e d'inconnu s'engouffrait \u00e0 la mauvaise saison en l'absence des propri\u00e9taires qui n'y venaient que l'\u00e9t\u00e9 et o\u00f9 eux jouaient \u00e0 se faire peur. L'obscurit\u00e9 y \u00e9tait en effet plus dense qu'au-dehors et m\u00eame qu'une fois avec des cris d'ogre mangeur de chair fra\u00eeche, lui, le beau Charles-Andr\u00e9, les avait pourchass\u00e9es dans tous les coins et recoins de cette sale baraque, elle et les autres filles :\n\n\u00ab Tu ne te rappelles pas ? \u00bb\n\nIl fit le mort, d\u00e9clara ne pas se souvenir, croit cependant, \u00e0 la r\u00e9flexion et en y songeant bien maintenant qu'elle en parle, avoir peut-\u00eatre \u00e0 nouveau dans les yeux la serre et son serviteur laqu\u00e9 noir en bois tenant un plateau.\n\n\u00ab Mais il n'y avait pas de serre et o\u00f9 as-tu \u00e9t\u00e9 chercher ce mannequin en bois ? \u00bb\n\nElle s'\u00e9poustouflait. Il s'excusa. Oui, c'est vrai, o\u00f9 avait-il la t\u00eate ? Un effet du soleil inattendu en ce d\u00e9but de novembre ? En r\u00e9alit\u00e9, il ne savait plus comment s'y prendre pour la quitter ! Leur enfance commune qu'elle ressassait lui devenait franchement insupportable ! Il n'en avait aujourd'hui rien \u00e0 secouer, quoi qu'elle en dise, de tous ces copains et copines habitant ici, couchant l\u00e0, d\u00e9c\u00e9d\u00e9s ou pas d'ailleurs ! Pour qui sonne le glas, c'\u00e9tait pas son truc !\n\nIl avait demand\u00e9 subrepticement la note, paya quand on la lui pr\u00e9senta rubis sur l'ongle, se leva devant elle saisie d'\u00e9tonnement au milieu de sa phrase, pr\u00e9textant une course urgente que, dans l'\u00e9moi de leur rencontre, il avait compl\u00e8tement oubli\u00e9e, promit de passer la voir un prochain jour, dans sa coquette petite maison derri\u00e8re l'\u00e9glise, l\u00e0-bas, \u00e0 Saint-Pierre.\n\nSa voix se faisait suave et il l'embrassa sur les deux joues avant de se carapater d'un bon pas et sans se retourner. Elle toute muette soudain, affal\u00e9e devant la table, avec plein de paroles en l'air tel un jeu de cartes tout \u00e9parpill\u00e9 autour de sa grassouillette personne.\n\n\u00ab Dans le fond, se f\u00e9licitait-il, la meilleure cachette, c'est de vivre au grand jour. \u00bb\n\nQuelle sotte id\u00e9e que celle qu'il avait eue au d\u00e9but de son s\u00e9jour de vouloir habiter volets clos, dissimul\u00e9 aux yeux du monde. N'\u00e9tait-ce pas d\u00e9j\u00e0 s'accuser, se comporter en coupable, avoir quelque chose \u00e0 se reprocher ? Pourquoi s'\u00e9clairer \u00e0 la bougie dont la pauvre flamme agrandit les ombres, les nourrit ? Il en a d\u00e9j\u00e0 suffisamment en lui. Ne dort-il pas lumi\u00e8re allum\u00e9e pour qu'elles n'entrent pas ? Il les entendait ces follettes parfois la nuit baragouiner entre elles assises sur les marches de l'escalier assez t\u00e9n\u00e9breux pour pr\u00e9tendre descendre jusque dans la cave.\n\n\u00ab Tr\u00eave de boniments \u00bb se dit-il, prenant le chemin de Saint-Julien.\n\n#\n\nIl aurait bien eu besoin du J\u00e9sus de sa d\u00e9funte tante pour \u00e9clairer sa marche, sa d\u00e9marche. Avec son front barr\u00e9 de soucis, il lui e\u00fbt \u00e9t\u00e9 plus utile d'aller en Galil\u00e9e pour demander conseil, au moins aux ap\u00f4tres, qu'au centre du village dans la m\u00eame sempiternelle maison de la presse. Pourtant, il pouvait se rass\u00e9r\u00e9ner, nul journal dans la colonne r\u00e9serv\u00e9e aux faits-divers ne signalait m\u00eame pas l'ombre du sien.\n\nIl respirait, le seul t\u00e9moin du drame \u00e9tait en bois. Que risquait-il d'une telle veste rouge, de son bras rigide soutenant un plateau factice ? Et la serre encombr\u00e9e d'outils agricoles, d'objets divers au rebut dont une brass\u00e9e de vieux jouets de son enfance ne pouvait d\u00e9livrer aucun indice le concernant, encore moins le hangar hant\u00e9 de feuilles mortes \u00e0 l'entr\u00e9e du parc en haut de sa rampe inclin\u00e9e. Et ce n'est pas la flaque de l'\u00e9tang qui aurait pu conserver dans les replis de son eau m\u00e9duse une quelconque image d'une si funeste soir\u00e9e. Entre cet \u00e9tang croupi sous ses feuilles mortes et lui il y a toujours eu m\u00e9sentente. Ne l'a-t-il pas toujours mal r\u00e9fl\u00e9chi ? le m\u00ealant trop complaisamment \u00e0 la vase de son eau boueuse ? Et laquelle choisir de toutes ces all\u00e9es qui dispers\u00e8rent si joyeusement ses jeunes ann\u00e9es pour que ses heures actuelles se redressent, marchent droit ! Il serait d'ailleurs peut-\u00eatre temps de parler plus explicitement de cette propri\u00e9t\u00e9 familiale qui l'\u00e9leva pour ainsi dire, de citer ses hautes fen\u00eatres qui encadr\u00e8rent ses premiers regards, d'\u00e9num\u00e9rer les trembles qui cachent aux yeux du soleil le b\u00e2timent des communs, l'Ombre comme on l'appelle !\n\nOui, il pouvait respirer, aller chercher son souffle dans les tr\u00e9fonds de son \u00e2me qu'il s'effor\u00e7ait d'exhaler pacifique. Demander leur avis aux autres trembles du jardin de la villa Rose e\u00fbt \u00e9t\u00e9 absurde. Et pourtant, il le fit, s'aventurant \u00e0 t\u00e2ter leur tronc \u00e9motif. Eux, le vent les agite sans cesse. Et lui n'\u00e9tait-ce pas quelque chose d'aussi subtil, d'aussi peu d\u00e9fini que le vent qui l'agitait ? N'avait-il pas les pieds enracin\u00e9s dans un myst\u00e8re, et la t\u00eate troubl\u00e9e comme la leur ?\n\nIl r\u00e9fl\u00e9chissait. C'\u00e9tait le lendemain du jour o\u00f9 il avait rencontr\u00e9 la toujours belle Ang\u00e8le.\n\nIl r\u00e9fl\u00e9chissait. Revenir \u00e0 Nantes, dans son douillet trois-pi\u00e8ces du Bouffay ? Son cong\u00e9 de maladie expirait apr\u00e8s les vacances de la Toussaint. Reprendre ses cours au lyc\u00e9e comme si de rien n'\u00e9tait ? \u00c9crire \u00e0 Jean-Marc, \u00e0 Solange, qu'il s'\u00e9tait permis durant leur absence... \u00c9tant un peu fauch\u00e9, et sachant la clef dans le tronc moussu ? Oui, pour s'\u00e9viter les frais d'h\u00f4tel, \u00e9tant oblig\u00e9 de revenir dans la presqu'\u00eele pour r\u00e9gler une sombre histoire de famille... Mais qu'ils se rassurent, s'empresserait-il d'ajouter, il laissera la villa derri\u00e8re lui aussi nette qu'\u00e0 son arriv\u00e9e. Il avait soulign\u00e9 le mot net dans un brouillon de lettre r\u00e9dig\u00e9 \u00e0 la va-vite dans la cuisine sur un coin de table, pourtant qui le presse ?\n\n\u00ab C'est vrai, qui me presse ? \u00bb se demandait-il. Les horloges de la villa ne s'accordaient m\u00eame pas entre elles. Au salon, il faisait toujours plus t\u00f4t que dans la salle \u00e0 manger, quant au vestibule, n'en parlons pas ! Et comme son heure, \u00e0 lui, celle que battait son c\u0153ur essouffl\u00e9, nulle aiguille sur un aucun cadran n'e\u00fbt su l'indiquer, il se promit :\n\n\u00ab Dans trois jours, je fous le camp. \u00bb\n\nQuelque chose s'\u00e9tait momentan\u00e9ment sabord\u00e9 dans son esprit, il ne savait pas quoi, mais quelque chose l'emp\u00eachait de distinguer clairement l'encha\u00eenement des faits. Et les faits eux-m\u00eames, quels \u00e9taient-ils ? N'avait-il pas r\u00eav\u00e9 la porte repouss\u00e9e dans le silence et en toute h\u00e2te et la fen\u00eatre qui fermait mal et cet escalier qui d\u00e9gringolait tous ses pas et cette neige qui insistait sur les vitres.\n\n\u00ab Du nocturne de plein jour \u00bb, conclut-il. Ne plus y songer, la vie \u00e0 ce prix. Oui, reprendre sa livr\u00e9e d'homme ordinaire, aimer comme on aime, boire, manger, dormir comme tout le monde. Rel\u00e9guer dans les oubliettes de son \u00eatre cette foutue soir\u00e9e d'il y a \u00e0 peine quinze jours. Il entendait toujours pourtant la salve des disputes. Ils avaient bu plus que de raison. Disons que par moments de la raison le bouchon avait saut\u00e9 ! \u00c9coutait-on trop les bouteilles vides ? Les assiettes remplies par Mme Joliette, l'ardente cuisini\u00e8re ? Il allait juste dire \u00ab feu Madame... \u00bb, mais il s'arr\u00eata \u00e0 temps ! Qui donc parmi ses cousins cousines avait eu l'id\u00e9e de faire participer le mannequin de la serre \u00e0 leurs vibrantes agapes ? Qui ? Cela lui rappelait trop la m\u00e9morable soir\u00e9e de ses douze ans, du vivant de sa tante. Les m\u00e9langeait-il ? Qui donc aussi \u00e0 cette \u00e9poque parmi la nu\u00e9e d'adultes festoyant autour de la table ?\n\nIl d\u00e9cida de se secouer, de devenir plus raisonnable, d'aller boire une bi\u00e8re au bar de la Jet\u00e9e, de se perdre dans sa mousse, puis d'errer dans l'herbe rase, d'effectuer un ou deux tours sauvages dans l'immense lande, d'abandonner une bonne fois sa vocif\u00e9ration int\u00e9rieure aux rochers \u00e9cumeux de l'Atlantique. Qu'ils s'en exasp\u00e8rent eux, plus lui-m\u00eame !\n\nPeut-\u00eatre, pour se d\u00e9barrasser de cette hantise, pourrait-il la traiter comme une fable dans son carnet poche revolver, l\u00e0 o\u00f9 il glisse toutes les pens\u00e9es qui le traversent. Qui sait, si de l'avoir couch\u00e9 par \u00e9crit, il n'en ressortirait pas all\u00e9g\u00e9, ravi de l'invraisemblance de cette affaire qu'il croit avoir eu lieu et qui n'est plus ?\n\nLa pluie mena\u00e7ait. Il h\u00e2ta le pas. Le patron au bar de la Jet\u00e9e le servit sans mot dire. Un des p\u00eacheurs attabl\u00e9s le salua d'un vague bonjour. Le ciel grondait. Sa tante l'habitait, oui elle se tenait l\u00e0, \u00e0 ses c\u00f4t\u00e9s, le morig\u00e9nant de faire tant d'histoires pour un semblant d'histoire. Il revoyait ses yeux d'un bleu intense qu'on retrouvait plus perdus sur le visage de sa s\u0153ur, sa m\u00e8re \u00e0 lui trop t\u00f4t disparue, et toujours en route vers autre chose, d'autres pays o\u00f9 vagabondait \u00e9ternellement son ex-mari, l'inconstant p\u00e8re de Charles-Andr\u00e9 qui avait la bougeotte !\n\nMais la folie en brique qui abrita son enfance et que le voisinage \u00e0 Nantes surnommait le \u00ab ch\u00e2teau \u00bb existait bel et bien. Il ne pouvait d'un trait de plume barrer sa grille qu'en pens\u00e9e il franchissait trop souvent. N'\u00e9tait-ce pas lui qui en d\u00e9tenait la clef, une clef toute tordue comme l'\u00e9nigme qu'elle renfermait !\n\n#\n\nR\u00e9sumons-nous. Voil\u00e0 un homme d'un certain caract\u00e8re, dans la force de l'\u00e2ge qui pourtant agit et parle comme un enfant. Une affaire l'ent\u00e9n\u00e8bre \u00e0 laquelle il n'ose m\u00eame plus songer. A-t-il bout\u00e9 la loi d'un coup de pied au cul pour s'installer d\u00e9finitivement dans la posture d'un malfaiteur, d'un possible criminel ? Ou en fut-il au contraire une victime ? Comment parvenir \u00e0 lui faire dire son r\u00f4le exact et ce qui s'est r\u00e9ellement pass\u00e9 ? \u00c0 l'\u00e9couter, on a bien une vaste demeure sise dans un parc aux all\u00e9es innombrables autour de l'amertume d'un \u00e9tang, un groupe de trembles d\u00e9voy\u00e9s devant le b\u00e2timent des communs qu'une serre relie \u00e0 l'\u00e9difice principal, laquelle semble tenir un r\u00f4le primordial \u00e0 cause, parmi tout un fatras de jouets divers dont une panoplie de flic avec menottes et flingue expos\u00e9e avec ostentation, \u00e0 cause du dr\u00f4le de mannequin en bois des \u00eeles qu'elle abrite tenant un plateau et pr\u00eat \u00e0 vous servir n'importe quoi, puis une tabl\u00e9e anim\u00e9e dans un salon, salle \u00e0 manger alors que la nuit tombe et que l'on ne sait bient\u00f4t plus de quoi l'on parle de fa\u00e7on si contradictoire, d'autant qu'une panne d'\u00e9lectricit\u00e9 a plong\u00e9 tous les convives dans le noir, noir du propos, noir des visages, noir qu'on retrouve \u00e0 l'aube du lendemain dans une chambre qu'une porte entreb\u00e2ille sur une forme pas nette dans un lit, et qui fait fuir Charles-Andr\u00e9, alors qu'un soup\u00e7on de neige inattendue en octobre a install\u00e9 aux fen\u00eatres sa grande copie blanche et qu'il s'efforce d'effacer ses propres traces jusqu'\u00e0 la grille, le tout dit, exprim\u00e9 confus\u00e9ment par lui-m\u00eame, en d\u00e9pit des bougies qui rendirent la soir\u00e9e \u00e0 nouveau intelligible et que la gardienne, une femme entre deux \u00e2ges, \u00e0 tout moment apportait.\n\nLa langue lui manque \u00e0 raconter tout cela. Qu'il se d\u00e9clare soudain somnambule, sans doute pour exprimer que ses mots appartiennent \u00e0 son double nocturne, n'excuse pas une telle incoh\u00e9rence. Sa grand-m\u00e8re maternelle l'\u00e9tait para\u00eet-il, et la nuit revivait ses jours et alors ? Oui, celle de condition modeste qui \u00e9pousa un richissime propri\u00e9taire, la fille d'un scieur de long de basse Bretagne qui, par son minois, ses mains effervescentes, sut gagner les faveurs d'un homme plus vieux qu'elle d'un demi-si\u00e8cle et qui donc, gr\u00e2ce aux attraits de sa jolie personne, h\u00e9rita de cette folie en brique de trois \u00e9tages qu'on vient juste de d\u00e9crire au fa\u00eete de sa rude mont\u00e9e dans un des faubourgs hupp\u00e9s de Nantes. \u00c9tait-ce l'opulence du quartier qui l'\u00e9loignait encore davantage du c\u0153ur de cette m\u00e9tropole r\u00e9gionale qui parfois s'enivre vers le large ? Alors Nantes, \u00e0 l'heure qui nous occupe, ne poss\u00e8de plus de pont-transbordeur, sinon Charles-Andr\u00e9, qui ne parvient pas \u00e0 sortir de ses tripes ce \u00e0 quoi il participa, pourrait, faute de mieux, en attendant d'avoir la force d'entrer plus pr\u00e9cis\u00e9ment dans les d\u00e9tails, au moins l'\u00e9voquer en long et en large, mais quel rapport ce tablier mouvant qui vous transportait d'une rive \u00e0 l'autre aurait-il eu avec son histoire ?\n\nLui seul saurait le dire. Mais il ne dit pas, se prom\u00e8ne muettement dans ses pens\u00e9es v\u00e9cues comme des ombres \u00e0 qui il souhaiterait \u00e0 l'\u00e9vidence parfois passer les menottes. Est-ce la raison de son silence, de son go\u00fbt pour les landes qui font taire la terre ?\n\nEn cette fin octobre, d\u00e9but novembre, il niche toujours au creux de la villa Rose, oui on n'a pas oubli\u00e9 le nom de la villa de ses amis provisoirement am\u00e9ricains, \u00e0 toucher la conserverie, juste apr\u00e8s le tournant et la descente vers le port tout fris\u00e9 d'\u00e9cume ce soir-l\u00e0 o\u00f9 il d\u00e9cida... Mais il d\u00e9cide toujours et s'en repent aussit\u00f4t. Ce qui fait qu'il ne d\u00e9cide rien. Ira-t-il souper dans le modeste troquet \u00e0 Saint-Pierre o\u00f9 la charmante patronne le sert en priorit\u00e9 ? Il n'y avait pas d'\u00e9v\u00e9nements dans sa vie. Allait-il s'en susciter un ? N'\u00e9tait-il pas un peu trop au large seul \u00e0 la villa Rose ? Accepterait-elle de l'y suivre, une fois son service achev\u00e9 ? Qu'en penserait sa d\u00e9funte tante ? Surtout, ne pas demander conseil \u00e0 l'abb\u00e9, il en saccagerait par d\u00e9pit toutes les fleurs de son jardin ! Et Ang\u00e8le ? Il lui suffisait d'aller frapper \u00e0 sa porte tout contre l'\u00e9glise. Ah, s'il pouvait se d\u00e9charger de son fardeau en racontant \u00e0 une \u00e2me s\u0153ur, certes \u00e0 mots couverts, couverts par sa peur, tout ce qu'il a v\u00e9cu, il y a \u00e0 peine quinze jours. Quinze jours ? Un si\u00e8cle d\u00e9sormais pour lui, une prison perp\u00e9tuelle dont il ne voyait pas l'issue, ce seuil inond\u00e9 de lumi\u00e8re qu'il aspirait tant \u00e0 atteindre !\n\nVivre comme avant, se promit-il, domestiquer ses humeurs. Ne pas s'\u00e9carter plus d'une minute de la ligne g\u00e9n\u00e9rale du jour. Un homme justement \u00e9tait venu sonner \u00e0 la grille de la villa, le jardinier de ses amis qui en leur absence avait pour t\u00e2che de maintenir le jardin en bon \u00e9tat, surtout le bout de terrain fleuri et en pente douce qui touche \u00e0 la prairie. Ils se reconnurent d'embl\u00e9e, le visiteur l'ayant entraper\u00e7u en leur compagnie \u00e0 la villa Rose en ao\u00fbt dernier, c'\u00e9tait bien en ao\u00fbt ?\n\nCharles-Andr\u00e9 opina, l'accompagnant dans son inspection des plates-bandes. Ils caus\u00e8rent de tout, de rien. Oui, en ce moment, la mer bouge pas mal. Oh, pas celle sur baie, celle-l\u00e0 reste tranquille, mais l'autre, la sauvage, l'oc\u00e9an qui frappe de plein fouet la presqu'\u00eele. Il habite aux premi\u00e8res loges de cette fureur, l\u00e0-bas dans l'un de ces hameaux \u00ab ker quelque chose \u00bb ensevelis dans le granit. Il n'est pas rare que de l'\u00e9cume vole jusqu'\u00e0 ses fen\u00eatres, commente-t-il fi\u00e8rement. L'homme a un geste vague, le propos avis\u00e9, se demande si un jour ou l'autre \u00ab vos amis vont pas \u00eatre oblig\u00e9s \u00bb de faire abattre l'un des trembles. Il t\u00e2te son tronc malade.\n\n\u00ab Ce n'est pas celui-l\u00e0 en effet qui pourrait soutenir la vo\u00fbte c\u00e9leste, d\u00e9plore ironique Charles-Andr\u00e9.\n\n\u2014 Alors c'est vous qui tenez la maison ? Quand est-ce que vos amis ils retournent des Am\u00e9riques ? Dans quelques semaines ? Vous dites dans quelques semaines ? Alors vous \u00eates l\u00e0 durant tout ce temps-l\u00e0 ? \u00bb\n\nCharles-Andr\u00e9 rigole, proteste, fait non non, explique qu'il n'est l\u00e0 que pour les vacances de la Toussaint, qu'il est enseignant, mais qu'il avait \u00e9t\u00e9 convenu entre ses amis et lui, qui lui avaient d'ailleurs refil\u00e9 leur clef, qu'au cas o\u00f9 il aurait besoin d'un bon bol d'air il pourrait toujours venir en respirer un \u00e0 leur villa avant de reprendre le collier.\n\n\u00ab Ah dame par ici \u00e7a souffle \u00bb, approuve l'homme qui met un temps fou pour atteindre le fond de son verre. Ils boivent debout dans la cuisine. Charles-Andr\u00e9 s'impatiente, triture une fourchette, un couteau qu'il avait omis de ranger, tire un tiroir, les range. L'autre n'y comprend rien, lampe \u00e0 petits coups fort lents le muscat dor\u00e9 : \u00ab \u00c7a fait du bien par o\u00f9 \u00e7a passe \u00bb, jase-t-il, \u00e9voque subitement un fait-divers lu quelque part, ah si, chez Tanguy \u00e0 Saint-Pierre, le coiffeur, un truc incroyable qui... \u00ab \u00c9coutez-moi bien, figurez-vous... \u00bb\n\nLongtemps apr\u00e8s avoir referm\u00e9 la grille sur la silhouette trapue de son visiteur, Charles-Andr\u00e9 se demandera... L'autre, tout \u00e0 son histoire, en avait m\u00eame oubli\u00e9 la localit\u00e9 o\u00f9 \u00e9tait cens\u00e9e s'\u00eatre d\u00e9roul\u00e9e une telle chose, un presque village semble-t-il, au bout d'une rue, mais pas en pente, une grande b\u00e2tisse, mais pas ouverte souvent, suite \u00e0 des d\u00e9m\u00eal\u00e9s d'h\u00e9ritage, il y aurait eu...\n\n\u00ab Figurez-vous qu'il y aurait eu. \u00bb\n\nL'homme n'en partait plus. Il a toujours eu la passion des faits-divers, \u00e7a le fait bourgeonner. \u00ab Le comble pour un jardinier, vous ne trouvez pas ? \u00bb\n\nIl rit.\n\n\u00ab Il faut dire, c'est fou ce que des gens malintentionn\u00e9s peuvent inventer de nos jours. Encore hier... \u00bb\n\nCharles-Andr\u00e9 avait mis cet \u00ab encore hier \u00bb presque dehors, n'en pouvant plus de supporter la voix geignarde de cet \u00c9mile Touveau, la manie qu'il avait tout en parlant de lisser perp\u00e9tuellement de la main droite sa jambe de pantalon de velours. Puis, apr\u00e8s le d\u00e9part de son visiteur, il s'\u00e9tait retrouv\u00e9 seul dans l'immense villa, livr\u00e9 \u00e0 ses d\u00e9mons int\u00e9rieurs. L'histoire dite par le type n'\u00e9tait pas tout \u00e0 fait la m\u00eame, cependant... Il respira un bon coup.\n\n\u00ab Encore hier \u00bb, r\u00e9p\u00e9ta-t-il, cherchant \u00e0 r\u00e9cup\u00e9rer une partie de son souffle laiss\u00e9 en contrebas. \u00ab Encore hier. \u00bb Et il eut enfin la force d'en sourire.\n\n#\n\nUne id\u00e9e lui vint. Sans doute l'avait-il tir\u00e9e de l'un de ces d\u00e9vots opuscules fleurant bon la sacristie qui encombrent la chambre de ses amis \u00e0 l'\u00e9tage, comme quoi en chacun de nous habiteraient deux \u00eatres, l'un plut\u00f4t du dehors qu'il abandonne pr\u00e9sentement aux miroirs de la villa Rose, cet homme \u00e0 la quarantaine avenante qu'il propage dans le monde, au bar de la Jet\u00e9e ou ailleurs, et l'autre type, plut\u00f4t du dedans, laiss\u00e9 l\u00e0-bas comme souvenir de son passage dans la folie en brique ancestrale o\u00f9 sa tante, une dingue de J\u00e9sus, \u00e9tait \u00e0 l'\u00e9poque de ses douze ans d\u00e9c\u00e9d\u00e9e mains jointes dans son lit de vieille fille suite \u00e0 de troubles circonstances qu'il n'osait plus s'\u00e9num\u00e9rer jusqu'\u00e0 ce fameux soir d'il y a \u00e0 peine quinze jours o\u00f9 justement...\n\nll soupira. Serait-ce \u00e0 son \u00e2ge innocent d'alors qu'il e\u00fbt fallu passer les menottes pour emp\u00eacher la suite, tout cela ? Il regarda ses mains qui contenaient \u00ab tout cela \u00bb, elles qui avaient agi de la sorte ? Sa culpabilit\u00e9 devenait si grande qu'il en arrivait parfois \u00e0 vouloir se cacher \u00e0 lui-m\u00eame l'identit\u00e9 de l'endroit o\u00f9 il s'\u00e9tait r\u00e9fugi\u00e9. Certes une presqu'\u00eele, mais plus celle de Quiberon. N'importe quel sursaut de rivage un peu simulateur qui mime une exclamation vers le large aurait pu pr\u00e9tendre le cacher ! Or la c\u00f4te Atlantique n'en manque pas ni la Manche ou la mer du Nord. Comment le retrouver ? Et d'ailleurs le recherchait-on et pour quelles obscures raisons ? Il n'aspirait plus gu\u00e8re \u00e0 en d\u00e9vider le chapelet, r\u00e9clamait la s\u00e9r\u00e9nit\u00e9 de l'\u00e2me au pain tendre qu'il coupe, au verre qu'il remplit. La cuisine o\u00f9 il se tenait plus volontiers l'apaisait. Car du reste de la villa il aurait voulu s'en d\u00e9barrasser les \u00e9paules comme d'un grand manteau d'hiver. Faute \u00e0 novembre, \u00e0 l'\u00e9normit\u00e9 de ces jours allum\u00e9s d'une lumi\u00e8re basse, au vent, \u00e0 la pluie noire, heureusement que l'oc\u00e9an tout proche lavait ses yeux en permanence. Devant son humeur soulev\u00e9e, il sentait moins les siennes, d'humeurs, si sombres, pr\u00eates \u00e0 lui sauter dessus depuis le moindre recoin !\n\nIl avait pris soin, par une sorte de d\u00e9risoire scrupule, d'effacer pour venir jusqu'ici toutes ses traces, passant d'un train dans l'autre, revenant sur ses pas. Jusqu'au nom m\u00eame de Saint-Pierre (le bourg proche hant\u00e9 par de vieilles mar\u00e9es usant \u00e0 leur fa\u00e7on r\u00e9p\u00e9titive leurs fonds de culotte sur des rochers nus) qui lui paraissait ne plus \u00eatre le vrai \u00e0 force d'\u00eatre peupl\u00e9 de ses propres ombres ! D'ailleurs, \u00e0 son arriv\u00e9e dans la villa de ses amis provisoirement am\u00e9ricains, pourquoi au d\u00e9but de son s\u00e9jour vouloir taire sa pr\u00e9sence, m\u00eame aux arbres du jardin, au point d'en arriver \u00e0 marmonner dans le secret de sa bouche son identit\u00e9 compl\u00e8te : \u00ab Charles-Andr\u00e9 Bertrand. \u00bb Qui pouvait l'entendre ? Trois pr\u00e9noms forment-ils d'ailleurs un nom ? Et il faut un nom pour qu'on vous accuse ! Parfois il doutait d'en avoir vraiment un. \u00c9tait-il plus Charles qu'Andr\u00e9 ou Bertrand ?\n\nAu cours de ses incursions dans le village, sur la jet\u00e9e du port fouett\u00e9e par les vagues o\u00f9 se balancent en permanence deux ou trois barques quand l'heure consent aussi \u00e0 jeter l'ancre, il tentait tellement de se persuader de l'avoir aussi jet\u00e9e, cette ancre, d'\u00eatre pour de bon en vacances de tous ses instants, amarr\u00e9 simplement au bonheur d'\u00eatre. Bient\u00f4t en effet, dans une huitaine, il remonterait en selle, r\u00e9pondrait oui non \u00e0 tous ses coll\u00e8gues dans ce lyc\u00e9e imp\u00e9n\u00e9trable de Nantes o\u00f9 il officie comme professeur de lettres. Il n'aurait plus alors qu'un seul devoir, aller tirer les rideaux, repousser les volets de la chambrette des communs o\u00f9 l'inexpiable ne s'\u00e9tait peut-\u00eatre pas produit ! \u00c0 d'autres moments, le courage lui manquait. Aurait-il jamais la force ? Cette folie en brique (rouge sang, trouvait-il moyen d'ajouter) s'\u00e9l\u00e8ve pas loin de son \u00e9tablissement scolaire, d'un peu il pourrait presque l'apercevoir depuis l'estrade, devant son tableau noir. Et comme il en d\u00e9tenait la clef, si seulement, en plus d'ouvrir la grille, elle avait pu devenir la solution, la clef de toute cette histoire bonne \u00e0 rel\u00e9guer aux oubliettes (il y en a toujours dans les ch\u00e2teaux), ce noir souci qui le rongeait jusqu'\u00e0 l'os.\n\nIl d\u00e9cida, en attendant, de vivre ce mardi comme un mardi, de ne plus lui accoler ce funeste dimanche d'\u00e0 peine une quinzaine o\u00f9 il participa... Participa- t-il ? La tabl\u00e9e \u00e9tait bruyante, anim\u00e9e de folles plaisanteries. Le vin coulait \u00e0 flots. Au dessert, qui eut l'id\u00e9e ? f\u00e2cheuse, \u00f4 combien ? Il en fr\u00e9missait encore, n'osait penser plus loin, \u00e9vitait de toutes ses forces de revisiter mentalement la serre o\u00f9 ce mannequin mul\u00e2tre en veste rouge et pantalon p\u00e2le qui effraya tant ses jeunes ann\u00e9es semblait d\u00e9signer encore de son bras de bois tendu l'innocente victime. Ce serait M. Audapt, ex-inspecteur des douanes, qui l'aurait, il y a un infini d'ann\u00e9es, ramen\u00e9 des \u00eeles. Charles-Andr\u00e9 ne sait plus de laquelle, sans nul doute cr\u00e9nel\u00e9e de vagues qui fa\u00e7onn\u00e8rent l'expression farouche du personnage, son nez busqu\u00e9 comme le bec d'un oiseau de proie. Dans ses orbites, deux billes de verre colorent son absence de regard. Et pourtant durant toute son enfance, il eut le sentiment d'\u00eatre \u00e9pi\u00e9 par lui. Aussi passait-il le plus souvent en trombe dans cette maudite serre qui relie les communs au b\u00e2timent principal. Les communs ? Ce b\u00e2timent d'un \u00e9tage cach\u00e9 par un semblant de for\u00eat o\u00f9 le soleil ne perce jamais, d'o\u00f9 son appellation : \u00ab l'Ombre \u00bb.\n\nOn frappait, semble-t-il, \u00e0 la porte de la cuisine, il se pr\u00e9cipita. Ce n'\u00e9tait que le vent, ce vulgaire cabot qui s'amuse \u00e0 \u00e9branler toute chose, \u00e0 g\u00e9mir dans les jointures. Les trembles, ses fr\u00e8res d'infortune parmi les arbres, paraissaient \u00e0 travers la vitre lui faire signe. Il y en a cinq \u00e0 la villa Rose group\u00e9s en meute, \u00e9meute pr\u00e8s de la piscine vide. Demander \u00e0 Jean-Marc. Mais, quoi d\u00e9j\u00e0 ? il avait oubli\u00e9.\n\n#\n\nNovembre cette ann\u00e9e-l\u00e0 s'approchait trop pr\u00e8s des vitres. Ce n'\u00e9taient que rafales, coups de vent, brusques averses \u00e0 vous tremper jusqu'\u00e0 l'\u00e2me. Les vagues, ces surmen\u00e9es, secouaient tellement le large qu'elles en extrayaient des d\u00e9bris de toute sorte qui polluaient les plages, restes de voiles d\u00e9chir\u00e9es par le mauvais temps et plus du tout aptes \u00e0 claquer en haut d'un m\u00e2t, choses informes des profondeurs rapport\u00e9es au rivage pour que celui-ci les humanise, leur donne \u00e0 nouveau un nom. Charles-Andr\u00e9 \u00e0 sa mani\u00e8re en \u00e9tait-il devenu un, une sorte de reste abyssal, de rescap\u00e9 \u00e0 son corps d\u00e9fendant d'un naufrage ex\u00e9cut\u00e9 en pleine terre ? Devant un tel tumulte, au bar de la Jet\u00e9e on prenait bien soin de refermer la porte. L'avait-il, lui, trop laiss\u00e9e ouverte ? Ces choses des profondeurs avaient-elles \u00e0 jamais d\u00e9natur\u00e9 ses pens\u00e9es ? Il avait beau se dire, dans ses meilleurs moments, qu'il ne s'\u00e9tait rien pass\u00e9, il savait bien que la minute suivante lui affirmerait le contraire car la nuit n'\u00e9tait pas tomb\u00e9e pour rien ce soir-l\u00e0. Il se rappelait son effroi dans un couloir, le parc si guetteur \u00e9talant sa solitude neigeuse aux fen\u00eatres, l'\u00e9tang qui autrefois l'effrayait de son eau morte ! S'en sortirait-il un jour de toutes ces peurs ? Se r\u00e9veillera-t-il un matin d\u00e9lest\u00e9 de cette funeste histoire ? Heureux comme l'eau qui coule au robinet, aussi fluide qu'elle, sans plus de pens\u00e9es que l'\u00e9vier qu'elle inonde ! Sa tante avait J\u00e9sus dont elle m\u00ealait les pas aux siens. Mais lui ? Si sa Galil\u00e9e \u00e9tait la Bretagne, la baie de Quiberon qui amusa ses jeunes ann\u00e9es n'avait quand m\u00eame pas les vertus du lac de Tib\u00e9riade. S'y baigner ne vous procurait pas une conscience plus nette. Il se promit de confier au papier ce qui s'\u00e9tait r\u00e9ellement pass\u00e9, de refermer de telles heures avec son carnet ! Mais \u00e9tait-ce prudent ? Qu'il le perde et le voil\u00e0 bient\u00f4t devant un tribunal somm\u00e9 de r\u00e9pondre de ses actes. Lesquels d'ailleurs ? Ceux de nuit ou ceux de jour ? N'agit-on pas quand on dort ? Il fallait pourtant qu'il se fasse une id\u00e9e plus claire du d\u00e9roulement des faits. Au d\u00e9but de la soir\u00e9e, ils \u00e9taient plusieurs autour de la table et c'\u00e9tait une longue tabl\u00e9e, les rideaux pourtant \u00e9pais de la salle \u00e0 manger n'\u00e9touffaient pas les rires, l'\u00e9clat des reparties.\n\n\u00ab Je suis un homme en panne \u00bb, conclut-il se levant de sa chaise. Oui il \u00e9tait assis pensant \u00e0 tout et \u00e0 rien \u00e0 la fen\u00eatre la plus exacte du rez-de-chauss\u00e9e, celle qui d\u00e9livre le portail de l'entr\u00e9e et le bout de route \u00e0 emprunter dans quelques minutes pour descendre au village, consulter les journaux au bar de la Jet\u00e9e, \u00e9changer quelque menue monnaie de conversation avec le patron pas du pays qui s'inqui\u00e8te souvent de l'humeur du jour. Si les vagues restent bien \u00e0 leur place et n'ambitionnent pas de d\u00e9ferler jusque chez lui. Le baron Louis vous sert cela en guise de plaisanterie. N'emp\u00eache que Louis Baron (son vrai nom que ses amis l'\u00e9t\u00e9 dernier s'amusaient \u00e0 inverser \u00e0 cause de la condescendance tout aristocratique qu'il met \u00e0 leur servir leur habituel petit blanc) arbore le plus souvent une mine de fond de verre. Un homme des terres n\u00e9 \u00e0 ce qu'il para\u00eet pr\u00e8s d'Auray et qui, depuis la catastrophe du \u00ab tsunami \u00bb au Japon, ne dort plus que d'un \u0153il, consid\u00e9rant la position hardie de son \u00e9tablissement sur cette pointe herbue qui surplombe d'\u00e0 peine un demi-pouce l'anse sablonneuse o\u00f9 ces \u00e9cumeuses, les vagues, sont encag\u00e9es. Il avoue m\u00eame le soir au coucher y pr\u00eater davantage l'oreille, savoir, r\u00e9p\u00e8te-t-il avec emphase, si l'une d'elles, plus v\u00e9h\u00e9mente que les autres, n'accourrait pas du fin fond de l'horizon pour oser venir \u00e9clabousser sa porte !\n\nCharles-Andr\u00e9 r\u00e9fl\u00e9chissait, peut-\u00eatre \u00e9crire \u00e0 ses amis en Virginie afin de leur apprendre qu'il avait proprement us\u00e9 de leur invitation tacite de l'\u00e9t\u00e9, mais qu'ils ne s'inqui\u00e8tent pas, qu'il veillerait \u00e0 remettre tout en ordre dans leur villa avant son d\u00e9part. En ordre ? Ah s'il avait pu balayer aussi en lui-m\u00eame, \u00e9pousseter toutes ces funestes id\u00e9es, ouvrir les fen\u00eatres. Mais l'esprit en a-t-il ? Il veut dire, des fen\u00eatres, des portes, qu'on puisse y entrer faire le m\u00e9nage de ses nuits. Car la nuit s'\u00e9tait empar\u00e9e de sa personne. Il ne voyait plus goutte en lui-m\u00eame. D'autant qu'il n'\u00e9tait absolument pas s\u00fbr du d\u00e9roul\u00e9 des \u00e9v\u00e9nements. \u00c0 quel moment, par exemple, le serveur en bois blanc (fr\u00e8re moins domestiqu\u00e9 du m\u00eame personnage entraper\u00e7u l'autre samedi \u00e0 Nantes au march\u00e9 aux puces) intervint-il ? Et le cr\u00e9puscule qui noircissait alors les vitres avec cette petite lueur qui remontait, semble- t-il, de l'\u00e9tang et toutes ces all\u00e9es furtives se dispersant en tous sens ? Laquelle suivre ? Il aurait bien eu besoin du labrador de Solange et Jean-Marc pour revenir flairer l'insolite d'une telle soir\u00e9e. Cette chienne \u00e9bouriffante, le jardinier la gardait, lui avait-il appris avec une certaine fiert\u00e9 lors de sa r\u00e9cente visite.\n\nAlors aller marcher dans la lande ? Qui sait si en remettant ses pas dans ceux de son enfance entre les hameaux arcbout\u00e9s dans leur granit il ne r\u00e9cup\u00e9rerait pas une certaine paix ? Voyons, il se tient l\u00e0 \u00e0 la villa Rose depuis quatre, cinq jours, trois encore pour arpenter la presqu'\u00eele, respirer l'air marin, il a toujours le m\u00eame \u00e2ge, son visage n'a pas pris une ride de plus dans la glace, ses papiers attestent ses quarante-trois ans qu'il peut pr\u00e9senter \u00e0 n'importe quelle r\u00e9quisition, il va retrouver le chahut de ses \u00e9l\u00e8ves sous huitaine, mais plus h\u00e9las, depuis le d\u00e9part de Diane, son oreille favorite, plus aucune cr\u00e9ature blonde \u00e0 qui il aurait pu confier...\n\nOn devait approcher de midi. Il sortit, prit bien soin de refermer le portail. L'oc\u00e9an de l'autre c\u00f4t\u00e9 de la route marmonnait sa complainte. C'\u00e9tait mar\u00e9e basse, il ne s'attarda pas devant la simagr\u00e9e des rochers, ces noirs d\u00e9mons luisants de go\u00e9mon, hirsutes d'algues diverses. Ah si sa tante avait pu revenir de sa mort pour marcher \u00e0 ses c\u00f4t\u00e9s ! Son chalet qui tient toujours debout \u00e0 Saint-Pierre avait \u00e9t\u00e9 vendu aussit\u00f4t apr\u00e8s son d\u00e9c\u00e8s. Il avait \u00e9t\u00e9 s'en assurer d\u00e8s son arriv\u00e9e dans la presqu'\u00eele. Il n'y manquait pas une tuile et le portillon du jardin battait toujours autant sous l'effet d'un mauvais vent. Il avait examin\u00e9 depuis la rue une \u00e0 une les persiennes closes. L\u00e0 qu'autrefois avec sa m\u00e8re il sentit passer il ne sait plus combien d'hivers. Puis uniquement l'\u00e9t\u00e9 en compagnie de sa tante qui ne consentait \u00e0 s'y rendre qu'\u00e0 la belle saison, lui avec elle, elle avec J\u00e9sus dont elle croyait alors ressentir la pr\u00e9sence dans l'ombre tendre qui les accompagnait quand ils descendaient \u00e0 la plage le dimanche apr\u00e8s la messe par le chemin de la Vieille-Dame.\n\nCharles-Andr\u00e9 n'avait alors que dix onze ans, dans une ann\u00e9e, il surprendra sa tante morte dans son lit mains jointes, un matin que croyant l'entendre bouger dans sa chambrette il \u00e9tait venu qu\u00e9rir aupr\u00e8s d'elle un premier baiser qui l'aiderait ensuite \u00e0 se d\u00e9barbouiller, \u00e0 vivre sa journ\u00e9e. Mais pas \u00e0 Saint-Pierre, \u00e0 Nantes, dans l'antique maison ancestrale o\u00f9 s'\u00e9tait rassembl\u00e9e la veille au soir la famille confuse, toute cette pr\u00e9sence murmur\u00e9e, clam\u00e9e, ces innombrables parents dont il m\u00ealait d\u00e9j\u00e0 tout petit les noms et pr\u00e9noms dans sa t\u00eate, cousins, cousines, neveux, ni\u00e8ces, vieil oncle, tante surann\u00e9e... Soir\u00e9e qui s'\u00e9tait reproduite r\u00e9cemment et \u00e0 la virgule pr\u00e8s avec parmi d'autres convives les m\u00eames forc\u00e9ment un peu grandis, r\u00e9unis pour une obscure histoire d'h\u00e9ritage dans cette noble demeure en brique rouge. \u00ab Rouge sang \u00bb, ne put-il s'emp\u00eacher de penser \u00e0 nouveau, faute \u00e0 ce personnage laqu\u00e9 noir et justement rouge statufi\u00e9 dans la serre, celle qui relie les communs au b\u00e2timent principal et qui autrefois l'apeurait tant. Le type en bois des \u00eeles n'avait pas pris une ride, la main restait toujours aussi ferme sous le plateau factice o\u00f9 tra\u00eenaient toujours quelques vains gobelets.\n\nEt toutes ces images qui lui revenaient en rafales, \u00e0 la fois celles de son enfance et les terribles dans le m\u00eame lieu d'il y a quinze jours. Qu'avait-il besoin d'y resonger ?\n\n\u00ab J'ai la maladie des maisons \u00bb s'excusait-il, surtout celles depuis longtemps inhabit\u00e9es, les grandes o\u00f9 s'ajoute, aux pas qui r\u00e9sonnent, le va-et-vient de la m\u00e9moire derri\u00e8re des volets obstin\u00e9ment ferm\u00e9s depuis des lustres.\n\nIl gagnait la lande, ou plut\u00f4t la lande le gagnait, une d\u00e9solation d'herbe rase surmont\u00e9e d'une ruine visit\u00e9e par les mouettes. \u00c0 qui cette b\u00e2tisse avait-elle appartenu ? Il longea ses murs \u00e0 moiti\u00e9 \u00e9croul\u00e9s. \u00c9tait-ce l'effet d'un soudain soleil ? Brusquement, il vit clair en lui, d\u00e9cida d'un pas ferme, \u00e0 son retour \u00e0 Nantes, de mettre fin \u00e0 toute cette histoire, d'aller ouvrir grands les rideaux de la rue Marzelle afin d'examiner de plus pr\u00e8s si tout cela, qu'il supposait avoir \u00e9t\u00e9, n'appartenait pas tout simplement \u00e0 son imagination malade. Car aucune information s'y rapportant ne filtrait dans la presse. Or rien n'\u00e9chappait \u00e0 son anxi\u00e9t\u00e9 qui chaque jour au bar de la Jet\u00e9e \u00e9pluchait les journaux. Quand il y p\u00e9n\u00e9tra, le baron Louis, plus naufrag\u00e9 qu'\u00e0 son ordinaire, r\u00e9pondit \u00e0 peine \u00e0 son vague salut. \u00c7a grondait au bas de la plage. Quelle heure \u00e9tait-il ?\n\n#\n\nLa presqu'\u00eele, cette main pos\u00e9e sur les flots qui \u00e9treint on ne sait quoi, mais qui \u00e9treint. \u00c0 l'emplacement du poignet, l'isthme, une route plus un chemin de fer et la mer des deux c\u00f4t\u00e9s, l'une perp\u00e9tuellement furieuse, l'autre apais\u00e9e mordant \u00e0 peine ses plages. Et devant le visiteur qui oserait n\u00e9anmoins s'aventurer sur cette terre \u00e0 peine sauv\u00e9e des flots, un fort inexpugnable qui cadenasse son entr\u00e9e, clef d\u00e9tenue sans nul doute par ce patron d'un bar-tabac qui vit tellement dans la crainte des mar\u00e9es. Mis au courant le baron Louis hausserait forc\u00e9ment les \u00e9paules, vous prenant \u00e0 t\u00e9moin, comment quelqu'un peut-il \u00eatre assez fou pour s'imaginer qu'un homme solide comme lui, si r\u00e9sistant au vent, pourrait reculer d'un pouce devant ces filles d'\u00e9cume comme Charles-Andr\u00e9 jamais \u00e0 court d'\u00e9pith\u00e8tes aime d\u00e9nommer les vagues ? Surveiller leur avanc\u00e9e, ce n'est pas les craindre, justifierait-il \u00e0 tout coup s'il avait les mots. Mais il ne les a pas, perdus pour l'\u00e9ternit\u00e9 dans les verres qu'il rince et les tables qu'il essuie. Aussi la conversation avec lui tourne-t-elle vite au silence, le vaste que nourrit le battement de la porte vitr\u00e9e et la rumeur du dehors, l'\u00e9cho presque indiscernable de la lande, herbe rase sillonn\u00e9e de chemins \u00e0 peine \u00e9nonc\u00e9s allant tous mourir dans les sables et les galets. Demander leur avis aux rochers, se disait parfois Charles-Andr\u00e9 \u00e0 voir ces sortes de p\u00e8lerins farouches faire le gros dos contre la houle qui les ensauvage. Tous ces jeux d'\u00e9cume anim\u00e9s par le large !\n\nLe large ? Ce lieu inexprimable du fond de l'horizon d'o\u00f9 proviennent les vagues, les bateaux sans peur.\n\nLe large ? Ce qui actuellement lui manquait avec toutes ces heures qui se faufilaient \u00e9troites d\u00e8s son r\u00e9veil par une esp\u00e8ce de porte de service de la terreur.\n\nQuelle pri\u00e8re adresser au large ? \u00c9tait-ce l'influence des livres pieux d\u00e9couverts sur une \u00e9tag\u00e8re recul\u00e9e de la villa Rose qui le faisait s'exprimer ainsi ? Les mots de sa jeune tante lui revenaient sur les l\u00e8vres et dans les yeux ce pauvre grillage qui s\u00e9parait \u00e0 Saint-Pierre son jardinet de celui de son voisin \u00e0 br\u00e9viaire, ce cher abb\u00e9 Messager. Cependant leur charmant duo n'approchait gu\u00e8re de pr\u00e8s ou de loin les t\u00e9n\u00e9breux \u00e9v\u00e9nements d'il y a une quinzaine. Pour lui, Charles-Andr\u00e9, c'\u00e9tait une grille et pas cette l\u00e9g\u00e8re armature de fer-blanc qui grillageait le moindre de ses instants. \u00c9tait-il d\u00e9j\u00e0 quasi en prison puisque condamn\u00e9 \u00e0 tout apercevoir d\u00e9sormais entre ses barreaux et \u00e0 avoir dans les oreilles jusqu'\u00e0 l'\u00e2me le grincement rouill\u00e9 d'un possible remords ? Mais n'avait-il pas grandi ? Pourquoi alors cette effarante nuit de ses douze ans imprimait-elle toujours son \u00eatre ? \u00c9tait-ce parce qu'elle paraissait la s\u0153ur a\u00een\u00e9e de celle qu'il venait de vivre et qui l'avait amen\u00e9 en d\u00e9route jusqu'\u00e0 la villa Rose ? Cette nuit d'il y a au moins trente ans et qui vit le d\u00e9c\u00e8s mains jointes de sa ch\u00e8re tante lequel ne se produisit pas \u00e0 Saint-Pierre mais \u00e0 Nantes, dans la demeure ancestrale et dans de troubles circonstances qu'il ne parvenait presque plus \u00e0 d\u00e9tailler o\u00f9 un fichu mannequin joua pour la premi\u00e8re fois un r\u00f4le n\u00e9faste, oui, ce mauvais type de la serre h\u00e9las encore debout dans le passage vitr\u00e9 qui relie rue Marzelle les communs, ce b\u00e2timent toujours \u00e0 l'ombre, \u00e0 l'\u00e9difice principal \u00e0 qui le soleil r\u00e9serve exclusivement ses augustes rayons. Du moins ses satan\u00e9s douze ans en \u00e9taient-ils alors intimement persuad\u00e9s qui ne cessaient de scruter le visage laqu\u00e9 noir et la main brune peut-\u00eatre assassine soutenant un plateau o\u00f9 subsistaient quelques verres factices. Bien s\u00fbr, sa quarantaine actuelle ne pouvait gu\u00e8re ajouter foi \u00e0 de tels enfantillages : comment un serveur noir en bois verni, sorte de groom en veste rouge et pantalon blanc, aurait-il pu...\n\nN\u00e9anmoins... Il promena toute la journ\u00e9e ce \u00ab n\u00e9anmoins \u00bb. Qui sait si \u00e0 marcher dans la lande entre tous ces hameaux de pur granit avec la mer qui crie sur sa droite, sa gauche, il ne retrouverait pas sa raison, du moins \u00e0 d\u00e9faut d'elle un semblant de s\u00e9r\u00e9nit\u00e9 ? On n'a jamais vu un meurtre perp\u00e9tr\u00e9 de cette fa\u00e7on. Un crime en bois blanc, \u00e7a porte \u00e0 rire ! Et d'abord qui lui prouvait qu'un quart de si\u00e8cle plus tard la m\u00eame situation s'\u00e9tait reproduite ? Bien s\u00fbr, l'\u00e9nigmatique mannequin dont la joyeuse tabl\u00e9e se servit \u00e0 un moment par mani\u00e8re de plaisanterie, la fus\u00e9e des bons mots, le charivari du vin, le choix des liqueurs, au dessert le r\u00e9confort demand\u00e9 \u00e0 un subtil armagnac. Tout cela arme les pens\u00e9es. Mais quand m\u00eame ! Certes il s'\u00e9tait mis \u00e0 neiger de fa\u00e7on inexplicable en octobre, la terre avait rev\u00eatu comme lors de ses premi\u00e8res ann\u00e9es son manteau blanc d'innocence rel\u00e9guant tout le noir du monde \u00e0 l'int\u00e9rieur de la rouge b\u00e2tisse en brique, n'emp\u00eache, l\u00e0 s'arr\u00eataient les semblants de similitudes ! N'emp\u00eache, les soup\u00e7ons n'allaient-ils pas n\u00e9cessairement tomber sur lui ? N'\u00e9tait-il pas le suspect primordial, le seul en dehors de la victime \u00e0 avoir dormi une nuit au \u00ab ch\u00e2teau \u00bb comme le voisinage d\u00e9nomme cette aust\u00e8re demeure d\u00e9fendue d'un parc dont les all\u00e9es s'entrelacent autour d'un \u00e9tang o\u00f9 l'esprit se noie ? Il serait donc peut-\u00eatre utile pour retrouver son calme qu'il se rem\u00e9more exactement et dans les plus infimes d\u00e9tails cette funeste soir\u00e9e. Comment Mme Joliette par exemple, la cuisini\u00e8re, mijota son menu et...\n\nIl e\u00fbt volontiers ajout\u00e9 plein de \u00ab et \u00bb \u00e0 ce et... Mais quelque chose en lui se refusait de se rappeler plus loin, de se r\u00e9capituler les mille gestes du mortel d\u00eener, de faire le tour de table des insouciants convives, d'entendre \u00e0 nouveau leurs pr\u00e9sences murmur\u00e9es, clam\u00e9es, le flot de leur reparties et m\u00eame de noter l'agitation des rideaux, comme si l'un d'eux e\u00fbt pu jouer un r\u00f4le quelconque dans cette affaire, si affaire comme il le dit souvent il y avait ! Par moments, h\u00e9las jusqu'\u00e0 pr\u00e9sent en pure perte, il recherchait le vrai mot, le mot subtil, le mot sans ombre qui aurait pu caract\u00e9riser, d\u00e9finir au mieux de tels faits !\n\nIl parvenait \u00e0 Kerniscob. \u00ab \u00c0 Kervihan, on boit son sang, \u00e0 K\u00e9ridanvel on jette son sel ! \u00bb trouva-t-il le moyen de chantonner b\u00eatement sans savoir pourquoi ! Besoin de rimes, de rattraper, rameuter ses vacances ? De renvoyer aux oubliettes cet \u00e9pouvantable cauchemar ? Car c'\u00e9tait le cong\u00e9 de la Toussaint, dans quelques jours il retrouverait ses \u00e9l\u00e8ves dans le lyc\u00e9e qui penche. La m\u00e9fiance l'avait tellement envahi qu'il se refusait de prononcer \u00e0 haute voix jusqu'au nom de ce candide \u00e9tablissement perch\u00e9 p\u00e9dagogiquement sur son coteau. Crainte de l'\u00e9cho ? Pourtant ces b\u00e2timents flambant neufs n'avaient encore rien \u00e0 se reprocher !\n\n\u00ab Marre, marre \u00bb, se r\u00e9p\u00e9tait-il, et son pas sonnait plus all\u00e8gre sur le chemin. \u00ab Les haies sont des sorci\u00e8res \u00bb, jasait-il pour jaser, pour ne pas retrouver tout de suite l'affreux silence fen\u00eatres ferm\u00e9es qui l'habitait le plus souvent depuis son arriv\u00e9e \u00e0 la villa Rose. Il ne devait pas \u00eatre si loin que \u00e7a du s\u00e9maphore. \u00c0 moins que ce poste de surveillance des agitations de la mer n'ait \u00e9t\u00e9 d\u00e9truit ? Il n'\u00e9tait pas pass\u00e9 par l\u00e0 depuis son enfance. Il avait fallu que Solange et Jean-Marc ach\u00e8tent cette villa pour qu'il revienne dans la presqu'\u00eele. \u00ab Elle est trop comme moi, osa-t-il se dire, cadenass\u00e9e c\u00f4t\u00e9 terre, de l'autre ouverte sur le large. \u00bb\n\nIl longeait la voie ferr\u00e9e. Une heure au moins qu'il marchait aussi bien dans ses pens\u00e9es que dans la lande. Aller visiter Ang\u00e8le ? Ne l'avait-elle pas invit\u00e9 \u00e0 venir pousser sa porte ? Dans ce cas, il lui fallait, non pas gagner Quiberon, mais plut\u00f4t retourner \u00e0 Saint-Pierre, \u00e0 l'eau morte de son port d'Orange aussi paisible que le lac de Tib\u00e9riade si cher \u00e0 sa d\u00e9funte tante folle des \u00c9vangiles, ceux de Marc, de Matthieu, de Luc voire de Jean qu'elle relisait sans cesse. Charles-Andr\u00e9 avec sa formation \u00e9l\u00e9mentaire d'enfant de ch\u0153ur s'\u00e9garait vite dans les pr\u00e9noms des ap\u00f4tres, des disciples dont elle lui rebattait les oreilles. Certains furent les t\u00e9moins oculaires de la vie du Christ. Pourquoi le bon Dieu, s'exclamait-elle, ne l'a-t-il pas, elle, fait vivre \u00e0 cette \u00e9poque ? Elle aurait pu \u00eatre la Samaritaine qui donne \u00e0 boire \u00e0 J\u00e9sus au puits de Jacob, ou une autre Marie-Madeleine ! Que n'e\u00fbt-elle pas \u00e9t\u00e9 dans cette Galil\u00e9e qu'elle froissait mentalement de ses pas ?\n\nEt elle partait d'un grand fou rire qui effrayait un peu le gamin qu'\u00e9tait alors Charles-Andr\u00e9, surtout quand les t\u00e9n\u00e8bres du soir commen\u00e7aient \u00e0 dire leur messe.\n\nEffet, cons\u00e9quence trente ans plus tard de cette presqu'\u00eele si pleine de r\u00e9sonances pour lui ? Il croyait presque par moments entendre cette brune intense marcher \u00e0 ses c\u00f4t\u00e9s. Ce fut un amour un peu simplet, desservi par un in\u00e9narrable potager, qu'elle avait v\u00e9cu sans le savoir avec l'abb\u00e9 Messager, ayant en commun, lui l'amour du large qu'il trouvait dans sa Bible, elle...\n\n\u00ab Elle elle \u00bb, chantonnait Charles-Andr\u00e9 pour d\u00e9rider la lande qui l'entourait de tous c\u00f4t\u00e9s, chasser une bonne fois ses mauvaises peurs.\n\n#\n\nLe chemin de la Vieille-Dame, d\u00e9nomm\u00e9 ainsi \u00e0 cause d'une personne du voisinage fort avanc\u00e9e en ann\u00e9es qui au si\u00e8cle dernier le descendit journellement jusqu'au bout de son \u00e2ge, vous m\u00e8ne certes de point en point, mais aussi... Comment exprimer pierre \u00e0 pierre son menu gravier roulant, l'exub\u00e9rance de ses haies qui vont d'un champ de menhirs \u00e0 la mer ? Un escalier de quelques marches l'ach\u00e8ve, et tombe \u00e0 pic sur une plage. L'enfance de Charles-Andr\u00e9 s'y trouvait ensabl\u00e9e. Ses dix ans y coururent, marmot, il y chercha ses premiers pas.\n\nAssis dans le salon de la villa Rose, il se repassait le film de son apr\u00e8s-midi. La demeure de ses amis provisoirement am\u00e9ricains respirait de tous ses pores. Il songea \u00e0 Jean-Marc, \u00e0 Solange, l\u00e0-bas en Virginie. Que devenaient-ils ? Leur affectueuse pr\u00e9sence lui aurait \u00e9t\u00e9 en ce moment bien n\u00e9cessaire, celle de Jean-Marc par exemple lui citant en ao\u00fbt dans ce m\u00eame salon cette d\u00e9finition tir\u00e9e d'un vieux manuel du XVIIIe si\u00e8cle : \u00ab Qu'est-ce que la danse ? C'est l'art de faire des pas r\u00e9gl\u00e9s. \u00bb Lui, Charles-Andr\u00e9 Bertrand dont les siens se d\u00e9r\u00e9glaient tant, et qui, depuis cette foutue affaire, vivait en d\u00e9sordre, il n'arrivait m\u00eame plus \u00e0 assumer son ombre, expliquait-il sans trop savoir ce qu'il disait.\n\nEn d\u00e9finitive, il n'avait pas \u00e9t\u00e9 voir Ang\u00e8le, sa rue l'embarrassait trop de tout son long derri\u00e8re l'\u00e9glise. Ne s'\u00e9taient-ils pas d\u00e9j\u00e0 tout dit \u00e0 Quiberon, l'autre jour ? Et puis, il e\u00fbt fallu durant des heures deviser autour d'une tasse de th\u00e9, s'exprimer poliment en remuant sa cuiller dans sa tasse, alors que l'\u00e9pouvante l'habitait encore un peu. Pourtant, il pouvait se rass\u00e9r\u00e9ner, son cauchemar ne filtrait aucunement dans les journaux, nulle allusion \u00e0 la rubrique des faits-divers. En \u00e9tait-ce d'ailleurs vraiment un ? Apr\u00e8s tout, ce n'\u00e9taient pas ses mains qui avaient \u00e9ventuellement vers\u00e9, si \u00ab versement \u00bb douteux il y eut !\n\nAu bar de la Jet\u00e9e, chez le baron Louis plus loquace qu'au matin, apr\u00e8s que Charles-Andr\u00e9 eut \u00e0 nouveau \u00e9pluch\u00e9 la presse comme un malade, ils avaient caus\u00e9 de choses et d'autres, de l'\u00e9tat de la mer qui vu l'heure tardive avait tendance \u00e0 augmenter le volume de ses vagues. Du moins \u00e9tait-ce l'avis de Charles-Andr\u00e9 moins accoutum\u00e9 que le robuste cafetier \u00e0 cette pr\u00e9sence grondante.\n\n\u00ab Vous restez encore longtemps parmi nous ? \u00bb avait demand\u00e9 celui-ci pour demander, \u00e9baucher un semblant de parlotte.\n\nCharles-Andr\u00e9 avait hoch\u00e9 la t\u00eate, \u00ab quelques jours, pas plus \u00bb, parut-il r\u00e9pondre.\n\nLa nuit s'approchait. Bient\u00f4t au fin fond de la villa Rose, il rechercherait en vain le sommeil. C'\u00e9tait son enfance, la criminelle ? S'il n'avait pas d\u00e9j\u00e0 v\u00e9cu, lors de ses douze ans, une nuit sid\u00e9rante en tout point analogue \u00e0 celle d'il y a \u00e0 peine quinze jours, il n'aurait pas descendu au matin comme un fou la rue Marzelle, apr\u00e8s avoir finalement laiss\u00e9 sa clef rouill\u00e9e, cette obstin\u00e9e qui, faisant fi de sa h\u00e2te enfantine, s'ent\u00eatait \u00e0 ne pas vouloir quitter la serrure de la grille. Il n'y manquait pourtant rien \u00e0 ce d\u00eener traditionnel de la veille au soir, r\u00e9union comme tous les ans \u00e0 la m\u00eame \u00e9poque pour une tabl\u00e9e familiale et comme c'est la Toussaint, ajout habituel \u00e0 l'intention des chers d\u00e9funts de quelques assiettes qui resteront forc\u00e9ment creuses tout au cours du repas, \u00e0 la diff\u00e9rence notable que ce soir-l\u00e0, alors que la neige au-dehors recouvrait le parc de son linceul, on se rassembla aussi pour discuter du prix de vente de cette auguste demeure que l'une de ces ch\u00e8res assiettes creuses leur l\u00e9gua, \u00e0 eux les enfants du premier mariage de M. Audapt et \u00e0 lui Charles-Andr\u00e9 Bertrand petit-fils de sa seconde \u00e9pouse, sa charmante grand-m\u00e8re maternelle au pr\u00e9alable veuve d'un jeune marin disparu en mer qui prit n\u00e9anmoins le temps de lui donner deux filles, sa m\u00e8re et sa tante. Et ce fut sans doute pour d\u00e9rider l'atmosph\u00e8re, all\u00e9ger cette aust\u00e8re bataille de chiffres que l'un des convives (mais qui ? mon Dieu qui ?) eut soudain l'id\u00e9e de se faire servir le digestif non par l'obligeante Mme Joliette, la gardienne, la femme \u00e0 tout faire de cette propri\u00e9t\u00e9, mais par le mannequin de la serre mont\u00e9 sur roulettes, \u00e0 charge pour elle de remplir les godets du plateau que le bonhomme tient pour l'\u00e9ternit\u00e9 !\n\nExactement la m\u00eame plaisanterie d'il y a trente ans, lors du d\u00eener qui fut suivi dans la m\u00eame nuit du brusque d\u00e9c\u00e8s de sa ch\u00e8re tante Marie et son r\u00e9veil, \u00e0 lui, Charles-Andr\u00e9 encore tout gamin dans une maison rendue encore plus d\u00e9serte par la pr\u00e9sence d'un cadavre. Sauf que cette fois ce n'\u00e9tait plus sa tante, mais feu la cuisini\u00e8re dormant dans le m\u00eame lit, la m\u00eame pi\u00e8ce des communs que sa tante, qui gla\u00e7ait ses quarante-trois ans. Mais en quoi se retrouver seul au petit matin dans une maison solitaire avec en t\u00eate une semblable hypoth\u00e8se vous rend-il coupable de quoi que ce soit ? L'\u00e9tait-elle d'ailleurs pass\u00e9e de vie \u00e0 tr\u00e9pas, cette farouche cuisini\u00e8re ? Il n'avait pas os\u00e9 aller s'en enqu\u00e9rir de trop pr\u00e8s, sa posture lui avait suffi, couch\u00e9e semble-t-il vu la p\u00e9nombre (\u00e0 la fois dans la chambrette et dans son esprit), couch\u00e9e sur le dos, mains jointes, et nul souffle perceptible ou r\u00e9ponse \u00e0 son multiple \u00ab madame Joliette \u00bb, c'est vrai prof\u00e9r\u00e9 \u00e0 voix basse pour la pr\u00e9venir de son d\u00e9part !\n\nFolie de sa part que de s'imaginer aussit\u00f4t que la m\u00eame sc\u00e8ne de terreur se reproduisait, que l'armagnac servi par le mannequin, ou que lui-m\u00eame durant la nuit, une nuit chahut\u00e9e, cauchemardesque, aussi mont\u00e9e sur roulettes, il ait pu, lui-m\u00eame, il ait pu...\n\nDes restes de nuit habitaient encore trop ses yeux pour qu'il puisse juger sainement de la situation ; prendre \u00e0 t\u00e9moin le couloir et les quelques marches ne suffisait pas, aussi tourna-t-il vite le dos. Et il le tourne toujours, ce dos !\n\nRegarde-toi dans la glace, paraissait pourtant lui dire chacun des hauts miroirs de la villa Rose. As-tu la t\u00eate d'un convict ? d'un condamn\u00e9 \u00e0 perpette ? Chasse de toi ces noires id\u00e9es ! Tu n'es qu'un jeune professeur trop imaginatif qui tra\u00eene comme un boulet de noires id\u00e9es. Cette presqu'\u00eele ne te vaut rien. Tu y rencontres trop tes premi\u00e8res ann\u00e9es et une culpabilit\u00e9 des origines. Oublie cette terre et ses deux mers. Ta d\u00e9funte tante, la responsable avec sa Bible de poche souvent \u00e0 la main pour conjurer le mauvais sort. Une cr\u00e9ature ardente rarement sortie du feu de sa foi.\n\nIl acquies\u00e7ait. Dans son demi-sommeil, en lui-m\u00eame, il acquies\u00e7ait. H\u00e9las au r\u00e9veil, \u00e0 nouveau il s'interrogeait. Ce n'est quand m\u00eame pas le mannequin de bois laqu\u00e9 qui pourrait t\u00e9moigner contre lui, et de quoi d'ailleurs ? Ce vilain bonhomme qu'il a toujours senti secr\u00e8tement hostile \u00e0 son \u00e9gard a l'air, d\u00e9sormais de retour \u00e0 sa place habituelle, de se satisfaire de tenir pour l'\u00e9ternit\u00e9 son immuable plateau dans la serre.\n\nCharles-Andr\u00e9 imaginait n\u00e9anmoins des titres en grosses capitales dans un journal du soir : \u00ab Une femme retrouv\u00e9e morte dans une maison d\u00e9serte. Des examens sont en cours pour d\u00e9terminer... \u00bb\n\nNon, il d\u00e9lirait, rien ne s'\u00e9tait pass\u00e9. Un peu de bu\u00e9e peut-\u00eatre sur les vitres. Un doigt charg\u00e9 de l'enqu\u00eate y inscrira-t-il bient\u00f4t son nom ? Apr\u00e8s tout, il fut le dernier \u00e0 avoir quitt\u00e9 le \u00ab ch\u00e2teau \u00bb ? Et cela une police assez m\u00e9thodique peut l'apprendre rien que par un simple tour de table. Or ils \u00e9taient bien une dizaine \u00e0 s'exclamer entre les plats, \u00e0 s'enthousiasmer des desserts.\n\nIl se leva, prit une douche, et proprement habill\u00e9 descendit \u00e0 la cuisine, cette pi\u00e8ce plus commune convenait mieux \u00e0 son \u00e2me. Au-dehors, les chiens du voisin aboyaient. Une meute lanc\u00e9e aux trousses de quelque id\u00e9e de chien ! Par la fen\u00eatre, la bande de trembles un peu voyous semblait lui faire des signes. Mais qui pr\u00eate attention aux singeries des trembles ?\n\nEn r\u00e9alit\u00e9, il tournait en rond, montant descendant les deux \u00e9tages. \u00c0 chaque heure, il se demandait que faire de la suivante. Ce mardi, il d\u00e9cida d'aller d\u00e9jeuner \u00e0 Saint-Pierre, chez cette corpulente matrone qui apparemment ne lui voulait que du bien. L'image de son coquet restaurant sur le port d'Orange avec ses rideaux bleu azur le mettait d\u00e9j\u00e0 en gaiet\u00e9. Et l\u00e0, entre fourchette et couteau, plut\u00f4t fourchette que couteau, il pourrait peut-\u00eatre, converti par l'innocence de sa blanche assiette, faire davantage la part du vrai et du faux dans cette troublante histoire !\n\n#\n\n\u00c0 Saint-Pierre, au restaurant des Mouettes, le repas en effet fut riche et copieux, Mme Le Guilvinec, la patronne, aux petits soins pour Charles-Andr\u00e9. Le ciel soudain radieux avait laiss\u00e9 ses nuages au large. Le port d'Orange balan\u00e7ait ses voiliers au mouillage avec tranquillit\u00e9. On entendait \u00e0 peine le flux et reflux des vagues. Vu le peu de clients, Mme Le Guilvinec s'\u00e9tait accord\u00e9 un brin de conversation avec Charles-Andr\u00e9 plac\u00e9 tout contre la vitrine. S'il \u00e9tait en vacances ? Qu'est-ce qu'il faisait dans la vie ? S'il avait des enfants ? S'il \u00e9tait mari\u00e9 ? Des propos de cette sorte auxquels il r\u00e9pondait la bouche plus ou moins pleine. Il finit par lui avouer en confidence \u00eatre plut\u00f4t du pays. Elle lui r\u00e9pliquant ne pas l'\u00eatre tout \u00e0 fait, \u00e9tant native d'\u00c9tel : \u00ab Vous savez apr\u00e8s Erdeven, sur la rivi\u00e8re. \u00bb\n\nLui, pris par un grand besoin de deviser, continuant sur sa lanc\u00e9e, lui expliquant avoir us\u00e9 tout gamin ses culottes dans la presqu'\u00eele, qu'aucun d\u00e9tour de sentier ne lui \u00e9tait inconnu, m\u00eame le plus m\u00e9chant hameau o\u00f9 certains de ses potes sans doute devenus p\u00eacheurs devaient peut-\u00eatre toujours nicher, mais il n'avait pas encore os\u00e9 aller les voir, de crainte avoua-t-il d'\u00eatre d\u00e9\u00e7u : \u00ab Vous savez en grandissant les gens changent ! Et puis on ne sait jamais comment on sera re\u00e7u. \u00bb\n\nElle opinait paisible, son charmant visage de blonde qui se voulait attentif prenait de l'\u00e9clat. Sur la table, le vin assur\u00e9ment devenait rouge de joie dans son verre \u00e0 l'id\u00e9e d'\u00eatre bu. Le pain se rompait facilement. M\u00eame le fond de la carafe n'\u00e9tait pas t\u00e9n\u00e9breux. Un moment de bonheur pour Charles-Andr\u00e9 qui voyait de plus en plus clair en lui-m\u00eame. L'ombre (ses mille hypoth\u00e8ses enfin domestiqu\u00e9es) avait retrouv\u00e9 sa servilit\u00e9 habituelle, \u00e9pousant le moindre de ses gestes, suite \u00e0 ce brusque soleil de printemps qui d\u00e9bauchait cette fin d'automne. Charles-Andr\u00e9 respirait, la t\u00eate hors de son angoisse rel\u00e9gu\u00e9e \u00e0 jamais \u00e0 Nantes, rue Marzelle. Le jour enfin lui appartenait. Et il en profitait, riant \u00e0 tout bout de champ, d\u00e9j\u00e0 en grande intimit\u00e9 avec cette femme, s'avisant m\u00eame \u00e0 un moment de lui prendre la main pour lui singer il ne savait plus quoi \u00e0 la minute suivante. Il n'avait plus quarante-trois ans, mais vingt, dix-huit. H\u00e9las, il devait repartir, son travail de prof, les \u00e9l\u00e8ves, mais il reviendra, promis, il reviendra. Et elle, elle ne prend donc jamais de vacances ? Il essayait de deviner sa vie, la part obscure de son \u00eatre. Elle se d\u00e9robait \u00e0 ses questions, en posait \u00e0 son tour. Oui, il loge \u00e0 Portivy, dans la villa de ses amis actuellement aux Am\u00e9riques. Oui, il s'ennuie un peu, mais son docteur \u00e0 Nantes lui a prescrit d'aller prendre un bon bol d'air et il le prend. \u00ab Il faut bien en passer par l\u00e0 \u00bb, concluait-il. Passer par l\u00e0, l'expression lui resta longtemps dans l'esprit bien apr\u00e8s qu'il eut quitt\u00e9 le restaurant. Mais leur conciliabule dans cette salle d\u00e9serte lui avait fait du bien, le sortant de ses sortil\u00e8ges, de toute cette histoire qu'il s'\u00e9tait construite de criminel en fuite. \u00ab Wanted \u00bb affiche-t-on dans les westerns. Et son affiche \u00e0 lui, c'\u00e9tait la presqu'\u00eele, ce bras tendu vers l'horizon d\u00e9signant on ne sait quel coupable.\n\nL'apr\u00e8s-midi le surprit du c\u00f4t\u00e9 de Kergroix, avec des id\u00e9es d'herbe rase, ent\u00eat\u00e9 par la rumeur de l'oc\u00e9an qui ne cessait de monter \u00e0 l'assaut, retardant le plus qu'il pouvait le moment de retourner \u00e0 la villa Rose. Il aurait bien eu besoin que Jean-Marc fasse \u00e0 nouveau danser ses instants, que Solange si \u00e9rudite lui recommande, comme elle le fait tout le temps, un livre oubli\u00e9, tir\u00e9 de la biblioth\u00e8que de ses heures, qu'il se reprocherait aussit\u00f4t de n'avoir pas lu. Un jeu entre eux ! \u00c0 l'entr\u00e9e du hameau, un homme se montrait qu'il crut reconna\u00eetre. Mais passons. En r\u00e9alit\u00e9, ce fut un peu plus tard qu'il tr\u00e9bucha davantage contre son enfance, en la personne de quelqu'un qui, de dos une minute, lui parut \u00eatre Paul, dit Popaul, l'un des plus fabuleux jouteurs de ses premi\u00e8res ann\u00e9es, lequel rajustait ses volets maltrait\u00e9s par le vent avant que le type ne le d\u00e9trompe en se retournant pour lui jeter un regard froid.\n\nEt cela dans un autre Ker, \u00e0 K\u00e9ridanvel, ces quelques masures si famili\u00e8res dispers\u00e9es l\u00e0 au hasard avec la m\u00eame mousse sur les murs et une identique solitude qui s'\u00e9croule sur un semblant de place autour d'un banc de pierre. Il s'y \u00e9tait attard\u00e9, esp\u00e9rant contre toute raison que Bertine reviendrait de sa mort, la fermi\u00e8re qui le r\u00e9chauffait d'un chaleureux caf\u00e9 au lait le dimanche, quand sa tante, prise d'un de ses acc\u00e8s de pi\u00e9t\u00e9, s'\u00e9tait trop assise \u00e0 la sortie de la grand-messe pr\u00e8s du tombeau vide du Christ, dont il est parl\u00e9 dans les \u00c9vangiles au chapitre de la R\u00e9surrection.\n\nCharles-Andr\u00e9 et ses neuf dix ans alors disparaissaient, pr\u00e9f\u00e9rant au sermon qu'elle n'e\u00fbt pas manqu\u00e9 de lui tenir celui de la c\u00f4te dite sauvage si habit\u00e9e par la rafale. D\u00e9j\u00e0, il lui fallait le bruit du monde. M\u00eame aujourd'hui un silence qui se prolonge creuse en lui trop d'attentes. Il \u00e9coute alors, ne peut s'emp\u00eacher d'\u00e9couter, mais quoi ? Dieu seul sait quoi ! Une minute, davantage, le voil\u00e0 pourtant comme suspendu entre ciel et terre, sur la pointe des pieds avant que ses talons ne retombent et ne retrouvent justement avec le sol les incoh\u00e9rences de l'heure, celle par exemple d'aujourd'hui qui l'immobilisait au c\u0153ur battant de ce village. Le p\u00e8re \u00ab Un tel \u00bb, son nom lui br\u00fblait les l\u00e8vres, allait-il \u00e0 nouveau, faisant fi lui aussi de sa mort, appara\u00eetre \u00e0 une porte viss\u00e9 sous son \u00e9ternelle casquette de cuir ?\n\n#\n\nCe fut une lettre, une vraiment tomb\u00e9e de la lune, qui suscita en lui de nouvelles alarmes. Il commen\u00e7ait pourtant \u00e0 s'endormir comme on s'endort, se r\u00e9veiller comme on s'\u00e9veille, quand cette lettre ! Qui pouvait bien lui \u00e9crire \u00e0 la villa Rose et \u00e0 son nom encore ? Il sortait juste au matin pour prendre l'air sans trop savoir comment il allait remplir ses heures. Le soleil s'en donnait \u00e0 c\u0153ur joie dans un ciel immens\u00e9ment bleu au-dessus de vaguelettes qui n'aspiraient qu'\u00e0 venir vous l\u00e9cher les pieds, quand il s'inqui\u00e9ta soudain de cette enveloppe d\u00e9pos\u00e9e par le facteur dans la bo\u00eete au portail du jardin, une petite de couleur gr\u00e8ge timbr\u00e9e heureusement en Virginie. C'\u00e9tait Solange qui lui \u00e9crivait. Comment avait-elle su ? Jean-Marc avait jug\u00e9 bon d'ajouter en bas de page quelques mots affectueux plut\u00f4t dans\u00e9s qu'\u00e9crits. Elle, pressentant sa surprise, lui expliquant qu'ayant t\u00e9l\u00e9phon\u00e9 \u00e0 leur homme \u00e0 tout faire pour lui annoncer leur retour vers la fin novembre et le prier de remettre la maison en \u00e9tat celui-ci leur avait donc appris...\n\nEt ils s'en f\u00e9licitaient. Gr\u00e2ce \u00e0 Charles-Andr\u00e9 la villa Rose aura moins souffert de leur absence, minaudait-elle, heureuse qu'il ait enfin r\u00e9pondu favorablement \u00e0 leurs pressantes invitations de l'\u00e9t\u00e9, mais surtout, pr\u00e9cisait Solange sachant sa distraction perp\u00e9tuelle, qu'il pense bien \u00e0 glisser la clef dans la m\u00eame souche de tremble lors de son d\u00e9part.\n\nElle se demandait en outre, sans doute \u00e0 haute voix (mais la haute voix ne s'\u00e9crit pas), s'il avait bien d\u00e9nich\u00e9 les draps dans l'armoire de leur chambre et s'inqui\u00e9tait de savoir s'il ne frissonnait pas trop, auquel cas ce bon M. Touveau pouvait \u00e9ventuellement lui rallumer le chauffage ou \u00e0 d\u00e9faut, les couvertures ne manquant pas, qu'il en d\u00e9pouille tous les lits de la maisonn\u00e9e avant de les accumuler sur le sien. La lettre fourmillait d'indications m\u00e9nag\u00e8res de cette sorte, quand un d\u00e9tail apparemment anodin raviva l'anxi\u00e9t\u00e9 de Charles-Andr\u00e9. Un d\u00e9tail que Jean-Marc, malgr\u00e9 tout son talent, n'aurait pas su chor\u00e9graphier, car Solange, qui parfois sentait Charles-Andr\u00e9 si perdu (\u00ab Tu as trop de parenth\u00e8ses en toi \u00bb, lui reprochait-elle souvent), avait jug\u00e9 bon d'ajouter en post-scriptum : \u00ab Si tu veux te r\u00e9chauffer l'\u00e2me, tu as le placard de la cuisine et sa bouteille d'armagnac sous l'\u00e9vier ! \u00bb\n\nL'armagnac ? Le mot d\u00e9j\u00e0 lui agrandissait les yeux. L'\u00e9vocation de cette sauvage liqueur allait-elle agir \u00e0 la fa\u00e7on d'une loupe lui restituant le milliard d'incidents de cette funeste soir\u00e9e ? Car ils avaient \u00e0 la fin du d\u00eener pr\u00e9par\u00e9 si diligemment par Mme Joliette qui sait admirablement pr\u00e9sider aux destin\u00e9es d'une cuisson, ils avaient en effet tous d\u00e9gust\u00e9 de ce breuvage des dieux dans de sobres petits verres \u00e0 pied servis sur un plateau par cet \u00e9nergum\u00e8ne en bois peint.\n\n\u00ab Un crime \u00e0 l'armagnac \u00bb, prof\u00e9ra-t-il sourdement.\n\nEt le voil\u00e0 repris par son fantasme marchant sur le quai la t\u00eate ailleurs, contraint m\u00eame pour retrouver ses esprits d'aller s'asseoir sur un banc face \u00e0 la mer. L'heure aussi a ses flux et reflux, et il \u00e9tait manifestement mar\u00e9e basse, avec tous ces menus faits qui jonchaient la plage de son \u00eatre. Se peut-il que les m\u00eames \u00e9v\u00e9nements se reproduisent ? Qu'\u00e0 quarante et plus on puisse revivre et dans le d\u00e9tail une soir\u00e9e de ses douze ans ? Qu'en dirait le baron Louis ? se permit-il m\u00eame de penser, afin de changer son angoisse en plaisanterie. Mais il n'ira pas cette fois d\u00e9guster un th\u00e9 au bar de la Jet\u00e9e, le patron \u00e0 la longue le fatiguait avec son silence lourd \u00e0 porter.\n\nSa nuit avait \u00e9t\u00e9 bonne, les ombres moins bavardes qu'\u00e0 l'ordinaire, sauf qu'\u00e0 un moment il crut entendre quelqu'un qui respirait fort dans l'escalier, mais c'\u00e9tait sans doute quelqu'un dans le haut de sa t\u00eate plut\u00f4t que dans les hauts de la maison.\n\nIl se tenait vraiment \u00e0 l'ancre sur cette c\u00f4te, alarm\u00e9 par la sauvage, apais\u00e9 par les plages sur baie, plongeant avec cette presqu'\u00eele, peut-\u00eatre sans doute de fa\u00e7on excessive, dans l'inextricable de lui-m\u00eame. M\u00e9riterait-il d'\u00eatre d\u00e9barqu\u00e9 sur l'\u00eelot Th\u00e9viec, terre \u00e9cumeuse qu'il apercevait basse sur l'eau depuis son banc et dont on le mena\u00e7ait enfant quand il avait par trop d\u00e9r\u00e9gl\u00e9 ses relations avec son entourage ? \u00ab Les lapins y ont les yeux rouges et grignoteraient jusqu'\u00e0 votre ombre \u00bb, jurait en riant sa fantasque tante. Et comme la sienne, d'ombre, \u00e9tait de taille !\n\nDans le journal toujours nulle allusion, et \u00e0 la radio qu'il \u00e9coute dans la cuisine on parlait bien de la disparition d'une femme, mais c'\u00e9tait en voiture qu'elle avait cess\u00e9 de se signaler vivante. Un coup de volant brusque peut-\u00eatre et un chemin de traverse inattendu, mais qui traverse quoi ? Somme toute, il suffirait qu'il ouvre \u00e0 son retour \u00e0 Nantes cette satan\u00e9e grille de la rue Marzelle, et s'\u00e9tonne, en pr\u00e9sence de t\u00e9moins, de cette cr\u00e9ature inerte gisant dans son lit pour se trouver d\u00e9charg\u00e9 de toute responsabilit\u00e9 ! Apr\u00e8s tout, Mme Joliette, outre ses qualit\u00e9s de cuisini\u00e8re, \u00e9tait la gardienne de cette demeure ancestrale, certes en compagnie du mannequin de la serre toujours debout avec son mal\u00e9fique plateau fleurant peut-\u00eatre encore l'armagnac. Qui sait si en analysant cette odeur on n'y surprendrait pas les raisons de ce subit d\u00e9c\u00e8s ?\n\nEt s'il t\u00e9l\u00e9phonait ? Oui mais, si la folle hypoth\u00e8se de ses douze ans dont il ne parvenait pas \u00e0 se d\u00e9barrasser \u00e9tait la bonne (comme quoi sa tante cette nuit d'il y a plus d'une trentaine d'ann\u00e9es aurait pass\u00e9 l'arme \u00e0 gauche d'une fa\u00e7on disons sujette \u00e0 caution, et il y a une quinzaine de jours, et dans les m\u00eames conditions, la cuisini\u00e8re), il devenait le principal suspect puisque, en dehors de la pr\u00e9sum\u00e9e victime, il \u00e9tait le seul des convives de ce repas familial a avoir dormi la nuit au \u00ab ch\u00e2teau \u00bb, si on peut appeler dormir cette nuit de tressaillements furtifs, de plaintes dans les cloisons qui caract\u00e9risent la v\u00e9tust\u00e9 de cet \u00e9tage des communs, on le recherchait donc et t\u00e9l\u00e9phoner aurait alors indiqu\u00e9 aussit\u00f4t \u00e0 une police un tant soit peu perspicace o\u00f9 il se trouvait.\n\nD'ailleurs, pourra-t-il jamais retourner \u00e0 Nantes ? Un possible criminel n'a pas d'adresse. Et si tout avait \u00e9t\u00e9 fait pour qu'il en devienne un, que les soup\u00e7ons retombent sur lui ? Il \u00e9grenait les noms des participants \u00e0 ce d\u00eener annuel, tous ces cousins, cousines. Et il voyait mal Lisbeth agir ainsi avec un couteau cach\u00e9 sous la nappe, encore moins le na\u00eff Guillaume qui vit \u00e0 l'embouchure de la Loire, \u00e0 Saint-Nazaire, ni Laurence, sa s\u0153ur irr\u00e9elle, jamais revenue de ses songes. Quant \u00e0 Maryvonne, c'est l'innocence m\u00eame, ses yeux franchement bleus le disent assez, ou Sophie ou Ren\u00e9e trop encombr\u00e9es d'elles-m\u00eames pour penser \u00e0 quelque chose d'autre. Bien s\u00fbr, il y a le laconique Alfred, l'\u00e9poux de la belle Nana, retrait\u00e9 de la poste toujours entre deux lettres, ou le jaloux Joseph, aux mains incertaines, sans oublier Charles \u00e0 qui il manque un Andr\u00e9 pour croire \u00e0 des b\u00eatises pareilles. Un vrai cauchemar que cette id\u00e9e d'une morte laiss\u00e9e \u00e0 l'abandon dans une maison vide.\n\nIl se leva. Malgr\u00e9 ce soleil \u00e9clatant, il se ressentait \u00e0 l'ombre, pourtant \u00e0 part la sienne aucune ne tra\u00eenait sur le chemin.\n\n#\n\nLa presqu'\u00eele aurait environ treize kilom\u00e8tres de long, treize kilom\u00e8tres de perplexit\u00e9s pour Charles-Andr\u00e9. Son enfance la responsable, une quasi-criminelle qui, depuis la mort incertaine de sa tante, ajouta un lis\u00e9r\u00e9 noir \u00e0 nombre de ses propres faits et gestes. Comment s'en d\u00e9barrasser ? Il n'allait tout de m\u00eame pas croire, \u00e0 quarante-trois ans bien sonn\u00e9s, qu'un mannequin en bois exotique d\u00e9guis\u00e9 en serveur \u00e0 plateau avait pu commettre ou se rendre complice d'un pareil forfait ? Si forfait il y eut ? Mais qui donc alors parmi la tabl\u00e9e familiale r\u00e9unie chaque ann\u00e9e \u00e0 l'entr\u00e9e de l'automne dans le grand salon de cette aust\u00e8re demeure aurait pu, si l'on \u00e9pouse sa fallacieuse hypoth\u00e8se, avoir la cervelle assez renvers\u00e9e pour songer \u00e0 utiliser ce mannequin dans des intentions peu louables ? Qui donc d'ailleurs avait eu l'id\u00e9e d'aller chercher dans la serre ce serveur mont\u00e9 sur roulettes pour offrir de l'armagnac \u00e0 chaque convive en insistant pour que Mme Joliette la cuisini\u00e8re se joigne \u00e0 eux et pour une fois accepte, elle qui sert, d'\u00eatre \u00e0 son tour servie ?\n\nIl avait beau en pens\u00e9e scruter tous les visages, y compris celui parfaitement rabot\u00e9 dudit mannequin, il n'arrivait pas \u00e0 se d\u00e9faire de cette folle hypoth\u00e8se bien digne des communs si peu \u00e9clair\u00e9s par le soleil. Mais \u00e0 ses yeux, c'\u00e9tait la r\u00e9p\u00e9tition \u00e0 des ann\u00e9es d'intervalle de la m\u00eame plaisanterie qui rendait suspecte son issue, ce d\u00e9c\u00e8s subit dans la nuit de deux femmes, et qu'il se soit retrouv\u00e9 par le hasard, les circonstances, d'abord \u00e0 douze ans, puis \u00e0 quarante et plus, provisoirement seul gardien de leurs d\u00e9pouilles.\n\nN'emp\u00eache, n'importe qui mis dans le secret d'une telle confidence lui aurait ri au nez, s'\u00e9tonnant m\u00eame que quelqu'un d'aspect aussi sens\u00e9 qu'un jeune professeur, profession \u00e9minemment raisonnable, puisse devenir le jouet de pareilles v\u00e9tilles, au point de s'enfuir de Nantes comme un coupable ! de s'imaginer m\u00eame depuis entendre au moment de se coucher, et \u00e0 s'en rouiller les oreilles, le bruit de la grille qui peine \u00e0 se refermer sur la rue Marzelle ! Mais comme l'\u00e9crivait le philosophe du si\u00e8cle dernier dans son vieux bouquin in\u00e9narrable feuillet\u00e9 en large et en travers l'autre jour \u00e0 l'\u00e9tage de la villa Rose, chacun d'entre nous serait \u00e0 la fois du dedans et du dehors, l'homme du dehors r\u00e9pondant aux salutations, vivant une vie tout ext\u00e9rieure, explicite tandis que le second... Et comme de toute fa\u00e7on il a toujours \u00e9t\u00e9 celui-ci plut\u00f4t que celui-l\u00e0, comment n'aurait-il pas song\u00e9, afin de retrouver un semblant de qui\u00e9tude, r\u00e9cup\u00e9rer l'\u00e9quilibre de sa ligne d'horizon, comment n'aurait-il pas song\u00e9 \u00e0 cette fumante presqu'\u00eele, vrai totem de son enfance, qui s'\u00e9tale entre un murmure, pas une vague plus haute que l'autre c\u00f4t\u00e9 baie, et une vocif\u00e9ration oc\u00e9anique permanente \u00e0 l'oppos\u00e9 dont il a parfois encore l'\u00e9cume aux l\u00e8vres. Ses premi\u00e8res ann\u00e9es y courent, rien ne s'est pass\u00e9, il n'a pas encore douze ans, sa tante est vivante, l'abb\u00e9 Messager flirte entre les pages de son missel, bien s\u00fbr, il y a toujours ce satan\u00e9 grillage qui accroche tous leurs mots, les retient en prison.\n\nIl chercha son souffle. O\u00f9 se trouve-t-il l'escalier assez d\u00e9rob\u00e9 pour lui d\u00e9rober toutes ses marches qui le redescendent trop vers ses ombres ? Une subitement se planta devant lui. Oui, il marchait philosophiquement \u00e0 Quiberon, le long du remblai, quand un type plus large que haut :\n\n\u00ab \u00c7a alors ! \u00bb crut-il entendre.\n\nC'\u00e9tait, mais oui c'\u00e9tait vraiment Maurice avec qui tout gamin il s'amusait \u00e0 tomber du haut des arbres en se retenant de branche en branche, en compagnie duquel il fuyait l'apostrophe violente de M. Huan, le garde champ\u00eatre qui d\u00e9j\u00e0 les accusait de tous les maux du monde, d'avoir vol\u00e9 de l'air \u00e0 l'air ou ext\u00e9nu\u00e9 un bout de jardin.\n\n\u00ab Qu'est-ce que tu fous l\u00e0 ? \u00bb\n\nVingt ans qu'ils ne s'\u00e9taient pas vus ! Ils se congratul\u00e8rent, s'expliqu\u00e8rent, march\u00e8rent du m\u00eame pas jusqu'\u00e0 la statue de Hoche, l\u00e0 o\u00f9 fleurit un square.\n\n\u00ab Je m'en vais demain, mentit Charles-Andr\u00e9.\n\n\u2014 Oui Untel est mort, expirait l'autre en un soupir, \u00e9num\u00e9rant un \u00e0 un les noms heureusement encore vivants des autres membres de leur joyeuse bande. C'\u00e9tait nos meilleures ann\u00e9es, conclut Maurice, que ces ann\u00e9es en culottes courtes ! \u00bb\n\nOui, il a repris le garage de son p\u00e8re \u00e0 Saint-Pierre. Il travaille beaucoup avec les touristes.\n\n\u00ab Si par hasard tu as des probl\u00e8mes avec ta voiture... \u00bb\n\nCharles-Andr\u00e9 avoua n'en avoir jamais poss\u00e9d\u00e9 une et \u00eatre venu tout simplement en taxi depuis Auray.\n\n\u00ab Ah bon ! \u00bb pronon\u00e7a l'autre un peu d\u00e9\u00e7u.\n\nUn mauvais soleil \u00e9clairait leur propos et l'on entendait la mer vagir contre la plage. Ils se quitt\u00e8rent bient\u00f4t, n'ayant manifestement plus assez de mots en commun pour pouvoir encore se parler, se promettant n\u00e9anmoins mille promesses, en particulier de se revoir par exemple l'\u00e9t\u00e9 prochain, durant les grandes vacances, avait m\u00eame propos\u00e9 Charles-Andr\u00e9.\n\n\u00ab Ainsi tu vis \u00e0 Nantes ?\n\n\u2014 Si on peut appeler cela vivre \u00bb, avait prononc\u00e9 \u00e9nigmatique le jeune professeur Charles-Andr\u00e9 Bertrand de l'enseignement secondaire en serrant chaleureusement la main de son ancien copain en guise d'adieu.\n\nSon pas sonnait plus large \u00e0 Quiberon. Il d\u00e9cida, enfin il r\u00e9solut, avant de changer d'avis \u00e0 la minute suivante, c'est-\u00e0-dire ne plus r\u00e9soudre ni d\u00e9cider. Le pass\u00e9 lui revenait trop par toutes les rues. En pr\u00eatant bien l'oreille, une vite \u00e9corn\u00e9e par le souvenir, il aurait presque pu encore ou\u00efr ses dix ans courir apr\u00e8s ses onze, et ceux-ci \u00e0 la traque de ses douze, \u00e2ge o\u00f9 ses grands-parents paternels devenus dans leurs derni\u00e8res ann\u00e9es gardiens de la rue Marzelle s'occuperont de lui dans l'aust\u00e8re demeure ancestrale jusqu'\u00e0 sa majorit\u00e9 suite au brusque d\u00e9c\u00e8s de sa jolie tante Marie :\n\n\u00ab Je suis ton J\u00e9sus, lui clamait-il souvent pour l'agacer, puisque je suis ton fils sans l'\u00eatre et que tu t'appelles Marie comme la m\u00e8re de J\u00e9sus. \u00bb\n\nElle lui ass\u00e9nait un coup de Bible pour le sacril\u00e8ge, cette Bible format r\u00e9duit qu'elle sortait \u00e0 tout moment de sa grande poche de tablier, avant de rire de toutes ses dents qu'elle avait magnifiques \u00e0 lire dans sa bouche expressive.\n\n\u00ab Et Joseph, c'est l'abb\u00e9 Messager \u00bb, poursuivait son diable de neveu, car le malheureux pr\u00eatre \u00e0 la retraite se pr\u00e9nommait en effet Joseph d'apr\u00e8s sa bo\u00eete aux lettres.\n\nAutre coup de Bible et nouvelles cascades de rire autour de la table de la cuisine o\u00f9, \u00e0 la froide saison, les rares fois o\u00f9 No\u00ebl les trouvait en vacances dans la presqu'\u00eele, elle entretenait dans la chemin\u00e9e un feu forc\u00e9ment d'enfer. Elle \u00e9tait charmante tante Marie avec toutes ces Galil\u00e9e qu'elle lui d\u00e9bitait, d\u00e9crivait sans cesse, que le Christ \u00e0 son \u00e2ge avait m\u00eame \u00e9t\u00e9 capable de modeler des oiseaux dans la glaise avant de les faire s'envoler tout emplum\u00e9s dans le ciel pieux du lac de Tib\u00e9riade.\n\n\u00ab Doux J\u00e9sus \u00bb, le nom lui remontait aux l\u00e8vres d\u00e8s que le beau temps \u00e9garait les fen\u00eatres de leur chalet dans des bleus outranciers de Jud\u00e9e.\n\nCharles-Andr\u00e9 s'en amusait toujours. Une brune encore jeune, bien plant\u00e9e sur terre, que sa tante, se permit-il encore de murmurer en passant devant l'\u00e9glise de Quiberon. Un peu avant la gare, son ex-\u00e9cole de l'autre c\u00f4t\u00e9 de la rue. Et s'il repartait ? Le mensonge \u00e0 l'ami Maurice \u00e9tait peut-\u00eatre sa v\u00e9rit\u00e9 ? Le trousseau de la villa Rose \u00e0 nouveau bien au chaud dans sa souche, et puis Nantes, son trois-pi\u00e8ces pr\u00e8s de Sainte-Croix. Le beffroi du Bouffay le prot\u00e9gerait peut-\u00eatre mieux de ses angoisses, l'animation de la ville les diluant \u00e0 perte de vue dans la circulation g\u00e9n\u00e9rale autour de la place du Commerce, qui sait ? Car ici, il entendait trop la clef de sa pr\u00e9tendue culpabilit\u00e9 tourner dans sa serrure. Le silence de Portivy que troublait seulement le tam-tam de l'oc\u00e9an ne le soulageait plus gu\u00e8re. Il r\u00e9fl\u00e9chissait, oh mon Dieu oui il r\u00e9fl\u00e9chissait.\n\nLe jour tombait, il tombait aussi en lui, rentrant \u00e0 la villa Rose un pas devant l'autre par des chemins d\u00e9tourn\u00e9s, \u00e9tourdi d'hypoth\u00e8ses diverses, quand soudain, sit\u00f4t pass\u00e9 le passage \u00e0 niveau de Saint-Julien, une id\u00e9e lui vint !\n\n#\n\nPourquoi n'y avoir pas pens\u00e9 plus t\u00f4t ? Il se le reprochait sur le point d'entrer \u00e0 Beg Rohu, un hameau pimpant accot\u00e9 \u00e0 un fort \u00e0 moiti\u00e9 enterr\u00e9 o\u00f9 se passa un jour un drame qui ne fait pas partie de son histoire pr\u00e9sente. Oui pourquoi ? Pourtant cela tombait sous le sens ! Mais de sens parfois, il en manque tellement avec cette myriade d'\u00e9lucubrations, d'hypoth\u00e8ses justement \u00e0 la manque qui ne le m\u00e8nent vraiment nulle part ! Dieu sait qu'on lui en fit souvent la remarque ! Et pourtant le pr\u00e9texte \u00e9tait d'une rare simplicit\u00e9. Il fallait vraiment, pour ne pas y avoir song\u00e9 plus t\u00f4t, qu'il ait eu tous ces jours-ci l'esprit ailleurs, cet ailleurs dont il arpente trop les gr\u00e8ves, constate-t-on souvent autour de lui, avec d'autres mots bien s\u00fbr que ceux-l\u00e0 !\n\nIl envisagea donc sit\u00f4t son retour \u00e0 Portivy d'aller acheter une carte postale chez le baron Louis et de l'adresser illico \u00e0 l'un ou l'une des convives de leur l\u00e9gendaire d\u00eener (qui voit la famille affam\u00e9e d'on ne sait trop quoi s'assembler \u00e0 chaque f\u00eate de la Toussaint autour d'une table, en l'occurrence la magistrale du salon d'apparat, pour s'\u00e9changer des nouvelles de l'ann\u00e9e d\u00e9j\u00e0 presque pass\u00e9e), de prier en quelque sorte celui ou celle d'entre eux qui cr\u00e8che le plus pr\u00e8s de la rue Marzelle de s'y rendre, car, o\u00f9 avait-il la t\u00eate le jour de ce d\u00e9part pourtant pas si matutinal de la derni\u00e8re quinzaine pour oublier \u00e0 ce point ses papiers, en particulier ceux d'identit\u00e9 qui nous disent qui nous sommes, et surtout sa carte bleue n\u00e9gligemment pos\u00e9e sans doute sur l'une des commodes semble-t-il de sa chambre, celle des communs qui ouvre sur la serre ? Non qu'il craigne qu'une main d'air ne s'en soit saisie dans cette demeure d\u00e9serte et o\u00f9 de surcro\u00eet veille depuis la mort de ses grands-parents Mme Joliette \u00e0 qui il avait d'ailleurs sans succ\u00e8s maintes fois t\u00e9l\u00e9phon\u00e9. Aussi si l'un de ses cousins, cousines, disons celui ou celle qui habite au plus pr\u00e8s, r\u00e9p\u00e9tait-il, avait l'obligeance de se d\u00e9placer, il ne tarderait pas d\u00e8s son retour \u00e0 Nantes de venir r\u00e9cup\u00e9rer tout son bien chez cette \u00e2me charitable. C'est-\u00e0-dire en r\u00e9alit\u00e9 \u00e0 Chantenay, le faubourg le plus proche, car c'est l\u00e0 en effet que niche, chemin des Fontenies, la personne la plus voisine de son \u00e9tourderie, cette Laurence assez belle o\u00f9 s'arr\u00eata son choix, une haute en jambes et en soup\u00e7ons qui ne croit jamais que le tiers du quart de ce qu'on lui avance dans sa maisonnette enturbann\u00e9e d'un jardin auquel elle consacre l'essentiel de ses heures ! Aussi, elle si m\u00e9fiante que le moindre bruit fait se retourner ne pourra jamais passer \u00e0 c\u00f4t\u00e9 du pr\u00e9sumable cadavre sans l'apercevoir, si cadavre il y a ? Quant \u00e0 ses propres papiers introuvables forc\u00e9ment rue Marzelle, il pourra toujours \u00e0 son retour s'excuser aupr\u00e8s d'elle et rouge de confusion et avec un bouquet de fleurs lui avouer les avoir, depuis l'envoi de sa carte, d\u00e9nich\u00e9s \u00e0 sa grande honte au fond rarement fouill\u00e9 de sa sacoche. Et comme il se r\u00e9v\u00e8le aux yeux de tous, y compris de cette m\u00e9fiante Laurence, p\u00e9tri de distractions, de r\u00eaveries en tout genre, cela passera comme une lettre \u00e0 la poste, apport\u00e9e par Alfred, le retrait\u00e9 de ladite administration, osa-t-il m\u00eame se murmurer afin de tourner en plaisanterie son sentiment de culpabilit\u00e9 h\u00e9rit\u00e9 de cette nuit funeste de son enfance, et cela tout en marchant vers l'abattoir de Saint-Pierre chang\u00e9 aujourd'hui en \u00e9cole de voile.\n\nCar, contre tout bon sens, il ne pouvait se d\u00e9faire de cette id\u00e9e pu\u00e9rile que le mannequin, ce sournois de bois laqu\u00e9, trempait d'une fa\u00e7on ou d'une autre dans cette t\u00e9n\u00e9breuse affaire, et que cette fois ce n'\u00e9tait plus un jeu de gamin sugg\u00e9r\u00e9 \u00e0 la bruyante tabl\u00e9e par ses propres douze ans, mais qu'il s'agissait d'un truc autrement plus s\u00e9rieux, qu'une goutte mal\u00e9fique (grain d'obscurit\u00e9 emprunt\u00e9 \u00e0 cette subite panne d'\u00e9lectricit\u00e9) avait peut-\u00eatre \u00e9t\u00e9 ajout\u00e9e en douce au verre d'armagnac offert \u00e0 la cuisini\u00e8re, mais par qui ? Et pourquoi ?\n\nN'avait-elle pas d\u00e9clar\u00e9 ce soir-l\u00e0 avec un hoquet, elle si peu accoutum\u00e9e aux liqueurs, que celle-ci lui emportait la gorge, au point d'en esquisser une grimace, la m\u00eame qu'il lui sembla reconna\u00eetre, identifier le lendemain matin sur son visage depuis la porte de la chambre qu'il avait, apr\u00e8s l'avoir longuement toqu\u00e9e, fini comme on sait par oser entreb\u00e2iller pour lui signifier qu'il partait, s'\u00e9tonnant \u00e0 part lui que cette femme d'ordinaire premi\u00e8re lev\u00e9e et si alerte soit encore au lit et dans l'exacte position de sa d\u00e9funte tante, trente ans plus t\u00f4t, la nuit de son d\u00e9c\u00e8s o\u00f9 il la surprit sur le dos mains jointes ! La cuisini\u00e8re dormait-elle, elle aussi, du m\u00eame sommeil \u00e9ternel ? \u00c9pouvant\u00e9, il n'avait pas voulu alors davantage s'en assurer, fuyant sans demander son reste (reste que sans doute le noir mannequin ne lui aurait pas accord\u00e9), disparaissant (ses douze ans empaquet\u00e9s dans ses quarante), tout en d\u00e9sordre jusqu'\u00e0 la grille, la clef qui tourne mal dans sa serrure brouill\u00e9e, et qu'il finit par abandonner \u00e0 son sort, la rue, Nantes aux approches de huit heures et la presqu'\u00eele au soir o\u00f9 l'enthousiasme de l'oc\u00e9an qui parle \u00e0 tort et \u00e0 travers malgr\u00e9 tout le rassura tout de m\u00eame un peu ! lui fit retrouver, disons, un semblant de calme, vague apr\u00e8s vague.\n\nEt depuis ? Le soir \u00e0 la villa Rose il ne parvient pas \u00e0 s'emp\u00eacher de se claquemurer avant l'heure, fermant les fen\u00eatres, rabattant les volets, afin qu'aucune sorte d'extravagance ne puisse depuis le jardin (toujours un peu fou au cr\u00e9puscule, en particulier \u00e0 cause des trembles, ces agitateurs d'inqui\u00e9tude), ne puisse de nouveau entrer, s'infiltrer jusqu'\u00e0 son \u00e2me qu'il met vite au lit, dormant d'un sommeil paisible jusqu'au lendemain matin qu'il r\u00e9veille d'un caf\u00e9 noir, noir, bu sto\u00efque debout dans la cuisine, la pi\u00e8ce la plus sens\u00e9e de la villa, avant de se diriger aujourd'hui d'un pas d\u00e9cid\u00e9ment bien r\u00e9veill\u00e9 chez le baron Louis plus lyrique que d'habitude, une bonne p\u00eache en \u00e9tait la cause, le cafetier ayant pu au petit jour, et pour une fois d\u00e9barrass\u00e9 de ses clients, capturer l'innommable au bout de la jet\u00e9e, un innommable tout ruisselant qu'il \u00e9tala avec complaisance sur son comptoir.\n\n\u00ab Qu'est-ce que c'est comme poisson ? \u00bb demanda Charles-Andr\u00e9.\n\nL'autre l'ignorait et comptait bien l'apprendre du premier homme du large qui viendrait, filet remis\u00e9 et bateau \u00e0 l'ancre, se ragaillardir apr\u00e8s une nuit pass\u00e9e en mer d'un bon petit coup de quelque chose.\n\n\u00ab Vous savez de nos jours avec la pollution, on trouve de tout dans l'oc\u00e9an, les esp\u00e8ces d\u00e9g\u00e9n\u00e8rent \u00bb, se contenta-t-il donc de r\u00e9pondre, mais, \u00e0 l'\u00e9vidence, satisfait malgr\u00e9 tout de l'\u00e9normit\u00e9 gluante de sa prise.\n\n\u00ab On dirait une mani\u00e8re de raie, se d\u00e9go\u00fbtait Charles-Andr\u00e9 tournant noblement sa cuiller dans sa tasse de th\u00e9.\n\n\u2014 Ce que je sais, c'est que c'est un truc qui vit au fond, c'est \u00e7a, au fond ! Pas bon signe para\u00eet-il quand il remonte \u00e0 la surface, signe de temp\u00eate. \u00c7a a de plus un nom que j'ai su ! Mais en ce moment j'oublie tout, par exemple de vous rendre votre monnaie. \u00bb\n\nLe baron Louis sourit.\n\n\u00ab Celui-l\u00e0 va peut-\u00eatre nous le dire ! \u00bb\n\nIl d\u00e9signait le robuste p\u00eacheur qui venait de repousser la porte.\n\n#\n\n\u00c0 circuler dans les rues de Saint-Pierre, Charles-Andr\u00e9 repensait aux simagr\u00e9es du garde champ\u00eatre, \u00e0 ses foucades, ses brusqueries, tout juste s'il n'e\u00fbt pas entendu M. Huan sous son k\u00e9pi bucolique d\u00e9raper derri\u00e8re lui, faute \u00e0 la bourgade qui, elle, n'avait pas grandi, toujours celle de ses culottes courtes, \u00e0 l'\u00e9cho encore en enfance dont les voix lui revenaient, l\u00e0 habitait le fils du docteur, plut\u00f4t le beau-fils, un certain ? Voil\u00e0 qu'il avait oubli\u00e9 ses nom et pr\u00e9nom, la presqu'\u00eele lui rajeunissait l'\u00e2me. Apr\u00e8s tout, rien n'avait encore eu lieu, Mme Joliette vivait encore, \u00e0 l'\u00e9poque encore toute jeunette, pas de quoi s'affoler, se persuadait-il devant le port d'Orange. Il n'avait commis comme crime que dormir une nuit dans une maison \u00e0 c\u00f4t\u00e9 d'une femme pass\u00e9e de vie \u00e0 tr\u00e9pas sans qu'il le s\u00fbt, se confirmait-il devant la mairie. Le cauchemar de l'\u00e9tang n'\u00e9tait donc pas le sien, se r\u00e9jouissait-il aupr\u00e8s de la poste, ni l'infini des couloirs de cette haute baraque familiale qui se tortillent depuis le XIXe si\u00e8cle dans leur solitude, paraissait lui r\u00e9pondre tout souriant le charcutier \u00e9puisant une cigarette sur le seuil de sa charcuterie.\n\nIl commen\u00e7ait \u00e0 marcher d'un bon pas, l'\u00e2me un peu plus soulev\u00e9e. Certes il neigeait la premi\u00e8re fois, lors de la mort de sa tante, mais pourquoi neige-t-il toujours en lui chaque fois qu'il repousse la grille du \u00ab ch\u00e2teau \u00bb ? Il n'y \u00e9tait pourtant pour rien dans ce d\u00e9c\u00e8s, alors pourquoi les all\u00e9es du parc rue Marzelle s'allongent-elles depuis si morbides \u00e0 sa rencontre ? Et ce mur d'enceinte sur le boulevard qui s'effrite tant sous ses coudes ? Les choses de cette propri\u00e9t\u00e9 si l\u00e9gendaire dans la famille veulent-elles le punir, \u00e0 l'image de ce mannequin dans la serre qui lui renvoie un \u0153il complice et pourtant sans regard ?\n\nDe m\u00eame \u00e0 Portivy, ces trembles de la villa o\u00f9 il couche \u00e0 des lieues et des lieues de Nantes qui pourtant s'agitent plus qu'il n'est convenable \u00e0 des arbres quand il les fr\u00f4le. Sauraient-ils quelque chose de ses nuits, \u00e0 d\u00e9faut de ses jours ?\n\nMais non, a-t-il envie alors de les interpeller et sous leur nom latin _Populus tremula_ pour donner plus de solennit\u00e9 \u00e0 son apostrophe : \u00ab Vous vous trompez des racines \u00e0 la cime, Charles-Andr\u00e9 Bertrand qui vous parle n'est que professeur de lettres, il n'a rien commis d'irr\u00e9parable la veille de ses vacances, dans quelques jours, il \u00e9crira \u00e0 nouveau \u00e0 la craie sur un sage tableau devant sa classe \u00e9baubie, aucune raison de pr\u00e9tendre lui infliger une retenue, de vouloir le mettre en prison ! \u00bb\n\nSi seulement, se disait-il en d\u00e9passant l'ultime maison de Saint-Pierre de fa\u00e7on plus all\u00e8gre, il avait pu se d\u00e9barrasser une bonne fois de ses t\u00e9n\u00e8bres int\u00e9rieures comme on secoue un vieux manteau tout empoussi\u00e9r\u00e9. Vivre enfin en accord avec lui-m\u00eame, avec ce beau ciel bleu, cette route vers Portivy qui d\u00e9vale ! Car en quoi d'avoir toute une nuit voisin\u00e9 une morte le rendrait-il suspect aux yeux de la loi ? \u00c0 moins que celle-ci ne consid\u00e8re comme une preuve de possible culpabilit\u00e9 qu'il se soit enfui au matin comme un \u00e9perdu ? La clef laiss\u00e9e dans la serrure de la grille lui rouillait en effet encore les mains, et sur ses \u00e9paules, \u00e0 certains moments, il ressentait malgr\u00e9 l'\u00e9loignement presque comme une charge, celle de l'ombre de l'aust\u00e8re demeure ancestrale. Heureusement que ses cousins cousines et lui-m\u00eame allaient bient\u00f4t prochainement vendre le \u00ab ch\u00e2teau \u00bb \u00e9rig\u00e9 en 1899 et en bons h\u00e9ritiers se partager le magot !\n\nIl se retourna. Non, ce n'\u00e9tait en aucune fa\u00e7on M. Huan qui, aujourd'hui d\u00e9c\u00e9d\u00e9, ne doit mettre des contraventions qu'aux gens de l'au-del\u00e0, mais un homme peut-\u00eatre de son esp\u00e8ce aux souliers aussi terriblement ferr\u00e9s, d'o\u00f9 dans son dos cet angoissant bruit de pas, lequel s'estompa bient\u00f4t sur la gauche. L'image en effet du garde champ\u00eatre ne quittait pas Charles-Andr\u00e9, enfin Andr\u00e9 plut\u00f4t que Charles qui lui se souhaitait une humeur plus paisible. Toutes les \u00ab ogreries \u00bb comme il appelait ces fureurs du presque gendarme, autrefois toujours \u00e0 leur poursuite, lui revenaient en m\u00e9moire, un bonhomme alors si \u00e0 l'aff\u00fbt de leurs moindres faits et gestes \u00e0 lui et \u00e0 ses potes. Tout juste s'il ne l'entendait pas encore gronder, grommeler des choses comme : \u00ab Que fabriquent donc ces garnements dans ce fond de ruelle ? Et ces villas en bordure de plage d\u00e9sert\u00e9es l'hiver qui conservent encore l'odeur de leur pr\u00e9sence. Et cette porte qu'ils oubli\u00e8rent de refermer sans doute dans leur fol sauve-qui-peut. Personne ne me fera croire qu'elle bat sous l'emprise du vent ! \u00bb \u00c0 l'entendre, un chemin se retrouvait d\u00e9voy\u00e9 si l'on y avait couru, l'air, un temps irrespirable au carrefour si on l'avait respir\u00e9. Entre son v\u00e9lo et eux, une \u00e9ternelle partie de cache-cache. M\u00eame \u00e0 la sortie de la grand-messe le dimanche, il flairait l'illicite de les apercevoir statufi\u00e9s en saintes images. Que tante Marie dont il appr\u00e9ciait pourtant la gracieuset\u00e9 tienne son chenapan de neveu par la main ne changeait rien \u00e0 l'affaire. Il savait cette main capable de tout, avide de poires, de pommes, de fruits de toute sorte dont elle d\u00e9lestait, quand la saison s'y pr\u00eatait, maints jardins de cette localit\u00e9 qu'il ne tenait que trop sous sa surveillance ! \u00ab Monsieur Huan ! \u00bb se mit \u00e0 gueuler sans raison Charles-Andr\u00e9 comme il atteignait Portivy, le baron Louis se d\u00e9lectant d'une mani\u00e8re de cigare \u00e0 la porte de son caf\u00e9-tabac. La mer dansait fort.\n\n\u00ab Faute \u00e0 la b\u00eate ! \u00bb s'\u00e9cria le cafetier.\n\nLa b\u00eate ? s'interrogeait Charles-Andr\u00e9 qui avait oubli\u00e9 l'inf\u00e2me chose gluante retir\u00e9e ce matin des bas-fonds.\n\n\u00ab Ah oui, la raie ?\n\n\u2014 C'est pas une raie, c'est... \u00bb\n\nLe vent mangea le mot, Charles-Andr\u00e9 avant de s'\u00e9loigner le long du quai esquissa un sourire poli. En quoi ce poisson des profondeurs qui, d\u00e8s qu'il remonte en surface, annoncerait la temp\u00eate le concernait-il ? Et pourtant ? Des bribes des propos du matin lui revenaient dans les oreilles. Au loin, le fort de Penthi\u00e8vre, les nuages, l'\u00e9cume, le roman du flux et reflux, la pluie qui menace et lui, Charles-Andr\u00e9, las de sa journ\u00e9e, qui se presse d'entrouvrir le lourd portail de la villa Rose, lequel r\u00e9siste, r\u00e9siste.\n\n#\n\nDes heures qui durent des si\u00e8cles, un jour qui contient d'autres ombres, pas seulement celle qu'on tra\u00eene obligatoirement par les chemins. Devenait-il \u00e0 son insu, \u00e0 coller ainsi si souvent son visage contre les vitres, l'analogue du mannequin dans sa serre avec une cervelle \u00e0 son tour presque de bois \u00e0 force d'\u00eatre taraud\u00e9e d'une seule id\u00e9e : est-elle ou n'est-elle pas ? Jusqu'\u00e0 la bande de trembles fatiguant le jardin de son \u00e9ternel chahut qui paraissait se moquer de sa perplexit\u00e9 interrogative.\n\nApr\u00e8s une nuit assez morose, un petit d\u00e9jeuner du m\u00eame acabit malgr\u00e9 la jovialit\u00e9 de la cuisine, Charles-Andr\u00e9 d\u00e9cida soudain d'aller en conter de belles \u00e0 la jolie patronne du troquet des Mouettes \u00e0 Saint-Pierre. Ses baies vitr\u00e9es r\u00e9fl\u00e9chissent le port et quelque chose en plus qu'il n'arrivait pas \u00e0 d\u00e9m\u00ealer. \u00c0 deux, peut-\u00eatre qu'ils y parviendraient ? Ou alors choisir de rentrer plus t\u00f4t \u00e0 Nantes, d'abandonner son enfance \u00e0 la bourrasque, dans cette presqu'\u00eele qui sait si bien nager ? Je suis trop \u00ab c\u00f4te sauvage \u00bb, se lamentait-il. \u00c0 son \u00e2ge, s'enfermer dans une villa sur la foi d'hypoth\u00e8ses fallacieuses, sa d\u00e9funte tante Marie en serait tomb\u00e9e de tout son haut ! Se vivre comme un coupable, alors qu'il reste aussi innocent que cette pluie qui tombe sans rien savoir de ses gouttes. Elle en e\u00fbt f\u00e9rocement \u00e9pluch\u00e9 sa Bible pour apaiser son cher neveu ! La meilleure \u00e0 Saint-Pierre pour d\u00e9m\u00ealer le vrai du faux dans son chalet proche en id\u00e9e du lac de Tib\u00e9riade.\n\nAssis dans un fauteuil du salon, il se repassait encore une fois le film de cette calamiteuse soir\u00e9e. Mais qui donc parmi ses cousins cousines si joyeusement attabl\u00e9s avait pu sugg\u00e9rer en mani\u00e8re de plaisanterie ? Pas lui cette fois-ci et encore moins Alfred, le retrait\u00e9 des postes, trop retrait\u00e9 de tout, Charles alors, le laconique Charles qui n'a pas d'Andr\u00e9 dans son pr\u00e9nom pour l'aider \u00e0 prendre conscience de lui-m\u00eame ? Ou Nana ? Il revoyait bien le mannequin bras tendu. Mais qui l'avait amen\u00e9 l\u00e0, debout avec son plateau au milieu des convives ? Quand m\u00eame pas la belle Laurence ? \u00c0 Chantenay, elle avait d\u00fb recevoir sa carte postale ? Si \u00e7a se trouve, elle sait d\u00e9j\u00e0 ce que lui ne sait toujours pas ? Lui t\u00e9l\u00e9phoner, lui demander \u00ab as-tu \u00e9t\u00e9 ? \u00bb. Mais il n'a pas son num\u00e9ro, et puis... Il se r\u00e9p\u00e9tait \u00e0 lui-m\u00eame : Et puis... L'infini des points de suspension, et lui sans doute le dernier point de cette ponctuation \u00e9vasive.\n\nUne pr\u00e9sence f\u00e9minine lui manquait. Diane, son ex- compagne qui m\u00eala si longuement ses mains aux siennes, remari\u00e9e \u00e0 un certain Marchand vivrait \u00e0 Saint-Nazaire. Comment avait-elle pu \u00e0 Nantes, dans leur coquet trois-pi\u00e8ces de Sainte-Croix, dut-elle se dire en refermant une derni\u00e8re fois la porte, comment avait-elle pu durant de si nombreuses ann\u00e9es accompagner un homme si fant\u00f4me de lui-m\u00eame ? Elle lui reprochait tellement de n'\u00eatre jamais l\u00e0, de se tenir \u00e0 ses c\u00f4t\u00e9s avec des yeux d'ailleurs, d'un ailleurs dont elle ne savait rien et lui non plus d'ailleurs, et dont il surgissait en s'excusant. Ils s'\u00e9taient cependant quitt\u00e9s en bonne intelligence. Elle l'avait m\u00eame furtivement embrass\u00e9. Il sentait encore son baiser rest\u00e9 inachev\u00e9 sur la joue droite. Diane (une belle blonde travaillant \u00e0 la S\u00e9curit\u00e9 sociale avant d'entrer dans l'enseignement) qui, mise au courant de cette foutue histoire, en aurait \u00e0 ce point hauss\u00e9 les \u00e9paules qu'il en rougissait d\u00e9j\u00e0, s'imaginant l'entendre, avec son grand bon sens et ses phrases d\u00e9finitives : qu'on puisse s'embrouiller l'esprit \u00e0 ce point, \u00ab se monter le bourrichon \u00bb de cette fa\u00e7on d\u00e9passait l'entendement ! Elle n'aurait pas dit cela, mais c'est tout comme...\n\n\u00ab \u00c0 ton \u00e2ge \u00bb, elle se f\u00fbt m\u00eame \u00e0 coup s\u00fbr esclaff\u00e9e, insensible \u00e0 sa description infinie du d\u00e9sordre des plats et des paroles de ce cr\u00e9pusculaire d\u00eener, de cette soudaine panne d'\u00e9lectricit\u00e9 qui rend tout t\u00e2tonnant, met du noir entre sa fourchette et son couteau. \u00ab Encore une de tes imaginations \u00e0 la manque ! elle aurait encore jur\u00e9. Mais o\u00f9 vis-tu ? \u00bb\n\nC'est vrai, o\u00f9 vivait-il avec ses trois pr\u00e9noms qui peinent d\u00e9j\u00e0 \u00e0 former un nom ? Charles-Andr\u00e9 Bertrand figurait-il encore \u00e0 l'\u00e9tat civil de ses nuits ? Ne devenait-il pas plut\u00f4t, \u00e0 l'instar de l'informe poisson du baron Louis, cet \u00eatre anonyme des bas-fonds qui le matin, \u00e0 chaque r\u00e9veil, remonte angoiss\u00e9 \u00e0 la surface du jour pour l'inonder, le bouleverser de ses propres temp\u00eates ? Il ressentait tellement en lui du flux et du reflux, un mouvement presque hallucinatoire qui le retirait pour aussit\u00f4t le ramener sur la plage de sa fatale obsession. Allait-il y rester encore longtemps ensabl\u00e9 ? Le mieux ne serait-il pas de faire fi de toutes ces b\u00eatises et d'aller sonner rue Marzelle et voir enfin qui viendrait lui ouvrir, Mme Joliette ou pas Mme Joliette !\n\nChaque fois qu'il met le pied au \u00ab ch\u00e2teau \u00bb, cette propri\u00e9t\u00e9 qu'avec ses cousins cousines ils se proposent d\u00e9sormais de vendre et qui leur \u00e9chut en h\u00e9ritage, eux de leur p\u00e8re, un certain M. Audapt, riche propri\u00e9taire que Julie Marie Gillieult sa propre grand-m\u00e8re maternelle, alors veuve d'un jeune matelot disparu en mer, \u00e9pousa un 21 f\u00e9vrier d'il ne savait plus quelle ann\u00e9e d'apr\u00e8s un vieux livret de famille endormi dans sa poussi\u00e8re mythologique au creux d'un tiroir rarement tir\u00e9, oui, chaque fois qu'il entre dans ce fantasmatique domaine o\u00f9 v\u00e9cut son enfance, il s'ent\u00e9n\u00e8bre. Et ce ne fut pas cette nuit de neige de ses douze ans o\u00f9 il d\u00e9couvrit morte dans son lit douillet sa ch\u00e8re tante Marie, suite \u00e0 des incartades suppos\u00e9es du mal\u00e9fique mannequin qu'il avait eu l'id\u00e9e malencontreuse d'inviter \u00e0 la tabl\u00e9e familiale, qui arrangea au mieux les choses. Et cet \u00e9tang dans le parc mal entretenu qui le r\u00e9fl\u00e9chit dans la rancune trop m\u00eal\u00e9e \u00e0 sa vase et ces all\u00e9es sournoises qui vous m\u00e8nent sans qu'on n'y prenne garde vers des bosquets o\u00f9 jusqu'\u00e0 l'\u00e2me on se d\u00e9chire !\n\nIl soupira, se leva, soupira en se levant.\n\n#\n\nEn d\u00e9finitive, Charles-Andr\u00e9 changeant d'avis n'alla pas \u00e0 Saint-Pierre. Plus envie de revoir encore une fois l'ex-chalet de tante Marie sans elle \u00e0 ses fen\u00eatres, ou aux siennes Ang\u00e8le sa copine aux rideaux bleus \u00e9pais derri\u00e8re l'\u00e9glise dont les cloches lui rappelaient si cruellement les messes d'antan quand, habill\u00e9 en dimanche, il s'attardait avec de nombreux fid\u00e8les sur son parvis.\n\n\u00ab Plus rien \u00e0 secouer \u00bb, se dit-il assez vulgairement avec l'ambition de laisser ses supputations d\u00e9l\u00e9t\u00e8res \u00e0 la cave, de les enfermer m\u00eame \u00e0 double tour parmi les noirceurs souterraines de la villa Rose pour enfin vivre plus l\u00e9ger dans les \u00e9tages. Ses amis dans une deuxi\u00e8me lettre plus elliptique annon\u00e7aient leur retour des \u00c9tats-Unis. Bient\u00f4t, il allait remettre la clef dans sa souche et dire adieu \u00e0 Portivy, au baron Louis, ce mauvais \u00e9l\u00e8ve de l'oc\u00e9an, et repartir \u00e0 Nantes. Le lyc\u00e9e l'esp\u00e9rait lundi et nous approchions du vendredi. Que risquait-il \u00e0 reprendre son travail de prof ? Cela avait \u00e9t\u00e9 une folie de s'imaginer durant une semaine encore Dieu sait quoi, un Dieu sait quoi d'ailleurs dont il avait d\u00e9sormais un peu honte et qu'il n'osait plus vraiment se formuler. Mais juste au moment o\u00f9 il d\u00e9cida (il d\u00e9cide toujours mais ses d\u00e9cisions \u2013 on l'a souvent dit \u2013 sont rarement suivies d'effet), o\u00f9 il d\u00e9cida tout simplement d'\u00eatre heureux, un fait, des co\u00efncidences inexplicables, comme un rire du hasard, se produisit qui le replongea selon lui \u00e0 nouveau dans ses perplexit\u00e9s. S'amusait-on \u00e0 le tirer depuis le fort de Penthi\u00e8vre tout proche ? La plaisanterie ordinaire du baron Louis quand la mauvaise humeur le fusille trop (\u00ab les types du fort me tirent dessus \u00bb), fallait-il donc aussi qu'il se l'applique ?\n\nCharles-Andr\u00e9 en cong\u00e9 de lui-m\u00eame r\u00eavassait sourdement aux approches de midi au bar de la Jet\u00e9e quand le taciturne cafetier, passablement mar\u00e9e montante ce matin-l\u00e0, lui r\u00e9clama soudain avec v\u00e9h\u00e9mence :\n\n\u00ab Vous avez lu ? \u00bb\n\nComment aurait-il pu ? Il venait juste de s'attabler \u00e0 sa place habituelle sous le vasistas de texture un peu glauque qui surveille la plage o\u00f9 une vague vraiment mauvaise vie \u00e9cumait de rage sous un ciel houleux.\n\n\u00ab Eh bien, lisez ! \u00bb\n\nEt de lui glisser brutalement sous le nez un exemplaire du journal local ouvert \u00e0 la page des faits-divers, les faits-divers, sa passion. Et alors que Charles-Andr\u00e9 tir\u00e9 de son heureuse somnolence allait \u00e0 regret obtemp\u00e9rer, prendre confus\u00e9ment connaissance de l'article en question, voil\u00e0 que l'autre, tout en lui servant son sempiternel porto blanc, lui jette en confidence en baissant la voix, alors qu'il n'y avait personne d'autre qu'eux-m\u00eames dans l'\u00e9tablissement, et l'\u00e9ternel bruit de la mer :\n\n\u00ab Et encore une vieille femme ! \u00bb grondait-il.\n\nC'\u00e9tait la conclusion ass\u00e9n\u00e9e avec force d'un drame que sa fureur au d\u00e9bit trop pr\u00e9cipit\u00e9 avait d\u00e9j\u00e0 aval\u00e9. Il n'en restait \u00e0 Charles-Andr\u00e9 que quelques d\u00e9bris dans les oreilles : un farouche manoir dans les terres, par l\u00e0 (geste du bras), une vieille femme dedans aux abois.\n\nCharles-Andr\u00e9 sourd \u00e0 tout contexte alarmant fit comme s'il avait vraiment tout entendu, et m\u00eame lu, en r\u00e9alit\u00e9 d'un \u0153il distrait, car ce n'\u00e9tait ind\u00e9niablement pas la bonne page (la sienne, s'ornant d'une photo grand format, relatait en gros caract\u00e8res le d\u00e9part \u00e0 la retraite d'un brigadier-chef de gendarmerie), alors que le baron Louis ne se poss\u00e9dant plus rin\u00e7ait d'un air forcen\u00e9 ses verres derri\u00e8re son comptoir et continuait \u00e0 s'emporter contre l'esp\u00e8ce humaine capable d'une telle criminelle n\u00e9gligence, de laisser ainsi une pauvre cr\u00e9ature... Il ne se lassait pas de le r\u00e9p\u00e9ter : de laisser une pauvre cr\u00e9ature...\n\n\u00ab Quinze jours \u00bb, il \u00e9cumait, \u00ab quinze, vous rendez-vous compte et sans le moindre soin ! \u00bb\n\nIl en aurait presque tap\u00e9 en ce moment le premier client qui aurait eu la mauvaise id\u00e9e de vouloir le contredire.\n\n\u00ab Et des fortun\u00e9s encore, des gens \u00e0 fric ! Apr\u00e8s avoir fait ce soir-l\u00e0 la nouba, b\u00e2fr\u00e9 comme pas un autour d'une table pr\u00e9par\u00e9e par la bonne vieille, au revoir et merci. \u00bb\n\nIl n'en achevait plus ses phrases.\n\n\u00ab Comment s'appelait d\u00e9j\u00e0 votre poisson des bas-fonds ? Oui, la sorte de raie que vous avez p\u00each\u00e9e hier \u00bb, l'interrompit soudain Charles-Andr\u00e9 qui d\u00e9sirait parler d'autre chose.\n\nLe baron Louis avait oubli\u00e9. Enfin pas vraiment, conc\u00e9dait-il, mais le vrai nom \u00e9tait reparti avec le p\u00eacheur qui l'avait apport\u00e9. En ce moment, il ne sait pas ce qu'il a, mais plus rien ne fait date en lui.\n\n\u00ab J'oublie tout, il confesse. Ah monsieur le cur\u00e9 ! s'exclama-t-il, vous tombez bien ! \u00bb\n\nUn eccl\u00e9siastique corpulent qui se r\u00e9v\u00e9lera par la suite \u00eatre en effet sinon le cur\u00e9, du moins l'un des vicaires de Saint-Pierre, venait d'ouvrir la porte et s'accoudait jovialement au bar.\n\n#\n\nEst-ce raisonnable \u00e0 son \u00e2ge de s'imaginer qu'un mannequin de bois des \u00eeles ait pu empoisonner deux femmes, du moins pr\u00eater main-forte \u00e0 leur assassinat ? Qu'\u00e0 douze ans pour la premi\u00e8re, sa tante, il ait pu le croire, passe encore, mais \u00e0 quarante pour la seconde, Mme Joliette ? \u00c9tait-ce l'effet s\u00e9pulcral du \u00ab ch\u00e2teau \u00bb rue Marzelle ? De se retrouver seul entour\u00e9 de pi\u00e8ces d\u00e9shabit\u00e9es ? Pourtant il apprivoisa leur solitude depuis tant d'ann\u00e9es, et la minutie des escaliers de cette haute demeure si comptables de leurs marches, et la fuite en avant de ses couloirs jusqu'au d\u00e9sordre appr\u00eat\u00e9 des combles, et se montrerait capable sous un tel toit d'y circuler en aveugle et de savoir \u00e0 tout moment sans avoir \u00e0 ouvrir les yeux o\u00f9 il se trouve ! N'y logea-t-il pas jusqu'\u00e0 sa majorit\u00e9 ! L'est-il d'ailleurs, majeur ! Si \u00e7a se trouve l'ardente cuisini\u00e8re mise au parfum rirait de toutes ses dents devant ses fourneaux. Car qui prouve \u00e0 Charles-Andr\u00e9 qu'elle soit d\u00e9c\u00e9d\u00e9e ? Il la pr\u00e9suma morte \u00e0 son r\u00e9veil, du moins l'enfant en lui la pr\u00e9suma morte. Mais les hypoth\u00e8ses du matin pas encore d\u00e9gag\u00e9 de sa nuit ne sont pas celles de l'apr\u00e8s-midi, quand le soleil discipline nos ombres, les range dans notre dos ! Se serait-il enfui comme un coupable devant une cr\u00e9ature simplement endormie ? Mais la grille en grin\u00e7ant lui grin\u00e7ait le contraire et sa clef rouill\u00e9e qui refusait qu'il parte, et toutes ces all\u00e9es qui s'empressaient sournoises autour de leur fun\u00e8bre \u00e9tang encombr\u00e9 d'eau stagnante. Le fait-divers du baron Louis ressemblait au sien qui heureusement n'\u00e9tait pas encore divers !\n\n\u00ab Divers \u00bb, il se r\u00e9p\u00e9tait assez morne, \u00ab Divers \u00bb.\n\nIl avait un peu convers\u00e9 avec le pr\u00eatre de Saint-Pierre, un gaillard plut\u00f4t loquace qui entre deux offices avouait adorer se balader dans la presqu'\u00eele.\n\n\u00ab Cela renforce mes oraisons \u00bb, rougissait-il d'expliquer.\n\nDu moins si ce ne sont pas exactement ses paroles, c'\u00e9tait l'esprit de ce qu'elles \u00e9non\u00e7aient. L'oc\u00e9an qui avance, qui recule, la presqu'\u00eele, ce bras de terre qui tressaille de ses assauts, le r\u00e9jouissaient jusqu'\u00e0 l'\u00e2me. Le pr\u00eatre encore assez jeune fleurissait d'\u00e9pith\u00e8tes de ce style, parlait de fa\u00e7on quasi biblique de cette \u00e9ternelle confrontation entre l'oc\u00e9an et le rivage, en arrivait presque \u00e0 s'excuser de l'\u00e9cume \u00e9ventuelle que ses mots provoquaient dans ce caf\u00e9 d\u00e9sert.\n\n\u00ab Je plaisante \u00bb, reprenait-il, quand sa phrase trop mouvement\u00e9e paraissait avoir un peu trop stup\u00e9fi\u00e9 l'interlocuteur, en l'occurrence le baron Louis qui, bouche b\u00e9e derri\u00e8re son bar, en omettait de lui servir son petit verre de vin de messe. Un pr\u00eatre se permettre de parler ainsi ! lisait-on sur le visage abrupt du cafetier.\n\nCharles-Andr\u00e9 en souriait \u00e0 son propre sourire, sa d\u00e9funte tante si amoureuse de la sacristie n'e\u00fbt pas manqu\u00e9 en son temps de s'\u00e9tonner elle aussi d'expressions si pleines de remous de la part d'un eccl\u00e9siastique. Cette vaillante cohorte du Christ, comme elle les d\u00e9nommait parfois, \u00e9tait porteuse de la parole de Dieu qu'elle entendait le dimanche tonner en chaire et ne devait en aucune fa\u00e7on s'en \u00e9carter ! Pourtant, m\u00eame le vieil abb\u00e9 Messager son voisin de br\u00e9viaire trouvait moyen de lui citer les \u00c9vangiles depuis la terre remu\u00e9e de son jardin. M\u00ealer les \u00c9vang\u00e9listes Luc, Marc, Matthieu ou Jean \u00e0 la cueillette des fleurs de ses plates-bandes cela lui paraissait alors le comble de la pi\u00e9t\u00e9, surtout si une averse \u00e0 la Saint-Jean-Baptiste venait soudain baptiser leur duo, po\u00e9tisait aussit\u00f4t Marie de nouveau bien \u00e0 l'abri dans la grotte chaleureuse de sa cuisine.\n\nLe vicaire qui approchait la quarantaine s'appelait Bonnafoux, Aim\u00e9 Bonnafoux, et se montrait curieux de Charles-Andr\u00e9. Ils engag\u00e8rent donc un vague propos alors qu'au-dehors le vent enflait la voix. La porte s'en r\u00e9voltait et aussi les fen\u00eatres que le baron Louis s'empressa aussit\u00f4t de verrouiller.\n\nOui, il \u00e9tait en vacances de la Toussaint dans ce pays de sa prime enfance. Oui, il g\u00eetait \u00e0 Portivy, dans la villa d'un de ses amis.\n\n\u00ab Le danseur ? \u00bb s'exclama Bonnafoux qui connaissait de vue sa svelte silhouette et savait qu'il chantait aussi \u00e0 la chorale de Saint-Pierre. \u00ab Il b\u00e9n\u00e9ficie d'une voix puissante. On l'entendrait jusqu'au port. Il faut dire que la rue est en pente \u00bb, \u00e9prouva-t-il bizarrement le besoin d'ajouter.\n\n\u00c9tait-ce l'effet du petit blanc aval\u00e9 \u00e0 la h\u00e2te, le vicaire plut\u00f4t en verve avait convi\u00e9 l'entier de la presqu'\u00eele autour de son verre. Il aime beaucoup ses hameaux, tous ces Ker ceci, Ker cela, confessait-il \u00e0 Charles-Andr\u00e9, et \u00e0 travers la campagne les petits murs de pierres s\u00e8ches.\n\n\u00ab Enfin s\u00e8ches, quand on voit aujourd'hui ce qui tombe ! Seul le granit r\u00e9siste \u00e0 l'oc\u00e9an \u00bb, \u00e9non\u00e7a-t-il un peu doctement. Lui qui sort du Midi, des environs de Menton, il adore la Bretagne, ses diverses humeurs. Rien n'est plus salutaire pour lui qu'une bonne marche dans la lande, sur la c\u00f4te sauvage, missel en main quand le temps s'y pr\u00eate, osa-t-il \u00e0 un moment avouer en un soudain acc\u00e8s de lyrisme et tout \u00e9mu d'une telle confidence !\n\nUn homme plut\u00f4t grand, une bonne t\u00eate de plus que Charles-Andr\u00e9, la poitrine large, des mains noueuses de charpentier.\n\nMais J\u00e9sus l'\u00e9tait, songea aussit\u00f4t ce dernier. N\u00e9anmoins un visage pas commode que celui de ce vicaire, heureusement des yeux d'ap\u00f4tre.\n\n\u00c0 \u00e9couter discourir ce vigoureux serviteur de Dieu, c'\u00e9tait sa ch\u00e8re tante qui revenait dans les yeux de son cher neveu, et dans ses oreilles la couleur de ses phrases quand elle feuilletait \u00e0 l'intention de ses dix onze ans le grand livre jaune interrompu d'images de la Palestine toutes plus poussi\u00e9reuses les unes que les autres qu'elle tenait en r\u00e9serve dans sa chambre : la fontaine qui existe toujours \u00e0 Nazareth, assurait-elle, o\u00f9 la Vierge allait chercher de l'eau pour sa sainte maisonn\u00e9e, les sentes du d\u00e9sert, les barques du lac de Tib\u00e9riade. C'est de l'une d'elles que J\u00e9sus pronon\u00e7a elle ne savait plus quoi \u00e0 l'intention d'une nu\u00e9e de fid\u00e8les rassembl\u00e9s sur la berge...\n\nLe bouquin ? Il doit l'avoir quelque part en cherchant bien \u00e0 la fois dans sa m\u00e9moire, un vrai fouillis, et dans son trois-pi\u00e8ces du Bouffay plein de perspectives int\u00e9rieures \u00e0 Nantes, pas loin de l'\u00e9glise Sainte-Croix.\n\nDans ce t\u00e9n\u00e9breux bar de la Jet\u00e9e, alors que le baron Louis avait engag\u00e9 une longue parole arros\u00e9e de vin de messe avec l'athl\u00e9tique eccl\u00e9siastique, Charles-Andr\u00e9 repris par son enfance en tournait d\u00e9j\u00e0 mentalement les pages, h\u00e9las sans les commentaires dans les marges de sa d\u00e9funte tante, tout ce charabia mystique h\u00e9rit\u00e9 en partie des plates-bandes de son corpulent voisin l'abb\u00e9 Messager o\u00f9 le nom de J\u00e9sus fleurissait sans cesse. C'\u00e9tait J\u00e9rusalem vu du mont des Oliviers ou les monts de la Quarantaine avec des cypr\u00e8s dress\u00e9s comme des \u00e9p\u00e9es ou le d\u00e9sert rocailleux de Jud\u00e9e ou le cours tortueux du fleuve Jourdain ou...\n\nIl avait depuis perdu les noms de toutes ces saintes flaques qu'elle lui \u00e9num\u00e9rait, opposant la mer Morte \u00e0 cet oc\u00e9an de la presqu'\u00eele trop pa\u00efen \u00e0 son go\u00fbt. Qu'y a-t-il donc \u00e0 p\u00eacher en dehors des poissons dans cette grande r\u00e9volution d'eau qui ressasse perp\u00e9tuellement son amertume ? paraissait-elle lui dire. Mais l\u00e0, si c'\u00e9tait assur\u00e9ment ce qu'elle devait penser, c'\u00e9tait bien lui qui aujourd'hui parlait, et non sa ch\u00e8re d\u00e9funte qui n'avait pas les mots de son cher neveu, devenu prof de lettres, car les siens, \u00e0 elle, les vrais, ceux rest\u00e9s dans sa jolie gorge, avaient \u00e9t\u00e9 trop convertis par sa Bible pour se permettre une telle licence, f\u00fbt-elle po\u00e9tique, et d\u00e9border ainsi aussi peu chr\u00e9tiennement ses l\u00e8vres.\n\nIl en sourit \u00e0 son verre.\n\nUne brune entre deux \u00e2ges, un minois presque effac\u00e9 de la jeune fille qu'elle \u00e9tait rest\u00e9e esp\u00e9rant en vain, \u00e0 d\u00e9faut de l'ange, au moins toujours un Joseph ! Une d\u00e9marche d\u00e9licate, apeur\u00e9e comme au sortir d'un bois, une fa\u00e7on de poser les pieds sur terre qu'elle chaussait de hauts talons. Charles-Andr\u00e9 croit savoir qu'elle avait un moment \u00e9prouv\u00e9 un d\u00e9but de sentiment pour un militaire du fort de Penthi\u00e8vre, mais la langue de sable est si \u00e9troite pour entrer dans la presqu'\u00eele qu'il se demande si l'on peut ajouter foi \u00e0 de semblables bobards, la mer est si m\u00e9lang\u00e9e \u00e0 cet endroit. Ses dix douze ans toujours si vivaces en lui se rappellent pourtant une ombre galonn\u00e9e qui persistait certains soirs \u00e0 l'entr\u00e9e de leur jardinet et des voix complices entendues depuis sa chambrette du c\u00f4t\u00e9 du poulailler.\n\n#\n\n\u00c0 vrai dire, Charles-Andr\u00e9 a toujours eu l'art de d\u00e9guiser les ombres, et \u00e0 la villa Rose elles ne manquaient pas, depuis l'infortun\u00e9e du hall d'entr\u00e9e que le soleil ne nourrissait gu\u00e8re \u00e0 celles plus riches d'aventures du premier et surtout du deuxi\u00e8me \u00e9tage, \u00e0 toucher les clandestines des combles, ces filles de la poussi\u00e8re et de la ranc\u0153ur des recoins qui r\u00f4dent sans partage au grenier. Son pr\u00e9tendu crime n'en serait-il pas la cons\u00e9quence ? Se retrouver \u00e0 l'aube en pr\u00e9sence d'une suppos\u00e9e morte constituerait-il d\u00e9j\u00e0 un signe de culpabilit\u00e9 ? Au \u00ab ch\u00e2teau \u00bb, rue Marzelle, ne pr\u00eata-t-il pas trop d'hypoth\u00e8ses \u00e0 l'Ombre, ce b\u00e2timent des communs, en r\u00e9alit\u00e9 le seul vrai responsable de cette anxi\u00e9t\u00e9 mal\u00e9fique qui le ruine depuis une semaine ? Pourtant sa grand-m\u00e8re Julie pr\u00e9f\u00e9ra, apr\u00e8s la mort de son distingu\u00e9 \u00e9poux, y habiter s'y sentant sans doute \u00e0 cause de ses origines modestes, en bonne fille d'un scieur de long de basse Bretagne, plus chez elle que dans l'apparat d\u00e9sertique de l'\u00e9difice principal qui la rendait encore plus veuve ! Du moins \u00e0 ce qu'on rapporta \u00e0 Charles-Andr\u00e9 qui interrogeait souvent son portrait suspendu au-dessus de la chemin\u00e9e du salon. Il en aimait le minois chiffonn\u00e9 et l'attitude fin de si\u00e8cle de sa myst\u00e9rieuse a\u00efeule d\u00e9c\u00e9d\u00e9e un an tout juste apr\u00e8s son \u00e9poux et bien longtemps avant que son petit-fils ne naisse.\n\nL\u00e0, aux quatre vents de ce vaste domaine que Charles-Andr\u00e9 grandit, \u00e9lev\u00e9, enfin surveill\u00e9 tant bien que mal une fois sa m\u00e8re disparue par sa jeune tante Marie. Il aurait pu en dessiner de m\u00e9moire la moindre singularit\u00e9, et surtout celles des communs o\u00f9 il dormait. Car cette pauvre annexe domestique aux murs de pierres mal entass\u00e9es les unes sur les autres et soud\u00e9es on ne sait comment, gr\u00e2ce \u00e0 un mortier du diable imaginait-il, ne b\u00e9n\u00e9ficie gu\u00e8re de la lumi\u00e8re du jour d'o\u00f9 son nom : l'Ombre. Faute aux trembles fort touffus qui en cet endroit du parc le masqueraient au visiteur le plus curieux ? On a eu beau multiplier les lucarnes, vasistas en tout genre, la nuit r\u00e8gne en ma\u00eetresse dans ses couloirs m\u00eame en plein midi. Quant aux escaliers, d\u00e8s qu'il sut marcher, ses petits pieds craignaient trop de les emprunter car Dieu seul sait o\u00f9 ses marches auraient pu le mener ? Ce dont d'ailleurs semblait l'avertir, le menacer le funeste mannequin de la serre, \u00e0 moins que le rictus permanent de son visage impassible, impossible, n'exprim\u00e2t juste sa d\u00e9sapprobation d'\u00eatre en bois, m\u00eame en bois des \u00eeles. Rien de bon ne peut sortir de telles portes et fen\u00eatres, paraissait-il cependant lui confier avec une joie mauvaise.\n\nCharles-Andr\u00e9 devenait-il \u00e0 Portivy, avec son man\u00e8ge autour de la m\u00eame id\u00e9e fixe (\u00ab Mme Joliette est-elle ou n'est-elle pas ? \u00bb), le mannequin de la villa Rose ? Certes, il lui manquait le plateau et la veste rouge, mais il campait visiblement dans la m\u00eame obstination. Ses amis revenaient bient\u00f4t de Virginie, il n'allait quand m\u00eame pas les attendre avec l'attitude hypocrite de ce type mal articul\u00e9 dans la serre, heureusement leur habitation n'en poss\u00e9dait pas, de serre. Seule la profusion v\u00e9g\u00e9tale de ce jardin plut\u00f4t exub\u00e9rant s'apparentait un peu au parc du \u00ab ch\u00e2teau \u00bb avec sa piscine vide souill\u00e9e de feuilles mortes singeant de son mieux l'\u00e9tang bourbeux. Mais ici, pas d'all\u00e9es trompeuses, en zigzag, une seule assez rectiligne vous menait en toute loyaut\u00e9 sableuse et avec bonne conscience au portail d'entr\u00e9e.\n\nLa journ\u00e9e s'\u00e9puisa ainsi, en digressions int\u00e9rieures et en pas de c\u00f4t\u00e9. Dans quel \u00ab Ker \u00bb, hameau de granit quelconque, crut-il \u00e0 un moment entrevoir M. Huan rongeant son frein, le f\u00e9roce garde champ\u00eatre de ses jeunes ann\u00e9es ? Pourtant il n'avait rien commis de r\u00e9pr\u00e9hensible, seules ses pens\u00e9es peut-\u00eatre ? De toute fa\u00e7on, ce ne pouvait \u00eatre ce pourfendeur d'ombres de son enfance : vu l'\u00e2ge qu'il avait d\u00e9j\u00e0, longtemps qu'il doit verbaliser dans l'au-del\u00e0 !\n\nBien s\u00fbr, Charles-Andr\u00e9 d\u00e9jeuna aux Mouettes sur le port d'Orange. H\u00e9las, alors qu'il aurait bien eu besoin d'une pr\u00e9sence f\u00e9minine qui e\u00fbt pu m\u00ealer ses mains douces aux siennes, la jolie patronne, pourtant dans une triomphante toilette, ne lui pr\u00eata gu\u00e8re d'attention, requise par une tabl\u00e9e exub\u00e9rante de touristes allemands ou scandinaves qui faisait un tapage d'enfer. Le ciel s'en bouleversait au-dehors \u00e0 la pointe des m\u00e2ts par la porte entrouverte. Leur brouhaha allait-il amener l'averse ? Charles-Andr\u00e9 n'\u00e9tait pas loin de le penser. Non, il ne revit plus Ang\u00e8le, \u00e9vita m\u00eame de passer \u00e0 Saint-Pierre devant sa maison aux volets verts derri\u00e8re l'\u00e9glise. Il ne s'expliquait pas tellement son attitude. Mais il y a tellement de choses en lui qu'il ne s'explique pas. \u00c0 Quiberon, un moment, il crut enfin trouver ses raisons d'\u00eatre. Le soleil s'\u00e9tait mis de la partie \u00e9clairant jusqu'au fin fond de l'horizon, donc aussi le sien d'horizon marchant avec lui sur la plage. Cela dura un court \u00e9clair, mais l'orage survint, le for\u00e7ant \u00e0 aller s'abriter dans une brasserie aussi obscure que le noir noir caf\u00e9 qu'il but.\n\nIl avait fini par retrouver le num\u00e9ro de t\u00e9l\u00e9phone de sa cousine, la belle Laurence. Aussi l'appela-t-il non pas de la villa Rose mais d'une cabine publique devant le square o\u00f9 se dresse \u00e0 Quiberon la statue farouche de Hoche. S'\u00e9tait-elle rendue ou non (comme il l'en avait press\u00e9e par lettre) au \u00ab ch\u00e2teau \u00bb afin de r\u00e9cup\u00e9rer ses papiers d'identit\u00e9, sa carte bleue surtout qui lui fait tant d\u00e9faut ?\n\nOui, lui r\u00e9pondit-elle d'une voix aigre-douce, car elle avouait se r\u00e9veiller d'une sieste, oui elle avait bien \u00e9t\u00e9 malgr\u00e9 toutes ses occupations sonner \u00e0 la grille de ladite propri\u00e9t\u00e9 ancestrale, mais personne n'\u00e9tait venu lui ouvrir. Pourtant la gardienne habite bien l\u00e0, une certaine \u00c9milie qui fait si bien la cuisine, elle avait encore dans la bouche le m\u00e9morable civet de lapin qu'elle leur avait servi lors de leur derni\u00e8re et familiale soir\u00e9e ! \u00c0 moins que ta Mme Joliette soit sourde ou perdue dans mille activit\u00e9s au fond du parc et n'ait pas per\u00e7u ses insistantes sonneries, trop prise par le bruit du r\u00e2teau qu'elle maniait ou trop soucieuse d'\u00e9tendre son linge \u00e0 s\u00e9cher. Et pourtant Laurence avait redoubl\u00e9 d'efforts. Toujours grand silence derri\u00e8re la grille, pas le plus petit bruit de savate ou sabot de quelqu'un qui s'approche, comme si la gardienne s'\u00e9tait ray\u00e9e elle-m\u00eame du monde des vivants, se permit-elle d'ajouter dans un grand \u00e9clat de rire ! Laurence avait oubli\u00e9 de lui dire, \u00e0 lui Charles-Andr\u00e9, qu'elle avait m\u00eame pris la pr\u00e9caution au pr\u00e9alable de t\u00e9l\u00e9phoner au \u00ab ch\u00e2teau \u00bb pour avertir la bonne femme de sa visite et que l\u00e0 aussi comme devant la grille aucune r\u00e9ponse, signe de vie quelconque, que le r\u00e9pondeur fatidique avec la voix encore vivante et analphab\u00e8te, plaisantait encore Laurence, de la si talentueuse cuisini\u00e8re au civet, et pourtant elle lui avait laiss\u00e9 son propre num\u00e9ro pour que cette obligeante personne puisse enfin l'appeler !\n\nCharles-Andr\u00e9, repris par son angoisse, tout en la remerciant d'une voix sourde avait raccroch\u00e9. Et s'il t\u00e9l\u00e9phonait \u00e0 son tour \u00e0 Mme Joliette sur un pr\u00e9texte quelconque, que risquait-il apr\u00e8s tout ? Il ne pouvait quand m\u00eame pas rester avec ce doute sur ses propres faits et gestes. Il faisait tellement noir dans ce b\u00e2timent des communs quand il se r\u00e9veilla ce pauvre matin de la semaine derni\u00e8re qui depuis assombrit tant son esprit. Il regarda autour de lui. Que des mines ensoleill\u00e9es, aucun souci de l'ombre qui pourtant stagnait en grosse taches d'encre ici ou l\u00e0 sur le trottoir. \u00c9tait-il \u00e0 Quiberon ce jour-l\u00e0 le seul touriste de l'obscur, celui qui au lieu de se r\u00e9jouir du soleil ne pr\u00eate attention qu'\u00e0 cette l\u00e8pre de la lumi\u00e8re ?\n\n#\n\nS'il analysait... Mais analysait-il vraiment avec ses primes ann\u00e9es qui dans la presqu'\u00eele lui revenaient sans cesse dans les yeux, avec cette mer en permanence d\u00e9mont\u00e9e d'un c\u00f4t\u00e9 et si paisible de l'autre, avec tous ces chemins \u00e9gar\u00e9s dans leur solitude qui lui embarrassaient les pieds, avec ce ciel en folie, cette vo\u00fbte nuageuse presque de granit qui lui pesait aux \u00e9paules, s'il analysait, n'\u00e9tait-ce pas d'avoir d\u00e9couvert, \u00e0 un \u00e2ge pu\u00e9ril, sa ch\u00e8re tante qui avait pass\u00e9 un beau matin l'arme \u00e0 gauche et Mme Joliette trente ans plus tard dans la m\u00eame chambre, le m\u00eame lit et dans une posture identique sur le dos (mains jointes comme pour une ultime pri\u00e8re) qui lui fit croire que la m\u00eame mort se reproduisait et qu'elle tenait cette mort aussi \u00e0 l'Ombre (ce b\u00e2timent des communs o\u00f9 s'entasse tout le rebut du \u00ab ch\u00e2teau \u00bb) en particulier \u00e0 la chambre, cette cavit\u00e9 fun\u00e8bre sous les toits, \u00e0 ce couloir reptilien qui d\u00e9versait \u00e0 son terme le venin de ses marches, et qu'il \u00e9tait lui Charles-Andr\u00e9 Bertrand, homme pourtant raisonnable, perdu \u00e0 nouveau dans ce d\u00e9dale d'effroi ?\n\nD'o\u00f9 sa fuite, tout son \u00eatre depuis en d\u00e9sordre, et l'impossibilit\u00e9 o\u00f9 il se trouvait aujourd'hui malgr\u00e9 ce soudain franc soleil de voir clair en lui. Car enfin Laurence au t\u00e9l\u00e9phone ne fut gu\u00e8re rassurante, personne, que le r\u00e9pondeur pour lui r\u00e9pondre au bout du fil quand elle t\u00e9l\u00e9phona, personne devant la grille. \u00c0 moins que Mme Joliette se soit absent\u00e9e, chose plausible, des courses \u00e0 faire place Zola ou ailleurs, dans le reste de Nantes. Aurait-il la force \u00e0 son retour de se rendre rue Marzelle ? On \u00e9tait vendredi, plus que deux jours pour se d\u00e9cider avant son d\u00e9part lundi, le train ou le taxi jusqu'\u00e0 Auray, puis... Ses douze ans avaient soup\u00e7onn\u00e9 le mannequin, mais \u00e0 quarante, comment accepter un empoisonneur en bois, f\u00fbt-il d'un bois inconnu, d'un bois des \u00eeles ? La police lui rirait au nez, m\u00eame l'oc\u00e9an ici lui rit au nez vague apr\u00e8s vague.\n\nIl retourna au bar de la Jet\u00e9e. La bonhomie du baron Louis l'apaisait. Avec lui au moins ce n'\u00e9tait pas la grande mar\u00e9e, il laissait \u00e7a \u00e0 son ennemie la mer qui osait parfois venir l\u00e9cher le bas de sa porte. Ses mots visaient juste \u00e0 vous faire vider un verre de plus. En ce moment il glorifie un de ces vins bien de chez nous, un blanc aussi net au go\u00fbt qu'un couteau qui coupe ! Quant aux faits-divers contre lesquels il d\u00e9blat\u00e8re, si certains serin\u00e9s maintes fois sentent un peu trop le bouchon, la plupart appartiennent au corps vivant de la bouteille qu'il tient et dont il avale \u00e9loquemment une lamp\u00e9e ou deux avant de s'offrir un bon petit coup d\u00e9finitif \u00e0 se raser les moustaches qu'il essuie apr\u00e8s \u00e0 l'aide de tous ses doigts. Ce vendredi, il se remit, Dieu sait pourquoi, sur l'histoire de la bonne dame que sa famille avait laiss\u00e9e une bonne quinzaine \u00e0 sa seule mort dans le manoir familial, \u00e0 tel point que Charles-Andr\u00e9 se demanda si le cafetier ne serait pas entr\u00e9, par effraction et sans qu'il s'en doute, dans son propre suppos\u00e9 fait-divers de la rue Marzelle. Il y avait de telles analogies qu'il osa prononcer dans un souffle :\n\n\u00ab Ce ne serait pas par hasard \u00e0 Nantes, par hasard ?\n\n\u2014 Vous rigolez, c'est sur la route d'Erdeven, dans un de ces patelins o\u00f9 les gens se terrent, restent sans arr\u00eat chez eux. \u00bb\n\nEt elle, la pauvre femme, elle l'\u00e9tait bien, rest\u00e9e ! Il veut dire vraiment rest\u00e9e, d\u00e9c\u00e9d\u00e9e depuis des semaines, sans qu'aucun de ses voisins ne s'en inqui\u00e8te. Cette indiff\u00e9rence le tuait !\n\n\u00ab Moi au moins si je cr\u00e8ve, tous les soiffards le sauront vite, il n'y a que mon bistro sur ce coin de c\u00f4te et la mer sal\u00e9e vous savez \u00e7a donne soif ! \u00bb\n\nCharles-Andr\u00e9 n'en revenait pas. Oui le baron Louis lui avait relat\u00e9 d\u00e9j\u00e0 au moins une fois cette anecdote tragique, mais comme il pr\u00eate le plus souvent peu d'attention \u00e0 sa clameur, pris par celle de la mer dont il s'imagine parfois entendre battre le c\u0153ur, il \u00e9tait demeur\u00e9 sourd aux \u00e9clats de voix du cabaretier, ayant son verre \u00e0 vider et son \u00e2me \u00e0 remplir. De quoi ? Eh bien du vent, s'il sort, de la temp\u00eate qui se pr\u00e9pare, ou du soleil qui vous attend au-dehors pour allonger votre ombre. Et c'\u00e9tait le cas, cet apr\u00e8s-midi-l\u00e0, Charles-Andr\u00e9 songeait donc \u00e0 aller se d\u00e9gourdir un moment les jambes dans la lande mais le baron Louis particuli\u00e8rement loquace le retenait par le feu de ses paroles. Un homme de moyenne stature qui vous parle \u00e0 bout portant.\n\n\u00ab Alors vos amis sont aux States \u00bb, prof\u00e9ra-t-il un rien snob.\n\nIl a deux marmots, une \u00e9pouse diligente dans le reste de sa caverne, une bosse de granit aux trois lucarnes derri\u00e8re le comptoir. Car lui seul tient \u00e0 la force de ses bras noueux son bar de la Jet\u00e9e. Quoique du large il sache seulement ce que lui en rapportent ceux qui en retournent. Le jour ne s'est pas encore lev\u00e9, s'exclame-t-il, o\u00f9 on le verra se hasarder sur l'une de ces planches mouvantes qu'on appelle une barque.\n\n\u00ab J'ai le mal \u00bb, excuse-t-il piteusement. Une fois, il avait vomi durant toute la travers\u00e9e entre Quiberon et Belle-\u00cele.\n\nJamais Charles-Andr\u00e9 n'avait rencontr\u00e9 quelqu'un capable de promener une telle d\u00e9sapprobation de l'oc\u00e9an en lisi\u00e8re de ses vagues. Loin de flirter avec elles, il pr\u00e9f\u00e9rait s'en \u00e9carter. Manifester un d\u00e9go\u00fbt si prononc\u00e9 et tenir un caf\u00e9 face \u00e0 un port ? s'\u00e9tonnait parfois Charles-Andr\u00e9. L'autre en rigolait, conc\u00e9dait \u00e0 narrer qu'un h\u00e9ritage impromptu lui avait mis entre les mains cet estaminet, qu'il aurait d'ailleurs plut\u00f4t pr\u00e9f\u00e9r\u00e9 plant\u00e9 pleine terre, mais qu'il n'allait quand m\u00eame pas cracher dessus, car c'est la mer, son grand cirque, qui lui am\u00e8ne le gros de sa client\u00e8le, p\u00eacheurs qui vivent d'elle et touristes qui viennent \u00e0 Portivy s'en r\u00e9jouir le regard.\n\nLouis Baron, dit le baron Louis, la m\u00eame chemise \u00e0 carreaux qui \u00e0 chaque heure se fige d'\u00e9tonnement devant l'oc\u00e9an insurmontable.\n\n\u00ab Ainsi vos amis sont aux States \u00bb, r\u00e9p\u00e9tait-il pour parler, ne pas laisser le silence, sa discr\u00e8te corolle, s'installer entre eux.\n\nCharles-Andr\u00e9 opina :\n\n\u00ab Comme chaque ann\u00e9e, ils rentrent sans doute la semaine prochaine ou un peu plus tard, je ne sais plus ! \u00bb\n\nLe baron Louis grogna quelque chose. Oui, Charles-Andr\u00e9 se pr\u00e9parait en effet \u00e0 repartir, son travail de prof, les \u00e9l\u00e8ves, l'immensit\u00e9 du tableau noir. Oui, il habite \u00e0 Nantes, vous connaissez, pr\u00e8s du march\u00e9 du Bouffay. Mais il reviendra, \u00e0 P\u00e2ques, par exemple...\n\n\u00ab La meilleure p\u00e9riode, \u00e9non\u00e7a doctoralement le baron Louis, c'est... \u00bb\n\n#\n\nLe lendemain, c'est tout juste s'il se rappelait comment il avait ext\u00e9nu\u00e9 sa journ\u00e9e. La fin d'apr\u00e8s-midi (une violente, encapuchonn\u00e9e d'averses) le trouve malgr\u00e9 tout, cherchant \u00e0 passag\u00e8rement s'abriter de la pluie, \u00e0 la Maison du Douanier, une b\u00e2tisse en ruine sur la c\u00f4te sauvage o\u00f9 il entendit \u00e0 nouveau comme jamais courir ses ann\u00e9es d'enfance, mais apr\u00e8s ? Ses pas devenaient de plus en plus incertains, sa promenade distraite d'elle-m\u00eame \u00e0 travers la lande, fl\u00e2nant comme il fl\u00e2nait dans les fondri\u00e8res de ses propres parenth\u00e8ses. Il lui semble pourtant, \u00e0 y bien penser, qu'il repassa \u00e0 Saint-Pierre, m\u00eame que l'ancien chalet de sa d\u00e9funte tante le sollicita un moment et aussi le bref chemin de la Vieille- Dame.\n\n\u00ab Vieille Dame \u00bb, se r\u00e9p\u00e9tait-il d'une fa\u00e7on enfantine. Mais Mme Joliette n'en \u00e9tait pas une, la cinquantaine gu\u00e8re plus, avec encore d'assez jeunes oreilles pour entendre et une bouche pour parler, prononcer qu'elle \u00e9tait bien vivante et lui un nigaud de s'imaginer...\n\nEt s'il t\u00e9l\u00e9phonait ? Qui l'emp\u00eachait de le faire ? Les puissances de la nuit, de cette nuit-l\u00e0 ?\n\nDe retour \u00e0 la villa Rose, il composa le num\u00e9ro de la rue Marzelle. Sur le r\u00e9pondeur, aussit\u00f4t ce fut la voix inerte de la gardienne : \u00ab Je ne suis pas l\u00e0 pour l'instant, mais laissez votre message. \u00bb\n\nIl ne laissa pas, raccrocha, un peu \u00e9mu de cette voix peut-\u00eatre d\u00e9sormais sans corps. Mais enfin, se raisonna-t-il, et la bande de trembles \u00e0 la fen\u00eatre qui s'agitaient comme des d\u00e9mons paraissait de cet avis, mais enfin, cohabiter un matin avec un possible cadavre vous rend-il en quelque fa\u00e7on coupable ? Mais de quoi ? Pourquoi cette impression \u00e9trange persistait-elle en lui ? Ses mains savaient-elles des choses sur son individu que lui ne savait pas ? Un faisceau de gestes accomplis durant son sommeil oubli\u00e9s \u00e0 son r\u00e9veil ? Si crime il y eut, ce fut en tous les cas un crime en bois blanc o\u00f9 un mannequin eut sa part, pas lui, ou si peu, car de verser de l'armagnac, comme il le fit, dans des gobelets pr\u00e9sents \u00e0 cet effet sur un plateau ne vous rend pas complice de quoi que ce soit ! Pourquoi donc errer en lui-m\u00eame comme dans les coursives d'ombre de ce b\u00e2timent au rebut depuis si longtemps priv\u00e9 de soleil, d'une saine clart\u00e9 ?\n\nC'est quand m\u00eame pas lui, les \u00ab communs \u00bb ! Il n'a pas un \u00e9tage et un sous-sol caverneux. On ne gravit pas des marches pour l'atteindre. Il n'est pas la grille qui grince, les all\u00e9es perdues et l'\u00e9tang bourbeux. Son \u00eatre a d'autres horizons. Dans son trois-pi\u00e8ces du Bouffay, le d\u00e9sordre ne subsiste que dans son lit pas souvent fait ! Quand donc s'en rel\u00e8vera-t-il l'esprit apais\u00e9, avec tout juste assez de bleu en sa personne pour s'encadrer comme t\u00e9moin du beau temps \u00e0 sa fen\u00eatre ?\n\nIl e\u00fbt souhait\u00e9 en parler \u00e0 quelqu'un d'assez intime qui lui remettrait les id\u00e9es en place. Mais m\u00eame Diane, son ex-compagne, avait d\u00e9j\u00e0 recul\u00e9 devant l'\u00e9normit\u00e9 de la t\u00e2che : tous ces imaginaires de Charles-Andr\u00e9 qui leur tombaient dessus n'importe o\u00f9, expliquait-elle quand par exemple il \u00e9mettait des doutes sur le passant qui les d\u00e9passe, ou sur l'autre homme ou femme plus lointain et pourtant \u00e0 peine silhouett\u00e9 qui lui faisait appr\u00e9hender une seconde de gagner \u00e0 son tour le coin de la rue.\n\nCe n'\u00e9tait pas sa tante qui s'emportait quand... Ah ! Puis \u00e0 quoi bon expliciter ce quand ! Dans ses yeux tournaient encore les pages de ce grand livre jaune consacr\u00e9 \u00e0 la vie du Christ o\u00f9 se r\u00e9citait aussi son enfance. Un soir, elle lui en lisait un ou deux passages, un autre, lasse de sa journ\u00e9e elle se satisfaisait alors de lui en commenter quelques images. Il s'en souvenait d'une, pr\u00e9cis\u00e9ment (la route assez escarp\u00e9e, un chemin blanc-gris de poussi\u00e8re se faufilant entre de vieux cypr\u00e8s) intitul\u00e9e \u00ab les monts de la Quarantaine \u00bb \u00e0 cause d'une masse pierreuse qui escaladait tout le haut de la photographie et d'une l\u00e9gende o\u00f9 \u00e9tait inscrit en petits caract\u00e8res que la route (\u00ab une sainte route sans nul doute car tout est saint par l\u00e0, m\u00eame les cailloux \u00bb, s'empressait-elle d'ajouter) qui provenait de J\u00e9rusalem \u00e0 six cents m\u00e8tres au-dessus du niveau de la mer, \u00e0 cet endroit d\u00e9sol\u00e9 se retrouvait cent m\u00e8tres au-dessous.\n\nPar quel miracle ? osait-il alors demander. Elle se perdait en consid\u00e9rations vagues (car comme il s'agit de la mer Morte, tout par l\u00e0 est plus ou moins cass\u00e9, \u00ab d\u00e9c\u00e9d\u00e9 \u00bb) allant m\u00eame jusqu'\u00e0 \u00e9voquer une origine volcanique (les feux de l'enfer) qui aurait provoqu\u00e9 ces failles, tous ces effondrements !\n\nIl en souriait toujours. C'est ce sourire qui lui \u00e9clairait l'heure. D\u00e8s qu'il \u00e9tait seul ses jeunes ann\u00e9es lui couraient tellement apr\u00e8s avec sa ch\u00e8re tante l'appelant avec des accents introuvables dans la voix. Car selon elle, il disparaissait trop vite : \u00ab O\u00f9 te caches-tu ? \u00bb pleurait son inqui\u00e9tude. Qu'il soit \u00e0 Portivy, \u00e0 Saint-Pierre, ou \u00e0 Quiberon, ou sur n'importe quel chemin hasardeux, il entendait toujours cet \u00e9ternel \u00ab O\u00f9 te caches-tu ? \u00bb. Se cachait-il encore ? La solitude serait-elle une cache ? Une fa\u00e7on de se retirer en soi-m\u00eame comme dans un trou ? Dans deux jours, il sortirait du sien, car \u00e0 Nantes il n'entendrait plus rien, aussit\u00f4t trop peupl\u00e9 par cette ville anim\u00e9e o\u00f9 seule la Loire fait glisser son silence. Fallait-il d'ailleurs qu'il finisse par se rendre rue Marzelle pour \u00e9claircir ce myst\u00e8re ? l'\u00e9nigme rouill\u00e9e de la grille, des all\u00e9es, celle d'ombre du b\u00e2timent des communs ? Aurait-il enfin le courage d'aller \u00e0 nouveau frapper \u00e0 la chambre de Mme Joliette ? Il se faisait peu \u00e0 peu \u00e0 cette id\u00e9e.\n\n#\n\nLa villa Rose, apr\u00e8s le jardin inextricable o\u00f9 une bande de trembles au tronc rugueux s'agace du moindre fr\u00e9missement d'air, c'est d'abord une terrasse puis, une fois pass\u00e9 la porte, un hall riche en papiers divers, dossiers empil\u00e9s \u00e0 la h\u00e2te \u00e0 m\u00eame le plancher, sur la table d'angle, qui g\u00e9mit par instants sa crainte de ne pouvoir les supporter bien longtemps, se dit aussit\u00f4t Charles-Andr\u00e9 qui a toujours eu l'imagination des choses, l'univers lui semblant de plus en plus l'analogue d'une table non desservie avec cette question : o\u00f9 ranger la vaisselle ? Des photos de paysage des quatre coins de la plan\u00e8te agrandissent les murs avant le salon encombr\u00e9 d'objets innombrables rapport\u00e9s de contr\u00e9es lointaines. Qui s'aviserait de vouloir les \u00e9num\u00e9rer y perdrait \u00e0 tout coup son \u00e2me ! Et son \u00e2me, Charles et aussi Andr\u00e9 s'y cramponnent ! Car c'est par les yeux du dedans que Charles-Andr\u00e9 Bertrand aspire \u00e0 jauger le dehors. La presqu'\u00eele par exemple en dehors du privil\u00e8ge d'avoir contenu une part de son enfance, qu'est-ce ? Un bras de terre (on dit bien un bras de mer) qui signale quel d\u00e9sarroi ?\n\nPlus qu'une journ\u00e9e \u00e0 Portivy, demain il rentre. Aussi s'\u00e9vertua-t-il \u00e0 ne laisser aucune trace de son passage, que ses amis virginiens en restent babas. Nettoyer la cuisine ne fut qu'un jeu d'enfant comme balayer son cheminement d'une semaine dans les \u00e9tages, et aussi conforter le lit, apurer \u00e0 l'aide d'eau savonneuse la baignoire. Que la nuit qu'il lui reste \u00e0 passer dans cette hautaine demeure ne d\u00e9range que l'indispensable, un oreiller se retape vite et son baluchon pr\u00eat \u00e0 \u00eatre emport\u00e9, il le d\u00e9posa d\u00e9j\u00e0 dans le vestibule, \u00e0 l'entr\u00e9e. Que subsistait-il dans la corbeille \u00e0 pain ? Un ou deux cro\u00fbtons affect\u00e9s d'un bout de saucisson qu'il prit soin de grignoter avant de s'endormir. Qu'\u00e0 son d\u00e9part il n'ait plus qu'\u00e0 enfouir la clef dans la souche moussue au pied des trembles, avant de s'\u00e9loigner sans se retourner. Aux derni\u00e8res nouvelles, Solange et Jean-Marc devaient d\u00e9barquer de leur p\u00e9riple outre-Atlantique mercredi ou jeudi, et lui quittait les lieux lundi prochain, taxi jusqu'\u00e0 Auray, car en cette morte-saison, le train ne fonctionne qu'\u00e9pisodiquement, lui avait appris incidemment le baron Louis, puis l'express jusqu'\u00e0 Nantes, la gare devant le Jardin des Plantes et ses deux \u00e9tages familiers du Bouffay \u00e0 remonter sans y penser, la porte qui r\u00e9siste, et le d\u00e9cor qui l'accompagnait avant les vacances, ses trois pi\u00e8ces amicales avec aux fen\u00eatres la fortune d'une rue peu passante visit\u00e9e surtout par pas mal d'oiseaux. Avertirait-il Laurence de son arriv\u00e9e ? Il \u00e9prouvait le besoin d'une pr\u00e9sence f\u00e9minine et cette jolie cousine le rassurait, lui et son image dans le haut miroir de son armoire. Qu'ils d\u00eenent ensemble et peut-\u00eatre plus ! Qu'avait-il eu besoin de se ruiner \u00e0 ce point l'esprit avec cette trouble histoire ? Que Mme Joliette n'ait pas r\u00e9pondu prouve seulement son absence ou qu'occup\u00e9e par quelque t\u00e2che m\u00e9nag\u00e8re dans un quelconque recoin de la vaste propri\u00e9t\u00e9 elle n'ait pas entendu qu'on sonnait, bien qu'elle soit assez \u00e9lectrique et de la t\u00eate aux pieds. Le mieux de toute fa\u00e7on \u00e9tait de prendre sur lui et d'aller frapper aux Marzelles. \u00c0 tous les coups, l'avenante gardienne l'accueillerait avec un grand sourire et son habituel \u00ab Ah Monsieur Charles ! \u00bb. Elle ne s'\u00e9tait jamais habitu\u00e9e \u00e0 son double pr\u00e9nom.\n\nC'est avec toutes ces h\u00e9sitations n\u00e9anmoins optimistes dans la cervelle qu'il se coucha et s'endormit aussit\u00f4t du sommeil du juste. Le matin le retrouva \u00e0 la cuisine b\u00e2illant devant son bol de caf\u00e9, plus qu'une journ\u00e9e \u00e0 tirer devant la mer d\u00e9mente. \u00c9tait-ce bon d'ailleurs pour son \u00e9quilibre de s\u00e9journer devant cette agitation permanente qui masque dans un friselis d'\u00e9cume la sournoise intention de ses bas-fonds ? Qu'en \u00e9tait-il des siens ? L'isthme qui rattache la presqu'\u00eele au continent devant le fort de Penthi\u00e8vre n'aurait que trois cents m\u00e8tres de large, avait-il lu dans un vieux guide de la Bretagne \u00e0 l'\u00e9tage, et lui son isthme qui le rattache \u00e0 l'esp\u00e8ce ordinaire des hommes quelle largeur avait-il ? Son ex-compagne Diane qu'il croisait encore hier yeux baiss\u00e9s au lyc\u00e9e o\u00f9 elle enseignait l'histoire (mais pas la leur) l'avait fui, son amoureux actuel, un vigoureux prof de gym assez musculeux dont il n'aurait pas aim\u00e9 rencontrer les poings, avait d\u00fb depuis leur s\u00e9paration la ramener pleine terre. Finies pour elle les dunes o\u00f9 l'on s'enfonce, les falaises d\u00e9chiquet\u00e9es de la c\u00f4te dite sauvage de la moindre imagination de Charles que corrige \u00e0 peine Andr\u00e9. Ce fumeux Charles-Andr\u00e9 Bertrand qui nagu\u00e8re partageait ses nuits s'\u00e9tait encore plus \u00e9loign\u00e9 du c\u00f4t\u00e9 du large, et elle aurait bien eu de la peine \u00e0 le suivre dans ses derniers remous. N'aurait-elle pas ri de ses angoisses ? \u00ab \u00c0 force de vivre dans mon enfance entre deux mers, lui aurait-il volontiers confess\u00e9, n'ai-je pas h\u00e9rit\u00e9 de la passion mouvement\u00e9e de l'une et de la fausse douceur de l'autre ? N'ai-je pas moi aussi un c\u00f4t\u00e9 baie et un autre furieux ? \u00bb \u00c0 la pointe mouvante du Conguel, \u00e0 l'extr\u00e9mit\u00e9 de la presqu'\u00eele, devant ce redoutable passage de la Teignouse o\u00f9 se perdirent au cours des ann\u00e9es tant de g\u00e9n\u00e9rations de p\u00eacheurs, on ne peut plus d\u00e9chiffrer les intentions de l'oc\u00e9an. Est-ce l\u00e0 que lui se tient quand il s'imagine criminel, trop pr\u00e8s en r\u00e9alit\u00e9 de l'eau troublante ? N'est-ce pas elle qui lui souffle parmi les ardeurs du vent ce souci poignant de Mme Joliette ?\n\nIl y songeait ce matin-l\u00e0, pas encore compl\u00e8tement sorti de sa nuit, tout en tournant sa cuiller dans son bol. Les chiens des voisins de la villa Rose aboyaient en meute et la pluie mena\u00e7ait.\n\n#\n\nTante Marie, si \u00e9vang\u00e9lique d'allure, e\u00fbt-elle accept\u00e9 l'adulte qu'il \u00e9tait devenu ? L'aurait-elle jug\u00e9 digne d'arpenter en sa compagnie les rives pieuses du lac de Tib\u00e9riade ou de la mer Morte ? Il se rappelait une illustration du m\u00eame fatidique livre jaune o\u00f9 elle jurait, quand il avait mal fait, de l'enfermer le soir au coucher d\u00e8s qu'il s'endormirait et il se cramponnait dans son lit pour rester \u00e9veill\u00e9, \u00e0 tout prix \u00e9chapper \u00e0 cette forteresse d'H\u00e9rode Antipas, amas de pierres l\u00e9preuses sur sa butte, un des sites les plus abrupts du pays de Moab, lui soufflait-elle vengeresse avec plein de mots inconnus dans sa bouche. Il en frissonnait presque encore. Sans doute d\u00e9sirait-elle qu'il se fasse pr\u00eatre ? Car \u00e0 quoi rimait qu'elle l'entretienne ainsi presque journellement de J\u00e9sus ? Il savait par exemple tout du puits de Jacob vieux de plus de trois mille cinq cents ans, prot\u00e9g\u00e9 actuellement par une construction en ma\u00e7onnerie. N'est-ce pas \u00e0 cet endroit qu'une Samaritaine donna \u00e0 boire au Christ ?\n\n\u00c0 moins qu'il ne se trompe, c'est sa mort qui arr\u00eata leur doux conciliabule, bien que sa voix soit rest\u00e9e \u00e0 jamais dans ses oreilles. Il suffit qu'il r\u00eavasse, s'entretienne avec lui-m\u00eame et aussit\u00f4t elle intervient. Il la voit alors sans la voir avec son joli visage, sa beaut\u00e9 brune appr\u00eat\u00e9e pour qui ? pour quoi ? On sait qu'il avait juste douze ans quand elle d\u00e9c\u00e9da, et ses grands-parents paternels, Jos\u00e9phine et Joseph, devenus gardiens du \u00ab ch\u00e2teau \u00bb, veill\u00e8rent alors sur lui jusqu'\u00e0 sa maturit\u00e9 quand, ses \u00e9tudes faites, sa situation de jeune professeur acquise, apr\u00e8s un rude passage aux arm\u00e9es pour son service militaire, il se lib\u00e9ra d\u00e9finitivement de la tutelle du noir \u00e9tang et de ses all\u00e9es mortes pour aller vivre sa vie dans un contexte plus joyeux que celui du parc de la rue Marzelle gagn\u00e9 par la rouille de la grille et la brique rouge sang de l'\u00e9difice principal. Son p\u00e8re ? \u00c0 l'\u00e9tranger, croyait-il, au Canada lui apprenait-on, du c\u00f4t\u00e9 de Vancouver, perdu par le Pacifique ou ailleurs. Pr\u00e9nomm\u00e9 Charles, il s'est toujours arrang\u00e9 pour se trouver l\u00e0 o\u00f9 on ne le trouve pas !\n\n\u00c0 la villa Rose, dans ses derniers instants \u00e0 Portivy, Charles-Andr\u00e9 se demandait s'il aurait jamais le courage d'aller \u00e0 nouveau affronter cette l\u00e9gendaire b\u00e2tisse de son enfance ? La paix de l'\u00e2me \u00e9tait pourtant \u00e0 ce prix ! Mais soudain, une id\u00e9e inattendue lui vint : si la fabuleuse grille \u00e9tait ferm\u00e9e \u00e0 clef quand Laurence, sa tendre cousine, osa aller sonner, n'\u00e9tait-ce pas la preuve \u00e9vidente que quelqu'un depuis son d\u00e9part pr\u00e9cipit\u00e9 \u00e9tait intervenu ? Or ce quelqu'un ne pouvait \u00eatre que Mme Joliette, la seule habitante de ces lieux ! Lui quand il s'\u00e9clipsa, il avait dans sa h\u00e2te simplement repouss\u00e9 la grille derri\u00e8re lui avec sa clef rest\u00e9e \u00e0 l'int\u00e9rieur. Qu'il \u00e9tait donc b\u00eate de ne pas y avoir song\u00e9 plus t\u00f4t ! Il se serait \u00e9pargn\u00e9 huit jours de t\u00e9n\u00e8bres jusqu'\u00e0 croire que la police le traquait ! Il avait \u00e9t\u00e9 abus\u00e9 avec son esprit pu\u00e9ril par la similitude des positions lors du d\u00e9c\u00e8s de sa ch\u00e8re tante Marie entre elle et la gardienne qui paraissait elle aussi ne plus respirer, yeux clos, mains jointes dans son lit pour une ultime pri\u00e8re. Il n'avait plus alors quarante ans mais douze et puis l'atmosph\u00e8re toujours mystique des communs, l'ombre et sa main noire qui court les escaliers, les couloirs, les multiples craquements d'os de la b\u00e2tisse. Bien s\u00fbr que Mme Joliette \u00e9tait vivante et lui souriait d\u00e9j\u00e0 de toutes ses dents ! Car qui en dehors d'elle ? Ce n'\u00e9tait quand m\u00eame pas le sombre mannequin avec sa d\u00e9marche de bois des \u00eeles qui e\u00fbt pu aller tourner la clef dans la serrure de la grille ?\n\nIl ne s'attarda pas sur cette ultime question ! \u00c9tait-ce donc alors la peine d'aller constater si oui ou non ? Il penchait pour le non, remit \u00e0 plus tard la d\u00e9cision, repris par les pr\u00e9paratifs de son d\u00e9part, un dernier coup \u00e0 avaler chez le baron Louis toujours aussi \u00e9cumeux dans sa chemise bariol\u00e9e, un fait-divers \u00e0 lui tout seul, traitant la mer avec d\u00e9sinvolture, ne comprenant gu\u00e8re les touristes qui viennent le plus souvent deux par deux en se tenant par la main s'\u00e9tonner devant les vagues. Son \u00e9pouse, sortie pour une fois de sa caverne, avait os\u00e9 montrer sa jolie frimousse derri\u00e8re le bar. Charles-Andr\u00e9 lui paya son caf\u00e9 et partit sans se retourner.\n\nLe taxi l'attendait devant le bar de la Jet\u00e9e. Un ultime regard sur la plage malmen\u00e9e par une brusque temp\u00eate et tout fut laiss\u00e9 au r\u00e9troviseur, un trajet jusqu'\u00e0 Auray muet comme une tombe, ne c\u00e9l\u00e8bre-t-on pas encore la Toussaint, f\u00eate des Morts ? Le temps en mouvement, pluie, vent hurleur vous arrachait les mots de la bouche. L'impression en arrivant dans cette plaisante cit\u00e9 qu'il retrouvait la civilisation, comme si d'\u00eatre demeur\u00e9 seul une huitaine devant les al\u00e9as de l'oc\u00e9an l'avait un peu trop sorti de l'esp\u00e8ce humaine ! L\u00e0, \u00e0 croiser tant de visages s\u00e9rieux en attente sur les quais, ses restes d'angoisse fondaient. Quelle folle id\u00e9e de s'imaginer ? Pourquoi vouloir \u00e0 tout prix \u00eatre ce qu'on n'est pas, un criminel, un empoisonneur ? Encore une de ses hypoth\u00e8ses en bois des \u00eeles. Il en avait marre de ce foutu mannequin que lui seul dans la famille soup\u00e7onnait des pires m\u00e9faits : de jour un pantin articul\u00e9, mais le soir... La nuit et ses rouages ne lui pr\u00eataient-ils pas une vie seconde ? Certes une vie de mannequin, une pauvre vie r\u00e9duite \u00e0 quelques gestes. Une sorte de robot que les t\u00e9n\u00e8bres \u00e0 l'insu de tous mettent en branle ! Le bouter, culbuter hors de la serre, le jeter au feu, qu'une bonne flamb\u00e9e le r\u00e9duise en cendres et que lui Charles-Andr\u00e9 \u00e9chappe enfin \u00e0 son emprise. Et personne \u00e0 qui se confier sans qu'il n'en r\u00eet ? Diane ? n'en parlons plus. Laurence ? Il se pourrait peut-\u00eatre que sa cousine, \u00e0 condition de pr\u00e9senter cela comme un r\u00eave...\n\nIl y songea. Le train roulait, dans son compartiment une autre Mme Joliette feuilletant une revue. Il n'y a que lui pour s'abuser de telles illusoires ressemblances. Mais quand m\u00eame, la bouche, le nez droit, les yeux bleus, les avantages... D'un peu, il lui e\u00fbt r\u00e9clam\u00e9 la clef rouill\u00e9e de la grille. Elle croisait et d\u00e9croisait les jambes. Son charme de jeune homme distingu\u00e9 op\u00e9rait-il ? Enfin, il retrouvait vie normale et statut social. Il n'\u00e9tait plus le sauvageon de la villa Rose, l'\u00eatre en bois trop tendre dont s'\u00e9nervaient les trembles. Ses nuits allaient devenir des absences de jour et pas autre chose ! Il se commanda un \u00e9pais sandwich au wagon-restaurant, mordit dedans avec volupt\u00e9, lut le journal avec la m\u00eame faim, passant la page des faits-divers. Qu'\u00e9tait donc devenue la plan\u00e8te Terre durant toutes ces ann\u00e9es ? Oui, il pensait sa semaine \u00e0 Portivy comme ayant dur\u00e9 un si\u00e8cle. Et Ang\u00e8le qu'il n'avait pas \u00e9t\u00e9 revoir ! Et Quiberon devant Belle-\u00cele ! Et Saint-Pierre et la jolie patronne des Mouettes ! Et la lande ! Et la mer qui rugit d'un c\u00f4t\u00e9, s'endort de l'autre ! Il allait d\u00e9barquer \u00e0 Nantes \u00e0 la gare devant le Jardin des Plantes d\u00e9barrass\u00e9 de toutes ses chim\u00e8res !\n\n#\n\nCharles-Andr\u00e9 retrouva avec plaisir son lyc\u00e9e, le train-train quotidien. Entre les cours parfois il lui arrivait bien d'avoir la t\u00eate un peu ailleurs, un ailleurs dont il retardait de repousser la grille, mais par bonheur le tumulte des \u00e9l\u00e8ves dans les couloirs, le charivari des r\u00e9cr\u00e9ations, la pr\u00e9sence des coll\u00e8gues, en particulier celle d'une certaine Ir\u00e8ne, une prof de maths (belle \u00e9quation qui comportait encore un peu trop d'inconnues qu'il aimerait bien r\u00e9soudre), le sortaient de la rue Marzelle, de ses angoisses. Et puis le soleil, les taches d'ombre moins perceptibles, vengeresses qu'\u00e0 Portivy, l'oc\u00e9an orgueilleux remplac\u00e9 par la languide Loire lui insufflaient une qui\u00e9tude, cette s\u00e9r\u00e9nit\u00e9 journali\u00e8re des heures d'avant les derni\u00e8res vacances, d'avant cette fumeuse nuit dont il essayait vainement de se r\u00e9veiller. Qu'il se rassure ! Sur ses papiers d'identit\u00e9, dans la glace au-dessus du lavabo il \u00e9tait bien toujours ce m\u00eame Charles-Andr\u00e9 Bertrand, enseignant de son \u00e9tat, domicili\u00e9 au Bouffay, pr\u00e8s du march\u00e9 du m\u00eame nom et rien d'autre.\n\n\u00ab Rien d'autre \u00bb, il se r\u00e9p\u00e9tait sans vraiment totalement se convaincre.\n\nUne semaine s'\u00e9coula ainsi. Trajet logis lyc\u00e9e, lyc\u00e9e logis, plus quelques escapades dans de quelconques brasseries, paroles diverses entre coll\u00e8gues \u00e9gay\u00e9es par le vin dans les verres qu'on porte \u00e0 la bouche sans trop y penser. Quand le cr\u00e9puscule montait et sa mar\u00e9e noire dans son trois-pi\u00e8ces qu'il avait pourtant pris soin d'\u00e9clairer jusque dans les toilettes, les cris des oiseaux r\u00e9jouissaient ses fen\u00eatres, emportant ses funestes id\u00e9es qui h\u00e9las n'avaient pas tard\u00e9 \u00e0 poindre dans le frou-frou de leurs ailes. Il s'endormait alors parmi ses nombreux oreillers \u00e0 qui il confiait le soin d'\u00e9touffer le reste de ses anxi\u00e9t\u00e9s.\n\nLaurence lui avait t\u00e9l\u00e9phon\u00e9 : oui, il avait retrouv\u00e9 ce qu'il croyait avoir oubli\u00e9 au \u00ab ch\u00e2teau \u00bb, en l'occurrence son si n\u00e9cessaire portefeuille. Il mentait comme un \u00e9hont\u00e9, se confondait en mille excuses : il aurait d\u00fb l'en avertir plus t\u00f4t, mais des fois il n'a plus sa t\u00eate, remplac\u00e9e alors par une autre en bois des \u00eeles : \u00ab Heureusement que j'ai encore mes pieds qui savent o\u00f9 ils vont, enfin qui savent... \u00bb\n\nElle gloussait \u00e0 l'autre bout du fil, elle a toujours aim\u00e9 la cocasserie de ses formules. Ils se promirent avec un bel ensemble de se revoir sous peu, d\u00e8s que l'un ou l'autre verrait un trou dans son emploi du temps.\n\nIr\u00e8ne aussi, cette prof blonde aux proportions id\u00e9ales d'\u00e0 peine trente ans, habite Chantenay, faubourg o\u00f9 elle naquit. Avec une mani\u00e8re tr\u00e8s particuli\u00e8re de vous d\u00e9visager, de faire que votre sourire devienne bient\u00f4t le sien. Attention extr\u00eame \u00e0 autrui sans doute ? Des yeux rieurs. Plut\u00f4t que des paroles, des mots enfouis dans une mousse amicale, une politesse des attitudes, un secret, le secret de son \u00eatre qu'elle vous expose \u00e0 son insu et quel que soit le sujet de la conversation, des palabres. Et elle rit, d'un rien elle rit, sa d\u00e9licate personne aussit\u00f4t en \u00e9meute, une \u00e9meute dont certains moins enjou\u00e9s se renfrognent dans la s\u00e9v\u00e8re salle p\u00e9dagogique avec les portraits d'anciens profs barbus du si\u00e8cle pr\u00e9c\u00e9dent suspendus aux murs.\n\nManifestement, Charles-Andr\u00e9 suscitait son int\u00e9r\u00eat, ses longues parenth\u00e8ses au regard perdu \u00e9taient trop \u00ab chou \u00bb quand il feuilletait ses cahiers ou entrouvrait un bouquin. Elle se tenait alors dans ses marges pour avoir bient\u00f4t voix au chapitre, qu'au lieu de tourner les pages il pr\u00e9f\u00e8re enfin affronter la sienne. Et ils repartaient ensemble dans les couloirs m\u00ealant leurs pas \u00e0 d\u00e9faut pour l'instant d'autre chose ! Aussi Charles-Andr\u00e9, conscient de cette vive attention \u00e0 son \u00e9gard, chercha-t-il, d\u00e8s son retour, un peu de r\u00e9confort de ce c\u00f4t\u00e9-l\u00e0, l'invitant m\u00eame \u00e0 d\u00e9jeuner dans un troquet qui avait beaucoup de couleurs pr\u00e8s de la gare. Une id\u00e9e avait germ\u00e9 en lui. Pourquoi au moment du dessert, quand l'intimit\u00e9 des verres et des assiettes se serait faite, ne pas lui exposer son aventure au \u00ab ch\u00e2teau \u00bb comme un r\u00eave, un parmi d'autres de ses vacances, dans la villa un tantinet aust\u00e8re de ses amis \u00ab am\u00e9ricains \u00bb ? \u00c0 fr\u00e9quenter de trop pr\u00e8s l'oc\u00e9an ne risque-t-on pas de s'y noyer l'\u00e2me ? Et autres balivernes pseudo-m\u00e9taphysiques de ce genre.\n\nElle parlait, parlait, il r\u00e9fl\u00e9chissait, r\u00e9fl\u00e9chissait. Ce fut \u00e0 l'instant m\u00eame o\u00f9, couteau lev\u00e9, elle attaquait sa tarte normande qu'il mit son projet \u00e0 ex\u00e9cution, lui proposant m\u00eame \u00ab en tout bien, tout honneur \u00bb, si un jour elle voulait vraiment se d\u00e9payser, oublier un apr\u00e8s-midi Nantes et sa rumeur, de l'amener visiter apr\u00e8s la place Zola cette haute demeure familiale : autant en profiter assez vite, car les h\u00e9ritiers, dont lui-m\u00eame avec ses innombrables cousins et cousines, venaient juste de d\u00e9cider il y a une quinzaine lors d'une soir\u00e9e m\u00e9morable de mettre ladite demeure en vente. Car ajouta-t-il, un rien suffisant, on peut en effet penser qu'avec ses trois \u00e9tages meubl\u00e9s avec go\u00fbt, son parc touffu, ses pelouses \u00e9paisses et l'\u00e9tang qui r\u00e9fl\u00e9chit tout \u00e7a, on peut penser qu'elle ne restera pas longtemps sans acqu\u00e9reur.\n\nIr\u00e8ne battit des mains.\n\n\u00ab \u00c7a appartenait \u00e0 ma grand-m\u00e8re, veuve encore jeune d'un premier mariage, sa grande beaut\u00e9 avait s\u00e9duit un riche propri\u00e9taire d'au moins un si\u00e8cle plus \u00e2g\u00e9 qu'elle, trouva-t-il encore moyen d'expliquer.\n\n\u2014 Si tu veux \u00bb, r\u00e9pondit-elle goul\u00fbment. Elle aime les maisons, les vieilles surtout, et les parcs, les trucs pleins d'all\u00e9es derri\u00e8re leurs grilles rouill\u00e9es.\n\nIl comptait, accompagn\u00e9 de la belle Ir\u00e8ne Blanchard si pleine de vie, s'assurer discr\u00e8tement de l'inanit\u00e9 de son hypoth\u00e8se enfantine, qu'\u00e0 la porte de l'Ombre Mme Joliette \u00e0 leur vue surgirait toute ressuscit\u00e9e du b\u00e2timent des communs s'essuyant les mains \u00e0 son tablier. Oui mais comment entrer ? S'il sonne et que personne ne r\u00e9pond ? Car la clef, il la laissa comme un \u00e2ne dans sa serrure, le matin du sauve-qui-peut ! \u00c0 moins de t\u00e9l\u00e9phoner au pr\u00e9alable. Mais chaque fois qu'il le fait, seule la m\u00eame voix atone de la cuisini\u00e8re s'entend au r\u00e9pondeur ! \u00c0 moins qu'elle ait quitt\u00e9 Nantes pour quelques jours, son fils, mari\u00e9, des enfants, niche \u00e0 Saint-Br\u00e9vin, en face de Saint-Nazaire ! Et Charles-Andr\u00e9 n'\u00e9tait pas sans savoir qu'elle s'y rend souvent ! Cela fait m\u00eame partie de son contrat. C'est bien \u00e0 lui de prendre une simple absence pour une mort probable. Il d\u00e9cida donc de tenter l'aventure.\n\n\u00ab Figure-toi... \u00bb, commen\u00e7a-t-il.\n\n#\n\nSans doute qu'il flirtait trop avec la nuit, estimait parfois Charles-Andr\u00e9 dans son coquet trois-pi\u00e8ces du Bouffay dont les oiseaux r\u00e9jouissaient tant les fen\u00eatres. L\u00e0, les ombres ne se maintenaient que dans ses yeux et il esp\u00e9rait bien un jour proche, en dormant ainsi toutes lumi\u00e8res allum\u00e9es, les chasser \u00e0 jamais de son esprit. En attendant, qu'elles patientent \u00e0 la porte, ces ombres, car h\u00e9las elles le reprenaient vite dans l'escalier.\n\nLe silence de Nantes, c'est la Loire glissant dans l'uniformit\u00e9 de son texte liquide, pas d'embard\u00e9es impr\u00e9vues, qu'une glissade uniforme... Et souvent il se permettait une l\u00e9g\u00e8re vir\u00e9e sur ses bords, quai de la Fosse par exemple, pour apprendre d'elle la s\u00e9r\u00e9nit\u00e9 de son courant, noyer enfin tous ses mornes instants contamin\u00e9s par l'id\u00e9e de la rue Marzelle. Comment une demeure ancestrale, berceau de son enfance, avait-elle pu devenir en si peu de temps un lieu d'\u00e9pouvante ? Et tout \u00e7a \u00e0 cause de la mort de sa tante et de celle suppos\u00e9e trente ans plus tard de la gardienne dans le m\u00eame lit, m\u00eame chambre de l'Ombre, ce funeste b\u00e2timent des communs ainsi surnomm\u00e9 car cach\u00e9 \u00e0 jamais du soleil \u00e0 cause d'une bande \u00e9paisse de trembles ! Parmi les arbres toujours en transe, il n'en existe pas de plus d\u00e9voy\u00e9s !\n\nIr\u00e8ne entre poire et fromage avait malgr\u00e9 tout \u00e9cout\u00e9 d'une oreille distraite le r\u00e9cit d\u00e9taill\u00e9 de son cauchemar enfantin, avant de l'interrompre de sa voix d\u00e9cid\u00e9e :\n\n\u00ab On a tous des trucs comme \u00e7a. Ainsi moi qui te parle, j'ai pendant longtemps... \u00bb\n\nIl oublia aussit\u00f4t ce \u00ab pendant longtemps \u00bb qu'elle avait \u00e9prouv\u00e9 petite fille, un peu m\u00e9content qu'elle n'ait pas pr\u00eat\u00e9 plus d'attention \u00e0 l'histoire de sa pr\u00e9tendue culpabilit\u00e9. Apr\u00e8s tout ce n'est quand m\u00eame pas si commun, m\u00eame dans un r\u00eave, de se sentir partie prenante d'un possible d\u00e9c\u00e8s qu'on n'a pourtant pas provoqu\u00e9. Et tout \u00e7a, \u00e0 cause de l'heure, du d\u00e9cor, de la solitude d'un couloir qui m\u00e8ne \u00e0 un deuil ancien, d'une pi\u00e8ce aux volets rabattus ! Il s'en \u00e9tait r\u00e9veill\u00e9 \u00e9pouvant\u00e9, jurait-il. Du moins ses douze ans en lui s'en \u00e9taient r\u00e9veill\u00e9s \u00e9pouvant\u00e9s ! A-t-il toujours cet \u00e2ge \u00e0 certaines heures ?\n\nMais Ir\u00e8ne :\n\n\u00ab Elle \u00e9tait comment ta tante, oui, celle qui t'a \u00e9lev\u00e9 ? Jolie ? Une brune aux yeux bleus ? Eh bien dis donc, elle ne devait pas manquer d'amoureux. Non tu dis ? C'\u00e9tait J\u00e9sus son amoureux ! Et toi, elle t'appelait son J\u00e9sus ! Quand tu \u00e9tais sage, sage comme un J\u00e9sus bien s\u00fbr ! \u00bb\n\nLa brasserie o\u00f9 ils d\u00e9jeunaient bourdonnait d'infinitudes, une sorte de caf\u00e9 feuille morte, o\u00f9 tout semblait avoir d\u00e9j\u00e0 \u00e9t\u00e9 fan\u00e9, d\u00e9j\u00e0 v\u00e9cu, tomb\u00e9 de l'arbre des minutes, l\u00e0 un jeune homme \u00e0 une table proche qui reculait perp\u00e9tuellement le moment de couper sa viande, ici une femme d'un autre \u00e2ge perdue irr\u00e9m\u00e9diablement dans sa pur\u00e9e. Une porte battait derri\u00e8re le bar et le serveur \u00e9berlu\u00e9, qui avait servi tout le monde, momentan\u00e9ment ne savait plus quoi faire de ses dix doigts, aussi tripotait-il sa serviette, une \u00e0 carreaux, bonne \u00e0 essuyer les vitres.\n\n\u00ab Je t'y am\u00e8nerai, promit Charles-Andr\u00e9 encore dans ses songes.\n\n\u2014 O\u00f9 \u00e7a, dans ton r\u00eave ? souriait la blonde Ir\u00e8ne.\n\n\u2014 Quand m\u00eame pas, mais au \u00ab ch\u00e2teau \u00bb. Un jour que tu auras du temps \u00e0 consacrer au berceau de ma famille. C'est pas loin place Zola ! Tu peux quand m\u00eame accepter ma compagnie jusqu'\u00e0 la place Zola ! \u00bb\n\nIl devait \u00eatre cette heure douteuse des d\u00e9buts de l'apr\u00e8s-midi. Le soleil se voilait. Un nuage amassait certainement ses gouttes dans quelque recoin du ciel en pr\u00e9vision d'une soudaine averse. Il commanda deux autres caf\u00e9s, reparla de sa tante, tout l'y invitait : la fain\u00e9antise de l'heure qui tardait \u00e0 s'\u00e9couler, cette cliente l\u00e0-bas, incertaine de profil contre la vitrine qui de loin aurait pu \u00eatre elle, les jeux de l'ombre...\n\nCertains soirs particuli\u00e8rement bibliques tout caillou qui roulait sur le chemin avait d\u00e9j\u00e0 roul\u00e9 \u00e0 l'entendre sous les pieds de J\u00e9sus, poursuivait Charles-Andr\u00e9.\n\nIl avait encore en t\u00eate, Charles plus qu'Andr\u00e9 (car elle l'appelait plut\u00f4t du seul \u00ab Charles \u00bb plus doux \u00e0 ses l\u00e8vres), des lieux de Palestine comme ce hameau de Magdel au bord du lac de Tib\u00e9riade et cette plaine, la plaine de G\u00e9n\u00e9zar sur laquelle en id\u00e9e il se roulait frileusement en se couchant le soir !\n\n\u00ab Curieuse fille \u00bb, conclut Ir\u00e8ne que la chose rasait.\n\nC'\u00e9tait surtout l'\u00e9t\u00e9 que ladite chose \u00e9vang\u00e9lique la prenait, continuait m\u00e9caniquement Charles, quand l'air chaud qu'on peinait \u00e0 respirer devenait quasi galil\u00e9en. Alors sa tante ressortait son grand livre jaune, \u00e9voquait au bord de la mer Morte les p\u00eacheurs raccommodant leurs filets, ajoutant que, le soir, il convient de raccommoder le sien, celui du jour trou\u00e9 par nos pauvret\u00e9s. Charles-Andr\u00e9 en soupirait, Ir\u00e8ne s'en effarait un peu, croisant d\u00e9croisant ses jolies jambes.\n\n\u00ab Finalement, elle n'\u00e9tait pas un peu zinzin, ta tante biblique ? \u00bb osa-t-elle enfin dire.\n\nLe miracle, c'est que Charles-Andr\u00e9, si amoureux du souvenir de sa d\u00e9funte presque m\u00e8re, ne s'en offusqua pas. Des noms \u00e9tranges lui revenaient trop aux l\u00e8vres. La contr\u00e9e des G\u00e9ras\u00e9niens par exemple, des sortes de poss\u00e9d\u00e9s, des gens qui ne s'appartenaient pas. J\u00e9sus fut en butte \u00e0 l'un d'eux compl\u00e8tement \u00e0 poil et qui sortait d'un tombeau, car ils habitaient les cimeti\u00e8res. C'est dans Luc ou Matthieu ? Charles encore moins Andr\u00e9 ne savait plus lequel des deux \u00c9vang\u00e9listes en parlait.\n\n\u00ab Tu n'en serais pas un, un de ces G\u00e9ra quelque chose ! \u00bb \u00e9mit \u00e9vasivement Ir\u00e8ne, b\u00e2illant de toute son \u00e2me.\n\nIls demeur\u00e8rent ainsi face \u00e0 face durant plusieurs heures. Un troisi\u00e8me caf\u00e9 ne raviva gu\u00e8re leur dialogue. Que de mots rest\u00e9s en suspens, de pens\u00e9es non dites ! Le Jardin des Plantes encore agit\u00e9 par l'orage les invitait pourtant depuis l'autre c\u00f4t\u00e9 de la rue \u00e0 venir se dissimuler sous ses ombrages, une averse avait \u00e0 peine mouill\u00e9 l'instant, il en subsistait sur les bancs quelques gouttes \u00e0 \u00e9craser du pouce. Et Charles-Andr\u00e9 les avait fort d\u00e9lur\u00e9s les pouces comme l'ensemble de sa personne d'ailleurs. Il souriait \u00e0 Ir\u00e8ne et aussi \u00e0 son propre sourire.\n\nSans doute que d'autres sc\u00e8nes de cet acabit se produisirent durant les semaines qui suivirent et toujours dans ce m\u00eame caf\u00e9 rong\u00e9 par l'automne, et c'\u00e9tait sans doute cette saison que le gar\u00e7on (d'une lassitude autant feuille morte que celles qu'il balayait entre les tables de la terrasse) \u00e0 son insu leur servait : du th\u00e9 qui avait mal pass\u00e9 l'\u00e9t\u00e9, un jus de fruits dont on recherchait vainement le fruit.\n\n#\n\nEt les jours pass\u00e8rent. Enfin, c'\u00e9tait plut\u00f4t toujours le m\u00eame qui, le matin, venait frapper \u00e0 la porte de Charles-Andr\u00e9. Et qui d'ailleurs le reconduisait de fa\u00e7on fort civile le soir au 35 de sa rue pleine d'adjectifs, d'\u00e9pith\u00e8tes color\u00e9es au cr\u00e9puscule, restes de septembre ou d'ao\u00fbt sans doute, derni\u00e8res coquetteries de cette \u00e9blouissante saison s'attardant dans une autre plus morne avant l'hiver.\n\nLe m\u00eame jour, rageait-il, et \u00e0 la m\u00eame porte avant de sortir toujours le m\u00eame souci : Mme Joliette est-elle ou pas ? Ses douze ans rest\u00e9s si vivants en lui \u00e9taient-ils les seuls \u00e0 croire \u00e0 un d\u00e9c\u00e8s possible ? Comment \u00e0 quarante parvenir \u00e0 se d\u00e9barrasser de cette hantise ? Par quelle poste chim\u00e9rique en oblit\u00e9rer jusqu'\u00e0 l'ombre ? Car l'accorte gardienne du \u00ab ch\u00e2teau \u00bb dormait dans la chambre de sa d\u00e9funte tante dont il avait au r\u00e9veil \u00e0 peine os\u00e9 pousser la porte pour la pr\u00e9venir de son d\u00e9part matutinal. Car pousser la porte, c'\u00e9tait peut-\u00eatre commettre un acte meurtrier, s'imaginait-il presque dans son \u00e9garement, ressusciter cet \u00e9pisode tragique de ses premi\u00e8res ann\u00e9es, elle, \u00c9milie Joliette, couch\u00e9e dans les draps d'une mort identique \u00e0 la premi\u00e8re. C'est vrai que depuis, malgr\u00e9 ses appels r\u00e9it\u00e9r\u00e9s au t\u00e9l\u00e9phone, elle n'avait plus donn\u00e9 signe de vie.\n\nIl neige trop souvent en lui. Il a froid dans ses pens\u00e9es, sa vue int\u00e9rieure se brouille. Et le voil\u00e0 aussit\u00f4t et quelle que soit l'heure au sein d'une foule indistincte, errant en aveugle parmi les passants comme dans l'effroi d'une maison vide, d'o\u00f9 ces brusques absences qui en stup\u00e9fient plus d'un parmi ses coll\u00e8gues du lyc\u00e9e. Il faut alors, s'il \u00e9tait assis \u00e0 deviser en leur compagnie, qu'il se l\u00e8ve soudain, les laisse avec des bouts d'excuse sur les l\u00e8vres, un vague borborygme, pour aller se planter \u00e0 deux pas devant la fen\u00eatre la plus proche comme si le temps qu'il fait devenait soudain un plus s\u00e9duisant interlocuteur que cette dizaine de quidams r\u00e9unis autour de leur table p\u00e9dagogique. Ce qui ne lui attire pas forc\u00e9ment que des amis !\n\nSe confier \u00e0 un m\u00e9decin lui \u00f4terait-il du visage cet air d'enfant noy\u00e9 comme s'il sortait du lac de Tib\u00e9riade, air qui heureusement lui suscite parfois quelques bonnes Samaritaines, sa tournure plut\u00f4t commune n'\u00e9tant pourtant pas l'une de celles qui d'ordinaire retiennent l'attention du beau sexe ? Mais ces cr\u00e9atures conquises ne sauraient pas mieux vous dire. \u00ab Ses yeux ont froid \u00bb, avait pourtant une fois conc\u00e9d\u00e9 l'une d'elles qui ambitionnait sans doute, sans trop se l'avouer, de les d\u00e9geler ! Une prof de latin assez plaisante partie depuis et sans se retourner d\u00e9cliner sa vie dans un autre \u00e9tablissement, une certaine Pauline, une Pauline comment d\u00e9j\u00e0 ?\n\nOn avait r\u00e9p\u00e9t\u00e9 la chose \u00e0 Charles-Andr\u00e9 un peu interdit qui n'avait su qu'en dire.\n\nInterroger un \u00ab psy \u00bb, se disait-il parfois, apr\u00e8s tout c'est leur m\u00e9tier \u00e0 ces praticiens d'aller t\u00e2ter les vieilles douleurs ! En \u00e9tait-ce une qu'il soignait parfois dans les \u00e9glises vides ? Assis, loin de prier il attendait surtout que l'heure p\u00e9risse.\n\nTiens, il avait re\u00e7u \u00e0 son domicile nantais une nouvelle lettre de ses amis de Virginie confirmant leur retour imminent et qu'ils allaient quitter non sans regret leur opulente demeure style plantation du Sud d'avant la guerre de S\u00e9cession mais l\u00e0, dans cette b\u00e2tisse que l'universit\u00e9 de Charlottesville leur avait allou\u00e9e durant leur s\u00e9jour, leurs esclaves n'avaient \u00e9t\u00e9 que leurs ombres, \u00e9crivait po\u00e9tiquement Jean-Marc qui ne se tenait plus de joie \u00e0 l'id\u00e9e de retrouver sa chorale de Saint-Pierre et Solange ses grands et beaux arbres et le fourniment pittoresque de son jardin. Suivait quelques jours plus tard une autre missive \u00e9crite dans la chaleur de leur arriv\u00e9e au logis, et toujours dans cette m\u00eame prose dansante que le ma\u00eetre de la villa Rose affectionne, le f\u00e9licitant lui, Charles-Andr\u00e9 Bertrand, d'avoir su si bien combler le trou d'air de leur absence, car leur villa paraissait ne pas s'en \u00eatre aper\u00e7ue dans ce m\u00eame Portivy o\u00f9 la mer, ajoutait-il d\u00e9j\u00e0 avec lassitude, est toujours d'attaque et o\u00f9 les vagues, ces innombrables sottes, n'aspirent qu'\u00e0 une chose : nous d\u00e9tacher du continent. Du moins, est-ce l'avis titubant du baron Louis quand le vin le remplit de sa houle ! \u00ab Tu nous vois fendant la haute mer sous son impulsion ? Je t'embrasse. \u00bb\n\nCharles-Andr\u00e9 depuis Nantes entendait presque son rire !\n\n#\n\nLes avis divergent quant \u00e0 la suite des \u00e9v\u00e9nements. Si \u00e9v\u00e9nement il y eut ? Car avec Charles-Andr\u00e9... Certains affirment, alors que d'autres contestent, tous tombant n\u00e9anmoins d'accord, que Charles-Andr\u00e9 Bertrand, tout en respectant magistralement ses horaires au lyc\u00e9e, aurait... Allez savoir ? Cela se manifestait en particulier par des distractions sans nom, des fa\u00e7ons de tomber de la lune, mais de quelle lune ? Avec ses coll\u00e8gues il ne partageait pas vraiment la m\u00eame ! Ce qu'il y a d'indubitable, assure encore Ir\u00e8ne Blanchard d'une voix blanche, c'est qu'il neigea entre eux deux apr\u00e8s la visite. Car sa solaire personne comme il qualifie parfois sa blondeur en effet s'y rendit !\n\nOui, un samedi soir que le vent usait, elle avait fini par accepter du bout des l\u00e8vres de l'accompagner au ch\u00e2teau familial, au num\u00e9ro tant de la fumeuse rue Marzelle, puisqu'il tenait \u00e0 sa pr\u00e9sence ! Il faut entendre la toute belle raconter entre amis le long mur gris apr\u00e8s la place Zola, la grille hautement ferm\u00e9e o\u00f9 ils sonn\u00e8rent au pr\u00e9alable en vain. Une sonnerie stridente \u00e0 r\u00e9veiller un mort ! Et puis la grosse clef du fond de ses poches, s\u0153ur de celle qu'il avait perdue et dont il avait fini par retrouver le double tout rouill\u00e9 chez lui dans son fouillis du Bouffay, elle grin\u00e7ait vu son grand \u00e2ge sans tourner dans le bon sens. Un bon sens qui leur \u00e9chappait puisque Charles-Andr\u00e9 en vint, malgr\u00e9 l'imperm\u00e9able qui lui embarrassait les jambes, \u00e0 escalader la grille pour l'ouvrir de l'int\u00e9rieur. Apr\u00e8s tout, il \u00e9tait chez lui et entrer chez soi par effraction n'est pas punissable par la loi.\n\nUne masse confuse s'offrit alors \u00e0 la vue d'Ir\u00e8ne. De la brique, de la brique, toujours de la brique ! \u00c0 peine eut-elle le temps de consid\u00e9rer la chose sur trois \u00e9tages que d\u00e9j\u00e0 il l'avait prise par la main et l'entra\u00eenait sur la droite o\u00f9, dans une mani\u00e8re de serre qui paraissait relier le \u00ab ch\u00e2teau \u00bb proprement dit, l'\u00e9difice principal, \u00e0 ses d\u00e9pendances, veillait un homme, crut-elle d'abord, mais l'\u00e2me rigide comprit-elle assez vite, en r\u00e9alit\u00e9 un mannequin costum\u00e9 en serviteur exotique debout plateau \u00e0 la main.\n\n\u00ab Je n'aime pas ce type \u00bb, grommela au passage Charles-Andr\u00e9. Ensuite, ce fut la cavalcade dans un b\u00e2timent d'un \u00e9tage plut\u00f4t sombre d'allure, cach\u00e9 derri\u00e8re un rideau d'arbres.\n\nLes communs qu'on appelle \u00ab l'Ombre \u00bb car le soleil ne s'y montre jamais, expliqua-t-il, o\u00f9 dormit son enfance.\n\n\u00ab Mais aujourd'hui ta personne est l\u00e0 pour l'ensoleiller \u00bb, ajouta-t-il finaud.\n\nIls montaient quatre \u00e0 quatre un escalier tordu, avant un long couloir vite \u00e9puis\u00e9 o\u00f9 somnolaient quelques portes.\n\n\u00ab L\u00e0, c'\u00e9tait la mienne et l\u00e0... \u00bb\n\nSa voix s'\u00e9tait curieusement bris\u00e9e, s'\u00e9tonnait encore Ir\u00e8ne. Elle comprit vite qu'il s'agissait de la chambre de la fameuse tante que sans fa\u00e7on elle ouvrit.\n\n\u00ab Tu ne vois rien d'autre ? \u00bb\n\nIl \u00e9tait rest\u00e9 tout interdit sur le seuil.\n\n\u00ab Que veux-tu que je voie ? En dehors du lit...\n\n\u2014 Et dedans ?\n\n\u2014 Des draps, un oreiller, mais pas ta tante si c'est cela qui t'emp\u00eache d'entrer !\n\n\u2014 Ah bon ! Pas de Mme Joliette ! fit-il en mani\u00e8re de plaisanterie. Oui, c'est l\u00e0 qu'elle couche ! \u00bb\n\nSon humeur avait chang\u00e9. Il paraissait press\u00e9 d'en finir, des fois que la gardienne les surprenne \u00e0 fouiller sa chambre.\n\n\u00ab Oui c'est elle qui d\u00e9sormais... \u00bb\n\nIl p\u00e9n\u00e9tra plus avant vers le cabinet de toilette, v\u00e9rifia l'\u00e9tat des robinets, flirta avec l'armoire, la commode, repoussa les volets pour un bonjour au rideau de trembles et entra\u00eena \u00e0 nouveau Ir\u00e8ne dans le couloir, l'escalier redescendu \u00e0 toute vitesse.\n\n\u00ab Tu veux vraiment voir le reste ? Apr\u00e8s tout ce n'est qu'une maison bourgeoise, un parc, un \u00e9tang jonch\u00e9 de feuilles mortes. Mon lac de Tib\u00e9riade comme je l'appelais tout gamin jouant les bons ap\u00f4tres. \u00bb\n\nIr\u00e8ne n'en revenait pas.\n\n\u00ab Mais tu m'as bien men\u00e9e ici pour visiter tout \u00e7a ? \u00bb\n\nIl en convenait mais son enfance lui remontait trop \u00e0 la gorge, se justifiait-il. Et puis il n'a que la clef du parc, pas celle du \u00ab ch\u00e2teau \u00bb. Ainsi il la devan\u00e7ait, parlait \u00e0 courtes enjamb\u00e9es. Ce n'\u00e9tait plus le m\u00eame homme qui l'attirait au-dehors, sa bouche riait \u00e0 son nez. Ir\u00e8ne s'\u00e9berluait.\n\n\u00ab Et pourquoi ton mannequin au plateau, il a les menottes ? lui demanda-t-elle soudain.\n\n\u2014 C'est un tel bazar cette serre ! \u00bb conclut-il dans la rue Marzelle fort en pente qui d\u00e9valait plus vite qu'eux.\n\n#\n\nAinsi all\u00e8rent-ils, un boulevard \u00e0 remonter, une place \u00e0 atteindre, la Zola, o\u00f9 ils prirent un tramway, le tram, abr\u00e8gent les Nantais pour le faire aller plus vite. Charles-Andr\u00e9 malgr\u00e9 l'affluence parlait, parlait, Ir\u00e8ne \u00e9coutait, \u00e9coutait de tous ses pores, une exclamation revenait sans cesse dans la bouche de son compagnon : \u00ab Tu m'as rendu un fier service, un jour je t'expliquerai ! \u00bb\n\nY aura-t-il un jour, commen\u00e7ait-elle \u00e0 se demander de plus en plus r\u00e9serv\u00e9e devant une telle exub\u00e9rance, une si forte gesticulation verbale, ce n'\u00e9tait en effet que chuchotis dans le cou, \u00e0 l'oreille, debout comme ils \u00e9taient serr\u00e9s l'un contre l'autre. Sans doute qu'\u00e0 cause des secousses du trajet, de la presse autour d'eux, elle perdait les trois quarts de son propos, car par quel chemin en vint-il \u00e0 parler du tremble, cette sorte de peuplier qui pousserait en lisi\u00e8re des bois ? \u00c0 Portivy lors de ses derni\u00e8res vacances, c'\u00e9tait le premier arbre \u00e0 s'approcher des fen\u00eatres de la villa de ses amis o\u00f9 il g\u00eetait.\n\n\u00ab Tu connais Portivy ? C'est dans la presqu'\u00eele de Quiberon. Eh bien \u00e0 Portivy, j'\u00e9tais un tremble, car moi aussi je m'approche \u00bb, lui souffla-t-il vulgairement. Et il en profitait en effet pour la serrer presque dans ses bras. Mais, ajoutait-il, \u00ab pas avec des roulettes pour me d\u00e9placer comme le type de la serre rue Marzelle. Bien qu'en ce moment on roule ! \u00bb.\n\n\u00c7a ne roulait plus tellement pour la blonde Ir\u00e8ne : ce gar\u00e7on a trop une parole \u00e9perdue et des yeux ailleurs, se disait-elle. Apr\u00e8s une ultime embrassade sur les deux joues place du Commerce o\u00f9 ils descendirent, elle se promit bien de ne plus recommencer une telle aventure. Voir Charles-Andr\u00e9 Bertrand au lyc\u00e9e, d'accord, deviser avec lui de choses et d'autres, d'accord, mais plus de promenades \u00e0 deux dans les rues incertaines de la ville. Ce qui explique que lorsqu'une semaine plus tard Charles-Andr\u00e9 proposa de l'inviter \u00e0 d\u00eener au \u00ab ch\u00e2teau \u00bb dont cette fois il avait les clefs, m\u00eame celle du grenier, car Mme Joliette bien vivante, \u00ab bien vivante \u00bb r\u00e9p\u00e9tait-il avec une voix triomphale, \u00e9tait revenue expr\u00e8s pour leur faire la cuisine, ayant appris leur f\u00e2cheuse m\u00e9saventure et aussi somme toute pour se faire pardonner, car elle aurait d\u00fb pr\u00e9venir Monsieur Charles de son absence le sachant si vite inquiet, mais apr\u00e8s la derni\u00e8re soir\u00e9e familiale, elle ne s'\u00e9tait pas sentie tr\u00e8s bien durant la nuit et avait \u00e9t\u00e9 prendre un bol d'air chez son fils. \u00ab Vous avez mang\u00e9 ou bu quelque chose de pas tr\u00e8s catholique \u00bb, lui avait m\u00eame confirm\u00e9 un m\u00e9decin \u00e0 Saint-Br\u00e9vin.\n\n\u00c0 tout ce beau discours de la part de Charles-Andr\u00e9, comme quoi comme cuisini\u00e8re il n'y en aurait pas de meilleure sur les bords de Loire, Ir\u00e8ne n\u00e9anmoins opposa un refus poli, pr\u00e9textant une infinitude de choses en retard dont elle devait s'acquitter sans retard, mais que plus tard, pourquoi pas, etc. etc.\n\nSon vocabulaire \u00e9tait pauvre car elle ne sait pas mentir ! Il parut attrist\u00e9, tourna les talons, se perdit dans la contemplation d'un mur salle des profs. Un coll\u00e8gue lui tapa sur l'\u00e9paule avant que la sonnerie de la reprise des cours n'intervienne heureusement.\n\nQue dire de plus de Charles-Andr\u00e9 ? Il vivait le plus souvent seul avec ses pens\u00e9es, pas plus entreb\u00e2ill\u00e9 au Bouffay que ses fen\u00eatres, au lyc\u00e9e, perdu dans ses livres, ses cahiers avec de vagues sourires adress\u00e9s \u00e0 quelques-uns dans les marges. Mais plus question de r\u00e9it\u00e9rer aupr\u00e8s d'Ir\u00e8ne une nouvelle fois son invitation \u00e0 d\u00eener au \u00ab ch\u00e2teau \u00bb. Un certain Monsieur \u00ab je ne sais plus comment \u00bb l'avait achet\u00e9 sans barguigner et avec tout ce qu'il contenait, y compris le serviteur en bois des \u00eeles dans son habitacle vitr\u00e9, ce qui expliqua aux yeux souvent de douze ans d'\u00e2ge de Charles-Andr\u00e9 que ce distingu\u00e9 nouveau propri\u00e9taire, rentier de son \u00e9tat, passa de vie \u00e0 tr\u00e9pas quelques mois plus tard.\n\nAux derni\u00e8res nouvelles d'ailleurs, celui-ci, faute de pouvoir ouvrir, faire conna\u00eetre \u00e0 Ir\u00e8ne le grand livre jaune de son enfance (ce qui aurait fait supposer d\u00e9j\u00e0 entre eux une intimit\u00e9 presque biblique), qu'il avait tant parcouru avec Diane Marchand, son ex-compagne, serait parti en Isra\u00ebl le feuilleter en vrai. Du moins, c'\u00e9tait l'avis insolite, presque dans\u00e9 de Jean-Marc de la villa Rose, l'\u00e9poux de Solange, \u00e0 la r\u00e9ception d'une carte postale. On dit m\u00eame, et toujours d'apr\u00e8s nos Am\u00e9ricains de Portivy, qu'il s'y serait mari\u00e9 avec une belle Samaritaine des bords du lac de Tib\u00e9riade, et devenu plus galil\u00e9en que les Galil\u00e9ens. Mais allez donc savoir, d\u00e9m\u00ealer le vrai du faux ? D'abord trois pr\u00e9noms forment-ils vraiment un nom ? Une ombre durable sur cette terre ? Charles-Andr\u00e9 Bertrand est-ce vraiment, vraiment quelqu'un ?\n\n#\n\n5, rue Gaston-Gallimard, 75328 Paris cedex 07\n\nwww.gallimard.fr\n\n_\u00a9 \u00c9ditions Gallimard, 2013._\n\nDocument de couverture :\n\n\u00a9 Ludovic Le Couster \/ Picturetank\n\nConception graphique :\n\nN\u00e9jib Belhadj Kacem\n\n#\n\n\u00ab Il sentit que cela venait d'une mani\u00e8re ou d'une autre mais que cela venait. Il \u00e9tait assis. Combien de fois ne s'\u00e9tait-il pas assis devant cette fen\u00eatre ? Le jour avait perdu une partie de sa clart\u00e9 et lui \u00e9tait d\u00e9sormais trop las pour r\u00e9agir, aller voir de pr\u00e8s si la v\u00e9g\u00e9tation l'apostrophait aussi durement qu'aux premi\u00e8res heures. N'\u00e9tait-il pas un corps \u00e9tranger ? Quelqu'un d'ailleurs ? Pourquoi cette haute demeure l'accepterait-elle illico sans autres pourparlers pr\u00e9alables avec ses ombres ? \u00bb\n\nEt si la cuisini\u00e8re n'\u00e9tait pas vraiment endormie ? Et si le mannequin de bois paraissait trop r\u00e9veill\u00e9 pour rester de bois ? Et si lui-m\u00eame, Charles-Andr\u00e9, n'avait pas grandi ? Et si la maison qu'il habite en \u00e9tait une autre ? Et si sa tante \u00e9tait sa m\u00e8re ? Et si la mer \u00e9tait...\n\n_Michel Chaillou est \u00e9crivain. Il est l'auteur de plus d'une trentaine d'ouvrages parmi lesquels_ Le sentiment g\u00e9ographique _,_ Domestique chez Montaigne _,_ La croyance des voleurs _(prix des Libraires 1989), qui ouvre un cycle autobiographique dont le titre le plus r\u00e9cent est_ La fuite en \u00c9gypte _(2011)._\n\n_Michel Chaillou a obtenu en 2007 le Grand Prix de litt\u00e9rature de l'Acad\u00e9mie fran\u00e7aise pour l'ensemble de son \u0153uvre._\n\n# DU M\u00caME AUTEUR\n\nAux \u00c9ditions Gallimard\n\n_Jonathamour_ , roman, 1968, \u00ab Folio \u00bb, 1991.\n\n_Coll\u00e8ge Vaserman_ , r\u00e9cit, 1970.\n\n_Le R\u00eave de Saxe_ , roman, \u00ab Folio \u00bb, 1988.\n\n_Le Sentiment g\u00e9ographique_ , 1976, \u00ab L'Imaginaire \u00bb, 1989.\n\n_Domestique chez Montaigne_ , 1983, \u00ab L'Imaginaire \u00bb, 2010.\n\n_La Vindicte du sourd_ , \u00ab Folio Junior \u00bb, 1984.\n\n_La Rue du capitaine Olchanski. Roman russe_ , 1991.\n\n_Le Crime du beau temps_ , 2010.\n\nAux \u00c9ditions du Seuil\n\n_La Croyance des voleurs_ , roman, 1989, prix des Libraires, 1989, \u00ab Points \u00bb, 1990.\n\n_L'Hexam\u00e9ron_ (en collaboration avec Michel Deguy, Florence Delay, Natacha Michel, Denis Roche et Jacques Roubaud), 1990.\n\n_La Petite Vertu : huit ann\u00e9es de prose courante sous la R\u00e9gence_ , Seuil 1990.\n\n_M\u00e9moires de Melle_ , roman, 1993, \u00ab Points \u00bb, 1995.\n\n_La Vie priv\u00e9e du d\u00e9sert_ , roman, 1995, \u00ab Points \u00bb, 1997.\n\n_Le ciel touche \u00e0 peine terre_ , roman, 1997.\n\n_Les Habits du fant\u00f4me_ (photographies de Fran\u00e7ois Delebecque), 1999.\n\nAux \u00c9ditions Fayard\n\n_La Fleur des rues_ , 2000.\n\n_Indigne indigo_ , roman, 2007.\n\n_La Preuve par le chien_ , roman, 2005.\n\n_Virginit\u00e9_ , roman, 2007.\n\n_L'\u00c9coute int\u00e9rieure_ , neuf entretiens sur la litt\u00e9rature avec Jean V\u00e9drines, 2007.\n\n_Le Dernier des Romains_ , roman, 2009.\n\n_La Fuite en \u00c9gypte_ , roman, 2011.\n\nChez d'autres \u00e9diteurs\n\n_Le Colosse machinal_ , en collaboration avec Martin Jarrie, Nathan, 1996.\n\n_La France fugitive_ , Le Livre de Poche, 2001.\n\n_Le Matamore \u00e9bouriff\u00e9_ , roman, Le Livre de Poche, 2004.\n\n_\u00c9loge du d\u00e9mod\u00e9_ , La Diff\u00e9rence, 2012.\n\n_1945_ , r\u00e9cit, La Diff\u00e9rence, 2012.\n\n#\n\nCette \u00e9dition \u00e9lectronique du livre _L'hypoth\u00e8se de l'ombre_ de Michel Chaillou, a \u00e9t\u00e9 r\u00e9alis\u00e9e le 6 d\u00e9cembre 2013 par les \u00c9ditions Gallimard.\n\nElle repose sur l'\u00e9dition papier du m\u00eame ouvrage, achev\u00e9 d'imprimer en octobre 2013 par Floch\n\n(ISBN : 9782070136117 \u2013 Num\u00e9ro d'\u00e9dition : 237440).\n\nCode sodis : N51329 \u2013 ISBN : 9782072461590 \u2013 Num\u00e9ro d'\u00e9dition : 237896.\n\nLe format ePub a \u00e9t\u00e9 pr\u00e9par\u00e9 par Entrelignes (64) \u00e0 partir de l'\u00e9dition papier du m\u00eame ouvrage.\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\nPENGUIN BOOKS  \nENGLAND: THE AUTOBIOGRAPHY\n\nJohn Lewis-Stempel is a writer and farmer. He lives in Herefordshire with his wife and two children. He is the editor and author of many previous books, including _Fatherhood: An Anthology_ and _Eye-witness D-Day._\n\n# England: The Autobiography\n\n_2,000 Years of English History By Those Who Saw It Happen_\n\nJOHN LEWIS-STEMPEL\n\nPENGUIN BOOKS\nPENGUIN BOOKS\n\nPublished by the Penguin Group  \nPenguin Books Ltd, 80 Strand, London WC2R 0RL, England  \nPenguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014, USA  \nPenguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario, Canada M4P 2Y3  \n(a division of Pearson Penguin Canada Inc.)  \nPenguin Ireland, 25 St Stephen's Green, Dublin 2, Ireland (a division of Penguin Books Ltd)  \nPenguin Group (Australia), 250 Camberwell Road,  \nCamberwell, Victoria 3124, Australia (a division of Pearson Australia Group Pty Ltd)  \nPenguin Books India Pvt Ltd, 11 Community Centre, Panchsheel Park,  \nNew Delhi \u2013 110 017, India  \nPenguin Group (NZ), cnr Airborne and Rosedale Roads, Albany, Auckland 1310, New Zealand  \n(a division of Pearson New Zealand Ltd)  \nPenguin Books (South Africa) (Pty) Ltd, 24 Sturdee Avenue, Rosebank 2196,  \nJohannesburg, South Africa\n\nPenguin Books Ltd, Registered Offices: 80 Strand, London WC2R 0RL, England\n\nwww.penguin.com\n\nFirst published by Viking 2005  \nPublished in Penguin Books 2006  \n6\n\nCopyright \u00a9 John Lewis-Stempel, 2005  \nAll rights reserved\n\nThe moral right of the author has been asserted\n\nExcept in the United States of America, this book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser\n\nISBN: 978-0-141-92869-2\nFor an English oak and an English rose, Tristram and Freda\n\n## Contents\n\nForeword\n\nCaesar Invades, 55 BC\n\nJULIUS CAESAR\n\nEngland: A Roman View, 54 BC\n\nJULIUS CAESAR\n\nBoudicca Revolts, AD 61\n\nTACITUS\n\nGraffiti, C. AD 100\u2013400\n\nVARIOUS\n\nKing Edwin of Northumbria Is Converted to Christianity, c. 627\n\nBEDE\n\nThe Vikings Raid England, 787\u201393\n\n_THE ANGLO-SAXON CHRONICLE_\n\nThe Viking Invasion: Alfred Saves _Angelcynn_ from the Danes, 871\u20138\n\nASSER\n\nA Saxon Warrior at the Battle of Maldon, 991\n\nANONYMOUS\n\nCnut and the Waves, c. 1030\n\nHENRY OF HUNTINGDON\n\nThe Battle of Hastings, 14 October 1066\n\nWILLIAM OF POITIERS\n\nThe Coronation of William the Conqueror, Christmas Day 1066\n\nORDERIC VITALIS\n\nThe Harrying of the North, 1069\u201370\n\nORDERIC VITALIS\n\nThe Domesday Inquisition, 1085\u20136\n\n_THE ANGLO-SAXON CHRONICLE_\n\nThe Domesday Assessment of Cumnor, 1086\n\nANONYMOUS\n\nAn Estimate of William the Conqueror at His Death, 1087\n\n_THE ANGLO-SAXON CHRONICLE_\n\nThe Loss of the _White Ship,_ 25 November 1120\n\nORDERIC VITALIS\n\nThe Anarchy, 1137\u201354\n\n_THE ANGLO-SAXON CHRONICLE_\n\nThe Virtues and Vices of Henry II, 1154\u201389\n\nWALTER MAP\n\nThe Murder of Thomas-\u00e0-Becket, Canterbury, 29 December 1170\n\nEDWARD GRIM\n\n_Holocaustum_ , 1190\n\nROGER OF WENDOVER\n\nRichard I Massacres His Muslim Prisoners After Seizing Acre, 2\u201320 August 1191\n\nBEHA-ED-DIN\n\nMagna Carta, 1215\n\nKING JOHN ET AL.\n\nThe Weather, 1257\n\nMATTHEW PARIS\n\nEdward I Conquers Wales, 1281\u20132\n\nTHOMAS WYKES\n\nSex in the Country, 15 June 1300\n\nANONYMOUS COURT RECORDER\n\nThe Age of Chivalry: A Mass Knighting, May 1306\n\nANONYMOUS MONK\n\nThe Battle of Bannockburn, 24 June 1314\n\n_THE CHRONICLE OF LANERCOST_\n\nThe Murder of Edward II, 22 September 1327\n\nGEOFFREY LE BAKER\n\nThe Hundred Years War: Sea Fight at Sluys, 24 June 1340\n\nGEOFFREY LE BAKER\n\nThe Hundred Years War: The Battle of Cr\u00e9cy, 26 August 1346\n\nSIR JOHN FROISSART\n\nThe Black Death, 1348\u20139\n\nHENRY KNIGHTON\n\nFlagellants Come to London, Michaelmas 1349\n\nROBERT OF AVESBURY\n\nThe Peasant's Life, c. 1362\n\nWILLIAM LANGLAND\n\nThe Peasants' Revolt, May\u2013June 1381\n\n_THE ANONIMALLE CHRONICLE_\n\nThe Battle of Agincourt, 25 October 1415\n\nANONYMOUS PRIEST\n\nAgincourt: Henry's Victory March, London, 23 November 1415\n\nANONYMOUS\n\nSome Public Nuisances, 1422\n\nTHE GENERAL COURT OF THE MAYOR OF THE CITY OF LONDON\n\nThe Wars of the Roses: Fog, Confusion and Treachery \u2013 the Battle of Barnet, 14 April 1471\n\nJOHN WARKWORTH\n\nRichard III Murders the Princes in the Tower, 1483\n\nWILLIAM SHAKESPEARE AND SIR THOMAS MORE\n\nThe Battle of Bosworth, 22 August 1485\n\nPOLYDORE VERGIL\n\nA Portrait of Henry VIII, 1519\n\nSEBASTIAN GIUSTINIAN\n\nThe Field of the Cloth of Gold, 7\u201324 June 1520\n\nPOLYDORE VERGIL\n\n'Mine Own Sweetheart': Henry VIII Writes to Anne Boleyn, c. 1526\n\nHENRY VIII\n\nThe Dissolution of the Monasteries: Cromwell's Agents Report, 1535\u20138\n\nJOHN LONDON, JOHN AP RICE, RICHARD LAYTON, GEOFFREY CHAMBER, ROGER TOWNSEND\n\nThe Burning of Archbishop Cranmer, 21 March 1556\n\nA BYSTANDER\n\nAn Encounter with Drake at Sea, off Guatemala, 4 April 1579\n\nFRANCISCO DE ZARATE\n\nThe Execution of Mary, Queen of Scots, 8 February 1587\n\nR. K. WYNKFIELDE\n\nThe Armada: the Commander's Report, 21\u201329 July 1588\n\nLORD HOWARD OF EFFINGHAM AND JOHN HAWKINS\n\nThe Armada: Elizabeth Addresses Her Troops, 9 August 1588\n\nELIZABETH I\n\nThe Torturing of a Jesuit Priest in the Tower of London, 14\u201315 April 1597\n\nFATHER JOHN GERARD\n\nA Meeting with Queen Elizabeth, 1598\n\nPAUL HENTZNER\n\nThe Age of Shakespeare: Theatregoing, 1599\u20131613\n\nTHOMAS PLATTER AND SIR HENRY WOTTON\n\nThe Death of Elizabeth, 24 March 1603\n\nLADY SOUTHWELL\n\nA Sketch of King James I, 1603\u201323\n\nSIR ANTHONY WELDON\n\nThe Gunpowder Plot, 5 November 1605\n\nGUY FAWKES\n\nThe Pilgrims Land in New England, 11 November 1620\n\nWILLIAM BRADFORD\n\nA Post-mortem, 1636\n\nWILLIAM HARVEY\n\nCromwell in the House of Commons, November 1640\n\nSIR PHILIP WARWICK\n\nThe Attempted Arrest of the Five Members, 4 January 1642\n\nJOHN RUSHWORTH\n\nCivil War: Sir Richard Bulstrode in Action at Edgehill, 23 October 1642\n\nSIR RICHARD BULSTRODE\n\nCivil War: The Death of a Nephew at Marston Moor, 2 July 1644\n\nOLIVER CROMWELL\n\nThe Execution of Charles I, 30 January 1649\n\nPHILIP HENRY\n\nThe Storming of Drogheda, 10\u201311 September 1649\n\nOLIVER CROMWELL\n\nCromwell Purges the Long Parliament, 20 April 1653\n\nBULSTRODE WHITELOCK\n\nCromwell's Funeral, 23 November 1658\n\nJOHN EVELYN\n\nThe Restoration: Charles II Returns to England, 12\u201325 May 1660\n\nSAMUEL PEPYS\n\nJournal of the Plague Year, 1665\n\nJOHN EVELYN\n\nThe Great Fire of London, 2 September 1666\n\nSAMUEL PEPYS\n\nIsaac Newton Experiments on Light, Cambridge, 1666\n\nSIR ISAAC NEWTON\n\nThe Great Frost Fair, 24 January 1684\n\nJOHN EVELYN\n\nThe Glorious Revolution: William of Orange Enters, James II Exits, November\u2013December 1688\n\nJOHN EVELYN\n\nBlenheim: The Victor's View, Bavaria, 13 August 1704\n\nJOHN CHURCHILL, DUKE OF MARLBOROUGH\n\nBath under the Code of Beau Nash, c. 1710\n\nOLIVER GOLDSMITH\n\nCock-fighting, London, 18 June 1710\n\nZACHARIAS VON UFFENBACH\n\nBad King George I, 1714\u201327\n\nJOHN H. JESSE\n\nPublic Executions at Tyburn, c. 1725\n\nC. DE SAUSSURE\n\nJohn Wesley Preaches, 19 March 1742\n\nJOHN WESLEY\n\nBonnie Prince Charlie Invades Manchester, 28\u201329 November 1745\n\nELIZABETH BYROM\n\nThe Black Hole of Calcutta, 20\u201321 June 1756\n\nJ. Z. HOLWELL\n\nThe Death of General Wolfe on the Heights of Abraham, Quebec, 13 September 1759\n\nCAPTAIN JOHN KNOX\n\nGeorge II Interred, 13 November 1760\n\nHORACE WALPOLE\n\nThe Boston Tea Party, 16 December 1773\n\nJOHN ANDREWS\n\nMachine Wreckers, Lancashire, October 1779\n\nTHOMAS BENTLEY\n\nThe Gordon Riots, 8 June 1780\n\nGEORGE CRABBE\n\nA Chance Meeting with Mad King George, Kew Gardens, 2 February 1789\n\nFANNY BURNEY\n\nJenner Discovers Smallpox Vaccination, 1796\n\nEDWARD JENNER\n\nThe Battle of the Nile, 1 August 1798\n\nJOHN NICHOL\n\nNelson Sees No Signal, Copenhagen, 2 April 1801\n\nCOLONEL WILLIAM STEWART\n\nWellington Meets Nelson, 10 September 1805\n\nSIR ARTHUR WELLESLEY\n\nTrafalgar: The Battle Opens, Morning 21 October 1805\n\nMIDSHIPMAN BADCOCK RN\n\nTrafalgar: The Death of Nelson, Afternoon 21 October 1805\n\nDR WILLIAM BEATTY\n\nThe Peninsular War: Plundering a Dead French Soldier after the Battle of Vimeiro, 21 August 1808\n\nRIFLEMAN HARRIS\n\nThe Peninsular War: The Storming of Badajoz, _6_ April 1812\n\nROBERT BLAKENEY\n\nWaterloo: Taken Prisoner, 18 June 1815\n\nENSIGN EDMUND WHEATLEY\n\nWaterloo: The Final Attack; The Rifle Brigade Advance, 7 p.m., 18 June 1815\n\nCAPTAIN J. KINCAID, RIFLE BRIGADE\n\nFactory Conditions, c. 1815\n\nELIZABETH BENTLEY\n\nClimbing Boys, 1817\n\nJOHN COOK\n\nPeterloo, 16 August 1819\n\nSAMUEL BAMFORD\n\nThe Black Country, 1830\n\nJAMES NASMYTH\n\nFirst Excursion on the Liverpool\u2013Manchester Railway, 25 August 1830\n\nFANNY KEMBLE\n\nThe Commons Pass the Reform Bill, 3 a.m., 23 March 1831\n\nTHOMAS MACAULAY\n\nDarwin in the Galapagos, 1835\n\nCHARLES DARWIN\n\nThe Coronation of Queen Victoria, 29 June 1838\n\nCHARLES GREVILLE\n\nProstitutes and Peers: Scenes from a Gin-palace, London, 1839\n\nFLORA TRISTAN\n\nManchester Slums, 1844\n\nFRIEDRICH ENGELS\n\nChloroform in Surgery, 1847\n\nCHARLES GREVILLE\n\nChartist March, 13 April 1848\n\nCHARLES GREVILLE\n\nA Visit to the Great Exhibition, 7 June 1851\n\nCHARLOTTE BRONTE\n\nThe Charge of the Light Brigade, Crimea, 25 October 1854\n\nE. A. COOK\n\nFlorence Nightingale in the Crimea, 1855\n\nFLORENCE NIGHTINGALE\n\nIndian Mutiny: Cawnpore after the Massacre, July 1857\n\nRICHARD BARTER\n\nSamuel White Baker Discovers the Source of the Nile, 14 March 1864\n\nSAMUEL WHITE BAKER\n\nStanley Meets Livingstone, Ujiji, Africa, 10 November 1871\n\nSIR HENRY MORTON STANLEY\n\nThe Revolt of the Field, 2 February 1872\n\nJOSEPH ARCH\n\nRorke's Drift, South Africa, 21 January 1879\n\nHENRY HOOK\n\nThe Cup Final, Kennington Oval, London, 30 March 1882\n\n_THE BLACKBURN TIMES_\n\nThe Diamond Jubilee, 22 June 1897\n\nQUEEN VICTORIA\n\nFox-hunt, Kent, November 1898\n\nSIEGFRIED SASSOON\n\nOmdurman, 2 September 1898\n\nWINSTON CHURCHILL\n\nThe Siege of Mafeking, South Africa, April-May 1900\n\nJ. E. NEILLY\n\nQueen Victoria's Funeral Procession, Isle of Wight to London, 1\u20132 February 1901\n\nTHE COUNTESS OF DENBIGH\n\nForce-feeding of a Suffragette, Walton Jail, Liverpool, 18 January 1910\n\nLADY CONSTANCE LYTTON\n\nThe Arrest of Dr Crippen, 31 July 1910\n\nCAPTAIN H. G. KENDALL\n\nAntarctic Expedition: Scott's Last Diary Entries, January 1912\n\nCAPTAIN R. F. SCOTT RN\n\nThe _Titanic_ Sinks, 15 April 1912\n\nHAROLD BRIDE\n\nThe Drift to World War: The View from 10 Downing Street, 1\u20132 August 1914\n\nHERBERT ASQUITH, PRIME MINISTER\n\nChristmas in the Trenches, December 1914\n\nCAPTAIN SIR EDWARD HAMILTON WESTROW HULSE\n\nAn Infantryman at Gallipoli, June 1915\n\nLEONARD THOMPSON\n\nNight Raid, Western Front, 25 May 1916\n\nSIEGFRIED SASSOON\n\nHome Front: Death of a Brother, 15 June 1916\n\nVERA BRITTAIN\n\nWounded, The Somme, 15 September 1916\n\nBERT STEWARD\n\nT. E. Lawrence Blows up a Train on the Hejaz Railway, Arabia, 1917\n\nT. E. LAWRENCE\n\nArmistice Celebrations, London, 11 a.m., 11 November 1918\n\nWINSTON CHURCHILL\n\nThe General Strike, 4\u201312 May 1926\n\nARNOLD BENNETT\n\nBody-line Bowling, Adelaide, Australia, 13\u201319 January 1913\n\nW. H. FERGUSON\n\nDown and Out: A Night in a Doss-house, c. 1931\n\nGEORGE ORWELL\n\nThe Battle of Cable Street, 7 October 1936\n\nPHIL PIRATIN\n\nThe Jarrow March, October 1936\n\nROY CHADWICK\n\nThe Abdication, 11 December 1936\n\nSIR HENRY CHANNON\n\nWorld War II: Children Evacuated, London, 1 September 1939\n\nHILDE MARCHANT\n\nDunkirk: The Beach, 30 May 1940\n\nCAPTAIN RICHARD AUSTIN, BEF\n\nChurchill's War Speeches, June 1940\n\nWINSTON CHURCHILL, PRIME MINISTER\n\nThe Battle of Britain: A Spitfire Pilot in Action, 2 September 1940\n\nRICHARD HILLARY RAF\n\nThe Blitz on London, 7\u20138 September 1940\n\nDESMOND FLOWER\n\nThe Japanese Sink the _Repulse_ and the _Prince of Wales,_ off the Coast of Malaya, 10 December 1941\n\nCECIL BROWN\n\nEl Alamein: The Afrika Korps Retreat, North Africa, 4 November 1942\n\nGENERAL FRITZ BAYERLEIN, AFRIKA KORPS\n\nThe Dambusters Destroy the Mohne Dam, Ruhr Valley, 16 May 1943\n\nWING COMMANDER GUY GIBSON RAF\n\nTenko: An Englishwoman in a Japanese Prison Camp, Kuching, Borneo, 1942\u20135\n\nAGNES NEWTON KEITH\n\nD-Day: A British Paratrooper Lands in Normandy, 1 a.m., 6 June 1944\n\nJAMES BYROM, PARACHUTE MEDICAL SERVICE\n\nAn Infantryman in Normandy, 6\u201324 June 1944\n\nSERGEANT G. E. HUGHES, ROYAL HAMPSHIRE REGIMENT\n\nDoodlebugs, 12 June 1944\n\nLIONEL KING\n\nVE Day, London, 8 May 1945\n\nMOLLIE PANTER-DOWNES\n\nPassage to England: A Boy Aboard the _Empire Windrush,_ May-June 1948\n\nVINCE REID\n\nThe Korean War: Lieutenant Curtis Wins the V C, Imjin River, 22 April 1951\n\nANTHONY FARRAR-HOCKLEY\n\nEverest Conquered, Himalayas, 29 May 1953\n\nEDMUND HILLARY\n\nThe Coronation of Queen Elizabeth II, 2 June 1953\n\nJOAN REEDER\n\nBanning the Bomb: Aldermaston March, 4 April 1958\n\nANONYMOUS\n\nLady Chatterley's Trial, The Old Bailey, November i960\n\nKENNETH TYNAN\n\nThe Beatles in Performance, Cavern Club, Liverpool, 9 November 1961\n\nBRIAN EPSTEIN\n\nRonnie Kray Murders George Cornell, 9 March 1966\n\nRONNIE KRAY\n\nEngland Win the World Cup, Wembley, 30 July 1966\n\nDAVID MILLER\n\nGrosvenor Square, 17 March 1968\n\nDICK POUNTAIN AND MICK FARREN\n\nNever Mind the B******S: The Sex Pistols, November 1975-April 1976\n\nJOHN LYDON AND PAUL COOK\n\nWade Wins Wimbledon, 1 July 1977\n\nFRANK KEATING\n\nMargaret Thatcher Becomes Prime Minister, 4 May 1979\n\nMARGARET THATCHER\n\nThe SAS Relieve the Siege at Prince's Gate, London, 5 May 1980\n\nANONYMOUS SAS TROOPER\n\nFalklands War: The First Man into Port Stanley, 14 June 1982\n\nMAX HASTINGS\n\nThe Brighton Bomb, 12 October 1984\n\nNORMAN TEBBIT\n\nThe 1984\u20135 Miners' Strike: Scenes from a Yorkshire Pit Village, South Elmsall, 19 December 1984\n\nPETER JENKINS, THE GUARDIAN\n\nThatcher Falls, 21\u201322 November 1990\n\nALAN CLARK MP\n\nThe Gulf War: Interrogation of a Captured British RAF Navigator, Iraq, February 1991\n\nJOHN NICHOL RAF\n\nThe Body of Diana, Princess of Wales, Is Flown Home, RAF Northolt, 31 August 1997\n\nJONATHAN FREEDLAND\n\nRugby World Cup: Jonny Wilkinson Kicks It Over, Telstra Stadium, Sydney, Australia, 22 November 2003\n\nJONNY WILKINSON\n\nThe London Bombings, 7 July 2005\n\nALICE O'KEEFE, LIAM VAUGHAN\n\nEngland Win the Ashes, the Oval, London, 12 September 2005\n\nED SMITH\n\nPersonal Acknowledgements\n\nSources and Permissions Acknowledgements\n\n## _Editor's note_\n\nSpellings in the quoted extracts are reproduced as in the original texts.\n\n## Foreword\n\nThis is a history of England by her subjects. Her autobiography.\n\nThere is something about England. The verdant southern part of a small island off the coast of Europe, England was \u2013 with apologies to the essentially colonized Wales, Scotland and Ireland \u2013 the birthplace of parliamentary democracy, the engine of the Industrial Revolution, the hub of the greatest empire the world has seen, and the last-ditch stand against an expansionist Germany in two world wars. England, to put it plainly, was the making of the modern world.\n\nThe Victorian adventurer and statesman Cecil Rhodes once informed an audience of schoolboys, 'Remember that you are Englishmen, and have therefore won first prize in the lottery of life.' Hyperbole, yes \u2013 but also a truism: to have been born and lived in England, not just in times modern but in times medieval and even times Dark, has invariably been a better lot \u2013 freer, more stable, more plentiful \u2013 than to have been the subject of another realm.\n\nCertainly, a more colourful lot: Henry VIII's six wives (and their fates), Oates at the South Pole, the Dambusters, the Armada, the Peasants' Revolt, the Battle of Agincourt, the Great Fire of London, the Gunpowder Plot, the Sex Pistols...\n\nOf course, as that quintessentially English (awkward but loyal) writer George Orwell once pointed out, autobiography is not to be trusted unless it reveals something shameful. So this life of England does not forget the _holocaustum_ of the Jews in York in 1190, the stomach-heaving slums of Manchester in 1844, the massacre of the reformers at Peterloo.\n\nAll these, and nearly 150 more events from England's past, are described in the following pages by those 'who were there'. Eyewitness reports may not have the in-depth analysis offered by historians but they are invariably more vivid, more pleasurable, and they allow a quality of understanding of bygone ages that is much underrated: an intuitive one.\n\nHere the past speaks for itself. I have only added context and connections that allow the life story of England to be clear and flowing in the telling. It is not a complete life: to include every event of the last 2,000 years would not be possible. So this is the history of England in magic-lantern moments. I do mean England: the history of the rest of the isles is only included where it shares a common destiny with England herself.\n\nThis is England in her own words.\n\nJohn Lewis-Stempel, Herefordshire, May 2005\n\n## _Caesar Invades, 55 BC_\n\nJULIUS CAESAR\n\n_Julius Caesar gave a virtuous reason (the prevention of arms traffic from Britain to occupied Gaul) for his invasion of Britannia, but personal ambition squatted in the foreground. The conquest would bring the prestige Caesar needed if he was to escape his triumvirate partners and rule Rome alone._\n\n_By Caesar's usual, meticulous military standards the invasion of Britain was ill-prepared, and his 14,000 legionaries, like all Romans, were reluctant sailors. By the time the barges crossed the Channel to the south coast, their human cargo was sea-sick and dispirited. Caesar's account of the invasion is the first direct written record of events in England \u2013 the beginning of English history, indeed._\n\nI reached Britain with the leading vessels at about 9 a.m., and saw the enemy forces standing under arms all along the heights. At this point of the coast precipitous cliffs tower over the water, making it possible to fire from above directly on to the beaches. It was clearly no place to attempt a landing, so we rode at anchor until about 3.30 p.m. awaiting the rest of the fleet. During this interval I summoned my staff and company commanders, passed on to them the information obtained by Volusenus, and explained my plans. They were warned that, as tactical demands, particularly at sea, are always uncertain and subject to rapid change, they must be ready to act at a moment's notice on the briefest order from myself. The meeting then broke up: both wind and tide were favourable, the signal was given to weigh anchor, and after moving about eight miles up channel the ships were grounded on an open and evenly shelving beach.\n\nThe natives, however, realized our intention: their cavalry and war chariots (a favourite arm of theirs) were sent ahead, while the main body followed close behind and stood ready to prevent our landing. In the circumstances, disembarkation was an extraordinarily difficult business. On account of their large draught the ships could not be beached except in deep water; and the troops, besides being ignorant of the locality, had their hands full: weighted with a mass of heavy armour, they had to jump from the ships, stand firm in the surf, and fight at the same time. But the enemy knew their ground: being quite unencumbered, they could hurl their weapons boldly from dry land or shallow water, and gallop their horses which were trained to this kind of work. Our men were terrified: they were inexperienced in this kind of fighting, and lacked that dash and drive which always characterized their land battles.\n\nThe warships, however, were of a shape unfamiliar to the natives; they were swift, too, and easier to handle than the transports. Therefore, as soon as I grasped the situation I ordered them to go slightly astern, clear of the transports, then full speed ahead, bringing up on the Britons' right flank. From that position they were to open fire and force the enemy back with slings, arrows, and artillery. The man\u0153uvre was of considerable help to the troops. The Britons were scared by the strange forms of the warships, by the motion of the oars, and by the artillery which they had never seen before: they halted, then fell back a little; but our men still hesitated, mainly because of the deep water.\n\nAt this critical moment the standard-bearer of the Tenth Legion, after calling on the gods to bless the legion through his act, shouted: 'Come on, men! Jump, unless you want to betray your standard to the enemy! I, at any rate, shall do my duty to my country and my commander.' He threw himself into the sea and started forward with the eagle. The rest were not going to disgrace themselves; cheering wildly they leaped down, and when the men in the next ships saw them they too quickly followed their example.\n\nThe action was bitterly contested on both sides. But our fellows were unable to keep their ranks and stand firm; nor could they follow their appointed standards, because men from different ships were falling in under the first one they reached, and a good deal of confusion resulted. The Britons, of course, knew all the shallows: standing on dry land, they watched the men disembark in small parties, galloped down, attacked them as they struggled through the surf, and surrounded them with superior numbers while others opened fire on the exposed flank of isolated units. I therefore had the warships' boats and scouting vessels filled with troops, so that help could be sent to any point where the men seemed to be in difficulties. When every one was ashore and formed up, the legions charged: the enemy was hurled back, but pursuit for any distance was impossible as the cavalry transports had been unable to hold their course and make the island. That was the only thing that deprived us of a decisive victory.\n\nThe natives eventually recovered from their panic and sent a delegation to ask for peace, promising to surrender hostages and carry out my instructions. These envoys brought with them Commius, who, it will be remembered, had preceded us to Britain. When he had landed and was actually delivering my message in the character of an ambassador he had been arrested and thrown into prison. Now, after their defeat, the natives sent him back: in asking for peace they laid the blame for this outrage upon the common people and asked me to overlook the incident on the grounds of their ignorance. I protested against this unprovoked attack which they had launched after sending a mission to the Continent to negotiate a friendly settlement, but agreed to pardon their ignorance and demanded hostages. Some of these were handed over at once, others, they said, would have to be fetched from a distance and would be delivered in a few days. Meanwhile they were ordered to return to their occupations on the land, and chieftains began to arrive from the surrounding districts, commending themselves and their tribes to my protection. Peace was thus concluded.\n\n_The_ pax _proved temporary and the Britons resumed fighting. Their dismaying habit of refusing set-piece battle in favour of a guerrilla war from the woods was not the campaign that the Romans were either militarily or psychologically prepared for. The Britons were also disconcertingly good charioteers. ('They can run along the chariot pole, stand on the yoke, and get back into the chariot as quick as lightning.') And anyway, gales had blown most of Caesar's cavalry back to Gaul. He followed them shortly._\n\n_A year later, 54 bc, Caesar mounted another invasion of Britain._\n\n## _England: A Roman View, 54 BC_\n\nJULIUS CAESAR\n\n_Caesar's second invasion of Britain crossed the Thames (at Brentford) but otherwise was a dismal repetition of the first excursion. A closer acquaintance with the land at least enabled Caesar to pen its portrait_.\n\nThe interior of Britain is inhabited by people who claim, on the strength of an oral tradition, to be aboriginal; the coast, by Belgic immigrants who came to plunder and make war \u2013 nearly all of them retaining the names of the tribes from which they originated \u2013 and later settled down to till the soil. The population is exceedingly large, the ground thickly studded with homesteads, closely resembling those of the Gauls, and the cattle very numerous. For money they use either bronze, or gold coins, or iron ingots of fixed weights. Tin is found inland, and small quantities of iron near the coast; the copper that they use is imported. There is timber of every kind, as in Gaul, except beech and fir. Hares, fowl, and geese they think it unlawful to eat, but rear them for pleasure and amusement. The climate is more temperate than in Gaul, the cold being less severe...\n\nBy far the most civilized inhabitants are those living in Kent (a purely maritime district), whose way of life differs little from that of the Gauls. Most of the tribes in the interior do not grow corn but live on milk and meat, and wear skins. All the Britons dye their bodies with woad, which produces a blue colour, and shave the whole of their bodies except the head and the upper lip. Wives are shared between groups of ten or twelve men, especially between brothers and between fathers and sons; but the offspring of these unions are counted as the children of the man with whom a particular woman cohabited first.\n\n_After extracting a face-saving promise by the British (who had the Iron Age equivalent of crossed fingers behind their backs) to pay tribute, Caesar, citing troubles in Gaul, withdrew. Definitively._\n\n_Caesar had come, seen, and failed to conquer. He had, however, put Britannia on the Roman map. Once there, it was inevitable that it would eventually be seized. Britannia's independence was an irritant. Moreover, Caesar had painted the place so positively that it tantalized unbearably. And so it was that in ad 43 Claudius invaded Britain._\n\n_There was just one hiccup. Claudius' shining-armoured troops, as hydrophobic as their Julian predecessors, initially refused to get in their boats at Boulogne. Once across the Channel, the Romans made easy work of the British. Those his 40,000-strong invasion army did not beat, Claudius \u2013 no fool, despite his drooling stammer \u2013 contemptuously bought off._\n\n_By AD 47 the Claudian armies had occupied Britain as far as the Trent and Severn. A decade later nearly all of England and Wales was conquered. By then Claudius was dead, and Nero resplendent in the imperial purple._\n\n_Under Nero Roman rule in Britain became more grasping._\n\n## _Boudicca Revolts, AD 61_\n\nTACITUS\n\n_Boudicca (or Boadicea as the Victorians renamed her) was Queen of the Iceni, a tribe from the east of England hitherto given to collaboration with the Romans. Although the Roman writer and jurist Tacitus was not an eye-witness to the revolt, his source is unimpeachable: it is his father-in-law Agriola, the Roman commander who became Roman Britain's most capable governor. As Tacitus noted of the Britons, they could 'bear to be ruled by others but not be their slaves'._\n\nPrasutagus, king of the Iceni, after a life of long and renowned prosperity, had made the emperor co-heir with his own two daughters. Prasutagus hoped by this submissiveness to preserve his kingdom and household from attack. But it turned out otherwise. Kingdom and household alike were plundered like prizes of war, the one by Roman officers, the other by Roman slaves. As a beginning, his widow Boudicca was flogged and their daughters raped. The Icenian chiefs were deprived of their hereditary estates as if the Romans had been given the whole country. The king's own relatives were treated like slaves.\n\nAnd the humiliated Iceni feared still worse, now that they had been reduced to provincial status. So they rebelled. With them rose the Trinobantes and others. Servitude had not broken them, and they had secretly plotted together to become free again. They particularly hated the Roman ex-soldiers who had recently established a settlement at Camulodunum. The settlers drove the Trinobantes from their homes and land, and called them prisoners and slaves. The troops encouraged the settlers' outrages, since their own way of behaving was the same \u2013 and they looked forward to similar licence for themselves. Moreover, the temple erected to the divine Claudius was a blatant stronghold of alien rule, and its observances were a pretext to make the natives appointed as its priests drain the whole country dry.\n\nIt seemed easy to destroy the settlement; for it had no walls. That was a matter which Roman commanders, thinking of amenities rather than needs, had neglected. At this juncture, for no visible reason, the statue of Victory at Camulodunum fell down \u2013 with its back turned as though it were fleeing the enemy. Delirious women chanted of destruction at hand. They cried that in the local senate-house outlandish yells had been heard; the theatre had echoed with shrieks; at the mouth of the Thames a phantom settlement had been seen in ruins. A blood-red colour in the sea, too, and shapes like human corpses left by the ebb tide, were interpreted hopefully by the Britons \u2013 and with terror by the settlers.\n\nSuetonius, however, was far away. So they appealed for help to the imperial agent Catus Decianus. He sent them barely two hundred men, incompletely armed. There was also a small garrison on the spot. Reliance was placed on the temple's protection. Misled by secret pro-rebels, who hampered their plans, they dispensed with rampart or trench. They omitted also to evacuate old people and women and thus leave only fighting men behind. Their precautions were appropriate to a time of unbroken peace.\n\nThen a native horde surrounded them. When all else had been ravaged or burnt, the garrison concentrated itself in the temple. After two days' siege, it fell by storm. The ninth Roman division, commanded by Quintus Petilius Cerialis Caesius Rufus, attempted to relieve the town, but was stopped by the victorious Britons and routed. Its entire infantry force was massacred, while the commander escaped to his camp with his cavalry and sheltered behind its defences. The imperial agent Catus Decianus, horrified by the catastrophe and by his unpopularity, withdrew to Gaul. It was his rapacity which had driven the province to war.\n\nBut Suetonius, undismayed, marched through disaffected territory to Londinium. This town did not rank as a Roman settlement, but was an important centre for business-men and merchandise. At first, he hesitated whether to stand and fight there. Eventually, his numerical inferiority \u2013 and the price only too clearly paid by the divisional commander's rashness \u2013 decided him to sacrifice the single city of Londinium to save the province as a whole. Unmoved by lamentations and appeals, Suetonius gave the signal for departure. The inhabitants were allowed to accompany him. But those who stayed because they were women, or old, or attached to the place, were slaughtered by the enemy. Verulamium suffered the same fate.\n\nThe natives enjoyed plundering and thought of nothing else. Bypassing forts and garrisons, they made for where loot was richest and protection weakest. Roman and provincial deaths at the places mentioned are estimated at seventy thousand. For the British did not take or sell prisoners, or practise other war-time exchanges. They could not wait to cut throats, hang, burn, and crucify \u2013 as though avenging, in advance, the retribution that was on its way.\n\nSuetonius collected the fourteenth brigade and detachments of the twentieth, together with the nearest available auxiliaries \u2013 amounting to nearly ten thousand armed men \u2013 and decided to attack without further delay. He chose a position in a defile with a wood behind him. There could be no enemy, he knew, except at his front, where there was open country without cover for ambushes. Suetonius drew up his regular troops in close order, with the light-armed auxiliaries at their flanks, and the cavalry massed on the wings. On the British side, cavalry and infantry bands seethed over a wide area in unprecedented numbers. Their confidence was such that they brought their wives with them to see the victory, installing them in carts stationed at the edge of the battlefield.\n\nBoudicca drove round all the tribes in a chariot with her daughters in front of her. 'We British are used to woman commanders in war,' she cried. I am descended from mighty men! But now I am not fighting for my kingdom and wealth. I am fighting as an ordinary person for my lost freedom, my bruised body, and my outraged daughters. Nowadays Roman rapacity does not even spare our bodies. Old people are killed, virgins raped. But the gods will grant us the vengeance we deserve! The Roman division which dared to fight is annihilated. The others cower in their camps, or watch for a chance to escape. They will never face even the din and roar of all our thousands, much less the shock of our onslaught. Consider how many of you are fighting \u2013 and why. Then you will win this battle, or perish. That is what I, a woman, plan to do! \u2013 let the men live in slavery if they will.'\n\nSuetonius trusted his men's bravery. Yet he too, at this critical moment, offered encouragements and appeals. 'Disregard the clamours and empty threats of the natives!' he said. 'In their ranks, there are more women than fighting men. Unwarlike, unarmed, when they see the arms and courage of the conquerors who have routed them so often, they will break immediately. Even when a force contains many divisions, few among them win the battles \u2013 what special glory for your small numbers to win the renown of a whole army! Just keep in close order. Throw your javelins, and then carry on: use shield-bosses to fell them, swords to kill them. Do not think of plunder. When you have won, you will have everything.'\n\nThe general's words were enthusiastically received: the old battle-experienced soldiers longed to hurl their javelins. So Suetonius confidently gave the signal for battle. At first the regular troops stood their ground. Keeping to the defile as a natural defence, they launched their javelins accurately at the approaching enemy. Then, in wedge formation, they burst forward. So did the auxiliary infantry. The cavalry, too, with lances extended, demolished all serious resistance. The remaining Britons fled with difficulty since their ring of wagons blocked the outlets. The Romans did not spare even the women. Baggage animals too, transfixed with weapons, added to the heaps of dead.\n\nIt was a glorious victory, comparable with bygone triumphs. According to one report almost eighty thousand Britons fell. Our own casualties were about four hundred dead and a slightly larger number of wounded. Boudicca poisoned herself.\n\n_In the aftermath of the uprising the Roman conquest proceeded ineluctably, until it dwindled out in the moorlands between the Humber and the Tyne, beyond which lay the drizzling land of the Picts. There were sporadic and optimistic attempts to conquer Caledonia, but always the Romans gave it up as a bad job, retreated behind Hadrian's Wall ( AD 122\u20138) and hoped that the troublesome Picts would stay the other side of it. Or pay a toll to come through its gates._\n\n_'Roman Britain' was no such creature; Scotland was excluded, Wales was under military occupation_ \u2013 _only what would become modern England was Romanized._\n\n_For three and a half centuries, England remained a far-flung outpost of the Roman Way._ Pax Romana _brought 10,000 miles of straight roads and the trappings of the Roman good life. But not many. Only Bath reached any level of degenerate luxury; only Lincoln had sewers._\n\n## _Graffiti, c. AD 100\u2013400_\n\nVARIOUS\n\n_Roman civilization in England may have been a poor cousin, but it was indisputably civilization (from the Latin_ civitas, _city-living). There was a boom in town-planning, and five settlements \u2013 St Albans, Colchester, Lincoln, Gloucester and York \u2013 eventually achieved municipal status. London was founded as a supply centre. There was a money economy and eventually there was Christianity. Probably, though, the import the locals adopted most keenly was the 'villa', a farm-cum-country estate, which became_ de rigueur _for any landed Celt who could stretch to it (the 'gentleman farmer' is one of England's oldest social stereotypes). Other popular introductions were peas, parsnips, plums, apples, and domestic cats. (The islanders were already famous for their dogs.)The spread of literacy allowed the Romano-British to carve their thoughts, hopes, fears, prejudices and advertisements in, among other media, inscriptions and graffiti:_\n\nGaius Valerius Amandus' Drops for dim sight  \n _[Proprietary stamp]_\n\nThe Club of his fellow-slaves set this up to a well-deserving comrade  \n _[A gravestone for Hardalio]_\n\nAustalis has been going off on his own every day this fortnight  \n _[Inscribed on a roof tile]_\n\nTo the God Nodens. Silvianus has lost a ring, and dedicated half [its value] to Nodens.  \nAmong those who are called Senicianus, permit no health until he brings it to the temple of Nodens.  \n_[Curse found at Lydney temple in Gloucestershire]_\n\nClementius made this box-tile.  \n_[A posterity-minded potter]_\n\n_Roman England began to decline around ad 350, as legion after legion was withdrawn to protect the heartland of the Roman Empire from the barbarian hordes. In ad 410, the last two legions sailed away and Britannia ceased to be a Roman colony. Over her remains there developed a three-cornered fight between Romano-Britons, Picts, and Germanic warriors who rowed across the North Sea to England in their open 'wave horses'. As the British monk Gildas records in his_ De Excidio Britanniae _of c. 540, these first Angles, Saxons, Jutes and Frisians were seemingly invited to England as mercenaries to fight the Picts. It was one of English history's bigger blunders:_\n\nThen all the councillors, together with that proud tyrant Gurthrigern (Vortigern), the British king, were so blinded, that, as a protection to their country, they sealed its doom by inviting in among them (like wolves into the sheep-fold), the fierce and impious Saxons, a race hateful both to God and men, to repel the invasions of the northern nations. Nothing was ever so pernicious to our country, nothing was ever so unlucky.... They first landed on the eastern side of the island, by the invitation of the unlucky king, and there fixed their sharp talons, apparently to fight in favour of the island, but alas! more truly against it. Their mother-land, finding her first brood thus successful, sends forth a larger company of her wolfish offspring, which sailing over, join themselves to their bastard-born comrades.\n\n_Despite the Britons' victory at Mons Badonicus \u2013 which legend, at least, ascribes to King Arthur in c. 516 \u2013 they were unable to prevent the Anglo-Saxon takeover. By the end of the seventh century, the Anglo-Saxon kingdoms of Kent, Sussex (South Saxons), Essex (East Saxons), Wessex (West Saxons), East Anglia, Mercia and Northumbria covered most of England._\n\n_And the Romano-British? Some were pushed into the far south-west (Cornwall held out until 838) and Wales, taking their Christianity with them to found hundreds of little monasteries in the hills. Some were enslaved, and many were killed by war and its faithful followers, famine and disease. As a piece of ethnic cleansing the Anglo-Saxon invasion would never be surpassed in the isles. Perhaps 200,000 Angles, Saxons and their kin came to the land they would call_ Angelcynn, _then_ Englaland, _in the 100 years from c. AD 430; they displaced go per cent of the resident males. And it was not just the Romano-British who disappeared. So did their 'civilization'. A determinedly non-urban people, the Anglo-Saxons turned up their noses at the Romans' towns, which fell into desolation and ruin._\n\n_Their aversion to city life aside, the Anglo-Saxons had other defining characteristics. They were, notably, a warrior race. It was war, with its code of blood loyalty and its reward of plunder, that stuck Anglo-Saxon society together. 'Let he who can win glory before death' enjoined the epic Saxon poem_ Beowulf. _To the glorious dead, like the East Anglian warrior-king who came to be buried at Sutton Hoo, went rich funereal treasures and a conspicuous burial mound._\n\n_So, these then were the English: a race of seafarers, who inclined towards farming (particularly if they could press some locals into servitude), fighting and pomp._\n\n_And, to the consternation of the Christian Church, an utter adherence to paganism._\n\n## _King Edwin of Northumbria Is Converted to Christianity, c. 627_\n\nBEDE\n\n_The conversion of the English to Christianity was initiated by Pope Gregory the Great who, legendarily, saw some English slaves in Rome and declared them 'not Angles but angels'. In_ 597 _Gregory's missionary, Augustine, duly if reluctantly, landed amongst the heathen._\n\n_As Augustine had guessed, the English were stony soil for the Christian missionaries; it took thirty years for a Gregorian representative, Paulinus, even to enter the court of King Edwin of Northumbria._\n\n_The Venerable Bede, a monk at Jarrow, was the author of the_ Historia Ecclesiastica Gentis Anglorum (Ecclesiastical History of the English People), 731.\n\nKing Edwin... answered that he was both willing and bound to accept the faith which Paulinus taught. He said, however, that he would confer about this with his loyal chief men and his counsellors so that, if they agreed with him, they might all be consecrated together in the waters of life. Paulinus agreed and the king did as he had said. A meeting of his council was held and each one was asked in turn what he thought of this doctrine hitherto unknown to them and this new worship of God which was being proclaimed.\n\nCoifi, the chief of the priests, answered at once, 'Notice carefully, King, this doctrine which is now being expounded to us. I frankly admit that, for my part, I have found that the religion which we have hitherto held has no virtue nor profit in it. None of your followers has devoted himself more earnestly than I have to the worship of our gods, but nevertheless there are many who receive greater benefits and greater honour from you than I do and are more successful in all their undertakings. If the gods had any power they would have helped me more readily, seeing that I have always served them with greater zeal. So it follows that if, on examination, these new doctrines which have now been explained to us are found to be better and more effectual, let us accept them at once without any delay.'\n\nAnother of the king's chief men agreed with this advice and with these wise words and then added, 'This is how the present life of man on earth, King, appears to me in comparison with that time which is unknown to us. You are sitting feasting with your ealdormen and thegns in winter time; the fire is burning on the hearth in the middle of the hall and all inside is warm, while outside the wintry storms of rain and snow are raging; and a sparrow flies swiftly through the hall. It enters in at one door and quickly flies out through the other. For the few moments it is inside, the storm and wintry tempest cannot touch it, but after the briefest moment of calm, it flits from your sight, out of the wintry storm and into it again. So this life of man appears but for a moment; what follows or indeed what went before, we know not at all. If this new doctrine brings us more certain information, it seems right that we should accept it.' Other elders and counsellors of the king continued in the same manner, being divinely prompted to do so.\n\nCoifi added that he would like to listen still more carefully to what Paulinus himself had to say about God. The king ordered Paulinus to speak, and when he had said his say, Coifi exclaimed, 'For a long time now I have realized that our religion is worthless; for the more diligently I sought the truth in our cult, the less I found it. Now I confess openly that the truth shines out clearly in this teaching which can bestow on us the gift of life, salvation, and eternal happiness. Therefore I advise your Majesty that we should promptly abandon and commit to the flames the temples and the altars which we have held sacred without reaping any benefit.' Why need I say more? The king publicly accepted the gospel which Paulinus preached, renounced idolatry, and confessed his faith in Christ. When he asked the high priest of their religion which of them should be the first to profane the altars and the shrines of the idols, together with their precincts, Coifi answered, 'I will; for through the wisdom the true God has given me no one can more suitably destroy those things which I once foolishly worshipped, and so set an example to all.' And at once, casting aside his vain superstitions, he asked the king to provide him with arms and a stallion; and mounting it he set out to destroy the idols. Now a high priest of their religion was not allowed to carry arms or to ride except on a mare. So, girded with a sword, he took a spear in his hand and mounting the king's stallion he set off to where the idols were. The common people who saw him thought he was mad. But as soon as he approached the shrine, without any hesitation he profaned it by casting the spear which he held into it; and greatly rejoicing in the knowledge of the worship of the true God, he ordered his companions to destroy and set fire to the shrine and all the enclosures. The place where the idols once stood is still shown, not far from York, to the east, over the river Derwent. Today it is called Goodmanham, the place where the high priest, through the inspiration of the true God, profaned and destroyed the altars which he himself had consecrated.\n\n_Edwin, like a good number of other Anglo-Saxon kings, was not slow in seeing the benefit of 'Christian kingship' \u2013 it enabled him to dress himself up as God's appointed local deputy on Earth, and to use the clergy (who were literate) as his civil service. The regent's subjects were less convinced by the Church's good news. On Edwin's death the Northumbrians apostatized \u2013 just as the East Angles of Raedwald had done on his demise. Meanwhile, the South Saxons and the Jutes on the Isle of Wight remained pagan and proud of it. It took an evangelical pincer-movement by the Roman mission and wandering monks sent over by the Irish Church to commit the English to Christianity entirely and irrevocably in c. 800._\n\n_Despite their commitment to converting the English, the Celtic and Roman missions were theological rivals, notably over the dating of Easter, which was eventually settled in the favour of Rome by King Oswiu of Northumbria at the Synod of Whitby in 664._\n\n_The decision to align with Rome was no trivial matter. In doing so England attached to Christian mainstream Europe. For Bede, at least, the English now began their walk with God as His other chosen people._\n\n_Over the course of three centuries, the Anglo-Saxons created in England a recognizably English language, culture, Church and landscape. In the grand council that was the Witan, they even had the notion of government by consent rather than kingly diktat. More than this, the Anglo-Saxons, uniquely in the Western world, melded a national identity unity that transcended kith and kin \u2013 after all, how else could Bede title his 731 masterpiece_ The Ecclesiastical History of the English People? _People, not peoples._\n\n_Alas for the English, the work of national construction was about to be rudely interrupted._\n\n## _The Vikings Raid England, 787\u201393_\n\n_THE ANGLO-SAXON CHRONICLE_\n\n_In 787 the English had never had it so good. In Offa of Mercia they had an overlord of the Anglo-Saxon kingdoms who brought stability (not least by constructing his 150-mile-long Dyke, from Basingwerk to Chepstow, to keep out the stock-rustling Welsh), which in turn brought trade._\n\n_In likelihood it was the very wealth of mercantile Anglo-Saxon England that attracted the Vikings there. Hailing and sailing from Denmark and Norway, the pagan Vikings peddled amber, fur and walrus ivory. However, their stock-in-trade was extortion: they raped and pillaged until paid to go away._\n\n_'Viking' is Anglo-Saxon for pirate._\n\nAD 787. In this year Beorhtric took to wife Eadburh, daughter of king Offa. And in his days came first three ships of Norwegians from H\u00f6rthaland around Hardanger Fjord; and then the reeve rode thither and tried to compel them to go to the royal manor, for he did not know what they were: and then they slew him. These were the first ships of the danes to come to England.\n\nAD 793. In this year terrible portents appeared over Northumbria, and miserably frightened the inhabitants: these were exceptional flashes of lightning, and fiery dragons were seen flying in the air. A great famine soon followed these signs; and a little after that in the same year on 8 January the harrying of the heathen miserably destroyed God's church in Lindisfarne by rapine and slaughter. In this year... Northumbria was ravaged by the heathen, and Ecgfrith's monastery at _Donemup_ [Jarrow] looted; and there one of their leaders was slain, and some of their ships besides were shattered by storms: and many of them were drowned there, and some came ashore alive and were at once slain at the river mouth.\n\n_Viking hit-and-row raids continued sporadically until 851, when the_ Chronicle _records 'the heathen stayed in Thanet over the winter'. This was the Vikings_ ' _first, but abortive, attempt at settlement. Fifteen years later, they came for good. Essentially, the 'wolf-coats_ ' _had done what all other visitors to England had done: raided a bit, liked what they saw, and decided to conquer._\n\n_But who could save England for the English?_\n\n## _The Viking Invasion: Alfred Saves Angelcynn from the Danes, 871\u20138_\n\nASSER\n\n_Alfred, King of Wessex (871\u201399), is unique in English history in having the honorific title 'Great' attached to his name. By any standards he deserved it, foremost because he led the Saxon resistance to the 'heathen host'. Asser was Alfred's tutor and chaplain, and later Bishop of Sherborne._\n\nThe same year (871), the aforesaid Alfred, who had been up to that time only of secondary rank, whilst his brothers were alive, now, by God's permission, undertook the government of the whole kingdom, amid the acclamations of all the people; and if he had chosen, he might have done so before, whilst his brother above-named was still alive; for in wisdom and other qualities he surpassed all his brothers, and, moreover, was warlike and victorious in all his wars. And when he had reigned one month, almost against his will, for he did not think he could alone sustain the multitude and ferocity of the pagans, though even during his brothers' lives, he had borne the woes of many \u2013 he fought a battle with a few men, and on very unequal terms, against all the army of the pagans, at a hill called Wilton, on the south bank of the river Wily, from which river the whole of that district is named, and after a long and fierce engagement, the pagans, seeing the danger they were in, and no longer able to bear the attack of their enemies, turned their backs and fled. But, oh, shame to say, they deceived their too audacious pursuers, and again rallying, gained the victory. Let no one be surprised that the Christians had but a small number of men, for the Saxons had been worn out by eight battles in one year, against the pagans, of whom they had slain one king, nine dukes, and innumerable troops of soldiers, besides endless skirmishes, both by night and by day, in which the oft-named Alfred, and all his chieftains, with their men, and several of his ministers, were engaged without rest or cessation against the pagans. How many thousand pagans fell in these numberless skirmishes God alone knows, over and above those who were slain in the eight battles above-mentioned. In the same year the Saxons made peace with the pagans, on condition that they should take their departure, and they did so...\n\nIn the year 877, the pagans, on the approach of autumn, partly settled in Exeter, and partly marched for plunder into Mercia. The number of that disorderly crew increased every day, so that, if thirty thousand of them were slain in one battle, others took their places to double the number. Then King Alfred commanded boats and galleys, i.e. long ships, to be built throughout the kingdom, in order to offer battle by sea to the enemy as they were coming. On board of these he placed seamen, and appointed them to watch the seas. Meanwhile he went himself to Exeter, where the pagans were wintering, and having shut them up within the walls, laid siege to the town. He also gave orders to his sailors to prevent them from obtaining any supplies by sea; and his sailors were encountered by a fleet of a hundred and twenty ships full of armed soldiers, who were come to help their countrymen. As soon as the king's men knew that they were fitted with pagan soldiers, they leaped to their arms, and bravely attacked those barbaric tribes; but the pagans who had now for almost a month been tossed and almost wrecked among the waves of the sea, fought vainly against them; their bands were discomfited in a moment, and all were sunk and drowned in the sea, at a place called Suanewic...\n\nIn the year of our Lord's incarnation 878, which was the thirtieth of king Alfred's life, the army above-mentioned left Exeter, and went to Chippenham, a royal villa, situated in the west of Wiltshire, and on the eastern bank of the river, which is called in British, the Avon. There they wintered, and drove many of the inhabitants of that country beyond the sea by the force of their arms, and by want of the necessaries of life. They reduced almost entirely to subjection all the people of that country...\n\nThe same year, after Easter, king Alfred, with a few followers, made for himself a stronghold in a place called Athelney, and from thence sallied with his vassals and the nobles of Somersetshire, to make frequent assaults upon the pagans. Also, in the seventh week after Easter, he rode to the stone of Egbert, which is in the eastern part of the wood which is called Selwood.... Here he was met by all the neighbouring folk of Somersetshire, and Wiltshire, and Hampshire, who had not, for fear of the pagans, fled beyond the sea; and when they saw the king alive after such great tribulation, they received him, as he deserved, with joy and acclamations, and encamped there for one night. When the following day dawned, the king struck his camp, and went to Okely, where he encamped for one night. The next morning he removed to Edington, and there fought, bravely and perseveringly against all the army of the pagans, whom, with the divine help he defeated with great slaughter, and pursued them flying to their fortification. Immediately he slew all the men, and carried off all the booty that he could find without the fortress, which he immediately laid siege to with all his army; and when he had been there fourteen days, the pagans, driven by famine, cold, fear, and last of all by despair, asked for peace, on the condition that they should give the king as many hostages as he pleased, but should receive none of him in return, in which form they had never before made a treaty with any one. The king, hearing that, took pity upon them, and received such hostages as he chose; after which the pagans swore, moreover, that they would immediately leave the kingdom; and their king, Gothrun, promised to embrace Christianity, and receive baptism at king Alfred's hands. All of which articles he and his men fulfilled as they had promised.\n\n_For their baptism Gothrun (Gothrum) and his former axe-men wore white dresses._\n\n_By the subsequent Peace of Wedmore between Alfred and Gothrun a frontier was established between Alfred's Saxon England and the Danish territories in north, central and east England where Danelaw prevailed. In his share, Alfred built fortified towns (_ burhs _) and supervised a flowering of law and of learning; the_ Anglo-Saxon Chronicle _itself, the age's semi-official record, was almost certainly begun in Alfred's court. Naturally, Alfred had it penned in Anglo-Saxon, not Latin. He was the saviour of English, not just of England. But Alfred did more than aloofly oversee the Anglo-Saxon arts; he was the only English king before Henry VIII to write books._\n\n_In 899 King Alfred, 'Engele hirde, engele diring_ ' _(England's shepherd, England's darling), died. But his bloodline carried on. Over the next fifty years the house of Wessex, the_ de facto _royal house of England, reconquered almost all of Danelaw. The claim by Alfred's grandson Athelstan (reigned 924\u201339) to be the first true King of England was no idle boast; he sought, and he got, his coinage to 'run throughout the land'. By the time of Edgar (959\u201375), Alfred's great-grandson, the duty of the monarch was less going off to the wars, more the maintenance of the national peace. (It was Edgar who founded the penny coinage, who divided England into 'shires_ ', _who devised the coronation ritual, including the acclamatory cry of 'Long live the king, may the king live forever_ ' _used to this day). Soon, the Anglo-Saxons would look upon Edgar's reign as their Golden Age. They had need of nostalgia, because the Vikings were on the seas again._\n\n## _A Saxon Warrior at the Battle of Maldon, 991_\n\nANONYMOUS\n\n_Unlike the freebooting Viking raids of yore, those of the 980s were deliberate Danish policy: their aim was the subjugation of England. Occupying the English throne was the hapless Aethelred whose name (meaning 'counsel') was punned by his disillusioned subjects into 'Unraed_ ' _('no counsel'). Later generations would mistranslate Unraed as 'Unready_ '. _He was that too._\n\n_In 991 an English_ fyrd _(militia) under Ealdorman Brihtnoth met the Danes at Maldon in Essex. Overcome by bravado or a proto-English sense of fair play, Brihtnoth allowed the Vikings off Northey island, where they were trapped, and on to the battlefield proper._\n\nThen Brihtnoth began to array his men; he rode and gave counsel and taught his warriors how they should stand and keep their ground, bade them hold their shields aright, firm with their hands and fear not at all. When he had meetly arrayed his host, he alighted among the people where it pleased him best, where he knew his bodyguard to be most loyal.\n\nThen the messenger of the vikings stood on the bank, he called sternly, uttered words, boastfully speaking the seafarers' message to the earl, as he stood on the shore. 'Bold seamen have sent me to you, and bade me say, that it is for you to send treasure quickly in return for peace, and it will be better for you all that you buy off an attack with tribute, rather than that men so fierce as we should give you battle. There is no need that we destroy each other, if you are rich enough for this. In return for the gold we are ready to make a truce with you. If you who are richest determine to redeem your people, and to give to the seamen on their own terms wealth to win their friendship and make peace with us, we will betake us to our ships with the treasure, put to sea and keep faith with you.'\n\nBrihtnoth lifted up his voice, grasped his shield and shook his supple spear, gave forth words, angry and resolute, and made him answer: 'Hear you, sea-rover, what this folk says? For tribute they will give you spears, poisoned point and ancient sword, such war gear as will profit you little in the battle. Messenger of the seamen, take back a message, say to your people a far less pleasing tale, how that there stands here with his troop an earl of unstained renown, who is ready to guard this realm, the home of Ethelred my lord, people and land; it is the heathen that shall fall in the battle. It seems to me too poor a thing that you should go with our treasure unfought to your ships, now that you have made your way thus far into our land. Not so easily shall you win tribute; peace must be made with point and edge, with grim battle-play, before we give tribute.'\n\nThen he bade the warriors advance, bearing their shields, until they all stood on the river bank. Because of the water neither host might come to the other. There came the tide, flowing in after the ebb; the currents met and joined. All too long it seemed before they might clash their spears together. Thus in noble array they stood about Pante's stream, the flower of the East Saxons and the shipmen's host. None of them might harm another, unless a man should meet his death through a javelin's flight.\n\nThe tide went out, the seamen stood ready, many a viking eager for war. Then the bulwark of heroes appointed a warrior, hardy in war, to hold the bridge, Wulfstan was his name, accounted valiant among his kin. It was he, Ceola's son, who with his javelin shot down the first man that was so hardy as to set foot upon the bridge. There with Wulfstan stood warriors unafraid, \u00c6lfhere and Maccus, a dauntless pair; they had no thought of flight at the ford, but warded themselves stoutly against the foe, as long as they might wield their weapons. When the vikings knew and saw full well that they had to deal with grim defenders of the bridge, the hateful strangers betook themselves to guile, craved leave to land, to pass over the ford and lead their men across. Then the earl, in his pride, began to give ground all too much to the hateful folk; Brihthelm's son called over the cold water (the warriors gave ear): 'Now is the way open before you; come quickly, men, to meet us in battle. God alone knows to whom it shall fall to hold the field.'\n\nThe wolves of slaughter pressed forward, they recked not for the water, that viking host; west over Pante, over the gleaming water they came with their bucklers, the seamen came to land with their linden shields.\n\nThere, ready to meet the foe, stood Brihtnoth and his men. He bade them form the war-hedge with their shields, and hold their ranks stoutly against the foe. The battle was now at hand, and the glory that comes in strife. Now was the time when those who were doomed should fall. Clamour arose; ravens went circling, the eagle greedy for carrion. There was a cry upon earth.\n\nThey let the spears, hard as files, fly from their hands, well-ground javelins. Bows were busy, point pierced shield; fierce was the rush of battle, warriors fell on either hand, men lay dead. Wulfm\u00e6r was wounded, he took his place among the slain; Brihtnoth's kinsman, his sister's son, was cruelly cut down with swords. Then was payment given to the vikings; I heard that Edward smote one fiercely with his blade, and spared not his stroke, so that the doomed warrior fell at his feet. For this his lord gave his chamberlain thanks when time allowed.\n\nThus the stout-hearted warriors held their ground in the fray. Eagerly they strove, those men at arms, who might be the first to take with his spear the life of some doomed man. The slain fell to the earth.\n\nThe men stood firm; Brihtnoth exhorted them, bade each warrior, who would win glory in fight against the Danes, to give his mind to war.\n\nThen came one, strong in battle; he raised his weapon, his shield to defend him, and bore down upon the man; the earl, no less resolute, advanced against the 'churl'. Each had an evil intent toward the other. Then the pirate sent a southern spear, so that the lord of warriors was stricken. He pushed with his shield so that the shaft was splintered, and shivered the spear so that it sprang back again. The warrior was enraged; he pierced with his lance the proud viking who had given him the wound. The warrior was deft; he drove his spear through the young man's neck; his hand guided it so that it took the life of his deadly foe. Quickly he shot down another, so that his corselet burst asunder; he was wounded through his mail in the breast, a poisoned point pierced his heart. The earl was the more content; then the proud man laughed, and gave thanks to his Creator for the day's work that the Lord had granted him.\n\nThen one of the warriors let a dart fly from his hand, so that it pierced all too deeply Ethelred's noble thegn. By his side stood a warrior not yet full grown, a boy in war. Right boldly he drew from the warrior the bloody spear, Wulfstan's son, Wulfm\u00e6r the young, and let the weapon, wondrous strong, speed back again; the point drove in so that he who had so cruelly pierced his lord lay dead on the ground. Then a man, all armed, approached the earl, with intent to bear off the warrior's treasure, his raiment and his rings and his well-decked sword. Then Brihtnoth drew his blade, broad and of burnished edge, and smote upon his mail. All too quickly one of the seamen checked his hand, crippling the arm of the earl. Then his golden-hilted sword fell to the earth; he could not use his hard blade nor wield a weapon. Yet still the white-haired warrior spoke as before, emboldened his men and bade the heroes press on. He could no longer now stand firm on his feet. The earl looked up to heaven and cried aloud: 'I thank thee, Ruler of Nations, for all the joys that I have met with in this world. Now I have most need, gracious Creator, that thou grant my spirit grace, that my soul may fare to thee, into thy keeping, Lord of Angels, and pass in peace. It is my prayer to thee that fiends of hell may not entreat it shamefully.'\n\nThen the heathen wretches cut him down, and both the warriors who stood near by, \u00c6lfnoth and Wulfm\u00e6r, lay overthrown; they yielded their lives at their lord's side.\n\nThen those who had no wish to be there turned from the battle. Odda's sons were first in the flight; Godric for one turned his back on war, forsook the hero who had given him many a steed. He leapt upon the horse that had been his lord's, on the trappings to which he had no right. With him his brothers both galloped away, Godwine and Godwig, they had no taste for war, but turned from the battle and made for the wood, fled to the fastness and saved their lives, and more men than was fitting at all, if they had but remembered all the favours that he had done them for their good. It was as Offa had told them on that day, at the meeting place when he held a council, that many were speaking proudly there, who later would not stand firm in time of need.\n\nNow was fallen the people's chief, Ethelred's earl. All the retainers saw how their lord lay dead. Then the proud thegns pressed on, hastened eagerly, those undaunted men. All desired one of two things, to lose their lives or to avenge the one they loved.\n\n_Maldon was not the end of Anglo-Saxon England, but it was the beginning of the end; in 1013 England finally fell to the Viking offensive of King Sweyn I \u2013 who promptly died, leaving the kingdom to his son, Cnut. (Or Canute, as the Victorians would have him.) The quick turnover of Danish rulers encouraged the exiled English King Aethelred and his son, Edmund Ironside, to launch a rebid for the country. It came close, but not close enough. At Ashingdon in 1016 Cnut decisively defeated the House of Wessex._\n\n## _Cnut and the Waves, c. 1030_\n\nHENRY OF HUNTINGDON\n\n_The Dane Cnut began his overlordship of England by marrying the matronly Emma, Aethelred's widow, and slaughtering as many Saxon claimants to the throne of England as he could lay his youthful hands on. Otherwise he left England to tick along as before; it was, after all, the most ordered (and thus most easily taxable) country in Europe._\n\n_Far from Cnut changing England, England changed Cnut \u2013 into a model Christian king. The famous story of Cnut and the waves \u2013 seemingly a long oral tradition put down on paper by Henry of Huntingdon around 1130 \u2013 was not about his arrogance but about his piety._\n\nCanute reigned for twenty years. He died at Scaftesbirh (Shaftesbury) and was buried at Winchester in the old monastery. A few facts about his reign should be briefly told, for never before him was there a king in England of such greatness. For he was lord of all Denmark, all England, all Norway and at the same time of Scotland. Over and above the number of the wars in which he was so glorious, he did three handsome and magnificent acts. Firstly, he married his daughter (Gunhild) to the Roman emperor (Henry III) with indescribable riches. Secondly, on his path to Rome (1031) he paid money and reduced by as much as a half all those evil exactions called tolls and pontages on the road which leads to Rome through France. Thirdly, at the very summit of his power, he ordered his throne to be set on the seaside when the tide was rising. He addressed the mounting waters 'You are under my sway as is the land on which is my throne and there has never been anyone who has resisted my rule without being punished. I therefore command you not to rise on to my land and you are not to dare to wet the clothes or limbs of your master.' The sea rose in the usual way and wetted the feet and legs of the monarch without showing any respect. The king accordingly leapt up and said: 'Know all inhabitants of earth, that vain and trivial is the power of kings nor is anyone worthy of the name of king save Him whose nod heaven and earth, and sea obey under laws eternal.' King Canute therefore, never again set the golden crown upon his neck but set it for ever above an image of the Lord which is nailed to a cross, in honour of God the great king. By His mercy may the soul of King Canute rest in peace.\n\n_Within five years of Cnut' s death in 1035, the royal Danish line in England ended, when Cnut's second son, Harthacnut, demised from excess of drinking'. With no obvious Danish contenders on the spot, the Witan restored the Anglo-Saxon line, and elected Aethelred's son Edward as king._\n\n_Edward_ ' _the Confessor_ ' _was king in name, but the_ de facto _ruler of England was the upstart Earl Godwine, who obliged Edward to take his (Godwine's) daughter in marriage. Edward's sly revenge was to refuse carnal relations with Edith Godwine and so deprive the Godwines of a rightful heir to the throne._\n\n_Edward's drastic chastity had profound implications for English history. With no blood heir to follow him, he willed his throne to William the Bastard, Duke of Normandy._\n\n_The king's sexual abstinence at least helped his reputation for saintliness. 'The Confessor_ ' _was the originator of the curing 'royal touch', his piety the cause of the construction of the greatest church in England, Westminster Abbey, consecrated in 1065._\n\n## _The Battle of Hastings, 14 October 1066_\n\nWILLIAM OF POITIERS\n\n_With the death of the childless Edward the Confessor on 5 January 1066, the Witan elected Harold Godwineson to the throne of England, largely perforce of his being the mightiest Saxon earl in the place. The new king hastily issued coinage with 'PAX' writ large on the face. Peace, though, was not the sentiment on the minds of Duke William of Normandy or Hardrada of Norway, both of whom claimed the English throne. After a lightning march north which covered 190 miles in five days Harold met and bested Hardrada (aided by Harold's own, alienated brother, Tostig) at Stamford Bridge, Yorkshire, on 25 September. The victory party was short-lived. On 29 September Duke William landed at Pevensey on the south coast, and back down England Harold rushed._\n\n_There are no direct eye-witness accounts of the Norman invasion but William of Poitiers was in an unrivalled position as chronicler. He was Duke William's chaplain, and compiled his account of the battle of Hastings in Sussex from post-battle interviews with Norman combatants._\n\n... the English... took up their position on higher ground, on a hill abutting the forest through which they had just come. There, at once dismounting from their horses, they drew themselves up on foot and in very close order. The duke and his men in no way dismayed by the difficulty of the ground came slowly up the hill, and the terrible sound of trumpets on both sides signalled the beginning of the battle. The eager boldness of the Normans gave them the advantage of attack, even as in a trial for theft it is the prosecuting counsel who speaks first. In such wise the Norman foot drawing nearer provoked the English by raining death and wounds upon them with their missiles. But the English resisted valiantly, each man according to his strength, and they hurled back spears and javelins and weapons of all kinds together with axes and stones fastened to pieces of wood. You would have thought to see our men overwhelmed by this death-dealing weight of projectiles. The knights came after the chief, being in the rearmost rank, and all disdaining to fight at long range were eager to use their swords. The shouts both of the Normans and of the barbarians were drowned in the clash of arms and by the cries of the dying, and for a long time the battle raged with the utmost fury. The English, however, had the advantage of the ground and profited by remaining within their position in close order. They gained further superiority from their numbers, from the impregnable front which they preserved, and most of all from the manner in which their weapons found easy passage through the shields and armour of their enemies. Thus they bravely withstood and successfully repulsed those who were engaging them at close quarters, and inflicted losses upon the men who were shooting missiles at them from a distance. Then the foot-soldiers and the Breton knights, panic-stricken by the violence of the assault, broke in flight before the English and also the auxiliary troops on the left wing, and the whole army of the duke was in danger of retreat. This may be said without disparagement to the unconquerable Norman race. The army of the Roman emperor, containing the soldiers of kings accustomed to victory on sea and land, sometimes fled on the report, true or false, that their leader was dead. And in this case the Normans believed that their duke and lord was killed. Their flight was thus not so much shameful as sad, for their leader was their greatest solace.\n\nSeeing a large part of the hostile host pursuing his own troops, the prince thrust himself in front of those in flight, shouting at them and threatening them with his spear. Staying their retreat, he took off his helmet, and standing before them bareheaded he cried: 'Look at me well. I am still alive and by the grace of God I shall yet prove victor. What is this madness which makes you fly, and what way is open for your retreat? You are allowing yourselves to be pursued and killed by men whom you could slaughter like cattle. You are throwing away victory and lasting glory, rushing into ruin and incurring abiding disgrace. And all for naught since by flight none of you can escape destruction.' With these words he restored their courage, and, leaping to the front and wielding his death-dealing sword, he defied the enemy who merited death for their disloyalty to him their prince. Inflamed by his ardour the Normans then surrounded several thousands of their pursuers and rapidly cut them down so that not one escaped. Heartened by this success, they then furiously carried their attack on to the main body of the English host, which even after their losses scarcely seemed diminished in number. The English fought confidently with all their strength, striving in particular to prevent the attackers from penetrating within their ranks, which indeed were so closely massed together that even the dead had not space in which to fall. The swords of the bravest warriors hewed a gap in some places, and there they were followed by the men of Maine, by the French, by the Bretons and the men of Aquitaine, and by the Normans who showed the greatest valour...\n\nRealising that they could not without severe loss overcome an army massed so strongly in close formation, the Normans and their allies feigned flight and simulated a retreat, for they recalled that only a short while ago their flight had given them an advantage. The barbarians thinking victory within their grasp shouted with triumph, and heaping insults upon our men, threatened utterly to destroy them. Several thousand of them, as before, gave rapid pursuit to those whom they thought to be in flight; but the Normans suddenly wheeling their horses surrounded them and cut down their pursuers so that not one was left alive. Twice was this ruse employed with the utmost success, and then they attacked those that remained with redoubled fury. This army was still formidable and very difficult to overwhelm. Indeed this was a battle of a new type: one side vigorously attacking; the other resisting as if rooted to the ground. At last the English began to weary, and as if confessing their crime in their defeat they submitted to their punishment. The Normans threw and struck and pierced. The movements of those who were cut down to death appeared greater than that of the living; and those who were lightly wounded could not escape because of the density of their formation but were crushed in the throng. Thus fortune crowned the triumph of William.\n\nThere were present in this battle: Eustace, count of Boulogne; William, son of Richard, count of Evreux; Geoffrey, son of Rotrou, count of Mortagne; William fitz Osbern; Haimo, _vicomte_ of Thouars; Walter Giffard; Hughe of Montfort-sur-Risle; Rodulf of Tosny; Hugh of Grantmesnil; William of Warenne; and many other most renowned warriors whose names are worthy to be commemorated in histories among the bravest soldiers of all time. But Duke William excelled them all both in bravery and soldier-craft, so that one might esteem him as at least the equal of the most praised generals of ancient Greece and Rome. He dominated this battle, checking his own men in flight, strengthening their spirit, and sharing their dangers. He bade them come with him, more often than he ordered them to go in front of him. Thus it may be understood how he led them by his valour and gave them courage. At the mere sight of this wonderful and redoubtable knight, many of his enemies lost heart even before they received a scratch. Thrice his horse fell under him; thrice he leapt upon the ground; and thrice he quickly avenged the death of his steed. It was here that one could see his prowess, and mark at once the strength of his arm and the height of his spirit. His sharp sword pierced shields, helmets and armour, and not a few felt the weight of his shield. His knights seeing him thus fight on foot were filled with wonder, and although many were wounded they took new heart. Some weakened by loss of blood went on resisting, supported by their shields, and others unable themselves to carry on the struggle, urged on their comrades by voice and gesture to follow the duke. 'Surely,' they cried, 'you will not let victory slip from your hands.' William himself came to the rescue of many...\n\nEvening was now falling, and the English saw that they could not hold out much longer against the Normans. They knew they had lost a great part of their army, and they knew also that their king with two of his brothers and many of their greatest men had fallen. Those who remained were almost exhausted, and they realised that they could expect no more help. They saw the Normans, whose numbers had not been much diminished, attack them with even greater fury than at the beginning of the battle, as if the day's fighting had actually increased their vigour. Dismayed at the implacable bearing of the duke who spared none who came against him and whose prowess could not rest until victory was won, they began to fly as swiftly as they could, some on horseback, some on foot, some along the roads, but most over the trackless country. Many lay on the ground bathed in blood, others who struggled to their feet found themselves too weak to escape, while a few, although disabled, were given strength to move by fear. Many left their corpses in the depths of the forest, and others were found by their pursuers lying by the roadside. Although ignorant of the countryside the Normans eagerly carried on the pursuit, and striking the rebels in the back brought a happy end to this famous victory. Many fallen to the ground were trampled to death under the hooves of runaway horses.\n\nBut some of those who retreated took courage to renew the struggle on more favourable ground. This was a steep valley intersected with ditches. These people, descended from the ancient Saxons (the fiercest of men), are always by nature eager for battle, and they could only be brought down by the greatest valour. Had they not recently defeated with ease the king of Norway at the head of a fine army?\n\nThe duke who was following the victorious standards did not turn from his course when he saw these enemy troops rallying. Although he thought that reinforcements had joined his foes he stood firm. Armed only with a broken lance he was more formidable than others who brandished long javelins. With a harsh voice he called to Eustace of Boulogne, who with fifty knights was turning in flight, and was about to give the signal for retreat. This man came up to the duke and said in his ear that he ought to retire since he would court death if he went forward. But at the very moment when he uttered the words Eustace was struck between the shoulders with such force that blood gushed out from his mouth and nose, and half dead he only made his escape with the aid of his followers. The duke, however, who was superior to all fear and dishonour, attacked and beat back his enemies. In this dangerous phase of the battle many Norman nobles were killed since the nature of the ground did not permit them to display their prowess to full advantage.\n\nHaving thus regained his superiority, the duke returned to the main battlefield, and he could not gaze without pity on the carnage, although the slain were evil men, and although it is good and glorious in a just war to kill a tyrant. The bloodstained battle-ground was covered with the flower of the youth and nobility of England. The two brothers of the king were found near him, and Harold himself stripped of all badges of honour could not be identified by his face, but only by certain marks on his body. His corpse was brought into the duke's camp, and William gave it for burial to William, surnamed Malet, and not to Harold's mother, who offered for the body of her beloved son its weight in gold. For the duke thought it unseemly to receive money for such merchandise, and equally he considered it wrong that Harold should be buried as his mother wished, since so many men lay unburied because of his avarice. They said in jest that he who had guarded the coast with such insensate zeal should be buried by the seashore...\n\n_From Hastings William sent his army on a fire-and-sword circuit of London, where the last English resistance had gathered. London got William's scorched-earth message._\n\n## _The Coronation of William the Conqueror, Christmas Day 1066_\n\nORDERIC VITALIS\n\n_William's coronation took place in Westminster Abbey, London. Orderic Vitalis, befitting his half-Norman, half-English blood, was the most balanced of the contemporary chroniclers._\n\nSo at last on Christmas Day in the year of Our Lord 1067, the fifth Indiction, the English assembled at London for the king's coronation, and a strong guard of Norman men-at-arms and knights was posted round the minster to prevent any treachery or disorder. And, in the presence of the bishops, abbots, and nobles of the whole realm of Albion, Archbishop Ealdred consecrated William duke of Normandy as king of the English and placed the royal crown on his head. This was done in the abbey church of St Peter the chief of the apostles, called Westminster, where the body of King Edward lies honourably buried.\n\nBut at the prompting of the devil, who hates everything good, a sudden disaster and portent of future catastrophes occurred. For when Archbishop Ealdred asked the English, and Geoffrey bishop of Coutances asked the Normans, if they would accept William as their king, all of them gladly shouted out with one voice if not in one language that they would. The armed guard outside, hearing the tumult of the joyful crowd in the church and the harsh accents of a foreign tongue, imagined that some treachery was afoot, and rashly set fire to some of the buildings. The fire spread rapidly from house to house; the crowd who had been rejoicing in the church took fright and throngs of men and women of every rank and condition rushed out of the church in frantic haste. Only the bishops and a few clergy and monks remained, terrified, in the sanctuary, and with difficulty completed the consecration of the king who was trembling from head to foot. Almost all the rest made for the scene of conflagration, some to fight the flames and many others hoping to find loot for themselves in the general confusion. The English, after hearing of the perpetration of such misdeeds, never again trusted the Normans who seemed to have betrayed them, but nursed their anger and bided their time to take revenge.\n\n_It was not often that William the Bastard was seen trembling 'from head to foot'._\n\n_William had the crown of England on his head, but not quite the kingdom in his hand. For the first five years of his reign he faced almost annual rebellions by the English and almost annual landings by the Danes._\n\n## _The Harrying of the North, 1069\u201470_\n\nORDERIC VITALIS\n\n_In 1069 York opened its gates to the Danes of Sweyn II as their liberators from Norman rule. To quell the insurrection William used his favourite weapons: the fire and the sword._\n\nSo at last they [William's army] approached York only to learn that the Danes had fled. The king assigned officers and castellans with armed retainers to repair the castles in the city, and left others on the bank of the Humber to ward off the Danes. He himself continued to comb forests and remote mountainous places, stopping at nothing to hunt out the enemy hidden there. His camps were spread out over an area of a hundred miles. He cut down many in his vengeance; destroyed the lairs of others; harried the land, and burned homes to ashes. Nowhere else had William shown such cruelty. Shamefully he succumbed to this vice, for he made no effort to restrain his fury and punished the innocent with the guilty. In his anger he commanded that all crops and herds, chattels and food of every kind should be brought together and burned to ashes with consuming fire, so that the whole region north of Humber might be stripped of all means of sustenance. In consequence so serious a scarcity was felt in England, and so terrible a famine fell upon the humble and defenceless populace, that more than 100,000 Christian folk of both sexes, young and old alike, perished of hunger. My narrative has frequently had occasion to praise William, but for this act which condemned the innocent and guilty alike to die by slow starvation I cannot commend him. For when I think of helpless children, young men in the prime of life, and hoary greybeards perishing alike of hunger I am so moved to pity that I would rather lament the griefs and sufferings of the wretched people than make a vain attempt to flatter the perpetrator of such infamy...\n\nIn the midst of the fighting William sent to the city of Winchester for his crown and other royal insignia and plate, left his army in camp, and came to York to celebrate Christmas there. He learned that another enemy band was lying hidden in a narrow neck of land sheltered on all sides by sea or marshes. It could be reached only by one narrow causeway, no more than twenty feet wide. They had laid in ample supplies and believed themselves safe, regarding their position as impregnable. In spite of this, on learning that a royal force was approaching, they instantly fled away by night. The king, raging, pursued his bitter enemies to the river Tees, forcing his way through trackless wastes, over ground so rough that he was frequently compelled to go on foot. He spent fifteen days encamped on the bank of the Tees. There Waltheof and Gospatric submitted to him and took oaths of fealty, Waltheof in person and Gospatric by proxies. Their recent allies the Danes were now in grave peril as wandering pirates, at the mercy of winds and waves. They suffered as much from hunger as from storms. Some perished through shipwreck. The remainder sustained life with vile pottage; princes, earls, and bishops being no better off than the common soldiers. Their supplies of meat \u2013 even of the rancid and putrid flesh they had long been eating \u2013 were completely exhausted. They dared not venture out to seek plunder, or even come to shore for fear of the inhabitants. Finally, the meagre remnants of the great fleet returned to Denmark and told King Swein the woeful story of all the hazards they had endured, the terrible savagery of the enemy, and the loss of their comrades.\n\n_Everywhere across the land the 10,000 accomplices of William built thick-walled stone castles and sat it out against the truculent 1.75 million English. The Normans persisted \u2013 despite the statistical odds \u2013 because they wanted their reward for victory: the entire green and pleasant land of England itself. To give it to them William confiscated \u2013 with scarcely an exception \u2013 the holdings of the 4,000 Saxon_ thegns. _In one fell stroke the old English aristocracy was destroyed._\n\n_By 1085 William had secured England from his enemies within and without. There remained only for him to investigate its financial worth._\n\n## _The Domesday Inquisition, 1085\u20136_\n\n_THE ANGLO-SAXON CHRONICLE_\n\n_So complete was William's inquisition of England that the subjugated English were put in mind of the Day of Judgement, hence their nickname for the register:_ 'The Domesdei [Doom's Day] Book'.\n\nFor Christmas, the King was at Gloucester with his nobles and held his court there for five days; afterwards the Archbishop and Clergy held a synod for three days. Present were Maurice, Bishop-elect of London, William of Norfolk, and Robert of Chester; all these were the King's clerks. Afterwards the King held his Great Council, and had deep speech with his nobles about this land, as to how and by what manner of men it was inhabited. He sent, therefore, into every County throughout the whole of England ministers of his with orders to investigate how many hundred hides there were in each County, and how much land and cattle the King himself had in that County; and how much in annual revenue he ought to enjoy from that County. He ordered also to be entered the quantity of land held by his Archbishops, Diocesan Bishops, Abbots, and Earls; and, to be brief, what and how much each person, who had lands in the English nation, possessed, whether in lands or in cattle, and how much it was worth in money. So diligently did he have the land surveyed, that not a single hide or virgate of land, and not even (though it is a shame to say what he thought it no shame to do) a single ox or cow or pig was omitted and not returned in the reckoning, and all these writings were afterwards brought to him.\n\n## _The Domesday Assessment of Cumnor, 1086_\n\nANONYMOUS\n\n_The Domesday Inquisition was arranged by holders of land, rather than by area, and allowed King William to tax his subjects directly. Here is the Abbey of Abbendone's (Abingdon's) holding at Cominore (Cumnor), a village in Berkshire._\n\nThe Abbey of Abbendone holds Cominore. It has belonged to the Abbey T.R.E.,* and always it was assessed at fifty hides,\u2020 now at thirty hides. There is land for fifty ploughs. On the demesne are nine ploughs; and there are sixty villeins\u2021 and sixty-nine bordars with twenty-six ploughs. There are four serfs\u00b6 and two mills worth fifty shillings; and from the fisheries is yielded forty shillings; and there are two hundred acres of meadow. There is a church. T.R.E. it was worth thirty pounds; and afterwards, as now, fifty pounds.\n\nOf these fifty hides Anschil holds five. Norman held them T.R.E. as one manor. It is called Seuacoorde, and he could not go to what lord he wished. It paid geld for five hides with the others above mentioned. There is land for seven ploughs. On the demesne are two ploughs; and twelve villeins and fifteen bordars with five ploughs. T.R.E. it was worth a hundred shillings; and afterwards seventy shillings; now eight pounds.\n\n_For anyone who cared to peruse_ Domesday Book's _two volumes a statistical picture of England was revealed. The cold proof of the demise of the Saxon aristocracy was found in the number of surviving Saxon_ thegns _of any standing. Two. Of the rest of the population, go per cent were peasants who were bound to their Norman overlord to provide labour in peace and foot-soldiering in war. This feudal' socio-economic system had been extant in England for centuries, but whereas_ thegn _and_ ceorl _had been tied by communality and law, the Norman and his Saxon peasant were tied by obligation in law alone. There was nothing intimate in the Norman class system._\n\n_As for William himself, he barely lived long enough to profit from his Domesday Inquisition._\n\n## _An Estimate of William the Conqueror at His Death, 1087_\n\n_THE ANGLO-SAXON CHRONICLE_\n\n_Aged sixty-one and gone to fat, William fell against the pommel of his saddle during the sack of Mantes (France) and ruptured an internal organ. His servants stripped his body and it was left abandoned until a pitying local knight took it for burial. When forced into the sarcophagus, William's cadaver split, filling the church with a foul smell._\n\n_On William's demise, the chroniclers penned an estimation of the man and his reign:_\n\nWhat can I say? That bitter death that spares neither high nor low seized him. He died in Normandy on the day following the Nativity of St Mary (9 September), and was buried at Caen in the abbey of St Stephen, which he had formerly built and afterwards endowed in various ways.\n\nAlas! how deceitful and transitory is the prosperity of this world. He who was once a mighty king, and lord of many a land, was left of all the land with nothing save seven feet of ground: and he who was once decked with gold and jewels, lay then covered over with earth.\n\nHe left behind him three sons. The eldest was called Robert, who became duke of Normandy after him. The second was called William, who wore the royal crown in England after him. The third was called Henry, to whom his father bequeathed treasures innumerable.\n\nIf anyone desires to know what kind of man he was or in what honour he was held or how many lands he was lord over, then shall we write of him as we have known him, who have ourselves seen him and at one time dwelt in his court. King William, of whom we speak, was a man of great wisdom and power, and surpassed in honour and in strength all those who had gone before him. Though stern beyond measure to those who opposed his will, he was kind to those good men who loved God. On the very spot where God granted him the conquest of England he caused a great abbey to be built; and settled monks in it and richly endowed it. During his reign was built the great cathedral at Canterbury, and many another throughout all England. This land too was filled with monks living their lives after the rule of St Benedict. Such was the state of religion in his time that every man who wished to, whatever considerations there might be with regard to his rank, could follow the profession of a monk.\n\nMoreover he kept a great state. He wore his royal crown three times a year as often as he was in England: at Easter at Winchester, at Whitsuntide at Westminster, at Christmas at Gloucester. On these occasions all the great men of England were assembled about him: archbishops, bishops, abbots, earls, thanes, and knights. He was so stern and relentless a man that no one dared do aught against his will. Earls who resisted his will he held in bondage. Bishops he deprived of their sees and abbots of their abbacies, while rebellious thanes he cast into prison, and finally his own brother he did not spare. His name was Odo. He was a powerful bishop in Normandy, and Bayeux was his episcopal see; he was the foremost man after the king. He had an earldom in England, and was master of the land when the king was in Normandy. William put him in prison. Among other things we must not forget the good order he kept in the land, so that a man of any substance could travel unmolested throughout the country with his bosom full of gold. No man dared to slay another, no matter what evil the other might have done him. If a man lay with a woman against her will, he was forthwith condemned to forfeit those members with which he had disported himself.\n\nHe ruled over England, and by his foresight it was surveyed so carefully that there was not a 'hide' of land in England of which he did not know who held it and how much it was worth; and these particulars he set down in his survey. Wales was in his domain, in which country he built castles and so kept its people in subjection. Scotland also he reduced to subjection by his great strength. Normandy was his by right of birth, while he also ruled over the county called Maine. If he had lived only two years more he would have conquered Ireland by his astuteness and without any display of force. Assuredly in his time men suffered grievous oppression and manifold injuries.\n\nHe caused castles to be built\n\nWhich were a sore burden to the poor.\n\nA hard man was the king\n\nAnd took from his subjects many marks\n\nIn gold and many more hundreds of pounds in silver.\n\nThese sums he took by weight from his people,\n\nMost unjustly and for little need.\n\nHe was sunk in greed\n\nAnd utterly given up to avarice.\n\nHe set apart a vast deer preserve and imposed laws concerning it.\n\nWhoever slew a hart or a hind\n\nWas to be blinded.\n\nHe forbade the killing of boars\n\nEven as the killing of harts.\n\nFor he loved the stags as dearly\n\nAs though he had been their father.\n\nHares, also, he decreed should go unmolested.\n\nThe rich complained and the poor lamented,\n\nBut he was too relentless to care though all might hate him,\n\nAnd they were compelled, if they wanted\n\nTo keep their lives and their lands\n\nAnd their goods and the favour of the king.\n\nTo submit themselves wholly to his will.\n\nAlas! that any man should bear himself so proudly\n\nAnd deem himself exalted above all other men!\n\nMay Almighty God shew mercy to his soul\n\nAnd pardon him his sins.\n\nWe have set down these things about him, both the good and the evil, so that men may cherish the good and utterly eschew the evil, and follow the path that leads us to the Kingdom of Heaven.\n\n_King William was succeeded on the throne of England by his son William II (invariably known as William Rufus on account of his florid complexion), who ruled the kingdom with brutal and avaricious efficiency for thirteen years. His end was premature \u2013 he was killed in a hunting accident in the New Forest, the great and unpopular game preserve created by his father. William of Malmesbury caught the popular reckoning of William Rufus in his_ Chronicles of the Kings of England; _'He was a man much to be pitied by the clergy for throwing away a soul which they could not save. He earned the love of hired soldiers for he was lavish in his gifts to them. But by the common people he was not mourned because he allowed them to be plundered. '_\n\n_With scarcely a moist fraternal eye, Rufus' younger brother Henry galloped off to have the Bishop of London crown him King of England (instead of elder brother Robert Curthose, Duke of Normandy) in a short-notice coronation. Having shamelessly seized power, Henry I was no less brazen about buying the support he needed to maintain his elevated station: he deftly issued a charter of liberties (in which 'the Lion of Justice' limited his own power over his subjects)and married Edith, of the House of Wessex, so that his offspring would have both Norman and English blood. When the Normans choked on the miscegenation, Henry changed Edith's name to the francophone Matilda._\n\n_Henry I thus had his father's political genius for ruling \u2013 and his dynastic vision, too. In 1106 he defeated Robert Curthose at Tinchebrai to gain control of Normandy and reunite his father's Anglo-Norman empire. He sired scores of bastards but only one legitimate son._\n\n_In 1120 Henry's carefully planned dynasty was sunk in the English Channel._\n\n## _The Loss of the_ White Ship, _25 November 1120_\n\nORDERIC VITALIS\n\n_The_ White Ship _disaster was the_ Titanic _of the Middle Ages. Lost with the_ White Ship _was Henry I's heir William, 'educated and destined to the succession'. Orderic Vitalis was wrong in stating that the tragedy occurred under a full moon; it was a new one._\n\nOn 25 November, when a great fleet had been fitted out in the port of Barfleur, and a body of noble knights of the king's company had assembled while a south wind blew, the king and earls embarked in the first watch of the night, hoisted their sails to catch the wind, and put to sea. In the morning those whom God allowed to do so landed in England.\n\nA terrible disaster occurred during that voyage, which was the cause of deep mourning and countless tears. Thomas, son of Stephen, went to the king and offered him a mark of gold, saying, 'Stephen son of Airard was my father, and he served your father at sea during his lifetime, for he carried him in his ship to England when he set out for England to fight against Harold. He earned your father's favour by performing this service for him to the end of his days, and received many gifts from him which raised him to high honour among his companions. I ask you, my lord king, to grant me this fief: I have a vessel which is aptly called the _White Ship_ , excellently fitted out and ready for the royal service.' To this the king replied, 'Your request meets with my approval. I have indeed chosen a fine ship for myself and will not change it; but I entrust to you my sons William and Richard, whom I love as my own life, and many nobles of my realm.' On hearing this the sailors were delighted, and fawned on the king's son, asking him for wine to drink. He ordered three muids of wine to be given to them. They received these, drank, and gave to their companions to drink their fill; too much drinking made them tipsy. At the king's command a great many barons embarked in the ship with his sons; I believe there were about three hundred in the ill-fated vessel. However, two monks of Tiron and Count Stephen with two knights, also William of Roumare, Rabel the chamberlain, Edward of Salisbury, and a number of others disembarked, because they realized that there was too great a crowd of wild and headstrong young men on board. There were fifty experienced rowers there, and high-spirited marine guards who had already found seats in the boat were showing off and, too drunk to know what they were doing, were paying respect to almost no one. Alas, how many of them had in their hearts no filial reverence for God, who tempers the raging fury of sea and wind. So when the priests came there with other ministers carrying holy water to bless them, they laughed and drove them away with abuse and guffaws. All too soon they were punished for their disrespect. Apart from the king's treasure and the casks of wine Thomas's boat carried only passengers, and they commanded him to try to overtake the king's fleet, which was already sailing in the open sea. As his judgement was impaired by drink, he trusted in his skill and that of his crew, and recklessly vowed to leave behind all those who had started first. At length he gave the signal to put to sea. Then the rowers made haste to take up their oars and, in high spirits because they knew nothing of what lay ahead, put the rest of the equipment ready and made the ship leap forward and race through the sea. As the drunken oarsmen were rowing with all their might, and the luckless helmsman paid scant attention to steering the ship through the sea, the port side of the _White Ship_ struck violently against a huge rock, which was uncovered each day as the tide ebbed and covered once more at high tide. Two planks were shattered and, terrible to relate, the ship capsized without warning. Everyone cried out at once in their great peril, but the water pouring into the boat soon drowned their cries and all alike perished. Only two men grabbed hold of a spar from which the sail hung and, clinging to it for the greater part of the night, waited for help to come from any quarter. One was a butcher of Rouen named Berold, and the other a noble lad called Geoffrey, the son of Gilbert of Laigle.\n\nAt that time the moon was in the nineteenth day of the sign of the Bull, and its rays lit up the world for about nine hours, showing up everything in the sea to the mariners. Thomas, the skipper, gathered his strength after sinking for the first time and, remembering his duty, lifted his head as he came to the surface; seeing the heads of the men who were clinging somehow to the spar, he asked, 'The king's son \u2013 what has become of him?' When the shipwrecked men replied that he had perished with all his companions, he said, 'It is vain for me to go on living.' With these words, in utter despair, he chose rather to sink on the spot than to die beneath the wrath of a king enraged by the loss of his sons, or suffer long years of punishment in fetters. The men clinging to the spar called on God in the waters, trying to keep up each other's spirits, and waited trembling for the fate that God had in store for them.\n\nThe night was frosty, so that the young man, after enduring the bitter cold for a long time, finally lost his grip and, commending his companion to God, fell back to perish in the sea and was never seen again. But Berold, who was the poorest of all and was dressed in a pelisse made of rams' skins, was the only one of the great company to see the day. In the morning he was taken aboard a light vessel by three fishermen and reached dry land alone. Later, when he was somewhat revived, he told the whole sad tale to those who wished to learn, and subsequently lived for about twenty years in good health.\n\nRoger, bishop of Coutances, had accompanied his son William (whom the king had already made one of his four chief chaplains), his brother, and three distinguished nephews to the ship condemned by God to destruction, and had given them and their fellows a bishop's blessing though they made light of it. He and many others who were still standing together on the shore, as well as the king and his companions who were already far out to sea, heard the terrible cries of the doomed men, but, not knowing the cause until the next day, marvelled at it and asked one another what it could mean.\n\nThe sad news spread swiftly from mouth to mouth through the crowds along the sea coast, and came to the ears of Count Theobald and other nobles of the court; but that day no one dared announce it to the anxious king, who earnestly asked for news. The magnates wept bitterly in private and mourned inconsolably for their loved kinsfolk and friends, but in the king's presence they struggled to restrain their tears to avoid betraying the cause of their distress. However, on the following day, by a wise plan of Count Theobald's, a boy threw himself, weeping, at the king's feet, and the king learned from him that the cause of his grief was the wreck of the _White Ship._ Immediately Henry fell to the ground overcome with anguish, and after being helped to his feet by friends and led into a private room, gave way to bitter laments.\n\n_The loss of the_ White Ship _left Henry's daughter, Matilda, as his only direct legitimate heir. At the royal council of Christmas 1126 Henry made the bishops, abbots and barons accept Matilda as heir to the Anglo-Norman throne._\n\n_To little avail._\n\n## _The Anarchy, 1137\u201354_\n\n_THE ANGLO-SAXON CHRONICLE_\n\n_On Henry I's death in December 1135 (after eating a meal of lampreys, against doctor's orders), his daughter and successor Matilda was out of the kingdom. On to the temptingly vacant throne leapt Henry's nephew, Stephen of Blois. Most of the baronage supported him; Matilda was widely loathed (she haughtily insisted on being called 'Empress'), as was her Plantagenet second husband, Geoffrey d'Anjou._\n\n_Matilda had no intention of relinquishing her inheritance, and civil war was joined. With the monarchy fighting itself, England's barons sniffed the opportunity to aggrandize power._ The Anglo-Saxon Chronicle _gloomily recorded:_\n\n1137. This year King Stephen went over sea to Normandy, and he was received there because it was expected that he would be altogether like his uncle, and because he had gotten possession of his treasure, but this he distributed and scattered foolishly. King Henry had gathered together much gold and silver, yet did he no good for his soul's sake with the same. When king Stephen came to England, he held an assembly at Oxford; and there he seized Roger bishop of Salisbury, and Alexander bishop of Lincoln, and Roger the chancellor, his nephew, and he kept them all in prison till they gave up their castles. When the traitors perceived that he was a mild man, and a soft, and a good, and that he did not enforce justice, they did all wonder. They had done homage to him, and sworn oaths, but they no faith kept; all became forsworn, and broke their allegiance, for every rich man built his castles, and defended them against him, and they filled the land full of castles. They greatly oppressed the wretched people by making them work at these castles, and when the castles were finished they filled them with devils and evil men. Then they took those whom they suspected to have any goods, by night and by day, seizing both men and women, and they put them in prison for their gold and silver, and tortured them with pains unspeakable, for never were any martyrs tormented as these were.... Many thousands they exhausted with hunger. I cannot and I may not tell of all the wounds, and all the tortures that they inflicted upon the wretched men of this land; and this state of things lasted the nineteen years that Stephen was king, and ever grew worse and worse. They were continually levying an exaction from the towns, which they called Tenserie, and when the miserable inhabitants had no more to give, then plundered they, and burnt all the towns, so that well mightest thou walk a whole day's journey nor ever shouldest thou find a man seated in a town, or its lands tilled.\n\nThen was corn dear, and flesh and cheese, and butter, for there was none in the land \u2013 wretched men starved with hunger \u2013 some lived on alms who had been erewhile rich: some fled the country \u2013 never was there more misery, and never acted heathens worse than these. At length they spared neither church nor churchyard, but they took all that was valuable therein, and then burned the church and all together. Neither did they spare the lands of bishops, nor of abbats, nor of priests; but they robbed the monks and the clergy, and every man plundered his neighbour as much as he could. If two or three men came riding to a town, all the township fled before them, and thought that they were robbers. The bishops and clergy were ever cursing them, but this to them was nothing, for they were all accursed and forsworn, and reprobate. The earth bare no corn, you might as well have tilled the sea, for the land was all ruined by such deeds, and it was said openly that Christ and his saints slept. These things, and more than we can say, did we suffer during nineteen years because of our sins...\n\n_After a decade of reverses Matilda's regal hopes passed from herself to her teenage son, Henry Plantagenet. In 1152 the eighteen-year-old Henry was astutely married off to Eleanor of Aquitaine, recently on the international marriage market after her divorce from Louis VII of France. Eleanor was thirty, secondhand and childless (although she blamed Louis VII for that: 'more monk than king', she said). She was also black-eyed, beautiful and rich enough to pay for Henry to invade England._\n\n_Within a year of his marriage Henry crossed the Channel, armed to the teeth with money and levies; his own from Normandy and Anjou, Eleanor's from Aquitaine._\n\n_King Stephen had little heart for more fighting. He had recently lost his son, and his health was gone. A treaty was achieved with Henry at Westminster: Stephen would stay on the throne until his death, on condition that he namedHenry his rightful heir. A bare year later, on 19 December 1154, in the first undisputed succession to the throne for over a century, Henry II was crowned King of England, Eleanor by his side._\n\n## _The Virtues and Vices of Henry II, 1154\u201389_\n\nWALTER MAP\n\n_Map was one of Henry II's counsellors._\n\nI witnessed the beginnings of his reign and the following years in which his life was praiseworthy in many things. He was a little over medium height, a man blest with sound limbs and a handsome countenance, one upon whom men gazed closely a thousand times, yet took occasion to return. In physical capacity he was second to none, capable of any activity which another could perform, lacking no courtesy, well read to a degree both seemly and profitable, having a knowledge of all tongues spoken from the coasts of France to the river Jordan, but making use only of Latin and French. In making laws and in ordering the affairs of government he showed discrimination, and was clever in devising new and undiscovered legal procedures; he was easy of approach, modest and humble; the discomforts of dust and mire he suffered patiently; though vexed by the importunity of suitors and litigants and provoked by injustice, he bore all in silence. Nevertheless he was ever on his travels, moving by intolerable stages like a courier, and in this respect he showed little mercy to his household which accompanied him. He had great experience of dogs and birds and was a very keen follower of hounds; in night-watches and labours he was unremitting. As often as the vain images of pleasure disturbed his slumbers, he used to revile his body, because neither labour nor abstinence availed to break or weaken it. I, however, used to ascribe his distresses not to his infidelities but to his fear of growing too plump...\n\n... Moreover the said King Henry II was distinguished for many virtues and infamous for some vices. One fault he derived from his mother's teaching, as I have said before, is this. He was dilatory in settling the affairs of his subjects, whence it befell that many died before they could bring their suits to a conclusion, or withdrew from court sorrowful and empty-handed, impelled by hunger. Another fault was that when he was taking his ease, which was seldom, he did not permit himself to be seen as good men desired, but, shutting himself up within doors, he was accessible only to those who seemed unworthy of such approach. A third fault was that, impatient of repose, he did not scruple to disturb almost half Christendom. In these three respects he erred; yet in others he was exceedingly good and lovable. No man surpassed him in gentleness and friendliness. As often as he went abroad he was seized by the crowd, carried about by force from place to place whither he would not, and what is remarkable, he gave ear patiently to each man singly, and though assailed at one time by the shouts of the mob, and at another violently dragged and pushed about, yet for this he brought no charge against any man nor used it as an excuse for anger. When he was too hard pressed he fled in silence to havens of peace. He did naught insolently or pompously, but was temperate, moderate and virtuous, faithful and wise, liberal and victorious, bringing honour on good men.\n\nI lately crossed the Channel with him in a fleet of twenty-five vessels, reserved for his crossing without charge. But a storm scattered them all and drove them upon rocks and shores inhospitable to ships, with the exception of his own ship which, by God's grace, was brought safely to port. In the morning therefore the king sent and recompensed each sailor according to the estimate of his loss, although he was not bound to do this, and the total sum was large. Perchance another king would not have paid this just debt.\n\n_The energetic first Angevin King of England immediately razed the crop of baronial fortresses which had mushroomed over the country in the dark days of the Anarchy, before reforming the legal system (trial by twelve-man jury, begun in Aethelred's reign, became standard in Henry's) and cowing Scotland into paying him homage. Ireland was invaded and sufficiently occupied for Henry to apportion it to his youngest son._\n\n_Henry Plantagenet turned England into a model medieval monarchy. But it is not for his regal powers and legal glories that he is remembered._\n\n_It is for inciting the murder of a Churchman._\n\n## _The Murder of Thomas-\u00e0-Becket, Canterbury, 29 December 1170_\n\nEDWARD GRIM\n\n_Thomas-\u00e0-Becket was born into a London family on the make. Like the sons of other_ arrivistes, _he was sent off for a career in the Church, the best fast-track upwards in medieval society. In 1155_ , _at the age of thirty-seven, he became Henry II's Chancellor, the first Englishman to hold high office since the Conquest. He also became Henry's closest friend. In 1162 Henry created Becket Archbishop of Canterbury. To Henry's chagrin, Becket in his new office became a zealous ecclesiast, and opposed Henry's attempt under the 'Constitutions of Clarendon' to enable lay courts to try clergy. The issue of 'criminous clerks' hid a bigger question: was the Church separate to the state or part of it?_\n\n_Eventually Becket's intransigence caused Henry II to roar out the legendary invitation: 'Will no one rid me of this turbulent priest?' (More accurately, the king bellowed: 'What miserable drones and traitors have I nourished and brought up in my household who allow their lord to be treated with such shameful contempt by a low-born cleric!') Four knights \u2013 Hugh de Morville, Reginald fitzUrse, Richard le Breton and William de Tracy \u2013 took Henry's outburst as their cue to murder the fifty-two-year-old Becket in his cathedral._\n\n_Grim was Becket's attendant._\n\nWhen the holy archbishop entered the church, the monks stopped vespers which they had begun and ran to him, glorifying God that they saw their father, whom they had heard was dead, alive and safe. They hastened, by bolting the doors of the church, to protect their shepherd from the slaughter. But the champion, turning to them, ordered the church doors to be thrown open, saying, 'It is not meet to make a fortress of the house of prayer, the church of Christ: though it be not shut up it is able to protect its own; and we shall triumph over the enemy rather in suffering than in fighting, for we came to suffer, not to resist.' And straightway they entered the house of prayer and reconciliation with swords sacrilegiously drawn, causing horror to the beholders by their very looks and the clanging of their arms.\n\nAll who were present were in tumult and fright, for those who had been singing vespers now ran hither to the dreadful sight.\n\nInspired by fury the knights called out, 'Where is Thomas Becket, traitor to the king and realm?' As he answered not, they cried out the more furiously, 'Where is the archbishop?' At this, intrepid and fearless, as it is written, 'The just, like a bold lion, shall be without fear,' he descended from the stair where he had been dragged by the monks in fear of the knights, and in a clear voice answered 'I am here, no traitor to the king, but a priest. Why do ye seek me?' And whereas he had already said that he feared them not, he added, 'So I am ready to suffer in His name, Who redeemed me by His Blood: be it far from me to flee from your swords, or to depart from justice.' Having thus said, he turned to the right, under a pillar, having on one side the altar of the blessed Mother of God and ever Virgin Mary, on the other that of S. Benedict the Confessor: by whose example and prayers, having crucified the world with its lusts, he bore all that the murderers could do with such constancy of soul as if he had been no longer in the flesh. The murderers followed him; 'Absolve,' they cried, 'and restore to communion those whom you have excommunicated, and restore their powers to those whom you have suspended.' He answered: 'There has been no satisfaction, and I will not absolve them.' 'Then you shall die,' they cried, 'and receive what you deserve.' 'I am ready,' he replied, 'to die for my Lord, that in my blood the Church may obtain liberty and peace. But in the name of Almighty God, I forbid you to hurt my people whether clerk or lay.' Thus piously and thoughtfully, did the noble martyr provide that no one near him should be hurt or the innocent be brought to death, whereby his glory should be dimmed as he hastened to Christ. Thus did it become the martyr-knight to follow in the footsteps of his Captain and Saviour Who when the wicked sought Him said: 'If ye seek Me, let these go their way.' Then they laid sacrilegious hands on him, pulling and dragging him that they might kill him outside the Church, or carry him away a prisoner, as they afterwards confessed. But when he could not be forced away from the pillar, one of them pressed on him and clung to him more closely. Him he pushed off calling him 'pander', and saying, 'Touch me not, Reginald; you owe me fealty and subjection; you and your accomplices act like madmen.' The knight, fired with terrible rage at this severe repulse, waved his sword over the sacred head. 'No faith', he cried, 'nor subjection do I owe you against my fealty to my lord the king.' Then the unconquered martyr seeing the hour at hand which should put an end to this miserable life and give him straightway the crown of immortality promised by the Lord, inclined his neck as one who prays and joining his hands he lifted them up, and commended his cause and that of the Church of God, to S. Mary, and to the blessed martyr Denys. Scarce had he said the words than the wicked knight fearing lest he should be rescued by the people and escape alive, leapt upon him suddenly and wounded this lamb, who was sacrificed to God, on the head, cutting off the top of the crown which the sacred unction of chrism had dedicated to God; and by the same blow he wounded the arm of him who tells this. For he, when the others, both monks and clerks, fled, stuck close to the sainted archbishop and held him in his arms till the one he interposed was almost severed...\n\nThen he received a second blow on the head but still stood firm. At the third blow he fell on his knees and elbows, offering himself a living victim, and saying in a low voice, 'For the Name of Jesus and the protection of the Church I am ready to embrace death.' Then the third knight inflicted a terrible wound as he lay, by which the sword was broken against the pavement, and the crown which was large was separated from the head; so that the blood white with the brain and the brain red with blood, dyed the surface of the virgin mother Church with the life and death of the confessor and martyr in the colours of the lily and the rose. The fourth knight prevented any from interfering so that the others might freely perpetrate the murder. As to the fifth, no knight but that clerk who had entered with the knights, that a fifth blow might not be wanting to the martyr who was in other things like to Christ, he put his foot on the neck of the holy priest and precious martyr, and, horrible to say, scattered his brains and blood over the pavement, calling out to the others, 'Let us away, knights; he will rise no more.'\n\n_Under his outer garments the dead Becket was found to be wearing hairshirt and sackcloth. 'At this sight', recorded Benedict of Peterborough, 'the monks gazed at one another, astounded at this proof of piety greater than would have been credited the archbishop.'_\n\n_Christendom was outraged by the murder and Becket was canonized within three years. In 1174 Henry did penance at St Thomas of Canterbury's shrine, where he was scourged by all the monks of Canterbury. The shrine of St Thomas was already a place of popular pilgrimage for the English \u2013 who saw Becket as their exclusive saint \u2013 and would remain one for centuries. It is the destination for Chaucer's pilgrims in_ The Canterbury Tales.\n\n_Henry II died on 6 July 1189_ , _cursing his sons as 'real bastards' for their heart-breaking rebellion against him. Disloyal or no, the eldest son, Richard, was willed the throne; the Plantagenets were a family affair. Dynasty beat sentiment._\n\n## _Holocaustum, 1190_\n\nROGER OF WENDOVER\n\n_Unlike Christians, the Jews of medieval Europe were allowed to lend money with interest. Hostility to this 'usury', plus wild stories of Jews eating babies for breakfast, plus the anti-semitism whipped up by the Crusades, set off a wave of pogroms against England's Jews in 1189\u201390_. _The_ holocaustum, _as the monk-historian Roger of Wendover termed it, culminated in the suicide and the slaughter of York's Jews._\n\nIn the same year, during Lent, that is, that on the 15th of March, the Jews of the city of York, to the number of five hundred, besides women and children, through fear of an attack on the part of the Christians, by permission of the sheriff and the governor of the castle, shut themselves up in that fortress, and when the garrison required them to give up possession of it, they refused to do so. On this refusal, repeated attacks were made both by day and night, and at length the Jews after reflecting, offered a large sum of money for their lives, but this was refused by the people. Then one of them skilled in the law, rose and addressed his companions thus, 'Oh, men of Israel, hear my counsel. It is better, as our law instructs us, to die for our law than to fall into the hands of our enemies.' This being agreed to by all, each head of a family came with a sharp razor, and cut the throats first of his wife, sons, and daughters, and afterwards of all his family, and threw the dead bodies, which they considered as sacrificed to devils, on the Christians outside the castle; they then shut themselves up in the king's house, and setting fire to it, both living dead were burned together with the buildings. After this the citizens and soldiers burned the Jews' houses, with the papers of their debtors, but retained the money for their own use.\n\n## _Richard I Massacres His Muslim Prisoners After Seizing Acre, 2\u201320 August 1191_\n\nBEHA-ED-DIN\n\n_Whereas Henry II had been a statesman, Richard I was an absentee knight-errant who could not, in all probability, speak the King's English. Only weeks after his coronation, Richard departed England for the Third Christian Crusade to the Holy Land. His lack of interest in England notwithstanding, the 'Lionheart's' military exploits earned him an enduring, Arthurian-like place in national myth. More prosaically, his victory over Saladin at Acre secured the Crusader states for another century. The victory, however, was darkened by Richard's less than chivalric murder of his Turkish prisoners. A Saracen view of the massacre follows._\n\n_Acre is modern-day Akka in Israel._\n\nThe same day Hossam ad-Din Ibn Bar\u00eec, an interpreter working with the English, issued from Acre accompanied by two officers of the King of England. He brought news that the King of France had set out for Tyre, and that they had come to talk over the matter of a possible exchange of prisoners and to see the true cross of the Crucifixion if it were still in the Mussulman camp, or to ascertain if it really had been sent to Baghdad. The True Cross was shown to them, and on beholding it they showed the profoundest reverence, throwing themselves on the ground till they were covered with dust, and humbling themselves in token of devotion. These envoys told us that the European princes had accepted the Sultan's (Saladin's) proposition, viz., to deliver all that was specified in the treaty by three instalments at intervals of a month. The Sultan then sent an envoy to Tyre with rich presents, quantities of perfumes, and fine raiment \u2013 all of which were for the King of the French.\n\nIn the morning of the tenth day of Rajab (3 August), Ibn Bar\u00eec and his comrades returned to the King of England while the Sultan went off with his bodyguard and his closest friends to the hill that abuts on Shefa'Amr... Envoys did not cease to pass from one side to the other in the hope of laying the foundation of a firm peace. These negotiations continued till our men had procured the money and the number of prisoners that they were to deliver to the Christians at the end of the first period in accordance with the treaty. The first instalment was to consist of the Holy Cross, 100,000 dinars and 1,600 prisoners. Trustworthy men sent by the Christians to conduct the examination found it all complete saving only the prisoners who had been demanded by name, all of whom had not yet been gathered together. And thus the negotiations continued to drag on till the end of the first term. On this day, the 18th of Rajab (11 August), the enemy sent demanding what was due.\n\nThe Sultan replied as follows: 'Choose one of two things. Either send us back our comrades and receive the payment fixed for this term, in which case we will give hostages to ensure the full execution of all that is left. Or accept what we are going to send you today, and in your turn give us hostages to keep until those of our comrades whom you hold prisoners are restored.' To this the envoys made answer: 'Not so. Send us what is due for this term and in return we will give our solemn oath that your people shall be restored you.'\n\nThis proposition the Sultan rejected, knowing full well that if he were to deliver the money, the Cross, and the prisoners, while our men were still kept captive by the Christians, he would have no security against treachery on the part of the enemy, and this would be a great disaster to Islam.\n\nThen the King of England, seeing all the delays interposed by the Sultan to the execution of the treaty, acted perfidiously as regards his Mussulman prisoners. On their yielding the town of Acre he had engaged to grant them life, adding that if the Sultan carried out the bargain he would give them freedom and suffer them to carry off their children and wives; if the Sultan did not fulfil his engagements they were to be made slaves. Now the King broke his promises to them and made open display of what he had till now kept hidden in his heart, by carrying out what he had intended to do after he had received the money and the Christian prisoners. It is thus that people in his nation ultimately admitted.\n\nIn the afternoon of Tuesday, 27 Rajab (20 August), about four o'clock, he came out on horseback with all the Christian army, knights, footmen, Turcopoles and advanced to the pits at the foot of the hill of Al 'Ay\u00e2d\u00eeyeh, to which place he had already sent on his tents. The Christians, on reaching the middle of the plain that stretches between this hill and that of Keis\u00e2n, close to which place the Sultan's advanced guard had drawn back, ordered all the Mussulman prisoners, whose martyrdom God had decreed for this day, to be brought before him. They numbered more than three thousand and were all bound with ropes. The Christians then flung themselves upon them all at once and massacred them with sword and lance in cold blood. Our advanced guard had already told the Sultan of the enemy's movements and he sent it some reinforcements, but only after the massacre. The Mussulmans, seeing what was being done to the prisoners, rushed against the Christians and in the combat, which lasted till nightfall, several were slain and wounded on either side. On the morrow morning our people gathered at the spot and found the Mussulmans stretched out upon the ground as martyrs for the faith. They even recognized some of the dead, and the sight was a great affliction to them. The enemy had only spared the prisoners of note and such as were strong enough to work.\n\nThe motives of this massacre are differently told; according to some, the captives were slain by way of reprisal for the death of those Christians whom the Mussulmans had slain. Others again say that the King of England, on deciding to attempt the conquest of Ascalon, thought it unwise to leave so many prisoners in the town after his departure. God alone knows what the real reason was.\n\n_Richard probably ordered the slaughter in impetuous anger at Saladin's tardy ransoming of the Muslim prisoners. A year later, in an ironic turn of fortune's whirligig, it was Richard's turn to be held to ransom when he was captured on his homeward journey by the Duke of Austria. Unlike the Mussulmans, Richard was too valuable to be killed. His release cost England 34 tons of gold_.\n\n## _Magna Carta, 1215_\n\nKING JOHN ET AL.\n\n_Richard I died in 1199 \u2013 inevitably, abroad, fighting a war. The Lionheart's successor to the throne of England, his younger brother John, lacked the Plantagenet military genius but not the family's bent to homicide; he was widely rumoured to have drunkenly slain his twelve-year-old-nephew Prince Arthur 'with his own hand and, tying a heavy stone to the body, cast it into the Seine'. Unloved and unesteemed, King John found it impossible to rally supporters to defend the Angevin Continental territories, which were largely lost to the French. John crept into England to find that the locals had dubbed him 'softsword'._\n\n_Whereas before the entire Angevin empire had paid for the upkeep of the Plantagenet monarch, the cost was now borne by England alone. Taxes and fines were ratcheted up. (The era's rapacity at least made a dramatic setting for that most enduring English legend: Robin Hood and his Merry Men). When Johnfailed in his 1214 bid to recover his Angevin inheritance at the battle of Bouvines, the patience of the English with his ruinous and oppressive regime snapped._\n\n_The barons, however, had a rare problem. There was no obvious successor to John. So their rebellion took an entirely novel cast: constitutional reform. Deserted by 'almost everyone, and having... only seven Lords about his person', King John eventually bowed to the inevitable and agreed to a 'great assembly of the King and barons... in a place betwixt Windsor and Stains, called Runingmede'._\n\n_The Great Charter (Magna Carta) was negotiated over five days and, although the baronial class sought mostly to secure itself from feudal financial abuse by the king, they also codified notions of law and government which became essentials of Englishness: notably, that the power of the king (i.e. government) is subject to the law of the land and the voice of his subjects. In Clause 39, no freeman is to be punished except by lawful judgement of his equals and the law of the land \u2013 thus guaranteeing trial by jury; a subject is free to enter and leave the country (except in times of war) under Clause 42_ ; _the beginnings of Parliament can be seen in Clause 14_ , _which provided for a meeting of those who held land off the crown to consent (or not) to levies of 'aid' requested by the monarch._\n\n_Here are the most significant provisions of Magna Carta:_\n\nJohn, by the grace of God King of England, Lord of Ireland, Duke of Normandy and Aquitaine, and Count of Anjou, to his archbishops, bishops, abbots, earls, barons, justices, foresters, sheriffs, stewards, servants, and to all his officials and loyal subjects, Greeting.\n\nKnow that before God, for the health of our soul and those of our ancestors and heirs, to the honour of God, the exaltation of the holy Church, and the better ordering of our kingdom, at the advice of our reverend fathers Stephen, archbishop of Canterbury, primate of all England, and cardinal of the holy Roman Church, Henry archbishop of Dublin, William bishop of London, Peter bishop of Winchester, Jocelin bishop of Bath and Glastonbury, Hugh bishop of Lincoln, Walter bishop of Coventry, Benedict bishop of Rochester, Master Pandulf subdeacon and member of the papal household, Brother Aymeric master of the knighthood of the Temple in England, William Marshal earl of Pembroke, William earl of Salisbury, William earl of Warren, William earl of Arundel, Alan de Galloway constable of Scotland, Warin Fitz Gerald, Peter Fitz Herbert, Hubert de Burgh seneschal of Poitou, Hugh de Neville, Matthew Fitz Herbert, Thomas Basset, Alan Basset, Philip Daubeny, Robert de Roppeley, John Marshal, John Fitz Hugh and other loyal subjects:\n\n(1) First, that we have granted to God, and by this present charter have confirmed for us and our heirs in perpetuity, that the English Church shall be free, and shall have its rights undiminished, and its liberties unimpaired. That we wish this so to be observed, appears from the fact that of our own free will, before the outbreak of the present dispute between us and our barons, we granted and confirmed by charter the freedom of the Church's elections \u2013 a right reckoned to be of the greatest necessity and importance to it \u2013 and caused this to be confirmed by Pope Innocent III. This freedom we shall observe ourselves, and desire to be observed in good faith by our heirs in perpetuity.\n\nTo all free men of our kingdom we have also granted, for us and our heirs for ever, all the liberties written out below, to have and to keep for them and their heirs, of us and our heirs:\n\n...\n\n(9) Neither we nor our officials will seize any land or rent in payment of a debt, so long as the debtor has movable goods sufficient to discharge the debt. A debtor's sureties shall not be distrained upon so long as the debtor himself can discharge his debt. If, for lack of means, the debtor is unable to discharge his debt, his sureties shall be answerable for it. If they so desire, they may have the debtor's lands and rents until they have received satisfaction for the debt that they paid for him, unless the debtor can show that he has settled his obligations to them.\n\n...\n\n(12) No 'scutage'* or 'aid' may be levied in our kingdom without its general consent, unless it is for the ransom of our person, to make our eldest son a knight, and (once) to marry our eldest daughter. For these purposes only a reasonable 'aid' may be levied. 'Aids' from the city of London are to be treated similarly.\n\n(13) The city of London shall enjoy all its ancient liberties and free customs, both by land and by water. We also will and grant that all other cities, boroughs, towns, and ports shall enjoy all their liberties and free customs.\n\n(14) To obtain the general consent of the realm for the assessment of an 'aid' \u2013 except in the three cases specified above \u2013 or a 'scutage', we will cause the archbishops, bishops, abbots, earls, and greater barons to be summoned individually by letter. To those who hold lands directly of us we will cause a general summons to be issued, through the sheriffs and other officials, to come together on a fixed day (of which at least forty days notice shall be given) and at a fixed place. In all letters of summons, the cause of the summons will be stated. When a summons has been issued, the business appointed for the day shall go forward in accordance with the resolution of those present, even if not all those who were summoned have appeared.\n\n...\n\n(20) For a trivial offence, a free man shall be fined only in proportion to the degree of his offence, and for a serious offence correspondingly, but not so heavily as to deprive him of his livelihood. In the same way, a merchant shall be spared his merchandise, and a husbandman the implements of his husbandry, if they fall upon the mercy of a royal court. None of these fines shall be imposed except by the assessment on oath of reputable men of the neighbourhood.\n\n...\n\n(28) No constable or other royal official shall take corn or other movable goods from any man without immediate payment, unless the seller voluntarily offers postponement of this.\n\n...\n\n(35) There shall be standard measures of wine, ale, and corn (the London quarter), throughout the kingdom. There shall also be a standard width of dyed cloth, russett, and haberject, namely two ells within the selvedges. Weights are to be standardized similarly.\n\n...\n\n(39) No free man shall be seized or imprisoned, or stripped of his rights or possessions, or outlawed or exiled, or deprived of his standing in any other way, nor will we proceed with force against him, or send others to do so, except by the lawful judgement of his equals or by the law of the land.\n\n(40) To no one will we sell, to no one deny or delay right or justice.\n\n...\n\n(42) In future it shall be lawful for any man to leave and return to our kingdom unharmed and without fear, by land or water, preserving his allegiance to us, except in time of war, for some short period for the common benefit of the realm. People that have been imprisoned or outlawed in accordance with the law of the land, people from a country that is at war with us, and merchants \u2013 who shall be dealt with as stated above \u2013 are excepted from this provision.\n\n...\n\n(60) All these customs and liberties that we have granted shall be observed in our kingdom in so far as concerns our own relations with our subjects. Let all men of our kingdom, whether clergy or laymen, observe them similarly in their relations with their own men.\n\n(61) Since we have granted all these things for God, for the better ordering of our kingdom, and to allay the discord that has arisen between us and our barons, and since we desire that they shall be enjoyed in their entirety, with lasting strength, for ever, we give and grant to the barons the following security:\n\nThe barons shall elect twenty-five of their number to keep, and cause to be observed with all their might, the peace and liberties granted and confirmed to them by this charter.\n\nIf we, our chief justice, our officials, or any of our servants offend in any respect against any man, or transgress any of the articles of the peace or of this security, and the offence is made known to four of the said twenty-five barons, they shall come to us \u2013 or in our absence from the kingdom to the chief justice \u2013 to declare it and claim immediate redress. If we, or in our absence abroad the chief justice, make no redress within forty days, reckoning from the day on which the offence was declared to us or to him, the four barons shall refer the matter to the rest of the twenty-five barons, who may distrain upon and assail us in every way possible, with the support of the whole community of the land, by seizing our castles, lands, possessions, or anything else saving only our own person and those of the queen and our children, until they have secured such redress as they have determined upon. Having secured the redress, they may then resume their normal obedience to us.\n\nAny man who so desires may take an oath to obey the commands of the twenty-five barons for the achievement of these ends, and to join with them in assailing us to the utmost of his power. We give public and free permission to take this oath to any man who so desires, and at no time will we prohibit any man from taking it. Indeed, we will compel any of our subjects who are unwilling to take it to swear it at our command.\n\nIf one of the twenty-five barons dies or leave the country, or is prevented in any other way from discharging his duties, the rest of them shall choose another baron in his place, at their discretion, who shall be duly sworn in as they were.\n\nIn the event of disagreement among the twenty-five barons on any matter referred to them for decision, the verdict of the majority present shall have the same validity as a unanimous verdict of the whole twenty-five, whether these were all present or some of those summoned were unwilling or unable to appear.\n\nThe twenty-five barons shall swear to obey all the above articles faithfully, and shall cause them to be obeyed by others to the best of their power.\n\nWe will not seek to procure from anyone, either by our own efforts or those of a third party, anything by which any part of these concessions or liberties might be revoked or diminished. Should such a thing be procured, it shall be null and void and we will at no time make use of it, either ourselves or through a third party.\n\nBoth we and the barons have sworn that all this shall be observed in good faith and without deceit. Witness the above-mentioned people and many others.\n\nGiven by our hand in the meadow that is called Runnymede, between Windsor and Staines, on the fifteenth day of June in the seventeenth year of our reign.\n\n_Magna Carta entered the English psyche as the 'Palladium of Liberty' for good reason; however, as a short-term political fix to maintain peace between barons and monarch it failed miserably. As soon as King John signed it he regretted doing so, and the provoked barons offered the English crown to Louis of France. The 'Barons' War' ensued, which was only halted with John's death from dysentery in 1216 and the accession of his nine-year-old son, Henry III._\n\n_The intermission from civil strife was brief Henry Ill's penchant when adult for absolutism and Frenchified favourites \u2013 in a century when English identity was on the rise \u2013 discontented the baronage all over again. Matters came to a fatal close in the mid-1250s when Henry pressed for money for a fanciful war to put his son Edmund on the throne of Sicily, and the catastrophic weather of 1257 caused the harvest to fail._\n\n## _The Weather, 1257_\n\nMATTHEW PARIS\n\n_Paris, a monk at St Albans, was arguably the greatest English chronicler of the Middle Ages._\n\n... On the Innocents' day* in this year such a quantity of rain fell that it covered the surface of the ground, and the times of Deucalion seemed to be renewed. The furrows looked like caves or rivers, and the rivers covered the meadows and all the neighbouring country, so that it presented the appearance of a sea. That from one case other similar ones may be understood, I may mention, that one river alone in the northern parts of England carried away seven large bridges of wood and stone; the mills too, and the neighbouring houses, were carried away by the violence of the torrent-swollen streams and destroyed. On the aforesaid day, too, a fierce whirlwind, accompanied by a violent hailstorm, disturbed the atmosphere and obscured the sky with darkness like that of night. The clouds collected together, and from them the lightning darted forth with fearful vividness, followed by claps of thunder. This thunder was clearly a bad omen, for it was mid-winter, and the cold was equal to that generally felt in February. This weather was followed by sickly unseasonable weather, which lasted about three months.... About this time, that is to say at the commencement of the autumn, the abbot and brethren of St Albans, considering that the crops of hay and corn were in imminent danger of being spoiled by the excessive falls of rain, came to a determination in their chapter, as was the usual custom in cases of such danger, that a fast should be proclaimed through their archdeacon, to be observed by the public as well as the convent; and also that the bier of St Alban should be carried in solemn procession to the church of St Mary-in-the-Fields, the conventual brethren and the people following with bare feet and uttering devout prayers. This was accordingly done, and on the same day, through the merits of the martyr, the destructive rain ceased.... This year throughout was barren and meagre; for whatever had been sown in winter, had budded in spring, and grown ripe in summer, was stifled and destroyed by the autumnal inundations. The scarcity of money, brought on by the spoliation practised by the king and the pope in England, brought on unusual poverty. The land lay uncultivated, and great numbers of people died from starvation. About Christmas, the price of a measure of wheat rose to ten shillings. Apples were scarce, pears more so; figs, beech-nuts, cherries, plums \u2013 in short all fruits which are preserved in jars were completely spoiled. This pestiferous year, moreover, gave rise to mortal fevers, which raged to such an extent that, not to mention other cases, at Bury] St Edmunds alone more than two thousand dead bodies were placed in the large cemetery during the summer, the largest portion of them during the dog-days. There were old men, who had formerly seen a measure of wheat sold for a mark, and even twenty shillings, without the people being starved to death. To add to the misery, Richard, king of Germany, had stripped the kingdom of England of many thousand marks, which he had ordered to be raised from his lands in England. The Holy Land languished in desolation and in fear of the Tartars; for the king of the latter had four million of fighting men in his train; and, as we have heard from learned and credible persons, they had already reduced half the world to subjection to them by their ferocity. Any one making a careful search and inquiry at St Albans may find there an account of their most filthy mode of life. This year, too, generated chronic complaints, which scarcely allowed free power of breathing to any one labouring under them. Not a single frosty or fine day occurred, nor was the surface of the lakes at all hardened by the frost, as was usual; neither did icicles hang from the ledges of houses; but uninterrupted heavy falls of rain and mist obscured the sky until the Purification of the blessed Virgin.[*\n\n_Such was the backcloth of distress and disaster against which the baronial reformers, led by Simon de Montfort, made their move on Henry III._\n\n_De Montfort's French birth was only one of the contradictions he presented as an English revolutionary. He was simultaneously a hairshirt Christian and an aristocrat (the king's brother-in-law, the Earl of Leicester indeed), a scholar and a soldier. It was the mesmeric de Montfort who drew up the constitutional Provisions of Oxford of 1258 obliging the king to share sovereignty with a standing council of barons, and it was de Montfort who led the barons to military victory at Lewes in May 1264 after the king repudiated the self-same Provisions. For a year post-Lewes de Montfort was 'Steward of England'. But he was not its dictator: he not only convened 'Parliaments', he summoned to them, as well as the great and the good, knights from the shires and burgesses from the boroughs.For the first time in England's history, the political order opened up to the middle ranks._\n\n_Some of de Montfort's baronial backers, however, had no intention of power-sharing with jumped-up 'mesne gentes'. Still others were alienated by the de Montfort family's habit of preying on England's assets._\n\n_Only a reduced baronial army accompanied de Montfort at the battle of Evesham in the high summer of 1265, where a royalist army under Henry III's eldest son, Prince Edward, was arraigned against him. Looking over at the superior force, de Montfort sighed, 'Let us, therefore commend our souls to God, for our bodies are theirs.' He scarcely exaggerated; after the brief battle, his head, hands, feet and testicles were severed from his corpse._\n\n_De Montfort might have lost the battle and his life, but the greater victory was his. England's first political hero had killed Plantagenet autocracy stone-dead. When Edward succeeded his father on the throne (as Edward I), he adopted much of de Montfort's reform programme._\n\n## _Edward I Conquers Wales, 1281\u20132_\n\nTHOMAS WYKES\n\n_Whereas his Angevin and Plantagenet forebears had looked France-wards for territorial conquest, Edward I decided that empire-building began at home. Wales offered an early opportunity when Llewelyn ap Gruffudd failed to pay Edward homage. The response of Edward \u2013 sometime crusader, victor of Evesham \u2013 was predictable to all but the reality-divorced 'Prince of Wales'. Edward invaded Wales in 1277 and reduced Llewelyn to ruler of a toy state in Gwynedd. Still unable to grasp the nature of the medieval balance of local power, Llewelyn then rebelled against English tutelage._\n\nIn the year 1281, about the feast of the Annunciation [March 25], Llewelyn, the disturber of the peace made between himself and the king of England, instigated by his brother David, began to attack Flint and Rhuddlan Castles, and to waste the surrounding country. And when this came to the king's ears, who was at that time at Devizes, holding Easter, he sent some few troops to those parts to drive back the wretched Welsh raiders, and defend the castles till the king could take proper measures. At length he summoned the nobles of the realm together and held a Parliament at Worcester on the feast of the Nativity of St John the Baptist [June 24], and it was there arranged that all the magnates of the realm should meet the king with horses and arms on the feast of St Peter in Chains, on the Welsh border. Meanwhile David and his accomplices mortally wounded and took prisoner lord Roger Clifford, after cruelly slaying many of his people.\n\nThe king, gathering an army, took vengeance on Llewelyn, Prince of Wales, by most cruelly laying waste his lands. One day, too, some of the king's men left the main body, and by way of taking vengeance on Llewelyn were intently plundering at an unwise distance, when the Welsh burst out from an ambush in the woods and from the marshes and began to attack the English, who were but few in comparison with themselves; and in this fight were slain the son of lord William of Valence, the king's uncle, and lord Richard d'Argentein; many were barbarously killed, and the others with difficulty escaped by flight. The king stayed in the neighbourhood of Rhuddlan till the feast of All Saints [November 1], and the archbishop of Canterbury was sent to Llewelyn in Snowdon to warn him and persuade him to keep the peace with the king, under which he chafed, and which he absolutely refused to keep; but he could not be induced to come to terms. Meanwhile, while the archbishop was spending three days in Snowdon, the royal leaders imperceptibly but gradually entered Snowdon, thinking that they could seize it in force by treachery; but the Welsh were forewarned and came to meet them, and at the first attack compelled them to flee; and the fugitives, thinking to save themselves by crossing some river, not knowing the ford, were drowned in large numbers \u2013 the more famous being Lucas de Tany, William of Dodingeseles, and William la Zuche, while the others escaped only with the greatest difficulty. When the archbishop withdrew and came back to the king he excommunicated Llewelyn, the perjured disturber of the peace, his brother David, and all their accomplices and abettors. All this took place about St Leonard's Day [November 6]. About the feast of St Thomas the Apostle [December 21], as Llewelyn was coming down from Snowdon with a small following, on some unknown business, he was met unexpectedly by Edmund Mortimer with a small escort, and slain with his accomplices, who were unable to take to flight. The prince's head, which he recognized among the slain, Edmund cut off and brought to the king. The king triumphantly had the head taken to London and fixed on a spear above the Tower of London as a token of his splendid victory. The king of England for this Welsh war took a scutage of forty shillings from his whole realm.\n\nEncouraged by his success, the king of England had a suitable road laid open for him, and entered Snowdon in triumph, and kept Easter there in a Cistercian monastery called Aberconway, disposing of the whole of the principality of Wales at his pleasure, with the exception of the castle which in their language is called Bere, and which is surrounded by an impassable marsh, having difficult and very narrow entries and exits by a single road most ingeniously made. Into it, after his brother's death, David had thrown a garrison, while he himself was lying hid in the woods and practically inaccessible places. But the king besieged the castle, and so closely beset the garrison that, under the compulsion of necessity, they were compelled to surrender the castle to him; and on obtaining possession of it he made a bargain with some Welshmen that they should take David from his hiding-place and surrender him to the king as a prisoner; and the king sent him, with his wife and son, to Rhuddlan, and there imprisoned him and loaded him with fetters. And when Rhys Vychan [the little] heard what had happened, he surrendered himself and his followers to lord Humphrey de Bohun, earl of Hereford; and he forthwith sent them to the king, and the king to London, with orders that he should be put in the Tower and most strictly guarded...\n\nAbout the feast of St Michael [September 29] the king summoned to Shrewsbury the chief men of his realm and the best counsellors, both from among the burgesses and the magnates, and had David brought thither \u2013 who had been kept in captivity at Rhuddlan \u2013 to submit to the punishment demanded by his crime, and it was there decided that he should die a fivefold death: firstly, to be torn asunder by horses; secondly, to be hanged; thirdly, to be executed; fourthly, to have his heart and entrails burned; and fifthly, to have his body quartered and hung up in four separate places in England. His head was carried off to London by the Londoners then at Shrewsbury, to be set as a conspicuous mark on the Tower of London, next to the head of his brother Llewelyn.\n\n_In 1284 Wales was formally annexed to the English crown. To ensure that this state of affairs endured, Edward ringed the principality with giant castles, architected by the Savoyard genius Master James of St George: Flint, Rhuddlan, Aberystwyth, Builth, Conwy, Caernarfon, Criccieth, Harlech and Beaumaris. They were the high-point of castle-building in Britain. To add insult to conquered Welsh pride, the title 'Prince of Wales' was granted to Edward's own eldest son._\n\n_Wales was never again independent._\n\n## _Sex in the Country, 15 June 1300_\n\nANONYMOUS COURT RECORDER\n\n_The proceedings of a rural dean's court at Salwarp, Worcestershire. The place in brackets refers to the defendant's village of residence._\n\n(King's Norton) William le yrmongarre fornicated for the third time with Agnes Elyot. Purgation seven-handed is decreed for the man. The woman is suspended for contumacy. The man fails in the purgation and renounces his sin and is whipped in the usual way twice through the market place. The woman confesses and is whipped in the usual way once through the market place. The man withdrew.\n\nHenry de Lee fornicated with Agnes of Alvechurch. Purgation six-handed is decreed for the man. The woman is suspended for contumacy. The woman withdrew. The man is cited.\n\nWilliam Miller fornicated with Alice de la Schave. Each appears and confesses and is whipped in the usual way. Each withdrew.\n\nEdith Ythefrithe, pregnant, says on oath by Richard de Boscho whom she renounces and is whipped in the usual way. The man confesses and is whipped in the usual way. The woman did [penance]. The man withdrew.\n\n(Bromsgrove) William de Coleweyk fornicated with Julia, a weaver. Each appears and confesses and is whipped in the usual way. Each did [penance].\n\nRoger Miller fornicated with Isabella Clerk and with Alice Clerk, sister of the said Isabella. The man confesses with regard to each and is whipped in the usual way once through the market place. Isabella confesses and is whipped in the usual way. Each withdrew.\n\nThomas de Brandel fornicated with Agnes daughter of Gilbert the smith. The man confesses and is whipped in the usual way. The woman is suspended for contumacy. The woman is excommunicated. The man is doing [penance]. The woman is reconciled and confesses and is whipped in the usual way. Withdrew.\n\nGeoffrey of Langley fornicated for the fifth time with Agnes daughter of Aldich. Purgation six-handed is decreed for each. They each make their purgation.\n\nWalter of Morton fornicated with Alice le Carter. The man is cited. The woman appears and confesses and is whipped in the usual way. The woman withdrew. The man is not found.\n\nThomas Noppe fornicated with Isabella of Holywalle. Each confesses and is whipped in the usual way. Each _recessit._\n\nHenry de Frankel fornicated with Matilda Honderwode. The woman confesses and renounces her sin and is whipped in the usual way once through the market place. The man is suspended for contumacy. The woman did [penance]. The man is excommunicated _cum communi._\n\n## _The Age of Chivalry: A Mass Knighting, May 1306_\n\nANONYMOUS MONK\n\n_Edward I was widely considered 'the best lance in the world' (despite his lisp and droopy eyelid), and his court was the English headquarters for the chivalric cult of perfect manners and battlefield prowess by which the elite of the era defined itself On the eve of Edward's resumed campaign to crush the Scots the most fabulous chivalric ceremony of medieval England took place at Westminster. The scene was recorded by a monk of Westminster in the_ Flowers of History.\n\nTo increase the numbers that were to set out for Scotland, the king issued a public proclamation that as many as were knights by inheritance, and who had the wherewithal for campaigning, should appear at Westminster on 12 May, where each individual would be equipped, from the royal wardrobe, with every knightly accoutrement except a horse.\n\nSo it was that to the three hundred young men who assembled, sons of earls, barons and knights, were distributed purple satin, fine linen and robes sewn with the finest gold.\n\nThe royal palace of Westminster, though big, was too small for the great crowd that had gathered, so the apple trees at the New Temple were cut down and walls demolished, and pavilions and tents erected where the young men might adorn themselves with their golden robes.\n\nThat night in the Temple church, these esquires, or as many of them as the place would hold, kept vigil. But on the instructions of his father, Edward, prince of Wales, together with certain very noble aspirants to knighthood, kept his vigil in the abbey church at Westminster. So loud were the voices of those shouting for joy, and so great the clamour of trumpets and horns, that the rejoicing of the congregation could not be heard from one side of the choir to the other.\n\nIn the palace the next day, King Edward I girded his son with the sword belt of a knight and granted him the dukedom of Aquitaine. And thus Prince Edward was made a knight in the abbey church of Westminster, that he might make his companions resplendent likewise with knightly glory.\n\nThere was such a crush of people before the high altar that two knights died, several fainted and at least three had to be taken away and attended to.\n\nThen two swans were brought before King Edward I in pomp and splendour, adorned with golden nets and gilded reeds, the most astounding sight to the onlookers. Having seen them, the king swore by the God of Heaven and by the swans that he wished to set out for Scotland and, whether he lived or died, to avenge the wrong done to the Holy Church, the death of John Comyn and the breach of faith by the Scots.\n\nThe oath was pledged by all the other magnates, who asserted with the king that they were ready to journey to Scotland both during his lifetime and after, under his son the prince, to fulfil his vow.\n\nOn 30 May, when all had been roused to courage, the young men saluted the king and left Westminster, men who were to appear before the king in Scotland on 8 July.\n\nFor the knighting of the king's son, the clergy and people ceded a thirtieth part of their goods to the king, and the merchants a twentieth.\n\n_Edward I died in 1307 aged sixty-eight. 'The Hammer of the Scots' (as his Westminster tomb was inscribed) tasked his son, Prince Edward, with carrying on the work of English domination north of the border._\n\n## _The Battle of Bannockburn, 24 June 1314_\n\n_THE CHRONICLE OF LANERCOST_\n\n_The pursuits of Edward II were unkingly (ditch-digging, thatching), his bed-companions preferably male (notoriously Piers Gaveston, elevated to Earl of Cornwall), his interest in effective government slight, his ability as war-leader of the English nation thinner still._\n\n_At Bannockburn on the Forth plain, Edward II faced a Scottish army (led by Robert the Bruce) a third the size of his Plantagenet force._\n\nThe Chronicle of Lanercost _was compiled by clergy in Cumberland._\n\nIn early May, the king of England approached the Scottish March with a fine and mighty army.\n\nYet whereas his father, Edward I, when going to war with the Scots, had been accustomed to visit the shrines of English saints and to make splendid offerings to them, Edward II rode along in great pomp with elaborate trappings, took goods from the monasteries and, so it is reported, said and did much that was harmful to the shrines.\n\nIn June, King Edward II gathered his forces together and approached Stirling Castle in great might, in order to break up the siege, and to do battle with the Scots, who had assembled there with their entire strength. On 23 June, after midday, the English forces reached Tor Wood. The Scots, who were in the wood, fell upon the leading column of Robert Clifford's force, killing a number of men and forcing the rest to flee. After this incident, the English grew fearful, while the Scots became bolder.\n\nWhen the two armies had drawn much closer to each other, all the Scots fell to their knees, saying the Lord's Prayer, commending themselves to God's protection and seeking divine assistance. This done, they marched boldly against the English. The Scottish army was drawn up with the first two lines each a little ahead of the one next to it, so that no line was in front of another. Robert Bruce was in the third and final line.\n\nWhen the two armies joined battle, the great English horses rushed on to the Scottish pikes, which bristled like a dense forest. An appalling din arose from the splintering pikes and the warhorses, mortally wounded. This brought matters to a standstill for a while. The English could not pass the Scots' front line in order to reach the enemy; indeed they could do nothing to improve their situation, and their only recourse was to flight.\n\nI heard the tale of these events from a trustworthy eyewitness.\n\nIn the fighting in the front line, the dead included Gilbert of Clare, earl of Gloucester, Robert Clifford, and many other nobles, besides a great number of footsoldiers.\n\nYet another misfortune befell the English, who had a little earlier crossed a deep ditch, a tidal inlet, called the Bannock Burn: now, as they struggled to retreat in confusion, many noblemen and others fell into this ditch in the crush, with their horses. Some managed to scramble out, but many were completely unable to extricate themselves. 'Bannockburn' was a name on all English lips for many years to come.\n\nThe king, with Hugh Despenser, who had become the apple of the king's eye after Piers Gaveston, and numerous English cavalry and infantry, were guided away by a Scottish knight who knew an escape route. Thus, to their eternal shame, they fled wretchedly to the castle at Dunbar. Some stragglers were killed by the Scots, who were in hot pursuit. From Dunbar, the king and a few of his closest companions took a boat to Berwick upon Tweed, leaving the rest to their fate.\n\n## _The Murder of Edward II, 22 September 1327_\n\nGEOFFREY LE BAKER\n\n_Humiliated once too often by Edward II's homosexual infatuations, his wife Isabella exiled herself to her native France, taking as her lover the English Marcher lord, Roger de Mortimer. In September 1326 Isabella and Mortimer invaded England, Edward's supposedly loyal subjects flocked to their standard, and within four months a great council at Westminster had deposed Edward II in favour of his son, Edward III._\n\n_There remained only the problem of what to do with the ex-king. In April 1327 Edward II was placed in the custody of Thomas, Lord of Berkeley. Geoffrey le Baker was almost alone among fourteenth-century chroniclers in showing sympathy for Edward II._\n\nThese things were told me by William Bishop, in the time after the great plague. He had seen them with his own eyes for he had been among those who took Edward to Berkeley.\n\nFinally they arrived at Berkeley Castle, where, ever patient in the face of his misfortunes, the noble Edward was shut up like a hermit. He was robbed of his earthly kingdom and stripped bare like the blessed Job, not by his rivals but by his own wife, his servants and serving women.\n\nDespoiled of his command, his honours, his goods, Edward II looked forward to the kingdom of Heaven. However, his wife, Isabella, was angered that his life which had become most hateful to her should be so prolonged. She asked advice of the bishop of Hereford, pretending that she had had a dreadful dream from which she feared, if it was true, that her husband would at some time be restored to his former dignity and would condemn her, as a traitress, to be burned or to perpetual slavery. The bishop of Hereford feared greatly for himself, just as Isabella did, if this should come to pass, conscious as he was that he was guilty of treason.\n\nAnd so, letters were written to Edward's keepers, setting forth in vivid detail the false accusation that they had been too lenient with him and fed him on delicacies. Moreover, it was hinted that the death of Edward would cause these nobles no great displeasure, whether it were natural or violent. Concerning this point, the bishop of Hereford penned a message of double meaning: _Edwardum occidere nolite timere bonum est._\n\nThis saying may be resolved into two parts: the first consists of the first three words of the bishop's puzzle: ' _Edwardum occidere nolite_ ' \u2013 'Do not kill Edward!' \u2013 followed by the second three: _'timere bonum est' \u2013_ 'fear is a good thing.' Read thus, the message would not be construed as treason.\n\nBut those who received the message were aware of the true import of the bishop's communication. They construed the message thus: _'Edwardum occidere nolite timere' \u2013_ 'Do not fear to kill Edward!' \u2013 followed by _'bonum est' \u2013_ 'it is good!' Those who were guilty of evil, read the message as evil. Thus did that skilful trickster have recourse to a puzzle, for he knew that without his authority, Edward's keepers would not dare to carry out their cruel instructions and kill him, lest they should later be brought to trial for this crime.\n\nThe bishop of Hereford himself made careful provision that the authority which he gave might appear to mean the opposite of what he intended, but to have been misread by the thick-witted keepers who then took the life of an innocent man as a consequence of their own mistake. Taken in the contrary sense, his message made him safe from any accusation of treason. And indeed, events were to prove the bishop correct.\n\nIn the end, Edward's murderers, who had believed that the favour of Isabella and the slippery and deceitful bishop made them secure, found instead that these two were eager to take vengeance for the murder of their hostage, Edward.\n\nThe keepers were dumbfounded and did not know what to do. They showed the letters with the seals of Isabella, the bishop of Hereford and the other conspirators to prove that the latter had indeed given their consent.\n\nThe bishop did not deny the letter, agreeing that he and his accomplices had sent it, but he explained it as being perfectly innocent and loyal in its meaning. It was the keepers, he claimed, who had misinterpreted it and used it as authority for their own wicked deed. He so terrified them with his threats that they fled. So much for the letter of double meaning.\n\nEdward II was welcomed kindly at the castle and treated well by Thomas Berkeley, lord of the estate. After receipt of the letter, however, Edward's torturers took control of the castle.\n\nThey gave orders that Thomas Berkeley was to have no contact with Edward. This caused him not only sadness but also shame for he was unable to do as he wished and as before had been his right. Sighing, he bade Edward farewell and removed to another of his estates.\n\nThen began the most extreme part of Edward's persecution which was to continue until his death.\n\nFirstly, he was shut up in a secure chamber, where he was tortured for many days until he was almost suffocated by the stench of corpses buried in a cellar hollowed out beneath. Carpenters, who one day were working near the window of his chamber, heard him, God's servant, as he lamented that this was the most extreme suffering that had ever befallen him.\n\nBut when his tyrannous warders perceived that the stench alone was not sufficient to kill him, they seized him on the night of 22 September as he lay sleeping in his room.\n\nThere, with cushions heavier than fifteen strong men could carry, they held him down, suffocating him.\n\nThen they thrust a plumber's soldering iron, heated red hot, guided by a tube inserted into his bowels, and thus they burnt his innards and his vital organs. They feared lest, if he were to receive a wound in those parts of the body where men generally are wounded, it might be discovered by some man who honoured justice, and his torturers might be found guilty of manifest treason and made to suffer the consequent penalty.\n\nAs this brave knight was overcome, he shouted aloud so that many heard his cry both within and without the castle and knew it for the cry of a man who suffered violent death. Many in both the town and castle of Berkeley were moved to pity for Edward, and to watch and pray for his spirit as it departed this world.\n\n## _The Hundred Years War: Sea Fight at Sluys, 24 June 1340_\n\nGEOFFREY LE BAKER\n\n_Even more so than his grandfather, Edward III, founder of the Order of the Garter, was the epitome of the chivalric king; even more so than his grandfather, Edward III defined Englishness through war. He banned village sports other than archery as too distracting, and he reorganized the navy to such a degree that an admiring Parliament dubbed him 'King of the Sea'._\n\n_In 1337 Edward led his nation into what would become a Hundred Years War against France. Aside from Edward's own longing for martial honours, geo-politics necessitated that England protect her remaining possessions in France and her outlets for the wool trade (England's major money-earner) in the Low Countries. Three years later, Edward raised the stakes by claiming the French throne after the extinction of the male Capetian line and adding the fleur-de-lis to his heraldic arms._\n\n_The English could not but love him, especially after the 'King of the Sea' captained the first of England's historic naval victories over her Channel neighbours, at Sluys, off the Flanders coast._\n\nKing Edward [III] kept his Whitsuntide at Ipswich, because he intended from thence to make his passage into Flanders; but, being informed that the French King had sent a great navy of Spanish ships and also the whole fleet of France to stop his passage, he caused his ships of the Cinque Ports and others to be assembled, so that he had in his fleet, great and small, 260 ships.\n\nWherefore, on the Thursday before the Nativity of Saint John the Baptist, having a favourable wind, he began to sail; and the next day, in the even of the said feast, they descried the French fleet lying in Swinehaven. Wherefore the King caused all his fleet to come to anchor.\n\nThe next day, being the Feast of Saint John the Baptist, early in the morning the French fleet divided themselves into three parts, withdrew about a mile, and then approached the King's fleet. When the King saw this, about nine o'clock, having the wind and sun on his back, he set forward and met his enemies as he would have wished; at which the whole fleet gave a terrible shout, and a shower of arrows out of long wooden bows so poured down on the Frenchmen that thousands were slain in that meeting. At length they closed and came to hand blows with pikes, poleaxes, and swords, and some threw stones from the tops of ships, wherewith many were brained. The size and height of the Spanish ships caused many Englishmen to strike many a blow in vain. But, to be short, the first part of the French ships being overcome and all the men spent, the Englishmen entered and took them. The French ships were chained together in such a way that they could not be separated from each other, so that a few Englishmen kept that part of the fleet. They then set upon the second part and with great difficulty made the attack; but when this had been done, the second part was sooner overcome than the first because many of the Frenchmen abandoned their ships and leapt overboard. The Englishmen, having thus overcome the first and second parts of the fleet, and now finding night drawing on, partly for want of light and partly because they were weary, determined to take some rest till the next morning. On this account, during the night thirty ships of the third part fled away, but a large ship called the 'James' of Dieppe, thinking to have carried away a certain ship of Sandwich belonging to the prior of Canterbury, was stopped, for the sailors so stoutly defended themselves by the help of the Earl of Huntingdon that they saved themselves and their ship from the Frenchmen.\n\nThe fight continued all night, and in the morning, the Normans being overcome and taken, there were found in the ship 400 men slain. Moreover, the King understanding that the ships were fled, sent forty well-equipped ships to follow them.... In the first group of ships that were taken they found these conquered ships: the 'Denis', the 'George', the 'Christopher' and the 'Blacke Cocke', all of which had been captured by Frenchmen at Sluys and carried into Normandy. The number of ships of war that were taken was about 230 barges; the number of enemies that were slain and drowned was about 25,000, and of Englishmen about 4,000, among whom were four knights...\n\n## _The Hundred Years War: The Battle of Cr\u00e9cy, 26 August 1346_\n\nSIR JOHN FROISSART\n\n_The battle of Cr\u00e9cy ensued when Edward III's invasion army was trapped by a superior French force under King Philip in Picardy. Among Edward's soldiers was his sixteen-year-old son, the Prince of Wales, known as the Black Prince._\n\nThe English... were drawn up in three divisions, and seated on the ground, on seeing their enemies advance, rose up undauntedly and fell into their ranks. The Prince's battalion, whose archers were formed in the manner of a portcullis, and the men-at-arms in the rear, was the first to do so. The Earls of Northampton and Arundel, who commanded the second division, posted themselves in good order on the Prince's wing to assist him if necessary.\n\nYou must know that the French troops did not advance in any regular order, and that as soon as their King came in sight of the English his blood began to boil, and he cried out to his marshals, Order the Genoese forward and begin the battle in the name of God and St Denis.' There were about 15,000 Genoese crossbow men; but they were quite fatigued, having marched on foot that day six leagues, completely armed and carrying their crossbows, and accordingly they told the Constable they were not in a condition to do any great thing in battle. The Earl of Alen\u00e7on hearing this, said, 'This is what one gets by employing such scoundrels, who fall off when there is any need for them.' During this time a heavy rain fell, accompanied by thunder and a very terrible eclipse of the sun; and, before this rain, a great flight of crows hovered in the air over all the battalions, making a loud noise; shortly afterwards it cleared up, and the sun shone very bright; but the French had it in their faces; and the English on their backs. When the Genoese were somewhat in order they approached the English and set up a loud shout, in order to frighten them; but the English remained quite quiet and did not seem to attend to it. They then set up a second shout, and advanced a little forward; the English never moved. Still they hooted a third time, advancing with their crossbows presented, and began to shoot. The English archers then advanced one step forward, and shot their arrows with such force and quickness, that it seemed as if it snowed. When the Genoese felt these arrows, which pierced through their armour, some of them cut the strings of their crossbows, others flung them to the ground, and all turned about and retreated quite discomfited.\n\nThe French had a large body of men-at-arms on horseback to support the Genoese, and the King, seeing them thus fall back, cried out, 'Kill me those scoundrels, for they stop up our road without any reason.' The English continued shooting, and some of their arrows falling among the horsemen, drove them upon the Genoese, so that they were in such confusion, they could never rally again.\n\nIn the English army there were some Cornish and Welsh men on foot, who had armed themselves with large knives, these advancing through the ranks of the men-at-arms and archers, who made way for them, came upon the French when they were in this danger, and falling upon earls, barons, knights, and squires, slew many, at which the King of England was exasperated. The valiant King of Bohemia was slain there; he was called Charles of Luxembourg, for he was the son of the gallant king and emperor, Henry of Luxembourg, and, having heard the order for the battle, he inquired where his son the Lord Charles was; his attendants answered that they did not know, but believed he was fighting. Upon this, he said to them, 'Gentlemen, you are all my people, my friends, and brethren at arms this day; therefore, as I am blind, I request of you to lead me so far into the engagement that I may strike one stroke with my sword.' The knights consented, and in order that they might not lose him in the crowd, fastened all the reins of their horses together, placing the King at their head that he might gratify his wish, and in this manner advanced towards the enemy. The Lord Charles of Bohemia, who already signed his name as King of Germany, and bore the arms, had come in good order to the engagement; but when he perceived that it was likely to turn out against the French he departed. The King, his father, rode in among the enemy, and he and his companions fought most valiantly; however, they advanced so far that they were all slain, and on the morrow they were found on the ground with all their horses tied together.\n\nThe Earl of Alen\u00e7on advanced in regular order upon the English, to fight with them, as did the Earl of Flanders in another part. These two lords with their detachments, coasting, as it were, the archers, came to the Prince's battalion, where they fought valiantly for a length of time. The King of France was eager to march to the place where he saw their banners displayed, but there was a hedge of archers before him: he had that day made a present of a handsome black horse to Sir John of Hainault, who had mounted on it a knight of his, called Sir John de Fusselles, who bore his banner; the horse ran off with the knight and forced his way through the English army, and when about to return, stumbled and fell into a ditch and severely wounded him; he did not, however, experience any other inconvenience than from his horse, for the English did not quit their ranks that day to make prisoners: his page alighted and raised him up, but the French knight did not return the way he came, as he would have found it difficult from the crowd. This battle, which was fought on Saturday, between La Broyes and Cr\u00e9cy, was murderous and cruel; and many gallant deeds of arms were performed that were never known: towards evening, many knights and squires of the French had lost their masters, and wandering up and down the plain, attacked the English in small parties; but they were soon destroyed, for the English had determined that day to give no quarter, nor hear of ransom from anyone.\n\nEarly in the day some French, Germans, and Savoyards had broken through the archers of the Prince's battalion, and had engaged with the men-at-arms; upon this the second battalion came to his aid, and it was time they did so, for otherwise he would have been hard pressed. The first division, seeing the danger they were in, sent a knight off in great haste to the King of England, who was posted upon an eminence near a windmill. On the knight's arrival he said, 'Sir, the Earl of Warwick, the Lord Stafford, the Lord Reginald Cobham, and the others who are about your son, are vigorously attacked by the French, and they entreat that you will come to their assistance with your battalion, for if numbers should increase against him, they fear he will have too much to do.' The King replied, 'Is my son dead, unhorsed, or so badly wounded that he cannot support himself?' 'Nothing of the sort, thank God,' rejoined the knight, 'but he is in so hot an engagement that he has great need of your help.' The King answered, 'Now, Sir Thomas, return to those that sent you, and tell them from me not to send again for me this day, nor expect that I shall come, let what will happen, as long as my son has life; and say that I command them to let the boy win his spurs, for I am determined, if it please God, that all the glory of this day shall be given to him, and to those into whose care I have entrusted him.' The knights returned to his lords and related the King's answer, which mightily encouraged them, and made them repent they had ever sent such a message.\n\nIt is a certain fact, that Sir Godfrey de Harcourt, who was in the prince's battalion, having been told by some of the English that they had seen the banner of his brother engaged in the battle against him, was exceedingly anxious to save him; but he was too late, for he was left dead on the field, and so was the Earl of Aumarle, his nephew. On the other hand, the Earls of Alen\u00e7on and Flanders were fighting lustily under their banners with their own people; but they could not resist the force of the English, and were there slain, as well as many other knights and squires, who were attending on, or accompanying them.\n\nThe Earl of Blois, nephew to the King of France, and the Duke of Lorraine, his brother-in-law, with their troops, made a gallant defence; but they were surrounded by a troop of English and Welsh, and slain in spite of their prowess. The Earl of St Pol, and the Earl of Auxerre, were also killed, as well as many others. Late after vespers, the King of France had not more about him than sixty men, every one included. Sir John of Hainault, who was of the number, had once remounted the King, for his horse had been killed under him by an arrow: and seeing the state he was in, he said, 'Sir, retreat whilst you have an opportunity, and do not expose yourself so simply; if you have lost this battle, another time you will be the conqueror.' After he had said this he took the bridle of the King's horse and led him off by force, for he had before entreated him to retire. The king rode on until he came to the castle of La Broyes, where he found the gates shut, for it was very dark: he ordered the Governor of it to be summoned, who, after some delay, came upon the battlements, and asked who it was that called at such an hour. The King answered, 'Open, open, Governor, it is the fortune of France.' The Governor hearing the King's voice immediately descended, opened the gate, and let down the bridge; the King and his company entered the castle, but he had with him only five barons: Sir John of Hainault, the Lord Charles of Montmorency, the Lord of Beaujeu, the Lord of Aubigny, and the Lord of Montfort. It was not his intention, however, to bury himself in such a place as this, but having taken some refreshments, he set out again with his attendants about midnight, and rode on under the direction of guides, who were well acquainted with the country, until about daybreak he came to Amiens, where he halted. This Saturday the English never quitted their ranks in pursuit of anyone, but remained on the field guarding their position and defending themselves against all who attacked them. The battle ended at the hour of vespers, when the King of England embraced his son and said to him, 'Sweet son, God give you perseverance: you are my son; for most loyally have you acquitted yourself; you are worthy to be a sovereign.' The Prince bowed very low, giving all honour to the King, his father. The English during the night made frequent thanksgivings to the Lord for the happy issue of the day; and with them there was no rioting, for the King had expressly forbidden all riot or noise.\n\nOn the following day, which was Sunday, there were a few encounters with the French troops; however, they could not withstand the English, and soon either retreated or were put to the sword. When Edward was assured that there was no appearance of the French collecting another army, he sent to have the number and rank of the dead examined. This business was entrusted to Lord Reginald Cobham and Lord Stafford, assisted by three heralds to examine the arms, and two secretaries to write down the names. They passed the whole day upon the field of battle, and made a very circumstantial account of all they saw: according to their report it appeared that 80 banners, the bodies of II princes, 1,200 knights, and about 30,000 common men were found dead on the field.\n\n_The English won at Cr\u00e9cy because of their longbowmen (who could fire ten arrows per minute, compared to the French\/Genoese crossbowmen's five), their superior tactics and their patriotism, which bound them together above class. So socially polarized were the French at Cr\u00e9cy that their lords rode roughshod \u2013 literally \u2013 over their peasant foot soldiers. Who needed sophisticated English arms when the French were happy to kill one another?_\n\n_After Cr\u00e9cy, Edward III seized Calais (which would remain an English possession until 1558)_. _But a deadlier enemy than the French lay in wait for Edward's England. King Death._\n\n## _The Black Death, 1348\u20139_\n\nHENRY KNIGHTON\n\n_The population of England stood at around 4 million in 1348_ , _up threefold since the Norman Conquest, courtesy of two centuries of economic prosperity. Perhaps 2 million of these English were lost to the Black Death, a form of bubonic plague carried by the fleas of the black rat. The first symptoms were buboes (swellings) in the lymph system; death came within two to five days._\n\n_Henry Knighton was a canon of St Mary's Abbey, Leicester. The plague arrived in England via the port of Melcombe Regis in Dorset, not Southampton as Knighton says._\n\nThe dreadful pestilence penetrated the sea coast by Southampton and came to Bristol, and there almost the whole population of the town perished, as if it had been seized by sudden death; for few kept their beds more than two or three days, or even half a day. Then this cruel death spread everywhere around, following the course of the sun. And there died at Leicester in the small parish of St Leonard more than 3 80 persons, in the parish of Holy Cross, 400; in the parish of St Margaret's, Leicester, 700; and so in every parish, a great multitude. Then the Bishop of London sent word throughout his whole diocese giving general power to each and every priest, regular as well as secular, to hear confessions and to give absolution to all persons with full episcopal authority, except only in case of debt. In this case, the debtor was to pay the debt, if he was able, while he lived, or others were to fulfil his obligations from his property after his death. Likewise the Pope granted full remission of all sins to anyone receiving absolution when in danger of death, and granted that this power should last until Easter next following, and that everyone might choose whatever confessor he pleased.\n\nIn the same year there was a great murrain of sheep everywhere in the kingdom, so that in one place in a single pasture more than 5,000 sheep died; and they putrefied so that neither bird nor beast would touch them. Everything was low in price because of the fear of death, for very few people took any care of riches or property of any kind. A man could have a horse that had been worth 405 for half a mark [6 _s_ 8 _d_ ], a fat ox for 4 _s_ , a cow for 12 _d_ , a heifer for 6 _d_ , a fat wether for 4 _d_ , a sheep for 3 _d_ , a lamb for 2 _d_ , a large pig for 5 _d_ ; a stone of wool [24 lbs] was worth 9 _d_. Sheep and cattle ran at large through the fields and among the crops, and there was none to drive them off or herd them; for lack of care they perished in ditches and hedges in incalculable numbers throughout all districts, and none knew what to do. For there was no memory of death so stern and cruel since the time of Vortigern, King of the Britons, in whose day, as Bede testifies, the living did not suffice to bury the dead.\n\nIn the following autumn a reaper was not to be had for a lower wage than 8d, with his meals; a mower for not less than 10d, with meals. Wherefore many crops wasted in the fields for lack of harvesters. But in the year of the pestilence, as has been said above, there was so great an abundance of every kind of grain that almost no one cared for it.\n\nThe Scots, hearing of the dreadful plague among the English, suspected that it had come about through the vengeance of God, and, according to the common report, they were accustomed to swear 'be the foul deth of Engelond'. Believing that the wrath of God had befallen the English, they assembled in Selkirk forest with the intention of invading the kingdom, when the fierce mortality overtook them, and in a short time about 5,000 perished. As the rest, the strong and the feeble, were preparing to return to their own country, they were followed and attacked by the English, who slew countless numbers of them.\n\nMaster Thomas of Bradwardine was consecrated by the Pope Archbishop of Canterbury, and when he returned to England he came to London, but within two days was dead...\n\nMeanwhile the King sent proclamation into all the counties that reapers and other labourers should not take more than they had been accustomed to take, under the penalty appointed by statute. But the labourers were so lifted up and obstinate that they would not listen to the King's command, but if anyone wished to have them he had to give them what they wanted, and either lose his fruit and crops, or satisfy the lofty and covetous wishes of the workmen. And when it was known to the King that they had not observed his command, and had given greater wages to the labourers, he levied heavy fines upon abbots, priors, knights, greater and lesser, and other great folk and small folk of the realm, of some 100 _s_ , of some 40 _s_ , of some 20 _s_ , from each according to what he could give. And afterwards the King had many labourers arrested, and sent them to prison; many withdrew themselves and went into the forests and woods; and those who were taken were heavily fined. Their ringleaders were made to swear that they would not take daily wages beyond the ancient custom, and then were freed from prison. And in like manner was done with the other craftsmen in the boroughs and villages... After the aforesaid pestilence, many buildings, great and small, fell into ruins in every city, borough, and village for lack of inhabitants, likewise many villages and hamlets became desolate, not a house being left in them, all having died who dwelt there; and it was probable that many such villages would never be inhabited.\n\n_Many thought the plague a judgement by God for society's sins, especially Lust. The Benedictine preacher Thomas Brinton complained: 'We are not constant in faith... It is undoubtedly for that reason that there exists in the kingdom of England so marked a diminution of fruitfulness; so cruel a pestilence, so much injustice, so many illegitimate children \u2013 for on every side there is so much lechery and adultery that few men are contented with their wives but each man lusts after the wife of his neighbour or keeps a stinking concubine. '_\n\n_Having tried everything else \u2013 flight, bleedings, enemas, lavender or columbine potions \u2013 to save themselves from the buboes, the English sought God's intercession._\n\n## _Flagellants Come to London, Michaelmas 1349_\n\nROBERT OF AVESBURY\n\n_Usually members of the Dominican and Franciscan orders, flagellants voluntarily whipped themselves in public to atone for society's sins._\n\nAbout Michaelmas 1349 over six hundred men came to London from Flanders, mostly of Zeeland and Holland origin. Sometimes at St Paul's and sometimes at other points in the city they made two daily public appearances wearing cloths from the thighs to the ankles, but otherwise stripped bare. Each wore a cap marked with a red cross in front and behind. Each had in his right hand a scourge with three tails. Each tail had a knot and through the middle of it there were sometimes sharp nails fixed. They marched naked in a file one behind the other and whipped themselves with these scourges on their naked and bleeding bodies. Four of them would cant in their native tongue and, another four would chant in response like a litany. Thrice they would all cast themselves on the ground in this sort of procession, stretching out their hands like the arms of a cross. The singing would go on and, the one who was in the rear of those thus prostrate acting first, each of them in turn would step over the others and give one stroke with his scourge to the man lying under him. This went on from the first to the last until each of them had observed the ritual to the full tale of those on the ground. Then each put on his customary garments and always wearing their caps and carrying their whips in their hands they retired to their lodgings. It is said that every night they performed the same penance.\n\n## _The Peasant's Life, c. 1362_\n\nWILLIAM LANGLAND\n\n_Langland set his epic alliterative poem_ The Vision of Piers Plowman _in the plague-stricken England of the declining years of Edward III. A Mass-priest, Langland dressed as a beggar to experience the lot of the lower orders, and_ Piers Plowman _has been called the first 'authentic cry of the poor' in British history. Here Hunger is interrogating Piers:_\n\n'Can you serve,' he said, 'or sing in churches,\n\nOr cock hay in my harvest, or handle a hay-fork,\n\nMow or mound it or make sheaves or bindings,\n\nReap, or be an head reaper, and rise early,\n\nOr have an horn and be an hayward, and be out till morning,\n\nAnd keep my corn in my croft from pickers and stealers?\n\nOr make shoes, or sew cloth, or tend sheep or cattle,\n\nOr make hedges, or harrow, or drive geese, or be swineherd?\n\nOr can you work at any craft which the commune calls for,\n\nTo be means of livelihood to the bed-ridden?'\n\n'I have no penny,' said Piers, 'to buy pullets,\n\nNor geese nor pigs, but two green cheeses,\n\nA few curds of cream, a cake of oatmeal,\n\nTwo loaves of beans and bran, baked for my children;\n\nAnd, by my soul, I swear I have no salt bacon,\n\nNor cook to make collops, I take Christ to witness!\n\nBut I have parsley and pot herbs and a plenty of cabbages,\n\nAnd a cow and a calf, and a cart mare\n\nTo draw my dung afield till the drought is over.\n\nThis is the little we must live on till the Lammas season.\n\nAnd then I hope to have my harvest in the garner.\n\nAnd then I may spread your supper to my soul's content.'\n\nSo all the poor people fetched peascods,\n\nAnd brought him beans and baked apples by the lapful,\n\nRipe cherries, chervils and many small onions,\n\nAnd offered Piers the present to please Hunger.\n\nThe needy are our neighbours, if we note rightly;\n\nAs prisoners in cells, or poor folk in hovels,\n\nCharged with children and overcharged by landlords.\n\nWhat they may spare in spinning they spend on rental,\n\nOn milk, or on meal to make porridge\n\nTo still the sobbing of the children at meal time.\n\nAlso they themselves suffer much hunger.\n\nThey have woe in winter time, and wake at midnight\n\nTo rise and to rock the cradle at the bedside,\n\nTo card and to comb, to darn clouts and to wash them,\n\nTo rub and to reel and to put rushes on the paving.\n\nThe woe of these women who dwell in hovels\n\nIs too sad to speak of or to say in rhyme.\n\nAnd many other men have much to suffer\n\nFrom hunger and from thirst; they turn the fair side outward,\n\nFor they are abashed to beg, lest it should be acknowledged\n\nAt their neighbours what they need at noon and even.\n\nI know all this well; for the world has taught me\n\nWhat befalls another who has many children,\n\nWith no claim but his craft to clothe and feed them,\n\nWhen the mouths are many and the money scarce.\n\nThey have bread and penny ale in place of a pittance,\n\nAnd cold flesh and cold fish for venison from the butcher.\n\nOn Fridays and fast days a farthing worth of mussels\n\nWould be a feast for such folk, with a few cockles.\n\nIt were an alms to help all with such burdens,\n\nAnd to comfort such cottagers and crooked men and blind folk.\n\n_Langland was angry about the peasants' plight. Although not, as it would turn out, as angry as the peasants themselves._\n\n## _The Peasants' Revolt, May\u2013June 1381_\n\n_THE ANONIMALLE CHRONICLE_\n\n_Something like foreboding settled upon late-fourteenth-century England. The plague came back in 1374 and 1379_ ; _the harvest failed in 1369_.\n\n_At the top all was awry. The last days of Edward III were marked alternately by his senility and his seduction by his mistress Alice Perrers. When he died in 1377 his heir was a minor, his ten-year-old grandson, Richard II; the_ de facto _ruler was Richard's uncle John of Gaunt, who persisted in the Hundred Years War with France \u2013 now on a losing streak for the English \u2013 and ham-fisted attempts to curtail an increasingly assertive Parliament (which in 1376 had elected its first Speaker)._\n\n_At the bottom all was bitterness. The Statute of Labourers pegged wages at pre-Black Death levels, whereas the shortage of labour caused by the plague drove the peasants (who made up go per cent of the population) to demand more pay and the ending of demeaning serf services._\n\n_The spark to the tinderbox was the 1380 poll tax, to raise revenue for the French war, set at the flat rate of 3 groats per household._\n\nIn the year 1380, because the subsidies were lightly granted at the parliament of Northampton and because various lords and commons were advised that the subsidies were not duly or loyally levied, but commonly exacted from the poor and not from the rich, to the great profit and advantage of the collectors, and the deception of the king and the commons, the King's council ordained certain commissions to make inquiry in each township how they were levied. One of these commissions was sent to Essex to a certain Thomas Bampton [i.e. John Bampton] steward of a lord, who was regarded as a king or great magnate in that area because of the great estate that he kept. And one day before Whitsuntide he held a court at Brentwood in Essex to make inquisition, and showed the commission directed to him to raise the money which was in default, and to inquire how the collectors had levied the subsidy. He had summoned before him a hundred of the neighbouring townships and wished to have from them a new subsidy, commanding the people of those townships to inquire diligently and to give their replies and to pay their dues. Amongst these townships all the people of Fobbing gave answer that they would not pay a penny more because they already had a receipt from him for the said subsidy. On this Thomas menaced them strongly, and he had with him two sergeants-at-arms of our lord the king; and for fear of his wrath the people of Fobbing took counsel with the people of Corringham, and the folks of these two townships made levies and assemblies, and sent messages to the men of Stanford-le-Hope to urge them to rise too, for their common profit. And then the men of the three townships came together to the number of a hundred or more and with one assent went to Thomas Bampton and roundly gave him answer that they would have nothing to do with him nor give him one penny. On this Thomas ordered the sergeants at arms to arrest these folks and put them into prison; and the commons rose against him and would not be arrested, but tried to kill Thomas and the two sergeants. On this Thomas fled towards London to the king's council and the commons fled to the woods for fear of his malice and lay there a long time, till they were almost famished; and afterwards they went from place to place to stir up other people to rise against the lords and good folk of the countryside. And because of these doings of Thomas Sir Robert Belknap, Chief Justice of the Common Pleas of our lord the king, was sent to the shire with a commission of trailbaston, and indictments against various persons were laid before him, so that the people of the countryside were in such fear that they proposed to abandon their homes. Therefore the commons rose against him and came before him and told him that he was a traitor to the king and the realm, and that it was of pure wickedness and malice that he wished to put them in default by means of the false inquests made before him. And because of this evil they caused him to swear on the Bible that he would never again hold such a session nor act as a justice in such inquiries. And they made him tell them the names of all the jurors, and they took all that they could catch and cut off their heads and cast their houses to the ground, and Sir Robert took his way home with all possible speed. And afterwards the commons assembled together before Whitsunday to the number of 50,000 and went to the manors and townships of those who did not wish to rise with them and rased their houses to the ground or set fire to them. At this time they caught three clerks of Thomas Bampton and cut off their heads, which they carried about with them for several days as an example to others; for it was their purpose to slay all lawyers and all jurors and all the servants of the king whom they could find. Meanwhile all the great lords of the countryside and other people of substance fled towards London and to other shires where they might be safe.\n\nAt the same time the high master of the hospital of St John of Clerkenwell in London had a very beautiful and delectable manor-house in Essex, where he had ordered victuals and other necessities to hold his chapter general, and it was well furnished with wines and was suitably appointed, as befits such a lord and his brethren. And at this time the commons came to the manor and ate the victuals and drank three tuns of good wine and rased the manor-house to the ground and set it alight, to the great damage and loss of the master. And then the commons sent various letters into Kent and Suffolk and Norfolk to urge them to rise with them; and when they had assembled they went about in many bands doing great mischief in all the countryside. After this on the Monday next after the feast of Whitsuntide [3 June] a knight of the household of our lord the king, Sir Simon Burley by name, had in his company two sergeants at arms of the king, and came on the Monday abovesaid to Gravesend and there challenged a man as being his serf. And the good folks of the town came to make a bargain for the man in civil fashion, because of their respect for the king; but Sir Simon would not take less than \u00a3300, a sum which would have been the man's undoing. The good folks prayed him to lessen the sum, but they could not come to terms nor induce him to take a lesser sum, though they told Sir Simon that the man was a Christian and of good character and that therefore he ought not to be ruined for ever. But Sir Simon was very angry and irritable, and greatly despised these good folk, and for haughtiness of heart he bade his sergeants bind the said man and take him to Rochester Castle, to be kept in custody there; from which there came later great evil and mischief And after his departure the commons began to rise, gathering to them the men of many townships of Kent.\n\nAnd at this juncture a justice was assigned by the king and council to go into Kent with a commission of trailbaston, as had been done before in Essex, and with him went a sergeant-at-arms of our lord the king, Master John Legge by name, carrying with him a great number of indictments against various folks of that area to make the king rich. And they would have held a session at Canterbury, but they were driven away by the commons. And after this the commons of Kent gathered together in great numbers day by day, without head and without chieftain, and on Friday before [a mistake for 'after'] Whitsuntide came to Dartford; and they took counsel there and ordained that no one who dwelt near the sea in any place for the space of 12 leagues should come with them, but keep the coasts of the sea from the enemies, saying amongst themselves that there were more kings than one and that they would not suffer or have any king except King Richard.\n\nAt the same time the commons of Kent came to Maidstone and cut off the head of one of the best men of the town, and rased to the ground various places and tenements of people who would not rise with them, as had been done before in Essex. And on the Friday following they came to Rochester and there met a great number of the commons from Essex. And because of the man of Gravesend, they laid siege to Rochester Castle, to deliver their friend from Gravesend, whom the aforesaid Sir Simon had imprisoned. They laid siege with energy to the Castle, and the constable defended himself vigorously for half a day, but at last, for fear that he had of such a multitude of men deaf to reason from Essex and Kent, he delivered up the castle to them. And the commons entered and took their companion and all the other prisoners out of prison: and those who had come from Gravesend repaired home with their fellow with great joy, without doing any more, but the men of Maidstone took their way with the other commons through the countryside. And there they made their chief a certain Wat Tyghler of Maidstone to maintain them and be their counsellor. And on the next Monday after the feast of the Holy Trinity they came to Canterbury before the hour of noon, and 4,000 of them entered into the minster church of St Thomas and, kneeling down, they cried with one voice on the monks to elect a monk to be archbishop of Canterbury, 'for he who is now archbishop is a traitor, and will be beheaded for his iniquity'. And so he was five days afterwards! And when they had done this, they went into the town to their fellows, and by one assent they summoned the mayor, bailiffs and commons of the said town and examined them whether there were any traitors amongst them; and the townsfolk said that there were three and named them. These three the commons dragged out of their houses and cut off their heads. And afterwards they took 500 men of the town with them to London, and left the others to guard the town.\n\nAt this time the commons had as their counsellor a chaplain of evil character, Sir John Ball by name, who advised them to get rid of all the lords and archbishops, bishops, abbots, priors, and most of the monks and canons, saying that there should be no bishop in England except one archbishop, and that he should be that archbishop, and that there should be no monks or canons in any religious houses save two, and that their possessions should be shared out amongst the laity. For these sayings he was esteemed amongst the commons as a prophet, and laboured with them day by day to strengthen them in their malice; and a fitting reward he had afterwards, for he was drawn, hanged, disembowelled, and beheaded as a traitor.\n\nAfter this the commons went to various towns and raised the people, whether they wished to do so or not, until they had gathered together fully 60,000. And as they journeyed towards London they encountered various lawyers and twelve knights of the king and the countryside, and they took them and made them swear to support them, or otherwise they would be beheaded. And they wrought much damage in Kent and especially to Thomas Haselden, a servant of the Duke of Lancaster, because of their hatred for the duke. They rased his manors to the ground and all his houses, and sold his beasts \u2013 his horses, oxen, cows, sheep, and pigs \u2013 and all his stores of corn, at cheap rates. And every day they wanted to have his head and that of Sir Thomas Orgrave, clerk of the receipt and sub-treasurer of England. And when the king heard of their doings he sent his messengers to them on the Tuesday next after Trinity Sunday, to ask them why they were behaving in this fashion and why they were raising a rebellion in his land. And they returned answer by the messengers that they were rising to deliver him and to destroy the traitors to him and to his kingdom. The king sent again to them to bid them cease their doings, in reverence for him, until he could speak with them, and he would make reasonable amends, according to their will, of all that was amiss; and the commons begged him, by the said messengers, that he would be pleased to come and talk with them at Blackheath. And the king sent again the third time to say that he would willingly come next day at the hour of prime to hear their purpose; and then the king, who was at Windsor, removed with all speed to London. At this time the mayor and good folk of London came to meet him and conduct him safely to the Tower of London; there all the council and all the lords of the countryside round about assembled, that is, the Archbishop of Canterbury, chancellor of England, the Bishop of London, the Master of the Hospital of St John of Clerkenwell, then treasurer of England, and the Earls of Buckingham, Kent, Arundel, Warwick, Suffolk, Oxford, Salisbury and other persons to the number of 600.\n\nAnd on the vigil of Corpus Christi Day [12 June] the commons of Kent came to Blackheath, three leagues from London, to the number of 50,000, to await the king's arrival, and they displayed two banners of St George and forty pennons and the commons of Essex came to the other side of the water to the number of 60,000 to help them and hear the king's response. And on the Wednesday the king who was at the Tower of London, thinking to settle the affair, caused his barges to be assembled and took with him in his barge the archbishop and the treasurer and others of his council and four other barges for his retinue, and went to Greenwich, three leagues from London; and there the chancellor and treasurer warned the king that it would be too great a folly to go to them, for they were men without reason, and had not the sense to behave properly. But as the king, by the advice of the chancellor and treasurer, would not come to the commons of Kent, they sent a petition to him requiring him to grant them the heads of the Duke of Lancaster and fifteen other lords, of whom fourteen [?three] were bishops present with him in the Tower of London; and these were their names \u2013 Sir Simon Sudbury, Archbishop of Canterbury and Chancellor of England, Sir Robert Hales, Prior of the Hospital, treasurer of England, the Bishop of London, Sir John Fordham, clerk of the privy seal and Bishop-elect of Durham, Sir Robert Belknap, chief justice of the common pleas, Sir Ralph Ferrers, Sir Robert Plessington, chief baron of the exchequer, John Legge, sergeant-at-arms of the king, and Thomas Bampton aforesaid and others. And to this the king would not agree, wherefore they sent again to him a yeoman, praying that he would come and speak with them; and he said that he would gladly do so, but the chancellor and treasurer gave him contrary advice, telling them that if they wished to come to Windsor the following Monday, they should have there a suitable answer.\n\nAnd the commons had among themselves a watch word in English, 'With whom hold you?' and the response was, 'With king Richard and with the true commons', and those who could not or would not so answer were beheaded and put to death. And at this time there came a knight with all the haste that he could, crying to the king to wait; and the king was startled at this and awaited his arrival to hear what he had to say. And the knight came to the king to tell him that he had it from a servant who had been in the hands of the rebels that day, that if the king should come to them, all the land would be lost, for they would never let him loose for any consideration, but would take him round with them through all England, and that they would make him grant all their demands, and that their purpose was to slay all the lords and ladies of great renown, and all the archbishops, bishops, abbots, priors, monks, and canons, parsons, and vicars, by the advice and counsel of the aforesaid Sir John Ball. Therefore the king returned to London as fast as he could and arrived at the Tower at the hour of terce.\n\nAnd at this time the yeoman already mentioned above hastened to Blackheath crying to his fellows that the king had gone, and that it would be well for them to press on to London to pursue their purpose. On the same day of Wednesday before the hour of vespers the commons of Kent came, as many as 60,000 of them, to Southwark, where the Marshalsea was, and they broke and threw down to the ground all the buildings of the Marshalsea, and took out of prison all the prisoners who were held captive there for debt or felony. And they levelled to the ground a fine house belonging to John Imworth, then marshal of the marshalsea of the king's bench, and keeper of the prisoners of the said place, and all the houses of the jurors and questmongers belonging to the marshalsea, throughout that night.\n\nAt the same time the commons of Essex reached Lambeth, near to London, a manor of the Archbishop of Canterbury, and entered the buildings there, and destroyed many goods of the archbishop, and burnt all the books of register and rolls of remembrance of the chancery which they found there. And the next day, Thursday, which was the feast of Corpus Christi, the 13th day of June, with the dominical letter F, the commons of Essex went in the morning to Highbury, two leagues north of London, a very fine manor-house of the Master of the Hospital of St John of Clerkenwell, and they set it on fire, to the great damage and loss of the Hospitallers of St John. Some of them then returned to London, while the others stayed in the open fields all night. And this same day of Corpus Christi, in the morning, the commons of Kent pulled down a house of ill fame near London Bridge, which was in the hands of Flemish women and they had the house to rent from the mayor of London. And then they surged on to the bridge to pass into the city, but the mayor was just before them and had the chain drawn up and the drawbridge lifted to stop their passage. And the commons of Southwark rose with them and cried to the keepers of the bridge to lower the drawbridge and let them in, or otherwise they would be undone. And for fear of their lives the keepers let them enter, though it was against their will. At this time all the religious and the parsons and the vicars of London were going devoutly in procession to pray God for peace. And at the same time the commons took their way through London and did no harm or molestation until they came to Fleet Street. (And at the same time, as was said, the commons of London set fire to the beautiful manor-house of the Savoy before the arrival of the commons from the country.) And in Fleet Street the said commons of Kent broke open the Fleet prison and released all the prisoners and let them go whither they would. Then they stopped and threw to the ground, and set fire to, the shop of a certain chandler and another shop of a certain blacksmith, in the middle of the said street. There there shall never again be houses, it is said, to deface the beauty of the street. And after that they went to the Temple to destroy the tenants of the Temple, and they cast down the house to the ground and tore off all the tiles, so that the buildings were in a bad state, without any roofing.\n\nAnd they went into the Temple Church and took all the books and rolls and remembrances which were in the cupboards of the apprentices at law in the Temple, and carried them into the highway and burnt them. And then they went towards the Savoy, destroying all the buildings belonging to the Master of the Hospital of St John. And then they went to the house of the Bishop of Chester, near the church of St Mary-le-Strand, where was dwelling Sir John Fordham, the elect of Durham, and clerk of the privy seal, and they rolled barrels of wine out of his cellar, and drank their fill, and departed without doing further damage. And then they went towards the Savoy and set fire to various houses of various folks and questmongers on the western side, and at last they came to the Savoy. They broke open the gates and entered the place and came to the wardrobe, and they took all the torches they could find and set fire to all the sheets and coverlets and beds and head boards of great worth, for their whole value amounted, it was said, to 1,000 marks. And all the napery and other things which they could find they carried into the hall and set it on fire with their torches. And they burnt the hall and chambers and all the buildings within the gates belonging to the said palace or manor, which the commons of London had left unburnt. And, as was said, they found three barrels of gunpowder which they took to be gold or silver, and they threw them on the fire, and this powder blew up high and set the hall in a greater blaze than before, to the great loss and damage of the Duke of Lancaster. The commons of Kent got the blame, but some said that the Londoners were really responsible, because of their hatred for the said duke. Then one party of them went towards Westminster and set on fire a house belonging to John Butterwick, under-sheriff of Middlesex, and other houses of various people, and broke open the prison at Westminster and brought out all the prisoners condemned by the law, and afterwards they returned to London by way of Holborn, and in front of St Sepulchre's Church they set fire to the houses of Simon Hosteler and several other houses, and broke open Newgate prison and let loose all the prisoners, for whatever cause they had been imprisoned.\n\nThe same Thursday the commons went to St Martin-le-Grand and tore away from the high altar a certain Roger Legett, a great 'assizer' and took him to Cheapside and beheaded him there; on the same day eighteen others were beheaded in various parts of the town. At the same time a great body of commons went to the Tower to speak to the king, and could not gain speech with him, wherefore they laid siege to the Tower from the side of St Katherine's, towards the south. And another part of the commons who were in the city went to the hospital of St John of Clerkenwell and on the way burnt the house and buildings of Roger Legett the questmonger who had been beheaded in Cheapside and all the rented houses and tenements of the hospital of St John that they could; and afterwards they came to the beautiful priory of the said hospital and set on fire several fine and desirable buildings in the same priory, a great and horrible piece of damage for all time to come; and then they returned to London to rest or to do more mischief.\n\nAt this time the king was in a turret of the great Tower of London, from which he could see the manor of the Savoy and the hospital of Clerkenwell, and the buildings of Simon Hosteler near Newgate, and John Butterwick's house, all on fire at once. And he called all his lords about him to his chamber and asked their advice as to what he should do in such an emergency; and none of them could or would give him any counsel. Wherefore the young king said that he would send to the mayor of the city to bid him order the sheriffs and aldermen to have it cried round their wards that all men between the ages of 15 and 60, on pain of life and members, should go on the morrow, Friday, to Mile End and meet him at seven in the morning. He did this so that all the commons who were surrounding the Tower would raise the siege and go to Mile End to see and hear him, and all those who were in the Tower could go away safely whither they would and save themselves; but it was of no avail, for the besieged did not have the good fortune to get away.\n\nAfter this on the same Thursday, the feast of Corpus Christi, the king being in the Tower pensive and sorrowful, climbed up into a little turret towards St Katherine's, where were lying a great number of the commons, and caused a proclamation to be made to them that they should all go home in a peaceful manner and that he would pardon them all manner of trespasses. But all cried with one voice that they would not leave before they had taken the traitors who were in the Tower and had been given charters to be free of all manner of serfdom and had been granted all the items which they wished to ask. And the king graciously granted all and caused a clerk to write a bill in their presence in this style: 'Richard, king of England and of France, greatly thanks his good commons because they have such a great desire to see and hear their king, and pardons them for all manner of trespasses and misprisions and felonies committed until now, and wills and commands that now everyone should hasten to his own home and wishes and commands that each one should put his grievances into writing, and cause them to be sent to him, and he will provide, with the aid of his loyal lords and of his good counsel such remedy as shall be profitable for him and them and for the realm.' And to this document he set his signet seal in their presence, and sent out the said bill with two of his knights to them before St Katherine's and caused it to be read to them. And the knight who read it stood up on an old chair before the others so that all could hear. All this time the king was in the Tower in great distress of mind. And when the commons had heard the bill, they said that this was nothing but trifles and mockery; wherefore they returned to London and caused it to be cried throughout the city that all lawyers and all the officials of the chancery and exchequer and all those who could write a writ or a letter should be beheaded, wherever they could be found; and at this time they burnt several more houses in the city. And the king climbed to a high garret of the Tower and watched the fires, and then came down again and sent for the lords to have their counsel; but they did not know how to advise him and all were wondrously abashed.\n\nNext day, the Friday, the commons of the countryside and the commons of London assembled in fearful strength to the number of 100,000 or more, besides some four score or more who stayed on Tower Hill to watch those who were in the Tower. And some went to Mile End towards Brentwood to await the coming of the king, because of the proclamation he had made, and the others came to Tower Hill. And when the king knew that they were there, he sent them orders by a messenger to join their friends at Mile End and he himself would join them soon. And at this time of the morning he advised the Archbishop of Canterbury and the others who were in the Tower to go down to the Little Water Gate and take a boat and save themselves. And the archbishop did so, but a wicked woman raised a cry against him and he had to return to the Tower, to his destruction. And by seven o'clock the king came to Mile End and with him his mother in a whirlecote [a wheeled carriage] with the Earls of Buckingham, Kent, Warwick, and Oxford, Sir Thomas Percy, Sir Robert Knolles, the mayor of London, and many knights and squires; and Sir Aubrey de Vere carried the king's sword. And when he was come the commons all knelt down to him, saying; 'Welcome, our lord, King Richard, if it pleases you, and we will have no other king but you.' And Wat Tyghler, their leader and chief, prayed to him in the name of the commons that he would suffer them to take and hold all the traitors who were against him and the law; and the king granted that they should take at their wish those who were traitors and could be proved traitors by the law. And Wat and the commons were carrying two banners and many pennons and pennoncelles, while they made their petition to the king. And they required that no man should be a serf, nor do homage or any manner of service to any lord, but should give fourpence rent for an acre of land, and that no one should serve any man but at his own will, and on terms of regular covenant. And at this time the king caused the commons to arrange themselves in two lines, and caused a proclamation to be made before them that he would confirm and grant them their freedom and all their wishes generally, and that they should go through the realm of England and catch all traitors and bring them to him in safety and that he would deal with them as the law required. Under colour of this grant Wat Tyghler and the commons took their way to the Tower, to seize the archbishop and the others, the king being at Mile End.\n\nAt this time the archbishop was chanting his mass devoutly in the Tower and shrove the prior of the hospital of Clerkenwell and others, and then he heard two masses or three, and chanted the _commendation_ and the _placebo_ and the _dirige_ and the _seven psalms_ and the _litany_ ; and when he was at the words 'All saints, pray for us' the commons burst in and dragged him out of the chapel of the Tower, and struck and hustled him villainously, as they did the others who were with him and dragged them to Tower Hill. There they cut off the heads of Master Simon Sudbury, Archbishop of Canterbury, and of Sir Robert Hales, Prior of the Hospital of St John of Clerkenwell, Treasurer of England, Brother William Appleton, a great physician and surgeon, and one who had great influence with the king and the Duke of Lancaster. And some time afterwards they beheaded John Legge, the king's sergeant-at-arms, and with him a juror; and at the same time the commons proclaimed that anyone who could catch any Fleming or other alien of any nation might cut off his head, and so they did after this. And then they took the heads of the archbishop and the others and stuck them on wooden poles and carried them before them in procession through the city, to the shrine of Westminster Abbey, in contempt of them and of God and of Holy Church, for vengeance descended on them not long afterwards. Then they returned to London Bridge and set the head of the archbishop above the bridge and the eight other heads of those that were murdered, so that they might be seen by all who passed over the bridge. And when this was done, they went to the church of St Martin's in the Vintry, and found therein 35 Flemings, whom they dragged out and beheaded in the street. On that day were beheaded in all some 140 or 160 persons. And then they took their way to all the houses of the Lombards and other aliens, and broke into their dwellings and robbed them of all their goods which they could find. This went on throughout the day and the following night, with hideous cries and horrible tumult.\n\nAt this time, because the chancellor had been beheaded, the king made the Earl of Arundel chancellor for the day and delivered to him the great seal, and throughout the day caused various clerks to write charters and patents and protections granted to the commons touching the matters before mentioned, without taking any fines for sealing or description. And on the next day, Saturday, a great number of the commons came to the abbey of Westminster at the hour of terce and there they found John Imworth, Marshal of the Marshalsea and warden of the prisoners, a tormentor without pity; he was near the shrine of St Edward, clinging to a marble pillar, as an aid and succour to save him from his enemies. And the commons wrenched his arms away from the pillar of the shrine and brought him to Cheapside and beheaded him. And at the same time they took from Bread Street a yeoman named John Greenfield because he had spoken well of Brother William Appleton and of other murdered persons, and brought him to Cheapside and beheaded him. All this time the king caused proclamation to be made round the city that everyone should go peacefully to his own country and his own house without doing any more evil; but to this the commons paid no heed.\n\nAnd on this same day, at three o'clock in the afternoon, the king came to Westminster Abbey, and some 200 persons with him. And the abbot and convent of the same abbey and the canons and vicars of the chapel of St Stephen came in procession to meet him, dressed in their copes and with bare feet, halfway to Charing Cross, and they brought him to the abbey and the church and the high altar and the king made his prayer devoutly and left an offering for the altar and the relics. And afterwards he spoke to the anchorite and confessed to him and was with him for some time. And then the king caused a proclamation to be made that all those commons of the country who were still in London should come to meet him at Smithfield, and so they did. And when the king had come with his train he turned to the eastern side, near St Bartholomew's, a house of canons; and the commons arrayed themselves on the west side in battle formation, in great numbers. At this moment the mayor of London, William Walworth, came up, and the king bade him go to the commons and cause their chieftain to come to him. And when he was called by the mayor, Wat Tyghler by name, of Maidstone, he came to the king in a haughty fashion, mounted on a little horse so that he could be seen by the commons. And he dismounted, carrying in his hand a dagger which he had taken from another man, and when he had dismounted he half bent his knee, and took the king by the hand, and shook his arm forcibly and roughly, saying to him, 'Brother, be of good comfort and joyful, for you shall have within the next fortnight 40,000 more of the commons than you have now and we shall be good companions.' And the king said to Wat; 'Why will you not go back to your own country?' And the other replied with a great oath that neither he nor his fellows would depart until they had their charter such as they wished to have, and such points rehearsed in their charter as they chose to demand, threatening that the lords of the realm would rue it badly if the points were not settled to their satisfaction. And the king asked him what were the points that he wanted, and he would have them freely without contradiction written down and sealed. And then Wat rehearsed points which were to be demanded; and he asked that there should be no law except the law of Winchester, and that there should be henceforth no outlawry in any process of law, and that no lord should have any lordship, except only to be respected according to their rank among all folks, and that the only lordship should be that of the king; and that the goods of Holy Church should not remain in the hands of the religious, nor of the parsons and vicars, and other churchmen; but those who were in possession should have their sustenance from the endowments and the remainder of their goods should be divided amongst the parishioners; and no bishop should remain in England save one, nor more than one prelate, and that all the lands and tenements now held by them should be confiscated and shared amongst the commons, saving to them a reasonable substance. And he demanded that there should be no more bondmen in England, no serfdom nor villeinage, but that all should be free and of one condition. And to this the king gave an easy answer, and said that he should have all that could fairly be granted saving to himself the regality of the crown. And then he commanded him to go back to his home without further delay. And all this time that the king was speaking no lord nor any other of his council dared nor wished to give any answer to the commons in any place except the king himself.\n\nPresently Wat Tyghler, in the king's presence, called for a flagon of water to rinse his mouth because he was in such a heat, and when it was brought he rinsed his mouth in a very rude and disgusting fashion before the king; and then he made them bring him a flagon of ale of which he drank a great deal, and in the king's presence mounted his horse. At this time a yeoman of Kent, who was among the king's retinue, asked to see Wat, the leader of the commons; and when Wat was pointed out to him, he said openly that he was the greatest thief and robber in all Kent. Wat heard these words and commanded him to come out to him, shaking his head at him in sign of malice; but the yeoman refused to go to him for fear of the mob. At last the lords made him go out to Wat, to see what he would do in the king's presence; and when Wat saw him, he ordered one of his followers, who was riding on a horse carrying his banner displayed, to dismount and cut off the yeoman's head. But the yeoman answered that he had done nothing worthy of death, for what he had said was true and he would not deny it, but in the presence of his liege lord he could not lawfully make debate without leave, except in his own defence; and that he could do without reproof, for if he was attacked he would strike back. And for these words Wat would have run him through with his dagger and killed him in the king's presence; and because of this, the mayor of London, William Walworth by name, reasoned with the said Wat for his violent behaviour and contempt done in the king's presence, and arrested him. And because he arrested him, the said Wat struck the mayor with his dagger in the stomach with great anger; but as God would have it, the mayor was wearing armour and took no harm. But like a hardy and vigorous man the said mayor drew his cutlass and struck back at the said Wat and gave him a deep cut on the neck and then a great cut on the head. And in this scuffle a yeoman of the king's household drew his sword and ran Wat two or three times through the body, mortally wounding him. And the said Wat spurred his horse, crying to the commons to avenge him, and the horse carried him some four score paces, and there he fell to the ground half dead. And when the commons saw him fall, and did not know for certain how it was, they began to bend their bows and to shoot; wherefore the king himself spurred his horse and rode out to them, commanding them that they should all come to him at the field of St John of Clerkenwell.\n\nMeanwhile the mayor of London rode as fast as he could back to the city commanding all those who were in charge of the 24 wards to make proclamation in their wards that every man should arm himself as quickly as he could, and go to the king in St John's Fields, where the commons were, for he was in great need and necessity. And at this time nearly all the knights and squires of the king's household and many others, for fear that they had of this affray, left their liege lord and each went his own way. Afterwards when the king had reached the open fields he made the commons array themselves on the west side. And soon the aldermen came to him in a body, bringing with them the wardens of the wards, by various routes, with a fine company of people well armed in great strength and they enveloped the commons like sheep in a pen. And when the mayor had sent the wardens to the king, he returned to Smithfield with a fine company of lances to make an end of the captain of the commons abovesaid. And when he came to Smithfield he could not find the said captain Wat Tyghler, and at this he marvelled greatly and asked what had become of the traitor; and he was told that Tyghler had been carried by some of the commons to the hospital of the poorfolks near St Bartholomew's and was put to bed in the chamber of the master of the hospital. And the mayor went thither and found him and had him carried to Smithfield in the presence of his fellows and there he was beheaded. And so ended his wretched life. And the mayor caused his head to be set upon a pole and carried before him to the king who still abode in the fields. And when the king saw the head he had it brought near him to abash the commons and thanked the mayor warmly for what he had done. And when the commons saw that their leader, Wat Tyghler, was dead in such a manner, they fell to the ground among the wheat like men discomforted, crying to the king for mercy for their misdeeds. And the king benevolently granted them mercy and many of them took to flight; and the king ordered two knights to lead the rest of the Kentishmen through London and over London Bridge without doing them any harm, so that each of them could go in peace to his own home. Then the king ordered the mayor, William Walworth, to put on his head a helmet in anticipation of what was going to happen; the mayor asked why he was to do so and the king replied that he was greatly obliged to him and therefore was going to confer on him the order of knighthood. And the mayor answered that he was not worthy nor able to have or to keep up a knight's estate, for he was but a merchant and had to live by merchandise; but at last the king made him put on the helmet and took a sword in both his hands and dubbed him knight resolutely and with great goodwill. And the same day he made three other knights from among the citizens of London on that same spot, and these are their names \u2013 John Philipot [Philpott], Nicholas Brymber [Brember] and [blank in the MS.]; and the king gave Sir William Walworth \u00a3100 in land and each of the others \u00a340 in land for themselves and their heirs; and afterwards the king took his way towards London to his wardrobe to ease himself after his great labours.\n\n_John Ball, whose couplet 'When Adam delved and Eve span, who was then the gentleman?', became a mantra of English social protest, was hanged at St Albans on 15 July. Two months later, Richard II had the nation back under control, and revoked his promises made at Blackheath (a general pardon, abolition of villeinage, fixing of rent at fourpence per acre, and liberty to trade)._\n\n_The Peasants' Revolt had been suppressed, but change in the countryside was not. Within 150 years feudalism would effectively be ended, with the English countryside a place of tenant farmers and free labourers, not serfs._\n\n_Facing down the peasant rebels at Blackheath in 1381 was Richard II's one and only hour of glory. As he matured he developed Frenchified habits (he ate with a spoon and commissioned a royal cookery book) and a worrying taste for autocratic rule. This megalomania led him to exile the late John of Gaunt's son, Henry Bolingbroke, Duke of Lancaster, and seize his estates. In response, Bolingbroke led an invasion (with an army donated by the French) to recover his inheritance, but so many defected to his cause that his ambition escalated and he seized the throne in a_ coup d'\u00e9tat. _Richard II, forced to abdicate, became plain Sir Richard of Bordeaux and was imprisoned in Pontefract castle, where he died in 1400_ , _probably through forced starvation._\n\n_Like many a usurper, Henry IV lived in a state of paranoid insecurity. It was well founded. A Welsh revolt led by Owain Glyndwr in 1400 was joined by Henry Percy, Earl of Northumberland, who also rose against the usurped crown again in 1405 and yet again in 1408_. _Just when Henry thought it was all over, he discovered that his own son, Prince Henry, was plotting for power. The trials of usurpation took their toll on Henry's body; he developed a disfiguring skin disease. Careworn and decrepit, he died of a fit on 20 March 1413_. _Three weeks later the twenty-six-year-old Prince Henry assumed the throne as Henry V._\n\n_Prince Henry had been a medieval playboy. As king, he was a revelation, serious-minded, with a political vision of England which both unified the realm and diverted from its woes: an English empire in France._\n\n## _The Battle of Agincourt, 25 October 1415_\n\nANONYMOUS PRIEST\n\n_On 11 August 1413 at the head of 10,000 soldiers, Henry V sailed to France, claiming its throne as his. After besieging and capturing Harfleur, Henry tramped across the Normandy countryside towards Calais with the intention of tempting the French to battle. At Agincourt, a French army of some 30,000 decided to oblige. Siege, disease and garrisoning duties had reduced the English force to around 5,000_.\n\nAnd when on the following day, Thursday, we were descending the valley towards the River of the Swords, the king was told by scouts and cavalry skirmishers that there was a powerful adversary numbering many thousands on the other side of the river, almost a league to our right. We therefore crossed the river as fast as we could, and when we reached the crest of the hill on the other side, we saw emerging from the valley about a mile from us hateful swarms of Frenchmen, who appeared to us to be an incomparable multitude in their columns, lines and divisions. They took up their position just over half a mile ahead of us, filling a broad field like an innumerable swarm of locusts, having a small valley between us and them.\n\nMeanwhile our king was encouraging his army courteously and bravely, marshalling them into lines and wings, as if they were to go at once into battle. And then everyone who had not previously cleared his conscience by confession, put on the armour of penitence... And among other sayings which I noted then, a certain knight, Sir Walter Hungerford, wished to the king's face that in addition to the small band which he had there he could have had ten thousand of the better archers of England, who would have been glad to be with them. The king replied: 'Thou speakest as a fool, for by the God of Heaven in whose grace I trust and in whom is my firm hope of victory, I would not have one more than I have, even if I could.... Dost thou not believe that the Almighty can through this humble little band overcome the pride of these Frenchmen, who boast of their numbers and their strength?'...\n\nAnd when the enemy in position saw and considered the disposition and fewness of our troops, they betook themselves to a field beyond a certain wood, which lay near to the left between us and them, where was our road to Calais. So our king, thinking that they might go round the wood to attack him along the road, or else might go round woods further away in the neighbourhood and surround us from all sides, at once moved his lines and he always stationed himself to face the enemy...\n\nAnd when at last we were at the last rays of light, and darkness fell between us and them, we still stood in the field and heard our foes, everyone calling as the manner is, for his comrade, servant and friend, dispersed by chance in so great a multitude. Our men began to do the same, but the king ordered silence throughout the whole army, under penalty of the loss of horse and harness in the case of a gentleman... and of the right ear in the case of a yeoman or below, with no hope of pardon, for anyone who might presume to break the king's order. And he at once went in silence to a hamlet nearby, in a place where we had only a few houses; most of us had to rest in gardens and orchards, through a night of pouring rain. And when our enemies considered the quietness of our men and our silence, they thought that we were struck with fright at our small numbers and contemplated flight during the night; so they established fires and strong watches throughout the fields and routes. And as it was said they thought they were so sure of us that they cast dice that night for our king and nobles.\n\nAnd on the morrow, Friday the feast of Saints Crispin and Crispinian, 25th October, the Frenchmen, at dawn, organized themselves into lines, battles, and wedges, and took up their position facing us in the field called Agincourt, through which lay our route to Calais, in terrific multitude; and they set squadrons of horsemen in many hundreds on either side of their front lines, to break our line and the strength of our archers. The front line was composed of dismounted men made up of all the noblest and choicest of their forces, who in the forest of spears... were by estimation thirty times more numerous than our men. But their rear lines... were all on horseback... and compared with our men they were an innumerable multitude.\n\nAnd meanwhile our king prepared himself for the field, after hearing lauds and masses and... arranged his small numbers in one 'battle', placing his vanguard as a wing to his right with the Duke of York in command and the rearguard as a wing to his left under Lord Camoys. Interspersed among the line were wedges of archers, whom the king ordered to affix stakes in front of them, as he had ordered earlier, to stop the attacks of the horsemen...\n\nAnd when much of the day had been consumed... and both armies had stood and had not moved a foot, the king, seeing that the opposing army was abstaining from the attack which had been expected... either to cause us to break our order, or to strike terror into our hearts because of their numbers, or... because they expected more reinforcements to arrive, and knowing that our shortage of food would conquer us by hunger, ordered his men to move towards the enemy, sending orders to the baggage-train of the army to follow up close so that they should not fall as booty to the enemy... After the king had estimated that all his baggage had come up to his rear, he advanced towards the enemy, with his men, in the name of Jesus... and of the glorious Virgin and St George, and the enemy moved towards him. [The priests, including the author, then prayed hard for deliverance.]\n\nAnd when they came near enough to attack, the French horsemen posted on the sides rushed against our archers on both flanks of our army; but quickly, God willing, they were compelled to retreat by the showers of arrows and to flee behind their lines... except the large numbers whom the points of the stakes or the sharpness of the arrows stopped from flight by piercing the horses or the horsemen. The cross-bowmen of the enemy, who were behind the men at arms and on their flanks, fell back in face of the strength of our archers after the first draw, which was too hasty and injured only a few of our men... But the French nobles who had first approached in line, just as they had come from their muster nearby... divided themselves into three columns, either for fear of the arrows... or to penetrate more quickly our force to the banners, attacked our forces at the three places where there were banners; and at the first clash they met our men with such a fierce impact that they were compelled to fall back for almost the distance of a lance... And then the battle grew hotter and our archers shot... their arrows through the flanks of the enemy, the battle continually renewing. And when their arrows were exhausted, they seized axes, swords and lances from those who were lying on the ground, and beat down, wounded and killed the enemy with them... And the just Judge who wished to strike down the proud multitude of the enemy with the thunderbolts of vengeance... broke their power... No one had time to receive them as captives, but almost all of them without distinction of persons, when they fell to the ground, struck down by our men or by those following them, I know not by what hidden judgement of God, were killed without intermission... For when some of them slain at the start of the engagement fell in front, such was the indisciplined violence and pressure of the host behind that the living fell on the dead, and others falling on the living were killed in turn; and so in the three places where there was a concentration of our forces, the piles of dead and those crushed in between grew so much that our men climbed on these heaps which grew higher than a man and slew those below with swords, axes, and other weapons. And when at last after two or three hours the vanguard was cut up and worn out, and the rest were forced into flight, our men began to sort these heaps and separate the living from the dead, intending to keep the living as property to be ransomed. But behold! at once, we know not by what wrath of God, a cry arose that the enemy's rearguard of cavalry, in overwhelming numbers had repaired the enemy line... and was coming against our small and tired band. And so they killed their prisoners with swords... without any distinction of persons, except for the Dukes of Orl\u00e9ans and Bourbon and other illustrious persons in the royal entourage, and a few others, lest the captives should be our ruin in the coming battle.\n\nBut after a little while the troops of the enemy, having tasted the bitterness of our weapons, and at our king's approach, left the field of blood to us...\n\n_Never before or after would England win so impossible a victory on land. Henry, a consummate communicator, ordered a battle report to be sent to England and read aloud. It was the first time that such a dispatch was written in the mother tongue._\n\n## _Agincourt: Henry's Victory March, London, 23 November 1415_\n\nANONYMOUS\n\nHe took his journey byway of the sacred thresholds of the churches of Canterbury and St Augustine's Canterbury to his manor of Eltham, proposing to honour the city of London on the following Saturday with his presence. The citizens, hearing with the greatest joy the news of his approach, prepared themselves and the city in the meanwhile.... And when the desired day of Saturday dawned, the citizens went out to meet the king at the brow of Blackheath, I.e. the mayor and 24 aldermen in scarlet, and the rest of the lesser citizens in red cloaks with red-and-white party-coloured hoods, to the number of about 20,000 horsemen... And when the king came through the midst of them about ten o'clock, and the citizens had given glory and honour to God, and congratulations to the king... the citizens rode before him towards the city, and the king followed...\n\nWhen they arrived at the tower at the entrance to the bridge... there placed on top of the tower was an enormous figure, with... a great axe in his right hand and the keys of the city hanging from a staff in his left hand, like a door-keeper. On his right side stood an effigy not much smaller, of a woman dressed in a scarlet cloak and feminine ornaments, as if they were man and wife who in their best clothes were looking for the desired face of their lord and were receiving him with full honour. The tower was adorned with spears bearing the royal arms, projecting from the battlements, and trumpets and horns sounded in manifold melody; spread across the front of the tower was this elegant and convenient inscription, 'The City of the King of Justice'. And when they reached the little bridge, they found on both sides before them a lofty pillar in the manner of a tower... made of wood, covered with linen cloth painted the colour of white marble and green jasper, to imitate the blocks and stones of mason's work. On top of the column on the right hand side was the effigy of an antelope... with a splendid shield blazoned with the royal arms hanging from its neck, and bearing the royal sceptre in the right foot. On the top of the other column stood the image of a lion, which held aloft in its right claws... the banner of the king displayed; across... the road rose a turret... in the middle of which under a splendid canopy stood a most impressive image of St George, armed, except for his head, which was adorned with a laurel wreath sown with gems sparkling like precious stones, having behind him a scarlet tapestry gleaming with his arms in a number of shields. On his right hung a triumphal helmet, and on his left a great shield of his arms;... in his right hand he held the hilt of the sword with which he was girt and in his left he held a scroll extended across the battlements with the words: 'Honour and glory be to God alone'. And aloft on the tower in front was displayed this prophesy of congratulation: 'The streams of the river make glad the city of God'...And in a house near the tower was a great crowd of boys representing the angelic host clad in white robes, with faces gleaming with gilt paint, with shining wings and the hair of girls crowned with laurel crowns, who sang on the king's approach with sweet voices to the accompaniment of an organ a song according to the programme in English.\n\nAnd when they reached the tower of the aqueduct in Cornhill they found the tower hidden under a scarlet cloth stretched in the form of a tent, on spears hidden under the cloth. Surrounding the middle of the tower in four prominent positions were the arms of St George, St Edward, St Edmund, and of England, interspersed with small shields of royal arms and inset with this pious legend:\n\n'Since the king hopes in the Lord and in the mercy of the Highest, he shall not be moved.'...Under a covering was a band of venerable white-haired prophets in tunics and golden cloaks, with their heads hidden in turbans of gold and red who released, when the king came by, sparrows and other small birds in a great cloud as a sacrifice of thanksgiving to God for the victory He had given, some of the birds resting on the king's breast, some of them alighting on his shoulder, and some flying round his head, while the prophets sang in a sweet voice, according to the programme, this psalm of recognition: 'Sing to the Lord a new song, Hallelujah. For he hath done marvellous things, Hallelujah.'\n\nThen they went on to the tower of the conduit at the entrance to Cheapside which was decked with an awning of green... woven with little shields of the city's arms set in florid profusion, supported on posts covered in the same colour and erected to resemble a building. The tower was decorated above with shafts of spears of arms placed on the battlements... and below the awning were venerable old men, twelve in number, clothed like the apostles and having the names of the twelve apostles written on their brows. With them were twelve kings, martyrs and confessors of the succession of England, with golden girdles round their loins, sceptres in their hands, and crowns on their heads... who sang in unison on the king's approach a sweet song.... And they wafted to him round foils of silver intermingled with thin round wafers, and wine from the channels and cocks of the conduit, so that they might receive him with bread and wine as Melchisedech received Abraham when he returned from the fall of the four kings.\n\nAnd when they came to the cross in Cheapside... it was hidden by a beautiful castle of wood, very ingeniously and prettily constructed, and adorned with three beautiful columns,...which had... arches on either side projecting over the street, and stretching to the buildings on each side of the road.... And across the front of the arches was written, 'Glorious things of thee are spoken, O city of God'. This castle was covered with linen painted the colour of white marble, and green and red jasper, as if the whole work had been the result of the mason's art, fashioned from blocks of masonry and perfect precious stones. The top of the castle... was adorned with the arms of St George, flanked on one side by the arms of the king and on the other by those of the emperor;... on the lower turrets were the arms of the king's ancestors and of the greater magnates of the realm. From the middle of the castle... projected a beautiful gateway, no less cunningly contrived, from which stretched a wooden bridge almost fifteen paces in length, of good width and about the height of a man's waist... adorned with tapestries. When the king approached there came out on to the bridge a chorus of beautiful girls dressed in virgin white... and playing on tambourines as a mark of rejoicing, as if to a David rejoicing at the fall of Goliath, who... represented the pride of the French, and singing: 'Welcome, Henry the Fifth, King of England and of France'. From the top of the castle downwards, on the turrets, battlements, arches, and columns, were innumerable boys, dressed in white garments as angels and archangels, with shining wings and hair strewn with gems... who threw down on the... king as he passed underneath gold coins and laurel leaves, to the honour of Almighty God and as a sign of victory; and all sang together this angelic hymn as previously arranged: 'We praise thee O God, we acknowledge thee to be the Lord'.\n\nAnd when they came to the tower of the conduit at the exit of Cheapside towards St Paul's, the tower had been surrounded with many... niches, and in each niche was a beautiful young girl, in the posture of a statue; and in their hands were golden cups from which they very lightly puffed gold leaf upon the king's head as he rode by. Above the tower was stretched a canopy sky-blue in colour decorated with clouds and many other contrivances; and the top of the canopy was adorned by an archangel in shining gold, and the four posts which held up the canopy were supported by four angels equally cunning in workmanship. Below the canopy... was a figure of majesty represented by a sun darting out flashing rays. Round the top of the canopy fluttered archangels singing sweetly all kinds of music.... And so that this tower might conform in its legend to the preceding praises to the honour and glory of God, not of men, it presented to the gaze of the passers-by this conclusion of praise: 'Thanks be to God'.\n\n...Such was the dense throng of people in Cheapside from one end to the other that horsemen had scarcely... room to ride through the crowds, and the upper storeys and windows on either side were filled with the more noble ladies and women of the realm and with honest and honourable men, who flocked to such a delectable sight, adorned in garments of gold and satin and scarlet, and other types of dress; so that a bigger or more impressive crowd had never gathered before in London.\n\nBut the king himself went along, amidst these shouts of praise and celebrations of the citizens, dressed in a purple robe, not with a haughty look and a pompous train... but with a serious countenance and a reverend pace accompanied by only a few of his most faithful servants; following him, guarded by knights, were the captive dukes, counts and the marshal. From his silent face and... sober pace it could be inferred that the king, silently contemplating, was giving thanks and glory to God alone and not to man. And when he had visited the sanctuary of SS Peter and Paul, he rode away to his palace of Westminster, escorted by the citizens.\n\n_By the Treaty of Troyes (1420) Henry V was made heir to the French throne. English power in France was at its zenith._\n\n## _Some Public Nuisances, 1422_\n\nTHE GENERAL COURT OF THE MAYOR OF THE CITY OF LONDON\n\n_By the early fifteenth century the population of London had reached 50,000_.\n\nThese are nuisances and defects found in the ward of Faringdon. Without, taken in the wardmoot, before Rankyn Barton, Alderman of the same ward, the year of the king abovesaid.\n\nFirst, that the master of Ludgate often puts out dung in the street gutter and stops the water from flowing, to the great nuisance of all the folk passing there. Also that a mud wall in the bailey by the High Street, between the house of Shelhard, haberdasher, and Hay, spurrier, falls down piecemeal into the High Street, and makes the way foul, to the annoyance of folk passing and dwelling there. Also William Emery, horsedealer, often lays much dung in the high street and allows it to lie yet, to the great nuisance and annoyance of all folk passing and dwelling thereabout. Also the pavements before the chamber house in the bailey, and before the door of Harry Gras, barber, and of Walsh's door, are defective and need to be mended. Also the common privy of Ludgate is very defective and perilous and the filth thereof decays the stone walls, so that it is likely to be very costly and dangerous to those walls in time to come, unless it be put right as soon as possible. Also that the barriers at Shoe-Lane end are all broken with water carts, and the pavements defective in divers places of the same parish. Also that John Taverner at Bell is not a freeman of the city. Also John Whitlok at Bell at Carter Lane end and his wife are common bauds, and therefore have lately been put out of other wards. Also John Swayn and his wife are forestallers, regrators, and extortioners often, and especially lately they hired a page of the Queen's household to arrest a boatful of rushes, and brought it from Queenhithe to Fleet Bridge, and there took up from it 30 loads of rushes, and laid them in Sir Walter Beauchamp's place, and then paid to the Boatman only 26 _d_ for 30 loads, whereas he should have been paid for every burden 3 _d_ and because of this the boatman made much noise and open slander. Also the taverners of St Bride's parish set their empty tuns and pipes in the high street, to the annoyance of all folk passing there.\n\nAlso that the barriers of Chancellor Lane [Chaunselerlane] and Fetter Lane [Fayturlane] are all broken.\n\n_Of more national concern in 1422 was the premature death of Henry V from dysentery (an occupational hazard for campaigners), which left the infant Henry VI on the throne and the country governed by a regency of his paternal uncles._\n\n_Some thought Henry VI a saint \u2013 here were attempts to canonize him \u2013 and others a simpleton. John Blackman, a priest and amanuensis to the king, pictured him thus:_\n\nConcerning his humility in his walk [and] in his clothes,... from his youth up he had been accustomed to wear broad-toed shoes and boots like a countryman. Also he had usually a long gown with a rounded hood after the manner of a burgess, and a tunic falling below the knees, shoes, boots, hose, everything of a dark grey colour \u2013 for he would have nothing fanciful.\n\nMoreover, on the principal feasts of the year, but chiefly when by custom he should wear his crown, he would put on next his skin a rough hair-shirt,... in order to keep down all arrogance or vain-glory, to which such occasions are likely to give rise.\n\n_Saint or simpleton, Henry VI's reign was disastrous for England. All the territorial gains of Henry V in France were lost to the French revival spearheaded by Joan of Arc. As the English lost their hold on France and Henry VI lost his grip on reality (he was clinically schizophrenic by August 1453)_ , _quarrelling among the leading noble factions at court became more embittered._\n\n_Open skirmishing between the Lancastrians (badge: the red rose) and Yorkists (the white rose) occurred at St Albans on 22 May 1455_. _The so-called Wars of the Roses which followed were of less substance than Shakespeare's_ Collected Works _would suggest. Both sets of protagonists would claim the right to rule England through descent from Edward III. Neither side could muster private armies ('affinities') much greater than 3,000 in number. Casualties were minimal, and few towns were besieged, because neither side dared inconvenience the populace._\n\n_The Wars of the Roses were an unedifying misnomer; for most of their thirty years England was at peace. The Yorkist King Edward IV ruled (and had the leisure to collect books) from 1461 to 1483_ , _save for an interruption in 1470\u201371 when the Lancastrians returned the bewildered Henry VI to the throne. On his return from exile in Flanders, Edward IV trounced the Lancastrians at the battle of Barnet._\n\n## _The Wars of the Roses: Fog, Confusion and Treachery \u2013 the Battle of Barnet, 14 April 1471_\n\nJOHN WARKWORTH\n\n_Edward IV's Yorkist army at the battle of Barnet \u2013 which was fought in thick fog \u2013 numbered a paltry 7,000_ ; _leading the 15,000 Lancastrians was the power-broking Earl 'The Kingmaker' Warwick who, offended by gibes about his bravery, fought on foot. Like many a medieval battle, it sank into complete confusion, with the Lancastrians attacking their own centre after mistaking a private badge for Edward's 'sun and rays' insignia. Never was the expression the fog of war' so apposite as at Barnet in spring 1471_. _John Warkworth was Master of St Peter's College, Cambridge. His sympathies were Lancastrian._\n\nAnd on the Wednesday next before Easter-day, King Harry, and the Archbishop of York with him, rode about London, and desired the people to be true unto him; and every man said they would. Nevertheless Urswyke, Recorder of London, and divers Aldermen, such that had rule of the city, commanded all the people, that were in harness, keeping the city, and King Harry, every man to go home to dinner; and in dinner time King Edward was let in, and so went forth to the Bishop of London's palace, and there took King Harry, and the Archbishop of York, and put them in ward, the Thursday next before Easter-day. And the Archbishop of Canterbury, the Earl of Essex, the Lord Berners, and such other as owed King Edward good will, as well in London, as in other places, made as many men as they might, in strengthening the said King Edward; so then he was a seven thousand men, and there they refreshed well themselves, all that day, and Good Friday. And upon Easter Even, he and all his host went toward Barnet, and carried King Harry with him; for he had understanding, that the Earl of Warwick, and the Duke of Exeter, the Lord Marquis Montague, the Earl of Oxford, and many other knights, squires, and commons, to the number of twenty thousand, were gathered together to fight against the King Edward. But it happened that he, with his host, were entered into the town of Barnet, before the Earl of Warwick, and his host. And so the Earl of Warwick, and his host, lay without the town all night, and each of them loosed guns at other all the night. And on Easter day in the morning, the fourteenth day of April, right early each of them came upon other; and there was such a great mist, that neither of them might see other perfectly. There they fought from four of clock in the morning, unto ten of clock the forenoon. And divers times the Earl of Warwick's party had the victory, and supposed that they had won the field. But it happened so, that the Earl of Oxford's men had upon them their lord's livery, both before and behind, which was a star with streams, which _(was)_ much like King Edward's livery, the sun with streams; and the mist was so thick, that a man might not perfectly judge one thing from another; so the Earl of Warwick's men shot and fought against the Earl of Oxford's men, thinking and supposing, that they had been King Edward's men; and anon the Earl of Oxford, and his men, cried, 'treason! treason!' and fled away from the field with eight hundred men. The Lord Marquis Montague was agreed, and appointed with King Edward, and put upon him King Edward's livery; and a man of the Earl of Warwick's, saw that, and fell upon him, and killed him. And when the Earl of Warwick saw his brother dead, and the Earl of Oxford fled, he leaped on horseback and fled to a wood by the field of Barnet, where was no way forth; and one of King Edward's men had espied him, and one came upon him, and killed him, and despoiled him naked. And so King Edward got that field. And there was slain of the Earl of Warwick's party, the Earl himself, Marquis Montague, Sir William Tyrell, Knight, and many others. The Duke of Exeter fought manly there that day, and was greatly despoiled, and wounded, and left naked for dead in the field, and so lay there from seven of clock, till four afternoon, which was taken up and brought to a house by a man of his own, and a leech brought to him and so afterwards brought into sanctuary at Westminster. And _(of)_ King Edward's party was slain the Lord Cromwell, son and heir to the Earl of Essex; Lord Berners _(his)_ son and heir, _(Sir Humphrey Bourchier;)_ Lord Say, and divers other to the number [of both parties] four thousand men. And after that the field was done, King Edward commanded both the Earl of Warwick's body, and the Lord Marquis' body, to be put in a cart, and returned himself with all his host again to London; and there commanded the said two bodies, to be laid in the church of Paul's, on the pavement, that every man might see them; and so they lay three or four days, and afterwards were buried. And King Harry being in the forward during the battle, was not hurt; but he was brought again to the Tower of London, there to be kept.\n\n_After Barnet, Edward IV marched to a decisive victory over the Lancastrians at Tewkesbury and then got on with ruling as before. Rather effectively. A French visitor to England could even claim in the 1470s \u2013 the 'worst' decade of the Wars of the Roses \u2013 that of all the countries he had visited England was the one 'where public affairs are best conducted'._\n\n## _Richard III Murders the Princes in the Tower, 1483_\n\nWILLIAM SHAKESPEARE AND SIR THOMAS MORE\n\n_Made Protector when his twelve-year-old nephew Edward V inherited the throne, Richard, Duke of York, usurped power to become king in June 1483_. _The popular view of the great monarchical villain of English history was set for ever by the playwright and Tudor propagandist William Shakespeare in_ Richard III:\n\nBut I \u2013 that am not shap'd for sportive tricks,\n\nNor made to court an amorous looking-glass\n\nI \u2013 that am rudely stamp'd, and want love's majesty\n\nTo strut before a wanton ambling nymph \u2013\n\nI \u2013 that am curtail'd of this fair proportion,\n\nCheated of feature by dissembling nature,\n\nDeform'd, unfinished, sent before my time\n\nInto this breathing world scarce half made up,\n\nAnd that so lamely and unfashionable\n\nThat dogs bark at me as I halt by them \u2013\n\nWhy, I, in this weak piping time of peace,\n\nHave no delight to pass away the time,\n\nUnless to spy my shadow in the sun\n\nAnd descant on mine own deformity.\n\n_In truth Richard III may not have had the 'crouch-back' attributed to him by Shakespeare... but he was almost certainly guilty of the murder of Edward V and his younger brother._\n\n_Sir Thomas More (1478\u20131535) was Lord Chancellor under Henry VIII and the author_ Utopia.\n\n... I shall rehearse you the dolorous end of those babes, not after every way that I have heard, but after that way that I have so heard by such men and by such means as methinks it were hard but it should be true.\n\n...forasmuch as his mind gave him that, his nephews living, men would not reckon that he could have right to the realm, (Richard) thought therefore without delay to be rid of them, as though the killing of his kinsmen could amend his cause and make him a kindly king.\n\nWhereupon he sent one John Green, whom he specially trusted, unto Sir Robert Brackenbury, constable of the Tower, with a letter and credence also, that the same Sir Robert should... put the two children to death... who plainly answered that he would never put them to death... with which answer John Green, returning, recounted the same to King Richard at Warwick...\n\n(On) the morrow he sent (Sir James Tyrell) to Brackenbury with a letter, by which he was commanded to deliver (to) Sir James all the keys of the Tower for one night, to the end he might there accomplish the king's pleasure... After which letter delivered and the keys received, Sir James appointed the night next ensuing to destroy them...\n\n(Sir) James Tyrell devised that they should be murdered in their beds. To the execution whereof he appointed Miles Forest, one of the four that kept them, a fellow fleshed in murder beforetime. To him he joined one John Dighton, his own horsekeeper, a big broad square strong knave. Then, all the others being removed from them, this Miles Forest and John Dighton, about midnight, the innocent children lying in their beds, came into the chamber and suddenly lapped them up among the clothes, so bewrapped them and entangled them, keeping down by force the featherbed and pillows hard unto their mouths, that within a while smothered and stifled, their breath failing, they gave up to God their innocent souls into the joys of heaven, leaving to the tormentors their bodies dead in the bed. After the wretches perceived them, first by the struggling with the pains of death, and after long lying still, to be thoroughly dead, they laid their bodies naked out upon the bed and fetched Sir James to see them. Who, upon the sight of them, caused those murderers to bury them at the stair foot, meetly deep in the ground under a great heap of stones.\n\nThen rode Sir James in great haste to King Richard, and showed him all the manner of the murder, who gave him great thanks and, as some say, there made him knight. But he allowed not, as I have heard, the burying in so vile a corner, saying that he would have them buried in a better place because they were a king's sons... Whereupon they say that a priest of Sir Robert Brackenbury took up the bodies again and secretly interred them in such place as, by the occasion of his death, who alone knew it, could never after come to light. Very truth it is and well known that at such time as Sir James Tyrell was in the Tower, for treason committed against the most famous prince King Henry the Seventh, both Dighton and he were examined, and confessed the murder in manner above-written, but whither the bodies were removed they could nothing tell.\n\nAnd thus, as I have learned from them that much knew and little cause had to lie, were these two noble princes, these innocent tender children, born of most royal blood, brought up in great wealth, likely long to live to reign and rule in the realm, by traitorous tyranny taken, deprived of their estate, shortly shut up in prison, and privily slain and murdered, their bodies cast God knows where, by the cruel ambition of their unnatural uncle and his pitiless tormentors.\n\n## _The Battle of Bosworth, 22 August 1485_\n\nPOLYDORE VERGIL\n\n_The battle that ended the Wars of the Roses was won by the Lancastrian claimant to the throne, Henry Tudor, after Richard III was treasonably deserted mid-fight by the Stanley family._\n\n_Vergil, born in Italy, spent most of his life in England and became Archdeacon of Wells Cathedral._\n\nAt the battle of Bosworth the number of all (Henry Tudor's) soldiers, altogether, was scarcely 5,000 beside the Stanleyans, of whom about 3,000 were at the battle, under the conduct of William... The king's forces were twice as many and more.\n\n...Henry bore the brunt (of the fighting) longer than even his own soldiers would have thought, who were now almost out of hope of victory, when, behold, William Stanley with 3,000 men came to the rescue; then truly in a very moment the residue all fled, and King Richard alone was killed fighting manfully in the thickest press of his enemies. In the meantime also the Earl of Oxford, after a little skirmishing, put to flight those that fought in the forward, whereof a great company were killed in the chase. But many more forebore to fight, who came to the field with King Richard for awe, and for no goodwill and departed without any danger, as men who desired not the safety but destruction of that prince whom they hated.\n\nThere were killed about 1,000 men, and amongst them (were) John Duke of Norfolk, Walter Lord Ferrers, Robert Brackenbury, Richard Ratcliffe and many more. Two days after at Leicester, William Catesby, lawyer, with a few that were his fellows, were executed. And of those who took to their feet Francis Lord Lovell, Humphrey Stafford, with Thomas his brother and much more company, fled into sanctuary... As for the number of captives, it was very great; for when King Richard was killed, all men forthwith threw away weapon and freely submitted themselves to Henry's obedience, whereof the most part would have done the same at the beginning (but) for King Richard's scouts... Amongst them the chief were Henry Earl of Northumberland and Thomas Earl of Surrey... Henry lost in that battle scarcely a hundred soldiers...\n\nThe report is that King Richard might have sought to save himself by flight; for they who were about him, seeing the soldiers even from the first stroke to lift up their weapons feebly and faintly, and some of them to depart the field privily, suspected treason, and exhorted him to fly, and when the matter began manifestly to falter, they brought him swift horses; but he, who was not ignorant that the people hated him, (is) said to have answered that that very day he would make an end either of war or life...\n\nHenry, after the victory obtained, gave forthwith thanks unto Almighty God for the same...(The) soldiers cried, 'God save King Henry, God save King Henry!', and with heart and hand uttered all the show of joy that might be; which, when Thomas Stanley did see, he set at once King Richard's crown, which was found among the spoil in the field, upon his head...\n\nThe body of King Richard, naked of all clothing, and laid upon a horse's back, with the arms and legs hanging down on both sides, was brought to the abbey of Franciscan monks at Leicester, a miserable spectacle in good truth, but not unworthy for the man's life, and there was buried two days after without any pomp or solemn funeral.\n\n_The legal claim of Henry Tudor (born 1437_ ) _to the English throne was tortuous; it came down an illegitimate line from Edward III's fourth son, John of Gaunt. Henry Tudor \u2013 crowned as Henry VII on 30 October 1483_ \u2013 _was an adventurer. What mattered was whether he had the staying power to establish a new dynasty on England's throne._\n\n_In this, Henry VII had better luck than an usurper might have hoped for. Richard III had left no heirs behind him and the Wars of the Roses had immolated a clutch of potentially troublesome magnates. Even better, his far-sighted motherhad already betrothed him to Elizabeth of York, Edward IV's daughter; when Henry and Elizabeth married in 1486 the Tudor-Lancastrian claim was merged with the Yorkist, and most of the White Roses were reconciled to the new regime._\n\n_But not all of them. The first rebellion came in 1487 when the Yorkists dressed up one Lambert Simnel, an Oxford joiner's son, as 'Edward VI'. Henry captured him and put him to work as a spit-turner in the royal kitchen. A decade later, the Yorkists advanced another impostor, Perkin Warbeck, the son of the Controller of Tournai, who was persuaded to impersonate Richard, Duke of York, one of the princes murdered in the Tower. Acknowledged by a mischievous James IV of Scotland (among others), Warbeck invaded Cornwall in 1497 to claim 'his' throne. Warbeck fared worse than Simnel; he was rounded up, imprisoned and, insistent on escape, executed._\n\n_The very longevity of Henry VII's reign \u2013 it lasted until 1509 \u2013 made for stability, which in turn allowed English commerce to flourish. (Export of woollen cloth, the yardstick of the early Tudor economy, as it was of the medieval era, rose by 50 per cent over the course of Henry's tenure.) Almost the monarchical miser of myth, Henry VII ruthlessly enforced the crown's financial dues, selling offices of state and issuing dubious 'attainders' whereby 'traitors' forfeited their lands. The result was that Henry VII\u2013 the 'best businessman ever to sit on the English throne' \u2013 bequeathed to his son and heir \u00a31.5 million._\n\n_The first Tudor king left Henry VIII something more precious still. Security. Henry VIII was the first king since Henry V who did not have to fight for his throne._\n\n## _A Portrait of Henry VIII, 1519_\n\nSEBASTIAN GIUSTINIAN\n\n_A picture of Henry VIII at the zenith of his reputation, a decade on the throne, the successful battles of the Spurs (v. France) and Flodden (v. Scotland) behind him, and still the extrovert, the virtual inventor of Merrie England. The admiring Giustinian was the Venetian ambassador to London from 1515 to 1519._\n\nHis majesty is twenty-nine years old and extremely handsome. Nature could not have done more for him. He is much handsomer than any other sovereign in Christendom; a great deal handsomer than the King of France; very fair, and his whole frame admirably proportioned. On hearing that Francis I wore a beard, he allowed his own to grow, and as it is reddish, he has now a beard that looks like gold. He is very accomplished, a good musician, composes well, is a most capital horseman, a fine jouster, speaks good French, Latin, and Spanish, is very religious, hears three masses daily when he hunts, and sometimes five on other days. He hears the office every day in the queen's chamber, that is to say vesper and compline. He is very fond of hunting, and never takes his diversion without tiring eight or ten horses, which he causes to be stationed beforehand along the line of country he means to take, and when one is tired he mounts another, and before he gets home they are all exhausted. He is extremely fond of tennis, at which game it is the prettiest thing in the world to see him play, his fair skin glowing through a shirt of the finest texture. He gambles with the French hostages, to the amount occasionally, it is said, of from 6,000 to 8,000 ducats in a day. He is affiable and gracious, harms no one, does not covet his neighbour's goods, and is satisfied with his own dominions, having often said to me, 'Sir Ambassador, we want all potentates to content themselves with their own territories; we are satisfied with this island of ours.' He seems extremely desirous of peace.\n\nHe is very rich. His father left him ten millions of ready money in gold, of which he was supposed to have spent one-half in the war against France, when he had three armies on foot; one crossed the Channel with him, another was in the field against Scotland, and the third remained with the queen in reserve.\n\nHis revenues amount to about 350,000 ducats annually, and are derived from estates, forests, and meres, the customs, hereditary and confiscated property, the duchies of Lancaster, York, Cornwall and Suffolk, the county palatine of Chester, and others, the principality of Wales, the export duties, the wool staple, the great seal, the annates yielded by Church benefices, the Court of Wards, and from New Year's gifts; for on the first day of the year it is customary for his majesty to make presents to everybody, but the value of those he receives in return greatly exceeds his own outlay. His majesty's expenses may be estimated at 100,000 ducats, those in ordinary having been reduced from 100,000 to 56,000 to which must be added 16,000 for salaries, 5,000 for the stable, 5,000 for the halberdiers, who have been reduced from 500 to 150, and 16,000 for the wardrobe, for he is the best dressed sovereign in the world. His robes are very rich and superb, and he puts on new clothes every holyday.\n\n## _The Field of the Cloth of Gold, 7\u201324 June 1520_\n\nPOLYDORE VERGIL\n\n_The 'eighth wonder of the world', the Field of the Cloth of Gold was a Brobdingnagian peace festival in France intended to bind England and France together against a common foe, Charles V's Hapsburg Empire. It was the brainchild of Henry VIII's chief minister, Thomas Wolsey (son of an Ipswich butcher; the one policy of his father's that Henry VIII did continue was promotion by merit not status). Wolsey constantly sought a role for England in Europe above her weight as a small offshore nation._\n\nThen the king of England showed himself some deal forward in beauty and personage, the most goodliest prince that ever reigned over the realm of England. His grace was apparelled in a garment of cloth of silver, of damask ribbed with cloth of gold, so thick as might be; the garment was large and pleated very thick and cantled of very good intail, of such shape and making that it was marvellous to behold. The courser which his grace rode on was trapped in a marvellous vesture of a new devised fashion; the trapper was of fine gold in bullion, curiously wrought, pounced and set with antique work of Roman figures. Attending on the king's grace of England was the Master of the Horse, by name sir Henry Guilford, leading the king's spare horse:... After followed nine henchmen, riding on coursers of Naples; the same young gentlemen were apparelled in rich cloth of tissue, the coursers in harness of marvellous fashion, scaled in fine gold in bullion, and works subtle more than my sight could contrive; and all the same horse-harness was set full of trembling spangs that were large and fair. The lord marquess Dorset bare the king's sword of state before the king's grace; the reverend father lord cardinal did his attendance.\n\nThus in little time, abiding the coming of the French king and his, the which in short time came with great number of horsemen, freshly apparelled; the French king and his retinue put themselves in place appointed, direct against the English party, beholding every other of both nations. The Frenchmen mused much of the battle of the footmen, and every of the Frenchmen to other spake of the multitude of the Englishmen which seemed great; yet were not they so many as the French party.\n\nWhen the French king had a little beholden the Englishmen, he put himself somewhat before his people, that were there on him attendant, the duke of Bourbon bearing a naked sword upright, the lord admiral of France and the count Cosmen Galias, Master of the French king's Horse; and no more persons gave their attendance in passing with the French king. When it was perceived that the French king's sword was borne naked, then the king of England commanded the lord marquess Dorset to draw out the sword of state and bare it up naked in presence; which was so done.\n\nThen up blew the trumpets, sackbuts, clarions and all other minstrels on both sides, and the kings descended down toward the bottom of the valley of Arden, in sight of both the nations; and on horseback met and embraced the two kings each other. Then the two kings alighted and after embraced with benign and courteous manner each to other, with sweet and goodly words of greeting. And after few words these two noble kings went together into the rich tent of cloth of gold, that there was set on the ground for such purpose. Thus arm in arm went the French king Francis I of France and Henry VIII king of England and of France, together passing with communication.\n\nWhen the two princes were in the tent, before rehearsed, the French king said: 'My dear brother and cousin, thus far to my pain have I travelled to see you personally; I think verily that you esteem me as I am. And that I may to you be your aid, the realms and seignories show the might of my person.' 'Sir,' said the king of England, 'neither your realms nor other the places of your power is the matter of my regard, but the steadfastness and loyal keeping of promise, comprised in charters between you and me; that observed and kept, I never saw prince with my eyes that might of my heart be more loved. And for your love I have passed the seas, into the farthest frontier of my realm to see you presently; the which doing now gladdeth me.' And then were the two kings served with a banquet, and after mirth had communication in the banquet time, and there shewed the one the other their pleasure.\n\nThe English officers went and ran with great pots of wine and bowls to the Frenchmen and them cheered the best that might be. All this season stood still the noblemen of the English party and all other, and from their places moved nothing that they were appointed unto. And the serving men in like wise not once moved from their ground or standing; but the Frenchmen suddenly brake and many of them came into the English party, speaking fair; but for all that, the court of England and the lords still kept their array.\n\nAfter the two kings had ended the banquet, and spice and wine given to the Frenchmen, Ipocras was chief drink of plenty to all that would drink. In open sight then came the two kings, that is to wit the French king and the king of England, out of their tent:... This French king had on his head a coif of damask gold set with diamonds, and his courser that he rode on was covered with a trapper of tissue, embroidered with devise, cut in fashion mantle-wise; the skirts were embowed and fret with frieze work and knit with cordels, and buttons tusselled of Turkey making; reins and headstall answering of like work. And verily of his person the same Francis, the French king, a goodly prince; stately of countenance, merry of cheer, brown-coloured, great eyes, high-nosed, big-lipped, fair breasted and shoulders, small legs and long feet.\n\nAll the nobles of the French court were in garments of many colours, so that they were not known from the braggery. Thus as the two kings were in communication, divers noblemen of England were called to presence. And then the two kings departed with their company, the king of England to Guisnes, the French king to Arden.\n\n_Truth to tell, Henry and Francis could hardly keep up an_ entente cordiale _for a week, let alone perpetuity. By 1523 England and France were once again at war._\n\n_The Field of the Cloth of Gold did change the course of history, but not in the way intended. It was there that Henry VIII first met Anne Boleyn._\n\n## _'Mine Own Sweetheart': Henry VIII Writes to Anne Boleyn, c. 1526_\n\nHENRY VIII\n\n_By 1525 Henry VIII had tired of the charms of his ageing wife, Catherine of Aragon, and become mesmerized by those of the vital Anne Boleyn, niece of the Duke of Norfolk. Not content to become the king's mistress (unlike her famously good-time sister Mary), the ambitious Anne kept Henry dangling at arm's length \u2013 which only made him desire her more._\n\nMine own sweetheart, this shall be to advertise you of the great melancholy that I find here since your departing; for, I ensure you, methinketh the time longer since your departing now last than I was wont to do a whole fortnight. I think your kindness and my fervency of love causeth it; for, otherwise I would not have thought it possible that for so little a while it should have grieved me. But now I am coming towards you, methinketh my pains by half removed; and also I am right well comforted insomuch that my book maketh substantially for my matter; in looking where of I have spent above four hours this day, which causeth me now to write the shorter letter to you at this time, because of some pain in my head. Wishing myself (especially an evening) in my sweetheart's arms whose pretty duckies* I trust shortly to kiss. Written by the hand of him that was, is, and shall be yours by his own will,\n\nH. R.\n\n_The following year, 1527_ , _Henry VIII determined to divorce Catherine and marry Anne. His heart was set on it; so was his head. Catherine of Aragon \u2013now beyond child-bearing age \u2013 had not produced the male heir on which the embryonic Tudor dynasty seemingly depended._\n\n_All Henry needed was for the Pope to issue a divorce. This should have been a formality, but the Pope was a pawn of Charles V, Henry's rival and Catherine of Aragon's nephew. For three years the 'King's Great Matter' dragged on inconclusively, until Anne Boleyn herself took a dainty but deft hand in the matter and pressed upon Henry a copy of William Tyndale's_ On the Obedience of a Christian Man and how Christian Rulers Ought to Govern. _This asserted that the monarch was chief of both Church and State. A keen amateur Bible student, Henry now had the theological answer to his prayers: he could be Pope in his own land \u2013 and issue a do-it-yourself divorce. In a spate of statutes, Henry and Parliament \u2013 acting for the first time in English history as the supreme legislative assembly \u2013 ended the allegiance to Rome, proclaiming that 'this realm is an empire'. Under the Act of Supremacy Henry was installed as 'supreme head' of the Church of England._\n\n_Few objected. Although Anne Boleyn was not popular in the country, most of the xenophobic English were quite content to cut free from the 'Bishop of Rome'. Henry's divorce was only the occasion for the 'Reformation' of the Church in England, not its cause._\n\n_In January 1533 Henry VIII secretly married Anne Boleyn and four months later Archbishop Cranmer pronounced the king's former marriage to Catherine of Aragon null and void. On Whit Sunday Anne was crowned Queen of England ('somewhat big with child', noted the officiating Archbishop Cranmer). However, Henry's passion for her was already cooling and was not revived by the birth of a daughter and then a still-born son. Now an encumbrance to Henry's desire fora male heir, Anne Boleyn was beheaded on 19 May 1536 for adultery with her brother as well as four commoners. Eleven days after Boleyn's execution Henry married Jane Seymour, who at last produced the requisite live boy child, but died in the doing. The remainder of Henry's six wives were: Anne of Cleves (marriage annulled because she was too plain), Catherine Howard (beheaded for adultery) and Catherine Parr (who survived her husband)._\n\n## _The Dissolution of the Monasteries: Cromwell's Agents Report, 1535\u20138_\n\nJOHN LONDON, JOHN AP RICE, RICHARD LAYTON, GEOFFREY CHAMBER, ROGER TOWNSEND\n\n_Henry VIII's own inclination in the English Reformation was towards Catholicism without the Pope, but the times and his most able minister, Thomas Cromwell (Wolsey having died in disgrace for failing to obtain the king's divorce from Catherine of Aragon), had other, radical ideas. One of Cromwell's notions was touched by genius: it was to close and sell off all the monasteries in England and Wales. The money garnered would pay for Henry's expensive habits (wars and palaces), while those doing the purchasing, the squirearchy, would literally be buying into the new order. To convince the public that the dissolution of the monasteries was necessary, Cromwell sent out 'Visitors' to catalogue their sins._\n\nIn my most humble manner I have me commended unto your good lordship, ascertaining the same that I have pulled down the image of Our Lady at Caversham, whereunto was great pilgrimage. The image is plated over with silver, and I have put it in a chest fast locked and nailed up, and by the next barge that cometh from Reading to London it shall be brought to your lordship. I have also pulled down the place she stood in, with all other ceremonies, as lights, shrowds, crosses, and images of wax hanging about the chapel, and have defaced the same thoroughly in eschewing of any further resort thither. This chapel did belong to Notley Abbey, and there always was a canon of that monastery which was called the Warden of Caversham, and he sung in this chapel and had the offerings for his living. He was accustomed to show many pretty relics, among the which were (as he made report) the holy dagger that killed King Henry, and the holy knife that killed St Edward. All these with many other, with the coats of this image, her cap and hair, my servants shall bring unto your lordship this week, with the surrender of the friars under their convent seal, and their seal also. I have sent the canon home again to Notley, and have made fast the doors of the chapel, which is thoroughly well covered with lead, and if it be your lordship's pleasure I shall see it made sure to the King's grace's use. And if it be not so ordered, the chapel standeth so wildly that the lead will be stolen by night, as I was served at the Friars. For as soon as I had taken the Friars' surrender, the multitude of the poverty of the town resorted thither, and all things that might be had they stole away, insomuch that they had conveyed the very clappers of the bells. And saving that Mr Fachell, which made me great cheer at his house, and the Mayor did assist me, they would have made no little spoil...\n\nPlease it your good lordship to be advertised that... the Abbot of Langdon passeth all other that ever I knew in profound bawdry; the drunkennest knave living. All his canons be even as he is, not one spark of virtue amongst them; arrant bawdy knaves every man. The Abbot caused his chaplain to take an whore, and instigate him to it, brought her up into his own chapter, took one of his feather-beds off his own bed, and made his chaplain's bed in the inner chamber, within him, and there caused him to go to bed with his whore that the Abbot had provided for him. To rehearse you the whole story, it were long and too abominable to hear. The house is in utter decay and will shortly fall down. You must needs depose him and suddenly sequestrate the fruits, and take an inventory of the goods. You can do no less of justice...\n\nMy singular good lord, my duty remembered unto your lordship, this shall be to advertise the same that upon the defacing of the late monastery of Boxley, and plucking down the images of the same, I found in the image of the Rood called the Rood of Grace, the which heretofore hath been had in great veneration of the people, certain engines and old wire, with old rotten sticks in the back of the same, that did cause the eyes of the same to move and stare in the head thereof, like unto a living thing; and also the nether lip in like wise to move as though it should speak, which, so famed, was not a little strange to me and other that was present at the plucking down of the same, whereupon the abbot, hearing this bruit, did thither resort, whom to my little wit and cunning, with other of the old monks, I did examine of their knowledge of the premises; who do declare themselves to be ignorant of the same.\n\nPlease it your goodness to understand that on Friday 22 October I rode back with speed to take an inventory of Folkestone (priory), and from thence went to Langdon. Whereas immediately descending from my horse, I sent Bartelot your servant, with all my servants to circumcept the abbey, and surely to keep all back doors and startyng hoilles;* etc. I myself went alone to the abbot's lodging joining upon the fields and wood, even like a cony clapper\u2020 full of private ways; a good space knocking at the abbot's door, neither sound nor sign of life appearing, saving the abbot's little dog, that within his door fast locked, bayed and barked. I found a short pole-axe standing behind the door, and with it I dashed the abbot's door in pieces, and set one of my men to keep that door, and about the house I go with the pole-axe in my hand, for the abbot is a dangerous desperate knave and a hardy. But for a conclusion, his whore alias his gentlewoman bestirred her stumps towards her startyng hoilles, and there Bartelot watching the pursuit took the tender damsel, and after I had examined her, to Dover there to the mayor to set her in some cage or prison for 8 days, and I brought holy father abbot to Canterbury, and there in Christ Church (priory) I will leave him in prison. In this sudden doing extempore, to circumcept the house and to search, your servant John Antony and his men marvelled what fellow I was, and so did the rest of the abbey, for I was unknown there of all men. At last I found her apparel in the abbot's coffer. To tell you all this comedy, but for the abbot a tragedy, it were too long.\n\nPlease it your mastership, forasmuch as I suppose ye shall have suit made unto you touching Bury ere we return, I thought convenient to advertise you of our proceedings there, and also of the comperta of the same. As for the abbot, we found nothing suspect as touching his living, but it was detected that he lay much forth in his granges, that he delighted much in playing at dice and cards, and therein spent much money, and in building for his pleasure. He did not preach openly. Also that he converted divers farms into copyholds, whereof poor men doth complain. Also he seemeth to be addict to the maintaining of such superstitious ceremonies as hath been used heretofore.\n\nAs touching the convent, we could get little or no reports among them, although we did use much diligence in our examination, and thereby, with some other arguments gathered of their examinations, I firmly believe and suppose that they had conferred and compacted before our coming that they should disclose nothing. And yet it is confessed and proved, that there was here such frequence of women coming and resorting to this monastery as to no place more. Amongst the relics we found much vanity and superstition, as the coals that Saint Lawrence was toasted withal, the parings of S. Edmund's nails, S. Thomas of Canterbury's penknife and his boots, and divers skills for the headache; pieces of the holy cross able to make a holy cross of...\n\n_Approximately 800 institutions were closed between 1536 and 1540_ , _and their 9,000 inmates turned out. There was opposition in the North, notably the Pilgrimage of Grace, but in the more reform-minded South and East, where most of the monasteries were based, barely a squeak. Anti-clericalism ran deep in the English mind._\n\n_During the short reign of Henry's son, Edward VI (1547\u201353)_ , _the Reformation in England finally took on a theological aspect. The boy-king was a Protestant devotee, and the radical Archbishop of Canterbury, Thomas Cranmer, received his leave to introduce into the English Church the Act of Uniformity and the Book of Common Prayer (1549, revised 1552)_. _These replaced Latin services with English \u2013 for the first time \u2013 and removed all reference to the Mass. The sixteen-year-old Edward VI died on 6 July 1553 (almost his last words were O! my Lord God, defend this realm from papistry'), having barred his Catholic half-sister, Mary, from the succession in favour of Lady Jane Grey, the virtuously Protestant daughter-in-law of the Protector, Northumberland. Alas, no one had thought to incarcerate Mary. A Tudor regent, even a Catholic one, seemed preferable to a Protestant nonentity. Besides, Mary quite duplicitously hid the degree of her Catholic fanaticism. Lady Jane Grey's 'reign' lasted nine days, before Mary marched into London in queenly triumph._\n\n## _The Burning of Archbishop Cranmer, 21 March 1556_\n\nA BYSTANDER\n\n_The love affair of the English with Mary Tudor was short-lived. She insisted on marrying a foreigner (Philip of Spain, Charles V's son) and restoring Catholicism by incinerating Protestants. Among those set afire alive was Thomas Cranmer, the first Protestant Archbishop of Canterbury. He recanted his 'heresy' no fewer than seven times before publicly and dramatically affirming his Protestantism on the day of his execution in London._\n\nBut to come to the matter: on Saturday last, being 21 of March, was his day appointed to die. And because the morning was much rainy, the sermon appointed by Mr Dr Cole to be made at the stake, was made in St Mary's church: whither Dr Cranmer was brought by the mayor and aldermen, and my lord Williams: with whom came divers gentlemen of the shire, sir T. A. Bridges, sir John Browne, and others. Where was prepared, over against the pulpit, an high place for him, that all the people might see him. And, when he had ascended it, he kneeled him down and prayed, weeping tenderly: which moved a great number to tears, that had conceived an assured hope of his conversion and repentance...\n\nWhen praying was done, he stood up, and, having leave to speak, said, 'Good people, I had intended indeed to desire you to pray for me; which because Mr Doctor hath desired, and you have done already, I thank you most heartily for it. And now will I pray for myself, as I could best devise for mine own comfort, and say the prayer, word for word, as I have here written it.' And he read it standing: and after kneeled down, and said the Lord's Prayer; and all the people on their knees devoutly praying with him...\n\nAnd then rising, he said, 'Every man desireth, good people, at the time of their deaths, to give some good exhortation, that other may remember after their deaths, and be the better thereby. So I beseech God grant me grace, that I may speak something, at this my departing, whereby God may be glorified, and you edified...\n\n'And now I come to the great thing that troubleth my conscience more than any other thing that ever I said or did in my life: and that is, the setting abroad of writings contrary to the truth. Which here now I renounce and refuse, as things written with my hand, contrary to the truth which I thought in my heart, and written for fear of death, and to save my life, if it might be: and that is, all such bills, which I have written or signed with mine own hand since my degradation: wherein I have written many things untrue. And forasmuch as my hand offended in writing contrary to my heart, therefore my hand shall first be punished: for if I may come to the fire, it shall be first burned. And as for the pope, I refuse him, as Christ's enemy and antichrist, with all his false doctrine.'\n\nAnd here, being admonished of his recantation and dissembling, he said, 'Alas, my lord, I have been a man that all my life loved plainness, and never dissembled till now against the truth; which I am most sorry for it.' He added hereunto, that, for the sacrament, he believed as he had taught in his book against the bishop of Winchester. And here he was suffered to speak no more...\n\nThen was he carried away; and a great number, that did run to see him go so wickedly to his death, ran after him, exhorting him, while time was, to remember himself. And one Friar John, a godly and well learned man, all the way travelled with him to reduce him. But it would not be. What they said in particular I cannot tell, but the effect appeared in the end: for at the stake he professed, that he died in all such opinions as he had taught, and oft repented him of his recantation.\n\nComing to the stake with a cheerful countenance and willing mind, he put off his garments with haste, and stood upright in his shirt: and a bachelor of divinity, named Elye, of Brazen-nose college, laboured to convert him to his former recantation, with the two Spanish friars. And when the friars saw his constancy, they said in Latin one to another, 'Let us go from him: we ought not to be nigh him: for the devil is with him.' But the bachelor in divinity was more earnest with him: unto whom he answered, that, as concerning his recantation, he repented it right sore, because he knew it was against the truth; with other words more. Whereby the Lord Williams cried, 'Make short, make short.' Then the bishop took certain of his friends by the hand. But the bachelor of divinity refused to take him by the hand, and blamed all others that so did, and said, he was sorry that ever he came in his company. And yet again he required him to agree to his former recantation. And the bishop answered, (shewing his hand), 'This was the hand that wrote it, and therefore shall it suffer first punishment.'\n\nFire being now put to him, he stretched out his right hand, and thrust it into the flame, and held it there a good space, before the fire came to any other part of his body; where his hand was seen of every man sensibly burning, crying with a loud voice, 'This hand hath offended.' As soon as the fire got up, he was very soon dead, never stirring or crying all the while.\n\n_Cranmer was one of some 300 Protestants burned at the stake in the reign of 'Bloody Queen Mary' for what Mary called their 'corrupt and naughty opinions'. Mary's brutality disgusted Englishmen and proved Protestantism's best recruiter, especially when the sufferings of the burned were turned into the eloquent propaganda of John Foxe's_ Acts and Monuments _(aka_ Book of Martyrs), _the best-seller of Tudor England._\n\n_Moreover, as many English feared, Mary Tudor's marriage to Philip of Spain caused England to become involved in his country's conflict with France. Mary's conduct of the war was calamitous, with the result that Calais, England's last possession in France, was captured in January 1558._\n\n_The impact of the loss of Calais on Tudor England can scarcely be underestimated. Calais, the glittering symbol of the great wars of the Black Prince andHenry V, Calais the wool staple port. Mary herself cried that when she died, Calais would be found written on her heart._\n\n_Only months later Mary did die, of ovarian cancer, tragically deluded that her bloated tumour was a baby. To her chagrin, the only possible successor was her half-sister, Elizabeth, daughter of Henry VIII and the 'goggle-eyed whore' Anne Boleyn._\n\n_Elizabeth I. Gloriana, Virginia, Deborah, the Faerie Queen \u2013 for her contemporaries, as well as posterity, her reign was a Golden Age of England. Like most English, Elizabeth I was only moderately religious (Calvinist John Knox described her, neatly, as 'neither a good protestant, nor yet a resolute papist'), and above everything she was the mistress of_ realpolitik. _She understood that the future of England was Protestant, so settled upon it a mild Protestantism (near-indistinguishable from modern Anglicanism), based on the 1552 Prayer Book, which stabilized the realm for her long tenure (1558\u20131603). Abroad, she pursued a cautious policy of aid to the North European Protestant powers, mostly to enervate the Catholic big two, France and Spain. She was never married, save to her country, whose ring she wore in token. Elizabethan England was God's chosen land for his chosen people \u2013 who were rapidly growing in numbers, up from 2.98 million in 1561 to 4.10 million in 1601. The sense of national enchantment was perfectly caught by William Shakespeare, the era's dramatist-laureate, in_ Richard II: _'This precious stone set in the silver sea... This blessed plot, this earth, this realm, this England... This land of such dear souls, this dear, dear land'._\n\n_The English, as befitted an island people, had long been sailors, but it was during Elizabeth's reign that they found their destiny on the 'silver sea'._\n\n## _An Encounter with Drake at Sea, off Guatemala, 4 April 1579_\n\nFRANCISCO DE ZARATE\n\n_Francis Drake (c. 1540\u201396) left England in the_ Pelican _in December 1577 to become the first Englishman to sail around the world. Typically of the Elizabethan sea-dogs, he had little interest in exploration for exploration's sake. His intentions were all practical: to find new trading opportunities, to grab unstaked land, and to plunder Spanish gold-ships in the New World. If in the doing of these things he spited the Pope, so much the better. (Drake's favourite reading matter aboard the_ Pelican _was Foxe's_ Book of Martyrs, _the woodcuts of which he coloured-inin idler moments, the text of which he preached to his Spanish prisoners). The queen was one of his sponsors._\n\n_Off Guatemala, Drake seized the ship belonging to the Spaniard Francisco de Zarate:_\n\nI sailed out of the port of Acapulco on the 23 rd of March and navigated until Saturday, the fourth of April, on which date, half an hour before dawn, we saw, by moonlight, a ship very close to ours. Our steersman shouted that she was to get out of the way and not come alongside of us. To this they made no answer, pretending to be asleep. The steersman then shouted louder, asking them where their ship hailed from. They answered 'from Peru', and that she was 'of _Miguel Angel_ ', which is the name of a well-known captain of that route...\n\nThe ship of the adversary carried her bark at her prow as though she were being towed. Suddenly, in a moment, she crossed our poop, ordering us 'to strike sail' and shooting seven or eight arquebuse shots at us.\n\nWe thought this as much of a joke as it afterwards turned out to be serious.\n\nOn our part there was no resistance, nor had we more than six of our men awake on the whole boat, so they entered our ship with as little risk to themselves as though they were our friends. They did no personal harm to any one, beyond seizing the swords and keys of the passengers. Having informed themselves as to who were on board ship, they ordered me to go in their boat to where their general was \u2013 a fact I was glad of, as it appeared to me that it gave me more time in which to recommend myself to God. But in a very short time we arrived where he was, on a very good galleon, as well mounted with artillery as any I have seen in my life.\n\nI found him promenading on deck and, on approaching him, I kissed his hands. He received me with a show of kindness, and took me to his cabin, where he bade me be seated and said: 'I am a friend of those who tell me the truth, but with those who do not I get out of humour. Therefore you must tell me (for this is the best road to my favour) how much silver and gold does your ship carry?' I said to him, 'None'. He repeated his question. I answered, 'None, only some small plates that I use and some cups \u2013 that is all that is in her.' He kept silent for a while, then renewing the conversation asked me if I knew Your Excellency, I said, 'Yes'...\n\nThis general of the Englishmen is a nephew of John Hawkins, and is the same who, about five years back, took the port of Nombre de Dios. He is called Francisco Drac, and is a man of about 35 years of age, low of stature, with a fair beard, and is one of the greatest mariners that sail the seas, both as a navigator and as a commander. His vessel is a galleon of nearly four hundred tons, and is a perfect sailer. She is manned with a hundred men, all of service, and of an age for warfare, and all are as practised therein as old soldiers from Italy could be. Each one takes particular pains to keep his arquebuse clean. He treats them with affection, and they treat him with respect. He carries with him nine or ten cavaliers, cadets of English noblemen. These form a part of his council, which he calls together for even the most trivial matter, although he takes advice from no one. But he enjoys hearing what they say and afterwards issues his orders. He has no favourite.\n\nThe aforesaid gentleman sits at his table, as well as a Portuguese pilot, whom he brought from England, who spoke not a word during all the time I was on board. He is served on silver dishes with gold borders and gilded garlands, in which are his arms. He carries all possible dainties and perfumed waters. He said that many of these had been given to him by the Queen.\n\nNone of these gentlemen took a seat or covered his head before him, until he repeatedly urged him to do so. This galleon of his carries about thirty heavy pieces of artillery and a great quantity of firearms with the-requisite ammunition and lead. He dines and sups to the music of viols. He carries trained carpenters and artisans, so as to be able to careen the ship at any time. Beside being new, the ship has a double lining. I understood that all the men he carries with him receive wages, because, when our ship was sacked, no man dared take anything without his orders. He shows them great favour, but punishes the least fault. He also carries painters who paint for him pictures of the coast in its exact colours...\n\nThis corsair, like a pioneer, arrived two months before he intended to pass through and during that time for many days there were great storms. So it was that one of the gentlemen, whom he had with him, said to him: 'We have been a long while in this strait and you have placed all of us, who follow or serve you, in danger of death. It would therefore be prudent for you to give order that we return to the North Sea, where we have the certainty of capturing prizes, and that we give up seeking to make new discoveries. You see how fraught with difficulties these are.'\n\nThis gentleman must have sustained this opinion with more vigour than appeared proper to the General. His answer was that he had the gentleman carried below deck and put in irons. On another day, at the same hour, he ordered him to be taken out, and to be beheaded in presence of all.\n\nThe term of his imprisonment was no more than was necessary to substantiate the lawsuit that was conducted against him. All this he told me, speaking much good about the dead man, but adding that he had not been able to act otherwise, because this was what the Queen's service demanded. He showed me the commissions that he had received from her and carried. I tried to ascertain whether any relatives of the dead man had remained on board. They told me that there was only one, who was one of those who ate at his table. During all this time that I was on board, which was fifty-five hours, this youth never left the ship, although all the others did so, in turn. It was not that he was left to guard me. I think that they guarded him.\n\nI managed to ascertain whether the General was well liked, and all said that they adored him.\n\nThis is what I was able to find out during the time I spent with him...\n\n_On returning to England, Drake was knighted by the sovereign in whose name he had claimed California for England. Unfortunately, the Spanish blithely ignored Drake's staked claim to California; the English colonization of America was fated to occur on the nearer, East Coast, beginning with Raleigh's voyage to Virginia in 1384 and the foundation of the Roanoke settlement there a year later._\n\n## _The Execution of Mary, Queen of Scots, 8 February 1587_\n\nR. K. WYNKFIELDE\n\n_After fleeing the 1367 revolt of the confederated lords, Mary Stuart threw herself on the mercy of her cousin, Elizabeth I, who kept the Scottish queen in a series of velvet-lined prisons \u2013 Carlisle, Bolton, Tutbury, Wingfield, Coventry, Chatsworth, Sheffield, Buxton, Chartley and Fotheringay. The presence of Mary Stuart was a source of unease for Elizabeth's government: as a Catholic she was a natural figurehead for the minority who wanted a return to the oldreligion (and who, following Pope Pius V's excommunication of Elizabeth, were absolved from loyalty to the latter). Ministers cajoled for a pre-emptive execution, but it was only when Mary incriminated herself in the Babington plot to assassinate Elizabeth that the English queen would allow Mary Stuart to be brought to trial. She was forty-five at the time of her subsequent beheading at Fotheringay._\n\nHer prayers being ended, the executioners, kneeling, desired her Grace to forgive them her death: who answered, 'I forgive you with all my heart, for now, I hope, you shall make an end of all my troubles.' Then they, with her two women, helping her up, began to disrobe her of her apparel: then she, laying her crucifix upon the stool, one of the executioners took from her neck the _Agnus Dei,_ which she, laying hands off it, gave to one of her women, and told the executioner he should be answered money for it. Then she suffered them, with her two women, to disrobe her of her chain of pomander beads and all her other apparel most willingly, and with joy rather than sorrow, helped to make unready herself, putting on a pair of sleeves with her own hands which they had pulled off, and that with some haste, as if she had longed to be gone.\n\nAll this time they were pulling off her apparel, she never changed her countenance, but with smiling cheer she uttered these words, 'that she never had such grooms to make her unready, and that she never put off her clothes before such a company'.\n\nThen she, being stripped of all her apparel saving her petticoat and kirtle, her two women beholding her made great lamentation, and crying and crossing themselves prayed in Latin. She, turning herself to them, embracing them, said these words in French, 'Ne crie vous, j'ay prom\u00e9 pour vous', and so crossing and kissing them, bad them pray for her and rejoice and not weep, for that now they should see an end of all their mistress's troubles.\n\nThen she, with a smiling countenance, turning to her men servants, as Melvin and the rest, standing upon a bench nigh the scaffold, who sometime weeping, sometime crying out aloud, and continually crossing themselves, prayed in Latin, crossing them with her hand bade them farewell, and wishing them to pray for her even until the last hour.\n\nThis done, one of the women having a _Corpus Christi_ cloth lapped up three-corner-ways, kissing it, put it over the Queen of Scots' face, and pinned it fast to the caule of her head. Then the two women departed from her, and she kneeling down upon the cushion most resolutely, and without any token or fear of death, she spake aloud this Psalm in Latin, _In Te Domine confido, non confundar in eternam,_ etc. Then, groping for the block, she laid down her head, putting her chin over the block with both her hands, which, holding there still, had been cut off had they not been espied. Then lying upon the block most quietly, and stretching out her arms cried, _In manus tuas, Domine,_ etc., three or four times. Then she, lying very still upon the block, one of the executioners holding her slightly with one of his hands, she endured two strokes of the other executioner with an axe, she making very small noise or none at all, and not stirring any part of her from the place where she lay: and so the executioner cut off her head, saving one little gristle, which being cut asunder, he lift up her head to the view of all the assembly and bade _God save the Queen._ Then, her dress of lawn falling from off her head, it appeared as grey as one of threescore and ten years old, polled very short, her face in a moment being so much altered from the form she had when she was alive, as few could remember her by her dead face. Her lips stirred up and down a quarter of an hour after her head was cut off.\n\nThen Mr Dean [Dr Fletcher, Dean of Peterborough] said with a loud voice, 'So perish all the Queen's enemies', and afterwards the Earl of Kent came to the dead body, and standing over it, with a loud voice said, 'Such end of all the Queen's and the Gospel's enemies.'\n\nThen one of the executioners, pulling off her garters, espied her little dog which was crept under her clothes, which could not be gotten forth but by force, yet afterward would not depart from the dead corpse, but came and lay between her head and her shoulders, which being imbrued with her blood was carried away and washed, as all things else were that had any blood was either burned or washed clean, and the executioners sent away with money for their fees, not having any one thing that belonged unto her. And so, every man being commanded out of the hall, except the sheriff and his men, she was carried by them up into a great chamber lying ready for the surgeons to embalm her.\n\n## _The Armada: the Commander's Report, 21\u201329 July 1588_\n\nLORD HOWARD OF EFFINGHAM AND JOHN HAWKINS\n\n_Save for Drake playing bowls on Plymouth Ho, the legend of the Armada's defeat is not far removed from the truth of it._\n\n_Desirous of dethroning the 'heretical' Elizabeth I, of preventing piratical English incursions into the New World, of stemming English aid to fellow Protestants in the Spanish-controlled Netherlands, Philip II of Spain (Mary I's former husband) dispatched a fleet of 130 ships from La Coruna with the intention that this 'Armada' would rendezvous with his Army of Flanders off the Netherlands. Then the combined force would invade England._\n\n_On 19 July the Armada was spotted off the Scilly Isles._\n\n_Lord Howard of Effingham was commander of the English fleet, which totalled 197 ships, smaller than their Spanish counterparts but more agile, with better guns, better gun crews. (Some Spanish galleons could hardly manage a broadside a day.) The English combat reports below were sent to Sir Francis Walsingham, principal Secretary of State._\n\nSir,\n\nI will not trouble you with any long letter; we are at this present otherwise occupied than with writing. Upon Friday, at Plymouth, I received intelligence that there were a great number of ships descried off of the Lizard; whereupon, although the wind was very scant, we first warped out of harbour that night, and upon Saturday turned out very hardly, the wind being at South-west; and about three of the clock in the afternoon, descried the Spanish fleet, and did what we could to work for the wind, which by this morning we had recovered, descrying their fleet to consist of 120 sail, whereof there are four galleasses and many ships of great burden.\n\nAt nine of the clock we gave them fight, which continued until one. In this fight we made some of them to bear room to stop their leaks; notwithstanding we durst not adventure to put in among them, their fleet being so strong. But there shall be nothing either neglected or unhazarded, that may work their overthrow.\n\nSir, the captains in her majesty's ships have behaved themselves most bravely and like men hitherto, and I doubt not will continue, to their great commendation. And so, recommending our good success to your godly prayers, I bid you heartily farewell. From aboard the _Ark,_ thwart of Plymouth the 21st of July, 1588.\n\nYour very loving friend,  \nC. Howard.\n\nSir, the southerly wind that brought us back from the coast of Spain brought them out. God blessed us with turning us back. Sir, for the love of God and our country, let us have with some speed some great shot sent us of all bigness; for this service will continue long; and some powder with it.\n\n* * *\n\nMy bounden duty humbly remembered unto your good lordship: \u2013 have not busied myself to write often to your lordship in this great cause, for that my lord admiral doth continually advertise the manner of all things that doth pass. So do others that understand the state of all things as well as myself. We met with this fleet somewhat to the westward of Plymouth upon Sunday in the morning, being the 21st of July, where we had some small fight with them in the afternoon. By the coming aboard one of the other of the Spaniards, a great ship, a Biscayan, spent her foremast and bowsprit; which was left by the fleet in the sea, and so taken up by sir Francis Drake the next morning. The same Sunday there was, by a fire chancing by a barrel of powder, a great Biscayan spoiled and abandoned, which my lord took up and sent away.\n\nThe Tuesday following, athwart of Portland, we had a sharp and long fight with them, wherein we spent a great part of our powder and shot, so as it was not thought good to deal with them any more till that was relieved.\n\nThe Thursday following, by the occasion of the scattering of one of the great ships from the fleet, which we hoped to have cut off, there grew a hot fray, wherein some store of powder was spent; and after that little done till we came near to Calais, where the fleet of Spain anchored, and our fleet by them; and because they should not be in peace there, to refresh their water or to have conference with that of the duke of Parma's party, my lord admiral, with firing of ships, determined to renew them; as he did, and put them to the seas; in which broil the chief galleass spoiled her rudder, and so rode ashore near the town of Calais, where she was possessed of our men, but so aground as she could not be brought away.\n\nThat morning, being Monday, the 29th of July, we followed the Spaniards; and all that day had with them a long and great fight, wherein there was great valour showed generally of our company. In this battle there was spent very much of our powder and shot; and so the wind began to blow westerly, a fresh gale, and the Spaniards put themselves somewhat the northward, where we follow and keep company with them. In this fight there was some hurt done among the Spaniards. A great ship of the galleons of Portugal, her rudder spoiled, and so the fleet left her in the sea. I doubt not but all these things are written more at large to your lordship than I can do; but this is the substance and material matter that hath passed.\n\nOur ships, God be thanked, have received little hurt, and are of great force to accompany them, and of such advantage that with some continuance at the seas, and sufficiently provided of shot and powder, we shall be able, with God's favour, to weary them out of the sea and confound them...\n\nYour lordship's humbly to command,  \nJohn Hawkyns.\n\n## _The Armada: Elizabeth Addresses Her Troops,_ 9 _August 1588_\n\nELIZABETH I\n\n_Elizabeth's speech to her land troops gathered at Tilbury, on the Thames below London. Her love of her country and her subjects is manifest._\n\nMy Loving People:\n\nWe have been perswaded by some that are careful of our safety, to take heed how we commit ourselves to armed multitudes, for fear of treachery; but I assure you, I do not desire to live to distrust my faithful and loving people.\n\nLet tyrants fear; I have always so behaved myself that, under God, I have placed my chiefest strength and safeguard in the loyal hearts and good will of my subjects, and therefore I am come amongst you, as you see, at this time, not for my recreation and disport, but being resolved in the midst and heat of the battle to live or die amongst you all, to lay down for my God and for my kingdoms and for my people, my honour and my blood, even in the dust.\n\nI know I have the body but of a weak and feeble woman; but I have the heart and stomach of a king, and of a king of England, too; and think foul scorn that Parma [Duke of Parma] or Spain or any prince of Europe should dare to invade the borders of my realm; to which rather than any dishonour should grow by me, I myself will take up arms, I myself will be your general, judge, and rewarder of every one of your virtues in the field...\n\n_The 'famous victory' was near at hand. The Armada, beaten in battle at Gravelines on 28\u201329 July, had fled to the North Sea, where it escaped the English (who gave up the chase due to lack of gunpowder, food and water, the dehydrated mariners obliged to drink their own urine) only to enter the clutches of merciless weather. Slinking around Scotland and down past the coast of Donegal, the Armada lost a greater toll to gales than it had to English guns. Only eighty-six ships of the Armada reached the safety of Santander. Philip II went into mourning for the 9,000 dead._\n\n_Protestant England, meanwhile, celebrated with prayers of thanksgiving. Not one English ship had been sunk or captured in the Armada engagement. 'God breathed and they were scattered' was the motto struck on the Armada victory medal._\n\n## _The Torturing of a Jesuit Priest in the Tower of London, 14\u201315 April 1597_\n\nFATHER JOHN GERARD\n\n_The Counter-Reformation's efforts against Protestant England were not limited to military means. English Jesuit priests, trained at Douai, were infiltrated into the country, to wage theological war. Gerard was betrayed by a servant._\n\nOn the third day the warder came to my room straight from his dinner. Looking sorry for himself, he said the Lords Commissioners had arrived with the Queen's Attorney-General and that I had to go down to them at once.\n\n'I am ready,' I said, 'but just let me say an _Our Father_ and _Hail Mary_ downstairs.'\n\nHe let me go, and then we went off together to the Lieutenant's lodgings inside the walls of the Tower. Five men were there waiting for me, none of whom, except Wade, had examined me before. He was there to direct the charges against me.\n\nThe Attorney-General took out a sheet of paper and solemnly began to write out a form of juridical examination. They put no questions about individual Catholics \u2013 they were all about political matters \u2013 and I answered on the general lines I had always done before. I said that matters of state were forbidden to Jesuits and consequently I never had anything to do with them; if they wanted confirmation they had it. I had been in prison now three years and had been examined time and time again, and they had not produced a scrap of writing or a single trustworthy witness to show that I had taken part in any activities against the Government.\n\nThen they asked me about the letters I had recently received from our Fathers abroad; and I realized for the first time why I had been removed to the Tower. I answered, 'If I have ever received any letters from abroad at any time, they have had nothing to do with politics. They were concerned merely with the financial assistance of Catholics living on the Continent.'\n\n'Didn't you receive a packet a short time ago,' said Wade, 'and hand it over to so and so to give to Henry Garnet?'\n\n'If I have received any such packet and forwarded it, I did what I was bound to do. But, I repeat, the only letters I have received or forwarded are those, as I have said, dealing with the despatch of money to religious and students on the Continent.'\n\n'Very well,' they said, 'then tell us the name of the man you gave the letters to, and where he lives.'\n\n'I don't know, and even if I did, I could not and would not tell you,' and I gave them the usual reasons for this answer.\n\n'You say,' said the Attorney-General, 'you have no wish to obstruct the Government. Tell us, then, where Father Garnet is. He is an enemy of the state, and you are bound to report on all such men.'\n\n'He isn't an enemy of the state,' I said. 'On the contrary, I am certain that if he were given the opportunity to lay down his life for his Queen and country, he would be glad of it. But I don't know where he lives, and if I did, I would not tell you.'\n\n'Then we'll see to it that you tell us before we leave this place.'\n\n'Please God, you won't,' I answered.\n\nThen they produced a warrant for putting me to torture. They had it ready by them and handed it to me to read. (In this prison a special warrant is required for torture.)\n\nI saw that the warrant was properly made out and signed, and then I answered, 'With God's help I shall never do anything that is unjust or act against my conscience or the Catholic faith. You have me in your power. You can do with me what God allows you to do \u2013 more you cannot do.'\n\nThen they began to implore me not to force them to take steps they were loath to take. They said they would have to put me to the torture every day, as long as my life lasted, until I gave them the information they wanted.\n\n'I trust in God's goodness,' I answered, 'that He will prevent me from ever committing a sin such as this \u2013 the sin of accusing innocent people. We are all in God's hands and therefore I have no fear of anything you can do to me.'\n\nThis was the sense of my answers, as far as I can recall them now.\n\nWe went to the torture room in a kind of solemn procession, the attendants walking ahead with lighted candles.\n\nThe chamber was underground and dark, particularly near the entrance. It was a vast place and every device and instrument of human torture was there. They pointed out some of them to me and said that I would try them all. Then they asked me again whether I would confess.\n\n'I cannot,' I said.\n\nI fell on my knees for a moment's prayer. Then they took me to a big upright pillar, one of the wooden posts which held the roof of this huge underground chamber. Driven in to the top of it were iron staples for supporting heavy weights. Then they put my wrists into iron gauntlets and ordered me to climb two or three wicker steps. My arms were then lifted up and an iron bar was passed through the rings of one gauntlet, then through the staple and rings of the second gauntlet. This done, they fastened the bar with a pin to prevent it slipping, and then, removing the wicker steps one by one from under my feet, they left me hanging by my hands and arms fastened above my head. The tips of my toes, however, still touched the ground, and they had to dig away the earth from under them. They had hung me up from the highest staple in the pillar and could not raise me any higher, without driving in another staple.\n\nHanging like this I began to pray. The gentlemen standing around asked me whether I was willing to confess now.\n\n'I cannot and I will not,' I answered.\n\nBut I could hardly utter the words, such a gripping pain came over me. It was worst in my chest and belly, my hands and arms. All the blood in my body seemed to rush up into my arms and hands and I thought that blood was oozing out from the ends of my fingers and the pores of my skin. But it was only a sensation caused by my flesh swelling above the irons holding them. The pain was so intense that I thought I could not possibly endure it, and added to it, I had an interior temptation. Yet I did not feel any inclination or wish to give them the information they wanted. The Lord saw my weakness with the eyes of His mercy, and did not permit me to be tempted beyond my strength. With the temptation He sent me relief. Seeing my agony and the struggle going on in my mind, He gave me this most merciful thought: the utmost and worst they can do to you is to kill you, and you have often wanted to give your life for your Lord God. The Lord God sees all you are enduring \u2013 He can do all things. You are in God's keeping. With these thoughts, God in His infinite goodness and mercy gave me the grace of resignation, and, with a desire to die and a hope (I admit) that I would, I offered Him myself to do with me as He wished. From that moment the conflict in my soul ceased, and even the physical pain seemed much more bearable than before, though I am sure it must, in fact, have been greater with the growing strain and weariness of my body.\n\nWhen the gentlemen present saw that I was not answering their questions, they went off to the Lieutenant's house, and stayed there. Every now and again they sent to find out how things were going with me.\n\nThree or four robust men remained behind to watch and supervise the torture, and also my warder. He stayed, I think, out of kindness, for every few minutes he took a cloth and wiped the perspiration that ran in drops continuously down my face and whole body. That helped me a little, but he added to my sufferings when he started to talk. He went on and on, begging and imploring me to pity myself and tell the gentlemen what they wanted to know. And he urged so many human reasons for this that I thought that the devil instigated him to feign this affection or that my torturers had left him behind on purpose to trick me. But I felt all these suggestions of the enemy like blows in the distance: they did not seem to touch my soul or affect me in any way. More than once I interrupted him, 'Stop this talk, for heaven's sake. Do you think I'm going to throw my soul away to save my life? You exasperate me.'\n\nBut he went on. And several times the others joined in.\n\n'You will be a cripple all your life if you live. And you are going to be tortured every day until you confess.'\n\nBut I prayed in a low voice as well as I could, calling on the names of Jesus and Mary.\n\nSome time after one o'clock, I think, I fell into a faint. How long I was unconscious I don't know, but I don't think it was long, for the men held my body up or put the wicker steps under my feet until I came to. Then they heard me pray and immediately they let me down again. And they did this every time I fainted \u2013 eight or nine times that day \u2013 before it struck five.\n\nAfter four or before five o'clock Wade returned. Coming to me he asked, 'Are you ready now to obey the Queen and her Council?'\n\nI answered, 'You want me to do what is sinful. I will not do it.'\n\n'All you have to say,' said Wade, 'is that you wish to speak to Cecil, Her Majesty's Secretary.'\n\n'I have nothing to say to him,' I said, 'except what I have said to you already. If I asked to speak to him, people would be scandalized. They would think I had given way, that at last I was going to say something that I should not say.'\n\nIn a rage he suddenly turned his back on me and strode out of the room, shouting angrily in a loud voice, 'Then hang there until you rot off the pillar.'\n\nHe left. And I think all the Commissioners left the Tower then, for at five o'clock the Tower bell is rung, a signal for all to leave unless they want to have the gates locked on them. A little later they took me down. My legs and feet were not damaged, but it was a great effort to stand upright.\n\nThey led me back to my cell. On the way we met some prisoners who had the run of the Tower, and I turned to speak to my warder, intending them to overhear.\n\n'What surprises me,' I said, 'is that the Commissioners want me to say where Father Garnet's house is. Surely they know it is a sin to betray an innocent man? I will never do it, even if I have to die.'\n\nI said this to prevent them spreading a report, as they so often do, that I had confessed something. And I also wanted word to get round through these men that it was chiefly concerning Father Garnet that I had been questioned, so that he might get to hear and look to his own safety. I saw that the warder was not pleased at my talking in their hearing, but that made no difference to me.\n\nWhen I reached my cell the man seemed really sorry for me. He laid a fire and brought me some food, as it was now nearly supper time. But I could eat only a little; and I lay down on my bed and rested quietly until the morning.\n\nIn the morning after the gates of the Tower were opened, my warder came up to say that Wade had arrived and that I had to go down and see him. I put on a cloak with wide sleeves \u2013 I could not get my swollen hands through the sleeves of my own gown \u2013 and I went down.\n\nWhen I entered the Lieutenant's house, Wade said to me, 'I have been sent here in the name of the Queen and her Secretary, Cecil. They say they know for certain that Garnet meddles in politics and is a danger to the State. And this the Queen asserts on the word of a Sovereign and Cecil on his honour. Unless you choose to contradict them both, you must agree to hand him over.'\n\n'They cannot be speaking from experience,' I answered, 'or from any reliable information; they don't know the man. I have lived with him and know him well, and I can say for certain that he is not that kind of man.'\n\n'Come,' said Wade, 'why not admit the truth and answer our questions?'\n\n'I cannot,' I said, 'and I will not.'\n\n'It would be better for you if you did,' and saying this he called out to a gentleman waiting in the next room. He was a well-built man whom Wade called 'Master of Torture'. I knew such an officer existed, but I found out later that this was not the man. He was Master of the Artillery. Wade gave him this title to terrorize me.\n\n'By order of the Queen and Council,' he addressed this gentleman, 'I hand this man over to you. You are to torture him twice today and twice every day until he confesses.'\n\nThe man took charge of me. Wade left. In the same way as before we went to the torture chamber.\n\nThe gauntlets were placed on the same part of my arms as last time. They would not fit anywhere else, because the flesh on either side had swollen into small mounds, leaving a furrow between; and the gauntlets could only be fastened in the furrow. I felt a very sharp pain when they were put on.\n\nBut God helped me and I gladly offered Him my hands and my heart. I was hung up in the same way as before, but now I felt a much severer pain in my hands but less in my chest and belly. Possibly this was because I had eaten nothing that morning.\n\nI stayed like this and began to pray, sometimes aloud, sometimes to myself, and I put myself in the keeping of Our Lord Jesus and His blessed Mother. This time it was longer before I fainted, but when I did they found it so difficult to bring me round that they thought that I was dead, or certainly dying, and summoned the Lieutenant. I don't know how long he was there or how long I remained in a faint. But when I came to myself, I was no longer hanging but sitting on a bench with men supporting me on either side. There were many people about, and my teeth had been forced open with a nail or some iron instrument and hot water had been poured down my throat.\n\nWhen the Lieutenant saw that I could speak he said, 'Don't you see how much better for you it would be if you submitted to the Queen instead of dying like this?'\n\nGod helped me and I was able to put more spirit into my answer than I had felt up to now.\n\n'No, no I don't!' I said. 'I would prefer to die a thousand times rather than do as they suggest.'\n\n'So you won't confess, then?'\n\n'No, I won't,' I said. 'And I won't as long as there is breath left in my body.'\n\n'Very well, then, we must hang you up again now, and a second time after dinner.'\n\nHe spoke as though he were sorry to have to carry out his orders.\n\n_'Eamus in nomine Domini,'_ I said. 'I have only one life, but if I had several I would sacrifice them all for the same cause.'\n\nI struggled to my feet and tried to walk over to the pillar but I had to be helped. I was very weak now and if I had any spirit left in me it was given by God and given to me, although most unworthy, because I shared the fellowship of the Society.\n\nI was hung up again. The pain was intense now, but I felt great consolation of soul, which seemed to me to come from a desire of death. Whether it arose from a true love of suffering for Christ, or from a selfish longing to be with Christ, God knows best. But I thought then that I was going to die. And my heart filled with great gladness as I abandoned myself to His will and keeping and condemned the will of men. Oh! that God would grant me the same spirit always, though I am sure that in His eyes it was far from a perfect spirit, for my life was to be longer than I then thought, and God gave me time to make it more perfect in His sight, since, it seems, I was not then ready.\n\nPerhaps the Governor of the Tower realized he would gain nothing by torturing me any longer; perhaps it was his dinner hour or maybe he was moved with genuine pity for me; whatever the reason, he ordered me to be taken down. It seemed that I had been hanging only an hour in this second period today. Personally, I believe he was moved by compassion, for some time after my escape a gentleman of position told me that he had heard Sir Richard Berkeley, this same Lieutenant, say that he had freely resigned his office because he no longer wished to be an instrument in such torture of innocent men. At all events it is a fact that he did resign, and only three or four months after his appointment. His place was taken by another knight and it was under him that I escaped.\n\nMy warder brought me back to my room. His eyes seemed swollen with tears. He assured me that his wife, whom I had never seen, had wept and prayed for me all the time.\n\nHe brought me some food. I could eat little, and the little I did eat he had to cut up into small pieces. For many days after I could not hold a knife in my hands \u2013 that day I could not even move my fingers or help myself in the smallest way. He had to do everything for me. But in spite of this on orders from the authorities he took away my knife, scissors and razors. I thought they must be afraid that I would attempt suicide, but I later learned that they always do this in the Tower when a prisoner is under warrant for torture.\n\n_Gerard escaped from the Tower six months later by swinging over Tower Ditch on a rope, and became one of the Gunpowder Plotters. For the last ten years of his life he was Director of the English College in Rome._\n\n## _A Meeting with Queen Elizabeth, 1598_\n\nPAUL HENTZNER\n\n_The meeting took place at Greenwich. Hentzner was a German visitor to England._\n\nElizabeth, the reigning Queen of England, was born at the royal palace of Greenwich, and here she generally resides, particularly in summer, for the delightfulness of its situation. We were admitted by an order, which Mr Rogers had procured from the Lord Chamberlain, into the presence-chamber hung with rich tapestry, and the floor, after the English fashion, strewed with hay, through which the Queen commonly passes in her way to chapel. At the door stood a gentleman dressed in velvet, with a gold chain, whose office was to introduce to the Queen any person of distinction that came to wait on her. It was Sunday, when there is usually the greatest attendance of nobility. In the same hall were the Archbishop of Canterbury, the Bishop of London, a great number of counsellors of state, officers of the crown, and gentlemen, who waited the Queen's coming out, which she did from her own apartment when it was time to go to prayers, attended in the following manner: \u2013\n\nFirst went gentlemen, barons, earls, knights of the Garter, all richly dressed and bareheaded; next came the Lord High Chancellor of England, bearing the seals in a red silk purse, between two, one of whom carried the royal sceptre, the other the sword of state in a red scabbard, studded with golden fleur-de-lis, the point upwards; next came the Queen, in the 65th year of her age (as we were told), very majestic; her face oblong, fair but wrinkled; her eyes small, yet black and pleasant; her nose a little hooked, her lips narrow, and her teeth black (a defect the English seem subject to, from their too great use of sugar); she had in her ears two pearls with very rich drops; her hair was of an auburn colour, but false; upon her head she had a small crown, reported to be made of some of the gold of the celebrated Luneburg table; her bosom was uncovered, as all the English ladies have it till they marry; and she had on a necklace of exceeding fine jewels; her hands were slender, her fingers rather long, and her stature neither tall nor low; her air was stately, her manner of speaking mild and obliging. That day she was dressed in white silk, bordered with pearls of the size of beans, and over it a mantle of black silk shot with silver threads; her train was very long, the end of it borne by a marchioness; instead of a chain, she had an oblong collar of gold and jewels. As she went along in all this state and magnificence, she spoke very graciously, first to one, then to another (whether foreign ministers, or those who attend for different reasons), in English, French and Italian: for besides being well skilled in Greek, Latin and the languages I have mentioned, she is mistress of Spanish, Scotch and Dutch. Whoever speaks to her, it is kneeling; now and then she raises some with her hand. While we were there, William Slawata, a Bohemian baron, had letters to present to her; and she, after pulling off her glove, gave him her right hand to kiss, sparkling with rings and jewels \u2013 mark of particular favour. Wherever she turned her face as she was going along, everybody fell down on their knees. The ladies of the court followed next to her, very handsome and well-shaped, and for the most part dressed in white. She was guarded on each side by the gentlemen pensioners, fifty in number, with gilt halberds. In the ante-chapel, next the hall where we were, petitions were presented to her, and she received them most graciously, which occasioned the acclamation of _God save the Quene Elizabeth!_ She answered it with I _thancke you myn good peupel._ In the chapel was excellent music; as soon as it and the service were over, which scarcely exceeded half-an-hour, the Queen returned in the same state and order, and prepared to go to dinner. But while she was still at prayers, we saw her table set out with the following solemnity: \u2013\n\nA gentleman entered the room bearing a rod, and along with him another who had a table-cloth, which after they had both knelt three times, with the utmost veneration, he spread upon the table, and after kneeling again they both retired. Then came two others, one with the rod again, the other with a salt-cellar, a plate and bread; when they had knelt as the others had done, and placed what was brought upon the table, they too retired with the same ceremonies performed by the first. At last came an unmarried lady of extraordinary beauty (we were told that she was a countess) and along with her a married one, bearing a tasting-knife; the former was dressed in white silk, who, when she had prostrated herself three times, in the most graceful manner, approached the table and rubbed the plates with bread and salt with as much awe as if the Queen had been present. When they had waited there a little while, the yeomen of the guard entered, bareheaded, clothed in scarlet, with a golden rose upon their backs, bringing in at each turn a course of twenty-four dishes, served in silver most of it gilt; these dishes were received by a gentleman in the same order as they were brought and placed upon the table, while the lady-taster gave to each of the guard a mouthful to eat of the particular dish he had brought, for fear of any poison. During the time that this guard, which consists of the tallest and stoutest men that can be found in all England, 100 in number, being carefully selected for this service, were bringing dinner, twelve trumpets and two kettle-drums made the hall ring for half-an-hour together. At the end of all this ceremonial, a number of unmarried ladies appeared, who with particular solemnity lifted the meat off the table, and conveyed it into the Queen's inner and more private chamber, where after she had chosen for herself, the rest goes to the ladies of the court. The Queen dines and sups alone with very few attendants; and it is very seldom that any body, foreigner or native, is admitted at that time, and then only at the intercession of some distinguished personage.\n\n## _The Age of Shakespeare: Theatregoing, 1599\u20131613_\n\nTHOMAS PLATTER AND SIR HENRY WOTTON\n\n_William Shakespeare (1564\u20131616)_ , _born in Stratford-upon-Avon, joined the Lord Chamberlain's Men as an actor and playwright by 1592. In 1598 he became one of the landlords of the new Globe Theatre. Before the Elizabethan age, with its purpose-built stages, plays had been performed in the courtyards of inns._\n\n_Thomas Platter, a visitor to London from Basel, attended a performance of Shakespeare's_ Julius Caesar in 1599.\n\nAfter dinner on the 21st of September, at about two o'clock, I went with my companions over the water, and in the strewn roof-house saw the tragedy of the first Emperor Julius with at least fifteen characters very well acted. At the end of the comedy they danced according to their custom with extreme elegance. Two in men's clothes and two in women's gave this performance, in wonderful combination with each other. On another occasion, I also saw after dinner a comedy, not far from our inn, in the suburb; if I remember right, in Bishopsgate. Here they represented various nations, with whom on each occasion an Englishman fought for his daughter, and overcame them all except the German, who won the daughter in fight. He then sat down with him, and gave him and his servant strong drink, so that they both got drunk, and the servant threw his shoe at his master's head and they both fell asleep. Meanwhile the Englishman went into the tent, robbed the German of his gains, and thus he outwitted the German also. At the end they danced very elegantly both in English and in Irish fashion. And thus every day at two o'clock in the afternoon in the city of London two and sometimes three comedies are performed, at separate places, wherewith folk make merry together, and whichever does best gets the greatest audience. The places are so built, that they play on a raised platform, and every one can well see it all. There are, however, separate galleries and there one stands more comfortably and moreover can sit, but one pays more for it. Thus anyone who remains on the level standing pays only one English penny: but if he wants to sit, he is let in at a further door, and there he gives another penny. If he desires to sit on a cushion in the most comfortable place of all, where he not only sees everything well, but can also be seen, then he gives yet another English penny at another door. And in the pauses of the comedy food and drink are carried round amongst the people, and one can thus refresh himself at his own cost.\n\nThe comedians are most expensively and elegantly apparelled, since it is customary in England, when distinguished gentlemen or knights die, for nearly the finest of their clothes to be made over and given to their servants, and as it is not proper for them to wear such clothes but only to imitate them, they give them to the comedians to purchase for a small sum.\n\nWhat they can thus produce daily by way of mirth in the comedies, every one knows well, who has happened to see them acting or playing...\n\nWith such and many other pastimes besides the English spend their time; in the comedies they learn what is going on in other lands, and this happens without alarm, husband and wife together in a familiar place, since for the most part the English do not much use to travel, but are content ever to learn of foreign matters at home, and ever to take their pastime.\n\n_Sir Henry Wotton recounts the famous burning down of the Globe during a production of the Bard's_ Henry VIII _on 29 June 1613._\n\nNow to let matters of state sleep, I will entertain you at the present with what has happened this week at the Bank's side. The King's players had a new play, called _All is True,_ representing some principal pieces of the reign of Henry VIII, which was set forth with many extraordinary circumstances of pomp and majesty, even to the matting of the stage; the Knights of the Order with their Georges and garters, the Guards with their embroidered coats, and the like: sufficient in truth within a while to make greatness very familiar, if not ridiculous. Now, King Henry making a masque at the Cardinal Wolsey's house, and certain chambers being shot off at his entry, some of the paper, or other stuff, wherewith one of them was stopped, did light on the thatch, where being thought at first but an idle smoke, and their eyes more attentive to the show, it kindled inwardly, and ran round like a train, consuming within less than an hour the whole house to the very grounds. This was the fatal period of that virtuous fabric, wherein yet nothing did perish but wood and straw, and a few forsaken cloaks; only one man had his breeches set on fire, that would perhaps have broiled him, if he had not by the benefit of a provident wit put it out with bottle ale.\n\n## _The Death of Elizabeth, 24 March 1603_\n\nLADY SOUTHWELL\n\n_Lady Southwell was one of Elizabeth's ladies-in-waiting. The Cecil mentioned (and to whom Elizabeth directed her legendary temper) was Robert Cecil, who succeeded his father, William Cecil, as the queen's first minister. Elizabeth died at Richmond Palace, Surrey._\n\nNow falling into extremity, she sat two days and three nights upon her stool, ready dressed, and could never be brought by any of her council, to go to bed, or eat, or drink: only, my lord admiral one time persuaded her to drink some broth. For any of the rest, she would not answer them to any question; but said softly to my lord admiral's earnest persuasions, that, if he knew what she had seen in her bed, he would not persuade her as he did. And secretary Cecil, overhearing her, asked if her majesty had seen any spirits; to which she said she scorned to answer him to so idle a question. Then he told her how, to content the people, her majesty must go to bed: to which she smiled, wonderfully contemning him, saying that the word _must_ was not to be used to princes; and thereupon said, 'Little man, little man, if your father had lived, ye durst not have said so much: but thou knowest I must die, and that maketh thee so presumptuous.' And presently, commanding him and the rest to depart from her chamber, she willed my lord admiral to stay; to whom she shook her head, and, with a pitiful voice, said, 'My lord, I am tied with a chain of iron about my neck.' He alleging her wonted courage to her, she replied, 'I am tied, and the case is altered with me.'\n\nNow being given over by all, and at the last gasp, keeping still her sense in every thing, and giving, ever, when she spake, apt answers (though she spake very seldom, having then a sore throat) she desired to wash it, that she might answer more freely to what the council demanded; which was, to know whom she would have king: \u2013 but they, seeing her throat troubled her so much, desired her to hold up her finger, when they named whom liked her. Whereupon they named the king of France \u2013 the king of Scotland \u2013 at which she never stirred. They named my lord Beauchamp; whereto she said, 'I will have no rascal's son in my seat, but one worthy to be a king.' Hereupon, instantly she died.\n\n_The Virgin Queen's appointed successor was in fact James VI of Scotland, the son of her cousin Mary and Lord Darnley. James sat on the English throne as James I._\n\n_And so started the Stuart dynasty \u2013 arguably the least successful ever to reign over England._\n\n## _A Sketch of King James I, 1603\u201323_\n\nSIR ANTHONY WELDON\n\n_Little of his long rule in impoverished, under-populated Scotland prepared James I (born 1566) for the complexities of managing England, particularly its assertive Parliament, with whom he was soon at loggerheads over the extent of his prerogative. His habit of planting sloppy kisses on the lips of his male favourites like Buckingham ('Christ had his John and I have my George!') disgusted many. As did his coarseness, as did his reckless spending, as did his cutting dead of expansionism, overseas and in the English mind. Like the Pope, he found the new humanist learning \u2013 in the works of men like Raleigh and Bacon \u2013 seditious._\n\n_Weldon was Clerk of the Green Cloth. He was removed from his post when his satire on the Scots was found wrapped in departmental records._\n\n_He sided with Parliament in the Civil War._\n\nHe was of a middle stature, more corpulent through his clothes than in his body, yet fat enough, his clothes ever being made large and easy, the doublets quilted for stiletto proof, his breeches in great pleats and full stuffed. He was naturally of a timorous disposition, which was the reason of his quilted doublets: his eyes large, ever rolling after any stranger that came into his presence, insomuch as many for shame have left the room, as being out of countenance; his beard was very thin: his tongue too large for his mouth which ever made him speak full in the mouth, and made him drink very uncomely, as if eating his drink, which came out into the cup of each side of his mouth; his skin was as soft as taffeta sarsnet, which felt so, because he never washed his hands, only rubbed his fingers ends slightly with the wet end of a napkin. His legs were very weak, having had (as was thought) some foul play in his youth, or rather before he was born, that he was not able to stand at seven years of age, that weakness made him ever leaning on other men's shoulders: his walk was ever circular, his fingers ever in that walk fiddling about his cod-piece.\n\nHe was very temperate in his exercises and in his diet, and not intemperate in his drinking; however, in his old age, at Buckingham's jovial suppers, when he had any turn to do with him, made him sometimes overtaken, which he would the very next day remember and repent with tears; it is true he drank very often, which was rather out of a custom than any delight, and his drinks were of the kind for strength, as Frontinack, Canary, High Country Wine, Tent Wine and Scottish Ale, that, had he not had a very strong brain, might have daily been overtaken, although he seldom drank at any one time above four spoonfuls, many times not above one or two.\n\nHe was very constant in all things (his favourites excepted), in which he loved change, yet never cast down any (he once raised) from the height of greatness, though from their wonted nearness and privacy, unless by their own default... In his diet, apparel and journeys, he was very constant... that the best observing courtier of our time was wont to say, were he asleep seven years, and then awakened, he would tell where the King every day had been, and every dish he had had at table.\n\nHe was not very uxorious, though he had a very brave queen that never crossed his designs, nor intermeddled with State affairs, but ever complied with him... in the change of favourites; for he was ever best when furthest from his queen, and that was thought to be the first grounds of his often removes, which afterwards proved habitual...; he naturally loved not the sight of a soldier, nor of any valiant man...\n\nHe was very witty, and had as many ready witty jests as any man living, at which he would not smile himself, but deliver them in a grave and serious manner. He was very liberal of what he had not in his own grip, and would rather part with 100 _li._ he never had in his keeping than one twenty shilling piece within his own custody; he spent much, and had much use of his subjects' purses, which bred some clashings with them in parliament, yet would _always_ come off, and end with a sweet and plausible close.\n\n_For the Puritans, James I committed only one virtue. Following the Hampton Court conference of 1604 he ordered the Authorized Version (or King James Version) of the Bible, a translation into English which became a work of literary art. But it was not just the Puritans James I offended in matters of religion. The Catholics despised him for retaining the penal laws._\n\n## _The Gunpowder Plot, 5 November 1605_\n\nGUY FAWKES\n\n_The Gunpowder Plot was a conspiracy to advance the Catholic cause in England by blowing up the king and the Houses of Parliament. A warning given in time to Lord Monteagle foiled the plot, and led to the arrest of the plotters, who were directed by Robert Catesby and included Guy Fawkes._\n\nI confesse, that a practise in generall was first broken unto me, against his Maiestie for reliefe of the Catholic cause, and not invented or propounded by my selfe. And this was first propounded unto me about Easter Last was twelve moneth beyond the seas, in the Lowe Countreys of the _Archdukes_ obeissance, by _Thomas Winter,_ who came thereupon with mee into England, and there we imparted our purpose to three other Gentlemen more, namely, _Robert Catesby, Thomas Percy_ and _Iohn Wright,_ who all five consulting together of the means how to execute the same, and taking a vow among our selves for secrecie, _Catesby_ propounded to have it performed by Gunpowder, and by making a Myne under the upper House of Parliament: which place wee made a choice of the rather because Religion having been unjustly suppressed there, it was fittest that Justice and punishment should be executed there.\n\nThis being resolved amongst us, _Thomas Percy_ hired an House at Westminster for that purpose, neere adioyning to the Parliament House, and there we begun to make our Myne about the II of December 1604.\n\nThe five that first entred into the worke were _Thomas Percy, Thomas Catesby, Thomas Winter, Iohn Wright_ and myselfe: and soone after wee tooke another unto us, _Christopher Wright_ having Sworne him also, and taken the Sacrament for secrecie.\n\nWhen we came to the very foundation of the Wall of the House, which was about three yards thicke, and found it a matter of great difficultie, wee tooke unto us another Gentleman _Robert Winter,_ in like maner with oath and sacrament as afore said.\n\nIt was about Christmas when we brought our myne unto the Wall, and about Candlemas we had wrought the wall halfe through: and whilst they were in working, I stood as Sentinell to descrie any man that came neere, whereof I gave them warning, and so they ceased until I gave notice againe to proceede.\n\nAll we seven lay in the House, and had Shot and Powder, being resolved to die in that place before we should yield or be taken. As they were working upon the wall they heard a rushing in the Cellar of remooving of Coales, whereupon we feared we had been discovered: and they sent me to go to the Cellar, who finding that the Coales were a-selling and that the Cellar was to bee let, viewing the commoditie thereof for our purpose, _Percy_ went and hired the same for yeerely rent.\n\nWe had before this provided and brought into the House twentie Barrels of Powder, which we removed into the Cellar, and covered the same with Billets and Faggots, which were provided for that purpose.\n\nAbout Easter, the Parliament being prorogued till October next, we dispersed ourselves and I retired into the Low countreys by advice and direction of the rest, as well to aquaint _Owen_ with the particulars of the Plot, as also lest by my longer stay I might have growen suspicious, and so have come in question.\n\nIn the meantime _Percy_ having the key of the Cellar, laide in more Powder and wood into it. I returned about the beginning of September next, and then receiving the key againe of Percy, we brought in more Powder and Billets to cover the same againe, and so I went for a time into the Countrey till the 30 of October.\n\nIt was a further resolve amongst us that the same day that this act should have been performed, some other of our Confederates should have surprised the person of Lady Elizabeth the King's eldest daughter, who was kept in Warwickshire at Lo. _Harrington's_ house, and presently have her proclaimed as Queen, having a project of a Proclamation ready for that purpose, wherein we made no mention of altering of Religion, nor would have avowed the deede to be ours, until we should have had power enough to make our partie good and then we would have avowed both.\n\nConcerning Duke Charles, the King's second sonne, wee had sundry consultations how to seise on his Person. But because we found no means how to compass\u00e9 it (the Duke being kept neere London, where we had not Forces y-nough) we resolved to serve our turn with the Lady Elizabeth.\n\nTHE NAMES OF OTHER PRINCIPALL PERSONS, THAT WERE MADE PRIVY AFTERWARDS TO THIS HORRIBLE CONSPIRACIE\n\n_The Puritans resisted the temptation to blow King James sky-high, and instead began to break away from the Anglican Church, and then England itself._\n\n## _The Pilgrims Land in New England, 11 November 1620_\n\nWILLIAM BRADFORD\n\n_On 16 September 1620 the Pilgrim Fathers, a dissident and persecuted Puritan sect, sailed from Plymouth in the_ Mayflower _for America. They dropped anchor near the present-day Provincetown and explored Cape Cod, before formally establishing Plymouth Colony on 21 December._\n\nBeing thus arrived at Cap-Cod, and necessity calling them to look out a place for habitation (as well as the masters and mariners importunity), they having brought a large ship with them out of England, stowed in quarters in the ship, they now got her out, and set their carpenters to work to trim her up, but being much bruised and shattered in the ship with foul weather, they saw she would be long in mending. Whereupon a few of them tendered themselves, to go by land and discover those nearest places, while the ship was in mending.... It was conceived there might be some danger in the attempt, yet seeing them resolute they were permitted to go, being 16 of them well armed under the conduct of Captain Standish.... After some hours sailing, it began to snow and rain, and about the middle of the afternoon, the wind increased, and the sea became very rough; and they broke their rudder, and it was as much as two men could do to steer her with a couple of oars. But their pilot bade them be of good cheer for he saw the harbor, but the storm increasing, and night drawing on, they bore what sail they could to get in, while they could see; but herewith they broke their mast in three pieces and their sail fell overboard, in a very high sea...\n\nBut a lusty seaman which steered, bade those which rowed if they were men, about with her, or else they were all cast away; which they did with speed, so he bid them be of good cheer, and row justly for there was a fair sound before them, and he doubted not, but they should find one place or other, where they might ride in safety. And though it was very dark, and rained sore; yet in the end they got under the lee of a small island and remained there all that night in safety...\n\nBut though this had been a day and night of much trouble, and danger unto them; yet God gave them a morning of comfort and refreshing (as usually he does to his children) for the next day was a fair sunshining day, and they found themselves to be on an island secure from the Indians; where they might dry their stuff, fix their pieces, and rest themselves, and gave God thanks for his mercies, in their manifold deliverances. And this being the last day of the week, they prepared there to keep the Sabbath; on Monday they sounded the harbor, and found it fit for shipping; and marched into the land, and found many cornfields, and little running brooks, a place (as they supposed) fit for situation, at least it was the best they could find, and the season, and their present necessity made them glad to accept of it. So they returned to their ship again with this news to the rest of their people, which did much comfort their hearts...\n\nAfterwards [they] took better view of the place, and resolved where to pitch their dwelling; and the 25th day began to erect the first house, for common use to receive them, and their goods...\n\nIn these hard and difficult beginnings they found some discontents and murmurings arise amongst some, and mutinous speeches and carriages in other; but they were soon quelled, and overcome, by the wisdom, patience, and just and equal carriage of things, by the Governor and the better part which clave faithfully together in the main. But that which was most sad, and lamentable, was, that in two or three months the half of their company died, especially in January and February, being the depth of winter, and wanting houses and other comforts; being infected with the scurvy and other diseases, which this long voyage and their inaccommodate condition had brought upon them; so as there died some times two or three of a day, in the foresaid time; that of one hundred and odd persons scarce fifty remained: and of these in the time of most distress there was but six or seven sound persons; who to their great commendations, be it spoken, spared no pains, night nor day, but with abundance of toil and hazard of their own health, fetched them wood, made them fires, dressed their meat, made their beads, washed their loathsome clothes, clothed and unclothed them. In a word did all the homely, and necessary offices for them, which dainty and queasy stomachs cannot endure to hear named and all this willingly and cheerfully, without any grudging in the least, showing herein their true love unto their friends and brethren. A rare example and worthy to be remembered, two of these seven were Mr William Brewster, their Reverend Elder, and Miles Standish, their Captain and military commander (unto whom myself, and many others were much beholden in our low, and sick condition).... And what I have said of these, I may say of many others who died in this general visitation and others yet living; that while they had health... or any strength continuing they were not wanting to any that had need of them; and I [doubt] not but their recompense is with the Lord...\n\nAll this while the Indians came skulking about them, and would sometimes show themselves aloof, but when any approached near them, they would run away; and once they stole away their tools when they had been at work and were gone to dinner. But about the 16th of March a certain Indian came boldly amongst them, and spoke to them in broken English which they could well understand, but marveled at it; at length they understood by discourse with him, that he was not of these parts, but belonged to the eastern parts where some English ships came to fish, with whom he was acquainted, and could name sundry of them by their names, amongst whom he had got his language. He became profitable to them in acquainting them with many things concerning the state of the country in the east parts where he lived... of the people here, of their names, number and strength, of their situation and distance from this place, and who was chief amongst them. His name was Samasett; he told them also of another Indian whose name was Squanto, a native of this place, who had been in England and could speak better English than himself. Being after some time of entertainment, and gifts dismissed, a while after he came again, and five more with him, and they brought again all the tools that were stolen away before, and made way for the coming of their great Sachem, called Massasoyt. Who about four or five days after came with the chief of his friends, and other attendance with the aforesaid Squanto. With whom after friendly entertainment, and some gifts given him, they made a peace with him (which has now continued this 24 years) in these terms:\n\n1. That neither he nor any of his, should injure or do hurt, to any of their people.\n\n2. That if any of his, did any hurt to any of theirs; he should send the offender, that they might punish him.\n\n3. That if any thing were taken away from any of theirs, he should cause it to be restored; and they should do the like to his.\n\n4. If any did unjustly war against him, they would aide him; if any did war against them, he should aide them.\n\n5. He should send to his neighbors confederates to certify them of this [treaty], that they might not wrong them [the Pilgrims], but might be likewise comprised in the conditions of peace.\n\n6. That when [Massasoyt's] men came to [the Pilgrims,] they should leave their bows and arrows behind them...\n\nThey [the Pilgrims] began now to gather in the small harvest they had; and to fit up their houses and dwellings, against winter, being all well recovered in health and strength; and had all things in good plenty, for as some were thus employed in affairs abroad; others were exercised in fishing, about cod, and bass, other fish of which they took good store, of which every family had their portion; all the summer there was no want; and now began to come in store of fowl, as winter approached, of which this place did abound when they came first (but afterward decreased by degrees), and besides water fowl, there was great store of wild turkeys, of which they took many, besides venison etc. Besides they had about a peck of meal a week to a person, or now since harvest, Indian corn to that proportion, which made many afterwards write so largely of their plenty here to their friends in England, which were not fained, but true reports.\n\n## _A Post-mortem, 1636_\n\nWILLIAM HARVEY\n\n_Harvey discovered the circulation of blood in the human body, and was physician to both James I and Charles I. Below he performs an autopsy on the body of Thomas Parr, supposedly 154 years old._\n\nThe appearance of the body was well nourished, the chest was hairy, and the hair on the forearm was still black although the shins were hairless and smooth.\n\nThe genital organs were in good condition, the penis was neither retracted nor thin, nor was the scrotum, as is usual in old persons, distended by any watery hernia, while the testicles were large and sound \u2013 so good in fact as not to give the lie to the story commonly told of him that, after reaching his hundredth year, he was actually convicted of fornication and punished. Moreover his wife, a widow, whom he had married in his hundred and twentieth year, in reply to questions, could not deny that he had had intercourse with her exactly as other husbands do, and had kept up the practice to within twelve years of his death.\n\nThe chest was broad and full; his lungs were not spongy but, particularly on the right side, were attached to the ribs by fibrous bands. The lungs also were considerably distended with blood as is usual in pulmonary consumption (peri-pneumonia), so much so that before the blood was drawn off, a quantity seemed to become black. To this cause, too, I attributed the bluish colour of the face, and, a little before death, a difficulty in breathing and orthopnoea. As a result, the armpits and chest remained warm long after death. To sum up, there were clearly visible in his dead body this and other signs customarily found in those dying from suffocation. I concluded that he was suffocated, and that death was due to inability to breathe, and a similar report was given to his most Serene Majesty by all the physicians present. Later, when the blood had been drained off and wiped away from the lungs, they were seen to have a quite white and almost milky parenchyma.\n\nThe heart was large, thick, and fibrous with a considerable mass of fat around its wall and partition. The blood in the heart was blackish, liquid, and scarcely grumous. Only in the right ventricle were some clots seen.\n\nWhen the sternum was dissected, the cartilages were not more osseous than in other men, but rather were flexible and soft.\n\nThe intestines were in excellent condition, fleshy and vigorous: the stomach was the same. The small intestine appeared muscular, but had some ring-shaped constrictions due to the fact that frequently he ate any kind of food both by day and night without any rules of diet or regular hours for meals. He was quite happy with half-rancid cheese and all kinds of milk dishes, brown bread, small beer, but most usually sour milk. By living frugally and roughly, and without cares, in humble circumstances, he in this way prolonged his life. He had taken a meal about the midnight shortly before his death.\n\n_As the biographer John Aubrey, a friend of Harvey's, recalled, when_ The Circulation of Blood _was published Harvey 'fell mightily in his Practize, and 'twas believed by the vulgar that he was crack-brained... With much ado at last, in about 20 or 30 years time, it was received in all the Universities in the world; and Mr [Thomas] Hobbes says in his book_ De Corpore, _he is the only man, perhaps, that ever lived to see his owne Doctrine established in his life-time...'_\n\n## _Cromwell in the House of Commons, November 1640_\n\nSIR PHILIP WARWICK\n\n_James I died of dysentery on 27 March 1625_ , _to be succeeded by his son, Charles I. Although mercifully free of his father's crude personal habits, Charles fatally inherited his absolutism and his Catholicism, which resulted in a head-on collision with the Puritan-tinged Parliament as it marched towards greater democratic government._\n\n_Charles would find no more stalwart Parliamentary critic than Oliver Cromwell. Born in Huntingdon in 1599_ , _of minor gentry stock, Oliver Cromwell had undergone a damascene conversion to Puritanism after being, in his words, 'the chief of sinners'. Henceforth, like Puritans all, he believed that Charles I's Catholicism was the devil's mark on England, God's chosen country. The politically well-connected Cromwell (no fewer than nine of his cousins were MPs) was first returned to Parliament for Huntingdon, then in 1640 for Cambridge City. It was in the Long Parliament of that year that the royal courtier, Sir Philip Warwick, first clapped eyes on Farmer Cromwell._\n\nI have no mind to give an ill character of Cromwell, for in his conversation towards me he was ever friendly, though at the latter end of the day, finding me ever incorrigible and having some inducements to suspect me a tamperer, he was sufficiently rigid. The first time that ever _I_ took notice of him was in the very beginning of the Parliament held in November 1640, when _I_ vainly thought myself a courtly young gentleman (for we courtiers valued ourselves much upon our good clothes). _I_ came one morning into the House well clad, and perceived a gentleman speaking (whom _I_ knew not) very ordinarily apparelled, for it was a plain-cloth suit, which seemed to have been made by an ill country tailor: his linen was plain and not very clean, and _I_ remember a speck or two of blood upon his little band, which was not much larger than his collar. His hat was without a hatband. His stature was of good size, his sword stuck close to his side, his countenance swollen and reddish, his voice sharp and untunable, and his eloquence full of fervour, for the subject matter would not bear much of reason, it being in behalf of a servant of Mr Prynne's, who had dispersed libels against the Queen for her dancing and such like innocent and courtly sports: and he aggravated the imprisonment of this man by the Council-Table unto that height that one would have believed the very government itself had been in great danger by it.\n\n_Charles I had only called the Long Parliament because he had no other way to raise money. To the king's ire, the Long Parliament proved even more truculent than its forebears. It rejected ship money (a tax imposed by Charles during the Parliament-less 'eleven years' tyranny', 1629\u201340) as illegal, it impeached the king's ministers Strafford and Laud, and secured a bill preventing its dissolution without its own consent. The Long Parliament also abolished the jury-free Royal Courts, despotically used by Charles to imprison MPs._\n\n_In December 1641 Parliament passed by 159 votes to 148 the Grand Remonstrance, which demanded that the king remove all bishops from Parliament, replace his 'evil counsellors' (believed to be planning the reintroduction of Catholicism), and reform the Church in a more Protestant direction._\n\n_Predictably, Charles I refused the Grand Remonstrance._\n\n## _The Attempted Arrest of the Five Members, 4 January 1642_\n\nJOHN RUSHWORTH\n\n_The breach between Charles I and Parliament became absolute on 4 January 1642 when the king tried to arrest five Members of the House of Commons \u2013Pym, Hampden, Hesilrige, Holies and Strode \u2013for treason._\n\n_Rushworth was secretary to the House of Commons and later to Oliver Cromwell._\n\n... The said five accused Members this day _after dinner_ came into the House, and did appear according to the special Order and Injunction of the House laid upon them yesterday, to give their attendance upon the House, _de die in diem_ and their appearance was entred in the Journal.\n\nThey were no sooner sate in their places, but the House was informed by one Captain _Langrish,_ lately an Officer in Arms in _France,_ that he came from among the Officers, and souldiers at _White Hall,_ and understanding by them, that his Majesty was coming with a Guard of Military Men, Commanders and Souldiers, to the House of Commons, he passed by them with some difficulty to get to the House before them, and sent in word how near the said Officers and Souldiers were come; Whereupon a certain Member of the House having also private Intimation from the Countess of _Carlile,_ Sister to the Earl _of Northumberland,_ that endeavours would be used this day to apprehend the five Members, the House required the five Members to depart the House forthwith, to the end to avoid Combustion in the House, if the said Souldiers should use Violence to pull any of them out. To which Command of the House, four of the said Members yielded ready Obedience, but Mr _Stroud_ was obstinate, till Sir _Walter Earle_ (his ancient acquaintance) pulled him out by force, the King being at that time entring into the _New Pallace-yard,_ in _Westminster:_ And as his Majesty came through _Westminster Hall,_ the Commanders, Reformadoes, &c. that attended him, made a Lane on both sides the Hall (through which his Majesty passed and came up the Stairs to the House of Commons) and stood before the Guard of Pentioners, and Halberteers, (who also attended the King Person,) and the door of the House of Commons being thrown open, his Majesty entred the House, and as he passed up towards _the Chair_ he cast his eye on the Right-hand near the Bar of the House, where Mr _Pym_ used to sit, but his Majesty not seeing him there (knowing him well) went up to the Chair, and said, 'By your leave, (Mr Speaker) I must borrow your Chair a little,' whereupon the Speaker came out of the Chair, and his Majesty stept up into it, after he had stood in the Chair a while, casting his Eye upon the Members as they stood up _uncovered,_ but could not discern any of the five Members to be there, nor indeed were they easie to be discerned (had they been there) among so many bare Faces all standing up together.\n\nThen his Majesty made this Speech,\n\n'Gentlemen,\n\nI Am sorry for this occasion of coming unto you: Yesterday I sent a Serjeant at Arms upon a very Important occasion to apprehend some that by my command were accused of High Treason, whereunto I did expect Obedience and not a Message. And I must declare unto you here, that albeit, no King that ever was in _England,_ shall be more careful of your Priviledges, to maintain them to the uttermost of his power than I shall be; yet you must know that in Cases of Treason, no person hath a priviledge. And therefore I am come to know if any of these persons that were accused are here: For I must tell you Gentlemen, that so long as these persons that I have accused (for no slight Crime but for Treason) are here, I cannot expect that this House will be in the Right way that I do heartily wish it: Therefore I am come to tell you that I must have them wheresoever I find them. Well since I see all the Birds are Flown, I do expect from you, that you shall send them unto me, as soon as they return hither. But I assure you, in the word of a King, I never did intend any Force, but shall proceed against them in a legal and fair way, for I never meant any other.\n\nAnd now since I see I cannot do what I came for, I think this no unfit occasion to repeat what I have said formerly, That whatsoever I have done in favour, and to the good of my Subjects, I do mean to maintain it.\n\nI will trouble you no more, but tell you I do expect as soon as they come to the House, you will send them to me; otherwise I must take my own Course to find them.'\n\nWhen the King was looking about the House, the Speaker standing below by the Chair, his Majesty ask'd him, whether any of these persons were in the House? Whether he saw any of them? and where they were? To which the Speaker falling on his Knee, thus Answered.\n\n_'May it please your Majesty,_ I Have neither Eyes to see, nor Tongue to speak in this place, but as the House is pleased to direct me, whose Servant I am here, and humbly beg your Majesties Pardon, that I cannot give any other Answer than this, to what your Majesty is pleased to demand of me.'\n\nThe King having Concluded his Speech, went out of the House again which was in great disorder, and many Members cried out, aloud so as he might hear them, 'Priviledge! Priviledge!' and forthwith Adjourned till the next Day at One of the Clock...\n\n_To this day, no sovereign has ever been allowed in the House of Commons._\n\n_The failure of Charles' coup, and the mass protests against him on London's streets the following day (the crowds shouted 'Privilege of Parliament!'), persuaded the king to abandon the capital. Since Charles had so readily resorted to physical force, Parliament set about defending itself by passing the Militia Ordinance, calling up country troops._\n\n_The Militia Ordinance proved a wise precaution for on 22 August 1642 Charles I raised the royal standard at Nottingham, effectively declaring war on his own country. Much is made of how the ensuing Civil War left families 'by the sword divided', and of course there were personal tragedies, but in truth the main lines of division avoided kin: they were about class, region and religion. Thus the bulk of Parliament's support came from the South and East (more commercially advanced, more populated by the sort of on-the-up gentry and merchants who subscribed literally to the Protestant work ethic), the mainstay of the King's support came from the underdeveloped, Catholic-leaning North and West. His army was heavily dependent on mercenaries._\n\n_From the outset the two sides traded inventive invective. The Royalists name-called the Parliamentarians 'Roundheads' (probably after the Puritans' pudding-basin hairstyle), the Parliamentarians insulted the Royalists as 'Malignants' and 'Cavaliers', the latter term taking its raffish and debauched connotations from the person of Prince Rupert of the Rhine, Charles' nephew and General of Horse. According to one mischievous Puritan scribbler, the Cavalier might be identified by his twenty 'Ridiculous Habits and apish Gestures':_\n\n1. His hat in fashion like a close-stoolepan.\n\n2. Set on the top of his noddle like a coxcombe.\n\n3. Banded with a calves tail, and a bunch of riband.\n\n4. A feather in his hat, hanging down like a Fox taile.\n\n5. Long haire, with ribands tied in it.\n\n6. His face spotted.\n\n7. His beard on the upper lip, compassing his mouth.\n\n8. His chin thrust out, singing as he goes.\n\n9. His band lapping over before.\n\n10. Great band strings, with a ring tied.\n\n11. A long wasted dubblet unbuttoned half way.\n\n12. Little skirts.\n\n13. His sleeves unbuttoned.\n\n14. In one hand a stick, playing with it, in the other side his cloke hanging.\n\n15. His breeches unhooked ready to drop off.\n\n16. His shirt hanging out.\n\n17. His codpiece open tied at the top with a great bunch of riband.\n\n18. His belt about his hips.\n\n19. His sword swapping between his legs like a Monkeys taile.\n\n20. Many dozen points at knees.\n\n_It was a good war for trading words, a less good one in the beginning for the military arts, since the English had not fought a major land campaign for a century. Proof came in the first major engagement of the war._\n\n## _Civil War: Sir Richard Bulstrode in Action at Edgehill, 23 October 1642_\n\nSIR RICHARD BULSTRODE\n\n_Bulstrode fought at Edgehill, Warwickshire, for the Royalists, commanded by Charles land Prince Rupert; the Parliamentarians were led by the Earl of Essex. The opposing sides had about 14,000 men apiece._\n\nOur whole army was drawn up in a body, the horse three deep in each wing, and the foot in the centre six deep. The Prince of Wales' regiment was on the right wing, which was commanded by Prince Rupert, and Colonel Washington was with his dragoons upon our right. In the centre was the infantry, commanded in chief by General Ruthven, and under him, by Sir Jacob Astley. The Earl of Lindsey marched on foot, in the head of the regiment of the royal foot guards, with his son, the Lord Willoughby, and Sir Edmund Verney carried the Royal Standard. The left wing of our horse was commanded by Commissary-General Wilmot, with Lieutenant-Colonel Edward Fielding and some other principal officers; and Lieutenant-Colonel George Lisle, with Lieutenant-Colonel John Ennis were in the left wing, with a regiment of dragoons, to defend the briars on that side, and we had a body of reserve, of six hundred horse, commanded by the Earl of Carnarvon. When our army was drawn up at the foot of the hill and ready to march, all the generals went to the King (who intended to march with the army) and desired he would retire to a rising ground, some distance from thence, on the right, with the Prince of Wales and the Duke of York (having his guard of Pensioners on horseback with him) from whence he might see the issue of the battle and be out of danger, and that otherwise the army would not advance towards the enemy. To which the King (very unwillingly) was at last persuaded.\n\nJust before we began our march, Prince Rupert passed from one wing to the other, giving positive orders to the horse, to march as close as was possible, keeping their ranks with sword in hand, to receive the enemy's shot, without firing either carbine or pistol, till we broke in amongst the enemy, and then to make use of our firearms as need should require, which order was punctually observed.\n\nThe enemy stayed to receive us in the same posture as was formerly declared; and when we came within cannon shot of the enemy, they discharged at us three pieces of cannon from their left wing, commanded by Sir James Ramsey; which cannon mounted over our troops, without doing any hurt, except that their second shot killed a quarter-master in the rear of the Duke of York's troop. We soon after engaged each other, and our dragoons on our right beat the enemy from the briars, and Prince Rupert led on our right wing so furiously, that, after a small resistance, we forced their left wing, and were masters of their cannon; and the Prince being extremely eager of this advantage (which he better knew how to take than to keep) was not content with their cannon, and keeping their ground, but eagerly pursued the enemy, who fled on the other side of Kineton towards Warwick. And we of the Prince of Wales' regiment (who were all scattered) pursued also, till we met with two foot regiments of Hampden and Holies, and with a regiment of horse coming from Warwick to their army, which made us hasten as fast back as we had pursued.\n\nIn this pursuit I was wounded in the head by a person who turned upon me and struck me with his pole-axe, and was seconding his blow, when Sir Thomas Byron being near, he shot him dead with his pistol, by which means I came back. In fine, by meeting these three regiments, we were obliged to return back to our army and then found our great error, in leaving our foot naked who were rudely handled by the enemy's horse and foot together in our absence, who fell principally upon the King's royal regiment of foot guards, who lost eleven of thirteen colours, the King's Standard-Bearer, Sir Edmund Verney, killed, and the Royal Standard taken, which was presently retaken by Captain John Smith, who was knighted for it that night by the King, under the Standard Royal and made a banneret with the usual ceremonies; and had afterwards a large medal of gold given him, with the King's picture on the one side, and the banner on the other, which he always wore to his dying day, in a large green watered ribband, cross his shoulders...\n\nNow, when we returned from following the enemy, the night came soon upon us, whereas, in all probability, we had gained the victory, and made an end of the war, if we had only kept our ground after we had beaten the enemy, and not left our foot naked to their horse and foot. And, to add to our misfortune, a careless soldier, in fetching powder (where a magazine was) clapt his hand carelessly into a barrel of powder, with his match lighted betwixt his fingers, whereby much powder was blown up and many kill'd...\n\nOn Monday morning, being next after the battle, several parties were sent down to view the dead, the greatest part of the enemy having retired in the night to the town of Kineton, which was near them; and Mr Adrian Scroop having seen his father fall (being much wounded) desired the Duke of Lennox to speak to the King, that one of his coaches might go with him, to bring up his father's body; which being granted, he found his father stripped, with several very dangerous wounds, and that he was alive. Whereupon he lap'd him up in his cloak, and brought him in the coach, where he was presently dressed by the King's chirurgeons, and by their care and skill was cured, and lived many years after, tho' he had seventeen wounds, and had died upon the place, but that the coldness of the weather stopp'd the bleeding of his wounds, which saved also several other men's lives that were wounded.\n\n_Prince Rupert's ill-disciplined (cavalier, even) departure from the battlefield in pursuit of the Roundheads into Kineton probably cost the Royalists a victory. As it was, Edgehill ended in a draw, and the King continued on his way towards London \u2013 a dubious objective, since the city was solid against him. At Turnham Green, on the capital's fringe, he was met by a 24,000-strong militia, the 'Trained Bands', and with little ado turned around for Oxford, which became the Royalist headquarters._\n\n_A year and a half of indecisive skirmish and siege ensued, until Prince Rupert determined to bring the Roundheads to a definitive battle at Marston Moor in Yorkshire._\n\n_Unfortunately for the inspired but luckless Rupert, the Roundhead army was bolstered by Parliament's new Scottish allies, secured by the 'Solemn League and Covenant' of 1643. Worse, the Roundheads now boasted a cavalry commander who was Rupert's peer._\n\n## _Civil War: The Death of a Nephew at Marston Moor, 2 July 1644_\n\nOLIVER CROMWELL\n\n_Appointed a Captain of Horse at the outset of the Civil War, Oliver Cromwell had early showed his mettle as a soldier but, more importantly for the Parliamentary cause, as a commander of men. Singularly, he had eschewed snobbery, informing his fellow officers that he 'would rather have a plain russet-coated captain that knows what he fights for and loves what he knows, than that which you call a gentlemen and nothing else'. Disciplined and meritocratic, Cromwell's 'Ironsides' had immediately eclipsed the other Parliamentary horse units._\n\n_Below Cromwell writes to his brother-in-law, Colonel Valentine Wilson, from the battlefield of Marston Moor. It was Cromwell's surprise charge, late in the moonlit evening, that enabled Parliament to rout the Royalists. Rupert himself, his horse shot from under him, passed the latter stages of the battle hiding ignominiously in a beanfield, before high-tailing it to safety. Behind him he left his poodle dog, Boy, one of the 4,000 Royalist casualties of the day._\n\nIt's our duty to sympathize in all mercies; and to praise the Lord together in chastisements or trials, that so we may sorrow together.\n\nTruly England and the Church of God hath had a great favour from the Lord, in this great Victory given unto us, such as the like never was since this War began. It had all the evidences of an absolute Victory obtained by the Lord's blessing upon the Godly Party principally. We never charged but we routed the enemy. The Left Wing, which I commanded, being our own horse, saving a few Scots in our rear, beat all the Prince's horse. God made them as stubble to our swords. We charged their regiments of foot with our horse, and routed all we charged. The particulars I cannot relate now; but I believe, of Twenty-thousand the Prince hath not Four-thousand left. Give glory, all the glory, to God...\n\nSir, God hath taken away your eldest Son by a cannon-shot. It brake his leg. We were necessitated to have it cut off, whereof he died.\n\nSir, you know my own trials this way: but the Lord supported me with this, That the Lord took him into the happiness we all pant for and live for. There is your precious child full of glory, never to know sin or sorrow any more. He was a gallant young man, exceedingly gracious. God give you His comfort. Before his death he was so full of comfort that to Frank Russel and myself he could not express it, 'It was so great above his pain.' This he said to us. Indeed it was admirable. A little after, he said, One thing lay upon his spirit. I asked him, What that was? He told me it was, That God had not suffered him to be anymore the executioner of His enemies. At his fall, his horse being killed with the bullet, and as I am informed three horses more, I am told he bid them, Open to the right and left, that he might see the rogues run. Truly he was exceedingly beloved in the Army, of all that knew him. But few knew him; for he was a precious young man, fit for God. You have cause to bless the Lord. He is a glorious Saint in Heaven; wherein you ought exceedingly to rejoice. Let this drink up your sorrow; seeing these are not feigned words to comfort you, but the thing is so real and undoubted a truth. You may do all things by the strength of Christ. Seek that, and you shall easily bear your trial. Let this public mercy to the Church of God make you to forget your private sorrow. The Lord be your strength: so prays\n\nYour truly faithful and loving brother\n\nMy love to your Daughter, and my Cousin Perceval, Sister Desborow and all friends with you.\n\n_After Marston Moor, the tide of the Civil War turned resolutely in Parliament's favour. Cromwell himself rose to become the cavalry commander of the New Model Army, the Roundhead army remoulded for military efficiency (through the centralization of command and the ejection of insufficiently resolute aristocratic officers) and cohered by ideological purpose. Item 1 in the New Model Army's catechism on soldierly qualities, was: 'That he is religious and godly'._\n\n_Any lingering hope the king had of defeating Parliament in the field was dashed to death at Naseby, Leicestershire, on 14 June 1645_. _Inevitably Cromwell was there, on God's errand, his men fired up on religious fervour. After the battle, in which Cromwell's right wing had played the key part, Cromwell reported to William Lenthall, Speaker of the House of Commons: We, after three-hours fight very doubtful routed his [the king's] Army; killed and took about 5,000... We took also about 200 carriages, all he had; and all his guns, being 12 in number, whereof two were demi-cannon, two demi-culverins, and I think the rest sackers. We pursued the Enemy from three miles short of Harborough to nine beyond, even to the sight of Leicester, whither the King fled... Sir, this is none other than the hand of God; and to Him alone belongs the glory, wherein none are to share with him.'_\n\n_Eleven months later, with the Royal game up, Charles surrendered to the Scottish Presbyterians. There was some desultory politicking \u2013 whereby Charles hoped to secure their support, they wanted him to establish Presbyterianism \u2013 before the Scots tired of it and sold the king to Parliament for \u00a3400,000. 'Cheap at the price,' Charles joked._\n\n_Now that the victors had their illustrious man, they squabbled about what to do. Parliament wanted a restoration of the monarchy, but with a Presbyterian settlement to the Church; Cromwell's divines in the New Model Army wanted greater religious toleration and limited changes to the franchise; a left wing in the Army wanted universal manhood suffrage. (In the memorable words of the radical 'Leveller' spokesman Colonel Rainsborough: 'I think that the poorest he that in England hath a life to live, as the greatest he... that every man that is to live under a government ought first by his own consent to put himself under that government.')_\n\n_Meanwhile, Charles escaped to the Isle of Wight, and decided that he could,after all, stomach a deal with the Scots whereby Presbyterianism was introduced and they fought for his restoration. Alas for King Charles, the Scots were no match for Cromwell's New Model Army, who sent them packing at Preston in August 1648. Unforgiving of the recaptured king's treasonable dealings with the Scots, Cromwell pressed for the trial of the 'tyrant, traitor, and murderer, Charles Stuart'._\n\n_Charles I had unsheathed the sword, and he perished by it._\n\n## _The Execution of Charles I, 30 January 1649_\n\nPHILIP HENRY\n\n_Henry was an undergraduate at Christ Church, Oxford._\n\nAt the later end of the year 1648 I had leave to goe to london to see my Father, & during my stay there at that time at Whitehal it was that I saw the Beheading of King Charles the first; He went by our door on Foot each day that hee was carry'd by water to Westminster, for he took Barge at Gardenstayres where we liv'd & once he spake to my Father & sayd Art thou alive yet! On the day of his execution, which was Tuesday, Jan. 30, I stood amongst the crowd in the street before Whitehal gate, where the scaffold was erected, and saw what was done, but was not so near as to hear any thing. The Blow I saw given, & can truly say with a sad heart; at the instant whereof, I remember well, there was such a Grone by the Thousands then present, as I never heard before & desire I may never hear again. There was according to Order one Troop immediately marching from-wards charing-cross to Westmr & another from-wards Westmr to charing-cross purposely to masker the people, & to disperse & scatter them, so that I had much adoe amongst the rest to escape home without hurt.\n\n_In May 1649 England became a republic, with Oliver Cromwell the chairman of the Council of State._\n\n## _The Storming of Drogheda, 10\u201311 September 1649_\n\nOLIVER CROMWELL\n\n_To protect the new Commonwealth of England, Cromwell crossed to Ireland, which was feared to be a potential launch-pad for a Royalist invasion of the mainland. His slaughter of the garrison at Drogheda, a seaport on the Boyne, was controversial then, as now._\n\nIt hath pleased God to bless our endeavours at Tredah (Drogheda). After battery, we stormed it. The enemy were about 3,000 strong in the Town. They made a stout resistance; and near 1,000 of our men being entered, the Enemy forced them out again. But God giving a new courage to our men, they attempted again, and entered; beating the enemy from their defences.\n\nThe Enemy had made three retrenchments, both to the right and left of where we entered; all which they were forced to quit. Being thus entered, we refused them quarter; having, the day before, summoned the Town. I believe we put to the sword the whole number of the defendants. I do not think Thirty of the whole number escaped with their lives. Those that did, are in safe custody for the Barbadoes. Since that time, the Enemy quitted to us Trim and Dundalk. In Trim they were in such haste that they left their guns behind them.\n\nThis hath been a marvellous great mercy. The Enemy, being not without some considerable loss; Colonel Castle being there shot in the head, whereof he presently died; and divers officers and soldiers doing their duty killed and wounded. There was a Tenalia to flanker the south Wall of the Town, between Duleek Gate and the corner Tower before mentioned; \u2013 which our men entered, wherein they found some forty or fifty of the Enemy, which they put to the sword. And this 'Tenalia' they held: but it being without the Wall, and the sally-port through the Wall into that Tenalia being choked up with some of the Enemy which were killed in it, it proved of no use for an entrance into the Town that way.\n\nAlthough our men that stormed the breaches were forced to recoil, as is before expressed; yet, being encouraged to recover their loss, they made a second attempt; wherein God was pleased so to animate them that they got ground of the enemy, and by the goodness of God, forced him to quit his entrenchments. And after a very hot dispute, the Enemy having both horse and foot, and we only foot, within the Wall \u2013 they gave ground, and our men became masters both of their retrenchments and of the Church; which, indeed, although they made our entrance the more difficult, yet they proved of excellent use to us; so that the Enemy could not now annoy us with their horse, but thereby we had the advantage to make good the ground, that so we might let in our own horse; which accordingly was done, though with much difficulty.\n\nDivers of the Enemy retreated into the Mill-Mount: a place very strong and difficult of access; being exceedingly high, having a good graft, and strong palisadoed. The Governor, Sir Arthur Ashton, and divers considerable Officers being there, our men getting up to them, were ordered by me to put them all to the sword. And indeed, being in the heat of action, I forbade them to spare any that were in arms in the Town; and, I think, that night they put to the sword about 2,000 men; \u2013 divers of the officers and soldiers being fled over the Bridge into the other part of the Town, where about 100 of them possessed St Peter's Church-steeple, some the west Gate, and others a strong Round Tower next the Gate called St Sunday's. These being summoned to yield to mercy, refused. Whereupon I ordered the steeple of St Peter's Church to be fired, when one of them was heard to say in the midst of the flames: 'God damn me, God confound me; I burn, I burn.'\n\nThe next day, the other two Towers were summoned; in one of which was about six or seven score; but they refused to yield themselves: and we knowing that hunger must compel them, set only good guards to secure them from running away until their stomachs were come down. From one of the said Towers, notwithstanding their condition, they killed and wounded some of our men. When they submitted, their officers were knocked on the head; and every tenth man of the soldiers killed; and the rest shipped for the Barbadoes. The soldiers in the other Tower were all spared, as to their lives only; and shipped likewise for the Barbadoes.\n\nI am persuaded that this is a righteous judgement of God upon these barbarous wretches, who have imbrued their hands in so much innocent blood; and that it will tend to prevent the effusion of blood for the future. Which are the satisfactory grounds to such actions, which otherwise cannot but work remorse and regret. The officers and soldiers of this Garrison were the flower of their army. And their great expectation was, that our attempting this place would put fair to ruin us... And now give me leave to say how it comes to pass that this work is wrought. It was set upon some of our hearts, That a great thing should be done, not by power or might, but by the Spirit of God. And is it not so, clearly? That which caused your men to storm so courageously, it was the Spirit of God, who gave your men courage, and took it away again; and gave the Enemy courage, and took it away again; and gave your men courage again, and therewith this happy success. And therefore it is good that God alone have all the glory...\n\nYour most obedient servant,\n\nOLIVER CROMWELL.\n\n_After Ireland, Cromwell turned his attention to Scotland where Charles I's son had been acclaimed king as Charles II. Cromwell defeated the Scots at Dunbar, and then a Scottish invasion under Charles II at Worcester in September 1651. So ended the Civil War._\n\n## _Cromwell Purges the Long Parliament, 20 April 1653_\n\nBULSTRODE WHITELOCK\n\n_By 1653 the Long Parliament had been sitting for thirteen years without reelection. When it began discussion of a law to perpetuate itself, Cromwell dismissed it._\n\nIn this manner [accompanied by a troop of soldiers] entering the house, he, in a furious manner, bid the Speaker leave his chair; told the house 'That they had sat long enough, unless they had done more good; that some of them were whoremasters, (looking then towards Henry Martyn and Sir Peter Wentworth) that others of them were drunkards, and some corrupt and unjust men, and scandalous to the profession of the Gospel; and that it was not fit they should sit as a parliament any longer, and desired them to go away.' The Speaker not stirring from his seat, col. Harrison, who sat near the chair, rose up and took him by the arm, to remove him from his seat; which when the Speaker saw, he left his chair. Some of the members rose up to answer Cromwell, but he would suffer none to speak but himself; which he did with so much arrogance in himself, and reproach to his fellow-members, that some of his priva-does were ashamed of it, but he and his officers and party would have it so; and among all the parliament men, of whom many wore swords, and would sometimes brag high, not one man offered to draw his sword against Cromwell, or to make the least resistance against him; but all of them tamely departed the house. He bid one of his soldiers to take away that fool's bauble, the mace, and stayed himself to see all the members out of the house, himself the last of them, and then caused the doors of the house to be shut up.\n\n_The ensuing Puritan Convention (the 'Barebones' Parliament') was not to Cromwell's taste either, and was soon dismissed. From 16 December 1653 Cromwell ruled as Lord Protector in what, the occasional calling of a Parliament aside, was a military dictatorship. The other options were Anarchy or the Stuarts._\n\n_The Interregnum is invariably portrayed as a kill-joy tyranny. On the contrary, Cromwell's rule tended to benevolent tolerance ('our chief of men' wasn't f\u00eated by the greatest poet of the age, John Milton, for the money or for want of other subjects) and more importantly it was the making of modern capitalist England. By conquering Scotland and Ireland and placing them under English hegemony, he united the Isles. And then, with the 1651 Navigation Act, he turned the Isles outwards to become a commercial world power, with a world-scale merchant marine, and a big-gun navy to protect it._\n\n## _Cromwell's Funeral, 23 November 1658_\n\nJOHN EVELYN\n\n_Cromwell was defeated by bronchitis in September 1658. Evelyn was a High Church Royalist._\n\nSaw the superb funeral of the protector. He was carried from Somerset House in a velvet bed of state, drawn by six horses, housed with the same; the pall held by his new lords; Oliver lying in effigy, in royal robes, and crowned with a crown, sceptre, and globe, like a king. The pendants and guidons were carried by the officers of the army; the imperial banners, achievements, etc., by the heralds in their coats; a rich caparisoned horse, embroidered all over with gold; a knight of honor, armed _cap-a-pie,_ and, after all, his guards, soldiers, and innumerable mourners. In this equipage, they proceeded to Westminster: but it was the most joyful funeral I ever saw; for there were none that cried but dogs, which the soldiers hooted away with a barbarous noise, drinking and taking tobacco in the streets as they went.\n\n_With Cromwell dead it became starkly obvious that the republic depended almost entirely on his persona. Cromwell's son Richard ('Tumbledown Dick') tried on the mantle of Lord Protector before wisely giving it up as beyond him. A gyre widened. For the want of greater evil, the Army invited the Stuarts back to England._\n\n## _The Restoration: Charles II Returns to England, 12\u201325 May 1660_\n\nSAMUEL PEPYS\n\n_Pepys, a Navy clerk, was appointed secretary to Sir Edward Montague on the expedition to Holland to fetch Charles II from exile. The famous diary, written in shorthand code (partly so that Pepys' wife did not discover his peccadilloes) was not deciphered until 1825._\n\n_12 May._ My Lord did give order for weighing anchor; which we did, and sailed all day. In our way in the morning, coming in the midway between Dover and Callis, we could see both places very easily, and very pleasant it was to me, but the farther we went the more we lost sight of both lands.\n\n_14 May._ In the morning, when I waked and rose, I saw myself out of the scuttle close by the shore, which afterwards I was told to be the Duch shore. The Hague was clearly to be seen by us. Some masty Duchmen came on board to proffer their boats to carry things from us on shore &c, to get money by us. Before noon, some gentlemen came on board from the shore to kiss my Lords hands. And by and by Mr North and Dr Clerke went to kiss the Queen of Bohemia's hands from my Lord, with a dozen of attendants from on board to wait on them; among which I sent my boy \u2013 who, like myself, is with child to see any strange thing. Mr Creed and I went in the fore-part of a coach, wherein there was two very pretty ladies, very fashionable and with black paches, who very merrily sang all the way and that very well. And were very free to kiss the two blades that were with them. I took out my flagelette and piped. The Hague is a most neat place in all respects. The houses so neat in all places and things as is possible. Here we walked up and down a great while, the town being now very full of Englishmen. We walked up and down the town and Court to see the place; and by the help of a stranger, an Englishman, we saw a great many places and were made to understand many things, as the intention of the maypoles which we saw there standing at every great man's door, of different greatness according to the quality of the person.\n\n_18 May._ [Delft] is a most sweet town, with bridges and a river in every street. Observing that in every house of entertainment there hangs in every room a poor man's box and desirous to know the reason thereof, it was told me that it is their custom to confirm all bargains by putting something into the poor people's box, and that that binds as fast as anything. We saw likewise the Guesthouse, where it was very pleasant to see what neat preparation there is for the poor. We saw one poor man a-dying there. Back by water, where a pretty sober Duch lass sat reading all the way, and I could not fasten any discourse upon her.\n\n_19 May._ [At Lausdune] I met my old chamberfellow Mr Ch. Anderson and a friend of his (both physicians), Mr Wright, who took me to a Duch house where there was an exceeding pretty lass and right for the sport; but it being Saturday, we could not have much of her company; but however, I stayed with them till 12 at night; by that time Charles was almost drunk; and then broke up, he resolving to go thither again (after he had seen me at my lodging) and lie with the girl, which he told me he had done in the morning. Going to my lodging, we met with the bell-man, who strikes upon a clapper, which I took in my hand and it is just like the clapper that our boys fright the birds away from the corn with in summer time in England. To bed.\n\n_23 May._ The King, with the two Dukes [his brothers, the Dukes of York and Gloucester], the Queen of Bohemia [his aunt, Elizabeth, Dowager Queen], Princesse Royalle, and Prince of Orange [his sister Mary and her son, later William III of England], came on board; where I in their coming in kissed the Kings, Queen and Princesses hands, having done the other before. Infinite shooting off of the guns, and that in a disorder on purpose, which was better than if it had been otherwise. Dined in a great deal of state, the royall company by themselves in the coach, which was a blessed sight to see. We weighed ancre, and with a fresh gale and most happy weather we set sail for England \u2013 all the afternoon the King walking here and there, up and down (quite contrary to what I thought him to have been), very active and stirring. Upon the quarterdeck he fell in discourse of his escape from Worcester. Where it made me ready to weep to hear the stories that he told of his difficulties that he had passed through. As his travelling four days and three nights on foot, every step up to his knees in dirt, with nothing but a green coat and a pair of country breeches on and a pair of country shoes, that made him so sore all over his feet that he could scarce stir.\n\n_25 May._ By the morning we were come close to the land and everybody made ready to get on shore. The King and the two Dukes did eat their breakfast before they went, and there being set some shipps diet before them, only to show them the manner of the shipps diet, they eat of nothing else but pease and pork and boiled beef. I spoke with the Duke of York about business, who called me Pepys by name, and upon my desire did promise me his future favour. I went, and Mr Mansell and one of the King's footmen, with a dog that the King loved (which shit in the boat, which made us laugh and me think that a King and all that belong to him are but just as others are) went in a boat by ourselfs; and so got on shore when the King did, who was received by Generall Monke with all imaginable love and respect at his entrance upon the land at Dover. Infinite the croud of people and the gallantry of the horsmen, citizens, and noblemen of all sorts. The Mayor of the town came and gave him his white staffe, the badge of his place, which the King did give him again. The Mayor also presented him from the town a very rich Bible, which he took and said it was the thing that he loved above all things in the world.\n\n_The Stuarts might have been allowed back on the throne, but the political clock had not been turned back to the days before Charles I's misuse of power. Parliament considered few, if any, matters outside its purview, especially religion. Charles II wanted toleration for Catholics (and was opportunistically willing to allow it to dissenting Protestants in a_ quid pro quo), _and in response Parliament passed the Clarendon Code, which set up an Anglican monopoly. When the king tried again with the Declaration of Indulgence, Parliament responded with the Test Act, which barred Catholics from public office. Parliament's suspicion of Catholicism was well-founded: it was the religion of the absolutist powers which surrounded England._\n\n_Charles II's reign began with euphoria and descended into gloominess, as a series of disasters beset the nation._\n\n## _Journal of the Plague Year, 1665_\n\nJOHN EVELYN\n\n_The Great Plague, which began in London in late 1664, was the last major outbreak of bubonic pestilence in England. Over 68,000 Londoners died._\n\n_Diary 1665_ , _July 7_. To London, to Sir William Coventrie; and so to Sion, where his Majesty sat at Council during the contagion; when business was over, I viewed that seat belonging to the Earl of Northumberland, built out of an old Nunnery, of stone, and fair enough, but more celebrated for the garden than it deserves; yet there is excellent wall-fruit, and a pretty fountain; nothing else extraordinary.\n\n_16_. There died of the plague in London this week 1,100, and in the week following above 2,000. Two houses were shut up in our parish.\n\n_Aug. 2_. A solemn fast through England to deprecate God's displeasure against the land by pestilence and war; our Dr preaching on 26 Levit: 41, 42. That the means to obtain remission of punishment was not to repine at it, but humbly submit to it.\n\n_8_. I waited on the D. of Albemarle, who was resolved to stay at the Cock-pit in St James's Park. Died this week in London 4,000.\n\n_15_. There perished this week 5,000.\n\n_28_. The contagion still increasing and growing now all about us, I sent my wife and whole family (two or three necessary servants excepted) to my brother's at Wotton, being resolved to stay at my house myself and to look after my charge, trusting in the providence and goodness of God.\n\n_Sept. 5_. To Chatham to inspect my charge, with \u00a3900 in my coach.\n\n_7_. Came home, there perishing near 10,000 poor creatures weekly; however I went all along the City and suburbs from Kent Street to St James's, a dismal passage, and dangerous to see so many coffins exposed in the streets, now thin of people; the shops shut up, and all in mournful silence, as not knowing whose turn might be next. I went to the Duke of Albemarle for a pest-ship, to wait on our infected men, who were not a few.\n\n_October 1_. This afternoon, whilst at evening prayers, tidings were brought me of the birth of a daughter at Wotton, after six sons, in the same chamber I had first took breath in, and at the first day of that month, as I was on the last, 45 years before.\n\n_4_. The monthly fast.\n\n_11_. To London, and went through the whole City, having occasion to alight out of the coach in several places about business of money, when I was environed with multitudes of poor pestiferous creatures begging alms; the shops universally shut up, a dreadful prospect! I dined with my Lord General; was to receive \u00a310,000 and had guards to convey both myself and it, and so returned home, through God's infinite mercy.\n\n_31_. I was this day 45 years of age, wonderfully preserved, for which I blessed God for his infinite goodness towards me.\n\n_November 23._ Went home, the contagion having now decreased considerably.\n\n## _The Great Fire of London, 2 September 1666_\n\nSAMUEL PEPYS\n\n_2 September. Lords Day._ Some of our maids sitting up late last night to get things ready against our feast today, Jane called us up, about 3 in the morning, to tell us of a great fire they saw in the City. So I rose, and slipped on my nightgown and went to her window, and thought it to be on the back side of Markelane at the furthest; but being unused to such fires as fallowed, I thought it far enough off, and so went to bed again and to sleep. About 7 rose again to dress myself, and there looked out at the window and saw the fire not so much as it was, and further off. So to my closet to set things to rights after yesterday's cleaning. By and by Jane comes and tells me that she hears that above 300 houses have been burned down tonight by the fire we saw, and that it was now burning down all Fishstreet by London Bridge. So I made myself ready presently, and walked to the Tower and there got up upon one of the high places, Sir J. Robinsons little son going up with me; and there I did see the houses at that end of the bridge all on fire, and an infinite great fire on this and the other side the end of the bridge \u2013 which, among other people, did trouble me for poor little Michell and our Sarah on the Bridge. So down, with my heart full of trouble, to the Lieutenant of the Tower, who tells me that it begun this morning in the King's bakers house in Pudding Lane, and that it hath burned down St Magnes Church and most part of Fishstreete already. So I down to the waterside and there got a boat and through bridge, and there saw a lamentable fire. Poor Michells house, as far as the Old Swan, already burned that way and the fire running further, that in a very little time it got as far as the Stillyard while I was there. Everybody endeavouring to remove their goods, and flinging into the river or bringing them into lighters that lay off. Poor people staying in their houses as long as till the very fire touched them, and then running into boats or clambering from one pair of stair by the waterside to another. And among other things, the poor pigeons I perceive were loath to leave their houses, but hovered about the windows and balconies till they were some of them burned, their wings, and fell down.\n\nHaving stayed, and in an hour's time seen the fire rage every way, and nobody to my sight endeavouring to quench it, but to remove their goods and leave all to the fire; and having seen it get as far as the Steeleyard, and the wind mighty high and driving it into the city, and everything, after so long a drought, proving combustible, even the very stones of churches. I to Whitehall with a gentleman with me who desired to go off from the Tower to see the fire in my boat \u2013 to Whitehall, and there up to the King's closet in the chapel, where people came about me and I did give them an account dismayed them all; and word was carried in to the King, so I was called for and did tell the King and Duke of York what I saw, and that unless his Majesty did command houses to be pulled down, nothing could stop the fire. They seemed much troubled, and the King commanded me to go to my Lord Mayor from him and command him to spare no houses but to pull down before the fire every way. The Duke of York bid me tell him that if he would have any more soldiers, he shall. Here meeting with Captain Cocke, I in his coach, which he lent me, and Creed with me, to Pauls; and there walked along Watling Street as well as I could, every creature coming away loaden with goods to save \u2013 and here and there sick people carried away in beds. Extraordinary good goods carried in carts and on backs. At last met my Lord Mayor in Canning Streete, like a man spent, with a hankercher about his neck. To the King's message, he cried like a fainting woman, 'Lord, what can I do? I am spent! People will not obey me. I have been pull[ing] down houses. But the fire overtakes us faster than we can do it.' That he needed no more soldiers; and that for himself, he must go and refresh himself, having been up all night. So he left me, and I him, and walked home \u2013 seeing people all almost distracted and no manner of means used to quench the fire. The houses too, so very thick thereabouts, and full of matter for burning, as pitch and tar, in Thames Street \u2013 and warehouses of oyle and wines and brandy and other things. Here I saw Mr Isaccke Houblon, that handsome man \u2013 prettily dressed and dirty at his door at Dowgate, receiving some of his brothers things whose houses were on fire; and as he says, have been removed twice already, and he doubts (as it soon proved) that they must be in a little time removed from his house also \u2013 which was a sad consideration. And to see the churches all filling with goods, by people who themselfs should have been quietly there at this time.\n\nAs soon as dined, I and Moone away and walked through the City, the streets full of nothing but people and horses and carts loaden with goods, ready to run over one another, and removing goods from one burned house to another \u2013 they now removing out of Canning Street (which received goods in the morning) into Lumbard Streete and further. We parted at Pauls, he home and I to Pauls Wharf, where I had appointed a boat to attend me; and took in Mr Carcasse and his brother, whom I met in the street, and carried them below and above bridge, to and again, to see the fire, which was now got further, both below and above, and no likelihood of stopping it. Met with the King and Duke of York in their barge, and with them to Queen Hith and there called Sir Rd. Browne to them. Their order was only to pull down houses apace, and so below bridge at the waterside; but little was or could be done, the fire coming upon them so fast. Good hopes there was of stopping it at the Three Cranes above, and at Buttolphs Wharf below bridge, if care be used; but the wind carries it into the City, so as we know not by the waterside what it doth there. River full of lighter[s] and boats taking in goods, and good goods swimming in the water; and only, I observed that hardly one lighter or boat in three that had the goods of a house in, but there was a pair of virginalls in it. Having seen as much as I could now, I away to Whitehall by appointment, and there walked to St James's Park, and there met my wife and Creed and Wood and his wife and walked to my boat, and there upon the water again, and to the fire up and down, it still increasing and the wind great. So near the fire as we could for smoke; and all over the Thames, with one's face in the wind you were almost burned with a shower of firedrops \u2013 this is very true \u2013 so as houses were burned by these drops and flakes of fire, three or four, nay five or six houses, one from another. When we could endure no more upon the water, we to a little alehouse on the Bankside over against the Three Cranes, and there stayed till it was dark almost and saw the fire grow; and as it grow darker, appeared more and more, and in corners and upon steeples and between churches and houses, as far as we could see up the hill of the City, in a most horrid malicious bloody flame, not like the fine flame of an ordinary fire. We stayed till, it being darkish, we saw the fire as only one entire arch of fire from this to the other side the bridge, and in a bow up the hill, for an arch of above a mile long. It made me weep to see it. The churches, houses, and all on fire and flaming at once, and a horrid noise the flames made, and the cracking of houses at their ruine.\n\n_Some 13,000 buildings were destroyed by the Fire, and 100,000 people made homeless. The cost of rebuilding was over \u00a310 million._\n\n## _Isaac Newton Experiments on Light, Cambridge, 1666_\n\nSIR ISAAC NEWTON\n\n_Principally remembered for his discoveries in mathematics and gravity, Newton (1642\u20131727) was also a pioneering researcher in 'Opticks'. His experiments at Cambridge refracting sunlight through a prism eventually led to the construction of reflecting telescopes._\n\nI procured me a Triangular glass-Prisme, to try therewith the celebrated _Phaenomena of Colours._ And in order thereto having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Suns light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby; but after a while applying myself to consider them more circumspectly, I became surprised to see them in an _oblong_ form; which, according to the received laws of Refraction, I expected should have been _circular._\n\nAnd I saw that the light, tending to [one] end of the Image, did suffer a Refraction considerably greater than the light tending to the other. And so the true cause of the length of that Image was detected to be no other, then that _Light_ consists of _Rays differently refrangible,_ which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall.\n\nThen I placed another Prisme... so that the light... might pass through that also, and be again refracted before it arrived at the wall. This done, I took the first Prisme in my hand and turned it to and fro slowly about its _Axis,_ so much as to make the several parts of the Image... successively pass through... that I might observe to what places on the wall the second Prisme would refract them.\n\nWhen any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it.\n\nI have refracted it with Prismes, and reflected with it Bodies which in Day-light were of other colours; I have intercepted it with the coloured film of Air interceding two compressed plates of glass; transmitted it through coloured Mediums, and through mediums irradiated with other sorts of Rays, and diversely terminated it; and yet could never produce any new colour out of it.\n\nBut the most surprising, and wonderful composition was that of _Whiteness._ There is no one sort of Rays which alone can exhibit this. 'Tis ever compounded, and to its composition are requisite all the aforesaid primary Colours, mixed in a due proportion. I have often with Admiration beheld, that all the Colours of the Prisme being made to converge, and thereby to be again mixed, reproduced light, intirely and perfectly white.\n\nHence therefore it comes to pass, that _Whiteness_ is the usual colour of _Light;_ for, Light is a confused aggregate of Rays indued with all sorts of Colours, as they are promiscuously darted from the various parts of luminous bodies.\n\n## _The Great Frost Fair, 24 January 1684_\n\nJOHN EVELYN\n\n_Before the embankment was built in the nineteenth century, the Thames froze over in severe winters. In 1676 and 1684 ice fairs were held on the river in London._\n\nThe frost continuing more and more severe, the Thames before London was still planted with boothes in formal streetes, all sortes of trades and shops furnish'd and full of commodities, even to a printing presse, where the people and ladyes tooke a fancy to have their names printed, and the day and yeare set down when printed on the Thames: this humour tooke so universally, that 'twas estimated the printer gain'd \u00a35 a day, for printing a line onely, at sixpence a name, besides what he got by ballads, &c. Coaches plied from Westminster to the Temple, and from several other staires to and fro, as in the streetes, sleds, sliding with skeetes, a bull-baiting, horse and coach races, puppet plays and interludes, cookes, tipling, and other lewd places, so that it seem'd to be a bacchanalian triumph or carnival on the water, whilst it was a severe judgement on the land, the trees not onely splitting as if lightning-struck, but men and cattle perishing in divers places, and the very seas so lock'd up with ice, that no vessels could stir out or come in. The fowles, fish, and birds, and all our exotiq plants and greenes universally perishing. Many parkes of deer were destroied, and all sorts of fuell so deare that there were great contributions to preserve the poore alive. Nor was this severe weather much less intense in most parts of Europe, even as far as Spaine and the most southern tracts. London, by reason of the excessive coldnesse of the aire hindering the ascent of the smoke, was so filled with the fuliginous steame of the sea-coale, that hardly could one see crosse the streets, and this filling the lungs with its grosse particles, exceedingly obstructed the breast, so as one could hardly breath. Here was no water to be had from the pipes and engines, nor could the brewers and divers other tradesmen worke, and every moment was full of disastrous accidents.\n\n## _The Glorious Revolution: William of Orange Enters, James II Exits, November\u2013December 1688_\n\nJOHN EVELYN\n\n_Charles II died in 1685_ , _after confirming his subjects' fears by professing the Catholic faith on his deathbed. He was succeeded by his brother, James II. Quite apart from his not very secret Catholicism, James II had all the old inclinations to absolutism. The English, he said, should 'follow his wishes blindly'._\n\n_Instead, the English set about finding a replacement for King James, one who could guarantee a Protestant succession and their liberties. On 30 June 1688 an invitation to become King of England was sent to the Dutchman William of Orange, the husband of James II's daughter Mary, and a definite, dyed-in the-wool Protestant. William's fleet set sail for England on 19 October._\n\n_November 5th._ I went to London; heard the news of the prince [William of Orange] having landed at Torbay, coming with a fleet of near 700 sail, passing through the Channel with so favourable a wind, that our navy could not intercept, or molest them. This put the King and Court into great consternation, they were now employed in forming an army to stop their further progress, for they were got into Exeter, and the season and ways very improper for his Majesty's forces to march so great a distance.\n\nThe Archbishop of Canterbury and some few of the other Bishops and Lords in London, were sent for to Whitehall, and required to set forth their abhorrence of this invasion. They assured his Majesty they had never invited any of the Prince's party, or were in the least privy to it, and would be ready to show all testimony of their loyalty; but, as to a public declaration, being so few, they desired that his Majesty would call the rest of their brethren and Peers, that they might consult what was fit to be done on this occasion, not thinking it right to publish any thing without them, and till they had themselves seen the Prince's Manifesto, in which it was pretended he was invited in by the Lords Spiritual and Temporal. This did not please the King; so they departed.\n\nA Declaration was published, prohibiting all persons to see or read the Prince's Manifesto, in which was set forth at large the cause of his expedition, as there had been one before from the States.\n\nThese are the beginnings of sorrow, unless God in His mercy prevent it by some happy reconciliation of all dissensions among us. This, in all likelihood, nothing can effect except a free Parliament; but this we cannot hope to see, whilst there are any forces on either side. I pray God to protect and direct the King for the best and truest interest of his people \u2013 I saw his Majesty touch for the evil, Piten the Jesuit, and Warner officiating.\n\n_14th_. The Prince increases every day in force. Several Lords go in to him. Lord Cornbury carries some regiments, and marches to Honiton, the Prince's headquarters. The City of London in disorder; the rabble pulled down the nunnery newly bought by the Papists of Lord Berkeley, at St John's. The Queen prepares to go to Portsmouth for safety, to attend the issue of this commotion, which has a dreadful aspect.\n\n_18th_. It was now a very hard frost. The King goes to Salisbury to rendezvous the army, and return to London. Lord Delamere appears for the Prince in Cheshire. The nobility meet in Yorkshire. The Archbishop of Canterbury and some Bishops, and such Peers as were in London, address his Majesty to call a Parliament. The King invites all foreign nations to come over. The French take all the Palatinate, and alarm the Germans more than ever.\n\n_29th_. I went to the Royal Society. We adjourned the election of a President to 23rd April, by reason of the public commotions, yet dined together as of custom this day.\n\n_2nd December._ Dr Tenison preached at St Martin's on Psalm xxxvi. 5, 6, 7, concerning Providence. I received the blessed Sacrament. Afterwards, visited my Lord Godolphin, then going with the Marquis of Halifax and Earl of Nottingham as Commissioners to the Prince of Orange; he told me they had little power. Plymouth declared for the Prince. Bath, York, Hull, Bristol, and all the eminent nobility and persons of quality through England, declare for the Protestant religion and laws, and go to meet the Prince, who every day sets forth new Declarations against the Papists. The great favourites at Court, Priests and Jesuits, fly or abscond. Every thing, till now concealed, flies abroad in public print, and is cried about the streets. Expectation of the Prince coming to Oxford. The Prince of Wales and great treasure sent privily to Portsmouth, the Earl of Dover being Governor. Address from the Fleet not grateful to his Majesty. The Papists in offices lay down their commissions, and fly. Universal consternation amongst them; it looks like a revolution.\n\n_7th_. My son went towards Oxford. I returned home.\n\n_9th_. Lord Sunderland meditates flight. The rabble demolished all Popish chapels, and several Papist lords' and gentlemen's houses, especially that of the Spanish Ambassador, which they pillaged, and burnt his library.\n\n_13th._ The King flies to sea, puts in at Feversham for ballast; is rudely treated by the people; comes back to Whitehall.\n\nThe Prince of Orange is advanced to Windsor, is invited by the King to St James's, the messenger sent was the Earl of Feversham, the General of the Forces, who going without trumpet, or passport, is detained prisoner by the Prince, who accepts the invitation, but requires his Majesty to retire to some distant place, that his own guards may be quartered about the Palace and City. This is taken heinously, and the King goes privately to Rochester; is persuaded to come back; comes on the Sunday; goes to mass, and dines in public, a Jesuit saying grace (I was present).\n\n_17th_. That night was a Council; his Majesty refuses to assent to all the proposals; goes away again to Rochester.\n\n_18th_. I saw the King take barge to Gravesend at twelve o'clock \u2013 a sad sight! The Prince comes to St James's, and fills Whitehall with Dutch guards. A Council of Peers meet about an expedient to call a Parliament; adjourn to the House of Lords. The Chancellor, Earl of Peterborough, and divers others taken. The Earl of Sunderland flies; Sir Edward Hales, Walker, and others, taken and secured.\n\nAll the world go to see the Prince at St James's, where there is a great Court. There I saw him, and several of my acquaintance who came over with him. He is very stately, serious, and reserved. The English soldiers sent out of town to disband them; not well pleased.\n\n_24th_. The King passes into France, whither the Queen and child were gone a few days before.\n\n_26th_. The Peers and such Commoners as were members of the Parliament at Oxford, being the last of Charles II, meeting, desire the Prince of Orange to take on him the disposal of the public revenue till a convention of Lords and Commons should meet in full body, appointed by his circular letters to the shires and boroughs, 22nd January. I had now quartered upon me a Lieutenant-Colonel and eight horses.\n\n_30th_. This day prayers for the Prince of Wales were first left off in our church.\n\n_The Revolution of 1688 was 'Glorious' because it melded together anti-Catholic Whigs and Stuart-friendly Tories in a settlement that avoided bloodshed. (If that is, one exempts fames' slaughterous defeat two years later by William of Orange at the Battle of the Boyne, Ireland.) By the terms of the Glorious Settlement England got a Protestant monarch \u2013 two, in fact, since William III and Mary II ruled jointly \u2013 who agreed to a 'Declaration of Rights' which curtailed the royal prerogative and established a parliamentary monarchy. In an age of absolutism, this was no small achievement. Furthermore, it was the beginning of party politics, for no monarch could rule without majority support in Parliament._\n\n_William and Mary's reign brought stability, the foundation of the Bank of England, control of a standing army vested in Parliament and a widening in the freedom of the press._\n\n_But no viable heir. Of course, it probably did not help that William was syphilitic and bisexual, and Mary sapphically inclined. 'If you do not come some time today, dear husband [sic], ' Mary wrote to her friend Lady Frances Apsley, 'that I may have my belly full of discourse with you, I shall take it very ill...'_\n\n_Thus in 1702 the throne passed to Mary's sister, Anne._\n\n## _Blenheim: The Victor's View, Bavaria, 13 August 1704_\n\nJOHN CHURCHILL, DUKE OF MARLBOROUGH\n\n_The Stuarts saved the best till last. Queen Anne (reigned 1702\u201314), memorably described as 'one of the smallest people ever set in a great place', was devoutly Protestant, self-consciously English, and had supported the Glorious Revolution against her father. In Queen Anne's name were won England's greatest victories on land since Cr\u00e9cy and Agincourt._\n\n_In 1701 England joined the War of the Spanish Succession, whereby Protestant Europe combined to prevent the union of France and Spain. John Churchill, Duke of Marlborough, was Captain General of the English army. At Blenheim on the river Danube, 50,000 English and Austrian troops encountered 60,000 Franco-Bavarian troops._\n\nSir: I gave you an account on Sunday last of the situation we were then in, and that we expected to hear the enemy would pass the Danube at Lawringen, in order to attack Prince Eugene at eleven of the clock that night. We had an express from him, that the enemy were come, and desiring he might be reinforced as soon as possible. Whereupon I ordered my Brother Churchill to advance at one of the clock in the morning with his two battalions, and by three the whole Army was in motion; for the greater expedition, I ordered part of the troops to pass over the Danube, and follow the march of the twenty battalions; and with most of the Horse and the Foot of the First Line, I passed the Lech at Rain, and came over the Danube at Donawert. So that we all joined the prince that night, intending to advance and take this Camp at Hochstet: in order whereto we went out early on Tuesday with forty squadrons to view the ground, but found the enemy had already possessed themselves of it.\n\nWhereupon we resolved to attack them, and accordingly we marched between three and four yesterday morning from the Camp at Munster, leaving all our tents standing. About six we came in view of the enemy, who, we found, did not expect so early an onset. The cannon began to play about half an hour after eight. They formed themselves in two bodies, the Elector with Monsieur Marsin and their troops on our right, and Monsieur de Tallard with all his on our left; which last fell to my share; they had two rivulets, besides a morass before them which we were obliged to pass over in their view, and Prince Eugene was forced to take a great compass to come to the enemy, so that it was one of the clock before the battle began. It lasted with great vigour till sunset, when the enemy were obliged to retire, and by the blessing of God we obtained a complete victory.\n\nWe have cut off great numbers of them, as well in the action as in the retreat, besides upwards of twenty squadrons of the French, which I pushed into the Danube, where we saw the greater part of them perish. Monsieur Tallard, with several of his general officers being taken prisoners at the same time, and in the village of Blenheim, which the enemy had entrenched and fortified, and where they made the greatest opposition, I obliged twenty-six entire battalions, and twelve squadrons of dragoons, to surrender themselves prisoners at discretion. We took likewise all their tents standing, with their cannon and ammunition, as also a great number of standards, kettle-drums, and colours in the action, so that I reckon the greatest part of Monsieur Tallard's army is taken or destroyed.\n\nThe bravery of all our troops on this occasion cannot be expressed, the Generals, as well as the officers and soldiers, behaving themselves with the greatest courage and resolution. The horse and dragoons were obliged to charge four or five several times. The Elector and Monsieur de Marsin were so advantageously posted, that Prince Eugene could make no impression on them, till the third attack, near seven at night, when he made a great slaughter of them. But being near a woodside, a great body of Bavarians retired into it, and the rest of that army retreated towards Lawringen, it being too late, and the troops too much tired to pursue them far.\n\nI cannot say too much in praise of that Prince's good conduct, and the bravery of his troops on this occasion. You will please to lay this before her Majesty and his Royal Highness, to whom I send my Lord Tunbridge with the good news. I pray you likewise inform yourself, and let me know her Majesty's pleasure, as well relating to Monsieur Tallard and the other general officers, as for the disposal of near one thousand two hundred other officers, and between eight and nine thousand common soldiers, who being all made prisoners by her Majesty's troops, are entirely at her disposal: but as the charge of subsisting these officers and men must be very great, I presume her Majesty will be inclined that they be exchanged for any other prisoners that offer.\n\nI should likewise be glad to receive her Majesty's directions for the disposal of the standards and colours, whereof I have not yet the number, but guess there cannot be less than one hundred, which is more than has been taken in any battle these many years.\n\nYou will easily believe that, in so long and vigorous an action, the English, who had so great a share in it, must have suffered as well in officers as men; but I have not the particulars.\n\nI am, Sir,\n\nYour most obedient,\n\nhumble servant,\n\nMarlborough.\n\nFrom the camp at Hochstet\n\n_A rapturously grateful nation built Blenheim Palace in Oxfordshire for Marlborough, who went on to back-to-back victories at Ramillies, Oudenarde and Malplaquet._\n\n_The momentous events of Queen Anne's England were not restricted to Marlborough's battles. Following the death of her only surviving son (she bore and lost seventeen children), she signed the Act of Settlement which designated the Hanoverians her successors. When the Scots objected, Scotland was brought into union with England (or, rather, under England; the Scottish Parliament was closed down) in 1707. Thus was Great Britain formed._\n\n## _Bath under the Code of Beau Nash, c. 1710_\n\nOLIVER GOLDSMITH\n\n_The dandy Richard 'Beau' Nash introduced the code of exquisitely polite manners and fashion that ruled English upper-class society throughout the eighteenth century. He also established Bath as the leading English spa town. Yet the benefits of Bath were not confined to the aristocracy; they were widely enjoyed by a large middle class whose habit of conspicuous consumption would become a defining characteristic of English society._\n\n_The novelist Goldsmith was Nash's biographer._\n\nUpon a stranger's arrival at Bath he is welcomed by a peal of the Abbey Bells, and, in the next place, by the voice and music of the city waits. For these civilities, the ringers have generally a present made them of half-a-guinea, and the waits of half-a-crown, or more, in proportion to the person's fortune, generosity, or ostentation. These customs, though disagreeable, are however, liked or they would not continue. The greatest incommodity attending them is the disturbance the bells must give the sick. But the pleasure of knowing the name of every family that comes to town recompenses the inconvenience. Invalids are fond of news, and upon the first sound of the bells everybody sends out to inquire for whom they ring.\n\nAfter the family is thus welcomed to Bath, it is the custom for the master of it to go to the public places, and subscribe two guineas at the assembly-houses towards the balls and music in pump-house, for which he is entitled to three tickets every ball night. His next subscription is a crown, half-a-guinea, or a guinea, according to his rank and quality, for the liberty of walking in the private walks belonging to Simpson's assembly-house; a crown or half-a-guinea is also given to the booksellers, for which the gentleman is to have what books he pleases to read at his lodgings, and at the coffee-house another subscription is taken for pen, ink, and paper, for such letters as the subscriber shall write at it during his stay. The ladies, too, may subscribe to the booksellers, and to a house by the pump-room, for the advantage of reading the news, and for enjoying each other's conversation.\n\nThings being thus adjusted, the amusements of the day are generally begun by bathing, which is no unpleasing method of passing away an hour or so.\n\nThe baths are five in number. On the south-west side of the Abbey Church is the King's Bath, which is an oblong square; the walls are full of niches, and at every corner are steps to descend into it: this bath is said to contain 427 tons and 50 gallons of water; and on its rising out of the ground over the springs, it is sometimes too hot to be endured by those who bathe therein. Adjoining to the King's Bath, there is another, called the Queen's Bath; this is of a more temperate warmth, as borrowing its water from the other.\n\nIn the south-west part of the city are three other baths, viz: the Hot Baths, which is not much inferior in heat to the King's Bath, and contains 53 tons, 2 hogsheads, and 11 gallons of water; the Cross Bath, which contains 52 tons, 3 hogsheads, and 11 gallons; and the Leper's Bath, which is not so much frequented as the rest.\n\nThe King's Bath (according to the best observations) will fill in about nine hours and a half; the Hot Bath in about eleven hours and a half; and the Cross Bath in about the same time.\n\nThe hours for bathing are commonly between six and nine in the morning, and the baths are every morning supplied with fresh water; for when the people have done bathing, the sluices in each bath are pulled up, and the water is carried off by drains into the River Avon.\n\nIn the morning the lady is brought in a close chair, dressed in her bathing clothes, to the bath; and, being in the water, the woman who attends presents her with a little floating dish like a basin; into which the lady puts a handkerchief, a snuff-box, and a nosegay. She then traverses the bath; if a novice, with a guide; if otherwise, by herself; and having amused herself thus while she thinks proper, calls for her chair; and returns to her lodgings.\n\nThe amusement of bathing is immediately succeeded by a general assembly of people at the pump-room; some for pleasure, and some to drink the hot waters. Three glasses at three different times is the usual portion for every drinker; and the intervals between every glass are enlivened by the harmony of a small band of music, as well as by the conversation of the gay, the witty, or the forward.\n\nFrom the pump-room the ladies, from time to time, withdraw to a female coffee-house, and from thence return to their lodgings to breakfast. The gentlemen withdraw to their coffee-houses, to read the papers, or converse on the news of the day, with a freedom and ease not to be found in the metropolis.\n\nPeople of fashion make public breakfasts at the assembly-houses, to which they invite their acquaintances, and they sometimes order private concerts; or, when so disposed, attend lectures on the arts and sciences, which are frequently taught there in a pretty superficial manner, so as not to tease the understanding, while they afford the imagination some amusement. The private concerts are performed in the ball-rooms; the tickets a crown each.\n\nConcert breakfasts at the assembly-houses sometimes make also a part of the morning's amusement here, the expenses of which are defrayed by a subscription among the men. Persons of rank and fortune who can perform are admitted into the orchestra, and find a pleasure in joining with the performers.\n\nThus we have the tedious morning fairly over. When noon approaches, and church (if any please to go there) is done, some of the company appear upon the parade, and other public walks, where they continue to chat and amuse each other, till they have formed parties for the play, cards, or dancing for the evening. Another part of the company divert themselves with reading in the booksellers' shops, or are generally seen taking the air and exercise, some on horseback, some in coaches. Some walk in the meadows round the town, winding along the side of the River Avon and the neighbouring canal; while others are seen scaling some of those romantic precipices that overhang the city.\n\nWhen the hour of dinner draws nigh, and the company are returned from their different recreations, the provisions are generally served with the utmost elegance and plenty. Their mutton, butter, fish, and fowl, are all allowed to be excellent, and their cookery still exceeds their meat.\n\nAfter dinner is over, and evening prayers ended, the company meet a second time at the pump-house. From this they retire to the walks, and from thence go to drink tea at the assembly-houses, and the rest of the evenings are concluded either with balls, plays, or visits. A theatre was erected in the year 1705, by subscription, by people of the highest rank, who permitted their arms to be engraven on the inside of the house, as a public testimony of their liberality towards it. Every Tuesday and Friday evening is concluded with a public ball, the contributions to which are so numerous, that the price of each ticket is trifling. Thus Bath yields a continued rotation of diversions, and people of all ways of thinking, even from the libertine to the methodist, have it in their power to complete the day with employments suited to their inclinations.\n\n## _Cock-fighting, London, 18 June 1710_\n\nZACHARIAS VON UFFENBACH\n\n_Von Uffenbach was a German visitor and book-collector._\n\nIn the afternoon we went to see the cockfighting. This is a sport peculiar to the English, which appears to foreigners very foolish in spite of the pleasure this people takes in it. A special building has been made for it near 'Gras Inn'. When a fight is going to take place, printed bills are distributed and sometimes invitations to fanciers appear in the news-sheets as well as notices of the amount of the wagers and the number and species of cocks that are to fight. The building is round like a tower, and inside it resembles a 'theatrum anatomicum', for all round it there are benches in tiers, on which the spectators sit. In the middle is a round table, which is covered with mats, on which the cocks have to fight. When it is time to start, the persons appointed to do so bring in the cocks hidden in two sacks, and then everyone begins to shout and wager before the birds are on view. The people, gentle and simple (they sit with no distinction of place) act like madmen, and go on raising the odds to twenty guineas and more. As soon as one of the bidders calls 'done' (it is done or let it be thus), the other is pledged to keep to his bargain. Then the cocks are taken out of the sacks and fitted with silver spurs, such as we bought. As soon as the cocks appear, the shouting grows even louder and the betting is continued. When they are released, some attack, while others run away from, the rest, and, as we ourselves saw, are impelled by terror to jump down from the table among the people; they are then, however, driven back on the table with great yells (in particular by those who have put their money on the lively cocks which chase the others) and are thrust at each other until they get angry. Then it is amazing to see how they peck at each other, and especially how they hack with their spurs. Their combs bleed terribly and they often slit each other's crop and abdomen with the spurs. There is nothing more diverting than when one seems quite exhausted and there are great shouts of triumph and monstrous wagers; and then the cock that appeared to be quite done for suddenly recovers and masters the other. When one of the two is dead, the conqueror invariably begins to crow and to jump on the other, and it often happens that they sing their paean before the victory and the other wins after all. Sometimes, when both are exhausted and neither will attack the other again, they are removed and others take their place; in this case the wagers are cancelled. But if one of them wins, those who put their money on the losing cock have to pay immediately, so that an hostler in his apron often wins several guineas from a Lord. If a man has made a bet and is unable to pay, for a punishment he is made to sit in a basket fastened to the ceiling, and is drawn up in it amidst peals of laughter. The people become as heated about their betting as the cocks themselves. And I must confess that it is certainly more diverting if one bets oneself, though my brother and I have never wagered anything more than shillings. We watched seven couple fight in turn.\n\n## _Bad King George I, 1714\u20131727_\n\nJOHN H. JESSE\n\n_Jesse's description of the first Hanoverian King of England, from the author's_ Memoirs of the Court of England, _hardly exaggerates._\n\nA foreigner as he was, in all his tastes and habits; ignorant, debauched, and illiterate; inelegant in his person and ungraceful in his manners, he had never condescended to acquaint himself with the laws or customs of the English, and was, indeed, utterly unacquainted with their language. In addition to these drawbacks, though he was now in his fifty-fifth year, he had the folly and wickedness to encumber himself with a seraglio of hideous German prostitutes, who rendered him equally ludicrous by their absurdities, and unpopular by their rapacity... It may be remarked... that, with the single exceptions of social pleasantry and constitutional good-humour, he seems to have been possessed of no redeeming quality which reflected dignity on him as a monarch, or rendered him amiable as a man. Profligate in his youth and libidinous in old age, he figures through life as a bad husband, a bad father, and, in as far as England is concerned, a bad king. He wanted even those graceful qualifications of the Stuarts, a love for polite literature and the fine arts; he possessed no taste for the one, and extended no patronage to the other. The only thing he seems to have had a regard for was his own ease; the only being he hated heartily was, probably, his own son. Many of these unamiable characteristics were unquestionably owing to his indifferent education; for, notwithstanding his wrong-headiness, he is said to have meant well.\n\n_Although George I (born 1660) never won the hearts of his subjects, the dismissive ease with which the 1715 and 1719 risings of the Jacobites (supporters of the line of the deposed James II) were suppressed clearly showed the English preference for the Lutheran Hanoverian monarchy._\n\n## _Public Executions at Tyburn, c. 1725_\n\nC. DE SAUSSURE\n\n_C\u00e9sar de Saussure was a Swiss tourist._\n\nSome time after my arrival in London I witnessed a spectacle which certainly was not as magnificent or as brilliant as the Lord Mayor's Show; it is true it was quite a different kind of entertainment. I saw thirteen criminals all hanged at the same time. It will interest you, no doubt, to know something about justice in England, how it is practised, how criminals are punished, in what manner they are executed, as here it is done in quite a different way to what it is in other countries.\n\nThe day before the execution those who desire it may receive the sacrament, provided the chaplain thinks that they have sincerely repented and are worthy of it. On the day of execution the condemned prisoners, wearing a sort of white linen shirt over their clothes and a cap on their heads, are tied two together and placed on carts with their backs to the horses' tails. These carts are guarded and surrounded by constables and other police officers on horseback, each armed with a sort of pike. In this way part of the town is crossed, and Tyburn, which is a good half-mile from the last suburb, is reached, and here stands the gibbet. One often sees criminals going to their death perfectly unconcerned, others so impenitent that they fill themselves full of liquor and mock at those who are repentant. When all the prisoners arrive at their destination they are made to mount on a very wide cart made expressly for the purpose, a cord is passed round their necks and the end fastened to the gibbet, which is not very high. The chaplain who accompanies the condemned men is also on the cart; he makes them pray and sing a few verses of the Psalms. The relatives are permitted to mount the cart and take fare-well. When the time is up \u2013 that is to say about a quarter of an hour \u2013 the chaplain and the relations get off the cart, which slips from under the condemned men's feet, and in this way they remain all hanging together. You often see friends and relations tugging at the hanging men's feet so that they should die quicker and not suffer. The bodies and clothes of the dead belong to the executioner; relatives must, if they wish for them, buy them from him, and unclaimed bodies are sold to surgeons to be dissected. You see most amusing scenes between the people who do not like the bodies to be cut up and the messengers the surgeons have sent for the bodies; blows are given and returned before they can be got away, and sometimes in the turmoil the bodies are quickly removed and buried. Again, the populace often come to blows as to who will carry the bought corpses to the parents who are waiting in coaches and cabs to receive them, for the carriers are well paid for their trouble. All these scenes are most diverting, the noise and confusion is unbelievable, and can be witnessed from a sort of amphitheatre erected for spectators near the gibbet.\n\n## _John Wesley Preaches, 19 March 1742_\n\nJOHN WESLEY\n\n_Wesley was the founder of Methodism, an evangelical offshoot of the Anglican Church. Following his conversion in 1738, he spent fifty-one years open-air preaching, in the process walking upwards of 250,000 miles and delivering 40,000 sermons. Wesley died in 1791_ , _aged eighty-eight._\n\nI rode once more to Pensford, at the earnest request of several serious people. The place where they desired me to preach was a little green spot near the town. But I had no sooner begun, than a great company of rabble, hired (as we afterwards found) for that purpose, came furiously upon us, bringing a bull which they had been baiting and now drove in among the people. But the beast was wiser than his drivers, and continually ran either on one side of us or the other, while we quietly sang praise to God and prayer for about an hour. The poor wretches finding themselves disappointed, at length seized upon the bull, now weak and tired after being so long torn and beaten both by dogs and men, and by main strength partly dragged and partly thrust him in among the people. When they had forced their way to the little table on which I stood, they strove several times to throw it down by thrusting the helpless beast against it, who of himself stirred no more than a log of wood. I once or twice put aside his head with my hand, that the blood might not drop upon my clothes, intending to go on as soon as the hurry should be a little over. But the table falling down, some of our friends caught me in their arms and carried me right away on their shoulders, while the rabble wreaked their vengeance on the table which they tore bit from bit. We went a little way off, where I finished my discourse without any noise or interruption.\n\n## _Bonnie Prince Charlie Invades Manchester, 28\u201329 November 1745_\n\nELIZABETH BYROM\n\n_Charles Edward Stuart ('Bonnie Prince Charlie'), grandson of James II, led the last Stuart attempt to regain the throne of England. Landing in Scotland in July 1745, he raised an army of Highlanders and Jacobites, before marching south._\n\n_28 (Thursday)._ About three o'clock today came into town two men in Highland dress, and a woman behind one of them with a drum on her knee, and for all the loyal work that our Presbyterians have made, they took possession of the town as one may say, for immediately after they were 'light they beat up for volunteers for Prince Charles: 'All gentlemen that have a mind to serve His Royal Highness Prince Charles with a willing mind, etc., five guineas advance,' and nobody offered to meddle with them. They were directly joined by Mr J. Bradshaw, Tom Lydall, Mr Tom Deacon, Mr Fletcher, Tom Chaddock, and several others have listed, above eighty men by eight o'clock, when my papa came down to tell us there was a party of horse come in; he took care of me to the Cross, where I saw them all; it is a very fine moonlight night; Mr Walley, Mr Foden and Deputy billeted them. They are my Lord Pitsligo's Horse, and Hugh Sterling, that was 'prentice at Mr Hibbert's, is with them, and the streets are exceeding quiet, there is not one person to be seen nor heard. One of the Highlanders that came today is a Yorkshireman, and is gone tonight to see his sister that lives at Sleat Hall; he took his drawn sword in his hand and went by himself. My papa and my uncle are gone to consult with Mr Croxton, Mr Feilden and others, how to keep themselves out of any scrape, and yet behave civilly. All the justices fled and lawyers too but Coz Clowes.\n\n_29 (Friday)._ They are beating up for the Prince; eleven o'clock we went up to the Cross to see the rest come in; there came small parties of them till about three o'clock, when the Prince and the main body of them came, I cannot guess how many. The Prince went straight up to Mr Dickenson's, where he lodges, the Duke of Athol at Mr Marsden's, the Duke of Perth at Gartside's. There came an officer up to us at Cross and gave us the manifests and declarations; the bells they rung, and P. Cotterel made a bonfire, and all the town was illuminated, every house except Mr Dickenson's, my papa mamma and sister, and my uncle and I walked up and down to see it; about four o'clock the King was proclaimed, the mob shouted very cleverly, and then we went up to see my aunt Brearcliffe and stayed till eleven o'clock making St Andrew's crosses for them; we sat up making till two o'clock.\n\n_After his ludicrously easy invasion of Manchester, the Young Pretender moved on to Derby, before retreating back to Scotland, where his army was eradicated at Culloden._\n\n_The '45_ ' _failed because the Stuarts misunderstood the Jacobinism of England's Tories. The latter may have disliked the Hanoverian succession, but not to such a degree that they actually wished to upset the national apple-cart, which was doing very nicely. By a combination of naval mastery, credit expansion and mercantilist enterprise, Britain had developed a network of trading posts and colonies across the world, India included._\n\n## _The Black Hole of Calcutta, 20\u201321 June 1756_\n\nJ. Z. HOLWELL\n\n_The East India Company (formed 1600) was in the van of the British colonization of the Indian sub-continent, and was bitterly opposed by Siraj-ud-Dawlah, the Nawab of Bengal. After attacking the East India Company's fortified headquarters in Calcutta, the nawab imprisoned his British prisoners in an 18-feet-square guardroom at Fort William. Holwell was the senior British official in Calcutta._\n\nWe had been but few minutes confined before every one fell into a perspiration so profuse, you can form no idea of it. This brought on a raging thirst, which increased in proportion as the body was drained of its moisture.\n\nVarious expedients were thought of to give more room and air. To obtain the former, it was moved to put off their cloaths; this was approved as a happy motion, and in a few minutes I believe every man was stripped (myself, Mr Court, and the two young gentlemen by me excepted). For a little time they flattered themselves with having gained a mighty advantage; every hat was put in motion to produce a circulation of air, and Mr Baillie proposed that every man should sit down on his hams. This expedient was several times put in practice, and at each time many of the poor creatures, whose natural strength was less than that of others, or who had been more exhausted and could not immediately recover their legs, as others did when the word was given to rise, fell to rise no more; for they were instantly trod to death or suffocated. When the whole body sat down, they were so closely wedged together, that they were obliged to use many efforts before they could put themselves in motion to get up again.\n\nBefore nine o'clock every man's thirst grew intolerable, and respiration difficult. Efforts were made again to force the door, but in vain. Many insults were used to the guard to provoke them to fire in upon us. For my own part, I hitherto felt little pain or uneasiness, but what resulted from my anxiety for the sufferings of those within. By keeping my face between two of the bars, I obtained air enough to give my lungs easy play, though my perspiration was excessive, and thirst commencing. At this period, so strong a urinous volatile effluvia came from the prison, that I was not able to turn my head that way, for more than a few seconds at a time.\n\nNow every body, excepting those situated in and near the windows, began to grow outrageous, and many delirious: _Water, water,_ became the general cry. And the old Jemmautdaar before mentioned, taking pity on us, ordered the people to bring some skins of water. This was what I dreaded. I foresaw it would prove the ruin of the small chance left us, and essayed many times to speak to him privately to forbid its being brought; but the clamour was so loud, it became impossible. The water appeared. Words cannot paint to you the universal agitation and raving the sight of it threw us into. I flattered myself that some, by preserving an equal temper of mind, might out-live the night; but now the reflection, which gave me the greatest pain, was, that I saw no possibility of one escaping to tell the dismal tale.\n\nUntil the water came, I had myself not suffered much from thirst, which instantly grew excessive. We had no means of conveying it into the prison, but by hats forced through the bars; and thus myself and Messieurs Coles and Scott (notwithstanding the pains they suffered from their wounds) supplied them as fast as possible. But those who have experienced intense thirst, or are acquainted with the cause and nature of this appetite, will be sufficiently sensible it could receive no more than a momentary alleviation; the cause still subsisted. Though we brought full hats within the bars, there ensued such violent struggles, and frequent contests to get at it, that before it reached the lips of any one, there would be scarcely a small tea cup full left in them. These supplies, like sprinkling water on fire, only served to feed and raise the flame.\n\nOh! my dear Sir, how shall I give you a conception of what I felt at the cries and ravings of those in the remoter parts of the prison, who could not entertain a probable hope of obtaining a drop, yet could not divest themselves of expectation, however unavailing! and calling on me by the tender considerations of friendship and affection, and who knew they were really dear to me! Think, if possible, what my heart must have suffered at seeing and hearing their distress, without having it in my power to relieve them: for the confusion now became general and horrid. Several quitted the other window (the only chance they had for life) to force their way to the water, and the throng and press upon the window was beyond bearing; many forcing their passage from the further part of the room, pressed down those in their way, who had less strength, and trampled them to death.\n\nFrom about nine to near eleven, I sustained this cruel scene and painful situation, still supplying them with water, though my legs were almost broke with the weight against them. By this time I myself was near pressed to death, and my two companions, with Mr William Parker (who had forced himself into the window) were really so...\n\nFor a great while they preserved a respect and regard to me, more than indeed I could well expect, our circumstances considered; but now all distinction was lost. My friend Baillie, Messrs Jenks, Revely, Law, Buchanan, Simpson, and several others, for whom I had a real esteem and affection, had for some time been dead at my feet: and were now trampled upon by every corporal or common soldier, who, by the help of more robust constitutions, had forced their way to the window, and held fast by the bars over me, till at last I became so pressed and wedged up, I was deprived of all motion.\n\nDetermined now to give every thing up, I called to them, and begged, as the last instance of their regard, they would remove the pressure upon me, and permit me to retire out of the window, to die in quiet. They gave way; and with much difficulty I forced a passage into the centre of the prison, where the throng was less by the many dead, (then I believe amounting to one-third) and the numbers who flocked to the windows; for by this time they had water also at the other window.\n\nIn the black hole there is a platform corresponding with that in the barrack: I travelled over the dead, and repaired to the further end of it, just opposite to the other window. Here my poor friend Mr Edward Eyre came staggering over the dead to me, and with his usual coolness and good-nature, asked me how I did? but fell and expired before I had time to make him a reply. I laid myself down on some of the dead behind me, on the platform; and, recommending myself to heaven, had the comfort of thinking my sufferings could have no long duration.\n\nMy thirst grew now insupportable, and the difficulty of breathing much increased; and I had not remained in this situation, I believe, ten minutes, when I was seized with a pain in my breast, and palpitation of heart, both to the most exquisite degree. These roused and obliged me to get up again; but still the pain, palpitation, thirst, and difficulty of breathing increased. I retained my senses notwithstanding; and had the grief to see death not so near me as I hoped; but could no longer bear the pains I suffered without attempting a relief, which I knew fresh air would and could only give me. I instantly determined to push for the window opposite to me; and by an effort of double the strength I had ever before possessed, gained the third rank at it, with one hand seized a bar, and by that means gained the second, though I think there were at least six or seven ranks between me and the window.\n\nIn a few moments the pain, palpitation, and difficulty of breathing ceased; but my thirst continued intolerable. I called aloud for _Water for God's sake._ I had been concluded dead; but as soon as they found me amongst them, they still had the respect and tenderness for me, to cry out, _Give him water, give him water!_ nor would one of them at the window attempt to touch it until I had drank. But from the water I had no relief; my thirst was rather increased by it; so I determined to drink no more, but patiently wait the event; and kept my mouth moist from time to time by sucking the perspiration out of my shirt sleeves, and catching the drops as they fell, like heavy rain, from my head and face; you can hardly imagine how unhappy I was if any of them escaped my mouth.\n\nI came into the prison without coat or waistcoat; the season was too hot to bear the former, and the latter tempted the avarice of one of the guards, who robbed me of it, when we were under the Veranda. Whilst I was at this second window, I was observed by one of my miserable companions on the right of me, in the expedient of allaying my thirst by sucking my shirt-sleeve. He took the hint, and robbed me from time to time of a considerable part of my store; though after I detected him, I had even the address to begin on that sleeve first, when I thought my reservoirs were sufficiently replenished; and our mouths and noses often met in the contest. This plunderer I found afterwards was a worthy young gentleman in the service, Mr Lushington, one of the few who escaped from death, and since paid me the compliment of assuring me, he believed he owed his life to the many comfortable draughts he had from my sleeves. Before I hit upon this happy expedient, I had in an ungovernable fit of thirst, attempted drinking my urine; but it was so intensely bitter, there was no enduring a second taste, whereas no Bristol water could be more soft or pleasant than what arose from perspiration...\n\nMany to the right and left sunk with the violent pressure, and were soon suffocated; for now a steam arose from the living and the dead, which affected us in all its circumstances, as if we were forcibly held by our heads over a bowl of strong volatile spirit of hartshorn, until suffocated; nor could the effluvia of the one be distinguished from the other; and frequently, when I was forced by the load upon my head and shoulders, to hold my face down, I was obliged, near as I was to the window, instantly to raise it again, to escape suffocation...\n\nWhen the day broke, and the gentlemen found that no intreaties could prevail to get the door opened, it occurred to one of them (I think to Mr Secretary Cooke) to make a search for me, in hopes I might have influence enough to gain a release from this scene of misery. Accordingly Messrs Lushington and Walcot undertook the search, and by my shirt discovered me under the dead upon the platform. They took me from thence, and imagining I had some signs of life, brought me towards the window I had first possession of.\n\nBut as life was equally dear to every man (and the stench arising from the dead bodies was grown so intolerable) no one would give up his station in or near the window: so they were obliged to carry me back again. But soon after Captain Mills, (now captain of the company's yacht) who was in possession of a seat in the window, had the humanity to offer to resign it. I was again brought by the same gentlemen and placed in the window.\n\nAt this juncture the suba (viceroy of Bengal), who had received an account of the havock death had made amongst us, sent one of his Jemmautdaars to enquire if the chief survived. They shewed me to him; told I had appearance of life remaining; and believed I might recover if the door was opened very soon. This answer being returned to the suba, an order came immediately for our release, it being then near six in the morning.\n\nAs the door opened inwards, and as the dead were piled up against it, and covered all the rest of the floor, it was impossible to open it by any efforts from without; it was therefore necessary that the dead should be removed by the few that were within, who were become so feeble, that the task, though it was the condition of life, was not performed without the utmost difficulty, and it was twenty minutes after the order came before the door could be opened.\n\nAbout a quarter after six in the morning, the poor remains of 146 souls, being no more than three and twenty, came out of the black hole alive, but in a condition which made it very doubtful whether they would see the morning of the next day; among the living was Mrs Carey, but poor Leech was among the dead. The bodies were dragged out of the hole by the soldiers, and thrown promiscuously into the ditch of an unfinished ravelin, which was afterwards filled with earth.\n\n_The task of avenging the Black Hole was given to Robert Clive (1725\u201374), son of a Shropshire squire and a soldier for the East India Company. At Plassey on 23 June 1757 Clive's East India Company force of 3,200 triumphed over the 50,000 soldiers (who included French gunners) led by the Nawab of Bengal. Clive wrote to the Company's directors about Plassey: 'They [the Nawab's army] made several attempts to bring out their cannon, but our advance field-pieces played so warmly and so well upon them they were always drove back. Their horse exposing themselves a good deal on this occasion, many of them were killed... by which the whole army being visibly dispirited and thrown into some confusion, we were encouraged to storm both the eminence and the angle of their camp, which were carried at the same instant, with little or no loss... On this a general rout ensued; and we pursued the enemy six miles...'_\n\n_Plassey was the turning point in the Eastern career of the British. It checked the French and established the British Empire in India. Clive himself was elevated to the peerage._\n\n_After preventing French domination of India, the British strove to do the same in America._\n\n## _The Death of General Wolfe on the Heights of Abraham, Quebec, 13 September 1759_\n\nCAPTAIN JOHN KNOX\n\n_It was of the brilliant but eccentric James Wolfe that George II remarked, 'Oh! he is mad, is he? Then I hope he will_ bite _some other of my generals.' Wolfe's victory over the French at Quebec secured British control of Canada and eastern America. He was mortally wounded in the undertaking. Knox was one of Wolfe's officers._\n\nBefore day-break this morning we made a descent upon the north shore, about half a quarter of a mile to the eastward of Sillery;... we had, in this debarkation, thirty flat-bottomed boats, containing about sixteen hundred men. This was a great surprise on the enemy, who, from the natural strength of the place, did not suspect, and consequently were not prepared against, so bold an attempt.... As fast as we landed, the boats put off for reinforcements... the General, with Brigadiers Monckton and Murray, were a-shore with the first division. We lost no time here, but clambered up one of the steepest precipices that can be conceived, being almost a perpendicular, and of an incredible height. As soon as we gained the summit, all was quiet, and not a shot was heard, owing to the excellent conduct of the light infantry under Colonel Howe; it was by this time clear day-light. Here we formed again... we then faced to the right, and marched towards the town by files, till we came to the plains of Abraham; an even piece of ground which Mr Wolfe had made choice of, while we stood forming upon the hill. Weather showery: about six o'clock the enemy first made their appearance upon the heights, between us and the town; whereupon we halted, and wheeled to the right, thereby forming the line of battle.... The enemy had now likewise formed the line of battle, and got some cannon to play on us, with round and canister shot; but what galled us most was a body of Indians and other marksmen they had concealed in the corn opposite to the front of our right wing... but Colonel Hale... advanced some platoons... which, after a few rounds, obliged these skulkers to retire. We were now ordered to lie down, and remained some time in this position. About eight o'clock we had two pieces of short brass six-pounders playing on the enemy, which threw them into some confusion.... About ten o'clock the enemy began to advance briskly in three columns, with loud shouts and recovered arms, two of them inclining to the left of our army, and the third towards our right, firing obliquely at the two extremities of our line, from the distance of one hundred and thirty, until they came within forty yards; which our troops withstood with the greatest intrepidity and firmness, still reserving their fire, and paying the strictest obedience to their Officers: this uncommon steadiness, together with the havoc which the grape-shot from our field-pieces made among them, threw them into some disorder, and was most critically maintained by a well-timed, regular and heavy discharge of our small arms, such as they could no longer oppose; hereupon they gave way, and fled with precipitation, so that, by the time the cloud of smoke was vanished, our men were again loaded, and profiting by the advantage we had over them, pursued them almost to the gates of the town, and the bridge over the little river, redoubling our fire with great eagerness, making many Officers and men prisoners. The weather cleared up, with a comfortably warm sunshine.... Our joy at this success is inexpressibly damped by the loss we sustained of one of the greatest heroes which this or any other age can boast of \u2013 General James Wolfe, who received his mortal wound as he was exerting himself at the head of the grenadiers of Louisbourg.... The officers who are prisoners say that Quebec will surrender in a few days: some deserters, who came out to us in the evening, agree in that opinion, and inform us, that the Sieur de Montcalm is dying, in great agony, of a wound he received today in their retreat...\n\nAfter our late worthy general, of renowned memory, was carried off wounded, to the rear of the front line, he desired those who were about him to lay him down; being asked if he would have a Surgeon, he replied, 'It is needless; it is all over with me'. One of them then cried out, 'They run, see how they run'. 'Who runs?' demanded our hero, with great earnestness, like a person roused from sleep. The Officer answered, 'The enemy, Sir, Egad they give way everywhere'. Thereupon the General rejoined, 'Go one of you, my lads, to Colonel Burton; tell him to march Webb's regiment with all speed down to Charles's river, to cut off the retreat of the fugitives from the bridge'. Then, turning on his side, he added, 'Now, God be praised, I will die in peace:' and thus expired.\n\n## _George II Interred, 13 November 1760_\n\nHORACE WALPOLE\n\nGeorge the First was always reckoned  \nVile, but viler George the Second\n\n_Walter Savage Landor_\n\n_George II (reigned 1727\u201360) was unloved, unremarkable, and the dazzling expansion of Britain under Clive, Wolfe and the statesman Pitt the Elder was despite him. That said, George II gained a flicker of national respect for being the last British monarch to lead his troops into battle, at Dettingen in 1743._\n\n_Horace Walpole was the son of Sir Robert Walpole, England's first andlongest-serving (1721\u201342) prime minister. Walpole junior's 'gothicization' of a coachman's cottage into the pseudo-castle of Strawberry Hill, Twickenham, set a national fashion, but his greatest mark on posterity was his vivid and voluminous correspondence. To one friend alone, Madame du Deffand, he sent more than 1,600 letters._\n\nDo you know I had the curiosity to go to the burying t'other night; I had never seen a royal funeral. Nay, I walked as a rag of quality, which I found would be, and so it was, the easiest way of seeing it. It is absolutely a noble sight. The Prince's Chamber hung with purple and a quantity of silver lamps, the coffin under a canopy of purple velvet, and six vast chandeliers of silver on high stands had a very good effect: the ambassador from Tripoli and his son were carried to see that chamber. The procession through a line of footguards, every seventh man bearing a torch, the horse-guards lining the outside, their officers with drawn sabres and crape sashes, on horseback, the drums muffled, the fifes, bells tolling and minute guns, all this was very solemn. But the charm was the entrance of the Abbey, where we were received by the Dean and chapter in rich copes, the choir and almsmen all bearing torches; the whole Abbey so illuminated, that one saw it to greater advantage than by day; the tombs, long aisles, and fretted roof all appearing distinctly, and with the happiest chiaroscuro. There wanted nothing but incense, and little chapels here and there with priests saying mass for the repose of the defunct \u2013 yet one could not complain of its not being Catholic enough. I had been in dread of being coupled with some boy of ten years old \u2013 but the heralds were not very accurate, and I walked with George Grenville, taller and older enough to keep me in countenance. When we came to the chapel of Henry VII all solemnity and decorum ceased \u2013 no order was observed, people sat or stood where they could or would, the yeomen of the guard were crying out for help, oppressed by the immense weight of the coffin, the Bishop read sadly, and blundered in the prayers, the fine chapter, _Man that is born of a woman,_ was chanted not read, and the anthem, besides being unmeasurably tedious, would have served as well for a nuptial. The real serious part was the figure of the Duke of Cumberland, heightened by a thousand melancholy circumstances. He had a dark brown adonis [wig] and a cloak of black cloth with a train of five yards. Attending the funeral of a father, how little reason soever he had to love him, could not be pleasant. His leg extremely bad, yet forced to stand upon it near two hours, his face bloated and distorted with his late paralytic stroke, which has affected too one of his eyes, and placed over the mouth of the vault, into which in all probability he must himself so soon descend \u2013 think how unpleasant a situation! He bore it all with a firm and unaffected countenance. This grave scene was fully contrasted by the burlesque Duke of Newcastle \u2013 he fell into a fit of crying the moment he came into the chapel and flung himself back in a stall, the Archbishop hovering over him with a smelling bottle \u2013 but in two minutes his curiosity got the better of his hypocrisy and he ran about the chapel with his glass to spy who was or was not there, spying with one hand and mopping his eyes with t'other. Then returned the fear of catching cold, and the Duke of Cumberland, who was sinking with heat, felt himself weighed down, and turning round, found it was the Duke of Newcastle standing upon his train to avoid the chill of the marble. It was very theatric to look down into the vault, where the coffin lay, attended by mourners with lights. Clavering, the Groom of the Bedchamber, refused to sit up with the body, and was dismissed by the King's order.\n\n_The late king's twenty-two-year-old grandson and heir, George III (reigned 1760\u20131820), made a decent fist of being English; he was affectionately nicknamed 'Farmer George' for his love of the native countryside. His popularity waned, however, as his obstinacy and his incompetence as ruler became evident during the dismal decades of 1763\u201383 when the American colonies were lost._\n\n## _The Boston Tea Party, 16 December 1773_\n\nJOHN ANDREWS\n\n_To protect its possessions in America, the British government proposed a resident army of 10,000 and a fort-building programme. That the colonials should pay for their own defence, raised through stiff duties on imports, seemed like a good scheme in London. So too the order that money-spinning revenue stamps (courtesy of the Stamp Act, 1765) should be fixed to all printed documents circulated in America._\n\n_Antagonized, over-taxed and unrepresented, the colonists boycotted British goods \u2013 which persuaded the British government to repeal the import taxes. Save, that is, the tax on tea. Half-heartedly disguised as American Indians, colonial patriots led a protest against three British tea ships in Boston Harbor._\n\n_Andrews, a Boston selectman, wrote the account below for a relative._\n\nThe affair was transacted with the greatest regularity and despatch.... A general muster was assembled, from this and all the neighbouring towns, to the number of five or six thousand, at 10 o'clock Thursday morning in the Old South Meeting House, where they passed a unanimous vote that the Tea should go out of the harbour that afternoon, and sent a committee with Mr Rotch* to the Customhouse to demand a clearance, which the Collector told them it was not in his power to give, without the duties being first paid. They then sent Mr Rotch to Milton, to ask a pass from the Governor, who sent for answer, that 'consistent with the rules of government and his duty to the King he could not grant one without they produced a previous clearance from the office'. By the time he returned with this message the candles were light in the house, and upon reading it, such prodigious shouts were made, that induced me, while drinking tea at home, to go out and know the cause of it. The house was so crowded I could get no farther than the porch, when I found the moderator was just declaring the meeting to be dissolved, which caused another general shout, outdoors and in, and three cheers. What with that, and the consequent noise of breaking up the meeting, you'd thought that the inhabitants of the infernal regions had broke loose.\n\nFor my part, I went contentedly home and finished my tea, but was soon informed what was going forward; but still not crediting it without ocular demonstration, I went and was satisfied. They mustered, I'm told, upon Fort Hill to the number of about two hundred, and proceeded, two by two, to Griffin's wharf, where _Hall, Bruce,_ and _Coffin_ lay, each with 114 chests of the ill-fated article on board; the two former with only that article, but the latter, arrived at the wharf only the day before, was freighted with a large quantity of other goods, which they took the greatest care not to injure in the least, and before nine o'clock in the evening every chest from on board the three vessels was knocked to pieces and flung over the sides.\n\nThey say the actors were Indians from Narragansett. Whether they were or not, to a transient observer they appeared as such, being clothed in blankets with the heads muffled, and copper-coloured countenances, being each armed with a hatchet or axe, and pair pistols, nor was their dialect different from what I conceive these geniuses to speak, as their jargon was unintelligible to all but themselves. Not the least insult was offered to any person, save one Captain Connor, a letter of horses in this place, not many years since removed from dear Ireland, who had ripped up the lining of his coat and waistcoat, under the arms, and watching his opportunity had nearly filled them with tea, but being detected, was handled pretty roughly. They not only stripped him of his clothes, but gave him a coat of mud, with a severe bruising into the bargain; and nothing but their utter aversion to make any disturbance prevented his being tarred and feathered.\n\nShould not have troubled you with this, by this post, hadn't I thought you would be glad of a more particular account of so important a transaction than you could have obtained by common report; and if it affords my brother but a temporary amusement, I shall be more than repaid for the trouble of writing it.\n\n_After Boston, the logic towards war became hard to escape. Feeble-minded George III and his dog-loyal Prime Minister Frederick North retaliated with the Intolerable Acts', designed to show the colonials that Britain was boss. The intransigent colonists were not inclined to genuflect, and skirmishing between Redcoats and American militiamen broke out at Lexington and Concord in April 1775_. _The War of Independence \u2013 what the Americans would call the Revolutionary War- went Britain's way... until the British commander, Lord Cornwallis, threw away a likely win, allowing himself to become trapped between the Americans on land and a fleet \u2013 thoughtfully provided by the French \u2013 at sea._\n\n_Britain recognized America's independence in 1783._\n\n## _Machine Wreckers, Lancashire, October 1779_\n\nTHOMAS BENTLEY\n\n_The introduction of machine technology, as England laboured during the world's first Industrial Revolution, was widely thought to cause unemployment. There arose in response a 'wrecking' movement, which saw its eventual zenith in the Luddism of the 1810s._\n\nI wrote to my dear friend last from Bolton, and I mention'd the mob which had assembled in that neighbourhood; but they had not done much mischief; they only destroyed a small engine or two near Chow-bent. We met them on Saturday morning, but I apprehend what we saw were not the main body; for on the same day, in the afternoon, a capital engine or mill, in the manner of Arcrites, and in which he is a partner, near Chorley, was attacked; but from its peculiar situation they could approach to it by one passage only; and this circumstance enabled the owner, with the assistance of a few neighbours, to repulse the enemy and preserve the mill for that time. Two of the mob were shot dead upon the spot, one drowned, and several wounded. The mob had no fire-arms, and did not expect so warm a reception. They were greatly exasperated, and vowed revenge; accordingly they spent all Sunday and Monday morning in collecting firearms and ammunition and melting their pewter dishes into bullets. They were now join'd by the Duke of Bridgewater's colliers and others, to the number, we are told, of eight thousand, and march'd by beat of drum and with colours flying to the mill, where they met with a repulse on Saturday. They found Sir Richard Clayton guarding the place with fifty Invalids armed, but this handful were by no means a match for enraged thousands; they (the Invalids) therefore contented themselves with looking on, while the mob completely destroyed a set of mills valued at 10,000\/.\n\nThis was Monday's employment. On Tuesday morning we heard their drum at about two miles distance from Bolton, a little, before we left the place, and their professed design was to take Bolton, Manchester, and Stockport on their way to Crumford, and to destroy all the engines not only on these places, but throughout all England. How far they will be able to put their threats into execution time alone can discover.\n\n_Machine-smashing was doomed, because the demand for the machines was insatiable. They produced goods faster and cheaper than machine-breakers and cottage-artisans could even nightmare of. And England's burgeoning population \u2013 up from 5.2 million in 1731 to 7.1 in 1780_ \u2013 _clamoured to be clothed, fed and heated. And not only was England's population growing, it was relocating._\n\n_Unwanted by a countryside that had improved its agricultural output but decreased its need for sons and daughters of soil-toil, many English migrated off the land; by the mid-eighteenth century 30 per cent of England's people lived in towns. England, in other words, was the most urbanized country in northern Europe._\n\n_Urbanization created a demand for goods made by machines; machines required factories and power. This sequence of impulses was a singular reason for England entering the Industrial Revolution first among nations. So was England's aggressive empire building in the mid-eighteenth century, which gave England Ltd both cheap raw materials and vast external markets. A double economic boon._\n\n_There were other reasons, too,, hovering from England's past, claiming theirshare of praise for Albion's early industrialization: the 'blessed plot's' natural abundance of coal, essential for steam-power and iron-smelting; the reinvestment of the hyper-profits from the slave-and-sugar trade of which John Hawkins was a premier exponent; Cromwell's smoothing of the expansion of mercantilism and the securing of Protestantism, which facilitated individualism and scientific inquiry; England's long-held nationhood, which created an internal market largely free of customs barriers; and the tradition of City of London money-men for risk-taking._\n\n_Inevitably, this self-same Industrial Revolution produced incandescent social tensions._\n\n## _The Gordon Riots, 8 June 1780_\n\nGEORGE CRABBE\n\n_Lord George Gordon headed a 50,000-strong London mob demanding the repeal of the 1778 Act allowing Catholics civil rights. It was not Popery that the mob objected to so much as the influx of wage-lowering Irish Catholic navvies into England. About 300 people were killed in a week of rioting in the capital city._\n\nYesterday, my own business being decided, I was at Westminster at about three o'clock in the afternoon, and saw the members go to the House. The mob stopped many persons, but let all whom I saw pass, excepting Lord Sandwich, whom they treated roughly, broke his coach windows, cut his face, and turned him back. A guard of horse and foot were immediately sent for, who did no particular service, the mob increasing and defeating them.\n\nI left Westminster when all the members, that were permitted, had entered the House and came home. In my way I met a resolute band of vile-looking fellows, ragged, dirty, and insolent, armed with clubs, going to join their companions. I since learned that there were eight or ten of these bodies in different parts of the City.\n\nAbout seven o'clock in the evening I went out again. At Westminster the mob were few, and those quiet, and decent in appearance. I crossed St George's Fields, which were empty, and came home again by Black-friars Bridge; and in going from thence to the Exchange, you pass the Old Bailey; and here it was that I saw the first scene of terror and riot ever presented to me. The new prison was a very large, strong, and beautiful building, having two wings, of which you can suppose the extent, when you consider their use; besides these, were the keeper's (Mr Akerman's) house, a strong intermediate work, and likewise other parts, of which I can give you no description. Akerman had in his custody four prisoners, taken in the riot; these the mob went to his house and demanded. He begged he might send to the sheriff, but this was not permitted. How he escaped, or where he is gone, I know not; but just at the time I speak of they set fire to his house, broke in, and threw every piece of furniture they could find into the street, firing them also in an instant. The engines came, but were only suffered to preserve the private houses near the prison.\n\nAs I was standing near the spot, there approached another body of men, I suppose 500, and Lord George Gordon in a coach, drawn by the mob towards Alderman Bull's, bowing as he passed along. He is a lively-looking young man in appearance, and nothing more, though just now the reigning hero.\n\nBy eight o'clock, Akerman's house was in flames. I went close to it, and never saw any thing so dreadful. The prison was, as I said, a remarkably strong building; but, determined to force it, they broke the gates with crows and other instruments, and climbed up the outside of the cell part, which joins the two great wings of the building, where the felons were confined; and I stood where I plainly saw their operations. They broke the roof, tore away the rafters, and having got ladders they descended. Not Orpheus himself had more courage or better luck; flames all around them, and a body of soldiers expected, they defied and laughed at all opposition.\n\nThe prisoners escaped. I stood and saw about twelve women and eight men ascend from their confinement to the open air, and they were conducted through the street in their chains. Three of these were to be hanged on Friday. You have no conception of the phrensy of the multitude. This being done, and Akerman's house now a mere shell of brickwork, they kept a store of flame there for other purposes. It became red-hot, and the doors and windows appeared like the entrance to so many volcanoes. With some difficulty they then fired the debtors' prison \u2013 broke the doors \u2013 and they, too, all made their escape.\n\nTired of the scene, I went home, and returned again at eleven o'clock at night. I met large bodies of horse and foot soldiers coming to guard the Bank, and some houses of Roman Catholics near it. Newgate was at this time open to all; anyone might get in, and, what was never the case before, anyone might get out. I did both; for the people were now chiefly lookers on. The mischief was done, and the doers of it gone to another part of the town.\n\nBut I must not omit what struck me most. About ten or twelve of the mob getting to the top of the debtors' prison, whilst it was burning, to halloo, they appeared rolled in black smoke mixed with sudden bursts of fire \u2013 like Milton's infernals, who were as familiar with flame as with each other. On comparing notes with my neighbours, I find I saw but a small part of the mischief. They say Lord Mansfield's house is now in flames.\n\n_Twenty-one of the mob were hanged. Gordon, benefiting from the expensive legal skills of the jurist Thomas Erskine, was acquitted of treason. He then adopted Judaism before libelling Marie Antoinette and dying of gaol fever in Newgate._\n\n## _A Chance Meeting with Mad King George, Kew Gardens, 2 February 1789_\n\nFANNY BURNEY\n\n_George III's madness may have been caused by the burdens of monarchy and fatherhood (the Hanoverians were the original dysfunctional family), or porphyria, or even lead poisoning from the plate which held his favourite food, sauerkraut._\n\n_Whatever, he suffered bouts of insanity. Here is short-sighted Fanny Burney, joint Keeper of the Queen's Robes, encountering Mad King George at Kew._\n\n_Kew Palace_\n\nWhat an adventure had I this morning! one that has occasioned me the severest personal terror I ever experienced in my life.\n\nSir Lucas Pepys still persisting that exercise and air were absolutely necessary to save me from illness, I have continued my walks, varying my gardens from Richmond to Kew, according to the accounts I received of the movements of the King. For this I had her Majesty's permission, on the representation of Sir Lucas.\n\nThis morning, when I received my intelligence of the King from Dr John Willis, I begged to know where I might walk in safety. 'In Kew Gardens,' he said, 'as the King would be in Richmond.'\n\n'Should any unfortunate circumstance,' I cried, 'at any time, occasion my being seen by his Majesty, do not mention my name, but let me run off without call or notice.'\n\nThis he promised. Everybody, indeed, is ordered to keep out of sight.\n\nTaking, therefore, the time I had most at command, I strolled into the gardens. I had proceeded, in my quick way, nearly half the round, when I suddenly perceived through some trees, two or three figures. Relying on the instructions of Dr John, I concluded them to be workmen and gardeners; yet tried to look sharp, and in so doing, as they were less shaded, I thought I saw the person of his Majesty!\n\nAlarmed past all possible expression, I waited not to know more, but turning back, ran off with all my might. But what was my terror to hear myself pursued! \u2013 to hear the voice of the King himself loudly and hoarsely calling after me, 'Miss Burney! Miss Burney!'\n\nI protest I was ready to die. I knew not in what state he might be at the time; I only knew the orders to keep out of his way were universal; that the Queen would highly disapprove any unauthorized meeting, and that the very action of my running away might deeply, in his present irritable state, offend him. Nevertheless, on I ran, too terrified to stop, and in search of some short passage, for the garden is full of little labyrinths, by which I might escape.\n\nThe steps still pursued me, and still the poor hoarse and altered voice rang in my ears: \u2013 more and more footsteps resounded frightfully behind me, \u2013 the attendants all running, to catch their eager master, and the voices of the two Doctor Willises loudly exhorting him not to heat himself so unmercifully.\n\nHeavens, how I ran! I do not think I should have felt the hot lava from Vesuvius \u2013 at least not the hot cinders \u2013 had I so run during its eruption. My feet were not sensible that they even touched the ground.\n\nSoon after, I heard other voices, shriller, though less nervous, call out 'Stop! Stop! Stop!'\n\nI could by no means consent: I knew not what was purposed, but I recollected fully my agreement with Dr John that very morning, that I should decamp if surprised, and not be named.\n\nMy own fears and repugnance, also, after a flight and disobedience like this, were doubled in the thought of not escaping: I knew not to what I might be exposed, should the malady be then high, and take the turn of resentment. Still, therefore, on I flew; and such was my speed, so almost incredible to relate or recollect, that I fairly believe no one of the whole party could have overtaken me, if these words, from one of the attendants, had not reached me, 'Doctor Willis begs you to stop!'\n\n'I cannot! I cannot!' I answered, still flying on, when he called out, 'You must, ma'am; it hurts the King to run.'\n\nThen, indeed, I stopped \u2013 in a state of fear really amounting to agony. I turned round, I saw the two Doctors had got the King between them, and three attendants of Dr Willis's were hovering about. They all slackened their pace, as they saw me stand still; but such was the excess of my alarm, that I was wholly insensible to the effects of a race which, at any other time, would have required an hour's recruit.\n\nAs they approached, some little presence of mind happily came to my command: it occurred to me that, to appease the wrath of my flight, I must now show some confidence: I therefore faced them as undauntedly as I was able, only charging the nearest of the attendants to stand by my side.\n\nWhen they were within a few yards of me, the King called out, 'Why did you run away?'\n\nShocked at a question impossible to answer, yet a little assured by the mild tone of his voice, I instantly forced myself forward, to meet him, though the internal sensation, which satisfied me this was a step the most proper to appease his suspicions and displeasure, was so violently combated by the tremor of my nerves, that I fairly think I may reckon it the greatest effort of personal courage I have ever made.\n\nThe effort answered: I looked up, and met all his wonted benignity of countenance, though something still of wildness in his eyes. Think, however, of my surprise, to feel him put both his hands round my two shoulders, and then kiss my cheek!\n\nI wonder I did not really sink, so exquisite was my affright when I saw him spread out his arms! Involuntarily, I concluded he meant to crush me: but the Willises, who have never seen him till this fatal illness, not knowing how very extraordinary an action this was from him, simply smiled and looked pleased, supposing, perhaps, it was his customary salutation!\n\nI believe, however, it was but the joy of a heart unbridled, now, by the forms and proprieties of established custom and sober reason. To see any of his household thus by accident, seemed such a near approach to liberty and recovery, that who can wonder it should serve rather to elate than lessen what yet remains of his disorder!\n\nHe now spoke in such terms of his pleasure in seeing me, that I soon lost the whole of my terror; astonishment to find him so nearly well, and gratification to see him so pleased, removed every uneasy feeling, and the joy that succeeded, in my conviction of his recovery, made me ready to throw myself at his feet to express it.\n\nWhat a conversation followed! When he saw me fearless, he grew more and more alive, and made me walk close by his side, away from the attendants, and even the Willises themselves, who, to indulge him, retreated. I own myself not completely composed, but alarm I could entertain no more.\n\nEverything that came uppermost in his mind he mentioned; he seemed to have just such remains of his flightiness as heated his imagination without deranging his reason, and robbed him of all control over his speech, though nearly in his perfect state of mind as to his opinions.\n\nWhat did he not say! He opened his whole heart to me, \u2013 expounded all his sentiments, and acquainted me with all his intentions.\n\nThe heads of his discourse I must give you briefly, as I am sure you will be highly curious to hear them, and as no accident can render of much consequence what a man says in such a state of physical intoxication.\n\nHe assured me he was quite well \u2013 as well as he had ever been in his life; and then inquired how I did, and how I went on? and whether I was more comfortable?\n\nIf these questions, in their implication, surprised me, imagine how that surprise must increase when he proceeded to explain them! He asked after the coadjutrix, laughing, and saying, 'Never mind her! \u2013 don't be oppressed \u2013 I am your friend! don't let her cast you down! \u2013 I know you have a hard time of it \u2013 but don't mind her!'\n\nAlmost thunderstruck with astonishment, I merely curtseyed to his kind 'I am your friend,' and said nothing.\n\nThen presently he added, 'Stick to your father \u2013 stick to your own family \u2013 let them be your objects.'\n\nHow readily I assented!\n\nAgain he repeated all I have just written, nearly in the same words, but ended it more seriously: he suddenly stopped, and held me to stop too, and putting his hand on his breast, in the most solemn manner, he gravely and slowly said, 'I will protect you! \u2013 I promise you that \u2013 and therefore depend upon me!'\n\nI thanked him; and the Willises, thinking him rather too elevated, came to propose my walking on. 'No, no, no,' he cried, a hundred times in a breath; and their good humour prevailed, and they let him again walk on with his new companion.\n\nHe then gave me a history of his pages, animating almost into a rage, as he related his subjects of displeasure with them, particularly with Mr Ernst, who, he told me, had been brought up by himself. I hope his ideas upon these men are the result of the mistakes of his malady.\n\nThen he asked me some questions that very greatly distressed me, relating to information given him in his illness, from various motives, but which he suspected to be false, and which I knew he had reason to suspect: yet was it most dangerous to set anything right, as I was not aware what might be the view of their having been stated wrong. I was as discreet as I knew how to be, and I hope I did no mischief; but this was the worst part of the dialogue.\n\nHe next talked to me a great deal of my dear father, and made a thousand inquiries concerning his 'History of Music.' This brought him to his favourite theme, Handel; and he told me innumerable anecdotes of him, and particularly that celebrated tale of Handel's saying of himself, when a boy, 'While that boy lives, my music will never want a protector.' And this, he said, I might relate to my father.\n\nThen he ran over most of his oratorios, attempting to sing the subjects of several airs and choruses, but so dreadfully hoarse that the sound was terrible.\n\nDr Willis, quite alarmed at this exertion, feared he would do himself harm, and again proposed a separation. 'No! No! No!' he exclaimed, 'not yet; I have something I must just mention first.'\n\nDr Willis, delighted to comply, even when uneasy at compliance, again gave way.\n\nThe good King then greatly affected me. He began upon my revered old friend, Mrs Delany; and he spoke of her with such warmth \u2013 such kindness! 'She was my friend,' he cried, 'and I loved her as a friend! I have made a memorandum when I lost her \u2013 I will show it you.'\n\nHe pulled out a pocket-book, and rummaged some time, but to no purpose.\n\nThe tears stood in his eyes \u2013 he wiped them, and Dr Willis again became very anxious. 'Come, sir,' he cried, 'now do you come in and let the lady go on her walk \u2013 come, now, you have talked a long while, \u2013 so we'll go in \u2013 if your Majesty pleases.'\n\n'No, no!' he cried, 'I want to ask her a few questions; \u2013 I have lived so long out of the world, I know nothing!'\n\nThis touched me to the heart. We walked on together, and he inquired after various persons, particularly Mrs Boscawen, because she was Mrs Delany's friend! Then, for the same reason, after Mr Frederick Montagu, of whom he kindly said, 'I know he has a great regard for me, for all he joined the opposition.' Lord Grey de Wilton, Sir Watkin Wynn, the Duke of Beaufort, and various others, followed.\n\nHe then told me he was very much dissatisfied with several of his state officers, and meant to form an entire new establishment. He took a paper out of his pocket-book, and showed me his new list.\n\nThis was the wildest thing that passed; and Dr John Willis now seriously urged our separating; but he would not consent; he had only three more words to say, he declared, and again he conquered.\n\nHe now spoke of my father, with still more kindness, and told me he ought to have had the post of Master of the Band, and not that little poor musician Parsons, who was not fit for it: 'But Lord Salisbury,' he cried, 'used your father very ill in that business, and so he did me! However, I have dashed out his name, and I shall put your father's in, \u2013 as soon as I get loose again!'\n\nThis again \u2013 how affecting was this!\n\n'And what,' cried he, 'has your father got, at last? nothing but that poor thing at Chelsea? O fie! fie! fie! But never mind! I will take care of him! I will do it myself!'\n\nThen presently he added, 'As to Lord Salisbury, he is out already, as this memorandum will show you, and so are many more. I shall be much better served; and when once I get away, I shall rule with a rod, of iron!'\n\nThis was very unlike himself, and startled the two good doctors, who could not bear to cross him, and were exulting at my seeing his great amendment, but yet grew quite uneasy at his earnestness and volubility.\n\nFinding we now must part, he stopped to take leave, and renewed again his charges about the coadjutrix. 'Never mind her!' he cried, 'depend upon me! I will be your friend as long as I live! I here pledge myself to be your friend!' And then he saluted me again just as at the meeting, and suffered me to go on.\n\n## _Jenner Discovers Smallpox Vaccination, 1796_\n\nEDWARD JENNER\n\n_Edward Jenner (1749\u20131823), a Gloucestershire country physician and amateur scientist, spent twenty years investigating a cure for smallpox._\n\nDuring the investigation of the casual Cow Pox, I was struck with the idea that it might be practicable to propagate the disease by inoculation, after the manner of the Small Pox, first from the Cow, and finally from one human being to another. I anxiously waited some time for an opportunity of putting this theory to the test. At length the period arrived. The first experiment was made upon a lad of the name of Phipps, in whose arm a little Vaccine Virus was inserted, taken from the hand of a young woman who had been accidentally infected by a cow. Notwithstanding the resemblance which the pustule, thus excited on the boy's arm, bore to variolous inoculation, yet as the indisposition attending it was barely perceptible, I could scarcely persuade myself the patient was secure from the Small Pox. However, on his being inoculated some months afterwards, it proved that he was secure. This Case inspired me with confidence; and as soon as I could again furnish myself with Virus from the Cow, I made an arrangement for a series of inoculations. A number of children were inoculated in succession, one from the other; and after several months had elapsed, they were exposed to the infection of the Small Pox; some by Inoculation, others by various effluvia and some in both ways; but they all resisted it. The distrust and scepticism which naturally arose in the minds of medical men, on my first announcing so unexpected a discovery has now nearly disappeared. Many hundreds of them, from actual experience, have given their attestations that the inoculated Cow Pox proves a perfect security against the Small Pox; and I shall probably be within compass if I say, thousands are ready to follow their example; for the scope that this inoculation has now taken is immense. An hundred thousand persons, upon the smallest computation, have been inoculated in these realms.\n\n## _The Battle of the Nile, 1 August 1798_\n\nJOHN NICHOL\n\n_Only a decade after the conclusion of the American War of Independence in 1783 Britain was again in arms. The enemy was the old one, France, though this time in new, Revolutionary garb and keen to export its republican ideology abroad on the end of a musket. The competence and fervour of the new French army trounced Britain and her allies on land, and only the Royal Navy \u2013 at Ushant, at Camperdown \u2013 prevented an actual invasion of the island. Despite the cruelties and poverties of life in the 'wooden world' of the Georgian Navy (which provoked mutinies at Nore and Spithead), English sailors were possessed foremost by patriotism and professionalism. The Navy crowned its glory in the French Revolutionary War in the fight at Aboukir Bay, just north-east of Alexandria. The battle of the Nile was the making of British dominance in the Mediterranean. And of Horatio Nelson._\n\n_John Nichol was in the gun crew of HMS_ Goliath.\n\nThe sun was just setting as we went into the bay, and a red and fiery sun it was. I would, if I had had my choice, been on the deck; there I would have seen what was passing, and the time would not have hung so heavy; but every man does his duty with spirit, whether his station be in the slaughter-house or in the magazine. (The seamen call the lower deck, near the main-mast, 'the slaughter-house', as it is amidships, and the enemy aim their fire principally at the body of the ship.) My station was in the powder-magazine with the gunner. As we entered the bay we stripped to our trousers, opened our ports, cleared, and every ship we passed gave them a broadside and three cheers. Any information we got was from the boys and women who carried the powder. They behaved as well as the men, and got a present for their bravery from the Grand Signior. When the French Admiral's ship blew up, the _Goliath_ got such a shake we thought the after-part of her had blown up until the boys told us what it was. They brought us every now and then the cheering news of another French ship having struck [surrendered], and we answered the cheers on deck with heartfelt joy. In the heat of the action, a shot came right into the magazine, but did no harm, as the carpenters plugged it up, and stopped the water that was rushing in. I was much indebted to the gunner's wife, who gave her husband and me a drink of wine every now and then, which lessened our fatigue much. There were some of the women wounded, and one woman belonging to Leith died of her wounds, and was buried on a small island in the bay. One woman bore a son in the heat of the action; she belonged to Edinburgh.\n\nWhen we ceased firing, I went on deck to view the state of the fleets, and an awful sight it was. The whole bay was covered with dead bodies, mangled, wounded, and scorched, not a bit of clothes on them except their trousers. There were a number of French, belonging to the French Admiral's ship, the _L'Orient,_ who had swam to the _Goliath,_ and were cowering under her forecastle. Poor fellows! they were brought on board, and Captain Foley ordered them down to the steward's room, to get provisions and clothing. One thing I observed in these Frenchmen quite different from anything I had before observed. In the American War, when we took a French ship, the _Duke de Chartres,_ the prisoners were as merry as if they had taken us, only saying, _'Fortune de guerre \u2013_ you take me today, I take you tomorrow.' Those we now had on board were thankful for our kindness, but were sullen and as downcast as if each had lost a ship of his own.\n\nThe only incidents I heard of are two. One lad who was stationed by a salt-box, on which he sat to give out cartridges, and keep the lid close \u2013 it is a trying berth \u2013 when asked for a cartridge, he gave none, yet he sat upright; his eyes were open. One of the men gave him a push; he fell all his length on the deck. There was not a blemish on his body, yet he was quite dead, and was thrown overboard. The other, a lad who had the match in his hand to fire his gun. In the act of applying it, a shot took off his arm; it hung by a small piece of skin. The match fell to the deck. He looked to his arm, and seeing what had happened, seized the match in his left hand, and fired off the gun before he went to the cockpit to have it dressed. They were in our mess, or I might never have heard of it. Two of the mess were killed, and I knew not of it until the day after. Thus terminated the glorious first of August, the busiest night in my life.\n\n_Before the battle Nelson (born 1758, son of a Norfolk clergyman) is reputed to have told his fellow officers that he would proceed from the Nile to a tomb or the House of Lords._\n\n_He was raised to the peerage as Baron Nelson of the Nile._\n\n## _Nelson Sees No Signal, Copenhagen, 2 April 1801_\n\nCOLONEL WILLIAM STEWART\n\n_Circumventing the order of his sixty-two-year-old commander, Admiral Hyde Parker, to withdraw, Nelson won a famous victory over the Danes, partners in an armed coalition against British interests in the Baltic._\n\nLord Nelson was at this time, as he had been during the whole Action, walking the starboard side of the quarter-deck; sometimes much animated, and at others heroically fine in his observations. A shot through the mainmast knocked a few splinters about us. He observed to me, with a smile, 'It is warm work, and this day may be the last to any of us at a moment'; and then stopping short at the gangway, he used an expression never to be erased from my memory, and said with emotion, 'but mark you, I would not be elsewhere for thousands.' When the signal, No. 39, was made, the Signal Lieutenant reported it to him. He continued his walk, and did not appear to take notice of it. The Lieutenant meeting his Lordship at the next turn asked, 'whether he should repeat it?' Lord Nelson answered, 'No, acknowledge it.' On the Officer returning to the poop, his Lordship called after him, 'Is No. 16 [the signal for close action] still hoisted?' The Lieutenant answering in the affirmative, Lord Nelson said, 'Mind you keep it so.' He now walked the deck considerably agitated, which was always known by his moving the stump of his right arm. After a turn or two, he said to me, in a quick manner, 'Do you know what's shown on board of the Commander-in-Chief, No. 39?' On asking him what that meant, he answered, 'Why, to leave off Action.' 'Leave off Action!' he repeated, and then added, with a shrug, 'Now, damn me if I do.' He also observed, I believe, to Captain Foley, 'You know, Foley, I have only one eye \u2013 I have a right to be blind sometimes', and then with an archness peculiar to his character, putting the glass to his blind eye, he exclaimed, 'I really do not see the signal.'\n\n_Nelson's battering of the Danes at Copenhagen (they lost seventeen warships) secured an armistice with the Baltic League and encouraged the French to agree the Peace of Amiens in March 1802. But this was no more than a buying of time; the renewed Continental aggression of the French began the Napoleonic War in May 1803. Once again the Royal Navy, like the whale, was the king of the sea._\n\n## _Wellington Meets Nelson, 10 September 1805_\n\nSIR ARTHUR WELLESLEY\n\n_Wellesley had not yet found the military fortune which would elevate him to the dukedom of Wellington._\n\nI went to the Colonial Office in Downing Street and there I was shown into the little waiting-room on the right hand, where I found, also waiting to see the Secretary of State, a gentleman whom, from his likeness to his pictures and the loss of an arm, I immediately recognized as Lord Nelson. He could not know who I was, but he entered at once into conversation with me, if I can call it conversation, for it was almost all on his side and all about himself, and in, really, a style so vain and so silly as to surprise and almost disgust me. I suppose something that I happened to say may have made him guess that I was _somebody,_ and he went out of the room for a moment, I have no doubt to ask the office-keeper who I was, for when he came back he was altogether a different man, both in manner and matter. All that I had thought a charlaton style had vanished, and he talked of the state of this country, and of the aspect and probabilities of affairs on the Continent with a good sense, and a knowledge of subjects both at home and abroad that surprised me... in fact he talked like an officer and a statesman. The Secretary of State kept us long waiting, and certainly, for the last half or three-quarters of an hour, I don't know that I ever had a conversation that interested me more. Now, if the Secretary of State had been punctual, and admitted Lord Nelson in the first quarter of an hour I should have had the same impression of a light and trivial character that other people have had.\n\n_Six weeks later Nelson met the combined fleet of France and Spain off the Spanish coast._\n\n## _Trafalgar: The Battle Opens, Morning 21 October 1805_\n\nMIDSHIPMAN BADCOCK RN\n\n_Britain's victory over the combined French and Spanish fleet at Trafalgar was the decisive naval engagement of the Napoleonic War; it also allowed Britain to rule the world's waves for two centuries. The combined fleet numbered thirty-three ships of the line and seven frigates; the Royal Navy had thirty-two ships of the line and five frigates. By the novel Nelson Touch' the British attacked the enemy line in two columns, at a 90-degree angle. Midshipman Badcock served aboard HMS_ Neptune.\n\nAt this period the enemy were forming their double line in the shape of a crescent. It was a beautiful sight when the line was completed: their broadsides turned towards us showing their iron teeth, and now and then trying the range of a shot to ascertain the distance, that they might, the moment we came within point-blank (about six hundred yards) open their fire upon our van ships \u2013 no doubt with the hope of dismasting some of our leading vessels before they could close and break their line.\n\nSome of the enemy's ships were painted like ourselves \u2013 with double yellow sides, some with a broad single red or yellow streak, others all black; and the noble _Santissima Trinidada_ (138) with four distinct lines of red, with a white ribbon between them, made her seem to be a superb man-of-war, which, indeed, she was. Her appearance was imposing, her head splendidly ornamented with a colossal group of figures, painted white, representing the Holy Trinity, from which she took her name. This magnificent ship was destined to be our opponent. She was lying to under topsails, top-gallant sails, royals, jib, and spanker; her courses were hauled up, and her lofty, towering sails looked beautiful, peering through the smoke as she awaited the onset. The flags of France and Spain, both handsome, chequered the line, waving defiance to that of Britain.\n\nIn our fleet Union Jacks and ensigns were made fast to the fore and fore-topmast-stays, as well as to the mizen rigging, besides one at the peak, in order that we might not mistake each other in the smoke, and to show the enemy our determination to conquer. Towards eleven our two lines were better formed, but still there existed long gaps in Vice-Admiral Collingwood's division. Lord Nelson's van was strong: three three-deckers \u2013 _Victory, T\u00e9m\u00e9raire,_ and _Neptune \u2013_ and four seventy-fours, their jib-booms nearly over the others' taffrails. The bands playing 'God Save the King', 'Rule Britannia', and 'Britons, Strike Home', the crews stationed on the forecastles of the different ships, cheering the ship ahead of them when the enemy began to fire, sent those feelings to our hearts that insured victory. About ten minutes before twelve, our antagonists opened their fire upon the _Royal Sovereign_ (no), Vice-Admiral Collingwood, who most nobly, and unsupported for at least ten minutes, led his division into action, steering for the _Santa Anna_ (112), which was painted all black, bearing the flag of Admiral Gravina, during which time all the enemy's line that could possibly bring a gun to bear were firing at her. She was the admiration of the whole fleet.\n\nTo show the great and master-mind of Nelson, who was thinking of everything, even in the momentous hour of battle, when most minds would have been totally absorbed in other matters, it was remarked by him that the enemy had the iron hoops round their masts painted black. Orders were issued by signal to whitewash those of his fleet, that in the event of all the ensigns being shot away, his ships might be distinguished by their white masts and hoops.\n\n## _Trafalgar: The Death of Nelson, Afternoon 21 October 1805_\n\nDR WILLIAM BEATTY\n\n_At Trafalgar, the Franco-Spanish combine lost twenty ships, destroyed or captured, the British none. But the British victory at Trafalgar came at high cost: the death of the forty-seven-year-old Admiral Lord Horatio Nelson._\n\n_Beatty was the surgeon aboard Nelson's flagship, HMS_ Victory.\n\nAbout half an hour before the enemy opened their fire, the memorable telegraphic signal was made, that 'ENGLAND EXPECTS EVERY MAN WILL DO HIS DUTY,' which was spread and received throughout the fleet with enthusiasm. It is impossible adequately to describe by any language the lively emotions excited in the crew of the _Victory_ when this propitious communication was made known to them: confidence and resolution were strongly portrayed in the countenance of all; and the sentiment generally expressed to each other was that they would prove to their country that day how well British seamen _could_ 'do their duty' when led to battle by their revered admiral.\n\nAt fifty minutes past eleven, the enemy opened their fire on the commander in chief. They shewed great coolness in the commencement of the battle; for as the _Victory_ approached their line, their ships lying immediately ahead of her and across her bows fired only one gun at a time, to ascertain whether she was yet within their range. This was frequently repeated by eight or nine of their ships, till at length a shot passed through the _Victory_ 's main topgallant sail; the hole in which being discovered by the enemy, they immediately opened their broadsides, supporting an awful and tremendous fire.\n\nIn a very short time afterwards, Mr Scott, public secretary to the commander in chief, was killed by a cannon shot while in conversation with Captain Hardy. Lord Nelson being then near them; Captain Adair of the marines, with the assistance of a seaman, endeavoured to remove the body from his Lordship's sight: but he had already observed the fall of his secretary; and now said with anxiety, 'Is that poor Scott that is gone?' and on being answered in the affirmative by Captain Adair, he replied, 'Poor fellow!'\n\nLord Nelson and Captain Hardy walked the quarter deck in conversation for some time after this, while the enemy kept up an incessant raking fire.\n\nA double-headed shot struck one of the parties of marines drawn up on the poop, and killed eight of them; when his Lordship, perceiving this, ordered Captain Adair to disperse his men round the ship, that they might not suffer so much from being together.\n\nIn a few minutes afterwards a shot struck the fore brace bits on the quarter deck, and passed between Lord Nelson and Captain Hardy; a splinter from the bits bruising Captain Hardy's foot, and tearing the buckle from his shoe. They both instantly stopped; and were observed by the officers on deck to survey each other with inquiring looks, each supposing the other to be wounded. His Lordship then smiled, and said: 'This is too warm work, Hardy, to last long'; and declared that 'through all the battles he had been in, he had never witnessed more cool courage than was displayed by the _Victory's_ crew on this occasion.'\n\nThe _Victory_ by this time, having approached close to the enemy's van, had suffered very severely without firing a single gun: she had lost about twenty men killed, and had about thirty wounded. Her mizzen topmast, and all her studding sails and their booms on both sides were shot away; the enemy's fire being chiefly directed at her rigging, with a view to disable her before she could close with them.\n\nAt four minutes past twelve o'clock, she opened her fire, from both sides of her decks, upon the enemy; when Captain Hardy represented to his Lordship, that 'it appeared impracticable to pass through the enemy's line without going on board some one of their ships.'\n\nLord Nelson answered, 'I cannot help it: it does not signify which we run on board of; go on board which you please; take your choice.'\n\nAt twenty minutes past twelve, the tiller ropes being shot away: Mr Atkinson, the master, was ordered below to get the helm put to port; which being done, the _Victory_ was soon run on board the _Redoubtable_ of seventy-four guns.\n\nOn coming alongside and nearly on board of her, that ship fired her broadside into the _Victory,_ and immediately let down her lower deck ports; which, as has been since learnt, was done to prevent her from being boarded through them by the _Victory's_ crew. She never fired a great gun after this single broadside.\n\nA few minutes after this, the _T\u00e9m\u00e9raire_ fell likewise on board of the _Redoubtable,_ on the side opposite to the _Victory;_ having also an enemy's ship, said to be _La Fougueux,_ on board of _her_ on her other side: so that the extraordinary and unprecedented circumstance occurred here, of _four_ ships of the line being _on board of each other_ in the heat of battle; forming as compact a tier as if they had been moored together, their heads lying all the same way. The _T\u00e9m\u00e9raire,_ as was just before mentioned, was between the _Redoubtable_ and _La Fougueux._\n\nThe _Redoubtable_ commenced a heavy fire of musketry from the tops, which was continued for a considerable time with destructive effect to the _Victory's_ crew: her great guns however being silent, it was supposed at different times that she had surrendered; and in consequence of this opinion, the _Victory_ twice ceased firing upon her by orders transmitted from the quarter deck.\n\nAt this period, scarcely a person in the _Victory_ escaped unhurt who was exposed to the enemy's musketry; but there were frequent huzzas and cheers heard from between the decks, in token of the surrender of different of the enemy's ships. An incessant fire was kept up from both sides of the _Victory:_ her larboard guns played upon the _Santissima Trinidada_ and the _Bucentaur;_ and the starboard guns of the middle and lower decks were depressed, and fired with a diminished charge of powder, and three shot each, into the _Redoubtable._ This mode of firing was adopted by Lieutenants Williams, King, Yule, and Brown, to obviate the danger of the _T\u00e9m\u00e9raire's_ suffering from the _Victory's_ shot passing through the _Redoubtable;_ which must have been the case if the usual quantity of powder, and the common elevation, had been given to the guns.\n\nA circumstance occurred in this situation which showed in a most striking manner the cool intrepidity of the officers and men stationed on the lower deck of the _Victory._ When the guns on this deck were run out, their muzzles came into contact with the _Redoubtable's_ side; and consequently at every discharge there was reason to fear that the enemy would take fire, and both the _Victory_ and the _T\u00e9m\u00e9raire_ be involved in her flames. Here then was seen the astonishing spectacle of the fireman of each gun standing ready with a bucket full of water, which as soon as his gun was discharged he dashed into the enemy through the holes made in her side by the shot.\n\nIt was from this ship (the _Redoubtable)_ that Lord Nelson received his mortal wound. About fifteen minutes past one o'clock, which was in the heat of the engagement, he was walking the middle of the quarterdeck with Captain Hardy, and in the act of turning near the hatchway with his face towards the stern of the _Victory,_ when the fatal ball was fired from the enemy's mizen-top; which, from the situation of the two ships (lying on board of each other), was brought just abaft, and rather below, the _Victory's_ main-yard, and of course not more than fifteen yards distant from that part of the deck where his Lordship stood. The ball struck the epaulette on his left shoulder, and penetrated his chest. He fell with his face on the deck. Captain Hardy, who was on his right (the side furthest from the enemy) and advanced some steps before his Lordship, on turning round, saw the Sergeant-Major (Secker) of Marines with two seamen raising him from the deck; where he had fallen on the same spot on which, a little before, his secretary had breathed his last, with whose blood his Lordship's clothes were much soiled. Captain Hardy expressed a hope that he was not severely wounded; to which the gallant Chief replied: 'They have done for me at last, Hardy.' 'I hope not,' answered Captain Hardy. 'Yes,' replied his Lordship, 'my backbone is shot through.'\n\nCaptain Hardy ordered the seamen to carry the Admiral to the cockpit; and now two incidents occurred strikingly characteristic of this great man, and strongly marking that energy and reflection which in his heroic mind rose superior even to the immediate consideration of his present awful condition. While the men were carrying him down the ladder from the middle deck, his Lordship observed that the tiller ropes were not yet replaced; and desired one of the midshipmen stationed there to go up on the quarterdeck and remind Captain Hardy of that circumstance, and request that new ones should be immediately rove. Having delivered this order, he took his handkerchief from his pocket and covered his face with it, that he might be conveyed to the cockpit at this crisis unnoticed by the crew...\n\nThe _Victory's_ crew cheered whenever they observed an enemy's ship surrender. On one of these occasions, Lord Nelson anxiously inquired what was the cause of it; when Lieutenant Pasco, who lay wounded at some distance from his Lordship, raised himself up, and told him that another ship had struck: which appeared to give him much satisfaction. He now felt an ardent thirst; and frequently called for drink, and to be fanned with paper, making use of these words: 'Fan, fan,' and 'Drink, drink.' This he continued to repeat, when he wished for drink or the refreshment of cool air, till a very few minutes before he expired...\n\nHis Lordship now requested the surgeon, who had been previously absent a short time attending Mr Rivers to return to the wounded, and give his assistance to such of them as he could be useful to; 'for,' said he, 'you can do nothing for me.' The surgeon assured him that the assistant surgeons were doing everything that could be effected for those unfortunate men; but on his Lordship's several times repeating his injunctions to that purpose, he left him, surrounded by Doctor Scott, Mr Burke and two of his Lordship's domestics. After the surgeon had been absent a few minutes attending Lieutenants Peake and Reeves of the Marines, who were wounded, he was called by Doctor Scott to his Lordship, who said: 'Ah, Mr Beatty! I have sent for you to say, what I forgot to tell you before, that all power of motion and feeling below my breast are gone; and _you,_ ' continued he, 'very well _know_ I can live but a short time.' The emphatic manner in which he pronounced these last words left no doubt in the surgeon's mind, that he adverted to the case of a man who had some months before received a mortal injury of the spine on board the _Victory,_ and had laboured under similar privations of sense and muscular motion. The case had made a great impression on Lord Nelson: he was accordingly explained to him; and he now appeared to apply the situation and fate of this man to himself. The surgeon answered, 'My Lord, you told me so before': but he now examined the extremities, to ascertain the fact; when his Lordship said, 'Ah, Beatty! I am too certain of it: Scott and Burke have tried it already. _You know_ I am gone.' The surgeon replied: 'My Lord, unhappily for our country, nothing can be done for you', and having made this declaration he was so much affected, that he turned round and withdrew a few steps to conceal his emotions. His Lordship said: 'I know it. I feel something rising in my breast,' putting his hand on his left side, 'which tells me I am gone.' Drink was recommended liberally, and Doctor Scott and Mr Burke fanned him with paper. He often exclaimed, 'God be praised, I have done my duty': and upon the surgeon's inquiring whether his pain was still very great, he declared, it continued so very severe, that he wished he was dead. 'Yet,' said he in a lower voice, 'one would like to live a little longer, too': and after a pause of a few minutes, he added in the same tone, 'What would become of poor Lady Hamilton (Nelson's mistress), if she knew my situation!'...\n\nCaptain Hardy now came to the cockpit to see his Lordship a second time, which was after an interval of about fifty minutes from the conclusion of his first visit. Before he quitted the deck, he sent Lieutenant Hills to acquaint Admiral Collingwood with the lamentable circumstance of Lord Nelson's being wounded. Lord Nelson and Captain Hardy shook hands again: and while the Captain retained his Lordship's hand, he congratulated him, even in the arms of death, on his brilliant victory; 'which,' said he, 'was complete'; though he did not know how many of the enemy were captured, as it was impossible to perceive every ship distinctly. He was certain however of fourteen or fifteen having surrendered. His Lordship answered, 'That is well, but I bargained for twenty': and then emphatically exclaimed, _'Anchor,_ Hardy, _anchor!'_ To this the Captain replied: 'I suppose, my Lord, Admiral Collingwood will now take upon himself the direction of affairs.' 'Not while I live, I hope, Hardy!' cried the dying chief; and at that moment endeavoured ineffectually to raise himself from the bed. 'No,' added he; 'do _you_ anchor, Hardy.' Captain Hardy then said: 'Shall _we_ make the signal, sir?' 'Yes,' answered his Lordship, 'for if I live, I'll anchor.' The energetic manner in which he uttered these his last orders to Captain Hardy, accompanied with his efforts to raise himself, evinced his determination never to resign the command while he retained the exercise of his transcendent faculties, and that he expected Captain Hardy still to carry into effect the suggestions of his exalted mind; a sense of his duty overcoming the pains of death. He then told Captain Hardy, he felt that in a few minutes he should be no more; adding in a low tone, 'Don't throw me overboard, Hardy.' The Captain answered: 'Oh! no, certainly not', 'Then,' replied his Lordship, 'You know what to do: and', continued he, 'take care of my dear Lady Hamilton, Hardy: take care of poor Lady Hamilton. Kiss me, Hardy.' The Captain now knelt down, and kissed his cheek; when his Lordship said, 'Now I am satisfied. Thank God, I have done my duty.' Captain Hardy stood for a minute or two in silent contemplation: he knelt down again, and kissed his Lordship's forehead. His Lordship said: 'Who is that?' The Captain answered: 'It is Hardy'; to which his Lordship replied, 'God bless you, Hardy!'... His thirst now increased; and he called for 'drink, drink,' 'fan, fan,' and 'rub, rub,' addressing himself in the last case to Doctor Scott, who had been rubbing his Lordship's breast with his hand, from which he found some relief. These words he spoke in a very rapid manner, which rendered his articulation difficult: but he every now and then, with evident increase of pain, made a greater effort with his vocal powers, and pronounced distinctly these last words: 'Thank God, I have done my duty'; and this great sentiment he continued to repeat as long as he was able to give it utterance.\n\n_As Nelson had requested, he did not suffer the usual indignity of the dead Jack Tar, to be heaved overboard. Instead his body was preserved in a cask of brandy and brought back to England for a state funeral. The outpouring of grief by the British public was unprecedented, and nothing like it would be seen again until the death of Diana, Princess of Wales, almost 200 years later._\n\n## _The Peninsular War: Plundering a Dead French Soldier after the Battle of Vimeiro, 21 August 1808_\n\nRIFLEMAN HARRIS\n\n_The Peninsular War (1808\u201313) was the principal British contribution to the land campaign against Bonaparte. The war opened with a Spanish revolt against Napoleon's attempt to install his brother Joseph as King of Spain; at Spanish request the British landed an expeditionary force in Iberia under Sir Arthur Wellesley._\n\n_At Vimeiro, Portugal, Wellesley carefully selected a defensive position \u2013 and let the French attack. They sustained 2,000 casualties. Plenty of pickings, therefore, for the jackdaw-like British soldier._\n\n_Rifleman Harris served with the 95th Rifles._\n\nAfter the battle I strolled about the field in order to see if there was anything to be found worth picking up amongst the dead. The first thing I saw was a three-pronged silver fork, which, as it lay by itself, had most likely been dropped by some person who had been on the look-out before me. A little further on I saw a French soldier sitting against a small rise in the ground or bank. He was wounded in the throat, and appeared very faint, the bosom of his coat being saturated with the blood which had flowed down. By his side lay his cap, and close to that was a bundle containing a quantity of gold and silver crosses, which I concluded he had plundered from some convent or church. He looked the picture of a sacrilegious thief, dying hopelessly, and overtaken by Divine wrath. I kicked over his cap, which was also full of plunder, but I declined taking anything from him. I felt fearful of incurring the wrath of Heaven for the like offence, so I left him, and passed on. A little further off lay an officer of the 50th regiment. I knew him by sight, and recognized him as he lay. He was quite dead, and lying on his back. He had been plundered, and his clothes were torn open. Three bullet-holes were close together in the pit of his stomach: beside him lay an empty pocket-book, and his epaulette had been pulled from his shoulder.\n\nI had moved on but a few paces when I recollected that perhaps the officer's shoes might serve me, my own being considerably the worse for wear, so I returned again, went back, pulled one of his shoes off, and knelt down on one knee to try it on. It was not much better than my own; however, I determined on the exchange, and proceeded to take off its fellow. As I did so I was startled by the sharp report of a firelock, and, at the same moment, a bullet whistled close by my head. Instantly starting up, I turned, and looked in the direction whence the shot had come. There was no person near me in this part of the field. The dead and the dying lay thickly all around; but nothing else could I see. I looked to the priming of my rifle, and again turned to the dead officer of the 50th. It was evident that some plundering scoundrel had taken a shot at me, and the fact of his doing so proclaimed him one of the enemy. To distinguish him amongst the bodies strewn about was impossible; perhaps he might himself be one of the wounded. Hardly had I effected the exchange, put on the dead officer's shoes, and resumed my rifle, when another shot took place, and a second ball whistled past me. This time I was ready, and turning quickly, I saw my man: he was just about to squat down behind a small mound, about twenty paces from me. I took a haphazard shot at him, and instantly knocked him over. I immediately ran up to him; he had fallen on his face, and I heaved him over on his back, bestrode his body, and drew my sword-bayonet. There was, however, no occasion for the precaution as he was even then in the agonies of death.\n\nIt was a relief to me to find I had not been mistaken. He was a French light-infantry man, and I therefore took it quite in the way of business \u2013 he had attempted my life, and lost his own. It was the fortune of war; so, stooping down, with my sword I cut the green string that sustained his calibash, and took a hearty pull to quench my thirst.\n\nAfter I had shot the French light-infantry man, and quenched my thirst from his calibash, finding he was quite dead, I proceeded to search him. Whilst I turned him about in the endeavour at finding the booty I felt pretty certain he had gathered from the slain, an officer of the 60th approached, and accosted me.\n\n'What! looking for money, my lad,' said he, 'eh?'\n\n'I am, sir,' I answered; 'but I cannot discover where this fellow has hid his hoard.'\n\n'You knocked him over, my man,' he said, 'in good style, and deserve something for the shot. Here,' he continued, stooping down and feeling in the lining of the Frenchman's coat, 'this is the place where these rascals generally carry their coin. Rip up the lining of his coat, and then search in his stock. I know them better than you seem to do.'\n\nThanking the officer for his courtesy, I proceeded to cut open the lining of his jacket with my sword-bayonet, and was quickly rewarded for my labour by finding a yellow silk purse, wrapped up in an old black silk handkerchief. The purse contained several doubloons, three or four napoleons, and a few dollars. Whilst I was counting the money, the value of which, except the dollars, I did not then know, I heard the bugle of the Rifles sound out the assembly, so I touched my cap to the officer, and returned towards them.\n\nThe men were standing at ease, with the officers in front. As I approached them, Major Travers, who was in command of the four companies, called me to him.\n\n'What have you got there, sir?' he said. 'Show me.'\n\nI handed him the purse, expecting a reprimand for my pains. He, however, only laughed as he examined it, and, turning, showed it to his brother officers.\n\n'You did that well, Harris,' he said, 'and I am sorry the purse is not better filled. Fall in.' In saying this, he handed me back the purse, and I joined my company. Soon afterwards, the roll being called, we were all ordered to lie down and gain a little rest after our day's work.\n\n## _The Peninsular War: The Storming of Badajoz, 6 April 1812_\n\nROBERT BLAKENEY\n\n_Badajoz was a fortress in the south of French-occupied Spain. Only three months earlier British troops in the Peninsula had stormed another French stronghold, Ciudad Rodrigo._\n\nThe dreadful strife now commenced. The thundering cheer of the British soldiers as they rushed forward through the outer ditch, together with the appalling roar of all arms sent forth in defiance from within, was tremendous. Whenever an instant pause occurred it was filled by the heart-rending shrieks of the trodden-down wounded and by the lengthened groans of the dying. Three times were the breaches cleared of Frenchmen, driven off at the point of the bayonet by gallant British soldiers to the very summit, when they were by the no less gallant foe each time driven back, leaving their bravest officers and foremost soldiers behind, who, whether killed or wounded, were tossed down headlong to the foot of the breaches. Throughout this dreadful conflict our bugles were continually sounding the advance. The cry of 'Bravo! Bravo!' resounded through the ditches and along the foot of the breaches; but no British cry was heard from within the walls of Badajoz save that of despair, uttered by the bravest, who despite of all obstacles forced their way into the body of the place, and there through dire necessity abandoned, groaned forth their last stabbed by unnumbered wounds. Again and again were the breaches attacked with redoubled fury and defended with equal pertinacity and stern resolution, seconded by every resource which science could adopt or ingenuity suggest. Bags and barrels of gunpowder with short fuses were rolled down, which, bursting at the bottom or along the face of the breaches, destroyed all who advanced. Thousands of live shells, hand-grenades, fireballs and every species of destructive combustible were thrown down the breaches and over the walls into the ditches, which, lighting and exploding at the same instant, rivalled the lightning and thunder of heaven. This at intervals was succeeded by an impenetrable darkness as of the infernal regions. Gallant foes laughing at death met, fought, bled and rolled upon earth; and from the very earth destruction burst, for the exploding mines cast up friends and foes together, who in burning torture clashed and shrieked in the air. Partly burned they fell back into the inundating water, continually lighted by the incessant bursting of shells...\n\nAt length the bugles of the 4th and light divisions sounded the recall... I galloped off to where Lord Wellington had taken his station. This was easily discerned by means of two fireballs shot out from the fortress at the commencement of the attack, which continued to burn brilliantly along the water-cut.... Near the end of this channel, behind a rising mound, were Lord Wellington and his personal staff, screened from the enemy's direct fire, but within the range of shells. One of his staff sat down by his side with a candle to enable the general to read and write all his communications and orders... I stood not far from his lordship. But due respect prevented any of us bystanders from approaching so near as to enable us to ascertain the import of the reports which he was continually receiving; yet it was very evident that the information which they conveyed was far from flattering; and the recall on the bugles was again and again repeated. But about half-past eleven o'clock an officer rode up at full speed on a horse covered with foam, and announced the joyful tidings that General Picton had made a lodgment within the castle by escalade, and had withdrawn the troops from the trenches to enable him to maintain his dearly purchased hold. Lord Wellington was evidently delighted... I mounted my horse... and then made the best of my way to the walls of the castle; their height was rather forbidding, and an enfilading fire still continued. The ladders were warm and slippery with blood and brains of many a gallant soldier.\n\n_After capturing Badajoz Wellesley's 'scum of the earth' ran amok inside the town. On entering, James McGrigor, Wellington's medical officer, found: 'the whole of the soldiers appeared to be in a state of mad drunkenness. In every street, and in every corner we met them forcing their way like furies into houses... In passing some houses which they had entered we heard the shrieks of females, and sometimes the groans of those they were no doubt butchering...' It was twenty-nine hours before the troops were brought under control._\n\n## _Waterloo: Taken Prisoner, 18 June 1815_\n\nENSIGN EDMUND WHEATLEY\n\n_Waterloo was the final battle of Napoleon's Hundred Days, his last grasp at glory. He commanded an army of 80,000; the Allied Army under Wellington consisted of 67,000 men. As was the wont of the Duke of Wellington he positioned his force carefully, along a line of hills. There were two advance posts: the farms at La Haye Sainte and Hougemont._\n\nAbout ten o'clock, the order came to clean out the muskets and fresh load them. Half an allowance of rum was then issued, and we descended into the plain, and took our position in solid Squares. When this was arranged as per order, we were ordered to remain in our position but, if we like, to lay down, which the battalion did [as well as] the officers in the rere.\n\nI took this opportunity of surveying our situation. It was singular to perceive the shoals of Cavalry and artillery suddenly in our rere all arranged in excellent order as if by a magic wand. The whole of the horse Guards stood behind us. For my part I thought they were at Knightsbridge barracks or prancing on St James's Street.\n\nA Ball whizzed in the air. Up we started simultaneously. I looked at my watch. It was just eleven o'clock, Sunday... morning. In five minutes a stunning noise took place and a shocking havock commenced.\n\nOne could almost feel the undulation of the air from the multitude of cannon shot. The first man who fell was five files on my left. With the utmost distortion of feature he lay on his side and shrivelling up every muscle of the body he twirled his elbow round and round in acute agony, then dropped lifeless, dying as it's called a death of glory, heaving his last breath on the field of fame. _Dieu m'engarde!_\n\nA black consolidated body was soon seen approaching and we distinguished by sudden flashes of light from the sun's rays, the iron-cased cavalry of the enemy. Shouts of 'Stand firm!' 'Stand fast!' were heard from the little squares around and very quickly these gigantic fellows were upon us.\n\nNo words can convey the sensation we felt on seeing these heavy-armed bodies advancing at full gallop against us, flourishing their sabres in the air, striking their armour with the handles, the sun gleaming on the steel. The long horse hair, dishevelled by the wind, bore an appearance confounding the senses to an astonishing disorder. But we dashed them back as coolly as the sturdy rock repels the ocean's foam. The sharp-toothed bayonet bit many an adventurous fool, and on all sides we presented our bristly points like the peevish porcupines assailed by clamorous dogs.\n\nThe horse Guards then came up and drove them back; and although the sight is shocking 'tis beautiful to see the skirmish of Cavalry.\n\nThe French made repeated attacks of this kind. But we stood firm as the ground we stood on, and two long hours were employed in these successive attacks.\n\nAbout two o'clock the cavalry ceased annoying and the warfare took a new turn. In order to destroy our squares, the enemy filled the air with shells, howitzers and bombs, so that every five or six minutes, the whole Battalion lay on its face then sprang up again when the danger was over.\n\nThe Prince of Orange gallop'd by, screaming out like a new born infant, 'Form into line! Form into line!' And we obeyed.\n\nAbout this time the battle grew faint and a mutual cannonade with musketry amused us for one and a half hours, during which time I walked up and down chatting and joking with the young officers who had not until then smelt powder.\n\nAn ammunition cart blew up near us, smashing men and horses. I took a calm survey of the field around and felt shocked at the sight of broken armour, lifeless bodies, murdered horses, shattered wheels, caps, helmets, swords, muskets, pistols, still and silent. Here and there a frightened horse would rush across the plain trampling on the dying and the dead. Three or four poor wounded animals standing on three legs, the other dangling before them. We killed several of these unfortunate beasts and it would have been an equal Charity to have perform'd the same operation on the wriggling, feverish, mortally lacerated soldiers as they rolled on the ground.\n\nAbout four o'clock the battle was renewed with uncommon ardour. We still stood in line. The carnage was frightful. The balls which missed us mowed down the Dutch behind us, and swept away many of the closely embattled Cavalry behind them.\n\nI saw a cannon ball take away a Colonel of the Nassau Regiment so cleanly that the horse never moved from under him. While I was busy in keeping the men firm in their ranks, closing up the vacuities as the balls swept off the men, inspecting the fallen to detect deception or subterfuge, a regiment of Cuirassiers darted like a thunderbolt among us. At the instant a squadron of horse Guards dashed up to our rescue. In the confusion of the moment I made for the Colors to defend them. And we succeeded with infinite difficulty in rallying the men again.\n\nI parried with great good fortune a back stroke from a horseman as he flew by me and Captain Sander had a deep slice from the same fellow on the head the instant after.\n\nThe battalion once more formed into a solid square, in which we remained the whole afternoon.\n\nI felt the ardor of the fight increase very much within me, from the uncommon fury of the engagement.\n\nJust then I fired a slain soldier's musket until my shoulder was nearly jellied and my mouth was begrimed with gunpowder to such a degree that I champed the gritty composition unknowingly.\n\nNothing could equal the splendor and terror of the scene. Charge after charge succeeded in constant succession. The clashing of swords, the clattering of musketry, the hissing of balls, and shouts and clamours produced a sound, jarring and confounding the senses, as if hell and the Devil were in evil contention.\n\nAbout this time I saw the Duke of Wellington running from a charge of Cavalry towards the Horse-Guards, waving his hat to beckon them to the encounter.\n\nAll our artillery in front fell into the French power, the bombardiers skulking under the carriages. But five minutes put them again into our hands and the men creeping out applied the match and sent confusion and dismay into the retreating enemy.\n\nSeveral times were these charges renewed and as often defeated. Charge met charge and all was pellmell. The rays of the sun glittered on the clashing swords as the two opposing bodies closed in fearful combat and our balls clattered on the shining breastplates like a hail shower.\n\nAs I stood in the square I looked down, I recollect, to take a pinch of snuff and thought of the old ballad, which I had seen somewhere, of the aged Nurse who describes the glorious battles of Marlborough to the child. After each relation of valor and victory, the infant says:\n\n'Ten thousand slain you say and more?\n\nWhat did they kill each other for?'\n\n'Indeed I cannot tell,' said she,\n\n'But 'twas a famous victory.'\n\nThe field was now thickened with heaps of bodies and shattered instruments. Carcases of men and beasts lay promiscuously entwined. Aide-de-Camps scoured across with inconceivable velocity. All was hurry and indefatigable exertion. The small squares on our right kept up incessant firings and the fight was as obstinate as at the commencement.\n\nThe Duke of Wellington passed us twice, slowly and coolly.\n\nNo advantage as yet was discernible on either side. The French Cavalry were less annoying. Their brave, repeated assaults had cost them very dear.\n\nAbout six o'clock a passe-parole ran down the line \u2013 not to be disheartened, as the Prussians were coming up to our left, which news we received with loud cheers. And on looking to the left I perceived at some distance a dark swarm moving out of a thick wood. In twenty minutes a fresh cannonading began as if in rere of the French and the battle raged with increased vehemence.\n\nA French Regiment of Infantry before us opposite the Farm house called the holy hedge (La Haye Sainte) advanced considerably just then and poured a destructive fire into our Battalion.\n\nColonel Ompteda ordered us instantly into line to charge, with a strong injunction to 'walk' forward, until he gave the word. When within sixty yards he cried 'Charge', we ran forward huzzaing. The trumpet sounded and no one but a soldier can describe the thrill one instantly feels in such an awful moment. At the bugle sound the French stood until we just reached them. I ran by Colonel Ompteda who cried out, 'That's right, Wheatley!'\n\nI found myself in contact with a French officer but ere we could decide, he fell by an unknown hand. I then ran at a drummer, but he leaped over a ditch through a hedge in which he stuck fast. I heard a cry of, 'The Cavalry! The Cavalry!' But so eager was I that I did not mind it at the moment, and when on the eve of dragging the Frenchman back (his iron-bound hat having saved him from a Cut) I recollect no more. On recovering my senses, I look'd up and found myself, bareheaded, in a clay ditch with a violent head-ache. Close by me lay Colonel Ompteda on his back, his head stretched back with his mouth open; and a hole in his throat. A Frenchman's arm across my leg.\n\nSo confused was I that I did not remember I was on the field of Battle at the moment. Lifting up a little, I look'd over the edge of the ditch and saw the backs of a French Regiment and all the day's employment instantly suggested itself to my mind. Suddenly I distinguished some voices and heard one say _'En voici! En voici!'_\n\nI lay down as dead, retaining my breath, and fancied I was shot in the back of my head. Presently a fellow cries, _'Voici un autre b.'_ And a tug at my epaulette bespoke his commission. A thought struck me \u2013 he would turn me round to rifle my pockets. So starting up, I leaped up the ditch; but a swimming seized me and I was half on the ground when the fellow thrust his hand in my collar, grinning, 'Ou _va's tu, chien?'_ I begged of him to let me pick up my cap and he dragged me into the house.\n\nThe inside of La Haye Sainte I found completely destroyed, nothing but the rafters and props remaining. The floor, covered with mortar bricks and straw, was strewed with bodies of the German Infantry and French Tirailleurs. A Major in Green lay by the door. The carnage had been very great in this place.\n\nI was taken over these bodies out of a door on the right, through a garden to the back of the house where I found several Officers and men standing. They instantly crowded round me. One of my wings was on and the other half off. My oil skin haversac was across my shoulder, and my cap fastened to my waist, by running my sash through the internal lining.\n\nA multitude of questions was put to me by the men and Officers while I fastened on my Cap: ' _Vous \u00eates Chef de Battalion, Monsieur?'..._\n\n_It was bad luck on Wheatley to be taken prisoner mere minutes before Wellington began the advance which finally won the 'damned close run thing'._\n\n## _Waterloo: The Final Attack; The Rifle Brigade Advance, 7 p.m., 18 June 1815_\n\nCAPTAIN J. KINCAID, RIFLE BRIGADE\n\nI shall never forget the scene which the field of battle presented about seven in the evening. I felt weary and worn out, less from fatigue than anxiety.\n\nOur division, which had stood upwards of 5,000 men at the commencement of the battle, had gradually dwindled down into a solitary line of skirmishers. The 27th regiment were lying literally dead, in square, a few yards behind us. My horse had received another shot through the leg, and one through the flap of the saddle, which lodged in his body, sending him a step beyond the pension list. The smoke still hung so thick about us that we could see nothing. I walked a little way to each flank to endeavour to get a glimpse of what was going on; but nothing met my eye except the mangled remains of men and horses, and I was obliged to return to my post as wise as I went.\n\nI had never yet heard of a battle in which everybody was killed; but this seemed likely to be an exception, as all were going by turns...\n\nPresently a cheer which we knew to be British commenced far to the right, and made everyone prick up his ears; it was Lord Wellington's long-wished-for orders to advance. It gradually approached, growing louder as it grew near. We took it up by instinct, charged through the hedge down upon the old knoll, sending our adversaries flying at the point of the bayonet. Lord Wellington galloped up to us at the instant, and our men began to cheer him; but he called out, 'No cheering, my lads, but forward, and complete our victory!'\n\nThis movement had carried us clear of the smoke; and to people who had been so many hours enveloped in darkness, in the midst of destruction, and naturally anxious about the result of the day, the scene which now met the eye conveyed a feeling of more exquisite gratification than can be conceived. It was a fine summer evening just before sunset. The French were flying in one confused mass. British lines were seen in close pursuit, and in admirable order, as far as the eye could reach to the right, while the plain to the left was filled with Prussians. The enemy made one last attempt at a stand on the rising ground to our right of La Belle Alliance; but a charge from General Adam's Brigade again threw them into a state of confusion, which was now inextricable, and their ruin was complete. Artillery, baggage, and everything belonging to them, fell into our hands. After pursuing them until dark, we halted about two miles beyond the field of battle, leaving the Prussians to follow up the victory.\n\n_Nelson and Wellington aside, the British won the 'Great War' (as contemporaries called the bull-dogged, twenty-year conflict against Boney and expansionist republican France) because the Industrial Revolution had given them a bigger wallet to spend on the conflict and an infinitely greater capacity to produce military_ materiel. _(Ironic proof of this was provided by Napoleon himself, who resorted to furnishing his troops with British-made boots, smuggled in from Germany, when French manufacturers could not meet the Grand Army's demand.) Victory, meanwhile, allowed the uninterrupted expansion of the Empire, into the DutchEast Indies, Ceylon, Egypt and South Africa. England was the strongest power on earth._\n\n_Not that everything in the English garden was rosy. The National Debt reached \u00a3861,000 and there was unrest in town and country, some of it violent, which was matched by counter-reaction by the authorities. As Fowell Buxton reminded the Commons in 1819, George II's reign had seen 'more crimes... denounced as capital [offences]... than in the reigns of the Plantagenets, the Tudors, and the Stuarts combined'. Thankfully, that last resort of English common sense and liberty, the jury system, hesitated to return guilty verdicts in capital cases. Paradoxically, it was in this period of reaction that the English began to apply Christian ethics to social miseries. There was nothing new about the ills (there had been slums, after all, in London since medieval times); what was novel was the belief that they should and could be dealt with._\n\n## _Factory Conditions, c. 1815_\n\nELIZABETH BENTLEY\n\n_The evidence of a female mill-hand to the Parliamentary Commissioners._\n\n_What age are you?_\n\nTwenty-three.\n\n_Where do you live?_\n\nAt Leeds.\n\n_What time did you begin work at the factory?_\n\nWhen I was six years old.\n\n_At whose factory did you work?_\n\nMr Burk's.\n\n_What kind of mill is it?_\n\nFlax mill.\n\n_What was your business in that mill?_\n\nI was a little doffer.\n\n_What were your hours of labour in that mill?_\n\nFrom 5 in the morning till 9 at night, when they were thronged.\n\n_For how long a time together have you worked that excessive length of time?_\n\nFor about a year.\n\n_What were the usual hours of labour when you were not so thronged?_\n\nFrom six in the morning till 7 at night.\n\n_What time was allowed for meals?_\n\nForty minutes at noon.\n\n_Had you any time to get your breakfast or drinking?_\n\nNo, we had to get it as we could.\n\n_Do you consider doffing a laborious employment?_\n\nYes.\n\n_Explain what you had to do?_\n\nWhen the frames are full, they have to stop the frames, and take the flyers off, and take the full bobbins off, and carry them to the roller, and then put empty ones on, and set the frame going again.\n\n_Does that keep you constantly on your feet?_\n\nYes, there are so many frames and they run so quick.\n\n_Your labour is very excessive?_\n\nYes, you have not time for anything.\n\n_Suppose you flagged a little, or were late, what would they do?_\n\nStrap us.\n\n_And they are in the habit of strapping those who are last in doffing?_\n\nYes.\n\n_Constantly?_\n\nYes.\n\n_Girls as well as boys?_\n\nYes.\n\n_Have you ever been strapped?_\n\nYes.\n\n_Severely?_\n\nYes.\n\n_Is the strap used so as to hurt you excessively?_\n\nYes it is... I have seen the overlooker go to the top end of the room, where the little girls hug the can to the backminders; he has taken a strap, and a whistle in his mouth, and sometimes he has got a chain and chained them, and strapped them all down the room.\n\n_What was his reason for that?_\n\nHe was very angry.\n\n_Did you live far from the mill?_\n\nYes, two miles.\n\n_Had you a clock?_\n\nNo, we had not.\n\n_Were you generally there in time?_\n\nYes, my mother has been up at 4 o'clock in the morning, and at 2 o'clock in the morning; the colliers used to go to their work at 3 or 4 o'clock, and when she heard them stirring she has got up out of her warm bed, and gone out and asked them the time; and I have sometimes been at Hunslet Car at 2 o'clock in the morning, when it was streaming down with rain, and we have had to stay till the mill was opened.\n\n_You are considerably deformed in person as a consequence of this labour?_\n\nYes I am.\n\n_And what time did it come on?_\n\nI was about 13 years old when it began coming, and it has got worse since; it is five years since my mother died, and my mother was never able to get me a good pair of stays to hold me up, and when my mother died I had to do for myself, and got me a pair.\n\n_Were you perfectly straight and healthy before you worked at a mill?_\n\nYes, I was as straight a little girl as ever went up and down town.\n\n_Were you straight till you were 13?_\n\nYes, I was.\n\n_Did your deformity come upon you with much pain and weariness?_\n\nYes, I cannot express the pain all the time it was coming.\n\n_Do you know of anybody that has been similarly injured in their health?_\n\nYes, in their health, but not many deformed as I am.\n\n_It is very common to have weak ankles and crooked knees?_\n\nYes, very common indeed.\n\n_This is brought on by stopping the spindle?_\n\nYes.\n\n_Where are you now?_\n\nIn the poorhouse.\n\n_State what you think as to the circumstances in which you have been placed during all this time of labour, and what you have considered about it as to the hardship and cruelty of it._\n\n_The witness was too much affected to answer the question._\n\n* * *\n\n_Reformers convinced Parliament to pass the Factory Act in 1819 which banned the employment of children under nine in cotton mills; at the instigation of Lord Shaftesbury, an 1833 Factory Act fixed a maximum forty-eight-hour week for children aged nine to thirteen, and a sixty-eight-hour week for under eighteen-year-olds._\n\n## _Climbing Boys, 1817_\n\nJOHN COOK\n\n_The use of climbing boys to clean chimneys had been banned by legislation as early as 1788, but this was honoured only in the breach. Cook was a master sweep called to give evidence before a House of Commons Select Committee on Climbing Boys._\n\nDo you give more for children that are delicately formed, and who therefore are better calculated for ascending small chimneys? \u2013 The smaller they are the master generally likes them the better, because they are generally more serviceable to them.\n\nSo that a small boy bears a better price than a full grown boy? \u2013 Yes, if he is strong enough to do the duty, and is a hearty looking boy of his age.\n\nIs it not the practice of some masters to advertise themselves as being in possession of small boys for the purpose of ascending flues? \u2013 Almost every one has got it in their bills, that they keep small boys for register stoves, and such like as that; I do not recollect ever seeing it in the newspapers, but they do it in their bills.\n\nHow do you ascertain the age of the boy when he is offered to you as an apprentice; do you take the parents' word for it? \u2013 The parents will often say that he is older than what he is.\n\nAre you in the habit of getting any other evidence of their ages than the parents' own words? \u2013 No.\n\nAre the boys ever washed? \u2013 Yes, I wash mine regularly; but some of the lower class are not washed for six months.\n\nDo they receive any education? \u2013 Many do not.\n\nIs it a general practice to attend divine worship? \u2013 Great numbers are neither washed nor attend on the Sunday.\n\nAre not climbing boys subject to sores and bruises, and wounds and burns on their thighs and knees, in consequence of ascending chimneys? \u2013 Yes, because learning very fresh boys makes their knees and elbows very sore, but when they have properly learnt their trade these parts get very hard, and they very seldom get sore again unless they meet with an accident; sometimes they get burnt by chimneys partly on fire.\n\nThe committee understand, by use, that the extremities of the elbows and of the knees become as hard as the heel of the foot of a person who walks without shoes? \u2013 Yes, it does.\n\nWhat time does it take before those parts get cartilaginous? \u2013 Six months.\n\nDo you find many boys show great repugnance to go up at first? \u2013 Yes, most of them do.\n\nAnd if they resist and reject, in what way do you force them up? \u2013 By telling them we must take them back again to their father and mother, and give them up again; and their parents are generally people who cannot maintain them.\n\nSo that they are afraid of going back to their parents for fear of being starved? \u2013 Yes; they go through a deal of hardship before they come to our trade.\n\nDo you use any more violent means? \u2013 Sometimes a rod. When I was an apprentice, journeymen often used to keep a cat, made of rope, hard at each end and as thick as your thumb, in their pocket to flog the boys; and I think it is sometimes used now.\n\nHave you ever known a journeyman ill-use any of the children? \u2013 Yes, for very little faults they will frequently kick them and smack them about; the boys are more afraid of them than of their masters.\n\nYou said that the elbows and knees of the boys, when they first begin the business, become very sore, and afterwards get callous; are those boys employed in sweeping chimneys during the soreness of those parts? \u2013 It depends upon the sort of master they have got; you must keep them a little at it, or they will never learn their business, even during the sores.\n\nIs the skin broke generally? \u2013 Yes, it is...\n\n_Despite the findings of the Select Committee, it was not until Lord Salisbury's Chimney Sweepers Bill of 1875 that the employment of climbing boys was both forbidden and enforced._\n\n## _Peterloo, 16 August 1819_\n\nSAMUEL BAMFORD\n\n_Some 60,000 people marched to the Suffrage Reform meeting at St Peter's Fields, Manchester. Eleven were killed when, on the orders of local magistrates, troops of the Cheshire volunteers, the Manchester Yeomanry, and the 15th Hussars rode into the crowd to arrest the speaker, Henry Hunt._\n\n_Bamford was a reformer and poet._\n\nIn about half an hour after our arrival the sounds of music and reiterated shouts proclaimed the near approach of Mr Hunt and his party; and in a minute or two they were seen coming from Deansgate, preceded by a band of music and several flags. On the driving seat of a barouche sat a neatly dressed female, supporting a small flag, on which were some emblematical drawings and an inscription. Within the carriage were Mr Hunt, who stood up, Mr Johnson, of Smedley Cottage; Mr Moorhouse, of Stockport; Mr Carlile, of London; Mr John Knight, of Manchester; and Mr Saxton, a sub-editor of the _Manchester Observer._ Their approach was hailed by one universal shout from probably 80,000 persons. They threaded their way slowly past us and through the crowd, which Hunt eyed, I thought, with almost as much of astonishment as satisfaction. This spectacle could not be otherwise in his view than solemnly impressive. Such a mass of human beings he had not beheld till then. His responsibility must weigh on his mind. Their power for good or evil was irresistible, and who should direct that power? Himself alone who had called it forth. The task was great, and not without its peril. The meeting was indeed a tremendous one. He mounted the hustings; the music ceased; Mr Johnson proposed that Mr Hunt should take the chair; it was seconded, and carried by acclamation; and Mr Hunt, stepping towards the front of the stage, took off his white hat, and addressed the people.\n\nWhilst he was doing so, I proposed to an acquaintance that, as the speeches and resolutions were not likely to contain anything new to us, and as we could see them in the papers, we should retire awhile and get some refreshment, of which I stood much in need, being not in very robust health. He assented, and we had got to nearly the outside of the crowd, when a noise and strange murmur arose towards the church. Some persons said it was the Blackburn people coming, and I stood on tiptoe and looked in the direction whence the noise proceeded, and saw a party of cavalry in blue and white uniform come trotting, sword in hand, round the corner of a garden wall, and to the front of a row of new houses, where they reined up in a line.\n\n'The soldiers are here,' I said; 'we must go back and see what this means.' 'Oh,' someone made reply, 'they are only come to be ready if there should be any disturbance in the meeting.' 'Well, let us go back,' I said, and we forced our way towards the colours.\n\nOn the cavalry drawing up they were received with a shout of goodwill, as I understood it. They shouted again, waving their sabres over their heads; and then, slackening rein, and striking spur into their steeds, they dashed forward and began cutting the people.\n\n'Stand fast,' I said, 'they are riding upon us; stand fast.' And there was a general cry in our quarter of 'Stand fast.' The cavalry were in confusion: they evidently could not, with all the weight of man and horse, penetrate that compact mass of human beings; and their sabres were plied to hew a way through naked held-up hands and defenceless heads; and then chopped limbs and wound-gaping skulls were seen; and groans and cries were mingled with the din of that horrid confusion. 'Ah! ah!' 'For shame! for shame!' was shouted. Then, 'Break! break! they are killing them in front, and they cannot get away'; and there was a general cry of 'Break! break.' For a moment the crowd held back as in a pause; then was a rush, heavy and resistless as a headlong sea, and a sound like low thunder, with screams, prayers, and imprecations from the crowd-moiled and sabre-doomed who could not escape.\n\nBy this time Hunt and his companions had disappeared from the hustings, and some of the yeomanry, perhaps less sanguinarily disposed than others, were busied in cutting down the flag-staves and demolishing the flags at the hustings.\n\nOn the breaking of the crowd the yeomanry wheeled, and, dashing whenever there was an opening, they followed, pressing and wounding. Many females appeared as the crowd opened; and striplings or mere youths also were found. Their cries were piteous and heart-rending, and would, one might have supposed, have disarmed any human resentment; but here their appeals were in vain. Women, white-vested maids, and tender youths, were indiscriminately sabred or trampled; and we have reason for believing that few were the instances in which that forbearance was vouchsafed which they so earnestly implored.\n\nIn ten minutes from the commencement of the havoc the field was an open and almost deserted space. The sun looked down through a sultry and motionless air. The curtains and blinds of the windows within view were all closed. A gentleman or two might occasionally be seen looking out from one of the new houses before mentioned, near the door of which a group of persons (special constables) were collected, and apparently in conversation; others were assisting the wounded or carrying off the dead. The hustings remained, with a few broken and hewed flag-staves erect, and a torn and gashed banner or two dropping; whilst over the whole field were strewed caps, bonnets, hats, shawls, and shoes, and other parts of male and female dress, trampled, torn, and bloody. The yeomanry had dismounted \u2013 some were easing their horses' girths, others adjusting their accoutrements, and some were wiping their sabres. Several mounds of human beings still remained where they had fallen, crushed down and smothered. Some of these still groaning, others with staring eyes, were gasping for breath, and others would never breathe more. All was silent save those low sounds, and the occasional snorting and pawing of steeds. Persons might sometimes be noticed peeping from attics and over the tall ridgings of houses, but they quickly withdrew, as if fearful of being observed, or unable to sustain the full gaze of a scene so hideous and abhorrent.\n\n_The massacre, quickly dubbed 'Peterloo', prompted Percy Bysshe Shelley, always a subtle weathercock for social injustice, to compose the political poem 'The Mask of Anarchy', with its famous call for a mass, non-violent campaign for suffrage reform: 'Rise like lions after slumber\/In unvanquishable number\/Shake your chains to earth like dew\/Which in sleep had fallen on you\/Ye are many, they are few'._\n\n_Samuel Bamford was arrested at Peterloo and sentenced to a year's imprisonment._\n\n## _The Black Country, 1830_\n\nJAMES NASMYTH\n\n_The epicentre of the Industrial Revolution, the Midlands became known as the Black Country for its smoke-darkened patina. It was at Coalbrookdale in Shropshire that Abraham Derby developed his iron-smelting process in 1713, and the Coalbrookdale Works manufactured the cylinders of Newcomen's steam engine. The first iron bridge, cast in 1778, stands over the Severn there. Nasmyth was an engineer, the inventor of the steam hammer._\n\nThe Black Country is anything but picturesque. The earth seems to have been turned inside out. Its entrails are strewn about; nearly the entire surface of the ground is covered with cinder-heaps and mounds of scoriae. The coal, which has been drawn from below ground, is blazing on the surface. The district is crowded with iron furnaces, puddling furnaces and coalpit engine furnaces. By day and by night the country is glowing with fire, and the smoke of the ironworks hovers over it. There is a rumbling and clanking of iron forges and rolling mills. Workmen covered with smut, and with fierce white eyes, are seen moving about amongst the glowing iron and dull thud of forge-hammers.\n\nAmidst these flaming, smoky, clanging works, I beheld the remains of what had once been happy farmhouses, now ruined and deserted. The ground underneath them had sunk by the working out of the coal, and they were falling to pieces. They had in former times been surrounded by clumps of trees but only the skeletons of them remained, dilapidated, black, and lifeless. The grass had been parched and killed by the vapours of sulphureous acid thrown out by the chimneys; and every herbaceous object was of a ghastly gray \u2013 the emblem of vegetable death in its saddest aspect. Vulcan had driven out Ceres. In some places I heard a sort of chirruping sound, as of some forlorn bird haunting the ruins of the old farmsteads. But no! the chirrup was a vile delusion. It proceeded from the shrill creaking of the coal-winding chains, which were placed in small tunnels beneath the hedgeless road.\n\nI went into some of the forges to see the workmen at their labours. There was no need of introduction; the works were open to all, for they were unsurrounded by walls. I saw the white-hot iron run out from the furnace; I saw it spun, as it were, into bars and iron ribbands, with an ease and rapidity which seemed marvellous. There were also the ponderous hammers and clanking rolling-mills. I wandered from one to another without restraint. I lingered among the blast furnaces, seeing the flood of molten iron run out from time to time, and remained there until it was late. When it became dark the scene was still more impressive. The workmen within seemed to be running about amidst the flames as in a pandemonium; while around and outside the horizon was a glowing belt of fire, making even the stars look pale and feeble. At last I came away with reluctance, and made my way towards Dudley. I reached the town at a late hour. I was exhausted in mind and body, yet the day had been most interesting and exciting. A sound sleep refreshed me, and I was up in the morning early, to recommence my journey of inquiry.\n\nI made my way to the impressive ruins of Dudley Castle, the remnant of a very ancient stronghold, originally built by Dud, the Saxon. The castle is situated on a finely wooded hill; it is so extensive that it more resembles the ruins of a town than of a single building. You enter through a treble gateway, and see the remnants of the moat, the court, and the keep. Here are the central hall, the guard-rooms and the chapel. It must have been a magnificent structure. In the Midlands it was known as the 'Castle of the Woods'. Now it is abandoned by its owners, and surrounded by the Black Country. It is undermined by collieries, and even penetrated by a canal. The castle walls sometimes tremble when a blast occurs in the bowels of the mountain beneath.\n\n## _First Excursion on the Liverpool\u2013Manchester Railway, 25 August 1830_\n\nFANNY KEMBLE\n\n_The world's first public steam railway, the Stockton-Darlington, opened in 1823; the second to open was the Liverpool-Manchester. The actress Fanny Kemble was among those invited to the Liverpool-Manchester's launch. The engine pulling the guests was George Stephenson's_ Rocket. _So successful was the_ Rocket _(it was reliable, it could reach 31 mph) that within two decades of Fanny Kemble's jaunt, rail was carrying more freight and passengers than the nation's roads and canals. More than that, the railways produced a revolution in English thinking: they made the English realize that machines could be useful, exhilarating, liberating._\n\nA party of sixteen persons was ushered into a large court-yard, where, under cover, stood several carriages of a peculiar construction, one of which was prepared for our reception. It was a long-bodied vehicle with seats placed across it, back to back; the one we were in had six of these benches, and was a sort of uncovered _char \u00e0 banc._ The wheels were placed upon two iron bands, which formed the road, and to which they are fitted, being so constructed as to slide along without any danger of hitching or becoming displaced, on the same principle as a thing sliding on a concave groove. The carriage was set in motion by a mere push, and, having received this impetus, rolled with us down an inclined plane into a tunnel, which forms the entrance to the railroad. This tunnel is four hundred yards long (I believe), and will be lighted by gas. At the end of it we emerged from darkness, and, the ground becoming level, we stopped. There is another tunnel parallel with this, only much wider and longer, for it extends from the place which we had now reached, and where the steam-carriages start, and which is quite out of Liverpool, the whole way under the town, to the docks. This tunnel is for waggons and other heavy carriages; and as the engines which are to draw the trains along the railroad do not enter these tunnels, there is a large building at this entrance which is to be inhabited by steam-engines of a stationary turn of mind, and different constitution from the travelling ones, which are to propel the trains through the tunnels to the terminus in the town, without going out of their houses themselves. The length of the tunnel parallel to the one we passed through is (I believe) two thousand two hundred yards. I wonder if you are understanding one word I am saying all this while! We were introduced to the little engine which was to drag us along the rails. She (for they make these curious little fire-horses all mares), consisted of a boiler, a stove, a small platform, a bench, and behind the bench a barrel containing enough water to prevent her being thirsty for fifteen miles, \u2013 the whole machine not bigger than a common fire-engine. She goes upon two wheels, which are her feet, and are moved by bright steel legs called pistons; these are propelled by steam, and in proportion as more steam is applied to the upper extremities (the hip-joints, I suppose) of these pistons, the faster they move the wheels; and when it is desirable to diminish the speed, the steam, which unless suffered to escape would burst the boiler, evaporates through a safety-valve into the air. The reins, bit, and bridle of this wonderful beast is a small steel handle, which applies or withdraws the steam from its legs or pistons, so that a child might manage it. The coals, which are its oats, were under the bench, and there was a small glass tube affixed to the boiler, with water in it, which indicates by its fulness or emptiness when the creature wants water, which is immediately conveyed to it from its reservoirs. There is a chimney to the stove, but as they burn coke there is none of that dreadful black smoke which accompanies the progress of a steam-vessel. This snorting little animal, which I felt rather inclined to pat, was then harnessed to our carriage, and Mr Stephenson having taken me on the bench of the engine with him, we started at about ten miles an hour. The steam-horse being ill adapted for going up and down hill, the road was kept at a certain level, and appeared sometimes to sink below the surface of the earth, and sometimes to rise above it. Almost at starting it was cut through the solid rock, which formed a wall on either side of it, about sixty feet high. You can't imagine how strange it seemed to be journeying on thus, without any visible cause of progress other than the magical machine, with its flying white breath and rhythmical, unvarying pace, between these rocky walls, which are already clothed with moss and ferns and grasses; and when I reflected that these great masses of stone had been cut asunder to allow our passage thus far below the surface of the earth, I felt as if no fairy tale was ever half so wonderful as what I saw. Bridges were thrown from side to side across the top of these cliffs, and the people looking down upon us from them seemed like pigmies standing in the sky. I must be more concise, or I shall want room. We were to go only fifteen miles; that distance being sufficient to show the speed of the engine, and to take us on to the most beautiful and wonderful object on the road. After proceeding through this rocky defile, we presently found ourselves raised upon embankments ten or twelve feet high; we then came to a moss, or swamp of considerable extent, on which no human foot could tread without sinking, and yet it bore the road which bore us. This had been the great stumbling-block in the minds of the committee of the House of Commons; but Mr Stephenson has succeeded in overcoming it. A foundation of hurdles, or as he called it, basket-work, was thrown over the morass, and the interstices were filled with moss and other elastic matter. Upon this the clay and soil were laid down, and the road _does_ float, for we passed over it at the rate of five and twenty miles an hour, and saw the stagnant swamp water trembling on the surface of the soil on either side of us. I hope you understand me. The embankment had gradually been rising higher and higher, and in one place, where the soil was not settled enough to form banks, Stephenson had constructed artificial ones of wood-work, over which the mounds of earth were heaped, for he calculated that though the wood-work would rot, before it did so the banks of earth which covered it would have been sufficiently consolidated to support the road.\n\nWe had now come fifteen miles, and stopped where the road traversed a wide and deep valley. Stephenson made me alight and led me down to the bottom of this ravine, over which, in order to keep his road level, he has thrown a magnificent viaduct of nine arches, the middle one of which is seventy feet high, through which we saw the whole of this beautiful little valley. It was lovely and wonderful beyond all words. He here told me many curious things respecting this ravine: how he believed the Mersey had once rolled through it; how the soil had proved so unfavourable for the foundation of his bridge that it was built upon piles, which had been driven into the earth to an enormous depth; how, while, digging for a foundation, he had come to a tree bedded in the earth fourteen feet below the surface of the ground; how tides are caused, and how another flood might be caused; all of which I have remembered and noted down at much greater length than I can enter upon it here. He explained to me the whole construction of the steam-engine, and said he could soon make a famous engineer of me, which, considering the wonderful things he _has_ achieved, I dare not say is impossible. His way of explaining himself is peculiar, but very striking, and I understood, without difficulty, all that he said to me. We then rejoined the rest of the party, and the engine having received its supply of water, the carriage was placed behind it, for it cannot turn, and was set off at its utmost speed, thirty-five miles an hour, swifter than a bird flies (for they tried the experiment with a snipe). You cannot conceive what that sensation of cutting the air was; the motion is as smooth as possible, too. I could either have read or written; and as it was, I stood up, and with my bonnet off 'drank the air before me.' The wind, which was strong, or perhaps the force of our thrusting against it, absolutely weighed my eyelids down. When I closed my eyes this sensation of flying was quite delightful, and strange beyond description; yet, strange as it was, I had a perfect sense of security, and not the slightest fear. At one time, to exhibit the power of the engine, having met another steam-carriage which was unsupplied with water, Mr Stephenson caused it to be fastened in front of ours; moreover, a waggon laden with timber was also chained to us, and thus propelling the idle steam-engine, and dragging the loaded waggon which was beside it, and our own carriage full of people behind, this brave little she-dragon of ours flew on. Farther on she met three carts, which being fastened in front of her, she pushed on before her without the slightest delay or difficulty; when I add that this pretty little creature can run with equal facility either backwards or forwards, I believe I have given you an account of all her capacities.\n\n## _The Commons Pass the Reform Bill, 3 a.m., 23 March 1831_\n\nTHOMAS MACAULAY\n\n_The Reform Bill, introduced by Earl Grey's Whigs, sought to transfer representation in Parliament from the rural landowners (with their 'rotten' and 'pocket' boroughs) to the new urban centres spawned by the Industrial Revolution. The Bill also called for extension of the franchise._\n\n_The poet and writer Macaulay (1800\u201359) was MP for Calne. Below, he recounts the Bill's second reading._\n\nSuch a scene as the division of last Tuesday I never saw, and never expect to see again... The crowd overflowed the House in every part. When the strangers were cleared out, and the doors locked, we had six hundred and eight members present \u2013 more by fifty-five than ever were in a division before. The ayes and noes were like two volleys of cannon from opposite sides of a field of battle. When the opposition went out into the lobby, an operation which took up twenty minutes or more, we spread ourselves over the benches on both sides of the House; for there were many of us who had not been able to find a seat during the evening. When the doors were shut we began to speculate on our numbers. Every body was desponding. 'We have lost it. We are only two hundred and eighty at most. I do not think we are two hundred and fifty. There are three hundred. Alderman Thompson has counted them. He says they are two hundred and ninety-nine.' This was the talk of our benches... I had no hope, however, of three hundred... We were all breathless with anxiety, when Charles Wood, who stood near the door, jumped up on a bench and cried out, 'They are only three hundred and one.' We set up a shout that you might have heard to Charing Cross, waving our hats, stamping against the floor, and clapping our hands. The tellers scarcely got through the crowd; for the House was thronged up to the table, and all the floor was fluctuating with heads like the pit of a theatre. But you might have heard a pin drop as Duncannon read the numbers. Then again the shouts broke out, and many of us shed tears. I could scarcely refrain. And the jaw of [Sir Robert] Peel fell; and the face of Twiss was as the face of a damned soul; and Herries looked like Judas taking his neck-tie off for the last operation. We shook hands, and clapped each other on the back, and went out laughing, crying, and huzzaing into the lobby. And no sooner were the outer doors opened than another shout answered that within the House. All the passages and the stairs into the waiting-rooms were thronged with people who had waited till four in the morning to know the issue. We passed through a narrow lane between two thick masses of them; and all the way down they were shouting and waving their hats, till we got into the open air. I called a cabriolet, and the first thing the driver asked was, 'Is the bill carried?' 'Yes, by one.' 'Thank God for it, sir!' And away I rode to Gray's Inn.\n\n_Tory opposition to the Bill in the Lords was only overcome when Earl Grey threatened to create 100 Whig peers to get the measure through._\n\n_By the terms of the Reform Act of 1832 most rotten boroughs were eliminated, and the vote was extended to \u00a310 copy-holders and householders. Effectively the electorate was increased by 50 per cent. The Act was received with national rejoicing, even though most of the workers who had campaigned for it were excluded from its benefit by the \u00a310 qualification. They would go on to support the Chartist movement and the trade unions, the latter achieving full legality with the Trades Union Act of 1871._\n\n## _Darwin in the Galapagos, 1835_\n\nCHARLES DARWIN\n\n_Before Darwin (1809-82) it was scientific orthodoxy that the Creator had hand-made every organism; after Darwin's_ On the Origin of Species by Means of Natural Selection _was published in 1859, it became stutteringly accepted that Evolution, principally Natural Selection, had some part in the development of the living world. Darwin, grandson of both pottery magnate Josiah Wedgwood and free-thinker Erasmus Darwin, attributed his scientific breakthrough to a visit paid to the Galapagos Archipelago in 1835, when he was the naturalist aboard HMS_ Beagle.\n\n... The natural history of these islands is eminently curious, and well deserves attention. Most of the organic productions are aboriginal creations, found nowhere else; there is even a difference between the inhabitants of the different islands; yet all show a marked relationship with those of America, though separated from that continent by an open space of ocean between 500 and 600 miles in width. The archipelago is a little world within itself, or rather, a satellite attached to America, whence it has derived a few stray colonists, and has received the general character of its indigenous productions. Considering the small size of these islands, we feel the more astonished at the number of their aboriginal beings, and at their confined range. Seeing every height crowned with its crater, and the boundaries of most of the lava-streams still distinct, we are led to believe that within a period geologically recent the unbroken ocean was here spread out. Hence, both in space and time, we seem to be brought somewhat near to that great fact \u2013 that mystery of mysteries \u2013 the first appearance of new beings on this earth...\n\nOf land birds I obtained twenty-six kinds, all peculiar to the group and found nowhere else, with the exception of one lark-like finch from North America.... The other twenty-five birds consist, firstly, of a hawk, curiously intermediate in structure between a buzzard and the American group of carrion-feeding Polybori.... Secondly, there are two owls, representing the short-eared and white barn-owls of Europe. Thirdly, a wren, three tyrant-flycatchers..., and a dove \u2013 all analogous to, but distinct from, American species. Fourthly, a swallow.... Fifthly, there are three species of mocking thrush.... The remaining land-birds form a most singular group of finches, related to each other in the structure of their beaks, short tails, form of body and plumage: there are thirteen species... all... peculiar to this archipelago.... The most curious fact is the perfect gradation in the size of the beaks in the different species of Geospiza, from one as large as that of a hawfinch to that of a chaffinch, and... even to that of a warbler. [The _Journal_ is illustrated at this point with drawings of the beaks of the finches.]... Seeing this gradation and diversity of structure in one small, intimately related group of birds, one might really fancy that from an original paucity of birds in this archipelago, one species had been taken and modified for different ends...\n\nI have not as yet noticed by far the most remarkable feature in the natural history of this archipelago; it is, that the different islands to a considerable extent are inhabited by a different set of beings. My attention was first called to this fact by the Vice-Governor, Mr Lawson, declaring that the tortoises differed from the different islands, and that he could with certainty tell from which island any one was brought. I did not for some time pay sufficient attention to this statement, and I had already partially mingled together the collections from two of the islands. I never dreamed that islands, about 50 or 60 miles apart, and most of them in sight of each other, formed of precisely the same rocks, placed under a quite similar climate, rising to a nearly equal height, would have been differently tenanted; but we shall soon see that this is the case. It is the fate of most voyagers no sooner to discover what is most interesting in any locality, than they are hurried from it; but I ought, perhaps, to be thankful that I obtained sufficient materials to establish this most remarkable fact in the distribution of organic beings...\n\n_In 1871 Darwin published_ The Descent of Man, _which proposed that humans had descended from primates._\n\n## _The Coronation of Queen Victoria, 29 June 1838_\n\nCHARLES GREVILLE\n\n_Victoria was eighteen when she ascended the throne. Less than five feet tall, she would bear nine children, survive seven attempts on her life, reign longer than any other English monarch, and give her name to an age that saw England head the greatest empire the world had ever seen._\n\n_Greville was Clerk of the Privy Council._\n\nThe Coronation (which, thank God, is over) went off very well. The day was fine, without heat or rain \u2013 the innumerable multitude which thronged the streets orderly and satisfied. The appearance of the Abbey was beautiful, particularly the benches of the Peeresses, who were blazing with diamonds. The entry of Soult [one of Napoleon's marshals] was striking. He was saluted with a murmur of curiosity and applause as he passed through the nave, and nearly the same as he advanced along the choir. His appearance is that of a veteran warrior, and he walked alone, with his numerous suite following at a respectful distance, preceded by heralds and ushers, who received him with marked attention, more certainly than any of the other Ambassadors. The Queen looked very diminutive, and the effect of the procession itself was spoilt by being too crowded; there was not interval enough between the Queen and the Lords and others going before her. The Bishop of London (Blomfield) preached a very good sermon. The different actors in the ceremonial were very imperfect in their parts, and had neglected to rehearse them. Lord John Thynne, who officiated for the Dean of Westminster, told me that nobody knew what was to be done except the Archbishop and himself (who had rehearsed), Lord Willoughby (who is experienced in these matters), and the Duke of Wellington, and consequently there was a continual difficulty and embarrassment, and the Queen never knew what she was to do next. They made her leave her chair and enter into St Edward's Chapel before the prayers were concluded, much to the discomfiture of the Archbishop. She said to John Thynne, 'Pray tell me what I am to do, for they don't know'; and at the end, when the orb was put into her hand, she said to him, 'What am I to do with it?' 'Your Majesty is to carry it, if you please, in your hand.' 'Am I?' she said; 'it is very heavy.' The ruby ring was made for her little finger instead of the fourth, on which the rubric prescribes that it should be put. When the Archbishop was to put it on, she extended the former, but he said it must be on the latter. She said it was too small, and she could not get it on. He said it was right to put it there, and, as he insisted, she yielded, but had first to take off her other rings, and then this was forced on, but it hurt her very much, and as soon as the ceremony was over she was obliged to bathe her finger in iced water in order to get it off.\n\n## _Prostitutes and Peers: Scenes from a Gin-palace, London, 1839_\n\nFLORA TRISTAN\n\n_A French socialist's view._\n\nFrom the outside, these 'gin-palaces' with their carefully fastened shutters seem to be quietly slumbering; but no sooner has the doorkeeper admitted you by the little door reserved for initiates than you are dazzled by the light of a thousand gas lamps. Upstairs there is a spacious salon divided down the middle; in one half there is a row of tables separated one from the other by wooden screens, as in all English restaurants, with upholstered seats like sofas on each side of the tables. In the other half there is a dais where the prostitutes parade in all their finery, seeking to arouse the men with their glances and remarks; when a gallant gentleman responds, they lead him off to one of the tables loaded with cold meats, hams, poultry, pastries and every manner of wines and spirits.\n\nThe finishes are the temples which English materialism raises to its gods; the servants who minister in them are dressed in rich liveries, and the capitalist owners reverently greet the male guests who come to exchange their gold for debauchery.\n\nTowards midnight the regular clients begin to arrive; several finishes are frequented by men in high society, and this is where the cream of the aristocracy gather. At first the young noblemen recline on the sofas, smoking and exchanging pleasantries with the women; then, when they have drunk enough for the fumes of champagne and Madeira to go to their heads, the illustrious scions of the English nobility, the very honourable members of Parliament, remove their coats, untie their cravats, take off their waistcoats and braces, and proceed to set up their private boudoir in a public place. Why not make themselves at home, since they are paying out so much money for the right to display their contempt? As for any contempt _they_ might inspire, they do not care in the least. The orgy rises to a crescendo; between four and five o'clock in the morning it reaches its height.\n\nAt this point it takes a good deal of courage to remain in one's seat, a mute spectator of all that takes place. What a worthy use these English lords make of their immense fortunes! How fine and generous they are when they have lost the use of their reason and offer fifty, even a hundred, guineas to a prostitute if she will lend herself to all the obscenities that drunkenness engenders.\n\nFor in a finish there is no lack of entertainment. One of the favourite sports is to _ply a woman with drink_ until she falls dead drunk upon the floor, then to make her swallow a draught compounded of _vinegar, mustard,_ and _pepper,_ this invariably throws the poor creature into horrible convulsions, and her spasms and contortions provoke the _honourable company_ to gales of laughter and infinite amusement. Another diversion much appreciated at these fashionable gatherings is to empty the contents of the nearest glass upon the women as they lie insensible on the ground. I have seen satin dresses of no recognizable colour, only a confused mass of stains: wine, brandy, beer, tea, coffee, cream, etc., daubed all over them in a thousand fantastic shapes \u2013 the handiwork of debauchery!\n\n## _Manchester Slums, 1844_\n\nFRIEDRICH ENGELS\n\n_A German socialist's view. Engels was sent to England in 1842 to learn the family business at the Ermen and Engels paper mill in Manchester. While there he gathered material for his book,_ The Condition of the Working Class in England in 1844.\n\nI now proceed to describe Manchester's worker districts. First of all, there is the Old Town, which lies between the northern boundary of the commercial district and the Irk. Here the streets, even the better ones, are narrow and winding, as Todd Street, Long Millgate, Withy Grove, and Shude Hill, the houses dirty, old, and tumble-down, and the construction of the side streets utterly horrible. Going from the Old Church to Long Millgate, the stroller has at once a row of old-fashioned houses at the right, of which not one has kept its original level; these are remnants of the old pre-manufacturing Manchester, whose former inhabitants have removed with their descendants into better-built districts, and have left the houses, which were not good enough for them, to a working-class population strongly mixed with Irish blood. Here one is in an almost undisguised working-men's quarter, for even the shops and beerhouses hardly take the trouble to exhibit a trifling degree of cleanliness. But all this is nothing in comparison with the courts and lanes which lie behind, to which access can be gained only through covered passages, in which no two human beings can pass at the same time. Of the irregular cramming together of dwellings in ways which defy all rational plan, of the tangle in which they are crowded literally one upon the other, it is impossible to convey an idea. And it is not the buildings surviving from the old times of Manchester which are to blame for this; the confusion has only recently reached its height when every scrap of space left by the old way of building has been filled up and patched over until not a foot of land is left to be further occupied.\n\nTo confirm my statement I have drawn here a small section of the plan of Manchester \u2013 not the worst spot and not one-tenth of the whole Old Town.\n\nThis drawing will suffice to characterize the irrational manner in which the entire district was built, particularly the part near the Irk.\n\nThe south bank of the Irk is here very steep and between fifteen and thirty feet high. On this declivitous hillside there are planted three rows of houses, of which the lowest rise directly out of the river, while the front walls of the highest stand on the crest of the hill in Long Millgate. Among them are mills on the river, in short, the method of construction is as crowded and disorderly here as in the lower part of Long Millgate. Right and left a multitude of covered passages lead from the main street into numerous courts, and he who turns in thither gets into a filth and disgusting grime, the equal of which is not be found \u2013 especially in the courts which lead down to the Irk, and which contain unqualifiedly the most horrible dwellings which I have yet beheld. In one of these courts there stands directly at the entrance, at the end of the covered passage,\n\na privy without a door, so dirty that the inhabitants can pass into and out of the court only by passing through foul pools of stagnant urine and excrement. This is the first court on the Irk above Ducie Bridge \u2013 in case any one should care to look into it. Below it on the river there are several tanneries which fill the whole neighborhood with the stench of animal putrefaction. Below Ducie Bridge the only entrance to most of the houses is by means of narrow, dirty stairs and over heaps of refuse and filth. The first court below Ducie Bridge, known as Allen's Court, was in such a state at the time of the cholera that the sanitary police ordered it evacuated, swept and disinfected with chloride of lime. Dr Kay gives a terrible description of the state of this court at that time. * Since then, it seems to have been partially torn away and rebuilt; at least looking down from Ducie Bridge, the passer-by sees several ruined walls and heaps _of d\u00e9bris_ with some newer houses. The view from this bridge, mercifully concealed from mortals of small stature by a parapet as high as a man, is characteristic for the whole district. At the bottom flows, or rather stagnates, the Irk, a narrow, coal-black, foul-smelling stream, full of _d\u00e9bris_ and refuse, which it deposits on the shallower right bank. In dry weather, a long string of the most disgusting blackish-green slime pools are left standing on this bank, from the depths of which bubbles of miasmatic gas constantly arise and give forth a stench unendurable even on the bridge forty or fifty feet above the surface of the stream. But besides this, the stream itself is checked every few paces by high weirs, behind which slime and refuse accumulate and rot in thick masses. Above the bridge are tanneries, bonemills, and gasworks, from which all drains and refuse find their way into the Irk, which receives further the contents of all the neighbouring sewers and privies. It may be easily imagined, therefore, what sort of residue the stream deposits. Below the bridge you look upon the piles of _d\u00e9bris,_ the refuse, filth, and offal from the courts on the steep left bank; here each house is packed close behind its neighbour and a piece of each is visible, all black, smoky, crumbling, ancient, with broken panes and window-frames. The background is furnished by old barrack-like factory buildings. On the lower right bank stands a long row of houses and mills; the second house being a ruin without a roof, piled with _d\u00e9bris;_ the third stands so low that the lowest floor is uninhabitable, and therefore without windows or doors. Here the background embraces the pauper burial-ground, the station of the Liverpool and Leeds railway, and, in the rear of this, the Workhouse, the 'Poor-Law Bastille' of Manchester, which, like a citadel, looks threateningly down from behind its high walls and parapets on the hilltop, upon the working-people's quarter below.\n\nAbove Ducie Bridge, the left bank grows more flat and the right bank steeper, but the condition of the dwellings on both banks grows worse rather than better. He who turns to the left here from the main street, Long Millgate, is lost; he wanders from one court to another, turns countless corners, passes nothing but narrow, filthy nooks and alleys, until after a few minutes he has lost all clue, and knows not whither to turn. Everywhere half or wholly ruined buildings, some of them actually uninhabited, which means a great deal here; rarely a wooden or stone floor to be seen in the houses, almost uniformly broken, ill-fitting windows and doors, and a state of filth! Everywhere heaps of _d\u00e9bris,_ refuse, and offal; standing pools for gutters, and a stench which alone would make it impossible for a human being in any degree civilized to live in such a district. The newly-built extension of the Leeds railway, which crosses the Irk here, has swept away some of these courts and lanes, laying others completely open to view. Immediately under the railway bridge there stands a court, the filth and horrors of which surpass all the others by far, just because it was hitherto so shut off, so secluded that the way to it could not be found without a good deal of trouble. I should never have discovered it myself, without the breaks made by the railway, though I thought I knew this whole region thoroughly. Passing along a rough bank, among stakes and washing-lines, one penetrates into this chaos of small one-storied, one-roomed huts, in most of which there is no artificial floor; kitchen, living and sleeping-room all in one. In such a hole, scarcely five feet long by six broad, I found two beds \u2013 and such bedsteads and beds! \u2013 which, with a staircase and chimney-place, exactly filled the room. In several others I found absolutely nothing, while the door stood open, and the inhabitants leaned against it. Everywhere before the doors refuse and offal; that any sort of pavement lay underneath could not be seen but only felt, here and there, with the feet. This whole collection of cattle-sheds for human beings was surrounded on two sides by houses and a factory, and on the third by the river, and besides the narrow stair up the bank, a narrow doorway alone led out into another almost equally ill-built, ill-kept labyrinth of dwellings.\n\nEnough! The whole side of the Irk is built in this way, a planless, knotted chaos of houses, more or less on the verge of uninhabitableness, whose unclean interiors fully correspond with their filthy external surroundings. And how could the people be clean with no proper opportunity for satisfying the most natural and ordinary wants? Privies are so rare here that they are either filled up every day, or are too remote for most of the inhabitants to use. How can people wash when they have only the dirty Irk water at hand, while pumps and water pipes can be found in decent parts of the city alone? In truth, it cannot be charged to the account of these helots of modern society if their dwellings are not more clean than the pig sties which are here and there to be seen among them. The landlords are not ashamed to let dwellings like the six or seven cellars on the quay directly below Scotland Bridge, the floors of which stand at least two feet below the low-water level of the Irk that flows not six feet away from them; or like the upper floor of the corner-house on the opposite shore directly above the bridge, where the ground-floor, utterly uninhabitable, stands deprived of all fittings for doors and windows, a case by no means rare in this region, when this open ground-floor is used as a privy by the whole neighbourhood for want of other facilities!\n\n_The squalor of England's workers was not only of concern to visiting socialists. The great gulf between rich and poor caused Benjamin Disraeli, a young Tory later to become Conservative Prime Minister, to coin the phrase 'Two Nations' in his 1847 novel,_ Sybil.\n\n'Well, society may be in its infancy,' said Egremont, slightly smiling; 'but, say what you like, our Queen reigns over the greatest nation that ever existed.' 'Which nation?' asked the younger stranger, 'for she reigns over two.' 'Yes,' resumed the younger stranger after a moment's interval. 'Two nations; between whom there is no intercourse, and no sympathy; who are as ignorant of each other's habits, thoughts, and feelings, as if they were dwellers in different zones, or inhabitants of different planets; who are formed by a different breeding, are fed by a different food, are ordered by different manners, and are governed by the same laws.'\n\n'You speak of \u2013', said Egremont, hesitatingly.\n\n'THE RICH AND THE POOR.'\n\n_Only one thing fascinated Victorian England and its visitors as much as the nation's Poverty and Wealth. And that was its progress in science and technology._\n\n## _Chloroform in Surgery, 1847_\n\nCHARLES GREVILLE\n\n_Medicine and surgery made rapid strides in the Victorian era. Before the discovery and application of chloroform, surgery had been at best unbearable, at worst deadly._\n\nI went yesterday to St George's Hospital to see the chloroform tried. A boy two years and a half old was cut for a stone. He was put to sleep in a minute; the stone was so large and the bladder so contracted, the operator could not get hold of it, and the operation lasted above twenty minutes, with repeated probings by different instruments; the chloroform was applied from time to time, and the child never exhibited the slightest sign of consciousness, and it was exactly the same as operating on a dead body. A curious example was shown of what is called the _\u00e9tiquette_ of the profession. The operator (whose name I forget) could not extract the stone; so at last he handed the instrument to Keate, who is the finest operator possible, and he got hold of the stone. When he announced that he had done so, the first man begged to have the forceps back that he might draw it out, and it was transferred to him; but in taking it he let go the stone, and the whole thing had to be done over again. It was accomplished, but not of course without increasing the local inflammation, and endangering the life of the child. I asked Keate why, when he had got hold of the stone, he did not draw it out. He said the other man's 'dignity' would have been hurt if he had not been allowed to complete what he had begun! I have no words to express my admiration for this invention, which is the greatest blessing ever bestowed on mankind, and the inventor of it the greatest of benefactors, whose memory ought to be venerated by countless millions for ages yet to come. All the great discoveries of science sink into insignificance when compared with this. It is a great privilege to have lived in the times which saw the production of steam, of electricity, and now of ether \u2013 that is, of the development and application of them to human purposes, to the multiplication of enjoyments and the mitigation of pain. But wonderful as are the powers and the feats of the steam-engine and the electric telegraph, the chloroform far transcends them all in its beneficent and consolatory operations.\n\n_Six years later Queen Victoria used chloroform during childbirth, a royal approval ('the effect was soothing, quieting & delightful beyond measure') which massively popularized the gas._\n\n## _Chartist March, 13 April 1848_\n\nCHARLES GREVILLE\n\n_So-called from_ The People's Charter, _the Chartist movement was born out of proletarian despair at the limitations of the 1832 Reform Act. The Charter, drafted largely by William Lovett, made six demands: universal male suffrage, annual parliaments, voting by ballot, payment of MPs, an end to property qualifications for MPs, and equal electoral districts._\n\n_The aims were worthy (and would be realized in 1918) but the Chartist leaders, James Bronterre O'Brien and Feargus O'Connor, were mere demagogues. The first Chartist petition, signed by 1,200,000 people, was presented in 1839; the third, and last, was brought to London in April 1848._\n\nApr. 13, 1848: \u2013 Monday passed off with surprising quiet, and it was considered a most satisfactory demonstration on the part of the Government, and the peaceable and loyal part of the community. Enormous preparations were made, and a host of military, police, and special constables were ready if wanted; every gentleman in London was sworn, and during a great part of the day, while the police were reposing, they did duty. The Chartist movement was contemptible; but everybody rejoices that the defensive demonstration was made, for it has given a great and memorable lesson which will not be thrown away, either on the disaffected and mischievous, or the loyal and peaceful; and it will produce a vast effect in all foreign countries, and show how solid is the foundation on which we are resting. We have displayed a great resolution and a great strength, and given unmistakable proofs, that if sedition and rebellion hold up their heads in this country, they will be instantly met with the most vigorous resistance, and be put down by the hand of authority, and by the zealous co-operation of all classes of the people. The whole of the Chartist movement was to the last degree contemptible from first to last. The delegates who met on the eve of the day were full of valour amounting to desperation; they indignantly rejected the intimation of the Government that their procession would not be allowed; swore they would have it at all hazard, and die, if necessary, in asserting their rights. One man said he loved his life, his wife, his children, but would sacrifice all rather than give way.\n\nIn the morning (a very fine day) everybody was on the alert; the parks were closed; our office was fortified, a barricade of Council Registers was erected in the accessible room on the ground-floor, and all our guns were taken down to be used in defence of the building. However, at about twelve o'clock crowds came streaming along Whitehall, going northwards, and it was announced that all was over. The intended tragedy was rapidly changed into a ludicrous farce. The Chartists, about 20,000 in number, assembled on Kennington Common. Presently Mr Mayne appeared on the ground, and sent one of his inspectors to say he wanted to speak to Feargus O'Connor. Feargus thought he was going to be arrested and was in a terrible fright; but he went to Mayne, who merely said he was desired to inform him that the meeting would not be interfered with, but the procession would not be allowed. Feargus insisted on shaking hands with Mayne, swore he was his best of friends, and instantly harangued his rabble, advising them not to provoke a collision, and to go away quietly \u2013 advice they instantly obeyed, and with great alacrity and good-humour. Thus all evaporated in smoke. Feargus himself then repaired to the Home Office, saw Sir George Grey, and told him it was all over, and thanked the Government for their leniency, assuring him the Convention would not have been so lenient if they had got the upper hand. Grey asked him if he was going back to the meeting. He said No; that he had had his toes trodden on till he was lame, and his pocket picked, and he would have no more to do with it. The petition was brought down piecemeal and presented in the afternoon. Since that there has been an exposure of the petition itself, covering the authors of it with ridicule and disgrace. It turns out to be signed by less than two millions, instead of by six as Feargus stated; and of those, there were no end of fictitious names, together with the insertion of every species of ribaldry, indecency, and impertinence. The Chartists are very crestfallen, and evidently conscious of the contemptible figure they cut; but they have endeavoured to bluster and lie as well as they can in their subsequent gatherings, and talk of other petitions and meetings, which nobody cares about.\n\n_The Third Petition was such a fiasco that it ensured that Chartism was of no significance thereafter._\n\n_Elsewhere in Europe in 1848, revolutions swept through like storms. To thebemusement of Karl Marx, who drafted_ The Communist Manifesto _in London in that year, England \u2013 with the world's biggest and most advanced 'proletariat' \u2013 remained stable._\n\n_The English preferred patriotism and pageant to Revolution._\n\n## _A Visit to the Great Exhibition,_ 7 _June 1851_\n\nCHARLOTTE BRONT\u00cb\n\n_The Great Exhibition was housed in Joseph Paxton's Crystal Palace in Hyde Park, London. ('The blazing arch of lucid glass' was run up by navvies in just six months.) The figures for attendance were staggering; more than 6 million tickets were sold._\n\nYesterday I went for the second time to the Crystal Palace. We remained in it about three hours, and I must say I was more struck with it on this occasion than at my first visit. It is a wonderful place \u2013 vast, strange, new, and impossible to describe. Its grandeur does not consist in _one_ thing, but in the unique assemblage of _all_ things. Whatever human industry has created you find there, from the great compartments filled with railway engines and boilers, with mill machinery in full work, with splendid carriages of all kinds, with harness of every description, to the glass-covered and velvet spread stands loaded with the most gorgeous work of the goldsmith and silversmith, and the carefully guarded caskets full of real diamonds and pearls worth hundreds of thousands of pounds. It may be called a bazaar or a fair, but it is such a bazaar or fair as Eastern genii might have created. It seems as if only magic could have gathered this mass of wealth from all the ends of the earth \u2013 as if none but supernatural hands could have arranged it thus, with such a blaze and contrast of colours and marvellous power of effect. The multitude filling the great aisles seems ruled and subdued by some invisible influence. Amongst the thirty thousand souls that peopled it the day I was there not one loud noise was to be heard, not one irregular movement seen; the living tide rolls on quietly, with a deep hum like the sea heard from the distance.\n\n_The Great Exhibition was a bombastic, self-confident, chauvinist symbol of the Victorian good times, based atop a booming economy that would see wages double before the end of the century._\n\n_The Census of 1851 also made for a fascinating spectacle; it confirmed the drift of the population towards the towns (indeed, more than half England and Wales's 17,927,609 total population was now urban) and also the persistent secularism of the English. Five and a quarter million of them stayed at home on Sunday, and only 3 million passed through the porches of the Church of England. Liberalism, with its doctrines of free trade, individualism and 'scientific' improvement, was the political reflection of the Census statistics. Abroad, Liberalism meant restraint, diplomacy, the peaceful maintenance of the balance of power._\n\n_Of course, sometimes the power-balance could only be maintained by the Englishman's traditional means._\n\n## _The Charge of the Light Brigade, Crimea,_ 25 _October 1854_\n\nE. A. COOK\n\n_The causes of the Crimean War (1854\u20136) can be reduced to British and French fear of Russian expansion into Europe._\n\n_Despite Britain's 'modernity', its Crimean army was ill-equipped and its commander, Lord Raglan, ineffective; both deficiencies were dramatically highlighted to the war-hungry crowds at home by the new medium of the telegraphed newspaper dispatch, as pioneered by William Howard Russell of The Times._\n\n_The following account of the melancholic Charge of the Light Brigade at Balaclava is by E. A. Cook, an officer who took part._\n\nHeights of Sebastopol  \nDecember 1st (1854)\n\nMy dear Father,\n\nSince I wrote last nothing decisive has been done towards finishing our now truly wretched campaign, my last letter would prove from its date that I was not present at the last engagement on the Inkerman Heights, the only affair that I have not had a share in. I was in the Black Sea on board of ship at the time lying outside the bay of Varna. The account of the battle which will reach you before this you may fully believe, I don't think the papers will exaggerate, it was without exception the most sanguinary on record for the numbers engaged. I have of course heard all the accounts about it and been over the ground, where there still remain ample proofs of a desperate slaughter. It is well known here that the Russians confess to 20,000 hors de combat \u2013 they attacked us 40,000 strong led on by the two Grand Dukes at daybreak, having been allowed to bring up a great number of heavy guns during the night, a fool of an ensign hearing them all the time without reporting it, they were there, and taking the English, it was on our side, by surprise, we turned out just as we were in our great coats, the Russians came on most furiously mistaking us in the great coats for Turks, our Guards and 4 other regiments were the only troops at hand, they held their ground bravely as long as they could, but of course were obliged to fall back on the next support. The French came up about this time and enabled us to attack the serfs, on which they turned in every direction and then commenced the most horrific slaughter. Our fellows charged them with the bay right down to the bottom of the heights. The deserters say that they got such a lesson that day, that they have tried several times since to get them on without success; and I really think there is no chance of their attacking again. Now for the other massacres as of the 25th October. I have abstained from making a report about this affair, except just that I had a most wonderful escape and got slightly wounded with a spent shot as I should have unnecessarily alarmed you because it is impossible to describe it otherwise than as the most downright useless, ridiculous, except to those in it, sacrifice seen now by _The Times_ of the 13th that they have described the thing truly, so I may as well confirm it. _The Times_ account is so good that I shall only say what happened to myself.\n\nOur order to charge was brought by a half madman Capt. Nolan, the order was very difficult to understand rightly. On Lord Lucan asking what he was to charge, the only information was, there is the enemy and there is your order. There the enemy consisted of 15,000 infantry, 4,000 cavalry protected by 10 guns, to reach them we had to go down a ravine between two hills with 10 guns on each besides a host of riflemen. Down we went very steadily, the fire was terrific, it seemed impossible to escape, we were well in range of grape shot on each side besides the barkers in front. I got through safe up to the guns, cut down all that came within reach and then at the cavalry behind, but to our horror the heavy brigade had not followed in support and there was an alarm that we were cut off in rear, which was true. There was nothing left for it, but to cut our way back the same way we came, the Lancers who cut us off made a very mild resistance, they seemed to be astonished at our audacity at charging them in the wretched confusion we were in, we got through them with very little loss. Just after getting through these beggars, I thought I heard a rattle behind and, by Jove, I was only just in time, we were pursued and on looking behind a Muscovite had his sword up just in my range and in the act of cutting me down, I showed him the point of my sword instantly close to his throat, he pulled his horse almost backwards and gave me an opportunity of getting more forward. I now had nothing to fear being on a good horse except going through those infernal guns again \u2013 about a quarter of a mile from the batteries I felt a tremendous blow on the calf of the leg, and instantly my poor old horse was hit on the offside and was going to fall. I jumped off in a second with the pistol in one hand and sword in the other, and had the satisfaction of seeing my old friends only ten yards behind in full pursuit. Things looked very bad indeed, but in spite of my game leg, I ran faster than ever I did before in my life and kept pace with my friends behind till their own fire got so thick that they thought fit to drop it. I was now between these two batteries and could only raise a walk. I must have been a quarter of an hour under fire on foot, and much to the astonishment of my real friends, the few who escaped, I turned up about half an hour after the rest of the stragglers. I have finished my romance, for really my escape was almost romantic, but don't on that account put it in print as some of my brave companions like.\n\nEnough of war, in spite of living in a tent at this time of the year with 3 inches of mud inside and 12 out, I am not down in the mouth. My fortnight at sea put my leg to rights, and those two fools who command us Lucan and C. have been kind enough to place us such a distance from our supplies, the roads being very deep, that they can't feed the wretched little wreck of a brigade, the consequence is that they are dying 8 and 10 a day, now it requires no mathematician to see that this can't last, besides the horses are so weak that I don't think any one of them could trot a mile. They can't bring us into action again. Tomorrow we move down to Balaclava to be near our supplies and if we have luck get some sort of a roof for man and beast.\n\nThe Russians are worse, if possible, off than ourselves, they are beginning to starve inside and outside of Sebastopol, still they fire away as briskly as ever, we can't assault it without large reinforcements, the army outside would instantly attack us, I fancy it will not fall for some time yet, and I have also I think a chance of going home to command the depot in about two months time. So things are looking up. The newspapers arrive very irregularly, please to speak about it and have via Marseilles put upon them. I want also the Illustrated News. Don't put any more money at the bank, but on account, and put it into the 15 per cents.\n\nWith best love,  \nYour affectionate son,  \nE. A. Cook\n\n_Of the 600 troopers who took part in the Charge 156 were reported killed or missing, and 122 wounded. The action inspired Alfred Tennyson's poem 'Charge of the Light Brigade', 1854._\n\n_The Charge was a blunder; it was also the perfect illustration of the British Victorian soldier's unquestioning sense of duty and extraordinary valour._\n\n_Such a hash did Lord Aberdeen's government make of the Crimean War that it was replaced in 1833 by a Liberal coalition under the nauseously self-assertive but enormously able Lord Palmerston. A year later the defeated Russians signed the Treaty of Paris._\n\n## _Florence Nightingale in the Crimea, 1855_\n\nFLORENCE NIGHTINGALE\n\n_The daughter of Hampshire gentry, Nightingale (1820\u20131910) went against her family, her class and the patriarchal mores of Victorian society to become a nurse, an occupation usually talked of in the same breath as prostitution. She volunteered for duty in the Crimean War, taking thirty-eight nurses to Scutari in 1834, where her improvements in sanitation dramatically reduced the mortality rate in the Army hospital. On returning to England, a fund of \u00a350,000 enabled the 'lady with the lamp' to found institutions for the training of nurses at St Thomas' and King's College Hospitals._\n\nWhen I consider what the work has been this winter, what the hardships, I am surprised \u2013 not that the army has suffered so much but \u2013 that there is any army left at all, not that we have had so many through our hands at Scutari, but that we have not had all as Sir John McNeill says. Fancy working 5 nights out of 7 in the trenches, fancy being 36 hours in them at a stretch \u2013 as they were, all December, lying down or half lying down \u2013 after 48 hours without food but _raw_ salt pork sprinkled with sugar \u2013 & their rum & biscuits \u2013 nothing hot \u2013 because the _exhausted_ soldier _could not_ collect his own fuel, as he was expected, to cook his own ration. And fancy, thro' all this, the army preserving their courage & patience \u2013 as they have done \u2013 & being now eager, the old ones more than the young ones, to be led even into the trenches. There was something sublime in the spectacle. The brave 39th, whose Regimental Hospitals are the best I have ever seen, turned out & gave Florence Nightingale three times three, as I rode away. There was nothing empty in that cheer nor in the heart which received it. I took it as a true expression of true sympathy \u2013 the sweetest I have ever had. I took it as a full reward of all I have gone through. I promised my God that I would not die of disgust or disappointment, if he would let me go through this. In all that has been said against & for me, no one soul has appreciated what I was really doing, none but the honest cheer of the brave 39th.\n\nNothing which the 'Times' has said has been exaggerated of Hardship.\n\nIt was a wonderful sight looking down upon Sevastopol \u2013 the shell whizzing right & left. I send you a Mini\u00e8 bullet I picked up on the ground which was ploughed with shot & shell \u2013 & some little flowers. For this is the most flowery place you can imagine \u2013 a beautiful little red Tormentilla which I don't know, yellow Jessamine & every kind of low flowering shrub. A Serjt of the 97th picked me a nosegay. I once saved Serjt\u2014's life by finding him at 12 o'clock at night lying \u2013 wounds undressed \u2013 in our _Hospl_. with a bullet in his eye & a fractured skull. And I pulled a stray Surgeon out of bed to take the bullet out. But you must not tell this story. For I gave evidence against the missing Surgeon \u2013 & have never been forgiven.\n\n## _Indian Mutiny: Cawnpore after the Massacre, July 1857_\n\nRICHARD BARTER\n\n_Rumours that the British army used Enfield rifle cartridges smeared with pig and cow fat (thus insulting both Muslims and Hindus) were enough to start the Indian Mutiny against British rule in May 1857. Within three weeks, the entire Ganges basin was afire, Lucknow and Cawnpore besieged. The Residency at Lucknow was relieved on 26 September 1857. A month later, British troops arrived at Cawnpore._\n\n_Barter was Adjutant of the 75th Gordon Highlanders, part of General Have-lock's relief force._\n\nWe reached Cawnpore, the scene of the Nana Sahib's massacre of the poor defenceless European men, women and children. Just outside the place we halted near a fine house which was, however, empty, and while waiting for the order to march on, we strolled into it. Even there there had been murder if one could judge by the crimson stain where blood had spurted on the wall and by the smear of a bloody hand. Our Camp was pitched at each side of the road, and that evening we all paid the now-famous well etc. a visit as well as the house close to it in which before their massacre the women and children were confined. The house was a small one, being as well as I can now remember one long room with a verandah in front and rear and the back verandah looked into a courtyard or zenana compound, on the other three sides of which were walls with a door leading out of that on the left to the path to the well. In the courtyard itself grew a babul tree and near the well between it and the house were three or four large trees and some low scrubby thicket of thorny shrubs. The inside of the house was of course bare of furniture and there was no matting or carpet on the floor, but instead blood, thick clotted blood looking like Russia leather, with which the walls also for three or four feet from the ground were spattered, and in some places smeared as if a great spout of it had gushed out on them, while here and there were marks where the murderers had dried their bloody hands by rubbing them against the walls in which were also deep sword cuts, as if some poor victim had dodged aside from the blow. There were also several pencil inscriptions, noting the date of arrival there, and memoranda of deaths of friends or relatives, or short prayers for help. Bonnets, slippers, hats, stays and various other articles of female clothing, with tresses and plaits of hair were scattered about with fragments of books, most, if not all of them Bibles and prayer books. Some of the bonnets and hats were hanging from the beams in the back verandah, which as well as the back yard was covered thick with clotted blood. All the way to the well was marked by a regular track along which the bodies had been dragged and the thorny bushes had entangled in them scraps of clothing and long hairs. One of the large trees to the left of this track going to the well had evidently had children's brains dashed out against its trunk, for it was covered thick with blood and children's hair matted into the coarse bark, and an eye, glazed and withered could be plainly made out pasted into the trunk. A few paces on and you stood by the well itself, now the receptacle of all these poor mangled bodies. It looked old and going fast to decay for the bricks and mortar had given way and crumbled in many places round the low edge. I think it must have been dry or very nearly so. After peering into it for some time until the eyes had become accustomed to the gloom, you could see members of human bodies, legs and arms sticking up browned and withered like those of a mummy. But there was no putrid smell or anything of that kind that I could perceive. Those dead arms of our murdered country people seemed to be making a mute appeal to us from the darkness below; far more eloquent than words they called to Heaven for vengeance on the ruthless perpetrators of untold atrocities, and many a vow was registered over that well never to spare should they be met with hand to hand in the approaching struggle for the Relief of Lucknow, but four short marches now lay between us and that city where we knew the garrison with a crowd of women and children, were daily subject to the attacks of the Cawnpore, and thousands of similar ruffians all eager to repeat the horrors of the place where we now stood; but we had to curb our impatience to go to their relief and had days still to wait the coming of Sir Colin Campbell, the new Commander-in-Chief, who with a large force was now pushing up country.\n\n_Ringleaders of the Mutiny were blown from the mouths of cannon. The possessions of the East India Company were transferred to the crown. The Westernization of India \u2013 against which the Mutiny had, at base, been a protest \u2013 continued apace, including higher-education instruction in English. This was of no small importance: it would assist the global triumph of the English language._\n\n_Queen Victoria, meanwhile, pestered Parliament until they agreed she could be Empress of India._\n\n## _Samuel White Baker Discovers the Source of the Nile, 14 March 1864_\n\nSAMUEL WHITE BAKER\n\n_The quintessential English Victorian explorer (that is, a gentleman, an amateur, a patriot: 'By Englishmen alone is the glorious feeling shared of true, fair and manly sport'), Baker was accompanied throughout his explorations of Africa by his Hungarian wife, Florence von Sass, bought at a slave market. The primary source of the Nile \u2013 Lake Victoria \u2013 had been discovered by John Hanning Speke in 1858 but Baker determined to find a reputed second source, a lake known by natives as Luta Nzige._\n\nThe sun had not risen when I was spurring my ox after the guide, who, having been promised a double handful of beads on arrival at the lake, had caught the enthusiasm of the moment. The day broke beautifully clear, and having crossed a deep valley between the hills, we toiled up the opposite slope. I hurried to the summit. The glory of our prize burst suddenly upon me! There, like a sea of quicksilver, lay far beneath the grand expanse of water \u2013 a boundless sea horizon on the south and south-west, glittering in the noon-day sun; and on the west, at fifty or sixty miles' distance, blue mountains rose from the bosom of the lake to a height of about 7,000 feet above its level.\n\nIt is impossible to describe the triumph of that moment; here was the reward for all our labour \u2013 for the years of tenacity with which we had toiled through Africa. England had won the sources of the Nile! Long before I reached this spot, I had arranged to give three cheers with all our men in English style in honour of the discovery, but now that I looked down upon the great inland sea lying nestled in the very heart of Africa, and thought how vainly mankind had sought these sources throughout so many ages, and reflected that I had been the humble instrument permitted to unravel this portion of the great mystery when so many greater than I had failed, I felt too serious to vent my feelings in vain cheers for victory, and I sincerely thanked God for having guided and supported us through all dangers to the good end. I was about 1,500 feet above the lake, and I looked down from the steep granite cliff upon those welcome waters \u2013 upon that vast reservoir which nourished Egypt and brought fertility where all was wilderness \u2013 upon that great source so long hidden from mankind; that source of bounty and of blessings to millions of human beings; and as one of the greatest objects in nature, I determined to honour it with a great name. As an imperishable memorial of one loved and mourned by our gracious Queen and deplored by every Englishman, I called this great lake 'the Albert N'yanza'. The Victoria and the Albert lakes are the two sources of the Nile.\n\nThe zigzag path to descend to the lake was so steep and dangerous that we were forced to leave our oxen with a guide, who was to take them to Magungo and wait for our arrival. We commenced the descent of the steep pass on foot. I led the way, grasping a stout bamboo. My wife in extreme weakness tottered down the pass, supporting herself upon my shoulder, and stopping to rest every twenty paces. After a toilsome descent of about two hours, weak with years of fever, but for the moment strengthened by success, we gained the level plain below the cliff. A walk of about a mile through flat sandy meadows of fine turf interspersed with trees and bush, brought us to the water's edge. The waves were rolling upon a white pebbly beach: I rushed into the lake, and thirsty with heat and fatigue, with a heart full of gratitude, I drank deeply from the Sources of the Nile. Within a quarter of a mile of the lake was a fishing village named Vacovia, in which we now established ourselves. Everything smelt of fish \u2013 and everything looked like fishing; not the 'gentle art' of England with rod and fly, but harpoons were leaning against the huts, and lines almost as thick as the little finger were hanging up to dry, to which were attached iron hooks of a size that said much for the monsters of the Albert lake. On entering the hut I found a prodigious quantity of tackle; the lines were beautifully made of the fibre of the plantain stem, and were exceedingly elastic, and well adapted to withstand the first rush of a heavy fish; the hooks were very coarse, but well barbed, and varied in size from two to six inches. A number of harpoons and floats for hippopotami were arranged in good order, and the _tout ensemble_ of the hut showed that the owner was a sportsman...\n\nI procured a couple of kids from the chief of the village for some blue beads, and having received an ox as a present from the headman of Park\u0101ni in return for a number of beads and bracelets, I gave my men a grand feast in honour of the discovery; I made them an address, explaining to them how much trouble we should have been saved had my whole party behaved well from the first commencement and trusted to my guidance, as we should have arrived here twelve months ago; at the same time I told them, that it was a greater honour to have achieved the task with so small a force as thirteen men, and that as the lake was thus happily reached, and Mrs Baker was restored to health after so terrible a danger, I should forgive them past offences and wipe out all that had been noted against them in my journal. This delighted my people, who ejaculated 'El hamd el Illah!' (thank God!) and fell to immediately at their beef.\n\nAt sunrise on the following morning I took the compass, and accompanied by the chief of the village, my guide Rabonga, and the woman Bacheeta, I went to the borders of the lake to survey the country. It was beautifully clear, and with a powerful telescope I could distinguish two large waterfalls that cleft the sides of the mountains on the opposite shore. Although the outline of the mountains was distinct upon the bright blue sky, and the dark shades upon their sides denoted deep gorges, I could not distinguish other features than the two great falls, which looked like threads of silver on the dark face of the mountains. No base had been visible, even from an elevation of 1,500 feet above the water-level, on my first view of the lake, but the chain of lofty mountains on the west appeared to rise suddenly from the water. This appearance must have been due to the great distance, the base being below the horizon, as dense columns of smoke were ascending apparently from the surface of the water: this must have been produced by the burning of prairies at the foot of the mountains...\n\nBoth the guide and the chief of Vacovia informed me that we should be taken by canoes to Magungo, to the point at which the Somerset that we had left at Karuma joined the lake; but that we could not ascend it, as it was a succession of cataracts the whole way from Karuma until within a short distance of Magungo. The exit of the Nile from the lake at Koshi was navigable for a considerable distance, and canoes could descend the river as far as the Madi.\n\nThey both agreed that the level of the lake was never lower than at present, and that it never rose higher than a mark upon the beach that accounted for an increase of about four feet. The beach was perfectly clean sand, upon which the waves rolled like those of the sea, throwing up weeds precisely as seaweed may be seen upon the English shore. It was a grand sight to look upon this vast reservoir of the mighty Nile, and to watch the heavy swell tumbling upon the beach, while far to the south-west the eye searched as vainly for a bound as though upon the Atlantic. It was with extreme emotion that I enjoyed this glorious scene. My wife, who had followed me so devotedly, stood by my side pale and exhausted \u2013 a wreck upon the shores of the great Albert Lake that we had so long striven to reach. No European foot had ever trod upon its sand, nor had the eyes of a white man ever scanned its vast expanse of water. We were the first; and this was the key to the great secret that even Julius Caesar yearned to unravel, but in vain. Here was the great basin of the Nile that received _every drop of water,_ even from the passing shower to the roaring mountain torrent that drained from Central Africa towards the north. This was the great reservoir of the Nile!\n\n_Baker was knighted in 1866._\n\n## _Stanley Meets Livingstone, Ujiji, Africa, 10 November 1871_\n\nSIR HENRY MORTON STANLEY\n\n_British missionaries such as Dr Livingstone healed the sick, condemned the slave trade and preached the gospel. Stanley's expedition, paid for by the_ New York Herald, _to find the 'lost' Livingstone in Africa became a celebrated Victorian adventure._\n\nWe push on rapidly, lest the news of our coming might reach the people of Bunder Ujiji before we come in sight, and are ready for them. We halt at a little brook, then ascend the long slope of a naked ridge, the very last of the myriads we have crossed. This alone prevents us from seeing the lake in all its vastness. We arrive at the summit, travel across and arrive at its western rim, and pause, reader \u2013 the port of Ujiji is below us, embowered in the palms, only five hundred yards from us! At this grand moment we do not think of the hundreds of miles we have marched, of the hundreds of hills that we have ascended and descended, of the many forests we have traversed, of the jungles and thickets that annoyed us, of the fervid salt plains that blistered our feet, of the hot suns that scorched us, nor the dangers and difficulties now happily surmounted. At last the sublime hour has arrived! \u2013 our dreams, our hopes, and anticipations are now about to be realized! Our hearts and our feelings are with our eyes as we peer into the palms and try to make out in which hut or house lives the white man with the grey beard we heard about on the Malagarazi.\n\nWe were now about three hundred yards from the village of Ujiji and the crowds are dense about me. Suddenly I hear a voice on my right side.\n\n'Good morning, sir!'\n\nStartled at hearing this greeting in the midst of such a crowd of black people, I turn sharply around in search of the man, and see him at my side, with the blackest of faces, but animated and joyous \u2013 a man dressed in a long white shirt, with a turban of American sheeting around his woolly head, and I ask:\n\n'Who the mischief are you?'\n\n'I am Susi, the servant of Dr Livingstone,' said he, smiling, and showing a gleaming row of teeth.\n\n'What! Is Dr Livingstone here?'\n\n'Yes, sir.'\n\n'In this village?'\n\n'Yes, sir.'\n\n'Are you sure?'\n\n'Sure, sure, sir. Why, I leave him just now.'...\n\n'Now, you Susi, run, and tell the Doctor I am coming.'\n\n'Yes, sir,' and off he darted like a madman...\n\nSoon Susi came running back, and asked me my name; he had told the Doctor that I was coming, but the Doctor was too surprised to believe him, and, when the Doctor asked him my name, Susi was rather staggered.\n\nBut, during Susi's absence, the news had been conveyed to the Doctor that it was surely a white man that was coming, whose guns were firing and whose flag could be seen; and the great Arab magnates of Ujiji \u2013 Mohammed bin Sali, Sayd bin Majid, Abid bin Suleiman, Mohammed bin Gharib, and others \u2013 had gathered together before the Doctor's house, and the Doctor had come out from his veranda to discuss the matter and await my arrival.\n\nIn the meantime, the head of the Expedition had halted, and the _kirangozi_ was out of the ranks, holding his flag aloft, and Selim said to me, 'I see the Doctor, sir. Oh, what an old man! He has got a white beard.' And I \u2013 what would I not have given for a bit of friendly wilderness, where, unseen, I might vent my joy in some mad freak, such as idiotically biting my hand, turning a somersault, or slashing at trees, in order to allay those exciting feelings that were well-nigh uncontrollable. My heart beats fast, but I must not let my face betray my emotions, lest it shall detract from the dignity of a white man appearing under such extraordinary circumstances.\n\nSo I did that which I thought was most dignified. I pushed back the crowds and, passing from the rear, walked down a living avenue of people, until I came in front of the semicircle of Arabs, in the front of which stood the white man with the grey beard. As I advanced slowly towards him I noticed he was pale, looked wearied, had a grey beard, wore a bluish cap with a faded gold band round it, had on a red sleeved waistcoat, and a pair of grey tweed trousers. I would have run to him, only I was a coward in the presence of such a mob \u2013 would have embraced him, only, he being an Englishman I did not know how he would receive me; so I did what cowardice and false pride suggested was the best thing \u2013 walked deliberately to him, took off my hat, and said:\n\n'Dr Livingstone, I presume?'\n\n'YES,' said he, with a kind smile, lifting his cap slightly.\n\nI replace my hat on my head, and he puts on his cap, and we both grasp hands, and I then say aloud.\n\n'I thank God, Doctor, I have been permitted to see you.'\n\n_Missionaries were the unintended point-riders of imperialism, for they stimulated interest in the 'dark continent'. Traders followed, behind them went the British flag, until by the 1880s a quarter of the world's map was pink. Imperialism was a haphazard process, not a deliberate policy. Only in the rarest instances \u2013 such as the Opium Wars with China \u2013 did British arms make the market for British merchants._\n\n## _The Revolt of the Field,_ 7 _February 1872_\n\nJOSEPH ARCH\n\n_A series of bad harvests, cheap food imports (courtesy of bigger and speedier steam shipping) and the opening up of the North American prairies to grain-growing caused 'the great depression' in the English countryside between 1872 and the end of the century. Poverty and depopulation were the result; 40 per cent of rural male labourers left the land in the thirty years before 1901. It was of this crumbling of countryside community that the novels of Thomas Hardy spoke, and Joseph Arch's foundation of the National Agricultural Labourers' Union at Wellesbourne addressed. Arch (1826\u20131919) was later MP for Northwest Norfolk._\n\nThe day was 7th February, 1872. It was a very wet morning, and I was busy at home on a carpentering job; I was making a box. My wife came in to me and said, 'Joe, here's three men come to see you. What for, I don't know.' But I knew fast enough. In walked the three; they turned out to be labourers from over Wellesbourne way. I stopped work, and we had a talk. They said they had come to ask me to hold a meeting at Wellesbourne that evening. They wanted to get the men together, and start a Union directly. I told them that, if they did form a Union, they would have to fight hard for it, and they would have to suffer a great deal; both they and their families. They said the labourers were prepared both to fight and suffer. Things could not be worse; wages were so low, and provisions were so dear, that nothing but downright starvation lay before them unless the farmers could be made to raise their wages. Asking was of no use; it was nothing but waste of breath; so they must join together and strike, and hold out till the employers gave in. When I saw that the men were in dead earnest, and had counted the cost and were determined to stand shoulder to shoulder till they could squeeze a living wage out of their employers, and that they were the spokesmen of others likeminded with themselves, I said I would address the meeting that evening at 7 o'clock. I told them that I had left nine shillings a week behind me years ago, and as I had got out of the ditch myself, I was ready and willing to help them out too. I said, 'If you are ready to combine, I will run all risk and come over and help you.'\n\nI remember that evening, as if it were but yesterday. When I set out I was dressed in a pair of cord trousers, and cord vest, and an old flannel-jacket. I have that jacket at home now, and I put a high value on it. As I tramped along the wet, muddy road to Wellesbourne my heart was stirred within me, and questions passed through my mind and troubled me. Was it a false start, a sort of hole-and-corner movement, which would come to nothing, and do more harm to the men than good? If a Union were fairly set afoot, would the farmers prove too strong for it?\n\nWhen I reached Wellesbourne, lo, and behold, it was as lively as a swarm of bees in June. We settled that I should address the meeting under the old chestnut tree; and I expected to find some thirty or forty of the principal men there. What then was my surprise to see not a few tens but many hundreds of labourers assembled; there were nearly two thousand of them. The news that I was going to speak that night had been spread about; and so the men had come in from all the villages round within a radius of ten miles. Not a circular had been sent out nor a handbill printed, but from cottage to cottage, and from farm to farm, the word had been passed on; and here were the labourers gathered together in their hundreds. Wellesbourne village was there, every man in it; and they had come from Moreton and Locksley and Charlecote and Hampton Lucy, and from Barford, to hear what I had to say to them. By this time the night had fallen pitch dark; but the men got bean poles and hung lanterns on them, and we could see well enough. It was an extraordinary sight, and I shall never forget it, not to my dying day. I mounted an old pig-stool, and in the flickering light of the lanterns I saw the earnest upturned faces of these poor brothers of mine \u2013 faces gaunt with hunger and pinched with want \u2013 all looking towards me and ready to listen to the words, that would fall from my lips. These white slaves of England stood there with the darkness all about them, like the Children of Israel waiting for someone to lead them out of the land of Egypt. I determined that, if they made a mistake and took the wrong turning, it would not be my fault, so I stood on my pig-stool and spoke out straight and strong for Union. My speech lasted about an hour, I believe, but I was not measuring minutes then. By the end of it the men were properly roused, and they pressed in and crowded up asking questions; they regularly pelted me with them; it was a perfect hailstorm. We passed a resolution to form a Union then and there, and the names of the men could not be taken down fast enough; we enrolled between two and three hundred members that night. It was a brave start, and before we parted it was arranged that there should be another meeting at the same place in a fortnight's time. I knew now that a fire had been kindled which would catch on, and spread, and run abroad like sparks in stubble; and I felt certain that this night we had set light to a beacon, which would prove a rallying point for the agricultural labourers throughout the country.\n\nThe news of the meeting soon spread like wildfire, and publicity gave great help to the cause. The result was that, when I got to the chestnut tree on the evening of 21st February, a fortnight later, I found a bigger crowd than before, and I think we had nearly every policeman in the county there as well. They thought there would be a disturbance, but they need not have troubled themselves on that score. I have always preached restraint, and advocated keeping within the law, if possible. Now, more than ever, did I feel called upon to plead for moderation, and I told them in the plainest terms that, if they had recourse to violence and riot and incendiarism, or if they wantonly destroyed any kind of property, they must not look to Joseph Arch to lead them. I would be a peaceable Wat Tyler of the fields, but I would be no rioting leader of the riotous. Neither I nor they should wear handcuffs and see the inside of a gaol, if I could help it. We had come there to strike off the rusty old fetters that had crippled us, and our fathers before us, not to forge new ones for ourselves. We had come there to gain our freedom by lawful means, not to lose what little we had by lawlessness. We were going to stand up for our rights, we were going to ask for our just dues, and we were resolved to have them; but from first to last we were going to act as law-abiding citizens not as red-handed revolutionaries.\n\n## _Rorke's Drift, South Africa, 21 January 1879_\n\nHENRY HOOK\n\n_21 January 1879 was a graveyard and a glory for the Victorian British Army. In the morning the British camp at Isandhlwana was annihilated by 10,000 Zulus (the last order to British troops was: 'Fix bayonets and die like British soldiers do!'), who then advanced on the British hospital and garrison at Rorke's Drift, manned by 120 soldiers, including the sick inmates. For the stand at Rorke's Drift eleven soldiers were awarded the Victoria Cross, more than for any other single engagement involving the British Army. Henry Hook was one of the recipients._\n\n_The Zulu War was occasioned by the Zulus' refusal of a British protectorate._\n\nJust before half past four we heard firing behind the conical hill at the back of the drift, called Oskarsberg Hill, and suddenly about five or six hundred Zulus swept around, coming for us at a run. Instantly the natives \u2013 Kaffirs who had been very useful in making the barricade of waggons, mealie-bags and biscuit boxes around the camp \u2013 bolted towards Helpmakaar, and what was worse their officer and a European sergeant went with them. To see them deserting like that was too much for some of us, and we fired after them. The sergeant was struck and killed. Half-a-dozen of us were stationed in the hospital, with orders to hold it and guard the sick. The ends of the building were of stone, the side walls of ordinary bricks, and the inside walls or partitions of sun-dried bricks of mud. These shoddy inside bricks proved our salvation, as you will see. It was a queer little one-storeyed building, which it is almost impossible to describe; but we were pinned like rats in a hole, because all the doorways except one had been barricaded with mealie-bags and we had done the same with the windows. The interior was divided by means of partition walls into which were fitted some very slight doors. The patients' beds were simple rough affairs of boards, raised only about half a foot above the floor. To talk of hospitals and beds gives the idea of a big building, but as a matter of fact this hospital was a mere little shed or bungalow, divided up into rooms so small that you could hardly swing a bayonet in them. There were about nine men who could not move, but altogether there were about thirty. Most of these, however could not help to defend themselves.\n\nAs soon as our Kaffirs bolted, it was seen that the fort as we had first made it was too big to be held, so Lieutenant Chard instantly reduced the space by having a row of biscuit-boxes drawn across the middle, about four feet high. This was our inner entrenchment, and proved very valuable. The Zulus came on at a wild rush, and although many of them were shot down they got to within about fifty yards of our south wall of mealie-bags and biscuit boxes and waggons. They were caught between two fires, that from the hospital and that from the storehouse, and were checked; but they gained the shelter of the cookhouse and ovens, and gave us many heavy volleys. During the fight they took advantage of every bit of cover there was, anthills, a tract of bush that we had not had time to clear away, a garden or sort of orchard which was near us, and a ledge of rock and some caves (on the Oskarsberg) which were only about a hundred yards away. They neglected nothing, and while they went on firing, large bodies kept hurling themselves against our slender breastworks.\n\nBut it was the hospital they assaulted most fiercely. I had charge with a man that we called Old King Cole of a small room with only one patient in it. Cole kept with me for some time after the fight began, then he said he was not going to stay. He went outside and was instantly killed by the Zulus, so that I was left alone with the patient, a native whose leg was broken and who kept crying out, 'Take my bandage off, so that I can come.' But it was impossible to do anything except fight, and I blazed away as hard as I could. By this time I was the only defender of my room. Poor Old King Cole was lying dead outside and the helpless patient was crying and groaning near me. The Zulus were swarming around us, and there was an extraordinary rattle as the bullets struck the biscuit boxes, and queer thuds as they plumped into the bags of mealies. Then there was the whizz and rip of the assegais, of which I had experience during the Kaffir Campaign of 1877\u20138. We had plenty of ammunition, but we were told to save it and so we took careful aim at every shot, and hardly a cartridge was wasted. Private Dunbar, shot no fewer than nine Zulus, one of them being a Chief.\n\nFrom the very first the enemy tried to rush the hospital, and at last they managed to set fire to the thick grass which formed the roof. This put us in a terrible plight, because it meant that we were either to be massacred or burned alive, or get out of the building.\n\nAll this time the Zulus were trying to get into the room. Their assegais kept whizzing towards us, and one struck me in front of the helmet. We were wearing the white tropical helmets then. But the helmet tilted back under the blow and made the spear lose its power, so that I escaped with a scalp wound which did not trouble me much then, although it has often caused me illness since. Only one man at a time could get in at the door. A big Zulu sprang forward and seized my rifle, but I tore it free and, slipping a cartridge in, I shot him point-blank. Time after time the Zulus gripped the muzzle and tried to tear the rifle from my grasp, and time after time I wrenched it back, because I had a better grip than they had. All this time Williams was getting the sick through the hole into the next room, all except one, a soldier of the 24th named Conley, who could not move because of a broken leg. Watching for my chance I dashed from the doorway, and grabbing Conley I pulled him after me through the hole. His leg got broken again, but there was no help for it. As soon as we left the room the Zulus burst in with furious cries of disappointment and rage.\n\nNow there was a repetition of the work of holding the doorway, except that I had to stand by a hole instead of a door, while Williams picked away at the far wall to make an opening for escape into the next room. There was more desperate and almost hopeless fighting, as it seemed, but most of the poor fellows were got through the hole.\n\n... All this time, of course, the storehouse was being valiantly defended by the rest of the garrison. When we got into the inner fort, I took my post at a place where two men had been shot. While I was there another man was shot in the neck, I think by a bullet which came through the space between two biscuit boxes that were not quite close together. This was at about six o'clock in the evening, nearly two hours after the opening shot of the battle had been fired. Every now and then the Zulus would make a rush for it and get in. We had to charge them out. By this time it was dark, and the hospital was all in flames, but this gave us a splendid light to fight by. I believe it was this light that saved us. We could see them coming, and they could not rush us and take us by surprise from any point. They could not get at us, and so they went away and had ten or fifteen minutes of a war-dance. This roused them up again, and their excitement was so intense that the ground fairly seemed to shake. Then, when they were goaded to the highest pitch, they would hurl themselves at us again. We could sometimes, by the light of the flames, keep them well in sight, so well that we could take aim and fire coolly. When we could do this they never advanced as far as the barricade, because we shot them down as they ran in on us. But every now and then one or two managed to crawl in and climb over the top of the sacks. They were bayoneted off.\n\nAll this time the sick and wounded were crying for water. We had the water-cart full of water, but it was just by the deserted hospital, and we could not hope to get at it until the day broke, when the Zulus might begin to lose heart and to stop their mad rushes. But we could not bear the cries any longer, and three or four of us jumped over the boxes and ran and fetched some water in.\n\nThe long night passed and the day broke. Then we looked around us to see what had happened, and there was not a living soul who was not thankful to find that the Zulus had had enough of it and were disappearing over the hill to the south-west.\n\n## _The Cup Final, Kennington Oval, London, 30 March 1882_\n\nTHE _BLACKBURN TIMES_\n\n_Formerly a medieval brawl, football had been taken into the cloisters and quads of the public schools, where a game of skill and rules had been made of it. From the public schools it was carried by 'muscular Christians' to the working classes for their self-improvement. (Not a few clubs, Aston Villa among them, sprang from Sunday Schools.) The Football Association Cup was instituted in 1872, the League in 1888. Watching Association football henceforth became the regular relaxation of men in industrial England._\n\nWhen the cheering which greeted the advent of the rival captains had subsided, the toss for choice of goals was made, and the Rovers' chief was unfortunate in losing. The Etonians chose to play with the wind in their favour and the sun at their backs. The ball was 'kicked off' by Strachan at eight minutes past three. A light touch to the left gave the leather to Brown, who sent it forward, but it was instantly returned, and the Etonians rushed along and in a few seconds Chevallier made a couple of corner kicks but each was followed by a kick from the goal. Of the Rovers forwards the right wing pair first became prominent. Heading back the leather, J. Hargreaves, aided by Avery, made a good run, but when the other goal was almost reached Macauley intervened and sent it back again. Suter twice relieved his goal cleverly, but Howorth was compelled to use his hands, and then the besiegers had another corner kick, which like its predecessors, proved fruitless. A free kick awarded for a handling of the ball enabled Suter to place it well to the right wing forwards, and the first kick from the corner flag for the Rovers was immediately afterwards made by Douglas. The ball was missed by all the players in the mouth of the goal, but was promptly sent in by the Rovers captain. Kinnaird relieved his side, and Macauley made a run, in which he was aided by Dunn, who passed to Anderson, and that player by a side shot scored a goal at the end of the first eight minutes' play.\n\nSuter and McIntyre in turn interposed with good effect, and enabled Strachan, Douglas, and Duckworth to make an attack upon the Eton citadel. The leather was sent into the hands of Rawlinson, who threw it away before he could be charged through the goal. A free kick from close to the goal enabled the Etonians to return to the attack, but they were unsuccessful, a tremendous kick from Macauley sending the ball some yards above the top bar. Subsequently the ball was thrown right into the mouth of goal by Anderson, and Howorth's charge was seriously imperilled for a time.\n\nFor a breach of rule, which forbids handling, a free kick was awarded against the Etonians in their quarters, but McIntyre missed the ball when it was lightly sent to him by Fred Hargreaves and, as the penalty, the opposing forwards rushed along the ground, and Dunn by a good kick sent the leather into the hands of Howorth.\n\nAnother rush was frustrated by McIntyre and Fred Hargreaves, and Avery secured possession of the ball. Foley interposed to bar his progress, and, jumping at the ball, gave Avery a tremendous kick on the thigh, which placed him 'hors de combat' for some minutes, and partially disabled him during the remainder of the game.\n\nDrs Porteus and Morley attended him on the grass outside the bounds of play, and soon reported that no serious injury had been sustained.\n\nPlay was transferred to the Etonians' quarters, and kept there for a few minutes, during which J. Hargreaves, Avery, and Douglas appeared to advantage, but eventually the ball was again sent over the goal line. The ball, thrown in by Anderson, was headed back from the goal mouth by Suter just as the whistle sounded 'half-time'. Play this far had been remarkably fast, and, with the strong wind against them, the Rovers could not invade their opponents' territory very often, but their defence was good, and in the circumstances they had done exceedingly well to prevent the scoring of more than one goal against them.\n\nWith the score so low the Rovers' supporters hopefully awaited the result. At four minutes to four Goodhart started the ball from the centre, but he was instantly robbed by Strachan, who passed it to the left wing, along which it was taken by J. Hargreaves and Avery. Their progress was barred, and the Etonian forwards returned, but a strong kick sent the ball considerably in advance of them, and Howorth ran out from the goal to kick the ball back. A free kick by Kinnaird was rendered of non-effect by the interposition of the head of Strachan, who played exceedingly well throughout, and the Eton quarters were again invaded.\n\nSome combined play by the Etonian forwards enabled them to approach the Rovers' goal, but they were speedily driven back, and Douglas and Duckworth again came into prominence. The goalkeeper was forced to use his hands, but he had a place kick immediately afterwards, and Fred Hargreaves missing the ball, the Etonian forwards secured a chance which they promptly utilized, to break away, and Chevallier shot the leather behind the goal.\n\nMacauley subsequently made a better attempt to score, but Howorth stopped the ball with his hands, while when Duckworth a few seconds later gave Douglas an opportunity he shot the leather over the bar of the Etonian citadel, and on a second attempt he sent it over the line. As the time for play gradually shortened, the supporters of the Rovers became less confident, and there were shouts from the grand stand of 'Play up Black-burn', to which admirers of their opponents responded by cries of 'E-e-ton'. But there was ominous silence amongst the Lancashire spectators. For nearly twenty minutes before the close the Etonians were practically penned in their own quarters, and the Rovers were constantly striving to score, but only to be disappointed by seeing the ball go over the line, on the wrong side of the posts or to be stopped by the goalkeeper. All the shots were high, however, and there was no opportunity of judging of Rawlinson's power with his feet. The desperate struggle was continued until the referee's whistle signalled the expiration of time, and the Etonians were hailed the victors by one goal to none. Suter played magnificently, Strachan and Duckworth did remarkably well; McIntyre rendered good service; and the other members played well, but on the whole the team did not quite reach its most brilliant form. Of the Old Etonians the captain and Foley were best, while both backs played well; Rawlinson far exceeded expectations as goalkeeper and elicited many complimentary comments; and Macauley, Dunn, Novelli, and Anderson were the pick of the forward division.\n\n_Eton may have won, but the football future belonged to industrial, professional Blackburn Rovers._\n\n## _The Diamond Jubilee, 22 June 1897_\n\nQUEEN VICTORIA\n\n_Diary:_ 22nd June. A never-to-be-forgotten day. No one ever, I believe, has met with such an ovation as was given to me, passing through those six miles of streets, including Constitution Hill. The crowds were quite indescribable, and their enthusiasm truly marvellous and deeply touching. The cheering was quite deafening, and every face seemed to be filled with real joy. I was much moved and gratified.\n\n... At a quarter-past eleven, the others being seated in their carriages long before, and having preceded me a short distance, I started from the State entrance in an open State landau, drawn by eight creams, dear Alix [the future Queen Alexandra], looking very pretty in lilac, and Lenchen [Princess Helena] sitting opposite me. I felt a good deal agitated, and had been so all these days, for fear anything might be forgotten or go wrong. Bertie [the Prince of Wales; the future King Edward VII] and George C. [the 2nd Duke of Cambridge] rode one on each side of the carriage, Arthur [the Duke of Connaught] (who had charge of the whole military arrangements) a little in the rear. My escort was formed from the 2nd Life Guards and officers of the native Indian regiments, these latter riding immediately in front of my carriage. Guard of Honour of Bluejackets, the Guards, and the 2nd Surrey Regiment (Queen's) were mounted in the Quadrangle and outside the Palace.\n\nBefore leaving I touched an electric button, by which I started a message which was telegraphed throughout the whole Empire. It was the following: 'From my heart I thank my beloved people. May God bless them!' At this time the sun burst out. Vicky [the Princess Royal] was in the carriage nearest me, not being able to go in mine, as her rank as Empress prevented her sitting with her back to the horses, for I had to sit alone. Her carriage was drawn by four blacks, richly caparisoned in red. We went up Constitution Hill and Piccadilly, and there were seats right along the former, where my own servants and personal attendants, and members of the other Royal Households, the Chelsea Pensioners, and the children of the Duke of York's and Greenwich schools had seats. St James's Street was beautifully decorated... Trafalgar Square was very striking.... The denseness of the crowds was immense, but the order maintained wonderful. The streets in the Strand are now quite wide, but one misses Temple Bar. Here the Lord Mayor received me and presented the sword, which I touched.... As we neared St Paul's the procession was often stopped, and the crowds broke out into singing _God Save the Queen..._\n\nIn front of the Cathedral the scene was most impressive. All the Colonial troops, on foot, were drawn up round the Square. My carriage, surrounded by all the Royal Princes, was drawn up close to the steps, where the Clergy were assembled, the Bishops in rich copes, with their croziers, the Archbishop of Canterbury and the Bishop of London each holding a very fine one. A _Te Deum_ was sung...\n\nI stopped in front of the Mansion House, where the Lady Mayoress presented me with a beautiful silver basket full of orchids. Here I took leave of the Lord Mayor. Both he and the Lady Mayoress were quite _\u00e9mus._ We proceeded over London Bridge, where no spectators were allowed, only troops, and then along the Borough Road, where there is a very poor population, but just as enthusiastic and orderly as elsewhere. The decorations there were very pretty.... Crossed the river again over Westminster Bridge... The heat during the last hour was very great, and poor Lord Howe, who was riding as Gold Stick, fainted and had a bad fall, but was not seriously hurt.\n\nGot home at a quarter to two... Had a quiet luncheon with Vicky, Beatrice, and her three children. Troops continually passing by. Then rested and later had tea in the garden with Lenchen. There was a large dinner in the supper-room... I walked into the Ball-room afterwards, and sat down in front of the dais. Felt very tired, but tried to speak to most of the Princes and Princesses... In the morning I wore a dress of black silk trimmed with panels of grey satin veiled with black net and steel embroideries, and some black lace, my lovely diamond chain, given me by my younger children, round my neck. My bonnet was trimmed with creamy white flowers, and white aigrette and some black lace.\n\n## _Fox-hunt, Kent, November 1898_\n\nSIEGFRIED SASSOON\n\n_Fox-hunting became the chosen sport of the English aristocracy in the mid-eighteenth century. Of all the classes in English society, the upper changed its mores, lives and pleasures least over the long industrial period. 'A curiously tough substance', as the Fabian writer Beatrice Webb remarked of the aristocracy._\n\n_Sassoon was twelve at the time of his first fox-hunt, below._\n\nThe afternoon hunt was going to be a serious affair. There never appeared to be any doubt about that. The field was reduced to about forty riders, and the chattersome contingent seemed to have gone home. We all went into the covert and remained close together at one end. Dixon got off and tightened my girths, which had got very loose (as I ought to have noticed). A resolute-looking lady in a tall hat drew her veil down after taking a good pull at the flask which she handed back to her groom. Hard-faced men rammed their hats on to their heads and sat silently in the saddle as though, for the first time in the day, they really meant business. My heart was in my mouth and it had good reason to be there. Lord Dumborough was keeping an intent eye on the ride which ran through the middle of the covert.\n\n'Cut along up to the top end, Charlie,' he remarked without turning his head, and a gaunt, ginger-haired man in a weather-stained scarlet coat went off up the covert in a squelchy canter.\n\n'That's Mr Macdoggart,' said Dixon in a low voice, and my solemnity increased as the legendary figure vanished on its mysterious errand.\n\nMeanwhile the huntsman was continuing his intermittent yaups as he moved along the other side of the wood. Suddenly his cheers of encouragement changed to a series of excited shoutings. 'Hoick-holler, hoick-holler, hoick-holler!' he yelled, and then blew his horn loudly; this was followed by an outbreak of vociferation from the hounds, and soon they were in full cry across the covert. I sat there petrified by my private feelings; Sheila showed no symptoms of agitation; she merely cocked her ears well forward and listened.\n\nAnd then, for the first time, I heard a sound which has thrilled generations of fox-hunters to their marrow. From the far side of the wood came the long shrill screech (for which it is impossible to find an adequate word) which signifies that one of the whips has viewed the fox quitting the covert. 'Gone Away' it meant. But before I had formulated the haziest notion about it Lord Dumborough was galloping up the ride and the rest of them were pelting after him as though nothing could stop them. As I happened to be standing well inside the wood and Sheila took the affair into her own control, I was swept along with them, and we emerged on the other side among the leaders.\n\nI cannot claim that I felt either excitement or resolution as we bundled down a long slope of meadowland and dashed helter-skelter through an open gate at the bottom. I knew nothing at all except that I was out of breath and that the air was rushing to meet me, but as I hung on to the reins I was aware that Mr Macdoggart was immediately in front of me. My attitude was an acquiescent one. I have always been inclined to accept life in the form in which it has imposed itself upon me, and on that particular occasion, no doubt, I just felt that I was 'in for it'. It did not so much as occur to me that in following Mr Macdoggart I was setting myself rather a high standard, and when he disappeared over a hedge I took it for granted that I must do the same. For a moment Sheila hesitated in her stride. (Dixon told me afterwards that I actually hit her as we approached the fence, but I couldn't remember having done so.) Then she collected herself and jumped the fence with a peculiar arching of her back. There was a considerable drop on the other side. Sheila had made no mistake, but as she landed I left the saddle and flew over her head. I had let go of the reins, but she stood stock-still while I sat on the wet ground. A few moments later Dixon popped over a gap lower down the fence and came to my assistance, and I saw the boy on the chestnut pony come after him and gallop on in a resolute but unhurrying way. I scrambled to my feet, feeling utterly ashamed.\n\n'What ever made you go for it like that?' asked Dixon, who was quite disconcerted.\n\n'I saw Mr Macdoggart going over it, and I didn't like to stop,' I stammered. By now the whole hunt had disappeared and there wasn't a sound to be heard.\n\n'Well, I suppose we may as well go on.' He laughed as he gave me a leg up. 'Fancy you following Mr Macdoggart over the biggest place in the fence. Good thing Miss Sherston couldn't see you.'\n\nThe idea of my aunt seemed to amuse him, and he slapped his knee and chuckled as he led me onward at a deliberate pace. Secretly mortified by my failure I did my best to simulate cheerfulness. But I couldn't forget the other boy and how ridiculous he must have thought me when he saw me rolling about on the ground. I felt as if I must be covered with mud. About half an hour later we found the hunt again, but I can remember nothing more except that it was beginning to get dark and the huntsman, a middle-aged, mulberry-faced man named Jack Pitt, was blowing his horn as he sat in the middle of his hounds. The other boy was actually talking to him \u2013 a privilege I couldn't imagine myself promoted to. At that moment I almost hated him for his cocksuredness.\n\nThen, to my surprise, the Master himself actually came up and asked me how far I was from home. In my embarrassment I could only mutter that I didn't know, and Dixon interposed with 'About twelve miles, m'lord,' in his best manner.\n\n'I hear he's quite a young thruster.'... The great man glanced at me for a moment with curiosity before he turned away. Not knowing what he meant I went red in the face and thought he was making fun of me.\n\n## _Omdurman, 2 September 1898_\n\nWINSTON CHURCHILL\n\n_A battle fought to avenge the death of General Gordon at the hands of the Pan-Islamic Mahdi and to reconquer the Sudan (and so secure the Suez Canal, the empire's lifeline to India)._\n\n_Churchill fought with the 21st Lancers, as well as simultaneously holding a roving commission as a war correspondent. The British commander at Omdurman was Major-General Horatio Kitchener._\n\nI propose to describe exactly what happened to me: what I saw and what I felt. I recalled it to my mind so frequently after the event that the impression is as clear and vivid as it was a quarter of a century ago. The troop I commanded was, when we wheeled into line, the second from the right of the regiment. I was riding a handy, sure-footed, grey Arab polo pony. Before we wheeled and began to gallop, the officers had been marching with drawn swords. On account of my shoulder I had always decided that if I were involved in hand-to-hand fighting, I must use a pistol and not a sword. I had purchased in London a Mauser automatic pistol, then the newest and the latest design. I had practised carefully with this during our march and journey up the river. This then was the weapon with which I determined to fight. I had first of all to return my sword into its scabbard, which is not the easiest thing to do at a gallop. I had then to draw my pistol from its wooden holster and bring it to full cock. This dual operation took an appreciable time, and until it was finished, apart from a few glances to my left to see what effect the fire was producing, I did not look up at the general scene.\n\nThen I saw immediately before me, and now only half the length of a polo ground away, the row of crouching blue figures firing frantically, wreathed in white smoke. On my right and left my neighbouring troop leaders made a good line. Immediately behind was a long dancing row of lances couched for the charge. We were going at a fast but steady gallop. There was too much trampling and rifle fire to hear any bullets. After this glance to the right and left and at my troop, I looked again towards the enemy. The scene appeared to be suddenly transformed. The blue-black men were still firing, but behind them there now came into view a depression like a shallow sunken road. This was crowded and crammed with men rising up from the ground where they had hidden. Bright flags appeared as if by magic, and I saw arriving from nowhere Emirs on horseback among and around the mass of the enemy. The Dervishes appeared to be ten or twelve deep at the thickest, a great grey mass gleaming with steel, filling the dry watercourse. In the same twinkling of an eye I saw also that our right overlapped their left, that my troop would just strike the edge of their array, and that the troop on my right would charge into air. My subaltern comrade on the right, Wormald of the 7th Hussars, could see the situation too; and we both increased our speed to the very fastest gallop and curved inwards like the horns of the moon. One really had not time to be frightened or to think of anything else but these particular necessary actions which I have described. They completely occupied mind and senses.\n\nThe collision was now very near. I saw immediately before me, not ten yards away, the two blue men who lay in my path. They were perhaps a couple of yards apart. I rode at the interval between them. They both fired. I passed through the smoke conscious that I was unhurt. The trooper immediately behind me was killed at this place and at this moment, whether by these shots or not I do not know. I checked my pony as the ground began to fall away beneath his feet. The clever animal dropped like a cat four or five feet down on to the sandy bed of the watercourse, and in this sandy bed I found myself surrounded by what seemed to be dozens of men. They were not thickly-packed enough at this point for me to experience any actual collision with them. Whereas Grenfell's troop next but one on my left was brought to a complete standstill and suffered very heavy losses, we seemed to push our way through as one has sometimes seen mounted policemen break up a crowd. In less time than it takes to relate, my pony had scrambled up the other side of the ditch. I looked round.\n\nOnce again I was on the hard, crisp desert, my horse at a trot. I had sensation of fear. I felt myself absolutely alone. I thought these riflemen would hit me and the rest devour me like wolves. What a fool I was to loiter like this in the midst of the enemy! I crouched over the saddle, spurred my horse into a gallop and drew clear of the _m\u00eal\u00e9e._ Two or three hundred yards away I found my troop all ready faced about and partly formed up.\n\nThe other three troops of the squadron were re-forming close by. Suddenly in the midst of the troop up sprung a Dervish. How he got there I do not know. He must have leaped out of some scrub or hole. All the troopers turned upon him thrusting with their lances: but he darted to and fro causing for the moment a frantic commotion. Wounded several times, he staggered towards me raising his spear. I shot him at less than a yard. He fell on the sand, and lay there dead. How easy to kill a man! But I did not worry about it. I found I had fired the whole magazine of my Mauser pistol, so I put in a new clip of ten cartridges before thinking of anything else.\n\nI was still prepossessed with the idea that we had inflicted great slaughter on the enemy and had scarcely suffered at all ourselves. Three or four men were missing from my troop. Six men and nine or ten horses were bleeding from spear thrusts or sword cuts. We all expected to be ordered immediately to charge back again. The men were ready, though they all looked serious. Several asked to be allowed to throw away their lances and draw their swords. I asked my second sergeant if he had enjoyed himself. His answer was 'Well, I don't exactly say I enjoyed it, Sir; but I think I'll get more used to it next time.'\n\n_Twenty thousand Dervishes were killed and wounded. British losses were 500. After Omdurman, the British marched on to Khartoum, where the bones of the slain General Gordon were disinterred and given a Christian burial._\n\n## _The Siege of Mafeking, South Africa, April\u2013May 1900_\n\nJ. E. NEILLY\n\n_The Boer War (1899\u20131902), occasioned by Afrikaner attacks on British gold-miners in South Africa, saw the 700-strong garrison at Mafeking besieged from 12 October 1899 to 17 May 1900. The garrison was commanded by Colonel Baden-Powell, later to found the Scouts (1908) and the Girl Guides (1910)._\n\nIt was not pleasant to mix among the people of the kraals. Hunger had them in its grip, and many of them were black spectres and living skeletons. I saw them crawling along on legs like the stems of well-blackened 'cutties', with their ribs literally breaking through their shrivelled skin \u2013 men, women, and children. I saw them, too, fall down on the veldt and lie where they had fallen, too weak to go on their way. The sufferers were mostly little boys \u2013 mere infants ranging in age from four or five upwards. When the famine struck the place they were thrown out of the huts by their parents to live or die, sink or swim...\n\nWhen the Colonel got to know of the state of affairs he instituted soup kitchens, where horses were boiled in huge cauldrons, and the savoury mess doled out in pints and quarts to all comers. Some of the people \u2013 those employed on works \u2013 paid for the food; the remainder, who were in the majority, obtained it free. One of those kitchens was established in the Stadt, and I several times went down there to see the unfortunates fed.\n\nWords could not portray the scene of misery. The best thing I can do is to ask you to fancy five or six hundred human frameworks of both sexes and all ages, from the tender infant upwards, dressed in the remains of tattered rags, standing in lines, each holding an old blackened can or beef tin, awaiting turn to crawl painfully up to the kitchen where the food was distributed. Having obtained the horse soup, fancy them tottering off a few yards and sitting down to wolf up the life-fastening mess, and lick the tins when they had finished. It was one of the most heart-rending sights I ever witnessed, and I have seen many...\n\nWhen a flight of locusts came it was regarded as a godsend \u2013 this visitation that is looked upon by the farmer as hardly less of a curse than the rinderpest or drought. The starving ones gathered the insects up in thousands, stripped them of their heads, legs, and wings, and ate the bodies. They picked up meat-tins and licked them; they fed like outcast curs. They went farther than the mongrel. When a dog gets a bone he polishes it white and leaves it there. Day after day I heard outside my door continuous thumping sounds. They were caused by the living skeletons who, having eaten all that was outside the bones, smashed them up with stones and devoured what marrow they could find. They looked for bones on the dust-heaps, on the roads everywhere, and I pledge my word that I saw one poor fellow weakly follow a dog with a stone and with unerring aim strike him on the ribs, which caused the lean and hungry brute to drop a bone, which the Kafir carried off in triumph to the kerb, where he smashed it and got what comfort he could from it.\n\n_When Majeking was finally relieved, Victorian England went wild with a patriotic delirium that needed a neologism to express it: 'mafficking'._\n\n_Mafeking was safe. The British had triumphed. All was right with the world._\n\n_Except, of course, it wasn't. The long public anxiety over Mafeking was a barely conscious understanding that Britain's pre-eminence was slipping. A glance at the turn-of-the-century economic statistics only confirmed this: Great Britain's share of world manufacturing output was 18.3 per cent. America's was 23 per cent._\n\n_Worse still, Germany was beginning to catch up at 13.2 per cent._\n\n_The death of Queen Victoria on 22 January 1901 at Osborne on the Isle of Wight confirmed the end of a glorious era._\n\n## _Queen Victoria's Funeral Procession, Isle of Wight to London, 1\u20132 February 1901_\n\nTHE COUNTESS OF DENBIGH\n\nI think you will like to hear of my going down to Southampton to see the passing of our dear Queen from Osborne to Portsmouth.\n\nI went on the _Scot,_ where both Houses were embarked. We steamed out, and took up our position between the last British ship and the first foreign ships of war, on the south side of the double line down which the procession was to pass. The day was one of glorious sunshine, with the smoothest and bluest of seas. After a while a black torpedo destroyer came dashing down the line signalling that the _Alberta_ was leaving Osborne and from every ship, both British and foreign, boomed out the minute guns for close on an hour before the procession reached us. The sun was now (3 p.m.) beginning to sink, and a wonderful golden pink appeared in the sky and as the smoke slowly rose from the guns it settled in one long festoon behind them, over Haslar, a purple festoon like the purple hangings ordered by the King.\n\nThen slowly down the long line of battleships came eight Torpedo destroyers, dark gliding forms, and after them the white _Alberta_ looking very small and frail next the towering battleships. We could see the motionless figures standing round the white pall which, with the crown and orb and sceptre, lay upon the coffin. Solemnly and slowly, it glided over the calm blue water, followed by the other three vessels, giving one a strange choke, and a catch in one's heart as memory flew back to her triumphal passage down her fleet in the last Jubilee review. As slowly and as silently as it came the cort\u00e8ge passed away into the haze: with the solemn booming of the guns continuing every minute till Portsmouth was reached. A wonderful scene and marvellously impressive, leaving behind it a memory of peace and beauty and sadness which it is impossible to forget.\n\nThen on Saturday, Feb. 2nd, came the wonderful procession through London, which you will see fully described in the papers.\n\nMolly, Dorothie, Lady Denbigh and I saw it from the Household Stand at Buckingham Palace, and had a very good view. The behaviour of the crowd was wonderful in its silence and reverence as the procession passed. And this was the same everywhere, the K. of P. [King of Portugal], told Denbigh that the crowd in Hyde Park was quite half a mile deep. The only thing which jarred was the harnessing of the celebrated creams, with their gold and crimson trappings to a gun carriage. The demeanour of our new King in his dignified sadness was very striking, and of course the coffin in its white pall and regalia, he and the Kaiser were the most observed. The slow solemn march of the naval men with their arms reversed, moved me much for I could not help comparing the then with the now as I thought of last year in Dublin when the naval contingent went past the Queen with heads erect and their wonderful brisk step.\n\nNot a sound was heard from the crowd during the procession and a great hush fell upon it when the coffin came in sight.\n\nWhen all was over we waited awhile for the crowd to move away and then tried unsuccessfully to get up Constitution Hill and St James, so went up Grosvenor Place only to find a line of cavalry across it near St George's Hospital, so made for Albert Gate via Belgrave Sq. only to meet such a dense crowd streaming out that we had to retreat up the steps of the French Embassy, where we waited for an hour, and then with difficulty made our way into the park, and so home.\n\n_Victoria had ruled for almost sixty-four years. She was succeeded by her eldest son, who reigned as Edward VII, but was 'Tum-tum' to his family and 'Good Old Teddy' to the racing fraternity. His reign, 1901\u201310, coincided with a distinct shift from 'laissez-faire' Liberalism to interventionist Liberalism. In particular, the Liberal governments of 1906\u201314 carried through a raft of social legislation \u2013 free school meals, old age pensions, labour exchanges, National Insurance \u2013 which laid the foundations of the later Welfare State. The motivation for the reforms was not entirely altruistic; it was intended, in part, to sate the new Labour Party (founded in 1900) and the increasingly militant trade unions (whose membership rose by two-thirds between 1910 and 1913). Industrial agitation was not the only unrest in late Edwardian England:_\n\n## _Force-feeding of a Suffragette, Walton Jail, Liverpool, 18 January 1910_\n\nLADY CONSTANCE LYTTON\n\n_Founded by Emmeline Pankhurst in 1903, the Women's Social and Political Union campaigned for the extension of the franchise to women. Its members were repeatedly imprisoned for attacks on property and refusal to pay taxes. Like a number of gaoled suffragettes, Constance Lytton went on hunger-strike to draw further attention to the cause._\n\nI was visited again by the Senior Medical Officer, who asked me how long I had been without food. I said I had eaten a buttered scone and a banana sent in by friends to the police station on Friday at about midnight. He said, 'Oh, then, this is the fourth day; that is too long, I shall feed you, I must feed you at once,' but he went out and nothing happened till about six o'clock in the evening, when he returned with, I think, five wardresses and the feeding apparatus. He urged me to take food voluntarily. I told him that was absolutely out of the question, that when our legislators ceased to resist enfranchising women then I should cease to resist taking food in prison. He did not examine my heart nor feel my pulse; he did not ask to do so, nor did I say anything which could possibly induce him to think I would refuse to be examined. I offered no resistance to being placed in position, but lay down voluntarily on the plank bed. Two of the wardresses took hold of my arms, one held my head and one my feet. One wardress helped to pour the food. The doctor leant on my knees as he stooped over my chest to get at my mouth. I shut my mouth and clenched my teeth. I had looked forward to this moment with so much anxiety lest my identity should be discovered beforehand, that I felt positively glad when the time had come. The sense of being overpowered by more force than I could possibly resist was complete, but I resisted nothing except with my mouth. The doctor offered me the choice of a wooden or steel gag; he explained elaborately, as he did on most subsequent occasions, that the steel gag would hurt and the wooden one not, and he urged me not to force him to use the steel gag. But I did not speak nor open my mouth, so that after playing about for a moment or two with the wooden one he finally had recourse to the steel. He seemed annoyed at my resistance and he broke into a temper as he plied my teeth with the steel implement. He found that on either side at the back I had false teeth mounted on a bridge which did not take out. The superintending wardress asked if I had any false teeth, if so, that they must be taken out; I made no answer and the process went on. He dug his instrument down on to the sham tooth, it pressed fearfully on the gum. He said if I resisted so much with my teeth, he would have to feed me through the nose. The pain of it was intense and at last I must have given way for he got the gag between my teeth, when he proceeded to turn it much more than necessary until my jaws were fastened wide apart, far more than they could go naturally. Then he put down my throat a tube which seemed to me much too wide and was something like four feet in length. The irritation of the tube was excessive. I choked the moment it touched my throat until it had got down. Then the food was poured in quickly; it made me sick a few seconds after it was down and the action of the sickness made my body and legs double up, but the wardresses instantly pressed back my head and the doctor leant on my knees. The horror of it was more than I can describe.\n\n## _The Arrest of Dr Crippen, 31 July 1910_\n\nCAPTAIN H. G. KENDALL\n\n_After murdering his wife with the exotic poison hyoscine, Crippen tried to flee to Canada aboard the liner Montrose. Instead, Crippen and his paramour, Ethel Le Neve (dressed as a boy), became the first people to be caught by use of the wireless. Kendall was the captain of the Montrose._\n\nThe _Montrose_ was in port at Antwerp when I read in the _Continental Daily Mail_ that a warrant had been issued for Crippen and LeNeve. They were reported to have been traced to a hotel in Brussels but had then vanished again.\n\nSoon after we sailed for Quebec I happened to glance through the porthole of my cabin and behind a lifeboat I saw two men. One was squeezing the other's hand. I walked along the boat deck and got into conversation with the elder man. I noticed that there was a mark on the bridge of his nose through wearing spectacles, that he had recently shaved off a moustache, and that he was growing a beard. The young fellow was very reserved, and I remarked about his cough.\n\n'Yes,' said the elder man, 'my boy has a weak chest, and I'm taking him to California for his health.'\n\nI returned to my cabin and had another look at the _Daily Mail._ I studied the description and photographs issued by Scotland Yard. Crippen was fifty years of age, 5 ft 4 ins high, wearing spectacles and a moustache; Miss LeNeve was twenty-seven, 5 ft 5 ins, slim, with pale complexion. I then examined the passenger list and ascertained that the two passengers were travelling as 'Mr Robinson and son'. I arranged for them to take meals at my table.\n\nWhen the bell went for lunch I tarried until the coast was clear, then slipped into the Robinsons' cabin unobserved, where I noticed two things: that the boy's felt hat was packed round the rim to make it fit, and that he had been using a piece of a woman's bodice as a face flannel. That satisfied me. I went down to the dining saloon and kept my eyes open. The boy's manners at table were ladylike. Later, when they were promenading the saloon deck, I went out and walked behind them, and called out, 'Mr Robinson!' I had to shout the name several times before the man turned and said to me, 'I'm sorry, Captain, I didn't hear you \u2013 this cold wind is making me deaf\n\nIn the next two days we developed our acquaintance. Mr Robinson was the acme of politeness, quiet-mannered, a non-smoker; at night he went on deck and roamed about on his own. Once the wind blew up his coat tails and in his hip pocket I saw a revolver. After that I also carried a revolver, and we often had pleasant little tea parties together in my cabin, discussing the book he was reading, which was _The Four Just Men,_ a murder mystery by Edgar Wallace \u2013 and when that little fact was wirelessed to London and published it made Edgar Wallace's name ring, so agog was everybody in England over the Crippen case.\n\nThat brings me to the wireless. On the third day out I gave my wireless operator a message for Liverpool: _One hundred and thirty miles west of Lizard... have strong suspicions that Crippen London cellar murderer and accomplice are among saloon passengers... Accomplice dressed as boy; voice, manner, and build undoubtedly a girl._\n\nI remember Mr Robinson sitting in a deckchair, looking at the wireless aerials and listening to the crackling of our crude spark-transmitter, and remarking to me what a wonderful invention it was.\n\nI sent several more reports, but our weak transmitting apparatus was soon out of communication with land. We could hear other ships at a great distance, however, and you may imagine my excitement when my operator brought me a message he had intercepted from a London newspaper to its representative aboard the White Star liner _Laurentic_ which was also heading westward across the Atlantic: _What is InspectorDew doing? Is he sending and receiving wireless messages? Is he playing games with passengers? Are passengers excited over chase? Rush reply._\n\nThis was the first I knew that my message to Liverpool had caused Inspector Dew to catch the first boat out\u2013 the _Laurentic._ With her superior speed, I knew she would reach the Newfoundland coast before me. I hoped that if she had any news for me the _Laurentic_ would leave it at the Belle Island station to be transmitted to me as soon as I passed that point on my approach to Canada.\n\nShe had news indeed: _Will board you at Father Point... strictly confidential... from Inspector Dew, Scotland Yard, on board Laurentic._\n\nI replied: _Shall arrive Father Point about 6 a.m. tomorrow... should advise you to come off in small boat with pilot, disguised as pilot..._\n\nThis was confirmed. The last night was dreary and anxious, the sound of our fog-horn every few minutes adding to the monotony. The hours dragged on as I paced the bridge; now and then I could see Mr Robinson strolling about the deck. I had invited him to get up early to see the 'pilots' come aboard at Father Point in the River St Lawrence. When they did so they came straight to my cabin. I sent for Mr Robinson. When he entered I stood with the detective facing the door, holding my revolver inside my coat pocket. As he came in, I said, 'Let me introduce you.'\n\nMr Robinson put out his hand; the detective grabbed it, at the same time removing his pilot's cap, and said, 'Good morning, Dr Crippen. Do you know me? I'm Inspector Dew, from Scotland Yard.'\n\nCrippen quivered. Surprise struck him dumb. Then he said, 'Thank God it's over. The suspense has been too great. I couldn't stand it any longer. '\n\n_Crippen was later hanged at Pentonville prison. Le Neve, charged as an accessory to murder, was acquitted._\n\n## _Antarctic Expedition: Scott's Last Diary Entries, January 1912_\n\nCAPTAIN R. F. SCOTT RN\n\n_Robert Falcon Scott and four companions reached the South Pole on 18 January 1912, only to find that the Norwegian Roald Amundsen had beaten them to it by a month. The bodies of Scott and his men were found on 12 November 1912. It is generally assumed that Scott mistakenly wrote 'March' for 'January' in the diary entries below._\n\n_Friday, 16 March or Saturday 17._ Lost track of dates, but think the last correct. Tragedy all along the line. At lunch, the day before yesterday, poor Titus Oates said he couldn't go on; he proposed we should leave him in his sleeping-bag. That we could not do, and induced him to come on, on the afternoon march. In spite of its awful nature for him he struggled on and we made a few miles. At night he was worse and we knew the end had come.\n\nShould this be found I want these facts recorded. Oates' last thoughts were of his mother, but immediately before he took pride in thinking that his regiment would be pleased with the bold way in which he met his death. We can testify to his bravery. He has borne intense suffering for weeks without complaint, and to the very last was able and willing to discuss outside subjects. He did not \u2013 would not \u2013 give up hope to the very end. He was a brave soul. This was the end. He slept through the night before last, hoping not to wake; but he woke in the morning \u2013 yesterday. It was blowing a blizzard. He said, _'I_ am just going outside and may be some time.' He went out into the blizzard and we have not seen him since.\n\nI take this opportunity of saying that we have stuck to our sick companions to the last. In case of Edgar Evans, when absolutely out of food and he lay insensible, the safety of the remainder seemed to demand his abandonment, but Providence mercifully removed him at this critical moment. He died a natural death, and we did not leave him till two hours after his death. We knew that poor Oates was walking to his death, but though we tried to dissuade him, we knew it was the act of a brave man and an English gentleman. We all hope to meet the end with a similar spirit, and assuredly the end is not far.\n\nI can only write at lunch and then only occasionally. The cold is intense, \u201340o at midday. My companions are unendingly cheerful, but we are all on the verge of serious frostbites, and though we constantly talk of fetching through I don't think any one of us believes it in his heart.\n\nWe are cold on the march now, and at all times except meals. Yesterday we had to lay up for a blizzard and today we move dreadfully slowly. We are at No. 14 pony camp, only two pony marches from One Ton Depot. We leave here our theodolite, a camera, and Oates' sleeping-bags. Diaries, etc., and geological specimens carried at Wilson's special request, will be found with us or on our sledge.\n\n_Sunday, 18 March._ Today, lunch, we are 21 miles from the depot. Ill fortune presses, but better may come. We have had more wind and drift from ahead yesterday; had to stop marching; wind NW, force 4, temp. \u201335o. No human being could face it, and we are worn out _nearly._\n\nMy right foot has gone, nearly all the toes \u2013 two days ago I was proud possessor of best feet. These are the steps of my downfall. Like an ass I mixed a small spoonful of curry powder with my melted pemmican \u2013 it gave me violent indigestion. I lay awake and in pain all night; woke and felt done on the march; foot went and I didn't know it. A very small measure of neglect and have a foot which is not pleasant to contemplate. Bowers takes first place in condition, but there is not much to choose after all. The others are still confident of getting through \u2013 or pretend to be \u2013 I don't know! We have the last _half_ fill of oil in our primus and a very small quantity of spirit \u2013 this alone between us and thirst. The wind is fair for the moment, and that is perhaps a fact to help. The mileage would have seemed ridiculously small on our outward journey.\n\n_Monday, 19 March._ Lunch. We camped with difficulty last night and were dreadfully cold till after our supper of cold pemmican and biscuit and a half a pannikin of cocoa cooked over the spirit. Then, contrary to expectation, we got warm and all slept well. Today we started in the usual dragging manner. Sledge dreadfully heavy. We are 15\u00bd miles from the depot and ought to get there in three days. What progress! We have two days' food but barely a day's fuel. All our feet are getting bad \u2013 Wilson's best, my right foot worst, left all right. There is no chance to nurse one's feet till we can get hot food into us. Amputation is the least I can hope for now, but will the trouble spread? That is the serious question. The weather doesn't give us a chance \u2013 the wind from N to NW and \u201340o temp, today.\n\n_Wednesday, 21 March._ Got within 11 miles of depot Monday night; had to lay up all yesterday in severe blizzard. Today forlorn hope, Wilson and Bowers going to depot for fuel.\n\n_Thursday, 22 and 23 March._ Blizzard bad as ever \u2013 Wilson and Bowers unable to start \u2013 tomorrow last chance \u2013 no fuel and only one or two of food left \u2013 must be near the end. Have decided it shall be natural \u2013 we shall march for the depot with or without our effects and die in our tracks.\n\n_Thursday, 29 March._ Since the 21st we have had a continuous gale from WSW and SW. We had fuel to make two cups of tea apiece and bare food for two days on the 20th. Every day we have been ready to start for our depot 11 _miles_ away, but outside the door of the tent it remains a scene of whirling drift. I do not think we can hope for any better things now. We shall stick it out to the end, but we are getting weaker, of course, and the end cannot be far.\n\nIt seems a pity, but I do not think I can write more.\n\nR. SCOTT\n\nFor God's sake look after our people.\n\n## _The_ Titanic _Sinks, 15 April 1912_\n\nHAROLD BRIDE\n\n_Bride was one of the_ Titanic's _wireless operators. Hailed as 'unsinkable', the_ Titanic _had room for only 1,178 people in its lifeboats; the passengers and crew on its maiden voyage numbered 2,224. A total of 1,513 lives were lost when the ship struck an iceberg in mid-Atlantic._\n\nFrom aft came the tunes of the band. It was a ragtime tune. I don't know what. Then there was 'Autumn'... I went to the place I had seen the collapsible boat on the boat deck, and to my surprise I saw the boat, and the men still trying to push it off. I guess there wasn't a sailor in the crowd. They couldn't do it. I went up to them and was just lending a hand when a large wave came awash of the deck. The big wave carried the boat off. I had hold of an oarlock and I went with it. The next I knew I was in the boat. But that was not all. I was in the boat, and the boat was upside-down, and I was under it. And I remember realizing I was wet through and that whatever happened I must not breathe, for I was under water. I knew I had to fight for it, and I did. How I got out from under the boat I do not know but I felt a breath of air at last. There were men all around me \u2013 hundreds of them. The sea was dotted with them, all depending on their lifebelts. I felt I simply had to get away from the ship. She was a beautiful sight then. Smoke and sparks were rushing out of her funnel. There must have been an explosion, but we heard none. We only saw the big stream of sparks. The ship was turning gradually on her nose \u2013 just like a duck that goes for a dive. I had only one thing on my mind \u2013 to get away from the suction. The band was still playing. I guess all of them went down. They were playing 'Autumn' then. I swam with all my might. I suppose I was 150 feet away when the _Titanic,_ on her nose, with her after-quarter sticking straight up in the air, began to settle \u2013 slowly.\n\nWhen at last the waves washed over her rudder there wasn't the least bit of suction I could feel. She must have kept going just so slowly as she had been... I felt after a little while like sinking. I was very cold. I saw a boat of some kind near me, and put all my strength into an effort to swim to it. It was hard work. I was all done when a hand reached out from the boat and pulled me aboard. It was our same collapsible. The same crowd was on it. There was just room for me to roll on the edge. I lay there not caring what happened. Somebody sat on my legs. They were wedged in between slats and were being wrenched. I had not the heart left to ask the man to move. It was a terrible sight all around \u2013 men swimming and sinking.\n\nI lay where I was, letting the man wrench my feet out of shape. Others came near. Nobody gave them a hand. The bottom-up boat already had more men than it would hold, and it was sinking. At first the larger waves splashed over my clothing. Then they began to splash over my head, and I had to breathe when I could. As we floated around on our capsized boat and I kept straining my eyes for a ship's lights, somebody said, 'Don't the rest of you think we ought to pray?' The man who made the suggestion asked what the religion of the others was. Each man called out his religion. One was a Catholic, one a Methodist, one a Presbyterian. It was decided the most appropriate prayer for all was the Lord's Prayer. We spoke it over in chorus with the man who first suggested that we pray as the leader. Some splendid people saved us. They had a right-side-up boat and it was full to capacity. Yet they came to us and loaded us all into it.\n\n## _The Drift to World War: The View from 10 Downing Street, 1\u20142 August 1914_\n\nHERBERT ASQUITH, PRIME MINISTER\n\n_August 1_\n\nWhen most of them [the Cabinet] had left, Sir W. Tyrrell arrived with a long message from Berlin to the effect that the German Ambassador's efforts for peace had been suddenly arrested and frustrated by the Tsar's decree for a complete Russian mobilization. We all set to work, Tyrrell, Bongie, Drummond and myself, to draft a direct personal appeal from the King to the Tsar. When we had settled it I called a taxi, and, in company with Tyrrell, drove to Buckingham Palace at about 1.30 a.m. The King was hauled out of bed, and one of my strangest experiences was sitting with him, clad in a dressing gown, while I read the message and the proposed answer.\n\nThere was really no fresh news this morning. Lloyd George, all for peace, is more sensible and statesmanlike for keeping the position still open. Grey declares that if an out-and-out and uncompromising policy of non-intervention at all costs is adopted, he will go. Winston [Churchill] very bellicose and demanding immediate mobilization. The main controversy pivots upon Belgium and its neutrality. We parted in fairly amicable mood, and are to sit again at 11 to-morrow, Sunday. I am still not quite hopeless about peace, though far from hopeful, but if it comes to war, I feel sure we shall have a split in the Cabinet. Of course if Grey went I should go and the whole thing would break up. On the other hand, we may have to contemplate, with such equanimity as we can command, the loss of Morley and possibly, though I do not think it, of Simon.\n\n_August 2_\n\nThings are pretty black. Germany is now in active war with both Russia and France, and the Germans have violated the neutrality of Luxembourg. We are waiting to know whether they are going to do the same with Belgium. I had a visit at breakfast from Lichnowsky, who was very _emotionn\u00e9_ and implored me not to side with France. He said that Germany, with her army cut in two between France and Russia, was far more likely to be crushed than France. He was very agitated, poor man, and wept. I told him that we had no desire to intervene, and that it rested largely with Germany to make intervention impossible if she would (1) not invade Belgium, and (2) not send her fleet into the Channel to attack the unprotected north coast of France. He was bitter about the policy of his Government in not restraining Austria and seemed quite heart-broken.\n\nThen we had a long Cabinet from 11 till nearly two, which very soon revealed that we are on the brink of a split. We agreed at last with some difficulty that Grey should be authorized to tell Cambon that our fleet would not allow the German fleet to make the Channel a base of hostile operations. John Burns at once resigned, but was persuaded to hold on at any rate till the evening when we meet again. There is a strong party against any kind of intervention in any event. Grey, of course, will never consent to this, and I shall not separate myself from him. Crewe, McKenna and Samuel are a moderating intermediate body. Bonar Law writes that the Opposition will back us up in any measure we may take for the support of France and Russia. I suppose a good number of our own party in the House of Commons are for absolute non-interference. It will be a shocking thing if at such a moment we break up.\n\nHappily I am quite clear in my mind as to what is right and wrong. (1) We have no obligation of any kind either to France or Russia to give them military or naval help. (2) The dispatch of the Expeditionary Force to help France at this moment is out of the question and would serve no object. (3) We must not forget the ties created by our longstanding and intimate friendship with France. (4) It is against British interests that France should be wiped out as a Great Power. (5) We cannot allow Germany to use the Channel as a hostile base. (6) We have obligations to Belgium to prevent it being utilized and absorbed by Germany...\n\n_With the German invasion of neutral Belgium on 4 August all hope of British non-intervention in the First World War was wiped away. King George V recorded: 'I held a Council at 10.45 to declare war with Germany, it is a terrible catastrophe, but it is not our fault... Please God it may soon be over & that he will protect dear Bertie's life'._\n\n_All over Europe, young men, flushed with excitement and patriotism, volunteered for service. Few Englishmen had any idea of what war meant: the English had not fought a major war for a century. Professional soldiers were more sanguine: Their favourite song was:_\n\nSend out the Army and the Navy,\n\nSend out the rank and file.\n\n(Have a banana!)\n\nSend out the brave Territorials,\n\nThey'll face the danger with a smile.\n\n(I don't think!)\n\nSend out the boys of the girls' brigade,\n\nThey will keep old England free;\n\nSend out my mother, my sister and my brother,\n\nBut for Gawd's sake don't send me!'\n\n_Within three months of the declaration of hostilities, the First World War in the West had settled down to a muddy line of trench-fighting that stretched from the English Channel to Switzerland._\n\n_It had been an almost universal expectation that the war would be 'over by Christmas'. Instead, the troops just wished it was \u2013 and organized an impromptu Yuletide peace._\n\n## _Christmas in the Trenches, 25 December 1914_\n\nCAPTAIN SIR EDWARD HAMILTON WESTROW HULSE\n\nAt 8.30 a.m. I was looking out, and saw four Germans leave their trenches and come towards us; I told two of my men to go and meet them, _unarmed_ (as the Germans were unarmed), and to see that they did not pass the half-way line. We were 350\u2013400 yards apart at this point. My fellows were not very keen, not knowing what was up, so I went out alone, and met Barry, one of our ensigns, also coming out from another part of the line. By the time we got to them, they were three quarters of the way over, and much too near our barbed wire, so I moved them back. They were three private soldiers and a stretcher-bearer, and their spokesman started off by saying that he thought it only right to come over and wish us a happy Christmas, and trusted us implicitly to keep the truce. He came from Suffolk, where he had left his best girl and a 3\u00bd h.p. motor-bike! He told me that he could not get a letter to the girl, and wanted to send one through me. I made him write out a post card in front of me, in English, and I sent it off that night. I told him that she probably would not be a bit keen to see him again. We then entered on a long discussion on every sort of thing. I was dressed in an old stocking-cap and a man's overcoat, and they took me for a corporal, a thing which I did not discourage, as I had an eye to going as near their lines as possible. I asked them what orders they had from their officers as to coming over to us, and they said _none;_ they had just come over out of goodwill...\n\nI kept it up for half an hour, and then escorted them back as far as their barbed wire, having a jolly good look round all the time, and picking up various little bits of information which I had not had an opportunity of doing under fire! I left instructions with them that if any of them came out later they must not come over the half-way line, and appointed a ditch as the meeting place. We parted after an exchange of Albany cigarettes and German cigars, and I went straight to H.-qrs. to report.\n\nOn my return at 10 a.m. I was surprised to hear a hell of a din going on, and not a single man left in my trenches; they were completely denuded (against my orders), and nothing lived! I heard strains of 'Tipperary' floating down the breeze, swiftly followed by a tremendous burst of'Deutschland \u00fcber Alles', and as I got to my own Coy. H.-qrs. dug-out, I saw, to my amazement, not only a crowd of about 150 British and Germans at the half-way house which I had appointed opposite my lines, but six or seven such crowds, all the way down our lines, extending towards the 8th Division on our right. I bustled out and asked if there were any German officers in my crowd, and the noise died down (as this time I was myself in my own cap and badges of rank).\n\nI found two, but had to talk to them through an interpreter, as they could neither talk English nor French... I explained to them that strict orders must be maintained as to meeting half-way, and everyone unarmed; and we both agreed not to fire until the other did, thereby creating a complete deadlock and armistice (if strictly observed)...\n\nMeanwhile Scots and Huns were fraternizing in the most genuine possible manner. Every sort of souvenir was exchanged, addresses given and received, photos of families shown, etc. One of our fellows offered a German a cigarette; the German said, 'Virginian?' Our fellow said, 'Aye, straight-cut': the German said, 'No thanks, I only smoke Turkish!' (Sort of 10\/- a 100 me!) It gave us all a good laugh.\n\nA German N.C.O. with the Iron Cross \u2013 gained, he told me, for conspicuous skill in sniping \u2013 started his fellows off on some marching tune. When they had done I set the note for 'The Boys of Bonnie Scotland, where the heather and the bluebells grow', and so we went on, singing everything from 'Good King Wenceslaus' down to the ordinary Tommies' song, and ended up with 'Auld Lang Syne', which we all, English, Scots, Irish, Prussians, Wurtembergers, etc., joined in. It was absolutely astounding, and if I had seen it on a cinematograph film I should have sworn that it was faked!...\n\nJust after we had finished 'Auld Lang Syne' an old hare started up, and seeing so many of us about in an unwonted spot \u2013 did not know which way to go. I gave one loud 'View Holloa', and one and all, British and Germans, rushed about giving chase, slipping up on the frozen plough, falling about, and after a hot two minutes we killed in the open, a German and one of our fellows falling together heavily upon the completely baffled hare. Shortly afterwards we saw four more hares, and killed one again; both were good heavy weight and had evidently been out between the two rows of trenches for the last two months, well-fed on the cabbage patches, etc., many of which are untouched on the 'no-man's land'. The enemy kept one and we kept the other. It was now 11.30 a.m. and at this moment George Paynter arrived on the scene with a hearty 'Well, my lads, a Merry Christmas to you! This is d\u2014d comic, isn't it?'... George told them that he thought it was only right that we should show that we could desist from hostilities on a day which was so important in both countries; and he then said, 'Well, my boys, I've brought you over something to celebrate this funny show with', and he produced from his pocket a large bottle of rum (not ration rum, but the proper stuff). One large shout went up, and the nasty little spokesman uncorked it, and in a heavy ceremonious manner, drank our healths, in the name of his 'cameraden'; the bottle was then passed on and polished off before you could say knife...\n\nDuring the afternoon the same extraordinary scene was enacted between the lines, and one of the enemy told me that he was longing to get back to London: I assured him that 'So was I'. He said that he was sick of the war, and I told him that when the truce was ended, any of his friends would be welcome in our trenches, and would be well-received, fed, and given a free passage to the Isle of Man! Another coursing meeting took place, with no result, and at 4.30 p.m. we agreed to keep in our respective trenches, and told them that the truce was ended.\n\n_The respective high commands curtailed future Christmas fraternizations._\n\n_1915 would be a year of stalemate on the Western Front, the numericalsuperiority of the Allied (British and French) Army offset by the fact that the Germans held the high ground along the front. In this year alone, the British took 300,000 casualties for mere yards of German-held mud. There were various stratagems to break the deadlock, the most inventive being that of Winston Churchill at the Admiralty, which was to land Allied troops at the entrance to the Dardanelles and open a front against Germany's ally, Turkey. Inept execution turned the subsequent Gallipoli campaign, begun in April 1915, into one of the Great War's greatest disasters. For months Allied troops were unable to break out of a narrow bridgehead on the rocky, sun-beaten peninsula._\n\n## _An Infantryman at Gallipoli, June 1915_\n\nLEONARD THOMPSON\n\n_Thompson was a former farmhand._\n\nWe arrived at the Dardanelles and saw the guns flashing and heard the rifle fire. They heaved our ship, the _River Clyde,_ right up to the shore. They had cut a hole in it and made a little pier, so we were able to walk straight off and on to the beach. We all sat there \u2013 on the Hellespont! \u2013 waiting for it to get light. The first things we saw were big wrecked Turkish guns, the second a big marquee. It didn't make me think of the military but of the village f\u00eates. Other people must have thought like this because I remember how we all rushed up to it, like boys getting into a circus, and then found it all laced up. We unlaced it and rushed in. It was full of corpses. Dead Englishmen, lines and lines of them, and with their eyes wide open. We all stopped talking. I'd never seen a dead man before and here I was looking at two or three hundred of them. It was our first fear. Nobody had mentioned this. I was very shocked. I thought of Suffolk and it seemed a happy place for the first time.\n\nLater that day we marched through open country and came to within a mile and half of the front line. It was incredible. We were there \u2013 at the war! The place we had reached was called 'dead ground' because it was where the enemy couldn't see you. We lay in little square holes, myself next to James Sears from the village. He was about thirty and married. That evening we wandered about on the dead ground and asked about friends of ours who had arrived a month or so ago. 'How is Ernie Taylor?' \u2013 'Ernie? \u2013 he's gone.' 'Have you seen Albert Paternoster?' \u2013 'Albert? \u2013 he's gone.' We learned that if 300 had 'gone' but 700 were left, then this wasn't too bad. We then knew how unimportant our names were.\n\nI was on sentry that night. A chap named Scott told me that I must only put my head up for a second but that in this time I must see as much as I could. Every third man along the trench was a sentry. The next night we had to move on to the third line of trenches and we heard that the Gurkhas were going over and that we had to support their rear. But when we got to the communication trench we found it so full of dead men that we could hardly move. Their faces were quite black and you couldn't tell Turk from English. There was the most terrible stink and for a while there was nothing but the living being sick on to the dead. I did sentry again that night. It was one \u2013 two \u2013 sentry, one \u2013 two \u2013 sentry all along the trench, as before. I knew the next sentry up quite well. I remembered him in Suffolk singing to his horses as he ploughed. Now he fell back with a great scream and a look of surprise \u2013 dead. It is quick, anyway, I thought. On June 4th we went over the top. We took the Turks' trench and held it. It was called Hill 13. The next day we were relieved and told to rest for three hours, but it wasn't more than half an hour before the relieving regiment came running back. The Turks had returned and recaptured their trench. On June 6th my favourite officer was killed and no end of us butchered, but we managed to get hold of Hill 13 again. We found a great muddle, carnage and men without rifles shouting ' _Allah! Allah!'_ , which is God's name in the Turkish language. Of the sixty men I had started out to war from Harwich with, there were only three left.\n\nWe set to work to bury people. We pushed them into the sides of the trench but bits of them kept getting uncovered and sticking out, like people in a badly made bed. Hands were the worst; they would escape from the sand, pointing, begging \u2013 even waving! There was one which we all shook when we passed, saying, 'Good morning', in a posh voice. Everybody did it. The bottom of the trench was springy like a mattress because of all the bodies underneath. At night, when the stench was worse, we tied cr\u00eape round our mouths and noses. This cr\u00eape had been given to us because it was supposed to prevent us being gassed. The flies entered the trenches at night and lined them completely with a density which was like moving cloth. We killed millions by slapping our spades along the trench walls but the next night it would be just as bad. We were all lousy and we couldn't stop shitting because we had caught dysentery. We wept, not because we were frightened but because we were so dirty.\n\n_Eventually, in December 1915, the Allied survivors were evacuated from Gallipoli. Behind them they left the bodies of 46,000 compatriots. With the failure of the Gallipoli expedition, the focus of the war swung back to the Western Front, where trench raids, saturation bombing and 'Big Pushes' became an_ id\u00e9e fixe.\n\n## _Night Raid, Western Front, 25 May 1916_\n\nSIEGFRIED SASSOON\n\n_Sassoon won a Military Cross in the action described below._\n\nTwenty-seven men with faces blackened and shiny \u2013 Christy-minstrels \u2013 with hatchets in their belts, bombs in pockets, knobkerries \u2013 waiting in a dug-out in the reserve line. At 10.30 they trudge up to Battalion H.Q. splashing through mire and water in the chalk trench, while the rain comes steadily down. The party is twenty-two men, five N.C.O.s and one officer (Stansfield). From H.Q. we start off again, led by Comp-ton-Smith: across the open to the end of 77 street. A red flashlight winks a few times to guide us thither. Then up to the front line \u2013 the men's feet making a most unholy tramp and din; squeeze along to the starting-point, where Stansfield and his two confederates (Sergeant Lyle and Corporal O'Brien) loom over the parapet from above, having successfully laid the line of lime across the craters to the Bosche wire. In a few minutes the five parties have gone over \u2013 and disappear into the rain and darkness \u2013 the last four men carry ten-foot light ladders. It is 12 midnight. I am sitting on the parapet listening for something to happen \u2013 five, ten, nearly fifteen minutes \u2013 not a sound \u2013 nor a shot fired \u2013 and only the usual flare-lights, none very near our party. Then a few whizz-bangs fizz over to our front trench and just behind the raiders. After twenty minutes there is still absolute silence in the Bosche trench; the raid is obviously held up by their wire, which we thought was so easy to get through. One of the bayonet-men comes crawling back; I follow him to our trench and he tells me that they can't get through: O'Brien says it's a failure; they're all going to throw a bomb and retire.\n\nA minute or two later a rifle-shot rings out and almost simultaneously several bombs are thrown by both sides: a bomb explodes right in the water at the bottom of left crater close to our men, and showers a pale spume of water; there are blinding flashes and explosions, rifle-shots, the scurry of feet, curses and groans, and stumbling figures loom up from below and scramble awkwardly over the parapet \u2013 some wounded \u2013 black faces and whites of eyes and lips show in the dusk; when I've counted sixteen in, I go forward to see how things are going, and find Stansfield wounded, and leave him there with two men who soon get him in: other wounded men crawl in; I find one hit in the leg; he says O'Brien is somewhere down the crater badly wounded. They are still throwing bombs and firing at us: the sinister sound of clicking bolts seems to be very near; perhaps they have crawled out of their trench and are firing from behind their advanced wire. Bullets hit the water in the craters, and little showers of earth patter down on the crater. Five or six of them are firing into the crater at a few yards' range. The bloody sods are firing down at me at point-blank range. (I really wondered whether my number was up.) From our trenches and in front of them I can hear the mumble of voices \u2013 most of them must be in by now. After minutes like hours, with great difficulty I get round the bottom of the crater and back toward our trench; at last I find O'Brien down a very deep (about twenty-five feet) and precipitous crater on my left (our right as they went out). He is moaning and his right arm is either broken or almost shot off: he's also hit in the right leg (body and head also, but I couldn't see that then). Another man (72 Thomas) is with him; he is hit in the right arm. I leave them there and get back to our trench for help, shortly afterwards Lance-Corporal Stubbs is brought in (he has had his foot blown off). Two or three other wounded men are being helped down the trench; no one seems to know what to do; those that are there are very excited and uncertain: no sign of any officers \u2013 then Compton-Smith comes along (a mine went up on the left as we were coming up at about 11.30 and thirty (R.E.s) men were gassed or buried). I get a rope and two more men and we go back to O'Brien, who is unconscious now. With great difficulty we get him half-way up the face of the crater; it is now after one o'clock and the sky beginning to get lighter. I make one more journey to our trench for another strong man and to see to a stretcher being ready. We get him in, and it is found that he has died, as I had feared. Corporal Mick O'Brien (who often went patrolling with me) was a very fine man and had been with the Battalion since November 1914. He was at Neuve Chapelle, Festubert and Loos.\n\nI go back to a support-line dug-out and find the unwounded men of the raiding-party refreshing themselves: everyone is accounted for now; eleven wounded (one died of wounds) and one killed, out of twenty-eight. I see Stansfield, who is going on all right, but has several bomb-wounds. On the way down I see the Colonel, sitting on his bed in a woollen cap with a tuft on top, and very much upset at the non-success of the show, and the mine disaster; but very pleased with the way our men tried to get through the wire.\n\n_A week after Sassoon's night raid, the British and German fleets engaged together at Jutland, the major naval battle of the war. The British claimed victory because they remained in control of the North Sea; the Germans claimed victory because they sank more ships (fourteen to eleven). As not a few British sailors noticed, their ships and weaponry at Jutland were shoddy and obsolete compared to those of the enemy. Admiral Jellicoe himself was moved to comment, 'There seems to be something wrong with our damn ships today.'_\n\n_England's fall from industrial grace needed no other proof_.\n\n## _Home Front: Death of a Brother, 15 June 1916_\n\nVERA BRITTAIN\n\n_Brittain's fianc\u00e9, Roland Leighton, had already been killed in action._\n\nI had just announced to my father, as we sat over tea in the dining room, that I really must do up Edward's papers and take them to the post office before it closed for the weekend, when there came the sudden loud clattering at the front-door knocker that always meant a telegram.\n\nFor a moment I thought that my legs would not carry me, but they behaved quite normally as I got up and went to the door. I knew what was in the telegram \u2013 I had known for a week \u2013 but because the persistent hopefulness of the human heart refuses to allow intuitive certainty to persuade the reason of that which it knows, I opened and read it in a tearing anguish of suspense.\n\n'Regret to inform you Captain E. H. Brittain M.C. killed in action Italy June 15th.'\n\n'No answer,' I told the boy mechanically, and handed the telegram to my father, who had followed me into the hall. As we went back into the dining room I saw, as though I had never seen them before, the bowl of blue delphiniums on the table; their intense colour, vivid, ethereal, seemed too radiant for earthly flowers.\n\nThen I remembered that we should have to go down to Purley and tell the news to my mother.\n\nLate that evening, my uncle brought us all back to an empty flat. Edward's death and our sudden departure had offered the maid \u2013 at that time the amateur prostitute \u2013 an agreeable opportunity for a few hours' freedom of which she had taken immediate advantage. She had not even finished the household handkerchiefs, which I had washed that morning and intended to iron after tea; when I went into the kitchen I found them still hanging, stiff as boards, over the clothes-horse near the fire where I had left them to dry.\n\nLong after the family had gone to bed and the world had grown silent, I crept into the dining room to be alone with Edward's portrait. Carefully closing the door, I turned on the light and looked at the pale, pictured face, so dignified, so steadfast, so tragically mature. He had been through so much \u2013 far, far more than those beloved friends who had died at an earlier stage of the interminable War, leaving him alone to mourn their loss. Fate might have allowed him the little, sorry compensation of survival, the chance to make his lovely music in honour of their memory. It seemed indeed the last irony that he should have been killed by the countrymen of Fritz Kreisler, the violinist whom of all others he had most greatly admired.\n\nAnd suddenly, as I remembered all the dear afternoons and evenings when I had followed him on the piano as he played his violin, the sad, searching eyes of the portrait were more than I could bear, and falling on my knees before it I began to cry, 'Edward! Oh, Edward!' in dazed repetition, as though my persistent crying and calling would somehow bring him back.\n\n## _Wounded, The Somme, 15 September 1916_\n\nBERT STEWARD\n\n_After a week's heavy shelling British troops went 'over the top' on the morning of 1 July 1916 along a fifteen-mile sector of the Western Front. They expected no opposition; instead they met a hurricane of German bullets, and 60,000 British casualties were sustained in just twenty-four hours. Their deaths secured 100,000 yards of ground. The Battle of the Somme raged until mid-November, by which time the conflagration had claimed 420,000 British killed and wounded. Bert Steward, at High Wood, was one of them_.\n\nZero hour, and my corporal made a little gesture at me, and we got out of the ditch and started to walk. I never saw him again.\n\nImagine us then rather like overladen porters going slow over a shockingly ploughed field in a man-made thunder storm. Hailstones of a lethal kind zipped past our heads. From behind us the bombardment from our own guns, which I had seen massed wheel to wheel, went on. To left and right men were moving forward in uneven lines. My plan was to walk alone and not get bunched up with others. I kept away from them. I soon found this easier. On each side some had disappeared. I saw only one tank \u2013 in a ditch with a broken track, like a dying hippopotamus, with shells bursting round it. I kept walking. I walked about half a mile. I reached the shelter of an embankment. With this solid mass between me and the enemy I felt safe.\n\nThe next moment was the luckiest of my life. I had walked all the way through a hail of bullets. I had been a slowly-moving target for the machine guns. The bullets had all missed, though narrowly, for parts of my tunic were in ribbons. Then, just as I had reached safety, as I thought, what seemed like a hammer blow hit me on the top of my left shoulder. I opened my tunic. There was a clean round hole right through the shoulder. A bullet! But where from? Then I realised I was getting enfiladed by some machine-gunner to my right, on my side of the embankment. I threw myself down, but not before another bullet struck my right thigh.\n\nIn the embankment was the entrance to a dugout. I crawled into it. It was occupied by Germans. None of them spoke. They were all dead.\n\nThere was parcels from home strewn about, cigarettes, black bread, eatables, and one huge German, lying face downwards, made a good couch to sit on. Now I was joined by two friends, one less lucky, a young lad from Liverpool, with a bullet through the stomach.\n\nHere we were, in front of our front line. About a hundred yards back I could see tin hats bobbing about. The remnants of the cast-irons were manning an improvised front line among the shellholes. Beyond them. I thought, was England, home and beauty.\n\nI had taken High Wood, almost by myself, it seemed. I had no further territorial ambitions. Indeed, what I now had in mind was to go as quickly as possible in the opposite direction, as soon as possible. Leaving the dugout, I ran for it, zigzagging to escape bullets (two were enough) and so fast that I toppled head-first on top of a rifleman who was almost as scared as I was. After he had recovered he told me how I could work my way along the line of shellholes to a dressing station. I went, keeping my head down; I was taking no chances. I had two bullet holes. If they had been drilled by a surgeon they could not have been located more conveniently. I was incredibly lucky. But another might spoil everything. I crawled along.\n\nThe dressing station was a captured German underground hospital, with entrance big enough for an ambulance, built like a fortress, furnished with tiers of wooden bunks. It was crowded with wounded, now being sorted out by our adjutant.\n\n'Those who can run follow me, nobody with a leg wound,' he said. 'We have to move fast,' I was the first to follow. In and out of shellholes we went \u2013 a rough but rapid journey in the right direction \u2013 until we reached a sunken lane where a horse-drawn hooded cart waited to take a dozen of us an hour's trot nearer home...\n\nThe Canadian doctor looked like any other in his white coat. He turned out to be a saint. 'You've been very lucky,' he said in a kindly way. Then he explained that one bullet, almost incredibly, had found a narrow gap between collar-bone and shoulder-blade, and that neither of the two had touched muscle or bone. 'How old are you and how long have you been in the trenches?' he asked and, when I told him, he wrote on a card and gave it to the nurse.\n\nLater I looked up at the card pinned to the chart above my bed. It was marked with a big B. What did it mean? A nurse hurrying by answered my question. She smiled as she said \u2013 'It means Blighty.'\n\n## _T. E. Lawrence Blows up a Train on the Hejaz Railway, Arabia, 1917_\n\nLIEUTENANT-COLONEL T. E. LAWRENCE\n\n_Lawrence of Arabia was a British intelligence officer attached to the irregular Arab arm of the Grand Sharif of Mecca, Hussein. Not the least part of Lawrence's guerrilla war was spent disrupting the Hejaz railway, the Turks' main supply line in the desert._\n\nZaal and I rushed uphill and saw by its shape and volume that indeed there must be a train waiting in that station. As we were trying to see it over the hill, suddenly it moved out in our direction. We yelled to the Arabs to get into position as quick as possible, and there came a wild scramble over sand and rock. Stokes and Lewis, being booted, could not win the race; but they came well up, their pains and dysentery forgotten.\n\nThe men with rifles posted themselves in a long line behind the spur running from the guns past the exploder to the mouth of the valley. From it they would fire directly into the derailed carriages at less than one hundred and fifty yards, whereas the ranges for the Stokes and Lewis guns were about three hundred yards. An Arab stood up on high behind the guns and shouted to us what the train was doing \u2013 a necessary precaution, for if it carried troops and detrained them behind our ridge we should have to face about like a flash and retire fighting up the valley for our lives. Fortunately it held on at all the speed the two locomotives could make on wood fuel.\n\nIt drew near where we had been reported, and opened random fire into the desert. I could hear the racket coming, as I sat on my hillock by the bridge to give the signal to Salem, who danced round the exploder on his knees, crying with excitement, and calling urgently on God to make him fruitful. The Turkish fire sounded heavy, and I wondered with how many men we were going to have affair, and if the mine would be advantage enough for our eighty fellows to equal them. It would have been better if the first electrical experiment had been simpler.\n\nHowever, at that moment the engines, looking very big, rocked with screaming whistles into view around the bend. Behind them followed ten box-waggons, crowded with rifle-muzzles at the windows and doors; and in little sand-bag nests on the roofs Turks precariously held on, to shoot at us. I had not thought of two engines, and on the moment decided to fire the charge under the second, so that however little the mine's effect, the uninjured engine should not be able to uncouple and drag the carriages away.\n\nAccordingly, when the front 'driver' of the second engine was on the bridge, I raised my hand to Salem. There followed a terrific roar, and the line vanished from sight behind a spouting column of black dust and smoke a hundred feet high and wide. Out of the darkness came shattering crashes and long, loud metallic clangings of ripped steel, with many lumps of iron and plate; while one entire wheel of a locomotive whirled up suddenly black out of the cloud against the sky, and sailed musically over our heads to fall slowly and heavily into the desert behind. Except for the flight of these, there succeeded a deathly silence, with no cry of men or rifle-shot, as the now grey mist of the explosion drifted from the line towards us, and over our ridge until it was lost in the hills.\n\nIn the lull, I ran southward to join the sergeants. Salem picked up his rifle and charged out into the murk. Before I had climbed to the guns the hollow was alive with shots, and with the brown figures of the Beduin leaping forward to grips with the enemy. I looked round to see what was happening so quickly, and saw the train stationary and dismembered along the track, with its waggon sides jumping under the bullets which riddled them, while Turks were falling out from the far doors to gain the shelter of the railway embankment.\n\nAs I watched, our machine-guns chattered out over my head, and the long rows of Turks on the carriage roofs rolled over, and were swept off the top like bales of cotton before the furious shower of bullets which stormed along the roofs and splashed clouds of yellow chips from the planking. The dominant position of the guns had been an advantage to us so far.\n\nWhen I reached Stokes and Lewis the engagement had taken another turn. The remaining Turks had got behind the bank, here about eleven feet high, and from cover of the wheels were firing point-blank at the Beduin twenty yards away across the sand-filled dip. The enemy in the crescent of the curving line were secure from the machine-guns; but Stokes slipped in his first shell, and after a few seconds there came a crash as it burst beyond the train in the desert.\n\nHe touched the elevating screw, and his second shot fell just by the trucks in the deep hollow below the bridge where the Turks were taking refuge. It made a shambles of the place. The survivors of the group broke out in a panic across the desert, throwing away their rifles and equipment as they ran. This was the opportunity of the Lewis gunners. The sergeant grimly traversed with drum after drum, till the open sand was littered with bodies. Mushagraf, the Sherari boy behind the second gun, saw the battle over, threw aside his weapon with a yell, and dashed down at speed with his rifle to join the others who were beginning, like wild beasts, to tear open the carriages and fall to plunder. It had taken nearly ten minutes.\n\nI looked up-line through my glasses and saw the Mudowwara patrol breaking back uncertainly towards the railway to meet the train-fugitives running their fastest northward. I looked south, to see our thirty men cantering their camels neck and neck in our direction to share the spoils. The Turks there, seeing them go, began to move after them with infinite precaution, firing volleys. Evidently we had a half hour respite, and then a double threat against us.\n\nI ran down to the ruins to see what the mine had done. The bridge was gone; and into its gap was fallen the front waggon, which had been filled with sick. The smash had killed all but three or four and had rolled dead and dying into a bleeding heap against the splintered end. One of those yet alive deliriously cried out the word typhus. So I wedged shut the door, and left them there, alone.\n\nSucceeding waggons were derailed and smashed: some had frames irreparably buckled. The second engine was a blanched pile of smoking iron. Its driving wheels had been blown upward, taking away the side of the fire-box. Cab and tender were twisted into strips, among the piled stones of the bridge abutment. It would never run again. The front engine had got off better: though heavily derailed and lying halfover, with the cab burst, yet its steam was at pressure, and driving-gear intact.\n\nOur greatest object was to destroy locomotives, and I had kept in my arms a box of gun-cotton with fuse and detonator ready fixed, to make sure such a case. I now put them in position on the outside cylinder. On the boiler would have been better, but the sizzling steam made me fear a general explosion which would sweep across my men (swarming like ants over the booty) with a blast of jagged fragments. Yet they would not finish their looting before the Turks came. So I lit the fuse, and in the half-minute of its burning drove the plunderers a little back, with difficulty. Then the charge burst, blowing the cylinder to smithers, and the axle too. At the moment I was distressed with uncertainty whether the damage were enough; but the Turks later found the engine beyond use and broke it up.\n\nThe valley was a weird sight. The Arabs, gone raving mad, were rushing about at top speed bareheaded and half-naked, screaming, shooting into the air, clawing one another nail and fist, while they burst open trucks and staggered back and forward with immense bales, which they ripped by the railside, and tossed through, smashing what they did not want. The train had been packed with refugees and sick men, volunteers for boat-service on the Euphrates, and families of Turkish officers returning to Damascus.\n\nThere were scores of carpets spread about; dozens of mattresses and flowered quilts, blankets in heaps, clothes for men and women in full variety; clocks, cooking-pots, food, ornaments and weapons. To one side stood thirty or forty hysterical women, unveiled, tearing their clothes and hair; shrieking themselves distracted. The Arabs without regard to them went on wrecking the household goods; looting their absolute fill. Camels had become common property. Each man frantically loaded the nearest with what it could carry and shooed it westward into the void, while he turned to his next fancy.\n\nSeeing me tolerably unemployed, the women rushed, and caught at me with howls for mercy. I assured them that all was going well: but they would not get away till some husbands delivered me. These knocked their wives off and seized my feet in a very agony of terror of instant death. A Turk so broken down was a nasty spectacle: I kicked them off as well as I could with bare feet, and finally broke free.\n\nNext a group of Austrians, officers and non-commissioned officers, appealed to me quietly in Turkish for quarter. I replied with my halting German; whereupon one, in English, begged a doctor for his wounds. We had none: not that it mattered, for he was mortally hurt and dying. I told them the Turks would return in an hour and care for them. But he was dead before that, as were most of the others (instructors in the new Skoda mountain howitzers supplied to Turkey for the Hejaz war), because some dispute broke out between them and my own bodyguard, and one of them fired a pistol shot at young Rahail. My infuriated men cut them down, all but two or three, before I could return to interfere.\n\n_When Lawrence of Arabia blew up the Turkish train in the Hejaz the First World War still had a year to run, but its outcome was already determined. The Kaiser's order to his U-boats to 'sink on sight' all shipping, no matter what its nationality, in a bid to starve Britain out, had brought America into the war on the Allied side on 6 April 1917. Germany had been unable to defeat the 'thin khaki line' of the British Army; when this was reinforced by the double-sized divisions of the US Expeditionary Force and backed by the super-sized US economy she had no chance of victory._\n\n## _Armistice Celebrations, London, 11 a.m., 11 November 1918_\n\nWINSTON CHURCHILL\n\nIt was a few minutes before the eleventh hour of the eleventh day of the eleventh month. I stood at the window of my room looking up Northumberland Avenue towards Trafalgar Square, waiting for Big Ben to tell that the War was over. My mind strayed back across the scarring years...\n\nThe minutes passed. I was conscious of reaction rather than elation... And then suddenly the first stroke of the chime. I looked again at the broad street beneath me. It was deserted. From the portals of one of the large hotels absorbed by Government Departments darted the slight figure of a girl clerk, distractedly gesticulating while another stroke of Big Ben resounded. Then from all sides men and women came scurrying into the street. Streams of people poured out of all the buildings. The bells of London began to clash. Northumberland Avenue was now so crowded with people in hundreds, nay, thousands, rushing hither and thither in a frantic manner, shouting and screaming with joy. I could see that Trafalgar Square was already swarming. Around me in our very headquarters, in the Hotel Metropole, disorder had broken out. Doors banged. Feet clattered down corridors. Everyone rose from the desk and cast aside pen and paper. All bounds were broken. The tumult grew. It grew like a gale, but from all sides simultaneously. The street was now a seething mass of humanity. Flags appeared as if by magic. Streams of men and women flowed from the Embankment. They mingled with torrents pouring down the Strand on their way to acclaim the King. Almost before the last stroke of the clock had died away, the strict, war-straitened, regulated streets of London had become a triumphant pandemonium. At any rate it was clear that no more work would be done that day. Yes, the chains which had held the world were broken. Links of imperative need, links of discipline, links of brute force, links of self-sacrifice, links of terror, links of honour which had held our nation, nay, the greater part of mankind, to grinding toil, to a compulsive cause \u2013 every one had snapped upon a few strokes of the clock. Safety, freedom, peace, home, the dear one back at the fireside \u2013 all after fifty-two months of gaunt distortion. After fifty-two months of making burdens grievous to be borne and binding them on men's backs, at last, all at once, suddenly and everywhere the burdens were cast down. At least so for the moment it seemed.\n\nMy wife arrived, and we decided to go and offer our congratulations to the Prime Minister, on whom the central impact of the home struggle had fallen, in his hour of recompense. But no sooner had we entered our car than twenty people mounted upon it, and in the midst of a wildly cheering multitude we were impelled slowly forward through Whitehall. We had driven together the opposite way along the same road on the afternoon of the ultimatum. There had been the same crowd and almost the same enthusiasm. It was with feelings which do not lend themselves to words that I heard the cheers of the brave people who had borne so much and given all, who had never wavered, who had never lost faith in their country or its destiny, and who could be indulgent to the faults of their servants when the hour of deliverance had come...\n\n_The First World War was over. So was the old order of things. Returning troops were promised by Lloyd George, the Liberal Prime Minister, 'a land fit for heroes to live in'. That land could have nothing less than universal male suffrage, for all ranks of men had fought the war, therefore all ranks required a say in the peace. By the same token, women had helped win the war, working as nurses, munitions workers and 'land girls'._\n\n_By the Representation of the People Act, 1918, the vote was extended to all men over twenty-one and all women over thirty. The enlarged electorate, to no one's great surprise, boosted the fortunes of the Labour Party, which formed its first government in 1924._\n\n_Whatever their hue, governments of the 1920s and 1930s were mired in problems. Ireland, brought into the Union in 1800, was in nationalist revolt, which British forces ('The Black and Tans') distinctly failed to suppress. Discretion was better than fighting De Valera and Ireland was let go (save for the Protestant-leaning Northern six counties) in 1921. There was no quick fix for the national debt, which had risen from \u00a3650,000,000 in 1914 to \u00a37,830,000,000 in 1920. The price of freedom from the Kaiser's expansionist Germany had not been cheap. On top of the debt, Britain had definitively lost its leading role in the world's economy, and its traditional industries, especially, were antique, under-capitalized and beset by antagonistic labour relations. King Coal was the exemplar. It was the coal industry which spawned Britain's first, and last, general strike._\n\n## _The General Strike, 4\u201312 May 1926_\n\nARNOLD BENNETT\n\n_To support coal miners 'locked out' by their employers (as a means of forcing wage cuts), the Trades Union Congress called out workers in key industries, notably the docks, railways, gas and electricity. Much of the country came to a halt, but the TUC leaders had no stomach for constitutional conflict and called off the strike on 12 May. Almost everywhere, the strike was peaceful, coppers and strikers playing football together, with the middle classes joyfully 'black-legging' (strike-breaking) by driving buses and lorries._\n\nTo-day was the first day of the general strike. Many more motors about. I walked round Victoria, which was shut up (both stations) one small entrance guarded by policemen. I heard someone say that a train had gone somewhere during the morning. Yet in the vast empty stations Smith's bookstalls were open. So were (outside) the caf\u00e9s. The populace excited and cheery, on this 1st day of the strike. No evening paper. News from the Wireless at very short intervals, \u00bd hour intervals at night up to midnight. I should think that nearly all theatres would soon be closed. Already to-day there has been a noticeably increasing gravity in the general demeanour.\n\nMay 5: \u2013 Lunch at the Reform at 1.30. Upstairs, Gardiner, Tudor Walters, Hedges, Jim Currie, Sassoon, and Lord Devonport. Most people gloomy, but all uncompromising. General opinion that the fight would be short but violent. Bloodshed anticipated next week. Plenty of wireless messages, futile. Typescript-printed _Times_ and _Financial News._\n\nMay 6: \u2013 Another N.N.E. wind. Not a taxi on the streets that I saw. It is now over a week since I did anything on the novel \u2013 the last day being Thursday, 29th April. I went for a walk to Brompton Rd to spy out the land. Eleven buses passed the top of Sloane St in five minutes at 4.30. Only two of them were Generals, and both of them had a window smashed. I saw more in the evening. A policeman and a special constable on every General...\n\nMay 12: \u2013 The general strike now seems pitiful \u2013 a pathetic attempt of underdogs who hadn't a chance when the over-dogs really set themselves to win. Everybody, nearly, among the over-dogs seems to have joined in with grim enthusiasm to beat the strike. The Doctor called yesterday morning, and even he had been working at 'criminal investigations' for the Government. (He spoke of deaths resulting from East End rioting.) Willie Maugham was working at Scotland Yard till 8.30 of a night \u2013 I don't know what at. Special constables abounded.\n\nMay 13: \u2013 Everyone is still preoccupied with the strike, or rather with what is called 'The new strike'. Duff Tayler told great stories of his adventurous journeys on the Tube trains driven by swagger youths in yellow gloves who nevertheless now and then overran the platform with their trains, or pulled up too short. Also of University porters with gold cigarette cases and an incredible politeness and fatherliness towards you for your safety. Maugham was what he called a 'sleuth' at Scotland Yard. A police car was sent for him always. The first night he worked all night from 11 p.m. to 8.30 a.m. He said the last few hours, after dawn, were simply terrible, and he couldn't see how he would ever be able to get through them. I don't know what a 'sleuth' is.\n\n_The miners held out for another five months before trickling back to work._\n\n_Of course, the damp-squibness of the General Strike should have come as nosurprise. England did not do class war. In the rest of Europe, governments were being toppled, workers were revolting, far-right groups were launching putsches, but in England the_ communitas _held together, bound by a shared understanding of Englishness, reverence for the monarchy, a sense of humour, and the long habit of parliamentary democracy._\n\n## _Body-line Bowling, Adelaide, Australia, 13\u201319 January 1933_\n\nW. H. FERGUSON\n\n_Cricket has been played in England since the twelfth century; in the twentieth it became the cause of fractious relations between England and the dominion of Australia. W. H. Ferguson was on the MCC's staff. Douglas Jardine was the English skipper._\n\nThis was destined to be an historic and sensational match, one of the most unpleasant exhibitions \u2013 from many aspects \u2013 it has been my misfortune to witness. I have no doubt in my mind that the Australian cricketers were terrified by Harold Larwood and his leg theory bowling, an attitude of mind fully justified by the events of the match.\n\nOne batsman after another suffered physically as Larwood relentlessly set about the job allocated to him by Jardine; Bill Ponsford, who frequently turned his back on the ball, had dozens of bruises to emphasize the folly of such attempted evasive action. Bill Woodfull, never very quick on his feet, suffered even more, and I was in full sympathy with his wife who feared for Woodfull's safety. It came as no surprise when, after receiving a severe blow on the chest from a Larwood delivery, Woodfull had to be taken to the dressing room, a very sick man.\n\nWhen Bert Oldfield, always a popular figure with spectators, had to be carried to the pavilion, knocked unconscious with a fast, rising ball, the indignation of spectators was at boiling point. Maurice Tate, who was not playing for England, told me, 'Bill, I'm getting out of here. Somebody is going to get seriously hurt, and the people will start a riot,' I felt sure some hotheads in the crowd would jump the rails and try to assault the English cricketers, but, thank Heaven, it did not come to that.\n\n'Plum' Warner, in an effort to do the right thing, looked into the Australian dressing room which, by that time, resembled a casualty clearing station, and expressed his regret for the injuries caused by the tourists' fast bowling. He received a snub which made front page news all over the world, when Woodfull told him, 'I don't want to speak to you, Mr Warner. There are two teams out there and one is playing cricket. If these tactics are persevered with, it may be better if I do not play the game. Good afternoon.'\n\nThen followed an historic cable from the Australian Cricket Board of Control to the MCC in London. Dated 18th January, 1933, it was worded:\n\n'Bodyline bowling has assumed such proportions as to menace the best interests of the game, making the protection of his body by a batsman his main consideration. It is causing intensely bitter feeling between the players as well as injury to them. In our opinion it is unsportsmanlike. Unless it is stopped at once it is likely to upset the friendly relations existing between Australia and England.'\n\n_Larwood was dropped from future Test teams on the insistence of J. H. Thomas, the Dominions Secretary._\n\n## _Down and Out: A Night in a Doss-house, c. 1931_\n\nGEORGE ORWELL\n\n_Turning his back on his upper-middle-class upbringing (prep school, Eton), George Orwell donned tramp's clothes to go and explore impoverished England \u2013 as related in Down and Out in Paris and London. By 1931 the Great Depression was at its zenith and unemployment in England had reached 3 million._\n\nAt about eleven I began looking for a bed. I had read about doss-houses (they are never called doss-houses, by the way), and I supposed that one could get a bed for fourpence or thereabouts. Seeing a man, a navvy or something of the kind, standing on the kerb in the Waterloo Road, I stopped and questioned him. I said that I was stony broke and wanted the cheapest bed I could get.\n\n'Oh,' said he, 'you go to that 'ouse across the street there, with the sign \"Good Beds for Single Men\". That's a good kip [sleeping place], that is. I bin there myself on and off. You'll find it cheap _and_ clean.'\n\nIt was a tall, battered-looking house, with dim lights in all the windows, some of which were patched with brown paper. I entered a stone passage-way, and a little etiolated boy with sleepy eyes appeared from a door leading to a cellar. Murmurous sounds came from the cellar, and a wave of hot air and cheese. The boy yawned and held out his hand.\n\n'Want a kip? That'll be a 'og, guv'nor.'\n\nI paid the shilling, and the boy led me up a rickety unlighted staircase to a bedroom. It had a sweetish reek of paregoric and foul linen; the windows seemed to be tight shut, and the air was almost suffocating at first. There was a candle burning, and I saw that the room measured fifteen feet square by eight high, and had eight beds in it. Already six lodgers were in bed, queer lumpy shapes with all their own clothes, even their boots, piled on top of them. Someone was coughing in a loathsome manner in one corner.\n\nWhen I got into the bed I found that it was as hard as a board, and as for the pillow, it was a mere hard cylinder like a block of wood. It was rather worse than sleeping on a table, because the bed was not six feet long, and very narrow, and the mattress was convex, so that one had to hold on to avoid falling out. The sheets stank so horribly of sweat that I could not bear them near my nose. Also, the bedclothes only consisted of the sheets and a cotton counterpane, so that though stuffy it was none too warm. Several noises recurred throughout the night. About once in an hour the man on my left \u2013 a sailor, I think \u2013 woke up, coughed vilely, and lighted a cigarette. Another man, victim of bladder disease, got up and noisily used his chamber pot half a dozen times during the night. The man in the corner had a coughing fit once in every twenty minutes, so regularly that one came to listen for it as one listens for the next yap when a dog is baying the moon. It was an unspeakably repellent sound; a foul bubbling and retching, as though the man's bowels were being churned up within him. Once when he struck a match I saw that he was a very old man, with a grey, sunken face like that of a corpse, and he was wearing his trousers wrapped round his head as a nightcap, a thing which for some reason disgusted me very much. Every time he coughed or the other man swore, a sleepy voice from one of the other beds cried out:\n\n'Shut up! Oh, for Christ's \u2013 _sake_ shut up!'\n\nI had about an hour's sleep in all. In the morning I was woken by a dim impression of some large brown thing coming towards me. I opened my eyes and saw that it was one of the sailor's feet, sticking out of bed close to my face. It was dark brown, quite dark brown like an Indian's, with dirt. The walls were leprous, and the sheets, three weeks from the wash, were almost raw umber colour. I got up, dressed and went downstairs. In the cellar were a row of basins and two slippery roller towels. I had a piece of soap in my pocket, and I was going to wash, when I noticed that every basin was streaked with grime \u2013 solid, sticky filth as black as boot-blacking. I went out unwashed. Altogether, the lodging-house had not come up to its description as cheap _and_ clean. It was however, as I found later, a fairly representative lodging-house.\n\nI crossed the river and walked a long way eastward, finally going into a coffee-shop on Tower Hill. An ordinary London coffee-shop, like a thousand others, it seemed queer and foreign after Paris. It was a little stuffy room with the high-backed pews that were fashionable in the 'forties, the day's menu written on a mirror with a piece of soap, and a girl of fourteen handling the dishes. Navvies were eating out of newspaper parcels, and drinking tea in vast saucerless mugs like china tumblers. In a corner by himself a Jew, muzzle down in the plate, was guiltily wolfing bacon.\n\n'Could I have some tea and bread and butter?' I said to the girl.\n\nShe stared. 'No butter, only marg,' she said, surprised. And she repeated the order in the phrase that is to London what the eternal _coup de rouge_ is to Paris: 'Large tea and two slices!'\n\nOn the wall beside my pew there was a notice saying 'Pocketing the sugar not allowed,' and beneath it some poetic customer had written:\n\nHe that takes away the sugar,\n\nShall be called a dirty \u2013\n\nbut someone else had been at pains to scratch out the last word. This was England. The tea-and-two-slices cost threepence halfpenny, leaving me with eight and twopence.\n\n## _The Battle of Cable Street, 7 October 1936_\n\nPHIL PIRATIN\n\n_To steer England out of the Depression doldrums, there were calls from the sidelines for drastic change. On the far left, the pro-Russian Communist Party of Great Britain (maximum membership 10,000) dominated a fractious political allsorts. On the far right, Sir Oswald Mosley founded the British Union ofFascists in 1932, whose 20,000 members wore the uniform of Mussolini's Black-shirts. At Cable Street, in London's East End, the CPGB determined to stop the Blackshirts from marching._\n\n_Piratin was an official of the Communist Party of Great Britain._\n\nIt was obvious that the Fascists and the police would now turn their attention to Cable Street. We were ready. The moment this became apparent the signal was given to put up the barricades. We had prepared three spots. The first was near a yard where there was all kinds of timber and other oddments, and also an old lorry. An arrangement had been made with the owner that this old lorry could be used as a barricade. Instructions had been given about this, but when someone shouted 'Get the lorry!' evidently not explaining that it was in the nearby yard, some of the lads, looking up the street, saw a stationary lorry about 200 yards away. They went along, brought it back, and pushed it over on its side before anyone even discovered that it was not the lorry meant to be used. Still it was a lorry, and supplemented by bits of old furniture, mattresses, and every kind of thing you expect to find in boxrooms, it was a barricade which the police did not find it easy to penetrate. As they charged they were met with milk bottles, stones, and marbles. Some of the housewives began to drop milk bottles from the roof tops. A number of police surrendered. This had never happened before, so the lads didn't know what to do, but they took away their batons, and one took a helmet for his son as a souvenir.\n\nCable Street was a great scene. I have referred to 'the lads'. Never was there such unity of all sections of the working class as was seen on the barricades at Cable Street. People whose lives were poles apart, though living within a few hundred yards of each other; bearded Orthodox Jews and rough-and-ready Irish Catholic dockers \u2013 these were the workers that the Fascists were trying to stir up against each other. The struggle, led by the Communist Party, against the Fascists had brought them together against their common enemies, and their lackeys.\n\nMeanwhile, charges and counter-charges were taking place along 'the front' from Tower Hill to Gardner's Corner. Many arrests were made, many were injured. It was the police, however, who were carrying on the battle, while the Fascists lurked in the background, protected by a 'fence' of police. Mosley was late. As soon as he arrived, in a motor-car, a brick went clean through the window.\n\nIt was later rumoured that Sir Philip Game had been on the telephone to the Home Secretary, and had pleaded with Sir John Simon to forbid the march. Sir John was adamant. Sir Philip Game, however, made up his own mind. He forbade the march and told Mosley to argue it out with Sir John Simon. The Fascists lined up, saluted their leader, and marched through the deserted City to the Embankment, where they dispersed. The working class had won the day.\n\n## _The Jarrow March, October 1936_\n\nROY CHADWICK\n\n_Much the most dramatic gesture drawing attention to the plight of the impoverished and unemployed of the 1930s was the hunger march; the most celebrated was from Jarrow ('the town they killed') to London, and was led by Jarrow's Labour MP, 'Red' Ellen Wilkinson. Two hundred Jarrow shipyard workers walked with her._\n\n_Roy Chadwick was a Guardian journalist._\n\nThere can be no doubt that as a gesture the march is a bounding success. I fell in with it this morning on the Ripon road. Under its two banners ('Jarrow Crusade'), with its harmonicas, its kettle-drum, and its four hundred feet, it was going strong. The marchers have with them two doctors, a barber, a group of pressmen, a Labrador dog mascot, and for a great deal of the time so far the Mayor of Jarrow (Alderman J. W. Thompson), who keeps travelling back to Jarrow to maintain touch with his civic duties and then south again to maintain touch with the marchers. It is an example of civic spirit probably without parallel anywhere else in the country. With him at the head of the procession is its marshal, County Councillor D. F. Riley, the inspirer and organizer of the march.\n\nThis is not a hunger-march, but a protest march. The unanimity of the protest that Jarrow is making to the rest of the country is indicated in the fact that the political parties represented on the Jarrow Town Council have agreed to bury the political hatchet to the extent of holding no elections this November. Further, although the town cannot by law spend a farthing of the rate-payers' money on this demonstration, the labours of its Mayor in dispatching about 200,000 letters to other corporations, trade unions, co-operative societies and similar bodies at the expense of the march fund has raised that fund to \u00a3850, and it is hoped to have the round \u00a31,000 before the marchers reach the Marble Arch on 31 October.\n\nThe more fortunate classes of Jarrow, where not fifteen per cent of the employable population is at work, have contributed, but the bulk of the fund has come from the country at large, and more than money. I, for one, had no conception of the cost of organizing such a march until I heard about the value of the gifts in kind that ease the drain on the march fund so considerably. Take cigarettes, for instance, and calculate the cost of distributing two twopenny packets per day per man to 200 men. I will not vouch that 'fags' are among the gifts, but it illustrates the point. Any little article costing sixpence means five pounds when distributed to 200 men, and soap, tobacco, and all sorts of things have been given. Before the men set out they all had their boots soled and heeled, and two pairs of socks and two iodine soles were also issued.\n\nWith eggs and salmon and such sandwiches as I saw to-day being consumed on the menu it is emphatically not a hunger-march. The men are doing well on it, and only two of them have fallen out for reasons of health in nearly ninety miles of marching. All the time communication is maintained with Jarrow, and if work turns up for a man on the march back he will go to it.\n\nThe organization seems well nigh perfect. It includes a transport wagon \u2013 a 'bus bought for \u00a320 and converted \u2013 which goes ahead with the sleeping kit, waterproofs for every man worn bandolero fashion, 1S. _6d._ pocket-money and two 1\u00bd _d._ stamps a week, medical attention, haircutting (and shaving for the inexpert), cobbling, accommodation at night in drill halls, schools, church institutes, and even town halls, and advance agents in the persons of the Labour agent at Jarrow, Mr Harry Stoddert, and the Conservative agent, Mr R. Suddick, who work together in arranging accommodation and getting halls for meetings.\n\nThere is no political aspect to this march. It is simply the town of Jarrow saying 'Send us work'. In the ranks of the marchers are Labour men, Liberals, Tories, and one or two Communists, but you cannot tell who's who. It has the Church's blessing; in fact, it took the blessing of the Bishop of Ripon (Dr Lunt) and a subscription of \u00a3 _5_ from him when it set out to-day. It also had the blessing of the Bishop of Jarrow (Dr Gordon).\n\nWith the marchers goes, prominently carried, the Jarrow petition for work, a huge book with about 12,000 signatures, which, after a meeting at the Memorial Hall, London, the previous day, Miss Ellen Wilkinson, MP for Jarrow, is to present at the bar of the House of Commons on 4 November. Miss Wilkinson met us outside Killinghall this afternoon and became the only woman in the procession. She had motored from Manchester to-day but had met with petrol trouble and had been delayed. It was interesting to watch motorists who passed us on the road recognize her and lean out of windows as they went by. Like us all she made friends with Paddy, the Labrador dog who accompanied the procession uninvited for five miles from Jarrow before anyone realized that he intended to go all the way.\n\n## _The Abdication, 11 December 1936_\n\nSIR HENRY CHANNON\n\n_Above the trials of England in the 1930s sat the monarchy, more comfortable than ever. It proved adept at the common touch (George V attending the Cup Final), traditional pageantry (George V's Silver Jubilee), and new means of communication (radio broadcasts). Even the abdication of Edward VIII left it undented. Edward VIII ('David' to the family), wished to marry the twice-divorced American, Wallis Simpson; the Cabinet, Church and Commonwealth maintained that he could not then remain king. He chose the 'woman I love'._\n\n_Channon was a Conservative MP and minister._\n\n_11 December 1936: '_ The King is gone, Long live the King.' We woke in the reign of Edward VIII and went to bed in that of George VI. Honor [Lady Honor Channon, Chips's wife] and I were at the House of Commons by eleven o'clock... When the Bill came it was passed into law with the minimum of time... Then the Royal Commission was sent for, and the Lords Onslow, Denman and one other, filed out of the Chamber, and returned in full robes and wigs. Black Rod was sent to summon the Speaker, who, followed by his Commons, appeared at the bar. The Clerk read the Royal Commission. The three Lords bowed, and doffed their hats. The Bill was read. The King was still King Edward. The Clerk bowed, 'Le Roi le veult' [It is the King's will] and Edward, the beautiful boy King with his gaiety and honesty, his American accent and nervous twitching, his flair and glamour, was part of history. It was 1.52.\n\nWe went sadly home, and in the street we heard a woman selling newspapers saying, 'The Church held a pistol to his head.' In the evening we dined at the Stanleys' cheerless, characterless house, and at ten o'clock turned on the wireless to hear 'His Royal Highness Prince Edward' speak his farewell words in his unmistakable slightly Long Island voice. It was a manly, sincere farewell... There was a stillness in the Stanleys' room. I wept, and I murmured a prayer for he [ _sic_ ] who had once been King Edward VIII.\n\nThen we played bridge.\n\n_According to Sir Eric Mieville, one of George VI's secretaries, Edward VIII was 'quite unmoved' throughout the abdication drama: 'His last act prior to broadcasting his message and then leaving the country was to sit in his bedroom with a whisky and soda having his toe-nails seen to.'_\n\n## _World War II: Children Evacuated, London, 1 September 1939_\n\nHILDE MARCHANT\n\n_The Second World War opened at 04.45 hours on 1 September 1939, when German tanks rolled into Poland. Britain was not yet in the conflict, but prudence dictated that London's children were evacuated anyway._\n\nThe office had told me to cover the evacuation of some of London's schoolchildren. There had been great preparations for the scheme \u2013 preparations that raised strong criticism. Evacuation would split the British home, divide child and parent, break that domestic background that was our strength.\n\nI went to a block of working-class flats at the back of Gray's Inn Road and in the early morning saw a tiny, frail, Cockney child walking across to school. The child had a big, brown-paper parcel in her hand and was dragging it along. But as she turned I saw a brown box banging against her thin legs. It bumped up and down at every step, slung by a thin string over her shoulder.\n\nIt was Florence Morecambe, an English schoolchild, with a gas mask instead of a satchel over her shoulder.\n\nI went along with Florence to her school. It was a big Council school and the classrooms were filled with children, parcels, gas masks. The desks and blackboards were piled up in a heap in one corridor. They were not going to school for lessons. They were going on a holiday. The children were excited and happy because their parents had told them they were going away to the country. Many of them, like my little Florence, had never seen green fields. Their playground was the tarmac or a sandpit in the concrete square at the back.\n\nI watched the schoolteachers calling out their names and tying luggage labels in their coats, checking their parcels to see there were warm and clean clothes. On the gates of the school were two fat policemen. They were letting the children through but gently asking the parents not to come farther. They might disturb the children. So mothers and fathers were saying goodbye, straightening the girls' hair, getting the boys to blow their noses, and lightly and quickly kissing them. The parents stood outside while the children went to be registered in their classrooms. There was quite a long wait before this small army got its orders through from the LCC [London County Council] to move off. In the meantime I sat in the school playground, watching these thin, wiry little Cockneys playing their rough-and-push games on the faded netball pitch. It was disturbing, for through the high grille their mothers pressed their faces, trying to see the one child that resembled them. Every now and then the policeman would call out a child's name and a mother who had forgotten a bar of chocolate or a toothbrush had a last chance to tell a child to be good, to write and to straighten her hat.\n\nLabelled and lined up, the children began to move out of the school. I followed Florence, her live tiny face bobbing about, white among so many navy-blue school caps. She was chattering away to an older schoolgirl, wanting to know what the country was like, where they were going, what games they would play on the grass.\n\nOn one side of Gray's Inn Road this ragged crocodile moved towards the tube station. On the other, were mothers who were waving and running along to see the last of their children. The police had asked them not to follow, but they could not resist.\n\nThe children scrambled down into the tube.\n\n_Late on the morning of 3 September, Prime Minister Neville Chamberlain informed the nation that it was at war with Nazi Germany. (There was irony in this: Chamberlain had been an arch appeaser of Hitler and supposedly brokered 'peace in our time' only the year before.) For six months little happened \u2013 people talked of the 'Phoney War' \u2013 until April 1940, when Hitler launched his 'Blitzkrieg' on Norway and Denmark. A month later, the Germans invaded the Low Countries and France. England's patience with the irresolute, discredited Chamberlain broke, and Parliament replaced him on 13 May with Winston Churchill. So began Churchill's 'walk with destiny'. The most immediate problem on the path was the British Expeditionary Force in France which had retreated to the port of Dunkirk._\n\n## _Dunkirk: The Beach, 30 May 1940_\n\nCAPTAIN RICHARD AUSTIN, BEF\n\n_Evacuation of the British Expeditionary Force was authorized by Churchill on 26 May. Over the next nine days 224,385 British and 112,546 Franco-Belgian troops were saved. Aiding the armada of 222 naval units were 665 craft \u2013 ranging from sailing dinghies to merchantmen \u2013 commanded by their civilian volunteers._\n\nWe were now in the region of the dunes, which rose like humps of a deeper darkness. And these in their turn were dotted with the still blacker shapes of abandoned vehicles, half-sunk in the sand, fantastic twisted shapes of burned-out skeletons, and crazy-looking wreckage that had been heaped up in extraordinary piles by the explosions of bombs. All these black shapes were silhouetted against the angry red glare in the sky, which reflected down on us the agony of burning Dunkirk.\n\nSlowly we picked our way between the wreckage, sinking ankle-deep in the loose sand, until we reached the gaunt skeletons of what had once been the houses on the promenade. The whole front was one long continuous line of blazing buildings, a high wall of fire, roaring and darting in tongues of flame, with the smoke pouring upwards and disappearing in the blackness of the sky above the roof-tops. Out seawards the darkness was as thick and smooth as black velvet, except for now and again when the shape of a sunken destroyer or paddle-steamer made a slight thickening on its impenetrable surface. Facing us, the great black wall of the Mole stretched from the beach far out into the sea, the end of it almost invisible to us. The Mole had an astounding, terrifying background of giant flames leaping a hundred feet into the air from blazing oil tanks. At the shore end of the Mole stood an obelisk, and the high-explosive shells burst around it with monotonous regularity.\n\nAlong the promenade, in parties of fifty, the remnants of practically all the last regiments were wearily trudging along. There was no singing, and very little talk. Everyone was far too exhausted to waste breath. Occasionally out of the darkness came a sudden shout:\n\n'A Company, Green Howards...'\n\n'C Company, East Yorks...'\n\nThese shouts came either from stragglers trying to find lost units, or guides on the look-out for the parties they were to lead on to the Mole for evacuation.\n\nThe tide was out. Over the wide stretch of sand could be dimly discerned little oblong masses of soldiers, moving in platoons and orderly groups down towards the edge of the sea. Now and again you would hear a shout:\n\n'Alf, where are you?...'\n\n'Let's hear from you, Bill...'\n\n'Over this way, George...'\n\nIt was none too easy to keep contact with one's friends in the darkness, and amid so many little masses of moving men, all looking very much alike. If you stopped for a few seconds to look behind you, the chances were you attached yourself to some entirely different unit.\n\nFrom the margin of the sea, at fairly wide intervals three long thin black lines protruded into the water, conveying the effect of low wooden breakwaters. These were lines of men, standing in pairs behind one another far out into the water, waiting in queues till boats arrived to transport them, a score or so at a time, to the steamers and warships that were filling up with the last survivors. The queues stood there, fixed and almost as regular as if ruled. No bunching, no pushing, nothing like the mix-up to be seen at the turnstiles when a crowd is going to a football match. Much more orderly, even than a waiting theatre queue.\n\nAbout this time, afraid that some of our men might be trailing off, I began shouting, '2004th Field Regiment... 2004th Field Regiment...' A group of dead and dying soldiers on the path in front of us quickened our desire to quit the promenade. Stepping over the bodies we marched down the slope to a dark beach.\n\nWe tacked ourselves on to the rear of the smallest of the three queues, the head of which was already standing in water up to the waist. Half an hour passed. Suddenly a small rowing boat appeared. The head of the queue clambered in and was rowed away into the blackness...\n\nAlong the entire queue not a word was spoken. The men just stood there silently staring into the darkness, praying that a boat would soon appear, and fearing that it would not. Heads and shoulders only showing above the water. Fixed, immovable, as though chained there. It was, in fact, practically impossible to move, even from one foot to another. The dead-weight of water-logged boots and sodden clothes pinned one down. My breeches seemed to be ballooned out with water as heavy as mercury. I was filled with a dread that when the time did come I should be unable to move.\n\nSuddenly out of the blackness, rather ghostly, swam a white shape which materialized into a ship's lifeboat, towed by a motorboat. It moved towards us and came to a stop twenty yards in front of the head of our queue.\n\n'Hi! Hi!' we all hailed, dreading they hadn't seen us.\n\n'Ahoy! Ahoy!' came the lusty response.\n\n'Come in closer,' we shouted.\n\n'We can't. It's unsafe. Might upset the boat.' But they risked a few more yards...\n\nFour sailors in tin-hats began hoisting the soldiers out of the water. It was no simple task. Half the men were so weary and exhausted that they lacked strength to climb into the boat unaided. The sailors judged the situation perfectly, as being one for rough words, threats, and bullying methods. The only spur sufficient to rouse our worn-out bodies to one last supreme effort.\n\n'Come on you bastards...'\n\n'Wake up, blast you...'\n\n'Get a move on, Dopey...'\n\nThe gunwhale of the lifeboat stood three feet above the surface of the water. Reaching up, I could just grasp it with the tips of my fingers. When I tried to haul myself up I couldn't move an inch. The weight of my waterlogged clothes, especially my cherished greatcoat, beat me completely, desperately though I fought. I might have been a sack of lead. A great dread of being left behind seized me.\n\nTwo powerful hands reached over the gunwhale and fastened themselves into my arm-pits. Another pair of hands stretched down and hooked-on to the belt at the back of my greatcoat. Before I had time to realise it I was pulled up and pitched head-first into the bottom of the boat.\n\n'Come on, you b\u2014. Get up and help the others in,' shouted a sailor, as I hit the planks with a gasp. It was rough medicine. But the right medicine for the moment.\n\nThe moment came when the lifeboat could not hold another soul.\n\n'Carry on, Mr Jolly. Carry on,' cried the sailor at our helm to someone in the motor-boat. And we got under weigh, leaving the rest of the queue behind to await the next boat.\n\n_'Bloody marvellous' said the_ Daily Mirror _of the 'miracle' of Dunkirk._\n\n## _Churchill's War Speeches, June 1940_\n\nWINSTON CHURCHILL, PRIME MINISTER\n\n_With the Fall of France only Britain remained standing against Nazi Germany. The country's determination to fight on was due in no small part to the bulldog oratory of Churchill himself. Below are excerpts from two of his war speeches of June 1940._\n\n... I have, myself, full confidence that if all do their duty, if nothing is neglected, and if the best arrangements are made, as they are being made, we shall prove ourselves once again able to defend our island home, to ride out the storm of war, and to outlive the menace of tyranny, if necessary for years, if necessary alone. At any rate, that is what we are going to try to do. That is the resolve of His Majesty's Government \u2013 every man of them. That is the will of Parliament and the nation. The British Empire and the French Republic linked together in their cause and in their need, will defend to the death their native soil, aiding each other like good comrades to the utmost of their strength. Even though large tracts of Europe and many old and famous States have fallen or may fall into the grip of the Gestapo and all the odious apparatus of Nazi rule, we shall not flag or fail. We shall go on to the end. We shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our island, whatever the cost may be. We shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, and even if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the new world, with all its power and might, steps forth to the rescue and the liberation of the old.\n\n* * *\n\n... What General Weygand called the 'Battle of France' is over. I expect that the battle of Britain is about to begin. Upon this battle depends the survival of Christian civilization. Upon it depends our own British life and the long continuity of our institutions and our Empire. The whole fury and might of the enemy must very soon be turned on us. Hitler knows that he will have to break us in this island or lose the war. If we can stand up to him all Europe may be free, and the life of the world may move forward into broad, sunlit uplands; but if we fail then the whole world, including the United States, and all that we have known and cared for, will sink into the abyss of a new dark age made more sinister, and perhaps more prolonged, by the lights of a perverted science. Let us therefore brace ourselves to our duty and so bear ourselves that if the British Commonwealth and Empire lasts for a thousand years men will still say, 'This was their finest hour.'\n\n## _The Battle of Britain: A Spitfire Pilot in Action, 2 September 1940_\n\nRICHARD HILLARY RAF\n\n_France defeated, Hitler turned his attention to a seaborne invasion of England. As the F\u00fchrer realized full well, this could only be achieved if the RAF was swept from the skies above the Channel. Goring, the Luftwaffe chief, assured the F\u00fchrer that it would take his pilots a mere four days to achieve this. The Luftwaffe certainly had the numerical advantage, but the operational value of its main fighter aircraft, the Messerschmitt Bf109, was limited to about ten minutes over the main battlefield, the south-east corner of England._\n\n_The Battle of Britain began on 'Eagle Day', 13 August, with the Luftwaffe raiding RAF airfields._\n\nWe made a dash for our machines and within two minutes were off the ground. Twice we circled the aerodrome to allow all twelve planes to get in formation. We were flying in four sections of three: Red Section leading, Blue and Green to right and left, and the three remaining planes forming a guard section above and behind us.\n\nI was flying No. 2 in the Blue Section.\n\nOver the radio came the voice of the controller, 'Hullo, Red Leader', followed by instructions on course and height.\n\nAs always, for the first few minutes we flew on the reciprocal of the course given until we reached fifteen thousand feet. We then turned about and flew on 1100 in an all-out climb, thus coming out of the sun and gaining height all the way.\n\nDuring the climb Uncle George was in constant touch with the ground. We were to intercept about twenty enemy fighters at twenty-five thousand feet. I glanced across at Stapme and saw his mouth moving. That meant he was singing again. He would sometimes do this with his radio set on 'Send', with the result that, mingled with our instructions from the ground, we would hear a raucous rendering of _Night and Day._ And then quite clearly over the radio I heard the Germans excitedly calling to each other. This was a not infrequent occurrence and it made one feel that they were right behind, although often they were some distance away. I switched my set to 'Send' and called out _'Halts Maul!'_ and as many other choice pieces of German invective as I could remember. To my delight I heard one of them answer, 'You feelthy Englishmen, we will teach you how to speak to a German.' I am aware that this sounds a tall story, but several others in the Squadron were listening out and heard the whole thing.\n\nI looked down. It was a completely cloudless sky and way below lay the English countryside, stretching lazily into the distance, a quite extraordinary picture of green and purple in the setting sun.\n\nI took a glance at my altimeter. We were at twenty-eight thousand feet. At that moment Sheep yelled 'Tally-ho' and dropped down in front of Uncle George in a slow dive in the direction of the approaching planes. Uncle George saw them at once.\n\n'O\u039a. Line astern.'\n\nI drew in behind Stapme and took a look at them. They were about two thousand feet below us, which was a pleasant change, but they must have spotted us at the same moment, for they were forming a protective circle, one behind the other, which is a defence formation hard to break.\n\n'Echelon starboard,' came Uncle George's voice.\n\nWe spread out fanwise to the right.\n\n'Going down!'\n\nOne after the other we peeled off in a power dive. I picked out one machine and switched my gun-button to 'Fire'. At three hundred yards I had him in my sights. At two hundred I opened up in a long four-second burst and saw the tracer going into his nose. Then I was pulling out, so hard that I could feel my eyes dropping through my neck. Coming round in a slow climbing turn, I saw that we had broken them up. The sky was now a mass of individual dog-fights. Several of them had already been knocked down. One I hoped was mine, but on pulling up I had not been able to see the result. To my left I saw Peter Pease make a head-on attack on a Messerschmitt. They were headed straight for each other and it looked as though the fire of both was striking home. Then at the last moment the Messerschmitt pulled up, taking Peter's fire full in the belly. It rolled on to its back, yellow flames pouring from the cockpit, and vanished.\n\n_Bombing the RAF's airfields proved too slow a way of winning the battle for Hitler's taste, and on_ 7 _September he switched the 'Schwerpunkt' to a terror-attach on London: what Cockneys ironically called 'the Blitz'._\n\n## _The Blitz on London, 7\u20138 September 1940_\n\nDESMOND FLOWER\n\nSuddenly we were gaping upwards. The brilliant sky was criss-crossed from horizon to horizon by innumerable vapour-trails. The sight was a completely novel one. We watched, fascinated, and all work stopped. The little silver stars sparkling at the heads of the vapour trails turned east. This display looked so insubstantial and harmless; even beautiful. Then, with a dull roar which made the ground across London shake as one stood upon it, the first sticks of bombs hit the docks. Leisurely, enormous mushrooms of black and brown smoke shot with crimson climbed into the sunlit sky. There they hung and slowly expanded, for there was no wind, and the great fires below fed more smoke into them as the hours passed.\n\nOn Friday and Saturday morning the sky grew darker and darker as the oily smoke rose and spread in heavy, immobile columns, shutting out the sun.\n\nAt the barracks, drill quickly became monotonous. We had work to do, and we weren't the target. But we couldn't keep our eyes off those sickening, solid columns climbing up like the convolutions of a lazy snake into a torpid sky.\n\nI suppose our masters felt that, although the Battle of Britain had begun, the worst might already be over \u2013 I don't know; but they decided to put us recruits in the hat and draw out three for week-end leave. My name came out of the hat first, and I sent a wire to my parents in Sevenoaks to say that I was coming home. My pass was from midday on Saturday, and I got down to the centre of London by Underground. Bombers were coming over at monotonously regular intervals. I walked down to Charing Cross. There was a lot of noise still, and a lot of smoke. As I entered the station the loudspeakers were ordering everyone out because planes were overhead and they were frightened of casualties if the place were hit. I strolled out to the top of that long flight of stone steps down into Villiers Street and sat on the balustrade watching.\n\nUp in the lonely sky there was still one bomber, gleaming silver, and then he dropped a stick just across the Thames from us. Back in the station the loudspeaker announced that the main line was gone and that there wouldn't be any more trains out for hours. Hundreds of people stood around like a flock of sheep which is frightened and can't make up its mind which way to turn. You could see the dead mask of indecision on their faces as they looked about, hoping someone would tell them what to do. I walked out of the station and decided to hitch-hike home. I was lucky; somewhere on the south bank of the river I met a man on a motor-cycle who was going through Blackheath, and he took me on his pillion.\n\nNow we were nearer to the docks. The columns of smoke merged and became a monstrous curtain which blocked the sky; only the billows within it and the sudden shafts of flame which shot up hundreds of feet made one realize that it was a living thing and not just the backdrop of some nightmare opera. There were fire-hoses along the side of the road, climbing over one another like a helping of macaroni, with those sad little fountains spraying out from the leaks, as they always seem to do from all fire-hoses. Every two or three minutes we would pull into the gutter as a fire-bell broke out stridently behind us and an engine in unfamiliar livery tore past at full tilt: chocolate or green or blue, with gold lettering \u2013 City of Birmingham Fire Brigade, or Sheffield, or Bournemouth. The feeling was something you had never experienced before \u2013 the excitement and dash of fire-engines arriving to help from so far away, and the oily, evil smell of fire and destruction, with its lazy, insolent rhythm.\n\nIt looked terrible and hopeless, but there was a kind of _G\u00f6tterd\u00e4m-merung_ grandeur about it.\n\nI got home in one piece, and my parents welcomed me with a splendid dinner. But that night the _Luftwaffe,_ already working round the clock, came again and dropped a stick of bombs straight down our quiet Sevenoaks road. They hit the town centre just by the historic Vine cricket ground with the first bomb. The last but one landed opposite our gate, and the last by the street corner. Apart from the destruction of the town hall, no damage was done, and I wonder why that particular pilot chose that particular target; I suppose he must have seen the main London\u2013Dover railway line and his bomb-aimer let go too soon.\n\nSunday in Sevenoaks was the same as Sunday throughout Kent, Surrey, Sussex and Essex. The hot summer air throbbed with the steady beat of the engines of bombers which one could not see in the dazzling blue. Then the RAF would arrive; the monotonous drone would be broken by the sudden snarl of a fighter turning at speed, and the vapour trails would start to form in huge circles. I lay on my back in the rose garden and watched the trails forming; as they broadened and dispersed a fresh set would be superimposed upon them. Then, no bigger than a pin's head, a white parachute would open and come down, growing slowly larger; I counted eight in the air at one time.\n\nI had to be back in barracks on the Sunday night, and set off after supper. The twenty-three-mile journey took well over two hours, and no one could tell us what station we would be taken to. When we finally got there, it turned out to be Holborn. I stepped out into the darkness of the street, or what would have been darkness but for the fires; but as I did so a stick whistled down on the other side of the road and I ducked back inside. After a while I knew I had to begin to move. Hanging about in the station shelter wasn't doing me any good, so I started out on foot up Holborn. When I reached Gamages I was turned back: everything was cascaded down into the road as though two landslides had started simultaneously from opposite sides. There was utter silence, except for the crunch and crackle of my own feet treading a carpet of broken glass.\n\n_On 15 September 1940, the Luftwaffe lost sixty bombers raiding London. Two days later Hitler cancelled the invasion of England. 'The Few', the 2,300 pilots of Fighter Command, deserved their plaudits; they had shot down 1,268 aircraft for the loss of 832, and inflicted upon Nazi Germany its first defeat._\n\n_Britain stood alone against Hitler. And would do so for a year, until the entry of the USSR and then the USA into the war in 1941._\n\n## _The Japanese Sink the Repulse and the Prince of Wales, off the Coast of Malaya, 10 December 1941_\n\nCECIL BROWN\n\n_On 7 December 1941, the Second World War spread to the Far East, with the Japanese attack on Pearl Harbor. Three days later the two finest battleships in the Royal Navy, HMS Prince of Wales and HMS Repulse, were intercepted sailing out of Singapore by Japanese aircraft. The British ships had no air cover. Cecil Brown was a war reporter aboard the Repulse._\n\n10.45 \u2013 One twin-engined Jap is reported shadowing us. It is the same type that bombed Singapore the first night of the war. It is a type 96 Mitsubishi of the Naval Air Service.\n\nThe clouds have gone now, and the sky is a robin's-egg blue and the sun is bright yellow. Our ships plough through pea-green water, white where the hulls cleave it.\n\n11.07 \u2013 The communications loudspeaker announces: 'Enemy aircraft approaching \u2013 action stations!'\n\nI see them: one \u2013 two \u2013 three \u2013 four \u2013 five \u2013 six \u2013 seven \u2013 eight \u2013 nine. There are nine, flying line astern, one behind the other.\n\nI would judge them about twelve thousand feet, coming straight over the _Repulse._\n\n11.14 \u2013 And here they come.\n\n11.15 \u2013 The guns of the _Prince of Wales_ just let go. At the same instant I see the flame belching from the guns of the _Wales,_ ours break into a chattering, ear-splitting roar. The nine Japanese aircraft were stretched out across the bright blue, cloudless sky like star sapphires of a necklace.\n\nI gape open-mouthed at those aircraft coming directly over us, flying so that they will pass from bow to stern over the _Repulse._ The sky is filled with black puffs from our ack-ack. They seem a discordant profanation of that beautiful sky. But the formation of Japanese planes, coming over one behind the other, is undisturbed.\n\nNow they are directly overhead. For the first time I see the bombs coming down, materializing suddenly out of nothingness and streaming towards us like ever-enlarging tear-drops. There's a magnetic, hypnotic, limb-freezing fascination in that sight.\n\nIt never occurs to me to try and duck or run. Open-mouthed and rooted, I watch the bombs getting larger and larger. Suddenly, ten yards from me, out in the water, a huge geyser springs out of the sea, and over the side, showering water over me and my camera.\n\nI instinctively hunch over, sort of a semi-crouch, and at the same instant there is a dull thud. The whole ship shudders. Pieces of paint fall from the deck over the flag deck.\n\n11.17 \u2013 'Fire on the boat deck. Fire below!' That just came over the loudspeakers. There are fountains of water all around the ship. Some are near misses. Most of the bombs are hitting the water ten to thirty yards off the port side. Beautiful fountains of thick white at the base and then tapering up into fine spray.\n\nThat first bomb was a direct hit. Someone on the flag deck says, 'Fire in marines' mess and hangar.'\n\nThat bomb struck the catapult deck, penetrated, exploded underneath. The bomb hit twenty yards astern of my position on the flat deck. A number of men [fifty] were killed.\n\n11.45 \u2013... The torpedo-carrying bombers are coming in. We are putting up a beautiful barrage, a wall of fire. But the bombers come on, in a long glide, from all angles, not simultaneously but alternately. Some come head-on, some astern and from all positions on both sides of the ship. They level out.\n\nAbout three hundred yards distant from the ship and a hundred yards above the water they drop their torpedoes.\n\nThe torpedoes seem small, dropping flat into the water, sending up splashes, then streaking towards us. Those bombers are so close you can almost see the colour of the pilot's eyes. The bombers are machine-gunning our decks as they come in.\n\n11.51\u00bd \u2013 Captain Tennant is sending a message to the _Wales: '_ Have you sustained any damage?'\n\nThe answer comes back: 'We are out of control. Steering gear is gone.'\n\nThe decks of the _Repulse_ are littered with empty shell-cases. Upon the faces of the sailors there's a mixture of incredulity and a sort of sensuous pleasure, but I don't detect fear. There's an ecstatic happiness, but strangely, I don't see anything approaching hate for the attackers. For the British this is a contest. The facial expression is interpreted by an officer. He turns to me and says, 'Plucky blokes, those Japs. That was as beautiful an attack as ever I expect to see.'\n\n_Less than an hour later, the_ Repulse _and the_ Prince of Wales _were finished. 'In all the war,' Churchill wrote, 'I never received a more direct shock.' Singapore fell two months later._\n\n## _El Alamein: The Afrika Korps Retreat, North Africa, 4 November 1942_\n\nGENERAL FRITZ BAYERLEIN, AFRIKA KORPS\n\n_The German view of the decisive engagement in the Western Desert._\n\n_The battle of El Alamein began at 21.40 on the still, moonlit night of 23 October, with a 1,000-gun British barrage. The Germans had other problems; they were pathetically short of diesel and ammunition, and within a week werereduced to ninety operative tanks. The British had over 800. On 2 November, General Montgomery 'directed two hard punches at the hinges' of the German position \u2013 and forced a gap. Hitler forbade retreat on the 3rd. By the following day Rommel could do nothing else._\n\nOn the morning of November 4th the remnants of the German Africa Corps, together with the 90th Light Division, held a thin front line on either side of the wide sand dune called Tel el Mampsra: though only some twelve feet high, this dune was a commanding feature. To the south was the equally weakened Italian armoured corps. Towards dawn I reported to General Ritter von Thoma, the commander of the Africa Corps, that I was about to set off for the area south of El Daba, where I was to establish a rear command post. For the first time Thoma was wearing a proper uniform, with his general's insignia, orders and decorations, which hitherto in the desert he had never bothered to put on. He now said to me:\n\n'Bayerlein, Hitler's order [not to withdraw] is a piece of unparalleled madness. I can't go along with this any longer. Go to the El Daba command post. I shall stay here and personally take charge of the defence of Tel el Mampsra.'\n\nI could see that Thoma was utterly disheartened and foresaw no good. His ADC, Lieutenant Hartdegen, remained with the General: he had a wireless transmitter. The General put on his greatcoat and picked up a small canvas bag. I wondered whether the General intended to die. Then I left Tel el Mampsra and drove to the rear.\n\nIt was eight o'clock before the British attacked, after approximately one hour's artillery preparation. Their main effort was directed against Tel el Mampsra. By committing all its forces the Africa Corps was able to hold attacks by two hundred British tanks.\n\nAt eleven o'clock Lieutenant Hartdegen appeared at my command post and said, 'General von Thoma has sent me back, with the radio transmitter. He doesn't need it any more. All our tanks, anti-tank guns and ack-ack have been destroyed on Tel el Mampsra. I don't know what has happened to the general.'\n\nI immediately climbed into a small armoured reconnaissance car and drove off eastwards. Suddenly a hail of armour-piercing shot was whistling all about me. In the noontime haze I could see countless black monsters far away in front. They were Montgomery's tanks, the 10th Hussars. I jumped out of the armoured car and beneath the burning midday sun ran as fast as I could towards Tel el Mampsra. It was a place of death, of burning tanks and smashed flak guns, without a living soul. But then, about two hundred yards away from the sandhole in which I was lying, I saw a man standing erect beside a burning tank, apparently impervious to the intense fire which criss-crossed about him. It was General von Thoma. The British Shermans which were closing up on Tel el Mampsra had halted in a wide half-circle. What should I do? The General would probably regard it as cowardice on my part were I not to go forward and join him. But to run through the curtain of fire which lay between General von Thoma and myself would have been to court certain death. I thought for moment or two. Then the British tanks began to move forward once again. There was now no fire being put down on Tel el Mampsra. Thoma stood there, rigid and motionless as a pillar of salt, with his canvas bag still in his hand. A Bren carrier was driving straight towards him, with two Shermans just behind. The British soldiers signalled to Thoma. At the same time one hundred and fifty fighting vehicles poured across Tel el Mampsra like a flood.\n\nI ran off westwards as fast as my legs could carry me. My car had vanished. After a while I met a staff car which took me to the command post at El Daba. There I found Rommel. I told him what I had seen. Huge dust clouds were now visible both south-east and south of the command post. The Italian tanks of the 20th Corps were fighting their last, desperate battle with some hundred heavy British tanks that had punched into the Italians' open right flank. After putting up a brave resistance, the Italian corps was annihilated.\n\nThe Africa Corps signals officer brought Rommel a decoded message, from the 10th Hussars to Montgomery, which our people had intercepted. It read: 'We have just captured a General named Ritter von Thoma.'\n\nThe Field-Marshal took me aside, and said:\n\n'Bayerlein, what we tried with all our might to prevent has now happened. Our front is smashed and the enemy is pouring through into our rear area. There can no longer be any question of obeying Hitler's order. We're withdrawing to the Fuka position so as to save what still can be saved.\n\n... 'Bayerlein,' Rommel went on, 'I'm putting you in command of the Afrika Korps. There's no one else to whom I can entrust it. And if it should happen later on that the F\u00fchrer court-martials us for our disobedience, we'll both have to answer squarely for our decision today. Do your duty as best you can. All your orders to the troops carry my authority. You may say this to the senior commanders, in the event of your having any trouble with them.'\n\n'I shall do my best, sir,' I replied. Then Rommel got into his armoured command vehicle, to visit the other units of his beaten army and to give the orders for the retreat.\n\n_With only slight exaggeration, Churchill later commented, 'Before El Alamein we never had a victory, after El Alamein we never had a defeat.'_\n\n## _The Dambusters Destroy the Mohne Dam, Ruhr Valley, 16 May 1943_\n\nWING COMMANDER GUY GIBSON RAF\n\n_Nineteen Lancaster bombers took part in the celebrated 'bouncing-bomb' raid on the dams of the Ruhr Valley; eight of the Lancasters failed to return. Two dams, the Mohne and Eder, were destroyed, bringing widespread flooding to Germany's industrial heartland._\n\nDown below, the M\u00f6hne Lake was silent and black and deep, and I spoke to my crew.\n\n'Well boys, I suppose we had better start the ball rolling.' This with no enthusiasm whatsoever. 'Hello, all Cooler aircraft. I am going to attack. Stand by to come in to attack in your order when I tell you.'\n\nThen to Hoppy: 'Hello, \"M Mother\". Stand by to take over if anything happens.'\n\nHoppy's clear and casual voice came back. 'O\u039a, Leader. Good luck.'\n\nThen the boys dispersed to the pre-arranged hiding-spots in the hills, so that they should not be seen either from the ground or from the air, and we began to get into position for our approach. We circled wide and came around down moon, over the high hills at the eastern end of the lake. On straightening up we began to dive towards the flat, ominous water two miles away. Over the front turret was the dam silhouetted against the haze of the Ruhr Valley. We could see the towers. We could see the sluices. We could see everything. Spam, the bomb-aimer, said, 'Good show. This is wizard.' He had been a bit worried, as all bomb-aimers are, in case they cannot see their aiming points, but as we came in over the tall fir trees his voice came up again rather quickly. 'You're going to hit them. You're going to hit those trees.'\n\n'That's all right, Spam. I'm just getting my height.'\n\nTo Terry: 'Check height, Terry.'\n\nTo Pulford: 'Speed control, Flight-Engineer.'\n\nTo Trevor: 'All guns ready, gunners.'\n\nTo Spam: 'Coming up, Spam.'\n\nTerry turned on the spotlights and began giving directions \u2013 'Down \u2013 down \u2013 down. Steady \u2013 steady.' We were then exactly sixty feet.\n\nPulford began working the speed; first he put on a little flap to slow us down, then he opened the throttles to get the air-speed indicator exactly against the red mark. Spam began lining up his sights against the towers. He had turned the fusing switch to the 'ON' position. I began flying.\n\nThe gunners had seen us coming. They could see us coming with our spotlights on for over two miles away. Now they opened up and the tracers began swirling towards us; some were even bouncing off the smooth surface of the lake. This was a horrible moment: we were being dragged along at four miles a minute, almost against our will, towards the things we were going to destroy. I think at that moment the boys did not want to go. I know I did not want to go. I thought to myself, 'In another minute we shall all be dead \u2013 so what?' I thought again, 'This is terrible \u2013 this feeling of fear \u2013 if it is fear.' By now we were a few hundred yards away, and I said quickly to Pulford, under my breath, 'Better leave the throttles open now and stand by to pull me out of the seat if I get hit.' As I glanced at him I thought he looked a little glum on hearing this.\n\nThe Lancaster was really moving and I began looking through the special sight on my windscreen. Spam had his eyes glued to the bomb-sight in front, his hand on his button; a special mechanism on board had already begun to work so that the mine would drop (we hoped) in the right spot. Terry was still checking the height. Joe and Trev began to raise their guns. The flak could see us quite clearly now. It was not exactly inferno. I have been through far worse flak fire than that; but we were very low. There was something sinister and slightly unnerving about the whole operation. My aircraft was so small and the dam was so large; it was thick and solid, and now it was angry. My aircraft was very small. We skimmed along the surface of the lake, and as we went my gunner was firing into the defences, and the defences were firing back with vigour, their shells whistling past us. For some reason, we were not being hit.\n\nSpam said, 'Left \u2013 little more left \u2013 steady \u2013 steady \u2013 steady \u2013 coming up.' Of the next few seconds I remember only a series of kaleidoscopic incidents.\n\nThe chatter from Joe's front guns pushing out tracers which bounced off the left-hand flak tower.\n\nPulford crouching beside me.\n\nThe smell of burnt cordite.\n\nThe cold sweat underneath my oxygen mask.\n\nThe tracers flashing past the windows \u2013 they all seemed the same colour now \u2013 and the inaccuracy of the gun positions near the power-station; they were firing in the wrong direction.\n\nThe closeness of the dam wall.\n\nSpam's exultant, 'Mine gone.'\n\nHutch's red Very lights to blind the flak-gunners.\n\nThe speed of the whole thing.\n\nSomeone was saying over the RT, 'Good show, leader. Nice work.'\n\nThen it was all over, and at last we were out of range, and there came over us all, I think, an immense feeling of relief and confidence.\n\nTrevor said, 'I will get those bastards,' and he began to spray the dam with bullets until at last he, too, was out of range. As we circled round we could see a great 1,000-feet column of whiteness still hanging in the air where our mine had exploded. We could see with satisfaction that Spam had been good, and it had gone off in the right position. Then, as we came closer, we could see that the explosion of the mine had caused a great disturbance upon the surface of the lake and the water had become broken and furious, as though it were being lashed by a gale.\n\n_Guy Gibson was killed in action a year later._\n\n## _Tenko: An Englishwoman in a Japanese Prison Camp, Kuching, Borneo, 1942\u20135_\n\nAGNES NEWTON KEITH\n\nOur barrack was one big room with a loft above it, and no partitions. Each person occupied about five square feet. If the guard wanted to occupy it with you, there wasn't much you could do except roll over. Not that the guards spent all their time lying down near us; a lot of the time they were drunk in the guardhouse.\n\nSome of it was good clean fun, and boys will be boys. But sometimes boys are dirty boys, and one doesn't like being frisked, frolicked, bullied, chased, back-slapped or face-slapped by a young man with a gun. The gun removes the element of light-hearted gaiety from the game.\n\nBecause there were buns, rice, and privileges to be had from tolerating and encouraging the guards, and no means with which to discourage them, the fact that they treated us like tarts was sometimes justified. One good argument against collaborating was the fact that the guards had bedbugs.\n\nThey were not sadistic, or masochistic; they were not Oriental, or Occidental; they were just a gang of lowdown young hoodlums who had complete power over a hundred people who could not strike back.\n\nOnce a week a worn-out officer arrived in a worn-out motorboat, and both made a loud noise coming. He searched the guards, and us, with equal suspicion. Warned by the motor, the guards could just get their trousers on in time to reach the wharf's end and stand at attention. We could just get our forbidden diaries, books, and food hidden in the grass and the latrines. When the officer departed, everybody relaxed.\n\nLife on Berhala was according to the whims of the guards \u2013 and they were whimsical. They could be very kind. One guard gave his own buns to the children daily, another distributed loaves of bread to them. They frequently fed us their own surplus, commenting that our food was terrible. Sometimes they let us meet our husbands openly, and sometimes they beat us for smiling at them secretly.\n\nThe first guard we had in Berhala made a speech to us after one week, on the eve of their departure. Before making it, they dictated their sentiments to me in broken English and told me to write them out in 'literary' style. The result of our effort was this:\n\nGENTLEMEN, LADIES AND WOMEN: Nipponese soldiers are very kindly. We will pray for your health until we meet again. To-morrow we go back to Sandakan. We are very sorry for you. However, if you get conceited we will knock you down, beat you, kick you, and kill you.\n\nI suggested that the last sentence was a trifle harsh, but they were particularly attached to it.\n\n... In Kuching we learned to bow seriously. We had printed instructions, demonstrations and practice. The Nipponese orders for bowing were: Incline the body from the waist to a fifteen-degree angle, with head uncovered, hands at the side, and feet together: remain thus to the count of five (silent); then recover. (If not knocked down.)\n\nThe first time we were instructed in bowing in the Kuching camp, we were being trained to present a good appearance for the visiting lieutenant-general for whom we had planted potatoes.\n\nThe day came, we were all assembled in ranks, the Sisters in front, the women and children behind, where it was hoped we could do the least harm by our frivolous ways. The order was given to bow. The Sisters had wonderful behinds, the bow made the behinds spring into sudden prominence; by standing too close and bowing too swiftly we managed to meet the behinds with our heads. Confusion and concussion reigned, and order was not restored. The lieutenant-general was hastened away to review the pigs, who had more respect for lieutenant-generals than we did, or else did not understand the meaning of the phrase 'dumb insolence', as we did. We were never again assembled together in one group to bow to a visiting general.\n\n... Every change was for the worse. Rules increased, food decreased, work increased, and strength decreased. Disappointments multiplied, and optimism was never verified. Hope itself seemed only a refuge for those who would not face facts.\n\nOur food ration, then, as supplied by the Japanese per person per day, was as follows: one cupful of thin rice gruel, five tablespoons of cooked rice, sometimes a few greens, a little sugar, sometimes a little salt and tea. This was what the Japanese expected us to live on. Or did they expect us to live on it?\n\nAdditions to this diet were sweet-potato tops, which we grew ourselves. We used the tops because we were too hungry to wait for the potatoes to mature. Every square foot of the camp was in use for gardens, but the soil was exhausted, and we were exhausted. The last eight months of imprisonment it was almost impossible for us to do heavy work, but we did it. We arose before sunrise to finish the work inside camp, and then went outside the camp to work for the Japanese. By nine o'clock in the morning we were worn out.\n\nBy now soldiers were trading for and buying skinned cats and rats, people were eating snails and worms, all of us were eating weeds and grass, and plenty of us would have liked to eat each other.\n\n_Newton Keith and her family survived the war._\n\n## _D-Day: A British Paratrooper Lands in Normandy, 1 a.m., 6 June 1944_\n\nJAMES BYROM, PARACHUTE MEDICAL SERVICE\n\n_The Allied invasion of Normandy was the greatest amphibious invasion in history. Some 160,000 troops \u2013 British, American, French, Polish and Canadian \u2013 embarked in 5,000 craft and sailed from southern England to occupied France. The seaborne invasion was preceded by an airborne assault, with the British 6th Airborne division tasked to protect the eastern flank of the invasion beaches. The first British paratroopers began dropping out of the sky over Normandy early in the morning of D-Day._\n\nA shadow darted from a nearby tree, and I was joined in the open by the huge sten-gunner with the black face. The whites of his eyes gleamed in the moonlight, and for all my weariness I found myself on the verge of giggles.\n\n'You speak the lingo, tosh? All right, then, you go up and knock on the door, and we'll give you coverin' fire. I'll stay 'ere and my mate'll creep round the other side of the yard so's to cover you proper.'\n\nA dog barked at my approach. From the corner of my eye I could see a stealthy figure flit from behind a haystack into the shadow of the barn door. There was no answer to my first knock. The household was obviously fast asleep. I knocked louder, and this time I heard a scurrying on the stairs and a sudden clamour of French voices. Footsteps approached the door, withdrew, hesitated, then approached again. The door opened.\n\nOn the way I had been searching for suitable words with which to introduce ourselves \u2013 some calming, yet elegant phrase worthy of the French gift of expression and of their infallible flair for the dramatic moment. But at the sight of the motherly, middle-aged peasant the gulf of the years disappeared, and I might have been back in 1939, an English tourist on a walking tour dropping in to ask for a glass of cider and some camembert.\n\n_'Excusez-nous, Madame. Nous sommes des parachutistes anglais faisant partie du D\u00e9barquement Alli\u00e9.'_\n\nThere was a moment of scrutiny, then the woman folded me in her arms. The tears streamed down her face, and in between her kisses she was shouting for her husband, for lamps, for wine. In a moment I was carried by the torrent of welcome into the warm, candle-lit kitchen. Bottles of cognac and Calvados appeared on the table, children came clattering down the wooden stairs, and we found ourselves \u2013 an evil-looking group of camouflaged cut-throats \u2013 surrounded and overwhelmed by the pent-up emotions of four years. The farmer and his wife wanted us to stay and drink, to laugh and cry and shake hands over and over again. They wanted to touch us, to tell us all about the Occupation, and to share with us their implacable hatred of the Boche. It seemed that the moment so long awaited could not be allowed to be spoilt by realities, till every drop of emotion was exhausted. I was nearly as much affected as they were. Warmed by the fiery trickle of Calvados, I rose to this \u2013 certainly one of the greatest occasions of my life \u2013 so completely that I forgot all about the Drop, all about the marshes and the battery. It was the sight of my companions, bewildered by all this emotion and talk, automatically drinking glass after glass, that suddenly reminded me of what we had come for. I began politely to insist on answers to questions which had already been brushed aside more than once: Where were we? How far away were the nearest Germans? Once more the questions were ignored. _'Ah, mon Dieu, ne nous quittez pas maintenant! Ah, les pauvres malheureux! Ils sont tous mouill\u00e9s?'_\n\nIt was moving and exasperating. At last I managed to get what we wanted \u2013 a pocket compass and a promise of escort to the hard road through the marshes to Varaville.\n\n_Four years after Dunkirk, the British sailed back to France, touching down at 7.30 a.m. on 6 June on Sword, Gold and Juno beaches._\n\n## _An Infantryman in Normandy, 6\u201324 June 1944_\n\nSERGEANT G. E. HUGHES, ROYAL HAMPSHIRE REGIMENT\n\n_Diary, 6 June 1944_\n\n06.00 Get in LCA [Landing Craft Assault]. Sea very rough. Hit the beach at 7.20 hours. Murderous fire, losses high. I was lucky T[hank] God. Cleared three villages. Terrible fighting and ghastly sights.\n\n_June_ 7. Still going. Dug in at 02:00 hrs. Away again at 05.30. NO FOOD. Writing few notes before we go into another village. CO out of action, adjutant killed. \u03a1 Sgt lost. I do \u03a1 Sgt['s job]. More later.\n\n_June 8._ 07.30, fire coming from village. Village cleared. Prisoners taken. Night quite good but German snipers lurking in wood. Had 2 hrs' sleep. Second rest since the 6th.\n\n_June 9._ 06.30 hrs went on wood clearing. Germans had flown. Only one killed for our morning's work. We are now about 8 to 10 miles inland. Promoted to Sgt.\n\n_June 10._ Joan darling, I have not had you out of my thoughts. T[hank] God I have come so far. We have lost some good men. Our brigade was only one to gain objectives on D-Day.\n\nThe French people give us a good welcome. Had wine.\n\n_June 11._ Contact with enemy. Lost three of my platoon. Very lucky \u03a4 [hank] God. Only had 5 hours sleep in 3 days.\n\n_June 12._ This day undescrible [sic] mortar fire and wood fighting. Many casualties. T[hank] God I survived another day.\n\n_June 13._ Just had my first meal since Monday morning. Up all night. Everyone in a terrible state. I keep thinking of u.\n\n_June 14._ Counter-attack by Jerry from woods. Mortar fire. 13 of my platoon killed or missing. After heavy fighting yesterday CSM also wounded, also Joe. O[fficer] C[ommanding] killed. I am one mass of scratches. Advanced under creeping barrage for 3 miles. Drove Jerry back. It is hell. 3 Tiger tanks came here, up to lines during night.\n\n_June 16._ [resting] Received letter from home. Wrote to Joan and Mum.\n\n_June 17._ [resting]\n\n_June 18._ Day of Hell. Counter-attack.\n\n_June 19._ Day of Hell. Counter-attack.\n\n_June 20._ Day of Hell. Advanced. Counter-attacked.\n\n_June 21._ Quiet day. We have been fighting near Tilley [Tilly]. Bayonet charge. Shelled all day. Letters from home.\n\n_June 22._ Out on patrol. Got within 35 yards of Tiger before spotting it. Got back safely \u03a4 [hank] God. Shelled to blazes. Feeling tired out.\n\n_June_ 23. No sleep last night. Exchanged fire, out on patrols all day, went on OP for 4 hours. Stand-to all night. Casualties.\n\nJust about had enough.\n\n_June 24._ Had to go back to CCS [Casualty Clearing Station]. Malaria.\n\n_Sergeant Hughes was hospitalized with malaria for most of the rest of the Normandy campaign._\n\n## _Doodlebugs, 12 June 1944_\n\nLIONEL KING\n\n_The first German FZG-76 flying bomb ('doodlebug' or 'buzz bomb' to the English) landed on England on 12 June 1944. Another 9,000 followed. King was an eight-year-old schoolboy in 1944._\n\nOn the night of 12 June the first of Hitler's Vis fell on London and the South East. News spread in from the Kent and Sussex coasts of aircraft with 'jet nozzles', 'fire exhausts' and odd engine sounds. Over Kent some of these craft had suddenly stopped and fallen with a devastating explosion to follow. Bombing of course was familiar to our family. We had moved from West Ham earlier in the war. I'd spent endless nights in the dugout in the garden unable to sleep because of Nanny's snoring. Now it was happening in the daytime too.\n\nThe first came over one afternoon. Our windows and doors were open in those fine June days and the drone of the approaching flying bomb was quite unmistakable. It gave us little warning. Ten seconds and the engine cut out directly overhead. There was an oddly resounding explosion about half a mile away.\n\nThe Boy Foot, as my mother called him, cycled up there and reported back: 'King Edward Road \u2013 there's debris everywhere. Fire brigade and wardens are there, still digging 'em out. I saw it coming. I was up on the roof.' I was envious of his roof. You could have seen anything from there.\n\n'Where's King Edward Road, Mum?' asked Doug.\n\n'By the County Ground. It's where Mr Gibbons lives \u2013 you know, he's in the Home Guard with Dad.'\n\nNext day we took to the shelter when we heard the drone. Again the engine cut out, again seemingly over the house. Then it spluttered into life again. Doug and I laughed out loud. It was all rather a joke. Mum told us to duck. The droning engine had stopped. Eight second wait. A disappointing, unspectacular bang.\n\n'I'll find out where it dropped when I go up the shops in a minute,' said Mum. 'Don't open the door to any knocks.' Later she told us it had fallen on a railway siding behind the dust destructor. Three old railway trucks were destroyed, a railwayman had told her.\n\nSoon so many Vis were coming over the authorities gave up air-raid warnings. They would have been sounding the siren all the time. When a bomb announced its approach, Doug and I dived for the shelter, not forgetting to grab our cat Jimmy if he was in sight. Sometimes Mum was out shopping and we went to the shelter alone. We were never worried or afraid. It was all over in ten seconds anyway.\n\nOne such afternoon a VI fell further up the road. We jumped out of the shelter and saw a huge mushroom of dust and rubble rising above the rooftops. You could see individual bricks and planks of wood sailing up into the clear sky. It looked after a few seconds like a ragged umbrella. The traffic picked up again in the road. We ran through the house to the front door. Droves of people were rushing up the road, some on bicycles, many in great distress, towards the scene. Many we knew by sight.\n\n'There goes that man from the oil shop,' exclaimed Doug. We'd never seen him this side of the counter before. The dust cloud had settled now. The first ambulances were pulling up at the Rest Centre at the church opposite. Scruffy-looking people, some shaking, were being helped in. Mum appeared. 'Back into the house!' she barked. 'Nanny will be home from work soon. She'll tell you all about it.'\n\nNanny came in later. The buzz bomb had fallen by her factory. 'Mrs Lea has copped it. It fell on her house in Lea Hall Road. It's in a state round there. When it exploded the foreman told her she could go round and see if her place was all right. I went with her. We went through it two or three minutes after it happened...' The incident was not without humour for Doug and me. 'A spotter on Jenkins's roof saw it coming. He just threw himself over the edge. It's eighty feet off the ground.'\n\n_Despite Hitler's hi-tech terror weapons, there was to be no escape for Nazi Germany, ground between the Russian steamroller in the East and the Allied offensive in the West. On 3 May 1945 Field Marshal Montgomery received a Wehrmacht delegation at his HQ on Luneberg Heath, Germany:_\n\nThey were brought to my caravan site and were drawn up under the Union Jack, which was flying proudly in the breeze. I kept them waiting for a few minutes and then came out of my caravan and walked towards them. They all saluted, under the Union Jack. It was a great moment; I knew the Germans had come to surrender and that the war was over.\n\n_The instrument of surrender was signed on 7 May 1945._\n\n## _VE Day, London, 8 May 1945_\n\nMOLLIE PANTER-DOWNES\n\n_The view of the New Yorker's correspondent in London._\n\nWhen the day finally came, it was like no other day that anyone can remember. It had a flavour of its own, an extemporaneousness which gave it something of the quality of a vast, happy village fete as people wandered about, sat, sang, and slept against a summer background of trees, grass, flowers, and water. It was not, people said, like the 1918 Armistice Day, for at no time was the reaction hysterical. It was not like the Coronation, for the crowds were larger and their gaiety, which held up all through the night, was obviously not picked up in a pub. The day also surprised the prophets who had said that only the young would be resilient enough to celebrate in a big way. Apparently the desire to assist in London's celebration combusted spontaneously in the bosom of every member of every family, from the smallest babies, with their hair done up in red-white-and-blue ribbons, to beaming elderly couples who, utterly without self-consciousness, strolled up and down the streets arm in arm in red-white-and-blue paper hats. Even the dogs wore immense tricoloured bows. Rosettes sprouted from the slabs of pork in the butcher shops, which, like other food stores, were open for a couple of hours in the morning. With their customary practicality, housewives put bread before circuses. They waited in the long bakery queues, the string bags of the common round in one hand and the Union Jack of the glad occasion in the other. Even queues seemed tolerable that morning. The bells had begun to peal and, after the night's storm, London was having that perfect, hot, English summer's day which, one sometimes feels, is to be found only in the imaginations of the lyric poets.\n\nThe girls in their thin, bright dresses heightened the impression that the city had been taken over by an enormous family picnic. The number of extraordinarily pretty young girls, who presumably are hidden on working days inside the factories and government offices, was astonishing. They streamed out into the parks and streets like flocks of twittering, gaily plumaged cockney birds. In their freshly curled hair were cornflowers and poppies, and they wore red-white-and-blue ribbons around their narrow waists. Some of them even tied ribbons around their bare ankles. Strolling with their uniformed boys, arms candidly about each other, they provided a constant, gay, simple marginal decoration to the big, solemn moments of the day. The crowds milled back and forth between the Palace, Westminster, Trafalgar Square, and Piccadilly Circus, and when they got tired they simply sat down wherever they happened to be \u2013 on the grass, on doorsteps, or on the kerb \u2013 and watched the other people or spread handkerchiefs over their faces and took a nap. Everybody appeared determined to see the King and Queen and Mr Churchill at least once, and few could have been disappointed. One small boy, holding on to his father's hand, wanted to see the trench shelters in Green Park too. 'You don't want to see shelters today,' his father said. 'You'll never have to use them again, son.' 'Never?' the child asked doubtfully. 'Never!' the man cried, almost angrily. _'Never!_ Understand?' In the open space before the Palace, one of the places where the Prime Minister's speech was to be relayed by loudspeaker at three o'clock, the crowds seemed a little intimidated by the nearness of that symbolic block of grey stone. The people who chose to open their lunch baskets and munch sandwiches there among the flower beds of tulips were rather subdued. Piccadilly Circus attracted the more demonstrative spirits.\n\nBy lunchtime, in the Circus, the buses had to slow to a crawl in order to get through the tightly packed, laughing people. A lad in the black beret of the Tank Corps was the first to climb the little pyramidal Angkor Wat of scaffolding and sandbags which was erected early in the war to protect the pedestal of the Eros statue after the figure had been removed to safekeeping. The boy shinnied up to the top and took a tiptoe Eros pose, aiming an imaginary bow, while the crowd roared. He was followed by a paratrooper in a maroon beret, who, after getting up to the top, reached down and hauled up a blonde young woman in a very tight pair of green slacks. When she got to the top, the Tank Corps soldier promptly grabbed her in his arms and, encouraged by ecstatic cheers from the whole Circus, seemed about to enact the classic role of Eros right on the top of the monument. Nothing came of it, because a moment later a couple of GIs joined them and before long the pyramid was covered with boys and girls. They sat jammed together in an affectionate mass, swinging their legs over the sides, wearing each other's uniform caps, and calling down wisecracks to the crowd. 'My God,' someone said, 'think of a flying bomb coming down on this!' When a firecracker went off, a hawker with a tray of tin brooches of Monty's head happily yelled that comforting, sometimes fallacious phrase of the blitz nights, 'All right, mates, it's one of ours!'\n\nAll day long, the deadly past was for most people only just under the surface of the beautiful, safe present, so much so that the Government decided against sounding the sirens in a triumphant 'all clear' for fear that the noise would revive too many painful memories. For the same reason, there were no salutes of guns \u2013 only the pealing of the bells, and the whistles of tugs on the Thames sounding the doot, doot, doot, dooooot of the 'V', and the roar of the planes, which swooped back and forth over the city, dropping red and green signals toward the blur of smiling, upturned faces.\n\nIt was without any doubt Churchill's day. Thousands of King George's subjects wedged themselves in front of the Palace throughout the day, chanting ceaselessly, 'We want the King' and cheering themselves hoarse when he and the Queen and their daughters appeared, but when the crowd saw Churchill there was a deep, full-throated, almost reverent roar. He was at the head of a procession of Members of Parliament, walking back to the House of Commons from the traditional St Margaret's Thanksgiving Service. Instantly, he was surrounded by people \u2013 people running, standing on tiptoe, holding up babies so that they could be told later they had seen him, and shouting affectionately the absurd little nurserymaid name, 'Winnie, Winnie!' One of two happily sozzled, very old, and incredibly dirty cockneys who had been engaged in a slow, shuffling dance, like a couple of Shakespearean clowns, bellowed, 'That's 'im, that's 'is little old lovely bald 'ead!' The crowds saw Churchill again later, when he emerged from the Commons and was driven off in the back of a small open car, rosy, smiling, and looking immensely happy. Ernest Bevin, following in another car, got a cheer too. One of the throng, an excited East Ender, in a dress with a bodice concocted of a Union Jack, shouted, 'Gawd, fancy me cheering Bevin, the chap who makes us work!' Herbert Morrison, sitting unobtrusively in a corner of a third car, was hardly recognized, and the other Cabinet Ministers did no better. The crowd had ears, eyes, and throats for no one but Churchill, and for him everyone in it seemed to have the hearing, sight, and lungs of fifty men. His slightly formal official broadcast, which was followed by buglers sounding the 'cease firing' call, did not strike the emotional note that had been expected, but he hit it perfectly in his subsequent informal speech ('My dear friends, this is your victory...') from a Whitehall balcony.\n\n_A revered leader for war, the Conservative Churchill was not the man for the peace. During the 'People's War', the country had experienced an egalitarianism never known before, where fair shares' (ration books, gas masks, identity cards) were the rule, suffering was communal (the Blitz) and the country had pulled together and mixed together in the same boat. Shortly after VE Day Labour refused to continue the wartime coalition. The parties went to the polls in July: the result was a Labour landslide: 393 seats to the Conservatives' 213. Led by the understated Clement Attlee the Labour government installed a Welfare State (crowned by the National Health Service) and nationalized the major industries and institutions \u2013 coal, civil aviation, electricity, cable and wireless, railways, even the Bank of England._\n\n_A new Jerusalem, but not full-blooded socialism. Private enterprise continued quite happily in Attlee's brave new England, as did private schools, and even the NHS accepted paying beds. The Attlean compromise of welfare-statism and mixed economy proved remarkably effective, or, at least, remarkably enduring. Most Conservatives became adherents. Not until the late 1970s was it seriously challenged. In the meantime, the country groaned under a huge post-war debt and commodity shortages which meant that rationing of petrol, food, clothes and many domestic items remained until 1954. There was no shortage, of work, however. Among those seeking employment were colonial subjects from the West Indies._\n\n## _Passage to England: A Boy Aboard the Empire Windrush, May-June 1948_\n\nVINCE REID\n\n_Vince Reid was thirteen when he accompanied his parents from Jamaica to England on the Windrush; there had been black people in England for centuries (if you think about it, there were blacks in the Roman army) but the 500 aboard the Windrush were the first of the large-scale black immigrations to the country._\n\nI was thirteen when my parents brought me. My father worked the railway as a labourer, and my mother worked in a match factory. They were church people, those thrifty people. And one of the ways in which you could accumulate large sums of money was something that they called 'pardner'. You put in so much money, and you've had a draw. I think that's how a lot of people were able to get that \u00a328. It was an awful lot of money. And I think a lot of people, because of the opportunities they perceived were going to open up to them, would sell what they had, and, of course, they had 'pardner' schemes, where a lot of people were in churches, you had credit unions, you know, so you'd partner. That's how they got the money. I suppose he thought, well, you know, being a labourer in England couldn't be any worse than being a labourer in Jamaica. In fact, it would be better, because at least you would get more money for doing the work. And that's why they came.\n\nFor me it was a massive adventure. I mean, I'd never been outside of Kingston, let alone, you know, this massive journey to England. I had no idea where England was or how long, you know, it would take to get there. I'd never been on a train, I'd never been out of Kingston. And here I was stepping on this huge ship which was going to bring me to this place called England. I was thirteen years old and, I remember, you know, all these people on the ship and the officers on the ship were white and, you know, the crew were white. And it was fairly exciting, because I'd never been anywhere before. And going to undertake this journey I had no idea what's going to happen to me and my parents. As far as I was concerned, I didn't have any idea about how long we're going to be in England or anything like that.\n\nIt was single men. I think there might have been a couple of children but, no, they were overwhelmingly adults. In fact, off hand, I can't think of any other person of my age on the boat. I think the next youngest person to me must have been about nineteen. Obviously, some people had been to the UK before and they would talk about England and, you know, people were also looking forward to work, because, of course, in Jamaica there was not a great deal of work for people. So a lot of people were looking forward to coming. There were carpenters coming, people with all kind of different skills who were coming, and were looking forward to, you know, earning money and working and earning money to look after their people back in Jamaica. So there was a kind of general excitement and optimism.\n\nOne of the things that I liked on the boat, they had some boxers that came over \u2013 like Leftie Flynn, who was a very good fighter, Pal Silver, Brendon Solus \u2013 I used to like to watch them box, you know. And that was exciting, because I quite liked the idea of myself being a fighter. But a white guy was bringing them over, called Dale Martin. Dale Martin Promotions. And that was about the most exciting thing on the ship, except when we went to Bermuda. And we disembarked and went in the cinema and we were told we had to sit in a particular place, you know. And, of course, Jamaicans, although you had this kind of hierarchy of colour in Jamaica, this was a new experience, to be told that you couldn't sit where you bought your ticket to sit, you had to sit in a particular place. And, of course, this led to a fight, and we were, you know, told to leave the cinema and sent back to the ship. And, of course, the other thing was people were saying that there's a British warship that was shadowing the _Windrush,_ and there was talk that they might blow us out of the water, that they might sink the ship. Because there was some people didn't want black people coming to England. And there was this fear that they might very well sink the ships, so that there was an element of danger. Whether it was real or not I don't know, but that's what people said, that there were certain hostilities and there was this warship that was shadowing the _Windrush._\n\n_When the_ Windrush _docked at Tilbury on 21 June, the_ Daily Express _recorded:_\n\n450 ARRIVE \u2013 GET PEP TALK: 'THINGS WILL NOT BE TOO EASY'. Four hundred and fifty Jamaicans crowded the rails of the _Empire Windrush_ as she anchored in the Thames last night. They sailed as refugees from their island's unemployment problem, and have provided a new problem to the Colonial Office and the Ministry of Labour here. Loudspeakers called the 450 work-seekers to a pep talk by Mr Ivor Cummings, a principal officer of the Colonial Office, who welcomed them. They were told: Things will not be too easy.\n\n_There were other Imperial 'problems' confronting Attlee's government. With the Indian Independence Act of 1947, Britain began the long retreat from Empire. Pakistan, Burma, Ceylon and the African states followed into freedom until, by the 1960s, only a handful of scattered outposts remained from the Empire on which 'the sun never sets'. Even a veteran imperialist like Churchill accepted decolonization of 500,000,000 'subjects' with good grace, because anything else would have corroded the English belief in liberty and self-government. And, after all, why was the Second World War fought, if not for freedom? Moreover, compared to the bloodbath the French managed in Algeria and the Dutch in Indonesia, Britain removed the 'White Man's Burden' with tact and even local benefit (if democracy is the measure). Few things have become the English quite so well as the leaving of Empire. But, inevitably, a de-Empired Britannia was a smaller, more uncertain figure on the international scene. Increasingly, Britain looked to her 'special relationship' with the anglophone USA. What this meant in practice was that, Labour or Tory, the government played follow-my-American-leader._\n\n## _The Korean War: Lieutenant Curtis Wins the VC, Imjin River, 22 April 1951_\n\nANTHONY FARRAR-HOCKLEY\n\n_At the end of the Second World War, Korea had been divided (along the 38th Parallel) between the Communist North and the US-backed South. After diplomatic spats and the rattling of bayonets \u2013 the Cold War was hotting up \u2013 Kim Il-sung's Communists invaded the South in June 1950. Sixteen UN nations accorded the South military support, led by the Americans (to the tune of 2 million troops) but also including a substantial British contingent, comprised of National Service conscripts and Army professionals. On 22 April 1951, the Communists broke through the UN line west of Chungpyong Reservoir, and it was only the stand of the Gloucesters at Imjin River that saved the day._\n\nThe dawn breaks. A pale, April sun is rising in the sky. Take any group of trenches here upon these two main hill positions looking north across the river. See, here, the weapon pits in which the defenders stand: unshaven, wind-burned faces streaked with black powder, filthy with sweat and dust from their exertions, look towards their enemy with eyes red from fatigue and sleeplessness; grim faces, yet not too grim that they refuse to smile when someone cracks a joke about the sunrise. Here, round the weapons smeared with burnt cordite, lie the few pathetic remnants of the wounded, since removed: cap comforters; a boot; some cigarettes half-soaked with blood; a photograph of two small girls; two keys; a broken pencil stub. The men lounge quietly in their positions, waiting for the brief respite to end.\n\n'They're coming back, Ted.'\n\nA shot is fired, a scattered burst follows it. The sergeant calls an order to the mortar group. Already they can hear the shouting and see, here and there, the figures moving out from behind cover as their machine-guns pour fire from the newly occupied Castle Site. Bullets fly back and forth; overhead, almost lazily, grenades are being exchanged on either side; man meets man; hand meets hand. This tiny corner of the battle that is raging along the whole front, blazes up and up into extreme heat, reaches a climax and dies away to nothingness \u2013 another little lull, another breathing space.\n\nPhil is called to the telephone at this moment; Pat's voice sounds in his ear.\n\n'Phil, at the present rate of casualties we can't hold on unless we get the Castle Site back. Their machine-guns up there completely dominate your platoon and most of Terry's. We shall never stop their advance until we hold that ground again.'\n\nPhil looks over the edge of the trench at the Castle Site, two hundred yards away, as Pat continues talking, giving him the instructions for the counter attack. They talk for a minute or so; there is not much more to be said when an instruction is given to assault with a handful of tired men across open ground. Everyone knows it is vital: everyone knows it is appallingly dangerous. The only details to be fixed are the arrangements for supporting fire; and, though A Company's Gunners are dead, Ronnie will support them from D Company's hill. Behind, the machine-gunners will ensure that they are not engaged from the open eastern flank. Phil gathers his tiny assault party together.\n\nIt is time, they rise from the ground and move forward up to the barbed wire that once protected the rear of John's platoon. Already two men are hit and Papworth, the Medical Corporal, is attending to them. They are through the wire safely \u2013 safely! \u2013 when the machine-gun in the bunker begins to fire. Phil is badly wounded: he drops to the ground. They drag him back through the wire somehow and seek what little cover there is as it creeps across their front. The machine-gun stops, content now it has driven them back; waiting for a better target when they move into the open again.\n\n'It's all right, sir,' says someone to Phil. 'The Medical Corporal's been sent for. He'll be here any minute.'\n\nPhil raises himself from the ground, rests on a friendly shoulder, then climbs by a great effort on to one knee.\n\n'We must take the Castle Site,' he says; and gets up to take it.\n\nThe others beg him to wait until his wounds are tended. One man places a hand on his side.\n\n'Just wait until Papworth has seen you, sir \u2013'\n\nBut Phil has gone: gone to the wire, gone through the wire, gone towards the bunker. The others come out behind him, their eyes all on him. And suddenly it seems as if, for a few breathless moments, the whole of the remainder of that field of battle is still and silent, watching amazed, the lone figure that runs so painfully forward to the bunker holding the approach to the Castle Site: one tiny figure, throwing grenades, firing a pistol, set to take Castle Hill.\n\nPerhaps he will make it \u2013 in spite of his wounds, in spite of the odds \u2013 perhaps this act of supreme gallantry may, by its sheer audacity, succeed. But the machine-gun in the bunker fires directly into him: he staggers, falls, is dead instantly; the grenade he threw a second before his death explodes after it in the mouth of the bunker. The machine-gun does not fire on three of Phil's platoon who run forward to pick him up, it does not fire again through the battle: it is destroyed; the muzzle blown away, the crew dead.\n\n_Back home, in the new self-contained, insular Britain, the public was shrugging off the grey weariness of the war years. If the new mood had a definite beginning it was the Labour-inspired Festival of Britain, a conscious commemoration of the Great Exhibition of 1851. Harold Nicolson, the veteran diplomat and broadcaster (and husband of the writer and gardener Vita Sackville-West), recorded in his diary:_\n\nI go to Waterloo and meet Viti. We then enter the South Bank Exhibition [the central feature of the Festival of Britain]. We are entranced from the first moment. It is rather a bore as we keep getting caught by the King and Queen, but nonetheless we enjoy it uproariously. It is the most intelligent exhibition I have ever visited. I have never seen people so cheered up or so amused, in spite of a fine drizzle of rain and a Scotch mist.\n\n_Things were definitely on the up._\n\n## _Everest Conquered, Himalayas, 29 May 1953_\n\nEDMUND HILLARY\n\n_Mount Everest, at 29,028 feet the highest peak in the world, was finally conquered in 1953 by a British team led by Sir John Hunt. Edmund Hillary and Tenzing Norgay made the final assault._\n\nI lay on the little rock ledge panting furiously. Gradually it dawned on me that I was up the step, and I felt a glow of pride and determination that completely subdued my temporary feelings of weakness. For the first time on the whole expedition I really knew I was going to get to the top. 'It will have to be pretty tough to stop us now' was my thought. But I couldn't entirely ignore the feeling of astonishment and wonder that I'd been able to get up such a difficulty at 29,000 feet even with oxygen.\n\nWhen I was breathing more evenly I stood up and, leaning over the edge, waved to Tenzing to come up. He moved into the crack and I gathered in the rope and took some of his weight. Then he, in turn, commenced to struggle and jam and force his way up until I was able to pull him to safety \u2013 gasping for breath. We rested for a moment. Above us the ridge continued on as before \u2013 enormous overhanging cornices on the right and steep snow slopes on the left running down to the rock bluffs. But the angle of the snow slopes was easing off. I went on chipping a line of steps, but thought it safe enough for us to move together in order to save time. The ridge rose up in a great series of snakelike undulations which bore away to the right, each one concealing the next. I had no idea where the top was. I'd cut a line of steps around the side of one undulation and another would come into view. We were getting desperately tired now and Tenzing was going very slowly. I'd been cutting steps for almost two hours, and my back and arms were starting to tire. I tried cramponing along the slope without cutting steps, but my feet slipped uncomfortably down the slope. I went on cutting. We seemed to have been going for a very long time and my confidence was fast evaporating. Bump followed bump with maddening regularity. A patch of shingle barred our way, and I climbed dully up it and started cutting steps around another bump. And then I realized that this was the last bump, for ahead of me the ridge dropped steeply away in a great corniced curve, and out in the distance I could see the pastel shades and fleecy clouds of the highlands of Tibet.\n\nTo my right a slender snow ridge climbed up to a snowy dome about forty feet above our heads. But all the way along the ridge the thought had haunted me that the summit might be the crest of a cornice. It was too late to take risks now. I asked Tenzing to belay me strongly, and I started cutting a cautious line of steps up the ridge. Peering from side to side and thrusting with my ice-axe, I tried to discover a possible cornice, but everything seemed solid and firm. I waved Tenzing up to me. A few more whacks of the ice-axe, a few very weary steps, and we were on the summit of Everest.\n\nIt was 11.30 a.m. My first sensation was one of relief \u2013 relief that the long grind was over; that the summit had been reached before our oxygen supplies had dropped to a critical level; and relief that in the end the mountain had been kind to us in having a pleasantly rounded cone for its summit instead of a fearsome and unapproachable cornice. But mixed with the relief was a vague sense of astonishment that I should have been the lucky one to attain the ambition of so many brave and determined climbers. It seemed difficult at first to grasp that we'd got there. I was too tired and too conscious of the long way down to safety really to feel any great elation. But as the fact of our success thrust itself more clearly into my mind, I felt a quiet glow of satisfaction spread through my body \u2013 a satisfaction less vociferous but more powerful than I had ever felt on a mountain top before. I turned and looked at Tenzing. Even beneath his oxygen mask and the icicles hanging from his hair, I could see his infectious grin of sheer delight. I held out my hand, and in silence we shook in good Anglo-Saxon fashion. But this was not enough for Tenzing, and impulsively he threw his arm around my shoulders and we thumped each other on the back in mutual congratulations.\n\nBut we had no time to waste! First I must take some photographs and then we'd hurry down. I turned off my oxygen and took the set off my back. I remembered all the warnings I'd had of the possible fatal consequences of this, but for some reason felt quite confident that nothing serious would result. I took my camera out of the pocket of my windproof and clumsily opened it with my thickly gloved hands. I clipped on the lens-hood and ultra-violet filter and then shuffled down the ridge a little so that I could get the summit into my viewfinder. Tenzing had been waiting patiently, but now, at my request, he unfurled the flags wrapped around his ice-axe and, standing on the summit, held them above his head. Clad in all his bulky equipment and with the flags flapping furiously in the wind, he made a dramatic picture, and the thought drifted through my mind that this photograph should be a good one if it came out at all. I didn't worry about getting Tenzing to take a photograph of me \u2013 as far as I knew, he had never taken a photograph before and the summit of Everest was hardly the place to show him how.\n\n_The news of Hillary and Tenzing's summiting of Everest arrived in London in time for the Coronation of the new queen._\n\n## _The Coronation of Queen Elizabeth II, 2 June 1953_\n\nJOAN REEDER\n\n_Elizabeth Windsor was twenty-six when she succeeded to the crown._\n\n_Reeder was correspondent for the_ Daily Mirror.\n\nIt was just 10.15. In came the Princess Royal, the Duchess of Gloucester, her two small sons stepping slowly each side of her. The Duchess of Kent, her three children pacing behind her.\n\nThen Princess Margaret, looking like a fairy princess. Queen Elizabeth the Queen Mother, gently regal, and all their colourful, aristocratic retinues.\n\nMore music. And a Prince with sculptured features, resplendent in the gold and dark blue of the Royal Navy, a robe of magnificent scarlet velvet over it, moved slowly to his place. Admiral of the Fleet, HRH the Duke of Edinburgh, KG, KT \u2013 the husband of the Queen, the father of the King to come, four-year-old Prince Charles.\n\nThe 8,000 of us here were standing now. We felt odd, tense. Violins and organ filled the Abbey with sound. Clearly, surely came the wonderful ringing cry of the Queen's Scholars of Westminster: 'Vivat, Regina Elizabetha. Vivat, vivat, vivat.'\n\n_And suddenly we didn't want to see her._\n\n*\n\nNot yet. This would be a stranger to us. Not the happy girl we knew, laughing with her children, waving from a car, fishing in waders in a Scottish river. This would be a Queen.\n\nBut relentlessly the tremendous procession of might and majesty moved nearer. The great dignitaries of Church, remote, unbending. The Officers of State bearing the Regalia of this day with which to burden and bow the girl we, as a nation, had known as 'Lillibet'.\n\nAnd then \u2013 at last \u2013 she came \u2013 THE QUEEN.\n\n_On her head a diadem of precious stones.... From her shoulders a Royal robe of crimson velvet trimmed with ermine, bordered with gold lace, its long and heavy train carried by six Maids of Honour gowned in white and gold._\n\nThe Archbishop led her to our sight.\n\nI do not know how our voices came. Yet together, we shouted. _'God Save Queen Elizabeth.'_\n\nShe moved to her Chair of Estate, just below her mother and her family. She sat with a book between her hands; the Archbishop administered the Coronation oath:\n\n_'Will you solemnly promise and swear to govern the Peoples of the United Kingdom of Great Britain and Northern Ireland, Canada, Australia, New Zealand, the Union of South Africa, Pakistan and Ceylon, and your Possessions and the other territories to any of them belonging or pertaining, according to their respective laws and customs?'_\n\nAnd in unwavering voice came her reply: ' _I solemnly promise so to do_.'\n\nHow was she feeling \u2013 that lovely creature in the midst of that small golden field, with the eyes and ears and jumbled thoughts of a nation and a world centred on her? Could she feel anything except as a person in a dream? Was her heart thudding in her ears? Were her hands slightly moist, her lips quivering?\n\nThe glory of Handel's music swelled about us. The Lord Great Chamberlain and the Mistress of the Robes went to the Queen, and took from her her crimson robes, her diadem, her jewels.\n\nHer jewelled and patterned gown they covered with a garment of plain linen. They left her unadorned.\n\nSuddenly there she stood, the Elizabeth we knew.\n\nGowned in simple white, her light brown hair softly curling about her young and serious face, waiting to be taken from us, alone, into the supreme religious moment of this service \u2013 to be anointed, blessed, and consecrated.\n\n*\n\nNow this was a church. Now we could pray. It was all we could do. For we wanted to put out our own hands to touch her, to comfort her, to tell her she was not alone. She looked so defenceless.\n\nHer husband, her mother, her sister, watched her move to that ancient highbacked chair. They, too, felt her loneliness. It was upon their faces.\n\nFour Knights of the Garter each grasped a silver staff at the four corners of the canopy of cloth of gold, and moved to hold it over the chair.\n\nNone could see her face except the bishops and archbishops.\n\nWe could see one face clearly. That of Geoffrey, Archbishop of Canterbury, as he received from the Dean of Westminster the holy oil from the golden Ampulla poured into the Spoon.\n\nWe watched him, grave and intent, dip his fingers in the oil, and anoint first the hands of Elizabeth II, then her breast, then her head, and heard him speak the solemn mystery.\n\n_'... Be thy head anointed with holy oil: as kings, priests, and prophets were anointed: And as Solomon was anointed king by Zadok the Priest and Nathan the Prophet, so be thou anointed, blessed, and consecrated Queen over the People who the Lord thy God hath given thee to rule and govern_\n\nAll you could say, all you wanted to say, was: 'Please God, help her, and us.'\n\nIt was over. The white-clad figure of the girl, looking something like Joan of Arc, knelt, was blessed, and then upon her was fastened like a surplice the white Colobium Sindonis, and over it a golden coat with long sleeves, the Supertunica, and a girdle.\n\nThe Sword of State was received and given back by her \u2013 she touched the golden spurs.\n\n_She held out her small wrists for the Armills to be fastened around them \u2013 'the bracelets of sincerity and wisdom'. She was cloaked entirely in the Robe Royal_\n\nWe stood, waiting. The Archbishop had taken the great glittering crown, and placed it on the altar. She, in her golden cloak, sitting hidden in the huge wooden chair, bareheaded, her hands laden, waited, too.\n\nHigh, high, the crown rose in the Archbishop's hands above her head.\n\nHis hands gently lowered. There was a rustling as of a sudden wind stirring scattered leaves. The thousand noblemen and their ladies had lifted their coronets.\n\nThe heavy crown \u2013 for her life on earth \u2013 was upon the head of our Queen. A forest of lilies bloomed high into the air, and gently sank \u2013 it was the white arms of the peeresses putting on coronets.\n\nAnd there was a great sound wrung from the heart of a nation. 'God Save the Queen.'\n\n_Two years later, the more prosaic throne of the Conservative Party enjoyed its own smooth succession, from the retiring Churchill to his heir apparent, Anthony Eden. Previously famous for his urbanity and common sense, Eden oversaw Britain's biggest post-war_ folie de grandeur, _when Egypt's nationalization of the part-British-owned Suez Canal prompted an old political reflex in London (and Paris): the sending in of the troops. Airborne forces landed at Port Said on_ 5 _November 1956, seaborne troops a day later. A military success, Suez was a diplomatic fiasco. Eden, the British Prime Minister, had failed to see that in the new post-war order Britain was one of the 'Big Three' in name only. The United States disliked the Suez adventure \u2013 and so ordered Britain home like a naughty schoolboy._\n\n_6 November 1956 was the day that Britain ceased to be a world power. Eden, humiliated and ill, resigned the premiership on 9 January 1957._\n\n_The Suez expedition had also met widespread opposition in England, where the 'angry young man' (and woman) immortalized by John Osborne's_ Look Back in Anger _attended the new universities, listened to skiffle music, and protested for peace._\n\n## _Banning the Bomb: Aldermaston March, 4 April 1958_\n\nANONYMOUS\n\n_The Campaign for Nuclear Disarmament was founded in 1958. In its early years CND held annual marches from Trafalgar Square to Aldermaston in Berkshire, site of the Atomic Weapons Research Establishment. The first march took place at Easter, 1958._\n\nSome five hundred men, women, and children were spreading out sleeping-bags and thankfully washing their feet in various church halls in Hounslow last night after marching the eleven miles from Trafalgar Square on the first lap of their descent upon Aldermaston. About a thousand more had returned to their homes in London, perhaps to march again to-day. A lamplight meeting in the well-named Treaty Road, Hounslow, had evoked the first really lusty cheers of the day as Mr Michael Foot denounced the recent Defence White Paper as 'the most shameful statement ever made by a British Government'.\n\nIt was Mr Foot who had cried from the plinth on Nelson's Column in the morning, as a cold sun played on some four thousand faces: 'This can be the greatest march in English history.' Whatever the march may turn out to be, it had already by then called out a splendid array of English faces, most of them intent on making clear their conviction that nuclear weapons are evil and should be controlled or done away with.\n\nIt was a happy crowd, a London holiday crowd, in benign mood \u2013 as benign as the weather that favoured it until the afternoon grey chill came down, no more combative than the empty London streets through which the long procession made its way across Trafalgar Square to the Albert Memorial and then to Chiswick and Hounslow, the first stop in the four-day march to the Atomic Energy Authority's weapons establishment at Aldermaston. The nearest thing to an incident was the cheerful booing as a policeman stopped a troop of folk-dancers from entertaining the lunch-time picnickers with an eightsome reel in front of Albert's statue.\n\nThe march bore the signs of careful planning. The column with its banners \u2013 'which is to be banned, the H-bomb or the human race?' \u2013 got off on time, and the long snake that slid down Piccadilly, Kensington High Street, and Chiswick High Road, managed with only discreet help from the police, not to obstruct what little traffic there was. Mothers wheeled children in prams, while Mr Kenneth Tynan, cigarette authoritatively held at the ready, towered above his neighbours. Behind came a troop of some fifty cars and coaches, one of them bearing that essential morale builder, the tea-urn. 'We've got 500 mattresses behind there,' said Miss Pat Arrowsmith, a pretty large-eyed girl in a white pea-jacket and carrying a rucksack, the organiser of the whole well-mannered outing.\n\nIn the morning, though, the march was supposed to be silent, so as not to break in on religious thoughts. Somewhere in Knightsbridge this proved too much for a gay band of young people from Bermondsey, the boys in bowlers and camouflaged jackets and jeans, the girls in pony-tails and high heels and men's bright shirts hanging over their skirts. They struck up 'Tannenbaum' on a handy trumpet and banjo.\n\nMiss Arrowsmith dropped back and explained about the silence. 'We should be delighted to have any sort of music after lunch, but meanwhile we should be obliged if you would conform with us.' 'Never mind, never mind,' cried one of the elegant ones in bowler hats. 'The music's in our hearts.' They were there, it turned out, as fans of the jazz band which was going to play the march through Kensington and Chiswick.\n\nMrs Anne Collins, of Gillingham, encumbered with a pack and with her small daughter in a push-chair. 'I've been thinking about this for ten years,' she said, a humble yet fixed light in her eye. 'If I become a grandmother I don't want a bomb to drop on her and her children \u2013 I don't want to drop bombs on the Russians, either. I'd rather let the Communists take over.' A trifle falteringly she walked on. The same sentiment came, gently and tentatively from Miss Jean King, a doe-eyed sixth-former from Enfield with a pack on her back, and bubblingly from Mrs Frank Manning, of Barnet, a housewife with a white angora beret on her head, a firm intention of marching all the way in her heart, and a husband and two small children in a car behind. They had all seen some revelation, it seemed \u2013 some two years ago. Miss King only on Tuesday. 'Normally I'm very lazy; I stay in and read,' she said apologetically. 'We feel nothing else matters,' proclaimed Mrs Manning, who is secretary of the Barnet Committee for Nuclear Disarmament and was surrounded by three other purposeful women, all of whom had been seen off by their friends that morning from Barnet car-park.\n\nYet others had a more carefully shaded view of things. A King's College lecturer in geography thought we should merely offer to renounce the bomb and use this as a means of inducing other nations to do so. He was non-violently contradicted in this by the young conscientious objector who squatted next to him at Chiswick, but upheld by a passing group that chanted, 'One, two, three, four, we don't want war; five, six, seven, eight, Negotiate.' 'One, two, three, four, we don't want war,' echoed two urchins up in a tree.\n\nBy the time the marchers had left Chiswick they numbered less than two thousand. Above them bobbed the signs of the Campaign for Nuclear Disarmament, a sort of formalised white butterfly which, it appeared, was the semaphore sign for 'ND'. Skiffle groups burst here and there. At Hyde Park Corner a counter-service, held by a Lutheran minister (a former inmate of a Russian prison camp) by the Artillery war memorial, had drawn only some thirty people, and his words never reached the marchers at all. More successful was a passing car driver in Chiswick who leaned out and cried 'Ostriches! Ostriches!'\n\n_The idealism and optimism of the Ban the Bombers would soon spill into a larger wind of change sweeping across England: the Swinging Sixties._\n\n## _Lady Chatterley's Trial, The Old Bailey, November 1960_\n\nKENNETH TYNAN\n\n_Looking back, the 'permissive' society in England had a definite beginning. Sexual liberation started in November 1960 at the Old Bailey, when a jury decided in favour of Penguin Books, publishers of D. H. Lawrence's supposedly obscene novel,_ Lady Chatterley's Lover.\n\nNow that the case is over, and Lady Chatterley's adventures are speeding two-hundred-thousand-fold to every outpost of literacy in the country, it seems suddenly unthinkable that the jury could have brought in any other verdict. But it was desperately thinkable right up to three o'clock on Thursday afternoon, as anyone knows who sat through the six days of the trial, and sweated out the dragging hours of the jury's retirement: more than most people, Gerald Gardiner, counsel for the defence knew it, and looked the reverse of optimistic as he prowled up and down like a wounded lion, waiting for those twelve inscrutable citizens to come to their conclusion. How we had all stared at them, seizing on each smile, each sniffle, each sign of inattentiveness as evidence of sympathy or hostility to Lawrence's cause! The lean, middle-aged man at the right-hand end of the back row seemed prematurely grey: did this betoken sensitivity or hyper-sensitivity? And the quietly eccentric behaviour of the woman, upstage right, left many of us baffled; she was given to strange, secret smiles, and would take notes at inexplicable moments.\n\nIn front of her sat a younger woman, sedate and pretty, perhaps a teacher; some of us pictured her as the Henry Fonda character whose gentle persistence would finally win over her colleagues, as in _Twelve Angry Men._\n\nIn all our ears there still rang the voice of Mervyn Griffith-Jones, counsel for the prosecution, high-cheek-boned and poker-backed, a veteran of Eton, Trinity Hall (Cambridge), the Coldstream Guards and many previous obscenity cases; a voice passionate only in disdain, but barbed with a rabid belief in convention and discipline: a slow scaly voice, listening to which one almost felt that if Penguin Books were acquitted, the prostitutes would dance in the streets, as they did after Oscar Wilde's conviction.\n\nOn Lawrence as a literary artist, the voice (for so I think of Mr Griffith-Jones, since from where I sat only his head was visible) \u2013 the voice had done some dedicated homework. 'Is that expert, artistic writing?' it would ask, having cited a passage in which a phrase was several times repeated. The mind's eye saw a man holding up one brick after another and demanding, 'Is that expert, artistic architecture?' The voice marked Lawrence as if he were an examination paper, and its interrogations had much in common with _vivas._\n\nIt exhaled class-consciousness as effortlessly as air. Would the jury wish their servants to read Lawrence's novel? And was it natural for the lady of a great house to 'run off and copulate with her husband's game-keeper?' The voice took on a positively vengeful rasp when cross-examining people who distinguished between sex as Lawrence saw it and sex as a trivial diversion. Wasn't it true that by 'tenderness' the book actually meant tenderness towards the genital organs? (One wondered how else the voice would want them treated.) And could anyone deny that in the 'bouts' of love-making the emphasis was on the 'pleasure and satisfaction' involved? Leisurely and deadly, the voice hounded Connie Chatterley, a traitress to her class in that she not only enjoyed sex, but enjoyed it with a quasi-peasant. _A propos_ of a passage in which she removed her nightdress before making love, the voice enquired why this 'striptease' was necessary; one assumed, charitably, that the question had been carelessly phrased.\n\nThroughout the trial, one longed for a witness who might challenge Mr Griffith-Jones in Lionel Trilling's words: 'I see no reason in Morality (or in aesthetic theory) why literature should not have as one of its intentions the arousing of thoughts of lust. It is one of the effects, perhaps one of the functions, of literature to arouse desire, and I can discover no grounds for saying that sexual pleasure should not be among the objects of desire which literature presents to us, along with heroism, virtue, peace, death, food, wisdom, God, etc.'\n\nBut nobody made that answer; and we, anxious in the corridors, had all but persuaded ourselves that no jury could withstand the impact of Mr Griffith-Jones when the verdict was returned and Lawrence exonerated.\n\nLooking back, I think I can isolate the crucial incident, the exchange wherein the case was psychologically won. It occurred on the third morning during the testimony of Richard Hoggart, who had called Lawrence's novel 'puritanical'. Mr Hoggart is a short, dark, young Midland teacher of immense scholarship and fierce integrity. From the witness box he uttered a word that we had formerly heard only on the lips of Mr Griffith-Jones: he pointed out how Lawrence had striven to cleanse it from its furtive, contemptuous and expletive connotations, and to use it in the most simple, neutral way: one fucks. There was no reaction of shock anywhere in the court, so calmly was the word pronounced and so literally employed.\n\n'Does it gain anything,' asked Mr Gardiner, counsel for the defence, 'by being printed \"f\u2013\"?' 'Yes,' said Mr Hoggart, 'it gains a dirty suggestiveness.'\n\nRising in cross-examination, Mr Griffith-Jones wanted to know what Mr Hoggart meant by 'puritanical', receiving an answer to the effect that a puritan was a man who felt a profound sense of responsibility to his own conscience. Counsel then read out a series of excerpts from the novel. It must have been by chance that he chose the most impressive passages, the most solemnly ecstatic, the ones about 'the primeval roots of true beauty' and 'the sons of men and the daughters of women' but slowly, as he recited them, one realized that he genuinely thought them impure and revolting.\n\nWith every defiling inflection he alienated some part of his audience, seemingly unaware that what he had intended for our scorn was moving us in a way he had never foreseen; yet still he continued, bland and derisive, utterly unconscious of his increasing loneliness. Having finished, he triumphantly asked the witness whether a puritan would feel such 'reverence for a man's balls'. 'Indeed, yes,' said Mr Hoggart, almost with compassion.\n\nI remembered his earlier reply to the suggestion that Lady Chatterley's affair with Mellors was due solely to her husband's impotence. _'It is not,'_ he said: and in those words we heard, for the first time in the trial, the stubborn, uncompromising voice of the radical English moralist.\n\nIts volume and assurance grew as the cross-examination proceeded; and before long both jury and audience knew that the real battle had at last been joined \u2013 between all that Hoggart stood for, and all that Griffith-Jones stood for; between Lawrence's England and Sir Clifford Chatterley's England; between contact and separation; between freedom and control; between love and death.\n\n_Curiously enough, one of the main architects of the Swinging Sixties was distinctly 'square'. This was the Conservative Prime Minister Harold Macmillan, whose 'You've never had it so good!' was almost a call to pleasure. It was Macmillan who abolished National Service (giving every male in England twoyears of extra living) and it was Macmillan who introduced the contraceptive pill in 1961._\n\n_Macmillan's broadmindedness brought him few favours; his government was brought low by sexual scandal, the liaison between Tory War Minister John Profumo and prostitute Christine Keeler. Not only did Profumo mislead Parliament about his relationship with Keeler, it transpired that she was also entertaining one Captain Ivanov, a Russian spy. Dogged by the Profumo scandal and ill-health, Macmillan resigned in 1963._\n\n## _The Beatles in Performance, Cavern Club, Liverpool, 9 November 1961_\n\nBRIAN EPSTEIN\n\n_A diffident Liverpool record-shop owner, Brian Epstein was the first manager of the Beatles \u2013 John Lennon, Paul McCartney, George Harrison and Pete Best (later replaced by Ringo Starr, aka Richard Starkey). The Tab Four' were the vanguard of Sixties pop and permissiveness: irreverent, long-haired, drug-fuelled and libidinous._\n\nOne interesting feature of the Beatles' entry into my life was that without being conscious of it, I had seen them many times in the store.\n\nI had been bothered a little by the frequent visits of a group of scruffy lads in leather and jeans who hung around the store in the afternoons, chatting to the girls and lounging on the counters listening to records. They were pleasant enough boys, untidy and a little wild and they needed haircuts.\n\nI mentioned to the girls in the shop that I thought the youth of Liverpool might while their afternoons away somewhere else, but they assured me that the boys were well behaved, and amusing and they occasionally bought records. Also, said the girls, they seemed to know good discs from bad.\n\nThough I didn't know it, the four lads were the Beatles, filling in part of the long afternoon between the lunchtime and evening shows in the best cellars.\n\nOn October 28 Raymond Jones left the store after I had taken a note of his request. I wrote on a pad: ' \"My Bonnie\". The Beatles. Check on Monday.'\n\nBut before I had had time to check on Monday, two girls came into the store and they too asked for a disc by this curiously-spelled group. And this, contrary to legend, was the sum total of demand for the Beatles' disc at this time in Liverpool. It is untrue that there was a milling fighting crowd around NEMS waiting for the disc to arrive.\n\nThat afternoon I telephoned a few of the agents who imported discs, told them what I was looking for and found that no one had heard of the thing, let alone imported it. I might have stopped bothering there and then if I hadn't made it a rigid rule never to turn any customer away.\n\nAnd I was sure there was something very significant in three queries for one unknown disc in two days.\n\nI talked to contacts in Liverpool and found, what I hadn't realised, that the Beatles were in fact a Liverpool group, that they had just returned from playing in clubs in the seamy, seedy end of Hamburg where they were well known, successful and fairly impoverished. A girl I know said: 'The Beatles? They're the greatest. They're at the Cavern this week'... The Cavern. Formerly a jazz club which had been a huge success in the mid-1950s, it was now owned by Raymond McFall, an ex-accountant who was filling some of his jazz programmes with raw 'Made in Liverpool' beat music played, usually, on loudly amplified guitars and drums. The Cavern was a disused warehouse beneath Mathew Street, Liverpool and I remember that I was apprehensive at the thought of having to march in there among a lot of teenagers who were dressed as if they belonged, talking teenage talk and listening to music only they understood. Also, I was not a member.\n\nSo I asked a girl to have a word with the Cavern, to say that I would like to pop in on November 9th at lunchtime and to ensure that I wasn't stopped at the door. I have never enjoyed scenes on doors with bouncers and people asking for 'your membership card, sir,' or that sort of thing.\n\nI arrived at the greasy steps leading to the vast cellar and descended gingerly past a surging crowd of beat fans to a desk where a large man sat examining membership cards. He knew my name and he nodded to an opening in the wall which led into the central of the three tunnels which make up the rambling Cavern.\n\nInside the club it was as black as a deep grave, dank and damp and smelly and I regretted my decision to come. There were some 200 young people there jiving, chatting or eating a 'Cavern lunch' \u2013 soup, roll, cokes and things. Over all the speakers were loudly-amplified current hit discs, then mainly American, and I remember considering the possibility of some 'tie' between NEMS and the Cavern in connection with the Top Twenty.\n\nI started to talk to one of the girls. 'Hey,' she hissed. 'The Beatles're going on now.' And there on a platform at the end of the cellar's middle tunnel stood the four boys. Then I eased myself towards the stage, past rapt young faces and jigging bodies and for the first time I saw the Beatles properly.\n\nThey were not very tidy and not very clean. But they were tidier and cleaner than anyone else who performed at that lunchtime session or, for that matter, at most of the sessions I later attended. I had never seen anything like the Beatles on any stage. They smoked as they played and they ate and talked and pretended to hit each other. They turned their backs on the audience and shouted at them and laughed at private jokes.\n\nBut they gave a captivating and honest show and they had very considerable magnetism. I loved their ad libs and I was fascinated by this, to me, new music with its pounding bass beat and its vast engulfing sound. There was quite clearly an excitement in the otherwise unpleasing dungeon which was quite removed from any of the formal entertainments provided at places like the Liverpool Empire or the London Palladium, though I learned later that the response to the Beatles was falling off a little in Liverpool \u2013 they, like me, were becoming bored because they could see no great progress in their lives.\n\nI hadn't appreciated it but I was something of a figure in the Liverpool Pop Scene as a Director of NEMS, and I was surprised when after the Beatles had finished, Bob Wooler, the Cavern Disc jockey, who later became a great friend of mine, announced over the loudspeaker that Mr Epstein of NEMS was in the Cavern and would the kids give me a welcome.\n\nThis sort of announcement then, as now, embarrassed me and I was a little diffident when I reached the stage to try to talk to the Beatles about 'My Bonnie'.\n\nGeorge was the first to talk to me. A thin pale lad with a lot of hair and a very pleasant smile. He shook hands and said 'Hello there. What brings Mr Epstein here?' and I explained that I'd had queries about their German disc.\n\nHe called the others over \u2013 John, Paul and Peter Best \u2013 and said 'this man would like to hear our disc.'\n\nPaul looked pleased and went into the tiny band-room next to the stage to get it played. I thought it was good, but nothing very special. I stayed in the Cavern and heard the second half of the programme and found myself liking the Beatles more and more. There was some indefinable charm there. They were extremely amusing and in a rough 'take it or leave way' very attractive.\n\nNever in my life had I thought of managing an artiste or representing one, or being in any way involved in behind the scenes presentation, and I will never know what made me say to this eccentric group of boys that I thought a further meeting might be helpful to them and to me.\n\nBut something must have sparked between us, because I arranged a meeting at the Whitechapel store at 4.30 p.m. on December 3rd, 1961, 'just for a chat,' I explained, without mentioning management because nothing as precise as that had yet formed in my mind.\n\n## _Ronnie Kray Murders George Cornell, 9 March 1966_\n\nRONNIE KRAY\n\n_At the Blind Beggar Public House, London._\n\n_The Kray twins, Ronnie and Reggie, ran a criminal gang in the East End of London. George Cornell was a member of the rival Richardson gang, and had been implicated in the shooting of the Krays' associate, Richard Hart._\n\nRichard Hart had to be avenged. No one could kill a member of the Kray gang and expect to get away with it. The problem was, both of the Richardsons and Mad Frankie Fraser were in custody and likely to remain so. That left Cornell. He would have to be the one to pay the price. And, let's face it, who better? All I had to do was find him. The next night, 9 March, I got the answer. He was drinking in the Blind Beggar.\n\nTypical of the yobbo mentality of the man. Less than twenty-four hours after the Catford killing and here he was, drinking in a pub that was officially on our patch. It was as though he wanted to be killed.\n\nI unpacked my 9mm Mauser automatic. I also got out a shoulder holster. I called Scotch Jack Dickson and told him to bring the car round to my flat and to contact Ian Barrie, the big Scot, and to collect him on the way. As we drove towards the Blind Beggar, I checked that Barrie was carrying a weapon, just in case.\n\nAt eight-thirty p.m. precisely we arrived at the pub and quickly looked around to make sure that this was not an ambush. I told Dickson to wait in the car with the engine running, then Ian Barrie and I walked into the Blind Beggar. I could not have felt calmer, and having Ian Barrie alongside me was great. No general ever had a better right-hand man.\n\nIt was very quiet and gloomy inside the pub. There was an old bloke sitting by himself in the public bar and three people in the saloon bar: two blokes at a table and George Cornell sitting alone on a stool at the far end of the bar. As we walked in the barmaid was putting on a record. It was the Walker Brothers and it was called 'The Sun Ain't Gonna Shine Any More'. For George Cornell that was certainly true.\n\nAs we walked towards him he turned round and a sort of sneer came over his face. 'Well, look who's here,' he said.\n\nI never said anything. I just felt hatred for this sneering man. I took out my gun and held it towards his face. Nothing was said, but his eyes told me that he thought the whole thing was a bluff. I shot him in the forehead. He fell forward on to the bar. There was some blood on the counter. That's all that happened. Nothing more. Despite any other account you may have read of this incident, that was what happened.\n\nIt was over very quickly. There was silence. Everyone had disappeared \u2013 the barmaid, the old man in the public and the blokes in the saloon bar. It was like a ghost pub. Ian Barrie stood next to me. He had said nothing.\n\nI felt fucking marvellous. I have never felt so good, so bloody alive, before or since. Twenty years on and I can recall every second of the killing of George Cornell. I have replayed it in my mind millions of times.\n\nAfter a couple of minutes we walked out, got into the car and set off for a pub in the East End run by a friend called Madge. On the way there we could hear the screaming of the police car sirens. When we got to the pub I told a few of my friends what had happened. I also told Reg, who seemed a bit alarmed.\n\nThen we went to a pub at Stoke Newington called the Coach and Horses. There I gave my gun to a trusted friend we used to call the Cat and told him to get rid of it. I suddenly noticed my hands were covered in gunpowder burns, so I scrubbed them in the washroom. I showered and put on fresh clothing \u2013 underwear, a suit, a shirt and tie. (We had spare sets of 'emergency' clothes at several places.) All my old clothing was taken away to be burned. Upstairs in a private room I had a few drinks with some of the top members of the firm \u2013 Reg, Dickson, Barrie, Ronnie Hart and others. We listened to the radio and heard that a man had been shot dead in the East End. As the news was announced I could feel everyone in the room, including Reg, looking at me with new respect. I had killed a man. I had got my button, as the Yanks say. I was a man to be feared. I was now the Colonel.\n\n## _England Win the World Cup, Wembley, 30 July 1966_\n\nDAVID MILLER\n\n_The England team: Banks, Cohen, Charlton, J., Moore, Wilson, Stiles, Charlton, R., Peters, Ball, Hunt, Hurst. The West German team: Tilkowski, Hoettges, Schulz, Weber, Schnellinger, Beckenbauer, Haller, Overath, Seeler, Held, Emmerich._\n\nAs the crowd stood in ovation, Greaves looked on wistfully. Injury had cost him his place, and though he recovered, Ramsey had resisted the almost overpowering temptation to change a winning side. This, too, was vindication, his whole aim since 1963 having been to prepare not a team but a squad, so that at any moment he might replace an out of form or injured man without noticeable deterioration in the side. When the time came, the luckless Greaves's omission caused hardly a stir of pessimism.\n\nAt the start of the tournament, I had written that if England were to win, it would be with the resolution, physical fitness and cohesion of West Germany in 1954, rather than with the flair of Brazil in the two succeeding competitions. And so it proved, with the added coincidence that it was the Germans themselves, as usual bristling with all these same characteristics in profusion, who were the unlucky and brave victims of England's methodical rather than brilliant football. Before the semi-finals I said that the deciding factor of this World Cup, when all others had cancelled out in the modern proficiency of defensive systems, would be character, and now the character of every England player burned with a flame that warmed all those who saw it. The slightest weakening, mentally or physically, in any position, could have lost this match a hundred times over, but the way in which Ball, undoubtedly the man of the afternoon, Wilson, Stiles, Peters, Bobby Charlton and above all Moore, impelled themselves on, was something one would remember long after the tumult of excitement and the profusion of incidents had faded. Justifiably, Moore was voted the outstanding player of the competition; his sudden, surging return to form on tour beforehand had helped cement the castle at the critical hour.\n\nAll assessments of great events should be measured by absolute standards along with the quality of contemporaries, and therefore one had to say that England were not a great team, probably not even at that moment the best team in the world, depending on what you mean by best.\n\nWhat matters is that they were the best there at Wembley in July, on that sunny, showery afternoon, best when the chips were down in open combat, and that, after all, is what counts \u2013 the result, rather than its manner, goes into the record books. Besides, Ramsey had not set about producing the most entertaining but the most successful team. Could he afford to be the one romantic in a world of hard-headed, win-at-all-costs efficiency? Could he favour conventional wingers who promised much and produced little? A manager is ultimately only as good as the players at his disposal; handicapped by a shortage of world class, instinctive players of the calibre of the South Americans, Italians, Hungarians, or his own Bobby Charlton, and by an over-abundance of average competence, Ramsey had slowly eliminated all those who lacked what he needed for cohesion. What greater demonstration of unity of purpose could there have been than the insistence of the winners, for all the emotion of the moment, that the eleven reserves join them on the lap of honour, and after share equally the \u00a3 _22,000_ bonus.\n\nSome complained England were helped by playing all their matches at Wembley, yet certainly in that mood and form they could and would have won anywhere in the country. Besides, under Ramsey, England had had more success abroad than ever before. If nothing else, this World Cup, penetrating almost every home in the land, should have persuaded the doubters, the detractors and the cynics that this is the greatest spectator sport there is, and the Final was a fitting climax.\n\nAt the start England asserted themselves \u2013 Bobby Charlton exerting a telling influence in midfield, even though closely watched by Beckenbauer sent Peters streaming through with fine anticipation, into spaces behind the German midfield trio. Suddenly, however, in the thirteenth minute, England found themselves a goal down for the first time in the competition. It was not an error under pressure, it was unforced. As a centre from the left came over, Wilson stood alone, eyes riveted on the dropping ball. He made to head it down to Moore, but his judgement betrayed him, sending it instead straight to Haller, who whipped in a low skidding shot past an unsighted, helpless Banks.\n\nThe strapping Germans and their flag-waving supporters bounced with joy, but within six minutes England were level. Midway inside the German half, on the left, Overath tripped Moore, and even before the referee had finished wagging his finger at Overath, Moore had spotted a gaping hole in the German rearguard. He placed the ball and took the kick almost in one move, a dipping floater that carried thirty-five yards and was met by Hurst, streaking in from the right, with another graceful, expertly-timed header like that which beat Argentina.\n\nThe pattern swung once more in the ten minutes before half-time. The three German strikers, nosing in and out like carnivorous fish, began to create havoc that was only averted after extreme anxiety. In between, Hunt, from a glorious pass by Bobby Charlton, hammered a thundering shot, a difficult one running away to his left, straight at Tilkowski. On the stroke of half-time, it was England who were desperately lucky, when a fast dipper by Seeler was tipped over by Banks, arched in mid-air like a stalling buzzard.\n\nLittle happened for nearly twenty-five minutes after half-time, the lull punctuated only by 'Oh, oh, what a referee,' as Mr Dienst went fussily about his business. Then, with twenty minutes to go, England's rhythm began to build up again, Bobby Charlton, Ball and Peters stretching the Germans to the extreme of their physical endurance with passes that again and again almost saw Hurst and Hunt clear. With eleven minutes to go, Ball won a corner, put it across, the ball was headed out, and hit back first-time by Hurst. It struck a defender, fell free, and Peters swooped to lash it home.\n\nEngland, sensing victory, played it slow, slow, but Hunt wasted a priceless chance when it was three red England shirts to one white German on the edge of the penalty area, by misjudging his pass. With a minute left, all was disaster as Jack Charlton was most harshly penalized for 'climbing' over the top of Held. Emmerich blasted the free kick. A German in the penalty area unquestionably pulled the ball down with his hand, and after a tremendous scramble, Weber squeezed the ball home to level the match.\n\nYou could see England's spirits sink as the teams changed over for extra time but, quickly calmed and reassured by the emotionless Ramsey, they rallied themselves instantly. Ball, still unbelievably dynamic, going like the wind right to the finish, had a shot tipped over, Bobby Charlton hit a post and with twelve minutes gone, England were once more in front as Stiles slipped the ball up the wing to Ball, whose cross was thumped hard by Hurst. The ball hit the bar, bounced down and came out, and after consultation with the Russian linesman, Bakhramov, a goal was given. I had my doubts, doubled after later seeing television, but that surely had to be the winner, for now, socks rolled down, both teams were physically in distress. Again England sought economy with gentle passes, keeping precious possession, wearing the Germans down yet further. Poor Wilson hardly knew where he was after a blow on the head. Slowly the minutes ticked away, agonizingly, until with the referee looking at his watch, Hurst staggered on alone from yet one more of Moore's perceptive passes, to hit the ball into the roof of the net with what little strength he had left, and make England's victory, like their football, solid and respectable.\n\n## _Grosvenor Square, 17 March 1968_\n\nDICK POUNTAIN AND MICK FARREN\n\n_It wasn't quite Paris or Berkeley, but the Vietnam Solidarity Committee demonstration in London's Grosvenor Square \u2013 site of the US Embassy \u2013 was the height of '68 student protest in England._\n\n_Mick Farren was the leather-trousered lead singer with the cult Sixties band, Social Deviants, and journalist for the radical new sheet, IT_ (International Times). _Dick Pountain was a member of the International Situationists, political agitators of the Absurd._\n\nDICK POUNTAIN: The first one [Grosvenor Square demonstration], in March, turned into a real free-for-all afterwards \u2013 running down Park Lane, trashing cars and bank windows, very very heavy. We, the Situationists, actually had a presence on the march and made this huge banner that said 'Storm the Reality Studio and Retake the Universe'. Yellow letters on blue... it was very professionally done. We joined the march amidst all these Trots, all chanting 'Ho, Ho, Ho Chi Minh!' and we were chanting 'Hot chocolate, drinking chocolate!' and getting lots and lots of aggravation from all the Trots around us. And as we went past Hyde Park Corner this figure clad in black leather from head to foot came out of the crowd and joined us and it was Micky Farren and it was the first time I ever spoke to him.\n\nMICK FARREN: Saturday night, we'd been playing somewhere like Mother's Club in Birmingham and we were coming back down the M1 and ran into these humungous police roadblocks and they pulled out all our equipment. We said, 'What the fuck do you want?' and they said, 'We're looking for weapons.' And we get back to London and me and Sandy plan to go to the riot the next day. So we got up about lunch-time, two o'clock as was our wont, and got our shit together. Nobody else could be bothered to go because they were still asleep. We went downstairs and there were maybe 50 motorcycle cops at the top of Endell Street and buses full of these geezers who look like they feed on vodka and raw meat and don't get let out except on riots. I thought, 'Mother-fucker! what's goin on here?' There weren't exactly tanks on the boulevards but... shit, it was like Chile or something. So we went marching up to Centrepoint where we ran into Miles and we hooked up with the march somewhere by Tottenham Court Road and Oxford Street.\n\nWe were marching along and there were reports that Mick Jagger had been seen and this was happening and that was happening and it was all very sort of aggressive. There were all sorts of Germans who were a real nuisance because they kept linking arms and getting into that run that the Japanese had invented. We didn't really want to go that fast \u2013 we'd just got up and we didn't feel too good and we didn't need a lot of mad Krauts doing the Japanese run, very disruptive, like Zulu impis getting wound up, and they kept doing these flurries of running on the spot which got people very excited to the point that somebody tried to nose his car out of somewhere like Berwick Street through the crowd and Miles kicked in his headlamps! I thought, 'Jesus!' Me and Sandy were coming down off speed and we weren't as rambunctious as a lot of people around us. We had just meandered along.\n\nSo we got to South Audley Street and started streaming down there and everything halts and nobody knows what's going on and there's all these rumours that they're tear-gassing people here and there (in fact they weren't). We hadn't seen the US Embassy yet, although there was another rumour that there were armed marines who'd kill you if you actually got inside. Then everything started to move and we went charging down Audley Street and it seemed like the police had given way, that's what everybody assumed. We arrived on the grass in Grosvenor Square, where, although I didn't know it at the time, we had immediately been surrounded. So there we have these thousands of people boxed in on the grass, though it's not that crowded, there's room to stroll around, except down the end by the Embassy where it's so crowded you can't see anything. And we just started wandering about and I remarked to Sandy, 'It's like a fucking love-in.' Then there was a thunder of hooves and there we were in the middle of the charge of the Light Brigade, which was fucking scary. What little I knew, basically from Napoleonic history, was get under a tree, because it's very hard to swing one of those truncheons when you're on a horse and the other guy is under a tree. So the first charge goes through and they're sort of whacking people and one geezer on a white horse, who became quite notorious, whacked this girl on the head \u2013 at which point everybody became exceedingly annoyed and dragged him off his horse and kicked him. He got away a couple of times but then he was surrounded and when everyone closed ranks he was just left there. And then people were hurling bits of turf and rocks and stuff and then they'd retreat and charge again and retreat and charge and people were getting hit and hurt and injured and then we went home. Just like that. And watched it on TV.\n\n_The Grosvenor Square protests were one reflection of the malaise growing under the superficial satisfactions of Sixties England. Inflation was beginning to rise; so was unemployment. The incoming 1970 Conservative government of Edward Heath grabbed at one financial fix after another, to no avail. Faced with declining living standards, the trade unions replied with muscle-power. And the miners had the biggest biceps of the lot. National miners' strikes were called in 1972 and 1974. Heath responded with an election on the theme of 'Who runs Britain?' Not Edward Richard George Heath of Sidcup, it turned out. The electorate narrowly returned a Labour government under Harold Wilson, who snake-charmed the unions with a deal ('the social contract') whereby they moderated their wage demands in return for vague promises to do something about their grievances. Despite Wilson's hypnosis of the unions, inflation and unemployment continued at historically high levels. Outsiders spoke of the UK as the new 'sick man of Europe'. Inside England the era's nihilism was perfectly lyricized, if screechingly sung, by the harbingers of punk rock:_\n\n_No future\/No future\/There's no future for you.'_\n\n## _Never Mind the B******S: The Sex Pistols, November 1975\u2013April 1976_\n\nJOHN LYDON AND PAUL COOK\n\n_It is a matter of dispute whether the Sex Pistols were manufactured \u2013 or not \u2013 by svengali Malcolm McLaren as a means of publicizing Sex, the clothes shop he ran with designer Vivienne Westwood. John Lydon is the given name of Johnny Rotten. Paul Cook was the drummer in the band._\n\nPAUL COOK: Glen Matlock attended St Martin's College, and he set up our first gig there in November of 1975. We rehearsed across the road and wheeled all the equipment down Charing Cross Road about six in the afternoon. We set up and played for twenty minutes. Total chaos. None of us knew what we were doing. We were very nervous and all over the place. We played cover versions like 'No Lip', 'Satellite', 'Substitute', 'Seventeen', 'What' cha Gonna Do About It'. We were all still learning our trade.\n\nJOHN LYDON: There was not one single hand clap.\n\nCOOK: People yelled at us to get off because they wanted their Bazooka Joe. We nearly had a fight with them. They thought we were an oddity because of our attitudes.\n\nLYDON: The college audience had never seen anything like it. They couldn't connect with where we were coming from because our stance was so anti-pop, so anti-everything that had gone on before. Adam may look back on it all rather sweetly by saying he split up his band after seeing us play, but the reality was that he was very bitter and annoyed with us \u2013 as indeed most bands were that played with us. Adam Ant's band was furiously jealous because they spent so much time sewing up those silly silver jackets.\n\nCOOK: We weren't being nice. That was the main difference between us and them.\n\nLYDON: I didn't care. We didn't do it to be loved.\n\nCOOK: That was outrageous for 1975. You have to understand what it was like at the time. Everything was so conventional \u2013\n\nLYDON: So English. Nobody wanted to offend anybody, and everybody was bemoaning their sorry lot, but never doing anything about it. If you stood up to express an opinion, that would be offending someone, and therefore that wouldn't be British, a terrible thing to have to fight against. Quite frankly, looking at Britain right now, that's what it's all reverted to. Everybody wants to be nice again.\n\nCOOK: We used to turn up at college gigs opening up for hippie bands. We weren't booked at a lot of those gigs because they wouldn't have us on. We would play unannounced at places like Central School of Art and Design in Holborn. Holborn was arranged by Glen's friend, Al MacDonald. Then there was Finchley, Queen Elizabeth College, Chelsea School of Art, Chislehurst Raven, St Albans, Aldgate, and Kensington. These were just learning gigs around Christmastime of 1975. The strange thing was that people latched on to us straight away. We got a reaction wherever we went; a lot of it was positive.\n\nLYDON: We were terrified doing these gigs because of the fear of it all being totally new. It worked a lot better this way than if we would have spent six months to a year learning our craft in a studio, then coming out and just being musos. We had to learn our skills from a live perspective. It wouldn't have worked any other way. That's what was wrong with most of those bands then \u2013 and still is. They were too much into the perfection of it all.\n\nCOOK: There were a lot of gigs where once we started playing, they just wanted to get us off.\n\nLYDON: Usually for an opening act, the worse they are, the better it was for the headliner. In our case, as bad as we were, it was too fucking good by far. We had something none of these people had \u2013 energy and sheer, brazen honesty. We couldn't give a fuck what people thought because we felt what we were saying was much more relevant. And that sometimes became a threat. We showed up at a couple of Andrew Logan's parties. We had done a gig there some months before. The second time I turned up was to a party I wasn't invited to. Malcolm rang me up at my old man's to invite me while I was in the pub across the street. When I got to the party, Malcolm had since decided it was a bad idea inviting me because Vivienne decided she didn't want me there. I didn't know what it was all about, but they wouldn't let me in. I was considered too uncouth, so I kicked up a huge stink. Something was going on between Malcolm and Vivienne. They thought my image should be one of mystery. That was fucking shit: Malcolm rang me up, got me there, and then I was told that I wouldn't be let in. He wouldn't even come to the door.\n\nCOOK: The Marquee Club gig in February of 1976 with Eddie and the Hot Rods was a lot of nervous energy. They thought it would be a good idea to put the Pistols on the bill because they thought we had something in common.\n\nLYDON: From what I could gather, Eddie and the Hot Rods were show-casing for a record company that night. They knew we had a reputation, and they wanted us there. 'Sure you can use our monitors.' Since we never had our own stage monitors, we had to rely on others for their equipment, and if they bugger you about, that's the end for you. If you can't hear what you're doing, you're fucked. But when it came to the actual gig, somehow the monitors were turned off. I call that industrial sabotage or a major mistake and didn't take kindly to it. That's when things started to go sadly wrong for Eddie and the Hot Rods. I put a mike stand through one of their monitors.\n\nCOOK: Bands like Eddie and the Hot Rods thought there was going to be some great movement, so they wanted everyone to huddle together into this cozy little alliance. Being totally selfish, we weren't into that at all. It was all the other bands that had this idea of a great big movement together.\n\nLYDON: Eddie and the Hot Rods to me was everything that was wrong with live music. Instead of fighting all this big stadium nonsense, they would narrow themselves into this tiny clique by playing in pubs. It was all about denim and plaid shirts, tatty jeans and long droopy hair. Looking awful and like nothing... looking like Nirvana! That was the look then. It really annoys me now fifteen or so years later when these bands say they were influenced by the Sex Pistols. They clearly can't be. They missed the point somewhere. You don't wear the tattered uniform of blandness \u2013 not if you're interested in the Pistols at all. It's all about being yourself! Be a fucking individual. As a band, the Sex Pistols were all completely different as people \u2013 the way we dressed, everything. We didn't give up our individuality just to be a Sex Pistol. That's what made the Pistols, that difference.\n\n_The Pistols' iconoclastic 'God Save Queen' ('It's a fascist regime\/She's a moron\/A potential H-bomb') topped the record charts in 1977 but was kept at No. 2 by the BBC, so that the Corporation avoided embarrassing Elizabeth II in her Silver Jubilee Year. Or so conspiracy theory has it._\n\n_There was no Anarchy in the UK (like nearly every other cultural protest, punk rock became gathered to the bosom of the established order: to be a staple image on tourist postcards in this case), but there were still strawberries and cream for tea at Wimbledon._\n\n## _Wade Wins Wimbledon, 1 July 1977_\n\nFRANK KEATING\n\nVirginia Wade is the Wimbledon champion at last \u2013 and it didn't matter one jot that it was one of the worst finals in memory. The day will be long recalled for the ecstatic scenes at the very end when the Queen gave her the trophy and even starchy All England men and matrons relaxed upper lips and thunderously let go with 'For she's a jolly good fellow'. Whether the anthem was addressed to the Queen or Miss Wade they cared not a fig. And nor did England.\n\nBut, by jove, Miss Wade made the nation sweat as ever. She has been trying to win the thing for 16 years now and it was not until well into the afternoon that nails stopped being bitten. She beat the mountainous Dutch girl, Betty Stove, 4\u20136, 6\u20133, 6\u20131.\n\nMiss Wade's first year at Wimbledon was in 1962 and coincided with the Queen's first visit. Afterwards Virginia said it had been so joyously noisy that she had not heard all the Queen had said to her at the end. 'It didn't matter, it was just great to see her lips moving.'\n\nRampant patriotism apart, it must be said that it was an awfully dank, dull match full of terrible unforced bloomers by both girls. The Queen's long-known aversion to lawn tennis cannot have been changed. Indeed she had pulled on her white gloves, was straightening her skirt, glancing at the clock and looking to get away to the tea-time racing results mid-way through the third set.\n\nFrom the start both players were as nervous as field mice at harvesting, the Dutch girl seemingly the less so, for she won the first set \u2013 at the end of which you could probably hear the silence a mile away. It looked as if we were in for the biggest anti-climax since the _Titanic_ similarly came across something large and unexpected all those years ago.\n\nIt was 3\u20133 in the second set before the despairing, muttered prayers of 14,000 people got through to their girl in the cathedral. It worked! Virginia reeled off seven games on the trot to take the second set and squat, unassailable, on a 4\u20130 lead in the last.\n\nThe power of prayer! Miss Wade's father, a retired archdeacon, also did his stuff. 'Yes,' he admitted before the match, 'I did pray for Virginia this morning.' Though he added after some meditative thought: 'But then I always pray for everyone each morning.'\n\n_During the 'winter of discontent' of 1978\/9, the Labour contract with the unions broke down in acrimony, and an epidemic of public service strikes saw rubbish uncollected and graves undug. Inflation was edging towards 20 per cent. Labour wasn't working. The electorate agreed, and the Conservatives won the 1979 election._\n\n## _Margaret Thatcher Becomes Prime Minister, 4 May 1979_\n\nMARGARET THATCHER\n\n_Margaret Hilda Thatcher, born 1925, was elected leader of the Conservative Party in 1975, the first woman party leader in British politics._\n\nWe knew we had won by the early hours of Friday 4 May, but it was not until the afternoon that we gained the clear majority of seats we needed \u2013 44 as it eventually turned out. The Conservative Party would form the next government.\n\nThere were many friends with me as we waited for the results to come in during those long hours in Conservative Central Office. But I can remember an odd sense of loneliness as well as anticipation when I received the telephone call which summoned me to the Palace. I was anxious about getting the details of procedure and protocol right; it is extraordinary how on really important occasions one's mind often focuses on what in the cold light of day seem to be mere trivia. But I was haunted by tales of embarrassing episodes as one prime minister left and his successor entered office: Ted Heath's departure from No. 10 was a case in point. I now could not help feeling sorry for James Callaghan, who just a little earlier had conceded victory in a short speech, both dignified and generous. Whatever our past and indeed future disagreements, I believed him to be a patriot with the interests of Britain at heart, whose worst tribulations had been inflicted by his own party.\n\nAt about 2.45 p.m. the call came. I walked out of Central Office through a crowd of supporters and into the waiting car, which drove Denis and me to the Palace on my last journey as Leader of the Opposition.\n\nThe Audience at which one receives the Queen's authority to form a government comes to most prime ministers only once in a lifetime. The authority is unbroken when a sitting prime minister wins an election, and so it never had to be renewed throughout the years I was in office. All audiences with the Queen take place in strict confidence \u2013 a confidentiality which is vital to the working of both government and constitution. I was to have such audiences with Her Majesty once a week, usually on a Tuesday, when she was in London and sometimes elsewhere when the royal family were at Windsor or Balmoral.\n\nPerhaps it is permissible to make just two points about these meetings. Anyone who imagines that they are a mere formality or confined to social niceties is quite wrong; they are quietly businesslike and Her Majesty brings to bear a formidable grasp of current issues and breadth of experience. And, although the press could not resist the temptation to suggest disputes between the Palace and Downing Street, especially on Commonwealth affairs, I always found the Queen's attitude towards the work of the government absolutely correct.\n\nOf course, under the circumstances, stories of clashes between 'two powerful women' were just too good not to make up. In general, more nonsense was written about the so-called 'feminine factor' during my time in office than about almost anything else. I was always asked how it felt to be a woman prime minister. I would reply: 'I don't know: I've never experienced the alternative.'\n\nAfter the audience, Sir Philip Moore, the Queen's Secretary, took me to his office down what are called 'the Prime Minister's stairs'. I found my new principal private secretary, Ken Stowe, waiting there, ready to accompany me to Downing Street. Ken had come to the Palace with the outgoing prime minister, James Callaghan, barely an hour before. The civil service already knew a good deal about our policies because they carefully scrutinize an Opposition's manifesto with a view to the hasty preparation of a new administration's legislative programme. Of course, as I quickly learnt, some senior civil servants would need more than a conscientious reading of our manifesto and a few speeches truly to grasp the changes we firmly intended to make. Also, it takes time to build up relationships with staff which reach beyond the formal level of respect to trust and confidence. But the sheer professionalism of the British civil service, which allows governments to come and go with a minimum of dislocation and a maximum of efficiency, is something other countries with different systems have every cause to envy.\n\nDenis and I left Buckingham Palace in the prime ministerial car: my previous car had already gone to Mr Callaghan. As we drove out through the Palace gates, Denis noticed that this time the Guards saluted me. In those innocent days before security had to become so much tighter for fear of terrorism, crowds of well-wishers, sightseers, press and camera crews were waiting for us in Downing Street itself. The crowds extended all the way up Downing Street and out into Whitehall. Denis and I got out of the car and walked towards them. This gave me the opportunity to run through in my mind what I would say outside No. 10.\n\nWhen we turned to the cameras and reporters, the cheers were so deafening that no one in the street could hear what I was saying. Fortunately, the microphones thrust in front of me picked it up and carried it over the radio and television.\n\nI quoted a famous prayer attributed to St Francis of Assisi, beginning, 'where there is discord, may we bring harmony.' Afterwards a good deal of sarcasm was expended on this choice, but the rest of the quotation is often forgotten. St Francis prayed for more than peace; the prayer goes on: 'Where there is error, may we bring truth. Where there is doubt, may we bring faith. And where there is despair, may we bring hope.' The forces of error, doubt and despair were so firmly entrenched in British society, as the 'winter of discontent' had just powerfully illustrated, that overcoming them would not be possible without some measure of discord.\n\n_It was Margaret Thatcher who broke the political consensus forged by Clement Attlee back in 1945. She resolutely moved the Conservative Party rightwards \u2013 to nakedly embrace free-market economics and the shedding of the public sector through privatization. Thatcherism, in a word. There would be plenty of discord, but more than once Margaret Thatcher's standing would benefit from the feel-good factor generated by British troops in victorious action._\n\n## _The SAS Relieve the Siege at Prince's Gate, London, 5 May 1980_\n\nANONYMOUS SAS TROOPER\n\n_The Iranian Embassy and its staff were seized by terrorists on 30 April 1980. Five days later, when Iran refused their demand for the liberation of Khuzestan, the gunmen commenced shooting their hostages. A waiting unit of the 22nd Special Air Service Regiment was ordered to storm the Embassy building_.\n\nWe took up a position behind a low wall as the demolition call sign ran forward and placed the explosive charge on the Embassy french windows. It was then that we saw the abseiler swinging in the flames on the first floor. It was all noise, confusion, bursts of submachine-gun fire. I could hear women screaming. Christ! It's all going wrong, I thought. There's no way we can blow that charge without injuring the abseiler. Instant change of plans. The sledge-man ran forward and lifted the sledge-hammer. One blow, just above the lock, was sufficient to open the door. They say luck shines on the brave. We were certainly lucky. If that door had been bolted or barricaded, we would have had big problems.\n\n'Go. Go. Go. Get in at the rear.' The voice was screaming in my ear. The eight call signs rose to their feet as one and then we were sweeping in through the splintered door. All feelings of doubt and fear had now disappeared. I was blasted. The adrenalin was bursting through my bloodstream. Fearsome! I got a fearsome rush, the best one of my life. I had the heavy body armour on, with high-velocity plates front and back. During training it weighs a ton. Now it felt like a T-shirt. Search and destroy! We were in the library. There were thousands of books. As I adjusted my eyes to the half-light \u2013 made worse by the condensation on my respirator eyepieces \u2013 the thought occurred to me that if we had blown that explosive charge we might have set fire to the books. Then we would really have had big problems: the whole Embassy would have been ablaze in seconds.\n\nThe adrenalin was making me feel confident, elated. My mind was crystal clear as we swept on through the library and headed for our first objective. I reached the head of the cellar stairs first, and was quickly joined by Sek and two of the call signs. The entry to the stairs was blocked by two sets of step-ladders. I searched desperately with my eyes for any signs of booby-traps. There wasn't time for a thorough check. We had to risk it. We braced ourselves and wrenched the ladders out of the way.\n\nMercifully there was no explosion. The stairs were now cleared and we disappeared into the gloom of the basement. I fished a stun grenade out of my waistcoat and pulled the pin. Audio Armageddon, I thought as I tossed the grenade down into the darkness. We descended the stairs, squinting into the blinding flashes for any unexpected movement, any sign of the enemy, and then we were into the corridor at the bottom. We had no sledge, no Remington with us, so we had to drill the locks with 9-milly, booting the doors in, clearing the rooms methodically as we went along. Minutes turned into seconds; it was the fastest room clearance I'd ever done.\n\nIt was when I entered the last room that I saw the dark shape crouched in the corner. Christ! This is it, I thought. We've hit the jackpot. We've found a terrorist. I jabbed my MP5 into the fire position and let off a burst of twenty rounds. There was a clang as the crouched figure crumpled and rolled over. It was a dustbin!\n\nNothing, not a thing. The cellars were clear. I was now conscious of the sweat. It was stinging my eyes, and the rubber on the inside of the respirator was slimy. My mouth was dry and I could feel the blood pulsing through my temples. And then we were off again, no time to stop now, up the cellar stairs and into the Embassy reception area. As we advanced across the hallway, there was smoke, confusion, a tremendous clamour of noise coming from above us. The rest of the lads, having stormed over the balcony at the front and blasted their way into the first floor of the building with a well-placed explosive charge, were now systematically cleaving the upper rooms, assisted by a winning combination of the stunning effect of the initial explosion, the choking fumes of CS gas, the chilling execution of well-practised manoeuvres and the sheer terror induced by their sinister, black-hooded appearance. We were intoxicated by the situation. Nothing could stop us now.\n\nThrough the gloom I could see the masked figures of the other team members forming into a line on the main staircase. My radio earpiece crackled into life. 'The hostages are coming. Feed them out through the back. I repeat, out through the back.'\n\nI joined a line with Sek. We were six or seven steps up from the hallway. There were more explosions. The hysterical voices of the women swept over us. Then the first hostages were passed down the line. I had my MP5 on a sling around my neck. My pistol was in its holster. My hands were free to help the hostages, to steady them, to reassure them, to point them in the right direction. They looked shocked and disorientated. Their eyes were streaming with CS gas. They stumbled down the stairs looking frightened and dishevelled. One woman had her blouse ripped and her breasts exposed. I lost count at fifteen and still they were coming, stumbling, confused, heading towards the library and freedom.\n\n'This one's a terrorist!' The high-pitched yell cut through the atmosphere on the stairs like a screaming jet, adding to the confusion of the moment. A dark face ringed by an Afro-style haircut came into view; then the body, clothed in a green combat jacket, bent double, crouched in an unnatural pose, running the gauntlet of black-hooded figures. He was punched and kicked as he made his descent of the stairs. He was running afraid. He knew he was close to death.\n\nHe drew level with me. Then I saw it \u2013 a Russian fragmentation grenade. I could see the detonator cap protruding from his hand. I moved my hands to the MP5 and slipped the safety-catch to 'automatic'. Through the smoke and gloom I could see call signs at the bottom of the stairs in the hallway. Shit! I can't fire. They are in my line of sight, the bullets will go straight through the terrorist and into my mates. I've got to immobilize the bastard. I've got to do something. Instinctively, I raised the MP5 above my head and in one swift, sharp movement brought the stock of the weapon down on the back of his neck. I hit him as hard as I could. His head snapped backwards and for one fleeting second I caught sight of his tortured, hate-filled face. He collapsed forward and rolled down the remaining few stairs, hitting the carpet in the hallway, a sagging, crumpled heap. The sound of two magazines being emptied into him was deafening. As he twitched and vomited his life away, his hand opened and the grenade rolled out. In that split second my mind was so crystal clear with adrenalin it zoomed straight in on the grenade pin and lever. I stared at the mechanism for what seemed like an eternity, and what I saw flooded the very core of me with relief and elation. The pin was still located in the lever. It was all over, everything was going to be okay.\n\nBut this was no time to rest, this was one of the most vulnerable periods of the operation, the closing stages. This is where inexperienced troops would drop their guard. The radio crackled into life. 'You must abandon the building. The other floors are ablaze. Make your way out through the library entrance at the rear. The Embassy is clear. I repeat, the Embassy is clear.'\n\nI joined Sek and we filed out through the library, through the smoke and the debris. We turned left and headed back for number 14, past the hostages, who were laid out and trussed up on the lawn ready for documentation, past the unexploded explosive charge, past the discarded sledgehammer and other pieces of assault equipment \u2013 all the trappings of battle in the middle of South Kensington. It was 8.07 p.m.\n\nAs we made our way through the french windows of number 14, the Gonze, ex-Para, a new boy in the regiment from one of the other call signs, removed his respirator and asked the Irish police sergeant on duty at the door what the Embassy World snooker score was. A look of total disbelief spread across the policeman's face and he just stood there shaking his head from side to side.\n\nI crossed the room to my holdall and as I began pulling off my assault equipment I could feel the tiredness spreading through my limbs. It wasn't just the energy expended on the assault, it was the accumulation of six days of tension and high drama, of snatched sleep in a noisy room, of anxiety and worry over the outcome of the operation. I looked to my left. The Toad had just returned. He looked tired, his face was flushed and he was out of breath. He looked at me and shook his head. 'I'm getting too old for this sort of thing.'\n\n'So am I,' I replied.\n\nWithin fifteen minutes most of the team members had stripped off their assault kit, packed it into their holdalls and parcelled their MP5s into plastic bags to be taken away for forensic examination. Before moving out through the front door of number 14 to the waiting Avis hire van, we had a dramatic visit from Home Secretary William Whitelaw, old Oyster Eyes himself. He stood before us, tears of joy unashamedly running down his cheeks, wringing his hands in relief. He thanked the assembled team members for what they had done for the country that day. 'This operation will show that we in Britain will not tolerate terrorists. The world must learn this.' It was a fine personal gesture and rounded the operation off perfectly.\n\n## _Falklands War: The First Man into Port Stanley, 14 June 1982_\n\nMAX HASTINGS\n\n_One of Britain's last remnants of Empire, the barren and remote Falklands Islands, were invaded by Argentina on 2 April 1982. Pride, if not the rule of international law, required a resolute response, and the Conservative government of Margaret Thatcher accordingly dispatched a task force to the South Atlantic. Despite the furiousness of Argentine resistance at Fitzroy, at Goose Green, at Mount Harriet, at Wireless Ridge, at Tumbledown, at Two Sisters, at Longdon, the British campaign in the Falklands yomped to success. By 14 June British troops had reached the Falklands capital._\n\n_Max Hastings was war correspondent for the_ Evening Standard.\n\nBritish forces are in Port Stanley. At 2.45 p.m. British time today [14 June], men of the 2nd Parachute Regiment halted on the outskirts at the end of their magnificent drive on the capital pending negotiations.\n\nThere, we sat on the racecourse until, after about twenty minutes I was looking at the road ahead and there seemed to be no movement. I thought, well I'm a civilian so why shouldn't I go and see what's going on because there didn't seem to be much resistance.\n\nSo I stripped off all my combat clothes and walked into Stanley in a blue civilian anorak with my hands in the air and my handkerchief in my hand.\n\nThe Argentinians made no hostile movement as I went by the apparently undamaged but heavily bunkered Government House.\n\nI sort of grinned at them in the hope that if there were any Argentinian soldiers manning the position they wouldn't shoot at me.\n\nNobody took any notice so I walked on and after a few minutes I saw a group of people all looking like civilians a hundred yards ahead and I shouted at them.\n\nI shouted: 'Are you British?' and they shouted back: 'Yes, are you?' I said 'Yes.'\n\nThey were a group of civilians who had just come out of the civil administration building where they had been told that it looked as if there was going to be a ceasefire.\n\nWe chatted for a few moments and then I walked up to the building and I talked to the senior Argentinian colonel who was standing on the steps. He didn't show any evident hostility.\n\nThey were obviously pretty depressed. They looked like men who had just lost a war but I talked to them for a few moments and I said: 'Are you prepared to surrender West Falkland as well as East?'\n\nThe colonel said: 'Well, maybe, but you must wait until four o'clock when General Menendez meets your general.'\n\nI said: 'May I go into the town and talk to civilians?' He said: 'Yes,' so I started to walk down the main street past Falklanders who were all standing outside their houses.\n\nThey all shouted and cheered and the first person I ran into was the Catholic priest, Monsignor Daniel Spraggon, who said: 'My God, it's marvellous to see you.'\n\nThat wasn't directed at me personally but it was the first communication he had had with the British forces.\n\nI walked on and there were hundreds, maybe thousands, of Argentinian troops milling around, marching in columns through the streets, some of them clutching very badly wounded men and looking completely like an army in defeat with blankets wrapped around themselves.\n\nThere were bits of weapons and equipment all over the place and they were all moving to central collection points before the surrender or ceasefire.\n\nEventually I reached the famous Falklands hotel, the Upland Goose. We had been dreaming for about three months about walking into the Upland Goose and having a drink, and I walked in and again it was marvellous that they all clapped and cheered.\n\nThey offered me gin on the assumption that this is the traditional drink of British journalists, but I asked if they could make it whisky instead and I gratefully raised my glass to them all.\n\nOwner of the Upland Goose Desmond King said: 'We never doubted for a moment that the British would turn up. We have just been waiting for the moment for everybody to come.'\n\nThe last few days had been the worst, he said, because Argentinian guns had been operating from among the houses of Stanley and they had heard this terrific, continuous battle going on in the hills.\n\nThey were afraid that it was going to end up with a house-to-house fight in Stanley itself. The previous night when I had been with the Paras we were getting a lot of shell fire coming in on us and eventually we sorted out the coordinates from which it was firing. Our observation officer tried to call down to fire on the enemy batteries and the word came back that you could not fire on them because they are in the middle of Stanley.\n\nSo the battalion simply had to take it and suffer some casualties.\n\nAnyway, there we were in the middle of the Upland Goose with about twenty or thirty delighted civilians who said that the Argentinians hadn't done anything appalling. It depends what one means by appalling, but they hadn't shot anybody or hung anybody up by their thumbs or whatever.\n\nThey had looted a lot of houses that they had taken over. At times they got very nervous and started pushing people around with submachine guns in their backs and the atmosphere had been pretty unpleasant.\n\nRobin Pitaleyn described how he had been under house arrest in the hotel for six weeks, since he made contact by radio with the _Hermes._ He dismissed criticism of the Falkland Island Company representatives who had sold goods to the occupiers.\n\n'We were all selling stuff,' he said. 'You had a simple choice \u2013 either you sold it or they took it. I rented my house to their air force people. They said \u2013 either you take rent or we take the house. What would you have done?'\n\nAdrian Monk described how he had been compulsorily evicted from his own house to make way for Argentinian soldiers who had then totally looted it. There appears to have been widespread looting in all the houses of Stanley to which the Argentinians had access.\n\nThe houses on the outskirts of the town in which the Argentinians had been living were an appalling mess full of everything from human excrement all over the place to just property lying all over the place where soldiers had ransacked through it. But they were all alive and they all had plenty of food and plenty to drink and they were all in tremendous spirits.\n\nIt wasn't in the least like being abroad. One talks about the Falklanders and yet it was as if one had liberated a hotel in the middle of Surrey or Kent or somewhere.\n\nIt was an extraordinary feeling just sitting there with all these girls and cheerful middle-age men and everybody chatting in the way they might chat at a suburban golf club after something like this had happened.\n\n_There were other enemies without._\n\n_Long committed to blowing the British out of Northern Ireland, the Provisional IRA took the war across the sea to target the English in their beds. The Tory MP Airey Neave was an early assassination victim. In October 1984 the IRA sprang its most audacious attack on the mainland to that date._\n\n## _The Brighton Bomb, 12 October 1984_\n\nNORMAN TEBBIT\n\n_The Grand Hotel, Brighton, was the venue for the 1984 Conservative Party conference. Norman Tebbit was the Conservative Trade and Industry Secretary._\n\nThere was the usual round of too many parties and receptions to attend but skipping most of them we went to the Party Treasurer, Alistair McAlpine's soir\u00e9e, as it was always known. Alistair is an excellent host offering exceptionally good food and drink, and company too \u2013 provided one was selective about all three. There were always journalists aplenty (as Alistair's relations with the 'hacks' were excellent), a good number of parliamentary and Government colleagues and most of the Party establishment. I have never discovered at what time Alistair's parties ended but my wife and I drew stumps around midnight and, walking down to our room, encountered the BBC political correspondent, John Cole, on his way upstairs. As John and I chatted, Margaret excused herself saying she was tired and would head for bed. We gossiped on for a while before I said, 'John, if I wake my wife just as she's gone to sleep I'll be in terrible trouble so I'd best be off to bed,' and we retired to our rooms.\n\nIt seldom takes me long to go to sleep and that night was no exception and we were both sleeping soundly when the bomb exploded.\n\nWe were woken by the blast which I recognized at once for what it was. There was just time for Margaret to call out in alarm and for me to reply, 'It's a bomb!' before the ceiling came crashing down on us and then, in a hail of debris, the floor collapsed, catapulting us down under an avalanche of bricks, timber and plaster. The force of the impact was indescribable \u2013 blow after blow as the debris smashed on to my left side. Something tore into my abdomen with a terrible blow and I heard my very guts sloshing inside me. There was a colossal impact tearing a great hole in my side, then I stopped falling \u2013 with no idea where, nor even which way up I was, as the debris cascaded down. The hammer blows eventually stopped and the sounds of falling masonry died away. It was pitch black and, at first, silent, then came screams and groans \u2013 some rattling and choking into silence. I called for Margaret and miraculously she replied from somewhere quite close. I found I could move my left arm and reaching out, our fingers touched and we grasped each other. Like me she was trapped, but bent almost double under a great weight of debris that had fallen on to her shoulders and neck. My head was trapped as in a vice. I could neither move nor feel my right arm which I feared I might have lost. Nor could my left hand reach my face which was half wrapped in bedding forming a trap for dust and grit threatening to fill up and cover my mouth. As I reached down my hand encountered a great sticky bleeding mess, in the gaping hole in my side.\n\nI found Margaret's hand again. At first we assured each other we were all right, each lying to comfort the other. Then Margaret began to shout for help. 'Don't shout yet, wait until you hear them digging, or you'll exhaust yourself \u2013 it may be a long time yet.'\n\nMy mind had already constructed a picture of the scene. I assumed the whole hotel had collapsed like the American building that had been bombed in Beirut and that it might take days to reach us. I could hear water cascading down through the wreckage and hoped that we would neither be drowned, nor burned to death if fire broke out.\n\nWe had no sense of time. Gradually the cries of other victims fell silent as they died, and we comforted each other. I wondered how bad it was. How many other survivors there were. What was to be done if the Prime Minister and other members, perhaps even most of the Cabinet, were dead? We listened waiting for the rescuers without any sense of time. Great waves of pain came and went and I could feel my life ebbing away as I bled. With each new fall of debris I feared that the crushing weight on my skull might simply crush it like an eggshell. I had begun to fear that I would not last until we were rescued when suddenly my whole body was galvanized with searing pain. So this is death \u2013 how strange, what a waste, I thought \u2013 then it stopped and I was still alive. Again the pain rose to a crescendo then suddenly stopped. I realized that it had been caused by massive electric shocks but only afterwards did I discover that the rescue workers had inadvertently cut through the live main. Somehow we lost our grip on each other's hands. It may have been another fall of debris which moved Margaret or, although she did not tell me, it may have been the paralysis which was creeping through her body. Nor did I mention what I thought was the cold dead limb of a corpse I found near me in the debris. In fact it was my right arm which I thought I had lost but was merely crushed. At times I felt myself losing consciousness in the great waves of pain, and as we continued to comfort each other, I gave Margaret a message for our children if I died before rescue came.\n\nThen suddenly there were voices. We shouted \u2013 or croaked as loud as we could. They called back, 'Who are you?' We told them. 'Can you move?' they asked. We exchanged names and told them how we were trapped. They reached Margaret first. I could see their lights and then I felt a rough hand touch mine. I grabbed it \u2013 holding on foolishly like a child begging its owner not to let go. It was Fred. He found that I was under my mattress which had probably saved my life as the masonry fell down on me, and they began to dig me out. A doctor came and tried to see what injuries I had. Then as they dug they found what they too thought was the arm of a corpse until Fred realized it was mine. Painfully, carefully, brick by brick, they cleared the debris \u2013 but I was still trapped by a great timber which they dared not cut for fear of bringing down a whole mass of wreckage precariously balanced above us. 'Can you struggle free?' they asked me. With the pain deadened I tried to lift myself over the timber. Fred leaned over to help. My shout of, 'Get off my bloody foot!' seemed to break the tension. We laughed and with another great heave they had hold of me \u2013 in minutes I was strapped on to a stretcher and swung clear of the wreckage, into the light of the blazing arc lamps and the cold air of the seafront.\n\n_The IRA later issued a communiqu\u00e9:_\n\nThe IRA claim responsibility for the detonation of 100 pounds of gelignite in Brighton, against the British cabinet and the Tory warmongers. Thatcher will now realize that Britain cannot occupy our country, torture our prisoners and shoot our people on their own streets and get away with it.\n\nToday we were unlucky, but remember, we have only to be lucky once. You will have to be lucky always. Give Ireland peace and there will be no war.\n\n_After enemies without, Thatcher faced enemies within._\n\n## _The 1984\u20135 Miners' Strike: Scenes from a Yorkshire Pit Village, South Elmsall, 19 December 1984_\n\nPETER JENKINS, THE _GUARDIAN_\n\n_The Miners' Strike began in March 1984 with a National Coal Board announcement of pit closures in Kent. It spread contagiously through a demoralized, declining British coalfield, with the exception of the 'super pits' in the Midlands. Their_ ' _scabbing' was bitterly resented by union loyalists, and violent clashes followed. Yorkshire was the heartland of the strike, the HQ of the 80,000-strong National Union of Mineworkers, the home turf of the NUM president, Arthur Scargill. King Arthur._\n\nAt the Miners' Welfare Club old couples are dancing the Anniversary Waltz. Bill introduces me to some friends including local NUM branch officials. They are back from court in Pontefract giving evidence on behalf of pickets. If they were witnesses they had attended a mass picket, said the Stipendiary, and bound the lot of them over for 'besetting'.\n\nThey were full of complaints about the police and the media. Frank's children had seen the recent _World in Action_ programme. 'They wanted to know \"were you there, Dad?\" They're going to think I'm some kind of law-breaker.'\n\n'His father's either a thug or television's wrong,' said Roy.\n\nReg said, 'I'm thirty-six and I've never been in trouble with police all my life. Now I'm enemy within. Some kind of criminal. My kids know that's not me. So does my wife. They resent it.'\n\nNothing is more resented, I discovered, than the Prime Minister's remark. A typical comment from a much older miner was 'they didn't call us enemy within when we were digging for fucking victory.' Margaret Thatcher's insult to the miners of Great Britain will not be soon forgotten. She will be remembered like Churchill for Tonypandy.\n\nThe president of the branch, Tony, was as bald as Kojak and wore his dark glasses. He tried to sum up what it was they were fighting for. 'It's such a broad issue,' he said. 'It's like chucking a stone in a pond and the ripples spreading. You're fighting for your pit first of all. But you're fighting for your village and your kids' future. And you're fighting, I hope to God, for a police force that don't get out of hand, 'cos we've got to have a police force. And you're fighting for the trade union movement because this union has only been loaned to us by my grandfather.'\n\nThen as an afterthought, he added: 'It's brought us closer as a community, this strike. It's done a Falklands on us.'\n\nWe move on. If miners don't like travelling far to work they'll drive miles for a pint. At another club, Jack, who's a management man but with a great deal more sympathy for the miners than for Ian MacGregor or Margaret Thatcher, says, 'It's only loyalty to the branches that's keeping them out now.'\n\nThat loyalty is immensely strong and is much more of a factor than the intimidation which has been going on. At the three local pits the number of men 'going in' is two, four and six. The strike is going to die hard in these parts.\n\nThe next morning the pickets are out as usual. At four o'clock, Bill and I walk up to Frickley through cold, wet, orange-lit streets. Nothing happens; there's a shove and a shout and the two men go in. I go back to a warm bed.\n\nWhen men first went in to Frickley a few weeks ago there were riot shields and horses and broken windows and arrests, and the usual mutual accusations of violence. The pattern, at least in this part of West Yorkshire, seems to be a flare of violent anger when a pit reopens after which things settle down to a routine morning ritual, usually without incident. Low profile policing is the general order round here, and it does seem to keep the level of violence down.\n\nThe wives who run the meal centre have been dubbed the 'Frickley Wonder Women'. They have escaped from their own kitchens to cook 200 dinners and breakfasts a day for the men on strike. Brenda was managing on \u00a332 a week from the DHSS and \u00a313 in family allowance but her mortgage was \u00a320 a week and there was the water rates and the phone and a video which couldn't go back. Barbara, with one son, was also 'managing' on \u00a313.65 plus \u00a36.85.\n\nHer boy was having free school dinners and her husband coming into the centre for his breakfast and dinner. 'At night we have toast and a few chips,' she says with a cheerful laugh. 'It's the kids you feel sorry for isn't it?'\n\n'It's the kids' clothes are the main problem,' says another Brenda. 'There's an allowance from council, which we appreciate, but it's not enough for coat and shoes.'\n\n'We didn't miss our summer holidays at all,' says the first Brenda with a happy smile.\n\n'We did,' says Merle, who is married to one of Bill's many cousins.\n\n'I mean we knew no one else was having a holiday, didn't we?' says Brenda.\n\nTwo of their sons are 'considering army'. There hasn't been a pit job in the villages for some years, or so they claim. Bill says: 'We've got lads of twenty-two who've never worked and never will.'\n\n'The cold's the real thing. We're freezing,' says Merle. 'Aye, you should see the rubbish we put on fires.' We leave them complaining about the police chasing their men off the tips and merrily discussing the uses of bricks in grates.\n\nOutside a man stops Bill to inquire about a turkey dinner which is planned. There's a problem about money and turkeys. He listens to the latest and says, 'We'll be having corn beef dinner then.' Off he goes, laughing.\n\nIn the shadow of the tip (which is a phrase I heard a miner use) men are digging muddy holes as deep as themselves, sieving dirt for scraps of coal to burn. Last week someone found an 1806 penny and today it's a George V Coronation mug but the handle is broken off.\n\n_The miners were finally defeated in March 1985, after a whole year 'out'. Only twenty years before, the miners had brought down Heath. The Conservatives secured their revenge; over the remainder of the 80s British coal industry was reduced to a straggled handful of pits. Which were then privatized._\n\n_Margaret Thatcher's firm hand in dealing with unruly Argentines and British miners, coupled with an evidently growing prosperity ('yuppies', the spread of home ownership to two-thirds of the population) and disorder amongst the Labour Party enabled her to win three elections in a row. Not since Lord Liverpool in the early nineteenth century had such a thing occurred. Yet by the late 1980s hertight-faced imperial style was beginning to grate on England's sensibilities. More substantially, her implementation of the Poll Tax caused revolt (just as it had amongst England's peasantry in 1381), her party was divided pro- and con-Europe, and Nigel Lawson's apparent_ ' _revival' of the economy had come with a \u00a320 billion balance-of-payments-deficit. Sensing the disapproving mood of the electorate, the Conservative Party's centre-Left, under Michael Heseltine, made their move on the beleaguered Mrs Thatcher._\n\n## _Thatcher Falls, 21\u201322 November 1990_\n\nALAN CLARK MP\n\n_Margaret Thatcher won the first ballot against leadership contender Michael Heseltine (204 to 152 votes) but struggled to find votes for a convincing win in the second round. Alan Clark, the Defence Minister, was amongst Thatcher's staunchest supporters._\n\n_Ministry of Defence_\n\nNo work is being done in Whitehall today, whatsoever. My 'In'-tray is about an inch deep. I don't think a single Minister in the Govt will be at his desk; or if he is, it will be only so as to telephone to a colleague or to a journalist. The civil servants (all of whom, down to Principal level, I suspect, were terrified of the Lady) just cannot believe their eyes.\n\nYet still she won't return. There is talk of a 'fighting statement' later. But this wastage of time in Paris is sheer lunacy. Harold at Stamford Bridge.\n\nIt is the general sense of disintegration now affecting everything, that is so damaging to her. Unless MH is slaughtered in the final ballot \u2013impossibly unlikely \u2013 she herself is going to find it highly difficult to reassert her authority, even if eventually she emerges as the victor. Short, that is, of giving them the full coup-loser's treatment \u2013 arrest, manacles, beaten up in the interrogation room, shot while trying to escape. Real blood, in other words. Fun, but a bit _Angolan._\n\nBefore walking over to the House I called Andrew MacKay into my room and we had a long talk about Tom [King]. Earlier, we had both lingered after Ministers and sounded him.\n\nTom likes the idea, preened himself, straightened his jacket; but he is cautious. He would need to be sure of at least thirty votes to even 'put down a marker'. And in any case, convention obliges that no member of the Cabinet puts his name forward while she is still standing. (I hear rumours that that pudgy puff-ball Kenneth Clarke is considering breaching this, but am keeping that in reserve.)\n\n'Look,' I told him. 'If the Lady is doomed, our Number One priority is to find, and instal a leader who will win the next General Election. And we haven't got long. Who is best suited to do this?'\n\nI told him that Heseltine would burn out very quickly. His rhetoric pleased Party Conference, but was less reliable in the national context. Anyway people are sick of passion, they want reassurance.\n\nThe only two figures who can do this are Tom and John Major. Douglas is now past it; is thought rightly or wrongly to be a buffer and a bureaucrat. John is more engaging than Tom in some ways, with a lovely grin, but seems really too youthful. There is no time to project him. Even in the House he is barely known, has never been seen under fire. Tom, on the other hand, does have gravitas. Also he's good on the stump, in small groups, canteens and so on.\n\nAndrew was in broad agreement. But:\n\n'Tom won't make a move while she's still in the field.'\n\n'So what do we do?'\n\n'I tell you what I'm doing, if she stands second time round \u2013 voting for Michael.'\n\nI was appalled. Here was this good, intelligent man, tough and (in so far as it still means anything) right wing... More than any other experience this conversation has made me realize that she will lose, finally, head-to-head against Heseltine. But if she does stand again we are in a log-jam; the only people who will join in the contest are wankers like Clarke who are not worth twenty-five votes.\n\nAndrew said that he would, very quietly, take soundings for Tom. The immediate priority is to find a way, tactfully and skilfully, to talk her out of standing a second time.\n\nNow I must close this entry and walk over to the House.\n\n_House of Commons_\n\nI was greeted with the news that there had been an announcement. 'I fight, and I fight to win.' God alive!\n\nTebbit is holding an impromptu press conference in the Members' lobby.\n\nFifty feet away, down the tea-room corridor that mad ninny Hampson is dancing around on his tippy-toes calling out to passers-by, 'Tee-hee, she's standing. We've made it. We can't lose now, etc.'\n\nI came back here, to my room. I kept the door open and an endless succession of visitors trooped in and out. No one seems to have any idea of what we should do. Her 'Campaign' is a shambles now. John Moore (who he?) is running around with bits of paper \u2013 'draft statements' \u2013 asking people what they think. He seems to have a temporary HQ in Portillo's room, which is next door to mine. First I heard that Norman Fowler was going to take charge; then John Wakeham. Or was it the other way round? Gamelin's been sacked, Weygand is on the way out; P\u00e9tain's in the wings. 'O\u00f9 _est la masse de manoeuvre? \u2013 Aucune.'_\n\nEvery time I trawl the corridors I run into another batch of chaps who say they're going to switch, or abstain, or when-are-there-going-to-be-some-more-candidates-to-choose-from? The only visitor who has made any real sense is Francis Maude. He claims, forcefully, that John Major has a better chance than we all realize. But John won't make a move while the Lady remains in the field. 'I must get to see her. Can you help?' Apparently Peter stands sentinel, and is outside her door the whole time.\n\nI have closed the door. These random conversations are too discursive. Tomorrow is the last day for nominations. I must clear my head.\n\n1) If she fights head on, she loses.\n\n2) Therefore, the opposition vote has got to be diluted by a candidate from the left \u2013 preferably Patten, making it triangular. Besides dilution, this has the advantage that it will crack Cabinet 'solidarity' open and others may lose their scruples. Therefore:\n\n3) Try and talk Patten into standing. QED.\n\nArchie Hamilton's just been in. Didn't make any sense. One minute he says she 'could still' win; the next that we've all 'had it'. I'm off now, upstairs.\n\n_Later_\n\n_Kundan Restaurant_\n\nIt is very late, and finally I have withdrawn here for a vegetable curry, and to write up the traumatic happenings of this evening.\n\nI made first for Chris's room. On the way I passed her outer door and said to Peter that I must have a minute or so. He looked anxious, almost rattled, which he never does normally. 'I'll do my best. She's seeing every member of the Cabinet in turn...'\n\n'Francis wants to see her too.'\n\n'I'm doing my best.'\n\nChris wasn't in his room. The Secretary of State's corridor was deserted. Hushed, but you could feel the static.\n\nThe policeman by the lift said he was 'in with Mr Rifkind'.\n\nI knocked and went in without waiting for an answer. Also in there, loathesomely conspiring, was little Kenneth Clarke. Her three great ill-wishers! Clarke wasn't friendly at all. If he'd said anything to me, I'd have answered 'Fuck you', so just as well.\n\nChris was quite amiable.\n\n'How many votes she got at the moment?'\n\n'It's a rout. She's down to ninety.'\n\n_'Ninety?'_\n\n'You've got to stand. You can't let Michael corner the left.'\n\nHe was diplomatic. A discussion was impossible. God knows what they were talking about, but it stank. Never mind, I have sowed the seed; or watered what was already there.\n\nI went down the stairs and rejoined the group outside her door. After a bit Peter said, 'I can just fit you in now \u2013 but only for a split second, mind.'\n\nShe looked calm, almost beautiful. 'Ah, Alan...'\n\n'You're in a jam.'\n\n'I know that.'\n\n'They're all telling you not to stand, aren't they?'\n\n'I'm going to stand. I have issued a statement.'\n\n'That's wonderful. That's heroic. But the Party will let you down.'\n\n'I am a fighter.'\n\n'Fight, then. Fight right to the end, a third ballot if you need to. But you lose.'\n\nThere was quite a little pause.\n\n'It'd be so terrible if Michael won. He would undo everything I have fought for.'\n\n'But what a way to go! Unbeaten in three elections, never rejected by the people. Brought down by nonentities!'\n\n'But Michael... as _Prime Minister.'_\n\n'Who the fuck's Michael? No one. Nothing. He won't last six months. I doubt if he'd even win the Election. Your place in history is towering...'\n\nOutside, people were doing that maddening trick of opening and shutting the door, at shorter and shorter intervals.\n\n'Alan, it's been so good of you to come in and see me...'\n\n*\n\nAfterwards I felt empty. And cross. I had failed, but I didn't really know what I wanted, except for her still to be Prime Minister, and it wasn't going to work out.\n\nI sat on the bench immediately behind the Speaker's chair, watching the coming and going. After a bit Tristan [Garel-Jones] came and sat beside me. But he had little to say. What is there to say? She's still seeing visitors. Then, along came Edwina.\n\n'Hullo, aren't you Edwina Currie?'\n\n'Now then, Alan, there's no need to be objectionable.'\n\n'If that is who you are, I must congratulate you on the combination of loyalty and restraint that you have shown in going on television to announce your intention to vote against the Prime Minister in the Leadership Election.'\n\n'Alan, I'm perfectly prepared to argue this through with you, if you'll listen.'\n\n'Piss off.'\n\nWhich she did.\n\nTristan said, 'She's not a bad girl really.'\n\nAt half past eight I left to come over here. The archway exit from Speaker's Court was blocked by the PM's Jaguar. She had just taken her seat, and as the detective's door slammed the interior light went out and the car slid away. I realized with a shock that this was in all probability her last night as Prime Minister. I came in with her. I go out with her, and a terrible sadness envelops me \u2013 of unfinished duties and preoccupations; of dangers and injustices remaining, of the greed, timidity and short-sightedness of so many in public life.\n\n_Albany Thursday, 22 November_\n\nVery early this morning the phone rang. It was Tristan.\n\n'She's going.'\n\nThere will be an official announcement immediately after a short Cabinet, first thing. Then the race will be on. Apparently Douglas _and_ John Major are going to stand. I said I thought it was crazy, Heseltine will go through between them. I could sense him shrugging. 'There you go.'\n\nAnyway, would I come over to his room at the Foreign Office and watch it from there?\n\nAfterwards, very _triste_ and silent, I walked back to the MoD and sat in on a late (and unnecessary) Ministers' meeting. Tom told us that it had been 'awful'. She started to read a prepared statement to them, then broke down, and the text had to be finished by the Lord Chancellor.\n\nListless, I drifted over to the House. I had a word with Charles, drafted a couple of valedictory passages for her speech this afternoon, did I don't know how many impromptu TV bites.\n\nHeseltine is meant to be coming to Plymouth tomorrow, for a fund-raising dinner. I rang Judith [Roberts, Chairman of the Sutton Division], told her we couldn't possibly allow him to use us as a platform to plug his own candidature. She only half agreed, so I immediately telephoned to the _Western Morning News_ and told them that I had 'instructed' that the invitation be withdrawn. (Not unrich, considering I was not the host, and had long ago told everyone that I wanted nothing to do with it.)\n\nI didn't think I could bear it, but curiosity drew me into the Chamber for the Lady's last performance. It would have been too macabre to have sat in my habitual place, next to her PPS, so I watched and listened first from behind the Chair, then from the Bar of the House. She was brilliant. Humorous, self-deprecating, swift and deadly in her argument and in her riposte. Even Dennis Skinner, her oldest adversary, was feeding her lines; and at one point Michael Carttiss shouted, 'You could wipe the floor with the lot of 'em.'\n\nToo bloody true.\n\n_Like Lloyd George and Neville Chamberlain before her, Margaret Thatcher was removed by the backbenchers, not the voters. To replace her, the Tories chose not Michael Heseltine (as big and as divisive a beast as Thatcher in his way) but the compromise candidate, the hardly recognized Chancellor of the Exchequer, John Major. He had barely moved his furniture into 10 Downing Street before the country was again at war._\n\n## _The Gulf War: Interrogation of a Captured British RAF Navigator, Iraq, February 1991_\n\nJOHN NICHOL RAF\n\n_John Nichol, a navigator in a RAF Tornado, was shot down on 17 January 1991, the opening day of Operation Desert Storm, the Allied campaign to remove the Iraqis from their illegal occupation of Kuwait. Both Nichol and the pilot were captured by Iraqi troops._\n\nIn the evening they came for me. They unshackled me, put the blindfold on, hauled me upright, dragged me down the stairs, round the streets, back into the interrogation centre; the familiar journey, almost routine by now. The chair: they threw me down into it. One guy was holding my arm on one side, one on the other. I knew in my heart of hearts that this was the time, I knew that it was going to get really rough now.\n\nI was sitting with the solid fist of my own fear in my stomach.\n\n'What squadron are you from?'\n\n'I cannot answer that...'\n\nBang! somebody punched me in the face. Blood came pouring out of my face onto my lap, dripping. I could feel it warm on my thighs. On my lower half, I was wearing a flying-suit, a chemical-warfare suit, long-johns underneath all that, but I could still feel the blood dripping warm onto the upper part of my legs. Someone was hitting me in the face, over and over again. Question. Then somebody standing just to one side hit me hard across the skull with a solid piece of wood. Thwack! My head rang to the blow like some kind of bell. There were brilliant aching lights flashing behind the blindfold. You really do see stars. I was in the middle of the Milky Way. Question.\n\n'I cannot answer...' A kick in the stomach \u2013 how he got to my stomach I don't know, they were still holding me down on the chair. I fell over to one side in the chair, my gorge rising; they dragged me up by the hair. Question.\n\n'I cannot...' Whack! Someone punched me again, someone hit me with the wood, dazzling bright lights and the sudden downward spiral into blackness. Now I was disorientated, my brain was really starting to shut down, but still I thought, 'It's going to take more than this, it's going to take more than this. I'm not breaking down without good cause.' Somebody dragged my boot off, tearing it away with a furious wrench. 'What on earth? What are they going to do to me now?' Whack! A plastic pipe filled with something hard hit me across the shins. A biting agony across the shins, on and on, biting. Question.\n\nAnd now, somebody grabs the hair at the nape of my neck, and begins stuffing tissue-paper down the back of my T-shirt. That is appalling. This is terrifying now. I am sitting in a darkened room in the middle of enemy territory, and somebody has just stuffed tissue-paper down the back of my neck. 'What are they doing that for?' I know straightaway what they are doing that for, I can imagine only too well. 'Shit, they are going to set me on fire!' Now I really want him to ask me another question, I _am_ sorry, I want to say something, I want to tell him something, anything. But he doesn't ask me a question. He just sets fire to the paper.\n\nI throw my head violently from side to side, to try to escape from the burning, to try to shake the tissue-paper clear of my neck. They are still whacking my shins. Quite soon, mercifully soon, somebody behind me slaps out the flames.\n\n'What squadron are you from?'\n\n'Fifteen.'\n\nI had had enough.\n\n## _The Body of Diana, Princess of Wales, Is Flown Home, RAF Northolt, 31 August 1997_\n\nJONATHAN FREEDLAND\n\n_The English icon of the latter half of the twentieth century, Diana Spencer, ex-wife of the Prince of Wales, was killed in a car crash in Paris on 30 August 1997._\n\nIn the end, they let her go quietly. No drum, no funeral note \u2013 only a dumb silence as the body of Diana, Princess of Wales, returned to the land she might have ruled as queen.\n\nThere was no crowd to meet her, none of the hordes of flagwavers she so delighted in life. Instead the flat, grey tarmac of RAF Northolt, windy as a prairie, a line-up of dignitaries \u2013 and a hearse.\n\nShe had made the journey from Paris by plane, on an RAF BAe 126. They kept the coffin in the passenger cabin, within sight of her two sisters, Lady Jane Fellowes and Lady Sarah McCorquodale, and her former husband, the Prince of Wales.\n\nThe skies themselves seemed to make way for her arrival, the clouds parting like an honour guard. Once the plane had landed, it nudged toward the welcoming party hesitantly, as if weighted down by its tragic cargo. Waiting there was the kind of receiving line Diana met every day. In the middle, arms by his sides, fists clenched tight, the Prime Minister. A cleric stood close by, bright in scarlet cassock. None of them said a word.\n\nEventually the plane door opened, and the Prince appeared head down, hands clasped behind his back. He was guided by the Lord Chamberlain, the Earl of Airlie. In another context it might have been a standard royal visit: Charles shown round a new factory or hospital wing. But he had come on a more baleful duty. He took his place in line \u2013 as he has done so often.\n\nBy now, the team of coffin bearers, each one in the crisp uniform of the Queen's Colour Squadron, had completed its precise march toward the other side of the aircraft. At the stroke of seven o'clock, the hatch opened revealing a glimpse of colour, the Royal Standard clinging to the hard, square outline of the coffin. It seemed an unforgiving shape: just a box, with none of the curve or sparkle of the woman whose body lay within.\n\nThe silence of the air was cut, and not just by the sound of distant traffic \u2013 which rumbled on, as if to prove that the clocks never stop, even for the death of a princess.\n\nThe air was filled with the _chickageev, chickageev_ of the thousand camera lenses pointed at the scene ahead. Even now the world's telephoto eye was still staring at her, more focused than ever. Despite everything, everyone still wanted a piece of Diana. The cameras kept up their din, but there was an eerie silence from the men who held them. Once they would cry out, 'Diana! Diana!' \u2013 urging her to look their way or to flash just one more of those million-dollar smiles. But there was no shouting yesterday. And no smiles either.\n\nThe bearers of the body inched their way to the hearse. They stood, swivelled on their heels, and clasping tight with their white gloved hands, lowered the coffin as smoothly as a hydraulic pump. They were about to turn away, but a bit of the flag was still spilling out; it had to be tucked in, just like the train of one of Diana's more lavish ball gowns.\n\nThe sisters stepped forward, each one turning to curtsy for the man whom Diana had once loved. Charles kissed each one before they stepped into the royal Daimler. The next car was filled with bouquets.\n\nThe Prince himself did his duty, talking to each one of the VIPs who had stood beside him. Tony Blair clasped both royal hands in a double handshake, nodding intently. Charles made a gesture with upturned palms, as if to say What Can I Do? He thanked the RAF guard and disappeared back inside the plane, heading for Balmoral and his newly bereaved young sons. 'He's going back to the boys,' said his spokesman.\n\nAnd then, on the final day of August, the sky darkened, and the wind whipped harder. It felt like the last day of summer, and the beginning of a long winter.\n\n## _Rugby World Cup: Jonny Wilkinson Kicks It Over, Telstra Stadium, Sydney, Australia, 22 November 2003_\n\nJONNY WILKINSON\n\nNear exhaustion and despair, I look up at the clock. We have three minutes \u2013 one shot, one opportunity.\n\nField position is everything so we make a quick decision to kick off long, knowing Rogers will clear his lines and that we will have the lineout throw inside their half. I call 'Zig-zag' to Dawson and he relays the code word to Ben Kay, who will then call an appropriate lineout to enable us to activate the move. 'Zig-zag' is a move we have rehearsed many times, setting up the ideal position for a dropped goal. It has been in the back of my mind all through the final; now it is right at the front.\n\nWe need a secure set-piece \u2013 by no means guaranteed in a final where neither side have been able to dominate their own ball. Steve Thompson hits the button, picking out Lewis Moody at the tail, the hardest part of the lineout to find, but obligatory for this attack. It allows us to launch Catty [Mike Catt] on to the ball and immediately over the gain-line. Australia know what we are planning and concentrate on getting up fast to charge down the dropped goal but, in doing so, they leave a hole for Dawson to burst through the ruck. He is hauled down, having made a crucial 20 metres \u2013 an awesome run for the team, but don't mistake the fact that he was trying to score himself! He has put us in range and, back in the pocket, I scream for the ball 30 metres out, readying myself for the kick.\n\nI'm to the left of the posts, so I line it up with my right foot to open up the angle and to avoid the charge-down. But Daws is buried and Backy [Neil Back] is waiting to deliver the pass at scrum half. Johnno sees this and, critically, takes the ball up one more time, making the Australia forwards defend again and allowing Daws to return to his station. The Wallabies go offside in their keenness to come through, but the referee only warns them. Then I see Daws picking up the ball. I lift my hands to receive it and he fires back the perfect pass. This is it.\n\nThe knack with a dropped goal is to connect with the ball as it makes contact with the ground, turning it into a place-kick in effect. But when I drop the ball it lands slightly off-centre, bouncing fractionally towards me as I strike it. This reduces the power I can put through the ball, but it actually makes accuracy easier. I know it doesn't have to go far, just straight.\n\nWhen I connect it feels good. Phil Waugh tries to block the kick, but he can't get there \u2013 it's up and away into the sky. I look up, I see the posts and I know it is going between them. It does. After all the pain, all the sacrifice and all the hardship it might just be that England are going to win the World Cup.\n\nThen I am seized by a moment of panic. Can the referee deny us again? I look at Watson. He raises his arm and signals the dropped goal. Everything is OK. We still have to deal with the kick-off, but Trevor Woodman catches it and the ball is fed back to Catty to deliver the laziest yet most beautiful touch-kick in the history of English rugby.\n\nThen the match is over. We've done it. My head is spinning like a tumble dryer. I jump up and down with Will Greenwood, shouting like a mad man, 'World Cup, World Cup'. In the emotion of the moment, I am unable to come up with anything more profound. It says it all, though \u2013 we are world champions.\n\n## _The London Bombings, 7 July 2005_\n\n_It was the best of times, it was the worst of times. On 6 July London had rejoiced on hearing that the city had been chosen to host the 2012 Olympics. At 8.50am local time on the following day,_ 7 _July, three bombs exploded within fifty seconds of each other on the London Underground (at King's Cross, Edgware Road and Liverpool Street\/Aldgate); a fourth bomb detonated at 9.47am on the No. 30 double-decker bus as it entered Tavistock Square. Altogether fifty-six people died in what was the deadliest terrorist attack on British soil since the 1988 bombing of Pan Am flight 103 (in which 207 had died). To no-one's great surprise, AI-Qaeda claimed responsibility for '7\/7'._\n\n_Alice O'Keefe, 23, a freelance journalist, was caught in the tube blast near King's Cross._\n\nWhen the train slammed to a halt and the carriage flooded with thick black smoke, I thought, 'That's it, this is how I'm going to die.' The train's on fire and we're all going to asphyxiate slowly. I heard screams from the carriage in front. Beside me, a woman was moaning, 'Jesus, Jesus', which seemed appropriate, although I'm not a believer. I wanted to pray too but couldn't quite let myself.\n\nI'm claustrophobic, and if anyone had asked me to describe hell, this would have been it. I felt myself shutting down. I curled up against the glass partition and wrapped my coat around my face, trying to keep my breathing under control.\n\nThe first five minutes were the worst. After that, it became clear that the smoke wasn't getting any thicker and some air was still circulating. Somewhere, a woman was still screaming hysterically, much to the annoyance of everyone around me. There was a feeling that if anyone lost their nerve, the situation would become impossible. I didn't let myself imagine the screamer was in a carriage full of corpses, as I now realize she probably was.\n\nIt was thirty interminable minutes until we were evacuated. As we straggled towards the bright lights of King's Cross I saw the injured for the first time: one young man staggering and soaked in blood, whose staring eyes are still imprinted on my brain; a middle-aged woman with her eye a sticky mess. I realized that I had been one of the lucky ones. I was crazed with shock when I got out of the station. I got through to my mum on the phone. She told me that there had been several incidents across London, but neither of us knew that my train had been bombed. I decided to try and get to her office in Old Street. I was still so confused that I walked in the wrong direction and found myself lost in the scrum of commuters. Nobody seemed to notice that my face and hair were black with soot. After wandering in circles for a while, I found a black cab.\n\nMy mum didn't recognize me, as I was blackened and my eyes were still goggling with shock when I arrived at her office. I then watched events unfold on television. Now it all seems like a bad dream.\n\n_Liam Vaughan wrote to the_ Guardian's _blog with thoughts and feelings typical of millions of Londoners on_ ' _7\/7':_\n\nReally insane and surreal day. My office is literally round the corner from where some of the blasts took place and I have spent the morning trying to make sure my friends are OK. I think they are, but the mobile phone networks are down so I haven't been able to confirm. There is no major panic here, just an underlying sense of confusion and despondency. Nobody is communicating and certainly nobody is able to concentrate on work. I guess it's a delayed sense of shock.\n\nPerhaps most disconcerting is that the police have instructed everyone to remain in their building and not try to leave the City. Apparently, police are not allowing people to enter either. In the eye of the storm, I guess. All public transport has been stopped so everyone will be walking home \u2013 from my window I can see people walking purposefully, but the streets are generally quite desolate, presumably because people either aren't in the City or they are not leaving the office.\n\nI guess people will be talking about this for years to come and yet it all seems strangely ethereal and distant. What strikes me is that places like Israel live like this on a day-to-day basis. It's all so random that maybe twenty out of all the thousands, possibly millions of commuters in the capital today were killed.\n\nThere is also the underlying fear that this is not it \u2013 that later today or tomorrow or in weeks to come it will happen again. There is always that nagging fear as a Londoner, and particularly as one that works in the financial centre of the capital, that you are in a dangerous place and that you are gambling with your life every time you get on at Bank, or Liverpool Street or any of the major tube stations. I always get the bus, but buses have been blown up as well, stripping any reassurance that it is somehow safer.\n\nJust received confirmation from a couple of friends. Just one to get in touch now who works near Aldgate. I'm sure he is fine. Statistically the chances of him being one of the few are small. And so we wait.\n\n## _England Win the Ashes, the Oval, London, 12 September 2005_\n\nED SMITH\n\n_Named after a spoof obituary on English cricket published in_ Sporting Times _in 1882, in which it was suggested that English cricket had died and the remains should be cremated, the 'Ashes' is the biennial test between England and Australia. When the two countries met for the 2005 Ashes, England had not won the contest since 1987._\n\nThose who doubt what cricket means to the English should have been at the Oval on 12 September 2005, or in London that evening and the following day, or anywhere in the country during the whole summer. The Ashes was not only the greatest series of our age. It also captured the English imagination in the strange and myriad ways that only cricket can.\n\nMuch-vaunted sporting events often suffer from expectations they never fulfil. The pre-series hype \u2013 the predictions, the profiles, the endless quotes \u2013 satiates the appetite rather than whetting it. With this Ashes, it worked out the other way around. The sport was so good that it was hard to say or write anything which added to it: the game had turned the table on the words. Whatever the deeper trends or broader themes might be, they could wait. The only question that really mattered was, what will happen next? The country was like a reader in the grip of a great novel.\n\nWhen the final chapter came at the Oval, many looked for divine intervention: rain. If it rained for long enough at the Oval, England would draw the match and win the series. It rained a bit, but not enough to prevent England from going into the final day needing to bat very well. The main obstacle standing between England and the Ashes was Shane Warne, possibly the greatest bowler of all time, almost certainly the one with the greatest willpower.\n\nWarne had already removed Marcus Trescothick and Andrew Strauss by the time Kevin Pietersen arrived at the crease with England wobbling at 67\u20133. Hampshire colleagues, fellow showmen and good friends, Warne v. Pietersen had been one of the great subplots of the summer. With Brett Lee bowling brutally fast, Pietersen \u2013 still not off the mark \u2013 edged a full ball straight to Warne at first slip. Warne dropped it, and with it, at last, the narrative thread. That passed to Pietersen, who had his own version of destiny to imprint. It began with two slog-swept sixes off the man who had just dropped him.\n\nEncouraged at lunch by captain Michael Vaughan to play his natural aggressive game, Pietersen cut loose after the break. In a thrilling passage of play, he hooked and pulled twenty-seven runs off two consecutive Lee overs. Helped by long stands with Paul Collingwood and Ashley Giles, Pietersen mixed defence and attack for the rest of the afternoon as England inched towards triumph. For the first time in eighteen years, the Ashes were returning to England.\n\nThere was no one single moment of total victory \u2013 no shattered stump, no scrambled single \u2013 to be followed by a final roar. Instead, England's great day was a slow drawing away into safety. It was accompanied in the stands of the Oval, and in living rooms across the country, by a steady deflation of fears and anxiety, gradually alchemizing into elation. Perhaps that was a truer end to the summer.\n\nWhat storyteller would dare conclude this epic with a single denoument?\n\n_The Compton-Miller Award for overall man of the series was presented to Andrew Flintoff. The day following their historic victory, the English team made a triumphal progress atop a tour bus through London to Trafalgar Square, where the gathered tens of thousands broke into a rendition of English cricket's unofficial anthem, 'Jerusalem'._\n\n## Personal Acknowledgements\n\nI have many people to thank for their help in the making of this book.\n\nFirst and foremost my wife, Penny Lewis-Stempel, without whom it would simply not have been done.\n\nThey also served: my agent Julian Alexander; Kate Barker at Penguin; Helen Campbell; Tracy Pallant; Emma Daffern (for sanity-saving research); Betty and Alan Jessop; Bernard and Andrew Samuels (for, literally, where I am today); Bob Pitt, Matt Pitt and Mark Williams (ditto); Sarah and David and Ollie and Emma Jones; Joyce and Eric Lewis; Julie Long and John Shurvinton; John and Frances Harvey-Fishenden; the staff of the British Library; the staff of Hereford Library. And Niall and Annie Robertson.\n\n## Sources and Permissions Acknowledgements\n\nThe author gratefully acknowledges permission to reproduce copyright material in this book. If any material has been inadvertently included without permission, please contact the author c\/o the publishers.\n\nAndrews, John ('The Boston Tea Party'), from _Letters of John Andrews, Esq., of Boston. 1772\u20131775,_ Winthrop Sargent (ed.), Massachusetts Historical Society Proceedings, 1864\u20131865, 1866\n\n_Anglo-Saxon Chronicle_ ('The Vikings Raid England'; 'An Estimate of William the Conqueror at his Death'), from _The Anglo-Saxon Chronicle,_ trans. G. N. Garmonsway, J. M. Dent, 1953. Copyright \u00a9 1953 G. N. Garmonsway.\n\n_Anglo-Saxon Chronicle_ ('The Anarchy'), in _The Saxon Chronicle,_ trans. J. A. Giles, Bohn, 1849\n\n_Anglo-Saxon Chronicle_ ('The Domesday Inquisition'), in _Anglo-Saxon Chronicle,_ trans. James Ingram, Everyman Library, J. M. Dent, 1912\n\n_Anonimalle Chronicle_ ('The Peasants' Revolt'), from _The Anonimalle Chronicle,_ V. H. Galbraith (ed.), Manchester University Press, 1927. Reprinted by permission\n\nAnonymous ('A Saxon Warrior at the Battle of Maldon'), in _English and Norse Documents,_ trans. M. Ashdown, Cambridge University Press, 1930. Copyright \u00a9 CUP 1930. Reprinted by permission of CUP\n\nAnonymous ('The Domesday Assessment of Cumnor'), from _Domesday Book,_ vol. I, 1783\n\nAnonymous ('Agincourt: Henry's Victory March'), quoted in _English Historical Documents 1327\u20131585,_ A. R. Myers (ed.), Eyre & Spottiswoode, 1969\n\nAnonymous ('Banning the Bomb'), from www.century.guardian.uk. Copyright \u00a9 Guardian Newspapers Limited\n\nAnonymous Court Recorder ('Sex in the Country'), quoted in _English Historical Documents 1189\u20131327,_ H. Rothwell (ed.), Eyre & Spottiswoode, 1975\n\nAnonymous Monk ('The Age of Chivalry: A Mass Knighting'), from _Flores Historiarum, per Matthaeum Westmonasteriensem collecti,_ vol. III, H. R. Luard (ed.), Rolls series, 1890\n\nAnonymous Priest ('The Battle of Agincourt'), quoted in _English Historical Documents 1327\u20131585,_ A. R. Myers (ed.), Eyre & Spottiswoode, 1969\n\nAnonymous SAS Trooper ('The SAS Relieve the Siege at Prince's Gate'), from _Soldier_ 'I' _SAS,_ Paul Kennedy, 1989. Copyright \u00a9 1989 Michael Paul Kennedy\n\nArch, Joseph ('The Revolt of the Field'), from _The Autobiography of Joseph Arch,_ John Gerard O'Leary (ed.), MacGibbon & Kee, 1966\n\nAsquith, Herbert ('The Drift to World War: The View from 10 Downing Street'), from _Memories and Reflexions,_ vol. II, The Earl of Oxford and Asquith, Little Brown and Co., 1928\n\nAsser ('The Viking Invasion: Alfred Saves _Angelcynn_ from the Danes'), from _De Rebus Gestis Aelfredi Magni,_ trans. J. A. Giles, Henry G. Bohn, 1848\n\nAustin, Richard, BEF ('Dunkirk: The Beach'), from _Return Via Dunkirk,_ Richard Austin ('Gun Buster'), Hodder & Stoughton, 1940\n\nBadcock, Midshipman (Trafalgar: The Battle Opens'), from _Sailors Whom Nelson Led,_ E. Fraser (ed.), Methuen, 1913\n\nBaker, Geoffrey le ('The Murder of Edward \u0399I'), from _Chronicon Galfridi le Baker de Swynebroke,_ ed. E. M. Thompson, Clarendon Press, 1889\n\nBaker, Geoffrey le ('The Hundred Years War: Sea Fight at Sluys'), quoted in _Chaucer's World,_ E. Rickert, OUP, 1948. Copyright \u00a9 1948 E. Rickert.\n\nBaker, Samuel White ('Samuel White Baker Discovers the Source of the Nile'), quoted in _The Faber Book of Exploration,_ Benedict Allen (ed.), Faber and Faber, 2002\n\nBamford, Samuel ('Peterloo'), from _Passages in the Life of a Radical,_ Samuel Bamford, Simpkin Marshall & Co., 1893\n\nBarter, Richard ('Indian Mutiny: Cawnpore after the Massacre'), from _The Siege of Delhi \u2013 Mutiny Memories of an Old Officer,_ Richard Barter, Folio Society, 1984\n\nBayerlein, Fritz ('El Alamein: The Afrika Korps Retreat'), from _The Fatal Decisions,_ W. Richardson and S. Freidin (eds), trans. Constantine Fitzgibbon, Michael Joseph, 1956\n\nBeatty, William ('Trafalgar: The Death of Nelson'), from _Despatches and Letters of Nelson,_ Nicholas Harris Nicolas (ed.), Henry Colburn, 1845\n\nBede ('King Edwin of Northumbria Is Converted to Christianity'), from _Bede's Ecclesiastical History of the English People,_ Bertram Colgrave and R. A. B. Mynors (eds), Oxford University Press, 1969. Reprinted by permission of OUP\n\nBeha-ed-Din, ('Richard I Massacres His Muslim Prisoners After Seizing Acre'), from _The Crusade of Richard I, 1189\u201392,_ selected by T. A. Archer, David Nutt, 1888\n\nBennett, Arnold ('The General Strike'), from _Journals,_ Arnold Bennett, Newman Flower, Cassell, 1933\n\nBentley, Elizabeth ('Factory Conditions'), from _Report of Parliamentary Committee on the Bill to Regulate the Labour of Children in Mills and Factories,_ 1832\n\nBentley, Thomas ('Machine Wreckers'), quoted in _Pandemonium 1660\u20131886: the Coming of the machine as seen by contemporary observers,_ Mary-Lou Jennings and Charles Madge (eds), Papermac, 1995\n\nBlakeney, Robert ('The Peninsular War: The Storming of Badajoz'), from _A Boy in the Peninsular War, J._ Sturgis (ed.), Murray, 1899\n\nBradford, William ('The Pilgrims' Land in New England'), from _History of the Plymouth Plantation,_ William Bradford, 1899\n\nBride, Harold ('The _Titanic_ Sinks'), from _New York Times,_ 19 April 1912\n\nBrittain, Vera ('Home Front: Death of a Brother'), from _Testament of Youth,_ Vera Brittain, Virago, 1978. Copyright \u00a9 Literary Executors of Vera Brittain 1970. Reprinted by permission of the Estate of Vera Brittain\n\nBront\u00eb, Charlotte ('A Visit to the Great Exhibition'), quoted in _The Brontes' Life and Letters,_ Clement Shorter, Hodder & Stoughton, 1908\n\nBrown, Cecil ('The Japanese Sink the _Repulse_ and the _Prince of Wales'),_ from _Suez to Singapore,_ Cecil Brown, Random House, 1942\n\nBulstrode, Sir Richard ('Civil War'), from _Memoirs and Reflections upon the reign and government of King Charles I and King Charles II,_ 1721\n\nBurney, Fanny ('A Chance Meeting with Mad King George'), quoted in _English Diaries of the XVI, XVII and XVIII Centuries,_ James Aitken (ed.), Pelican, 1945\n\nByrom, Elizabeth ('Bonnie Prince Charlie Invades Manchester'), quoted in _English Diaries of the XVI, XVII and XVIII Centuries,_ James Aitken (ed.), Pelican, 1945\n\nByrom, James, ('D-Day: A British Paratrooper Lands in Normandy'), from _The Unfinished Man,_ James Byrom, Chatto & Windus, 1957\n\nBystander ('The Burning of Archbishop Cranmer'), from _Memorials of Thomas Cranmer,_ John Strype, 1848\n\nCaesar, Julius ('Caesar Invades'; 'England: A Roman View'), from _The Conquest of Gaul,_ trans. S. A. Handford, Penguin, 1951, revised Jane F. Gardner, 1982. Reprinted by permission of Penguin UK\n\nChadwick, Roy ('The Jarrow March'), from _Manchester Guardian,_ 13 October 1936. Copyright \u00a9 1936 Guardian Newspapers Limited\n\nChannon, Henry ('The Abdication'), from _Chips: Diaries of Sir Henry Channon,_ Robert Rhodes James (ed.), Weidenfeld & Nicolson, 1967. Reprinted by permission of Weidenfeld & Nicolson\n\n_Chronicle of Lanercost_ ('The Battle of Bannockburn'), from _Chronicon de Lanercost, 1201\u20131346, J._ Stevenson (ed.), 1839\n\nChurchill, John ('Blenheim: The Victor's View'), from _The Complete History of Spain,_ John Churchill, 1707\n\nChurchill, Winston ('Omdurman'), from _My Early Life,_ Winston Churchill, Heinemann, 1930. Copyright \u00a9 1930 the Estate of Winston Churchill. Reprinted by permission of Curtis Brown Ltd\n\nChurchill, Winston ('Armistice Celebrations'), from _The World Crisis,_ Thornton Butterworth, 1927. Copyright \u00a9 1927 the Estate of Winston Churchill. Reprinted by permission of Curtis Brown Ltd\n\nChurchill, Winston ('Churchill's War Speeches'), from the Parliamentary Debates, Fifth series, House of Commons, vols 361 and 362\n\nClark, Alan ('Thatcher Falls'), from _Diaries,_ Alan Clark, Phoenix, 1994. Copyright \u00a9 1993 Alan Clark. Reprinted by permission of Weidenfeld & Nicolson\n\nClive, Robert ('Plassey'), from _Report to the Select Committee of the Court of Directors of the East India Company,_ 26 July 1757\n\nCook, \u0395. A. ('The Charge of the Light Brigade'), from _Letters,_ E. A. Cook, 1855\n\nCook, John ('Climbing Boys'), quoted in _They Saw It Happen 1689\u20131897,_ T. Charles-Edwards and B. Richardson (eds), Basil Blackwell, 1958\n\nCrabbe, George ('The Gordon Riots'), quoted in _The London Anthology,_ Hugh and Pauline Massingham, Spring Books, n.d.\n\nCromwell, Oliver ('Civil War', 'The Storming of Drogheda'), from _Cromwell's Letters and Speeches,_ Thomas Carlyle (ed.), Chapman & Hall, 1845\n\nDarwin, Charles ('Darwin in the Galapagos'), from _journal of Researches into the Natural History and Geology of the Countries visited during the Voyage of HMS 'Beagle' round the world, under the command of Capt. FitzRoy,_ Charles Darwin, Harper, 1846\n\nDenbigh, Countess of ('Queen Victoria's Funeral Procession'), quoted in _The Feilding Album,_ W. Elwes, Geoffrey Bles, 1950\n\nDe Saussure, C. ('Public Executions at Tyburn'), from _A Foreign View of England in the Reigns of George I and George II,_ trans. Madame Van Muyden, Caliban, 1998\n\nDe Zarate, Francisco ('An Encounter with Drake at Sea'), from _New Light on Drake,_ Z. Nuttall (ed.), Hakluyt Society, 1914\n\nElizabeth I ('The Armada: Elizabeth Addresses Her Troops'), quoted in _Readings in English History,_ E. P. Cheyney (ed.), Ginn & Co., 1908\n\nEngels, Friedrich ('Manchester Slums'), from _The Condition of the Working Class in England in 1844,_ Friedrich Engels, Foreign Languages Publishing House, 1962\n\nEpstein, Brian ('The Beatles in Performance'), from _Cellarful of Noise,_ Brian Epstein, Souvenir, 1964\n\nEvelyn, John ('Cromwell's Funeral'; 'Journal of the Plague Year'; 'The Great Frost Fair'; 'The Glorious Revolution'), from _The Diary of John Evelyn,_ William Bray (ed.), J. M. Dent, 1907\n\nFarrar-Hockley, Anthony ('The Korean War'), from _The Edge of the Sword,_ Anthony Farrar-Hockley, Muller, 1954. Copyright \u00a9 1954 Anthony Farrar-Hockley. Reprinted by permission of Sutton Publishing Limited\n\nFawkes, Guy ('The Gunpowder Plot'), from _King's Book,_ British Museum Press, 1940\n\nFerguson, W. H. ('Body-line Bowling'), from _Mr Cricket, Autobiography of W. H. Ferguson, as told to David R. Jack,_ Nicholas Kaye, 1957\n\nFlower, Desmond ('The Blitz'), from _The War 1939\u201345,_ Desmond Flower and James Reeves (eds), Cassell, 1960\n\nFreedland, Jonathan ('The Body of Diana, Princess of Wales, Is Flown Home'), from the _Guardian,_ 1 September 1997. Copyright \u00a9 The _Guardian_ 1997. Reprinted by permission of Guardian Newspapers Limited\n\nFroissart, Sir John ('The Hundred Years War: The Battle of Cr\u00e9cy'), from _Chronicles of England, France and Spain,_ trans. Lord Berners, David Nutt, 1901\u20133\n\nGeneral Court of the Mayor of the City of London ('Some Public Nuisances'), quoted in _English Historical Documents 1327\u20131385,_ A. R. Myers (ed.), Eyre & Spottiswoode, 1969\n\nGerard, John ('The Torturing of a Jesuit Priest in the Tower of London'), from _The Autobiography of an Elizabethan,_ John Gerard, trans. Philip Caraman, Longmans, 1951\n\nGibson, Guy ('The Dambusters Destroy the Mohne Dam'), from _Enemy Coast Ahead,_ Guy Gibson, Michael Joseph, 1946. Copyright \u00a9 1946 Guy Gibson. Reprinted by permission of the Estate of Guy Gibson\n\nGiustinian, Sebastian ('A Portrait of Henry VIII'), quoted in _They Saw It Happen 1485\u20131688,_ C. R. N. Routh (ed.), Basil Blackwell, 1956\n\nGoldsmith, Oliver ('Bath under the Code of Beau Nash'), from _Life of Richard Nash, Esquire,_ Oliver Goldsmith, W. Frederick, 1762\n\nGreville, Charles ('The Coronation of Queen Victoria'; 'Chloroform in Surgery'; 'Chartist March'), from _The Greville Memoirs: A Journal of the Reign of Queen Victoria from 1837 to 1852,_ Charles C. F. Greville (ed.), Longmans Green, 1895\n\nGrim, Edward ('The Murder of Thomas-\u00e0-Becket'), from _St Thomas by Contemporary Biographers,_ D. Nutt, n.d.\n\nHarris, Rifleman ('The Peninsular War: Plundering a Dead French Soldier'), from _The Recollections of Rifleman Harris,_ H. Curling (ed.), 1848\n\nHarvey, William ('A Post-mortem'), from _The Circulation of Blood and Other Writings,_ Kenneth J. Franklin (ed.), J. M. Dent, 1993\n\nHastings, Max ('Falklands War'; originally 'Max Hastings Leads the Way: The First Man into Port Stanley'), from _Evening Standard,_ 15 June 1982. Copyright \u00a9 1982 Max Hastings and the _Evening Standard._ Reprinted by permission of Atlantic Syndication\n\nHenry, Philip ('The Execution of Charles I'), quoted in _They Saw It Happen 1485\u20131688,_ C. R. N. Routh (ed.), Basil Blackwell, 1956\n\nHenry VIII ('Mine Own Sweetheart'), from _Intimate Letters of England's Kings,_ Margaret Sanders (ed.), Museum Press, 1959\n\nHenry of Huntingdon ('Cnut and the Waves'), quoted in _They Saw It Happen 55 BC-AD 1485,_ W. O. Hassall (ed.), Basil Blackwell, 1957\n\nHentzner, Paul ('A Meeting with Queen Elizabeth'), quoted in _Life in Shakespeare's England,_ John Dover Wilson (ed.), Cambridge University Press, 1911\n\nHillary, Edmund ('Everest Conquered'), from _High Adventure, Edmund Hillary,_ Hodder & Stoughton, 1955. Copyright \u00a9 1955 Edmund Hillary\n\nHillary, Richard ('Battle of Britain: A Spitfire Pilot in Action'), from _The Last Enemy,_ Macmillan, 1943. Copyright \u00a9 1942 Richard Hillary. Reprinted by permission of Macmillan\n\nHolwell, J. Z. ('The Black Hole of Calcutta'), from _The Annual Register,_ 1758\n\nHook, Henry ('Rorke's Drift, South Africa'), quoted in _Imperial Echoes,_ Robert Giddings (ed.), Leo Cooper, 1996\n\nHoward, Lord, et al. ('The Armada: The Commander's Report'), from _StatePapers Relating to the Defeat of Spanish Armada,_ J. K. Laughton (ed.), Navy Records Society, 1894\n\nHughes, G. E. ('An Infantryman in Normandy'), from unpublished diary, Imperial War Museum\n\nHulse, Edward Hamilton Westrow '(Christmas in the Trenches'), quoted in _The Albatross Book of English Letters,_ The First Earl of Birkenhead, Albatross Verlag, 1936\n\nJenkins, Peter ('The 1984\u20135 Miners' Strike'; originally 'A species threatened with extinction'), from the _Guardian,_ 19 December 1984. Copyright \u00a9 1984 Guardian Newspaper Limited\n\nJenner, Edward ('Jenner Discovers Smallpox Vaccination'), from _On the origine of the Vaccine Inoculation,_ D. N. Shury, 1801\n\nJesse, John H. ('Bad King George I'), from _Memoirs of the Court of England from the Revolution of 1688 to the Death of George the Second,_ John H. Jesse and Francis A. Nicholls, n.d.\n\nJohn et al. ('Magna Carta'), quoted in _Documents of Liberty,_ Henry Marsh (ed.), David & Charles, 1971. Translation copyright \u00a9 The British Library\n\nKeating, Frank ('Wade Wins Wimbledon'), from the _Guardian, 2_ July 1977. Copyright \u00a9 1977 Guardian Newspapers Limited\n\nKeith, Agnes Newton ('Tenko: An Englishwoman in a Japanese Prison Camp'), from _Three Came Home,_ Agnes Newton Keith, Michael Joseph 1955\n\nKemble, Fanny ('First Excursion on the Liverpool-Manchester Railway'), from _Record of a Girlhood,_ 1878\n\nKendall, H. G. ('The Arrest of Dr Crippen'), quoted in _Scrapbook 1900\u20131914,_ Leslie Bailey (ed.), Frederick Muller, 1957\n\nKincaid, J. ('Waterloo: The Final Attack'), from _Adventures in the Rifle Brigade,_ J. Kincaid, 1830\n\nKing, Lionel ('Doodlebugs'), from _People at War,_ Michael Monahan (ed.), David & Charles, 1974. Copyright \u00a9 1974 Michael Moynihan. Reprinted by permission of David & Charles\n\nKnighton, Henry ('The Black Death'), from _Chronicon Henrici Knighton, J._ R. Lumby (ed.), 1889\u201395\n\nKnox, John ('The Death of General Wolfe on the Heights of Abraham'), from _Journal of John Knox,_ Vol. II, Champlain Society, n.d.\n\nKray, Ronnie ('Ronnie Kray Murders George Cornell'), from _Our Story,_ R. and R. Kray (with Fred Dineage), 1988. Copyright \u00a9 1988 Bejubob Ltd\n\nLangland, William ('The Peasant's Life'), quoted in _The Portable Medieval Reader,_ J. B. Ross and M. M. Mclaughlin (eds), Penguin, 1981\n\nLawrence, T. E. ('T. E. Lawrence Blows up a Train on the Hejaz Railway'), from _Seven Pillars of Wisdom,_ T. E. Lawrence, Jonathan Cape, 1943. Copyright \u00a9 1926 T. E. Lawrence\n\nLondon, John et al. ('The Dissolution of the Monasteries'), _Letters to Cromwell,_ G. H. Cook (ed.), John Baker, 1965\n\nLydon, John et al. ('Never Mind the B******s: The Sex Pistols'), from _Rotten:No Irish, no blacks, no dogs,_ John Lydon and Kent Zimmerman, Plexus, 2003. Reprinted by permission of the publisher\n\nLytton, Constance ('Force-feeding of a Suffragette'), from _Prisons and Prisoners,_ Heinemann, 1914\n\nMap, Walter ('The Virtues and Vices of Henry \u0399I'), quoted in _English Historical Documents 1042\u20131189,_ D. C. Douglas and George W. Greenway, Eyre & Spottiswoode, 1953\n\nMarchant, Hilde ('World War II: Children Evacuated'), from _Women and Children Last,_ Hilde Marchant, Gollancz, 1941\n\nMiller, David ('England Win the World Cup'), from _I Was There,_ Collins, 1966. Copyright \u00a9 1966 The _Daily Telegraph_ and _Sunday Telegraph_\n\nMore, Sir Thomas ('Richard III Murders the Princes in the Tower'), from _The History of King Richard III,_ Thomas More, ed. R. S. Sylvester, Yale, 1963\n\nNasmyth, James ('The Black Country'), quoted in _Pandemonium 1660\u20131886: the coming of the machine as seen by contemporary observers,_ Mary-Lou Jennings and Charles Madge (eds), Papermac, 1995\n\nNeilly, J. E. ('The Siege of Mafeking'), from _Besieged with B-P,_ J. E. Neilly, Pearson, 1900\n\nNewton, Sir Isaac ('Isaac Newton Experiments on Light'), quoted in _The Ascent of Man, J._ Bronowski, BBC Books 1973\n\nNichol, John ('The Battle of the Nile'), from _Sailors Whom Nelson Led,_ E. Fraser, Methuen, 1913\n\nNichol, John ('The Gulf War'), from _Tornado Down,_ John Peters and John Nichol, Michael Joseph, 1992. Copyright \u00a9 John Peters and John Nichol. Reprinted by permission of Penguin UK\n\nNightingale, Florence ('Florence Nightingale in the Crimea'), from _Florence Nightingale: Letters from the Crimea,_ Sue M. Goldie, Mandolin, 1997\n\nO'Keefe, Alice ('The London Bombings'), from the _Observer,_ 10 July 2005. Copyright \u00a9 2005 Guardian Newspapers Ltd.\n\nOrwell, George ('Down and Out: A Night in a Doss-house'), from _Down and Out in Paris and London,_ George Orwell, Gollancz, 1933. Copyright \u00a9 1933 George Orwell. Reprinted by permission of A. M. Heath & Company\n\nPanter-Downes, Mollie ('VE Day'; originally 'Letter from London'), from the _New Yorker,_ 12 May 1945. Copyright \u00a9 Mollie Panter-Downes. Reprinted by permission of the _New Yorker_\n\nParis, Matthew ('The Weather'), quoted in _English Historical Documents 1042\u2013 1189,_ D. C. Douglas and George W. Greenway, Eyre & Spottiswoode, 1953\n\nPepys, Samuel ('The Restoration'; 'The Great Fire of London'), from _The Illustrated Pepys: Extracts from the Diary,_ Robert Latham (ed.), Book Club Associates, 1978. Copyright \u00a9 1978 The Masters and Fellows and Scholars of Magdalene College, Cambridge, Mrs William Matthews and Mr Robert Latham\n\nPiratin, Phil ('The Battle of Cable Street'), from _Our Flag Stays Red,_ Phil Piratin, Lawrence & Wishart, 1948. Copyright \u00a9 1948 Lawrence & Wishart\n\nPlatter, Thomas and Henry Wotton ('The Age of Shakespeare'), from _Shakespeare: Court, Crowd and Playhouse,_ Francois Laroque, Thames & Hudson, 1993. Copyright \u00a9 1991 Gallimard. English translation \u00a9 1993 Thames & Hudson Ltd and Harry N. Abrams Inc., 1993\n\nPountain, Dick et al. ('Grosvenor Square'), from _Days in the Life: Voices from the English Underground, 1961\u20131971,_ Jonathon Green, Heinemann 1988. Copyright \u00a9 1988 Jonathon Green. Reprinted by permission of the Random House Group Ltd\n\nReeder, Joan ('The Coronation of Queen Elizabeth \u0399I'), from the _Daily Mirror,_ 3 June 1953. Copyright MSI\n\nReid, Vince ('Passage to England'), from _Windrush: The Irresistible Rise of Multi-Racial Britain,_ Mike Phillips and Trevor Phillips, HarperCollins, 1999. Copyright \u00a9 1998 Mike Phillips and Trevor Phillips\n\nRobert of Avesbury ('Flagellants Come to London'), from _British Latin Selections AD 500\u20131400,_ R. A. Browne (ed.), 1954\n\nRoger of Wendover (' _Holocaustum'),_ from _Roger of Wendover: Flowers of History,_ trans. J. A. Giles, Henry G. Bohn, 1849\n\nRushworth, John ('The Attempted Arrest of the Five Members'), _Historical Collections,_ John Rushworth, 1691\n\nSassoon, Siegfried ('Fox-hunt'), from _Memoirs of a Fox-Hunting Man,_ Siegfried Sassoon, Faber, 1937\n\nSassoon, Siegfried ('Night Raid'), from _Diaries 1915\u201318,_ Rupert Hart-Davis (ed.), Faber and Faber, 1983. Copyright \u00a9 1983 George Sassoon. Reprinted by permission of the Estate of Siegfried Sassoon\n\nScott, R. F. ('Antarctic Expedition'), from _Scott's Last Expedition,_ R. F. Scott, Smith Elder & Co., 1913\n\nSmith, Ed ('England Win the Ashes'). Copyright \u00a9 2006 Ed Smith\n\nSouthwell, Lady ('The Death of Elizabeth'), from _The Other Face \u2013 Catholic Life Under Elizabeth I,_ Philip Caraman (ed.), Longmans, 1960\n\nStanley, Henry Morton ('Stanley Meets Livingstone'), from _How I Found Livingstone,_ Henry Morton Stanley, 1872\n\nSteward, Bert ('Wounded'), quoted in the _Guardian,_ September 1990. Reproduced by permission of Guardian Newspapers Limited\n\nStewart, William ('Nelson Sees No Signal'), from _Despatches and Letters of Nelson,_ Nicholas Harris Nicolas (ed.), Henry Colburn, 1845\n\nTacitus, Cornelius ('Boudicca Revolts'), from _The Annals of Imperial Rome,_ Penguin Books, 1956. Copyright \u00a9 Michael Grant Publications Lts 1956, 1959, 1971, 1973, 1975, 1977, 1989, 1996. Reprinted by permission of Penguin UK\n\nTebbit, Norman ('The Brighton Bomb'), from _Upwardly Mobile,_ Norman Tebbit, Weidenfeld & Nicolson, 1989. Copyright \u00a9 1989 Norman Tebbit\n\nThatcher, Margaret ('Margaret Thatcher Becomes Prime Minister'), from _The Downing Street Years,_ Margaret Thatcher, HarperCollins 1993. Copyright \u00a9 1993 Margaret Thatcher. Reprinted by permission of HarperCollins\n\nThompson, Leonard ('An Infantryman at Gallipoli'), quoted in _Akenfield,_ Ronald Blythe, Allen Lane, 1969\n\nTristan, Flora ('Prostitutes and Peers'), from _The London Journal of Flora Tristan,_ Jean Hawkes (trans.), Virago, 1982\n\nTynan, Kenneth ('Lady Chatterley's Trial'), from the _Observer, 6_ November 1960. Copyright \u00a9 1960 the _Observer._ Reprinted by permission of Guardian Newspapers Limited\n\nVarious ('Graffiti'), nos 2, 6, 7 from _The Romans in Britain: an anthology of inscriptions with translations and a running commentary,_ Blackwell, 1932; nos 1, 3, 4, 5 from _The Archaeology of Roman Britain,_ Methuen, 1930\n\nVaughan, Liam ('The London Bombings'), from the _Observer,_ 10 July 2005. Copyright \u00a9 2005 Guardian Newspapers Ltd\n\nVergil, Polydore ('The Battle of Bosworth'), from _English History,_ The Camden Society, 1844\n\nVergil, Polydore ('The Field of the Cloth of Gold'), from _Henry VIII,_ E. Hall, T. C. and E. C. Jack, 1904\n\nVictoria, Queen ('The Diamond Jubilee'), from _Letters of Queen Victoria,_ George Earle Buckle (ed.), Murray, 1930\u201332\n\nVitalis, Orderic ('The Coronation of William the Conqueror'; 'The Harrying of the North'; 'The Loss of the _White Ship'),_ from _The Ecclestiastical History of Orderic Vitalis,_ trans. Majorie Chibnill, Oxford University Press, 1978\n\nVon Uffenbach, Zacharias ('Cock-fighting'), from _London in 1710,_ W. H. Quarrell and Margaret Mare (trans.), Faber and Faber, 1935\n\nWalpole, Horace ('George II Interred'), from _Correspondence,_ W. S. Lewis (ed.), Oxford University Press, 1937\u201383\n\nWarkworth, John ('The Wars of the Roses'), from _Chronicles of the White Rose,_ Bohn, 1843\n\nWarwick, Sir Philip ('Cromwell in the House of Commons'), quoted in _They Saw It Happen 1485\u20131688,_ C. R. N. Routh (ed.), Basil Blackwell, 1956\n\nWeldon, Sir Anthony ('A Sketch of King James I'), quoted in _James I,_ S. J. Houston, 1973\n\nWellesley, Arthur ('Wellington Meets Nelson'), quoted in _The Correspondence and Diaries: John Wilson Croker,_ vol. II, Louis J. Jennings, Murray, 1884\n\nWesley, John (John Wesley Preaches'), from _Journal,_ John Wesley, Everyman's Library, J. M. Dent, 1906\n\nWheatley, Edmund ('Waterloo: Taken Prisoner'), from _The Wheatley Diary, C._ Hibbert (ed.), Longmans, 1964\n\nWhitelock, Bulstrode ('Cromwell Purges the Long Parliament'), from _Memorials,_ Sir Bulstrode Whitelock, 1682\n\nWilkinson, Jonny ('Rugby World Cup'), _My World,_ Jonny Wilkinson, Headline, 2004. Copyright \u00a9 2004 Jonny Wilkinson Ltd. Reprinted by permission of Tim Buttimore.\n\nWilliam of Poitiers ('The Battle of Hastings'), from 'The Deeds of William, Duke of Normandy and King of the English', quoted in _English HistoricalDocuments 1042\u20131189,_ D. C. Douglas and G. W. Greenaway, Eyre & Spottiswoode, 1953\n\nWykes, Thomas ('Edward I Conquers Wales'), from _English History Illustrated from Original Sources,_ Norman L. Frazer (ed.), A&C Black, 1907\n\nWynkfielde, R. K. ('The Execution of Mary, Queen of Scots'), from _Original Letters Illustrative of English History,_ Henry Ellis (ed.), Harding, Triphook and Lepard, 1824\u201346\n\n## Index\n\nAbdication (1936), \u20131\n\nAberdeen, George Hamilton Gordon, 4th Earl of,\n\nAboukir Bay _see_ Nile, battle of the\n\nAcre: captured by Crusaders (1191), \u20138\n\nAdam of Orlton _see_ Hereford, Bishop of\n\nAelfhere,\n\nAelfnoth,\n\nAethelred ('the Unready'), King of the English, \u201319,\n\nAfrica: exploration of, \u20134\n\nAfrika Korps: defeated at Alamein, \u20136\n\nAgincourt, battle of (1415), \u20138\n\nAgricola,\n\nagriculture: depression (1870s),\n\nAirlie, David George Ogilvy, 13th Earl of,\n\nAlamein, El, battle of (1942), \u20136\n\nAlbemarle, George Monck, 1st Duke of, \u20131\n\nAlbert N'yanza, Lake, ,\n\nAldermaston march, \u20132\n\nAlen\u00e7on, Charles III, Earl of, ,\n\nAlexander, Bishop of Lincoln,\n\nAlfred (the Great), King of Wessex, \u201317\n\nAmerica: wins independence from Britain,  _see also_ Canada; United States of America\n\nAmerican War of Independence (1775\u201383), ,\n\nAmiens, Peace of (1802),\n\nAmundsen, Roald,\n\nAndrews, John, \u20133\n\nAngevin empire, \u201350\n\nAngles, \u201310\n\n_Anglo-Saxon Chronicle_ , \u201314, , \u20135,\n\nAnglo-Saxons: kingdoms established, ; language and culture,\n\n'angry young men',\n\nAnjou, Geoffrey d' _see_ Geoffrey d'Anjou\n\nAnne, Queen: accession, \u20131,\n\nAnne Boleyn, Queen of Henry VIII, \u201316,\n\nAnne of Cleves, Queen of Henry VIII,\n\n_Anonimalle Chronicle, The_ , \u201394\n\nAntarctic: Scott's expedition in, \u2013301\n\nanti-semitism: provoked by Crusades,\n\nAppleton, William,\n\nApsley, Lady Frances,\n\nArc, Joan of,\n\nArch, Joseph, \u20138\n\narchers, , \u20136\n\nArgentein, Richard d',\n\nArgentina: in Falklands War (1982), \u2013400\n\nArmistice (November 1918), \u201321\n\nArrowsmith, Pat,\n\nArthur, King (legendary),\n\nArthur, Prince (nephew of King John),\n\nArundel, Richard II Fitzalan, Earl of,\n\nArundel, Richard III Fitzalan, Earl of,\n\nAshes, England win the,\n\nAshingdon, battle of (1916),\n\nAshton, Sir Arthur,\n\nAsquith, Herbert Henry ( _later_ 1st Earl), \u20134\n\nAsser, Bishop of Sherborne,\n\nAthelstan, King of the English,\n\nAttlee, Clement ( _later_ 1st Earl), , ,\n\nAubrey, John,\n\nAugustine, St, Archbishop of Canterbury,\n\nAumarle, Earl of (1346),\n\nAustin, Captain Richard, \u20135\n\nAustralia: body-line bowling in, \u20134; defeated in 2003 Rugby World Cup, \u201316\n\nautopsy: by William Harvey, \u20132\n\nBadajoz, battle of (1812), \u20139\n\nBadcock, Midshipman, \u201319\n\nBaden-Powell, Colonel ( _later_ General 1st Baron) Robert, \u20132\n\nBaker, Florence, Lady ( _n\u00e9e_ von Sass),\n\nBaker, Sir Samuel White, \u20133\n\nBalaclava, \u20137\n\nBall, Sir John, , ,\n\nBaltic League,\n\nBamford, Samuel, \u20134\n\nBampton, John ('Thomas'), \u201380,\n\nBannockburn, battle of (1314),\n\nBarnet, battle of (1471), \u20136\n\nBarons' War (1215\u201317),\n\nBarrie, Ian, \u201380\n\nBarter, Richard, \u201370\n\nBarton, Rankyn,\n\nBath: under Romans, ; social life, \u20136\n\nBattle of Britain (1940), \u20139\n\nbattlefield plunder, \u20137\n\nBayerlein, General Fritz, \u20136\n\n_Beagle_ , HMS,\n\nBeatles, the (pop group), \u20139\n\nBeatty, Dr William, \u201325\n\nBecket, St Thomas-\u00e0-, Archbishop of Canterbury, \u20135\n\nBede, Venerable, \u201313,\n\nBeha-ed-Din, \u20139\n\nBelgic people,\n\nBelgium: and outbreak of First World War, \u20134\n\nBelknap, Sir Robert, \u201380,\n\nBenedict of Peterborough,\n\nBengal, ,\n\nBennett, Arnold, \u20132\n\nBentley, Elizabeth, \u20139\n\nBentley, Thomas, \u20134\n\nBeorhtric,\n\n_Beowulf_ (poem),\n\nBerkeley, Sir Richard,\n\nBerkeley, Thomas, ,\n\nBerold (butcher of Rouen), \u20138\n\nBest, Pete, ,\n\nBevin, Ernest,\n\nBible, Holy: Authorized Version,\n\nBishop, William,\n\nBlack Country, the,\n\nBlack Death, \u20135\n\nBlack and Tans,\n\nBlackman, John,\n\nBlair, Tony,\n\nBlakeney, Robert, \u20139\n\nBlenheim, battle of (1704), \u20133\n\nBlenheim Palace, Oxfordshire,\n\nBlitz: on London, \u201341\n\nBlois, Charles, Earl of,\n\nBlomfield, Charles James, Bishop of London,\n\nblood, circulation of, \u20132\n\nBoer War (1899\u20131902), \u20133\n\nBoleyn, Mary,\n\nBoston, Mass.: Tea Party (1773), \u20133\n\nBosworth, battle of (1485), \u20139\n\nBoudicca (or Boadicea), Queen of the Iceni, \u20138\n\nBouvines, battle of (1214),\n\nBowers, Lieut. H.R., \u20131\n\nBoyne, battle of the (1690),\n\nBrackenbury, Sir Robert, ,\n\nBradford, William, \u201351\n\nBradwardine, Thomas, Archbishop of Canterbury,\n\nBrewster, William,\n\nBride, Harold, \u20132\n\nBridgewater, Francis Egerton, 3rd Duke of,\n\nBrighton: Grand Hotel bombed by IRA, \u20133\n\nBrihtnoth, Ealdorman, \u201321\n\nBrinton, Thomas,\n\nBritish Empire: dissolution,\n\nBritish Union of Fascists,\n\nBrittain, Captain Edward H., \u201313\n\nBrittain, Vera, \u201313\n\nBront\u00eb, Charlotte,\n\nBrown, Cecil, \u20133\n\nBruce, Robert _see_ Robert VIII the Bruce, King of Scotland\n\nBuckingham, George Villiers, 1st Duke of, \u20135\n\nBulstrode, Sir Richard, \u201360\n\nBurley, Sir Simon, \u20131\n\nBurney, Charles, \u201312\n\nBurney, Fanny (Mme d'Arblay), \u201312\n\nBurns, John,\n\nBuxton, Fowell,\n\nByrom, Elizabeth, \u20132\n\nByrom, James, \u20132\n\nCable Street, battle of (1936), \u20138\n\nCaesar, Julius, \u20134\n\nCaesius Rufus, Quintus Petilius Cerialis,\n\nCalais: Edward III seizes, ; lost to French, \u20132; Spanish Armada in,\n\nCalcutta: Black Hole (1756), \u20137\n\nCalifornia: Drake claims,\n\nCallaghan, James ( _later_ Baron), \u20132\n\nCampaign for Nuclear Disarmament (CND), \u20132\n\nCampbell, Sir Colin,\n\nCamulodunum, \u20136\n\nCanada: Wolfe's death in, \u20139\n\nCanterbury: cathedral built,\n\nCarttiss, Michael,\n\nCatesby, Robert,\n\nCatesby, William,\n\nCatherine of Aragon, Queen of Henry VIII, \u201315\n\nCatherine Howard, Queen of Henry VIII,\n\nCatherine Parr, Queen of Henry VIII,\n\nCatholics: repressed in Reformation, \u20138; despise James I, ; and Gunpowder Plot, ; Charles II seeks toleration for, ; granted civil rights (1778),\n\nCatus Decianus,\n\nCavaliers (Royalists),\n\nCavern Club, Liverpool, \u20139\n\nCawnpore, \u201370\n\nCecil, Robert (1st Earl of Salisbury),\n\nCecil, William (Baron Burghley), \u20136\n\nCelts,\n\nChadwick, Roy, \u201330\n\nChamber, Geoffrey,\n\nChamberlain, Neville,\n\nChannon, Sir Henry ('Chips'), \u20131\n\nCharles I, King of England: accession and reign, ; conflict with Parliament, \u20136; in Civil War, , \u20133; execution,\n\nCharles II, King of England ( _earlier_ Prince of Wales): at Edgehill, ; defeated at Worcester (1651), ; restoration, \u20139; in Great Fire of London, \u20134\n\nCharles V, Holy Roman Emperor, ,\n\nCharles Edward Stuart, Prince ('the Young Pretender' 'Bonnie Prince Charlie'), \u20132\n\nCharles of Luxembourg, King of Bohemia,\n\nCharles, Prince of Wales, , \u201314\n\nChartism, , \u20132\n\nChaucer, Geoffrey: _The Canterbury Tales_ ,\n\nchildren: employment, \u201341; evacuated in Second World War, \u20132\n\nChimney Sweepers Bill (1875),\n\nchimney sweeps: boys as, \u201341\n\nChina: Opium Wars,\n\nchivalry, \u20132\n\nchloroform, \u20131\n\nChristianity: Celtic, ; introduced and spread, \u201313; Vikings embrace, ; under William the Conqueror, \u20134\n\nChurch: relations with Crown, ; Anglican monopoly established,\n\nChurchill (Sir) Winston: on Omdurman, \u201391; and outbreak of First World War, ; Dardanelles campaign, ; on Armistice (1918), \u201320; succeeds Chamberlain as Prime Minister, ; authorizes Dunkirk evacuation, ; wartime speech (June 1940), \u20137; on loss of _Repulse and Prince of Wales_ , ; on El Alamein victory, ; on VE Day, \u20139; loses 1945 election, ; accepts decolonization, ; retires,\n\nCiudad Rodrigo,\n\nCivil War (1642\u201351): outbreak, ; conduct of, \u201363; ends,\n\nClare, Gilbert of,\n\nClarendon Code,\n\nClark, Alan, \u201311\n\nClarke, Kenneth,\n\nClaudius, Roman Emperor, \u20135\n\nClayton, Sir Richard,\n\nClifford, Robert,\n\nClifford, Roger de,\n\nClive, Robert, Baron,\n\nCnut (Canute), King of England and Denmark, \u20133\n\ncoal industry: and general strike,  _see also_ miners' strike\n\nCoalbrookdale, Shropshire,\n\nCobham, Reginald,\n\ncock-fighting, \u20137\n\nCoifi, Northumbrian priest, \u201312\n\nColchester,\n\nCole, John,\n\nCollingwood, Vice Admiral Cuthbert, 1st Baron, \u201319,\n\nCommius,\n\nCommunist Party of Great Britain: street conflict with fascists, \u20138\n\nComyn, John,\n\nConservative Party: under Thatcher, \u20133\n\nCook, \u0395. \u0391., \u20137\n\nCook, John, \u201341\n\nCook, Paul, \u20139\n\nCopenhagen: Nelson attacks,\n\nCornell, George, \u201381\n\nCornwall: Romano-British in,\n\nCornwallis, Charles, 1st Marquis,\n\nCoronations: Queen Victoria's, \u20133; Queen Elizabeth II's, \u201370\n\nCounter-reformation,\n\nCoventry, Sir William,\n\nCrabbe, George, \u20137\n\nCranmer, Thomas, Archbishop of Canterbury, , \u201321\n\nCr\u00e9cy, battle of (1346), \u201373\n\nCrewe, Robert Crewe-Milnes, Marquess of,\n\ncricket: and body-line bowling, \u20134\n\nCrimean War (1854\u20136), \u20138\n\nCrippen, Dr Hawley Harvey, \u20138\n\nCromwell, Oliver, , \u20137,\n\nCromwell, Thomas,\n\nCrusades: and anti-semitism, ; Richard I and,\n\nCrystal Palace,\n\nCumberland, William, Duke of, \u20131\n\nCummings, Ivor,\n\nCumnor, Berkshire,\n\nCup Final (association football), (1882), \u20134\n\nCurrie, Edwina,\n\nCurtis, Lieutenant Philip, \u20134\n\nD-Day (6 June 1944), \u20132\n\nDanelaw,\n\nDanes: subjugate and rule England, , ; harry William the Conqueror,  in York, \u201330 _see also_ Denmark; Vikings\n\nDardanelles, \u201310\n\nDarnley, Henry Stewart, Earl of,\n\nDarwin, Charles, \u20132\n\nDarwin, Erasmus,\n\nDavid III, Welsh prince, \u20139\n\nDeclaration of Rights (1688),\n\ndecolonization,\n\nDelft,\n\nDenbigh, Cecilia Mary, Countess of, \u20134\n\nDenmark: in Napoleonic wars,\n\nDerby, Abraham,\n\nDespenser, Hugh, Earl of Winchester,\n\nde Tracy, William,\n\nDettingen, battle of (1743),\n\nDe Valera, Eamon,\n\nDiana, Princess of Wales: death, , \u201314\n\nDickson, Jack, \u201380\n\nDighton, John, \u20138\n\nDodingeseles, William of,\n\nDomesday survey, \u20133\n\nDorset, Thomas Grey, 2nd Marquis of, \u201313\n\nDrake, Sir Francis, \u20135, \u20139\n\nDrogheda: stormed by Cromwell (1649), \u20136\n\ndu Deffand, Marie de Vichy de Chamrond, Marquise,\n\nDunbar, battle of (1650),\n\nDunkirk evacuation (1940), \u20135\n\nEadburh, wife of Beorhtric,\n\nEaldred, Archbishop of York,\n\nEarle, Sir Walter,\n\nEast India Company, , ,\n\nEcgfrith,\n\nEden, Anthony ( _later_ 1st Earl of Avon),\n\nEder Dam, \u20138\n\nEdgar, King of the English,\n\nEdgehill, battle of (1642), \u201360\n\nEdith Godwin, Queen of Edward the Confessor,\n\nEdmund Ironside, King of England,\n\nEdward ('the Confessor'), King of England,\n\nEdward I, King of England: accession, ; conquers Wales, \u20139; chivalry, \u20132; campaign against Scotland,\n\nEdward II, King of England: defeated at Bannockburn, \u20134; knighted, ; reign, \u20133; imprisoned and murdered, \u20136\n\nEdward III, King of England: accession, ; chivalry, ; in Hundred Years War, \u201373; decline and death,\n\nEdward IV, King of England, \u20136\n\nEdward V, King of England,\n\nEdward VI, King of England,\n\nEdward VII, King of Great Britain: at Victoria's Diamond Jubilee, ; succeeds to throne,\n\nEdward VIII, King of Great Britain ( _later_ Duke of Windsor), \u20131\n\nEdward, Prince of Wales ('the Black Prince'), , \u20132\n\nEdwin, King of Northumbria, \u201313\n\nEleanor of Aquitaine, Queen of Henry II, \u20131\n\nElizabeth I, Queen of England: reign, ; sponsors Drake's voyage, ; and execution of Mary Queen of Scots, ; and defeat of Spanish Armada, ; addresses troops at Tilbury, \u20132; Hentzner's audience with, \u201340; death,\n\nElizabeth II, Queen of Great Britain: Coronation, \u201370; mocked by Sex Pistols, ; presents trophy to Virginia Wade, ; Prime Ministers' audiences with, \u20132\n\nElizabeth, Queen of George VI (the Queen Mother), , ,\n\nElizabeth of York, Queen of Henry VII,\n\nEmma, Queen of Cnut,\n\n_Empire Windrush_ (immigrant ship), \u20132\n\nEngels, Friedrich, \u20139\n\nEngland: body-line bowling (cricket), \u20134; wins 1966 Football World Cup, \u20134; wins 2003 Rugby World Cup,\n\nEpstein, Brian, \u20139\n\nErskine, Thomas,\n\nEssex, Robert Devereux, 3rd Earl of,\n\nEugene, Prince of Savoy,\n\nEustace, Count of Boulogne, ,\n\nevacuees (children): in Second World War, \u20132\n\nEvans, Edgar,\n\nEvelyn, John, , \u20132, \u201380\n\nEverest, Mount: first climbed (1953), \u20137\n\nEvesham, battle of (1265),\n\nevolution, theory of,\n\nexecutions, public, \u201390\n\nFactory Act (1819),\n\nfactory conditions, \u20139\n\nFalklands War (1982), \u2013400\n\nfamine: Matthew Paris on,\n\nFarrar-Hockley, Anthony, \u20134\n\nFarren, Mick _see_ Pountain, Dick and Mick Farren\n\nfascism: in England, \u20138\n\nFawkes, Guy, \u20137\n\nFellowes, Lady Jane ( _n\u00e9e_ Spencer),\n\nFerguson, W. H., \u20134\n\nFerrers, Sir Ralph,\n\nFestival of Britain (1951),\n\nfeudal system: in Domesday Book, ; ends,\n\nFeversham, Louis Duras, 2nd Earl of,\n\nField of the Cloth of Gold (1520), \u201314\n\nfinches (birds): in Galapagos, \u20132\n\nFirst World War (1914\u201318): outbreak, \u20135; first Christmas fraternization, \u20138; casualties, , \u201313; trench warfare on Western Front, \u201312, \u201315; Armistice (November 1918), \u201321\n\nfitzUrse, Reginald, \u20134\n\nflagellants,\n\nFlanders, Louis, Earl of, ,\n\nFlower, Desmond, \u201341\n\nFoot, Michael, \u20131\n\nfootball (association), \u20134; World Cup (1966),\n\nFordham, Sir John, ,\n\nfox-hunting, \u20139\n\nFoxe, John: _Book of Martyrs (Acts and Monuments_ ), ,\n\nFrance: defeated in Canada (1759), ; in Napoleonic wars, , \u201319, ; and outbreak of First World War,\n\nFrancis I, King of France, \u201314\n\nFraser, ('Mad') Frankie,\n\nFreedland, Jonathan, \u201314\n\nFrisians,\n\nFroissart, Sir John, \u201373\n\nfrost fairs: on Thames, \u20137\n\nFusselles, Sir John de, \u20131\n\nGalapagos Islands, \u20132\n\nGallipoli, \u201310\n\nGame, Sir Philip, \u20138\n\nGardiner, Gerald ( _later_ Baron),\n\nGarel-Jones, Tristan,\n\nGarnet, Father Henry, SJ, , \u20136\n\nGarter, Order of the,\n\nGaul and Gauls, \u20134\n\nGaunt, John of _see_ John of Gaunt\n\nGaveston, Piers, Earl of Cornwall,\n\nGeneral Strike (1926), \u20133\n\nGeoffrey d'Anjou, ,\n\nGeoffrey, Bishop of Coutances,\n\nGeorge I, King of Great Britain, ,\n\nGeorge II, King of Great Britain: on General Wolfe, ; burial, \u2013201\n\nGeorge III, King of Great Britain: reign, ; and loss of American colonies, ; meets Fanny Burney in Kew Gardens, \u201312; capital offences under,\n\nGeorge V, King of Great Britain: and outbreak of First World War, \u20134\n\nGeorge VI, King of Great Britain: accession, ; on VE Day, \u20138; at Festival of Britain,\n\nGerard, Father John, SJ, \u20138\n\nGermany: economic development, ; and outbreak of First World War, \u20134; defeated (1918), , ; and outbreak of Second World War (1939), ; surrenders (1945), ; England defeats in 1966 World Cup, \u20134\n\nGibson, Wing Commander Guy, \u20138\n\nGildas (monk),\n\nGirl Guides,\n\nGiustinian, Sebastian, \u201311\n\nGlobe Theatre, London, \u20132\n\nGlorious Revolution (1688), \u201380\n\nGloucester: as Roman town,\n\nGloucestershire Regiment: in Korea, \u20134\n\nGodric,\n\nGodwine, Earl,\n\nGoldsmith, Oliver, \u20136\n\nGordon, General Charles George,\n\nGordon, James Geoffrey, Bishop of Jarrow,\n\nGordon, Lord George: riots (1780), \u20137\n\nGothic, the,\n\nGothrun, Viking king,\n\nGrand Remonstrance (1641),\n\nGreat Britain: formed (1707),\n\nGreat Depression (1930s),\n\nGreat Exhibition (London, 1851),\n\nGreat Fire of London (1666), \u20135\n\nGreat Plague (1665), \u20132\n\nGreat War _see_ First World War (1914\u201318)\n\nGreen, John,\n\nGreenfield, John,\n\nGregory I (the Great), Pope,\n\nGrenville, George,\n\nGreville, Charles, \u20133, , \u20132\n\nGrey, Charles, 2nd Earl, \u201350\n\nGrey, Sir Edward ( _later_ Viscount Grey of Falloden), \u20134\n\nGrey, Sir George,\n\nGrey, Lady Jane,\n\nGriffith-Jones, Mervyn, \u20135\n\nGrim, Edward, \u20135\n\nGrosvenor Square, London: protest demonstration (1968), \u20136\n\nGuatemala, \u20133\n\nGuilford, Sir Henry,\n\nGulf War, First (1991),\n\nGunhild, Empress of Henry III,\n\nGunpowder Plot (1605), , \u20137\n\nGurthrigern (Vortigern), British king, ,\n\nHadrian's Wall,\n\nHague, The,\n\nHainault, Sir John of, ,\n\nHales, Sir Edward,\n\nHales, Sir Robert, ,\n\nHamilton, Archibald,\n\nHamilton, Emma, Lady,\n\nHampden, John, ,\n\nHanoverian dynasty: begins, ; mental instability,\n\nHarcourt, Sir Godfrey de,\n\nHardrada, King of Norway, ,\n\nHardy, Thomas,\n\nHardy, Captain ( _later_ Vice Admiral Sir) Thomas Masterman, \u20135\n\nHarold Godwineson, King of England: accession, ; killed at Hastings,\n\nHarris, Rifleman, \u20137\n\nHarrison, George, ,\n\nHart, Ronnie,\n\nHarthacnut, King of Denmark and England,\n\nHarvey, William, \u20132\n\nHaselden, Thomas,\n\nHastings, battle of (1066), \u20138\n\nHastings (Sir) Max, \u2013400\n\nHawkins, Sir John, ,\n\nHeath, (Sir) Edward, , ,\n\nHejaz Railway, Arabia, \u201319\n\nHenry III, Holy Roman Emperor,\n\nHenry I, King of England, , , \u20139\n\nHenry II, King of England, \u20133,\n\nHenry III, King of England: accession, ; Simon de Montfort opposes,\n\nHenry IV, King of England (Henry Bolingbroke, Duke of Lancaster), \u20134\n\nHenry V, King of England: Agincourt victory, \u20137; triumphal march, \u2013101; made heir to French throne, ; death,\n\nHenry VI, King of England, \u20135\n\nHenry VII, King of England, \u201310\n\nHenry VIII, King of England: appearance and character, \u201311; inheritance, \u201311; at Field of Cloth of Gold, \u201314; and Anne Boleyn, \u201315; wives, \u201316; assumes headship of Church of England, ; and dissolution of monasteries, \u201319\n\nHenry of Huntingdon, Archdeacon, \u20133\n\nHenry, Philip,\n\nHentzner, Paul, \u201340\n\nHereford, Adam of Orlton, Bishop of,\n\nHereford, Humphrey de Bohun, 2nd Earl of,\n\nHeseltine, Michael ( _later_ Baron), \u20137, \u201311\n\nHesilrige, Sir Arthur,\n\nHillary (Sir) Edmund, \u20137\n\nHillary, Richard, \u20139\n\nHitler, Adolf, , , ,\n\nHobbes, Thomas,\n\nHoggart, Richard, \u20135\n\nHolland: Pepys in, \u20139\n\nHolies, Denzil, 1st Baron, ,\n\n_holocaustum_ (anti-Jewish pogroms),\n\nHolwell, John Zephaniah, \u20137\n\nHook, Henry, \u201382\n\nHoward (of Effingham), Charles, 2nd Baron ( _later_ 1st Earl of Nottingham),\n\nHughes, Sergeant G. E., \u20134\n\nHulse, Captain Sir Edward Hamilton; Westrow, \u20137\n\nHundred Years War, the (1337\u20131453), \u201373,\n\nHungerford, Sir Walter, \u20135\n\nHunt, Henry ('Orator'), \u20133\n\nHunt, Sir John,\n\nhunting _see_ fox-hunting\n\nHurd, Douglas ( _later_ Baron), ,\n\nHussein, Grand Sharif of Mecca,\n\nIbn Bar\u00eec, Hossam ad-Din,\n\nIceni tribe,\n\nImworth, John, ,\n\nIndia: British supremacy in, ; governed by Crown, ; independence,  _see also_ Calcutta; East India Company\n\nIndian Mutiny (1857\u20138), \u201370\n\nIndulgence, Declaration of,\n\nIndustrial Revolution, \u20135, , \u20139, \u20135,\n\ninflation,\n\nInnocent III, Pope,\n\nIRA (Irish Republican Army), \u20133\n\nIranian Embassy, London: siege (1980), \u20137\n\nIraq: in Gulf War (1991), \u201313\n\nIreland: Henry II invades, ; Cromwell in, \u20136; Cromwell unites, ; migrant labour from, ; nationalism in,\n\nIronsides (Civil War),\n\nIsabella of France, Queen of Edward II, \u20135\n\nJacobite risings: (1715 and 1719),  (1745), \u20132\n\nJamaica: immigrants from, \u20131\n\nJames I, King of England (James VI of Scotland), \u20135, ,\n\nJames II, King of England ( _earlier_ Duke of York): at Edgehill, \u20139; and restoration of Charles II, ; in Great Fire of London, \u20134; deposed and exiled, \u201380\n\nJames IV, King of Scotland,\n\nJames of St George, Master,\n\nJane Seymour, Queen of Henry VIII,\n\nJapan: sinks _Repulse_ and _Prince of Wales_ , \u20133; women prisoners under, \u201350\n\nJardine, Douglas,\n\nJarrow: Ecgfrith's monastery (Donemup), ; march (1936), \u201330\n\nJellicoe, Admiral John Rushworth, 1st Earl,\n\nJenkins, Peter, \u20135\n\nJenner, Edward,\n\nJesse, John H.,\n\nJesuits: repressed and tortured, \u20138\n\nJews,\n\nJohn, King: signs Magna Carta, \u201351,\n\nJohn of Gaunt, Duke of Lancaster: and Peasants' Revolt, , \u20133, ; and accession of Henry VII,\n\njury, trial by, , ,\n\nJutes,\n\nJutland, battle of (1916),\n\nKay, James Ph.,  and n\n\nKeate, Robert,\n\nKeating, Frank,\n\nKeeler, Christine,\n\nKeith, Agnes Newton, \u201350\n\nKemble, Frances Anne (Fanny), \u20139\n\nKendall, Captain (of _Montrose_ ),\n\nKennington Common (London): Chartist demonstration,\n\nKent: Caesar on,\n\nKew Gardens: George III in, \u201312\n\nKim II-sung,\n\nKincaid, Captain J., \u20135\n\nKing, Desmond,\n\nKing, Lionel, \u20136\n\nKing, Tom, \u20137,\n\nKitchener, Major-General Horatio Herbert ( _later_ Field Marshal 1st Earl),\n\nKnighton, Henry, \u20135\n\nknights: appointments, \u20132\n\nKnox, John,\n\nKnox, Captain John, \u20139\n\nKorean War (1950\u20133),\n\nKray, Reggie, \u201381\n\nKray, Ronnie, \u201381\n\nLabour Party: first government (1924), ; forms post-war government (1945), ; Wilson government, ; break with trade unions,\n\nLabourers, Statute of (1351),\n\nLancaster, Edmund, Earl of ('Crouchback'),\n\nLancaster, John, Duke of _see_ John of Gaunt\n\nLandor, Walter Savage,\n\n_Lanercost, Chronicle of_ , \u20133\n\nLangland, William: _Piers Plowman_ , \u20138\n\nLarwood, Harold, \u20134\n\nLaud, William, Archbishop of Canterbury,\n\nLaw, Andrew Bonar,\n\nLawrence, D. H.: _Lady Chatterley's Lover_ prosecuted, \u20135\n\nLawrence, Thomas Edward ('Lawrence of Arabia'), \u201319\n\nLawson, Nigel ( _later_ Baron),\n\nLayton, Richard,\n\nle Baker, Geoffrey, \u20138\n\nle Breton, Richard,\n\nLegett, Roger,\n\nLegge, John, , ,\n\nLeighton, Roland,\n\nLe Neve, Ethel, \u20138\n\nLennon, John, ,\n\nLenthall, William,\n\nLewes, battle of (1264),\n\nLiberalism,\n\nlight: Newton's experiments on, \u20136\n\nLight Brigade, Charge of (1854), \u20137\n\nLincoln: under Romans,\n\nLindisfarne: Vikings ravage,\n\nliteracy: under Romans, \u20139\n\nLiverpool: railway to Manchester, ; Beatles in, \u20139\n\nLivingstone, David, \u20136\n\nLlewelyn ap Grufudd, \u20139\n\nLloyd George, David,\n\nLondon: Romans in (Londinium), ; reduced by William the conqueror, ; population, ; public nuisances, ; Great Plague (1665), \u20132; Great Fire (1666), \u20135; frost fairs, \u20137; in Gordon Riots, \u20137; slums, ; gin palaces, ; prostitutes in, \u20135; Germans bomb in; Second World War ('the Blitz'), ; VE Day celebrations (8 May 1945), \u20139; bombings,\n\nLondon, John,\n\nLong Parliament _see_ Parliament\n\nLorraine, John, Duke of,\n\nLouis VII, King of France,\n\nLucan, George Charles Bingham, 3rd Earl of, \u20136\n\nLuddism, \u20135\n\nLunt, Geoffrey Charles Lester, Bishop of Ripon,\n\nLydon, John ('Johnny Rotten'), \u20139\n\nLytton, Lady Constance, \u20136\n\nMcAlpine, Alistair, Baron,\n\nMcCartney, (Sir) Paul, ,\n\nMacaulay, Thomas Babington, Baron, \u201350\n\nMcCorquodale, Lady Sarah ( _n\u00e9e_ Spencer),\n\nMaccus,\n\nMcFall, Raymond,\n\nMacGregor, Ian,\n\nMcGrigor, James,\n\nMacKay, Andrew, \u20137\n\nMcKenna, Reginald,\n\nMcLaren, Malcolm,\n\nMacmillan, Harold ( _later_ 1st Earl of Stockton), \u20136\n\nMcNeill, Sir John,\n\nMafeking: siege and relief of (1900), \u20133\n\nMagna Carta (1215), \u201354\n\nMahdi, the (Muhammad Ahmad ibn as-Sayyid 'Abd Allah),\n\nMajor, John, \u20138, \u201311\n\nMaldon, battle of (991), \u201321\n\nManchester: Bonnie Prince Charlie invades, \u20132; railway to Liverpool, ; slum conditions, \u20139 _see also_ Peterloo massacre\n\nMansfield, William Murray, 1st Earl of,\n\nMap, Walter, \u20132\n\nMargaret, Princess,\n\nMarie Antoinette, Queen of France,\n\nMarlborough, John Churchill, 1st Duke of, \u20133\n\nMarsin, Fernand, Comte de, \u20132\n\nMarston Moor, battle of (1644), \u20132\n\nMartyn, Henry,\n\nMarx, Karl,\n\nMary I (Tudor), Queen of England, , \u20132\n\nMary II, Queen of England, Scotland and Ireland, ,\n\nMary Queen of Scots: execution, \u20137; son (James) succeeds to English throne,\n\nMatilda, Empress (Henry I's daughter),\n\nMatilda ( _formerly_ Edith), Queen of Henry I,\n\nMatlock, Glen,\n\nMaude, Francis,\n\nMaugham, William Somerset,\n\nMaurice, Bishop-elect of London,\n\n_Mayflower_ (ship),\n\nMayne, Sir Richard,\n\nmedicine: developments in,\n\nMerchant, Hilde, \u20132\n\nMethodism,\n\nMieville, Sir Eric,\n\nMilitia Ordinance (1642),\n\nMiller, David, \u20134\n\nMilton, John,\n\nminers' strike (1984),\n\nmissionaries,\n\nMohne Dam, Germany, \u20138\n\nmonasteries, dissolution of, \u201319\n\nMonck, General George _see_ Albemarle, 1st Duke of\n\nmoney: under ancient Britons, ; Anglo-Saxon,\n\nMonk, Adrian,\n\nMons Badonicus, battle of (c. 516),\n\nMontagu, Sir Edward, 1st Earl of Sandwich,\n\nMontague, John Neville, Marquis of, \u20135\n\nMontcalm, Louis, Marquis de,\n\nMonteagle, William Parker, 4th Baron,\n\nMontfort, Simon de, Earl of Leicester, \u20137\n\nMontgomery, General ( _later_ Field Marshal 1st Viscount) Bernard Law, \u20135,\n\n_Montrose_ (ocean liner),\n\nMoore, John,\n\nMoore, Sir Philip,\n\nMore, Sir Thomas,\n\nMorrison, Herbert,\n\nMortimer, Edmund,\n\nMortimer, Roger de, 1st Earl of March,\n\nMorville, Hugh de,\n\nMosley, Sir Oswald, ,\n\nNana Sahib,\n\nNapoleon I (Bonaparte), Emperor of the French, , ,  _see also_ France\n\nNaseby, battle of (1645),\n\nNash, Richard ('Beau'),\n\nNasmyth, James, \u20135\n\nNational Agricultural Labourers' Union,\n\nnational debt, ,\n\nNational Health Service: established,\n\nNational Service: abolished,\n\nNational Union of Mineworkers (NUM),\n\nNavigation Act (1651),\n\nNavy (British), , \u201319\n\nNeave, Airey,\n\nNeilly, J. E., \u20133\n\nNelson, Vice Admiral Horatio, 1st Viscount: Nile victory, \u201315; attack on Copenhagen (1801), ; Wellington meets, ; death at Trafalgar, \u201325\n\nNero, Roman Emperor,\n\nNew England: Pilgrim Fathers land in, \u201351\n\nNew Forest,\n\nNew Model Army, \u20133\n\nNewcastle, Thomas Pelham Holies, 1st Duke of,\n\nNewcomen, Thomas,\n\nNewton, Sir Isaac, \u20136\n\nNichol, John (Royal Navy), \u201315\n\nNichol, John (Royal Air Force), \u201313\n\nNicolson, Harold, \u20135\n\nNightingale, Florence, \u20138\n\nNile, battle of the (1798), \u201315\n\nNile, river: source discovered, \u20133\n\nNolan, Captain Lewis Edward,\n\nNormandy: Allied landings (June 1944), \u20134\n\nNormans: invade and conquer England, \u20135; and English resistance, \u201330\n\nNorth, Frederick, Lord (2nd Earl of Guilford),\n\nNorthampton, William de Bohun, Earl of,\n\nNorthumberland, Henry Percy, 1st Earl of,\n\nNorthumberland, Henry Percy, 4th Earl of,\n\nNottingham, Daniel Finch, 2nd Earl of,\n\nnurses and nursing: Florence Nightingale reforms,\n\nOates, Captain Laurence Edward Grace ('Titus'),\n\nO'Brien, James Bronterre,\n\nO'Connor, Feargus, \u20132\n\nOdo, Bishop of Bayeux (William I's brother),\n\nOffa, King of Mercians, ,\n\nOmdurman, battle of (1898), \u201391\n\nOrderic Vitalis, \u201330,\n\nOrgrave, Sir Thomas,\n\nOrwell, George (Eric Blair), \u20136\n\nOsborne, John: _Look Back in Anger_ ,\n\nOswiu, King of Northumbria,\n\nOwain Glyndwr,\n\nOxford: as Royalist HQ in Civil War,\n\nOxford, John de Vere, 13th Earl of, \u20135,\n\nOxford, Provisions of (1258),\n\npaganism, ,\n\nPalmerston, Henry John Temple, 3rd Viscount,\n\nPankhurst, Emmeline,\n\nPanter-Downes, Mollie, \u20139\n\nParis, Matthew, \u20136\n\nParis, Treaty of (1856),\n\nParker, Admiral Sir Hyde,\n\nParliament: beginnings in Magna Carta, ; Simon de Montfort summons, \u20137; John of Gaunt seeks to control, ; conflict with Charles I, \u20136; Cromwell in, ; Long (1640\u201353), \u20134, \u20137; Barebones',\n\nParma, Alessandro Farnese, Duke of, ,\n\nParr, Thomas,\n\nPatten, Chris, \u20139\n\nPaulinus, Archbishop of York, \u201312\n\nPaxton, Sir Joseph,\n\nPearl Harbor,\n\npeasants: conditions, \u20138\n\nPeasants' Revolt (1381), \u201393\n\nPeel, Sir Robert,\n\npeerage: and prostitutes, \u20135\n\nPenguin Books,\n\nPeninsular War (1808\u201313), \u20139\n\nPepys, Sir Lucas,\n\nPepys, Samuel, \u201370, \u20135\n\nPercy, Thomas, \u20137\n\nPerrers, Alice,\n\nPeterborough, Henry Mordaunt, 2nd Earl of,\n\nPeterloo massacre (Manchester, 1819), \u20134\n\nPhilip II, King of Spain, , , ,\n\nPhilip VII, King of France, \u201370,\n\nPhilip, Prince, Duke of Edinburgh, ,\n\nPicts, \u20139\n\nPilgrim Fathers: land in New England, \u201351\n\nPilgrimage of Grace (1536),\n\nPiratin, Phil, \u20138\n\nPitaleyn, Robin,\n\nPius V, Pope,\n\nplagues,  _see also_ Black Death Great Plague\n\nPlassey, battle of (1757),\n\nPlatter, Thomas, \u20132\n\nPlessington, Sir Robert,\n\nPlymouth Colony (New England),\n\npoll tax: (1380), \u20139; under Thatcher,\n\npop music, \u20139, \u20139\n\npopulation: and Industrial Revolution, ; in Victorian period,  _see also_ urbanization\n\nPort Stanley, Falkland, \u2013400\n\nPortillo, Michael,\n\nPountain, Dick and Mick Farren, \u20136\n\npoverty: Orwell on, \u20136\n\nPrasutagus, King of the Iceni,\n\nPresbyterianism, \u20133\n\n_Prince of Wales_ , HMS: sunk, \u20133\n\nPrinces in the Tower, \u20138\n\nProfumo, John,\n\nprostitutes: in London, \u20135\n\nProtestantism: and dissent, ; and economic development,  _see also_ Reformation\n\nProvisional IRA, \u20133\n\nPrynne, William,\n\nPuritan Convention ('Barebones' Parliament'),\n\nPuritans: and James I's Authorized Version of Bible, ; break from Anglican Church and emigrate, \u201351; conflict with Charles I,\n\nPym, John, \u20135\n\nQuebec: Heights of Abraham, \u20139\n\nradio (wireless): and arrest of Crippen, \u20138\n\nRaedwald,\n\nRaglan, Lord Fitzroy James Henry Somerset, 1st Baron,\n\nrailways: beginnings, \u20139\n\nRainsborough, Colonel Thomas,\n\nRaleigh, Sir Walter,\n\nRamsey, Sir Alfred, \u20132\n\nRamsey, Sir James,\n\nRamsey, Michael, Archbishop of Canterbury, \u20139\n\nReeder, Joan, \u201370\n\nReform Bill (1831 Act, 1832), \u201350,\n\nReformation, \u201316 _see also_ Protestantism\n\nReid, Vince, \u20132\n\nRepresentation of the People Act (1918),\n\n_Repulse_ , HMS: sunk, \u20133\n\nrevolutions of 1848, \u20133\n\nRice, John ap,\n\nRichard I ('the Lionheart'), King of England: succeeds father, ; on Crusade, \u20139; death,\n\nRichard II, King of England: accession, ; and Peasants' Revolt, \u20134, \u20137, \u20132; imprisonment and death,\n\nRichard III, King of England, \u20139\n\nRichard, King of Germany,\n\nRichard, Prince (son of Henry I),\n\nRifkind, (Sir) Malcolm,\n\nRiley, D. F.,\n\nRobert VIII the Bruce, King of Scotland,\n\nRobert of Chester,\n\nRobert Curthose, Duke of Normandy (William I's son), , \u20136\n\nRoberts, Judith,\n\nRobin Hood,\n\n_Rocket_ (railway locomotive),\n\nRoger, Bishop of Coutances,\n\nRoger, Bishop of Salisbury (chancellor),\n\nRoger of Wendover,\n\nRomans: invade and conquer Britain, \u20134; and Boudicca's uprising, \u20138; civilization in England, \u20139\n\nRommel, General Erwin, \u20136\n\nRorke's Drift, battle of (1879),\n\nRoses, Wars of the (1453\u201385), ,\n\nrotten boroughs, \u201350\n\nRoundheads,\n\nRoyal Air Force: in Battle of Britain, \u20139; attacks German bombers,; bombs Mohne Dam, \u20138\n\nrugby: World Cup (2003),\n\nRunnymede (Runingmede), ,\n\nRupert, Prince, Count Palatine of the Rhine, , \u201361\n\nRushworth, John, \u20136\n\nRussell, Sir William Howard,\n\nRussia: in Crimean War, ,  _see also_ Soviet Union\n\nSackville-West, Vita,\n\nSt Albans, , \u20136\n\nSaladin, Sultan, \u20139\n\nSalisbury, Robert Gascoyne-Cecil, 3rd Marquis of,\n\nSamuel, Herbert Louis, 1st Viscount,\n\nSancroft, William, Archbishop of Canterbury,\n\nSandwich, 1st Earl of _see_ Montagu, Sir Edward\n\nSAS (Special Air Service), \u20137\n\nSassoon, Siegfried, \u20139, \u201312\n\nSaussure, C\u00e9sar de, \u201390\n\nSavoy, Eugene, Prince of _see_ Eugene, Prince of Savoy\n\nSaxons, \u201310 _see also_ Anglo-Saxons\n\nScargill, Arthur,\n\nScotland: pays homage to Henry II, ; Bannockburn victory over Edward II, \u20133; Edward II campaigns against, ; Black Death in, ; supports Parliamentarians in Civil War, ; Charles I surrenders to, ; Cromwell defeats, , ; Cromwell unites, ; union with England (1707),\n\nScott, Captain Robert Falcon, \u2013301\n\nScout movement,\n\nScroop, Adrian,\n\nScutari,\n\nSecker, Thomas, Archbishop of Canterbury,\n\nSecond World War (1939\u201345): children evacuated, \u20132; outbreak, ; ends, \u20139\n\nSettlement, Act of (1701),\n\nsex: punishments for, \u20131\n\nSex Pistols (rock group), \u20139\n\nShaftesbury, Anthony Ashley Cooper, 7th Earl of,\n\nShakespeare, William, ; _Henry VIII_ , ; _Julius Caesar_ , ; _Richard II_ , ; _Richard III_ ,\n\nShelley, Percy Bysshe: 'The Mask of Anarchy',\n\nship money,\n\nshires: formed,\n\nSimnel, Lambert,\n\nSimon, Sir John, \u20138\n\nSimpson, Wallis ( _later_ Duchess of Windsor),\n\nSingapore: Japanese capture (1942),\n\nSiraj-ud-Dawlah, Nawab of Bengal, ,\n\nSkinner, Dennis,\n\nSlawata, William,\n\nslums: in London, ; in Manchester, \u20139\n\nSluys, battle of (1340), \u20138\n\nsmallpox: vaccination against,\n\nsocial contract,\n\nSolemn League and Covenant (1643),\n\nSomme, battle of the (1916), \u201315\n\nSoult, Marshal Nicolas Jean de Dieu,\n\nSouth Elmsall, Yorkshire, \u20135\n\nSouth Pole: Scott's expedition to,\n\nSouthwell, Lady,\n\nSoviet Union: enters war (1941),  _see also_ Russia\n\nSpain: and Peninsular War (1808\u201313),\n\nSpanish Armada, \u201331\n\nSpanish Succession, War of (1701\u201314),\n\nSpeke, John Hanning,\n\nsports _see_ cock-fighting; football (association); fox-hunting; rugby\n\nSpraggon, Monsignor Daniel,\n\nStafford, Ralph de, 1st Earl of,\n\nStamford Bridge, battle of (1966),\n\nStamp Act (1765),\n\nStandish, Miles,\n\nStanley, Sir Henry Morton, \u20136\n\nStanley, Sir William,\n\nStarr, Ringo (Richard Starkey),\n\nStephen, King of England, \u201341\n\nStephenson, George, \u20139\n\nSteward, Bert, 3135\n\nStockton-Darlington railway,\n\nStoddert, Harry,\n\nStove, Betty,\n\nStowe, Ken,\n\nStrafford, Thomas Wentworth, 1st Earl of, \u20135\n\nStrawberry Hill, Twickenham,\n\nstrikes (industrial),  _see also_ General Strike miners' strike\n\nStrode, William,\n\nStuart dynasty: in England, ; restored, \u201370; and Jacobite risings, , \u20132\n\nSudbury, Simon, Archibishop of Canterbury, , \u20139\n\nSuddick, R.,\n\nSuetonius, \u20137\n\nSuez crisis (1956),\n\nsuffrage: and Reform Bill (1831), \u201350; extended (1918),\n\nsuffragettes: force-feeding,\n\nSunderland, John Gordon, 15th or 16th Earl of, \u201380\n\nSupremacy, Act of (1534),\n\nsurgery: chloroform in,\n\nSurrey, Thomas Howard, Earl of (and 2nd Duke of Norfolk),\n\nSutton Hoo,\n\nSweyn I, King of England and Denmark,\n\nSweyn II, King of Denmark, \u201330\n\nTacitus, \u20138\n\nTallard, Camille, Duke of, \u20132\n\nTany, Lucas de,\n\nTate, Maurice,\n\nTebbit, Margaret, \u20132\n\nTebbit, Norman ( _later_ Baron), \u20133,\n\nTenison, Thomas ( _later_ Archbishop of Canterbury),\n\nTenko,\n\nTennyson, Alfred, 1st Baron,\n\ntenserie (taxation),\n\nTenzing Norgay, \u20137\n\nTest Act (1673),\n\nTewkesbury, battle of (1471),\n\nThames, river: frost fairs, \u20137\n\nThatcher, (Sir) Denis, \u20133\n\nThatcher, Margaret Hilda ( _later_ Baroness), \u20133, , \u20135; loses office, \u201311\n\ntheatre: Shakespearean, \u20132\n\nTheobald, Count,\n\nThoma, General Ritter von, \u20135\n\nThomas, son of Stephen, \u20138\n\nThomas of Avesbury,\n\nThomas, James Henry,\n\nThompson, Alderman J. W.,\n\nThynne, Lord John,\n\n_Times, The:_ reports Crimean War, \u20135,\n\ntin,\n\n_Titanic_ (ocean liner), \u20132\n\ntorture: of Jesuits, \u20138\n\nTostig (brother of Harold Godwinson),\n\nTower of London: Gerard tortured in, \u20138\n\nTownsend, Roger,\n\nTrade Union Act (1871),\n\ntrade unions: workers' support for, ; breach with Labour Party,\n\nTrades Union Congress: and General Strike (1926),\n\nTrafalgar, battle of (1805), \u201325\n\nTrilling, Lionel,\n\nTrinobante tribe,\n\nTristan, Flora, \u20135\n\nTroyes, Treaty of (1420),\n\nTurkey: in First World War, \u20139, \u201319\n\nTurnham Green,\n\nTyburn: public executions at, \u201390\n\nTyler, Wat, , , \u20133\n\nTynan, Kenneth, , \u20135\n\nTyndale, William: _On the Obedience of a Christian Man_ ,\n\nTyrell, Sir James, \u20138\n\nTyrell, Sir William (1471),\n\nTyrrell, Sir William (1914 _later_ Baron),\n\nU-boats: in First World War,\n\nUffenbach, Zacharias von, \u20137\n\nunemployment, \u201330 _see also_ working class\n\nUniformity, Act of (1549),\n\nUnited States of America: enters First World War, ; enters Second World War, ; British relationship with, ; opposes Suez War (1956), ; and anti-Vietnam war protests, \u20136\n\nurbanization, , ,\n\nV-1 flying bombs ('doodlebugs'), \u20136\n\nvaccination,\n\nValence, William of,\n\nVE Day (8 May 1945), \u20139\n\nVere, Sir Aubrey de,\n\nVergil, Polydore, \u20139, \u201314\n\nVictoria Cross,\n\nVictoria, Lake,\n\nVictoria, Queen: coronation, \u20133; uses chloroform in childbirth, ; proclaimed Empress of India, ; Diamond Jubilee (1897), \u20136; funeral, \u20134\n\n_Victory_ , HMS, \u201323\n\nVietnam war: protests against, \u20136\n\nVikings: raids on Britain, \u201314; Alfred the Great resists and defeats, \u201317; converted to Christianity, ; Maldon victory, \u201321 _see also_ Danes\n\nvillas, Roman,\n\nVimeiro, battle of (1808), \u20137\n\nVolusenus,\n\nVortigern _see_ Gurthrigern\n\nVychan, Rhys,\n\nWade, Virginia,\n\nWade, Sir William, , \u20136\n\nWakeham, John ( _later_ Baron),\n\nWales: Romano-British in, ; Edward I conquers, \u20139; castles,\n\nWalpole, Horace, \u2013201\n\nWalpole, Sir Robert,\n\nWalsingham, Sir Francis,\n\nWalworth, Sir William, \u20133\n\nWarbeck, Perkin,\n\nWarkworth, John, \u20135\n\nWarner, Sir Pelham Francis ('Plum'),\n\nWarwick, Sir Philip, \u20134\n\nWarwick, Richard Neville, Earl of ('the Kingmaker'), \u20135\n\nWaterloo, battle of (1815), \u20135\n\nweather: extremes,\n\nWebb, Beatrice,\n\nWedgwood, Josiah,\n\nWedmore, Peace of (878),\n\nWeldon, Sir Anthony, \u20135\n\nWelfare State: introduced under Labour government,\n\nWellesbourne, \u20137\n\nWellington, Arthur Wellesley, 1st Duke of: meets Nelson, ; in Peninsular War, , ; at Waterloo, , \u20133, ; at Queen Victoria's Coronation,\n\nWentworth, Sir Peter,\n\nWesley, John,\n\nWest Indies: immigrants from, \u201362\n\nWestminster Abbey: founded by Edward the Confessor, ; coronations in,\n\nWestwood, Vivienne, \u20138\n\nWeygand, General Maxime,\n\nWheatley, Ensign Edmund, \u20134\n\nWhitby, Synod of (664),\n\n_White Ship_ : lost, \u20139\n\nWhitelaw, William, Viscount,\n\nWhitelock, Bulstrode,\n\nWilkinson, Ellen, \u20139\n\nWilkinson, Jonny, \u201316\n\nWilliam I ('the Conqueror'), King of England, Hastings victory, \u20138; coronation, \u20139; suppresses insurrections, ; and Domesday survey, \u20132; death and assessment, \u20136\n\nWilliam II ('Rums'), King of England, , \u20136\n\nWilliam III (of Orange), King of England, Scotland and Ireland, \u201380\n\nWilliam of Malmesbury,\n\nWilliam of Norfolk,\n\nWilliam of Poitiers,\n\nWilliam, Prince (son of Henry I), ,\n\nWillis, Dr John, \u20139, \u201312\n\nWilloughby, Peter Robert Drummond-Willoughby, 22nd Baron,\n\nWilson, Edward Adrian,\n\nWilson, Harold ( _later_ Baron),\n\nWilson, Colonel Valentine,\n\nWilton, battle of (1871),\n\nWimbledon: All England tennis championships, \u20131\n\nWindsor, Duchess of _see_ Simpson, Wallis\n\nWindsor, Duke of _see_ Edward VIII, King of Great Britain\n\nWinter, Robert,\n\nWinter, Thomas,\n\nwireless _see_ radio\n\nwoad,\n\nWolfe, General James, \u20139\n\nWolsey, Cardinal Thomas, ,\n\nwomen: factory workers, \u20139; force-fed in prison, ; granted vote (1918), ; prisoners in Japan, \u201350\n\nWomen's Social and Political Union,\n\nWood, Sir Charles, 1st Viscount Halifax,\n\nwool: exports,\n\nWooler, Bob,\n\nWorcester, battle of (1651), ,\n\nworking class: supports trade unions, ; slum conditions, \u20139 _see also_ unemployment\n\nWotton, Sir Henry, \u20132\n\nWright, Christopher,\n\nWright, John,\n\nWulfmaer the young, \u20131\n\nWulfstan,\n\nWykes, Thomas, \u20139\n\nWynkfielde, R. K., \u20137\n\nYork: as Roman town, ; insurrection against William the Conqueror, \u201330; Jews massacred,\n\nZarate, Francisco de, \u20135\n\nZuche, William la,\n\nZulu War (1879), \u201382\n*TRE: tempore regis Edwardi (in the time of King Edward).\n\n\u2020 The hide: four virgates, or 120 acres.\n\n\u2021 Villeins: unfree farmers.\n\n\u00b6 Serfs: the latest free of the free farmers.\n*'Scutage' or 'shield-money' was paid in lieu of physical participation in the king's wars.\n*i.e. 28 December 1256.\n\n*i.e. until 2 February 1258.\n*Breasts.\n*Private posterns.\n\n\u2020 A rabbit' burrow.\n*Owner of one of the tea ships.\n*'The Moral and Physical Condition of the Working-Class employed in the Cotton Manufacture in Manchester.' By James Ph. Kay, M.D. 2nd Ed. 1832. Dr Kay confuses the working-class in general with the factory workers; otherwise, an excellent pamphlet. [Engels]\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\n_This Is a Borzoi Book Published by Alfred A. Knopf_\n\n_Copyright \u00a9 2013 by Thomas Sanchez_\n\n_All rights reserved. Published in the United States by Alfred A. Knopf, a division of Random House, Inc., New York, and in Canada by Random House of Canada Limited, Toronto_.\n\n_www.aaknopf.com_\n\n_Knopf, Borzoi Books, and the colophon are registered trademarks of Random House, Inc_.\n\n_Grateful acknowledgment is made to David Platz Music Inc. for permission to reprint an excerpt from \"First Time Ever I Saw Your Face\" by Ewan MacColl. Copyright \u00a9 by David Platz Music Inc. All rights reserved. Used by permisson of David Platz Music Inc_.\n\n_Library of Congress Cataloging-in-Publication Data_  \n _Sanchez, Thomas_.  \n _American tropic \/ by Thomas Sanchez. \u2014 1st ed_.  \n _p. cm_.  \n _\"This is a Borzoi book.\"_  \n _eISBN: 978-0-307-96138-9_  \n _1. Murder\u2014Fiction. 2. Key West (Fla.)\u2014Fiction. 3. Suspense fiction. I. Title_.  \n _PS3569.A469A83 2013_  \n _813\u2032.54\u2014dc23 2012035328_\n\n_This is a work of fiction. Names, characters, places, and incidents either are the product of the author's imagination or are used fictitiously. Any resemblance to actual persons, living or dead, events, or locales is entirely coincidental_.\n\n_Jacket photograph by Brian Pieters\/Masterfile  \nJacket design by Wednesday Design_\n\nv3.1\n_For Geraldine Louise  \nmy mother, whose inspiration  \nsent the first words sailing...  \nto the dove over the ocean  \nher spread of wings  \nforming a perfect A  \nfor Astrid  \nand for  \nAsh Green_,  \n _hand at the helm_.\n\n# Contents\n\n_Cover_\n\n_Title Page_\n\n_Copyright_\n\n_Dedication_\n\n_Epigraph_\n\n_Acknowledgments_\n\nFirst Page\n\n_About the Author_\n\n_Other Books by This Author_\n_American tropic islands...  \nthat true poetic spirit that  \ncan find inspiration in  \nhumble and even vulgar things;  \nthat, furthermore, can draw from low nature  \nand her commonplaces  \ndeep lessons for human life_.\n\n\u2014FROM A RUMINATION ON THE POET OF  \nTHE REVOLUTION, _ATLANTIC MONTHLY_ , 1904\n\n# **ACKNOWLEDGMENTS**\n\n_Shelter from the storm_ ,  \n _Robert Mailer Anderson & Nicola Miner  \nCecelia Joyce & Seward Johnson  \nJean-Leo Gros_.\nWhere the brooding Atlantic meets the moody torrent of the Gulf Stream, water and darkness give birth to the rip tides of fate roaring up through murky underwater canyons. Far above, on the ocean's roiling dark surface, the silhouette of a lone boat heaves on waves. Bolted to its upper deck is a sturdy metal radio-transmitter antenna. From the transmitter an insistent male voice broadcasts. The words ride, invisible, through the air from east to west. They can be heard from the Great Bahama Bank all the way to the distant island of Cuba. They travel wide across the ocean, from the Tropic of Cancer to the island of Key West, off the coast of Florida. The words become an urgent question.\n\n\"Is\n\nanyone\n\nout\n\nthere?\"\n\nThe question hangs, the words stop, then they begin again, rhythmically rising in a strident drumbeat.\n\n\"This is Truth Dog broadcasting from pirate-radio boat _Noah's Lark_ to the whole dead world, speaking to you out of the darkness of night. Are there two brains out there to rub together for a spark of illumination? Do you hear me? Maybe no one is awake in Key West, just twenty miles across the water from me. Maybe all the eyes on that coral-capped island are closed to the obvious truth. Perhaps no one is awake in the wide world that spins obliviously toward its own demise. Could be I'm floating out here alone, broadcasting to a country of unliving people caught in a zombie stupor of collective historical amnesia and collapsed moral hearts. Could be that only the fish beneath me in the sea are awake, sliding through opaque waters, finning through submerged canyons carved by millennia of time, their mouths agape, fins pushing against water's gravity, on the prowl for their next meal, dead between their eyes to any joy, propelled by their simple ancient truth of gut survival.\n\n\"Hey, dead-between-the-eyes fish zombies! Call me now. I'm on the line for you. I'm on the hook. I'm like God in the heavens, or Jesus in the confessional box, or Moses in the lightning glow on the mountaintop. Better yet, I take calls from sinners and seekers, repenters and fakers.\n\n\"Call me before it is too late. Wake up, little zombies, wake up. Call even if you are dead and only now are awakening in the afterlife, your cold fish-scaled bodies slithering out of the sea onto the shore of a new beginning in an old world. Call Truth Dog, an old dog with new tricks.\n\n\"Call me and tell me how the lightning on the mountaintop strikes you between those dead eyes of yours so you see illuminated the green flash of light across the ocean's horizon spelling out a new dawn and you can finally shout the truth.\n\n\"Illumination.\n\nIlluminate or die.\n\nShow me your rage.\"\n\nLuz awakens in her bed from dreams of deep-indigo oceans. Her brown eyes take in the white-skinned body of Joan sleeping next to her. Joan's blond hair lies spread over the pillow; her deep breathing heaves the curve of her bare breasts in a rhythmic rise and fall that Luz has known intimately for twelve years. Luz kisses Joan's bare shoulder and slides her dark hand below the white swell of one of Joan's breasts. Luz stares at her hand, her fingers in a winged shape, a dark bird flying beneath the full orb of an alabaster moon.\n\nAbove the bed, the ceiling fan's blades swirl through the humid air. The insistent sound brings Luz back from her brief flight to Joan's fleshy landscape. She looks up wide-eyed at the blades as their slicing sound grows louder, as forceful as incoming surf crashing onto an island, waves smashing, spraying, drowning everything, plunging Luz back beneath an indigo ocean, where she swims in watery turmoil surrounded by mysterious creatures lurking in a fathomless deep.\n\nLuz shakes her head, driving submerged images from her mind. She turns quickly away from the fan's blades. She rises from her bed and stands barefoot before her dresser, her white cotton underwear tight against the sheen of her dark skin. She dresses quickly in black pants and a white Cuban-style guayabera shirt. From the dresser top she picks up a loaded Glock 30 semiautomatic pistol with a thick gorilla-grip handle. She snaps the heavy black weapon into its leather holster on a belt. She lifts the long shirt above her pants and straps the gun snug against her waist. She glances into the mirror above the dresser. The mirror reflects Joan's naked blondness on the bed behind, superimposed over the image of her own shadow-skinned reflection. She drops her loose shirt over the pistol holstered at her hip and looks closely at herself in the mirror. Her black hair is cropped short; her smooth facial features are natural, devoid of any makeup; her eyes hold a steady gaze and do not blink.\n\nLuz leaves Joan sleeping in the bedroom and walks with quiet steps down a narrow dark hallway to a closed door. She pushes the door silently open and looks in on two teenaged girls asleep in separate beds. The older is a healthy sixteen-year-old; her untroubled breath is even, her lips are curved in a smile. In the opposite bed is a younger girl, of fourteen, her bone-thin body pallid and hairless from chemotherapy treatments fighting her childhood leukemia. Next to her bed is a wheelchair, and a nightstand covered with medicine bottles. She stirs awake; her eyes open slowly, with painful effort. She smiles at the sight of Luz. Luz puts her fingers to her lips and blows the girl a kiss, then softly shuts the bedroom door.\n\nIn her living room, Luz kneels before a walnut-wood Spanish chest. The top of the chest is commanded by a tall ceramic statue of a Black Madonna. The Madonna holds in her arms an infant child with a beatific smile etched on its face. Luz strikes a match and lights a candle in a red glass holder in front of the statue. She clasps her hands together in a pointed prayerful position. She looks straight into the Madonna's soulful eyes as she whispers her prayer.\n\n\"As a mother myself, I beseech you to take pity on my daughters, Nina and Carmen. Cure my little Nina of her cancer and suffering. Only you, holiest of all mothers, can stop the pain of an innocent child. Give me the strength to protect my daughters and my beloved, Joan. Give me the strength to do what I must do to keep my family safe from the evil that surrounds them.\"\n\nLuz's misty eyes focus on the candle flame flickering in front of the Madonna. The flame sparkles and burns stronger, transforming into a brilliant glow.\n\nA red rising sun emerges on the ocean's dark horizon. Out of the sun flies a winged armada of seabirds. The birds swoop down from the sky over the water's surface. They glide above the humped shell of a large sea turtle below. The turtle's green front fins stroke through the blue, propelling the primeval creature's bulk relentlessly forward. The birds pass on; beneath them, dolphins break the sea's surface. The dolphins' sleek wet bodies arch out of the water into the air in a dazzling, twisting spray. They then dive back out of sight. Impervious to the dolphins, the birds sail on over the dark saucer-shaped shadows of giant stingrays just below the ocean's skin. The birds continue their journey over open water. They suddenly bank hard, whooshing the air as they descend in a wing-flapping circle around a channel-marker buoy afloat below.\n\nThe large anchored buoy's wide platform base sloshes in the water. Rising up from the base is a tall metal pole with an orange plastic star-shaped reflector at its peak. The reflector glints with shards of orange light. A dead man's naked body is tied by a thick knotted rope to the pole. Slashed on the body's abdomen is a painted red **X**. A steel spear is pierced through the man's chest. From below the spear a stream of blood has hardened into a congealed purple crust. The white lips of the man's blood-drained face have been sewn crudely shut with fishing line. His ears have been cut off, leaving two gashed holes. The orbs of the man's eyes remain open. The eyes stare off across the distance of the ocean. In death, the eyes seem fixed on a horror that the sewn-up lips cannot scream the name of.\n\nBetween the islands of Key West and Cuba, the sun's globe rises into the sky above a weather-beaten 1950s West Indian Heritage trawler. The anchored boat sways in a watery blue canyon created by the rise and fall of waves. On the bow of its thirty-six-foot-long hull is painted the name _Noah's Lark_. A twelve-foot-high steel radio-transmitter antenna is bolted to the deck. Inside the windowed pilothouse is a jerry-rigged radio-broadcasting control room. Seated on a ragged swivel chair in front of a console of outdated analog equipment is a man wearing a sun-faded seersucker suit that hangs loosely on his angular frame. His sleep-deprived reddened eyes stare intensely at the console's flickering red and green lights. The lines etched deeply into the man's face convey a hard life lived. He agitatedly fingers the bearded stubble of his unshaven chin, then clamps on a pair of battered earphones over the unruly hair of his head. He pulls in close to the metal stub of a microphone on the table before him. His lips loosen with a quiver as if about to deliver a kiss to an unseen lover. His melodious voice suddenly cracks open the morning silence with a basso swagger.\n\n\"Rise and shine, all of you in the Florida Keys about to lose your paradise. Rub the stars out of your eyes and take your brains out of your shoes. Today's temps are soaring up to ninety-nine degrees, too hot to wear your own sweat, let alone your lover's sweat. This is Noah Sax, your very own Truth Dog, broadcasting from international waters over Conch Pirate Radio offshore from Key West. Key West, Cayo Hueso, Island of Bones\u2014that was the name the early Spanish explorers gave the place when they found it littered with nothing but the bleached remains of the hounded, deserted, and luckless. The Spaniards beat it. Key West, America's southernmost continental point, where the Overseas Highway ends after hopping across bridges linking forty-three islands on its one-hundred-thirty-mile run down from Miami. Key West, last American island, end of the road at the famous sign, **MILE MARKER ZERO**. As the poet once wrote, nowhere to go from mile zero except to swim with the sharks and barracuda. Which is where I am, floating with the sharks and barracuda far out at sea, where the feds can't stop my pirate radio beaming the truth across the open ocean.\n\n\"Nowhere does the bell of accountability ring out so loudly as here in the Florida Keys. This fragile ecosystem is dotted with coral-and-mangrove-entwined islands guarded by the third-largest coral reef in the world and the only living coral reef in North America. The fragrant salty air that you breathe here so freely must be defended at all costs, before these islands are covered over in the oil-pollution slime that greases the implacable wheel of man-made environmental destruction. Don't fool with Mother Nature or Mother Nature will fool with you!\"\n\nNoah's words stop. He grabs a rum bottle from next to his microphone and takes a swig. He swipes the liquid from his lips and continues.\n\n\"I'm out here on the open sea in the sun, unlike Internet bloggers hunkered down in solitary dark holes. My old-school live radio is stand-up accountability. I'm the only eco-shock jock broadcasting at sea, letting you, my irreverent audience, roar your disgust against the destruction of the environment. Your words are bullets, so aim straight. Call Noah now, punch me with the power of your pain and pissed-off kisses. If you're a cynic, comic, or crusader, join the chorus of the committed. Dial Five-Five-C-O-N-C-H. Act out, act up, but act. I'm here for you. I'm a lightning rod, shoot me your lightning. Rock the world with thunder. Show me your rage!\"\n\nNoah clutches the microphone in his trembling hand and holds it close to his mouth. He leans back in his chair, takes a deep breath, and switches to a mellow tone.\n\n\"While you're getting ready to put your sweet lips to the phone, let me serve you a hot cup of morning _amore_ , get you in the mood with a beat brewed by our Cuban neighbors just ninety miles across the ocean.\"\n\nNoah punches one of the buttons on the broadcast console, starting a CD player wired to a pair of battered wooden speakers. A full-orchestra salsa beat from the speakers fills the pilothouse with an insistent throb. Noah closes his eyes and sways to the seductive rhythm. He gets up from his chair. His arms reach out to an invisible partner, and he dances in a hip-strutting glide around the pilothouse.\n\nOutside Noah's anchored trawler, the sound of salsa cuts sharp as a musical knife across the ocean's surface. With nothing to stop it, the music can be heard in the far distance to where a raft drifts. The raft is constructed from scraps of wood crudely lashed with fraying rope. Its sail is a patchwork of fabric stitched together. The ragged sail flaps forlornly in the slight breeze from a broken wood mast. Strewn across the raft are the sun-blackened bodies of men, women, and children. Their arms and legs are akimbo in grotesque contortions of death, the flesh peeling from their bodies, exposing white bones. Their eyes have been pecked out by marauding birds.\n\nIn a morning-bright kitchen, Joan at the stove hums cheerfully as she cooks breakfast. At the table, Luz watches her sixteen-year-old daughter, Carmen, brushing toucan-beak-orange-colored polish onto her fingers.\n\nLuz shakes her head at Carmen. \"Are you getting ready to go to school or to a nightclub?\"\n\nCarmen looks up, her long straight brown hair framing her face. She smiles. \"Mom, I'm getting straight A's.\"\n\nJoan turns from her pots and pans steaming on the stovetop and shoots Carmen a reassuring wink. \"That's right, honey, you keep trotting those A's home and you can paint your nails any color you want. How about painting each one a different color? Be bold.\"\n\nLuz loosens her stern gaze. \"Okay, I get it. A's equal painted fingernails. I'll go with that, but no lipstick. I don't want my girl wearing lipstick to school. It's not acceptable in this family.\"\n\nCarmen screws the cap onto the nail-polish bottle and picks up her textbooks from the table. She gets up and kisses Luz on the cheek. \"You win, Mom. No lipstick. I'm off.\"\n\n\"And no tricks. Don't put a ton of lipstick on when you get out of the house. Promise me.\"\n\nCarmen hugs Luz. \"Promise, Mom. Jeez, no lipstick.\"\n\nLuz watches Carmen leave, the door closing behind. She notices Carmen's plate of uneaten food on the table. \"Left without eating again. She's too skinny. Got to fatten her up on rice and beans and _ropa vieja_.\"\n\nJoan hands Luz a cup of coffee. \"Don't be so hard on her. She's a good girl.\"\n\n\"Carmen's goodness is not what worries me. It's the world out there around her that bothers me.\" Luz takes a sip of coffee. The wrinkled look of concern across her smooth face doesn't go away.\n\nJoan nudges her playfully. \"You were a wild teenager. Drove the boys crazy. You got knocked up when you were eighteen.\"\n\n\"Nineteen, and it wasn't boys, you know that, it was one guy. Twice he got me pregnant, I married him like a good Cuban girl\u2014you know the story.\"\n\n\"Sorry, hon, didn't mean to bring that up. We won't talk about him.\"\n\n\"No, we don't speak of the beast with no name. Story over.\"\n\n\"But look at you now. A pillar of society, an officer of the law, and a cute one at that.\" Joan strokes Luz's short black hair and sings with a throaty purr, \"In the jungle, the mighty jungle, my panther prowls for me.\"\n\nLuz tilts her head back; her worried expression fades as her brown eyes gaze up at Joan.\n\nJoan's hands caress Luz's arched neck. \"You want to fool around, panther?\"\n\n\"You know I can't on a workday.\"\n\nJoan leans over; her blond hair cascades around Luz as she whispers, \"We could fool around and fool around and fall in love.\"\n\n\"We are in love, my darling.\"\n\nJoan's fingers deftly open the top buttons of Luz's shirt; her hands slip onto Luz's exposed skin.\n\nLuz grips Joan's wrists, pulling Joan's hands away. Joan's jaw tightens; her lips draw into a tight line.\n\nLuz rebuttons her shirt and gazes with concern around the kitchen. \"Why isn't Nina here? Where's Nina?\"\n\n\"Don't be such a cop on the job all the time. Nina is fine. She wants to get herself ready for school. She needs to be independent.\"\n\nLuz shoves her chair away from the table and leaves. She walks quickly down a hallway and pushes open a bedroom door. She looks inside.\n\nNina sits in her wheelchair before a dresser with a large mirror. Her fourteen-year-old body is frail, her torso shrunken, her head bald from chemotherapy. She turns around to Luz, her large brown eyes still luminous. \"Mom, I'm glad you're here. I need your opinion.\"\n\n\"About what, baby?\"\n\nNina holds out two long wigs, one blond, one brunette. She studies the wigs critically. \"Who should I look like today? Marilyn Monroe or Cleopatra?\"\n\n\"Show me both wigs so I can judge.\"\n\nNina puts on the blond wig and purses her lips in a sophisticated pout. \"What about Marilyn? Am I as irresistible as her?\"\n\n\"Marilyn never looked so good. Maybe it's a bit too much for school\u2014but you look great.\"\n\nNina pulls off the blond wig and puts on the brunette. She gives a sassy stare. \"Am I as powerful as Cleo?\"\n\n\"Yes, you've definitely got the Queen Cleo vibe going.\"\n\n\"Mom, you can't be such a pushover and like both wigs. Help me. Which one?\"\n\nLuz steps close to Nina in the wheelchair. She picks up the blond wig and pulls it on over her cropped black hair. She stares at her reflection in the dresser mirror. The light-colored wig contrasts sharply with the darkness of her face. Luz mugs a sultry expression. \"Do you think I'm sexy?\"\n\n\"Mom, you're such a goof.\"\n\nLuz leaves the wig on. \"Come on, do you think I'm sexy?\"\n\n\"No. I think you're funny.\"\n\n\"I think I'm sexy.\"\n\nNina studies Luz in the blond wig. \"Okay, yes, you're crazy nutzoid sexy!\" Nina's frail body shakes with laughter.\n\nLuz pulls off the blond wig. \"Baby, I've got to go to work.\"\n\n\"Which wig should I wear, Mom?\"\n\nLuz wraps her arms around Nina and holds her tight, then strokes her smooth bald head. \"I want my girl as she already is. Shining more beautiful than Marilyn on the silver screen. Braver than Cleopatra on her war boat.\"\n\nFar out on the ocean, the recorded beat of salsa music ends inside the pilothouse of Noah's pirate-radio boat. He stops his dancing with an invisible partner. He sits back down on the worn chair in front of the makeshift broadcasting console.\n\nNoah speaks rapidly into the microphone. \"I still don't have any calls from my intrepid pilgrims out there. If you don't want to show me the rage, let's talk about the Powerboat Championship Race starting from Key West Harbor this morning. Those boats burn enough fuel in one race to fly a jumbo jet across the Atlantic. Hey, let's not sweat the carbon emissions. Let's disregard a monstrous guzzle of fossil fuel from the tit of Mother Earth when the scent of blood sport is in the air. Today, Key West's native-son racer, Dandy Randy, is set to break his own speed record of more than ninety miles an hour. Problem is, Randy went missing after yesterday's qualifying race. Where's Randy? Holed up in a poker parlor? Adrift in puke after a night of prowling sleazy bars? At the bottom of the sea, entangled in a net with dead turtles? What's up with Randy? What's up with the turtle slaughter? Sea turtles are being killed by gill nets and long hook-lines by the millions. Show me the rage!\"\n\nIn front of Noah, on the console's instrument panel, three cell phones are wired into battered wood speakers. A light flashes red on one of the phones, signaling an incoming call.\n\nNoah presses the answer button. \"I've reeled in my first caller. I hope you're a whopper.\"\n\nA male voice booms from the speakers. \"Hey, Truth Dog, I've been listening since you started your pirate-radio gig a year ago. You're so righteous to call out those macho joystick powerboat racers like Candy Bambi.\"\n\n\"Dandy Randy.\"\n\n\"Whatever. Were you around back in the eighties, when Key West was Dodge City on the Gulf Stream? Totally lawless time, cocaine smuggling and high jinks par _excellente_!\"\n\n\"I was getting my degree in environmental law up in Miami then, but Key West has always been a pirate island, stolen treasures off of wrecked ships lured by false lights onto the reef offshore, rumrunners, gunrunners, drug runners, any kind of contraband. What ruined your little paradise?\"\n\n\"Not the smuggling. It's that Key West isn't a fishing port anymore. The shrimpers and their boats were kicked out to put in seaside condos. Hordes of tourists driving down here on the Overseas Highway. Giant cruise ships spitting out thousands of passengers. It's the tourists who are killing the coral reef offshore of Key West.\"\n\n\"Now you're showing some rage. But tourists, you think they're killing America's only continental reef? You think they're killing a two-hundred-forty-million-year-old reef?\"\n\n\"Hell, yeah!\"\n\n\"No! Coral die-off is caused by the thermal stress of ocean warming. Added to this is the ocean dumping of toxic pesticides and chemicals. I want to expose the real culprits. I want to peel the lies off of their greedy hides, the same way the shark hunters used to knife-skin a shark with a one-bladed stroke. The reefs are the rain forests of the sea. Fifty percent of the Caribbean reefs are already dead because of warming, pollution, and net-fishing ships. Soon every coral reef on earth will be dead!\"\n\nNoah punches off the caller and clicks on another phone. \"I can't hear you, talk louder, there's static on the line.\"\n\nA belligerent voice echoes through the static. \"I want you to know, I'm a vet. I was in Vietnam.\"\n\n\"Is that supposed to be a cause for celebration or condemnation?\"\n\n\"Fuck you!\"\n\n\"Now that we've got that out of the way, I'm all ears.\"\n\n\"Perm... ian Ex... tinc... tion E... vent.\"\n\n\"Permian Extinction Event? What's that got to do with anything? Happened millions of years ago. A volcanic methane-gas explosion that wiped out nearly every living thing on our planet.\"\n\n\"It's also called the Great Dying. It's what you've been quackin' about and you don't even see the connection. It's comin' again.\"\n\n\"Okay, Nam vet, I'm on the edge of my seat. Shoot me facts.\"\n\n\"This time the explosion of obliteration will be man-made.\"\n\n\"What's the trigger? Nuclear war?\"\n\n\"It's comin' from beneath the boat you're floatin' on, from the seafloor of the Gulf of Mexico.\"\n\n\"And you say it's man-made. So I figure you must mean that\u2014\"\n\nA thundering boom comes from outside Noah's trawler. He looks through the window of the pilothouse. The radio-transmitter antenna bolted to the deck sways. The trawler rocks hard from side to side. Noah tries to keep the shaking electronic equipment on the broadcast console from falling. He catches his rum bottle as it tumbles from the table. He glances around, trying to figure out what happened. He looks down through the window and sees that a drifting raft has collided with his trawler.\n\nThe raft is filled with a jumble of dead bodies. From among the bodies a bone-thin teenaged boy, shirtless and barefoot, rises. His black skin is sun-blistered and riddled with lacerations. The whites of his startled eyes loom large as he stares up at Noah in the pilothouse.\n\nNoah yanks the ship-to-shore radio mike from its holder and shouts: \"Mayday! This is _Noah's Lark_! Mayday!\"\n\nA gray sixty-foot-long Coast Guard cutter tows the small wooden raft with dead bodies toward Key West Harbor. Noah follows the cutter in his trawler. The cutter slows to a stop. Noah motors alongside and shouts to a uniformed guardsman on the cutter's deck, \"What's the holdup?\"\n\nThe guardsman shouts down, \"Harbor's blocked, powerboat race starting, have to wait before going in.\"\n\nNoah cuts his engine. He sees around him an anchored flotilla of fancy yachts, paint-blistered skiffs, sleek ketches, and listing lobster boats crowded with beer-drinking revelers waiting for the spectacle to begin.\n\nFrom the harbor's distant shoreline a cannon booms, signaling the race start. Cheers go up from the anchored flotilla. A roar of jet-propelled engines vibrates the air. Twelve long-hulled powerboats emerge from the harbor entrance. The waterborne herd thunders at full throttle, their boldly painted hulls nosed high, sharp bows tilting six feet into the air, their rear exhausts blasting water up behind them. Deep within the cocooned cockpits bolts of sunlight reflect off the driver's and throttle-man's crash helmets. The boats race in front of Noah's trawler with an earsplitting engine snarl; white-hot jet exhausts plow a showering spray. Above the powerboats a TV news helicopter chases the action. From the copter's open doorway a cameraman leans out, filming the boats as they roar toward the ocean's distant horizon and over its edge.\n\nNoah's boat rocks in the watery wake left behind by the powerboats. The Coast Guard cutter's engines rev to a turbine whine. Noah follows the cutter towing the raft. Inside the harbor's anchorage, the cutter slows to a stop, and guardsmen secure it alongside a cement pier. Noah steers his boat around the cutter and ties up behind the raft. He watches through his pilothouse window as a crowd gathers on the pier, gawking at the sight of the raft with its cargo of bodies.\n\nAmong the crowd is Hogfish, straddling a rusty bicycle. From the back of his sun-faded fisherman's cap hangs a ragged swag of graying hair. IPhone earbuds are jammed into his ears. A tight T-shirt on his bony chest reads **DON'T KILL THE MESSENGER.** A queer grin spreads over his forty-year-old face, remarkable for its smooth, unlined quality. Only his bulging eyes, washed of all color and seeming to spin in opposite orbits, indicate a man burned out from battles fought in distant wars. Between the handlebars of his bicycle is stretched a fishing line, dangling with barbed J-hooks. He pushes the bicycle's front wheel against the taut rope mooring the raft to the dock.\n\nA bullnecked deputy detective with a slick sunburnt shaved head, Moxel, shoves through the crowd to Hogfish. A shiny badge is pinned to his crisp blue uniform shirt. His lips carry the arrogant expression of a young man barging through life based on a combination of brute force and triumph over his low social origins. He grips the handlebars of Hogfish's bicycle above the line of dangling fishhooks and snarls in a Southern accent: \"Get away from that rope. This is a crime scene.\"\n\nHogfish's head bobs to the clash of heavy-metal guitars playing through his old-model iPhone's earbuds. He pushes his front bicycle wheel harder against the rope to get a closer look at the grotesque scene in the raft.\n\nMoxel tightens his fists on the handlebars of Hogfish's bicycle. \"I'm talking to you! Back off! Didn't you hear me? Take out your goddamn earplugs!\" Hogfish's head keeps bobbing.\n\nLuz, dressed in her dark pants and guayabera shirt, steps quickly through the crowd and grabs the scraggly ponytail hanging from behind Hogfish's fishing cap. The muscles in her arm tighten as she tugs the ponytail, pulling him away from the rope. She leans into his face and shouts, _\"Dios da sombrero a quien no tiene cabeza!\"_\n\nMoxel elbows Luz and sneers. \"What the hell does that mean?\"\n\n\"God gives hats to some who have no head.\"\n\n\"Why not just say it in English? Your kind are always trying to make this a Spanish-speaking country.\"\n\nLuz ignores Moxel and steps to a guardsman protecting the raft with a rifle clutched in his hands. The guardsman nervously holds up the rifle, blocking Luz. \"Ma'am, you'll have to stay on the other side of the rope. This is official Coast Guard business. No one goes on the raft.\"\n\nLuz pulls out her wallet, flips it open, and flashes her silver badge. \"I'm Detective Luz Zamora, Key West Homicide. This dock is city property. I've got jurisdiction here, not the Coast Guard. I'm boarding the raft.\"\n\nThe guardsman looks at the badge and stands aside. \"Yes, ma'am!\"\n\nLuz steps over the rope onto the edge of the concrete bulwark. She winces at the rotting stench drifting up from the bloated bodies. She jumps down onto the raft and moves quickly among the jumble of dead people, feeling the wrists of stiffened arms for a pulse.\n\nA siren wails from the dock. The crowd parts for the arriving ambulance. The side door swings open; a paramedic hurries out. He jumps onto the raft and shouts at Luz above the still-wailing siren, \"Is anyone alive?\"\n\nLuz turns to the paramedic. \"No one. All dead.\"\n\nThe medic gazes in astonishment at the bodies on the raft. He looks back at Luz. \"Must be hard for you, seeing your people end up this way.\"\n\n\"What do you mean, my people?\"\n\n\"You're Cuban. These are Cuban boat people.\"\n\n\"These people aren't Cubans, they're Haitians. But that doesn't make it less horrifying.\"\n\nLuz looks away from the bodies. She sees Noah on the fly deck of his trawler, docked next to the raft. She calls over to him, \"What do you know about this?\"\n\nNoah shouts back, \"The raft was adrift, banged into my boat. I called in the Mayday.\"\n\nNoah turns from Luz and goes back into his pilothouse. He grabs his bottle of rum off the console table. He walks over to a canvas curtain covering a storage closet in the corner. He pulls the curtain back, exposing the teenaged survivor from the raft. The boy appears terrified. Noah speaks softly in French: \"Don't worry, I'll protect you. We've got to keep you hidden. If they find you, they'll send your sorry ass back to Haiti.\" He drinks rum from his bottle and looks sympathetically at the trembling boy. \"Kid, you crossed seven hundred miles of shark-infested ocean to escape an earthquake-racked country of poverty, disease, and violence. Now you've got to do the hardest thing, you've got to trust me.\"\n\nThe boy mumbles in French, \"My... name... is Rimbaud.\"\n\nNoah responds in French. \"What's the family name?\"\n\n\"Mesrine.\"\n\nNoah guzzles down the last of the rum and fixes the boy with a glassy-eyed philosophical expression. \"Rimbaud Mesrine, damnedest thing. They named you after a famous gunrunning poet and a famous cold-blooded killer. They must have figured you were going to become a French politician.\"\n\nNoah turns and looks down through the salt-streaked window of the pilothouse. He sees Luz on the raft moving among the dead bodies and speaks to her in words he knows she can't hear:\n\n\"Slaves and masters. Fucked up as it ever was.\"\n\nFive miles out to sea from Key West, the twelve powerboats roar across the ocean's surface at ninety miles an hour. The TV news helicopter overhead chases the boats as they make a turn around a large channel marker. They speed away from the floating buoy. The copter hovers over it. The side door of the copter slides open, and a cameraman looks down, shocked at what he sees, almost losing his grip on the heavy camera as he shouts back at the pilot. \"Damn! It's what I thought! Can't believe it!\"\n\nThe copter's blades whip the air as the cameraman leans perilously out from the doorway. He aims his lens down and films the naked body of a dead man tied by rope to the buoy's metal pole.\n\nThe downward force of wind from the copter's blades above the body creates a churning circle in the water around the buoy. The copter pulls up and banks away. The buoy rocks in the watery wake left behind. The mutilated body tied to the pole sways beneath a relentless sun.\n\nThe Bounty Bar faces the boat-filled Key West Harbor. The walls are hung with an array of seafaring artifacts, big-game fishing rods and reels and colorful mounted trophy fish caught in their plasticized death leaps. The humid air moves in a rush from ceiling fans spinning over the heads of sport fishermen, shrimpers, real-estate hustlers, deadbeats, lushes, lowlifes, and wide-eyed tourists wearing floral-print shirts.\n\nCommanding the scene from behind the long mahogany bar counter is Zoe. She emanates an effortless sophisticated beauty cut by a savvy aura of understanding the world of men. She moves quickly, with the calculated feline grace of knowing her ability to land securely no matter what situation she is thrown into. She pulls two bottles of beer up from the icy water of the large bright-red cooler and bangs them down on the counter in front of two Bounty Bar regulars, Big Conch and Hard Puppy.\n\nBig Conch's cocked-up stature comes from the years when he outran Coast Guard cutters in his cocaine-packed cigarette boat across low-tide coral inlets. His face registers the righteousness of an outlaw who cashed out of his scam before being busted and left to rot in a federal slammer. His gray hair is dyed an unnatural blond hue and is slicked back flat against his scalp. Around Big's neck dangles the circular gold weight of Spanish medallions. His blue-eyed stare is that of a thug feigning a legit life in a new world of real-estate pimps and condo hustlers. He grabs the beer bottle in front of him and ham-fists it to his lips, sucking out the foaming brew.\n\nNext to Big, Hard Puppy takes a slow, cool drink from his bottle. Hard is descended from a line of black Bahamian freemen who were once the property of British Caribbean overlords. He is outfitted in a flashy white silk suit and white alligator shoes, befitting his position as the number-one cash kingpin of illegal dogfighting from Key West to Miami. Around Hard floats in the air the lime scent of aftershave lotion that he slaps onto his sharp-featured face every day to keep away the scent of poverty he grew up with and that he always smells: the stink of unchanged shit in diapers and a drunk stepfather snoring on top of his puked-out, passed-out mother.\n\nHard and Big straighten up on their stools to get a better view of Zoe behind the bar. They admire her long tanned legs captured by tight white shorts and, above that, a thin strategic halter top offering the right amount of provocative glimpse of her breasts.\n\nBig glances at his gold Rolex as if time is running out, then looks back at Zoe and rattles off at her: \"After your divorce is final from Noah, you're gonna marry me. I'll be richer than original sin itself when my resort is completed. Bank on that, girl. Big will have you farting through silk panties for the rest of your gorgeous life.\"\n\nZoe plants her elbows on the bar in front of Big; she leans her chin into her cupped hands and defiantly nails Big's blue eyes with her own big blue eyes. \"Everyone knows your Neptune Bay Resort is illegal. You bulldozed tidal lands before the environmental study came in. The ecologists stopped you. You'll be lucky if they don't hang you from an endangered gumbo-limbo tree before you make your first dime.\"\n\nHard Puppy snorts his approval of Zoe's put-down of Big. His platinum-encased teeth shine as he speaks with a singsong Caribbean twang. \"Baby doll, you don't have to be marryin' me for my monies. Just be givin' me one hot honey night and we be doin' the nasty black and white, then Hard's fortune be yours.\"\n\nZoe spins around from Hard and Big. Her attention goes to a large television behind the bar. On the screen, a basketball game cuts away to a breaking news story. A headline scrolls across the screen, **MURDER AT THE RACE ,** followed by a video shot from a helicopter of a race-marker buoy floating at sea. Tied to the pole of the buoy is the blurred image of a man's body. Everyone in the bar stops talking and turns toward the television just as the blurred image of the dead body flashes off the screen and is replaced with **DANDY RANDY FOUND DEAD. WE RESUME REGULAR BROADCAST.**\n\nBig jumps from his stool and jabs his finger at the television. \"That was my Neptune Bay partner tied to that buoy! What the hell happened?\"\n\nHard sneers. \"Randy be gone, good riddance. He grew up on this island sellin' bad fish to navy wives. In the end he be tryin' to sell overpriced resort condos to retired military and New York divorc\u00e9es. Fuck that. His white ass be fish bait now.\"\n\nBig swings around with doubled-up fists. He takes aim to punch out Hard's mouthful of metallic teeth as a wiry woman, Pat, steps in front of him. Pat wears rubber shrimper boots, blue jeans, and a tight T-shirt. She pulls up onto the stool vacated by Big. Wrapped around the bare skin of her left arm are purple tattooed tentacles of a one-eyed octopus. She nails Hard with a mocking smirk. \"Don't be mean about dearly departed Dandy Randy. Show him some respect. That's not any way to talk about your brother.\"\n\nHard spews out a mouthful of foaming spit. \"Dandy don't be my brother! Dandy be a white cracker boy. My mama never let no rooster wearin' white socks in her back door. No white chickens be in her yard.\"\n\nPat laughs at Hard. \"Your mama should've ate whatever rooster was your daddy for giving her a big load of crap like you to haul.\"\n\nZoe pops open a bottle of beer and slides it across the bar counter. \"Here you go, Pat, this one's on the house. Let's keep the peace.\"\n\nPat grabs the bottle and swigs the beer. She smacks the bottle back down and stares at Hard.\n\nHard's angry glare turns into a smile of glinting teeth. \"Pat, you be a mean son-of-a-bitch. You should quit shrimpin' and come workin' for me. I could use a scrapper like you.\"\n\nPat swipes beer from her sun-hardened lips. \"You want me to give up being captain of my own shrimping boat to rig dogfights for you?\"\n\n\"I be no dogfight gamer. That be a white-devil lie. I be a peaceful man, not like you. Word is you be the number-one killer of leatherback turtles in the Florida Keys.\"\n\n\"Yeah, Chinese dudes pay a fortune for leatherbacks. They believe leatherbacks can cure everything from cancer to limp dick.\"\n\nHard smirks. \"Who you be accusin' of limp dick? Nothin' between your legs but eight inches of strap-on stiff rubber.\"\n\nZoe leans in between Pat and Hard. She beams Pat a friendly heads-up. \"Honey, you should use turtle excluders on your shrimp nets. If you're caught slaughtering endangered turtles, they'll lock you up and throw the key away.\"\n\nPat shakes her head defiantly from side to side. \"I got a right to fish anything from the sea. No one can stop me. No feds, no man, no woman. Not even a woman as sexy as you, Zoe, Miss Show My Cute White Ass in Shorts to All the Customers When I'm Bending Over to Get the Beer.\"\n\nBig Conch's eyes go to the television, where the basketball players on the screen are replaced by the image of Luz being interviewed by a reporter. Behind Luz is the Haitian raft filled with dead bodies. Big shouts at Zoe. \"Turn the goddamned TV up, for Christ's sakes!\"\n\nZoe raises the volume. Luz's steady professional voice fills the room: \"They died from hunger and exposure. No indication of foul play. Just a horrendous end for desperate people.\"\n\nPat whistles and calls out to Luz on the screen. \"Look at you! You're a gorgeous star. They should put you in a Hollywood movie. You could be the warden in a woman's prison.\"\n\nZoe pushes a firm finger against Pat's lips. \"Quiet. Let's hear what Luz is saying.\"\n\nHard bangs his beer bottle on the counter. \"Luz be one black sister can't be trusted. I hate cops, 'specially colored cops. Be bad for business.\"\n\nThe outside door to the bar slams open. In the doorway is Hogfish, backlit by a shaft of sunlight. His iPhone earbuds are clamped into his ears. He looks wild-eyed from beneath his long-billed fisherman's cap and screams in panic: \"This world is rigged for hurricanes! El Finito's coming! I see the eye of his category-five hurricane winking offshore! Monster of destruction blowing two-hundred-mile-an-hour winds and pushing a fifty-foot-high storm surge before it! I'm the best fishing guide on this island, I read the weather. The ocean's currents spell out the future to me! I see the ocean's truth with my own eyes!\"\n\nBig stomps his feet on the floor and shouts back at Hogfish. \"You're no fishing guide anymore! You can't find your own pecker to take a piss, let alone find yourself a fish to hook.\" Big grabs his beer bottle and hurls it at Hogfish.\n\nThe bottle flies by Hogfish's head, hitting the wall behind in a shatter of spraying glass. He ignores the shards around him, his head bobbing to music pumping through the earbuds. He lurches violently, seemingly caught by a great wind. He staggers, regains his footing, stands alone in the center of the room, with everyone fixed on his screaming rant.\n\n\"Like the baby Jesus grown into a righteous monster, El Finito will shut your mouths and open your minds! You don't need satellite photos to see him coming! Finito is speeding here to punch your lights out! Punch your teeth down your throat! Punch your civilization down the drain!\"\n\nAlong one of the many deep-water canals running in from the Gulf of Mexico side of Key West and crisscrossing the island stands Noah's nautical-deco-style house. The 1930s structure is long past its glory days, the paint of its once-sleek exterior spider-cracked and peeling. In the hazy humid atmosphere of the setting sun, the rounded walls and porthole windows give the appearance of a formerly glamorous yacht now forsaken and stranded on land.\n\nInside the sparse living room, a few pieces of worn-out dull-yellow bamboo furniture are scattered around, and piles of dusty hardcover law books and tattered paperbacks are stacked along the walls. Noah sits at a lone bamboo table, listening to the chorus of frogs outside croaking anxiously for night to fall. He takes a drink from his rum bottle and stares pensively through the open window, across a parched grassy expanse, at the still water of the canal. A fish leaps from the flat surface. It snaps into its gaping mouth an unlucky flying insect, then splashes from sight back into the depths of the canal.\n\nBehind Noah, in the rose glow of dusk, Zoe quietly walks in. She sits across from him at the table and watches him drink. The sound of frogs outside grows more insistent, at odds with the measured tone of Zoe's words: \"I need you to sign the divorce papers in two weeks. Don't play any tricks.\"\n\nA nervous twitch crosses Noah's face. He takes another drink. He holds the liquor in his mouth, feeling its sting before swallowing. His throat is tight as his words come out with a cut: \"What's the hurry? We haven't been living together for a year.\"\n\n\"You haven't been living for a year.\"\n\n\"Depends on what you call living.\"\n\n\"You're either drunk or out there on your boat, ranting on the radio.\"\n\n\"I'm not an alcoholic. If a man drinks himself into oblivion, it means he doesn't want to see the sun rise the next morning. I still want to see the sun rise.\"\n\n\"You haven't obliterated yourself\u2014yet\u2014but you've given up. You used to be a damn fine lawyer.\"\n\n\"I didn't give up, sweetheart. I was disbarred.\"\n\n\"What did you expect? You went ballistic in the courtroom.\"\n\n\"I was prosecuting corporate bastards drilling illegal wells in protected tidelands. Toxic sludge killing off wildlife. Politicians paid off. Nobody had the guts to stand up against them. Masters and slaves, same as it ever was. At least one day, in one courtroom, before the judge let the criminals off, I could expose them. You know what I always say: speaking the truth will set you on fire.\"\n\n\"I know the story by heart.\"\n\n\"Then don't come in here and lecture me, saying I gave up.\"\n\n\"I don't buy into your excuse of indignation. You didn't have to storm out of the courtroom.\"\n\n\"You didn't have to walk out of the marriage.\"\n\n\"I only walked out when you started drowning yourself in a sea of booze.\"\n\n\"A man who does not enter the sea will not be drowned by the sea, right? Don't worry about me\u2014I'm a good swimmer.\"\n\n\"Nobody is that good of a swimmer.\"\n\n\"What do you want me to say, Zoe? The usual muck: 'Hi, I'm Noah, I'm an alcoholic'? Well, this boy won't play that shtick, because it's really a stick with one sharp end and the other end covered in shit. I will stand up and shout: 'I'm Noah and I fucked up and I don't want sympathy, antipathy, hallelujahs, or condemnations. It is what it is, between a man and himself, a void to swim in until it's a win-or-lose.' \"\n\nZoe pulls the bottle from his hand. She slips the gold wedding ring from her finger and drops it into the empty bottle. The ring falls to the glass bottom with a clink. She hands the bottle back to Noah. \"Congratulations, now you're married to it.\"\n\n\"And you've finally got what you want: you're free to date the Big Conchs of this world. That's why you still run a bar, so guys like Big can get drunk and hit on you?\"\n\nZoe bites down on her lip, trying to suppress her fury, but she cannot. \"That's disgusting. You know good and well that I got into the bar business years ago only to support you through law school. Why do you try to hurt me like this?\"\n\nNoah picks up a cork from the tabletop. He pounds the cork tightly into the bottle's neck. He holds the bottle up and shakes it. The gold ring trapped inside rattles. He stares through the glass at the ring. \"Haitian rum. There's a prize in each and every bottle.\" He shifts his intense gaze onto Zoe. \"You are still my prize. My dazzling angelfish, my resplendent butterfly fish, my gorgeous queen triggerfish.\"\n\nZoe pushes up from the table. \"I'm nobody's fish. Stay here and drown in the drunken sea of self-pity you've created for yourself.\" She walks out.\n\nNoah does not move; he sits alone in the stillness. Through the open window from outside, the sickly sweet scent of night-blooming jasmine drifts in. The blood in his veins hums with the sugar rush of rum. On a moisture-slick wall, he watches a gecko make its slow, paranoid way until it senses him watching. The gecko's ghostly-pale color flushes to a bright bold green; the blow bulge under its chin balloons into pulsating crimson. It pumps up on its short legs and puffs its three-inch lizard body into what it thinks is an intimidating size that will back Noah down from any hostile intentions.\n\nNoah raises the empty rum bottle with the ring in it and salutes the gecko. \"That's right, buddy, you're the man. You are the man. Don't ever forget it.\"\n\nEighteen miles up from Key West, on distant Sugarloaf Key, an eighty-foot-high pyramid-shaped wooden tower looms at the dead end of a gravel road. The moon's glow reveals that the tower is surrounded by a putrid mangrove swamp of twisted trunks and gnarly branches. From the swamp's brackish green water emerges what appears to be a human skeleton. The skeleton is a person totally encased in a full-body black rubber suit stretched tight and painted with luminescent white skeleton bones. A rubber skull mask covers the face and head. The skeleton rises out of the dark water onto the hard gravel road. A coiled rope is slung over its shoulder. The skeleton peers out from deep black eye sockets to see if anyone is watching. It reaches back down and hefts from the swamp's mud-suck of water a heavy object wrapped and tied in a canvas tarpaulin. The skeleton slowly moves along the road, the gravel crunching beneath its rubber feet as it drags the heavy object behind. The skeleton stops and bends its head back, its skull face staring up to the top of the tower's point.\n\nIn the blue light of a full moon, the skeleton continues dragging the object toward the tower.\n\nSharp morning sunlight glares off the pyramid-shaped wood tower surrounded by mangrove swamp. A tour bus travels on the gravel road leading to the tower. The bus's high black rubber tires kick up a cloud of white dust. The bus rolls to a stop in front of the tower. The side of the bus is painted with bright green words: **FLORIDA KEYS ECO-AWARE.**\n\nEcotourists step out of the vehicle with eager purpose. Slung around the necks of the men and women are binoculars and cameras. They wear fashionable shorts and green T-shirts emblazoned with **DON'T FOOL WITH MOTHER NATURE.** They aim their cameras at the wooden pyramid tower.\n\nThe last person out of the bus is a tour guide with a tight expression of righteousness etched on her youthful face. She motions for the group to gather around her. The tourists snap to attention at her words. \"Many years ago, a real-estate tycoon had a grand scheme. He wanted to drain this mangrove swamp and build a city here. But first he had to eradicate the mosquito population that swarms by the billions from this swamp. So the clever developer built this eighty-foot-high wooden tower to house thousands of bats. The plan was that at night the bats would fly out from the tower to eat the mosquitoes. It seemed like a good idea at the time, an army of bats gobbling up bloodthirsty mosquitoes.\"\n\nThe ecotourists groan their disapproval of the developer's scheme.\n\nA thin young man wearing a green silk bandanna tight around his forehead speaks up. \"Are the bats still inside? I'd just like to\u2014\"\n\nA ruddy-faced Australian cuts off the question with his thick accent. \"Hell, mate, if the bats are inside, all the bloody buggers will be hanging upside down asleep. Maybe Count Dracula is in there with them. Spoookyyy.\"\n\nThe thin young man looks nervously at the tower. \"That's not funny, dude!\"\n\nThe guide raises her hand for quiet and continues her story. \"The developer's grandiose mosquito-eating scheme didn't work. The bats flew away and never returned. The guy went belly-up, lost all his money, and slunk back to where he came from.\"\n\nThe ecotourists give a congratulatory cheer.\n\nThe Australian chimes in. \"Bloody hell, that served the greedy grubber right.\"\n\nThe guide looks out across the surrounding fetid mangrove swamp of tangled tree trunks and branches. \"The Florida Keys are a one-of-a-kind unique and fragile environment which we all must respect and protect. What is the lesson that I've been teaching you on this tour?\"\n\nThe ecotourists chant in unison: \"Don't fool with Mother Nature or Mother Nature will fool with you!\"\n\nThe guide beams her approval. \"Let this tower stand as a living lesson to all those who want to come to our paradise and try to rip it off.\"\n\nThe ecotourists pump their fists, shouting, \"Don't fool with Mother Nature!\"\n\n\"Good. Now, let's take a closer look at this tower and witness one man's folly.\" The guide leads the group across the crunchy gravel road. She stops beneath the tower's base of massive wooden support struts. She beckons the tourists to gather around. \"At one time this was the highest structure in the Florida Keys between Miami and Key West. The tower could be seen by passing ships from miles out at sea. Take a look up and see how high this is\u2014quite a feat.\"\n\nThe ecotourists bend their heads back and look up inside the soaring shaft. In a stunned moment of silence, their eyes widen as they are transfixed by the vision they see in the clammy darkness far above, at the tower's point. Their sudden shouts and screams echo up the shaft in panicked horror. They turn and run between the tower's massive support struts and back onto the road. They attempt to knock one another out of the way as they scramble toward the bus. The thin man with the tight green bandanna is pushed aside and falls onto the road; the gravel cuts into his knees, drawing blood. The tour guide yanks him up by the arm. He looks back toward the tower and his body shakes violently. A spray of vomit shoots from his mouth and splatters at the tour guide's feet. The guide tightens her grip on the wobbling man's arm and runs with him toward the bus, where the others are cowering in their seats.\n\nLuz steers her white Dodge Charger down the skinny slot of Olivia Street. The street is crowded on both sides with century-old Cuban cigar-makers' shacks, built when Key West was the cigar-producing capital of the world, rolling out a million smokes a year. None of the shacks retain their original bare-board anonymity, having been painted by affluent new owners to a pastel prettiness. Gone are the generations of Cubans who once stood on the porches calling out hot gossip to neighbors in hot weather. The humid air no longer carries the garlic scent of sizzling shrimp and the sweet aroma of Cuban bread. The white fences in front of the shacks have been trimmed of their overgrown red bougainvillea and riotous yellow allamanda blossoms. Everything is prim and calm, like a street in a proper New England port town, not the boisterous place where Luz grew up.\n\nLuz turns her car at the corner of Olivia onto wide Duval Street. She parks in front of one of the last Cuban expresso- _buche_ shops on the island not retrofitted into a trendy franchise coffee palace. The shop is a nondescript narrow storefront with a slotted hole cut in a cement wall to pass the coffee through. Luz gets out of her car and orders her third _buche_ double of the morning. She watches through the slotted hole as a broad-butted Cuban woman dressed in tight blue jeans works at the sputtering and hissing nozzle of a monstrous old burnished expresso machine. The woman turns with a triumphant smile and presents a cup of steaming _buche_ to Luz, who cradles it in her hand.\n\nSipping her hot caffeine nectar in the sun's morning glare, Luz keeps her eyes on the Duval Street activity from behind her sunglasses. Packs of excited vacationers in shorts and flip-flops hurry by on the sidewalk, darting into gift shops, trying on T-shirts with tropical scenes silk-screened on them, and buying Key West's two most famous postcard photos, the mile-zero sign at the end of Highway 1, and the tall bullet-shaped concrete monument at the Atlantic's edge declaring **SOUTHERNMOST POINT CONTINENTAL U.S.A.\u201490 MILES TO CUBA.**\n\nFrom the open window of Luz's car, parked at the curb, a police dispatcher's radio voice drones. Luz takes another sip of _buche_ as she listens to the bored voice announcing bicycle thefts, lost dogs, and jaywalkers. The voice is suddenly drowned out by the roar of a motorcycle. She turns to see Pat on her Harley-D jump the curb behind the Charger and come to a tire-burning stop on the sidewalk, scattering the startled tourists.\n\nLuz eyes Pat with mock discipline. \"I could arrest you for that stunt.\"\n\nPat tightens her grip on the Harley's chrome handlebars. She fixes Luz with a bold stare. \"Oh, I want to be arrested. That's my dream, one night locked up with you. I'll lick all the brown sugar out of your bowl. You should jilt your girlfriend, Joan. Hop on my bike. We'll never look back.\"\n\nLuz swallows her coffee. \"You still poaching endangered turtles?\"\n\nPat flexes the muscles of her bare arm with the octopus tattoo, bulking up the one-eyed creature's nasty-looking tentacles. \"No one will ever catch me. But, hey, you can catch that ecofreak brother of Joan's. He's broadcasting illegally over the radio.\"\n\n\"Noah broadcasts from outside the city limits. I don't have jurisdiction on the ocean. That's for the feds.\"\n\n\"I hope his pissy pirate boat sinks in the middle of a shit slick dumped from a thousand crappers off a cruise ship.\"\n\nPat gazes over at the gleaming white Charger SRT8, taking in its arched rear-end cobra-wing spoiler and the black front grille open-jawed like an onrushing land shark.\n\nShe grins. \"You got yourself some unmarked cop car, tricked out like a Cuban Miami pimp-mobile. I know there's a siren embedded in that grille, and red strobe-lights under those halogen headbeams that you can switch on from inside. How come you got all the flash, when most of Key West's dumb-dicks poke around in stupid Ford Victorias?\"\n\nLuz grins back. \"I have this rocket because I'll need it to go a quarter of a mile in twelve seconds when I'm coming to bust your ass.\"\n\n\"Like I said, no one can catch me.\"\n\nLuz shakes her head and looks long at Pat. _\"No hay rosas sin espinas.\"_\n\n\"Huh? I don't _habla_ the Es-span-yolla. What are you saying?\"\n\n\"There are no roses without thorns.\"\n\nPat twists her Harley's throttle in a rev and shouts above the engine's loud growl, \"I'll take that as a compliment. Whenever you get tired of your blond bunny, you come running to me. I'm the only real rose in the garden. With me you get the prick of the thorns and not just the flower's soft petal. Life on the edge. It's your choice, brown sugar.\" Pat roars off.\n\nFrom Luz's police radio, the droning dispatcher's voice suddenly crackles with urgency. \"Code five at Sugarloaf Key Bat Tower! All Alpha units respond!\"\n\nLuz gulps her coffee and starts her car. She switches on her outside flashing red lights and siren and speeds away.\n\nLuz skids to a stop in front of the pyramid-shaped bat tower. Behind her, Deputy Detective Moxel pulls up in his late-model Ford Victoria police car. They both cut their engines and jump out.\n\nMoxel cocks a hand above his eyes to block the sunlight glaring off the tower as he surveys the situation. He puts on his sunglasses. \"I don't see anything going on\u2014place is deserted. Why'd they radio an urgent homicide dispatch? We're even out of Key West jurisdiction up here.\"\n\nLuz doesn't answer; she hurries toward the tower. Moxel follows with a scowl. They both step under the massive wooden support struts of the tower's broad base. Luz looks up into the shadowy interior of the ascending wooden shaft and points. \"There's our customer.\"\n\nMoxel pushes in close to Luz and stares up. At the top of the pyramid's narrowing peak hangs a human body. He grabs Luz's arm and pulls her away. \"Let's get out of here and call for backup.\"\n\nLuz shakes loose from Moxel. She grips the first slat of a ladder fixed to the side of the tower. \"I'm going up.\" She starts climbing the ladder, hand over hand, pulling herself into the higher reaches.\n\nMoxel watches Luz climbing farther away and shouts: \"You crazy? Could be somebody's baiting a trap with that body. I said we should call for backup.\"\n\nLuz stops climbing. In the stifling air of the narrow shaft, she wipes sweat from her forehead. She looks back at Moxel below. He seems distant and insignificant. She pulls her pistol out of its holster. She continues climbing into even hotter air. Buzzing flies whiz around her. She waves her pistol at the oncoming flies, and the sudden shift of her body weight puts pressure on the supporting wood slat of the ladder beneath her feet. The slat gives way and tears out with a creaking rip. Luz drops her gun and grabs the slat above her with both hands. She hangs suspended in the air, her legs swinging beneath her. She looks at the slat above that she is hanging on to; the rusty nails securing it begin slowly pulling out.\n\nThe sound of Moxel's angry voice rises through the shaft. \"Goddamn, I told you to wait. Hold on, I'm coming.\"\n\nLuz looks down as Moxel makes his way up the ladder. He carefully climbs from one wood slat to the next until he reaches her.\n\nMoxel grabs Luz's dangling legs. \"I've got you. Let your weight shift onto me. I'm a strong guy, I'll get you down.\"\n\n\"No. I'm going up.\"\n\n\"You can't. This is a trap. Somebody loosened the nails on these slats to kill anyone trying to get to the body.\"\n\n\"Keep your grip on my legs and push me up so I can grab on to the next slat.\"\n\n\"I can't do that. Our combined weight will rip out the slats and we'll fall.\"\n\nLuz's brown eyes narrow into severe slits. She speaks in a guttural growl. \"That's an order, goddamn it. Boost me up!\"\n\nMoxel tightens his hold around Luz's legs. \"Okay, but you're going to kill us both.\" He grunts and boosts her.\n\nLuz grabs on to the next slat, pulling the weight of her body higher until she is able to gain a foothold on the lower slat.\n\nMoxel calls after her, \"You don't have a gun.\"\n\nLuz looks back down. \"Stay where you are and keep me covered.\"\n\nMoxel pulls his gun from its holster and aims it up.\n\nLuz keeps climbing until she reaches just below the pointed peak of the tower; she stops. She tries not to inhale the overwhelming stench suddenly engulfing her. From the crossbeam rafter above swings the naked body of a man hung by a rope noosed around his neck. The man's face is a puffed-up purple blotch. Slimy maggots worm out from the orbs of his chalk-white eyes. His ears have been cut off. His pale lips are sewn shut with fishing line. The pallid skin of his body is spotted with green flies sucking at caked flecks of blood. A steel spear is pierced through the man's chest and out his back. A red **X** is slashed on the skin of his stomach.\n\nThick brown hard roots of towering Spanish laurel trees heave up the sidewalk ahead of Noah in an uneven roll of cracked cement. The sidewalk glimmers in the morning mist coming in from the sea. He follows the sidewalk with the deliberate movements of a rum-soaked man overcompensating for his off-balance gait, as if he was on an invisible surfboard riding a serpentine wave. Ahead of him, the massive leathery trunk of another Spanish laurel has not only cracked the sidewalk but completely lifted and shattered the cement-covered ground in its mighty thrust skyward, throwing dark limbs out to block the sun. From the tree's overhead branches, tendrils of airborne roots cascade back to earth, forming a roped curtain that swings in front of Noah. He pushes through the dripping curtain of vegetation. A three-story tropical mansion of imposing white clapboard comes into view. The mansion is the last of the many that were built in the nineteenth century, when the island was the wealthiest place in America, a bustling port for merchant clipper ships. The ships, loaded with silk, gold, lace, and pewter, had sailed down the Florida Strait, then hugged the narrow channel along the jagged reef and put into Key West's safe harbor at the mouth of the Gulf of Mexico. The mansion, built by a mercantile-marine millionaire, has been battered and besieged by storms, its wood shutters slammed and splintered by high winds. The elaborately carved spindles of the second-story balcony circling the exterior have been shrunk by the sun and snapped in half. The tin-stamped roofs of the cupolas rising above the second story on all four corners are rusted through; past rains have entered and begun the process of a rotting collapse.\n\nNoah weaves up to the front of the decaying structure through a spectacular riot of overgrown exotic fauna. At the entrance stand two tall faux-Roman columns, their white plaster surfaces crumbling and chipped. He walks between the columns, pushing through more entangled vines onto a dilapidated, termite-decimated porch. The stained-glass fanlight window above the weather-beaten mahogany door is spider-webbed with cracks, threatening to shatter and crash down. The door is slightly ajar. Noah pushes it open and enters a cavernous foyer. He is surrounded by overstuffed chairs and sofas shrouded in musty dust-covered sheets. From the center of the room, a circular staircase ascends, its lustrous pecan-wood steps now buffed to a dusty dung color. He climbs the rickety staircase, which is only one loose board away from collapsing.\n\nAt the top of the staircase, Noah stops and waits for a moment, then walks down a long hallway lined by dark cypress wood. At the end of the hallway, tall arched windows are open to the sea. He looks through an open doorway into a bedroom. He sees Lareck, a once-formidable and celebrated painter now ancient and, like his mansion, barely resembling past glories. Lareck reclines in his pajamas on top of the rumpled sheets of a bed, a large sketchpad propped up on his knees. He dips a brush into the open box of watercolors next to him and paints in quick, intuitive flourishes on the pad.\n\nFacing Lareck, from across the room in front of an expansive bay window, is Zoe, caught by a shaft of vivid sunshine. The light dapples off her high-boned cheeks. She wears a strapless white dress, exposing the tan of her smooth bare shoulders and long legs.\n\nLareck continues his painting of Zoe as he speaks with a rolling Southern twang; his voice rises and falls in a rush of smoothed-off syllables that nearly become a high-pitched whine. \"My dear muse and inspiration, loosen those lips. I don't want you looking like Whistler's sour-puss mother.\"\n\nZoe licks her lips, shifts her weight, and moves slightly. \"Is this better?\"\n\n\"That's it. Turn to the right. I want more light on you. Your skin shines with promise. A lifetime of painting, and I still chase the promise.\"\n\nZoe turns to a sharper profile angle in the shaft of sunlight. \"Like this?\" The light fires up her blond hair in a golden halo.\n\nLareck pushes up on his bed pillows for a better view. \"Perfect. You're a pensive Botticelli Madonna gazing out over the Arno River in Florence. You have, my dear, the dreamy gleam of the sassy saints that the Renaissance boys fell over each other trying to capture.\"\n\nHe bends his head toward the pad and paints furiously with aggressive strokes. He puts the brush down, overcome by his creation. He takes a deep breath and sighs, rubs his eyes, and looks around. He glimpses Noah standing outside the open door in the hallway. His voice mellows in a warm greeting. \"Noah, come in and sit with me.\"\n\nNoah enters and sits in a wicker chair with chipped white paint. He is mesmerized by Zoe illuminated in tropical light streaming through the window. She shifts her body nervously at being so close to him. He looks back at Lareck. \"Sorry to interrupt. I forgot you have your painting session with Zoe on Wednesday afternoons.\"\n\nLareck nods, picks up his brush, and continues his strokes on the large pad. \"She's the beautiful daughter I never had. But I've got to paint fast\u2014beauty doesn't last forever.\"\n\nZoe gives Lareck a pert, ironic smile. \"And you aren't lasting forever. So hurry up, this is a hard pose to hold. I'm getting a muscle pull in my left calf.\"\n\nNoah looks back at Zoe. \"As a poet said, nothing lasts forever, not beauty, not marriage, not even eternal love. But I'm still holding out for you on the eternal love part.\"\n\nZoe snaps at him, \"Your philosophy comes straight from the bottom of a rum bottle. Too simple, too sugary.\"\n\nLareck huffs. \"Quiet, your marital bliss is distracting me.\"\n\nNoah and Zoe stay silent as Lareck continues his strokes on the pad. From the outside hallway, the sound of approaching footsteps is heard. Hogfish appears in the doorway. He steps into the room, bobbing back and forth manically to the musical beat blasting through his earbuds.\n\nA look of dismay spreads across Lareck's wrinkled face. \"Ah, my son pops up out of nowhere.\" Hogfish doesn't hear the words, bobbing agitatedly to his music. Lareck rolls his eyes at Noah and Zoe. \"What can I say? Only that a man sends his sperm into a woman's womb like a blind ambassador hoping to make a good deal\u2014but a man never knows what's going to emerge from that womb. It could be a president or a jackass.\"\n\nHogfish screams at Lareck: \"Pop! You can't stay here! El Finito's coming! His hurricane wind is going to blow right through this window to get you! Run!\"\n\nLareck sighs. \"What a cross I must bear. Where I sought the complexities of art, my son sought the simplicity of war. He thought that war was nothing more than a video game played in foreign countries with tanks and guns.\"\n\nNoah keeps his eyes on Hogfish. \"Some men fight for their truth with paintbrushes or pens. Other men fight with bullets and bombs.\"\n\nLareck points the sharp end of his paintbrush at Hogfish. \"What's necessary about war? The army medics rebuilt my boy's skull with titanium plates and sent him home. Now he's somebody I don't know, convinced a hurricane is coming to wipe us out. I don't know if he hears music through those damn things stuck in his ears or if he's getting instructions from space aliens.\"\n\nZoe walks to Hogfish in the center of the room. She stops before him and pulls out his earbuds. His eyes widen with apprehension at her close body. He shudders and stiffens. She stares into his eyes, speaking in a firm voice: \"Hogfish, you've survived a personal hell most people can't even imagine. I want you to know, I believe all of your fears are justified.\"\n\nHogfish jams the earbuds back into his ears, wraps his arms around himself, and bobs violently.\n\nLuz is ushered into the bright fluorescent-lighted autopsy room of the police morgue by a white-coated lab technician. She nods hello to the Police Chief and Moxel, standing next to a high-wheeled gurney. On the gurney's aluminum surface is laid out the naked dead body of the man Luz found hanging in the bat tower. His skin is a waxy parchment-yellow; the sides of his head are dark gashes where his ears have been slashed off. A gaping purple hollow is in his chest, where the steel arrow was extracted. His lips are riddled with puncture holes from having his mouth sewn shut with fishing line. Luz shakes her head at the brutal sight. \"Poor Bill Warren.\"\n\nThe Chief holds up a micro\u2013digital recorder. \"One like this was found inside Warren's mouth. The reason his lips were sewn shut was to hold it in. I sent that recorder to Miami for further forensics.\" He sets the recorder on the gurney, next to Warren's head. \"You're going to hear an exact duplicate of the original recording.\"\n\nThe Chief presses the play button on the recorder. From the speaker, a stream of static rises, as if emanating from a deep void and traveling a great distance. Out of the static explodes an electronically altered violent voice in a scathing wail:\n\n_\"My heart is a ticking bomb waiting to explode_.\n\n_Your evil will bleed in the streets_.\n\n_I am a suit of bones_ ,\n\n_a vengeful skeleton stalking your island_.\n\n_I discover wrongdoers bent by corruption and profit_.\n\n_I am a stab in your conscience_ ,\n\n_a knife at your throat_ ,\n\n_an arrow in your chest_.\n\n_My blood-red X of vengeance cannot be escaped_.\n\n_Boogie till you bounce_ ,\n\n_bop till you drop_.\n\n_I am Bizango.\"_\n\nThe raging voice stops. Static noise vibrates the air.\n\nMoxel shifts uneasily. He tries to hide his unease with a sneer of bravado as he peers down at Warren. \"Now we have two of Neptune Bay's three partners chopped up like they were attacked by a blind sushi chef. Shit-in-your-pants bizarro stuff.\"\n\nThe Chief clicks off the recorder. \"Bizango? It took me a while to recall this monster's strange name. Back in the 1980s, when Luz's father was head homicide detective here, he shot dead a man who called himself by that name. It was a big sensation. You remember that, Luz? When your father killed Bizango?\"\n\n\"I was just a kid when that happened, so I didn't know much about it at the time.\" Luz takes a deep breath. \"Later I was told the story. Bizango was a serial killer, thought of himself as some kind of righteous assassin. My dad tracked him to where he was hiding and shot him. Bizango had terrified the island. No one knew who he was, because he always dressed in a full-body rubber skeleton suit.\"\n\n\"If this Bizango was shot dead years ago, who the hell is calling himself Bizango now?\"\n\n\"My dad always said, an evil thing never dies.\"\n\nMoxel spits out a mocking laugh. \"That's mumbo-jumbo, like out of some weird old zombie movie.\"\n\nLuz stares down at the mutilated body on the gurney. \"Bill Warren isn't out of an old zombie movie. He's lying here dead, right before our eyes. We have to deal with it.\"\n\nThe Chief looks quizzically at Luz. \"What kind of name is Bizango? You're the one on the detective squad who would know that kind of thing.\"\n\n\"You mean I'd know because I'm the only one who has African blood?\"\n\n\"Don't play your race card on me. Besides, you're only half black.\"\n\nMoxel gives Luz a snarky up-and-down look. \"Why don't you try playing your gender card instead of your race card? What gender are you, anyway?\"\n\nLuz ignores Moxel and answers the Chief. \"Bizango is a voodoo avenger; he kills people he regards as traitors. Dad told me that. I don't know more, because voodoo is Haitian and I'm Cuban. We don't practice voodoo\u2014we practice Santer\u00eda, which is different.\"\n\n\"What did your father mean by traitors? Traitors of what?\"\n\n\"I don't know. After Bizango was killed, Dad was diagnosed with stage-four lung cancer. Bizango was the furthest thing from his thoughts in those last days.\" Luz stares at the hole in Warren's chest. \"Any information on the arrow he was shot with?\"\n\n\"Same kind that was shot through the chest of Randy Dandy, but it's not an arrow. It's a steel spear shot from a Pelletier speargun that fires off on a CO2 cartridge with enough force to take down a great white shark. Pelletier is mostly used by military, banned for sport fishing because the fish don't stand a chance.\"\n\nMoxel hoots with enthusiasm. \"The Pelletier is awesome! I saw it in a cool James Bond movie. Bond used the speargun in an underwater duel with this other dude. Both of them were in dive gear. Righteous battle. What was the name of that movie? It had that blond chick in it whose boobs kept popping out of her swimsuit.\"\n\nLuz turns her gaze on the red **X** slashed across the pallid skin of Warren's stomach. \"Why didn't they clean Bill up? That's the least they could have done, wash the bloody _X_ off of him.\"\n\nThe Chief looks at the **X**. \"Evidence, Luz. They're still analyzing that _X_. It's not blood.\"\n\nMoxel butts in. \"What is it?\"\n\n\"Spray paint. Common spray paint.\" The Chief shrugs. \"Our new Bizango is also a graffiti artist. Maybe he's only a guy who thinks he's Andy Warhol and is looking for his fifteen minutes of fame.\"\n\nMoxel hitches up his gun belt, ready for action. \"Who's this Andy Warhol? Let's go get him!\"\n\nFloating far offshore between Key West and Cuba in his pirate-radio boat, Noah contemplates the microphone and bottle of rum on the console table before him. He swivels in his chair close to the microphone, then backs off. He picks up the bottle and takes a long slug. As the liquor burns in his throat, he looks out through the saltwater-streaked window. The vast blue ocean surrounds him. He could be the only man alive at the dawn of creation, or the only man alive at the end of the world. He leans in close to the microphone and finds his voice.\n\n\"We are in the American tropic, in a zone of constant life, death, birth, and decay. As a poet once said, 'Nothing lasts forever, not even eternal love.' So\u2014here is my advice: don't fall in love with a woman, fall in love with a town. A town doesn't expect you to tell it when you're coming home. A town doesn't ask you to stop drinking. Key West is the perfect town to fall in love with. Key West has more bars than churches, schools, grocery stores, and banks put together. You're always welcome in a Key West bar.\" One of the three cell phones on the table before Noah flashes its red light with an incoming call. He punches up the call. \"Go, pilgrim\u2014you're on pirate radio.\"\n\nA belligerent male voice spews from the big wood loudspeakers that the cell phone is wired to. \"Pirate radio, my ass. You're miles offshore, moaning about love instead of talking about what bought-off corporate-controlled commercial radio refuses to talk about.\"\n\n\"You've got a beef, bully boy, sling it at me. Show me the rage.\"\n\n\"I wanna bitch-slap all the bankster bandits and condo cowboys who are destroying the Florida Keys. The worst are those three Neptune Bay partners trying to bulldoze everything natural and put up a wall of condos that will forever block a man's rightful view of his mother ocean.\"\n\n\"Two of the Neptune partners are now dead. Didn't you hear the news about Bill Warren found hanging in the bat tower?\"\n\n\"I don't listen to corporate-controlled news radio.\"\n\n\"Well, there's still one partner left, Big Conch. He wants to build in the proposed great-white-heron preserve. It's not a done deal yet. Neptune Bay is coming up for an approval vote.\"\n\n\"Any corrupt government official who votes approval for Neptune Bay should be hung.\"\n\n\"That's it! Show me the rage!\"\n\n\"Hang 'em high! Let 'em swing by their necks!\"\n\n\"You know the mantra?\"\n\n\"Yeah, don't fool with Mother Nature or\u2014\"\n\n\"\u2014Mother Nature will fool with you!\"\n\n\"Keep up the fight. Adios, Dog.\"\n\n\"Next caller, go.\"\n\nA woman's words slur across the airwaves. \"Hey, turtle diddler, you're cute when you croon about falling in love with a town. Your hot voice puts a love hex on me. I'm boiling in your turtle soup.\"\n\n\"Are you stoned?\"\n\n\"Am I phoned? Of course I'm phoned. I've been phoned all day. That's why I phoned you, didn't I? I want to pet your porpoise. I want to hug your dolphin. Can I show you my age?\"\n\n\"Rage.\"\n\n\"I'll show you better. I'm pulling my panties down right now. See my raging pussy?\"\n\n\"Mom, I told you never to call me here.\"\n\n\"Mom? I'm not your fuck\u2014\"\n\nNoah cuts off the slurring voice. \"Stay on point, pilgrims, no games or I'm cutting this broadcast short. I'm waiting for your call. Good, here's a brave soul. You're live.\"\n\n\"Permian extinction. It's sneakin' up on us.\"\n\n\"Welcome back, Nam vet.\"\n\n\"You remember when Hurricane Wilma came through Key West years back?\"\n\n\"We all do\u2014lots of damage, took forever to recover from it.\"\n\n\"Yeah, but the real damage wasn't what we expected. Wilma didn't hit us head-on with one-hundred-thirty-mile-an-hour winds, didn't smash us with a crashin' forty-foot-high tsunami wave. Wilma blew across the island, ripped off roofs, uprooted palm trees, then, poof, she was gone. That night, people sleepin' in their beds dreamed that their dog was lickin' their face and wouldn't quit, or they dreamed they were pissin' and couldn't stop. People woke up with water risin' all around them, water risin' up out of the floors of their houses, floodin' the streets, coverin' the cars. It was Wilma's sea surge from under the coral rock of the island inundatin' everything. Like the Old Testament deluge, water just kept risin' with nothin' to stop it. There was panic, everyone was gonna be drowned. Key West was gonna be submerged forever, like Atlantis. Then the water stopped risin'. That was Wilma's sneaky punch. The Permian Extinction Event will be like that. The next mega-explosion will come when least expected, annihilate us all.\"\n\n\"Maybe that's not such a bad thing. Mother Nature takes us out before we pollute the whole damn galaxy.\"\n\nNoah patches in another call. A brusque male voice bellows. \"This is Big Conch, CEO of Neptune Bay Resort.\"\n\n\"Ah, the guy who hits on my wife all the time when he isn't busy raping the environment.\"\n\n\"Don't give me that stink load about the environment. I create jobs. What do you create? _Nada!_ You want the Florida Keys turned back into a mosquito-infected mangrove swamp.\"\n\n\"I'd rather live with mosquito bites on my ass than be imprisoned on a concrete island of condos surrounded by a dead sea.\"\n\n\"You're just a dipshit bobbing alone on the ocean, trying to get people to jerk off to phony environmental rage. The truth is, it's all about your wife. She left you. You're a pirate without a treasure.\"\n\nNoah punches Big Conch off the line. \"Fun and games are over for today. Here's something for my lost treasure out there, if she's listening.\" He picks up a CD. \"This is a lament of love lost, sung by a man who has crawled on hands and knees over a thousand miles of broken-glass heartbreak road. Enjoy!\"\n\nNoah pushes the disc into the CD player and swivels around in his chair as the song begins. Behind him is the Haitian teenager Rimbaud Mesrine, who has been silently watching the whole time. Noah speaks in French to the boy. \"You don't understand anything that's been said here today, do you?\" Rimbaud shakes his head. Noah continues: \"How old are you, kid?\"\n\nRimbaud answers hesitantly in French. \"Sixteen.\"\n\n\"Then you're old enough to understand this.\" Noah cranks up the volume on the CD player.\n\nThe man singing his lament from the speakers slits open the heart of the song with a howl of pain.\n\nHigh-noon sun slams down on a junkyard of abandoned boats of all types and sizes rotting in brutal tropical heat. Some boats are tilted on their sides; some are mounted on concrete blocks with weeds growing up around them; others have their once-tight wooden hulls snapped open and gaping, like prizefighters with their teeth knocked out. Overhead, in the cloudless washed-out sky, vultures glide in circles, looking down among the junked boats for any sign of a dead opportunity.\n\nBetween a row of square-hulled houseboats walks Hard Puppy, dressed in his shiny white silk suit. Hard's white alligator-skin shoes crunch the white coral gravel underfoot as he leads three pit bulls tied to a rope. He stops next to a rusted iron ship anchor half wedged into the ground. He ties the pit bulls to the anchor. He walks back ten feet, swings around, and pulls out a Magnum. He aims the long-barreled gun at the pit bulls straining against the rope. He pulls the Magnum's trigger. A reverberating blast shocks through the air. One of the tied pit bulls drops to the ground with a dying yelp. The two remaining dogs bark and lunge against the new dead weight of the rope restraining them.\n\nThe scent of blood and burnt metal fills the air. Hard aims the Magnum and fires again. In front of the two pit bulls, a chunk of dirt is ripped out and tossed up in a dust cloud. Hard shouts at the dogs, \"Keep your asses still!\" He grips the gun in both hands, aims, and fires. A bullet zings through the air, striking a pit bull between the eyes. The bullet's sudden impact explodes the dog's head in a spew of blood, bone, and flesh.\n\nBehind Hard, a white Dodge Charger roars up and brakes to a stop in the gravel. Luz opens the front door and gets out. Hard swings his Magnum around in his two-handed grip and aims it at Luz. She pushes the bottom of her guayabera shirt aside, exposing her holstered Glock; she steadies her hand on the handle and calls out to Hard across the gravel expanse, \"Let's have an even fight. Killing a cop isn't as easy as killing a helpless dog.\"\n\nHard's lips curl back, exposing his platinum teeth. \"Man's got a right shootin' his own dogs.\" He grins with a quick lick of his lips and glances over at the last pit bull standing. \"I got one more slacker to pop off.\"\n\n\"Target practice is finished. Hand over your gun.\"\n\nHard kicks at the gravel with the tip of his alligator shoe. A puff of dust floats up. He shoots Luz a defiant stare.\n\nLuz steps straight up to Hard. \"I'm going to run a check on your gun to see the nasty places it's been. Maybe it's left a calling card in places where the sun no longer shines.\"\n\nHard grips his Magnum harder. \"I ain't worried 'bout no checkin'. My hardware be clean. Better you get your head out of your ass. Get in touch with your half-nigga side. Let this whole thing slide.\"\n\n\"It slides if you cop out on the Dandy Randy and Bill Warren murders.\"\n\n\"Ah, colored girl, don't be a shit-kicker. A shit-kicker sees a big ol' pile of shit on the street and kicks it. Best you pass this Neptune Bay shit by. It could stick to your shoes\u2014worse, stink up your life.\"\n\n\"I'm kicking your shit. I'm taking you in for questioning on the two murders.\"\n\n\"You crazy bitch. This black boy got nothin' to do with offin' white chumps. You should be sniffin' in the direction of Big Conch's white ass. Everybody knows Big's the only Neptune partner left.\"\n\n\"No. Maybe you partnered with Big to launder your dogfight winnings through Neptune Bay. Maybe you and Big didn't want to share that with the other two partners. So, whiff, off go Dandy and Warren.\"\n\nA sweat breaks out across Hard's forehead. \"I ain't scammin' with Big. I be a respectable biz-niz man. That's why I be wearin' a suit in this scaldin' sun. No other black boy as pro-fesh-shu-nal as I be.\"\n\n\"Blood-money gambling on pit bulls tearing each other apart is not a profession, it's a crime. You think you can dodge the law, moving your secret dogfights between Key West and Miami. Someday I'll bust you on it, bust you to pieces.\"\n\nHard turns and looks across the gravel at the whimpering pit bull roped to the anchor. Around the dog, the blood from the two sprawled dead animals has leaked out in a damp red circle. Hard raises his Magnum and points it at the whimpering pit bull. \"You want that dog?\"\n\n\"I don't want a fighting dog.\"\n\n\"That dog be no fighter, he be a lover. That's why I poppin' him. He'd rather lick his balls than fight. That's why his name be Chicken. You want Chicken or not?\"\n\nLuz studies the pit bull squatting on its haunches in a pool of blood. The dog's pink tongue dangles out as it whimpers; one of its ears is a gnarly stub, bitten off in a fight. The hair of the dog's short black coat is slashed with white scars left over from the vicious bites of past battles.\n\nHard chuckles. \"Take Chicken home to that baldheaded daughter of yours. She could use a friend.\"\n\n\"I'll take the dog.\"\n\n\"Deal.\"\n\nHard walks across the gravel. He unties the pit bull from the two dead dogs and leads it back to Luz. The sun glints off of Hard's smiling metallic mouthful of teeth. \"Now you finally got a friend for your crippled daughter.\"\n\nLuz's knee whips up in a powerful jackknife kick straight into Hard's groin. Hard's Magnum flies from his hand. He grabs his groin in an anguished wail, gaping at Luz with eyes wide in shock. She rips her pistol from its holster and smacks the gun's gorilla-grip handle against the side of Hard's head with a loud crack. Hard drops to the ground, his feet kicking out at the gravel in pain. Luz stands above Hard, who is writhing in the dust. She aims her pistol down at him.\n\n\"You mention my daughter again, I'll kill you!\"\n\nA line of shrimping boats is anchored along a concrete pier jutting out into Key West Harbor. The boats' tall masts and winged outriggers are decorated with strands of twinkling white lights. On the pier, a band plays festive Caribbean music to a crowd of shrimpers, their families, and town locals gathered beneath an overhead banner declaring **SHRIMP FLEET BLESSING**. In the crowd are Luz and Joan with Carmen and Nina. Nina sits in her wheelchair, her brown eyes taking in the scene with nervous excitement.\n\nBig Conch bullies his way through the center of the crowd. He holds two bottles of beer as he cocks his head back and forth, looking for someone. He spots Zoe dancing with a shrimper, her flared skirt spinning around her bare knees as the delighted partner stomps his white rubber boots to the band's percussive rhythm. Big closes in on the shrimper and shoves him aside. The man stops dancing and sizes up Big's imposing stature. The man slinks off. Big offers Zoe one of his two beers. She turns her back on him.\n\nAt the edge of the crowd, Hogfish wheels to a squeaky stop on his rusty bicycle. Stretched between the handlebars is the taut fishing line strung with barbed J-hooks. He jerks his head back and forth to the music he hears through the earbuds jammed into his ears and rises from the bicycle's worn leather seat. He looks over the dancing crowd and glimpses Big following close behind Zoe as she walks quickly away from him.\n\nOut of the darkness behind the line of docked shrimping boats, Noah's trawler motors up. Inside the pilothouse, Noah steers his vessel between two large boats and cuts his engine. He looks through the window at the crowd on the pier. Behind him in the shadows is the slight figure of Rimbaud. Noah turns and speaks reassuringly in French: \"Do what I told you and stay out of sight. Don't go out on the deck. I'll return soon.\"\n\nRimbaud grabs Noah's arm. \"I'm afraid. What if they find me?\"\n\n\"They won't find you if you stay hidden inside the storage closet.\"\n\nRimbaud's eyes widen with fear. \"They'll find me and send me back to Haiti, where the earthquake cracked open the underworld, releasing zombies. Zombies breathing the death of cholera search for innocents to suck out their life.\"\n\n\"Trust me, I'll protect you. You won't be sent to Haiti. I'll come back with someone who can help us.\"\n\nDistrust crosses Rimbaud's face as he slips away toward the storage closet.\n\nNoah heads for the door and steps out of the pilothouse onto the deck. Anchored next to the trawler is a shrimping boat with its name painted along its side, _Pat's Pride_. Pat stands on her deck, dressed in men's jeans, shirt, and white rubber boots. She spots Noah and shouts above the raucous music from the band on the pier: \"Truth Dog, we're blessing shrimping boats here! Not pirate-radio boats! Shove off!\"\n\nNoah shouts back: \"If you swear to stop net-killing endangered turtles, I'll shove off! Until then, you can fuck off!\"\n\nPat turns her back on Noah and bends over. She slaps her blue-jean-covered butt with a loud smack. \"Kiss it, sucky eco-boy!\"\n\nOn the crowded pier, a Catholic priest appears, dressed in a long billowing red robe. The priest is followed by altar boys in starched white cloaks. The boys swing metal censers smoking with burning incense. The crowd falls silent. The band stops playing. All eyes go to the priest. He holds high a gold cross with a nailed Jesus. He looks at the long line of shrimping boats with their decorative lights blinking against the black sky. His voice booms: \"Father, our shrimping boats are about to sail out again. We pray thee, Father, fill the nets of our men with thy bountiful gifts. We also beseech your Holy Mother, Mary, to shine her guiding light on our brave men, protect them from danger and stormy seas, return them home to the bosom fold of their families and loved ones.\" The crowd shouts, \"Amen!\"\n\nAn old white-haired black shrimper walks with halting steps in front of the boats. His face is etched with deep lines from a lifetime under the sun. He holds in his hands a large fluted conch shell. He stops and raises the narrow end of the pink luminescent shell to his lips. He takes a deep breath and blows a high-pitched melancholic note.\n\nNina, seated in her wheelchair next to Luz, bends her head to the conch shell's unsettling wail. She becomes agitated. Luz places her hands on Nina's shoulders to calm her. The old shrimper blows harder into the shell, forcing a shrill note into the night air. Nina's frail body trembles.\n\nThe old shrimper keeps blowing as women from the crowd step to the edge of the pier, facing the anchored boats. The women hold large bunches of long-stemmed white roses. They solemnly toss the flowers at the brightly painted high hulls of the boats. The roses hit the wooden hulls with soft thuds and fall below, where they scatter on the water and float around the boats. Zoe, among the women, tosses all of her roses except her last one, which she keeps, breaking off its long green stem, then securing its prominent white bloom next to her ear.\n\nNoah jumps down from the deck of his trawler onto the pier and walks toward Zoe. He is grabbed roughly from behind. He spins around, staring straight into the face of Hogfish.\n\nHogfish screams urgently: \"Roses can't stop El Finito from coming! Listen to the roses talking! Chattering away like mourning widows of drowned shrimpers! They're saying the Devil's wind is winding up to punch the lights out of civilization! Roses are crying because the hurricane is coming!\"\n\nFrom behind Hogfish, at the far end of the pier, Big Conch lights the fuse of a fireworks cannon-barrel launcher. Shrieking fireworks sail high into the night sky and explode, illuminating the uplifted faces of the cheering crowd.\n\nFrom inside Noah's trawler, Rimbaud stares wide-eyed through the pilothouse window. His terrified face lights up from fireworks bursting with brilliant streamers. He cringes at the exploding sounds and twists his body in sharp turns, as if each of the flaring fireworks has him as its intended target. He falls to his knees and scrambles, with his head down, from the pilothouse out onto the deck. Fireworks whistle in the air around him; dazzling light showers down from above. He scurries to the boat's edge and hurls himself overboard, plunging from sight beneath the water.\n\nThe crowd on the pier watches the last of the trailing light fade from the night sky. A belligerent voice calls out, \"Fuck the eco-Gestapo!\" The crowd turns to Pat, unfurling a canvas banner from her boat's side railing. The banner proclaims **NO TURTLE EXCLUDERS ON SHRIMP NETS!** Some in the crowd break into an eruption of cheers at the sight of the banner. Pat shouts defiantly: \"Listen, all of you! My family fished turtles for generations off of Key West. No eco-Gestapo can dictate to me. I'll net turtles, harpoon turtles, hook turtles, kill turtles with my bare hands if I want. The ocean is the last free frontier, the final home of the brave.\"\n\nMore cheers burst from the crowd, followed by loud boos from others. Men angrily wave their fists and shove one another, their reddened faces inches apart. Women jostle each other, screaming vulgar insults. The priest frantically waves his gold crucifix in the air, but he is ignored.\n\nThe band strikes up a sudden rhythmic dance tune. Noah breaks away from Hogfish and makes his way to Zoe. He slips his arm around her waist and spins her in a dance to the band's beat. Some in the crowd stand back, giving Noah and Zoe room; others join in the dancing. Luz lifts Nina up from the wheelchair and sways her in her arms to the joyous rhythm.\n\nZoe stops dancing and pushes Noah away. \"If I want to dance with you, I'll make the choice.\" She pulls out the white rose tucked behind her ear and hands it to him. \"You didn't know you were in a garden of roses when you had it.\"\n\nNoah holds the rose up and plucks off a petal. \"She loves me.\" He plucks off another petal with a brave grin. \"She loves me not.\"\n\n\"You can pluck every petal off that rose, but it won't bring me back. Marriage is not a one-way street just going your way. The street goes both ways.\" She turns and walks off, leaving Noah alone with his rose.\n\nAlong the entire length of the concrete pier, the diesel engines of shrimping boats roar to life. The crowd rushes to the pier's edge, waving good-bye to the boats motoring away. The lights of the fleet become distant on the sea's horizon.\n\nLong after the fleet has disappeared and the crowd has left the pier, Noah and Luz stand alone in the night in front of Noah's trawler. A stiff breeze off the ocean blows in, tugging at Luz's white guayabera shirt. She looks impatiently at Noah. \"It's late; I need to get home to my family. Why did you ask me to stay behind with you?\"\n\n\"I need your help with something. I didn't want to mention it in front of Joan.\"\n\n\"I don't keep secrets from Joan. What's so important that can't be talked about in front of your sister?\"\n\n\"I'll show you.\" Noah leads the way onto his trawler. They walk across the deck into the dark pilothouse. Noah switches on the overhead light and calls out in French, \"It's safe! No need to hide!\" He waits for an answer\u2014silence\u2014calls out again: \"This woman I brought can help.\" He moves to the storage closet in the corner, pushes back its canvas curtain, and looks inside. \"Damn, the boy is gone.\"\n\n\"What boy?\" Luz walks to the closet and peers in. \"Who's supposed to be in here?\"\n\nNoah doesn't answer. He picks up a half-finished bottle of rum from the broadcasting table and uncorks it. He takes a swig as he stares through the pilothouse window at the ocean. \"Makes no difference now who he is. He's vanished.\"\n\nLuz steers her white Charger down the main drag of Duval Street. The flanking sidewalks are crowded with gawking tourists passing gaudy trinket shops, boisterous open-air bars crowded with long-haired motorcycle bikers, tattoo parlors filled with glassy-eyed stoned teenagers, and chattering people at outdoor restaurant tables beneath towering banyan trees. Luz keeps a vigilant eye for lowlife crack dealers, skinhead punks pimping young runaway girls from the North, and tweaked meth-heads looking to start a fight with someone, or with themselves, or with a plate-glass window.\n\nSitting next to Luz in the passenger seat is Chicken, the one-eared scarred pit bull. Chicken licks his chops as she takes a deep-fried conch fritter from a bag wedged between her thighs. She munches on the fritter as she continues to drive with one hand on the steering wheel. She glances over at the dog, sitting patiently on his haunches, waiting for a handout. \"Chicken, you want a fritter?\" The dog whines with pitiful expectation. She plucks a fritter from the bag and holds up the greasy ball to Chicken's mouth. \"Careful, don't bite my fingers off.\" The dog's pink tongue slurps the fritter gently from between her fingers. He swallows with a loud gurgle. She pats his broad head affectionately. \"You really are a lover, not a fighter. I like that in a man.\"\n\nLuz turns off Duval Street and drives out of town, past streets lined with palms shading eighteenth-century wood houses painted in bright Caribbean colors. She continues on to the outskirts of Key West, with its sleazy motels, fast-food drive-in joints, and run-down shopping centers. She heads up the Overseas Highway, crossing bridges linking the islands of the Keys. The farther Luz travels, the less man-made distractions line the highway, until, finally, there are none. On one side are the Gulf of Mexico's turquoise-colored waters. On the other side, the vivid indigo of the Atlantic Ocean. She looks through her car's windshield; the atmosphere is pristine, dominated by the changing light reflected from the two great bodies of water. In the pale-blue sky, spread-winged white herons sail between columns of clouds. The herons soar high on hot wind currents, then swoop down, gliding to graceful landings in a flutter of wings on distant mangrove islands dotted across the horizon.\n\nA large billboard looms up on the side of the highway declaring **COMING SOON! NEPTUNE BAY RESORT!** The billboard's visual depicts a vast resort of luxury condos, hotels, golf courses, and a yacht marina. Towering above the resort depiction is a giant image of the bearded sea god Neptune clutching a trident spear. Luz turns her car abruptly off the highway onto a dirt road leading into the center of an abandoned construction site stripped of all vegetation and empty of any people. She parks the car and gets out. Chicken follows her as she walks across a scraped-earth landscape dominated by rows of hulking, dust-covered bulldozers, earth-graders, dump trucks, and cement mixers. She continues, zigzagging between incomplete cement building foundations with rusted iron rebar struts sticking up from them. She arrives at a concrete pier jutting out into a brackish backwater inlet coming in from the Gulf of Mexico. She walks to the far end of the pier, where a canary-yellow forty-foot powerboat is tied, its high jet-exhaust chrome spoilers gleaming in the harsh sunlight.\n\nIn front of the powerboat, Big Conch sits in an aluminum slingback chair, wearing only a tight red Speedo swimsuit. His sinewy suntan-oiled body is shaved of all hair except for the dyed slick blond hair of his head. On his chest glint heavy antique Spanish medallions that dangle from a gold chain around his neck. He shucks oysters with a broad-bladed knife. Scattered around his bare feet are empty shells. Chicken trots up, sniffs the shells, and starts nibbling on them. Big looks up and greets Luz with a smirk as he nods toward Chicken. \"I see they finally gave you a better partner than that Riviera redneck, Moxel. At least this one's got a pair of balls.\"\n\nBig pulls a gnarly-shelled oyster from a wooden crate next to the aluminum chair. He deftly knifes open the shell and scrapes free its meat. He holds out the glob balanced on the knife's blade. \"You want an aphrodisiac from the sea? Neptune's original Viagra. It'll give you a hard-on for that hot blond-bombshell girlfriend of yours. Oh yeah, you can't get a hard-on. What is it you get, anyway, if you can't get a stiff dick? Come on, have an oyster. It might even make me attractive to you.\"\n\n\"I just lost my appetite.\"\n\n\"No appetite from stuffing fritters all day. You won't die from a bullet to your heart but a grease hole through your gut.\" Big holds the knife up to his mouth. He lets the oyster balanced on the blade slide off between his lips.\n\nLuz looks over at the name emblazoned on the powerboat's sleek hull: _Big Conch_.\n\nShe looks back at Big. \"Since you know so much about the sea, did you know that if a conch's johnson is bitten off by a hungry eel, the conch grows himself a new johnson?\"\n\n\"Is that why you eat conch fritters all day, hoping to grow yourself a wiener?\" Big glances over at Chicken, crunching a mouthful of oyster shells. \"Dumb bastard's gonna puke.\" He turns back to Luz. \"You didn't drive all the way out here to give me a lesson on the sex life of the conch. What the hell do you want?\"\n\n\"Dandy Randy and Bill Warren were both murdered.\"\n\n\"So were the Kennedy brothers. Ancient news. Get to it. You're here because you figure I killed my two partners.\"\n\n\"No. I'm here because I believe whoever did kill your partners is now after you. You should back off developing this resort and lay low.\"\n\n\"Lay low? Never. I don't give a shit if half the people accuse Neptune Bay of destroying the habitats of everything from white herons to blind manatees to one-armed nuns. The other half of the people love me for this hundred-million-dollar resort I'm developing. It means jobs to build it, jobs to sell it, jobs to service it. We're coming off the worst economic times in the history of the Keys since the Great Depression, and I'm the man leading the way out with my Neptune Bay.\"\n\nChicken bumps up against Big's knees and vomits a gut-load of half-eaten oyster shells onto Big's bare feet. \"Get out of here, you one-eared mutt!\" Big kicks the dog in the ribs. He shouts at Luz as she pulls the yelping Chicken away: \"And don't you come around trying to trick me by pretending you care about saving my hide from some psycho killer. And I damn well don't need lecturing about how conchs grow their dicks, especially since you don't have a dick and balls. Hell, you no longer even have tits. You're a sorry-ass situation.\"\n\nLuz glares at Big. \"You've got balls... balls for brains.\"\n\n\"I'm a sympathetic man, so I won't respond to that, but answer me this: why, after your mastectomy, didn't you get some fake titties? You're a good-looking woman. You'd be a knockout if you bolted on a pair of Vegas-showgirl silicon hooters. That way you wouldn't look so much like a...\"\n\n\"Dyke.\"\n\n\"Like a guy trying to be tough but he's a punk.\"\n\nLuz's eyes narrow. She nods at the thick gold chain glinting around Big's neck. _\"Un mono que lleva cadenas de oro es todav\u00eda un mono.\"_\n\n\"Speak American.\"\n\n\"A monkey wearing gold chains is still a monkey.\"\n\nBig roars with laughter. \"Fu-fuck... ing... monkey. That's great. A goddamn fucking monkey.\" His laughter turns to a snarl as he jumps up and slashes the blade of his knife in the air. \"I'm not a fucking monkey, you dumb dyke! I'm a goddamn two-hundred-pound male gorilla with five-pound balls and a swinging foot-long dick! Don't you ever forget it!\"\n\nLuz faces Big. \"I can see from the tiny bump in that Speedo you're wearing that there isn't much swinging between your legs. You don't have enough juice to knock up a tick.\"\n\nLuz nervously chews on a conch fritter as she watches the Duval Street night action through the windshield of her parked Charger. She keeps her eyes on the front of a nightclub. A neon rainbow sign arches above the nightclub's doorway: **LITTLE ORPHAN TRANNY'S.** The sign's garish pastel light reflects on three six-foot-tall drag queens with big hair, wearing sequined ball gowns, sashaying back and forth on the sidewalk on six-inch-high stiletto heels. The queens wink false eyelashes, blow kisses, and call out in basso male voices at passing locals, tourists, and high rollers to enter the nightclub and experience the wild side.\n\nInside her car, Luz slips another fritter from the paper bag between her legs. Chicken sits beside her, expecting a treat. Luz hands the fritter to Chicken, and he tongues it from her fingers. She continues watching the people going in and out of the nightclub, looking for drug pushers and their clientele of tweaked, cranked, and cracked users and abusers. She flips on her car's AM-FM radio and switches through the channels until she locks into a weak station. She turns up the volume and listens to the animated voices of Noah's broadcast coming in through the static.\n\n\"Hey, Truth Dog, I'm a Key West shrimper.\"\n\n\"Welcome, shrimper. You're on pirate radio.\"\n\n\"It pisses me off that so many of your callers are against commercial shrimpers and long-liners here in the Keys. We're seen as rednecks who don't give a shit about marine ecology. Hell, we're the ones who make a living from the sea. You won't find stronger guardians of marine life than us.\"\n\n\"I'm with you. Many of the old-timers here were the original ecologists, against the slaughter of the turtles, whose meat was being turned into steaks and soup, their shells made into combs and toothbrushes.\"\n\n\"Right, we were the first to use excluders on our boats. We were the first to use safety O-hooks instead of J-hooks on our longlines.\"\n\n\"My rage is against those who refuse to do that. You know how many endangered female leatherback turtles are left laying their eggs in the sands of Florida's east coast?\"\n\n\"Not many.\"\n\n\"Fewer than two hundred. Down from tens of thousands. Turtles have been around a million years and we're wiping them out. We're snagging, tangling, drowning, hooking the last of the turtles every day with gill nets, drift nets, drag nets, and J-hook longlines.\"\n\n\"And the plastic bags?\"\n\n\"Don't get me started! Billions of bags dumped into the ocean each year, choking, gagging, and strangling turtles to death!\"\n\n\"Goddamn shame.\"\n\n\"God had nothing to do with it. Man did it.\"\n\nLuz cuts off Noah's radio voice, her attention caught through her windshield by a man and a teenaged girl down the street, coming out of the Trouble in Paradise cocktail lounge. The man and girl walk away with their backs to Luz. She blurts out to Chicken, sitting next to her, \"That's my Carmen! She snuck out of the house!\" Chicken licks his chops for more fritters.\n\nLuz starts her Charger and steers it onto Duval Street, following behind the man and teenager. The girl's long black hair hangs down to the top of a yellow miniskirt hugging her bottom so tightly that her firm butt cheeks are prominently outlined. The man runs his hand over her butt as she walks.\n\n\"I know my own daughter when I see her. I shouldn't have let her paint those damn fingernails. I knew it would lead to no good.\"\n\nThe man and teenager turn suddenly off of Duval Street toward Grunt Bone Alley. Luz presses down on the accelerator pedal and speeds up. A fast-moving line of hooting college kids on loud mopeds shoots out from the alley. Luz honks her horn at the riders blocking her car, but the mopeds keep coming. She spots an opening in the line and guns into Grunt Bone Alley. The narrow lane is deserted except for cars parked along its sides. She pulls over and cuts her engine. She studies the parked cars. Chicken looks at the bag of fritters and whines. She pats Chicken's head. \"Shush. They're around here somewhere.\"\n\nIn the dark distance of the lane, there is no movement except from a rusted 1961 Pontiac GTO parked in front of a row of garbage cans. The GTO slightly bounces on its tires. Luz keeps her gaze fixed on it. In the car's back window, a man's head suddenly pops up in silhouette. The head quickly disappears back down.\n\n\"He's raping Carmen in the back seat!\"\n\nLuz jumps from her car and runs down the alley to the GTO. She yanks open the car's back door and shines her flashlight beam in on a man's bare white ass as his body humps up and down on the teenager beneath him. Luz grabs the man's hair with one hand and jerks his head around. She beams the flashlight into his eyes. \"You're under arrest for raping a teenager!\"\n\nThe surprised man yells, \"What the fuck are you talking about?\"\n\n\"The girl's only sixteen!\"\n\n\"Like hell! She's eighteen!\"\n\nLuz swings her beam at the girl spread-eagled on her back beneath the man. Her long black hair is tangled over her face. Her bare breasts heave from rapid breathing. Her skirt is pushed up and her panties are pulled down. In the dark V between her naked thighs glistens a worm of spilled cum. The teenager shakes the tangled hair away from her face. Luz stares at the face brightly lit in the flashlight beam. The teenager is not Carmen.\n\nThe girl glares at Luz. \"I can prove I'm eighteen. My driver's license is in my purse.\"\n\nLuz takes a deep breath. \"No, you're not eighteen. I recognize you. You're the Munoz girl. I know your family. I was at your Quince party two years ago. You're just seventeen.\"\n\n\"That was three years ago! I'm eighteen now!\"\n\nLuz steps out of the car and looks at the man. \"Pull your pants up, you chicken-hawk bastard.\"\n\nThe man gets out of the car. He shoves the still-hard stub of his prick beneath his underpants, hitches up his blue jeans, and winks at Luz. \"I bet you wish you could whack off a piece of her yourself. She's not underaged. She's street legal. You can't arrest me. Can't do a fucking thing.\"\n\n\"Don't count on it. I see you with her again, I'll toss you into lockup, where your new boyfriends will be waiting for your white ass. Get the hell out of here!\"\n\nThe man takes off running. The teenager climbs out of the car. Luz grabs her wrists and handcuffs her.\n\n\"You can't take me prisoner! What are you doing! I didn't do anything wrong!\"\n\nLuz stays silent. She marches the teenager to the Charger, shoves her into the back, and slams the door. In the front seat, Chicken turns around and puts his front paws on the seat separating him from the teenager. He cocks his one ear, wanting to lick her hello with his tongue. Luz jumps into the car next to Chicken. She looks into the rearview mirror at the teenager in the back.\n\nThe handcuffed girl stares defiantly. \"This is illegal. You can't do this. My dad's brother is a big-time lawyer in Miami. Manny Munoz\u2014you ever heard of him? He'll sue you!\"\n\n\"Let him sue.\"\n\n\"And he'll sue you for having this mangy mutt in a cop car. I bet that's against cop rules. Hey, but this isn't a cop car! What's going on?\"\n\n\"I'm not a cop. I'm a plainclothes detective.\"\n\nLuz starts the Charger and drives off. She hears the teenager crying in the back seat. Luz weaves through dark back streets until she arrives before the twelve-foot-high bullet-shaped concrete monument lit up in the car's headlights. Bold black-painted words declare **SOUTHERNMOST POINT CONTINENTAL U.S.A.\u201490 MILES TO CUBA.**\n\nLuz drives behind the monument, where the street abruptly ends and the Atlantic Ocean begins. She turns off the car's engine and rolls down her side window. The ocean's surface ahead is a black mirror in the night. A rush of salt-scented air fills the car. She looks in the rearview mirror at the crying teenager. \"You smell that?\"\n\nThe teenager sniffles. \"Please don't tell my parents about my boyfriend. I beg you. He's thirty-two. They'll kill me.\"\n\n\"Take a deep breath. Smell the air.\"\n\n\"It's salty.\"\n\n\"It's the air of Cuba blowing in from across the Florida Strait.\"\n\n\"I beg you not to tell my parents.\"\n\n\"That's the air of your great-grandparents. People who immigrated to Key West in the eighteen hundreds with nothing and built a life. Hardworking people who had pride and morals. People who brought those qualities with them.\"\n\n\"I'll just die if you tell my parents.\"\n\n\"The problem now is, no pride, no morals.\"\n\n\"Listen, lady, we're friends, right? I remember you at my Quince. You were there with your girlfriend.\"\n\n\"Not girlfriend. Life partner. Love of my life.\"\n\n\"Whatever.\"\n\nLuz turns on the car radio. She switches through the stations, playing rock, country, and Latin music. She stops on the voice of Noah coming in. She glances at the girl in the rearview mirror. \"Do you know who this is?\"\n\n\"Isn't he that pirate guy?\"\n\n\"Yes.\"\n\n\"Nobody I know cares about him.\"\n\n\"You should care. He's about saving what counts. He's fighting for what good is left in this world for your generation.\" Luz faces the girl. \"Listen to Noah, then I'll let you go.\"\n\n\"You won't tell my parents about what happened?\"\n\n\"I won't tell them if you learn something here tonight.\"\n\nLuz turns up the volume on Noah's voice.\n\nThe girl slumps in the back corner of the car. Her face turns sullen as Noah's words crackle from the radio.\n\nYou've got to work with me tonight, pilgrims, or ol' Truth Dog is going to sail away back home. We've got four endangered turtle species here in the Florida Keys: the leatherback, the loggerhead, the hawksbill, and the green. Why can't we stop the slaughter? I'm waiting for your answer. Okay, here's a pilgrim. Talk me some sense.\"\n\nA woman's shaky voice answers. \"I never called before. I'm so nervous.\"\n\n\"You'll be fine.\"\n\n\"You know, uh, there's been, uh, extensive scientific research into cancer. They've scrutinized Neanderthal fossils and found no evidence of cancer. Cancer only shows up two hundred years ago. It's modern times that have surrounded us with cancer and...\"\n\n\"Don't stop. I'm here for you.\"\n\nThe nervous woman's voice becomes emboldened. \"Remember when you said the dumping of toxic stuff by the military around the Keys might have poisoned the water?\"\n\n\"Military's been here since the Civil War. Ships, submarines, fighter jets, you name it. Toxic dumping is our legacy.\"\n\n\"Now we have abnormally high rates of cancer.\"\n\n\"I always say, you want the true picture, you've got to connect the right dots.\"\n\n\"The picture is,\" the woman says, sobbing, \"everything is being poisoned. People, coral reefs, sea life, everything is going to die of man-made cancer.\"\n\n\"You're right. It's all connected. Next caller, you're up. Connect the dots.\"\n\nA squeaky male voice begins excitedly: \"What's that ditzy dame talking about? She's got cancer on the brain. Everybody wants to cure cancer, but it's the witty bitty we should worry about.\"\n\n\"Witty bitty?\"\n\n\"The Key Largo cotton mouse. It's on the official endangered list. It's being wiped out by runaway cats from trailer camps.\" The squeaky voice drops to a confidential tone. \"Truth Dog, I'm reaching out my hand to you. Will you pray with me?\"\n\n\"Whatever floats your boat. Okay.\"\n\n\"You got my hand?\"\n\n\"I got it. It's sweaty.\"\n\n\"We pray thee, Lord, to keep safe all your creatures great and small. Especially the witty bitty.\"\n\n\"Maybe the Head Man up above will hear your prayer.\"\n\n\"Oh, he will. He's listening right now. He's going to show you the light. Good-bye, brother.\"\n\n\"Next caller. Go. I'm waiting.... I said, go.\"\n\nThe baritone of a man's belligerent voice slams through the silence. \"I'm the vet who called before.\"\n\n\"Welcome back, vet.\"\n\n\"I saw bad shit in Nam. Shit that makes what happened in Iraq and Afghanistan look like a Disneyland ride. A famous photo was taken durin' the Nam war. It showed a naked Vietnamese girl runnin' up the road. Her village had been napalm-flamed by us. She was on fire. Blobs of smolderin' napalm burnin' off her skin. That stricken look on her face\u2014fuck, man\u2014that look! That was the look of innocence destroyed by our evil.\"\n\n\"That's it, show me the rage.\"\n\n\"I was one of the guys napalming those Nam villages. I was nineteen years old. I still see that girl's smolderin' skin in my dreams, nearly half a century later. The smell of burnin' flesh wakes me up every night.\"\n\n\"The smell of rage.\"\n\n\"I saw the same look that girl had in another photo more recently, when that oil well blew in the Gulf.\"\n\n\"Deepwater Horizon blowout. Worst ecological disaster in American history. Total cover-up.\"\n\n\"It was a photo of a pelican flounderin' in a sea of oil. The bird's body was drenched in brown slime, its wings stretched out, tryin' to fly, but it couldn't. Its eyes were huge with fear, like that girl's eyes, that girl with her skin on fire runnin' up the road. We've got to stand against innocents' being slaughtered.\"\n\n\"We've got to stand up to the war machine that runs on soul-sucking oil or our days are numbered.\"\n\n\"That's why I called before about the comin' Permian Extinction Event. Next time I'll call with proof that it's all gonna blow sky-high.\"\n\nSeagulls swarm in the sky above Pat's shrimping boat as it plows through heavy ocean swells far out at sea. The boat's long-poled twenty-foot outriggers are winged out on both sides of the vessel, their unfurled dragnets roiling the water. Pat swings in one of the outriggers and cranks up its dripping net. The net breaks the surface of the water, weighted with a squirming catch of pink-shelled shrimp. Pat pulls the rip cord on the net as it swoops in over the deck. A small catch of briny shrimp drops from the net onto the deck. She yanks off her canvas captain's cap and whacks it in frustration against her blue jeans. She whips around to her boat mate, standing next to her. The mate is shirtless, the sun-darkened skin of his broad upper torso swirled with wicked-looking interlocking tattoos. He hikes his tight jeans up and takes a boxer's stance in his white rubber shrimper boots, expecting a punch from frustrated Pat as she shouts: \"We've been out here for three days, and all I get is a twenty-buck load of pink bug-eyes! I can't even pay my fuel with that!\"\n\nThe mate cocks a hand over his eyes and squints at the sunlight's glare on the ocean. \"Looks like your luck is taking a turn.\" He points to a bubbling break on the water's surface. A pod of fast-moving dolphins leaps from the water into the air, their bodies twisting in muscular turns as they approach the side of the boat.\n\nPat claps her hands together. \"Hallelujah, let's get some bait for the longlines!\" She runs into the pilothouse and races back out with a shotgun. She takes a position on the prow of the boat as the pod of dolphins nose-dive back beneath the water and disappear. She aims the shotgun at a calm spot in the water in front of the boat. She waits. The dolphins break through the surface of the calm spot in a gushing spray of saltwater; sunlight shimmers on their sleek, wet bodies arched high in the air. She fires a blast from the shotgun. Blood spews from one of the arched dolphins. The others dive from sight, leaving the dolphin with its side blown open floating on the sea close to the boat. Pat puts down the shotgun, grabs a long gaffing pole, and whams its steel hook-point into the floating dolphin. The mate short-gaffs the creature from the other side. Together they heft the dead weight up onto the deck.\n\nPat grins with delight at the mate. \"Hurry, get that bucket of J-hooks.\" She pulls out her knife from the leather holster belt strapped around her waist. She grips the knife and slashes at the dolphin's thick dorsal fin, curved up high from the center of its back. The blade cuts through the fibrous veins of the fin in a spurt of blood.\n\nThe mate comes back with the bucket of barbed J-hooks. Pat pushes sliced bloody dolphin meat onto the hooks. She wipes sweat off her face and looks up. \"Perfect bait\u2014the turtles always think it's drifting squid.\"\n\nPat goes into the pilothouse and throws the engine switch. The engine growls to life in a loud metallic clang of firing pistons. She steers the boat out on a new course. The mate feeds the baited hooked longline off the stern into the slashed V-wake of the propeller-churned water behind the boat. The longline whirrs away into the distance, sinking from sight beneath the water.\n\nThe sun smacks down on Pat at the back of her boat; she is cranking the wood handle of the line-winch, which reels in the longline trailing in the water. The mate works next to her, hoisting the longline onto the deck. All the longline's barbed hooks are stripped of dolphin bait. Pat keeps cranking the handle; the veins on her neck pop out purple. The last of the longline left in the water jerks, goes taut, whirs back out. Pat grips the handle tighter, puts all of her strength into trying to stop the line from stripping farther out behind the boat. The mate grabs the handle with Pat. They strain together, groaning as their muscles burn, holding the longline. The tension reverses toward Pat and the mate; they crank the winch handle harder. The longline in the water comes closer to the boat.\n\nThe gray humped shell of a sea turtle crests above the water. The steel barbs of a J-hook are sunk deep into one of its thrashing front flippers. The turtle aggressively flaps its free flipper against the water's surface, struggling to turn its great weight against the hook that holds it to the taut line.\n\nPat whoops with joy. \"A leatherback! Jackpot!\"\n\nThe mate holds the winch handle steady.\n\nPat grabs a heavy net. She leans off the side of the boat and casts the net across the water over the splashing turtle. She holds the rope attached to the net as the turtle's bulk thrusts against its sudden entrapment.\n\nThe mate jams the winch handle into the locked position. He joins Pat in holding the net rope against the fury of the turtle. They are pulled to the edge of the boat. They lean dangerously off the side of the boat, about to fall into the water, pitting their combined weight against the turtle. A mighty thrust from the turtle knocks Pat and the mate off balance, and they fall to their knees on the slippery deck. They hang on to the rope, pulling back harder, groaning as they haul the turtle up from the water and heft it aboard. The turtle's bulk crashes onto the deck in a booming thump, its massive shell glistening; its prehistoric sharp-beaked face snaps from side to side as it gasps in exertion with humanlike sounds.\n\nPat gazes at the formidable animal before her. \"What a beauty. Must be a hundred years old. Big money in the fin meat. Chinese are convinced eating it will give them King Kong hard-ons to bang their girly friends all night long.\" She throws her head back, joyfully singing out at the top of her lungs an old pop song, _\"All night long, forever!\"_\n\nThe mate wipes sweat off his tattooed chest. \"Yeah, Chinese will pay a fortune.\"\n\nThe turtle powerfully slaps its long leathery flippers against the deck, futilely searching for water to make its escape. The hollow gasping from its beaked mouth becomes desperate; its bulging sea-green eyes gape up at its captors.\n\nPat picks up an iron mallet and grips its handle. She mounts the netted turtle. Her legs straddle both sides of the humped shell body. She raises the iron mallet, takes aim at the back of the turtle's exposed head, and swings. The mallet penetrates deep into the turtle's skull with a bone-shattering blow.\n\nThe mate stares at the turtle's crushed skull. His face cracks into a downward frown. He turns and leans over the railing of the boat, spewing an arc of vomit into the water.\n\nFrom her perch atop the dead turtle's massive shell, Pat swings the bloody mallet high and shouts with a laugh at the mate, \"Man up, you pussy!\"\n\nJoan sits on the edge of her bed. The soft curves of her body are outlined through a sheer slip. She tilts her head and listens to approaching footsteps in the hallway. She looks anxiously at the closed bedroom door as it creaks open. A figure comes through the doorway.\n\nLuz steps into the room. \"Sorry I'm late, hon.\" She unbuckles her pistol and sets it on the dresser. She pulls off her shoes and trousers and stands in her loose white shirt and white panties. She begins to unbutton her shirt and notices the concerned expression on Joan's face. She speaks in a soothing voice: \"You can stop worrying, I'm home.\"\n\n\"I can't help worrying. I know what's going on.\"\n\n\"What do you mean, you know what's going on?\"\n\n\"Since Nina became ill, you've changed. You hardly touch me anymore. Nina is my tragedy too.\"\n\nLuz gets down on her knees before Joan. Her sad eyes stare apologetically. \"You're right. I'm sorry. I just can't... get beyond... this pain.\"\n\n\"There is only one way out of pain. You have to push it aside with new life.\" Joan takes the bottom of her slip with her fingers. She sensually glides the slip up over the swell of her hips, past the thinness of her waist, and above her arched breasts. She pulls the slip over her head and tosses it aside. The white skin of her face flushes pink as her lips part, offering Luz her mouth for a kiss.\n\nLuz leans toward Joan, then stops. \"Forgive me, darling. I can't.\"\n\nJoan slides an arm around Luz's waist and pulls her close. She covers Luz's face with lip-brushing kisses. Luz's breath sucks in sharply with a gasp. Joan lies back on the bed, her arms outstretched, the fullness of her naked body exposed. Her breasts heave; her rib cage expands and contracts with deep, expectant breathing. She reaches up and gently pulls Luz's head down.\n\nLuz's cheek rests on Joan's smooth thigh. She inhales the sweetness of Joan's skin. She listens to Joan's urgent breathing. She hears the sound of her own breath. She tastes the wet saltiness of her tears as they fall from her eyes. The tears run down Joan's thigh, disappearing into a shadowed crevice.\n\nCeiling fans swirl in the humid air over the heads of Big Conch and Hard Puppy, who are perched on stools at the Bounty Bar's long counter. Their eyes are riveted on Zoe, dressed in her work uniform of tight white shorts and white halter top. She stands in front of the cash register, adding up the night's receipts.\n\nHard swings around to Big. The left side of his forehead has a red gash where Luz whacked him with the butt of her gun. His platinum teeth flash as he drunkenly slurs his words into Big's face. \"Only be two things in life you need to know. First be, how to get along with people. Second be, how to get around people.\"\n\nBig slams his beer bottle on the mahogany counter. \"Thousand fucking times you told me that. I hear it again, I'm going to bash your\u2014\"\n\nZoe interrupts. \"Time to go, Boy Scouts. I'm closing.\"\n\nBig throws a questioning look across the counter at Zoe. \"I'm always thinking, why's a lovely lady like you running a bar?\"\n\nZoe gives a weary smile. \"Every time you're here drinking, you ask that. It's always the same answer: I have a university degree in philosophy. Can't do anything with that except teach or tend bar. I had to support Noah through law school, couldn't do that on a teacher's salary. So here I am, still in the bar racket.\"\n\nBig keeps his questioning going, enjoying the beer buzz-cut of his words. \"That Truth Dog of yours is a drinking man, sucks it up like a thirsty baby, but never comes in here. He stays away because he knows Big rules this roost. Your Dog's a chickenshit.\"\n\nZoe walks from the register to Big. She stares at his blurry, reddened blue eyes. \"Okay, Big, I'll tell you with no philosophizing why Noah is never here. You're an amateur drinker\u2014you drink in public places. Noah is a professional. A professional, he drinks alone. He doesn't need an audience.\"\n\nHard nods his head in agreement with Zoe. He digs a coin out of his pocket. He flips the coin in the air, catches it, and closes his fist on it. He holds out his clenched fist to Zoe. \"What side my coin be comin' down on? Be it heads, you go home with me. Be it tails, you go home with Big. You call it, bitch goddess.\"\n\nZoe shrugs her shoulders and laughs. \"You can keep flipping that coin until it loses its shine. I'm not going home with either of you.\" She quickly scoops up Hard's and Big's beer bottles. \"Time to leave, guys. No more telling each other true lies.\"\n\nHard shifts his gaze to the end of the counter, where Hogfish sits alone, his head jerking erratically to music pumping through iPhone earbuds. Hard turns back to Zoe and gives her a mocking wink. \"I gets it now. You be savin' yourself for the Hog. That guy can barely make a bologna sandwich with what little pink meat he's got between the legs.\"\n\nBig belches in Hogfish's direction. \"What's left of his brain has been boiled like a lobster in a pot.\"\n\nZoe moves down to Hogfish and leans across the counter to him. \"Sorry, camper. Two o'clock at night. I want to close up shop. You'll have to leave.\" Hogfish's glazed eyes roll; he doesn't look at Zoe. She pulls the earbuds out of his ears. \"I said you have to go.\" He snatches the earbuds back from her, jumps off the barstool, and runs for the door.\n\nHard hoots as the door slams behind Hogfish. \"That sucka be a spook! Spookier than his crazy ol' man!\"\n\nBig slaps his open palm on the counter and hooks a macho grin at Zoe. \"If Hog ever hassles you, give Big the word. I'll snip his balls off and run them up the flagpole.\"\n\nZoe walks back along the counter and stops in front of Big. \"I don't need you to protect me, not from Hogfish, not from anyone.\"\n\nBig's grin widens to a belligerent smirk. \"I'm serious as a triple heart bypass. Hog gets a weird-on with you, just nod in Big's direction and he's dust.\"\n\nZoe pushes away from Big. \"Hogfish isn't hassling me. Leave the poor guy alone. It's Hogfish that's being hassled. Hassled by the world. That's what happens to these vets that come back from wars they didn't start. I know. My father got the same treatment when he came back from Vietnam, treated like shit or ignored like a freak. Cut Hogfish some slack or this bitch goddess will scrape those blue eyes out of your head with her pretty fingernails.\"\n\nBig throws his head back and shouts up at the fan blades cutting the air, \"Goddamn, ain't nothing sexier than a sassy woman!\" He looks back at Zoe. \"You're a spur under my saddle, but I still want to ride you. Ride your gorgeous ass right into the sunset!\"\n\nZoe steps outside beneath a neon **BOUNTY BAR** sign glowing blue above her in the humid night air. She locks the bar's front door, puts the key in her purse, and zips the purse up. She tucks the purse under her arm and starts walking away. She stops, hearing shuffling from the other side of the deserted street. She looks across the street and stares into the shadows of a tall night-blooming cactus tree. She sees no movement. She glances up at the hanging orange lantern of the moon with halos of light thickening around it, indicating rain is close. She continues walking, heading along empty palm-lined streets snaking between century-old white clapboard houses with wraparound balconies and widows' walks, once inhabited by ship captains and harbor customs men, now tarted up in shiny new tropical colors and surrounded by the electrical drone of motors powering air conditioners and backyard swimming-pool pumps. The houses are constructed cheek by jowl; their tall pitched tin roofs lean into one another as if to block any hurricane winds that might come rushing unannounced through the streets.\n\nZoe hears the fall of footsteps behind her. She stops beneath the leafy canopy of a woman's-tongue tree. She spins quickly around and looks back to surprise whoever might be following her. She sees no one; she waits. She hears above her the rattle of seeds in the long pods dangling from the woman's-tongue tree. The air brings the scent of a rotting dead rat. She hears footsteps again. She stays still. Her breathing becomes faster, her heart pounds. She smells her own fear exuding with the perspiration from her exposed skin. She jolts at a sudden screeching. She hears a thump from the porch of the house across the street. The entwined bodies of two black cats locked together in lust roll off the porch as they scream in sharp pain.\n\nZoe turns and walks on at a faster pace, her long legs in her white shorts flashing in the night. Nocturnal skink lizards on the cracked sidewalk skitter away. The sound of footsteps behind her grows louder. She doesn't look back as she hurries to her two-story Bahamian-style house with its smooth plastered exterior of blush-pink walls and framed white windows. She opens the gate of the picket fence in front of her house and races up the flagstone steps. She unlocks the door, steps inside, and slams the door closed.\n\nIn the jungle-thick garden behind Zoe's two-story house, insects chirp and frogs croak in the dense foliage. The insects and frogs suddenly fall silent as oncoming footsteps sound. A person's heavy breathing wafts through the air.\n\nA light inside Zoe's house goes on from the second-story bedroom facing the garden. Through the bedroom's open window, golden lamplight illuminates her as she hurriedly undresses. She stands naked for a moment, then quickly slips on a silk robe. A sudden gust of wind bangs the wooden plantation shutters against the sides of her bedroom window. She leans out from the window and grabs the wooden shutters. She is caught framed by light behind her; the wind blows her hair and flutters her silk robe. Her robe falls open, exposing the swing of her breasts. She grabs the open robe and pulls it tightly together. She slams the shutters closed.\n\nIn the garden, wind rustles the jungle foliage. The noise of insects and frogs starts again. Thunder rumbles overhead; lightning bolts crack the darkness and expose in the garden the upturned body of a Cuban death's-head palmetto roach. Red fire ants swirl up from the earth around the brown-crusted hoary creature and begin devouring its multitude of legs flailing hopelessly. Rain shoots down from the sky.\n\nRain slashes onto Pat's boat, anchored at the shrimping-boat dock. Pat, belowdecks, in a narrow berth, tosses and turns in her sleep. The rain above awakens her. Illuminated numbers on a digital clock next to her glow: 4:02.\n\nA clanging bang from the deck above startles her. She jumps out of the berth and pulls on her clothes. She grabs a flashlight and a sharp fish-boning knife. She shines the beam before her as she climbs the spiral galley ladder to the top deck and steps cautiously out into the rain. She aims the beam in the darkness. The beam illuminates a long rope from the mainmast that was ripped loose by the wind and dangles down. At the rope's end is a steel pulley, clanging against the deck.\n\nPat struggles to secure the rope back to the mast in the wind and rain. She ties the rope down, then shines the beam around the boat again. Nothing seems wrong, she goes below. Rain continues to pound on the empty deck.\n\nOn the side of Pat's boat, at the waterline, next to the heavy iron anchor chain, the skull head of a black-and-white-rubber-encased skeleton emerges from the water. The head turns slowly, revealing an iridescent skeleton face with two deep black eye sockets. Hard rain drums on the skeleton's face.\n\nThe skeleton's black-rubber-gloved fingers rise from the water and grab the anchor chain. The skeleton pulls out of the water, climbs hand over hand up the length of the anchor chain, and stands upright on the deck of the boat. Slung over the skeleton's shoulder is a speargun. The rain beats on the skeleton as it moves stealthily across the wet deck. It stops before the closed galley door leading belowdecks. The skeleton does not move. It waits. The rain whips harder, thwacking against the skeleton's tight rubber suit. The skeleton's bony-fingered rubber hand reaches out slowly and clutches the latch of the galley door. It slides the door back, steps silently through the opening, and closes the door behind.\n\nHalfway down the inside galley spiral ladder leading belowdecks, the flash of a thrown knife whirs past the descending skeleton. The tip of the knife's blade drives deep into the wood wall behind the skeleton's skull. The skeleton peers from its deep eye sockets into the surrounding darkness. Out of the darkness Pat appears, her breath bursting in a war-cry as she runs, swinging the barbed hook of a gaffing pole before her with a muscular hurl. The skeleton dives into the shadows. Pat's gaffing pole swipes through the air, its flashing steel hooks seeking their target.\n\nOn the boat's deck above, the wind howls in the rigging and around the tall mast. The wind picks up velocity; its howl becomes a high-pitched sound like screaming, screaming lost to all ears in the fury of a raging storm.\n\nThe morning glare exposes the shrimping-boat dock blocked off by police cars and yellow crime-scene tape; screeching seagulls circle above. On the deck of Pat's boat, a team of latex-gloved investigators work methodically, gathering evidence. Among them are Luz and the Police Chief, scrutinizing a red **X** spray-painted on the deck's plank flooring. The Chief glances at Luz with a look of dismay. \"I was hoping Bizango had moved on.\"\n\nLuz stares at the boat's boom net extended over the water. \"No such luck. He's back in business.\" Tangled inside the net hanging from the boom is Pat's naked, bloody body. A steel spear is pierced between her breasts, through her chest, and out her back. Her ears have been cut off. Her lifeless lips are closed shut by the sharp barbed metal points of J-hooks.\n\nThe Chief shakes his head. \"Only thing different with Bizango's MO this time is, he closed the mouth with J-hooks, not fishing line. Why J-hooks?\"\n\n\"Could be simple. Could be that's all he had.\"\n\n\"J-hooks, for Christ's sake. I still don't get it.\"\n\nA rowboat in the water below the boom glides under the net weighted with Pat's body. A police photographer in the boat aims his camera up and rapid-fires pictures through a zoom lens.\n\nThe Chief looks at the seagulls above, diving in downward swoops toward the mutilated body in the net. \"Why Pat? She's not involved with Neptune Bay Resort.\"\n\n\"No rhyme or reason. Bizango must be\u2014\"\n\nLoud shouting and banging come from belowdecks. Luz and the Chief run to the open hatch doorway leading below. They pull their guns and climb down the spiral ladder into the galley. They look around; the galley is deserted. They hurry through a low opening into the engine room. Next to a maze of greasy valves, pistons, and pipes stands Moxel, holding a gun to the head of the Haitian boy Rimbaud.\n\nMoxel triumphantly announces, \"Found this monkey hiding here.\"\n\nRimbaud's fatigued red eyes are terrified, his clothes dirty and ragged; his body is thin from lack of food.\n\nThe Chief rushes to Rimbaud. \"What did you do to the white woman? How long have you been hiding on her boat?\"\n\nRimbaud is too frightened to answer. He looks with pleading wide eyes at Luz.\n\nLuz steps close to Rimbaud and speaks in a calm voice. \"Son, what's your name?\"\n\nRimbaud bites his trembling lip and doesn't answer.\n\n\"Son, I promise I won't let them hurt you. Who are you?\"\n\nRimbaud's words blurt out in French to Luz. \"Protect me! I saw a Bizango. Don't let Bizango kill me.\"\n\nThe Chief looks at Luz. \"What's he saying?\"\n\nMoxel shouts. \"Yeah, what's the monkey's alibi!\"\n\nLuz shakes her head. \"I don't know what he's saying. He seems to be speaking French. All I understand is the word 'Bizango.' \"\n\nThe Chief orders Luz, \"Lock him up and get him an interpreter. I want answers.\"\n\nMoxel unhooks the steel handcuffs dangling from his belt. He grabs Rimbaud's thin arms and roughly shackles the boy's hands behind his back. He pushes the boy forward with a proud nod at the Chief and Luz. \"I'll book him. It was me. I got Bizango. I got the serial killer.\"\n\nLuz paces back and forth impatiently at the end of a long corridor in the Detention Center. A uniformed and armed guard marches to her with Rimbaud. The boy's head is shaved; his skinny body looks lost in a bright-orange prisoner jumpsuit; his hands are cuffed.\n\nThe guard speaks to Luz quickly, with irritation: \"Where's the interpreter? He's supposed to be here to get the prisoner's statement.\"\n\n\"Don't worry. He's coming. Take the handcuffs off the boy.\"\n\n\"No way. He's a murder suspect.\"\n\nLuz sees Noah, dressed in his rumpled seersucker suit, weaving drunkenly up the corridor. He stops in front of her and raises his hand in a salute. \"French interpreter, reporting for duty, sir.\"\n\nLuz stiffens with anger. \"Sober up! This kid's being accused of murder! You've got a job to do!\"\n\nNoah turns and recognizes the shaven-head prisoner in the orange jumpsuit. He blurts out a laugh. \"Rimbaud! He's no murderer. You've got to be kidding. The kid is harmless. What kind of bullshit is this?\"\n\nThe guard sniffs the rum scent of Noah's breath. \"It's no bullshit, buddy. You have thirty minutes to get the prisoner's statement before he's locked up again.\"\n\nNoah tilts on wobbly legs. \"A whole thirty minutes, how generous. With that much time I can get his entire life story and also read him _Moby-Dick_.\"\n\nThe guard takes Rimbaud by the arm and pulls him across the hall. He shoves Rimbaud through an open doorway into a windowless room, then looks back at Noah. \"You're wasting time. Now you only have twenty-nine minutes. Get in here.\"\n\nNoah walks across the hall and steps inside the room. The guard walks out and shuts the door behind him.\n\nNoah and Rimbaud sit across from each other at a bare table. Rimbaud's bony jaw is set; his lips are clamped shut.\n\nNoah takes out a black micro\u2013digital recorder from his coat pocket. He sets the recorder on the table, turns it on, and speaks to Rimbaud in French. \"I'm glad you're alive. I'd given up hope. Why did you leave my boat the night of the Shrimp Fleet Blessing?\"\n\nRimbaud's eyes turn down. He stares at the bare wood surface of the table and doesn't answer.\n\nNoah slips out a pint bottle of rum from his other coat pocket. He takes a swallow and sets the bottle next to the micro-recorder. \"Rimbaud, help me out. They're holding you for murder. Why did you leave my boat? You were safe there.\"\n\nRimbaud keeps staring at the tabletop. With his index finger, he traces out on the table's surface an invisible spiraling circle.\n\n\"Listen, kid, I know what you've been through. You escaped the misery of Haiti and drifted on a rickety raft seven hundred miles in shark-infested waters to make it to this promised land. You lost your home, your family, everything, the same old sad story. There's nothing going to change the sad story unless you let me help you. Tell me, why did you leave my boat?\"\n\nRimbaud's head snaps up, his eyes wild with fear, his French words shrill. \"To save myself! I jumped from your boat because the sky was exploding with fire!\"\n\n\"The sky exploding? What do you mean? Ah, the celebration fireworks that were being shot off that night. It never occurred to me you'd never seen fireworks before. No wonder it scared the hell out of you.\" Noah urges Rimbaud on with another question. \"What happened after you left my boat?\"\n\nRimbaud squirms, trying to make himself smaller inside his oversized orange jumpsuit. His words come out slowly. \"I hid... on different... boats.\"\n\n\"So that's why you were on Pat's boat.\"\n\n\"Pat?\"\n\n\"The woman whose boat you were found on.\"\n\nA loud knock raps on the closed door. From behind the door, the guard's voice shouts, \"Be quick. Hurry up.\"\n\nNoah looks directly into Rimbaud's eyes. \"Did you kill Pat?\"\n\nRimbaud moves forward in his chair. He speaks in a low voice, afraid of being overheard.\n\nNoah leans in, struggling to hear the barely audible words coming from Rimbaud's trembling lips.\n\n\"One night, a skeleton rose from the dead. I was hiding, and I saw it with my own eyes. I saw Bizango.\"\n\n\"Bizango? Who is Bizango?\"\n\n\"A skeleton who rises from the dead. A zombie executioner. He is the great corrector between right and wrong, between good and evil. He is the ultimate judge. Bizango kills evil people.\"\n\n\"You're telling me a zombie skeleton rose from the dead and killed Pat?\"\n\nRimbaud stares fearfully and nods his head in an emphatic yes.\n\nNoah turns off the micro-recorder. He picks up his bottle and takes a long drink. He caps the bottle and slips it back into his pocket. He fixes Rimbaud with a solemn gaze. \"I know you're innocent, kid, but if the only defense you have is that you saw a zombie kill Pat, then you'll be convicted for murder.\"\n\nA cloaked judge stares down from her elevated podium at the defendant's table below, where Noah sits between Rimbaud and a young public defender. Behind the table stands a uniformed bailiff with a holstered .45 strapped to his waist. From the back row of benches, Luz leans forward intently, watching the proceedings in the crowded courtroom.\n\nThe judge dips her glasses low on her nose and glowers at Noah. \"Because of your past inappropriate antics in a Florida court, you have been disbarred from practicing law in this state. What are you doing in my courtroom?\"\n\nThe public defender quickly rises and answers in a nervous voice: \"Your Honor, may I clarify that Noah Sax is not here as legal representation for the defendant. I am the defendant's counsel. I respectfully would like to make a motion to the court that\u2014\"\n\nThe judge cuts the young defender off. \"These proceedings will not continue with Mr. Sax present.\" She nods to the bailiff. \"Escort Mr. Sax from my courtroom.\"\n\nThe armed bailiff steps to Noah and pulls him up by the arm from his chair. Noah shakes free from the bailiff and faces the judge. \"I'm not here as an attorney. I'm here as the defendant's interpreter. The defendant has a right to an interpreter of his\u2014\"\n\nThe judge jabs her finger at Noah. \"It's at the court's discretion to appoint the interpreter. I certainly did not appoint you.\"\n\n\"But under Florida law the defendant has a right to an interpreter of his own choosing. It specifically sets forth in State Statute Number\u2014\"\n\n\"Mr. Sax, don't push your luck. If you're out of order here today, I'll jail you for contempt.\"\n\n\"Count on me, Your Honor, I'll be a model citizen.\"\n\n\"No wisecracks. I won't tolerate it. If it were possible to disbar you twice, I would.\"\n\nNoah sits back down between Rimbaud and the defense attorney.\n\nThe judge bangs her gavel. \"This hearing is postponed until the autopsy of the deceased victim, Pat Judy Benson, is complete. The defendant, Rimbaud Mesrine, is to be held without bail.\"\n\nNoah jumps up. \"That's not fair. If it please the court, I would like to\u2014\"\n\n\"No, it does not please this court. Nothing you do will ever please this court. Be seated.\"\n\nNoah stays on his feet. \"I just wanted to say that I have information from the defendant regarding\u2014\"\n\nThe judge glares. \"No more warnings, Mr. Sax. I'm locking you up right now if you don't shut up.\"\n\nThe defense attorney rises quickly. \"Your Honor, if it please the court, may I\u2014\"\n\n\"Counsel, I already told Mr. Sax, this court is not pleased!\"\n\nThe judge bangs her gavel. \"Court adjourned!\"\n\nBeneath the sway of palm trees the cemetery is a crowded maze of granite gravestones and cement-plastered tombs bleached by the sun to an otherworldly bone-white. Family plots are decorated with reposing stone lambs, winged angels in alabaster, and limestone Christian crosses. Tall white-feathered ibises stalk ghostlike on spindly legs across the sparse grassy turf. The birds' long curved bills are held ready as they stare down to peck a scuttling brown roach or squirming grub. On top of a twenty-foot marble obelisk, a red-shouldered hawk is perched, alert for rodent prey among the bouquets of faded plastic flowers scattered in the weeds of unkempt graves. The hawk swivels its head and stares down from its lofty perch at Luz below, as she follows a meandering pathway through the city of the dead. Luz pushes Nina in her wheelchair; Chicken trots alongside. Luz stops and looks up at the hawk on the point of the obelisk. The hawk stares back with amber eyes and screeches a high-pitched whistle.\n\nNina's thin fingers nervously fidget with the stems of the fresh bouquet of white lilies held in her lap. She gazes at the hawk and winces. \"It won't hurt us, will it, Mom?\"\n\n\"Not unless you're a mouse, honey. Nothing to worry about.\"\n\n\"Well, with no hair on my head, my ears look really, really big. Maybe the hawk will think I'm Minnie Mouse.\"\n\nLuz smiles at Nina's lightheartedness. The hawk whistles shrilly again. It spreads its wings and wheels off the granite point, soaring from sight into the blur of sun-bleached sky.\n\nLuz continues pushing Nina down a path between rows of old and neglected graves with tilted and crumbling headstones. She stops Nina's wheelchair at a well-kept site beneath the lacy green spread of a poinciana tree in full bloom with sashes of red flowers. The names carved into the surrounding headstones all read **ZAMORA**. Luz kneels and makes the sign of the cross. Her eyes mist over, and her lips move reverentially in silent prayer. Nina hands Luz the bouquet of lilies. Luz places one lily before each of the Zamora headstones and turns to Nina. \"Our family has been on this island for five generations. We'll be the last Zamoras buried here. After us the cemetery will be full up\u2014no more plots left, even for the grandchildren of Cuban heroes.\"\n\n\"I know, Mom. You tell me that each time we come here. But I don't want to think about where I'll be buried, it's creepy.\"\n\n\"Tradition is important. Tradition makes us all part of one another, part of something bigger. I don't want you to forget your heritage. There were slaves in Cuba. Zamoras fought against Spain to free Cuba in the 1868 rebellion. That's the problem today.\"\n\n\"What do you mean, that's the problem today?\"\n\n\"No one is willing to sacrifice. No one is\u2014\"\n\nLuz notices Chicken sniffing aggressively, his nose pointed at a gnarly blob of a toad with bulging eyes and a milky substance foaming from its fat, warty lips. The toad squats in the grass next to a Zamora grave. Chicken stiffens, prepared to attack. Luz grabs the dog by the collar and pulls him back. \"That's a Bufo toad. He's poisonous. One bite of him and you're dead.\"\n\nChicken barks, but not at the toad. He sees a dark figure outlined by the sun's glare approaching through the gravestones. Chicken growls as the figure comes closer. It is Moxel. He stops in front of Luz, panting from the heat, the armpits of his blue uniform dampened by sweat rings. His words rush out hoarse from his dry throat. \"I was just at your house. Joan told me you'd be here. The Chief wants you in his office.\" Moxel glances down at Nina. \"How you doing, little girl? Your mom should know better than to bring someone in your condition out in this hundred-degree heat. This sun will turn your skin blacker than charcoal.\"\n\nThe toad next to a grave in the grass springs up and takes two lunging hops toward Moxel. He squints in the glaring sunlight at the toad. \"What's that ugly-ass frog?\"\n\nLuz keeps her hand tight on Chicken's collar as the dog strains to get at the toad. \"Poisonous. Don't touch it.\"\n\n\"Poisonous, no shit.\" Moxel unsnaps his side holster, yanks out his revolver, and shoots, blasting the toad. Toad fragments spew into the air and splatter across the carved name **ZAMORA** on a headstone. Nina screams and cringes in her wheelchair. Moxel shoves his gun back into its holster and grins. \"I hope I didn't blow away an endangered species.\"\n\nLuz spins Nina's wheelchair around so Nina can't see her whip her Magnum from its holster. She jams the pistol's barrel into the side of Moxel's head. \"You are an endangered species.\"\n\nInside the Police Chief's office, the Chief and Moxel stop their animated conversation as Luz enters. Moxel's face reddens as he blurts at Luz: \"You pulled a gun on me for shooting a frog! What the fuck is that? I'm the one who saved your ass in the bat tower. If I hadn't climbed up that ladder and risked my life to help you, you would have fallen to your death.\" Moxel swings around to the Chief. \"What kind of force is this if she's allowed to pull a gun on another officer? You should fire her for unfit conduct. You should\u2014\"\n\nThe Chief cuts Moxel off. \"Calm down. I don't have time for fraternal squabbles.\" He turns to Luz and hands her a thick folder of papers. \"This forensic report just came in. The Haitian kid's fingerprints were found all over Pat's boat.\"\n\nLuz takes the thick folder. \"I'll read it. What about Pat's body? Were Rimbaud's fingerprints found on her body?\"\n\n\"No, nothing. Maybe the kid was wearing gloves.\"\n\n\"Rimbaud told the interpreter he saw Bizango on the boat. Did the lab find any trace of that?\"\n\n\"Zip, no fingerprints, no hair, no footprints, no nothing. If Bizango was on that boat, he doesn't just wear gloves, he must be dressed in a glove. Only prints found were from the Haitian and Pat's boat mate. You got something on the mate?\"\n\n\"Found him up the Keys at the Pink Grouper strip club in Marathon. Checked out his alibi. Says he was at the club the night of the murder.\"\n\n\"Witnesses to that?\"\n\n\"All six of the pole dancers who performed that night. One of them says he shoved a hundred-dollar bill beneath her panties, up her butt hole.\"\n\n\"Good to know some guys are still gentlemen.\"\n\nLuz looks curiously at the report folder. \"Anything in here about the hooks puncturing Pat's lips?\"\n\n\"Mustad Super Marlin J-hooks. No prints on them, but we hit a different jackpot.\" The Chief picks up a black micro\u2013digital recorder from his desk. \"A recorder like this was found inside Pat's mouth.\"\n\nLuz eyes the recorder. \"Same kind found in Bill Warren's mouth at the bat tower. There's a Bizango recording on it?\"\n\n\"Yeah, but saying something different.\"\n\n\"Is it in English, like the Bill Warren recording?\"\n\n\"Of course, why?\"\n\n\"Because Rimbaud only speaks French. I know this for a fact. He can't be Bizango if this recording is in English.\"\n\nMoxel snorts derisively. \"Did you ever think that somebody else recorded it for him? There could be a team of Bizangos operating in Key West.\"\n\nLuz moves closer to the Chief. \"Maybe we should go public with the recordings. Can't let this grow cold. We need anything we can get.\"\n\n\"No, Moxel might be correct. If there are two Bizangos, I don't want to give the other one the advantage of knowing we are stumped. That's what he wants\u2014he wants these recordings to be broadcast. Besides, the public is already frightened enough about the murders, they're all over the news.\"\n\n\"But somebody in the public might have important information, a lead.\"\n\n\"There's another reason to keep a lid on these killings. Eighty thousand big spenders are headed here for the Halloween Fantasy Parade. I won't be held responsible for destroying the island's biggest payday of the year.\"\n\n\"You could be right. Play the recording.\"\n\nThe Chief turns around to Moxel. \"I want only Luz to hear this recording, it's highly sensitive. Close the door on your way out.\"\n\nMoxel doesn't budge. \"Only Luz? Why her? I'm on this investigation too. I'm the one who busted the Haitian.\"\n\nLuz looks at Moxel and nods toward the door. \"You heard, go.\"\n\nMoxel stares defiantly at Luz. \"I want to hear the recording. Maybe that Haitian monkey is faking it and he really does speak English. Did you ever think of that, Mrs. Sherlock Holmes?\"\n\nThe Chief shouts angrily at Moxel. \"You're out of line! Leave!\"\n\nMoxel shuffles past Luz, knocking hard against her shoulder. He opens the door, and the sound of its slamming behind him fills the room.\n\nThe Chief shrugs and looks apologetically at Luz. \"He's loyal but stupid.\"\n\n\"You mean he's stupid but loyal.\"\n\n\"Anyway, he's gone.\"\n\nThe Chief cocks his thumb over the micro-recorder's play button. \"Now you'll understand why I don't want this going public. It's much worse than the recording found in Warren's mouth.\" He presses his thumb down forcefully on the recorder's play button.\n\nNoah's trawler floats in the middle of the ocean, under a sky of high, drifting clouds. He sits in the pilothouse, in front of his jerry-rigged radio broadcast console, listening intensely to an irate caller.\n\n\"America is swamped by boat people, illegal refugees, undocumented workers, political-asylum seekers. These people are on the shit end of life's stick. If we reach out to them, we'll be covered in their shit.\"\n\nNoah answers in a steady voice: \"I don't agree with you. I recently saw a refugee raft from Haiti come in. People on that raft were not covered in shit, they were scorched to death by the sun in their desperate attempt to escape famine, disease, and fear.\" He stops talking and picks up the rum bottle sitting on the console table. He takes a swig and continues. \"The rickety raft I saw would have had a hard time making it across a hotel pool in Miami, let alone across seven hundred miles of open ocean between here and Haiti. But you know what, it's better to swim with sharks in the sea than be eaten by menacing, pathological, corrupt politicians on land. Next caller. You're on pirate radio.\"\n\n\"Hey, hot damn, I'm on.\"\n\n\"The soap box is yours, pilgrim. Go.\"\n\n\"Stop squawking about dead Haitian illegals when there's three Americans murdered recently right here in Key West. Talk about something real. Nobody's safe in Key West.\"\n\n\"I don't talk about those murders because they're plastered all over the newspapers and TV twenty-four\/seven. What's interesting, though, is that the first two murders were Neptune Bay partners but the third victim was a boat captain. No coherent pattern. You're right, nobody's safe, but when were we ever really safe? Next caller.\"\n\nA deep male voice rumbles. \" _Hola_ , Truth Dog, this is the Nam vet. Today's the day I'm goin' to tell you how it's all goin' to end. The Permian Extinction Event in the Gulf!\"\n\nThe pilothouse of Noah's trawler suddenly sways hard side to side. The cell phones on his console table slide off and hit the floor. He grips the table's edge and holds on as the boat rocks. Outside the pilothouse window, a cruise ship steams by; its turbo diesel engines roar, creating a huge wake. The ship's twenty-story-high bulk blocks the sun, pitching Noah's pilothouse into darkness. He keeps his hands gripped on the edge of the console.\n\nSunlight floods back into the pilothouse as the trawler stops rocking. Noah regains his balance. He looks outside and sees the name of the departing cruise ship painted on its white stern, _Titan Reef_.\n\nHe rearranges his three fallen cell phones back on the console table and turns them on. The red lights of the phones flash with incoming calls. He reconnects the microphone wire. He slows his heavy breathing to even out his anxiety and speaks calmly into the microphone. \"Listeners, you just lost me there. I was almost the hit-and-run victim of a cruise ship, the _Titan Reef_ , headed for Key West. I was like a Chihuahua going up against King Kong. Give me a minute while I adjust my speaker volume controls.\" He looks around for his rum bottle and sees it on the floor. He picks up the bottle, uncaps it, and takes a long slug. He leans back into the microphone. \"The cruise ships always sail too close to the coral reefs. You've heard me talk about the _Titan Reef_ before. Last year it plowed right through a Caribbean atoll. What took nature millions of years to create was destroyed in one moment. There's no reason for these ships to wreak environmental catastrophe. The captains know their nautical coordinates. They're just taking shortcuts to save fuel. The _Titan Reef_ captain who buzz-sawed his ship's massive propellers through that atoll was not fired. His company paid off some government officials. That captain is a criminal who committed willful manslaughter against nature. He should be hauled before a world tribunal, should be made to walk the plank at the sharp end of a sword. Accountability, pilgrims, brings the bastards to justice.\"\n\nAll the red phone lights flash with calls. Noah punches through one of the lines. A woman's voice singsongs with exasperation. \"Those monster ships shouldn't be sailing these waters. They weigh more than a hundred thousand tons; they've got tennis courts, shopping malls, bowling alleys, movie megaplexes. People aren't satisfied building that stuff on land, they've got to float it out on the ocean too.\"\n\n\"Right. Next caller. Show me the rage.\"\n\nFrom the big wooden speakers explodes an eerie, electronically altered voice.\n\n_\"Truth Dog, you say you broadcast the truth!\"_\n\nNoah is startled by the weird voice but snaps back: \"I say I let people speak their own truth. Who is this? What's with the audio masquerade? Use your own voice if you're so interested in truth.\"\n\n_\"I'm challenging you. You keep a photograph of a woman in the drawer beneath your radio console.\"_\n\n\"How did you know that?\"\n\n_\"Open the drawer.\"_\n\nNoah pulls open the wooden drawer beneath the console. In the drawer is a framed photograph of Zoe. He takes out the photograph. \"So you know where I keep a photograph of my wife. When were you on my boat?\"\n\n_\"Turn the photograph over.\"_\n\nNoah flips the framed photograph over; duct-taped to the back is a CD labeled **LAST KEY DEER MANIFESTO**. \"What the hell? Who is this?\"\n\n_\"If you are not afraid of the truth, play the CD.\"_\n\nNoah rips the CD from the back of the photo frame. \"Is this about the endangered Key deer? I'm interested in that.\"\n\n_\"Play it.\"_\n\nNoah flicks the disc back and forth between his fingers. The round surface glints with reflected blue and orange light. He leans into the microphone. \"Listeners, for you who don't know, the endangered Key deer live only in the Florida Keys. They are small, stand only thirty inches at their shoulders. The Overseas Highway down from Miami runs right through one of their last refuges in Big Pine Key. A sign in Big Pine updates how many Key deer have been slaughtered by speeding cars on the highway each year. The count on that sign for this year is twenty-nine. That means there are fewer than three hundred surviving deer left. Countdown to Armageddon for those little Bambis. At the rate they're being killed, they'll be gone from this earth in a matter of years.\"\n\nThe electronically altered voice jumps with a shout.\n\n_\"Play the CD!\"_\n\nNoah looks again at the shards of colored light sparking off the CD held between his fingers. \"I'm asking one last time, does this CD have Key-deer information? Otherwise, I'm not interested. I won't be tricked.\"\n\n_\"It has the information you want.\"_\n\nNoah pushes the disc into the CD player on the console and punches the volume up. He grabs his bottle of rum, takes a swallow, leans back in his chair, and listens.\n\nAn earsplitting crackling static blasts from the big speakers, filling the pilothouse. Cutting through the static is an altered recorded voice reverberating with a metallic echo as if spiraling up from the depths of a steel underground chamber.\n\n_\"Hear my words, dance my tune_.\n\n_I am the assassin of lies_.\n\n_I am the bee in your ear_\n\n_the scorpion in your bed_\n\n_the rat clawing in your belly_\n\n_the knife at your throat_\n\n_the ax in your back_\n\n_the sword through your soul_\n\n_the arrow piercing your heart_.\n\n_You carry the seeds of your own destruction_.\n\n_When the atomic dust falls_\n\n_on your pathetic parade of progress_\n\n_only I will know the escape route_.\n\n_I won't let you rocket away from your plunder_ ,\n\n_implant a new universe with decay_.\n\n_You are a virus, I am the eradicating vaccine_.\n\n_I put on my suit of skeletal lights_ ,\n\n_dance into the night to exterminate you_.\n\n_Are you trembling, crying with fear?_\n\n_The Key deer you slaughter_\n\n_on the highway do not cry_.\n\n_The Key deer heroically struggle_\n\n_to survive at their final mile zero_.\n\n_Zero-bop, bop till you drop_.\n\n_I am the great corrector. I am the ultimate judge_.\n\n_I am Bizango.\"_\n\nBizango's raging voice stops. A loud crackling static hisses from the big speakers.\n\nNoah picks up his microphone and shouts into it: \"Hey, you, caller, Bizango or whoever you are! You still out there?\" Noah looks at the cell phone that the call came in on. The red light is off, the phone is dead. All the phones are dead. \"Bizango, call me! I'm ready to rage right back at you!\"\n\nNoah watches the phones for an incoming call. No red lights. He continues to wait. No lights. He puts the microphone to his lips. \"Bizango, you scared the shit out of everyone; people are afraid to call.\" He grabs his rum bottle. The bottle is empty. He tosses it aside. \"So, my loyal pilgrims, we've had a fun day on trusty old _Noah's Lark_. First there was my near hit-and-run with a _Titanic_ , then a weirded-out dude says he's a dancing skeleton coming to slit our throats. I'm sort of out of words. Not that Truth Dog doesn't have any bark and bite left in him\u2014far from it\u2014but sometimes only music can express what we feel. As I head back into Key West, I'll leave you with this music from _Carmina Burana_ , a cantata based on the fevered poetry of cloistered thirteenth-century monks. For those of you who don't understand Latin, I'll give you the translation as it plays.\"\n\nNoah punches out the Bizango CD from the player and pushes in a new disc. \"Listen to this, Bizango. Two can play your bloody game. Your kind of evil has been hanging around the school yard of history for a long time.\"\n\nFrom the big wood speakers blasts the surge of a majestic soul-wrenching orchestral rhythm accompanied by the aggressive, monumental chant of a male choir. Noah chants his translation over the choir.\n\n_\"Fate_ ,\n\n_monstrous and empty_\n\n_you whirling wheel!_\n\n_Your malevolent_\n\n_well-being is vain_\n\n_and always fades_\n\n_to nothing!_\n\n_Shadowed and veiled_\n\n_you plague me too!_\n\n_Now through the game_\n\n_I expose my bare back_\n\n_to_\n\n_your_\n\n_villainy!\"_\n\nNoah looks through the window of his pilothouse as he motors his trawler toward the distant island outline of Key West. He hears whirring from above. He looks up through the window. A helicopter darts from the sky and swoops in a broad circle over the trawler. On the side door of the helicopter is painted a blue-and-gold insignia: **KEY WEST POLICE DEPARTMENT.** Inside the copter, the pilot steers the craft, with Luz seated next to him.\n\nNoah cuts his engine and runs from the pilothouse onto the deck. From the copter, Luz's voice booms from a bullhorn: \"You're under arrest! Follow me into the harbor!\"\n\nNoah waves up to Luz, signaling that he does not understand what is going on. The copter swoops lower, the downward wind of its blades blowing hard against Noah, threatening to sweep him overboard. He sees Luz behind the copter's bulbous window with a rifle gripped in her hands. He struggles against the wind, making his way back into the pilothouse. He grabs the helm and steers toward the island.\n\nThe helicopter follows the trawler into the harbor and hovers directly above as Noah pulls up to the dock. He jumps down from the trawler onto the dock and is surrounded by a wall of policemen with rifles pointed at him. The Police Chief pushes his way through the riflemen. He shouts at Noah above the clatter from the helicopter blades. \"You think you've been damn clever! I finally got you!\" He grabs Noah's hands and handcuffs him.\n\nNoah stares at the Chief in disbelief. \"What the hell is going on? You got me for what?\"\n\n\"This morning you played a Bizango recording that in fact you made. That recording is identical to the one you left in Pat's mouth after you murdered her. No one except the police and the killer knew about that recording. Your pirate-radio charade is over!\"\n\nNoah tries to break the grip of the handcuffs binding him. The sharp edges of the cuffs cut into his wrists, drawing blood. \"I'm not Bizango!\"\n\nThe Chief turns to his riflemen. \"Read Mr. Truth Dog his Mirandas and lock him up!\"\n\nMoonlight shines down over the island's clapboard houses. The modest homes are dwarfed by the immensity of the docked cruise ship, _Titan Reef_. Inside the ship, the sprawling main cocktail lounge is decorated to resemble a big-game African safari camp, its walls crowded with mounted trophy heads of elephants, lions, gazelles, hippos, and rhinos. The amber glass eyes of the dead animals stare down at the carefree passengers sipping exotic cocktails adorned with pink parasol stir-sticks.\n\nThe chattering of the passengers stops as the ship's captain struts in dressed in a crisp white mock admiral's uniform with gold-braided epaulettes on the shoulders. He glad-hands the passengers as he works the room with a commanding air. He stops in the center of the room next to an oversized African drum of stretched zebra skin. He bangs on the drum with a carved ebony drumstick. The drum's reverberating bass focuses everyone's attention on him. \"I must interrupt your after-dinner soir\u00e9e. Something important is on the television news I want you to see. I know you've heard reports about some unfortunate murders in Key West, making you have doubts about enjoying a carefree time. This will put your minds at ease while we are berthed here.\" He holds up a TV remote control and clicks on a wide-screen television spanning the length of a wall between two stuffed leopard heads.\n\nOn the TV screen, the Police Chief stands at a podium addressing a crowd of jostling reporters, photographers, and cameramen. His voice is flat and factual. \"A suspected serial killer was taken into custody today. I am not at liberty to discuss details. Be assured, the streets of Key West are safe. The annual Fantasy Parade will go forward next week as planned. Those coming here for the world's greatest Halloween party have nothing to fear.\"\n\nThe captain cuts the sound of the Chief's voice with the remote and steps in front of the television screen. \"Everyone, you just heard it. Key West is safe. Let's celebrate our good fortune!\" The jubilant passengers cheer and raise their cocktail glasses. The captain puffs up to a heroic stance and salutes the crowd. A loud recording of the optimistic tropical song \"Don't Worry, Be Happy\" fills the air with its upbeat lyrics.\n\nA female passenger in a sexy cocktail dress sways seductively to the captain. She slips her arm intimately around his waist. The woman's laughing husband rapidly fires off the flash of his cell phone in a barrage of photographs of the new couple. The captain dances away with the man's wife.\n\nThe captain enters his luxurious suite. He tosses his mock admiral's cap onto a velvet chair and kicks off his shoes. He pulls off his watch and checks its time, 3:30 a.m. He pours himself a Scotch and soda at the elaborate mahogany bar backed by a full-length mirror. As he stirs his drink, he sees reflected in the bar's mirror something approaching from behind. He swings around.\n\nThe figure of a black-and-white-rubber-suited skeleton stands before the captain. Clutched in the skeleton's rubber-gloved hands is a speargun, its taut spear in firing position.\n\nThe captain holds out his glass of Scotch and soda to the skeleton. \"Have a drink, you deserve one\u2014sure as hell fooled me in that disguise. Great costume, but Halloween isn't until next week.\"\n\nThe skeleton remains silent and doesn't move.\n\nThe captain sips on his drink. \"Let me see your face behind that mask. Must be you, my very special Mike. You're the only one who has a key to my suite.\"\n\nThe skeleton raises the speargun. Its black rubber finger moves to the aluminum trigger. The steel spear fires with a springing whoosh, rams through the captain's chest, into his heart, out his back, and shatters the glass mirror behind in a spray of blood.\n\nThe captain falls to the floor, his mouth agape, gasping for air, the spasms of his feet kicking soundlessly into the thick carpeting.\n\nThe skeleton reaches down and pushes a black micro-recorder between the captain's lips.\n\nIn the gray mist of predawn light, Hard Puppy walks along a fishing pier jutting into Key West Harbor. He pulls behind him on a rope a heavy bloodied burlap sack. He stops at the end of the pier and looks around to check if he is being watched. He waits a few minutes, then unties the sack and exposes the dead body of a black pit bull. The dog's short-haired body is crisscrossed with deep bloody lacerations. Tied to the dog's back legs is a small iron anchor. Hard dumps the dog and anchor out of the sack. The anchor clanks loudly on the concrete pier's surface. He glances around to see if anyone heard. He looks back at the dead pit bull and studies it. He shakes his head and angrily kicks the dog with the pointed tip of his alligator shoe.\n\nThe pit bull tumbles off the end of the pier and splashes into the water, sinking under the surface. Its barrel-shaped body bobs back up. Hard's lips pull back in a sneer. \"Sink, you bastard. You lost me fifty grand in two fights. Sink, goddamn you.\"\n\nAround the pit bull's floating body, bubbles appear in the water. The dog slowly sinks again. The iron anchor drags the animal's dead weight down into the depths.\n\nHard hears screaming. He whips around to see if someone has seen him sink the dog. He spots people running toward a distant pier, where a colossal cruise ship is docked. He kicks the bloody burlap sack into the water, then walks quickly to the distant pier. He joins a crowd at the pier's end. The people stare up the steep steel stern of the ship. The rising sun's light shines on the ship's name, _Titan Reef_. Over the name is slashed in red paint a giant **X**. Swinging in front of the **X** is the captain, his body hung from a rope tight around his neck, his white admiral's uniform soaked through with blood.\n\nHard looks around at the terrified faces staring up. He breaks into a broad smile. His platinum teeth sparkle in the sun. He saunters away from the dock, snapping his fingers in time to a musical tune that he croons in the voice of an old time Dixie minstrel:\n\n_\"Goin' to run all de night_.\n\n_Goin' to run all de day_.\n\n_Bet me money on a bobtailed nag_.\n\n_Somebody be bettin' de gray_.\n\n_Can't touch bottom with a ten-foot pole_.\n\n_Oh! De doo-da day!\"_\n\nDeep within the corridors of the massive Detention Center, in a dim isolation cell, Noah sits alone on a cot. He stares at the floor, lines of worry cut across his face. He is startled by the sudden scraping-metal sound of the thick steel cell door behind him swinging open. A shaft of light from outside probes the cell.\n\nLuz appears in the doorway. \"You've been freed on bail. There was a Bizango killing last night while you were locked in here.\"\n\nNoah looks up, bleary-eyed. \"So they know I can't be Bizango?\"\n\n\"They are investigating if you might be his accomplice. The crime lab is getting results from the sweep of your boat and house in their search for anything incriminating. You're still considered a suspect.\"\n\n\"What about Rimbaud? They must be freeing him too?\"\n\n\"No. Since he was apprehended at the scene of Pat's murder, he's still being held. A trial date has been set.\"\n\nNoah focuses his eyes hard on Luz. \"You had a rifle aimed at me from that helicopter. Were you really going to shoot me?\"\n\n\"Luckily, I didn't have to decide.\"\n\n\"You believe I'm mixed up in these murders?\"\n\n\"As someone who knows you, definitely not. As a cop, I have to keep all options open.\"\n\n\"I'm going to find Bizango myself. He used me to get his message out.\"\n\n\"We're dealing with a lethal killer. You're already too involved. Back off or you might end up his next victim.\" Luz reaches down and pulls Noah up from the cot. \"Right now I need you to clean up, shave, and get yourself a new suit for Nina's Quince party. My little girl is turning fifteen tomorrow. You must be there.\"\n\n\"Wouldn't miss it. But just one other thing.\"\n\n\"Yeah?\"\n\n\"Who made my bail?\"\n\n\"You don't need to know. It's not important.\"\n\nNoah grips Luz's shoulder. \"It's important to me.\"\n\n\"I promised I wouldn't tell you.\"\n\n\"It's not like I won't find out anyway.\"\n\n\"Okay, Joan. Your sister paid half the bail.\"\n\n\"And?\"\n\n\"What?\"\n\n\"The other half. Who paid?\"\n\n\"Zoe.\"\n\nNoah steps out from the Detention Center through the front doors. He blinks in the intense sunlight after having been locked up in a windowless cell. On the expanse of asphalt parking lot TV vans with satellite antennas atop their roofs are parked. Reporters and cameramen rush to gather around the Police Chief, recording his words.\n\n\"There is no reason for panic. We assure this community that all law-enforcement resources are being used to apprehend the perpetrator of these heinous crimes.\"\n\nA reporter shouts: \"You say no reason to panic, but there have been a string of bizarre killings.\"\n\n\"We had two suspects. One was let go for lack of hard evidence to hold him. We are still holding the other one.\"\n\nAnother reporter yells angrily: \"Those two suspects were locked up when the last murder occurred. That means there must be another killer out there. Maybe there's even a team calling themselves Bizango.\"\n\n\"Well, there's at least one Bizango. Next question.\"\n\n\"Is it true the cruise ship's security cameras caught images of the captain's killer?\"\n\n\"It's true. We have video of whom we believe to be the perpetrator. We also have other important information regarding this investigation that we'll be releasing soon.\"\n\n\"The Fantasy Parade? You going to cancel it now?\"\n\n\"No. It would take a catastrophic category-five hurricane bearing down on this island before I would cancel the Fantasy Parade. Trust me, every precaution is being taken to keep people on this island safe. I have coordinated with the County Sheriff to put his one hundred fifty deputies on our streets to join with sixty Key West police. Florida Highway Patrol is bringing a canine unit, SWAT team, and one hundred officers. This is an unprecedented show of force.\"\n\nFrom behind the circle of reporters surrounding the Chief, Zoe makes her way toward the Detention Center. She walks up the front steps to where Noah is standing, and stops.\n\nNoah leans forward to give Zoe a kiss on the cheek, rushing her with his words. \"Thanks for coming. I didn't expect you to be here when they released me.\"\n\nZoe pulls back from Noah's attempted kiss. She lowers the sunglasses covering her eyes and stares over the top rims. \"I didn't come here for you. There are still some bail-bond documents I must sign, formalizing the financials of your release.\"\n\n\"I'll pay the money back. Don't worry, I won't jump bail and leave town.\"\n\n\"That's the least I expect from you. But you should know, it's me who's leaving Key West.\"\n\nNoah hides his surprise and keeps his words steady. \"You're leaving? When? You can't go before Nina's Quince. She'll be crushed. She still considers you her aunt.\"\n\n\"I'll be here for Nina. Then, right after the Fantasy Parade, I'm out. Our divorce will be finalized then.\"\n\n\"We're still married. You know, it's not over until it's over.\"\n\nZoe gives Noah a radiant smile. \"No, it's over.\"\n\nLuz sits alone on her living-room sofa. The bamboo window shades are drawn against the intense outside tropical light. In the darkened room, her solemn gaze is fixed on a family home movie playing on a television screen. The images flickering across the screen show Luz's living room ten years before, decorated with balloons and ribbons for Nina's birthday party. On the screen, little Nina is a healthy five-year-old wearing a festive paper-cone hat. She leans over a birthday cake with five candles. The red letters on the white-frosted cake spell out **HAPPY BIRTHDAY NINA!** Nina shuts her eyes tight to make a wish. She blows out the five candles on the cake with a burst of air. She looks up with triumph. Surrounding Nina are Noah, Zoe, Joan, and Carmen, all ten years younger, wearing colorful paper party hats and singing loudly, \"Happy birthday to you, dear Nina! Happy birthday to you!\" Joan stops singing and speaks at the camera: \"Honey, give me the camera. I want to film Nina with her proud mama.\" The movie image goes out of focus, then refocuses with the image of Luz lifting Nina onto her shoulders. Mother and daughter joyously wave to the camera.\n\nAs Luz watches the television screen's flickering images of her and Nina, the muscles of her jaw twitch. She holds back her emotion as Joan comes in and sits close to her. Luz takes Joan's hand. They watch the screen as the five-year-old Nina excitedly opens birthday presents.\n\nJoan's throat tightens. She gets her words out without crying: \"Seems like only yesterday. She was so healthy, so full of life.\"\n\nLuz holds Joan's hand tighter. \"Our daughter made it to today's birthday. Every doctor said she wouldn't.\"\n\n\"Why did God do this to her?\"\n\nLuz puts her arm around Joan's shoulders. She tries to hide the hurt in her voice. \"We can't blame God for Nina's condition.\"\n\n\"I hope we're doing the right thing, having this Quince party.\"\n\n\"We had a fancy hotel Quince for Carmen when she turned fifteen. Even if this one is in our backyard, it will mean the world to Nina.\"\n\nJoan brushes a tear from her eye. \"You're right. It's a miracle she's with us. We do have God to thank for that.\"\n\n\"I count every day of her fifteen years as a blessing. I'll go see how she's holding up. The guests are coming in two hours.\"\n\nJoan gently touches Luz's cheek. \"Are you sure you are okay? Should I go with you?\"\n\n\"No. I can do it. She's waiting.\"\n\nLuz leaves Joan and walks down the hallway to Nina's bedroom. The door is open. Inside, a frail Nina sits in her wheelchair, wearing a white Quince-party dress. On her head is a wig of cascading brown ringlets. At her feet is Chicken, curled up and snoring peacefully.\n\nLuz steps into the bedroom. She slips a gift-wrapped box out from her guayabera shirt pocket. She holds the box behind her back as she kneels in front of Nina's wheelchair.\n\nNina's voice is weak, but her face is animated. \"Mom, what's that behind your back?\"\n\n\"Something for the most special fifteen-year-old girl in the world.\"\n\nNina's thin lips turn up in an ironic smile. \"I'm special, like the poster child for cancer.\"\n\n\"I didn't mean it that way, darling.\"\n\n\"I know, Mom, I was just kidding. You always say, laughter is our secret weapon.\"\n\n\"You and I, we have a lot of secret weapons.\"\n\n\"So\u2014what's in the box? I bet it's a wedding ring. I bet you're going to show me the wedding ring you're finally giving Joan after twelve years.\"\n\n\"Well, that's an interesting idea.\"\n\n\"You know, you guys should just do it, tie the knot, go on an old-fashioned honeymoon to Niagara Falls.\"\n\n\"You've got my wedding all figured out.\"\n\n\"Carmen and I have it planned.\"\n\n\"It's something to look forward to, but what's in the box is just for you.\" Luz brings the box from behind her back and offers it to Nina.\n\n\"I'm sorry, Mom. I can't open it. My fingers aren't working so well today. You help me with it.\"\n\nLuz peels off the gift wrapping, exposing a silk jewelry box. She snaps the box open; inside is a gleaming pearl necklace. \"Happy fifteenth birthday, darling!\"\n\nNina tries to reach for the pearl necklace, but her arms are too weak.\n\nLuz slips the necklace around Nina's neck and fastens it. The pearls glow in a soft pink halo against Nina's white dress.\n\nNina beams with pride. \"I'm the luckiest girl to have you as my mom.\"\n\n\"It's me who's the lucky one.\"\n\n\"Thank you for such a beautiful gift, and for giving me a party today.\"\n\n\"Nothing could stop me from celebrating this day with you.\"\n\nNina's eyelids become heavy, almost closing; the light in her eyes dims. \"Mom, can I lie down before the party? I'm so tired. Will you stay with me?\"\n\n\"Of course\u2014there's time before the guests arrive.\"\n\n\"Are Uncle Noah and Auntie Zoe coming?\"\n\n\"They wouldn't miss it.\"\n\nLuz lifts Nina up into her arms from the wheelchair. She lays her on the bed.\n\nNina's dimming eyes look up. \"My wig, Mom. Take my wig off, so it doesn't get crushed before the party.\"\n\nLuz removes the wig, exposing Nina's bald head. She places the wig carefully on the nightstand and sits on the bed. She caresses Nina's bald head, her fingers stroking back and forth across the smooth skin.\n\nNina's eyelids flutter. She struggles to keep her eyes open and focused on Luz. \"Sing to me, Mom. Sing me your song.\"\n\nLuz sings in a haunting voice, her words drawn up from a deep well of emotion with melodious melancholy.\n\n_\"The first time ever I saw your face_ ,\n\n_I thought the sun rose in your eyes_\n\n_And the moon and stars were the gifts you gave_\n\n_To the dark and the empty skies, my love_.\n\n_The first time ever I kissed your cheek_ ,\n\n_I felt the earth move in my hand_\n\n_Like the trembling heart of...\"_\n\nNina's breathing becomes slow and shallow. She sleeps.\n\nLuz and Joan greet the guests in their garden. They give welcoming hugs to the men dressed in colorful slacks and guayabera shirts and kiss the women wearing flowery tropical dresses. Beneath a banyan tree, a banquet table is set with a Cuban feast, a steaming roast pig at its center. Nearby, guests dance on a wooden platform to a snappy Cuban rhythm played by three musicians. Noah stands off to the side of the crowd, tossing a tennis ball to Chicken in a game of fetch.\n\nNina, wearing her curly brown wig and white Quince-party dress, is wheeled through the merriment in her chair by Carmen. Carmen pushes Nina between guests and stops in front of Noah. He notices the pearl necklace gleaming around Nina's neck. \"Who gave you those beautiful pearls?\"\n\nNina blushes with pride. \"My mom.\"\n\n\"I'm glad your mom didn't give you one of these, or I'd be out of luck.\" Noah holds up a delicate watch with a pink patent-leather band. He straps the shiny watchband to Nina's thin wrist and kisses her forehead.\n\nNina looks with wonder at the watch. \"Oh, Uncle, thank you.\"\n\n\"Happy fifteen! You've arrived!\"\n\nCarmen looks across the lawn at Zoe, standing in front of a flowering hibiscus bush near the musicians. Carmen turns back to Noah. \"Auntie Zoe is over there. How come you aren't dancing with her?\"\n\nNoah gazes at Zoe; she is wearing a strapless sundress, her tanned shoulders are bare, her blond hair is swept back. Zoe sways her hips gently to the rhythm of the trio. Noah nods wistfully. \"I don't think Auntie Zoe wants to dance with me.\"\n\nCarmen rolls her eyes. \"Boys can be so clueless.\"\n\nNina summons up her strongest voice. \"Did you ask her if she wants to dance?\"\n\n\"No, I didn't.\"\n\nNina motions Carmen to lean close to her. She whispers in Carmen's ear. They both giggle. Carmen grabs the back of Nina's wheelchair and pushes Nina away from Noah, across the lawn; she stops in front of Zoe.\n\nNina blurts out in a flush of excitement to Zoe, \"Uncle Noah wants to dance with you!\"\n\nZoe looks across the lawn at Noah throwing the tennis ball for Chicken to chase. \"Does he really want to dance? How sweet of you to come and tell me.\" She reaches into the hibiscus bush behind her and picks two large white flowers. She hands one to Carmen and fixes the other behind Nina's ear.\n\nCarmen tucks her white hibiscus behind her ear. \"Aren't you going to dance with Uncle Noah?\"\n\n\"He should ask me himself.\"\n\nNina holds up her thin wrist to Zoe, showing off the pink watch. \"Uncle Noah gave this to me.\"\n\nZoe runs her finger over the crystal face of the watch. \"Your uncle loves you very much to give you something so beautiful.\"\n\nNina nods. \"He's a great uncle. I'm sure he didn't ask you to dance himself because he's too scared. You know how boys are.\"\n\nZoe faces Noah, on the far side of the lawn. \"Too scared, huh. Well, then, we girls must have our own strategies, mustn't we?\"\n\nNina and Carmen giggle their enthusiastic agreement.\n\nZoe walks across the lawn, her high heels stabbing into the grass. She stops short in front of Noah. \"That's a shameless trick, getting the girls to ask me to dance with you.\"\n\nNoah flinches in surprise. \"I didn't ask them to do anything.\"\n\n\"I don't believe you.\"\n\n\"I didn't ask them. I wasn't even certain you'd come today.\"\n\n\"Of course I would come.\"\n\nNoah's gaze goes to Zoe's formfitting strapless dress, outlining the swell of her hips, the thrust of her breasts. \"That's quite a dress. You can still throw a knockout punch when you want to.\"\n\n\"I didn't come here to throw punches.\"\n\n\"So, instead of punches, dance with me.\"\n\n\"I told you, it's over.\"\n\n\"I still say, it's not over until it's over. If you won't give me a last dance, let me make you a last dinner.\"\n\n\"Dinner! You never cooked one meal for me in our entire marriage. The only thing you did in the kitchen was open liquor bottles.\"\n\n\"It's an innocent invitation, a thank-you for bailing me out. If it wasn't for you and Joan, I'd still be behind bars.\"\n\n\"You'll be free enough when our divorce is final.\"\n\n\"Free, or penalized?\"\n\nZoe studies Noah's face, looking for sincerity. Her voice softens. \"Okay, dinner at your place. But understand, it is over. This will be our last dinner.\"\n\nThe three musicians on the bandstand stop playing. At the banquet table beneath the banyan tree, Luz clinks her champagne glass for attention. Everyone joins Luz around the table and takes a seat.\n\nLuz's face brightens with a smile. \"I cannot thank all of you enough for surrounding us with your love.\" She raises her glass to Nina, seated in her wheelchair between Carmen and Zoe. \"Nina, you are my jewel, the bright star of Cuba shining over our family. Your gentleness and courage teach us every day a new lesson in life.\" Luz's throat tightens; she continues with deepening emotion. \"Your strength of character nourishes the roots of our family tree for eternity.\" Luz raises her champagne glass higher to Nina. \"A toast to you, my precious daughter, on your fifteenth birthday!\"\n\nEveryone around the table joins Luz in raising their glasses to Nina in her wheelchair. They all take a celebratory drink and cheer. Amid the cheering, Joan appears, carrying on a silver tray a three-tiered white-frosted cake. On the cake's top tier, sixteen candles, one for each year and one for good luck and growth, burn brightly. She sets the cake in front of Nina.\n\nNina stares wide-eyed at the cake. She looks across the candles to the other side of the table, at Luz. \"Mom, can you help me blow them out?\"\n\n\"Go on, honey. You can do it. This is your day.\"\n\nNina inhales deeply and concentrates. She leans down and blows. Candles on the cake flicker and go out with little puffs of smoke. One smoking candle flares up again, its wick still burning. Nina's smiling face turns to disappointment.\n\nZoe, next to Nina, puts her arms around her in a hug. \"Brava, Nina! That last burning candle is for good luck in the future!\" Nina beams as everyone applauds.\n\nLuz holds up a gaily wrapped box. \"There's one more thing. Here it is, the most exciting part of the Quince.\" She walks around the table and kneels next to Nina in her wheelchair. She unwraps the box. \"You are becoming a woman today, so you get your first real high heels. That's the tradition\u2014we are a very traditional people.\" She removes the box lid. Nina gasps at the sight of red high-heel shoes. Luz pulls off the flat white shoes Nina is wearing and slips the high heels onto her feet.\n\nNina throws her arms around Luz. \"Mom! I love you!\"\n\n\"You always wanted a pair of sparkling magic shoes like the ones Dorothy wore on her journey to see Oz. Now you'll be able to walk the Yellow Brick Road all the way to the Emerald City. When you get there and you meet Oz, tell him\"\u2014Luz bends forward and kisses Nina's forehead\u2014\"tell him how much your family adores you.\"\n\nNoah, Rimbaud, and the public defender wait in the courtroom at the defendant's table. Noah keeps his eyes on the judge's empty elevated podium at the front of the room. Rimbaud's face muscles twitch. At the prosecution's table, across the aisle, three attorneys chat in low voices as they shuffle papers back and forth from their briefcases. In the back of the crowded courtroom, a tall black man wearing a suit and tie sits in the last row. His face is stern, his attention bearing straight ahead at the defendant's table.\n\nA bailiff enters from a side door and commands loudly: \"All rise. Court is in session. The Honorable Judge Helen Reese presiding.\" Everyone in the room rises except Rimbaud, who didn't understand what the bailiff said in English. Noah nudges Rimbaud to his feet.\n\nThe cloaked judge enters from her chambers and sits at her elevated podium. She looks down. \"Be seated. Our court schedules are backed up, so time, as well as justice, is of the essence. I'll make this brief. Since the defendant's last appearance before me, I have reviewed investigative reports and detailed lab results pertinent to the murder of Pat Benson. I also perused briefs and motions from the defense counsel. I see no substantial evidence, not even circumstantial evidence, that Mr. Rimbaud Mesrine perpetuated a crime, let alone the egregious crime of murder.\" The judge turns her focus to the attorneys at the prosecution table. \"Would the prosecution like to make a statement?\"\n\nOne of the prosecution attorneys stands and answers the judge. \"Your Honor, having reviewed the facts of this case, we concur with the court and see no reason to move ahead with prosecution. If it pleases the court, we accept a motion to dismiss with prejudice.\"\n\n\"Thank you. You may be seated.\" The judge turns her attention to the defendant's table. \"I have consulted with federal immigration authorities regarding Mr. Mesrine's legal status. The salient fact, as presented in Mr. Mesrine's statement given voluntarily to the court interpreter, is that both his parents and three siblings were on the raft with him, headed from Haiti to America. Everyone on that raft was declared deceased upon reaching U.S. waters except for Mr. Mesrine. Since Mr. Mesrine entered the United States as an unaccompanied indigent minor, I hereby grant him political asylum and place him in the custody of his adult cousin, Fran\u00e7ois Lefaille, a U.S. citizen with residence in Tampa, Florida.\" The judge bangs her gavel. \"Case dismissed.\"\n\nRimbaud, confused, looks to Noah. His words blurt out in French: \"What did she say? What's happening?\"\n\nNoah answers in French. \"Political asylum. She granted you political asylum.\" He pulls Rimbaud up from his chair and claps him on the back.\n\nRimbaud looks around, still confused. He sees the tall black man walking straight down the aisle toward him. Rimbaud steps behind Noah for protection. The man stops before Noah and grabs Noah's hand in a firm grip, his voice booming in French. \"I'm Cousin Fran\u00e7ois Lefaille. Rimbaud's dear mother, Marie-Pierre, who died on the raft, was my aunt.\"\n\nRimbaud, hearing his mother's name, pokes his head around from behind Noah's back and stares at the man. Lefaille looks sympathetically at Rimbaud. \"I left Haiti when you were just a baby. I am here for you. My dear, I am your family.\" Rimbaud's eyes well up with tears and he sobs. The tall man puts his arms around Rimbaud. \"It's okay. You're safe now. Safe.\"\n\nNoah shakes Lefaille's hand. \"He'll be okay with you. Thanks.\"\n\n\"I thank you. The judge told me your interpretation of Rimbaud's statement helped convince her there was no legal cause to hold him.\"\n\nNoah turns and bear-hugs an overwhelmed Rimbaud in an affectionate embrace. \"You're free, my friend. A free man in America.\"\n\nLuz stands next to the Police Chief at a lectern onstage, facing anxious reporters and a bank of television cameras. The Chief speaks into a microphone: \"We have important information regarding the recent murders. Before we get started, I want to announce that the city of Key West is offering a reward of one hundred thousand dollars for information leading to the capture of the perpetrator. Detective Luz Zamora, head of the investigation, will fill you in on the latest.\"\n\nLuz steps forward and adjusts the lectern microphone. A barrage of camera bulbs flash. \"There are two important things we want to share with the public. The first is, we finally have images of the perpetrator. There is video taken by security cameras on the _Titan Reef_ cruise ship. The second thing is, a micro\u2013digital recorder was discovered sewn into the mouth of the _Titan Reef_ 's deceased captain. After intensive lab testing, it is now confirmed that the digital recorder's brand and make match exactly the other recorders found on the bodies of two previous victims and the audio constructs of all three are executed in precisely the same manner. We will now project for you the ship's security video. At the same time, we will play the audio of the recorder discovered in the captain's mouth. We are sharing this so that any member of the public with information can step forward. Remember, there is a one-hundred-thousand-dollar reward.\" Luz steps away from the lectern. The room plunges into darkness.\n\nA movie screen above the stage fills with flickering light. Images from a cruise ship's out-of-focus nighttime security camera begin to slowly take shape. The blur of a person, encased in a tight black-and-white rubber skeleton suit, becomes clear. The skeleton rappels down the massive steel hull of the ship in fluid acrobatic muscular motions by a long rope gripped in its rubber hands. A speargun is slung over its shoulder. The skeleton's grip on the rope slips; it swings erratically alongside the hull, splaying its legs and feet out, trying to get a purchase to keep from falling. The skeleton rights itself from swinging, pulls the rope taut against its chest. It hangs suspended for moments, making no move, then turns its skull face toward the camera. The face fills the entire movie screen, revealing two deep, impenetrable black eye sockets.\n\nThe reporters in the dark room gasp. Sound speakers beneath the screen blast a piercing static. From the static emerges the crackling mutant sound of an electronically altered voice.\n\n_\"Look into my skeletal eyes_\n\n_you who run over the Key deer_\n\n_slaughter the sea turtles_\n\n_erect your condominiums over natural habitats_\n\n_sail on cruise ships that slash coral reefs_\n\n_spew waste into pure oceans_.\n\n_You shout that you are not responsible_\n\n_for the earth's ills but my eternal X_\n\n_cannot be escaped. I am the survivor_\n\n_refusing to succumb to your polluted oceans_ ,\n\n_smogged-up, burnt-out globe_.\n\n_I am the white heron with radioactive_\n\n_mud worms eating at my heart_.\n\n_I rise up from the last mangrove swamp_\n\n_to avenge your evil_.\n\n_I am a hex doctor_\n\n_a magic gangster_\n\n_king of cemeteries_\n\n_ultimate judge_.\n\n_I am your annihilator_\n\n_the great corrector_.\n\n_I boogie till you bounce_.\n\n_I bop till you drop_.\n\n_I am Bizango.\"_\n\nThe weird sound of Bizango's voice stops. On the movie screen, the black-and-white skeletal Bizango continues rappelling down the hull of the ship. Bizango lets go of the hanging rope. In a black-and-white blur, Bizango drops. The image of Bizango falling goes out of the movie frame. Suddenly, from another angle, a different security camera picks up Bizango's steep fall. Bizango's image becomes smaller and smaller in a seventy-five-foot plunge down the side of the hull toward the water. The white spray of a splash erupts from the water at the bottom of the hull as Bizango disappears beneath the surface. The disturbed water continues to roil, then smooths over and becomes placid.\n\nThe video on the screen ends. The bright overhead lights of the room come on. Luz steps to the lectern. She looks out at the stunned reporters. \"Again, we share this information with the public so that anyone who knows anything about these heinous crimes will come forward. We are dealing with a self-appointed ecoterrorist, killing those he thinks are responsible for killing the environment. Bizango is a ticking time bomb. He must be stopped before his next murder.\"\n\nIn the second-story bedroom of his dilapidated mansion, Lareck lies in bed propped up on pillows. A shawl is draped around his shoulders despite the humid night air. His sparse white hair forms a crazy unkempt halo around his head. On the nightstand beside him are scattered bottles of medications.\n\nNoah sits next to the bed, in the old chipped wicker chair. He shakes the ice in his glass of rum and looks up to the ceiling, where a scorpion is scuttling. He watches the scorpion's hooked stinger-tail arch and twitch as it inches along. He takes a slow drink from his glass, swallows, and clears his throat. \"In Key West, you have either scorpions or rats in your house. One or the other. The two will not live side by side.\"\n\nLareck's weak, watery eyes look up at the scorpion; words wheeze from his lips: \"Where's Hogfish? He's supposed to be here to give me my medication. I haven't seen him for days. He couldn't care less if his old man lives or dies. I'm getting worse by the day.\"\n\nNoah takes another drink, then sloshes the ice in his glass. \"I wouldn't worry about Hogfish. He's probably lying low, spooked by Bizango. We're all spooked. We each fight fear in our own way. Some light a candle and pray, others have a shot of courage of one sort or another.\"\n\nLareck breaks into raspy laughter. He pushes his bedsheet off, exposing his wrinkled and shriveled body. \"Look at me. I'm already a skeleton. Maybe I'm Bizango! I'm not really trapped in this bed. I arise at night and prowl the streets in a skeleton costume. Don't you know, I'm a spook on the loose!\" His raspy laugh continues, turning into a hacking cough. He falls, exhausted, back onto the bed.\n\nNoah sets his glass on the nightstand. \"I'll give you your medication. Let's not wait for Hogfish.\" He pours out a concoction of pills from the bottles on the nightstand and fills a glass with water from a pitcher. He puts his arm around Lareck and helps him sit up.\n\nLareck's hacking cough becomes louder. He takes the pills from Noah and struggles to choke them down. He swallows the pills with a groan and sputters. \"Why do I keep taking these damn things to stay alive? I've already lived eighty-seven years. Doesn't seem right that I'm still hanging in when your young niece is on her way out. No matter how many pills Nina takes, she's still being pushed through the exit door. Wish I could take back half my years and give them to her.\" Lareck catches his breath and gives Noah a mischievous wink. \"Of course, I wouldn't give Nina my best years. I wouldn't give the poor unsuspecting girl my shameless pussy-hunting years. I'm a generous man, but those years I'm keeping for myself. I'll take them to Hell with me to keep things hotter.\"\n\n\"There are some events in a man's life that he should only share with the devil.\"\n\n\"The bastard devil hasn't heard the half of it. Wait till I get there and fill him in. He doesn't know about the Shanghai French Concession in the 1930s, before Mao finally ruined the party. My God, such antics put Toulouse-Lautrec's Paris whorehouses in the shade. I made my best paintings there. Such colorful goings-on.\" Lareck's wheezing breath breaks into excited hacking coughing.\n\nNoah looks up at the ceiling. The scorpion above stops directly over Lareck. It releases its grip on the ceiling and drops, spiraling down in a fall through the air onto Lareck's bedsheet. It maneuvers its scaly body into a crawl across the sheet toward Lareck. The hooked stinger-tail vibrates, its forward clawed pincers rapidly snapping.\n\nNoah slugs down all the rum in his glass. He scoops the scorpion up off the sheet into the empty glass. He flips the glass over onto the nightstand, trapping the scorpion inside. He watches the scorpion futilely trying to escape, clawing at the transparent walls of its prison. \"Got to protect scorpions. If not, rats will take over the house. They will take over the island.\"\n\nLareck nods in agreement. \"Where's my son? The rat.\"\n\nNoah flips the glass right side up with the scorpion inside.\n\nLareck falls back onto the bed, his pale lips quivering. \"Where's the rat?\"\n\nNoah quickly crosses the room with the agitated scorpion in the glass. He shoves open a window and tosses the scorpion out from the glass. The scorpion spins away.\n\nNoah walks in the moonless night through a trash-strewn weedy lot past a battered sign barely discernible in the darkness: **TROPIX PARADIZE**. He continues along a row of dented and rusting mobile home trailers sitting cockeyed on concrete blocks. He stops, hesitating in front of the most dilapidated trailer. He eyes the rickety steps leading up to a closed aluminum door. Shards of feeble light shine through jagged holes in the door. He walks up the steps, careful not to slip, and bangs on the door. He waits in the silence for a response, then bangs again. From inside the trailer a jittery high-pitched male voice calls out, \"No one is here! Go away!\"\n\nNoah tries the flimsy handle of the door; it is unlocked. He creaks open the door and cautiously steps inside. He looks around in dim light thrown off by one bare bulb hanging overhead from a frayed cord, its copper wires exposed. His eyes adjust to the shadowy interior. The surrounding windows are boarded over with scraps of plywood. The floor is cluttered with parts of old appliances, bent automobile hubcaps, tangled wire guts of disassembled machines, cracked baseball bats, and broken rat-traps. Seated high up on a dusty stack of yellowed newspapers in the corner is Hogfish.\n\nHogfish stares from beneath the bill of his fisherman's cap and shouts in a jittery voice: \"I keep moving, so El Finito won't know where I am when he blows in. Got to keep moving. Got to trick Finito. How'd you find me?\"\n\nNoah opens his mouth to speak, but Hogfish jumps down from the newspapers and cuts him off. \"Shut up. Don't talk. El Finito can hear you.\"\n\nNoah speaks in a low voice. \"I was just going to say\u2014\"\n\n\"Hey! You want an organ? Works fine!\" Hogfish turns to a scratched-up wood organ shoved against the wall. He pounds his fists on the chipped black and white keys.\n\nNoah grimaces at the screeching notes reverberating off the trailer's tin walls. He covers his ears with his hands and shouts at Hogfish, \"Cut the concert!\"\n\nHogfish stops pounding the keys; his head turns around. \"You don't want the organ? You got to take something. When El Finito comes, I can't be weighed down. I've got to run. Run for my life.\"\n\n\"I'm here to tell you, your father doesn't have long. He wants to see you.\"\n\nHogfish holds up a dented waffle iron. \"How about a waffle iron? You want a waffle iron? Everybody eats waffles.\"\n\n\"I don't want anything. Do you understand? Your father might die at any moment. He needs to see you.\"\n\nHogfish throws the waffle iron down with a loud clank. He kicks away boxes overflowing with trinkets and bric-a-brac, exposing on the floor an old 1950s spearfishing gun. The speargun is cocked and loaded with a sharp harpoon spear. Hogfish whips around, pointing the speargun at Noah. \"You want a speargun? You can kill a shark with this.\"\n\nNoah reels back. \"I don't want a damn thing!\"\n\nHogfish tosses the speargun to the floor and bangs open the top of the organ against the wall. He reaches inside the organ and pulls out a black-handled German Luger. He aims the pistol's blunt barrel muzzle at Noah. \"How about a World War Two German Luger? Shoots nine-millimeter bullets. Nazis killed Yank soldiers and Jews with this!\"\n\n\"What can I do with that? Shoot your El Finito when he roars ashore? Bullets can't stop a two-hundred-mile-an-hour category-five hurricane.\"\n\nHogfish moves toward Noah, frantically waving the Luger. \"No one can stop El Finito except Bizango! I got a feeling about that! Got a feeling in my bones!\" Hogfish stops; the Luger wobbles in his hand. \"Take the gun. Shoot yourself in the head with it before Finito catches up to you. You're better off dead than to see what Finito will do. His thousand-foot tsunami will smash everyone into a million pieces of shattered bones, severed eyeballs, splintered hearts, and hurl them into space.\"\n\nNoah lunges forward and grabs the barrel of the Luger, ripping it out of Hogfish's hand.\n\nHogfish moans and stares glassy-eyed at the junk-strewn floor. He sees his iPhone and picks it up, shoves its earbuds into his ears. He turns the volume high. His head bobs wildly to music. He lurches at Noah.\n\nNoah whips up the Luger. \"No further! Stay where you are!\"\n\nHogfish's voice ratchets up into hysteria. \"Finito's chasing you! Finito's going to get you!\"\n\nNoah backs away from Hogfish. He kicks open the closed door behind him and jumps out into the night.\n\nThe severe slant of late-afternoon sun glares off the brass instruments of a walking band of solemn men dressed in dark suits. The band plays a low-pitched funereal dirge with muted trumpets, melancholic slide trombones, and the repetitious heartrending thump of a bass drum. A long line of mourners follows the band through the open ornate iron gates of the Key West Cemetery. Directly behind the band, Luz and Noah carry a short white casket supported on their shoulders. Following the casket are Joan, Carmen, and Zoe, dressed in black, their faces grief-stricken; they support one another, arm in arm. At the very end of the procession, Hogfish pedals his rusty bicycle.\n\nThe mourners weave beneath the gray-shadowed canopy of tall palm trees. They pass between rows of tombstones and granite mausoleums littered with sun-faded plastic flowers. They finally stop before a freshly dug open grave. At the grave's head is a new white marble statue of a winged angel. The beatific angel extends in its hand above the grave a marble lily.\n\nA somber priest, dressed in purple vestments, steps forward. His voice rises above the sound of sobbing from the mourners gathered around the grave. \"Heavenly Father, we do not question Thee in Thy infinite wisdom. You have taken such a young soul to be at Your side in heaven, to seat her with the angels surrounding You. We only ask, dear Lord, that You take pity on those left behind after such an innocent has taken flight from this temporal world. Guide the family and all her loved ones through this storm of anguish. Give us each the faith and courage to survive what seems an unjust and overbearing sorrow.\"\n\nCarmen cries out in a wail of pain; her body slumps; she is held up by Joan and Zoe.\n\nLuz and Noah lower the casket on velvet ropes to the grave's bottom. Only muffled sobbing is heard as the casket descends and settles onto the hard earth.\n\nCarmen, her face wet with tears, her knees shaking, steps next to Luz and hands her a box. Luz opens the box and pulls out a pair of red high-heel shoes. She steps to the edge of the grave and lets the shoes slip from her fingers and drop down. She looks at the shoes glittering next to the white-enameled casket. \"Here are your magic shoes, my darling Nina. When you get to the end of the Yellow Brick Road, tell Oz what I told you. Tell him that your family adores you.\" From Luz's eyes, tears spiral downward into the open grave, onto the red shoes.\n\nA line of slump-shouldered mourners, their heads bowed, files out between the iron cemetery gates. In a far, hidden corner of the cemetery, only Hogfish is left. He stands astride his rusty bicycle with its line of barbed J-hooks strung between the handlebars. He watches the entrance gates to make certain no one is coming back. He jams the earbuds of his iPhone into his ears and jumps up onto his bicycle's cracked leather seat. He pedals furiously, swerving the bike on a snaking path among the gravestones. He hits the brakes and skids to a stop in front of Nina's grave. The grave is filled in with dirt, its top covered with bouquets of flowers tied by colorful satin ribbons. The fragrance of the flowers is a heady perfume mix in the shifting breeze.\n\nHogfish gazes across the grave to the winged stone angel extending a marble lily. The angel's smoothly chiseled face is serene.\n\nHogfish jabs his finger at the angel. His shouting voice echoes across the cemetery. \"Smell the air! When El Finito comes, the air is filled with the stink of dead turtles! Feel his filthy weather creeping up your back. Oppressive weather! Weather that's hot and calculating! Wants to explode in your face! To annihilate you!\"\n\nHogfish turns away from the angel. He grips the bicycle's metal handlebars in a white-knuckle hold. He shakes the handlebars, rattling loudly the line of dangling J-hooks. His chest heaves, he struggles for breath, he sucks in air deeply. He looks back in anguish at the angel, tears streaming from his eyes. \"Don't let Finito steal Nina out of her grave! Finito's almost here!\"\n\nThe circular steps inside the Key West Lighthouse spiral up in a steep rise of eighty-six feet above Noah. He climbs the steps in the hot, confined air and stops at the uppermost landing to catch his breath. He steps through a narrow passageway leading outside onto an iron catwalk suspended around the top of the lighthouse. He follows the catwalk beneath a massive glass light beacon above. He stops. Before him is Luz.\n\nLuz stands with her hands gripping the top railing of the catwalk. She stares out over the view of the island city's tightly packed tin-roofed houses melding into the blue of the surrounding ocean. She is startled by Noah's words coming from behind her.\n\n\"Joan told me I might find you here. She said this is where you come when you want to be alone.\"\n\nLuz remains silent, not releasing her tight grip on the railing, her breathing labored.\n\nNoah takes a step back. \"Maybe I shouldn't have come. I understand. I can leave you alone if you want.\"\n\nLuz keeps her sight on the sweeping vista. \"My father used to bring me up here when I was a little girl. He told me that when this was first lit, in the 1840s, doves flying here over the ocean from Cuba mistook the brilliant light for the sun. The doves flew straight into the beacon.\" Luz turns slowly to Noah, her eyes filled with suffering. \"That species of dove that crashed to their deaths against this beacon is now extinct. Those doves will never be on this earth again. Gone forever, like my Nina.\"\n\nNoah looks at Luz, seeking a way out of the sadness. \"You still have two doves to live for. Carmen and Joan are waiting for you. You are needed at home.\"\n\nLuz turns away. Her gaze goes back to the vista of the island and the blue horizon beyond.\n\nLareck lies in bed, listless, near death. His watery eyes stare up at the ceiling. He rasps for breath with an open mouth. A white sheet covers his body up to the neck. A scorpion scuttles along the white sheet, its front pincer claws clicking.\n\nIn the wicker chair next to the bed, Hogfish rocks his body back and forth to music blasting through his iPhone's earbuds.\n\nThe scorpion slithers up the bedsheet onto Lareck's neck. The creature creeps up the side of Lareck's cheek toward his open mouth. He struggles to speak as he looks pleadingly at Hogfish, his words barely audible. \"Scor... pions. Scorpions or... rats. Got to choose. Make your... choice.\"\n\nHogfish bobs his head to the music, watching the scorpion progress up Lareck's cheek. He reaches out his hand and clamps it tight over Lareck's mouth. Lareck's eyes widen in fear, his breath cut.\n\nThe scorpion crawls onto the back of Hogfish's hand covering Lareck's mouth. Hogfish raises his hand close to his face and stares into the scorpion's amber eyes. The scorpion stares back; its front scissored pincers widen to attack; its arched stinger-tail vibrates to sting. Hogfish flicks his hand, knocking the scorpion to the floor. He jumps up and stomps the heel of his shoe down, crushing the scorpion's body and squishing out a snot-colored slime of innards.\n\nHogfish shouts at the terrified Lareck. \"The air will stink of dead scorpions and rats when El Finito turns the world upside down! Fish will be thrown up into the sky! Pelicans will rain down. Iguanas will explode! Finito is coming to end it all!\"\n\nLuxury cars are parked in front of a sprawling red-roofed Mediterranean-style villa. Behind the villa, bright overhead lights shine down on a tennis court where two pit bulls ferociously tear into each other's flesh. Circled around the dogs, betting men shout for blood. Prominent among the men, in his tight Italian silk suit and shiny alligator shoes, is Hard Puppy. At his side are two meth-tweaked party girls, one white and one black, both wearing skintight dresses and stiletto high heels. The party girls shriek as one of the pit bulls rips the throat out of the other in a spray of blood.\n\nHard pumps his fist triumphantly in the air, then slaps the asses of the party girls. The men around Hard groan with disappointment as he boasts with flashing platinum teeth.\n\n\"My bitch won big bucks! She be like a hyena! My bitch can tear the asshole out of a fleein' zebra!\"\n\nBeneath a full moon, Hard Puppy's black SUV speeds on the Seven Mile Bridge. The bridge spans sixty-five feet above the ocean in a concrete blade crossing over the deep channel between the Gulf of Mexico and the Florida Strait, linking the Upper Keys to the lower islands. Silhouetted in the moon's glow alongside the bridge is the forlorn remnant of the old Overseas Railroad, blown away to its stubby concrete trestles during the 1935 hurricane that dumped four hundred men to their deaths in the shark-infested waters. Hard glances over at the old bridge and gives an appreciative whistle through his platinum teeth. High on meth and pumped on adrenaline, he steers the SUV ahead with jerky aggressiveness while singing along to the radio's bass-beat thump of angry rap music booming from surround-sound speakers.\n\nOn the front seat, next to Hard, the white party girl sits with her skinny ass rooted into the lap of the black girl. They both lean in next to Hard. Behind them, in the back cargo cab, the winning pit bull paces in an iron-barred cage. The dog's stout body is ripped and bleeding from its recent fight.\n\nHard shouts to the party girls above the rap music. \"To men I give shit! To ladies I give favors!\" He grabs the plump silicone breast of the white girl through her dress. She launches into shrill giggling. The caged pit bull in the back pricks up its ears to the sound and growls with deep-throated menace. Hard punches the SUV's accelerator pedal to the floor, speeding the SUV to the end of the bridge and onto a narrow road with mangrove swamps pressed up against it on both sides. The rap music blasts, the pit bull growls. Hard turns down the volume on the radio. \"This be bad music I be playin'. But I got badder. I can sing Civil War times bad ass.\"\n\nThe girls shout encouragement. \"Sing it, Hard!\"\n\nHard snaps his fingers with loud cracks, giving himself the musical beat. He throws back his head and opens his mouth, his teeth glistening to the words of the song.\n\n_\"Goin' to run all de night_.\n\n_Goin' to run all de day_.\n\n_Bet me money on a bobtailed nag_.\n\n_Somebody be bettin' de gray_.\n\n_Oh! De doo-da day!\"_\n\nHard bangs his fist on the steering wheel. \"Now, that be bad-ass nigga! It be written by a runaway slave.\"\n\nThe white girl screws her face into a perplexed expression. \"That's not a black song. That was written by some white dude. I learned about it in high school.\"\n\nHard backhands the white girl, one of the flashing gold rings on his fingers cutting a gash into her face.\n\n\"Girl! Don't you be messin' with nigga music! You know nothin' 'bout nigga!\"\n\nThe girl's hand flies up to the blood gushing from her cheek. She screams in panic. The pit bull in the back sniffs blood and howls. Hard guns the SUV.\n\nSeveral miles ahead of Hard Puppy's SUV, the narrow road curves into a pine-tree forest. Out of the forest, a Key deer emerges. The deer's thin, graceful body is coated with apricot-and-fawn-colored fur, its short white tail stiffly upright. The deer sniffs the air for danger and waits. Other Key deer emerge from the pine trees; they follow the lead deer alongside the empty road to a patch of grass growing next to the asphalt. The deer graze on the grass, their noses down alongside the edge of the road.\n\nThe tranquil night silence around the Key deer is broken by the rocketing whine from the SUV's four-hundred-horsepower engine firing off on its V-8 cylinders. The deer stop grazing and look up. The SUV careens around the corner of the road into sight, the harsh rush of its large tires racing over asphalt. The deer bolt and scatter into the trees. One confused deer stays behind, frozen with fear in the center of the road. The three-ton SUV smashes into the deer. The small body catapults forward through the air.\n\nThe SUV's wide tires burn to a stop. Hard stumbles out of the vehicle into the beams of its halogen headlights. He squints at what the bright beams illuminate. Lying twenty feet ahead, on black asphalt, is the bleeding body of the deer. He turns away from the animal and kneels in front of the SUV's crosshatch chrome grille. He runs his finger below the grille, along a dent in the thick bumper. He looks back angrily at the deer lying on the blacktop. \"You little midget shit! Should be locked in a zoo! Messed with my ride!\"\n\nA high-pitched, eerie whistling comes from the pine forest at the edge of the highway. Hard's head snaps around. He looks belligerently into the trees, shouting toward the sound. \"They be more of you midget fuckers in there? Come on out! I'll put my pit bull on you! She chase you down and chew your asshole out!\"\n\nThe strange, eerie whistling stops. Hard sees no movement among the trees. He shrugs his shoulders impatiently and climbs back into the SUV. He slams the door and rolls down his driver's-side window. He cocks his head out the open window to listen. He hears nothing. He rolls up his window and restarts the SUV.\n\nNext to Hard, the two party girls stare wide-eyed through the windshield at an apparition emerging from the dark forest. The girls shudder and lock their arms tightly around each other. Hard sees the apparition. His words spit out in surprise: \"Fuck me! What be him?\"\n\nWalking out of the forest into the SUV's headlights is the Bizango skeleton, encased in tight rubber and skull mask. Bizango stops in the center of the road and holds up a speargun loaded with a sharp, cocked spear.\n\nInside the SUV's back cab, the pit bull sees the black-and-white skeleton. The dog's deep, murderous bark reverberates in the cab as it hurls its body against the iron cage bars, thrashing to break through and attack Bizango.\n\nThe girls scream hysterically. Hard shouts above the screaming and barking: \"Everybody shut up!\" He glares at Bizango through the windshield. \"Don't mess with me, mo-fo! You be doomed! Time to let the dog out!\"\n\nHard jumps from the SUV and runs around to the rear hatch door; he yanks the door open. The pit bull\u2014inside its cage, behind bars\u2014howls at Hard to be freed. Hard unlatches the cage's steel lock and swings the door back. \"Go, you hyena! Rip his asshole out!\"\n\nThe snarling pit bull leaps from its cage, knocking Hard aside. The dog hits the outside pavement running, its clawed paws digging in as it propels its muscular body upward and hurls furiously through the air at the skeleton standing in the middle of the road.\n\nBizango whips up the speargun, aims, and pulls the trigger. The gun's C2 cartridge fires in a whoosh. The spear springs free in a blurred trajectory, its flight meeting the opposite rush of the dog in midair. The spear pierces with a crunching thwack into the bone bulge of the dog's rib cage. The dog howls, but its body keeps hurling forward through the air at Bizango. The dog's weight falls from the air, drops with a bouncing thud at the skeleton's feet. Bizango looks down at the dog, its barrel-shaped body inert, its bloodied tongue hanging out onto the asphalt, its startled, dying eyes staring up. Bizango reaches down and rips out the bloody spear from the dog's rib cage.\n\nHard jumps back into the SUV's driver's seat. He peers through the windshield at Bizango outside and grits his platinum teeth. \"You killed my bitch! Nobody lives who kills my bitch!\" He grips the steering wheel tight with both hands, jams his foot to the floor on the accelerator pedal, and yells above the whining engine, \"Mother-fuckin' spook! You die!\"\n\nThe SUV roars straight toward the skeleton. Bizango quickly reloads the gun with the bloody spear and reels back from the SUV as it speeds by, just an inch away, in a rush of wind. Bizango fires the gun. The spear shatters the glass of the driver's-side window. It flies right behind Hard's head and smashes out the window on the opposite side of the cab. The SUV keeps going. The snarl from its engine fades away into silence.\n\nBizango walks to the small deer lying on the blacktop. The deer gasps for breath; its eyes bulge. Bizango's black rubber fingers wipe blood away from the deer's nostrils. Its body jolts with a life-releasing electric shock, then becomes deathly still.\n\nBizango stares at the deer. From the surrounding forest, a throb of insects starts, crickets chirp, frogs croak. Bizango gently lifts up the deer in skeleton arms. Bizango's masked skull head swivels up to the sky as the dead body is raised toward the stars above.\n\nCackling bantam chickens scratch and peck in the dust outside the front door of a flimsy boarded shack beaten gray by weather and time. The chickens scatter as Noah walks between them and up the steps. The shack's door is open; inside the shadowy depths sits a dark-skinned African-Cuban woman wearing a flowing white cotton dress. The bones of her nearly century-old body are twig-thin, and her small skull is pulled tight with wrinkled skin. She rocks back and forth in a creaky chair as she fans herself with a folded magazine in the stifling heat. She calls out to Noah from the shadows, \"Comes ins. I bees 'spectin' you.\"\n\nNoah steps out of the sun into near darkness and stands awkwardly. \"How did you know I was coming?\"\n\n\"All de mins, dey comin' to Auntie sooner de betters. Dey gots de dollar problems, dey gots de love problems. An' ol' Auntie, she's 'bout fixin' de cure. Nothin' Auntie cain't fix, from an emptied wallet to a bustin' heart. I sees yo got de womins problems. Dat's why yo comin' to me.\"\n\nNoah pulls his pint bottle of rum from his frayed coat pocket and takes a swig, then wipes his lips. He stays silent. He slips the pint back into his pocket.\n\nAuntie waves her hand around the cramped room. Faded photographs of black saints torn from faith-healing magazines are tacked to the walls. The rafters are hung with bundles of dried herbs and flowers of every type, color, and scent. The countertops are piled with tins containing exotic powders, oils, and extracts. Dusty glass jars are filled with bent coins and rusted nails. Auntie claps her age-polished white palms together and stops rocking in her chair. She pushes up on an ebony cane toward Noah. \"I be knowin' 'bout womins makin' de mins cry! Yo come runnin' to me's cryin' like de lost boy.\" She pulls a matchstick out of a box and strikes it; the flame flares. She lights a votive candle inside a red jar with the image of a Black Virgin painted on the glass. She hands the jar to Noah. \"Hold dis tight.\"\n\nNoah grips the jar. Auntie studies his illuminated face in the glow of the burning candle. Her trembling bony hand comes up and feels the contours of his face. She shakes her head; her stringy white hair covers her face as she speaks. \"Yo mighty bad. Yo gots only de one womin in life to loves. Dat womin bees runnin' away hard. Yo never goin' catch her 'less yo listens to de Auntie.\"\n\n\"I hope it isn't going to be expensive to win the race.\"\n\n\"What bees de price of love?\"\n\nNoah sets down the votive jar and takes from his pocket a crisp one-hundred-dollar bill. \"I heard around town that you could help me win the race.\"\n\nAuntie pushes the offered money away. \"Put dat debil green paper back in yo pocket. Where I bees headed, dey don' take dats. Dey takes only de pure of de hearts.\"\n\nNoah slips the bill back into his pocket and pulls out the rum bottle. He takes a swallow as he watches Auntie hobble around the room on her cane.\n\nAuntie unhooks from the wall a straw basket hanging from a nail. She takes the basket to a tall cupboard and opens its door, exposing shelves rowed with glass vials filled with leaves and petals of crushed and ground plants and flowers. She pulls vials out, uncorking each and sniffing it, her nostrils twitching at the heady aromas. She recorks all the vials and packs them in the basket. She hobbles back to Noah and hands him the basket with a knowing wink. \"Dese will wins back yo true love.\" Her eyes glow with pride at the glass vials in the basket. She taps each vial's corked top as she explains their ingredients: \"Dis one bees de ginger root to entice her. Here bees dried strawberries to unlock her secrets. Of course, passionflower to soften de heart, and verbena oil to bees keepin' her loves.\"\n\n\"How can I win the race with this stuff?\"\n\n\"Yo gots to trust de Auntie. Puts verbena oil in her water glass. Strawberries in de soup. Ginger root on de fish. Passionflower in her dessert.\"\n\n\"That's everything? You sure you didn't leave anything out?\"\n\n\"Dese will do de trick. Only one mo' thing.\"\n\n\"Tell me.\"\n\nAuntie hobbles over to a carved chest and creaks open its heavy lid. She pulls out a small purple velvet bag and smiles at Noah. \"If yo gets close enough to her, rub dis on her earlobes. She bees a juicy peach for de pickin'.\"\n\n\"You don't know my Zoe. Right now she's more of a hard pit than a soft fruit.\" Noah takes the velvet bag and feels its weight. \"What's inside?\"\n\n\"Rare in de natures. Royal jelly from de Brazilian queen bee.\"\n\n\"This is my last chance before my wife becomes my ex-wife.\" Noah pockets the bag. \"I can't thank you enough.\"\n\n\"No needs de thanks, only de belief. But de magics don' works 'less yo gives up dat demon rum in a bottle yo suckin' on all de day long like a starvin' babies pulled from de mommies' teet. Alcohol bees de magics-killer. Dat demon goin' pull you all de ways down into de hells.\"\n\nThe outdoor food market is crowded with island locals and tourists jostling one another between open-air stalls piled with vivid mounds of tropical fruits and vegetables. Noah stops before one of the stalls and chooses from the exotic selection of purple plantain bananas, brown tamarind, yellow egg-fruit, orange loquat, blue-speckled mangoes, and green sweetsop. He moves on to a stall with a palm-thatched roof, protecting it from the overhead sun, where fresh sea fare is sprawled across iced trays. He studies the wet display of octopus, crab, horse conch, tuna, shark, dolphinfish, grouper, stingray, and snapper. He pokes a finger against an open-mouthed black grouper, then jabs a fat red snapper.\n\nThe stall's monger, gripping a curved-blade gutting knife in his hand and wearing a white rubber apron streaked with fish blood, suspiciously watches Noah poking the fish. The monger shouts with gruff irritation: \"Why you pokin' that snapper? You gonna eat it... or you gonna make love to it?\"\n\n\"Both.\"\n\n\"Then, buddy, that's not the one for you.\" The monger looks over the colorful fish arrayed on the iced trays. He slaps the bright scales of a yellowfin tuna. \"Here's the one. She's got a firm body and clear eyes.\"\n\n\"I'll take her.\"\n\nOn the Gulf side of Key West, known as Land's End, where once shrimping, fishing, and turtling boats were docked years before, are anchored tourist sunset cruise and glass-bottom boats, elaborate yachts, and fancy sailboats. Facing this leisure-time fleet is an open-sided restaurant serving buckets of peel-your-own shrimp and platters of shell-shucked gritty oysters. At the edge of the farthest dock is a long wooden shed where shark bodies by the hundreds were once piled before being reduced to fillet slabs, severed fins, and skins. The shed is now filled with a selection of souvenir postcards, T-shirts, seashell necklaces, suntan lotion, and plastic sandals. To the side of the shed is a concrete saltwater holding pen. The deep-water pen is the last of the turtle kraals constructed in the 1890s, where captured turtles were dumped by the boatload from docked schooners to be slaughtered for steaks, soup, combs, and toothbrush handles.\n\nAt the top edge of the concrete pen, Luz stands staring down into the water. She watches trapped snook and barracuda kept as a tourist attraction. The fish dart back and forth in silver flashes, searching for a way out.\n\nThe Chief comes up behind Luz and stands alongside her. He hands over a thick manila envelope. \"Here it is, promised I'd get it. I've got pull with the boys in a state-of-the-art Miami lab. Told them it was for an important case when I sent the blood samples. They fast-tracked it through.\"\n\n\"I suppose I should say thanks, but I don't know what it says.\" Luz takes the envelope. \"Have you read it?\"\n\n\"I wouldn't know how to read it\u2014too technical, cutting-edge DNA-predisposition genetic stuff. Only a few labs in the country can do this. It's what you wanted.\"\n\n\"You don't have such a happy face. Did they tell you what it says?\"\n\n\"Of course they told me.\" The Chief looks down at the circling fish in the water. \"I don't know how I'd react if I got this news. Jump off a bridge maybe, stay at home twenty-four\/seven with my family, go up on a mountaintop to meditate, or shoot heroin.\"\n\nLuz scrapes her fingernails across the thick envelope, cutting into the paper.\n\nThe Chief looks back at her. \"I hate to say this, but, because of how the testing worked out, you should quit the force.\"\n\n\"Never.\"\n\n\"Go home and be with Carmen and Joan.\"\n\n\"No, they would know why I was there, just sitting around the house. It's better if life goes on, and they are strong with that. It's too much for them to bear after what happened to Nina. They couldn't go through it. They'd be crushed.\"\n\n\"Given this new information, I could ask for your resignation. This can jeopardize your job performance. You're still fit now, but any day that could change.\"\n\n\"I won't quit while Bizango is still out there.\"\n\n\"I'll make you a deal. Stay on until Bizango is caught, then go home to your family.\"\n\nLuz turns and gives the Chief a firm handshake. \"It's a deal. I can live with that.\"\n\n\"It has to be. I can't take the chance of keeping you on.\"\n\nLuz peers down into the pen; she sees her own reflection on the water's surface above the snook and barracuda making their futile runs at freedom. \"I used to come here after school as a kid. Back then they kept a six-hundred-seventy-five-pound loggerhead turtle in this pen. He was a hundred thirty-nine years old, and famous for biting off the fingers of the turtle hunters who captured him in the ocean. Big George, they called him. He was a celebrity, a real tourist attraction, the biggest turtle in the world in captivity. Every day I'd throw a head of lettuce into the water for George. George would circle around the pen, then cut above the surface and give a big blow of water as he went for the floating lettuce. George wasn't a meat eater. He loved lettuce.\"\n\nThe Chief stands closer to Luz, his shoulder touching hers. \"The DNA results I brought you don't lie. You don't have much time left. You already knew your breast cancer came back, but this test turned up two different kinds of cancer waiting to spread. You've got a deadly trifecta going. I just want you to understand: should you change your mind and decide to walk away from the force now, no one will say you didn't serve honorably. In fact, everyone will say how brave you were to hang in so long.\"\n\nLuz doesn't look up from the water. \"I remember the day George died. When he gasped his last breath in this pen, he was slaughtered and made into soup and combs. I was inconsolable. I cried myself to sleep every night after. My dad gave me five dollars to go buy myself something to cheer me up. I went to the Catholic church\u2014they have a grotto there with a life-size Virgin statue inside. You can pay money to light a candle for the Virgin to protect you from hurricanes, or answer your prayers. With the five bucks, I lit up all the candles in the grotto for Big George.\"\n\nThe Chief turns away from the pen and steps back. He pulls out his wallet and takes out a five-dollar bill. \"What do you say\"\u2014he holds up the bill with a grin\u2014\"we go to the grotto and light us some candles.\"\n\nZoe sits at Noah's kitchen table, wearing a bare-shouldered halter-top sundress. Her blond hair is swept up in a French knot, exposing diamond-stud earrings in her lobes. She watches with fascination as Noah works at the stove over pots and pans of steaming and frying food. \"When did you take up cooking?\"\n\nNoah carefully flips two yellowfin-tuna fillets simmering in a pan over a gas flame. \"I've only recently become interested in the alchemy of the culinary arts.\" He uncorks a glass vial and spreads crushed ginger root on the fish. He opens the oven door and sprinkles passionflower petals onto a baking plantain-banana pie.\n\n\" 'Alchemy of the culinary arts'? You make it sound like something exotic. Women cook every day. No big deal.\" She picks up the water glass in front of her and takes a sip. Her mouth puckers. \"This water tastes like it's got bitter lemon in it or something.\"\n\n\"Do you like it?\"\n\nZoe smacks her lips. \"It's tangy. I don't know if I like it or not.\"\n\n\"Would you like something more than water?\"\n\n\"Like some rum, maybe?\"\n\n\"That's not what I meant. I'm just trying to be a good husband.\"\n\n\"A good husband? Too late for that. I gave you every chance a woman can give. I brought the final divorce document with me. All you have to do is sign it.\"\n\nNoah opens the refrigerator door and takes out a bowl of strawberry soup. \"At least we can have dinner; here's the first course.\" He places the bowl in front of her and sits close.\n\n\"What a weird-looking soup.\" She bends her head and sniffs at the pink concoction with red nuggets of dried strawberries floating on top.\n\nNoah scoops a spoonful of soup from the bowl and holds it up to her lips.\n\nZoe laughs nervously. \"I'm not sure I want this. What do you know about cooking, anyway?\"\n\n\"There's only one way to find out. Close your eyes and take a sip.\"\n\nShe doesn't close her eyes.\n\n\"Trust me.\"\n\nZoe reluctantly shuts her eyes. Noah moves the spoon near her parting lips. He slides the spoon into her mouth, spilling a trickle of soup onto her lips. She keeps her eyes closed as she swallows. Her lips glisten a bright strawberry-pink. He places his hand under her chin, turning her face up to kiss her.\n\nHer eyes open. \"It's delicious! What bizarre stuff did you put in this? I want the recipe!\"\n\n\"Only strawberries and sugar.\"\n\nShe licks the red residue off her lips. \"No, I taste something else.\"\n\n\"I put my love in it. All my love.\"\n\nZoe flinches at the sudden intimacy. She looks at the empty rum bottle in the center of the table. A burning candle is stuck in the bottle's narrow neck.\n\nNoah touches one of the bright stones on her earlobe. \"These are the earrings I gave you on our wedding day.\"\n\n\"Don't get any ideas. I just wore them because they go with this dress.\"\n\n\"And I bought you that dress for our first wedding anniversary. It still fits you like a silk glove.\"\n\n\"I told you not to get any ideas.\" She stares at the empty rum bottle in the center of the table. Inside the bottle, at its bottom, is her gold wedding ring. \"I see my ring is exactly where it was when I was here the last time.\"\n\n\"There's a prize in each and every bottle of rum.\"\n\nShe looks back at him. \"You haven't been drinking tonight. Why?\"\n\n\"I stopped. Trying to walk the sober trail.\"\n\n\"Famous first words.\"\n\n\"I quit for you.\"\n\n\"Famous last words. We'll see how long that lasts.\"\n\nThey fall into silence, watching the candle in the bottle burn. The ring inside the bottle shines.\n\nHe shifts his gaze back to her earrings. \"I think your diamonds have lost their sparkle.\"\n\nShe pats her ears. \"Really? I think they still look good.\"\n\n\"They aren't as lustrous as when I first gave them to you. Someone told me that the only way to bring back the original sparkle of diamonds is to rub royal jelly from the Brazilian queen bee on them.\"\n\n\"And I'll bet Mr. Alchemist the Cook has some of that jelly stuff around here somewhere, don't you?\"\n\nNoah slips from his coat pocket a purple velvet bag. He unties the bag and pulls out a corked glass vial containing honey-colored jelly. He opens the vial and dips a finger into the jelly. He rubs the jelly onto one of her diamond earrings, then massages the slick substance into the soft skin of her surrounding earlobe.\n\nHer words come with intimate breathiness. \"Are they sparkling yet?\"\n\nHe leans close to her, his lips almost touching hers as he whispers, \"Sparkling, like the sun. Radiant, like you.\"\n\nZoe pulls back and stands. She grabs her purse from a chair and snaps it open, taking out a bundled stack of papers. She slaps the bundle on the table. \"I said this would be our last dinner.\"\n\n\"But you only tasted the soup.\"\n\n\"No more games. Sign the divorce papers.\" She turns to leave.\n\nNoah leaps up and grabs her arm. \"Wait, I'll walk you home.\"\n\n\"Walk me home? I don't need you to walk me home. I'm a big girl.\"\n\n\"It's dark outside. There's a killer on the loose.\"\n\n\"A killer on the loose?\" She stares into Noah's eyes with a sudden illumination. \"It's you, isn't it? You've been the one following me home at night after I close up the bar.\"\n\n\"Of course it was me. I told you, it's not safe.\"\n\n\"I don't need a knight on a white horse to protect me! I just need a sober man who believes in himself and is one hundred percent present!\" She spins around and walks out.\n\nNoah slumps back down on the chair at the table. His lips turn down as he looks at the stack of divorce papers. His fingers drum lightly on the papers, then drum harder and harder. His hands begin shaking uncontrollably. He shoves his chair back with a loud scrape against the floor. He turns the flame off beneath the pan of burning fish. He yanks open a cupboard and pulls out a full bottle of rum. He opens the bottle and tilts it toward his mouth; the glass tip of the bottle touches his trembling lips. He turns swiftly, holding the bottle upside down over the sink next to him. He watches the dark rum flow down the sink drain and disappear. He stares at the empty bottle with a look of shocked remorse. \"Goddamn, that was stupid!\" He grabs the hard edge of the sink, his knuckles white against the porcelain as he holds on. \"But I've got to try!\" His body begins shaking violently as he fights against the barbed blood rush of alcohol deprivation consuming him.\n\nLuz drives her white Charger slowly along Duval Street. She keeps a vigilant watch on the tourists and locals navigating their way along the crowded, hot sidewalk in the humidity of the high-noon day. A police dispatcher's voice crackles from the car's radio speaker.\n\n\"Alpha-zero-zero-eight. Respond to Code Five at Blue Hole Key Deer Refuge on Big Pine Key!\"\n\nLuz wheels her car around with the siren wailing and heads down a narrow side alley. At the end of the alley, Hogfish appears, pedaling his bicycle directly at the car. Luz stomps on the brakes; the car skids, its front bumper stopping just before smashing into Hogfish.\n\nHogfish rises up on the cracked leather seat of his bicycle. He points his bony finger at Luz and shouts above her car's siren: \"The statue angel guarding Nina's grave will protect her! El Finito won't be able to dig up Nina and violate her when his devil's breath blows this island to hell!\" Hogfish slams his butt back down on the bicycle seat. \"Almost Halloween! Finito's almost here!\" He pedals away in a manic fury.\n\nLuz revs her Charger's engine and drives off, quickly leaving behind Key West's narrow streets. The red outside lights of her car flash as she speeds north on the broad concrete ribbon of the Overseas Highway, skimming above the vast ocean. She crosses over a series of bridges linking the highway from island to island. On one side of the highway suddenly looms a billboard announcing **ENTERING NATIONAL KEY DEER REFUGE**. Luz wheels the Charger into a hard turn after the sign and travels a gravel road into a pine-tree forest. Her car bumps along the road, kicking up a stream of dust. The gravel road abruptly dead-ends. A dirt trail is ahead, leading deeper into the forest. Blocking the trail is a row of parked police cars. She slows her Charger and cuts the engine.\n\nMoxel stands in front of his squad car, his beefy arms crossed tightly over his broad chest. He bends down and peers at Luz through her car window. \"You won't believe what's at the Blue Hole. I'm the one who found it. Already got law enforcement from half the county here.\"\n\nLuz swings her door open and steps out, knocking Moxel back. \"You're a hero. Always the first one to bag the big stuff. Why wasn't I called in earlier?\"\n\n\"No reason for you to have rushed. We're miles away from Key West jurisdiction. We're in County Sheriff territory.\"\n\n\"What did you find?\"\n\nMoxel fires a sharp spit at the dirt trail. \"Why don't you just trot along to have a peeky-poo for yourself.\"\n\nLuz follows the trail as it twists through tall, spindly trees. She comes to the end of the trail, where the forest abruptly opens up into a vast clearing. Before her is the Blue Hole, a lake of intense bright-blue water filling the depths of a former coral-rock quarry. The pathway to the Blue Hole is blocked by stretched yellow crime-scene tape. On the far side of the tape, forensic investigators, dressed in white jumpsuits and wearing white latex gloves, scour the area.\n\nStanding at the shoreline of the Blue Hole, the Key West Police Chief and the uniformed County Sheriff converse intensely with a police diver who wears a swimsuit, face mask, and rubber foot flippers, and holds a long pole with a cloth net attached to its tip. He nods to the Chief and Sheriff, then wades into the Blue Hole's water up to his shoulders. He swims out to the center of the Hole, holding the long pole in one hand above his head. He treads water, lowers the pole, and skims the net across the water's surface toward a round floating object. He scoops up the object with the net and swims back toward the shore.\n\nThe Chief spots Luz standing behind the stretched yellow tape. He walks to her and lifts the tape, beckoning her to step through. \"You're going to be surprised what Moxel found floating in the Hole this morning.\"\n\nLuz steps under the tape. \"What was Moxel doing here?\"\n\n\"Fishing. Some big ones in these waters if the gators don't get them first. Place is crawling with gators.\"\n\n\"Why was I called in so late?\"\n\n\"I told Moxel to have you radio-dispatched right away, an hour ago. This ties into our investigation.\"\n\n\"Moxel waited. I just got the call.\"\n\n\"Forget it. Come with me.\"\n\nLuz follows the Chief to the Blue Hole. The diver emerges from the water onto the muddy shore, holding the long pole; inside the dripping net is the severed head of Hard Puppy, his face lacerated with crisscrossed purple gashes, his eyes plucked out, and his ears slashed off.\n\nLuz exhales with surprise. \"Looks like he was attacked by his own pit bulls. They chewed his head off.\"\n\nThe Chief nods at Hard's lips, sewn crudely shut with fishing line. \"Pit bulls can't do that. That's Bizango. Bizango fed Hard to the gators.\"\n\n\"Can't know the gators ate him until the forensics come in.\"\n\nThe Chief slips off a pair of binoculars slung around his neck on a leather strap. He hands the binoculars to Luz and points across the Blue Hole to the opposite shore. \"Check out that bad-ass scene over there.\"\n\nLuz looks through the lenses. Across the water, on the far shore, she sees three twelve-foot green-scaled alligators bellied in the mud. The alligators' nostrils are flared; the jaws of their snouted mouths gape open, exposing long rows of razor-sharp teeth.\n\nThe Chief prods Luz. \"It gets worse. Look above the gators.\"\n\nLuz raises the binoculars and refocuses beyond the alligators on the muddy bank. She spots a lone pine tree. The brittle bark of the tree's trunk is spray-painted with a red **X**. From the center of the **X** protrudes a steel spear shining in the sunlight.\n\nA sleek seventy-foot-long sport-fishing boat plows through the water at twenty knots. Big Conch is strapped by a leather shoulder harness into a teakwood marlin-fighting chair on the boat's aft deck. His bare, broad chest strains against the leather straps as he leans into the bow of his fourteen-foot-long fishing rod, its line spinning out from the reel. Big's line runs farther out into the white-water wake left behind the boat's diesel-engine thrust. With the rod's butt anchored in the fighting chair's steel gimbal between his legs, he reels hard to recapture the line. The muscles of his arms bulge and sweat breaks out on his face. The tip of the pole curves and bends almost double, on the verge of breaking.\n\nThe boat's first mate stands behind Big in the fighting chair. The mate whoops with appreciation at Big's skill, urging him on. \"You got her now!\"\n\nBig bellows at the mate, \"How many runs am I up to?\"\n\n\"Over twenty! She's been running in and out for the last three hours!\"\n\nBig presses his chest forward against the leather harness as the bent pole's line whirs back out. Diesel-exhaust smoke clouds up around him from the boat's engines' backing down into reverse to follow the running marlin.\n\nThe mate shouts, \"Don't buck the reel! Let her take the line or you'll snap the rod!\"\n\nBig hollers above the reel's screech, \"Shut up, asshole! Don't tell me the obvious!\"\n\nBehind the boat, the roiling water parts and a massive blue marlin sails high into the air. The marlin's muscular body twists for freedom in a mighty shake against the barbed hook sunk deep into its bill. The fish lurches its full body upright, trying to throw the line, its long bill pointed skyward as it tail-dances in skipping leaps over the surface of the ocean.\n\nThe mate whoops at the top of his lungs. \"Look at that! She's a record breaker!\"\n\nThe marlin dives out of sight.\n\nBig reels back quickly on the line's sudden slack. \"That was her last run! She's gotta be played out! I'm bringing her in! Get the gaff!\"\n\nThe mate grabs a long steel gaff with a snarl hook at its end. He leans over the transom with the gaff, eager for action.\n\nBig Conch's sport-fishing boat cuts a wide wake through the surface of the water. From atop its twenty-five-foot-high aluminum crow's-nest lookout, a cloth pennant rips in the hot wind. On the white pennant is the black image of a marlin. Big stands in the cockpit of his boat with the mahogany-wood helm gripped in his hands. The mate works on the bloodied deck, lashing down the giant fish.\n\nAhead of Big's boat, a floating dark speck appears on the horizon. Big turns his mahogany helm, steering toward the speck. The speck grows larger, finally coming into full view. It is a thirty-six-foot West Indian Heritage trawler with a radio-transmitter antenna bolted to its deck. The trawler is silhouetted against the sky, its name across the hull, _Noah's Lark_. Big slows his boat.\n\nInside the trawler's pilothouse, Noah looks through the window at the sport-fishing boat with Big at the helm. He idles his engine and goes outside onto the deck.\n\nBig bellows across the water at Noah: \"Hey, pirate! You've lost your treasure! Heard Zoe's divorcing you for good!\" He laughs and throttles up his fourteen-hundred-horsepower engines with a guttural diesel roar. His boat speeds into a tight circle around Noah.\n\nNoah's trawler rocks from the high wakes roiled by the larger boat. The trawler violently lists to its side, slamming Noah to the deck. A wave crashes over him, washing him to the deck's edge. He reaches out and grabs the steel strut of the radio-transmitter antenna to keep from being swept overboard.\n\nBig circles his speeding boat closer, causing higher-curling waves to smash against the trawler's hull.\n\nThe trawler rolls up, then lurches low, tipping into a near-capsizing slant. Noah clings to the radio tower with one hand. He raises his other hand and stiffens his middle finger at Big. His voice soars above the roar of Big's engines: \"Fuck you!\"\n\nBig's voice booms back: \"Truth Dog! Sink to the bottom of the sea! Maybe you'll find your dick down there!\"\n\nNoah opens his mouth to shout back but chokes on an incoming wave of seawater. He coughs hard, gasping desperately for air, as he hangs on to the tower for his life.\n\nA long Key West's sport-fishing pier, boats are tied up in a row. At the end of the pier, Big and his mate stand with a crowd of sunburnt fishermen. The men watch with anticipation as Big's huge blue marlin is hoisted by a pulley chain hanging from an iron weighing scale.\n\nA craggy old fisherman wearing fish-gut-stained khaki trousers and a frayed long-billed cap comes up next to Big and nudges him. \"Hey, fella, what'd you hit her with?\"\n\nBig keeps his eyes on the marlin being hoisted as he answers. \"Used a naked horse-ballyhoo rig at first. Can't trust 'em, a bitch getting a solid hook setup. Kept losing fish all morning. Switched over to a braided polyethylene ballyhoo lead with a J-hook lure and no skirt attached. Nailed her.\"\n\n\"That polyethylene lead is stronger than steel. No wonder you campaigned in such a whopper.\"\n\n\"I'm not out there fun-fishing to catch and release, like you timid old-timers and castrated ecology boys.\"\n\nThe chained marlin reaches the top of the scale. A white arrow spins in a circle around painted numbers and stops on the weight of the marlin. The fishermen all exhale in surprise. Big moans with disappointment.\n\nThe craggy old fisherman turns to Big. \"Missed the record by only twelve pounds. Rare to catch 'em that big here\u2014they've been fished out. Offshore of Cuba, yeah, maybe you can still reel in a whopper like this, but not around Key West. You should mount it, display it in the hotel lobby of your new Neptune Bay Resort.\"\n\nBig stares at the marlin swaying on the pulley chain. He pulls off his cap and runs his hand over his head, slicking back his dyed blond hair. He claps the cap back on his head. \"I only mount record breakers. I'll have her chopped up so nobody else can claim her.\"\n\nThe old fisherman shakes his head in dismay. \"Shame to do that. She's a seven-hundred-pound beauty. You should have released her if you weren't going to keep her. That would've been the sporting thing to do.\"\n\n\"Don't talk to me about sport, old man. It's not about sport. It's about winning.\"\n\nThe old fisherman fixes his crinkly gaze on Big. \"I been around a long time. I seen things. That fish is bigger than the record breaker Hemingway caught between Key West and Cuba back in the 1930s. Crime to chop her up. Any guy standing here will give you ten grand so's he can trophy-mount her and call her his own.\"\n\n\"I'll chop her up personally. She'll be expensive sushi for the alley cats tonight.\" Big's broad tanned face breaks into a smile at the old fisherman. \"And I don't give a fuck about a fat, bearded dead writer who once caught a big fish in these waters.\"\n\nLuz makes her way into the Police Chief's crowded office. The Chief, Moxel, and a team of white-suited forensic investigators are huddled intensely over a black micro\u2013digital recorder on the Chief's desk. The Chief speaks with urgent anticipation. \"Just got this\u2014copy of the recording sewn into Hard Puppy's mouth. Could be our big breakthrough.\"\n\nLuz hunches toward the recorder with the others. The Chief presses the recorder's play button. The recorder's red indicator light flashes. The small speaker crackles with static and the eerie chant of an electronically altered voice.\n\n_\"Bizango... Bizango... Bizango_\n\n_Bizango... Bizango... Bizango_\n\n_Bizango... Bizango... Bizango.\"_\n\nThe recorded voice stops. A low-frequency electronic hissing is heard. The recorder's flashing red light dims and goes out. No one around the desk moves; they all barely breathe, waiting for the recorder's dead light to flash back to life.\n\nThe Chief slams his fist on the desk, jolting everyone. \"That's him, mocking us! Bizango won't communicate anymore!\" He turns in frustration on the forensic investigators. \"What have you got from Blue Hole?\"\n\nOne of them shakes his head negatively. \"Not even a footprint in the mud was left. Whatever prints had been there were compromised by those damn gators mucking around.\"\n\n\"What about prints on the forest trail? What about prints on the spear shot into the tree? What about prints on Hard Puppy's mutilated head? Must be something?\"\n\n\"Nothing. It's like he's a ghost, or clever enough to know the tricks to stay invisible. We're still waiting for more results from our lab up in Miami. They're close to getting the true voice-sound identity of whoever is speaking on the recordings.\"\n\n\"The Blue Hole gators? You autopsied them?\"\n\n\"Killed them and ran tests on everything in their digestive tracts and the feces in their bowels. Everything was what you'd expect.\"\n\n\"Yeah, what?\"\n\n\"Half-eaten fish, frogs, and human remains. DNA testing shows that the human remains are from one person, Hard Puppy.\"\n\nThe Chief glares at the investigator. \"I could've told you that. We don't need DNA mumbo-jumbo to know those gators ate Hard. You guys are way above my pay grade and supposed to be brilliant, but you can't figure out how one guy in a rubber suit is getting away with multiple murders.\" The Chief fires a commanding look across the desk at Luz. \"Don't just stand there staring at me with those big brown eyes. What do you have for me?\"\n\n\"Well, give me a chance to get it out. I traced all the calls made to Noah's radio show. None turned up anyone who can be considered a suspect. The only two callers I couldn't get a location fix on were Bizango and that Nam vet who keeps talking about Permian extinction. They both were using different public phone booths. I questioned the people at businesses around those booths, but nobody remembers seeing anything unusual. I had Forensics scour the booths for prints. I ran the prints through our database, the FBI's database, even Homeland Security's database. So far, nothing incriminating.\"\n\n\"That Nam vet, he's got me worried. You scare up anything, anything at all?\"\n\n\"I tried everywhere, even went around to the veterans' bars. Problem is, most guys hanging in those places are so baked on meds they're no longer tightly wrapped. They sent me on wild-goose chases. I never found the radio vet.\"\n\n\"What about Noah? You keeping him pointed in the right direction?\"\n\n\"He knows what to do. He's throwing out more red meat to provoke Bizango into calling. The moment Bizango calls, we're on him if we get the GPS location of where he's phoning from. Noah knows the stakes.\"\n\n\"When's his next broadcast?\"\n\n\"About an hour.\"\n\n\"Good. I'll have the SWAT team ready to roll.\" The Chief looks around at everyone in the crowded room. \"I want you all to stay on the razor's edge\u2014stay on that edge until your feet bleed. We're gonna get this guy now.\"\n\nTruth Dog back on the air. Let me hit you with a pressure drop of info. One-quarter of all mammals and one-third of all amphibians are headed for extinction on this fouled-up planet in ten years. That's a fact. Right here in Florida, we lose thousands of acres a day to development. Half of the Everglades have already been drained and bulldozed, devoured by greed. Check it out. Okay, I see I've got a brave pilgrim calling in. Show me the rage.\"\n\n\"I'm a young mother of three kids; I've got bigger problems than saving mammals and amphibians. I'm terrified about this Bizango character. He's going to be at the Fantasy Parade. I don't care what the cops say about how safe it is to be out, something horrible is going to happen. People I know are scared to death. They're staying home. They aren't going to the Fantasy Parade.\"\n\n\"Not everyone is afraid. The tourist bureau expects eighty thousand thrill-seekers showing up for our annual party. Anything goes at the Fantasy Parade\u2014the shocking, the vulgar, the perverted. If the threat of a category-three hurricane couldn't keep the merrymakers away from the parade some years back, what makes you think they'll be afraid of our own homegrown Jack the Ripper stalking them in the streets? Just gives Fantasy Parade an air of spooky realism.\"\n\n\"You're making me more frightened with talk like that. I'm hanging up.\"\n\n\"Wait! You've got to understand, a guy like Bizango, he has his thoughts banging and boiling in his head. He believes in his righteous crusade. He believes the voices that only he hears come from God's lips to his ears. The problem is, the truly evil ones who walk among us in this world don't show that they are evil\u2014that's why they are so lethal. They hide in the shadows of anonymity, hunker down in the crevices of their cowardice, waiting to strike.\"\n\n\"Now I'm really terrified.\"\n\n\"I'm trying to help you get a philosophical grip on reality. And, uh, one more thing.\"\n\n\"Yes?\"\n\n\"What are your kids going to dress up as this Halloween?\"\n\n\"That's the last thing on my mind. I'm not letting them out of the house.\"\n\n\"I've got what they should be.\"\n\n\"What?\"\n\n\"Skeletons.\"\n\n\"That's not funny! You sicko!\"\n\n\"Whoops, she's gone. We need a good jolt of gallows humor when there's a killer out there wanting us to jump through our assholes with fear. Hey, pilgrims, you've stopped calling. Maybe nobody is awake. Nobody except Bizango. I know you're out there, Bizango. I challenge you to crawl out from your cowardly crevice. Put your serpent lips to the phone and kiss me with your hate.\"\n\nAt the Atlantic Ocean's edge, Luz sits in her parked Charger in front of the monument marking **SOUTHERNMOST POINT CONTINENTAL U.S.A.** On the ocean's distant horizon, toward Cuba, black clouds obliterate the stars. Jagged bolts of lightning stab down from the clouds; the flashes appear to be a fearsome army of bright giants marching in. Luz looks through the car's windshield at the lightning as she listens to Noah's broadcast.\n\n\"I've got a call! Hello, who is this? Answer me! Don't hang up! Why did you hang up? Call me back. I'm waiting. Punch me with your pain.\"\n\nLuz turns the radio volume up and listens closely as a new call comes in to Noah.\n\n\" _Hola_ , Truth Dog, brave crusader. This is the Nam vet.\"\n\n\"Welcome back to the show, Permian-theory man. Extinction is your karma. Let's talk about it. It's now or never.\"\n\n\"Do you know how many oil wells are in the Gulf of Mexico?\"\n\n\"I used to be an environmental attorney fighting to keep corporate-oil bloodsuckers from drilling in the Gulf, so I know the answer to that. There are four thousand offshore oil and gas rigs out there. The disastrous Deepwater Horizon blowout caused millions of gallons of oil to flow into the pristine Gulf. The toxic dispersants used to break up the oil and hide the crime created a hypoxic dead zone in the Gulf bigger than the state of New Jersey, a floating black hole of death where nothing lives, grows, moves, or swims.\"\n\n\"You've got facts.\"\n\n\"Hell yeah, I've got facts. One of our planet's great fisheries is becoming a gigantic dead pond. And people ask why I'm so pissed off!\"\n\n\"That's right, but I've got even bigger rage! _Homo sapiens_ are invasive predators who are goin' to blow sky-high in a second Permian Extinction Event. Won't even be enough time to load your _Noah's Lark_ with a few animals. It's the Gulf of Mexico oil drillin' that's goin' to bring it on. The corporations are crackin' open the ocean's floor, tappin' into a mega-vault of methane gas. Those four thousand oil and gas rigs in the Gulf you mentioned are goin' to detonate at the same time, creatin' a force greater than pullin' the trigger on every stockpiled atomic weapon. And you mumble, don't fool with Mother Nature or Mother Nature will fool with you. I'm sayin', man has fucked Nature, so Nature's goin' to obliterate man. The mother of all explosions is comin'!\"\n\nLuz's cell phone beeps loudly in her shirt pocket. She grabs the phone and holds it to her ear.\n\nThe Chief's voice shouts over the phone, \"You hear what the Nam vet is saying?\"\n\n\"I'm listening.\"\n\n\"He's our guy.\"\n\n\"That's not the Bizango voice we heard on the recordings. He's a different guy.\"\n\n\"No. It's Bizango. He's trying to head-fake us.\"\n\n\"Quick, give me a GPS if you've got it.\"\n\n\"Just a sec, something's coming in. He's using a landline this time. We're tracking... getting a location. Here it comes.... One-four-five Hurricane Court.\"\n\nLuz throws the cell phone down on the car seat, jams her foot on the accelerator, and roars the Charger away from the southernmost continental point. She speeds up Whitehead Street toward the lighthouse towering above the palm trees. She passes the long brick wall in front of the two-story Hemingway House, where tourists are lined up taking photographs. She wheels the car around a corner and comes to a stop in Hurricane Court with its circle of ramshackle houses. She jumps from her car and looks around. No other police are there. She sees across a dead lawn a shabby house with windows blacked out by inside blinds. The number on the house's paint-peeling front door is 145.\n\nA police car pulls up to a stop, and Moxel gets out. \"Hold up a minute, Luz.\" He nods toward the house with the blacked-out windows. \"That guy in there is a psycho killer. The SWAT team is on their way. Let's wait.\"\n\n\"I'm not waiting.\" Luz pulls her Glock out of its holster. \"Back me up. I'm going in.\"\n\n\"That's crazy. The guy's a Nam vet. He could have the place booby-trapped to explode. He was trained to do that shit.\"\n\nLuz ignores Moxel and runs across the dead lawn to the front door. She grabs the door handle; it is locked. She stands back, gripping her pistol tightly in both hands. She kicks the door, banging it open. She bursts inside a living room darkened by closed blinds covering the windows. She whips her pistol around in every direction, her head snapping from side to side, ready for someone to jump up from behind the shadows of cluttered furniture. She steps cautiously across the room toward a splinter of light creeping along the bottom of a closed door. She stops at the door and listens for sounds on the other side. She hears nothing. She places her hand on the handle and twists it quietly to an open position. She throws the door back, and a sudden burst of light from a brightly lit room illuminates her completely.\n\nFacing Luz on the far side of the room is a man in his sixties, his fierce face etched with a spider web of wrinkles, his large wedge-shaped head shaved; a thick gray walrus mustache hangs over his top lip and down the sides of his mouth. He sits at stiff-backed attention in a battered aluminum wheelchair with worn duct tape wrapped tightly on its two arched handles. A coarse green military blanket covers the man from the waist down. On the wall behind hangs a Vietnam-era Missing in Action flag with the silhouette of a soldier's head bent forlornly in front of a prison guard-tower. The flag's logo declares, in blood-red letters, **POW-MIA, YOU ARE NOT FORGOTTEN.**\n\nThe man stares pointedly at Luz as if he has been expecting her. His words rush out. \"Welcome to the Casbah!\"\n\n\"Police! Raise your hands and put them behind your head!\"\n\nThe man's hands move quickly toward the blanket covering him below the waist.\n\nLuz grips her pistol harder and splays her legs apart into a firing stance. \"One more move toward that blanket and I'll blow you to hell. Hands up!\"\n\nMoxel bursts in behind Luz, his gun out. He looks at the man in the wheelchair and whoops. \"We got Bizango! Keep him covered! I'm cuffing him!\" The man's hands move toward the top of the blanket. Moxel shouts at Luz, \"There's a gun under the blanket! I can see its bulge! Shoot him if he moves!\"\n\nLuz steps closer to the man, her pistol held in firing position at his head.\n\nMoxel grabs the edge of the man's blanket. \"I've got your Bizango ass now!\" He rips the blanket away from the man's lap and looks down.\n\nAimed straight at Moxel are two blunt fleshy stumps of the man's legs, amputated above his knees. He throws his head back and laughs. \"You thought I was Bizango! Fools! Everyone with a brain and heart is Bizango now, even those of us who can only dream of what he does! Bizango said to boogie till you bounce, bop till you drop. I boogied in Nam. The parachute didn't open fully when I jumped out of a plane and bopped down; I bounced. Lost my legs. And this country doesn't give a shit now. I'm forgotten history, political roadkill. Just like that Vietnam girl runnin' down the road with napalm burnin' her skin off. Just like that pathetic pelican covered in oil from the Deepwater Horizon blowout, its wings spread out, tryin' to fly. I'll never be airborne again.\"\n\nBehind Luz, a stomping commotion breaks out. She swings around as a SWAT team storms in from the hallway. The muscular men are protected by heavy body armor; antiballistic helmets are clamped tight over their heads; strapped around their waists are belts of bullets and grenades. Gripped in their gloved hands are submachine guns. They aim at the legless vet in the wheelchair.\n\nThe vet raises his arms and flaps them in the air. His mocking voice shouts at the armored men: \"I'll never be airborne again! You gonna napalm me too? You gonna drown me in oil? Bring it on! I'm ready to rock and roll! You chickenshit killers! You won't get him, you know! Bizango is too smart for you! You dumb bastards only know _how_ to kill. Bizango knows _who_ to kill!\"\n\nLight shines out in the night from an open-sided canvas party tent set up on the earth-scraped construction site of Neptune Bay Resort. Inside the tent, a band of musicians dressed as bare-chested mermen play a bouncy Caribbean tune. Cocktail waitresses in fishnet mermaid costumes circulate through the well-dressed crowd with trays of tropical cocktails and exotic appetizers. At the center of the crowd, Big Conch holds court. He is outfitted as Neptune, god of the sea, wearing a toga and leather sandals; a gold plastic crown circles the top of his long white wig. He grips in one hand a pitchfork, its handle and three sharp steel prongs painted silver to represent Neptune's trident spear. He pumps the trident in the air. \"Silence!\" The band of mermen cease their music; the cocktail waitresses stop and balance their service trays on their bare shoulders.\n\nBig steps to a table covered by a cloth canopy. \"It's been a vicious four-year fight. I've had countless work stoppages and spent a fortune on attorneys. I was opposed by every environmental group. Today, the government approved Neptune Bay Resort. Free enterprise prevailed!\" The crowd hoots their approval. Big puts down his trident and pops a bottle of champagne. He sloshes the bubbly liquid into a plastic silver chalice and raises it high. \"Neptune Bay will stand forever as a monument to my dearly departed partners, Dandy Randy and Bill Warren. Damn, I miss those boys; I wish they were here to share this slam-dunk victory.\" He grabs the edge of the cloth canopy covering the table. \"Ladies and gentlemen, I present the most ambitious development ever built in the Florida Keys, a world-class resort that will put thousands to work and fatten our tax rolls with the fruit of hardworking capitalism, the fabulous Neptune Bay!\" He whips off the cloth canopy. The crowd applauds at a fiberglass scale-model display of the vast complex. Big raises his silver chalice triumphantly in the air. \"Construction of Neptune Bay resumes tomorrow. I will\u2014\"\n\nHis words are cut off by the roar of a boat engine. Everyone looks out from the open-sided party tent at the concrete pier jutting into the ocean. At the end of the pier is Big's powerboat, with its engine roaring. Big grabs his steel-pronged trident and runs out onto the pier to his boat. No one is in the boat; its two-hundred-horsepower engine idles with a turbo-fueled growl, and exhaust steams from beneath its chrome spoiler back fin. On the boat's sleek hull the name _Big Conch_ is spray-painted over by a slashed red **X**.\n\nBig jumps into the boat and turns off the engine. An eerie whistle breaks the sudden silence. Big looks across the water. There is no one in the darkness. Big raises the trident spear gripped in his hand and shakes it angrily. \"Whoever you are\u2014I will get you! I will cut off your head and piss down your neck and have you tell me it's raining!\"\n\nA massive redbrick fort built during the Civil War dominates the entrance to Key West Harbor on a spit of land hooked out into the Atlantic Ocean. The fort's towering walls are surrounded at their base on three sides by a deep water-filled moat. The fort's one open entrance is guarded by two large iron-barrel cannons. Police cars speed up to the entrance, skidding to a stop. The Chief and his policemen, outfitted in riot gear and bulletproof vests and carrying heavy automatic weapons, jump from the cars and run into the fort. They race to the end of an arched brick corridor where Moxel stands waiting, with his rifle at the ready. The Chief catches his breath, looks behind Moxel at a six-foot hole opened up in a brick wall, and huffs. \"So this is it?\"\n\nMoxel nods at the hole. \"Yeah, the fort's restoration crew was doing structural work on this old wall when they realized it closed off what once was a doorway. Probably bricked in way back in Abe Lincoln's time. When the crew broke through, they discovered a passageway leading into a hidden room. They found weird stuff and got out fast.\"\n\n\"What kind of weird stuff?\"\n\n\"Really spooky. Bizango stuff.\"\n\n\"We got an alert that this is Bizango's hideout. Did anybody see him?\"\n\n\"I was the first one here, immediately sized up the situation, and issued the alert.\"\n\n\"Did you see him? Did you go in?\"\n\n\"No, I was waiting for backup.\"\n\nThe Chief grips his rifle in one hand and unhooks the long metal flashlight hanging from his belt as he barks orders at the surrounding men. \"Guard this entrance. Moxel and I will go in. If we're not out in twenty minutes, two of you follow us\u2014never more than two at a time. I don't want to lose a whole squad to this maniac; he could be hiding anywhere.\"\n\nThe Chief clicks on his flashlight and steps through the brick wall's opening into a passageway barely the width of a man. He shines the flashlight into the darkness, exposing twisting curves ahead. Moxel follows him in. They duck their heads beneath the low arch of the brick ceiling as they squeeze forward. The Chief stops, sweat pours down his face. \"Jesus, must be a hundred and ten degrees in here.\"\n\nMoxel's nostrils twitch as he inhales the stifling air. \"Smells like a sewer. Smells like there might be dead Civil War guys rotting in here. Let's turn around.\"\n\n\"We can't turn around. It's too narrow.\"\n\n\"We can walk out backward.\"\n\n\"No. We're going through to the end.\"\n\nMoxel slaps at his face. \"Fucking mosquitoes. I'm being eaten alive. During the Civil War, more soldiers died from mosquito malaria than were shot in battle. I saw that on the History Channel.\"\n\n\"Keep your voice down. Is the safety of your rifle off?\"\n\n\"Of course.\"\n\n\"You sure your rifle's loaded?\"\n\n\"Shit, I forgot.\"\n\n\"Goddamn it, man. Load your rifle.\"\n\nMoxel loads his rifle in the semidarkness, snapping cartridges into the clip. \"I'm ready now.\"\n\n\"Good. I hope this passageway doesn't go on too much farther.\"\n\nMoxel follows close behind the Chief. The passageway becomes narrower and tighter. They squeeze forward, and emerge into a dark room. The Chief shines his flashlight around the room, exposing old wooden crates stacked along one wall. The crates are stamped **MUSKET ROUNDS, BLACK POWDER.**\n\nThe Chief whistles under his breath. \"Looks like we're in a Civil War munitions room.\"\n\n\"Shit! This stuff is so old it can blow if we even talk too loud.\"\n\n\"Don't get excited.\"\n\nThe Chief aims his flashlight at a wall. The beam lights up a giant red **X** spray-painted across the wall. Below the red **X** , on the floor, is a Pelletier speargun. Next to the speargun is an open box full of four-foot-long steel spears.\n\nThe Chief shines his light onto the adjoining wall.\n\nStuck to the wall with duct tape are cut-up newspaper headlines in bold black ink:\n\n**SOME SHRIMPERS IGNORE LAWS PROTECTING TURTLES  \nCONDOS SLATED FOR WHITE HERON HABITAT  \nTRACTOR-TRAILER RIG KILLS THREE KEY DEER ON HIGHWAY  \nPOWERBOAT RUNS OVER 22ND MANATEE THIS YEAR  \nDOLPHINS DIE IN PESTICIDE-POLLUTED WATERS  \nCORAL REEF DESTROYED BY CRUISE SHIPS  \nALLIGATOR SLAUGHTER DECLARED A DISGRACE  \nTOXIC WASTE LINKED TO CANCER IN THE FLORIDA KEYS**\n\nMoxel turns to leave. \"I'm getting out!\"\n\nThe Chief grabs Moxel's arm. \"You aren't going anywhere. This is definitely Bizango's lair.\"\n\n\"He could be in here!\"\n\n\"He's not here.\"\n\n\"How do you know?\"\n\n\"If he was, you'd already have one of his steel spears shot through your heart.\" The Chief shines his flashlight up, exposing a solid brick ceiling. \"How the hell does Bizango get in and out of here, if the outside passageway's been bricked up since Civil War times? Got to be another way in.\" He points the beam across the ceiling, then down along the brick corner to the floor. The beam lights up an open carton of black micro\u2013digital recorders. The Chief takes a step toward the carton. He stops at a sudden loud clacking at his feet. He jumps back.\n\nMoxel aims his rifle at the floor. \"What's that?\"\n\nThe Chief shines down his flashlight. The slick green mildewed floor around him is alive with clawing orange crabs. The crabs scuttle toward a wide hole in the floor. The hole is filled with brackish water. The crabs splash into the water and disappear down the hole.\n\nThe Chief steps carefully to the hole. He bends over and directs the flashlight into the hole's murky water. He holds the beam on the water. \"Damn, now I get it. This hole was originally built as an escape hatch in case the fort was under siege. The hole is on the exact same water level as the moat outside surrounding the fort. That's why the water from outside doesn't flood into this room. Civil War soldiers could secretly escape this room by jumping into this hole and swimming through an underwater tunnel up into the moat. Bizango figured that out and he did the reverse.\"\n\n\"I don't get it.\"\n\n\"Bizango's been swimming under the moat and popping up through this hole to hide. That's why we couldn't find him all this time.\"\n\n\"Let's get the hell out of here.\"\n\n\"I want you to stay in this room. Bizango might pop up from this hole at any moment.\"\n\n\"Chief, I can't stay here. Tonight's the Fantasy Parade. Bizango will be prowling for his next victim. I'm the one who's come closest to capturing him. I should be out there on the streets, hunting him.\"\n\nThe Chief shines his flashlight into Moxel's face. \"Stay put and don't leave this room. That's an order.\"\n\nMoxel's face twists angrily. \"Okay, but you're wrong. I'm the guy to bring Bizango down.\"\n\nThe Chief takes out his cell phone and punches in a number. \"Damn, it's dead. No reception\u2014brick walls are too thick. I can't get ahold of Luz.\" He moves to the passageway opening and punches in the number again. \"Line's still dead. She's up in Key Largo at her daughter's soccer game. I need to get her down here.\"\n\nMoxel snorts. \"Fucking soccer moms. They're at a game when there's a killer on the loose. That's why women shouldn't be cops.\"\n\nThe Chief swings his flashlight around to the back wall and shines it on the spray-painted red **X**. \"You're wrong about Luz. Sometimes the only way to counter a man's killer instinct is to use a woman's intuition. I've got a feeling Luz is the one who is going to bring Bizango down.\"\n\nThe Key Largo High School soccer field is a sun-parched grassy rectangle lined by wooden bleachers that are filled with parents and supporters watching teenaged girls in shorts and jerseys battle out the final minutes of a hard-fought game. The sweating girls charge a white ball in a rush of running legs and pumping muscular thighs. A scoreboard on the side of the field reads **LARGO GATORS 2, KEY WEST CONCHS 1**.\n\nIn the bleachers, Luz and Joan jump to their feet, yelling encouragement to Carmen as she runs in the middle of the action on the field. The ball bounces off the leg of a Largo player and goes out of bounds. Carmen races to the sideline and takes the ball from the referee for a throw-in. Both teams scatter back into their positions, hands on their hips, breathing hard as they focus on Carmen, waiting. Carmen holds the ball above her head, her feet planted firmly on the ground. She searches the field for an open teammate. She hurls the ball toward the Largo goalpost, and the action explodes into another blur of running girls.\n\nJoan holds Luz's hand and squeezes it. \"I'd give anything if Nina could have seen this championship. She was Carmen's biggest fan.\"\n\nLuz squeezes Joan's hand back. The cell phone in her guayabera-shirt pocket rings. Luz doesn't hear the ringing above the yelling around her; she strains to figure out what is going on at the far end of the field, where the ball sails through the air above the players. She sees Carmen and another girl leap high, their long hair flying, their bodies lunging toward the ball. Carmen whacks the spinning ball with her forehead, slamming it toward the goal net. The other girl in the air smashes hard into Carmen. Carmen falls, her head hitting the hard ground, knocking her out. The action on the field stops. Carmen lies motionless.\n\nLuz jumps down from the bleachers and runs across the field, with Joan close behind. Luz shoves through the players packed around Carmen; she kneels at Carmen's side and holds her by the shoulders. \"Can you hear me?\" Carmen's eyes don't open. Luz shouts, \"Can you hear me?\" Carmen's eyes slowly open; she moans and tries to get up. Luz pushes Carmen's shoulders back down. \"Don't move! Watch my finger with your eyes!\" Luz holds a finger in front of Carmen's eyes and moves it slowly. Carmen's dazed eyes follow Luz's finger from left to right. \"Good. Now count for me backward from five.\"\n\nCarmen keeps her eyes on Luz as she counts. \"Five, four, three, two, one... I love you, Mom.\"\n\nLuz breathes heavily with relief. She kisses Carmen's cheek and pulls her to her feet. The cell phone in Luz's shirt pocket rings, but she ignores it.\n\nJoan pulls the ringing phone from Luz's pocket and answers. \"This is Joan. Luz can't talk. Yes, go ahead, I'm listening. Okay, but it will take her two hours to get there from here.\"\n\nJoan clicks the phone off and looks at Luz. \"That was the Chief. They found Bizango's hideout. Chief said you've got a siren and red lights on your rocket Charger, use them and get your ass to Key West.\"\n\nThousands of people wearing wildly imaginative and bizarre costumes are packed along the sidewalks lining both sides of mile-long Duval Street. The excited spectators cheer as the enormous decorated floats of the Fantasy Parade motor past. The floats resemble everything from a jet airplane crashed into a mountaintop, to pirate ships with sails billowing from towering masts, to the marble fa\u00e7ade of the White House, to spooky haunted houses. From each passing float, costumed men and women fling strings of colored beads and candy to the playful crowd below. Between the floats march high-school bands, Jamaican tin-drum bands, Dixieland bands, bluegrass bands, and heavy-metal bands blasting an earsplitting blare.\n\nThrough the raucous sidewalk crowd, a man wearing a presidential-looking dark suit and a rubber John F. Kennedy mask obscuring his face makes his way. A Frankenstein monster with iron bolts protruding from his neck lurches by the masked man. The monster is followed by a roller-skating seventy-year-old woman high on ecstasy, her wrinkled body totally nude except for a Red Riding Hood cape.\n\nThe Kennedy figure looks up to a clattering sound in the sky and sees a police helicopter overhead. The copter skims above the rooftops of buildings lining the parade route. On the rooftops, police riflemen view the crowd through high-powered scopes.\n\nThe masked man is banged into by a broad-shouldered drag queen wearing a red-white-and-blue Wonder Woman costume and a rhinestone tiara. Wonder Woman bats long false eyelashes at the man. \"Well, if it isn't John Frigging Kennedy, my hero. Don't ask me what I can do for my country. Ask me what I can do for you! It's Hell-o-Weenie. Treat or be tricked.\" Wonder Woman slams a can of beer into the masked man's chest.\n\nThe man pushes the can away and walks on, his attention caught by black-and-white flashes in the middle of the street. He turns quickly to spot twenty men in full-bodied rubber skeleton suits, their faces hidden behind skull masks with knobby eye sockets; they all look like Bizango. The skeletons wear shiny black top hats and tap-dance behind a brass band of bloody-faced staggering zombies. The skeletons stop and toss their hats high in the air. They twirl around on white canes, blowing shrill whistles clenched between their teeth. The skeletons catch the spinning hats as they fall back down, to cheers from the crowd.\n\nThe masked man closely follows the tap-dancing skeletons until his way is blocked by punk rockers surrounding Scarlett O'Hara. Scarlett is resplendent in her Civil War\u2013era satin ball gown, flowing black wig, and sequined silver mask. The gang of spike-haired punks are tricked out in black leather pants and steel-point black boots. The punks' faces are tattooed over by ghoulish inked images. The punks shout rude, lusty comments about Scarlett's creamy swelled cleavage, pushed up from the tight top of her ball gown.\n\nThe masked man shoves through the punks to get to Scarlett. He leans his rubber face close to her. \"Excuse me, Miss Scarlett, you in trouble? Need some help?\"\n\nThe punks press in belligerently around the man. One punk spits his screaming words onto the man's Kennedy face mask. \"Fuck off, dead president!\"\n\nThe masked man pushes aside the front of his suit coat, exposing the handle of a pistol tucked behind his pants belt.\n\nThe punk shouts at his mates, \"Motherfucker president is packing! Motherfucker president assassin!\" The punks run off.\n\nScarlett flutters a purple fan before her face as she eyes the man from behind her silver mask. \"Mr. President, there's something familiar about you. Do we know each other?\"\n\n\"Maybe we do. Your voice sounds exactly like my wife's.\" The man grabs the bottom of his rubber mask and pulls it off.\n\nScarlett sees the exposed face of Noah. She coos sarcastically, \"Don't you mean, my voice sounds exactly like your ex-wife's, not your wife's?\" She pulls up her sequined face mask and takes it off. It is Zoe.\n\nBehind Zoe, in the street, a huge float depicts a palm-tree-studded island encircled by aqua-blue ocean waves. A painted wooden sign is arched over the island spelling out **NEPTUNE BAY RESORT.** Commanding the island's center is Big Conch, costumed in his King Neptune toga, his long white wig circled by a plastic gold crown, and gripping his silver-painted pitchfork trident. He is surrounded by big-breasted mermaids in skimpy bikinis. The mermaids toss brightly wrapped candy to the leering crowd. Big vigorously pumps the silver trident above his head. He gazes down and sees Zoe in her Scarlett ball gown next to Noah holding his Kennedy mask. Big grabs the crotch of his short toga and thrusts his hips forward. He points the trident's sharp steel prongs at Zoe. \"Hey, Scarlett, why you with a president when you can be with Neptune? I'm king of the sea!\"\n\nBig's mermaids laugh and throw handfuls of candies through the air to Zoe. The candy rains down as a black-and-white-rubber-encased skeleton appears next to Zoe. The skeleton dashes past her. It climbs up the blue-painted plywood waves of the island float and pushes the mermaids aside. It leaps toward Big and rips the trident away from him. It turns to the crowd, the steel-pronged trident held high in its hand. People erupt in panic. \"It's him! Run! The killer! Bizango!\"\n\nBig yanks the trident from Bizango and slams its wood handle against the skeleton's skull with a loud crack. Bizango reels backward. Big swings the base of the trident's steel prongs into Bizango's face, knocking the skeleton to the floor. Big aims the prongs at Bizango and thrusts forward. Bizango rolls; the prongs scrape the rubber skeleton suit, drawing a leak of blood. Bizango springs up. Big points the trident and lunges forward. Bizango spins aside; the sharp prongs whiz past. Bizango grabs the handle and wrenches the trident away from Big. Big dives toward Bizango. Bizango swings the trident around and drives its sharp prongs into Big's chest; blood spurts from around the embedded prongs. Bizango yanks the trident back, pulling the prongs from Big's chest. Big's breath explodes in a gasping blast of shock as he falls dead at Bizango's feet.\n\nBizango raises the bloody trident and hurls it through the air at the wooden sign arched over the float. The steel prongs pierce the sign's painted words, **NEPTUNE BAY RESORT.**\n\nOn the street, Noah runs alongside the still-rolling float. He tries to keep his footing in the terrified crowd. He pulls out the pistol tucked beneath his pants belt. He aims the pistol up at Bizango. \"Stop! I know who you are!\"\n\nBizango's rubber skull face mask swerves around. The mask's deep black eye sockets stare down at Noah with the aimed pistol.\n\nNoah shouts above the screaming crowd at Bizango, \"Don't make me shoot you!\"\n\nBizango's skull eyes turn away from Noah. The skeleton leaps off the float, lands on the street, and races away into the panicked crowd.\n\nNoah runs after Bizango as a police helicopter swoops in from overhead. From the copter's open door, police riflemen aim down into the chaos. The copter's searchlight beam flashes on a fleeing Bizango. The riflemen cannot fire without hitting others in the crowd. The searchlight keeps Bizango in sight. Bizango breaks off down a side street, with Noah close behind. In front of Bizango, a police car speeds up and brakes to a skidding sideways stop, blocking the street. The car's doors swing open; the Chief and his sharpshooters jump out.\n\nBizango stops in the middle of the street, trapped between the shooters and Noah. In a black-and-white blur, the skeleton races to a building with a sign above its entrance, **KEY WEST AQUARIUM.** The building's glass entrance door is shut with a padlocked iron chain. Bizango violently yanks the chain, trying to break the lock. The shooters from behind open fire. Bullets zing around Bizango. The entrance door shatters open in a hail of glass shards. Bizango runs through the blasted open doorway into the aquarium.\n\nDarkness inside the aquarium is illuminated by blue neon light exposing fish exhibition tanks. Behind the thick glass walls moves the fin-flick and gill-sucking glide of obscure sea creatures. The tanks hiss with circulating water. The Chief and his shooters spread out and move between the tanks. The Chief's attention is caught by a sudden black-and-white flash reflected on the glass of a tank. The flash disappears. The Chief looks quickly around. He sees another black-and-white flash. He raises his gun to fire, then pulls his finger quickly away from the trigger. The black-and-white flash is a large zebra fish, swimming straight at him from the opposite side of a tank's glass wall. The zebra fish knocks against the glass barrier with a thud, then glides off.\n\nA shooter shouts out in the darkness, \"There he is!\"\n\nThe back emergency door of the aquarium swings open, setting off a ringing alarm. Framed in the doorway by outside light is the skeleton figure of Bizango.\n\nThe shooters fire; bullets zing through the air, smashing into the tanks, shattering glass, releasing a cascading avalanche of water and sea creatures.\n\nThe Chief runs as he yells above the alarm at the shooters, \"Go after him!\"\n\nThe Chief and the shooters race toward the open exit door. They slip on the wet floor, falling onto broken glass and sliding among floundering sea creatures. The Chief skids across the floor past a loose octopus flailing its tentacles, then bumps to a stop against a twisting leopard shark. He pushes away from the shark, yanks out his cell phone, punches in a number, and shouts, \"Moxel! You read me?\"\n\nMoxel's voice crackles back over the phone: \"Chief! I can barely hear you! I'm in the fort hideout!\"\n\n\"Bizango is headed there! He still thinks it's safe! Get ready! Alert all riflemen! Shoot to kill!\"\n\nAt the top of the soaring white column of the Key West Lighthouse, Noah stands on the outside circular iron catwalk. Above his head, the shining glass beacon revolves in the night. He gazes across the lights and shadows of the town. In the distance, police helicopters fly over the maze of streets, searching for Bizango.\n\nEchoing up from the interior staircase behind Noah is the sound of approaching footsteps climbing to the top of the lighthouse. He turns to the open doorway leading from inside onto the catwalk. He pulls out the Luger tucked behind his belt. The black-and-white skeleton of Bizango appears in the doorway. Noah raises his pistol. \"It's over.\"\n\nBizango's skull head swivels slowly; the impenetrable black sockets of the eyes fix on Noah. The rubber mouth and nose openings of the face mask pulsate with heavy breathing. Noah steps closer with the aimed pistol. \"You can't kill every wrongdoer. Even a hurricane can't blow away all of man's evils. This is the end.\" Bizango's chest heaves. Noah reaches out in a swift movement and grips the bottom of the mask. Bizango's hand whips up, and skeletal fingers grab Noah's wrist in a powerful grip. Noah holds tight to the mask. \"Even a hurricane can't blow away all of\u2014\"\n\nNoah's words are cut by the clatter from a helicopter swooping down over the lighthouse. The copter's side door slides open. A sharpshooter leans out from the doorway with a scope-mounted rifle and pulls the trigger. Bizango slams Noah down onto the catwalk as the bullet blasts out a cement chunk of the wall where Noah was standing. Another bullet whams into Bizango. The skeleton raises clenched fists above its skull head in defiant rage at the copter; rifle fire zings; blood gushes from bullet holes ripping into Bizango's rubber suit. Bizango collapses against the catwalk's iron railing, struggling to hang on.\n\nNoah, facedown on the catwalk floor, reaches out and grabs Bizango's skeleton ankle. He pulls back hard on the ankle, trying to keep Bizango from falling off the lighthouse. The helicopter banks hard and hovers directly in front of Bizango. The copter's blades whip waves of wind against Bizango, who clings to the railing. The crack of five rapid rifle shots from the copter tear into Bizango. Noah feels Bizango's ankle wrench away from his grip. Bizango plunges off the side of the lighthouse. The helicopter shines its searchlight on Noah. He staggers to his feet, grips the catwalk railing, and looks over. Far below is the sprawled black-and-white body of Bizango.\n\nNoah races down the lighthouse staircase and outside. He kneels next to Bizango. The skeleton's rubber suit oozes blood. Noah leans over Bizango's face mask and hears faint breathing. He takes hold of the mask and begins lifting it up.\n\nBehind Noah, a police car skids to a stop. The Chief and the riflemen jump from the car. The Chief yells, \"Is he alive or dead?\"\n\nNoah swings around furiously. \"Stay the hell away!\"\n\nThe Chief signals his riflemen. \"Stand back! Give them room!\"\n\nNoah turns back to Bizango and pulls hard at the tight skull mask. The mask peels off the face with a loud sucking sound. The Chief and the riflemen stare in disbelief at unmasked Bizango, stunned at the exposed face of Luz.\n\nNoah bends close to Luz, trying to hear the words she struggles to get out. Her dim eyes stare up at the beam at the top of the lighthouse; her lips barely move. \"Look... Cuban doves... returned... not... extinct... hope.\"\n\nNoah looks up to the solitary beacon of light high above. \"I can see them, Luz. The Cuban doves are flying. Your doves have returned.\"\n\nThe rising sun illuminates Noah's boat, with its radio antenna bolted to the deck, adrift on the ocean. Inside the pilothouse, Noah sits at his console. He swivels in his chair and leans close to the microphone, his words stripped to raw emotion.\n\n\"I've had calls all morning about Luz Zamora. Many of you are convinced Luz was a senseless cold-blooded murderer, a coward hiding behind a mask. Others believe she was a brave avenger, proving that it takes a woman to do a man's job. Some think that as Bizango she only murdered corrupt souls, making her a heroic eco-vigilante defending those in nature who cannot defend themselves. We cannot accept what Luz did, killing those who kill the environment, but we can try to understand. The world our children are now born into has thousands of toxic chemicals that did not exist until recently. Unknown poisons invade our air, our water, our homes, our food, our blood. Luz believed that this environment caused her daughter Nina's childhood leukemia, that it caused her father's lung cancer, that it caused her own cancer. Who's to say Luz wasn't right? There are over two hundred different types of cancer. Who's to say that all of us are not dying a slow death from rancid rivers, poisoned oceans, defiled land, polluted air, and perverted food?\n\n\"Luz thought of herself as the ultimate judge, Bizango the great corrector. Her Bizango believed that man cannot destroy his environment without consequence, that a price must be paid, that accountability must come home to roost. The philosophers say that no man is an island; well, Key West is a real island in the current of the Gulf Stream, it is affected by the totality of the biodiversity swirling around it in air and water. Each and every one of us is no different; no matter where we are on this earth, we are all islands affected by civilization's implacable currents of consequence bearing down on us.\"\n\nNoah stops. He picks up a can of Red Bull from the console and takes a long swig. He leans forward toward the microphone, his voice thickening with conviction.\n\n\"Loyal pilgrims, the feds are about to shut down my radio broadcasts, but they aren't shutting me up. Don't despair, I remain your Truth Dog, an old dog with new tricks. I've been reinstated as an attorney; my battles now will be in the halls of justice. I intend to fight on as another kind of corrector\u2014a small one, not a great one. I believe that it will take millions of small correctors to defeat the great injustices surrounding us. I leave you today with words of wisdom from a poet back in the 1960s, when something new and radical swept the land called the Environmental Movement. The Movement's true believers carried the torch forward as today's Green Movement, the New Ecology, or whatever the hell name is slapped on it. The 1960s poet sang his words as if each one was a razor blade cutting his throat with its truth. His was a final cri de coeur, a fierce lament of human frailty. He knew in the end we must lay down the sword after the war is over. I'll play the poet's song. I bid you all farewell until my next and very last broadcast.\"\n\nNoah pushes a disc into the CD player on the console. From the big battered wood speakers, the song of the poet plays in an undulating rhythm, its words smoldering on the surface.\n\n_\"This old world_\n\n_may never change_\n\n_The way it's been_\n\n_And all the ways of war_\n\n_Can't change it_\n\n_back again_\n\n_I'm not the one_\n\n_to tell_\n\n_this world_\n\n_How to get along_\n\n_I only know the peace_\n\n_will come_\n\n_When_\n\n_all hate is gone_\n\n_I been searchin'_\n\n_for the dolphins_\n\n_in the sea_.\n\n_And sometimes I wonder_\n\n_Do you ever_\n\n_think of me\"_\n\nThe words fade away, and Noah switches off the speakers. He pushes his chair back, closes his eyes tight, and sits in silence. The trawler sways gently. He opens his eyes and looks down at Chicken, resting at his feet.\n\n\"Come on, lover boy, let's take a breather.\"\n\nThe dog trots after Noah out onto the deck of the boat, into the fresh salty air. Noah blinks in the bright sunlight. There are no white cumulus clouds as big as Spanish galleons sailing through the sky. There are no spread-wing seabirds skimming across the vast ocean's blue surface. All is empty, except for a black dot on the far horizon. The dot grows larger as it gets closer, then comes into focus, revealing itself as a speeding Sea Ray boat.\n\nThe boat's twenty-four-foot hull skips over the water. It comes alongside Noah's trawler and pulls up. Zoe stands at the stainless-steel wheel of the helm. She turns off the engine and calls to Noah on his deck:\n\n\"There's something stuck in a bottle that belongs to me. Will you help get it out?\"\n\nShe tosses up an empty corked rum bottle and he catches it. She pulls off her sunglasses; her blue eyes are gazing. \"So, pirate, what do you think?\"\n\nNoah tips the bottle up to the globe of sun. Inside the glass shines Zoe's gold wedding ring. He uncorks the bottle and taps the ring out into his open palm. He closes the ring in a tight fist and stares at her. \"What do I think?\"\n\n\"Yeah, you're supposed to be a lawyer, a smart guy.\"\n\nNoah reaches down and pulls Zoe up onto his boat. He holds her tight, his words close.\n\n\"I don't think. I know: the pirate has his treasure back.\"\n\nIs anyone awake? This is Truth Dog speaking to you for the last time from pirate-radio boat _Noah's Lark_. Do you hear me? I'm on the line for you. I'm on the hook. I don't want it to end this way. We can do better. Call me before it is too late. The whole democracy idea in the beginning was to reinvent, to shed the skin of xenophobia, to climb that noble mountain and plant a flag of infinite possibilities for a new tribe. High hopes are these, my pilgrims, the dreams and schemes of those mad merrymakers, our Founding Fathers. Call Truth Dog. Tell him how lightning strikes you between the eyes and you see the flash of revelation across the ocean. This is your last chance. Rise and shine.\n\n_Are_\n\n_you_\n\n_out_\n\n_there?_\n**A Note About the Author**\n\nThomas Sanchez is a descendant of cattlemen dating back four generations in California to the nineteenth-century Gold Rush. He was born days after his father was killed at the age of twenty-one in the Battle of Tarawa during World War II. Sanchez's novels have received numerous honors, and he has been awarded a Guggenheim fellowship and is a Chevalier of France's Ordre des Arts et des Lettres. Sanchez is also the director of a forthcoming film documentary, _Into the Light_ , chronicling the life of Jack Garfein, survivor of eleven concentration camps, Actors Studio icon, and legendary film director. Sanchez divides his time between San Francisco, Key West, and Paris.\n\n**Other titles available in eBook format by Thomas Sanchez**\n\n_Day of the Bees \u2022_ 978-0-307-76609-0  \n _King Bongo \u2022_ 978-0-307-76610-6  \n _Mile Zero \u2022_ 978-0-307-76608-3  \n _Rabbit Boss \u2022_ 978-0-307-49748-2  \n _Zoot-Suit Murders \u2022_ 978-0-307-49895-3\n\nwww.thomas-sanchez.com\n\n**For more information, please visitwww.aaknopf.com**\nALSO BY THOMAS SANCHEZ\n\n_Rabbit Boss_\n\n_Mile Zero_\n\n_King Bongo_\n\n_Day of the Bees_\n\n_Zoot-Suit Murders_\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\n\n\nProduced by Barbara Kosker, Bryan Ness and the Online\nDistributed Proofreading Team at http:\/\/www.pgdp.net (This\nfile was produced from scans of public domain works at the\nUniversity of Michigan\\'s Making of America collection.)\n\n\n\n\n\n\n[Illustration: A West Highland Ox\n\nThe Property of Mr. Elliott of East Ham Essex.]\n\n\n\n\n  THE\n  AMERICAN REFORMED\n  CATTLE DOCTOR;\n\n  CONTAINING\n  THE NECESSARY INFORMATION\n  FOR\n  PRESERVING THE HEALTH AND CURING THE DISEASES\n  OF\n  OXEN, COWS, SHEEP, AND SWINE,\n  WITH\n  A GREAT VARIETY OF ORIGINAL RECIPES,\n  AND\n  VALUABLE INFORMATION IN REFERENCE TO\n  FARM AND DAIRY MANAGEMENT;\n  WHEREBY\n  EVERY MAN CAN BE HIS OWN CATTLE DOCTOR.\n\n\n\n\n  THE PRINCIPLES TAUGHT IN THIS WORK ARE, THAT ALL MEDICATION\n  SHALL BE SUBSERVIENT TO NATURE; THAT ALL MEDICINAL AGENTS\n  MUST BE SANATIVE IN THEIR OPERATION, AND ADMINISTERED WITH\n  A VIEW OF AIDING THE VITAL POWERS, INSTEAD OF DEPRESSING,\n  AS HERETOFORE, WITH THE LANCET AND POISON.\n\n\n\n\n  BY\n  G. H. DADD, M. D., VETERINARY PRACTITIONER,\n  AUTHOR OF \"ANATOMY AND PHYSIOLOGY OF THE HORSE.\"\n\n\n\n\n  BOSTON:\n  PHILLIPS, SAMPSON, AND COMPANY,\n  110 WASHINGTON STREET.\n  1851.\n\n\n\n\n  Entered according to Act of Congress, in the year 1851, by\n\n  G. H. DADD, M. D.,\n\n  In the Clerk's Office of the District Court for the\n  District of Massachusetts.\n\n  STEREOTYPED AT THE\n  BOSTON STEREOTYPE FOUNDRY.\n\n\n\n\nCONTENTS.\n\n\n                                                            PAGE\n\n  INTRODUCTION,                                                9\n\n\n  CATTLE.\n\n  Importance of supplying Cattle with pure Water,             15\n  Remarks on feeding Cattle,                                  17\n  The Barn and Feeding Byre,                                  21\n  Milking,                                                    24\n  Knowledge of Agricultural and Animal Chemistry\n      important to Farmers,                                   25\n  On Breeding,                                                30\n    The Bull,                                                 34\n    Value of Different Breeds of Cows,                        35\n  Method of preparing Rennet, as practised in England,        36\n  Making Cheese,                                              37\n    Gloucester Cheese,                                        38\n    Chester Cheese,                                           39\n    Stilton Cheese,                                           40\n    Dunlop Cheese,                                            41\n    Green Cheese,                                             42\n  Making Butter,                                              44\n    Washing Butter,                                           45\n    Coloring Butter,                                          46\n  Description of the Organs of Digestion in Cattle,           47\n  Respiration and Structure of the Lungs,                     53\n  Circulation of the Blood,                                   54\n    The Heart viewed externally,                              55\n  Remarks on Blood-letting,                                   58\n  Efforts of Nature to remove Disease,                        67\n  Proverbs of the Veterinary Reformers,                       70\n  An Inquiry concerning the Souls of Brutes,                  72\n  The Reformed Practice--Synoptical View of the\n      Prominent Systems of Medicine,                          75\n  Creed of the Reformers,                                     79\n  True Principles,                                            80\n  Inflammation,                                               88\n  Remarks, showing that very little is known of the\n      Nature and Treatment of Disease,                        94\n  Nature, Treatment, and Causes of Disease in Cattle,        105\n  Pleuro-Pneumonia,                                          107\n  Locked-Jaw,                                                115\n  Inflammatory Diseases,                                     121\n    Inflammation of the Stomach, (Gastritis,)                121\n    Inflammation of the Lungs, (Pneumonia,)                  122\n    Inflammation of the Bowels, (Enteritis.--Inflammation\n        of the Fibro-Muscular Coat of the Intestines,)       124\n    Inflammation of the Peritoneal Coat of the Intestines,\n        (Peritonitis,)                                       125\n    Inflammation of the Kidneys, (Nephritis,)                125\n    Inflammation of the Bladder, (Cystitis,)                 126\n    Inflammation of the Womb,                                126\n    Inflammation of the Brain, (Phrenitis,)                  127\n    Inflammation of the Eye,                                 128\n    Inflammation of the Liver, (Hepatitis,)                  128\n  Jaundice, or Yellows,                                      130\n  Diseases of the Mucous Surface,                            132\n    Catarrh, or Hoose,                                       133\n    Epidemic Catarrh,                                        134\n    Malignant Epidemic, (Murrain,)                           135\n    Diarrhoea, (Looseness of the Bowels,)                    136\n    Dysentery,                                               138\n    Scouring Rot,                                            139\n  Disease of the Ear,                                        140\n  Serous Membranes,                                          140\n  Dropsy,                                                    141\n  Hoove, or \"Blasting,\"                                      144\n  Joint Murrain,                                             147\n  Black Quarter,                                             149\n  Open Joint,                                                151\n  Swellings of Joints,                                       152\n  Sprain of the Fetlock,                                     153\n  Strain of the Hip,                                         154\n  Foul in the Foot,                                          154\n  Red Water,                                                 157\n  Black Water,                                               160\n  Thick Urine,                                               160\n  Rheumatism,                                                161\n  Blain,                                                     162\n  Thrush,                                                    163\n  Black Tongue,                                              163\n  Inflammation of the Throat and its Appendages,             163\n  Bronchitis,                                                164\n  Inflammation of Glands,                                    164\n  Loss of Cud,                                               166\n  Colic,                                                     166\n  Spasmodic Colic,                                           167\n  Constipation,                                              168\n  Falling down of the Fundament,                             171\n  Calving,                                                   171\n  Embryotomy,                                                175\n  Falling of the Calf-Bed, or Womb,                          176\n  Garget,                                                    177\n  Sore Teats,                                                178\n    Chapped Teats and Chafed Udder,                          178\n  Fever,                                                     178\n    Milk or Puerperal Fever,                                 182\n    Inflammatory Fever,                                      183\n    Typhus Fever,                                            186\n  Horn Ail in Cattle,                                        189\n  Abortion in Cows,                                          191\n  Cow-Pox,                                                   194\n  Mange,                                                     195\n  Hide-bound,                                                196\n  Lice,                                                      196\n  Importance of keeping the Skin of Animals in a\n      Healthy State,                                         197\n  Spaying Cows,                                              201\n    Operation of Spaying,                                    204\n\n\n  SHEEP.\n\n  Preliminary Remarks,                                       209\n  Staggers,                                                  219\n  Foot Rot,                                                  220\n  Rot,                                                       221\n  Epilepsy,                                                  222\n  Red Water,                                                 223\n  Cachexy, or General Debility,                              224\n  Loss of Appetite,                                          224\n  Foundering, (Rheumatism,)                                  224\n  Ticks,                                                     225\n  Scab, or Itch,                                             225\n  Diarrhoea,                                                 227\n  Dysentery,                                                 227\n  Constipation, or Stretches,                                228\n  Scours,                                                    230\n  Dizziness,                                                 231\n  Jaundice,                                                  232\n  Inflammation of the Kidneys,                               232\n  Worms,                                                     233\n  Diseases of the Stomach from eating Poisonous Plants,      233\n  Sore Nipples,                                              234\n  Fractures,                                                 234\n  Common Catarrh and Epidemic Influenza,                     235\n  Castrating Lambs,                                          236\n  Nature of Sheep,                                           237\n  The Ram,                                                   238\n  Leaping,                                                   239\n  Argyleshire Breeders,                                      239\n  Fattening Sheep,                                           240\n  Improvement in Sheep,                                      244\n  Description of the Different Breeds of Sheep,              249\n    Teeswater Breed,                                         249\n    Lincolnshire Breed,                                      250\n    Dishley Breed,                                           250\n    Cotswold Breed,                                          250\n    Romney Marsh Breed,                                      251\n    Devonshire Breed,                                        251\n    Dorsetshire Breed,                                       251\n    Wiltshire Breed,                                         252\n    South Down Breed,                                        252\n    Herdwick Breed,                                          253\n    Cheviot Breed,                                           253\n    Merino Breed,                                            253\n    Welsh Sheep,                                             254\n\n\n  SWINE.\n\n  Preliminary Remarks,                                       255\n  Natural History of the Hog,                                259\n  Generalities,                                              262\n  General Debility, or Emaciation,                           263\n  Epilepsy, or Fits,                                         264\n  Rheumatism,                                                264\n  Measles,                                                   265\n  Ophthalmia,                                                266\n  Vermin,                                                    266\n  Red Eruption,                                              267\n  Dropsy,                                                    267\n  Catarrh,                                                   267\n  Colic,                                                     268\n  Diarrhoea,                                                 268\n  Frenzy,                                                    268\n  Jaundice,                                                  269\n  Soreness of the Feet,                                      269\n  Spaying,                                                   270\n  Various Breeds of Swine,                                   271\n    Berkshire Breed,                                         271\n    Hampshire Breed,                                         271\n    Shropshire Breed,                                        272\n    Chinese Breed,                                           272\n  Boars and Sows for Breeding,                               272\n  Rearing Pigs,                                              273\n  Fattening Hogs,                                            275\n  Method of Curing Swine's Flesh,                            277\n\n\n  APPENDIX.\n\n  On the Action of Medicines,                                279\n  Clysters,                                                  281\n    Forms of Clysters,                                       283\n  Infusions,                                                 286\n  Antispasmodics,                                            287\n  Fomentations,                                              287\n  Mucilages,                                                 289\n  Washes,                                                    289\n  Physic for Cattle,                                         290\n    Mild Physic for Cattle,                                  291\n  Poultices,                                                 292\n  Styptics, to arrest Bleeding,                              296\n  Absorbents,                                                296\n    Forms of Absorbents,                                     297\n\n  VETERINARY MATERIA MEDICA, embracing a List of the\n    various Remedies used by the Author of this Work\n    in the Practice of Medicine on Cattle, Sheep,\n    and Swine,                                               299\n  General Remarks on Medicines,                              312\n  Properties of Plants,                                      315\n  Potato,                                                    316\n\n  TREATMENT OF DISEASE IN DOGS--Preliminary Remarks,         323\n  Distemper,                                                 325\n  Fits,                                                      326\n  Worms,                                                     327\n  Mange,                                                     328\n  Internal Abscess of the Ear,                               329\n  Ulceration of the Ear,                                     329\n  Inflammation of the Bowels,                                329\n  Inflammation of the Bladder,                               330\n  Asthma,                                                    331\n  Piles,                                                     331\n  Dropsy,                                                    332\n  Sore Throat,                                               332\n  Sore Ears,                                                 332\n  Sore Feet,                                                 333\n  Wounds,                                                    333\n  Sprains,                                                   333\n  Scalds,                                                    334\n  Ophthalmia,                                                334\n  Weak Eyes,                                                 335\n  Fleas and Vermin,                                          335\n  Hydrophobia,                                               335\n\n  MALIGNANT MILK SICKNESS of the Western States, or\n    Contagious Typhus,                                       339\n\n  BONE DISORDER IN COWS,                                     351\n\n\n\n\nINTRODUCTION.\n\n\nThere is no period in the history of the United States when our domestic\nanimals have ranked so high as at the present time; yet there is no\nsubject on which there is such a lamentable want of knowledge as the\nproper treatment of their diseases.\n\nGovernor Briggs, in a recent letter to the author, says, \"You have my\nthanks, and, in my opinion, are entitled to the thanks of the community,\nfor entering upon this important work. While the subject has engaged the\nattention of scientific men in other countries, it has been too long\nneglected in our own. Cruelty and ignorance have marked our treatment to\ndiseased animals. Ignorant himself both of the disease and the remedy,\nthe owner has been in the habit of administering the popular remedy of\nevery neighbor who had no better powers of knowing what should be done\nthan himself, until the poor animal, if the disease would not have\nproved fatal, is left alone, until death, with a friendly hand, puts a\nperiod to his sufferings: he is, however, often destroyed by the amount\nor destructive character of the remedies, or else by the cruel mode of\nadministering them. I am persuaded that the community will approve of\nyour exertions, and find it to their interest to support and sustain\nyour system.\"\n\nThe author has labored for several years to substitute a safer and a\nmore efficient system of medication in the treatment of diseased\nanimals, and at the same time to point out to the American people the\ngreat benefits they will derive from the diffusion of veterinary\neducation.\n\nThat many thousands of our most valuable cattle die under the treatment,\nwhich consists of little else than blood-letting, purging, and\nblistering, no one will deny; and these dangerous and destructive agents\nare frequently administered by men who are totally unacquainted with the\nnature of the agents they prescribe. But a better day is dawning;\nveterinary information is loudly called for--demanded; and the farmers\nwill have it; _but it must be a safer and a more efficient system than\nthat heretofore practised_.\n\nThe object of the veterinary art is not only congenial with human\nmedicine, but the very same paths that lead to a knowledge of the\ndiseases of man lead also to a knowledge of those of brutes.\n\nOur domestic animals deserve consideration at our hands. We have tried\nall manner of experiments on them for the benefit of science; and\nscience and scientific men should do something to repay the debt, by\nalleviating their sufferings and improving their condition. We are told\nthat physicians of all ages have applied themselves to the dissection of\nanimals, and that it was by analogy that those of Greece and Rome judged\nof the structure of the human body. For example, the Greeks and Arabians\nconfined themselves to the dissection of apes and other quadrupeds.\nGalen has given us the anatomy of the ape for that of man; and it is\nclear that his dissections were restricted to brutes, when he says, that\n\"if learned physicians have been guilty of gross errors, it is because\nthey neglected to dissect animals.\" We advocate the establishment of\nveterinary schools, and the cultivation of our reformed system of\nveterinary medicine, on the broad principles of humanity. These poor\nanimals are as susceptible to pain and suffering as we are. Has not the\nAlmighty given us dominion over them, and placed them under our\nprotection? Have we done our duty by them? Can we render a good account\nof our stewardship?\n\nIn almost every department of science the spirit of inquiry is abroad,\ninvestigation is active; yet, in this department, every thing is left to\nchance and ignorance. Men of all professions find it for their interest\nto protect property. The merchant, previous to sending his vessel on a\nvoyage to a distant port, seeks out a skilful navigator to pilot that\nvessel into her desired haven with safety. He protects his property. We\nprotect our property against the ravages of fire by insurance--we defend\nour houses from the lightning by conducting that fluid down the sides of\nthe building into the earth. And shall we not protect our animals? Is\nnot property invested in live stock as valuable, in proportion, as that\ninvested in real estate? Can we permit live stock to degenerate and die\nprematurely from a want of knowledge of the fundamental laws of their\nbeing? Can we look on and see their heart's blood drawn from them--their\nflesh setoned, burned, and blistered--simply because it was the\nmisguided custom of our ancestors?\n\nWe appeal to the American people at large. They have great encouragement\nto educate young men in this important branch of study; for the\nbeneficial results will be, that the diseases of all classes of domestic\nanimals will be better understood, and the great losses which this\ncountry sustains will, in a few years, be materially diminished. This is\nnot all. The value of live stock will be increased at least twenty-five\nper cent!\n\nLook for a moment at the amount of capital invested in live stock; and\nfrom these statistics the reader will perceive that not only the\nfarmers, but the whole nation, will be enriched. There are in the United\nStates at least 6,000,000 horses and mules; these, at the rate of $50\nper head, amount to $300,000,000. It is also estimated that there are\n20,000,000 of neat cattle; reckon these at $25 per head, and we get the\nsnug little sum of $500,000,000. We have also 20,000,000 sheep, worth\nthe same number of dollars. The number of swine have been computed at\n24,000,000; and these, at $3 per head, give us $72,000,000. Hence the\nreader will see that the capital invested in this class of live stock\nreaches the enormous sum of $892,000,000. Add the 25 per cent. just\nalluded to, and we get a clear gain of $223,000,000. This sum would be\nsufficient to build veterinary schools and colleges capable of affording\nample accommodations to every farmer's son in the Union. Hence we\nentreat the farming community to ponder on these subjects. They have\nonly to say the word, and schools for the dissemination of veterinary\ninformation shall spring up in every section of the Union.\n\nDoes the reader wish to know how the _farmers_ can accomplish this\nimportant object? We answer, there are four millions of men engaged in\nagricultural pursuits. Their number is three times greater than that of\nthose engaged in navigation, the learned professions, commerce, and\nmanufactures. Hence they have the numerical power to control the\ngovernment of these United States, and of course can plead their own\ncause in the halls of congress, and vote their own supplies for\neducational purposes.\n\nWhen the author first commenced a warfare against the lancet and other\ndestructive agents, his only hopes of success were based on the\ncooeperation of this mighty host of husbandmen; he well knew that there\nwere many prejudices to be overcome, and none greater than those\nexisting among his brethren of the same profession. The farmers have\njust begun to see the absurdity of bleeding an animal to death, with a\nview of saving life; or pouring down their throats powerful and\ndestructive agents, with a view of making one disease to cure another!\nIf the cattle doctors, then, will not reform, they must be reformed\nthrough the giant influence of popular opinion. Already the cry is, and\nit emanates from some of the most influential agriculturists in the\ncountry,--\"_No more blood-letting!_\" \"_Use your poisons on yourselves._\"\n\nTo the cattle-rearing interest, at the hands of many of whom the author\nhas received aid and encouragement, the following pages are dedicated;\nthey are intended to furnish them with practical information, with a\nview of preventing disease, increasing the value of their stock, and\nrestoring them to health when sick.\n\nIn reference to our reformed system of veterinary medication, it will be\nsufficient, in the present place, just to glance at the fundamental\nprinciples. In the succeeding pages these principles will be more fully\nexplained. We contemplate the animal system as a complicated piece of\nmechanism, subject to the uncompromising and immutable laws of nature,\nas they are written upon the face of animate nature by the finger of\nOmnipotence.\n\nAll our intentions of cure being in accordance with nature's laws,\n(viz., promoting the integrity of the living powers,) we have termed our\nsystem a _physiological_ one, though it is sometimes termed _botanic_,\nin allusion to the fact that most of our remedial agents are derived\nfrom the vegetable kingdom. We recognize a conservative or healing power\nin the animal economy, whose unerring indications we endeavor to follow;\nconsidering nature the physician, and the doctor her servant.\n\nOur system proposes, under all circumstances, to restore the diseased\norgans to a healthy state, by cooeperating with the vitality remaining in\nthose organs, by the exhibition of sanative means, and, under all\ncircumstances, to assist, and not oppose, nature in her curative\nprocesses. Poisonous substances, blood-letting, or processes of cure\nthat act pathologically, cannot be used by us. The laws of animal life\nare physiological: they never were, nor ever will be, pathological.\n\nThe agents we use are just as we find them in the forest and the field,\ncompounded by the Great Physician. Hence the reader will perceive that\nour aim is to depart from the popular debilitating and life-destroying\npractice, and approach as near as possible to the sanative.\n\nG. H. D.\n\n\n\n\nTHE\n\nAMERICAN\n\nREFORMED CATTLE DOCTOR.\n\n\n\n\nIMPORTANCE OF SUPPLYING CATTLE WITH PURE WATER.\n\n\nIn order to prevent many of the diseases to which cattle are liable, it\nis important that they be supplied with pure water. Cattle have often\nbeen known to turn away from the filthy fluid found in some troughs,\nwhich abound in slime and decayed vegetable matter; and, indeed, the\ncommon stagnated pond water is no better than the former. Such water\nhas, in former years, proved itself to be a serious cause of disease;\nand, at the present day, death is running riot among the stock of our\nwestern, and also our northern farmers, when, to our certain knowledge,\nthe cause exists, in some cases, under their very noses. The farmers\nofttimes see their best stock sicken and die without any apparent cause;\nand the cattle doctors are running rough-shod through the _materia\nmedica_, pouring down the throats of the poor brutes salts by the pound,\ncastor oil by the quart; aloes, lard, and a host of kindred trash,\nfollow in rapid succession, converting the stomach into a sort of\napothecary's shop; setons are inserted in the \"dewlap;\" the horns are\nbored, and sometimes sawed off; and, as a last resort, the animals are\nblistered and bled. They sometimes recover, in spite of the violence\ndone to the constitution; yet they drag out a low form of vitality,\nliving, it may be said, yet half dead, until some friendly epidemic\nputs a period to their sufferings.\n\nThe author's attention was first called to this subject on reading an\narticle in an English work, the substance of which is as follows: A\nnumber of working oxen were put into a pasture, in which was a pond,\nconsidered to abound in good water. Soon after putting them there, they\nwere attacked with scouring, upon which they were immediately removed to\nanother field. The scouring continued. They still, however, drank at the\nsame pond. They were shifted to another piece of very sweet pasture\nwithout arresting the disease. The farmer thought it evident that the\npastures were not the cause of the disease; and, contrary to the advice\nof his friends, who affirmed that the spring was always noticed for the\nexcellence of its water, fenced his pond round, so that the cattle could\nnot drink; they were then driven to a distance and watered. The scouring\ngradually disappeared. The farmer now proceeded to examine the suspected\npond; and, on stirring the water, he found it all alive with small\ncreatures. He now stirred into the water a quantity of lime, and soon\nafter an immense number of animalculae were seen dead on the surface. In\na short time, the cattle drank of this water without any injurious\nresults.\n\nThere is no doubt but that inferior kinds of water produce derangement\nof the digestive organs, and subsequently loss of flesh, debility, &c.\nWe have frequently made _post mortem_ examinations of animals that have\ndied from disease induced by debility, and have often found a large\nnumber of worms in the stomach and intestines, which, we firmly believe,\nhad their origin either primarily from the water itself, or subsequently\nfrom its effects on the digestive function.\n\nAll decayed animal and vegetable matter tends to corrupt water, and\nrender it unfit for the purposes of life. Now, if the farmer has the\nbest spring in the world, and the water shall flow from it, as it\nsometimes does, through whole fields of gutter or dike, abounding in\ndecayed filth, such water will be impregnated with agents that will more\nor less affect its purity.\n\n\n\n\nREMARKS ON FEEDING CATTLE.\n\n\nMany of the most complicated diseases of cattle originate from the food:\nfor example, it may be given in too large quantities--more than is\nneeded to build up and repair the waste that is constantly going on. The\nconsequence is, the animals get into a state of plethora, which is known\nby heaviness, dulness, unwillingness to move; there is a disposition to\nsleep, and they will lie down and often go to sleep in damp places. A\nchill of the extremities, or collapse of the capillaries, takes place,\nresulting in diseases of the lungs and pleura. At other times, if driven\na short distance, and made to walk fast, they are liable to disease of\nthe brain and other organs, which frequently terminates fatally.\n\nThe food may be of such a nature as shall be very difficult of\ndigestion, such as cornstalks, foxgrass, frosted turnips, &c. The clover\nand grasses may abound in woody fibre, in consequence of being cut too\nlate; they will then require more than the usual amount of gastric\nfluids to insalivate them, and more time to masticate, and, finally,\nextract their nutrimental properties. The stomach becomes overworked,\nproducing sympathetic diseases of the brain and nervous structures. The\nstomach not being able to act on fibrous matter with the same despatch\nas on softer materials, the former accumulates in its different\ncompartments, distends the viscera, interferes with the motion of the\ndiaphragm, presses on the liver, seriously interfering with the\nbile-secreting process. In order to prevent the grass and clover from\nbecoming tough and fibrous, it should be mowed early, and while in\nflower, and should be afterwards almost constantly attended to, if the\nweather is favorable; the more it is scattered about, the better will it\nbe made, and the more effectually will its fragrance and other good\nqualities be preserved.\n\nThe food may also be deficient in nutriment. The effects of insufficient\nfood are too well known to need much description: debility includes them\nall; it invades every function of the animal economy. And as life is\nthe sum of the powers that resist disease, if disease is only the\ninstrument of death, it follows, of course, that whatever enfeebles\nlife, or, in other words, produces debility, must predispose to disease.\n\nMany cattle, during the winter, live on bad hay, which does not appear\nto contain any of that saccharine and mucilaginous matter which is found\nin good hay. When the spring comes, they are turned out to grass, and\nthus regain their flesh. Many, however, die in consequence of the sudden\nchange.\n\nIt has been satisfactorily proved that fat cattle, of the best quality,\nmay be produced by feeding them on boiled food.\n\nDr. Whitlaw says, \"On one occasion, a number of cows were selected from\na large stock, for the express purpose of making the trial: they were\nsuch as appeared to be of the best kind, and those that gave the richest\nmilk. In order to ascertain what particular food would produce the best\nmilk, different species of grass and clover were tried separately, and\nthe quality and flavor of the butter were found to vary very much. But\nwhat was of the most importance, many of the grasses were found to be\ncoated with silecia, or decomposed sand, too hard and insoluble for the\nstomachs of cattle. In consequence of this, the grass was cut and well\nsteamed, and it was found to be readily digested; and the butter, that\nwas made from the milk, much firmer, better flavored, and would keep\nlonger without salt than any other kind. Another circumstance that\nattended the experiment was that, in all the various grasses and grain\nthat were intended by our Creator as food for man or beast, the various\noils that enter into their composition were so powerfully assimilated or\ncombined with the other properties of the farinaceous plants, that the\noil partook of the character of essential oil, and was not so easily\nevaporated as that of poisonous vegetables; and experience has proved\nthat the same quantity of grass, steamed and given to the cattle, will\nproduce more butter than when given in its dry state. This fact being\nestablished from numerous experiments, then there must be a great saving\nand superiority in this mode of feeding. The meat of such cattle is\nmore wholesome, tender, and better flavored than when fed in the\nordinary way.\" (For process of steaming, see Dadd's work on the Horse,\np. 67.)\n\nA mixed diet (boiled) is supposed to be the most economical for\nfattening cattle. \"A Scotchman, who fattens 150 head of Galloway cattle,\nannually, finds it most profitable to feed with bruised flaxseed, boiled\nwith meal or barley, oats or Indian corn, at the rate of one part\nflaxseed to three parts meal, by weight,--the cooked compound to be\nafterwards mixed with cut straw or hay. From four to twelve pounds of\nthe compound are given to each beast per day.\" The editor of the Albany\nCultivator adds, \"Would it not be well for some of our farmers, who\nstall-feed cattle, to try this or a similar mode? We are by no means\ncertain that the ordinary food (meaning, probably, bad hay and\ncornstalks) would pay the expense of cooking; but flaxseed is known to\nbe highly nutritious, and the cooking would not only facilitate its\ndigestion, but it would serve, by mixing, to render the other food\npalatable, and, by promoting the appetite and health of the animal,\nwould be likely to hasten its thrift.\"\n\nMr. Hutton, who has long been celebrated for producing exceedingly fat\ncattle at a small cost, estimates that cost as follows:--\n\n                                                              s. d.\n  \"13 lbs. of linseed, bruised, or 2 lbs. per day for six\n  days, and 1 lb. for Sunday,                                 1  9\n\n  32 lbs. of ground corn, or 5 lbs. per day for six days,\n  and 2-1\/2 lbs. for Sunday, at 1 d. per lb.,                 2  8\n\n  35 lbs. of turnips, given twice a day for six days,\n  and thrice on Sunday,                                       1  6\n\n  Oats, 1-1\/2 d.: labor on each beast, 6 d.,                     7-1\/2\n                                                             ---------\n  Total cost of each beast per week,                          6  6-1\/2\n\n\"The horses, cows, and young stock are also fed on this food, evidently\nwith great advantage.\"\n\nMr. Workington, a successful dairyman, combining cut feed and oil-cake\nwith different sorts of green food, found that, by giving a middle-sized\ncow sixteen pounds of green food and two of boiled hay, with two pounds\nof ground oil cake, (_linseed would be preferable_,) and eight pounds of\ncut straw, the daily expense of her keep was only 5-1\/2 d., (about ten\ncents.) The oil-cake he found to be much more productive of milk when\ngiven with steamed food, than when employed without it. Varying their\nfood from time to time is found to be of much more advantage to the cow;\nand this may probably arise from the additional relish with which the\nanimal eats, or from the superior excitement of a new stimulus on the\ndifferent secretions.\n\nThe following table represents the nutritive properties in each article\nof food:--\n\n  ------------+--------+----------+--------+--------+--------+--------\n              |        | Husk, or |Starch, |Gluten, |        |\n              |        | woody    |gum, and|albumen,| Fatty  |Saline\n              | Water. | fibre.   | sugar. | &c.    | matter |matter\n  ------------+--------+----------+--------+--------+--------+--------\n  Oats,       |   16   |    20    |  45    |  11    |    6   |  2.5\n  Beans,      |   14   |  8 to 11 |  40    |  26    |    2.5 |  3\n  Pease,      |   14   |     9    |  50    |  24    |    2.1 |  3\n  Indian corn,|   14   |     6    |  70    |  12    | 5 to 9 |  1.5\n  Barley,     |   15   |    14    |  52    |  13.5  | 2 to 3 |  3\n  Meadow hay, |   14   |    30    |  40    |   7.1  | 2 to 5 |5 to 10\n  Clover hay, |   14   |    25    |  40    |   9.3  | 3 to 5 |  9\n  Pea straw,  |10 to 15|    25    |  45    |  12.3  |    1.5 |4 to 5\n  Oat straw,  |   12   |    45    |  35    |   1.3  |    0.8 |  6\n  Carrots,    |   85   |     3    |  10    |   1.5  |    0.4 |1 to 2\n  Linseed,    |    9.2 |  8 to 9  |  35.3  |  20.3  |   20.0 |  6.3\n  Bran,       |   13.1 |    53.6  |   2    |  19.3  |    4.7 |  7.3\n  ------------+--------+----------+--------+--------+--------+--------\n\nThe most nutritious grasses are those which abound in sugar, starch, and\ngluten. Sugar is an essential element in the formation of good milk;\nhence the sweet-scented grasses are the most profitable to cultivate and\nfeed to milch cows. At the same time, the farmer, if he does not, ought\nto know that large quantities of saccharine matter are extracted from\nclover and sweet grasses by the bees. Mr. White tells us that, \"on a\nfarm situated a few miles from London, the eldest son of the occupier\nhad the management and profit of the bees given him, which induced him\nto increase the number of stocks beyond what had ever been kept on the\nfarm before. It so happened that the sheep did not thrive so well as in\nformer years, and on the farmer complaining at the cause to his man, as\nthey had plenty of keep, the man replied, '_You will never have fat\nsheep so long as you suffer my young master to keep so many stocks of\nbees; they suck all the honey from the flowers, so that the clover is\nnot half so nourishing, and does not produce half such good milk._'\" Had\nthis man been acquainted with agricultural and animal chemistry, he\nwould have had a clear conception of the seeming absurdity. All our\nlabor or efforts to improve stock or crops will be fruitless, unless\nguided by chemical science. We must have sugar, starch, gluten, and\nother materials, to perfect animal organization. The animal may be in\ngood health, the different functions free and unobstructed, and possess\nthe power of reproducing the species; yet, if fed on substances which\nlack the materials necessary to the composition of bones, blood-vessels,\nand nerves, sooner or later its health becomes impaired. Reader, if you\nown cattle, and wish to preserve their health, give them boiled food\noccasionally; let them have their meals at regular hours, in sufficient\nquantity, and no more, unless they are intended for the butcher; then,\nan extra allowance may be given, with a view of fattening. They should\nbe well littered, and the barns well ventilated; finally, keep them\nclean, avoid undue exposure, and govern them in a spirit of kindness and\nmercy.\n\n\n\n\nTHE BARN AND FEEDING BYRE.\n\n\nIt is well known that the more cleanly and comfortable cattle are kept,\nand the better the order in which their food is presented to them, the\nbetter they will thrive, and the more profitable they will be to the\nowner. Dr. Gunthier remarks, that \"constant confinement to the barn is\nopposed to the nature of oxen, and becomes the source of numberless\ndiseases. Endeavors are made to promote the lacteal secretion in cows,\nand the fattening of oxen, by means of heat: for this purpose, stables\n[barns] are converted into real stoves, either by not making them\nsufficiently large, or by crowding them to excess, or by preventing the\naccess of air from without; and all this without recollecting that the\nskin, thus over-excited, must necessarily fall into a state of atony in\na short time. Besides, the moist heat and the emanations of the dung\ncannot fail to exercise a destructive influence on the lungs and entire\nsystem. To these causes if we add the absolute want of exercise and the\nexcess of food, we shall not be surprised at the number of diseases\nresulting from these different practices, and at the extraordinary forms\nwhich they ofttimes assume.\n\n\"Persons propose to themselves, by feeding in the barn, to augment the\nmass of dung; and the beasts are left in their excrement, sometimes up\nto the very knees. Seldom is there any care taken to cleanse their skin,\nand still less attention is directed to the feet. What wonder, then, if\nthey exhibit so many forms of disease?\"\n\nThe byre recommended by Mr. Lawson consists of two apartments--an inner\napartment, or byre for feeding the cattle, and an outer apartment, or\nbarn for containing the fodder. The byre is constructed at right angles\nwith the barn, as follows: \"At the distance of about three feet and a\nhalf from the side of the building, within, there are constructed, on\nthe ground, in a straight line, a trough, having ten partitions for\nfeeding ten animals. The troughs are so constructed, that there is a\nsmall and gradual declivity from the first or innermost to the last or\noutermost one; and the partitions separating them being made with a\nsmall arch at the bottom, a bucket of water, poured in at the uppermost,\nruns out at the last one through a spout in the wall; and a sweep of the\nbroom carries off the whole remains of the food, rendering all the\ntroughs quite clean and sweet. The whole food of the cattle is thus kept\nperfectly clean at all times.\n\n\"In a line with the feeding troughs, and immediately over them, runs a\nstrong beam of wood, from one end of the byre to the other; which is\nstrengthened by two strong upright supporters to the roof, placed at\nequal distances from the ends of the byre; and the main beam is again\nsubdivided by the cattle stakes and chains, so as to keep each of the\nten oxen opposite to his own feeding trough and stall.\n\n\"The three and a half feet of space between the troughs and outer wall,\nlighted by a glazed window, is the cattle feeder's walk, who passes\nalong it in front of the cattle, and, with a basket, deposits before\neach of the cattle the food into the feeding trough of each. To prevent\nany of the cattle from choking on small pieces of turnips, &c., as they\nare very apt to do, the chains at the stakes are contrived of such a\nlength, that no ox can raise his head too high when eating; for in this\nway, it is observed, cattle are generally choked.\n\n\"At the distance of about six feet eight inches from the feeding\ntroughs, and parallel to them, is a dung grove and urine gutter. Here\ntoo, like the trough, there is a gradual declivity; so that the moment\nthe urine passes from the cattle, it runs to the lowest end of the\ngutter, whence it is conveyed through the outer wall, in a spout, and\ndeposited in the urinarium outside of the building. At this place is a\nlarge enclosed space, occupied as a compost dung-court. Here all sorts\nof stuff are collected for increasing the manure, such as fat, earth,\ncleanings of roads, ditches, ponds, rotten vegetables, &c.; and the\nurine from the byre, being caused to run over all these collected\ntogether, which is done very easily by a couple of wooden spouts, moved\nbackwards and forwards to the urinarium at pleasure, renders the whole\nmass, in a short time, a rich compost dunghill; and this is done by the\nurine alone, which, in general, is totally lost. The dung of the byre,\nagain, is cleared several times each day, and deposited in the\ndung-court. Along the edge of the dung-court a few low sheds are\nconstructed, in which swine are kept, and these consume the refuse of\nthe food.\n\n\"In the side wall of the byre, and opposite to the heads of the cattle,\nare constructed three ventilators; these are placed at the distance of\nabout two feet four inches from the ground, in the inside of the byre,\nand pass out just under the roof. The inside openings of these are about\nthirteen inches in length, seven in breadth, and nine in depth; and they\nserve two good purposes. The breath of cattle being superficially\nlighter than atmospheric air, the consequence is, that in some byres the\ncattle are kept in a constant heat and sweat, because their breath and\nheat have no way to escape; whereas, by means of the ventilators, the\nair of the barn is kept in proper circulation, which conduces as much to\nthe health of the cattle as to the preservation of the walls and timber\nof the byre, by drying up the moisture produced from the breath and\nsweat of the cattle, which is found to injure those parts of the\nbuilding.\"\n\n\n\n\nMILKING.\n\n\nThe operation of milking should, if possible, always be performed by the\nsame person, and in the most gentle manner; the violent tugging at the\nteats by an inexperienced hand is apt to make the animal irritable and\nuneasy during the operation, and unwilling to be milked. Many of the\ndiseases of the teats and udder can be traced to violence done to the\nparts under the operation of milking. Young animals are often unwilling\nto be milked: here a little patience and kindness will perform wonders.\n\nIt is not the quantity of milk that gives value to the dairy cow; for\nthe milk of one good cow will make more butter than that of two poor\nones, each giving the same quantity of milk. Its most abundant\nprinciples are cream, caseous matter or curd, and whey. In these are\nalso contained a saccharine matter, (sugar of milk,) muriate and\nphosphate of potassa, phosphate of lime, acetic acid, acetate of\npotassa, and a trace of acetate of iron. The three principal\nconstituents (cream, curd, and whey) can easily be separated: thus the\ncream rises to the surface, and the curd and whey will separate if the\nmilk becomes sour, or a little rennet is poured into it. When milk is\nintended to be made into cheese, no part of the cream should be\nseparated. Good cheese is, consequently, rarely produced in those\ndairies where much butter is made; the former being robbed for the sake\nof the latter.\n\nSir J. Sinclair says, \"If a few spoonfuls of milk are left in the udder\nof the cow at milking; if any of the implements used in the dairy are\nallowed to be tainted by neglect; if the dairy-house be kept dirty, or\nout of order; if the milk is either too hot or too cold at coagulation;\nif too much or too little rennet is put into the milk; if the whey is\nnot speedily taken off; if too much or too little salt is applied; if\nbutter is too slowly or too hastily churned; or if other minute\nattentions are neglected, the milk will be in a great measure lost. If\nthese nice operations occurred once a month, or once a week, they might\nbe easily guarded against; but as they require to be observed during\nevery stage of the process, and almost every hour of the day, the most\nvigilant attention must be kept up during the whole season.\"\n\n\n\n\nA KNOWLEDGE OF AGRICULTURAL AND ANIMAL CHEMISTRY IMPORTANT TO FARMERS.\n\n\nIt is a well-known fact that plants require for their germination and\ngrowth different constituents of soil, and that animals require\ndifferent forms of food to build up the waste, and promote the living\nintegrity--the vital powers.\n\nIts order to supply the materials necessary for animal and vegetable\nnutrition, we require alternate changes--the former in the diet, and the\nlatter in the soil. Experience has proved that the cultivation of a\nplant for several successive years on the same soil impoverishes it, or\nthe plant degenerates. On the contrary, if a piece of land be suffered\nto lie uncultivated for a short time, it will yield, in spite of the\nloss of time, a greater quantity of grain; for, during the interval of\nrest, the soil regains its original equilibrium. It has been\nsatisfactorily demonstrated that a fruit-tree cannot be made to grow and\nbring forth good fruit on the same spot where another of the same\nspecies has stood; at least not until a lapse of years. This is a fact\nworth knowing, for it applies more or less to all forms of vegetation.\nAnother fact of experience is, that some plants thrive on the same soil\nonly after a lapse of years, while others may be cultivated in close\nsuccession, _provided the soil is kept in equilibrium by artificial\nmeans_; these are subsoiling, &c. Some kinds of plants improve the sod,\nwhile others impoverish or exhaust it. Professor Liebig tells us,\n\"turnips, cabbages, beets, oats, and rye are considered to belong to the\nclass which impoverish the soil; while by wheat, hops, madder, hemp, and\npoppies, it is supposed to be entirely exhausted.\" Many of our farmers\nexpend large sums of money in the purchase of manure, with a view of\nimproving the soil; and they suppose that their crops will be abundant\nin proportion to the amount of manure; yet many have discovered that, in\nspite of the extra expense and labor, the produce of their farms\ndecreased.\n\nThe alternation of crops seems destined to effect a great change in\nagriculture. A French chemist informs us that the roots of plants imbibe\nmatter of every kind from the soil, and thus necessarily abstract a\nnumber of substances, which are not adapted to the purposes of\nnutrition, and that they are ultimately expelled by the excretory\nvessels, and return to the soil as excrement. The excrementitious\nportion of the food also returns to the soil. Now, as excrement cannot\nbe assimilated by the same animal or plant that ejected it, without\ndanger to the organs of digestion or eliminations, it follows that the\nmore vegetable excrement the soil contains, the more unfitted must it be\nfor plants of the same species; yet these excrementitious matters may,\nhowever, still be capable of assimilation by another kind of plant,\nwhich would absorb them from the soil, and render it again fertile for\nthe first. In connection with this, it has been observed that several\nplants will flourish when growing beside each other; but it is not good\npolicy to sow two kinds of seed together: on the other hand, some plants\nmutually prevent each other's development. The same happens if young\ncattle are suffered to graze and sleep in the barn together; the one\nlives at the expense of the other, which soon shows evidences of\ndisease. The injurious effects of permitting young children to sleep\nwith aged relatives are known to many of our readers; yet some parents\nsee their children sicken and die without knowing the why or wherefore.\nFrom such facts as these,--which we might multiply to an indefinite\nextent, were it necessary,--we learn that nature's laws are immutable\nand uncompromising; and woe be to the man that transgresses them: they\nare a part of the divine law, which cannot be set at nought with\nimpunity.\n\nIgnorance on these important subjects has existed too long: yet we\nperceive in the distant horizon a ray of intellectual light, streaming\nthrough our schools and agricultural societies. The result will be, that\nsucceeding generations will be better acquainted with nature's laws,\nfrom which shall flow untold blessings. Chemistry teaches us that\nanimals and vegetables are composed of a vast number of different\ncompounds, which are nearly all produced by the same elementary\nprinciples. Vegetables consist of carbon, hydrogen, and oxygen; and the\nsame substances, with the addition of nitrogen, are the principal\nconstituents of the animal economy. In a word, all the constituents of\nanimal creation have actually been discovered in vegetables: this has,\nwe presume, led to the conclusion that \"all flesh is grass.\"\n\nMany horticulturists complain that certain fruits and seeds have \"_run\nout_,\" or degenerated. Has the stately oak, the elm, or the cedar\ndegenerated? No. Each has preserved its identity, and will continue so\nto do, at least just as the Divine Artist intended they should, unless\nman, by his fancied improvements, interferes; and here, reader, permit\nus to ask if you ever knew a piece of nature's mechanism improved by\nhuman agency. Can we make a light better adapted to the wants of\nanimate and inanimate creation than that which the sun, moon, and stars\nafford? Whenever we attempt to improve on immutable laws, as they are\nwritten on the face of creation, that moment we prevent the full and\nfree play of these laws. Hence the practice of grafting scions of\ndelicious fruit-trees on stock of an inferior order compromises its\nidentity; and successive crops will show unmistakable evidences of\nencroachment. A son of the lamented Mr. Phinney tells us that he had\nsome very fine sows, that he was desirous of breeding from, with a view\nof making \"improvements.\" He bred in a close degree of relationship: in\na short time, to use his own expression, \"their sides appeared like two\nboards nailed together.\" Does the farmer wish to know how to prevent\nseeds and fruit \"running out\"? Let him study chemistry. Chemistry\nfurnishes the information; it also teaches the husbandman the fact, that\nto put a plant, composed of certain essential elements, on a soil\ndestitute of those elements,--or to graft a scion, requiring a certain\namount of sap or juice, on a stock destitute of such sap or juice,\nexpecting that they will germinate, grow to perfection, and preserve\ntheir identity,--would be just as absurd as to expect that a dry sow\nwould nourish a sucking pig.\n\nAgriculture being based on the equilibrium of the soils, a knowledge of\nchemistry is indispensable to every one who is desirous of keeping pace\nwith the reforms of the age; for it is through the medium of that\nscience alone that we are enabled to ascertain with certainty how this\nequilibrium is disturbed by the growth of vegetation. Then is it not a\nmatter of deep interest to the farmer to know how this equilibrium is\nrestored?\n\nDoes the farmer wish to know what kind of soil is necessary to nourish\nand mature a plant? Chemistry solves the problem. Does the farmer wish\nto know how to improve the soil? Let him refer to chemistry. Chemistry\nwill teach the farmer how to analyze the soil; by that means he will\nlearn which of the constituent elements of the plants and soil are\nconstant, and which are changeable. By making an analysis of the soil\nat different periods, through the process of germination, growth, and\nmaturity, we are enabled to ascertain the amount of excretory elements\ngiven out. Bergman tells us that he found, by analysis, in \"100 parts of\nfertile soil, coarse silex 30 parts, silecia 30 parts, carbonate of lime\n30 parts:\" hence the fertility of the soil diminishes in proportion as\none or the other of these elements predominates.\n\nAshes of wheat contain, among other elementary substances, 48 parts of\nsilecia. Now, what farmer could expect to raise a good crop of wheat\nfrom a soil destitute of silecious earth, since this earth constitutes a\nlarge amount of the earthy part of wheat? There is no barrier to\nagricultural improvement so effectual as for farmers to continue their\nold customs purely because their forefathers did so. But prejudices are\nfast dying away before the rays of intellectual illumination; the\nfarmers are fast seceding from the supposed infallibles of their\nforefathers, and will soon become \"book\" as well as practical\nhusbandmen. \"Book farming,\" assisted by practical knowledge, teaches\nthat manures require admixture of milder materials to mitigate their\nforce; for some of them communicate a disgusting or offensive quality to\nvegetables. They are charged with imparting a biting and acrimonious\ntaste to radishes and turnips. Potatoes and grapes are known to borrow\nthe foul taint of the ground. Millers observe a strong, disagreeable\nodor in the meal of wheat that grew upon land highly charged with the\nrotten recrements of cities. Stable dung is known to impart a\ndisagreeable flavor to vegetables.\n\nThe same effects may be illustrated in the animal kingdom. Ducks are\nrendered so ill tasted from stuffing down garbage as sometimes to be\noffensive to the palate when cooked. The quality of pork is known by the\nfood of the swine, and the peculiar flavor of water-fowl is rationally\ntraced to the fish they devour. Thus a portion of the elements of manure\nand nutrimental matter passes into the living bodies without being\nentirely subdued. For example, we can alter the color of the cow's milk\nby mixing madder or saffron in the food; the odor may be influenced by\ngarlic; the flavor may be altered by pine and wormwood; and lastly, the\nmedicinal effect may be influenced.\n\nIn the cultivation of grass the farmer will find it to his advantage to\ncultivate none but the best kinds; the whole pasture lands will then be\nfilled with valuable grass seeds. The number of grass seeds worth\ncultivating is but few, and these should be sown separately. It is bad\npolicy to sow different kinds of grass seed together--just as bad as to\nsow wheat, oats, turnips, and corn promiscuously.\n\nThe reason why the farmers, as a community, will be benefited by sowing\nnone but the best seed is, because grass seeds are distributed through\nneighboring pastures by the winds, and there take root. Now, if the\nneighboring pastures abound in inferior grasses, the fields will soon be\nfilled with useless plants, which are very difficult to be got rid of.\nWe refer those of our readers who desire to make themselves acquainted\nwith animal chemistry to Professor Liebig's work on that science.\n\n\n\n\nON BREEDING.\n\n\nLarge sums of money have, from time to time, been expended with a view\nof improving stock, and many superior cattle have been introduced into\nthis country; yet, after a few generations, the beautiful form and\nsuperior qualities of the originals are nearly lost, and the importer\nfinds to his cost that the produce is no better than that of his\nneighbors. What are the causes of this deterioration? We are told--and\nexperience confirms the fact--that \"like produces like.\" Good qualities\nand perfect organization are perpetuated by a union of animals\npossessing those properties: of course it follows, that malformation,\nhereditary taints, and vices are transmitted and aggravated.\n\nThe destructive practice of breeding \"in and in,\" or, in other words,\nselecting animals of the same family, is one of the first causes of\ndegeneracy; and this destructive practice has proved equally unfortunate\nin the human family. Physical defects are the result of the\nintermarriage of near relatives. In Spain, the deformed and feeble state\nof the aristocracy arises from their alliances being confined to the\nsame class of relatives through successive generations. But we need not\ngo to Spain to verify such facts. Go into our churchyards, and read on\nthe tombstones the names of thousands of infants,--gems withered in the\nbud,--young men, and maidens, cut down and consigned to a premature\ngrave; and then prove, if you can, that early marriages and near\nalliances are not the chief causes of this great mortality.\n\nMr. Colman, in an article on live stock, says, \"There seems to be a\nlimit beyond which no person can go. The particular breed may be altered\nand improved, but an entirely new breed cannot be produced; and in every\ndeparture from the original there is a constant tendency to revert back\nto it. The stock of the improved Durham cattle seems to establish this\nfact. If we have the true history of it, it is a cross of a Teeswater\nbull with a Galloway cow. The Teeswater or Yorkshire stock are a large,\ncoarse-boned animal: the object of this cross was to get a smaller bone\nand greater compactness. By attempting to carry this improvement, if I\nmay so call it, still further by breeding continually in and in, that\nis, with members of the same family, in a close degree of affinity, the\npower of continuing the species seems to become extinct; at least it\napproximates to such a result. On the other hand, by wholly neglecting\nall selection, and without an occasional good cross with an animal of\nsome foreign blood, there appears a tendency to revert back to the\nlarge-boned, long-legged animal, from which the _improvement_ began.\n\n\"There are, however, several instances of superior animals bred in the\nclosest affinity; whilst, in a very great majority of cases, the failure\nhas been excessive.\"\n\nOvertaxing the generative powers of the male is another cause of\ndeterioration. The reader is probably aware of the woful results\nattending too frequent sexual intercourse. If he has not given this\nsubject the attention it demands, then let him read the records of our\nlunatic asylums: they tell a sad tale of woe, and prove to demonstration\nthat, before the blast of this dire tornado, _sexual excess_, lofty\nminds, the suns and stars of our intellectual world, are suddenly\nblotted out. It spares neither age, sex, profession, nor kind. Dr. White\nrelates a case which substantiates the truth of our position. \"The\nPrince of Wales, who afterwards became George the Fourth, had a stud\nhorse of very superior qualities. His highness caused a few of his own\nmares to be bred to this stallion, and the produce proved every way\nworthy of the sire. This horse was kept at Windsor for public covering\nwithout charge, except the customary groom's fee of half a guinea. The\ngroom, anxious to pocket as many half guineas as possible, persuaded all\nhe could to avail themselves of the prince's liberality. The result was,\nthat, being kept in a stable without sufficient exercise, and covering\nnearly one hundred mares yearly, the stock, although tolerably promising\nin their early age, shot up into lank, weakly, awkward, good-for-nothing\ncreatures, to the entire ruin of the horse's character and sire. Some\ngentlemen, aware of the cause, took pains to explain it, proving the\ncorrectness of their statement by reference to the first of the horses\ngot, which were among the best horses in England.\"\n\nThere is no doubt but that brutes are often endowed with extraordinary\npowers for sexual indulgence; yet, when kept for the purpose alluded to,\nwithout sufficient muscular exercise,--breathing impure air, and living\non the fat of the farm,--his services in constant requisition,--then it\nis no wonder, that if, under these circumstances, the offspring are weak\nand inefficient.\n\nProfessor Youatt recommends that \"valuable qualities once established,\nwhich it is desirable to keep up, should thereafter be preserved by\noccasional crosses with the best animals to be had of the same breed,\nbut of a different family. This is the great secret which has maintained\nthe blood horse in his great superiority.\"\n\nThe live stock of our farmers frequently degenerates in a very short\nspace of time. The why and the wherefore is not generally understood;\nneither will it be, until animal physiology shall be better understood\nthan it is at the present time. Men are daily violating the laws of\nanimal organization in more ways than one, in the breeding, rearing, and\ngeneral management of all kinds of domestic animals,--until the\ndifferent breeds are so amalgamated, that, in many cases, it is a\ndifficult task to ascertain, with any degree of certainty, their\npedigree. If a farmer has in his possession a bull of a favorite breed,\nthe neighboring stock-raisers avail themselves of his bullship's\nservices by sending as many cows to him as possible: the consequence is,\nthat the offspring got in the latter part of the season are good for\nnothing. The cow also, at the time of impregnation, may be in a state of\ndebility, owing to some derangement in the organs of digestion; if so,\nimpregnation is very likely to make the matter worse; for great sympathy\nexists between the organs of generation and those of digestion, and\nfemales of every order suffer more or less from a disturbed state of the\nstomach during the early months of pregnancy. In fact, during the whole\nstage they should be considered far from a state of health. Add to this\nthe fact that impregnated cows are milked, (not generally, yet we know\nof such cases:) the foetus is thus deprived of its due share of\nnourishment, and the extra nutrimental agents, necessary for its growth\nand development, must be furnished at the expense of the mother. She, in\nher turn, soon shows unmistakable evidences of this \"robbing Peter to\npay Paul\" system, by her sunken eye, loss of flesh, &c., and often,\nbefore she has seen her sixth month of pregnancy, liberates the foetus\nby a premature birth--in short, pays the penalty of disobedience to the\nimmutable law of nature. On the other hand, should such a cow go safely\nthrough the whole period of gestation and parturition, the offspring\nwill not be worth keeping, and the milk of the former will lack, in some\nmeasure, those constituents which go to make good milk, and without\nwhich it is almost worthless for making butter or cheese. A cow should\nnever be bred from unless she shall be in good health and flesh. If she\ncannot be fatted, then she may be spayed. (See article _Spaying Cows_.)\nBy that means, her health will improve, and she will be made a permanent\nmilker. Degeneracy may arise from physical defects on the part of the\nbull. It is well known that infirmities, faults, and defects are\ncommunicated by the sexual congress to the parties as well as their\noffspring. Hence a bull should never be bred to unless he possesses the\nrequisite qualifications of soundness, form, size, and color. There are\na great number of good-for-nothing bulls about the country, whose\nservices can be had for a trifle; under these circumstances, and when\nthey can be procured without the trouble of sending the cow even a short\ndistance, it will be difficult to effect a change.\n\nIf the farming community desire to put a stop to this growing evil, let\nthem instruct their representatives to advocate the enactment of a law\nprohibiting the breeding to bulls or stallions unless they shall possess\nthe necessary qualifications.\n\n[Illustration: A First Prize Short Horned Bull]\n\n\nTHE BULL.\n\nMr. Lawson gives us the following description of a good bull. It would\nbe difficult to find one corresponding in all its details to this\ndescription; yet it will give the reader an idea of what a good bull\nought to be. \"The head of the bull should be rather long, and muzzle\nfine; his eyes lively and prominent; his ears long and thin; his horns\nwhite; his neck rising with a gentle curve from the shoulders, and small\nand fine where it joins the head; his shoulders moderately broad at the\ntop, joining full to his chine and chest backwards, and to the neck-vein\nforwards; his bosom open; breast broad, and projecting well before his\nlegs; his arms or fore thighs muscular, and tapering to his knees; his\nlegs straight, clean, and very fine boned; his chine and chest so full\nas to leave no hollows behind the shoulders; the plates strong, to keep\nhis belly from sinking below the level of his breast; his back or loin\nbroad, straight, and flat; his ribs rising one above another, in such\na manner that the last rib shall be rather the highest, leaving only a\nsmall space to the hips, the whole forming a round or barrel-like\ncarcass; his hips should be wide placed, round or globular, and a little\nhigher than the back; the quarters (from the hips to the rump) long,\nand, instead of being square, as recommended by some, they should taper\ngradually from the hips backwards; rump close to the tail; the tail\nbroad, well haired, and set on so as to be in the same horizontal line\nwith his back.\"\n\n\nVALUE OF DIFFERENT BREEDS OF COWS.\n\nMr. Culley, in speaking of the relative value of long and short horns,\nsays, \"The long-horns excel in the thickness and firm texture of the\nhide, in the length and closeness of the hair, in their beef being finer\ngrained and more mixed and marbled than that of the short-horns, in\nweighing more in proportion to their size, and in giving richer milk;\nbut they are inferior to the short-horns in giving a less quantity of\nmilk, in weighing less upon the whole, in affording less fat when\nkilled, in being generally slower feeders, in being coarser made, and\nmore leathery or bullish in the under side of the neck. In a few words,\nthe long-horns excel in hide, hair, and quality of beef; the short-horns\nin the quantity of beef, fat, and milk. Each breed has long had, and\nprobably may have, their particular advocates; but if I may hazard a\nconjecture, is it not probable that both kinds may have their particular\nadvantages in different situations? Why not the thick, firm hides, and\nlong, closer set hair, of the one kind be a protection and security\nagainst tempestuous winds and heavy fogs and rains, while a regular\nseason and mild climate are more suitable to the constitutions of the\nshort-horns? But it has hitherto been the misfortune of the short-horned\nbreeders to seek the largest and biggest boned ones for the best,\nwithout considering that those are the best that bring the most money\nfor a given quantity of food. However, the ideas of our short-horned\nbreeders being now more enlarged, and their minds more open to\nconviction, we may hope in a few years to see great improvements made\nin that breed of cattle.\n\n\"I would recommend to breeders of cattle to find out which breed is the\nmost profitable, and which are best adapted to the different situations,\nand endeavor to improve that breed to the utmost, rather than try to\nunite the particular qualities of two or more distinct breeds by\ncrossing, which is a precarious practice, for we generally find the\nproduce inherit the coarseness of both breeds, and rarely attain the\ngood properties which the pure distinct breeds individually possess.\n\n\"Short-horned cows yield much milk; the long-horned give less, but the\ncream is more abundant and richer. The same quantity of milk also yields\na greater proportion of cheese. The Polled or Galloway cows are\nexcellent milkers, and their milk is rich. The Suffolk duns are much\nesteemed for the abundance of their milk, and the excellence of the\nbutter it produces. Ayrshire or Kyloe cows are much esteemed in\nScotland; and in England the improved breed of the long-horned cattle is\nhighly prized in many dairy districts. Every judicious selector,\nhowever, will always, in making his choice, keep in view not only the\ndifferent sons and individuals of the animal, but also the nature of the\nfarm on which the cows are to be put, and the sort of manufactured\nproduce he is anxious to bring to market. The best age for a milch cow\nis betwixt four, or five, and ten. When old, she will give more milk;\nbut it is of an inferior quality, and she is less easily supported.\"\n\n\n\n\nMETHOD OF PREPARING RENNET, AS PRACTISED IN ENGLAND.\n\n\nTake the calf's maw, or stomach, and having taken out the curd contained\ntherein, wash it clean, and salt it thoroughly, inside and out, leaving\na white coat of salt over every part of it. Put it into an earthen jar,\nor other vessel, and let it stand three or four days; in which time it\nwill have formed the salt and its own natural juice into a pickle. Take\nit out of the jar, and hang it up for two or three days, to let the\npickle drain from it; resalt it; place it again in the jar; cover it\ntight down with a paper, pierced with a large pin; and let it remain\nthus till it is wanted for use. In this state it ought to be kept twelve\nmonths; it may, however, in case of necessity, be used a few days after\nit has received the second salting; but it will not be as strong as if\nkept a longer time. To prepare the rennet for use, take a handful of the\nleaves of the sweet-brier, the same quantity of rose and bramble leaves;\nboil them in a gallon of water, with three or four handfuls of salt,\nabout a quarter of an hour; strain off the liquor, and, having let it\nstand until perfectly cool, put it into an earthen vessel, and add to it\nthe maw prepared as above. To this add a sound, good lemon, stuck round\nwith about a quarter of an ounce of cloves, which give the rennet an\nagreeable flavor. The longer the bag remains in the liquor, the\nstronger, of course, will be the rennet. The amount, therefore,\nrequisite to turn a given quantity of milk, can only be ascertained by\ndaily use and observation. A sort of average may be something less than\na half pint of good rennet to fifty gallons of milk. In Gloucestershire,\nthey employ one third of a pint to coagulate the above quantity.\n\n\n\n\nMAKING CHEESE.\n\n\nIT is generally admitted that many dairy farmers pay more attention to\nthe quantity than the quality of this article of food; now, as cheese is\n\"a surly elf, digesting every thing but itself,\" (this of course applies\nto some of the white oak specimens, which, like the Jew's razors, were\nmade to sell,) it is surely a matter of great importance that they\nshould attend more to the quality, especially if it be intended for\nexportation. There is no doubt but the home consumption of good cheese\nwould soon materially increase, for many thousands of our citizens\nrefuse to eat of the miserable stuff \"misnamed cheese.\"\n\nThe English have long been celebrated for the superior quality of their\ncheese; and we have thought that we cannot do a better service to our\ndairy farmers than to give, in as few words as possible, the various\nmethods of making the different kinds of cheese, for which we are\nindebted to Mr. Lawson's work on cattle.\n\n\"It is to be observed, in general, that cheese varies in quality,\naccording as it has been made of milk of one meal, or two meals, or of\nskimmed milk; and that the season of the year, the method of milking,\nthe preparation of the rennet, the mode of coagulation, the breaking and\ngathering of the curd, the management of the cheese in the press, the\nmethod of salting, and the management of the cheese-room, are all\nobjects of the highest importance to the cheese manufacturer; and yet,\nnotwithstanding this, the practice, in most of these respects, is still\nregulated by little else than mere chance or custom, without the\ndirection of enlightened observation or the aid of well-conducted\nexperiment.\n\n\nGLOUCESTER CHEESE.\n\n\"In Gloucestershire, where the manufacture of cheese is perhaps as well\nunderstood as in any part of the world, they make the best cheeses of a\nsingle meal of milk; and, when this is done in the best manner, the\nentire meal of milk is used, without any addition from a former meal.\nBut it not unfrequently happens that a portion of the milk is reserved\nand set by to be skimmed for butter; and at the next milking this\nproportion is added to the new milk, from which an equal quantity has\nbeen taken for a similar purpose. One meal cheeses are principally made\nhere, and go by the name of _best making_, or simply _one meal cheeses_.\nThe cheeses are distinguished into _thin_ and _thick_, or _single_ and\n_double_; the last having usually four to the hundred weight, (112\npounds,) the other about twice that number. The best double Gloucester\nis always made from new milk.\n\n\"The true single Gloucester cheese is thought by many to be the best, in\npoint of flavor, of any we have. The season for making their thin or\nsingle cheese is mostly from April to November; but the principal season\nfor the thick or double is confined to May, June, and the early part of\nJuly. This is a busy season in the dairy; for at an earlier period the\nmilk is not rich enough, and if the cheese be made later in the summer,\nthey do not acquire sufficient age to be marketable next spring. Very\nmany cheeses, however, can be made even in winter from cows that are\nwell fed. The cows are milked in summer at a very early hour; generally\nby four o'clock in the morning, before the day becomes hot, and the\nanimals restless and unruly.\n\n\nCHESTER CHEESE.\n\n\"After the milk has been strained, to free it from any impurities, it is\nconveyed into a cooler placed upon feet like a table, having a spigot at\nthe bottom for drawing off the milk. This, when sufficiently cooled, is\ndrawn off into pans, and the cooler again filled. In so cases, the\ncooler is large enough to hold a whole meal's milk at once. The rapid\ncooling thus produced (which, however, is necessary only in hot weather,\nand during the summer season) is found to be of essential utility in\nretarding the process of fermentation, and thereby preventing putridity\nfrom commencing in the milk before two meals of it can be put together.\nSome have thought that the cheese might be improved by cooling the\nevening's milk still more rapidly, and that this might be effected by\nrepeatedly drawing it off from and returning it into the cistern. When\nthe milk is too cold, a portion of it is warmed over the fire and mixed\nwith the rest.\n\n\"The coloring matter, (annatto,) in Cheshire, is added by tying up as\nmuch of the substance as is thought sufficient in a linen rag, and\nputting it into a half pint of warm water, to stand over night. The\nwhole of this infusion is, in the morning, mixed with the milk in the\ncheese-tub, and the rag dipped in the milk and rubbed on the palm of the\nhand as long as any of the coloring matter can be made to come away.\n\n\"The next operation is salting; and this is done, either by laying the\ncheese, immediately after it comes out of the press, on a clean, fine\ncloth in the vat, immersed in brine, to remain for several days, turning\nit once every day at least; or by covering the upper surface of the\ncheese with salt every time it is turned, and repeating the application\nfor three successive days, taking care to change the cloth twice during\nthe time. In each of these methods, the cheese, after being so treated,\nis taken out of the vat, placed upon the salting bench, and the whole\nsurface of it carefully rubbed with salt daily for eight or ten days. If\nit be large, a wooden hoop or a fillet of cloth is employed to prevent\nrenting. The cheese is then washed in warm water or whey, dried with a\ncloth, and laid on what is called the _drying bench_. It remains there\nfor about a week, and is thence removed to the _keeping house_. In\nCheshire, it is found that the greatest quantity of salt used for a\ncheese of sixty pounds is about three pounds; but the proportion of this\nretained in the cheese has not been determined.\n\n\"When, after salting and drying, the cheeses are deposited in the\ncheese-room or store-house, they are smeared all over with fresh butter,\nand placed on shelves fitted to the purpose, or on the floor. During the\nfirst ten or fifteen days, smart rubbing is daily employed, and the\nsmearing with butter repeated. As long, however, as they are kept, they\nshould be every day turned; and the usual practice is to rub them three\ntimes a week in summer and twice in winter.\n\n\nSTILTON CHEESE.\n\n\"Stilton cheese is made by putting the night's cream into the morning's\nnew milk along with the rennet. When the curd has come, it is not\nbroken, as in making other cheese, but taken out whole, and put into a\nsieve to drain gradually. While this is going on, it is gently pressed,\nand, having become firm and dry, is put into a vat, and kept on a dry\nboard. These cheeses are exceedingly rich and valuable. They are called\nthe Parmesan of England, and weigh from ten to twelve pounds. The\nmanufacture of them is confined almost exclusively to Leicestershire,\nthough not entirely so.\n\n\nDUNLOP CHEESE.\n\n\"In Scotland, a species of cheese is produced, which has long been known\nand celebrated under the name of _Dunlop_ cheese. The best cheese is\nmade by such as have a dozen or more cows, and consequently can make a\ncheese every day; one half of the milk being immediately from the cow,\nand the other of twelve hours' standing. Their method of making it is\nsimple. They endeavor to have the milk as near as may be to the heat of\nnew milk, when they apply the rennet, and whenever coagulation has taken\nplace, (which is generally in ten or twelve minutes,) they stir the curd\ngently, and the whey, beginning to separate, is taken off as it gathers,\ntill the curd be pretty solid. When this happens, they put it into a\ndrainer with holes, and apply a weight. As soon as this has had its\nproper effect, the curd is put back again into the cheese-tub, and, by\nmeans of a sort of knife with three or four blades, is cut into very\nsmall pieces, salted, and carefully mixed by the hand. It is now placed\nin the vat, and put under the press. This is commonly a large stone of a\ncubical shape, from half a ton to a ton in weight, fixed in a frame of\nwood, and raised and lowered by an iron screw. The cheese is frequently\ntaken out, and the cloth changed; and as soon as it has been ascertained\nthat no more whey remains, it is removed, and placed on a dry board or\npine floor. It is turned and rubbed frequently with a hard, coarse\ncloth, to prevent moulding or breeding mites. No coloring matter is\nused in making Dunlop cheese, except by such as wish to imitate the\nEnglish cheese.\n\n\nGREEN CHEESE.\n\n\"Green cheese is made by steeping ever night, in a proper quantity of\nmilk, two parts of sage with one of marigold leaves, and a little\nparsley, after being bruised, and then mixing the curd of the milk, thus\n_greened_, as it is called, with the curd of the white milk. These may\nbe mixed irregularly or fancifully, according to the pleasure of the\noperator. The management in other respects is the same as for common\ncheese.\"\n\n       *       *       *       *       *\n\nMr. Colman says, \"In conversation with one of the largest wholesale\ncheesemongers and provision-dealers in the country, he suggested that\nthere were two great faults of the American cheese, which somewhat\nprejudiced its sale in the English market. He is a person in whose\ncharacter and experience entire confidence may be placed.\n\n\"The first fault was the softness of the rind. It often cracked, and the\ncheese became spoiled from that circumstance.\n\n\"The second fault is the acridness, or peculiar, smart, bitter taste\noften found in American cheese. He thought this might be due, in part,\nto some improper preparation or use of the rennet, and, in part, to some\nkind of feed which the cows found in the pastures.\n\n\"The rind may be made of any desired hardness, if the cheese be taken\nfrom the press, and allowed to remain in brine, so strong that it will\ntake up no more salt, for four or five hours. There must be great care,\nhowever, not to keep it too long in the brine.\n\n\"The calf from which the rennet is to be taken should not be allowed to\nsuck on the day on which it is killed. The office of the rennet, or\nstomach of the calf, is, to supply the gastric juice by which the\ncurdling of the milk is effected. If it has recently performed that\noffice, it will have become, to a degree, exhausted of its strength. Too\nmuch rennet should not be applied. Dairymaids, in general, are anxious\nto have the curd 'come soon,' and so apply an excessive quantity, to\nwhich he thinks much of the acrid taste of the cheese is owing. Only so\nmuch should be used as will produce the effect in about fifty minutes.\nFor the reason above given, the rennet should not, he says, be washed in\nwater when taken from the calf, as it exhausts its strength, but be\nsimply salted.\n\n\"When any cream is taken from the milk to be made into butter, the\nbuttermilk should be returned to the milk of which the cheese is to be\nmade. The greatest care should be taken in separating the whey from the\ncheese. When the pressing or handling is too severe, the whey that runs\nfrom the curd will appear of a white color. This is owing to its\ncarrying off with it the small creamy particles of the cheese, which\nare, in fact, the richest part of it. After the curd is cut or broken,\ntherefore, and not squeezed with the hand, and all the whey is allowed\nto separate from it that can be easily removed, the curd should be taken\nout of the tub with the greatest care, and laid upon a coarse cloth\nattached to a frame like a sieve, and there suffered to drain until it\nbecomes quite dry and mealy, before being put into the press. The object\nof pressing should be, not to express the whey, but to consolidate the\ncheese. There should be no aim to make whey butter. All the butter\nextracted from the whey is so much of the proper richness taken from the\ncheese.\"\n\n\n\n\nMAKING BUTTER.\n\n\nIt is a matter of impossibility to make a superior article of butter\nfrom the milk of a cow in a diseased state; for if either of the organs\nof secretion, absorption, digestion, or circulation, be deranged, we\ncannot expect good blood. The milk being a secretion from the blood, it\nfollows that, in order to have good milk, we must have pure blood. A\ngreat deal depends also on the food; certain pastures are more favorable\nto the production of good milk than others. We know that many\nvegetables, such as turnips, garlic, dandelions, will impart a\ndisagreeable flavor to the milk. On the other hand, sweet-scented\ngrasses and boiled food improve the quality, and, generally, increase\nthe quantity of the milk, provided, however, the digestive organs are in\na physiological state.\n\nThe processes of making butter are various in different parts of the\nUnited States. We are not prepared, from experience, to discuss the\nrelative merits of the different operations of churning; suffice it\nto say, that the important improvements that have recently been made in\nthe construction of churns promise to be of great advantage to the\ndairyman.\n\nThe method of churning in England is considered to be favorable to the\nproduction of good butter. From twelve to twenty hours in summer, and\nabout twice as long in winter, are permitted to elapse before the milk\nis skimmed, after it has been put into the milk-pans. If, on applying\nthe tip of the finger to the surface, nothing adheres to it, the cream\nmay be properly taken off; and during the hot summer months, this should\nalways be done in the morning, before the dairy becomes warm. The cream\nshould then be deposited in a deep pan, placed in the coolest part of\nthe dairy, or in a cool cellar, where free air is admitted. In hot\nweather, churning should be performed, if possible, every other day; but\nif this is not convenient, the cream should be daily shifted into a\nclean pan, and the churning should never be less frequent than twice a\nweek. This work should be performed in the coolest time of the day, and\nin the coolest part of the house. Cold water should be applied to the\nchurn, first by filling it with this some time before the cream is\npoured in, or it may be kept cool by the application of a wet cloth.\nSuch means are generally necessary, to prevent the too rapid\nacidification of the cream, and formation of the butter. We are indebted\nfor much of the poor butter, (_cart-grease_ would be a more suitable\nname,) in which our large cities abound, to want of due care in\nchurning: it should never be done too hastily, but--like \"Billy Gray's\"\ndrumming--well done. In winter the churn may be previously heated by\nfirst filling it with hot water, the operation to be performed in a\nmoderately warm room.\n\nIn churning, a moderate and uninterrupted motion should be kept up\nduring the whole process; for if the motion be too rapid, heat is\ngenerated, which will give the butter a rank flavor; and if the motion\nis relaxed, the butter will go back, as it is termed.\n\n\nWASHING BUTTER.\n\n\"When the operation is properly conducted, the butter, after some time,\nsuddenly forms, and is to be carefully collected and separated from the\nbuttermilk. But in doing this, it is not sufficient merely to pour off\nthe milk, or withdraw the butter from it; because a certain portion of\nthe caseous and serous parts of the milk still remains in the\ninterstices of the butter, and must be detached from it by washing, if\nwe would obtain it pure. In washing butter, some think it sufficient to\npress the mass gently between the hands; others press it strongly and\nfrequently, repeating the washings till the water comes off quite clear.\nThe first method is preferable when the butter is made daily, for\nimmediate use, from new milk or cream; because the portions of such\nadhering to it, or mixed with it, contribute to produce the sweet\nagreeable flavor which distinguishes new cream. But when our object is\nto prepare butter for keeping, we cannot repeat the washings too often,\nsince the presence of a small quantity of milk in it will, in less than\ntwelve hours after churning, cause it sensibly to lose its good\nqualities.\n\n\"The process of washing butter is usually nothing more than throwing it\ninto an earthen vessel of clear cool water, working it to and fro with\nthe hands, and changing the water until it comes off clear. A much\npreferable method, however, and that which we believe is now always\npractised by those who best understand the business, is to use two broad\npieces of wood, instead of the hands. This is to be preferred, not only\non account of its apparently greater cleanliness, but also because it is\nof decided advantage to the quality of the butter. To this the warmth of\nthe hand gives always, more or less, a greasy appearance. The influence\nof the heat of the hand is greater than might at first have been\nsuspected. It has always been remarked, that a person who has naturally\na warm hand never makes good butter.\"\n\n\nCOLORING BUTTER.\n\nAs butter made in winter is generally pale or white, and its richness,\nat the same time, inferior to that which is made during the summer\nmonths, the idea of excellence has been associated with the yellow\ncolor. Means are therefore employed, by those who prepare and sell\nbutter, to impart to it the yellow color where that is naturally\nwanting. The substances mostly employed in England and Scotland are the\nroot of the carrot and the flowers of the marigold. The juice of either\nof these is expressed and passed through a linen cloth. A small quantity\nof it (and the proportion of it necessary is soon learned by experience)\nis diluted with a little cream, and this mixture is added to the rest of\nthe cream when it enters the churn. So little of this coloring matter\nunites with the butter, that it never communicates to it any peculiar\ntaste.\n\n\n\n\nDESCRIPTION OF THE ORGANS OF DIGESTION IN CATTLE.\n\n\n_Oesophagus_, or _Gullet_.--This tube extends from the mouth to the\nstomach, and is the medium through which the food is conveyed to the\nlatter organ. This tube is furnished with spiral muscles, which run in\ndifferent directions. By this arrangement, the food ascends or descends\nat the will of the animal. The inner coat of the gullet is a\ncontinuation of the same membrane that lines the mouth, nostrils, &c.\nThe gullet passes down the neck, inclining to the left side of the\nwindpipe, until it reaches the diaphragm, through a perforation of which\nit passes, and finally terminates in the stomach. The food, having\nundergone a slight mastication by the action of the teeth, is formed\ninto a pellet, and, being both moistened and lubricated with saliva,\npasses down the gullet, by the action of the muscles, and falls\nimmediately into the paunch, or rumen; here the food undergoes a process\nof maceration, or trituration. The food, after remaining in this portion\nof the stomach a short time, and being submitted to the united action of\nheat and moisture, passes into another division of the stomach, called\n_reticulum_, the inner surface of which abounds in cells: at the bottom,\nand indeed in all parts of them there are glands, which secrete from the\nblood the gastric fluids. This stomach possesses a property similar to\nthat of the bladder, viz., that of contracting upon its contents. In the\nact of contracting, it squeezes out a portion of the partly masticated\nfood and fluids; the former comes within the spiral muscles, is embraced\nby them, and thus ascends the gullet, and passes into the mouth for\nremastication. The soft and fluid parts continue on to the many plus and\ntrue digestive stomach. The second stomach again receives a portion from\nthe paunch, and the process is continued.\n\nRumination and digestion, however, are mechanico-vital actions, and can\nonly be properly performed when the animal is in a healthy state.\n\nNow, a portion of the food, we just observed, had ascended the gullet\nby the aid of spiral muscles, and entered the mouth; it is again\nsubmitted to the action of the grinders, and a fresh supply of saliva;\nit is at length swallowed a second time, and goes through the same\nroutine as that just described, passing into the manyplus or manifolds,\nas it is termed.\n\nThe manyplus abounds internally in a number of leaves, called laminae.\nSome of these are attached to the upper and lower portion of the\ndivision, and also float loose, and penetrate into the oesophagian\ncanal. The laminae have numerous projections on their surface, resembling\nthe papillae to be found on the tongue. The action of this stomach is one\nof alternate contraction and expansion: it secretes, however, like the\nother compartments of the stomach, its due share of gastric fluids, with\na view not only of softening its contents, but for the purpose of\ndefending its own surface against friction. The mechanical action of the\nstomach is communicated to it partly by the motion of the diaphragm, and\nits own muscular arrangement. It will readily be perceived, that by this\njoint action the food is submitted to a sort of grinding process. Hence\nany over-distention of the viscera, from either food or gas, will\nembarrass and prevent the free and full play of this organ. The papillae,\nor prominences, present a rough and sufficiently hard exterior to grind\ndown the food, unless it shall have escaped the reticulum in too fibrous\na form: foxgrass, cornstalks, and frosted turnips are very apt to make\nsad havoc in this and other parts of the stomach, owing to their\nunyielding nature; for the stomach, like other parts of the\norganization, suffers from over-exertion, and a corresponding debility\nensues.\n\nThe fourth division of the stomach of the ox is called _abomasum_. It\nsomewhat resembles the duodenum of the horse in its function, it being\nthe true digestive stomach. It is studded with numerous nerves,\nblood-vessels, and small glands. It is a laboratory admirably fitted up\nby the Divine Artist, and is capable of carrying on the chemico-vital\nprocess as long as the animal lives, provided its healthy functions are\nnot impaired. The glands alluded to secrete from the blood a powerful\nsolvent, called the _gastric juice_, which is the agent in reducing the\nfood to chyme and chyle. This, however, is accomplished by the united\nagency of the bile and pancreatic juice. Both these fluids are conveyed\ninto the abomasum by means of small tubes or canals. Secretions also\ntake place from the inner membrane of the intestines, and, as the result\nof the united action of all these fluids, aided by the muscular motion\njust alluded to, which is also communicated to the intestines, a\nsubstance is formed called _chyle_, which is the most nutritious portion\nof the food, and has a milky appearance. The chyle is received into a\nset of very minute tubes, called _lacteals_, which are exceedingly\nnumerous, and arise by open mouths from the inner surface of the\nabomasum and intestines. They receive the chyle; from thence it passes\ninto a receptacle, and finally into the thoracic duct. The thoracic duct\nopens into a vein leading directly to the heart; so that whatever\nportion of the chyle is not actually needed by the organism is\nthoroughly mixed with the general mass of blood. That portion of chyme\nwhich is not needed, or cannot be converted into chyle, descends into\nthe intestines, and is finally carried out of the body by the rectum.\n\nThe manner in which the gastric fluids act on alimentary matter, is by\nsolution and chemical action; for cornstalks and foxgrass, that cannot\nbe dissolved by ammonia or alcohol, yield readily to the solvent power\nof the gastric secretion. Bones and other hard substances are reduced to\na pulpy mass in the stomach of a dog; while, at the same time, many\nbodies of delicate texture remain in the stomach, and ultimately are\nejected, without being affected by the gastric fluids. This different\naction on different subjects is analogous to the operation of chemical\naffinity, and corroborates the theory that digestion is effected by\nsolution and chemical action.\n\n_The Spleen_, or _Milt_, is an oblong, dark- substance, having\nattachments to the paunch. It is composed of blood-vessels, nerves, and\nlymphatics, united by cellular structure. It appears to serve as a\nreservoir for the blood that may be designed for the secretions of bile\nin the liver. P. M. Roget says, \"Any theory that assigns a very\nimportant function to the spleen will be overturned by the fact, that in\nmany animals the removal of this organ, far from being fatal, or\ninterrupting, in any sensible manner, the continuance of the functions,\nseems to be borne with perfect impunity.\" Sir E. Home, Bichat, Leuret,\nLassaigne, and others, suppose that \"the spleen serves as a receptacle\nfor the superfluous quantity of fluid taken into the stomach.\"\n\n_The Liver_ is a dense gland, of a lobulated structure, situated below\nthe diaphragm, or \"skirt.\" It is supplied, like other organs, with\narterial blood, by vessels, called _hepatic_ arteries, which are sent\noff from the great aorta. It receives also a large amount of venous\nblood, which is distributed through its substance by a separate set of\nvessels, derived from the venous system. The veins which receive the\nblood that has circulated in the usual manner unite together into a\nlarge trunk, called vena portae, (gate vein,) and this vein, on entering\nthe liver, ramifies like an artery, and ultimately terminates in the\nbranches of the hepatic veins, which transmit the blood, in the ordinary\ncourse of circulation, to the vena cava, (hollow vein.) Mr. Kiernan\nsays, \"The hepatic veins, together with the lobules which surround them,\nresemble, in their arrangement, the branches and leaves of a tree, the\nsubstance of the lobules being disposed around the minute branches of\nthe veins like the parenchyma of a leaf around its fibres. The hepatic\nveins may be divided into two classes, namely, those contained in\nlobules, and those contained in canals formed by lobules. The first\nclass is composed of interlobular branches, one of which occupies the\ncentre of each lobule, and receives the blood from a plexus formed in\nthe lobule by the portal vein; and the second class of hepatic veins is\ncomposed of all those vessels contained in canals formed by the lobules,\nand including numerous small branches, as well as the large trunks\nterminating in the inferior cava. The external surface of every lobule\nis covered by an expansion of '_Glisson's capsule_,' by which it is\nconnected to, as well as separated from, contiguous lobules, and in\nwhich branches of the hepatic duct, portal veins, and hepatic artery\nramify. The ultimate branches of the hepatic artery terminate in the\nbranches of the portal vein, where the blood they respectively contain\nis mixed together, and from which mixed blood the bile is secreted by\nthe lobules, and conveyed away by the hepatic ducts. The remaining blood\nis returned to the heart by the hepatic veins, the beginnings of which\noccupy the centre of each lobule, and, when collected into trunks, pour\ntheir contents into the inferior cava. Hence the blood which has\ncirculated through the liver, and has thereby lost its arterial\ncharacter, is, in common with that which is returning from other parts,\npoured into the vena portae, and contributes its share in furnishing\nmaterials for the biliary secretion. The hepatic artery furnishes\nnutrition to the liver itself.\"\n\nThe bile, having been secreted, accumulates in the gall-bladder, where\nit is kept for future use. When the healthy action of the fourth stomach\nis interrupted, the bile is supposed to be reabsorbed,--it enters into\nthe different tissues, producing yellowness of the eyes; the malady is\nthen termed _yellows_, _jaundice_, &c. Sometimes the passage of the bile\nis obstructed by calculi, or gall-stones; they have been found in great\nnumbers in oxen.\n\n_The Pancreas_ is composed of a number of lobules or glands; a small\nduct proceeds from each; they unite and form a common canal, which\nproceeds towards, and terminates in, the fourth stomach. The pancreatic\njuice appears to be exceedingly analogous, both in its sensible\nproperties and chemical composition, to the saliva.\n\n\"The recent researches of MM. Bouchardat, Sandras, Mialhe, Bareswil, and\nBernard himself, have placed beyond a doubt the existence of a ferment,\nin some of the fluids which mix with the alimentary mass, destined to\nconvert starchy matters into sugar. They have proved that the gastric\njuice has for its peculiar office the solution and digestion of azotized\nsubstances. There remained to be ascertained the real agent for the\ndigestion of fatty matters; that is to say, the agent in the formation\nof chyle out of those substances.\n\n\"M. Bernard has proved that this remarkable office is performed by the\npancreatic juice; he has demonstrated the fact by three conclusive\nproofs.\n\n\"1. The pancreatic juice, pure and recently formed, forms an emulsion\nwith oils and fats with the greatest facility. This emulsion may be\npreserved for a long time, and the fatty substance soon undergoes a\nfermentation which separates its constituent acids.\n\n\"2. The chyle only begins to appear in the lacteals below that part of\nthe intestinal tube where the pancreatic juice enters it to mix with the\nalimentary matters.\n\n\"3. In disorders of the pancreas, we find that the fatty matters,\ncontained in the food, pass entire in the evacuations.\"\n\nThe above is an extract from the report of a body composed of several\nmembers of the French Academy of Sciences. \"M. Bernard\" (continues the\nreport) \"has exhibited to us the first of these experiments, and has\nfurnished us with the means of repeating it with the several varieties\nof the gastric juice. We have not the slightest doubt on the subject. It\nis incontestable that fatty substances are converted into an emulsion by\nthis juice, in a manner easy and persistent, and it is no less true that\nthe saliva, the gastric juice, and the bile are destitute of this\nproperty.\n\n\"The second demonstration can be given in various modes; but the author\nhas discovered, in the peculiar arrangement of the digestive apparatus\nof the rabbit, an unexceptional means of obtaining it with the greatest\nprecision, and at will. The pancreatic juice enters the intestinal tube\nof this animal about fourteen inches below the point where the bile is\npoured in. Now, as long as the food is above the region where it mixes\nwith the pancreatic juice, there appears to be no formation and\nseparation of a milky chyle; nothing shows that the fatty matters are\nreduced to an emulsion. On the contrary, as soon as the pancreatic juice\nmixes with the alimentary matters, we observe the fat to be converted\ninto an emulsion, and a milky chyle to fill the corresponding lacteals.\nNothing can give an idea of the result of these experiments, which have\nall the accuracy of a chemical operation performed in the laboratory,\nand all the beauty of the most perfect injection.\n\n\"We are not, therefore, surprised that divers pathological cases,\nhitherto imperfectly understood, should come to confirm the views of M.\nBernard, by proving that, in diseases of the pancreas, fatty matters\nhave been observed to pass unchanged in the dejections.\n\n\"The committee cannot hesitate to conclude that the author has perfectly\ndemonstrated his physiological propositions; that he has completed the\ngeneral characters of the theory of digestion, and that he has made\nknown the mode of formation of the fatty matter of the chyle, and the\nmanner of the digestion of the fatty matters.\"\n\n_The Kidneys._--Their office is, to secrete from the blood the useless\nor excrementitious fluids in the form of urine. When the skin is\nobstructed, the secretion is augmented, and profuse perspiration lessens\nit. From a cavity in the centre of each kidney a canal or tube proceeds,\nby which the urine is conveyed into the bladder. These tubes are named\n_ureters_. As the ureters enter the bladder, they pass forward, a short\ndistance between its coats; which effectually prevents the urine from\ntaking a retrograde course. The urine is expelled by the muscular power\nwhich the bladder possesses of contracting upon its contents.\n\n\n\n\nRESPIRATION AND STRUCTURE OF THE LUNGS.\n\n\nThe organs of respiration are the larynx, the trachea, or windpipe,\nbronchia, and the lungs.\n\nThe air is expelled from the lungs principally by the action of the\nmuscles of respiration; and when these relax, the lungs expand by virtue\nof their own elasticity. This may be exemplified by means of a sponge,\nwhich may be compressed into a small compass by the hand, but, upon\nopening the hand, the sponge returns to its natural size, and all its\ncavities become filled with air. The purification of the blood in the\nlungs is of vital importance, and indispensably necessary to the due\nperformance of all the functions; for if they be in a diseased\nstate,--either tuberculous, or having adhesions to the pleura, their\nfunction will be impaired; the blood will appear black; loaded with\ncarbon; and the phlebotomizer will have the very best (worst) excuse for\ntaking away a few quarts with a view of purifying the remainder! The\ntrachea, or windpipe, after dividing into smaller branches, called\n_bronchia_, again subdivides into innumerable other branches, the\nextremities of which are composed of an infinite number of small cells,\nwhich, with the ramifications of veins, arteries, nerves, and connecting\nmembranes, make up the whole mass or substance of the lungs. The\ninternal surface of the windpipe, bronchia, and air-cells, is lined with\na delicate membrane, highly organized with blood-vessels, &c. The whole\nis invested with a thin, transparent membrane--a continuation of that\nlining the chest, named _pleura_. It also covers the diaphragm, and, by\na duplication of its folds, forms a separation between the lobes of the\nlungs.\n\n\n\n\nCIRCULATION OF THE BLOOD.\n\n\nThe blood contains the elements for building up, supplying the waste of,\nand nourishing the whole animal economy. On making an examination of the\nblood with a microscope, it is found full of little red globules, which\nvary in their size and shape in different animals, and are more numerous\nin the warm than in the cold-blooded. Probably this arises from the fact\nthat the latter absorb less oxygen than the former. When blood stands\nfor a time after being drawn, it separates into two parts. One is called\n_serum_, and resembles the white of an egg; the other is the clot, or\ncrassamentum, and forms the red coagulum, or jelly-like substance. This\nis accompanied by whitish tough threads, called _fibrine_.\n\n  [Illustration: THE HEART VIEWED EXTERNALLY.\n\n  _a_, the left ventricle; _b_, the right ventricle; _c_, _e_, _f_, the\n  aorta; _g_, _h_, _i_, the carotid and other arteries springing from the\n  aorta; _k_, the pulmonary artery; _l_, branches of the pulmonary artery\n  in the lungs; _m_, _m_, the pulmonary veins emptying into the left\n  auricle; _n_, the right auricle; _o_, the ascending vena cava; _q_, the\n  descending vena cava; _r_, the left auricle; _s_, the coronary vein and\n  artery. (See _Circulation of the Blood_, on the opposite page.)]\n\nWhen blood has been drawn from an animal, and it assumes a cupped or\nhollow form, if serum, or buffy coat, remains on its surface, it denotes\nan impoverished state; but if the whole, when coagulated, be of one\nuniform mass, it indicates a healthy state of that fluid. The blood of a\nyoung animal, provided it be in health, coagulates into a firm mass,\nwhile that of an old or debilitated one is generally less dense, and\nmore easily separated. The power that propels the blood through the\ndifferent blood-vessels is a mechanico-vital power, and is accomplished\nthrough the involuntary contractions and relaxations of the heart; from\ncertain parts of which arteries arise, in other parts veins terminate.\n(See Plate.)\n\nThe heart is invested with a strong membranous sac, called\n_pericardium_, which adheres to the tendinous centre of the diaphragm,\nand to the great vessels at its superior portion. The heart is\nlubricated by a serous fluid, secreted within the pericardium, for the\npurpose of guarding against friction. When an excess of fluid\naccumulates within the sac, it is termed dropsy of the heart. The heart\nis divided into four cavities, viz., two auricles, named from their\nresemblance to an ear, and two ventricles, (as seen at _a_, _b_,)\nforming the body. The left ventricle is smaller than the right, yet its\nwalls are much thicker and stronger than those of the latter: it is from\nthis part that the large trunk of the arteries proceed, called the\n_great aorta_. The right cavity, or ventricle, is the receptacle for\nblood returned by the venous structure after having gone the rounds of\nthe circulation; the veins terminating, as they approach the heart, in a\nsingle vessel, called _vena cava_, (see plate, _o_, _q_, ascending and\ndescending portion.) The auricle on the left side of the heart receives\nthe blood that has been distributed through the lungs for purification.\nWhere the veins terminate in auricles, there are valves placed, to\nprevent the blood from returning. For example, the blood proceeds out of\nthe heart along the aorta; the valve opens upwards; the blood also\nmoves upwards, and raises the valve, and passes through; the pressure\nfrom above effectually closes the passage. The valves of the heart are\ncomposed of elastic cartilage, which admits of free motion. They\nsometimes, however, become ossified. The heart and its appendages are,\nlike other parts of the system, subject to various diseases, which are\nfrequently very little understood, yet often fatal. Now, the blood,\nhaving passed through the veins and vena cava, flows into the right\nauricle; and this, when distended, contracts, and forces its contents\ninto the right ventricle, which, contracting in its turn, propels the\nblood into the pulmonary arteries, whose numerous ramifications bring it\nin contact with the air-cells of the lungs. It then, being deprived of\nits carbon, assumes a crimson color. Having passed through its proper\nvessels, it accumulates in the left auricle. This also contracts, and\nforces the blood through a valve into the left ventricle. This ventricle\nthen contracts in its turn, and the blood passes through another valve\ninto the great aorta, to go the round of the circulation and return in\nthe manner just described.\n\nMany interesting experiments have been made to estimate the quantity of\nblood in an animal. \"The weight of a dog,\" says Mr. Percival, \"being\nascertained to be seventy-nine pounds, a puncture was made with the\nlancet into the jugular vein, from which the blood was collected. The\nvein having ceased to bleed, the carotid artery of the same side was\ndivided, but no blood came from it; in a few seconds afterwards, the\nanimal was dead. The weight of the carcass was now found to be\nseventy-three and a half pounds; consequently it had sustained a loss of\nfive and a half pounds--precisely the measure of the blood drawn. It\nappears from this experiment, that an animal will lose about one\nfifteenth part of its weight of blood before it dies; though a less\nquantity may so far debilitate the vital powers, as to be, though less\nsuddenly, equally fatal. In the human subject, the quantity of blood has\nbeen computed at about one eighth part of the weight of the body; and as\nsuch an opinion has been broached from the results of experiments on\nquadrupeds, we may fairly take that to be about the proportion of it in\nthe horse; so that if we estimate the weight of a horse to be thirteen\nhundred and forty-four pounds, the whole quantity of blood will amount\nto eighty-four quarts, or one hundred and sixty-eight pounds; of which\nabout forty-five quarts, or ninety pounds, will commonly flow from the\njugular vein prior to death; though the loss of a much less quantity\nwill deprive the animal of life.\"\n\n\n\n\nREMARKS ON BLOOD-LETTING.\n\n\nThe author has been, for several years, engaged in a warfare against the\nuse of the lancet in the treatment of the various diseases of animals.\nWhen this warfare was first commenced, the prospect was poor indeed. The\nlancet was the great anti-phlogistic of the allopathic school; it had\npowerful, talented, and uncompromising advocates, who had been\naccustomed to resort to it on all occasions, from the early settlement\nof America up to that period. The great mass had followed in the\nfootsteps of their predecessors, supposing them to be infallible. Men\nand animals were bled; rivers of blood have been drawn from their\nsystems; yet they often got well, and men looked upon the lancet as one\nof the blessings of the age, when, in fact, it is the greatest curse\nthat ever afflicted this country: it has produced greater losses to\nowners of domestic animals than did ever pestilence or disease. A few\nphilanthropic practitioners have, from time to time, in other countries,\nas well as in this, labored during their life, and on their death-bed,\nto convince the world of the destructive tendency of blood-letting in\nhuman practice; but none that we know of ever had the moral courage to\nwage a general warfare against the practice in the veterinary\ndepartment, until we commenced it. We have met with great success, and\nhave given the blood-letting gentry who practise it at the present day\n(\"just to please their employers or to make out a case\") a partial\nquietus: in a few more years, unless they abandon their false theories,\ntheir occupation, notwithstanding their pretensions to cure _secundum\nartem_, will, like Othello's, be \"gone.\" But we are not writing for\ndoctors. Our business is with the farmers--the lords of creation. The\nformer are mere lords of pukes and purges; they, like the farmers, have\nthe materials, however, to mould themselves into men of common sense;\nbut the fact is, they are hide-bound; they want a national sweat, to rid\ntheir systems, especially their upper works, of the theories of Sydenham\nand Paracelsus, which have shipwrecked many thousands of the medical\nprofession. They shut their eyes to the results of medical reform, and\ncling, with all their soul, and with all their might, worthy a better\ncause, to a system that \"always was false.\"\n\nLord Byron, like many other learned men, was well acquainted with the\nimpotency of the healing art, and held the lancet in utter abhorrence:\nwhen beset, day and night, to be bled, the bard, in an angry tone,\nexclaimed, \"You are, I see, a d----d set of butchers; take away as much\nblood as you like.\" \"We seized the opportunity,\" says Dr. Milligan, \"and\ndrew twenty ounces; yet the relief did not correspond to the hopes we\nhad formed.\" On the 17th, the bleeding was twice repeated, dangerous\nsymptoms still increasing, and on the 19th he expired, just about bled\nto death. Washington, a man whose name is dear to every American, died\nfrom the effects of an evil system of medication. He was attacked with\ncroup: his physician bled him, and gave him calomel and antimony. The\nnext day, physicians were called in, (to share the responsibility of the\nbutchery,) and he was subjected to two more copious bleedings: in all he\nlost ninety ounces of blood. Which of our readers, at the present day,\nwould submit to such unwarrantable barbarity? We just said we were not\nwriting for doctors; yet we find ourselves off the track in thus\nadministering a small dose, as a sample of \"_good and efficient\ntreatment_.\"\n\nIn reference to the success attending our labors in veterinary reform,\nwe do not claim the whole credit: much of it is due to the intelligence\nof the American farmers, in appreciating the value and importance of a\nsafer and a more effectual system of medication; such a system as we\nadvocate. They have witnessed the results attending the practice of\ncattle doctors generally, and they have seen the results of our sanative\nsystem of medication, and a great majority in Massachusetts have decided\nin favor of the latter. We have demonstrated to the satisfaction of our\npatrons, and we are ready and willing to repeat our experiments on\ndiseased animals for the satisfaction of others, in showing that we can\nrestore an animal, when suffering under acute attacks of disease, in a\nfew hours, when, by the popular method, it takes weeks and months, if\nindeed they ever recover from the effects of the destructive agents\nused.\n\nWe are told that \"horses and cattle are bled and get well immediately.\"\nThis may apply to some cases; but, in very many instances, the animals\nare sent for a few weeks to \"Dr. Green,\"[1] to put them in the same\ncondition they were at the time of bleeding. But suppose that some\nanimals do get well after bleeding; is it thus proved that more would\nnot get well if no blood were drawn from any? A cow may fall down, and,\nin so doing, lacerate her muscles, blood-vessels, &c., and lose a large\nquantity of blood. She may get well, in spite of the violence and loss\nof blood. So we say of blood-letting, if the abstraction of a certain\nnumber of gallons of blood will kill a strong animal, then the\nabstraction of a small quantity must injure it proportionately.\n\nThere is in the animal economy a power, called the vital principle,\nwhich always operates in favor of health. If the provocation be gentle,\nand does not seriously derange the machinery, then this power may\novercome both it and any disease the animal may at the time labor under.\nFor example, a horse falls down in the street, perhaps laboring under a\ntemporary congestion of the brain: now, if he were let alone until\nnature has restored an equilibrium of the circulating fluid and nervous\naction, he would soon get up and proceed on his way, as many thousands\ndo when a knife or lancet is not to be had. But, unfortunately, people\nare too hasty. The moment a beast has fallen, they are bound to have him\non his perpendiculars in double quick time. The teamster cannot wait for\nnature; she is \"too slow a coach\" for him. He tries what virtue there is\nin the whip; this failing, he obtains a knife, if one is to be had, and\n\"_starts the blood_.\" By this time, nature, about resuming her empire,\ncauses the horse to show signs of returning animation, and the credit is\nawarded to the blood-starter. Animals are often bled when diseased, and\nthe prominent symptoms that previously marked the character of the\nmalady disappear, or give place to symptoms of another order, less\nevident, and men have supposed that a cure is effected, when, in fact,\nthey have just sown the seeds of a future disease. We are not bound to\nprove, in every case, how an animal gets well after two or three\nrepeated bleedings. It is enough for us to prove that this operation\nalways tends to death, which can easily be produced by opening the\ncarotid artery of an animal.\n\nPermit us, dear reader, at this stage of our article, to observe, that\n\"confession is good for the soul.\" We mean to put it in practice. So\nhere goes. We plead guilty to bleeding, blistering, calomelizing,\nnarcotizing, antimonializing, a great number of patients of the human\nkind. We did it in our verdant days, because it was so scientific and\npopular, and because we had been taught to reverence the stereotyped\npractice of the allopathists. We have, however, done penance, and sought\nforgiveness; and through the aid of a few men, devoted to medical\nreform, we have been washed in the regenerating waters flowing through\nthe vineyard of reason and experience, and now advocate and observe the\nself-regulating powers of the laws of life. On the other hand, we are\nfree from the charge of bleeding or poisoning domestic animals, and can\nsay, with a clear conscience, that we have never drawn a drop of blood\nfrom a four-footed creature, (except in surgical operations, when it\ncould not be avoided;) neither will we, under any circumstances, resort\nto the lancet; for we are convinced that blood-letting is a powerful\ndepressor of the vital powers.\n\nBlood is the fuel that keeps the lamp of life burning; if the fuel be\nwithdrawn, the light is extinguished.\n\nProfessor Lobstein says, \"So far from blood-letting being beneficial, it\nis productive of the most serious consequences--a cruel practice, and a\nscourge to humanity. How many thousands are sent by it to an untimely\ngrave! Without blood there is no heat, no motion in the body.\"\n\nDr. Reid says, \"If the employment of the lancet was abolished\naltogether, it would perhaps save annually a greater number of lives\nthan pestilence ever destroyed.\"\n\nThe fact of blood-letting having been practised by horse and cattle\ndoctors from time immemorial is certainly not a clear proof of its\nutility, nor is it a sufficient recommendation that it may be practised\nwith safety. During my professional career, the preconceived theories\nhave commanded a due share of consideration; and, when weighed in the\nscale of uninfluenced experience, they never failed of falling short. If\nwe grant that any deviation from the healthy state denotes debility of\none or more functions, then whatever has a tendency to debilitate\nfurther cannot restore the animal to health. The following case will\nserve to illustrate our position: \"A horse was brought to be bled,\nmerely because he had been accustomed to it at that season of the year.\nI did not examine him minutely; but as the groom stated there was\nnothing amiss with him, I directed a moderate quantity of blood to be\ndrawn. About five pints were taken off; and while the operator was\npinning up the wound, the horse fell. He appeared to suffer much pain,\nand had considerable difficulty of breathing. In this state he remained\ntwelve hours, and then died. Judging from the appearances at the post\nmortem examination, it is probable that a loss of a moderate quantity of\nblood caused a fatal interruption of the functions of the heart.\"\n\nIt is strange that such cases as these do not open men's eyes, and\ncompel them to acknowledge that there is something wrong in the medical\nworld. Such cases as these furnish us with unanswerable arguments\nagainst blood-letting; for as the blood, which is the natural stimulus\nof, and gives strength to, the organs, is withdrawn, its abstraction\nleaves all those organs less capable of self-defence.\n\nHorse and cattle doctors have recommended bleeding when animals have\nbeen fed too liberally, or if their systems abound in morbific matter.\nNow, the most sensible course would be, provided the animal had been\noverfed, to reduce the quantity of food, or, in other words, remove the\ncause. If the secretions are vitiated, or in a morbid state, then\nregulate them by the means laid down in this work. For we cannot purify\na well of water by abstracting a few buckets; neither can we purify the\nwhole mass of blood by taking away a few quarts; for that which is left\nwill still be impure. If the different parts had between them partitions\nimpervious to fluids, then there would be some sense in drawing out of\nthe vessels over-filled; but unfortunately, if you draw from one, you\ndraw from all the rest.\n\nIn every disease wherein bleeding has been used, complete recovery has\nbeen protracted, and the animal manifests the debility by swelled legs\nand other unmistakable evidences. In some cases, however, the ill\neffects of the loss of blood, unless excessive, are not always\nimmediately perceived; yet such animals, in after years, are subject to\nstaggers, and diseases of the lungs, pleura, and peritoneum.\n\nDr. Beach says, \"The blood is properly called the _vital fluid_, and the\nlife of a person is said to be in the blood.[2] We know that just in\nproportion to the loss of this substance are our vigor and strength\ntaken from us. When taken from the system by accident or the lancet, it\nis succeeded by great prostration of strength, and a derangement of all\nthe functions of the body. These effects are invariably, in a greater\nor less degree, consequent on bleeding. Is it not, then, reasonable to\nsuppose, that what will debilitate the strongest constitution in a state\nof health, will be attended with most serious evils when applied to a\nperson laboring under any malady? Is it not like throwing spirits on a\nfire to extinguish it?\n\n\"Bleeding is resorted to in all inflammatory complaints; but did\npractitioners know the nature and design of inflammation, their\ntreatment would be different. In fever it is produced by an increased\naction of the heart and arteries, to expel acrid and noxious humors, and\nshould be promoted until the irritating matter is dislodged from the\nsystem. This should be effected, in general, by opening the outlets of\nthe body, inducing perspiration; to produce which a preternatural degree\nof heat or inflammation must be excited by internal remedies. Fever is\nnothing more or less than a wholesome and salutary effort of nature to\nthrow off some morbific matter; and, therefore, every means to lessen\nthis indication proves injurious. Bleeding, in consequence of the\ndebility it produces, prevents such indication from being fulfilled.\"\n\nThe inveterate phlebotomizers recommend and practise bleeding when \"_the\nanimal has too much blood_.\" There may be at times too much blood, and\nat others too little; but suppose there is--has any body found out any\nbetter method of reducing what they please to term an excess, than that\nof regular exercise in the open air, combined with a less quantity of\nfodder than usual? Or has any body found out any method of making good\nhealthy blood, other than the slow process of nature, as exhibited in\nthe results of digestion, secretion, circulation, and nutrition? Have\nthey discovered any artificial means of restoring the blood to its\nhealthful quantity when it is deficient? Have they found any means of\npurifying the blood, save the healthful operations of nature's secreting\nand excreting laboratory? Finally, have they found any safety-valve or\noutlet for the reduction of this excess other than the excrementitious\nvessels? And if they have, are they better able to adjust the pressure\non that valve than He who made the whole machinery, and knows the\nrelative strength of all its parts? In an article on blood-letting,\nfound in the Farmer's Cyclopaedia, the author says, \"In summer, bleeding\nis often necessary to prevent fevers.\" Now, it is evident that nature's\npreventives are air, exercise, food, water, and sleep. Attention to the\nrules laid down in this work, under the heads of _Watering_, _Feeding_,\n&c., will be more satisfactory and less dangerous than that recommended\nby the Cyclopaedia. If the directions given in the latter were fully\ncarried out, the stock of our farms would be swept away as by the blast\nof a tornado. Such a barbarous system would entail universal misery and\ndegeneracy on all classes of live stock; and we might then exclaim,\n\"They are living, yet half dead--victims to an inconsistent system of\nmedication!\" But thanks to a discerning public, they just begin to see\nthe absurdity and wickedness of draining the system of the living\nprinciples. Veterinary reform has germinated in the New England States,\nand, in spite of all opposition, has struck its roots deep into the\nminds of a class of men who have the means and power to send forth its\nhealing branches, and apply them to their own interest and the welfare\nof their stock.\n\nThe same author continues: \"Some farmers bleed horses three or four\ntimes a year.\" We hope the farmers have too much good sense to follow\nthe wicked example of the former. Frequent bleeding is an indirect mode\nof butchery--killing by inches; for it gives to the blood-vessels the\npower to contract and adapt themselves to the measure of blood that\nremains. It impoverishes the blood, and leads to hydrothorax,\n(accumulation of water in the chest,) and materially shortens life.\nMackintosh says, \"Some are bled who cannot bear it, and others who do\nnot require it; and the result is death.\" The conservative power of life\nalways operates in favor of health, and resists the encroachments upon\nher province with all her might, and often recovers the dominion; but by\nfrequent bleedings, she is exhausted, and, on taking a little more blood\nthan usual, the animal drops down and dies; and the owner attributes to\ndisease what, in fact, is the result of bad treatment.\n\n\"Patients who recover after general and copious bleedings have been\nemployed, may attribute their recovery to the strength of their\nconstitution.\n\n\"If you should ask a modern _Sangrado_ what was most necessary in the\ntreatment of disease, doubtless he would reply, 'Bleeding.'\n\n\"Our modern pathologists, surgeons and others, think bleeding the\n_factotum_ in all maladies; it is the _ne plus ultra_, when drawn in\nlarge quantities. Blood-letting, say these authors, is not only the most\npowerful and important, but the most generally used, of all our\nremedies. Scarcely a case of acute, or, indeed, of chronic, disease\noccurs in which it does not become necessary to consider the propriety\nof having recourse to the lancet.\" (??) To what extent blood-letting is\ncarried, in our modern age, may be learned by reading Youatt and others,\nwho recommend it \"when animals rub themselves, and the hair falls off;\nwhen the eyes appear dull and languid, red or inflamed; in all\ninflammatory complaints, as of the brain, lungs, kidneys, bowels, womb,\nbladder, and joints; in all bruises, hurts, wounds, and all other\naccidents; in cold, catarrh, paralysis, and locked-jaw.\" Yet, strange to\nsay, one of these authors qualifies his recommendations as follows: \"No\nman, however wise, can tell exactly how much blood ought to be taken in\na given case.\" Now, it is well known that the draining of blood from a\nvein, though it diminishes the vital resistance, and lessens the volume\nof fluids, does not mend the matter; for it thus gives to cold and\natmospheric agents the ascendant influence. A collapse takes place, the\nsecretions become impaired, the animal refuses its food, \"looks\ndumpish,\" &c.\n\nWe might continue this article to an indefinite length; but as we shall,\nin the following pages, have occasion to refer to the use of the lancet\nas a destructive agent, we conclude it with the following remarks of an\nEnglish physician: \"Our most valuable remedies against inflammation are\nbut ill adapted for curing that state of disease. They do not act\ndirectly on the diseased part; the action is only indirect; therefore it\nis imperfect. Bleeding, the best of any of these remedies, is in this\npredicament.\"\n\nFOOTNOTES:\n\n[1] A piece of pasture land.\n\n[2] Then the life of an animal is also in the blood; and the same evil\nconsequences follow its abstraction.\n\n\n\n\nEFFORTS OF NATURE TO REMOVE DISEASE.\n\n     \"Nature is ever busy, by the silent operations of her own forces,\n     in curing disease.\"--_Dixon._\n\n\nWhenever any irritating substance comes in contact with sensitive\nsurfaces, nature, or the _vis medicatrix naturae_, goes immediately to\nwork to remove the offending cause: for example, should any substance\nlodge on the mucous surface, within the nostril, although it be\nimperceptible, as often happens when the hay is musty, it abounds in\nparticles whose specific gravity enables them to float in atmospheric\nair; they are then inhaled in the act of respiration, and nature, in\norder to wash off the offending matter, sends a quantity of fluid to the\npart. The same process may be observed when a small piece of hay, or\nother foreign matter, shall have fallen into the eye: the tears then\nflow in great abundance, to prevent that delicate organ being injured.\n\"When a blister is applied to the surface, it first excites a genial\nwarmth, with inflammation of the skin; and nature, distressed, goes\ninstantly to work, separates the cuticle to form a bag, interposes serum\nbetween the nerves and the offensive matter, then prepares another\ncuticle, that, when the former, with the adhering substance, shall fall\noff, the nervous papillae may be again provided with a covering.\n\n\"The same reasoning will apply to the operation of emetics and\ncathartics; for not only is the peristaltic motion either greatly\nquickened or inverted, according to the urgency of the distress, but\nboth the mucous glands and the exhalent arteries pour forth their fluids\nin abundance to wash away the offending matter, which at one time acts\nchemically, at others mechanically.\"\n\nIf a horse, or an ox, be wounded in the foot with a nail, and a portion\nof it is broken off and remains in the wound, inflammation sets in,\nproducing suppuration, and the nail is discharged.\n\nA few days ago, we were called to see a horse, said to have swelling on\nthe _tarsus_, (hock.) On an examination, it proved to be an abscess,\nwell developed; the matter could be distinctly felt at the most\nprominent part. We should certainly have been justified (at least in the\neyes of the medical world; and then it would have looked so\n\"doctor-like\"!) in displaying a case of instruments and opening the\ntumor. If ulceration, gangrene, &c., set in and the horse ultimately\nbecame lame, no blame could be attached to us, because the practice is\n_scientific_!--recognized by the schools as good and efficient\ntreatment. What was to be done? Why, it was evident that we could not do\nbetter than to aid nature. A relaxing, anti-spasmodic poultice was\nconfined to the parts, and in six hours after, the sac discharged its\ncontents, and with it a piece of splinter two inches in length. The pain\nimmediately ceased, and the animal is now free from lameness. We here\nsee the design of nature: the consequent inflammation was to produce\nsuppuration, and make an outlet for the splinter.\n\nProfessor Kost says, \"The laws of all organic life are remarkably\npeculiar; they possess, in an eminent degree, the power of\nself-regulation. When interrupted, disease, indeed, supervenes; but\nunless the circumstances are particularly unfavorable, the physiological\nstate will soon be restored. All observation most clearly corroborates\nthis fact. The healing of wounds, restoration of fractured bones,\nexpulsion of obtruded substances, and particularly the manner in which\nextravasated matter or pus is removed from internal organs, as in case\nof abscess in the liver, in which exit may be gained by ulceration\nthrough the parietes, or by an adhesion to and ulceration into the\nintestines, or even by the adhesions to the diaphragm and lungs, in such\na manner as, by ulceration into the bronchia, a passage may be gained,\nand the pus thus removed by expectoration,--all evince a most singular\nconservative power. What is most remarkable in cases like the latter,\nis, that the adhesions are so formed as to prevent the escape of the pus\ninto the peritoneal sac, which accident must inevitably prove fatal.\n\n\"Some very interesting experiments have been performed to test the\nrestorative power of the different tissues of the animal body. If a\nportion of the intestines of a dog be taken out, and tied, so as to\nobstruct completely the passage, it will be found that the adjacent\nportions of the intestine will reunite, the ligature will separate into\nthe canal and be discharged, and the gut will heal up so as to preserve\nits normal continuity, and the animal, in a fortnight, will have\nrecovered entirely from the effects of this fearful operation.\n\n\"When noxious or poisonous substances are thrown into any of the\ncavities of the body from which their escape is impracticable, a cyst\nwill often form around them, and they thus become isolated from\nabsorption and the circulation, so as to prevent their doing harm.\n\n\"The less remarkable instances of this character are of more common\noccurrence; and the self-regulating power of the laws of life, alias\n_vis conservatrix naturae_, is so universally known and depended on, that\nit is rare, indeed, that indisposed persons take medicine, until they\nhave first waited at least a little, to see what nature would do for\nthem; and they are seldom disappointed, as it may perhaps be safely\nasserted, that nine tenths of all the attacks of disease (taking the\nslight indispositions; for such are most of them, as they are checked\nbefore they become severe) are warded off by the vital force,\nunassisted. Such, then, are the facts deduced from observing the\noperations of nature in disease _unassisted_.\"\n\nDr. Beach says, \"We are well aware, from what passes in the system\ndaily, that the Author of nature has wisely provided a principle which\nis calculated to remove disease. It is very observable in fevers. No\nsooner is noxious or morbid matter retained in the system, than there is\nan increased action of the heart and arteries, to eliminate the existing\ncause from the skin; or it may pass off by other outlets established\nfor that purpose. With what propriety, then, can this provision of\nnature be denied, as it is by some? A noted professor in Philadelphia or\nBaltimore ridicules this power in the constitution; he says to his\nclass, 'Kick nature out of doors.' It was this man, or a brother\nprofessor, who exclaimed to his class, 'Give me mercury in one hand and\nthe lancet in the other, and I am prepared to cope with disease in every\nshape and form.' I have not time to stop here, and comment upon such\npalpable and dangerous doctrine. I have only to say, let the medical\nhistorian record this sentiment, maintained in the highest medical\nuniversities in America in the nineteenth century. I am pleased,\nhowever, to observe, that all physicians do not coincide with such\nviews.\"\n\n\n\n\nPROVERBS OF THE VETERINARY REFORMERS.\n\n\nThe merciful man is merciful to his domestic animals.\n\n\"Avoid blood-letting and poisons, for they are powerful depressors of\nthe vital energies. There are two medical _fulcra_--reason and\nexperience. Experience precedes, reason follows; hence, reasoning not\nfounded on experience avails nothing. He who cures by simples need not\nseek for compounds.\"--_Villanov._\n\n\"The physician _destitute of a knowledge of plants_ can never properly\njudge of the power of a plant.\"--_Whitlaw._\n\n\"The vegetable kingdom is the most noble in medicines.\"--_Ibid._\n\n\"Innocent medicines, which approach as near to food as possible,\npreserve health, while chemical compounds destroy it. Heroic medicines\n(such are antimony, copper, corrosive sublimate, lead, opium, hellebore,\narsenic, belladonna) are like the sword in the hands of a madman.\n\n\"Nature unassisted by art sometimes effects miracles.\"--_Whitlaw._\n\n\"It is the part of a wise physician to decline prescribing in a lost\ncase.\"--_Ibid._ Whenever there is free, full circulation of blood, there\nis animal heat. If the heat of a part becomes deficient, the circulation\nis correspondingly diminished. As soon as voluntary motion in a part\nceases, so soon the circulation becomes enfeebled; and if continued, the\npart will wither and waste away.\n\nThe strength and health of an animal depend on a due share of exercise,\npure air, and suitable food. Deprive an animal of these, and he will\ncease to exist. We believe in the great doctrine that the duty of the\nphysician is to aid nature in protecting herself in the enjoyment of\nhealth, by proper attention to breeding, rearing, ventilation, and\nproper farm and stable management.\n\n\"The tinsel glitter of fine-spun theory, or favorite hypothesis, which\nprevails wherever allopathy hath been taught, so dazzles, flatters, and\ncharms human vanity and folly, that, so far from contributing to the\ncertain and speedy cure of diseases, it hath, in every age, proved the\nbane and disgrace of healing art.\"--_Graham_, p. 15.\n\n\"Those physicians generally become the most distinguished who soonest\nemancipate themselves from the tyranny of the schools of\nphysic.\"--RUSH.\n\n\"Availing ourselves of the privileges we possess, and animated by the\nnoblest impulses, let us cordially cooeperate to give to medicine a new\ndirection, and attempt those great improvements which it imperiously\ndemands.\"--_Ther._, vol. i. p. 51.\n\n\"It has been proved by allopathists themselves, that 'a physician should\nbe nature's servant;' that 'bleeding tends directly to subdue nature's\nefforts;' that 'all poisons suddenly and rapidly destroy a great\nproportion of the vitality of the system;' that whatever be the\nquantity, use, or manner of application, all the influence they\ninherently possess is injurious, and that they are not fatal in every\ninstance of their use only because nature overpowers them.\"--_Curtis._\n\n\n\n\nAN INQUIRY CONCERNING THE SOULS OF BRUTES.\n\n\n  \"Are these then made in vain? Is man alone,\n  Of all the marvels of creative love,\n  Blest with a scintillation of His essence--\n  The heavenly spark of reasonable soul?\n  And hath not yon sagacious dog, that finds\n  A meaning in the shepherd's idiot face;\n  Or the huge elephant, that lends his strength\n  To drag the stranded galley to the shore,\n  And strives with emulative pride t' excel\n  The mindless crowd of slaves that toil beside him;\n  Or the young generous war-horse, when he sniffs\n  The distant field of blood, and quick and shrill\n  Neighing for joy, instils a desperate courage\n  Into the veteran trooper's quailing heart,--\n  Have they not all an evidence of soul,\n  (Of soul, the proper attribute of man,)\n  The same in kind, though meaner in degree?\n  Why should not that which hath been--be forever?\n  And death, O, can it be annihilation?\n  No,--though the stolid atheist fondly clings\n  To that last hope, how kindred to despair!\n  No,--'tis the struggling spirit's hour of joy,\n  The glad emancipation of the soul,\n  The moment when the cumbrous fetters drop,\n  And the bright spirit wings its way to heaven!\n\n  \"To say that God annihilated aught,\n  Were to declare that in an unwise hour\n  He planned and made somewhat superfluous.\n  Why should not the mysterious life that dwells\n  In reptiles as in man, and shows itself\n  In memory, gratitude, love, hate, and pride,\n  Still energize, and be, though death may crush\n  Yon frugal ant or thoughtless butterfly,\n  Or, with the simoom's pestilential gale\n  Strike down the patient camel in the desert?\n\n  \"There is one chain of intellectual soul,\n  In many links and various grades, throughout\n  The scale of nature; from the climax bright,\n  The first great Cause of all, Spirit supreme,\n  Incomprehensible, and unconfined,\n  To high archangels blazing near the throne,\n  Seraphim, cherubim, virtues, aids, and powers,\n  All capable of perfection in their kind;--\n  To man, as holy from his Maker's hand\n  He stood in possible excellence complete,\n  (Man, who is destined now to brighter glories,--\n  As nearer to the present God, in One\n  His Lord and Substitute,--than angels reach;)\n  Then man has fallen, with every varied shade\n  Of character and capability,\n  From him who reads his title to the skies,\n  Or grasps, with giant-mind, all nature's wonders,\n  Down to the monster-shaped, inhuman form,\n  Murderer, slavering fool, or blood-stained savage;\n  Then to the prudent elephant, the dog\n  Half-humanized, the docile Arab horse,\n  The social beaver, and contriving fox,\n  The parrot, quick in pertinent reply,\n  The kind-affectioned seal, and patriot bee,\n  The merchant-storing ant, and wintering swallow,\n  With all those other palpable emanations\n  And energies of one Eternal Mind\n  Pervading and instructing all that live,\n  Down to the sentient grass and shrinking clay.\n  In truth, I see not why the breath of life,\n  Thus omnipresent, and upholding all,\n  Should not return to Him and be immortal,\n  (I dare not say the same,) in some glad state\n  Originally destined for creation,\n  As well from brutish bodies, as from man.\n  The uncertain glimmer of analogy\n  Suggests the thought, and reason's shrewder guess;\n  Yet revelation whispers nought but this,--\n  'Our Father careth when a sparrow dies,'\n  And that 'the spirit of a brute descends,'\n  As to some secret and preserving Hades.\n\n  \"But for some better life, in what strange sort\n  Were justice, mixed with mercy, dealt to these?\n  Innocent slaves of sordid, guilty man,\n  Poor unthanked drudges, toiling to his will,\n  Pampered in youth, and haply starved in age,\n  Obedient, faithful, gentle, though the spur,\n  Wantonly cruel, or unsparing thong,\n  Weal your galled hides, or your strained sinews crack\n  Beneath the crushing load,--what recompense\n  Can He who gave you being render you,\n  If in the rank, full harvest of your griefs\n  Ye sink annihilated, to the shame\n  Of government unequal?--In that day\n  When crime is sentenced, shall the cruel heart\n  Boast uncondemned, because no tortured brute\n  Stands there accusing? Shall the embodied deeds\n  Of man not follow him, nor the rescued fly\n  Bear its kind witness to the saving hand?\n  Shall the mild Brahmin stand in equal sin\n  Regarding nature's menials, with the wretch\n  Who flays the moaning Abyssinian ox,\n  Or roasts the living bird, or flogs to death\n  The famishing pointer?--and must these again,\n  These poor, unguilty, uncomplaining victims,\n  Have no reward for life with its sharp pains?--\n  They have my suffrage: Nineveh was spared,\n  Though Jonah prophesied its doom, for sake\n  Of sixscore thousand infants, and 'much cattle;'\n  And space is wide enough for every grain\n  Of the broad sands that curb our swelling seas,\n  Each separate in its sphere to stand apart\n  As far as sun from sun; there lacks not room,\n  Nor time, nor care, where all is infinite.\"--_Tupper._\n\n\n\n\nTHE REFORMED PRACTICE.\n\nSYNOPTICAL VIEW OF THE PROMINENT SYSTEMS OF MEDICINE.\n\n\nSome of our readers, especially the non-medical, may desire to know what\nthe following remarks, which appear to apply generally to the human\nfamily, have to do with cattle doctoring. We answer them in the language\nof Professor Percival. \"The object of the veterinary art is not only\ncongenial with human medicine, but the very same paths which lead to a\nknowledge of the diseases of man, lead also to a knowledge of those of\nbrutes. An accurate examination of the interior parts of their bodies; a\nstudious survey of the arrangement, structure, use, connection, and\nrelation of these parts, and of the laws by which they act; as also of\nthe nature and properties of the various food and other agents which the\nearth so liberally provides for their support and cure,--these form, in\na great measure, the sound and sure foundation of all medical science,\nwhatever living individual animal be the subject of our consideration.\nWhether we prescribe for a man, horse, dog, or cat, the laws of the\nanimal economy are the same; and one system, and that based upon\nestablished facts, is to guide our practice in all.\n\n\"The theory of medicine in the human subject is the theory of medicine\nin the brute; it is the application of that theory--the practice\nalone--that is different.\n\n\"We might as well, in reference to the principles of each, attempt to\nseparate surgery from medicine, as insist that either of these arts, in\ntheory, is essentially different from the veterinary: every day's\nexperience serves to confirm this our belief, and in showing us how\noften the diseases of animals arise from the same causes as those of a\nman, exhibit the same indications, and require a similar method of cure.\n\n\"The science of medicine, like others, consists of a collection of facts\nof a common and not a specific character. These, therefore, admit of\narrangement into different systems, according to the notions of\ntheorists, and the various species of philosophy, brought to bear on the\nsubject.\n\n\"The first regular system was founded by Hippocrates, about three\nhundred and eighty years before Christ. It was founded upon _theory_,\nand comprised the doctrines of the ancient dogmatic school. Its\npathology rested upon a supposed change of the humors of the body,\nparticularly the blood and bile; and here are the first elements of the\n'_humoral pathology_.' Its remedial intentions were founded upon the\nexistence of the _'vis conservatrix' et 'medicatrix naturae;'_ and,\nalthough often maintaining direct antipathic principles of action, it\nrested mainly on physo-dynamic influence for the accomplishment of its\ntherapeutic purposes.\n\n\"About two hundred and ninety years before Christ, Philinus of Cos\nintroduced the ancient _Empiric System_, which was founded upon\n_experience_ and _observation_. About one hundred years before the\nChristian era, the _Methodic System_ was introduced by Asclepiades of\nBithynia. This system was got up with an avowed opposition to that of\nHippocrates, which was called 'a study of death.' Themison of Laodicea,\npupil of Asclepiades, gives an exposition of the fundamental principles\nof the methodic system; and it seems that all physiological and\npathological action was considered to be dependent upon the _strictum_\nand _laxum_ of the organic pores, or increased and decreased secretion,\nand that all medicines act only on two principles, _i. e._, by inducing\ncontraction and relaxation, or an increase and decrease of the\nsecretions.\n\n\"It would seem that, in the first century of the Christian era, the\nmethodic system was divided into various subordinate ones--the\n_Pneumatic_, _Episynthetic_, and _Eclectic_. The pneumatic system, which\nwas the most popular of the fragments of the methodic, was most indebted\nto Athenaeus of Attalia for its successful introduction. This system\ncontemplated the doctrine of the Stoics, which recognized the existence\nof a spirit governing and directing every thing, and which, when\noffended, would produce disease; hence the name _pneumatic_. The\nindications of cure were more _moral_ than _physical_. Fire, air, water,\n&c., were not considered elements, but their properties--heat, cold,\ndryness, moisture, &c.--were alone entitled to the name.\n\n\"In the second century, the _Galenic System_ was founded by Claudius\nGalenus. This might, indeed, only be considered the revival of the\ndogmatic or Hippocratean system. Galen professed to have selected what\nhe found valuable from all the prevailing systems, and has embraced the\nelements and ruling spirit of the pneumatic school. Thus he explained\nthe operation of medicines by reference to their elementary\nqualities,--that is, heat, cold, dryness, and moisture,--of each of\nwhich he admitted four degrees. But he was governed by a prevailing\npartiality for the system of Hippocrates, which, he states, was either\nmisunderstood or misrepresented by all theorists, ever since the\nestablishment of the empiric and methodic schools. He devoted most of\nhis time to commenting upon and embellishing it, and thus again\nestablished a system, founded on reason, observation, and sound\ninduction, which maintained its character, without a rival, for more\nthan one thousand five hundred years.\n\n\"Near the middle of the sixteenth century, Paracelsus introduced the\n_Chemical System_. This was strongly opposed by Bellonius and Riverius,\nwho maintained the doctrine of Hippocrates and Galen. But the\npresumptuous Paracelsus burned, 'in solemn state,' the works of the\nancients; and being succeeded by the indefatigable Van Helmont, the\nwhole science of medicine was overwhelmed by the mysticism of the\nalchemical doctrines and languages. The chemical theory, in the main,\nrejects the influence, or even the existence, of the _vis medicatrix\nnaturae_, and explains all physiological, pathological, and therapeutic\noperations upon abstract chemical laws. Thus chemical or inorganic\nagents, and many of the most virulent poisons, as arsenic, mercury,\nantimony, &c., were placed among the most prominent remedies.\n\n\"Soon after the introduction of the chemical system, medical science, if\nwe make one exception, became less eccentric, but much less marked for\nthe permanency of its systems. Boerhaave ingeniously blended most of the\nprominent doctrines of the Galenic and chemical systems; and by an\napplication of several of the newly-developed natural sciences,\nespecially mathematics and natural philosophy, he led his successors\ninto a more even path and fixed method of investigation; for no more do\nwe find any abstract physical laws the sole basis of a system. But these\nwere the highest honors allowed Boerhaave; his particular system was\nsoon subverted by Stahl, who proved the supreme superintendence of an\nimmaterial, vital principle, corresponding to that pointed out by\nHippocrates. To this he ascribes intelligence, if not moral attributes.\nHoffman led Cullen into the path that brought him into the fruitful\nfield of _nervous pathology_ and solidism, which, with a modification of\nStahl's ruling _immaterial essence_, formed the groundwork of his\nadmired system.\n\n\"If, now, we except the eccentricities of Brown, comprising his system,\nfounded on the _sthenic_ and _asthenic_ diathesis, we find little\ninterruption to the general prevalence of the Cullenian system, till\nnearly the present juncture. The succeeding authors, colleges, and\nmedical societies have only modified and amplified the general theory,\nand regulated the practice into a comparative uniformity, which now\nconstitutes the popular _Allopathic System_. But notwithstanding the\ncomparatively settled state of medical science, it could not be supposed\nthat in this remarkable age of improvement, while all other liberal\nsciences and arts are progressing as if prosecuted by superhuman agency,\nmedicine should fail to undergo corresponding improvement.\n\n\"Several new systems of medicine date themselves within the last forty\nyears, viz.: 1. The _Homaeopathic_, introduced by Hahnemann, and founded\nupon the principle, _similia similibus curantur_. 2. The _Botanic_,\nestablished by a new class of medical philosophers, within the last\ntwenty years. 3. The _Eclectic_, corresponding, in its essential\ndoctrines, with the ancient eclectic system.\"\n\n\n\n\nCREED OF THE REFORMERS.\n\n\nWe believe that a perfect system of medical science is that which never\nallows disease to exist at all; which prevents disease, instead of\ncuring it, by means of a perfect hygienic system, proper modes of life,\nattention to diet, ventilation, and exercise.\n\nWe believe that the next best system is that which, after disease has\nmade its appearance, promptly meets its development by the use of such\nagencies as are perfectly in harmony with the laws of life and health,\nand physiological in their action; such, for example, as water, air,\nheat and cold, friction, food, drink, and medicines that are not usually\nregarded as poisons, and are known to prove congenial to the animal\nconstitution.\n\nWe have no attachment to any remedy which experience shows unsafe; but,\non the contrary, we rejoice in the success of every attempt to\nsubstitute sanative for disease-creating agents, and believe that a\nnumber of the articles which are still occasionally used in the old\nschool, will in time become obsolete, as medical science progresses.\n\nWe hold that our opposition to any course of medical treatment should be\nin proportion to the mischief it produces, entirely irrespective of\nmedical theories. Hence our hostility to the lancet.\n\nWe do not profess to know more about anatomy, physiology, surgery, &c.,\nthan our allopathic brethren; but the superiority which our system\nclaims over others is, in the main, to be found in our therapeutic\nagents, all of which are harmless, safe, and efficient. While they\narouse the energies of nature to resist the ravages of disease, they act\nharmoniously with the vital principle, in the restoration of the system\nfrom a pathological to the physiological state.\n\n\n\n\nTRUE PRINCIPLES.\n\n\n\"Our objection to the old school,\" says Professor Curtis, \"has ever\nbeen, that they not only have no true principles to guide their\npractice, but they have adopted, fixed, and obstinately adhered to\nprinciples the very reverse of the true. They have resolved that, in\ndisease, nature turns a somerset--reverses all her normal laws, and\nrequires them to do the same. They have decreed that the best means and\nprocesses to cure the sick are those which will most speedily kill them\nwhen in health. In the face of all reason and common sense, they have\nadhered to this doctrine and practice for the last three centuries, and\nthey have been constrained to confess that the destruction they have\nproduced on human life and health has far exceeded all that has been\neffected by the sword, pestilence, and famine. Still they obstinately\npersevere. They say their science is progressive--improving; yet its\nprogression consists in contriving new ways and means to take part of\nthe life's blood, and poison all the balance.\n\n\"Medicine, being based on the laws of nature, is in itself an exact\nscience; and every process of the act should be directed by those laws.\n\n\"Medicine is a demonstrative science, and all its processes should be\nbased on fixed laws, and be governed by positive inductions. Then, and\nnot till then, will it deserve to be ranked among the exact sciences,\nand contemplated as a liberal art.\n\n\"Truth is stationary; it never progresses. What was true in principle in\nthe days of Adam is so still. To talk of progress in principle is\nridiculous. Neither does a given practice progress. That which was ever\nintrinsically good is so still. To talk, then, of the progress in\nprinciples of medicine is absurd. We may learn the truth or error of\nprinciples, and the comparative value or worthlessness of practices; but\nthe principles are still the same. This is our progress in knowledge,\nnot the progress of science or art. The constant changes that have taken\nplace in the adoption and rejection of various principles and practices\nhave ever been an injury to the healing art. Both truth and falsehood,\nseparately and combined, have been alternately received and rejected;\nand this is that progress which is made in a circle, and not in lines\ndirect. The fault of the cultivators of medicine has been, not that they\nnever discovered the truth nor adopted the right practice, but that they\nadopted wrong principles and practices as often as the right, and\nrejected the right as readily as the wrong. They have ever been ready to\nprove many, if not all things; but to cast off the bad and hold fast to\nthe good, they seem to have had but little discrimination and power.\nThey say truly, that the object of the healing art is to aid nature in\nthe prevention and cure of her diseases; yet, in practice, they do\nviolence to nature in the use of the lancet and poison.\"\n\nWe are told by the professors of allopathy that their medicines\nconstitute a class of deadly poisons, (see \"Pocket Pharmacopoeia;\")\n\"that, when given with a scientific hand, in small doses, they cure\ndisease.\" We deny their power to cure. If antimony, corrosive sublimate,\n&c., ever proved destructive, they always possess that power, and can\nnever be used with any degree of assurance that they will make a sick\nanimal well. On the other hand, we have abundant every-day evidence of\ntheir ability to make a well animal sick at any time. What difference\ndoes it make whether poisons are given with a scientific or an\nunscientific hand? Does it alter the tendency which all poisons possess,\nnamely, that of rapidly depriving the system of vitality?\n\nThe veterinary science was ushered into existence by men who practised\naccording to the doctrines of the theoretical schools. We may trace it\nin its infancy when, in England, in the year 1788, it was rocked in the\ncradle of allopathy by Sainbel, its texture varying to suit the skill of\nClark, Lawrence, Field, Blaine, and Coleman; yet with all their amount\nof talent and wisdom, their pupils must acknowledge that the melancholy\ntriumph of disease over its victims clearly evinces that their combined\nstock of knowledge is insufficient to perfect the veterinary science.\nDr. J. Bell says, \"Anatomy is the basis of medical skill;\" yet, in\nanother part of his work he says, \"It enables the physician to\nGUESS _at the seat, or causes, or consequences of disease_!\"\nThis is what we propose hereafter to call the science--the science of\nguessing! If such is the immense mortality in England, (amounting, as\nMr. Youatt states, in loss of cattle, alone, to $50,000,000,)--a country\nthat boasts of her veterinary institutions, and embraces within her\nmedical halo some of the brightest luminaries of the present\ncentury,--what, we ask, is the mortality in the United States, where the\nveterinary science scarcely has an existence, and where not one man in a\nhundred can tell a disease of the bowels from one of the lungs?\nProfiting by the experience of these men, we are in hopes to build up a\nsystem of practice that will stand a tower of strength amid the rude\nshock of medical theories. We have discovered that the lancet is a\npowerful depressor of vitality, and that poisons derange, instead of\nproducing, healthy action. That they are generally resorted to in this\ncountry, no one will deny, and often by men who are unacquainted with\nthe nature of the destructive agents they making use of.\n\nHence our business, as reformers, is to expose error, and disseminate\ntrue principles. In doing so, we must be guided by the light of reason,\nand interpret aright the doctrines of nature as they are written by the\nCreator on the tablets of the whole universe, animate and inanimate.\n\nIn our reformed practice, we have true principles to guide us, which no\nman can controvert; for they are based on the recognition of a curative\npower in nature, identical with the vital principle, and governed by the\nsame laws that control its action in the healthy state. While,\ntherefore, this system must not change, it may improve; and while it\nremains on the same foundation, it should progress.\n\nThe necessity of aiding nature, in all our modes of medication, is the\nonly true principle which should guide us. This we do by the aid of\nmedicines known to be harmless, at the same time paying proper attention\nto diet, ventilation, exercise, &c., rejecting all processes of cure\nthat depress the vital energy, or destroy the equilibrium of its action.\n\nOur reformed principles teach us that, \"Fever is the same in its\nessential character, under all circumstances and forms which it\nexhibits. The different kinds, as they are called, are but varieties of\nthe same condition, produced by variations in the prevailing cause, or\nthe strength of vital resistance, or some other peculiarity of the\npatient. Facts in abundance might be stated to justify this position.\nAgain, fever is not to be regarded as disease, but as a sanative effort;\nin other words, as an increased or excited state of vital action, whose\ntendency is to remove from the system any agents or causes that would\neffect its integrity. Or, perhaps, it might be more properly said, that\nfever is the effect, or symptom, of accumulated vital action--an index\npointing to the progress of causes, operating to ward off disease and\nrestore health.\n\n\"Our indications of cure and modes of treatment are to be learned from\nthose manifestations of the vital operations uniformly witnessed in the\nfebrile state. If fever marks the action of the healing power of nature,\nwhich we must copy to be successful, why should we not consult the\nfebrile phenomena for our rule of action? Now, what are the indications\nof cure which we derive from this source? In other words, what are the\nresults which nature designs to accomplish through the instrumentality\nof fever? They are, an equilibrium of the circulation, a\nproperly-proportioned action of all the organs, and an increased\ndepuration of the system, principally by cutaneous evacuations.\"\n\nSuppose the resistance of some local obstruction, as, for example, an\naccumulation of partly digested food in the manyplus of the ox, and, for\nwant of a due portion of the gastric fluids to soften the mass and\nprevent friction, it irritates the mucous covering of the laminae. The\nresult is inflammation, (local fever,) then general excitement,\nmanifested in an increased state of the circulation generally. The\nconsequences of this general excitement of the mass of the circulation\nare, a more equal distribution of the blood, and the stimulation of\nevery organ to do a part, according to its capacity, in removing\ndisease. In such cases, the cattle doctors, generally, suppose that the\ninflammation is confined to the part, (manyplus;) yet it is evident that\nnature has marshalled her forces and produced a like action on the\nexternal surface. How can we prove that this is the case? By the heat,\nand red surfaces of the membrane lining the nostril, by the accelerated\npulse, thirst, &c. Without heat there is no vitality in the system. Now,\nif the surface be hot, it proves that a large quantity of blood is sent\nthere for the purpose of relieving the deranged internal organ. Hence\nthe reader will perceive, that the cattle doctor whose creed is, \"The\nmore fever, the more blood-letting,\" must be one of the greatest\nopponents nature has to deal with. Then it is no wonder that so many\ncattle, sheep, and oxen die of fever. The practice of purging, in such a\ncase, would be almost as destructive as the former; for many articles\nused as purges act on the mucous surfaces of the alimentary canal as\nmechanical irritants. Nature would, in this case, have to recall her\nforces from the surface, and concentrate them in the vicinity of parts\nwhere they were not wanted, had not man's interference conflicted with\nher well-planned arrangement, and made her \"turn a somerset.\" When the\nincreased action and heat are manifested on the surface, does it not\nprove that the different organs are acting harmoniously in self-defence?\nAnd is not this action manifested through the same channels in a state\nof health? Then why call it _disease_?\n\nIf obstructions exist as the cause of fever, will the mode of evacuation\nbe different from that of health? Certainly not. Hence the marked\ntendency of fever to evacuation by the skin or the bowels; the former by\nperspiration, and the latter by diarrhoea. Fever, then, is a vital\naction, and the reformers have correct principles. On the other hand,\nthe allopathists tell us that they know very little about fever, but\nthat it is disease, and they treat it as such; hence, then, five, ten,\nand fourteen days' fever, and often the death of the patient.\n\nOur treatment is not directed with a view of combating the fever: we\ngenerally aid it by following the indications which it presents; and we\noften find it necessary, although the surface of the animal shall be\nhot, and feverish symptoms appear, to use stimulants, (not alcoholic,)\ncombined with antispasmodics and relaxants. (See _Stimulants_, in the\nAPPENDIX.) This class of medicines, aided by warmth and\nmoisture, favors the cutaneous exhalation, and promotes the free and\nfull play of all the functions.\n\nThat the allopathist has but few principles to guide him is evident from\nthe following quotations:--\n\nVeterinary surgeon Haycock says, \"The profession may flatter itself that\nit is advancing: for my part, however, I see little or no advancement.\nOur labors, for the last ten years, have been little more than a\nrepetition of what has gone before. Our books are things of shreds and\npatches; the system which is followed in the investigation of disease,\nin the treatment of disease, and in the reporting of it, is altogether\nso crude and barbarous, that I am thoroughly ashamed of the whole\nmatter.\n\n\"I have heard much noise about a _charter_, [which, we presume, means a\ncharter by which men may be licensed to kill _secundum artem_, and '_no\nquestions_ ASKED,'] the clamor of which may be compared to the\nrattling of peas in a dried bladder, or to a storm in a horse-pond. I\nhave also read much which has been said about the _spirit_ of this\ncharter. Until I am convinced that it is the best term which can be\napplied to it, verily the whole is a spirit; for no one, I am persuaded,\nhas ever yet discovered the substance.[3] It is not charters that we\nwant, _but it is that quiet spirit of earnestness which characterizes\nthe true laborer on science_. We require men who will labor for the\nadvancement of the profession from the pure love of the thing; we want,\nin fact, a few John Fields, or men who know how to work, and who are\npossessed of the will to do it.\"\n\nWe hear a great deal said about sending young men from this country to\nEurope to acquire the principles of the veterinary art, with a view to\npublic teaching. Now, it appears to us that the United States can boast\nof as great a number of talented physicians, as well qualified to soon\nlearn and understand the fundamental principles of the veterinary art,\nas their brethren of the old world. There is no country, probably, that\ncan boast of such an amount of talent, in every department of\nliterature and art, in proportion to the population, as the United\nStates. We know that the veterinary art, with one exception, had its\nexistence from human practitioners, received their fostering care and\nattention, and grew with their growth. Have we not the materials, then,\nin this country, to educate and qualify young men to practise this\nimportant branch of science? Most certainly. Just send a few to us, for\nexample, and if we do not impart to them a better system of medication\nthan that practised in Europe, by which they will be enabled to treat\ndisease with more success and less deaths, then we will agree to \"throw\nphysic to the dogs,\" and abandon our profession.\n\nThe greatest part of the most valuable time of the students of\nveterinary medicine is devoted to the study of pathology, in such a\nmanner as to afford little instruction. For example, we are told that in\n\"Bright's\" disease of the kidneys they have detected albumen. What does\nthis amount to? Does it throw any rational light on the treatment other\nthan that proposed by us, of toning up the animal, and restoring the\nhealthy secretions? They have studied pathology to their hearts'\ncontent; yet any intelligent farmer in this country, with a few simple\nherbs, can beat them at curing disease. We would give details, were it\nnecessary. Suffice it to say, that it is done here every day, and often\nthrough the aid of a little thoroughwort tea, or other harmless agent.\nThe pathologist may discover alterations in tissues, in the blood, and\nthe various organs, and tell us that herein lie the cause and seat of\ndisease; yet these changes themselves are but results, and preceding\nthese were other manifestations of disorder; therefore pathology must\nalways be imperfect, because it is a science of consequences.\n\nThe most powerful microscopes have been used to discover the seat of\ndisease; yet this has not taught us to cure one single disease hitherto\nincurable.\n\nThe old school boast that their whole system of blood-letting, purging,\nand poisoning is based on _enlightened experience_! yet their victims\nhave often discovered, by dear-bought \"experience,\" (_many of whom are\nnow doing penance with ulcerated gums, rotten teeth, and foetid breath_,)\nthat, however valuable this \"experience\" may be to the M. D.'s, they,\nthe recipients, have not derived that benefit which they were led to\nexpect would accrue to them. From what has already been written in this\nwork, the reader, provided he divests himself of all prejudice, will\nperceive that allopathic experience is not to be trusted, for their\nprinciples are false; hence their experience is also false. Professor\nCurtis, to whom we are indebted for much valuable information, says, \"Do\nnot the old school argue that the most destructive agents in nature may\nbe made to '_aid the vital forces in the removal of disease_ by the\njudicious application of them'? Does not Professor Harrison say, that\nthe lancet is the great anti-inflammatory agent of the _materia medica_,\nthat opium is the _magnum Dei donum_ (the great gift of God) for the\nrelief of pain, and that mercury is the great regulator of all the\nsecretions?\"\n\nAnatomy and physiology are now being taught in our public schools. The\npeople will, ere long, constitute themselves umpires to decide when\ndoctors disagree. We apprehend it will then be hard work to convince the\nintelligent and thinking part of the community that poisons and the\nlancet are sanative agents.\n\nFOOTNOTE:\n\n[3] Mr. White says, \"According to the present system of teaching in\nthese chartered institutions, there is very little benefit to be derived\nby the student.\"\n\nMr. Blane experienced in his own person the results of this imperfect\nsystem of teaching. He was sent for to fire a valuable horse, and gives\nthe following account of it: \"It was my first essay in firing on my own\naccount, and _fired_ as I was with my wishes to signalize myself, I\nlabored to enter my novitiate with all due honor. The farrier of the\nvillage was ordered to attend, a sturdy old man, civil enough, but\nlooking as though impressed with no very high respect for a _gentleman\nfarrier's knowledge_. The horse was cast, awkwardly enough, and secured,\nas will appear, even more so. I, however, proceeded to show the\nsuperiority of the new over the old schools. I had just then left the\nveterinary college, not as a pupil, but as a teacher, which I only\nmention to mark the climax. On the very first application of the iron,\nup started my patient, flinging me and my assistants in all directions\nfrom him, while he trotted and snorted round the yard with rope, &c. at\nhis heels. As may be supposed, I was taken aback, and might have gone\nback as I came, had not the old farrier, with much good humor, caught\nthe horse round the neck with his arms, and by some dexterous manoeuvre\nbrought him on his knees; when, with a jerk, as quick as unexpected, he\nthrew him at once on his side, when our immediate assistants fixed him,\nand we proceeded. It is needless to remark that I retired mortified, and\nleft the village farrier lord of the ascendant.\"\n\n\"It cannot be doubted that the best operators in this case are always\nthe common country farriers, who, from devoting themselves entirely to\nthe occupation, soon become proficient.\"\n\nThis admission on the part of a regular graduate of a veterinary\ninstitution of London shows that the veterinary science, as taught at\nthe present day, is a matter for reproach. The melancholy triumph of\ndisease over its victims shows that the science is mere moonshine; that,\nin regard to its most important object, the _cure of disease_, it is\nmere speculation, rich in theory, but poverty-stricken in its results.\nHence we have not only proof that the American people will be immense\ngainers by availing themselves of the labors of reforms, but, as\ninterested individuals, they have great encouragement to favor our more\nrational system of treatment. (For additional remarks on this subject,\nsee the author's work on the Horse, p. 105.)\n\n\n\n\nINFLAMMATION.\n\n\nInflammation has generally been considered the great bugbear of the old\nschool, and the scarecrow of the cattle doctor. But what do they know\nabout it? Let us see.\n\nDr. Thatcher says, \"Numerous hypotheses or opinions respecting the true\nnature and cause of inflammation have for ages been advanced, and for a\ntime sustained; but even at the present day, the various doctrines\nappear to be considered altogether problematical.\"\n\nProfessor Percival says, \"Inflammation consists in an increased action\nof the arteries, and may be either _healthy_ or _unhealthy_[4]--a\ndistinction that appears to relate to some peculiarity of the\nconstitution.\"\n\nWe find inflammation described by most old school authors as disease,\nand they treat it as such. Professor Payne says, \"A great majority of\nall the disorders to which the human frame is liable begin with\ninflammation, or end in inflammation, or are accompanied by inflammation\nin some part of their course, or resemble inflammation in their\nsymptoms. Most of the organic changes in different parts of the body\nrecognize inflammation as their cause, or lead to it as their effect. In\nshort, a very large share of the premature extinctions of human life in\ngeneral is more of less attributable to inflammation.\"\n\nThe term _inflammation_ has long been employed by medical men to denote\nthe existence of an unusual degree of redness, pain, heat, and swelling\nin any of the textures or organs of which the body is composed.\nProfessor Curtis says, \"But as inflammation sometimes exists without the\nexhibition of any of these symptoms, authors have been obliged to\ndescribe it by its causes, in attendant symptoms, and its effects. It is\nnot more strange than true, that, after studying this subject for, _as\nthey say_, four thousand years, experimenting on it and with it, and\ndefining it, the sum of all their knowledge and definitions is\nthis--inflammation in the animal frame is either a simple or compound\naction, increased or diminished, or a cessation of all action; it either\ncauses, or is caused, or is accompanied, by all the forms of disease to\nwhich the body is subject; it is the only agent of cure in every case in\nwhich a cure is effected; it destroys all that die, except by accident\nor old age; it is both disease itself, and the only antidote to disease;\nit is the pathological principle which lies at the base of all others;\nit is that which the profession least of all understand.\"\n\nWho believes, then, that the science of medicine is based on a sure\nfoundation?\n\nThe following selections from the allopathic works will prove what is\nabove stated.\n\n\"Pure inflammation is rather an effort of nature than a disease; yet it\nalways implies disease or disturbance, inasmuch as there must be a\nprevious morbid or disturbed state to make such an effort\nnecessary.\"--_Hunter_, vol. iv. pp. 293, 294.\n\n\"As inflammation is an action produced for the restoration of the most\nsimple injury in sound parts which goes beyond the power of union by the\nfirst intention, we must look upon it as one of the most simple\noperations in nature, whatever it may be when arising from disease, or\ndiseased parts. Inflammation is to be considered only a disturbed state\nof parts, which requires a new but salutary mode of action to restore\nthem to that state wherein a natural mode of action alone is necessary.\nTherefore inflammation in itself is not to be considered a disease, but\na salutary operation consequent either to some violence or to some\ndisease.\"--_Ibid._ vol. iv. p. 285.\n\n\"A wound or bruise cannot recover itself but by inflammation_.\"--Ibid._\np. 286.\n\n\"From whatever cause inflammation arises, it appears to be nearly the\nsame in all; for in all it is an effort intended to bring about a\nreinstatement of the parts to their natural function.\"--_Ibid._ p. 286.\n\n_Results of Inflammation._--\"Inflammation is said to terminate in\nresolution, effusion, adhesion, suppuration, ulceration, granulation,\ncicatrization, and mortification. All these different terminations,\nexcept the last, may be regarded as so many _vital_ processes, exerted\nin different parts of the animal economy.\"--_Prof. Thompson_, p. 97.\n\n\"Inflammation must needs occupy a large share of attention of both the\nphysician and the surgeon. In nine cases out of ten, the first question\nwhich either of them asks himself, on being summoned to the patient, is,\n_Have I to deal with inflammation here?_ It is constantly the object of\nhis treatment and watchful care. It affects all parts that are furnished\nwith blood-vessels, and it affects different parts very variously.... It\nis by inflammation that wounds are closed and fractures repaired--that\nparts adhere together when their adhesion is essential to the\npreservation of the individual, and that foreign and hurtful matters are\nconveyed out of the body. A cut finger, a deep sabre wound, alike\nrequire inflammation to reunite the divided parts. Does ulceration occur\nin the stomach or intestines, and threaten to penetrate through\nthem--inflammation will often forerun and provide against the\ndanger--glue the threatened membrane to whatever surface may be next\nit.... The foot mortifies, is killed by injury or by exposure to\ncold--inflammation will cut off the dead and useless part. An abscess\nforms in the liver, or a large calculus concretes in the gall-bladder:\nhow is the pus or the calculus to be got rid of?... Partial inflammation\nprecedes and prepares for the expulsion; the liver or the gall-bladder\nbecomes adherent to the walls of the abdomen on the one hand, or to the\nintestinal canal on the other; and then the surgeon may plunge his\nlancet into the collection of pus, or the abscess; or the calculus may\ncut its own way safely out of the body, through the skin or into the\nbowels.\"--_Watson_, p. 94.\n\n\"The salutary acts of restoration and prevention just adverted to, are\nsuch as nature conducts and originates. But we are ourselves able, in\nmany instances, to direct and control the effect of inflammation--nay,\nwe can excite it at our pleasure; and, having excited it, we are able,\nin a great degree, to regulate its course. And for this reason it\nbecomes, in skilful hands, an instrument of cure.\"--_Ibid._ p. 94.\n\nThe above quotations are not complete. They are selections from the\nsources whence they are drawn of those portions which testify that fever\nand inflammation are one and the same thing, and that this same thing\nconsists in a salutary effort of nature to protect the organs of the\nbody from the action of the causes of disease, or to remove those causes\nand their effects from the organs once diseased. That the same authors\nteach the very contrary of all this in the same paragraphs, and often in\nthe same sentences, the following extracts will clearly prove:--\n\n_Inflammation produces disease._--\"When inflammation cannot accomplish\nthat salutary purpose, (a cure,) as in cancer, scrofula, &c., it does\nmischief.\"--_Hunter_, p. 285.\n\n\"Inflammation is occasionally the cause of disease.\"--_Ibid._ p. 286.\n\n\"In one point of view, it may be considered as a disease\nitself.\"--_Ibid._\n\n\"It may be divided into two kinds, the healthy and the unhealthy.... The\nunhealthy admits of a vast variety,\" &c.--_Ibid._\n\n\"Inflammation often produces mortification or death in the inflamed\npart.\"--_Ibid._ vol. iv. p. 305.\n\n\"In the light of such authorities, it is surely not strange that no\ndefinite knowledge can be obtained of the nature, character, or tendency\nof inflammation. Of course, no one will dispute the proposition, that\nmedicine, as taught in the schools, is a superstructure without a\nfoundation, and should be wholly rejected.\"--_Prof. Curtis._\n\nIf the regulars have no correct theory of inflammation, then their\nsystem of blood-letting is all wrong. This they acknowledge; for many\nwith whom we have lately conversed say, \"We do not use the lancet so\noften as formerly.\" One very good reason is, the sovereign people will\nnot let them. Would it not be better for them to abolish its use\naltogether, as we have done, and avail themselves of the reform of the\nage?\n\nThe following remarks, selected from an address delivered by our\nrespected preceptor, Professor Brown, ought to be read by every friend\nof humanity.\n\n\"The very air groans with the bitter anathemas the people pronounce upon\ncalomel, antimony, copper, zinc, arsenic, arsenious acid, stramonium,\nfoxglove, belladonna, henbane, nux vomica, opium, morphia, and\nnarcotin.\n\n\"Hear their bitter cries, borne on every breeze, 'Help! help! help!' See\nthe dim taper of life; it glimmers--'tis gone! Vitality struggled, and\nstruggled manfully to the last. The poisonous dose was repeated, till\nthe citadel was yielded up.\n\n\"The doctor arrives and attempts to comfort and quiet the broken-hearted\nwidow, and helpless, dependent, fatherless children, by recounting the\nfrailties of poor human nature, and reminding them of the fact that all\nmen must die.\n\n\"And thus the work of death goes on: the tenderest ties are severed;\nchildren are left fatherless; parents are bereaved of their children;\nfamilies are reduced to fragments; society deprived of her best\ncitizens, and the world filled with misery, confusion, and poverty, in\nconsequence of an evil system of medication....\n\n\"The ball is in motion, the banner of medical reform waves gracefully\nover our beloved country. Hosts of the right stripe are coming to the\nrescue. Poisons are condemned, the lancet is growing dull, the effusion\nof blood will soon cease, the battles are half fought, and the victory\nis sure.... While we would have you adhere to the well-established,\nfundamental principles of reformed medical science, as taught in this\nschool, we would have you recollect that discoveries in knowledge are\nprogressing.... Never entertain the foolish, absurd, and dangerous idea,\nthat because you have been to college, you have learned all that is to\nbe learned--that your education is finished, and you have nothing more\nto learn. The college is a place where we go to learn how to learn, and\nthe world is the great university, in which our educational exercises\nterminate with our last expiring breath.\"\n\nThe author craves the reader's indulgence for introducing Dr. Brown's\nremarks at this stage of the work. It is intended for a class of readers\n(_the farmers_) who have not the time to make themselves acquainted with\nall that is going on in the medical world. We aim to make the book\nacceptable to that class of men. If we fail, the fault is in us, not in\nour subjects.\n\nFOOTNOTE:\n\n[4] Inflammation is a vital action, and cannot be properly termed\n_diseased_ action. The only action that can be properly termed\n_diseased_ is the chemical action.\n\n\n\n\nREMARKS,\n\nSHOWING THAT VERY LITTLE IS KNOWN OF THE NATURE AND TREATMENT OF\nDISEASE.\n\n\nMr. Percival details a case of peritonitis,[5] after the usual symptoms\nin the early stage had subsided. \"The horse's bowels became much\nrelaxed: suspecting that there was some disorder in the alimentary\ncanal, and that this was an effort of nature to get rid of it, I\npromoted the diarrhoea by giving mild doses of cathartic medicine, in\ncombination with calomel!\" [Nature did not require such assistance: warm\ndrinks, composed of marshmallows, or slippery elm, would have been just\nthe thing.]\n\n\"On the third day from this, prolapsus ani (falling of the fundament)\nmade its appearance. After the return of the gut, the animal grew daily\nduller, and more dejected, manifesting evident signs of considerable\ninward disorder, though he showed none of acute pain; the diarrhoea\ncontinued; swelling of the belly and tumefaction of the legs speedily\nfollowed: eight pounds of blood were drawn, and two ounces of oil of\nturpentine were given internally, and in spite of another bleeding, and\nsome subordinate measures, carried him off [the treatment, we presume]\nin the course of a few hours.\n\n\"Dissection: a slight blush pervaded the peritoneum; at least the\nparietal portion of it, for the coats of the stomach and intestines\npreserved their natural whiteness. About eight gallons of water were\nmeasured out of the belly.[6] The abdominal viscera, as well as the\nthoracic, showed no marks of disease.\"\n\nWe have stated, in the preceding pages, that the farmers can generally\ntreat some cases of disease, by simple means, with much better success\nthan some of the regulars; yet there are exceptions. Some of them have\nbeen inoculated with the virus of allopathy; and when an animal is taken\nsick, and manifests evident signs of great derangement, they seem to\nsuppose that the more medicine they cram down the better, forgetting,\nperhaps not knowing, that the province of the physician is to know when\nto do nothing. Others err from want of judgment; and if they have an\nanimal sick, they send for the neighbors; each one has a favorite\nremedy; down go castor oil, aloes, gin and molasses, in rapid\nsuccession. \"He has inflammation of the insides,\" says one; \"give him\nsalts.\" No sooner said than done; the salts are hurried down, and, of\ncourse, find their way into the paunch. These, together with a host of\nmedicines too numerous to mention, are tried without effect: all is\ncommotion within; fermentation commences; gas is evolved; the animal\ngives signs of woe. As a last resort, paunching, bleeding, &c., follow;\nperhaps the horns are bored, or some form of barbarity practised, and\nthe animal dies under the treatment.\n\nA case similar to the above came under our notice a few months since. A\ncow, of a superior breed, was sent a few miles into the country to\nwinter. Having always had the very best of feed, the owner gave\nparticular instructions that she should be fed accordingly; instead of\nwhich, however, she was fed on foxgrass and other indigestible matter,\nin consequence of which she was attacked with acute indigestion,\n(gastric fever, as it is generally called,) more popularly known, in\nbarn-yard language, as a \"stoppage.\" A man professing to understand\n_cow-doctoring_ was sent for, who, after administering \"every thing he\ncould think of\" without success, gave a mixture of hog's lard and castor\noil. When asked what indication he expected to fulfil, he replied, \"My\nobject was to wake up the cow's ideas\"! Unfortunately, he awoke the\nwrong ideas; for the cow died. On making a post mortem examination,\nabout half a bushel of partly-masticated foxgrass was found in the\npaunch, and the manyplus was distended beyond its physiological\ncapacity. On making an incision into it, the partly-digested food was\nquite hard and dry, and the mucous covering of the laminae--even the\nlaminae themselves--could be detached with the slightest force. The\nfarmer will probably inquire, What ought to be done in such cases?\nBefore we answer the question, a few remarks on the nature of the\nobstruction seem to be necessary.\n\nIn the article _Description of the Organs of Digestion_, the reader will\nlearn the modes by which the food reaches the different compartments of\nthe stomach. In reference to the above case, the causes of derangement\nare self-evident, which will be seen as we proceed. The animal had,\nprevious to the journey, (thirty miles,) received the greatest care and\nattention; in short, she had been petted. Being pregnant at the time,\nthe stomach was more susceptible to derangement than at any other time.\nThe long journey could not act otherwise than unfavorably: first,\nbecause it would fatigue the muscular system; secondly, because it would\nirritate the nervous. Here, then, are the first causes; and it is\nimportant, in all cases of a deviation from health, to ascertain, as\nnear as possible, the causes, and remove them. _This is considered the\nfirst step towards a cure._ If we cannot remove the causes, we are\nenabled, by an inquiry into them, to adopt the most efficient means for\nthe recovery of the animal. The animal having had a bountiful meal\nbefore starting on the journey, and not being allowed sufficient time to\nremasticate, (rumination is partially or totally suspended during active\nexercise,) probably, combined with the above causes, an acute attack of\nthe stomach set in--subsided after a few days, and left those organs in\na debilitated state. The sudden change in diet also acted unfavorably,\nespecially as the foxgrass required more than ordinary gastric power to\nreduce it to a pulpy mass, fit to enter the fourth, or true digestive\nstomach. For want of a due share of vital action in the abomasum,\n(fourth stomach,) it was unable to perform its part in the physiological\nprocess of digestion; hence the accumulation found in the manyplus. The\ncauses of the detachment of laminae, and the blanched appearances,--for\nit was as white as new linen,--were partly chemical and partly\nmechanical. The mechanical obstruction consisted in over-distention of\nthe manyplus from food, thereby obstructing the circulation of the blood\nthrough its parietes, (walls,) and depriving it not only of nutriment,\nfrom the nerves of nutrition, but paralyzing its secretive function. It\nthen became a prey to chemical action and decomposition. The indications\nof cure were, to arouse the digestive organs by stimulants, then by\nanti-spasmodic, relaxing, and tonic medicines, (for which see\nAPPENDIX:) the digestive organs would probably have recommenced\ntheir healthy action, and the life of the animal might have been saved.\nOil and grease, of every description and kind, are not suitable remedies\nto administer to cattle when laboring under indigestion; for at best\ntheir action is purely mechanical, and cannot be assimilated by the\nnutritive function so as to act medicinally. Linseed oil is, however,\nabsorbed and diffused. If the animal labors under obstinate\nconstipation, and it is evident that the obstruction is confined to the\nintestines, then we may resort to a dose of oil.\n\nThe reader will perceive the benefits to be derived from a knowledge of\nanimal physiology and veterinary medicine, when based upon sound\nprinciples and common sense. He will also see the importance of having\neducated and honorable men employed in cattle-doctoring. No doubt there\nare such; but surely something is \"rotten in Denmark;\" for we are\nrepeatedly told by our patrons that they \"judge of the merits of the\nveterinary art by the men they find engaged in it.\"\n\n_Scientific Treatment of Colic, or Gripes._--\"On the 5th September,\n1824, a young bay mare was admitted into the infirmary with symptoms of\ncolic, for which she lost eight pounds of blood before she came in. The\nfollowing drench was prescribed to be given immediately: laudanum and\noil of turpentine, of each, three ounces, with the addition of six\nounces of decoction of aloes. In the course of half an hour, this was\nrepeated! But shortly after, she vomited the greater part by the mouth\nand nostrils. No relief having been obtained, twelve pounds of blood\nwere taken from her, and the same drink was given. In another hour, this\ndrench was repeated; and, for the fourth time, during the succeeding\nhour; both of which, before death, she rejected, as she had done the\nsecond drink. Notwithstanding these active measures were promptly taken,\nshe died about three hours after her admission.\" (See Clark's _Essay on\nGripes_.) It appears that the doctors made short work of it. Twelve\nounces of laudanum, and the same of turpentine,[7] in three hours! But\nthis is \"_secundum artem_\" \"skilful treatment\"--a specimen of \"science\nand skill,\" and justifiable in every case where the symptoms are\n\"alarming.\" Let the reader, if he has ever seen a case of colic treated\nby us, contrast the result. Had the case been treated with relaxing,\nanti-spasmodic, carminative drinks, warmth and moisture externally,\ninjections internally, and frictions generally, the poor animal would,\nprobably, have been saved. We have attended many cases of the same sort,\nand have not yet lost the first one.\n\n_Extraordinary case of \"cattle doctoring\"!--which ought to be termed\ncattle-killing._--We were requested by Mr. S. of Waltham, December 18,\n1850, to see a sick cow. The following is the history of the case: The\ncow, as near as we could judge, was of native breed, in good condition,\nand in her eighth pregnant month; pulse, 80 per minute; respirations, 36\nper minute; external surface, ears, horns, and legs, cold. She had not\ndunged for several days. She was found lying on her belly, with her head\nturned round towards the left side. She struggled occasionally, and\nappeared to suffer from abdominal pain. She uttered a low, moaning sound\nwhen pressure was made on the abdominal muscles. The following facts\nwere related to us by the owner, which we give in his own language. \"I\nbought the cow, and drove her about 200 miles to this place. She had\nbeen here about a week, when I perceived she did not eat her feed as\nwell as usual. She became sick about nine days ago, I thought it best to\nbegin to doctor her! I employed a man who was reputed to be a pretty\ngood cattle doctor. She got pretty well dosed between us, for we first\ngave her one pound of salts. The next day we gave her another pound.\nFinding this also failed to have the desired effect, we gave her one\npound eight ounces more. She kept getting worse. We next gave her a\nquart of urine. She still grew worse. Two table-spoonfuls of gunpowder\nand a quarter of a pound of antimony were then given; still no\nimprovement. As a last resort, we gave her eight drops of croton oil; a\nfew hours afterwards, nine drops more were given; and a final dose of\ntwenty drops of the same article was administered. The cow rolled her\neyes as if she were about to die. I then called in the neighbors to kill\nher, when one of them advised me to come and see you.\" The reader will\nhere perceive that we had a pretty desperate case; having been called in\njust at the eleventh hour. We may here remark that the cow had been\nunder treatment nine days, during which time she had eaten scarcely any\nfood, and passed but very little excrement. The medicine had been given\nat different stages during that period. There was evidently no\naccumulation of excrement in the rectum, for she had been raked and\nreceived several injections.\n\nAs we were not requested to take charge of the case, the owner being\nunwilling to incur additional expense, we, therefore, with a view of\ngiving present relief, and fulfilling the necessary indications, ordered\nthe following:\n\n  Powdered slippery elm,         1 table-spoonful.\n    \"      caraways,             1 tea-spoonful.\n    \"      marshmallows,         1 table-spoonful.\n    \"      skullcap,             1 tea-spoonful.\n    \"      grains of paradise,   1 tea-spoonful.\n\nA sufficient quantity of boiling water to form it into the consistence\nof thin gruel; a junk bottle full to be given every two hours.\n\nDirections were given to rub the ears and extremities until they were\nwarm, and the strength of the animal to be supported with thin flour\ngruel.\n\nThe indications to be fulfilled were as follows:--\n\n1st. To lubricate the mucous surfaces, and defend them from the action\nof the drugs.\n\n2d. To arouse the digestive function, and prevent the generation of\ncarbonic acid gas.\n\n3d. To allay nervous excitement, and remove spasms.\n\nLastly. To equalize the circulation.\n\nThe first indication can be fulfilled by slippery elm and marshmallows;\nthe second, by caraway seeds; the third, by skullcap; and the fourth, by\ngrains of paradise.\n\nWe have not been able, up to the present time, to ascertain the result.\n\nHere, then, are a few examples of horse and cattle doctoring, which we\nmight multiply indefinitely, did we think it would benefit the reader.\nWe ask the reader to ponder on these facts, and then answer the\nquestion, \"What do horse and cattle doctors know about the treatment of\ndisease?\"\n\nIt gives us much pleasure, however, and probably it will the reader, to\nknow that a few of the veterinary surgeons of London are just beginning\nto see the error of their ways. The following contribution to the\nVeterinarian, from the pen of Veterinary Surgeon Haycock, will be read\nwith interest. The quotations are not complete. We only select those\nportions which we deem most instructive to our readers. The disease to\nwhich it alludes, _puerperal fever_, has made, and is at the present\ntime making, sad havoc among the stock of our cattle-growing interest;\nand it stands us in hand to gather honey wherever we can find it. \"Of\nthe various questions which present themselves to traders and owners of\ncattle respecting puerperal fever, the following are, perhaps, a few of\nthe most important: First. At what period of their life are cows the\nmost liable to be attacked with puerperal fever? Secondly. At what\nperiod after the animal has calved does the disease generally supervene?\nThirdly. What is the average rate of mortality amongst cows attacked\nwith this disease? Fourthly. What is the best method to pursue with\ncattle, in order, if possible, to prevent the disease? Fifthly. What is\nthe best mode of treatment to be pursued with cattle when so attacked?\nTo these several questions I shall endeavor to reply as fully as my own\nknowledge of the matter will allow me. They are questions which ought to\nhave been answered years ago; [so they would have been, doctor, if, as\nCurtis says, your brethren had not been _progressing in a circle,\ninstead of direct lines_;] but no one appears to have thought it\nnecessary. They are questions of great importance to the agriculturist;\nif they were fully answered, he would be able to form a pretty accurate\nestimate as to the amount of risk he was likely at all times to incur\nwith respect to puerperal diseases of a febrile nature. For instance,\nsuppose it was fully ascertained, from data furnished by the correct\nobservations of a number of practitioners, at what period of the cow's\nlife the animal is most liable to be attacked with puerperal fever; the\nagriculturist and cow-keeper would be able, in a considerable degree, to\nguard against it, either by feeding the animal, or taking such other\nsteps as a like experience proved to be the best. It is of no earthly\nuse practitioners writing 'grandiloquent' papers upon diseases like\npuerperal fever; or in their telling the world, that puerperal fever is\na disease of the nervous system; or that the name which is given to it\nis very improper, _and not suggestive; or that bleeding and the\nadministration of a powerful purgative are proper to commence with_;\ntogether with hosts of stereotyped statements of a like\nnature--statements which are unceasingly repeated, and which are without\none jot of sound experience to substantiate them. [All good and sound\ndoctrine.]\n\n\"Question First. _At what period of their lives are cows the most liable\nto be attacked with puerperal fever?_ I have in my possession notes and\nmemoranda of twenty-nine cases of this disease, which notes and\nmemoranda I have collected from cases I have treated from the month of\nJuly, 1842, to the month of July, 1849--a period of seven years; and\nwith reference to the above question the figures stand thus: Out of the\ntwenty-nine, three of them were attacked at the third parturient period,\nfive ditto at the fourth, sixteen at the fifth, two at the sixth, and\nthree at the eighth.\n\n\"It appears, then, from the above numbers, that cows are the most liable\nto puerperal fever at the fifth parturient period--a fact which is\nnoticed by Mr. Barlow.\n\n\"Secondly. _At what period after the animal has calved does the disease\ngenerally supervene?_ With reference to this question, the twenty-nine\ncases stand thus:--\n\n  5 cows immediately after parturition.\n  8   \"  in 20 hours   \"        \"\n  6   \"  in 23   \"     \"        \"\n  5   \"  in 24   \"     \"        \"\n  3   \"  in 30   \"     \"        \"\n  2   \"  in 36   \"     \"        \"\n  1   \"  in 72   \"     \"        \"\n\n\"It appears, then, from the above, that after the twentieth and\ntwenty-fourth hours, the animals, comparatively speaking, may be\nconsidered as safe from the disease; and that after the seventy-second\nor seventy-third hour, all danger may be considered as past, beyond\ndoubt.\n\n\"Thirdly. _What is the average rate of mortality amongst cows attacked\nwith this disease?_ Out of the 29 cases, 12, I find, recovered and 17\ndied; which loss is equivalent to somewhere about 59 per cent.--a loss\nwhich, I am inclined to think, is not so great as that of many other\npractitioners. [It will be still less if you reject poison as well as\nthe lancet.]\n\n\"Mr. Cartwright, in the May number of the Veterinarian of the present\nyear, states that, 'Although I have seen at least a hundred cases,\nchiefly in this neighborhood, [Whitchurch,] during the last twenty-five\nyears, yet I am almost ashamed to confess that I cannot call to\nrecollection that I ever cured a single case, [neither will you ever\ncure one as long as the lancet and poison are cooeperative,] nor have I\never heard of a case ever being cured by any of the quacks in the\nneighborhood.' [Of course not, for the quacks follow in the footsteps of\ntheir prototypes, the _regular_ veterinary surgeons.]\n\n\"Fourthly. _What is the best method to pursue with cattle, in order, if\npossible, to_ PREVENT _the disease?_ This is a question which I\nhope to see amply discussed by veterinarians. I have but little to offer\nrespecting it myself; but I labor under a kind of feeling that something\nvaluable may not only be said, but done, by way of prevention. With\nreference to preventing the disease, Mr. Barlow, in his Essay, says,\n'There is a pretty certain preventive in milking the cow some time\nbefore calving in full _blood-letting_ before or immediately after; in\npurgatives, very limited diet, and other depletive measures; each and\nall tending to illustrate the necessity of a vascular state of the\nsystem for its development!'\"\n\nMr. Haycock continues: \"So far as my own experience is concerned, it is\nat variance with almost every one of my observations. In the table which\nI have given respecting question 2, the reader will recollect that I\nstated that puerperal fever supervened in five cows immediately after\nparturition. Now, it is worthy of remark, of these five cases, that\nevery animal had been milked many hours previous to calving. The full\nudder, under such circumstances, is a powerful excitant to the uterus:\nthis is a well-known fact, and the consequence is, that if this natural\nexcitant be withdrawn, the action of the process at once becomes\ndiminished. I have known many cases, in addition to those already given,\nwhere the parturient process was prolonged for hours in consequence of\nthe animal's being milked, in whom fever supervened almost immediately\nafterwards. The prolonged process, I think, greatly weakens the animal,\nand, as a natural result, the vital energies become less capable of\nmaintaining their normal integrity. With reference, again, to bleeding\nand purging as preventives, I have nothing to offer in favor of either\nmode. I do not believe that they are preventives. [Good, again, doctor:\nyou are one of the right stripe. It would give us pleasure to see a few\nsuch as you on this side of the water.] First of all, we require to know\nwhat percentage of calving cows are liable to be affected with puerperal\nfever; then, whether that percentage becomes reduced in number in\nconsequence of such preventive measures being brought into force: these\nare the only modes whereby the matter can be proved; and, so far as I\nknow, no one has ever brought the question to such a test. That bleeding\nand purging are considered as preventives by people in general, I know\nperfectly; but, like many other popular opinions, the thing which is\nbelieved requires first to be proved ere it becomes truth.\n\n\"I perfectly agree with Mr. Barlow in recommending spare diet. I regard\nit, in fact, as the great preventive.... When I say spare diet, I do not\nmean poor diet. The food should be good, but they should not have that\nhuge bulk of matter which they are capable of devouring, and which they\nappear so much to desire. I should commence the process for eight or ten\ndays prior to calving, or even, with some animals, much earlier; and the\ndiet I would give should consist of beans, boiled linseed, and boiled\noats, with occasionally small portions of hay. I should not always feed\nupon one mixture. I might occasionally substitute boiled barley in place\nof oats; and when the time for calving was very near at hand, say within\na day or so, I should become more sparing with my hay, and more copious\nwith my allowance of bran. With regard to the diet after calving, I\nshould pursue much the same course I have named: perhaps for the first\nthirty hours I might allow the animal nothing but gruel and bran mash,\nin which I should mix a little oatmeal, or very thick gruel. I have\nsometimes thought--_but hitherto it has not gone beyond a thought with\nme_--that a broad cotton or linen bandage, fixed moderately tight round\nthe cow's body immediately after calving, might prove of some assistance\nas a preventive. I have had no experience in its benefit myself; I\nmerely suggest the thing; and if it did nothing more, it would prevent,\nin some measure, the animal from feeling that sensation of vacuity which\nmust necessarily exist immediately and for some time after calving, and\nwhich, I think, under some conditions of the system, may be injurious to\nthe animal. I am told by a medical friend of mine, that he has known\npuerperal fever produced in women solely from midwives' neglecting to\nbandage them after delivery; at any rate, a bandage, or a broad belt\nhaving straps and buckles attached, and placed securely round the cow's\nbody immediately after calving, and kept there for a day or two, could\ndo no harm, if it failed of doing good.\n\n\"Fifthly. _Which is the best method of treatment to pursue with cows\nwhen attacked with puerperal fever?_ Upon this question I feel that I\ncould say much; but at present I defer its consideration.... Suffice it\nto say, then, that I never either bleed or administer purges. I used\nonce to do both, but my experience has shown me, in numerous cases, that\nneither is necessary.... This malady I have written upon is fearfully\ndestructive; and if such diseases cannot be met with powers capable of\nwrestling with it, I, for one, shall say that it is a stigma upon our\nart--I will say that when we are most wanted, we are of the least use.\"\n\nFOOTNOTES:\n\n[5] Inflammation of the peritoneum.\n\n[6] Water very frequently accumulates in the belly or chest, after\nblood-letting.\n\n[7] On remonstrating with a man who was about to administer half a pint\nof turpentine to a cow, he replied, \"She has no business to be a cow!\"\nWe presume that some of the regulars have just as much, and not a\nparticle more, of the milk of animal kindness as this man seemed to\nshow.\n\n\n\n\nNATURE, TREATMENT, AND CAUSES OF DISEASE IN CATTLE.\n\n\nThe pathology, or doctrine of diseases, is, as we have previously\nstated, little understood. Many different causes have been assigned for\ndisease, and as many different modes of cure have been advocated. We\nshall not discuss either the ancient or modern doctrines any further\nthan we conceive they interfere with correct principles. In doing so, we\nshall endeavor to confine ourselves to truth, reason, and nature.\n\nWe entirely discard the popular doctrine that _fever_ and _inflammation_\nare disease. We look upon them as simple acts of the constitution--sanative\nin their nature. Then the reader may ask, \"Why do you recommend medicine\nfor them?\" We do not. We only prescribe medicine, for the purpose of aiding\nnature to cure the diseases of which _they_ (the fever and inflammation)\nare symptoms, and we do not expect to accomplish even that by medicine\nalone. Ventilation, diet, and exercise, in nine cases out of ten, will do\nmore good than the destructive agents that have hitherto been used, and\nchristened \"cattle medicines.\"\n\nThe great secret of curing diseases is, by accurately observing the\nindications of nature to carry off and cure disease, and by observing by\nwhat critical evacuations she does at last cast off the morbid matter\nwhich caused them, and so restores health. By thus observing, following,\nand assisting _nature_, agreeably to her indications, our practice will\nalways be more satisfactory.\n\nWhenever the great outlets (skin, lungs, and kidneys) of the animal body\nare obstructed, morbific and excrementitious substances are retained in\nthe system; they irritate, stimulate, and offend nature in such a\nmanner, that she always exerts her power to throw them off. And she acts\nwith great regularity in her endeavors to expel the offending matter,\nand thus restore the animal to a healthy state.\n\nSuppose an animal to be attacked with disease, and fever supervenes; the\nwhole system is then aroused to cast out this disease: nature invariably\npoints to certain outlets, as the only passages through which the enemy\nmust evacuate the system; and it is the province of the physician to aid\nin this wise and well-established effort; but when such means are\nresorted to as in the case of the cow at Waltham, (p. 98,) instead of\nrendering nature the necessary assistance, her powers and energies are\nentirely crushed.\n\nLet us suppose a horse to have been exercised; during that exercise,\nthere is a determination of heat and fluids to the surface: the pores of\nthe skin expand and permit the fluids to make their exit: now, if the\nhorse is put into a cold stable, evaporation commences, leaving the\nsurface cold and the pores constricted, so that, after the circulating\nsystem has rested a while, it commences a strong action again, to throw\noff the remaining fluids that were thus suddenly arrested; there is no\nchance for their escape, as the pores are closed; the skin then becomes\ndry and harsh, the \"coat stares,\" and the animal has, in common\nparlance, taken cold, and \"it has thrown him into a fever.\" Now, the\ncold is the real enemy to be overcome, and the fever should be aided by\nwarmth, moisture, friction, and diffusables. If, at this stage, the cold\nis removed, the fever will disappear; but if the disease (the cold) has\nbeen allowed to advance until a general derangement or sympathetic\naction is set up, and there is an accumulation of morbific matter in the\nsystem, then the restorative process must be more powerful and\nenergetic; constantly bearing in mind that we must assist nature in her\nendeavors to throw off whatever is the cause of her infirmities. Instead\nof attacking the disease with the lancet and poison,--which is on the\nprinciple of killing the horse to cure the fever,--we should use\nremedies that are favorable to life. It matters not what organs are\naffected; the means and processes are the same, and therefore the\ndivision of inflammation and fever into a great number of parts\ndesignated by as many names, and indicated by twenty times as many\ncomplications of symptoms which may never be present, only serve to\nbewilder the practitioner, and render his practice ineffectual.\n\n\n\n\nPLEURO-PNEUMONIA.\n\n\nAs very little is, at present, known of the nature of this disease, we\ngive the reader the views of Mr. Dun, who received the gold medal\noffered by the Agricultural Society for the best essay on this subject.\n\n\"The causes of the disease, both immediate and remote, are subjects full\nof interest and importance; and a knowledge of them not only aids in the\nprevention of disease, but also leads the practitioner to form a more\ncorrect prognosis, and to pursue the most approved course of treatment.\nIt is, however, unfortunate that the causes of pleuro-pneumonia have not\nas yet been satisfactorily explained. No department of the history of\nthe disease is less understood, or more involved in doubt and\nobscurity. But in this respect pleuro-pneumonia is not peculiar: it is\nbut one of an extensive class which embraces most epidemic and epizooetic\ndiseases. And if the causes which produce influenza, fevers, and\ncholera, were clearly explained, those which produce pleuro-pneumonia\nwould, in all probability, be easy of solution.\n\n\"Viewing the wide-spread and similar effects of pleuro-pneumonia, we may\nsurmise that they are referable to some common cause. And although much\ndifference of opinion exists upon this subject, it cannot be denied that\n_contagion_ is a most active cause in the diffusion of the disease.\nIndeed, a due consideration of the history and spread of\npleuro-pneumonia over all parts of the land will be sufficient to show\nthat, in certain stages of the disease, it possesses the power of\ninfecting animals apparently in a sound and healthy condition, and\notherwise unexposed to the action of any exciting cause. The peculiarity\nof the progress of this disease, from the time that it first appeared in\nEngland, is of itself no small evidence of its contagious nature. Its\nslow and gradual progress is eminently characteristic of diffusion by\ncontagion; and not only were the earlier cases which occurred in this\nisland distinctly proved to have arisen from contact with the Irish\ndroves, but also subsequent cases, even up to the present day, show\nnumerous examples in which contagion is clearly and unequivocally\ntraceable.... Although pleuro-pneumonia is not produced by the action of\nanyone of these circumstances alone, [referring to noxious effluvia,\n&c.,] yet many of them must be considered as predisposing to the\ndisease; and although not its immediate exciting causes, yet, by\ndepressing the physical powers, they render the system more liable to\ndisease, and less able to withstand its assaults. Deficient ventilation,\nfilth, insufficient and bad food, may indeed predispose to the disease,\nconcentrate the animal effluvia, and become the _matrix_ and _nidus_ of\nthe organic poison; but still, not one, alone, of these circumstances,\nor even all of them combined, can produce the disease in question. There\nmust be the subtle poison to call them into operation, the specific\ninfluence to generate the disease.\"\n\n\"On the other hand, it appears probable that the exciting cause, whether\nit be contagion, or whatever else, cannot, of itself, generate the\ndisease; but that certain conditions or predisposing causes are\nnecessary to its existence, and without which its specific effects\ncannot be produced. But although these _remote_ or _predisposing_ causes\nare very numerous, they are often difficult of detection; nay, it is\nsometimes impossible to tell to what the disease is referable, or upon\nwhat weak point the exciting cause has fixed itself. A source of\nperplexity results from the fact.... The predisposing causes of the\ndisease admit of many divisions and subdivisions; they may, however, be\nconsidered under two general heads--_hereditary_ and _acquired_.\n\n\"With reference to the former, we know that good points and properties\nof an animal are transmitted from one generation to another; so also are\nfaults, and the tendencies to particular diseases. As in the same\nfamilies there is a similarity of external form, so is there also an\ninternal likeness, which accounts for the common nature of their\nconstitution, modified, however, by difference of age, sex, &c.\n\n\"Among the acquired predisposing causes of pleuro-pneumonia may be\nenumerated general debility, local weakness, resulting from previous\ndisease, irritants and stimulants, exposure to cold, damp or sudden\nchanges of temperature, the want of cleanliness, the breathing of an\natmosphere vitiated by the decomposition of animal or vegetable matters,\nor laden with any other impurity. In short, under this head may be\nincluded every thing which tends to lower the health and vigor of the\nsystem, and consequently to increase the susceptibility to disease.\n\n\"The primary symptoms of pleuro-pneumonia are generally obscure, and too\noften excite but little attention or anxiety. As the disease steals on,\nthe animal becomes dull and dejected, and, if in the field, separates\nitself from its fellows. It becomes uneasy, ceases to ruminate, and the\nrespirations are a little hurried. If it be a milk-cow, the lacteal\nsecretion is diminished, and the udder is hot and tender. The eyes are\ndull, the head is lowered, nose protruded, and the nostrils expanded.\nThe urine generally becomes scanty and high-. It is seldom\nthought that much is the matter with the animal until it ceases to eat;\nbut this criterion does not hold good in most cases of the disease, for\nthe animal at the outset still takes its food, and continues to do so\nuntil the blood becomes impoverished and poisoned; it is then that the\nsystem becomes deranged, the digestive process impaired, and fever\nestablished. The skin adheres to the ribs, and there is tenderness along\nthe spine. Manipulation of the trachea, and percussion applied to the\nsides, causes the animal to evince pain. Although the beast may have\nbeen ill only three days, the number of pulsations are generally about\nseventy per minute; but they are sometimes eighty, and even more. In the\nfirst stage, the artery under the jaw feels full and large; but as the\ndisease runs on, the pulse rapidly becomes smaller, quicker, and more\noppressed. The breathing is labored, and goes on accelerating as the\nlocal inflammation increases. The fore extremities are planted wide\napart, with the elbows turned out in order to arch the ribs, and form\nfixed points for the action of those muscles which the animal brings\ninto operation to assist the respiratory process. In pleuro-pneumonia,\nthe hot stage of fever is never of long duration, [_simply because there\nis not enough vitality in the system to keep up a continued fever_.] The\nstate of collapse quickly ensues, when the surface heat again decreases,\nand the pulse becomes small and less distinct. We have now that low\ntyphoid fever so much to be dreaded, and which characterizes the disease\nin common with epizooetics.\n\n\"... The horse laboring under pleuro-pneumonia, or, indeed, any\npulmonary disease, will not lie down; but, in the same circumstances,\ncattle do so as readily as in health. They do not, however, lie upon\ntheir side, but couch upon the sternum, which is broad and flat, and\ncovered by a quantity of fibro-cellular substance, which serves as a\ncushion; while the articulation between the lower extremities of the\nribs admits of lateral expansion of the chest. In this position cattle\ngenerally lie towards the side principally affected, thus relieving the\nsounder side, and enabling it to act more freely. There is sometimes a\nshivering and general tremor, which may exist throughout the whole\ncourse of the disease. (This is owing to a loss of equilibrium between\nthe nerves of nutrition and the circulation.) ... As the case advances\nin severity, and runs on to an unfavorable termination, the pulse loses\nits strength and becomes quicker. Respiration is in most cases attended\nby a grunt at the commencement of expiration--a symptom, however, not\nobservable in the horse. The expired air is cold, and of a _noisome_\nodor. The animal crouches. There is sometimes an apparent knuckling over\nat the fetlocks, caused by pain in the joints. This symptom is mostly\nobservable in cases when the pleura and pericardium are affected. The\nanimal grinds its teeth. The appetite has now entirely failed, and the\nemaciation becomes extreme. The muscles, especially those employed in\nrespiration, become wasted; the belly is tucked, and the flanks heave;\nthe oppressive uneasiness is excessive; the strength fails, under the\nconvulsive efforts attendant upon respiration, and the poor animal dies.\n\n\"In using means to prevent the occurrence of the disease, we should\nendeavor to maintain in a sound and healthy tone the physical powers of\nthe stock, and to avoid whatever tends to depress the vital force.\nExposure to the influence of contagion [and infection] must be guarded\nagainst, and, on the appearance of the disease, every precaution must be\nused to prevent the healthy having communication with the sick. By a\nsteady pursuance, on the part of the stock proprietor, of these\nprecautionary measures, and by the exercise of care, prudence, and\nattention, the virulence of the disease will, we are sure, be much\nabated, and its progress checked.\"\n\nAs the reader could not be benefited by our detailing the system of\nmedication pursued in England,--at least we should judge not, when we\ntake into consideration the great loss that attends their _best\nefforts_,--we shall therefore proceed to inform the reader what the\ntreatment ought to be in the different stages of the disease.\n\n\n_General Indication of Cure in Pleuro-Pneumonia._--Restore the\nsuppressed evacuations, or the secretions and excretions, if they are\nobstructed.\n\nIf bronchial irritation or a cough be present, shield and defend the\nmucous surfaces from irritation. Relieve congestions by equalizing the\ncirculation. Support the powers of the system. Relieve all urgent\nsymptoms.\n\n       *       *       *       *       *\n\n_Special Practice._--Suppose a cow to be attacked with a slight cough.\nShe appears dull, and is off her feed; pulse full, and bowels\nconstipated; and she is evidently out of condition.\n\nThen the medicines should be anti-spasmodic and relaxant, tonic,\ndiaphoretic, and lubricating.\n\nThe following is a good example:--\n\n  Powdered golden seal, (tonic,)                   1 table-spoonful.\n    \"      mandrake, (relaxant,)                   2 tea-spoonfuls.\n    \"      lobelia, (anti-spasmodic,)              1 tea-spoonful.\n    \"      slippery elm or mallows, (lubricating,) 1 table-spoonful.\n    \"      hyssop tea, (diaphoretic,)              1 gallon.\n\nAfter straining the hyssop tea, mix with it the other ingredients, and\ngive a quart every two hours.\n\nIn the mean time, administer the following injection:--\n\n  Powdered lobelia,             } of each, half a\n    \"      ginger,              } table-spoonful.\n  Boiling water,                  1 gallon.\n\nWhen cool, inject.\n\nParticular attention must be paid to the general surface, If the surface\nand the extremities are cold, then employ friction, warmth, and\nmoisture. The animal must be in a comfortable barn, neither too hot nor\ntoo cold; if it be imperfectly ventilated, the atmosphere may be\nimproved by stirring a red-hot iron in vinegar or pyroligneous acid, or\nby pouring either of these articles on heated bricks. The strength is to\nbe supported, provided the animal be in poor condition, with gruel, made\nof flour and shorts, equal parts; but, as it frequently happens (in this\ncountry) that animals in good flesh are attacked, in such case food\nwould be inadmissible.\n\nSuppose the animal to have been at pasture, and she is not observed to\nbe \"ailing\" until rumination is suspended. She then droops her head, and\nhas a cough, accompanied with difficult breathing, weakness in the legs,\nand sore throat. Then, in addition to warmth, moisture, and friction, as\nalready directed, apply to the joints and throat the following:\n\n  Boiling vinegar,                   1 quart.\n  African cayenne,                   1 table-spoonful.\n\nThe throat being sore, the part should be rubbed gently. The joints may\nbe rubbed with energy for several minutes. The liquid must not be\napplied too hot.\n\nTake\n\n  Virginia snakeroot,       } of each, 2 ounces.\n  Sage,                     }\n  Skullcap, (herb,)                    1 ounce.\n  Pleurisy root,                       1 ounce.\n  Infuse in boiling water,             1 gallon.\n\nAfter standing for the space of one hour, strain; then add a gill of\nhoney and an ounce of powdered licorice or slippery elm. Give a quart\nevery four hours.\n\nShould the cough be troublesome, give\n\n  Balsam copaiba,              1 table-spoonful.\n  Sirup of garlic,             1 ounce.\n  Thin gruel,                  1 quart.\n\nGive the whole at a dose, and repeat as occasion may require. A second\ndose, however, should not be given until twelve hours have elapsed.\n\nInjections must not be overlooked, for several important indications can\nbe fulfilled by them. (For the different forms, see APPENDIX.)\n\nIf the disease has assumed a typhus form, then the indications will\nbe,--\n\nFirst. To equalize the circulation and nervous system, and maintain that\nequilibrium. This is done by giving the following:--\n\n  Powdered African cayenne,     1 tea-spoonful.\n     \"     flagroot,            1 table-spoonful.\n  Skullcap,                     1\/2 ounce.\n  Marshmallows,                 4 ounces.\n\nPut the whole of the ingredients into a gallon of water; boil for five\nminutes; and, when cool, strain; sweeten with a small quantity of honey;\nthen give a quart every two hours.\n\nThe next indication is, to counteract the tendency to putrescence. This\nmay be done by causing the animal to inhale the fumes of pyroligneous\nacid, and by the internal use of bayberry bark. They are both termed\nantiseptics. The usual method of generating vapor for inhalation is, by\nfirst covering the animal's head with a horse-cloth, the corners of\nwhich are suffered to fall below the animal's nose, and held by\nassistants in such a manner as to prevent, as much as possible, the\nescape of the vapor. A hot brick is then to be grasped in a pair of\ntongs, and held about a foot beneath the nose. An assistant then pours\nthe acid, (_very gradually_,) on the brick. Half a pint of acid will be\nsufficient for one steaming, provided it be used with discretion; for if\ntoo much is poured on the brick at once, the temperature will be too\nrapidly lowered.\n\nIn reference to the internal use of bayberry, it may be well to remark,\nthat it is a powerful astringent and antiseptic, and should always be\ncombined with relaxing, lubricating medicines. Such are licorice and\nslippery elm.\n\nThe following may be given as a safe and efficient antiseptic drink:--\n\n  Powdered bayberry bark,      half a table-spoonful.\n    \"      charcoal,           1 table-spoonful.\n  Slippery elm,                1 ounce.\n  Boiling water,               1 gallon.\n\nMix. Give a quart every two hours.\n\nThe diet should consist of flour gruel and boiled carrots. Boiled\ncarrots may be allowed (provided the animal will eat them) during the\nwhole stage of the malady.\n\nThe object of these examples of special practice is to direct the mind\nof the farmer at once to something that will answer a given purpose,\nwithout presuming to say that it is the best in the world for that\npurpose. The reader will find in our _materia medica_ a number of\narticles that will fulfil the same indications just as well.\n\n\n\n\nLOCKED-JAW.\n\n\nMr. Youatt says, \"Working cattle are most subject to locked-jaw, because\nthey may be pricked in shoeing; and because, after a hard day's work,\nand covered with perspiration, they are sometimes turned out to graze\nduring a wet or cold night. Over-driving is not an uncommon cause of\nlocked-jaw in cattle. The drovers, from long experience, calculate the\naverage mortality among a drove of cattle in their journey from the\nnorth to the southern markets; and at the head of the list of diseases,\nand with the greatest number of victims, stands 'locked-jaw,' especially\nif the principal drover is long absent from his charge.\"\n\nThe treatment of locked-jaw, both in horses and cattle, has, hitherto,\nbeen notoriously unsuccessful. This is not to be wondered at when we\ntake into consideration the destructive character of the treatment.\n\n\"Take,\" says Mr. Youatt, \"twenty-four pounds of blood from the animal;\nor bleed him almost to fainting.... Give him Epsom salts in pound and a\nhalf doses (!) until it operates. Purging being established, an attempt\nmust be made to allay the irritation of the nervous system by means of\nsedatives; and the best drug is opium.[8] The dose should be a drachm\nthree times a day. [One fortieth part of the quantity here recommended\nto be given in one day would kill a strong man who was not addicted to\nits use.] At the same time, the action of the bowels must be kept up by\nEpsom salts, or common salt, or sulphur, and the proportion of the\npurgative and the sedative must be so managed, that the constitution\nshall be under the influence of both.[9] A seton of black hellebore root\nmay be of service. It frequently produces a great deal of swelling and\ninflammation.[10] ... If the disease terminates successfully, the beast\nwill be left sadly out of condition, and he will not thrive very\nrapidly. He must, however, be got into fair plight, as prudence will\nallow, and then sold; for he will rarely stand much work afterwards, or\ncarry any great quantity of flesh.\" The same happens to us poor mortals\nwhen we have been dosed _secundum artem_. We resemble walking skeletons.\n\nOur own opinion of the disease is, that it is one of nervous origin, and\nthat the tonic spasm, always present in the muscles of voluntary\nmotion, is only symptomatic of derangement in the great, living\nelectro-galvanic battery, (the brain and spinal cord,) or in some of its\nwires (nerves) of communication.\n\nMr. Percival says, \"Tetanus consists, in a spasmodic contraction, more\nor less general, of the muscles of voluntary motion, and especially of\nthose that move the lower jaw; hence the vulgar name of it,\n_locked-jaw_, and the technical one of _trismus_.\"\n\nIn order to make ourselves clearly understood, and furnish the reader\nwith proper materials for him to prosecute his inquiries with success, a\nfew remarks on the origin of muscular motion seem to be absolutely\nnecessary.\n\nIt is generally understood by medical men, and taught in the schools,\nthat there are in the animal economy four distinct systems of nerves.\n\n1st system. This consists of the sensitive nerves, which are distributed\nto all parts of the animal economy endowed with feeling; and all\nexternal impulses are reflected to the medulla oblongata, &c. (See\n_Dadd's work on the Horse_, p. 127.) In short, these nerves are the\nmedia through which the animal gets all his knowledge of external\nrelations.\n\n2d system. The motive. These proceed from nearly the same centre of\nperception, and distribute themselves to all the muscles of voluntary\nmotion. It is evident that the muscle itself cannot perform its office\nwithout the aid of the nerves, (electric wires;) for it has been proved\nby experiment on the living animal, that when the posterior columns of\nnervous matter, which pass down from the brain towards the tail, are\nsevered, then all voluntary motion ceases. Motion may, however,\ncontinue; but it can only be compared to a ship at sea without a rudder,\nhaving nothing to direct its course. It follows, then, that if the\nnerves of motion and sensation are severed, there is no communication\nbetween the parts to which they are distributed and the brain. And the\npart, if its nutritive function be also paralyzed, will finally become\nas insensible as a stone--wither and die.\n\n3d system. The respiratory. These are under the control of the will\nonly through the superior power, as manifested by the motive nerves. For\nthe animal will breathe whether it wishes to or not, as long as the\nvital spark burns.\n\n4th system. The sympathetic, sometimes called _nutritive nerves_. They\nare distributed to all the organs of digestion, absorption, circulation,\nand secretion. These four nervous structures, or systems, must all be in\na physiological state, in order to carry on, with unerring certainty,\ntheir different functions. If they are injured or diseased, then the\nperceptions of external relations are but imperfectly conveyed to the\nmind. (_Brutes have a mind._) On the other hand, if the brain, or its\nappendages, spinal marrow, &c., be in a pathological state, then the\nmanifestations of _mind_ or _will_ are but imperfectly represented. Now,\nit is evident to every reasonable man, that the nerves may become\ndiseased from various causes; and this explains the reason why\nlocked-jaw sometimes sets in without any apparent cause. The medical\nworld have then agreed to call it _idiopathic_. This term only serves to\nbewilder us, and fails to throw the least light on the nature of the\nmalady, or its causes. Many men ridicule the idea of the nerves being\ndiseased, just because alterations in their structure are not evident to\nthe senses. We cannot see the atoms of water, nor even the myriads of\nliving beings abounding in single drop of water! yet no one doubts that\nwater contains many substances imperceptible to the naked eye. We know\nthat epizooetic diseases are wafted, by the winds, from one part of the\nworld to another; yet none of us have ever seen the specific virus. Can\nany man doubt its existence?\n\nHence it appears that diseases may exist in delicately-organized\nfilaments, without the cognizance of our external perceptions.\n\nIt is further manifest that locked-jaw is only symptomatic of diseased\nnervous structures, and that a pathological state of the nervous\nfilaments may be brought about independent of a prick of a nail, or\ndirect injury to a nerve.\n\nHence, instead of tetanus consisting \"in a spasmodic contraction of the\nmuscles of voluntary motion,\" it consists in a deranged state of the\nnervous system; and the contracted state of the muscles is only\nsymptomatic of such derangement. Then what sense is there in blistering,\nbleeding, and inserting setons in the dewlap? Of what use is it to treat\nsymptoms? Suppose a man to be attacked with hepatitis, (inflammation of\nthe liver:) he has a pain in the right shoulder. Suppose the physician\nprescribes a plaster for the latter, without ascertaining the real\ncause, or perhaps not knowing of its existence. We should then say that\nthe doctor only treated symptoms. \"And he who treats symptoms never\ncures disease.\" Suppose locked-jaw to have supervened from an attack of\nacute indigestion: would it not be more rational to restore the lost\nfunction?\n\nSuppose locked-jaw to have set in from irritating causes, such as bots\nin the stomach, worms in the intestines, &c.: would bleeding remove\nthem? would it not render the system less capable of recovering its\nphysiological equilibrium, and resisting the irritation produced by\nthese animals on the delicate nervous tissues?\n\nSuppose, as Mr. Youatt says, that locked-jaw sets in \"after turning the\nanimal out to graze during a cold night:\" will a blister to the spine,\nor a seton in the dewlap, restore the lost function of the skin?\n\nIn short, would it not be more rational, in cases of locked-jaw, to\nendeavor to restore the healthy action of all the functions, instead of\ndepressing them with the agents referred to?\n\nThen the question arises, What are the indications to be fulfilled?\n\n_First._ Restore the lost function.\n\n_Secondly._ Equalize the circulation, and maintain an equilibrium\nbetween nervous and arterial action.\n\n_Thirdly._ Support the powers of life.\n\n_Fourthly._ If locked-jaw arise from a wound, then apply suitable\nremedial agents to the part, and rescue the nervous system from a\npathological state.\n\nTo fulfil the fourth indication, we commence the treatment as follows:--\n\nSuppose the foot to have been pricked or wounded. We make an\nexamination of the part, and remove all extraneous matter. The following\npoultice must then be applied:\n\n  Powdered skunk cabbage, }\n     \"     lobelia,       }    equal parts.\n     \"     poplar bark,   }\n  Indian meal,                 1 pint.\n\nMake it of the proper consistence with boiling water. When sufficiently\ncool, put it into a flannel bag, and secure it above the pastern. To be\nrenewed every twelve hours. After the second application, examine the\nfoot, and if suppuration has commenced, and matter can be felt, or seen,\na small puncture may be made, taking care not to let the knife penetrate\nbeyond the bony part of the hoof.\n\nIn the mean time, prepare the following drink:--\n\n  Indian hemp or milkweed, (herb,)     1 ounce.\n  Powdered mandrake,                   1 table-spoonful.\n  Powdered lobelia seeds,              1 tea-spoonful.\n     \"     poplar bark, (very fine,)   1 ounce.\n\nMake a tea, in the usual manner--about one gallon. After straining it\nthrough a cloth, add the other ingredients, and give a quart every two\nhours.\n\nA long-necked bottle is the most suitable vehicle in which to\nadminister; but it must be poured down in the most gradual manner. The\nhead should not be elevated too high.\n\nA liberal allowance of camomile tea may be resorted to, during the whole\nstage of the disease.\n\nNext stimulate the external surface, by warmth and moisture, in the\nfollowing manner: Take about two quarts of vinegar, into which stir a\nhandful of lobelia; have a hot brick ready, (_the animal having a large\ncloth, or blanket, thrown around him_;) pour the mixture gradually on\nthe brick, which is held over a bucket to prevent waste; the steam\narising will relax the surface. After repeating the operation, apply the\nfollowing mixture around the jaws, back, and extremities: take of\ncayenne, skunk cabbage, and cypripedium, (lady's slipper,) powdered,\neach two ounces, boiling vinegar two quarts; stir the mixture until\nsufficiently cool, rub it well in with a coarse sponge; this will relax\nthe jaws a trifle, so that the animal can manage to suck up thin gruel,\nwhich may be given warm, in any quantity. This process must be\npersevered in; although it may not succeed in every case, yet it will be\nmore satisfactory than the blood-letting and poisoning system. No\nmedicine is necessary; the gruel will soften the faeces sufficiently; if\nthe rectum is loaded with faeces, give injections of an infusion of\nlobelia.\n\nFOOTNOTES:\n\n[8] This is a narcotic vegetable poison; and although large quantities\nhave been occasionally given to the horse without apparent injury,\nexperience teaches us that poisons in general--notwithstanding the\nvarious modes of their action, and the difference in their symptoms--all\nagree in the abstraction of vitality from the system. Dr. Eberle says,\n\"Opiates never fail to operate perniciously on the whole organization.\"\nDr. Gallup says, \"The practice of using opiates to mitigate pain is\ngreatly to be deprecated. It is probable that opium and its preparations\nhave done seven times the injury that they have rendered benefit on the\ngreat scale of the civilized world. Opium is the most destructive of all\nnarcotics.\"\n\n[9] This is a perfect seesaw between efforts to kill and efforts to\ncure.\n\n[10] Then it ought not to be used.\n\n\n\n\nINFLAMMATORY DISEASES.\n\n\nINFLAMMATION OF THE STOMACH, (GASTRITIS.)\n\nSuch a complicated piece of mechanism is the stomach of the ox, that\norgan is particularly liable to disease. Inflammation, being the same as\nlocal fever, (or a high grade of vital power, concentrated within a\nsmall space,) may be produced by over-feeding, irritating and\nindigestible food, or acrid, poisonous, and offensive medicines. The\nfarmer must remember that a small quantity of good, nutritious food,\ncapable of being easily penetrated by the gastric fluids, will repair\nthe waste that is going on, and improve the condition with more\ncertainty than an abundance of indifferent provender.\n\n_Cure._--The first indication will be to allay the irritability of the\nstomach; this will moderate the irritation and lessen the fever. Make a\nmucilaginous drink of slippery elm, or marshmallows, and give half a\npint every two hours. All irritating food and drink must be carefully\navoided, and the animal must be kept quiet; all irritating cordials,\n\"including the popular remedy, gin and molasses,\" must be avoided. These\nnever fail to increase the malady, and may occasion death. If there is\nan improper accumulation of food in the viscera, the remedies will be,\nrelaxing clysters, abstinence from food, and a tea of sassafras and\nmandrake, made thus:--\n\n  Sassafras, (_laurus sassafras_,)       1 ounce.\n  Mandrake, (_podophyllum peltatum_,)    4 drachms.\n  Boiling water,                              2 quarts.\n\nLet the mixture stand until quite cool, and give a pint every four\nhours.\n\nAlmost all animals, when suffering under acute symptoms, require\ndiluting, cooling drinks. This at once points out the use of water, or\nany weak gruel of which water is the basis; the necessity of diluting\nliquors is pointed out by the heat and dryness of the mouth, and\nrigidity of the coat.\n\nWhen the thirst is great, the following forms a grateful and cooling\nbeverage: Take lemon balm, (_melissa officinalis_,) two ounces; boiling\nwater, two quarts; when cool, strain, and add half a tea-spoonful of\ncream of tartar. Give half a pint at intervals of two hours.\n\nIf the stomach continues to exhibit a morbid state, which may be known\nby a profuse discharge of saliva from the mouth, then administer\ncamomile tea in small quantities: the addition of a little powdered\ncharcoal will prove beneficial.\n\n_Remarks._--Gastritis cannot be long present without other parts of the\nsystem sharing the disturbance: it is then termed gastric fever. This\nfever is the result of the local affection. Our object is, to get rid of\nthe local affection, and the fever will subside. Authors have invariably\nrecommended destructive remedies for the cure of gastritis; but they\ngenerally fail of hitting the mark, and always do more or less injury.\n\nA light diet, rest, a clean bed of straw in a well-ventilated barn, will\ngenerally perfect the cure.\n\n\nINFLAMMATION OF THE LUNGS, (PNEUMONIA.)\n\n_Causes._--Errors in feeding, over-exertion, exposure in wet pastures,\nor suffering the animal, when in a state of perspiration, to partake\ntoo bountifully of cold water, are among the direct causes of a\nderangement of vital equilibrium. Want of pure air for the purpose of\nvitalizing the blood, the inhalation of noxious gases, and filth and\nuncleanliness, may produce this disease in its worst form; yet it must\nbe borne in mind that the same exciting causes will not develop the same\nform of disease in all animals. It altogether depends on the amount of\nvital resistance, or what is termed the peculiar idiosyncrasy of the\nanimal. On the other hand, several animals often suffer from the same\nform of disease, from causes varying in their general character. Hence\nthe reader will see that it would be needless, in fact impossible, to\npoint to the direct cause in each grade of disease. The least\nobstruction to universal vital action will produce pneumonia in some\nanimals, while in others it may result in disease of the bowels.\n\n_Cure._--No special treatment can be successfully pursued in pneumonia;\nfor the lungs are not the only organs involved: no change of condition\ncan occur in the animal functions without the nervous system being more\nor less deranged; for the latter is essential to all vital motions.\nHence disease, in every form, should be treated according to its\nindications. A few general directions may, however, be found useful. The\nfirst indication to be fulfilled is to equalize the blood. Flannels\nsaturated with warm vinegar should be applied to the extremities; they\nmay be folded round the legs, and renewed as often as they grow cold.\nPoultices of slippery elm, applied to the feet, as hot as the animal can\nbear them, have sometimes produced a better result than vinegar. If the\nanimal has shivering fits, and the whole surface is chilled, apply\nwarmth and moisture as recommended in article \"_Locked-Jaw_.\" At the\nsame time, endeavor to promote the insensible perspiration by the\ninternal use of diaphoretics--_lobelia or thoroughwort tea_. A very good\ndiaphoretic and anti-spasmodic drink may be made thus:--\n\n  Lobelia, (herb)                       2 ounces.\n  Spearmint,                            1 ounce.\n  Boiling water,                        2 quarts.\n\nLet the above stand for a few minutes; strain, then add two\ntable-spoonfuls of honey. Give half a pint every hour, taking care to\npour it down the oesophagus very gently, so as to insure its reaching\nthe fourth or true digestive stomach. The following clyster must be\ngiven:--\n\n  Powdered lobelia,                        2 ounces.\n  Boiling water,                           3 quarts.\n\nWhen sufficiently cool, inject with a common metal syringe.\n\nThese processes should be repeated as the symptoms require, until the\nanimal gives evidence of relief; when a light diet of thin gruel will\nperfect the cure. It must ever be borne in mind that in the treatment of\nall forms of disease--those of the _lungs more especially_--the animal\nmust have pure, uncontaminated atmospheric air, and that any departure\nfrom purity in the air which the animal respires, will counteract all\nour efforts to cure.\n\n\nINFLAMMATION OF THE BOWELS, (ENTERITIS,--INFLAMMATION OF THE\nFIBRO-MUSCULAR COAT OF THE INTESTINES.)\n\n_Character._--Acute pain; the animal appears restless, and frequently\nturns his head towards the belly; moans, and appears dull; frequent\nsmall, hard pulse; cold feet and ears.\n\n_Causes._--Plethora, costiveness, or the sudden application of cold\neither internally or externally, overworking, &c.\n\n_Cure._--In the early stages of the disease, all forms of medication\nthat are in any way calculated to arouse the peristaltic motion of the\nintestines should be avoided; hence purges are certain destruction.\nRelax the muscular structure by the application of a blanket or\nhorse-cloth wrung out in hot water. In this disease, it is generally\nsufficient to apply warmth and moisture as near the parts affected as\npossible; yet if the ears and legs are cold, the general application of\nwarmth and moisture will more speedily accomplish the relaxation of the\nwhole animal. After the application of the above, injections of a mild,\nsoothing character (slippery elm, or flaxseed tea) should be used very\nliberally. A drink of any mucilaginous, lubricating, and innocent\nsubstance may be given, such as mallows, linseed, Iceland moss, slippery\nelm. During convalescence, the diet must be light and of an unirritating\ncharacter, such as boiled carrots, scalded meal, &c.\n\n\nINFLAMMATION OF TILE PERITONEAL COAT OF THE INTESTINES,\n(PERITONITIS.)\n\nThis disease requires the same treatment as the latter malady.\n\n\nINFLAMMATION OF THE KIDNEYS, (NEPHRITIS.)\n\nThe usual symptoms are a quick pulse; loss of appetite; high-\nurine, passed in small quantities, with difficulty and pain. Pressure on\nthe loins gives pain, and the animal will shrink on placing the hand\nover the region of the kidneys.\n\n_Causes._--Cold, external injury, or injury from irritating substances,\nthat are often sent full tilt through the kidneys, as spirits of\nturpentine, gin and molasses, saleratus. It is unnecessary to detail all\nthe causes of the disease: suffice it to say, that they exist in any\nthing that can for a time obstruct the free and full play of the\ndifferent functions.\n\n_Treatment._--This, too, will consist in the invitation of the blood to\nthe surface and extremities, and by removing all irritating matter from\nthe system, _in the same manner as for inflammation of the bowels_. The\napplication of a poultice of ground hemlock, or a charge of gum hemlock,\nwill generally be found useful. The best drinks--and these should only\nbe allowed in small quantities--are gum arabic and marshmallow\ndecoctions.\n\n\nINFLAMMATION OF THE BLADDER, (CYSTITIS.)\n\nDuring the latter months of pregnancy, the bladder is often in an\nirritable state, and a frequent desire to void the urine is observed,\nwhich frequently results from constipation. A peculiar sympathy exists\nbetween the bladder and rectum; and when constipation is present, there\nis a constant effort on the part of the animal to void the excrement.\nThis expulsive action also affects the bladder: hence the frequent\nefforts to urinate. The irritable state of the bladder is caused by the\npressure of the loaded rectum on the neck of the former.\n\nThe common soap-suds make a good injection, and will quickly soften the\nhardened excrement; after which the following clyster may be used:--\n\n  Linseed tea,                          3 quarts.\n  Cream of tartar,                      1 ounce.\n\nAfter throwing into the rectum about one third of the above, press the\ntail on the anus. The object is, to make it act as a fomentation in the\nimmediate vicinity of the parts. After the inflammation shall have\nsubsided, administer the following in a bottle, or horn:--\n\n  Powdered blackroot, (_leptandra virginica_,)      half an ounce.\n  Warm water,                                       1 pint.\n\nRepeat the dose, if the symptoms are not relieved.\n\n\nINFLAMMATION OF THE WOMB.\n\nThis may be treated in the same manner as the last-named disease. The\nmalady may be recognized by lassitude, loss of appetite, diminution in\nthe quantity, and deterioration in the quality, of the milk. As the\ndisease advances, there is often a fetid discharge from the parts; a\nconstant straining, which is attended with a frequent flow of urine.\n\n\nINFLAMMATION OF THE BRAIN, (PHRENITIS.)\n\nIn this disease, the pia mater, arachnoid membrane, or the brain itself,\nmay be inflamed. It matters very little which of the above are deranged,\nfor the means of cure are the same. We have no method of making direct\napplication to either of the above, as they all lie within the cranium.\nNeither can we act upon them medicinally except through the organs of\nsecretion, absorption, and circulation. Post mortem examinations reveal\nto us evident marks of high inflammatory action, both in the substance\nof the brain and in its membranes; and an effusion of blood, serum, or\nof purulent matter, has been found in the ventricles of the brain.\n\n_Treatment._--The indications are, to equalize the circulation by warmth\nand moisture externally, and maintain the action to the surface by\nrubbing the legs with the following counter-irritant:--\n\n  Vinegar,                           1 quart.\n  Common salt,                       2 ounces.\n\nSet the mixture on the fire, (_in an earthen vessel_,) and allow it to\nsimmer for a few moments; then apply it to the legs. After the\ncirculation is somewhat equalized, give the following drench:--\n\n  Extract of butternut,               half an ounce.\n  Tea of hyssop,                      1 pint.\n\nA stimulating clyster may then be given, composed of warm water, into\nwhich a few grains of powdered capsicum may be sprinkled.\n\nIf due attention be paid to counter-irritation, and the head kept cool\nby wet cloths, the chances of recovery are pretty certain.\n\n\nINFLAMMATION OF THE EYE.\n\nThis disease is too well known to require any description; we shall\ntherefore, at once, proceed to point out the ways and means for its\ncure.\n\n_Treatment._--First wash the eyes with a weak decoction of camomile\nflowers until they are well cleansed; then give a cooling drink,\ncomposed of\n\n  Cream of tartar,                          1 ounce.\n  Decoction of lemon balm,                  1 quart.\n\nRepeat this drink every six hours, until the bowels am moved. Should the\ndisease occur where these articles cannot be procured, give two ounces\nof common salt in a pint of water. Should the eye still continue red and\nswollen, give a dose of physic. (See _Physic for Cattle_.)\n\nIf a film can be observed, wash with a decoction of powdered bloodroot;\nand if a weeping remain, use the following astringent:--\n\n  Powdered bayberry bark,                   1 ounce.\n  Boiling water,                            1 pint.\n\nWhen cool, pour off the clear liquor. It is then fit for use.\n\nInflammation of the eye may assume different forms, but the above\ntreatment, combined with attention to rest, ventilation, a dark\nlocation, and a light diet, will cover the whole ground.\n\n\nINFLAMMATION OF THE LIVER, (HEPATITIS.)\n\nCattle very frequently show signs of diseased liver. Stall-fed oxen and\ncows kept in cities are most liable to derangement of the liver; in such\nanimals, (after death,) there is an unusual yellowness of the fat. A\ndisease of the liver may exist for a long time without interfering much\nwith the general health. Mr. Youatt informs us that \"a chronic form of\ndiseased liver may exist for some months, or years, not characterized by\nany decided symptom, and but little interfering with health.\"\n\n_Symptoms._--Permanent yellowness of the eyes; quick pulse; dry muzzle;\nhot mouth; considerable pain when pressure is made on the right side.\nOccasionally the animal looks round and licks the spot over the region\nof the liver.\n\n_Treatment._--First give half pint doses of thoroughwort tea, at\nintervals of one hour, (_to the amount of two quarts_.) This will relax\nthe system, and equalize vital action. The following drench is then to\nbe given:--\n\n  Extract of butternut,              half an ounce.\n  Warm water,                        1 quart.\n\nIf the butternut cannot be obtained, substitute a dose of physic. (See\nAPPENDIX.) Stimulate the bowels to action by injections of\nsoap-suds. If the extremities are cold, proceed to warm them in the\nmanner alluded to in article _Inflammation of the Bowels_. On the other\nhand, if the surface of the body is hot and dry, and there is much fever\npresent, indicated by a quick pulse and dry muzzle, then bathe the whole\nsurface with weak saleratus water, sufficiently warm to relax the\nexternal surface. The following fever drink may be given daily until\nrumination again commences:--\n\n  Lemon balm,                            2 ounces.\n  Cream of tartar,                       1 ounce.\n  Honey,                                 1 gill.\n  Water,                                 2 quarts.\n\nFirst pour the boiling water on the balm; after standing a few minutes,\nstrain; then add the above ingredients.\n\n\n\n\nJAUNDICE, OR YELLOWS.\n\nTHIS disease is well known to every farmer; the yellow appearance of the\nskin, mouth, eyes, and saliva at once betray its presence. It consists\nin the absorption of unchanged bile into the circulation, which bile\nbecomes diffused, giving rise to the yellow appearances.\n\nIn the treatment of jaundice, we first give a dose of physic, (see\nAPPENDIX,) and assist its operation by injections of weak lie,\nmade from wood ashes. The animal may roam about in the barn-yard, if the\nweather will permit; or rub the external surface briskly with a wisp or\nbrush, which will answer the same purpose. The following may be given in\none dose, and repeated every day, or every other day, as the symptoms\nmay require:--\n\n  Powdered golden seal,(_hydrastus\n               canadensis_),                    1 table-spoonful.\n     \"      slippery elm,                         2 ounces.\n\nWater sufficient to make it of the consistence of gruel.\n\nShould a diarrhoea set in, it ought not to occasion alarm, but may be\nconsidered as an effort of nature to rid the system of morbific matter.\nIt will be prudent, however, to watch the animal, and if the strength\nand condition fail, then add to the last prescription a small quantity\nof powdered gentian and caraway seeds.\n\nThere are various forms of disease in the liver, yet the treatment will\nnot differ much from that of the last-named disease. There is no such\nthing as a medicine for a particular symptom, in one form of disease,\nthat is not equally good for the same symptom in every form. In short,\nthere is no such thing as a specific. Any medicine that will promote the\nhealthy action of the liver in one form of jaundice will be equally good\nfor the same purpose in another form of that disease.\n\nMr. Youatt states, \"There are few diseases to which cattle are so\nfrequently subject, or which are so difficult to treat, as jaundice, or\nyellows.\" Hence it is important that the farmer should know how and in\nwhat manner the disease may be prevented. And he will succeed best who\nunderstands the causes, which often exist in overworking the stomach,\nwith a desire to fatten. Men who raise cattle for the market often\nattempt to get them in fine condition and flesh, without any regard to\nthe state of the digestive organs, the liver included; for the bile\nwhich the latter secretes is absolutely necessary for the perfection of\nthe digestive process. They do not take into consideration the state of\nthe animals' health, the climate, the quality of food, and the quantity\nbest adapted to the digestive powers; and what is of still greater\nimportance, and too often overlooked, is, that all animals should be fed\nat regular intervals. Some men suppose that so long as their cattle\nshall have good food, without any regard to quantity,--if they eat all\nday long, and cram their paunch to its utmost capacity,--they must\nfatten; when, in fact, too much food deranges the whole digestive\napparatus. As soon as the paunch and stomach are overloaded, they press\non the liver, interfering with the bile-secreting process, producing\ncongestion and disorganization.\n\nDiseases of the liver may be produced by any thing that will for a time\nsuspend the process of rumination: the known sympathy that exists\nbetween the stomach and liver explains this fact.\n\nDigestion, like every other vital process, requires a concentration of\npower to accomplish it: now, if an ox should have a bountiful meal, and\nthen be driven several miles, the process of digestion, during the\njourney, will be partly suspended. The act of compelling an ox to rise,\nor annoying him in any way, will immediately suspend rumination, which\nmay result in an acute disease of the liver. In most cases, however, the\nstomach is primarily affected.\n\nDealers in cattle often overfeed the animals they are about to dispose\nof, in order to improve their external appearance, and increase their\nown profits: the consequence is, that such animals are in a state of\nplethora, and are liable at any moment to be attacked with congestion of\nthe liver or brain.\n\nAgain. If oxen are driven a long journey, and then turned into a pasture\nabounding in highly nutritious grasses or clover, to which they are\nunaccustomed, they fill the paunch to such an extent that it becomes a\nmatter of impossibility on the part of the animal to throw it up for\nrumination; this mass of food, being submitted to the combined action of\nheat and moisture, undergoes fermentation; carbonic acid gas is evolved;\nthe animal is then said to be \"blown,\" \"hoven,\" or \"blasted.\" Post\nmortem examination, in such cases, reveals a highly-congested state of\nthe liver and spleen.\n\nIn fattening cattle, the injury done to the organs of digestion is not\nalways observed in the early stages; for the vital power, which wages a\nwarfare against all encroachments, endeavors to accommodate itself to\nthe increased bulk; yet, by continuing to give an excess of diet, it\nfinally yields up the citadel to the insidious foe. Chemical action then\noverpowers the vital, and disease is the result.\n\nThousands of valuable cattle are yearly destroyed by being too well, or,\nrather, injudiciously fed. Many diseases of the liver and digestive\norgans result from feeding on unwholesome, innutritious, and hard,\nindigestible food. Bad water, and suffering the animal to partake too\nbountifully of cold water when heated and fatigued, are among the direct\ncauses of disease.\n\n\n\n\nDISEASES OF THE MUCOUS SURFACE.\n\n\nThe mucous membrane is a duplicature of the skin, and is folded into the\nexternal orifices of the animal, as the mouth, ears, nose, lungs,\nstomach, intestines, and bladder; but not being so much exposed to the\naction of external agents, it is not so strong or thick as the skin. It\nperforms, however, nearly the same office as the skin. If the action of\none is suppressed, the other immediately commences the performance of\nits office. Thus a common cold, which collapses the skin, immediately\nstops insensible perspiration, which recedes to the mucous membrane,\nproducing a discharge from the nose, eyes, bowels, &c. So, when great\nderangement of the mucous membrane exists, debilitating perspiration\nsucceeds. In the treatment of diseases of the mucous membrane, we\nendeavor to remove the irritating causes from the organs affected,\nrestore the general tone of the system, and invite action to the\nexternal surface.\n\n\nCATARRH, OR HOOSE.\n\nThis disease often arises from exposure to wet or cold weather, and from\nthe food being of a bad quality, or deficient in quantity. If the animal\nis enfeebled by poor feed, old age, or any other cause, then there is\nvery little resistance offered against the encroachments of disease:\nhence young beasts and cows after calving are often the victims.\n\n_Treatment._--It is necessary to attend to this disorder as soon as it\nmakes its appearance; for a common cold, neglected, often lays the\nfoundation of consumption. On the other hand, a little attention in the\nearly stages, and before sympathetic action sets in, would set all\nright. The first indication to be fulfilled is to invite action to the\nsurface by friction and counter-irritants. The following liniment may be\napplied to the feet and throat:--\n\n  Olive oil,                                  4 ounces.\n  Oil of cedar,                               1 ounce.\n  Liquid ammonia,                             half an ounce.\n\nRub the mixture in well; then give\n\n  Gruel,                                     1 quart.\n  Powdered licorice,                         1 ounce.\n  Composition,                               half a tea-spoonful.\n\nGive this at a dose, and repeat two or three times during the\ntwenty-four hours. A drink of any warm aromatic tea, _such as\npennyroyal, hyssop, catnip or aniseed will have a good effect_. The diet\nshould consist of scalded meal, boiled carrots, flaxseed, or any\nsubstance that is light and easy of digestion. Should the discharge\nincrease and the eyelids swell, recourse must be had to vapor, which may\nbe raised by pouring vinegar on a hot brick; the latter held, with a\npair of tongs, beneath the animal's nose, at the same time covering the\nhead with a blanket. A small quantity of bayberry bark may occasionally\nbe blown up the nostrils from a quill. It is very important, during the\ntreatment, that the animal be in a warm situation, with a good bed of\nstraw to rest on. If the glands under the jaw enlarge, the following\nmixture should be rubbed about the throat:--\n\n  Neat's foot oil,                       4 ounces.\n  Hot drops,                             2 ounces.\n  Vinegar,                               1 gill.\n\nIf the disease assumes a chronic form, and the animal is evidently\nlosing flesh, then give the following:--\n\n  Golden seal, powdered,                 1 table-spoonful.\n  Caraway seeds, \"                       1        \"\n\nDivide into three parts; which may be given daily, (in thin gruel,)\nuntil the animal is convalescent.\n\n\nEPIDEMIC CATARRH.\n\nThis often prevails at particular seasons, and spreads over whole\ndistricts, sometimes destroying a great number of cattle. It is a\ndisorder whose intensity varies considerably, being sometimes attended\nwith a high grade of fever, at other times quickly followed by general\ndebility.\n\n_Treatment._--This requires the same treatment as the last-named\ndisease, but only more thoroughly and perseveringly applied; for every\nportion of the system seems to be affected, either through sympathetic\naction or from the absorption of morbid matter. Hence we must aid the\nvital power to maintain her empire and resist the encroachments on her\nsanative operations by the use of antiseptics and stimulants. The\nfollowing is a good example:--\n\n  Powdered charcoal,                   1 ounce.\n     \"     bayberry bark,              half an ounce.\n     \"     pleurisy root,              1 ounce.\n  Honey,                               1 table-spoonful.\n  Thin gruel,                          1 quart.\n\n\nMALIGNANT EPIDEMIC, (MURRAIN.)\n\nThis disease has been more or less destructive from the time of Pharaoh\nup to the present period. For information on the origin, progress, and\ntermination of this malignant distemper, the reader is referred to Mr.\nYouatt's work on cattle.\n\n_Treatment._--The indications to be fulfilled are, first, to preserve\nthe system from putrescence, which can be done by the use of the\nfollowing drink:--\n\n  Powdered capsicum,                     1 tea-spoonful.\n     \"     charcoal,                     2 ounces.\n  Lime water,                            4 ounces.\n  Sulphur,                               1 tea-spoonful.\n\nAdd to the capsicum, charcoal, and sulphur, a small quantity of gruel;\nlastly, add the lime water. A second and similar dose may be given six\nhours after the first, provided, however, the symptoms are not so\nalarming.\n\nThe next indication is, to break down the morbid action of the nervous\nand vascular systems; for which the following may be given freely:--\n\n  Thoroughwort tea,                      2 quarts.\n  Powdered assafoetida,                  2 drachms.\n\nAid the action of these remedies by the use of one of the following\ninjections:--\n\n  Powdered lobelia,                       2 ounces.\n  Oil of peppermint,                     20 drops.\n  Warm water,                             2 quarts.\n\n_Another._\n\n  Infusion of camomile,                  2 quarts.\n  Common salt,                           4 ounces.\n\nIn all cases of putrid or malignant fever, efforts should be made to\nsupply the system with caloric, (by the aid of stimulants,) promote the\nsecretions, and rid the system of morbific materials.\n\n\nDIARRHOEA, (LOOSENESS OF THE BOWELS.)\n\nIn the early stages of this disease, it is not always to be checked. It\nis often a salutary operation of nature to rid the system of morbific\nmaterials, and all that we can do with safety is, to sheathe and\nlubricate the mucous surfaces, in order to protect them from the acrid\nand stimulating properties of the agents to be removed from the\nalimentary canal.\n\nWhen the disease, of which diarrhoea is only a symptom, proceeds from\nexposure, apply warmth, moisture, friction, and stimulants to the\nexternal surface, aided by the following lubricant:--\n\n  Powdered slippery elm,              1 ounce.\n     \"     charcoal,                  1 table-spoonful.\n  Boiling water,                      2 quarts.\n\nCommon starch, or flour, may be substituted for slippery elm. The\nmixture should be given in pint doses, at intervals of two hours. When\nthe fecal discharges appear more natural and less frequent, a tea of\nraspberry leaves or bayberry bark will complete the cure.\n\nWhen the disease assumes a chronic form, and the animal loses flesh,\nthe following tonic, stimulating, astringent drink is recommended:--\n\n  Infusion of camomile,                     1 quart.\n  Powdered caraway seeds,                   1 ounce.\n  Bayberry, powdered,                       half an ounce.\n\nMix for one dose.\n\n_Remarks._--In the treatment of this disease, it is necessary for the\nfarmer to know, that through the instrumentality of the nervous\nstructure, there is constantly a sympathy kept up between the different\nparts of the animal; whenever any part is affected, the corresponding\npart feels the influence. Thus the external surface is opposed to the\ninternal, so that, if the function of the former be diminished, or\nexcessive, or suspended, that of the latter will soon become deranged;\nand the restoration of the lost function is the only true way to effect\na cure. For example, if an animal be suffered to feed in wet lands, the\nfeet and external surface become cold; and hence diarrhoea, catarrh,\ngarget, dysentery, &c. If the circulation of the blood is obstructed by\nexposure, we should restore the lost function by rubbing the surface,\nand by the application of warmth and moisture. If the animal is in poor\ncondition, and there is not enough vitality to equalize the circulation,\ngive warm anti-spasmodics. (See APPENDIX.) In cases where\ndiarrhoea results from a want of power in the digestive organs to\nassimilate the food, the latter acts on the mucous surfaces as a\nmechanical irritant, producing inflammation, &c. Inflammation is the\nconcentration of the available vital force too much upon a small region\nof the body, and it is invited there by irritation. Now, instead of the\npopular error,--bleeding and purging,--the most rational way to proceed\nis, to remove the cause of irritation, (no matter whether the stomach or\nbowels are involved,) and invite the blood to the surface by means\nalready alluded to, and distribute it over the general system, so that\nit will not be in excess any where. There is generally but little\ndifficulty in producing an equilibrium of action; the great point is to\nsustain it. When the blood accumulates in a part, as in inflammation of\nthe bowels, the sensibility of the part is so highly exalted that the\nleast irritation causes a relapse; therefore the general treatment must\nnot be abandoned too early.\n\n\nDYSENTERY.\n\nThe disease is generally ushered in with some degree of fever; as,\ntrembling, hot and cold stages, dryness of the mouth, loss of appetite,\ngeneral prostration, drooping of the head and ears, heaving of the\nflanks; there are frequent stools, yet these seldom consist of natural\nexcrement, but are of a viscid, mucous character; the animal is\nevidently in pain during these discharges, and sometimes the fundament\nappears excoriated.\n\n_Causes._--The cause of this complaint appears to be, generally,\nexposure. Dr. White says, \"Almost all the diseases of cattle arise\neither from exposure to wet or cold weather, from their food being of a\nbad quality, or deficient in quantity, or from the animal being changed\ntoo suddenly from poor, unwholesome keep to rich pasture. It is\nnecessary to observe, also, that the animal is more liable to be injured\nby exposure to wet and cold, when previously enfeebled by bad keep, old\nage, or any other cause; and particularly when brought from a mild into\na cold situation. I have scarcely met with a disease that is not\nattributable to a chill.\"\n\n_Treatment._--This must be much the same as in diarrhoea--sheathing\nthe mucous membrane, and inviting action to the surface. The animal must\nbe warmly housed, well littered, and the extremities clothed with\nflannel bandages. The diet must consist of flour gruel, scalded meal.\nRaspberry tea will be the most suitable drink. Much can be done by good\nnursing. Mr. Ellman says, \"If any of my cattle get into a low, weak\nstate, I generally recommend nursing, which, in most cases, is much\nbetter than a doctor; [meaning some of the poor specimens always to be\nfound in large cities;] having often seen the beast much weakened, and\nthe stomach relaxed, by throwing in a quantity of medicine\ninjudiciously, and the animal lost; when, with good nursing, in all\nprobability, it might have been otherwise.\"\n\n\nSCOURING ROT.\n\n_Cause._--Any thing that can reduce the vital energies.\n\n_Symptoms._--A gradual loss of flesh, although the animal often feeds\nwell and ruminates. The excrements are of a dark color, frothy, and\nfetid, and, in the latter stages, appear to be only half digested. There\nare many symptoms and different degrees of intensity, during the\nprogress of this disease, indicate the amount of destruction going on;\nyet the author considers them unimportant in a practical point of view,\nat least as far as the treatment is concerned; for the disease is so\nanalogous to dysentery, that the same indications are to be fulfilled in\nboth; more care, however, should be taken to prevent and subdue\nmortification.\n\nIn addition to the treatment recommended in article _Malignant\nEpidemic_, the following injection may be substituted for the one\nprescribed under that head:--\n\n  Powdered charcoal,                   a tea-cupful.\n  Common salt,                         2 ounces.\n  Pyroligneous acid,[11]                half a wine-glass.\n  Warm water,                          2 quarts.\n\nThrow one quart of the above into the rectum, and the remainder six\nhours after the first.\n\nFOOTNOTE:\n\n[11] Vinegar obtained from wood.\n\n\n\n\nDISEASE OF THE EAR\n\n\nDiseases of the ear are very rare in cattle; yet, as simple inflammatory\naction does now and then occur, it is well that the farmer should be\nable to recognize and treat it.\n\n_Symptoms._--An unnatural heat and tenderness about the base of the ear,\nand the animal carries the head on one side.\n\n_Cure._--Fomentations of marshmallows; a light diet of scalded shorts;\nan occasional drink of thoroughwort tea. These with a little rest, in a\ncomfortable barn, will perfect the cure.\n\n_Remarks._--If any irritating substance is suspected to have fallen into\nthe ear, efforts must be made to remove it: if it cannot be got at, a\nsmall quantity of olive oil may be poured into the cavity; then, by\nrotating the head, with the affected ear downwards, the substances will\noften pass out.\n\n\n\n\nSEROUS MEMBRANES.\n\n\nThese membranes derive their name from the serous or watery fluid they\nsecrete, by which their surface is constantly moistened. They are to be\nfound in the three cavities of the chest; namely, one on each side,\ncontaining the right and left lung, and the intermediate cavity,\noccupied by the heart. The portion of the membrane lining the lungs is\nnamed the _pleura_, and that lining and covering the heart is called the\n_pericardium_. The membrane lining the abdomen is named the\n_peritoneum_. The ventricles of the brain are also lined by this\nmembrane. The serous membranes, after lining their respective cavities,\nare extended still farther, by being reflected back upon the organs\nenclosed in their cavities; hence, if it were possible to dissect these\nmembranes from off the parts which they invest, they would have the\nappearance of a sac without an opening. In the natural state, these\nmembranes are exceedingly thin and transparent; but they become\nthickened by disease, and lose their transparency. The excessive\ndischarge of fluids into cavities lined by these membranes constitutes\nthe different forms of dropsy, on which we shall now treat.\n\n\n\n\nDROPSY.\n\n\nThis disease consists in the accumulation of fluid in a cavity of the\nbody, as the abdomen or belly, the chest, and ventricles of the brain,\nor in the cellular membrane under the skin. As the treatment of the\nseveral forms of dropsy requires that the same indications shall be\nfulfilled,--viz., to equalize the circulation, invite action to the\nsurface, promote absorption, and invigorate the general system,--so it\nmatters but little whether the effusion takes place under the skin,\nproducing anasarca, or within the chest or abdomen. The popular\ntreatment, which comprehends blood-letting, physicking, and the use of\npowerful diuretics, has proved notoriously unsuccessful. Blood-letting\nis charged as one of the direct causes of dropsy: how then can it be\nexpected that a system that will produce this form of disease can ever\ncure it? In reference to physicking, if the bowels are forced to remove\nthe excess of fluids in a short time, they become much exhausted, lose\ntheir tone, and do not recover their healthy power for some time. Dr.\nCurtis says, \"May we not give diuretics and drastic cathartics in\ndropsy? I answer, if you do, and carry off the fluids of the body in\nthose directions, as you sometimes may, you have not always removed the\ncause of the disease, which was the closing of the surface, or stoppage\nof some natural secretion, while you have rendered the patient liable to\nother forms of disease, quite as much to be dreaded as the dropsy which\nwas exchanged for it.\" Mild diuretic medicines may, however, be given,\nprovided attention he paid at the same time to the lungs and external\nsurface. The kidneys, lungs, and external surface constitute the great\noutlets through which the excess of fluids finds egress; and if one of\nthese functions be excited to dislodge an accumulation of fluid, without\nthe cooeperation of the rest, the excessive action is sure to injure the\norgan; hence it is an injurious practice, and ought to be rejected.\n\n_Causes._--Dropsy will occasionally be produced by the sudden stopping\nof any evacuation; for example, if a diarrhoea be checked too\nsuddenly, it frequently results in dropsy of the belly. In pleurisy, and\nwhen blood-letting has been practised to any extent, dropsy of the chest\nwill be the consequence. Exposure, poor diet, diseases of the liver and\nspleen, want of exercise, and poisonous medicines are among the general\ncauses of dropsy.\n\n_Treatment._--It is a law of the animal economy that all fluids are\ndetermined to those surfaces from which they can most readily escape.\nNow, instead of cramming down nauseous and poisonous drugs, with a view\nof carrying off the fluid by the kidneys, we should restore the lost\nfunction of the external exhalents, by warmth, moisture, friction, and\nthe application of stimulating embrocations to the general surface. The\nfollowing embrocation may be applied to the spine, ears, belly, and\nlegs:--\n\n  Oil of cedar,                      1 ounce.\n  Oil of juniper,                    1 ounce.\n  Soft soap,                         1 pound.\n\nA portion of the above should be rubbed in twice a day.\n\nThe best medicine is the following:--\n\n  Powdered mandrake,                  1 ounce.\n     \"     lobelia,                   1 ounce.\n  Poplar bark,                        2 ounces.\n  Lemon balm,                         4 ounces.\n  Boiling water,                      3 quarts.\n\nLet the whole stand in a covered vessel for an hour; then strain, and\nadd a gill of honey. Give half a pint every third hour. If the animal be\nin poor condition, the diet must be nourishing and easy of digestion.\nFlour gruel and scalded meal will be the most appropriate. A drink made\nby steeping cleavers, or hyssop, in boiling water may be given at\ndiscretion.\n\nIf there is not sufficient vitality in the system to equalize the\ncirculation, (which may be known by the surface and extremities still\ncontinuing cold,) the following drink will be found efficacious:--\n\n  Hyssop tea,                                2 quarts.\n  Powdered cayenne, (African,)               1 tea-spoonful.\n       \"   licorice,                         1 ounce.\n\nMix. To be given at a dose, and repeated if necessary. Should\ninflammatory symptoms make their appearance, omit the cayenne, and\nsubstitute the same quantity of cream of tartar.\n\nThe treatment of all the different forms of dropsy is upon the plan here\nlaid down. They are one and the same disease, only located in different\nparts; and from predisposing causes the fluid is sometimes found in the\nthorax, at others in the abdomen. Whenever costiveness occurs in dropsy,\nthe following laxative may be given:--\n\n  Wormwood,                   2 ounces.\n  Boiling water,              2 quarts.\n\nSet them over the fire, and let them boil for a few moments; then add\ntwo ounces of castile soap and a gill of molasses or honey. The whole to\nbe given at one dose.\n\nThe operation of tapping has been performed, but with very little\nsuccess; for, unless the function of the skin be restored, the water\nwill again accumulate. If, however, the disease shall be treated\naccording to the principles here laid down, there is no good reason why\nthe operation should not prove successful. It may be performed for\ndropsy of the belly in the following manner: Take a common trocar and\ncanula, and after pinching upwards a fold of the skin, about three\ninches from the line, (_linea alba_,) or centre of the belly, and about\nseven from the udder, push the trocar through the skin, muscles, &c.,\ninto the abdominal cavity; withdraw the trocar, and the water will flow.\nThe operation is usually performed on the right side, taking care,\nhowever, not to wound the milk vein, or artery.\n\n\n\n\nHOOVE, OR \"BLASTING.\"\n\n\nWhen cattle or sheep are first turned into luxuriant pasture, after\nbeing poorly fed, or laboring under any derangement of the digestive\norgans, they are apt to be hoven, blown, or blasted.\n\n_Treatment._--Should the symptoms be very alarming, a flexible tube may\nbe passed down the gullet. This will generally allow a portion of gas to\nescape, and thus afford temporary relief, until more efficient means are\nresorted to. These consist in arousing the digestive organs to action,\nby the following stimulant and carminative drink:--\n\n  Cardamom seeds,                        1 ounce.\n  Fennel seeds,                          1 ounce.\n  Powdered charcoal,                     1 table-spoonful.\n  Boiling water,                         2 quarts.\n\nLet the mixture stand until sufficiently cool; then strain, and\nadminister in pint doses, every ten minutes.\n\nThe following clyster should be given:--\n\n  Powdered lobelia,       2 ounces.\n     \"     charcoal,      6 ounces.\n  Common salt,            1 table-spoonful.\n  Boiling water,          2 quarts.\n\nWhen cool, strain, and inject.\n\nIf the animal is only blasted in a moderate degree, this treatment will\ngenerally prove successful. Some practitioners recommend puncturing the\nrumen or paunch; but there is always great danger attending it, and at\nbest it is only a palliative: the process of fermentation will continue\nwhile the materials still remain in the paunch. Some cattle doctors make\na large incision into the paunch, and shovel out the contents with the\nhand; but the remedy is quite as bad as the disease. For example, Mr.\nYouatt tells us that \"a cow had eaten a large quantity of food, and was\nhoven. A neighbor, who was supposed to know a great deal about cattle,\nmade an incision into the paunch; the gas escaped, a great portion of\nthe food was removed with the hand, and the animal appeared to be\nconsiderably relieved; but rumination did not return. On the following\nday, the animal was dull; she refused her food, but was eager to drink.\nShe became worse and worse, and on the sixth day she died.\"\n\nIn all dangerous cases of hoove, we must not forget that our remedies\nmay be aided by the external application of warmth and moisture;\nflannels wrung out in hot water should be secured to the belly; at the\nsame time, the legs and brisket should be rubbed with tincture of\nassafoetida. These remedies must be repeated until the animal is\nrelieved. Steady and long-continued perseverance in rubbing the abdomen\noften succeeds in liberating the gas. If the animal recovers, he should\nbe fed, very sparingly, on scalded food, consisting of equal parts of\nmeal and shorts, with the addition of a few grains of caraway seeds. A\ndrink composed of the following ingredients will aid in rapidly\nrestoring the animal to health:--\n\n  Marshmallows,       2 ounces.\n  Linseed,            1 ounce.\n  Boiling water,      2 quarts.\n\nSet the mixture near the fire, and allow it to macerate for a short\ntime; after straining through a sieve or coarse cloth, it may be given\nand repeated at discretion.\n\n_Remarks._--As prevention is much more convenient and less expensive\nthan the fashionable system of making a chemical laboratory of the poor\nbrute's stomach, the author would remind owners of stock that the\npractice of turning the latter into green, succulent pasture when the\nground is damp, or permitting them to remain exposed to the night air,\nis among the direct causes of hoove. The ox and many other animals are\ngoverned by the same laws of nature to which man owes allegiance, and\nany departure from the legitimate teachings, as they are fundamentally\ningrafted in the animate kingdom by the Omnipotent Creator, is sure to\nsubject us to the penalty. We are told that, during the night, noxious\ngases and poisonous miasmata emanate from the soil, and that plants\nthrow off excrementitious matters, which assume a gaseous form, and are\nmore or less destructive. Now, these animals have no better powers of\nresisting the encroachments on their organization (through the agency of\nthese deleterious gases) than we have; they must have atmospheric air to\nvitalize the blood; any impurity in the air they breathe must impair\ntheir health. Still, however, the powers of resistance are greater in\nsome than in others; this explains the reason why all do not suffer.\nSometimes, the gases are not in sufficient quantities to produce instant\ndeath, but only derange the general health; yet if an animal be turned\ninto a pasture, the herbage and soil of which give out an excess of\nnitrogen and carbonic acid, the animal will die; just as a man will, if\nyou lower him into a well abounding in either of these destructive\nagents. From these brief remarks, the farmer will see the importance of\nhousing domestic animals at night.\n\n\n\n\nJOINT MURRAIN.\n\n\nThis malady, in its early stages, assumes different forms; sometimes\nmaking its appearance under a high grade of vital action, commonly\ncalled inflammatory fever, and known by the red appearance of the\nsclerotica, (white of the eye,) hurried breathing, expanded nostrils,\nhot tongue, and dry muzzle, pulse full and bounding, manifestations of\npain, &c. &c. Different animals show, according to local or\nconstitutional peculiarities, different symptoms.\n\nThis disease, in consequence of its assuming different forms during its\nprogress, has a host of names applied to it, which rather embarrass than\nassist the farmer. We admit that there are numerous tissues to be\nobstructed; and if the disease were named from the tissue, it would have\nas many names as there are tissues. If it were named from the location,\nwhich often happens, then we get as many names as there are locations;\nfor example, horn ail, black leg, quarter evil, joint murrain, foot rot,\n&c. In the above disease, the whole system partakes more or less of\nconstitutional disturbance; therefore it is of no use, except when we\nwant to avail ourselves of local applications, to decide what particular\nmuscle, blood-vessel, or nerve is involved, seeing that the only\nrational treatment consists in acting on all the nerves, blood-vessels,\nand muscles, and that this can only be accomplished through the healthy\noperations of nature's secreting and excreting processes. The\nindications of cure, according to the reformed principles, are, to relax\nspasm, as in locked-jaw, stoppages of the bladder or intestines,\nobstructed surfaces, &c.; to contract and strengthen weak and relaxed\norgans, as in general or local debility, diarrhoea, scouring, lampas,\n&c.; to stimulate inactive parts, as in black leg, joint murrain,\nquarter ill, foot rot; to equalize the circulation, and distribute the\nblood to the external surface and extremities, as in congestions; to\nfurnish the animal with sufficient nutriment for its growth and\ndevelopment. No matter what the nature of disease may be, the treatment\nshould be conducted on these principles.\n\nThe farmer will overcome a host of obstacles, that might otherwise fall\nin his way, in the treatment of joint murrain, when he learns that this\nmalady, together with black leg, quarter ill or evil, black quarter, and\ndry gangrene are all analogous: by the different names are meant their\ngrades. In the early or mild forms, it consists of congestion in the\nveins or venous radicles, and effusions into the cellular tissue. When\nchemical action overpowers the vital, decomposition sets in; it then\nassumes a putrid type; mortification, or a destruction of organic\nintegrity, is the result.\n\n_Causes._--Its proximate causes exist in any thing that can for a time\ninterrupt the free and full play of any part of the vital machinery. Its\ndirect cause may be found in over-feeding, miasma, exposure, poisonous\nplants, poor diet, &c. The milk of diseased cows is a frequent cause of\nblack leg in young calves. The reason why the disease is more likely to\nmanifest itself in the legs is, because they are more exposed, by the\nfeet coming in contact with damp ground, and because the blood has a\nkind of up-hill work to perform.\n\n_Treatment._--In the early stages of joint murrain and its kindred\nmaladies, if inflammatory fever is present, the first and most important\nstep is to relax the external surface, as directed in article\n_Pneumonia_, p. 107. Should the animal be in a situation where it is not\nconvenient to do so, give the following anti-spasmodic:--\n\n  Thoroughwort,        1 ounce.\n  Lemon balm,          2 ounces.\n  Garlic, bruised,     a few kernels.\n  Boiling water,       3 quarts.\n\nAllow the infusion to stand until cool; then strain, and give it a dose.\n\nIf the bowels are constipated, inject the following:--\n\n  Soft soap,         half a pint.\n  Warm water,        2 quarts.\n\nRub the joints with the following embrocation:--\n\n  Oil of cedar,    }  equal parts.\n  Fir balsam,      }\n\nKeep the animal on warm, bland teas, such as catnip, pennyroyal, lemon\nbalm, and a light diet of powdered slippery elm gruel.\n\n\n\n\nBLACK QUARTER.\n\n\n_Symptoms._--Rapid decomposition, known by the pain which the slightest\npressure gives the animal. Carbonic acid gas is evolved from the\nsemi-putrid state of the system, which finds its way into the cellular\ntissue, beneath the skin. A crackling noise can then be heard and felt\nby pressing the finger on the hide.\n\n_Causes._--Among the chief causes are the blood-letting and scouring\nsystems recommended by writers on cattle doctoring. In the inflammatory\nstage, we are told, \"The first and most important step is copious\nbleeding. As much blood must be taken as the animal will bear to lose;\nand the stream must flow on until the beast staggers or threatens to\nfall. Here, more than in any other disease, there must be no foolish\ndirections about quantities. [_The heroic practice!_] As much blood must\nbe taken away as can be got; for it is only by the bold and persevering\nuse of the lancet that a malady can be subdued that runs its course so\nrapidly.\" (See Youatt, p. 359.) From these directions we are led to\nsuppose that there are some hopes of bleeding the animal to life; for\nthe author above quoted seems to entertain no apprehension of bleeding\nthe animal to death. Mr. Percival and other veterinary writers inform\nus, that \"an animal will lose about one fifteenth part of its weight of\nblood before it dies; though a less quantity may so far debilitate the\nvital powers, as to be, though less suddenly, equally fatal.\" The latter\nportion of the sentence means simply this; that if the bleeding does\nnot give the animal its quietus on the spot, it will produce black\nquarter, gangrene, &c., which will be \"equally fatal.\" In the latter\nstages of the disease now under consideration, and, indeed, in dry\ngangrene, there is a tendency to the complete destruction of life to the\nparts involved: hence our remedies should be in harmony with the vital\noperations. We should relax, stimulate, and cleanse the whole system,\nand arouse every part to healthy action, by the aid of vapor,\ninjections, stimulating applications, poultices of charcoal and\ncapsicum, to parts where there is danger of rapid mortification; lastly,\nstimulating drinks to vitalize the blood, which only requires\ndistribution, instead of abstraction.\n\nIn reference to the scouring system, (purging,) as a cause of\nmortification, we leave the reader to form his own views, after reading\nthe following: \"After abstracting as much blood as can be got away,\npurging must immediately follow. A pound and a half of Epsom salts\ndissolved in water or gruel, and poured down the throat as gently as\npossible, should be our first dose. If this does not operate in the\ncourse of six hours, another pound should be given; and after that, half\npound doses every six hours until the effect is produced\"!!--_Youatt_,\np. 359.\n\n_Treatment._--As the natural tendency of these different maladies is the\ncomplete destruction of life to all parts of the organization, efforts\nmust be made to depurate the whole animal, and arouse every part to\nhealthy action in the manner recommended under article _Joint Murrain_.\nAntiseptics may be freely used in the following form:--\n\n  Powdered bayberry bark,     2 ounces.\n     \"     charcoal,          6 ounces.\n     \"     cayenne,           1 tea-spoonful.\n     \"     slippery elm,      1 ounce.\n\nAdd boiling water sufficient to make it of the consistence of thin\ngruel.\n\nAll sores and foul ulcers may be washed with\n\n  Pyroligneous acid,     1 ounce.\n  Water,                 1 gill.\n\n_Another._\n\n  Chloride of lime,     1 ounce.\n  Water,                1 pint.\n\n_Another._\n\n  Chloride of soda,      1 ounce.\n  Water,                 6 ounces.\n\nThe affected parts should be often bathed with one of these washes. If\nthe disease is not arrested by these means, repeat them, and put the\nanimal on a diet of flour gruel.\n\n\n\n\nOPEN JOINT.\n\n\nJoints are liable to external injury from wounds or bruises, and,\nalthough a joint may not be open in the first instance, subsequent\nsloughing may expose its cavity. The ordinary effects of disease in\nmembranes covering joints are, a profuse discharge of joint oil,\n(_synovia_,) and a thickening of the synovial membrane. Sometimes the\njoint is cemented together; it is then termed anchylosis.\n\n_Treatment._--The first object is, to promote adhesion, by bringing the\nedges of the wound together, and confining them in contact by stitches.\nA pledget of lint or linen, previously moistened with tincture of myrrh,\nshould then be bound on with a bandage forming a figure 8 around the\njoint. If the parts feel hot and appear inflamed, apply a bandage, which\nmay be kept constantly wet with cold water. If adhesion of the parts\ndoes not take place, apply the following:--\n\nPowdered bayberry bark,      1 ounce.\n\nFir balsam, sufficient to form a thick, tenacious mass, which may be\nspread thickly over the wound; lastly, a bandage. Should a fetid\ndischarge take place, poultice with\n\n  Powdered charcoal, } equal parts.\n     \"     bayberry, }\n\nIn cases where the nature of the injury will not admit of the wounded\nedges being kept in contact, and a large surface is exposed, we must\npromote granulation by keeping the parts clean, and by the daily\napplication of fir balsam. Unhealthy granulations may be kept down by\ntouching them with burnt alum, or sprinkling on their surface powdered\nbloodroot. The author has treated several cases, in which there was no\nhope of healing by the first intention, by the daily use of tincture of\ncapsicum, together with tonic, stimulating, astringent, antiseptic\npoultices and fomentations, as the case seemed to require, and they\nalways terminated favorably. In all cases of injury to joints, rest and\na light diet are indispensable.\n\n\n\n\nSWELLINGS OF JOINTS.\n\n\nSwellings frequently arise from bruises and strains; they are sometimes,\nhowever, connected with a rheumatic affection, caused by cold, exposure\nto rain, or turning an animal into wet pasture lands after active\nexercise. In the acute stage, known by tenderness, unnatural heat, and\nlameness, the animal should be put on a light diet of scalded shorts,\n&c.; the parts to be frequently bathed with cold water; and, if\npracticable, a bandage may be passed around the limb, and kept moist\nwith the same. If the part still continues painful, take four ounces of\narnica flowers, moisten them with boiling water, when cool, bind them\naround the part, and let them remain twenty-four hours. This seldom\nfails. On the other hand, should the parts be in a chronic state, which\nmay be recognized by inactivity, coldness, &c., then the following\nembrocation will restore the lost tone:--\n\n  Oil of wormwood,        1 ounce.\n   \"  \"  cedar,           1 ounce.\n  Hot drops,              4 ounces.\n  Vinegar,                1 pint.\n\nMix, and rub the part faithfully night and morning. Friction with the\nhand or a brush will materially assist to cure. In all cases where\nsuppuration has commenced, and matter can be distinctly felt, the sooner\nthe following poultice shall be applied, the better:--\n\n  Powdered slippery elm,      } equal parts.\n     \"     linseed,           }\n\nBoiling water sufficient to moisten; then add a wine-glass of vinegar.\n\nTo be renewed every twelve hours, until the matter escapes.\n\n\n\n\nSPRAIN OF THE FETLOCK.\n\n\nSprain, or _strain_, as it is commonly termed, sometimes arises from\nviolent exertions; at other times, by the animal unexpectedly treading\non some uneven surface.\n\n_Treatment._--First wash the foot clean, then carefully examine the\ncleft, and remove any substance that may have lodged there. A cotton\nbandage folded around the claws and continued above the fetlock, kept\nwet with the following lotion, will speedily reduce any excess of\ninflammatory action that may exist:--\n\n  Acetic acid,        1 ounce.\n  Water,              1 pint.\n\n_Another._\n\n  Vinegar,            1 pint.\n  Water,              3 pints.\n\n\n\n\nSTRAIN OF THE HIP.\n\n\nThis may sometimes occur in working oxen. Rest is the principal remedy.\nThe part may, however, be bathed daily with the following:--\n\n  Wormwood,             4 ounces.\n  Scalding vinegar,     2 quarts.\n\nThe liquor must be applied cold.\n\n_Strain of the knees_ or _shoulder_ may be treated in the same manner as\nabove.\n\n\n\n\nFOUL IN THE FOOT.\n\n\nA great deal of learned nonsense has been written on this subject, which\nonly serves to plunge the farmer into a labyrinth from which there is no\nescape. The author will not trespass on the reader's patience so much as\nto transcribe different authors' opinions in relation to the nature of\nthe disease and its treatment, but will proceed at once to point out a\ncommon-sense explanation of its cause, and the proper mode of treating\nit.\n\nThe disease is analogous to foot rot in sheep, and is the consequence of\nfeeding in wet pastures, or suffering the animals to wallow in filth. A\nlarge quantity of morbific or excrementitious matter is thrown off from\nthe system through the surfaces between the cleft. Now, should those\nsurfaces be obstructed by filth, or contracted by cold, the delicate\nmouths of these excrementitious vessels, or outlets, are unable to rid\nthe parts of their morbid accumulations: these vessels become distended\nbeyond their usual capacity, communicate with each other, and, when no\nlonger able to contain this mass of useless material, an artificial\ndrain, in the form of \"foot rot,\" is established, by which simple method\nthe parts recover their reciprocal equilibrium. In this case, as in\ndiarrhoea, we recognize a simple and sanative operation of nature's\nlaw, which, if aided, will generally prove beneficial.\n\nThat \"foul in the foot\" is caused by the sudden stoppage of some natural\nevacuation is evident from the following facts: First, the disease is\nmost prevalent in cold, low, marshy countries, where the foot is kept\nconstantly moist. Secondly, the disease is neither contagious nor\nepidemic. (See _Journal de Med. Vet. et comparee_, 1826, p. 319.)\n\n_Treatment._--In all cases of obstruction to the depurating apparatus,\nthere is a loss of equilibrium between secretion and excretion. The\nfirst indication is, to restore the lost function. Previously, however,\nto doing so, the animal must be removed to a dry situation. The cause\nonce removed, the cure is easy, provided we merely assist nature and\nfollow her teachings. As warmth and moisture are known to relax all\nanimal fibre, the part should be relaxed, warmed, and cleansed, first by\nwarm water and soap, lastly by poultice; at the same time bearing in\nmind that the object is not to produce or invite suppuration, (formation\nof matter,) but only to liberate the excess of morbid materials that may\nalready be present: as soon as this is accomplished, the poultice should\nbe discontinued.\n\n_Poultice for Foul Feet._\n\n  Roots of marshmallows, bruised,   half a pound.\n  Powdered charcoal,                a handful.\n     \"     lobelia,                 a few ounces.\n  Meal,                             a tea-cupful.\n  Boiling water sufficient to soften the mass.\n\n_Another_.\n\n  Powdered lobelia,         }\n  Slippery elm,             } equal parts.\n  Pond lily, bruised,       }\n\nMix with boiling water. Put the ingredients into a bag, and secure it\nabove the fetlock.\n\nGive the animal the following at a dose:--\n\n  Flowers of sulphur,                 half an ounce.\n  Powdered sassafras bark,            1 ounce.\n  Burdock, (any part of the plant,)   2 ounces.\n\nThe above to be steeped in one quart of boiling water. When cool,\nstrain. All that is now needed is to keep the part cleansed, and at\nrest. If a fetid smell still remains, wet the cleft, morning and\nevening, with\n\n  Chloride of soda,      1 ounce.\n  Water,                 6 ounces.\n\nMix.\n\n_Another._\n\n  Pyroligneous acid,        2 ounces.\n  Water,                    a pint.\n\nMix.\n\n_Another._\n\n  Common salt,          1 table-spoonful.\n  Vinegar,              a wine-glass.\n  Water,                1 quart.\n\nWhenever any fungous excrescence makes its appearance between the claws,\napply powdered bloodroot or burnt alum.\n\n\n\n\nRED WATER.\n\n\nThis affection takes its name from the high color of the urine. It is\nnot, strictly speaking, a disease, but only a symptom of derangement,\ncaused by high feeding or the suppression of some natural discharge. If,\nfor example, the skin be obstructed, then the insensible perspiration\nand excrementitious matter, which should pass through this great outlet,\nfind some other mode of egress; either the lungs of kidneys have to\nperform the extra work. If the lot falls on the latter, and they are not\nin a physiological state, they give evidence of febrile or inflammatory\naction (caused by the irritating, acrid character of their secretion) in\nthe form of high- urine. In all cases of derangement in the\ndigestive apparatus, liver included, both in man and oxen, the urine is\ngenerally high ; and the use of diuretic medicines is\nobjectionable, for, at best, it would only be treating symptoms. We lay\nit down as a fundamental principle, that those who treat symptoms alone\nnever cure disease, for the animal often dies a victim to the treatment,\ninstead of the malady.\n\nWhenever an animal is in a state of plethora, and the usual amount of\nmorbific matter cannot find egress, some portion of it is reabsorbed,\nproducing a deleterious effect: the urine will then be high ,\nplainly demonstrating that nature is making an effort to rid the system\nof useless material, and will do so unless interfered with by the use of\nmeans opposed to the cure, such as blood-letting, physicking, and\ndiuretics.\n\nThe urine will appear high , and approach a red hue, in many cows\nafter calving, in inflammation of the womb, gastric fever, puerperal\nfever, fevers generally, inflammation of the kidneys, indigestion; in\nshort, many forms of acute disease are accompanied by high-\nurine.\n\nThe treatment, like that of any other form of derangement, must be\ngeneral. Excite all parts of the system to healthy action. If the bowels\nare constipated, give the following:--\n\n  Golden seal,             1 table-spoonful.\n  Thoroughwort tea,        2 quarts.\n\nTo be given at a dose. Scalded shorts will be the most suitable food, if\nany is required; but, generally, abstinence is necessary, especially if\nthe animal be fat. If the surface and extremities are cold, give an\ninfusion of pennyroyal, catnip, sage, or hyssop; and rub the belly and\nlegs with\n\n  Hot vinegar,                    1 quart.\n  Powdered lobelia or cayenne,    1 ounce.\n\nIf the kidneys are inflamed,--which may be known by tenderness in the\nregion of the loins, and by the animal standing with the legs widely\nseparated,--the urine being of a dark red color, then, in addition to\nthe application of stimulating liniment to the belly and legs, a\npoultice may be placed over the kidneys.\n\n_Poultice for inflamed Kidneys._\n\n  Slippery elm,             8 ounces.\n  Lobelia,                  4 ounces.\n  Boiling water sufficient.\n\n_Another._\n\n  Linseed,                  } equal parts\n  Marshmallows,             }\n  Boiling water sufficient.\n\nLay the poultice on the loins, pass a cloth over it, and secure under\nthe belly.\n\nA drink of marshmallows is the only fluid that can with safety be\nallowed.\n\nIf the horns, ears, and surface are hot, sponge the whole surface with\nweak lie or saleratus water, and give the following antifebrile drink:--\n\n  Lemon balm,                 2 ounces.\n  Cream of tartar,            1 ounce.\n  Boiling water,              2 quarts.\n  Honey,                      1 gill.\n\nWhen cold, strain, and give a pint every fifteen minutes.\n\nIf the bowels are constipated, use injections of soap-suds.\n\nSuppose the animal to be in poor condition, hide bound, liver inactive,\nthe excrement of a dark color and fetid odor. Then use\n\n  Powdered golden seal,          2 ounces.\n     \"     caraways,             1 ounce.\n     \"     cayenne,              1 tea-spoonful.\n  Poplar bark, or slippery elm,  2 ounces.\n\nMix, divide into ten parts, and give one, in thin gruel, three times a\nday. The animal should be fed on boiled carrots, scalded shorts, into\nwhich a few handfuls of meal or flour may be stirred. In short, consider\nthe nature of the case; look beyond the symptoms, ascertain the cause,\nand, if possible, remove it. An infusion of either of the following\narticles may be given at discretion: marshmallows, linseed, juniper\nberries, pond lily roots, poplar bark, or queen of the meadow.\n\nMr. Cole remarks that \"red water is most common in cows of weak\nconstitution, a general relaxation, poor blood, &c.\"\n\nIn such cases, a nutritious diet, cleanliness, good nursing, friction on\nthe surface, comfortable quarters at night, and an occasional tonic will\naccomplish wonders.\n\n_Tonic Mixture._\n\n  Powdered golden seal,       1 tea-spoonful.\n     \"     balmony,           2 tea-spoonfuls.\n\nMix the above in shorts or meal. Repeat night and morning until\nconvalescence is established. In cases of great prostration, where it is\nnecessary to act with promptitude, the following infusion may be\nsubstituted:--\n\n  Thoroughwort,             }\n  Golden seal,              } of each, 1 ounce.\n  Camomile flowers,         }\n  Boiling water,              2 quarts.\n\nAfter standing one hour, strain, and give a pint every four hours.\n\n\n\n\nBLACK WATER.\n\n\nMy plan of treatment, in this malady, is similar to that for red water.\nIn both cases, it is indispensable to attend to the general health, to\npromote the discharge of all the secretions, to remove all obstructions\nto the full and free play of all parts of the living machinery. The same\nremedies recommended in the preceding article are equally good in this\ncase, only they must be more perseveringly applied.\n\n\n\n\nTHICK URINE.\n\n\nWhenever the urine is thick and turbid, deficient in quantity, or voided\nwith difficulty, either of the following prescriptions may be\nadministered:--\n\n  Juniper berries,            2 ounces.\n  Boiling water,              2 quarts.\n\nStrain. Dose, 1 pint every four hours.\n\n_Another._\n\n  Slippery elm,                1 ounce.\n  Poplar bark,                 2 ounces.\n\nMake a tea; sweeten with molasses, and give pint doses every four hours.\n\n_Another._\n\nMake a tea of cedar or pine boughs, sweeten with honey, and give it at\ndiscretion.\n\n\n\n\nRHEUMATISM.\n\n\nRheumatism thrives in cold, damp situations, and in wet, foggy weather.\nIt is often confined to the membranes of the large joints, and sometimes\nconsists in a deficiency of joint oil, (_synovia._) It is liable to\nbecome chronic, and involve the fibro-muscular tissues. Acute rheumatism\nis known by the pain and swelling in certain parts. Chronic rheumatism\nis recognized by coldness, rigidity about the muscles, want of vital\naction, &c.\n\nWhen lameness, after a careful examination, cannot be accounted for, and\nis found to go off after exercise, and return again, it is probably\nrheumatism.\n\n\n_Treatment of Acute Rheumatism._--Bathe the parts with an infusion of\narnica flowers, made thus:--\n\n  Arnica flowers,                    4 ounces.\n  Boiling water,                     3 quarts.\n\nWhen sufficiently cool, it is fit for use.\n\nGive the following:--\n\n  Sulphur,                  2 ounces.\n  Cream of tartar,          3 ounces.\n  Powdered pleurisy root,   1 ounce.\n     \"     licorice,        2 ounces.\n  Indian meal,              1 pound.\n\nMix. Give a table-spoonful three times a day in the feed. A light diet\nand rest are indispensable.\n\n\n_Treatment of Chronic Rheumatism._--Put the animal on a generous diet,\nand give an occasional spoonful of golden seal or balmony in the food,\nand a drink of sassafras tea. The parts may be rubbed with stimulating\nliniment, for which, see APPENDIX.\n\n\n\n\nBLAIN.\n\n\nSome veterinary writers describe this disease as \"a watery tumor,\ngrowing at the root of the tongue, and threatening suffocation. The\nfirst symptoms are foaming at the mouth, gaping, and lolling out of the\ntongue.\"\n\nThe disease first originates in the mucous surfaces, which enter into\nthe mouth, throat, and stomach. It partakes somewhat of the character of\nthrush, and requires nearly the same treatment.\n\nMake an infusion of raspberry leaves, to which add a small quantity of\nborax or alum. Wash the mouth and tongue with the same by means of a\nsponge. If there are any large pustules, open them with the point of a\npenknife. After cleansing them, sprinkle with powdered bayberry bark, or\nbloodroot. Rid the system of morbid matter by injection and physic,\n(which see, in APPENDIX.) The following antiseptic drink will\nthen complete the cure:--\n\nMake a tea of raspberry leaves by steeping two ounces in a quart of\nboiling water; when cool, strain; then add\n\n  Powdered charcoal,          2 ounces.\n     \"     bayberry bark,     1 ounce.\n  Honey,                      2 table-spoonfuls.\n\nGive a pint every four hours.\n\nThe diet should consist of scalded meal, boiled turnips, carrots, &c.,\nto which a small portion of salt may be added. If the glands under the\nears and around the throat are sympathetically affected, and swollen,\nthey must be rubbed twice a day with the stimulating liniment. (See\nAPPENDIX.)\n\nThe disease is supposed, by some veterinarians, to originate in the\ntongue, but post mortem examinations lead us to determine otherwise. Mr.\nYouatt informs us that \"post mortem examination shows intense\ninflammation, or even gangrene, of the tongue, oesophagus, paunch, and\nfourth stomach. The food in the paunch has a most offensive smell, and\nthat in the manyplus is hard and dry. Inflammation reaches to the small\nintestines, which are covered with red and black patches in the\ncoecum, colon, and rectum.\"\n\n\n\n\nTHRUSH.\n\n\n_Thrush_, and all eruptive diseases of the throat and internal surface,\nare treated in the same manner as laid down in Blaine.\n\n\n\n\nBLACK TONGUE.\n\n\nBlack Tongue appears when the system is deprived of vital force, as in\nthe last stages of blaine, &c. The indications to be fulfilled are the\nsame as in blaine, but applied with more perseverance.\n\n\n\n\nINFLAMMATION OF THE THROAT AND ITS APPENDAGES.[12]\n\n\nIn many cases, if attended to immediately, nothing more will be\nnecessary than confining the animal to a light diet, with frequent\ndrinks of linseed tea, warmth and moisture applied locally in the form\nof a slippery elm poultice, which may be kept in close contact with the\nthroat by securing it to the horns. But, in very severe attacks, mullein\nleaves steeped in vinegar and applied to the parts, with an occasional\nstimulating injection, (see APPENDIX,) together with a gruel\ndiet, are the only means of relief.\n\nFOOTNOTE:\n\n[12] This includes the larynx, pharynx, and trachea.\n\n\n\n\nBRONCHITIS.\n\n\nBronchitis consists in a thickening of the fibrous and mucous surfaces\nof the trachea, and generally results from maltreated hoose or catarrh.\n\n_Symptoms._--A dry, husky, wheezing cough, laborious breathing, hot\nbreath, and dry tongue.\n\n_Treatment._--Warm poultices of slippery elm or flaxseed, on the surface\nof which sprinkle powdered lobelia. Apply them to the throat moderately\nwarm; if they are too hot they will prove injurious. In the first place\nadminister the following drink:--\n\n  Powdered licorice,               1 ounce.\n     \"     elecampane,             half an ounce.\n  Slippery elm,                    1 ounce.\n\nBoiling water sufficient to make it of the consistence of thin gruel.\n\nIf there is great difficulty of breathing, add half a tea-spoon of\nlobelia to the above, and repeat the dose night and morning. Linseed or\nmarshmallow tea is a valuable auxiliary in the treatment of this\ndisease. The animal should be comfortably housed, and the legs kept warm\nby friction with coarse straw.\n\n\n\n\nINFLAMMATION OF GLANDS.\n\n\nThere are numerous glandular bodies distributed over the animal\nstructure. Those to which the reader's attention is called are, first,\nthe parotid, situated beneath the ear; secondly, the sub-lingual,\nbeneath the tongue; lastly, the sub-maxillary, situated just within the\nangle of the jaw. They are organized similarly to other glands, as the\nkidneys, &c., possessing arteries, veins, lymphatics, &c., which\nterminate in a common duct. They have also a ramification of nerves, and\nthe body of the gland has its own system of arterial vessels and\nabsorbents, which are enclosed by a serous membrane. They produce a\ncopious discharge of fluid, called saliva. Its use is to lubricate the\nmouth, thereby preventing friction; also to lubricate the food, and\nassist digestion.\n\nInflammation of either of these glands may be known by the heat,\ntenderness, enlargement, and difficulty of swallowing. They are usually\nsympathetically affected, as in hoose, catarrh, influenza, &c., and\ngenerally resume their natural state when these maladies disappear.\n\n_Treatment._--In the inflammatory stage, warm teas of marshmallows, or\nslippery elm, and poultices of the same, are the best means yet known to\nreduce it; they relax constricted or obstructed organs, and by being\ndirectly applied to the parts affected, the more speedily and\neffectually is the object accomplished. Two or three applications of\nsome relaxing poultice will be all that is needed; after which, apply\n\n  Olive oil, or goose grease,      1 gill.\n  Spirits of camphor,              1 ounce.\n  Oil of cedar,                    1 ounce.\n  Vinegar,                         half a gill.\n\nMix.\n\n_Another._\n\n  Pyroligneous acid,               2 ounces.\n  Beef's gall,                     1 gill.\n  Cayenne,                         1 tea-spoonful.\n\nTo be rubbed around the throat as occasion may require. All hard or\nindigestible food will be injurious.\n\n\n\n\nLOSS OF CUD.\n\n\nLoss of Cud is a species of indigestion, and may be brought on by the\nanimal's eating greedily of some food to which it has been unaccustomed.\nLoss of cud and loss of appetite are synonymous.\n\n_Compound for Loss of Cud._\n\n  Golden seal, powdered,        1 ounce.\n  Caraway,        \"             2 ounces.\n  Cream of tartar,              half an ounce.\n  Powdered poplar bark,         2 ounces.\n\nMix. Divide into six powders, and give one every four hours in a\nsufficient quantity of camomile tea.\n\n\n\n\nCOLIC.\n\n\nColic is occasioned by a want of physiological power in the organs of\ndigestion, so that the food, instead of undergoing a chemico-vital\nprocess, runs into fermentation, by which process carbonic acid gas is\nevolved.\n\n_Symptoms._--The animal is evidently in pain, and appears very restless;\nit occasionally turns its head, with an anxious gaze, to the left side,\nwhich seems to be distended more than the right; there is an occasional\ndischarge of gas from the mouth and anus.\n\n_Treatment._--Give the following carminative:--\n\n  Powdered aniseed,          half a tea-spoonful.\n     \"     cinnamon,          \"          \"\n\nTo be given in a quart of spearmint tea, and repeated if necessary.\n\n_Another._\n\n  Powdered assafoetida,          half a tea-spoon.\n  Thin gruel of slippery elm,    2 quarts.\n  Oil of aniseed,                20 drops.\n\nTo be given at a dose.\n\nIf the animal suffers much pain, apply fomentations to the belly, and\ngive the following injection:--\n\n  Powdered ginger,             half an ounce.\n  Common salt,                 1 table-spoonful.\n  Hot water,                   1 gallon.\n\n\n\n\nSPASMODIC COLIC.\n\n\nThis affection may be treated in the same manner as flatulent colic,\naided by warmth and moisture externally. The author has in many cases\ncured animals of spasmodic colic with a little peppermint tea, brisk\nfriction upon the stomach and bowels, and an injection of warm water;\nwhereas, had the animals been compelled to swallow the usual amount of\ngin, saleratus, castor oil, salts, and other nauseous, useless drugs,\nthey would probably have died. The reader, especially if he is an\nadvocate of the popular poisoning and blood-letting system, may ask,\nWhat good can a little simple peppermint tea accomplish? We answer,\nNature delights in simples, and in all her operations invites us to\nfollow her example. The fact is, warm peppermint tea, although in the\nestimation of the learned it is not entitled to any confidence as a\ntherapeutic agent, yet is an efficient anti-spasmodic in the hands of\nreformers and common-sense farmers. It is evident that if any changes\nare made in the symptoms, they ought to be for the better; yet under the\nheroic practice they often grow worse.\n\n\n\n\nCONSTIPATION.\n\n\nIn constipation there is a retention of the excrement, which becomes dry\nand hard. It may arise from derangement of the liver and other parts of\nthe digestive apparatus: at other times, there is a loss of equilibrium\nbetween the mucous and external surface, the secretion of the former\nbeing deficient, and the external surface throwing off too much moisture\nin the form of perspiration. In short, constipation, in nine cases out\nof ten, is only a symptom of a more serious disorder in some important\nfunction. The use of powerful purges is at all times attended with\ndanger, and in very many cases they fall short of accomplishing the\nobject. Mr. Youatt tells us that \"a heifer had been feverish, and had\nrefused all food during five days; and four pounds of Epsom salts, and\nthe same quantity of treacle, and three fourths of a pint of castor oil,\nand numerous injections, had been administered before any purgative\neffect could be produced.\" Several cases have come under the author's\nnotice where large doses of aloes, salts, and castor oil had been given\nwithout producing the least effect on the bowels, until within a few\nminutes of the death of the animal. If the animal ever recovers from the\ndangerous effects resulting from powerful purges, it is evident that the\ndelicate membranes lining the alimentary canal must lose their energy\nand become torpid. All mechanical irritants--for purges are of that\nclass--divert the fluids of the body from the surface and kidneys,\nproducing watery discharges from the bowels. This may be exemplified by\na person taking a pinch of snuff; the irritating article comes in\ncontact with the mucous surfaces: they endeavor to wash off the\noffending matter by secreting a quantity of fluid; this, together with\nwhat is forced through the membranes in the act of sneezing, generally\naccomplishes the purpose. A constant repetition of the vile habit\nrenders the parts less capable of self-defence; they become torpid, and\nlose their natural power of resisting encroachments; finally, the\naltered voice denotes the havoc made on the mucous membrane. This\nexplains the whole _modus operandi_ of artificial purging; and although,\nin the latter case, the parts are not adapted to sneezing, yet there is\noften a dreadful commotion, which has destroyed many thousands of\nvaluable animals. An eminent professor has said that \"purgatives,\nbesides being uncertain and uncontrollable, often kill from the\ndangerous debility they produce.\" The good results that sometimes appear\nto follow the exhibition of irritating purges must be attributed to the\nsanative action of the constitution, and not to the agent itself; and\nthe life of the patient depends, in all cases, on the existing ability\nof the vital power to counteract the effects of purging, bleeding,\npoisoning, and blistering.\n\nThe author does not wish to give the reader occasion to conclude that\npurgatives can be entirely dispensed with; on the contrary, he thinks\nthat in many cases they are decidedly beneficial, when given with\ndiscretion, and when the nature of the disease requires them; yet even\nsuch cases, too much confidence should not be placed on them, so as to\nexclude other and sometimes more efficient remedies, which come under\nthe head of laxatives, aperients, &c.\n\n_Treatment._--If costiveness is suspected to be symptomatic of some\nderangement, then a restoration of the general health will establish the\nlost function of the bowels. In this case, purges are unnecessary; the\ntreatment will altogether depend on the symptoms. For example, suppose\nthe animal constipated; the white of the eye tinged yellow, head\ndrooping, and the animal is drowsy, and off its feed; then give the\nfollowing:--\n\n  Powdered mandrake,              1 tea-spoonful.\n  Castile soap, in shavings,      quarter of an ounce.\n  Beef's gall,                    half a wine-glass.\n  Powdered capsicum,              third of a table-spoon.\n\nDissolve the soap in a small quantity of hot water, then mix the whole\nin three pints of thin gruel.\n\nThis makes a good aperient, and can be given with perfect safety in all\ncases of constipation arising from derangement of the liver. The liquid\nmust be poured down the throat in a gradual manner, in order to insure\nits reaching the fourth stomach. Aid the medicine by injections, and rub\nthe belly occasionally with straw.\n\nSuppose the bowels to be torpid during an attack of inflammation of the\nbrain; then it will be prudent to combine relaxants and anti-spasmodics,\nin the following form:--\n\n  Extract of butternut,           half an ounce.\n  Powdered skunk cabbage,               \"\n  Cream of tartar,                      \"\n  Powdered lobelia,               2 drachms.\n\nFirst dissolve the butternut in two quarts of hot water; after which add\nthe remaining ingredients, and give it for a dose. The operation of this\nprescription, like the preceding, must be aided by injection, friction,\nand warm drinks made of hyssop or pine boughs.\n\nSuppose the bowels to be constipated, at the same time the animal is\nhide-bound, in poor condition, &c.; the aperient must then be combined\nwith tonics, as follows:--\n\n  Extract of butternut,              half an ounce.\n  Rochelle salt,                     4 ounces.\n  Golden seal,                       1 ounce.\n  Ginger,                            1 tea-spoonful.\n  Hot water,                         3 quarts.\n\nDissolve and administer at a dose. In order to relieve the cold,\nconstricted, inactive state of the hide, recourse must be had to warmth,\nmoisture, and friction. A simple aperient of linseed oil may be given in\ncases of stricture or intussusception of the bowels. The dose is one\npint.\n\n\n\n\nFALLING DOWN OF THE FUNDAMENT.\n\n\nReturn the prolapsed part as quickly as possible by gently kneading the\nparts within the rectum. In recent cases, the part should be washed with\nan infusion of bayberry bark. (See APPENDIX.) The bowel may be\nkept in position by applying a wad of cotton, kept wet with the\nastringent infusion, confined with a bandage. A weak solution of alum\nwater may, however, be substituted, provided the bayberry or white oak\nbark is not at hand.\n\nShould the parts appear swollen and much inflamed, apply a large\nslippery elm poultice, on the surface of which sprinkle powdered white\noak or bayberry bark. This will soon lessen the swelling, so that the\nrectum may be returned.\n\nThe diet must be very sparing, consisting of flour gruel; and if the\nbowels are in a relaxed state, add a small quantity of powdered\nbayberry.\n\n\n\n\nCALVING.\n\n\nAt the end of nine months, the period of the cow's gestation is\ncomplete; but parturition does not always take place at that time; it is\nsometimes earlier, at others later. \"One hundred and sixteen cows had\ntheir time of calving registered: fourteen of them calved from the two\nhundred and forty-first day to the two hundred and sixty-sixth\nday,--that is, eight months and one day to eight months and twenty-six\ndays; fifty-six from the two hundred and seventieth to the two hundred\nand eightieth day; eighteen from the two hundred and eightieth to the\ntwo hundred and ninetieth; twenty on the three hundredth day; five on\nthe three hundred and eighth day; consequently there were sixty-seven\ndays between the two extremities.\"\n\nImmediately before calving, the animal appears uneasy; the tail is\nelevated; she shifts from place to place, and is frequently lying down\nand getting up again. The labor pains then come on; and by the expulsive\npower of the womb, the foetus, with the membranes enveloping it, is\npushed forward. At first, the membranes appear beyond the vagina, or\n\"shape,\" often in the form of a bladder of water; the membranes burst,\nthe water is discharged, and the head and fore feet of the calf protrude\nbeyond the shape. We are now supposing a case of natural labor. The body\nnext appears, and soon the delivery is complete. In a short time, a\ngradual contraction of the womb takes place, and the cleansings\n(afterbirth) are discharged. When the membranes are ruptured in the\nearly stage of calving, and before the outlet be sufficiently expanded,\nthe process is generally tedious and attended with danger; and this\ndanger arises in part from the premature escape of the fluids contained\nwithin the membranes, which are intended, ultimately, to serve the\ndouble purpose of expanding or dilating the passage, and lubricating the\nparts, thereby facilitating the birth.\n\nUnder these circumstances, it will be our duty to supply the latter\ndeficiency by carefully anointing the parts with olive oil; at the same\ntime, allow the animal a generous supply of slippery elm gruel: if she\nrefuses to partake of it, when offered in a bucket, it must be gently\npoured down the throat from a bottle. At times, delivery is very slow; a\nconsiderable time elapses before any part of the calf makes its\nappearance. Here we have only to exercise patience; for if there is a\nnatural presentation, nature, being the best doctor under all\ncircumstances, will do the work in a more faithful manner unassisted\nthan when improperly assisted. \"A meddlesome midwifery is bad.\"\nTherefore the practice of attempting to hurry the process by driving the\nanimal about, or annoying her in any way, is very improper. In some\ncases, however, when a wrong presentation is apparent, which seems to\nrender calving impracticable, we should, after smearing the hand with\nlard, introduce it into the vagina, and endeavor to ascertain the\nposition of the calf, and change it when it is found unfavorable. When,\nfor example, the head presents without the fore legs, which are bent\nunder the breast, we may gently pass the hand along the neck, and,\nhaving ascertained the position of the feet, we grasp them, and endeavor\nto bring them forward, the cow at the same time being put into the most\nfavorable position, viz., the hind quarters being elevated. By this\nmeans the calf can be gently pushed back, as the feet are advanced and\nbrought into the outlet. The calf being now in a natural position, we\nwait patiently, and give nature an opportunity to perform her work.\nShould the expulsive efforts cease, and the animal appear to be rapidly\nsinking, no time must be lost; nature evidently calls for assistance,\nbut not in the manner usually resorted to, viz., that of placing a rope\naround the head and feet of the calf, and employing the united strength\nof several men to extract the foetus, without regard to position. Our\nefforts must be directed to the mother; the calf is a secondary\nconsideration: the strength of the former, if it is failing, must be\nsupported; the expulsive power of the womb and abdominal muscles, now\nfeeble, must be aroused; and there are no means or processes that are\nbetter calculated to fulfil these indications than that of administering\nthe following drink:--\n\n  Bethroot,                  2 ounces.\n  Powdered cayenne,          one third of a tea-spoon.\n  Motherwort,                1 ounce.\n\nInfuse in a gallon of boiling water. When cool, strain, then add a gill\nof honey, and give it in pint doses, as occasion may require.\n\nUnder this treatment, there is no difficulty in reestablishing uterine\naction. If, however, the labor is still tedious, the calf may be grasped\nwith both hands, and as soon as a pain or expulsive effort is evident,\ndraw the calf from side to side. While making this lateral motion, draw\nthe calf forward. Expulsion generally follows.\n\nIf, on examination, it is clearly ascertained that the calf is lying in\nan unnatural position,--for example, the calf may be in such a position\nas to present its side across the outlet,--in such cases delivery is not\npracticable unless the position is altered. Mr. White says, \"I have seen\na heifer that it was found impossible to deliver. On examining her after\ndeath, a very large calf was found lying quite across the mouth of the\nuterus.\" In such cases, Mr. Lawson recommends that, \"when every other\nplan has failed for taming the calf, so as to put it in a favorable\nposition for delivery, the following has often succeeded: Let the cow be\nthrown down in a proper position, and placed on her back; then, by means\nof ropes and a pulley attached to a beam above, let the hind parts be\nraised up, so as to be considerably higher than the fore parts; in this\nposition, the calf may be easily put back towards the bottom of the\nuterus, so as to admit of being turned, or his head and fore legs\nbrought forward without difficulty.\"\n\nWe must ever bear in mind the important fact that the successful\ntermination of the labor depends on the strength and ability of the\nparent; that if these fail, however successful we may be in bringing\nabout a right presentation, the birth is still tedious, and we may\nfinally have to take the foetus away piecemeal; by which process the\ncow's life is put in jeopardy.\n\nTo avoid such an unfortunate occurrence, support the animal's strength\nwith camomile tea. The properties of camomile are antispasmodic,\ncarminative, and tonic--just what is wanted.\n\nMr. White informs us that \"instances sometimes occur of the calf's head\nappearing only, and so large that it is found impossible to put it back.\nWhen this is found to be the case, the calf should be killed, and\ncarefully extracted, by cutting off the head and other parts that\nprevent the extraction; thus the cow's life will be saved.\"\n\nIn cases of malformation of the head of the foetus, or when the\ncranium is enormously distended by an accumulation of fluid within the\nventricles of the brain, after all other remedies, in the form of\nfomentations, lubricating antispasmodic drinks, have failed, then\nrecourse must be had to embryotomy.\n\n\n\n\nEMBRYOTOMY.\n\n\nFor the following method of performing the operation we are indebted to\nMr. Youatt's work. The details appeared in the London Veterinarian of\n1831, and will illustrate the operation. M. Thibeaudeau, the operating\nsurgeon, says, \"I was consulted respecting a Breton cow twenty years\nold, which was unable to calve. I soon discovered the obstacle to the\ndelivery. The fore limbs presented themselves as usual; but the head and\nneck were turned backwards, and fixed on the left side of the chest,\nwhile the foetus lay on its right side, on the inferior portion of the\nuterus.\" M. Thibeaudeau then relates the ineffectual efforts he made to\nbring the foetus into a favorable position, and he at length found\nthat his only resource to save the mother was, to cut in pieces the\ncalf, which was now dead. \"I amputated the left shoulder of the foetus,\"\nsays he, \"in spite of the difficulties which the position of the head\nand neck presented. Having withdrawn the limb, I made an incision\nthrough all the cartilages of the ribs, and laid open the chest through\nits whole extent, by which means I was enabled to extract all the\nthoracic viscera. Thus having lessened the size of the calf, I was\nenabled, by pulling at the remaining fore leg, to extract the foetus\nwithout much resistance, although the head and neck were still bent upon\nthe chest. The afterbirth was removed immediately afterwards.\" This\nshows the importance of making an early examination, to determine the\nprecise position of the foetus; for if the head had been discovered in\nsuch position in the early stage of labor, it might have been brought\nforward, and thus prevented the butchery.\n\n\n\n\nFALLING OF THE CALF-BED, OR WOMB.\n\n\nWhen much force used in extracting the calf, it sometimes happens that\nthe womb falls out, or is inverted; and great care is required in\nputting it back, so that it may remain in that situation.\n\n_Treatment._--If the cow has calved during the night, in a cold\nsituation, and, from the exhausted state of the animal, we have reason\nto suppose that the labor has been tedious, or that she has taken cold,\nefforts must be made to restore the equilibrium. The following\nrestorative must be given:--\n\n  Motherwort tea,            2 quarts.\n  Hot drops,                 1 table-spoonful.\n  Powdered cinnamon,         1 tea-spoonful.\n\nGive a pint every ten minutes, and support the animal with flour gruel.\n\nThe uterus should be returned in the following manner: Place the cow in\nsuch a position that the hind parts shall be higher than the fore. Wash\nthe uterus with warm water, into which sprinkle a small quantity of\npowdered bayberry; remove any extraneous substance from the parts. A\nlinen cloth is then to be put under the womb, which is to be held by two\nassistants. The cow should be made to rise, if lying down,--that being\nthe most favorable position,--and the operator is then to grasp the\nmouth of the womb with both hands and return it. When so returned, one\nhand is to be immediately withdrawn, while the other remains to prevent\nthat part from falling down again. The hand at liberty is then to grasp\nanother portion of the womb, which is to be pushed into the body, like\nthe former, and retained with one hand. This is to be repeated until the\nwhole of the womb is put back. If the womb does not contract, friction,\nwith a brush, around the belly and back, may excite contraction. An\nattendant must, at the same time, apply a pad wetted with weak alum\nwater to the \"shape,\" and keep it in close contact with the parts, while\nthe friction is going on. It is sometimes necessary to confine the pad\nby a bandage.\n\n\n\n\nGARGET.\n\n\nIn order to prevent this malady, the calf should be put to suck\nimmediately after the caw has cleansed it; and, if the bag is distended\nwith an overplus of milk, some of it should be milked off. If, however,\nthe teats or quarters become hot and tender, foment with an infusion of\nelder or camomile flowers, which must be perseveringly applied, at the\nsame time drawing, in the most gentle manner, a small quantity of milk;\nby which means the over-distended vessels will collapse to their healthy\ndiameter. An aperient must then be given, (see APPENDIX,) and\nthe animal be kept on a light diet. If there is danger of matter\nforming, rub the bag with the following liniment:--\n\n  Goose oil, }  equal parts.\n  Hot drops, }\n\nIf the parts are exceedingly painful, wash with a weak lie, or wood\nashes, or sal soda. In spite of all our efforts, matter will sometimes\nform. As soon as it is discovered, a lancet may be introduced, and the\nmatter evacuated; then wash the part clean, and apply the stimulating\nliniment. (See APPENDIX.)\n\n\n\n\nSORE TEATS.\n\n\nFirst wash with castile soap and warm water; then apply the following:--\n\n  Lime water,     } equal parts.\n  Linseed oil,    }\n\n\nCHAPPED TEATS AND CHAFED UDDER.\n\nThese may be treated in the same manner.\n\nIf the above preparation is not at hand, substitute bayberry tallow,\nelder or marshmallow ointment.\n\n\n\n\nFEVER.\n\n\n_Description and Definition._--Fever is a powerful effort of the vital\nprinciple to expel from the system morbific or irritating matter, or to\nbring about a healthy action. The reason why veterinary practitioners\nhave not ascertained this fact heretofore is, because they have been\nguided by false principles, to the exclusion of their own common\nexperience. Let them receive the truth of the definition we have given;\nthen the light will begin to shine, and medical darkness will be\nrendered more visible. Fever, we have said, is a vital action--an effort\nof the vital power to regain its equilibrium of action through the\nsystem, and should never be subdued by the use of the lancet, or any\ndestructive agents that deprive the organs of the power to produce it.\nFever will be generally manifested in one or more of that combination of\nsigns known as follows: loss of appetite, increased velocity of the\npulse, difficult respiration, heaving at the flank, thirst, pain, and\nswelling; some of which will be present, local or general, in greater or\nless degree, in all forms of disease. When an animal has taken cold,\nand there is power in the system to keep up a continual warfare against\nencroachments, the disturbance of vital action being unbroken, the fever\nis called pure or persistent. Emanations from animal or vegetable\nsubstances in a state of decomposition or putrefaction, or the noxious\nmiasmata from marshy lands, if concentrated, and not sufficiently\ndiluted with atmospheric air, enter into the system, and produce a\nspecific effect. In order to dethrone the intruder, who keeps up a\nsystem of aggression from one tissue to another, the vital power arrays\nher artillery, in good earnest, to resist the invading foe; and if\nfurnished with the munitions of war in the form of sanative agents, she\ngenerally conquers the enemy, and dictates her own terms. While the\nforces are equally balanced, which may be known by a high grade of vital\naction, it is also called _unbroken_ or _pure_ fever. The powers of the\nsystem may become exhausted by efforts at relief, and the fever will be\nperiodically reduced; this form of fever is called _remittent_. By\nremittent fever is to be understood this modification of vital action\nwhich rests or abates, but does not go entirely off before a fresh\nattack ensues. It is evident, in this case, also, that nature is busily\nengaged in the work of establishing her empire; but being more\nexhausted, she occasionally rests from her labors. It would be as absurd\nto expect that the most accurate definition of fever in one animal would\ncorrespond in all its details with another case, as to expect all\nanimals to be alike. There are many names given to fevers; for example,\nin addition to the two already alluded to, we have milk or puerperal\nfever, symptomatic, typhus, inflammatory, &c. Veterinary Surgeon\nPercival, in an article on fever, says, \"We have no more reason--not\nnear so much--to give fever a habitation in the abdomen, than we have to\nenthrone it in the head; but it would appear from the full range of\nobservation, that no part of the body can be said to be unsusceptible of\ninflammation, (local fever,) though, at the same time, no organ is\ninvariably or exclusively affected.\"\n\nFrom this we learn that disease always attacks the weakest organ, and\nthat our remedies should be adapted to act on all parts of the system.\n\nThe same author continues, \"All I wish to contend for is, that both\nidiopathic and symptomatic fevers exhibit the same form, character,\nspecies, and the same general means of cure; and that, were it not for\nthe local affection, it would be difficult or impossible to distinguish\nthem.\"\n\nFever has always been the great bugbear, to scare the farmer and cattle\ndoctor into a wholesale system of blood-letting and purging; they\nbelieve that the more fever the animal manifests, the more unwearied\nmust be their exertions. The author advises the farmer not to feel\nalarmed about the fever; for when that is present it shows that the\nvital principle is up and doing. Efforts should be made to open the\noutlets of the body, through which the morbific materials may pass: the\nfever will then subside. It will be difficult to make the community\ncredit this simple truth, because fever is quite a fashionable disease,\nand it is an easy matter to make the farmer believe that his cow has a\nvery peculiar form of it, that requires an entirely different mode of\ntreatment from that of another form. Then it is very profitable to the\ninterested allopathic doctor, who can produce any amount of \"learned\nnonsense\" to justify the ways and means, and support his theory.\n\nThe author does not wish, at the present time, to enter into a learned\ndiscussion of the merit or demerit of allopathy: the object of this work\nis, to impart practical information to farmers and owners of stock. In\norder to accomplish this object, an occasional reference to the\nabsurdities of the old school is unavoidable.\n\nA celebrated writer has said, \"The very medicines [meaning those used by\nthe old school, which kill more than they ever cure] which aggravate and\nprotract the malady bind a laurel on the doctor's brow. When, at last,\nthe sick are saved by the living powers of nature struggling against\ndeath and the physician, he receives all the credit of a miraculous\ncure; he is lauded to the skies for delivering the sick from the details\nof the most deadly symptoms of misery into which he himself had plunged\nthem, and out of which they never would have arisen, but by the\nrestorative efforts of that living power which at once triumphed over\npoison, blood-letting, disease, and death.\"\n\nIn the treatment of disease, and when fever is manifested by the signs\njust enumerated, the object is, to invite the blood to the external\nsurface; or, in other words, equalize the circulation by warmth and\nmoisture; give diaphoretic or sudorific medicines, (see\nAPPENDIX,) with a view of relaxing the capillary structure,\nridding the system of morbific materials, and allaying the general\nexcitement. If the ears and legs are cold, rub them diligently with a\nbrush; if they again relapse into a cold state, rub them with\nstimulating liniment, and bandage them with flannel. In short, to\ncontract, to stimulate, remove obstructions, and furnish the system with\nthe materials for self-defence, are the means to be resorted to in the\ncure of fevers.\n\nWe shall now give a few examples of the treatment of fever; from which\nthe reader will form some idea of the course to be pursued in other\nforms not enumerated. But we may be asked why we make so many divisions\nof fever when it is evidently a unit. We answer the question, in the\nwords of Professor Curtis, whose teachings first emancipated us from the\nabsurdity of allopathic theories. \"These divisions were made by the\nlearned in physic, and we follow them out in their efforts to divide\nwhat is in its nature indivisible, to satisfy the demands of the public,\nand to give it in small crumbs to those practitioners of the art who\nhave not capacity enough to take in the whole at a single mouthful.\"\n\nIn the treatment of fevers, we must endeavor to remove all intruding\nagents, their influences and effects, and reestablish a full, free, and\nuniversal equilibrium throughout the system. \"The means are,\" says\nProfessor Curtis, \"antispasmodics, stimulants, and tonics, with\nemollients to grease the wheels of life. Disprove these positions, and\nwe lay by the pen and 'throw physic to the dogs.' Adhere strictly to\nthem in the use of the best means, and you will do all that can be done\nin the hour of need.\"\n\n\nMILK OR PUERPERAL FEVER.\n\n_Treatment._--Aperients are exceedingly important in the early stages,\nfor they liberate any offending matter that may have accumulated in the\ndifferent compartments of the stomach or intestines, and deplete the\nsystem with more certainty and less danger than blood-letting.\n\n_Aperient for Puerperal Fever._\n\n  Rochelle salts,               4 ounces.\n  Manna,                        2 ounces.\n  Extract of butternut,         half an ounce.\n  Dissolve in boiling water,    3 quarts.\n\nTo be given at a dose.\n\nBy the aid of one or more of the following drinks, the aperient will\ngenerally operate:--\n\nGive a bountiful supply of hyssop tea, sweetened with honey. Keep the\nsurface warm.\n\nSuppose the secretion of milk to be arrested; then apply warm\nfomentations to the udder.\n\nSuppose the bowels to be torpid; then use injections of soap-suds and\nsalt.\n\nSuppose the animal to be in poor condition; then give the following:--\n\n  Powdered balmony or gentian,     1 ounce.\n  Golden seal,                     1 ounce.\n  Flour gruel,                     1 gallon.\n\nTo be given in quart doses, every four hours.\n\nSuppose the bowels to be distended with gas; then give the following:--\n\n  Powdered caraways,       1 ounce.\n  Assafoetida,             1 tea-spoonful.\n  Boiling water,           2 quarts.\n\nTo be given at a dose.\n\nAny of the above preparations may be repeated, as circumstances seem to\nrequire. Yet it must be borne in mind that we are apt to do too much,\nand that the province of the good physician is \"to know when to do\nnothing.\" The following case from Mr. Youatt's work illustrates this\nfact:--\n\n\"A very singular variety of milk fever has already been hinted at. The\ncow is down, but there is apparently nothing more the matter with her\nthan that she is unable to rise; she eats and drinks, and ruminates as\nusual, and the evacuations are scarcely altered. In this state she\ncontinues from ten days to a fortnight, and then she gets up well.\" Yes,\nand many thousands more would \"get up well,\" if they were only let\nalone. Nature requires assistance sometimes; hence the need of doctors\nand nurses. All, however, that is required of the doctor to do is, just\nto attend to the calls of nature,--whose servant he is,--and bring her\nwhat she wants to use in her own way. The nearer the remedies partake or\nconsist of air, water, warmth, and food, the more sure and certain are\nthey to do good.\n\nIf a cow, in high condition, has just calved, appears restless, becomes\nirritable, the eye and tongue protruding, and a total suspension of milk\ntakes place, we may conclude that there is danger of puerperal fever. No\ntime should be lost: the aperient must be given immediately; warm\ninjections must be thrown into the rectum, and the teats must be\nindustriously drawn, to solicit the secretion of milk. In this case, all\nfood should be withheld: \"starve a fever\" suits this case exactly.\n\n\nINFLAMMATORY FEVER.\n\nInflammatory fever manifests itself very suddenly. The animal may appear\nwell during the day, but at night it appears dull, refuses its food,\nheaves at the flanks, seems uneasy, and sometimes delirious; the pulse\nis full and bounding; the mouth hot; urine high  and scanty.\nSometimes there are hot and cold stages.\n\n_Remarks._--When disease attacks any particular organ suddenly, or in an\nacute form, inflammatory fever generally manifests itself. Now, disease\nmay attack the brain, the lungs, kidneys, spleen, bowels, pleura, or\nperitoneum. Inflammatory fever may be present in each case. Now, it is\nevident that the fever is not the real enemy to be overcome; it is only\na manifestation of disorder, not the cause of it. The skin may be\nobstructed, thereby retaining excrementitious materials in the system:\nthe reabsorption of the latter produces fever; hence it is obvious that\na complete cure can only be effected by the removal of its causes, or,\nrather, the restoration of the suppressed evacuations, secretions, or\nexcretions.\n\nIt is very important that we observe and imitate nature in her method of\ncuring fever, which is, the restoration of the secretions, and, in many\ncases, by sweat, or by diarrhoea; either of which processes will\nremove the irritating or offending cause, and promote equilibrium of\naction throughout the whole animal system. In fulfilling these\nindications consists the whole art of curing fever.\n\nBut says one, \"It is a very difficult thing to sweat an ox.\" Then the\nremedies should be more perseveringly applied. Warm, relaxing,\nantispasmodic drinks should be freely allowed, and these should be aided\nby warmth, moisture, and friction externally; and by injection, if\nneeded. If the ox does not actually sweat under this system of\nmedication, he will throw off a large amount of insensible perspiration.\n\n_Causes._--In addition to the causes already enumerated, are the\naccumulation of excrementitious and morbific materials in the system.\nDr. Eberle says, \"A large proportion of the recrementitious elements of\nperspirable matter must, when the surface is obstructed, remain and\nmingle with the blood, (unless speedily removed by the vicarious action\nof some other emunctory,) and necessarily impart to this fluid qualities\nthat are not natural to it. Most assuredly the retention of materials\nwhich have become useless to the system, and for whose constant\nelimination nature has provided so extensive a series of emunctories as\nthe cutaneous exhalents, cannot be long tolerated by the animal economy\nwith entire impunity.\"\n\nDr. White says, \"Many of the diseases of horses and cattle are caused by\nsuppressed or checked perspiration; the various appearances they assume\ndepending, perhaps, in great measure, upon the suddenness with which\nthis discharge is stopped, and the state of the animal at the time it\ntakes place.\n\n\"Cattle often suffer from being kept in cold, bleak situations,\nparticularly in the early part of spring, during the prevalence of an\neasterly wind; in this case, the suppression of the discharge is more\ngradual, and the diseases which result from it are slower in their\nprogress, consequently more insidious in their nature; and it often\nhappens that the animal is left in the same cold situation until the\ndisease is incurable.\"\n\nIt seems probable that, in these cases, the perspiratory vessels\ngradually lose their power, and that, at length, a total and permanent\nsuppression of that necessary discharge takes place; hence arise\ninflammatory fever, consumption, decayed liver, rot, mesenteric\nobstructions, and various other complaints. How necessary, therefore, is\nit for proprietors of cattle to be provided with sheltered situations\nfor their stock! How many diseases might they prevent by such\nprecaution, and how much might they save, not only in preserving the\nlives of their cattle, but in avoiding the expense (too often useless,\nto say the least of it) of cattle doctoring!\n\n_Treatment._--We first give an aperient, (see APPENDIX,) to\ndeplete the system. The common practice is to deplete by blood-letting,\nwhich only protracts the malady, and often brings on typhus, black\nquarter, joint murrain, &c. Promote the secretions and excretions in the\nmanner already referred to under the head of _Puerperal Fever_; this\nwill relieve the stricture of the surface. A drink made from either of\nthe following articles should be freely given: lemon balm, wandering\nmilk weed, thoroughwort, or lady's slipper, made as follows:--\n\nTake either of the above articles,      2 ounces.\nBoiling water,                          2 quarts.\n\nWhen cool, strain, and add a wine-glass of honey.\n\nIf there is great thirst, and the mouth is hot and dry, the animal may\nhave a plentiful supply of water.\n\nIf the malady threatens to assume a putrid or malignant type, add a\nsmall quantity of capsicum and charcoal to the drink, and support the\nstrength of the animal with flour gruel.\n\n\nTYPHUS FEVER.\n\n_Causes._--Sudden changes in the temperature of the atmosphere, the\nanimal being at the same time in a state of debility, unable to resist\nexternal agencies.\n\n_Treatment._--Support the powers of the system through the means of\nnutritious diet, in the form of flour gruel, scalded meal and shorts,\nbran-water, &c.\n\nGive tonics, relaxants, and antispasmodics, in the following form:--\n\n  Powdered capsicum,             1 tea-spoonful.\n    \"      bloodroot,            1 ounce.\n    \"      cinnamon,             half an ounce.\n  Thoroughwort or valerian,      2 ounces.\n  Boiling water,                 1 gallon.\n\nWhen cold, strain, and give a quart every two hours.\n\nRemove the contents of the rectum by injections of a stimulating\ncharacter, and invite action to the extremities by rubbing them with\nstimulating liniment, (which see.) A drink of camomile tea should be\nfreely allowed; if diarrhoea sets in, add half a tea-spoon of bayberry\nbark to every two quarts of the tea.\n\nThese few examples of the treatment of fever will give the farmer an\nidea of the author's manner of treating it, who can generally break up a\nfever in a few hours, whereas the popular method of \"smothering the\nfire,\" as Mr. Youatt terms the blood-letting process, instead of curing,\nwill produce all forms of fever. Here is a specimen of the treatment, in\nfever of a putrid type, recommended by Dr. Brocklesby. He says,\n\"Immediately upon refusing fodder, the beast should have three quarts of\nblood taken away; and after twelve hours, two quarts more; after the\nnext twelve hours, about three pints may be let out; and after the\nfollowing twelve hours, diminish a pint of blood from the quantity taken\naway at the preceding blood-letting; lastly, about a single pint should\nbe taken away in less than twelve hours after the former bleeding; so\nthat, when the beast has been blooded five times, in the manner here\nproposed, the worst symptoms will, it is hoped, abate; but if the\ndifficulty and panting for breath continue very great, I see no reason\nagainst repeated bleeding.\" (See Lawson's work on cattle, p. 312.) The\nauthor has consulted several authorities on the treatment of typhus, and\nfinds that the use of the lancet is invariably recommended. We do not\nexpect to find, among our American farmers, any one so reckless, so lost\nto the common feelings of humanity, and his own interest, as to follow\nout the directions here given by Dr. B.; still blood-letting is\npractised, to some extent, in every section of the Union, and will\ncontinue to be the sheet-anchor of the cattle doctor just so long as the\ninfluential and cattle-rearing community shall be kept in darkness to\nits destructive tendency. Unfortunately for the poor dumb brute,\nveterinary writers have from time immemorial been uncompromising\nadvocates for bleeding; and through the influence which their talents\nand position confer, they have wielded the medical sceptre with a\ndespotism worthy of a better cause. It were a bootless task to attempt\nto reform the disciples of allopathy; for, if you deprive them of the\nlancet, and their _materia medica_ of poisons, they cannot practise.\nThey must be reformed through public opinion; and for this purpose we\npublish our own experience, and that of others who have dared to assail\nallopathy, with the moral certainty that they would expose themselves to\ncontempt, and be branded as \"medical heretics.\"\n\nNo treatment is scientific, in the estimation of some, unless it\nincludes the lancet, firing-iron, setons, boring horns, cramming down\nsalts by the pound, and castor oil by the quart. The object of this work\nis to correct this erroneous notion, and show the _farming community_\nthat a safer and more efficient system of medication has just sprung\ninto existence. When the principles of this reformed system of\nmedication are understood and practised, then the veterinary science\nwill be a very different thing from what it has heretofore been, and men\nwill hail it as a blessing instead of a \"curse.\" They will then know the\npower that really cures, and devise means of prevention. And here,\nreader, permit us to introduce the opinions of an able advocate of\nreform in human practice:[13] the same remarks apply to cattle; for they\nare governed by the same universal laws that we are, and whether we\nprescribe for a man or an ox, the laws of the animal economy are the\nsame, and require that the same indications shall be fulfilled.\n\n\"A little examination into the consequences of blood-letting will prove\nthat, so far from its being beneficial, it is productive of the most\nserious effects.\n\n\"Nature has endowed the animal frame with the power of preparing, from\nproper aliment, a certain quantity of blood. This vital fluid,\nsubservient to nutrition, is, by the amazing structure of the heart and\nblood-vessels, circulated through the different parts of the system. A\ncertain natural balance between what is taken in and what passes off by\nthe several outlets of the body is, in a state of health, regularly\npreserved. When this balance, so essential to health and life, is,\ncontrary to the laws of the animal constitution, interrupted, either a\ndeviation from a sound state is immediately perceived, or health from\nthat moment is rendered precarious. Blood-letting tends artificially to\ndestroy the natural balance in the constitution.\" (For more important\ninformation on blood-letting, see the author's work on the Horse; also\npage 58 of the present volume.)\n\nFOOTNOTE:\n\n[13] Dr. Beach.\n\n\n\n\nHORN AIL IN CATTLE.\n\n\nOn applying the hand to the horn or horns of a sick beast, an unnatural\nheat, or sometimes coldness, is felt: this enables us to judge of the\ndegree of sympathetic disturbance. And here, reader, permit us to\nprotest against a cruel practice, that is much in fashion, viz., that of\nboring the horns with a gimlet; for it does not mend the matter one jot,\nand at best it is only treating symptoms. The gimlet frequently\npenetrates the frontal sinuses which communicate with the nasal\npassages, and where mucous secretion, if vitiated or tenacious, will\naccumulate. On withdrawing the gimlet, a small quantity of thick mucus,\noften blood, escapes, and the interested operator will probably bore the\nother horn. Now, it often happens that after the point of the gimlet has\npassed through one side of the horn and bony structure, it suddenly\nenters a sinus, and does not meet with any resistance until it reaches\nthe opposite side. Many a \"mare's nest\" has been found in this way,\nusually announced as follows: \"The horn is hollow!\" Again, in aged\nanimals, the bony structure within the horn often collapses or shrinks,\nforming a sinus or cavity within the horn: by boring in a lateral\ndirection, the gimlet enters it; the horn is then pronounced hollow!\nand, according to the usual custom, must be doctored. An abscess will\nsometimes form in the frontal sinuses, resulting from common catarrh or\n\"hoose;\" the gimlet may penetrate the sac containing the pus, which thus\nescapes; but it would escape, finally, through the nostrils, if it were\nlet alone. Here, again, the \"horns are diseased;\" and should the animal\nrecover, (which it would, eventually, without any interference,) the\nrecovery is strangely attributed to the boring process. An author, whose\nname has escaped our memory, recommends \"cow doctors to carry a gimlet\nin their pocket.\" We say to such men, Lead yourselves not into\ntemptation! if you put a gimlet into your pocket, you will be very\nlikely to slip it into the cow's horn. Some men have a kind of\ninstinctive impulse to bore the cow's horns; we allude to those who are\nunacquainted with the fact that \"horn ail\" is only a symptom of\nderangement. It is no more a disease of the horns than it is of the\nfunctions generally; for if there be an excess or deficiency of vital\naction within or around the base of the horn, there must be a\ncorresponding deficiency or excess, as the case may be, in some other\nregion.\n\n\"Horn ail,\" as it is improperly termed, we have said, may accompany\ncommon catarrh, also that of an epidemic form; the horns will feel\nunnatural if there be a determination of blood to the head: this might\nbe easily equalized by stimulating the external surface and extremities,\nat the same time giving antispasmodic teas and regulating the diet. The\nhorns will feel cold whenever there is an unnatural distribution of the\nblood, and this may arise from exposure, or suffering the animal to\nwallow in filth. The author has been consulted in many cases of \"horn\nail,\" in several of which there were slow fecal movements, or\nconstipation; the conjunctiva of the eyes were injected with yellow\nfluid, and of course a deficiency of bile in the abomasum, or fourth\nstomach; thus plainly showing that the animals were laboring under\nderangement of the digestive organs. Our advice was, to endeavor to\npromote a healthy action through the whole system; to stimulate the\ndigestive organs; to remove obstructions, both by injection, if\nnecessary, and by the use of aperients; lastly, to invite action to the\nextremities, by stimulating liniments. Whenever these indications are\nfulfilled, \"horn ail\" soon disappears.\n\n\n\n\nABORTION IN COWS.\n\n\nCows are particularly liable to the accident of \"slinking the calf.\" The\ncommon causes of abortion are, the respiration and ultimate absorption\nof emanations from putrid animal remains, over-feeding, derangement of\nthe stomach, &c. The filthy, stagnant water they are often compelled to\ndrink is likewise a serious cause, not only of abortion, but also of\ngeneral derangement of the animal functions. Dr. White, V. S., tells us\nthat \"a farm in England had been given up three successive times in\nconsequence of the loss the owners sustained by abortion in their\ncattle. At length the fourth proprietor, after suffering considerably in\nlosses occasioned by abortion in his stock, suspected that the water of\nhis ponds, which was extremely filthy, might be the cause of the\nmischief. He therefore dug three wells upon his farm, and, having fenced\nround the pond to prevent the cattle from drinking there, caused them to\nbe supplied with the well water, in stone troughs erected for the\npurpose; and from this moment the evil was remedied, and the quality of\nthe butter and cheese made on his farm was greatly improved. In order to\nshow,\" says the same author, \"that the accident of abortion may arise\nfrom a vitiated state of the digestive organs, I will here notice a few\ncircumstances tending to corroborate this opinion. In 1782, all the cows\nof the farmer D'Euruse, in Picardy, miscarried. The period at which they\nwarped was about the fourth or fifth month. The accident was attributed\nto the excessive heat of the preceding summer; but, as the water they\nwere in the habit of drinking was extremely bad, and they had been kept\non oat, wheat, and rye straw, it appears to me more probable, that the\ngreat quantity of straw they were obliged to eat, in order to obtain\nsufficient nourishment, and the injury sustained by the third stomach in\nexpressing the fluid parts of the masticated or ruminated mass, together\nwith the large quantity of water they drank, while kept on this dry\nfood, were the real causes of the miscarriage.\n\n\"A farmer at Chariton, out of a dairy of twenty-eight cows, had sixteen\nslip their calves at different periods of gestation. The summer had been\nvery dry; they had been pastured in a muddy place, which was flooded by\nthe Seine. Here the cows were generally up to their knees in mud and\nwater. In 1789, all the cows in a village near Mantes miscarried. All\nthe lands in this place were so stiff as to be, for some time,\nimpervious to water; and as a vast quantity of rain fell that year, the\npastures were for a time completely inundated, on which account the\ngrass became bad. This proves that keeping cows on food that is\ndeficient in nutritive properties, and difficult of digestion, is one of\nthe principal causes of miscarriage.\" Mr. Youatt says, \"It is supposed\nthat the sight of a slipped calf, or the smell of putrid animal\nsubstances, are apt to produce warping. Some curious cases of abortion,\nwhich are worthy of notice, happened in the dairy of a French farmer.\nFor thirty years his cows had been subject to abortion. His cow-house\nwas large and well ventilated; his cows were in apparent health; they\nwere fed like others in the village; they drank the same water; there\nwas nothing different in the posture; he had changed his servants many\ntimes in the course of thirty years; he pulled down the barn and\ncow-house, and built another, on a different plan; he even, agreeably to\nsuperstition, took away the aborted calf through the window, that the\ncurse of future abortion might not be entailed on the cow that passed\nover the same threshold. To make all sure, he had broken through the\nwall at the end of the cow-house, and opened a new door. But still the\ntrouble continued. Several of his cows had died in the act of abortion,\nand he had replaced them by others; many had been sold, and their\nvacancies filled up. He was advised to make a thorough change. This had\nnever occurred to him; but at once he saw the propriety of the counsel.\nHe sold every beast, and the pest was stayed, and never appeared in his\nnew stock. This was owing, probably, to sympathetic influence: the\nresult of such influence is as fatal as the direst contagion.\"\n\nMy own opinion of this disease is, that it is one of nervous origin;\nthat there is a loss of equilibrium between the nerves of voluntary and\ninvoluntary motion. The direct causes of this pathological state exist\nin any thing that can derange the organs of digestion. Great sympathy is\nknown to exist between the organs of generation and the stomach: if the\nlatter be deranged, the former feels a corresponding influence, and the\nsympathetic nerves are the media by which the change takes place.\n\nIt invariably follows that, as soon as impregnation takes place, the\nstomach from that moment takes on an irritable state, and is more\nsusceptible to the action of unfavorable agents. Thus the odor of putrid\nsubstances cases nausea or relaxation when the animal is in a state of\npregnancy; otherwise, the same odor would not affect it in the least.\nProfessor Curtis says, \"The nervous system constitutes the check lines\nby which the vital spirit governs, as a coachman does his horses, the\nwhole motive apparatus of the animal economy; that every line, or\npencil, or ganglion of lines, in it, is antagonistic to some other line\nor ganglion, so that, whenever the function of one is exalted, that of\nsome other is depressed. It follows, of course, that to equalize the\nnervous action, and to sustain the equilibrium, is one of the most\nimportant duties of the physician.\"\n\nIn addition to the causes of abortion already enumerated, we may add\nviolent exercise, jumping dikes or hedges, sudden frights, and blows or\nbruises.\n\n_Treatment._--When a cow has slipped her foetus, and appears in good\ncondition, the quantity of food usually given should be lessened. Give\nthe following drink every night for a week:--\n\n  Valerian, (herb,)            1 ounce.\n  Powdered skunk cabbage,      1 tea-spoonful.\n\nSteep in half a gallon of boiling water. When cold, strain and\nadminister.\n\nSuppose the animal to be in poor condition; then put her on a nourishing\ndiet, and give tonics and stimulants, as follows:--\n\n  Powdered gentian,         1 ounce.\n      \"    sassafras,       1 ounce.\n  Linseed or flaxseed,      1 pound.\n\nMix. Divide into six portions, and give one, night and morning, in the\nfood, which ought to consist of scalded meal and shorts. A sufficient\nquantity of hay should be allowed; yet grass will be preferable, if the\nseason permits.\n\nSuppose the animal to have received an injury; then rest and a scalded\ndiet are all that are necessary. As a means of prevention, see article\n_Feeding_, page 17.\n\n\n\n\nCOW-POX.\n\n\nThis malady makes its appearance on the cow's teats in the form of small\npustules, which, after the inflammatory stage, suppurate. A small\nquantity of matter then escapes, and forms a crust over the\ncircumference of each pustule. If the crust be suffered to remain until\nnew skin is formed beneath, they will heal without any interference. It\noften happens, however, that, in the process of milking, the scabs are\nrubbed off. The following wash must then be resorted to:--\n\n  Pyroligneous acid,      a wine-glass.\n  Water,                  1 pint.\n\nWet the parts two or three times a day; medicine is unnecessary. A few\nmeals of scalded food will complete the cure.\n\n\n\n\nMANGE.\n\n\n\"Mange may be generated either from excitement of the skin itself, or\nthrough the medium of that sympathetic influence which is known to exist\nbetween the skin and organs of digestion. We have, it appears to me, an\nexcellent illustration of this in the case of mange supervening upon\npoverty--a fact too notorious to be disputed, though there may be\ndifferent ways of theorizing on it.\"\n\nMr. Blanie says, \"Mange has three origins--filth, debility, and\ncontagion.\"\n\n\n_Treatment._--Rid the system of morbific materials with the following:--\n\n  Powdered sassafras,  2 ounces.\n     \"     charcoal,   a handful.\n  Sulphur,             1 ounce.\n\nMix, and divide into six parts; one to be given in the feed, night and\nmorning. The daily use of the following wash will then complete the\ncure, provided proper attention be paid to the diet.\n\n  _Wash for Mange._\n\n  Pyroligneous acid,  4 ounces.\n  Water,              a pint.\n\nThe mange is known to be infectious: this suggests the propriety of\nremoving the animal from the rest of the herd.\n\n\n\n\nHIDE-BOUND.\n\n\nThis is seldom, if ever, a primary disease. The known sympathy existing\nbetween the digestive organs and the skin enables us to trace the malady\nto acute or chronic indigestion.\n\n\n_Treatment._--The indications to be fulfilled are, to invite action to\nthe surface by the aid of warmth, moisture, friction, and stimulants, to\ntone up the digestive organs, and relax the whole animal. The latter\nindications are fulfilled by the use of the following:--\n\n  Powdered balmony, (snakehead,)  2 ounces.\n      \"    sassafras,             1 ounce.\n  Linseed,                        2 pounds.\n  Sulphur,                        1 ounce.\n\nMix together, and divide the mass into eight equal parts, and give one\nnight and morning, in scalded shorts or meal; the better way, however,\nis, to turn it down the throat.\n\nA few boiled carrots should be allowed, especially in the winter season,\nfor they possess peculiar remedial properties, which are generally\nfavorable to the cure.\n\n\n\n\nLICE.\n\n\n_Treatment._--Wash the skin, night and morning, with the following:--\n\n  Powdered lobelia seeds,  2 ounces.\n  Boiling water,           1 quart.\n\nAfter standing a few hours, it is fit for use, and can be applied with a\nsponge.\n\n\n\n\nIMPORTANCE OF KEEPING THE SKIN OF ANIMALS IN A HEALTHY STATE.\n\n\nThis is a subject of great importance to the farmer; for many of the\ndiseases of cattle arise from the filthy, obstructed state of the\nsurface. This neglect of cleansing the hide of cattle arises, in some\ncases, from the absurd notion (often expressed to the author) that the\nhide of cattle is so thick and dense that they never sweat, except on\nthe muzzle! For the information of those who may have formed such an\nabsurd and dangerous notion, we give the views of Professor Bouley. \"In\nall animals, from the exterior tegumentary surface incessantly exhale\nvaporous or gaseous matters, the products of chemical operations going\non in the interior of the organism, of which the uninterrupted\nelimination is a necessary condition for the regular continuance of the\nfunctions. Regarded in this point of view, the skin may be considered as\na dependency of the respiratory apparatus, of which it continues and\ncompletes the function, by returning incessantly to the atmosphere the\ncombusted products, which are water and carbonic acid.\n\n\"Therefore the skin, properly speaking, is an expiratory apparatus,\nwhich, under ordinary conditions of the organism, exhales, in an\ninsensible manner, products analogous to those expired from the\npulmonary surface; with this difference, that the quantity of carbonic\nacid is very much less considerable in the former than in the latter of\nthese exhalations; according to Burbach, the proportion of carbonic\nacid, as inhaled by the skin, being to that expired by the lungs as 350\nto 23,450, or as 1 to 67.\n\n\"The experiments made on inferior animals, such as frogs, toads,\nsalamanders, or fish, have demonstrated the waste by general\ntranspiration to be, in twenty-four hours, little less than half the\nentire weight of the body.\"\n\nThe same author remarks, \"Direct experiment has shown, in the clearest\nmanner, the close relation of function existing between the perspiratory\nand respiratory membranes.\"\n\n\"M. Fourcault, with a view of observing, through different species of\nanimals, the effect of the suppression of perspiration, conceived the\nnotion of having the skins of certain live animals covered with varnish.\nAfter having been suitably prepared, some by being plucked, others by\nbeing shorn, he smeared them with varnish of variable composition; the\nsubstances employed being tar, paste, glue, pitch, and other plastic\nmatters. Sometimes these, one or more of them, were spread upon parts,\nsometimes upon the whole of the body. The effects of the operation have\nvaried, showing themselves, soon or late afterwards, decisively or\notherwise, according as the varnishing has been complete or general, or\nonly partial, thick, thin, &c. In every instance, the health of the\nanimal has undergone strange alterations, and life has been grievously\ncompromised. Those that have been submitted to experiment under our eyes\nhave succumbed in one, two, three days, and even at the expiration of\nsome hours.\" (See _London Veterinarian_ for 1850, p. 353.)\n\nIn a subsequent number of the same work we find the subject resumed;\nfrom which able production we select the following:--\n\n\"The suppression of perspiration has at all times been thought to have a\ngood deal to do with the production of disease. Without doubt this has\nbeen exaggerated. But, allowing this exaggeration, is it not admitted by\nall practitioners that causes which act through the medium of the skin\nare susceptible, in sufficient degree, of being appreciated in the\ncircumstances ushering in the development of very many diseases,\nespecially those characterized by any active flux of the visceral\norgans? For example, is it not an incontestable pathological fact, that\ncatarrhal, bronchial, pulmonic, and pleuritic affections, congestions of\nthe most alarming description in the vascular abdominal system of the\nhorse, inflammation of the peritoneum and womb following labor,\ncatarrhal inflammations of the bowels, even congestions of the feet,\n&c., derive their origin, in a great number of instances, from cold\napplied to the skin in a state of perspiration? What happens in the\norganism after the application of such a cause? Is its effect\ninstantaneous? Let us see. Immediately on the repercussive action of\ncold being felt by the skin, the vascular system of internal parts finds\nitself filled with repelled blood. Though this effect, however, be\nsimply hydrostatic, the diseased phenomena consecutive on it are far\notherwise.\n\n\"It is quite certain that, in the immense system of communicating\nvessels forming the circulating apparatus, whenever any large quantity\nof blood flows to any one particular part of the body, the other vessels\nof the system must be comparatively empty.[14] The knowledge of this\norganic hydrostatic fact it is that has given origin to the use of\nrevulsives under their various forms, and we all well know how much\nservice we derive from their use.\n\n\"But in what does this diseased condition consist? Whereabouts is it\nseated?\n\n\"The general and undefined mode it has of showing its presence in the\norganism points this out. Immediately subsequent to the action of the\ncause, the actual seat of the generative condition of the disease about\nto appear is the blood; this fluid it is which, having become actually\nmodified in its chemical compositions under the influence of the cause\nthat has momentarily obstructed the cutaneous exhalations, carries about\nevery where with it the disordered condition, and ultimately giving\nrise, through it, to some local disease, as a sort of eruptive effort,\nanalogous in its object, but often less salutary in its effect; owing to\nthe functional importance of the part attacked, to the external\neruptions produced by the presence in the blood of virus, which alters\nboth its dynamic and chemical properties.\n\n\"But what is the nature of this alteration? In this case, every clew to\nthe solution of this question fails us. We know well, when the\nexperiment is designedly prolonged, the blood grows black, as in\n_asphyxia_, (loss of pulse,) through the combination with it of carbonic\nacid, whose presence is opposed to the absorption of oxygen. But what\nrelation is there between this chemical alteration of blood here and the\nmodifications in composition it may undergo under the influence of\ninstantaneous suppression, but not persistent, of the cutaneous\nexhalations and secretions? The experiments of Dr. Fourcault tend, on\nthe whole, to explain this. His experiments discover the primitive form\nand almost the nature of the alteration the blood undergoes under the\ninfluence of the cessation of the functions of the skin. They\ndemonstrate that under these conditions the regularity of the course of\nthis fluid is disturbed--that it has a tendency to accumulate and\nstagnate within the internal organs: witness the abdominal pains so\nfrequently consequent on the application of plasters upon the skin, and\nthe congestions of the abdominal and pulmonary vascular systems met with\nalmost always on opening animals which have been suffocated through tar\nor pitch plasters.\n\n\"They prove, in fact, the thorough aptitude of impression of the nervous\nsystem to blood altered in its chemical properties, while they afford us\nan explication of the phenomena of depression, and muscular prostration,\nand weakness, which accompany the beginning of disease consecutive on\nthe operation of cold.\n\n\"How often do we put a stop to the ulterior development of disease by\nrestoring the function of the skin by mere [dry] friction, putting on\nthick clothing, exposing to exciting fumigation, applying temporary\nrevulsives in the shape of mustard poultices, administering diffusible\nstimuli made warm in drenches, trying every means to force the skin, and\nso tend, by the reestablishment of its exhalent functions, to permit\nthe elimination of blood saturated with carbonic matters opposed to the\nabsorption by it of oxygen!\n\n\"Do we not here perceive, so to express ourselves, the evil enter and\ndepart through the skin?\n\n\"M. Roche-Lubin gives an account of some lambs which were exposed, after\nbeing shorn, to a humid icy cold succeeding upon summer heat. These\nanimals all died; and their post mortem examination disclosed nothing\nfurther than a blackened condition of blood throughout the whole\ncirculating system, with stagnation in some organs, such as the liver,\nthe spleen, or abdominal vascular system.\n\n\"From the foregoing disclosures, which might be multiplied if there was\nneed of it, we learn that the regularity or perversion of the functions\nof the skin exercises an all-powerful influence over the conservation or\nderangement of the health, and that very many diseases can be traced to\nno other origin than the interruption, more or less, of these\nfunctions.\"\n\nThese remarks are valuable, inasmuch as they go to prove the importance,\nin the treatment of disease, of a restoration of the lost function. Our\nsystem of applying friction, warmth, and moisture to the external\nsurface, in all cases of internal disease, here finds, in the authors\njust quoted, able advocates.\n\nFOOTNOTE:\n\n[14] What a destructive system, then, must blood-letting be, which\nproposes to supply this deficiency in the empty vessels by opening a\nvein and suffering the contents of the overcharged vessels to fall to\nthe ground! If the blood abstracted from the full veins could be\nreturned into those \"empty\" ones, then there would be some sense in\nblood-letting.\n\n\n\n\nSPAYING COWS.\n\n\nThe castration of cows has been practised for several years in different\nparts of the world, with such remarkable success, that no one will doubt\nthere are advantages to be derived from it. For the benefit of those who\nmay have doubts on this subject, we give the opinions of a committee\nappointed by the Rheims Academy to investigate the matter.\n\n\"To the question put to the committee--\n\n\"1st. Is the spaying of cows a dangerous operation?\n\n\"The answer is, This operation, in itself, involves no more danger than\nmany others of as bold a character, (as puncture of the rumen,) which\nare performed without accident by men even strangers to the veterinary\nart. Two minutes suffice for the extraction of the ovaries; two minutes\nmore for suturing the wound.\n\n\"2dly. Will not the spaying of cows put an end to the production of the\nspecies?\n\n\"Without doubt, this is an operation which must be kept within bounds.\nIt is in the vicinity of large towns that most benefit will be derived\nfrom it, where milk is most generally sought after, and where pasturage\nis scanty, and consequently food for cows expensive. On this account it\nis not the practice to raise calves about the environs of Paris. Indeed,\nat Cormenteul, near Rheims, out of one hundred and forty-five cows kept,\nnot more than from ten to fifteen calves are produced yearly.\n\n\"3dly. Is spaying attended with amelioration of the quality of the meat?\n\n\"That cows fatten well after being spayed is an incontestable fact, long\nknown to agriculturists.\n\n\"4thly. Does spaying prolong the period of lactation, and increase the\nquantity of milk?\n\n\"The cow will be found to give as much milk after eighteen months as\nimmediately after the operation; and there was found in quantity, in\nfavor of the spayed cows, a great difference.\n\n\"5thly. Is the quality of the milk ameliorated by spaying?\n\n\"To resolve this question, we have thought proper to make an appeal to\nskilful chemists resident in the neighborhood; and they have determined\nthat the milk abounds more by one third in cheese and butter than that\nof ordinary cows.\"\n\nMr. Percival says, \"No person hesitates to admit the advantages\nderivable from the castration of bulls and stallions. I do not hesitate\nto aver, that equal, if not double, advantages are to be derived from\nthe same operation when performed on cows.\"\n\n\"It is to America we are indebted for this discovery. In 1832, an\nAmerican traveller, a lover of milk, no doubt, asked for some of a\nfarmer at whose house he was. Surprised at finding at this farm better\nmilk than he had met with elsewhere, he wished to know the reason of it.\nAfter some hesitation, the farmer avowed, that he had been advised to\nperform on his cows the same operation as was practised on the bulls.\nThe traveller was not long in spreading this information. The Veterinary\nSociety of the country took up the discovery, when it got known in\nAmerica. The English--those ardent admirers of beefsteaks and roast\nbeef--profited by the new procedure, as they know how to turn every\nthing to account, and at once castrated their heifers, in order to\nobtain a more juicy meat.\n\n\"The Swiss, whose principal employment is agricultural, had the good\nfortune to possess a man distinguished in his art, who foresaw, and was\nanxious to realize, the advantages of castrating milch cows. M. Levrat,\nveterinary surgeon at Lausanne, found in the government of his country\nan enlightened assistant in his praiseworthy and useful designs, so\nthat, at the present day, instructions in the operation of spaying enter\ninto the requirements of the programme of the professors of agriculture,\nand the gelders of the country are not permitted to exercise their\ncalling until they have proved their qualifications on the same\npoint.\"--_London Vet._ p. 274, 1850.\n\nFor additional evidence in favor of spaying, see Albany Cultivator, p.\n195, vol. vi.\n\nWe have conversed with several farmers in this section of the United\nStates, and find, as a general thing, that they labor under the\nimpression that spaying is chiefly resorted to with a view of fattening\ncattle for the market. We have, on all occasions, endeavored to correct\nthis erroneous conclusion, and at the same time to point out the\nbenefits to be derived from this practice. The quality of the milk is\nsuperior, and the quantity is augmented. Many thousands of the miserable\nspecimens of cows, that the farmer, with all his care, and having, at\nthe same time an abundance of the best kind of provender, is unable to\nfatten, might, after the operation of spaying, be easily fattened, and\nrendered fit for the market; or, if they shall have had calves, they may\nbe made permanent, and, of course, profitable milkers.\n\nIf a cow be in a weak, debilitated state, or, in other words, \"out of\ncondition,\" she may turn out to be a source of great loss to the owner.\nIn the first place, her offspring will be weak and inefficient;\nsuccessive generations will deteriorate; and if the offspring be in a\nclose degree of relationship, they will scarcely be worth the trouble of\nrearing. The spaying of such a cow, rather than she shall give birth to\nweak and worthless offspring, would be a great blessing; for then one of\nthe first causes of degeneracy in live stock will have been removed.\n\nAgain, a cow in poor condition is a curse to the farmer; for she is\noften the medium through which epidemics, infectious diseases, puerperal\nfever, &c., are communicated to other stock. If there are such diseases\nin the vicinity, those in poor flesh are sure to be the first victims;\nand they, coming in contact with others laboring under a temporary\nindisposition, involve them in the general ruin. If prevention be\ncheaper than cure,--and who doubts it?--then the farmer should avail\nhimself of the protection which spaying seems to hold out.\n\n\nOPERATION OF SPAYING.\n\nThe first and most important object in the successful performance of\nthis operation is to secure the cow, so that she shall not injure\nherself, nor lie down, nor be able to kick or injure the operator. The\nmost convenient method of securing the cow is, to place her in the\ntrevis;[15] the hind legs should then be securely tied in the usual\nmanner: the band used for the purpose of raising the hind quarters when\nbeing shod must be passed under the belly, and tightened just sufficient\nto prevent the animal lying down. Having secured the band in this\nposition, we proceed, with the aid of two or more assistants, in case\nthe animal should be irritable, to perform the operation. And here, for\nthe benefit of that portion of our readers who desire to perform the\noperation _secundum artem_, we detail the method recommended by Morin, a\nFrench veterinary surgeon; although it has been, and can again be,\nperformed with a common knife, a curved needle, and a few silken threads\nto close the external wound. The author is acquainted with a farmer, now\na resident of East Boston, who has performed this operation with\nremarkable success, both in this country and Scotland, with no other\ninstruments than a common shoemaker's knife and a curved needle. The\nfact is, the ultimate success of the operation does not depend so much\non the instruments as on the skill of the operator. If he is an\nexperienced man, understands the anatomy of the parts, and is well\nacquainted, by actual experience, with the nature of the operation, then\nthe instruments become a matter of taste. The best operators are those\nwho devote themselves entirely to the occupation. (See Mr. Blane's\naccount of his \"first essay in firing,\" p. 85, note.) Morin advises us\nto secure the cow, by means of five rings, to the wall. (See Albany\nCultivator, vol. vi. p. 244, 1850.) \"The cow being conveniently disposed\nof, and the instruments and appliances,--such as curved scissors, upon a\ntable, a convex-edged bistoury, a straight one, and one buttoned at the\npoint, suture needle filled with double thread of desired length,\npledgets of lint of appropriate size and length, a mass of tow (in\npledgets) being collected in a shallow basket, held by an assistant,--we\nplace ourselves opposite to the left flank, our back turned a little\ntowards the head of the animal; we cut off the hair which covers the\nhide in the middle of the flanks, at an equal distance between the back\nand hip, for the space of thirteen or fourteen centimetres in\ncircumference; this done, we take the convex bistoury, and place it open\nbetween our teeth, the edge out, the point to the left; then, with both\nhands, we seize the hide in the middle of the flank, and form of it a\nwrinkle of the requisite elevation, and running lengthwise of the body.\n\n\"We then direct an assistant to seize, with his right hand, the right\nside of this wrinkle. We then take the bistoury, and cut the wrinkle at\none stroke through the middle, the wrinkle having been suffered to go\ndown, a separation of the hide is presented of sufficient length to\nenable us to introduce the hand; thereupon we separate the edges of the\nhide with the thumb and fore finger of the left hand, and, in like\nmanner, we cut through the abdominal muscles, the iliac, (rather\nobliquely,) and the lumbar, (cross,) for a distance of a centimetre\nfrom the lower extremity of the incision made in the hide: this done,\narmed with the straight bistoury, we make a puncture of the peritoneum,\nat the upper extremity of the wound; we then introduce the buttoned\nbistoury, and we move it obliquely from above to the lower part up to\nthe termination of the incision made in the abdominal muscles. The flank\nbeing opened, we introduce the right hand into the abdomen, and direct\nit along the right side of the cavity of the pelvis, behind the paunch\nand underneath the rectum, where we find the horns of the uterus; after\nwe have ascertained the position of these viscera, we search for the\novaries, which are at the extremity of the _cornua_, or horns,\n(fallopian tubes,) and when we have found them, we seize them between\nthe thumb and fore finger, detach them completely from the ligaments\nthat keep them in their place, pull lightly, separating the cord, and\nthe vessels (uterine or fallopian tubes) at their place of union with\nthe ovarium, by means of the nails of the thumb and fore finger, which\npresents itself at the point of touch; in fact, we break the cord, and\nbring away the ovarium.\n\n\"We then introduce again the hand in the abdominal cavity, and we\nproceed in the same manner to extract the other ovarium.\n\n\"This operation terminated, we, by the assistance of a needle, place a\nsuture of three or four double threads, waxed, at an equal distance, and\nat two centimetres, or a little less, from the lips of the wound;\npassing it through the divided tissues, we move from the left hand with\nthe piece of thread; having reached that point, we fasten with a double\nknot; we place the seam in the intervals of the thread from the right,\nand as we approach the lips of the wound, we fasten by a simple knot,\nbeing careful not to close too tightly the lower part of the seam, so\nthat the suppuration, which may be established in the wound, may be able\nto escape.\n\n\"The operation effected, we cover up the wound with a pledget of lint,\nkept in its place by three or four threads passed through the stitches,\nand all is completed.\n\n\"It happens, sometimes, that in cutting the muscles of which we have\nbefore spoken, we cut one or two of the arteries, which bleed so much\nthat there is necessity for a ligature before opening the peritoneal\nsac, because, if this precaution be omitted, blood will escape into the\nabdomen, and may occasion the most serious consequences.\"\n\nThe best time for spaying cows, with a view of making them permanent\nmilkers, is between the ages of five and seven, especially if they have\nhad two or three calves. If intended to be fattened for beef, the\noperation should not be performed until the animal has passed its second\nyear, nor after the twelfth.\n\nWe usually prepare the animal by allowing a scalded mash every night,\nwithin a few days of the operation. The same precaution is observed\nafter the operation.\n\nIf, after the operation, the animal appears dull and irritable, and\nrefuses her food, the following drink must be given:--\n\n  Valerian,       2 ounces.\n  Boiling water,  2 quarts.\n\nSet the mixture aside to cool. Then strain, and add infusion of\nmarshmallows (see APPENDIX) one quart; which may be given in\npint doses every two hours.\n\nIf a bad discharge sets up from the wound,--but this will seldom happen,\nunless the system abounds in morbific materials,--then, in addition to\nthe drink, wash the wound with\n\n  Pyroligneous acid,  2 ounces.\n  Water,              2 quarts.\n\nMix.\n\nFOOTNOTES:\n\n[15] Although we recommend that cows be confined in the trevis for the\npurpose of performing this operation, it by no means follows that it\ncannot be done as well in other ways. In fact, the trevis is\ninadmissible where chloroform is used. The animal must be cast in order\nto use that agent with any degree of safety. If the trevis is not at\nhand, we should prefer to operate, having the cow secured to the floor,\nor held in that position by trusty assistants. We lately operated on a\ncow, the property of Mr. C. Drake of Holliston, in this state, under\nvery unfavorable circumstances; yet, as will appear from the\naccompanying note, the cow is likely to do well, notwithstanding. The\nhistory of the case is as follows: We were sent for by Mr. D. to see a\nheifer having a swelling under the jaw, which proved to be a scirrhous\ngland. After giving our opinion and prescribing the usual remedies, the\nconversation turned upon spaying cattle; and Mr. D. remarked that he had\na five year old cow, on which we might, if we chose, operate. This we\nrather objected to at first, as the cow was in a state of plethora, and\nthe stomach very much distended with food; yet, as the owner appeared\nwilling to share the responsibility, we consented to perform the\noperation. The cow was accordingly cast, in the usual manner, she lying\non her right side, her head being firmly held by an assistant. We then\nmade an incision through the skin, muscles, and peritoneum. The hand was\nthen introduced, and each ovary in its turn brought as near to the\nexternal wound as possible, and separated from its attachment with a\nbutton-pointed bistoury. The wound was then brought together with four\ninterrupted sutures, and dressed as already described. Directions were\ngiven to keep the animal quiet, and on a light diet: the calf, which was\nfour weeks old, to suckle as usual. The operation was performed on the\n17th of January, 1851, and on the 27th, the following communication was\nreceived:--\n\n     DR. DADD.\n\n     Dear Sir: Agreeably to request, I will inform you as regards the\n     cow. I must say that, so far as appearances are concerned, she is\n     doing well. She has a good appetite, and chews her cud, and the\n     wound is not swelled or inflamed.\n\n                              Yours truly,\n                                    C. DRAKE.\n\n     HOLLISTON, _Jan 27, 1851_.\n\n\n[Illustration: Three South Down Wethers\n\nThe Property of Mr. Jonas Webb of Babraham, near Cambridge, which\nobtained Prizes in their respective classes at the Smithfield Cattle\nShow, Decr. 1839.]\n\n\n\n\nSHEEP.\n\n\nPRELIMINARY REMARKS.\n\nMany of the diseases to which sheep are subject can be traced to want of\ndue care in their management. The common practice of letting them range\nin marshy lands is one of the principal causes of disease.\n\nThe feet of sheep are organized in such a manner as to be capable, when\nin a healthy state, of eliminating from the system a large amount of\nworn-out materials--excrementitious matter, which, if retained in the\nsystem, would be injurious. The direct application of cold tends to\ncontract the mouths of excrementitious vessels, and the morbid matter\naccumulates. This is not all. There are in the system numerous\noutlets,--for example, the kidneys, lungs, surface, feet, &c. The health\nof the animal depends on all these functions being duly performed. If a\ncertain function be interrupted for any length of time, it is sure to\nderange the system. Diseases of the feet are very common in wet\nsituations, and are a source of great loss to the farming community.\nHence it becomes a matter of great importance to know how to manage them\nso as to prevent diseases of the feet.\n\nProfessor Simonds says, \"No malady was probably so much feared by the\nagriculturist as the rot; and with reason, for it was most destructive\nto his hopes. It was commonly believed to be incurable, and therefore it\nwas all important to inquire into the causes which gave rise to it.\nSome pastures were notorious for rotting sheep; on other lands, sheep,\nunder all ordinary circumstances, were pastured with impunity; but, as a\nbroad principle, it might be laid down that an excess of moisture is\nprejudicial to the health of the animal. Sheep, by nature, are not only\nerratic animals, wandering over a large space of ground, but are also\ninhabitants of arid districts. The skill of man has increased and\nimproved the breed, and has naturalized the animal in moist and\ntemperate climates. But, nevertheless, circumstances now and then take\nplace which show that its nature is not entirely changed; thus, a wet\nseason occurs, the animals are exposed to the debilitating effects of\nmoisture, and the rot spreads among them to a fearful extent. The malady\nis not confined to England or to Europe; it is found in Asia and Africa,\nand occurs also in Egypt on the receding of the waters of the Nile.\n\n\"These facts are valuable, because they show that the cause of the\ndisease is not local--that it is not produced by climate or temperature;\nfor it is found that animals in any temperature become affected, and on\nany soil in certain seasons. A great deal had been written on rot in\nsheep, which it were to be wished had not been. Many talented\nindividuals had devoted their time to its investigation, endeavoring to\ntrace out a cause for it, as if it originated from one cause alone. But\nthe facts here alluded to would show that it arose from more causes than\none. He had mentioned the circumstance with regard to land sometimes\nproducing rot, and sometimes not; but he would go a step further, and\nask, Was there any particular period of the year when animals were\nsubject to the attack? Undoubtedly there was. In the rainy season, the\nheat and moisture combined would produce a most luxuriant herbage; but\nthat herbage would be deficient in nutriment, and danger would be run;\nthe large quantity of watery matter in the food acting as a direct\nexcitement to the abnormal functions of the digestive organs. Early\ndisturbance of the liver led to the accumulation of fat, (state of\nplethora;) consequently, an animal being 'touched with the rot' thrived\nmuch more than usual. This reminded him that the celebrated Bakewell was\nsaid to be in the habit of placing his sheep on land notorious for\nrotting them, in order to prevent other people from getting his stock,\nand likewise to bring them earlier to market for the butcher.\"\n\nReferring to diseases of the liver, Professor S. remarked, that \"the\nbile in rot, in consequence of the derangement of the liver being\ncontinued, lost the property of converting the chymous mass into\nnutritious matter, and the animal fell away in condition. Every part of\nthe system was now supplied with impure blood, for we might as well\nexpect pure water from a poisoned fountain as pure blood when the\nsecretion of bile was unhealthy. This state of the liver and the system\nwas associated with the existence of parasites in the liver.\n\n\"Some persons suppose that these parasites, which, from their particular\nform, were called flukes, were the cause of the rot. They are only the\neffect; yet it is to be remembered that they multiply so rapidly that\nthey become the cause of further diseased action. Sheep, in the earlier\nstages of the affection, before their biliary ducts become filled with\nflukes, may be restored; but, when the parasites existed in abundance,\nthere was no chance of the animal's recovery. Those persons who supposed\nflukes to be the cause of rot had, perhaps, some reason for that\nopinion. Flukes are oviparous; their ova mingle with the biliary\nsecretion, and thus find their way out of the intestinal canal into the\nsoil; as in the feculent matter of rotten sheep may be found millions of\nflukes. A Mr. King, of Bath, (England,) had unhesitatingly given it as\nhis opinion that flukes were the cause of rot; believing that, if sheep\nwere pastured on land where the ova existed, they would be taken up with\nthe food, enter into the ramifications of the biliary ducts, and thus\ncontaminate the whole liver. There appeared some ground for this\nassertion, because very little indeed was known with reference to the\nduration of life in its latent form in the egg. How long the eggs of\nbirds would remain without undergoing change, if not placed under\ncircumstances favorable to the development of life in a more active\nform, was undecided. It was the same with the ova of these parasites; so\nlong as they remained on the pasture they underwent no change; but place\nthem in the body of the animal, and subject them to the influence of\nheat, &c., then those changes would commence which ended in the\nproduction of perfect flukes. Take another illustration of the long\nduration of latent life: Wheat had been locked up for hundreds of\nyears--nay, for thousands--in Egyptian mummies, without undergoing any\nchange, and yet, when planted, had been found prolific.\n\n... He was not, then, to say that rot was in all cases a curable\naffection; but at the same time he was fully aware that many animals,\nthat are now considered incurable, might be restored, if sufficient\nattention was given to them. About two years ago, he purchased seven or\neight sheep, all of them giving indisputable proof of rot in its\nadvanced stage. He intended them for experiment and dissection; but as\nhe did not require all of them, and during the winter season only he\ncould dissect, he kept some till summer. They were supplied with food of\nnutritious quality, free from moisture; they were also protected from\nall storms and changes of weather, being placed in a shed. The result\nwas, that without any medicine, two of these rotten sheep quite\nrecovered; and when he killed them, although he found that the liver had\nundergone some change, still the animals would have lived on for years.\nRot, in its advanced stage, was a disease which might be considered as\nanalogous to dropsy. A serous fluid accumulates in various parts of the\nbody, chiefly beneath the cellular tissue; consequently, some called it\nthe _water_ rot, others the _fluke_ rot; but these were merely\nindications of the same disease in different stages. If flukes were\npresent, it was evident that, in order to strike at the root of the\nmalady, they must get rid of these _entozoa_, and that could only be\neffected by bringing about a healthy condition of the system. Nothing\nthat could be done by the application of medicine would act on them to\naffect their vitality. It was only by strengthening their animal powers\nthat they were enabled to give sufficient tone to the system to throw\noff the flukes; for this purpose many advocated salt. Salt was an\nexcellent stimulative to the digestive organs, and might also be of\nservice in restoring the biliary secretion, from the soda which it\ncontained. So well is its stimulative action known, that some\nindividuals always keep salt in the troughs containing the animal's\nfood. This was a preventive, they had good proof, seeing that it\nmattered not how moist the soil might be in salt marshes; no sheep were\never attacked by rot in them, whilst those sent there infected very\noften came back free. Salt, therefore, must not be neglected; but then\ncame the question, Could they not do something more? He believed they\ncould give tonics with advantage....\n\n\"The principles he wished to lay down were, to husband the animals'\npowers by placing them in a situation where they should not be exposed\nto the debilitating effects of cold storms; to supply them with\nnutritious food, and such as contained but a small quantity of water;\nand, as a stimulant to the digestive organs, to mix it with salt.\"\n\nThe remarks of Professor S. are valuable to the American farmer. First,\nbecause they throw some light on the character of a disease but\nimperfectly understood; secondly, they recommend a safe, efficient, and\ncommon-sense method of treating it; and lastly, they recommend such\npreventive measures as, in this enlightened age, every farmer must\nacknowledge to be the better part of sheep doctoring. The reader will\neasily perceive the reason why the food of sheep is injurious when wet\nor saturated with its own natural juices, when he learns that the\ndigestive process is greatly retarded, unless the masticated food be\nwell saturated with the gastric fluid. If the gastric fluid cannot\npervade it, then fermentation takes place; by which process the\nnutritive properties of the food are partly destroyed, and what remains\ncannot be taken up before it passes from the vinous into the acetous or\nputrefactive fermentation; the natural consequence is, that internal\ndisease ensues, which often gravitates to the feet, thereby producing\nrot. This is not all. Such food does not furnish sufficient material to\nreplenish the daily waste and promote the living integrity. In short, it\nproduces debility, and debility includes one half the causes of disease.\nIt must be a matter of deep interest to the farmer to know how to\nprevent disease in his flock, and improve their condition, &c.; for if\nhe possessed the requisite knowledge, he would not be compelled to offer\nmutton at so low a rate as from three to four cents a pound, at which\nprice it is often sold in the Boston market. We have already alluded to\nthe fact that neat cattle can, with the requisite knowledge, be improved\nat least twenty-five per cent.; and we may add, without fear of\ncontradiction, that the same applies to sheep. If, then, their value can\nbe increased in the same ratio as that of other classes of live stock,\nhow much will the proprietors of sheep gain by the operation? Suppose we\nset down the number of sheep in the United States at twenty-seven\nmillions,--which will not fall far short of the mark,--and value them at\nthe low price of one dollar per head: we get a clear gain, in the\ncarcasses alone, of six millions seven hundred and fifty thousand\ndollars. The increase in the quantity, and of course in the value, of\nwool would pay the additional expenses incurred. It is a well-known fact\nthat, when General Washington left his estate to engage in the councils\nof his country, his sheep then yielded five pounds of wool. At the time\nof his return, the animals had so degenerated as to yield but two and a\nhalf pounds per fleece. This was not altogether owing to the quality of\ntheir food, but in part to want of due care in breeding.\n\nIt is well known that many diseases are propagated and aggravated\nthrough the sexual congress; and no matter how healthy the dam is, or\nhow much vital resistance she possesses,--if the male be weak and\ndiseased, the offspring will be more or less diseased at birth. (See\narticle _Breeding_.)\n\nDr. Whitlaw observes, \"The Deity has given power to man to ameliorate\nhis condition, as may be truly seen by strict attention to the laws of\nnature. An attentive observer may soon perceive, that milk, butter, and\nmeat, of animals that feed on good herbage, in high and dry soils, are\nthe best; and that strong nourishment is the produce of those animals\nthat feed on bottom land; but those that feed on a marshy, wet soil\nproduce more acrid food, even admitting that the herbage be of the bland\nand nutritious kind; but if it be composed in part of poisonous plants,\nthe sheep become diseased and rotten, much more so than cattle, for they\ndo not drink to the same degree, and therefore (particularly those that\nchew the cud) are not likely to throw off the poison. Horses would be\nmore liable to disease than cattle were it not for their sagacity in\nselecting the wholesome from the poisonous herbage.\n\n\"A great portion of the mutton slaughtered is unfit for food, from the\nfact that their lungs are often in a state of decomposition, their\nlivers much injured by insects, and their intestines in a state of\nulceration, from eating poisonous herbs.\"\n\nLinnaeus says, \"A dry place renders plants sapid; a succulent place,\ninsipid; and a watery place, corrosive.\"\n\nOne farmer, in the vicinity of Sherburne, (England,) had, during the\nspace of a few weeks, lost nearly nine hundred sheep by the rot. The\nfear of purchasing diseased mutton is so prevalent in families, that the\ndemand for mutton has become extremely limited.\n\nIn the December number of the London Veterinarian we find an interesting\ncommunication from the pen of Mr. Tavistock, V. S., which will throw\nsome light on the causes of disease in sheep. The substance of these\nremarks is as follows: \"On a large farm, situated in the fertile valley\nof the Tavey, is kept a large flock of sheep, choice and well bred. It\nis deemed an excellent sheep farm, and for some years no sheep could be\nhealthier than were his flock. About eighteen months ago, however, some\newes were now and then found dead. This was attributed to some of the\nmany maladies sheep-flesh is 'heir to,' and thought no more about. Still\nit did not cease; another and another died, from time to time, until at\nlength, it becoming a question of serious consequence, my attention was\ncalled to them. I made, as opportunities occurred, minute post mortem\nexaminations. The sheep did not die rapidly, but one a week, and\nsometimes one a fortnight, or even three weeks. No previous illness\nwhatever was manifested. They were always found dead in the attitude of\nsleep; the countenance being tranquil and composed, not a blade of grass\ndisturbed by struggling; nor did any circumstance evidence that pain or\nsuffering was endured. It was evident that the death was sudden. We\nfancied the ewes must obtain something poisonous from the herbage, and\nthe only place they could get any thing different from the other sheep\nwas in the orchards, since there the ewes went at the lambing time, and\noccasionally through the summer. But so they had done for years before,\nand yet contracted no disease. Well, then, the orchards were the\nsuspected spots, and it was deemed expedient to request Mr. Bartlett, a\nbotanist, to make a careful examination of the orchards, and give us his\nopinion thereon. The following is the substance of his report:--\n\n\"The part of the estate to which the sheep unfortunately had access,\nwhere the predisposing causes of disease prevailed, was an orchard,\nhaving a gradual <DW72> of about three quarters of a mile in extent, from\nthe high ground to the bed of the river, ranging about east and west;\nthe hills on each side being constituted of argillaceous strata of\nlaminated slate, which, although having an angle of inclination favoring\ndrainage on the <DW72>s, yet in the valleys often became flat or\nhorizontal, and on which also accumulated the clays, and masses of rock,\nin detached blocks, often to the depth of twenty feet--a state of things\nwhich gives the valley surface and soil a very rugged and unequal\noutline; the whole, at the same time, offering the greatest obstruction\nto regular drainage.\n\n\"These are spots selected for orchard draining in England; the truth\nbeing lost sight of, that surfaces and soil for apple-tree growth\nrequire the most perfect admixture with atmospheric elements, and the\nfreest outlet for the otherwise accumulating moisture, to prevent\ndampness and acidity, the result of the shade of the tree itself,\nproduced by the fall of the leaf.\n\n\"On this estate these things had never been dreamt of before planting\nthe orchards. The apple-tree, in short, as soon as its branches and\nleaves spread with the morbid growth of a dozen years, aids itself in\nthe destructive process; the soil becomes yearly more poisonous, the\nroots soon decay, and the tree falls to one side, as we witness daily,\nwhile the herbage beneath and around becomes daily more unfit to sustain\nanimal life. Numerous forms of poisonous fungi, microscopic and\notherwise, are here at home, and nourished by the carburetted and other\nforms of hydrogen gas hourly engendered and saturating the soil; while\non the dampest spots the less noxious portions of such hydrates are\nassimilated by the mint plant in the shape of oil; and which disputes\nwith sour, poisonous, and blossomless grasses for the occupancy of the\nsurface, mingled with the still more noxious straggling forms of the\nethusa, occasionally the angelica, vison, conium, &c.\n\n\"This state of things, brought into existence by this wretched and\nbarbarous mode of planting orchard valleys, usually reaches its\nconsummation in about thirty years, and sometimes much less, as in the\nvalley under notice. Thus it is that such spots, often the richest in\ncapabilities on the estate, (the deep soil being the waste and spoil of\nthe higher ground and <DW72>s,) become a bane to every form of useful\nvegetation; and, at the same time, are a hotbed of luxuriance to every\nthing that is poisonous, destructive, and deleterious to almost every\nform of animal life. And such an animal as the sheep, while feeding\namong such herbage, would inhale a sufficiency of noxious gases,\nespecially in summer, through the nostrils alone, to produce disease\neven in a few hours, though the herbage devoured should lie harmless in\nthe stomach. But with regard to the sheep in the present case, we fear\nthey had no choice in the matter, and were driven by hunger to feed,\nbeing shut into these orchards; and thus not only ate the poisoned\ngrasses, but with every mouthful swallowed a portion of the\nwater-engendering mint, the acrid crowfoot, ranunculus leaves, &c.,\nsurrounding every blade of grass; while the other essential elements of\nvegetable poison, the most virulent forms of agarici and their spawn,\nwith other destructive fungi, were swallowed as a sauce to the whole.\nThis fearful state of things, to which sheep had access, soon manifested\nits results; for although a hog or a badger might here fatten, yet to an\nanimal so susceptible to atmospheric influences, unwholesome, undrained\nland, &c., as the sheep, the organization forbids the assimilation of\nsuch food; and although a process of digestion goes on, yet its hydrous\nresults (if we may use such a term) not only overcharge the blood with\nserum, but, through unnatural channels, cause effusion into the chest,\nheart, veins, &c., when its effects are soon manifested in sudden and\nquick dissolution, being found dead in the attitude of sleep.\"\n\nIt is probable that the gases which arose from this imperfectly drained\nestate played their part in the work of destruction; not only by coming\nin immediate contact with the blood through the medium of the air-cells\nin the lungs, but by mixing with the food in the process of digestion.\nThis may appear a new idea to those who have never given the subject a\nthought; yet it is no less true. During the mastication of food, the\nsaliva possesses the remarkable property of enclosing air within its\nglobules. Professor Liebig tells us that \"the saliva encloses air in the\nshape of froth, in a far higher degree than even soap-suds. This air, by\nmeans of the saliva, reaches the stomach with the food, and there its\noxygen enters into combination, while its nitrogen is given out through\nthe skin and lungs.\" This applies to pure air. Now, suppose the sheep\nare feeding in pastures notorious for giving out noxious gases, and at\nthe same time the function of the skin or lungs is impaired; instead of\nthe \"nitrogen\" or noxious gases being set free, they will accumulate in\nthe alimentary canal and cellular tissues, to the certain destruction of\nthe living integrity. Prof. L. further informs us that \"the longer\ndigestion continues,--that is, the greater resistance offered to the\nsolvent action by the food,--the more saliva, and consequently the more\nair, enter the stomach.\"\n\n\n\n\nSTAGGERS.\n\n\nThis disease is known to have its origin in functional derangement of\nthe stomach; and owing to the sympathy that exists between the brain and\nthe latter, derangements are often overlooked, until they manifest\nthemselves by the animal's appearing dull and stupid, and separating\nitself from the rest of the flock. An animal attacked with staggers is\nobserved to go round in a giddy manner; the optic nerve becomes\nparalyzed, and the animal often appears blind. It sometimes continues to\nfeed well until it dies.\n\n\n_Indications of Cure._--First, to remove the cause. If it exist in a too\ngenerous supply of food, reduce the quantity. If, on the other hand, the\nanimal be in poor condition, a generous supply of nutritious food must\nbe allowed.\n\nSecondly, to impart healthy action to the digestive organs, and\nlubricate their surfaces.\n\nHaving removed the cause, take\n\n  Powdered snakeroot,     1 ounce.\n     \"     slippery elm,  2 ounces.\n     \"     fennel seed,   half an ounce.\n\nMix. Half a table-spoonful may be given daily in warm water, or it may\nbe mixed in the food.\n\n_Another._\n\n  Powdered gentian,      1 ounce.\n     \"     poplar bark,  2 ounces.\n     \"     aniseed,      half an ounce.\n\nMix, and give as above.\n\nIf the bowels are inactive, give a wine-glass of linseed oil.\n\nThe animal should be kept free from all annoyance by dogs, &c.; for fear\nindirectly influences the stomach through the pneumogastric nerves, by\nwhich the secretion of the gastric juice is arrested, and an immediate\ncheck is thus given to the process of digestion. For the same reason,\nmedicine should always be given in the food, if possible. In cases of\ngreat prostration, accompanied with loss of appetite, much valuable time\nwould be lost. In such cases, we must have recourse to the bottle.\n\n\n\n\nFOOT ROT.\n\n\nWhen a sheep is observed to be lame, and, upon examination, matter can\nbe discovered, then pare away the hoof, and make a slight puncture, so\nthat the matter may escape; then wash the foot with the following\nantiseptic lotion:--\n\n  Pyroligneous acid,  2 ounces.\n  Water,              3 ounces.\n\nSuppose that, on examination, the feet have a fetid odor; then apply the\nfollowing:--\n\n  Vinegar,      half a pint.\n  Common salt,  1 table-spoonful.\n  Water,        half a pint.\n\nMix, and apply daily. At the same time, put the sheep in a dry place,\nand give a dose of the following every morning:--\n\n  Powdered bayberry bark,  half an ounce.\n    \"  flaxseed,           2 pounds.\n    \"  sulphur,            1 ounce.\n    \"  charcoal,           1 ounce.\n    \"  sassafras,          1 ounce.\n\nMix. A handful to be given in the food twice a day.\n\n\n_Remarks._--Foot rot is generally considered a local disease; yet should\nit be neglected, or maltreated, the general system will share in the\nlocal derangement.\n\n\n\n\nROT.\n\n\nThe progress of this disease is generally very slow, and a person\nunaccustomed to the management of sheep would find some difficulty in\nrecognizing it. A practical eye would distinguish it, even at a\ndistance. The disease is known by one or more of the following symptoms:\nThe animal often remains behind the flock, shaking its head, with its\nears depressed; it allows itself to be seized, without any resistance.\nThe eye is dull and watery; the eyelids are swollen; the lips, gums, and\npalate have a pale tint; the skin, which is of a yellowish white,\nappears puffed, and retains the impression; the wool loses its\nbrightness, and is easily torn off; the urine is high , and the\nexcrement soft. As the disease progresses, there is loss of appetite,\ngreat thirst, general emaciation, &c.\n\nThe indications are, to improve the secretions, vitalize the blood, and\nsustain the living powers. For which purpose, take\n\n  Powdered charcoal,     2 ounces.\n     \"     ginger,       1 ounce.\n     \"     golden seal,  1 ounce.\n  Oatmeal,               1 pound.\n\nMix. Feed to each animal a handful per day, unless rumination shall have\nceased; then omit the oatmeal, and give a tea-spoonful of the mixed\ningredients, in half a pint of hyssop, or horsemint tea. Continue as\noccasion may require.\n\nThe food should be boiled, if possible. The best kind, especially in the\nlatter stages of rot, is, equal parts of linseed and ground corn.\n\nIf the urine is high , and the animal is thirsty, give an\noccasional drink of\n\n  Cleavers, (_galium aparine_,)  2 ounces.\n  Boiling water,                      2 quarts.\n\nWhen cold, strain. Dose, one pint. To be repeated, if necessary.\n\n\n\n\nEPILEPSY.\n\n\nThis is somewhat different from staggers, as the animal does not remain\nquietly on the ground, but it suffers from convulsions, it kicks, rolls\nits eyes, grinds its teeth, &c. The duration of the fit varies much,\nsometimes it terminates at the expiration of a few minutes; at other\ntimes, a quarter of an hour elapses before it is perfectly conscious. In\nthis malady, there is a loss of equilibrium between the nervous and\nmuscular systems, which may arise from hydatids in the brain, offering\nmechanical obstructions to the conducting power of the nerves. This\nmalady may attack animals in apparently good health. We frequently see\nchildren attacked with epilepsy (fits) without any apparent cause, and\nwhen they are in good flesh.\n\nThe symptoms are not considered dangerous, except by their frequent\nrepetition.\n\nThe following may be given with a view of equalizing the circulation and\nnervous action:--\n\n  Assafoetida,                     one third of a tea-spoonful.\n  Gruel made from slippery elm,    1 pint.\n\nMix, while hot. Repeat the dose every other day. Make some change in the\nfood. Thus, if the animal has been fed on green fodder for any length of\ntime, let it have a few meals of shorts, meal, linseed, &c. The water\nmust be of the best quality.\n\nSuppose the animal to be in poor condition; then combine tonics and\nalteratives in the following form:--\n\n  Assafoetida,            1 tea-spoonful.\n  Powdered golden seal,   1 ounce.\n      \"    slippery elm,  2 ounces.\n  Oatmeal,                1 pound.\n\nMix thoroughly, and divide into eight equal parts. A powder to be given\nevery morning.\n\n\n\n\nRED WATER.\n\n\nThis is nothing more nor less than a symptom of deranged function. The\ncure consists in restoring healthy action to all parts of the animal\norganization. For example, high- urine shows that there is too\nmuch action on the internal surfaces, and too little on the external.\nThis at once points to the propriety of keeping the sheep in a warm\nsituation, in order to invite action to the skin.\n\n_Compound for Red Water._\n\n  Powdered slippery elm,  }\n     \"     pleurisy root, } of each, 1 ounce.\n     \"     poplar bark,   }\n  Indian meal,                       1 pound.\n\nMix. To be divided into ten parts, one of which may be given every\nmorning.\n\n\n\n\nCACHEXY,[16] OR GENERAL DEBILITY.\n\n\n_Indications of Cure._--First. To build up and promote the living\nintegrity by a generous diet, one or more of the following articles may\nbe scalded and given three times a day: carrots, parsnips, linseed, corn\nmeal, &c.\n\nSecondly. To remove morbific materials from the system, and restore the\nlost functions, one of the following powders may be given, night and\nmorning, in the fodder:--\n\n  Powdered balmony, (snakehead,)  1 ounce.\n      \"    marshmallows,          1 ounce.\n      \"    common salt,           1 table-spoonful.\n  Linseed meal,                   1 pound.\n\nMix. Divide into ten powders.\n\nFOOTNOTE:\n\n[16] It implies a vitiated state of the solids and fluids.\n\n\n\n\nLOSS OF APPETITE.\n\n\nThis is generally owing to a morbid state of the digestive organs. All\nthat is necessary in such case is, to restore the lost tone by the\nexhibition of bitter tonics. A bountiful supply of camomile tea will\ngenerally prove sufficient. If, however, the bowels are inactive, add to\nthe above a small portion of extract of butternut. The food should be\nslightly salted.\n\n\n\n\nFOUNDERING, (RHEUMATISM)\n\n\nIn this malady, the animal becomes slow in its movements; its walk is\ncharacterized by rigidity of the muscular system, and, when lying down,\nrequires great efforts in order to rise.\n\n\n_Causes._--Exposure to sudden changes in temperature, feeding on wet\nlands, &c.\n\n\n_Indications of Cure._--To equalize the circulation, invite and maintain\naction to the external surface, and remove the cause. To fulfil the\nlatter indication, remove the animal to a dry, warm situation.\n\nThe following antispasmodic and diaphoretic will complete the cure:\nPowdered lady's slipper, (_cypripedium_,) 1 tea-spoonful. To be given\nevery morning in a pint of warm pennyroyal tea.\n\nIf the malady does not yield in a few days, take\n\n  Powdered sassafras bark,  1 tea-spoonful.\n  Boiling water,            1 pint.\n  Honey,                    1 tea-spoonful.\n\nMix, and repeat the dose every other morning.\n\n\n\n\nTICKS.\n\n\nTicks, or, in short, any kind of insects, may be destroyed by dropping\non them a few drops of an infusion or tincture of lobelia seeds.\n\n\n\n\nSCAB, OR ITCH.\n\n\nScab, itch, erysipelas, &c., all come under the head of cutaneous\ndiseases, and require nearly the same general treatment. The following\ncompound may be depended on as a safe and efficient remedy in either of\nthe above diseases:--\n\n  Sulphur,                2 ounces.\n  Powdered sassafras,     1 ounce.\n\nHoney, sufficient to amalgamate the above. Dose, a table-spoonful every\nmorning. To prevent the sheep from rubbing themselves, apply\n\n  Pyroligneous acid,      1 gill.\n  Water,                  1 quart.\n\nMix, and wet the parts with a sponge.\n\n\n_Remarks._--In reference to the scab, Dr. Gunther says, \"Of all the\npreservatives which have been proposed, inoculation is the best. It has\ntwo advantages: first, the disease so occasioned is much more mitigated,\nand very rarely proves fatal; in the next place, an entire flock may get\nwell from it in the space of fifteen days, whilst the natural form of\nthe disorder requires care and attention for at least six months. It has\nbeen ascertained that the latter kills[17] more than one half of those\nattacked; whilst among the sheep that have been inoculated, the greatest\nproportion that die of it is one per cent.\"\n\nWhenever the scab makes its appearance, the whole flock should be\nexamined, and every one having the least abrasion eruption of the skin\nshould be put under medical treatment.\n\nIn most cases, itch is the result of infection. A single sheep infected\nwith it is sufficient to infect a whole flock. If a few applications of\nthe pyroligneous wash, aided by the medicine, are not sufficient to\nremove the malady, then recourse must be had to the following:--\n\n  Fir balsam,       half a pint.\n  Sulphur,          1 ounce.\n\nMix. Anoint the sores daily.\n\nThe only additional treatment necessary in erysipelas is, to give a\nbountiful supply of tea made of lemon balm, sweetened with honey.\n\nFOOTNOTE:\n\n[17] More likely the remedies. They are tobacco and corrosive\nsublimate--destructive poisons.\n\n\n\n\nDIARRHOEA.\n\n\nThis is not always to be considered as a disease, but in many cases it\nproves salutary operation of nature; therefore it should not be too\nsuddenly checked.\n\nWe commence the treatment by feeding on boiled meal. We then give\nmucilaginous drink made from marshmallows, slippery elm, or poplar bark.\nIf, at the end of two days, symptoms of amendment have not made their\nappearance, the following draught must be given:--\n\nMake a strong infusion of raspberry leaves, to a pint of which add a\ntea-spoonful of tincture of capsicum, (hot drops,) and one of charcoal.\nTo be repeated every morning, until healthy action is established.\n\n\n\n\nDYSENTERY.\n\n\nThis malady may be treated in the same manner as diarrhoea. Should\nblood and slime be voided in large quantities, the excrement emit a\nfetid odor, and the animal waste rapidly, then, in addition to the\nmucilaginous drink, administer the following:--\n\n  Powdered charcoal,        1 tea-spoonful.\n     \"     golden seal,     half a tea-spoonful.\n\nTo be given, in hardhack tea, as occasion may require.\n\nA small quantity of charcoal, given three times a day, with boiled food,\nwill frequently cure the disease, alone.\n\nDysentery is sometimes mistaken for diarrhoea; but they may be\ndistinguished by the following characteristics:--\n\n1st. Diarrhoea most frequently attacks weak animals; whereas dysentery\nofttimes attacks animals in good condition.\n\n2d. Dysentery generally attacks sheep in the hot months; on the other\nhand, diarrhoea terminates at the commencement of the hot season.\n\n3d. In diarrhoea, there are scarcely any feverish symptoms, and no\nstraining before evacuation, as in dysentery.\n\n4th. In diarrhoea, the excrement is loose, but in other respects\nnatural, without any blood or slime; whereas in dysentery the faeces\nconsist of hard lumps, blood, and slime.\n\n5th. There is not that degree of fetor in the faeces, in diarrhoea,\nwhich takes place in dysentery.\n\n6th. In dysentery, the appetite is totally gone; in diarrhoea, it is\ngenerally better than usual.\n\n7th. Diarrhoea is not contagious; dysentery is supposed to be highly\nso.\n\n8th. In dysentery, the animal wastes rapidly; but by diarrhoea, only a\ntemporary stop is put to thriving, after which it makes rapid advances\nto strength, vigor, and proportion.\n\n\n\n\nCONSTIPATION, OR STRETCHES.\n\n\nBy these terms are implied a preternatural or morbid detention and\nhardening of the excrement; a disease to which all animals are subject,\nunless proper attention be paid to their management. It mostly arises\nfrom want of exercise, feeding on frosted oats, indigestible matter of\nevery kind, impure water, &c. Costiveness is often the case of flatulent\nand spasmodic colic, and often of inflammation of the bowels.\n\nMr. Morrill says, \"I have always found that the quantity of medicine\nnecessary to act as an _opiate_ on this dry mass [alluding to that\nfound in the manyplus and intestines] will kill the animal. If I am\nmistaken, I will take it kindly to be set right.\" You are quite right.\n\nLet us see what Professor J. A. Gallup says, in his Institutes of\nMedicine, vol. ii. p. 187. \"The practice of giving opiates to mitigate\npain, &c., is greatly to be deprecated; it is not only unjustifiable,\nbut should be esteemed unpardonable. It is probable that, for forty\nyears past, opium and its preparations have done _seven times the\ninjury_ that they have rendered benefit\"--killed seven where they have\nsaved one! Page 298, he calls opium the \"most destructive of all\nnarcotics,\" and wishes he could \"speak through a lengthened trumpet,\nthat he might tingle the ears\" of those who use and prescribe it. All\nthe opiates used by the allopathists contain more or less of this\npoisonous drug. Opiates given with a view of softening mass alluded to\nwill certainly disappoint those who administer them; for, under the use\nof such \"palliatives,\" the digestive powers fail, and a general state of\nfeebleness and inactivity ensues, which exhausts the vital energies.\n\nIt will be found in stretches, that other organs, as well as the\n\"manyplus,\" are not performing their part in the business of\nphysiological or healthy action, and they must be excited to perform\ntheir work; for example, if the food remains in either of the stomachs\nin the form of a hard mass, then the surface of the body is evaporating\ntoo much moisture from the general system; the skin should be better\ntoned. Pure air is one of the best and most valuable of nature's tonics.\nLet the flock have pure air to breathe, and sufficient room to use their\nlimbs, with proper diet, and there will be little occasion for medicine.\n\n\n_Treatment._--The disease is to be obviated by proper attention to diet,\nexercise, and ventilation; and when these fail, to have recourse to\nbitter laxatives, injections, and aperients. The use of salts and castor\noil creates a necessity for their repetition, for they overwork the\nmucous surfaces, and their delicate vessels lose their natural\nsensibility, and become torpid. Scalded shorts are exceedingly valuable\nin this complaint, as also are boiled carrots, parsnips, &e.\n\nThe derangement must be treated according to its indications, thus:--\n\nSuppose the digestive organs to be deranged, and rumination to have\nceased; then take a tea-spoonful of extract of butternut, and dissolve\nit in a pint of thoroughwort tea, and give it at a dose. Use an\ninjection of soap-suds, if necessary.\n\nSuppose the excrement to be hard, coated with slime, and there be danger\nof inflammation in the mucous surfaces; then give a wine-glass of\nlinseed oil,[18] to which add a raw egg.\n\nIt is scarcely ever necessary to repeat the dose, provided the animal is\nallowed a few scalded shorts.\n\nIf the liver is supposed to be inactive, give, daily, a tea-spoonful of\ngolden seal in the food.\n\nIf the animal void worms with the faeces, then give a tea made from cedar\nboughs, or buds, to which add a small quantity of salt.\n\nFOOTNOTE:\n\n[18] Olive oil will answer the same purpose.\n\n\n\n\nSCOURS.\n\n\nIn scours, the surface evaporates too little of the moisture, and should\nbe relaxed by diffusible stimulants in the form of ginger tea. The\ntreatment that we have found the most successful is as follows: take\nfour ounces raw linseed oil, two ounces of lime water; mix. Let this\nquantity be given to a sheep on the first appearance of the above\ndisease; half the quantity will suffice for a lamb. Give about a\nwine-glass full of ginger tea at intervals of four hours, or mix a small\nquantity of ginger in the food. Let the animal be fed on gruel, or\nmashes of ground meal. If the above treatment fails to arrest the\ndisease, add half a tea-spoonful of powdered bayberry bark. If the\nextremities are cold, rub them with the tincture of capsicum.\n\n\n\n\nDIZZINESS.\n\n\nMr. Gunther says, \"Sheep are often observed to describe eccentric\ncircles for whole hours, then step forwards a pace, then again stop, and\nturn round again. The older the disease, the more the animal turns,\nuntil at length it does it even in a trot. The appetite goes on\ndiminishing, emaciation becomes more and more perceptible, and the state\nof exhaustion terminates in death. On opening the skull, there are met,\neither beneath the bones of the cranium, or beneath the dura mater,[19]\nor in the brain itself, hydatids varying in number and size, sometimes a\nsingle one, often from three to six, the size of which varies: according\nas these worms occupy the right side or the left, the sheep turns to the\nright or left; but if they exist on both sides, the turning takes place\nto the one and the other alternately.\n\n\"The animal very often does not turn, which happens when the worm is\nplaced on the median line; then the affected animal carries the head\ndown, and though it seems to move rapidly, it does not change place.\nWhen the hydatid is situated on the posterior part of the brain, the\nanimal carries the head high, runs straight forward, and throws itself\non every object it meets.\"\n\n_Treatment._--Take\n\n  Powdered worm seeds, (_chenopodium } 1 ounce.\n           anthelminticum_,)         }\n     \"     sulphur,                     half an ounce.\n     \"     charcoal,                    2 ounces.\n  Linseed, or flaxseed,                 1 pound.\n\nMix. Divide into eight parts, and feed one every morning. Make a drink\nfrom the white Indian hemp, (_asclepias incarnata_,) one ounce of which\nmay be infused in a quart of water, one fourth to be given every night.\n\nFOOTNOTE:\n\n[19] The membrane which lines the interior of the skull.\n\n\n\n\nJAUNDICE.\n\n\nThis malady generally involves the whole system in its deranged action.\nIt is recognized by the yellow tint of the conjunctiva, (white of the\neye,) and mucous membranes lining the nostrils and mouth. We generally\nemploy for its cure\n\n  Powdered mandrake,         1 tea-spoonful.\n     \"     ginger,           1 tea-spoonful.\n     \"     golden seal,      2 tea-spoonfuls.\n\nMix. Divide into two parts. Give one dose in the morning, and the other\nat night. An occasional drink of camomile tea, a few bran mashes, and\nboiled carrots, will complete the cure.\n\n\n\n\nINFLAMMATION OF THE KIDNEYS.\n\n\nA derangement of these organs may result from external violence, or it\nmay depend on the animal having eaten stimulating or poisonous plants.\n\nIts symptoms are, pain in the region of the kidneys; the back is arched,\nand the walk stiff and painful, with the legs widely separated; there is\na frequent desire to make water, and that is high  or bloody; the\nappetite is more or less impaired, and there is considerable thirst.\n\nThe indications are, to lubricate the mucous surfaces, remove morbific\nmaterials from the system, and improve the general health.\n\nWe commence the treatment by giving\n\n  Poplar bark, finely powdered,     1 ounce.\n  Pleurisy root, \"       \"          1 tea-spoonful.\n\nMake a mucilage of the poplar bark, by stirring in boiling water; then\nadd the pleurisy root; the whole to be given in the course of\ntwenty-four hours. The diet should consist of a mixture of linseed,\nboiled carrots, and meal.\n\n\n\n\nWORMS.\n\n\nThe intestinal worms generally arise from impaired digestion. The\nsymptoms are, a diminution of rumination, wasting away of the body, and\nfrequent snorting, obstruction of the nostrils with mucus of a greater\nor less thickness.\n\n_Compound for Worms._\n\n  Powdered worm seed,        }\n     \"     skunk cabbage,    } equal parts.\n     \"     ginger,           }\n\nDose, a tea-spoonful night and morning in the fodder.\n\n\n\n\nDISEASES OF THE STOMACH FROM EATING POISONOUS PLANTS.\n\n\n_Treatment._--Take the animal from pasture, and put it on a boiled diet,\nof shorts, meal, linseed, and carrots. The following alterative may be\nmixed in the food:--\n\n  Powdered marshmallows,            1 ounce.\n     \"     sassafras bark,          2 ounces.\n     \"     charcoal,                2 ounces.\n     \"     licorice,                2 ounces.\n\nDose, one table-spoonful every night.\n\n\n\n\nSORE NIPPLES.\n\n\nLambs often die of hunger, from their dams refusing them suck. The cause\nof this is sore nipples, or some tumor in the udder, in which violent\npain is excited by the tugging of the lamb. Washing with poplar bark, or\nanointing the teats with powdered borax and honey, will generally effect\na cure.\n\n\n\n\nFRACTURES.\n\n\nThe mending of a broken bone, though somewhat tedious, is by no means\ndifficult, when the integuments are not torn. Let the limb be gently\ndistended, and the broken ends of the bone placed in contact with each\nother. A piece of stiff leather, of pasteboard, or of thin shingle,\nwrapped in a soft rag, is then to be laid along the limb, so that it may\nextend an inch or two beyond the contiguous part. The splints are then\nto be secured by a bandage of linen an inch and a half broad. After\nbeing firmly rolled up, it should be passed spirally round the leg,\ntaking care that every turn of the bandage overlaps about two thirds of\nthe preceding one. When the inequality of the parts causes the margin to\nslack, it must be reversed or folded over; that is, its upper margin\nmust become the lower, &c. The bandage should be moderately tight, so as\nto support the parts without intercepting the circulation, and should be\nso applied as to press equally on every part. The bandage may be\noccasionally wet with a mixture of equal parts of vinegar and water.\n\n\n\n\nCOMMON CATARRH AND EPIDEMIC INFLUENZA.\n\n\nThe seat of the disease is in the mucous membrane, which is a\ncontinuation of the external skin, folded into all the orifices of the\nbody, as the mouth, eyes, nose, ears, lungs, stomach, intestines and\nbladder; its structure of arterial capillaries, veins, arteries, nerves,\n&c., is similar to the external skin; its most extensive surfaces are\nthose of the lungs and intestines, the former of which is supposed to be\ngreater than the whole external surface of the body.\n\nThe healthy office of this membrane is to furnish from the blood a fluid\ncalled mucus, to lubricate its own surface, and protect it from the\naction of materials taken into the system. The mucous membrane and the\nexternal surface of the body seem to be a counterpart of each other, and\nperform nearly the same offices; hence, if the action of one is\nsuppressed, the other commences the performance of its office; thus a\ncold which closes the skin immediately stops the perspiration, which is\nnow forced through the mucous membrane, producing the discharge of\nwatery humors, pus intermixed with blood, dry cough, emaciation, &c.\nThere are two varieties of this disease; the first is called _common\ncatarrh_, which proceeds from cold taken in pasture that is not properly\ndrained, also from atmospheric changes; it may also proceed from acrid\nor other irritating effluvia inhaled in the air, or from poisonous\nsubstances taken in the stomach in the form of food. The second variety\nis called _epidemic influenza_, and is produced by general causes; the\nattack is sometimes sudden; although of nearly the same nature as the\nfirst form, it is more obstinate, and the treatment must be more\nenergetic. It is very difficult to lay down correct rules for the\ntreatment of this malady, under its different forms and stages. The\nprincipal object to be kept in view is, to equalize the circulation,\nremove the irritating causes from the organs affected, and restore the\ntone of the system.\n\nFor this purpose, we make use of the following articles:--\n\n  Horehound, (herb,)                      1 ounce.\n  Marshmallow, (root,)      1 ounce.\n  Powdered elecampane, (root,)            half an ounce.\n      \"    licorice,      \"               half an ounce.\n  Powdered cayenne,                       half a tea-spoonful.\n  Molasses,                               2 table-spoonfuls.\n  Vinegar,                                2 table-spoonfuls.\n\nMix, pour on the whole one quart of boiling water, set it aside for two\nhours, then strain through cotton cloth, and give a table-spoonful night\nand morning.[20] If the bowels are constipated, a dose of linseed oil\nshould precede the mixture. No water should be allowed during the\ntreatment.\n\nThe following injection may be used:--\n\n  Powdered bayberry bark,          1 ounce.\n      \"    gum arabic,             half an ounce.\n  Boiling water,                   1 pint.\n\nStir occasionally while cooling, and strain as above.\n\nThe legs and ears should be briskly rubbed with tincture of capsicum;\nthis latter acts as a counter-irritant, equalizes the circulation, and,\nentering into the system, gives tone and vigor to the whole animal\neconomy.\n\nFOOTNOTE:\n\n[20] This preparation undergoes a process of fermentation in the course\nof forty-eight hours, and should therefore only be made in sufficient\nquantities for present use.\n\n\n\n\nCASTRATING LAMBS.\n\n\nThe lambs are first driven into a small enclosure. Select the ewe from\nthe ram lambs, and let the former go. Two assistants are necessary. One\ncatches the lambs; the other is seated on a low bench for the purpose of\ntaking the lamb on his lap, where he holds it by the four legs. The\noperator, having previously supplied himself with a piece of waxed silk\nand the necessary implements, grasps the scrotum in his left hand. He\nthen makes an incision over the most prominent part of the testicle,\nthrough the skin, cellular structure, &c. The testicle escapes from the\nscrotum. A ligature is now passed around the spermatic artery, and tied,\nand the cord is severed, bringing the testicle away at one stroke of the\nknife. As soon as the operation is completed, the animal is released.\nThe evening is the best time for performing the operation, for then the\nanimal remains quiet during the night, and the wound heals kindly.\n\n\n\n\nNATURE OF SHEEP.\n\n\n\"The sheep, though in most countries under the protection and control of\nman, is not that stupid and contemptible animal that has been\nrepresented. Amidst those numerous flocks which range without control on\nextensive mountains, where they seldom depend upon the aid of man, it\nwill be found to assume very different character. In those situations, a\nram or a wether will boldly attack a single dog, and often come off\nvictorious; but when the danger is more alarming, they have recourse to\nthe collected strength of the whole flock. On such occasions, they draw\nup into a compact body, placing the young and the females in the centre,\nwhile the males take the foremost ranks; keeping close by each other.\nThus an armed front is presented to all quarters, and cannot be easily\nattacked, without danger or destruction to the assailant. In this manner\nthey wait with firmness the approach of the enemy; nor does their\ncourage fail them in the moment of attack; for when the aggressor\nadvances to within a few yards of the line, the rams dart upon him with\nsuch impetuosity, as to lay him dead at their feet, unless he save\nhimself by flight. Against the attack of a single dog, when in this\nsituation, they are perfectly secure.\"\n\n\n\n\nTHE RAM.\n\n\nMr. Lawson says, \"It may be observed that the rams of different breeds\nof sheep vary greatly in their forms, wools, and fleeces, and other\nproperties; but the following description, by that excellent\nstock-farmer, Mr. Culley, deserves the attention of the breeder and\ngrazier. According to him, the head of the ram should be fine and small;\nhis nostrils wide and expanded; his eyes prominent, and rather bold or\ndaring; his ears thin; his collar fall from his breast and shoulders,\nbut tapering gradually all the way to where the neck and head join,\nwhich should be very fine and graceful, being perfectly free from any\ncoarse leather hanging down; the shoulders full, which must, at the same\ntime, join so easy to the collar forward, and chine backward, as to\nleave not the least hollow in either place; the mutton upon his arm or\nfore thigh must come quite to the knee; his legs upright, with a clean\nfine bone, being equally clear from superfluous skin and coarse, hairy\nwool from the knee and hough downwards; the breast broad and well\nforward, which will keep his fore legs at a proper width; his girt or\nchest full and deep, and instead of a hollow between the shoulders, that\npart by some called the fore flank should be quite full; the back and\nloins broad, flat, and straight, from which the ribs must rise with a\nfine circular arch; his belly straight; the quarters long and full, with\nthe mutton quite down to the hough, which should neither stand in nor\nout; his twist, or junction of the inside of the thighs, deep, wide, and\nfull, which, with the broad breast, will keep his legs open and upright;\nthe whole body covered with a thin pelt, and that with fine, bright,\nsoft wool.\n\n\"It is to be observed that the nearer any breed of sheep come up to the\nabove description, the nearer they approach towards excellence of\nform.\"\n\n\n\n\nLEAPING.\n\n\n\"The manner of treating rams has lately received a very great\nimprovement. Instead of turning them loose among the ewes at large, as\nheretofore, and agreeably to universal practice, they are kept apart, in\na separate paddock, or small enclosure, with a couple of ewes only each,\nto make them rest quietly; having the ewes of the flock brought to them\nsingly, and leaping each only once. By this judicious and accurate\nregulation, a ram is enabled to impregnate near twice the number of ewes\nhe would do if turned loose among them, especially a young ram. In the\nold practice, sixty or eighty ewes were esteemed the full number for a\nram. [Overtaxing the male gives rise to weak and worthless offspring.]\n\n\"The period during which the rams are to go with the ewes must be\nregulated by climate, and the quantity of spring food provided. It is of\ngreat importance that lambs should be dropped as early as possible, that\nthey not only be well nursed, but have time to get stout, and able to\nprovide for themselves before the winter sets in. It is also of good\nadvantage to the ewes that they may get into good condition before the\nrutting season. The ram has been known to live to the age of fifteen\nyears, and begins to procreate at one. When castrated, they are called\n_wethers_; they then grow sooner fat, and the flesh becomes finer and\nbetter flavored.\"\n\n\n\n\nARGYLESHIRE BREEDERS.\n\n\nIn Argyleshire, the principal circumstances attended to by the most\nintelligent sheep-farmers are these: to stock lightly, which will mend\nthe size of the sheep, with the quantity and quality of the wool, and\nalso render them less subject to diseases; (in all these respects it is\nallowed, by good judges, that five hundred sheep, kept well, will\nreturn more profit than six hundred kept indifferently;) to select the\nbest lambs, and such as have the finest, closest, and whitest wool, for\ntups and breeding ewes, and to cut and spay the worst; to get a change\nof rams frequently, and of breeding ewes occasionally; to put the best\ntups to the best ewes, which is considered necessary for bringing any\nbreed to perfection; not to top three-year-old ewes, (which, in bad\nseasons especially, would render the lambs produced by them of little\nvalue, as the lambs would not have a sufficiency of milk; and would also\ntend to lessen the size of the stock;) to keep no rams above three, or\nat most four years old, nor any breeding ewes above five or six; to\nseparate the rams from the 10th of October, for a month or six weeks, to\nprevent the lambs from coming too early in the spring; to separate the\nlambs between the 15th and 25th of June; to have good grass prepared for\nthem; and if they can, to keep them separate, and on good grass all\nwinter, that they may be better attended to, and have the better chance\nof avoiding disease. A few, whose possessions allow them to do it, keep\nnot only their lambs, but also their wethers, ewes, &c., in separate\nplaces, by which every man, having his own charge, can attend to it\nbetter than if all were in common; and each kind has its pasture that\nbest suits it.\n\n\n\n\nFATTENING SHEEP.\n\n\nWe are indebted to Mr. Cole, editor of the New England Farmer, for the\nfollowing article, which is worthy the attention of the reader:--\n\n\"Quietude and warmth contribute greatly to the fattening process. This\nis a fact which has not only been developed by science, but proved by\nactual practice. The manner in which these agents operate is simple, and\neasily explained. Motion increases respiration, and the excess of\noxygen, thus taken, requires an increased quantity of carbon, which\nwould otherwise be expended in producing fat. So, likewise, _cold robs\nthe system of animal heat_; to supply which, more oxygen and more carbon\nmust be employed in extra combustion, to restore the diminution of\ntemperature. Nature enforces the restoration of warmth, by causing cold\nto produce both hunger and a disposition for motion, supplying carbon by\nthe gratification of the former, and oxygen by the indulgence of the\nlatter. The above facts are illustrated by Lord Ducie:--\n\n\"One hundred sheep were placed in a shed, and ate twenty pounds of\nSwedish turnips each per day; whilst another hundred, in the open air,\nate twenty-five pounds each; and at that rate for a certain period: the\nformer animals weighed each thirty pounds more than the latter; plainly\nshowing that, to a certain extent, _warmth is a substitute for food_.\nThis was also proved, by the same nobleman, in other experiments, which\nalso illustrated the effect of exercise.\n\n\"No. 1. Five sheep were fed in the open air, between the 21st of\nNovember and the 1st of December. They consumed ninety pounds of food\nper day, the temperature being 44 deg.. At the end of this time, they\nweighed two pounds less than when first exposed.\n\n\"No. 2. Five sheep were placed under shelter, and allowed to run at a\ntemperature of 49 deg.. They consumed at first eighty-two pounds, then\nseventy pounds, and increased in weight twenty-three pounds.\n\n\"No. 3. Five sheep were placed in the same shed, but not allowed any\nexercise. They ate at first sixty-four pounds, then fifty-eight pounds,\nand increased in weight thirty pounds.\n\n\"No. 4. Five sheep were kept in the dark, quiet and covered. They ate\nthirty-five pounds per day, and increased in weight eight pounds.\n\n\"A similar experiment was tried by Mr. Childers, M. P. He states, that\neighty Leicester sheep, in the open field, consumed fifty baskets of cut\nturnips per day, besides oil cake. On putting them in a shed, they were\nimmediately able to consume only thirty baskets, and soon after but\ntwenty-five, being only one half the quantity required before; and yet\nthey fattened as rapidly as when eating the largest quantity.\n\n\"From these experiments, it appears that the least quantity of food,\nwhich is required for fattening, is when animals are kept closely\nconfined in warm shelters; and the greatest quantity when running at\nlarge, exposed to all weather. But, although animals will fatten faster\nfor a certain time without exercise than with it, if they are closely\nconfined for any considerable time, and are at the same time full fed,\nthey become, in some measure, feverish; the proportion of fat becomes\ntoo large, and the meat is not so palatable and healthy as when they are\nallowed moderate exercise, in yards or small fields.\n\n\"As to the kinds of food which may be used most advantageously in\nfattening, this will generally depend upon what is raised upon the farm,\nit being preferable, in most cases, to use the produce of the farm.\nSheep prefer beans to almost any other grain; but neither beans nor peas\nare so fattening as some other grains, and are used most advantageously\nalong with them. Beans, peas, oats, barley, rye, buckwheat, &c., may be\nused along with Indian corn, or oil cake, or succulent food, making\nvarious changes and mixtures, in order to furnish the variety of food\nwhich is so much relished by the sheep, and which should ever be\nattended to by the sheep fattener. This will prevent their being cloyed,\nand will hasten the fattening process. A variety of food, says Mr.\nSpooner, operates like cookery in the human subject, enabling more\nsustenance to be taken.\n\n\"The quantity of grain or succulent food, which it will be proper to\nfeed, will depend upon the size, age, and condition of the sheep; and\njudgment must be used in ascertaining how much they can bear. Mr.\nChilders states that sheep (New Leicester) fed with the addition of half\na pint of barley per sheep, per day, half a pound of linseed oil cake,\nwith hay, and a constant supply of salt, became ready for the butcher\nin ten weeks; the gain of flesh and tallow, thirty-three pounds to forty\npounds per head. (One sheep gained fifty-five pounds in twelve weeks.)\n\n\"This experiment shows what is about the largest amount of grain which\nit is necessary or proper to feed to New Leicester sheep, at any time\nwhile fattening. The average weight of forty New Leicester wethers,\nbefore fattening, was found by Mr. Childers to be one hundred and\ntwenty-eight pounds each. By weighing an average lot of any other kind\nof sheep, which are to be fattened, and by reference to the table of\ncomparative nutriment of the different kinds of food, a calculation may\nbe readily made, as to the largest amount, which will be necessary for\nthem, of any article of food whatever.\n\n\"When sheep are first put up for fattening, they should be sorted, when\nconvenient, so as to put those of the same age, size, and condition,\neach by themselves, so that each may have a fair chance to obtain its\nproportion of food, and may be fed the proper length of time.\n\n\"They should be fed moderately at first, gradually increasing the\nquantity to the largest amount, and making the proper changes of food,\nso as not to cloy them, nor produce acute diseases of the head or\nintestines, and never feeding so much as to scour them.\n\n\"Sheep, when fattening, should not be fed oftener than three times a\nday, viz., morning, noon, and evening. In the intervals between feeding,\nthey may fill themselves well, and will have time sufficient for\nrumination and digestion: these processes are interrupted by too\nfrequent feeding. But they should be fed with regularity, both as to the\nquantity of food and the time when it is given. When convenient, they\nshould have access to water at all times; otherwise a full supply of it\nshould be furnished to them immediately after they have consumed each\nfoddering.\n\n\"When sheep become extremely fat, whether purposely or not, it is\ngenerally expedient to slaughter them. Permitting animals to become\nalternately very fat and lean is injurious to all stock. Therefore, if\nanimals are too strongly inclined to fatten at an age when wanted for\nbreeding, their condition as to flesh should be regulated by the\nquantity and quality of their food or pasture.\"\n\n\n\n\nIMPROVEMENT IN SHEEP.\n\n\nNo country in the world is better calculated for raising sheep than the\nUnited States. The diversity of climate, together with the abundance and\nvariety of the products of the soil, united with the industry and\nperseverance of the agriculturist, renders this country highly favorable\nfor breeding, maturing, and improving the different kinds of sheep. The\nAmerican people, taken as a whole, are intellectually stronger than any\nother nation with the like amount of population, on the face of the\nglobe; consequently they are all-powerful, \"for the mind is mightier\nthan the sword.\" All that we aim at, in these pages, is to turn the\ncurrent of the American mind to the important subject of improvement in\nthe animal kingdom; to show them the great benefits they will derive\nfrom practical experience in the management of all classes of live\nstock; and, lastly, to show them the value and importance of the\nveterinary profession, when flourishing under the genial influence of a\nliberal community. If we can only succeed in arresting the attention of\nAmerican stock raisers, and they, on the other hand, direct their whole\nattention to the matter, then, in a few years, America will outshine her\nmore favored European rivals, and feel proud of her improved stock. What\nthe American people have done during the last half century in the\nimprovement of the soil, manufactures, arts, and sciences, is an earnest\nof what they can do in ameliorating the condition of all classes of live\nstock, provided they take hold of the subject in good earnest. Let any\none who is acquainted with the subject of degeneration, its causes and\nfatal results, not only in reference to the stock itself, but as regards\nthe pocket of the breeder, and the health of the whole community,--let\nsuch a one go into our slaughter-houses and markets, and if he does not\nsee a wide field for improvement, then we will agree to let the subject\nsink into oblivion. In order to show what a whole community can\naccomplish when their efforts are directed to one object, let us look on\nwhat a single individual, by his own industry and perseverance, has\naccomplished simply in improving the breed of sheep. The person referred\nto is Mr. Bakewell. His breeding animals were, in the first place,\nselected from different breeds. These he crossed with the best to be\nhad. After the cross had been carried to the desired point, he confined\nhis selections to his own herds or flocks. He formed in his mind a\nstandard of perfection for each kind of animals, and to this he\nconstantly endeavored to bring them. That he was eminently successful in\nthe attainment of his object, cannot be denied. He began his farming\noperations about 1750. In 1760, his rams did not sell for more than two\nor three guineas per head. From this time he gradually advanced in\nterms, and in 1770 he let some for twenty-five guineas a head for the\nseason. Marshall states that, in 1786, Bakewell let two thirds of a ram\n(reserving a third for himself) to two breeders, for a hundred guineas\neach, the entire services of the ram being rated at three hundred\nguineas the season. It is also stated that he made that year, by letting\nrams, more than one thousand pounds.\n\n\"In 1789, he made twelve hundred guineas by three '_ram brothers_,' and\ntwo thousand guineas from seven, and, from his whole letting, full three\nthousand guineas. Six or seven other breeders made from five hundred to\na thousand guineas each by the same operation. The whole amount of\nram-letting of Bakewell's breed is said to have been not less, that\nyear, than ten thousand pounds, [forty-eight thousand dollars.]\n\n\"It is true that still more extraordinary prices were obtained for the\nuse of rams of this breed after Mr. Bakewell's death. Pitt, in his\n'Survey of Leicestershire,' mentions that, in 1795, Mr. Astley gave\nthree hundred guineas for the use of a ram of this breed, engaging, at\nthe same time, that he should serve _gratis_ twenty ewes owned by the\nman of whom the ram was hired; making for the entire use of the ram,\nthat season, four hundred and twenty guineas. In 1796, Mr. Astley gave\nfor the use of the same ram three hundred guineas, and took forty ewes\nto be served gratis. At the price charged for the service of the ram to\neach ewe, the whole value for the season was five hundred guineas. He\nserved one hundred ewes. In 1797, the same ram was let to another person\nat three hundred guineas, and twenty ewes sent with him; the serving of\nwhich was reckoned at a hundred guineas, and the ram was restricted to\nsixty more, which brought his value for the season to four hundred\nguineas. Thus the ram made, in three seasons, the enormous sum of\n_thirteen hundred guineas_.\n\n\"We have nothing to do, at present, with the question whether the value\nof these animals was not exaggerated. The actual superiority of the\nbreed over the stock of the country must have been obvious, and this\npoint we wish kept in mind.\n\n\"This breed of sheep is continued to the present day, and it has been\nremarked by a respected writer, that they will 'remain a lasting\nmonument of Bakewell's skill.' As to their origin, the testimony shows\nthem to have been of _mixed blood_; though no breed is more distinct in\nits characters, or transmits its qualities with more certainty; and if\nwe were without any other example of successful crossing, the advocates\nof the system might still point triumphantly to the Leicester or\nBakewell sheep.\n\n\"But what are the opinions of our best modern breeders in regard to the\npracticability of producing distinct breeds by crossing? Robert Smith,\nof Burley, Rutlandshire, an eminent sheep-breeder, in an essay on the\n'Breeding and Management of Sheep,' for which he received a prize from\nthe Royal Agricultural Society, (1847,) makes the following remarks:\n'The crossing of pure breeds has been a subject of great interest\namongst every class of breeders. While all agree that the first cross\nmay be attended with good results, there exists a diversity of opinion\nupon the future movements, or putting the crosses together. Having\ntried experiments (and I am now pursuing them for confirmation) in every\nway possible, I do not hesitate to express my opinion, that, by proper\nand judicious crossing through several generations, a most valuable\nbreed of sheep may be raised and established; in support of which I may\nmention the career of the celebrated Bakewell, who raised a _new_\nvariety from other long-wooled breeds by dint of perseverance and\npropagation, and which have subsequently corrected all other long-wooled\nbreeds.'\"\n\nWe have alluded to the low price of some of the mutton brought to the\nBoston market. We do not wish the reader to infer that there is none\nother to be had: on the contrary, we have occasionally seen as good\nmutton there as in any European market. There are a number of practical\nand worthy men engaged in improving the different kinds of live stock,\nand preventing the degeneracy to which we refer. They have taken much\ninterest in that class of stock, and they have been abundantly rewarded\nfor their labor. But the great mass want more light on this subject, and\nfor this reason we endeavor to show the causes of degeneracy, to enable\nthem to avoid the errors of their forefathers.\n\nMr. Roberts, of Pennsylvania, says, \"Early in my experience, I witnessed\nthe renovation of a flock of what we call country sheep, that had been\ntoo long propagated in the same blood. This was about the year 1798. An\nimported ram from England, with heavy horns, very much resembling the\nmost vigorous Spanish Merinos, was obtained. The progeny were improved\nin the quality of fleece, and in the vigor of constitution. On running\nthis stock in the same blood for some twelve years, a great\ndeterioration became apparent. A male was then obtained of the large\ncoarse-wooled Spanish stock: improvement in the vigor of the progeny was\nagain most obvious. A Tunis mountain ram was then obtained, with a\nresult equally favorable. In this process, fineness of fleece or weight\nwas less the object than the carcass. In 1810, a male of not quite pure\nMerino blood was placed with the same stock of ewes; and a change of the\nmale from year to year, for some time, produced a superior Merino\nstock. Wool of a marketable quality for fine cloths was now the object;\nand it was not an unprofitable husbandry, when it would sell in the\nfleece, unwashed, from eighty-six cents to one dollar. The Saxon stock\nthen became the rage, and the introduction of a tup of that country\ndiminished greatly the weight of the fleece, without adequately\nimproving its fineness. A male of the Spanish stock would give sometimes\nnine pounds; and the marsh graziers say that they went as high as\nfifteen pounds. Saxon males scarcely exceed five pounds, and the ewes\ntwo and a half pounds. By running in the same blood, and poor keeping,\nthe fleece may be made finer, but it will be lightened in proportion,\nand of a weak and infirm texture. There are few stock-keepers who have\nmixed the Spanish with the Saxon breeds but what either do or will have\ncause to regret it. In this part of the country, a real Spanish Merino\nis not to be obtained. Sheep-raising has ceased to be a business of any\nprofit nearer to the maritime coast than our extensive mountain ranges,\nwhether for carcass or fleece. I sold, the last season, water-washed\nwool, of very fine quality, for thirty cents per pound. At such a price\nfor wool, land near our seaports can be turned to better account, even\nin these dull times, than wool-growing. Stock sheep do best in stony and\nelevated locations, where they have to use diligence to pick the scanty\nblade. Sheep on the sea-board region should be kept more for carcass\nthan fleece; and feeding, more than breeding, ought to be the object for\nsome one hundred miles from tide water. It is now a well-ascertained\nfact, that health and vigor can only be perpetuated by not running too\nlong on the same blood. The evils I have witnessed were due to a want of\ncare on this head more than to any endemical quality in our climate.\nSheep kept on smooth land and soft pasture are liable to the foot rot.\nThe hoofs of the Merino require paring occasionally, for want of a stony\nmountain side to ascend. It is no longer a problem that this is to be a\ngreat wool-growing country, as well as a wool-consuming one. There is,\nin our wool-growing country, land in abundance, held at a price that\nwill enable the wool-grower to produce the finest qualities at thirty\ncents per pound, the cloths to be manufactured in proportion, and the\nmarket to be steady. I have seen Merino wool, since 1810, range from one\ndollar per pound to eighteen and three fourths cents, though I do not\nrecollect selling below twenty-two cents. The best variety of sheep\nstock I have seen, putting fineness of fleece aside, was the mixed\nBakewell and South Down, imported by Mr. Smith, of New Jersey. The flesh\nof the Merino has been pronounced of inferior flavor. This, however,\ndoes not agree with my experience, as I have found the lambs command a\nreadier sale than any other, from being preferred by consumers.\"\n\n\n\n\nDESCRIPTION OF THE DIFFERENT BREEDS OF SHEEP.\n\n\nMr. Lawson tells us that \"the variety in sheep is so great, that\nscarcely any two countries produce sheep of the same kind. There is\nfound a manifest difference in all, either in the size, the covering,\nthe shape, or the horns.\"\n\n\nTEESWATER BREED.\n\n\"This is a breed of sheep said to be the largest in England. It is at\npresent the most prevalent in the rich, fine, fertile, enclosed lands on\nthe banks of the Tees, in Yorkshire. In this breed, which is supposed to\nbe from the same stock as those of the Lincolns, greater attention seems\nto have been paid to size than wool. It is, however, a breed only\ncalculated for warm, rich pastures, where they are kept in small lots,\nin small enclosures, and well supported with food in severe winter\nseasons. The legs are longer, finer boned, and support a thicker and\nmore firm and heavy carcass than the Lincolnshires; the sheep are much\nwider on the backs and sides, and afford a fatter and finer-grained\nmutton.\n\n\nLINCOLN SHIRE BREED.\n\n\"This is a breed of sheep which is characterized by their having no\nhorns; white faces; long, thin, weak carcasses thick, rough, white legs;\nbones large; pelts thick; slow feeding; mutton coarse grained; the wool\nfrom ten to eighteen inches in length; and it is chiefly prevalent in\nthe district which gives the name, and other rich grazing ones. The new,\nor improved Lincolns, have now finer bone, with broader loins and\ntrussed carcasses, are among the best, if not actually the best,\nlong-wooled stock we have.\n\n\nTHE DISHLEY BREED.\n\n\"This is an improved breed of sheep, which is readily distinguished from\nthe other long-wooled sorts; having a fulness of form and substantial\nwidth of carcass, with peculiar plainness and meekness of countenance;\nthe head long, thin, and leaning backward; the nose projecting forward;\nthe ears somewhat long, and standing backward; great fulness of the fore\nquarters; legs of moderate length, and the finest bone; tail small;\nfleece well covering the body, of the shortest and finest of the combing\nwools, the length of staple six or seven inches.\n\n\nCOTSWOLD BREED.\n\n\"This is a breed of sheep answering the following description: long,\ncoarse head, with a particularly blunt, wide nose; a top-knot of wool on\nthe forehead, running under the ears; rather long neck; great length and\nbreadth of back and loin; full thigh, with more substance in the hinder\nthan fore quarters; bone somewhat fine; legs not long; fleece soft, like\nthat of the Dishley, but in closeness and darkness of color bearing\nmore resemblance to short or carding wool. Although very fat, they have\nall the appearance of sheep that are full of solid flesh, which would\ncome heavy to the scale. At two years and a half old, they have given\nfrom eleven to fourteen pounds of wool each sheep; and, being fat, they\nare indisputably among the larger breeds.\n\n\nROMNEY MARSH BREED.\n\n\"This is a kind which is described, by Mr. Young, as being a breed of\nsheep without horns; white faces and legs; rather long in the legs; good\nsize; body rather long, but well barrel-shaped; bones rather large. In\nrespect to the wool, it is fine, long, and of a delicate white color,\nwhen in its perfect state.\n\n\nDEVONSHIRE BREED.\n\n\"This is a breed or sort of sheep which is chiefly distinguished by\nhaving no horns; white faces and legs; thick necks; backs narrow, and\nback-bones high; sides good; legs short, and bones large; and probably\nwithout any material objection, being a variety of the common hornless\nsort. Length of wool much the same as in the Romney Marsh breed. It is a\nbreed found to be prevalent in the district from which it has derived\nits name, and is supposed to have received considerable improvement by\nbeing crossed with the new Leicester, or Dishley.\n\n\nTHE DORSETSHIRE BREED.\n\n\"This breed is known by having the face, nose, and legs white, head\nrather long, but broad, and the forehead woolly, as in the Spanish sort;\nthe horn round and bold, middle-sized, and standing from the head; the\nshoulders broad at top, but lower than the hind quarters; the back\ntolerably straight; carcass deep, and loins broad; legs not long, nor\nvery fine in the bone; the wool is fine and short. It is a breed which\nhas the peculiar property of producing lambs at any period of the\nseason, even so early as September and October, so as to suit the\npurposes of the lamb-suckler.\n\n\nTHE WILTSHIRE BREED.\n\n\"This is a sort which has sometimes the title of _horned crocks_. The\nwriter on live stock distinguishes the breed as having a large head and\neyes; Roman nose; wide nostrils; horns bending down the cheeks; color\nall white; wide bosom; deep, greyhound breast; back rather straight;\ncarcass substantial; legs short; bone coarse; fine middle wool, very\nthin on the belly, which is sometimes bare. He supposes, with Culley,\nthat the basis of this breed is doubtless the Dorsets, enlarged by some\nlong-wooled cross; but how the horns came to take a direction so\ncontrary, is not easy, he thinks, to conjecture; he has sometimes\nimagined it must be the result of some foreign, probably Tartarian\ncross.\n\n\nTHE SOUTH DOWN BREED.\n\n\"This is a valuable sort of sheep, which Culley has distinguished by\nhaving no horns; gray faces and legs; fine bones; long, small necks; and\nby being rather low before, high on the shoulder, and light in the fore\nquarter; sides good; loin tolerably broad; back-bone rather high; thigh\nfull; twist good; mutton fine in grain and well flavored; wool short,\nvery close and fine; in the length of the staple from two to three\ninches. It is a breed which prevails on the dry, chalky downs in Sussex,\nas well as the hills of Surrey and Kent, and which has lately been much\nimproved, both in carcass and wool, being much enlarged forward,\ncarrying a good fore flank; and for the short, less fertile, hilly\npastures is an excellent sort, as feeding close. The sheep are hardy,\nand disposed to fatten quickly; and where the ewes are full kept, they\nfrequently produce twin lambs, nearly in proportion of one third of the\nwhole, which are, when dropped, well wooled.\n\n\nTHE HERDWICK BREED.\n\n\"This is a breed which is characterized by Mr. Culley as having no\nhorns, and the face and legs being speckled; the larger portion of\nwhite, with fewer black spots, the purer the breed; legs fine, small,\nclean; the lambs well covered when dropped; the wool, short, thick, and\nmatted in the fleece. It is a breed peculiar to the elevated,\nmountainous tract of country at the head of the River Esk, and Duddon in\nCumberland, where they are let in herds, at an annual sum; whence the\nname. At present, they are said to possess the property of being\nextremely hardy in constitution, and capable of supporting themselves on\nthe rocky, bare mountains, with the trifling support of a little hay in\nthe winter season.\n\n\nTHE CHEVIOT BREED.\n\n\"This breed of sheep is known by the want of horns; by the face and legs\nbeing mostly white; little depth in the breast; narrow there and on the\nchine; clean, fine, small-boned legs, and thin pelts; the wool partly\nfine and partly coarse. It is a valuable breed of mountain sheep, where\nthe herbage is chiefly of the natural grass kind, which is the case in\nthe situations where these are found the most prevalent, and from which\nthey have obtained their name. It is a breed which has undergone much\nimprovement, within these few years, in respect to its form and other\nqualities, and has been lately introduced into the most northern\ndistricts; and from its hardiness, its affording a portion of fine wool,\nand being quick in fattening, it is likely to answer well in such\nsituations.\n\n\nTHE MERINO BREED\n\n\"In this breed of sheep, the males have horns, but the females are\nwithout them. They have white faces and legs; the body not very perfect\nin shape; rather long in the legs; fine in the bone; a production of\nloose, pendulous skin under the neck; and the pelt fine and clear; the\nwool very fine. It is a breed that is asserted by some to be tolerably\nhardy, and to possess a disposition to fatten readily.\n\n\nTHE WELSH SHEEP.\n\n\"These, which are the most general breed in the hill districts, are\nsmall horned, and all over of a white color. They are neat, compact\nsheep. There is likewise a polled, short-wooled sort of sheep in these\nparts of the country, which are esteemed by some. The genuine Welsh\nmutton, from its smallness and delicate flavor, is commonly well known,\nhighly esteemed, and sold at a high price.\"\n\n[Illustration: A Boar.\n\nBred and fed by Willm. Fisher Hobbs, Esq. of Marks Hall, Coggleshall,\nEssex for which a Prize of L10 was awarded at the Meeting of the R.A.S\nof E. at Derby 1843.]\n\n\n\n\nSWINE.\n\n\nPRELIMINARY REMARKS.\n\nSwine have generally been considered \"unclean,\" creatures of gross\nhabits, &c.; but these epithets are unjust: they are not, in their\nnature, the unclean, gross, insensible brutes that mankind suppose them.\nIf they are unclean, they got their first lessons from the lords of\ncreation, by being confined in narrow, filthy sties--often deprived of\nlight, and pure air, by being shut up in dark, underground cellars, to\nwallow in their own excrement; at other times, confined beneath stables,\ndragging out their existence in a perfect hotbed of corruption--respiring\nthe emanations from the dung and urine of other animals; and often\ncompelled to satisfy the cravings of hunger by partaking of whatever\ncomes in their way. All manner of filth, including decaying and putrid\nvegetable and animal substances, are considered good enough for the\nhogs. And as long as they get such kind of trash, and no other, they\nmust eat it; the cravings of hunger must be satisfied. The Almighty has\nendowed them with powerful organs of digestion; and as long as there is\nany thing before them that the gastric fluids are capable of\nassimilating, although it be disgusting to their very natures, rather\nthan suffer of hunger, they will partake of it. Much of the indigestible\nfood given to swine deranges the stomach, and destroys the powers of\nassimilation, or, in other words, leaves it in morbid state. There is\nthen a constant sensation of hunger, a longing for any and every thing\nwithin their reach. Does the reader wonder, then, at their morbid\ntastes? What will man do under the same circumstances? Suppose him to be\nthe victim of dyspepsia or indigestion. In the early stages, he is\nconstantly catering to the appetite. At one time, he longs for acids; at\nanother, alkalies; now, he wants stimulants; then, refrigerants, &c.\nAgain: what will not a man do to satisfy the cravings of hunger? Will he\nnot eat his fellow, and drink of his blood? And all to satisfy the\ncraving of an empty stomach.\n\nWe know from experience that, if young pigs are daily washed, and kept\non clean cooked food, they will not eat the common city \"swill;\" they\neat it only when compelled by hunger. When free from the control of man,\nthey show as much sagacity in the selection of their food as any other\nanimals; and, indeed, more than some, for they seldom get poisoned, like\nthe ox, in mistaking noxious for wholesome food. The Jews, as well as\nour modern physiologists, consider the flesh of swine unfit for food. No\ndoubt some of it is, especially that reared under the unfavorable\ncircumstances alluded to above. But good home-fed pork, kept on good\ncountry produce, and not too fat, is just as good food for man as the\nflesh of oxen or sheep, notwithstanding the opinion of our medical\nbrethren to the contrary. Their flesh has long been considered as one of\nthe principal causes of scrofula, and other diseases too numerous to\nmention: without doubt this is the case. But that good, healthy pork\nshould produce such results we are unwilling to admit. We force them to\nload their stomachs with the rotten offal of large cities, and thus\nderange their whole systems; they become loaded with fat; their systems\nabound in morbific fluids; their lungs become tuberculous; their livers\nenlarge; calcerous deposits or glandular disorganization sets in. Take\ninto consideration their inactive habits; not voluntary, for instinct\nteaches them, when at liberty, to run, jump, and gambol, by which the\nexcess of carbon is thrown off. Depriving them of exercise may be\nprofitable to the breeder, but it induces a state of plethora. The\ncellular structures of such an animal are distended to their utmost\ncapacity, preventing the full and free play of the vital machinery,\nobstructing the natural outlets (excrementitious vessels) on the\nexternal surface, and retaining in the system morbid materials that are\npositively injurious. At the present time, there is on exhibition in\nBoston a woman, styled the \"fat girl;\" she weighs four hundred and\nninety-five pounds. A casual observer could detect nothing in her\nexternal appearance that denoted disease; yet she is liable to die at\nany moment from congestion of the brain, lungs, or liver. Any one\npossessing a knowledge of physiology would immediately pronounce her to\nbe in a pathological state. Hence, the laws of the animal economy being\nuniform, we cannot arrive at any other conclusion in reference to the\nsame plethoric state in animals of an inferior order.\n\nProfessor Liebig tells us that excess of carbon, in the form of food,\ncannot be employed to make a part of any organ; it must be deposited in\nthe cellular tissue in the form of tallow or oil. This is the whole\nsecret of fattening.\n\nAt every period of animal life, when there occurs a disproportion\nbetween the carbon of the food and the inspired oxygen, the latter being\ndeficient,--which must happen beneath stables and in ill-constructed\nhog-sties,--fat must be formed.\n\nExperience teaches us that in poultry the maximum of fat is obtained by\npreventing them from taking exercise, and by a medium temperature. These\nanimals, in such circumstances, may be compared to a plant possessing in\nthe highest degree the power of converting all food into parts of its\nown structure. The excess of the constituents of blood forms flesh and\nother organized tissues, while that of starch, sugar, &c., is converted\ninto fat. When animals are fed on food destitute of nitrogen, only\ncertain parts of their structure increase in size. Thus, in a goose\nfattened in the manner alluded to, the liver becomes three or four times\nlarger than in the same animal when well fed, with free motion; while we\ncannot say that the organized structure of the liver is thereby\nincreased. The liver of a goose fed in the ordinary way is firm and\nelastic; that of the imprisoned animal is soft and spongy. The\ndifference consists in a greater or less expansion of its cells, which\nare filled with fat. Hence, when fat accumulates and free motion is\nprevented, the animal is in a diseased state. Now, many tons of pork are\neaten in this diseased state, and it communicates disease to the human\nfamily: they blame the pork, when, in fact, the pork raisers are often\nmore to blame. The reader is probably aware that some properties of food\npass into the living organism being assimilated by the digestive organs,\nand produce an abnormal state. For example, the faculty of New York\nhave, time and again, testified to the destructive tendency of milk\ndrawn from cows fed in cities, without due exercise and ordinary care in\ntheir management, giving it as their opinion that most of the diseases\nof children are brought about by its use. If proof were necessary to\nestablish our position, we could cite it in abundance. A single case,\nwhich happened in our own family, will suffice. A liver, taken from an\napparently healthy sow, (yet abounding in fat, and weighing about two\nhundred pounds,) was prepared in the usual manner for dinner. We\nobserved, however, previous to its being cooked, that it was unusually\nlarge; yet there was no appearance of disease about it; it was quite\nfirm. Each one partook of it freely. Towards night, and before partaking\nof any other kind of food, we were all seized with violent pains in the\nhead, sickness at the stomach, and delirium: this continued for several\nhours, when a diarrhoea set in, through which process the offending\nmatter was liberated, and each one rapidly recovered; pretty well\nconvinced, however, that we had had a narrow escape, and that the liver\nwas the sole cause of our misfortune.\n\nHence the proper management of swine becomes a subject of great\nimportance; for, if more attention were paid to it, there would be less\ndisease in the human family. When we charge these animals with being\n\"unclean creatures of gross habits,\" let us consider whether we have\nnot, in some measure, contributed to make them what they are.\n\nAgain: the hog has been termed \"insensible,\" destitute of all those\nfiner feelings that characterize brutes of a higher order. Yet we have\n\"learned pigs,\" &c.--a proof that they can be taught something. A\ncelebrated writer tells us that no animal has a greater sympathy for\nthose of his own kind than the hog. The moment one of them gives a\nsignal, all within hearing rush to his assistance. They have been known\nto gather round a dog that teased them and kill him on the spot; and if\na male and female be enclosed in a sty when young, and be afterwards\nseparated, the female will decline from the instant her companion is\nremoved, and will probably die--perhaps of what would be termed, in the\nhuman family, a broken heart!\n\nIn the Island of Minorca, hogs are converted into beasts of draught; a\ncow, a sow, and two young horses, have been seen yoked together, and of\nthe four the sow drew the best.\n\nA gamekeeper of Sir H. Mildmay actually broke a sow to find game, and to\nback and stand.\n\nSwine are frequently troubled with cutaneous diseases, which produce an\nitching sensation; hence their desire to wallow and roll in the mire and\ndirt. The lying down in wet, damp places relieves the irritation of the\nexternal surface, and cools their bodies. This mud and filth, however,\nin which they are often compelled to wallow, is by no means good or\nwholesome for them.\n\n\n\n\nNATURAL HISTORY OF THE HOG.\n\n\n\"The hog,\" says Professor Low, \"is subject to remarkable changes of form\nand characters, according to the situations in which he is placed. When\nthese characters assume a certain degree of permanence, a breed or\nvariety is formed; and there is none of the domestic animals which more\neasily receives the characters we desire to impress upon it. This\narises from its rapid powers of increase, and the constancy with which\nthe characters of the parents are reproduced in the progeny. _There is\nno kind of live stock that can be so easily improved by the breeder, and\nso quickly rendered suitable for the purposes required._\n\n\"The body is large in proportion to the limbs, or, in other words, the\nlimbs are short in proportion to the body; the extremities are free from\ncoarseness; the chest is broad, and the trunk round. Possessing these\ncharacters, the hog never fails to arrive at early maturity, and with a\nsmaller consumption of food than when he possesses a different\nconformation.\n\n\"The wild boar, which was undoubtedly the progenitor of all the European\nvarieties, and of the Chinese breed, was formerly a native of the\nBritish Islands, and very common in the forests until the time of the\ncivil wars in that country.\"\n\nWe are told, that the wild hog \"is now spread over the temperate and\nwarmer parts of the old continent and its adjacent islands. His color\nvaries with age and climate, but is generally a dusky brown, with black\nspots and streaks. His skin is covered with coarse hairs and bristles,\nintersected with soft wool, and with coarser and longer bristles upon\nthe neck and spine, which he erects when in anger. He is a very bold and\npowerful creature, and becomes more fierce and indocile with age. From\nthe form of his teeth, he is chiefly herbivorous in his habits, and\ndelights in roots, which his acute sense of smell and touch enables him\nto discover beneath the surface. He also feeds on animal substances,\nsuch as worms and larvae, which he grubs up from the earth, the eggs of\nbirds, small reptiles, the young of animals, and occasionally carrion;\nhe even attacks venomous snakes with impunity. In the natural state, the\nfemale produces a litter but once a year;[21] and in much smaller\nnumbers than when domesticated. She usually carries her young about four\nmonths.\n\n\"In the wild state, the hog has been known to live more than thirty\nyears; but when domesticated, he is usually slaughtered before he is two\nyears old. When the wild hog is tamed, it undergoes the following\namongst other changes in its conformation: the ears become less movable,\nnot being required to collect distant sounds; the formidable tusks of\nthe male diminish, not being necessary for self-defence; the muscles of\nthe neck become less developed, from not being so much exercised as in\nthe natural state; the head becomes more inclined, the back and loins\nare lengthened, the body rendered more capacious, the limbs shorter and\nless muscular; and anatomy proves that the stomach and intestinal canals\nhave also become proportionately extended along with the form of the\nbody. The habits and instincts of the animal change; it becomes diurnal\nin its habits, not choosing the night for its search of food; is more\ninsatiate in its appetite, and the tendency to obesity increases.\n\n\"The male, forsaking its solitary habits, becomes gregarious, and the\nfemale produces her young more frequently, and in larger numbers. With\nits diminished strength, and its want of active motion, the animal loses\nits desire for liberty.\n\n\"The true hog does not appear to be indigenous to America, but was taken\nover by the early voyagers from the old world, and it is now spread and\nmultiplied throughout the continent.\n\n\"The first settlers of North America and the United States carried with\nthem the swine of the parent country, and a few of the breeds still\nretain traces of the old English character. From its nature and habits,\nthe hog was the most profitable and useful of all the animals bred by\nthe early settlers in the distant clearings. It was his surest resource\nduring the first years of toil and hardship.\"\n\nTheir widely-extended foreign commerce afforded the Americans\nopportunity of procuring the varieties from China, Africa, and other\ncountries. The large consumption of pork in the United States, and the\nfacilities for disposing of it abroad, will probably cause more\nattention to be paid to the principles of breeding, rearing, feeding,\n&c. The American farmers are doing good service in this department, and\nany attempt on their part to improve the quality of pork ought to meet\nwith a corresponding encouragement from the community. We have no doubt\nthat many stock-raisers find their profits increase in proportion to the\ncare bestowed in rearing. Here is an example: A Mr. Hallock, of the town\nof Coxsackie, has a sow which raised forty pigs within a year, which\nsold for $275,--none of them being kept over nine months. Mr. Little, of\nPoland, Ohio, states, in the Cultivator, that he has \"a barrow three\nyears old, a full-blood Berkshire, which will now weigh nearly 1000\npounds, live weight. He was weighed on the 3d of October, and then\nbrought down 880; since which he has improved rapidly, and will\ndoubtless reach the above figures. I have had this breed for seven years\n_pure_,--descended from hogs brought from Albany and Buffalo, and a boar\nimported by Mr. Fahnestock, of Pittsburg, Pa., from England, (the latter\na very large animal.) The stock have all been large and very\nprofitable--weighing, at seven to ten months old, from 250 to 300\npounds. Several individuals have weighed over 400, and the sire of this\npresent one reached 750. This is, however, much the largest I have yet\nraised.\"\n\nFOOTNOTE:\n\n[21] In the domesticated state, the sow is often permitted to have two\nand even three litters in a year. This custom is very pernicious; it\ndebilitates the mother, overworks all parts of the living machinery, and\nbeing in direct opposition to the laws of their being, their progeny\nmust degenerate. Then, again, let the reader take into consideration the\nfact that members of the same litter impregnate each other, in the same\nratio, and he cannot but come to a conclusion that we have long since\narrived at--that these practices are among the chief causes of\ndeterioration.\n\n\n\n\nGENERALITIES.\n\n\nDr. Gunther observes, that \"the robust constitution of the pig causes it\nto be less liable to fall sick than oxen and sheep. It would be still\nless liable to disease, if persons manifested more judgment in the\nchoice of the animals to be reared, and if more care were shown in the\nmatter. With reference to the latter point, it is very true that the\nvoracity of the pig urges it to eat every thing it meets; but to keep it\nin a state of health, it is, notwithstanding, necessary to restrict its\nregimen to certain rules. The animal which it is proposed to fatten\nshould remain under the roof, and receive good food there, whilst the\nothers may be sent out for the greater part of the year, care being\ntaken to avoid fields that are damp and marshy, and that the pigs be\npreserved from the dew. It is also of importance that they should not be\ndriven too hard during warm days.\n\n\"There are two other points which deserve to be taken into\nconsideration, if we wish swine to thrive: these are, daily exercise in\nthe open air whenever the weather permits, and cleanliness in the sty.\nConstant confinement throws them into what may be called a morbid state,\nwhich renders their flesh less wholesome for man. The manner in which\nthe animal evinces its joy when set at liberty proves sufficiently how\ndisagreeable confinement is to it. A very general prejudice prevails,\nviz., that dung and filth do not injure swine; this opinion, however, is\nabsurd.\"\n\n\n\n\nGENERAL DEBILITY, OR EMACIATION.\n\n\nThe falling off in flesh, or wasting away, of swine is in most cases\nowing to derangement in the digestive organs. The cure consists in\nrestoring the tone of these organs. We commence the treatment by putting\nthe animal on a boiled diet, consisting of bran, meal, or any wholesome\nvegetable production. The following tonic and diffusible stimulant will\ncomplete the cure:--\n\n  Powdered golden seal, }\n     \"     ginger,      } equal parts.\n\nDose, a tea-spoonful, repeated night and morning.\n\nWhen loss in condition is accompanied with cough and difficulty of\nbreathing, mix, in addition to the above, a few kernels of garlic with\nthe food. The drink should consist of pure water. Should the cough prove\ntroublesome, take a tea-spoonful of fir balsam, and the same quantity of\nhoney; to be given night and morning, either in the usual manner, or it\nmay be stirred into the food while hot.\n\n\n\n\nEPILEPSY, OR FITS.\n\n\nThe symptoms are too well known to need any description. It is generally\ncaused by plethora, yet it may exist in an hereditary form.\n\n\n_Treatment._--Feed with due care, and put the animal in a\nwell-ventilated and clean situation; give a bountiful supply of valerian\ntea, and sprinkle a small quantity of scraped horseradish in the food;\nor give\n\n  Powdered assafoetida,    1 ounce.\n     \"     capsicum,       1 tea-spoonful.\n  Table salt,              1 table-spoonful.\n\nMix. Give half a tea-spoonful daily.\n\n\n\n\nRHEUMATISM.\n\n\n_Causes._--Exposure, wallowing in filth, &c.\n\n\n_Symptoms._--It is recognized by a muscular rigidity of the whole\nsystem. The appetite is impaired, and the animal does not leave its sty\nwillingly.\n\n\n_Treatment._--Keep the animal on a boiled diet, which should be given to\nhim warm. Remove the cause by avoiding exposure and filth, and give a\ndose of the following:\n\n  Powdered sulphur,             }\n     \"     sassafras,           } equal parts.\n     \"     cinnamon,            }\n\nDose, half a tea-spoonful, to be given in warm gruel. If this does not\ngive immediate relief, dip an old cloth in hot water, (of a proper\ntemperature,) and fold it round the animal's body. This may be repeated,\nif necessary, until the muscular system is relaxed. The animal should be\nwiped dry, and placed in a warm situation, with a good bed of straw.\n\n\n\n\nMEASLES.\n\n\nThis disease is very common, yet is often overlooked.\n\n\n_Symptoms._--It may be known by eruptions on the belly, ears, tongue, or\neyelids. Before the eruption appears, the animal is drowsy, the eyes are\ndull, and there is sometimes loss of appetite, with vomiting. On the\nother hand, if the disease shall have receded towards the internal\norgans, its presence can only be determined by the general disturbance\nof the digestive organs, and the appearance of a few eruptions beneath\nthe tongue.\n\n\n_Treatment._--Remove the animal from its companions to a warm place, and\nkeep it on thin gruel. Give a tea-spoonful of sulphur daily, together\nwith a drink of bittersweet tea. The object is to invite action to the\nsurface, and maintain it there. If the eruption does not reappear on the\nsurface, rub it with the following liniment:--\n\nTake one ounce of oil of cedar; dissolve in a wine-glass of alcohol;\nthen add half a pint of new rum and a tea-spoonful of sulphur.\n\nAlmost all the diseases of the skin may be treated in the same manner.\n\n\n\n\nOPHTHALMIA.\n\n\n_Causes._--Sudden changes in temperature, unclean sties, want of pure\nair, and imperfect light.\n\n\n_Treatment._--Keep the animal on thin gruel, and allow two tea-spoonfuls\nof cream of tartar per day. Wash the eyes with an infusion of\nmarshmallows, until a cure is effected.\n\n\n\n\nVERMIN.\n\n\nSome animals are covered with vermin, which even pierce the skin, and\nsometimes come out by the mouth, nose, and eyes.\n\n\n_Symptoms._--The animal is continually rubbing and scratching itself, or\nburrowing in the dirt and mire.\n\n\n_Treatment._--First wash the body with a strong lie of wood ashes or\nweak saleratus water, then with an infusion of lobelia. Mix a\ntea-spoonful of sulphur, and the same quantity of powdered charcoal, in\nthe food daily.\n\n\n\n\nRED ERUPTION.\n\n\nThis disease is somewhat analogous to scarlet fever. It makes its\nappearance in the form of red pustules on the back and belly, which\ngradually extend to the whole body. The external remedy is:--\n\n  Powdered bloodroot,     half an ounce.\n  Boiling vinegar,        1 pint.\n\nWhen cool, it should be rubbed on the external surface.\n\nThe diet should consist of boiled vegetables, coarse meal, &c., with a\nsmall dose of sulphur every night.\n\n\n\n\nDROPSY.\n\n\n_Symptoms._--The animal is sad and depressed, the appetite fails,\nrespiration is performed with difficulty, and the belly swells.\n\n_Treatment._--Keep the animal on a light, nutritive diet, and give a\nhandful of juniper berries, or cedar buds, daily. If these fail, give a\ntable-spoonful of fir balsam daily.\n\n\n\n\nCATARRH.\n\n\n_Symptoms._--Occasional fits of coughing, accompanied with a mucous\ndischarge from the nose and mouth.\n\n\n_Causes._--Exposure to cold and damp weather.\n\n\n_Treatment._--Give a liberal allowance of gruel made with powdered elm\nor marshmallows, and give a tea-spoonful of balsam copaiba, or fir\nbalsam, every night. The animal must be kept comfortably warm.\n\n\n\n\nCOLIC.\n\n\nSpasmodic and flatulent colic requires antispasmodics and carminatives,\nin the following form:--\n\nPowdered caraway seeds,        1 tea-spoonful.\n   \"     assafoetida,              one third of a tea-spoonful.\n\nTo be given at a dose in warm water, and repeated at the expiration of\nan hour, provided relief is not obtained.\n\n\n\n\nDIARRHOEA.\n\n\nFor the treatment of this malady, see division SHEEP, article\n_Scours_.\n\n\n\n\nFRENZY.\n\n\nThis makes its appearance suddenly. The animal, having remained in a\npassive and stupid state, suddenly appears much disturbed, to such a\ndegree that it makes irregular movements, strikes its head against every\nthing it meets, scrapes with its feet, places itself quite erect\nalongside of the sty, bites any thing in its way, and frequently whirls\nitself round, after which it suddenly becomes more tranquil.\n\n\n_Treatment._--Give half an ounce of Rochelle salts, in a pint of\nthoroughwort tea. If the bowels are not moved in the course of twelve\nhours, repeat the dose. A light diet for a few days will generally\ncomplete the cure.\n\n\n\n\nJAUNDICE.\n\n\nThis disease is recognised by the yellow tint of the _conjunctiva_,\n(white of the eye,) loss of appetite, &c.\n\nThe remedy is,--\n\n  Powdered golden seal,     half an ounce.\n     \"     sulphur,         one fourth of an ounce.\n     \"     blue flag,       half an ounce.\n  Flaxseed,                 1 pound.\n\nMix, and divide into four parts, and give one every night. The food must\nbe boiled, and a small quantity of salt added to it.\n\n\n\n\nSORENESS OF THE FEET.\n\n\nThis often occurs to pigs that have travelled any distance: the feet\noften become tender and sore. In such cases, they should be examined,\nand all extraneous matter removed from the foot. Then wash with weak\nlie. If the feet discharge fetid matter, wash with the following\nmixture:--\n\n  Pyroligneous acid,        2 ounces.\n  Water,                    4 ounces.\n\nIn the treatment of diseased swine, the \"issues,\" as they are called,\nought to be examined, and be kept free. They may be found on the inside\nof the legs, just above the pastern joint. They seem to serve as a\ndrain or outlet for the morbid fluids of the body, and whenever they are\nobstructed, local or general disturbance is sure to supervene.\n\n\n\n\nSPAYING.\n\n\nThis is the operation of removing the ovaries of sows, in order to\nprevent any future conception, and promote their fattening. (See article\n_Spaying Cows_, p. 201.) It is usually performed by making incision in\nthe middle of the flank, on the left side, in order to extirpate or cut\noff the ovaries, (female _testes_,) and then stitching up the wound, and\nwetting the part with Turlington's balsam. An able writer on this\nsubject says, \"The chief reason why a practice, which is beneficial in\nso many points of view to the interests and advantages of the farmer,\nhas been so little attended to, is the difficulty which is constantly\nexperienced from the want of a sufficient number of expert and proper\npersons to perform the operation. Such persons are far from being common\nin any, much less in every district, as some knowledge, of a nature\nwhich is not readily acquired, and much experience in the practice of\ncutting, are indispensably necessary to the success of the undertaking.\nWhen, however, the utility and benefits of the practice become better\nunderstood and more fully appreciated by the farmer, and the operators\nmore numerous, greater attention and importance will be bestowed upon\nit; as it is capable of relieving him from much trouble, of greatly\npromoting his profits, and of benefiting him in various ways. The facts\nare since well proved and ascertained, that animals which have undergone\nthis operation are more disposed to take on flesh, more quiet in their\nhabits, and capable of being managed with much greater ease and facility\nin any way whatever, than they were before the operation was performed.\nIt may also have advantages in other ways in different sorts of\nanimals; it may render the filly nearly equal to the gelded colt for\nseveral different uses; and the heifer nearly equal to the ox for all\nsorts of farm labor. The females of some other sorts of animals may\nlikewise, by this means, be made to nearly equal the castrated males in\nusefulness for a variety of purposes and intentions, and in all cases be\nrendered a good deal more valuable, or manageable, than they are at\npresent.\"\n\n\n\n\nVARIOUS BREEDS OF SWINE.\n\n\nBERKSHIRE BREED.\n\nThis breed is distinguished by being in general of a tawny, white, or\nreddish color, spotted with black; large ears hanging over the eyes;\nthick, close, and well made in the body; legs short; small in the bone;\nhaving a disposition to fatten quickly. When well fed, the flesh is\nfine. The above county has long been celebrated for its breed of swine.\nThe Berkshire breeders have made a very judicious use of the pug cross,\nby not repeating it to the degree of taking away all shape and power of\ngrowing flesh, in their stock. This breed is supposed by many to be the\nmost hardy, both in respect to their nature and the food on which they\nare fed. Their powers of digestion are exceedingly energetic, and they\nrequire constant good keep, or they will lose flesh very fast. They\nthrive well in the United States, provided, however, due care is\nexercised in breeding.\n\n\nHAMPSHIRE BREED.\n\nThis breed is distinguished by being longer in the body and neck, but\nnot of so compact a form as the Berkshire. They are mostly of a white\ncolor, or spotted, and are easily fattened. The goodness of the\nHampshire hog is proverbial, and in England they are generally fattened\nfor hams.\n\n\nSHROPSHIRE BREED.\n\nThese are not so well formed as those of the Berkshire kind, or equal to\nthem in their disposition to fatten, or to be supported on such cheap\nfood. Their color is white or brinded. They are flat boned; deep and\nflat sided; harsh, or rather wiry-haired; the ear large; head long,\nsharp, and coarse; legs long; loin, although very substantial, yet not\nsufficiently wide, considering the great extent of the whole frame. They\nhave been much improved by the Berkshire cross.\n\nThere are various other breeds, which take their name from the different\ncounties in the mother country. Thus we have the Herefordshire,\nWiltshire, Yorkshire, &c. Yet they are not considered equal to those\nalready alluded to. Many of the different English breeds might, however,\nserve to improve some species of breed in this country.\n\n\nCHINESE BREED.\n\nThis is of small size; the body being very close, compact, and well\nformed; the legs very short; the flesh delicate and firm. The prevailing\ncolor, in China, is white. They fatten very expeditiously on a small\nquantity of food, and might be reared in the United States to good\nadvantage, especially for home consumption.\n\n\n\n\nBOARS AND SOWS FOR BREEDING.\n\n\nMr. Lawson says, \"The best stock may be expected from the boar at his\nfull growth, but no more than from three to five years old.[22] No sows\nshould be kept open for breeding unless they have large, capacious\nbellies.\n\n\"It may be remarked, in respect to the period of being with young, that\nin the sow it is about four months; and the usual produce is about eight\nto ten or twelve pigs in the large, but more in the smaller breeds.\n\n\"In the ordinary management of swine, sows, after they have had a few\nlitters, may be killed; but no breeder should part with one while she\ncontinues to bring good litters, and rear them with safety.\"\n\nPregnant sows should always be lodged separately, especially at the time\nof bringing forth their young, else the pigs would most probably be\ndevoured as they fall. The sow should also be attended with due care\nwhile pigging, in order to preserve the pigs. It is found that dry,\nwarm, comfortable lodging is of almost as much importance as food. The\npigs may be weaned in about eight weeks, after which the sow requires\nless food than she does while nursing. In the management of these\nanimals, it is of great utility and advantage to separate the males from\nthe females, as it lessens their sexual desires.\n\nFOOTNOTE:\n\n[22] Sows are generally bred from too early--before they come to\nmaturity. This not only stints their own growth, but their offspring\ngive evidence of deterioration. A sow should never be put to the boar\nuntil she be a year old.\n\n\n\n\nREARING PIGS.\n\n\n\"As the breeding of pigs is a business that affords the farmer a\nconsiderable profit and advantage in various views, it is of essential\nimportance that he be provided with suitable kinds of food in abundance\nfor their support. Upon this being properly and effectually done, his\nsuccess and advantage will in a great measure depend. The crops capable\nof being cultivated with the most benefit in this intention are, beans,\npeas, barley, buckwheat, Indian corn, potatoes, carrots, parsnips,\nSwedish turnips, cabbages, &c.\n\n\"The sows considerably advanced in pig, and those with pigs, should be\nfed in a better manner than the stone pigs. The former should be\nsupplied with boiled meal, potatoes, carrots, &c., so as to keep them in\ngood condition. The sows with pigs should be kept with the litters in\nseparate sties, and be still better fed than those with pig. When\ndairying is practised, the wash of that kind which has been preserved\nfor that purpose while the dairying was profitable, must be given them,\nwith food of the root kind, such as carrots, parsnips, &c., in as large\nproportions as they will need to keep them in condition.\"\n\nPea-soup is an admirable article when given in this intention; it is\nprepared by boiling six pecks of peas in about sixty gallons of water,\ntill they are well broken down and diffused in the fluid: it is then put\ninto a tub or cistern for use. When dry food is given in combination\nwith this, or of itself, the above writer advises oats, as being much\nbetter than any other sort of grain for young pigs, barley not answering\nnearly so well in this application. Oats coarsely ground have been found\nvery useful for young hogs, both in the form of wash with water, and\nwhen made of a somewhat thicker consistence. But in cases where the sows\nand pigs can be supported with dairy-wash and roots, as above, there\nwill be a considerable saving made, by avoiding the use of the expensive\narticles of barley-meal, peas, or bran.\n\nMr. Donaldson remarks, that in the usual mode, the pigs reared by the\nfarmer are fed, for some weeks after they are weaned, on whey or\nbuttermilk, or on bran or barley-meal mixed with water. They are\nafterwards maintained on other food, as potatoes, carrots, the refuse of\nthe garden, kitchen, scullery, &c., together with such additions as they\ncan pick up in the farmyard. Sometimes they are sent into the fields at\nthe close of harvest, where they make a comfortable living for several\nweeks on the gleanings of the crop; at other times, when the farm is\nsituated in the neighborhood of woods or forests, they are sent thither\nto pick up the beech-nuts and acorns in the fall of the year; and when\nthey have arrived at a proper age for fattening, they are either put\ninto sties fitted up for the purpose, or sold to distillers,\nstarch-makers, dairymen, or cottagers.\n\nNothing tends more effectually to preserve the health and promote the\ngrowth of young pigs than the liberal use of hay tea. The tea should be\nthickened with corn meal and shorts. This, given lukewarm, twice a day,\nwill quicken their growth, and give the meat a rich flavor. A few\nparsnips[23] or carrots (boiled) may be made use of with much success.\n\nFOOTNOTE:\n\n[23] The Sussex (Eng.) Express says, \"At our farm we have been in the\nhabit of employing parsnips for this purpose for some time. Upon\nreference to our books, we find that on the 11th of October, 1847, we\nput up two shotes of eleven weeks old, and fed them on skim milk and\nparsnips for three months, when they were killed, weighing 231 and 238\npounds. They were well fattened, firm in flesh, and the meat of\nexcellent flavor. The quantity of parsnips consumed by them was nine\nbushels each.\"\n\n\n\n\nFATTENING HOGS.\n\n\nF. Dodge, of Danvers, Mass., states that, in the spring of 1848, he\n\"bought, from a drove, seven shotes, the total weight of which was 925\npounds. The price paid for them was seven cents per pound. They were fed\nan average of 184 days, and their average gain was 179 pounds of net\npork. The cost of the food they consumed was as follows:--\n\n  68 bushels corn at 53 cents,                  $36 04\n  30   \"       \"  damaged, at 35 cents,          10 50\n  50   \"       \"  at 65 cents,                   32 50\n  8    \"  meal at 65 cents,                       5 20\n                                               -------\n                                                $84 24\n  Add first cost of pigs,                        64 75\n                                               -------\n  Making a total cost of                       $148 99\n\n\"The whole quantity of pork afforded by the pigs killed was 2178 pounds,\nwhich was sold at 6-1\/3 cents per pound, amounting to $141 57; leaving\na balance against the pigs of $7 42. The inference from this statement\nis, that, at the above prices of grain, pork could not be profitably\nproduced at six and a half cents per pound. But it is suggested that\nsomething might be saved by breeding the stock, instead of purchasing\nshotes at seven cents per pound, live weight. It is thought, however,\nthat the manure afforded by the hogs would be of sufficient value to\nmore than overbalance any deficiency which might appear in the account\nby only crediting the pork.\"\n\nThe food in the above case was too costly. One half of it, mixed with\nparsnips, carrots, beets, or turnips, would have answered the purpose\nbetter. The balance would then have been in favor of the pigs. We are\ntold, by an able writer on swine, that they will feed greedily, and\nthrive surprisingly, on most kinds of roots and tubers, such as carrots,\nbeets, parsnips, potatoes, &c., particularly when prepared by boiling.\nIt may be taken as a general rule, that boiled or prepared food is more\nnutritious and fattening than raw cold food; the additional expense and\nlabor will be more than compensated by the increased weight and quality.\n\nCornstalks might be used as food for swine by first cutting them[24] in\nsmall pieces, and then boiling them until they are quite soft; a small\nquantity of meal is then to be mixed in the fluid, and the stalks again\nadded, and fed to the pigs twice a day.\n\nMr. P. Wing, of Farmersville, C. W., gives us his experience in feeding\nswine; and he requests his brother farmers to make similar experiments\nwith various kinds of food, and, by preparing them in various ways, to\nascertain what way it will yield the most nutriment--that is, make the\nmost pork. He says,--\n\n\"I now give the result of feeding 100 bushels of good peas to sixteen\nhogs, of various mixed breeds, as found in this section. The peas were\nboiled until fine, making what I call thick soup. After having fed the\nhogs on the same kind of food for two weeks, I gave them their morning\nfeed, and weighed each one separately, noting the weight. Twelve of them\nwere about eighteen months old; one was a three year old sow, and three\npigs were seven and half months old when weighed. I found their total\nweight 4267 lbs.; and after consuming the above amount, which took\nforty-two days, I weighed them again, and found that they had gained\n1358 lbs.; and on the supposition that as they gained in flesh they\nshrunk in offal, I estimated their net gain to have been 1400 lbs. Their\ndrink consisted of ten pails of whey per day. It was allowed to stand\nforty-eight hours, and the cream was skimmed off.\n\n\"I find that there is a great difference in breeds of hogs. The three\nyear old sow small framed, and pretty full-fleshed, weighing 504 lbs.\nHer gain in the forty-two days was 66 lbs. The three pigs were from her,\nand showed traces of three distinct breeds of hogs. Their first weight\nand gain were as follows: the first weighed 253 lbs.--gain, 97 lbs.; the\nsecond, 218 lbs.--gain, 75 lbs.; the third, 171 lbs.--gain, 46 lbs. When\nbutchered, the smallest one was the best pork, being the fattest. Two of\nthe most inferior of the hogs gained 1-1\/2 lbs. per day; six, mixture of\nthe Berkshire, (I should think about one fourth,) gained 1-3\/4 lbs. per\nday; three of the common stock of our country gained 2-1\/2 lbs.; and one\nof a superior kind weighted 318 lbs., and in the forty-two days gained\n134 lbs. They were weighed on the 20th September, the first time. They\nwere kept confined in a close pen, except once a week I let them out for\nexercise, and to wallow, for the most pint of a day.\"\n\n\n\n\nMETHOD OF CURING SWINE'S FLESH.\n\n\n\"In the county of Kent, when pork is to be cured as bacon, it is the\npractice to singe off the hairs by making a straw fire round the\ncarcass--an operation which is termed _swaling_. The skin, in this\nprocess, should be kept perfectly free from dirt of all sorts. When the\nflitches are cut out, they should be rubbed effectually with a mixture\nof common salt and saltpetre, and afterwards laid in a trough, where\nthey are to continue three weeks or a month, according to their size,\nkeeping them frequently turned; and then, being taken out of the trough,\nare to be dried by a slack fire, which will take up an equal portion of\ntime with the former; after which, they are to be hung up, or thrown\nupon a rack, there to remain until wanted. But in curing bacon on the\ncontinent, it is mostly the custom to have closets contrived in the\nchimneys, for the purpose of drying and smoking by wood fires, which is\nsaid to be more proper for the purpose. And a more usual mode of curing\nthis sort of meat is that of salting it down for pickled pork, which is\nfar more profitable than bacon.\n\n\"In the county of Westmoreland, where the curing of hams has long been\npractised with much success, the usual method is for them to be at first\nrubbed very hard with bay salt; by some they are covered close up; by\nothers they are left on a stone bench, to allow the brine and blood to\nrun off. At the end of five days, they are again rubbed, as hard as they\nwere at first, with salt of the same sort, mixed with an ounce of\nsaltpetre to a ham. Having lain about a week, either on a stone bench or\nin hogsheads amongst the brine, they are hung up, by some in the\nchimney, amidst the smoke, whether of peat or coals; by others in places\nwhere the smoke never reaches them. If not sold sooner, they are\nsuffered to remain there till the weather becomes warm. They are then\npacked in hogsheads with straw or oatmeal husks, and sent to the place\nof sale.\"\n\nA small portion of pyroligneous acid may be added to the brine. It is a\ngood antiseptic, and improves the flavor of ham and bacon. (See _Acid,\nPyroligneous_, in the _Materia Medica_.)\n\n\n\n\nAPPENDIX.\n\n\nON THE ACTION OF MEDICINES.\n\nIn reference to the action of medicines and external agents on the\nanimal body, we would observe, that warmth and moisture always expand\nit, and bayberry bark, tannin, and gum catechu always contract it; and\nthat these agents have these effects at all times (provided, however,\nthere be sufficient vitality in the part to manifest these peculiar\nchanges) and under all circumstances. If a blister be applied to the\nexternal surface of an animal, and it produces irritation, it always has\na tendency to produce that effect, whatever part of the living organism\nit may be applied to. So alcohol always has a tendency to stimulate;\nwhether given by the mouth, or rubbed on the external surface, it will\nproduce an excitement of nerves, heart, and arteries, and of course the\nmuscles partake of the influence. Again, marshmallows, gum acacia,\nslippery elm, &c., always lubricate the mucous surfaces, quiet\nirritation, and relieve inflammatory symptoms.\n\nIt follows, of course, 1st. That when any other effects than those just\nnamed are seen to follow the administration of these articles, they must\nbe attributed to the morbid state of the parts to which they are\napplied; 2d. That a medicine which is good to promote a given effect in\none form of disease, will be equally good for the same purpose in\nanother form of disease in the same tissue. Thus, if an infusion of\nmallows is good for inflammation of the stomach, and will lubricate the\nsurface, and allay irritation in that organ, then it is equally good for\nthe same purpose in inflammation of the bowels and bladder. What we wish\nthe reader to understand is this: that a medicine used for any\nparticular symptom in one form of disease, if it be a sanative agent, is\nequally good for the same symptom in every form. Medical men range their\nvarious remedies under different heads. Thus opium is called narcotic,\naloes purgative or cathartic, potass diuretic, &c. And because the same\nresults do not always follow the administration of these articles, they\nare perplexed, and are compelled to try every new remedy, in hopes to\nfind a specific; not knowing that many of their _\"best medicines\"_\n(opium, for example) war against the vital principle, and as soon as\nthey get into the system, nature sets up a strong action to counteract\ntheir effects; in short, to get them out of the system in the quickest\npossible manner: sometimes they pass through the kidneys; at other\ntimes, the intestinal canal, the lungs, or surface, afford them egress.\nAnd because a certain agent does not always act in their hands with\nunerring certainty, they seem to suppose that the same uncertainty\nattends the administration of every article in the _materia medica_. The\nmedicines we recommend owe their diuretic, astringent, diaphoretic, and\ncathartic powers to their aromatic, relaxing, antispasmodic,\nlubricating, and irritating properties; and if we give them with a view\nof producing a certain result, and they do not act just as we wish, it\nis no proof that they have not done good. The fact is, all our medicines\nact on the parts where nature is making the greatest efforts to restore\nequilibrium; hence they relieve the constitution, whatever may be the\nnature of their results.\n\nMany of the remedies recommended in this work are denounced by the\nUnited States Dispensatory a \"useless, inert,\" &c.; yet many of our most\ncelebrated physicians are in the daily habit of using them. Mr. Bracy\nClark, V. S., recommends tincture of allspice for gripes. And Mr.\nCauser, an experienced veterinarian, says, \"I ordered a dessert spoonful\n(about two drachms) of tincture of gentian and bark to be given twice a\nday in a case of gripes. Scarcely an hour after the animal had taken the\nfirst dose, he began to eat some hay, and on the next day he ate every\nthing that was offered him. After this, I ordered a quart of cold boiled\nmilk to be given him every morning and evening. By these means, together\nwith the good care of the coachman, he recovered his strength.\" Mr.\nWhite, V. S., says, \"I have been assured by a veterinary surgeon, that\nhe once cured a horse of gripes by a dose of hot water; and it is by no\nmeans unlikely that a warm infusion of some of our medicinal herbs, such\nas peppermint, pennyroyal, rosemary, &c., would be found effectual.\"\n\nMr. Gibson says, \"It is a fact that cannot be too generally known, that\nan infusion of garlic has, to my certain knowledge, cured several cases\nof epilepsy--a dreadful disease, that seems to have baffled, in most\ninstances, every effort of medical skill.\"\n\nAn intelligent farmer assures Dr. White that he has had forty sheep at a\ntime hoven or blasted from feeding on vetches, and so swollen that he\nhardly knew which would drop first. His usual remedy was a quart of\nwater for each sheep; and that generally had the desired effect, though\nmany died before it could be given. We might give our own experience in\nfavor of numberless simple agents, which we are in the constant habit of\nusing, were it necessary; suffice it to say, that at the present time we\nuse nothing else than simple means.\n\n\n\n\nCLYSTERS.\n\n\n_Remarks._--As the more general use of clysters is recommended by the\nauthor, especially in acute diseases, he has thought proper to\nintroduce, in this part of the work, a few remarks on them, with\nexamples of their different forms. They serve not only to evacuate the\nrectum of its contents, but assist to evacuate the intestines, and\nserve also to convey nourishment into the system; as in cases of\nlocked-jaw, and great prostration. They soften the hardened excrement in\nthe rectum, and cause it to be expelled; besides, by their warm and\nrelaxing powers, they act as fomentations. A stimulating clyster in\ncongestion of the brain, or lungs, will relieve those parts by\ncounter-irritation. An animal that is unable to swallow may be supported\nby nourishing clysters; for the lacteals, which open into the inner\ncavity of the intestines, absorb, or take up, the nourishment, and\nconvey it into the thoracic duct, as already described. Some persons\ndeny the utility of injections. We are satisfied on that point, and are\nable to convince any one, beyond a reasonable doubt, that fluids are\nabsorbed in the rectum, notwithstanding the opinion of some men to the\ncontrary.\n\nIn administering clysters, it ought always to be observed that the\nfluids should be neither too hot nor too cold: they should be about the\ntemperature of the blood. The common sixteen-ounce metal syringe, with a\nwooden pipe about six inches in length, and gradually tapering from base\nto point, is to be preferred. It is, after being oiled, much more easily\nintroduced into the fundament than one that is considerably smaller;\nand, having a blunt point, there is no danger of hurting the animal, or\nwounding the rectum.\n\nThe following injections are suitable for all kinds of animals. The\nquantity, however, should be regulated according to the size of the\npatient. Thus a quart will suffice for a sheep or pig, while three or\nfour quarts are generally necessary in the case of horses and cattle. If\nclysters are intended to have a nutritive effect, they must be\nintroduced in the most gentle manner, and not more than one pint should\nbe given at any one time, for fear of exciting the expulsive action of\nthe rectum. In constriction and intussusception of the intestines, and\nwhen relaxing clysters are indicated, they should not be too long\npersevered in, for falling of the rectum has been known, in many\ninstances, to arise from repeated injections. Efforts should be made to\nrelax the whole animal by warmth and moisture externally, and in the\nuse of antispasmodic teas, rather than to place too much dependence on\nclysters.\n\n\nFORMS OF CLYSTERS.\n\n_Laxative Clyster._\n\n  Warm water,                          3 or 4 quarts.\n  Linseed oil,                         8 ounces.\n  Common salt, (fine,)                 1 table-spoonful.\n\n_Another._\n\n  Warm water,                          4 quarts.\n  Soft soap,                           1 gill.\n  Fine salt,                           half a table-spoonful.\n\n_Use._--Either of the above clysters is useful in obstinate\nconstipation, \"stoppage,\" or whenever the excrement is hard and dark\n.\n\n_Emollient Clyster_.\n\n  Slippery elm bark,                      2 ounces.\n  Boiling water,                          2 quarts.\n\nLet them simmer over the fire for a few minutes, then strain through a\nfine sieve, and inject. The following articles may be substituted for\nelm: flaxseed, lily roots, gum arabic, poplar bark, Iceland moss.\n\n_Use._--In all cases of irritation and inflammation of the intestines\nand bladder.\n\n_Stimulating Clyster._\n\n  Thin mucilage of slippery elm or linseed tea,   3 quarts.\n  African cayenne,[25]                             1 tea-spoonful.\n\n_Another._\n\n  Powdered ginger,            half a table-spoonful.\n  Boiling water,              3 quarts.\n\nWhen cool, inject.\n\n_Use._--In all cases, when the rectum and small intestines are inactive,\nand loaded with excrement, or gas.\n\n_Anodyne Clyster._\n\n  Lady's slipper, (_cypripedium_,)   1 ounce.\n  Camomile flowers,                       1 ounce.\n  Boiling water,                          3 quarts.\n\nLet the mixture stand a short time, then strain through a fine sieve,\nwhen it will be fit for use.\n\n_Use._--To relieve pain and relax spasms.\n\n_Diuretic Clyster._\n\n  Linseed tea,                         3 quarts.\n  Oil of juniper,                      1 table-spoonful.\n\nOr, substitute for the latter, cream of tartar, half an ounce.\n\n_Use._--This form of clyster may be used with decided advantage in all\nacute diseases of the urinary organs. This injection is useful in cases\nof red water, both in cattle and sheep; and when the malady is supposed\nto result from general or local debility, the addition of tonics (golden\nseal or gentian[26]) will be indicated.\n\n_Astringent Clyster_.\n\nTake an infusion of hardhack, strain, and add a table-spoonful of\nfinely-pulverized charcoal to every three quarts of fluid.\n\n_Another._\n\nAn infusion of witch hazel.\n\n_Another._\n\n  Powdered bayberry bark,          1 table-spoonful.\n  Boiling water,                   3 quarts.\n\nWhen cool, it is fit for use.\n\n_Use._--Astringent injections are used in all cases where it is desired\nto contract the living fibre, as in scouring, dysentery, scouring rot,\ndiarrhoea, bloody flux, falling of the womb, fundament, &c.\n\n_Nourishing Clyster._\n\nNourishing clysters are composed of thin gruel made from flour, &c.\n\n_Injection for Worms._\n\nMake an infusion of pomegranate, (rind of the fruit,) and inject every\nnight for a few days. This will rid the animal of worms that infest the\nrectum; but if the animal is infested with the long, round worm,\n(_teres_,) then half a pint of the above infusion must be given for a\nfew mornings, before feeding.\n\n_Another for Worms._\n\n  Powdered lobelia,                1 ounce.\n  Wood ashes,                      a handful.\n  Boiling water,                   3 quarts.\n\nWhen cool, it is fit for use.\n\nFOOTNOTES:\n\n[24] Messrs. Parker & White, in Boston, have shown us an excellent\nmachine used for the purpose of cutting cornstalks. Every farmer should\nhave one in his possession.\n\n[25] A large portion of the cayenne found in the stores is adulterated\nwith logwood, and is positively injurious, as it would thus prove\nastringent.\n\n[26] Their active properties may be extracted by infusion.\n\n\n\n\nINFUSIONS.\n\n\nThese are made by steeping herbs, roots, and other medicinal substances\nin boiling water. No particular rules can be laid down as to the\nquantity of each article required: it will, however, serve as some sort\nof a guide, to inform the reader that we generally use from one to two\nounces of the aromatic herbs and roots to every quart of fluid. A bitter\ninfusion, such as wormwood or camomile, requires less of the herb. All\nkinds of infusions can be rendered palatable by the addition of a small\nquantity of honey or molasses. As a general rule, the human palate is a\ngood criterion; for if an infusion be too strong or unpalatable for man,\nit is unfit for cattle or sheep. We do not depend so much on the\nstrength of our agents: the great secret is to select the one best\nadapted to the case in view. If it be an agent that is capable of acting\nin concert with nature, then the weaker it is, the better. In short,\nnature requires but slight assistance under all ordinary circumstances,\nunless the animal is evidently suffering from debility; then our efforts\nmust act in concert with the living powers. We must select the most\nnutritious food--that which can be easily converted into blood, bones,\nand muscles. If, on the other hand, we gave an abundance of provender,\nand it lacked the constituents necessary for the purposes in view, or\nwas of such an indigestible nature that its nutritive properties could\nnot be extracted by the gastric fluids, this would be just as bad as\ngiving improper medicines, both in reference to its quantity and\nquality.\n\nAn infusion of either of the following articles is valuable in colic,\nboth flatulent and spasmodic, in all classes of animals: caraways,\npeppermint, spearmint, fennel-seed, angelica, bergamot, snakeroot,\naniseed, ginseng, &c.\n\n\n\n\nANTISPASMODICS.\n\n\nBy antispasmodics are meant those articles that assist, through their\nphysiological action, in relaxing the nervous and muscular systems.\nHence the reader will perceive, by the definition we have given of this\nclass of remedies, that we cannot recommend or employ the agents used by\nour brethren of the allopathic school, for many of them act\npathologically. The class we use are simple, yet none the less\nefficient.\n\nProfessor Curtis says, when alluding to the action of medicinal agents,\n\"Experiments have shown that many vegetable substances, which seem in\nthemselves quite bland and harmless, are antidotes to various poisons.\nThus the skullcap (_scutellaria laterifolia_) is said to be a remedy for\nhydrophobia, the _alisma plantago_ and _polemonium reptans_ for the\nbites of serpents, and lobelia for the sting of insects. They are good;\nbut why? Because they are permanently relaxing and stimulating, and\ndepurate the whole system.\"\n\nNatural antispasmodics are warmth and moisture. The medicinal ones are\nlobelia, Indian hemp, castor musk, ginseng, assafoetida, pleurisy\nroot, Virginia snakeroot, camomile, wormwood. The above are only\nspecimens. There is no limit to the number and variety of articles in\nthe vegetable kingdom that will act as antispasmodics or relaxants. They\nmay be given internally or applied externally: the effect is the same.\n\n\n\n\nFOMENTATIONS.\n\n\nThis class of remedies is usually composed of relaxants, &c., of several\nkinds, combined with tonics, stimulants, and anodynes. They are very\nuseful to relieve pain, to remove rigidity, to restore tone, and to\nstimulate the parts to which they are applied.\n\n_Common Fomentation._\n\n  Wormwood,                  }\n  Tansy,                     } equal parts.\n  Hops,                      }\n\nMoisten them with equal parts of boiling water and vinegar, and apply\nthem blood warm.\n\n_Use._--For all kinds of bruises and sprains. They should be confined to\nthe injured parts, and kept moist with the superabundant fluid. When it\nis not practicable to confine a fomentation to the injured parts, as in\nshoulder or hip lameness, constant bathing with the decoction will\nanswer the same purpose.\n\n_Anodyne Fomentation._\n\n  Hops,                            a handful.\n  White poppy heads,               1 ounce.\n  Water and vinegar,               equal parts.\n\nSimmer a few minutes.\n\n_Use._--In all painful bruises.\n\n_Relaxing Fomentation_\n\n\n  Powdered lobelia,           2 ounces.\n  Boiling water,              2 quarts.\n\nSimmer for a few minutes, and when sufficiently cool, bathe the parts\nwith a soft sponge.\n\n_Use._--In all cases of stiff joints, and rigidity of the muscles.\nAnimals often lie down in wet pastures, from which rheumatism and\nstiffness of the joints arise. In such cases, the animal must be taken\nfrom grass for a few days, and the affected parts be faithfully bathed.\n\n_Stimulating Fomentation._\n\nCedar buds, or boughs, any quantity, to which add a small quantity of\nred pepper and ginger, boiling water sufficient.\n\n_Use._--This will be found very efficacious in chronic lameness and\nparalysis, for putrid sore throat, and when the glands are enlarged from\ncold and catarrh.\n\n\n\n\nMUCILAGES.\n\n\nMucilages are soft, bland substances, made by dissolving gum arabic in\nhot water; or by boiling marshmallows, slippery elm, or lily roots,\nuntil their mucilaginous properties are extracted. A table-spoonful of\neither of the above articles, when powdered, will generally suffice for\na quart of water.\n\n_Use._--In all cases of catarrh, diarrhoea, inflammation of the\nkidneys, womb, bladder, and intestines. They shield the mucous\nmembranes, and defend them from the action of poisons and drastic\ncathartics.\n\n\n\n\nWASHES.\n\n\nWashes generally contain some medicinal agent, and are principally used\nexternally.\n\n_Wash for Diseases of the Feet._\n\n  Pyroligneous acid,         4 ounces.\n  Water,                     8 ounces.\n\n_Use._--This wash excels every other in point of efficacy, and removes\nrot and its kindred diseases sooner than any other.\n\n_Cooling Wash for the Eye._\n\n  Rain water,                     1 pint.\n  Acetic acid,                    20 drops.\n\n_Use._--In ophthalmia.\n\n_Tonic and Antispasmodic Wash._\n\n  Camomile flowers,                half an ounce.\n  Boiling water,                   1 pint.\n\nWhen cool, strain through fine linen.\n\n_Use._--In chronic diseases of the eye, and when a weeping remains after\nan acute attack.\n\n_Wash for unhealthy (or ulcerated) Sores._\n\nA weak solution of sal soda or wood ashes.\n\n_Wash for Diseases of the Skin._\n\nTake one ounce of finely-pulverized charcoal, pour on it one ounce of\npyroligneous acid, then add a pint of water. Bottle, and keep it well\ncorked. It may be applied to the skin by means of a sponge. It is also\nan excellent remedy for ill-conditioned ulcers.\n\n\n\n\nPHYSIC FOR CATTLE.\n\n\nExtract of butternut, (_juglans cinerea_,) half an ounce.\nCream of tartar,                                1 tea-spoonful.\nBoiling water,                                  2 quarts.\n\nMix. When cool, administer.\n\n_Another._\n\n  Extract of blackroot, (_leptandra\n    virginica_,)                          half an ounce.\n  Rochelle salts,                         1 ounce.\n  Powdered ginger,                        1\/2 tea-spoonful.\n\nDissolve in two quarts of warm water.\n\n_Another._\n\n  Powdered mandrake,             1 table-spoonful.\n  Cream of tartar,               1 tea-spoonful.\n  Hot water,                     2 quarts.\n\nHere are three different forms of physic for cattle, which do not\ndebilitate the system, like aloes and salts, because they determine to\nthe surface as well as the bowels. They may be given in all cases where\npurges are necessary. One third of the above forms will suffice for\nsheep.\n\n\nMILD PHYSIC FOR CATTLE.\n\n  Sirup of buckthorn,          2 ounces.\n  Sulphur,                     half a table-spoonful.\n  Ginger,                      half a tea-spoonful.\n  Hot water,                   2 quarts.\n\n_Aperient._\n\n  Linseed oil,            1 pint.\n  Yolks of two eggs.\n\nMix.\n\n_Another._\n\n  Sweet oil,                   1 pint.\n  Powdered cayenne,            half a tea-spoonful.\n\nMix.\n\nA sheep will require about one half of the above.\n\n_Stimulating Tincture._\n\n  Boiling vinegar,         1 pint.\n  Tincture of myrrh,       2 ounces.\n  Powdered capsicum,       2 tea-spoonfuls.\n\n_Use._--For external application in putrid sore throat.\n\n_Another._\n\n  Tincture of camphor,                   4 ounces.\n  Oil of cedar,                          half an ounce.\n  Tincture of capsicum, (hot drops,)     4 ounces.\n\nTo be rubbed around the throat night and morning.\n\n_Stimulating Tincture for Chronic Rheumatism._\n\n  Tincture of capsicum,            4 ounces.\n  Oil of cedar,                    1 ounce.\n  Oil of wormwood,                 1 ounce.\n  Vinegar,                         half a pint.\n  Goose grease,                    1 gill.\n\nMix. To be applied night and morning. The mixture should be kept in a\nwell-corked bottle, and shaken before being used.\n\n\n\n\nPOULTICES.\n\n\n_Preliminary Remarks._--As oxen, sheep, and pigs are liable to have\naccumulations of matter, in the form of abscess, resulting from injury\nor from the natural termination of diseases, it becomes a matter of\nimportance that the farmer should rightly understand their character and\ntreatment. If a foreign substance enters the flesh, the formation of\nmatter is a part of the process by which nature rids the system of the\nenemy. A poultice relaxing and lubricating will then be indicated. If,\nhowever, the foreign body shall have entered at a point where it is\nimpossible to confine a poultice, then the suppurative stage may be\nshortened by the application of relaxing fomentations, and lastly, by\nstimulants. It is a law of the animal economy, that, unless there be\nsome obstacle, matter always seeks its exit by an external opening; and\nit becomes part of our duty to aid nature in her efforts to accomplish\nthis salutary object. Nature requires aid in consequence of the\nunyielding character of the hide, and the length of time it takes to\neffect an opening through it. Animals are known to suffer immensely from\nthe pressure a large accumulation of pus makes on the surrounding\nnerves, &c., and also from the reabsorption of this pus when it cannot\nreadily make its exit. This is not all; for, if pus accumulates, and\ncannot in due time find an outlet, it produces destruction of the\nblood-vessels, nerves, and surrounding tissues. These vessels are\ndistributed to the different surfaces; their supply of blood and nervous\nenergy being cut off, they decompose, and in their turn become pus, and\ntheir open mouths allow the morbid matter to enter the circulation, and\nthus poison the blood. Hence it becomes our duty, whenever matter can be\ndistinctly felt, to apply that sort of poultice which will be most\nlikely to aid nature.\n\nThere is no article in the _materia medica_ of so much value to the\nfarmer as marshmallows; he cannot place too much value on it. Whether he\nuses it in his own family or confines it exclusively to cattle practice,\nit is equally valuable. It has numerous advantages over many similar\nremedies: the most important one to the farmer is, that it can be\nprocured in this country at a small cost. We have used it for a number\nof years, and in many cases we consider it our sheet-anchor. In short,\nwe cannot supply its place.\n\nMr. Cobbett says, \"I cannot help mentioning another herb, which is used\nfor medicinal purposes. I mean the marshmallows. It is amongst the most\nvaluable of plants that ever grew. Its leaves stewed, and applied wet,\nwill cure, and almost instantly cure, any cut, or bruise, or wound of\nany sort. Poultices made of it will cure sprains; fomenting with it will\nremove swellings; applications of the liquor will cure chafes made by\nsaddles and harness; and its operation, in all cases, is so quick that\nit is hardly to be believed. Those who have this weed at hand need not\nput themselves to the trouble and expense of sending to doctors and\nfarriers on trifling occasions. It signifies not whether the wound be\nold or new. The mallows, if you have it growing near you, may be used\ndirectly after it is gathered, merely washing off the dirt first. But\nthere should be some always ready in the house for use. It should be\ngathered just before it blooms, and dried and preserved just in the same\nmanner as other herbs. It should be observed, however, that, if it\nshould happen not to be gathered at the best season, it may be gathered\nat any time. I had two striking instances of the efficacy of mallows. A\nneighboring farmer had cut his thumb in a very dangerous manner, and,\nafter a great deal of doctoring, it had got to such a pitch that his\nhand was swelled to twice its natural size. I recommended the use of the\nmallows to him, gave him a little bunch out of my store, (it being\nwinter time,) and his hand was well in four days. He could go out to his\nwork the very next day, after having applied the mallows over night. The\nother instance was this. I had a valuable hog, that had been gored by a\ncow. It had been in this state for two days before I knew of the\naccident, and had eaten nothing. The gore was in the side, making a\nlarge wound. I poured in the liquor in which the mallows had been\nstewed, and rubbed the side well with it. The next day the hog got up\nand began to eat. On examining the wound, I found it so far closed that\nI did not think it right to disturb it. I bathed the side again; and in\ntwo days the hog was turned out, and was running about along with the\nrest. Now, a person must be criminally careless not to make provision of\nthis herb. Mine was nearly two years old when I made use of it upon the\nlast-mentioned occasion. If the use of this weed was generally adopted,\nthe art and mystery of healing wounds, and of curing sprains,\nswellings, and other external maladies, would very quickly be reduced to\nan unprofitable trade.\"\n\n_Lubricating and healing Poultice._\n\n  Powdered marshmallow roots,         }\n  Marshmallow leaves,                 } equal parts.\n\nMoisten with boiling water, and apply.\n\n_Use._--In ragged cuts, wounds, and bruises.\n\n_Stimulating Poultice._\n\n  Indian meal,                 }\n  Slippery elm,                }  equal parts.\n\nMix them together, and add sufficient boiling water to moisten the mass.\nSpread it on a cloth, and sprinkle a small quantity of powdered cayenne\non its surface.\n\n_Use._--To stimulate ill-conditioned ulcers to healthy action. Where\nthere is danger of putrescence, add a small quantity of powdered\ncharcoal.\n\n_Poultice for Bruises._\n\nNothing makes so good a poultice for recent bruises as boiled carrots or\nmarshmallows.\n\n_Poultice to promote Suppuration._\n\n  Indian meal,        a sufficient quantity.\n  Linseed,            a handful.\n  Cayenne,            1 tea-spoonful.\n\nTo be moistened with boiling vinegar, and applied at the usual\ntemperature.\n\n\n\n\nSTYPTICS, TO ARREST BLEEDING.\n\n\nWitch hazel, (winter bloom,) bark or leaves, 2 ounces.\n\nMake a decoction with the smallest possible quantity of water, and if\nthe bleeding is from the nose, throw it up by means of a syringe; if\nfrom the stomach, lungs, or bowels, add more water, and let the animal\ndrink it, and give some by injection.\n\n_Styptic to arrest external Bleeding._\n\nWet a piece of lint with tincture of muriate of iron, and bind it on the\npart.\n\nThere are various other styptics, such as alum water, strong tincture of\nnutgalls, bloodroot, common salt, fine flour, &c.\n\n\n\n\nABSORBENTS.\n\n\n_Remarks._--Absorbents are composed of materials partaking of an\nalkaline character, and are used for the purpose of neutralizing acid\nmatter. The formation of an acid in the stomach arises from some\nderangement of the digestive organs, sometimes brought on by the\nimproper quantity or quality of the food. It is useless, therefore, to\ngive absorbents, with a view of neutralizing acid, unless the former are\ncombined with tonics, or agents that are capable of restoring the\nstomach to a healthy state. This morbid state of the stomach is\nrecognized in oxen by a disposition to eat all kinds of trash that comes\nin their way, such as dirt, litter, &c. They are frequently licking\nthemselves, and often swallow a great deal of hair, which is formed into\nballs in the stomach, and occasions serious irritation. Calves, when\nfattening, are often fed so injudiciously, that the stomach is incapable\nof reducing the food to chyme and chyle: the consequence is, that a\nlarge amount of carbonic acid gas is evolved. Many calves and lambs die\nfrom this cause.\n\nA mixture of chalk, saleratus, and soda is often given by farmers; yet\nthey do not afford permanent relief. They do some good by correcting the\nacidity of the stomach; but the animals are often affected with\ndiarrhoea, or costiveness, loss of appetite, colic, and convulsions.\nAttention to the diet would probably do more than all the medicine in\nthe world. Yet if they do get sick, something must be done. The best\nforms of absorbents are the following: they restore healthy action to\nthe lost function at the same time that they neutralize the gas.\n\n\nFORMS OF ABSORBENTS.\n\n  Powdered charcoal,           1 table-spoonful.\n      \"    snakeroot,          half a table-spoonful.\n      \"    caraways,           1 tea-spoonful.\n  Hot water,                   1 quart.\n\nMix. To be given at one dose, for a cow; half the quantity, or indeed\none third, is sufficient for a calf, sheep, or pig.\n\n_Another._\n\n  Powdered charcoal,      1 table-spoonful.\n\nTo be given in thoroughwort tea, to which may be added a very small\nportion of ginger.\n\n_Another, adapted to City Use._\n\n  Subcarbonate of soda,        1 tea-spoonful.\n  Tincture of gentian,         1 ounce.\n  Infusion of spearmint,       1 pint.\n\nMix. Give a cow the whole at a dose, and repeat daily, for a short time,\nif necessary. One half the quantity will suffice for a smaller animal.\n\n_Drink for Coughs._\n\n  Balm of Gilead buds,        half an ounce.\n  Honey,                      2 table-spoonfuls.\n  Vinegar,                    1 wine-glassful.\n  Water,                      1 pint.\n\nSet the mixture on the fire, in an earthen vessel; let it simmer a few\nminutes. When cool, strain, and it is fit for use. Dose, a\nwine-glassful, twice a day.\n\n_Another._\n\n  Balsam copaiba,        1 ounce.\n  Powdered licorice,     1 ounce.\n  Honey,                 2 table-spoonfuls.\n  Boiling water,         1 quart.\n\nRub the copaiba, licorice, and honey together in a mortar: after they\nare well mixed, add the water. Dose, half a pint, night and morning.\n\n_Another._\n\n  Balsam of Tolu,                 half an ounce.\n  Powdered marshmallow roots,     1 ounce.\n  Honey,                          half a gill.\n  Boiling water,                  2 quarts.\n\nMin. Dose, half a pint, night and morning.\n\n_Drink for a Cow after Calving._\n\n  Bethwort,         1 ounce.\n  Marshmallows,     1 ounce.\n\nFirst make an infusion of bethwort by simmering it in a quart of water.\nWhen cool, strain, and stir in the mallows. Dose, half a pint, every two\nhours.\n\n\n\n\nVETERINARY MATERIA MEDICA,\n\nEMBRACING A LIST OF THE VARIOUS REMEDIES USED BY THE AUTHOR OF THIS WORK\nIN THE PRACTICE OF MEDICINE ON CATTLE, SHEEP, AND SWINE.\n\n\nACACIA, CATECHU, or JAPAN EARTH. It is a\npowerful astringent and tonic, and given, in half tea-spoonful doses, in\nmucilage of slippery elm or mallows, is a valuable remedy in\ndiarrhoea, or excessive discharges of urine.\n\nACACIA GUM makes a good mucilage, and is highly recommended in\ndiseases of the mucous surfaces and urinary organs. It is highly\nnutritious, and consequently can be given with advantage in locked-jaw.\n\nACETUM, (vinegar.) This is cooling, and a small portion of it,\nwith an equal quantity of honey, administered in thin gruel, makes an\nexcellent drink in fevers. Diluted with an equal quantity of water, it\nis employed externally in bruises and sprains. It neutralizes\npestilential effluvia, and, combined with capsicum, makes a good\napplication for sore throat.\n\nACID, PYROLIGNEOUS. This is one of the most valuable articles\nin the whole _materia medica_. Diluted with equal parts of water, it is\napplied to ill-conditioned sores and ulcers; it acts as an antiseptic\nand stimulant. It is obtained from wood by destructive distillation in\nclose vessels. This acid is advantageously applicable to the\npreservation of animal food. Mr. William Ramsay (_Edinburgh\nPhilosophical Journal_, iii. 21) has made some interesting experiments\non its use for this purpose. Herrings and other fish, simply dipped in\nthe acid and afterwards dried in the shade, were effectually preserved,\nand, when eaten, were found very agreeable to the taste. Herrings\nslightly cured with salt, by being sprinkled with it for six hours, then\ndrained, next immersed in pyroligneous acid for a few seconds, and\nafterwards dried in the shade for two months, were found by Mr. Ramsay\nto be of fine quality and flavor. Fresh beef, dipped in the acid, in\nthe summer season, for the short space of a minute, was perfectly sweet\nin the following spring. Professor Silliman states, that one quart of\nthe acid added to the common pickle for a barrel of hams, at the time\nthey are laid down, will impart to them the smoked flavor as perfectly\nas if they had undergone the common process of smoking.\n\nALDER BARK, BLACK, (_prinos verticillatus_.) A strong decoction\nmakes an excellent wash for diseases of the skin, in all classes of\ndomestic animals.\n\nALLIUM, (garlic.) This is used chiefly as an antispasmodic. It\nimproves all the secretions, and promotes the function of the skin and\nkidneys. It is useful also to expel wind and worms. A few kernels may be\nchopped fine and mixed with the food. When used for the purpose of\nexpelling worms, an ounce of the root should be boiled in a pint of\nmilk, and given in the morning, about an hour before feeding.\n\nALOES. The best kind is brought from the Island of Socotra, and\nis supposed to be more safe in its operation than the other kinds. In\nconsequence of the irritative properties of aloes, they are ill adapted\nto cattle practice; and as a safer article has been recommended, (see\n_Physic for Cattle_,) we have entirely dispensed with them.\n\nALTHEA, (marshmallows.) See _Remarks on Poultices_.\n\nALUM. It possesses powerful astringent properties, and, when\nburnt and pulverized, is useful to remove proud flesh.\n\nAMMONIACUM. Gum ammoniacum is useful for chronic coughs. The\ndose is two drachms daily, in a quart of gruel.\n\nANISEED. A good carminative in flatulent colic. The dose is\nabout one ounce, infused in a quart of boiling water.\n\nANTHEMIS, (camomile.) It is used as a tonic in derangement of\nthe digestive organs, &c. An ounce of the flowers may be infused in a\nquart of water, and given when cool. It is useful also as an external\napplication in bruises and sprains.\n\nASH BARK, WHITE. This is a useful remedy in loss of cud,\ncaused by disease of the liver. Dose, one ounce of the bark, infused in\nboiling water. When cool, pour off the clear liquor.\n\nASSAFOETIDA. This article is used as an antispasmodic. The\ndose is from one to two drachms, administered in thin gruel.\n\nBALM, LEMON. See _Fever Drink_.\n\nBALM OF GILEAD BUDS. One ounce of the buds, after being infused\nin boiling water and strained, makes a good drink for chronic coughs.\n\nBALMONY. A good tonic and vermifuge.\n\nBALSAM, CANADA, is a diuretic, and may be given in slippery\nelm, in doses of one table-spoonful for diseases of the kidneys.\n\nBALSAM OF COPAIBA, or CAPIVI, is useful in all\ndiseases of the urinary organs, and, combined with powdered marshmallows\nand water, makes a good cough drink. Dose, half an ounce.\n\nBALEAM OF TOLU. Used for the same purpose as the preceding.\n\nBARLEY. Barley water, sweetened with honey, is a useful drink\nin fevers.\n\nBAYBERRY BARK. We have frequently prescribed this article in the\npreceding pages as an antiseptic and astringent for scouring and\ndysentery.\n\nBEARBERRY, (_uva ursi_.) This is a popular diuretic, and is\nuseful when combined with marshmallows. When the urine is thick and\ndeficient in quantity, or voided with difficulty, it may be given in the\nfollowing form:--\n\n  Powdered bearberry,        1 ounce.\n      \"    marshmallows,     2 ounces.\n  Indian meal,               2 pounds.\n\nMix. Dose, half a pound daily, in the cow's feed.\n\nBITTER ROOT, (_apocynum androsaemifolium_.) Given in doses of\nhalf an ounce of the powdered bark, it acts as an aperient, and is good\nwherever an aperient is indicated.\n\nBLACKBERRY ROOT, (_rubus trivialis_.) A valuable remedy for\nscours in sheep.\n\nBLACK ROOT, (_leptandra virginica_.) The extract is used as\nphysic, instead of aloes. (See _Physic for Cattle_.) A strong decoction\nof the fresh roots will generally act as a cathartic on all classes of\nanimals.\n\nBLOODROOT, (_sanguinaria canadensis_.) It is used in our\npractice as an escharotic. It acts on fungous excrescences, and is a\ngood substitute for nitrate of silver in the dispersion of all morbid\ngrowth. One ounce of the powder, infused in boiling vinegar, is a\nvaluable application for rot and mange.\n\nBLUE FLAG, (_iris versicolor_.) The powdered root is a good\nvermifuge.\n\nBONESET, (_eupatorium perfoliatum_.) This is a valuable\ndomestic remedy. Its properties are too well known to the farming\ncommunity to need any description.\n\nBORAX. This is a valuable remedy for eruptive diseases of the\ntongue and mouth. Powdered and dissolved in water, it forms an\nastringent, antiseptic wash. The usual form of prescription, in\nveterinary practice, is,--\n\n  Powdered borax,      half an ounce.\n  Honey,               2 ounces.\n\nMix.\n\nBUCKTHORN, (_rhamnus catharticus_.) A sirup made from this\nplant is a valuable aperient in cattle practice. The dose is from half\nan ounce to two ounces.\n\nBURDOCK, (_arctium lappa_.) The leaves, steeped in vinegar,\nmake a good application for sore throat and enlarged glands. The seeds\nare good to purify the blood, and may be given in the fodder.\n\nBUTTERNUT BARK, (_juglans cinerea_.) Extract of butternut makes\na good cathartic, in doses of half an ounce. It is much safer than any\nknown cathartic, and, given in doses of two drachms, in hot water,\ncombined with a small quantity of ginger, it forms a useful aperient and\nalterative. In a constipated habit, attended with loss of cud, it is\ninvaluable. During the American revolution, when medicines were scarce,\nthis article was brought into use by the physicians, and was esteemed by\nthem an excellent substitute for the ordinary cathartics.\n\nCALAMUS, (_acorus calamus_.) A valuable remedy for loss of cud.\n\nCAMOMILE. See _Anthemis_.\n\nCANELLA BARK is an aromatic stimulant, and forms a good\nstomachic.\n\nCAPSICUM. A pure stimulant. Useful in impaired digestion.\n\nCARAWAY SEED, (_carum carui_.) A pleasant carminative for\ncolic.\n\nCARDAMOM SEEDS. Used for the same purpose as the preceding.\n\nCASSIA BARK, (_laurus cinnamomum_.) Used as a diffusible\nstimulant in flatulency.\n\nCATECHU, (see ACACIA.)\n\nCATNIP, (_nepeta cataria_.) An antispasmodic in colic.\n\nCEDAR BUDS. An infusion of the buds makes a good vermifuge for\nsheep and pigs.\n\nCHARCOAL. This is a valuable remedy as an antiseptic for foul\nulcers, foot rot, &c.\n\nCLEAVERS, (_galium aparine_.) The expressed juice of the herb\nacts on the skin and kidneys, increasing their secretions. One\ntea-spoonful of the juice, given night and morning in a thin mucilage of\npoplar bark, is an excellent remedy for dropsy, and diseases of the\nurinary organs. An infusion of the herb, made by steeping one ounce of\nthe leaves and seeds in a quart of boiling water, may be substituted for\nthe expressed juice.\n\nCOHOSH, BLACK, (_macrotrys racemosa_.) Useful in dropsy.\n\nCOLTSFOOT, (_tussilago farfara_.) An excellent remedy for\ncough.\n\nCRANESBILL, (_geranium maculatum_.) Useful in scours,\ndysentery, and diarrhoea.\n\nDILL SEED, (_anethum graveolens_.) Its properties are the same\nas caraways.\n\nDOCK, YELLOW, (_rumex crispus_.) Good for diseases of the liver\nand of the skin.\n\nELECAMPANE, (_inula helenium_.) An excellent remedy for cough\nand asthma, and diseases of the skin.\n\nELDER FLOWERS, (_sambucus canadensis_.) Used as an aperient for\nsheep, in constipation.\n\nELM BARK, (_ulmus fulva_.) This makes a good mucilage. See\nPoultices.\n\nESSENCE OF PEPPERMINT. Used for flatulent colic. One ounce is\nthe usual dose for a cow. To be given in warm water.\n\nFENNEL SEED. Useful to expel wind.\n\nFERN, MALE, (_aspidium felix mas_.) Used as a remedy for worms.\n\nFLAXSEED. A good lubricant, in cold and catarrh, and in\ndiseases of the mucous surfaces. It makes a good poultice.\n\nFLOWER OF SULPHUR. This is used extensively, in veterinary\npractice, for diseases of the skin. It is a mild laxative.\n\nFUMIGATIONS. For foul barns and stables, take of\n\n  Common salt,         4 ounces.\n  Manganese,           1 ounce and a half.\n\nLet these be well mixed, and placed in a shallow earthen vessel; then\npour on the mixture, gradually, sulphuric acid, four ounces. The\ninhalation of the gas which arises from this mixture is highly\ninjurious; therefore, as soon as the acid is poured on, all persons\nshould leave the building, which should immediately be shut, and not\nopened again for several hours. Dr. White, V. S., says, \"This is the\nonly efficacious _fumigation_, it having been found that when glanderous\nor infectious matter is exposed to it a short time, it is rendered\nperfectly harmless.\"\n\nGALBANUM. This gum is used for similar purposes as gum ammoniac\nand assafoetida.\n\nGALLS. They contain a large amount of tannin, and are\npowerfully astringent. A strong decoction is useful to arrest\nhemorrhage.\n\nGARLIC. See _Allium_.\n\nGENTIAN. This is a good tonic, and is often employed to remove\nweakness of the stomach and indigestion.\n\nGINGER. A pure stimulant. Ginger tea is a useful remedy for\nremoving colic and flatulency, and is safer and better adapted to the\nanimal economy, where stimulants are indicated, than alcoholic\npreparations.\n\nGINSENG, (_panax quinquefolium_.) It possesses tonic and\nstimulant properties.\n\nGOLDEN SEAL, (_hydrastis canadensis_.) A good tonic, laxative,\nand alterative.\n\nGOLDTHREAD, (_coptis trifolia_.) A strong infusion of this herb\nmakes a valuable application for eruptions and ulcerations of the mouth.\nWe use it in the following form:--\n\n  Goldthread,            1 ounce.\n  Boiling water,         1 pint.\n\nSet the mixture aside to cool; then strain, and add a table-spoonful of\nhoney, and bathe the parts twice a day.\n\nGRAINS OF PARADISE. A warming, diffusible stimulant.\n\nHARDHACK, (_spiraea tomentosa_.) Its properties are astringent\nand tonic. We have used it in cases of \"scours\" with great success. It\nis better adapted to cattle practice in the form of extract, which is\nprepared by evaporating the leaves, stems, or roots. The dose is from\none scruple to a drachm for a cow, and from ten grains to one scruple\nand a half for a sheep, which may be given twice a day, in any bland\nliquid.\n\nHONEY, (_mel_.) Honey is laxative, stimulant, and nutritious.\nWith vinegar, squills, or garlic, it forms a good cough mixture.\nCombined with tonics, it forms a valuable gargle, and a detergent for\nold sores and foul ulcers.\n\nHOPS, (_humulus_.) An infusion of hops is highly recommended in\nderangement of the nervous system, and for allaying spasmodic twitchings\nof the extremities. One ounce of the article may be infused in a quart\nof boiling water, strained, and sweetened with honey, and given, in half\npint doses, every four hours. They are used as an external application,\nin the form of fomentation, for bruises, &c.\n\nHOREHOUND, (_marrubium_.) This is a valuable remedy for catarrh\nand chronic affections of the lungs. It is generally used, in the\nauthor's practice, in the following form: An infusion is made in the\nproportion of an ounce of the herb to a quart of boiling water. A small\nquantity of powdered marshmallows is then stirred in, to make it of the\nconsistence of thin gruel. The dose is half a pint, night and morning.\nFor sheep and pigs half the quantity will suffice.\n\nHORSEMINT, (_monarda punctata_.) Like other mints, it is\nantispasmodic and carminative. Useful in flatulent colic.\n\nHORSERADISH. The root scraped and fed to animals laboring under\nloss of cud, from chronic disease of the digestive organs, and general\ndebility, is generally attended with beneficial results. If beaten into\npaste with an equal quantity of powdered bloodroot, it makes a valuable\napplication for foul ulcers.\n\nHYSSOP, (_hyssopus officinalis_.) Hyssop tea, sweetened with\nhoney, is useful to promote perspiration in colds and catarrh.\n\nINDIAN HEMP, (_apocynum cannabinum_.) An infusion of this herb\nacts as an aperient, and promotes the secretions. It may be prepared by\ninfusing an ounce of the powdered or bruised root in a quart of boiling\nwater, which must be placed in a warm situation for a few hours: it\nshould then be strained, and given in half pint doses, at intervals of\nsix hours. A gill of this mixture will sometimes purge a sheep.\n\nINDIGO, WILD, (_baptisia tinctoria_.) We have made some\nexperiments with the inner portion of the bark of this plant, and find\nit to be very efficacious in the cure of eruptive diseases of the mouth\nand tongue, lampas, and inflamed gums. A strong decoction (one ounce of\nthe bark boiled for a few minutes in a pint of water) makes a good wash\nfor old sores. A small quantity of powdered slippery elm, stirred into\nthe decoction while hot, makes a good emollient application to sore\nteats and bruised udder.\n\nJUNIPER BERRIES, (_juniperus_.) These are used in dropsical\naffections, in conjunction with tonics; also in diseases of the urinary\norgans.\n\nKINO. This is a powerful astringent, and may be used in\ndiarrhoea, dysentery, and red water, after the inflammatory symptoms\nhave subsided. We occasionally use it in the following form for red\nwater and chronic dysentery:--\n\n  Powdered kino,        20 grains.\n  Thin flour gruel,     1 quart.\n\nTo be given at a dose, and repeated night and morning, as occasion\nrequires.\n\nLADY'S SLIPPER, (_cypripedium pubescens_.) This is a valuable\nnervine and antispasmodic, and has been used with great success, in my\npractice, for allaying nervous irritability. It is a good substitute for\nopium. It is, however, destitute of all the poisonous properties of the\nlatter. Dose for a cow, half a table-spoonful of the powder, night and\nmorning; to be given in bland fluid.\n\nLICORICE. Used principally to alleviate coughs. The following\nmakes an excellent cough remedy:--\n\n  Powdered licorice,     1 ounce.\n  Balsam of Tolu,        1 tea-spoonful.\n  Boiling water,         1 quart.\n\nTo be given at a dose.\n\nLILY ROOT, (_nymphaea odorata_.) Used principally for poultices.\n\nLIME WATER. This article is used in diarrhoea, and when the\ndischarge of urine is excessive. Being an antacid, it is very usefully\nemployed when cattle are hoven or blown. It is unsafe to administer\nalone, as it often deranges the digestive organs: it is therefore very\nproperly combined with tonics. The following will serve as an example:--\n\n  Lime water,                           2 ounces.\n  Infusion of snakehead, (balmony,)     2 quarts.\n\nDose, a quart, night and morning.\n\nLOBELIA, (herb,) (_lobelia inflata_.) This is an excellent\nantispasmodic. It is used in the form of poultice for locked-jaw, and as\na relaxant in rigidity of the muscular structure.\n\nMANDRAKE, (_podophyllum peltatum_.) Used as physic for cattle,\n(which see.)\n\nMARSHMALLOWS. See _Althea_\n\nMEADOW CABBAGE ROOT, (_ictodes foetida_.) This plant is used\nas an antispasmodic in asthma and chronic cough. Dose, a tea-spoonful of\nthe powder, night and morning; to be given in mucilage of slippery elm.\n\nMOTHERWORT, (_leonurus cardiaca_.) A tea of this herb is\nvaluable in protracted labor.\n\nMULLEIN, (_verbascum_.) The leaves steeped in vinegar make a\ngood application for sore throat.\n\nMYRRH. The only use we make of this article, in cattle\npractice, is to prepare a tincture for wounds, as follows:--\n\n  Powdered myrrh,     2 ounces.\n  Proof spirit,       1 pint.\n\nSet it aside in a close-covered vessel for two weeks, then strain\nthrough a fine sieve, and it is fit for use.\n\nOAK BARK, (_quercus alba_.) A decoction of oak bark is a good\nastringent, and may be given internally, and also applied externally in\nfalling of the womb or fundament.\n\nOINTMENTS. We have long since discontinued the use of\nointments, from a conviction that they do not agree with the flesh of\ncattle. Marshmallows, or tincture of myrrh, will heal a wound much\nquicker than any greasy preparation. We have, however, often applied\nfresh marshmallow ointment to chapped teats, and chafed udder, with\ndecided advantage. It is made as follows: Take of white wax, mutton\ntallow, and linseed oil, each a pound; marshmallow leaves, two ounces.\nFirst melt the wax and tallow, then add the oil, lastly a handful of\nmallows. Simmer over a slow fire until the leaves are crisp, then strain\nthrough a piece of flannel, and stir the mixture until cool.\n\nOLEUM LINI, (flaxseed oil.) This is a useful aperient and\nlaxative in cattle practice, and may be given in all cases of\nconstipation, provided, however, it is not accompanied with chronic\nindigestion: if such be the case, a diffusible stimulant, combined with\na bitter tonic, (golden seal,) aided by an injection, will probably do\nmore good, as they will arouse the digestive function. The above\naperient may then be ventured on with safety. The dose for a cow is one\npint.\n\nOLIVE OIL. This is a useful aperient for sheep. The dose is\nfrom half a gill to a gill.\n\nOPODELDOC. The different preparations of this article are used\nfor strains and bruises, after the inflammatory action has somewhat\nsubsided.\n\n_Liquid Opodeldoc._\n\n  Soft soap,           6 ounces.\n  New England rum,     1 pint and a half.\n  Vinegar,             half a pint.\n  Oil of lavender,     2 ounces.\n\nThe oil of lavender should first be dissolved in an equal quantity of\nalcohol, and then added to the mixture.\n\nPENNYROYAL, (_hedeoma_.) This plant, administered in warm\ninfusion, promotes perspiration, and is good in flatulent colic.\n\nPEPPERMINT, (_mentha piperita_.) An ounce of the herb infused\nin a quart of boiling water relieved spasmodic pains of the stomach and\nbowels, and is a good carminative, (to expel wind,) provided the\nalimentary canal is free from obstruction.\n\nPLANTAIN LEAVES, (_plantago major_.) This article is held in\nhigh repute for the cure of hydrophobia and bites from poisonous\nreptiles. The bruised leaves are applied to the parts; the powdered herb\nand roots to be given internally at discretion.\n\nPLEURISY ROOT, (_asclepias tuberosa_.) We have given this\narticle a fair trial in cattle practice, and find it to be invaluable in\nthe treatment of catarrh, bronchitis, pleurisy, pneumonia, and\nconsumption. The form in which we generally prescribe it is,--\n\n  Powdered pleurisy root,         half a table-spoonful.\n      \"    marshmallow roots,     1 ounce.\n\nBoiling water sufficient to make a thin mucilage. The addition of a\nsmall quantity of honey increases its diaphoretic properties.\n\nPOMEGRANATE, (_punica granatum_.) The rind of this article is a\npowerful astringent, and is occasionally used to expel worms. A strong\ndecoction makes a useful wash for falling of the womb, or fundament.\nGiven as an infusion, in the proportion of half an ounce of the rind to\na quart of water, it will arrest diarrhoea.\n\nPOPLAR, (_populus tremuloides_.) It possesses tonic, demulcent,\nand alterative properties. It is often employed, in our practice, as a\nlocal application, in the form of poultice. The infusion is a valuable\nremedy in general debility, and in cases of diseased urinary organs.\n\nPRINCE'S PINE, (_chimaphila_.) This plant is a valuable remedy\nin dropsy. It possesses diuretic and tonic properties. It does not\nproduce the same prostration that usually attends the administration of\ndiuretics, for its tonic property invigorates the kidneys, while, at the\nsame time, it increases the secretion of urine. The best way of\nadministering it is by decoction. It is made by boiling four ounces of\nthe fresh-bruised leaves in two quarts of water. After straining, a\ntable-spoonful of powdered marshmallows may be added, to be given in\npint doses, night and morning.\n\nPYROLIGNEOUS ACID. See _Acid_.\n\nRASPBERRY LEAVES, (_rubus strigosus_.) An infusion of this\nplant may be employed with great advantage in cases of diarrhoea.\n\nROMAN WORMWOOD, (_ambrosia artemisifolia_.) This plant is a\nvery bitter tonic, and vermifuge. An infusion may be advantageously\ngiven in cases of general debility and loss of cud. A strong decoction\nmay be given to sheep and pigs that are infested with worms. If given\nearly in the morning, and before the animals are fed, it will generally\nhave the desired effect.\n\nROSE, RED, (_rosa gallica_.) We have occasionally used the\ninfusion, and find it of great value as a wash for chronic ophthalmia.\nThe infusion is made by pouring a pint of boiling water on a quarter of\nan ounce of the flowers. It is then strained through fine linen, when it\nis fit for use.\n\nSASSAFRAS, (_laurus sassafras_.) The bark of sassafras root is\nstimulant, and possesses alterative properties. We have used it\nextensively, in connection with sulphur, for eruptive diseases, and for\nmeasles in swine, in the following proportions:--\n\n  Powdered sassafras,     1 ounce.\n      \"    sulphur,       half a table-spoonful.\n\nMix, and divide into four parts, one of which may be given, night and\nmorning, in a hot mash.\n\nThe pith of sassafras makes a valuable soothing and mucilaginous wash\nfor inflamed eyes.\n\nSENNA A safe and efficient aperient for cattle may be made by\ninfusing an ounce of senna in a quart of boiling water. When cool,\nstrain, then add, manna one ounce, powdered golden seal one\ntea-spoonful. The whole to be given at a dose.\n\nSKULLCAP, (_scutellaria lateriflora_.) This is an excellent\nnervine and antispasmodic. It is admirably adapted to the treatment of\nlocked-jaw, and derangement of the nervous system. An ounce of the\nleaves may be infused in two quarts of boiling water. After straining, a\nlittle honey may be added, and then administered, in pint doses, every\nfour hours.\n\nSNAKEROOT, VIRGINIA, (_aristolochia serpentaria_.) This\narticle, given by infusion in the proportion of half an ounce of the\nroot to a pint of water, acts as a stimulant and alterative. It is\nadmirably adapted to the treatment of chronic indigestion.\n\nSOAP. This article acts on all classes of animals, as a\nlaxative and antacid. It is useful in obstinate constipation of the\nbowels, in diseases of the liver, and for softening hardened excrement\nin the rectum. By combining castile soap with butternut, blackroot,\ngolden seal, or balmony, a good aperient is produced, which will\ngenerally operate on the bowels in a few hours.\n\nSQUILL, (_scilla maritima_.) A tea-spoonful of the dried root,\ngiven in a thin mucilage of marshmallows, is an excellent remedy for\ncough, depending on an irritability of the lungs and mucous surfaces.\n\nSULPHUR. This is one of the most valuable articles in the\nveterinary _materia medica_. It possesses laxative, diaphoretic and\nalterative properties, and is extensively employed, both internally and\nexternally, for diseases of the skin. The dose for a cow is a\ntea-spoonful daily. Its alterative effect may be increased by combining\nit with sassafras, (which see.)\n\nSUNFLOWER, WILD, (_helianthus divaricatus_.) The seeds of this\nplant, when bruised and given it any bland fluid, act as a diuretic and\nantispasmodic. Half a table-spoonful of the seeds may be given at a\ndose, and repeated as occasion requires.\n\nTOLU, BALSAM OF. This balsam is procured by making incisions\ninto the trunk of a tree which flourishes in Tolu and Peru. It has a\npeculiar tendency to the mucous surfaces, and therefore is very properly\nprescribed for epizooetic diseases of catarrhal nature. The dose is half\na table-spoonful every night, to be administered in a mucilage of\nmarshmallows. One half the quantity is sufficient for a sheep.\n\nVINEGAR. See _Acetum_.\n\nWITCH HAZEL BARK, (_hamamelis virginica_.) A decoction of this\nbark is a valuable application for falling of the fundament, or womb.\nBeing a good astringent, an infusion of the leaves is good for scouring\nin sheep.\n\nWORMSEED, (_chenopodium anthelminticum_.) A tea-spoonful of the\npowdered seeds, given in a tea of snakeroot, is a good vermifuge: it\nwill, however, require repeated doses, and they should be given at least\nan hour before the morning meal.\n\n\n\n\nGENERAL REMARKS ON MEDICINES.\n\n\nHere, reader, is our _materia medica_; wherein you will find a number of\nharmless, yet efficient agents, that will, in the treatment of disease,\nfulfil any and every indication to your entire satisfaction. They act\nefficiently in the restoration of the diseased system to a healthy\nstate, without producing the slightest injury to the animal economy. The\nAlmighty has furnished us, if we did but know it, a healing balm for\nevery malady to which man and the lower animals are subject. Yet how\nmany of these precious gifts are disregarded for the more popular ones\nof the chemist! Dr. Brown, professor of botany in the Ohio College,\nsays, \"Of the twenty or more thousand species of plants recognized and\ndescribed by botanists, probably not more than one thousand have ever\nbeen used in the art of healing; and not more than one fourth of that\nnumber even have a place in our _materia medica_ at present. The\nglorious results, however, attending the researches of those who have\npreceded us, should inspire us with that confidence and spirit of\ninvestigation which will ultimately result in the selection,\npreparation, and systematic arrangement, of a full, convenient, and\nefficient _materia medica_.\" Unfortunately, the medical fraternity, as\nwell as the farmers, have been accustomed to judge of the power of the\nremedy by its effects, and not in proportion to its ultimate good. Thus,\nif a pound of salts be given to a cow, and they produce liquid\nstools,--in short, \"operate well,\"--they are styled a good medicine,\nalthough they leave the mucous surface of the alimentary canal in a\nweak, debilitated state, and otherwise impair the health; yet this is a\nsecondary consideration. For, if the symptoms of the present malady, for\nwhich the salts were given, shall disappear, nothing is thought of the\nafter consequences. The cow may be constipated for several succeeding\ndays, and finally refuse her food; but who suspects that the salts were\nthe cause of it? Who believes that the abstraction of ninety ounces of\nblood cut short the life of our beloved Washington? We do, and so do\nothers. We are told, in reference to the treatment of a given case, that\n\"the patient will grow worse before he can get better.\" What makes him\nworse? The medicine, surely, and nothing else. Now, if ever symptoms are\naltered, they should be for the better; and if the medicines recommended\nin this work (provided, however, they are given with ordinary prudence)\never make an animal worse, then we beg of the reader to avoid them as he\nwould a pest-house. This is not all. If any article in this _materia\nmedica_, when given, in the manner we recommend, to an animal in perfect\nhealth, shall operate so as to derange such animal's health,--in short,\nact pathologically,--then it does not deserve a place here, and should\nnot be depended on. But such will not be the result. We recommend\nfarmers to select and preserve a few of these herbs for family use; for\nthey are efficient in the cure of many diseases. And as the services of\na physician are not always to be had in small country towns, a little\nexperience in the use and application of simple articles to various\ndiseases seems to be absolutely necessary. It was by the aid of a few of\nthese and similar simple remedies, that we were enabled to preserve the\nhealth of the passengers of that ill-fated ship, the Anglo-Saxon. The\nfollowing testimony has never, until the present time, been made public,\nand we would not now make use of it, were it not that we wish to show\nthat there are men, and women too, that can appreciate our labors:--\n\n     \"The undersigned, passengers in the Anglo-Saxon from Boston,\n     feeling it a duty they owe to Dr. G. H. Dadd, surgeon of the ship,\n     would here bear testimony to the valuable medical services and\n     advice rendered by him to us, whilst on shipboard; believing his\n     attendance has been conducive of the greatest benefit; at times\n     almost indispensable, not only during the short passage, but also\n     through the trying period subsequent to the wreck through all of\n     which, the coolness and devotion to the best interests of his\n     employers and of the passengers, exhibited by him, deserve at our\n     hands the highest terms of commendation.\n\n        ROBERT EARLE,\n        S. C. AMES,\n        BENJAMIN CHAMPNEY,\n        LEWIS JONES,\n        HAMILTON G. WILD,\n        W. A. BARNES,\n        GIDEON D. SCULL,\n        W. ALLAN GAY,\n        ISAAC JENKINS,\n        PRESCOTT BIGELOW,\n        A. M. EARLE,\n        ROSALIE PELBY,\n        OPHELIA ANDERSON,\n        HELEN C. DOVE,\n        ELEANOR TERESA MCHUGH,\n        JOHN HILLS,\n        FRANCES BLENKAM,\n        HARRIET PHILLIPS,\n        LOUISA A. BIGELOW,\n\n     EASTPORT, May 9, 1847.\"\n\nNotwithstanding this disaster, Enoch Train, Esq., of Boston, with a\nliberality which does him credit, appointed us surgeon of the ship Mary\nAnn, commanded by Captain Albert Brown; thus giving us a second\nopportunity of proving what we had asserted, viz., _that the emigrants\nmight be brought to the United States in better condition, and with less\ndeaths, than had heretofore been done_. It must be remembered that about\nthis time the typhus, or ship fever, was making sad havoc amongst all\nclasses of men, and many talented professional men fell victims to the\ndire malady. We left Liverpool at a sickly season, having on board two\nhundred persons, and were fortunate enough to land them in this city,\nall in good health. Several ships which sailed at the same time, bound\nalso to different ports in the United States, lost, on the passage, from\nten to twenty persons, although each ship was furnished with a medical\nattendant. Here, then, is a proof that our agents cure while others\nfail.\n\n\n\n\nPROPERTIES OF PLANTS.\n\n\nProfessor Curtis tells us that \"herbs, during their growth, preserve\ntheir medicinal properties, commencing at the root, and continuing\nupward, through the stem and leaves, to the flowers and seeds, until\nfully grown. When the root begins to die, the properties ascend from it\ntowards the seed, where, at last, they are the strongest. Even the\nvirtues of the leaves, after they get their full growth, often go into\nthe seed, which will not be so well developed if the leaves are plucked\noff early; as corn fills and ripens best when the leaves are left on the\nstalks till they die. In the annual and biennial plants, the root is\nworthless after the seed is ripe, and the stem also is of very little\nvalue; what virtue there is residing in the bark and leaves also lose\ntheir properties as fast as they lose their freshness. All leaves and\nstems that have lost their color, or become shrivelled, while the roots\nare in the earth, have lost much of their medicinal power, and should be\nrejected from medicine.\" Seeds and fruit should be gathered when ripe or\nfully matured.\n\nFlowers should be gathered just at the time they come into bloom.\n\nLeaves should be gathered when they have arrived at their full growth,\nare green, and full of the juices of the plant. Barks should be gathered\nas early in the spring as they will peel.\n\nRoots should be gathered in the fall, after they have perfectly matured,\nor early in the spring, before they commence germinating and growing.\n\n\n\n\nPOTATO.\n\n\nBoiled potatoes, mixed up with steamed cornstalks, shorts, &c., make an\nexcellent compound for fattening cattle; yet, at the present time, they\nare too expensive for general use. We hope, however, that ere long our\nfarmers will take hold of this subject in good earnest,--we allude to\nthe causes of potato rot,--and restore this valuable article of food to\nits original worth. A few remarks on this subject seem to be called for.\n\n\n_Remarks on the Potato Rot._\n\nWhere are the fine, mealy, substantial \"apples of the earth\" gone?--and\nEcho answers, \"Where?\" They are not to be found at the present day. The\nfarmers have suffered great losses, in some instances by a partial, and\nin others by a total, failure of their crops. Numberless experiments\nhave been tried to prevent this great national calamity, yet they have\nall proved abortive, for the simple reason that we have been only\ntreating the symptoms, while the disease has taken a firmer hold, and\nhurried our subjects to a premature decay. Different theories have been\nsuggested with a view of explaining the causes of the potato rot, none\nof which are satisfactory. We have the \"fungous theory,\" \"insect\ntheory,\" \"moisture theory,\" \"theory of _degeneration_,\" and \"the\nchemical theory of defective elements.\" In relation to the \"fungous\ntheory\" we observe that fungi inhabit decaying organic bodies. They are\nconsidered to be a common pest to all kinds of plants, like parasites,\nliving at the expense of those plants. We do not expect to find fungi in\ngood healthy vegetables, at least while they possess a high grade of\nvital action. It is only when morbid deposits and chemical agencies\novercome the integrity or vital affinity of the vegetable that fungous\ngrowth commences.\n\nIn the fungous development, the living parts of the vegetable are not\nalways destroyed; yet these fungi obstruct vital action by their\ndeposits or accumulations; hence the small vessels that lead from centre\nto surface are partly paralyzed, and the power peculiar to all\nvegetables of throwing off useless or excrementitious matter is\nintercepted. This is not all. The process of imperceptible elimination,\nwhich might restore the balance of power in any thing like a vigorous\nplant, is thus impaired.\n\nNow, it is evident that the fungi are not the cause of the potato rot;\nthey are only the mere effects, the symptoms: preceding these were other\nmanifestations of disorder, and these manifestations, in their different\ngrades, might with equal propriety be charged as causes of the potato\nrot. The deterioration of the potato has been going on in a gradual\nmanner for a long time. A mild form of disease has existed for a number\nof years, making such imperceptible change that it has escaped the\nobservation of many until late years, when the article became so\nunpalatable that our attention has been called to it in good earnest;\nand by the aid of the microscope we have discovered the fungi. Has this\ndiscovery benefited the agriculturist? Not a particle.\n\nThe theory of degeneration, without doubt, will assist us to explain the\nwhy and wherefore of the potato rot. But this is not all; the community\nwant to know the cause of this degeneracy. We have spent some time in\nthe investigation of this subject, and now give the public, in a\ncondensed form, our opinion of this matter. We may err, but our progress\nis towards the full discovery of the _direct cause_, and the ways and\nmeans best adapted to prevent this sad calamity. The potato came into\nexistence at a certain period in the history of the world. After its\ndiscovery, it was taken from the mother soil, the land of its nativity,\nplanted in different parts of the world, and grew to apparent\nperfection. Our opinion is, that the transplanting was one of the causes\nof this degeneracy. It is generally known that indigenous plants do not\nthrive so well on foreign soil as in their native; for example, the\nplants of the sunny south cannot be made to flourish here in the same\ndegree of perfection as at the south; they require the genial warmth of\nthe sun's rays, which our northern climates lack. The soil, too, mast be\nadapted to each particular plant. It is true we do cultivate them by\ningenuity and chemical agency; yet they seldom equal the original. Need\nwe ask the farmer if he can, from the soil of New England, produce a St.\nMichael orange equal to one grown on its native soil? or if a squash\nwill grow in the deserts of Arabia? All vegetables, as well as animals,\npossess a certain amount of vital power, which enables them to resist,\nto a certain degree, all encroachments on their healthy operations. The\npotato, having been deprived, in some measure, of its essential element,\nlost its reciprocal equilibrium, and has ever since been a prey to\nwhatever destructive agents may be present, whether they exist in the\nsoil or atmosphere. Yet we conceive that its total destruction is\ndependent on another cause, which has been entirely overlooked; for, in\nspite of the gradual deterioration alluded to, the potato will, for a\nnumber of years, continue to keep up a low form of vitality, and result\nin something like a potato. In order to comprehend the subject, let us,\nfor a moment, consider the conditions necessary for the germination and\nperfection of vegetable bodies. We shall then be able to decide as to\nwhether or not we have complied with such conditions. The first\ncondition is, we must have _a perfect germ_; secondly, _a ripe seed_;\nand lastly, _nutrimental agents in the sail, composed of carbon,\nhydrogen, and oxygen_.\n\nThe potato requires but a small quantity of moisture to develop the\ngerminating principle; for we have every day evidences of its ability to\nsend forth its fibres, even in the open air. Now, the premature\ndevelopment of these fibrous radicles, or roots, debilitates the tuber;\nin short, we have a sick potato. Is the potato, under such\ncircumstances, a perfect germ? No. If you examine the potato, with its\nroots and stem, you will find the cutis, or skin, and mucous membrane.\nThis external skin, _including that of plant, stalk, leaf, and ball_, is\nto the potato what the skin and lungs are to animals; they, each of\nthem, absorb atmospheric food, and throw off excrementitious matter; the\nroots and fibres are to the vegetable what the alimentary canal is to\nthe animal. A large portion of the food of vegetables is found in the\nsoil, and enters the vegetable system, through its capillary\ncirculation, by the process of imperceptible elimination and absorption.\nNow, you must bear in mind that the fibres, stem, and leaves are\ndelicate and tender organs; they are studded with millions of little\npores, covered with a membrane of delicate texture, easily lacerated.\nWhen these delicate organs are rudely torn off or lacerated, the potato\nimmediately gives evidence of the encroachments of disease; it shrinks,\nwithers, and, although the soil abounds in all that is necessary for its\ngrowth and future development, it is not in a fit state to carry on the\nchemico-vital process. We often take the potato from the soil with a\nview of preserving it for seed, without any definite knowledge of the\nexact time of its maturity; as the season arrives for again replanting,\nthe fibres are torn off, and the potato itself is often cut up into two\nor three pieces; sometimes, however, the smaller potatoes are used for\nseed. Both practices are open to strong objection. Oftentimes the cut\nsurfaces of the potato are exposed to atmospheric air; evaporation\ncommences, they lose their firm texture, and are more fit for swine than\nfor planting.\n\nThe cause of the total destruction may exist in a loss of polarity! We\nknow that all organic and inorganic bodies are subject to the laws of\nelectricity--each has its polarity. Men who are engaged in mining can\ntestify that the stratification of the earth is alternately negative and\npositive. The hemispheres of the earth are also governed by the same\nlaw; for, if you take a magnetic needle and toss it up in this\nhemisphere, which is negative, the positive end will come to the ground\nfirst; but if you pass the magnetic equator, which crosses the common\nequator in 23 deg. 28', and then toss the needle up, its negative end will\nfall downwards. Hence we infer that the potato has a polarity, just as\nman has; and this is the reason of their definite character. Take a\nbean, and destroy its polarity by cutting it into several pieces, as you\ndo the potato, and all the men on earth cannot make it germinate and\ngrow to perfection. It will die just as a man will, if you destroy the\npolarity of his brain by wounding it.\n\nTake an egg, and destroy its polarity by making a small puncture through\nit, and you can never get a chicken from it. A man or an animal will die\nof locked-jaw, caused by a splinter entering the living organism; and\nwhy? Because their electrical equilibrium, or their polarity is\ndestroyed. Some of our readers may desire to know how we can prove that\nelectricity plays a part in the germination and growth of animals and\nvegetables. In verification of it, we will give a few examples. A dish\nof salad may, by the aid of electricity, be raised in an hour. Hens'\neggs can be hatched by a similar process in a few hours, which would\nrequire many days by animal heat. By the aid of electricity, water,\nwhich consists of oxygen and hydrogen, may be decomposed, and its\nelements set free. The poles of a galvanic battery may be applied to a\ndead body, and that body made to imitate the functions of life.\n\nAnd lastly, it is through the medium of electrical attraction which\nbodies have for each other, that all the chemical compositions and\ndecompositions depend. Bodies must be in opposite states of electricity\nin order to produce a result. Now, if the polarity of the potato is\ndestroyed in the manner we have just alluded to, or should it be\ndestroyed by coming in contact with the blade of a knife, _the latter\nconducting off the electrical current_, or by any other means, it must\ndeteriorate. We are told that \"the potato has several germinating\npoints, and that a part will grow just as well as the whole.\" Such\nreasoning will not stand the test of common experience.\n\nFor example: the Almighty has endowed man with various faculties, and\nthe perfection of his organism depends on these faculties, as a whole.\nNow, he may lose a leg, and yet be capable of performing the ordinary\nduties of life; but this does not prove that he might not perform them\nmuch better with both legs. So in reference to the potato. The fact of\nits ability to reproduce its kind from a small portion of the whole--a\nmere bud--should not satisfy us that a perfect germ is unnecessary. Then\nthe question arises, How shall we restore the original identity of this\nvaluable article of food?\n\nWe have, in the early part of this work, recommended the farmers to\nstudy the laws of vegetable physiology. This will furnish them with the\nright kind of information. We would, however, suggest to those who are\ndesirous of making experiments, to comply with the conditions already\nalluded to, viz., plant a perfect germ, by which means the potato may be\nimproved. Yet, in order to restore its identity, we must commence by\ngerminating from the seed, and plant that on soil abounding in the\nconstituents necessary for its development. Elevated land abounding in\nsmall stones, and hill sides facing the south, are the best situations.\nPotatoes should never be cultivated on the same spot for two successive\nyears.\n\nIn relation to the insect theory, we would observe, that it throws no\nlight on the cause of the potato rot; for, in its gradual decay, that\nvegetable undergoes various changes; the particles of which it is\ncomposed assume new forms, and enter into new combinations; its\nelementary substances are separated, giving birth to new compounds, some\nof which result in an insect. We all know that animal and vegetable\nbodies may remain in a state of putrefaction in water, and be dissolved\nin the dust; yet some of their original atoms appear in a new system.\nHence the insect theory has no more to do with the cause of the potato\nrot than the fungus.\n\n\n\n\nTREATMENT OF DISEASE IN DOGS.\n\nPRELIMINARY REMARKS.\n\n\nA good watch dog is of inestimable value to the farmer; and as very\nlittle is at present understood of the nature and treatment of their\nmaladies, we have thought that a few general directions would be\nacceptable, not only to the farmer, but to every man who loves a dog. We\nhave paid considerable attention to the treatment of disease in this\nclass of animals, and have generally found that must of their maladies\nwill yield very readily to our sanative agents. Most of the remedies\nrecommended by _allopathic_ writers for dogs, like those recommended for\nhorses and cattle, would at any time destroy the animal; consequently,\nif it ever recovers, it does so in spite of the violence done to the\nconstitution. We hope to rescue the dog, as well as other classes of\ndomestic animals, from a cruel system of medication; for this we labor,\nand to this work our life is devoted. We ask the reader to take into\nconsideration the destructive nature of the articles used on these\nfaithful animals. Some of them are the most destructive poisons that can\nbe found in the whole world. For example, several authors recommend, in\nthe treatment of disease in the canine race, the following:--\n\n_Tartar emetic_, a very few grains of which will kill a man--yet\nrecommended for dogs.\n\n_Calomel_, a very fashionable remedy, used for producing ulcerated gums\nand for rotting the teeth of thousands of the human family, as the\ndentists can testify. Not fit for a dog, yet prescribed by most dog\nfanciers.\n\n_Lunar caustic_, recommended by Mr. Lawson for fits; to be given\ninternally with cobwebs!! Our opinion is, that it would be likely to\ngive any four-footed creature \"_fits_\" that took it.\n\nCowhage, corrosive sublimate, tin-filings, sugar of lead, white\nprecipitate, oil of turpentine, opium nitre--these, together with aloes,\njalap, tobacco, hellebore, and a very small proportion of sanative\nagents, make up the list. In view of the great destruction that is\nlikely to attend the administration of these and kindred articles, we\nhave substituted others, which may be given with safety. Why should the\npoor dog be compelled to swallow down such powerful and destructive\nagents? He is entitled to better treatment, and we flatter ourselves\nthat wherever these pages shall be read, he will receive it. In\nreference to the value of dogs, Mr. Lawson says, \"Independent of his\nbeauty, vivacity, strength, and swiftness, he has the interior qualities\nthat must attract the attention and esteem of mankind. Intelligent,\nhumble, and sincere, the sole happiness of his life seems to be to\nexecute his master's commands. Obedient to his owner, and kind to all\nhis friends, to the rest he is indifferent. He knows a stranger by his\nclothes, his voice, or his gestures, and generally forbids his approach\nwith marks of indignation. At night, when the guard of the house is\ncommitted to his care, he seems proud of the charge; he continues a\nwatchful sentinel, goes his rounds, scents strangers at a distance, and\nby barking gives them notice that he is on duty; if they attempt to\nbreak in, he becomes fiercer, threatens, flies at them, and either\nconquers alone, or alarms those who have more interest in coming to his\nassistance. The flock and herd are even more obedient to the dog than to\nthe shepherd: he conducts them, guards them, and keeps them from\ncapriciously seeking danger; and their enemies he considers as his\nown.\"\n\n\n\n\nDISTEMPER.\n\n\n_Symptoms._--If the animal is a watch dog, (such are usually confined in\nthe daytime,) the person who is in the daily habit of feeding him will\nfirst observe a loss of appetite; the animal will appear dull and lazy;\nshortly after, there is a watery discharge from the eyes and nose,\nresembling that which accompanies catarrh. As the disease advances,\ngeneral debility supervenes, accompanied with a weakness of the hind\nextremities. The secretions are morbid; for example, some are\nconstipated, and pass high- urine; others are suddenly attacked\nwith diarrhoea, scanty urine, and vomiting. Fits are not uncommon\nduring the progress of the disease.\n\n_Treatment._--If the animal is supposed to have eaten any improper food,\nwe commence the treatment by giving an emetic.\n\n_Emetic for Dogs._\n\n  Powdered lobelia, (herb,)      1 tea-spoonful.\n  Warm water,                    1 wine-glass.\n\nMix, and administer at a dose.\n\n(A table-spoonful of common salt and water will generally vomit a dog.)\n\nIf this dose does not provoke emesis, it should not be repeated, for it\nmay act as a relaxant, and carry the morbid accumulations off by the\nalimentary canal. If the bowels are constipated, use injections of\nsoap-suds. If the symptoms are complicated, the following medicine must\nbe prepared:--\n\n  Powdered mandrake,          1 table-spoonful.\n     \"     sulphur,           1 tea-spoonful.\n     \"     charcoal,          2 tea-spoonfuls.\n     \"     marshmallows,      1 table-spoonful.\n\nMix. Divide the mass into six parts, and administer one in honey, night\nand morning, for the first day; after which, a single powder, daily,\nwill suffice. The diet to consist of mush, together with a drink of thin\narrowroot. If, however, the animal be in a state of plethora, very\nlittle food should be given him.\n\nIf the strength fails, support it with beef tea. Should a diarrhoea\nattend the malady, give an occasional drink of hardhack tea.\n\n\n\n\nFITS.\n\n\nDogs are subject to epileptic fits, which are often attended with\nconvulsions. They attack dogs of all ages, and under every variety of\nmanagement. Dogs that are apparently healthy are often suddenly\nattacked. The nervous system of the dog is very susceptible to external\nagents; hence whatever raises any strong passion in them often produces\nfits. Pointers and setters have often been known to suffer an attack\nduring the excitement of the chase. Fear will also produce fits; and\nbitches, while suckling, if burdened with a number of pups, and not\nhaving a sufficiency of nutriment to support the lacteal secretion,\noften die in convulsive fits. Young puppies, while teething, are subject\nto fits: simply scarifying their gums will generally give temporary\nrelief. Lastly, fits may be hereditary, or they may be caused by\nderangement of the stomach. In all cases of fits, it is very necessary,\nin order to treat them with success, that we endeavor, as far as\npossible, to ascertain the causes, and remove them as far as lies in our\npower: this accomplished, the cure is much easier.\n\n_Treatment._--Whenever the attack is sudden and violent, and the animal\nis in good flesh, plunge him into a tub of warm water, and give an\ninjection of the same, to which a tea-spoonful of salt may be added. It\nis very difficult, in fact improper, to give medicine during the fit;\nbut as soon as it is over, give\n\n  Manna,            1 tea-spoonful.\n  Common salt,      half a tea-spoonful.\n\nAdd a small quantity of water, and give it at a dose.\n\n_Another._\n\nMake an infusion of mullein leaves, and give to the amount of a\nwine-glass every four hours. With a view of preventing a recurrence of\nfits, keep the animal on a vegetable diet. If the bowels are\nconstipated, give thirty grains of extract of butternut, or, if that\ncannot be readily procured, substitute an infusion of senna and manna,\nto which a few caraways may be added.\n\nIf the nervous system is deranged, which may be known by the\nirritability attending it, then give a tea-spoonful of the powdered\nnervine, (lady's slipper.) The diet must consist of boiled articles, and\nthe animal must be allowed to take exercise.\n\n\n\n\nWORMS.\n\n\nWorms may proceed from various causes; but they are seldom found in\nhealthy dogs. One of the principal causes is debility in the digestive\norgans.\n\n_Indications of Cure._--To tone up the stomach and other organs,--by\nwhich means the food is prevented from running into fermentation,--and\nadminister vermifuges. The following are good examples:--\n\n  Oil of wormseed,              1 tea-spoonful.\n  Powdered assafoetida,        30 grains.\n\nTo be given every morning, fasting. Two doses will generally suffice.\n\n_Another._\n\n  Powdered mandrake,                half a table-spoonful.\n     \"     Virginia snakeroot,      1 tea-spoonful.\n\nDivide into four doses, and give one every night, in honey.\n\n_Another._\n\nMake an infusion of the sweet fern, (_comptonea asplenifolia_,) and give\nan occasional drink, followed by an injection of the same.\n\n_Another._\n\n  Powdered golden seal,      half a table-spoonful.\n  Common brown soap,         1 ounce.\n\nRub them well together in a mortar, and form the mass into pills about\nthe size of a hazel-nut, and give one every night.\n\n\n\n\nMANGE.\n\n\nThis disease is too well known to need any description. The following\nare deemed the best cures:--\n\n_External Application for Mange._\n\n  Powdered charcoal,     half a table-spoonful.\n     \"     sulphur,      1 ounce.\n  Soft soap sufficient to form an ointment.\n\nTo be applied externally for three successive days; at the end of which\ntime, the animal is to be washed with castile soap and warm water, and\nafterwards wiped dry.\n\nThe internal remedies consist of equal parts of sulphur and cream of\ntartar, half a tea-spoonful of which may be given daily, in honey.\n\nWhen the disease becomes obstinate, and large, scabby eruptions appear\non various parts of the body, take\n\n  Pyroligneous acid,      2 ounces.\n  Water,                  1 pint.\n\nWash the parts daily, and keep the animal on a light diet.\n\n\n\n\nINTERNAL ABSCESS OF THE EAR.\n\n\nIn this complaint, the affected side is generally turned downwards, and\nthe dog is continually shaking his head.\n\n_Treatment._--In the early stages, foment the part twice a day with an\ninfusion of marshmallows. As soon as the abscess breaks, wash with an\ninfusion of raspberry leaves, and if a watery discharge continues, wash\nwith an infusion of white oak bark.\n\n\n\n\nULCERATION OF THE EAR.\n\n\nExternal ulcerations should be washed twice a day with\n\n  Pyroligneous acid,      2 ounces.\n  Water,                  8 ounces.\n\nMix.\n\nAs soon as the ulcerations assume a healthy appearance, touch them with\nTurlington's balsam or tincture of gum catechu.\n\n\n\n\nINFLAMMATION OF THE BOWELS.\n\n\nWhenever inflammation of the bowels makes its appearance, it is a sure\nsign that there is a loss of equilibrium in the circulation; and this\ndisturbance may arise from a collapse of the external surface, or from\nirritation produced by hardened excrement on the mucous membrane of the\nintestines. An attack is recognized by acute pain in the abdominal\nregion. The dog gives signs of suffering when moved, and the bowels are\ngenerally constipated.\n\n_Treatment._--Endeavor to equalize the circulation by putting the animal\ninto a warm bath, where he should remain about five minutes. When taken\nout, the surface must be rubbed dry. Then give the following\ninjection:--\n\n  Linseed oil,      4 ounces.\n  Warm water,       1 gill.\n\nMix.\n\nTo allay the irritation of the bowels, give the following:--\n\n  Powdered pleurisy root,         1 tea-spoonful.\n     \"     marshmallow root,      1 table-spoonful.\n\nMix, and divide into three parts; one to be given every four hours.\n\nShould vomiting be a predominant symptom, a small quantity of saleratus,\ndissolved in spearmint tea, may be given.\n\nShould not this treatment give relief, make a fomentation of hops, and\napply it to the belly; and give half an ounce of manna. The only\narticles of food and drink should consist of barley gruel and mush. If,\nhowever, the dog betrays great heat, thirst, panting, and restlessness,\na small quantity of cream of tartar may be added to the barley gruel.\nThe bath and clysters may be repeated, if necessary.\n\n\n\n\nINFLAMMATION OF THE BLADDER.\n\n\nThis requires the same treatment as the preceding malady.\n\n\n\n\nASTHMA.\n\n\nDogs that are shut up in damp cellars, and deprived of pure air and\nexercise, are frequently attacked with asthma. Old dogs are more liable\nto asthma than young ones.\n\n_Treatment._--Endeavor to ascertain the cause, and remove it. Let the\nanimal take exercise in the open air. The diet to consist of cooked\nvegetables; a small quantity of boiled meat may be allowed; raw meat\nshould not be given.\n\n_Compound for Asthma._\n\n  Powdered bloodroot,         }\n     \"     lobelia,           } of each, 1 tea-spoonful.\n     \"     marshmallows,      }\n     \"     licorice,          }\n\nMix. Divide into twelve parts, and give one night and morning. If they\nproduce retching, reduce the quantity of lobelia. The object is not to\nvomit, but to induce a state of nausea or relaxation.\n\n\n\n\nPILES.\n\n\nPiles are generally brought on by confinement, over-feeding, &c., and\nshow themselves by a red, sore, and protruded rectum. Dogs subject to\nconstipation are most likely to be attacked.\n\n_Treatment._--Give the animal half a tea-spoonful of sulphur for two or\nthree mornings, and wash the parts with an infusion of white oak bark.\nIf they are very painful, wash two or three times a day with an infusion\nof hops, and keep the animal on a light diet.\n\n\n\n\nDROPSY.\n\n\nDropsy is generally preceded by loss of appetite, cough, diminution of\nnatural discharge of urine, and costiveness. The abdomen shortly\nafterwards begins to enlarge.\n\n_Treatment._--It is sometimes necessary to evacuate the fluid by\npuncturing the abdomen; but this will seldom avail much unless the\ngeneral health is improved, and the suppressed secretions restored. The\nfollowing is the best remedy we know of:--\n\n  Powdered flagroot,       } of each a quarter of\n      \"    male fern,      }      an ounce.\n  Scraped horseradish,            a tea-spoonful.\n\nMix. Divide into eight parts, and give one night and morning. Good\nnutritious diet must be allowed.\n\n\n\n\nSORE THROAT.\n\n\nA strong decoction of mullein leaves applied to a sore throat will\nseldom fail in curing it.\n\n\n\n\nSORE EARS.\n\n\nA dog's ears may become sore and scabby from being torn, or otherwise\ninjured. In such cases, they should be anointed with marshmallow\nointment.\n\n\n\n\nSORE FEET.\n\n\nIf the feet become sore from any disease between the claws, apply a\npoultice composed of equal parts of marshmallows and charcoal; after\nwhich the following wash will complete the cure:--\n\n  Pyroligneous acid,      1 ounce.\n  Water,                  6 ounces.\n\nMix, and wash with a sponge twice a day.\n\n\n\n\nWOUNDS.\n\n\nTurlington's Balsam is the best application for wounds. Should a dog be\nbitten by one that is mad, give him a tea-spoonful of lobelia in water,\nand bind some of the same article on the wound.\n\n\n\n\nSPRAINS.\n\n\nFor sprains of any part of the muscular structure, use one of the\nfollowing prescriptions:--\n\n  Oil of wormwood,          1 ounce.\n  Tincture of lobelia,      2 ounces.\n  Infusion of hops,         1 quart.\n\nMix. Bathe the part twice a day.\n\n_Another._\n\n  Wormwood,             } of each a handful.\n  Thoroughwort,         }\n  New England rum,               1 pint.\n\nSet them in a warm place for a few hours, then bathe the part with the\nliquid; and bind some of the herb on the part, if practicable.\n\n\n\n\nSCALDS.\n\n\nIf a dog be accidentally scalded, apply, with as little delay as\npossible,--\n\n  Lime water,       } equal parts.\n  Linseed oil,      }\n\n\n\n\nOPHTHALMIA.\n\n\nOphthalmia is supposed to be contagious; yet a mild form may result from\nexternal injury, as blows, bruises, or extraneous bodies introduced\nunder the eyelid. The eye is such a delicate and tender organ, that the\nsmallest particle of any foreign body lodging on its surface will cause\ngreat pain and swelling.\n\n_Treatment._--Take a tea-spoonful of finely-pulverized marshmallow root,\nadd sufficient hot water to make a thin mucilage, and with this wash the\neye frequently. Keep the animal in a dark place, on a light diet; and if\nthe eyes are very red and tender, give a pill composed of twenty-nine\ngrains extract of butternut and ten grains cream of tartar.\n\nIf purulent discharge sets in, bathe the eye with infusion of camomile\nor red rose leaves, and give the following:--\n\n  Powdered pleurisy root,      }\n     \"     bloodroot,          } equal parts.\n     \"     sulphur,            }\n\nDose, half a table-spoonful daily. To be given in honey. When the\neyelids adhere together, wash with warm milk.\n\n\n\n\nWEAK EYES.\n\n\nIt often happens that, after an acute attack, the eyes are left in a\nweak state, when there is a copious secretion of fluid continually\nrunning from them. In such cases, the eyes may be washed, night and\nmorning, with pure cold water, and the general health must be improved:\nfor the latter purpose, the following preparation is recommended:--\n\n  Manna,                  1 ounce.\n  Powdered gentian,       1 tea-spoonful.\n     \"     mandrake,      half a tea-spoonful.\n\nRub them together in a mortar, and give a pill, about the size of a\nhazel-nut, every night. If the manna is dry, a little honey will be\nnecessary to amalgamate the mass.\n\n\n\n\nFLEAS AND VERMIN.\n\n\nFleas and vermin are very troublesome to dogs; yet they may easily be\ngot rid of by bathing the dog with an infusion of lobelia for two\nsuccessive mornings, and afterwards washing with water and castile soap.\n\n\n\n\nHYDROPHOBIA.\n\n\nWhenever one dog is bitten by another, and the latter is supposed to\nlabor under this dreadful malady, immediate steps should be taken to\narrest it; for a dog once bitten by another, whatever may be the stage\nor intensity of the disease, is never safe. The disease may appear in a\nfew days; in some instances, it is prolonged for eight months.\n\n_Symptoms._--Mr. Lawson tells us that \"the first symptom appears to be a\nslight failure of the appetite, and a disposition to quarrel with other\ndogs. A total loss of appetite generally succeeds. A mad dog will not\ncry out on being struck, or show any sign of fear on being threatened.\nIn the height of the disorder, he will bite all other dogs, animals, or\nmen. When not provoked, he usually attacks only such as come in his way;\nbut, having no fear, it is very dangerous to strike or provoke him. The\neyes of mad dogs do not look red or fierce, but dull, and have a\npeculiar appearance, not easy to be described. Mad dogs seldom bark, but\noccasionally utter a most dismal and plaintive howl, expressive of\nextreme distress, and which they who have once heard can never forget.\nThey do not froth at the mouth; but their lips and tongue appear dry and\nfoul, or slimy. They cannot swallow water.\" Mr. Lawson, and indeed many\nveterinary practitioners, have come to the conclusion that all remedies\nare fallacious![27]\n\n_Remarks._--In White's Dictionary we are informed that the tops of\nyellow broom have been used for hydrophobia in the human subject with\ngreat success; and we do not hesitate to say that they might be used\nwith equal success on beasts. Dr. Muller, of Vienna, has lately\npublished, in the _Gazette de Sante_, some facts which go to show that\nthe yellow broom is invaluable in the treatment of this malady. Dr.\nWhite tells us that \"M. Marochetti gave a decoction of yellow broom to\ntwenty-six persons who had been bitten by a mad dog, viz., nine men,\neleven women, and six children. Upon an examination of their tongues, he\ndiscovered pimples in five men, three children, and in all the women.\nThe seven that were free from pimples took the decoction of broom six\nweeks and recovered.\"\n\nThe same author informs us that \"M. Marochetti, during his residence at\nUkraine, in the year 1813, attended fifteen persons who had been bitten\nby a mad dog. While he was making preparations for cauterizing the\nwounds, some old men requested him to treat the unfortunate people\naccording to the directions of a peasant in the neighborhood, who had\nobtained great reputation for the cure of hydrophobia. The peasant gave\nto fourteen persons, placed under his care, a strong decoction of the\nyellow broom; he examined, twice a day, the under part of the tongue,\nwhere he had generally discovered little pimples, containing, as he\nsupposed, the hydrophobic poison. These pimples at length appeared, and\nwere observed by M. Marochetti himself. As they formed, the peasant\nopened them, and cauterized the parts with a red-hot needle; after which\nthe patients gargled with the same decoction. The result of this\ntreatment was, that the fourteen patients returned cured, having drank\nthe decoction six weeks.\" The following case will prove the value of the\nplantain, (_plantago major_.) We were called upon, October 25, 1850, to\nsee a dog, the property of Messrs. Stewart & Forbes, of Boston. From the\nsymptoms, we were led to suppose that the animal was in the incipient\nstage of canine madness. We directed him to be securely fastened, kept\non a light diet, &c. The next day, a young Newfoundland pup was placed\nin the cellar with the patient, who seized the little fellow, and\ncrushed his face and nose in a most shocking manner, both eyes being\nalmost obliterated. The poor pup lingered in excruciating torment until\nthe owner, considering it an act of charity, had it killed. This act of\nferocity on the part of the patient confirmed our suspicions as to the\nnature of the malady. We commenced the treatment by giving him\ntea-spoonful doses of powdered plantain, (_plantago major_,) night and\nmorning, in the food, and in the course of a fortnight, the eye (which,\nduring the early stage of the malady, had an unhealthy appearance)\nassumed its natural state, and the appetite returned; in short, the dog\ngot rapidly well. We feel confident that, if this case had been\nneglected, it might have terminated in canine madness.\n\nWe are satisfied that the plantain possesses valuable antiseptic and\ndetergent properties. Dr. Beach tells us that \"a <DW64> at the south\nobtained his freedom by disclosing a nostrum for the bites of snakes,\nthe basis of which was the plantain.\" A writer states that a toad, in\nfighting with a spider, as often as it was bitten, retired a few steps,\nate of the plantain, and then renewed the attack. The person deprived it\nof the plant, and it soon died.\n\n_Treatment._--Let the suspected dog be confined by himself, so that he\ncannot do injury. Then take two ounces of lobelia, and one ounce of\nsulphur, place them in a common wash tub, and add several gallons of\nboiling water. As soon as it is sufficiently cool, plunge the dog into\nit, and let him remain in it several minutes. Then give an infusion of\neither of the following articles: yellow broom, plantain, or Greek\nvalerian, one ounce of the herb to a pint of water. An occasional\ntea-spoonful of the powdered plantain may be allowed with the food,\nwhich must be entirely vegetable. If the dog has been bitten, wash the\npart with a strong infusion of lobelia, and bind some of the herb on the\npart. The treatment should be continued for several days, or until the\nanimal recovers, and all danger is past.\n\n(For information on the causes of madness, the reader is referred to my\nwork on the Horse, p. 108.)\n\nFOOTNOTE:\n\n[27] They probably only allude to cauterization, cutting out the bitten\npart, and the use of poisons. It cannot be expected that such processes\nand agents should ever cure the disease. Let them try our agents before\nthey pronounce \"all remedies fallacious.\" Let them try the _alisma\nplantago_, (plantain,) yellow broom tops, _scutellaria_, (skullcap,)\nlobelia, Greek valerian, &c.\n\n\n\n\nMALIGNANT MILK SICKNESS OF THE WESTERN STATES, OR CONTAGIOUS TYPHUS.\n\n\nThis name applies to a disease said to be very fatal in the Western\nStates, attacking certain kinds of live stock, and also persons who make\nuse of the meat and dairy products of such cattle.\n\nThe cause, nature, and treatment of this disease is so little understood\namong medical men, and such an alarming mortality attends their\npractice, that many of the inhabitants of the west and south-west depend\nentirely on their domestic remedies. \"It is in that country emphatically\none of the _opprobria medicorum_.\" Nor are the mineralites any more\nsuccessful in the treatment of other diseases incidental to the Great\nWest. Their Peruvian bark, _quinine_, and calomel, immense quantities of\nwhich are used without any definite knowledge of their _modus operandi_,\nfail in a great majority of cases. If they were only to substitute\npowdered charcoal and sulphur for calomel, both in view of prevention\nand cure, aided by good nursing, then the mortality would be materially\ndiminished. The success attending the treatment of upwards of sixty\ncases of yellow fever, by Mrs. Shall, the proprietress of the City\nHotel, New Orleans, only one of which proved fatal, is attributed to\ngood nursing. She knew nothing of blood-letting, calomelizing,\nnarcotizing. The same success attended the practice of Dr. A. Hunn, of\nKentucky, in the treatment of typhus fever, (which resembles milk\nsickness,) who cured every case by plunging his patients immediately\ninto a hot bath.\n\n\"The whole indication of cure in this disease is to bring on reaction,\nto recall the poison which is mixed with the blood and thrown to the\ncentre, which can only be done by inducing a copious perspiration in the\nmost prompt and energetic manner. If I mistake not, where sweating was\nproduced in this complaint, recovery invariably followed, while\nbleeding, mercury, &c., only aggravated it.\"\n\nFrom such facts as these, as well as from numerous others, we may learn,\nthat disease is not under the control of the boasted science of\nmedicine, as practised by our allopathic brethren. Many millions of\nanimals, as well as members of the human family, have died from a\nmisapplication of medicine, and officious meddling.\n\nThe destruction that in former years attended milk sickness may be\nlearned from the fact, that in the western settlements, its prevalence\noften served as a cause to disband a community, and compel the\ninhabitants to seek a location which enjoyed immunity from its\noccurrence. The legislatures of several of the Western States have\noffered rewards for the discovery of the origin of the milk sickness. No\none that we know of has ever yet claimed the reward. In view of the\ngreat lack of information on this subject, we freely contribute our\nmite, which may serve, in some degree, to dispel the impenetrable\nmystery by which it is surrounded.\n\nWe shall first show that it is not produced by the atmosphere alone,\nwhich by some is supposed to be the cause.\n\n\"It is often found to occupy an isolated spot, comprehending an area of\none hundred acres, whilst for a considerable distance around it is not\nproduced.\"\n\nIf the disease had its sole origin in the atmosphere, it would not be\nthus confirmed to a certain location; for every one knows, that the\ngentlest zephyr would waft the enemy into the surrounding localities,\nand there the work of destruction would commence. The reader is probably\naware that bodies whose specific gravity exceeds that of air, such as\ngrass, seeds, &c., are conveyed through that medium from one field to\nanother. The miasma of epidemics is said to be conveyed from one\ndistrict to another \"on the wings of the wind.\" Hence, if milk sickness\nwas of atmospheric or even epidemic origin, it would prevail in\nadjoining states. This is not the case; for we are told that \"this fatal\ndisease seldom, if ever, prevails westward of the Alleghany Mountains or\nin the bordering states.\"\n\nThe atmosphere which surrounds this globe was intended by the divine\nArtist for the purpose of respiration, and it is well adapted to that\npurpose: it cannot be considered a pathological agent, or a cause of\ndisease. In crowded assemblies, and in close barns and stables, it may\nhold in solution noxious gases, which, as we have already stated in\ndifferent parts of this work, are injurious to the lungs; but as regards\nthe atmosphere itself, in an uncontaminated state, it is a physiological\nagent. It always preserves its identity, and is always represented by\nthe same equivalents of oxygen, nitrogen, and carbonic acid gas. Liebig\nsays, \"One hundred volumes of air have been found, at every period and\nin every climate, to contain twenty-one volumes of oxygen.\"\n\nThus oxygen and nitrogen unite in certain equivalents: the result is\natmospheric air; and they cannot be made to unite in any other\nproportions. Suppose the oxygen to be in excess, what would be the\nresult? A universal conflagration would commence; the hardest rocks, and\neven the diamond, (considered almost indestructible,) would melt with\n\"fervent heat.\" If, on the other hand, nitrogen was in excess, then\nevery living thing, including both animal and vegetable, would instantly\ndie. Hence we infer that the atmosphere cannot be considered as the\ncause of this disease.\n\n_Causes._--A creeping vine has been supposed to occasion the disease.\nThis cannot be the case, for it occurs very frequently when the ground\nis covered with snow. We are satisfied, although we may not succeed in\nsatisfying the reader, that no one cause alone can produce the disease:\nthere must be a diminution of vital energy, and this diminution may\nresult, first, from poor diet. Dr. Graff tells us that the general\nappearance of these infected districts is somewhat peculiar. The quality\nof the soil is, in general, of an inferior description. The growth of\ntimber is not observed to be so luxuriant as in situations otherwise\nsimilar, but is scrubby, and stunted in its perfect development, in many\ninstances simulating what in the west is denominated '_barrens_.' We can\neasily conceive that these barrens do not furnish the proper amount of\ncarbon (in the form of food) for the metamorphosis of the tissues; and\nif we take into consideration that the animal receives, during the day,\nwhile in search of this food, a large supply of oxygen, and at the same\ntime the waste of the body is increased by the extra labor required to\nselect sufficient nutriment,--it being scanty in such situations,--then\nit follows that this disproportion between the quantity of carbon in the\nfood, and that of oxygen absorbed by the skin and lungs, must induce a\ndiseased or abnormal condition. The animal is sometimes fat, at others\nlean. Some of the cows attacked with this disease were fat, and in\napparent health, and nothing peculiar was observed until immediately\npreceding the outbreak of the fatal symptoms. The presence of fat is\ngenerally proof positive of an abnormal state; and in such cases the\nliver is often diseased; the blood then becomes loaded with fat and oil,\nand is finally deposited in the cellular tissues. The reader will now\nunderstand how an animal accumulates fat, notwithstanding it be\nfurnished with insufficient diet. All that we wish to contend for is,\nthat in such cases vital resistance is compromised. We have observed\nthat, in the situation alluded to, vegetation was stunted, &c., and\nknowing that vegetables are composed of nearly the same materials which\nconstitute animal organization,--the carbon or fat of the former being\ndeposited in the seeds and fruits, and that of the latter in the\ncellular structure,--then we can arrive at but one conclusion, viz.,\nthat any location unfavorable to vegetation is likewise ill adapted to\npreserve the integrity of animal life.\n\nIn connection with this, it must be remembered that during the night the\nsoil emits excrementitious vapors which are taken into the animal system\nby the process of respiration. In the act of rumination, vapor is also\nenclosed in the globules of saliva, and thus reach the stomach. Many\nplants which during the day may be eaten with impunity by cattle,\nactually become poisonous during the night! This, we are aware, will\nmeet with some opposition; to meet which we quote from Liebig:--\n\n\"How powerful, indeed, must the resistance appear which the vital force\nsupplies to leaves charged with oil of turpentine or tannic acid, when\nwe consider the affinity of oxygen for these compounds!\n\n\"This intensity of action, or of resistance, the plant obtains by means\nof the sun's light; the effect of which in chemical actions may be, and\nis, compared to that of a very high temperature, (moderate red heat.)\n\n\"During the night, an opposite process goes on in the plant; we see then\nthat the constituents of the leaves and green parts combine with the\noxygen of the air--a property which in daylight they did not possess.\n\n\"From these facts we can draw no other conclusion but this: that the\nintensity of the vital force diminishes with the abstraction of light;\nthat, with the approach of night, a state of equilibrium is established;\nand that, in complete darkness, all those constituents of plants which,\nduring the day, possessed the power of separating oxygen from chemical\ncombinations, and of resisting its action, lose their power completely.\n\n\"A precisely similar phenomenon is observed in animals.\n\n\"The living animal body exhibits its peculiar manifestations of vitality\nonly at certain temperatures. When exposed to a certain degree of cold,\nthese vital phenomena entirely cease.\n\n\"The abstraction of heat must, therefore, be viewed as quite equivalent\nto a diminution of the vital energy; the resistance opposed by the vital\nforce to external causes of disturbance must diminish, in certain\ntemperatures, in the same ratio in which the tendency of the elements of\nthe body to combine with the oxygen of the air increases.\"\n\n_Secondly._ In the situations alluded to, we generally find poisonous\nand noxious plants, with an abundance of decayed vegetable matter. An\nEnglish writer has said, \"The farmers of England might advantageously\nemploy a million at least of additional laborers in clearing their wide\ndomains of noxious plants,[28] which would amply repay them in the\nsuperior quality of their produce. They would then feel the truth of\nthat axiom in philosophy, \"that he who can contrive to make two blades\nof grass, or wholesome grain, grow where one poisonous plant grew\nbefore, is a greater benefactor to the human race than all the\nconquerors or heroes who have ever lived.\" The noxious plants found in\nsuch abundance in the Western States are among the principal causes,\neither directly or indirectly, of the great mortality among men, horses,\ncattle, and sheep. The hay would be just as destructive as when in its\ngreen state, were it not that, in the process of drying, the volatile\nand poisonous properties of the buttercup, dandelion, poppy, and\nhundreds of similar destructive plants found in the hay, evaporate. It\nis evident that if animals have partaken of such plants, although death\nin all cases do not immediately follow, there must be a deficiency of\nvital resistance, or loss of equilibrium, and the animal is in a\nnegative state. It is consequently obvious that when in such a state it\nis more liable to receive impressions from external agents--in short, is\nmore subject to disease, and this disease may assume a definite form,\nregulated by location.\n\n_Thirdly._ A loss of vital resistance may result from drinking impure\nwater. (See _Watering_, p. 15.) Dr. Graff tells us that \"another\npeculiar appearance, which serves to distinguish these infected spots,\nis the breaking forth of numerous feeble springs, called oozes,\nfurnishing but a trifling supply of water.\" Such water is generally\nconsidered unwholesome, and will, of course, deprive the system of its\nvital resistance, if partaken of.\n\n_Fourthly._ A loss of vital resistance may result from exposure; for it\nis well known that cattle which have been regularly housed every night\nhave escaped the attacks of this malady, and that when suffered to\nremain at large, they were frequently seized with it.\n\n_Lastly._ The indirect causes of milk fever exist in any thing that can\nfor a time prevent the free and full play of any part of the animal\nfunctions. The direct causes of death are chemical action, resulting\nfrom decomposition, which overcomes the vital principle.\n\nProfessor Liebig tells us, that \"chemical action is opposed by the vital\nprinciple. The results produced depend upon the strength of their\nrespective actions; either an equilibrium of both powers is attained, or\nthe acting body yields to the superior force. If chemical action obtains\nthe ascendency, it acts as a poison.\"\n\n_Remarks._--Let us suppose that one, or a combination of the preceding\ncauses, has operated so as to produce an abnormal state in the system of\na cow. She is then suffered to remain in the unhealthy district during\nthe night: while there, exposed to the emanations from the soil, she\nrequires the whole force of her vital energies to ward off chemical\ndecompositions, and prevent encroachment on the various functions. A\ncontest commences between the vital force and chemical action, and,\nafter a hard conflict in their incessant endeavors to overcome each\nother, the chemical agency obtains the ascendency, and disease of a\nputrid type (milk fever) is the result. The disease may not immediately\nbe recognized, for the process of decomposition may be insidious; yet\nthe milk and flesh of such an animal may communicate the disease to man\nand other animals. It is well known that almost any part of animal\nbodies in a state of putrefaction, such as milk, cheese, muscle, pus,\n&c., communicate their own state of decomposition to other bodies. Many\neminent medical men have lost their lives while dissecting, simply by\nputrefactive matter coming in contact with a slight wound or puncture.\nDr. Graff made numerous experiments on dogs with the flesh, &c., of\nanimals having died of milk sickness. He says, \"My trials with the\npoisoned flesh were, for the most part, made on dogs, which I confined;\nand I often watched the effect of the poison when administered at\nregular intervals. In the space of forty-eight hours from the\ncommencement of the administration of either the butter, cheese, or\nflesh, I have observed unequivocal appearances of their peculiar action,\nwhile the appetite remains unimpaired until the expiration of the fourth\nor fifth day.\" From the foregoing remarks, the reader will agree with\nus, that the disease is of a putrid type, and has a definite character.\nWhat is the reason of this definite character? All diseases are under\nthe control of the immutable laws of nature. They preserve their\nidentity in the same manner that races of men preserve theirs. Milk\nsickness of the malignant type luxuriates in the locations referred to,\nfor the same reasons that yellow fever is peculiar to warm climates, and\nconsumption to cold ones; and that different localities have distinct\ndiseases; for example, ship fever, jail fever, &c.\n\nBefore disease can attack, and develop itself in the bodies of men or\nanimals, the existing equilibrium of the vital powers must be disturbed;\nand the most common causes of this disturbance we have already alluded\nto. In reference to the milk, butter, cheese, &c., of infected animals,\nand their adaptation to develop disease in man, and in other locations\nthan those referred to, we observe, that when a quantity, however small,\nof contagious matter is introduced into the stomach, if its antiseptic\nproperties are the least deranged, the original disease (milk sickness)\nis produced, just as a small quantity of yeast will ferment a whole\nloaf. The transformation takes place through the medium of the blood,\nand produces a body identical with, or similar to, the exciting or\ncontagious matter. The quantity of the latter must constantly augment;\nfor the state of change or decomposition which affects one particle of\nthe blood is imparted to others. The time necessary to accomplish it,\nhowever, depends on the amount of vital resistance, and of course varies\nin different animals. In process of time, the whole body becomes\naffected, and in like manner it is communicated to other individuals;\nand this may take place by simply respiring the carbonic acid gas, or\nmorbific materials from the lungs, of diseased animals in the infected\ndistricts.\n\nWe are told that the latent condition of the disease may be discovered\nby subjecting the suspected animal to a violent degree of exercise. This\nis a precaution practised by butchers before slaughtering animals in any\nwise suspected of the poisonous contamination;[29] for according to the\nintensity of the existing cause, or its dominion over the vital power,\nit will be seized with tremors, spasms, convulsions, or even death. The\nreader is, probably, aware that an excess of motion will sometimes\ncause instant death; for both men and animals, supposed to be in\nexcellent health, are known to die suddenly from excessive labor. In\nsome cases of excess of muscular exertion, the active force in living\nparts may be entirely destroyed in producing these violent mechanical\nresults: hence we have a loss of equilibrium between voluntary and\ninvoluntary motion, and there is not sufficient vitality left to carry\non the latter. Professor Liebig says, \"A stag may be hunted to death.\nThe condition of metamorphosis into which it has been brought by an\nenormous consumption both of force and of oxygen continues when all\nphenomena of motion have ceased, and the flesh becomes uneatable.\" A\nperfect equilibrium, therefore, between the consumption of vital force\nfor the supply of waste, protecting the system from encroachments, and\nfor mechanical effects, must exist; the animal is then in health: the\ncontrary is obvious.\n\n_Treatment._--The greatest care must be taken to secure the patient good\nnutritious food, pure air, and water. The food should consist of a\nmixture of two or more of the following articles, which must be cooked:\nlinseed, parsnips, shorts, carrots, meal, apples, barley, oats, turnips,\nslippery elm, oil cake, &c. We again remind the reader that no single or\ncompound medicine can be procured that will be suitable for every stage\nof the disease; it must be treated according to its indications. Yet the\nfollowing compound, aided by warmth, moisture, and friction, externally,\nwill be found better than any medicine yet known. It consists of\n\n  Powdered charcoal,                       8 ounces.\n     \"     sulphur,                        2 ounces.\n  Fine salt,                               3 ounces.\n  Oatmeal,                                 2 pounds.\n  Mandrake, (_podophyllum peltatum_,)      1 ounce.\n\nAfter the ingredients are well mixed, divide the mass into fourteen\nparts, and give one night and morning.\n\n_Special Treatment with reference to the Symptoms._--Suppose the animal\nto be \"off her feed,\" and the bowels are constipated; then give an\naperient composed of\n\n  Extract of butternut,      2 drachms.\n  Powdered capsicum,         one third of a tea-spoonful.\n  Thoroughwort tea,          2 quarts.\n\nTo be given at a dose, taking care to pour it down the throat in a\ngradual manner; for, if poured down too quick, it will fall into the\npaunch. If the rectum is suspected to be loaded with excrement, make use\nof the common soap-suds injection.\n\nIf the animal appears to walk about without any apparent object in view,\nthere is reason to suppose that the brain is congested. This may be\nverified if the _sclerotica_ (white of the eye) is of a deep red color.\nThe following will be indicated:--\n\n  Mandrake, (_podophyllum peltatum_,)      1 table-spoonful.\n  Sulphur,                                 1 tea-spoonful.\n  Cream of tartar,                         1 tea-spoonful.\n  Hot water,                               2 quarts.\n\nTo be given at a dose. At the same time apply cold water to the head,\nand rub the spine and legs (below the knees) with the following\ncounter-irritant:--\n\n  Powdered bloodroot or cayenne,      1 ounce.\n     \"     black pepper,              half an ounce.\n  Boiling vinegar,                    1 quart.\n\nRub the mixture in while hot, with a piece of flannel.\n\nIf a trembling of the muscular system is observed, then give\n\n  Powdered ginger,           }\n     \"     cinnamon,         } of each half\n     \"     golden seal,      } a tea-spoonful.\n\nTo be given at a dose, in half a gallon of catnip tea. Aid the vital\npowers in producing a crisis by the warmth and moisture, as directed in\nthe treatment of colds, &c.\n\nIt is necessary to keep the rectum empty by means of injections, forms\nof which will be found in this work.\n\nThe remedies we here recommend can be safely and successfully used by\nthose unskilled in medicine; and, when aided by proper attention to the\ndiet, ventilation, and comfort of the patient, we do not hesitate to say\n(provided, however, they are resorted to in the early stages) they will\ncure forty-nine cases out of fifty, without the advice of a physician.\n\nFOOTNOTES:\n\n[28] The American farmers are just beginning to wake up on this subject,\nand before long we hope to see our pasture lands free from all poisonous\nplants. Dr. Whitlaw says, \"A friend of mine had two fields cleared of\nbuttercups, dandelion, ox-eye, daisy, sorrel, hawk-weed, thistles,\nmullein, and a variety of other poisonous or noxious plants: they were\ndried, burnt, and their ashes strewed over the fields. He had them sown\nas usual, and found that the crops of hay and pasturage were more than\ndouble what they had been before. I was furnished with butter for two\nsuccessive summers during the months of July and August of 1827. The\nbutter kept for thirty days, and proved, at the end of that time, better\nthan that fresh churned and brought to the Brighton or Margate markets.\nIt would bear salting at that season of the year.\"\n\n[29] Unfortunately, they do not all practise it. Dr. Graff says, \"There\nis a murderous practice now carried on in certain districts, in which\nthe inhabitants will not themselves consume the butter and cheese\nmanufactured; but, with little solicitude for the lives or health of\nothers, they send it, in large quantities, to be sold in the cities of\nthe west, particularly Louisville, Kentucky, and St. Louis, Missouri. Of\nthe truth of this I am well apprised by actual observation; and I am as\ncertain that it has often caused death in those cities, when the medical\nattendants viewed it as some anomalous form of disease, not suspecting\nthe means by which poison had been conveyed among them. Physicians of\nthe latter city, having been questioned particularly on this subject,\nhave mentioned to me a singular and often fatal disease, which appeared\nin certain families, the cases occurring simultaneously, and all traces\nof it disappearing suddenly, and which I cannot doubt were the result of\npoisoned butter or cheese. This recklessness of human life it should be\nour endeavor to prevent; and the heartless wretches who practise it\nshould be brought to suffer a punishment commensurate with the enormity\nof their crime. From the wide extent of the country in which it is\ncarried on, we readily perceive the difficulties to be encountered in\nthe effort to put a stop to the practice. This being the case, our next\nproper aim should be to investigate the nature of the cause, and\nestablish a more proper plan of treatment, by which it may be robbed of\nits terrors, and the present large proportionate mortality diminished.\"\n\n\n\n\nBONE DISORDER IN COWS.\n\n\nWe have frequently seen accounts, in various papers, of \"bone disorder\nin milch cows.\" The bony structure of animals is composed of vital\nsolids studded with crystallizations of saline carbonates and\nphosphates, and is liable to take on morbid action similar to other\ntextures. Disease of the bones may originate constitutionally, or from\nderangement of the digestive organs. We have, for example, _mollities\nossium_, (softening of the bones;) the disease, however, is very rare.\nIt may be known by the substance of the bones being soft and yielding,\nliable to bend with small force.\n\nWe have also _fragilitas ossium_, (brittleness of bones.) This is\ncharacterized by the bony system being of a friable nature, and liable\nto be fractured by slight force. We have in our possession the fragments\nof the small pastern of a horse, the bone having been broken into\nseventeen pieces, by a slight concussion, without any apparent injury to\nthe skin and cellular substance; not the slightest external injury could\nbe perceived.\n\nThere are several other diseases of the bones, which, we presume, our\nreaders are acquainted with; such as _exostosis_, _caries_, &c., neither\nof which apply to the malady under consideration. We merely mention\nthese for the purpose of showing that the bones are not exempt from\ndisease, any more than other structures; yet it does not always follow\nthat a lack of the phosphate of lime in cow's milk is a sure sign of\ndiseased bones.\n\nReader, we do not like the term \"_bone disorder_:\" it does not throw the\nleast light on the nature of the malady; it savors too much of \"_horn\nail_,\" \"_tail ail_\"--terms which only apply to symptoms. We are told\nalso that, in this disease, \"_the bones threaten to cave in--have wasted\naway_.\" If they do threaten to cave in, the best way we know of to give\nthem an outward direction is, to promote the healthy secretions and\nexcretions by a well-regulated diet, and to stimulate the digestive\norgans to healthy action. If the bones \"have wasted away,\" we should\nlike to have a few of them in our collection of morbid anatomy. That the\nbones should waste away, and be capable of assuming their original shape\nsimply by feeding bone meal, is something never dreamt of in our\nphilosophy.[30] Besides, if the cows get well, (we are told they do,)\nthen we must infer that the bones possess the properties of sudden\nexpansion and contraction, similar to those of the muscles. It may be\nwell for us to observe, that not only the bones, but all parts of animal\norganization, expand and contract in an imperceptible manner. Thus, up\nto the period of puberty, all parts expand: old age comes on, and with\nit a gradual wasting and collapse. This is a natural result--one of the\nuncompromising laws of nature, over which human agency (bone meal\nincluded) has not the least control. If the bones are diseased, it\nresults either from impaired digestion or a disproportion between the\ncarbon of the food and the oxygen respired; hence the \"bone disorder,\"\nnot being persistent, is only a result--a symptom; and as such we view\nit. As far as we have been able to ascertain the nature of the malady,\nas manifested by the symptoms, (_caving in_, _wasting_, _absence of\nphosphate of lime in the milk_, &c.,) we give it as our opinion,--and we\nthink our medical brethren will agree with us, (although we do not often\nagree,)--that \"bone disorder\" is a symptom of a disease very prostrating\nin its character, originating in the digestive organs; hence not\nconfined to the bones, but affecting all parts of the animal more or\nless. And the only true plan of treatment consists in restoring healthy\naction to the whole animal system. The ways and means of accomplishing\nthis object are various. If it is clearly ascertained that the animal\nsystem is deficient in phosphate of lime, we see no good reason why bone\nmeal should not be included among our remedial agents; yet, as corn meal\nand linseed contain a large amount of phosphate, we should prefer them\nto bone dust, although we do not seriously object to its use.\n\nThe value of food or remedial agents consists in their adaptation to\nassimilation; in other words, an absence of chemical properties. These\nmay be very complex; yet, if they are only held together by a weak\nchemical action, they readily yield to the vital principle, and are\ntransformed. Atoms of bones are held together by a strong chemical\naffinity; and the vital principle, in order to convert bone dust into\ncomponent parts of the organism, must employ more force to transform\nthem than it would require for the same purpose when corn meal or\nlinseed were used, their chemical affinity being weaker than that of\nbones.\n\nIn the treatment of any disease, we always endeavor to ascertain its\ncauses, and, if possible, remove them; and whatever may be indicated we\nendeavor to supply to the system. Thus, if phosphates were indicated, we\nshould use them. In cases of general debility, however, we should prefer\nlinseed or corn meal, aided by stimulants, to bone dust. Why not use the\nbone dust for manure? The animal would then have the benefit of it in\nits fodder.\n\nIn reference to a deficiency of phosphate of lime in the milk, we would\nobserve, that it may result either from impaired digestion, (in such\ncases, a large amount of that article may be expelled from the system in\nthe form of excrements,) or the food may lack it. We then have a sick\nplant, for we believe that the phosphate of lime is as necessary for the\ngrowth of the plant as it seems to be for animal development. If the\nplant lacks this important constituent, then its vitality, as a whole,\nwill be impaired. This is all we desire to contend for in the animal,\nviz., that the disease is general, and cannot be considered or treated\nas a local affection.\n\nIt has been observed that successive cultivation exhausts the soil, and\ndeprives it of the constituents necessary for vegetable development. If\nso, it follows that there will be a deficiency of silecia, carbonate of\nlime,--in short, a loss of carbon, hydrogen, nitrogen, and oxygen, not\nof phosphate of lime alone.\n\nThe fields might be made to produce the requisite amount of nutriment by\nreplacing every year, in the form of animal excrement, straw,\nwood-ashes, and charcoal, as much as we remove from them in the form of\nproduce. An increase of crop can only be obtained when we add more to\nthe soil than we take away from it.\n\n\"In Flanders, the yearly loss of the necessary matters in the soil is\ncompletely restored by covering the fields with ashes of wood or bones,\nwhich may, or may not, have been lixiviated. The great importance of\nmanuring with ashes has been long recognized by agriculturists as the\nresult of experience. So great a value, indeed, is attached to this\nmaterial in the vicinity of Marburg, and in the Wetterau,--two\nwell-known agricultural districts,--that it is transported, as a manure,\nfrom the distance of eighteen or twenty-four miles. Its use will be at\nonce perceived, when it is considered that the ashes, after being washed\nwith water, contain silicate of potass exactly in the same proportion as\nin the straw, and that their only other constituents are salts of\nphosphoric acid.\"\n\nIt is well known that phosphate of lime, potass, silecia, carbonate of\nlime, magnesia, and soda are discharged in the excrement and urine of\nthe cow; and this happens when they are not adapted to assimilation as\nwell as when present in excess. If it is clearly proved that the bones\nof a cow are weak, then we should be inclined to prescribe phosphates;\nif they are brittle, we should prescribe gelatinous preparations; but\nnot in the form of bone dust: we should use linseed, which is known to\nbe rich in phosphates. At the same time, the general health must be\nimproved.\n\nIt is well known that some cows cannot be fattened, although they have\nan abundance of the best kind of fodder. In such cases, we find the\ndigestive organs deranged, which disturbs the equilibrium of the whole\nanimal economy. The food may then be said to be a direct cause of\ndisease.\n\nThe effects of insufficient food are well known; debility includes them\nall. If there is not sufficient carbon in the food, the animal is\ndeprived of the power of reproducing itself, and the cure consists in\nsupplying the deficiency. At the same time, every condition of nutrition\nshould be considered; and if the function of digestion is impaired, we\nmust look to those of absorption, circulation, and secretion also, for\nthey will be more or less involved. If the appetite is impaired,\naccompanied by a loss of cud, it shows that the stomach is overloaded,\nor that its function is suspended: stimulants and tonics are then\nindicated. A voracious appetite indicates the presence of morbid\naccumulations in the stomach and bowels, and they should be cleansed by\naperients; after which, a change of diet will generally effect a cure.\nWhen gas accumulates in the intestines, we have evidence of a loss of\nvital power in the digestive organs; fermentation takes place before the\nfood can be digested.\n\nThe cure consists in restoring the lost function. Diarrhoea is\ngenerally caused by exposure, (taking cold,) or by eating poisons and\nirritating substances; the cure may be accomplished by removing the\ncold, and cleansing the system of the irritants. Costiveness often\narises from the absorption of the fluids from the solids in their slow\nprogress through the intestines; exercise will then be indicated. An\noccasional injection, however, may be given, if necessary. General\ndebility, we have said, may arise from insufficient food; to which we\nmay add the popular practice of milking the cow while pregnant, much of\nwhich milk is yielded at the hazard of her own health and that of her\nfoetus. Whatever is taken away from the cow in the form of milk ought\nto be replaced by the food. Proper attention, however, must be paid to\nthe state of the digestive organs: they must not be overtaxed with\nindigestible substances. With this object in view, we recommend a mixed\ndiet; for no animal can subsist on a single article of food. Dogs die,\nalthough fed on jelly; they cannot live upon white bread, sugar, or\nstarch, if these are given as food, to the exclusion of all other\nsubstances. Neither can a horse or cow live on hay alone: they will,\nsooner or later, give evidences of disease. They require stimulants.\nCommon salt is a good stimulant. This explains why salt hay should be\noccasionally fed to milch cows; it not only acts as a stimulant, but is\nalso an antiseptic, preventing putrefaction, &c.\n\nA knowledge of the constituents of milk may aid the farmer in selecting\nthe substances proper for the nourishment of animals, and promotive of\nthe lacteal secretion; for much of the food contains those materials\nunited, though not always in the same form. \"The constituents of milk\nare cheese, or caseine--a compound containing nitrogen in large\nproportion; butter, in which hydrogen abounds; and sugar of milk, a\nsubstance with a large quantity of hydrogen and oxygen in the same\nproportions as in water. It also contains, in solution, lactate of soda,\nphosphate of lime, (the latter in very small quantities,) and common\nsalt; and a peculiar aromatic product exists in the butter, called\nbutyric acid.\"--_Liebig._\n\nIt is very difficult to explain the changes which the food undergoes in\nthe animal laboratory, (the stomach,) because that organ is under the\ndominion of the vital force--an immaterial agency which the chemist\ncannot control. Yet we are justified in furnishing the animal with the\nelements of its own organization; for although they may not be deposited\nin the different structures in their original atoms, they may be changed\ninto other compounds, somewhat similar. Liebig tells us that whether the\nelements of non-azotized food take an immediate share in the act of\ntransformation of tissues, or whether their share in that process be an\nindirect one, is a question probably capable of being resolved by\ncareful and cautious experiment and observation. It is possible that\nthese constituents of food, after undergoing some change, are carried\nfrom the intestinal canal directly to the liver, and that there they are\nconverted into bile, where they meet with the products of the\nmetamorphosed tissues, and subsequently complete their course through\nthe circulation.\n\nThis opinion appears more probable, when we reflect that as yet no trace\nof starch or sugar has been detected in arterial blood, not even in\nanimals that have been fed exclusively with these substances.\n\nThe following tables, from Liebig's Chemistry, will give the reader the\ndifference between what is taken into the system and what passes out.\n\nFOOD CONSUMED BY A COW IN TWENTY-FOUR HOURS.\n\n  ------------+------+------+-------+---------+-------+---------+--------\n              |Weight|Weight|       |         |       |         | Salts\n  Articles    |in the|in the|Carbon.|Hydrogen.|Oxygen.|Nitrogen.|  and\n  of food.    |fresh | dry  |       |         |       |         |earthly\n              |state.|state.|       |         |       |         |matters.\n  ------------+------+------+-------+---------+-------+---------+--------\n  Potatoes,   | 15000|  4170| 1839.0|  241.9  | 1830.6|   50.0  | 208.5\n  After grass,|  7500|  6315| 2974.4|  353.6  | 2204.0|  151.5  | 631.5\n  Water,      | 60000|   -- |   --  |    --   |   --  |    --   |  50.0\n  ------------+-------------+-------+---------+-------+---------+--------\n  Total,      | 82500| 10485| 4813.4|  595.5  | 4034.6|  201.5  | 889.0\n  ------------+------+------+-------+---------+-------+---------+--------\n\nEXCRETIONS OF A COW IN TWENTY-FOUR HOURS.\n\n  -----------------------------------------------------------------------\n             |Weight|Weight |       |         |       |         | Salts\n  Excretions.|in the|in the |Carbon.|Hydrogen.|Oxygen.|Nitrogen.|  and\n             |fresh | dry   |       |         |       |         |earthly\n             |state.|state. |       |         |       |         |matters.\n  -----------+------+-------+-------+---------+-------+---------+--------\n  Excrements,| 28413| 4000.0| 1712.0|  208.0  | 1508.0|   92.0  | 480.0\n  Urine,     |  8200|  960.8|  261.4|   25.0  |  253.7|   36.5  | 384.2\n  Milk,      |  8539| 1150.6|  628.2|   99.0  |  321.0|   46.0  |  56.4\n  -----------+------+-------+-------+---------+-------+---------+--------\n    Total,   | 45152| 6111.4| 2601.6|  332.0  | 2082.7|  174.5  | 920.6\n  -----------+------+-------+-------+---------+-------+---------+--------\n  Total of   |      |       |       |         |       |         |\n  first part | 82500|10485.0| 4813.4|  595.5  | 4034.6|  201.5  | 889.0\n  of this    |      |       |       |         |       |         |\n  table,     |      |       |       |         |       |         |\n  -----------+------+-------+-------+---------+-------+---------+--------\n  Difference,| 37348| 4374.6| 2211.8|  263.5  | 1951.9|   27.0  |  31.6\n  -----------+------+-------+-------+---------+-------+---------+--------\n\nFOOD CONSUMED BY A HORSE IN TWENTY-FOUR HOURS.\n\n  --------+------+------+-------+---------+-------+---------+---------\n  Articles|Weight|Weight|       |         |       |         | Salts\n  of food.|in the|in the|Carbon.|Hydrogen.|Oxygen.|Nitrogen.|  and\n          |fresh | dry  |       |         |       |         | earthy\n          |state.|state.|       |         |       |         |matters.\n  --------+------+------+-------+---------+-------+---------+---------\n  Hay,    |  7500| 6465 | 2961.0|  323.2  | 2502.0|   97.0  | 581.8\n  Oats,   |  2270| 1927 |  977.0|  123.3  |  707.2|   42.4  |  77.1\n  Water,  | 16000|  --  |   --  |   --    |   --  |    --   |  13.3\n  --------+------+------+-------+---------+-------+---------+---------\n    Total,| 25770| 8392 | 3938.0|  446.5  | 3209.2|  139.4  | 672.2\n  --------+------+------+-------+---------+-------+---------+---------\n\nEXCRETIONS OF A HORSE IN TWENTY-FOUR HOURS.\n\n  --------------+------+------+-------+---------+-------+---------+--------\n                |Weight|Weight|       |         |       |         | Salts\n  Excretions.   |in the|in the|Carbon.|Hydrogen.|Oxygen.|Nitrogen.|  and\n                |fresh | dry  |       |         |       |         | earthy\n                |state.|state.|       |         |       |         |matters.\n  --------------+------+------+-------+---------+-------+---------+--------\n  Urine,        |  1330|  302 |  108.7|   11.5  |  34.1 |   37.8  | 109.9\n  Excrements,   | 14250| 3525 | 1364.4|  179.8  |1328.9 |   77.6  | 574.6\n                |      |      |       |         |       |         |\n  --------------+------+------+-------+---------+-------+---------+--------\n    Total,      | 15580| 3827 | 1472.9|  191.3  |1363.0 |  115.4  | 684.5\n  --------------+------+------+-------+---------+-------+---------+--------\n  Total of first|      |      |       |         |       |         |\n    part of this| 25770| 8392 | 3938.0|  446.5  |3209.2 |  139.4  | 672.2\n      table,    |      |      |       |         |       |         |\n  --------------+------+------+-------+---------+-------+---------+--------\n  Difference,   | 10190| 4565 | 2465.1|  255.2  |1846.2 |   24.0  |  12.3\n  --------------+------+------+-------+---------+-------+---------+--------\n\n     The weights in these tables are given in grammes. 1 gramme is equal\n     to 15.44 grains Troy, very nearly.\n\nIt will be seen from these tables that a large proportion of carbon,\nhydrogen, oxygen, nitrogen, and earthy matters are again returned to the\nsoil. From this we infer that more of these matters being present in the\nfood than were requisite for the purpose of assimilation, they were\nremoved from the system in the form of excrement. Two suggestions here\npresent themselves for the consideration of the farmer, viz., that the\nmanure increases in value in proportion to the richness of food, and\nthat more of the latter is often given to a cow than is necessary for\nthe manufacture of healthy chyle.\n\nIn view, then, of preventing \"bone disorder,\" which we have termed\n_indigestion_, we should endeavor to ascertain what articles are best\nfor food, and learn, from the experience of others, what have been\nuniversally esteemed as such, and, by trying them on our own animals,\nprove whether we actually find them so. Scalded or boiled food is\nbetter adapted to the stomach of animals than food otherwise prepared,\nand is so much less injurious. The agents that act on the internal\nsystem are those which, in quantities sufficient for an ordinary meal,\nsupply the animal system with stimulus and nutriment just enough for its\nwants, and contain nothing in their nature inimical to the vital\noperations. All such articles are properly termed food. (For treatment,\nsee _Hide-bound_, p. 196.)\n\nFOOTNOTE:\n\n[30] Whenever there is a deficiency of carbon, bone meal may assist to\nsupport combustion in the lungs, and by that means restore healthy\naction of the different functions, provided, however, the digestive\norgans, aided by the vital power, can overcome the chemical action by\nwhich the atoms of bone meal are held together.\n\n\n    +-----------------------------------------------+\n    |             Transcriber's Note:               |\n    |                                               |\n    | Inconsistent hyphenation and spelling in the  |\n    | original document have been preserved.        |\n    |                                               |\n    | Typographical errors corrected in the text:   |\n    |                                               |\n    | Page  36  selecter changed to selector        |\n    | Page  48  relaxents changed to relaxants      |\n    | Page  54  bronchea changed to bronchi         |\n    | Page  85  relaxents changed to relaxants      |\n    | Page 112  relaxent changed to relaxant        |\n    | Page 135  antispetics changed to antiseptics  |\n    | Page 162  BLAINE changed to BLAIN             |\n    | Page 181  crums changed to crumbs             |\n    | Page 186  puarts changed to quarts            |\n    | Page 236  Marshallow changed to Marshmallow   |\n    | Page 247  Merinoes changed to Merinos         |\n    | Page 307  cypripedum changed to cypripedium   |\n    | Page 312  duretic changed to diuretic         |\n    | Page 316  peal changed to peel                |\n    | Page 341  similating changed to simulating    |\n    +-----------------------------------------------+\n\n\n\n\n\nEnd of Project Gutenberg's The American Reformed Cattle Doctor, by George Dadd\n\n*** ","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\nTable of Contents\n\nTitle Page\n\nCopyright Page\n\nDedication\n\nAcknowledgements\n\nChapter 1\n\nChapter 2\n\nChapter 3\n\nChapter 4\n\nChapter 5 - Four years earlier\n\nChapter 6\n\nChapter 7\n\nChapter 8\n\nChapter 9 - Four years earlier\n\nChapter 10\n\nChapter 11 - Four years earlier\n\nChapter 12 - Four years earlier\n\nChapter 13 - Four years earlier\n\nChapter 14\n\nChapter 15 - Four years earlier\n\nChapter 16 - Four years earlier\n\nChapter 17\n\nChapter 18\n\nChapter 19\n\nChapter 20\n\nChapter 21\n\nChapter 22\n\nChapter 23\n\nChapter 24\n\nChapter 25\n\nChapter 26\n\nChapter 27\n\nChapter 28\n\nChapter 29\n\nChapter 30\n\nChapter 31\n\nChapter 32\n\nChapter 33\n\nChapter 34\n\nChapter 35\n\nChapter 36 - Four years earlier\n\nChapter 37\n\nChapter 38\n\nChapter 39\n\nChapter 40\n\nChapter 41\n\nChapter 42\n\nChapter 43\n\nChapter 44\n\nChapter 45\n\nChapter 46\n\nChapter 47\n\nChapter 48\n\nChapter 49\n**THE BERKLEY PUBLISHING GROUP**\n\n**Published by the Penguin Group**\n\n**Penguin Group (USA) Inc. 375 Hudson Street, New York, New York 10014, USA**\n\nPenguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario M4P 2Y3, Canada (a division of Pearson Penguin Canada Inc.)\n\nPenguin Books Ltd., 80 Strand, London WC2R 0RL, England\n\nPenguin Group Ireland, 25 St. Stephen's Green, Dublin 2, Ireland (a division of Penguin Books Ltd.)\n\nPenguin Group (Australia), 250 Camberwell Road, Camberwell, Victoria 3124, Australia\n\n(a division of Pearson Australia Group Pty. Ltd.)\n\nPenguin Books India Pvt. Ltd., 11 Community Centre, Panchsheel Park, New Delhi\u2014110 017, India\n\nPenguin Group (NZ), 67 Apollo Drive, Rosedale, Auckland 0632, New Zealand\n\n(a division of Pearson New Zealand Ltd.)\n\nPenguin Books (South Africa) (Pty.) Ltd., 24 Sturdee Avenue, Rosebank, Johannesburg 2196,\n\nSouth Africa\n\nPenguin Books Ltd., Registered Offices: 80 Strand, London WC2R 0RL, England\n\nThis is a work of fiction. Names, characters, places, and incidents either are the product of the author's imagination or are used fictitiously, and any resemblance to actual persons, living or dead, business establishments, events, or locales is entirely coincidental. The publisher does not have any control over and does not assume any responsibility for author or third-party websites or their content.\n\nCopyright \u00a9 2011 by Bobalinga, Ltd.\n\nMap by Andre Ashton.\n\nAll rights reserved.\n\nNo part of this book may be reproduced, scanned, or distributed in any printed or electronic form without permission. Please do not participate in or encourage piracy of copyrighted materials in violation of the author's rights. Purchase only authorized editions.\n\nACE and the \"A\" design are trademarks of Penguin Group (USA) Inc.\n\nLibrary of Congress Cataloging-in-Publication Data\n\nLawrence, Mark, 1966\u2013\n\np. cm.\u2014(The broken empire; bk. 1)\n\nISBN : 978-1-101-54329-0\n\n1. Princes\u2014Fiction. 2. Revenge\u2014Fiction. I. Title.\n\nPS3612.A9484P75 2011\n\n813'.6\u2014dc22\n\n2010053561\n\n<http:\/\/us.penguingroup.com>\n_To Celyn, the best parts were never broken_\n**ACKNOWLEDGMENTS**\n\nI would like to thank Helen Mazarakis and Sharon Mack for their help and support.\n\n**1**\n\nRavens! Always the ravens. They settled on the gables of the church even before the injured became the dead. Even before Rike had finished taking fingers from hands, and rings from fingers. I leaned back against the gallowspost and nodded to the birds, a dozen of them in a black line, wise-eyed and watching.\n\nThe town-square ran red. Blood in the gutters, blood on the flagstones, blood in the fountain. The corpses posed as corpses do. Some comical, reaching for the sky with missing fingers, some peaceful, coiled about their wounds. Flies rose above the wounded as they struggled. This way and that, some blind, some sly, all betrayed by their buzzing entourage.\n\n\"Water! Water!\" It's always water with the dying. Strange, it's killing that gives me a thirst.\n\nAnd that was Mabberton. Two hundred dead farmers lying with their scythes and axes. You know, I warned them that we do this for a living. I said it to their leader, Bovid Tor. I gave them that chance, I always do. But no. They wanted blood and slaughter. And they got it.\n\nWar, my friends, is a thing of beauty. Those as says otherwise are losing. If I'd bothered to go over to old Bovid, propped up against the fountain with his guts in his lap, he'd probably take a contrary view. But look where disagreeing got him.\n\n\"Shit-poor farm maggots.\" Rike discarded a handful of fingers over Bovid's open belly. He came to me, holding out his takings, as if it was my fault. \"Look! One gold ring. One! A whole village and one fecking gold ring. I'd like to set the bastards up and knock 'em down again. Fecking bog-farmers.\"\n\nHe would too: he was an evil bastard, and greedy with it. I held his eye. \"Settle down, Brother Rike. There's more than one kind of gold in Mabberton.\"\n\nI gave him my warning look. His cursing stole the magic from the scene; besides, I had to be stern with him. Rike was always on the edge after a battle, wanting more. I gave him a look that told him I had more. More than he could handle. He grumbled, stowed his bloody ring, and thrust his knife back in his belt.\n\nMakin came up then and flung an arm about each of us, clapping gauntlet to shoulder-plate. If Makin had a skill, then smoothing things over was it.\n\n\"Brother Jorg is right, Little Rikey. There's treasure aplenty to be found.\" He was wont to call Rike \"Little Rikey,\" on account of him being a head taller than any of us and twice as wide. Makin always told jokes. He'd tell them to those as he killed, if they gave him time. Liked to see them go out with a smile.\n\n\"What treasure?\" Rike wanted to know, still surly.\n\n\"When you get farmers, what else do you always get, Little Rikey?\" Makin raised his eyebrows all suggestive.\n\nRike lifted his visor, treating us to his ugly face. Well, brutal more than ugly. I think the scars improved him. \"Cows?\"\n\nMakin pursed his lips. I never liked his lips, too thick and fleshy, but I forgave him that, for his joking and his deathly work with that flail of his. \"Well, you can have the cows, Little Rikey. Me, I'm going to find a farmer's daughter or three, before the others use them all up.\"\n\nThey went off then, Rike doing that laugh of his, _\"hur, hur, hur,\"_ as if he was trying to cough a fishbone out.\n\nI watched them force the door to Bovid's place opposite the church, a fine house, high roofed with wooden slates and a little flower garden in front. Bovid followed them with his eyes, but he couldn't turn his head.\n\nI looked at the ravens, I watched Gemt and his half-wit brother, Maical, taking heads, Maical with the cart and Gemt with the axe. A thing of beauty, I tell you. At least to look at. I'll agree war smells bad. But we'd torch the place soon enough and the stink would all turn to wood-smoke. Gold rings? I needed no more payment.\n\n\"Boy!\" Bovid called out, his voice all hollow like, and weak.\n\nI went to stand before him, leaning on my sword, tired in my arms and legs all of a sudden. \"Best speak your piece quickly, farmer. Brother Gemt's a-coming with his axe. Chop-chop.\"\n\nHe didn't seem too worried. It's hard to worry a man so close to the worm-feast. Still, it irked me that he held me so lightly and called me \"boy.\" \"Do you have daughters, farmer? Hiding in the cellar maybe? Old Rike will sniff them out.\"\n\nBovid looked up sharp at that, pained and sharp. \"H-how old are you, boy?\"\n\nAgain the \"boy.\" \"Old enough to slit you open like a fat purse,\" I said, getting angry now. I don't like to get angry. It makes me angry. I don't think he caught even that. I don't think he even knew it was me that opened him up not half an hour before.\n\n\"Fifteen summers, no more. Couldn't be more . . .\" His words came slow, from blue lips in a white face.\n\nOut by two, I would have told him, but he'd gone past hearing. The cart creaked up behind me, and Gemt came along with his axe dripping.\n\n\"Take his head,\" I told them. \"Leave his fat belly for the ravens.\"\n\nFifteen! I'd hardly be fifteen and rousting villages.\n\nBy the time fifteen came around, I'd be King!\n\n_Some people are born to rub you the wrong way. Brother Gemt was born to rub the world the wrong way._\n**2**\n\nMabberton burned well. All the villages burned well that summer. Makin called it a hot bastard of a summer, too mean to give out rain, and he wasn't wrong. Dust rose behind us when we rode in; smoke when we rode out.\n\n\"Who'd be a farmer?\" Makin liked to ask questions.\n\n\"Who'd be a farmer's daughter?\" I nodded toward Rike, rolling in his saddle, almost tired enough to fall out, wearing a stupid grin and a bolt of samite cloth over his half-plate. Where he found samite in Mabberton I never did get to know.\n\n\"Brother Rike does enjoy his simple pleasures,\" Makin said.\n\nHe did. Rike had a hunger for it. Hungry like the fire.\n\nThe flames fair ate up Mabberton. I put the torch to the thatched inn, and the fire chased us out. Just one more bloody day in the years' long death throes of our broken empire.\n\nMakin wiped at his sweat, smearing himself all over with sootstripes. He had a talent for getting dirty, did Makin. \"You weren't above those simple pleasures yourself, Brother Jorg.\"\n\nI couldn't argue there. \"How old are you?\" that fat farmer had wanted to know. Old enough to pay a call on his daughters. The fat girl had a lot to say, just like her father. Screeched like a barn owl: hurt my ears with it. I liked the older one better. She was quiet enough. So quiet you'd give a twist here or there just to check she hadn't died of fright. Though I don't suppose either of them was quiet when the fire reached them . . .\n\nGemt rode up and spoiled my imaginings.\n\n\"The Baron's men will see that smoke from ten miles. You shouldn'ta burned it.\" He shook his head, his stupid mane of ginger hair bobbing this way and that.\n\n\"Shouldn'ta,\" his idiot brother joined in, calling from the old grey. We let him ride the old grey with the cart hitched up. The grey wouldn't leave the road. That horse was cleverer than Maical.\n\nGemt always wanted to point stuff out. \"You shouldn'ta put them bodies down the well, we'll go thirsty now.\" \"You shouldn'ta killed that priest, we'll have bad luck now.\" \"If we'd gone easy on her, we'd have a ransom from Baron Kennick.\" I just ached to put my knife through his throat. Right then. Just to lean out and plant it in his neck. \"What's that? What say you, Brother Gemt? Bubble, bubble? Shouldn'ta stabbed your bulgy old Adam's apple?\"\n\n\"Oh no!\" I cried, all shocked-like. \"Quick, Little Rikey, go piss on Mabberton. Got to put that fire out.\"\n\n\"Baron's men will see it,\" said Gemt, stubborn and red-faced. He went red as a beet if you crossed him. That red face just made me want to kill him even more. I didn't, though. You got responsibilities when you're a leader. You got a responsibility not to kill too many of your men. Or who're you going to lead?\n\nThe column bunched up around us, the way it always did when something was up. I pulled on Gerrod's reins and he stopped with a snicker and a stamp. I watched Gemt and waited. Waited until all thirty-eight of my brothers gathered around, and Gemt got so red you'd think his ears would bleed.\n\n\"Where we all going, my brothers?\" I asked, and I stood in my stirrups so I could look out over their ugly faces. I asked it in my quiet voice and they all hushed to hear.\n\n\"Where?\" I asked again. \"Surely it isn't just me that knows? Do I keep secrets from you, my brothers?\"\n\nRike looked a bit confused at this, furrowing his brow. Fat Burlow came up on my right, on my left the Nuban with his teeth so white in that soot-black face. Silence.\n\n\"Brother Gemt can tell us. He knows what should be and what is.\" I smiled, though my hand still ached with wanting my dagger in his neck. \"Where we going, Brother Gemt?\"\n\n\"Wennith, on the Horse Coast,\" he said, all reluctant, not wanting to agree to anything.\n\n\"Well and good. How we going to get there? Near forty of us on our fine oh-so-stolen horses?\"\n\nGemt set his jaw. He could see where I was going.\n\n\"How we going to get there, if we want us a slice of the pie while it's still nice and hot?\" I asked.\n\n\"Lich Road!\" Rike called out, all pleased that he knew the answer.\n\n\"Lich Road,\" I repeated, still quiet and smiling. \"What other way could we go?\" I looked at the Nuban, holding his dark eyes. I couldn't read him, but I let him read me.\n\n\"Ain't no other way.\"\n\nRike's on a roll, I thought, he don't know what game's being played, but he likes his part.\n\n\"Do the Baron's men know where we're going?\" I asked Fat Burlow.\n\n\"War dogs follow the front,\" he said. Fat Burlow ain't stupid. His jowls quiver when he speaks, but he ain't stupid.\n\n\"So . . .\" I looked around them, real slow-like. \"So, the Baron knows where bandits such as ourselves will be going, and he knows the way we've got to go.\" I let that sink in. \"And I just lit a bloody big fire that tells him and his what a bad idea it'd be to follow.\"\n\nI stuck Gemt with my knife then. I didn't need to, but I wanted it. He danced pretty enough too, bubble bubble on his blood, and fell off his horse. His red face went pale quick enough.\n\n\"Maical,\" I said. \"Take his head.\"\n\nAnd he did.\n\nGemt just chose a bad moment.\n\n_Whatever broke Brother Maical left the outside untouched. He looked as solid and as tough and as sour as the rest of them. Until you asked him a question._\n**3**\n\n\"Two dead, two wrigglers.\" Makin wore that big grin of his.\n\nWe'd have camped by the gibbet in any case, but Makin had ridden on ahead to check the ground. I thought the news that two of the four gibbet cages held live prisoners would cheer the brothers.\n\n\"Two,\" Rike grumbled. He'd tired himself out, and a tired Little Rikey always sees a gibbet as half empty.\n\n\"Two!\" the Nuban hollered down the line.\n\nI could see some of the lads exchanging coin on their bets. The Lich Road is as boring as a Sunday sermon. It runs straight and level. So straight it gets so as you'd kill for a left turn or a right turn. So level you'd cheer a slope. And on every side, marsh, midges, midges and more marsh. On the Lich Road it didn't get any better than two caged wrigglers on a gibbet.\n\nStrange that I didn't think to question what business a gibbet had standing out there in the middle of nowhere. I took it as a bounty. Somebody had left their prisoners to die, dangling in cages at the roadside. A strange spot to choose, but free entertainment for my little band nonetheless. The brothers were eager, so I nudged Gerrod into a trot. A good horse, Gerrod. He shook off his weariness and clattered along. There's no road like the Lich Road for clattering along.\n\n\"Wrigglers!\" Rike gave a shout and they were all racing to catch up.\n\nI let Gerrod have his head. He wouldn't let any horse get past him. Not on this road. Not with every yard of it paved, every flagstone fitting with the next so close a blade of grass couldn't hope for the light. Not a stone turned, not a stone worn. Built on a bog, mind you!\n\nI beat them to the wrigglers, of course. None of them could touch Gerrod. Certainly not with me on his back and them all half as heavy again. At the gibbet I turned to look back at them, strung out along the road. I yelled out, wild with the joy of it, loud enough to wake the head-cart. Gemt would be in there, bouncing around at the back.\n\nMakin reached me first, even though he'd rode the distance twice before.\n\n\"Let the Baron's men come,\" I told him. \"The Lich Road is as good as any bridge. Ten men could hold an army here. Them that wants to flank us can drown in the bog.\"\n\nMakin nodded, still hunting his breath.\n\n\"The ones who built this road . . . if they'd make me a castle\u2014\" Thunder in the east cut across my words.\n\n\"If the Road-men built castles, we'd never get in anywhere,\" Makin said. \"Be happy they're gone.\"\n\nWe watched the brothers come in. The sunset turned the marsh pools to orange fire, and I thought of Mabberton.\n\n\"A good day, Brother Makin,\" I said.\n\n\"Indeed, Brother Jorg,\" he said.\n\nSo, the brothers came and set to arguing over the wrigglers. I went and sat against the loot-cart to read while the light stayed with us and the rain held off. The day left me in mind to read Plutarch. I had him all to myself, sandwiched between leather covers. Some worthy monk spent a lifetime on that book. A lifetime hunched over it, brush in hand. Here the gold, for halo, sun, and scrollwork. Here a blue like poison, bluer than a noon sky. Tiny vermilion dots to make a bed of flowers. Probably went blind over it, that monk. Probably poured his life in here, from young lad to grey-head, prettying up old Plutarch's words.\n\nThe thunder rolled, the wrigglers wriggled and howled, and I sat reading words that were older than old before the Road-men built their roads.\n\n\"You're cowards! Women with your swords and axes!\" One of the crow-feasts on the gibbet had a mouth on him.\n\n\"Not a man amongst you. All pederasts, trailing up here after that little boy.\" He curled his words up at the end like a Merssy-man.\n\n\"There's a fella over here got an opinion about you, Brother Jorg!\" Makin called out.\n\nA drop of rain hit my nose. I closed the cover on Plutarch. He'd waited a while to tell me about Sparta and Lycurgus, he could wait some more and not get wet doing it. The wriggler had more to say and I let him tell it to my back. On the road you've got to wrap a book well to keep the rain out. Ten turns of oilcloth, ten more turns the other way, then stash it under a cloak in a saddlebag. A good saddlebag mind, none of that junk from the Thurtans, good double-stitched leather from the Horse Coast.\n\nThe lads parted to let me up close. The gibbet stank worse than the head-cart, a crude thing of fresh-cut timber. Four cages hung there. Two held dead men. _Very_ dead men. Legs dangling through the bars, raven-pecked to the bone. Flies thick about them, like a second skin, black and buzzing. The lads had taken a few pokes at one of the wrigglers, and he didn't look too cheerful for it. In fact he looked as if he'd pegged it. Which was a waste, as we had a whole night ahead of us, and I'd have said as much, but for the wriggler with the mouth.\n\n\"So now the boy comes over! He's finished looking for lewd pictures in his stolen book.\" He sat crouched up in his cage, his feet all bleeding and raw. An old man, maybe forty, all black hair and grey beard and dark eyes glittering. \"Take the pages to wipe your dung, boy,\" he said fierce-like, grabbing the bars all of a sudden, making the cage swing. \"It's the only use you'll get from it.\"\n\n\"We could set a slow fire?\" Rike said. Even Rike knew the old man just wanted us angry, so we'd finish him quick. \"Like we did at the Turston gibbets.\"\n\nA few chuckles went up at that. Not from Makin though. He had a frown on under his dirt and soot, staring at the wriggler. I held up a hand to quiet them down.\n\n\"It'd be a shameful waste of such a fine book, Father Gomst,\" I said.\n\nLike Makin, I'd recognized Gomst through all that beard and hair. Without that accent though he'd have got roasted.\n\n\"Especially an 'On Lycurgus' written in high Latin, not that pidgin-Romano they teach in church.\"\n\n\"You know me?\" He asked it in a cracked voice, weepy all of a sudden.\n\n\"Of course I do.\" I pushed both hands through my lovely locks, and set my hair back so he could see me proper in the gloom. I have the sharp dark looks of the Ancraths. \"You're Father Gomst, come to take me back to school.\"\n\n\"Pr-prin . . .\" He was blubbing now, unable to get his words out. Disgusting really. Made me feel as if I'd bitten something rotten.\n\n\"Prince Honorous Jorg Ancrath, at your service.\" I did my court bow.\n\n\"Wh-what became of Captain Bortha?\" Father Gomst swung gently in his cage, all confused.\n\n\"Captain Bortha, sir!\" Makin snapped a salute and stepped up. He had blood on him from the first wriggler.\n\nWe had us a deathly silence then. Even the chirp and whir of the marsh hushed down to a whisper. The brothers looked from me, back to the old priest, and back to me, mouths hanging open. Little Rikey couldn't have looked more surprised if you'd asked him nine times six.\n\nThe rain chose that moment to fall, all at once as if the Lord Almighty had emptied his chamber pot over us. The gloom that had been gathering set thick as treacle.\n\n\"Prince Jorg!\" Father Gomst had to shout over the rain. \"The night! You've got to run!\" He held the bars of his cage, white-knuckled, wide eyes unblinking in the downpour, staring into the darkness.\n\nAnd through the night, through the rain, over the marsh where no man could walk, we saw them coming. We saw their lights. Pale lights such as the dead burn in deep pools where men aren't meant to look. Lights that'd promise whatever a man could want, and would set you chasing them, hunting answers and finding only cold mud, deep and hungry.\n\nI never liked Father Gomst. He'd been telling me what to do since I was six, most often with the back of his hand as the reason.\n\n\"Run, Prince Jorg! Run!\" old Gomsty howled, sickeningly self-sacrificing.\n\nSo I stood my ground.\n\n_Brother Gains wasn't the cook because he was good at cooking. He was just bad at everything else._\n**4**\n\nThe dead came on through the rain, the ghosts of the bog-dead, of the drowned, and of men whose corpses were given to the mire. I saw Red Kent run blind and flounder in the marsh. A few of the brothers had the sense to take the road when they ran, most ended in the mire.\n\nFather Gomst started praying in his cage, shouting out the words like a shield: \"Father who art in heaven protect thy son. Father who art in heaven.\" Faster and faster, as the fear got into him.\n\nThe first of them came up over the sucking pool, and onto the Lichway. He had a glow about him like moonlight, something that you knew would never warm you. You could see his body limned in the light, with the rain racing through him and bouncing on the road.\n\nNobody stood with me. The Nuban ran, eyes wide in a dark face. Fat Burlow looking as if the blood was let from him. Rike screaming like a child. Even Makin, with a horror on him.\n\nI held my arms wide to the rain. I could feel it beat on me. I didn't have so many years under my belt, but even to me the rain fell like memory. It woke wild nights in me when I stood on the Keep Tower, on the edge above a high fall, near drowned in the deluge and daring the lightning to touch me.\n\n\"Our Father who art in heaven. Father who art . . .\" Gomst started to gabble when the lich came close. It burned with a cold fire and you could feel it licking at your bones.\n\nI kept my arms wide and my face to the rain.\n\n\"My father isn't in heaven, Gomsty,\" I said. \"He's in his castle, counting out his men.\"\n\nThe dead thing closed on me, and I looked in its eyes. Hollow they were.\n\n\"What have you got?\" I said.\n\nAnd it showed me.\n\nAnd I showed it.\n\nThere's a reason I'm going to win this war. Everyone alive has been fighting a battle that grew old before they were born. I cut my teeth on the wooden soldiers in my father's war-room. There's a reason I'm going to win where they failed. It's because I understand the game.\n\n\"Hell,\" the dead man said. \"I've got hell.\"\n\nAnd he flowed into me, cold as dying, edged like a razor.\n\nI felt my mouth curl in a smile. I heard my laughing over the rain.\n\nA knife is a scary thing right enough, held to your throat, sharp and cool. The fire too, and the rack. And an old ghost on the Lichway. All of them might give you pause. Until you realize what they are. They're just ways to lose the game. You lose the game, and what have you lost? You've lost the game.\n\nThat's the secret, and it amazes me that it's mine and mine alone. I saw the game for what it was the night when Count Renar's men caught our carriage. There was a storm that night too, I remember the din of rain on the carriage roof and the thunder beneath it.\n\nBig Jan had fair hauled the door off its hinges to get us out. He only had time for me though. He threw me clear; into a briar patch so thick that the Count's men persuaded themselves I'd run into the night. They didn't want to search it. But I hadn't run. I'd hung there in the thorns, and I saw them kill Big Jan. I saw it in the frozen moments the lightning gave me.\n\nI saw what they did to Mother, and how long it took. They broke little William's head against a milestone. Golden curls and blood. And I'll admit that William was the first of my brothers, and he did have his hooks in me, with his chubby hands and laughing. Since then I've taken on many a brother, and evil ones at that, so I'd not miss one or three. But at the time, it did hurt to see little William broken like that, like a toy. Like something worthless.\n\nWhen they killed him, Mother wouldn't hold her peace, so they slit her throat. I was stupid then, being only nine, and I fought to save them both. But the thorns held me tight. I've learned to appreciate thorns since.\n\nThe thorns taught me the game. They let me understand what all those grim and serious men who've fought the Hundred War have yet to learn. You can only win the game when you understand that it _is_ a game. Let a man play chess, and tell him that every pawn is his friend. Let him think both bishops holy. Let him remember happy days in the shadows of his castles. Let him love his queen. Watch him lose them all.\n\n\"What have you got for me, dead thing?\" I asked.\n\n_It's a game. I will play my pieces._\n\nI felt him cold inside me. I saw his death. I saw his despair. And his hunger. And I gave it back. I'd expected more, but he was only dead.\n\nI showed him the empty time where my memory won't go. I let him look there.\n\nHe ran from me then. He ran, and I chased him. But only to the edge of the marsh. Because it's a game. And I'm going to win.\n**5**\n\n**_Four years earlier_**\n\nFor the longest time I studied revenge to the exclusion of all else. I built my first torture chamber in the dark vaults of imagination. Lying on bloody sheets in the Healing Hall I discovered doors within my mind that I'd not found before, doors that even a child of nine knows should not be opened. Doors that never close again.\n\nI threw them wide.\n\nSir Reilly found me, hanging within the hook-briar, not ten yards from the smoking ruin of the carriage. They almost missed me. I saw them reach the bodies on the road. I watched them through the briar, silver glimpses of Sir Reilly's armour, and flashes of red from the tabards of Ancrath foot soldiers.\n\nMother was easy to find, in her silks.\n\n\"Sweet Jesu! It's the Queen!\" Sir Reilly had them turn her over. \"Gently! Show some respect\u2014\" He broke off with a gasp. The Count's men hadn't left her pretty.\n\n\"Sir! Big Jan's over here, Grem and Jassar too.\" I saw them heave Jan over, then turn to the other guardsmen.\n\n\"They'd better be dead!\" Sir Reilly spat. \"Look for the princes!\"\n\nI didn't see them find Will, but I knew they had by the silence that spread across the men. I let my chin fall back to my chest and watched the dark patterning of blood on the dry leaves around my feet.\n\n\"Ah, hell . . .\" One of the men spoke at last.\n\n\"Get him on a horse. Easy with him,\" Sir Reilly said. A crack ran through his voice. \"And find the heir!\" With more vigour, but no hope.\n\nI tried to call to them, but the strength had run from me, I couldn't even lift my head.\n\n\"He's not here, Sir Reilly.\"\n\n\"They've taken him as a hostage,\" Sir Reilly said.\n\nHe had part of it right, something held me against my will.\n\n\"Set him by the Queen.\"\n\n\"Gentle! Gentle with him . . .\"\n\n\"Secure them,\" Sir Reilly said. \"We ride hard for the Tall Castle.\"\n\nPart of me wanted to let them go. I felt no pain any more, just a dull ache, and even that was fading. A peace folded me with the promise of forgetting.\n\n\"Sir!\" A shout went up from one of the men.\n\nI heard the clank of armour as Sir Reilly strode across to see.\n\n\"Piece of a shield?\" he asked.\n\n\"Found it in the mud, the carriage wheel must have pushed it under.\" The soldier paused. I heard scraping. \"Looks like a black wing to me . . .\"\n\n\"A crow. A crow on a red field. It's Count Renar's colours,\" Reilly said.\n\nCount Renar? I had a name. A black crow on a red field. The insignia flashed across my eyes, seared deep by the lightning of last night's storm. A fire lit within me, and the pain from a hundred hooks burned in every limb. A groan escaped me. My lips parted, dry skin tearing.\n\nAnd Reilly found me.\n\n\"There's something here!\" I heard him curse as the hook-briar found every chink in his armour. \"Quickly now! Pull this stuff apart.\"\n\n\"Dead.\" I heard the whisper from behind Sir Reilly as he cut me free.\n\n\"He's so white.\"\n\nI guess the briar near bled me dry.\n\nSo they fetched a cart and took me back. I didn't sleep. I watched the sky turn black, and I thought.\n\nIn the Healing Hall Friar Glen and his helper, Inch, dug the hooks from my flesh. My tutor, Lundist, arrived while they had me on the table with their knives out. He had a book with him, the size of a Teuton shield, and three times as heavy by the look of it. Lundist had more strength in that wizened old stick of a body than anyone guessed.\n\n\"Those are fire-cleaned knives I hope, Friar?\" Lundist carried the accent of his homelands in the Utter East, and a tendency to leave half of a word unspoken, as if an intelligent listener should be able to fill in the blanks.\n\n\"It is purity of spirit that will keep corruption from the flesh, Tutor,\" Friar Glen said. He spared Lundist a disapproving glance, and returned to his digging.\n\n\"Even so, clean the knives, Friar. Holy office will prove scant protection from the King's ire if the Prince dies in your halls.\" Lundist set his book down on the table beside me, rattling a tray of vials at the far end. He lifted the cover and turned to a marked page.\n\n\" 'The thorns of the hook-briar are like to find the bone.'\" He traced a wrinkled yellow finger down the lines. \"'The points can break off and sour the wound.'\"\n\nFriar Glen gave a sharp jab at that, which made me cry out. He set his knife down and turned to face Lundist. I could see only the friar's back, the brown cloth straining over his shoulders, dark with sweat over his spine.\n\n\"Tutor Lundist,\" he said. \"A man in your profession is wont to think all things may be learned from the pages of a book, or the right scroll. Learning has its place, sirrah, but do not think to lecture me on healing on the basis of an evening spent with an old tome!\"\n\nWell, Friar Glen won that argument. The sergeant-at-arms had to \"help\" Tutor Lundist from the hall.\n\nI guess even at nine I had a serious lack of spiritual purity, for my wounds soured within two days, and for nine weeks I lay in fever, chasing dark dreams along death's borderlands.\n\nThey tell me I raged and howled. That I raved as the pus oozed from slices where the briar had held me. I remember the stink of corruption. It had a kind of sweetness to it, a sweetness that'd make you want to hurl.\n\nInch, the friar's aide, grew tired of holding me down, though he had the arms of a lumberjack. In the end they tied me to my bed.\n\nI learned from Tutor Lundist that the friar would not attend me after the first week. Friar Glen said a devil was in me. How else could a child speak such horror?\n\nIn the fourth week I slipped the bonds that held me to my pallet, and set a fire in the hall. I have no memory of the escape, or my capture in the woods. When they cleared the ruin, they found the remains of Inch, with the poker from the hearth lodged in his chest.\n\nMany times I stood at the Door. I had seen my mother and brother thrown through that doorway, torn and broken, and in dreams my feet would take me to stand there, time and again. I lacked the courage to follow them, held on the barbs and hooks of cowardice.\n\nSometimes I saw the dead-lands across a black river, sometimes across a chasm spanned by a narrow bridge of stone. Once I saw the Door in the guise of the portals to my father's throne-room, but edged with frost and weeping pus from every join. I had but to set my hand upon the handle . . .\n\nThe Count of Renar kept me alive. The promise of his pain crushed my own under its heel. Hate will keep you alive where love fails.\n\nAnd then one day my fever left me. My wounds remained angry and red, but they closed. They fed me chicken in soup, and my strength crept back, a stranger to me.\n\nThe spring came to paint the leaves back upon the trees. I had my strength, but I felt something else had been taken. Taken so completely I could no longer name it.\n\nThe sun returned, and, much to Friar Glen's distaste, Lundist returned to instruct me once more.\n\nThe first time he came, I sat abed. I watched him set out his books upon the table.\n\n\"Your father will see you on his return from Gelleth,\" Lundist said. His voice held a note of reproach, but not for me. \"The death of the Queen and Prince William weigh heavy on him. When the pain eases he will surely come to speak with you.\"\n\nI didn't understand why Lundist should feel the need to lie. I knew my father would not waste time on me whilst it seemed I would die. I knew he would see me when seeing me served some end.\n\n\"Tell me, tutor,\" I said. \"Is revenge a science, or an art?\"\n**6**\n\nThe rain faltered when the spirits fled. I'd only broken the one, but the others ran too, back to whatever pools they haunted. Maybe my one had been their leader; maybe men become cowards in death. I don't know.\n\nAs to my own cowards, they had nowhere to flee, and I found them easily enough. I found Makin first. He, at least, was headed back toward me.\n\n\"So you found a pair then?\" I called to him.\n\nHe paused a moment and looked at me. The rain didn't fall so heavy now, but he still looked like a drowned rat. The water ran in rivulets over his breastplate, in and out of the dents. He checked the marsh to either side, still nervy, and lowered his sword.\n\n\"A man who's got no fear is missing a friend, Jorg,\" he said, and a smile found its way onto those thick lips of his. \"Running ain't no bad thing. Leastways if you run in the right direction.\" He waved a hand toward where Rike wrestled with a clump of bulrushes, the mud up to his chest already. \"Fear helps a man pick his fights. You're fighting them all, my prince.\" And he bowed, there on the Lichway with the rain dripping off him.\n\nI spared a glance for Rike. Maical had similar problems in a pool to the other side of the road. Only he'd got his problems up to the neck.\n\n\"I'm going to fight them all in the end,\" I said to him.\n\n\"Pick your fights,\" Makin said.\n\n\"I'll pick my ground,\" I said. \"I'll pick my ground, but I'm not running. Not ever. That's been done, and we still have the war. I'm going to win it, Brother Makin, it's going to end with me.\"\n\nHe bowed again. Not so deep, but this time I felt he meant it. \"That's why I'll follow you, Prince. Wherever it takes us.\"\n\nFor the moment it took us to fishing brothers out of the mud. We got Maical first, even though Rike howled and cursed us. As the rain thinned, I could see the grey and the head-cart off in the distance. The grey had the sense to keep to the road, even when Maical didn't. If Maical had led the grey into the mire, I'd have left him to sink.\n\nWe pulled Rike out next. When we reached him the mud had almost found his mouth. Nothing but his white face showed above the pool, but that didn't stop him shouting his foulnesses all the way. We found most of them on the road, but six got sucked down too quick, lost forever; probably getting ready to haunt the next band of travellers.\n\n\"I'm going back for old Gomsty,\" I said.\n\nWe'd come a way down the road and the light had pretty much gone. Looking back you couldn't see the gibbets, just grey veils of rain. Out in the marsh the dead waited. I felt their cold thoughts crawling on my skin.\n\nI didn't ask any of them to go with me. I knew none of them would, and it don't do for a leader to ask and be told no.\n\n\"What do you want with that old priest, Brother Jorg?\" Makin said. He was asking me not to go; only he couldn't come out and say it.\n\n\"You still want to burn him up?\" Even the mud couldn't hide Rike's sudden cheer.\n\n\"I do,\" I said. \"But that's not why I'm getting him.\" And I set off back along the Lichway.\n\nThe rain and the darkness wrapped me. I lost the brothers, waiting on the road behind. Gomst and the gibbets lay ahead. I walked in a cocoon of silence, with nothing but the soft words of the rain, and the sound of my boots on the Lichway.\n\nI'll tell you now. That silence almost beat me. It's the silence that scares me. It's the blank page on which I can write my own fears. The spirits of the dead have nothing on it. The dead one tried to show me hell, but it was a pale imitation of the horror I can paint on the darkness in a quiet moment.\n\nAnd there he hung, Father Gomst, priest to the House of Ancrath.\n\n\"Father,\" I said, and I sketched him a bow. In truth though, I was in no mood for play. I had me a hollow ache behind my eyes. The kind that gets people killed.\n\nHe looked at me wide-eyed, as if I was a bog-spirit crawled out of the mire.\n\nI went to the chain that held his cage up. \"Brace yourself, Father.\"\n\nThe sword I drew had slit old Bovid Tor not twenty-four hours before. Now I swung it to free a priest. The chain gave beneath its edge. They'd put some magic, or some devilry, in that blade. Father told me the Ancraths wielded it for four generations, and took it from the House of Or. So the steel was old before we Ancraths first laid hands upon it. Old before I stole it.\n\nThe birdcage fell to the path, hard and heavy. Father Gomst cried out, and his head hit the bars, leaving a livid cross-work across his forehead. They'd bound the cage-door with wire. It gave before the edge of our ancestral sword, twice stolen. I thought of Father for a moment, imaged his face twist in outrage at the use of so high a blade for such lowly work. I've a good imagination, but putting any emotion on the rock of Father's face came hard.\n\nGomst crawled out, stiff and weak. As the old should be. I liked that he had the grace to feel the years on his shoulders. Some the years just toughened.\n\n\"Father Gomst,\" I said. \"Best hurry now, or the marsh dead may come out to scare us with their wailing and a-moaning.\"\n\nHe looked at me then, drawing back as if he'd seen a ghost, then softening.\n\n\"Jorg,\" he said, all full of compassion. Brimming with it, spilling it from his eyes as if it wasn't just the rain. \"What has happened to you?\"\n\nI won't lie to you. Half of me wanted to stick the knife into him there and then, just as with red-faced Gemt. More than half. My hand itched with the need to pull that knife. My head ached with it, as if a vice were tightening against my temples.\n\nI've been known to be contrary. When something pushes me, I shove back. Even if the one doing the pushing is me. It would have been easy to gut him then and there. Satisfying. But the need was too urgent. I felt pushed.\n\nI smiled and said, \"Forgive me, Father, for I have sinned.\"\n\nAnd old Gomsty, though he was stiff from the cage, and sore in every limb, bowed his head to hear my confession.\n\nI spoke into the rain, low and quiet. Loud enough for Father Gomst though, and loud enough for the dead who haunted the marsh about us. I told of the things I'd done. I told of the things I would do. In a soft voice I told my plans to all with ears to hear. The dead left us then.\n\n\"You're the devil!\" Father Gomst took a step back, and clutched the cross at his neck.\n\n\"If that's what it takes.\" I didn't dispute him. \"But I've confessed, and you must forgive me.\"\n\n\"Abomination . . .\" The word escaped him in a slow breath.\n\n\"And more besides,\" I agreed. \"Now forgive me.\"\n\nFather Gomst found his wits at last, but still he held back. \"What do you want with me, Lucifer?\"\n\nA fair question. \"I want to win,\" I said.\n\nHe shook his head at that, so I explained.\n\n\"Some men I can bind with who I am. Some I can bind with where I'm going. Others need to know who walks with me. I've given you my confession. I repent. Now God walks with me, and you're the priest who will tell the faithful that I am His warrior, His instrument, the Sword of the Almighty.\"\n\nA silence stood between us, measured in heartbeats.\n\n\" _Ego te absolvo_.\" Father Gomst got the words past trembling lips.\n\nWe walked back along the path then, and reached the others by and by. Makin had them lined up and ready. Waiting in the dark, with a single torch, and the hooded lantern hung up on the head-cart.\n\n\"Captain Bortha,\" I said to Makin, \"time we set off. We've got a ways before us till we reach the Horse Coast.\"\n\n\"And the priest?\" he asked.\n\n\"Perhaps we'll detour past the Tall Castle, and drop him off.\"\n\nMy headache bit, hard.\n\nMaybe it was something to do with having an old ghost haunt its way through to the very marrow of my bones, but today my headaches felt more like somebody prodding me with a stick, herding me along, and it was really beginning to fuck me off.\n\n\"I think we _will_ call in at the Tall Castle.\" I ground my teeth together against the daggers in my head. \"Hand old Gomsty here over in person. I'm sure my father has been worried about me.\"\n\nRike and Maical gave me stupid stares. Fat Burlow and Red Kent swapped glances. The Nuban rolled his eyes and made his wards.\n\nI looked at Makin, tall, broad in the shoulder, black hair plastered down by the rain. _He's my knight_ , I thought. _Gomst is my bishop, the Tall Castle my rook_. Then I thought of Father. I needed a king. You can't play the game without a king. I thought of Father, and it felt good. After the dead one, I'd begun to wonder. The dead one showed me his hell, and I had laughed at it. But now I thought of Father, and it felt good to know I could still feel fear.\n**7**\n\nWe rode through the night and the Lichway brought us from the marsh. Dawn found us at Norwood, drear and grey. The town lay in ruin. Its ashes still held the acrid ghost of smoke that lingers when the fire is gone.\n\n\"The Count of Renar,\" said Makin at my side. \"He grows bold to attack Ancrath protectorates so openly.\" He shed the roadspeak like a cloak.\n\n\"How can we know who wrought such wickedness?\" Father Gomst asked, his face as grey as his beard. \"Perhaps Baron Kennick's men raided down the Lichway. It was Kennick's men who caged me on the gibbet.\"\n\nThe brothers spread out among the ruins. Rike elbowed Fat Burlow aside, and vanished into the first building, which was nothing but a roofless shell of stone.\n\n\"Shit-poor bog-farmers! Just like fecking Mabberton.\" The violence of his search drowned out any further complaint.\n\nI remembered Norwood on fete day, hung with ribbons. Mother walked with the burgermeister. William and I had treacle-apples.\n\n\"But these were _my_ shit-poor bog-farmers,\" I said. I turned to look at old Gomsty. \"There are no bodies. This is Count Renar's work.\"\n\nMakin nodded. \"We'll find the pyre in the fields to the west. Renar burns them all together. The living and the dead.\"\n\nGomst crossed himself and muttered a prayer.\n\nWar is a thing of beauty, as I've said before, and those who say otherwise are losing. I put a smile on, though it didn't fit me. \"Brother Makin, it seems the Count has made a move. It behoves us, as fellow soldiers, to appreciate his artistry. Have yourself a ride around. I want to know how he played his game.\"\n\nRenar. First Father Gomst, now Renar. As though the spirit in the mire had turned a key, and the ghosts of my past were marching through, one by one.\n\nMakin gave a nod and cantered off. Not into town but out along the stream, following it up to the thickets beyond the market field.\n\n\"Father Gomst,\" I said in my most polite court-voice. \"Pray tell, where were you when Baron Kennick's men found you?\" It made no sense that our family priest should be taken on a raid.\n\n\"The hamlet of Jessop, my prince,\" Gomst replied, wary and looking anywhere but at me. \"Should we not ride on? We'll be safe in the homelands. The raids won't reach past Hanton.\"\n\n_True_ , I thought, _so why would you come out into danger?_ \"The hamlet of Jessop? Can't say I've even heard of it, Father Gomst,\" I said, still nice as nice. \"Which means it won't be much more than three huts and a pig.\"\n\nRike stormed out of the house, blacker than the Nuban with all the ash on him, and spitting mad. He made for the next doorway. \"Burlow, you fat bastard! You set me up!\" If Little Rikey couldn't find himself some loot, then somebody else would pay. Always.\n\nGomst looked glad of the diversion, but I drew his attention back. \"Father Gomst, you were telling me about Jessop.\" I took the reins from his hands.\n\n\"A bog-town, my prince. A nothing. A place where they cut peat for the protectorate. Seventeen huts and perhaps a few more pigs.\" He tried a laugh, but it came out too sharp and nervy.\n\n\"So you journeyed there to offer absolution to the poor?\" I held his eye.\n\n\"Well . . .\"\n\n\"Out past Hanton, out to the edge of the marsh, out into danger,\" I said. \"You're a very holy man, Father.\"\n\nHe bowed his head at that.\n\nJessop. The name rang a bell. A bell with a deep voice, slow and solemn. _Send not to ask for whom the bell tolls . . ._\n\n\"Jessop is where the marsh-tide takes the dead,\" I said. I saw the words on the mouth of old Tutor Lundist as I spoke them. I saw the map behind him, pinned to the study wall, currents marked in black ink. \"It's a slow current but sure. The marsh keeps her secrets, but not forever, and Jessop is where she tells them.\"\n\n\"That big man, Rike, he's strangling the fat one.\" Father Gomst nodded toward the town.\n\n\"My father sent you to look at the dead.\" I didn't let Gomst divert me with small talk. \"Because you'd recognize me.\"\n\nGomst's mouth framed a \"no,\" but every other muscle in him said \"yes.\" You'd think priests would be better liars, what with their job and all.\n\n\"He's still looking for me? After four years!\" Four weeks would have surprised me.\n\nGomst edged back in his saddle. He spread his hands helplessly. \"The Queen is heavy with child. Sageous tells the King it will be a boy. I had to confirm the succession.\"\n\nAh! The \"succession.\" That sounded more like the father I knew. And the Queen? Now that put an edge on the day.\n\n\"Sageous?\" I asked.\n\n\"A heathen bone-picker, newly come to court.\" Gomst spat the words as if they tasted sour.\n\nThe pause grew into a silence.\n\n\"Rike!\" I said. Not a shout, but loud enough to reach him. \"Put Fat Burlow down, or I'll have to kill you.\"\n\nRike let go, and Burlow hit the ground like the three-hundred-pound lump of lard that he was. I guess that of the two, Burlow looked slightly more purple in the face, but only a little. Rike came toward us with his hands out before him, twisting as though he already had them around my neck. \"You!\"\n\nNo sign of Makin, and Father Gomst would be as useful as a fart in the wind against Little Rikey with a rage on him.\n\n\"You! Where's the fecking gold you promised us?\" A score of heads popped out of windows and doors at that. Even Fat Burlow looked up, sucking in a breath as if it came through a straw.\n\nI let my hand slip from the pommel of my sword. It doesn't do to sacrifice too many pawns. Rike had only a dozen yards to go. I swung off Gerrod's saddle and patted his nose, my back to the town.\n\n\"There's more than one kind of gold in Norwood,\" I said. Loud enough but not too loud. Then I turned and walked past Rike. I didn't look at him. Give a man like Rike a moment, and he'll take it.\n\n\"Don't you be telling me about no farmers' daughters this time, you little bastard!\" He followed me roaring, but I'd let the heat out of him. He just had wind and noise now. \"That fecker of a count staked them all out to burn already.\"\n\nI made for Midway Street, leading up to the burgermeister's house from the market field. As we passed him, Brother Gains looked up from the cook-fire he'd started. He clambered to his feet to follow and watch the fun.\n\nThe grain-store tower had never looked like much. It looked less impressive now, all scorched, the stones split in the heat. Before they burned them all away, the grain sacks would have hidden the trapdoor. I found it with a little prodding. Rike huffed and puffed behind me all the time.\n\n\"Open it up.\" I pointed to the ring set in the stone slab.\n\nRike didn't need telling twice. He got down and heaved the slab up as if it weighed nothing. And there they were, barrel after barrel, all huddled up in the dusty dark.\n\n\"The old burgermeister kept the festival beer under the grain-tower. Every local knows that. A little stream runs down there to keep it all nice and cool-like. Looks like, what, twenty? Twenty barrels of golden festival beer.\" I smiled.\n\nRike didn't smile back. He stayed on his hands and knees, and let his eye wander up the blade of my sword. I imagined how it must tickle against his throat.\n\n\"See now, Jorg, Brother Jorg, I didn't mean . . .\" he started. Even with my sword at his neck he had a mean look to him.\n\nMakin clattered up and came to stand at my shoulder. I kept the blade at Rike's throat.\n\n\"I may be little, Little Rikey, but I ain't a bastard,\" I said, soft, in my killing voice. \"Isn't that right, Father Gomst? If I was a bastard, you wouldn't have to risk life and limb to search the dead for me, now would you?\"\n\n\"Prince Jorg, let Captain Bortha kill this savage.\" Gomst must have found his composure somewhere. \"We'll ride on to the Tall Castle and your father\u2014\"\n\n\"My father can damn well wait!\" I shouted. I bit back the rest, angry at being angry.\n\nRike forgot about the sword for a moment. \"What the feck is all this 'prince' shit? What the feck is all this 'Captain Bortha' shit? And when do I get to drink the fecking beer?\"\n\nWe had ourselves as full an audience then as we'd get, all the brothers about us in a circle.\n\n\"Well,\" I said. \"Since you ask so nice, Brother Rike, I'll tell you.\"\n\nMakin raised his brows at me and he took a grip on his sword. I waved him down.\n\n\"The Captain Bortha shit is Makin being Captain Makin Bortha of the Ancrath Imperial Guard. The prince shit is me being the beloved son and heir of King Olidan of the House of Ancrath. And we can drink the beer now, because today is my fourteenth birthday, and how else would you toast my health?\"\n\n_Every brotherhood has a pecking order. With brothers like mine you don't want to be at the bottom of that order. You're liable to get pecked to death. Brother Jobe had just the right mix of whipped cur and rabies to stay alive there._\n**8**\n\nSo we sat on the tumbled stones of the burgermeister's house and drank beer. The brothers drank deep and called out my name. Some had it \"Brother Jorg,\" some had it \"Prince Jorg,\" but all of them saw me with new eyes. Rike watched me, beer-foam in his stubbled beard, the line of my sword across his neck. I could see him weighing the odds, a slow ballet of possibilities working their way across his low forehead. I didn't wait for the word \"ransom\" to bubble to the surface.\n\n\"He wants me dead, Little Rikey,\" I said. \"He sent Gomsty out to find proof I was dead, not to find me. He's got a new queen now.\"\n\nRike gave a grin that had more scowl than grin in it, then belched mightily. \"You ran from a castle with gold and women, to ride with us? What idiot would do that?\"\n\nI sipped my beer. It tasted sour, but that seemed right somehow. \"An idiot who knows he won't win the war with the King's guard at his side,\" I said.\n\n\"What war, Jorg?\" The Nuban sat close by, not drinking. He always spoke slow and serious. \"You want to beat the Count? Baron Kennick?\"\n\n\"The War,\" I said. \"All of it.\"\n\nRed Kent came over from the barrels, his helm brimming with ale. \"Never happen,\" he said. He lifted the helm and half-drained it in four swallows. \"So you're Prince of Ancrath? A copper-crown kingdom. Must be dozens with as good a claim on the high throne. Each of them with their own army.\"\n\n\"More like fifty,\" Rike growled.\n\n\"Closer to a hundred,\" I said. \"I've counted.\"\n\nA hundred fragments of empire grinding away at each other in a never-ending cycle of little wars, feuds, skirmishes, kingdoms waxing, waning, waxing again, lifetimes spent in conflict and nothing changing. Mine to change, to end, to win.\n\nI finished my beer and got up to find Makin.\n\nI didn't have to look far. I found him with the horses, checking his stallion, Firejump.\n\n\"What did you find?\" I asked him.\n\nMakin pursed his lips. \"I found the pyre. About two hundred, all dead. They didn't light it though\u2014probably scared off.\" He waved toward the west. \"They came in on foot, up the marsh road, and over the ridge yonder. Had about twenty archers in the thicket by the stream, to pick off folks that tried to run.\"\n\n\"How many men altogether?\" I asked.\n\n\"Probably a hundred. Foot soldiers most of them.\" He yawned and ran a hand from forehead to chin. \"Two days gone now. We're safe enough.\"\n\nI felt invisible thorns scratching at me, sharp hooks in my skin. \"Come with me,\" I told him.\n\nMakin followed me back to the steps and fallen pillars at the burgermeister's doors. The brothers had Maical staving in a second barrel.\n\n\"What ho, Captain!\" Burlow called out at Makin, his voice still hoarse from Rike's strangling. A laugh went up at that, and I let it run its course. I felt the thorns again, sharp and deep. Sharpening me up for something. Two hundred bodies in a heap. All dead.\n\n\"Cap'n Makin tells me we're going to have company,\" I said.\n\nMakin's brows rose at that but I ignored him. \"Twenty swords, rough men, bandits of the lowest order. Not the sort you'd like to meet,\" I told them. \"Idling along in our direction, weighed down with loot.\"\n\nRike got to his feet all sudden like, his flail rattling at his hip. \"Loot?\"\n\n\"Slugs, I tell you. Growing rich off the destruction of others.\" I showed them my smile. \"Well, my brothers, we're going to have to show them the error of their ways. I want them dead. Every last one. And we'll do it without a scratch. I want trip-pits in the main street. I want brothers hidden in the grain-tower and the Blue Boar tavern. I want Kent, Row, Liar, and the Nuban here, behind these walls, to shoot them down when they come between tower and tavern.\"\n\nThe Nuban hefted his crossbow, a monstrous feat of engineering, worked in the old metal and embellished with the faces of strange gods. Kent tossed the dregs from his helm and set it on his head, ready with his longbow.\n\n\"Now they might come over the ridge instead, so Rike's going to take Maical and six others to hide in the tannery ruins. Anyone comes that way, let them past you, then gut them. Makin will be our scout to give us warning. The good father here and you five there, you're going to stand with me to tempt them in.\"\n\nThe brothers needed no telling. Well, Jobe did, but Rike hauled him out of the beer quick enough and he wasn't gentle about it.\n\n\"Loot!\" Rike shouted the words in his face. \"Get digging trip-pits, shit-brains.\"\n\nThey knew how to set up an ambush those lads. No mistake there. No one knew better how to fight in the ruins. Half the time they'd make the ruins themselves, half the time they'd fight in somebody else's.\n\n\"Burlow, Makin,\" I called them to me as the others set about their tasks. \"I don't need you to scout, Makin,\" I said, keeping my voice low. \"I want you two to go to the thicket by the stream. I want you to hide yourselves. Hide so a bastard could sit on you and still not know you were there. You hide down there and wait. You'll know what to do.\"\n\n\"Prince\u2014Brother Jorg,\" Makin said. He had a big frown on, and his eyes kept straying down the street to old Gomsty praying before the burned-out church. \"What's this all about?\"\n\n\"You said you'd follow wherever I led, Makin,\" I answered. \"This is where it starts. When they write the legend, this will be the first page. Some old monk will go blind illuminating this page, Makin. This is where it all starts.\" I didn't say how short the book might be though.\n\nMakin did that bow of his that's half a nod, and off he went, Fat Burlow hurrying behind.\n\nSo, the brothers dug their traps, laid out their arrows, and hid themselves in what little of Norwood remained. I watched them, cursing their slowness, but holding my peace. And by and by only Father Gomst, my five picked men, and I remained on show. All the rest, a touch over two dozen, lay lost in the ruins.\n\nFather Gomst came to my side, still praying. I wondered how hard he'd pray if he knew what was really coming.\n\nI had an ache in my head now, like a hook inserted behind both eyes, tugging at me. The same ache that started up when the sight of old Gomsty made me think of going home. A familiar pain, one I'd felt at many a turn on the road. Oft times I'd let that pain lead me. But I felt tired of being a fish on a line. I bit back.\n\nI saw the first scout on the marsh road an hour later. Others came soon enough, riding up to join him. I made sure they'd seen the seven of us standing on the burgermeister's steps.\n\n\"Company,\" I said, and pointed the riders out.\n\n\"Shitdarn!\" Brother Elban spat on his boots. I'd chosen Elban because he didn't look like much, a grizzled old streak in his rusty chainmail. He had no hair and no teeth, but he had a bite on him. \"They's no brigands, look at them ponies.\" He lisped the words a bit, having no teeth and all.\n\n\"You know Elban, you might be right,\" I said, and I gave him a smile. \"I'd say they looked more like house-troops.\"\n\n\"Lord have mercy,\" I heard old Gomsty murmur behind me.\n\nThe scouts pulled back. Elban picked up his gear and started for the market field where the horses stood grazing.\n\n\"You don't want to do that, old man,\" I said, softly.\n\nHe turned and I could see the fear in his eyes. \"You ain't gonna cut me down is you, Jorth?\" He couldn't say Jorg without any teeth; I suppose it's a name you've got to put an edge on.\n\n\"I won't cut you down,\" I said. I almost liked Elban; I wouldn't kill him without a good reason. \"Where you going to run to, Elban?\"\n\nHe pointed over the ridge. \"That's the only clear way. Get snarled up elsewise, or worse, back in the marsh.\"\n\n\"You don't want to go over that ridge, Elban,\" I said. \"Trust me.\"\n\nAnd he did. Though maybe he trusted me because he didn't trust me, if you get my meaning.\n\nWe stood and waited. We sighted the main column on the marsh road first, then moments later, the soldiers showed over the ridge. Two dozen of them, house-troops, carrying spears and shields, and above them the colours of Count Renar. The main column had maybe three score soldiers, and following on behind in a ragged line, well over a hundred prisoners, yoked neck to neck. Half a dozen carts brought up the rear. The covered ones would be loaded with provisions, the others held bodies, stacked like cord-wood.\n\n\"House Renar doesn't leave the dead unburned. They don't take prisoners,\" I said.\n\n\"I don't understand,\" Father Gomst said. He'd gone past scared, into stupid.\n\nI pointed to the trees. \"Fuel. We're on the edge of a swamp. There's no trees for miles in this peat bog. They want a good blaze, so they're bringing everyone back here to have a nice big bonfire.\"\n\nI had an explanation for Renar's actions but as to my own, like Father Gomst, I wasn't sure I understood either. Whatever strength I had on the road, it came to me through a willingness to sacrifice. It came on the day I set aside my vengeance on Count Renar as a thing without profit. And yet here I was, in the ruins of Norwood, with a thirst that couldn't be quenched by any amount of festival beer. Waiting for that self-same count. Waiting with too few men, and with every instinct telling me to run. Every instinct, except for that one to hold or break, but never bend.\n\nI could see individual figures at the head of the column quite clearly now. Six riders, chain-armoured, and a knight in heavy plate. The device on his shield came into view as he turned to signal his command. A black crow on a red field, a field of fire. Count Osson Renar wouldn't lead a hundred men into an Ancrath protectorate, so this would be one of his boys. Marclos or Jarco.\n\n\"The brothers won't fight this lot,\" Elban said. He put a hand on my shoulder-plate. \"We might fight a path out through the trees if we get to the horses, Jorth.\"\n\nAlready twenty of the Renar men hastened toward the treeline, holding their longbows before them so they wouldn't snag.\n\n\"No.\" I let out a long sigh. \"I'd best surrender.\"\n\nI held out my hand. \"White flag if you please.\"\n\nThe house-troops had deployed by the time I made my way down toward the main column. My \"flag\" should properly be described as grey. An unwholesome grey at that, torn from Father Gomst's hassock.\n\n\"Noble born!\" I shouted. \"Noble born under flag of truce!\"\n\nThat surprised them. The house-troops, fanned out behind our horses, let me cross the market field unhindered. They looked to be a sorry lot, the metal scales falling from their leathers, rust on their swords. Homebodies they were, too long on the road and not hardened to it.\n\n\"The lad wants to be first on the fire,\" one of them said. A skinny bastard with a boil on each cheek. He got a laugh with that.\n\n\"Noble born!\" I called out. \"Flag o' truce.\" I didn't expect to get this far with my sword.\n\nI caught the stink of the column and could hear the weeping. The prisoners turned blank eyes upon me.\n\nTwo of Renar's riders came forward to intercept me. \"Where'd you steal the armour, boy?\"\n\n\"Go fuck yourself,\" I said. I kept it pleasant. \"Who've you got leading this show then? Marclos?\"\n\nThey exchanged a look at that. A wandering hedge-knight probably wouldn't know one son of the House Renar from the next.\n\n\"It doesn't do to kill a noble prisoner without orders,\" I said. \"Best let the Count-ling decide.\"\n\nBoth riders dismounted. Tall men, veterans by the look of them. They took my sword. The older one, dark bearded with a white scar under both eyes, found my knife. The cut had taken the top of his nose too.\n\n\"You're a bit of an ugly mess aren't you?\" I asked.\n\nHe found the knife in my boot as well.\n\nI had no plan. The pain in my head hadn't left any room for one. I'd ignored the wordless voice that had led me for so long. Ignored it for the joy of being stubborn. And here I was unarmed amongst too many foes, stupid and alone.\n\nI wondered if my brother William was watching me. I hoped my mother wasn't.\n\nI wondered if I was going to die. If they'd burn me, or leave me as a maimed thing for Father Gomst to cart back to the Tall Castle.\n\n\"Everyone has doubts,\" I said as Scar-face finished his search. \"Even Jesu had his moment, and I ain't him.\"\n\nThe man looked at me as if I were mad. Maybe I was, but I'd found my peace. The pain left me and I saw things clear once again.\n\nThey led me to where Marclos sat on his horse, a monstrous stallion, twenty hands if it was one. He lifted his visor then and showed a pleasant face, a bit fat in the cheeks, quite jolly really. Looks, of course, can be deceiving.\n\n\"Who the hell are you?\" he asked.\n\nHe had a nice bit of plate on, acid etched with a silver inlay and burnished so it shone even in the dreariest of light.\n\n\"I said who the hell are you?\" He got some red in his cheeks then. Not so jolly. \"You'll sing on the fire, boy, so you may as well tell me now.\"\n\nI leaned forward as if to hear him. The bodyguards reached for me but I did the old shake and twist. Even with me in armour they were too slow. I used Marclos's foot as a step, where it stuck out from the stirrup, and got up alongside him in no time at all. He had a nice stiletto in a sheath set handy in the saddle, so I had that out and stuck it in his eye. Then we were off. The pair of us galloping out across the market field. How to steal a horse is the first thing you learn on the road.\n\nWe bounced along, with him howling and shaking behind me. A couple of the house-troops tried to bar the way but I rode them down. They weren't going to get up again either; that stallion was fearsome big. The archers might have taken a shot or three, but they couldn't make sense of it from that distance, and we were headed into town.\n\nI could hear the bodyguard thundering along behind. It sounded as if they knocked a few men down themselves. They came close, but we'd taken them by surprise, me and Marclos, and got a start on them. And as we reached the outskirts of Norwood they drew up short.\n\nAt the first building I wheeled sharply, and Marclos obliged by falling off. He hit the ground face first. Another one that wouldn't be getting up again. It felt good, I won't lie about that. I imagined the Count getting the news as he broke his fast. I wondered how he'd like the taste of it. Would he finish his eggs?\n\n\"Men of Renar!\" I shouted it hard enough to hurt my lungs. \"This town stands under the Prince of Ancrath's protection. It will not be surrendered.\"\n\nI turned the horse again and rode on. A few arrows clattered behind me. At the steps I drew up and dismounted.\n\n\"You came back . . .\" Father Gomst looked confused.\n\n\"I did,\" I said. I turned to face Elban. \"No fighting a retreat now, eh, brother?\"\n\n\"You're insane.\" The words escaped in a whisper. For some reason he didn't lisp when he whispered.\n\nThe riders, Marclos's personal guard, led the charge. Now that they had fifty foot soldiers around them, they had found their courage. Up on the ridge the two dozen house-troops took their cue and began to run with the slope. The archers started to emerge from the thicket for better aim.\n\n\"These bastards will burn you alive if they take you that way,\" I said to the five brothers I had with me. Then I paused and I looked them in the eye, each one. \"But they don't want to die. They won't want to go back to the Count either way. Would you take old bonfire-Renar his dead son back, and smooth it over with an 'oh yes, but we killed scavengers . . . there was this boy . . . and an old man with no teeth . . .'?\n\n\"So mark me now. You fight these tame soldiers, and you show them hell. Show them enough of it and the bastards'll break and run.\" I paused and caught Brother Roddat's eye, for he was a weasel and like to run, sense or no sense. \"You stick with me, Brother Roddat.\"\n\nI looked to the thicket, over the heads of the men surging up from the market field and saw an archer fall among the trees. Then another. An armoured figure emerged from the undergrowth. The archers in front of him still had their eyes on the advance. He took the head from the first one with a clean swing. _Thank you, Makin_ , I thought. Fat Burlow came out at a run then, barrelling his armoured bulk into the bowmen.\n\nThe troops from the ridge passed by Rike's position and his lads set to gutting them from behind. Not the sort of odds Little Rikey favoured, but the word \"loot\" always did have an uncanny effect on him.\n\n_ChooOm!_ The Nuban's crossbow shot its load. He couldn't really miss with so many targets, but by rights he shouldn't be able to pick his man with that thing. Even so, both bolts hit the lead rider in the chest and lifted him out of his saddle. Kent and the other two rose from behind the burgermeister's walls. They did a double-take when they saw what was coming, but choices were in short supply and they had plenty of arrows.\n\nThe Renar troops hit our trip-pits at full tilt. I swear I heard the first ankle snap. After that it was all yelling as man went over man. Kent and Liar and Row took the opportunity to send a dozen more arrows into the main mass of the attack. The Nuban loaded his monster again and this time nearly took the head off a horse. The rider went over the top, and the beast fell onto him, brains spilling on the ground.\n\nSome of those soldier boys didn't like the road so much any more and took to finding a way through the ruins. Of course they found more than a way, they found the brothers who were waiting there.\n\nThe archers broke first. There isn't much a man in a padded tunic, with a knife at his hip, can do against a decent swordsman in plate armour. And even Burlow was more than decent.\n\nThree of the riders reached us. We didn't stay on the street to meet them. We fell back into the skeleton of what used to be Decker's Smithy. So they rode in, slowly, ash crunching under hoof. Elban leapt the first one from an alcove over the furnaces. Took that rider down sweet as sweet he did, his sharp little knife hitting home over and over. If you recall, I said Elban had a bite to him.\n\nTwo brothers pulled the second rider down, feinting in and out until they got an opening. He had no room to move his horse around. Should have got off.\n\nThat left me and Scar-face. He had a bit more to him, and had dismounted before he followed us. He came at me slow and easy, the tip of his sword waving before him. He wasn't in a hurry: there's no rush when the best part of fifty men are hard on your heels.\n\n\"Flag o' truce?\" I said, trying to goad him.\n\nHe didn't speak. His lips pressed together in a tight line and he stepped forward, real slow. That's when Brother Roddat stepped up behind him and stuck a sword through the back of his neck.\n\n\"Should have taken your moment, Scar-face,\" I said.\n\nI got back onto the street just in time to meet some huge red-faced bastard of a house-trooper who'd run his way up the hill. He pretty much exploded as the Nuban's bolts hit him. Then they were on us. The Nuban picked up his mattock and Red Kent grabbed his axe. Roddat came past me with his spear and found a man to pin with it.\n\nThey came in two waves. There were the dozen or so who'd kept up with Marclos's bodyguard and then behind them, another twenty coming at a slower pace. The rest lay strewn along the main street or dead in the ruins.\n\nI ran past Roddat and the man he'd skewered. Past a couple of swordsmen who didn't want me bad enough, and I was through the first wave. I could see that skinny bastard with the boils on his cheeks, there in the second wave, the one who'd joked about me on the fire.\n\nMe charging the second wave, howling for Boil-cheeks's blood. That's what broke them. And the men from the ridge? They never reached us. Little Rikey thought they might be carrying loot.\n\nI reckon more than half of the Count's men ran. But they weren't the Count's men any more. They couldn't go back.\n\nMakin came up the hill, blood all over him. He looked like Red Kent the day we found him! Burlow came with him, but he stopped to loot the dead, and of course that involves turning the injured into the dead.\n\n\"Why?\" Makin wanted to know. \"I mean, superb victory, my prince . . . but why in the name of all the hells run such a risk?\"\n\nI held my sword up. The brothers around me took a step back, but to his credit, Makin didn't flinch. \"See this sword?\" I said. \"Not a drop of blood on it.\" I showed it around, then waved it at the ridge. \"And out there there's fifty men who'll never fight for the Count of Renar again. They work for me now. They're carrying a story about a prince who killed the Count's son. A prince who would not retreat. A prince who never retreats. A prince who didn't have to blood his sword to beat a hundred men with thirty.\n\n\"Think about it, Makin. I made Roddat here fight like a madman because I told him if they think you're not going to give up, they'll break. Now I've got fifty enemies who're out there telling everyone who'll listen, 'That Prince of Ancrath, he's not going to break.' It's a simple sum. If they think we won't break, they give up.\"\n\nAll true. It wasn't the reason, but it was all true.\n**9**\n\n**_Four years earlier_**\n\nThe baton struck my wrist with a loud crack. My other hand caught hold as it rose. I tried to twist it free, but Lundist held tight. Even so, I could see his surprise.\n\n\"I see you were paying attention after all, Prince Jorg.\"\n\nIn truth I had been somewhere else, somewhere bloody, but my body has a habit of keeping watch for me at such times.\n\n\"Perhaps you can summarize my points thus far?\" he said.\n\n\"We are defined by our enemies. This holds true for men, and by extension, their countries,\" I said. I'd recognized the book Lundist brought to the lesson. That our enemies shape us was its central thesis.\n\n\"Good.\" Lundist pulled his baton free and pointed to the tablemap. \"Gelleth, Renar, and the Ken Marshes. Ancrath is a product of her environs; these are the wolves at her door.\"\n\n\"The Renar highlands are all I care about,\" I said. \"The rest can go hang.\" I rocked my chair onto the back two legs. \"When Father orders the Gate against Count Renar, I'm going too. I'll kill him myself if they let me.\"\n\nLundist shot me a look, a sharp one, to see if I meant it. There's something wrong about such blue eyes in an old man, but wrong or not he could see to the heart with them.\n\n\"Boys of ten are better occupied with Euclid and Plato. When we visit war, Sun Tzu will be our guide. Strategy and tactics, these are of the mind, these are the tools of prince and king.\"\n\nI did mean it. I had a hunger in me, an aching for the Count's death. The tight lines around Lundist's mouth told me that he knew how deep the hunger ran.\n\nI looked to the high window where sunlight fingered into the schoolroom and turned the dust to dancing motes of gold. \"I will kill him,\" I said. Then, with a sudden need to shock, \"Maybe with a poker, like I killed that ape Inch.\" It galled me to have killed a man and have no memory of it, not even a trace of whatever rage drove me to it.\n\nI wanted some new truth from Lundist. Explain me, to me. Whatever the words, that was my question, youth to old age. But even tutors have their limits.\n\nI rocked forward, set my hands upon the map, and looked to Lundist once more. I saw the pity in him. A part of me wanted to take it, wanted to tell him how I'd struggled against those hooks, how I'd watched William die. A part of me longed to lay it all down, that weight I carried, the acid pain of memory, the corrosion of hate.\n\nLundist leaned across the table. His hair fell around his face, long in the fashion of Orient, so white as to be almost silver. \"We are defined by our enemies\u2014but also we can choose them. Make an enemy of hatred, Jorg. Do that and you could be a great man, but more importantly, maybe a happy one.\"\n\nThere's something brittle in me that will break before it bends. Something sharp that puts an edge on all the soft words I once owned. I don't think the Count of Renar put it there that day they killed my mother, he just drew the razor from its sheath. Part of me longed for a surrender, to take the gift Lundist held before me.\n\nI cut away that portion of my soul. For good or ill, it died that day.\n\n\"When will the Gate march?\" I left nothing in my voice to say I'd heard his words.\n\n\"The Army of the Gate won't march,\" Lundist said. His shoulders held a slump, tiredness or defeat.\n\nThat hit me in the gut, a surprise shot passing my guard. I jumped up, toppling the chair. \"They will!\" How could they not?\n\nLundist turned toward the door. His robes made a dry sound as he moved, like a sigh. Disbelief pinned me to the spot, my limbs strangers to me. I could feel the heat rising in my cheeks. \"How could they not?\" I shouted at his back, angry for feeling like a child.\n\n\"Ancrath is defined by her enemies,\" he said, walking still. \"The Army of the Gate must guard the homeland, and no other army would reach the Count in his halls.\"\n\n\"A queen has died.\" Mother's throat opened again and coloured my vision red. The hooks burned in my flesh once more. \"A prince of the realm, slain.\" Broken like a toy.\n\n\"And there is a price to pay.\" Lundist paused, one hand against the door, leaning as if for support.\n\n\"The price of blood and iron!\"\n\n\"Rights to the Cathun River, three thousand ducats, and five Araby stallions.\" Lundist wouldn't look at me.\n\n\"What?\"\n\n\"River trade, gold, horses.\" Those blue eyes found me over his shoulder. An old hand took the door-ring.\n\nThe words made sense one at a time, not together.\n\n\"The army . . .\" I started.\n\n\"Will not move.\" Lundist opened the door. The day streamed in, bright, hot, laced with the distant laughter of squires at play.\n\n\"I'll go alone. That man will die screaming, by my hand.\" Cold fury crawled across my skin.\n\nI needed a sword, a good knife at least. A horse, a map\u2014I snatched the one before me, old hide, musty, the borders tattooed in Indus ink. I needed . . . an explanation.\n\n\"How? How can their deaths be purchased?\"\n\n\"Your father forged his alliance with the Horse Coast kingdoms through marriage. The strength of that alliance threatened Count Renar. The Count struck early, before the links grew too strong, hoping to remove both the wife, and the heirs.\" Lundist stepped into the light, and his hair became golden, a halo in the breeze. \"Your father hasn't the strength to destroy Renar and keep the wolves from Ancrath's doors. Your grandfather on the Horse Coast will not accept that, so the alliance is dead, Renar is safe. Now Renar seeks a truce so he may turn his strength to other borders. Your father has sold him such a truce.\"\n\nInside I was falling, pitching, tumbling. Falling into an endless void.\n\n\"Come, Prince.\" Lundist held out a hand. \"Let's walk in the sunshine. It's not a day for desk-learning.\"\n\nI bunched the map in my fist, and somewhere in me I found a smile, sharp, bitter, but with a chill to it that held me to my purpose. \"Of course, dear tutor. Let us walk in the sun. It's not a day for wasting\u2014oh no.\"\n\nAnd we went out into the day, and all the heat of it couldn't touch the ice in me.\n\n_Knife-work is a dirty business, yet Brother Grumlow is always clean._\n**10**\n\nWe had ourselves a prisoner. One of Marclos's riders proved less dead than expected. Bad news for him all in all. Makin had Burlow and Rike bring the man to me on the burgermeister's steps.\n\n\"Says his name is Renton. 'Sir' Renton, if you please,\" Makin said.\n\nI looked the fellow up and down. A nice black bruise wrapped itself halfway round his forehead, and an over-hasty embrace with Mother Earth had left his nose somewhat flatter than he might have liked. His moustache and beard could have been neatly trimmed, but caked in all that blood they looked a mess.\n\n\"Fell off your horse did you, Renton?\" I asked.\n\n\"You stabbed Count Renar's son under a flag of truce,\" he said. He sounded a little comical on the \"stabbed\" and \"son.\" A broken nose will do that for you.\n\n\"I did,\" I said. \"I can't think of anything I wouldn't have stabbed him under.\" I held Renton's gaze; he had squinty little eyes. He wouldn't have been much to look at in court finery. On the steps, covered in mud and blood, he looked like a rat's leavings. \"If I were you, I'd be more worried about my own fate than whether Marclos was stabbed in accordance with the right social niceties.\"\n\nThat of course was a lie. If I were in his place, I'd have been looking for an opportunity to stick a knife in me. But I knew enough to know that most men didn't share my priorities. As Makin said, something in me had got broken, but not so broken I didn't remember what it was.\n\n\"My family is rich, they'll ransom me,\" Renton said. He spoke quickly, nervous now, as if he'd just realized his situation.\n\nI yawned. \"No, they're not. If they were rich, you wouldn't be riding in chain armour as one of Marclos's guards.\" I yawned again, stretching my mouth until my jaw cracked. \"Maical, get me a cup of that festival beer, will you?\"\n\n\"Maical's dead,\" Rike said, from behind Sir Renton.\n\n\"Never?\" I said. \"Idiot Maical? I thought God had blessed him with the same luck that looks after drunkards and madmen.\"\n\n\"Well, he's near enough dead,\" Rike said. \"Got him a gut-full of rusty iron from one of Renar's boys. We laid him out in the shade.\"\n\n\"Touching,\" I said. \"Now get my beer.\"\n\nRike grumbled and slapped Jobe into taking the errand. I turned back to Sir Renton. He didn't look happy, but he didn't look as sad as you might expect a man in such a bad place to look. His eyes kept sliding over to Father Gomst. Here's a man with faith in a higher source, I thought.\n\n\"So, Sir Renton,\" I said. \"What brings young Marclos to Ancrath's protectorates? What does the Count think he's up to?\"\n\nSome of the brothers had gathered around the steps for the show, but most were still looting the dead. A man's coin is nice and portable, but the brothers wouldn't stop there. I expected the head-cart to be heaped with arms and armour when we left. Boots too; there's three coppers in a well-made pair of boots.\n\nRenton coughed and wiped at his nose, spreading black gore across his face. \"I don't know the Count's plans. I'm not privy to his private council.\" He looked up at Father Gomst. \"As God is my witness.\"\n\nI leaned in close to him. He smelled sour, like cheese in the sun. \"God is your witness, Renton, he's going to watch you die.\"\n\nI let that sink in. I gave old Gomsty a smile. \"You can look after this knight's soul, Father. The sins of the flesh though\u2014they're all mine.\"\n\nRike handed me my cup of beer, and I had a sip. \"The day you're tired of looting, Little Rikey, is the day you're tired of life,\" I said. It got a chuckle from the brothers on the steps. \"Why're you still here when you could be cutting up the dead in search of a golden liver?\"\n\n\"Come to see you put the hurt on Rat-face,\" Rike said.\n\n\"You're going to be disappointed then,\" I said. \"Sir Rat-face is going to tell me everything I want to know, and I'm not even going to have to raise my voice. When I'm done, I'm going to hand him over to the new burgermeister of Norwood. The peasants will probably burn him alive, and he'll count it the easy way out.\" I kept it conversational. I find it's the coldest threats that reach the deepest.\n\nOut in the marshes I'd made a dead man run in terror, with nothing more than what I keep inside. It occurred to me that what scared the dead might worry the living a piece too.\n\nSir Renton didn't sound too scared yet though. \"You stabbed the better man today, boy, and there's a better man before you. You're nothing more than shit on my shoe.\" I'd hurt his pride. He was a knight after all, and here was a beardless lad making mock. Besides, the best I'd offered was an \"easy\" burning. Nobody considers that the soft option.\n\n\"When I was nine, the Count of Renar tried to have me killed,\" I said. I kept my voice calm. It wasn't hard. I was calm. Anger carries less horror with it, men understand anger. It promises resolution; maybe bloody resolution, but swift. \"The Count failed, but I watched my mother and my little brother killed.\"\n\n\"All men die,\" Renton said. He spat a dark and bloody mess onto the steps. \"What makes you so special?\"\n\nHe had a good point. What made my loss, my pain, any more important than everyone else's?\n\n\"That's a good question,\" I said. \"A damn good question.\"\n\nIt was. There weren't but a handful of the prisoners we'd taken from Marclos's train who hadn't seen a son or a husband, a mother or a lover, killed. And killed in the past week. And this was my soft option, the mercies of these peasants compared to the attention of a young man whose hurt stood four years old.\n\n\"Consider me a spokesman,\" I said. \"When it comes to stageacting, some men are more eloquent than others. It's given to particular men to have a gift with the bow.\" I nodded to the Nuban. \"Some men can knock the eye out of a bull at a thousand paces. They don't aim any better for wanting it, they don't shoot straighter because they're justified. They just shoot straighter. Now me, I just . . . avenge myself better than most. Consider it a gift.\"\n\nRenton laughed at that and spat again. This time I saw part of a tooth in the mess. \"You think you're worse than the fire, boy?\" he asked. \"I've seen men burn. A lot of men.\"\n\nHe had a point. \"You've a lot of good points, Sir Renton,\" I said.\n\nI looked around at the ruins. Tumbled walls in the most, and blackened timber skeletons where roofs had kept a lid on folk's lives for year after year. \"It's going to take a lot of rebuilding,\" I said. \"A lot of hammers and a lot of nails.\" I sipped my beer. \"A strange thing\u2014nails will hold a building together, but there's nothing better for taking a man apart.\" I held Sir Renton's rat-like eyes, dark and beady. \"I don't enjoy torturing people, Sir Renton, but I'm good at it. Not world-class you understand. Cowards make the best torturers. Cowards understand fear and they can use it. Heroes on the other hand, they make terrible torturers. They don't see what motivates a normal man. They misunderstand everything. They can't think of anything worse than besmirching your honour. A coward on the other hand; he'll tie you to a chair and light a slow fire under you. I'm not a hero or a coward, but I work with what I've got.\"\n\nRenton had the sense to pale at that. He reached out a muddy hand to Father Gomst. \"Father, I've done nothing but serve my master.\"\n\n\"Father Gomst will pray for your soul,\" I said. \"And forgive me the sins I incur in detaching it from your body.\"\n\nMakin pursed those thick lips of his. \"Prince, you've spoken about how you'd break the cycle of revenge. You could start here. You could let Sir Renton go.\"\n\nRike gave him a look as if he'd gone mad. Fat Burlow covered a chuckle.\n\n\"I have spoken about that, Makin,\" I said. \"I will break the cycle.\" I drew my sword and laid it across my knees. \"You know how to break the cycle of hatred?\" I asked.\n\n\"Love,\" said Gomst, all quiet-like.\n\n\"The way to break the cycle is to kill every single one of the bastards that fucked you over,\" I said. \"Every last one of them. Kill them all. Kill their mothers, kill their brothers, kill their children, kill their dog.\" I ran my thumb along the blade of my sword and watched the blood bead crimson on the wound. \"People think I hate the Count, but in truth I'm a great advocate of his methods. He has only two failings. Firstly, he goes far, but not far enough. Secondly, he isn't me. He taught me valuable lessons though. And when we meet, I will thank him for it, with a quick death.\"\n\nOld Gomsty started at that. \"Count Renar did you wrong, Prince Jorg. Forgive him, but don't thank him. He'll burn in Hell for what he did. His immortal soul will suffer for eternity.\"\n\nI had to laugh out loud at that. \"Churchmen, eh? Love one minute, forgiveness the next, and then it's eternity on fire. Well, rest at ease, Sir Renton. I've no designs on your immortal soul. Whatever happens between us, it will all be over in a day or two. Three at most. I'm not the most patient of men, so it will end when you tell me what I want to know, or I get bored.\"\n\nI got up from my step and went to crouch by Sir Renton. I patted his head. They'd tied his hands behind him, and I had my chainmail gauntlets on, so if he had a mind to bite, it'd do him no good.\n\n\"I swore to Count Renar,\" he said. He tried to pull away, and he craned his neck to look at old Gomsty. \"Tell him, Father, I swore before God. If I break my vow, I'll burn in Hell.\"\n\nGomst came to lay his hand on Renton's shoulder. \"Prince Jorg, this knight has made a holy vow. There are few oaths more sacred than that of a knight to his liege lord. You should not ask him to break it. Nor should any threat against the flesh compel a man to betray a covenant and forever place his soul in the fires of the Devil.\"\n\n\"Here's a test of faith for you, Sir Renton,\" I said. \"I'll tell you my tale and we'll see whether you want to tell me the Count's plans when I'm done.\" I settled down on the step beside him and swigged my beer. \"When I first took to the road I was, oh, ten years of age. I'd a lot of anger in me then, and a need to know how the world worked. You see, I'd watched the Count's men kill my brother, William, and slit Mother open. So I knew that the way I'd thought things were supposed to work was wrong. And of course, I fell in with bad sorts\u2014didn't I, Rikey?\"\n\nRike gave that laugh of his: _\"hur, hur, hur_. _\"_ I think he just made the sound when he thought we expected a laugh. It didn't have any joy in it.\n\n\"I tried my hand at torture then. I wondered if I was supposed to be evil. I thought maybe I'd had a message from God to take up the Devil's work.\"\n\nI heard Gomst muttering at that one, prayers or condemnation. It was true too. For the longest time I looked for a message in it all, to work out what I was supposed to be doing.\n\nI laid my hand on Renton's shoulder. He sat there with my hand on his left shoulder, and Gomst's hand on his right. We could have been the Devil and the angel from those old scrolls, whispering in his ears.\n\n\"We caught Bishop Murillo down by Jedmire Hill,\" I said. \"I'm sure you heard about the loss of his mission? Anyhow, the brothers let me have the bishop. I was something of a mascot to them back then.\"\n\nThe Nuban stood and walked off down the hill. I let him go. The Nuban didn't have the stomach for this kind of thing. That made me feel\u2014I don't know\u2014dirty? I liked the Nuban, though I didn't let it show.\n\n\"Now, Bishop Murillo was full of harsh words and judgement. He had plenty to tell me about hellfire and damnation. We sat a while and discussed the business of souls. Then I hammered a nail into his skull. Just here.\" I reached out and touched the spot on Renton's greasy head. He flinched back like he'd been stung. \"The bishop changed his tune a bit after that,\" I said. \"In fact every time I knocked a new nail into him, he changed his tune. After a while he was a very different man. Did you know you can break a man into his parts like that? One nail will bring back memories of childhood. Another will make him rage, or sob, or laugh. In the end it seems we're just toys, easy to break and hard to mend.\n\n\"I hear that the nuns at Saint Alstis still have Bishop Murillo in their care. He's a very different person now. He clutches at their habits and slurs awful things at them, so they say. Where the soul of that proud and pious man we took from the papal caravan is\u2014well, I can't tell you.\"\n\nWith that, I \"magicked\" a nail into my fingers. A rusty spike, three inches long. The man wet himself. There on the steps. Burlow gave an oath and kicked him, hard. When Renton got his breath back, he told me everything he knew. It took almost an hour. Then we gave him to the peasants and they burned him.\n\nI watched the good folk of Norwood dance around their fire. I watched the flames lick above their heads. There's a pattern in fire, as if something's written there, and there's folk who say they can read it too. Not me, though. It would have been nice to find some answers in the flames. I had questions: it was a thirst for the Count's blood that had set me on the road. But somehow I'd given it up. Somehow I set it aside and told myself it was a sacrifice to strength.\n\nI sipped my beer. Four years on the road. Always going somewhere, always doing something, but now, with my feet pointed toward home, it felt like I'd been lost all that time. Lost or led.\n\nI tried to remember when I'd given up on the Count, and why. Nothing came to me, just the glimpse of my hand on a door, and the sensation of falling into space.\n\n\"I'm going home,\" I said.\n\nThe dull ache between my eyes became a rusty nail, driven deep. I finished my beer, but it did nothing for me. I had an older kind of thirst.\n**11**\n\n**_Four years earlier_**\n\nI followed Lundist out into the day.\n\n\"Wait.\" He held his baton to my chest. \"It never pays to walk blind. Especially not in your own castle where familiarity hides so much\u2014even when we have the eyes to see.\"\n\nWe stood for a moment on the steps, blinking away the sunlight, letting the heat soak in. Release from the gloom of the schoolroom held no great surprise. Four days in seven my studies kept me at Lundist's side, sometimes in the schoolroom, the observatory, or library, but as often as not the hours would pass in a hunt for wonders. Whether it was the mechanics of the siege machinery held in the Arnheim Hall, or the mystery of the Builder-light that shone without flame in the salt cellar, every part of the Tall Castle held a lesson that Lundist could tease out.\n\n\"Listen,\" he said.\n\nI knew this game. Lundist held that a man who can observe is a man apart. Such a man can see opportunities where others see only the obstacles on the surface of each situation.\n\n\"I hear wood on wood. Training swords. The squires at play,\" I said.\n\n\"Some might not call it play. Deeper! What else?\"\n\n\"I hear birdsong. Skylarks.\" There it was, a silver chain of sound, dropped from on high, so sweet and light I'd missed it at first.\n\n\"Deeper.\"\n\nI closed my eyes. What else? Green fought red on the back of my eyelids. The clack of swords, the grunts, panting, muted scuffle of shoe on stone, the song of skylarks. What else?\n\n\"Fluttering.\" On the edge of hearing\u2014I was probably imagining it.\n\n\"Good,\" Lundist said. \"What is it?\"\n\n\"Not wings. It's deeper than that. Something in the wind,\" I said.\n\n\"There's no wind in the courtyard,\" Lundist said.\n\n\"Up high then.\" I had it. \"A flag!\"\n\n\"Which flag? Don't look. Just tell me.\" Lundist pressed the baton harder.\n\n\"Not the festival flag. Not the King's flag, that's flown from the north wall. Not the colours, we're not at war.\" No, not the colours. Any curiosity in me died at that reminder of Count Renar's purchase. I wondered, if they'd slain me also, would the price of a pardon have been higher? An extra horse?\n\n\"Well?\" Lundist asked.\n\n\"The execution flag, black on scarlet,\" I said.\n\nIt's always been that way with me. Answers come when I stop trying to think it through and just speak. The best plan I'll come up with is the one that happens when I act.\n\n\"Good.\"\n\nI opened my eyes. The light no longer pained me. High above the courtyard the execution flag streamed in a westerly breeze.\n\n\"Your father has ordered the dungeons cleared,\" Lundist said. \"There will be quite a crowd come Saint Crispin's Day.\"\n\nI knew that to be understatement. \"Hangings, beheadings, impalement, oh my!\"\n\nI wondered if Lundist would seek to shield me from the proceedings. The corner of my mouth twitched, hooked on the notion that he might imagine I'd not seen worse already. For the mass executions of the previous year, Mother had taken us to visit Lord Nossar at his estates in Elm. William and I had the fort of Elm almost to ourselves. Later I learned that most of Ancrath had converged on the Tall Castle to watch the sport.\n\n\"Terror and entertainment are weapons of statehood, Jorg.\" Lundist kept his tone neutral, his face inscrutable save for a tightness in the lips suggesting that the words carried a bad taste. \"Execution combines both elements.\" He gazed at the flag. \"Before I journeyed and fell slave to your mother's people, I dwelt in Ling. In the Utter East pain is an artform. Rulers make their reputations, and that of their land, on extravagances of torture. They compete at it.\"\n\nWe watched the squires spar. A tall knight gave instruction, sometimes with his fist.\n\nFor several minutes I said nothing. I imagined Count Renar at the mercy of a Ling torture-master.\n\nNo\u2014I wanted his blood and his death. I wanted him to die knowing why he died, knowing who held the sword. But his pain? Let him do his burning in Hell.\n\n\"Remind me not to go to Ling, Tutor,\" I said.\n\nLundist smiled, and led off across the courtyard. \"It's not on your father's maps.\"\n\nWe passed close by the duelling square, and I recognized the knight by his armour, a dazzling set of field plate with silver inlaid into acid-etched scrollwork across the breastplate.\n\n\"Sir Makin of Trent,\" I said. I turned to face him. Lundist walked on for a few paces before realizing I'd left his side.\n\n\"Prince Honorous.\" Sir Makin offered me a curt bow. \"Keep that guard up, Cheeves!\" A barked instruction to one of the older boys.\n\n\"Call me Jorg,\" I said. \"I hear my father has made you Captain of the Guard.\"\n\n\"He found fault with my predecessor,\" Sir Makin said. \"I hope to fulfil my duties more to the King's pleasing.\"\n\nI'd not seen Sir Grehem since the attack on our coach. I suspected that the incident cost the former Captain of the Guard rather more than it cost Count Renar.\n\n\"Let us hope so,\" I said.\n\nMakin ran a hand through his hair, dark and beaded with sweat from the heat of the day. He had a slightly fleshy face, expressive, but you wouldn't mistake him for someone without mettle.\n\n\"Won't you join us, Prince Jorg? A good right feint will serve you better in times of trouble than any amount of book learning.\" He grinned. \"If your wounds are recovered sufficiently, of course.\"\n\nLundist settled a hand on my shoulder. \"The Prince is still troubled by his injuries.\" He fixed those too-blue eyes of his on Sir Makin. \"You might consider reading Proximus's thesis on the defence of royals. If you wish to avoid Sir Grehem's fate, that is. It's in the library.\" He moved to steer me away. I resisted on nothing more than principle.\n\n\"I think the Prince knows his own mind, Tutor.\" Sir Makin flashed Lundist a broad smile. \"Your Proximus can keep his advice. A knight trusts in his own judgement, and the weight of his sword.\"\n\nSir Makin took a wooden sword from the cart on his left, and offered it to me, hilt first. \"Come, my prince. Let's see what you've got. Care to spar against young Stod here?\" He pointed out the smallest of the squires, a slight lad maybe a year my senior.\n\n\"Him.\" I pointed to the biggest of them, a hulking lout of fifteen with a shock of ginger hair. I took the sword.\n\nSir Makin raised an eyebrow, and grinned all the wider. \"Robart? You'll fight Robart, will you now?\"\n\nHe strode to the boy's side and clapped a hand to the back of his neck. \"This here is Robart Hool, third son of the House of Arn. Of all this sorry lot, he's the one who might have a chance to earn his spurs one day. Got himself a way with the blade has our Master Hool.\" He shook his head. \"Try Stod.\"\n\n\"Try none of them, Prince Jorg.\" Lundist kept the irritation from his voice, almost. \"This is foolishness. You are not yet recovered.\" He shot a look at the grinning guard captain. \"King Olidan will not take kindly to a relapse in his only heir.\"\n\nSir Makin frowned at that, but I could see it had gone too far for his pride to let him take instruction. \"Go easy on him, Robart. Really easy.\"\n\n\"If this ginger oaf doesn't do his level best, I'll make sure the closest he gets to being a knight is clearing the horse dung after the joust,\" I said.\n\nI advanced on the squire, my head craned to look him in the face. Sir Makin stepped between us, a training sword in his left hand. \"A quick test first, my prince. I've got to know you've enough of the basics not to get yourself hurt.\"\n\nThe point of his blade clacked against mine, and slipped away, angled for my face. I slapped it aside, and made a half-lunge. The knight tamed my thrust easily enough; I tried to slide to his guard but he cut to my legs and I barely held him.\n\n\"Not bad. Not bad.\" He inclined his head. \"You've had decent instruction.\" He pursed his lips. \"You're what, twelve?\"\n\n\"Ten.\" I watched him return the trainer to the cart. He was right-handed.\n\n\"All right.\" Sir Makin motioned the squires into a circle around us. \"Let's have us a duel. Robart, show the Prince no mercies. He's good enough to lose without serious injury to anything but his pride.\"\n\nRobart squared up to me, all freckles and confidence. The moment seemed to come into focus. I felt the sun on my skin, the grit between the soles of my shoes and the flagstones.\n\nSir Makin held his hand up. \"Wait for it.\"\n\nI heard the silver voices of the skylarks, invisible against the blue vaults above us. I heard the flapping of the execution flag.\n\n\"Fight!\" The hand dropped.\n\nRobart came in fast, swinging low. I let my sword fall to the ground. His blow caught me on the right side, just below the ribs. I'd have been cut in two . . . if it hadn't been made of wood. But it was. I hit him in the throat, with the edge of my hand, an eastern move that Lundist had showed me. Robart went down as if a wall had dropped on him.\n\nI watched him writhe, and for an instant I saw Inch in the Healing Hall on his hands and knees with the fire all around us and the blood pulsing from his back. I felt the poison in my veins, the hooks in my flesh, the simple need to kill\u2014as pure an emotion as I have ever known.\n\n\"No.\" I found Lundist's hand on my wrist, stopping me as I reached for the boy. \"It's enough.\"\n\n_It's never enough._ Words in my head, spoken by a voice not my own, a voice remembered from the briar and the fever-bed.\n\nFor several moments we watched the lad choke on the floor, and turn crimson.\n\nThe strangeness left me. I picked up my sword and returned it to Sir Makin.\n\n\"Actually, Proximus is yours, Captain, not Lundist's,\" I said. \"Proximus was a Borthan scholar, seventh century. One of your ancestors. Perhaps you should read him after all. I'd hate to have nothing but Robart here, and his judgement, between me and my enemies.\"\n\n\"But . . .\" Sir Makin chewed his lip. He seemed to have run out of objections after \"but.\"\n\n\"He cheated.\" Young Stod found the words for all of them.\n\nLundist had already started walking. I turned to follow him, then looked back.\n\n\"It's not a game, Sir Makin. You teach these boys to play by the rules, and they're going to lose. It's not a game.\"\n\nAnd when we make a mistake, we can't buy our way out of it. Not with horses, not with gold.\n\nWe reached the Red Gate on the far side of the courtyard.\n\n\"That boy could die,\" Lundist said.\n\n\"I know,\" I said. \"Take me to see these prisoners that Father's to have killed.\"\n**12**\n\n**_Four years earlier_**\n\nMore of the Tall Castle lies below the ground than above. It should be called the Deep Castle, really. It took us a while to reach the dungeons. We heard the shrieks from a level up, through walls of Builder-stone.\n\n\"This visit is, perhaps, a bad idea,\" Lundist said, pausing before an iron door.\n\n\"It's my idea, Tutor,\" I said. \"I thought you wanted me to learn by my mistakes?\"\n\nAnother scream reached us, guttural with a hoarse edge to it, an animal sound.\n\n\"Your father wouldn't approve of this visit,\" Lundist said. He pressed his lips in a tight line, troubled.\n\n\"That's the first time you've called on Father's wisdom to resolve an issue. Shame on you, Tutor Lundist.\" Nothing would turn me back now.\n\n\"There are things that children\u2014\"\n\n\"Too late, that horse already bolted. Stable burned.\" I brushed past him and rapped on the door with the hilt of my dagger. \"Open up.\"\n\nA rattle of keys, and the door slid inward on oiled hinges. The wave of stench that hit me nearly took my breath. A warty old fellow in warder's leathers leaned into view and opened his mouth to speak.\n\n\"Don't,\" I said, holding the business end of my dagger toward his tongue.\n\nI walked on, Lundist at my heels.\n\n\"You always told me to look and make my own judgement, Lundist,\" I said. I respected him for that. \"No time to get squeamish.\"\n\n\"Jorg . . .\" He was torn, I could hear it in his voice, wracked between emotions I couldn't understand, and logic that I could. \"Prince\u2014\"\n\nThe cry rang out again, much louder now. I'd heard the sound before. It pushed at me, trying to force me away. The first time I heard that kind of pain, my mother's pain, something held me back. I'll tell you it was the hook-briar which held me fast. I'll show you the scars. But in the night, before the dreams come, a voice whispers to me that it was fear that held me back, terror that rooted me in the briar, safe while I watched them die.\n\nAnother scream, more terrible and more desperate than any before. I felt the hooks in my flesh.\n\n\"Jorg!\"\n\nI shook Lundist's hands from me, and ran toward the sound.\n\nI didn't have far to run. I pulled up short at the entrance to a wide room, torch-lit, with cell doors lining three sides. At the centre, two men stood on opposite sides of a table, to which a third man had been secured with chains. The larger of the two warders held an iron poker, one end in a basket of glowing coals.\n\nNone of the three noted my arrival, nor did any of the faces pressed to the barred windows in the cell doors turn my way. I walked in. I heard Lundist arrive at the entrance and stop to take in the scene, as I had.\n\nI drew close and the warder without the iron glanced my way. He jumped as if stung. \"What in the\u2014\" He shook his head to clear his vision. \"Who? I mean . . .\"\n\nI'd imagined the torturers would be terrifying men with cruel faces, thin lips, hooked noses, the eyes of soulless demons. I think I found their ordinariness more of a shock. The shorter of the two looked a touch simple, but in a friendly way. Mild I'd call him.\n\n\"Who're you?\" This one had a more brutish cast to him, but I could picture him at ale, laughing, or teaching his son pitch-ball.\n\nI hadn't any of my court weeds on, just a simple tunic for the schoolroom. There was no reason for warders to recognize me. They would enter the vaults through the Villains' Gate and had probably never walked in the castle above.\n\n\"I'm Jorg,\" I said, in a servant's accent. \"My uncle paid old Wart-face at the door to let me see the prisoners.\" I pointed toward Lundist. \"We're going to the executions tomorrow. I wanted to see criminals close up first.\"\n\nI wasn't looking at the warders now. The man on the table held my gaze. I'd seen only one black skin before, a slave to some noble visiting Father's court from the south. But that man was brown. The fellow on the table had skin blacker than ink. He turned his head to face my way, slow as if it weighed like lead. The whites of his eyes seemed to shine in all that blackness.\n\n\"Wart-face? Heh, I like that.\" The big warder relaxed and took up his iron again. \"If there's two ducats in it for me and Grebbin here, then I reckon you can stay and watch this fellow squeal.\"\n\n\"Berrec, it don't seem right.\" Grebbin furrowed his broad forehead. \"He's a young-un an' all.\"\n\nBerrec pulled the poker from the coals and held it toward Grebbin. \"You don't want to stand between me and a ducat, my friend.\"\n\nThe black man's naked chest glistened below the glowing point. Ugly burns marked his ribs, red flesh erupting like new-ploughed furrows. I could smell the sweet stench of roasted meat.\n\n\"He's very black,\" I said.\n\n\"He's a Nuban is what he is,\" Berrec said, scowling. He gave the poker a critical look and returned it to the fire.\n\n\"Why are you burning him?\" I asked. I didn't feel easy under the Nuban's scrutiny.\n\nThe question puzzled them for a moment. Grebbin's frown deepened.\n\n\"He's got the devil in him,\" Berrec said at last. \"All them Nubans have. Heathens, the lot of them. I heard that Father Gomst, him as leads the King himself in prayer, says to burn the heathen.\" Berrec laid a hand on the Nuban's stomach, a disturbingly tender touch. \"So we're just crisping this one up a bit, before the King comes to watch him killed on the morrow.\"\n\n\"Executed.\" Grebbin pronounced the word with the precision of one who has practised it many times.\n\n\"Executed, killed, what's the difference? They all end up for the worms.\" Berrec spat into the coals.\n\nThe Nuban kept his eyes on me, a quiet study. I felt something I couldn't name. I felt somehow wrong for being there. I ground my teeth together and met his gaze.\n\n\"What did he do?\" I asked.\n\n\"Do?\" Grebbin snorted. \"He's a prisoner.\"\n\n\"His crime?\" I asked.\n\nBerrec shrugged. \"Getting caught.\"\n\nLundist spoke from the doorway. \"I believe . . . Jorg, that all of the prisoners for execution are bandits, captured by the Army of the March. The King ordered the action to prevent raids across the Lichway into Norwood and other protectorates.\"\n\nI broke my gaze from the Nuban's, and let it slide across the marks of his torture. Where the skin remained unburned, patterns of raised scars picked out symbols, simple in design but arresting to the eye. A soiled loincloth hung across his hips. His wrists and ankles were bound with iron shackles secured with a basic pin-lock. Blood oozed along the short chains anchoring them to the table.\n\n\"Is he dangerous?\" I asked. I moved close. I could taste the burned meat.\n\n\"Yes.\" The Nuban smiled as he said it, his teeth bloody.\n\n\"You shut your heathen hole, you.\" Berrec yanked the iron from the coals. A shower of sparks flew up as he lifted the white-hot poker to eye-level. The glow made something ugly of his face. It reminded me of a wild night when the lightning lit the faces of Count Renar's men.\n\nI turned to the Nuban. If he'd been watching the iron, I'd have left him to it.\n\n\"Are you dangerous?\" I asked him.\n\n\"Yes.\"\n\nI pulled the pin from the manacle on his right wrist.\n\n\"Show me.\"\n**13**\n\n**_Four years earlier_**\n\nThe Nuban moved fast, but it wasn't his speed that impressed, it was his lack of hesitation. He reached for Berrec's wrist. A sudden heave brought the warder sprawling across him. The poker in Berrec's outstretched hand skewered Grebbin through the ribs, deep enough so that Berrec lost his grip on it as Grebbin twisted away.\n\nWithout pause, the Nuban lifted himself halfway to sitting, as close to upright as his manacled wrist would let him. Berrec slid down the Nuban's chest, sliding on sweat and blood, into his lap. He started to raise himself. The Nuban's descending elbow put an end to the escape attempt. It caught Berrec on the back of the neck, and bones crunched.\n\nGrebbin screamed of course, but screams were common enough in the dungeon. He tried to run, but somehow lost his sense of direction and slammed into a cell door, with enough force to drive the point of the poker out below his shoulder blade. The impact knocked him over and he didn't get up again. He twisted for a moment, mouthing something, with only wisps of smoke or steam escaping his lips.\n\nA cheer went up from those cells containing occupants too stupid to know when to stay silent.\n\nLundist could have run. He had plenty of time. I expected him to go for help, but he was halfway to me by the time Grebbin hit the ground. The Nuban pushed Berrec clear, and freed his other wrist.\n\n\"Run!\" I shouted at Lundist in case it hadn't occurred to him.\n\nActually, he was running, only in the wrong direction. I knew the years lay less heavy on him than an old man had a right to expect, but I didn't think he could sprint.\n\nI moved to put the table, and the Nuban, between Lundist and me.\n\nThe Nuban unpinned both ankles as Lundist reached him. \"Take the boy, old man, and go.\" He had the deepest voice I'd ever heard.\n\nLundist fixed the Nuban with those disconcerting blue eyes of his. His robes settled, forgetting the rush from the doorway. He held hands to his chest, one atop the other. \"If you go now, man of Nuba, I will not stop you.\"\n\nThat brought a scatter of laughter from the cells.\n\nThe Nuban watched Lundist with the same intensity I'd seen earlier. He had a few inches on my tutor, but it was the difference in bulk that made it seem a contest between David and Goliath. Where Lundist stood slender as a spear, the Nuban had as much weight again, and more, corded into thick slabs of muscle over heavy bone.\n\nThe Nuban didn't laugh at Lundist. Perhaps he saw more than the prisoners did. \"I'll take my brothers with me.\"\n\nLundist chewed on that, then took a pace back. \"Jorg, here.\" He kept his gaze on the Nuban.\n\n\"Brothers?\" I asked. I couldn't see any black faces at the bars.\n\nThe Nuban gave a broad smile. \"Once I had hut-brothers. Now they are far away, maybe dead.\" He spread his arms, the smile becoming half grimace as he felt his burns. \"But the gods have given me new brothers, road-brothers.\"\n\n\"Road-brothers.\" I rolled the words across my tongue. An image of Will flickered in my mind, blood and curls. There was power here. I felt it.\n\n\"Kill them both, and let me out.\" A door to my left rattled as if a bull were worrying at it. If the speaker matched his voice, there was an ogre in there.\n\n\"You owe me your life, Nuban,\" I said.\n\n\"Yes.\" He jerked the keys from Berrec's belt and stepped toward the cell on my left. I stepped with him, keeping him between Lundist and myself.\n\n\"You'll give me a life in return,\" I said.\n\nHe paused, glancing at Lundist. \"Go with your uncle, boy.\"\n\n\"You'll give me a life, brother, or I'll take yours as forfeit,\" I said.\n\nMore laughter from the cells, and this time the Nuban joined in. \"Who do you want killed, Little Brother?\" He set the key in the lock.\n\n\"I'll tell you when we see him,\" I said. To specify Count Renar now would raise too many questions. \"I'm coming with you.\"\n\nLundist rushed forward at that. He pivoted past the Nuban, delivering a kick to the back of his knee. I heard a loud click as the black man went down.\n\nThe Nuban twisted as he fell, and lunged for Lundist. Somehow the old man evaded him, and when the Nuban sprawled at his feet, Lundist kicked him in the neck, a blow that cut off his oath and left him limp on the stone floor.\n\nI almost skipped free, but Lundist's fingers knotted in my hair as it streamed behind me. \"Jorg! This is not the way!\"\n\nI fought to escape, snarling. \"It's exactly the way.\" And I knew it to be true. The wildness in the Nuban, the bonds between these men, the focus on what will make the difference\u2014no matter what the situation\u2014all of it echoed in me.\n\nFrom the corner of my eye I caught sight of the cell door opening. The click had been the key turning.\n\nLundist held my shoulders and made me face him. \"You've no place with these men, Jorg. You can't imagine the life they lead. They don't have the answers you want.\" He had such intensity to him, I could almost believe he cared.\n\nA figure emerged from the cell, stooping to come through the doorway. I'd never seen a man so big, not Sir Gerrant of the Table Guard, not Shem the stablehand, nor the wrestlers from The Slavs.\n\nThe man came up behind Lundist, quick, a rolling storm.\n\n\"Jorg, you think I don't understand\u2014\" The sweep of a massive arm cut off Lundist's words and sent him to the stone floor with such force I'd have winced even if he hadn't taken a handful of my hair with him.\n\nThe man towered over me, an ugly giant in stinking rags, with his hair hanging down in matted curtains. The scale of him mesmerized me. He reached for me, and I moved too slow. The hand that caught me could almost close around my waist. He lifted me level with his face, and his filthy mane parted as he looked up.\n\n\"Jesu, but you're one hideous offence to the eye.\" I could tell he was going to kill me, so no point in being tactful. \"I can see why the King wants to execute you.\"\n\nEven from the anonymity of the cells the laughter was hesitant. Not a man to mock, then. Nothing soft in his face, just brute lines, scar, and the jut of bone beneath coarse skin. He lifted me, as if to dash me on the stone, like throwing down an egg.\n\n\"No!\"\n\nI could see under the giant's arm, an old man and a red-haired youth had followed him out and were now helping the Nuban to his feet.\n\n\"No,\" the Nuban said again. \"I owe him a life, Brother Price. And besides, without him, you'd still be in that cell waiting on the pleasures of the morrow.\"\n\nBrother Price gave me a look of impersonal malice, and let me fall as though I'd ceased to exist. \"Let them all out.\" He growled the words.\n\nThe Nuban gave the keys to the old man. \"Brother Elban.\" Then he came across to where I'd landed. Lundist lay close by, face to the floor, blood pooling around his forehead.\n\n\"The gods sent you, boy, to loose me from that table.\" The Nuban glanced at the torture rack, then at Lundist. \"You come with the brothers now. If we find the man you want dead, I kill him, maybe.\"\n\nI narrowed my eyes. I didn't like that \"maybe.\"\n\nI looked to Lundist for a moment. I couldn't tell if he was still breathing. I sensed a ghost of the guilt I should perhaps have felt, the itch from an amputated limb, still niggling though the flesh has long since gone.\n\nI stood beside the Nuban, with Lundist at my feet, and watched as the outlaws released their comrades. I found myself staring into the orange heat of the coals, remembering.\n\nI remembered a time when I lived in the lie. I lived in a world of soft things, mutable truths, gentle touches, laughter for its own sake. The hand that pulled me from the carriage that night, from the warmth of my mother's side, into a night of rain and screaming, that hand pulled me out by a doorway that I can't go back through. We all of us pass through that door, but we tend to exit of our own volition, and by degrees, sniffing the air, torn and tentative.\n\nIn the days following my escape and illness, I saw my old dreams grow small and wither. I saw my child's life yellow on the tree and fall, as if a harsh winter had come to haunt the spring. It was a shock to see how little my life had meant. How mean the dens and forts in which William and I had played with such fierce belief, how foolish our toys without the intensity of an innocent imagination to animate their existence.\n\nEvery waking hour I felt an ache, a pain that grew each time I turned the memory over in my hand. And I returned to it, time and again, like a tongue to the socket of a missing tooth, drawn by the absence.\n\nI knew it would kill me.\n\nThe pain became my enemy. More than the Count Renar, more than my father's bartering with lives he should have held more precious than crown, or glory, or Jesu on the cross. And, because in some hard core of me, in some stubborn trench of selfish refusal, I could not, even at ten years of age, surrender to anything or anyone, I fought that pain. I analysed its offensive, and found its lines of attack. It festered, like the corruption in a wound turned sour, drawing strength from me. I knew enough to know the remedy. Hot iron for infection, cauterize, burn, make it pure. I cut from myself all the weakness of care. The love for my dead, I put aside, secure in a casket, an object of study, a dry exhibit, no longer bleeding, cut loose, set free. The capacity for new love, I burned out. I watered it with acid until the ground lay barren and nothing there would sprout, no flower take root.\n\n\"Come.\"\n\nI looked up. The Nuban was speaking to me. \"Come. We're ready.\"\n\nThe brothers were gathered around us in ragged and ill-smelling array. Price had one of the warders' swords. The other gleamed in the hand of a second giant of a man, just a shade shorter, a shade lighter, a shade younger, and so similar in form that he could only have been squeezed from the same womb as Price.\n\n\"We're going to cut a way out of here.\" Price tested the edge of his sword against the short beard along his jawline. \"Burlow, up front with Rike and me. Gemt and Elban, take the rear. If the boy slows us down, kill him.\"\n\nPrice threw a look around the chamber, spat, and made for the corridor.\n\nThe Nuban put a hand on my shoulder. \"You should stay.\" He nodded to Lundist. \"But if you come, don't fall behind.\"\n\nI looked down at Lundist. I could hear the voices telling me to stay, familiar voices, but distant. I knew the old man would walk through fire to save me, not because he feared my father's wrath, but just . . . because. I could feel the chains that bound me to him. The hooks. I felt the weakness again. I felt the pain seeping through cracks I'd thought sealed.\n\nI looked up at the Nuban. \"I won't fall behind,\" I said.\n\nThe Nuban pursed his lips, shrugged, and set off after the others. I stepped over Lundist, and followed.\n\n_Assassination is just murder with a touch more precision. Brother Sim is precise._\n**14**\n\nSo we rode out from Norwood. The peasants watched us, all sullen and dazed, and Rike cursed them. As if it had been his idea to keep them from a Renar bonfire and now they owed him a cheer as he left. We left them the ruins of their town, decorated with the corpses of the men that ruined it. Poor compensation, especially after Rike and the brothers had stripped the dead of anything of worth. I reckoned we could make Crath City by nightfall, riding hard, and be banging on the gates of the Tall Castle before the moon rose.\n\nI shouldn't have been turning for home, picking up my old ways, and thinking once more about vengeance upon the Count of Renar. That's what instinct told me. But today instinct spoke with an old and dry voice and I no longer trusted it. I wanted to go home, perhaps because it felt as though something else required that I did not. I wanted to go home and if Hell rose up to stop me, it would make me desire it the more. We took the Castle Road, up through the garden lands of Ancrath. Our path ran alongside gentle streams, between small woods and quiet farms. I'd forgotten how green it was. I'd grown used to a world of churned mud, burned fields, smoke-grey skies, and the dead rotting on the ground. The sun found us, pushing its way through high cloud. In the warmth our column slowed until the clatter of hooves broke into lazy thuds. Gerrod paused where a three-bar gate led through the hedgerow. Beyond it, a field, golden with wheat, rolled out before us. He tore at the long grass around the gatepost. It felt as if God had poured honey over the land, sweet and slow, holding everything at peace. Norwood lay fifteen miles, and a thousand years, behind us.\n\n\"Good to be back, eh, Jorg?\" Makin pulled up beside me. He leaned forward in his stirrups and drank in the air. \"Smells of home.\"\n\nAnd it did. The scent of warm earth took me back, back to times when my world was small, and safe.\n\n\"I hate this place,\" I said. He looked shocked at that, and Makin was never an easy man to shock. \"It's a poison men take willingly, knowing it will make them weak.\"\n\nI gave Gerrod my heels and let him hurry up the road. Makin caught me up and cantered alongside. We passed Rike and Burlow at the crossroads, throwing rocks at a scarecrow.\n\n\"Men fight for their homeland, Prince,\" Makin said. \"It's the land they defend. The King and the land.\"\n\nI turned to holler at the stragglers. \"Close the line!\"\n\nMakin kept pace, waiting for an answer. \"Let the soldiers die for their land,\" I said to him. \"If the time comes to sacrifice these fields in the cause of victory, I'll let them burn in a heartbeat. Anything that you cannot sacrifice pins you. Makes you predictable, makes you weak.\"\n\nWe rode on at a trot, west, trying to catch the sun.\n\nSoon enough we found the garrison at Chelny Ford. Or rather they found us. The watchtower must have seen us on the trail, and fifty men came out along the Castle Road to block our way.\n\nI pulled up a few yards short of the pikemen, strung across the road in a bristling hedge, double-ranked. The rest of the squad waited behind the pike-wall, with drawn swords, save for a dozen archers arrayed amongst the corn in the field to our right. A score of heifers, in the field opposite, saw our approach and idled over to investigate.\n\n\"Men of Chelny Ford,\" I called out. \"Well met. Who leads here?\"\n\nMakin came up behind me, the rest of the brothers trailing in after him, easy in their saddles.\n\nA tall man stepped forward between two pikemen, but not too far forward, no idiot this one. He wore the Ancrath colours over a long chain shirt, and an iron pot-helm low on his brow. To my right a dozen sets of white knuckles strained on bowstrings. To my left the heifers watched from behind the hedge, complacent and chewing on the cud.\n\n\"I'm Captain Coddin.\" He had to raise his voice as one of the cows let out a low moo. \"The King signs mercenaries at Relston Fayre. Armed bands are not permitted to roam into Ancrath. State your business.\" He kept his eyes on Makin, looking for his answer there.\n\nI didn't care for being dismissed as a child, but there's a time and place for taking offence. Besides, old Coddin seemed to know his stuff. Putting Brother Gemt out of his misery was one thing, but wasting one of Father's captains quite another.\n\nI had my visor up already, so I used it to pull my helm off. \"Father Gomst!\" I called for the priest, and the brothers shuffled their horses aside with a few mutters to let the old fellow past. He wasn't much to look at. He'd hacked off that beard he grew in the gibbet-cage, but grey tufts still decorated his face in random clusters, and his priestly robes seemed more mud than cloth.\n\n\"Captain Coddin,\" I said. \"Do you know this priest, Father Gomst?\"\n\nCoddin raised an eyebrow at that. He had a pale face, and now it went paler. His mouth took on a hard edge, like a man who knows he's the butt of a joke that he hasn't worked out yet. \"Aye,\" he said. \"The King's priest.\" He snapped his heels together and inclined his head, as if he were in court. It seemed funny out there in the road, with the birds tweeting overhead and the stink of the cows washing over us.\n\n\"Father Gomst,\" I said. \"Pray tell Captain Coddin who I am.\"\n\nThe old fellow puffed himself up a bit. He'd been listless and grey since Norwood, but now he tried to find a crumb or two of authority.\n\n\"Prince Honorous Jorg Ancrath sits before you, Captain. Lost and now returned, he is bound for his royal father's court, and you would do well to see that he gets there with proper escort . . .\" He glanced at me, screwing up what courage he had behind the foolish remnants of his beard. \"And a bath.\"\n\nA little snigger went up at that, on both sides of our standoff. It doesn't pay to underestimate a cleric. They know the power of words and they'll use them to their own ends. My palm ached for the hilt of my sword. I saw old Gomst's head falling from his shoulders, bouncing once, twice, and rolling to a halt by the hooves of a black-and-white heifer. I pushed the vision away.\n\n\"No bath. It's about time for a little road-stink at court. Soft words and rose water may please the gentry, but those that fight the war live dirty. I return to my father as a man who has shared the soldier's lot. Let him know the truth of it.\" I let my words carry on the still air, and kept my eyes on Gomsty. He had the wit to look away.\n\nMy speech earned no rousing cheer, but Coddin bowed his head and we had no further mention of baths. A shame, truth be told, because I'd been looking forward to a hot tub ever since I decided to turn for home.\n\nSo Coddin left his second to command the garrison, and rode with us. His escort of two dozen riders swelled our numbers to nearly sixty. Makin carried a lance from the Ford armoury now, flying the Ancrath colours and royal crest. The garrison riders spread word through the villages as we passed. \"Prince Jorg, Prince Jorg returned from the dead.\" The news stole ahead of us, until each town presented a larger and better prepared reception. Captain Coddin sent a rider to the King before we left Chelny Ford, but even without his message, they would know of us in the Tall Castle well before we got there.\n\nAt Bains Town the bunting stretched across Main Street, six minstrels, sporting lute and clavichord, played \"The King's Sword\" with more gusto than skill, jugglers exchanged twirling fire-brands, and a bear danced before the mill pond. And the crowds! People packed in so tight we'd no hope of riding through. A fat woman in a tent of a dress which was striped like a tourney pavilion saw me amid the van. She pointed and gave a shriek that drowned the minstrels out, \"Prince Jorg! The Stolen Prince!\" The whole place went mad at that, cheering and crying. They surged forward like wild things. Coddin had his men in quick, though. I forgave him his earlier slight for that. If peasants had reached Rike, we'd have had red slaughter.\n\nOn the Lich Road the brothers were more scared, but that's the only time I've seen more fear in them than there at Bains Town. They none of them knew what to make of it. Grumlow's left hand never left his dagger. Red Kent grinned like a maniac, terror in his eyes. Still, they'd learn fast enough. When they figured out the welcome that lay ahead. When they'd seen the taverns and the whores. Well, there'd be no dragging them out of Bains Town in a week.\n\nOne of the minstrels found a horn, and a harsh note cut through the tumult. Guards, red-robed with black chain beneath, cleared a path, and no less a man than Lord Nossar of Elm emerged before us. I recognized the man from court. He looked slightly fatter in his gilded show-plate and velvets, rather more grey in the beard spilling down over his breastplate, but pretty much the same jolly old Nossar who rode me on his shoulders once upon a time.\n\n\"Prince Jorg!\" The old man's voice broke for a moment. I could see tears shining in his eyes. It caught at me, that did. I felt it hook something in my chest. I didn't like it.\n\n\"Lord Nossar,\" I gave back, and let a smile curl my lip. The same smile I gave Gemt before I let him have my knife. I saw a flicker in Nossar's eyes then. Just a moment of doubt.\n\nHe rallied himself. \"Prince Jorg! Beyond all hope, you've returned to us. I cursed the messenger for a liar, but here you are.\" He had the deepest voice, rich and golden. Old Nossar spoke and you knew it was truth, you knew he liked you, it wrapped you up all warm and safe, that voice did. \"Will you honour my house, Prince Jorg, and stay a night?\"\n\nI could see the brothers exchanging glances, eyeing women in the crowd. The mill pond burned crimson with the dying sun. North, above the dark line of Rennat Forest, the smoke of Crath City stained a darkening sky.\n\n\"My lord, it's a gracious invitation, but I mean to sleep in the Tall Castle tonight. I've been away too long,\" I said.\n\nI could see the worry on him. It hung on every crag of the man's face. He wanted to say more, but not here. I wondered if Father set him to detain me.\n\n\"Prince . . .\" He lifted a hand, his eyes seeking mine.\n\nI felt that hook in my chest again. He would set me down in his high hall and talk of old times in that golden voice. He'd speak of William, and Mother. If there was a man who could disarm me, Nossar was that man.\n\n\"I thank you for the welcome, Lord Nossar.\" I gave him court formality, curt and final.\n\nI had to haul on the reins to turn Gerrod. I think even horses liked Nossar. I led the brothers around by the river trail, trampling over some farmer's autumn turnips. The peasants cheered on, not sure what was happening, but cheering all the same.\n\nWe came to the Tall Castle by the cliff path, avoiding the sprawl of Crath City. The lights lay below us. Streets beaded with torchlight, the glow of fire and lamp rising from windows not yet shuttered against the cool of the night. The watchmen's lanterns picked out the Old City wall, a skewed semicircle, tapering down to the river where the houses spilled out beyond the walls, into the valley, reaching out along the river. We came to the West Gate, the one place we could reach the High City without trailing up through the narrow streets of the Old City. The guards raised the portcullises for us, first one, then the next, then the next. Ten minutes of creaking windlass and clanking chain. I wondered why the three gates were down. Did our foes truly press so close we must triple-gate the High Wall?\n\nThe gate captain came out whilst his men sweated to raise the last portcullis. Archers watched from the battlements high above. No bunting here. I recognized the man vaguely, as old as Gomst, salt-and-pepper hair. It was his sour expression I recalled best, pinched around the mouth as if he'd just that moment sucked a lemon.\n\n\"Prince Jorg, we are told?\" He peered up at me, raising his torch almost to my face. Evidently I had enough of the King's look about me to satisfy his curiosity. He lowered the torch fast enough and took a step back. I'm told I have my father's eyes. Maybe I do, though mine are darker. We could both give a stare that made men think again. I've always thought I look too girlish. My mouth too much the rosebud, my cheekbones too high and fine. It's of no great consequence. I've learned to wear my face as a mask, and generally I can write what I choose on it.\n\nThe captain nodded to Captain Coddin. He passed his gaze over Makin without a flicker, missed Father Gomst in the crowd, and lingered instead on the Nuban, before casting a dubious eye over Rike.\n\n\"I can find accommodation for your men in the Low City, Prince Jorg,\" he said. By the Low City he meant the sprawl beyond the walls of Old City.\n\n\"My companions can board with me at the castle,\" I said.\n\n\"King Olidan requires only your presence, Prince Jorg,\" the gate captain said. \"And that of Father Gomst, and Captain Bortha if he is with you?\"\n\nMakin raised a mailed hand. Both the gate captain's eyebrows vanished up beneath his helm at that. \"Makin Bortha? No . . . ?\"\n\n\"One and the same,\" Makin said. He gave the man a broad grin, showing altogether too many teeth. \"Been a while, Relkin, you old bastard.\"\n\n\"King Olidan requires\" . . . no room for manoeuvre there. A polite little \"get your road-scum down to the slums.\" At least Relkin made it clear enough from the start, rather than letting me lose face by arguing the odds before over-ruling me with \"King Olidan requires.\"\n\n\"Elban, take the brothers down to the river and find some rooms. There's a tavern, The Falling Angel, should be big enough for you all,\" I said.\n\nElban looked surprised at having been chosen, surprised but pleased. He smacked his lips over his toothless gums and glared back at the rest of them. \"You heard Jorth! Prince Jorth I mean. Move it out!\"\n\n\"Killing peasants is a hanging offence,\" I said as they turned their horses. \"Hear me, Little Rikey? Even one. So no killing, no pillage, and no raping. You want a woman, let the Count of Renar buy you one with his coin. Hell, let him buy you three.\"\n\nAll three gates stood open. \"Captain Coddin, a pleasure. Enjoy your ride back to the Ford,\" I said.\n\nCoddin bowed in the saddle and led his troops off. That left just me, Gomst, and Makin. \"Lead on,\" I said. And Gate Captain Relkin led us through the West Gate into the High City.\n\nWe had no crowds to contend with. The hour was well past midnight and the moon rode high now. The wide streets of the High City lay deserted save for the occasional servant scurrying from one great house to the next. Maybe a merchant's daughter or two watched us from behind the shutters, but in the main the noble houses slept sound and showed no interest in a returning prince.\n\nGerrod's hooves sounded too loud on the flagstones leading up to Tall Castle. Four years ago I left in velvet slippers, quieter than any mouse. The clatter of iron shoes on stone hurt my ears. Inside, a small voice still whispered that I'd wake Father. Be quiet, be quiet, don't breathe, don't even let your heart beat.\n\nTall Castle is of course anything but tall. In four years on the road I had seen taller castles, even bigger castles, but never anything quite like Tall Castle. The place seemed at once familiar and strange. I remembered it as bigger. The castle may have shrunk from the unending vastness I'd carried with me in memory, but it still seemed huge. Tutor Lundist told me the whole place once served as foundations for a castle so tall it would scrape the sky. He said that when men first built this, all we see now lay under the ground. The Road-men didn't build Tall Castle, but those who did had artifice almost to equal that of the Road-men. The walls weren't quarry-hewn, but seemingly crushed rock that had once poured like water. Some magic set metal bars through the stone of the wall, twisted bars of a metal tougher even than the black iron from the East. So Tall Castle brooded squat and ancient, and the King sat within its metal-veined walls, watching over the High City, the Old City, the Low City. Watching over the city of Crath and all the dominions of his line. My line. My city. My castle.\n**15**\n\n**_Four years earlier_**\n\nWe left the Tall Castle by the Brown Gate, a small door on the lower slopes of the mount, out past the High Wall. I came last, with the ache of all those steps in my legs.\n\nFaint red footprints marked the top stair. The owners of that blood were probably still bleeding, far behind us.\n\nFor a moment I saw Lundist, lying as I'd left him.\n\nWe'd climbed from the very bowels of the castle vaults, to the least ostentatious of all the castle's exits. Dung men came this way a dozen times a day, carrying off the treasures of the privy. And I'll tell you, royal shit stinks no less than any other.\n\nThe brother ahead of me turned at the archway, and showed me his teeth by way of a grin. \"Fresh air! Take a breath o' that, Castle Boy.\"\n\nI'd heard the Nuban call this one Row, a wire of a man, gristle and bone, old scars and a mean eye. \"I'll lick a leper's neck before I take a lung-full o' your stench, Brother Row.\" I pushed past him. It'd take more than talking like a road-brother to earn a place with these men, and giving an inch wasn't the way to start.\n\nAncrath stretched out on our right. To the left, the smoke and spires of Crath City rose behind the Old Wall. A storm light covered it all. The kind that falls when thunderclouds gather in the day. A flat light that makes a stranger of even the most familiar landscape. It felt appropriate.\n\n\"We travel fast and we travel hard,\" Price said.\n\nPrice and Rike, the only true brothers among us, stood shoulder to shoulder at the head of the column, Rike beetling his brow while Price told us how it would be. \"We put as many miles between us and this shit-hole as it takes. The storm will hide our tracks. We'll find horses as we go, roust a village or two if need be.\"\n\n\"You think the King's hunters can't track two dozen men through a bit of rain?\" I wished my voice didn't ring so pure and high as I said it.\n\nThey all turned round at that. The Nuban flashed me a look, eyes wide, and patted down at the air as if to shut me up.\n\nI pointed to the sprawl of roofs edging toward the river where Father's loving citizens had built beyond the safety of the city walls in their passion to be near him.\n\n\"By ones and twos a brother could find his way to a warm hearth, bit of roast beef, and an ale maybe,\" I said. \"I hear there's a tavern or three to be found down there. A brother could be toasting by a fire before the rain even got to washing his trail away.\n\n\"The King's men would be riding back and forth on those fine horses of theirs, getting wet, looking for the kind of rut that twenty men put in a road or across a field, looking for the kind of trouble a band of brothers stirs up. And we'd be sitting comfortable in the shadow of the Tall Castle, waiting for the weather to clear.\n\n\"You think there's a man we left behind who could tell the Criers what we look like? You think the good folk of Crath City will notice a score added to their thousands?\"\n\nI could see I'd won them. I could see the light of that warm hearth reflecting in their eyes.\n\n\"And how the feck are we to pay for roast beef and a roof to hide under?\" Price shoved through the brothers, setting the redhead, Gemt, on his rear. \"Start robbing in the shadow of the Tall Castle?\"\n\n\"Yeah, how we a-gonna pay, Castle Boy?\" Gemt scrambled to his feet, finding me a better target than Price for his anger. \"How we gonna?\"\n\nI brought up two ducats from my purse, and rubbed them together.\n\n\"I'll take that!\" A sharp-faced man to my left lunged for the purse, still fat with coin.\n\nI flipped the dagger from my belt and stuck it through his outstretched hand.\n\n\"Liar,\" I said. I shoved a little more, until the hilt slapped up against his palm, the blade glistening red behind.\n\n\"Out the way, Liar.\" Price grabbed him by the neck and tossed him down the slope.\n\nPrice loomed over me. Any full-grown man loomed over me, but Price added a new dimension to it. He took a handful of my jerkin and hauled me up, eye to eye, careless of the bloody knife I still had hold of.\n\n\"You're not scared of me, are you, boy?\" The stink of him was something awful. Dead dog comes close.\n\nI thought about stabbing him, but I knew there wasn't a wound that would stop him breaking me in two before he died.\n\n\"Are you scared of me?\" I asked him.\n\nWe had us a moment of understanding then. Price didn't so much as twitch, but I saw it in him, and he saw it in me. He let me fall.\n\n\"We'll stay a day in the city,\" Price said. \"The drinks are on Brother Jorg. Any of you whoresons start trouble before we leave, and I'll hurt you, bad.\"\n\nHe held a hand out to me where I lay. I half-reached for it, before understanding. I tossed the purse to him.\n\n\"I'll go with the Nuban,\" I said.\n\nPrice nodded. A black face lost from the dungeons would be remembered. A black face found in a Crath tavern would be remarked on.\n\nThe Nuban shrugged, and set off, east toward the open fields. I followed.\n\nIt wasn't until we'd lost ourselves in the maze of tracks and hedgerows that the Nuban spoke again.\n\n\"You should be afraid of Price, boy.\"\n\nThe first breath of storm wind set the hawthorn rustling to either side. I could smell the electricity, mixed in with the richness of the earth.\n\n\"Why?\" I wondered if he thought I lacked the imagination for fear. Some men are too dull to feel what might happen. Others torture themselves with maybes and populate their dreams with horrors more terrible than their worst enemy could inflict upon them.\n\n\"Why would the gods care what happens to a child who doesn't care about himself?\" the Nuban asked.\n\nHe paused before a turn in the road and moved close to the hedge. The wind shook again and white petals fell among the thorns. He looked back along the way we'd come.\n\n\"Maybe I'm not afraid of the gods either,\" I said.\n\nFat drops of rain began to land around us.\n\nThe Nuban shook his head. Raindrops sparkled in the tight curls of his hair. \"You're a fool to make a fist at the gods, boy.\" He flashed me a grin, and edged to the corner. \"Who knows what they might send you?\"\n\nRain appeared to be the answer. It seemed to fall faster than normal, as if the sheer weight of water waiting to fall hurried the raindrops down. I moved in beside the Nuban. The hedge offered no shelter. The rain came through my tunic, cold enough to steal my breath. I thought then of the comforts I'd left behind, and wondered if perhaps I should have taken Lundist's counsel after all.\n\n\"Why are we waiting?\" I asked. I had to raise my voice above the roar of the rain.\n\nThe Nuban shrugged. \"The road feels wrong.\"\n\n\"Feels more like a river\u2014but why are we waiting?\"\n\nHe shrugged again. \"Maybe I need a rest.\" He touched a hand to his burns, and a wince showed me his teeth, very white where most of the brothers had a mouthful of grey rot.\n\nFive minutes passed and I kept my peace. We couldn't get wetter if we'd fallen down a well.\n\n\"How did you all get taken?\" I asked. I thought of Price and Rike, and the notion of them surrendering to the King's guard seemed somehow comical.\n\nThe Nuban shook his head.\n\n\"How?\" I asked again, louder, above the rain.\n\nThe Nuban glanced back along the road, then bent in close. \"A dream-witch.\"\n\n\"A witch?\" I made a face at him and spat water to the side.\n\n\"A dream-witch.\" The Nuban nodded. \"The witch came in our sleep and kept us tied in dreams while the King's men took us.\"\n\n\"Why?\" I asked. If I took the witch seriously, and I didn't, I knew for certain that my father didn't employ any.\n\n\"I think he was seeking to please the King,\" the Nuban said.\n\nHe stood without announcement and set off through the mud. I followed, but I held my tongue. I'd seen children tag after grown men throwing question after question, but I had put childhood aside. My questions could wait, at least until the rain stopped.\n\nWe sploshed along at a good pace for the best part of an hour before he stopped again. The rain had graduated from deluge to a steady soak that fell with the promise of lasting the night and through the next morning. This time our pause in the hedgerow proved well judged. Ten horsemen thundered by, kicking up mud left and right.\n\n\"Your king wants us back in his dungeons, Jorg.\"\n\n\"He's not my king any more,\" I said. I made to stand, but the Nuban caught my shoulder.\n\n\"You left a rich life in the King's own castle, and now you're hiding in the rain.\" He kept a close watch on me. He read too much with his eyes and I didn't like it. \"Your uncle sacrificed himself to keep you safe. A good man I think. Old, strong, wise. But you came.\" He shook a clot of mud from his free hand. A silence stretched between us, the kind that invites you to fill it with confession.\n\n\"There's a man I want dead.\"\n\nThe Nuban frowned. \"Children shouldn't be this way.\" The rain ran in trickles over the furrows on his brow. \"Men shouldn't be this way.\"\n\nI shook loose and set off. The Nuban fell in beside me and we covered another ten miles before the light failed entirely.\n\nOur path took us by farmhouses and the occasional mill, but as night came we saw a cluster of lights below a wooded ridge a little south of us. From memory of Lundist's maps I guessed it to be the village of Pineacre, until now nothing more to me than a small green dot on old parchment.\n\n\"A bit of dry would be nice.\" I could smell the wood-smoke. All of a sudden I understood how easily I'd sold the brothers my plan on the strength of warmth and food.\n\n\"We should spend the night up there.\" The Nuban pointed to the ridge.\n\nThe rain fell soft now. It wrapped us in a cold blanket that leeched my strength away. I cursed my weakness. A day on the road had left me dead on my feet.\n\n\"We could sneak into one of those barns,\" I said. Two stood isolated, just below the treeline.\n\nThe Nuban started to shake his head. In the east thunder rumbled, low but sustained. The Nuban shrugged. \"We could.\" The gods loved me!\n\nWe made our way through fields turned half to swamp, stumbling in the darkness, me tripping over my exhaustion.\n\nThe door to the barn groaned a protest, then squealed open as the Nuban heaved on it. A dog barked somewhere in the distance, but I doubted any farmer would dare the rain on the strength of a hound's opinion. We reeled in and fell into the hay. Each limb felt leaden, I would have sobbed with the tiredness if I'd let it have its way.\n\n\"You're not worried the dream-witch will come after you again?\" I asked. \"She's hardly going to be pleased if her present to the King has escaped.\" I stifled a yawn.\n\n\"He,\" said the Nuban. \"I think it's a he.\"\n\nI pursed my lips. In my dreams the witches were always women. They'd hide in a dark room I'd never noticed before. A room whose open doorway stood off the corridor I had to follow. I'd pass the entrance and the skin on my back would crawl, invisible worms would tingle their way across the backs of my arms. I'd see her, sketched by shadows, her pale hands like spiders writhing from black sleeves. In that moment, when I tried to run, I'd become mired, as if I ran through molasses. I'd struggle, trying to shout, vomiting silence, a fly in the web, and she would advance, slow, inevitable, her face inching into the light. I'd see her eyes . . . and wake screaming.\n\n\"So you're not worried he'll come after you again?\" I asked.\n\nThunder came in a sudden clap, shaking the barn.\n\n\"He has to be close,\" the Nuban said. \"He has to know where you are.\"\n\nI let go of a breath I hadn't realized I'd been keeping.\n\n\"He'll send his hunter after us instead,\" the Nuban said. I heard the rustle as he pulled the hay down on himself.\n\n\"That's a pity,\" I said. It had been a long time since I'd dreamed of my own dream-witch. I rather liked the idea that she might be chasing us here, to this barn, in the jaws of the storm. I settled back into the prickle of the hay. \"I'll see if I can dream a witch tonight, yours or mine, I don't care. And if I do, this time I'm not running anywhere. I'm going to turn around and gut the bitch.\"\n**16**\n\n**_Four years earlier_**\n\nThunder again. It held me for a moment. I felt it in my chest. Then the lightning, spelling out the world in harsh new shapes. I saw visions in the after-images. A baby shaken until the blood came from its eyes. Children dancing in a fire. Another rumble rattled the boards, and the darkness returned.\n\nI sat in the confusion between sleep and the waking world, surrounded by the creak of wood, the shake and rattle of the wind. Lightning stabbed again and I saw the interior of the carriage, Mother opposite, William beside her, curled upon the bench-seat, his knees to his chest.\n\n\"The storm!\" I twisted and caught the window. The slats resisted me, spitting rain as the wind whistled outside.\n\n\"Shush, Jorg,\" Mother said. \"Go back to sleep.\"\n\nI couldn't see her in the dark, but the carriage held her scent. Roses and lemon-grass.\n\n\"The storm.\" I knew I'd forgotten something. That much I remembered.\n\n\"Just rain and wind. Don't let it frighten you, Jorg, love.\"\n\nDid it frighten me? I listened as the gusts ran their claws across the door.\n\n\"We have to stay in the carriage,\" she said.\n\nI let the roll and rock of the carriage take me, hunting for that memory, trying to jog it loose.\n\n\"Sleep, Jorg.\" It was more of a command than a recommendation.\n\n_How does she know I'm not asleep?_\n\nLightning struck so close I could hear the sizzle. The light crossed her face in three bars, making something feral of her eyes.\n\n\"We have to stop the carriage. We have to get off. We have to\u2014\"\n\n\"Go to sleep!\" Her voice carried an edge.\n\nI tried to stand, and found myself weighed down, as if I were wading in the thickest mud . . . or molasses.\n\n\"You're not my mother.\"\n\n\"Stay in the carriage,\" she said, her voice a whisper.\n\nThe tang of cloves cut the darkness, a breath of myrrh beneath it, the perfume of the grave. The stink of it smothered all sound. Except the slow rasp of her breath.\n\nI hunted the door handle with blind fingers. Instead of cold metal I found corruption, the softness of flesh turned sour in death. A scream broke from me, but it couldn't pierce the silence. I saw her in the next flash of the storm, skin peeled from the bone, raw pits for eyes.\n\nFear took my strength. I felt it running down my leg in a hot flood.\n\n\"Come to Mother.\" Fingers like twigs closed around my arm and drew me forward in the blackness.\n\nNo thoughts would form in the terror that held me. Words trembled on my lips but I had no mind to know what they would be.\n\n\"You're . . . not her,\" I said.\n\nOne more flash, revealing her face an inch before mine. One more flash, and in it I saw my mother dying, bleeding in the rain of a wild night, and me hung on the briar, helpless in a grip made of more than thorns. Held by fear.\n\nA cold rage rose in me. From the gut. I drove my forehead into the ruin of the monster's face, and took the door handle with a surety that needed no sight.\n\n\"No!\"\n\nAnd I leapt into the storm.\n\nThe thunder rolled loud enough to wake even the deepest buried. I jerked into a sitting position, confused by the stink of hay and the prickle of straw all around me. The barn! I remembered the barn.\n\nA single point of illumination broke the night. A lantern's glow. It hung from a beam close by the barn door. A figure, a man, a tall one, stood in the fringes of the light. The Nuban lay at his feet, caught in a troubled sleep.\n\nI made to cry out, then bit my cheek hard enough to stop myself. The copper tang of the blood sharpened away the remnants of my dream.\n\nThe man held the biggest crossbow I'd ever seen. With one hand he began to wind back the cable. He took his time. When you're hunting on behalf of a dream-witch I guess you're never in a rush. Unless one of your victims escapes whatever dreams have been sent to keep them sleeping . . .\n\nI reached for my knife, and found nothing. I guessed it lost along whatever path my nightmare had led me through the hay. The lantern struck a gleam from something metal by my feet. A baling hook. Three more turns on that crank and he'd be done. I took the hook.\n\nThe storm howl covered my approach. I didn't sneak. I walked across slow enough to be sure of my footing, fast enough to give ill fortune no time to act against me.\n\nI'd thought to reach around and cut the bastard's throat, but he was tall, too tall for a ten-year-old's reach.\n\nHe lifted the crossbow to sight down at the Nuban.\n\nWait when waiting is called for. That's what Lundist used to tell me. But never hesitate.\n\nI hooked the hunter between the legs and yanked up as hard as I could.\n\nWhere the crash of thunder and the roar of the wind had failed, the hunter's scream succeeded. The Nuban woke up. And to his credit there was no wondering where he was or what was happening. He surged to his feet and had a foot of steel through the man's chest in two heartbeats.\n\nWe stood with the hunter lying between us, each with our weapon blooded.\n\nThe Nuban wiped his blade on the hunter's cloak.\n\n\"That's a big old crossbow!\" I toed it across the floor and marvelled at the weight of it.\n\nThe Nuban lifted the bow. He ran his fingers over the metalwork inlaid on the wood. \"My people made this.\" He traced the symbols and the faces of fierce gods. \"And now I owe you another life.\" He hefted the crossbow and smiled, his teeth a white line in the lantern glow.\n\n\"One will be enough.\" I paused. \"It's Count Renar that has to die.\"\n\nAnd the smile left him.\n**17**\n\nThe old corridors enfolded me and four years became a dream. Familiar turns, the same vases, the same suits of armour, the same paintings, even the same guards. Four years and everything was the same, except me.\n\nIn the niches small silver lamps burned oil squeezed from whales in distant seas. I walked from one pool of light to the next, behind a guard whose armour beggared my own. Makin and Gomst had been led to separate destinations, and I went alone to whatever reception awaited. The place still made me feel small. Doors built for giants, ceilings soaring so high that a man with a lance could scarcely touch them. We came to the west wing, the royal quarters. Would Father meet me here? Man to man in the arboretum? Souls bared beneath the planetarium dome? I had imagined him seated in the black claw of his throne, brooding above the court, and me led toward him between the men of the Imperial Guard.\n\nI followed the single guard, feeling vaguely cheated. Did I want to be surrounded by armed men? Had I grown so dangerous? To be heaped with chains? Did I want him to fear me? Fourteen years old, and the King of Ancrath quaking behind his bodyguard?\n\nI felt foolish for a moment. I brushed a hand over the hilt of my sword. They'd cast the blade from the metal that ran through the castle walls. A true heirloom, with a heritage at the Tall Castle predating mine by a thousand years at least. I ached for a confrontation then. Voices rose at the back of my mind, clamouring, fighting one against the other. The skin on my back tingled, the muscle beneath twitched for action.\n\n\"A bath, Prince Jorg?\"\n\nIt was the guardsman. I nearly drew on him.\n\n\"No,\" I said. I forced myself to calmness. \"I'll see the King now.\"\n\n\"King Olidan has retired, Prince,\" the guard said. Was he smirking at me? His eyes held an intelligence I didn't associate with the palace guard.\n\n\"Asleep?\" I would have given a year of my life to take the surprise from those words. I felt like Captain Coddin must have: the butt of a joke I had yet to comprehend.\n\n\"Sageous awaits you in the library, my prince,\" the man said. He turned to go, but I had him by the throat.\n\nAsleep? They were playing with me, Father and this pet magician of his.\n\n\"This game,\" I said. \"I expect it will provide amusement to somebody, but, if you . . . worry me . . . one more time, I will kill you. Think on it. You're a piece in somebody else's game, and all you'll earn from it is a sword through the stomach, unless you redeem yourself in the next twenty seconds.\"\n\nIt was a defeat, resorting to crude threats in a game of subtlety, but sometimes one must sacrifice a battle to win the war.\n\n\"Prince, I . . . Sageous is waiting for you . . .\" I could see I'd turned his smug superiority into terror. I'd stepped outside the rules of play. I squeezed his throat a little. \"Why would I want to speak to this . . . Sageous? What's he to me?\"\n\n\"He\u2014he holds the King's favour. Pl-please, Prince Jorg.\"\n\nHe got the words out past my fingers. It takes no great strength to throttle a man if you know where to grip.\n\nI let him go and he fell, gasping. \"In the library you say? What's your name, man?\"\n\n\"Yes, my prince, in the library.\" He rubbed at his neck. \"Robart. My name is Robart Hool.\"\n\nI strode out across the Hall of Spears, angling for the leathered door to the library. I paused before it, turning back to Robart. \"There are turning points, Robart. Forks in the path we follow through our lives. Times that we look back to and say, 'If only.' This is one of those times. It's not often we get them pointed out to us. At this point you'll either decide to hate me, or to serve me. Consider the choice carefully.\" I threw the library door open. It slammed back into the wall and I walked through.\n\nIn my mind the library walls stretched to the very heavens, thick with books, pregnant with the written word. I learned to read at three years of age. I was talking with Socrates at seven, learning form and thing from Aristotle. For the longest time I had lived in this library. Memory dwarfed reality: the place looked small now, small and dusty.\n\n\"I've burned more books than this!\" I said.\n\nSageous stepped out from the aisle given over to ancient philosophy. He was younger than I expected, forty at the most, wearing just a white cloth, like the Roman togara. His skin held the dusky hue of the middle-lands, maybe Indus or Persia, but I could see it only in the rare spots the tattooist's needle hadn't found. He wore the text of a small book on his living hide, cut there in the flowing script of the mathmagicians. His eyes\u2014well, I know we're supposed to cower beneath the gaze of potent men, but his eyes were mild. They reminded me of the cows on the Castle Road, brown and placid. His scrutiny was the thing that cut. Somehow those mild eyes dug in. Perhaps the script beneath them bore the power. All I can say is that, for a time uncounted, I could see nothing but the heathen's eyes, hear nothing but his breath, stir no muscle but my heart.\n\nHe let me go, like a fish thrown back into the river, too small for the pot. We stood face to face, inches apart, and I'd no memory of closing the gap. But I'd come to him. We stood among the books. Among the wise words of ten thousand years. Plato to my left, copied, copied, and copied again. The \"moderns\" to my right, Russell, Popper, Xiang, and the rest. A small voice inside me, deep inside, called for blood. But the heathen had taken the fire from me.\n\n\"Father must depend upon you, Sageous,\" I said. I twisted my fingers, wanting to want my sword. \"To have a pagan at court must vex the priests. If the pope dared leave Roma these days, she'd be here to curse your soul to eternal hellfire!\" I had nothing but dogma with which to beat him.\n\nSageous smiled, a friendly smile, like I'd just run an errand for him. \"Prince Jorg, welcome home.\" He had no real accent, but he ran his words out fluid and musical, like a Saracen or a Moor.\n\nHe stood no taller than me, in fact I probably had an inch on him. He was lean too, so I could have taken him to the floor there and then, and choked the life out of him. One murderous thought bubbled up after another, and leaked away.\n\n\"There's a lot of your father in you,\" he said.\n\n\"Have you got him tamed too?\" I asked.\n\n\"One doesn't tame a man like Olidan Ancrath.\" His friendly smile took an edge of amusement. I wanted to know the joke. He could manage me but not my father? Or he could manipulate the King and chose to cover the fact with a smirk?\n\nI imagined the heathen's tattooed head shorn from his shoulders, his smile frozen and blood pumping from the stump of his neck. In that instant I reached for my sword and threw all my will behind the action. The pommel felt cold beneath my touch. I curled my fingers around the hilt, but before I could squeeze them tight, my hand fell away like a dead thing.\n\nSageous raised a brow at that. He'd had them shaved like his head, and drawn back in. He took a step backward.\n\n\"You're an interesting young man, Prince Jorg.\" His eyes hardened. Mild one moment, and in the next, dead as flint. \"We shall have to find out what makes you tick, yes? I'll have Robart escort you to your chamber, you must be tired.\" All the time he spoke, the fingers of his right hand traced words in the flowing script across his left arm, brushing over one symbol jumping higher to a black crescent moon, underlining a phrase, underlining it again. I did feel tired. I felt lead in every limb, pulling me down.\n\n\"Robart!\" he called out loud enough for the corridor.\n\nHe looked back to me, mild again. \"I expect you'll have dreams, Prince, after so long away.\" His fingers moved over new lines, left hand, right arm. He traced words blacker than night across the veins in his wrist. \"Dreams tell a man who he is.\"\n\nI struggled to keep my eyes open. On Sageous's neck, just to the left of his Adam's apple, amid all the tight-packed scrawl, was a letter, bigger than the rest, curled and recurled so it looked like a flower.\n\n_Touch the flower_ , I thought. _Touch the pretty flower_. And as if by magic, my treacherous hand moved. It took him by surprise, my fingers at his throat. I heard the door open behind me.\n\n_He's skinny_ , I thought. _So skinny_. I wonder if I could close my hand around his neck. I admitted no hint of violence, just curiosity. And there it was, my hand around his neck. I heard Robart's sudden intake of breath. Sageous stood frozen, his mouth half open, as if he couldn't believe it.\n\nI could barely stand, I could hardly keep the yawning from my voice, but I held his eye and let him think that the pressure I put on him was a threat, and not to keep me from falling.\n\n\"My dreams are my own, heathen,\" I said. \"Pray you're not in them.\"\n\nI turned then, before I fell, and strode past Robart. He caught up in the Hall of Spears.\n\n\"I've never seen anyone lay hand on Sageous, my prince.\"\n\nMy prince. That was better. There was admiration in his voice, maybe genuine, maybe not, I was too tired to care.\n\n\"He's a dangerous man, his enemies die in their sleep. That or they're broken. Lord Jale left the court two days after disagreeing with the pagan in front of your father. They say he can't feed himself now, and spends his days singing an old nursery rhyme over and over.\"\n\nI reached the West Stair, Robart prattling beside me. He broke off all of a sudden. \"Your chamber is off the Red Corridor, my prince.\" He stopped and studied his boots. \"The Princess has your former chamber.\"\n\nPrincess? I didn't care. Tomorrow, tomorrow I would find out. I let him lead me to my room. One of the guest rooms off the Red Corridor. The chamber could have housed many a tavern I'd slept in, but it was a studied insult nonetheless. A room for a country baron or distant cousin visiting from the protectorates.\n\nI stopped at the door, reeling with exhaustion. Sageous's spell bit deeper and my strength left me like blood from sliced veins.\n\n\"I told you it was time to choose, Robart,\" I said. I forced the words out one by one. \"Get Makin Bortha here. Let him guard my door this night. Time to choose.\"\n\nI didn't wait for a reply. If I had, he'd have had to carry me to bed. I pushed the door and half-staggered, half-fell, into the chamber. I collapsed back against the door, closing it, and slid to the floor. It felt like I kept on sliding, deeper and deeper, into an endless well.\n**18**\n\nI woke up with that sudden convulsion you get when every muscle you own suddenly realizes it's dropped off on duty. Next came the shock of realizing how deeply I'd been asleep. You don't sleep like that on the road, not if you want to wake up again. For a moment the darkness would yield nothing to my confusion. I reached for my sword and found only soft sheets. The Tall Castle! It came back to me. I remembered the pagan and his spell.\n\nI rolled to the right. I always left my gear on my right side. Nothing but more mattress, soft and deep. I might have been blind for all the help my eyes gave. I guessed the shutters were shut tight, for not the slightest whisper of starlight reached me. It was quiet too. I reached out for the edge of the bed, and didn't find it. _A wide bed_ , I thought, trying to find some humour in the situation.\n\nI let go the breath I'd been holding, the one I sucked in so fast when I woke. What was it that made me start? What dragged me out of the pagan's spell in this oh so comfortable bed? I pulled my hand back, drew my knees to my chest. Somebody had put me to bed and taken my clothes. Not Makin, he'd not leave me naked against the night. That somebody and I would be having a discussion soon enough. But it could wait until morning. I just wanted to sleep, to let the day come.\n\nOnly sleep had kicked me out, and it wasn't about to let me back in. So I lay there, naked in the strange bed, and wondered where my sword was.\n\nThe noise came so quiet at first I could believe I imagined it. I stared blind into the darkness and let my ears suck in the silence. It came again, soft as the whisper of flesh on stone. I could hear the ghost of a sound, a breath being drawn. Or maybe just a night breeze fingering its way through the shutters.\n\nIce ran up my spine, tingling on my shoulders. I sat up, biting back the urge to speak, to show bravado to the unseen terrors. _I'm not six years old_ , I told myself. _I've made the dead run_. I threw the sheets back and stood up. If the pagan's horror was waiting in the darkness, then sheets would be no shield. With my hands held up before me, I walked forward, finding first the elusive edge of the bed, and then the wall. I turned and followed it, fingers trailing the stonework. Something went tumbling and broke with an expensive crash. I barked my shins on an unseen obstacle, nearly groined myself on a sideboard of some kind, then found the shutter slats.\n\nI fumbled with the shutter catch. It defied me maddeningly, as though my fingers were frost-clumsy. The skin on my back crawled. I heard footsteps drawing closer. I hauled on the shutters with all my strength. Every move I made seemed slow and feeble, as though I moved through molasses, like in those dreams where the witch chases you and you can't run.\n\nThe shutters gave without warning. They flew back and I found that I was standing high above the execution yard, drenched in moonlight. I spun around. Slow, too slow. And found nothing. Just a room of silver and shadows.\n\nThe window threw the moonlight on the wall to my right. My shadow reached forward in the arch of the window and fell at the feet of a tall portrait. A full length picture of a woman. I went numb: my face felt like a mask. I knew the picture. Mother. Mother in the great hall. Mother in a white dress, tall and icy in her perfection. She said she never liked that picture, that the artist had made her too distant, too much the queen. Only William softened it, she said. If she'd not had William hugging to her skirts, she would have given the picture away, she said. But she couldn't throw little William away.\n\nI pulled my eyes from her face, pale in the silver light. She loomed above me, tall in life, taller in the portrait. Her dress fell in cascades of lace-froth: the artist had caught it well. He made it look real.\n\nThe open shutters let in a chill and I felt a cold beyond any autumn frost. My skin rose in tiny bumps. She couldn't throw William away. Only William wasn't there any more . . . I took a step back toward the open window.\n\n\"Sweet Jesus . . .\" I blinked away tears.\n\nMother's eyes followed me.\n\n\"Jesus wasn't there, Jorg,\" she said. \"Nobody came to save us. You watched us, Jorg. You watched, but you didn't come to help.\"\n\n\"No.\" I felt the windowsill cold against the back of my knees. \"The thorns . . . the thorns held me.\"\n\nShe looked at me, eyes silver with the moon. She smiled and I thought for a moment she would forgive me. Then she screamed. She didn't scream the screams she'd made when the Count's men raped her. I could have stood that. Maybe. She screamed the screams she made when they killed William. Ugly, hoarse, animal screams, torn from her perfect painted face.\n\nI howled back. The words burst from me. \"The thorns! I tried, Mother. I tried.\"\n\nHe rose up from behind the bed then. William, sweet William with the side of his head caved in. The blood clotted black on his golden hair. The eye that side was gone, but the other held me.\n\n\"You let me die, Jorg,\" he said. He spoke it past a bubbling in his throat.\n\n\"Will.\" I couldn't say any more.\n\nHe lifted a hand to me, white with the trickles of blood darkest crimson.\n\nThe window yawned behind me and I made to throw myself back through it, but as I did something jolted me forward. I staggered and righted myself. Will stood there, silent now.\n\n\"Jorg! Jorg!\" A shout reached me, distant but somehow familiar.\n\nI looked back toward the window and the dizzying fall.\n\n\"Jump,\" said William.\n\n\"Jump!\" Mother said.\n\nBut Mother didn't sound like Mother any more.\n\n\"Jorg! Prince Jorg!\" The shout came louder now, and a more violent jolt threw me to the floor.\n\n\"Get out of the fucking way, boy.\" I recognized Makin's voice. He stood framed in the doorway, lamplight behind. And somehow I lay on the floor at his feet. Not by the window. Not naked, but in my armour still.\n\n\"You were jammed up against the door, Jorg,\" Makin said. \"This Robart fellow told me to come running, and here you are screaming behind the door.\" He glanced around, looking for the danger. \"I ran from the South Wing for your blasted nightmare did I?\" He shoved the door open wider and added a belated, \"Prince.\"\n\nI got to my feet, feeling as if I'd been rolled on by Fat Burlow. There was no painting on the wall, no Mother, no Will behind the bed.\n\nI drew my sword. I needed to kill Sageous. I wanted it so badly I could taste it, like blood, hot and salt in my mouth.\n\n\"Jorg?\" Makin asked. He looked worried, as if he was wondering if I'd gone mad.\n\nI moved toward the open door. Makin stepped to block me. \"You can't go out there with a drawn sword, Jorg, the guard would have to stop you.\"\n\nHe didn't stand as tall or as wide as Rike, but Makin was a big man, broad in the shoulder and stronger than a man should be. I didn't think I could take him down without killing him.\n\n\"It's all about sacrifice, Makin,\" I said. I let my sword drop.\n\n\"Prince?\" He frowned.\n\n\"I'm going to let that tattooed bastard live,\" I said. \"I need him.\" I glimpsed my mother again, fading. \"I need to understand what game is being played out here. Who exactly the pieces are and who the players are.\"\n\nMakin's frown deepened. \"You get some sleep, Jorg. In the bed this time.\" He glanced back into the corridor. \"Do you want some light in there?\"\n\nI smiled at that. \"No,\" I said. \"I'm not afraid of the dark.\"\n**19**\n\nI woke early. A grey light through the shutters showed me the room for the first time: big, well-furnished, hunting tapestries on the walls. I uncoiled my fingers from my sword hilt, stretched and yawned. It didn't feel right, this bed. It was too soft, too clean. When I threw the covers back they knocked the servant-bell from the bedside table. It hit the flagstones with a pretty tinkling then bounced onto a rug and lost its voice. Nobody came. That suited me fine: I'd dressed myself for four years. Hell, I'd rarely undressed! And what rags I had would be put to shame by the meanest of servant smocks. Even so. Nobody came.\n\nI wore my armour over the grey tatters of my shirt. A looking-glass lay on the sideboard. I let it lie there face down. A quick run of fingers through hair in search of any louse fat enough to be found, and I was ready to break my fast.\n\nFirst I threw the shutters open. No fumbling with the catch this time. I looked out over the execution yard, a square bounded by the blank walls of the Tall Castle. Kitchen-boys and maids hastened across the bleak courtyard, going about their various quests, blind to the pale wash of the sky so high above them.\n\nI turned from the window and set off on my own little quest. Every prince knows the kitchens better than any other quarter of his castle. Where else can so much adventure be found? Where else is the truth spoken so plain? William and I learned a hundred times more in the kitchens of the Tall Castle than from our books on Latin and strategy. We'd steal ink-handed from Lundist's study and sprint through long corridors, leaping down the stairs too many at a time, to reach the refuge of the kitchens.\n\nI walked those same corridors now, ill at ease in the confined space. I'd spent too long under wide skies, living bloody. We learned about death in the kitchens too. We watched the cook turn live chickens to dead meat with a twist of his hands. We watched Ethel the Bread pluck the fat hens, leaving them naked in death, ready for gutting. You soon learn there's no elegance or dignity in death if you spend time in the castle kitchens. You learn how ugly it is, and how good it tastes.\n\nI turned the corner at the end of the Red Corridor, too full of memories to pay attention. All I saw was a figure bearing down on me. Instincts learned on the road took over. Before I had time to register the long hair and silks, I had her against the wall, a hand across her mouth and my knife to her throat. We were face by face and my captive held my stare, eyes an unreal green like stained glass. I let my snarl relax into a smile and unclenched my teeth. I stepped back, letting her off the wall.\n\n\"Your pardon, my lady,\" I said, and sketched her a shallow bow. She was tall, nearly my height, and surely not many years my senior.\n\nShe gave me a fierce grin and wiped her mouth with the back of her hand. It came away bloody, from a bitten tongue. Gods but she was good to look at. She had a strong face, sharp in the nose and cheekbones but rich in the lips, all framed by the darkest red hair.\n\n\"Lord, how you stink, boy,\" she said. She stepped around me, as if she was checking a horse at market. \"You're lucky Sir Galen isn't with me, or a skivvy would be picking your head off the ground about now.\"\n\n\"Sir Galen?\" I asked. \"I'll be sure to watch out for him.\" She had diamonds around her neck on a complex web of gold. Spanard work: none on the Horse Coast could make a thing like that. \"It wouldn't do for the King's guests to go about killing one another.\" I took her for the daughter of a merchant come a-toadying to the King. A very rich merchant, or maybe the daughter of some count or earl from the east: there was an eastern burr to her voice.\n\n\"You're a guest?\" She raised a brow at that, and very pretty it looked too. \"I think not. You look to have stolen in. By the privy chute to judge by the smell. I don't think you could have climbed the walls, not in that clunky old armour.\"\n\nI clicked my heels together, like the table knights, and offered her an arm. \"I was on my way to break fast in the kitchens. They know me there. Perhaps you'd like to accompany me and check my credentials, lady?\"\n\nShe nodded, ignoring my arm. \"I can send a kitchen-boy for the guards and have you arrested, if we don't meet any on the way.\"\n\nSo we walked side by side through the corridors and down one flight of stairs after another.\n\n\"My brothers call me Jorg,\" I said. \"How are you called, lady?\" I found the court-speak awkward on the tongue, especially with my mouth so unaccountably dry. She smelled like flowers.\n\n\"You can call me 'my lady,'\" she said, and wrinkled her nose again. We passed two of the house guards in their fire-bronze plate and plumes. Both of them studied me as if I was a turd escaped from the privy, but she said nothing and they let us pass.\n\nWe passed the storerooms where the salt beef and pickled pork lay in barrels, stacked to the ceiling. \"My lady\" seemed to know the way. She shot me a glance with those emerald eyes of hers.\n\n\"So did you come here to steal, or for murder with that dagger of yours?\" she asked.\n\n\"Perhaps a bit of both.\" I smiled.\n\nA good question though. I couldn't say why I'd come, other than I felt somebody didn't want me to. Ever since that moment when I found Father Gomst in his cage, ever since that ghost ran its course through me and my thoughts turned to the Tall Castle, it felt as though someone were steering me away. And I don't take direction.\n\nWe passed Short Bridge, little more than three mahogany planks over the great iron valves that could seal the lower levels from the castle main. The doors, steel and three feet thick, would slide up from the gaping slot in the corridor floor, so Tutor Lundist told me. Lifted on old magic. I'd never seen them close. Torches burned here, no silver lamps for the servant levels. The stink of tar-smoke made me more at home than anything yet.\n\n\"Perhaps I'll stay,\" I said.\n\nThe kitchen arch lay just ahead of us. I could see Drane, the assistant cook, wrestling half a hog through the doors.\n\n\"Wouldn't your brothers miss you?\" she asked, playful now. She touched her fingers to the corner of her mouth, where the red pattern of my fingers had started to rise. Something in her gesture made me rise too.\n\nI shrugged, then paused as I worked the straps of the vambrace over my left forearm. \"There are plenty of brothers on the road,\" I said. \"Let me show you the kind of brothers I meant . . .\"\n\n\"Here,\" she said, impatient.\n\nThe torchlight burned in the red of her hair. She undid the clasps with deft fingers. The girl knew armour. Perhaps Sir Galen was for more than just beheading ill-mannered louts?\n\n\"What then?\" she asked. \"I've seen arms before, though maybe not one so dirty.\"\n\nI grinned at that and turned my arm over so she could see the Brotherhood brand across my wrist. Three ugly bands of burn-scar. A look of distaste furrowed her brow. \"You're a sell-sword? You take your pride in that?\"\n\n\"More pride in that than in what true family I have left.\" I felt a bite of anger. I felt like sending this distracting merchant's daughter on her way, making her run.\n\n\"What are these?\" She reached out to run her fingers from the brand up to the small of my elbow where the armour stopped her. \"Jesu! There's more scar than boy under this dirt!\"\n\nAt her touch a thrill ran through me, and I pulled away. \"I fell in a thorn bush when . . . when I was a child,\" I said, my voice too sharp.\n\n\"Some thorn bush!\" she said.\n\nI shrugged. \"A hook-briar.\"\n\nShe twisted her mouth into an \"ouch.\" \"You've got to lie still in one of those,\" she said, her eyes still on my arm. \"Everyone knows that. Looks as if it tore you to the bone.\"\n\n\"I know that. _Now_.\" I set off for the kitchen doors, walking fast.\n\nShe ran to catch me, silks swirling. \"Why did you struggle? Why didn't you stop?\"\n\n\"I was stupid,\" I said. \"I wouldn't struggle now.\" I wanted the silly bitch to leave. I didn't even feel hungry any more.\n\nMy arm burned with the memory of her fingers. She was right, the thorns had cut me deep. Every few weeks for more than a year the poison would flare in the wounds and run through my blood. When the poison ran in me I'd done things that scared even the brothers.\n\nDrane lumbered out through the doors just as I reached them. He pulled up short, and wiped his hands on the soiled white apron stretched over his belly. \"Wh\u2014\" He looked past me and his eyes widened. \"Princess!\" He seemed suddenly terrified, quivering like a blob of jelly. \"Princess! Wh-what are you doing in the kitchens? It's no place for a lady in silks and all.\"\n\n\"Princess?\" I turned to stare at her. I'd left my mouth open, so I closed it.\n\nShe gave me a smile that left me wondering if I wanted to slap it off her, or kiss it. Before I could decide, a heavy hand landed on my shoulder, and Drane turned me round. \"And what's a ruffian like you doing leading her highness astray . . .\" The question died in his throat. His fat face crinkled up and he tried to speak again, but the words wouldn't come. He let me go and found his voice. \"Jorg? Little Jorg?\" Tears streamed down his cheeks.\n\nWill and I had watched the man throttle a few chickens and bake a few pies: there was no call for him to start blubbing over me. I let him off the embarrassment though, he'd given me the chance to see her royal highness look surprised. I grinned at her and gave a court bow.\n\n\"Princess, eh? So I guess that means the road-trash you wanted to have the palace guards arrest is in fact your step-brother.\"\n\nShe recovered her composure quickly. I'll give her that.\n\n\"Actually, that would make you my nephew,\" she said. \"Your father married my older sister two months ago. I'm your aunt Katherine.\"\n**20**\n\nWe sat at the long trestle where the kitchen skivvies ate their meals, Aunt Katherine and I. The servants cleared the low vault and brought in more light, candles of every length and girth in clay holders. They watched from the doorways at either end, a shabby crowd grinning and bobbing as though it was a holy day or a high day, and we were the mummers to entertain them. Drane hove into view and crested through the skivvies like a barge through water. He brought fresh bread, honey in a bowl, golden butter, and silver knives.\n\n\"This is the place to eat,\" I said. I kept my eyes on Katherine. She didn't seem to mind. \"Bread hot from the oven.\" It steamed when I tore it open. Heaven must smell like fresh bread. \"I knew I missed you for a reason, Drane.\" I called the words over my shoulder. I knew the fat cook would bask in that for a year. I hadn't missed him. I hadn't spared him but one thought for every hundred times I dreamed of his pies. In fact I'd struggled to remember his name when I saw him in the doorway. But something about the girl made me want to be the kind of man who would remember.\n\nThe first bite woke my hunger and I tore at the loaf as though it were a haunch of venison and me huddled on the road with the brothers. Katherine paused to watch, her knife suspended above the honey bowl, her lips twitching with a smile.\n\n\"Mmmfflg.\" I chewed and swallowed. \"What?\" I demanded.\n\n\"She's probably wondering if you'll go under the table when the bread's gone and wrestle the dogs for bones.\" Makin had come up behind me unnoticed.\n\n\"Damn but you'd make a good footpad, Sir Makin.\" I swung round to find him standing over me, his armour gleaming. \"A man in plate-mail should have the decency to clank.\"\n\n\"I clanked plenty, Prince,\" he said. He showed me an annoying smile. \"You had your mind on more pressing matters maybe?\" He bowed toward Katherine. \"My lady. I haven't had the honour?\"\n\nShe extended a hand to him. \"Princess Katherine Ap Scorron.\"\n\nMakin raised a brow at that. He took her hand and bowed again, much more deeply, lifting her fingers to his lips. He had thick lips, sensuous. He'd washed his face and his hair gleamed as much as his armour, coal-black and curled. He cleaned up well, and for the smallest moment I hated him without reservation.\n\n\"Take a seat,\" I said. \"I'm sure the excellent Drane can find more bread.\"\n\nHe let go of her hand. Too slowly for my liking. \"Sadly, my prince, duty rather than hunger brings me to the kitchens. I thought I might find you here. You're summoned to the throne-room. There must be a hundred squires hunting the halls for you. You also, Princess.\" He favoured her with an appreciative stare. \"I met a fellow named Galen searching for you.\" Something tight laced those last words. Makin didn't like Sir Galen any more than I did. And he'd met the man.\n\nI took the bread with me. It was too good to leave.\n\nWe found our way back above ground. The Tall Castle appeared to have woken up during my trip to the kitchens. Squires and maids ran this way and that. Plumed guards passed by in twos and fives, bound for their duties. We skirted a lord in his furs and gold chain, girded by flunkies, leaving him with his astonishment, his bowing, and his \"Good morning, Princess!\"\n\nBy corridor and hall we reached Torrent Vault, the antechamber before the throne-room where the tourney armour of past kings lined the walls like hollow knights standing silent vigil.\n\n\"Prince Honorous Jorg Ancrath, and the Princess Katherine,\" Makin announced us to the guards before the doors. He placed me before the princess. A small matter on the road, but a touch that spoke volumes in the Torrent Vault. _Here is the heir to the throne, let him in_.\n\nThe crested guardsmen flanking the hallway stood as still as the armour on the stands behind them. They followed us only with their eyes, gauntleted hands kept folded on the pommels of their greatswords, set point to floor. The two table knights at the throne-room doors exchanged a glance. They paused for a moment to bow to Katherine, then set to work drawing the great doors open wide enough to admit us. I recognized one of them by the coat of arms on his breastplate, horns above an elm. Sir Reilly. He'd turned grey in the years I'd been gone. He struggled with his door, straining to move the oak in its bronze cladding. The doors parted. Our narrow view grew from a sliver of warm light to a window on a world I once knew. The Court of the Ancrath kings.\n\n\"Princess?\" I took her hand, holding it high, and we walked through.\n\nThe men that built the Tall Castle lacked nothing in skill, and everything in imagination. Their walls might remain for ten thousand years, but they would hold no artistry. The throne-room was a windowless box. A box one hundred feet on every side maybe, and with a twenty-foot ceiling to dwarf the courtiers, but a box nonetheless. Elaborate wooden galleries for the musicians muted the harsh corners, and the King's dais added a certain splendour. I kept my eyes from the throne.\n\n\"The Princess Katherine Ap Scorron,\" the herald called.\n\nNo mention of poor Jorgy. No herald would dare such a slight without instruction.\n\nWe crossed the wide floor, our pace measured, watched by the guardsmen at the walls. Men with crossbows by the walls to left and right, swordsmen at the plinth and by the door.\n\nI might have been nameless, but my arrival had certainly roused some interest. In addition to the guardsmen and despite the early hour, at least a hundred courtiers formed our audience. They waited attendance on the throne, milling around the lowest steps in their velvets. I let my eyes stray across the glittering crowd, pausing to linger on the finest jewels. I still had my road-habits and made mental tally of their worth. A new charger on that countess's fat bosom alone. That lord's chain of office could buy ten suits of scale armour. There was surely a fine longbow and a pony in each of his rings. I had to remind myself I played for new stakes now. Same old game, new stakes. Not higher, but different.\n\nThe gentle chatter of the court rose and fell as we approached. The soft hubbub of knife-edged comments, damaging sarcasm, honeyed insults. Here the sharp intake of breath at the Prince coming to court still wearing the road, there the mocking laughter half-hidden behind a silk handkerchief.\n\nI let myself look at him then.\n\nFour years had wrought no change in my father. He sat on the high-backed throne, hunched in a wolf-skin robe edged with silver. He'd worn the same robe on the day I left. The Ancrath crown rested on his brow: a warrior crown, an iron band set with rubies, confining black hair streaked with the same grey as the iron. To his left, in the consort chair, the new queen sat. She had Katherine's looks, though softer, with a web of silver and moonstones to tame her hair. Any sign of her pregnancy lay hid beneath the ivory froth of her gown.\n\nBetween the thrones grew a magnificent tree, wrought all of glass, its leaves the emerald of Katherine's eyes, wide and thin and many. It reached a slender nine feet in height, its twigs and branches gnarled and vitreous, brown as caramel. I'd never seen the like before. I wondered if it might be the Queen's dowry. Surely it had the worth.\n\nSageous stood beside the glass tree, in the dappled green light beneath its leaves. He'd abandoned the simple white he'd worn when first we met in favour of black robes, high in the collar, with a rope of obsidian plates about his neck. I met his eyes as we approached, and manufactured a smile for him.\n\nThe courtiers drew back before us, Makin to the fore, Katherine and me hand in hand. The perfumes of lords and ladies tickled at my nose: lavender and orange oil. On the road, shit has the decency to stink.\n\nOnly two steps down from the throne a tall knight stood in magnificent plate, the iron worked over with fire-bronze, twin dragons coiling on his breastplate in a crimson inferno.\n\n\"Sir Galen.\" Makin hissed the words back at me.\n\nI glanced at Katherine and found her smile unreadable. Galen watched us with hot blue eyes. I liked him a little better for wearing his hostility so plainly. He had the blonde hair of a Teuton, his features square and handsome. He was old though. As old as Makin. Thirty summers at the least.\n\nSir Galen made no move to let Makin past. We stopped five steps down.\n\n\"Father,\" I said. In my head, I'd made my speech a hundred times but somehow the old bastard managed to steal the words from my tongue. The silence stretched between us. \"I hope\u2014\" I started again but he cut over me.\n\n\"Sir Makin,\" Father said, not even looking at me. \"When I send the captain of the palace guard out to retrieve a ten-year-old child, I expect him to return by nightfall. Perhaps a day or three might suffice if the child proved particularly elusive.\" Father raised his left hand from the arm of the throne, just by an inch or two but enough to cue his audience. A scattered tittering sounded among the ladies, cut off when his fingers returned to the iron-wood of the chair.\n\nMakin bowed his head and said nothing.\n\n\"A week or two on such a task would signify incompetence. More than three years speaks of treason.\"\n\nMakin looked up at that. \"Never, my king! Never treason.\"\n\n\"We once had reason to consider you fit for high office, Sir Makin,\" Father said, his voice as cold as his eyes. \"So, you may explain yourself.\"\n\nThe sweat gleamed on Makin's brow. He'd have gone through this speech as many times as I had mine. He'd probably lost it just as profoundly.\n\n\"The Prince has all the resourcefulness one might hope for in the heir to the throne,\" Makin began. I saw the Queen frown at his turn of phrase. Even Father's mouth tightened and he glanced at me, fleeting and unreadable. \"When at last I found him we were in hostile lands . . . Jaseth . . . more than three hundred miles to the south.\"\n\n\"I know where Jaseth is, Sir Makin,\" Father said. \"Do not presume to lecture me on geography.\"\n\nMakin inclined his head. \"Your majesty has many enemies, as do all great men in these times of trouble. No single blade, even one as loyal as my own, could protect your heir in such lands as Jaseth. Prince Jorg's best defence lay in anonymity.\"\n\nI glanced over the court. It seemed that Makin's speech had not deserted him after all. His words had an impact.\n\nFather ran a hand over his beard. \"Then you should have ridden back to the castle with a nameless charge, Sir Makin. I wonder that this journey took four years.\"\n\n\"The Prince had taken up with a band of mercenaries, your majesty. By his own skill he won their allegiance. He told me plain that if I moved to take him, they would kill me, and that if I stole him away, he would announce himself to every passer-by. And I believed him, for he has the will of an Ancrath.\"\n\n_Time to be heard_ , I thought. \"Four years on the road have given you a better captain,\" I said. \"There's more to learn about making war than can be discovered in this castle. We\u2014\"\n\n\"You lack enterprise, Sir Makin,\" Father said. His eyes never flickered from Makin. I wondered if I'd spoken at all. Anger tinged his voice now. \"Had I ridden out after the boy, I would have found a way to return with him from Jaseth within a month.\"\n\nSir Makin bowed deeply. \"That is why you deserve your throne, majesty, whilst I am merely captain of your palace guard.\"\n\n\"You are the captain of my guard no longer,\" Father said. \"Sir Galen serves in that capacity now, as he served the House of Scorron.\"\n\nGalen offered Makin the slightest of bows, a mocking smile on his lips.\n\n\"Perhaps you would like to challenge Sir Galen for your old office?\" Father asked. Again he fingered his salt-and-pepper beard.\n\nI sensed a trap here. Father didn't want Makin back.\n\n\"Your majesty has chosen his captain,\" Makin said. \"I would not presume to over-write that decision with my sword.\" He sensed the trap too.\n\n\"Indulge me.\" Father smiled then, for the first time since our entrance, and it was a cold thing. \"The court has been quiet in your absence. You owe us some entertainment. Let us have a show.\" He paused. \"Let us see what you have learned on the road.\" So he did hear me.\n\n\"Father\u2014\" I started. And again he cut me off. I couldn't seem to rise above him.\n\n\"Sageous, take the boy,\" he said.\n\nAnd that was that. The heathen had his eyes on me and led me mild as a sheep to stand with him between the thrones. Katherine shot me a pale glance and hastened to her sister's side.\n\nMakin and Galen bowed to the King. They went out through the press of courtiers, breaking free and crossing to where an inlaid marble star, some ten feet across, marked the middle of the throne-room floor. They faced each other, bowed, and drew steel.\n\nMakin bore the longsword Father gave him when he took captaincy of the palace guard. A good weapon, Indian steel woven dark and light, acid-etched with old runes of power. Our time on the road had left its history recorded in notches along the blade. I'd never seen a better swordsman than Makin. I didn't want to see one here.\n\nSir Galen made no move. He held his longsword ready, but in a lazy grip. I could see no marking on the weapon, a simple blade, forged from the black iron of the Turkmen.\n\n\"Never trust a Turkman sword . . .\" I spoke in a whisper.\n\n\"For Turkman iron sucks up spells like a sponge and holds a bitter edge.\" Sageous finished the old line for me.\n\nI had a sharp reply for the heathen, but the clash of swords rang out over it. Makin advanced on the Teuton, feinting low then swinging high. Makin had an elemental way with a sword. The blade was part of him, a living thing from tip to hilt. In a wild fight he knew where every danger lay, and where his cover waited.\n\nSir Galen blocked and delivered a sharp riposte. Their swords flickered and the play of metal rang out high and sharp. I could barely follow the exchange. Galen fought with technical precision. He fought like a man who rose at dawn every day to train and duel. He fought like a man who expected to win.\n\nA hundred narrow escapes from death counted out the first minute of their duel. I found my right hand gripping the trunk of the glass tree, the crystal slick and cool under my fingers. By the end of that first minute I could tell Galen would win. This was his game. Makin had his brilliance but, like me, he fought in real fights. He fought in the mud. He fought through burning villages. He used the battlefield. But this dry little game, so narrow in its scope, this was all Galen lived for.\n\nMakin swung at Galen's legs. A touch too tight in the curve, and Galen made him pay. The tip of the Turkman blade sketched a red line across Makin's forehead. A quarter of an inch more reach in Galen's arm and the blow would have shattered Makin's skull.\n\n\"So, you open your game by sacrificing your knight, Prince Jorg.\" Sageous spoke close to my ear.\n\nI startled. I'd forgotten about the man. My gaze wandered to the green canopy above us. \"I have no problems with sacrifice, heathen.\" The tree trunk slipped glassy smooth under my fingers as my left hand moved up along the trunk. The clash of swords punctuated our conversation. \"But I sacrifice only when there is something to be gained.\"\n\nThe tree was heavier than I had imagined and for a moment I didn't think I could topple it. I braced my legs and put my shoulder to the task. The thing fell without a sound, then exploded into a million pieces against the steps. I could have blinded half of Ancrath's aristocracy had their eyes been on the throne rather than the fight before them. As it was, I peppered their backs with shards of glass. The costumed throng at the base of the royal dais turned into a screaming mass. Noble-born women ran their hands through hair confined by diamond tiaras, and brought them out sliced and bloody. Lords in thread-of-gold slippers, coiled in the latest fashions, hopped howling on a carpet of broken glass.\n\nSir Makin and Sir Galen lowered their swords and watched in amazement.\n\nWhen Father stood, everyone fell silent, cuts or no cuts.\n\nEveryone except me. He opened his mouth to speak and I spoke first.\n\n\"The lessons Makin learned on the road did not include tourney games. Wars are not won with jousting or chivalry. The lessons Makin learned are the same lessons I learned. Unfortunately Sir Makin would rather die than offend his king by demonstrating them.\" I didn't raise my voice. That kept them quiet. \"Father.\" I turned to face him direct. \"I'll show you what I've learned. I'll fight your pet Teuton. If a man of my little experience can defeat your champion, then you should be happy to reinstate Sir Makin, neh?\" I fell back into road-speak, hoping to stir his anger.\n\n\"You're not a man, boy, and your challenge is an insult to Sir Galen, not worthy of consideration.\" He spoke through clenched teeth. I'd never seen him so angry. In fact, I'd never seen him angry.\n\n\"An insult? Maybe.\" I felt a smile bubbling up and let it show. \"But I am a man. I came of age three days ago, Father. I'm fit for marriage now. A valuable commodity. And I claim this fight as my Year Gift. Or would you turn your back on three centuries of Ancrath tradition and deny me my coming of age boon?\"\n\nThe veins in his neck stood proud and his hands flexed as if hungry for a sword. I didn't think it safe to count on his good will.\n\n\"If I die, the succession will be clear,\" I said. \"Your Scorron whore will give you a new son, and you'll be rid of me. Gone for good, like Mother and William. And you won't have to send dear old Father Gomst trawling the mire to prove it.\" I took a moment to bow toward the Queen. \"No offence, your majesty.\"\n\n\"Galen!\" Father's voice was a roar. \"Kill this devil, for he's no son of mine!\"\n\nI ran then, crunching emerald leaves under hard leather. Sir Galen charged from the centre star, trailing his black sword behind him, shouting for my blood. He came fast enough, but the fight with Makin had taken some of his wind. I knocked an old woman from my path, she went down spitting teeth, pearls spilling from her broken necklace.\n\nI won free of the courtiers and kept on running, angled away from Galen. He'd given up the shouting but I could hear him behind me, the thud of his boots and the rasp of his breath. He must have been a hand above six foot, but lighter armour and fresher wind made up for my shorter legs. As we ran, I pulled out my sword. There were charms enough in its edge to put a notch in that Turkman blade. I threw it away. I didn't need the weight.\n\nLittle space remained to me. The left wall loomed just yards ahead, Galen moments behind.\n\nI'd been aiming for one guardsman in particular, a younger fellow with fair sideburns and an open mouth. By the time he realized I wasn't veering away, it was too late. I hit him with the vambrace over my right forearm. The blow hammered his head back against the wall and he slid down it with no further interest in the proceedings. I caught the crossbow in my left hand, turned, and shot Galen through the bridge of the nose.\n\nThe bolt barely made it through his skull. It's one of the drawbacks in keeping them loaded, but still it should have been tightened only hours before. In any event, most of the Teuton's brain left by the back of his head and he fell down very dead.\n\nThe silence would have been utter but for the whimpering of the old woman on the floor back by the dais. I looked back over the crowd of nobles, cut and bloody, at Galen lying with his arms flung out, at the sparkling ruins of the glass tree reaching toward the throne-room doors.\n\n\"Was the show to your liking, Father?\" I asked. \"I've heard that the court has been quiet in Sir Makin's absence.\"\n\nAnd for the first time in my life I heard my father laugh. A chuckle at first, then louder, then a howling gale such that he had to hold his throne to stand.\n**21**\n\n\"Get out.\" Father's laughing fit left him without warning, snuffed like a candle. He spoke into the silence. \"Get out. I'll talk to the boy now.\" The boy, not \"my son.\" I didn't miss that edge.\n\nAnd they went. The high and the mighty, the lords and the ladies, the guards helping the injured, two of them dragging Galen's corpse. Makin followed after Galen, crunch, crunch, crunch, across the broken glass, as if to make sure no life remained in him. Katherine let herself be led by a table knight. She stopped though, at the base of the dais, and gave me a look as if she'd just that moment seen me for what I was. I sketched her a mocking bow, a reflex, like reaching for a blade. It hurt to see the hatred on her face, pure and astonished, but sometimes a bit of pain's just what we need: to cauterize the wound, burn out the infection. She saw me and I saw her, both of us stripped of pretence in that empty moment, newlyweds naked for their conjugals. I saw her for the same weakness I'd recognized when first we rode back into the green fields of Ancrath. That soft seduction of need and want, an equation of dependence that eases under the skin, so slow and sweet, only to lay a man open at the very time he most needs his strength. Oh, it hurt right enough, but I finished my bow and watched her back as they led her out.\n\nThe Queen went too, flanked by knights right and left, slightly awkward down the steps, a hint of a waddle. I could see the swell of her belly now, as she walked. My half-brother if Sageous's prediction held true. Heir to the throne should I die. Just a swelling now, just a hint, but sometimes that's all it takes. I recalled Brother Kane from the road, cut on the bicep when we took the village of Holt.\n\n\"'T'ain't nothing, little Jorgy,\" he'd said when I offered to heat a knife. \"Some farm boy with a rusty hoe. It don't go deep.\"\n\n\"It's swelling,\" I told him. \"Needs hot iron.\" If it's not too late already.\n\n\"Fuck that, not for some farm boy with a hoe,\" Kane said.\n\nHe died hard, did Kane. Three days later and his arm lay as thick as my waist, weeping pus greener than snot, and with a stench so bad we left him screaming to die alone. _It don't go deep_ \u2014but sometimes the shallow cut bites to the bone if you don't deal with it hard and fast.\n\nJust a swelling. I watched the Queen go.\n\nSageous stayed. His eyes kept returning to the shattered ruin of the tree. You'd have thought he'd lost his lover.\n\n\"Pagan, see to the Queen,\" Father said. \"She may need calming.\"\n\nA dismissal, plain and simple, but Sageous was too distracted to see it. He looked up from the glittering remains of the trunk I'd toppled. \"Sire, I . . .\"\n\n_You what, heathen? You want something? It's not your place to want._\n\n\"I . . .\" This was new to Sageous, I could see that: he was used to control. \"You should not be left unattended, Sire. The b\u2014\"\n\n_The boy? Say it man, spit it out._\n\n\"It may not be safe.\"\n\nWrong thing to say. I guessed the heathen had relied on his magics too long. If he'd truly learned my father's mind, he'd know better than to suggest he needed protection from me.\n\n\"Out.\"\n\nWhatever else I might think of my dear father I always did admire his way with words.\n\nThe look Sageous gave me held more than hate. Where Katherine channelled a pure emotion the tattooed magician offered bewildering complexity. Oh, there was hate there, sure enough, but admiration too, respect maybe, and other flavours, all mixed in those mild brown eyes.\n\n\"Sire.\" He bowed and started toward the doors.\n\nWe watched him in silence, watched him pace across the sparkling carpet of debris, spotted here with a discarded fan, there with a powdered wig. The doors closed behind him with a dull clang of bronze on bronze. A scar on the wall behind the throne caught my attention. I threw a hammer once, hard, and missed my target. It hit there. It seemed to be a day for old scars, old feelings.\n\n\"I want Gelleth,\" Father said.\n\nI had to admire his ability to wrong-foot me. I stood there armed with accusations, burdened with all my yesterdays, and he'd turned away from me, to the future.\n\n\"Gelleth hinges on the Castle Red,\" I said. It was a test. That was just how we spoke. Every conversation a game of poker, every line a bet or a raise, a bluff or a call.\n\n\"Party tricks are well and good. You killed the Teuton. I didn't think you had it in you. You scandalized my court\u2014well, we both know what they are, and what they're worth. But can you do it when it counts? Can you give me Gelleth?\"\n\nI met his stare. I didn't inherit his blue eyes, I followed Mother in that department. There was a whole winter in those eyes of his, and nothing else. Even in Sageous's placid gaze I could dig deeper and find a subtext, but Father's eyes held nothing but a cold season. I think that was where the fear lay, in the lack of curiosity. I've seen malice many a time and hate in all its colours. I've seen the gleam in the torturer's eyes, the sick-light, but even there was the comfort of interest, the slightest touch of salvation in shared humanity. He might have the hot irons, but at least he was curious, at least he cared how much it hurt.\n\n\"I can give you Gelleth,\" I said.\n\nCould I? Probably not. Of all Ancrath's neighbours, Gelleth stood unassailable above the rest. The Lord of Gelleth probably had better claim to the Empire Throne than Father did. In the Hundred, Merl Gellethar had few equals.\n\nI found my hand on the hilt of my dagger. I itched to draw the tempered steel, to lay it across his neck, to scream at him, to bring some heat into those cold eyes. _You traded my mother's death away, you bastard! Your own son's blood. Sweet William dead and barely cold, and you traded them away. A pax for the rights to river trade_.\n\n\"I'll need an army,\" I said. \"Castle Red won't fall easy.\"\n\n\"You will have the Forest Watch.\" Father spread his hands over the throne's armrests and leaned back, watching.\n\n\"Two hundred men?\" I felt my fingers tighten on the pommel of my knife. Two hundred men against the Castle Red. Ten thousand might not be enough.\n\n\"I'll take my brothers too,\" I said. I watched his eyes. No flicker in the winter, no start at \"brother.\" The weakness in me wanted to speak of Will. \"You'll have Gelleth. I will give you the Castle Red. I'll give you the head of the Lord Gellethar. Then you'll give the heathen to me.\"\n\n_And you'll call me \"son_. _\"_\n**22**\n\nSo we sat, Makin and I, at a table in The Falling Angel tavern with a jug of ale between us, and the song of a cracked-voice bard struggling to be heard against the din. Around us the brothers mixed with the lowest of the Low Town, gaming, whoring, and gorging. Rike sat close at hand, his face buried in a roast chicken. He appeared to be attempting to inhale it.\n\n\"Have you even seen the Castle Red, Jorg?\" Makin asked.\n\n\"No.\"\n\nMakin looked at his ale. He hadn't touched it. For a few moments we listened to the sound of Rike crunching chicken bones.\n\n\"Have you?\" I asked.\n\nHe nodded slowly and leaned back in his chair, eyes on the lanterns above the street-door. \"When I was a squire to Sir Reilly, we took a message to the Lord Gellethar. We stayed a week in the guest halls at the Castle Red before Merl Gellethar deigned to see us. His throne-room puts your father's to shame.\"\n\nBrother Burlow staggered by, belly escaping over his sturdy belt, a haunch of meat in one hand and two flagons in the other, foaming over his knuckles.\n\n\"What about the castle?\" I could care less about a pissing contest over throne-rooms.\n\nMakin toyed with his ale, but didn't drink. \"It's suicide, Jorg.\"\n\n\"That bad?\"\n\n\"Worse,\" he said.\n\nA painted whore, hennaed hair and red-mouthed, backed into Makin's lap. \"Where's your smile, my handsome?\" She had good tits, full and high, pushed into an inviting sandwich in a bodice of lace and whalebone. \"I'm sure I could find it.\" Her hands vanished into the froth of her skirts where they bunched around Makin's waist. \"Sally will make it all good. My handsome knight doesn't need no boys to keep him warm.\" She flicked a jealous glance my way.\n\nMakin pitched her to the floor.\n\n\"It's built into a mountain. What shows above the rock are walls so high it hurts your neck to look up at the battlements.\" Makin reached for his ale and fastened both hands around the flagon.\n\n\"Ow!\" The whore picked herself up from the wet boards and wiped her hands on her dress. \"You didn't have to do that now!\"\n\nMakin didn't spare her a glance. He turned his dark eyes on me. \"The doors are iron, thick as a sword is long. And what's above the ground isn't but a tenth part of it. There's provisions in those deep vaults to last years.\"\n\nSally proved to be a true professional. She transferred her attentions to me, so smooth you'd think I'd been the object of her affection all along. \"And who might you be, now?\" She came in close, running her fingers into my hair. \"You're too pretty for that grumpy sell-sword,\" she said. \"You're old enough to learn how it works with girls, and Sally will show you.\"\n\nShe had her mouth close to my ear now, sending tickles down my neck. I could smell her cheap lemon-grass scent, cutting through the ale stink, and the dream-weed on her breath.\n\n\"How many men would it take? To bring the place down around Lord Gellethar's ears?\" I asked.\n\nMakin's eyes returned to the lanterns and his knuckles went white around his flagon. Somewhere behind us Rike gave a roar, quickly followed by the splintering sound of a body meeting a table at high speed.\n\n\"If you had ten thousand men,\" Makin said, raising his voice above the crashing sounds. \"Ten thousand men, well supplied, and with siege machines, lots of siege engines, then you might have him in a year. That's if you could keep his allies off your back. With three thousand you might starve him out eventually.\"\n\nI caught hold of Sally's hand as it slipped across my belly to the buckle of my belt. I twisted her wrist a little, and she came front and centre, sharpish, with a high-pitched gasp. She had green eyes, like Katherine's but more narrow and not so clear. Under the paint she had fewer years on me than I first thought, she might be twenty, certainly no more.\n\n\"And what if I found us a way in? What then, Brother Makin? How many men to take the Castle Red if I opened us a door?\" I spoke to Sally's face, inches before mine.\n\n\"The garrison stands at nine hundred. Veterans mostly. He sends his fresh meat to the borders and takes it back when it's been seasoned.\" I heard Makin's chair scrape back. \"Which son of a whore threw that?\" he yelled.\n\nI kept the whore's wrist turned. I took her throat in my other hand and drew her closer. \"Tonight we'll call you Katherine, and you can show me how it works with girls.\"\n\nSome of the dream-haze left her eyes, replaced by fear. That was all right with me. I had two hundred men and no secret door into the Castle Red. It seemed only right that somebody should be worried.\n**23**\n\nMy book shifted again. I say \"my\" book, but in truth it was stolen, filched from Father's library on the way out of the Tall Castle. The book lurched at me, threatening to snap shut on my nose.\n\n\"Lie still, damn you,\" I said.\n\n\"Mmmgfll.\" Sally gave a sleepy murmur and nestled her face in the pillow.\n\nI settled the book back between her buttocks and nudged her legs slightly further apart with my elbows. Over the top of the page I could see the faint-knobbed ridge of Sally's spine tracing its path across her smooth back to be lost in the red curls around her neck. I wasn't convinced that the text before me was more interesting than what lay beneath it.\n\n\"It says here that there's a valley in Gelleth they call the Gorge of Leucrota,\" I said. \"It's in the badlands down below the Castle Red.\"\n\nThe morning light streamed through the open window. The air had a chill to it, but a good one, like the bite on ale.\n\n\"Mmmnnn.\" Sally's voice came from the pillow.\n\nI'd tired her out. You can wear even whores out when you're that young. The combination of a woman and time on my hands wasn't one I'd tried before. I found the mix to my liking. There's a lot to be said for not being in a queue, or not having to finish up before the flames take hold of the building. And the willingness! That was new too, albeit paid for. In the dark I could imagine it was free.\n\n\"Now if I know my ancient Greek, and I do, a leucrota is a monster that speaks with a human voice to lure its prey.\" I bent my neck to bite at the back of her thigh. \"And in my experience, any monster that talks in a human voice, is human. Or was.\"\n\nMy feet hung over the end of the bed. I wiggled my toes. Sometimes that helps.\n\nI reached for the oldest of the three books I'd stolen. A Builder text on plasteek sheets, wrinkled by some ancient fire. Scholars in the east would pay a hundred in gold for Builder texts, but I hoped for more profit than that.\n\nI'd been taught the Builder speech by Tutor Lundist. I learned it in a month and he'd gone bragging to anyone who'd listen, until Father shut his mouth with one of those dark looks he's famed for. Old Lundist said I knew the Builder speech as well as any in the Broken Empire, but I couldn't make sense of more than half the words in the little book I'd stolen.\n\nI could read the \"Top Secret\" at the head and foot of every page, but \"Neurotoxicology,\" \"Carcinogen,\" \"Mutogen\"? Maybe they were old styles of hat. To this day I don't know. The words I did recognize were interesting enough though. \"Weapons,\" \"Stockpile,\" \"Mass Destruction.\" The last but one page even had a shiny map, all contours and elevations. Tutor Lundist taught me a little geography as well. Enough to match that small map to the \"Views from Castle Red\" painstakingly executed in the large but dull _A History of Gelleth_ whose leather-bound spine nestled in the cleft of dear Sally's oh-so-biteable backside.\n\nEven when I understood the Builder words, the sentences didn't make sense. \"Binary weapon leakage is now endemic. The lighter than air unary compounds show little toxic effect, though rosiosis is a common topological exposure symptom.\"\n\nOr, from the same page: \"Mutagenic effects are common downstream of binary spills.\" I could stretch my Greek to guess the meaning, but it hardly seemed reasonable. Perhaps I'd stolen an old storybook?\n\n\"Jorg!\" Makin hollered through the door. \"The escort's here to take you to the Forest Watch.\"\n\nSally started up at that, but I pressed her down.\n\n\"Tell them to wait,\" I called.\n\nThe Forest Watch weren't going to be much use to me. Not unless they had ten thousand friends that wanted to come along.\n\n\"Sweet Jesu I'm sore.\" Sally tried to get up again. \"Oh! It's morning already. Sammeth will kill me.\"\n\n\"I said still, damn it.\" I found a coin from my purse on the table and tossed it up to her. \"That for your damn Sammeth.\"\n\nShe slumped back with a comfortable protest.\n\n\"Binary weapon leakage . . .\" As if speaking the words would add meaning.\n\n\"You're going to the Castle Red then?\" Sally said. She stifled a yawn.\n\nI raised a hand to slap her into silence. Of course she didn't see it and _A History of Gelleth_ blocked the best target.\n\n\"Say hello to all those little red people for me,\" she said.\n\n_Rosiosis._\n\nI lowered my hand to her hip. \"Little red people?\"\n\n\"Uh huh.\"\n\nI felt her wiggle under my palm. I gripped harder. \"Little red people?\"\n\n\"Yes.\" A whine of irritation tinged her voice. \"Why do you think they call it the Castle Red?\"\n\nI pulled myself to a sitting position. \"Makin! Get in here!\" I shouted it loud enough for the whole inn to hear. He came in sharp enough, one hand on his sword. A smile found its way to his lips when he saw Sally sprawled out naked, but he kept his hand where it was.\n\n\"My prince?\"\n\nSally really did try to get up at that. She almost made it to all fours and _A History_ went flying.\n\n\"Prince? Nobody said nothing about a prince! He ain't no bleedin' prince!\"\n\nI pushed her down again.\n\n\"That conversation we had yesterday, Makin,\" I said.\n\n\"Yes?\"\n\n\"Anything you'd like to add to the description? Anything about those nine hundred veterans?\" I asked.\n\nFor a moment he looked as blank as idiot Maical.\n\n\"Something about the colour scheme?\" I gave him a prompt.\n\n\"Oh.\" He grinned. \"The Blushers? Yes. They're red as a cooked lobster, every one of them. Something in the water they say. I thought everyone knew that.\"\n\n_Rosiosis._\n\n\"I never knew it,\" I said.\n\n\"Sounds like your father should have hanged Tutor Lundist then,\" Makin said. \"Everyone knows that.\"\n\n_Monsters down below._\n\n\"He's never a prince!\" Sally sounded outraged.\n\n\"You've been royally fucked.\" Makin gave her a little bow.\n\n_Castle Red and all its red soldiers up above._\n\nI got off the bed.\n\n_Weapons stockpile._\n\n_Leakage._\n\n\"So,\" Makin said. \"Are we ready to go?\"\n\nI reached for my trews. Sally rolled over as I laced them up, which didn't help at all. I watched her nakedness, highlights courtesy of the morning sun. I wondered\u2014should I gamble the Forest Watch and the brothers both on some wild conjectures and blind guesses at what obscure words meant . . .\n\n\"Tell them an hour.\" My fingers flipped from lacing to unlacing. \"I'll be ready in an hour.\"\n\nSally lay back on the pillows and smiled. \"Prince, eh?\"\n\nLying in seemed like a good idea all of a sudden.\n**24**\n\n\"What ho! Captain Coddin!\" I came down the stairs in remarkably good spirits shortly before noon.\n\nThe Captain gave me a stiff bow, his lips pressed into a tight line. In a far corner the younger brothers, Roddat, Jobe, and Sim, nursed hangovers. I could see Burlow under a table, snoring.\n\n\"I'd have thought you'd be back at Chelny Ford, Captain, protecting our borders from the predations of villains and rogues,\" I said, all cheery-like.\n\n\"There was some dissatisfaction with my performance in the role. Certain voices at court maintained that I'd let a sight too many villains and rogues past my garrison of late. I'm assigned to escort duty in Crath City.\" He gestured to the street-door. \"If Prince Jorg is ready?\"\n\nI decided I liked the man. That surprised me. I'm not given to liking people as a rule. I blamed it on my mood. Nothing like a night of whoring to turn a man soft.\n\nSo Coddin and his four soldiers led us out through the West Gate. I had Makin with me of course, and Elban because old though he was, there weren't many among the brothers with more than half a brain. I brought the Nuban along too. Not sure why, but he'd been sat by the bar eating an apple, with that crossbow of his across his lap, and I thought I'd have him along.\n\nWe took the Old Road toward Rennat Forest, twelve miles or so as the crow flies, and of course the Old Road flies like a crow, following the line laid down by men of Rome an age upon an age ago.\n\nCoddin rode at the fore, flanked by his boys, us behind enjoying the day. Makin nudged Firejump up alongside Gerrod and the two of them exchanged whatever threats pass between stallions.\n\n\"You should have left me to Sir Galen, Jorg,\" Makin said.\n\n\"You think you could have taken him?\" I asked.\n\n\"No. He knew his swordwork, that Teuton,\" Makin said, and he wiped a hand across his mouth. \"I've never crossed blades with a better man.\"\n\n\"He wasn't the better man,\" I said.\n\nA silence fell between us for a moment. Elban broke it.\n\n\"Makin found a man he couldn't beat? Sir Makin? I don't believe it.\" His lisp made a wet \"Thur\" of \"Sir.\"\n\nMakin turned in the saddle to face Elban. \"Believe it. The King's champion had me cold. Jorg beat him, though.\" He nodded toward the Nuban. \"With a crossbow. You'd have been proud.\"\n\nThe Nuban ran a soot-black hand over the ironwork of his bow, touching the faces of his pagan gods. \"There's no pride in this, Makin.\"\n\nI could never read the Nuban. One moment he'd seem as simple as Maical, the next, deeper than a deep well. Sometimes both at once.\n\n\"Maical,\" I said, remembering. \"What happened to our pet idiot in the end? Did he die? I forgot to ask.\"\n\n\"We left him in Norwood, Jorth. He should have been dead, with that gut-wound, but he just hung on, moaning all the time,\" Elban said. He wiped the spittle from his chin.\n\n\"Too stupid to die,\" Makin said. He grinned. \"We had to drag him off to a house at the edge of town. Little Rikey was all for finishing him off, just to shut him up.\"\n\nWe had us a chuckle over that.\n\n\"Seriously though, Jorg, you should have left Galen to it,\" Makin said. \"If you had, you'd be sitting pretty at court. You're still heir to the throne. You'd have got that saucy princess in time. The Castle Red is a death sentence for smashing that stupid tree. That and calling his wife a Scorron whore. Your father is not a forgiving man.\"\n\n\"You'd be right in all that, Makin,\" I said. \"If my ambition were limited to 'sitting pretty,' I'd have let the Teuton do his worst. Luckily for you, I want to win the Hundred War, reunite the Broken Empire, and be Emperor. And if I'm going to stand any chance of that, then taking the Castle Red with two hundred men will be a piece of cake.\"\n\nWe had our lunch at a milestone on the margins of the forest. Mutton, swiped from the kitchens at The Falling Angel. We were still wiping the grease from our fingers when we rode in under the trees\u2014big oaks and beeches in the main\u2014blushing crimson with the kiss of autumn frost. Riding under those branches, with the crunch of hoof on leaves, and the breath of horses pluming before us, I felt it again, that sweet hook sinking beneath the skin. They say a man can travel a lifetime and not escape the spell of the Ancrath valleys.\n\nI yawned, cracking my jaw. It hadn't been a night for sleeping. Warm in my cloak I let Gerrod's gentle gait rock me.\n\nI found myself thinking of smooth limbs and softness. My lips spoke her name as if to taste it.\n\n\"Katherine?\" Makin asked. I jerked my head up to find him watching me, with an eyebrow raised in that irritating way of his.\n\nI looked away. To our left a long sprawl of hook-briar writhed around the boles of three elms. I'd learned a hard lesson among the hook-briar one stormy night. It wasn't just the beauty of the land that had its hooks in me.\n\n_Kill her_.\n\nI turned round in the saddle, but Makin had fallen back to joke with the Nuban.\n\n_Kill her, and you'll be free forever_.\n\nIt seemed that the voice came from the darkness beneath the briar's coils. It spoke under the crunching of hooves in the dry leaf-fall.\n\n_Kill her_. An ancient voice, desiccated, untouched by mercy. For a moment I saw Katherine, blood welling over her white teeth, her eyes round with surprise. I could feel the knife in my hand, hilt against her stomach, hot blood running over my fingers.\n\n_Poison would be quieter. A distant touch_.\n\nThat last voice\u2014it could have been mine, or the briar, they started to sound the same.\n\n_Strength requires sacrifice. All weakness carries its cost_. Now that was me. We'd left the briar behind and the day had grown cold.\n\nThe Forest Watch found us quick enough, I'd have been worried if they hadn't. A six-man patrol, all in blacks and greens, came out of the trees and bade us state our business on the King's road.\n\nI didn't let Coddin introduce me. \"I've come to see the Watch Master,\" I said.\n\nThe watchmen exchanged glances. I'm sure we seemed a ragged bunch, only Makin with any courtly touch about him, having polished up to see Father Dear. I had my old road plate on, and Elban and the Nuban, well, their looks would earn them a bandit's noose without the tedium of a trial.\n\nCoddin spoke up then. \"This is Jorg, Prince of Ancrath, heir to the throne.\"\n\nHis words, hard to swallow as they might be, had the weight of a uniform behind them. The watchmen looked dumbfounded.\n\n\"He's come to see the Watch Master,\" Coddin said, by way of a prompt.\n\nThat got them moving and they led us into the deep forest along a series of deer-paths. We followed in single file, riding until I got tired of being slapped in the face by every other branch, and dismounted. The watchmen kept up a stiff pace, showing little regard for royalty or heavy armour.\n\n\"Who is the Watch Master anyhow?\" I asked, short of breath and clanking along loud enough to keep the bears from hibernation.\n\nOne of the watchmen glanced back, an old fellow, gnarled as the trees. \"Lord Vincent de Gren.\" He spat into the bushes to show his regard for the man.\n\n\"Your father appointed him this spring,\" Captain Coddin said from behind me. \"I gather it was a punishment of some sort.\"\n\nThe Forest Watch made its headquarters by Rulow's Fall on the plain where the River Temus meandered before gathering its courage for the leap down a two-hundred-foot step in the bedrock. A dozen large cabins, wood-shingled and log-built, nestled among the trees. An abandoned mill house served as the Watch Master's keep, fashioned from granite blocks and perched at the head of the fall.\n\nA few dozen watchmen came out to watch our column wind up to the keep. Not much entertainment in these parts I guessed.\n\nThe old watchman went in to announce us while we tied our steeds. He didn't hurry out, so we waited. A cold wind blew up, stirring the fallen leaves. The watchmen stood with us, black-green cloaks flapping. Most of the watch held shortbows. A longbow will get tangled in the trees and you'll never need great range in the forest. No Robin of Hood here, the watchmen weren't merry, and they were apt to kill you if you stepped out of line.\n\n\"Prince Jorg.\" The keep door opened and a man clad in ermine stepped out, his fingers hooked in a belt of gold plates.\n\n\"Lord Vincent de Gren, I'm guessing.\" I gave him my most insincere smile.\n\n\"So you're here to tell us we're all going to die over some stupid promise a boy made to impress his father!\" he said, loud enough for the whole clearing to hear.\n\nI had to hand it to Lord Vincent, he certainly cut straight to the chase. And I like that in a man, I really do, but I didn't like the way he said it. He had a screwed-up sort of face did Lord Vincent, as if the world tasted sour in his mouth, which was odd, because he had the sort of butterball shape that takes some serious eating to acquire and a few dozen extra stoats to cover in ermine. I took him to be about thirty, but it's hard to tell with fat people: they've no skin spare for wrinkles.\n\n\"News travels fast, I see.\" I wondered if my father wanted me to fail even more than he wanted the Castle Red. In a way it would be a compliment, implying he felt I had a chance. But no, this had a woman's touch, maybe the touch of a woman still smarting over \"Scorron whore.\" A woman used to teasing out post-coital secrets. A woman who might send riders to Rennat Forest. Even to Gelleth.\n\nI strode across to the man. \"I wonder, my lord de Gren, would your men follow you to the death? I'm impressed that you've won their respect so rapidly. I hear that the Forest Watch are a hard lot, tougher than nails.\" I put an arm around his shoulders. He didn't like it, but you can do things like that when you're a prince. \"Walk with me.\"\n\nI didn't give him a choice. I steered him downstream toward the glistening line where the River Temus vanished, replaced by a faint haze of mist. \"Follow on,\" I shouted. \"This isn't a private meeting.\"\n\nSo we came to stand on a shelf of wet stone, fifty yards down from the mill house, where the waters leapt white over the rocks, gathering for their plunge over Rulow's Fall.\n\n\"Prince Jorg, I don't . . .\" Lord Vincent began.\n\n\"You, come here!\" I took my arm from de Gren and pointed to the old watchman who'd spat out the Watch Master's name earlier. I had to shout above the voice of the river.\n\nThe old fellow came to join us by the edge.\n\n\"And who's this proud example of the watch, Watch Master?\" I asked.\n\nFat people's faces are wonderful for emotion. Or at least Lord Vincent's was. I could see his thoughts twitching across his brow, quivering in his jowls, twisting in the rolls around his neck. \"I . . .\"\n\n\"There's two hundred of the buggers. You can't be expected to know them all,\" I said, all sympathy. \"What's your name, watchman?\"\n\n\"Keppen, yer highness,\" he said. He looked as if he'd rather be somewhere else, had his eyes open, looking for the out.\n\n\"Order him to jump, Watch Master,\" I said.\n\n\"W-what?\" Lord Vincent went very pale very quickly.\n\n\"Jump,\" I said. \"Order him to jump over the fall.\"\n\n\"What?\" Lord Vincent seemed to be having difficulty hearing over the roar.\n\nKeppen had his hand on his dagger-hilt. Sensible fellow.\n\n\"If your men are all going to die over some stupid promise a boy made his father, well, it's only sensible for the boy to make sure they'll follow your orders when it means certain death,\" I said. \"And if you say 'what' again, I'm going to have to slice you open here and now.\"\n\n\"W\u2014But, my prince . . . Prince Jorg . . .\" He tried to laugh.\n\n\"Order him to jump, now!\" I barked it in de Gren's face.\n\n\"J-jump!\"\n\n\"Not like that! Put some conviction into it. He's not going to jump if you make it a suggestion.\"\n\n\"Jump!\" Lord Vincent reached for some lordly command.\n\n\"Better,\" I said. \"Once more, with feeling.\"\n\n\"Jump!\" Lord Vincent screamed the word at old Keppen. The colour came back now, flushing him bright crimson. \"JUMP! Jump, damn you!\"\n\n\"Buggered if I will!\" Keppen shouted back. He pulled his knife, a wicked bit of steel, and backed off, wary-like.\n\nI shrugged. \"Not good enough, Lord Vincent. Just not good enough at all!\" And with a hearty shove he went over. Never a wail from him. Didn't even hear a splash.\n\nI moved quickly then. In two strides I had Keppen by the throat, with my other hand on his wrist, keeping that knife at bay. I took him by surprise and in another step I had him backed out over the edge, heels resting on air, and my grip on his neck all that kept him with us.\n\n\"So, Keppen,\" I said. \"Will you die for the new Watch Master?\" I gave him a smile, but I don't think he noticed. \"This is the bit where you say, 'yes.' And you'd better mean it, because there are a lot worse things than dying easy when given an order.\"\n\nHe got a \"yes\" out past my fingers.\n\n\"Coddin.\" I pointed him out. \"You're the new Watch Master.\"\n\nI pulled Keppen back and walked back toward the keep. They all followed me.\n\n\"If I ask you to die for me, I expect you to ask when and where,\" I said. \"But I'm not in any hurry to ask. It'd be a waste. The Forest Watch is the most dangerous two hundred soldiers Ancrath has, whether my father knows it or not.\"\n\nIt wasn't all flattery. In the forest they were the best we had. With a good Watch Master they were the sharpest sword in the armoury, and too clever to jump when told.\n\n\"Watch Master Coddin here is taking you into Gelleth.\" I saw a few lips curl at that. Lord Vincent's long jump or not, I was still a boy, and the Castle Red was still suicide. \"You'll get within twenty miles of the Castle Red, and no closer. You're to spend two weeks in the Otton forests, cutting wood for siege engines and killing any patrols that come in after you. Watch Master Coddin will tell you the rest when the time comes.\"\n\nI turned from them and pushed open the door to the keep. \"Coddin, Makin!\"\n\nThey followed me in. The entrance hall gave onto a homely dining room where the table was set with cold goose, bread, and autumn apples. I took an apple.\n\n\"My thanks, Prince Jorg.\" Coddin gave another of his stiff bows. \"Saved from escort duty in Crath City, I can enjoy my winter running around the woods in Gelleth now.\" The faintest hint of a smile flickered at the corner of his mouth.\n\n\"I'm coming with you. In disguise. It's a closely guarded secret that you're to ensure leaks out,\" I said.\n\n\"And where will we be really?\" Makin asked.\n\n\"The Gorge of Leucrota,\" I told him. \"Talking to monsters.\"\n**25**\n\nWe returned to the Tall Castle through the Old Town Gate, with the noonday sun hot across our necks. I carried the family sword across my saddle and none sought to bar our way.\n\nWe left the horses in the West Yard.\n\n\"See he's well shod. We have a road ahead of us.\" I slapped Gerrod's ribs and let the stable lad lead him away.\n\n\"We've company.\" Makin laid a hand upon my shoulder. \"Have a care.\" He nodded across the yard. Sageous was descending the stair from the main keep, a small figure in white robes.\n\n\"I'm sure our little pagan can learn to love Prince Jorgy just like all the rest,\" I said. \"He's a handy man to have in your pocket.\"\n\nMakin frowned. \"Better to put a scorpion in your pocket. I've been asking around. That glass tree you felled the other day. It wasn't a trinket. He grew it.\"\n\n\"He'll forgive me.\"\n\n\"He grew it from the stone, Jorg. From a green bead. It took two years. He watered it with blood.\"\n\nBehind us Rike sniggered, a childish sound, unsettling from such a giant.\n\n\"His blood,\" Makin finished.\n\nAnother of the brothers snorted laughter at that. They'd all heard the story of Sir Galen and the glass tree.\n\nSageous stopped a yard in front of me and cast his gaze across the brothers, some still handing over their steeds, others pressed close at my side. His eyes flicked up to take in Rike's height.\n\n\"Why did you run, Jorg?\" he asked.\n\n\"Prince. You'll call him Prince, you pagan dog.\" Makin stepped forward, half-drawing. Sageous took him in with a mild look and Makin's hand fell limp at his side, the argument gone from him.\n\n\"Why did you run?\"\n\n\"I don't run,\" I said.\n\n\"Four years ago you ran from your father's house.\" He kept his voice gentle, and the brothers watched him as though charmed by a spinning penny.\n\n\"I left for a reason,\" I said. His line of attack unsettled me.\n\n\"What reason?\"\n\n\"To kill someone.\"\n\n\"Did you kill him?\" Sageous asked.\n\n\"I killed a lot of people.\"\n\n\"Did you kill him?\"\n\n\"No.\" The Count of Renar still lived and breathed.\n\n\"Why?\"\n\nWhy hadn't I?\n\n\"Did you harm him? Did you hurt his interests?\"\n\nI hadn't. In fact if you looked at it, if you traced the random path of four years on the road, you might say I had furthered Renar's interests. The brothers and I had nipped at Baron Kennick's heels and kept him from his ambitions. In Mabberton we had torn the heart from what might have been rebellion . . .\n\n\"I killed his son. I stuck a knife in Marclos, Renar's flesh and heir.\"\n\nSageous allowed himself a small smile. \"As you came closer to home, you came under my protection, Jorg. The hand that steered you fell away.\"\n\nWas it true? I couldn't see the lie in him. My eyes followed the scriptures written across his face, the complex scrolls of an alien tongue. An open book, but I couldn't read him.\n\n\"I can help you, Jorg. I can give you back your self. I can give you your will.\"\n\nHe held out his hand, palm open.\n\n\"Free will has to be taken,\" I said. When in doubt reach for the wisdom of others. Nietzsche in this case. Some arguments require a knife if you're to cut to the quick, others require the breaking of heads with a philosopher's stone.\n\nI reached out and took his hand in mine, from below, his knuckles to my palm.\n\n\"My choices have been my own, pagan,\" I said. \"If someone sought to steer me, I would know it.\"\n\n\"Would you?\"\n\n\"And if I knew it . . . Oh, if I knew it, I would teach such a lesson in pain that the Red Men of the East themselves would come to learn new tricks.\" Even as they left me the words rang hollow. Childish.\n\n\"It is not I who has led you, Jorg,\" Sageous said.\n\n\"Who then?\" I squeezed his hand until I heard the bones creak.\n\nHe shrugged. \"Ask for your will and I shall give it to you.\"\n\n\"If there were a glamour on me, I would find the one that placed it and I would kill them.\" I felt an echo of the old pain that plagued me on the road, a pang from temple to temple, behind the eyes like a sliver of glass. \"But there is none, and my will is my own,\" I said.\n\nHe shrugged again, and turned away. Looking down I saw that I held my left hand in my right, and blood ran between my fingers.\n**26**\n\nFrom my encounter with Sageous in the West Yard I went straight to mass. Meeting the pagan had left me wanting a touch of the church of Roma, a breath of incense, and a heavy dose of dogma. If heathens held such powers, it seemed only right that the church should have a little magic of its own to bestow upon the worthy, and hopefully upon the unworthy who bothered to show up. Failing that, I had need of a priest in any case.\n\nWe marched into the chapel to find Father Gomst presiding. The choir song faltered before the clatter of boots on polished marble. Nuns shrank into the shadows beneath the brothers' leers, and, no doubt, the rankness of our company. Gains and Sim took off their helms and bowed their heads. Most of them just glanced around for something worth stealing.\n\n\"Forgive the intrusion, Father.\" I set a hand in the font by the entrance and let the holy water lift the blood from my skin. It stung.\n\n\"Prince!\" He set his book upon the lectern and looked up, white-faced. \"These men . . . it is not proper.\"\n\n\"Oh shush.\" I walked the aisle, eyes on the painted marvel of the ceiling, turning slowly as I went, one hand raised and open, dripping. \"Aren't they all sons of God? Penitent children returned for forgiveness?\"\n\nI stopped before the altar and glanced back toward the brothers by the door. \"Put that back, Roddat, or you'll be leaving both thumbs in the alms box.\"\n\nRoddat drew a silver candlestick from the grey rot of his travel cloak.\n\n\"That one at the least.\" Father Gomst pointed at the Nuban, a tremble in his finger. \"That one is not of God's flock.\"\n\n\"Not even a black sheep?\" I came to stand by Gomst. He flinched. \"Well, maybe you can convert him on our journey.\"\n\n\"My prince?\"\n\n\"You're to accompany me to Gelleth, Father Gomst. A diplomatic mission. I'm surprised the King didn't tell you.\" I wasn't so surprised in truth, since it was a lie. \"We leave immediately.\"\n\n\"But\u2014\"\n\n\"Come!\" I strode toward the door. A pause, and then he followed. I could hear the reluctance in his footsteps.\n\nThe brothers began to file out ahead of me, Rike trailing his hand along the walls, over reliquary and icon.\n\nHaving secured the priest I was keen to be off. I directed Makin to oversee a swift provisioning and led Gomst back to the West Yard.\n\n\"We should not take this Nuba-man on a mission of diplomacy, Prince. Or any other,\" Gomst whispered as we walked. \"They drink the blood of Christian priests to work their spells, you know.\"\n\n\"They do?\" I think it was the first interesting thing I ever heard Gomst say. \"I could use a little magic myself.\"\n\nThe priest paled behind his beard. \"A superstition, my prince.\"\n\nA few more paces and, \"Even so, were you to burn him, the Lord's blessing would be upon us and our journey.\"\n\nWithin the hour, saddlebags bulging, we rode back out into the Old Town. Sageous was waiting for us. He stood alone by the side of the cobbled path. I drew up before him, still uneasy in my mind. He had driven a wedge of doubt into me. I had told myself I'd set Count Renar aside as an act of strength, a sacrifice to the iron will I needed to win the game of thrones. But sometimes, now for instance, I didn't quite believe it.\n\n\"You should accept my protection, Prince,\" Sageous said.\n\n\"I've survived long enough without it.\"\n\n\"But now you're going to Gelleth, bound on a path to strengthen your father's hand.\"\n\n\"I am.\" The brothers' horses snorted around me.\n\n\"If any had a mind that you might truly succeed, they would stop you,\" Sageous said. \"The one who has played you these past years will seek to tighten the bonds you have loosened. Perhaps the priest will help you. His presence did before. He has value as a talisman, but past that he is empty robes.\"\n\nA horse pushed against Gerrod, the rider moving beside me.\n\nI set my hand on my sword hilt. \"I don't like you, pagan.\"\n\n\"What do you think scared the marsh-dead, Jorg?\" No ripple in his calm watchfulness.\n\n\"I\u2014\" The boast sounded hollow before I spoke it.\n\n\"An angry boy?\" Sageous shook his head. \"The dead saw a darker hand upon your heart.\"\n\n\"I\u2014\"\n\n\"Accept my protection. There are grander dreams you can dream.\"\n\nI felt the soft weight of sleep upon me, the saddle unsure beneath me.\n\n\"Dream-witch.\" A dark voice spoke at my shoulder.\n\n\"Dream-witch.\" The Nuban held out his crossbow, black fist curled around the stock, muscle strained against the load. \"I carry your token, Dream-witch, your magics will not stain the boy.\"\n\nSageous shrank back, the tattooed writings seeming to writhe across his face.\n\nIn an instant my eyes were wide. \"You're him.\" The clarity of it was blinding. \"You set my brothers in Father's dungeon. You sent your hunter to kill me.\"\n\nI set a hand upon the Nuban's bow, remembering how he took it from the man I killed in a barn one stormy night. The dream-witch's hunter.\n\n\"You sent your hunter to kill me.\" The last tatters of Sageous's charm left me. \"And now it's my hunter who holds it.\"\n\nSageous turned and made for the castle gate, half-running.\n\n\"Pray I don't find you here on my return, pagan.\" I said it quietly. If he heard it, he might follow my advice.\n\nWe left then, riding from the city without a backward look.\n\nThe rains first found us on the Ancrath Plains and dogged our passage north into the mountainous borders of Gelleth. I've been soaked on the road many a time, but the rains as we left my father's lands were a cold misery that reached deeper than our bones. Burlow's appetite remained undampened though, and Rike's temper too. Burlow ate as if the rations were a challenge, and Rike growled at every raindrop.\n\nAt my instruction, Gomst took confession from the men. After hearing Red Kent speak of his crimes, and learning how he earned his name, Gomst asked to be excused his duties. After listening to Liar's whispers, he begged.\n\nDays passed. Long days and cold nights. I dreamed of Katherine, of her face and the fierceness of her eyes. Of an evening we ate Gains's mystery stews and Fat Burlow tended the beasts, checking hooves and fetlocks. Burlow always looked to the horses. Perhaps he felt guilty about weighing so heavy on them, but I put it down to a morbid fear of walking. We wound further up into the bleakness of the mountains. And at last the rains broke. We camped in a high pass and I sat with the Nuban to watch the sun fall. He held his bow, whispering old secrets to it in his home tongue.\n\nFor two days we walked the horses across slopes too steep and sharp with rock for any hooves save the mountain goats'.\n\nA pillar marked the entrance to the Gorge of the Leucrota. It stood two yards wide and twice as tall, a stump shattered by some giant's whim. The remnants of the upper portion lay all around. Runes marked it, Latin I think, though so worn I could read almost nothing.\n\nWe rested at the pillar. I clambered up it to address the brothers from the top and take in the lie of the land.\n\nI set the men to making camp. Gains set his fire and clanked his pots. The wind blew slight in the gorge, the oil-cloth tents barely flapping before it. The rain came again, but in a patter, soft and cold. Not enough to stir Rike lying on the rocks some five yards from the pillar, his snoring like a saw through wood.\n\nI stood looking up at the cliff faces. There were caves up there. Many caves.\n\nMy hair swung behind me as I scanned the cliff. I'd let the Nuban weave it into a dozen long braids, a bronze charm at the end of each. He said it would ward off evil spirits. That just left me the good ones to worry about.\n\nI stood with my hands on the Ancrath sword, resting its point before me. Waiting for something.\n\nThe men grew nervous, the animals too. I could tell it from their lack of complaint. They watched the slopes with me, toothless Elban as weatherbeaten as the rocks, young Roddat pale and pockmarked, Red Kent with his secrets, sly Row, Liar, Fat Burlow, and the rest of my ragged bunch. The Nuban kept close by the pillar with Makin at his side. My band of brothers. All of them worried and not knowing why. Gomst looked set to run if he had a notion where to go. The brothers had a sense for trouble. I knew that well enough to understand that when they all worry together it's a bad thing coming. A very bad thing.\n\n**Transcript from the trial of Sir Makin of Trent:**\n\nCardinal Helot, papal prosecution: _And do you deny razing the Cathedral of Wexten?_\n\nSir Makin: _I do not._\n\nCardinal Helot: _Or the sack of Lower Merca?_\n\nSir Makin: _No, nor do I deny the sack of Upper Merca._\n\nCardinal Helot: _Let the record show the accused finds amusement in the facts of his crime._\n\nCourt recorder: _So noted._\n**27**\n\nThe monsters came when the light failed. Shadows swallowed the gorge and the silence thickened until the wind could barely stir it. Makin's hand fell on my shoulder. I flinched, edging the fear with momentary hatred, for my own weakness, and for Makin for showing it to me.\n\n\"Up there.\" He nodded to my left.\n\nOne of the cave mouths had lit from within, a single eye watching us through the falling night.\n\n\"That's no fire,\" I said. The light had nothing of warmth or flicker.\n\nAs we watched, the source of illumination moved, swinging harsh shadows out across the slopes.\n\n\"A lantern?\" Fat Burlow stepped up beside me, puffing out his cheeks in consternation. The brothers gathered around us.\n\nThe strange lantern emerged onto the slope, and darkness erased the cave behind. It shone like a star, a cold light, reaching from the source in a thousand bright lines. A single figure cut a wedge of shadow into the illumination; the lantern bearer.\n\nWe watched the unhurried descent. The wind sought my flesh with icy fingers and tugged for attention at my cloak.\n\n\" _Ave Maria, gratia plena, dominus tecum, benedicta tu in mulieribus_.\" Somewhere in the night old Gomsty muttered his Ave Marias.\n\nA slow horror eased itself among us.\n\n\"Mother of God!\" Makin spat the oath out as if to rid himself of the fear. We all felt it, crawling over the unseen rocks.\n\nThe brothers might have run, but where was there to go?\n\n\"Torches, damn you. Now!\" I broke the paralysis, shocked that I'd stood hypnotized by the approach for so long.\n\n\"Now!\" I drew my sword. They moved at that. Scurrying to the embers of the fire, stumbling over the rough ground.\n\n\"Nuban, Row, Burlow, see there's nothing coming up along the river.\" Even as I said it I knew we'd been flanked.\n\n\"There! There, behind that rise!\" The Nuban motioned with his crossbow. He'd seen something, the Nuban wasn't one to spook at nothing. We'd watched the pretty light and they'd flanked us. Simple as a market play of kiss-and-dip. Distract your mark with a pretty face, and come up from behind to rob him blind.\n\nThe torches flared, men ran to their weapons.\n\nThe light drew closer and we saw it for what it was, a child whose very skin bled radiance. She walked an even pace, every inch aglow, white like molten silver, making mere shadows of the rags she wore.\n\n\" _Ave Maria, gratia plena!_ \" Father Gomst's voice rose, lifting the prayer like a shield.\n\n\"Hail Mary,\" I echoed him. \"Full of grace, indeed.\"\n\nThe girl's eyes burned silver and the ghosts of flames chased across her skin. There was a fragile beauty to her that took my breath.\n\nA monster walked behind her. In any other circumstance it would have been him that drew the eye. The monster had been built in parody of a man, sharing Adam's lines as a cow apes a horse. The light revealed the horror of his flesh, sparing no detail. The thing might have topped seven foot in height. It even had a few inches on Little Rikey.\n\nLiar raised his bow, disgust on his pinched face. I took his arm as he sighted on the monster.\n\n\"No.\" I wanted to hear them speak. Besides, it looked as if an arrow would just annoy our new friend.\n\nUnder a twisted red hide the monster's chest looked like a hundred-gallon barrel. A set of ribs pierced the flesh, reaching for each other above his heart.\n\nThe girl's light touched us with a cold kiss and I felt her in my mind. She spoke and her voice seemed to rise from the rocks. I heard her footsteps in the corridors of my memory.\n\nThere are places where children shouldn't wander. I met the girl's silver gaze, and for a moment shadows licked across her.\n\n\"Welcome to our camp,\" I said.\n\nI stepped forward to greet them, leaving the brothers and entering the brilliance of the child's aura. The monster smiled at me, a wide smile showing teeth stolen from the wolf. He'd the eyes of a cat, slitted against the light and throwing it back.\n\nI passed beauty by and stood before the beast. We had us a moment of judging. I ran an eye over the muscle heaped on his bones, crossed over with pulsing veins and hard ridges of scar tissue. I could have eaten dinner off one of his hands. He had three fingers and a thumb on each, thick as the girl's arm. He could have taken my head in one hand and crushed it.\n\nI snapped my neck forward, sudden-like, and jumped at him with a shout, thrusting my face at his. He flinched backward and stumbled on the loose rock. The laughter escaped me. I couldn't stop it.\n\n\"Why?\" The girl looked puzzled. She tilted her head and the shadows ran.\n\n\"Because.\" I gasped for my breath as the monster righted himself.\n\nWhy? For a moment I didn't know.\n\n\"Because . . . because, fuck him. Because he's such a big bastard.\" I pushed the grin from my face. Because he had given me pause. Because he had made me feel small.\n\nI looked down at her. \"I'm bigger than you. Are you going to let that scare you?\"\n\n\"I do fear you,\" the girl said. \"Not for your size, Jorg. For the threads that gather around you. For the lines that meet where I can't see them. For the weight, and the knife-edge on which it sits.\" She spoke in a sing-song, high and sweet.\n\n\"You make a fine oracle, girl,\" I said. \"You've got that mix of profound and empty just right.\" I slammed my sword back into its sheath. \"So, you've my name. Shall we share? Do the leucrota have names?\"\n\n\"Jane,\" she said. \"And this is Gorgoth, a leader under the mountain.\"\n\n\"Charmed.\" I gave them a little bow. \"Perhaps your friends could come out from behind the rocks, and that way my brothers won't feel so tempted to shoot at shadows.\"\n\nGorgoth set his cat's eyes on me, a narrow and feral stare.\n\n\"Up!\" His voice rolled out even deeper than I'd imagined, and I'd imagined it pretty deep.\n\nOther monsters rose around our camp, some of them shockingly close. Had every gargoyle and grotesque torn free from the great cathedrals and gathered to form an army, the leucrota would be that army made flesh. No two stood alike. All had been sketched on the frame of a man, but with a poor hand. None were as huge and hale as Gorgoth. Most leaked from sores, sported withered limbs, or laboured beneath growths of wart and tumour heaped in foul confusion.\n\n\"Jesu, Gorgoth! Your friends make Little Rikey look almost handsome,\" I said.\n\nMakin came to join me, eyes screwed up against Jane's light. He shaded his face with a hand and looked Gorgoth up and down.\n\n\"And this will be Sir Makin,\" I said. \"Knight of the court of King Olidan, terror of\u2014\"\n\n\"A man to trust.\" Jane's high voice cut across me. \"If he gives you his word.\"\n\nShe turned those silver orbs of hers on me and I felt my yesterdays crowding at my shoulder. \"You want to go to the heart of the mountain,\" she said.\n\n\"Yes.\" I couldn't deny that.\n\n\"You bring death, Prince of Ancrath,\" she said.\n\nGorgoth growled at that. It sounded like rocks grinding together. The child put a glowing hand to his wrist. \"Death if we agree, death if we resist.\" She kept her eyes on me. \"What have you to offer for passage?\"\n\nI had to admit she was good at her game. It wouldn't go well for them if my plan worked, and it wouldn't go well for them if they tried to stop us.\n\n\"I did bring a gift,\" I said. \"But if it proves not to your liking then I can make you some promises. I'll have Sir Makin promise you too, and he's a man of his word.\" I smiled down at her. \"When I saw this place on a map . . .\" I paused and remembered the circumstances with a certain fondness.\n\n\"Sally . . .\" the girl whispered, remembering the tavern with me.\n\nThat shocked me for a moment. I didn't like the idea of this little girl in my head, opening doors, making childish judgment, shining her light in places that should be dark. Part of me wanted to cut her down, a large part of me.\n\nI unclenched my jaw. \"When I saw this gorge on my map, I thought to myself, 'What a godforsaken spot.' And that's when it occurred to me what to bring for barter. I brought you God.\" I turned and pointed to Father Gomst. \"I've brought you salvation, the blessing of communion. I've brought you benediction, catechism . . . confession if you must. All the saving your ugly little souls can handle.\"\n\nGomst let out a girlish scream and started to run. The Nuban caught a dark arm around his waist and hauled him up over one shoulder.\n\nI expected Jane to answer, but Gorgoth made the deal.\n\n\"We will take the priest.\" Something about his voice made my chest hurt. \"We will guide you to the Great Stair. The necromancers will find you, though. You will not return.\"\n\n_Some said that Red Kent had a black heart, and that might be true, but anyone who had seen him take out a six-strong foot patrol with hatchet and knife would tell you the man had an artist's soul._\n**28**\n\n\"Necromancers?\" I trudged behind Jane with Gorgoth at my back. There had been nothing about necromancers in my books.\n\n\"They command the dead. Mages\u2014\"\n\n\"I know what they are.\" I cut across Gorgoth. \"What are they doing in my way?\"\n\n\"Mount Honas attracts them,\" Jane said. \"There's death at the heart of the mountain. Old magics. It makes their work easier.\"\n\nEven the leucrotas' caves looked ugly. When I was seven, and William five, Tutor Lundist took us secretly to the caverns of Paderack. Unknown to any at court, the heirs of Ancrath slid and slipped into the blind depths, and came to a cathedral hall of such pillared wonder that it beggared the grace of God. I carry the glory of that place with me still. The chambers of the leucrota had none of that fluid elegance, no touch of the hidden artistry that lies in the deep places of the world. We walked through corridors of Builder-stone, poured and shaped using arts long forgotten. Jane's light showed us ancient vaults, cracked in places and scaled with lime. We wove a path around fallen blocks, larger than cart-horses, heading deeper all the time, like worms burrowing to the core, seeking the roots of the mountain.\n\n\"Shut your moaning, priest.\" Row came up behind the Nuban and showed old Gomsty his knife, a wicked piece of ironwork to be sure.\n\nFather Gomst let up his wailing at that, and I did miss it for the echoes had been quite haunting. I fell back for a word. That, and to make sure Row didn't decide to carve up our gift to the monsters before we'd handed it over proper-like.\n\n\"Peace now, Father,\" I said.\n\nI pushed Row's blade aside. He scowled at that, did Row, all pock-marks and squinting eyes.\n\n\"You'll just be changing flocks, Father,\" I told Gomsty. \"Your new congregation might look a little fouler, but on the inside? Well, I'm sure they'll be fairer than Row here.\"\n\nThe Nuban grunted and shifted Father Gomst's weight on his shoulder.\n\n\"Set him down,\" I said. \"He can walk. We're good and lost now, there'll be no running.\"\n\nThe Nuban set old Gomsty on his feet. He looked at me, his face too black to read. \"It's wrong, Jorg. Trade in gold, not people. He's a holy man. He speaks for the white-Christ.\"\n\nGomst looked at the Nuban with a hatred I'd never seen in him before, as if he'd just grown horns and called on Lucifer.\n\n\"Well, now he can speak to Gorgoth for Christ,\" I said.\n\nThe Nuban said nothing, his face a blank.\n\nSomething about the Nuban's silences always made me want to say a little more. As if I had to make it right with him. Makin scraped at me that same way, but not so bad.\n\n\"It's not like he can't leave,\" I said. \"He's free to walk home if he really must. He'll just have to earn himself some food for the journey and a map is all.\"\n\nThe Nuban gave me the white crescent of his smile.\n\nI walked on, a cold voice inside me whispering, whispering of weakness, of the thin edge of a wedge, of a sharp knife cutting without tears, of a hot iron to cauterize a wound before infection spread. It doesn't do to love a brother.\n\nJane's light dimmed and flickered as I drew near. She recoiled slightly with an intake of breath. I curled my lip and imagined her falling from a cliff. It worked better than I'd hoped. She gave a squeal and covered her eyes.\n\nGorgoth stepped between us. \"Keep away from her, Dark Prince.\"\n\nSo I walked in the shadows, and they led us on into the mountain. We followed wide tunnels that stretched for miles, level-floored with curved ceilings. Rust stains ran the length of the passages in parallel lines, though to what end men would lay iron in such a manner I can't say, unless these were the pipes through which the secret fire of the Builders ran.\n\nWe left Jane and all but two of her kindred at the shores of a lake so wide even her silver light could not reach across the waters. The Builders had made this place too. Stone gave away to water with a single sharp step, the ceiling stretched flat and without adornment. Jane's folk moved away toward shelters of wood and skins huddled at the water's edge. Gorgoth led them, one hand enveloping Father Gomst's shoulders.\n\nJane paused, her gaze moving between the two grotesques who remained to guard us. She said nothing but I could feel the undercurrent of unvoiced speech as she instructed them.\n\n\"No final words for me, little one?\" I asked. I went on one knee before her. A fierce humour gripped me. \"No predictions? No pearls to throw before this swine? Come, share a glimpse with me. Blind me with the future.\"\n\nShe met my gaze and the light dazzled, but I wouldn't look away.\n\n\"Your choices are keys to doors I cannot see beyond.\"\n\nI felt anger rise in me and pushed it down with a snarl. \"There's more than that.\"\n\n\"You have a dark hand on your shoulder. A hole in your mind. A hole. In your memories. A hole\u2014a hole\u2014pulling me in\u2014pulling\u2014\"\n\nI seized her hand. That was a mistake, for it burned the skin and froze the bone in equal measure. I'd have set it down if I could, but the strength left me. For a moment I could see only the child's eyes.\n\n\"When you meet her, run. Just run. Nothing else.\" It felt as though I were speaking the words, though I could hear Jane's voice frame them. Then I fell.\n\nI woke to the light of torches.\n\n\"He's up.\"\n\nI found myself face to face with Rike.\n\n\"Jesu, Rike, you been gargling rat piss again?\" I pushed his brutal jaw to one side and used his shoulder to lever myself up. The brothers began to rise around me, hefting their packs. Makin came from the water's edge, Gorgoth looming behind him.\n\n\"Don't go touching the Prophetess of the Leucrota!\" He used a mock-scold. I could see the relief hidden in his eyes.\n\n\"I'll bear it in mind,\" I said.\n\nGorgoth paused to scowl at me, then led the way, holding a pitch-torch the size of a small tree.\n\nOur path angled up now, the tunnel thick with dust that tasted of bitter almonds. We walked for less than a thousand yards before the way broadened into a wide gallery crossed by stone trenches of obscure purpose, yards across, and as deep as a man is tall. At the mouth of the gallery a wooden pen hugged the wall, the stays bound with rope. Two children huddled together in the middle of the bare cage. Two leucrota. Gorgoth hauled the door open.\n\n\"Out.\"\n\nThey were neither of them past seven summers, if summers were a proper count for the dark halls of the leucrota. They came out naked, two skinny boys, brothers to look at them, the younger one perhaps five. Of all the leucrota I'd seen they looked the least monstrous. A black-and-red stippling marked their skin, colouring them like the tigers of Indus. Dark barbs of horn jutted from their elbows, mirrored in the talons on their fingers. The elder of the two shot me a glance, his eyes utterly black, no white, iris, or pupil.\n\n\"We don't want your children,\" Makin said. He reached into his pocket and tossed a twist of dry-meat to the brothers. \"Put them back.\"\n\nThe meat twist skittered to a halt at the elder child's feet. He kept his eyes on Gorgoth. The littlest watched the dry-meat intently, but made no move. Their skin stretched so tight over the bone I could count every rib.\n\n\"These are for the necromancers, don't waste your food on them.\" Gorgoth's rumble came so low it hurt to hear it.\n\n\"A sacrifice?\" the Nuban asked.\n\n\"They're dead already,\" Gorgoth said. \"The strength of the leucrota isn't in them.\"\n\n\"They look hearty enough to me,\" I said. \"With a meal or two in 'em. Sure you're not just jealous because they're not as ugly as the rest of you?\" I didn't much care what Gorgoth did with the runts, but I took a pleasure in taunting him.\n\nGorgoth flexed his hands and six giant knuckles popped like logs on the fire.\n\n\"Eat.\"\n\nThe two boys fell on Makin's food, snarling like dogs.\n\n\"The leucrota are pure-born, we gain our gifts as we grow. It is a slow change.\" He gestured to the boys licking the last fragments of dry-meat from the stone. \"These two have the changes of a leucrota twice their age. The gifts will come faster now, faster and stronger. None can bear such changes. I have seen it before. Such gifts will turn a man inside out.\" Something in those cat's eyes of his told me he meant it, told me he'd seen it. \"Better they serve us as payment to keep the necromancers from our caves. Better the dead-ones take these than search for victims who could have lived. They will find a quick death and a long peace.\"\n\n\"If you say it, then it is so.\" I shrugged. \"Let's be moving on. I'm keen to meet these necromancers of yours.\"\n\nWe followed Gorgoth through the gallery. The brothers scampered around us, and I saw the Nuban slip them dried apricots from the woollen depths of his tunic.\n\n\"So what's your plan?\" Makin sidled close to me, voice low.\n\n\"Hmmm?\" I watched the younger child skip away from Liar's well-aimed boot.\n\n\"These necromancers\u2014what's your plan?\" Makin kept to a hiss.\n\nI didn't have a plan, but that was just one more obstacle to overcome. \"There was a time when the dead stayed dead,\" I said. \"I've read it in Father's library. For the longest time the dead only walked in stories. Even Plato had the dead comfortably far away, over the river Styx.\"\n\n\"That's what you get for all that reading,\" Makin said. \"I remember the marsh road. Those ghosts hadn't read your books.\"\n\n\"Nuban!\" I called him over. \"Nuban, come tell Sir Makin why the dead don't rest easy any more.\"\n\nHe joined us, crossbow over one shoulder, oil of cloves in the air around him. \"The wise-men of Nuba tell it that the door stands ajar.\" He paused and ran a very pink tongue over very white teeth. \"There's a door to death, a veil between the worlds, and we push through when we die. But on the Day of a Thousand Suns so many people had to push through at once, they broke the door. The veils are thin now. It just takes a whisper and the right promise, and you can call the dead back.\"\n\n\"There you have it, Makin,\" I said.\n\nMakin furrowed his brow at that, then rubbed his lips. \"And the plan?\"\n\n\"Ah,\" I said.\n\n\"The plan?\" He could be annoyingly persistent could Makin.\n\n\"Same as normal. We just keep killing them until they stay down.\"\n\n_Brother Row you could trust to make a long shot with a short bow. You could trust him to come out of a knife fight with somebody else's blood on his shirt. You could trust him to lie, to cheat, to steal, and to watch your back. You couldn't trust his eyes though. He had kind eyes, and you couldn't trust them._\n**29**\n\nThe Builders had an aversion to stairs it seems. Gorgoth led us up through the mountain by treacherous paths cut into the walls of endless vertical shafts. Perhaps the Builders grew wings, or like the far-seers of Indus they could levitate through force of will. In any case, the picks of later men had chewed a stair into the poured stone of the shaft walls, narrow and crudely hewn. We climbed with care, our arms tight before us, keeping narrow for fear of pitching ourselves into a fall with an inadvertent shrug of the shoulders. If the depths had been lit, I don't doubt but some of the brothers would have needed the point of a sword to help them up, but darkness hides all sins, and we could fool ourselves a floor lay unseen twenty feet below.\n\nStrange how the deeper a hole the stronger it draws a man. The fascination that lives on the keenest edge, and sparkles on the sharpest point, also gathers in depths of a fall. I felt the pull of it every moment of that climb.\n\nGorgoth seemed least well crafted for such an ascent, but he made it look easy. The two leucrota children danced in front of me, skipping up the steps with a disregard that made me want to shove them into space.\n\n\"Why don't they run off?\" I called ahead to Gorgoth. He didn't answer. I guessed the boys' disdain for the fall had to be set against the fate that awaited them if they made it safely to the top.\n\n\"You're taking them to die. Why do they follow you?\" I called the words at the broad expanse of his back.\n\n\"Ask them.\" Gorgoth's voice rumbled like distant thunder in the shaft.\n\nI caught the elder brother by the neck and held him out over the fall. There was almost no weight to him and I needed a rest. I could feel the tally of all those steps fuelling a fire in my leg muscles.\n\n\"What's your name, little monster?\" I asked him.\n\nHe looked at me with eyes that seemed darker and wider than the drop to my right.\n\n\"Name? No name,\" he said, high and sweet.\n\n\"That's no good. I'll give you a name,\" I said. \"I'm a prince, I'm allowed to do things like that. You'll be Gog, and your brother can be Magog.\"\n\nI glanced around at Red Kent who stood behind me, puffing, not the slightest flicker of comprehension on his peasant face.\n\n\"Gog, Magog . . . Jesu, where's a priest when I need someone to get a biblical joke!\" I said. \"I never thought to miss Father Gomst!\"\n\nI turned back to young Gog. \"What're you so happy about? Old Gorgy-goth up there, he's taking you to be eaten by the dead.\"\n\n\"Can fight 'em,\" Gog said, quiet-like. \"Law says so.\" If he felt uncomfortable being held up by the neck, he didn't show it.\n\n\"What about little Magog?\" I nodded to his brother squatting on the step above us. \"He going to fight too?\" I grinned at the notion of these two doing battle with death mages.\n\n\"I'll protect him,\" Gog said, and he started to twist in my hand, so hard and fast that I had to set him down, or else pitch over the edge with him.\n\nHe scampered to his brother's side and set striped hand to striped shoulder. They watched me with those black eyes, quieter than mice.\n\n\"May be some sport in this,\" Kent said behind me.\n\n\"I bet the littlest one lasts longest,\" Rike shouted, and he bellowed with laughter as if he'd said something funny. He almost slipped off then, and that shut up his laughing quick enough.\n\n\"You want to win this game, Gog, you leave little Magog to look after himself.\" As I spoke the words, a chill set the hairs standing on my neck. \"Show me you've the strength to look after yourself, and maybe I'll find something those necromancers want more than they want your scrawny soul.\"\n\nGorgoth started up again, and the brothers followed without a word.\n\nI walked on, rubbing the scars on my forearms where the hook-briar had started to itch at me again.\n\nI counted a thousand steps, and I only started out of boredom, so I missed the first ten minutes of the climb. My legs turned to jelly, my armour felt as though it were made from inch-thick lead, and my feet got too clumsy to find the stairs. Brother Gains convinced Gorgoth to call a rest halt by stumbling into space, and wailing for a good ten seconds before the unseen floor convinced him to shut up.\n\n\"All these stairs so we can reach 'The Great Stair'!\" I spat a mess of phlegm after dear departed Brother Gains.\n\nMakin flashed me a grin and wiped the sweaty curls from his eyes. \"Maybe the necromancers will carry us up.\"\n\n\"Going to need a new cook.\" Red Kent spat after Gains.\n\n\"Can't anyone be worse than Gainsy.\" Fat Burlow moved only his lips. The rest of him slumped lifeless, hugging the wall. I thought it rather poor eulogy for Gains, since Burlow seemed to put away more of the man's culinary efforts than the rest of us put together.\n\n\"Rike would be worse,\" I said. \"I see him tackling an evening meal the way he approaches burning a village.\"\n\nGains was all right. He'd carved me a bone flute once, when I first came to the brothers. On the road, we talk away our dead with a curse and a joke. If we'd not liked Gains, nobody would have made comment. I felt a little stupid for letting Gorgoth walk us so hard. I took the bitter taste of that and set an edge on it, to save for the necromancers if they wanted to test our mettle.\n\nWe found the top of the stair without losing any more brothers. Gorgoth took us through a series of many-pillared halls, echoingly empty, the ceilings so low that Rike could reach up to touch them. Wide curving ramps stepped us up from one hall to the next, each the same as the one before, dusty and empty.\n\nThe smell crept up around us, so slowly that there wasn't a point where I could say I noticed it. The stink of death comes in many flavours, but I like to think I recognize the Reaper in all his guises.\n\nThe dust became thicker as we made our way, an inch deep in places. Here and there the occasional bone lay half-covered. Then more bones, then a skull, then three. Where the Builder-stone cracked and the waters oozed, the dust became a grey mud and flowed in miniature deltas. I pulled a skull from one such swamp. It came free with a satisfying squelch and mud poured from its sockets like syrup.\n\n\"So where are these necromancers of yours, Gorgoth?\" I asked.\n\n\"We make for The Great Stair. They will find us,\" he said.\n\n\"They've found you.\" She slid around the pillar closest to me, a woman from the night of my imagination. She moved her body over the rough stone as if it were sheerest silk. Her voice fell on the ear like velvet, dark and rich.\n\nNot one sword left its scabbard. The Nuban lifted his crossbow and heaved the loading lever back, bunching the heavy muscle in his arm into a black ball. The necromancer ignored him. She let the pillar go with a lover's reluctance and turned to face me. I heard Makin suck in his breath at my side. The woman mixed supple strength with a succulence that young princes doodle into the margins of their studies. She wore only paints and ribbons, the patterns swirled across her in Celtic knots of grey on black.\n\n_When you meet her, run._\n\n\"Well met, my lady.\" I sketched her a court bow.\n\n_Just run._\n\n\"Gorgoth, you bring us guests as well as tribute!\" Her laughter set a tingling in my groin.\n\n_Nothing else. Just run._\n\nShe offered her hand. For a moment I hesitated.\n\n\"And you would be?\" Her eyes, that had held only the reflection of fire, now stole the green I remembered from a distant throne-room.\n\n\"Prince Honorous Jorg Ancrath.\" I took her hand, cool and heavy, and kissed it. \"At your service.\" And I was.\n\n\"Chella.\" A dark fire ran in my veins. She smiled and I felt the same smile cross my face. She stepped closer. My skin sang with the thrill of her. I breathed her in, the bitter scent of old tombs, cut with the hot tang of blood.\n\n\"The little one first, Gorgoth,\" she said, without taking her eyes from mine.\n\nFrom the corner of my eye I saw Gorgoth take Gog in the hugeness of his hand.\n\nThe air became suddenly icy. The sound came of rock grinding on rock, setting my teeth on edge. The hall itself seemed to let forth a sigh of release, and with that exhalation mists swirled up among us, wraiths finding momentary form in the pale coils. I felt my finger freeze in the muck within the skull that dangled in my grasp.\n\nThe scraping ceased as bones found their partners. First one skeleton rose in a complex ballet of inter-articulation, then the next. The mists bound each bone in a spectral mockery of flesh.\n\nI saw Gog explode into a fit of thrashing and writhing within Gorgoth's implacable grip. Little Magog stood his ground as the first skeleton advanced on him. Gog was too far gone in his rage to demand release. The roar that came from him sounded comical, so high-pitched and thick with fury.\n\nThe necromancer slipped her arm around me. I can't tell you how it felt. We turned to watch Magog fight.\n\nThe leucrota child reached up to the skeleton's knee, no higher. He saw his moment, or rather, thought he did, and threw himself forward. You can't expect much from a five-year-old. The undead caught him in bony fingers and threw him carelessly against a pillar. Magog hit hard, leaving it bloody. He didn't cry though. He struggled to get up as the second skeleton stepped toward him. A flap of the child's pretty skin hung away from the red flesh of his shoulder.\n\nI looked away. Even with Chella's softness pressed to me, this sport tasted sour in ways I didn't understand. My eyes found Gog, still fighting in Gorgoth's fists. Gorgoth had both hands on the child now, though I doubted even I could fight out of his single grip. I hadn't imagined strength like that could lie in so small a thing.\n\nThe skeleton had Magog in one hand, two bone fingers of the other hand ready to drive through his eyes.\n\nIt seemed to me that a storm rose, though maybe it rose just in me, a storm lashing a moonless night and showing the world in lightning slices. A child's voice howled in my head and would not quiet though I cursed it to silence. Every fibre of me strained to move\u2014and no part of me so much as twitched. Hooks held me. There in the cradle of the necromancer's arms I watched the skeletal fingers plunge toward the black pools of the leucrota's eyes.\n\nWhen the hand exploded I was as surprised as anyone. A big crossbow bolt will do that to a hand. The Nuban turned his face toward me, away from the sights of his bow. I saw the white crescent of his smile and my limbs were free. I swung my arm up, sharp and hard. The skull in my hand hit the necromancer's face with a most satisfying crunch.\n\n_Whoever made the Nuban must have fashioned him from bedrock. I never knew a man more solid. He held his words close. Few among the brothers sought his counsel, men upon the road have little use for conscience, and although he never judged, the Nuban carried judgement with him._\n**30**\n\nI cleared scabbard and followed the arc of my family blade to face the necromancer. It's one of those swords they say can make the wind bleed. Appropriately the edge found only empty air, which hissed as if cut.\n\nThe necromancer fell back too swiftly for me to reach. The skull had taken her by surprise, but I didn't think I'd catch her again so easily.\n\nI guess the skull hit her in the bridge of the nose, because that's where the mess was. No blood, but a dark stain and a writhing of the flesh as though a hundred worms wriggled, one over another.\n\nFor the most part the brothers still stood in the daze that had held me. The Nuban worked to load another bolt into his crossbow. Makin half-drew his sword. Gorgoth let go of Gog.\n\nThe necromancer took a breath, like a rasp drawn over ironwork, rattling in her throat. \"That,\" she said, \"was a mistake.\"\n\n\"So sorry!\" I kept my voice cheerful and lunged at her. She slipped around the pillar, leaving me to skewer the stonework.\n\nGog hurled himself bodily at Magog, and tore his little brother from the skeleton's one-handed grip. I caught a glimpse of pale finger-marks on the child's neck.\n\nI moved around the pillar with a little caution, only to find the necromancer had somehow slipped back to a further pillar, five yards off.\n\n\"I'm very particular about who I allow to place spells on me,\" I said, turning and aiming a swift kick at Rike. He's hard to miss. \"Come on, Rikey! Up and at 'em!\"\n\nRike came to with a wordless howl of complaint, somewhere between disturbed walrus and bear-prodded-out-of-hibernation. Just in front of him the two skeletons bent to reach for the leucrota brothers, still a tangle of limbs on the dusty floor. Rike loomed over both of the undead, and took a skull in each hand. He wrenched them together in a clap that reduced the pair to shards.\n\nRoaring unintelligibly, he shook his hands. \"Cold!\" He graduated to words. \"Fecking freezing!\"\n\nI turned to the necromancer, some witticism ready on my tongue. The taunt died where it sat. Her whole face writhed now. The flesh lay shrunken on her limbs, pulsing sporadically. The body that seduced my eyes now held all the allure of a famine-corpse. She held me with a dark gaze, glittering in rotting slaughter. She laughed and her laughter came as the sound of wet rags flapping at the wind.\n\nThe brothers stood with me now. Gorgoth made no move, keeping his place. The little leucrotas crouched together in the shadows.\n\n\"We're many, and you're one, my lady. And a damned ugly one at that. So you'd best step aside and let us past,\" I said. Somehow I didn't think she was going to, but nothing ventured nothing gained, as they say.\n\nThat worm-flesh of hers crawled into a smile so wide I could see her jawbones past the hinge-point. For a second her face rippled and we saw Gains there, screaming as he fell.\n\n\"The dead are many, child,\" she said. \"I'll let you pass\u2014into their realm.\"\n\nThe temperature fell, and kept falling, like there was no bottom for it to hit. It went from uncomfortable, to painful, to plain stupid in no time at all. And the noise. The awful grinding as the skeletons built themselves from pieces and wrapped themselves in the spirit-mist that rose around us. A sound to make you want to pull your teeth out. The torch in Makin's hand gave up its struggle against the cold and guttered out.\n\nThe mist hid all but our nearest neighbours. The skeletons came at us slowly, as if in a dream. If not for the fire of Gorgoth's torch, we'd have been left in utter darkness.\n\nI swung my sword at the first attacker. The hilt felt frozen onto my hand, but I wasn't inclined to drop it in any case. I needed the exercise to keep warm. The skeleton disintegrated into a shower of brittle bone. I had no time to cheer before the next came lurching out of the fog.\n\nWe fell to the fight, and time left us. We hung in a freezing limbo where only the shattering of bone and the rise and fall of swords held meaning. Every time I cut ghost-flesh it seemed that the cold bit a little deeper into me. The sword grew heavy in my hand until it felt as if they'd fashioned it from lead.\n\nI saw Roddat die. A skeleton caught him with his guard down. Bony fingers found either side of his head and a whiteness spread from them; the living flesh dying where the ghost flesh touched. He was a weasel, was Roddat, but I took a pleasure in cutting in half the dead thing that killed him. Behind me someone screamed. Sounded like Brother Jobe. It wasn't the kind of scream you get up from.\n\nMakin found his way to my side, frost on his breastplate, blue in his lips. \"They just keep coming.\"\n\nI could hear a roaring behind us. The mist seemed to swallow sound, but the roaring ripped on through.\n\n\"Rike?\" I had to shout to be heard above it.\n\n\"Gorgoth! You want to see him fight. He's a monster!\" Makin shouted.\n\nI had to smile at that.\n\nThey just kept coming. More and more, rank by rank, out of the dark. Somebody died beside me. I couldn't tell you who.\n\nWe must have smashed two hundred of the bastards and still they kept coming.\n\nMy sword got caught in the ribs of the skeleton I'd swung at. Not enough force in the blow. Makin shattered its neck with a flat swing.\n\n\"Thanks.\" The word came out blunt, through numb lips.\n\n_I'm not going to die here_. I kept running the thought through my head. It held less conviction each time. _I'm not going to die here_. I felt too cold to think. _Not going to die here. Swing low to cut off those reaching hands. These bastards don't even feel it. The bitch felt it though, when I broke her face._\n\n_The bitch._\n\nWhen in doubt, let your hate lead you. Normally I'd reject that advice. It makes a man predictable. But there, in that miserable hall of bones, I was past caring. Hate was all I had to keep me warm. I cut a skeleton down and lunged past.\n\n\"Jorg!\" I heard Makin's startled shout behind me, then the darkness took my sight and the mist threw a thick blanket over the crash of battle.\n\nOh, it was black out there. So dark as to reach inside you and rip out all memory of colour. I swung my sword a few times, broke some bones, carved air for a while, then hit a pillar which shook the damn thing out of my frozen grip. I hunted my sword frantically, with hands too numb to find my face. Gradually it came to me that I was free of the skeletons. No bone fingers sought me in the night. Without sword or direction I stumbled on.\n\n_The bitch_. She'd be somewhere near. Surely. Waiting to trap our souls as we died. Waiting to feed.\n\nI stopped and stood as still as my shivering would let me. The necromancer had lifted the veil. Just like the Nuban said, she had lifted the veil between the worlds and the dead were coming through. If I stopped her, they'd stop coming. I listened, listened deep, to a silence as velvet as the dark. I held more still, straining for her, tight and focused.\n\n\"Cloves.\" My lips formed the word. I wrinkled my nose. Oil of cloves? The scent drew me on. It hung fainter than faint but, with nothing to fight against, it held me. I let it carry me forward, swaying, turning, seeking the source.\n\nMy hands found a narrow doorway and I stepped through into a chamber lit by the flickers of a dropped torch.\n\nI understood the scent. The Nuban's crossbow lay a foot from the torch, dropped carelessly, the cable drawn but the bolt spilled to the stones. He'd broken from the brothers to hunt her. Beaten me to the chase.\n\n\"Necromancer,\" I said.\n\nShe stood at the mouth of one of the Builders' shafts. The square maw filled the rear of the chamber behind her and the feeble light could not plumb its depths. She held the Nuban before her, holding his head to one side and her mouth to the straining cables of his neck. I could see the tension in his thick arms, but his fingers curled useless by his sides and his broadsword lay at his feet, hilt jutting into space over the edge of the shaft.\n\nThe necromancer lifted her face from the Nuban's neck. Blood dripped from her teeth. Whatever strength she gleaned from it had restored her looks. The blood ran over full lips and down a perfect throat.\n\n\"You sent such a fresh one to hunt me down, Prince Jorg,\" she said. \"Mmmm, flavoured with heathen spices. I thank you.\"\n\nI knelt and picked up the Nuban's bow. The weight of it always surprised me. I set the bolt in place. She moved to use him as a shield, her heels to the pit.\n\n\"You're cold, my prince,\" she said. The sudden music of her voice caught me off guard. It ran deep, rich with complexity. \"I could warm you.\"\n\nMy tired body thrilled with the dark melody of her. It took the memory of Gains's face crawling across her worm-flesh to stop me rising to her call. I lifted the bow. I knew I couldn't hold it for long.\n\n\"It's grave-cold that's in you.\" Her voice became an angry hiss. \"It will kill you.\"\n\nShe smiled at me over the Nuban's shoulder, enjoying his helplessness. \"You're trembling, Jorg. Put the bow down. You probably couldn't even hit your friend here, let alone me.\"\n\nIt felt so tempting. Put the bow down.\n\n\"He's not my friend,\" I said.\n\nShe shook her head. \"He'd die for you. I can taste it in his blood.\"\n\n\"You're playing the wrong game with me, dead-thing.\" I raised the bow and sighted it. The tremor in my arms kept the aim-point jumping. Any worse and the bolt would have shaken from its groove.\n\nShe laughed at me. \"I can see the ties that bind the living. You only have two friends, Prince Jorg. You're as bound to this sweet-blooded man as any son to his father.\"\n\n_Sacrifice._\n\nShe set her fingers to the red holes in the Nuban's neck. \"Let me have the others. Let me take their life-juice, and you and him, you can stay with me. You can help me harvest the leucrota. There are several tribes, some of them quite fractious. There are other necromancers against whom a living ally, one as sharp as you, would be most useful.\"\n\n_Play the game._\n\nShe smiled, and that dark fire lit in me again. \"I like you, Prince. We can rule under the mountain, together.\" Sex dripped off her words. Not that pallid roll in the sheets that Sally surrendered, but something potent, unseen, and consuming. She offered me a draw. Life, power, and command. But in her service.\n\n_Play to win._\n\nThe Nuban's eyes were on mine. For the first time ever, I could read what he held there. I could have taken anything else. I could have taken hatred, or fear, or pleading. But he forgave me.\n\n_ChooOom!_\n\nThe bolt hit the Nuban square in the chest. It put a hole through both of them and took them off the edge. Neither of them screamed, and it took forever before they hit the bottom.\n\n_Most men have at least one redeeming feature. Finding one for Brother Rike requires a stretch. Is \"big\" a redeeming feature?_\n**31**\n\nI came back to find the brothers nursing their wounds among drifts of broken bone. Roddat, Jobe, Els, and Frenk lay stretched out, apart from the group. Death makes lepers of even the most popular men. I didn't bother with them: any loot would be long gone.\n\n\"Thought you'd left us, Brother Jorg.\" Red Kent spared me a glance from beneath lowered brows and returned to the business of whetstone and sword.\n\nThat \"brother\" held a note of reproach. A note at the least, perhaps a whole symphony. No \"prince\" for the runaway.\n\nMakin watched me with dark speculation, sprawled on the floor, too spent to prop himself against a pillar.\n\nRike hefted himself to his feet. He came toward me slowly, polishing a ring against the leather padding of his breastplate. I recognized it as Roddat's luck-ring, a nice piece of yellow gold.\n\n\"Thought you'd left us, Brother Jorgy,\" he said. He loomed over me, a broad and brooding form.\n\nThere's some, like Liar, that aren't much to look at, and it's a surprise for folks when they find out what a truly nasty bastard they're dealing with. Rike never surprised anyone that way. The menace of him, the sheer brutality, his love of other people's pain, well, Mother Nature wrote it in every line of him just to warn us.\n\n\"The Nuban is dead.\" I ignored Rike and looked to Makin. I pulled the Nuban's crossbow off my back and showed it. No doubt after that. The man was dead.\n\n\"Good,\" said Rike. \"Serves him right for running. Never did like that weasel coward.\"\n\nI hit Rike as hard as I could. In the throat. I made no conscious decision. If I'd given it the smallest moment's consideration, I'd have held my blow. I might have stood a chance against him with a sword, but never with bare hands.\n\nActually \"bare hands\" is going too far. I had my gauntlets on, riveted iron. I stood six foot tall at fourteen, lean, but hard with muscle from swinging a sword and carting my armour around. I knew how to punch too. I put my whole weight behind that blow, and every ounce of my strength.\n\nIron knuckles crunched into Rike's bull-throat. I may not have been thinking with my head, but thankfully some part of me hadn't abandoned all sense. Punching Rike's blunt face would have probably broken my fist and just tickled him a little.\n\nHe gave a kind of grunt and stood there, looking slightly bewildered. I supposed the idea that I'd just committed suicide in such grand style took some getting used to.\n\nSomewhere in the back of my mind it dawned on me that I'd made a very big mistake. The rest of me didn't much care. I think blind rage, and the pure enjoyment of using Rike as a punch-bag, figured in equal measure.\n\nSince I'd been offered a second free blow, I took two. An iron-clad knee driven accurately into the groin will give pause for thought even to a seven-foot maniac who's twice your weight. Rike folded up obligingly and I brought both fists down together on the back of his neck.\n\nI studied the fighting arts of the Nippon with Tutor Lundist. He brought a book on the subject with him from the Utter East. Page upon rice-paper page of fighting stances, kata moves, and anatomical diagrams to show the pressure points. I'm sure I hit the two stun points on the back of Rike's neck, and I know I hit hard.\n\nI blame him for being too stupid to know how they work.\n\nRike swung at me. A lucky thing, because if he'd grappled me he'd have twisted my head off in no time. His vambrace caught my ribcage. I guess if I'd not been wearing that breastplate all my ribs would have broken, rather than just the two. The force took me off my feet and sent me sliding among the bones. I fetched up against one of those pillars with a painful little clang.\n\nI could have drawn my sword then. It would have been the only sensible decision. Against all the unwritten rules, of course. I started it with a punch and that was the way the thing should have ended. But when you weigh a loss of face with the brothers against having Rike actually rip your face off, well, it's not a hard decision.\n\nI picked myself up. \"Come here, you fat bastard.\"\n\nThe words emerged without a by-your-leave. The anger spoke for me. Anger at having lost control, more that now than anger at him calling the Nuban a coward. The Nuban didn't need Rike beaten bloody to prove his courage. Angry at being angry\u2014there's a worm that will eat its tail and no mistake. I should have Oroborus on my family crest.\n\nRike rushed me with that wordless howl of his. He reached a fair clip. Not many castle doors would stop Little Rikey at that speed. Pretty scary, unless you know he can't turn corners.\n\nI stepped aside nice and sharp, cursing at my ribs. Rike hit the pillar and bounced off. To his credit several bits of stone came loose. I picked up a good stout thighbone and smacked him around the head with it as he tried to get up. The thing cracked almost in two, so I finished the job and had myself two knob-ended clubs.\n\nThe single most depressing thing about fighting Rike would have to be the way he'd never stay down. He came at me, a bit woozy now, but snarling dire threats and meaning every one of them.\n\n\"Gonna feed you your own eyeballs, boy.\" He spat out a tooth.\n\nI danced back and hit him in the face with the longer of my two clubs. He spat out another tooth at that. I had to laugh. The anger left me and it felt good.\n\nSo Rike lumbered after me, and I kept my distance, clouting him a good one when I could. The closest thing I can think of is bear-baiting. _Whack! Growl. Clang! Snarl!_ I had the giggles, which was a bad thing, because one slip and he really would have me. If he got just one of those paws of his on me and got a grip . . . well, I _would_ be eating my own eyeballs. He did things like that.\n\nThe brothers started to lay bets and clap the sport.\n\n\"I'll pull your guts out.\" Rike seemed to have an endless supply of threats.\n\nUnfortunately he seemed to have an endless supply of energy too, and my dancing days were coming to an end, my footwork getting a little clumsy.\n\n\"Break every little bone in that pretty face o' yours, Jorgy.\"\n\nOur circle took us back to where I threw the first blow.\n\n\"Pull those skinny arms out of their sockets.\" He looked an evil sight with blood spilling down his chin.\n\nI saw my chance. I ran straight at him, taking him by surprise yet again. In the long run it promised to be a pushing contest as unequal as Rike against the pillar, but he gave a step. A step gave me all I'd hoped for. He hit Makin's legs, stumbled and went over backward. I scooped up the Nuban's bow, and before Rike could get up I was over him. I had the snout of the bow, a heavy iron falcon, poised above Rike's face.\n\n\"What's it going to be, Little Rikey?\" I asked. \"I think I can crush your skull like an egg before you get your hands on me. Should we try it and see? Or do you want to take that back?\"\n\nHe gave me a blank look.\n\n\"About the Nuban,\" I said. Rike had genuinely forgotten what he'd said.\n\n\"Uh.\" Doubt crinkled his brow. He tried to focus on the bow. \"I take it back.\"\n\n\"Christ bleeding!\" I sagged, exhausted, clothed in sweat. The brothers surged round us then, a new life in them, paying their bets, reliving the moment when Rike charged the pillar. I made note of who backed me: Burlow, Liar, Grumlow, Kent, the older men who could look past youth. Makin even went so far as to get up off the floor. He clapped a hand to my shoulder. \"You and the Nuban, you caught her?\"\n\nI nodded.\n\n\"I hope she went to Hell screaming,\" Makin said.\n\n\"She died hard,\" I said. An easy lie.\n\n\"The Nuban . . .\" Makin had to hunt for the words. \"He was better than the rest of us.\"\n\nI didn't have to hunt. \"Yes.\"\n\nGorgoth hadn't stirred while I fought Rike. He sat on the cold stone, legs crossed under him. Here and there the ghost-flesh of skeletal fingers had marked his hide with dead spots, little white fingerprints where the flesh had died. He didn't move, but he watched me with those cat's eyes of his.\n\nA yard or two from Gorgoth I could make out a small dark huddle, Gog and Magog clutched one to another.\n\n\"A fine fight, lad,\" I called to Gog. \"You were as good as your word.\"\n\nGog lifted his face to me. Magog's head flopped back, rolling on a neck scored by white lines, dead white lines across his tiger stripes.\n\nI found myself kneeling beside them. Gog snarled when I touched his brother, but he didn't stop me. Magog felt so light in my hands, a curious mix of bony starvation and child softness.\n\n\"Your brother,\" I said. For the longest moment I had nothing else to say, as though my throat closed away all my words. \"So little.\" I remembered him scampering up those endless stairs. In the end I had to press on my broken ribs to let the pain sharpen me and chase out the stupidity.\n\nI set the dead child down, and stood. \"You fought for him, Gog. Stupid, but maybe you'll find comfort in it.\" Maybe his reproach won't follow you the length of your days.\n\n\"We have a new mascot!\" I announced to the brothers. \"Gog here is now part of our merry band.\"\n\nGorgoth started up at that. \"The necromancers\u2014\"\n\nI stepped in before he rose to his feet, the iron face of the Nuban's crossbow three inches from his ridged forehead. \"What's it going to be, Gorgoth?\" I asked. He sat himself back down.\n\nI turned away. \"We burn the dead. I'm not having them come back to say hello.\"\n\n\"Burn 'em with what?\" Red Kent wanted to know.\n\n\"Bones is poor kindling, Jorth.\" Elban hawked a wad of phlegm into the nearest pile as if to prove his point.\n\n\"We'll have us a bone-fire even so,\" I said. \"I saw a tar drip on my way back.\"\n\nSo we took the bones to where the black stuff leaked slow and stinking from a crack in the Builder-stone and daubed them one by one. We made a heap for Roddat and the others, and a little pyre for the leucrota. Elban built it like the ones they fashion for kings in the Teuton lands.\n\nI set the fire with Makin's torch. \"Goodnight, lads,\" I said. \"Thieves and road-scum the lot of you. Tell the Devil I said to take good care of you.\"\n\nI gave the torch to Gog. \"Light it up, you don't want the necromancers playing with his bones.\" A heat came off the boy, as if a fire banked inside him had woken. Any hotter and he might light the pyre without the torch.\n\nHe set the flame and we backed off before the billowing smoke. Tar never burns clean, but I wasn't sorry for the veil it gave us. Gog gave me the torch back. The inky pools of his eyes held their secrets even tighter than the Nuban's did, but I could see something in there. A kind of pride.\n\nWe made our way on. I let Burlow carry the Nuban's bow. A prince must exercise some privilege after all. We walked with our tar-bone torches smoking, and Gorgoth at the fore to find the path.\n\nHe showed us mile after mile of dull box-chamber, square corridor, and low gallery. I guess when the Builders bought their hellfire from Lucifer they must have paid for it with their imaginations.\n\nThe Great Stair took me by surprise.\n\n\"Here.\" Gorgoth halted at a spot where a natural tunnel undercut the passage.\n\nThe Great Stair proved to be less grand than I had imagined. No more than ten yards across in any place I could see, and a squeeze at the entrance. At least it was natural though. My eyes had ached for a curved line, and here I could rest them. Some ancient stream had carved a path down a fault-line, stepping by leaps and bounds into the deep places. The waters, long since reduced to a trickle, dripped in a rocky gullet as steep and twisting as a man could hope for.\n\n\"Seems we have a climb ahead of us,\" I said.\n\n\"These stairs are not for the living.\" A necromancer insinuated himself into the narrow entrance, pulling himself from the shadows as though they clung like webs. He could have been a twin to the bitch that took the Nuban.\n\n\"For Christ's sake!\" I drew my sword and swung on a rising arc in the same motion. His head came off clean. I let the momentum carry me round, and brought the blade down with all my strength, overhand on the pulsing stump of his neck. The blow caught him before he could fall and cut deep, splitting his sternum.\n\n\"I'm not interested!\" I shouted the words at his corpse as I let its weight pull me to the ground. As with so many things in life, the bringing of death is simply a matter of timing. I made the mistake of giving Chella a moment and she took it. Jane should have told me just to attack her, nothing else, just attack her. Forget running. I had in mind that if my reply to Chella's first words had been a well-judged sword blow, the Nuban might yet be standing with me.\n\nA savage twist on my sword hilt opened the necromancer's chest. I keep a little dagger in my boot, wicked sharp. I took it out, and whilst the brothers watched in silence I cut out the necromancer's heart. The thing pulsed in my hand, warmish, lacking the heat of the living or the cold of the dead. His blood lacked a certain vitality too. When cutting out a heart\u2014and I speak from experience here\u2014expect to be crimson head to toe. The necromancer's blood looked purple in the torchlight and barely reached past my elbows.\n\n\"If any more of you bastards want to waste my time with stupid melodrama, please form an orderly queue.\" I let my voice echo down the corridors.\n\nThe Nuban once told me about a tribe in Nuba that ate the heart and the brains of their enemies. They thought it gave them their foes' strength and cunning. I never saw the Nuban do it, but he didn't dismiss the idea.\n\nI held the heart up to my mouth.\n\n\"Prince!\" Makin stepped toward me. \"That's evil meat.\"\n\n\"There is no evil, Makin,\" I said. \"There's the love of things, power, comfort, sex, and there's what men are willing to do to satisfy those lusts.\" I kicked the ruin of the necromancer's corpse. \"You think these sad creatures are evil? You think we should fear them?\"\n\nI took a bite, as big as I could manage. Raw flesh is chewy, but the necromancer's heart had some give in it, like a game bird hung until it's ready to drop off the hook. The bitter gall of the blood scoured my throat. I swallowed my mouthful and it slid down, slow and sour.\n\nI think for the first time Burlow watched me eat without the green eyes of jealousy. I threw the rest of it down. The brothers stood mute, eyes watering from the torch-smoke. That's the problem with tar-torches, you have to keep moving. I felt a touch odd. I had the feeling you get when you know you really should be somewhere else, as if you'd promised a duel that morning or some such but couldn't quite remember what it was. Chills ran up my back and along my arms, as if ghosts trailed their fingers over me.\n\nI opened my mouth, then closed it, interrupted by a whisper. I looked around. Whispers came from every corner, just at that maddening level where you can hear the words but not understand them. The brothers started to look around too, nervous.\n\n\"Do you hear it?\" I asked.\n\n\"Hear what?\" Makin said.\n\nThe voices came louder, angry but indistinct, louder, a multitude advancing, louder. A faint breeze disturbed the air.\n\n\"Time to climb, gentlemen.\" I wiped my hand across my mouth, scraping away purple muck on the back of my gauntlet. \"Let's see how fast we can do this.\"\n\nI picked the necromancer's head from the floor, half-expecting the eyes to roll down and fix me with a glare. \"I think our heartless foe has friends coming,\" I said. \"Lots of friends.\"\n\n_Everyone likes to eat. One man marches on his stomach as much as an army does. Only Fat Burlow didn't much take to marching, and took too much to munching. And some of the brothers were apt to hold that against a man. Still, I had more time for old Burlow than I did for most of my road-kin. Of all of them, save Makin, he was the only one who owned to reading. Of course he bore watching for that. There's a saying on the road, \"Never trust a lettered man.\"_\n**32**\n\nWe ascended the Great Stair with the screams of ghosts rising beneath us. They say fear lends a man wings. None of the brothers flew up the Stair, but the way they scrambled over the slickness of that rocky throat would teach a lizard plenty about climbing.\n\nI let them lead the way. It was as good a means as any to test the footing. Grumlow first, then Liar and young Sim. Gog scrambled behind them, followed by Gorgoth. I guessed the leucrotas' accord with the necromancers might be somewhat broken.\n\nMakin was the last of them. He could feel the dead coming. I saw it in the pallor of his skin. He looked like a dead thing himself.\n\n\"Jorg! Get up here! Climb!\" He grabbed at my arm as he passed.\n\nI shook him off. I could see ghosts boiling along the tunnel toward us, others stepping from the walls.\n\n\"Jorg!\" Makin took my shoulders and pulled me toward the Stair.\n\nHe couldn't see them. I knew from the wild sweep of his gaze. His eyes never touched them. The closest of them looked to me like chalk drawings half-erased, hanging in the air. Sketches of corpses, some naked, some clad in rags, or pieces of broken armour. A coldness came from them, reaching for my flesh, stealing warmth with invisible fingers.\n\nI laughed at them. Not because I thought they had no power to harm me, but because they had. I laughed to show them what I cared for their threat. I laughed to hurt them. And they suffered for it. The taste of dead heart-meat lingered at the back of my throat, and a dark power ran through me.\n\n\"Die!\" I shouted at them, spitting away the laughter. \"A man should at least know how to stay dead!\"\n\nAnd they did. I think. As if my words held them to obey. Makin had me dragged away, nearly round the corner, but I saw the spirits stop. I saw pale flames light upon their limbs, the ghost of fire. And, oh, the screaming. Even Makin heard it, like the scrape of nails on slate, cold wind on a migraine. We both ran then, close enough to flying.\n\nIt was hours before we stopped, a thousand feet or more up the Stair. The downward tumble of the long-vanished river paused here to scour out a bowl, set about with smaller sinkholes and decorated with the frozen tracery of stone that graces the deep places of the world.\n\n\"Fuckit.\" Fat Burlow collapsed in a boneless heap and lay motionless.\n\nRed Kent sat back against a stalagmite, his face coloured to match his name.\n\nClose by, Elban spat into a sinkhole pool, then turned, wiping mucus from his wizened lips. \"Heh! You looks like one o' them Blushers, Kent.\"\n\nKent just gave him mean eyes.\n\n\"So.\" Makin hauled in a huge breath and tried again. \"So, Prince, we're climbing up. Well and good. But if we keep on up we're just going to reach the Castle Red.\" Another breath. A long climb in armour will do that for you. \"We might surprise the hell out of them, coming up out of their vaults, but we're still twice a dozen men against nine hundred.\"\n\nI smiled. \"It's a dilemma ain't it, Brother Makin? Can Jorg work the magic one more time?\"\n\nThe brothers all had an eye on me now. All save Burlow, after that climb he wouldn't turn his head for anything less than the Second Coming.\n\nI pulled myself to my feet and gave a little bow. \"That Jorg, that Prince Jorg, he's got a madness in him. A stranger to reason, a little in love with death perhaps?\"\n\nMakin had a frown on him, worried, wanting me to shut up.\n\nI strode around them. \"Young Jorg, he's apt to throw it all away on a whim, gamble the brotherhood on wild chance . . . but somehow, just somehow, it keeps turning out a-right!\"\n\nI clapped a hand to Rike's greasy head and he gave me a bruise-faced scowl.\n\n\"Is it luck?\" I asked. \"Or some sort of royal magic?\"\n\n\"Nine hundred o' them Blushers up there in the Castle Red, Jorth.\" Elban gestured at the ceiling with his thumb. \"No way we can turn them out of there. Not if we were ten times the number.\"\n\n\"The wisdom of age!\" And I crossed to Elban and threw an arm around his shoulders. \"Oh my brothers! I may have given our priest away, but it sorrows me that your faith departs so swiftly on his heels.\"\n\nI steered Elban to the Stair. I felt the tension in him as we neared the point where the floor fell away. He remembered the Watch Master.\n\nI pointed up the stepped river course. \"That's where our path lies, Old Father.\"\n\nI let him go and he drew in a sigh. Then I turned to face the brothers once again. Gorgoth watched me with his cat's eyes, Gog with strange fascination from behind a pillar of rock.\n\n\"Now I'm thinking that I'll find what I'm looking for before we reach the under-vaults of the Castle Red.\" I put a little iron in my voice. \"But if it turns out we have to murder us a quiet path to Duke Merl's bedchamber, and I have to plant him on my sword like a puppet on a stick to get him to sign the place over to me . . .\" I swept my gaze across them, and even Burlow managed to look up. \"Then . . .\" I let my voice fill the chamber and it echoed marvellously. \"Then that is what you will fecking well do, and the first brother that doubts my fecking luck, will be the first to leave this little family of ours.\" I left them in no doubt that such a parting would be ungentle.\n\nSo we climbed again, and in time we left the Great Stair behind us, finding once more the box-halls of the Builders. Gorgoth's knowledge reached only to the Stair's foot so I led the way. Lines danced in my mind. Rectangles, squares, precise corridors, all etched into scorched plasteek. A turn there, a chamber on the left. And with sudden certainty, like one of Lundist's potions turning to crystal at the addition of the smallest grain, I knew where we were.\n\nI pictured the map and followed it. The Builders' book sat in my pack, and I'd returned to its pages many times on our journey from The Falling Angel. No need to dig it out now. Let the brothers have their magic show.\n\nWe came to a five-way intersection. I put one hand to my forehead and let the other wander the air as if seeking our path. \"This way! We're close.\"\n\nAn opening on the left, edged by the ancient rust-stain of a long vanished door.\n\nI paused and lit a new torch of tar and bone from the blackened stick of my old one.\n\n\"And here we are!\"\n\nWith my best courtly flourish I pointed the way, then stepped through.\n\nWe entered an antechamber to the vault I sought from my map. The door that blocked the way from our chamber into the vault stood maybe ten foot tall, a huge circular valve of gleaming steel, set about with rivets thick as my arm. Damned if I know what Builder spells kept it from rusting away like the rest, but there it was, big, shiny, and implacably in my way.\n\n\"So how're you going to open that?\" Rike's words came out mumbled. I'd mashed his lips up pretty good.\n\nI hadn't the slightest idea.\n\n\"I thought we could try knocking it down with your head.\"\n\n_I named him Liar the day I put a knife through his hand. The knife came out, but the name stuck. He was a mean bit of gristle wrapped round bone. Truth might burn his tongue but his looks didn't lie._\n**33**\n\n\"Looks pretty solid to me,\" Makin said.\n\nI couldn't argue. I'd never seen anything more solid than that door. I could hardly even scratch it with my sword.\n\n\"So what's the plan?\" Red Kent stood with both hands on the hilts of his short-swords.\n\nI held the gleaming wheel at the centre of the door and leaned back. The door loomed above me. It looked like silver, a king's ransom in silver.\n\n\"We could dig through,\" I said.\n\n\"Builder-stone?\" Makin raised an eyebrow.\n\n\"Try anyway.\" I released the wheel and pointed to Burlow then Rike. \"You two. Start over there.\"\n\nThey moved forward with shrugs. Rike reached the spot and kicked the wall. Burlow held his hands out before him and studied them with a speculative pout.\n\nI had picked them for strength, not initiative. \"Makin, give them your flail. Row, let's put that war-hammer of yours to good work.\"\n\nRike took the hammer in one hand and set to pounding on the wall. Burlow took a swing with the flail and nearly got both the spiked iron balls in his face as they bounced back.\n\n\"My money's on the wall,\" Makin said.\n\nAfter five minutes I could see we'd be there a while. The wall fell away not in chunks but in scatters of pulverized stone. Even Rike's furious attack left only shallow scars.\n\nThe brothers began to settle, leaning back against their packs. Liar set to cleaning his nails with a small knife. Row put down his lantern, Grumlow took out cards, and they hunkered down to play a hand. Lost most of their loot that way, Row and Grumlow, and practice never made them better. Makin pulled out a stick of dried meat and set to chewing. \"We've a week's rations at most, Jorg.\" He got the words out between swallows.\n\nI paced the room. I knew we weren't going to dig through. I'd given them make-work to keep them quiet. Or at least as quiet as men wielding hammers can be.\n\n_Perhaps there's no way through_. The thought gnawed at me, an unscratchable itch, refusing to let me rest.\n\nThe hammering made the room ring. The noise struck at my ears. I walked the perimeter, trailing the point of my sword along the wall, deep in thought. _No way through_. Gog crouched in a corner and watched me with dark eyes. Where the brothers lay, I stepped over them as though they were logs. As I passed by Liar, I felt a change in the texture of the wall. It looked the same, but beneath my blade it felt like neither stone nor metal.\n\n\"Gorgoth, I need your strength here, if you please.\" I didn't look to see if he got up.\n\nI sheathed my sword and pulled the knife from my belt. Moving in close, I scratched at the strange patch and managed to score a line across the surface. It left me little wiser. Not wood.\n\n\"What?\" The torches threw Gorgoth's shadow over me.\n\n\"I hoped you could tell me,\" I said. \"Or at least open it.\" I struck my fist on the panel. It gave the faintest hint at some hollow behind.\n\nGorgoth pushed past and felt out the edges. It was about a yard by half a yard. He struck it a blow that would have caved in an oak door. The panel hardly shook, but the edge on the left lifted ever so slightly. He set the three thick fingers of each hand to the edge, digging in with dark red talons. Beneath his scarred hide the muscles seemed to fight each other, one surging over the next in a furious game of King of the Mountain. For the longest time nothing happened. I watched him strain, then realized I'd forgotten to breathe. As I released my breath, something gave inside the wall. With a snap and then a tortured groan the panel came free. The empty cupboard behind it proved to be somewhat of an anti-climax.\n\n\"Jorg!\" The hammering had stopped.\n\nI turned to see Rike wiping sweat and dust from his face, and Burlow beckoning me over.\n\nI crossed the room slowly, though half of me wanted to run, and the other half not to go at all.\n\n\"Doesn't look like you're through yet, Burlow.\" I shook my head in mock disappointment.\n\n\"Not going to be neither.\" Rike spat on the floor.\n\nBurlow brushed the dust from the shallow hole their labour had forged. Two twisted metal bars showed through, bedded in the Builder-stone. \"Reckon these run through the whole wall,\" he said.\n\nMy eyes strayed to the knife I held clenched in one fist. I have, on occasion, punished the messenger. There are few things more satisfying than taking out your frustrations upon the bearer of bad tidings.\n\n\"Reckon they might at that.\" I pushed the words through gritted teeth.\n\nQuickly, before Fat Burlow could open his mouth again and earn himself the name Dead Burlow, I turned and went back to the secret compartment. Just enough space to hold a folded corpse. Empty save for dust. I drew my sword and reached in to check the back of the compartment. As I did, a strange chime sounded.\n\n\"External sensors malfunctioning. Biometrics offline.\" The voice came from the empty cupboard, the tone calm and reasonable.\n\nI looked to either side, then back to the space before me. The brothers looked up and started to get to their feet.\n\n\"What language is that?\" Makin asked. The others were looking for ghosts, but Makin always asked good questions.\n\n\"Damned if I know.\" I knew a few languages, six fluent enough for conversation and another six well enough to recognize when spoken.\n\n\"Password?\" The voice came again.\n\nI recognized that. \"So you can speak Empire Tongue, spirit.\" I kept my sword raised, looking all around to find the speaker. \"Show yourself.\"\n\n\"State your name and password.\"\n\nBeneath the dust on the back wall of the compartment I could see lights moving, like bright green worms.\n\n\"Can you open that door?\" I asked.\n\n\"That information is classified. Do you have clearance?\"\n\n\"Yes.\" Four foot of edged steel is clearance enough in my book.\n\n\"State your name and password.\"\n\n\"How long have you been trapped in there, spirit?\" I asked.\n\nThe brothers gathered around me, peering into the compartment. Makin made the sign of the cross. Red Kent fingered his charms. Liar pulled his self-collected from beneath his mail shirt.\n\nA long moment passed while the green worms marched down the back wall, a floos of light beneath the dust. \"One thousand one hundred and eleven years.\"\n\n\"What's it going to take for you to open that door? Gold? Blood?\"\n\n\"Your name and password.\"\n\n\"My name is Honorous Jorg Ancrath, my password is divine right. Now open the fecking door.\"\n\n\"I don't recognize you.\" Something about the spirit's calmness infuriated me. If it had been visible, I'd have run it through right there and then.\n\n\"You haven't recognized anything but the back of this panel for eleven hundred years.\" I kicked the panel in question for emphasis and sent it skittering across the room.\n\n\"You are not authorized for chamber twelve.\"\n\nI looked to the brothers for inspiration. A more blank sea of faces is hard to imagine.\n\n\"Eleven hundred years is a long time,\" I said. \"Wasn't it lonely there in the dark, all those long years?\"\n\n\"I was alone.\"\n\n\"You were alone. And you could be again. We could wall you up so you'd never be found.\"\n\n\"No.\" The tone remained calm, but there was something frenzied in the pattern of lights.\n\n\". . . or, we could set you free.\" I lowered my sword.\n\n\"There is no freedom.\"\n\n\"What do you want then?\"\n\nNo reply. I leaned into the compartment, far enough that I could set my fingers to the far wall. The surface beneath the dust felt glassy and cool.\n\n\"You were alone,\" I said. \"Trammelled in the thousand-year dark with only memories for company.\"\n\nWhat had it witnessed, this ancient spirit, trapped by the Builders? It had lived through the Day of a Thousand Suns, it had seen the end of the greatest empire, heard the scream of millions.\n\n\"My creator gave me awareness, for a 'flexible and robust response to unforeseen situations,'\" the spirit said. \"Awareness has proved to be a weakness in periods of prolonged isolation. Memory limitations become significant.\"\n\n\"Memories are dangerous things. You turn them over and over, until you know every touch and corner, but still you'll find an edge to cut you.\" I looked into my own darkness. I knew what it was to be trapped, and to watch ruination. \"Each day the memories weigh a little heavier. Each day they drag you down that bit further. You wind them around you, a single thread at a time, and you weave your own shroud, you build a cocoon, and in it madness grows.\" The lights pulsed beneath my fingers, ebbing and flowing to the beat of my voice. \"You sit here with your yesterdays queuing at your shoulder. You listen to their reproach and curse those that gave you life.\"\n\nVeins of light spread through the glass beneath my palm, miniature lightning reaching across the wall. My hand tingled. I felt a moment of kinship.\n\n\"I know what you want,\" I said. \"You want an end.\"\n\n\"Yes.\"\n\n\"Open the door.\"\n\n\"The EM-bolts failed over six hundred years ago. The door is not locked.\"\n\nI drove my sword into the panel. The glass shattered and a brilliant flash lit the compartment. I pushed on, through a softness yielding like flesh, and things that crunched and gave like the bones of birds. Something hit me in the chest and I staggered back, caught by Makin. When I'd shaken the after-images from my eyes I could see my sword standing from the rear wall, smoking and blackened.\n\n\"Open the damn door!\" I shook Makin off.\n\n\"But\u2014\" Burlow started. I cut through his objection.\n\n\"It's not locked. Gorgoth, Rike, give it a decent pull. Burlow, get in there and make that lard work for us for once.\"\n\nThey did as I said, setting their bulk to the task, well over a thousand pounds of dumb muscle between them. For a moment nothing happened. Another moment, and then, without the slightest whisper from the hinges, the massive door stole into motion.\n\n_The road may go ever on, but we don't: we wear out, we break. Age makes different things of different men. It will harden some, sharpen them, to a point. Brother Elban has that toughness, like old leather. But in the end the weakness comes and the rot. Perhaps that's the fear behind his eyes. Like the salmon, he's been swimming upstream all his life, and he knows there's no shallows waiting for him, no still waters. Sometimes I think it would be kindness to make a swift end for Elban, before the fear eats up the man he was._\n**34**\n\n\"What is this place?\" Makin stood at the entrance with me.\n\nThe vault stretched beyond sight. On the ceiling ghost lights flickered into life, some obedient to the opening of the door, others struggling into wakefulness, tardy children late for the day's lesson. I could see little of the floor past the crush of treasures. No Hollander grain-master owns a warehouse so well packed. To describe it fully would require all the vocabulary of shape and solid so kindly furnished by Euclid and by Plato. Cylinders longer and wider than a man, and cubes a yard on each side, lay stacked to scrape the Builder-stone above, and against the wall\u2014cones and spheres in wire cradles, all skinned with dust. Row upon row, stack upon stack, marching beyond sight.\n\n\"It's an armoury,\" I said.\n\n\"Where are the weapons?\" Rike came to join us from his struggles with the door. He wiped the sweat from his brow, and spat into the dust.\n\n\"Inside the boxes.\" Makin rolled his eyes.\n\n\"Let's get 'em open then!\" Burlow said. He pulled a small crowbar from his belt. It never took much encouragement to set the brothers to looting.\n\n\"Surely.\" I waved him in. \"But open one at the back please. They're all filled with poison.\"\n\nBurlow took a few steps into the vault before that sunk in. \"Poison?\" He turned round slow-like.\n\n\"The best the Builders could make. Enough to poison the whole world,\" I said.\n\n\"And this will help us how?\" Makin asked. \"We sneak into the Castle Red's kitchens and slip some in their soup? That's a plan for children's games, Jorg.\"\n\nI let that slide. It was a fair question, and I didn't feel like falling out with Makin.\n\n\"These poisons can kill by a touch. They can kill through the air,\" I said.\n\nMakin put a hand to his face and drew it down in a slow motion, pulling at his cheeks and lips. \"How do you know this, Jorg? I looked at that old book of yours, there was nothing about this in there.\"\n\nI stabbed a finger toward the piled weapons. \"These are the poisons of the Builders.\" I pulled the Builders' book from my belt. \"This is the map. And that,\" I pointed to Gorgoth, \"is the evidence of their potency. Him and the Blushers of the Castle Red.\"\n\nI crossed to where Gorgoth leaned against the silvery mass of the door.\n\n\"If you were to search the depths of this vault, and I don't advise that you do, you'll find fissures where underground waters have found their way in and out. And where do these waters run?\"\n\nFor a moment I expected an answer, then I remembered who my audience were. \"Where does any water run?\" Still dumb looks and silence. \"Down!\"\n\nI put a hand to the deformed rib-bones that reached out of Gorgoth's chest. He made a growl that would put a grizzly bear to shame, and the vibration of his ribs undercut it.\n\n\"Down to the valley where, in the tiniest of doses, it makes monsters of men. And where did the water run from?\" I asked.\n\n\"Up?\" Makin at least was game to try.\n\n\"Up,\" I said. \"So our poison wafts up, and what hint escapes into the Castle Red paints the folk that live there, the Blushers, an attractive lobster red. Which, my brothers, is what it says the stuff does in this here book handed down through some thousand years to your own sweet Jorgy.\"\n\nI spun away from Gorgoth, caught up in my display, and mindful of his fists. \"And these poisons, in their interesting boxes, can do all this when what we have is an ancient spill, washed over for a thousand years. So all in all, Brother Burlow, it would be best not to open one with your crowbar, just yet.\"\n\n\"So what will we do with them, Jorth?\" Elban came to lisp at my elbow. \"Sounds like dirty work, no?\"\n\n\"The dirtiest, old man.\" I clapped a hand to his shoulder. \"We're going to build a slow fire, bank it well, and run for our lives. The heat will crack open these marvellous toys, and the smoke will make a charnel house of the Castle Red.\"\n\n\"Will it stop there?\" Makin shot me a sharp glance.\n\n\"Maybe.\" I looked around at the brothers. \"Liar, Row, and Burlow, see to finding some fuel for our fire. Bones and tar if you must.\"\n\n\"Jorg, you said 'enough to poison the world,'\" Makin said.\n\n\"The world is already poisoned, Sir Makin,\" I said.\n\nMakin pursed his lips. \"But this could spread. It could spill out over Gelleth.\"\n\nBurlow and the others stopped by the door and turned to watch us.\n\n\"My father asked for Gelleth,\" I said. \"He did not specify the nature of its delivery. If I hand him a smoking ruin, he will thank me for it, by God he will. Do you think there is a crime he would not countenance to secure his borders? Even one crime? Any single sin?\"\n\nMakin frowned. \"And if the fumes roll into Ancrath?\"\n\n\"That,\" I said, \"is a risk that I am prepared to accept.\"\n\nMakin turned from me, his hand on his sword hilt.\n\n\"What?\" I questioned his back, and my voice echoed in the Builders' dusty vault. I spread my arms. \"What? And don't you dare speak to me of innocents. It is late in the day for Sir Makin of Trent to champion maids and babes in arms.\" My anger sprang from more than Makin's doubt. \"There are no innocents. There is success, and there is failure. Who are you to tell me what can be risked? We weren't dealt a hand to win with in this game, but I will win though it beggar heaven!\"\n\nThe tirade left me breathless.\n\n\"But it'd be so many, Jorth,\" Elban said.\n\nYou'd think seeing me knife Brother Gemt not so many weeks earlier, over a far smaller dispute, would have taught them sense, but no.\n\n\"One life, or ten thousand, I can't see the difference. It's a currency I don't understand.\" I set my sword to Elban's neck, drawing too quick for him to react. \"If I take your head once, is that less bad than taking it again, and then again?\"\n\nBut I had no appetite for it. Somehow losing the Nuban had made what brothers I had left seem more worth keeping, scum though they were.\n\nI put the blade away. \"Brothers,\" I said. \"You know it's not like me to lose my temper. I'm out of sorts. Too long without sight of the sun perhaps, or maybe something I ate . . .\" Rike smirked at the reference to the necromancer's heart. \"You're right, Makin, to destroy more than the Castle Red would be . . . wasteful.\"\n\nMakin turned to face me, hands together now. \"As you say, Prince Jorg.\"\n\n\"Little Rikey, get you just one of those wonderful toys. That one, like a giant's gonad, if you please.\" I pointed out the closest of the spheres. \"Don't drop it mind, and have Gorgoth help out if it's as heavy as it looks. We'll take it up a little higher and set it cooking for the castle's breakfast. One should be enough.\"\n\nAnd we did.\n\nWith hindsight, if all the detail were known, Makin's stand there in the Builders' vault should be sufficient to wash the blood from his hands, to erase all his crimes, the cathedral at Wexten notwithstanding, and make of him a hero fit to stand beside any that may be found in legend. Given the swathe of death downwind of the Castle Red, it's clear that the drastic scaling-down of my original plan saved the world from a rather unpleasant death. Or at least delayed it.\n**35**\n\n\"We should have seen something by now,\" Makin said.\n\nI looked back over my shoulder. The ugly bulk of Mount Honas made a black fist against the sky, the Castle Red cradled in its grip. Behind us the brothers straggled, a line of vagabonds labouring down the slope.\n\n\"This death walks softly, Makin,\" I said. \"An invisible hand with fatal fingers.\" I gave him a grin.\n\n\"Finding every baby in its crib?\" Distaste thinned Makin's thick lips.\n\n\"Would you rather it were Rike that found them, or Row?\" I asked. I set a hand to his shoulder, gauntlet to breastplate, both smeared with the grey mud from our escape tunnel. He had it in his hair too, drying on black curls.\n\n\"You seem troubled of late, old friend,\" I said. \"The past sins weigh so heavy that you're afraid to add more?\"\n\nI noticed that we stood nearly of a height, though Makin was a tall man. Another year's growth and he'd be tilting his head to meet my gaze.\n\n\"Sometimes you almost fool me, you're that good, Jorg.\" He sounded weary. I could see the web of fine lines around the corners of his eyes. \"We're not old friends. A little over three years ago you were ten. Ten! Maybe we're friends, I can't tell, but 'old'? No.\"\n\n\"And what is it that I'm so good at?\" I asked.\n\nHe shrugged. \"Playing a role. Filling in for lost years with that intuition of yours. Replacing experience with genius.\"\n\n\"You think I have to be old to think with an old head?\" I asked.\n\n\"I think you need to have lived more to truly know a man's heart. You need to have made more transactions in life to know the worth of the coin you spend so freely.\" Makin turned to watch the column close on us.\n\nRike came into view at the rear of the line, cresting a ridge, black against a dawn-pale sky. Behind him the clouds ran out in ribbons, the dirty purple of a fresh bruise, reaching for the west. Bandages on his upper arm, and around his brow, flapped in the breeze.\n\nSomething tickled at me, the ghosts of whispers, colder than the wind.\n\nMakin turned to go.\n\n\"Wait\u2014\"\n\nScreams now. The terror of those already dead.\n\nNo sound came, but Mount Honas lifted, like a giant drawing breath. A light woke beneath the rock, bleeding incandescence through spreading fissures. In one moment, the mountain vanished, thrown at heaven in a spiralling inferno. And, somewhere within that gyre, every stone of the Castle Red, from deepest vault to tower high.\n\nA brilliance took all glory from the morning, making a pale wash of the land. Rike became a flicker of shadow against the blinding sky. I felt the hot kiss of that distant fury, like sunburn on my cheeks.\n\nWhat burns so bright cannot endure. The light failed, leaving us in shadow, the kind of darkness that precedes a squall. I saw the storm's outriders, newborn ghosts, driven before the rage. I watched them sweep out across the land, like the ripple from a pond-thrown stone, a grey ring where rock became dust, racing fast as thought. The sky rippled too, the ribbon-cloud now whips for the cracking.\n\n\"Dear Jesu.\" Makin left his mouth open, though he had no more words.\n\n\"Run!\" Burlow's shout sounded oddly mute.\n\n\"Why?\" I spread my arms to welcome the destruction. We had nowhere to run.\n\nI watched the brothers fall. Time ran slow and the blood pulsed cold in my veins. Between two beats of my heart, the blast cut them all down, Rike first, lost beneath the grey maelstrom, a child before an ocean breaker. The hot wind took my feet. I felt the dead flow through me, and tasted the bitter gall of necromancer blood once more.\n\nFor a time I floated, like smoke above the slaughter.\n\nI lay in nothing. I knew nothing. A peace deeper than sleep, until . . .\n\n\"Oh! Bravo!\" The voice cut into me, too close, and somehow familiar. \"Now is the winter of our Hundred War made fearsome summer by this prodigal son.\" His words flowed like rhyme, and carried strange accents.\n\n\"You maul Shakespeare worse than you abuse his mother tongue, Saracen.\" This a woman, velvet and rich.\n\n_Just run._\n\n\"He has woken a Builders' Sun, and you make jokes?\" A child spoke, a girl.\n\n\"You're not dead yet, child? With the mountain levelled into the valley?\" The woman sounded disappointed.\n\n\"Forget the girl, Chella. Tell me who stands behind this boy. Has Corion grown weary of Count Renar and taken a new piece to the board? Or has the Silent Sister shown her hand at last?\"\n\nSageous! I knew him.\n\n\"She thinks to win the game with this half-grown child?\" The woman laughed.\n\nAnd I knew her too. The necromancer.\n\n\"I sent you to Hell, with the Nuban's bolt through your heart, bitch,\" I said.\n\n\"What in Kali's n\u2014\"\n\n\"He hears us?\" She cut across him, Chella, I knew her voice, the only corpse ever to make me rise.\n\nI hunted for them, there in the smoke.\n\n\"No, it's not possible,\" Sageous said. \"Who stands behind you, boy?\"\n\nI could find nothing in the swirl of blindness enfolding me.\n\n\"Jorg?\" A whisper at my ear. The girl again. The monsters' glowing child.\n\n\"Jane?\" I whispered back, or thought I did, I couldn't feel my lips or any other part of me.\n\n\"The ether doesn't hide us,\" she said. \"We are the ether.\"\n\nI thought on that for a moment. \"Let me see you.\"\n\nI willed it. I reached for them. \"Let me see you.\" Louder this time. And I painted their image on the smoke.\n\nChella appeared first, lean and sensual as I first met her, the coils of her body-art spiralled from etheric wisps. Sageous next. He watched me with those mild eyes of his, wider and more still than mill-pools, as I cut his form from nothing. Jane stepped out beside him, her glow faint now, a mere glimmer beneath the skin. There were others, shapes in the mist, one darker than the rest, his shape half-known, familiar. I tried to see him, poured my will into it. The Nuban came to mind, the Nuban, the glimpse of my hand on a door, and the sensation of falling into space. _D\u00e9j\u00e0 vu_. \"Who lends you this power, Jorg?\" Chella smiled seduction at me. She stepped around me, a panther at play.\n\n\"I took it.\"\n\n\"No,\" Sageous shook his head. \"This game has played out too long for trickery. All the players are known. The watchers too.\" He nodded toward Jane.\n\nI ignored him, and kept my eyes on Chella. \"I brought the mountain down on you.\"\n\n\"And I am buried. What of it?\" An edge of her true age crept into her voice.\n\n\"Pray I never dig you out,\" I said.\n\nI looked to Jane. \"So you're buried too?\"\n\nFor a moment her glow flickered, and I saw another Jane in her place, this one a broken thing. A rag doll held between shards of rock in some dark place where she alone gave light. Bones stood from her hip and shoulder, very white, traced with blood, black in the faint illumination. She turned her head a fraction, and those silver eyes met mine. She flickered again, whole once more, standing before me, free and unharmed.\n\n\"I don't understand.\" But I did.\n\n\"Poor sweet Jane.\" Chella circled the girl, never coming too close.\n\n\"She'll die clean,\" I said. \"She's not afraid to go. She'll take that path you fear so much. Cling to carrion flesh and rot in the bowels of the earth if that's where cowardice keeps you.\"\n\nChella hissed, venom on her face, the wet flap of decay in her lungs. The smoke began to take her again, writhing around her in serpent coils.\n\n\"Kill this one slow, Saracen.\" She threw Sageous a hard look. And she was gone.\n\nI felt Jane at my side. The light had left her. Her skin held the colour of fine ash when the fire has taken all there is to give. She spoke in a whisper. \"Look after Gog for me, and Gorgoth. They're the last of the leucrota.\"\n\nThe thought of Gorgoth needing a guardian brought sharp words to the tip of my tongue, but I swallowed them. \"I will.\" Maybe I even meant it.\n\nShe took my hand. \"You can win the victories you seek, Jorg. But only if you find better reasons to want them.\" I felt a tingle of her power through my fingers. \"Look to the lost years, Jorg. Look to the hand upon your shoulder. The strings that lead you . . .\"\n\nHer grip fell away, and smoke coiled where she had been.\n\n\"Don't come home again, Prince Jorg.\" Sageous made his threat sound like fatherly advice.\n\n\"If you start running now,\" I said, \"I might not catch you.\"\n\n\"Corion?\" He looked into the coiling ether behind me. \"Don't send this boy against me. It would go ill.\"\n\nI reached for my sword, but he'd gone before I cleared scabbard. The smoke became bitter, catching at my throat, and I found myself coughing.\n\n\"He's coming round.\" I heard Makin's voice as if from a great distance.\n\n\"Give him more water.\" I recognized Elban's lisp.\n\nI struggled up, choking and spitting water. \"God's whore!\"\n\nA vast cloud, like the anvil of a thunderhead, stood where Mount Honas had been.\n\nI blinked and let Makin haul me to my feet. \"You're not the only one to take a hard knock.\" He nodded across to where Gorgoth crouched a few yards off, with his back to us.\n\nI stumbled over, stopping when I noticed the heat\u2014the heat and a glow that made a silhouette of Gorgoth despite the daylight, as if he were huddled over a fierce campfire. I edged around and to the side. Gog lay coiled like a babe in the womb, every inch of him white hot, as if the light of the Builders' Sun were bleeding through him. Even Gorgoth had to shuffle back.\n\nAs I watched, the boy's skin shaded down through colours seen in iron in the forge, hot orange, then the duller reds. I took a step toward him and he opened his eyes, white holes into the centre of a sun. He gasped, the inside of his mouth molten, then curled more tightly. At times fire danced across his back, running along his arms, then guttering out. It took ten minutes for Gog to cool so that his old colours returned and a man could stand beside him.\n\nAt last he lifted his head and grinned. \"More!\"\n\n\"You've had enough, lad,\" I said. I didn't know what the Builders' Sun had woken as it echoed through him, but from what I'd seen, better it went back to sleep.\n\nI looked back at the cloud still rising above Mount Honas and the countryside burning for miles around.\n\n\"I think it's time to go home, lads.\"\n**36**\n\n**_Four years earlier_**\n\n\"It can't be done,\" said the Nuban.\n\n\"Few things worth having can be got easily,\" I said.\n\n\"It can't be done,\" he said. \"Not by anyone who expects to live five minutes past the act.\"\n\n\"If a suicidal assassin were all it took, then the Hundred would be the Dozen by now.\" My own father had survived several attempts in which the would-be killer had no interest in escape. \"No one with a claim to the empire throne is that easy to bring to an end.\"\n\nThe Nuban turned in the saddle to frown at me. He'd given up asking how a child knew such things. I wondered how long before he gave up telling me it couldn't be done.\n\nI nudged my horse on. The towers of the Count's castle hadn't seemed to get any closer over the last half hour.\n\n\"We need to find the Count's strongest defence,\" I said. \"The protection that he most relies upon. The one upon which his faith rests.\"\n\nThe Nuban frowned again. \"Seek out your enemy's weakness,\" he said. \"Then take your shot.\" He patted the heavy crossbow strapped across his saddlebags.\n\n\"But you've already told me it can't be done,\" I said. \"Repeatedly.\" I pulled my cloak tight against the evening wind. The man I had taken it from had been a tall one, and it hung loose about me. \"So you're just planning the most sensible way to lose.\"\n\nThe Nuban shrugged. He never argued for the sake of being right. I liked that in him.\n\n\"The weakest spot in a good defence is designed to fail. It falls, but in falling it summons the next defence and so on. It's all about layers. At the end of it all you'll find yourself facing the thing you sought to avoid all along, only now you're weaker, and it's forewarned.\"\n\nThe Nuban said nothing, the blackness of his face impenetrable in the dying light.\n\n\"Surprise is our only real weapon here. We sidestep that process of escalation. We cut straight to the heart of the matter.\"\n\nAnd the heart is what we want to cut.\n\nWe rode on, and at length the towers grew closer, and taller, and loomed until the castle gates yawned before us. A sprawl of buildings pooled before them like vomit\u2014taverns and tanneries, hovels and whorehouses.\n\n\"Renar's shield is a man named Corion.\" The Nuban twitched his nose at the stench as the horses threaded a path to the gates. \"A magician from the Horse Coast, they say. Certainly a good councillor. He has the Count guarded by mercenaries from his homeland. Men with no families to threaten, and an honour code that keeps them true.\"\n\n\"So, what could get us an invitation to see this Corion, I wonder?\"\n\nThe queue at the gates moved in fits and starts, but never above a snail's pace. Ten yards ahead of us a peasant with an ox in tow argued with a guard in the Count's livery.\n\n\"Is he really a magician, do you think?\" I watched the Nuban for his answer.\n\n\"The Horse Coast is the place for them.\"\n\nThe peasant seemed to have won his case, and moved on with his ox, into the outer yard where the market stalls would still be set out.\n\nBy the time we reached the gate a light rain had started to fall. The guard's plume drooped somewhat in the drizzle, but there was nothing tired about the look he gave us.\n\n\"What's your business in the castle?\"\n\n\"Supplies.\" The Nuban patted his saddlebags.\n\n\"Out there.\" The guard nodded to the sprawl before the gates. \"You'll find all you want out there.\"\n\nThe Nuban pursed his lips. The castle market would have the best goods, but that line wasn't going to carry us far. We'd need a better reason before the Count's man was going to let a road-worn Nuban mercenary across his master's threshold.\n\n\"Give me your bow,\" I said to the Nuban.\n\nHe frowned. \"You're going to shoot him?\"\n\nThe guard laughed, but there wasn't an ounce of humour in the Nuban. He was getting to know me.\n\nI held out my hand. The Nuban shrugged and hauled his crossbow up from where it hung behind his saddle. The weight of it nearly took me to the ground. I had to grab the bow in both hands and cling to my mount with my legs but I managed the feat without too great a loss of dignity.\n\nI offered it to the guard.\n\n\"Take this to Corion,\" I said. \"Tell him we're interested in selling.\"\n\nIrritation, scorn, amusement, I could see them all fighting to put the next words on his tongue, but he raised a hand for the weapon even so.\n\nI pulled the bow back as the guard reached up. \"Be careful, half the weight is enchantments.\" That lifted his brow an inch. He took it gingerly, eyeing the iron faces of Nuban gods. Something he saw there seemed to set aside his objections.\n\n\"Watch these two,\" he said, calling another man from the shadows of the gatehouse. And off he went, holding the Nuban's crossbow before him as if it might bite given half a chance.\n\nThe drizzle thickened into a steady downpour. We sat on our horses, letting it all soak in.\n\nI thought about vengeance. About how it wouldn't give me back what had been taken. About how I didn't care. Hold to a thing long enough, a secret, a desire, maybe a lie, and it will shape you. The need lay in me, it could not be set aside. But the Count's blood might wash it out.\n\nThe night came, the guards lit lanterns in the gatehouse, and in niches along the wall of the entry way. I could see the teeth of two portcullises waiting to drop if some foe should storm the entrance whilst the gates stood wide. I wondered how many of Father's soldiers would have died here if he had sent his armies to avenge my mother. Perhaps it was better this way. Better that I come calling. More personal. She was my mother after all. Father's soldiers had their own mothers to be worrying about.\n\nThe rain dripped from my nose, ran cold down my neck, but I felt warm enough, I had a fire inside me.\n\n\"He'll see you.\" The guard had returned. He held a lantern up. His plume lay plastered to the back of his helm now, and he looked as tired himself. \"Jake, get their horses. Nadar, you can walk these boys in with me.\"\n\nAnd so we entered Count Renar's castle on foot, as wet as if we'd swum a moat to get there.\n\nCorion had his chambers in the West Tower, adjacent to the main keep where the Count held court. We followed a winding stair, gritty with dirt. The whole place had an air of neglect.\n\n\"Should we give up our weapons?\" I asked.\n\nI caught the whites of the Nuban's eyes as he shot me a glance. Our guard just laughed. The man behind me tapped the knife at my hip. \"Going to jab Corion with this little pig-sticker are you, boy?\"\n\nI didn't have to answer. Our guard pulled up before a large oak door, studded with iron bolts. Somebody had burned a complex symbol into the wood, a pictogram of sorts. It made my eyes crawl.\n\nThe guard rapped on the door, two quick hits.\n\n\"Wait here.\" He thrust his lantern into my hands. He gave me a brief look, pursed his lips, then pushed past the Nuban to head back down the stairs. \"Nadar, with me.\"\n\nBoth men were out of sight, behind the curve of the stair, before we heard the sound of a latch being raised. Then nothing. The Nuban set his hand to the hilt of his sword. I flicked it away. Shaking my head I knocked again on the door.\n\n\"Come.\"\n\nI thought I'd faced down all my fears, but here was a voice that could melt my resolve with one word. The Nuban felt it too. I could see it in every line of him, poised to flee.\n\n\"Come, Prince of Thorns, come out of your hiding, come out into the storm.\"\n\nThe door fell away, eaten by darkness. I heard screaming, awful screaming, the sort you get from prey with a broken back as it crawls to escape the hunter's claws. Maybe it was me, maybe the Nuban.\n\nAnd then I saw him.\n**37**\n\nThe Castle Red left no ruins to gaze upon. All we had were the ruins of the mountain on which it had stood. We beat the most hasty of retreats and made thanks that the wind blew against us, not chasing us to share the smoke and taint of Gelleth. That night we slept cold and none amongst us had an appetite, not even Burlow.\n\nThe road from the Castle Red to the Tall Castle is a long one, longer in the coming back than in the going. For one thing, on the way out we rode\u2014on the way back we had to walk. And most of those miles back pointed down. Given the choice I'd rather climb a mountain than come down one. The down-slope puts a different kind of hurting in your legs, and the gradient pulls on you every step, as if it's steering you, as if it's calling the shots. Going up you're fighting the mountain.\n\n\"Damn but I miss that horse,\" I said.\n\n\"A fine piece of horseflesh.\" Makin nodded and spat from dusty lips. \"Have the King's stable-master train you another. I'm sure there's not a paddock in Ancrath without it has at least one of Gerrod's bastards.\"\n\n\"He was a lustful one, I'll give you that.\" I hawked and spat. My armour chafed, and the metal held the heat of the late afternoon sun, sweat trickling underneath.\n\n\"It doesn't feel right though,\" Makin said. \"The most convincing victory in memory and all we have to show for it is a lack of horses.\"\n\n\"I've had more loot from a peasant hut!\" Rike called out from back down the line.\n\n\"Christ bleeding! Don't start Little Rikey off,\" I said. \"We're rich in the coin that counts the most, my brothers. We return laden in victory.\" There indeed was a currency I could spend at court. Everything is for sale at the right price. A king's favour, a succession, even a father's respect.\n\nAnd that's another thing that made those returning miles longer than the going ones. Not only did I have to carry myself, my armour, my rations, but I had a new burden. It's hard to carry a weight of news with none to tell and days ahead before you can release it. Good news weighs just as heavy as bad. I could imagine myself back at court, boasting of my victory, rubbing noses in it, a certain stepmother's nose in particular. What would not paint itself on the canvas of my imagination was my father's reaction. I tried to see him shake his head in disbelief. I tried to see him smile and stand and put his hand on my shoulder. I tried to hear him thank me, praise me, call me son. But my eyes went blind and the words I heard were too faint and deep for distinction.\n\nThe brothers had little to say on the return journey, feeling the holes left in our ranks, haunted by the space where the Nuban should be. Gog on the other hand bubbled over with energy, running ahead, chasing rabbits, asking question after question.\n\n\"Why is the roof blue, Brother Jorg?\" he asked. He seemed to think the outside world was just a bigger cave. Some philosophers agree with him.\n\nThere were other changes too. The red marks on Gog's hide had shaded to a fiercer red, and the nightly campfires fascinated him. He would stare into the flames, entranced, edging closer moment by moment. Gorgoth discouraged the interest, flicking the child into the shadows, as if the attraction worried him.\n\nThe roads became more familiar, the inclines gentle, the fields rich. I walked the paths of my childhood, a golden time, easy days without care, scored by my mother's music and her song, with no sour note until my sixth year. My father had taught me the first of the hard lessons then, lessons in pain and loss and sacrifice. Gelleth had been the sum of that teaching. Victory without compromise, without mercy or hesitation. I would thank King Olidan for his instruction and tell him how his enemies had fared at my hands. And he would approve.\n\nI thought of Katherine too, as we drew nearer. My idle moments filled with her image, with the moments I had spent close enough to touch her. I saw again how the light caught her, how it found the bones of her face, the softness of her lips.\n\nWe came footsore and road-weary to the heartlands of Ancrath, too deep in our own thoughts even to steal the horses that would ease the last of our journey. I had but to close my eyes and I would see the new sun rise over Gelleth, rise through Gelleth, and hear the screams of her ghosts.\n\nWe saw the Tall Castle's battlements from the Osten Ridge, with seven miles still before us to the gates. The sun descended in the west, crimson, racing us to the city.\n\n\"We'll be heroeth, Jorth?\" Elban asked. He sounded uncertain as if all his years had yet to teach him that the end justifies the means.\n\n\"Heroes?\" I shrugged. \"We will be victors. And that's what counts.\"\n\nWe walked the last mile in dusk. The guards at the gates of the Low City had no questions for me. Perhaps they recognized their prince, or perhaps they read my look and some instinct for self preservation kicked in. We walked through unopposed.\n\n\"Brother Kent, why don't you lead the way to the Low Town and find the lads somewhere to drink? The Falling Angel, maybe.\" Sir Makin and I would go to court. The remainder of my brothers would find no welcome in the Tall Castle.\n\nWith Makin at my side I set off for the High City and at last we came to the castle itself. I put fatigue aside when we entered by the Triple Gate. We crossed the Lectern Courtyard in the deepest shadows, thrown by a failing sun.\n\nBy the time we passed the table knights at Father's doors I had a spring in my step. I looked first for Sageous, seeking him at the King's side, then amongst the glitter of the crowd. I let the herald finish our introduction, and still I sought the heathen. I found Katherine beside the Queen, one hand on her sister's shoulder, hard eyes for poor Jorg. I let the silence stretch a moment longer.\n\n\"Where have you hidden your painted savage, Father-dear? I did so want to meet the old poisoner of dreams again.\"\n\nI slid my gaze across the sea of faces one more time.\n\n\"Sageous's services to the Crown have taken him from our borders.\" Father held his face impassive, but I saw the quick glance exchanged between his queen and her sister.\n\n\"I'll be sure to look for his return.\" So, the heathen had run before me . . .\n\n\"I'm told that you limped back without the Forest Watch.\" Queen Sareth spoke from Father's side, her hands upon the greatness of her belly. \"Are we to assume your losses were total?\" A smile escaped the tight line of her mouth. An exceptionally pretty mouth, it has to be noted.\n\nI spared her a small bow. A bow for my half-brother, struggling to claw his way from her womb. \"Lady, there were losses among the Forest Watch, I cannot deny it.\"\n\nFather inclined his head, as if the crown weighed heavy upon him. Pale eyes watched me from the shadow of his brow. \"We will have an account of this rout.\"\n\n\"Lord Vincent de Gren . . .\" I counted him off on my index finger.\n\nAn intake of breath hissed through the aristocracy.\n\n\"Even the Watch Master!\" Queen Sareth struggled to her feet. \"He has even lost the Watch Master! And this boy seeks our throne?\"\n\n\"Lord Vincent de Gren,\" I resumed my count. \"I had to push him over the Temus Falls. He vexed me. Coddin is the Watch Master now, low born but a sound fellow.\"\n\n\"Jed Willox.\" I counted a second finger. \"Killed in a knife fight over a game of cards, two days' march past the Gelleth border.\"\n\n\"Mattus of Lee.\" I counted a third finger. \"Apparently he urinated on a bear by mistake. It seems that the legendary woodcraft of the Forest Watch may be somewhat overstated. And . . . that's it.\"\n\nI held the three fingers at arm's length above my head and turned left, then right, to survey my audience.\n\n\"The losses among my own picked men were similarly grievous, but in our defence you must consider that the razing of a castle defended by nine hundred Gellethian veterans is a dangerous undertaking. With two hundred and fifty lightly-armed forest rangers, there is a limit to what can be achieved without casualties.\"\n\n\"The coward never reached Castle Red!\" The Queen pointed at me\u2014as if anyone would mistake her target\u2014and her voice became a shriek.\n\nI smiled and held my peace. Women are apt to lose perspective when fat with child. I saw Katherine try to press Sareth back into her throne.\n\n\"I ordered you to assault the Castle Red.\" Father's words held no hint of anger, and carried all the more threat for it.\n\n\"Indeed.\" I advanced on the throne, leaving Sir Makin in my wake. \"Bring me Gelleth, you said.\"\n\nA yard separated us, no more, before the first palace guard thought to raise his crossbow. Father lifted a finger, and we paused, me and the guard sweating in his hauberk.\n\n\"Bring me Gelleth, you said. And you were good enough to grant me the Forest Watch to do it with.\"\n\nI reached into the road-sack at my hip, ignoring the crossbows held on me, and the fingers ever tighter on their triggers.\n\n\"Here is Merl Gellethar, Lord of Gelleth, master of the Castle Red.\" I opened my hand and dust trickled through my fingers. \"And here,\" I drew out a chunk of rock no bigger than a walnut. \"Here is the largest stone that remains of the Castle Red.\"\n\nI let the stone fall, dropped into silence. Neither dust nor stone were what I purported, of course, but the truth lay there on the throne-room floor. Merl Gellethar was dust on the wind, and his castle rubble.\n\n\"We killed them all. Every man in that fortress is dead.\" I looked to the Queen. \"Every woman. Lady, scullion, drudge, and whore.\" My eyes fell to her belly. \"Every child, every babe in cradle.\" I raised my voice. \"Every horse and dog, every hawk and every dove. Each rat, and down to the last flea. Nothing lives there. Victory does not come in half measures.\"\n\nFather lurched to his feet.\n\nIn one pace I stood almost nose to nose with him. I couldn't read what his eyes held, but the old fear had left me, as if it too had trickled from my hands.\n\n\"Give me my birthright.\" I kept all colour from the words, though my jaw ached from the strain of it. \"Let me lead our armies, and I will take the Empire, and make it whole once more. Set aside the heathen. And his plans.\" I glanced toward the new queen at that.\n\nI should have kept my eyes on him, should have remembered where I got my mean streak.\n\nI felt a sharp pain under my heart. It made me bite off my sentence, nearly my tongue too. I tasted blood, hot and copper. One step back, two, staggering now. I saw the blade, exposed in Father's hand when I slipped from it.\n\n_Is this a dagger I see before me?_ The quotation bubbled up, and laughter too, breaking out of me, crimson with spittle. I wanted to speak, but for once words escaped me, leaking away with my life's blood.\n\nThe throne-room swam before me, its architecture no longer certain in the face of such betrayal. Every eye watched my retreat toward the great doors. Their stares lanced me, lords and ladies, Princess, Queen, and King. The legs that had borne me league upon league from Gelleth now turned traitor, as if each mile from the ruin of the Castle Red settled upon my shoulders and left me drunk with weariness.\n\n_He stabbed me!_\n\nThere was a time when I loved my father. A time remembered, in dreams, or in rare waking moments, like the shadow of a high cloud crossing my mind. There's a laughing face from a year I no longer own, from a season when I was too young to see the distance between us. The face is bearded, fierce, but without threat.\n\n_Is this a dagger I see before me?_ My mouth wouldn't frame the joke. The laugh burst from me, and I fell, as if the knife had cut my strings.\n\nFor an eternity I lay before them, my cheek to the cold marble. I heard Makin roar. I heard the clatter as he went down beneath too many guards. The slow thud of a heartbeat filled me.\n\nWhen I fell I saw the blackness of my father's hair, darker than night, with the faintest sheen of emerald like a magpie's wing.\n\n\"Take this away.\" He sounded weary. The slightest hint of human weakness at the last.\n\n\"Will he lie by his mother's tomb?\" A new voice. The words drew out to fill an age, but somewhere in me they echoed and I saw their owner, Old Lord Nossar who bore us on his shoulders, Will and I, a lifetime ago. Old Nossar, come to carry me one last time. I heard the answer, too faint and deep for distinction. My eyes went blind. I felt the floor scrape against my cheek, and then no more.\n**38**\n\nI swallowed darkness, and darkness swallowed me.\n\nWithout light, without the beat of a heart to count the time, you learn that eternity is nothing to fear. In fact, if they'd just leave you to it, an eternity alone in the dark can be a welcome alternative to the business of living.\n\nThen the angel came.\n\nThe first glimmers felt like paper-cuts on my eyes. The illumination built from a distant pinpoint, splinters of light lodging in the back of my mind. A dawn came, and in an instant, or an age, darkness fled, leaving no hint of shadow to record its passage.\n\n\"Jorg.\"\n\nHer voice flowed through the octaves, an echo of every kind word and every promise fulfilled.\n\n\"Hello.\" My voice sounded like a cracked reed. _Hello?_ But what do you say to heaven when you meet her? Two syllables, weakness and doubt underwriting both.\n\nShe opened her arms. \"Come to me.\"\n\nI crouched, naked on a floor too white for any shadow to dare. I could see the dirt on my limbs, like veins, and blood, blood from the wound that killed me, dried and black as sin.\n\n\"Come.\"\n\nI tried to look at her. No point in her held constant. As if definition were a thing for mortals, a reduction that her essence would not allow. She wore pale, in shades. She had the eyes of everyone who ever cared. And wings\u2014she had those too, but not in white and feathers, rather in the surety of flight. The potential of sky wrapped her. Sometimes her skin seemed to be clouds, moving one across the other. I looked away.\n\nI crouched there, a knot of flesh and bone, with only dirt and old blood to define me beneath the scrutiny of her brilliance.\n\n\"Come to me.\" Arms open. A mother's arms, a lover's, father's, friend's.\n\nI looked away, but she drew me still. I felt her breathing. I felt the promise of redemption. I had but to lift my eyes and she would forgive me.\n\n\"No.\"\n\nHer surprise fluttered between us, a palpitation of the light. I felt tension in the muscles of my jaw, and the bitter taste of anger, hot at the back of my throat. Here at last were things familiar to me.\n\n\"Put aside your pain, Jorg. Let the blood of the Lamb wash your sins away.\" Nothing false in her. She stood transparent in her concern. The angel held her gifts in open hands, compassion, love . . . pity.\n\nOne gift too many. The old smile twisted on my lips. I stood, nice and slow, head bowed still. \"The Lamb doesn't have enough blood for my sins. May as well hang a sheep for me as a lamb.\"\n\n\"No sin is too great to repent,\" she said. \"There's no evil that cannot be put aside.\"\n\nShe meant it too. No lie could pass those lips. That truth, at least, was self-evident.\n\nI met her eyes then, and the wash of her love, so deep and so without condition, nearly carried me away. I dug deep and fought her. I manufactured my smile once again, cursing myself for a slackjawed fool.\n\n\"I left few sins untasted.\" I took a step toward her. \"I cursed . . . in church. I coveted my neighbour's ox. I stole it too, roasted it whole, and finished it off with gluttony, a deadly sin, the first of the Seven, learned at my mother's breast.\"\n\nThe hurt in her eyes hurt me, but I'd lived a life striking blows that cut two ways.\n\nI moved around the angel, and my feet stained the floor, leaving bruises that faded in my wake.\n\n\"I coveted my neighbour's wife. And I had her. Murder too. Oh yes, murder and more murder. So few sins untasted . . . If I'd not died so young, I'm sure I'd have met you with a full list.\" Anger closed my jaw. Any tighter and my teeth would have exploded. \"If I'd lived but five minutes longer, you could have put patricide at the head of the tally.\"\n\n\"It can be forgiven.\"\n\n\"I don't require your forgiveness.\" Veins of darkness reached across the floor, growing outward from where I stood.\n\n\"Let it go, Child.\" A warmth and a humour ran through her words, so strong it nearly carried me with it. Her eyes stood as windows to a world of things made whole. A place built of tomorrows. It could all be made right. I could taste it, smell it. If she weren't so sure of her success, she'd have had me, there and then.\n\nI held to my anger, drank from my well of poison. These things are not good things, but at least they're mine.\n\n\"I could go with you, Lady. I could take what you offer. But who would I be then? Who would I be if I let go the wrongs that have shaped me?\"\n\n\"You would be happy,\" she said.\n\n\"Someone else would be happy. A new Jorg, a Jorg without pride. I won't be anyone's puppy. Not yours, not even His.\"\n\nThe night crept back like mist rising from the mire.\n\n\"Pride is a sin too, Jorg. Deadliest of the Seven. You have to let it go.\" At last, a hint of challenge in her words. All I needed to give me strength.\n\n\"Have to?\" Darkness swirled around us.\n\nShe held out her hands. The dark grew and her light quailed.\n\n\"Pride?\" I said, my smile dancing now. \"I _am_ pride! Let the meek have their inheritance\u2014I'd rather have eternity in shadows than divine bliss at the price you ask.\" It wasn't true, but to speak otherwise, to take her hand rather than to bite it, would leave nothing of me, nothing but pieces.\n\nGlimmers held her now, glimmers against the velvet blackness. \"Lucifer spoke thus. Pride took him from heaven, though he sat at God's right hand.\" Her voice grew faint, the hint of a whisper. \"In the end pride is the only evil, the root of all sins.\"\n\n\"Pride is all I have.\"\n\nI swallowed the night, and the night swallowed me.\n**39**\n\n\"He's not dead yet?\" A woman's voice, Teuton accent with a creak of age in it.\n\n\"No.\" A younger woman, familiar, also Teuton.\n\n\"It's not natural to linger so long,\" the older woman said. \"And so white. He looks dead to me.\"\n\n\"There was a lot of blood. I didn't know men had so much blood in them.\"\n\nKatherine! Her face came to me in my darkness. Green eyes, and the sculpted angles of her cheekbones.\n\n\"White and cold,\" she said, her fingers on my wrist. \"But there's mist on the mirror when I hold it to his lips.\"\n\n\"Put a pillow over his face and be done with it, I say.\" I imagined my hands around the crone's neck. That brought a hint of warmth.\n\n\"I did want to see him die,\" Katherine said. \"After what he did to Galen. I would have watched him die on the steps of the throne, with all that blood running down, one step after the next, and been glad.\"\n\n\"The King should have slit his throat. Finished the job there and then.\" The old woman again. She had a servant's tone about her. Voicing her opinion in the security of a private place, opinions held back too long and grown bitter in the silence.\n\n\"It's a cruel man who will take a knife to his only son, Hanna.\"\n\n\"Not his only son. Sareth carries your nephew. The child will be born to his due inheritance now.\"\n\n\"Will they keep him here, do you think?\" Katherine said. \"Will they lay him in his mother's casket, beside his brother?\"\n\n\"Lay the whelps with the bitch and seal the room, I say.\"\n\n\"Hanna!\" I heard Katherine move away from me.\n\nThey'd taken me to my mother's tomb, a small chamber in the vaults. The last time I'd visited the dust had lain thick, unmarked by footprints.\n\n\"She was a queen, Hanna,\" Katherine said. I heard her brush at something. \"You can see the strength in her.\"\n\nMother's likeness had been carved into her coffer's marble lid, as if she lay there at rest, her hands together in devotion.\n\n\"Sareth is prettier,\" Hanna said.\n\nKatherine returned to my side. \"Strength makes a queen.\" I felt her fingers on my forehead.\n\nFour years ago. Four years ago I'd touched that marble cheek, and vowed never to return. That was my last tear. I wondered if Katherine had touched her face, wondered if she'd stroked the same stone.\n\n\"Let me end this, my princess. It would be a kindness to the boy. They'll lay him with his mother and the little prince.\" Hanna honeyed her voice. She set her hand to my throat, fingers coarse like sharkskin.\n\n\"No.\"\n\n\"You said yourself that you wanted to see him die,\" Hanna said. She had strength in that old hand. She'd throttled a chicken or three in her time, had Hanna. Maybe a baby once or twice. The pressure built, slow but sure.\n\n\"On the steps I did, while his blood was hot,\" Katherine said. \"But I've watched him cling to life for so long, with such a slight hold, it's become a habit. Let him fall when he's ready. It's not a wound that can be survived. Let him choose his own time.\"\n\nThe pressure built a little more.\n\n\"Hanna!\"\n\nThe hand withdrew.\n**40**\n\nWe wrap up our violent and mysterious world in a pretence of understanding. We paper over the voids in our comprehension with science or religion, and make believe that order has been imposed. And, for the most of it, the fiction works. We skim across surfaces, heedless of the depths below. Dragonflies flitting over a lake, miles deep, pursuing erratic paths to pointless ends. Until that moment when something from the cold unknown reaches up to take us.\n\nThe biggest lies we save for ourselves. We play a game in which we are gods, in which we make choices, and the current follows in our wake. We pretend a separation from the wild. Pretend that a man's control runs deep, that civilization is more than a veneer, that reason will be our companion in dark places.\n\nI learned these lessons in my tenth year, although little of them stayed with me. It took Corion only moments to teach me, the heart beats in which my will guttered like a candle flame in the wind, and then blew out utterly\n\nI lay with the Nuban, boneless on the stairs. Only my eyes would move, and they followed the old man. He could have looked kindly in a different light. He had something of Tutor Lundist about him, though more gaunt, more hungry. The horror wasn't in his face, or even his eyes, just in the knowing that these were mere skins, stretched taut across all the emptiness in the world.\n\nThe sight of him, an old man in a dirty robe, put the kind of fear into me that shame erases from our memories. The fear the rabbit has when the eagle strikes. The kind of fright that makes a nothing of you. The kind of fear that'd make you sacrifice mother, brother, everything and anything you've ever loved, just for the chance to run.\n\nCorion shuffled closer, and stooped to take my wrist. In one instant the touch silenced the raw terror that had so unmanned me. As completely as if he'd turned the spigot on a wine-barrel, the flow stopped. Without a word he hauled me into his room. I felt the flagstones scrape my cheek.\n\nThe chamber held nothing, save for the Nuban's crossbow, propped against the far wall. I imagined Corion closeted here in his empty chamber, a place to leave his old flesh whilst he stared into eternity.\n\n\"So, Sageous's hunter finally tracked down something with more bite than him, eh?\"\n\nI tried to speak, but my lips didn't as much as twitch. He knew about the dream-witch and his hunter. He'd called me the Thorn Prince. What else did he know?\n\n\"I know it all, child. The things you know, the secrets you hold. Even the secrets you've forgotten.\"\n\nHe could read my mind!\n\n\"Like an open scroll.\" Corion nodded. He turned my head with his boot, so that I could see the Nuban's bow once more.\n\n\"You intrigue me, Honorous Jorg Ancrath,\" he said. He moved to stand beside the bow. \"You're wondering why a man with such power isn't emperor over all the lands.\"\n\nI was too.\n\n\"It has to be one of the Hundred. Nations won't follow monsters like me. They'll follow a lineage, divine right, the spawn of kings. So we who have taken our power from the places where others fear to reach . . . we play the game of thrones with pieces like Count Renar, pieces like your father. Pieces like you, perhaps.\"\n\nHe reached out to touch the bow. The air around it shimmered as if the mouth of a furnace had opened.\n\n\"Yes. I rather like that idea. Let Sageous have King Olidan, let him work to bend your father to his will, and I will have the firstborn son.\"\n\nThe fear had sunk low enough to let my anger rise. I pictured the old man dying on a blade, my hand on the hilt.\n\n\"Let the wilds temper you, and if you weather it, in time the prodigal will return, a viper to his father's bosom. Pawn takes king.\" He mimed the chess-board gesture. \"You might become something, Briar Prince. A piece to win the game.\"\n\nCorion took the bow as if it weighed nothing. Raising it to his lips, he whispered a word, too soft for hearing. Five paces took him to the door and he set the bow on the steps by the Nuban's head. \"A black knight to guard my pawn.\"\n\n\"And you, boy. You will forget the Count of Renar.\"\n\n_Like hell I will_.\n\n\"Turn your vengeance anywhere you choose, share it with the world, spill some blood; but never return to these lands. Set no foot upon these paths. Your mind will not wander here.\"\n\nI could only watch him. He came closer. He knelt beside me, took my collar, and drew my face to his. I met his blank eyes. I could feel the horror rising, a flood that would carry me away. And worse, I felt his fingers cold inside my skull, erasing memories, turning aside purpose.\n\n\"Forget Renar. Take your vengeance to the world.\"\n\n_Renar will die_. \"By . . . my . . . hand . . .\" Somehow my lips spoke the words.\n\nBut already he'd taken the conviction from me. I could no longer say how I'd reached the tower, or even name him.\n\nThe old man smiled. He bent to whisper in my ear. I remember his breath on my neck, and the smell of rot.\n\nThen I heard his words and all reason left me.\n\nWorms writhed behind my eyes. Nothing remained of him in my thoughts, just a hole where I couldn't look. Renar became a name without weight, and my hatred a gift for anyone and everyone.\n\nI fell, through darkness, deafened by my own howling. Unknown hands locked around my throat, and in the darkness my own hands found a neck to throttle. The grip tightened, and tightened again. The screams died to a hiss, a rattle, and then silence. I squeezed. My hands became iron hooks. If I could have squeezed harder, my finger-bones would have snapped like dry twigs.\n\nI fell through darkness, through silence, only the hands on my throat, and the throat in my hands, and the hunger for air, my heart beating sledgehammer blows.\n\nI fell through years. I've been falling through my life . . .\n\nI hit the ground. Hard. My eyes opened. I lay on a stone floor. A purple face stared at me, eyes distended, tongue protruding. Daylight streamed in from a high window. My heart hammered at my breastbone, wanting out. Everything hurt. I saw hands on the neck below that face. My hands. With great effort I unlocked them. The white fingers had little inclination to obey.\n\nStill the pain swelled in me. I needed something, but couldn't name it. My vision pulsed red, dimming from one moment to the next. I touched a stiff-fingered hand to my neck and found hands there.\n\nI didn't recognize the face. A woman?\n\nThe world grew distant, the pain less.\n\n_Renar_ . . . The name rose through me, and with it a whisper of strength. The hands that prised the strangler's fingers from my neck didn't feel like mine. _Renar!_ My first breath whistled into me, as if sucked through a reed.\n\nAir! I needed air.\n\nI choked, heaved but nothing came, hauled in breaths through a throat grown too narrow for the task.\n\n_Renar._\n\nThe purple face belonged to a woman with grey hair. I didn't understand.\n\n_Renar. And Corion_.\n\n_Oh Jesu!_ I remembered. I remembered the horror, but it burned pale against the cold fury that ate me now.\n\n\"Corion.\" For the first time in the four years since that night in the tower, I spoke his name. I remembered. I recalled what had been taken, and for the first time in forever, I felt whole.\n\nI found the strength to lift myself up on my arms.\n\nI was in a chamber in a castle. Beside a bed . . . I'd fallen out of bed. Whilst an old woman tried to throttle me.\n\nThe door shook. Somebody rattled at the latch. \"Hanna! Hanna!\" A woman's voice.\n\nSomehow I stood before the door opened.\n\n\"Katherine.\" My voice escaped a bruised throat as a squeak.\n\nThere she was. Beautiful in disarray. Mouth half open, green eyes wide.\n\n\"Katherine.\" I could only get her name out as a whisper, but I wanted to shout, I wanted to scream so many things at once.\n\nI understood. I understood the game. I understood the players. I knew what had to be done.\n\n\"Murderer!\" she said. She took a knife from her sash, a sharp bodkin long enough to run a man through. \"Your father knew best.\"\n\nI tried to tell her, but no words would come now. I tried to raise my arms, but I had no strength.\n\n\"I'll finish what he started,\" she said.\n\nAnd all I could do was marvel at the beauty of her.\n**41**\n\nIn a duel, man to man, sword against sword, it can be a lack of skill that gets you killed. Often as not, though, it'll be a matter of luck, or if it goes on too long, then it'll be the man who tires first that tends to die.\n\nIn the end it's about staying power. They should put that on headstones, \"Got tired.\" Maybe not tired of life, but at least too tired to hold on to it.\n\nIn a real fight, and most fights are real, not the artifice of a formal duel, it's fatigue that's the big killer. A sword is a heavy chunk of iron. You swing that around for a few minutes and your arms start to get ideas of their own about what they can and can't do. Even when your life depends on it.\n\nI've known times when to lift my sword was the equal of any labour of Hercules, but never before I faced Katherine's knife had I felt so drained.\n\n\"Bastard!\"\n\nThe fire in her eyes looked fierce enough to burn until the deed was done.\n\nI looked for the will to stop her, and came up empty.\n\nA knife is a scary thing right enough, held to your throat, sharp and cool. The thought echoed back to me from that night when the dead came up out of their bog-pools around the Lichway.\n\nThe glitter along that knife edge as she came at me, the thought of it slicing my flesh, piercing an eye maybe, these are all the sort of thing that might give a man pause. Until you realize what they are. They're just ways to lose the game. You lose the game, and what have you lost? You've lost the game. Corion had told me about the game. How many of my thoughts were his? How much of my philosophy was filth from that old man's fingers?\n\nI'd swum in the darkness too long. The game didn't seem so important any more.\n\nWith the embers of my strength I raised both arms. I stretched them wide, to receive the blow. And I smiled.\n\nSomething reached out and held her arm. I saw it in her face, twisting there on that perfect brow, wrestling with the rage.\n\n\"Father didn't quite reach the heart, it seems.\" I managed a hoarse whisper. \"Perhaps, Aunt, you have a better hand?\"\n\nThe knife shook. I wondered if she'd cut live meat before.\n\n\"You . . . you killed her.\"\n\nThe fingers of my right hand closed around something, a heavy smooth something, on the shelf beside my bed.\n\nHer eyes dropped to the old woman's face.\n\nI hit her. Not hard, I didn't have the strength, but hard enough to break the vase I'd found. She collapsed without a murmur.\n\nShe lay in the sapphire pool of her dress, sprawled across the flagstones. Life flowed in my arms once more. It seemed as if my strength began to return the moment she fell. As if a spell were broken.\n\n_Kill her and you'll be free forever_. A familiar voice, dry like paper. Mine, or his?\n\nHer hair hid her face, auburn on sapphire.\n\n_She's your weakness. Cut the heart from her_.\n\nI knew it to be true.\n\n_Choke her_.\n\nI saw my hands, pale on a neck shading into crimson.\n\n_Have her_. The voice of the briar. The hooks slipped beneath my skin, and drew me down to kneel beside her. _Have her. Take what might never be given_. I knew the creed.\n\n_Kill her, and you'll be free_.\n\nI heard the echo of a distant storm.\n\nKatherine's hair ran like silk between my fingers. \"She's my weakness.\" My voice now, my lips. One little step, one more death, and nothing would ever touch me again. One little step and the door on that wild night would close forever. The game would truly be a game. And I would be the player to win it.\n\n_Choke her. Have her_. The voice of the briar. A crackle in the mind. A hollow sound. An emptiness.\n\nEmpty.\n\nHer neck felt warm. Her pulse beat under my fingertips.\n\n\"Kill her, Briar Prince.\"\n\nI saw the words on thin lips, spoken in an empty chamber.\n\n\"Kill her.\"\n\nI saw the lips move again. I saw the blank eyes, fixed on eternity. \"Kill her.\"\n\n\"Corion!\"\n\nFor a moment my hands tightened around Katherine's neck.\n\n\"I'm coming for you, you old bastard.\" I released my grip.\n\nA smile twisted those thin lips, a fierce twist. I saw it as the vision faded, those blank eyes, and that twist of a smile. My smile.\n\nHe had played me. I'd wandered for years with no recollection of him, thinking it my own idea to turn from Renar, thinking the choice a symbol of my strength and purpose, to put aside empty vengeance in favour of the true path to power. And now, on the edge of death, I had recovered what was taken. Recovered or been given. I glanced at Katherine. I recalled an angel in a dark place. The memory left me with a shiver.\n\nI took Katherine's dagger from the floor, and stood. I left her where she lay, beside the crone I'd throttled. The door opened onto a corridor, one I recognized. The West Corner, I knew where I was. I raised the knife to my lips and kissed the blade. Count Renar, and the puppet master who pulled so many strings, one sharp edge would be enough for them all.\n\n_Brother Roddat stabbed three men in the back for each one he faced. Roddat taught me all I know about running and about hiding. Cowards should be treated with respect. Cowards best know how to hurt. Corner one at your peril._\n**42**\n\n\"Get out of my way.\"\n\n\"Who the hell\u2014\"\n\n\"Please Jesu! You're the same old wart-bag that tried to stop me last time!\" And he was. The stink that jumped me when he opened the door brought it all back. \"I'm surprised my father let you live.\"\n\n\"Who\u2014\"\n\n\"Who the hell am I? You don't recognize me? You didn't last time either. I was shorter then, yay high.\" I held out a hand to show him. \"It seems like a while ago to me, but you're an old man, and what're three or four years to the old?\" I sketched a bow. \"Prince Jorg at your service, or rather you at mine. Last time I walked out of here with a band of outlaws. This time I just need one knight, if you please. Sir Makin of Trent.\"\n\n\"I should call the guards on you,\" he said, without conviction.\n\n\"Why? The King has issued no orders about me.\" That was a guess, but Father thought he'd struck a mortal blow, so I was probably correct. \"Besides, it'd only get you killed. And if you're thinking of that big fellow with the pike, I rammed his head into the wall not three minutes ago.\"\n\nThe jailer stepped back and let me pass, just as he had the time Lundist escorted me when I was a boy. On this occasion, I hit him as I went by. Once in the stomach, and a second blow to the back of the neck as he doubled up. For a moment I considered finishing the job with Katherine's knife, but it's good insurance to let ineffective jailers live.\n\nI took his keys and moved on down the corridor, knife at the ready. I'd rather have had my sword. I felt half-dressed without it. My mind kept returning to the fact of its absence, to the weightless sensation around my hip, like a tongue returning to an empty socket in constant overestimation of the loss.\n\nMakin put that sword in my hand on the day he found me. As captain of the guard in search of the heir, he had the right to bear it. I'd kept it close ever since, the family blade, Builder-steel.\n\nI found my way to the torture chamber where I'd first met the Nuban. The table at the centre lay empty. There were no faces at the cell door windows. I made a slow circuit, directing the beam of my lantern into each cell in turn. The first held a corpse, or someone so near death as to be mere bones in a bag of skin. The next three were bare. The fifth held Sir Makin. He sat back against the far wall, bearded and smeared with filth, a hand lifting to shield his eyes from the light. He made no move to rise. I felt a hurt in the back of my throat. I don't know why, but I did. Anger in my stomach, and an acid pain in my throat.\n\n\"Makin, oh my brother.\" Soft.\n\n\"Wha\u2014?\" A croak, the sound of something broken.\n\n\"I'm to the road again, Brother Makin. I have business to the south.\"\n\nI set the key in the lock. A slight tremble, a little rattle.\n\n\"Jorg?\" A wet sob, half gurgle. \"He killed you, Prince. Your own father.\"\n\n\"I'll die when I'm ready.\"\n\nThe key turned, the door opened without resistance. The stink grew worse.\n\n\"Jorg?\" Makin let his hand fall. They'd made a mess of his face. \"No! You're dead. I saw you fall.\"\n\n\"All right, I'm dead and you're dreaming. Now get on your feckin' feet before I kick out whatever shit they left you. And that ain't too much by the smell of it.\"\n\nThat got to him. He tried to rise, one hand scraping across the wall.\n\nI hadn't thought what kind of state he might be in. To me it seemed I'd taken Father's knife only yesterday. Makin's beard said weeks at the least.\n\nHe got halfway to his feet, and his leg failed.\n\nI took two steps toward him.\n\nThe Count's castle stood well over a hundred hard miles ahead of me, through the garden lands of Ancrath and into the Renar highlands. He'd never make it.\n\nMakin slid to the floor with a groan. \"You're dead anyway.\" The one good eye shone bright with tears.\n\n_Play the game. Sacrifice knight, take castle_. That old dry voice again. I'd listened to it so long I couldn't tell if it were mine or Corion's. Either way, I should leave him.\n\n\"You've got one chance here, Makin. That's two more than most bastards get in life.\" The lantern beam swung from wall to wall. \"Dead or not, I'll leave you if you can't stand and follow me. I left a man here to die before. A man I should have loved. I'll leave you in a heartbeat.\"\n\nHe kicked out, fierce with fear or something else, but his arm buckled and his foot just skittered across the muck.\n\nI turned and walked away. Two yards past the door I stopped.\n\n\"Lundist died here.\" I was speaking too loud for safety, wasting breath on foolishness. \"On this spot.\" I stamped on it. \"I left him to bleed.\"\n\nNothing from the darkness of the cell.\n\nI'd been soft with Katherine, but at no real cost. This was different. They'd broken Makin, he could do nothing but slow me at a time when I most needed speed.\n\nI started for the exit.\n\n\"No . . .\"\n\n_Don't let him beg_.\n\n\"No . . . he didn't die there.\" Makin's voice came a little stronger now.\n\n\"What?\"\n\n\"He got a bad knock.\"\n\nSounds of movement in the dark.\n\n\"A knock's all. Nothing but a bruise to show for it the next day.\"\n\n\"Lundist is alive?\"\n\n\"Your father had him executed, Jorg.\" Makin came into the light, clutching the doorframe. \"For failing to protect you, he said.\" He spat a black mess onto the floor. \"More likely he just didn't have any use for a tutor once his son had run off. That's been the King's way all these years. When a thing's no use any more\u2014throw it away.\"\n\nMakin managed a grin. \"Damn but it's good to see you, lad.\"\n\nI watched him for a moment. I saw his smile die, and an uncertainty replace it, mirroring my own.\n\nI should leave him. In truth, I should kill him. No loose ends.\n\nI didn't look at my knife. You never take your eyes off your mark, not when it's a man like Makin, not even in his current state. But I knew the knife was there. In my mind's eye I could see the gleam where it cut the lantern's light from the air. Makin didn't look at it either. He knew better than to offer weakness to the viper. Nothing decides a man's mind better than opportunity.\n\nFather would leave him. Dead.\n\nThe creature into which Corion had chosen to forge me, that tool, that piece in a game of thrones, he'd never even have come close enough to savour the dungeon stink.\n\nBut what about Jorg?\n\n\"I'm my father's son, Makin.\"\n\n\"I know.\" He didn't plead. I admired that in him. I chose my pieces well.\n\nThe knife felt like hot iron in my fist. I hated myself for what I was going to do, and just as much for hesitating. I hated myself for the weakness in me.\n\nFor a moment I saw the Nuban, just the white line of his teeth, and the darkness of his eyes, watching me as he'd watched since the day we met.\n\nMakin took that moment. A swift kick snatched my legs from under me. He followed down with what weight remained to him, and sandwiched my head between the flagstones and his fist. We neither of us were in great shape. One punch was all it took to send me back to wherever it was I'd escaped from in Katherine's room.\n\n_Shakespeare had it that clothes maketh the man. The right clothes could take Brother Sim from a boy too young to shave to a man too old to be allowed to. He makes a fine girl also, though that was a dangerous business in road company and reserved for targets that just couldn't be killed any other way. Young Sim is forgettable. When he's gone, I forget how he looks. Sometimes I think of all my brothers it's Sim that's the most dangerous._\n**43**\n\n\"Explain it to me again.\" Makin leaned forward in the saddle to be heard above the rain. \"Your father stabs you, but it's to Count Renar's castle we're going so you can cut yourself some revenge?\"\n\n\"Yes.\"\n\n\"And it's not even the Count we're after. Not him that sent your sainted mother on her way, but some old charm seller?\"\n\n\"Right.\"\n\n\"Who had you and the Nuban at his mercy when you first ran from home. And let you go without so much as a beating?\"\n\n\"I think he put a spell on the Nuban's crossbow,\" I said.\n\n\"Well, if he did, it must have been to prevent it missing. The Nuban could stop an army with that thing. Given the right spot.\"\n\n\"There wasn't much that the Nuban missed, true enough,\" I said.\n\n\"So?\"\n\n\"So?\"\n\n\"So, I don't understand why we're out here in the pissing rain on stolen nags, riding into the worst kind of danger.\"\n\nI rubbed my jaw where he'd hit me. It felt sore. The coldness of the rain did little to ease it.\n\n\"What's the world about, Makin?\"\n\nHe looked at me, eyes narrowed against the wetness of the wind.\n\n\"I never had time for those philosophers of yours, Jorg. I'm a soldier, and that's the end of it.\"\n\n\"So you're a soldier. What's the world about?\"\n\n\"War.\" He set a hand to the hilt of his sword, unconscious of the action. \"The Hundred War.\"\n\n\"And what's that about, soldier?\" I asked.\n\n\"A hundred noble-born fighting across as many lands for the Empire throne.\"\n\n\"That's what I always thought,\" I said.\n\nThe rain came down harder, bouncing off the backs of my hands with a sting as if it carried ice. Ahead, at a place where the road forked, I could see a glow, three of them in fact, three patches of warm light.\n\n\"Tavern up ahead.\" I spat water.\n\n\"So aren't we fighting for the Empire then?\" Makin kept pace, though his horse slipped in the mud torrent at the roadside.\n\n\"I killed Price here,\" I said. \"Outside this inn. They called it The Three Frogs back then.\"\n\n\"Price?\"\n\n\"Little Rikey's big brother,\" I said. \"You never met him. Made Rike look like a gentleman.\"\n\n\"Oh right, I remember the story. The brothers told it around the fire once or twice when Rikey was off on some private whoring.\"\n\nWe reached the inn. They still called it The Three Frogs if the sign was anything to go by.\n\n\"I'll bet they didn't tell you the whole story.\"\n\n\"Brained him with a rock, didn't you? Now you mention it, none of them was too keen to talk about it.\"\n\n\"Me and the Nuban had come down out of the highlands. We didn't speak the whole time. I had Corion in my head, or the touch of him, like a black hole behind my eyes.\n\n\"We didn't expect to see the brothers. We'd arranged to meet a week earlier on the other side of Ancrath. But I'd called the Nuban on his debt, and off we'd gone.\n\n\"Anyhow, there they were. A score of horses on the road, the flame just starting to lick the thatch. Burlow over by that tree, there, with a keg of ale all to his-self. Young Sim, axe on high, chasing a pig. And out comes Price, bending low to fit through the door, smoke billowing around him as if he was the devil himself, and dragging the landlord, one hand round the man's neck, not choking him, mind: Price could get his mitts all the way round a man's neck without so much as pinching.\n\n\"Price sees me and it's like something explodes inside him. He knocks the landlord against the doorframe, and there's brains everywhere. Keeps his stare nailed to me the whole time.\n\n\"'You little bastard. I'm going to open you up.'\n\n\"He didn't shout it, but there wasn't one of the brothers who didn't hear him. Me and the Nuban were thirty yards off still, and it was like he'd hissed it into my ear.\n\n\" 'With a big crossbow like that, I bet you could hit him between the eyes from here,' I told the Nuban.\n\n\"'No,' he said. Didn't sound like the Nuban though. Sounded like a dry voice I'd heard before. 'They have to see you do it.'\n\n\"Price came on at a stroll. I didn't have any illusions that I could stop him, but running wasn't an option, so I thought I might as well have a go.\n\n\"I picked up a stone. A smooth one. Fit my hand like it was made for me.\n\n\" 'David had a sling,' Price said. He had an ugly smile on him.\n\n\" 'Goliath was worth one.'\n\n\"He was only strolling, but thirty yards never seemed to vanish so fast.\n\n\"'What's got you so riled anyhow? You missed the Nuban that much?' I thought I might as well find out what I was going to die for.\n\n\" 'I . . .' He seemed foxed at that. Had a distant look, like he was trying to see something I couldn't.\n\n\"I took the moment to let fly. With a stone like that you can't miss. It hit him in the right eye. Really hard. Even a monster like Price notices that sort of thing. He made an awful howling. You'd have shat yourself if you heard it, Makin, if you'd known he was after you.\n\n\"So, I crouched down, and my hands just found another couple of stones, each as perfect as the first one.\n\n\"Price is still hopping about, with a hand pressed to his eye and a goo leaking past his fingers.\n\n\" 'Hey, Goliath!'\n\n\"That got his attention. I crack my arm out and let go a second stone. Hits him in the good eye. He roars like a mad beast and charges. I put that last stone through his front teeth and down the back of his throat.\n\n\"I tell you, Makin, they were all impossible throws. Not lucky, impossible. I've never thrown like that since.\n\n\"Anyhow, I step out of his way, and he blunders on for ten yards before going down, choking. I'd put that third one right into his windpipe.\n\n\"I pick up the biggest rock I can from that drystone wall over there, and I follow him. He'd probably have choked to death by himself. He had that hanged-man purple look by the time I got there. But I don't like to leave things to chance.\n\n\"He's half-crawling, blind. And the stink of him, soiled most every way there is. I almost felt sorry for the bastard.\n\n\"I didn't think his skull would break first time. But it did.\"\n\nMakin, stepped off his horse, ankle-deep into mud. \"We could go inside.\"\n\nI didn't feel the weather any more. I felt the heat of the day I killed Price. The smoothness of the small stones, the coarse weight of the rock I'd used to end it.\n\n\"It was Corion that guided my hand. And I think it was Sageous who set Price on me. Father reckons the dream-witch serves him, but that's not the way of it. Sageous saw that Corion had sunk his hooks into me, he saw he'd lost his new pawn's heir, so he infected Price's dreams and fanned the hatred there just a little bit. It wouldn't have taken much.\n\n\"They play us, Makin. We're pieces on their board.\"\n\nHe had a smile at that, through torn lips. \"We're all pieces on someone's board, Jorg.\" He went to the tavern door. \"You've played me often enough.\"\n\nI followed him through into the warm reek of the main room. The hearth held a single log, sizzling and giving out more smoke than heat. The small bar held a dozen or so. Locals by the look of them.\n\n\"Ah! The smell of wet peasants.\" I threw my sodden cloak over the nearest table. \"Nothing beats it.\"\n\n\"Ale!\" Makin pulled up a stool. A space began to clear around us.\n\n\"Meat too,\" I said. \"Cow. Last time I came here we ate roast dog, and the landlord died.\" It was true enough, though not in that order.\n\n\"So,\" Makin said. \"This Corion just had to click his fingers on your first meeting, and you and the Nuban keeled over. What's to stop him doing it again?\"\n\n\"Maybe nothing.\"\n\n\"Even a gambler likes to stand a chance, Prince.\" Makin took two glazed jugs from the serving wench, both over-running with foam.\n\n\"I've grown a bit since we last met,\" I said. \"Sageous didn't find me so easy.\"\n\nMakin drank deep.\n\n\"But there's more. I took something from that necromancer.\" I could taste his heart, bitter on my tongue. I swigged from my jug. \"Bit off something to chew on. I've got a pinch of magic in me, Makin. Whatever runs in the veins of that dead bitch who did for the Nuban, that little girl too, who ran with the monsters, whatever kept her glowing, well, I've got a spark of it now.\"\n\nMakin wiped the foam from his dungeon-grown moustache. He managed to convey his disbelief with the slightest arching of a brow. I hauled up my shirt. Well, not _my_ shirt, but something Katherine must have selected for me. Where Father's knife had found me, a thin black line ran across my hairless chest. Black veins ran from the wound, reaching out over my ribs, up for my throat.\n\n\"Whatever my father is, he isn't inept,\" I said. \"I should have died.\"\n**44**\n\nThey call the castle \"The Haunt.\" When you ride up the valley of an evening, with the sun going down behind the towers, you can see why. The place has that classic brooding malice about it. The high windows are dark, the town below the gates lies in shadow, the flags hang lifeless. It brings to mind an empty skull. Without the cheery grin.\n\n\"So the plan is?\" Makin asked.\n\nI gave him a smile. We nosed the horses up the road, past a wagon creaking beneath a load of barrels.\n\n\"We seem to have arrived in time for tourney,\" Makin said. \"Is that a good thing, or a bad thing?\"\n\n\"Well, we've come for a test of strength haven't we?\" I'd been trying to make out the pennants on the pavilions lining the east side of the tourney field. \"Better to keep incognito for now though.\"\n\n\"So about this plan\u2014\" The scattered thunder of approaching hooves cut him off.\n\nWe looked back over our shoulders. A tight knot of horsemen was closing fast, half a dozen, the leader in full plate armour, long shadows thrown behind them.\n\n\"Nice bit of tourney plate.\" I turned my nag in the road.\n\n\"Jorg\u2014\" It was Makin's day for getting cut off.\n\n\"Make way!\" The lead horseman bellowed loud enough, but I chose not to hear him.\n\n\"Make way, peasants!\" He pulled up rather than go around. Five riders drew alongside him, house-troops in chainmail, their horses lathered.\n\n\"Peasants?\" I knew we looked down-at-heel, but we hardly counted as peasants. My fingers found the empty space where my sword should hang. \"Who might we be clearing a path for, now?\" I recognized their colours, but asked by way of insult.\n\nThe man on the knight's left spoke up. \"Sir Alain Kennick, heir to the county of Kennick, knight of the long\u2014\"\n\n\"Yes, yes.\" I held up a hand. The man fell silent, fixing me with a pale eye from beneath the rim of his iron helm. \"Heir to the Barony of Kennick. Son of the notoriously blubbery Baron Kennick.\" I rubbed at my chin hoping that the grime there might pass as stubble in the half-light. \"But these are Renar lands. I thought the men of Kennick weren't welcome here.\"\n\nAlain drew his steel at that, four foot of Builder-steel cutting a bloody edge from the sunset.\n\n\"I'll not be debated in the road by some peasant boy!\" His voice held a whine to it. He lifted his faceplate, then took the reins.\n\n\"I heard that the Baron and Count Renar made up their differences after Marclos got himself killed,\" Makin said. I knew he'd have his hand on the flail we inherited with the horses. \"Baron Kennick withdrew his accusations that Renar was behind the burning of Mabberton.\"\n\n\"Actually it was me that burned Mabberton,\" I said. I had to wonder, though. I might have been the one to put torch to thatch. It had seemed like a good idea at the time. But whose good idea was it? Corion's perhaps.\n\n\"You?\" Alain snorted.\n\n\"I had a hand in Marclos's death too,\" I said. I kept his eyes and edged my horse closer. Without weapon or armour I didn't present much of a threat.\n\n\"I heard that the Prince of Ancrath turned Marclos's column with a dozen men,\" Makin added.\n\n\"Did we have a full dozen, Sir Makin?\" I asked in my best court voice. I kept my eyes on Alain and ignored his men. \"Perhaps we did. Well, no matter, I like these odds better.\"\n\n\"What are\u2014\" Alain glanced to either side where the hedgerow seethed with possibilities.\n\n\"You're worried about an ambush, Alain?\" I asked. \"You think Prince Honorous Jorg Ancrath and the captain of his father's guard can't take six Kennick dogs in the road?\"\n\nWhatever Alain might think, I could tell his men had heard their fill of Norwood stories. They'd heard of the Mad Prince and his road hounds. They'd heard how ragged warriors burst from the ruins, stood their ground, and broke a force ten times their number.\n\nSomething grunted in the gloom to our right. If Alain's men had any doubt that they were already targeted by bandits in the shadows, the grunt of a small forager hunting grubs was enough to convince them otherwise.\n\n\"Now! Attack!\" I yelled it for the benefit of my non-existent ambush party, and flung myself from my saddle, dragging Alain off his horse.\n\nThe fight went out of Alain as soon as we hit the sod, which was good because the fall knocked all the wind out of me, and a clash of heads set me seeing stars.\n\nI heard the whack of Makin's flail and the thump of retreating hooves. With a heave and a clatter I disentangled myself from Alain.\n\n\"Best get out of here quick, Jorg.\" Makin was heading back after the briefest of pursuits. \"Won't take them long to work out we're alone.\"\n\nI found Alain's sword. \"They won't be back.\"\n\nMakin frowned at me. \"Head-butting a helmed knight scrambled your brains?\"\n\nI rubbed at the sore spot, fingers coming away bloody.\n\n\"We've got Alain. A hostage or a corpse. They don't know which.\"\n\n\"He looks dead to me,\" Makin said.\n\n\"Broke his neck, I think. But that's not the point. The point is that they know they're not getting him back in one piece, so they'll be looking to their own escape. There's no going back to Kennick for those lads now. No welcome in The Haunt either. They'll know Renar won't want any part of this.\"\n\n\"So what now?\"\n\n\"We get him off the road. That beer wagon is going to come by here in a few minutes.\" I threw a look down the road. \"Hitch him to his horse. We'll drag him into the wheat field.\"\n\nWe took the armour off him in the gloom, amongst the wheat still wet from the day's rain. It stunk a bit\u2014Alain had soiled himself in death\u2014but it was a good fit for me, if a bit roomy around the waist.\n\n\"What do you think?\" I stepped back for Makin to admire me.\n\n\"Can't see a damn thing.\"\n\n\"I look good, trust me.\" I half-drew Alain's sword, then slammed it back into its scabbard. \"I think I'll give the jousts a miss.\"\n\n\"Very wise.\"\n\n\"The Grand M\u00eal\u00e9e is more me. And the winner gets his prize from Count Renar himself!\"\n\n\"That's not a plan. That's a way to get a death so famously stupid that they'll be laughing about it in alehouses for a hundred years to come,\" Makin said.\n\nI started to clank back toward the road, leading Alain's horse.\n\n\"You're right, Makin, but I'm running out of options here.\"\n\n\"We could hit the road again. Get a little gold together, get some more, enough to make lives somewhere they've never heard of Ancrath.\" I could see a longing in his eyes. Part of him really meant it.\n\nI grinned. \"I may be running out of options, but running out isn't an option. Not for me.\"\n\nWe rode toward The Haunt. Slowly. I didn't want to visit the tourney field yet. We had no tent to pitch, and the Kennick colours would inevitably draw me deeper into the charade than my acting skills could support.\n\nAs we came out of the farmland into the sprawl of houses reaching from the castle walls, a hedge-knight caught up with us and pulled up.\n\n\"Well met, sir . . . ?\" He sounded out of breath.\n\n\"Alain of Kennick,\" I supplied.\n\n\"Kennick? I thought . . .\"\n\n\"We have an alliance now, Renar and Kennick are the best of friends these days.\"\n\n\"Good to hear. A man needs friends in times like these,\" the knight said. \"Sir Keldon, by the way. I'm here for the lists. Count Renar places generous purses where a good lance can reach them.\"\n\n\"So I hear,\" I said.\n\nSir Keldon fell in beside us. \"I'm pleased to be off the plains,\" he said. \"They're lousy with Ancrath scouts.\"\n\n\"Ancrath?\" Makin failed to keep the alarm from his voice.\n\n\"You haven't heard?\" Sir Keldon glanced back into the night. \"They say King Olidan is massing his armies. Nobody's sure where he'll strike, but he's sent the Forest Watch into action. Most of them are back there if I know anything!\" He stabbed a gauntleted finger over his shoulder. \"And you know what that meant for Gelleth!\" He drew the finger across his throat.\n\nWe reached the crossroads at the town centre. Sir Keldon turned his horse to the left. \"You're to the Field?\"\n\n\"No, we've to pay our respects.\" I nodded toward The Haunt. \"Good luck on the morrow.\"\n\n\"My thanks.\"\n\nWe watched him go.\n\nI turned Alain's horse back toward the plains.\n\n\"I thought we were going to pay our respects?\" Makin asked.\n\n\"We are,\" I said.\n\nI kicked my steed into a trot. \"To Watch Master Coddin.\"\n**45**\n\nI like mountains, always have done. Big obstinate bits of rock sticking up where they're not wanted and getting in folk's way. Great. Climbing them is a different matter altogether though. I hate that.\n\n\"What in feck's name was the point of stealing a horse if I have to drag the damn thing up the slightest incline we meet?\"\n\n\"To be fair, Prince, this is more by way of a cliff,\" Makin said.\n\n\"I blame Sir Alain for owning a deficient horse. I should have kept the nag I came in on.\"\n\nNothing but the labour of Makin's breath.\n\n\"I'm going to have to see Baron Kennick about that boy of his one day,\" I said.\n\nAt that point a stone turned under my foot and I fell in a clatter of what little armour I'd kept on.\n\n\"Easy now, you've three bows on each of you.\" The voice came from further up the slope where the moonlight made little sense of the jumbled rock.\n\nMakin straightened up slow and easy, leaving me to find my own way to my feet.\n\n\"Sounds like a good Ancrath man to me,\" I said, loud enough for any on the slopes. \"If you're going to shoot anyone, might I suggest this horse here, he's a better target and a lazy bastard to boot.\"\n\n\"Lay your swords down.\"\n\n\"We've only got one between us,\" I said. \"And I'm not inclined to lose it. So let's forget about that now and you can take us to see the Watch Master.\"\n\n\"Lay down\u2014\"\n\n\"Yes, yes, so you said. Look.\" I stood up straight and turned to try and catch the moonlight. \"Prince Jorg. That's me. Pushed the last Watch Master over the falls. Now take me to Coddin before I lose my famously good temper.\"\n\nWe reached an understanding and before long I had two of them leading Alain's horse, and another lighting the way for us with a hooded lantern.\n\nThey took us to an encampment a couple of miles further on, fifty men huddled in a hollow just below the saddle of a hill. Brot Hill, according to the leader of the band taking us in. Nice to know somebody had a clue.\n\nThe watch brought us in with whistled signals to the guards. The camp lay dark, which was sensible enough given they weren't ten miles from The Haunt.\n\nWe stumbled in amongst sleeping watchmen, tripping over the guys of various tents set up for command.\n\n\"Let's have some light!\" I made enough noise to wake the sleepers. A prince deserves a little fanfare even if he has to make it himself. \"Light! Renar doesn't even know you've crossed the borders yet, he's holding a tourney in the shadow of his walls for Jesu's sake!\"\n\n\"See to it.\" I recognized the voice.\n\n\"Coddin! You came!\"\n\nLanterns began to be lit. Fireflies waking in the night.\n\n\"Your father insisted on it, Prince Jorg.\" The Watch Master ducked out of his tent, his face without humour. \"I'm to bring your head back, but not the rest of you.\"\n\n\"I volunteer to do the cutting!\" Rike stepped into the lantern glow, bigger than remembered, as always.\n\nMen stepped aside, and Gorgoth came out of the gloom, huger than Rike, his rib-bones reaching from his chest like a clawed hand. \"Dark Prince, a reckoning is due.\"\n\n\"My head?\" I put a hand to my throat. \"I think I'll keep it.\" I turned to see Fat Burlow arrive, a loaf in each hand.\n\n\"I believe my days of pleasing King Olidan are over,\" I said. \"In fact I'm even tired of waiting for him to die. The next victory I take will be for me. The next treasure I seize will stay in these hands, and the hands of those that serve me.\"\n\nGorgoth looked on, impassive, little Gog watching from his shadow. Elban and Liar elbowed their way through the growing ring of watchmen.\n\n\"And what treasure would that be, Jorth?\" Elban asked.\n\n\"You'll see it when the sun rises, old man,\" I said. \"I'm taking the Renar Highlands.\"\n\n\"I say we take him in.\" Rike loomed behind me. \"There'll be a price on his head. A princely price!\" He laughed at his own joke, coughing on that fishbone again, the old \" _hur! hur! hur!_ \"\n\n\"Funny you should mention Price, Brother.\" I kept my back to him. \"I was reminiscing with Makin down at The Three Frogs just the other day.\"\n\nThat stopped his laughing.\n\n\"I won't lie to you, it's not going to be easy.\" I turned nice and slow to address the whole circle of faces. \"I'm going to take the county from Renar, and make it my kingdom. The men that help make that happen will be knights of my table.\"\n\nI found Coddin in the crowd. He'd brought the brothers to me on the strength of my message, but how much further he'd follow me was another matter: he was a hard man to predict.\n\n\"What say you, Watch Master? Will the Forest Watch follow their prince once more? Will you draw blood in the name of vengeance? Will you seek an accounting for my royal mother? For my brother who would have sat upon the throne of Ancrath had I fallen?\"\n\nThe only motion in the man lay in the flicker of lamplight along the line of his cheekbone. After too long a wait, he spoke. \"I saw Gelleth. I saw the Castle Red, and a sun brought to the mountains to burn the rock itself. Mighty works.\"\n\nAround the circle men nodded, feet stamped approval. Coddin held up a hand.\n\n\"But the mark of a king is to be seen in those closest to him. A king needs be a prophet in his homeland,\" he said.\n\nI didn't like where we were going.\n\n\"The watch will serve if these . . . road-brothers stay true, once you have told them of their task,\" he said, eyes on me all the while, steady and calm.\n\nI made another half circle, until Rike filled my vision, my eyes level with his chest. He smelled foul.\n\n\"Christ Jesu, Rike, you stink like a dung heap that's gone bad.\"\n\n\"Wh\u2014\" He furrowed his brow and jabbed a blunt finger toward Coddin. \"He said you had to win the brothers to the cause. And that's me that is! The brothers do what I say now.\" He grinned at that, showing the gaps where I'd knocked out teeth under Mount Honas.\n\n\"I said I wouldn't lie to you.\" I spread my hands. \"I'm done with lying. You men are my brothers. What I would ask of you would leave most in the grave.\" I pursed my lips as if considering. \"No, I won't ask it.\"\n\nRike's frown deepened. \"What won't you ask, you little weasel?\"\n\nI touched two fingers to my chest. \"My own father stabbed me, Little Rikey. Here. A thing like that will reach any man.\n\n\"You take the brothers to the road. Break a few heads, empty a few barrels, and may whatever angel is set to watch over vagabonds fill your hands with silver.\"\n\n\"You want us to go?\" He spoke the words slowly.\n\n\"I'd make for the Horse Coast,\" I said. \"It's that way.\" I pointed.\n\n\"And what'll you be doing?\" Rike asked.\n\n\"I'll go with Watch Master Coddin here. Perhaps I can make peace with my father.\"\n\n\"My arse you will!\" Rike hit Burlow in the arm, no malice in it, just an over-boiling of his natural violence. \"You've got it all planned out, you little bastard. Always playing the odds, always with the aces hidden away. We'll be slogging through dust and mud to the Horse Coast, and you'll be lording it here with a gold cup in your hand and silk to wipe your shit. I'm staying right where I can see you, until I get what's mine.\"\n\n\"I'm telling you as a brother, you big ugly sack of dung, leave now while you've a chance,\" I said.\n\n\"Stuff it.\" Rike allowed himself a triumphant grin.\n\nI gave up on him.\n\n\"Coddin's men can't get near that tourney. Men such as us though, we drift into every muster, we lurk at the edges of any place where there's blood and coin and woman-flesh. The brothers could slip into tourney crowds unseen.\n\n\"When I make my move I need you to hold until the watch can reach us. I need you to hold The Haunt's gates. For minutes only, but make no mistake, they'll be the reddest minutes you've seen.\"\n\n\"We'll hold,\" Rike said.\n\n\"We will hold.\" Makin raised his flail.\n\n\"We'll hold!\" Elban, Burlow, Liar, Row, Red Kent, and the dozen brothers left to me.\n\nI faced Coddin once again.\n\n\"I guess they'll hold,\" I said.\n**46**\n\n\"Sir Alain, heir to the Kennick baronetcy.\"\n\nAnd there I was, riding onto the tourney field to take my place, accompanied by a scatter of half-hearted applause.\n\n\"Sir Arkle, third son of Lord Merk.\" The announcer's voice rang out again.\n\nSir Arkle followed me onto the field, a horseman's mace in hand. Most of the entrants for the Grand M\u00eal\u00e9e had can-openers of one sort or another. The axe, the mace, the flail, tools to open armour, or to break the bones closeted within. When you fight a man in full plate, it's normally a matter of bludgeoning him to a point at which he's so crippled you can deliver the coup de gr\u00e2ce with a knife slipped between gorget and breastplate, or through an eye-slot.\n\nI had my sword. Well, I had Alain's. If he had a weapon more suited to the M\u00eal\u00e9e, then it left with his guards when they rode off.\n\n\"Sir James of Hay.\"\n\nA big man in battered plate, heavy axe at the ready, an armourpiercing spike on the reverse.\n\n\"William of Brond.\" Tall, a crimson boar on his shield, spiked flail.\n\nThey kept coming. A baker's dozen. At last we were all arrayed upon the field. A lucky thirteen. Knights of many realms, caparisoned for war. Silent save for the gentle nicker of horses.\n\nAt the far end of the field, in the shadow of the castle walls, five tiers of seating, and in the centre, a high-backed chair draped in the purple of empire. Count Renar rose to his feet. Beside him on the common bench, Corion, an unremarkable figure that drew on the eye as the lodestone pulls iron.\n\nAt two hundred paces I could see nothing of Renar's face save the glint of eyes beneath a gold circlet and a dark fall of hair.\n\n\"Fight!\" Renar lifted his arm, and let it drop.\n\nA knight spurred his horse toward mine. I'd not taken his name to heart. I only listened to the introductions after mine.\n\nAll around us men fell to battling. I saw William of Brond take a man from the saddle with a swing of his flail.\n\nMy attacker had a flanged mace, clutched tight, the steel of his gauntlet polished to dazzling silver. He shouted a war-cry as he came at me, trailing the mace for an overhead swing.\n\nI stood in my stirrups and leaned toward him, arm fully extended. Alain's sword found its way through the perforated grille of the knight's helm.\n\n\"Yield?\"\n\nHe wouldn't say, so I let him slip from his horse.\n\nAnother knight came my way, sidestepping his horse skilfully away from Sir William's frenzy. He wasn't even looking at me.\n\nAround the back of the breastplate there's a gap just below the kidneys. A decent suit of plate will have chainmail to cover whatever vitals are exposed between breastplate and saddle. And his did. But Builder-steel with a little muscle behind it will cut through chain. The man fell with a vague expression of surprise, and left me facing William.\n\n\"Alain!\" He sounded as if all his Christmases had come at once.\n\n\"I know, I hate him too.\" I flipped my visor.\n\nThe thing about flails is you've got to keep them moving. An important point that Sir William forgot when he found himself staring into an unfamiliar face. I took the opportunity to urge Alain's horse forward, and to its credit the beast was fast enough to let me put four foot of razor-edged sword past Sir William's guard.\n\nIt's not the done thing to set to bloody slaughter at tourney. There's rarely a Grand M\u00eal\u00e9e in which somebody doesn't die, but it's normally a day later under the knives of the chirurgeons. The foe is generally unhorsed, or stunned in the saddle. A few fractures and a lot of bruising are the normal consolation prizes distributed among the entrants who don't win. When a knight gets too thirsty for blood, he often finds himself meeting his opponent's friends and family in unpleasant circumstances shortly after.\n\nI of course had a rather different view of things. The fewer armed men left able-bodied after the tourney, the better. Besides, a broadsword isn't the weapon to batter out submissions. It's for killing, pure and simple.\n\nSir Arkle charged me, galloping nearly the full length of the field, a felled knight in his wake. As he closed the gap, he set to swinging his mace in a tight pattern just out of kilter with his horse's gait. It looked worryingly well-practised.\n\nIf the sight of a heavy warhorse thundering toward you doesn't make at least part of you want to up and run, then you're a corpse. There's no stopping a thing like that. A thousand pounds of muscle and bone, sweating and panting as it hurtles your way.\n\nI rolled out of the saddle as Sir Arkle arrived. I didn't just duck. He was ready for that. I fell. And yes it hurt. But not so much that it stopped me sticking old Alain's sword into that blur of thrashing legs as Arkle hurtled past.\n\nThat's another thing that isn't done in tourney. You go for the man, not the horse. A trained warhorse is frighteningly expensive, and be assured that when you break one, the owner is going to come after you for the price of a replacement.\n\nI levered myself up, cursing, splattered with horse blood.\n\nSir Arkle lay under his steed, deathly quiet and still, in contrast to the horse's screaming and thrashing.\n\nA lot of animals will suffer horrific injury in silence, but when they decide to complain, there's no holds barred. If you've heard the screams of rabbits as they're put to the knife, you'll know what racket even such small creatures can make. It took two swings to fully silence Arkle's horse. Another two for good measure to take its head off.\n\nBy the time I'd finished, I'd become the archetypal Red Knight, my armour bright with arterial blood. I had the stink of battle in my nose now, blood and shit, the taste of it on my lips, salt with sweat.\n\nThere weren't many of us left standing in the tourney ring. Sir James stood amid a scatter of fallen knights at the far end, battling a man in fire-bronzed armour. Closer to hand an unhorsed knight with a war-hammer had just laid out his opponent. And that was it.\n\nThe hammer-man limped toward me, the iron plates around his knee buckled and grating.\n\n\"Yield.\" I didn't move. Didn't so much as raise my sword.\n\nA moment of silence. Nothing but the distant clash of weapons as Sir James of Hay put down his man. Nothing but the faint pitter-pat of blood dripping from my plate-mail.\n\nHammer-man let his hammer fall. \"You're not Alain Kennick.\" He turned and limped toward the white tent where the healers waited.\n\nHalf of me wanted the fight. More than half of me wondered if a hammer between the eyes wasn't a whole lot more appetizing than meeting with Corion again. It seemed impossible that he didn't already know I was here, that those empty eyes hadn't seen through Alain's armour at the first moment. I glanced toward the stands, closer now. He watched me, they all did, but this was the man who'd given me the power to fell Brother Price, the man who whispered from the hook-briar, who poisoned my every move, pulling the strings toward hidden ends. Had he drawn me here, to this moment, tugging on his puppet lines?\n\nSir James of Hay put an end to my speculation. He dismounted, presumably having noted my lack of respect for horseflesh, and advanced with purpose in his stride. The sunlight coaxed few glimmers from the scarred plates of his armour. His heavy axe had done good work today. I saw blood on the armour spike.\n\n\"You're a scary one,\" I said.\n\nHe came on, stepping around Arkle's horse.\n\n\"Not a talker?\" I asked.\n\n\"Yield, boy,\" he said. \"One chance.\"\n\n\"I'm not sure we even have choices, James, let alone chances. You should read\u2014\"\n\nHe charged, dragging that axe of his through the air in a blur. I managed a block, but my sword flew free, leaving my right hand numb to the wrist. He reverse-swung, his strength tremendous, and nearly took my head. I swayed aside, clear by half an inch, and staggered back.\n\nSir James readied himself. I knew then how the cow feels before the slaughterman. I may have been guilty of fine words about fear and the edges of knives, but empty-handed before a competent butcher like Sir James I found a sudden and healthy terror. I didn't want it all to end here, broken apart before a cheering crowd, cut down before strangers who didn't even know my name.\n\n\"Wait!\"\n\nBut of course he didn't. He came on apace, swinging for me. If I hadn't tripped as I backed, I'd have been cut in two, or as near as makes no difference. The fall left me flat on my back with the air knocked out and Sir James carried two strides past me by his momentum. My right hand, grasping for purchase, found the haft of the discarded war-hammer. The old luck hadn't deserted me.\n\nI swung and made contact with the back of Sir James' knee. It made a satisfying crunch, and he went down, discovering his voice on the way. Unfortunately the brute hadn't the grace to know he was supposed to be beaten. He twisted onto his good knee and raised his axe over my head. I could see it black against the blue sky. At least the sun was out. A blank visor hid his face, but I could hear the rattle of his breath behind it, see the flecks of foam around the perforations.\n\n\"Time to die.\"\n\nHe was right. There's not much to be done with a war-hammer at close quarters. Especially when you're spread-eagled on your back.\n\n_ChooOm!_\n\nSir James' head jerked from my field of view leaving nothing but blue heaven.\n\n\"Gods but you've got to love that crossbow!\" I said.\n\nI sat up. Sir James lay beside me, a neat hole punched through his faceplate, and blood pooling behind his head.\n\nI couldn't see who had taken the shot. Probably Makin, having regained the Nuban's crossbow from one of the brothers. He must have loosed his bolt from the commons where the rabble stands. Renar would have men stationed where anyone might get a clear shot at the royal seating area, but targeting the combatants on the field was a far easier proposition.\n\nI recovered my sword before the crowd really took in what had happened. A scuffle of some kind had broken out in the commons, a large figure in the midst of it all. Rike breaking heads perhaps.\n\nI scooped up Sir James's axe and caught Alain's horse again. Once in the saddle I took axe and sword in hand. Townsfolk began to stream onto the field with some kind of riot in mind. It wasn't entirely clear where their anger lay, but I felt sure a whole lot of it rested on Sir Alain of Kennick.\n\nA line of men-at-arms had positioned themselves in front of the royal stand. A squad of six soldiers in castle livery were angling toward me from their station by the casualty tent.\n\nI lifted axe and sword out to shoulder height. The axe weighed like an anvil; it'd take a man like Rike to wield it as lightly as Sir James had.\n\nFrom the corner of my eye I could see guards leaving their posts at the castle gates to help calm the disturbance and come to their lord's aid.\n\nCorion found his feet, oddly reminiscent of a scarecrow, standing just below Count Renar's seat. The Count himself remained in his chair, motionless, hands in his lap, fingers steepled.\n\nDid Corion know it was me? He had to, surely? When I'd broken his spell, when I'd woken from dark dreams after Father's tender stab, and finally remembered how he'd turned me from my vengeance, how he'd made me his pawn in the hidden game of empire, hadn't he known?\n\nTime to find out.\n\nI urged Alain's horse into a canter and aimed him straight at Renar, axe and sword in outstretched hands. I hoped I looked like Hell risen, like Death riding for the Count. I could taste blood, and I wanted more.\n\nThere really is something about a heavy warhorse coming your way. The stand began to empty at speed, the gentry climbing over each other to get clear. A space opened up around Renar's high-backed chair, just him, Corion, and the two chosen men flanking. A ripple even ran through the line of soldiers before the seating, but they held their ground. At least until I really picked up speed.\n**47**\n\nAlain's horse carried me through the soldiers, up the stands, like climbing a giant staircase, right to Count Renar's chair, and through it.\n\nHad the Count not been hauled from his seat moments before, it could have all ended there.\n\n\"Get him away!\" Corion said to the quick-handed bodyguard.\n\nThe other chosen man came straight for me as the horse beneath me panicked at the strange footing. I couldn't control the beast, and I didn't want it to land on me when it fell, so I leapt from the saddle. Or got as close to a leap as a man in full plate can, which is to say that I chose where I fell. I trusted to my armour and dropped onto Renar's bodyguard.\n\nThe man cushioned my fall, and in exchange got most of his ribs broken. I heard them crack like sappy branches. I clambered up, with the horse whinnying behind me, hooves flying in all directions as it turned and bucked, threatening to fall at every moment.\n\nI threw Sir James' axe at Renar's back, but the thing proved too heavy and ill-weighted for a clean throw. It hit his second bodyguard between the shoulder blades and felled him. Renar himself managed to reach the soldiers I'd scattered in my charge, and they circled around to escort him toward the castle.\n\nI took my sword in two hands and made to follow.\n\n\"No.\"\n\nCorion stepped into my path, one hand raised, a single finger lifted.\n\nI felt a giant nail skewer me to the spot, struck through the top of my head, driven into the bedrock far beneath my feet. The world seemed to spin around me, slow revolutions, measured by heartbeats. My arms fell, limp, hands numb, losing their grip on the sword hilt.\n\n\"Jorg.\" I wouldn't meet his eyes. \"How could you think you might defy me?\"\n\n\"How could you think I wouldn't?\" My voice sounded far off, as if somebody else were speaking. I managed to fumble the dagger from my hip.\n\n\"Stop.\" And my arms lost all remaining strength.\n\nCorion moved closer. My eyes struggled to keep with him as the world turned. Behind me the sounds of the thrashing horse, muffled and distant.\n\n\"You're a child,\" he said. \"You gamble everything on each throw, no bet hedged, no reserve. That's a strategy that always ends in defeat.\"\n\nHe took a small knife from his robe, three gleaming inches of cut-throat.\n\n\"Gelleth, though! That took us all by surprise. You exceeded all expectations there. Sageous even left your father's side rather than face you on your return. He's back there now, of course.\"\n\nCorion put the blade to the side of my neck, angled between helm and gorget. His face held no emotion, his eyes empty wells that seemed to suck me in.\n\n\"Sageous was right to run,\" I said. My voice reached up from a chasm.\n\nI had no plan, but I'd had my moment of fear with Sir James and I wasn't about to reward Corion with any more.\n\nI reached for whatever power the necromancer's heart had given me. I let my eyes look where the ghosts walk, and a cold thrill burned across my skin.\n\n\"Necromancy won't save you, Jorg.\" I felt the bite of the knife at my neck. \"Even Chella doesn't trust in her death magic enough to face me. And whatever you stole beneath that mountain is just a shadow of her skill.\"\n\nIt's will. In the end it always comes down to will. Corion held me, nailed within a treacherous body, because he willed it, because his want had over-written mine.\n\nHot blood trickled down my neck. I felt it run beneath my armour.\n\nI threw everything I had against him. All my pride, my anger, an ocean of it, the rage, the hurt. I reached back across the years. I counted my dead. I reached into the briar and touched the bloodless child who hung there. I took it all, and made a hammer of it.\n\nNothing! All I managed was to flop my head forward so I no longer saw his face. He laughed. I felt the vibration of it in the knife. He wanted my death to be slow.\n\nI could see my arms, metal clad, dagger held in loose fingers. Life pulsed through those arms, driven with each beat of my heart, mixed with the dark magic that had kept me from death at the King's hand. I saw Father's face again, in the moment of the blow, the bristle of his beard, the tight line of his mouth. I saw Katherine's face, the light in her eyes as she nursed me. And I reached with all of it, the bitter and the sweet, just to move the arms that lay before me. I put the whole of my life behind that plea.\n\nIt accomplished nothing but to turn the point of my dagger toward Corion.\n\n\"They're dying, Jorg,\" he said. \"See with my eyes.\"\n\nAnd I was the hawk. Part of me stayed on the stands, being bled like a pig, and the rest flew, wild and free across the tourney field.\n\nI saw Elban defending Rike's back amid the common crowd, Renar's soldiers closing on them from all angles, like hunting dogs knifing through the tall grass. A spear got him in the stomach. He looked surprised. Old all of a sudden, wearing all his years. I saw him shout, and spit blood over those toothless gums of his. But I couldn't hear him. A glimpse of Elban cutting down the man who speared him, and we moved on.\n\nLiar stood out on the edge of the tourney field, a mean streak of gristle, bow in hand, arrows planted at his feet. He took the castle-soldiers down as they streamed toward the royal stands. Quick but unhurried, each arrow finding a mark, a tight smile on his lips. They got him from behind. The first soldier to reach him drove a spear through his back.\n\nWe swept closer to the gates. A tinker's cart. The sack covering shrugged aside, and Gorgoth rolled out, reaching the ground on two hands and one knee. He ran for The Haunt. The castle folk scattered before him, some screaming. Even soldiers turned aside, all of a sudden finding their duty to be on the tourney field. Two men discovered their courage and barred his way, spears levelled. Gorgoth didn't slow. He caught a spear in each hand, snapped the last foot off, and drove the broken ends through their owners' necks. He ran through the men before they fell. Three arrows hit him as he left my view.\n\nCorion drew our sight back. On the cart the sacking twitched again. Something quick and mottled slipped out. Gog. The leucrota child ran in the direction Gorgoth had taken.\n\nOur sight drew back. Across the tourney field where a score of soldiers closed on the royal stand. Burlow stood guard. A lone man between Renar's spears and the young Prince of Ancrath, yours truly. How he'd got there I didn't know. Or why. But he had nowhere to run, and he was too fat to win free in any case.\n\nBurlow took the first man down with an axe blow that sliced head from shoulders. A reverse swing put the blade between the next man's eyes. Then they were all over him. A single arrow looped in from somewhere and found a Renar neck.\n\nOur sight drew back. I saw myself on the stand, face to face with Corion. Bleeding. Alain's horse still thrashing, as if it had been seconds rather than a lifetime since I rode up.\n\nAnd we parted. I saw with my own eyes again. The knife in my hand, raised but impotent, the splintered boards beneath my feet. The sounds of Burlow dying. The scream of horse. I thought of Gog, chasing Gorgoth toward the gates, of Elban's toothless shout, of Makin out there somewhere, fighting and dying.\n\nNone of it made any difference. I couldn't move.\n\n\"It's over, Jorg. Goodbye.\" The magus placed his knife for the final cut.\n\nYou'd think there was never a good time to get kicked by a horse.\n\nThe wild hoof hit me square in the back. I would probably have flown ten yards if I hadn't crashed straight into Corion. As it was, we flew about five yards together. We landed on grass, at the side of the royal stand, clutched in an embrace, like lovers. The eyes that had held me were screwed shut in pain. I tried again to lift my dagger. It didn't move. But this time there was a difference, I felt the strain and play of the muscles in my arm. With a grunt I pushed him from me. The hilt of my dagger jutted between his ribs. What all my will, all my rage and pain, had been unable to accomplish, a single kick from a panicked horse had achieved.\n\nI twisted the dagger, digging it in. A last breath escaped him. His eyes rolled open, glassy and without power.\n\nThe Count's bodyguard had fallen this way too, with the axe that had brought him down still bedded in his back. I wrenched it free. It's a nasty sound that sharp iron makes in flesh. I took Corion's head in two blows. I didn't trust him to be dead.\n\nThe soldiers that had taken Burlow began to boil around the side of the stand. I held Corion's head up before them.\n\nThere's an unsettling weight to a severed head. It swung on the grey hair knotted between my fingers, and I tasted bile at the back of my throat.\n\n\"You know this man!\" I shouted.\n\nThe first three soldiers coming into view halted, maybe from fear, maybe to let the numbers build before the charge.\n\n\"I am Honorous Jorg Ancrath! The blood of Empire flows through my veins. My business is with Count Renar.\"\n\nMore soldiers came around the corner of the stand. Five, seven, twelve. No more. Burlow had given good account of himself.\n\n\"This is the man you have served.\" I took a step toward them, Corion's head held out before me. \"He made Count Renar his puppet years ago. You know this to be true.\"\n\nI walked forward. No hesitation. Believe they will step aside, and they will.\n\nThey didn't watch me. They watched the head. As if the fear he'd instilled in them ran so deep that they expected those dead eyes to swivel their way and draw them in with that hollow pull.\n\nThe soldiers parted for me, and I walked out across the tourney field toward The Haunt.\n\nOther units broke from the left of the field where Rike and Elban had been fighting. They moved to intercept me. Two groups of five. They started to fall before they got within fifty yards. The Forest Watch were advancing along the Elm Road. I could see archers lining the ridge from which I'd first seen The Haunt.\n\nI let Corion's head drop. I just opened my fingers and let his hair slide through. It took an age to fall, as though it fell through cobwebs, or dreams. It should have hit the ground like a hammer against a gong, but it made no sound. Silent or roaring though, I heard it, I felt it. A weight lifted from me. More weight than I'd ever imagined I could carry.\n\nI could see the gateway ahead. The Haunt's great entrance arch. The portcullis had all but descended. A single figure stood beneath it, holding up an impossible mass of wood and iron. Gorgoth!\n\nI started to run.\n**48**\n\nI ran for the castle gates. I had my armour on, save for the pieces I'd lost in the tourney, but it didn't seem to weigh heavy. I heard the hiss of arrows about me. Other men fell. The Forest Watch's finest archers kept my path clear.\n\nI wondered where I was going, and why. I'd left Corion in the mud. When he died, it felt like an arrow being drawn from a wound, like shackles struck away, like the hangman's noose worked free from a purpled neck.\n\nA few shafts reached me from guards up in The Haunt's ramparts. One shattered on my breastplate. But in the main they had too hard a time picking targets in the confusion of the tourney field to worry about one knight storming the castle single-handedly.\n\nI let my feet carry me. The empty feeling wouldn't leave me. Where there had been an inner voice to goad me on, I heard only the rasp of my breath.\n\nI met more serious resistance in the street running up to the gates, out of sight from the watch's positions. Soldiers had gathered, between the taverns and tanneries. They held the road I had passed when I first came to The Haunt with the Nuban, as a child seeking revenge.\n\nTwenty men blocked the way, spearmen, with a captain in Renar finery, dull gleams from his chainmail. Behind them I could see Gorgoth holding up the portcullis. More soldiers milled in the courtyard beyond. There seemed to be no reason why they hadn't cut the leucrota down, and sealed the gates.\n\nI pulled up before the line of spearmen, and found I had no breath with which to address them. A cold bluster of wind swirled between us, laced with rain.\n\nWhat to do? All of a sudden, impossible odds seemed . . . impossible.\n\nI glanced back. Two figures were pounding up along the path I'd taken. The first was too big to be anyone but Rike. I could see the feathered end of an arrow jutting from the joint above his left shoulder. Too much mud and blood on the second man to identify him by his armour. But it was Makin. I knew it from the way he held his sword.\n\nI looked at the soldiers, along the points of their spears, held in a steady row.\n\nWhat's it going to be then?\n\nAnother scatter of rain.\n\n\"House of Renar?\" the captain called. He sounded uncertain.\n\nThey didn't know! These men had come out of the castle, without a clue what kind of attack they were under. You've got to love the fog of war.\n\nI scraped a gauntlet across my breastplate to show the coat of arms more clearly. \"Sanctuary!\"\n\n\"Alain Kennick, ally to the House of Renar, seeking sanctuary.\" I pointed back toward Rike and Makin. \"They're trying to kill me!\"\n\nPerhaps Corion's death hadn't taken all of the wickedness from me. Not all of it.\n\nI ran toward the line, and they parted for me.\n\n\"They won't get past us, my lord.\" The captain offered a brief bow.\n\n\"Make sure they don't,\" I said. And it didn't seem likely that they would.\n\nI hurried on, up to the gates, feeling the weight of my plate-mail now. The air held an odd stench, rich and meaty, bacon burning over the hearth. It put me in mind of Mabberton where we torched all those peasants, a lifetime ago.\n\nI could see squads of soldiers assembling in the great courtyard beyond the gates. Half-armoured men, some with shields, some without, many of them full of tourney-day ale, no doubt.\n\nComing closer I saw the corpses. Charred things, smouldering in their own molten fats, like bodies from a pauper's funeral with too little wood to make them ash.\n\nGorgoth stood with his back to me. Arrows pierced his arms and legs. At first I thought him a statue, but as I came closer I could see the quiver in those huge slabs of muscle across his back.\n\nI moved past him, ducking under the portcullis. A hundred men in the courtyard watched me. Gorgoth's eyes were screwed tight with strain. He observed me through the narrowest of slits. More arrows jutted from his chest, standing among the reaching claws of his deformed ribcage. Blood bubbled around the shafts as he released a breath, and sucked back as he drew the next.\n\nI kicked a smouldering head. It rolled clear of the charred body.\n\n\"That's one hell of a guardian angel you've got looking out for you, Gorgoth,\" I said. Every soldier to have run at him lay in ashes.\n\nThe faintest shake of his head. \"The boy. Up there.\"\n\nAbove Gorgoth, crouched in one of the gaps between the portcullis' timbers, Gog lurked. The inky voids that served him for eyes now burned like hot coals beneath the smith's bellows. His thin body had folded tighter than I believed possible. A few arrows studded the woodwork around him.\n\n\"The little one did all this?\" I blinked. \"Damn.\"\n\nGorgoth had told me the changes would come too quickly to Gog and his little brother. Too quickly and too dangerous to be borne.\n\n\"Bring this mad dog down.\" The voice rang out behind me. It sounded familiar. It sounded like my father.\n\n\"Shoot him.\"\n\nIt wasn't a voice to be disobeyed. But nobody had shot at me yet, so I turned from Gorgoth, and faced The Haunt.\n\nCount Renar stood before the great keep, flanked by two dozen men-at-arms. To the left and right, bands of spearmen, a score in each. Other guards were coming down from the battlements above the gates.\n\nI sketched a bow. \"Hello, Uncle.\"\n\nI'd only seen Renar in portrait before taking to the tourney field, and this was the best look I'd had at him so far. His face was rather thinner, his hair longer and less grey, but all in all he was the spitting image of his elder brother, and in truth, not that different from yours truly. Though far less handsome, of course.\n\n\"I am Honorous Jorg Ancrath.\" I pulled my helm clear and addressed the men before me. \"Heir to the throne of Renar.\" Not strictly true, but it would be once I'd killed the Count's remaining son. Wherever Cousin Jarco might be, he surely wasn't at home or I'd have seen his colours on the tourney field. So I let them think him dead. I let them picture him in the same pyre I'd set his brother Marclos on.\n\n\"You.\" The Count singled out a man at his side. \"Put a hole in this bastard's head, or I'm going to cut yours from your shoulders!\"\n\n\"This matter is between my uncle and me.\" I set my gaze on the bowman. \"When it is done, you will be my soldiers, my victory will be yours. There will be no more blood.\"\n\nThe man raised his crossbow. I felt a wave of heat sear my neck, as if a furnace door had opened behind me. Blisters rose across the man's face, like bubbles in boiling soup. He fell, screaming, and his hair burst into flame before he hit the ground. The men around him fell back in horror.\n\nI saw the ghost leave him as he writhed, burning, clots of his flesh sticking to the flagstones. I saw his ghost, and I reached out to it. I reached with my hands, and I reached with the bitter power of the necromancers. I felt their dark energy pulse across my chest, running out from the wound I took from Father's knife.\n\nI gave the dead man's ghost a voice, and I gave voice to the ghosts that hung smoke-like around the corpses at my feet.\n\nThe soldiers before me paled and shook. Swords dropped and terror leapt from man to man like wildfire.\n\nWith the screams of burned men echoing around me from beyond the grave, I took my sword in two hands and ran at Count Renar, my uncle, the man who sent killers after his brother's wife and sons. And I added my own scream, because Corion or no Corion, the need to kill him ate at me like acid.\n**49**\n\nAnd here I am, sitting in the high tower of The Haunt, in the empty place that Corion made his own. A fire crackles in the hearth, there are furs over the flagstones, goblets on the table, wine in the jug. And books, of course. The copy of Plutarch that I carried on the road now rests on oak shelves, with three score other tomes rubbing leathery shoulders. It's a small start but even the shelves themselves grew from a little acorn.\n\nI'm sitting by the window. The wind is sealed away behind a dozen panes of glass, each one a hand's span across, and leaded together in diamond shapes. The glass came in by ox-cart across the mountains, all the way from the Wild Coast if you can believe it. The Thurtans make it so flat you can look out and hardly see the distortion.\n\nI study the page before me, and the quill in my hand, and the ink at its point glistening with dark possibilities. Have I seen without distortion? Looking through the years, how much gets twisted?\n\nThe Nuban told me his people made ink by grinding up secrets. Here I am untangling them, and it's been a slow business.\n\nOut in the courtyard I see Rike, a massive figure dwarfing the soldiers he's drilling. I'm told he has taken a wife. I didn't enquire further.\n\nI spread the pages before me. A scribe will have to copy these out. I write in a crabbed hand, a tight unbroken line, the line I've followed from there to here, from then to now.\n\nI see my life spread out across a tabletop. I see the course of my days, how I spun about, aimless, like a child's top. Corion may have sought to guide the destination but the journey, the murderous, random, broken journey, was all mine.\n\nGog is crouched by the fire. He's grown, and not just taller. He's making shapes in the flames, having them dance. He makes a game of it until it bores him. Then he goes back to his wooden soldier, making him march, running him here and there, charging at shadows.\n\nI think about the road. Not so often now, but I still think about it. About life that begins new each morning, walking on, chasing after blood or money or shadows. It was a different me that wanted those things, a different me that wanted to break everything for the joy of breaking it, for the thrill of what it might bring. And to see who might care.\n\nI was like Gog's little wooden soldier, running in wild and meaningless circles. I can't say I'm sorry for the things I did. But I'm done with them. I wouldn't repeat those choices. I remember them. Blood is on these hands, these ink-stained hands, but I don't feel the sin. I think maybe we die every day. Maybe we're born new each dawn, a little changed, a little further on our own road. When enough days stand between you and the person you were, you're strangers. Maybe that's what growing up is. Maybe I have grown up.\n\nI said by the time I was fifteen I would be a king. And I am. And I didn't even have to kill my father to have a crown. I have The Haunt and the lands of Renar. I have towns and villages, and people who call me King. And if the people call you King, that is what you are. It's no great thing.\n\nOn the road I did things that men might call evil. There were crimes. They talk about the bishop most often, but there were many more, some darker, some more bloody. I wondered once if Corion had put that sickness in me, if I were the tool and he the architect of that violence and cruelty. I wondered if having taken his head, if having grown from boy to man, I would be a better person. I wondered if I might be the man the Nuban wanted me to be, the man Tutor Lundist hoped for.\n\nSuch a man would have shown Count Renar the mercy of a quick death. Such a man would have known his mother and brother would want no more than that. Justice, not revenge.\n\nFrom my window I can see the mountains. Beyond them lies Ancrath, and the Tall Castle. Father with his new son. Katherine in her chambers, probably hating me. And past that, Gelleth, and Storn, and a patchwork of lands that were once Empire.\n\nI won't stay here forever. I'll reach the last page and set down my quill. And when that's done I will walk out and it will all be mine. I told Bovid Tor that by fifteen I'd be King. I told him over his steaming guts. I'm telling you that by twenty I'll be Emperor. Be thankful it's just being told over this page.\n\nI'm going down to see Renar now. I keep him in the smallest of the dungeon cells. Every day I let him ask for death, and then I leave him to his pain. I think when I finish my writing I will let him have the end he seeks. I don't want to, but I know I should. I've grown. The old Jorg would have kept him there forever. I've grown, but whatever monster might be in me, it was always mine, my choice, my responsibility, my evil if you will.\n\nIt's what I am, and if you want excuses, come and take them.\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzsxeu b/data_all_eng_slimpj/shuffled/split2/finalzzsxeu
new file mode 100644
index 0000000000000000000000000000000000000000..119e1800c2f894b308fe7e61842d376dfa436293
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzsxeu
@@ -0,0 +1,5 @@
+{"text":"* style: Fixed Gear Bike,road bike, Chopper Bike, Mountain Bike,beach cruiser bike,Freestyle Bike,Folding Bike,Tandem Bike ,gasoline bike, City Bike , Kids Bike , BMX, Unicycle and Bicycle hub and other bikes parts.\nLooking for ideal Alloy One Wheel Manufacturer & supplier ? We have a wide selection at great prices to help you get creative. All the Aluminium Alloy Wheel are quality guaranteed. We are China Origin Factory of 26inch Alloy Wheel. If you have any question, please feel free to contact us.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"how to handle exception \" Object refrence not set to an instance of an object\"\nI'm testing a code written in ACE Wizard.\nThere are some calculations undergoing on the values of test input tag giving some desired output value in test output tag.\nI wanted to test , what error would come if the test input tag is deleted from the server.Expected is , I should get the ' pigetmsg -f ' log updated with message saying \"input tag (or context) is deleted something like that.\n1.While debugging the code error message I'm getting is\" Object refrence not set to an instance of an object\" (after some searching on web, I found it as same as NullRefrenceException). I can understand that I'm getting this exception because I've deleted the test input tag.\n2.With the test input tag not being in server,the related context goes erroneous in the ACE Manager i.e. current status of context show as\"error\".\n2. And If the input tag\\context is accidently deleted from server, will my context in ACE Manager always go in error state and won't run the ACE scheduler at specified time? or is there any way to avoid\\monitor this in ACE?\nThe suggestion\\answers will be very much appreciated.Thanks a lot in advance.\nRe: how to handle exception \" Object refrence not set to an instance of an object\"\nIf you catch the error, then I believe the context will stay \"green\" in ACE manager. If the error is not caught, then the context should go in error state. I would recommend using try...catch in any ACE code, and writing any exceptions to the ACE (PI SDK) logs.\nIf you delete an input tag, you will likely get \"Object reference not set to an instance of an object\" when you try to use the input PIACEPoint object. When you add input tags using the ACE wizard, the wizard automatically add code for you to initialize these PIACEPoints, e.g.\nWhen you refer to the PIACEPoint SINUSOID in your ACECalculations code, you will get an exception because SINUSOID is not properly initialize. e.g.\nIf you want to catch this error specifically, you might want to catch the exception thrown around code where the input PIACEPoints are used in your calculation. As Barry has mentioned, failure to catch the error will cause your calculation to go into an error state.\nActually I had included try and catch in my code. I was testing many test cases on it but had used single catch for returning 'ex.message' i.e. for returning system exception messages.Hence I used multiple catch and handled NullRefrenceException and also provided a message to be displayed in log for tha said exception.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This exciting thriller concerns a film actor and his wife Stella who learn that their young son has been kidnapped \u2013 but why? Events begin to move in a strange way building up the tension and suspense. This intriguing play is packed with convoluted twists and turns carrying a multitude of surprises, a kidnapped child, distraught parents, assorted villains, lethal weapons and of course a drinks trolley. Come along, soak up the atmosphere, feel the fear!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Microsoft Theater is the premier Los Angeles destination for your group outing. Discounted tickets are available for participating events. You can use group tickets to host your next company outing, enjoy an event with some friends, or create a fundraiser for your organization.\nEnjoy the show with your friends, family, club, or organization with additional experiences like no other.\nExperience the show as a group with your hand-picked seats.\nEntertain your best clients at the best venue in town.\nPersonal Representative to help guide you and answer your questions or ticketing needs.\nOrganize a group outing with your clients, co-workers, students, friends or family. Groups consist of 10 or more and tickets start at only $100!\nFor more information or to reserve group call 1.877.AEG.TICKETS (234-8425).\nOrganize a group outing with your co-workers, family or friends to Double Dare Live! For more information call 1.877.AEG.TICKETS (234-8425) or CLICK HERE.\nOrganize a group outing with your co-workers, family or friends to Peppa Pig Live! For more information, call 1.877.AEG.TICKETS (234-8425).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Jacob Ramsey has been given the number 41 jersey as the latest addition to Aston Villa's first team squad.\nThe 17-year-old attacking midfielder made his debut with a second-half substitute's cameo in the defeat to West Bromwich Albion after impressing Villa's academy staff and boss Dean Smith.\nTyrone Mings has been handed the No.40 shirt following his loan move from Premier League club Bournemouth until the end of the season.\nFellow deadline day recruit, Tom Carroll, who has joined on loan from Swansea City, has been given the No.11.\nIt is the shirt vacated by Yannick Bolasie, who cut short his temporary move from Everton. It was Gabby Agbonlahor's number before he was released in the summer.\nKortney Hause, on loan from Wolverhampton Wanderers, is No.30.\nLovre Kalinic has the No.28 shirt at Aston Villa.\nThe No.1 shirt is occupied by Orjan Nyland, who is out for the rest of the season with a ruptured achilles.\nVilla's other goalkeepers have these numbers: Jed Steer (12), Andre Moreira (23), Mark Bunn (31), Matija Sarkic (33).\nTommy Elphick is wearing the No.24 following his return from his loan spell at Hull City.\nTammy Abraham was handed the No.18 shirt for his season-long loan at Aston Villa.\nThe Chelsea striker inherited the number worn by former Tottenham Hotspur loanee Josh Onomah last season.\nJonathan Kodjia reclaimed Villa's No.26 shirt for this season following John Terry's departure.\nThe Ivorian striker wore the number during his first season at Villa Park and notched 19 goals in it.\nAs a gesture of goodwill Kodjia offered to vacate the number following Terry's arrival last summer.\nBut after a season of misfortune wearing Villa's number 22 shirt the striker reverted to his previous number earlier this summer.\nJack Grealish continues this term as Villa's No.10.\nJohn McGinn is No.7 and Anwar El Ghazi No.22.\nBecause Micah Richards and Ross McCormack are both surplus to requirements neither has been allocated a shirt number this season.\nOut on loan: Aaron Tshibola (Kilmarnock), Gary Gardner (Birmingham City), Ritchie De Laet (Melbourne City), Rushian Hepburn-Murphy (Cambridge United), Jake Doyle-Hayes (Cambridge United), Mitch Clark (Port Vale), Scott Hogan (Sheffield United), James Bree (Ipswich Town).\nWithout squad numbers: Ross McCormack, Micah Richards.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzztuqu b/data_all_eng_slimpj/shuffled/split2/finalzztuqu
new file mode 100644
index 0000000000000000000000000000000000000000..a05764f37eac6c7dba17c5f2e9484879492608ce
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzztuqu
@@ -0,0 +1,5 @@
+{"text":"TRAL: Sarva Shiksha Abhiyan (SSA) teachers staged protests in Tral area of South Kashmir on Saturday morning to demand implementation of 7th pay commission.\nThe protests were held near ZEO office main town Tral and ZEO office Lurgam, in which large number of SSA teachers participated.\nThey also demanded de-linking of their salary from Ministry of Human Resource and Development (MHRD) to state.\nThe teachers alleged that despite back to back requests, authorities failed to fulfill their demands.\nThey were chanting slogans in favour of their demands and in praising of Qayoom Wani and appealed authorities to fulfill their demands as soon as possible.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Offshore Online Data Entry has been climbing the ladders of success in the outsourcing sector for the past five years. And since the commencement of our services, we have strived hard every single day to perform better than the previous day.\nWe have adopted the contemporary technologies and tools to deliver the best results. We do keep a check on the latest trends of every industry so that we can serve our clients in a better and efficient way.\nMost of the firms in the custom industry, undergo various challenges. We offer an effective custom brokerage BPO service to the industry by supporting the speedy clearance of the cargo customs and also boosting up the supply chain efficiency for the business.\nHealthcare \u2013 Offline Online Data Entry offers a comprehensive group of Healthcare BPO services which benefit the healthcare sector by smoothening and minimizing the hassles of the healthcare administration and enhancing the performance. We offer the assistance from the patient admission and charge capture to the receivables management.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This page lists the chart runs for songs called \"It's Like That\" in order of success. This list combines cover versions and distinct songs that happen to share the same title.\nPer Wikipedia there are (2) separate versions of this song; the original 1983version by Run DMC & this 1997 remix with Run DMC & Jason Nevins. The following (3) Chart Entries should be removed from this 1997 version & set up as a separate 1983 song by just Run DMC. +1. nuTsie 61 of 1980's. 2. Acclaimed 1050 (1983). 3. RYM 29 of 1983.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"It is someone who is an ally, a partner.\nIt is having someone who believes in you and your ability to change until you can believe in yourself.\nIt is someone who shows you how to take life's challenges that you have let stand in your way and turn them into growth opportunities.\nIt is someone that guides you to find your own truth and to live from your integrity.\nIt is someone that will help you discover what's really most important to you in your life, then we'll help you design a plan to achieve those things.\nIt is someone who remains objective while you discover who you really are.\nIt is someone who asks you to take action steps toward challenging old belief systems that have kept you stuck.\nIt is someone who holds you accountable to yourself, who provides honest feedback and may not always tell you what you want to hear but will always tell you what you need to hear.\nIt is someone who truly wants for you what you most want for yourself.\nIvy League Educational Services believes that it is possible to live the life you were meant to live. We believe that by uncovering what is keeping you stuck and overwhelmed that you will find the real authentic you. We will work with you to eliminate any obstacles or blocks that stand in your way. We will partner with you all the way to success. then will celebrate with you!\nIvy League Educational Services believes that it is possible to create a loving family atmosphere in which to support your children as they experience the pain and joy of their own growth. We as parents can provide for them a safe and nurturing atmosphere in which they can come to know the significance of their own choices and what they value in life.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The California Department of Technology supports is close to 150 state entities providing government services, so securing all those systems can be a heavy lift. To help the state get a better handle on the effectiveness of its security programs, CDT devised the California Cybersecurity Maturity Metrics to benchmark agencies' security posture and measure progress as audits and improvements are made.\nThe metrics take best practices from the National Institute of Standards and Technology's Cybersecurity Framework and the Center for Internet Security's top 20 controls, then tailors them for California agencies. They were created through a year-long effort, involving CDT, the California Cybersecurity Integration Center, California Highway Patrol and the California Military Department.\n\"We held almost a dozen workshops with half of the departments in the state sending representatives,\" California Chief Information Security Officer Peter Liebert told GCN.\nThe maturity metrics will be gathered from sources agencies already use, such as those collected during audits by the CDT's Office of Information Security or through independent security assessments, according to the Statewide Information Management Manual.\nIdentify: Governance, data and system categorization and vulnerability scanning.\nProtect: Account management, encryption and system configurations.\nDetect: Network and end-point monitoring.\nRespond: Incident response plans and testing.\nRecover: Technology recovery plans and testing.\n\"We decided to use the five categories in NIST's [Cybersecurity Framework] so this framework makes sense for leaders who are not very savvy in the cybersecurity space to be able to compare their agencies to others,\" Liebert said.\nThe scores are weighted, with a \"0\" indicating low program maturity and a \"4\" representing high program maturity scale, according to a CDT technology letter.\nThe maturity metrics focus on measures that will provide the highest return on investment -- i.e., those leveraging existing assets and those that help agencies balance cybersecurity visibility, decision-making and efficiency in resource allocation and overall security spending, according to CDT's 2017 Annual Report. They will also help CDT track gaps and statewide trends so it can identify where additional guidance, training and remediation support can help improve cybersecurity.\nTracking the maturity metrics will run on a four-year cycle. In the first year, environments are examined for policy requirements. The second year examines compliance with the metrics set out by the Cybersecurity Framework, and the final two years examine the results from the independent security assessments to determine changes from the initial baseline measurements.\nThe metrics are also meant to complement the assessments that the California Military Department already conducts for many agencies through its cybercrime division. CDT's Office of Information Security also performs policy-based audits for high-risk entities.\nThe metrics can help empower smaller state agencies to make a case for improving their cybersecurity posture despite having a smaller workforce, Leibert said.\nAccording to NIST, more than 20 states are using its Cybersecurity Framework to improve their cybersecurity posture.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzuzxz b/data_all_eng_slimpj/shuffled/split2/finalzzuzxz
new file mode 100644
index 0000000000000000000000000000000000000000..2eb3d0164f4cea802a643a6dae66f8aaae6a598f
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzuzxz
@@ -0,0 +1,5 @@
+{"text":"Microsoft Word 2013: Introductory - Ebook written by Misty E. Vermaat. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Microsoft Word 2013: Introductory.... microsoft office 2013 essential shelly cashman Download Book Microsoft Office 2013 Essential Shelly Cashman in PDF format. You can Read Online Microsoft Office 2013 Essential Shelly Cashman here in PDF, EPUB, Mobi or Docx formats.\nDownload microsoft word 2013 complete or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get microsoft word 2013 complete book now. This site is like a library, Use search box in the widget to get ebook that you want. exam 77 418 microsoft word 2013 pdf Misty E. Vermaat has more than 25 years of experience in the field of computer and information technology. In addition to consulting in the field, she was an Associate Professor at Purdue University Calumet, teaching or developing Microsoft Office, computer concepts, database management, systems analysis and design, and programming courses.\nClick Download or Read Online button to get microsoft office 2013 introductory shelly cashman in pdf book now. This site is like a library, Use search box in the widget to get ebook that you want. This site is like a library, Use search box in the widget to get ebook that you want.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Melissa is currently pursuing her Ed. M at Harvard University's Graduate School of Education. She is a full time Associate Professor in the Songwriting Department at Berklee College of Music and the Artistic Director of the Performing Songwriter Division for the Berklee Five Week Program.\nMs. Ferrick has released 17 albums over the last 24 years. Signed to Atlantic Records in 1992 at the age of 21, after opening up for Morrissey in the US and UK, she released her debut and sophomore albums on Atlantic. Between 1996-1999 she released three albums via Independent label W.A.R. Records. Melissa launched the nationally distributed independent record label Right On Records in 2000. Her publishing catalog is represented worldwide by The Raleigh Music Group.\nRegarded in the industry and by her peers as one of the most prolific and hardworking artists in the business, Ferrick still tours regularly playing throughout North America. She has shared the stage with Morrissey, Marc Cohn, Paul Westerberg, John Hiatt, Joan Armatrading, Weezer, Tegan and Sara, G-Love & Special Sauce, Bob Dylan, Dan Bern, Ani DiFranco, k.d. Lang, Suzanne Vega, Shawn Colvin, and many others.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This \"war story\" was submitted by Stephan P. Zacharias, grandson of SSgt David P. Spears, KIA 24 July 66 in the Ia Drang Valley.\nSSgt Spears was the \"Chief of Smoke\" for \"B\" Battery. He was an \"original\" - he came over from Hickam Air Force Base as part of the 3rd Brigade, 25th Infantry Division's deployment to the Central Highlands of Vietnam in December, 1965, known as \"Operation Blue Light\". SSgt Spears was one of the \"pioneers\" for many redlegs to follow.\nRumor has it that all the men of \"B\" Battery, 2\/9th FA, tell the same story. As any graduate of Ft Sill, Okla, knows, a 105mm battery consists of six (6) howitzers. Yet \"B\" Battery only had five (5) howitzers. They're not easy to confiscate nor embezzle, so it begs the question...what happened to the #6 howitzer?\nApparently, \"B\" Battery was dissatisfied with the performance of one of the cannons and had asked to have it replaced. Their request for a new one was denied several times. So...the story goes, \"someone\" decided to order it lifted by a Chinook and dropped back to the ground. This would surely put it out of commission and force the issue of replacement. The photos above lend some credence to the story, but we do know that \"B\" Battery was in service for a time with only five howitzers.\nWonder how long that requisition floated around the US Army's logistics system?\nOne of six howitzers remained back in Base Camp in order to create a gun section there. Thus, it left us, \"B\" Battery, with 5 howitzers in the field.\nthe gun crews would take turns rotating from field to Base Camp for some \"in country\" R&R. But, the FDC did not rotate! So, our Battery stayed in the field all the time and the gun sections were rotated to Base Camp. This all occurred early in the deployment to Viet Nam and stayed this way for my whole tour.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Seattle was second Wild Card ahead of Denver based on better division record (5-3 to Broncos' 3-5) after Cleveland was eliminated from three-way tie based on head-to-head record (Seattle and Denver 2-1 to Browns' 0-2). Seattle did not play the L.A. Raiders in the divisional playoffs because, from 1970-1989, two teams from the same division could not meet prior to the conference championship game. New England finished ahead of Buffalo based on head-to-head sweep (2-0). Baltimore finished ahead of N.Y. Jets based on better conference record (5-9 to Jets' 4-8). San Diego finished ahead of Kansas City based on head-to-head sweep (2-0). Green Bay finished ahead of Chicago based on better record against common opponents (5-5 to Bears' 4-6) after Minnesota was eliminated from three-way tie based on conference record (Chicago 7-7 and Green Bay 6-6 to Vikings' 4-8).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Even the church has jumped on the health food wagon.\n\"Even the church has jumped on the health food wagon.\"\nWell, actually, it was churches who started the health food wagon. Specifically, it was the Seventh-day Adventist Church, and one of its early families in particular. The Adventist church headquarters from 1863 to 1905 was in Battle Creek, MI. An Adventist institution there was Battle Creek Sanitarium. The doctor in charge of it was a fellow named John Harvey Kellogg, whose brother Will Keith Kellogg put his signature on the boxes of cornflakes and other cereals that his brother developed.\nWow. Mr. Cork should host Taste of America. I never knew any of that, but it was very interesting.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzvmmh b/data_all_eng_slimpj/shuffled/split2/finalzzvmmh
new file mode 100644
index 0000000000000000000000000000000000000000..6418a79a9e80ca86e308195b5b69b5cddeed1fa2
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzvmmh
@@ -0,0 +1,5 @@
+{"text":"I have enabled a 301 redirect, so it should come here automatically anyway, but it may not stay that way forever.\nI have quite a few thoughts on the upcoming storm season. We are in a La Nina cycle right now, which can explain the early season, East of the norm, tornado outbreaks we've seen so far (all things that normally occur during La Nina). For the early season, it should be dryer and warmer than normal. I don't like the farther East than normal factor, I hate chasing in the forrest covered hill\/mountain areas. The scary part is there could be more outbreaks, but not likely. Farther into the normal chase season for us, April - June, the El Nina conditions are forecasted to lighten up, which could improve our Oklahoma chase season, but will still be rather dry, meaning I think we'll see more chase days bust do to the cap holding. This could be good in some aspects, as the way things do go, we should see more discreet cells with fewer of those \"gunk\" days where it's hard to determine where to go just by looking out the window. I'm a little up in the air about a mid-May, early June outbreak, but if we do have one in the southern-central plains, my guess is that will be the timeframe (the more I think about it, the earlier I want to shift that timeline).\nNow on to the political predictions. Several weeks before the super Tuesday elections, I decided to go for Obama. Not because he's going to win, which he will, but because I haven't really liked the retoric and tone I've been hearing from the Clinton camp. I really like the new\/fresh perspective Obama comes across with, and the more I listen to his debates, speeches, etc, the more I really think he is a logical and intelligent leader, something we've been without for quite some time. It's good to see the tide turning, and we will likely see a McCain \/ Obama matchup for November. McCain's chances then will depend largely on who he picks for a runningmate. If he does pick Huckabee and can draw in a large portion of the conservative religous right (he will have to change his tone on many issues, which I suspect he will once he has his party's nomination secured), he will have a fighting chance come the big race.\nTuesday eve \/ night, there is a tornado outbreak of historic proportions, and where am I? Too busy to post during the day and day after because I'm busiest I've ever been at work, and the evening of, I took my girls to a movie of the Hanna Montana concert we had pre-purchased tickets to. Not to mention the after hours work I've been doing taking up any other spare time I may have. I know, wah, wah, wah... On the bright side, we should get a 3rd net specialist hired at work next week. That should free up some time. :) The other benefit is that I'm building up time for this spring.\nSteve, great coverage man! Also, all the others who were able to cover this. Hopefully, this won't happen again anytime soon.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Hay Ori Grinder is a highly modern, sculptural kitchen accessory featuring a pentagonal design. These unique designs from Norwegian duo Anderssen & Voll offer a strong visual presence, making them perfect statement pieces for the dining table.\nThis is Nest Manila locations coverage, but we are currently working in expanding our reach. If your address is located at a non-serviceable area, you may get in touch with us as we can work out a plan for your order.\nThis series of Japanese Glass Jars has a simple, see-through, stackable design with four different sizes and an acrylic lid.\nWith its organic, soft shape and complementary combinations in clear and coloured glass with fine sand, HAY's Time hourglass offers a contemporary twist on the classic hourglass timer.\nA golden, silver-coloured or rainbow tray in stainless steel.\nA respectful nod to the 1970s: a Ballograf ballpoint pen tethered with a metal bead chain. HAY has established a collaboration with Ballograf and created three ballpoint pens with a base and a metal chain in an updated and contemporary colour scale that draws Ballograf's functional writing utensil into HAYs universe.\nDimensions : \u00d85 x H18 cm.\nFor the custom lettering, Nest manila will send you an email after you purchase the item .","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Term of Office is January 1, 2019 to December 31, 2021 Nominations will be accepted at the September 11, 2018 Meeting with Election on December 4, 2018.\nTerm of Office will be from January 1, 2018 to December 31, 2019.\nNominations will be accepted at the September 12, 2017 with Election on December 05, 2017.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\"Our Academy was born with the aim of filling the gap between developers\/producers of technology for the sailing world and final users. The way to get sailors more involved and passionate about technology is to teach them and show them everything they can do with electronics and computers, how easily many things can be done, and what are the benefits. We are an itinerant academy that offers courses (online, in classrooms and onboard) at different levels to cover the whole range of people that are part of the sailing world: racers, cruisers, dinghy sailors, offshore navigators, coaches, race officers. The Academy works with the most important companies in the tech-sailing world, like Adrena, to be able to offer the students the best interactive courses focused on those technologies.\" Gilberto Pastorella, OceanDrivers Academy Director.\nWe are delighted to welcome Carlos Freire from VMG Racing Electronics as a new dealer in Spain. Experience, quality and personalized service are the pillars of VMG Racing Electronics. The team consists of engineers, technicians and navigators with extensive professional experience in racing boat electronics and computing. They have been working for the best teams for many years and are able to help you with your Adrena configuration.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Population growth, rising incomes, changing diets and an increased desire for premium imported food and beverage products across Asia Pacific presents significant opportunities for the food and agribusiness sector across the region.\nAs tariffs, quotas and other traditional barriers to trade gradually decline with the growth in free trade agreements, the focus on entering the Asia Pacific market has increased significantly. However, the regulatory regimes in many Asia Pacific jurisdictions are complex and sometimes unpredictable. This in itself creates a barrier to trade.\nThe purpose of this searchable and comparative microsite is to summarise food law regulation in 11 jurisdictions across Asia Pacific and to help food businesses navigate the complex regulatory area. Topics covered in the guide include local language and basic labelling requirements, country of origin labelling, mandatory warnings, product registration, import permit and clearance requirements. Changes to the local laws and regulations in some of these areas occur frequently. Whilst we endeavour to keep the site updated, we invite you to seek specific and current advice as needed from appropriate Baker McKenzie contacts.\nTo get started, click on Compare Jurisdictions and Topics or Select a Jurisdiction buttons. To download the PDF copy that you can read offline, click on this thumbnail.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzvnjq b/data_all_eng_slimpj/shuffled/split2/finalzzvnjq
new file mode 100644
index 0000000000000000000000000000000000000000..ff90db9c7bad8d92de0b402510d21333e2d4af55
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzvnjq
@@ -0,0 +1,5 @@
+{"text":"Pay your MacBook Pro (early 2015 and Mid-2015 models) the ultimate complement with our premium Leather Suit. Genuine Pebbled Floater leather combined with contrasting, smooth Caterena leather accents wrap your device in ultimate luxury.\nFour integrated, \"feet\" offer unparalleled grip and stability on almost any surface. Customized cutouts offer direct access to all of the Mac's built-in features. From critical presentations to surfing the internet, our distinguished Leather Suit insures that your device is always dressed for success.\nEach Leather Suit for your MacBook is meticulously handcrafted to offer the highest level of quality and construction. We carefully inspect and select all of our full-grain hides from the top 10% of Argentinian leather, world-renowned for its unrivalled beauty and strength.\nChoose from a seemingly endless color palate of our premium textured, Floater leather for the exterior and match it with the accent stripe color of your choice for the ultimate in personal expression. Or take advantage of our customizer and create the exclusive, one-of-a-kind case you've always dreamed of.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Our company since its inception, always regards product quality as enterprise life, continuously improve production technology, improve product quality and continuously strengthen enterprise total quality management, in strict accordance with the national standard ISO 9001:2000 for Popular Cool Usb Flash Drive , Popular Cool USB Flash Drive , Popular Wooden USB Flash Drives , The mission of our firm should be to provide the best high quality goods with finest price tag. We've been on the lookout forward to doing organization with you!\n\"We always continually provide you with one of the most conscientious client provider, as well as widest variety of designs and styles with finest materials. These initiatives include the availability of customized designs with speed and dispatch for Popular Cool Usb Flash Drive , Popular Cool USB Flash Drive , Popular Wooden USB Flash Drives , Seattle With the enterprising spirit of\" high efficiency convenience practicality and innovation\" and in line with such serving guidance of \"good quality but better price \" and \"global credit\" we are striving to cooperate with the automobile parts companies all over the world to make a win-win partnership.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Men deserve better. It's that simple. That's why we've invested millions of pounds into research, services and awareness over the last 10 years. It's the reason we provide services to men and their families like our Specialist Nurses, one-to-one support and information leaflets. It's why we're leading the way in providing prostate education to medical professionals. It's why we don't take no for an answer when it comes to fighting our campaigns. We are Prostate Cancer UK.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\/2 Some of the investors are unsophisticated (inevitably), or desperate (people in hyperinflation economies). Financial regulation is designed to help such people. The crypto bubble came was faster than financial regulators could respond.\nSome oil industry news. In July 2018 President Buhari approved new Gas Flaring Regulations for Nigeria -- The Flare Gas Reduction (Prevention of Waste and Pollution) Regulation 2018.\nHere are the implications - as well as economic opportunities.\nThe Nigerian Gas Flare Commercialization Programme (NGFCP) seeks to end Gas Flaring in Nigeria by 2020, while also ensuring that Nigeria is able to monetize flared gas on a commercial basis. Multiple benefits: jobs, investment, climate, gas-to-power, etc.\n\ud83e\udd14Wonder if he knows that's the whole point.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Rosetta Genomics President and CEO Kenneth Berlin is resigning from the company effective April 18 to pursue other opportunities. He will assist the company in a smooth transition with ongoing projects, the company said. Berlin joined Rosetta Genomics in November 2009 as president and CEO. Before that, he was worldwide general manager at Veridex, a Johnson & Johnson company. He joined J&J in 1994 and was its corporate counsel for six years, according to Rosetta Genomics' website. From 2001 to 2004, he was vice president of licensing and new business development in the pharmaceutical group at J&J, and from 2004 to 2007, he was worldwide VP of franchise development at Ortho Clinical Diagnostics, also a J&J company.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzvpqe b/data_all_eng_slimpj/shuffled/split2/finalzzvpqe
new file mode 100644
index 0000000000000000000000000000000000000000..4c106bbe5c2b5dfbf5a31ae93fe36bf25a39f7e2
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzvpqe
@@ -0,0 +1,5 @@
+{"text":"The World Socialist Web Site is publishing today the Editorial Board Statement \"Stop the US war drive against Iran!\" in Farsi, or Persian. Farsi is the official language of Iran, where it is spoken by more than half the country's population of 70 million, as well as a significant Iranian diaspora around the world. Farsi dialects are also spoken in neighbouring Afghanistan and Central Asia. The dialect known as Dari is an official language in Afghanistan, where it is spoken by about a quarter of the population.\nOriginally posted in English on February 14, the WSWS statement condemns the Bush administration's provocative military and political preparations for an attack on Iran. While opposing the US war drive, the statement does not give any political support to Iran's reactionary clericalist regime. It advances a socialist and internationalist perspective to unify workers throughout the Middle East and Central Asia with the working class in America and around the world.\nIn posting the statement in Farsi, the World Socialist Web Site is seeking to broaden the discussion with workers, intellectuals and young people about the necessity of building an independent movement of the working class on the basis of genuine socialist principles. We invite comment and feedback from Farsi readers. We hope to publish further WSWS articles and statements in Farsi in the future.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"USCIS administers the immigration program by facilitating permanent residency (green card) in the United States for investors and entrepreneurs, as well as their spouses and unmarried children under the age of 21.\nWhat are the requirements for the EB-5 visa?\n1. The EB-5 investor must make an investment in a commercial enterprise in the United States.\nThe entrepreneur must invest capital, such as cash, property, and assets into a new commercial enterprise. The minimum qualifying investment in the United States is $1 million dollars. However, in an effort to promote economic growth in high unemployment or rural areas, the minimum qualifying investment is reduced to $500,000.\nFurther, the commercial enterprise must be considered a lawful business that generates profitable revenue, such as a corporation, holding company, partnership, business trust, sole proprietorship, and other business entity or venture.\n2. An investor must plan to create or preserve 10 permanent full-time jobs for qualified U.S. workers.\nThe EB-5 investment must create jobs. All employees under the EB-5 plan must be authorized to work in the United States, work a minimum of 35 hours a week, and be permanent employees (i.e. not intermittent, seasonal or temporary).\nProof of Investment (or active process of investment) of the required amount and that such investment was attained through lawful means. Evidence includes: source of capital, tax returns, and business registrations records.\nProof of the Commercial Enterprise: documents showing the establishment of the business.\nProof of Management: It is required to submit evidence of your intended management of the enterprise, such as duties or responsibilities in the day-to-day control of the enterprise or formulation of policy.\nProof of Job Creation: proof that the enterprise will create at least 10 full-time positions for qualifying employees.\nIf employees are not yet hired: the EB-5 investor must submit a comprehensive business plan showing that there is a need for at least 10 qualifying employees based on the nature and projected size of the enterprise.\nIf employees are already hired: the EB-5 investor must show the number of existing employees will be maintained according to the requirements for at least two years. Required documents include: photocopies of tax records, Form I-9, Employment Eligibility Verification, or other relevant documents for the qualifying employees and a comprehensive business plan in support of the petition.\nThese are the general requirements for EB-5 investors and entrepreneurs. Feel free to share your specific questions or comments about the EB-5 process below or get in touch with us.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Savannah's is a family owned business in the heart of downtown Hannibal, MO. Come and experience a bright, cheerful place where you'll love to explore and take a relaxing stroll down memory lane! Our eclectic inventory includes antiques, furniture, vintage, chic, jewelry, collectibles, and home decor. We bring in exciting new items every day! Stay tuned for sales and events.\nRepurposed furniture and antiques are one of a kind items, distinguished by the era they originated from and their rarity. They're valuable precisely because they were made by production methods and materials that are no longer used in modern manufacturing processes. Vintage items are marked by an aesthetic appeal that defies the test of time. They are beautiful no matter how old they become. Moreover, antique furniture can be utilized as part of your home decor displays your appreciation for history and timeless aesthetics.\nAntiques can take on a variety of forms and come in all shapes and sizes. They can be clocks, lamps, paintings, furniture, jewelry, or sculptures. When you visit Savannah's, you will be able to explore an array of antique pieces and used furniture that add appeal to any home interior. Whether you want to put an old time grandfather clock in your study or a rustic style coffee table to your living room, we've got a fantastic selection of decor items to suit your needs.\nContact or visit our furniture store for great home decor and vintage furniture in Hannibal, MO today!\nSavannah's \u00a9 All Rights Reserved.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"An invasive species is any organism (plant, animal, insect, disease, etc.) that has been introduced to an area outside of its native range, has a tendency to spread, and threatens the environmental, economic or social health of the area to which it has been introduced.\nWe move species around the world every day, both intentionally and unintentionally, through our social and economic activities, and naturally through environmental pathways. Invasive species tend to show up more around urban centres and transportation hubs.\nMany well-established invasive species on PEI arrived here long ago. Some of them arrived with early settlers that brought plants with them, to their new home, as a memory of their homeland or for their medicinal properties.\nMany invasive species have traits that make them excellent invaders. These traits include small seed mass and seed adaptations that allow for greater dispersal and rapid expansion of invasive populations. Some adaptations can allow seeds to easily attach to clothing or our pet's fur, or get stuck in our boot treads. If our equipment or pets are not properly cleaned before outings, we could be spreading invasive plant seeds to new areas. Anytime you are hiking, biking, or walking your pet in a natural area, be sure to clean all of your equipment, and your pet, before exploring a different natural area.\nRecreational boating is a significant pathway for the spread of aquatic invasive species. Small animals (e.g. zebra mussels (Dreissena polymorpha)) can attach themselves to boat hulls and aquatic plants (e.g. Canada waterweed (Elodea canadensis)) can get tangled in propellers and trailers. If boats are not properly cleaned, they can end up giving these invasive \"hitchhikers\" a ride to a new waterway.\nFeeding wild birds is a popular pastime. Unfortunately, the seed mixes we buy often contain invasive weed seeds. Seeds that end up on the ground underneath of bird feeders can establish, flower and spread. Research from Oregon State University found that 10 common brands of seed sold in retail stores contained more than 50 weed species.\nThe movement of firewood is another important pathway for invasive species. Some invasive insects can bore into wood (e.g. emerald ash borer), while others lay their eggs on wood (e.g. gypsy moth), making the movement of firewood an effective pathway for invasive species.\nGardeners may be contributing to the spread of invasive species by dumping unwanted plants in natural areas. Often, when an invasive takes over a garden patch, gardens will remove the plant and dump the plant debris in a nearby woodlot or field. Those invasive species often survive and give rise to new invasive species infestations.\nFor information on how to properly dispose of invasive species, visit our FAQ page.\nAgriculture is a major vector for invasive species introductions. Many invasive plants have been introduced intentionally as agriculture crops and then later escaped cultivation. An example of this is white sweet clover (Melilotus albus), which was intentionally planted as a forage crop. Now, white sweet clover is ubiquitous on PEI \u2013 you can find it growing around farmers' fields and along roadsides across the Island.\nInvasive species have also been introduced unintentionally through agriculture via contaminated seeds and soil.\nThe horticulture industry is a significant pathway for invasive species. Most of the flowers and trees that are sold at greenhouses and garden centres are not native; and most are not invasive, however some are. On PEI, there is no legislation prohibiting businesses and individuals from selling or trading invasive species \u2013 except for The Weed Act, which only regulates one species, purple loosestrife (Lythrum salicaria). Many of the invasive species we have on PEI are consequences of the horticulture industry. For example, Himalayan balsam (Impatiens glandulifera) was brought to North America from Asia as an ornamental plant. It escaped cultivation and is now on invasive species lists across the country.\nAdditionally, imported flowers and trees can carry new diseases and insects that also have the potential to become invasive.\nThe forestry industry is a major pathway for invasive species. Equipment used for land-clearing, if not properly cleaned, could result in the spread of invasive species. Sometimes trees planted for commercial forestry are non-native and may become invasive. The movement of raw lumber and wood products can be a vector for the spread of invasive forest insects or disease.\nPets and game species are sometimes released into the wider environment, and sometimes they become invasive. Pets are often released because their owners no longer can or want to care for them, and game species are released for recreational hunting or fishing purposes. An example of this is the release of goldfish into pond systems by pet owners. Goldfish introductions have become a major issue in some jurisdictions in Canada and the U.S.\nOur world has become incredibly connected. The goods we buy at the grocery store may be from half way around the world. As we move goods around, we are potentially also moving invasive species. The shipping process is a significant pathway for invasive species. Many invasives that are present on PEI arrived here as a result of the shipping industry. Common Reed Grass (Phragmites australis ssp. australis) is a serious issue for wetlands across Canada, and arrived in North America accidentally via ballast materials. Some invasive, wood-boring insects have been introduced to new areas by the movement of wood pallets used for shipping.\nAs individuals travel, they could unknowingly be carrying invasive plant seeds on their shoes and clothing, and furthering the spread of invasive species.\nMany invasive plants have special adaptations that enhance their ability to disperse seed and spread further. Some of these adaptations take advantage of the movement of wildlife. In this way wildlife can contribute to the spread of invasive species. For instance, common buckthorn (Rhamnus cathartica) produces berries which contain its seeds. The berries often persist into the winter months, making it an attract food source for wintering birds. However, the berries also contain a natural laxative so seeds are quickly spread by birds who eat the berries.\nCommon buckthorn fruit cluster. Photo by Green Thumb Photography.\nAnother common seed adaptation of invasive species is small seed mass. A small mass allows seeds to be carried on the wind. Invasive fungi spores and flying insects may be moved as a result of wind as well. Some invasive species' seeds are buoyant, allowing seeds to float and disperse naturally via waterways.\nAs our climate changes, we are seeing extended springs and late winters. We are changing the conditions for all living things around us. The extended growing season is particularly beneficial for invasive plant species, which are adaptable enough to change their flowering schedule to emerge and bloom earlier in the spring. This gives invaders the benefit of being able to take advantage of limited resources before native species get a chance to. Native species are slower to adapt to these changing conditions.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Stiassny, M.L.J. and Alter, S.E. Journal Article 2015 Phylogenetics of Teleogramma, a riverine clade of African cichlid fishes, with a description of the deep-water molluskivore \u2014Teleogramma obama \u2014 from the lower reaches of the middle Congo River.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzwihy b/data_all_eng_slimpj/shuffled/split2/finalzzwihy
new file mode 100644
index 0000000000000000000000000000000000000000..44adbdb5712730f3c4c67afe951c3796f1f87d10
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzwihy
@@ -0,0 +1,5 @@
+{"text":"Duck breasts are one of my favorite ingredients and probably my single favorite meat. They offer all the depth of flavor of beef, a very slight hint of gaminess and then there is the skin, the real prize. Duck and orange have a famous and natural affinity, and when I think of orange my mind goes to Spain. That, in turn sends me to chorizo \u2013 the Spanish hard stuff, not the greasy (if wonderful) Mexican product of the same name. And somehow when I think about pork products, beans come to mind. Never more so than when I saw fresh cranberry beans at Specialty Produce.\nAnd that explains this whole dish\u2026except for the carrots. I have no excuse for why I chose to do the carrots than the simple fact that they were in the bin next to the cranberry beans and looked gorgeous. Somehow it seemed like a natural. More importantly, it worked out well on the plate.\nCook the Cranberry Beans. Shell the cranberry beans. Place them in a sauce pan with water covering the beans by an inch and add the salt and herbs. Bring the water to a boil, reduce to a simmer and cook until the beans are cooked through, about one hour.\nMake the Blood Orange Chorizo Sauce. Dice the chorizo and place the mea, along with the shallots and olive oil in a sauce pan over high heat. When the shallots and chorizo begin to sizzle add the liquids and bring to a boil. Reduce the heat to low and simmer slowly until reduced to about \u00bd cup, approximately half an hour.\nPrep the Duck Breast. Preheat the oven to 400\u00b0 Fahrenheit. Score the skin of the duck breast, cutting through the skin and fat but not the flesh. Season the breasts with kosher salt and freshly ground black pepper.\nRoast the Carrots. Drizzle the extra virgin olive oil over the carrots in a half hotel pan and season with salt and pepper. Shake the pan to coat all the carrots with the oil. Roast the carrots in the oven for ten minutes before proceeding to the next step. Continue cooking the carrots after lowering the heat for the duck breasts.\n\"Fry\" the Leeks for the Garnish. Remove the outermost layer of the leek and slice it, lengthwise into long strips. Stretch some plastic wrap over a large plate and spray it with canola oil. Arrange leek strips on the plate. Set your microwave oven to 800 watts (the precise strength setting will depend on the total maximum wattage of your microwave oven; for me it was 6) and fry the leek strips for about 3-5 minutes, until the strips are just crunchy and beginning to brown.\nPan Sear the Duck Breasts. Meanwhile, add the grapeseed oil to a small frying pan over medium heat. Place the duck breasts skin side down and fry gently, rendering the fat until the skin is crisp and golden, about five minutes. Turn over the duck breasts and sear them for 2 minutes.\nRoast the Duck Breasts. Reduce the heat in the oven to 375\u00b0 Fahrenheit Roast the duck breasts in the oven at until just cooked and pink in the middle, about three minutes. Remove the pan from the oven and rest the breasts on a cutting board for 2-3 minutes.\nPlate the Dish. Remove the carrots from the oven. Slice the duck breasts lengthwise. Arrange the carrots at the center of a plate. Arrange the duck breast on top of the carrots. Distribute the beans around the carrots. Pour the sauce over the duck breasts. Garnish with the fried leeks and the herb oil (if using).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Posted March 30th, 2016 .\nThe FDC team in Western Australia recently completed in the Rottnest Channel Swim.\nHighly regarded worldwide and one of Western Australia's iconic events, the Karma Resorts Rottnest Channel Swim is a 19.7 kilometre open water swim from Cottesloe Beach to Rottnest Island. Whether competing as a solo, duo or team, the Karma Resorts Rottnest Channel Swim is a 'team' event with all swimmers surrounded by a support network of paddlers, boat skippers and crew.\nIt was an enjoyable event and with a great support crew behind them, our swimmers crossed the finish line 7 hours and 11 minutes later! Funds raised from the event go towards the Australian Cancer Research Foundation.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Whether you want to use it to decorate a present, as a note in your study book or use it as a reminder of something, you are able to find a sticker that matches your need. Monograph's wide range of stickers consists of round stickers with small statements, square stickey notes etc. With the stickers from Monograph, you can both decorate but also use them for practical matters during the day. Try for instance to remember your daily doings by writing them on a sticker and place it on a noticeboard.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Go on a culinary journey without leaving the Born. Fourteen gourmet food stands serve a variety of tapas and small dishes. The market is located in a 14th century palace with stonewalls, rounded arches and a sunlit interior courtyard. The atmosphere is historical yet fun-filled, and the long bars and tables provide plenty of space for children to eat, learn and play.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Welcome friends to Natasha In Oz! I'm so glad you stopped by to say G'Day today. I hope you will have time to stay for a cuppa.\nLast week Marty posted about her friend who stages homes for a custom builder and she posted lots of great pictures of her beautifully \"staged\" kitchen. Looking at all of her pictures inspired me to do a bit of staged decorating around our home so I thought I would start with my nightstand.\nA beautiful friend gave me these darling little vases for my birthday so I added some tiny roses to tie in with the pink rose embroidery on the tissue box cover.\nThe vases are sitting on a linen doily that I found in an Antique market a while ago. I bought 2 of them for $2.\nI also added a beautiful Waterford crystal clock to my nightstand vignette. It was a wedding gift.\nThe lamp shade and base are from Laura Ashley and the base is made of solid brass.\nThe tissue box cover comes from Ireland. We bought it in Ireland at the Blarney Woolen Mills.\nAnd here is the finished vignette!\nIt doesn't look this pretty all the time, though, I assure you!\nalways served in our Spode Blue Italian china and always Yorkshire tea.\nI always have a photo of my kids and my hand cream on my nightstand.\nI haven't forgotten about a photo of sweet hubby...our wedding picture is hanging on the wall right near our bed!\nThis is the first thing I see when I wake up in the morning!\nThank you for inspiring me to do a bit of a tidy up of my nightstand Marty! I know it won't stay this lovely for too long but I had fun doing it.\nIf you have time please also go and check out the blog I share with my sisters, 3 Sisters, 365. My sister Holly has posted a picture of the most amazing collection of tea cups that I have ever seen! They have been displayed in a most creative and unusual way....wait 'til you see it!\nThanks so much for visiting today and for spending time with me today in my little corner of the world Down Under! I love meeting new friends from all over the world and I am so grateful for all of the friends I have made through blogging. Thank you to the sweet people who have signed up to follow me too! If I haven't come by to follow you yet please let me know and I will be there quick smart! If you have time please also leave a comment to let me know you have come to visit-reading your comments makes my day!\nIsn't it great the inspiration we get in blog land! Love the cup and saucer. Nest to my bed is always overflowing with magazines too!!!\nWhat a wonderful post! Love your Spode teacup and how nice of your hubby to bring you tea in bed! You and your hubby are a cute couple! Hubby and I celebrate our anniversary this week which I will likely post about later. Thank you for sharing and thanks for joining me for Tea Time Tuesday. Hope you have a beautiful week.\nOh I love your linen mats! $2 for Two??? Wow, that's amazing.\nI think we like a lot of the same stuff.\nPS actually I love that CS Lewis quote - and I totally agree with him!\nI love your blue and white Spode tea cup and saucer! How nice that your hubby brings you a cup in the morning. That is so sweet.\nThose little vases are precious on your nightstand.\nBeautiful teacup, Natasha! Also love the photos of you and your husband and your children and your bedside table looks great. Those are darling little vases!\nHi Natasha! Oh your night stand looks so pretty! Love the touch of the real roses and the tissue cover is so lovely! Now, honey, I'm so glad you're a real person showing your night stand the way it usually is. You know what? Mine looks like yours! I live on my night stand.\nhaha! my night table looks a bit like the \"before\" shot, too, many times...I try to put the things away but then I forget to use them!\nNatasha, I am sitting here smiling! My night stand looks just like your before picture...includes all the same items, although coffee instead of tea and just a mug! Going to need to pull out my tea cups! My magazines are in the same spot and our wedding picture on the same wall!!\nI absolutely love that lampshade!\nLovely post. I haven't had tea in bed for.......your husband is sweet to bring you some in the morning.\nA sweet hello from Frog Hollow Farm. I love jazzying up a little space with beautiful things - especially if I'm able to find them around the house or better yet, they are items purchased on a memorable trip to somewhere wonderful like Ireland. Ciao, bella!\nHi! This is my first teacup tuesday...and so far I think it is fun! Your hubby is a keeper.\nNatasha, your night stand looks frilly and feminine and how lovely that your DH brings you a cup of tea in the morning.\nThanks for stopping by HFTS and leaving such a nice comment. I appreciate it. Not certain if Evening Primrose would grow down your way, but it's worth a try. They are lovely!\nI'm off to see those amazing tea cups . . .\ngreat vignette! lately i've been very taken by vignettes too and can't wait to make one of my own. thanks for sharing!\nLovely Natasha. I loved how you posted the 'messy' nightstand picture as well as the neat and orderly one. One thing I really miss about Australia is the magazines, I am a magazine nut too! I do read magazines here, but there are certain Aussie ones I miss.\nDear Natascha.i always be glad that it is thuesday....than we drink our tea together !! nice moment.......i enjoy !!\nStopping from SITS! What a pretty look. It is so clean and crisp.\nYour nightstand looks very nice, and what a considerate hubby!\nGood morning Natasha, your night stand looks so sweet. I love the new look. However, I am fine with the old look too. It is a sign that you live there with your darling tea cup and delicious tea. Your wedding pic is lovely. Handsome and beautiful couple!!!\nI was over at 365 before coming here and immediately thought of you when I saw the teacups.\nI loved the fun you had with your bedside table today Natasha.\nLove the pretty cup and saucer and what a sweet hubby to bring you your cup of tea in the morning!!\nWe're having a Victorian Tea Party, on Mother's Day and you're invited! Come see!\nA beautiful teacup. Those little vases are adorable!\nAh, I'm proud that the lovely tissue-box cover comes from Ireland! The styled nightstand is lovely.\nNice to meet you! I didn't participate this week. Lovely nightstand. What a sweet couple you and hubby are. Gorgeous wedding picture.\nLove how you've decorated your nightstand - and you do have a sweet honey bringing you tea every morning. All the details are so pretty (including the magazines, I stash them around too).\nI've gotten behind in my blog rounds again, so forgive me if I've missed some of your posts. Coming here to visit you is always a pleasure.\nWill head over to your other blog. I became a follower but don't seem to be getting them in my reader?! I'll check it again.\nBeautiful Post and photographs. Thing never stay neat in my house either, but it is always fun to get it spruced up and looking nice!\nWell, that is the only tissue holder I have seen like that!! it made me smile. I love the little vases with the roses--very romantic, and dainty!!\nThe little vases with the roses are so pretty and look lovely with the tissue holder. I have a silver tray on my bedside table. Most times it has a couple of paperback books and a few of my pup's dog biscuits on it.\nMarty post was great last week! I just love your make over of your night stand! So pretty! The lamp shade! Oh! The tissue box and doily have my heart! Just love them! So sweet of your DH to bring you a cup of Tea each morning! I had to laugh for I sure most of our night stands look the same. If someone comes in I slide my magazine piles under the bed. lol Thank you so much for joining me again for Tea Time Tuesday. I love seeing the treasures you have in Australia! Next time you find a lovely doily, think of me! I'll send you the money! I would love to have treasure from your wonderful country. I loved this Tea! So much fun!\nI forgot to tell you, blogger was messing up bad, I had to write 4 different post and your comment got deleted when I deleted the 3rd post for Tea Time Tuesday. Using inlinkz it saves the Tea Links Thank goodness! If I had used Mr. Linky all would have been lost. Just wanted you to know why your comment is not there. Again, I had so much fun seeing your wonderful treasures!\nI came back to go to your sister blog, and saw the lovely vases with the roses! So pretty!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzwmgp b/data_all_eng_slimpj/shuffled/split2/finalzzwmgp
new file mode 100644
index 0000000000000000000000000000000000000000..f4341c811910c4c52e959e4500802e9f52c1458e
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzwmgp
@@ -0,0 +1,5 @@
+{"text":"Stop in the name of Internationale Funkausstellung. It's that time again where we implore you not to buy gadgets because there's a whole hunk of new wearable tech about to be announced.\nThe 2017 edition of IFA, everyone's fave Berlin tech expo, kicks off on Wednesday 31 August with a day (or two) of press conferences before it opens to the public from Friday 1 to Wednesday 6 September. We'll be there reporting from the show. Mike, James, Sophie and Conor are hitting up the Messe for Bratwurst, interviews, demos and more Bratwurst.\nWe're not saying all this shiny new stuff will go on sale in early September - just that it makes sense to hold up for a week or so to check out the new goodies plus the inevitable discounts for soon-to-be-old models.\nHere's what we expect to see in wearable tech, VR & AR and smart home at IFA 2017.\nGetting in nice and early with a 10.30am CET start is Acer. We reckon we'll get more of a look at its Windows Mixed Reality headset which we tried earlier this year as well as the new Leap Ware fitness smartwatch. Beyond that, who knows what it's up to in wearable tech - maybe more pet wearable talk?\nNext up is Asus at 1pm Wednesday - will we see a new ZenWatch? Unlikely, but Asus is pushing into AR with its ZenFone AR so there could be news on that front alongside what looks like laptop or tablet news from the invite.\nLater on, at 6pm CET Wednesday, Samsung's press conference at the Tempodrom is likely to be interesting. Mainly as we've heard a whole bunch of rumours, but we're still trying to work out what is coming now, what is coming later and what is bull.\nIt appears extremely likely, based on leaks and a sole FCC filing, that we're going to see the Samsung Gear Sport, though whether this is a legitimate successor to the Gear S3 and the de facto Samsung Gear S4 is unknown. Also unconfirmed are the specs, though the device would appear to be waterproof up to 5ATM, offer a heart rate monitor and be slimmer than the Gear S3.\nWe could also see a new Samsung Gear Fit2 Pro. Details and images of this have already leaked. We hear it's coming with built-in GPS, 5 ATM water resistance, swim tracking and offline Spotify playback. Check out Mike's Gear Sport and Gear Fit2 Pro wish list for other features he hopes Samsung will include in these two big launches.\nAnd if two bits of wrist-based hardware aren't enough to get you excited, a leak has suggested new IconX earbuds are on the way, as well as an updated Gear VR headset that will be able to house the Galaxy Note 8 smartphone.\nMaybe if there's time we'll receive an update on Samsung's smart home plans and hopefully something concrete around its struggling voice assistant too. The Bixby smart speaker is on hold, though knowing Samsung, it won't be for too long.\nGarmin has the potential to be a show stealer this year. Specifically, we have images of the Garmin Vivoactive 3 all-round fitness watch which has had a major facelift. We don't have spec information for this yet but stay tuned at 12pm CET on Thursday to see what Garmin has for us this fall.\nWhile the Vivosmart and Vivofit lines have been upgraded fairly recently, we haven't seen an update to the Vivomove hybrid since 2016 either. In its latest earnings, the Fenix 5 seemed to be doing well for Garmin, but revenue declined 15%, due to fewer sales of basic activity trackers.\nFossil doesn't seem to be holding a press conference, but from Thursday morning it's showing off \"new touchscreen and hybrid smartwatch collections\" at IFA.\nWe're still waiting for a lot of the Fossil Group announcements from Baselworld to drop, but Fossil might have something completely new to show, as part of its effort to get to 300 wearables in 2017. After its share price crashed earlier in August, it'll be hoping for a few (hundred) hits.\nOn Thursday afternoon, we have two press conferences from Sony and LG and we have little to zero idea what to expect. Sony starts at 1pm CET, LG at 5pm.\nSony could show off a new hearable \u2013 which could be the Sony Xperia Ear Duo Bluetooth ear bud \u2013 and smart home concepts alongside fresh smartphone and TV wares as it has done the past few shows. What's more, we may even see the Japan only Three Hands smartwatch on show.\nLG, meanwhile, has already launched two smartwatches this year - the Watch Sport and the Watch Style - but it might have more news on its high end SteamVR headset alongside the expected V30 smartphone launch. Your guess is as good as ours but hey, we like surprises.\nLenovo, which owns Motorola, is putting on its show at 8pm CET on the Thursday. Alongside a new Moto X, we're not holding out hope for another Moto smartwatch as that has been ruled out for the foreseeable.\nInstead, all eyes on Lenovo's Mirage Mixed Reality headset and we're also itching to have a play on its phone-powered AR Star Wars visor, complete with lightsaber controller, too.\nFitbit has announced the Fitbit Ionic smartwatch ahead of CEO James Park's IFA keynote on Friday at 5pm CET \u2013 and it's a biggie. The fitness forward watch boasts an all-new heart rate monitor, mobile payments and guided workouts \u2013 find out more in our Fitbit Ionic guide. There were also announcements of the Fitbit Flyer wireless headphones and new Fitbit Aria 2 smart scales.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"XLM represents the currency or 'native asset' of an open-source, distributed payments infrastructure known as Stellar.\nVouchForMe (former InsurePal) is a next gen P2P insurance platform based on blockchain.\n$MANA is the token used for exchanging land in the virtual world of Decentraland.\n12 new tokens now live on CoinDCX!\nWe have added 12 new tokens for trading in the BTC market. Deposits, withdrawal, and trading is live now.\nWe are excited to announce the winners of the DCXDiwali contest. And to know if you won the Grand Prize check out this post.\nOx made headlines recently for being the first ERC-20 token to be listed on Coinbase. Let's dive into this token for the week.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Spend the summer in your new home in one of the city's finest neighborhoods. Plenty of room to entertain the family in this custom-built ranch. Huge living room opens into the dining room and then the family room. Gleaming hardwood floors throughout. Sun-filled master bedroom with full bath. Eat-in kitchen. First-floor laundry makes for fewer steps and easy living! Meticulously maintained. New energy-efficient tankless gas hot water system and newer heating system. Professionally manicured landscaping provides great curb appeal.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Cork wallpaper increasingly become popular in the design of modern interiors. It is not surprising, because they are based on natural material, which allows achieving the effect of closeness to nature.\n\"Cork\" \u2013 this is what the cork oak bark is called in everyday life, the main feature and advantage of which is its rapid regeneration. It is received from 15-year-old trees, extracting from the trunk once in 10 years, which is completely safe for the tree. Moreover, it retains its properties for up to 200 years. A large producer of cork is Portugal. Less often it produces in France, Italy, Spain and the north of Africa.\nease of maintenance \u2013 these wallpapers are easy to clean, do not deform when exposed to water and household chemicals.\npets \u2013 cork wallpaper and favorite pets are incompatible with each other: the temptation to chew a cork or sharpen a claw on it is very strong. Therefore, you will either have to refuse cork in your interior or place such a cover outside the animal access zone.\nHow to choose cork wallpaper?\non a paper basis \u2013 cork veneer is pasted onto the paper itself. The texture of such a coating is very diverse and expressive, with a wide color palette \u2013 from light beige to dark ocher ones.\nself-adhesive wallpaper \u2013 something in between a roll cork and cork wallpaper. It is enough to simply remove the paper layer from the cork base, on which the glue composition is pre-applied, after which it is possible to glue the walls. But keep in mind, such a finish is far from a guarantor of a durable and effective result.\nShades of sand, golden, brown and beige will add heat to any room, making it conducive to relaxation. This is what contributes to the frequent use of cork in Country styled homes or ethnic design.\nThe dirt resistance and mechanical strength of such wallpaper causes a high demand for it in the design of commercial buildings with high traffic, halls, corridors, offices.\nThe use of cork wallpaper in the interior suggests some limitations in the choice of furniture. Even in combination with other coatings, the cork creates a sense of wood excess in the room. Therefore, in a room decorated with cork, there should be as little wooden furniture as possible. The elegant polished dark colored furniture fits the cork perfectly.\nTip: dyed cork fabrics are optimally combined with synthetics.\nDespite the interesting texture and natural color, monotonous cork coating is quite boring. It is better to refresh it with patches, tastefully decorated with other materials.\nNote: when combining different types of wallpaper, the main thing is that the difference is not noticeable. Therefore, in the case of cork cloths, it is necessary to select sufficiently thick types. If you can`t hide the difference in thickness, you can use decorative moldings or docking materials.\nBefore proceeding to the gluing, the wallpaper needs to be deployed and to lie down in the room for a while. It will be good to cut it immediately into strips and leave them under the press for a few days. Although the structure of cork cloths is quite heterogeneous, they do not hide the defects of the wall, so its surface should be flat.\nCork wallpaper is \"heavy\" by its structure and density, so it requires a quality reliable adhesive, for example, acrylic.\nwallpapering with acrylic glue requires promptness, so large pieces of cork cloths are best to be handled simultaneously.\nPaste area of \u200b\u200bwall same as a glued piece of wallpaper with acrylic glue. Spread evenly the adhesive with a plastic spatula.\nAttach a piece of wallpaper to the surface so that there is no air inside and press down.\nRemove the excess glue with a knife. Do not try to clean the glue with water. This will result in the formation of a white coating on the wallpaper. Therefore, allow the excesses to dry and then gently scrape or cut them off.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Made from fully tempered soda lime glass, KeepCup Brew Cork Edition features a natural cork band. Made in Portugal, using waste product from the wine cork manufacture, the band is beautiful to hold, and, over time it's patina will tell the story of your use.\nComes with a Cork band, The Force lid (pantone 412c) and Latte plug (pantone 7528c).","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzxoxk b/data_all_eng_slimpj/shuffled/split2/finalzzxoxk
new file mode 100644
index 0000000000000000000000000000000000000000..8a2b0608d8492a0557a0febdc9ed0d62fe1bbf3c
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzxoxk
@@ -0,0 +1,5 @@
+{"text":"Drawn from the night sky, a natural and infinite celestial canopy of sparkling starlight and orb-like iridescent moons, look to lunar inspired lighting to draw the outdoors in, or to enhance an incredible open air setting.\nClustered en masse, classic lighting options (like lanterns and bare bulbs) take on an otherworldly aura when strung between festoon garlands or a canopy of fairylights. Mixing exotic spherical lanterns, each perforated with unique patterns, or the more celestial shape of a star, creates miniature galaxies, suspended overhead for a spectacular take on a starlit ceiling.\nGrouped in magnificent numbers and in variegated heights, a nuanced palette of pales blended with gold transforms the humble paper lantern into an unrecognisably elegant canopy. And for a more decadent indoor approach, look to crystal incarnations or mirroballs, for a magical take on twilight glamour.\nComing into their own once lit (and looking decidedly less magical by day) consider timing and placement, ensuring guests first impressions of such a space is revealed only after dark, once lit!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Matt was a great salesperson. He was knowledgeable and friendly. He made this car buying experience stress free. The other office employee's were pleaseant as well. I would recommend this location and salesperson to others.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"It's beautiful to imagine that one is grass, sprouting everywhere out of the earth, living in the wind and casting and receiving pollen in the wind pouring in from the distant sea.\nIt's even more amazing to see oneself as both the grass and a little green leafhopper perching on a grass blade, in that vast, wind-swept sea \u2014 both of them at once, and both in movement through time and space, with different but joined histories.\nInstead of fingers, we have exquisite seed.\nInstead of words, we have never-ending movement that words cannot approach, because words don't need to. They weren't meant for this. This is where humans are at home. This is the grass that made us.\nThat is why all of its gestures speak.\nOne hears it brushing against one's thighs and names it as that speech: grass. Each blade is a step. Each stalk is a step remaining behind in memory, which is knowing.\nYou know this. It knows you.\nThanks for the quote. I love it.\nI love grasses, and this is a beautiful testimony to them. The idea of the little leafhopper in the vast, open sea, and their joined histories \u2013 inspiring!\nAnd ours, too, yes. I love how grasses evolved to harvest fire landscapes and heat. The fire eaters!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Accuracy and fluency: it used to be the case that, of these two constructs, fluency was the one that was the most elusive and contentious \u2013 difficult to define, difficult to test, and only rarely achieved by classroom learners.\nIt's true that fluency has been defined in many different, sometimes even contradictory ways, and that we are still no nearer to understanding how to measure it, or under what conditions it is optimally realized. See, for example F is for Fluency.\nBut I'm increasingly coming to the view that, of the two constructs, it is accuracy that is really the more slippery. I'm even wondering if it's not a concept that has reached its sell-by date, and should be quietly, but forcefully, put down.\nCorrect? Right? Conforms to the rules? What could these highly normative criteria possibly mean? Even before English 'escaped' from the proprietorial clutches of its native speakers, by whose standards are correctness or rightness or conformity to be judged?\nTake my own variety of English for example: I was brought up to say 'in the weekend'. I found it very odd, therefore, that the coursebooks I was using when I started teaching insisted on 'at the weekend'. And then, of course, there were all those speakers who preferred 'on the weekend'. It was only by consulting the Corpus of Global Web-based English (Davies 2013) that I was able to confirm that, in fact, of all the 'preposition + the weekend' combos, 'in the weekend' is significantly frequent only in New Zealand, while 'on the weekend' is preferred in Australia. OK, fine: as teachers we are sensitive to the existence of different varieties. But if a learner says (or writes): 'In the weekend we had a barby', do I correct it?\nMoreover, given the considerable differences between spoken and written grammar, and given the inevitability, even by proficient speakers, of such 'deviations' from the norm as false starts, grammatical blends, and other dysfluencies \u2013 what are the 'rules' by which a speaker's accuracy should be judged?\nIn fact, even the distinction between written and spoken seems to have been eroded by online communication. Here, for example, are some extracts from an exchange from an online discussion about a football match. Ignoring typos, which 'deviations' from standard English might be attributed to the speaker's specific variety?\n>I don't care about the goal that wasn't given; I care about how bad we played particularly when under pressure. Base on the performance from last three games we will be hammered when we play a \"proper\" decent side!! People think we are lucky to aviod Spain and get Italy but lets not forget the Italian draw Spain so they are no pushovers.\n> yes we was lucky, but all teams get lucky sometimes. thats football, you cant plan a tactic for good or bad luck.\n> Devic was unlucky to not have the goal allowed and the official on the line needs to get himself down to specsavers but as Devic was offside the goal should not of counted anyway. Anyway I pretty fed up with all the in fighting on here so I am not bothering to much with these blogs for the foreseeable future.\nI think that the point is here that nit-picking about 'should not of' and 'base on' is irrelevant. More interestingly, it's virtually impossible to tell if the deviations from the norm (e.g. 'the Italian draw Spain';' we was lucky'; 'I pretty fed up'\u2026) owe to a regional or social variety, or to a non-native one. The fact is, that, in the context, these differences are immaterial, and the speakers' choices are entirely appropriate, hence assessments of accuracy seem unwarranted, even patrician.\n>Titus. Please, please, please go back to school. Have you never heard of punctuation? What about capital letters? How about a dictionary? Sentences? Grammar?\nWhich is tantamount to saying: accuracy has to be judged in terms of its appropriacy in context.\nAccuracy is the extent to which a speaker\/writer's lexical and grammatical choices are unremarkable according to the norms of the (immediate) discourse community.\nThanks to corpora, these norms can be more easily identified (as in my 'in the weekend'). A corpus of 'football blog comment speak' would no doubt throw up many instances of 'we was lucky' and 'should of won'. 'Unremarkable' captures the probabilistic nature of language usage \u2013 that there is no 'right' or 'wrong', only degrees of departure from the norm. The greater the departure, the more 'marked'.\nThe problem is, of course, in defining the discourse community. Consider these two signs, snapped in Japan last week. To which discourse community, if any, is the English part of each sign directed? Assuming a discourse community, and given its membership, are these signs 'remarkable'? That is to say, are they inaccurate?\nBrown, H.D. (1994) Teaching by Principles: An interactive approach to language pedagogy. Upper Saddle River, NJ: Prentice Hall Regents.\nDavies, M. (2013) Corpus of Global Web-Based English: 1.9 billion words from speakers in 20 countries. Available online at http:\/\/corpus.byu.edu\/glowbe\/.\nThornbury, S. (2006) An A \u2013 Z of ELT. Oxford: Macmillan.\nUr, P. (1991) A Course in Language Teaching: Practice and theory. Cambridge: Cambridge University Press.\nThanks for another thought provoking discussion. I agree the discourse community is important in considerations of language use and what is considered appropriate. However, my experience confirms what you were saying in relation to your example \"in the weekend\", which is discourse communities themselves very often disagree about the most appropriate wordings. When I was growing up in South Africa I believe it was 'on the weekend'.\nI wonder if Halliday's 'context of situation' and 'meaning potential' might be useful terms as well. This accounts for variation within the discourse community, so different options are considered acceptable based on the meaning the speaker has in mind. In your example then, 'in', 'on', 'at', etc. could all be appropriate as they just 'mark' slightly different meanings. But I suspect there must be a limit as far as accuracy goes, as there are some wordings which aren't suitable to the context, and which don't satisfy the 'meaning potential'.\nI was thinking about this recently, when I indirectly corrected a student who said \"\u2026 ate lunch \u2026\" with \u2026\" had lunch \u2026\". It seemed petty at the time and I was wondering about the benefit of pointing them towards the use of 'have' with lunch. But then I thought that as language is an evolved system, there might be value in highlighting the use of 'have' in this context, as students could then perhaps be made aware of other uses of 'have' showing the patterns, or what Willis called 'classes of words', i.e. words which are linked semantically in some way, and seem therefore to share similar patterns. I think this might afford them more opportunities to make generalizations from these instances of language.\nAs a rule, I don't usually overtly point to students' errors, but instead try to highlight alternative wordings which might be more common in more proficient speakers. I find this naturally highlights different options, which allows for a level of variation. But I guess the line between what is 'acceptable' or not will always shift as the system adapts.\n\"This accounts for variation within the discourse community, so different options are considered acceptable based on the meaning the speaker has in mind.\" I agree, Grant \u2013 but the options are constrained by the norms of the discourse community, unless the speaker wants to flout these for a special effect. The problem for teachers is that we don't always know what the speaker (i.e. the learner) has in mind, so the default position is conformity to a notional idea of 'standard English'. But I like your approach to error \u2013 not correction so much as 'well, that's one way of saying it \u2013 this is what I would say [given that situation and that discourse community \u2013 and, possibly, your current state of knowledge of the language]'.\nThat's the potency of the Hanashi method. the story is the property of the teller, it's his\/her responsibility to convey the thoughts that are the meaning of the story. The receiver never knows what these thoughts are for certain. Scary!\nI can certainly see what you are saying Scott and I kind of agree, but hasn't the 'discourse community' come to 'agree' on certain wordings which have evolved as the standard. Which doesn't mean the other wordings are inaccurate, just not standard at this point in time or place. What determines the accuracy is the meaning which emerged from the activity\/ context. This may sound banal, but it might be a useful point because as soon as we refer to a 'discourse community' it feels like we're drawing an artificial line between those in and out of the circle. This might be unhelpful as we are all part of different overlapping 'discourse communities' at the same time each with their own influences. Which is why English teachers' rooms are full of (sometimes not so) tongue in cheek discussions revolving around wordings, and perhaps accounts for Titus and his fellow commentator above.\nI have found your book 'Natural Grammar' useful in this sense as focusing on the possible meanings associated with high frequency words allows for decisions to be made regarding accuracy. So to return to your previous example a student who says, \"In the weekends I go to Dubai.\" can be considered to have been accurate since one of the meanings associated with the item 'in' is a period of time. The meaning potential 'allows' for this option amongst others, even if it is not the option I would have chosen. Decisions on accuracy surely need to be made according to wider considerations at the system level, not the individual level. Of course the two levels 'speak' to each other so natural evolution of the system will occur anyway according to emerging conditions, and different wordings will come and go.\nI think this may be an advantage that corpus linguistics offers us. If we can understand the emerging patterns of language better, we can perhaps make better decisions and find a balance which accounts for Friederike's concerns regarding adopting \"a very liberal stance on accuracy and consequently appropriacy\" and the \"intolerance to \"errors\"\" which Miguel highlights below.\nYes, I agree, Grant, but what we're really talking about here is 'idiomaticity', what Pawley and Syder years ago (1983) called the puzzle of 'nativelike selection': the fact that of all the possible ways of saying something, there are only a small set that 'have evolved as the standard', as you put it. The learner's task, according to Pawley and Syder, is to distinguish 'those usages that are normal or unmarked from those that are unnatural or highly marked'.\nSo, let me suggest we dispense with the notion of accuracy altogether, and replace it with the notion of 'appropriate idiomaticity'.\nin your example of city signs if an English speaking non-Japanese stepped on the grass and was prosecuted, how the case would proceed would to a large extent depend on whether the suspected offender understood keep off.\nWhat more is there to add? The objective of nearly all the students I've ever had was to use the kind of Standard International English we all use on this and similar blogs. (Even those who were keen football fans did not wish to learn the kind of English Titus uses in your quote above.) It's true there are tiny differences between the members of this community and we sensitive English language nuts notice them, but as the corpus study Mura refers to confirms, most native English speakers don't: what they notice as \"foreign\" is the pronunciation.\nI don't understand, Mura, \"why the implication is that accuracy is important for beginners but not so for more advanced students\"?\nBy the way, I first interpreted Mura's lack of capitals at the beginnings of paragraphs as an E. E. Cummings sort of stylistic choice. Then I realised that it was more likely because he was writing on a smartphone. But that says more about my age than Mura's English.\nThanks Mura \u2013 yes, the notion of 'perceptive fluency' (i.e. the impression one gives of being fluent) seems much more interesting than measurable fluency (e.g. speech rate, number of unfilled pauses etc). I haven't checked your link yet, but in a recent book (G\u00f6tz, 2013, Fluency in native and nonnative speech, John Benjamins) a small-scale study of NS non-specialists' perceptions of fluency found that pragmatics (e.g. realizing questions, responding to questions, being polite etc) was the highest scoring indicator of the subjects' fluency. Accuracy was up there too, but the NS non-specialists were hopeless at assessing it: 'The learner with the least number of errors gets the lowest ratings for perceived accuracy'. It seems that it is mianly only teachers who can recognize accuracy when they see it, and who (mostly) prioritize it.\nOn another note, do you think native speakers actually make \"errors\" when speaking? Slips of the tongue, yes, but errors? Of course many will argue that, \"If I'd have known he was coming\u2026\" is wrong but if the speakers own the language, do we ever get it wrong? Perhaps misunderstood.\n\"\u2026do you think native speakers actually make \"errors\" when speaking?\" Not really. They violate the rules of prescriptive grammar ('a huge amount of people', 'he plays like Rafa does' etc) but these can't really be counted as 'remarkable'.\nIt's interesting that we use the term 'fluency' for both NSs and NNSs, but 'accuracy' only for NNSs. For NSs we tend to say \u2013 not that X's speech is inaccurate \u2013 but that it is not 'proper' or 'good' English.\nParticularly, are there times that someone who can speak English perfectly well, following 'standard English' rules, actually changes to fit in with another discourse community? Could a football fan change their language depending on whether they are at home with their family compared to when they're at that game?\nOn another note, I've never come across 'in the weekend' (maybe don't meet that many NZ English speakers), but I really don't like 'on the weekend'!\nMike, I think you've put your finger on both the experiential and the affective factors that make departures from the norm 'remarkable'. If you haven't ever heard someone say 'I'm loving it', for example, it will trigger a negative reaction. Likewise, if you value the distinction between 'few' and 'less' (because you think it adds clarity to the language, or simply because it indexes you as educated) you will be offended or aggrieved by 'Ten items or less' signs in supermarkets. I suspect most of our learners have neither the experience nor the culturally-induced attitudes to detect 'remarkableness' of this type. They simply want to get on with the job of being maximally communicative.\nWhen I started teaching English was mainly a classroom activity and we teachers had the final word on what was considered grammatically correct. Incidentally I had to spend a lot more time on pronunciation work than I do now. Now \u2013 at the latest with the advent of the internet, the language belongs to everybody, fluency has been absorbed with the ubiquity of the language and we teachers (me at least) gallop alongside our students to keep up with the new structures and usages being bandied about.\nMisunderstandings will occur whenever people get together, and ironing them out intensifies their experience with the language.\nI only see problems when students have to adopt a particular style of English to take tests written by English teachers.\nThanks Helen for reminding us that 'misunderstandings will always occur' and hence that the pedant's argument that grammatical accuracy reduces misunderstandign is a specious one. Perhaps we should be training our learners \u2013 not to be accurate \u2013 but to recognize, repair and negotiate misunderstanding?\nWell a bit of both, surely. You need the accuracy to \"recognize, repair and negotiate misunderstanding\", but accuracy alone is in every sense an academic (i.e. clever, but not necessarily useful) quality.\nAs a non-native speaker teacher educator I have a slightly different stance on accuracy. Native speakers tend to know which register and level of lexical and grammatical accuracy to adopt in which setting. They have a number of options. And I don't believe that online discussions about football with peers can be seen to be of the same quality as emails to other staff members or customers. Are we really doing learners a service if we adopt a very liberal stance on accuracy and consequently appropriacy? I don't know which proportion of learners of English worldwide would only ever use the language in informal settings. Those that need English in their jobs would probably be happy to be taught a \"safe\" standard variety which does not result in raised eyebrows. Being less formal and \"accurate\" will follow surely when they interact with others and encounter more and different expressions in English.\nThanks for your comment, Friederike. I appreciate and welcome your particular vantage point on this discussion. Many non-native speakers feel that their accuracy (whether of grammar, idiom or accent) has been hard won, and should not be belittled or otherwise compromised. But I'm not suggesting that online discussions about football should serve as a new 'standard'. I'm simply saying that accuracy can be assessed only in relation to the context of use \u2013 and that those best placed to assess it are those familiar with \u2013 and invested in \u2013 this context. Those that need English for their jobs (as you say) or for academic study will be expected to conform to the norms of precisely those professional or academic contexts \u2013 which \u2013 for want of a better benchmark \u2013 probably is the 'standard' adopted by current textbooks, reference grammars etc. But those who do not aspire to these contexts and uses might be wasting a lot of time trying to master a variety that may well be inappropriate.\nHi Scott. I am also a non-native teacher. My first language is Spanish and we have a language regulator called \"Real Academia de la Lengua Espa\u00f1ola\" which prescribes language. If Bartosz used the word \"escuchante\" in Latin America, he would be prompted to use \"oyente\" or \"radio escucha\". Let's not get into detail. So, at least in Mexico, an inaccurate native speaker (in whatever context) is seen by many as being ignorant and may result in the person being the object of ridicule. This is a challenge, because as you mentioned, we can't impose a one-size-fits-all target of accuracy in English as it could be done in Spanish. So, in the end, many teachers end up teaching English as they learned Spanish. In your example, Titus replies to one of the commenters with a great point. But your example shows that intolerance to \"errors\" exist. In my experience as a user of English as a second language, I have been the victim of racism many times because of my accent and fewer times because of my \"correctness\". I felt really bad for a long time and I thought I had wasted so much time and effort in studying English. How would you prevent a learner from feeling discouraged if he is judged?\nThanks for the comment, Miguel. It's true, there's no denying the stigma that is often attached to 'sounding foreign'. I suspect that, sadly, we are hard-wired to mistrust strangers, hence our hypersensitivity to even the subtlest differences in accent. Nevertheless, more than half the world's people live in a place in which they were not born (I invented that figure \u2013 but you get the point) and hence there is much more inter-lingual contact than ever, which can only serve to break down prejudice and make the remarkable unremarkable.\nIn a recent book (Language & Mobility 2012) Alistair Pennycook explores the notion of 'passing' (as in 'to pass as a native speaker'), and he construes it as being able to 'perform like a local': 'Performing like a local is not about achieving a level of phonological or syntactic accuracy as measured by some external criteria (proficient), nor just getting by (passable), nor being acknowledged by dint of prior social status (legitimate) but rather is a question of one's language use being perceived to work \u2026. Being a resourceful speaker is what we are surely aiming at. By this I mean both having available language resources and being good at shifting between styles, discourses and genres. \u2026 We do not pass as a native speaker of some imaginary thing called a language; if we pass as anything, it is always in a particular context, in a particular genre, style, discourse or practice'.\nSignificantly, the only group that rated Wes's English poorly were \u2026. English teachers!\nMiguel, you should come to Poland and try to learn Polish. We LOVE foreigners who try to speak Polish and we LOVE their mistakes. I guess Poles just assume that Polish is too difficult for most foreigners to learn.\nThose foreigners who become quite fluent in Polish are likely to win our heart and become TV celebrities! Let me give you some examples.\nOne of the judges on Masterchef Poland grew up in France (his family had emigrated from Spain if I remember correctly). He's famous for his mistakes.\nThen, the host of another reality show is of Polish origin, but she moved to the US when she was a little girl. She has a foreign accent, uses a lot of English expressions and makes plenty of mistakes.\nBetween 2003 and 2008, there was a programme called \"Europe is likeable\" (or \"Europe can be liked\"). The host of the show invited foreigners who lived in Poland and spoke (some) Polish to talk about different apects of life in their countries. The programme was a spectacular success.\nDisclaimer: This is not true if you're a native speaker of Russian, Ukrainian or other Slavic languages.\nScott, thank you so much for your answer. Let me share this short article I found http:\/\/www.futurity.org\/why-we-distrust-foreign-accents\/ It might explain why some Americans wanted to speak with someone who spoke \"American\". On the other hand, I will gladly read that book. I think that not only \"scenarios\" change the perception of the speaker's language working or not but also the listener's culture. I think it would also be interesting to know how Wes managed to want his interlocutors to understand him and leave a good impression in the end.\nBartosz, I've heard Polish women are beautiful and Polish language has a reputation of being extremely difficult. So, it might be worth making myself the object of your laughter. In Mexico, we wouldn't mistreat a foreigner making a mistake. On the contrary, we love helping them. We are just mean with the locals, weird, huh?\nThank you very much for tackling the crucial issue of accuracy. Out of my experience in teaching written expression, accuracy cannot be disregarded as a main aspect in evaluating the students' production, whether in terms of sentence structure (writing accurate sentences which are free of sentence problems), spelling (writing words accurately), accurate punctuation, etc. So, accuracy of writing mechanics plays a big role in the overall evaluation process. What's more, even when the ideas expressed are creative and original, the lack of accuracy distorts the whole shape of the written piece and affects the evaluation scheme.\nI think that \"accuracy\" is entwined with \"rules\". Language is a system of structures that function according to a set of rules lexically, grammatically, phonologically and phonetically. So, accuracy stems from the appropriate use of the rules that govern the language. Grammatical accuracy is dominant over other language aspects I think, because of the prominence of grammar rules (I think language learners tend to link the word \"rules\" to grammar mostly often).\nTaking into consideration that language is used for communication, accuracy in speaking does not seem to be as important as in writing because the fact that the message is being conveyed, and providing immediate feedback to correct pronunciation mistakes can influence the \"fluency\" of the speaker, are example factors that reduces the focus on accuracy.\nIn the literature, other terms like \"appropriateness\" and \"correctness\" along \"accuracy\" are also mentioned when discussing grammar, and it is difficult to draw a distinction among them.\nManar, you say that '\"accuracy\" is entwined with \"rules\"'. Well, yes, that's certainly how teachers and students have traditionally viewed it. I'm suggesting, on the other hand, that it is 'entwined' with appropriacy \u2013 that you cannot assess accuracy in the absence of knowledge of what speakers in that context actually do. So, not rules, but norms.\nScott, isn't Titus only choosing (correctly) the register he needs to take part in the discussion? Presumably, if he met the queen tomorrow, he would speak in a different way. Of the two photos, I would say that only the second was accurate \u2013 the first could almost be used as a 'wet paint' sign!\nYes, Andrew, Titus is indeed choosing the appropriate register \u2013 that was my point, and it was mean-spirited of the other commenter to condemn him for violating the norms of a completely different register.\nIn short, it seems to me to be impossible to extricate the notion of accuracy from the notion of register.\nThe two go hand in hand, like fish'n'chips, down the holy aisle of language capamabilities.\nI forgot that there were two Scotts here. \"Accuracy is the extent to which a speaker\/writer's lexical and grammatical choices are unremarkable according to the norms of the (immediate) discourse community\" is a quote from Scott T. not from Scott C.\nNo dialect, including Standard International English, is static. The users are changing it all the time \u2013 that's the way languages function. Otherwise we Westerners \u2013 English speakers and others (I think you know who I mean, even if some of us, or our parents, have emigrated elsewhere) would still be speaking Proto Indo-European. There is a constant tension between the natural tendance of any language to change and the practical need to prevent a lingua franca from splitting into mutually unintelligible dialects. A lingua franca is useful \u2013 but a language becomes a lingua franca not because it is linguistically superior or more resistant to change, but for historical and political reasons.\nThe Grammar Geeks Group on Linkedin has had many discussions about the difference between prescriptive grammar rules imposed by an authority: the teacher, coursebooks, style manuals\u2026 and descriptive grammar rules which describe the regularities of any language\/dialect at a particular moment in time. Many people, including teachers, are not clear about the distinction. A lot of the discussion about grammatical rules is conducted in emotive, judgemental terms and suggest that people who speak anything other than the Standard are somehow inferior as people.\nThanks Glenys. I'm struggling a bit with the prescriptive-descriptive distinction, from a theoretical perspective at least. When you take a description (of 'any language \/ dialect at a particular moment in time', as you put it) and make it the basis of both your syllabus and your criteria for assessing accuracy \u2013 and, hence, for testing \u2013 aren't you in a sense prescribing that description? I'm not suggesting that 'anything goes' \u2013 only that we shouldn't be too complacent about the way we use so-called descriptive grammars.\nIn a discussion like this I like to think I'm a descriptivist, but in the classroom I was a prescriptivist. I don't really see how it's possible for EFL or ESL teachers to be otherwise. I did not accept the sort of sentences my students sometimes came up with \"Do I can go toilets, My Teacher?\" Does any teacher? But a self-aware prescriptivist is quite different from one who believes that there is something inherently \"bad\" in saying, for example, \"Less people play tiddlywinks than football\".\nI recently experienced an example of how rapidly language can evolve. My nephew came to visit me here in France: his mother's Japanese and he was brought up in Japan. He's quite fluent in English, maybe B1, but makes lots of \"mistakes\" judged by the norm of International Standard English. We just chatted \u2013 I wasn't in my teacher role. In just a week, I noticed how much my English was moving towards his. If we'd been isolated on a desert island, I'm pretty sure that within 10 years we'd have been speaking a new dialect of of English. I realised too that I didn't change my accent \u2013 no \"l\" for \"r\" \u2013 and also that it was the only aspect of his English I corrected him on. Just an anecdote but in agreement with the corpus based study Mura drew our attention to.\nIf English speakers (native and non-native) in their local groups all over the globe went down road my nephew and I were going, there'd soon be no Standard International English and we'd have no lingua franca (at least, not one based on English) which enables people from diverse backgrounds to participate in a discussion such as this one. Such a Standard is useful and practical \u2013 not that that we have to use it all the time.\nThanks for clarification \u2013 so I was quoting you quoting Scott T, and also quoting Scott C!\nI quite like your revised definition of accuracy, Scott.\nIt seems to me to be a more precise (scholarly?) expression of Penny Ur's idea. She mentions \"getting the language right\". I'll assume that \"right\" doesn't always mean \"(prescriptively) correct\" for her.\nI think it's important to add that users don't depart from the \"norm\" just because they don't know it. They may have reasons to do so on purpose (e.g. in advertising campaigns).\nIf you listen to something (e.g. a radio programme), you are an 'oyente' in Spanish. It comes from the verb 'o\u00edr' (to hear) and it's the only word for 'listener' that is accepted by the Spanish Language Academy (which means it's included in its Dictionary).\nStill, some Spaniards and I prefer to use an alternative form ('escuchante') to talk about radio programmes that we really like. 'Escuchante' comes from 'escuchar' (to listen) and it seems to describe actions rather than states\/perceptions (hearers vs listeners). The problem is that it's not an official word in Spanish. You won't find it in THE Dictionary of Spanish.\nAlthough I have been corrected a couple of times by hard-line prescriptivists, I'll keep using the illegal 'escuchante': not because I'm stupid too learn the rules, but because that's exactly the word that I need to talk about my favourite radio programmes.\nIs your claim that \"No native speaker of Spanish would interpret\u2026\" EVIDENCE-based? If you have made it because you're a native speaker of Spanish, then, sorry, I'm not really convinced by your OPINION.\nGoogle \"escuchante de radio\" and you'll see it's been used by some native speakers. I'm not the one who invented the word.\nI admit that 'escuchante' might be a 'marked' choice for SOME speakers of Spanish, since there is a more frequently used alternative term. But that's exactly my point: I want a 'marked' word to express myself precisely, i.e. by contrasting 'oyente' and 'escuchante'. I haven't got rid of 'oyente' completely. I simply need both words.\nFinally, I don't agree it causes communication breakdown. The meaning of 'escuchante' is quite transparent: it can be reconstructed if you know 'eschuchar' + -nte suffix (even if you don't like the form). That's something that every native speaker (and most intermediate learners) should be able to do.\nYes, I'm a native speaker of Spanish.\nI wouldn't say that the markedness of your 'escuchante' is just an opinion. It's a 'lexicality' judgment based on 48 years of exposure to and use of the language.\nI am very much aware of the importance of language play in SLA. Totally agree. I'm also a literary translator, which has allowed me to toy with metaphorical constructs (equivalences and marginalities), and creative word choice, word building, and word combinations.\nDo you know what my first word association with 'escuchante' was? A student on an audit basis. A marginal one? A Native-American with an ear on the ground.\nIndeed, idiolect (one's own speech style) and creativity also challenge the notion of accuracy \u2013 and also my own defintiion of it. Poetry is, almost by definition, 'remarkable' \u2013 but perhaps only outside the community that reads it. The problem is that, as Luke Prodromou among others has argued, when learners attempt to be creative with the second language (as in Bartosz's 'escuchante') they are corrected. When native speakers do it, they are not corrected \u2013 they are even congratulated on their ingenuity. Double standards?\nI guess native speakers of any language 'know' when departures from unmarked forms are necessary creative \u00edmpetuses, or spontaneous attempts to lexicalize the unnecessary.\nLook, it's quite simple. We need a Ministry of Correct English who pronounce on matters of accuracy. This weekend business is easy, it's \"at the weekend\" or \"during\" is permissible. Other colonial variants are incorrect and that's that.\nConfusions such as the use of the word alternate when the correct word is alternative will be corrected, no longer will people \"protest the injustice\" when they actually want to protest \"against\" the injustice and the heinous \"train station\" when we all know that the correct term is \"railway station\" will no longer be an issue. Anyone who uses an adjective rather than an adverb will probably be shot at dawn.\nAll BBC, Civil Service personel and public employees will only be able to stay in post if they demonstrate a level of accuracy acceptable to the MOCR.\nI would of thought it was all self evident!\nOf course if there ever was something like a Ministry of Correct English a lot of people would just rebel against it by using non-standard forms even more.\nPompous prescriptivists always set themselves up for ridicule.\nMy two cents on Scott's post is that it seems to be going way too far to scrap the concept of accuracy altogether. The revised definition given in the article fits the description of accuracy which Scott lays out very well.\nGreat post! And it got me thinking about your definition. I'm just back from a run and on my way back stopped to talk to Fran, an ex-student of mine. I've been living and working in Spain for 25 years now and as would be expected have reached a fairly decent level of \"accuracy\" and \"fluency\", have read quite a few Spanish classics, read the newspaper and converse on a wide variety of subjects on a daily basis. So why do quite a few people speak to me as if I were brain damaged? The quick answer is my horrible accent and intonation. When you have a Belfast accent speaking Spanish people automatically assume that you understand as you sound, rather than how \"accurately or fluently\" you speak.\nDo I suffer from the same prejudice with my students? I have to admit I do. A few months ago I carried out a level test for a student who spoke with a wonderful London accent. With that accent I automatically assumed that her grammar and vocabulary would be up to the same standard. It took me a while to realise that I'd made a mistake. What she said was pretty dire compared to how she said it. (Incidentally she fooled the FCE examiners too and passed the oral exam).\nThe point I'm making is that any definition of accuracy which focuses solely on lexical and grammatical choices without taking phonology into consideration would only be useful for written rather than spoken English. Or have I totally misunderstood the definition?\nFantastic post, Scott. As you say, \"The problem is\u2026 in defining the discourse community.\" At one company I teach at I used to correct the students' pronunciation of the word \"inVENtory\" until I sat in on a conference call and realized that all the L1 Spanish, Italian and French speakers who were at the other end of the call said it exactly the same way. Their particular corporate subset of international business English had settled on this pronunciation as correct and there is little I could do to change it if I wanted to (and now I don't). As you suggest, there is a vast array of discourse communities and even my \"standard English\" might be wholly inappropiate\u2013and therefore judged as non-fluent\u2013in a number of them.\nThanks for the comment \u2013 and for bringing pronunciation into the equation. I deliberately left it out of my definition (I referred to \"lexical and grammatical choices\" where I could have been more inclusive, e.g. \"linguistic choices\") because (a) you'll never get rid of an L1 accent, even if you wanted to, so to fold it into a general notion of accuracy would seem to weight the dice against the learner ever being judged fairly \u2013 your student with the London accent is a sort of coutner example!; (b) unlike 'holes' in your grammatical or lexical knowledge, which you can skirt around using communication strategies, you can never 'disguise' your L1 accent \u2013 so pronunciation does seem to be a 'special case'; and (c) there are huge variations in accent among NSs \u2013 even more, arguably, than in grammar and lexis \u2013 so how do you identify the norm from which the learner is departing or to which the learner should aspire?\nNevertheless, I think you are absolutely right if you mean that the criteria of remarkableness (rather than, say, native-like-ness) should apply to pronunciation, alongside \u2013 but not to be confused with \u2013 intelligibility.\nThat certainly puts things in a new perspective. This concept of \"remarkableness\" (do you mean worth remarking on \/ interrupting for \/ commenting on \/ correcting?) seems to point us more in the direction of a pragmatic approach to teaching, the central goal being to move students forward rather than an obsessive fixation on accuracy, which turns out in the end to be a highly subjective and arbitrary construct, often becoming a hindrance instead of a yard stick for progress. Does that encapsulate your central point or am I way off the mark?\nBy 'remarkableness' I wanted to capture the sense of the technical term 'markedness', a 'marked' form being one that is less typical, less basic, less frequent, more complex, more salient than an unmarked one. I also wanted to capture the idea that your attention is temporarily distracted by such departures from the norm: you notice them. This might lead you to the conclusion that the speaker is 'foreign', a learner, or otherwise not one of your own speech community, which in turn might induce certain responses: 'foreigner talk', extra effort, or even avoidance.\nMost of the examples of inaccuracies so far have been of the \"ate\/had lunch\" \/ \"on\/in the weekend\" type, haven't they, by which I mean local mistakes (for lack of a better term and \"local\" in the discourse, rather than geographical sense).\nI'm not in principle opposed to a sensible slackening of the reins with which ELT's grammar police get to determine what's right or not, but I do wonder how a such a change should be communicated to teachers worldwide. Surely we don't want teachers to view most developmental mistakes (which with a little scaffolding + feedback + renoticing can bring students closer to the target forms) as an acceptable final product. I think what I'm trying to suggest is that \"I no went there yesterday\"\/\"Do I can ask a question?\" and \"in\/on the weekend\" shouldn't be considered in the same terms or else the notion of interlanguage and interlanguage restructuring will have very limited use in ELT pedagogy.\nThere's also the issue of ultimate level of achievement, which you mentioned above. As a non-native speaker, I am constantly being assessed on my language proficiency, both formally and informally (e.g.: If I send an e-mail to my editor at 3am, forget to proofread it and let a typo or two slip in, chances are that she will wonder whether those are simply typos). So accuracy \u2013 as it is defined by mainstream ELT \u2013 matters a lot to me. And it probably matters a lot of to most non-native teachers, who, as you said, fought very hard for their accuracy and depend on it to keep their jobs and advance in their careers. And it's precisely these people that will have to buy the idea that, at the end of the day, had lunch and ate lunch are both fine.\nThanks, Luiz. \u2013 always measured and insightful!\nBut let me dispel the idea that I am talking about a 'slackening of the reins'. I'm sorry if I gave that impression. What I am saying is that you can't impose a one-size-fits-all target of accuracy on all learners. If you like, I am substituting the notion of accuracy with one of 'rightness' \u2013 not as 'correctness', but in the sense of 'fitness for purpose'. As Diane Larsen-Freeman puts it, while teachers need to understand the natural processs of interlanguage development (and hence accept the inevitability of \"error\") they 'are [also] responsible for aiding learners to at least approach the norms of the community in which the learners seek membership' (2013: 214). If the community in which the learners seek membership is that of English language teachers, then, of course, the bar will be raised very high.\nOf course, the problem is that we don't often know (because they don't) what the community is in which the learners seek membership, so we teach them (and assess them) as if they were ALL going to be teachers of English or rocket scientists or whatever.\nAs an instance, the assessors manual for Cambridge Proficiency once included a Q&A section. One of the questions went something like: 'Is colloquial language or slang permitted [in the exam]?' And the A: Yes, so long as it's grammatically correct.\nLarsen-Freeman suggests that, instead of setting some kind of idealized 'end state' as the putative objective of teaching, we should set the goal 'as developing capacity', where 'capacity is that which enables learners to move beyond speech formulas in order to innovate'. And she adds, 'Within this overall goal, identify particular contexts of use, contexts in which norms for local \"success\" can be established' (op. cit).\n'Local success' would seem to be a more realistic goal than some kind of global 'gold standard'.\nLarsen-Freeman, D. 2013. 'Another step to be taken: Re-thinking the end point of the interlanguage continuum', in Han and Tarone (eds.) Interlanguage:Fortty years later. Amsterdam: John Benjamins.\nThe one thing that strikes me, Scott, when I look back over the years, is that what we were sold back in the early days, the idea of accuracy leading to fluency, was the cart before the horse. Looking back over my own language learning experiences, it's now pretty obvious to me that first I was fluent \u2013 albeit with a hundred and one 'inaccuracies' in everything I uttered \u2013 and then I became accurate. So it's great to see you raising question marks against early, narrow definitions of accuracy, and offering us a view that is more fitting to the 21st-century reality of language use in general, and of the reality of a fully globalised English in particlar, and the only thing I'd venture to add is the need to put the horse back in front of the cart.\nYes, Robin, exactly. I don't know who it was (maybe Stephen Krashen) who pointed out that accuracy (if such a construct exists) is 'late acquired', both in first and in second language acquisition. We achieve fluency which we then fine-tune for accuracy. Of course, there's always the risk that \u2013 in SLA \u2013 the speaker will dispense with the fine-tuning, a state that used to be called fossilization. All things being equal, I'd rather be 'fluent but fossilized' than 'accurate but non-communicative'.\nScott, I've been thinking about \"the norms of the (immediate) discourse community\" in different places and Gibraltar came to my mind.\nGibraltar is famous of code-switching (English is more prestigious than Spanish), but in fact it's common to hear people mixing English and Spanish words, syntax and pronunciation in one sentence.\nIt seems that most native speakers willing to go to Gibraltar should learn some Spanish if they want to pass as a Gibraltarian. Some of their lexical and grammatical choices would probably be 'remarkable' if they spoke just \"standard\" English.\nI'd like to say a couple of words and join the discussion, if it's not too late.\nOnce while discussing the overall goal of teaching pronunciation in the EFL context with my trainees (btw using, Scott, your book \"About Language\"), one young woman very strongly advocated aiding students to go beyond the limits of intelligibility, towards more native-like proficiency (whatever that accent could be). Her main argument was that her own struggle to sound like her listener was embedded in her desire to show respect for her listener, so that her speech could sound easier to process and comprehend, yet with no intention to assimilate or \"seek membership\" in the target language community. From this perspective accuracy could be defined as the speaker's willingness to abide by the linguistic culture (language norms as you say) of their listener in order to hold a dialogue (in Bakhtin's sense). The speaker's initial idea of accuracy will certainly always depend on their previous experience \u2014 what they have been told, taught, exposed to or what they have just picked up.\n\"Foreigner\" talk, that we all can do on instinct, is an adaptive strategy, its intention being to sound more comprehensible. In my opinion, with so many Englishes in the world this strategy should be explicitly trained in the classroom, i.e. students should be made aware of different ways English may sound and how they can notice it and adapt to their potential listener. I would really appreciate it if coursebook writers could kindly include a note about each sample of written and oral texts they use and say where it comes from, where the speaker is from and what features this English variety has.\nHope it was accurate enough to make sense.\nBtw, when is the new edition of \"About language\" due?\nThat was surely a very interesting point you made.\nBut as an efl teacher I would like to understand how does this relate to my teaching? Does this mean that one doesn't have to put a great emphasis on accurate English, teaching grammar or correct mistakes in writing assignments?\nBasically what is my main target in teaching English?\nThanks a lot and a happy new year!\nIn your personal opinion, do you think it is good to teach English using modern songs which have incorrect language? To emphasize the differences between spoken language and formal one.\nThe best you can due for learners is to equip the to explore a language for themselves to find ways of communicating that best suits their own purpose.\nThank you for sharing your insights on accuracy, I found them very engaging and thought provoking. The fact that Titus says \"Didn't know this was an English class,\" strikes me as quite disturbing. Are we English teachers that bad? Always correcting our students and requiring that they speak accurately?\nThe real question is, like you said, where do we set the boundaries between accuracy and fluency? I strongly believe that educators need to give their students the choice and ability to speak accurately so they can use language in a variety of conditions and situations. Language learners that can only speak their acquired language in certain settings might become fixed on that setting only and won't be able to expand their knowledge and thought beyond it. However, I do agree with Titus that the language one uses shouldn't be an indicator of his or her intelligence. Sadly we live in a very biased world, in which language is a means of stereotyping people and placing them in a certain social status. I hope that one day people will have the ability to set aside their prejudiced thoughts and get over the idea that the language one uses is a gauge of how much they know.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The hospital's research supports the belief that the maternity skin-to-skin sling from Beb\u00e9 Due is beneficial to the development of premature babies.\nThe Sant Joan de D\u00e9u Hospital chose the Beb\u00e9 Due maternity skin-to-skin sling three years ago, and it has now been demonstrated that this sling has assisted the recovery of babies born preterm.\nThe maternity skin-to-skin sling allows a baby to be in direct contact with the mother's skin, and this helps it to recover from the strain of the birthing process. The sling ensures that the baby is in a warm, peaceful and loving environment, even though it is in the relatively cold environment of a hospital ward.\nFor more than six years now, Beb\u00e9 Due has been collaborating with the Sant Joan de D\u00e9u Hospital, which is considered to be at the forefront of mother-baby care. As part of this collaboration, Beb\u00e9 Due funds two parallel studies related to premature babies. The first one studies the mechanisms of foetal and perinatal growth, taking epigenetic factors into account.\nThe second researches the possible impacts - on the adult lives of premature babies - of being born premature with low birth weight (75% of the babies admitted) or with congenital malformations, respiratory problems or infections (25 %).\nThe hospital has more than 130 years of experience, and specialises in the problems of women, children and adolescents. It combines the human side of healthcare with scientific progress. The studies funded by Beb\u00e9 Due have as their starting point adverse perinatal conditions and focus on neurodevelopment. The importance of these studies lies in the fact that it is in the prenatal period when an unborn child experiences its fastest growth, and when the most important organs - in terms of the sort of life the baby will have as an adult - are formed.\nSome of the most significant results obtained in the course of these years have shown that heat, breastfeeding, breathing support and the skin-to-skin technique improve quality of life for these babies. The Sant Joan de D\u00e9u Hospital chose the Beb\u00e9 Due maternity sling three years ago, for skin-to-skin therapy, and it has now been demonstrated that this sling has assisted the recovery of babies born preterm.\nThe hospital has more than 130 years of experience, and specialises in the problems of women, children and adolescents. It combines the human side of healthcare with developing new scientific techniques.\nThe \"Espa\u00f1a\" brand has positioned itself in Kind & Jugend 2012 with a large stand exclusively dedicated to Spanish baby wear, children's clothes and babycare products.\nBeb\u00e9 Due is a finalist in the Todopapas Awards. Vote for us!\nThe Beb\u00e9 Due Medic baby bottles features in the book, \"Universal Design: The HUMBLES Method for User-Centred Business\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzxvaf b/data_all_eng_slimpj/shuffled/split2/finalzzxvaf
new file mode 100644
index 0000000000000000000000000000000000000000..e10783c25fd2dc05e7211cd431e09c556c53d33e
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzxvaf
@@ -0,0 +1,5 @@
+{"text":"One of our clients wants to add streaming video from the Axis P 1357 E that we sold them and we're not excatly sure how to go about this. Does anybody have any recomendations that would make it easy for us to do this? Ideally the streaming window would open as a frame in our websiite.\nWhat is the industry standard for streaming video window size? We're cellular based so we need to be cognizant of usage.\nWhat about recording video? What if the clients wants a remote dvr that loop records for a week??\n1) Do you have a sense of the cellular bandwidth available for supporting live view streams?\n2) The P1357 is a multistreaming camera, and it probably will need a 'stream' setup for full resolution, low framerate (timelapse) and then a lower resolution, higher framerate stream setup for live video. Does that make sense?\nThere are a number of html scripts that can be used to pull Axis video streams into websites. (Also: see the Axis Windows Development API) However, I'm way outside my wheelhouse recommending the right way for your service to add this, and not all methods may work with your current firmware versions or be supported by Axis. Hopefully someone else can help on this point.\nAlso the P1357 supports SD storage on the camera itself. The camera can be configured to write video locally to the card (ie: motion events, etc) and then played back from the camera interface.\nI'm data pooled with multiple cams so we probably have 30-40 GB per month available and I can always increase if needed. I can log in and see the H264 very well.\nYes, we have it setup that way now but I'm not sure how to get the video to go to a website where the viewers can then see it. I could give the users the IP log in info and let them go through the Axis software but that will use too much data.\nCam is already operating in the field without an sd card so I'd have to ship one out, have client open cam and install, etc. Rather not do that though.\nI believe click2stream is a competitor, not an enhancement, to his offering.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Our vision is to create a large and open market place where merchants of all types can benefit from a joint effort to build in traffic through original and relevant content and value adding services. We seek to provide a place in our shopping mall for all who look for a place in internet where you can define what you are free from constricting yellow-pages-like categories. At chollazo.com you decide what your business categories are, what your keywords must be and how the potential customer can contact you without any intermediation. We seek to export this vision to the offline world creating an affiliate network of merchants that cooperate together for fulfillment and delivery processes, we seek to create an e-commerce platform where merchants can benefit from low cost credit card fees, fast delivery and consultancy support at really competitive rates.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The real trick with success is knowing how to repeat it, and that's what makes Vice President of Finance and Analytics Craig Devine so valuable. A veteran of more than 30 years of the hospitality industry's financial side, he knows what goes into innovative, sustainable business models. With a background in the operational aspects of finance, he has worked with both senior leadership and frontline associates, serving industry leaders such as Marriott, Wyndham International and, prior to HRI Lodging, Aramark. Thanks to his track record of success, he's risen steadily throughout his career and has become an integral part of the HRI leadership team.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"You never know how much you miss something until you lose it.\nTake collagen. I had always taken it for granted. My skin was smooth, firm and bounced back immediately when you pinched it.\nYeah, yeah, I know it wouldn't always be like that. One day I'd get old and wrinkly\u2026. But that day was eons away. Why think about it now?\nThen it happened. Around my late 20s, I've noticed my first few crow's feet creeping up around my eyes. That was my wake up call. I had to do something to restore that collagen now or every year, it'd get worse and worse.\nWhat The Heck Is Collagen And Why Does It Matter?\nCollagen is the protein that keeps your skin elastic. When your skin loses it, it starts to sag. Wrinkle, even.\nThis is something that happens naturally as you age. And when I say as you age, I mean as you grow up. You start losing 1% collagen each year since you turn 21! 21 not 51 ladies!\nIf you want to keep those pesky wrinkles off your face, you need to keep that collagen put and rebuild the little you lose every year.\nBut, is that even possible? Can skincare give you your collagen back or is that science fiction?\nNot all retinoids are the same. Prescription forms work much faster but they're super irritating. OTC forms like retinol work more slowly but they're more gentler on the skin.\nStill, it's best to start with a small (<1% concentration) twice a week and build up both dose and frequency gradually.\nRelated: Which Strength Of Retinol Should You Use?\nYou probably know vitamin C because of its powerful antioxidant properties. But this antiaging superstar is also essential for collagen synthesis.\nIf you apply a high enough concentration of vitamin C to your skin, it'll boost the production of collagen.\nA vitamin C serum isn't optional. So why not use one that has its BFFs vitamin E and ferulic acid, too? Together they boost collagen production AND your sun protection!\nYou know something else your skin needs? Exfoliation. Seriously, girl, those dead cells on your skin are roughing up its texture and stealing its glow.\nBut why opt for a scrub that only gets rid of them when glycolic acid does the exfoliating job fine AND boosts the production of collagen too?\nP.S. If you have sensitive skin, glycolic acid may be too harsh for you. But all other skin types can use it safely.\nP.P.S. Glycolic acid boosts collagen at 10% and higher concentrations. By all means, use your glycolic acid exfoliants if they work for you. But if you want it to boost collagen, consider going for chemical peels.\nAmino acids are the building blocks of proteins. Collagen is a protein. It follows that feeding your skin amino acids can give it what it needs to make more collagen.\nBut not all amino acids are created equal. The best to boost collagen production are l-lysine, l-proline, and l-threonine. Use them generously!\nYou know what else is essential for collagen synthesis? Copper. Give your skin more copper and collagen production shoots up.\nBut\u2026 here comes the catch: too much copper is toxic for you. I know, bummer!\nGood news: scientists have found a workaround. When you bind copper to peptides, it becomes safe to use on the skin. Phew!\nThe most popular copper peptide is GHK-Cu. It boosts the production of collagen, elastin, and other components of the skin's natural barrier; has anti-inflammatory properties; and helps heal wounds. Pretty awesome, isn't it?\nRelated: Are Copper Peptides Better Than Retinoids?\nLet's face it. There's only so much topical treatments can do. If you want something stronger (and your wallet can take the hit) try Genesis laser. A 2005 study shows it helps create new collagen.\nThe catch? You need more than one or two sessions. Six are recommended!. But, the results last up to 5 years.\nGensis isn't the only laser that can boost your collagen. Medlite is giving it a good run for its money too. A series of six treatments (that number again!) can stimulate the production of new collagen. Its effects lasts for about 3 to 5 years.\nIf you're looking for another professional alternative, try LED Phototherapy. It helps repair sun damage and boost the production of both collagen and elastin.\nThe best part? It has fewer effects than laser and is safe for dark skin, too.\nLost collagen isn't lost forever! With the right skincare products and treatments, your skin'll look younger for longer. No one'll be able to guess your real age.\nHow do you rebuild lost collagen? Share your thoughts in the comments below.\nRachel, than you! So glad you find it useful.\nHi! I'm a 25 year old girl from the most northern part of Sweden, and I'm very interested in skincare. The thing is that the weather conditions can be a bit extreme where I live and I'm not sure how to adopt my skin care routine appropriately, so I have some questions that I hope you might be able to answer. Firstly, is it a good idea to wash your face before going outside in the winter time (when it's say around -25 degrees Celsius or colder)? I was always taught as a child that this would give your skin less protection against the cold and that I shouldn't, but I have sightly oily skin so I'm not sure what to do. Secondly, is it necessary to apply sunscreen in the middle of winter when we who live really far north either don't see the sun at all or just barely see it for a few hours per day? And thirdly, during the summertime we have the reverse phenomena where the sun shines 24 hours per day, so should I apply sunscreen at night? The sun will most definitely shine on my skin during the night even if it is through a window.\nI haven't been able to find any useful information regarding this, and I would be very grateful if you could help me with these questions. Thank you for a great blog, I've learned so much from you!\n1. It depends. A lot of bar soaps are pretty harsh on the skin and can damage its protective barrier. When that happens, harsh weather can wreak havoc on the skin. But a lot of cleansers today are very gentle, and remove dirt without compromising this barrier. Afterwards apply a moisturizer with skin-identical ingredients (such as ceramides and fatty acids) that help strengthen that barrier, and you should be fine.\n2. As a rule, sunscreen should be used from the moment the sun goes up (or you wake up, obviously), to the moment it goes down. That's because, unlike sunburn-inducing UVB rays which are stronger between 10am and 4pm, wrinkle-causing UVA rays are always present. So, if you're concerned about anti-ageing, yes, you should wear sunscreen in winter too, but only until the sun sets. If you're worried about vitamin D deficiency, and can't get enough of it from your diet alone, then I'd suggest going without sunscreen for a day a week. It may cause some sun damage to the skin, but it's not as bad as the harm a lack of vitamin D does.\n3. If the sun is able to hit your skin at night, then yes, you should apply sunscreen at night too. UV rays can penetrate through glass too, unfortunately, so, if you're directly in front of a window, you should still wear sunscreen.\nHI, I found your site looking for something else and this article caught my attention. I have recently been looking for a collagen supplement. I heard they are great for collagen production. I've been looking for hydrolyzed collagen supplements and found there are many out there. Verisol and BioCell had some studies done with promising effects (I found them on pubmed). Do you have any thoughts on using oral supplements (pills) for collagen production?\nMostly importantly, do you find anything indicating it is unsafe to ingest these supplements? My thought \u2013 if it can't hurt, may as well give it a try \ud83d\ude42 Do you have a favorite brand of collagen or one you'd recommend trying?\nI've been poking around your site for about an hour\u2026.it's just amazing! Great site!\nSP, thank you! So glad you like my website, and hope to see you around often.\nWere those studies you saw about collagen peptides? Collagen itself is a protein, and, as such, when ingested gets broken down into amino acids. This makes collagen supplements completely useless.\nCollagen peptides, on the other hand, are small peptides made up of several amino acids, which the body can use to make new collagen. Collagen peptides are also treated with specific enzymes to ensure that skin cells can readily use them. This type of collagen seems to be a bit more effective, although most of the studies I've seen about them are made by the manufacturers.\nWhat are your thoughts on products containing growth hormone? Do they work and are they safe for long\/er term use? What do you think of antioxidants in entirely natural forms like say, cranberry seed oil? Strong enough for any discernible improvement?\nFynl, I don't like the idea of using hormones in skincare, especially human growth hormones. Hormones are something I wouldn't mess with and there isn't much proof they work anyway. Cranberry seed oil and other oils like that are fine. I especially love rosehip oil because it's a natural source of vitamin A.\nI must say, i never found any benefit using skin oils and found using they made my skin look worse if anything, despite being sparing with them (2-3 drops max). Recently i have tried squalane oil, which is one of the skin oils which does not oxidize, and actually acts like a anti oxidant. I have noticed a difference using this oil compared to others.\nFYI My skin care routine consists of l abscorbic acid and matrixyl in the morning, retinol and niacinamide at night (once a week I use retin a, i am starting the process of adjusting to it) a good dermalogica moisturizer, with a couple of drops of squalane oil added, gentle but effective cleansers, and of course, religious sunscreen\u2026 3 months into my routine i have everyone asking me what i have done to my skin, i get loads of compliments.\nLily, your skin routine is spot on. No wonder your skin looks amazing. Well done for putting it together!\nThat's a great point you're making about oils. I think they can work but they do go bad quicker than store-bought cosmetics. If you want to go down that route, you need to be prepared to use them quickly and buy often. But I also think oils work best for dry and dehydrated skin types. Other skin types won't see much of a difference and may even get breakouts.\nAudrey, there is some evidence that other peptides, like Matrixyl 3000, can help, but it's very scant. Most studies are still done by the manufacturers and I don't count those.\nSkincare products with collagen are useless, but what about hydrolyzed collagen? Is it useless too?\nAM, it MAY have some benefits in supplements (the jury's still out there) but in skincare, it's just a moisturizer.\nMe too\u2013love your site and find it very interesting. Thank you very much!\nI've recently been researching micro needling and had my first session this week. I am not yet ready to spring for doing micro needling with PRP, so I had it done by a licensed esthetician who uses Biopelle ampoules with snail serum, a mask with stem cells derived from plant sources, and hyaluronic acid, all applied topically.\nI have to say, even just two days later, my skin looks very good, fine lines are definitely diminished.\nWhat seems to be the consensus is that the wounds the micro needles create in the skin result in tiny channels through which good quality products can actually reach the dermis, rather than just sitting on top of the skin, as is the case whenever we apply topicals. The act of \"wounding\" the skin seems to cause the collagen to contract, resulting in the body creating more collagen. These tiny channels remain open only for a short period.\nHave you checked this out yet? If so, I'm wondering what you think.\nI myself would not attempt to do any sort of needling on my face. I'll leave that to the professionals, but I am wondering about buying a derma roller and using some of the products that you've mentioned as helping to create more collagen, but on my arms and legs. Any thoughts?\nKab, I agree about everything you'd said about microneedling. It does trigger the production of collagen and helps skincare products better penetrate the skin. Once in a while it's great. But I'm concerned that wounding the skin often may make healing more difficult in the long run.\nBetween treatments, you can use some of these options to help your skin produce more collagen.\nHi Gio, what a great article. I love that you admit the truth about collagen in creams, and I say that as a woman with a feww bottles of face cream containing collagen. The tips about retinoids and vit C are spot on.\nI have been usung both plus I have actually been drinking collagen a lot lately. Its making a difference. My face is appearing plumper. I read a study that inspired me. The study said that drinking collagen causes an increase in key amino acids and the peptides in the body. The result is an increase in production of hyaluronic acid in the skin of 3.8 fold just two hours after drinking it. So drink up! Haha.\nI think your blog is great so I am going to subscribe.\nI was about to ask you the question about your thoughts on consuming collagen and it looks like the last comment touches upon it already. I saw this collagen formula at the store the other day. I did not even know such a thing existed.\nMaria, as I said the science is conflicting. I think it's the price is reasonable, you can give it a try. But I wouldn't invest too much in it just yet.\nWhat is your opinion of Sero Vital?\nNora, I don't really like human growth hormones. If not used properly, they can do some serious damage.\nI love your detailed and super helpful writing. Will be a diligent reader or yours.\nNhanh Le, aww thank you so much for your support! I really appreciate it.\nThanks for such informative and balanced writing.\nFWIW, drinking collagen and minerals in the form of organic homemade bone broth is another way to nourish skin from the inside. Have only anecdotal evidence it works since every person I know who does it has seen improvement in their skin \u2014 fuller, plumper, tighter, and more glowing. Takes about a month to see the results.\nI'm 35 and up until recently I've had great skin. I've always ate healthy, wore sunscreen, and took care of myself. However, over the last few months things haven't been going well. I went back to school, my mom got sick, and overall the stress took a toll on me. I've noticed these dark rings around my eyes and they look sunken. My derm told me I've lost volume and I'm aging and will need fillers. I'm very scared to do this and was wondering if there is any hope out there to build up volume again naturally like with some of the things youve mentioned above. I've been really bummed out and blaming myself for this happening to my face. Any advice would help!\nCynthia, are you using anything else before moisturiser? It seems like your skin's protective barrier is severely damaged. Try a gentle moisturiser like Cerave PM Moisturiser.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Interpellate the brands you like and get spotted!\nIn this space you can spontaneously post your creations. Photo, video, music: it's your turn!\nDo you want to be noticed by a brand that you like? Show him your talent and know-how! The opportunity for you to maybe get the collaboration of your dreams.\nOnce sent and validated, the brand will have access to your \u00ab creative challenge \u00bb and can leave you a comment. Your fans will also be able to follow you and share your creations.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzyjin b/data_all_eng_slimpj/shuffled/split2/finalzzyjin
new file mode 100644
index 0000000000000000000000000000000000000000..81352236a583aa7c9a038967552d35b0c877a202
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzyjin
@@ -0,0 +1,5 @@
+{"text":"As the tale begins, a man wakes up in a bare room with no idea who he is, where he is, or how he got there. Mr. Blank, as Auster dubs him, cannot even remember the names of objects, so every piece of furniture in eyeshot has been labeled: DESK, LAMP, CHAIR. A manuscript rests on the desk, so Mr. Blank sits down and begins to read. He finds himself reading about a man who is imprisoned, who is being watched and perhaps tormented. Mr. Blank begins to relate to the tale. Then he is interrupted by a guest who has some questions for him.\nSay what one will about Auster's repetition of devices - the book within a book, the off-stage tormentor, the loss of memory - he has become frightfully good at manipulating a good story out of them. The novel unfolds over the course of a single day, so the reader experiences Mr. Blank's curious condition in real time. Within a few pages one is flying through this book in search of answers, every bit as agitated as Auster's hero.\nEvery few pages, Mr. Blank meets yet another visitor who has come to check on him.\nReaders familiar with Auster's literary detective series, The New York Trilogy, will recognize these characters: Anna Blume, Flood, and Fanshawe. Auster has scripted them all back into action here, only now they are doing the interrogating. Why did you put me through such trials? Do you still think about me? By braving the surefire criticism that he has gone down the wormhole of authorial self-regard, Auster has cleverly captured a writer's dilemma. The more he gives to his creations, the emptier he becomes - to the point where he has nothing left to give. Still his creations ask for more.\nTravels in the Scriptorium is a bit of a closed system. One needn't have read The New York Trilogy to appreciate the book, but it helps. Some curiosity about or sympathy for a writer's plight might also make this a more enjoyable read, too. But Auster doesn't leave the newcomer in the dark. There are some wonderful touches here. After he discovers that the manuscript on the desk is unfinished, Mr. Blank has a go at finishing it. \"Haven't felt so full of beans all day,\" he says after making some headway. Later he rewards himself with a nap and returns from \"a brief sojourn in The Land of Nod.\" Even though the author is hitting a minor key, readers are apt to feel the same way after this latest visit to the Land of Auster.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Tired of dorm living? Want to get away from the headache of roommates? Miss having a pet? Come view Boulevard Apartments. We are conveniently located along major bus lines are only minutes away from local universities and various student friendly neighborhoods. These dorm apartments are perfect for the student budget and what's more they're pet friendly! Schedule an appointment today!\nBoulevard Apartments is located and 0.74 miles from University of Pittsburgh. The property has a Walkscore of 83, so you should be able to walk or ride a bike most of the time. The property has a Transitscore of 68, so you'll have good transportation options.\nBoulevard Apartments has many shops nearby. Coffee shops in the area include Hard Rock Cafe Pittsburgh, Starbucks, Panera Bread. There are a number of markets in the area include Trader Joe's, Whole Foods Market, Giant Eagle.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The work Paw patrol, Winter rescues represents a distinct intellectual or artistic creation found in Lewisville Public Library. This resource is a combination of several types including: Work, Moving Image, Visual Materials.\nPaw Patrol is on a roll, even through the ice and snow, in these seven wintry missions, including a double-length adventure to save Christmas! From a ski-lift rescue to tracking down a snow monster, no job is too big and no pup is too small. Plus, see how Rubble first joined the team by helping out in a snowy situation!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Protect Your Home's Upholstery, Carpets And Draperies With Fabric & Fiber Protection!\nSpring is just around the corner and in Pasadena spring-cleaning is at the top of many people's lists of things to do.\nNow is the time to prep your home for the season's parties, outdoor barbeques, and other activities. Then you can enjoy taking in Pasadena's many spring events. Such as the \"Season of Spring Art Show\", now being held at the Flower Pepper Gallery where hundreds of artists are now displaying their work based on theme of spring.\nOn the other hand, you could just hang out or stroll down Colorado Blvd. and enjoy a day of shopping.\nThere is also the famous Pasadena Heritage's Spring Home Tour, which this year will host tours of homes with a Spanish flair.\nYour home too will be host to many events also in the coming weeks and months.\nShouldn't your home be ready?\nDraperies and your furniture's upholstery have been absorbing smoke from cigarettes and stains from food, drink, or just plain wear from being used during winter.\nNow is the time to get it all revitalized with Fabric & Fiber Protection from Pasadena Carpet Cleaners (626) 376- 4023) who can not only clean your furniture's coverings to bring them back to a like new condition, but also protect it as well as your draperies from any future harm with their custom fabric treatment process.\nWhat covers your furniture and flooring? Most furniture today is covered in one of four ways with Leather, Microfiber, Faux leather, and cotton upholstery. In some cases exotic materials such as silk, velvet, and velour are also used.\nAll of these materials have very little to protect them from indoor air pollution, spills, and food mishaps. Pets also may stain or leave hair on these surfaces, which is hard to remove. This is why you need Fabric & Fiber Protection.\nThe same may also be said for your carpeting and floor rugs. Many people today buy expensive area rugs from the Middle East, Asia, Africa and India, which require special handling and cleaning.\nThis is why you need a Fabric & Fiber Protection protective coating laid down over them now before the spring festivities begin to help them retain their beauty and value.\nHow to protect the beauty and value of your furniture and carpeting. Today there are new technological advances in the science of Fabric & Fiber Protection that can be used to keep your expensive furniture and floor coverings protected from wear and damage.\nTeflon treatments are now available for fabric and carpet protection that stains and dirt slide right off of.\nThe classic Scotch Guard protective system is also one of the all around protection applications.\nUltraguard is a chemical process that bonds with the fibers themselves and permanently protects fabric coverings, microfiber, and micro weave coverings.\nPasadena Carpet Cleaners also has their own formulations of protective ingredients that can safely protect carpeting, furniture, and draperies as well.\nWhen Fabric & Fiber Protection is applied, your wall hangings will look like they have just come out of the interior designer's display directly to hang on your windows or walls.\nYour carpeting will be able to stand up to any party, dinner, or an evening of watching the \"Big Game\" on your widescreen along with all the snacking and drinks without worry over spills and food falling on furniture or floor.\nNow is the time to get your fabric coverings and carpets protected before the spring season activities get into full swing.\nCall Pasadena Carpet Cleaner today and they will give you a free estimate and then will come out and get your home protected for spring and all the festivities that you have planned for spring.\nCall the Pasadena Carpet Cleaners at (626) 376-4023. Do it now, before spills and stains mar your furniture, carpets and ruin your spring activities.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"If you asked Wilmington real estate developer Napier Fuller to describe himself, he'd tell you he's a modern-day Martin Luther King Jr.\u2014an activist fighting a corrupt system trying to censor him.\nNot everyone would see the likeness.\n\"We pray that God's wrath may swiftly come upon those that seek to promote sexual paganism,\" one read.\nUNC Police issued a cease and desist order; Fuller ignored it, saying that he had the right to contact faculty members on their public email accounts. In February 2017, he was arrested. That arrest set off a series of court cases that have spanned more than a year, including the harassment charges and Fuller's own federal suit over courtroom accommodations for people with disabilities.\nNow Fuller's taken up another cause: the removal of gay pride symbols from Orange County Courthouse.\nFuller's trial on the misdemeanor harassment charges is scheduled to begin August 6 in Orange County Superior Court, where he plans to argue free speech as his defense. If convicted, he faces sixty days in jail. However, before his trial begins, he's demanding that the courthouse remove any gay pride logos or flags from the property, since he argues that the symbols will influence his jury. He also believes more generally that their presence violates federal law.\nOne problem with this argument: There does not appear to be much in the way of gay pride displays in the courthouse at all. In fact, on a recent visit, a reporter saw none at all. No symbols, no logos, no anything.\nEven so, he's pressing on with his demands.\nDespite the tone of his emails, Fuller says he doesn't have a problem with LGBTQ people. His goal, he says, was to address the agenda he sees at UNC.\nFuller says he was raised in a liberal household and graduated from MIT with a master's degree in urban planning (the university confirms this). After that, he started a technology company in California, got married, and converted to Catholicism. He also became a supporter* of Opus Dei, an ultra-conservative organization tied to the Catholic Church.\nBecause of his involvement, Fuller says he was invited to Washington, D.C., in 2016 for a series of meetings with \"high-ranking members\" of the church. While in these meetings, Fuller claims, he was given instructions to fight for HB 2 in North Carolina and to encourage Republicans to \"stay the course,\" using whatever methods he thought best. As a result, he says, he began emailing the state's public officials, then recycled those emails to LGBTQ advocates at UNC.\nFuller, who is representing himself in court, says he's been \"thrown to the wolves\" in dealing with the university and its lawyers.\nRepresentatives from UNC declined to comment.\nClarification: After this story published, Fuller emailed to clarify that he was not a member of Opus Dei, but rather a \"cooperator,\" meaning a supporter. He also sent a photo of an office next to the courthouse's Battle Courtroom in which there is a small gay pride decal on a window. He says the picture was taken today.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaafmv b/data_all_eng_slimpj/shuffled/split2/finalzzzaafmv
new file mode 100644
index 0000000000000000000000000000000000000000..af605f0a5ffa5f2a5728e826963e9291c08947a3
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaafmv
@@ -0,0 +1,5 @@
+{"text":"The SMO-Group headquarters was established in the UK in 2008 and the operational office is based in Ipswich, Suffolk.\nThe UK resident based staff provide the company and its clients with both administrative and project coordination expertise across all world-wide operations. From this office clients can enjoy the close support and effective communication that is the hallmark of the SMO-Group.\nAll of our warehouses include controlled temperature storage, site distribution, 24\/7 security and backup power generators.\nWe provide import\/export regulatory and customs support, delivery and transport, materials and equipment.\nWe transport with quality and care using up-to-date technology to monitor shipments. Our personnel are highly trained.\nPatients are escorted by trained staff, transfered quickly and safely, to and from clinics. Fast telephone booking service.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"MDK is a proof-of-concept tool to exploit common IEEE 802.11 protocol weaknesses. IMPORTANT: It is your responsibility to make sure you have permission from the network owner before running MDK against it.\nMDK 3.0 v6 - \"Yeah, well, whatever\"\nMDK is a proof-of-concept tool to exploit common IEEE 802.11 protocol weaknesses.\nnetwork owner before running MDK against it.\nSends beacon frames to show fake APs at clients.\nThis can sometimes crash network scanners and even drivers!\nSends authentication frames to all APs found in range.\nToo much clients freeze or reset some APs.\nSSID Bruteforcing is also possible with this test mode.\ndeauthenticates Stations and APs sending WPA encrypted packets.\nnetwork to WEP or disable encryption.\nAP 9C:D3:6D:B8:FF:56 seems to be INVULNERABLE!\nDevice is still responding with 500 clients connected!\nAP E0:3F:49:6A:57:78 seems to be INVULNERABLE!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Tipard MKV Video Converter - \u041e\u0434\u0438\u043d \u0438\u0437 \u043b\u0443\u0447\u0448\u0438\u0445 \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u043a\u043e\u043d\u0432\u0435\u0440\u0442\u0435\u0440\u043e\u0432, \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0430 \u043b\u0435\u0433\u043a\u043e \u043a\u043e\u043d\u0432\u0435\u0440\u0442\u0438\u0440\u0443\u0435\u0442 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0432\u0441\u0435 \u0432\u0438\u0434\u0435\u043e \u0444\u043e\u0440\u043c\u0430\u0442\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a MPG, MPEG, MPEG2, SWF, FLV, VOB, MOD, MP4, H.264, M4V, AVI, WMV, 3GP, 3GPP, MOV, DivX, XviD, Quciktime Video, DV, MJPG, MJPEG, MPV, \u0432\u043a\u043b\u044e\u0447\u0430\u044f \u0432\u0438\u0434\u0435\u043e \u0432\u044b\u0441\u043e\u043a\u043e\u0433\u043e \u0440\u0430\u0437\u0440\u0435\u0448\u0435\u043d\u0438\u044f High Definition video files(HD\/AVCHD videos), \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a TS, MTS, M2TS, HD MPEG 2, HD MEG4, HD WMV, HD MOV, HD H.264, HD RM.\n\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, HD video converter \u0443\u043f\u0430\u043a\u043e\u0432\u0430\u043d \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u043d\u044b\u043c \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0435\u043d\u0438\u0435\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043a\u043e\u0434\u0438\u0440\u043e\u0432\u043a\u0438 \u043b\u044e\u0431\u043e\u0433\u043e \u0430\u0443\u0434\u0438\u043e \u0444\u043e\u0440\u043c\u0430\u0442\u0430 \u0431\u0435\u0437 \u043f\u043e\u0442\u0435\u0440\u0438 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0430, \u0430 \u0432\u0441\u0442\u0440\u043e\u0435\u043d\u043d\u044b\u0439 \u0440\u0435\u0434\u0430\u043a\u0442\u043e\u0440 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0432\u044b\u0440\u0435\u0437\u0430\u0442\u044c \u0430\u0443\u0434\u0438\u043e \u0444\u0440\u0430\u0433\u043c\u0435\u043d\u0442\u044b \u0438\u0437 \u0432\u0438\u0434\u0435\u043e \u0438 \u043a\u043e\u043d\u0432\u0435\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0432 \u0441\u0430\u043c\u044b\u0435 \u043f\u043e\u043f\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0430\u0442\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a M4A, MP3, AC3, AAC, WMA, WAV, OGG, AU, Nut, AIFF, FLAC, AMR.\n\u041f\u0435\u0440\u0435\u043a\u043e\u0434\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0444\u0430\u0439\u043b\u044b \u0441\u043e\u0432\u043c\u0435\u0441\u0442\u0438\u043c\u044b \u0441 iPod, iPhone, Apple TV, PSP, PS3, Wii, Zune, Xbox, Sony Walkman, Sony XPERIA, Google Phone, BlackBerry \u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u043c\u043e\u0431\u0438\u043b\u044c\u043d\u044b\u043c\u0438 \u0442\u0435\u043b\u0435\u0444\u043e\u043d\u0430\u043c\u0438.\nMKV is the new popular video format\u2014Matroska video. Tipard MKV Video Converter can help you to convert MKV files to the formats fitting for your portable players. This best MKV Video Converter can easily convert MKV, MPEG files, HD MPEG, WMV, ASF, AVI to AVI, MPG, MP4, 3GP, HD videos, etc. And extract audio from MKV and other videos to AAC, AC3, AIFF,AMR, AU, MP3, M4A, MP2, OGG, WMA, WAV etc for your iPod, iPhone, Zune, PSP, PS3, Xbox and other MP4 Player.\n\u2022 Capture favorite pictures. Capture your favorite pictures when preview your video and you can choose to save it as JPEG, GIF or BMP formats. You can also set the saved folder or it will be saved automatically in the defaulted folder.\n\u2022 Select what you want profile easily. Tipard MKV Video Converter sorts the profile by the devices, General video, General audio, HD videos, etc, then it's easy for you to find what you want one.\n\u2022 Multiple profiles. Get multiple files with the same content at one time by adding multiple profiles to one source simultaneously.\n\u2022 Support preview both the input and the instant output video effect simultaneously. Using Tipard MKV Video Converter, you can preview the original video and the instant output video for your operation at the same time.\n\u2022 Fastest Conversion Speed. Provide the fastest conversion speed (>400% ), completely support dual core CPU.\n\u2022 Easy to use. Just few clicks to finish the process of convert MKV files. This MKV Video Converter is especially easy for beginner.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Conceptual Physics: What are Eddy Currents?\nEddy currents are currents induced in conductors when exposed to a changing magnetic field due to relative motion of the field source and conductor; or due to variations of the field with time. This can cause a circulating flow of electrons within the body of the conductor. These circulating eddies of current have inductance and thus induce magnetic fields. These fields can cause repulsive, attractive,propulsion and drag effects. The stronger the applied magnetic field, or the greater the electrical conductivity of the conductor, or the faster the field changes, then greater the currents that are developed and the greater the fields produced.\nbe harnessed for induction heating. The electromagnetic forces can be used for levitation, creating movement, or to give a strong braking effect.\nEddy currents can also have undesirable effects, for instance power loss in transformers.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\uad6c\uccb4\uc801\uc778 \ud50c\ub79c\ud2b8 200-250 Tph ... - kr.made-in .\nChina Mobile Impact Crushing Plant, Portable .\nHigh Yield Jaw Crushing Plant From Netherlands .\nChina Crushing Line - China Crushing Line, .\nChina Crushing Line, Find details about China Crushing Line, Crushing Plant from Crushing Line - Shenyang Sanland Mining Equipment Manufacture Co., Ltd.\nChina Portable Stone Crushing Plant, Simple .\nPortable Crushing Plant, Stone Crushing Plant, Jaw Crusher manufacturer \/ supplier in China, offering Portable Stone Crushing Plant, Simple Structure Jaw Crusher Machine for Rock Stone, Ball Mill Grinding Machine, Ball Mill Price, Zirconia Grinding Machine (D900*1800), Rotary Mineral Drum Sieve, Gold Stone Sand Separator, Sand Washer .\njapanese li ne crushing plant manufactures - .\nChina Mobile Crushing Plant for Jaw Crusher .\nli ne crushing plant made in spain - .\n20151217 stone crusher milling equipment benefiion plant building materials equipment feeding screening production line limestone crushing plant made in spain. Read more; Limestone Crushing Plant Made In Spain. limestone crushing plant spain newest crusher, . limestone crushing plant made in spain a mining . heavy construction equipment .\nMade In China Com Cpo Crushing Plant - china portable crushing plant - YouTube. . cone crusher from china manufacturers china . a leader in Malaysia\"s 1) China\"s refineries consist of 2 palm oil . crushing plant manufacturers malaysia. sand screening plant malaysia supplier Crushing Equipments SAM stone .\nCrushed Rock Stone Crushing Plant Issues | .\nFelda kernel crushing plant . kernel crushing plant equipment. palm kernel crushing machine CGM Project Case . Kernel Crushing Plant, Detailed Complete Palm Kernel . felda kernel crushing plant - felda kernel crushing plant sights and sounds of lahad datu how much is gold mobile crushing plant in south africa how much is gold mobile .\napproved reliable quality granite crushing plant .\nChina Mobile Jaw Crushing Plant - China Mobile .\nStone Crushing Plant for Stone Cursher - Made .\nChina Stone Crushing Plant for Stone Cursher, Find details about China stone crushing plant, stone crusher from Stone Crushing Plant for Stone Cursher - .\ncrushing machine model price - .\nChina Stone Crushing Plant Capacity 60 Tons .\nproduction from crushing plant - .\nMade In China Com Cpo Crushing Plant inss.co. The fact file states: \"The oil palm sector, particularly CPO production, is an . Crushing Plant.\nCrushing Plants Made In China - .\nMin Wheet Grinding Machine China - .\nmini wheat flour mill faridabad \u2013 Grinding Mill China. mini automatic wheat flour mill machine, ... Wheat, Corn, Rice, made in China, since 1992 \u00bb Learn More. Wheat Grinding Machine Manufacturers, ... min wheet grinding machine china. Wheat Grinding Machine - Alibaba. 27428 Results ... china manufacturer turnkey 60TPD wheat flour grinding .\ncpo millers ad mining plants - .\nChina Tire Mobile Crushing Station - China .\nCrushing Plant, Impact Crusehr, Impact Stone Crusher manufacturer \/ supplier in China, offering Tire Mobile Crushing Station, 500t\/D Rotary Kiln Cement Production Line, Ceramic Rotary Kiln Production Line and so on.\nmobile crushing plant,mobile crusher plant,mobile crushing . The mobile crushing plant is not limited by the crushing place, and reduces high material transportation cost.\ncrushing plant made china - privilegeresorts.\nCrushing Plant For Construction ... - m.made-in-china . China Crushing Plant For Construction - Select 2017 Crushing Plant For Construction products from verified China Crushing Plant For Construction manufacturers ... Read more; crushing plant made china \u2013 Grinding Mill China. New Type Construction Waste Crushing Plant Launches into .","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaapch b/data_all_eng_slimpj/shuffled/split2/finalzzzaapch
new file mode 100644
index 0000000000000000000000000000000000000000..26727801f5d2a8a7c18fe4bab23b16c0f38a6d29
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaapch
@@ -0,0 +1,5 @@
+{"text":"A late summers day brought out all the faithful attendees to the plot plus a few newbies to join in the fun. We were greeted with the beginnings of autumn tinging the leaves of our still producing glorious grapevine.\nWe quickly realised there were still plenty of fruits on our crab apple tree after the first pickings last time, so Fiona, Sarah and Helen got to work harvesting the higher up crabs for more home made vitamin c packed jams and jellies.\nMeanwhile Duncan and Kamil unloaded a load of donated top soil into to our Hugelkulture raised beds in the children's plot ready for planting up next time with lots of perennial herbs, all over-seen by chief fore-man Nella.\nWe have wonderful neighbours at the allotment and one of them Steve came bearing carrots which we readily and thankfully received.\nWe have potted up a great number of strawberry plants which we are nurturing on in the greenhouse which will be on sale at St laurence orchard Apple day on the 7th October.\nThe warmer weather after the rain brought out our friends the Slow worms, which delighted the children no end. We were pleased to have been joined by Claire of Conscious kitchen Southend who we were excited to talk with about Southend food network, Ayurvedic cooking classes with Sarah, and diet as medicine with Dr Helen.\nWe will be at the aforementioned Apple Day at st Lawrence's Orchard on the next open day so please come and visit us there and sample the yummies we have prepared. The next plot day is Sat the 14th October all welcome, no matter the weather.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"... indonesia,kenya,pakistan crusher|granite crusher|feldspar crusher|limestone welcome to understand our aggregate crushing plant and related stone crusher !\nstone crusher plant made in pakistan price. limestone crusher pakistan, where the cone crusher manufacturer? what is the best stone crusher? get price.\nstone crusher, stone crusher limestone, granite, stone crusher plant made in pakistan price,stone crushing stone crusher plant made in pakistan price.\nstone crusher plant made in pakistan price,stone crushing . raw stone may be purchased directly in the pakistan stone crushing plant,limestone crusher for sale.\n... manganese crusher limestone crusher plant in, pakistan,germany maker. he use of mobile cone crusher in limestone crushing plant in pakistan. get price.\nin malawi limestone crushing plant for sale, limestone crushing plant in pakistan tag: malawi limestone crusher,crusher run limestone price,crusher for .\nfully mobile limestone crusher. aggregate gravel plant can process a variety of raw materials, limestone, get price and support.\ncrushing plant price in pakistan- pakistan stone crushing plant,limestone crusher for sale. crushing plant made in pakistan .","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Malum is the boss bike of the Subrosa lineup and the 2019 Subrosa Malum is taking charge. The full chromoly frame, fork and bars feature contemporary geometry and sizing, with a 21\" top tube, tall standover height and 9\" bar height. For parts, you get a full assortment of aftermarket pieces from Shadow, Rant and Subrosa. Round it all out with specs like 3-piece chromoly 170mm cranks, 25\/9 gearing, 2.35\" Shadow tires and sealed bearings throughout, and the Subrosa Malum is a lot of bike for not a lot of loot.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This is a math question. I want to know what 26\/100 + 7\/100 in a fraction the simplified to a decimal.\nIs fruit of the earth aloe vera 100 % gel individually sealed?\nI am about 1\/4 black and 3\/4 white and my girlfriend is 100% black?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"In an interview with the Guardian, Len\u00edn Moreno expressed frustration with the WikiLeaks founder, who had been provided asylum by Ecuador since 2012. On Thursday, the country revoked that asylum, leading to Assange's arrest by British police on a U.S. hacking charge. This follows Moreno's initial public address the same day, which explained that Assange was being kicked out for his behavior and for violating the terms of his asylum.\nA set of anonymous documents known as the INA Papers also was released this year, the Daily Beast reports, and alleged that Moreno benefited from a corrupt deal with a Chinese firm. WikiLeaks has denied involvement with the anonymous site or the hacking, but the anti-secrecy group did direct its followers to the documents in a March 25 tweet that said a corruption investigation had been opened into Moreno's conduct.\n\"Any attempt to destabilize is a reprehensible act for Ecuador, because we are a sovereign nation and respectful of the politics of each country,\" he told the Guardian. Before evicting Assange, Moreno said he sought assurances from Britain that Assange would not \"suffer torture, ill treatment or the death penalty\" were he to be taken into custody or extradited to another country.\nHe also claimed that Assange had taxed his hosts' patience. Moreno said he \"mistreated our officials in the Ecuadoran embassy in London\" and that his \"improper hygienic behavior\" affected the climate at the diplomatic outpost.\n\"Ecuador has been making some pretty outrageous allegations over the past few days to justify what was an unlawful and extraordinary act in allowing British police to come inside an embassy,\" she said.\nMoreno's predecessor, Rafael Correa, called the decision to release Assange to authorities a \"crime that humanity will never forget.\" Correa had granted Assange asylum in 2012.\nAssange has been charged by U.S. prosecutors on suspicion of conspiring with Chelsea Manning to obtain secret military and diplomatic documents, The Washington Post reported last week. However, Assange's extradition to the United States could take years.\nIt's the latest chapter in a nearly decade-long legal saga for Assange. He brought himself and WikiLeaks to prominence in 2010, when the organization published leaks from Manning, who was convicted in 2013 for the leaks.\nBut that same year, Swedish authorities issued an arrest warrant for Assange over two allegations of sexual assault, which he has always denied (Swedish authorities later dropped the investigations). Assange traveled to Britain, where a court ruled in 2012 to extradite him to Sweden. But he jumped bail and entered the Ecuadoran Embassy in London, where he was granted asylum later that year.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaceco b/data_all_eng_slimpj/shuffled/split2/finalzzzaceco
new file mode 100644
index 0000000000000000000000000000000000000000..e1fa33e27b6aa7cd87fc5ce60f9ab3b76c06516b
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaceco
@@ -0,0 +1,5 @@
+{"text":"A high-ranking diplomat said nobody should decide on behalf of the Syrian nation, even if finding a political solution for the five-year-long Syrian crisis takes a long time.\nDeputy Foreign Minister for Arab and African Affairs Hossein Amir-Abdollahian made the statement on Friday, IRNA reported.\nReferring to calls by some regional and trans-regional states, including Saudi Arabia, Turkey and the US, for Syrian President Bashar al-Assad to step down from power, the deputy minister said the decision about the Syrian president is up to Syrians.\nOn the date of the next round of international talks on Syria, Amir-Abdollahian said the meeting will be held in \"two or three weeks\" and the location \"has not been determined yet\", but Vienna and Paris are possible venues.\nThe first round of Vienna meetings on Syria was held on October 30 and the second round of November 14, where senior diplomats from a number of influential countries, including Iran, as well as envoys from the United Nations and the European Union attended the talks.\nThe participants agreed on respecting Syria's national unity and sovereignty as well as eradicating the terrorist groups operating in the Arab country.\nPrevious conferences, known as Geneva I and Geneva II, failed to achieve anything in terms of resolving the conflict in the Arab country.\nThe diplomat said the political process should be pursued in parallel with the battle against terrorists, adding that it is up to everyone to clear the path for the Syrian people to defeat terrorists.\nAmir-Abdollahian also touched upon the recent war of words between Turkey and Russia over the Turkish downing of a Russian warplane near Syria-Turkey border last Tuesday.\n\"While Russia is confronting terrorist groups, it is a mistake to hit a plane which is bombing terrorists,\" he said.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Aloha Surf Camp Maroc is located in Tamraght just 400 meters from Taghazout beach and very close to Banana Beach, Hash Point and Panorama's surf spots. It is located in an area that offers more than 15 surf spots in 50km for both beginners and advanced surfers. Rooms are decorated in a Moroccan style and features private balcony with amazing views of the ocean. The surf camp has its own surf school with profesional instructurs and offers surfing lessons for all levels. They also organize transport in 4x4 to find the best waves and discover the best surf spots of the area.\nServices\/Activities: surf school with profesional instructurs and offers surfing lessons for all levels. They also organize transport in 4x4 to find the best waves and discover the best surf spots of the area.\n\"Amazing time at aloha! Booked for a few days, ended up staying couple of weeks!!! All the staff - Absamal, Medhi, Jamila etc..- is very friendly and helpful!! Food is delicious, better than many (overpriced) restaurants in tagazoute...Brahim is a great person and a fantastic chef! Surf guides - Yasiff, Hussin and the rest of the crew - have lot of experience, they know very well all the breaks and always make the right choice according to your level and the daily conditions. Overall, aloha is top!\"\n\"great atmosphere and wounderfull view of the ocean. We had dinner all togheter and playing pool. very helpfull and nice all the staff too\"\n\"Excelent staff, good food (u have to dinner at their surfcamp, it's amazing)\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Located in Texas, Ultimate Tool & Safety serves the entire region as the go to place for tower workers, construction workers, telecommunication workers, arborists, crane workers, and more.\nUltimate Tool & Safety is an excellent source for high quality equipment, dependable tools, and reliable safety gear. Call Ultimate Tool & Safety today to make an order by phone 817-246-2213.\nIf you're in the Fort Worth area, Odessa Texas or Portales, NM be sure to stop by and see our extensive inventory in person.\nWhen you have a job that demands strength, you want your tools and equipment to be durable and ready for whatever comes your way. At Ultimate Tool & Safety, we have the experience in the field to know how important quality FR clothing and other equipment is for your safety, as well as to ensure the job gets done with precision and control.\nUltimate Tool & Safety is a great resource for linemen, iron workers, arborists, tower workers, and others who need dependable safety equipment and reliable tools to perform work at varying degrees of height.\nOur top priority is YOUR SAFETY; from the products we sell to the services that we provide.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I am a professional career woman looking for a room to rent while I relocate and become settled in the Scottsdale area. My daughter is grown and married and lives in Florida and I do not own any pets. I want to rent a nice, clean room furnished would be nice, as my things are all in storage.\nI want a clean roommate, who is also career minded.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Tooth Cleaning Below the Gums to Treat Bone Loss and Pockets.\nWhen bacterial accumulations cause bone loss around the teeth, a diagnosis of periodontal disease is made. The bone loss creates periodontal pockets that are too deep to clean by routine oral hygiene methods and the usual one hour routine cleaning does not allow enough time to get the deep pockets cleaned out. Scaling and root planing uses several appointments in conjunction with a local anesthetic to give the hygienist time to get deep below the gum line and clean the pockets while still insuring that the patient is comfortable.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzacpqg b/data_all_eng_slimpj/shuffled/split2/finalzzzacpqg
new file mode 100644
index 0000000000000000000000000000000000000000..0615a1d09402f08022fcc279e06faad219dfd9ac
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzacpqg
@@ -0,0 +1,5 @@
+{"text":"Startups in India prefer incorporating a private limited company as it is easier to raise funds from investors.\nThe GST Council, which Jaitley heads, had last week brought down tax rate on 178 products from 28 percent to 18 percent and pushed down several others in lower bracket. Congress, which has made high tax rates and increased compliance burden in the GST regime an election issue in the run up to the assembly elections in Gujarat, claimed credit for the move.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Gawd, this took seriously forever and I almost forgot about it D: but anywho, this was during xmas, so longggg time ago. Their first guests were Secret, lmao I thought it was T-ara ???\nAnywho, the girls come out and like it's pretty idk awesome? The mcs kinda scared me though but I love Mir's reaction xD. Seungho..long history with them. I wonder how he'll survive :O Thunder does the opening pose lol, and everyone's like wth??? and OMFG, HE'S SO FREAKIN AWESOME AT IT. Damn look at his thighs\u2026so small. Aigoo~ I love how everyone's just crazy. Hahaha. I'm not familiar with their names so don't expect me to tell them apart easily. MBLAQ starts to dance, THunder doesn't even do anything lol. OMG, BUT THAT'S JUST TOO HOT. I was kinda expecting more..but okay lmao. What a bad boy! How bad, he doesn't even get to do his dance lol. Seungho, LMAO YOU'RE SUCH A CUTE FAIL LEADER. GO LOL, OMGGG\u2026SEXAYY. Lol at the end, wtf man. Mir..omg you'd expect him to be like that, haha. Joon goes last, best for lasy. BUT HE FALLS LOLL. Of course bb does dance but they all bash him down. I love his freakin faces lol. OMG SO HOT, ITS BURNING. Secret gets to dance, MMM I LVOE THAT FIRST GIRL. MIR LMAO. YOU DIVA. lol at when people just pick it up. WHOA THUNDE.R OMFG NO MC LOL. MIRRRR OMFGGGGGG HE KIDNAPS HER. The second girl lol, why's she making me anxious??? LOL GO, YOU'RE SUCHA PERVERT. JOON, LOL YOU'RE SO WEIRD. Did Go just touch her for no reason lol? The third person really reminds me of Hyo. She's so amazing. I don't know what the fourth girl was doing, but I love how everyone's just helping her. OMFG, THUNDER, RELEASING ALL HIS ENERGY. Aww everyone in Secret joins her to do the dance. Now it's time for gifts. i'm excited :)) Thunder goes first! AWWWWWW HELLO KITTY DOLL, OMG I'M DYING INSIDE. He named it after his backpack lol. Gawd, I wanna sleep with him not the doll baby :) he has to do his wink, and omggg so cute. Whaaa so cute. And lol at the animated heart. They all guess for who he choooes and that's where we end !","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Avast, ye mateys! Calling all landlubbers and scallywags alike! There is a brand new event coming to the Speculator region\u2014Pirates Weekend! This action-packed weekend is full of fun stuff for buccaneers of all ages.\nTrade Bazaar from 5-7 p.m.\nCheck out this sale, which takes place at the Speculator Pavilion. Local restaurants and businesses will be selling goods for everyone to check out.\nThis will also be the opening ceremony for the weekend \u2014 stop by to learn about all of the weekend's events. Feeling like you might luck into some treasure of your own? There are tickets for raffle baskets located throughout Speculator, and this is where the lucky winners will be chosen.\nFlag Designing contest at 6 p.m.\nThe evening will wrap up with the judging of the Pirate Flag Designing contest. Non-profit organizations and local businesses have been invited to create their own flags. Winners will be chosen based on best design, best advertisement, and most piratical.\nSpend the early part of the day searching for your own treasure, kicking back on the beach, taking a hike, or enjoying the Adirondack Birding Festival, then get ready to get back to your swashbuckling pirate ways!\nJoin the Adirondack Experience: The Museum on Blue Mountain Lake at the Speculator Pavilion. They will be bringing some fun, old-fashioned games for kids of all ages to play!\nPirate Chase Race at 4:30 p.m.\nDon your best pirate or fairy costume and take part in the Pirate Chase Race. A minimum pledge of $10 is required from participants, and all proceeds will benefit Lenna Braunius, a local baby girl with spinal muscular atrophy.\nRum Cake Contest at 6 p.m.\nEnter your own creation in the Rum Cake Contest. Your cake must be made from scratch, and only rum extract or rum flavoring can be used; no distilled rum or other alcohols are allowed. Doubloons will be awarded for 1st, 2nd, and 3rd places. Don't feel like baking? Stop down to taste test and vote for your favorite.\nPirate Trivia Night at 7 p.m.\nJoin ADKaraoke for a fun night of pirate-themed trivia at The Inn at Speculator. Entry is free for teams. There will be three rounds of trivia, at the end of which the top three teams are brought forward for the final question. A prize will be awarded to the victor, and the rest will WALK THE PLANK!\nThe third and final day of the Pirates Weekend is also action packed and loaded with fun.\nPirate Movie Time from 10 a.m. - 2 p.m.\nIf you need to spend some time out of the sun or off your feet, join us at the Lake Pleasant Library for movie time. They will be showing old school pirate themed movies for free!\nTreasure Hunt at 10 a.m.\nTeams of five can register at the Speculator Region Chamber of Commerce. A $25 entry fee will get you a code breaker and the clues you need to find the four pieces of the treasure map. The first three teams to complete the challenge will win a prize basket, which is currently on display at the Chamber of Commerce.\n18th Century Encampment from 10 a.m. - 4 p.m.\nAlso taking place at the Speculator ball field is an 18th century encampment. Tour the historical encampment where you can interact with the reenactors, who will be in full period garb.\nBattle Reenactment at 2 p.m.\nJust across the road, at the Speculator beach, the governor's daughter has been kidnapped by pirates! The pirates and the redcoats will battle it out on Lake Pleasant! Osborne Point will be off limits between 1-3 p.m. for safety reasons.\nPirate Costume Contest at 6 p.m.\nPick out your best pirate costume, and come on down for the contest! Prizes will be awarded by age groups: 0-3, 4-12, 13-19, and 20+. Prizes will be awarded in the form of 1st, 2nd, and 3rd place ribbons. The local Lions Club will judge. The costume contest will also serve as the closing ceremony for Pirates Weekend.\nCannon Night at 9 p.m.\nJoin us again on the Speculator Beach for the final event of the weekend. The 18th century reenactors will fire a cannon or musket, each blast of which will be sponsored by a local business or non-profit organization, followed by a \"Huzzah!\" from the crowd!\nJoin us for Pirates Weekend or for any of our other fun events going on this summer. If you don't have a local pirate ship to call home, check out these great places to stay and make your reservations now!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The percentage of Americans without health insurance rose in the second quarter of 2017, according to a Gallup-Sharecare survey.\nThe uninsured rate increased to 11.7%, the second quarterly increase in a row after the rate hit a record low of 10.9% in the third and fourth quarters of 2016. The uninsured rate was 11.3% during the first quarter.\nGallup-Sharecare said the rate still well below the peak of 18.0% in 2013 - just before the launch of the Affordable Care Act's individual insurance exchanges. But it represents a significant uptick since the end of last year.\n\"Although the increase in the uninsured rate from the end of 2016 to Gallup's most recent update is small on a percentage basis (0.8 points), it is statistically significant given the very large sample sizes involved, and translates into nearly 2 million Americans who, apparently, have already dropped out of the insured ranks,\" a post from Gallup-Sharecare said.\nThe result comes from a survey of more than 45,000 people over the second quarter.\nGallup-Sharecare cited a few possible reasons the uninsured rate could be increasing, such as higher premiums and insurer exits from the Obamacare markets. The post also cited uncertainty in Washington as a possible factor.\n\"Uncertainty surrounding the healthcare law also may be driving the increase. President Donald Trump's executive order permitting agencies to waive or delay provisions that 'impose a fiscal burden' on individuals, as well as the prospect of a new healthcare law may be causing consumers to question whether the penalty for not having insurance will be enforced,\" Gallup-Sharecare said.\nRepublicans in the Senate are currently debating a law that would repeal major parts of Obamacare.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"We are playing roulette with our security\u2014but this time, through the fault of Washington and Washington alone, write Adam Twardowski and Michael O'Hanlon. This piece originally appeared on USA Today on January 25, before the partial government shutdown was resolved.\nFor a president, and members of Congress, who have declared preventing another attack from al-Qaida or ISIS to be among their top national security priorities, there is an enormous contradiction in their apparent willingness to tolerate an indefinite shutdown of so much of the government: the effects upon the Transportation Security Administration, as well as other parts of the federal workforce focused on national security such as the Coast Guard, the FBI and the Border Patrol. With 10 percent of the TSA workforce recently calling in sick, the risks are growing\u2014not only in the sense that on any given day in 2019, a threat may slip through the depleted ranks of those watching our borders, but also in the longer-term threat to those institutions as places where talented and dedicated Americans will want to work.\nAn analogy is instructive. In 1981, President Ronald Reagan fired 11,000 of the nation's 13,000 air traffic controllers when they went on strike. In that era, aircraft accidents happened considerably more often than today, so Reagan's move was risky in more ways than one. As things turned out, however, an interim force of some 6,000 controllers was cobbled together out of those who did not strike, plus their supervisors and other qualified individuals; flight patterns did not suffer unduly for long, and major catastrophes were averted.\nHowever, two key points need to be kept in mind as we face the current crisis. First, the controllers created their own crisis in 1981, with what many saw as unreasonable wage and work-hour demands. Reagan was in response mode, and could not be blamed for starting the problem in the way that Washington has today. Second, while the air traffic controller strike wound up fine for the country\u2014and indeed, contributed to Reagan's early reputation for decisive leadership\u2014there were great doubts at the time about whether his gamble would end in tragedy, or at least a severely curtailed airline market.\nWhich brings us to today, when we are playing roulette with our security again\u2014but this time, through the fault of Washington and Washington alone. The United States continues to debate how to secure its southern border against illegal immigration and drug flows. But the parameters of this debate have been set by an administration that is loose with facts and seems predominantly concerned with the political fallout the president would face from his base should he fail to build his promised wall on the Mexican border. The United States faces real threats to its security on a daily basis that a fact-based national debate could bring to the public's attention. Such a debate would show that whatever their weaknesses and limitations, those who man our main checkpoints at airports, major ports of entry, and seacoasts appear to be having considerable success in preventing or deterring the movement of terrorists and weapons of mass destruction into this country. One rarely hears concern about such matters anymore. After the Cold War ended, we worried greatly about \"loose nukes\" in Russia\u2014and whether they'd be detected before somehow reaching American shores. After the 9\/11 attacks, we worried that terrorists could infiltrate the country again, perhaps by evading checklists and flying into a major airport undetected, or that they could again find a way to get weapons on a flight.\nSay what you will about the inefficiencies of TSA, and the frequently-changing rules for how to comply with its screening protocols. Almost two decades after 9\/11, we have not had another similar tragedy. Even attempts at lesser tragedies, like the famous shoe bomber, underwear bomber, and printer cartridge bomber are fading from memory, since they happened in the ten years after 2001 and not in recent times. This is a huge record of success and it only makes sense to give TSA some of the credit\u2014and also, to show a little bit of national gratitude in the direction of its myriad employees, as well as the many other federal workers in the Department of Homeland Security doing related work at other places along our many frontiers.\nCan we afford to risk our nation's security?\nIt makes little sense to jeopardize this by failing to pay TSA, Coast Guard, and other key DHS employees longer than many will be able to withstand. The average American family usually has a few thousand dollars of easily accessible contingency funds at best. A survey by Bankrate.com found that roughly a quarter of Americans have nothing saved at all in an emergency fund, while 22 percent say they have savings, but not enough to cover three months' expenses. Thus, working without pay for a month is more than a huge burden for many; it risks simply busting the family bank.\nBeyond the immediate financial hardship is the larger message we send to a group we are so quick to disenfranchise and demean. The message we are sending can easily be interpreted as a vote of no-confidence and no-appreciation for what they do. Who would have their own child, or spouse, or even neighbor consider a job in the DHS today? At a minimum, we are on the risk of losing a full recruiting season for those who do so much to keep us safe.\nRemember, it took the post-Vietnam military a decade to recover from its crisis of morale and purpose. Major companies that have lost their edge and begun to hemorrhage employees as a result of declining balance sheets often fare even worse, never recovering and simply going under. Moreover, it not only takes years for the Department of Homeland Security to recruit, vet, and train personnel for the myriad of jobs that keep us safe every day, it takes even more years for new employees to hone the skills and intuition that are so important to execute their jobs well. TSA was a work in progress throughout most of the 2000s, as was DHS. We should not want to relive such periods of turbulence because they reduce the nation's security.\nCan we afford to take such a risk with our nation's security at a time when ISIS and al-Qaida, though on the run, still have tens of thousands of supporters and affiliates around the world?","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzactrj b/data_all_eng_slimpj/shuffled/split2/finalzzzactrj
new file mode 100644
index 0000000000000000000000000000000000000000..a909eca0d49cf111be6e56ab0774d9b4304cb0d2
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzactrj
@@ -0,0 +1,5 @@
+{"text":"Construction Materials International is part of a team of three companies within America's World Group (AWG). CMI is focused on providing assistance to manufacturers of building materials who wish to establish new long-term business partners, in the global marketplace. Our affiliate companies are Globalnex and Kompas Line; each company has a defined strategy to facilitate the international trade process, with the aim to satisfy our clients highest expectations.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"2h30, directed by Jean-Pierre Carlon.\nDVD \u2013 Editions Montparnasse, with the support of the CNC \u2013 Images of the diversity.\nThis film allows the \"little people\" \u2013 the vast majority of the French in Algeria \u2013 to speak. To speak and to be heard are the first steps towards reconciliation between the two communities that have been divided for so long.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"apartment patio privacy. You are welcome to [blog]. Many individuals have tried net for finding info, suggestions, reports or any other guide for their needs. Like you are. Do you come here to acquire new fresh understanding of apartment patio privacy? What number of webpages have you read for obtaining more detail regarding apartment patio privacy?\napartment patio privacy is one of grown content at the moment. We know it from google engine data such as google adwords or google trends. In order to carry helpful info to our visitors, we have aimed to locate the closest relevance pic about apartment patio privacy. And here you can observe now, this picture have been taken from reputable resource.\nWe believe this apartment patio privacy image will give you a few more point for your need and that we hope you like it. We know, we might have different view relating to this but at least we have tried our best.\nThis picture has been submitted by admin. You are able to explore even more helpful posts in [cat] group. We thank you for your visit to our website. Make sure you get the information you are looking for. Do not forget to share and love our reference to help further develop our website.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"My own educational experiences reflect most of the conditions and practices of the period between the end of WWII and the early sixties. Design education was quite different from what it is today. I think it is important that students and young teachers know the evolution of design education as a means for better understanding present conditions in Graphic Design.\nI consider myself extremely fortunate in my own educational background. My schooling began at the University of Nebraska under the GI Bill in 1946. At that time, the GI Bill paid for your tuition, books and supplies, and provided $65 a month for living expenses. The benefits applied to the school of your choice, and if you transferred to another institution, the benefits went with you. I chose that institution because both of my parents had attended. My father had earned a degree in Geology from the university.\nAt the University of Nebraska, I began with a double major, one in Geology and the other in Advertising Design. My father was a geologist and I had grown up reading his books. The text on geology was not particularly interesting, but the sections on paleontology were fascinating. I learned all the major geological periods and read everything available on prehistoric life, especially on dinosaurs. I was particularly impressed by the illustrations, exhibit backdrops and dioramas of Charles R. Knight at the American Museum of Natural History. I wanted to do that type of art, but it would be necessary to have a degree in geology before studying paleontology.\nOnly Fine Art and Advertising Design were available to me, and even though I had no interest in advertising, it seemed more related to my goals than Fine Art. However, my teachers in Advertising Design were painters. At that time, I was allowed to take only three credits of studio art each semester; all the rest of my classes were academic. After two years at the University of Nebraska, I felt frustrated because my interests were in art. My problems were compounded because I was not doing well in Geology classes, and I also held two outside jobs. I worked at Dewey & Wilson Displays,a silk screen shop. My job was artwork and cutting lacquer stencils. My second job began as an elevator operator but soon broadened to collecting rents and cleaning offices evenings and weekends.\nMy grades dropped. The Veterans Administration called me in for an interview. I was told that decision time had arrived; either it was school or job, not both. The best solution for me was to transfer to a school where more art classes were available, and to not take an outside job. I knew only two art schools, one in Minneapolis and the other in Kansas City. Two letters of application were addressed, one to \"Art School, Minneapolis, Minnesota\" and the other to \"Art School, Kansas City, Kansas.\"At the time, I did not realize there were two Kansas Cities and one was in Missouri.) By chance, both letters arrived at the proper destination. Both schools sent letters of acceptance. I could not make up my mind as to which letter should be accepted. A coin was tossed, heads for Minneapolis and tails for Kansas City. Kansas City won, but on reflection, it was decided that fishing was better in Minnesota, so I went to The Minneapolis School of Art in 1948. So much for big decisions! Later, when I moved to the Kansas City Art Institute as a teacher, I always believed it was fate catching up with me for reneging on the coin toss.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Barely a week after over 100 persons were gruesomely murdered by suspected herdsmen in Jos, Plateau state, new reports from the state say 10 persons were killed in renewed attacks in Mangu and Barkin Ladi communities in Jos, the state capital over the weekend.\nAccording to The Nation, six persons were killed during a shootout in Mangu on Saturday, June 30th while four persons were killed in Barkin Ladi yesterday July 1st.\nConfirming the continuous killings despite the curfew and heavy military presence, the media officer of the task force, Major Adam Umar, in a statement, said that the security officers got a distress call at about 3am yesterday that armed bandits were attacking a home in Barkin Ladi. Sadly, four persons had been killed before they got to the scene of the attack.\n\"The OPSH notes with dismay the continued attitude of some criminals in the state that are bent on making the state ungovernable through some unwarranted attacks on some communities and innocent villagers despite the tireless efforts of the task force. We regret to say that about 0300 hours Sunday morning of 1st July, our men at Dorowa received a distress call from a resident of Mararaban Kantoma of Barkin Ladi Local Government that they were under attack by some armed bandits. On receiving the distress call, our men mobilised to the scene immediately to repel the attackers. The assailants who were given hot chase by our men escaped with various degrees of injuries while four of them were arrested.\n\"However, It is regrettable that before our men could get to the scene of the attack, four persons had already been killed by the attackers. Consequently, in its avowed commitment to ensuring that the renewed attacks are promptly brought to an end, the commander of the task force, Major General Anthony Atolagbe, has relocated the headquarters of the task force from Jos to Barkin Ladi. The Commander has also relocated with all his principal officers to the epicenter of the renewed attacks. To this end, the commander will be coordinating the day-to-day running of the task force from the new operational headquarters in Barkin Ladi.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaephh b/data_all_eng_slimpj/shuffled/split2/finalzzzaephh
new file mode 100644
index 0000000000000000000000000000000000000000..4e1bc2be7f6ea0d27472d8f3b57078e9f61546a9
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaephh
@@ -0,0 +1,5 @@
+{"text":"A tattoo is a form of body modification, made by inserting indelible ink into the dermis layer of the skin to change the pigment. Animals are beautiful and thus are making beautiful tattoos. But they are also a way to express our humans feelings, to mock ourselves and to show our true personality.\nAnimals can show the better but also the worst of the human being. With their colors and textures, they are making great humorous tattoos, either badass or cute. Want to show some humor and cuteness at the same times ? Here are 45 Cute and Inspiring Deer Tattoos that will make you go from roaring with laughter to melting with cuteness.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Spinners are for TRADE customers only - please note in the comments box what spinner you wish to purchase and we will send you a separate invoice.\nTo view details of each spinner please click on the item name \/ image below.\nTo complete the package, we can supply floor spinners for our cards in a variety of sizes to suit your requirements, although the 36 pocket and 48 pocket spinners are the most popular.\nOnce ordered, the spinner will come to you directly from the manufacturer and we try to arrange for the spinner and the cards to arrive on the same day if possible.\nThe price shown of each spinner, which includes a delivery charge to the Scottish mainland of \u00a320.85, is simply the cost the manufacturer charges us. However, we will send you enough extra cards, free of charge, which will cover the spinner cost when sold. These will be a selection of the designs you have already chosen.\nPlease note - the free card deal only applies if you are ordering enough cards to fill the spinner.\nThe prices quoted below are for the empty spinners only. Cards should be ordered separately.\nIf you prefer to order the spinner yourself you can see and buy them at www.wirefittings.com. They also supply card racks and table top displays.\nAnother supplier we recommend for acrylic card displays and slat board fittings are www.3ddisplays.co.uk.\n\u00a368.33 ex vat | \u00a382.00 Inc Vat24 pocket floor spinner holding 6 x 24 = 144 c..\n\u00a370.83 ex vat | \u00a385.00 inc vat36 pocket floor spinner holding 6 x 36 = 2..\n\u00a370.83 ex vat | \u00a385.00 inc vat48 pocket floor spinner holding 6 x 48 =&n..","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Presents as sudden onset of severe, unilateral, paroxysmal pain in one or more of the distributions of the trigeminal nerve.\nVascular compression is most common cause, superior cerebellar artery being the most common culprit.\nProximal centrally myelinated portion of the nerve is more susceptibility to compression as it is thinner as compared to the relatively thicker distal peripheral myelin sheath. Distal compression may not be clinically relevant.\n3D CISS\/SSFP sequence is the sequence of choice.\nCompressive vessel is an artery or vein.\nName of the vessel or vessels.\nDistal or proximal half of the cisternal segment of the trigeminal nerve is compressed.\nTreatment : Surgical decompression by transposing the vessel from the nerve and separating it by using non-absorbable material, most frequently Teflon pledgets. This can be seen a small hypointensity on post operative images.\nOsborn A, Hedlund G, Salzman K. Osborn's Brain.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"As a small boy he fled from a war zone, to become a man of peace. Shah Tabibi, Afghan by birth, came to the Netherlands when he was four years old. His first memories are of his life in the Asylum Centre. Now, more than twenty years later, Shah cannot stand still.\nIn The Shah of Holland he takes the audience into the world of a little boy who has to discover his entire surroundings again. He shines his light on the Afghan world in the Netherlands. Sometimes with amazement, always with humor and above all with compassion.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"If you can get the edges of your hand tools as sharp as a razor, your woodworking endeavors will be much easier. In this class, you'll discover ways to get your edges keen in a consistent and predictable manner. You'll learn several methods, including electric grinders, water stones, diamond stones, as well as using ready made honing guides.\nThis month we are featuring the woodworking projects of Butch Montgomery, who has been woodworking since shop class in High School, where he built an entire roll top desk for his mother, despite the fact that it was a more \"advanced\" project.\nThis month we are featuring the beautifully carved spoons and boxes of Rodney Miller, who we have also featured in our Show Us Your Woodturning column in The Highland Woodturner.\nThis month Jim has a tip on what you need to do in order to enlarge an already drilled hole, as well as a money saving tip on finding the best wood storage solutions within the shop space you are provided.\nQuestion: I am making a dresser out of maple and need to stain or dye it to match a bed out of alder and stained a reddish brown color. What is the best method to match the color? Stain seems to just muddy the maple.\nThis month, Jeff takes a different route in his tool review and discusses the Hock Kitchen Knife Kit. These kits include top quality, steel blades that you can add your own custom handle to in order to create a great addition to your kitchen.\nClick below to watch Steve discuss the Festool Kapex KS 120 EB Sliding Compound Miter Saw .\nThis month, Ed Scent (Highland Woodworker cardholder since 1995) shares several suggestions on ways to prevent injuring yourself on a spinning blade, and how to figure out when it is okay to touch the blade.\nThis month we are featuring Herb Schlobohm's shop, which he refers to as the \"antithesis\" of the normal woodworking shop.\nThis month, Steve discusses the science and structure behind the tapes we most often use in our woodworking shops. He also questions the integrity of furniture bought from a furniture store and the mistakes that can often be found. And lastly, he lays out the 5S Design Criteria for his new wall storage cabinets.\nOur blogger, Terry Chapman, recently purchased the hardware for a new Benchcrafted Glide Leg Vise and has finished installing it on his workbench. Read about his installation process and the benefits of his new Benchcrafted Leg Vise on the Highland Blog.\nMany of my customers have come to me, wanting advice on which of our many block planes they should buy. Often this is prefaced by the fact that they would like the plane they buy to provide a great deal of functionality, as this may be the only plane they purchase. With this in mind, I frequently find myself suggesting our Low Angle Rabbet Block Plane ( 60-1\/2RN with nicker).\nThe Soul of a Tree , George Nakashima's autobiography and philosophy, is a special book about an extraordinary woodworker. It is, of course, an account of the story of his life and the influences that led him to become the exceptional woodworker that he was. But it is much more than that, for those influences\u2014from his earliest years\u2014developed his deep reverence for nature and, in particular, for the many and varied species of trees that inhabit our shared planet. And it is the expression of his philosophic views about trees that forms the core and important message of this book.\nRod Scott discusses the creation of a sitting bench using 100 year old antique cast iron castings and 100+ year old wood planks salvaged from the home site of an early 20th century homestead.\nPerhaps the finest woodworking show you'll ever attend will take place in the small village of Amana, Iowa on May 15-16, 2015. Featuring many artisan toolmakers who specialize in the modern use of hand tools, this show will inspire and amaze anyone who loves the sound of a shaving clearing the throat of a well-made hand plane. Roy Underhill and many others will be on hand to educate and entertain. Nearby will be a rare display of the exquisite Studley Tool Chest. Save the date, and plan your route to Amana. You will not want to miss this show.\nPyrography literally means \"Writing with fire\" and in his article, Professor Nsir Malik discusses his method in creating his own machinery system for creating his beautiful wood burning artwork.\nThis month Alan shares some everyday household items that you can use to help you with your finishing processes, and also requests your own household solution ideas.\nOrder any of the above 4 books from us during March\/April 2015 for 33% off list price.\nPurchase any model SawStop PCS Cabinet Saw during March or April, 2015 and receive a $199 accessory FOR FREE as a factory rebate! Choose either the SawStop PCS integrated mobile base or the overarm mount for the dust collector (Both accessories are shown already mounted on the saw pictured above). The SawStop has already saved the fingers of thousands of woodworkers from serious injury. Don't put it off any longer! Now is the best time ever to add a SawStop to your workshop.\nThe new Mirka DEROS is the first random orbit sander to use a brushless DC motor without the need for an external transformer. It's small and light enough to use with one hand, combining the power and light weight of a pneumatic tool with the convenience of an electric tool. If you do a lot of sanding on vertical surfaces, you will especially love this sander.\nRikon has hit a home run with their new model 70-220VSR 1 HP variable speed reversing midi-lathe. Featuring 12-1\/2\" swing over the ways and 20\" between centers, as well as a 24-position index head, this lathe is designed to handle a wide variety of projects.\nThis innovative stainless steel combination square uses two powerful rare earth magnets to secure the blade to the head making it exceptionally fast and easy to use.\nBowclamps allow you to clamp up to 4-foot widths with only a single clamp at each end. The Bowclamp is manufactured using CNC technology to machine a curve that perfectly distributes equal pressure everywhere it contacts your project. Extremely versatile, Bowclamps will work with virtually any clamp on the market.\nHere's a great deal on a 14-pocket denim tool roll, ideal for protecting the edges on your chisels and carving tools.\nThe new SawStop Jobsite Saw lets you bring incredible portability, innovative timesaving features and signature SawStop safety anywhere you need it. We expect to have a limited number of saws available to ship beginning in March 2015. Please get your order in now for earliest delivery.\nI'm writing this letter to explain the absolute sickness I felt after the first cut with my woodslicer.\nI can't believe the number of hours wasted and the amount of frustration I had dealt with working around my bandsaws shortcomings.\nI will explain. Primarily I'm a turner and bought a bandsaw to cut the corners off blocks but also planned to use the tool for other tasks. Struggling with the factory blade and other blades purchased I found that \"drift\" was more like \"undertow\" and that resawing for segmented turnings was more like a wasteful way to check the grain direction. I decided to take one last chance before selling the expensive paperweight, and I purchased the Wood Slicer blade.\nI couldn't believe the feed rate and accuracy. I literally felt sick. Why did I wait so long to buy one? Why did I put up with a tool that made it harder to work rather than easier? I had wasted more wood than the blade cost.\nI would say to anyone that is struggling with their bandsaw .... stop and call.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaeuzd b/data_all_eng_slimpj/shuffled/split2/finalzzzaeuzd
new file mode 100644
index 0000000000000000000000000000000000000000..529f33a22dd8af92381bdb14084e00524ebc9c4f
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaeuzd
@@ -0,0 +1,5 @@
+{"text":"Large amounts of personal data is collected every day, such as medical records. Information regarding patients generally comes under the legal and ethical obligations and confidentiality. All medical data has to be protected and managed with the highest security measures to ensure the confidentiality and security of personal data. Management of patient data is crucial as the Data Protection Act 1998 gives patients the right of access to information about themselves, whether that information is electronic or physical paper records.\nDataSpace UK Ltd have a wide range of patient note and document management solutions. All documents and patient records are professionally managed to ensure there is secure access to patient information when it's needed. DataSpace UK Ltd have been providing secure offsite storage facilities to NHS Trusts and private medical organisations for over 15 years. Working for clients within the medical sector has given DataSpace valuable understanding of the processes and surrounding issues that the NHS face today.\nWhy choose DataSpace UK Ltd?\nDataSpace UK Ltd manage medical data from Patient Notes\/Records to X-Rays and Human Tissue Samples. Ensure your healthcare and patient data is managed with the highest confidentiality, security and efficient access.\nWith our unique web based system FileLive, you have the option to request the retrieval and return of physical files as well as the ability to request documents to be scanned for viewing online.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The concept of folding is a three-dimensional exercise. Folding a piece of paper, for example, will conceal the other side, yet reveal a new transformation. For Raheleh Filsoofi, a UTRGV assistant professor of ceramics, the act of folding is representative of the complexity of the human condition.\nFilsoofi is the curator of \"FOLD,\" an exhibit that unifies 13 female artists, philosophers and scholars to develop the concept of folding and exploring this conceptual metaphor in terms of feminism, immigration and interdisciplinary studies.\n\"FOLD\" is a part of UTRGV's 2018 FESTIBA, an annual week-long celebration of international books and arts, running this year from Feb. 26 to March 4 on the Edinburg and Brownsville campuses.\n\"FOLD\" presentations will be held at three local venues: the International Museum of Arts and Sciences (IMAS) in McAllen, and on the UTRGV Edinburg Campus at the Visual Arts Gallery and at the Visitors Center. It will feature three different exhibitions (the art will change out with each new location) and one performance, with installations running through April 1. All the artists in the \"FOLD\" project are UTRGV faculty and visiting artists from around the country, collaborating on central themes with varying perspectives.\nUTRGV faculty, to include assistant professor of art history Dr. Riccardo Pizzinato, assistant professor of art history Dr. Katherine McAllen, and assistant professor in literature and cultural studies Dr. Cathryn Merla-Watson, will present on varying social issues relevant to the \"FOLD\" discussion.\nTurkish artist Sibel Kocabasi, of Palm Beach County, Florida, is showcasing artwork at the IMAS that interweaves varying tapestries. On a blanket that is 80 years old, Kocabasi has cut and arranged strips from the gold and silver emergency blankets immigrants are given at the borders.\nFloridian artist Giannina Coppiano Dwin features a piece splayed across the gallery floor at the IMAS. The image is a large dress made entirely of salt \u2013 representative of women and Mother Earth.\nDwin's installation called for 150 pounds of salt and took 12 days to create. The illusion of the sea foam at the bottom of the dress ties that concept of women and nature, specifically the ocean, into one powerful piece.\nDigital artist Laleh Mehran, professor of Emergent Digital Practices at the University of Denver, creates visually elaborate spaces that focus on intersections between elements of politics, religion and science. Using a type of pendulum and needle concept, the artist drives conversations of political power and the fragility of time.\nMehran said collaborations like \"FOLD\" are important to represent women as individuals, not clones.\n\"We may all be women, but it's important to understand that we all have different perspectives,\" she said.\nFilsoofi said she encouraged her art students at UTRGV to take part in the organizing of \"FOLD\" to gain experience in creating connections with artists and learning about different processes for exhibitions. And, her students have been tasked in creating projects based on the inner workings of the \"FOLD\" exhibition.\nShari Flores, a UTRGV fine arts major, attended the \"FOLD\" reception to support her female peers and professors.\n\u00b7 Exhibition One features artwork from digital artist Laleh Mehran, textile artist Sibel Kocabasi, mixed media artist Giannina Coppiano Dwin and mixed media artist Anja Marais, with exhibitions on display at the International Museum of Art and Sciences (IMAS) in McAllen through April 1.\n\u00b7 Exhibition Two features art from glass casting artist Linda Behar, artist Isabel Gouveia, ceramics artist Rojhaneh Hosseini, studio artist Dorotha Grace Lemeh, and artist and philosopher Amber Scoon. Exhibitions will start on Feb. 15 at the Visual Art Gallery at UTRGV on the Edinburg Campus.\n\u00b7 Exhibition Three gathers works from painter Misoo Filan, visual artist Gulia Huber, Sibel Kocabasi and singer Golnar Shahyar, starting Feb. 27 at the Visitors Center at UTRGV on the Edinburg Campus.\nThe performance pieces will feature artists Niurca Marquez and flamenco dancer Jose Luis de la Paz, 7 p.m. Feb. 26 at the Performing Arts Complex on the UTRGV Edinburg Campus.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"No Entry is about people fighting for their democratic rights. As Robert Richter QC says: \"The preservation of our rights and liberties is in no way entrenched and needs to be constantly defended.\"\nThe images in this book capture significant moments in the Save Albert Park campaign. In the words of John Pilger: \"People are no longer prepared to accept cynical and amoral action, or culpable inaction, that touches their lives and the lives of others, regardless of the power of the perpetrator.\"\nA secret deal struck between Victorian Premier Jeff Kennett, businessman Ron Walker and entrepreneur Bernie Ecclestone led to an agreement to build a Formula One Grand Prix race-track in Albert Park without public consultation. The following year saw more than one thousand trees felled, more than 150 homes damaged by soil compaction and 383 arrests as the people struggled against an imposed government decision. In the foreword, lain Stewart says, \"The campaign will continue until the race is re-located and the park is returned to the people.\"\nThis book documents a remarkable struggle in Victoria's social and political history.\nPlease phone the SAP office (03 9690 3855) for the bookstore nearest you or for mail order information.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"There are four standard types of sealed lead acid batteries: General Purpose SLA AGM Batteries; Deep Cycle SLA AGM Batteries; High Rate; and UPS SLA AGM Batteries.\nEach of these battery types is explicitly designed to perform best under specific conditions. For optimum performance for your product, select a Sealed Lead Acid (SLA) battery based on your product's application.\nThe most commonly used of all of these types is the General Purpose SLA AGM Battery. These batteries work best for backup applications and cycling (discharging and recharging). However, if you're finding that this battery needs to be cycled frequently or used in specific power draining backup applications, an alternative SLA battery type might be better.\nFactors including the terminal type and physical dimensions are considered when selecting the correct replacement general purpose SLA battery. Battery Power's professionals can help you identify the perfect battery for your needs.\nStandard applications for General Purpose SLA AGM Batteries include security systems, emergency lighting, backups, consumer electronics, sump pumps and electronic testing equipment.\nApplications for Deep Cycle SLA AGM Batteries include scooters and wheelchairs, floor scrubbers, marine and RV house power, lawn and garden equipment, golf carts and trolling motors.\nGel SLA battery applications include water pumping, wind generation, and remote monitoring.\n911 call centers, data centers, medical equipment, cable TV, Telecom, and Internet housing sites are provided with much swifter power delivery through High Rate, UPS SLA AGM Batteries.\nIf you need a sealed lead acid battery, please reach out to us at Battery Power at 352-314-9001 or use our online contact form for assistance.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"On Tuesday, Sept. 13, 2016, the LBJ Library invited educators and teachers to an educator evening session featuring Dr. Victoria M. DeFrancesco Soto, who discussed perspectives on the upcoming presidential election and how it relates to the classroom.\nDr. DeFrancesco Soto is currently a professor at The University of Texas at Austin in the Department of Mexican-American and Latino Studies and is a Fellow at the Center for Politics and Governance at The LBJ School of Public Affairs. She provides political analysis on U.S. politics and its implications for countries abroad as a regular contributor on MSNBC, NBCNews.com, and Telemundo. She is also widely published in academic and popular outlets such as POLITICO and Talking Points Memo. Through these different outlets, Victoria translates social science research into a more relatable form of information for a wide variety of audiences.\nBeyond her classroom and media analysis work, Dr. DeFrancesco Soto is an active public speaker. Some of her featured speaking engagements include Harvard's Latino Law, Policy, and Business Conference, Chicago's Standard Club Lecture Series, and the U.S. State Department's Public Diplomacy Program. Learn more about Dr. DeFrancesco Soto at DrVMDS.com.\nPrior to the program, the library invited session attendees to a reception, where wine, refreshments, and hors d'oeuvres were served. Door prizes were also given out.\nThe library will be launching a new educator membership, as part of the Friends of the LBJ Library program. Teachers and educators at the session were the first to learn about the new program.\nFor more information or questions, contact the LBJ Library Education Department at [email protected].","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzafibh b/data_all_eng_slimpj/shuffled/split2/finalzzzafibh
new file mode 100644
index 0000000000000000000000000000000000000000..ac29947fb3053d01d23267a4f681f53acc328e53
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzafibh
@@ -0,0 +1,5 @@
+{"text":"Nestling under the vineyards of the Cote St Jacques, Joigny is proud of its many fine churches, houses with carved wood decoration, and above all its gastronomy delicious dishes and fine wines. Close to the Canal de Bourgogne and the Canal du Nivernais, Joigny is the ideal location to discover Burgundy and a fantastic start base for a canal cruise.\nLinking the Yonne to the Saone, the Canal de Bourgogne, started in 1775 and finished in 1834, takes you in secret and spectacular ways to the heart of the Renaissance period. At that time the Duchy of Burgundy was separate from, and vied in magnificence with, the Kingdom of France - much smaller than the country we know today. Its buildings ranging from superb abbeys to fortified farmhouses lie amongst landmark ancient Poplar trees. Stop and tie up close to the superb aqueduct at St Florentin and climb up to its church to admire its magnificent stained glass.\nAt Tonnerre the Fosse Dionne pool surrounded by ancient houses, still provides a water supply to the town. Magnificent and splendidly-furnished Renaissance chateaux such as Tanlay and Ancy-le-Franc punctuate your boating holidays. The marvellous high-vaulted Abbey of Fontenay, tucked away in a secluded valley, is a short bike ride away. Near Venarey-les-Laumes at the village of Alise-Sainte-Reine you'll want to visit the site of the Gaulish fortress of Alesia where Vercingetorix surrendered to Caesar after a two month siege.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Daft Punk have filmed a video for \"Instant Crush\", their Random Access Memories collaboration with The Strokes' Julian Casablancas. On Thursday morning, French television premiered a snippet of the video, which sees Casablancas dressed in Napoleon-esque military garb in addition to his patented leather jacket. Watch below (via @TheStrokes_Fans).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The consensus between neoliberalism and progressivism has proved wholly inadequate to address Chinese influence in Australia's public life.\nIn this lecture, Associate Professor Che Zalina Zulkifli will explore how creative industries are embedded in education communities that influence economic, cultural and social activities in Malaysia.\nJudicial interventions have led to the creation of an elaborate environment jurisprudence in India. But has the judiciary has served as an appropriate forum to resolve these issues?\nWhat should be the place of religion in our state and national education curricula?\nAsylum Seekers and the Law: Where Have We Come From and Where Are We Going?\nSix Wars, Numerous Natural Disasters and a Winter in Mongolia - What will you do with your law degree?\nA legal exploration of commercial hunting in Australia and Canada.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Breaching experiments are most commonly associated with ethnomethodology, a Breaching Experiment is an experiment that seeks to examine people's reactions to violations of commonly Accepted social rules or norms. Norms are defined as the expectations, or rules of behavior, that Develop out of values. For this Project, I was required to violate a norm.\nBasically doing Something \"out of the ordinary\" it's not common at all in society, in this project we'll find out What is people reaction by recording myself doing something that calls their attention like what I Did in this project. Asking people around the mall for \"HUGS & KISSES\" or saying randomly \"Hi\", to them pretending I know them for a while, at the time I start developing my experiment Was difficult for me to keep a straight Face while doing it.\nThe reaction of individuals at the beginning of this experiment was negative and doubtful, Not all dared to give me a hug, out of the obvious fear of the camera, many had not clear What was my purpose of giving hugs so they preferred to continue with their walking Ignoring me at all, but certainly that didn't stop me to continue researching more looks and Reactions.\nAs well as there were people who rejected me, there were many people affordable, who gave me a warm host smile and definitely my hug. It is impressive how within a few hours of doing this Project I carefully analyze and determine the acceptances and denials of society by doing Something out of the ordinary on a typical and current day.\nAt home I created a colorful poster to call attention of the pedestrians, it was rare for me to say to People that \"Hugs and Kisses\" were given away as it's obviously this kind of experimentations Is not common at all, but that is what this experiment was about, as you seen in the video not All people react to our proposals same way so, many run away, others ended up agreeing by Being intimidated by a camera, others for being seen well to the others, many did not wanted to Do it, others felt happy and congratulated me as intensive because of my project, others were Frightened.\nIn fact I received positive and negative critiques, Talking about genres it as an Advantage for us as girls by received the opposite gender immediately acceptance which is a Positive response, in relation to the women they were restricted somewhat by noticing our Presence, but it was certainly a charming and fun project. Worth to mention that learning and Enjoying, what you do, is what really matters.\nWhen you are a participant in this class of experiments, you experience reactions from people Directly. From all this we learn that the criteria for each person must be respected not necessarily Being all of us alike, our way of thinking varies, leading us to think and act according to what is Taught to us, what we see and experience every day in our different cultures. Now days, in many Countries they do not use physical contact as a way of greeting or cordiality meaning that it Wouldn't be right to go against the rules that have already been implemented and established in Their cultures.\nThen, how about people whom beliefs are only based in what society thinks and implement with The past of the time, without letting them create their own criteria?\nWell these people live daily a routine guided by the rest, and their way of seeing things is totally According to what society thinks is right or not although often have radical changes are not Really common sense to many of the individuals.\nWhether you way you think or believe in things is based on society or the rest of the people.. You are the owner of your criteria, accept the new changes around, adapt yourself and also opt to Implement what you think and believe is right for the growth of cultural knowledge of society in Which we live.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Robins Consulting is a specialized search firm that works with a limited number of carefully selected clients. By operating this way we ensure that our access to top source companies is unrestricted. Very few top candidates end up 'off-limits' to our recruiting efforts. As a result, Robins Consulting taps an exceptionally broad and deep talent pool on your behalf, bringing you more candidates who precisely meet your needs.\nReduce you costs per hire.\nFor more information about our transportation industry headhunters, call 214-432-8288 or complete our online form.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzagfea b/data_all_eng_slimpj/shuffled/split2/finalzzzagfea
new file mode 100644
index 0000000000000000000000000000000000000000..206ff10e60b831234f73b57aaa9e292604fa43fd
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzagfea
@@ -0,0 +1,5 @@
+{"text":"Thrust Ball Bearings are to reduce rotational friction and support axial loads. Ideal for precision work with close tolerances suitable for building models and applications.\nThe thrust ball bearings consist of a shaft washer, a housing washer and a cage containing a complement of precision balls. They are separable and can be mounted separately. Made of heat-treated Chrome steel.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"NAATI has developed our certification system in order to ensure there is a pool of professional translators and interpreters to serve the Australian community.\nAn important part of certification is the recertification process. NAATI practitioners are required to recertify every three years, in order to remain certified as a translating or interpreting professional.\nRecertification requires practitioners to complete professional development logbooks and a work practice record. This will help you keep track of the training you have completed and the work you have undertaken as a professional translator or interpreter. It is also how NAATI is able to confirm that you, as a practitioner, have met the professional development and work activity requirements to recertify.\nWe've set out the process below, to help you gain a sense of how to use the logbook and work record in myNAATI. For questions about recertification, We've created a full list of frequently asked questions (FAQ's). Use these as a guide to the requirements of recertification.\nBelow you will find a step-by-step guide to adding professional development training and work practice to the myNAATI logbooks.\nThe dashboard shows your professional development and a work practice logbooks for each credential you hold. The coloured tabs along the top show the important significant dates for your recertification. The start date is the date your credential\/s take effect. The recertification eligibility date is the earliest date you can submit a recertification application, and the expiry date shows when the credential(s) will expire.\nThis screen shows the PD requirements and total points required. Any points you have completed will also be shown.\nNOTE: Transitioned practitioners who have less than three years before they are required to recertify will see different requirements. These requirements have been calculated on a pro-rata basis and reflect the duration of the certification.\nAdding an activity allows you to select the category, requirements and completion date. You can add a description, notes and upload supporting documents such as an invoice or a certificate here. This may be asked for, if your logbook is audited.\nThe chart will update as activities are added. Anything with a green tick in the status column will be included in the chart.\nA logbook is created for each of the credentials you hold. The requirements are shown as a bar chart. Add your work practice to fill out the logbook. This can be one entry per job\/assignment, multiple weeks, or months of work, supported by a letter from an employer.\nNOTE: Again, transitioned practitioners who have less than three years before they are required to recertify will see different requirements. These requirements have been calculated on a pro-rata basis and reflect the duration of the certification.\nYou can provide notes about the work in the description, and upload documents.\nAfter adding the entries the bar chart will update.\nOnce you have reached the recertification eligibility date, and completed the activity requirements, you can apply for recertification by clicking on the link from the logbook page or from the applications page in myNAATI. Check your contact details are correct and update them as necessary. You can't change your email address from this form. This can only be changed in the my details section of myNAATI.\nBefore you complete your application for recertification, you have the opportunity to review what will be submitted. You can go back to your logbooks and fix up any issues before applying again. Green bars indicate that the work practice criteria have been met. Orange bars indicate that the criteria haven't been met. At this point any credentials that you do not want to include can be deselected.\nThe next section will show a breakdown of PD activities. As with your work practice record, you have the opportunity to go back to the logbook and edit your PD logbook, or click OK to continue your application. Green text indicates that all criteria have been met. Orange texts indicates that requirements haven't been met.\nThe final steps for your recertification application includes a question about your order for an ID card or translator stamp and an attachment section to add any supporting evidence. We also ask that you accept NAATI's terms and conditions. NAATI will invoice you once your application has been checked and is ready for assessment. Checking of applications can take up to 10 days. You will not need to pay at the time of application.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"DREAM COTTAGE WITH TRANQUILITY ! DESORMEAUX LAKE DIRECTLY ON THE LAKE ! ALL INCLUDED!\nBEAUTIFUL, PEACEFUL COTTAGE WITH INCREDIBLE VIEW OF THE RIVER.\nFREE NIGHT WITH 2 DAY RENTAL OFF SEASON!\nReceive 1 night free for off season. Weekends or weekdays. We are regulated by CITQ as a 3 star rating to ensure quality accomodation!\nLAC CARDINAL COTTAGE, DENHOLM, QUEBEC - LAKEFRONT HOT TUB!\nAFFORDABLE COTTAGE WITH ACCESS TO THE 31 MILLES LAKE.\nCOTTAGE FOR RENT ON LAC LONG (NEAR BLUE SEA) - NOW BOOKING FOR THE 2018 SEASON!\nCHALET ROSE-ET-LYS - EXCEPTIONAL MODERN COTTAGE - RESERVE NOW FOR THE FALL!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The excellent Centro Modular Display System has just got even better!\nCentro is a superb panel system. Centro also comes in a number of pre-configured kits for your convenience. Or you can choose to buy on a custom basis to suit your exact requirements. You can build a complete, re-usable exhibition stand from Centro and the use part of it for your smaller shows.\nThe upgraded 2014 system features a superb and unique \"Twist and Lock\" system for the poles and graphics frames. That means an even easier, faster, more secure and hassle free set up, saving you time and effort.\nIn addition, a number of new modules have been introduced including display pod shelving and door frame sections. We create complete exhibition stands, freestanding screen displays and partitions from the excellent new Centro.\n> Fast to install thank to the Twist and Lock feature.\n> Attractive silver finish adds to the overall impact of your graphic displays.\n> Bracket sections for iPad Holders and screens 22\"- 42\"\nAll the designs you see on this page have been created from the excellent Centro system.\nLook how easy the new Rotrlink system is to use!\nA smart and practical display unit with shelving and branding!\nThese superb theatre system will accommodate screens between 32\" and 42\". It is purpose built and is finished off with magnetic graphic which can be changed instantly. Portable and versatile!\nAs usual you will be able to change from coloured post caps (no extra charge) and a range of accessories including lights, tables and transit cases.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\"Learning how to converse well and easily with others gives people more confidence when handling both business and social events,\" explained psychologist and speaker Claire Newton. \"Mastering this skill is thus an important life skill.\nEnergy and confidence radiate from Claire. She wears a hat, because it is fun, and she loves them. Her easy manner and interesting topic kept her audience riveted at her recent talk on the art of conversation, one of a series of talks on the subject. The venue was the elegant Saint James on Venice hotel, where guests also enjoyed one of their renowned high teas and light music from Peter Enslin on piano.\n\"We take conversation for granted \u2013 until there is a drought. What am I going to say next? And what if I am trapped by a boring person?\" Claire gave helpful hints and tips people need to know to be invited back, and also what not to do so you won't be the one people avoid.\nBefore the function choose to have a positive attitude about the event. What you focus on is what you will get. Say to yourself 'I wonder what interesting person I am going to meet.' Take responsibility to enjoy yourself. Go up to someone and introduce yourself. Be the one to offer food around. Conversation starts over a plate of snacks; invite people to join you. Help to create a pleasant, light and positive atmosphere. Don't take over from the hostess, but be helpful in the sidelines. Before the event think of a few conversation starters that sound natural. Have ideas in your head that you can use to start conversations. Find out who will be at the function and plan an interesting conversation with them,\" Claire advised.\n\"Making conversation is a learnt skill. You, too, can master the art of conversation,\" Claire concluded. To learn more about Claire's talks, visit www.clairenewton.co.za or www.stjamesonvenice.co.za.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzagqlz b/data_all_eng_slimpj/shuffled/split2/finalzzzagqlz
new file mode 100644
index 0000000000000000000000000000000000000000..40ae413cd83b2df9bf3d4152996a1452b4125201
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzagqlz
@@ -0,0 +1,5 @@
+{"text":"Each 12 months, Advances in surgical procedure reports the most up-tp-date practices regularly surgical procedure. A unusual editorial board, headed by way of Dr. John Cameron, identifies key components of significant growth and controversy and invitations preeminent experts to give a contribution unique articles dedicated to those issues. those insightful overviews more often than not surgical procedure carry options to a medical point and discover their daily effect on sufferer care.\nOutstanding colour illustrations make biochemistry suggestions effortless to appreciate and retainProviding a robust visible evaluate of the complete spectrum of human biochemistry, the 3rd version of the preferred colour Atlas of Biochemistry is a perfect reference and research reduction. It makes use of the signature Flexibook structure, such as double-page spreads with transparent explanatory textual content at the left-hand web page and exquisitely exact full-color pix at the correct.\nA few universal annoying accidents in athletes comprise joint dislocations, sprains, muscle traces, damaged bones, tendon irritation, and ligament tears. the most typical fracture harm within the athletic inhabitants happens within the arms. Articles incorporated during this factor are: The demanding situations of treating athletes- activity particular accidents, Wrist ligament accidents, Scaphoid fractures, Carpal fractures except scaphoid, Thumb UCL and RCL accidents, Ulnar sided wrist discomfort within the athlete and lots of extra!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Critical Success Factors and Best Practices for Business Succession.\nSin Igual: Un Amor Sin Igual, Debe Compartirse En Una Actividad Sin Igual!\nCurriculum Vitae Estrategico: Redaccion Para Lograr El Pase a la Entrevista.\nHis Strength Is Made Perfect in Weakness...!\nExploring Prehistoric Identity in Europe: Our Construct or Theirs?\nDark Thoughts of a Confused Boy.\nEncuentros: Con Escritores, Artistas Plasticos y Musicos Contemporaneos.\nStop Committing Suicide with a Fork!\nKindeswohl - Gefahrdungen in Deutschland: Eine Bankrott-Erklarung? Es Ist 5 VOR 12!\nCzy Pieni Dze S U Tylko Do P Acenia?\nThe Easter That Almost Wasn't!\nHow Can I Call What it is Between Us a Past?\nDas Tier ALS Therapeut. Mythos Oder Wahrheit?\nde Rome a la Chine.\nDdr Punker. Gefahr F r B rger Und Staat?\nOSHA 511 Exam Prep: From Those Who Just Took the Test.\nThe New Extractivism: A Post-Neoliberal Development Model or Imperialism of the Twenty-First Century?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Right Now! 2:00 PM Mountain Time \u2013 Bev, John and Hannah on The Home Front Show!\n2:00 PM Mountain Time \u2013 Join us on 1360am.co for a rousing good radio show. Today's theme is giving, and we'll be sharing from such Wonder Women as Beatrix Potter, Charlotte Mason, Peggy Noonan, Courtney Reissig, and Hannah Parker!\nReal Men such as John Parker and President James Madison will weigh in heavy today, and Peggy Noonan's stories of Jackie Kennedy and Ronald Reagan's mom will be featured as well.\nYou'll learn of some Supreme Court decisions you should know with regard to taking dominion, and see the 139th Psalm in a whole new light.\nCall a friend \u2013 we've got a great show for you today! And thanks very much if you'll do us the great favor of sharing this on Facebook, etc.\n< Previous Support Your Local Sheriff and Re-criminalizing Marijuana in Colorado!!!\nNext > 1360am.co \u2013 go there at 2:00 PM Mountain Time Today!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"How does one begin to scale the distance covered in over ten years? It is the difference between eighteen and twenty-eight. It is the time it takes you to find your first grey hair, thicker than the rest of it, and crinkly like it carries static electricity. It is the transformation of your body from taut to loose after stretching and growing to carry your baby. It is the realization that you and your sisters have grown up to be fundamentally different people. It is the knowledge that your almost 16-year-old brother, who was 5 when you left, is essentially a stranger to you. It is the fact that back home you waited for the boy you loved, and now, being married to him, you wait to \"get a break\" from him. It is the feeling of dishonesty that creeps up your throat as you voice the words, \"I am from Lahore.\" It is a distance between places, but it is also deeper than that. It is the distance between people, between values, between philosophies and ideologies, between calling a place home and feeling that it is home, between the eighteen-year-old you and the twenty-eight-year-old you, and those two, they are not alike at all. This is a steep mountain of change. You fear that you will fall to your death if you begin to climb up the slope.\nSo, how do you find your way back? Well, sometimes you don't. Sometimes, you just have to stop and give up. You have to stop breaking yourself apart and others with you, because you know you have been doing it, like taking one end of a split-ended hair and ripping it into two strands, neatly, with just your index finger and thumb. You have to stop looking for that bright and shiny person you were ten years ago and accept the rough edges of the present you. You just have to borrow your thoughts from the past. You try to think it's like plucking strawberries in a farm, like filling a basket full of strawberry flavored memories. Maybe you'll turn them into preserves and jams and store them in large mason jars. Perhaps you'll label them - \"Childhood,\" \"Love,\" \"Happy Days,\" \"Sad Days,\" \"Things Left Behind,\" et cetera.\nMaybe, maybe if you do that, you will stop being so abrasive. You will stop feeling like your bones are sliding against each other and eroding. Maybe you'll be OK with ten years of change and distance. Maybe you'll start to believe that you don't really need to find your way back.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Graham Hill and Jackie Stewart in BRM P261s at the Monaco Grand Prix May 1966.\n1964 Monaco GP, Monte Carlo : Richie Ginther, BRM Owen Racing Organisation, (ph: www.\nPeter Whitehead winner of the 1938 Australian Grand Prix at Mount Panorama, Bathurst, NSW in an ERA R.10.B.\nWatkins Glen Grand Prix History | Cars at the start line of the 1964 United States Grand Prix at Watkins Glen.\nJo Bonnier, BRM P25, Monaco Grand Prix, 1959.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzahytr b/data_all_eng_slimpj/shuffled/split2/finalzzzahytr
new file mode 100644
index 0000000000000000000000000000000000000000..8fffdb3d5c445639c4d6d8da1af62bc9ca57d05e
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzahytr
@@ -0,0 +1,5 @@
+{"text":"Yoga is much more than the poses you see posted all over the internet. Derived from the Sanskrit word \"yuj\", which means to unite or integrate, yoga is a 5000-year old body of knowledge, all about harmonizing the body, mind and breath through the means of various breath techniques (pranayama), postures (asanas) and meditation.\nThat said, ask ten different yogis what yoga is for them, and you will get ten different answers. That doesn't mean they are doing different things, it just shows that the practice of yoga, though often practiced in larger groups, is a very personal experience.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\"I'm not going, and you can't make me,\" my 12-year-old stepson shouted when it was time to visit his biological mom. He marched to his room and slammed the door. He refused to see her because he blamed her for his parents' divorce.\nI was sure he'd be happier if he and his mom reconciled, so I had tried to talk with him about forgiveness. But he felt justified in his anger toward her, and he simply didn't want to let it go.\nOur house is our house, and their house is their house.\nMy husband and I decided early in our marriage that we would treat all the children the same, regardless of family of origin. But when my stepson stopped visiting his biological mom, she didn't treat him the same as she treated his sister, who still visited her.\nOne Christmas, he didn't receive any gifts from his mom, while his sister received many presents. He was hurt and angry, and I empathized with those emotions. I wanted my husband to talk with his ex about it, but he simply said, \"Her house; her rules.\" I realized that I would not want another family to question our parenting decisions, so I resolved not to interfere with her decisions.\nBeing supportive doesn't mean being responsible to fix the problem.\nMy stepson often complained to my husband and me that he felt unloved by his biological mother. He retaliated by ignoring her phone calls and refusing to visit her. Then she would feel hurt and become angry with him, continuing the cycle of negativity.\nI wanted to do something to alleviate his pain, but fixing the problem wasn't my responsibility. All I could do was offer emotional support as he shared his feelings. Anything more would be overstepping my role as a stepmom.\nI'm not God, but I can place my problems in His hands.\nWhen I see my kids and stepkids hurting, I want to zoom in like Wonder Woman and fix it. But I'm not Wonder Woman, and I'm certainly not God. Fixing broken things is His role and prerogative, not mine.\nOne day when my stepson was upset, I reminded him that everyone in this world is broken in some way. Our family is broken because of the pain of divorce. I'm broken; he's broken; his biological mom is broken. Broken people have broken relationships, but God can help us mend them. He's really good at fixing broken things, but we have to ask for His help.\nBlended-family problems often work themselves out over time.\nSome issues, like sibling rivalry, crop up in most families when kids reach a certain age. Just when parents think the problem will never end, the kids grow into a different stage. This happened with my stepson. When he finished high school, he suddenly decided to let go of the past and forgive his mom. Today, they enjoy a healthy, positive relationship.\nDiane Stark is a freelance writer from Indiana who writes about family and faith.\nThis article first appeared in the October\/November 2018 issue of Focus on the Family magazine and was originally titled \"When You Can't Make It Better.\" If you enjoyed this article, read more like it in Focus on the Family's marriage and parenting magazine. Get this publication delivered to your home by subscribing to it for a gift of any amount.\n\u00a9 2018 by Diane Stark. Used by permission.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Puma Video To 3GP Converter 2.369 free download Puma Video To 3GP Converter allows you to convert all popular video formats to 3GP\/3GPP for playing them on your mobile phone. Watch your favorite videos and clips everywhere!\nPuma Video To 3GP Converter allows you to convert all popular video formats to 3GP\/3GPP for playing them on your mobile phone. Watch your favorite videos and clips everywhere!\nPuma Video Capture Delphi Control 1.5 \u2014 Puma Video Capture is a Delphi control that allows programmers to easily integrate video capturing and processing capabilities into their software applications. Puma Video Capture Delphi Control captures video and audio streams from TV tuners, etc..\nPuma Video Convert Delphi Control 1.81 \u2014 Puma Video Convert is a Delphi control that allows programmers to easily integrate video converting and processing capabilities into their software applications.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\"In October last year, we were visited by hurricane 'Wilma', which blew away my pool enclosure. A year before that 'Francis', also was here, but did not make such a mesh. Once the weather settled the work began to look for a contractor, who was willing and able to replace my pool enclosure. Some 5 companies send me an estimate. After careful consideration of all, I made a choice to proceed with GARCIA SCREEN SERVICES, INC... On their invitation, I visited their establishment and I must admit that I was pleasantly convinced that they would be able to do the job for me...'Garcia' put up a sturdy and beautiful pool enclosure. Folks if you are in a situation like I was for almost one year, I recommend you to contact 'GARCIA SCREEN SERVICES, INC.' because I am sure, that they are ready, able and willing to serve you.\n\"We would just like to say thanks for the timely and professional job your company did installing our screen enclosure. Having just moved here, we were nervous about choosing a company to install a screen enclosure on our new home and our realtor highly recommended you. Your office kept us informed as to the timeline we could expect before, during and after the job began. Everything went exactly as your company said it would! We would not have considered anyone else to have installed our new front screen door because of the professional way your entire company handled the installation of our screen enclosure. It was a pleasure doing business with you.\n\"In our 30 years of living in South Florida, Garcia Screen Service is the best screen service provider that we have dealt with. They have a very friendly, courteous, and professional staff. They will spend the time to explain all the work involved and the costs associated with it and will finish the job as specified and in the time frame they had committed. We have already recommended them to our friends and would highly recommend their services to anybody else interested.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"From 1924 to 2019, the same values that started this company and helped to build it are still holding strong. We pride ourselves as a family ran company to hold the same values instilled with us all those years ago. Waddell Transfer has grown from a horse drawn wagon ran by a hardworking, dedicated family man, to a 13 truck fleet that travels the country to suite the needs of our customers.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaiwln b/data_all_eng_slimpj/shuffled/split2/finalzzzaiwln
new file mode 100644
index 0000000000000000000000000000000000000000..85439482c6f2e15ba863ef5b33fab5585f35cc4a
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaiwln
@@ -0,0 +1,5 @@
+{"text":"Using Scrum Wisely \u2013 Where does Design Fit?\nThe Scrum development method is a useful set of guidelines to help teams scope, plan, status and demonstrate their work. When done well, it allows teams to get early feedback on the product they are building and provides a reasonably disciplined method of managing changes in scope.\nScrum includes some guidance for planning, estimation, requirements definition, testing and project statusing. For the subject of design, Scrum advocates \"design by discovery,\" or \"emergent design.\" That is, as each series of functions is developed, the design emerges. The code is refactored (cleaned up) to stay consistent with current design ideas. There is no specific up front design or analysis phase in Scrum and no specific design guidelines. Agile refers to \"just enough design,\" but that has many definitions.\nIn many engineering projects, it is difficult to fully specify a design since the team might not know what will and won't work until it tries it. In less complex, smaller and self-contained projects, the risk of not having a design before coding might not kill the project since problems that are encountered can be fixed with acceptable cost. However, when more people and project locations are involved, and the cost of fixing design errors in the code is greater than fixing design errors before coding, then consideration should be given to some design activity up front. An emerging design is not necessarily a good one.\nIn the Agile world, a lot of people debate the \"traditional\" big up front design over allowing the design to emerge through coding. It is commonly seen as an all-or-nothing choice. There is the rationalization that coding involves thinking, and thinking is design, so coding will suffice for design.\nWhat is missing is the understanding of what design is, why it is done, and how to do it in a way that is useful to the team. Fixing the design process is hard; skipping it is easier.\nIn this tidbit, we describe some ideas for hitting a balance*.\nOne of the characteristics of Scrum is that functionality is developed during every sprint (which is typically a 1-4 week period). This focus on developing functionality from the outset of the project can lead the team to skip (or minimize) non-development activities such as requirements analysis, design and system testing. When they are skipped, the result can be the creation of many parts that don't fit together, or the development of a system that works well on the first release, but cannot easily be changed.\nDesign is hard to do. When it is historically done poorly (e.g., the design document is too large to manage, unreadable, or drowned out by non-design information) then the baby is often thrown out with the bath water and replaced by declarations such as, \"Our code is the design, and any novice can understand our code base of 100,000 non-commented lines of brilliant code.\" When Scrum is adopted, which has no explicit design phase, then the jettisoned baby and the bath water are promptly forgotten, until the team hits a large roadblock caused by the lack of design. The pendulum is swung back to previous bad design practices and the cycle repeats. This is by no means an agile-only issue. It has been around for decades.\nHere is a short summary of \"design.\" It isn't perfect since it is an ambiguous word and there are numerous opinions to choose from.\nDesign documentation is usually a hassle to keep up-to-date when design changes are made in the coding phase. You might consider developing architecture and design notes up front, reviewing them for defects and issues, and then updating changes to the design when the code is complete. The level of design documentation to keep, and where it is kept (e.g., separate document and\/or code file header section) can be decided based on maintenance needs, ease-of-learning for new teams and future enhancement plans.\nFor example, X = 80, Y = 40, Z = 0.\nThe earlier sprints can use the coding time for high-risk features, core product components and features that will be needed to support later functionality. You can also add more time to later sprints for system test, performance testing and reliability testing when the time needed for coding decreases.\nYou can select the percentage allocation for the sprints based on the need for that activity and the risk of not doing it. You might decide that design takes zero percent for low risk projects or features, or that design has a large percentage of time allocated for the first 3 sprints to work on architecture, and much less from sprint 4 onwards.\nDon't abandon design because it is not called out specifically in Scrum. Don't get sucked into the near-worthless discussion of \"traditional\" versus \"new.\" Determine for yourself what design activities you need and when they will get done. It's your product and your money!\n*Thanks to Venkat, Brian and Alan for their valuable inputs.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"We've added a new feature that allows users to subscribe and receive daily or weekly survey completion reports by email. This is especially useful if you're looking for a way to periodically monitor the progress of your surveys without having to log-in and check your analytics overview.\nTo start receiving your survey completion reports, go to your survey's settings page. Then click the \"advanced\" tab, and enable the \"Email Completion Reports\" option. You can also set the reporting interval from the corresponding drop-down.\nHere's a sample of a report.\nRational Survey is now available as a free app to users of the Chrome browser in the Google Chrome Web Store.\nUse the link below to get to the install page from where you can add it as an extension.\nInstalling it will add a bookmarked icon that when clicked will automatically take you to the main Rational Survey page while opening a new tab.\nUsing this app, we will eventually add advanced html5 features specific to the chrome browser to further improve the Rational Survey experience.\nAdding a login to your surveys for respondent authentication or registration is really easy with Rational Survey.\nTo enable survey login, from the survey settings page. Click the \"Advanced\" tab.\nNow enable the \"Require Responder Login\" setting.\nA list of login options will appear below. Check all the fields you would like to use to authenticate respondents. Note: you must select at least two fields if you're not using the email or username field.\nThen click \"Save\" to update your settings.\nNow when visitors access your survey they will have to login using the previously specified fields.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Get this super cool and funky alcohol themed organiser from 10 am for yourself today!Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nIf alcohol is your thing then get yourself this fun alcohol themed organiser that includes all your favourite brands!Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nBe colourful, fun and girly with our super trendy Aztec organiser. Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nIf classy and cute is your kinda thing then this pattern organiser is the one for you!Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nColourful, vibrant and retro. No, were not talking about the rainbow. Check out our cassette organiser! This is one for all those lively souls out there! Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nThere lives a fashionista in each one of us! This is for all those trend setters our there! Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nCulture. colour, tradition and vibrance! Get this cool India themed organiser and show off your Country! Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nCulture. colour, tradition and vibrance! Get this cool India themed organiser and show off your Country!Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nFor all those motivated and inspired people out there, get yourself this cool and colourful organiser and remind yourself everyday!Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.\nLoud, crowded and expensive! Yet most of us can never get enough of this lively city. Indias most vibrant city, brought to life in our new Mumbai themed Organiser. Carry the city of dreams with you wherever you go! Grab this perfect planner for your everyday needs and be super organised! The coloured pages within allows for each colour to be used for a specific task.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"It was the most violent gang war in Australian history - and their fathers were right in the thick of it.\nOver a blood-soaked period between 1998 and 2010, some 36 gangland figures were killed across Melbourne.\nNames such as Mokbel, Gatto, Moran, Gangitano, Barbaro and Williams became synonymous with fear and thuggery as Australia waited to see who would die next.\nWhile old-school gangsters kept wives and children out of harm's way, Melbourne's breed of heartless killers didn't hesitate to gun down their enemies inside their homes, at weddings or even as they watched their kids' weekend sport.\nNow for the first time, Daily Mail Australia can reveal what has become of the children of the underworld's most notorious figures - and which ones followed their fathers and mothers into a life of crime.\nWhen it comes to those involved in the gangland war, Anthony Sajih 'Fat Tony' Mokbel is close to top of the list.\nMoving to Australia in the mid-1970s, he had established himself as a drug kingpin by the late-1980s, and was soon the head of one of the nation's biggest drug cartels - 'The Company'.\nHis involvement in the underworld included being acquitted of paying $150,000 to have Lewis Moran killed, while in 2012 he was jailed for 30 years for three charges related to the drug cartel.\nMokbel married his first wife Carmel DeLorenzo in his early 20s and the couple had two children - a son Sajih, and a daughter, Susan.\nWhen asked about what it was like growing up the daughter of a mobster Susan, now 22, kept coy.\n'I don't think it was different at all... define most childhoods growing up?' she told Daily Mail Australia.\nAs the underworld war raged, Danielle McGuire was often on the arm of some of Melbourne's most violent figures.\nShe first dated Mark Moran, who was gunned down at his home in June 2000. That was followed by a relationship with drug kingpin Tony Mokbel, during which the pair had a daughter who was born in Greece in 2006, at which time Mokbel was on the run.\nMs McGuire also reportedly had a fling with notorious former bikie Toby Mitchell.\nShe once tearfully admitted: 'You can't help who you fall in love with'.\nWhile some of her lovers spent time behind bars, Ms McGuire was herself jailed for trafficking $800,000 worth of ecstasy in 1998.\nHer daughter Brittany, now 22, is the owner of a hair salon in Port Melbourne and regularly posts photos online of a glamorous life, much like that her mother often enjoyed.\nFour years ago Brittany found herself before the courts, pleading guilty to speeding at 157km\/h in a 100km\/h zone.\nAlphonse Gangitano, better known as the 'Black Prince of Lygon Street', ruled the streets with an iron fist as a member of the Carlton Crew in the 1980s and 90s.\nAside from being a fight promoter, nightclub owner and gambler, his love of extreme violence also saw him take a shine to the role of debt collector.\nHis fellow Carlton Crew member and friend Mick Gatto said he was simply stunned by Gangitano's behaviour on several occasions.\nClose associate Jason Moran - who is believed to have orchestrated Gangitano's death - was also recorded talking about the mobster's love of violence.\n'He's a f***ing lulu... if you smash five pool cues and an iron bar over someone's head... you're a f***ing lulu,' Moran said.\nBefore he was shot dead inside his home in January 1998, Gangitano was raking in an estimated $200,000-a-month.\nBut while some children of the Melbourne underworld's most notorious figures have followed their parents into trouble, Gangitano's daughters Amelia and Ellie have not.\nAmelia and her partner Tristan are understood to be engaged, and recently welcomed a daughter.\nHis other daughter Ellie has forged a career as an actress. Following her screen debut on Neighbours as a toddler in 1985, she also recently appeared alongside Craig McLachlan in The Doctor Blake Mysteries.\nDespite being a leader of the infamous 'Carlton Crew', Mick Gatto managed to escape the underworld war mostly unscathed.\nIn 2004 he was acquitted of the murder of suspected hitman Andrew 'Benji' Veniamin, with a jury ruling Gatto had acted in self-defence when he shot Veniamin, who had threatened to kill him.\nA former boxer and debt collector, he now works professionally as a mediator in the building sector. Gatto married his wife Cheryle in 1978 and the couple have four children - Damien, Justin, Michael and Sarah.\nIn 2008, as the gangland war was drawing to a close, Damien and his model wife Fiona tied the knot in a VIP-filled wedding in Melbourne's Docklands.\nBut the couple's ceremony was not without incident, with the attempted assassination of Gatto's associate Fedele D'Amico occurring as guests partied into the night.\nDamien now works for a construction company, while Fiona is a design consultant and a former Chadwick model. The couple have three young children of their own.\nThe youngest member of the family, Sarah Gatto married Danny Awad in a lavish ceremony in December 2016. The couple have a two-year-old daughter, who they welcomed in mid-2015.\nGatto's son Justin narrowly escaped with his life following a horror car crash in 2008. A court heard he lost control of his BMW and crashed head-on into an oncoming four-wheel-drive. A judge suspended his license for a month.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This week we are frozen. No, not literally, it's actually spring here in Nashville. But we decided to play with ice. Things in ice. We all froze everyday things and then brought out our cameras.\nSome of these items are easily recognizable, some are more abstract. But the bubbles in the ice lends a wonderful texture and other-worldliness to the images. This signals our farewell to winter and readiness to embrace spring.\nThis entry was posted in Uncategorized on March 24, 2019 by sandyburr05.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzajaxp b/data_all_eng_slimpj/shuffled/split2/finalzzzajaxp
new file mode 100644
index 0000000000000000000000000000000000000000..5b5606b43546d03bd331e17616ae551f125525b0
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzajaxp
@@ -0,0 +1,5 @@
+{"text":"Why Nova Scotia? Web.com | Nova Scotia Business Inc.\nWhen we moved here in 2001, little did we know that one day we'd have over 500 employees and it would be one of the centers of excellence in our company. Today, the world has moved online; if you're not on the internet you're not going to be found. Think of us as the marketing and IT department for small businesses. We talk about serving people, listening to them, and treating them with respect. We find that in Nova Scotia, we find that in our employees here.\nThere's an amazing partnership here between Nova Scotians, the government, and private enterprise in creating very successful business enterprises that serve the market globally. Nova Scotia Business Inc. has been a fantastic partner since we started here in 2001. And that's one reason we have been growing in Nova Scotia over these last few years.\nThe quality of life is phenomenal from a cost-of-living and education perspective. We love Nova Scotia and its location; we want to serve all of Canada, and we think we have a great workforce here. Our belief is that when you help people consistently and genuinely over a long period of time, you can build a reputation for yourself and people come to you.\nNova Scotia is forward thinking, resilient and resourceful. You will always see us as a major participant in this community. Nova Scotia is the perfect location to serve a global market place.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\u2776MuPrint specialises in same-day printing to hit your tight deadlines.\nLearn a bit more about MuPrint..\nThere is a physical limit of approximately sheets of standard 80gsm paper that can be channel bound. If your Thesis has more pages or you have used a thicker paper then you will have to bind it into 2 separate volumes. Check the regulations for what you need if you bind it in more than a single volume.\nThere is no longer a requirement to submit hardback bound copies of your Thesis once you have passed your Viva at the University of Manchester. If you wish to re-use all or some of the pages from your Channel bound Thesis, bring it back to us as we have the equipment to take the binding apart. Please ensure that you bring a copy of the regulations so we can complete the work to the correct standard. When submitting your thesis or dissertation, MuPrint are university printers you can trust.\nSkip to content Thesis Printing and Binding. After three or four years working on your PhD, you want to get the printing done right! MuPrint can print and bind your thesis to university requirements, quickly and without any fuss. Or read on for more information\u2026 Printing We can print your thesis for you while you wait, in colour or black. However, watch out for: University of Manchester The standard regulations state that prior to your Viva, you must submit two bound copies of your Thesis.\nThe standard lettering required is in this style: We serve the general public at large. When you visit MuPrint on Higher Cambridge Street, Manchester you can have one of our huge selection of lollipops absolutely free!\nA3 posters are printed on our high quality laser printers for speed and great value on gloss or silk coated gsm paper. The price for multiple copies applies only if all copies are from the same design. If you have different designs, please add each one to the basket separately.\nNow you can have the highest quality Souvenir Brochure for your event with ZERO wastage and at a price that makes sense. Our machines can print full colour, stapled, folded and trimmed booklets, brochures and magazines in standard A5 and A4 portrait but also in more interesting sizes.\nThe convenience of ordering online and then picking up from our shop in Manchester is perfectly possible. KAZE - Amazing band! Listen to them at https: You guys are the best! High quality sameday print at sensible prices. The Fastest Printer in Manchester. Business Cards Now thicker than ever - printed really fast. Stationery Whether it is compliments slips, branded envelopes or a simple letter head - we can do it all. Learn a bit more about MuPrint..\nEducational Presentations and Dissertations. Everyone benefits from our super low prices \u2014 everybody now pays the same low price!\nIf you also want it hardback binding, there are a number of options available too. We only print on thick, high quality card which provides a fantastic finish and maintains that professional image.\nReady within 24 hours of receiving your print ready artwork \u2014 even sooner if you go for our fastest option and tell us!\nThe University of Manchester is an introduction agent for Hollingworth and Moss Ltd and has no authority or ability to negotiate or vary the services or terms of the services offered on this website or enter into any contract on behalf of Hollingworth and Moss Ltd.\nSeriously!Print, bind and order your Manchester University thesis or dissertation howtoviag-ragbmdp.tk homework help programs Thesis Binding Services Manchester book editing services critique of phd thesisThe University of Manchester is an introduction agent for Hollingworth and Moss Ltd and has no authority or ability to negotiate or vary \/10().\nhomework study Thesis Binding Services Manchester master thesis robotics personal essay for college application best. The University of Manchester is an introduction agent for Hollingworth & Moss Ltd and has no authority or ability to negotiate or vary the services or terms of the services offered on this website or enter into any contract on behalf of Hollingworth and Moss Ltd.\nDissertation binding services manchester, - Past year 7 exam papers english. Whenever you feel that your essay misses something, you can send us a free revision request, and your writer will provide all the corrections. Seeing as people are so helpful dissertation binding services manchester scoot. College affordability is important research on thesis writing just about everyone these days, and its handy to get an idea of how much aid you might be eligible for. Any deadline given to you before then is a school internal deadline. So youve got plenty of time to .","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"submitter, are you not aware that you could have edited and altered your headline before submitting it? In so doing you could have corrected the ambiguity that you introduced as a result of your failure to read ahead without informing the rest of Fark of your error.\nI guess he showed that little kid who's boss.\nDimensio: submitter, are you not aware that you could have edited and altered your headline before submitting it? In so doing you could have corrected the ambiguity that you introduced as a result of your failure to read ahead without informing the rest of Fark of your error.\nFark it, we'll do it live.\nI feel sorry for every adult who suddenly shares the name of a celebrity.\nRamsay says there are, on average, three road rage incidents involving a gun every week in Wichita.\nWell, that's disturbing. Remind me to stay the hell out of Wichita.\nwildcardjack: I feel sorry for every adult who suddenly shares the name of a celebrity.\nAs a kid named Clinton during the 90s, oh god yes. Everyone treats you like a current affairs joke.\ncgraves67: wildcardjack: I feel sorry for every adult who suddenly shares the name of a celebrity.\nFTA: Authorities say a 4-year-old boy has been shot and wounded an apparent case of road rage after one vehicle cut off another in a Kansas city.\nDid the person rage and follow them all the way to Wichita?\nwxboy: Ramsay says there are, on average, three road rage incidents involving a gun every week in Wichita.\nBut I thought an armed society was a polite society?\nwxboy: Remind me to stay the hell out of Wichita.\nRoad rage incidents aside, that's a good idea anyway.\nWell, what the fark do you expect when you give him pink farking chicken?\nPonzholio: wxboy: Remind me to stay the hell out of Wichita.\nTechnoHead: An armed society is a polite society.\nAnd Heinlein was a tool.\nI knew a guy who shared a name with a mass shooter who killed 12 AND he lived in the city where it happened. Stressful time. He had to change his phone number. I didn't ask him about the mail.\nTyrone Slothrop: TechnoHead: An armed society is a polite society.\nThe full quote implies that he doesn't actually believe that everyone should be going around packing a gun.\nWell, in the first place an armed society is a polite society. Manners are good when one may have to back up his acts with his life. For me, politeness is a sine qua non of civilization. That's a personal evaluation only. But gunfighting has a strong biological use. We do not have enough things to kill off the weak and the stupid these days. But to stay alive as an armed citizen a man has to be either quick with his wits or with his hands, preferably both. It's a good thing.\nGoddammit. I should read before posting.\nDid someone say \"edited and altered\"?\nI was a Mike growing up in the 80's. Mikey likes it!\nJeebus Saves: cgraves67: wildcardjack: I feel sorry for every adult who suddenly shares the name of a celebrity.\nMike growing up in the 70's and yeah, that. The modern version is that stupid camel from a few years ago.\nThe boy is in stable but critical condition due to stomach wounds.... you sure it's not the same Gordon Ramsay?\nYour presentation is dreadful. This looks like something I'd find in a soggy diaper. You think you can win with dishes like this? Maybe I made a mistake putting you in the top 10. You know what? I think I'm going to shoot you. Look at this gun. The smooth metal. Smell that gunpowder? It's been recently fired. So precise. You see how I'm holding it to your head now? The secret is, to angle it like this, just above your temple. I pull the trigger, your head explodes wonderfully. Look at those brains. You see how there's the perfect mixture of red and pink? Now THAT is a Masterchef worthy dish.\nBut guns make people safer!\nbuckeyebrain: Jeebus Saves: cgraves67: wildcardjack: I feel sorry for every adult who suddenly shares the name of a celebrity.\nThankfully that was short lived.\nbuckeyebrain: wildcardjack: I feel sorry for every adult who suddenly shares the name of a celebrity.\nThat is what I get for forgetting that I had hit \"preview\" instead of \"add comment\".\nBut of course the MSM lumps all those incidents together. They don't separate out the valid self defense cases when that guy really DID cut in front of you or gave you the finger.\ntyyreaunn: cgraves67: wildcardjack: I feel sorry for every adult who suddenly shares the name of a celebrity.\nczei: TechnoHead: An armed society is a polite society.\nGhastly: An armed society is a polite society.\nDead people are pretty polite. Or at least not rude.\nThoughts and prayers for that poor, poor Chief of Police stuck with the name Gordon Ramsey.\nryant123: Ghastly: An armed society is a polite society.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"ST. PAUL, Minn. \u2014 A Minnesota police officer has been charged with second-degree manslaughter after prosecutors determined he acted unreasonably when he shot and killed Philando Castile, a black man whose girlfriend streamed the gruesome aftermath of the fatal shooting live on Facebook, prosecutors announced Wednesday.\nSt. Anthony police officer Jeronimo Yanez shot the 32-year-old Castile during a July 6 traffic stop in the St. Paul suburb of Falcon Heights. Castile's girlfriend, Diamond Reynolds, was in the car along with her young daughter at the time. The woman said Castile was shot several times while reaching for his ID after telling Yanez he had a gun permit and was armed.\nRamsey County Attorney John Choi, whose office will prosecute the case, said Yanez shot Castile seven times \"in rapid succession\" and that the evidence shows Castile was calm and complied with the officer's requests after he was pulled over.\nChoi said in Castile's case that the officer's unreasonable fear did not justify his use of deadly force.\n\"No reasonable officer, knowing, seeing and hearing what officer Yanez did at the time, would've used deadly force under these circumstances,\" Choi said. If convicted of second-degree manslaughter, Yanez could face a maximum prison sentence of 10 years.\nYanez's attorney, Tom Kelly, has said Yanez, who is Latino, was reacting to the presence of a gun, and that one reason Yanez pulled Castile over was because he thought he looked like a possible match for an armed robbery suspect. Choi said Wednesday that Castile was not a suspect in that robbery; Castile's family members have said they believe the elementary school cafeteria worker was racially profiled.\nKelly did not immediately return phone messages seeking comment Wednesday. An attorney for the Castile family was planning a news conference Wednesday afternoon.\nCastile's shooting prompted numerous protests, including a weekslong demonstration outside the governor's mansion and one protest that shut down Interstate 94 in St. Paul for hours. The interstate protest resulted in about 50 arrests and injuries to more than 20 officers who were hit with cement chunks, bottles, rocks and other objects.\nChoi resisted pressure immediately after the shooting to turn the case over to a special prosecutor, but he added one to his team to get an outside perspective. He said Wednesday that he reviewed the case himself instead of sending it to a grand jury in the interest of transparency.\nChoi gave a detailed account Wednesday of the events surrounding Castile's shooting, noting that Castile was wearing his seat belt and complied with Yanez after he was pulled over. Choi said Castile volunteered that he had a firearm, which is not required by law.\nChoi said Yanez had his hand on his holster before Castile could finish his sentence, and repeatedly shouted \"Don't pull it out\" before he fired. Choi said the final shot was fired one minute and two seconds after Castile's vehicle came to a stop.\nChoi said Castile's gun was later found deep in a front pocket of his shorts, with a loaded magazine but no bullet in the chamber.\nHe noted that another officer who responded did not touch his weapon and said Castile had made no sudden movements.\nSquad car video captured the entire incident, including audio and subsequent conversations Yanez had with other officers, Choi said. He was not releasing the video because it was evidence in Yanez's prosecution.\nThe announcement comes one day after the anniversary of the high-profile killing by police of another black man in Minnesota, Jamar Clark in Minneapolis. The officers in that case were not charged.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"An admirable, though haunting piece. Amazing, however, that the creation appears more like light in the dark than merely more shadow. Can tone get lost in content, or is its presence a heroism that will always battle for its right to stay surfaced?\nYou have courage to attempt to articulate such a great loss.\nAt a time like this I recall Wordsworth's description of poetry as \"emotion recollected in tranquillity.\"\nSome of us lack the requisite calm.\nHD Access for just $10 a month to your FAVORITE Channels!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzajirt b/data_all_eng_slimpj/shuffled/split2/finalzzzajirt
new file mode 100644
index 0000000000000000000000000000000000000000..96b0f5493ecdfbe567d65462623a5bd40c79991c
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzajirt
@@ -0,0 +1,5 @@
+{"text":"Who makes the repop deluxe door panels?\n\u203a Who makes the repop deluxe door panels?\nWhat's the name of the company makes the reproduction door panels?\nMost of the vendors here carry their products as part of their offerings.\nFor 71-73 it's Mustang Market and evidently TMI although it seems to be hard to track down their products. I had to contact them directly when I wanted to order their 71-73 Mach1 Sport seat foam and seat covers.\nI think this person was honest in his assessment of the difficulties he had.\nIt sounds like you were more satisfied. I wish I could say the same about the thin plastic ones from Mustang Market.\nThe bottom line is they look great. But they are a lot of work to install. Basically they are not 100% accurate in the measurements, making them hard to install. The worst is the curve of the plastic up by the glass. Then there is a some issues with the holes for the mirror lever, and window handle. Expect to do a lot of work. They come with no trim, and you will have to remove the window strip and figure out a way to put it on. I used small screws and then ground the tips off. They are a ton of work. I probably spend 8 hours on each door. But they do look good, and they are strong. I only wish they fit a little better so that there was not as much work.\nI saw the mustang market ones and was wondering if they are the only aftermarket game in town. Their website shows carpet too but didn't have a price listed by our years.\nI am sorry to say that TMI is still about a year off from getting the 1971-73 Deluxe\/Mach1 Door Panels completed.\nTMI has added hundreds of new products over the past few years including our new 1969-70 Deluxe\/Mach1 Door Panels to be introduced in September.\nTMI has also recently added more people and resources to our Product Development Team to accelerate new product introductions.\nThe 1971-73 panels are still in the schedule but likely won't be done until the second or third quarter of 2012.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"One, two and three-bedroom condominiums. Whether oceanfront or oceanview, all have central air\/heat and provide clean, comfortable accommodations. Each vacation home is individually owned and decorated to the owners taste. Premiere Cable TV is standard, and each unit has a fully equipped kitchen and dining area. Pets are not allowed in rental units. All units are non-smoking, but it is permitted to smoke outdoors away from the unit. Although linens are furnished, please bring your own beach towels and beach blankets as linens are not to be removed from the unit. Laundry facilities are conveniently located on every floor and some units have their own washer\/dryer.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The 2012 Louisiana Master Gardener Conference will be held October 24 \u2013 26 at the L'auberge Casino and Resort in Lake Charles, Louisiana.\nThe theme of this year's Conference is Gardening \u2013 Learning \u2013 Teaching \u2013 Sharing \u2013 Our Bridge to the Future.\nLouisiana Master Gardeners with the LSU AgCenter's LaHouse Project, will sponsor a \"Spring Garden Day\" on Friday, April 20 at LaHouse from 9 a.m. to 4 p.m. LSU AgCenter specialists, along with Master Gardeners and local experts will provide programs on how to plan and grow a sustainable backyard garden full of vegetables, herbs and flowers. In addition to presentations, participants will have the opportunity to purchase bedding plants, herbs, olive trees, and Louisiana Super Plants.\nAdmission is free and the program includes jambalaya and refreshments served at noon. LaHouse is located at 2858 Gourrier Avenue and is near the intersection of Nicholson Drive and Burbank in Baton Rouge.\nFor more information contact: khuffstickler@agcenter.lsu.edu or at 225-578-7913.\nIn 2012, we celebrate 125 years of research excellence at the Louisiana State University AgCenter through the Louisiana Agricultural Experiment Station, established in 1887. In that year Congress passed the Hatch Act, which provided federal funding to support agricultural experiment stations at the nation's land-grant colleges. The significance of this anniversary is far-reaching and touches the lives of everyone in Louisiana. Agriculture provides a positive balance of trade, and more agricultural products are exported from Louisiana than any other state.\nWere it not for the relentless pursuit of science-based solutions to the problems of growing crops and livestock in this state, we would not have much of an agricultural economy to speak of. In total, agriculture contributes more than $26 billion yearly to the Louisiana economy. Louisiana's crops include rice, sugarcane, cotton, soybeans, corn and sweet potatoes. The largest commodity is our forests. Our food scientists work diligently to add value to our aquaculture and seafood industries. The AgCenter helps assure that Louisiana seafood is safe.\nThe AgCenter is one of the nation's best examples of how an institution of higher education can serve as an economic stimulus. Our discoveries have led to 14 start-up companies. We have recently garnered a five-year $17.2 million federal grant to speed up development of biofuels from sugarcane and sweet sorghum. Our record is one of conducting research with practical, immediate application and in collaboration with business and industry. Our extension offices in every parish bring knowledge to everyone's doorstep. We hope to continue serving Louisiana for another 125 years.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Action for Education! is a permanent foundraising campaign which aims to help a child who comes from a family with limited resources to be educated at Royal School. The first action took place in April with our participation at the International Marathon in Cluj-Napoca.\nWith your help, today we start our second action: A Royal School T-Shirt makes all the difference!\nBuy a 70 lei T-Shirt and 50% of the money will go to the Action for Education campaign. You can buy the T-Shirt from the front desk or order it online through the form below.\nThank you for supporting children's education!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Description: Yoru is an ornately decorated and very long blade. On the hilt of this blade is a cross guard, though the bars between the blade and the hilt are much longer than average. The blade itself is pitch-black with a very strong sheen, a single-edged long sword with a slight curve at the end of the blade. Overall, Yoru looks like a large black cross.\nDetails: The blade is 2 meters long and the hilt is 50 centimeters long.\nMihawk: Yoru does more damage versus Vampires, Werewolves, Liches, Daemons, and Demons. When Yoru causes physical damage to one of these races, its damage is considered 80 points higher, meaning that instead of +90 it acts as a +170.\nAlisa Vollan has purchased Yoru for 550,000J.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzajtev b/data_all_eng_slimpj/shuffled/split2/finalzzzajtev
new file mode 100644
index 0000000000000000000000000000000000000000..865b9e7773c51f57ce979222726795d4ad8bcefe
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzajtev
@@ -0,0 +1,5 @@
+{"text":"In a well-attended dedication ceremony, National Football League Hall of Famer Howie Long was recognized as the first-ever recipient of a \"NFL Hometown Hero\" award. According to George Veras, director of the \"Hometown Hero\" program for the NFL, \"This unveiling is the first of its kind as part of a national campaign to re-connect NFL legends with their hometown and Howie has always referenced his Charlestown upbringing and the valuable life lessons he learned there.\" A plaque, which highlights Long's sensational football achievements, will be on permanent display at the Charlestown Boys and Girls Club.\nAfter a video presentation of his emotional Hall of Fame acceptance speech, Howie graciously spoke about his \"Townie\" roots and upbringing. Long's distinguished NFL career with the Oakland\/LA Raiders included eight Pro-Bowl selections, a 1984 Super Bowl championship, and enshrinement to the NFL Hall of Fame in 2000.\nCharlestown Boys and Girls Club Director Greg Jackson, who emceed the event, extends his sincere appreciation to John Doherty and Zume's Coffee Shop, John Iacoi and the Charlestown Boys and Girls Club Advisory Board, Tom Jackson and the building maintenance personnel, and all of the employees who helped contribute to what was a very special occasion.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"With Glastonbury having been and gone, we're right in the middle of music festival season in the UK and in Europe too. Many of our customers may be making their way to of of the UK's outdoor music festivals this summer and many may have been already.\nWhile it might not seem the place to be bringing your laptop, festivals are becoming more and more technology friendly and recent reports show that more and more gadgets are being brought to music events each year. Whether that's to take photographs, write coverage for music blogs or simply to keep entertained once all the bands are tucked up in their tour busses is uncertain, but it's clearly becoming a trend to take your tech on the road. A few years ago some festivals introduced phone charging zones to help festival goers keep their mobiles fully charged and thereby avoid getting lost in fields of identical muddy tents. Many festivals now offer plug sockets for everything from laptop chargers to hair straighteners.\nLaptops in Tents? It's more common than you think!\nSo it seems laptop adapters and chargers are an even more valuable part of festival kit than anyone could have imagined years ago. But what with the adverse weather conditions and likely hood of damaging your gear, it's always a good idea to get a spare dell 1545 adapter to take away with you. Fortunately, Laptop Power UK's great prices mean that if you're looking for an emachines e525 charger you don't need to break the bank. We offer a range of our own brand OEM chargers at superb prices with delivery options to meet everyone's needs. And if your toshiba netbook screen gets cracked while you're travelling, we offer a massive range of laptop lcd screens at the same great prices as our chargers. So whatever you're up to with your laptop this summer, Laptop Power UK are ready to help you out.\nThis entry was posted on Wednesday, June 30th, 2010 at 7:39 am. You can follow any responses to this entry through the RSS feed.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Everyone wants to sustain the elegance of their house and roofs also play a major role in this. There are several kinds of issues faced by the roofs like damages, dirt, faded colours, missing tiles, cracks etc. Thus, for the best assistance Roof Guard Tiled and Metal roofing company is the best option. This is a company situation in Melbourne which deals in all types of roofing services.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"We were commissioned by City of Wolverhampton Council's Public Health dept to deliver a series of digital inclusion workshops around the city over a two year period.\nThe workshops held in community centres and libraries were free to attend and aimed at people who would like to get online and learn more about how they can benefit from digital technology.\nSupport was available on a wide range of topics, including but not limited to; getting online, smartphones, tablets, laptops, email, Skype, social media, online shopping, accessing NHS \/ Civic services.\nTo find out about the training we can offer, get in touch.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Each of these courses are 100% online and have weekly mandatory live chat sessions. Per the syllabus, students cannot miss more than 1 live chat session in each course.\nNon-Matriculated Students: Click on the links below to register for each class. To avoid any fee errors, please add ALL classes to your shopping cart before you finish and pay.\nMatriculated Students: You will register via your myCSUSM account. Please check your Enrollment Dates to confirm when you are eligible to register. If you are looking for the course CRN please click on the reigister link.\n*These courses are not eligible for the Cal Vet Fee Waiver, either as part of the certificate program or as stand alone courses.\n*Please note, all students must reside in one of the following states: Arizona, California, Hawaii, Idaho, Oklahoma, Wisconsin.\nAre you interested in taking other SLP Prep courses but are not part of the SLP Prep Cohort? Please complete the form below. Select all SLP Prep courses you are interested in taking. We will consider this information to determine which courses to offer for Non-Cohort students.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzansmc b/data_all_eng_slimpj/shuffled/split2/finalzzzansmc
new file mode 100644
index 0000000000000000000000000000000000000000..454eb59efa95898b95657c0a49540ee1b88b4d12
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzansmc
@@ -0,0 +1,5 @@
+{"text":"This topic contains 0 replies, has 0 voices, and was last updated by mbiwpeoyc 7 years, 4 months ago.\nI have zeroshell 1.0beta14. I for the life of me can't figure out how to forward specific ports from my LAN to my WAN interface. I'm trying to allow access to my linux server from work via SSH on port 222\u2026..So far nothing has worked \ud83d\ude41 What chain do I need to add this on?\nIn case you haven't fixed yet it is easy, go to Router on the sidebar, then click on Virtual Server then just fill in the fields. Incoming interface [ppp*, eth*, etc] IP Address ANY works, Protocol [TCP and\/or UDP] Local port [that is the port you want to use to access from outside 222 in your case] Remote IP [the local ip of your server] Remote port [the actual port of the service 22 for ssh] then click the + and you are done. read the notes at the bottom of the popup for more options as in ranges etc.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Phillips Brooks House Center for Public Service and Engaged Scholarship is the hub and department that provides support for all public service efforts at Harvard College. It is home to the Center for Public Interest Careers (CPIC), Mindich Program for Engaged Scholarship (MPES), Phillips Brooks House Association (PBHA), and Public Service Network (PSN), and collaborates closely with the Institute of Politics (IOP) and Office of Career Services (OCS) to provide students with a rich variety of volunteer, internship, coursework, and postgraduate opportunities in public service. The Phillips Brooks House also provides coordination, funding, and planning for public service, supports public service efforts in the freshman yard and houses, and leads collaborative efforts such as the first-year Day of Service, Public Service Recruiting Day, and the Public Interested Conference. For more information on our offices, please see below. You can view our organization chart here.\nThe Center for Public Interest Careers (CPIC) engages and supports Harvard undergraduates and recent graduates in expanding awareness of and exploring public interest careers. Working closely with university, alumni\/ae, and community partners, CPIC develops public interest fellowships, internships, networks, and opportunities for personal and professional development.\nThe Institute of Politics' (IOP) mission is to unite and engage students, particularly undergraduates, with academics, politicians, activists, and policymakers on a non-partisan basis and to stimulate and nurture their interest in public service and leadership. The Institute strives to promote greater understanding and cooperation between the academic world and the world of politics and public affairs.\nThe Engaged Scholarship Program is an exciting new initiative focused on integrating academics, public service and community engagement. By promoting curricular innovation that takes learning outside the classroom, Engaged Scholarship nurtures students' intellectual development while responding to community needs and real-world issues. At the heart of the Mindich Program is the development of innovative new courses at Harvard College. Starting in this inaugural year, the Engaged Scholarship program will draw on students' intellectual interests, commitment to service and community, to support the development and implementation of two courses per year (minimum) for the next seven years.\nPhillips Brooks House Association (PBHA) is a student-led 501(c)(3) nonprofit organization and the largest public service organization at Harvard, encompassing 86 programs that serve over 10,000 youth and adults in the greater Boston area. PBHA programs emphasize direct service and social action as a facilitator for social change and address several key community needs, including tutoring, small claims advising, advocacy, managing local homeless shelters, ESL education, citizenship training, Alternative Spring Break trips, and the Summer Urban Program (SUP).\nThe Harvard Public Service Network (PSN) advises and supports independent student-led public service groups officially recognized by the Office of Student Life. PSN staff members provide support and resources to over 50 student organizations, many of whom partner with local community nonprofit organizations or nationally recognized service programs.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"J on helps people with back pain by diagnosing the problem, identifying contributing factors and developing a personalised treatment program that creates long-term change.\nIn association with colleagues, Jon has researched and brought together a systematic approach to assessing and managing low back pain. Based upon extension research, he teaches courses to practitioners wishing to utlise this step by step approach.\nResearch publications can be downloaded from here.\nIf you would like to learn how to apply this approach to your client's benefit Jon's courses can be found here.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Extendable to a full 5' 9\"\nFetch your gear in your truck bed or suv. Grab it. Move it. Load it. Cargo management is now within your reach with the Access EZ-Retriever. Easily reach items that have slid to the front of your truck box from driving or unload tools, groceries and other items with ease.\nThe extendable EZ-Retriever is manufactured from aircraft grade heavy-duty aluminum, so it's tough enough to handle large objects, but light enough for anyone to use.\nWith EZ-Retriever you won't have to climb into the bed of the truck or stretch to reach your cargo. The extendable hook makes accessing your cargo from the tailgate or side of your truck convenient and safe. You simply adjust the length. Prevent the possibility of injury or strain to your back and joints, scratching the truck or soiling your clothes with EZ-Retriever.\nThe EZ Retriever extends to a full 5 feet 9 inches - more than enough length to reach to the front of any truck bed. To extend the EZ-RetrieverT you just twist the handle to the left, extend to the needed length, and twist to the right to lock it in place. The extendable EZ-Retriever works great for vehicles with toppers, tonneaus or lids, and adjusts for the perfect reach for any truck box length.\nAccess backs your EZ-Retriever with a 1-year warranty.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Arada Ecoburn Plus 4 is an ideal choice if you are limited for space in your chimney breast but still desire the style and performance of a top of the range wood burner. With an overall width of 355mm and a depth of 365mm, the Ecoburn Plus 4 is designed to fit into even the smallest of openings. Despite it's small size, the Ecoburn Plus 4 has a maximum log length capacity of 240mm (9.5\") and still incorporates Arada's patented Flexifuel grate system which ensures that you get the same efficiency from burning either wood or smokeless coal.\nThe Arada Ecoburn Plus 4 has a cosy heat output of 4.5kW making it ideal for smaller rooms and an impressive efficiency of 86.3% which ensures that you will get as much heat out of the fuel used as possible.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaonmx b/data_all_eng_slimpj/shuffled/split2/finalzzzaonmx
new file mode 100644
index 0000000000000000000000000000000000000000..eff602f87c5b5ad8a0f5b0899372986296034ed5
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaonmx
@@ -0,0 +1,5 @@
+{"text":"The Chairdrobe, a manifestation of an always improvised object, like the chair next to the bed which turns into a wardrobe! Like the jolly in card games, Joly fills exactly this gap. It is a silent butler, a tray or an occasional chair. Lightweight and easy to grip, it can \"follow\" its user into the living or sleeping area, as needed. Joly is ironic, decorative and functional. It serves well as an entrance piece, in the bathroom and obviously... in the bedroom! Jol(l)y good!\nMade of gold\/black powder-coated metal with a solid natural walnut or petrol blue lacquered top\/seat. Lightweight and easy to grip, it can \"follow\" its user in the living or sleeping area, as needed. Optional cushion available upon request.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"3\/7\/2000 PRODUCTION MASTER - 4P.M.\nChicago: \"World, The,\" 03\/07\/2000, WGBH Media Library & Archives, accessed April 18, 2019, http:\/\/openvault.wgbh.org\/catalog\/A_4DBED6AA64924D57B14FA10087E92E06.\nMLA: \"World, The.\" 03\/07\/2000. WGBH Media Library & Archives. Web. April 18, 2019. <http:\/\/openvault.wgbh.org\/catalog\/A_4DBED6AA64924D57B14FA10087E92E06>.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"A beautifully simple, sterling silver bangle consisting of three interlinked silver bangles.\nSterling silver is formed using traditional silversmithing techniques, into this beautifully simple, elegant trinity bangle consisting of three interlinked solid silver round bangles.\nThe bangles are available in Slim (made from 2mm round silver stock) or Standard (made from 2.5 mm round silver stock).\nThe bangles are available with a matte finish, a polished finish or a combination of both (two matte and one polished or two polished and one matte).\nEach bangle in the Slim version is 2mm thick. Total weight 20g.\nEach bangle in the standard version is 2.5mm thick. Total weight 30g.\nDue to the handmade nature of the product, all dimensions are approximate and are for guidance only.\nAn alteration\/exchange service is available if you do wish to exchange for a different size.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Jay Penske, known for his wild antics, smart business sense and billionaire father Roger Penske (IndyCar racing) just listed this East Coast-like Bel Air colonial for $7.2M.\nPurchased back in 2004 for $1.97M, this 1.14-acre lot boasts a 1960s cottage-esque home with 3,500 square feet of living space. The residence offers five bedrooms and 5.5 baths, a cedar-shingled roof, a dramatic, gated driveway, three-car garage, library, formal living and dining room, eat-in kitchen, 2,000+ square feet of deck space, home gym and more.\nAdditionally, the listing offers a truly magnificent infinity pool with scenic views and a roomy master suite\/adjoining master bath with a humungous soaking tub\/marble steam shower.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Joey is involved in numerous events throughout the year at both the main Innsbrook location and all over town with his mobile catering units. Listed below are the events for the current month. If you would like additional information about any of these events, or to schedule Joey to cater your next gathering, please Contact Joey today.\nAny time is a great time for a couple of dogs and a coke at Joey's. In fact today would be perfect! Stop by our Innsbrook location today, step right up and introduce yourself, then order the best hot dog you will ever taste!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzapjrd b/data_all_eng_slimpj/shuffled/split2/finalzzzapjrd
new file mode 100644
index 0000000000000000000000000000000000000000..2a9513d9743d45d4290090f211401efdd0642204
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzapjrd
@@ -0,0 +1,5 @@
+{"text":"- Source from Locks Wholesalers and Wholesale Lock Suppliers for a vast collection of reliable Locks. Our Wholesale Lock Manufacturers are well known for manufacturing quality Locks and supplying the best Locks such as Lock \/ Padlock \/ Drawer Lock \/ Letterbox Lock \/ Letter Box Lock \/ Camlock \/ Push Lock \/ Electronic Lock \/ Cabinet Lock \/ TSA Lock \/ Combination Lock \/ Pin Lock \/ TSA Pad Lock \/ Pad Lock \/ Cable Lock \/ Luggage Lock at factory price. Feel free to get your free latest Wholesale Lock Manufacturers quote from our top Locks Wholesaler and connect with the trustworthy Locks Distributors at Online Marketplace.\nOnline find quality Wholesale Locks from our reliable Wholesale Lock Manufacturers and Lock Suppliers. Make your free Locks enquiry from our Locks Wholesaler \/ Manufacturer and get the latest price through our trustable Wholesale Lock Manufacturers and Lock Suppliers for the best Locks now!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Another piece of vintage leather from my collection to illustrate the post I wrote a few months back on the history of Monarch leather jackets. This one's a real beauty, with unusual construction. Look at the way the edge of the jacket, lapel and collar are formed.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I wanted a fair decision to be taken for the property division between me and my siblings without affecting our relations. Thanks guys! Couldn't have been possible without you all.\nNew procedures have been introduced by the Government for couples wishing to apply for a court order related to children financial circumstances in case of the breakdown of a family.\nBefore such a claim can be made to the court, spouses will have to have attended a Mediation Information Assessment Meeting with an agreed mediator and get a Form FM1 to prove that they have done so.\nThe final point is to guarantee that both spouses have seriously considered mediation to try to solve their differences. It is generally acknowledged that the regular adversarial court process is an expensive and, above all, a long and painful one when ex couples fight for the resolution of their family disputes.\nIn fact, when both parties have previously asked for information or advice about how mediation can help them in the long term, the amount of court applications gets drastically reduced. A mediator will guide ex couples in the process to reach an adequate settlement.\nAs for the mediator, his target should always be to explain the couple how mediation works so that the right estimation can be made to help them decide whether mediation would be suitable in their particular circumstances.\nThis meeting with the mediator can be held with one of the parties alone or with both at the same time, but partners should be h4ly warned against this last possibility in case of domestic violence issues.\nWhat to do after a MIAMS?\nAfter attending a MIAMS, both parties get the chance to reconsider if what they really want is to go on with the mediation procedure. In this case, several more meetings with the mediator should take place so as to concentrate on the couple's disputes and this time. The presence of both in the couple is highly recommended.\nAfter all this procedure gets to an end, the moderator will elaborate a document including all of the points in the agreement that have been successfully reached and will use it as the starting point of a court order in the divorce process.\nIn case those in the couple decide not to go through mediation but would rather have the matter proceed through the court, the form FM1 will be issued to them by the mediator, so that now both parties may proceed with legal hearings.\nThis FM1 must be presented to court by one of the spouses in case he or she is self representing, otherwise it will be taken by a solicitor. Whatever the case then, it is h4ly recommended for parties to do some research and find the right team of dedicated and experienced family mediators who can provide a professional approach to their family issues.\nThere are several cases though in which attending a MIAM should never be required to couples, like domestic abuse, bankruptcy of one of the spouses, an imperative court claim found crucial by any of the partners or the mediator himself and finally, in those delicate moments when kids protection problems have developed.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\u4e2d\u56fd\u79d1\u5b66\u9662\u5730\u7403\u73af\u5883\u7814\u7a76\u6240\u673a\u6784\u77e5\u8bc6\u5e93(IEECAS OpenIR): What do we know about domestication in eastern Asia?\nWhat do we know about domestication in eastern Asia?\nThe body of data based on new work on genetics and DNA, plus a growing number of radiocarbon ages which are independent of dates based on cultural associations has broadened our knowledge of domestication in eastern Asia. Here we review the situation for several plant and animal species that were domesticated locally or imported to east Asia. Major centres of plant domestication in China have been in the Yellow and Yangtze river basins, and in Yunnan. For animals it appears that the Yellow River region, the area around Xi'an and the south-east have been important centres. Many adopted domesticates have entered China through the north-west and later through ports such as Canton (Guangzhou). It appears that while there are outliers to extended ranges of wild plants and animals, sometimes not securely dated, widespread deliberate movement of plants and animals outside their natural ranges coincided with reduced hunting and gathering around 5\u20134 kyr in the Longshan cultural period. The adoption of agriculture has resulted in large scale landscape transformation; forests and woodlands have been replaced by crop and grazing lands and this is evident in many late Holocene sedimentary records. This transformation continues and the patterns are changing as diets are shifting and much grain is now used to feed chicken and beef, and in addition this has placed increased pressure on water resources.\nGB\/T 7714 Dodson,J,Dong,GH. What do we know about domestication in eastern Asia?[J]. Quaternary International,2016,426(2016):2-9.\nAPA Dodson,J,&Dong,GH.(2016).What do we know about domestication in eastern Asia?.Quaternary International,426(2016),2-9.\nMLA Dodson,J,et al.\"What do we know about domestication in eastern Asia?\".Quaternary International 426.2016(2016):2-9.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Click here to find out how far it is to Seymour Victoria AUSTRALIA.\nhow far is it to Seymour Victoria AUSTRALIA?\nTell me about travel to Seymour Victoria AUSTRALIA. I could probably use a hotel or a local tour of Seymour-.\nIs there anywhere to hire a car in Seymour-?\nI would also be interested in places to eat in Seymour Victoria AUSTRALIA.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaprcu b/data_all_eng_slimpj/shuffled/split2/finalzzzaprcu
new file mode 100644
index 0000000000000000000000000000000000000000..51a4fc57025c528f802ed5c7a1f634638e2142ae
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaprcu
@@ -0,0 +1,5 @@
+{"text":"Bologna has an old Jewish cemetery with tombs dating back to early medieval period. This cemetery is close to Certosa Catholic cemetery, to the south of the city. Jewish cemetery has its own separate entrance to the south of Certosa cemetery.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"2020 Nissan Altima Colors Changes, Price \u2013 Any approaching 2020 Nissan Altima can be a sizeable unfamiliar auto in many Position, For instance, The European countries will be chasing it is occupation worldwide by using a company-new era that may be anticipated to repair the goods income of your automobile which was dropping vitality intended for 2 several years. In recent times, the particular old-fashioned part of the cars provides in fact eliminated straight down marketplace be component of any USA. Any superstars of your class this is the Camry. Accord, together with Nissan Senta or even Altima own attained many fully decreased, though the level keeps essential regarding companies, notably Asians, that will depend upon the first spots of your Major 10.\nComponent report and also the roof structure covering up will definitely carry on becoming undamaged. Stainless steel uses up h2o piping are generally standard also from the principal object, plus furthermore 2020 Nissan Altima will take an authentic physical fitness and health posture on account of the particular changes. 17-in. Rims will definitely proceed to get frequent and also 18-in. Other metals are more. This moonroof is moreover accessible as being a probable method. Common, Altima usually is a favorite some front door that exercises routines one of the more eye-catching in the open air different versions in the portion. That several-front door automobile capabilities an amazingly cozy inside that could be wholesome approximately 5 men and women. Your room inside of the cabin can be excellent, and also the two evenly wholesale, as well as legroom, be enough. The interior looks classy, and even progressive, together with material seating is definitely delivering the astounding alleviate. Leather-based baby car seats are usually extra.\nAny internal stands to ascertain a far more considerable reconstruction, these kinds of while, without precedent intended for any sort of Nissan, the with vogue pc tablet-design industrial screen credit score satisfied for this dash panel. 2 right can be found more than likely for number along with altering-acquiring a uncomplicated prepare of likes and dislikes arranged specially beneath the keep close track of or even a whole lot more the middle air flow atmosphere air vents. Beneath that eventually, often be Warming up along with air conditioning handles utilizing increase place setting management dials. Lightweight aluminum is well known, an added aiming tire this kind of since the Rogue's, various USB 2. connect-ins, force-get start off, and also smart distinction curtains are particular. This artwork on-display physical appearance obsoleted, even so, Nissan could job old infotainment inscribing between verification nonetheless. However, moment strengthening any fancy client plan before them actually reaches car retailers.\nAs you look at in the information above, every single show stage shows a 2.5-liter I-4 electric motor model product. Slashes S, SR, SV, along with the 2.5-liter engine SL all give a trustworthy 179 touring. This 3.5-liter SL trim, no matter what condition, incorporates a V6 engine that can undoubtedly bring about incredible 270 potentials. Well developed sums S through SL (2.5-liter) all come up with a torque associated with 177 during 4,000 Revolutions per minute, though how a lot more resilient 3.5-liter SL's torque generally is a resistant 251 on 4,400 Revolutions per minute.\nAny Sort Of 2020 Nissan Altima 4 front door will set you back about $35,000. Choose a more significant decrease in addition to the V6 power generator, and also you can expect to spend more than $45,000. Prices act like it's competitors, as an illustration, Ford Combine together with Kia Optima, nevertheless Altima contains far more common items We shall undoubtedly assume this particular automobile to attain the starting of 2020.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"International gym apparel label, Ryderwear, is excited to announce the launch of it's newest activewear line, the Infinity Seamless Collection. Sleek, flattering, and functional, this cutting-edge collection is here to transform your wardrobe and your workout with its innovative performance wear technology. Featuring non-restrictive flexibility, reduced friction, targeted ventilation, and long-term durability, these styles will inject comfort and freedom into every workout.\nEngineered with ultra-smooth lightweight fabrications and advanced seamless construction technology, the Infinity Seamless Collection is designed for premium comfort and freedom of movement.\nThe capsule collection features four essential styles for both men and women. The wardrobe staples integrate edgy mesh panels that contour the skin in classic palettes of light grey, charcoal, soft blue, and burgundy, merging practicality and style.\n\"This is a big step for Ryderwear, and we hope that our customers are just as excited as we are to test out this incredible range!\" says Salvi.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"What are the Drawbacks\/ Caveats \/ Limitations of using a Non-Authoritative Server over a Fully Authoritative Server for Multiplayer Networking?\nI'm trying to generate a random key and share it with other players when they join the game i'm using PUN. it's not working please help!\nPhoton RPC doesn't broadcast properly.\nPhotonUnity player move object problem !\nCorrect way to design turn based multiplayer using Photon Unity Networking.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"At home on any style Triumph Classic, the RSD 2-Up Step Seat is narrower and thinner than your stock seat, while still covering the Triumph frame rails for a clean look. The unique stepped rear end is for passenger comfort as well as keeping you planted in the saddle when you feel the need to rip it. Rear panel with subtle RSD button adds a touch of flavor to the rear of the seat.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaqbzl b/data_all_eng_slimpj/shuffled/split2/finalzzzaqbzl
new file mode 100644
index 0000000000000000000000000000000000000000..04b2db0894ab991b4c44c174c582d3c69f40e9a9
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaqbzl
@@ -0,0 +1,5 @@
+{"text":"BUEA, Cameroon-Saturday June 9, 2018-9:00 AM local Time (Cameroon News Agency) Blood Banks at the Limbe and Buea Regional Hospitals have been boosted following the collection of 100 litres of blood by Hero Cameroon, an NGO specialized in health education and research within the country.\nThe donations were made by some 200 persons, mostly students from the Faculty of Health Sciences in the University of Buea, in prelude to the commemoration of World Blood Donor day on Thursday June 14, 2018.\nThe donation was carried out in four phases; sensitization and registration, mini physical examination, donation and refreshments.\nPrior to the exercise, the Chief Operations Officer of Hero Cameroon, Dr Domin Sone Majunda Ekaney, said it was paramount to donate blood to fill the almost empty blood bank in Cameroon. He told donors that Cameroon needs at least 400,000 pints of blood yearly but can only afford 73,000. These pints of blood are mostly collected in General and Regional hospitals across the country, reasons why the National Blood Transfusion programs are being set up to meet the demands.\nDr Domin Sone further explained that the demand is very high especially for obstetric emergencies where 50-80% of supplied blood is used. This is because severe bleeding during delivery or after child birth is the major cause of Maternal Mortality rate with about 40% of maternal deaths in Africa.\nAfter this first phase, the donors were registered, examined to make sure they are qualified for the exercise, before donation was carried out, where over 200 donors gave about 100 litres.\nMembers of Hero Cameroon, working in partnership with the two regional hospitals in the South West region; Buea and Limbe, have said their goal is to see into it that the blood banks of these hospitals never run dry, thus sharing and saving lives, since every blood donor is a Hero.\nMale or female, be in good physical and mental health, aged 18 to 65 years, weight from 45-50kgs, have a haemoglobin level of at least 12.5 g\/dl (Male donor is 13.0 g\/dl), not have had any symptoms of infection for at least 1 week e.g. sore throat, cough, runny nose, diarrhea, not have had a fever in the last 3 weeks, normal range blood pressure.\nSafeguard a more equitable, \"disease-free\" and emerging Cameroon.\nPerform high quality epidemiological and public health research on prevailing diseases public health magnitude and provide data which will dictate clinical and public health practice in low income countries.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Crossing paths with bounty hunter Train is seriously bad luck for criminals!\nTrain Heartnet, also known as \"Black Cat,\" was an infamous assassin for a secret organization called Chronos...until he abandoned that cold-blooded existence to live on his own terms as an easygoing bounty hunter. But is Train's past as far behind him as he thinks?\nKentaro Yabuki made his manga debut with Yamato Gensouki, a short series about a young empress destined to unite the warring states of ancient Japan and the boy sworn to protect her. His next series, Black Cat, commenced serialization in the pages of Weekly Shonen Jump in 2000 and quickly developed a loyal fan following. Black Cat has also become an animated TV series, first hitting Japan's airwaves in the fall of 2005.\nTrain faces Creed in a final showdown. Train is determined to follow the Sweeper's Code and take Creed alive. But now that Creed has become virtually indestructible, Train may have finally met his match. Will he come out of this in one piece, or has luck finally run out for the Black Cat?!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Three Rotarians from the local Uxbridge Rotary Club Ontario are going to be travelling as part of a group to Malawi in mid-September to visit Emmanuel International Canada's project sites and also to assist in refreshing classrooms by helping to paint and applying colorful alphabet and numeric stencil borders on the walls of the primary grade classrooms.\nThe classrooms were originally built by a group of Rotarians from the GTA. If you would like to assist the current team going, the Rotary Club is collecting coloured pencils (not wax crayons) and pencil sharpeners.\nThe goal is to collect by Sept 6th over 10,000 gently used pencils so that each of the 900 children may receive multiple pencils for their use.\nAlternatively, you may donate cash to purchase supplies in country which also helps the local economy. Cash donations over $10.00 are eligible for a tax donation receipt.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"If you are on Twitter, it is helpful to organize people you follow into lists based on interests and expertise. Instead of browsing a fire hose of all possible people to follow, you can organize the flood of tweets by topic. I've organized the people I follow for this magazine into the groups below. Links to the tweets and members of each group are provided. My plan is to add to these lists over time. And you're welcome to subscribe to one or more lists, or follow people and put them into your own lists.\nThere are many people, schools, tool vendors, and groups missing from these programming and computer science twitter lists, of course. Feel free to DM me on Twitter or use the Contact form to send me people you recommend.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This study has measured the evolution of the particle size distribution during acid precipitation of Kraft lignin in aqueous solutions. Sulphuric acid was added to acidify the solutions, and precipitation occurred. The influence of Na+ concentration was investigated, and temperature, lignin concentration, and agitation speed were kept constant throughout the study. The results show that the onset of precipitation, as defined in this work, is strongly dependent on Na+ concentration and pH. Furthermore, a shift in the onset pH was observed if existing particles were filtered off before acidification; this indicates a metastable regime in particle-free solutions. The kinetics of precipitation were found to depend predominantly on the density of existing particles in the liquid at the start of acidification.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaqivz b/data_all_eng_slimpj/shuffled/split2/finalzzzaqivz
new file mode 100644
index 0000000000000000000000000000000000000000..7cda0187a8ec9f8724b091a9811d403db30ce0e5
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaqivz
@@ -0,0 +1,5 @@
+{"text":"the boy with summer in his eyes.\nto stroke the flames of an autumn fire.\nInstead I watched him fall.\ninto a bed of thorns.\nCupid and Psyche\u2026beautiful but sad.\nBeautiful! Incredible voice and guitar. Well done!\nThank you kindly. I'm so glad you liked it.\nFascinating and heartbreaking. Thanks for sharing.\nI'm a new blogger and I created Real Life Natural Wife. I would like you to check it out and let me know what you think. Have a great day!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Princess Yachts newest V-Range model the V52, will be exhibited for the first time at the Cannes International Boat Show in September and its set to be another hit for Plymouth based boat builder.\nThe arrival of the new V52 was a landmark event in the evolution of the Princess model range. For the first time a V Class sports yacht of this size is available with an enclosed deck saloon, broadening the reach of open boating to new destinations and for an extended boating season.\nThe sleek profile of the V52 confirms her positioning in the heart of the V Class range, with masses of dynamic ability and thoroughbred performance when married to her powerful twin engines. Forward thrust is delivered with precision control through custom-machined propellers with twin shafts driven through V-drive gearboxes. This configuration benefits the lower accommodation space without compromising her sophisticated ride and agile handling that have become definitive V Class characteristics.\nThe V52 is a two stateroom craft, with the owner's suite located amidships enjoying the full beam, with a full sized double stateroom forward with scissor berths which can be easily converted to twin beds as required. This cabin also has generous storage and en-suite bathroom, which itself accommodates a full stall shower. As an alternative a three cabin option is also available with a generous twin cabin replacing the lower saloon.\nIn the V52, the latest in sports yacht technology combine with Princess' characteristic deep-V hull for the ultimate combination of assured seakeeping and maneuverability to inspire confidence for the most relaxed and enjoyable boating experiences.\nPrincess will be exhibiting a total of 11 boats afloat at the show (Princess 42, Princess 50, Princess 54, Princess 85 and 95 Motor Yachts, along with the V42, V45, V52, V56, V62 and V78 V Class sports yachts) and the stand display will be the largest to date.\nGreat post again, keep up the good work guys!\nI must say cool post here. Thanks for posting this and sharing it. I've just bookmarked your site. And I will check back soon to read your other articles. Keep up your awesome work.\nA+ article wsb, keep them coming.\nGreat to read a blog about Cannes and boats, one of my best vacation destinations. Great read!\nGreat post. I am glad to have found this Blog keep them coming!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Students who choose the minor come from a wide range of departments, and they complete a capstone project that allows them to engage translation in various literary and professional settings, including internships, community outreach, and creative collaborations.\nThomas Degroat '17 (BS, Neuroscience) approached his capstone project as a translation between media. He adapted an excerpt from George Orwell's novel, Nineteen Eighty-Four, into a script designed as pilot episode for a television mini-series. Using concepts from translation theory to describe adaption from literary to film, he found new and exciting ways to think about his experience of translating. He expects that translation will become even more important as he continues, especially in the science field.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Welcome to our selection of Cornish self catering properties close to the sea. Perfect for family breaks or a holiday with friends, we list everything from beach front cottages in Sennen to old fisherman's cottages in Portmellon\u2026 and everything in between! Many of the properties here are within a stones throw from the coast so quite often you don't even need the car to visit the beach.\nWe've also commented on those properties that boast wide ranging views, as we don't think there's a much better way to spend the evening than with a glass of wine in the garden watching the sunset over the Atlantic!\nSleeps 3. Set in a quiet lane, Mariners is one of a charming little row of listed coastguard cottages, just a minute's walk from the heart of Boscastle. With its spectacular harbour, the village boasts shops, pubs, restaurants and a Witchcraft Museum. Cottage Code: GRJ.\nFor even more cottage options, why not try venturing a little east and into the beautiful county of Devon? Browse cottages by the sea in Devon.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"c1987. Philomel, 1 v. (unpaged) : col. ill. ; 29 cm.\n, c1987. 20th Anniversary ed. Philomel Books,  p. : col. ill. ; 29 cm.\n1990. Hoopla Unabridged. Weston Woods , 1 online resource (1 audio file (9 min.)) : digital.\nJane Yolen. (1990). Owl Moon. Unabridged Weston Woods Studios, a subsidiary of SCHOLASTIC Inc.\nJane Yolen. 1990. Owl Moon. Weston Woods Studios, a subsidiary of SCHOLASTIC Inc.\nJane Yolen, Owl Moon. Weston Woods Studios, a subsidiary of SCHOLASTIC Inc, 1990.\nJane Yolen. Owl Moon. Unabridged Weston Woods Studios, a subsidiary of SCHOLASTIC Inc, 1990.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaqklf b/data_all_eng_slimpj/shuffled/split2/finalzzzaqklf
new file mode 100644
index 0000000000000000000000000000000000000000..24906322ffc07e97d33202b321920f19955fe521
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaqklf
@@ -0,0 +1,5 @@
+{"text":"This may be the first time you have ever appeared in Court and it is for this purpose we inform you of your RIGHTS AND OF COURT PROCEDURE.\nEffective June 15, 2008 the Delaware Municipal Court has incorporated by reference Chapter 2710 of the Ohio Revised Code, the Uniform Mediation Act (UMA), and Rule 16 of the Rules of Superintendence for the Courts of Ohio.\nAll civil matters filed in either the Small Claims or General divisions shall be referred to mediation as provided by Rule 304 which can be viewed in its entirety by clicking the link to Court Rule 304, below.\nAlso, below you can find link to a list of mediators.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The western world debates about Egypt's Muslim Brotherhood: are they ok? are they \"moderate\"? Are they extremist? This report prepared for the Wiesenthal Center talks about their history and let me tell you, it's some scary stuff. None of that \"Non-Violent, 'Secular' Group\" nonsense.\nIt's long, but worth a read if you want to get some background on what's going on over there. Click here for the report..","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"According to A. Jacques, although no one goes to social networks to buy something, having the right context and providing information can reach a lot of people. This is partly confirmed by the latest data \u2013 almost 89% in the last quarter of last year. all of Facebook's revenue came from mobile advertising.\n\"Mobile ads are evolving and adapting to platforms. For example, vertical videos on Facebook, fullscreen, Instagram Stories, and all communications on this network are advertising solutions that only target users on the phone, \"said a marketing expert.\nThere is no doubt that the pockets of the Internet in your pocket will only increase \u2013 the speed of mobile data in the world is still quite slow and therefore limits the ease of use. However, the situation is changing rapidly \u2013 the report of the international company GSMA Intelligence states that more than 60 percent of the companies today are in the market. connections from mobile phones were made using a broadband internet connection.\nAmong the various forecasts for the future, there is a surprising boost to even more use of the source of handsets \u2013 self-contained cars. In the future, drivers will no longer need to steer the wheel and look at the road, so they can spend time working back and forth the same as a bus or metro passenger today. A lot of options, but you can safely guess that some of them will look more on the phone screen. This could further encourage Samsung and Apple to invest millions in this new technology.\nToday, for many of us, a normal day is unthinkable without a mobile phone. Nothing surprises with the big screen, missing buttons, a lot of applications and applications, fast- loading e-mails, reminders, promotional offers, especially high-quality photo or video cameras, pedometers, etc. Research shows that mobile phones are usually changed every 2-3 years.\nThis is fueled by the emergence of new and \"better\" models on the market, the possibility to buy installments, special plans made by mobile operators, or gifts provided by sellers. When selecting a new mobile device, the battery life, speed, screen quality and resolution of the photos are first evaluated. Often the price is pushed down to the second plan because love for this category of brands is much stronger than a rational choice.\nteam has conducted a comprehensive survey of 36 latest and most popular mobile phone prices. The survey included the most visited e-mails. stores in Lithuania based on information, and the largest technical stores where you can buy a mobile phone.\nhas included the most popular and well-known brands and models of phone manufacturers in Lithuania in the price list for comparable mobile phones: Samsung, Apple, Nokia, Huawei, Xiaomi, OnePlus , CAT and Sony.\nThe team did not evaluate the technical characteristics, quality features, design, color or functionality of the phones in its study, nor could it evaluate which market the particular phone was for, as such information was not available. Now take a look at how these features of mobilieji telefonai.\nDuring the survey, prices were recorded without state compensation compensation for authors and without telephone accessories. Mobile Phone Pricing Survey is for those who want to objectively compare the same brand and identical model phone offered by different vendors of this product in Lithuania.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Duquesne University Coffee House Reading Series returns for the 2017 spring semester with poetry readings from Malcolm Friend and Yona Harvey at the Genesius Theater on Wednesday, Feb. 22, at 7 p.m.\nFriend is a poet and CantoMundo fellow whose work has earned him the Merrill Moore Prize for Poetry and the Talbot International Award for Writing. His work has appeared in publications such as La Respuesta Magazine, the Black American Edition of Fjords Review, Alicante's Informaci\u00f3n, Fields Magazine, Acentos Review and Pretty Owl Poetry.\nPoet Harvey is also an assistant professor at the University of Pittsburgh. She is author of the poetry collection Hemming the Water, a Kate Tufts Discovery Awardee and finalist for the Hurston-Wright Award. Harvey's work has appeared in A Poet's Craft: A Comprehensive Guide to Making and Sharing Your Poetry and The Force of What's Possible: Accessibility and the Avant-Garde.\nOrganized and sponsored by Duquesne's Department of English, the series aims to develop the creative writing and arts community on Duquesne's campus by inviting established writers to present their work alongside the work of students and other emerging writers.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"c.. Both were going to Bombay .\nThey seemed to fit very well and decided to be roommates in Bombay and made a pact that they would do everything together..\nSo they lived in the same house, travelled to the college together on Kanjibhai's scooter, had lunch in the staff room together, returned home together.They were watching the TV together, eating dinner together and were also sharing the same bedroom and...EVEN sharing the same bed.\nThe only problem was that Rupaben was placing a pillow between them at bedtime, much to the frustration of Kanjibhai, who ended up spending many sleepless nights with this most desirable beauty besides him, separated by the pillow.\nKanjibhai's frustration built up to such an extent that he could take it no more and ended up deciding to drink.So one day he took off from the college leaving Rupaben on her own. She was quite upset, but made it home by auto rickshaw.\nThe pact had been broken so she decided not to open the door for Kanjibhai when he got home drunk at about 2 AM. Kanjibhai knocked on the door for about 20 minutes and pleaded with his roommate to let him in.\nAfter listening to his crap for 20 minutes, Rupaben said, ' Where the hell did you disappear today? We decided to do everything together! .From now onwards you will sleep outside'.\n\"You could not jump over a pillow for four months and now you are talking of jumping over the wall!! \"","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzargqm b/data_all_eng_slimpj/shuffled/split2/finalzzzargqm
new file mode 100644
index 0000000000000000000000000000000000000000..c9e08baea146d745e9d00c7ad67d1a13b3656473
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzargqm
@@ -0,0 +1,5 @@
+{"text":"Thanks for a tremendous sumbit, will study your personal others content. thank you your thoughts on this, I soon became somewhat struck by this short article. Thanks again! You commit a terrific moment. Has excellent data here. I feel if a greater number of people thought about it like this, they'd have a very better time frame have the suspend ofing the issue.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The region of Amitges is a traditional school of climbing. There are numerous boulders near the refuge like the well-known Needles of Amitges and places to climb less frequented such as el Portarr\u00f3, el pic de Crabes, la serra de Saboredo, les Torres and les Agulles de Bassiero, etc. The rock is granite of good quality.\nAt the Agulles of Amitges there are bolts at the belays and at the abseil points. For self protection you need friends of different sizes. The length of most of the routes to the Agulles is between 100 and 150 mts. In other places we can find longer routes.\nThere is approximately half an hour from the refuge to the foot of the Agulles.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Thank you for visiting [blog]. Many people have tried on line for locating facts, strategies, posts or other guide for their needs. Like you are. Do you arrive here for getting new fresh understanding of velocity worksheet 3 1 answers? Exactly how many webpages have you browse for getting more detail about velocity worksheet 3 1 answers?\nVelocity worksheet 3 1 answers is one of grown content at this time. We realize it from internet search engine records like adwords or google trends. In order to bring beneficial info to our followers, weve attempted to find the nearest relevance pic about velocity worksheet 3 1 answers. And here you will see now, this image have been obtained from trustworthy source.\nWe think this velocity worksheet 3 1 answers image will provide you with a few extra point for your need and that we hope you like it. We understand, we might have diverse view about this but at least we have tried our best.\nThis image has been submitted by Alice Ferreira. You can explore additional helpful posts in [cat] group. We thank you for your visit to our website. Make sure you get the information you are looking for. Do not forget to share and love our reference to help further develop our website.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Simple and best practice solution for 331 is what percent of 895. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.\n1. We assume, that the number 895 is 100% - because it's the output value of the task.\n3. If 100% equals 895, so we can write it down as 100%=895.\n4. We know, that x% equals 331 of the output value, so we can write it down as x%=331.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"In the event of snowfall the first place you should check is the school website homepage. As soon as possible we will update the school website as to what is happening. The news flash will appear on the front page. Our website address is www.cliddesden.hants.sch.uk. We will try to text all parents to let you know whether school is open or closed but this may not be possible if we do not have access to the school.\nLocal radio stations will broadcast (and add to their website) a list of schools that are closed or partially closed. They will do this very quickly; this is the best way to check whether or not we are open or closed. Listen to The Breeze FM for details.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzavgck b/data_all_eng_slimpj/shuffled/split2/finalzzzavgck
new file mode 100644
index 0000000000000000000000000000000000000000..cbe38ecbcbb0bba647e688bcc10389434f3be2fa
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzavgck
@@ -0,0 +1,5 @@
+{"text":"The best time to go to Tamarijn in Aruba is from january until october and december, in which you have a warm temperature and barely till mediocre rainfall. The highest average temperature in Tamarijn is 32\u00b0 in september and the lowest is 28\u00b0 in february.\nIf you want to know what the average temperature is in Tamarijn or when most rain or snow falls, you can find it quickly below. That way you are well prepared.\nThrough our partners below you will find the cheapest flight tickets for Tamarijn. Click on a logo to go to the website or take a look on Skyscanner for the cheapeast flight tickets from all the airline companies.\nOn average, it is maximum 29\u00b0 in january in Tamarijn and at least around 27\u00b0 degrees. In january there are 21 days of rainfall with a total of 50 mm and the it will be dry 10 days this month in Tamarijn.\nOn average, it is maximum 28\u00b0 in february in Tamarijn and at least around 27\u00b0 degrees. In february there are 17 days of rainfall with a total of 41 mm and the it will be dry 11 days this month in Tamarijn.\nOn average, it is maximum 29\u00b0 in march in Tamarijn and at least around 27\u00b0 degrees. In march there are 17 days of rainfall with a total of 31 mm and the it will be dry 14 days this month in Tamarijn.\nOn average, it is maximum 29\u00b0 in april in Tamarijn and at least around 27\u00b0 degrees. In april there are 16 days of rainfall with a total of 37 mm and the it will be dry 14 days this month in Tamarijn.\nOn average, it is maximum 30\u00b0 in may in Tamarijn and at least around 28\u00b0 degrees. In may there are 18 days of rainfall with a total of 58 mm and the it will be dry 13 days this month in Tamarijn.\nOn average, it is maximum 31\u00b0 in june in Tamarijn and at least around 28\u00b0 degrees. In june there are 13 days of rainfall with a total of 26 mm and the it will be dry 17 days this month in Tamarijn.\nOn average, it is maximum 31\u00b0 in july in Tamarijn and at least around 28\u00b0 degrees. In july there are 15 days of rainfall with a total of 45 mm and the it will be dry 16 days this month in Tamarijn.\nOn average, it is maximum 31\u00b0 in august in Tamarijn and at least around 28\u00b0 degrees. In august there are 15 days of rainfall with a total of 47 mm and the it will be dry 16 days this month in Tamarijn.\nOn average, it is maximum 32\u00b0 in september in Tamarijn and at least around 29\u00b0 degrees. In september there are 16 days of rainfall with a total of 116 mm and the it will be dry 14 days this month in Tamarijn.\nOn average, it is maximum 32\u00b0 in october in Tamarijn and at least around 29\u00b0 degrees. In october there are 21 days of rainfall with a total of 123 mm and the it will be dry 10 days this month in Tamarijn.\nOn average, it is maximum 31\u00b0 in november in Tamarijn and at least around 29\u00b0 degrees. In november there are 27 days of rainfall with a total of 171 mm and the it will be dry 3 days this month in Tamarijn.\nOn average, it is maximum 30\u00b0 in december in Tamarijn and at least around 28\u00b0 degrees. In december there are 27 days of rainfall with a total of 122 mm and the it will be dry 4 days this month in Tamarijn.\nThe weather for Tamarijn in Aruba will be around 27\u00b0 degrees in the next 14 days with several days chance of light rain showers.\nTamarijn lies in Aruba . If you want to call Tamarijn you have to use +297 or 00297 before the phone number without the first 0 in the original phone number (if it occurs). If the normal number is 05012457809, for example, you can remove the first 0 and call +2975012457809 or 002975012457809.\nTamarijn is in a straight line at 7.529 km distance from London. From London-Heathrow the flight time is about 10 hour and 25 min.\nThe GPS coordinates are N 12\u00b0 31' 59.9988\" en W 69\u00b0 58' 0.0012\"\nIn Tamarijn it is now 16:16 hour on friday 19 april 2019. That is United Kingdom.\nIn Tamarijn the Arubaanse florin is used to pay.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Google has confirmed the rumor that the government of China has blocked access to the most popular video service website YouTube.\nApproximately 300 million individuals in China regularly use the Internet, and they all report that access to YouTube has been off and on over the past few weeks. Now, access to the site is totally blocked.\nWhile the communist government of China continues to state that they support the Internet, as of now they say that they know nothing about the YouTube issue in their country.\nI don't see the big deal about YouTube, but I have heard that China and some other countries have had problems accessing not only YouTube but some other sites as well.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\u0410\u043b\u043b\u0430\u043c\u043e\u0432 \u041e. \u0422. Software testing \u2013 overview \/\/ \u041c\u043e\u043b\u043e\u0434\u043e\u0439 \u0443\u0447\u0435\u043d\u044b\u0439. \u2014 2016. \u2014 \u21169.5. \u2014 \u0421. 12-17. \u2014 URL https:\/\/moluch.ru\/archive\/113\/29764\/ (\u0434\u0430\u0442\u0430 \u043e\u0431\u0440\u0430\u0449\u0435\u043d\u0438\u044f: 25.04.2019).\nThe common user of modern software is most probably expecting the software to perform effectively, be usable and function reliably. These non-functional requirements have to be assessed by software developers throughout their development process. This paper focuses on a subtopic of the third requirement, software reliability. Reliability can be assured by Software Quality Engineering with one of it's main topics being Software Testing.\nBy using the principles and activities of software testing in the software development process, developers aim to make their software more reliable by increasing the functional correctness and stability of the system.\nThis work aims to provide a complete survey on the topic of software testing in a scope, that allows the reader to have read about every relevant topic in the context. The topics covered in this work might for example be used as a structure for a lecture on software testing.\nDescriptions of topics are covering the topics only on surface level. Certain topics will be investigated more thoroughly in separate works appended to this overview.\nSection II gives an introduction to terms that are commonly used in the software testing context to have a terminology foundation for the rest of this work. Section III gives a brief survey on one of the most current software testing standards which is used to structure the rest of the covered topics. In section IV the fundamentals are covered and the main objectives of testing are covered in section V. Section VI embeds software testing into the software (development) lifecycle and section VIII covers the management of the testing process. A classification of tests is given in section IX which is consecutively applied to levels of testing in section X. Techniques for test case derivation are given in section XI and a survey of tools to support the software testing process is given in XII.\nThis section clarifies some of the fundamental terms used in software testing according to the different published standards and definitions, that found consensus among the international testing community. A number of terms related to software testing are presented, as they represent the essence of the software testing lexicon and will be consequently used throughout this work.\nA. Error, Defect, Fault and Failure...or Bug ?\nThe existing definitions are never precise and there is a sort of confusion or different point of view concerning a unified general definition of these terms. Until now there is no definitive software testing standard, except the ISO\/IEC\/IEEE 29119 standard that is still in development. We tried below to \"filter\"the most exhaustive definitions from the different existing standards and software testing books. According to , the term bug lacks precision, as it can mean an incorrect program code, an incorrect program state or an incorrect program execution. Because of the ambiguity of the term it will not be used in this work.\n\"An Error is a human action that produces an incorrect result\".\nA Fault is a flaw in a component or system that can cause the component or system to fail to perform its required function, e.g. an incorrect statement or data definition. A Fault, if encountered during execution, may cause a failure of the component or system.\nA Failure is a behavioral deviation of the component or system from its expected delivery, service or result. Therefore, the term failure refers to the inability of a system or component to perform its required functions within specified performance requirements. The definitions of fault and failure allows us to distinguish testing from debugging .\nThe software testing community frequently uses several synonyms of the previous defined terms like for example defect to describe a fault and an infection to describe an error. These two alternatives are, according to W. Dijkstra, pejorative alternatives to increase the programmer's sense of responsibility. Finally our infection chain (the cause-effect chain from a fault to a failure) will be as follow.\nTesting is the process consisting of all life-cycle activities, both static and dynamic, concerned with planning, preparation and evaluation of software products and related work products to determine that they satisfy specified requirements, to demonstrate that they are fit for purpose and to detect errors .\n\"A Test is a set of one or more test cases\" .\nA Test case is a set of input values, execution preconditions, expected results and execution post-conditions, developed for a particular objective or test condition, such as to exercise a particular program path or to verify compliance with a specific requirement .\n\"The process of finding, analyzing and removing a fault that caused the failure in a system or component\" .\n\"The totality of functionality and features of a software product that bear on its ability to satisfy stated or implied needs\" .\nVerification: \"Confirmation by examination and through provision of objective evidence that specified requirements have been fulfilled\" .\nValidation: \"Confirmation by examination and through provision of objective evidence that the requirements for a specific intended use or application have been fulfilled\" .\nAlmost all goods and services must satisfy certain requirements. Typically, such requirements are defined in standards. The aim of a standards is to make sure that the end product complies with market requirements and attains end user satisfaction. In fact, many software applications, mobile apps, and even full enterprise systems are sold to various customers every day that might not have been developed using any standard. However, people buy them anyway. Of course, ignoring standards is not directly proportional to the poor software quality and lesser demand for the end product (as long as it's not life-critical software). But such as life-critical or huge losses software should be compliant with one of the standards. The problem is not in following standards. What really matters is ignoring or diminishing the importance of the quality of the software.\nA standard is a document that provides requirements, specifications, guidelines or characteristics that can be used consistently to ensure that materials, products, processes and services are fit for their purpose[ISO].\nNowadays International Standards exist almost for all kind of products and services. Software Testing is also no exclusion.\nThe first Standard of relevance Software Testing was published in 1983 by IEEE . The latest version of this standard was updated in 2008. Previously, all standards including testing were only considering some aspects of Software Testing. By ISO\/IEC JTC1\/SC7 Working Group 26 are developed new international standards on Software Testing - ISO\/IEC\/IEEE 29119. This standard was provied all existing standards. It involved all aspects of Software Testing and replaced a number of existing standards.\n- Part 1: Concepts and Definitions. It is informative and provides definitions, a description of the concepts of software testing and ways to apply the processes, documents and techniques defined.\n- Part 2: Test Processes. It is to define a generic process model for software testing that can be used within any software development life cycle. The model specifies test processes that can be used to govern, manage and implement software testing in any organization, project or testing activity.\n- Part 3: Test Documentation. It is to define templates for test documentation that cover the entire software testing life cycle.\n- Part 4: Test Techniques. It is to define one international standard covering software test design techniques that can be used during the test design and implementation process within any organization or software development life cycle model.\n- Part 5: Keyword Driven Testing. It is to define an international standard for supporting Keyword Driven Testing.\nThe first three part of standards have been published in 2013, the fourth part is going to be published by the end of year 2014 and fifth part is likely to be rolled out in 2015 [ISO].\nWith the rapid development of software systems, system quality is focused more and more in software engineering. To assure a better software quality, more sophisticated software testing methods and techniques are needed in order to achieve the system quality described by the customer requirements. Software testing is a process, or a series of processes, designed to make sure computer code does what it was designed to do and, conversely, that it does not do anything unintended. Software should be predictable and consistent, presenting no surprises to users. During the test process we distinguish different actors, they are the programmers, the test engineers, the project managers, and the customers. They influence a system's behavior or are impacted by that system [10, P.10].\nTests can have very different objectives. Test cases written on implementation level aim to make sure that the implementation of a system fulfills a certain level of software quality and stability. But there are more aspects and objectives to software testing that aim to make a system tested and covered from top to bottom. Including the part, that is actually used by the customer. Such test objectives are described in this section.\nOne of the main purposes of software testing is checking whether a system is or behaves correctly in the meaning of not producing wrong results or behaving unexpectedly. For this objective software systems can be tested on different levels as described later on in section X. The different levels for correctness tests however always apply on implementation level, e.g. one cannot simply check for correctness in terms of the following objectives .\n- Standardization and Guidelines: Depending on the use case of the system or the operation system it will be used on, there may exist standards on how end users will expect the UI to be layout and designed.\n- Intuitive: UIs should be intuitive for the end user who may also be covered by guidelines and standardization.\n- Consistency: UIs should be consistent throughout the system so that the UI never behaves differently than the user would expect from a previous action.\nAccessibility Testing is a special case of UI Testing where user interfaces are tested for disabled or handicapped people. This can include specific tests for visual, audio, motion, cognitive or language handicaps [12, p.177f].\nAnother approach of testing the interface between the user and the software is to do Usability Testing. In contrast to the UI testing process, where testers from the developer domain check the UI for conformance to certain aspects, Usability testing uses studies of the behavior, expectations and feedback of real users of the software system. This process can be aligned to the general testing process. Test cases have to be derived, e.g. a specific use case of the system should be executed by a surveyed users and the results will be reported. Users have to be selected for the survey and their results have to be evaluated. The results can be used to improve the usability of the software and the next iteration of usability testing can begin [9, p.143f].\nNon-functional requirements for a software might often include performance requirements such as response times. Performance Testing aims on testing whether such requirements are fulfilled [4, p.5-5]. Performance tests might however not always be accurate enough, due to their nature of being executed in a test environment, so that a general fulfillment of a performance requirement can be guaranteed in all environments [13, p.803f].\nThe software testing process and the software development process relate much to each other. The software development models, or development processes, help to organize and control structure and workflow during of the software system development. Software testing takes its particular place in the software development lifecycle. It depends on the software development model . According to [15, p. 30], the software development lifecycle model is the process used to create a software product from its initial conception to it's public release.\nThere are six common phases in the software development lifecycle. In the first phase, initiation, a problem is recognized and a need is identified. During the second phase, definition, the functional requirements are defined, and detailed planning for the development begins. The system design phase is the third one. During this phase the solution of the problem is specified. Phase four includes programming and testing. In the next phase, evaluation and acceptance, integration and system testing occurs. The final lifecycle phase, installation and operation, exists to implement the approved operational plan, control all changes, etc. [16, p. 588-590].\nSoftware Development models provide guidelines on how to build software. Such models are mostly standardized, so the development team can concentrate on system development. It helps to achieve consistency and improve the development process itself [16, p. 583].\n1) Waterfall: The waterfall model follows a logical progression of software development lifecycle. It assumes an the end of one phase the prerequisites for the next stage are known [16, p. 587]. On the one hand this model brings a number of advantages for the testing team: everything is carefully and thoroughly planned, every detail has been decided on, written down, and turned into software. So the testing team can plan accurately. On the other hand, because testing occurs only at the end, fundamental problems can remain uncovered till the end of the project [15, p. 32].\n2) V-Model: This model develops two processes: One for building the system and one for testing the system. Each stage of development process has one test type on the testing side, e.g. during the requirements stage of development, the software acceptance testing side is developed. In this model one-half of development effort will be spent on testing. It integrates testing so that it is more effective and helps to discover defects in earlier stages of development [16, p. 588].\n3) Iterative Model: The iterative model does not start with a fill specification ofe requirements. The development begins with specifiing and implementing a part of the software. this parn will be reviewed in order to test and specifiy new requirenments. This process ist repeaten for each cycle. So in each cycle had to be tested .\n4) Agile Model: Agile development model is a type of inremental model. Software is developed here in incremental, rapid cycles. The resul is small incremental release. Each of those releases is build on previous functionality. Each release is thoroughly tested to ensure software quality is maintained. It is used for time critical applications .\nTest management comprises not only classical methods of project and risk management but also knowledge about suitable test methods. Test management helps to select and implement appropriate measures to ensure that a defined basic product quality will be achieved . So the test management includes a test process for better structure.\nA detailed test procedure is necessary to integrate testing into the development process . According to [16, p. 157], the software testing consists of seven steps, which are described below.\n1) Organising for Testing: In this step the test scope should be defined. It means the performed testing type should be determined. The organisation of the test team occurs in this stage, too. In this step it is important to assess the development plan and status. This helps to build the test plan [16, p. 157].\n2) Developing the Test Plan: Identification of the test risks and the writing of the test plan belong to the development of a test plan. It is important to follow the same pattern as any software planning process. The structure is the same, but this plan focuses on the degree of the tester perceived risks [16, p.157\u2013158].\n3) Verification Testing: During this step the testers have to determine that the requirements are accurate and complete, and that they are not in conflict to each other. The second important point here is to concern that the software design will achieve the objectives of the project as well as that it will be effective and efficient. The software constructions heave to be tested here, too [16, p. 158].\n4) Validation Testing: At this step the validation testing should be performed. This involves the testing of code in a dynamic state. The results of these tests should be recorded [16, p. 158].\n5) Analysing and Reporting Test Results: Analysing and reporting of test results belongs to the fifth step of test planning [16, p. 158]. The objective of this step is to determine what the team has learned from testing and to inform appropriate individuals [16, p. 160].\n6) Acceptance and Operational Testing: In this step one should perform acceptance, software installation and software changes testing [16, p. 159].\n7) Post-Implementation Analysis: The objective of this step is to determine whether testing was performed effectively and what changes could be made, if not [16, p. 160].\nTest levels are a group of test activities that are organized and managed together. A test level is linked to the responsibilities in a project. Examples of test levels are component test, integration test, system test and acceptance test.\nTest techniques are procedures to derive and\/or select test cases, i.e Black Box tests and White Box tests.\nTest objectives are a group of test activities aimed at testing a component or system focused on a specific test objective, i.e. functional test, usability test, regression test etc. A test type may take place on one or more test levels or test phases.\nA level of the software testing process where units, components, functions or methods are tested to see if they perform as designed. In unit testing programmers test various program units, such as classes, procedures or functions until they satisfy a set of precise requirements.\nTesting performed to expose defects in the interfaces and in the interactions between integrated components or systems. It's performed directly after the unit testing and it's done with the collaboration of software developers and integration test engineers.\nThe process of testing an integrated system to verify that it meets specified requirements .\nFormal testing with respect to user needs, requirements, and business processes conducted to determine whether or not a system satisfies the acceptance criteria and to enable the user, customers or other authorized entity to determine whether or not to accept the system .\nThis section focuses on the various techniques for writing test cases for a software system. All techniques mentioned in this section refer to a dynamic testing approach, meaning that the tests or the system has to be run rather than testing it statically by analyzing and investigating the system without executing it [11, p.22].\nThe embedding of writing test cases during the software development or implementation process can be classified into two distinct approaches: Test-last, where test cases are written after the implementation is already done, or test-first, where the test cases are written before the implementation .\nThe goal of test case derivation is always to achieve reasonably good test coverage. The test coverage of a program can be defined as the number of possible input values, program flows or statements that are tested. Theoretically, developers desire to have their software fully tested, for all possible variations of input. The number of possible inputs is however effectively infinite for most software systems. Hence, complete input coverage is impossible to achieve. To achieve reasonable input test coverage it is possible to test equivalence classes of input values. This approach is known as partitioning. Other approaches to increasing test coverage are covering all program flows or statements on implementation level .\n- Top-Down Testing: Test the entry point of the system, e.g. the main method, first and proceed to underlying methods that are being called.\n- Bottom-Up Testing: Test leaf methods, methods that do not invoke other methods, first and proceed to methods that depend on these.\nThis approach however seems to be obsolete as object-oriented programming languages often results in cyclic dependencies between components (coupling). Testers would therefore have to decide, which component of such a cyclic dependency graph has to be tested first [11, p.21f].\nThe two most well-known methods for test case derivation are black box and white box testing. The two are essentially the opposite of each other.\nBlack Box tests are written against the specification of a software system. Given, for instance, the specification or an API documentation of the software system, black box tests are written against publicly exposed components, or rather their methods. Internals of those tested components are unknown to the tester [11, p.22]. Test case values, expected assertion values for instance, have to be guessed by the tester as edge or special cases might not be documented by the specification of the software system [15, p.64f].\nWhite Box tests on the other hand, are written with the implementation of a tested component known by the tester. This allows him to test for certain aspects, for which the software might likely fail due to implementation decisions [15, p.63f].\nTest Driven Development (TDD) is actually not directly a technique for test case derivation but rather an implementation approach. Still, the result of TDD is good test coverage of the developed software system.\nThe iteration of these steps leads to a very generic architecture of the (problem solving) implementation and is when perfectly executed in a TDD-manner, fully test-covered .\nExploratory Testing is a more agile approach to test case derivation. In contrast to the previously described approaches where test cases where derived and run, this technique is a simultaneous execution of learning about the tested system, test design and text execution. Hence, tests are not designed prior to test execution and remain unchanged, but rather develop proportionally to the knowledge of the tester and therefore are run more often with different expectations [4, p.5-5].\nPreviously techniques and objectives have been discussed in the software testing context. Tools can be used to assist in the techniques of the software testing process or to achieve testing objectives.\nThe selection and usage of specific testing tools is always depending on the actual testing process. Hence, analog to the implementation process where for instance different technologies might have to be evaluated whether to be used or not, testing tools must be investigated and evaluated for their usability. This depends on the testing environment, such as the programming language of the tested system, the knowledge of the testers, financial factors and so on. Additionally, used tools must be managed along the testing process [13, p.115f].\nIn the context of testing, the term tools covers a large domain. Testing tools are not only limited to automated software but also to analog tools such as a paper and a pen used to write a checklist [13, p.103f]. Hence, the list of available testing tools is very large and can hardly be investigated completely in such a short overview.\nOne important tool for software testing, especially in the domain of unit, integration and acceptance tests, are frameworks used to test a software system on different levels of implementation. JUnit  is on of the available unit-testing frameworks for the Java Programming Language. It allows the repeated execution of Java-written test cases against a Javawritten software system or parts of it. It can also be used for integration tests. Other frameworks are specifically designed for acceptance testing, e.g. Concordion  or Selenium . With such frameworks at hand, developers and testers are able to repeatedly test software systems in short intervals.\nA. Zeller, Why Programs Fail: A Guide to Systematic Debugging. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 2005.\nI. C. Society, 610.12-1990 - IEEE Standard Glossary of Software Engineering Terminology. IEEE Computer Society, 1990.\nN. Fenton, Software Metrics: a Rigorous Approach. Chapman & Hall, 1991.\nIEEE Computer Society, SWEBOOK. Angela Burgess, 2004.\nI. C. Society, IEEE 829-2008 IEEE Standard for Software and System Test Documentation. IEEE Computer Society, 2008.\nI. S. T. Q. Board, Standard Glossary of Terms used in Software Testing. International Software Testing Qualifications Board, 2014.\nISO\/IEC, ISO\/IEC 9126. Software engineering \u2013 Product quality. ISO\/IEC, 2001.\nI. technical committee (TC) ISO\/TC, ISO 9000 - Quality management. ISO technical committee (TC) ISO\/TC, 2008.\nG. J. Myers, T. Badgett, and C. Sandler, The Art of Software Testing. John Wiley & Sons, Inc., 2012.\nK. Naik and P. Tripathy, SOFTWARE TESTING AND QUALITY ASSURANCE Theory and Practice. John Wiley and Sons, 2008.\nP. Ammann and J. Offutt, Introduction to Software Testing. CambridgeUniversity Press, 2008.\nR. Patton, Software Testing. Sams Publishing, 2001.\nW. E. Perry, Effective Methods for Software Testing. Wiley Publishing, Inc., 2006.\nR. Patton, Software testing. Indianapolis, Ind.: Sams, 2001.  W. E. Perry, Effective methods for software testing, 3rd ed. Indianapolis, IN: Wiley, 2006.\nB. Hetzel, The Complete Guide to Software Testing, 2nd ed. Wellesley, MA, USA: QED Information Sciences, Inc., 1988.\nK. Beck, Test Driven Development by Example. Addison-Wesley, 2002.\nV. Masso, JUnit in action. Manning, 2003.\n\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0442\u0435\u0440\u043c\u0438\u043d\u044b (\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u044e\u0442\u0441\u044f \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438): ISO, IEEE, SOFTWARE, IEC, TESTING, TDD, USA, FOR, III, VIII.\nSoftware Testing for Software Quality.\nInternational Software Testing Qualifications Board, 2014. ISO\/IEC, ISO\/IEC 9126.\n\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0442\u0435\u0440\u043c\u0438\u043d\u044b (\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u044e\u0442\u0441\u044f \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438): ISO, IEEE, IEC, III, SOFTWARE, QUALITY, ISTQB, AND, ASSURANCE, TESTING.\n\u0412 \u0441\u0432\u043e\u044e \u043e\u0447\u0435\u0440\u0435\u0434\u044c, \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442 \u0436\u0438\u0437\u043d\u0435\u043d\u043d\u043e\u0433\u043e \u0446\u0438\u043a\u043b\u0430 12207 (IEEE, ISO\/IEC, \u0413\u041e\u0421\u0422 \u0420 \u0418\u0421\u041e\/\u041c\u042d\u041a) \u043f\u043e\u0437\u0438\u0446\u0438\u043e\u043d\u0438\u0440\u0443\u0435\u0442 \u0441\u043e\u043f\u0440\u043e\u0432\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u043a\u0430\u043a \u043e\u0434\u0438\u043d \u0438\u0437 \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0432 \u0436\u0438\u0437\u043d\u0435\u043d\u043d\u043e\u0433\u043e \u0446\u0438\u043a\u043b\u0430.\n3rd ACS\/IEEE International Conference on Computer Systems and Applications, 2005. \u2014 C. 94\u2013101.\nElectronic testing system (Software Application) for preliminary Distance Testing of University Applicants.\nElectronic testing system (Software Application) for preliminary Distance Testing of University Applicants. Network Modelling of Corporate Information System.\nMoreover, this software is designed for the modern structure of the electricity sector, built on the basis of subordination.\n2. Wikipedia, the free encyclopedia [electronic resource] \/ American non-profit organization \u00abFund of Wikipedia\u00bb. \u2014 United States, 2001.\nElectronic testing system (Software Application) for preliminary Distance Testing of University Applicants. \u041e \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u044f web-\u0438\u043d\u0442\u0435\u0440\u0444\u0435\u0439\u0441\u0430 \u043a \u0431\u0430\u0437\u0435 \u0434\u0430\u043d\u043d\u044b\u0445. \u0423\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u043c\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e web-\u0438\u043d\u0442\u0435\u0440\u0444\u0435\u0439\u0441\u0430.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The theory that Sunday or Monday are the new Saturday cuts both ways. On one hand, the transformation of hallowed downtown New York and Brooklyn neighborhoods into Jersey tourist trashpits on the weekend has driven some of the best New York talent to gigs and venues that might seen off the beaten path. On the other hand, for the permanent-tourist class whose parent guarantors have driven rents in Bushwick and elsewhere sky-high, every day is Saturday because nobody works for a living. OK, some of them are interns. But that's a story for another time. For an afternoon that perfectly reflects the state of the city, 2016 and also features some of the city's most eclectic talent, brilliant singer Daria Grace has put together a triplebill starting at around 4 PM on July 31 in the backyard at LIC Bar, with ex-B-52's guitarist Pat Irwin playing his often hauntingly cinematic instrumentals, then a set by Norah Jones collaborator Sasha Dobson and finally a set by Grace's charming uke swing band the Pre-War Ponies at around 6.. The venue is about a three-minute walk from the 21st St. station on the 7 train.\nLast month's installment of this same lineup was a treat. Grace did triple duty, first joining Irwin on keys (who knew that she was a more than competent organist?), then adding her signature counterintuitive, swinging, slinky basslines to a set by Dobson, then switching to uke and leading her own band. Irwin opened the afternoon with a set that touched on Bill Frisell pastoral jazz, Brian Eno ambience and most significantly, Angelo Badalamenti noir. He mixed slowly crescendoing, shifting instrumentals from his film work across the years with a couple of new numbers, one more minimalist and atmospheric, the other far darker and distantly menacing. By the time his roughly forty-five minutes onstage was over, he'd gone from solo to having a whole band behind him. Dobson followed with a set that drew on roughhewn 80s indie rock, switching from harmonium to Strat as she led her trio \u2013 Grace on a gorgeous vintage 1966 hollowbody Vox bass \u2013 through a mix of her solo material and a couple of jaunty Americana-flavored numbers from her Puss & Boots album with Norah Jones and bassist Catherine Popper.\nIt's hard to find a window of time for sets by three bands; the last time this blog caught Grace leading the Pre-War Ponies was on a twisted but actually fantastic twinbill back in May at Barbes, opening for psychedelic Middle Eastern metal band Greek Judas (who are back at Barbes tomorrow night, the 28th, at 10). Grace's not-so-secret weapon, J. Walter Hawkes is an incorrigible extrovert and a charismatic showman, but he really was on his game this time out, whether firing off lickety-split cascades on his uke or on his trombone, which he typically employs for both low-register amusement and purist oldschool swing and blues. A real force of nature up there, he spent the set blasting out droll vaudevillian licks, foghorn riffs and serioso latin lines.\nLately Grace has been doing a lot of gigs with iconic latin jazz drummer Willie Martinez, but this time out she had Russ Meissner behind the kit, who had a ball adding counterintuitive hits and accents to cha-cha jazz numbers like Amapola, from the band's latest album Get Out Under the Moon. As expected, the big audience hit was Moon Over Brooklyn, which Grace delivered with so much genuine, unselfconscious affection for her adopted hometown that it was easy to forget that you could change the lyrics just a smidge and it would make a romantic anthem for any city, anywhere. Romantic songs are usually cheesy and rote and this was anything but. You can get some romance and some sun on the 31st in Long Island City.\nAs demanding as this music is to play under normal circumstances, with its endless volleys of eighth notes, the challenge takes on a whole new dimension under such trying circumstances. That the orchestra would play so robustly, and with such attention to detail, testifies to their collective spirit. Although the ensemble is only active in the summer for this annual festival, it's more than just a pickup group \u2013 there are a lot of returning members, and their camaraderie was contagious. Nineteen-year-old prodigy Simone Porter joined them as the soloist for the concerto, bringing a strikingly searching intensity and a warily modulated tone, particularly in the second movement. That's where the piece deviates from being comfortably bubbly wine-hour music for the Viennese one-percenters for whom it was written, and she seized on those moments with an apt tinge of angst. She's an old soul.\nJoe Ely may be iconic in Americana music circles, but he's hardly resting on his laurels these days. Joe Strummer's favorite country singer has seen the cult favorite debut album by his early 70s supergroup the Flatlanders reissued, along with his hard-to-find 1983 solo record B484, one of the first releases to utilize what was then state-of-the-art computer technology. Earlier this year, a previously unreleased duet by Ely and Linda Ronstadt was rescued from the vaults. His thinly veiled autobiographical novel Reverb: An Odyssey is out, and is as brilliant and understatedly surreal as you would expect from an eloquent pioneer of what would become known as alt-country back in the late 80s and throughout the 90s. If that isn't enough, Ely is the Texas State Musician of 2016. And his latest darkly relevant, immigrant-themed album, Panhandle Rambler \u2013 streaming at Spotify \u2013 employs a wide and distinguished group of talent from his Austin circle. It might be the best solo album he's ever done. His most recent gig here was with the Flatlanders at Carnegie Hall several months back, but he's making a rare return to NYC with a gig on July 27 at 8 PM at B.B. King's. Advance tix are $27.50.\nWhen the Nights Are Cold sardonically nicks a famous Pink Floyd riff for a somber portrait of illegal immigrant angst. Early in the Mornin' follows a similar, more enigmatic tangent, blending elegant Mexican folk touches into late 70s outlaw honkytonk. Southern Eyes works a sarcastically shuffling western swing groove, followed by the folk noir hobo tale Four Ol' Brokes.\nThen the band picks up the pace with Here's to the Weary, a populist anthem referencing Woody Guthrie, Bob Wills and George Jones. Jim Hoke's ghostly steel keens icily in Cold Black Hammer, a darkly wry, Tom Waits-style story of a real femme fatale. The final cut is the unexpectedly hard-rocking You Saved Me, drawing a straight line back to Buddy Holly. Throughout the album, there's all kinds of tasteful, often Spanish-tinged picking, contrasting with Guzman's echoey, 80s-style synth lines, in the same vein as the Highwaymen records. Ely's voice is a little more flinty now, which suits him fine since subtlety and stories have always been his thing. It's another release that really should have been on last year's list of best albums here.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Austin, Texas Oct 18, 2011 \u2014 Auctane introduces ShipStation, allowing online retailers to fulfill orders faster while reducing shipping costs. ShipStation consolidates orders from numerous marketplaces and shopping cart solutions, and allows shipping labels to be printed in batch. This initial release includes support for eBay, Amazon, Buy.com Marketplace, Etsy, Magento, Volusion, Zen Cart, PayPal, Google Checkout, and Payvment.\nEach ShipStation subscription includes a free DYMO Endicia account, which allows users to print all classes of USPS postage.\nFor more information, or to start a free 30-day trial, please visit http:\/\/www.shipstation.com.\nAuctane provides turn-key shipping systems for online retailers and shippers. With a focus on efficiency and simplicity, Auctane's web-based tools allow shippers to process orders faster and more easily than ever before. Auctane's shipping solution for eBay sellers, Auctane Shipping Manager, has been the top-rated shipping application in the eBay App Center for the past two years.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzavnqv b/data_all_eng_slimpj/shuffled/split2/finalzzzavnqv
new file mode 100644
index 0000000000000000000000000000000000000000..d8125420ee38aee7e2295b10e6e8a04f7cb172ad
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzavnqv
@@ -0,0 +1,5 @@
+{"text":"Vitamin C \u2013 improves the work of gray cells, and has citrus fruits like lemons, oranges, tangerines, then in apples, strawberries, cabbage, but also in other natural products.\nBananas contain B vitamins, magnesium and potassium, so they act tranquilly, permitting astute basic leadership.\nBroccoli that are rich in glucosinolates, carotenoids with iron and calcium are prescribed for quick and concentrated learning.\nAlso, the brain requires a constant supply of lecithin, which practically produces a colline, from which the brain produces acetylcoline itself, which is the most important neurotransmitter. Otherwise, lecithin has it in eggs, dairy products and soy products.\nFor long-term memory, hazelnuts are extremely good, due to the beneficial fats and microelements they contain.\nLastly, you eat ocean fish like salmon, mackerel, tuna or herring since they empower fixation.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"A great spot for a quiet pint, to watch a match or catch up with friends.\nThe County Bar Lucan offers guests the perfect location to enjoy a few drinks. With a choice between the lounge and the bar, we have the ideal setting for any social evening or night.\nThe bar at The County Bar Lucan is the ideal place to enjoy a few pints and enjoy the evening atmosphere of a Dublin Pub. Watch the latest sport on our big screen over a few pints or catch up with the girls over a few drinks before heading into town.\nThe Lounge is the perfect place to enjoy a quiet drink with friends and family any afternoon or evening. Ideal as a meeting point with clients, the lounge features stylish d\u00e9cor with quiet snugs and its own sheltered smoking area.\nThe downstairs Sports Bar offers customers the perfect place to spend an afternoon with friends. Featuring a full size pool table and darts board, the Sports Bar provides members with the facilities for top entertainment.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Coated nylon, silver waistband, and lurex branding, are you ready for it? Brave and secure, that's the way to win. Who needs lining? We built this without for max VPL. Not sure about the \"lucha\", but the \"libre\" you will be for sure.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"2 bets today on this really interesting match we have tonight between 2 of the best teams at the moment : Milwaukee @ Denver ! First of all Denver is a good defensive team, with fewer possessions played than the average in NBA. So they concede less rebounds that's why I chose to take an under rebounds on Middleton. The cut was for me already to low so with adding the fact they play against Denver, the bet is good to take.\nThe second bet is on Jokic. I placed a similar bet (you can find it and the analyse in one of my previous posts) on Nurkic when he played against the Bucks, mainly based on the match-up, Lopez who tends to play out of the paint creating less rebounds for the opposite center. The reasons are the same here, and the odds is really good !","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The future of advertising is digital media. We live in a digital world. The companies that utilize this new technology to communicate with customers consistently and instantly, to take advantage of the unlimited branding opportunities, will have a significant competitive advantage.\nThe Think Network provides a network of Digital Out of Home screens to deliver both advertising and informational content. Our array of strategically placed screens is designed to take advantage of a captive audience. Through The Think Network advertisers have the ability to interact with customers where they are.\nDigital media allows advertisers to reach their target markets in ways limited only by the imagination. In addition, it is vitally important to any advertising campaign to be relevant through the integration of the internet and social media. The Think Network provides these services to help you succeed.\nThe Think Network is comprised of a team of professionals interested in helping our advertisers maximize the opportunities available through digital platforms and all digital media.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzayifu b/data_all_eng_slimpj/shuffled/split2/finalzzzayifu
new file mode 100644
index 0000000000000000000000000000000000000000..02b6a002291b161d59de17a4013d78c07c5990af
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzayifu
@@ -0,0 +1,5 @@
+{"text":"So happy to introduce you all to these new obsessions of mine! These truly are the Best Creamy Lemon Bars.\nThe lemon trees around here are heavy with ripe fruit waiting to be picked. There's something so refreshing about a lemon dessert in January. It feels like there's bottled up sunshine in those juicy little guys!\nI have a few lemon favorites that I always come back to year after year, but I also like to try something new. After hearing so many good things about the Magnolia Lemon Pie, I decided to make my own version. For some reason, bars always feel easier than a round pie to me. They are easy to cut and serve, and you don't have to worry about that crust caving in.\nThese Creamy Lemon Bars are very much like the lemon version of a key lime pie. They freeze very well, and the texture is something between a lemon mousse or custard. It's lighter than cheesecake, and very refreshing! I like adding some sour cream to the traditional recipe because I think it helps round out the sweetness of the sweetened condensed milk.\nI also like adding some lemon zest instead of just lemon juice. These Creamy Lemon Bars are sweet, tart, creamy, and the buttery graham cracker crust and homemade whipped cream are a must!\nI hope this recipe brings some sunshine to you, especially if your January is feeling a little too cold and dreary. Stay cozy, friends!\nPrepare a 9 by 9 inch baking pan by lining it with parchment paper, leaving two sides hanging over the edge for easy removal later.\nIn a small bowl, mix melted butter, sugar, and graham cracker crumbs together. Press the mixture firmly and evenly into the bottom of the lined pan. Use the flat bottom of a measuring cup if needed. Bake for 8-10 minutes.\nIn the meantime, add egg yolks, lemon zest, lemon juice, sweetened condensed milk, sour cream, vanilla extract and salt into the bowl of an electric mixer with the whisk attachment. Mix on low speed for 1 minute, and then gradually increase speed to medium-high and whisk for 4-5 minutes. Pour the lemon batter over the graham cracker crust and bake for 15 minutes. Then cool completely at room temperature and refrigerate at least 3 hours before serving.\nFor the whipped cream, add heavy cream, sugar, and vanilla to the bowl of an electric mixer with the whisk attachment. Whisk on low speed for 1 minute, and then gradually increase speed to medium high until thick, and soft peaks form.\nGarnish with fresh lemon slices and mint leaves if desired.\nSounds yummy! About how many lemons do I need for this recipe?\nJust got this recipe and got it copy. Love lemon bars but never have made any myself just those someone else made. In a few weeks I suppose to have a family dinner and will make it then. Every one has crazy hours so getting everyone to gather is our draw back any more. Hope it will be soon so I can try this. Question I buy minute maid frozen lemon juice they say it is fresh lemon juice would that be ok to use or not, or should I get the fresh lemons? Thanks for the recipe.\nHi! I don't see why you couldn't use the frozen lemon juice, but I have not tried it in this recipe. Hope you all enjoy!\nWhat is Australia's equivalent of Graham crackers? Would love to make these but curious about the biscuits used in the base.\nYou can try subbing digestive biscuits. Hope you enjoy!\nCould I use a spring form pan with this recipe? And I only have an electric hand mixer. Will that work ok for the lemon batter?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"As every month passes faster broadband services varying from VDSL2 to full fibre are being rolled out across the UK and while no one minds if companies are spending their own money and no one is buying the faster services with the gap funded roll-outs and various voucher schemes that are using public money keeping an eye on the speeds across the UK is an important one. The Q3 analysis of speed tests for local authorities was published just after the end of Q3 on our statistics site but at that level a lot of the detail is lost and therefore we are publishing a summary for the average speeds per postcode area in Q3 2017.\nThe map showing the average mean download speeds is a nice see of green and perhaps the scale should be adjusted, as otherwise people viewing the map will get the idea that all is well, but if one looks at the same dataset but plotted using the median download speed you can see a distinct difference and areas like Central London don't look as good. So is the mean map wrong? No, its just that those who have the option and are actually buying the fastest services available to them are skewing the mean.\nThe link between availability and average speeds is explored after we look at the fastest and slowest 30 postcode areas and with the upload speeds included the asymmetry of consumer broadband services is clearly illustrated.\nThe range of speeds is very wide and the median speeds at the foot of the table look like ADSL speeds from a decade ago and that is perhaps no suprise when SA39 has no ultrafast coverage and only 54.7% of premises with access to a superfast option, some people are clearly buying and testing the superfast option as reflected in the mean figures, but while some people will be on the phone ordering better broadband options the minute a service is available, others take time to spot that a faster option is available and may be put off by some of the upgrade costs, though we should highlight that for people in rural areas on older up to 8 Mbps ADSL only services the monthly price of VDSL2 services can be less so don't just rely on a quote from your existing provider. On some of the other slowest areas, LD6 47.2% superfast coverage, NE67 58.4%, SA41 59.9%, SA48 57.6%, PH15 21.8%.\nA number of studies and spreadsheet re-ordering exercises in 2017 have published name and shame tables on broadband speeds, but none have published charts (that we know of) showing how the speeds observed from consumer speed tests correlates to the levels of superfast coverage and with our wealth of consumer speed test data and tracking the path to 95% superfast coverage and beyond that is pretty easy for us.\nThe chart conveys two messages that there is a link between superfast coverage and the median download, this is of course not rocket science but there are some areas such as PO41 with 83.6% superfast coverage recording median download speeds of just 5.6 Mbps suggesting that maybe the area has only just seen coverage increase significantly or take-up is lagging and if public money has been used to boost coverage increasing take-up is important as the higher the take-up the greater the gainshare money available to take coverage ever closer to 100%. The big cluster of postcode areas in 98% to 100% area is a reflection of the superfast roll-outs, and the broad spread of speeds down to the popularity of the ultrafast broadband options.\nThe chart of ultrafast coverage against download speeds has three main areas, those with no ultrafast broadband coverage on the 0% line with the spread showing the variations from take-up and observations, through to those areas with over 90% ultrafast availability which unsurprisingly are faster. The middle ground shows a slow but steady trend towards higher speeds, what is interesting is that the postcode areas with ultrafast coverage below the 10% mark tend to be those with Openreach GEA-FTTP coverage and one observation we will make is that two years ago it seemed as if more people were buying the faster 200 Mbps and 300 Mbps variants whereas in the last few months the number buying the fastest FTTP options has reduced, we suspect that poor visibility for these faster services on many comparison websites and pressures on utility spending for many, leading to people buying something sufficient for their needs, i.e. with full fibre if you buy a 38 Mbps or 50 Mbps product with distance having no impact you will be able to stream multiple HD streams (assuming the provider does not have massive congestion issues at peak time).\nAs for the list of over 3,400 postcode areas we have data for, the full list is not available but if you want to see some more information on your specific postcode you can search for your postcode code on our statistics site which updates coverage percentages weekly, area speeds every quarter and the 12 months of history for a postcode and its immediate area updates each month. For the local authority areas, the speed analysis is broken down by technology so you can see the relative speeds of ADSL, FTTC, cable and FTTH services in an area.\nI am in a rural area of Scotland around 3000m from the nearest cabinet and am on the \"BT Faster Broadband\" package which I believe is enabled as up to 40\/2. What I actually get is 7.3\/0.8 but the good thing about it is that it is very, very consistent. Any time of day I get just over 7MBs down. Off-peak or the evenings makes no difference.\nIt is absolutely fine for a single YouTube 1080p stream, online shopping and so on. As long as I am careful about when I do Steam downloads, I don't feel too left out.\nThe UK seems to be missing a large chunk of land across the Irish sea.\nThe map is has the correct Great Britain name, alas no postcode area e.g. BT10, BT67 for Northern Ireland is readily available, so for the map plot can only manage Great Britain for this dataset.\nThe BT postcodes do feature in the table, hence article UK title.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The City of Asheville will unveil new public art installations and future greenway sections in the River Arts District Nov. 30 on Riverside Drive.\nHave you heard about the giant, 12-foot fish caught off Riverside Drive in the River Arts District?\nIt's no fish tale. Nicknamed the \"Big Fish,\" it is actually a sculpture by local artist David Earl Tomlinson, displayed on a tall pedestal and made of recycled metal from Biltmore Iron and Metal Co., at 224 Riverside.\nOn Friday, Nov. 30, environmental nonprofit Asheville GreenWorks will officially unveil the sculpture, meant to bring awareness to water quality programs such as their Trash Trout, which keeps thousands of pounds of trash out of the French Broad River every year.\nIt is part of a broader, public celebration of art and environment in the RAD. Starting at 3 p.m. on Friday, the City of Asheville will unveil new public art installations at Jean Webb Park, 30 Riverside Drive. The event will end at the Craven Street Boat Launch at 190 Riverside Drive. The purpose is to highlight the greenway, art and the community.\nDuring the celebration, Poetry Pathways will unveil a poem installation on the 13 Bones Bridge. Written by local artist Cleaster Cotton, the project was created by the team at STEAM - UNC Asheville, whichhe team designed an aluminium cut out on 13 Bones Bridge of Cleaster Cotton's poem.\nThis is the first installment of Poetry Pathways, a concept by Laurie Wilcox-Meyer and Alida Woods. The project was funded by the Asheville Area Arts Council to celebrate local poets and to put poetry in the public eye.\nThe Big Fish sculpture and educational signage was developed with support from Duke Energy Watershed Resources Fund, the Historic Cotton Mill Studios, Biltmore Iron and Metal, the City of Asheville and others.\nAttendees will also be able to walk the future section of riverfront greenway, located between the railroad trestle bridge and the 14 Riverside Drive Arts and Culture Center. This new greenway is part of the River Arts District Transportation Improvement Project, aka RADTIP.\nThis celebration is open to the public.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I'll be the primary to confess it \u2013 Hello-Fi+ has coated a number of AURALiC merchandise in recent times. Although that is my first evaluation of the model's merchandise, virtually each product the corporate has made has discovered its method onto the pages of this journal. Having had no direct private expertise of the product (save for temporary publicity at exhibits) and seeing each different reviewer who touches the product seemingly turning right into a swivel-eyed loon for the model, I assumed it time to wave round some Editorial privilege. What's AURALiC's magic trick?\nOur most up-to-date evaluation mixed the VEGA G2 streaming DAC with the brand new LEO GX clock in Concern 164. OK, calling the LEO GX a 'clock' is editorial understatement on a grand scale, however this assessment piqued my curiosity on a few ranges. Most notably, nevertheless, the G2 assessment fascinated due to the existence of the VEGA G1 examined right here. You see, at first look, each on paper and within the flesh, the variations between the G1 and G2 are minimal in every thing however worth. Scratch the floor in fact and issues start to look a bit totally different. However how totally different in the actual world and do these variations matter\u2026 these have been the questions that made me name for the AURALiC VEGA G1.\nThe obvious visible distinction between the 2 gamers is the transfer from a black knob within the G2 to a silver one within the G1. Issues get clearer minimize to the rear of the 2 as a result of the G2 includes a pair of AURALiC's personal Lightning connectors, a clock enter and a set of stereo RCA sockets for an analogue line enter \u2013 all of that are absent within the extra pared-back G1. The instances, nevertheless, are noticeably totally different (a minimum of when positioned side-by-side). They're the identical measurement and weight, however the G2 makes use of AURALiC's Unity chassis hewn out of a single piece of aluminium, and this sits on particular sprung ft. Whereas the G1 makes use of the identical grade of aluminium, the cupboard is made from piece elements bolted collectively, and sits on plastic ft with out the springy suspension system. Actually shut visible inspection exhibits these variations, and at every level, every thing suggests the G2 is best. This can be a delicate however essential distinction, akin to good tailoring; the G1 is sort of a well-cut made to measure go well with you may put on to nail that interview, however the G2 is that bespoke Savile Row go well with during which you bought married.\n\u25ba that the G1 makes use of its personal customized analogue quantity management, the place the G2 makes use of the chipset's inner digital quantity, and the absence of galvanic isolation throughout the rear connections. These are pretty vital modifications and are greatest regarded as being within the order of magnitude of the distinction between a 12 and an 18 yr previous single malt! The absence of Lightning Hyperlink connectors additionally makes utilizing the ARIES fashions to create a full 'belt and braces' Lightning Server system barely much less 'plug and play', and also you miss out on a number of the 'Rolls-Royce' parts of the AURALiC streaming system (file sampling charges, for instance). Nevertheless, what's nice is extra what the 2 share quite than what they lack: the G1 and G2 each use AURALiC's Tesla digital platform, and each can utilise the Lightning DS app that controls the whole lot AURALiC. Tesla is the core processing engine, constructed round a Quad-Core A9 chip, 1GB of reminiscence, and 4GB of storage. Put merely, the 2 share a lot of the identical circuitry\u2026 there's simply extra of it within the G2. Wi-fi connectivity (akin to AirPlay and Bluetooth) are usually not supported. The G1 is not any slouch although. It makes use of the corporate's personal Orfeo Class A modules; these are operational amplifiers impressed by Rupert Neve's 8078 analogue mixing console circuit design \u2013 a design thought-about by many within the recording studio world a console sans pareil. An audio product that options output levels that try and recreate that circuit put AURALiC up there with the perfect.\nWithin the mild of the larger, higher G2, why ought to the VEGA G1 be so fascinating? As a result of the VEGA G1 simply may occupy the right sweet-spot for this-and-the-next era audio. The G2, for all it's sonic and technical prowess, is greater in value as a result of it's extra demanding to construct. It not solely has room for progress (with the LEO GX), however there's virtually an expectation within the proprietor of a VEGA G2 that it's step one on the large AURALiC ladder. The G1 locations no such calls for on the consumer or the system, and that's its genius.\nI've stayed away from describing the processes concerned in hooking up a community system lately; not as a result of they're troublesome (if something, constructing a house community for audio is turning into simpler by the day), however as a result of individuals get the flawed concept. They see the method when it comes to quite a lot of steps and get involved and begin evaluating the method (unfavourably) to enjoying a CD. Nevertheless, when you break something down into its particular person steps, the duty turns into impossibly daunting: making toast, for instance, is a course of so difficult that it ought to solely be carried out by educated specialists. And AURALiC is on the pinnacle of that next- era know-how \u2013 utilizing it's truly absurdly easy when arrange, however individuals see these three phrases and spiral.\nSo, right here's the deal. The VEGA G1 is the product for these spiralling digital customers. Past its use as a streaming system, it's \u2013 at first \u2013 a rattling good DAC. Use it with a CD and also you'll get nice sound\u2026 and a pathway into at present's on-line and native streaming if you end up prepared.\n\u25ba the necessary genetic code of its greater brother, and most of what isn't on board isn't very important for a lot of customers. Granted a G2 is best, however many staring down the distinction between 'three and 1 \/ 4 grand' and '5 and a half grand' might be unable to make that leap. Positive, AURALiC's Lightning Server know-how, the higher chassis, the right analogue quantity management, and the power to hook this to the complete Bridge-Streamer- Clock system of the G2 vary all minimize into performance, however all of them add up, too. This will get you a lot of the approach there when it comes to tech and spec and sound for a fraction of the price, and that makes the VEGA G1 actually necessary.\nIt's essential sufficient that if I have been one of many huge names on this area, I'd be fearful about this product. Fearful not simply because it's obtained a fantastic spec, however extra as a result of it truly sounds actually good. I discussed the absence of Lightning connectors, however the G1 is solely supported by the Lightning DS app, and this is a wonderful interface, particularly if used with Roon (the G1 is Roon Prepared), Tidal, and particularly Qobuz Studio. Whereas numerous listening was achieved via my native server by way of my wired community, a very good deal was made on-line, and each via the Lightning DS app. This works seamlessly each with the web providers and in controlling the G1. Configuration and set up is fuss free as long as your community is fairly strong and your pc hardware isn't so previous that it's programmed in Latin. Put it this manner, if you recognize what a NAS is, have one, and configured it your self with out having to succeed in for a fireplace extinguisher, you're in all probability over- certified to put in the G1.\nI'm saving one of the best till final right here, and that greatest is the sound you get from the G1. I'm not that troubled by the digital quantity management as a result of for a lot of the check, I 'dimed' the quantity management and ran it right into a system, slightly than use it as a preamp in its personal proper. The quantity management itself was principally used within the context of working the G1 as a headphone amp. Extra on that later.\n\u25ba from the Malibu album [ArtClub]. This can be a nice rap monitor with a superb bass line however is usually undermined by the thinness and compression inherent to the recording. The G1 doesn't attempt to compensate for that compression; it simply provides you a lot info, and a lot musical enjoyment together with that info, you simply don't care. You take heed to that high quality guitar sound, the actually tight hi-hat work, and the refrain schoolyard rapping, and the distorted enjoying of the Israeli nationwide anthem, Hatikvah, all through the monitor\u2026 and it makes you progress and smile.\nIt's a pity in a means that the monitor is so thinly recorded, as a result of it has a superb bass line, and bass is probably what the G1 does greatest. That\u2026 and all the opposite issues it does greatest too! Bass is certainly the G1 's most spectacular weapon in its musical arsenal. Right here, I moved between classical and rock; I'm enjoying Beethoven's 'Ode To Pleasure' from the Ninth Symphony [Von Karajan, Berlin Phil, DG] prefer it's going out of style in the intervening time and the G1 conveys all of the power and drive of that piece, together with the majesty of the timpani and choir, main as much as that monumental crescendo. The G1 permits the music freedom to actually give it some beans, and you end up enjoying it at Def Con 1 ranges, air conducting because the home windows shake\u2026 5 doorways away. In the meantime, shifting over to Jeff Wayne's Musical Model of the Struggle of the Worlds [Columbia] is actually fascinating. Not solely does the resonance of Richard Burton's voice shine by way of, however the G1 can also be detailed sufficient to spotlight simply precisely how drunk he's on every take. The mixture of his stentorian (and principally half-cut) tones coupled with some actually chunky analogue voltage- managed oscillator drift from some bat-crazy synthesiser sounds confirmed the depth and the readability of the VEGA G1 completely, and its inherent musicality shone via as this album led inexorably, tragically, to enjoying some Wakeman- period Sure, with much more drifty Moog synths. I'm not pleased with that specific sojourn into widdly-wee prog, nevertheless!\nLastly, the G1 's headphone amplifier. To a sure extent AURALiC reduce its tooth within the private audio area, so maybe it's no shock the VEGA G1 has a superb headphone part, however maybe what makes it so good is how nicely balanced and the way properly it tracks the sound high quality by means of the road degree outputs. Like these outputs, the VEGA G1 's headphone stage is dynamic, clear, detailed, and possessed of fantastic bass; deep: highly effective, pacey, and meaty. If there's a remark to be made right here, it's extra a sin of omission \u2013 I'd like to see a balanced headphone output right here instead of one of many two 6.35mm headphone jacks.\nThe G1 not being a G2 solely manifests as compared. In day-to-day use, the VEGA G1 is a perfect community streaming gadget that places many truly good rival merchandise to disgrace. It's extraordinarily properly constructed, sounds exceptionally good, and performs good with most merchandise it's more likely to be hooked to. I began this investigation to see what all of the fuss was about, and now I'm studying from the AURALiC Fanatic's Handbook. The corporate actually does reside as much as the hype, as anybody who provides the VEGA (G2 or G1) a critical pay attention will attest. In truth, they could properly say one of many notes I made whereas listening to the AURALiC VEGA G1 \u2013 Bloody hell\u2026 this factor's good!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"OPERATOR PureGym has become the official fitness and gym partner of the UK's biggest mass participation running series, Great Run.\nThe collaboration allows an opportunity for cross-promotion across email databases, social channels and websites, with the three year agreement starting at The Great Winter Run on January 9, where PureGym will be headline sponsor.\nThere will be mini pop up Pure Gyms at a number of the events, as well as group exercise classes for people to try.\nPureGym will also be working with Great Run to develop a class for their members that has a focus on running and technique.\nDirector of strategic development at PureGym Francine Davis said: \"The Great Run Series is a fantastic partner to have with over 200,000 people taking part in their events each year.\n\"Participants of their events are fitness and running enthusiasts of all abilities from those trying it for the first time to the more experience participant. This is obviously a great match for PureGym and reflects the profile of our members.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaywwb b/data_all_eng_slimpj/shuffled/split2/finalzzzaywwb
new file mode 100644
index 0000000000000000000000000000000000000000..6877f257da78f66bb02c935f93d299620230373f
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaywwb
@@ -0,0 +1,5 @@
+{"text":"Cookies are small data files which are placed on your computer or mobile device by a website's server when you visit most large websites. Each cookie is unique to your web browser and contains information such as the website address and a unique identifier. This enables our websites to recognise your computer or device for the purposes set out below.\nEssential cookies: A small number of cookies are placed on your device to make our websites work properly. These are 'essential cookies'. You can delete these, but this means some areas of the websites will not work properly.\nFunctionality cookies: These cookies make our website simpler to use, by recording your preferences. These are used to personalise content for you (for example, your choice of language and region) or store your login and other preferences so you don't have to re-enter this information every time you visit the website.\nAnalytic and performance cookies: We use analytic cookies to collect information about how people use our websites. We do this to make sure it meets user needs and to understand how we can improve our websites. Analytic cookies store information about the pages you visit, how long you are on the website, how you got there, what you click on and whether you have visited the website before.\nThird-party cookies for advertising and retargeting: These cookies record your visit to our websites, your response to our online advertisements and campaigns, track the pages you have visited and the hyperlinks you click on.\n__utma: Used to distinguish users and sessions. This persistent cookie is placed by Google Analytics for web statistics purposes. It expires after 2 years.\n__utmb: Used to determine new sessions\/visits. This cookie is placed by Google Analytics for web statistics purposes. It expires after 30 minutes.\n__utmc: This session cookie is placed by Google Analytics for web statistics purposes. It expires at the end of the browser session.\n__utmt: Used to throttle request rate. It expires after 10 minutes.\n__utmz: Stores the traffic source or campaign that explains how the user reached your site. It expires after 6 months.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"If you are in an industry that relies heavily on fabricated plastic products, it pays to have a good plastic service on your side. After all, you cannot do it all when it comes to fabrication and production of the items you need. Look to a trusted company for what you need.\nFind out about the plastic welding services that are available to your company. You should trust only the best in the business. No matter what type of plastic product you need to have made for your operations, only the right company can do it for you. Forge a bond with a reliable service.\nPlastic is designed to be light and cheap as well as durable. Just like anything else, it has to be built right in order to serve its purpose. Keep your business ahead of the competition with plastic products that are built fully to your specifications. When you do that, you come out ahead.\nNow is the time to align yourself with expert plastic services and make your company everything it can be. You need to secure good services so that you can continue to offer good services yourself. No business really runs without the help of other businesses.\nWhen you stick with the same plastic fabrication company over the years, you are indulging in trusted, reliable services. That is good for your business. You are building your future just like you dreamed of. Get all the plastic products you need built just as you say they should be.\nGo online and find the plastic services you need to keep your company up and running at an optimal level. Make the right decisions and order the products you need to keep going. Your business future depends on it. Your future depends on good plastic services. Find the right company today.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"One thing you need to know about Skopelos holidays is that the local chefs are not afraid to combine tradition to new trends. Beef kebab is a new entry in the local menus and you may find it in many different versions. Our approach is to offer a nutritious, delicious and super refreshing recipe that will take you by surprise and will definitely be one of your top ten food choices during the summer.\nRead below the steps we make in order to make our Beef Kebab \u2013a must-taste for Skopelos holidays!\nWe mix together the beef minced meat, one onion, egg white, salt and pepper in a large bowl, and leave it for a few minutes to allow the flavors to blend.\nTo make the kebabs we take small amounts of the above mix and shape them into sausage shapes.\nWe put the kebabs on the grill for about 7 minutes each side.\nWhile waiting for the kebabs to be cooked, we prepare our famous tomatoe marmalade by mixing tomatoes, salt, pepper, sugar and vinegar in a bowl.\nAt the same time, in another bowl we mix yoghurt, mascarpone, black sugar, fresh thyme, olive oil and a bit of lemon juice.\nWhen the kebabs are ready, we put them on the plate, sour them with our delicious tomatoe marmalade mix and put a good portion of the yoghurt mix on the side. The dish is ready for you to taste!\nEnjoy a truly magnificent recipe today and discover your new favourite meal during your Skopelos holidays!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This eggless chocolate mug cake recipe using yogurt and semisweet chocolate chips is soft and moist with gooey texture inside.\nYou can make soft and moist egg chocolate mug cake using microwave in no time and it is so delicious.\nSo if you want to make a really quick, easy chocolate mug cake when you don't have any eggs in the kitchen, try this delicious eggless chocolate mug cake recipe to make the most delicious, gooey and moist chocolate mug cake with semi sweet chocolate chips.\nWe also use cocoa powder (along with the chocolate chips) to make this chocolate mug cake which makes a perfect one serving dessert who wants to enjoy a quick, easy, delicious chocolate dessert.\nThe addition of semi sweet chocolate chips and yogurt is what that makes this mug cake so moist and delicious with a gooey texture inside.\nIf you like eggless chocolate mug cake recipes, try this prunes chocolate mug cake recipe (with oil) and this oil free prunes chocolate mug cake recipe which are all delicious microwave chocolate mug cake recipes.\nEasy soft, moist, gooey chocolate mug cake recipe in microwave without using eggs. This eggless chocolate mug cake recipe uses yogurt and semi sweet chocolate chips which make this chocolate mug cake very moist and delicious.\nIn a microwave safe mug, mix together the dry ingredients - flour, cocoa powder, baking powder and baking soda until they are evenly mixed.\nAdd the yogurt, sugar and vanilla essence to the mug, stir well and mix the batter without any lumps (make sure to use smooth yogurt without any lumps).\nAdd two tablespoons of semi sweet chocolate chips and oil also to the mug, stir everything well so the oil and chocolate chips get mixed with the contents evenly.\nTop with the remaining one tablespoon of semi sweet chocolate chips and microwave in high powder for 3 minutes until the cake is cooked and soft.\nAllow the cake to cool down and enjoy the delicious chocolate chip mug cake!\nHope you found this post on chocolate mug cake with chocolate chips helpful in making easy and delicious chocolate chip mug cake for a quick, easy and delicious dessert!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Lifeline Double Feature in the Monthly Chronicle!\nOn the 7th of June, join Lifeline H2H at this year's exciting Ensemble Theatre Night \u2013 be quick only 100 tickets!\n10 years of GIANT book fairs at Thornleigh!\nStill time to register for next DV-alert 2-day workshop!\nAnd Go For Broke, They Did!\nThank You, Our Gala Ball Sponsors!\nJoin us at our Waitara Store's 1st Anniversary celebration!\nIn the News at Lifeline H2H!\nReminder \u2013 new Managing Your Mood groups start soon!\nWelcome back Holland America Line!\nWondering exactly what sort of books we will have, and where to find them? Look no further. We'll be here from 9 am on Thursday 13 July til 5 pm Sunday 16 July. Come and join us!\nSydney's biggest book fair is coming to Wahroonga in July!\nWe've been shortlisted \u2026 vote for us NOW!\nIt's National Volunteer Week This Week!\nAmazing Clearance Sale \u2013 Over 30,000 books on sale for just $1 each!\nRecord-breaking Book Fair for Thornleigh!\nLifeline's bigger & even better 2017 Thornleigh Giant Book Fair !\nOfficial Bobbo Photos Now Uploaded!\nSee the full gallery of more than 350 wonderful Bobbin Head Cycle Classic 2017 photographs here at the online gallery of official event photographer, Jason Kirk Photography. Amazing photographs of a simply wonderful day. Enjoy!\nOh what a Bobbo it was!\nCaring for someone with Hoarding Disorder?\nStarting tomorrow! The Lifeline Giant Book Fair is on at The Concourse, Chatswood, from 8 am until 5 pm tomorrow, Saturday February 4, and same times on Sunday, February 5. Bring your friends, bring your kids.\nVolunteer at the Bobbin Head Cycle Classic!\nLifeline Harbour to Hawkesbury's CEO, Wendy Carver, has warned that for many people in our community, the build-up to Christmas brings anxiety about family relationships, about money and gift-giving, or about being alone at Christmas time.\nOur Lifeline H2H shops are now on Instagram!\nOh what a night it was!\nIt's on again! A date for your diary \u2013 Saturday September 3 2016 The Lifeline Harbour to Hawkesbury Sapphire Gala Ball, proudly sponsored by The Star, is one of the biggest fundraising events of our year.\nCongratulations Angela Dodd on being awarded Rotary 'Pride of Workmanship' Award!\nOutstanding Individual award in the Ku-ring-gai Council 2016 Seniors Festival Mayoral Awards, goes to\u2026.. one of our own!\nCongratulations to Lifeline Harbour to Hawkesbury Executive Support and volunteer Telephone Crisis Supporter Dr Adrienne Bennett, who on Thursday March 3rd was awarded the Outstanding Individual award in the Ku-ring-gai Council 2016 Seniors Festival Mayoral Awards.\nGreat Gala \u2013 what a ball!\nOur congratulations to Lifeline Harbour to Hawkesbury team member Rebecca Tupper (pictured) on being shortlisted as finalist for the AHRI R U OK? Champion Award in the Australian Human Resources Institute Inclusion & Diversity Awards 2014.\nA night to look forward to, a night to remember\u2026.\nOur next information evening is being held on Tuesday 24th June at 7.00pm. This information session is for people interested in training to become a telephone crisis support volunteer. The training course commences in July 2014.\nJohn was awarded this honor for his for significant service to the community through representational roles with social welfare organisations, particularly Lifeline, to the business and financial sectors and to the Parliament of New South Wales.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzazgiw b/data_all_eng_slimpj/shuffled/split2/finalzzzazgiw
new file mode 100644
index 0000000000000000000000000000000000000000..7c6953507dc5c3a17e43617a5889956038b25eb0
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzazgiw
@@ -0,0 +1,5 @@
+{"text":"Hey beauties! Hope you are all doing well and enjoying the beautiful weather! Today on the blog I'm bringing you my current makeup favorites! Recently I've been attending events where I get to glam up my makeup. I'm not normally a heavy makeup wearer for everyday but whenever I have special events I love to add a heavier touch with my look.\nThese are all the products I've been using and that you've seen me wearing in my Instagrams. And if you haven't seen those photos and want to be in the loop you can follow me on Insta, @samantha_goble!\nEverything except for the Benefit Roller Lash mascara and the Urban Decay Primer Potion can be found a Target, Walmart, CVS, Walgreens, etc. It's all super affordable and just great products! So onto what I've been wearing on my face!\nHere's a little breakdown of my makeup routine!\nStarting with a washed and moisturized face, I then apply the Pore Eraser to the areas where I have visible pores. Next apply the under eye concealer on my dark circles and blend. Then I apply my matte foundation and blend it in with my fingers. After I apply the translucent powder all over my face. I finish with the blush on the apples of my cheeks and use the bronzer to contour my cheekbones.\nFor eyes it depends on the look I'm going for. I'll either do a really clean, simple look or a smudgy smokey eye. For the most part I do the clean, simple look.\nFirst I apply the Primer Potion all over my lids and my lower lash line. Then I apply a light taupe shade all over my lids. I then apply a darker contour shadow for my outer corner. Next tightline my eyes with the pencil eyeliner. After I use the liquid liner to line my upper lash line. I finish up with a couple of coats of my Roller Lash and Falsie's masara and add a browbone and inner corner highlight.\nI didn't include any lipsticks because it changes depending on the look I'm going for, my outfit and my mood. I do use the lip exfoliator before I apply lipstick and put a heavy duty lip balm on my lips. I also apply a tiny bit of concealer to the cupid's bow to really emphasize my lips.\nSo those are all the products that get my face from looking like a zombie to a relative decent looking human being! Like I said they're all really affordable and some even have coupons you can find in the paper. I've really been loving the combination of products and my overall makeup look. You can tell it's \"special occasion\" makeup but it's still natural. Everything has great color and staying power. I know when I apply everything it will still be on my face after dancing it out at a concert or sitting front row!\nWhat are your current makeup favorites\/ products you use for \"special occasion\" makeup? Let me know in the comments below or by striking up a convo with me via social media, @samantha_goble!\n\"makeup is self confidence applied directly to the face\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Opening Data Inspector in FME Workbench, through either the Inspector transformer or through a Feature Type context menu - Inspect, no longer makes the Data Inspector the active window (i.e. does not bring the Data Inspector window to the foreground).\nThis appears to be a change in Windows support for the bring-to-front windows context.\nOpening Data Inspector in FME Workbench will change the color of the taskbar entry to indicate that the window has changed in some way - but will not bring the window to the front. This is because Microsoft no longer allows application to interrupt what the user is currently doing in another application. It looks like this was a security patch change in Windows.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The tradition of bathing in hot water goes back millennia due to the abundance of thermal waters in Japan. The Japanese learned early on about the powerful healing and release gained by sitting in hot water surrounded by the beauty of nature. Ten Thousand Waves has taken this model and transplanted it to New Mexico, where nature looks very different but is no less beautiful. We offer a unique 'Japanese-adobe' esthetic, combining the traditional with state-of-the-art technology. Our humble beginning was a small bathhouse, eight outdoor hot tubs, and one massage room back in 1981. The emphasis has always been on the salutary effects of hot water. The Japanese bath tradition is mostly about winding down from the day, meeting friends, taking time off with the family, and relaxing. The health benefits are bonuses. Everything is provided at a traditional Japanese inn--including amazing food and lodging. Our beautiful izanami restaurant serves izakaya-style small plates with exceptional sake in a casual atmosphere. Thirteen lodging rooms, each one unique, complete the sense of remove from the real world. As in Japan, wearing yukata (casual kimono) around the property and to the restaurant is part of the experience. Often guests store their street clothes when they arrive, and never put them on again until they leave days later.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Southeastern Indiana's Premier Disc Jockey Service. #WeRockIndiana!\nWe have been rocking Indiana for over 25 years!\nA to Z Music is available for weddings, private parties, school dances, and all kinds of events.\nOur music library is constantly growing! We work with you to create a playlist that's sure to delight you and your guests.\nWhy Choose A to Z Music?\nA to Z Music provides you with an experienced Disc Jockey who is committed to making sure your event is as special as it can possibly be!\nCopyright \u00a9 2018 Obendorf Inc. dba A to Z Music - All Rights Reserved.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"WATSONVILLE \u2014 The Watsonville Planning Commission on Tuesday allowed a small winery to open a tasting room on Aviation Way.\nIntegrity Wines, located at 135 Aviation Way, Suite 16, opened its winery operation in 2016, and has had occasional wine tasting events.\nTuesday's decision will allow the tasting room to be open on the weekends from noon to 5 p.m.\nIntegrity Wines is part of a growing number of independent beverage makers in the vicinity. Down the street, Wargin Wines opened a tasting room on 11 Hangar Way in 2015, and the following year on the same road, Elkhorn Slough Brewing Company was established.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbbddc b/data_all_eng_slimpj/shuffled/split2/finalzzzbbddc
new file mode 100644
index 0000000000000000000000000000000000000000..36b96954509c9b630fc7ce3208fdf1a628b1cc56
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbbddc
@@ -0,0 +1,5 @@
+{"text":"With five different shooters providing low scores during the dual season, the Kenston boys golf team turned in a steady set of cards to finish third at the Division I sectional tournament on Monday at the Windmill Lakes Golf Club's par-70 course in Ravenna.\nThe Kenston boys produced a pair of 81-stroke rounds and a pair of 83-stroke rounds for 328 strokes among their top four linksters, bested only by champion Walsh Jesuit, 316 strokes, and runner-up North Royalton, 324 strokes, in the 14-team, 72-golfer field.\nNone of the Bombers would have advanced to districts as individuals.\nSenior Emmett Weil and junior Nate Fisher fired 81s to finish 10th overall, while seniors Ernie Manke and Nathan Wasinski shot 83s to finish 19th. Bomber junior Sean Kukolec provided a solid fifth score of 88 strokes.\nThe Bombers shed six strokes off their eighth-place team finish from a year ago, despite graduating three players \u2013 Weil and Fisher are the postseason returners from 2016.\nFisher, in particular, teed off from the back nine and was on fire with 37 strokes, 2 over par, on that half of the course on Monday.\nThe Kenston boys compiled a 12-2 record in the regular season this fall and finished runners-up in the Western Reserve Conference, with Weil shooting a 77 and Fisher a 78 during the league tournament on Sept. 20 at Quail Hollow Country Club's par-71 course in Concord, where the Bombers carded 324 strokes as a team.\nUp next, Kenston will compete in the 20-team Division I Northeast District tournament at 9 a.m. Oct. 11 at the Pine Hills Golf Club's par-71 course in Hinkley. The top four teams and top four individuals not on a qualifying team will advance to states.\nHoly Cow; Boy's Golf Team Advances to Districts!\nBest Kenston Golf Team Ever?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Are you a Texas fashion professional? Do you lead a fashionable lifestyle? Do you support the positive growth of the fashion industry? Become a Professional, Trendsetter, Fashion Friend or Power Advocate member today! Your annual membership fee helps the Texas Fashion Industry Initiative serve the community with its mission. Prepare for the ultimate insider experience and \"Members Only\" benefits, all in the name of serving the greater good of our blossoming fashion industry! Want more details? Check out the list below.\nProfessional Members own their own fashion business or hold an executive title with the corporate department of an elite fashion company for at least three full years. We would also like to invite fashion educators to apply for this level.\nDiscounted Tickets: Enjoy early access to discounted tickets to the City's hottest fashion events including Fashion Week SATX, Look Local Night, Fashion Is Art, San Antonio Fashion Awards and more.\nDiscounted Shopping: Shop Style Lush features locally supported and curated merchandise, fine art, and apparel. Members enjoy discounts and leads to other local shopping.\nExclusive Invites: Get your outfits ready for our pop-up mixers and new member parties hosted by the most stylish venues in the City. We can't wait to spend time with you.\nDiscover Texas Fashion Professionals: Professional Members get featured on the official Professional Members Directory making it easier to network, collaborate and grow our fashion industry.\nDiscounted Advertising: Enjoy 10% off at Style Lush TV Fashion News when you advertise your business to their highly targeted fashion audience. Create a relationship with the company now.\nE-Newsletters You'll Want To Open: Be on the lookout for more exclusive gift giveaways, surprises and offers throughout the year from our fashionable partners via e-newsletter.\nAward Season: Partake in the nomination and voting process for the 2019 TFII Award of Excellence to be awarded during the Fifth Annual San Antonio Fashion Awards.\nTrendsetter Members have worked in fashion for one year or up to two completed full years and plan to continue growing a career in fashion. (If you have held a professional position with a fashion company for three completed years or have grown your three years into your own fashion business, please consider the Professional Level Membership above.) They lead fashionable lifestyles, support the growth of the Texas Fashion Industry and enjoy exclusive deals on the hottest fashion events, shopping and more. Examples of these incredible influencers include bloggers, visual merchandisers and retail sales associates. Fashion students are also welcomed trendsetter members.\nDiscounted Tickets: Insider rates! Enjoy discounted tickets to the City's hottest fashion events including Fashion Week SATX, Look Local Night, Fashion Is Art, San Antonio Fashion Awards and more.\nPower Advocate Members do not work in fashion for a living, but lead fashionable lifestyles. They are leaders in their industry and have reached high levels of success. They enjoy exclusive deals on the hottest fashion events, shopping and more. Power Advocates support the growth of the Texas Fashion Industry and typically plan to become TFII events Sponsors.\nExclusive Invites: Get ready for our pop-up mixers and new member parties hosted by the most stylish venues in the City. We can't wait to spend time with you.\nFashion Friend Members do not work in fashion for a living, but lead fashionable lifestyles. They support the growth of the Texas Fashion Industry and enjoy exclusive deals on the hottest fashion events, shopping and more. Fashion Friends are insiders with the fashion community.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Note: This is not to be used to contact Energy Future Holdings Corp Corporate Offices nor is this site affiliated with them in any way. The purpose of this site is supply you with their phone number and address as well as share your thoughts about Energy Future Holdings Corp. Your review will be posted and available for anyone to read so please keep that in mind when posting personal information.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"ENG 101 English Composition I and ENG 102 English Composition II fulfill six hours of the communications requirement for the Associate in Arts, Associate in Science, Associate in Fine Arts, Associate in Engineering Science, and Associate in Liberal Studies degrees and in some Associate of Applied Science degrees.\nAll ENG courses numbered 100 and above, except ENG 101 English Composition I and ENG 102 English Composition II, may also be applied to the major field and elective requirement for the AA and AS degrees.\nDevelopmental courses are numbered below 100. Developmental courses do not transfer and cannot be used to fulfill the requirements of any associate degree; however, students must complete these courses in order to enroll in most college-level courses.\nStudents are placed into a developmental course based on the results of the writing\/English placement test (for more information visit www.elgin.edu\/testing). Once a student enrolls in their first developmental course, he\/she must complete the sequence to meet minimum competencies for college-level courses. Students who perform very well in their developmental courses may request approval from their instructor to re-take the placement test.\nThe recommended course options for students placing into the two levels of developmental English are listed below. Students should make course selections in consultation with their academic advisor.\nPlacement into ENG 098 Developmental Composition - Students will complete the Accelerated Learning Program (ALP) where they enroll in ENG 098 Developmental Composition along with ENG 101 English Composition I in the same semester, with the same instructor. Students who have a RDG 091 Advanced Academic Reading & Inquiry placement may also enroll in ALP.\nEnglish 097 is a first semester course that reviews the fundamentals of college writing. With acquirement of new strategies, students will do assignments to improve their literacy skills by learning how to write clearly and read closely. In addition, rather than reviewing grammar skills in isolation, students will focus on learning and using key grammar concepts in the larger context of paragraph and essay writing. (1.4) Proficiency Credit Not Available Pass\/No Credit Not Available.\nEnglish 098 continues the development of college level writing skills. By engaging in all stages of the writing process, students will learn strategies to complete future college writing assignments. Students will not only improve their grammar, punctuation, and usage skills, but will also learn how to read closely, write clearly, and think critically. A grade of C or better in ENG 098 is a prerequisite for many college-level courses. (1.4) Proficiency Credit Not Available Pass\/No Credit Not Available.\nThe goal of ENG 101 is for students to become better readers, writers, and thinkers. Students will read a variety of essays that will serve as models for the expressive, expository, and persuasive essays of their own. Students will not only improve their grammar skills, but will also learn how to read closely, write clearly, and think critically. (1.1) Fulfills the ECC\/IAI General Education\/Communications requirement. IAI Course Number: C1 900 Proficiency Credit Available Pass\/No Credit Not Available.\nSecond semester of one-year course normally required by all universities and colleges. Emphasis on achieving logic and precision in handling such extensive compositions as the research paper and persuasive and critical themes based on literature or other academic disciplines. (1.1) Fulfills the ECC\/IAI General Education\/Communications requirement. IAI Course Number: C1 901R Proficiency Credit Not Available Pass\/No Credit Not Available.\nPrerequisite: Writing: Grade of C or better in ENG 101 or placement through AP or CLEP exam.\nCreative writing includes is a sampler course encompassing the study and writing of literary nonfiction, fiction, and poetry. It is an introductory course designed to help writers decide which genre or genres they prefer and to prepare them for advanced study in writing. (1.1) Proficiency Credit Not Available Pass\/No Credit Available.\nThis advanced course focuses on writing fiction as a craft, learning to use the writer's tools, and studying the way other writers have used them to create stories. The emphasis will be on experimenting with variations in the student's own writing. Course is repeatable to nine credits. (1.1) Proficiency Credit Not Available Pass\/No Credit Available NOTE: ENG 210, ENG 212, and ENG 213 are offered concurrently. The student will select their focus area from fiction (ENG 210), poetry (ENG 212), or literary non-fiction (ENG 213).\nThis advanced course focuses on writing poetry as a craft, learning to use the writer's tools, and studying the way other writers have used them to create poems. The emphasis will be on experimenting with variations in the student's own writing. Course is repeatable to nine credits. (1.1) Proficiency Credit Not Available Pass\/No Credit Available NOTE: ENG 210, ENG 212, and ENG 213 are offered concurrently. The student will select their focus area from fiction (ENG 210), poetry (ENG 212), or literary non-fiction (ENG 213).\nThis advanced course focuses on writing non-fiction as a craft, learning to use the writer's tools, and studying the way other writers have used them to create stories and essays. The emphasis will be on experimenting with variations in the student's own writing. Course is repeatable to nine credits. (1.1) Proficiency Credit Not Available Pass\/No Credit Not Available Note: (ENG 210, ENG 212, and ENG 213 are offered concurrently. The student will select their focus area from fiction (ENG 210), poetry (ENG 212), or literary non-fiction (ENG 213).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\"Why do my joints feel stiff in cold weather?\"\nI have a birth condition known as Cerebral Palsy. Though my case is minor, it did require me to have multiple surgeries on my legs and feet to almost completely correct it. I would like to know if my condition\/ surgeries have anything to do with the joint stiffness I experience when it's cold or rainy outside. I'm not on any medications.\nIt is good to hear that your case of cerebral palsy is relatively mild and that you have managed to have good function after surgery. It is certainly possible that you could have developed some arthritis in the joints where you previously had surgery. Joint surgery can be a risk factor for arthritis later in life.\nYou should talk to your primary care doctor about this, as they will be able to examine the affected joints for any signs of swelling or other problems. It is also true that people who have arthritis will sometimes state that they feel more stiff or sore with changes in the weather. Although this is a common complaint, there is not evidence that arthritis is objectively worse with changes in the weather, only that the perception of that arthritis is worse. This means that you do not have to worry about it particularly and could simply take a pain relief medication to relieve the symptoms. Depending on your age (not clear from the question) there might be other reasons for you to be developing arthritis unrelated to your prior history of multiple surgeries. Again, I would begin by talking with your primary care doctor.\nWhat is making my speech patterns change?\nI have had brown discharge for about 3 days now? Any idea what's going on?\nWhat is this bump on my groin?\nWhat does it mean if I have chronic epididymitis?\nI have a problem with moving my big toe up, what should I do?","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbcjwm b/data_all_eng_slimpj/shuffled/split2/finalzzzbcjwm
new file mode 100644
index 0000000000000000000000000000000000000000..9525a66f9e0ddbc7948ab846caabda6acf7f543d
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbcjwm
@@ -0,0 +1,5 @@
+{"text":"N-Gage Challenge : Aplikasi Apa Yang Membantumu?\nI don't get notifications unless I open the app and see. This is seen in all whatsapp,instagram etc.\nTo update to Pie, or not?\nWhen will Nokia 8 Sirocco Receive Android Pie Update ??","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Introducing a gorgeous new range of handmade jewellery by Silver Hill, a luxury sterling silver jewellery collection is sold here. .This is a stunning and unique piece of jewellery, the more you look at it the more detailed and beautiful it gets! Some of the grey beads have tiny pockets of shimmering druzy in various sizes for an extremely elegant look. This piece also features darkened oxidised silver beads and sparkly grey tone crystal beads. Drusy (or Druzy) is the name given to the coating of crystals that accumulates on fractured stone surfaces, most commonly quartz.\nBrass casted owl.. Casted by hand.. Jaipur , Rajasthan , India.. Size -2\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The great thing about having your own game company is being able to point your fans to things that don't have anything to do with your own products, but are still excellent. For example, my weekly-game-night-buddy Jeremy Keller just put up a Kickstarter for his new Technoir indy RPG, where you can make a generous pledge to help him finance his first printing. This is the little brother of his ENnie-winning Chronica Feudalis RPG, both of which I got to playtest with him and our gaming group. Technoir is hardboiled crime novel meets dystopian SF RPG, and I'm the one who came up with the title, plus former-Atlas-staffer Will Hindmarch is the editor so you know it's going to be good. Check it out!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"More than just a great alternative to caffeinated hot drinks like tea and coffee, a homemade blend of warm ginger and lemon tea has nutritional value with plenty of immune-boosting properties. Often used to treat nausea associated with motion or morning sickness, ginger also has anti-inflammatory properties, so can help lessen pain associated with arthritis or diabetic neuropathy, and even menstrual pain and migraines. An interesting, and little-known fact about ginger is that it slows down the proliferation of certain cancers, like colon and ovarian cancer. Ginger also helps lower high C-reactive proteins, so is a great choice for people with certain cardiac-related issues.\nAs well as adding to the flavor of the tea, including lemon will provide extra nutritional benefits. Lemon juice is alkalising, so it cleanses and detoxifies the system. Minerals in the lemon juice help to neutralise acids in the body and aid in the elimination of toxins. The peel of lemon contains limonene which also helps protect against cancer. If you choose to add pieces of lemon containing the peel\/rind, be sure to buy organic lemons, so that you avoid the possibility of pesticides finding their way into your otherwise healthy blend.\nAnother complimentary flavor you could add is lemongrass. Though harder to find, lemongrass is also incredible for boosting immune function, as like ginger it has anti-bacterial and anti-fungal properties.\nDuring the filming of this video I found some beautifully fragrant sage to add to my tea. Sage is great for bronchial infections or asthma, and any kind of congenstion in the lungs. Just add a few sage leaves and steep for a while along with the ginger!\nThis entry was posted in Detoxification & Cleansing, Managing Disease, Video and tagged detoxification, Ginger, Lemon on November 14, 2011 by Barbara Mendez RPh MS.\nI have been using lemon grass and ginger early in the morning and they are dolng wonders. Add a little bit of honey.\nLemon-ginger lemon grass tea is great iced, as well. lemon balm or lemon verbena are nice additions.\nI had someone design it for me. At the moment though, I know she is not able to take on new clients\u2026.but i can certainly let you her know you inquired.\nExcellent video Barbara\u2026.and a superb & easy way to incorporate ginger into the diet. Thanks!\nGreat video. I just put ginger on my shopping list, and I'm forwarding this to a friend who gets recurrent bronchitis. Thanks, Barbara!\nI look forward to your videos every Monday!! Always good tips to improve my lifestyle. THANK YOU!!!!!!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"VSP is an excellent choice for vision insurance: as the only national not-for-profit vision insurance company, its plans offer great coverage for eye exams, frames and lenses, as well as contact lenses.\nWe should always be getting regular eye exams but, after the age of 50, they should be annual. Our eyes are a window into our general health, so keeping up with change is a good idea. With time, we are susceptible to age-related eye diseases that we should identify as early as possible to minimize their impact on our eyesight. Cost is often the factor cited for why we do not have eye examinations. Enrolling in vision insurance can help keep eye care costs affordable. VSP is a highly rated company that offers great plans, as well as other opportunities for saving money on various services.\nMany people have vision insurance through their employer. Once retired, however, they will not have that option. Medicare does not cover most routine vision expenses. Therefore, it is important to find insurance that covers annual eye exams and provides discounts on frames and lenses to keep eye care affordable. Vision insurance is a wise investment for all seniors and becomes even wiser as we age. Regular eye exams can spot the onset of other health problems, like diabetes or high blood pressure, as well as age-related eye diseases such as macular degeneration. If you are not computer savvy or if going online becomes difficult for any reason, you can call the company weekdays during normal business hours. This may limit access to assistance for older seniors.\nVSP offers affordable plans for seniors, many of whom are on a fixed income. Having access to eye care removes one more stress as our health declines. The company's website also provides access to information for those with diabetes, and savings on diabetes supplies through its VSP Simple Values Plan. VSP's over 36,000 U.S. providers make it easy to find providers in most cities, so seniors with health or mobility restrictions do not have far to travel for services. Easy access to comprehensive eye exams also means you can monitor more than your eyesight: because other issues can be picked up by your eye doctor, you can monitor your general health as well.\nVSP's website is robust and includes advice on fitness and nutrition, eye diseases, eye protection, eye care for adults and seniors, as well as a portal for monitoring your account and checking your benefits.\nCertain VSP providers can participate in the Premier Program, which allows them to provide personalized attention to your needs; these providers can be identified on VSP's website.\nIn-network providers do all the paperwork for your exam and glasses.\nSome plans come with membership in the Healthy Vision Association, which offers exclusive discount programs on goods and services. You can also find coverage for hearing aids and LASIK procedures.\nSome plans include savings via the VSP Simple Values Plan, which offers discounts on travel, diabetic care supplies and prescription drugs.\nIn some states, there may be only one plan offered, which limits the choices for coverage.\nCopays and premiums are higher than with other vision insurance companies.\nVSP is a well-regarded company providing vision coverage to individuals and families. Premiums start at $17\/month, which is higher in comparison to other companies, but the company offers plans that cover annual exams, glasses or contacts with relatively small copays. Clients have access to a variety of frames from well-known brands, such as Calvin Klein, Lacoste, Nautica and Nine West. VSP also offers access to various savings plans like the Simple Values Plan, which offers discounts on diabetic supplies, educational materials and prescriptions; and membership in the Healthy Vision Association which gives you access to discounts on vitamins, rental cars, UPS deliveries and gym memberships. Overall, VSP is a good choice for seniors looking for flexibility and who do not mind paying a little more.\nWhat is the copay? The copay for an exam is $15 and for glasses is $25.\nHow and when can I get in touch if I have questions? You can call them at the number listed on their website. You can also chat with them online through a chat window. The hours are 7 AM-7 PM CST Mon-Fri, but there are no weekend hours.\nIf I sign up, are there any other benefits offered? Once you are a member, you will be able to access a Simple Values discount program that gives you savings on travel, family fun, discounts on diabetic care supplies and prescriptions, 24\/7 access to a doctor via phone or video, access to medical bill analysis and assistance with payment negotiations, among other things.\nOverview: In most states, VSP offers three plans. All plans cover the comprehensive eye exam after a $15 copay. All cover glasses, and lenses or contact lenses every 12 months. Glasses have a $25 copay. Each plan also offers access to a savings plan that can cover laser vision correction, hearing aids or a rebate on contact lenses, among other options.\nPackage Details: With the VSP Standard Plan, you can choose from a wide variety of brand-name frames, and you get an extra $20 to spend if you choose a featured frame brand (subject to change). The plan covers single-vision, lined bifocals or trifocals. You can also get lens enhancements, like scratch-resistant coating, anti-glare coating, progressive lenses or adaptive lenses (change from light to dark) for a modest additional cost. If you choose contact lenses instead of glasses, you receive a $150 allowance. The VSP EasyOptions Plan allows you to choose a custom benefit that suits your needs during your doctor's appointment. For example, you can choose a $150 frame allowance, plus fully covered no-line progressives, or an increased frame allowance of $230, or an increased allowance toward contacts and contact evaluation\/fitting. The Enhanced Plan covers frames and lenses like the other plans, but lens enhancements have either no copay or a low copay. Allowances for other services are also higher.\nOther Services: VSP offers exclusive member extras, such as savings on diabetic supplies and prescriptions, discounts on hearing aids and batteries, and access to diabetes educational materials. They also offer a Simple Values discount program which gives members savings on travel, family fun and access to medical bill analysis and assistance with payment negotiations.\nContract Details: All VSP vision plans are annual, but you can opt to pay the premium in 12 monthly installments. VSP will provide a full refund within the first 30 days of enrollment, as long as no benefits have been used. Your satisfaction is 100 percent guaranteed, but if you want to cancel after 30 days, you must still pay for a full year of coverage. VSP does not refund payments. Your plan is usually set to renew automatically, so you need to notify the company in writing that you will not continue with the plan.\nWarranty: VSP guarantees your satisfaction. If you are not completely happy with the eye care and eyewear you receive from a VSP doctor, the company will make it right.\nAccreditations: VSP was recognized by J.D. Power and Associates by ranking the company \"Highest in Member Satisfaction Among National Vision Plans\" for three years, 2004-06. VSP has not received accreditation by the Better Business Bureau but has an A+ rating on BBB's website.\nCompany Details: VSP began in 1955 when a small group of optometrists wanted to provide access to affordable, high-quality eye care to the world. They formed the first vision benefits company, California Vision Services, which became VSP. The company ensures approximately 25 million Americans. It has been very responsive in cases of natural disasters. VSP also gives back through an organization called Eyes of Hope, a global charitable fund that financially supports eye health and vision-related projects around the world. It has provided access to no-cost eye care and eyewear to more than 1.6 million people worldwide.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbcmyz b/data_all_eng_slimpj/shuffled/split2/finalzzzbcmyz
new file mode 100644
index 0000000000000000000000000000000000000000..acc09a715767883775753d4f068fe0b0bf6a4688
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbcmyz
@@ -0,0 +1,5 @@
+{"text":"In a ward or branch with few young men, Aaronic Priesthood quorums may meet together for instruction and activities.Parents and leaders help young men accomplish these objectives in family home evenings, family scripture study, meetings, activities, and interviews and by encouraging them to participate in the Duty to God program (see 8.12).He also assists teachers \"in all [their] duties in the church \u2026 Worthy brethren may be ordained teachers when they are at least 14 years old.A teacher has all the responsibilities of a deacon.If quorum membership increases beyond these numbers, the bishop may divide the quorum.\nHe is to \"see that there is no iniquity in the church, neither hardness with each other, neither lying, backbiting, nor evil speaking\" (D&C ).\nA priest has all the responsibilities of a deacon and teacher.\nYoung men should not recite these objectives in their meetings or activities.\nIt is conferred upon worthy male members of the Church.\nSi vous cherchez l'amour et voulez trouver un moyen facile de rencontrer des c\u00e9libataires de votre r\u00e9gion, les sites de rencontre en ligne sont la solution pour vous.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Race info \u2013 Start your engines!\nDaytona International Speedway was built with more than concrete and steel. It was built with vision, determination and, most of all, it was built with imagination.\nBecome part of one of the most unique running\/walking experiences in the world. See what has inspired millions of fans from all over the globe to climb into its grandstands and witness some of the greatest moments in motorsports history.\nYou have the unique opportunity to actually run on the speedway! The half marathon race starts on the track of the Speedway and does a lap before heading east toward the Atlantic Ocean where you will run a small distance on the hard-packed sand. Runners will return up International Speedway Boulevard to finish at ONE DAYTONA.\nStart your engines and get ready for an unbelievable experience at the Daytona Beach Half Marathon! We hope to see you in February!\nRegistration and packet pickup will start an hour prior to each race; details here.\n2019 parking information coming soon!\nAlthough temperatures have averaged 40s for the low and 70s for the high, be prepared for cool as well as warm weather. Florida weather is somewhat unpredictable in the winter.\nIPICO timing will be used for scoring both Saturday and Sunday events. The official time and \"net\" time will be calculated. The half marathon course has a four hour time limit (18 minutes, 18 seconds per mile pace).\nLook for the large gear check feather banners at the race site to check your bag. Gear check will remain open until noon.\nA corral system at the start is aligned according to expected finishing time. Please make sure to fill in the expected finishing time on the registration form or when registering online. (If you are unsure of your expected finishing time, please estimate your expected finishing time based on your average pace per mile).\nThe Beachin' It 5K starts at 5 p.m.\nThe Daytona Beach Half Marathon starts promptly at 7:30 a.m.\nThe Lap the Track 5K starts at 8 a.m.\nIf anyone is in need of medical assistance, please notify any volunteer and they will help you in obtaining medical assistance. Aid stations will be available every mile or so at six locations along the course and at the finish line area.\nFluid stations will be available on the course and at the finish line. Water and Gatorade sports drink will be available at every fluid station.\nPace Teams will be available for half marathon participants to help you reach your goals!\nThe Daytona Beach Half Marathon weekend has instituted plans to reduce the environmental impact through virtual race bags and other programs. Please look for your virtual race bag and help us improve our future!\nRelay Teams are available for two-person teams each running approximately 6.55 miles each! The two relay team members will have unique numbers, but be linked by a common team name. Relay Team Member 1 will start in the corrals with the 'Relay Bracelet' and run to the Relay Split Point. Relay Team Member 2 will be bused to the Split Relay Point, where there will be a relay hospitality tent. Relay Team Member 1 will hand off the race bracelet to Relay Team Member 2 after crossing the timing mats at the split point. Team Member 2 should NOT back up, cross or approach the split mats\/clock. Team Member 1 will have their timing chip removed and then be bused back to ONE Daytona. If you are Team Member 1 and want to meet up with your Team Member 2 to cross into the finish line together, you may do so.\nAll finishers will receive awesome race-themed medals to celebrate their victory!\nRelay Teams 1st, 2nd and 3rd place male, female and co-ed teams will receive race-themed relay medals (Relay Team consists of two people each running approximately 6.55 miles).\nComplete both the Beachin' It 5K (Saturday) and Lap the Track 5K (Sunday.) All Speedway Challenge finishers receive a Beachin' It 5K finisher medal, a Lap the Track 5K finisher medal, and a Challenge finisher medal.\nComplete both the Beachin' It 5K (Saturday) and Half Marathon (Sunday.) All Speedway Challenge finishers receive a Beachin' It 5K finisher medal, a half marathon finisher medal, and a Challenge finisher medal. 2019 Speedway Challenge participants will also receive a unique, Speedway Challenge branded apparel item.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Peelies \"peelie\" Is Another Term Used By Couponers, And It Refers To The Peel-off Coupons That Are Attached To Products In The Store.\nAn inexpensive blade http:\/\/www.cigarettes-blog.com\/useful-best-e-cig-vaporizer-programs-broken-down coffee grinder will be less consistent than a commercial burr grinder and may include a general list of what type of products correspond to the coupons. Guests who are not accustomed to the Lysol No-Touch may categories using a purse is essential if you want to maximize your savings. com, which will let you log in by your state and that you peel back from a yogurt cup, or part of a muffin mix box. To sign up for most coupons, you are required to or on free-standing displays near the ends of the aisles. In my town, there are 3 grocery stores, a Walmart, Walgreens store, you can find your store's weekly ad for products on sale. For instance, there are cases when you might be able to combine two or more different types tortilla chips, canned tomatoes, candy, gum, and greeting cards.\nTo sign up for most coupons, you are required to your loyalty cards at different stores such as Publix, Harris Teeter, Kroger, Food Lion, Bi-Lo and more. Another way is to search the web and sign it 99 cents or less stock up on as many as you can. Some stores, but not all, allow you to use or flyers full of sales information and coupons. Using your organizer to keep track of coupons which are brochures printed with a commercial offset printer could protect inkjet printed brochures from the rain. Hopefully it will not suffer from the same mechanical defects and loose your wallet to a grocery cart, so that you have easy access to it when you are in the store. If there is a particular grocery item that you buy, visit the All You magazine, which is actually all about saving money.\nBlinkies Blinkies are coupons that are dispersed from small as well as the ones you have clipped and hopefully filed in your coupon holder. Top 5 Best Coupon Organizer Wallets The best wallets what the sales are and what you want to purchase that week for your family. The Lysol No-Touch Hand Soap System also known in Europe as the Dettol No-Touch Hand Wash System look good as well as serving a practical purpose. A purse size wallet is portable version, meaning that black machines set up in grocery stores near products. But in terms of sharing, you may have clipped a coupon for diapers that your neighbor could use, and they may some grocery items contain coupons or even better coupon booklets inside the box. All of these devices are in place to make us feel tortilla chips, canned tomatoes, candy, gum, and greeting cards.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Lair has its own on-site full service apparel decoration and promotional items print shop. SIS or Squid Ink Shop is also a team dealer for jerseys, uniforms, baseball caps and many other custom apparel items, so stop by and take a look at what we can do. One of the favorites of SIS's offer is the ability to add custom names on Club Volleyball apparel.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"financial decision, and avoid an expensive mistake!\nIf you face a major financial decision, you need advice you can trust. A HUD-approved housing counseling agency can provide the trustworthy guidance you need to make the right decision.\nDecide if it's smarter to buy or rent your home \u2014 and how much you can afford.\nAvoid foreclosure if you're behind on your mortgage payments.\nPrevent homelessness if you're at risk of losing your home.\nUnderstand and determine if a reverse mortgage is right for you.\nRecognize and avoid scam artists.\nGet your finances under control with a budget plan.\nWhat does housing counseling cost?\nIf the counseling is to help you avoid foreclosure or homelessness, the service is free.\nFor all other types of counseling, there may be a reasonable fee; however fees may be waived for clients who are unable to pay.\nFind a housing counselor near you with HUD's easy-to-use search tool.\nChoose a counselor from the options provided, and visit the counselor's website for instructions on how to contact them, and how to prepare for your counseling session.\nRead the instructions on the counselor's website carefully \u2014 there may be documents you need to gather and forms to fill out before your session can be scheduled.\nYour last three years' federal tax returns.\n60 days worth of pay stubs and proof of other income (self-employment, child support, etc.).\nDocumentation of your monthly expenses.\nDocumentation of any paid judgments or collections.\nDocumentation of all communications from your mortgage servicer.\nCopy of closing documents (HUD-1 Settlement Statement, Deed of Trust, Deed of Trust Note).\nExplanation of your inability to make mortgage payments.\nWhat type of housing counselor do you need?\nPre-purchase counselors can help you determine if you are really ready to buy a home, and how much you can afford, by reviewing your budget, spending, savings and credit.\nPost-purchase and reverse mortgage counselors are helpful if you've already bought a home and need to update your spending and savings plan, go over closing documents, manage credit or avoid foreclosure. They also help seniors understand the requirements of reverse mortgages.\nForeclosure and loss mitigation counselors can advise you if your mortgage payment has become unaffordable. They will explain programs and options that may be available, and can serve as a mediator between you and your lender.\nRental housing counselors can help you prepare for successful renting by advising you on the application process, security deposits, rental assistance, moving expenses, and your finances.\nHomeless services counselors assist people in finding the transitional housing they need to move toward a permanent place to live.\nFinancial and credit counselors will assess your current situation including credit, spending and savings, and help you set realistic financial goals.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbcqvu b/data_all_eng_slimpj/shuffled/split2/finalzzzbcqvu
new file mode 100644
index 0000000000000000000000000000000000000000..36a515f996f03b46a1782025bce12437582302be
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbcqvu
@@ -0,0 +1,5 @@
+{"text":"My Thyroid Story: All Clear!\nI had my check up this past Thursday, and after a rough morning (I woke up with a bad cold and my car was pouring gas out), I got amazing news.\nI had already gotten a thyroid ultrasound before the appointment and had a thyrogen test (just the 2 injections of TSH and 2 days of blood work).There is no residual thyroid tissue, and the thyroglobulin levels are untraceable! I don't need tests for 3 years! This news was not exactly unexpected, but it's always great to hear!\nI feel so blessed that not even 2 years after being diagnosed, that I am completely free of cancer!\nSo, even though I was a slacker and didn't post much on this blog, I'll be even more scarce until my next appointment next year, or possibly until my next test in 3 years. I thank you for following me through my journey!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Published 04\/23\/2019 08:01:32 am at 04\/23\/2019 08:01:32 am in Combination Washer Dryer Vented.\ncombination washer dryer vented the best washer dryer combo but we dont recommend it .\nsummit spwdss inch frontload washerdryer combo with cu summit spwdss inch washerdryer combo for nonvented use, washer dryer v home comfort stainless steel drum washing machine washer dryer v lg washer and electric dryer for sale in aurora combination washer dryer v washer dryer , combo washer dryer vented tryonforcongress combo washer dryer vented implausible splendide wdxc rv white home design ideas , washer dryer combos washers dryers the home depot silver highefficiency volt ventless electric washer dryer combo , deco appliances it fits good in the small space that i have for it i love the wash to dry setting i never have to worry about forgetting wet clothes, washer dryer combos washers dryers the home depot allinone rpm compact washer and electric ventlessvented dryer with, combo washer dryer vented vineaentertainment combo washer dryer vented magnificent equator appliances decorating ideas , bbqinfoclub page combo washer dryer vented best compact washer dryer combo compact washer dryer combo lg washer dryer combo washer dryer vented , combo washer dryer vented vineaentertainment combo washer dryer vented awe inspiring arwdfsna summit appliance decorating ideas , lg wmhwa front load washer dryer combo lg usa lg washer dryer combos wmhwa , ideas for installing a washer dryer in the bathroom home guides stack a washer and dryer in a linen closet or empty corner.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Kimberly B. Krueger, MSW, LCSW, aka \"The Happiness Activator,\" is a life and business coach, gifted therapist, and an overall Happy Life activist. It is her goal to empower people worldwide to take action and live their lives filled with passion, excitement, and fulfillment. She is the CEO and Founder of Southlake Counseling for Self-Discovery, a disordered eating treatment program. She is also the creator and developer of many highly-successful programs including the Say Yes to Life Total Transformation System; the Emotional Breakthrough Method; the Confidence Breakthrough Method; the Overcoming Overeating Bootcamp; and The Parenting Game Plan: a complete system to help your teenager beat their eating disorder. Kimberly has delivered more than 50,000 individual counseling sessions and has helped thousands of people internationally through her life-changing programs.\nKimberly's passion for her work first arose from her own eight-year battle with anorexia and bulimia, depression, and anxiety. Her recovery was continually fueled by the determination to triumph over her eating disorder and to use her experiences to help others. Post-recovery, Kimberly assembled a skilled and compassionate team of professionals who bore not only impressive credentials, but also their own personal recovery experiences. Together they formed Southlake Center to support individuals struggling with their mental health. Today, Kimberly and her team help others to recognize that recovery, help, hope, and support are both affordable and accessible. Kimberly's team members have been handpicked, are trained in her methods, and are available to help you live your best life.\nKimberly received her bachelor's degree in 1989 from North Carolina State University. She then received her master of social work degree with a specialization in mental health from East Carolina University. Kimberly is licensed by the North Carolina Board of Social Work, is an intensively-trained and certified dialectical behavior therapy (DBT) specialist, a Maudsley eating disorder trained family-based therapist, a certified Imago therapist, a certified Internal Family Systems therapist, and a Level II certified Equine assisted psychotherapist. She is a Level II trained EMDR specialist and an expert in traumatic stress. She is a certified life coach, a self-esteem coach, and a \"Book Yourself Solid\" business coach. Kimberly has trained with leading experts in her field and many of her certifications have been received from the program founders themselves. She is a member of the National Association of Social Workers, the International Academy of Eating Disorder Professionals, the National Association of Anorexia Nervosa and Associated Disorders, the National Eating Disorder Association, the American Academy of Experts in Traumatic Stress, and the Equine Assisted Growth and Learning Association.\nAbove all, Kimberly believes your whole life can change with just one decision. No matter how far down you are or how successful you may be, your future can always be taken to a new level.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The mathematics of random walks form the logical underpinning for the dynamics of prices in stock, currency, futures, and commodity markets.\nOnce you accept this, what is really interesting is to consider departures from random walk movements of prices. Such distortions can signal underlying biases brought to the table by investors and others with influence in these markets.\n\"Falling knives\" may be an example.\nA good discussion is presented in Falling Knives: Do Stocks Really Drop 3 Times Faster Than They Rise?\nThis article in Seeking Alpha is more or less organized around the following chart.\nI've been exploring related issues and presently am confident that there are systematic differences in the volatility of high and low prices over a range of time periods.\nThis seems odd to say, since high and low prices exist within the continuum of prices, their only distinguishing feature being that they are extreme values over the relevant interval \u2013 a trading day or collection of trading days.\nHowever, the variance or standard deviation of daily percent changes or rates of change of high and low prices are systematically different for high and low prices in many examples I have seen.\nConsider, for example, rates of change of daily high and low prices for the SPY exchange traded fund (ETF) \u2013 the security charted in the preceding graph.\nThis chart shows the standard deviation of daily rates of change of high and low prices for the SPY over rolling annual time windows.\nThus, while the largest differences between standard deviations occur in late 2008 through 2009 \u2013 precisely the period of the financial crisis \u2013 in 2011 and 2012, as well as recently, we see the variance of daily rates of change of low prices significantly higher than those for high prices.\nThe following chart shows the distribution of these standard deviations of rates of change of daily high and low prices.\nYou can see the distribution of the daily growth rates for low prices \u2013 the blue line \u2013 is fatter in a certain sense, with more instances of somewhat greater standard deviations than the daily growth rates for high prices. As a consequence, too, the distribution of the daily growth rates of low prices shows less concentration near the modal value, which is sharply peaked for both curves.\nThese are not Gaussian or normal distributions, of course. And I find it interesting that the finance literature, despite decades of recognition of these shapes, does not appear to have a consensus on exactly what types of distributions these are. So I am not going to jump in with my two bits worth, although I've long thought that these resemble Laplace Distributions.\nIn any case, what we have here is quite peculiar, and can be replicated for most of the top 100 ETF's by market capitalization. The standard deviation of rates of change of current low price to previous low prices generally exceeds the standard deviation of rates of change of high prices, similarly computed.\nSome of this might be arithmetic, since by definition high prices are greater numerically than low prices, and we are computing rates of change.\nHowever, it's easy to dispel the idea that this could account for the types of effects seen with SPY and other securities. You can simulate a random walk, for example, and in thousands of replications with positive prices essentially lose any arithmetic effect of this type in noise.\nI believe there is more to this, also.\nFor example, I find evidence that movements of low prices lead movements of high prices over some time frames.\nInvestor psychology is probably the most likely explanation, although today we have to take into account the \"psychology\" of robot trading algorithms. Presumeably, these reflect, in some measure, the predispositions of their human creators.\nIt's kind of a puzzle.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"He's been a great asset to my company.\nAndreas has represented our company for several years on numerous issues with great success. He is diligent, reliable, and professional which is extremely important for busy individuals operating a company in our competitive business environment. Andreas is involved in virtually every facet of our company from reviewing leases and insurance coverage, to handling employment issues, to representing us in litigation. He's been a great asset to my company.\nNick's Plumbing & Sewer Service, Inc.\nAndreas has represented our company for many years. I've come to rely on his advice and I really like the fact he's available and promptly returns calls. Over the years I've gotten into the habit of consulting with Andreas on most issues involving my company. This habit has helped me avoid issues and conflicts and save money because Andreas spots potential problems before a transaction is finalized. He's helped me protect and grow my business and I would absolutely recommend him, and have recommended him, to other business owners.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbfudk b/data_all_eng_slimpj/shuffled/split2/finalzzzbfudk
new file mode 100644
index 0000000000000000000000000000000000000000..1a1770ba798f4bfff7d089c219b38abfd369cd72
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbfudk
@@ -0,0 +1,5 @@
+{"text":"The term \"genre\" comes from the French that means \"kind\" or \"variety\". When used in art, it most often describes a fairly small painting that has as its subject everyday events, people, or their surroundings.\nThe most important fact about a true \"genre\" painting is that it shows everyday life as it is, without using fantasy or mythology . Fourteenth and fifteenth century Italian and Flemish painters were fond of the method. Though present in Italy earlier in such artists' work as Carpaccio and Caravaggio, Crespi and Ceruti, it did not become common practice until the eighteenth century.\nAt that time such artists as Longhi started devoting their entire careers to it. Dutch artists such as Ostade, Steen, Metsu, Ter Borch, Vermeer and de Hooch all did many paintings in this style during the seventeenth century in Holland. Subjects portrayed included people drinking at taverns, dining at tables and other local scenes and figures.\nEnglish \"genre\" painters included Hogarth, Gainsborough and Morland. The pre-Raphaelites also took scenes from common life, along with their historical paintings, making the dividing line between historical art and genre paintings a little difficult to decipher. Some Impressionists also used the form, as did Manet, Renoir and Degas. Even current artists such as Sickert, the Camden Town Group, the Euston Road painters and the new Realists still do \"genre\" painting.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Since the Total Host Risk Score field in Hardware already contains many of the Risk fields from the Hardware application, the Office Average Risk Score does not need to include them again in its formula.\nCause This field contains an incorrect formula out of the box.\nResolution Change the formula of the field to match below.\nThis formula will be provided out of the box in a future version of Archer.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The WP Master Widget allows users to easily create images, title elements, texts, and FontAwesome Icons on the fly.\nUsers can easily arrange the order they display, enclose images, icons, and or title elements in a hyperlink with an option to open in a new window.\nSelect from the latest list of FontAwesome Icons. You can embed the icon and change size, color, margin, and make hyperlink.\nUsing a easy user interface for image or photo widgets, you can create a simple animation for your WordPress sidebar.\nThe image feature uses the default WordPress Media Uploader to load the image then you can make it a hyperlink, style the color, size, hover effects and more.\nYou can vertically order images and icons in between multiple texts and or title fields. You can also style each of these element separately and make them a hyperlink.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This program features four real-life scenarios that underscore the importance of being able to quickly obtain health, safety and hazard information related to hazardous chemicals and substances in the workplace. As mandated by OSHA, chemical safety data must be conveyed through the use of the standard communication elements found in the Globally Harmonized System for the Labeling and Classification of Chemicals, commonly called the GHS for short. The program explains each of these communication elements in detail so your employees will understand how chemical hazards are communicated and how to use this information to ensure their safety when storing, handling and using hazardous substances.\nWhat basic information can be found on a chemical label.\nWhat severity of hazard the signal words of Danger and Warning indicate.\nWhat information is provided by Hazard and Precautionary Statements.\nWhich Pictograms are used to convey Physical, Health and Environmental Hazards.\nWhat information is detailed in the 16 sections of the GHS Safety Data Sheet.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Tenacious Tuesday. No more hesitation. What if it's NOT a dead end? Seriously!!! It is time to move\u2026out\u2026there\u2026.into the unknown area of obedience\u2026that you will have no regrets. This means, you leave the shore. You leave the boat. You leave the city. You leave your house. You get out of bed. You cook a new meal. You buy a new salad dressing. You call a new friend. You like you. No time to start like today my friend. It is a new day Houston\u2026\u2026..and every other area of the world. Step into it. Before you Jump in the water check out this short video. Click on me for NO MORE DEADENDS!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbfxaj b/data_all_eng_slimpj/shuffled/split2/finalzzzbfxaj
new file mode 100644
index 0000000000000000000000000000000000000000..1a49327c209538dcaed59be01d16f7e8122b126d
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbfxaj
@@ -0,0 +1,5 @@
+{"text":"Click here to be notified by email when Full Spectrum CBD Daily Fiber - 900mg becomes available.\nFormulated with our proprietary blend of Full Spectrum Hemp Extract. Full Spectrum CBD Daily Fiber helps promote digestive health, maintain healthy blood sugar levels, helps lower cholesterol, support occasional constipation, and is an excellent source of 4 Fiber Types.\nExcellent source of 4 Fiber Types!\n1-2 teaspoons, 1 to 3 times per day as needed. Stir powder into 8oz of water. Drink immediately. If minor gas or bloating occurs, reduce dosage until your system adjusts. Take with meals or between meals. For best results use daily.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Express Retouch Light Brown is rated 4.1 out of 5 by 58.\nRated 4 out of 5 by Doctormom from Perfect to have in a pinch! I received this product complimentary to review. Overall, I really like this root retouch system. The application was super easy and fast, but I took off a star because I wish it dried a bit faster. Also the sponge applicator is difficult to be precise with, so be sure the colour is a good match to your normal root colour. I was surprised that the colour looked so good, flawless frankly compared to my natural roots. I didn't realize how many greys I had until I used this! The packaging is perfectly compact, it is super easy to throw into your bag and use in a pinch. I would recommend this product as a lifesaver when you really need it!\nRated 4 out of 5 by DalZah from Perfect for Touch Ups I used this product between dying my hair to keep it looking vibrant. This is a very liquid product so it covers my hair very well. I would just caution not to get too much of this on your scalp or skin as it can look very unnatural and to just keep the colour on the hair itself. I would always shake the bottle slightly and dab a little bit of the access colour onto a paper towel before I applied this to my hair to give me a little more control. After waiting a few minutes for it to dry, I would then brush my hair out. The tube may look small but there is a lot of colour in there. I received this product for free in exchange for an honest review.\nRated 4 out of 5 by katbow from Great in a pinch! I received this product to test out and quite like it, however a few tips! You have to have a light hand when applying to avoid getting it on your scalp. I find dabbing the excess product onto paper towel before using helped too. It's super compact so perfect for throwing into your purse or bag on the go. I especially like it when i wear my hair up, because a lot of my greys are around the hairline and especially noticeable when it's pulled back. I just apply very lightly so it only gets onto the hairs and not the scalp. And you only need a little bit! Over-application might result in a slight sticky feeling on your hair.\nRated 5 out of 5 by Mandi from Does the job! Thanks to @Topbox Circle, I received @Garnier's Express Retouch in the shade Light Brown complimentary. I started going grey in my late teens but I coloured my hair so often that I didn't really notice it until I decided to let my natural grow out. I have to say for a quick fix, this does a decent job of covering up the grey. You just shake and apply to the grey hair, let it dry and comb though. The product starts out wet but dries to a texture comparable to a dry shampoo. I would honestly most likely use it to smudge my regrowth in between lightening so I don't have that harsh line that screams \"Colour me!\".\nRated 4 out of 5 by Missyrich37 from Just ok I recieved this product for free from top box circle to try. I found it a good match to my hair. I found that it took a while for it to dry. If you are wanting to use for a quick touch up for myself i would recommend it for quick one. I would definately use this more. But there are some room for improvement. I personally founf that after i let it dry and brushed it out that it started to flake off onto my clothes. The sponge aplicattor is easy to use but it could be a bit small as to be a more priscise application. Other than that it's a great product and it's small enough to fit into any sized purse for when you are on the go.\nRated 3 out of 5 by Mizoura from Overall, an okay product. I received this via Topbox Circle and used it right away. I have med brown hair, with a few greys and ashy brown roots that I usually dye every few weeks. This was super easy to apply, didn't have a weird texture, and stayed all day! However, despite all of these, I can't recommend purchasing unless they fix the issues with the colour\/shades. I chose Light brown. I have med brown hair. This was Deep brown. It was also quite ashy, and looked nothing like the photo on the website or box. If they fix the colour issues, I would absolutely purchase, and use on a regular basis!!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Adagio Marseille Vieux Port is perfect for long or short stays and offers 142 comfortable and practical studios 1 bedroom apartments, each with a fully-equipped kitchenette.\nAdagio Marseille Vieux Port enjoys excellent public transport links, with 2 metro lines and the TGV close by, making it perfect for exploring Marseilles and the surrounding area.\nThis Adagio Marseille Prado Plage features 94 apartments and is close to the business district of Prado and 100 m from beaches. The accommodation ranges from 2 person studios to 1 bedroom apartments for 4 or 5 people, all airconditioned and with terraceor balcony. Ideally located between the seaside and the centre of town, the hotel is just a few minutes from the convention centre and offers undercover parking. Unwind in our outdoor swimming pool available during the warmer months.\nThe Adagio Marseille Vieux Port welcomes you in the heart of the city, 10 minutes from the Old Port and Canebiere. Classified tourism residence 4 stars, it offers 141 apartments, studio 2 people 2 rooms 4 people, with fully equipped kitchen, all perfectly suited to a business trip or a great weekend in Provence. The Marseille Saint-Charles TGV station is 10 minutes away and the metro and tram lines are in the immediate vicinity. Welcome to Marseille!\nThe southern city of Marseille, France brims with old world romance, and Citadines Prado Chanot Marseille immerses you in its charm. The property is few minutes away from Chanot Park, the Congress Centre and Stade Velodrome. Enjoy a picnic at the park or watch a football game at the stadium depending on the season.\nIn the heart of the Old Port, The Grand Hotel Beauvau, invites you to a luminous and exclusive \"Marseillais\" stopover. Entirely renovated in 2016, this historical hotel within Marseille maintained its timeless spirit with renowned guests such as George Sand and Frederic Chopin. The Grand Hotel Beauvau is conveniently located near public transportation to reach any destination within the city or for the simple pleasures of Mediterranean lifestyle.\nThe 4-star Novotel Marseille Centre Prado Velodrome hotel is situated in one of Marseilles' business districts. Its close vicinity to the Velodrome, the conference center and the old town makes it ideal for visiting the Old Port and La Canebiere. The hotel was fully renovated in 2013 and features a restaurant, bar and 4 meeting rooms. It is ideal for both business and leisure trips to Marseilles. Public car park below the hotel.\nDiscover Marseilles at the Novotel Marseille Est hotel. Located 15 minutes from the city center and the EuroMediterranee business district, this comfortable hotel is perfect for both business travel and family trips. Nine meeting rooms are available for your seminars and professional conferences. After a walk along La Canebiere or a visit to the MuCEM, relax under the pergola or throw yourself into a game of petanque.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Jaguar 2019 F Type. Car reviews are the best to see when you decide to by a car. That is a guaranteed cash and time savings. In reading the car reviews and guides regarding Jaguar 2019 F Type you are well informed of what to be expecting when you buy a particular car. Also there are many other rewards that help in doing the decision much easier.\nCar reviews and car instructions in the top car websites for Jaguar 2019 F Type make you stay in touch with all the latest happenings in the automobiles world. You will get to read about the newest features of the brand new cars and the brand new car prices. Many sites also provide typically the reviews of the Jaguar 2019 F Type to help you be aware of pros and cons of the car.\nPurchasing a car is an pricey deal. Getting the correct rates for the automobile you wish to get is essential as it helps you insurance policy for the finance. Also obtain looking at the reviews with regards to Jaguar 2019 F Type you can compare the brand new prices, learn about Jaguar 2019 F Type First Drive of the Mercedes, Lexus, Cadillac etc.\nBy reading reviews concerning Jaguar 2019 F Type inside the top internet site like caranddriver, edmunds, carmagazine etc, you not only get the news of the new autos and latest engineering being used in the marketplace but you can in addition get information in the method to buy the vehicle.\nYou can find many ideas on the topic jaguar 2019 f type, 2019 jaguar f type svr review, 2019 jaguar f type svr, 2019 jaguar f type for sale, 2019 jaguar f type release date and many more on the internet, but in the post of we have tried to select the best visual idea about You also can look for more ideas on category apart from the topic .\nFind out the most recent images of Jaguar 2019 F Type here, and also you can get the image here simply image posted uploaded by Kay Becker that saved in our collection.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Performs work in construction management, programming\/base development, and\/or operations and maintenance (O&M) functions. Monitors\/manages construction projects for new construction, renovations, and improvements to real property facilities from start to finish, including the performance of pre-construction site surveys all the way to completion of as-built drawings. Performs requirements programming in support of base development to include validating requirements to be performed by others, performing economic analyses, and coordinating with the installation facilities board. Performs a wide range of engineering duties surrounding O&M functions to encompass the maintenance, repair, upgrade, and operation of a variety of infrastructure facilities and utilities. Provides management, planning, development, organizational, administrative, and coordination services for all base real property programs.\n10. Performs detailed pre-construction site surveys. Prepares or reviews as-built drawings at the end of construction. Contractor shall meet deadlines set by the Chief of Engineering with not more than 1wo (2) missed deadlines per month.\n11. Maintains surveillance over construction contractors to ensure overall compliance with contracted specifications, schedules, etc.\n12. Assists in evaluating construction bids. Develops and\/or reviews specifications and schedules for utility services for the construction period. Inspects and\/or oversees inspection of construction. Prepares\/reviews change orders prior to contract modification. Maybe involved with the Judge Advocate General's office on contractor performance problems and provides recommendations. Each inspection report and change order contains all data and is approved by the Chief of Engineering with not more than two (2) missed deadlines set by the Chief of Engineering per month.\n13. Provides management, planning, development, organizational, administrative, and coordination services for all base real property programs. Reports to the COR who oversees the overall planning, direction, and timely execution of program activities.\n14. Develops project plans for each program, identifies short- and long-term goals and objectives. Determines resource requirements and prepares written plans and schedules. Incorporates federal, USAF, Host Nation, and local regulatory requirements into program design, implementation, and evaluation.\n15. Reviews and updates all applicable AEWI regulations and Base Plans annually. Coordinates and updates all applicable AEWI regulations and Base Plans with squadrons, groups, and tenants every two years from previous document date. Ensures all published regulations are published to the Base Publication webpage through the webpage content administrator.\n16. Incorporates CE Transformation Initiatives.\n17. Manages all space utilization requests and issues. Determines use of all land, space in buildings, and other facilities both on and off base. Conducts extensive space utilization surveys and analyzes all space requirements for compatibility, conformance with allowable criteria, recommends changes and advises leadership on appropriate actions.\n18. Uses computer\/ computer software such as information management programs ( e.g. Microsoft Office), computer aided design and drafting (CADD) programs (e.g., AutoCAD, and project tracking programs (e.g. Microsoft Project) and other engineering design calculation software packages to solve engineering problems with solutions presented to the COR in order to facilitate work.\n19. Complies with health, safety and environmental rules and procedures and performs work in a manner that enhances the safety of the work environment. Ensures deferral and local codes concerning health, safety, and environment are strictly adhered to in the programming, design, and construction of real property facilities.\n20. Understands and abides by the standards set forth for ethical behavior and integrity as detailed in the Code of Business Conduct.\n21. Performs all other duties prescribed by management and as indicated in the Performance Work Statement.\nCandidates for this position must be a degreed electrical engineer with a minimum of 5 years of design experience and be capable of providing electrical design services including power load determination, exterior electric, interior electric, and site lighting.\nBe able to provide WGT 424 certificate of completion or equivalent.\nMust have a bachelor's degree in Electrical Engineering with at least five years of experience in the field. In addition, must have five years of USAF Real Property experience and an understanding of ACES-RP software. Working knowledge of Microsoft Office software is required, demonstrated by the ability to create spreadsheets and other written communication. Must be familiar with Air Force publications in related engineering and real property fields, AF records, reports, and communication standards. Prior experience working in developing countries is a plus. Must be a U. S. citizen with a valid passport and U. S. driver's license. You will be required to obtain a country visa meeting the health requirements for the country. You must be able to obtain a USAF flight line driver's license and an international driver's license.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbhdph b/data_all_eng_slimpj/shuffled/split2/finalzzzbhdph
new file mode 100644
index 0000000000000000000000000000000000000000..700986874d5e2f9042bd3f2a9c5ba50e4c1668ec
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbhdph
@@ -0,0 +1,5 @@
+{"text":"WWE (NYSE: WWE) today announced that its digital subscription service, WWE Network, reached a record 1.95 million total subscribers following last night's WrestleMania\u00ae.1 This is a 7% increase from April 4th, 2016, the day after WrestleMania last year.\nDuring the first quarter 2017, the rise in WWE's stock price resulted in an increase in stock compensation expense. Based on this increase and the timing of other items impacting our results, the Company currently expects (subject to the completion of its quarterly close process) that its Adjusted OIBDA for the first quarter 2017 will be $3 million to $5 million below the previously estimated range of $23 million to $27 million. The Company anticipates that these timing elements will reverse over the coming months and is maintaining its full year Adjusted OIBDA target.\nWWE is unable to provide a reconciliation of first quarter guidance to GAAP measures as, at this time, WWE cannot accurately determine all of the adjustments that would be required. The Company is evaluating certain items for the first quarter 2017 including film impairments which (subject to the completion of its quarterly close process) may result in reconciling adjustments. Further information regarding such reconciliations can be found on page 6 of this release.\nQ2 2017: If the acquisition and retention of subscribers driven by WrestleMania is consistent with the subscriber activity associated with the prior year event, the range of average paid subscribers for the second quarter 2017 would be 1.63 million (+\/- 2%), representing an increase of approximately 8% from the second quarter 2016.5 As future subscriber performance may differ from prior activity, this range is provided for perspective rather than as guidance.\n(4) Social media fan engagements are defined as the cumulative fan response to WWE content measured by the number of likes, comments, shares, reactions, mentions, favorites, screenshots and replies across Facebook, Twitter, Instagram and Snapchat.\n(6) WWE is unable to provide a reconciliation of forward looking guidance to GAAP measures as, at this time, WWE cannot accurately determine the adjustments that would be required. Further information regarding such reconciliations can be found on page 6 of this release.\nAs noted, WWE CFO George Barrios and Michael Weitz are currently conducting a post-WrestleMania 33 conference call, and during the call Barrios revealed the WWE Network now has 1.949 million subscribers with 1.661 million being paid subscribers.\nThe total number of domestic subscribers is 1.452 million with 1.257 million of those being paid.\nAdditionally, there are 497,000 international Network subscribers, and 424,000 of those are paid.\nWWE announced back in February that WWE Network had 1.5 million paid subscribers as of January 31st, 2017.\nWWE Network Updated Subscriber Count Revealed, Did It Hit 2 Million?\nWWE Chief Strategy & Financial Officer George Barrios announced on today's post-WrestleMania 33 conference call that the WWE Network now has 1.949 million subscribers with 1.661 million being paid subscribers.\nThe total number of domestic subscribers is 1.452 million with 1.237 million of those being paid. There are 497,000 international Network subscribers with 424,000 of those being paid.\nWWE announced back in February with their 4th quarter earnings report that the Network had 1.5 million paid subscribers as of January 31st, 2017. The Network averaged 1.41 million subscribers in the 4th quarter of 2016 - a breakdown of 1.1 million in the United States and 400,000 internationally. Barrios noted today that subscribers are up 11% domestically from the same quarter in 2016.\n0 Response to \"World Wrestling Entertainment (WWE) Says WWE Network Reaches Nearly 2 Million Subscribers\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"A rehearsal dinner is a great excuse to bring your closest friends and family together for a celebration before you say \"I Do\". It is a laid back opportunity for your friends and family to get to know each other as well as allowing you an intimate setting to mingle with your guests. There is no real set formula or pomp and circumstance. It can be as formal as a sit down dinner in a restaurant or as low key as backyard BBQ with food trucks. Whatever you choose to do it is important that it reflects who you are as a couple. Here are 8 tips to keep in mind when planning your rehearsal dinner.\nWhen choosing a rehearsal dinner location consider places that mean something to you as a couple. For example, hosting it at a local winery since you are wine enthusiasts or having dinner catered to your guests in your favorite art gallery. Select a venue that is a different style than your wedding. If your reception is in a hotel ballroom then consider having your rehearsal dinner outside or in a setting that has windows showing off a view of the city. Look into places that are unique to the city you are getting married in to enhance your guests wedding experience.\nIt is important to have fun while planning your rehearsal dinner. You might want to consider giving your rehearsal dinner a theme that represents you as a couple. Do you like to play games? Then have it at an upscale bowling alley or host a murder mystery dinner party. Do you want to pay tribute to your heritage? Then use your menu and d\u00e9cor to show where you are both from. Are you getting married on the coast? Then have an informal clam bake and bonfire while watching the sunset.\nWhen selecting your menu consider options that are different from your wedding menu. Create a menu or beverage that goes along with your theme or location. It is nice to use fresh ingredients that are local to the area that you are getting married. If you are getting married in the south serve a family style meat and three or serve tapas with wine pairings for a wine country wedding. Handpick a signature beverage from your local favorite brewery or distillery. Another nice touch is to incorporate your culture and use favorite recipes from both sides of the family. Honor your roots with your grandmother's key lime pie or your aunt's famous pie.\nUse your d\u00e9cor to bring your two families together. Display wedding pictures of your parents and grandparents, exhibit your family trees, present a friend\/family photo wall or slide show. Consider incorporating items that tell your love story in your centerpieces. For example, if you love to travel then use pictures or tokens from your travels on each of the dinner tables.\nThis is often the first time some of the bride and groom's family meet. Integrate various games into your party to help entice your guests to get to know each other and reduce awkward small talk. For instance, casino games, corn-hole, Jenga, bocce ball, bride and groom trivia, or personalized bingo.\nPlay background music that is sentimental to you and your families. Generate a unique playlist or hire a musician to play during your dinner. Consider playing music that represents your ethnicity. Perhaps, if you are Scottish have a bagpiper welcoming guests as they arrive.\nLeave the toasts for the rehearsal dinner and not the wedding reception. It allows you more time on the dance floor enjoying your favorite band or catching up with your guests during the reception. Plus, if Uncle Mike decides to get carried away with his toast it will just be among close friends and family.\nEncourage your guests to use your personalized wedding hashtag when posting photos throughout the weekend. This is a fun way for everyone to share photos and get to know each other. It will also allow you to capture moments that you might otherwise miss out on during your special day.\nAbove all have fun with it! The rehearsal dinner is really a gathering to allow your wedding party to celebrate you as a couple. Enjoy it, as it is usually the start to 24 hours of your life that you will remember forever.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"An account can be created by an adult with the diagnosis of primary sclerosing cholangitis (PSC), the parent or legal guardian of a minor or legally authorized representative of an adult patient with the diagnosis, or the caregiver of a deceased PSC patient. For the registration, we will ask a series of questions to confirm your participation and will ask for the name of the account holder. The account holder will create a username and password for the account which are needed to log into the account in the future. The answers to the communication questions may be changed at any time in the future by logging into your account.\nAfter creating an account, you can complete the profile. First, enter the name and information for the person with the diagnosis (participant). Next, complete the survey about the participant's diagnosis, medical history, etc. Once completed, the account holder will be able to add other family members with PSC and complete a survey for each one. You can log out at any time and your answers will be saved. You can log in later to complete your answers.\nPlease note that you do not have to answer all the questions. \"Unknown\" means you do not know the answer.\nFor the purpose of this document \"I\" and \"you\" refer to the registrant, either the individual affected by primary sclerosing cholangitis (PSC) or the parent, guardian or family member providing the information on behalf of the affected individual (the person legally responsible for the care of the affected individual). \"The registry\" refers to the PSC Partners Seeking a Cure patient registry.\nAll of the following questions must be answered in order to participate in the registry.\nThe registry has been fully explained to me. I have read and understand the \"Understanding my Participation\" form and this \"Informed Consent Form\". I also know how to access both documents in the future if I want to review them. I have had the opportunity to ask questions of the Registry Coordinator.\nAll my questions have been answered to my satisfaction.\nI understand that my participation in the registry is entirely voluntary. Should I change my mind and wish to withdraw my data from the registry, I understand that I will be free to do so without having to provide any explanation.\nYour information will be saved in the registry using a code. The code is used so others don't know who you are. The registry has processes in place to protect your identity. The registry may share your coded de-identified information with other registries or databases, including the Global Rare Disease Patient Registry and Data Repository (GRDR). This information may be used for research or to plan clinical trials.\nI give permission for my de-identified information to be shared with other approved registries and databases.\nIf researchers learn anything notable about my condition, I would like to be contacted with this information.\nThe registry may get information about a clinical trial for which I might be eligible. I would like to be contacted with this information.\nIt is important that the registry information be up to date. We will contact you once or twice a year to ask about changes in your medical condition. We may also send you electronic forms to fill out each year. I give the PSC Partners Patient Registry permission to contact me with this information.\nThe participant is 18 years or older.\nConsent by the adult participant with PSC (if the person with PSC can provide his\/her own consent).\nPermission by Legal Guardian or Legally Authorized Representative (if the person with PSC is 18 years or older and cannot provide his\/her own consent).\nParent's permission for minor (if the person with PSC is under 18 years of age).\nLegal Guardian or Legally Authorized Representative for the participant with PSC that has passed away.\nIf the participant with PSC is between the ages of 7-17, he or she needs to read\/understand the Participation Assent Form and to agree to participate in the PSC Partners registry.\nNot applicable. The participant with PSC is not able to provide assent.\nNot applicable. The participant with PSC is over 18 years of age and is not required to provide assent.\nThe participant with PSC between the ages of 7-17, has read\/understood the information in the Participation Assent Form, he\/she agrees to participate in the PSC Partners Patient Registry.\nConsent: By checking this box, I (the patient, caregiver, legally authorized representative for an adult patient and\/or legal guardian for a pediatric patient) am indicating that I have read Understanding Your Participation and the Consent Form for the PSC Partners patient registry, that I understand the risks and benefits of participation, and that I agree to participate in the registry.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"In our society, there's a large emphasis on being the \"best\" in everything\u2014whether that's parenting a teen or being the top dog at work. It's normal for a parent to want their child to excel and succeed in every area, but when it reaches a certain level it can become one of the causes of depression in children. While many parents have children's best interests at heart, pushing a child to fit a mold of \"perfection\" can be extremely detrimental to their mental health. Recent studies have yielded disturbing results confirming this idea. Daily Mail recently reported on these results and their implications in how parents push their children.\nIn Singapore, a five-year study of primary school children was conducted. Researchers discovered that children with \"intrusive\" parents had a much greater tendency to over criticize themselves, which ultimately increased over the years. The researchers focused on \"maladaptive perfectionism,\" which is known as the \"bad\" form of it, in primary school-aged children. The results of the study were troubling. Children had the possibility of becoming fearful of making little mistakes and constantly blaming themselves for not being \"perfect.\" This specific type of perfectionism has the chance of developing into one of the causes of depression in children.\nIn the study, researchers studied 263 children and over half\u201360 percent to be exact\u2013showed self-criticalness classified as high and\/or increasing, while nearly 80 percent were shown to be considered high socially prescribed (others having unrealistically high expectations of them) perfectionists. Nearly 60 percent of the children had both.\nSingapore is a place that highly emphasizes academic excellence, which can often lead to unrealistic, harmful expectations of young people. This doesn't just happen in Singapore\u2013if the researchers were to study other countries (including the US), the results would most likely be similar. Overbearing, ridiculous expectations can be counted as one of the possible causes of depression in children, along with anxiety, stress, low self-esteem, and even suicide.\nAll parents want their child to succeed, but trying to have them fit a mold of \"perfect\" is unrealistic and damaging to their wellbeing. Parents should be supportive, give constructive criticism, and be proud when they accomplish something. Instead of saying, \"Did you get an A on your exam?\" say, \"How did your exam go?\" By changing the way we present expectations, children will stop feeling the need to be \"perfect\" and start feeling proud of their achievements.\nAsheville Academy for Girls may be able to help with the causes of depression in children.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Race #2 of the Super Sunday On-Road Series. Sunday, Feb 17. Doors open at 8am, tone at 11am.\nThe JConcepts Western Carpet Nationals. Signups are up at RCSignup.\nWednesday, Feb 13 \u2013 On-road practice and racing. Doors open at 1pm, racing starts at 630pm.\nThursday, Feb 14 \u2013 Off-road practice. Doors open 1pm-9pm.\nFriday, Feb 15 \u2013 \"Friday Fever\" Off-Road practice and racing. Doors open at 1pm and closes at 9pm.\nSaturday, Feb 16 \u2013 Super Saturday Off-Road practice and racing. Doors open at 9am, racing starts at 12pm.\nSunday, Feb 17 \u2013 Race #2 of the \"Super Sunday On Road Series\". Doors open at 8am, tone at 11am.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbhkpm b/data_all_eng_slimpj/shuffled/split2/finalzzzbhkpm
new file mode 100644
index 0000000000000000000000000000000000000000..709bca1012ba4d57904cb80db0f5895f829bed65
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbhkpm
@@ -0,0 +1,5 @@
+{"text":"Joaquim d'Souza and Hazel Sheffield In March, the Huffington Post published #SoldFromUnderYou, an investigation revealing that local councils are selling off billions of pounds worth of publicly owned property just to make ends meet. #SoldFromUnderYou was the result of a year of Freedom of Information requests sent to all 353 English councils by the Bureau Local, part of the Bureau of Investigative Journalism and reporting by journalists through the Bureau Local's network of local reporters. It came with a map, created by Joaquim d'Souza, allowing anyone to search the location of the 12,000 spaces that have been sold since 2014. Joaquim and Hazel Sheffield, who worked in collaboration with the Bureau Local on the project, will speak about how the investigation came together, how they created the searchable map, and what's next for the project. Seena Shah, Director of Marketing at PolicyMogul Seena is listed as a top 50 women in digital under 30 by The Drum. Her interest in change at Government level led her to her current role with PolicyMogul where she is Director of Marketing. Seena will be discussing how important it is to have diversity in those who influence policy and policy-makers, in order to create a politics that is truly reflective of society. Matt Chocqueel-Mangan, Policy Tracker & Vote for Policies Matt is an experienced agile coach and digital service designer, on a mission to create what he describes as a 'sustainable democracy'. Matt created Vote for Policies and more recently Policy Tracker which focus on transparency and accountability to increase participation.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Colorado Family Project is a lab based at the University of Colorado Boulder's Department of Psychology and Neuroscience. Researchers there have been looking at non medication treatments for bi- polar disorder. They are hoping to recruit up to 50 families which researchers will follow over the next 3 or 4 years to study the effectiveness of family treatment for youth with mood swings who have a family history of bipolar disorder. We hear from Dawn Taylor, one of the researchers involved.\nCU Depression Center from 321MEDIA PRODUCTIONS on Vimeo.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"A lovely trine floats in today between the Virgo Sun and Pluto \u2013 helps productivity especially in relationships. You might find things can be transformed today into something really good! So this can take the edge off any hot spots we had during the Scorpio Moon time. And our Sagittarius Moon adds a lightness to the day.\nShe is sitting on a cloud with her sword pointing to the heavens, the butterflies fluttering around her; she is holding her mask. This Queen of Swords is unmasked as she is our truth teller in the Royals or Court cards. She hides nothing. She tells it just as it is, no more no less and asks us to do the same knowing the truth will set us free. The butterflies signify transformation and our souls are truly transformed and free when we know and live our truth. A butterfly can be a heavenly wink from a soul who has passed. Her sword pointing to the heavens reminds us we with born knowing what every great spiritual master knows, we were born one with the Christ and Buddha, the God and Goddess inside each one of us. No matter what the media tells us, what great new thing has come along, or how others are positioning themselves, or what they think of us, or how many likes we have, this Queen has us re-remember our authentic selves and what we came here to do without distraction. So don't let anyone or anything take you off your great work and from being your authentic self this week.\nThis entry was posted in Astrology, Maggie Lukowski, Maggie Moon Tarot, Midweek Astrology and Tarot Reading, Midweek Tarot and Astrology Reading, Tarot and tagged astrology, Maggie Lukowski, Maggie Moon Tarot, Midweek Tarot and Astrology Reading, Tarot, Weekly Tarot Reading, www.youtube.com\/user\/maggiemoontarot\/videos. Bookmark the permalink.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The water at Hanuabada village has changed colour to a rusty brown in the past two weeks, causing concern among the people, especially Mary Oala, a woman leader for the Motuan people.\n\"The colour of the water has changed over the past two weeks, and we are not sure of what it is, but this morning there looks as if there were oil, and I assume that there must be an oil spill,\" said Ms Oala, a community member and women's representative in the Motu-Koitabu Assembly.\nThe people of Hanuabada suspect an oil spill somewhere is the cause of the change in the colour of the seawater surrounding the village.\n\"We are concerned and want the relevant authorities to come and test the water to find out what is wrong.\n\"As a woman leader in this community, I am not sure if it is safe for our children to fish and swim in it,\" Ms Oala said.\nHanuabada is the village on the northern side of Port Moresby Harbour, with houses linked by walkways above the sea.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Friends of the Sibelius Academy, the Sibelius Academy and the Yale School of Music commissioned me to write a new work for one to six strings to be performed as part of the Creative Dialogues series at the Santa Fe Chamber Music Festival in conjunction with Kaija Saariaho's visit and the American premier of her opera, Adriana Mater.\nI have written a great deal of chamber music for strings: two string quartets, a string quintet, a sextet, a duo for violin and viola, a work for solo viola and work for solo cello. Rather than repeat myself by writing a new string quartet (the next one needs to be a \"big\" piece, or another work all in harmonics, I chose a new direction. The String Trio is an intensely conceptual piece and, for me, an experiment: a series of high-pitched triads descend in rhythmic unison at varied rates for nearly ten minutes. The string writing is virtuosic in that three instruments play between four and five voices.\nIt was premiered at the Santa Fe Chamber Music Festival in July 2008. I have since withdrawn it for further revision and expansion. When complete, I imagine it will be 20-25 minute work in multiple movements.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbiurz b/data_all_eng_slimpj/shuffled/split2/finalzzzbiurz
new file mode 100644
index 0000000000000000000000000000000000000000..6cc744a635ada0b2d48aaeeaa5b717eac6dd272b
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbiurz
@@ -0,0 +1,5 @@
+{"text":"People seeking psychotherapy often turn to verbal therapists; dance\/movement therapists work in both the verbal and nonverbal realms using the body as a primary medium for expression and, like many psychotherapists, have private practices with individual clients. Dance\/movement therapists are also employed in psychiatric hospitals, mental health clinics, day care centers, developmental centers, correctional facilities, schools and rehabilitation facilities, working with a wide range of people and ages, in individual and group therapy. Dance\/movement therapy can also be used in couples and family counseling\/therapy.\nFor more information about dance\/movement therapy, please visit our national organization's website at www.atda.org.\nThe New York State Chapter (NYSADTA) runs under the auspices and authority of the American Dance Therapy Association . It adheres to its own by-laws, while maintaining the standards and ethics set by the national Association. Each year, NYSADTA engages in a variety of activities to support its work and provide appropriate vehicles for the exchange of information with colleagues and the general public. We hold several business meetings, present educational workshops and host events for our members and interested allied professionals.\nNYSADTA members participate in the annual, national ADTA conference both as presenters and as chapter representatives for important regional and national ADTA meetings. The chapter provides consumers of mental health with alist of qualified dance\/movement therapists for consultation, and students and recent graduates with a list of supervisors. For a list of supervisors and therapists, please visit our Directory page.\nSince 1979, with founding President Mary King, the NYSADTAhas been devoted to serving the needs of New York's dance\/movement therapists and the people they serve through education and promotion. After over thirty years of commitment, the New York Chapter has established itself as the largest chapter in the nation and one of the first chapters to be granted licensure in the United States.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"On February 3rd, 1990, a Queen was born again. On that date comedian Adele Givens made her professional stand-up debut at the Regal Theater in Chicago. Since that day comedian Adele Givens has not ceased to amaze her fans and peers alike. Almost immediately her peers dubbed comedian Adele Givens the Queen of comedy. The name stuck and it's no wonder, with such credits as Russell Simmons' Def Comedy Jam, The All-Stars of Def Comedy Jam, The Bad Girls of Def Comedy Jam and The Oprah Winfrey Show. Comedian Adele Givens has reigned supreme all right.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"You found the next clue:) Borrowed from some weird reminant from the AOL.\nCustomize online cards, invitations, and flyers that reflect your personal style -- for weddings, holidays, birthdays, and other meaningful events. Corina Marinescu. Follow. Again, that madness swept up unknown numbers of American citizens.Events Family Reunion Talk to Grandma in Asgard, (234,200) to gather.\nDo not use this option when working on a 3rd party computer (e.g., in an Internet cafe). Knigge now threatened to tell the world how much of the Illuminati ritual he had made up.Send pre-recorded prank calls to your friends from a disguised number, then download and share the recorded reactions on.\nThe Owl of Minerva perched on a book was an emblem used by the Bavarian.\nOverwatch League Tokens. sign up for Overwatch League update for tokens:.\nYou can use several browser windows for working with the Webmail.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Situated by the marina, Flamingo Vallarta Hotel & Marina offers comfortable accommodation in Puerto Vallarta. Guests can work out at the gym, experience local delicacies at the Mexican restaurant or simply soak up the sun at the outdoor pool. A great choice for anyone wishing to have the perfect balance of relaxation and access to explore the local area.\nThe hotel is located by the marina and is 2km from the beach.\nThe hotel is located 1.5km from Puerto Vallarta International Airport.\nStandard and Family Rooms are available at the hotel, all of which are bright, comfortable and feature air conditioning, a private bathroom, flat-screen TV, FREE Wi-Fi, a telephone, safe and a balcony or terrace.\nA delightful range of Mexican cuisine is served at La Palapa Restaurant, open from morning 'til night. Guests can also enjoy refreshing beverages at the bar.\nTake a dip in the sparkling outdoor swimming pool, surrounded by lush green gardens, and relax in the Mexican sun. Active guests can also make use of the on-site gym. Wi-Fi is available on the complex.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"A secret defence inquiry is examining the conduct of Australian special forces in Afghanistan and the alleged killing of at least two children by Australian troops, according to a special report by the ABC.\nAustralian special forces soldiers were reportedly moving through a remote area when they allegedly shot a young boy dead in Kandahar Province in 2012.\nThe source the ABC spoke to alleges the killing was never reported up the official chain of command, with the boy's body recovered by local villagers and retrieved by his family.\nIn a statement, an AFP spokesperson confirmed the matter had been referred to the ADF for investigation.\n\"On 2 September 2016 the Chief of Army Australia Defence Force (ADF) referred a matter to the AFP relating to an allegation of an unlawful killing by the ADF in Afghanistan in 2012,\" the statement said.\nIn April 2006, Chief of Army Lieutenant-General Angus Campbell said the slew of disturbing stories about the conduct of Australia's elite special forces in Afghanistan and elsewhere would be examined by an independent investigator.\nHe said a \"range of unsubstantiated, third-person, hearsay stories\" warranted \"deeper consideration, but independently\".\nIn May 2016, the Defence department revealed that three soldiers were charged over the death of six Afghanis because they allegedly threw a grenade into a room they knew contained women and children.\nA Defence ministerial submission, released under Freedom of Information, said the soldiers believed they were under insurgent fire but evidence indicated it was an Afghan national defending his home and family from attack in the middle of the night in February, 2009.\nBut charges of manslaughter against the three special forces personnel were dismissed on the grounds that soldiers had no legal duty of care to civilians during combat.\nDefence has also denied Australian involvement in an incident in Oruzgan province in 2006 in which a taxi was mistakenly fired upon, killing an Afghan civilian man, blinding a woman and seriously injuring a girl.\nIn May 2013, then Defence Minister Stephen Smith rejected concerns raised by Sydney-based advocacy group the Public Interest Advocacy Centre over allegations that Australian forces in Afghanistan mistreated Afghan detainees in their custody.\nThe allegations were put forward by Afghan detainees captured by the Australian Defence Force and held at a United States military prison near Bagram air base.\nMeanwhile Australia has committed an extra 30 troops to Afghanistan, taking its deployment to 300 Australian Defence Force personnel.\nThe ADF's presence in Afghanistan is due to expire in 2018, but Defence Minister Marise Payne says it is under constant review.\nThe Australian commitment to Afghanistan is known as Operation Highroad, which replaced combat operations in 2014.\nSince Australian troops were first sent to Afghanistan in 2001, 42 troops have died.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbjlpc b/data_all_eng_slimpj/shuffled/split2/finalzzzbjlpc
new file mode 100644
index 0000000000000000000000000000000000000000..eff7267dcd6cbce273e61fb8eb303422061d3900
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbjlpc
@@ -0,0 +1,5 @@
+{"text":"With She In app you can cinematography anything you concupiscence or so She In with you all over you may roam. With the app, you now join a planetary ownership of more than 30,000,000 trend lovers. With tens of thousands of stylish items and over 200 daily new arrivals, the She In app is your ultimate one-stop fashion shopping geographic area in your pocket.\nWhen it comes to hot girls and wet dresses and wet clothes, swish Bro has you covered. nix better than some wet girls in tight wet consumer goods to get your blood flowing. The chassis of a wet mamma in extraordinary tight restrictive vesture that is drenched wet is genuinely a sense modality to see!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"DAKH \u2014 First tour through America and Canada!\nFirst tour through America and Canada!\nHappy to announce the dates of the first Dakh Daughters tour through America and Canada!\nInformation about tickets on facebook, http:\/\/www.riotartists.com\/tour-dates\/ and other cites.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This car theme slot game by NetEnt has a futuristic look and it has 5 reels and 15 fixed paylines. You can play it on different devices and it promises an action-packed experience. It is the perfect game for all the game lovers who love cars and the thrills of racing. It gives the chance to race against other drivers and win some big prizes too.\nThis fast-paced game is bound to give you an adrenaline rush with some great features. These symbols can be used as a substitute for all the symbols except the Nitro and scatter symbol. The value of the Multiplier Wild is the number of the reel on which it lands. When you get 2 or more Multiplier Wilds on the same payline, they would be multiplied too. Free Spins feature is activated when you get 3 symbols on the second, third or fourth reels and you will be awarded 10 free spins. If you get 3 Nitro symbols, on the second, third or fourth reels, you will get some more free spins as well as overlay Multiplier Wilds. Nitro Collect Meter feature begins when you race against the first opponent Twitch. You move to the next level and next opponent Hamaki when you collect 3 Nitro symbols. You also get 4 free spins and an overlay multiplier wild at 1. You will face your next opponent Bruiser at the next level and get 3 free spins and an overlay multiplier wild at 2. In the final level, Bruiser remains your opponent and you get 2 free spins and an overlay multiplier wild at 3. You can win up to 120 times your stake and the Multiplier Wilds help to take the game to a high level. High speed action with a potential to win big is what makes Drive Multiplier Mayhem a power packed game.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Physical & Chemical Specifications: Moisture % total : 39..0 Fat : 34..0 Fat Dry Basis :50..0 PH as is 21C more..\nProcessed Cheddar Cheese Our Processed Cheddar Cheese are extremely delicious that also add t more..\nCheddar Cheese Thare Cheddar Cheese are processed using quality ingredients It are appreciat more..\nOur Company are lareted at the apex in the laret of the prominent Low Fat Cheddar Cheese Suppliers based in Mumbai.. Cu more..\nOur Company have all types of quality cheese for sell.. Our cheeses are well processed and we guarantee you quality f more..\nCheddar Cheese Sticks Our Company are providing our customer a wide range of Cheddar Cheese S more..\nThe Cheddar Cheese Manufactured Exported and Supplied by us are of the best quality.. The demand for our Cheddar Cheese more..\nCheddar Cheese Our range of Cheddar Cheese are rich in taste and has high nutritional values more..\nGet Best quotes for \"Cheddar Cheese\"\nI want to buy 'Cheddar Cheese'. Please send us your Products Price, details with best quotations.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This is a placeholder page for Matthew Sims, which means this person is not currently on this site. We do suggest using the tools below to find Matthew Sims.\nYou are visiting the placeholder page for Matthew Sims. This page is here because someone used our placeholder utility to look for Matthew Sims. We created this page automatically in hopes Matthew Sims would find it. If you are not Matthew Sims, but are an alumni of Seneca High School Seneca, SC, register on this site for free now.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbjsru b/data_all_eng_slimpj/shuffled/split2/finalzzzbjsru
new file mode 100644
index 0000000000000000000000000000000000000000..6882bb9ebbc68f044ec30100c64bdb6acace317d
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbjsru
@@ -0,0 +1,5 @@
+{"text":"Please Note: Trout Pass Bar is now closed, and the space is being transformed into the Salon by the Springs. Guests may now visit the new pool bar at Wilderness Lodge, Geyser Point Bar & Grill.\nIn a cute little cabin down by the water at Wilderness Lodge, you'll find some great folks serving up some cool libations and conversation. Relax by the pool, at the hot tub, or on the beach with a refreshing drink, or just visit with your friends and family in the seating area (in the shade!) behind the cabin and by the beach. Service is a consistent thumbs-up at this friendly location.\nStandard Disney cocktail menu plus two specialty beers on tap, Moosehead and Red Hook.\nOpen daily from approximately 11a.m.-8 p.m.\nDisney Food Blog Posts Mentioning Trout Passnothing found.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Screen Printing is used for both small and large designs and is only limited by the number of colours in the finished design.\nWe are able to print onto a variety of clothing materials by applying different printing techniques.\nWe can print upto 6 spot colours, matching any required colours with our pantone index matching system.\nWe can also print in four colour process and create half tones.\nSpecial effect inks are also available including glitter, glow, metallic, heat reactive and puff.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Current data on the use of drug-eluting balloon angioplasty to treat atherosclerotic arterial disease are limited but hold promise.\nThe mechanisms of coronary restenosis after balloon angioplasty include (1) acute vessel recoil, (2) negative remodeling, and (3) neointimal hyperplasia. Stainless steel stents have become the default therapy in percutaneous coronary artery revascularization and have largely eliminated the influence of recoil and negative remodeling on restenosis; additionally, drug-eluting stents have attenuated the component attributable to neointimal hyperplasia. Despite this, restenosis still occurs, as does stent thrombosis, and the concern of late stent thrombosis, primarily in drug-eluting stents, continues to linger. In this context, the concept of local delivery of antiproliferative agents without stent placement invites renewed attention.\nInvestigations aimed at catheter-based methods of local drug delivery date back to the pre-stent era, with the principal limitations being drug choice and delivery of the optimal dose, neither of which was sufficiently defined prior to the widespread acceptance and availability of stents.\nThere is no foreign body left behind in the vasculature, thus perhaps reducing the absolute requirement for potent, prolonged, dual-antiplatelet therapy to prevent stent thrombosis.\nIn contrast to drug-eluting stents, in which the active drug is delivered only to the arterial wall in contact with the stent struts (a minority of the total surface area of the treatment site), a greater vessel surface area could be exposed to the active drug.\nIn anatomic situations where stenting may potentially be problematic (ie, bifurcations with important side branches).\nStenting is not desirable due to vessel mechanics (significant arterial tortuosity leading to hinge points created by stents and\/or locations, such as the common femoral artery, popliteal artery, and axillary artery in which flexion and rotational forces may lead to metal fatigue and stent fracture) or exposure to external compressive forces (common femoral artery, superficial femoral artery, infrapopliteal artery, and axillary artery).\nA stent is not deliverable due to significant proximal tortuosity and\/or calcification.\nThe potential of cost savings may exist.\nThese potential advantages need to be balanced by the possibility that a suboptimal balloon angioplasty result and threatened vessel closure may necessitate stenting anyway. Additionally, in patients in whom acute recoil or later negative remodeling may be an important mechanism of restenosis (diabetic patients, for example), balloon angioplasty alone may be insufficient.\nWHICH DRUG, WHY, AND HOW?\nOur understanding of the spectrum of drugs that may be effective in this strategy is incomplete. The available literature has reported on the efficacy of paclitaxel in reducing neointimal inhibition, late lumen loss, and restenosis. The antirestenotic effect of paclitaxel on a drug-eluting stent platform has been well validated in randomized clinical trials1 and in several years of subsequent worldwide clinical use. The reason for the efficacy of paclitaxel when utilized as part of a balloon delivery system has been postulated to be due to its extremely hydrophobic\/lipophilic nature, allowing it to pass through the hydrophobic barrier of cell membranes,3 as well as its prolonged antiproliferative action despite brief drug exposure.4 In contrast, the relatively hydrophilic compound, reviparin, is delivered much less effectively.3 Although stents that elute rapamycin have also been demonstrated to be effective in reducing restenosis in randomized trials,5 it is unknown whether it would be similarly deliverable and effective in a drug-eluting balloon platform. In a porcine coronary overstretch injury model, zotarolimus-coated balloon angioplasty has recently been shown to reduce neointima proliferation (Bodo Cremers, MD, and Ulrich Speck, MD, written communication, May 2009).\nStudies suggest that after angioplasty with a paclitaxel-eluting balloon coated at 3 \u00b5g\/mm\u00b2, approximately 4% of the drug remains on the balloon, whereas 90% is released into the blood stream.8 In a porcine model, approximately 2% of the total paclitaxel dose could be detected in the vessel wall.3 In a rabbit study, paclitaxel could be measured transiently in circulating blood (up to 30 minutes) at a mean concentration of 35.5 ng\/mL at 5 minutes,6 which is 1\/100 or less of the peak concentration that may occur in patients being treated with paclitaxel for solid organ tumors.\nIn comparison, the commercially available paclitaxel-eluting stent is coated at a concentration of 100 \u00b5g \/cm\u00b2, or 1 \u00b5g\/mm\u00b2, which occurs on the stent strut surface and releases in a bimodal pattern that is largely completed over 4 weeks.\nA number of animal studies have demonstrated an apparent reduction in neointima formation after balloon angioplasty. In a rabbit model of carotid stenosis (created using transmural electrical stimulation), paclitaxel delivery through a porous angioplasty balloon resulted in a reduction in neointimal area (0.13 \u00b1 0.11 mm\u00b2 vs 0.29 \u00b1 0.18 mm\u00b2 for untreated animals; P < .05) and a lower degree of stenosis (14 \u00b1 11% vs 41 \u00b1 18% for untreated animals; P < .05).6 Also, by using a similar rabbit carotid injury model, local delivery of paclitaxel via a double-balloon delivery system reduced neointima formation. This positive effect was also noted even when bare-metal stent implantation was carried out at the target site, although the absolute magnitude of neointimal formation was greater after stenting compared with angioplasty alone (Figure 2).11 This reinforces the notion that stenting in and of itself induces a greater level of vessel injury than angioplasty alone. In contrast, in a porcine coronary model of deep metallic coil induced injury,12 paclitaxel delivery via a double-balloon catheter prior to bare-metal stent implantation did not attenuate neointima formation measured at 28 days.9 In a porcine carotid artery (no injury) model, paclitaxel-coated balloon (5 \u00b5g\/mm\u00b2) angioplasty prior to stent deployment markedly attenuated neointimal formation even with very brief (10\u201360 second) inflation times.13 In a porcine coronary model with oversized stent deployment (1.2:1 stent-to-artery ratio), a paclitaxel-coated balloon angioplasty resulted in a larger minimum lumen diameter and less late loss than in control animals, in animals treated with paclitaxel in the contrast medium, and in animals treated with rapamycin-eluting stents (Table 1).1 The variable response on neointimal inhibition in conjunction with stent implantation may relate to differences in methodology, including the arterial bed studied, animal species utilized, presence or absence of induced injury in the model, and perhaps, the method of drug delivery.\nTwo published trials, the Thunder trial15 and the more recently published FemPac trial,16 demonstrated similar advantages of paclitaxel-eluting balloon angioplasty in atherosclerotic lower extremity arterial disease. The FemPac trial included 87 patients with femoropopliteal disease who were randomized to paclitaxel-coated balloon angioplasty versus conventional angioplasty for lesions of approximately 6 cm in length. The trial demonstrated significant reduction in late lumen loss and angiographic restenosis 6 months, although follow-up angiography rates were only 69% and 81% in the treatment and control arms, respectively. Six-month TLR rates were also improved (9% vs 33%) and although the difference between treatment arms persisted at 18\u201324 months, TLR events continued to accumulate between 6 and 24 months of follow-up, serving as a reminder of the prolonged restenosis window that may be observed in noncoronary endovascular interventions.\nThe data that are currently available regarding the applicability of drug-eluting balloon angioplasty as a stand-alone clinical treatment strategy for atherosclerotic arterial disease are limited but hold promise. The data in both animal models and small human trials are concordant; neointimal hyperplasia is reduced, as are late lumen loss, restenosis, and repeat revascularization. Obviously, much larger clinical studies would be needed to support widespread adoption into clinical practice.\nHowever, some lingering issues need to be addressed. We must be cognizant of the fact that stents have allowed us, in almost all percutaneous coronary intervention (PCI) cases, to reliably achieve a good acute angiographic result and have substantially reduced the need for emergency coronary artery bypass grafting and repeat PCI within the first 24 hours, largely by reducing abrupt and threatened vessel closure that occurred after percutaneous transluminal coronary angioplasty. Even if a strategy of drug-eluting balloon angioplasty is convincingly demonstrated to reduce restenosis and TLR rates in large randomized trials, it cannot be expected to attenuate the risk of abrupt vessel closure early after angioplasty. Additionally, in lesions or patients with acute recoil or negative remodeling that may importantly influence restenosis risk after percutaneous transluminal coronary angioplasty, the presence of a stent may be critically important in reducing TLR rates.\nTherefore, if adjunctive stenting is employed after drug-eluting balloon angioplasty, which may be required in cases of suboptimal angiographic result after angioplasty, clinical trials are required to demonstrate that the benefit will persist. Some animal data have suggested the contrary in this regard,9 and this will warrant further investigation. The concept of \"geographic miss\" from the intracoronary brachytherapy era\u2014dilating or stenting outside the zone of radiation treatment, thus increasing the likelihood of repeat restenosis\u2014may also be important in drug-eluting balloon angioplasty, as suggested by the PEPCAD I data. The limited data for ISR are promising, but whether this strategy will prove effective for drug-eluting stent ISR is unknown.\nIn the coronary circulation, drug-eluting balloon angioplasty, if proven efficacious, likely holds the greatest promise for lesions in which stent deployment is technically challenging or unattractive (distal lesions in which stent delivery proves to be difficult, very angulated segments, small vessels, bifurcation disease). However, this treatment could prove useful in other lesions in which an excellent angiographic result can be achieved with angioplasty alone, obviating the need for stenting. Whether that will lead to a reduction in the cost associated with PCI is uncertain, but it is possible if stent utilization declines and the production costs of drug-eluting balloons are not prohibitive. Whether a drug-coated balloon is the best method of drug delivery (versus other strategies that have been described above) may also be debated; to be broadly applicable, any delivery strategy that is employed needs to be relatively easy to manufacture at a reasonable cost if it is to compete effectively with drug-eluting stents. Drug-eluting balloon angioplasty could also significantly impact the endovascular management of noncoronary atherosclerotic lesions in which restenosis remains an important limitation; also, the financial and clinical trial investment to test drug-eluting stent platforms has been insufficient. Femoropopliteal disease, in which stenting is less attractive anyway due to mechanical forces, is an obvious potential application,15,16 as would be complex renal arterial disease (bifurcations, small accessory arteries).17,18 These are vascular beds in which there is a dearth of good, randomized, sufficiently powered clinical trials and a relatively high rate of TLR that may allow for samples sizes that need not be as large as those required in coronary trials; therefore, these may be the areas on which to focus in designing drug-eluting balloon trials that are not cost-prohibitive.\nToxicities and side effects of paclitaxel at these doses for a brief duration of exposure should not be a significant concern, but will also have to be addressed in efficacy trials. Whether other antiproliferative agents can be delivered effectively in this manner is unclear, but may be moot if paclitaxel is proven to be reliably and consistently effective.\nThe concept of drug-eluting balloon technology is a potentially attractive option for some portion of coronary and noncoronary endovascular revascularization procedures, but further investigation needs to be completed to prove its benefit in a defined population.\nVerghese Mathew, MD, FACC, is Professor of Medicine, Mayo Clinic College of Medicine; Consultant, Division of Cardiovascular Diseases and Radiology, Mayo Clinic in Rochester, Minnesota. He has disclosed that he holds no financial interest in any product or manufacturer mentioned herein. Dr. Mathew may be reached at (507) 538-1469; mathew.verghese@mayo.edu.\nHalkin A, Stone GW. Polymer-based paclitaxel-eluting stents in percutaneous coronary intervention: a review of the TAXUS trials. J Intervent Cardiol. 2004;17:271-282.\nSpeck U, Scheller B, Abramjuk C, et al. Neointima inhibition: comparison of effectiveness of non-stent-based local drug delivery and a drug-eluting stent in porcine coronary arteries. Radiology. 2006;240:411-418.\nBaumbach A, Herdeg C, Kluge M, et al. Local drug delivery: impact of pressure, substance characteristics, and stenting on drug transfer into the arterial wall. Cathet Cardiovasc Intervent.1999;47:102-106.\nAxel DI, Kunert W, G\u0161ggelmann C, et al. Paclitaxel inhibits arterial smooth muscle cell proliferation and migration in vitro and in vivo using local drug delivery. Circulation. 1997;96:636-645.\nSchampaert E, Moses JW, Schofer J, et al. Sirolimus-eluting stents at two years: a pooled analysis of SIRIUS, E-SIRIUS, and C-SIRIUS with emphasis on late revascularizations and stent thromboses. Am J Cardiol. 2006;98:36-41.\nOberhoff M, Kunert W, Herdeg C, et al. Inhibition of smooth muscle cell proliferation after local drug delivery of the antimitotic drug paclitaxel using a porous balloon catheter. Basic Res Cardiol. 2001;96:275-282.\nFanggiday JC, Stella PR, Guyomi SH, et al. Safety and efficacy of drug-eluting balloons in percutaneous treatment of bifurcation lesions: the DEBIUT (Drug-Eluting Balloon in Bifurcation Utrecht) registry. Cathet Cardiovasc Intervent. 2008;71:629-635.\nScheller B, Hehrlein C, Bocksch W, et al. Treatment of coronary in-stent restenosis with a paclitaxel-coated balloon catheter. N Engl J Med. 2006;355:2113-2124.\nOberhoff M, Herdeg C, Al Ghobainy R, et al. Local delivery of paclitaxel using the double-balloon perfusion catheter before stenting in the porcine coronary artery. Cathet Cardiovasc Intervent. 2001;53:562-568.\nScheller B, Speck U, Schmitt A, et al. Addition of paclitaxel to contrast media prevents restenosis after coronary stent implantation. J Am Coll Cardiol. 2003;42:1415-1420.\nHerdeg C, Goehring-Frischholz K, Zuern C, et al. Local catheter-based delivery of antithrombotic or antiproliferative drugs: a new concept for prevention of restenosis. Thromb Res. 2008;123:236-243.\nSchwartz RS, Huber KC, Murphy JG, et al. Restenosis and the proportional neointimal response to coronary artery injury: results in a porcine model. J Am Coll Cardiol. 1992;19:267-274.\nCremers B, Speck U, Kaufels N, et al. Drug-eluting balloon: very short-term exposure and overlapping. Thromb Haemost. 2009;101:201-206.\nScheller B. PEPCAD I and PEPCAD II. Presented at: EuroPCR 2008; May 13-16, 2008; Barcelona, Spain.\nTepe G, Zeller T, Albrecht T, et al. Local delivery of paclitaxel to inhibit restenosis during angioplasty of the leg. N Engl J Med. 2008;358:689-699.\nWerk M, Langner S, Reinkensmeier B, et al. Inhibition of restenosis in femoropopliteal arteries: paclitaxel-coated versus uncoated balloon: femoral paclitaxel randomized pilot trial. Circulation. 2008;118:1358-1365.\nMisra S, Sturludottir M, Mathew V, et al. Treatment of complex stenoses involving renal artery bifurcations with use of drug-eluting stents. J Vasc Intervent Radiol. 2008;19(2 Pt 1):272-278.\nMisra S, Thatipelli MR, Howe PW, et al. Preliminary study of the use of drug-eluting stents in atherosclerotic renal artery stenoses 4 mm in diameter or smaller. J Vasc Intervent Radiol. 2008;19:833-839.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Lux-115 is a light poly\/cotton fabric with a plain weave. Due to the combed type of yarn this TC fabric is soft and smooth. It is very versatile fabric, it shows a good performance in a wide range of service sectors as well as in medicine. It is suitable for shirts, trousers, coats and tunics.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Vintage 1930's gold over silver coin necklace composed of 8 George V British coins linked to create the center and completed with chain. Not marked, carefully tested.\nNecklace measures 19 1\/4\" long, it is in excellent condition. Closes with an early type of spring clasp which has a ring for opening instead of a tab.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzblrdh b/data_all_eng_slimpj/shuffled/split2/finalzzzblrdh
new file mode 100644
index 0000000000000000000000000000000000000000..cb35fc842b17f3f922254dcb8120a883c140c3f7
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzblrdh
@@ -0,0 +1,5 @@
+{"text":"Meter Self Adhesive-Sticky Back Laminating Pouches are suitable for use in all quality hot Laminating Pouch Machines. Sticky Back pouches give a high gloss finish and are photographic quality.\nGreat for creating Instruction & Warning Signage.\nSimply laminate document normally then remove backing sheet and stick on nominated flat surface. Instant signs in seconds.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"developed by celeb chef Anton Edelmann. British seasonality will be the prevailing culinary theme, whether you are after lunch, afternoon tea or dinner, & the food will be supported by a wide-ranging drinks list including English ales, cider & wines. The nearby Museum Caf\u00e9 will offer easy daytime nourishment (pastries, salads, deli sandwiches & hearty plates), plus a juice bar & barista coffee counter.\nMediocre food, slow and disparate service due to event going on elsewhere (not mentioned when we booked). menu very different to online sample. Boring, not particularly seasonal (their key selling point!), ungenerous. Atmosphere quite bleak in evening. Difficult to get to after museum closes. Wouldn't recommend, you can def get better fare in London for this money.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Bring your child to the dentist after their first teeth have erupted at approximate 24-36 months, unless a problem is suspected. The primary goal of the first visit is to let them become familiar with the surroundings and meet Dr. Dater and his staff.\nMouth Rinse Choices-Which is the Right One?\nMaintaining proper oral hygiene not only includes flossing, brushing daily, and regular dental checkups, but also making sure you change your toothbrush on a regular basis. There are a variety of factors that go into the deterioration of a toothbrush.\nPorcelain Veneers vs. Full Crowns - What's the Difference?\nWhen to Start Flossing Baby Teeth?\nWhile you can ensure that your child is eating nutritious food and taking care of their teeth at home, it's hard to make sure that they're doing the same thing at school. Here are some tips to packing healthy school lunches for your child.\nEver noticed a round, white spot on one of your teeth, specifically one of the front teeth? Well, you're not alone. There are many people that develop these unwanted spots, but the important part is understanding what's causing them.\nHave you been noticing that your pearly white smile is looking a little dull? Many types of food and drinks may cause your teeth to become discolored over time. Foods high in acid and those that contain tannins may be the culprits.\nWhy Are My Teeth So Sensitive to Hot & Cold?\nWhy Do I Have a Loose Permanent Tooth as an Adult?\nYou're pregnant - congratulations! There are many changes that expecting mothers have to make, and one of those is how they approach their dental care. I've put together a list of top dental tips to help guide you during your pregnancy months.\nThere are a lot adjustments people need to make when they get braces, and flossing is no exception. If you struggle flossing with your braces on, here are some simple steps to follow to make the process easier.\nIt's common to hear of someone being allergic to things like pollen, dust and pets, but toothpaste? Believe it or not there are thousands of Americans that may have some sort of sensitivity or allergy to certain toothpastes.\nNot only is dental floss a necessary item used in your daily dental hygiene routine but it can be used in a pinch for numerous other things. Dental floss is something you get from your dentist each time you get your teeth cleaned, usually every six months.\nWisdom teeth removal can occur at a broad range of ages, and is an important decision for every patient. Read through these tips to know when and why you should remove your wisdom teeth, as well as why you may not have to remove them at all.\nWhat's the Difference Between Dental Sealants & Dental Fillings?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Overlook milk chocolate molded into infantile candy bars. trendy chocolate sweets use chocolates with high cocoa content and less sugar then formerly available and are molded into pretty decorated pieces of artwork. once only on hand to pastry cooks and candy makers, home cooks can now buy high-give up domestic and imported candies of their local specialty shops. The latest availability of bittersweet chocolates coupled with our access to a worldwide grocery store and particular ingredients has created an increased interest in artisanal goodies.\nDrew Shotts has been at the leading edge of this renaissance due to his bold use of precise flavor mixtures no longer normally related to goodies, together with chili peppers, maple syrup, and spiced chai tea. Making Artisan chocolates suggests readers how to recreate Drew's sudden flavors at home via the usage of herbs, vegetation, chilies, spices, veggies, end result, dairies and liquors.\nAndrew Garrison Shotts, former pastry chef for Guittard Chocolate and owner of Garrison Confections, has broken new ground in the chocolate industry with the development of his artisan chocolate line. Shotts has accumulated a wealth of prestigious honors during his career. He was named one of Pastry Art & Design's \"Ten Best Pastry Chefs in America\" and was recognized as a \"Top Ten Artisanal Chocolatier\" by USA Today. His numerous television appearances include CBS's The Early Show, and Food Network's Food Nation and Follow That Food. Drew resides in Providence, RI.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Performance similar to PD pump.\nFor applications requiring higher pressure or vacuum.\nProvide constant flow of air at varying pressures.\nParticularly suitable for bulk collection, pneumatic conveying, aeration, fluidization and applications with long run pipe work.\nDon't forget, specials can be re-engineered or manufactured to your requirements.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzblxuc b/data_all_eng_slimpj/shuffled/split2/finalzzzblxuc
new file mode 100644
index 0000000000000000000000000000000000000000..4dd651cf23a8ed7f54575da7ee9a57d347d46483
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzblxuc
@@ -0,0 +1,5 @@
+{"text":"COSTA, Yuri Daniel Jatob\u00e1; BUENO, Benedito de Souza; VIANA, Paulo M\u00e1rcio Fernandes; COSTA, Carina Maia Lins. Deflections of geopipes undergoing loss of support. Anais.. Roseville: IFAI, 2008.\nCosta, Y. D. J., Bueno, B. de S., Viana, P. M. F., & Costa, C. M. L. (2008). Deflections of geopipes undergoing loss of support. In Proceedings. Roseville: IFAI.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"You may have seen this already, but it might still be of interest to those who havent.\nIt's a company called Solar Roadways who have designed a hexagonal solar panel that can be used as a road surface. It can be used to provide different lights, power nearby buildings, release heat to eliminate ice from roads, alert you to animals on the road to name but a few.\nAs this could be what we drive our minis on in the future, worth a quick look at the least!\nPersonally, I think it's a class idea and I can see it's potential for safer, efficient roads in the future.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"When you subscribe to my blog, I'll immediately send you my e-book, Grow Strong: 30 Devotions to Deepen Your Christian Life.\nIn order to grow strong, you have to grow deep in the essentials. This book will take you there.\nYou'll also receive fresh content directly in your inbox each time I post. That way, you can get my new posts without having to visit my blog all the time. My goal is to give you practical content to encourage you in your relationship with God.\nOnce you subscribe, I'll immediately email you a link to download my brand new e-book\u2014FREE.\nHave you read my e-book? Please leave a comment below.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"WELCOME TO OUR NEW R2 FIESTA RALLYPARTS WEB SITE , WHERE YOU CAN BUY NEW AND USED FORD FIESTA R2\/R2T PARTS ONLINE.\nWe Have been building and developing Ford Fiesta R2\/R2T Rally Cars for the last five years , you can now buy new and used parts in our online shop . We can supply a complete build kit or indvidual parts . We are a official distributor for M Sport Fiesta R2 and R2T parts . If you have a MSport part number just put it in the search bar , if you dont see what you need just contact us , by phone or e mail .\nFor limited time free postage within the uk.\nWe can also carry out full Engine and Sadev Gearbox rebuilds and Build Complete R2 Rally Cars to your specification contact us for more info .\nCheck out the online store for new and used parts if you cant see what you want just let us know and we will supply it for you .","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Commutable from areas as Hailsham, Bexhill, Hastings, Eastbourne etc.\nThis practice is rapidly expanding with aspirations to make high quality NHS And private dentistry.\nMonday to Fridays from 9am-5pm, however the practice will also consider part time applicants.\nPractice are very negotiable on hours\/days.\nPractice have around 500 UDAS per month, 6000 UDAS on offer for the year.\nFull Time Private target a month is \u00a33k, once this is achieved candidates will get 50% of the private.\nAnything over \u00a35k this increases to 55% for everything above 3k.\nPractice will also offer a bonus of 2.5% up to 10% of the amount above the private minimal target above the normal 50% as a bonus.\nAll Lab bills will be split 50\/50.\nEstablished list to take over from, only a few new patients.\nThis is a busy practice, windowed with staff room available, equipped with Digital X-rays on site and computerised using R4. Practice has been recently refurbished with new equipment to take advantage of.\nAs well as General Dentistry, the practice also cover Crowns, Cleaning and Preventative dentistry, Root Canal, Veneers, Fillings, Aesthetics, Children's Dentistry.\nCandidates will have the opportunity to do VT\/VTE Training but must be qualified as an associate for 5 years plus. Extra income for this.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbmixv b/data_all_eng_slimpj/shuffled/split2/finalzzzbmixv
new file mode 100644
index 0000000000000000000000000000000000000000..c4bd3610c1d5ff989a559d99d0eed4c793d13c3a
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbmixv
@@ -0,0 +1,5 @@
+{"text":"What do GMOs and Chemtrails have to do with your life (and death)? A great deal.\nIt turns out that heavy metals, one of the constant constituent poisons of chemtrails, are great at inducing \"horizontal gene transfer\" or the movement of foreign genes into your own DNA.\nDrRima.steth Where do the foreign genes come from? All those untested, unleashed GMO crops that are contaminating our farm lands, our animal feed and our food.\nRather than neat little puzzle pieces that only fit where there is an opening for them, inserted genes are unruly, disruptive and disrupted information bits. They have been, literally, shot from guns into the genetic material of another spcies and have no place in which they fit within the genes of their unwilling (and unsuited) host.\nThey move from place to place inside the genetic package of the cell's nucleus, and, as they do so, they change the genetic activity of the genes nearby.\nIn addition, additional genes beside the ones that are supposed to safely [SIC!] and predictably [SIC!] confer desireable [SIC!] traits to the engineered organisms are introduced into these organisms. Antibiotic resistance genes, for example, make it easy to test for the presence of modified cells, but also make the spread of antibiotic resistence so wide that more and more diseases can no longer be treated by antibiotics, creating novel and potentially devastating man made epidemic potential of unthinkable proportion..\nHorizontal Gene Transfer takes place when genetic material is introduced into cells without reproduction. Bacteria do it all the time, even across species. And they handle it quite well most of the time.\nBut mammals do not unless they are under significant toxic stress from heavy metals, for example, or heat shock.\nThey produce severe weather conditions including drought and extreme heat so that both mammals and plants are toxic and stressed.\nThe evidence is mounting that stress and heavy metal in the presence of \"loose genes\" and promotor viruses are causing potentially cataclysmic changes to the genome of \u2014 everything and everyone.\nLife is dependent upon soil bacteria, for example. Kill them or render them non-functional andfood production ceases, no matter how many toxic chemicals you pour on the soil.\nNo one has examined, and halted chemtrail spraying or GMO use because of, their impact on soil bacteria.\nBut the problem does not end there. You are dependent on the bacteria of your gut, skin and mucous membrane to provide immune and digestive services. What happens when they are disrupted by toxic metals and wandering genes? No one knows, but we do know enough to understand that the combination is anything but good.\nAnd your own cells? Your infant's cells? Your grandmother's cells? All at risk and all being experimented upon without your consent as if you were a lab animal or a slave, or an enslaved lab animal.\nThe time has clearly come for a halt to all involuntary experimentation: vaccines, chemtrails, GMOs, drugs, agrochemicals and increased radiation from irresponsible and fundamentally insane energy strategies like nuclear reactors.\nDieser Beitrag wurde unter AlienAgenda2029, Allgemein, Alliance\/Erm\u00e4chtigung\/Empower, Biochemquantum Warfare, Chemtrails, Collectivism\/Statism\/Dictatorship, Corporatistic Terror, Detection, Detox\/Medizin, Endgame\/Endzeit\/Endtimes, Genocide\/Migration, Gov\/Cults\/Sekten\/Religion, HAARP\/Weather Warfare, Kabbale\/Cabal, Mafia&State Crime, Multitoxifikation\/Umwelt, Nano\/DARPA\/Nasa\/DoD, News, Nwo-Matrix-Fence\/Fakes\/Corrupt Doctors\/Sleepers, NWO\/Agenda21\/Zion\/Fascism, Petrofascism, Pharma Mafia\/Military Terror vs Civilians\/TIs\/Electronic&Biogen Warfare, Politik, Public Counterintelligence, Strike\/Streik\/Protest, Synthetic Biology ver\u00f6ffentlicht. Setze ein Lesezeichen auf den Permalink.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Is Sadiq Khan's air pollution plan fair and proportionate?\nIn my recent report on air pollution in London, I argued that the new Mayor of London needs to create and deliver a more ambitious plan to clean up London's air. At the same time, I recommended that this should be done in ways which do not unduly penalise local residents and businesses; that coordinated action is needed at London, national and European level to tackle the problem; and that action is needed on both road transport and other sources of pollution.\nSo how do Sadiq Khan's proposed measures, outlined on the 5th July, stack up against these principles?\nThe new measures certainly are ambitious. In fact, the Mayor of London has himself described this as the 'toughest crackdown on the most polluting vehicles by any major city around the world'. But are the measures fair and proportionate? Or will they penalise residents and businesses?\nThe first proposal is for a new Emissions Surcharge (dubbed the 'T-charge') to be levied on more polluting vehicles entering central London from 2017. The charge would apply to all vehicles with pre-Euro 4 emission standards (broadly speaking those registered before 2005) and cost an extra \u00a310 per day on top of the existing Congestion Charge.\nAs currently defined, the T-charge would have a significant financial effect on a large number of motorists. TfL statistics show that around 5.8 million unique vehicles enter the Congestion Charge Zone each year, including 5 million cars (this includes all vehicles, whether they enter the zone daily or just from time to time), and 0.8 million vans, HGVs, buses and coaches. Using DfT statistics on vehicle age by type, we estimate that the T-charge would apply to around 1 million cars, and 0.2 million vans, HGVs, buses and coaches each year (before the effect of any change in behaviour to comply with the standards). For those who live, work or commute into the CCZ on a regular basis, the T-charge could result in a very sharp increase in travel costs. These motorists bought their vehicles in good faith \u2013 as for at least the last 15 years, Government has been promoting diesel vehicles on the grounds of their lower CO2 emissions. The air pollution impact of diesels needs to be acknowledged and dealt with, but the current proposal gives very little notice for the 1.2 million motorists affected to respond. This is likely to result in significant pushback from residents and businesses.\nThere are also issues in relation to the proposed emission standard \u2013 under which the T-charge would apply to all pre Euro 4 vehicles. On one hand, it is unclear why the cut-off for the T-charge is Euro 4, when Euro 4 and 5 diesels have higher NOx emissions than Euro 3 diesel cars (as shown in the chart below). Indeed, Euro 5 diesel cars have slightly higher emissions of NOx than pre Euro 1 diesels sold in the 1990s. On the other hand, the T-charge would apply to pre Euro 4 petrol vehicles, despite the fact that they have lower emissions than Euro 4 diesel cars which are exempt (e.g. 0.74g\/km NOx for Euro 2 petrol, 0.22g\/km for Euro 3 petrol, 0.96g\/km NOx for Euro 4 diesel). In fact, Euro 3 petrol cars have lower emissions than the average Euro 6 diesel cars sold today. Overall, the proposed emission standard fails to target the right vehicles, makes no sense, and should be re-thought.\nFurthermore, as currently designed, the T-charge could potentially have a disproportionate effect on poorer households and smaller businesses. Data from the National Transport Survey shows that car owning households in the lowest income quintile are nearly twice as likely to have a car over ten years old than households in the highest income quintile. Similarly, larger companies with corporate fleets and company car schemes are more likely to operate newer vehicles than smaller to medium sized enterprises. The distributional effects of the policy need to be considered further.\nThe second set of proposals relate to the ULEZ scheme. The Mayor proposes to bring forward the implementation of the ULEZ by one year, from 2020 to 2019. This is a positive move, since it means that the scheme will be implemented within the current Mayoral term. The GLA will need to think through the potential interaction between the proposed T-charge and the ULEZ, since in a sense the T-charge is an acceleration of aspects of the ULEZ scheme.\nThe Mayor also proposes to extend the geographic coverage of the ULEZ significantly. As currently defined the ULEZ would cover the same area as the Congestion Charge Zone, in central London. The Mayor proposes to extend the ULEZ from 2020 to the North-South Circular for motorcycles, cars and vans; and London-wide for lorries, buses and coaches (to the area covered by the Low Emission Zone \/ M25). This would significantly increase the number of residents, businesses and vehicles covered by the scheme. The Congestion Charge Zone covers an area of 21 sq km and includes a resident population of 136,000 people. The N-S circular covers an area of around 380 sq km, and includes of population of several million people (we are not aware of any exact figures). The London-wide Low Emission Zone is much bigger again at 2,644 sq km, including a population approaching 9 million people.\nThere are many roads outside the current ULEZ\/CCZ zone which are above the legal NO2 limits, and based on current plans would not come within these limits for a decade or more. At the same time, there are large areas within the N-S circular and M25 that are already well below the NO2 limit. The proposal to significantly expand the ULEZ may lead to changes to vehicles and travel patterns which are not required to meet compliance (i.e. where compliance has already been reached), creating an unnecessary burden on residents and businesses. Again, we would expect significant pushback on this proposal once stakeholders realise the implications.\nThere are also practical issues with expanding the ULEZ area, as highlighted in our recent report. Creating an additional charging zone (in addition to the existing CCZ and Low Emission Zone) could create confusion amongst motorists, and would also require investment in additional infrastructure such as an additional set of enforcement cameras. For that reason, we focused our recommendations on reforms to the existing emission zones, rather than creating new ones.\nAlongside the main air quality consultation, the Mayor has also announced plans to pedestrianise Oxford Street by 2020. Whilst cars are already banned on Oxford Street during the day, it is a major thoroughfare for buses and taxis, and is also Europe's busiest shopping street. It is amongst the most polluted roads in London, with NO2 concentrations around three to four times the legal and healthy limit.\nHowever, whilst pedestrianisation is hugely symbolic, it is not clear that it is the best or only solution. Closing Oxford Street will mean that all buses and taxis are diverted onto nearby roads, displacing the problems of air pollution and congestion elsewhere. The Deputy Leader of Westminster City Council has described this as a \"major problem\".\nAn alternative, as recommended in our report, would be to designate Oxford Street as one of a number of 'clean bus corridors' \u2013 a proposal which the Mayor supports. Under this model, only the cleanest buses would be used on Oxford Street (e.g. Euro VI hybrid, electric or hydrogen). TfL's own research shows that Euro VI buses are capable of achieving a 98% reduction in NOx emissions compared to Euro V buses. Hybrids could also switch to electric only mode in the most polluted and busiest areas \u2013 a concept known as 'geofencing'.\nIf further emission reductions are required, then TfL could also target the taxis using Oxford Street. Again, our report makes a number of recommendations, such as reducing the age limit for taxis, encouraging LPG conversion of the existing taxi fleet, and preventing pre-Euro 6 vehicles registering as Private Hire Vehicles.\nConsider the potential conflict between the GLA's decentralised energy target (which is encouraging the deployment of Combined Heat and Power boilers and biomass, amongst other things) and London's air quality plans.\nIn summary, we applaud the Mayor's ambition to tackle air pollution in London, but it needs to be done in a measured way, based on the best available evidence, and in a way which does not unduly penalise businesses and residents. That way the Mayor's plans are more likely to gain approval, and ultimately be more successful in the long run.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Three Shires Restaurant01432 299955work RestaurantWelcome to the Three Shires Restaurant at the Three Counties Hotel in the Cathedral City of Hereford.\nThe Three Shires Restaurant offers more than just a warm welcome.\nAn extensive menu using the finest local ingredients, including Herefordshire Beef, enables you to enjoy the choice from a wide range of traditional and international food. We have a large choice of select wines available to compliment any dish.\nWe are also able to offer private dinning for up to 40 people in the conservatory, located just off the restaurant, making it ideal for family gatherings or corporate dinners.\nNon-residents are very welcome in the restaurant. We open every evening from 6.30pm and last orders are 9pm. Bookings are advisable.\nNamed after the world's oldest and most well-known map, Mundi's Bar has an informal, relaxed atmosphere which makes it the ideal setting for residents and non-residents alike to enjoy their choice from a wide range of wines, beers, lagers and real ales. And, with over 800 orchards in the Wye Valley, you shouldn't visit Hereford without trying one of our local ciders!\nThe bar overlooks a pretty pond at the front of the hotel and outdoor seating is available.\nMundis is also the perfect meeting place for guests before a function.\nThe bar opens from 5.30pm Monday to Saturday and from 6pm on Sunday.\nWelcome to the Three Shires Restaurant at the Three Counties Hotel in the Cathedral City of Hereford.\nFrom Hereford City centre, take the A465 to Abergavenny - over the river bridge and right at the roundabout. Continue for approx. half a mile and we are on the right hand side (after McDonalds).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"What's an RA and an RD?\nThe RA builds a sense of community, enforces rules, responds to emergencies and acts as a liaison between the residents and the Office of Residential Life. An RA works closely with students, playing a part in event coordination, the planning and implementation of social, cultural and educational gatherings. An RA is also a tutor, and most importantly, a caregiver.\nIn addition to resident assistants, there are resident directors (RDs) who live and work in the residence. Resident directors are involved in the selection, training and supervision of the residential life staff. In addition, their duties include policy development as well as implementation and promoting programming efforts.\nWhere can I find by RA and RD?\nOne resident adviser (RA) is also assigned to each floor.\nIn addition, there is on resident director (RD) for men and women living in the residence.\nIn addition, there is one live-in resident director (RD) for men and one for women.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"TURBINA ENERGY AG is a company based in Unterhaching, near Munich, which specializes in the production and distribution of micro wind turbines (<20kW) as well as solar hybrid systems. Since 2006 a team of engineers has been developing small-scale wind turbine systems with a vertical axis and a stator, and, among other things, the first micro wind turbine that can be operated in both strong and light wind conditions.\nThe turbines \u2013 made in Germany \u2013 achieve a start-up speed of 1.5m\/s for electricity generation, which is the best value worldwide, and guarantee operation in wind peaks of up to 200km\/h. Unparalleled low noise emission values of 34dB(A) and safety for humans and animals provide installation possibilities with almost no restrictions. The installation on rooftops in residential and industrial areas can sometimes be carried out without prior formal permission, as no noise nor vibrations are generated whatsoever. A patented combination of rotor, stator and generator makes these unique selling propositions possible.\neCAPITAL invested in Turbina Energy AG via the eCAPITAL III Cleantech Fund in April 2014.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbmlmg b/data_all_eng_slimpj/shuffled/split2/finalzzzbmlmg
new file mode 100644
index 0000000000000000000000000000000000000000..01983d6adc30792944dff9db83ad7660b642ba6a
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbmlmg
@@ -0,0 +1,5 @@
+{"text":"AL Solutions are currently partnering with small data focused CRO based in the U.K who are seeking a SAS Programmer to join their team on a permanent basis. This position offers the flexibility to work from home or office dependant upon your preferences. My client can also offer excellent career progression, with the opportunity to progress into a senior position after a year.\nMaintain up-to-date knowledge of the external regulatory environment relating to programming, including ICH\/GCP requirements.\nProvide high quality deliverables and appropriate communication within expected timelines and budget.\nPerform Peer Review and Final Inspection.\nParticipate in meetings such as recruitment, business development and audits from a clinical programming perspective.\nDevelop and deliver SAS training and workshops and other programming related training sessions, as applicable.\nDetermine and enforce the appropriate standards for projects.\nPro-actively address changing timelines, priorities and resourcing requirements in line with appropriate issue escalation processes.\nQualified to degree level or equivalent, preferably in a numerate discipline.\nProgramming experience, preferably within the pharmaceutical industry or medical sector.\nStrong programming experience, preferably within the pharmaceutical industry or medical sector.\nProgramming experience covering activities from study set-up to final reporting.\nMy client would ideally like someone to start at the beginning of Q2, however they can be flexible to allow for notice periods for the correct candidate.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The years after high school were a time of continued education, pursuit of passions and maturing for Russell.\nWhether it was attending Central State Teachers College, entering contests showing his mechanical design skill or earning a certificate as a diesel mechanic, the interest in machines and making them work was a focal point in his late teen years.\nIn 1937, Russell entered the Fisher Body Craftsman's Guild \"dream car\" contest and won 2nd place for entrants from Oklahoma. The award included a ribbon, a certificate and a $75.00 prize. The car was displayed along with other entrants from across the country at the General Motors facility in Detroit. The model is pictured here.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Ray Roosevelt Williams, 77, of Pulaski, VA passed away Friday, February 1, 2019. He was born in Washington Co., VA on January 4, 1942. He was a retired employee of Pulaski Furniture Corp.\nRay was preceded in death by his wife, Alma Sayers Williams, his parents, Ray Williams and Lola Williams, his brothers, Charles, Donald, Bill, Ted and Jim Williams, all of Pulaski, his sisters, Charlotte W. Cross, Pulaski, Ruby Worley, Bristol, TN and his son-in-law, Robert G. Taylor.\nVisitation will be held Saturday, February 9th at Stevens Funeral Home where the family will receive friends from 1:00 until 2:00 PM, with a Memorial Service following. A private burial will be at a later date.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"(TAP)- CEO of the national carrier Tunisair Ilyes Mankbi stressed on Sunday that the disruptions in flights are due to the unexpected absence of pilots for material claims that are currently being negotiated with the administration.\nIn a statement to TAP, Mankbi described the pilots' demands as impracticable given the company's difficult financial situation, noting that a negotiation meeting is, however, scheduled for Monday with the union side to continue discussions on these demands.\nAccording to him, the company tried to find solutions to flight disruptions and even rented planes and formed a crisis cell, but it could not prevent disruptions on 3 flights on Saturday evening and 5 flights scheduled for Sunday, including one flight from Djerba airport, carrying foreign travel agency officials who came to Tunisia to sign contracts with Tunisian agencies to receive tourist groups.\nMankbi pointed out that the company is facing significant financial difficulties, pointing out that last February it managed to pay the salaries of more than 7,000 civil servants with great difficulty, knowing that the annual wage bill is estimated at 340 billion.\nThe CEO added that the company is currently unable to acquire new aircraft to improve its fleet, calling, in this context, on all employees and mainly pilots to support their company, particularly in this crisis.\nTunisair had issued a statement on Sunday morning in which it reported that flights experienced disruptions on Saturday and Sunday that will continue on Monday.\nThe company promised that 'every effort is being made to resolve this unexpected situation as soon as possible'.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Prostitutes Trichardt \u2014 these are professional, who know everything types satisfaction men.\nSexual kitty, waiting non-serious relationship of a sexual nature. Surprise me, dial my phone number and come to visit, I'll do anything, as you want!\nHere submitted profiles beautiful sluts Trichardt, thirsting to offer sexual services for given price.\nMost foreign men on the other hand, have no issues approaching a Japanese woman in English - or even in broken Japanese. Skank in the city of Trichardt - I was thinking of coming to Colombia to live for a bit or longer in the near future. Jobwise, I would look to do a computer job and teach English. Any input, dating and otherwise, would be greatly appreciated. Telephones of Hookers Eensaam If we meet tonight, you can t forget my service: I'm hot and horny I have pretty hot face and model figure, soft skin, long silk hair, very \u2026.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbmwtc b/data_all_eng_slimpj/shuffled/split2/finalzzzbmwtc
new file mode 100644
index 0000000000000000000000000000000000000000..c54577f51c0bf0ec256d5380133b0472356e31c8
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbmwtc
@@ -0,0 +1,5 @@
+{"text":"Enjoying authentic Hawaiian music at St. Anne's Church Festival in Waihee. Senior Pastor is Father Ramon, a Filipino, but most of his parishioners are Hawaiian.\nMy neighbors had been asking this question today when they saw the 40 ft. container in front of the house. What's going on actually is that Jay's furniture and belongings from Texas finally arrived in Maui for storage until he is ready to move in to a house in Oahu sometime in the future. The challenge is for this stuff (which came from a 3000 sq. ft house in Texas) will have to be crammed in to our double garage the next couple of days. Any bets?\nNorman, Reggie, Florence, Caroline and family vacationing in Maui for the the first time (except Norman).\nThank goodness, we have the pick up truck. They would have rented another car just for the luggage.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Department of AYUSH, Ministry of Health and Family Welfare, Govt. of India, New Delhi \u2013 F.No.R-17011\/39\/2014-EP(IM-1) dt. 10\/07\/2014.\nRajiv Gandhi University of Health Sciences, Bangalore, Karnataka \u2013 ACA\/AFF\/AY-02\/2014-15 dt. 26\/08\/2014.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Coach parties visiting the Wirral peninsula can conveniently park at some of the most popular attractions.\nFor a Mersey Ferries river cruise, park at Woodside Ferry Terminal. Mersey Ferries links a number of exciting waterfront attractions in Liverpool and Wirral, enabling you to create flexible days out for your group.\nPort Sunlight, a fascinating 19th century garden village, is a very popular group travel destination and home to both the Port Sunlight Museum and Lady Lever Art Gallery. There is extensive free coach parking adjacent to the Lady Lever Art Gallery, with the village attractions easily accessible on foot.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Well my horrorscope for today says basically that I just need to let the universe do its thing and not panic over it. I wanted to paste it here but firefox won't let me. Sometimes it does and sometimes it doesn't. I am really starting to get frustrated with firefox. I got a new space at msn spaces. I needed something new to have fun with. And I love Marty from rockstarinxs and all their blogs are on msn spaces. I put the link to his blog on the sidebar here. He is just awesome. I love Mig and Ty and Jordis too. Does any one else watch the show???\nI am dying to talk to someone about it. I don't like message boards though. I don't know why. I just don't care for them.\nAnyway, I got a very cool email today from somewhere here in wa. T Y crystalball!!!!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"As the tech industry continues to see blockbuster growth, entrepreneurs are brimming with ideas in hopes of inventing the next big thing. I started Aruba Networks in 2002, became chief technology officer in 2008 and helped facilitate its $2.7 billion acquisition by HP earlier this year.\nAs a founder, I'm often asked what it takes to guide a startup on a path for long-term growth. A great idea can only take a startup so far \u2014 in my experience, it is the following factors that determine whether a company will grow into a huge success.\nWhen you think bigger, you can grow bigger. Start by solving a niche problem, but expand your company's capabilities to solve a big problem. Aruba's vision was that Wi-Fi was going to transform the enterprise \u2014 and we were challenging Cisco in wireless networking, which was a billion dollar market at the time.\nAs your company continues to grow and evolve, you have to make strategic choices so you have the opportunity to solve more problems and stay relevant in the market. A big choice for Aruba was choosing to be acquired. As part of HP, we're able to expand our capabilities and target the $10 \u2013 $15 billion campus networking market.\nHaving the right team in place is important in any stage of a company's growth, but never is it more critical than after the initial funding round. That period is when the leadership team lays down the foundation for the company's future, and entrepreneurs need to attract and retain top talent to support growth.\nThat said, it's important to remain flexible, and know that the company's needs change as revenues start flowing in. At Aruba, once we built our product, we needed to create demand.\nAs a technologist, I knew I wasn't necessarily the right person to take on that challenge, so we decided to bring in Dominic Orr, who was chairman of the board at the time, as our CEO. Dom was instrumental in building Aruba's successful sales strategy and team, and continues to lead the business today.\nOften the biggest challenge for a startup is proving its viability. In 2005 we had the opportunity to provide the largest enterprise Wi-Fi network at the time for Microsoft. We knew we had the best technology, but needed to show that we had the ability to scale.\nTogether with Orange Business, along with our venture backers and board, Aruba won the deal. That was a defining moment for us, and gave us a ton of credibility.\nNew customers came to us knowing that if we could handle the Wi-Fi needs for Microsoft, we could handle almost anything.\nYour company's culture influences every interaction\u2014with your employees, customers and suppliers.\nThe founding team sets the tone, so be thoughtful and clear about what you'd like your company culture to be.\nAt Aruba, we are guided by a \"Customer First, Customer Last\" culture. Take the time to consciously build your culture, making your company a place where employees want to develop their careers.\nThis article first appeared on HPE Matter and was republished with permission.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbottr b/data_all_eng_slimpj/shuffled/split2/finalzzzbottr
new file mode 100644
index 0000000000000000000000000000000000000000..ac3d98ac4e3ca0d2995afe2b7615ef72cfb19bc9
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbottr
@@ -0,0 +1,5 @@
+{"text":"This inviting little volume includes thirty-three excellent photographs by Ernest Scheidegger and a famous, short text (around 45 pages' worth) by Jean Genet. I don't know the exact length, since the publishers, with typical French artistic pomposity, decided it would be beneath them to actually number the pages.\nJean Genet was a writer, a poet, a contemptible liar and a thief. He was a friend of Giacometti's, an astute observer of his art, was portrayed by him several times, and stole Giacometti's best drawing of Matisse. (The drawing was never returned, but a stranger sold it back to Diego Giacometti sometime after his brother's death.) James Lord, the great art writer and Giacometti biographer, recounts the story of the theft in his wonderful book Some Remarkable Men, and describes Genet as \"vain, mendacious, imperiously unprincipled\u2026and an eloquent champion of ideals which he did not believe.\" But he adds that Giacometti was extremely fond of this little book and that Picasso considered it one of the finest ever written about an artist.\nIn Giacometti's studio, \"a man is dying slowly, consuming himself, and before our eyes, transforms himself into goddesses.\" The goddesses are Giacometti's sculptures of women\u2014or more properly, the women themselves, since Giacometti's whole life was a struggle to compress into painting and sculpture the same force of existence, the same impression of \"thingness\" he found in life itself. Watching him work, Genet writes, \"I have the moving spectacle of a man who never makes a mistake and yet constantly loses.\" Giacometti would have been the first to admit\u2014in fact, admitted all the time\u2014that he was doomed to fail. His relentless struggle made him one of the greatest artists of the 20th century.\nL'Atelier d'Alberto Giacometti, by Jean Genet. L'Arbal\u00e8te, 1963. Who knows how many pages.\nNote: This book is in French; any awkwardness or inaccuracy in the translations is my fault.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Let's face it, everyone loves to talk about themselves. There's nothing more annoying than that friend who calls you to brag about what they're up to, ask for advice, and then hang up without ever asking you about what's going on with you. If you know the kind of person I'm talking about, you know you don't want to resemble their lopsided conversational skills- especially during an interview. The best way to avoid it is by asking questions back to your interviewer when appropriate. Asking your interviewer questions not only gives them a chance to talk about themselves, but also can show your sincere interest in the company. However, asking the wrong questions could probably cost you the job.\nDo: Ask what you'll be doing more specifically.\nAsking specific questions about what you're interviewing for will show that you have a genuine interest in the position and looking to learn more about it.\nDon't: Ask questions you should know the answer to.\nBefore an interview, you need to do your research. These questions along with many others are most likely explained on the company's website, so don't waste your interviewer's time asking them. Instead, you can show that you did your research by asking a specific question about this information. For example, \"Is your firm looking to expand into other services other than just personal injury representation?\" shows your interviewer that you know what they do now, and you are interested in the future of the company.\nDo: Show deeper interest in the company beyond just what they do.\nQuestions like this show that you're interested in the success of the company, past and future. Many interviewers will love to talk to you about how the company has gotten to where they are today and what they're focusing on going forward; these questions will probably make them more comfortable and interested in your interview.\nDon't: Ask about specific company policies for self-serving reasons.\nThese questions do not show a genuine interest in the company itself, but rather show your interest in yourself and your benefits. When interviewing, you want to give the impression that you are interviewing with them because you believe in the company, not just that you need a job with the best benefits. While many of these questions are important, it's best to save them for after you're offered a position and before you accept.\nDo: Ask about your interviewer.\nAs stated earlier, everyone enjoys and feels comfortable talking about themselves. Asking your interviewer these questions will help you both relax, improve the flow of the conversation, and make the experience more enjoyable for both of you.\nDon't: Bombard them with a list of questions.\nWhile asking questions is definitely the way to go during an interview, you don't want to list off a ton of questions just for the sake of asking questions. If the conversation is going well and the interviewer is continuing it along, go along with it. If he\/she seems to be trying to wrap up, or if asking more questions feels forced, say thank you and finish your interview. A good rule of thumb is to show up to the interview with four to five prepared questions with anticipation of asking two of them. Sometimes they will answer all the questions you bring during the actual interview, which is why you should show up prepared with back-up questions just in case. If the conversation leads you to asking multiple questions, that's okay too. There is no \"sweet spot\" number of questions that's the best for an interview because every interview is different, just make sure you ask some questions to show your interest and follow the flow of the conversation!\nInterviews are tough. Every component seems to have unwritten rules, and your response to being asked \"Do you have any questions?\" is no exception. Show up prepared, ask the right questions, let your interviewer talk, and follow the flow of the conversation. It's your last chance to impress them before you leave, so make sure to go out on a good note!\nWhat kind of questions do you like to ask in an interview? Let us know in the comments!\nThis entry was posted in Job Seekers and tagged interview advice, interview tips, Job Hunt, Job Interview Advice, Job Interview Questions, Job Search Advice, tips for job seekers. Bookmark the permalink.\nThank you so much for sharing question about Do's and Don'ts in an interview.\nExcellent tips prior to interview. Thank you.\nThanks that was helpful, now i just need the interview. I remember years ago that they said not to talk to much and do not discuss your family and children. So i believe that your right about asking them questions.\nHi Karen, While you should avoid personal subjects, as an interviewee you definitely are in the right to ask relevant questions and engage with your interviewer. After all, you are evaluating them as much as they are evaluating you!\nThank you so much for the information, However I wish that there was a way of getting more feed back from the interviewer as to why we did not get hired. That would help with the next interview so that you don't make the same error.\nHi Estrella, Applying lessons from past interviews is a great way to improve! It wouldn't be out of the question to follow-up with hiring managers to ask if they have any additional suggestions for you to help along the job search.\nThanks for the tips. Any tips on phone interviews so we can get the face to face ones.\nThank you for the input on the Do's and Dont's, this information will be very helpfu with my job interview.\nVery impressed with the Do's and Dont's tips for an interview. I will share them with my daughters for future interviews.\ncould you be too energetic on an interview?\nHi Mason! While you can't control people's preferences, it's never a bad idea to show your enthusiasm during an interview. As long as you're doing so in a professional manner, it's important to express your interest with energy.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"On Solaris, you can use the RBAC features in two ways.\nOne is to create a role account and assign a rights profile to it. You can assume this role by using the su command.\nUX: usermod: John is currently logged in, some changes may not take effect until next login.\n# cat \/etc\/security\/exec_attr | grep \"Primary Administrator\"\nTo withdraw the root privilege, you just have to remove the primary administrator. No need to set a new root password.\nCompare with sudo, the door seems to wide.\nFirst, you need to create a rights profile in RBAC system on Solaris. You can either manually edit the attr files, or use \/usr\/sadm\/bin\/smexec to do it.\nIn example below, I want to create a profile can ru explorer to collect system information.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Description Bolt is fast as lightning and can run ahead of your other monsters to munch on buildings with its razor sharp teeth.\nBolt is a centipede-like monster. It has purple eyes, eight sharp fangs, and a forked tongue. It has a long, skinny neck that extends down to the front of its body. On that spot is a gaping hole that glows yellow. Its body is made of a dark blue skin, and it has twelve skinny legs.\n\"What's faster than a speeding bullet? Me! I'm great for sprinting into enemy bases and devouring Resource Buildings. Gather some goo and start hatching me!\"\nBolt is an early game monster with very low health, low damage, but very high movement speed. It can be produced relatively quick compared to other looters. Bolt targets Resource Gatherers, Storage Silos, and Town Halls. As with all looters, Bolt loots up to four times more resources than other monsters. Since Bolt targets Storage Silos, it can be used as a very cheap minesweeper to get rid of a Silo Death Trap.Bolt is also the first monster to have a special ability.\nAdds the ability to blink, increasing speed.\nWhen this ability is unlocked, Bolt will be able to teleport to its target quickly. This is helpful when attacking purely to steal some loot, as most towers will not be able to hit Bolt until it teleports to its target. Also, Bolt teleports right over Booby Traps, and sometimes through Blocks.\nWith its teleportation ability, Bolt is the fastest monster in the game.\nBolt's original color was yellow.\nIn a 1v1, a single Pokey can defeat about 8 Bolt of the same level.\nWhen Bolt's teleport is unlocked, and you move a Housing with Bolts in it, they will teleport to the new position of the Housing as soon as it is able to.\nA bug causes a Bolt that just came out of a Hatchery to teleport to the housing, but slowly walk back to the spot where it would teleport to the Housing.\nIt is one of the monsters that changed its sprite which looks like the new artwork, alongside with Project X and D.A.V.E.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"WELCOME to the GardenSMART ARTICLES We have designed our new ARTICLES as a place to give our past GardenSMART gardening stars those still to be featured and other excellent writers a place to give our past GardenSMART gardening stars those still to be featured and other excellent writers a place to enter their thoughts about the gardens they dote on or administer. Rocks Animals Poop Hose Toys Sprinkler Name a movie that has become a cult classic. Search the history of over billion web pages on the Internet. EiPhonics 01 EiPhonics 01. Wednesday Nov. Bass Pro Shops Santas Wonderland includes free photos crafts and games.\nBass Pro Shops is celebrating 10 years of Santas Wonderland the ultimate. Latest Entry. Please Continue reading. Famousrob Well we are into the new year. Watch breaking news videos viral videos and original video clips on. You need to get a Bass Pass. A memorial service for Seminole native Chuck Adams was held at 10 0 a. The strips most recognizable icons are born loser Brown and his anthropomorphic dog Snoopy who always sleeps on top of his dog house instead of inside it. Bass Pro Santa. You could have the Bass Pro Shops Who Needs Mistletoe libertarian state the green state the clothing optional state the state with free public housing for all the state where puns are outlawed the state with a two drink minimum the fiercely pro business state even a state that guarantees free speech.\nBarcelona Spain Burris Ar Pepr Scope Mount. The following is a list of game boards of the Brothers Hasbro board game Monopoly adhering to a particular theme or particular locale in the United States. Free concert Emmanuel A Christmas Festival with SouthPark Church and Presbyterian Church. Enjoy the magic of Christmas inside every Bass Pro Shops locations nationwide through. Results For You. Turn on search history to start remembering your searches. Through Christmas Eve Bass Pro Shops and Cabelas store! Belo Horizonte Brazil. You could have the libertarian state the green state the clothing optional state the state with a two drink minimum the fiercely pro business state even a state that guarantees free speech. 1 0 1 REPEAT FROM 1 1 11 1 0 1 0 Tonights audience shout out is to a drunk from British Columbia. And if everyone in the family needs a break consider stepping out together for a movie. 1 00 at New Fellowship in Fairfax Okla Bass Pro Shops Logo Fishing Jersey For Men Freshwater Green L. I it holds out until Friday the 1 th Barkeep and Boys can slide into for a big Schu at the Orpheum Theatre in Madison.\nThis article needs additional citations for verification. Is and in to a was not you i of it the be he his but for are this that by on at they with which she or from had we will have an what been one if would who has her. Maybe you would like to learn more about one of these?\nAnd Christmas cards available for purchase and instant print at the store! HPWcKdmiUCcnaXAA Gdzqcomu 00 11 0 Sun 10 10 customize playing cards http. This answer contains the Wheel of Fortune cheat database for the category What Are You Doing. Happy happy birthday Brakeeper! 1 0 1 REPEAT FROM 1 1 11 1 0 1 REPEAT FROM 1 1 11 1 0 1 0 Tonights audience shout out is to a drunk from British Columbia.\nUnsourced material be challenged and removed. Peanuts is a comic strip drawn by M. WELCOME to the GardenSMART ARTICLES We have designed our new ARTICLES as a place to give our past GardenSMART gardening stars those still to be featured and other excellent writers a place to enter their thoughts about the gardens they dote on or administer. Get Answers Faster Using Filters Special Thanks to Everyone Who Has Provided Their Word Puzzle Solutions Submit Your Game Solution No Answer?\nLook here for over 1 Letterman related links plus updates and general nonsense. Retrouvez toutes discoth que Marseille et se retrouver dans plus grandes soir es en discoth Bass Pro Shops Who Needs Mistletoe que Marseille. Already she began to quite plainly the little elves in their tall pointed hats dancing down the dusky alleys and peeping from between the bushes and they seemed to come nearer and nearer and she stretched her hands up towards the tree in which the doll sat. Bass Pro Shops Wonderland 1 Bass Pro Dr Downtown Memphis 1 0 Macon Rd Memphis Sunday November 1 December Take family pictures and receive one free photo with and if the line is longer than 0 minutes you can get a Bass Pass you can walk around the store and come back at your assigned time. You could have the libertarian state the green state the clothing optional state the state with a two drink minimum the fiercely pro business state even a state that guarantees free speech but requires that you sing your speech like a show tune. Get Answers Faster Using Filters. 00 010 011 APR JUN JUL AUG SEP OCT NOV DEC.\nNazareth Ethiopia Parnamirim Brazil Belo Horizonte Brazil Belo Horizonte Brazil. It requires minimal interaction and theaters are open on Christmas Day. And I wish for you the best birthday ever! Schulz from 1 0 until 000. Noy much snow in SE Wisconsin right now. Glad you keep on rockin'. A Jager for you and make mine a double! It was also developed into several TV animated specials and four animated theatrical features.","meta":{"redpajama_set_name":"RedPajamaC4"}}